LMFDB - Embedded newform 185.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [185,2,Mod(1,185)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(185, 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("185.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.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:	$1.47723243739$
Analytic rank:	$1$
Dimension:	$1$
Coefficient field:	$\mathbb{Q}$
Coefficient ring:	$\mathbb{Z}$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	185.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$

$=$

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

\(q+1.00000 q^{2} -2.00000 q^{3} -1.00000 q^{4} -1.00000 q^{5} -2.00000 q^{6} -2.00000 q^{7} -3.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} +2.00000 q^{12} -2.00000 q^{13} -2.00000 q^{14} +2.00000 q^{15} -1.00000 q^{16} +2.00000 q^{17} +1.00000 q^{18} +2.00000 q^{19} +1.00000 q^{20} +4.00000 q^{21} -8.00000 q^{23} +6.00000 q^{24} +1.00000 q^{25} -2.00000 q^{26} +4.00000 q^{27} +2.00000 q^{28} +2.00000 q^{29} +2.00000 q^{30} -6.00000 q^{31} +5.00000 q^{32} +2.00000 q^{34} +2.00000 q^{35} -1.00000 q^{36} -1.00000 q^{37} +2.00000 q^{38} +4.00000 q^{39} +3.00000 q^{40} +10.0000 q^{41} +4.00000 q^{42} -4.00000 q^{43} -1.00000 q^{45} -8.00000 q^{46} -10.0000 q^{47} +2.00000 q^{48} -3.00000 q^{49} +1.00000 q^{50} -4.00000 q^{51} +2.00000 q^{52} -6.00000 q^{53} +4.00000 q^{54} +6.00000 q^{56} -4.00000 q^{57} +2.00000 q^{58} -6.00000 q^{59} -2.00000 q^{60} +2.00000 q^{61} -6.00000 q^{62} -2.00000 q^{63} +7.00000 q^{64} +2.00000 q^{65} -14.0000 q^{67} -2.00000 q^{68} +16.0000 q^{69} +2.00000 q^{70} -3.00000 q^{72} +2.00000 q^{73} -1.00000 q^{74} -2.00000 q^{75} -2.00000 q^{76} +4.00000 q^{78} -6.00000 q^{79} +1.00000 q^{80} -11.0000 q^{81} +10.0000 q^{82} +18.0000 q^{83} -4.00000 q^{84} -2.00000 q^{85} -4.00000 q^{86} -4.00000 q^{87} +2.00000 q^{89} -1.00000 q^{90} +4.00000 q^{91} +8.00000 q^{92} +12.0000 q^{93} -10.0000 q^{94} -2.00000 q^{95} -10.0000 q^{96} -10.0000 q^{97} -3.00000 q^{98} +O(q^{100})\)

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	$-0.384973\pi$
$2$	1.00000	0.707107	0.353553	+	0.935414i	$0.384973\pi$
$3$	−2.00000	−1.15470	−0.577350	−	0.816497i	$-0.695913\pi$
$3$	−2.00000	−1.15470	−0.577350	+	0.816497i	$0.695913\pi$
$4$	−1.00000	−0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−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	$0.623376\pi$
$8$	−3.00000	−1.06066
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	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
$15$	2.00000	0.516398
$16$	−1.00000	−0.250000
$17$	2.00000	0.485071	0.242536	−	0.970143i	$-0.422021\pi$
$17$	2.00000	0.485071	0.242536	+	0.970143i	$0.422021\pi$
$18$	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	$0.426318\pi$
$20$	1.00000	0.223607
$21$	4.00000	0.872872
$22$	0	0
$23$	−8.00000	−1.66812	−0.834058	−	0.551677i	$-0.813988\pi$
$23$	−8.00000	−1.66812	−0.834058	+	0.551677i	$0.813988\pi$
$24$	6.00000	1.22474
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	4.00000	0.769800
$28$	2.00000	0.377964
$29$	2.00000	0.371391	0.185695	−	0.982607i	$-0.440546\pi$
$29$	2.00000	0.371391	0.185695	+	0.982607i	$0.440546\pi$
$30$	2.00000	0.365148
$31$	−6.00000	−1.07763	−0.538816	−	0.842424i	$-0.681128\pi$
$31$	−6.00000	−1.07763	−0.538816	+	0.842424i	$0.681128\pi$
$32$	5.00000	0.883883
$33$	0	0
$34$	2.00000	0.342997
$35$	2.00000	0.338062
$36$	−1.00000	−0.166667
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	2.00000	0.324443
$39$	4.00000	0.640513
$40$	3.00000	0.474342
$41$	10.0000	1.56174	0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000	1.56174	0.780869	+	0.624695i	$0.214777\pi$
$42$	4.00000	0.617213
$43$	−4.00000	−0.609994	−0.304997	−	0.952353i	$-0.598656\pi$
$43$	−4.00000	−0.609994	−0.304997	+	0.952353i	$0.598656\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−8.00000	−1.17954
$47$	−10.0000	−1.45865	−0.729325	−	0.684167i	$-0.760166\pi$
$47$	−10.0000	−1.45865	−0.729325	+	0.684167i	$0.760166\pi$
$48$	2.00000	0.288675
$49$	−3.00000	−0.428571
$50$	1.00000	0.141421
$51$	−4.00000	−0.560112
$52$	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
$56$	6.00000	0.801784
$57$	−4.00000	−0.529813
$58$	2.00000	0.262613
$59$	−6.00000	−0.781133	−0.390567	−	0.920575i	$-0.627721\pi$
$59$	−6.00000	−0.781133	−0.390567	+	0.920575i	$0.627721\pi$
$60$	−2.00000	−0.258199
$61$	2.00000	0.256074	0.128037	−	0.991769i	$-0.459132\pi$
$61$	2.00000	0.256074	0.128037	+	0.991769i	$0.459132\pi$
$62$	−6.00000	−0.762001
$63$	−2.00000	−0.251976
$64$	7.00000	0.875000
$65$	2.00000	0.248069
$66$	0	0
$67$	−14.0000	−1.71037	−0.855186	−	0.518321i	$-0.826557\pi$
$67$	−14.0000	−1.71037	−0.855186	+	0.518321i	$0.826557\pi$
$68$	−2.00000	−0.242536
$69$	16.0000	1.92617
$70$	2.00000	0.239046
$71$	0	0		−	1.00000i	$-0.5\pi$
$71$	0	0			1.00000i	$0.5\pi$
$72$	−3.00000	−0.353553
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−1.00000	−0.116248
$75$	−2.00000	−0.230940
$76$	−2.00000	−0.229416
$77$	0	0
$78$	4.00000	0.452911
$79$	−6.00000	−0.675053	−0.337526	−	0.941316i	$-0.609590\pi$
$79$	−6.00000	−0.675053	−0.337526	+	0.941316i	$0.609590\pi$
$80$	1.00000	0.111803
$81$	−11.0000	−1.22222
$82$	10.0000	1.10432
$83$	18.0000	1.97576	0.987878	−	0.155230i	$-0.0496119\pi$
$83$	18.0000	1.97576	0.987878	+	0.155230i	$0.0496119\pi$
$84$	−4.00000	−0.436436
$85$	−2.00000	−0.216930
$86$	−4.00000	−0.431331
$87$	−4.00000	−0.428845
$88$	0	0
$89$	2.00000	0.212000	0.106000	−	0.994366i	$-0.466196\pi$
$89$	2.00000	0.212000	0.106000	+	0.994366i	$0.466196\pi$
$90$	−1.00000	−0.105409
$91$	4.00000	0.419314
$92$	8.00000	0.834058
$93$	12.0000	1.24434
$94$	−10.0000	−1.03142
$95$	−2.00000	−0.205196
$96$	−10.0000	−1.02062
$97$	−10.0000	−1.01535	−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000	−1.01535	−0.507673	+	0.861550i	$0.669494\pi$
$98$	−3.00000	−0.303046
$99$	0	0
$100$	−1.00000	−0.100000
$101$	10.0000	0.995037	0.497519	−	0.867453i	$-0.334245\pi$
$101$	10.0000	0.995037	0.497519	+	0.867453i	$0.334245\pi$
$102$	−4.00000	−0.396059
$103$	−4.00000	−0.394132	−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000	−0.394132	−0.197066	+	0.980390i	$0.563141\pi$
$104$	6.00000	0.588348
$105$	−4.00000	−0.390360
$106$	−6.00000	−0.582772
$107$	6.00000	0.580042	0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000	0.580042	0.290021	+	0.957020i	$0.406338\pi$
$108$	−4.00000	−0.384900
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	0	0
$111$	2.00000	0.189832
$112$	2.00000	0.188982
$113$	2.00000	0.188144	0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000	0.188144	0.0940721	+	0.995565i	$0.470012\pi$
$114$	−4.00000	−0.374634
$115$	8.00000	0.746004
$116$	−2.00000	−0.185695
$117$	−2.00000	−0.184900
$118$	−6.00000	−0.552345
$119$	−4.00000	−0.366679
$120$	−6.00000	−0.547723
$121$	−11.0000	−1.00000
$122$	2.00000	0.181071
$123$	−20.0000	−1.80334
$124$	6.00000	0.538816
$125$	−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
$129$	8.00000	0.704361
$130$	2.00000	0.175412
$131$	18.0000	1.57267	0.786334	−	0.617802i	$-0.211977\pi$
$131$	18.0000	1.57267	0.786334	+	0.617802i	$0.211977\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	−14.0000	−1.20942
$135$	−4.00000	−0.344265
$136$	−6.00000	−0.514496
$137$	−6.00000	−0.512615	−0.256307	−	0.966595i	$-0.582506\pi$
$137$	−6.00000	−0.512615	−0.256307	+	0.966595i	$0.582506\pi$
$138$	16.0000	1.36201
$139$	−4.00000	−0.339276	−0.169638	−	0.985506i	$-0.554260\pi$
$139$	−4.00000	−0.339276	−0.169638	+	0.985506i	$0.554260\pi$
$140$	−2.00000	−0.169031
$141$	20.0000	1.68430
$142$	0	0
$143$	0	0
$144$	−1.00000	−0.0833333
$145$	−2.00000	−0.166091
$146$	2.00000	0.165521
$147$	6.00000	0.494872
$148$	1.00000	0.0821995
$149$	−6.00000	−0.491539	−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000	−0.491539	−0.245770	+	0.969328i	$0.579041\pi$
$150$	−2.00000	−0.163299
$151$	−20.0000	−1.62758	−0.813788	−	0.581161i	$-0.802599\pi$
$151$	−20.0000	−1.62758	−0.813788	+	0.581161i	$0.802599\pi$
$152$	−6.00000	−0.486664
$153$	2.00000	0.161690
$154$	0	0
$155$	6.00000	0.481932
$156$	−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	$0.244931\pi$
$158$	−6.00000	−0.477334
$159$	12.0000	0.951662
$160$	−5.00000	−0.395285
$161$	16.0000	1.26098
$162$	−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	$0.284443\pi$
$164$	−10.0000	−0.780869
$165$	0	0
$166$	18.0000	1.39707
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	−12.0000	−0.925820
$169$	−9.00000	−0.692308
$170$	−2.00000	−0.153393
$171$	2.00000	0.152944
$172$	4.00000	0.304997
$173$	2.00000	0.152057	0.0760286	−	0.997106i	$-0.475776\pi$
$173$	2.00000	0.152057	0.0760286	+	0.997106i	$0.475776\pi$
$174$	−4.00000	−0.303239
$175$	−2.00000	−0.151186
$176$	0	0
$177$	12.0000	0.901975
$178$	2.00000	0.149906
$179$	14.0000	1.04641	0.523205	−	0.852207i	$-0.324736\pi$
$179$	14.0000	1.04641	0.523205	+	0.852207i	$0.324736\pi$
$180$	1.00000	0.0745356
$181$	10.0000	0.743294	0.371647	−	0.928374i	$-0.378793\pi$
$181$	10.0000	0.743294	0.371647	+	0.928374i	$0.378793\pi$
$182$	4.00000	0.296500
$183$	−4.00000	−0.295689
$184$	24.0000	1.76930
$185$	1.00000	0.0735215
$186$	12.0000	0.879883
$187$	0	0
$188$	10.0000	0.729325
$189$	−8.00000	−0.581914
$190$	−2.00000	−0.145095
$191$	22.0000	1.59186	0.795932	−	0.605386i	$-0.206981\pi$
$191$	22.0000	1.59186	0.795932	+	0.605386i	$0.206981\pi$
$192$	−14.0000	−1.01036
$193$	14.0000	1.00774	0.503871	−	0.863779i	$-0.331909\pi$
$193$	14.0000	1.00774	0.503871	+	0.863779i	$0.331909\pi$
$194$	−10.0000	−0.717958
$195$	−4.00000	−0.286446
$196$	3.00000	0.214286
$197$	10.0000	0.712470	0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000	0.712470	0.356235	+	0.934396i	$0.384060\pi$
$198$	0	0
$199$	−26.0000	−1.84309	−0.921546	−	0.388270i	$-0.873073\pi$
$199$	−26.0000	−1.84309	−0.921546	+	0.388270i	$0.873073\pi$
$200$	−3.00000	−0.212132
$201$	28.0000	1.97497
$202$	10.0000	0.703598
$203$	−4.00000	−0.280745
$204$	4.00000	0.280056
$205$	−10.0000	−0.698430
$206$	−4.00000	−0.278693
$207$	−8.00000	−0.556038
$208$	2.00000	0.138675
$209$	0	0
$210$	−4.00000	−0.276026
$211$	−28.0000	−1.92760	−0.963800	−	0.266627i	$-0.914091\pi$
$211$	−28.0000	−1.92760	−0.963800	+	0.266627i	$0.914091\pi$
$212$	6.00000	0.412082
$213$	0	0
$214$	6.00000	0.410152
$215$	4.00000	0.272798
$216$	−12.0000	−0.816497
$217$	12.0000	0.814613
$218$	2.00000	0.135457
$219$	−4.00000	−0.270295
$220$	0	0
$221$	−4.00000	−0.269069
$222$	2.00000	0.134231
$223$	10.0000	0.669650	0.334825	−	0.942280i	$-0.391323\pi$
$223$	10.0000	0.669650	0.334825	+	0.942280i	$0.391323\pi$
$224$	−10.0000	−0.668153
$225$	1.00000	0.0666667
$226$	2.00000	0.133038
$227$	−8.00000	−0.530979	−0.265489	−	0.964114i	$-0.585534\pi$
$227$	−8.00000	−0.530979	−0.265489	+	0.964114i	$0.585534\pi$
$228$	4.00000	0.264906
$229$	−18.0000	−1.18947	−0.594737	−	0.803921i	$-0.702744\pi$
$229$	−18.0000	−1.18947	−0.594737	+	0.803921i	$0.702744\pi$
$230$	8.00000	0.527504
$231$	0	0
$232$	−6.00000	−0.393919
$233$	−14.0000	−0.917170	−0.458585	−	0.888650i	$-0.651644\pi$
$233$	−14.0000	−0.917170	−0.458585	+	0.888650i	$0.651644\pi$
$234$	−2.00000	−0.130744
$235$	10.0000	0.652328
$236$	6.00000	0.390567
$237$	12.0000	0.779484
$238$	−4.00000	−0.259281
$239$	−6.00000	−0.388108	−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000	−0.388108	−0.194054	+	0.980991i	$0.562164\pi$
$240$	−2.00000	−0.129099
$241$	10.0000	0.644157	0.322078	−	0.946713i	$-0.395619\pi$
$241$	10.0000	0.644157	0.322078	+	0.946713i	$0.395619\pi$
$242$	−11.0000	−0.707107
$243$	10.0000	0.641500
$244$	−2.00000	−0.128037
$245$	3.00000	0.191663
$246$	−20.0000	−1.27515
$247$	−4.00000	−0.254514
$248$	18.0000	1.14300
$249$	−36.0000	−2.28141
$250$	−1.00000	−0.0632456
$251$	−14.0000	−0.883672	−0.441836	−	0.897096i	$-0.645673\pi$
$251$	−14.0000	−0.883672	−0.441836	+	0.897096i	$0.645673\pi$
$252$	2.00000	0.125988
$253$	0	0
$254$	−2.00000	−0.125491
$255$	4.00000	0.250490
$256$	−17.0000	−1.06250
$257$	−30.0000	−1.87135	−0.935674	−	0.352865i	$-0.885208\pi$
$257$	−30.0000	−1.87135	−0.935674	+	0.352865i	$0.885208\pi$
$258$	8.00000	0.498058
$259$	2.00000	0.124274
$260$	−2.00000	−0.124035
$261$	2.00000	0.123797
$262$	18.0000	1.11204
$263$	22.0000	1.35658	0.678289	−	0.734795i	$-0.262722\pi$
$263$	22.0000	1.35658	0.678289	+	0.734795i	$0.262722\pi$
$264$	0	0
$265$	6.00000	0.368577
$266$	−4.00000	−0.245256
$267$	−4.00000	−0.244796
$268$	14.0000	0.855186
$269$	−30.0000	−1.82913	−0.914566	−	0.404436i	$-0.867468\pi$
$269$	−30.0000	−1.82913	−0.914566	+	0.404436i	$0.867468\pi$
$270$	−4.00000	−0.243432
$271$	0	0		−	1.00000i	$-0.5\pi$
$271$	0	0			1.00000i	$0.5\pi$
$272$	−2.00000	−0.121268
$273$	−8.00000	−0.484182
$274$	−6.00000	−0.362473
$275$	0	0
$276$	−16.0000	−0.963087
$277$	−10.0000	−0.600842	−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000	−0.600842	−0.300421	+	0.953807i	$0.597127\pi$
$278$	−4.00000	−0.239904
$279$	−6.00000	−0.359211
$280$	−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	$0.727839\pi$
$282$	20.0000	1.19098
$283$	−16.0000	−0.951101	−0.475551	−	0.879688i	$-0.657751\pi$
$283$	−16.0000	−0.951101	−0.475551	+	0.879688i	$0.657751\pi$
$284$	0	0
$285$	4.00000	0.236940
$286$	0	0
$287$	−20.0000	−1.18056
$288$	5.00000	0.294628
$289$	−13.0000	−0.764706
$290$	−2.00000	−0.117444
$291$	20.0000	1.17242
$292$	−2.00000	−0.117041
$293$	−14.0000	−0.817889	−0.408944	−	0.912559i	$-0.634103\pi$
$293$	−14.0000	−0.817889	−0.408944	+	0.912559i	$0.634103\pi$
$294$	6.00000	0.349927
$295$	6.00000	0.349334
$296$	3.00000	0.174371
$297$	0	0
$298$	−6.00000	−0.347571
$299$	16.0000	0.925304
$300$	2.00000	0.115470
$301$	8.00000	0.461112
$302$	−20.0000	−1.15087
$303$	−20.0000	−1.14897
$304$	−2.00000	−0.114708
$305$	−2.00000	−0.114520
$306$	2.00000	0.114332
$307$	34.0000	1.94048	0.970241	−	0.242140i	$-0.0778494\pi$
$307$	34.0000	1.94048	0.970241	+	0.242140i	$0.0778494\pi$
$308$	0	0
$309$	8.00000	0.455104
$310$	6.00000	0.340777
$311$	−6.00000	−0.340229	−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000	−0.340229	−0.170114	+	0.985424i	$0.554414\pi$
$312$	−12.0000	−0.679366
$313$	22.0000	1.24351	0.621757	−	0.783210i	$-0.286419\pi$
$313$	22.0000	1.24351	0.621757	+	0.783210i	$0.286419\pi$
$314$	18.0000	1.01580
$315$	2.00000	0.112687
$316$	6.00000	0.337526
$317$	34.0000	1.90963	0.954815	−	0.297200i	$-0.0960529\pi$
$317$	34.0000	1.90963	0.954815	+	0.297200i	$0.0960529\pi$
$318$	12.0000	0.672927
$319$	0	0
$320$	−7.00000	−0.391312
$321$	−12.0000	−0.669775
$322$	16.0000	0.891645
$323$	4.00000	0.222566
$324$	11.0000	0.611111
$325$	−2.00000	−0.110940
$326$	16.0000	0.886158
$327$	−4.00000	−0.221201
$328$	−30.0000	−1.65647
$329$	20.0000	1.10264
$330$	0	0
$331$	−26.0000	−1.42909	−0.714545	−	0.699590i	$-0.753366\pi$
$331$	−26.0000	−1.42909	−0.714545	+	0.699590i	$0.753366\pi$
$332$	−18.0000	−0.987878
$333$	−1.00000	−0.0547997
$334$	12.0000	0.656611
$335$	14.0000	0.764902
$336$	−4.00000	−0.218218
$337$	2.00000	0.108947	0.0544735	−	0.998515i	$-0.482652\pi$
$337$	2.00000	0.108947	0.0544735	+	0.998515i	$0.482652\pi$
$338$	−9.00000	−0.489535
$339$	−4.00000	−0.217250
$340$	2.00000	0.108465
$341$	0	0
$342$	2.00000	0.108148
$343$	20.0000	1.07990
$344$	12.0000	0.646997
$345$	−16.0000	−0.861411
$346$	2.00000	0.107521
$347$	−28.0000	−1.50312	−0.751559	−	0.659665i	$-0.770698\pi$
$347$	−28.0000	−1.50312	−0.751559	+	0.659665i	$0.770698\pi$
$348$	4.00000	0.214423
$349$	2.00000	0.107058	0.0535288	−	0.998566i	$-0.482953\pi$
$349$	2.00000	0.107058	0.0535288	+	0.998566i	$0.482953\pi$
$350$	−2.00000	−0.106904
$351$	−8.00000	−0.427008
$352$	0	0
$353$	−26.0000	−1.38384	−0.691920	−	0.721974i	$-0.743235\pi$
$353$	−26.0000	−1.38384	−0.691920	+	0.721974i	$0.743235\pi$
$354$	12.0000	0.637793
$355$	0	0
$356$	−2.00000	−0.106000
$357$	8.00000	0.423405
$358$	14.0000	0.739923
$359$	12.0000	0.633336	0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000	0.633336	0.316668	+	0.948536i	$0.397436\pi$
$360$	3.00000	0.158114
$361$	−15.0000	−0.789474
$362$	10.0000	0.525588
$363$	22.0000	1.15470
$364$	−4.00000	−0.209657
$365$	−2.00000	−0.104685
$366$	−4.00000	−0.209083
$367$	−2.00000	−0.104399	−0.0521996	−	0.998637i	$-0.516623\pi$
$367$	−2.00000	−0.104399	−0.0521996	+	0.998637i	$0.516623\pi$
$368$	8.00000	0.417029
$369$	10.0000	0.520579
$370$	1.00000	0.0519875
$371$	12.0000	0.623009
$372$	−12.0000	−0.622171
$373$	−6.00000	−0.310668	−0.155334	−	0.987862i	$-0.549645\pi$
$373$	−6.00000	−0.310668	−0.155334	+	0.987862i	$0.549645\pi$
$374$	0	0
$375$	2.00000	0.103280
$376$	30.0000	1.54713
$377$	−4.00000	−0.206010
$378$	−8.00000	−0.411476
$379$	16.0000	0.821865	0.410932	−	0.911666i	$-0.365203\pi$
$379$	16.0000	0.821865	0.410932	+	0.911666i	$0.365203\pi$
$380$	2.00000	0.102598
$381$	4.00000	0.204926
$382$	22.0000	1.12562
$383$	−24.0000	−1.22634	−0.613171	−	0.789950i	$-0.710106\pi$
$383$	−24.0000	−1.22634	−0.613171	+	0.789950i	$0.710106\pi$
$384$	6.00000	0.306186
$385$	0	0
$386$	14.0000	0.712581
$387$	−4.00000	−0.203331
$388$	10.0000	0.507673
$389$	−30.0000	−1.52106	−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000	−1.52106	−0.760530	+	0.649303i	$0.775061\pi$
$390$	−4.00000	−0.202548
$391$	−16.0000	−0.809155
$392$	9.00000	0.454569
$393$	−36.0000	−1.81596
$394$	10.0000	0.503793
$395$	6.00000	0.301893
$396$	0	0
$397$	−30.0000	−1.50566	−0.752828	−	0.658217i	$-0.771311\pi$
$397$	−30.0000	−1.50566	−0.752828	+	0.658217i	$0.771311\pi$
$398$	−26.0000	−1.30326
$399$	8.00000	0.400501
$400$	−1.00000	−0.0500000
$401$	18.0000	0.898877	0.449439	−	0.893311i	$-0.351624\pi$
$401$	18.0000	0.898877	0.449439	+	0.893311i	$0.351624\pi$
$402$	28.0000	1.39651
$403$	12.0000	0.597763
$404$	−10.0000	−0.497519
$405$	11.0000	0.546594
$406$	−4.00000	−0.198517
$407$	0	0
$408$	12.0000	0.594089
$409$	26.0000	1.28562	0.642809	−	0.766027i	$-0.277769\pi$
$409$	26.0000	1.28562	0.642809	+	0.766027i	$0.277769\pi$
$410$	−10.0000	−0.493865
$411$	12.0000	0.591916
$412$	4.00000	0.197066
$413$	12.0000	0.590481
$414$	−8.00000	−0.393179
$415$	−18.0000	−0.883585
$416$	−10.0000	−0.490290
$417$	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	$0.300608\pi$
$420$	4.00000	0.195180
$421$	26.0000	1.26716	0.633581	−	0.773676i	$-0.281584\pi$
$421$	26.0000	1.26716	0.633581	+	0.773676i	$0.281584\pi$
$422$	−28.0000	−1.36302
$423$	−10.0000	−0.486217
$424$	18.0000	0.874157
$425$	2.00000	0.0970143
$426$	0	0
$427$	−4.00000	−0.193574
$428$	−6.00000	−0.290021
$429$	0	0
$430$	4.00000	0.192897
$431$	−30.0000	−1.44505	−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000	−1.44505	−0.722525	+	0.691345i	$0.757018\pi$
$432$	−4.00000	−0.192450
$433$	34.0000	1.63394	0.816968	−	0.576683i	$-0.195653\pi$
$433$	34.0000	1.63394	0.816968	+	0.576683i	$0.195653\pi$
$434$	12.0000	0.576018
$435$	4.00000	0.191785
$436$	−2.00000	−0.0957826
$437$	−16.0000	−0.765384
$438$	−4.00000	−0.191127
$439$	22.0000	1.05000	0.525001	−	0.851101i	$-0.324065\pi$
$439$	22.0000	1.05000	0.525001	+	0.851101i	$0.324065\pi$
$440$	0	0
$441$	−3.00000	−0.142857
$442$	−4.00000	−0.190261
$443$	6.00000	0.285069	0.142534	−	0.989790i	$-0.454475\pi$
$443$	6.00000	0.285069	0.142534	+	0.989790i	$0.454475\pi$
$444$	−2.00000	−0.0949158
$445$	−2.00000	−0.0948091
$446$	10.0000	0.473514
$447$	12.0000	0.567581
$448$	−14.0000	−0.661438
$449$	−22.0000	−1.03824	−0.519122	−	0.854700i	$-0.673741\pi$
$449$	−22.0000	−1.03824	−0.519122	+	0.854700i	$0.673741\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−2.00000	−0.0940721
$453$	40.0000	1.87936
$454$	−8.00000	−0.375459
$455$	−4.00000	−0.187523
$456$	12.0000	0.561951
$457$	−18.0000	−0.842004	−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000	−0.842004	−0.421002	+	0.907060i	$0.638322\pi$
$458$	−18.0000	−0.841085
$459$	8.00000	0.373408
$460$	−8.00000	−0.373002
$461$	18.0000	0.838344	0.419172	−	0.907907i	$-0.362320\pi$
$461$	18.0000	0.838344	0.419172	+	0.907907i	$0.362320\pi$
$462$	0	0
$463$	−32.0000	−1.48717	−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000	−1.48717	−0.743583	+	0.668644i	$0.766875\pi$
$464$	−2.00000	−0.0928477
$465$	−12.0000	−0.556487
$466$	−14.0000	−0.648537
$467$	−16.0000	−0.740392	−0.370196	−	0.928954i	$-0.620709\pi$
$467$	−16.0000	−0.740392	−0.370196	+	0.928954i	$0.620709\pi$
$468$	2.00000	0.0924500
$469$	28.0000	1.29292
$470$	10.0000	0.461266
$471$	−36.0000	−1.65879
$472$	18.0000	0.828517
$473$	0	0
$474$	12.0000	0.551178
$475$	2.00000	0.0917663
$476$	4.00000	0.183340
$477$	−6.00000	−0.274721
$478$	−6.00000	−0.274434
$479$	18.0000	0.822441	0.411220	−	0.911536i	$-0.365103\pi$
$479$	18.0000	0.822441	0.411220	+	0.911536i	$0.365103\pi$
$480$	10.0000	0.456435
$481$	2.00000	0.0911922
$482$	10.0000	0.455488
$483$	−32.0000	−1.45605
$484$	11.0000	0.500000
$485$	10.0000	0.454077
$486$	10.0000	0.453609
$487$	−12.0000	−0.543772	−0.271886	−	0.962329i	$-0.587647\pi$
$487$	−12.0000	−0.543772	−0.271886	+	0.962329i	$0.587647\pi$
$488$	−6.00000	−0.271607
$489$	−32.0000	−1.44709
$490$	3.00000	0.135526
$491$	20.0000	0.902587	0.451294	−	0.892375i	$-0.350963\pi$
$491$	20.0000	0.902587	0.451294	+	0.892375i	$0.350963\pi$
$492$	20.0000	0.901670
$493$	4.00000	0.180151
$494$	−4.00000	−0.179969
$495$	0	0
$496$	6.00000	0.269408
$497$	0	0
$498$	−36.0000	−1.61320
$499$	14.0000	0.626726	0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000	0.626726	0.313363	+	0.949633i	$0.398544\pi$
$500$	1.00000	0.0447214
$501$	−24.0000	−1.07224
$502$	−14.0000	−0.624851
$503$	24.0000	1.07011	0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000	1.07011	0.535054	+	0.844818i	$0.320291\pi$
$504$	6.00000	0.267261
$505$	−10.0000	−0.444994
$506$	0	0
$507$	18.0000	0.799408
$508$	2.00000	0.0887357
$509$	−18.0000	−0.797836	−0.398918	−	0.916987i	$-0.630614\pi$
$509$	−18.0000	−0.797836	−0.398918	+	0.916987i	$0.630614\pi$
$510$	4.00000	0.177123
$511$	−4.00000	−0.176950
$512$	−11.0000	−0.486136
$513$	8.00000	0.353209
$514$	−30.0000	−1.32324
$515$	4.00000	0.176261
$516$	−8.00000	−0.352180
$517$	0	0
$518$	2.00000	0.0878750
$519$	−4.00000	−0.175581
$520$	−6.00000	−0.263117
$521$	−18.0000	−0.788594	−0.394297	−	0.918983i	$-0.629012\pi$
$521$	−18.0000	−0.788594	−0.394297	+	0.918983i	$0.629012\pi$
$522$	2.00000	0.0875376
$523$	−20.0000	−0.874539	−0.437269	−	0.899331i	$-0.644054\pi$
$523$	−20.0000	−0.874539	−0.437269	+	0.899331i	$0.644054\pi$
$524$	−18.0000	−0.786334
$525$	4.00000	0.174574
$526$	22.0000	0.959246
$527$	−12.0000	−0.522728
$528$	0	0
$529$	41.0000	1.78261
$530$	6.00000	0.260623
$531$	−6.00000	−0.260378
$532$	4.00000	0.173422
$533$	−20.0000	−0.866296
$534$	−4.00000	−0.173097
$535$	−6.00000	−0.259403
$536$	42.0000	1.81412
$537$	−28.0000	−1.20829
$538$	−30.0000	−1.29339
$539$	0	0
$540$	4.00000	0.172133
$541$	10.0000	0.429934	0.214967	−	0.976621i	$-0.431036\pi$
$541$	10.0000	0.429934	0.214967	+	0.976621i	$0.431036\pi$
$542$	0	0
$543$	−20.0000	−0.858282
$544$	10.0000	0.428746
$545$	−2.00000	−0.0856706
$546$	−8.00000	−0.342368
$547$	12.0000	0.513083	0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000	0.513083	0.256541	+	0.966533i	$0.417417\pi$
$548$	6.00000	0.256307
$549$	2.00000	0.0853579
$550$	0	0
$551$	4.00000	0.170406
$552$	−48.0000	−2.04302
$553$	12.0000	0.510292
$554$	−10.0000	−0.424859
$555$	−2.00000	−0.0848953
$556$	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	$0.280765\pi$
$558$	−6.00000	−0.254000
$559$	8.00000	0.338364
$560$	−2.00000	−0.0845154
$561$	0	0
$562$	−22.0000	−0.928014
$563$	−12.0000	−0.505740	−0.252870	−	0.967500i	$-0.581374\pi$
$563$	−12.0000	−0.505740	−0.252870	+	0.967500i	$0.581374\pi$
$564$	−20.0000	−0.842152
$565$	−2.00000	−0.0841406
$566$	−16.0000	−0.672530
$567$	22.0000	0.923913
$568$	0	0
$569$	18.0000	0.754599	0.377300	−	0.926091i	$-0.376853\pi$
$569$	18.0000	0.754599	0.377300	+	0.926091i	$0.376853\pi$
$570$	4.00000	0.167542
$571$	20.0000	0.836974	0.418487	−	0.908223i	$-0.362561\pi$
$571$	20.0000	0.836974	0.418487	+	0.908223i	$0.362561\pi$
$572$	0	0
$573$	−44.0000	−1.83813
$574$	−20.0000	−0.834784
$575$	−8.00000	−0.333623
$576$	7.00000	0.291667
$577$	−14.0000	−0.582828	−0.291414	−	0.956597i	$-0.594126\pi$
$577$	−14.0000	−0.582828	−0.291414	+	0.956597i	$0.594126\pi$
$578$	−13.0000	−0.540729
$579$	−28.0000	−1.16364
$580$	2.00000	0.0830455
$581$	−36.0000	−1.49353
$582$	20.0000	0.829027
$583$	0	0
$584$	−6.00000	−0.248282
$585$	2.00000	0.0826898
$586$	−14.0000	−0.578335
$587$	12.0000	0.495293	0.247647	−	0.968850i	$-0.420343\pi$
$587$	12.0000	0.495293	0.247647	+	0.968850i	$0.420343\pi$
$588$	−6.00000	−0.247436
$589$	−12.0000	−0.494451
$590$	6.00000	0.247016
$591$	−20.0000	−0.822690
$592$	1.00000	0.0410997
$593$	10.0000	0.410651	0.205325	−	0.978694i	$-0.434175\pi$
$593$	10.0000	0.410651	0.205325	+	0.978694i	$0.434175\pi$
$594$	0	0
$595$	4.00000	0.163984
$596$	6.00000	0.245770
$597$	52.0000	2.12822
$598$	16.0000	0.654289
$599$	36.0000	1.47092	0.735460	−	0.677568i	$-0.236966\pi$
$599$	36.0000	1.47092	0.735460	+	0.677568i	$0.236966\pi$
$600$	6.00000	0.244949
$601$	−26.0000	−1.06056	−0.530281	−	0.847822i	$-0.677914\pi$
$601$	−26.0000	−1.06056	−0.530281	+	0.847822i	$0.677914\pi$
$602$	8.00000	0.326056
$603$	−14.0000	−0.570124
$604$	20.0000	0.813788
$605$	11.0000	0.447214
$606$	−20.0000	−0.812444
$607$	−8.00000	−0.324710	−0.162355	−	0.986732i	$-0.551909\pi$
$607$	−8.00000	−0.324710	−0.162355	+	0.986732i	$0.551909\pi$
$608$	10.0000	0.405554
$609$	8.00000	0.324176
$610$	−2.00000	−0.0809776
$611$	20.0000	0.809113
$612$	−2.00000	−0.0808452
$613$	2.00000	0.0807792	0.0403896	−	0.999184i	$-0.487140\pi$
$613$	2.00000	0.0807792	0.0403896	+	0.999184i	$0.487140\pi$
$614$	34.0000	1.37213
$615$	20.0000	0.806478
$616$	0	0
$617$	−22.0000	−0.885687	−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000	−0.885687	−0.442843	+	0.896599i	$0.646030\pi$
$618$	8.00000	0.321807
$619$	12.0000	0.482321	0.241160	−	0.970485i	$-0.422472\pi$
$619$	12.0000	0.482321	0.241160	+	0.970485i	$0.422472\pi$
$620$	−6.00000	−0.240966
$621$	−32.0000	−1.28412
$622$	−6.00000	−0.240578
$623$	−4.00000	−0.160257
$624$	−4.00000	−0.160128
$625$	1.00000	0.0400000
$626$	22.0000	0.879297
$627$	0	0
$628$	−18.0000	−0.718278
$629$	−2.00000	−0.0797452
$630$	2.00000	0.0796819
$631$	−22.0000	−0.875806	−0.437903	−	0.899022i	$-0.644279\pi$
$631$	−22.0000	−0.875806	−0.437903	+	0.899022i	$0.644279\pi$
$632$	18.0000	0.716002
$633$	56.0000	2.22580
$634$	34.0000	1.35031
$635$	2.00000	0.0793676
$636$	−12.0000	−0.475831
$637$	6.00000	0.237729
$638$	0	0
$639$	0	0
$640$	3.00000	0.118585
$641$	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	$-0.282654\pi$
$643$	32.0000	1.26196	0.630978	+	0.775800i	$0.282654\pi$
$644$	−16.0000	−0.630488
$645$	−8.00000	−0.315000
$646$	4.00000	0.157378
$647$	8.00000	0.314512	0.157256	−	0.987558i	$-0.449735\pi$
$647$	8.00000	0.314512	0.157256	+	0.987558i	$0.449735\pi$
$648$	33.0000	1.29636
$649$	0	0
$650$	−2.00000	−0.0784465
$651$	−24.0000	−0.940634
$652$	−16.0000	−0.626608
$653$	2.00000	0.0782660	0.0391330	−	0.999234i	$-0.487540\pi$
$653$	2.00000	0.0782660	0.0391330	+	0.999234i	$0.487540\pi$
$654$	−4.00000	−0.156412
$655$	−18.0000	−0.703318
$656$	−10.0000	−0.390434
$657$	2.00000	0.0780274
$658$	20.0000	0.779681
$659$	−4.00000	−0.155818	−0.0779089	−	0.996960i	$-0.524824\pi$
$659$	−4.00000	−0.155818	−0.0779089	+	0.996960i	$0.524824\pi$
$660$	0	0
$661$	−30.0000	−1.16686	−0.583432	−	0.812162i	$-0.698291\pi$
$661$	−30.0000	−1.16686	−0.583432	+	0.812162i	$0.698291\pi$
$662$	−26.0000	−1.01052
$663$	8.00000	0.310694
$664$	−54.0000	−2.09561
$665$	4.00000	0.155113
$666$	−1.00000	−0.0387492
$667$	−16.0000	−0.619522
$668$	−12.0000	−0.464294
$669$	−20.0000	−0.773245
$670$	14.0000	0.540867
$671$	0	0
$672$	20.0000	0.771517
$673$	50.0000	1.92736	0.963679	−	0.267063i	$-0.0860531\pi$
$673$	50.0000	1.92736	0.963679	+	0.267063i	$0.0860531\pi$
$674$	2.00000	0.0770371
$675$	4.00000	0.153960
$676$	9.00000	0.346154
$677$	2.00000	0.0768662	0.0384331	−	0.999261i	$-0.487763\pi$
$677$	2.00000	0.0768662	0.0384331	+	0.999261i	$0.487763\pi$
$678$	−4.00000	−0.153619
$679$	20.0000	0.767530
$680$	6.00000	0.230089
$681$	16.0000	0.613121
$682$	0	0
$683$	4.00000	0.153056	0.0765279	−	0.997067i	$-0.475617\pi$
$683$	4.00000	0.153056	0.0765279	+	0.997067i	$0.475617\pi$
$684$	−2.00000	−0.0764719
$685$	6.00000	0.229248
$686$	20.0000	0.763604
$687$	36.0000	1.37349
$688$	4.00000	0.152499
$689$	12.0000	0.457164
$690$	−16.0000	−0.609110
$691$	40.0000	1.52167	0.760836	−	0.648944i	$-0.224789\pi$
$691$	40.0000	1.52167	0.760836	+	0.648944i	$0.224789\pi$
$692$	−2.00000	−0.0760286
$693$	0	0
$694$	−28.0000	−1.06287
$695$	4.00000	0.151729
$696$	12.0000	0.454859
$697$	20.0000	0.757554
$698$	2.00000	0.0757011
$699$	28.0000	1.05906
$700$	2.00000	0.0755929
$701$	−30.0000	−1.13308	−0.566542	−	0.824033i	$-0.691719\pi$
$701$	−30.0000	−1.13308	−0.566542	+	0.824033i	$0.691719\pi$
$702$	−8.00000	−0.301941
$703$	−2.00000	−0.0754314
$704$	0	0
$705$	−20.0000	−0.753244
$706$	−26.0000	−0.978523
$707$	−20.0000	−0.752177
$708$	−12.0000	−0.450988
$709$	−46.0000	−1.72757	−0.863783	−	0.503864i	$-0.831911\pi$
$709$	−46.0000	−1.72757	−0.863783	+	0.503864i	$0.831911\pi$
$710$	0	0
$711$	−6.00000	−0.225018
$712$	−6.00000	−0.224860
$713$	48.0000	1.79761
$714$	8.00000	0.299392
$715$	0	0
$716$	−14.0000	−0.523205
$717$	12.0000	0.448148
$718$	12.0000	0.447836
$719$	−12.0000	−0.447524	−0.223762	−	0.974644i	$-0.571834\pi$
$719$	−12.0000	−0.447524	−0.223762	+	0.974644i	$0.571834\pi$
$720$	1.00000	0.0372678
$721$	8.00000	0.297936
$722$	−15.0000	−0.558242
$723$	−20.0000	−0.743808
$724$	−10.0000	−0.371647
$725$	2.00000	0.0742781
$726$	22.0000	0.816497
$727$	−8.00000	−0.296704	−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000	−0.296704	−0.148352	+	0.988935i	$0.547397\pi$
$728$	−12.0000	−0.444750
$729$	13.0000	0.481481
$730$	−2.00000	−0.0740233
$731$	−8.00000	−0.295891
$732$	4.00000	0.147844
$733$	−46.0000	−1.69905	−0.849524	−	0.527549i	$-0.823111\pi$
$733$	−46.0000	−1.69905	−0.849524	+	0.527549i	$0.823111\pi$
$734$	−2.00000	−0.0738213
$735$	−6.00000	−0.221313
$736$	−40.0000	−1.47442
$737$	0	0
$738$	10.0000	0.368105
$739$	36.0000	1.32428	0.662141	−	0.749380i	$-0.269648\pi$
$739$	36.0000	1.32428	0.662141	+	0.749380i	$0.269648\pi$
$740$	−1.00000	−0.0367607
$741$	8.00000	0.293887
$742$	12.0000	0.440534
$743$	6.00000	0.220119	0.110059	−	0.993925i	$-0.464896\pi$
$743$	6.00000	0.220119	0.110059	+	0.993925i	$0.464896\pi$
$744$	−36.0000	−1.31982
$745$	6.00000	0.219823
$746$	−6.00000	−0.219676
$747$	18.0000	0.658586
$748$	0	0
$749$	−12.0000	−0.438470
$750$	2.00000	0.0730297
$751$	4.00000	0.145962	0.0729810	−	0.997333i	$-0.476749\pi$
$751$	4.00000	0.145962	0.0729810	+	0.997333i	$0.476749\pi$
$752$	10.0000	0.364662
$753$	28.0000	1.02038
$754$	−4.00000	−0.145671
$755$	20.0000	0.727875
$756$	8.00000	0.290957
$757$	42.0000	1.52652	0.763258	−	0.646094i	$-0.223599\pi$
$757$	42.0000	1.52652	0.763258	+	0.646094i	$0.223599\pi$
$758$	16.0000	0.581146
$759$	0	0
$760$	6.00000	0.217643
$761$	−22.0000	−0.797499	−0.398750	−	0.917060i	$-0.630556\pi$
$761$	−22.0000	−0.797499	−0.398750	+	0.917060i	$0.630556\pi$
$762$	4.00000	0.144905
$763$	−4.00000	−0.144810
$764$	−22.0000	−0.795932
$765$	−2.00000	−0.0723102
$766$	−24.0000	−0.867155
$767$	12.0000	0.433295
$768$	34.0000	1.22687
$769$	−38.0000	−1.37032	−0.685158	−	0.728395i	$-0.740267\pi$
$769$	−38.0000	−1.37032	−0.685158	+	0.728395i	$0.740267\pi$
$770$	0	0
$771$	60.0000	2.16085
$772$	−14.0000	−0.503871
$773$	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
$775$	−6.00000	−0.215526
$776$	30.0000	1.07694
$777$	−4.00000	−0.143499
$778$	−30.0000	−1.07555
$779$	20.0000	0.716574
$780$	4.00000	0.143223
$781$	0	0
$782$	−16.0000	−0.572159
$783$	8.00000	0.285897
$784$	3.00000	0.107143
$785$	−18.0000	−0.642448
$786$	−36.0000	−1.28408
$787$	−10.0000	−0.356462	−0.178231	−	0.983989i	$-0.557037\pi$
$787$	−10.0000	−0.356462	−0.178231	+	0.983989i	$0.557037\pi$
$788$	−10.0000	−0.356235
$789$	−44.0000	−1.56644
$790$	6.00000	0.213470
$791$	−4.00000	−0.142224
$792$	0	0
$793$	−4.00000	−0.142044
$794$	−30.0000	−1.06466
$795$	−12.0000	−0.425596
$796$	26.0000	0.921546
$797$	14.0000	0.495905	0.247953	−	0.968772i	$-0.420242\pi$
$797$	14.0000	0.495905	0.247953	+	0.968772i	$0.420242\pi$
$798$	8.00000	0.283197
$799$	−20.0000	−0.707549
$800$	5.00000	0.176777
$801$	2.00000	0.0706665
$802$	18.0000	0.635602
$803$	0	0
$804$	−28.0000	−0.987484
$805$	−16.0000	−0.563926
$806$	12.0000	0.422682
$807$	60.0000	2.11210
$808$	−30.0000	−1.05540
$809$	10.0000	0.351581	0.175791	−	0.984428i	$-0.443752\pi$
$809$	10.0000	0.351581	0.175791	+	0.984428i	$0.443752\pi$
$810$	11.0000	0.386501
$811$	52.0000	1.82597	0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000	1.82597	0.912983	+	0.407997i	$0.133772\pi$
$812$	4.00000	0.140372
$813$	0	0
$814$	0	0
$815$	−16.0000	−0.560456
$816$	4.00000	0.140028
$817$	−8.00000	−0.279885
$818$	26.0000	0.909069
$819$	4.00000	0.139771
$820$	10.0000	0.349215
$821$	6.00000	0.209401	0.104701	−	0.994504i	$-0.466612\pi$
$821$	6.00000	0.209401	0.104701	+	0.994504i	$0.466612\pi$
$822$	12.0000	0.418548
$823$	26.0000	0.906303	0.453152	−	0.891434i	$-0.350300\pi$
$823$	26.0000	0.906303	0.453152	+	0.891434i	$0.350300\pi$
$824$	12.0000	0.418040
$825$	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	$0.637017\pi$
$828$	8.00000	0.278019
$829$	−46.0000	−1.59765	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	−46.0000	−1.59765	−0.798823	+	0.601566i	$0.794544\pi$
$830$	−18.0000	−0.624789
$831$	20.0000	0.693792
$832$	−14.0000	−0.485363
$833$	−6.00000	−0.207888
$834$	8.00000	0.277017
$835$	−12.0000	−0.415277
$836$	0	0
$837$	−24.0000	−0.829561
$838$	24.0000	0.829066
$839$	0	0		−	1.00000i	$-0.5\pi$
$839$	0	0			1.00000i	$0.5\pi$
$840$	12.0000	0.414039
$841$	−25.0000	−0.862069
$842$	26.0000	0.896019
$843$	44.0000	1.51544
$844$	28.0000	0.963800
$845$	9.00000	0.309609
$846$	−10.0000	−0.343807
$847$	22.0000	0.755929
$848$	6.00000	0.206041
$849$	32.0000	1.09824
$850$	2.00000	0.0685994
$851$	8.00000	0.274236
$852$	0	0
$853$	−54.0000	−1.84892	−0.924462	−	0.381273i	$-0.875486\pi$
$853$	−54.0000	−1.84892	−0.924462	+	0.381273i	$0.875486\pi$
$854$	−4.00000	−0.136877
$855$	−2.00000	−0.0683986
$856$	−18.0000	−0.615227
$857$	14.0000	0.478231	0.239115	−	0.970991i	$-0.423143\pi$
$857$	14.0000	0.478231	0.239115	+	0.970991i	$0.423143\pi$
$858$	0	0
$859$	−14.0000	−0.477674	−0.238837	−	0.971060i	$-0.576766\pi$
$859$	−14.0000	−0.477674	−0.238837	+	0.971060i	$0.576766\pi$
$860$	−4.00000	−0.136399
$861$	40.0000	1.36320
$862$	−30.0000	−1.02180
$863$	−6.00000	−0.204242	−0.102121	−	0.994772i	$-0.532563\pi$
$863$	−6.00000	−0.204242	−0.102121	+	0.994772i	$0.532563\pi$
$864$	20.0000	0.680414
$865$	−2.00000	−0.0680020
$866$	34.0000	1.15537
$867$	26.0000	0.883006
$868$	−12.0000	−0.407307
$869$	0	0
$870$	4.00000	0.135613
$871$	28.0000	0.948744
$872$	−6.00000	−0.203186
$873$	−10.0000	−0.338449
$874$	−16.0000	−0.541208
$875$	2.00000	0.0676123
$876$	4.00000	0.135147
$877$	−14.0000	−0.472746	−0.236373	−	0.971662i	$-0.575959\pi$
$877$	−14.0000	−0.472746	−0.236373	+	0.971662i	$0.575959\pi$
$878$	22.0000	0.742464
$879$	28.0000	0.944417
$880$	0	0
$881$	38.0000	1.28025	0.640126	−	0.768270i	$-0.278882\pi$
$881$	38.0000	1.28025	0.640126	+	0.768270i	$0.278882\pi$
$882$	−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	$0.891318\pi$
$884$	4.00000	0.134535
$885$	−12.0000	−0.403376
$886$	6.00000	0.201574
$887$	−14.0000	−0.470074	−0.235037	−	0.971986i	$-0.575521\pi$
$887$	−14.0000	−0.470074	−0.235037	+	0.971986i	$0.575521\pi$
$888$	−6.00000	−0.201347
$889$	4.00000	0.134156
$890$	−2.00000	−0.0670402
$891$	0	0
$892$	−10.0000	−0.334825
$893$	−20.0000	−0.669274
$894$	12.0000	0.401340
$895$	−14.0000	−0.467968
$896$	6.00000	0.200446
$897$	−32.0000	−1.06845
$898$	−22.0000	−0.734150
$899$	−12.0000	−0.400222
$900$	−1.00000	−0.0333333
$901$	−12.0000	−0.399778
$902$	0	0
$903$	−16.0000	−0.532447
$904$	−6.00000	−0.199557
$905$	−10.0000	−0.332411
$906$	40.0000	1.32891
$907$	−40.0000	−1.32818	−0.664089	−	0.747653i	$-0.731180\pi$
$907$	−40.0000	−1.32818	−0.664089	+	0.747653i	$0.731180\pi$
$908$	8.00000	0.265489
$909$	10.0000	0.331679
$910$	−4.00000	−0.132599
$911$	−10.0000	−0.331315	−0.165657	−	0.986183i	$-0.552975\pi$
$911$	−10.0000	−0.331315	−0.165657	+	0.986183i	$0.552975\pi$
$912$	4.00000	0.132453
$913$	0	0
$914$	−18.0000	−0.595387
$915$	4.00000	0.132236
$916$	18.0000	0.594737
$917$	−36.0000	−1.18882
$918$	8.00000	0.264039
$919$	−26.0000	−0.857661	−0.428830	−	0.903385i	$-0.641074\pi$
$919$	−26.0000	−0.857661	−0.428830	+	0.903385i	$0.641074\pi$
$920$	−24.0000	−0.791257
$921$	−68.0000	−2.24068
$922$	18.0000	0.592798
$923$	0	0
$924$	0	0
$925$	−1.00000	−0.0328798
$926$	−32.0000	−1.05159
$927$	−4.00000	−0.131377
$928$	10.0000	0.328266
$929$	−14.0000	−0.459325	−0.229663	−	0.973270i	$-0.573762\pi$
$929$	−14.0000	−0.459325	−0.229663	+	0.973270i	$0.573762\pi$
$930$	−12.0000	−0.393496
$931$	−6.00000	−0.196642
$932$	14.0000	0.458585
$933$	12.0000	0.392862
$934$	−16.0000	−0.523536
$935$	0	0
$936$	6.00000	0.196116
$937$	−30.0000	−0.980057	−0.490029	−	0.871706i	$-0.663014\pi$
$937$	−30.0000	−0.980057	−0.490029	+	0.871706i	$0.663014\pi$
$938$	28.0000	0.914232
$939$	−44.0000	−1.43589
$940$	−10.0000	−0.326164
$941$	−14.0000	−0.456387	−0.228193	−	0.973616i	$-0.573282\pi$
$941$	−14.0000	−0.456387	−0.228193	+	0.973616i	$0.573282\pi$
$942$	−36.0000	−1.17294
$943$	−80.0000	−2.60516
$944$	6.00000	0.195283
$945$	8.00000	0.260240
$946$	0	0
$947$	32.0000	1.03986	0.519930	−	0.854209i	$-0.325958\pi$
$947$	32.0000	1.03986	0.519930	+	0.854209i	$0.325958\pi$
$948$	−12.0000	−0.389742
$949$	−4.00000	−0.129845
$950$	2.00000	0.0648886
$951$	−68.0000	−2.20505
$952$	12.0000	0.388922
$953$	−54.0000	−1.74923	−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000	−1.74923	−0.874616	+	0.484817i	$0.838886\pi$
$954$	−6.00000	−0.194257
$955$	−22.0000	−0.711903
$956$	6.00000	0.194054
$957$	0	0
$958$	18.0000	0.581554
$959$	12.0000	0.387500
$960$	14.0000	0.451848
$961$	5.00000	0.161290
$962$	2.00000	0.0644826
$963$	6.00000	0.193347
$964$	−10.0000	−0.322078
$965$	−14.0000	−0.450676
$966$	−32.0000	−1.02958
$967$	28.0000	0.900419	0.450210	−	0.892923i	$-0.351349\pi$
$967$	28.0000	0.900419	0.450210	+	0.892923i	$0.351349\pi$
$968$	33.0000	1.06066
$969$	−8.00000	−0.256997
$970$	10.0000	0.321081
$971$	12.0000	0.385098	0.192549	−	0.981287i	$-0.438325\pi$
$971$	12.0000	0.385098	0.192549	+	0.981287i	$0.438325\pi$
$972$	−10.0000	−0.320750
$973$	8.00000	0.256468
$974$	−12.0000	−0.384505
$975$	4.00000	0.128103
$976$	−2.00000	−0.0640184
$977$	−2.00000	−0.0639857	−0.0319928	−	0.999488i	$-0.510185\pi$
$977$	−2.00000	−0.0639857	−0.0319928	+	0.999488i	$0.510185\pi$
$978$	−32.0000	−1.02325
$979$	0	0
$980$	−3.00000	−0.0958315
$981$	2.00000	0.0638551
$982$	20.0000	0.638226
$983$	−10.0000	−0.318950	−0.159475	−	0.987202i	$-0.550980\pi$
$983$	−10.0000	−0.318950	−0.159475	+	0.987202i	$0.550980\pi$
$984$	60.0000	1.91273
$985$	−10.0000	−0.318626
$986$	4.00000	0.127386
$987$	−40.0000	−1.27321
$988$	4.00000	0.127257
$989$	32.0000	1.01754
$990$	0	0
$991$	−22.0000	−0.698853	−0.349427	−	0.936964i	$-0.613624\pi$
$991$	−22.0000	−0.698853	−0.349427	+	0.936964i	$0.613624\pi$
$992$	−30.0000	−0.952501
$993$	52.0000	1.65017
$994$	0	0
$995$	26.0000	0.824255
$996$	36.0000	1.14070
$997$	−6.00000	−0.190022	−0.0950110	−	0.995476i	$-0.530289\pi$
$997$	−6.00000	−0.190022	−0.0950110	+	0.995476i	$0.530289\pi$
$998$	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	185.2.a.c.1.1	✓	1
3.2	odd	2		1665.2.a.b.1.1		1
4.3	odd	2		2960.2.a.k.1.1		1
5.2	odd	4		925.2.b.c.149.2		2
5.3	odd	4		925.2.b.c.149.1		2
5.4	even	2		925.2.a.a.1.1		1
7.6	odd	2		9065.2.a.e.1.1		1
15.14	odd	2		8325.2.a.y.1.1		1
37.36	even	2		6845.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.c.1.1	✓	1	1.1	even	1	trivial
925.2.a.a.1.1		1	5.4	even	2
925.2.b.c.149.1		2	5.3	odd	4
925.2.b.c.149.2		2	5.2	odd	4
1665.2.a.b.1.1		1	3.2	odd	2
2960.2.a.k.1.1		1	4.3	odd	2
6845.2.a.a.1.1		1	37.36	even	2
8325.2.a.y.1.1		1	15.14	odd	2
9065.2.a.e.1.1		1	7.6	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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.a (trivial)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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