LMFDB - Embedded newform 185.2.a.d.1.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(1,185)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage: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")

magma://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:traces = [5,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	yes
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.368464.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{5} - 2x^{4} - 6x^{3} + 6x^{2} + 6x - 4$ x^5 - 2x^4 - 6x^3 + 6x^2 + 6x - 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1.09027$ of defining polynomial
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)

$f(q)$	$=$	$q+1.46516 q^{2} +0.744131 q^{3} +0.146703 q^{4} +1.00000 q^{5} +1.09027 q^{6} +3.94357 q^{7} -2.71538 q^{8} -2.44627 q^{9} +1.46516 q^{10} -4.52210 q^{11} +0.109166 q^{12} +1.36924 q^{13} +5.77797 q^{14} +0.744131 q^{15} -4.27188 q^{16} +2.29957 q^{17} -3.58418 q^{18} +4.84765 q^{19} +0.146703 q^{20} +2.93453 q^{21} -6.62562 q^{22} -4.41859 q^{23} -2.02060 q^{24} +1.00000 q^{25} +2.00616 q^{26} -4.05274 q^{27} +0.578534 q^{28} -9.55595 q^{29} +1.09027 q^{30} -4.75908 q^{31} -0.828243 q^{32} -3.36504 q^{33} +3.36924 q^{34} +3.94357 q^{35} -0.358875 q^{36} -1.00000 q^{37} +7.10259 q^{38} +1.01889 q^{39} -2.71538 q^{40} +5.21439 q^{41} +4.29957 q^{42} -1.19485 q^{43} -0.663407 q^{44} -2.44627 q^{45} -6.47395 q^{46} +5.34785 q^{47} -3.17884 q^{48} +8.55174 q^{49} +1.46516 q^{50} +1.71118 q^{51} +0.200872 q^{52} +1.03384 q^{53} -5.93792 q^{54} -4.52210 q^{55} -10.7083 q^{56} +3.60728 q^{57} -14.0010 q^{58} +14.6197 q^{59} +0.109166 q^{60} +1.30772 q^{61} -6.97283 q^{62} -9.64703 q^{63} +7.33026 q^{64} +1.36924 q^{65} -4.93033 q^{66} +7.23975 q^{67} +0.337354 q^{68} -3.28801 q^{69} +5.77797 q^{70} +15.1787 q^{71} +6.64256 q^{72} -4.81551 q^{73} -1.46516 q^{74} +0.744131 q^{75} +0.711165 q^{76} -17.8332 q^{77} +1.49285 q^{78} +4.64520 q^{79} -4.27188 q^{80} +4.32304 q^{81} +7.63993 q^{82} -5.89279 q^{83} +0.430505 q^{84} +2.29957 q^{85} -1.75066 q^{86} -7.11087 q^{87} +12.2792 q^{88} -10.3435 q^{89} -3.58418 q^{90} +5.39969 q^{91} -0.648221 q^{92} -3.54138 q^{93} +7.83547 q^{94} +4.84765 q^{95} -0.616321 q^{96} +6.37000 q^{97} +12.5297 q^{98} +11.0623 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$5 q - q^{3} + 6 q^{4} + 5 q^{5} - 2 q^{6} + 7 q^{7} - 6 q^{8} + 2 q^{9} + 7 q^{11} + 2 q^{13} + 4 q^{14} - q^{15} + 8 q^{16} - 8 q^{17} - 6 q^{18} + 14 q^{19} + 6 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23}+ \cdots + 18 q^{99}+O(q^{100})$ 5 * q - q^3 + 6 * q^4 + 5 * q^5 - 2 * q^6 + 7 * q^7 - 6 * q^8 + 2 * q^9 + 7 * q^11 + 2 * q^13 + 4 * q^14 - q^15 + 8 * q^16 - 8 * q^17 - 6 * q^18 + 14 * q^19 + 6 * q^20 - 9 * q^21 + 2 * q^22 + 2 * q^23 + 12 * q^24 + 5 * q^25 - 20 * q^26 - 7 * q^27 - 14 * q^28 + 2 * q^29 - 2 * q^30 + 8 * q^31 - 22 * q^32 - 21 * q^33 + 12 * q^34 + 7 * q^35 - 36 * q^36 - 5 * q^37 - 32 * q^38 + 12 * q^39 - 6 * q^40 - 9 * q^41 + 2 * q^42 + 14 * q^43 + 18 * q^44 + 2 * q^45 - 28 * q^46 - 5 * q^47 - 30 * q^48 + 2 * q^49 + 10 * q^51 + 20 * q^52 - 15 * q^53 - 12 * q^54 + 7 * q^55 - 14 * q^56 + 4 * q^57 + 12 * q^59 + 12 * q^61 + 10 * q^62 + 24 * q^63 + 12 * q^64 + 2 * q^65 - 10 * q^66 - 2 * q^67 - 4 * q^68 - 30 * q^69 + 4 * q^70 + 13 * q^71 + 26 * q^72 - 5 * q^73 - q^75 + 18 * q^76 - 7 * q^77 + 10 * q^78 + 36 * q^79 + 8 * q^80 + 21 * q^81 - 2 * q^82 - 9 * q^83 + 30 * q^84 - 8 * q^85 - 8 * q^86 - 6 * q^87 + 8 * q^88 - 16 * q^89 - 6 * q^90 - 4 * q^91 + 12 * q^92 - 16 * q^93 + 20 * q^94 + 14 * q^95 + 30 * q^98 + 18 * q^99

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

)

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

$2$	1.46516	1.03603	0.518013	−	0.855372i	$-0.326672\pi$
$2$	1.46516	1.03603	0.518013	+	0.855372i	$0.326672\pi$
$3$	0.744131	0.429624	0.214812	−	0.976655i	$-0.431086\pi$
$3$	0.744131	0.429624	0.214812	+	0.976655i	$0.431086\pi$
$4$	0.146703	0.0733516
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.09027	0.445102
$7$	3.94357	1.49053	0.745265	−	0.666769i	$-0.232323\pi$
$7$	3.94357	1.49053	0.745265	+	0.666769i	$0.232323\pi$
$8$	−2.71538	−0.960033
$9$	−2.44627	−0.815423
$10$	1.46516	0.463325
$11$	−4.52210	−1.36347	−0.681733	−	0.731601i	$-0.738773\pi$
$11$	−4.52210	−1.36347	−0.681733	+	0.731601i	$0.738773\pi$
$12$	0.109166	0.0315136
$13$	1.36924	0.379759	0.189879	−	0.981807i	$-0.439190\pi$
$13$	1.36924	0.379759	0.189879	+	0.981807i	$0.439190\pi$
$14$	5.77797	1.54423
$15$	0.744131	0.192134
$16$	−4.27188	−1.06797
$17$	2.29957	0.557727	0.278863	−	0.960331i	$-0.410042\pi$
$17$	2.29957	0.557727	0.278863	+	0.960331i	$0.410042\pi$
$18$	−3.58418	−0.844800
$19$	4.84765	1.11213	0.556063	−	0.831140i	$-0.312311\pi$
$19$	4.84765	1.11213	0.556063	+	0.831140i	$0.312311\pi$
$20$	0.146703	0.0328038
$21$	2.93453	0.640367
$22$	−6.62562	−1.41259
$23$	−4.41859	−0.921339	−0.460670	−	0.887572i	$-0.652391\pi$
$23$	−4.41859	−0.921339	−0.460670	+	0.887572i	$0.652391\pi$
$24$	−2.02060	−0.412453
$25$	1.00000	0.200000
$26$	2.00616	0.393440
$27$	−4.05274	−0.779949
$28$	0.578534	0.109333
$29$	−9.55595	−1.77449	−0.887247	−	0.461294i	$-0.847385\pi$
$29$	−9.55595	−1.77449	−0.887247	+	0.461294i	$0.847385\pi$
$30$	1.09027	0.199056
$31$	−4.75908	−0.854756	−0.427378	−	0.904073i	$-0.640563\pi$
$31$	−4.75908	−0.854756	−0.427378	+	0.904073i	$0.640563\pi$
$32$	−0.828243	−0.146414
$33$	−3.36504	−0.585778
$34$	3.36924	0.577820
$35$	3.94357	0.666585
$36$	−0.358875	−0.0598126
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	7.10259	1.15219
$39$	1.01889	0.163154
$40$	−2.71538	−0.429340
$41$	5.21439	0.814351	0.407175	−	0.913350i	$-0.366514\pi$
$41$	5.21439	0.814351	0.407175	+	0.913350i	$0.366514\pi$
$42$	4.29957	0.663438
$43$	−1.19485	−0.182214	−0.0911068	−	0.995841i	$-0.529040\pi$
$43$	−1.19485	−0.182214	−0.0911068	+	0.995841i	$0.529040\pi$
$44$	−0.663407	−0.100012
$45$	−2.44627	−0.364668
$46$	−6.47395	−0.954532
$47$	5.34785	0.780064	0.390032	−	0.920801i	$-0.372464\pi$
$47$	5.34785	0.780064	0.390032	+	0.920801i	$0.372464\pi$
$48$	−3.17884	−0.458826
$49$	8.55174	1.22168
$50$	1.46516	0.207205
$51$	1.71118	0.239613
$52$	0.200872	0.0278559
$53$	1.03384	0.142009	0.0710046	−	0.997476i	$-0.477380\pi$
$53$	1.03384	0.142009	0.0710046	+	0.997476i	$0.477380\pi$
$54$	−5.93792	−0.808048
$55$	−4.52210	−0.609760
$56$	−10.7083	−1.43096
$57$	3.60728	0.477796
$58$	−14.0010	−1.83842
$59$	14.6197	1.90333	0.951664	−	0.307143i	$-0.0993729\pi$
$59$	14.6197	1.90333	0.951664	+	0.307143i	$0.0993729\pi$
$60$	0.109166	0.0140933
$61$	1.30772	0.167436	0.0837179	−	0.996489i	$-0.473321\pi$
$61$	1.30772	0.167436	0.0837179	+	0.996489i	$0.473321\pi$
$62$	−6.97283	−0.885550
$63$	−9.64703	−1.21541
$64$	7.33026	0.916282
$65$	1.36924	0.169833
$66$	−4.93033	−0.606881
$67$	7.23975	0.884476	0.442238	−	0.896898i	$-0.354185\pi$
$67$	7.23975	0.884476	0.442238	+	0.896898i	$0.354185\pi$
$68$	0.337354	0.0409101
$69$	−3.28801	−0.395829
$70$	5.77797	0.690600
$71$	15.1787	1.80138	0.900692	−	0.434458i	$-0.143060\pi$
$71$	15.1787	1.80138	0.900692	+	0.434458i	$0.143060\pi$
$72$	6.64256	0.782833
$73$	−4.81551	−0.563613	−0.281806	−	0.959471i	$-0.590934\pi$
$73$	−4.81551	−0.563613	−0.281806	+	0.959471i	$0.590934\pi$
$74$	−1.46516	−0.170322
$75$	0.744131	0.0859248
$76$	0.711165	0.0815762
$77$	−17.8332	−2.03229
$78$	1.49285	0.169031
$79$	4.64520	0.522626	0.261313	−	0.965254i	$-0.415845\pi$
$79$	4.64520	0.522626	0.261313	+	0.965254i	$0.415845\pi$
$80$	−4.27188	−0.477611
$81$	4.32304	0.480338
$82$	7.63993	0.843689
$83$	−5.89279	−0.646818	−0.323409	−	0.946259i	$-0.604829\pi$
$83$	−5.89279	−0.646818	−0.323409	+	0.946259i	$0.604829\pi$
$84$	0.430505	0.0469719
$85$	2.29957	0.249423
$86$	−1.75066	−0.188778
$87$	−7.11087	−0.762365
$88$	12.2792	1.30897
$89$	−10.3435	−1.09641	−0.548205	−	0.836344i	$-0.684689\pi$
$89$	−10.3435	−1.09641	−0.548205	+	0.836344i	$0.684689\pi$
$90$	−3.58418	−0.377806
$91$	5.39969	0.566042
$92$	−0.648221	−0.0675817
$93$	−3.54138	−0.367224
$94$	7.83547	0.808167
$95$	4.84765	0.497358
$96$	−0.616321	−0.0629030
$97$	6.37000	0.646776	0.323388	−	0.946267i	$-0.395178\pi$
$97$	6.37000	0.646776	0.323388	+	0.946267i	$0.395178\pi$
$98$	12.5297	1.26569
$99$	11.0623	1.11180
$100$	0.146703	0.0146703
$101$	−4.62142	−0.459848	−0.229924	−	0.973209i	$-0.573848\pi$
$101$	−4.62142	−0.459848	−0.229924	+	0.973209i	$0.573848\pi$
$102$	2.50715	0.248245
$103$	18.3734	1.81039	0.905193	−	0.425001i	$-0.139726\pi$
$103$	18.3734	1.81039	0.905193	+	0.425001i	$0.139726\pi$
$104$	−3.71801	−0.364581
$105$	2.93453	0.286381
$106$	1.51475	0.147125
$107$	−17.8700	−1.72755	−0.863777	−	0.503875i	$-0.831907\pi$
$107$	−17.8700	−1.72755	−0.863777	+	0.503875i	$0.831907\pi$
$108$	−0.594549	−0.0572105
$109$	−3.03189	−0.290402	−0.145201	−	0.989402i	$-0.546383\pi$
$109$	−3.03189	−0.290402	−0.145201	+	0.989402i	$0.546383\pi$
$110$	−6.62562	−0.631728
$111$	−0.744131	−0.0706298
$112$	−16.8465	−1.59184
$113$	−20.1901	−1.89933	−0.949663	−	0.313273i	$-0.898575\pi$
$113$	−20.1901	−1.89933	−0.949663	+	0.313273i	$0.898575\pi$
$114$	5.28526	0.495010
$115$	−4.41859	−0.412035
$116$	−1.40189	−0.130162
$117$	−3.34953	−0.309664
$118$	21.4203	1.97190
$119$	9.06850	0.831308
$120$	−2.02060	−0.184455
$121$	9.44942	0.859038
$122$	1.91602	0.173468
$123$	3.88019	0.349865
$124$	−0.698172	−0.0626977
$125$	1.00000	0.0894427
$126$	−14.1345	−1.25920
$127$	−13.5915	−1.20605	−0.603025	−	0.797722i	$-0.706038\pi$
$127$	−13.5915	−1.20605	−0.603025	+	0.797722i	$0.706038\pi$
$128$	12.3965	1.09571
$129$	−0.889128	−0.0782834
$130$	2.00616	0.175952
$131$	21.1799	1.85049	0.925246	−	0.379367i	$-0.123858\pi$
$131$	21.1799	1.85049	0.925246	+	0.379367i	$0.123858\pi$
$132$	−0.493661	−0.0429677
$133$	19.1170	1.65766
$134$	10.6074	0.916341
$135$	−4.05274	−0.348804
$136$	−6.24420	−0.535436
$137$	7.17856	0.613305	0.306653	−	0.951821i	$-0.400791\pi$
$137$	7.17856	0.613305	0.306653	+	0.951821i	$0.400791\pi$
$138$	−4.81747	−0.410090
$139$	−12.9602	−1.09927	−0.549636	−	0.835404i	$-0.685234\pi$
$139$	−12.9602	−1.09927	−0.549636	+	0.835404i	$0.685234\pi$
$140$	0.578534	0.0488950
$141$	3.97950	0.335134
$142$	22.2393	1.86628
$143$	−6.19185	−0.517788
$144$	10.4502	0.870848
$145$	−9.55595	−0.793578
$146$	−7.05551	−0.583918
$147$	6.36361	0.524862
$148$	−0.146703	−0.0120589
$149$	−15.8451	−1.29809	−0.649043	−	0.760752i	$-0.724830\pi$
$149$	−15.8451	−1.29809	−0.649043	+	0.760752i	$0.724830\pi$
$150$	1.09027	0.0890204
$151$	14.2944	1.16326	0.581632	−	0.813452i	$-0.302414\pi$
$151$	14.2944	1.16326	0.581632	+	0.813452i	$0.302414\pi$
$152$	−13.1632	−1.06768
$153$	−5.62536	−0.454783
$154$	−26.1286	−2.10550
$155$	−4.75908	−0.382258
$156$	0.149475	0.0119676
$157$	−1.95398	−0.155945	−0.0779723	−	0.996956i	$-0.524845\pi$
$157$	−1.95398	−0.155945	−0.0779723	+	0.996956i	$0.524845\pi$
$158$	6.80597	0.541454
$159$	0.769314	0.0610105
$160$	−0.828243	−0.0654784
$161$	−17.4250	−1.37328
$162$	6.33397	0.497643
$163$	3.01431	0.236099	0.118049	−	0.993008i	$-0.462336\pi$
$163$	3.01431	0.236099	0.118049	+	0.993008i	$0.462336\pi$
$164$	0.764967	0.0597339
$165$	−3.36504	−0.261968
$166$	−8.63390	−0.670120
$167$	4.16008	0.321916	0.160958	−	0.986961i	$-0.448542\pi$
$167$	4.16008	0.321916	0.160958	+	0.986961i	$0.448542\pi$
$168$	−7.96837	−0.614773
$169$	−11.1252	−0.855783
$170$	3.36924	0.258409
$171$	−11.8587	−0.906854
$172$	−0.175289	−0.0133657
$173$	−3.79279	−0.288361	−0.144180	−	0.989551i	$-0.546055\pi$
$173$	−3.79279	−0.288361	−0.144180	+	0.989551i	$0.546055\pi$
$174$	−10.4186	−0.789831
$175$	3.94357	0.298106
$176$	19.3179	1.45614
$177$	10.8790	0.817715
$178$	−15.1549	−1.13591
$179$	−13.0017	−0.971793	−0.485897	−	0.874016i	$-0.661507\pi$
$179$	−13.0017	−0.971793	−0.485897	+	0.874016i	$0.661507\pi$
$180$	−0.358875	−0.0267490
$181$	−16.6739	−1.23936	−0.619681	−	0.784854i	$-0.712738\pi$
$181$	−16.6739	−1.23936	−0.619681	+	0.784854i	$0.712738\pi$
$182$	7.91143	0.586434
$183$	0.973111	0.0719345
$184$	11.9982	0.884516
$185$	−1.00000	−0.0735215
$186$	−5.18869	−0.380454
$187$	−10.3989	−0.760441
$188$	0.784546	0.0572189
$189$	−15.9822	−1.16254
$190$	7.10259	0.515276
$191$	8.73937	0.632359	0.316179	−	0.948699i	$-0.397600\pi$
$191$	8.73937	0.632359	0.316179	+	0.948699i	$0.397600\pi$
$192$	5.45467	0.393657
$193$	21.6457	1.55809	0.779047	−	0.626966i	$-0.215703\pi$
$193$	21.6457	1.55809	0.779047	+	0.626966i	$0.215703\pi$
$194$	9.33309	0.670077
$195$	1.01889	0.0729645
$196$	1.25457	0.0896119
$197$	−2.60609	−0.185676	−0.0928380	−	0.995681i	$-0.529594\pi$
$197$	−2.60609	−0.185676	−0.0928380	+	0.995681i	$0.529594\pi$
$198$	16.2081	1.15186
$199$	−6.57573	−0.466141	−0.233071	−	0.972460i	$-0.574877\pi$
$199$	−6.57573	−0.466141	−0.233071	+	0.972460i	$0.574877\pi$
$200$	−2.71538	−0.192007
$201$	5.38732	0.379992
$202$	−6.77113	−0.476415
$203$	−37.6845	−2.64494
$204$	0.251035	0.0175760
$205$	5.21439	0.364189
$206$	26.9200	1.87561
$207$	10.8091	0.751281
$208$	−5.84924	−0.405572
$209$	−21.9216	−1.51635
$210$	4.29957	0.296698
$211$	−2.00196	−0.137820	−0.0689102	−	0.997623i	$-0.521952\pi$
$211$	−2.00196	−0.137820	−0.0689102	+	0.997623i	$0.521952\pi$
$212$	0.151668	0.0104166
$213$	11.2950	0.773918
$214$	−26.1824	−1.78979
$215$	−1.19485	−0.0814884
$216$	11.0047	0.748777
$217$	−18.7678	−1.27404
$218$	−4.44221	−0.300864
$219$	−3.58337	−0.242142
$220$	−0.663407	−0.0447269
$221$	3.14866	0.211802
$222$	−1.09027	−0.0731743
$223$	−7.43402	−0.497819	−0.248910	−	0.968527i	$-0.580072\pi$
$223$	−7.43402	−0.497819	−0.248910	+	0.968527i	$0.580072\pi$
$224$	−3.26623	−0.218234
$225$	−2.44627	−0.163085
$226$	−29.5818	−1.96775
$227$	−0.633009	−0.0420143	−0.0210071	−	0.999779i	$-0.506687\pi$
$227$	−0.633009	−0.0420143	−0.0210071	+	0.999779i	$0.506687\pi$
$228$	0.529200	0.0350471
$229$	15.9122	1.05151	0.525754	−	0.850636i	$-0.323783\pi$
$229$	15.9122	1.05151	0.525754	+	0.850636i	$0.323783\pi$
$230$	−6.47395	−0.426880
$231$	−13.2703	−0.873119
$232$	25.9480	1.70357
$233$	−8.89467	−0.582709	−0.291355	−	0.956615i	$-0.594106\pi$
$233$	−8.89467	−0.582709	−0.291355	+	0.956615i	$0.594106\pi$
$234$	−4.90761	−0.320820
$235$	5.34785	0.348855
$236$	2.14476	0.139612
$237$	3.45663	0.224533
$238$	13.2868	0.861257
$239$	−0.0826797	−0.00534810	−0.00267405	−	0.999996i	$-0.500851\pi$
$239$	−0.0826797	−0.00534810	−0.00267405	+	0.999996i	$0.500851\pi$
$240$	−3.17884	−0.205193
$241$	−19.6320	−1.26461	−0.632305	−	0.774719i	$-0.717891\pi$
$241$	−19.6320	−1.26461	−0.632305	+	0.774719i	$0.717891\pi$
$242$	13.8449	0.889987
$243$	15.3751	0.986314
$244$	0.191846	0.0122817
$245$	8.55174	0.546351
$246$	5.68511	0.362469
$247$	6.63759	0.422340
$248$	12.9227	0.820594
$249$	−4.38501	−0.277888
$250$	1.46516	0.0926651
$251$	−3.16254	−0.199618	−0.0998089	−	0.995007i	$-0.531823\pi$
$251$	−3.16254	−0.199618	−0.0998089	+	0.995007i	$0.531823\pi$
$252$	−1.41525	−0.0891524
$253$	19.9813	1.25621
$254$	−19.9138	−1.24950
$255$	1.71118	0.107158
$256$	3.50239	0.218900
$257$	−11.7279	−0.731569	−0.365784	−	0.930700i	$-0.619199\pi$
$257$	−11.7279	−0.731569	−0.365784	+	0.930700i	$0.619199\pi$
$258$	−1.30272	−0.0811037
$259$	−3.94357	−0.245041
$260$	0.200872	0.0124575
$261$	23.3764	1.44696
$262$	31.0320	1.91716
$263$	0.755431	0.0465819	0.0232909	−	0.999729i	$-0.492586\pi$
$263$	0.755431	0.0465819	0.0232909	+	0.999729i	$0.492586\pi$
$264$	9.13736	0.562366
$265$	1.03384	0.0635084
$266$	28.0096	1.71738
$267$	−7.69693	−0.471044
$268$	1.06209	0.0648777
$269$	13.4542	0.820320	0.410160	−	0.912014i	$-0.365473\pi$
$269$	13.4542	0.820320	0.410160	+	0.912014i	$0.365473\pi$
$270$	−5.93792	−0.361370
$271$	7.94268	0.482483	0.241242	−	0.970465i	$-0.422445\pi$
$271$	7.94268	0.482483	0.241242	+	0.970465i	$0.422445\pi$
$272$	−9.82348	−0.595636
$273$	4.01808	0.243185
$274$	10.5178	0.635401
$275$	−4.52210	−0.272693
$276$	−0.482361	−0.0290347
$277$	6.88638	0.413762	0.206881	−	0.978366i	$-0.433669\pi$
$277$	6.88638	0.413762	0.206881	+	0.978366i	$0.433669\pi$
$278$	−18.9888	−1.13888
$279$	11.6420	0.696988
$280$	−10.7083	−0.639943
$281$	16.0874	0.959693	0.479847	−	0.877352i	$-0.340692\pi$
$281$	16.0874	0.959693	0.479847	+	0.877352i	$0.340692\pi$
$282$	5.83061	0.347208
$283$	24.9263	1.48172	0.740859	−	0.671661i	$-0.234419\pi$
$283$	24.9263	1.48172	0.740859	+	0.671661i	$0.234419\pi$
$284$	2.22677	0.132134
$285$	3.60728	0.213677
$286$	−9.07206	−0.536442
$287$	20.5633	1.21381
$288$	2.02611	0.119389
$289$	−11.7120	−0.688941
$290$	−14.0010	−0.822168
$291$	4.74011	0.277870
$292$	−0.706450	−0.0413419
$293$	26.0732	1.52321	0.761607	−	0.648039i	$-0.224411\pi$
$293$	26.0732	1.52321	0.761607	+	0.648039i	$0.224411\pi$
$294$	9.32373	0.543771
$295$	14.6197	0.851194
$296$	2.71538	0.157828
$297$	18.3269	1.06343
$298$	−23.2157	−1.34485
$299$	−6.05011	−0.349887
$300$	0.109166	0.00630272
$301$	−4.71199	−0.271595
$302$	20.9437	1.20517
$303$	−3.43894	−0.197562
$304$	−20.7086	−1.18772
$305$	1.30772	0.0748796
$306$	−8.24207	−0.471168
$307$	−18.2979	−1.04432	−0.522158	−	0.852849i	$-0.674873\pi$
$307$	−18.2979	−1.04432	−0.522158	+	0.852849i	$0.674873\pi$
$308$	−2.61619	−0.149071
$309$	13.6722	0.777785
$310$	−6.97283	−0.396030
$311$	−1.44118	−0.0817216	−0.0408608	−	0.999165i	$-0.513010\pi$
$311$	−1.44118	−0.0817216	−0.0408608	+	0.999165i	$0.513010\pi$
$312$	−2.76669	−0.156633
$313$	−18.5015	−1.04576	−0.522882	−	0.852405i	$-0.675143\pi$
$313$	−18.5015	−1.04576	−0.522882	+	0.852405i	$0.675143\pi$
$314$	−2.86290	−0.161563
$315$	−9.64703	−0.543549
$316$	0.681465	0.0383354
$317$	−24.1703	−1.35754	−0.678769	−	0.734352i	$-0.737486\pi$
$317$	−24.1703	−1.35754	−0.678769	+	0.734352i	$0.737486\pi$
$318$	1.12717	0.0632086
$319$	43.2130	2.41946
$320$	7.33026	0.409774
$321$	−13.2976	−0.742198
$322$	−25.5305	−1.42276
$323$	11.1475	0.620263
$324$	0.634204	0.0352336
$325$	1.36924	0.0759518
$326$	4.41646	0.244605
$327$	−2.25612	−0.124764
$328$	−14.1591	−0.781803
$329$	21.0896	1.16271
$330$	−4.93033	−0.271406
$331$	−0.308401	−0.0169513	−0.00847563	−	0.999964i	$-0.502698\pi$
$331$	−0.308401	−0.0169513	−0.00847563	+	0.999964i	$0.502698\pi$
$332$	−0.864491	−0.0474451
$333$	2.44627	0.134055
$334$	6.09519	0.333514
$335$	7.23975	0.395550
$336$	−12.5360	−0.683894
$337$	−17.7374	−0.966219	−0.483110	−	0.875560i	$-0.660493\pi$
$337$	−17.7374	−0.966219	−0.483110	+	0.875560i	$0.660493\pi$
$338$	−16.3002	−0.886614
$339$	−15.0241	−0.815996
$340$	0.337354	0.0182956
$341$	21.5211	1.16543
$342$	−17.3749	−0.939525
$343$	6.11940	0.330417
$344$	3.24449	0.174931
$345$	−3.28801	−0.177020
$346$	−5.55706	−0.298749
$347$	13.4103	0.719902	0.359951	−	0.932971i	$-0.382793\pi$
$347$	13.4103	0.719902	0.359951	+	0.932971i	$0.382793\pi$
$348$	−1.04319	−0.0559207
$349$	−18.0187	−0.964521	−0.482261	−	0.876028i	$-0.660184\pi$
$349$	−18.0187	−0.964521	−0.482261	+	0.876028i	$0.660184\pi$
$350$	5.77797	0.308846
$351$	−5.54917	−0.296193
$352$	3.74540	0.199631
$353$	−16.5967	−0.883355	−0.441678	−	0.897174i	$-0.645617\pi$
$353$	−16.5967	−0.883355	−0.441678	+	0.897174i	$0.645617\pi$
$354$	15.9395	0.847175
$355$	15.1787	0.805604
$356$	−1.51743	−0.0804234
$357$	6.74815	0.357150
$358$	−19.0496	−1.00680
$359$	0.294342	0.0155348	0.00776739	−	0.999970i	$-0.497528\pi$
$359$	0.294342	0.0155348	0.00776739	+	0.999970i	$0.497528\pi$
$360$	6.64256	0.350094
$361$	4.49968	0.236825
$362$	−24.4300	−1.28401
$363$	7.03160	0.369063
$364$	0.792152	0.0415200
$365$	−4.81551	−0.252055
$366$	1.42577	0.0745260
$367$	23.2638	1.21436	0.607181	−	0.794563i	$-0.292300\pi$
$367$	23.2638	1.21436	0.607181	+	0.794563i	$0.292300\pi$
$368$	18.8757	0.983964
$369$	−12.7558	−0.664040
$370$	−1.46516	−0.0761702
$371$	4.07703	0.211669
$372$	−0.519531	−0.0269364
$373$	−37.2311	−1.92776	−0.963878	−	0.266345i	$-0.914184\pi$
$373$	−37.2311	−1.92776	−0.963878	+	0.266345i	$0.914184\pi$
$374$	−15.2361	−0.787838
$375$	0.744131	0.0384267
$376$	−14.5215	−0.748887
$377$	−13.0844	−0.673880
$378$	−23.4166	−1.20442
$379$	−23.0305	−1.18300	−0.591498	−	0.806306i	$-0.701463\pi$
$379$	−23.0305	−1.18300	−0.591498	+	0.806306i	$0.701463\pi$
$380$	0.711165	0.0364820
$381$	−10.1138	−0.518148
$382$	12.8046	0.655140
$383$	−12.8637	−0.657302	−0.328651	−	0.944451i	$-0.606594\pi$
$383$	−12.8637	−0.657302	−0.328651	+	0.944451i	$0.606594\pi$
$384$	9.22462	0.470742
$385$	−17.8332	−0.908866
$386$	31.7145	1.61423
$387$	2.92294	0.148581
$388$	0.934499	0.0474420
$389$	−16.1194	−0.817287	−0.408644	−	0.912694i	$-0.633998\pi$
$389$	−16.1194	−0.817287	−0.408644	+	0.912694i	$0.633998\pi$
$390$	1.49285	0.0755932
$391$	−10.1608	−0.513856
$392$	−23.2212	−1.17285
$393$	15.7606	0.795016
$394$	−3.81834	−0.192365
$395$	4.64520	0.233725
$396$	1.62287	0.0815524
$397$	−12.9491	−0.649897	−0.324948	−	0.945732i	$-0.605347\pi$
$397$	−12.9491	−0.649897	−0.324948	+	0.945732i	$0.605347\pi$
$398$	−9.63452	−0.482935
$399$	14.2256	0.712169
$400$	−4.27188	−0.213594
$401$	−17.2452	−0.861185	−0.430593	−	0.902546i	$-0.641695\pi$
$401$	−17.2452	−0.861185	−0.430593	+	0.902546i	$0.641695\pi$
$402$	7.89330	0.393682
$403$	−6.51632	−0.324601
$404$	−0.677976	−0.0337306
$405$	4.32304	0.214814
$406$	−55.2140	−2.74022
$407$	4.52210	0.224152
$408$	−4.64650	−0.230036
$409$	31.2920	1.54729	0.773644	−	0.633621i	$-0.218432\pi$
$409$	31.2920	1.54729	0.773644	+	0.633621i	$0.218432\pi$
$410$	7.63993	0.377309
$411$	5.34178	0.263491
$412$	2.69544	0.132795
$413$	57.6539	2.83696
$414$	15.8370	0.778348
$415$	−5.89279	−0.289266
$416$	−1.13406	−0.0556020
$417$	−9.64410	−0.472274
$418$	−32.1187	−1.57098
$419$	−11.8203	−0.577459	−0.288730	−	0.957411i	$-0.593233\pi$
$419$	−11.8203	−0.577459	−0.288730	+	0.957411i	$0.593233\pi$
$420$	0.430505	0.0210065
$421$	19.1673	0.934155	0.467077	−	0.884216i	$-0.345307\pi$
$421$	19.1673	0.934155	0.467077	+	0.884216i	$0.345307\pi$
$422$	−2.93319	−0.142786
$423$	−13.0823	−0.636082
$424$	−2.80728	−0.136333
$425$	2.29957	0.111545
$426$	16.5490	0.801800
$427$	5.15707	0.249568
$428$	−2.62158	−0.126719
$429$	−4.60754	−0.222454
$430$	−1.75066	−0.0844242
$431$	9.78469	0.471312	0.235656	−	0.971837i	$-0.424276\pi$
$431$	9.78469	0.471312	0.235656	+	0.971837i	$0.424276\pi$
$432$	17.3128	0.832963
$433$	35.2661	1.69478	0.847391	−	0.530969i	$-0.178172\pi$
$433$	35.2661	1.69478	0.847391	+	0.530969i	$0.178172\pi$
$434$	−27.4978	−1.31994
$435$	−7.11087	−0.340940
$436$	−0.444787	−0.0213014
$437$	−21.4198	−1.02465
$438$	−5.25022	−0.250865
$439$	24.4934	1.16901	0.584503	−	0.811392i	$-0.301290\pi$
$439$	24.4934	1.16901	0.584503	+	0.811392i	$0.301290\pi$
$440$	12.2792	0.585390
$441$	−20.9199	−0.996184
$442$	4.61330	0.219432
$443$	−26.1850	−1.24409	−0.622044	−	0.782982i	$-0.713698\pi$
$443$	−26.1850	−1.24409	−0.622044	+	0.782982i	$0.713698\pi$
$444$	−0.109166	−0.00518080
$445$	−10.3435	−0.490330
$446$	−10.8921	−0.515754
$447$	−11.7909	−0.557689
$448$	28.9074	1.36575
$449$	39.6969	1.87341	0.936705	−	0.350119i	$-0.113859\pi$
$449$	39.6969	1.87341	0.936705	+	0.350119i	$0.113859\pi$
$450$	−3.58418	−0.168960
$451$	−23.5800	−1.11034
$452$	−2.96195	−0.139319
$453$	10.6369	0.499766
$454$	−0.927461	−0.0435279
$455$	5.39969	0.253142
$456$	−9.79515	−0.458700
$457$	20.6802	0.967380	0.483690	−	0.875239i	$-0.339296\pi$
$457$	20.6802	0.967380	0.483690	+	0.875239i	$0.339296\pi$
$458$	23.3140	1.08939
$459$	−9.31954	−0.434999
$460$	−0.648221	−0.0302234
$461$	−5.51764	−0.256982	−0.128491	−	0.991711i	$-0.541013\pi$
$461$	−5.51764	−0.256982	−0.128491	+	0.991711i	$0.541013\pi$
$462$	−19.4431	−0.904574
$463$	20.9783	0.974944	0.487472	−	0.873139i	$-0.337919\pi$
$463$	20.9783	0.974944	0.487472	+	0.873139i	$0.337919\pi$
$464$	40.8219	1.89511
$465$	−3.54138	−0.164227
$466$	−13.0321	−0.603702
$467$	−7.62261	−0.352732	−0.176366	−	0.984325i	$-0.556434\pi$
$467$	−7.62261	−0.352732	−0.176366	+	0.984325i	$0.556434\pi$
$468$	−0.491387	−0.0227144
$469$	28.5504	1.31834
$470$	7.83547	0.361423
$471$	−1.45402	−0.0669976
$472$	−39.6982	−1.82726
$473$	5.40326	0.248442
$474$	5.06453	0.232622
$475$	4.84765	0.222425
$476$	1.33038	0.0609777
$477$	−2.52906	−0.115798
$478$	−0.121139	−0.00554078
$479$	32.7445	1.49613	0.748067	−	0.663623i	$-0.230982\pi$
$479$	32.7445	1.49613	0.748067	+	0.663623i	$0.230982\pi$
$480$	−0.616321	−0.0281311
$481$	−1.36924	−0.0624320
$482$	−28.7641	−1.31017
$483$	−12.9665	−0.589995
$484$	1.38626	0.0630118
$485$	6.37000	0.289247
$486$	22.5271	1.02185
$487$	−24.3487	−1.10335	−0.551673	−	0.834061i	$-0.686010\pi$
$487$	−24.3487	−1.10335	−0.551673	+	0.834061i	$0.686010\pi$
$488$	−3.55095	−0.160744
$489$	2.24304	0.101434
$490$	12.5297	0.566034
$491$	9.88214	0.445975	0.222987	−	0.974821i	$-0.428419\pi$
$491$	9.88214	0.445975	0.222987	+	0.974821i	$0.428419\pi$
$492$	0.569235	0.0256631
$493$	−21.9745	−0.989683
$494$	9.72516	0.437555
$495$	11.0623	0.497213
$496$	20.3302	0.912855
$497$	59.8584	2.68502
$498$	−6.42475	−0.287900
$499$	38.4155	1.71971	0.859857	−	0.510535i	$-0.170553\pi$
$499$	38.4155	1.71971	0.859857	+	0.510535i	$0.170553\pi$
$500$	0.146703	0.00656076
$501$	3.09564	0.138303
$502$	−4.63364	−0.206809
$503$	−14.2482	−0.635297	−0.317649	−	0.948209i	$-0.602893\pi$
$503$	−14.2482	−0.635297	−0.317649	+	0.948209i	$0.602893\pi$
$504$	26.1954	1.16684
$505$	−4.62142	−0.205650
$506$	29.2759	1.30147
$507$	−8.27859	−0.367665
$508$	−1.99391	−0.0884657
$509$	28.0410	1.24290	0.621448	−	0.783455i	$-0.286545\pi$
$509$	28.0410	1.24290	0.621448	+	0.783455i	$0.286545\pi$
$510$	2.50715	0.111019
$511$	−18.9903	−0.840081
$512$	−19.6614	−0.868921
$513$	−19.6462	−0.867402
$514$	−17.1833	−0.757925
$515$	18.3734	0.809629
$516$	−0.130438	−0.00574221
$517$	−24.1835	−1.06359
$518$	−5.77797	−0.253870
$519$	−2.82233	−0.123887
$520$	−3.71801	−0.163046
$521$	31.3715	1.37441	0.687204	−	0.726464i	$-0.258838\pi$
$521$	31.3715	1.37441	0.687204	+	0.726464i	$0.258838\pi$
$522$	34.2503	1.49909
$523$	−37.1439	−1.62419	−0.812095	−	0.583525i	$-0.801673\pi$
$523$	−37.1439	−1.62419	−0.812095	+	0.583525i	$0.801673\pi$
$524$	3.10715	0.135737
$525$	2.93453	0.128073
$526$	1.10683	0.0482601
$527$	−10.9438	−0.476720
$528$	14.3750	0.625593
$529$	−3.47608	−0.151134
$530$	1.51475	0.0657964
$531$	−35.7638	−1.55202
$532$	2.80453	0.121592
$533$	7.13975	0.309257
$534$	−11.2773	−0.488014
$535$	−17.8700	−0.772585
$536$	−19.6587	−0.849126
$537$	−9.67497	−0.417506
$538$	19.7127	0.849873
$539$	−38.6719	−1.66571
$540$	−0.594549	−0.0255853
$541$	−4.01732	−0.172718	−0.0863590	−	0.996264i	$-0.527523\pi$
$541$	−4.01732	−0.172718	−0.0863590	+	0.996264i	$0.527523\pi$
$542$	11.6373	0.499866
$543$	−12.4076	−0.532460
$544$	−1.90460	−0.0816591
$545$	−3.03189	−0.129872
$546$	5.88714	0.251946
$547$	−40.4991	−1.73162	−0.865809	−	0.500375i	$-0.833195\pi$
$547$	−40.4991	−1.73162	−0.865809	+	0.500375i	$0.833195\pi$
$548$	1.05312	0.0449869
$549$	−3.19903	−0.136531
$550$	−6.62562	−0.282517
$551$	−46.3238	−1.97346
$552$	8.92819	0.380009
$553$	18.3187	0.778989
$554$	10.0897	0.428669
$555$	−0.744131	−0.0315866
$556$	−1.90131	−0.0806333
$557$	41.5078	1.75874	0.879370	−	0.476139i	$-0.157964\pi$
$557$	41.5078	1.75874	0.879370	+	0.476139i	$0.157964\pi$
$558$	17.0574	0.722098
$559$	−1.63604	−0.0691973
$560$	−16.8465	−0.711893
$561$	−7.73812	−0.326704
$562$	23.5707	0.994268
$563$	8.82377	0.371877	0.185939	−	0.982561i	$-0.440467\pi$
$563$	8.82377	0.371877	0.185939	+	0.982561i	$0.440467\pi$
$564$	0.583805	0.0245826
$565$	−20.1901	−0.849405
$566$	36.5212	1.53510
$567$	17.0482	0.715958
$568$	−41.2161	−1.72939
$569$	−1.06707	−0.0447338	−0.0223669	−	0.999750i	$-0.507120\pi$
$569$	−1.06707	−0.0447338	−0.0223669	+	0.999750i	$0.507120\pi$
$570$	5.28526	0.221375
$571$	3.43435	0.143723	0.0718616	−	0.997415i	$-0.477106\pi$
$571$	3.43435	0.143723	0.0718616	+	0.997415i	$0.477106\pi$
$572$	−0.908363	−0.0379806
$573$	6.50323	0.271676
$574$	30.1286	1.25754
$575$	−4.41859	−0.184268
$576$	−17.9318	−0.747158
$577$	30.2801	1.26058	0.630289	−	0.776361i	$-0.282936\pi$
$577$	30.2801	1.26058	0.630289	+	0.776361i	$0.282936\pi$
$578$	−17.1600	−0.713761
$579$	16.1073	0.669395
$580$	−1.40189	−0.0582102
$581$	−23.2386	−0.964101
$582$	6.94504	0.287881
$583$	−4.67514	−0.193625
$584$	13.0760	0.541087
$585$	−3.34953	−0.138486
$586$	38.2015	1.57809
$587$	−10.4265	−0.430347	−0.215173	−	0.976576i	$-0.569032\pi$
$587$	−10.4265	−0.430347	−0.215173	+	0.976576i	$0.569032\pi$
$588$	0.933562	0.0384994
$589$	−23.0703	−0.950597
$590$	21.4203	0.881860
$591$	−1.93927	−0.0797709
$592$	4.27188	0.175573
$593$	19.5382	0.802337	0.401169	−	0.916004i	$-0.368604\pi$
$593$	19.5382	0.802337	0.401169	+	0.916004i	$0.368604\pi$
$594$	26.8519	1.10175
$595$	9.06850	0.371772
$596$	−2.32453	−0.0952166
$597$	−4.89320	−0.200265
$598$	−8.86439	−0.362492
$599$	−9.95917	−0.406921	−0.203460	−	0.979083i	$-0.565219\pi$
$599$	−9.95917	−0.406921	−0.203460	+	0.979083i	$0.565219\pi$
$600$	−2.02060	−0.0824906
$601$	0.201892	0.00823534	0.00411767	−	0.999992i	$-0.498689\pi$
$601$	0.201892	0.00823534	0.00411767	+	0.999992i	$0.498689\pi$
$602$	−6.90384	−0.281380
$603$	−17.7104	−0.721222
$604$	2.09704	0.0853272
$605$	9.44942	0.384174
$606$	−5.03860	−0.204679
$607$	33.5993	1.36375	0.681876	−	0.731468i	$-0.261164\pi$
$607$	33.5993	1.36375	0.681876	+	0.731468i	$0.261164\pi$
$608$	−4.01503	−0.162831
$609$	−28.0422	−1.13633
$610$	1.91602	0.0775773
$611$	7.32249	0.296236
$612$	−0.825258	−0.0333591
$613$	8.63736	0.348859	0.174430	−	0.984670i	$-0.444192\pi$
$613$	8.63736	0.348859	0.174430	+	0.984670i	$0.444192\pi$
$614$	−26.8094	−1.08194
$615$	3.88019	0.156464
$616$	48.4240	1.95106
$617$	8.37257	0.337067	0.168533	−	0.985696i	$-0.446097\pi$
$617$	8.37257	0.337067	0.168533	+	0.985696i	$0.446097\pi$
$618$	20.0320	0.805806
$619$	−0.670360	−0.0269441	−0.0134720	−	0.999909i	$-0.504288\pi$
$619$	−0.670360	−0.0269441	−0.0134720	+	0.999909i	$0.504288\pi$
$620$	−0.698172	−0.0280393
$621$	17.9074	0.718598
$622$	−2.11156	−0.0846657
$623$	−40.7904	−1.63423
$624$	−4.35260	−0.174243
$625$	1.00000	0.0400000
$626$	−27.1077	−1.08344
$627$	−16.3125	−0.651459
$628$	−0.286655	−0.0114388
$629$	−2.29957	−0.0916897
$630$	−14.1345	−0.563131
$631$	15.0416	0.598798	0.299399	−	0.954128i	$-0.403214\pi$
$631$	15.0416	0.598798	0.299399	+	0.954128i	$0.403214\pi$
$632$	−12.6135	−0.501738
$633$	−1.48972	−0.0592109
$634$	−35.4134	−1.40645
$635$	−13.5915	−0.539362
$636$	0.112861	0.00447522
$637$	11.7094	0.463943
$638$	63.3141	2.50663
$639$	−37.1313	−1.46889
$640$	12.3965	0.490015
$641$	18.9440	0.748241	0.374121	−	0.927380i	$-0.377945\pi$
$641$	18.9440	0.748241	0.374121	+	0.927380i	$0.377945\pi$
$642$	−19.4831	−0.768937
$643$	−27.9869	−1.10369	−0.551847	−	0.833945i	$-0.686077\pi$
$643$	−27.9869	−1.10369	−0.551847	+	0.833945i	$0.686077\pi$
$644$	−2.55630	−0.100732
$645$	−0.889128	−0.0350094
$646$	16.3329	0.642609
$647$	20.3334	0.799387	0.399694	−	0.916649i	$-0.369117\pi$
$647$	20.3334	0.799387	0.399694	+	0.916649i	$0.369117\pi$
$648$	−11.7387	−0.461140
$649$	−66.1119	−2.59512
$650$	2.00616	0.0786881
$651$	−13.9657	−0.547358
$652$	0.442209	0.0173182
$653$	−12.5212	−0.489991	−0.244996	−	0.969524i	$-0.578787\pi$
$653$	−12.5212	−0.489991	−0.244996	+	0.969524i	$0.578787\pi$
$654$	−3.30558	−0.129259
$655$	21.1799	0.827566
$656$	−22.2753	−0.869703
$657$	11.7800	0.459583
$658$	30.8997	1.20460
$659$	−10.5140	−0.409565	−0.204783	−	0.978807i	$-0.565649\pi$
$659$	−10.5140	−0.409565	−0.204783	+	0.978807i	$0.565649\pi$
$660$	−0.493661	−0.0192157
$661$	12.9804	0.504880	0.252440	−	0.967613i	$-0.418767\pi$
$661$	12.9804	0.504880	0.252440	+	0.967613i	$0.418767\pi$
$662$	−0.451858	−0.0175620
$663$	2.34301	0.0909951
$664$	16.0012	0.620966
$665$	19.1170	0.741327
$666$	3.58418	0.138884
$667$	42.2238	1.63491
$668$	0.610296	0.0236131
$669$	−5.53188	−0.213875
$670$	10.6074	0.409800
$671$	−5.91363	−0.228293
$672$	−2.43050	−0.0937588
$673$	2.47979	0.0955890	0.0477945	−	0.998857i	$-0.484781\pi$
$673$	2.47979	0.0955890	0.0477945	+	0.998857i	$0.484781\pi$
$674$	−25.9882	−1.00103
$675$	−4.05274	−0.155990
$676$	−1.63210	−0.0627730
$677$	−23.8883	−0.918103	−0.459052	−	0.888410i	$-0.651811\pi$
$677$	−23.8883	−0.918103	−0.459052	+	0.888410i	$0.651811\pi$
$678$	−22.0127	−0.845394
$679$	25.1205	0.964038
$680$	−6.24420	−0.239454
$681$	−0.471041	−0.0180503
$682$	31.5319	1.20742
$683$	−36.3338	−1.39028	−0.695138	−	0.718876i	$-0.744657\pi$
$683$	−36.3338	−1.39028	−0.695138	+	0.718876i	$0.744657\pi$
$684$	−1.73970	−0.0665191
$685$	7.17856	0.274279
$686$	8.96592	0.342320
$687$	11.8408	0.451753
$688$	5.10428	0.194599
$689$	1.41558	0.0539292
$690$	−4.81747	−0.183398
$691$	2.36561	0.0899922	0.0449961	−	0.998987i	$-0.485672\pi$
$691$	2.36561	0.0899922	0.0449961	+	0.998987i	$0.485672\pi$
$692$	−0.556414	−0.0211517
$693$	43.6249	1.65717
$694$	19.6483	0.745838
$695$	−12.9602	−0.491609
$696$	19.3087	0.731896
$697$	11.9908	0.454185
$698$	−26.4004	−0.999270
$699$	−6.61880	−0.250346
$700$	0.578534	0.0218665
$701$	−36.1238	−1.36438	−0.682189	−	0.731176i	$-0.738972\pi$
$701$	−36.1238	−1.36438	−0.682189	+	0.731176i	$0.738972\pi$
$702$	−8.13044	−0.306864
$703$	−4.84765	−0.182832
$704$	−33.1482	−1.24932
$705$	3.97950	0.149877
$706$	−24.3169	−0.915180
$707$	−18.2249	−0.685417
$708$	1.59598	0.0599807
$709$	24.4167	0.916989	0.458495	−	0.888697i	$-0.348389\pi$
$709$	24.4167	0.916989	0.458495	+	0.888697i	$0.348389\pi$
$710$	22.2393	0.834627
$711$	−11.3634	−0.426161
$712$	28.0866	1.05259
$713$	21.0284	0.787520
$714$	9.88714	0.370017
$715$	−6.19185	−0.231562
$716$	−1.90739	−0.0712825
$717$	−0.0615245	−0.00229767
$718$	0.431259	0.0160944
$719$	−26.7224	−0.996576	−0.498288	−	0.867012i	$-0.666038\pi$
$719$	−26.7224	−0.996576	−0.498288	+	0.867012i	$0.666038\pi$
$720$	10.4502	0.389455
$721$	72.4568	2.69843
$722$	6.59276	0.245357
$723$	−14.6088	−0.543307
$724$	−2.44612	−0.0909092
$725$	−9.55595	−0.354899
$726$	10.3024	0.382360
$727$	2.85449	0.105867	0.0529336	−	0.998598i	$-0.483143\pi$
$727$	2.85449	0.105867	0.0529336	+	0.998598i	$0.483143\pi$
$728$	−14.6622	−0.543419
$729$	−1.52804	−0.0565940
$730$	−7.05551	−0.261136
$731$	−2.74765	−0.101625
$732$	0.142758	0.00527650
$733$	−23.9471	−0.884507	−0.442253	−	0.896890i	$-0.645821\pi$
$733$	−23.9471	−0.884507	−0.442253	+	0.896890i	$0.645821\pi$
$734$	34.0853	1.25811
$735$	6.36361	0.234725
$736$	3.65966	0.134897
$737$	−32.7389	−1.20595
$738$	−18.6893	−0.687964
$739$	27.0438	0.994823	0.497411	−	0.867515i	$-0.334284\pi$
$739$	27.0438	0.994823	0.497411	+	0.867515i	$0.334284\pi$
$740$	−0.146703	−0.00539291
$741$	4.93924	0.181447
$742$	5.97351	0.219295
$743$	38.5442	1.41405	0.707026	−	0.707188i	$-0.250037\pi$
$743$	38.5442	1.41405	0.707026	+	0.707188i	$0.250037\pi$
$744$	9.61619	0.352547
$745$	−15.8451	−0.580521
$746$	−54.5497	−1.99721
$747$	14.4154	0.527430
$748$	−1.52555	−0.0557796
$749$	−70.4714	−2.57497
$750$	1.09027	0.0398111
$751$	−42.9011	−1.56548	−0.782741	−	0.622348i	$-0.786179\pi$
$751$	−42.9011	−1.56548	−0.782741	+	0.622348i	$0.786179\pi$
$752$	−22.8454	−0.833086
$753$	−2.35334	−0.0857606
$754$	−19.1708	−0.698158
$755$	14.2944	0.520227
$756$	−2.34465	−0.0852739
$757$	17.3376	0.630146	0.315073	−	0.949067i	$-0.397971\pi$
$757$	17.3376	0.630146	0.315073	+	0.949067i	$0.397971\pi$
$758$	−33.7434	−1.22562
$759$	14.8687	0.539700
$760$	−13.1632	−0.477480
$761$	41.5752	1.50710	0.753550	−	0.657390i	$-0.228340\pi$
$761$	41.5752	1.50710	0.753550	+	0.657390i	$0.228340\pi$
$762$	−14.8184	−0.536815
$763$	−11.9565	−0.432853
$764$	1.28209	0.0463845
$765$	−5.62536	−0.203385
$766$	−18.8474	−0.680983
$767$	20.0179	0.722805
$768$	2.60624	0.0940445
$769$	−10.1940	−0.367603	−0.183802	−	0.982963i	$-0.558840\pi$
$769$	−10.1940	−0.367603	−0.183802	+	0.982963i	$0.558840\pi$
$770$	−26.1286	−0.941609
$771$	−8.72712	−0.314300
$772$	3.17550	0.114289
$773$	−1.79833	−0.0646816	−0.0323408	−	0.999477i	$-0.510296\pi$
$773$	−1.79833	−0.0646816	−0.0323408	+	0.999477i	$0.510296\pi$
$774$	4.28258	0.153934
$775$	−4.75908	−0.170951
$776$	−17.2970	−0.620926
$777$	−2.93453	−0.105276
$778$	−23.6176	−0.846732
$779$	25.2775	0.905661
$780$	0.149475	0.00535206
$781$	−68.6398	−2.45613
$782$	−14.8873	−0.532368
$783$	38.7277	1.38402
$784$	−36.5321	−1.30472
$785$	−1.95398	−0.0697406
$786$	23.0918	0.823658
$787$	−44.7062	−1.59360	−0.796802	−	0.604241i	$-0.793477\pi$
$787$	−44.7062	−1.59360	−0.796802	+	0.604241i	$0.793477\pi$
$788$	−0.382321	−0.0136196
$789$	0.562139	0.0200127
$790$	6.80597	0.242146
$791$	−79.6211	−2.83100
$792$	−30.0383	−1.06737
$793$	1.79058	0.0635852
$794$	−18.9725	−0.673310
$795$	0.769314	0.0272847
$796$	−0.964680	−0.0341922
$797$	1.95203	0.0691444	0.0345722	−	0.999402i	$-0.488993\pi$
$797$	1.95203	0.0691444	0.0345722	+	0.999402i	$0.488993\pi$
$798$	20.8428	0.737826
$799$	12.2977	0.435062
$800$	−0.828243	−0.0292828
$801$	25.3030	0.894038
$802$	−25.2671	−0.892211
$803$	21.7762	0.768467
$804$	0.790336	0.0278730
$805$	−17.4250	−0.614151
$806$	−9.54748	−0.336296
$807$	10.0117	0.352429
$808$	12.5489	0.441469
$809$	32.1732	1.13115	0.565574	−	0.824698i	$-0.308655\pi$
$809$	32.1732	1.13115	0.565574	+	0.824698i	$0.308655\pi$
$810$	6.33397	0.222553
$811$	43.5729	1.53005	0.765025	−	0.644000i	$-0.222726\pi$
$811$	43.5729	1.53005	0.765025	+	0.644000i	$0.222726\pi$
$812$	−5.52844	−0.194010
$813$	5.91039	0.207286
$814$	6.62562	0.232228
$815$	3.01431	0.105587
$816$	−7.30995	−0.255900
$817$	−5.79223	−0.202645
$818$	45.8478	1.60303
$819$	−13.2091	−0.461564
$820$	0.764967	0.0267138
$821$	−42.7990	−1.49370	−0.746848	−	0.664995i	$-0.768434\pi$
$821$	−42.7990	−1.49370	−0.746848	+	0.664995i	$0.768434\pi$
$822$	7.82658	0.272983
$823$	52.9850	1.84694	0.923470	−	0.383670i	$-0.125340\pi$
$823$	52.9850	1.84694	0.923470	+	0.383670i	$0.125340\pi$
$824$	−49.8908	−1.73803
$825$	−3.36504	−0.117156
$826$	84.4724	2.93917
$827$	23.3945	0.813508	0.406754	−	0.913538i	$-0.366661\pi$
$827$	23.3945	0.813508	0.406754	+	0.913538i	$0.366661\pi$
$828$	1.58572	0.0551077
$829$	0.375803	0.0130522	0.00652608	−	0.999979i	$-0.497923\pi$
$829$	0.375803	0.0130522	0.00652608	+	0.999979i	$0.497923\pi$
$830$	−8.63390	−0.299687
$831$	5.12437	0.177762
$832$	10.0369	0.347966
$833$	19.6653	0.681362
$834$	−14.1302	−0.489288
$835$	4.16008	0.143965
$836$	−3.21596	−0.111226
$837$	19.2873	0.666666
$838$	−17.3187	−0.598263
$839$	15.8320	0.546583	0.273291	−	0.961931i	$-0.411888\pi$
$839$	15.8320	0.546583	0.273291	+	0.961931i	$0.411888\pi$
$840$	−7.96837	−0.274935
$841$	62.3161	2.14883
$842$	28.0832	0.967810
$843$	11.9711	0.412307
$844$	−0.293693	−0.0101093
$845$	−11.1252	−0.382718
$846$	−19.1677	−0.658998
$847$	37.2644	1.28042
$848$	−4.41646	−0.151662
$849$	18.5485	0.636581
$850$	3.36924	0.115564
$851$	4.41859	0.151467
$852$	1.65701	0.0567681
$853$	−9.32579	−0.319309	−0.159655	−	0.987173i	$-0.551038\pi$
$853$	−9.32579	−0.319309	−0.159655	+	0.987173i	$0.551038\pi$
$854$	7.55595	0.258559
$855$	−11.8587	−0.405557
$856$	48.5238	1.65851
$857$	−5.99313	−0.204721	−0.102361	−	0.994747i	$-0.532640\pi$
$857$	−5.99313	−0.204721	−0.102361	+	0.994747i	$0.532640\pi$
$858$	−6.75080	−0.230469
$859$	−44.6541	−1.52358	−0.761788	−	0.647826i	$-0.775678\pi$
$859$	−44.6541	−1.52358	−0.761788	+	0.647826i	$0.775678\pi$
$860$	−0.175289	−0.00597730
$861$	15.3018	0.521483
$862$	14.3362	0.488292
$863$	−21.8515	−0.743832	−0.371916	−	0.928266i	$-0.621299\pi$
$863$	−21.8515	−0.743832	−0.371916	+	0.928266i	$0.621299\pi$
$864$	3.35665	0.114196
$865$	−3.79279	−0.128959
$866$	51.6706	1.75584
$867$	−8.71525	−0.295986
$868$	−2.75329	−0.0934527
$869$	−21.0061	−0.712582
$870$	−10.4186	−0.353223
$871$	9.91295	0.335888
$872$	8.23273	0.278795
$873$	−15.5827	−0.527396
$874$	−31.3834	−1.06156
$875$	3.94357	0.133317
$876$	−0.525691	−0.0177615
$877$	−11.3951	−0.384786	−0.192393	−	0.981318i	$-0.561625\pi$
$877$	−11.3951	−0.384786	−0.192393	+	0.981318i	$0.561625\pi$
$878$	35.8868	1.21112
$879$	19.4019	0.654409
$880$	19.3179	0.651206
$881$	−48.2087	−1.62419	−0.812096	−	0.583523i	$-0.801674\pi$
$881$	−48.2087	−1.62419	−0.812096	+	0.583523i	$0.801674\pi$
$882$	−30.6510	−1.03207
$883$	−36.2461	−1.21978	−0.609890	−	0.792486i	$-0.708786\pi$
$883$	−36.2461	−1.21978	−0.609890	+	0.792486i	$0.708786\pi$
$884$	0.461918	0.0155360
$885$	10.8790	0.365693
$886$	−38.3653	−1.28891
$887$	−23.8002	−0.799134	−0.399567	−	0.916704i	$-0.630840\pi$
$887$	−23.8002	−0.799134	−0.399567	+	0.916704i	$0.630840\pi$
$888$	2.02060	0.0678069
$889$	−53.5990	−1.79765
$890$	−15.1549	−0.507995
$891$	−19.5493	−0.654925
$892$	−1.09059	−0.0365158
$893$	25.9245	0.867530
$894$	−17.2755	−0.577780
$895$	−13.0017	−0.434599
$896$	48.8865	1.63318
$897$	−4.50207	−0.150320
$898$	58.1624	1.94090
$899$	45.4775	1.51676
$900$	−0.358875	−0.0119625
$901$	2.37739	0.0792023
$902$	−34.5486	−1.15034
$903$	−3.50634	−0.116684
$904$	54.8239	1.82342
$905$	−16.6739	−0.554260
$906$	15.5848	0.517771
$907$	−9.82566	−0.326256	−0.163128	−	0.986605i	$-0.552158\pi$
$907$	−9.82566	−0.326256	−0.163128	+	0.986605i	$0.552158\pi$
$908$	−0.0928643	−0.00308181
$909$	11.3052	0.374971
$910$	7.91143	0.262261
$911$	31.2125	1.03412	0.517058	−	0.855950i	$-0.327027\pi$
$911$	31.2125	1.03412	0.517058	+	0.855950i	$0.327027\pi$
$912$	−15.4099	−0.510273
$913$	26.6478	0.881914
$914$	30.2999	1.00223
$915$	0.973111	0.0321701
$916$	2.33437	0.0771298
$917$	83.5243	2.75821
$918$	−13.6546	−0.450670
$919$	28.5950	0.943263	0.471631	−	0.881796i	$-0.343665\pi$
$919$	28.5950	0.943263	0.471631	+	0.881796i	$0.343665\pi$
$920$	11.9982	0.395567
$921$	−13.6160	−0.448663
$922$	−8.08424	−0.266240
$923$	20.7833	0.684092
$924$	−1.94679	−0.0640446
$925$	−1.00000	−0.0328798
$926$	30.7366	1.01007
$927$	−44.9463	−1.47623
$928$	7.91465	0.259811
$929$	−45.3832	−1.48898	−0.744488	−	0.667636i	$-0.767306\pi$
$929$	−45.3832	−1.48898	−0.744488	+	0.667636i	$0.767306\pi$
$930$	−5.18869	−0.170144
$931$	41.4558	1.35866
$932$	−1.30488	−0.0427426
$933$	−1.07242	−0.0351095
$934$	−11.1684	−0.365440
$935$	−10.3989	−0.340080
$936$	9.09526	0.297288
$937$	−27.0457	−0.883543	−0.441772	−	0.897128i	$-0.645650\pi$
$937$	−27.0457	−0.883543	−0.441772	+	0.897128i	$0.645650\pi$
$938$	41.8311	1.36583
$939$	−13.7675	−0.449285
$940$	0.784546	0.0255891
$941$	31.3367	1.02155	0.510773	−	0.859716i	$-0.329359\pi$
$941$	31.3367	1.02155	0.510773	+	0.859716i	$0.329359\pi$
$942$	−2.13037	−0.0694113
$943$	−23.0402	−0.750293
$944$	−62.4538	−2.03270
$945$	−15.9822	−0.519903
$946$	7.91665	0.257393
$947$	−27.4446	−0.891830	−0.445915	−	0.895075i	$-0.647122\pi$
$947$	−27.4446	−0.891830	−0.445915	+	0.895075i	$0.647122\pi$
$948$	0.507099	0.0164698
$949$	−6.59359	−0.214037
$950$	7.10259	0.230439
$951$	−17.9858	−0.583231
$952$	−24.6244	−0.798083
$953$	−35.3324	−1.14453	−0.572265	−	0.820069i	$-0.693935\pi$
$953$	−35.3324	−1.14453	−0.572265	+	0.820069i	$0.693935\pi$
$954$	−3.70548	−0.119969
$955$	8.73937	0.282799
$956$	−0.0121294	−0.000392292 0
$957$	32.1561	1.03946
$958$	47.9760	1.55004
$959$	28.3091	0.914150
$960$	5.45467	0.176049
$961$	−8.35116	−0.269392
$962$	−2.00616	−0.0646812
$963$	43.7147	1.40869
$964$	−2.88008	−0.0927612
$965$	21.6457	0.696801
$966$	−18.9980	−0.611251
$967$	31.4137	1.01020	0.505098	−	0.863062i	$-0.331456\pi$
$967$	31.4137	1.01020	0.505098	+	0.863062i	$0.331456\pi$
$968$	−25.6588	−0.824705
$969$	8.29519	0.266480
$970$	9.33309	0.299667
$971$	6.60982	0.212119	0.106060	−	0.994360i	$-0.466177\pi$
$971$	6.60982	0.212119	0.106060	+	0.994360i	$0.466177\pi$
$972$	2.25558	0.0723477
$973$	−51.1095	−1.63850
$974$	−35.6748	−1.14310
$975$	1.01889	0.0326307
$976$	−5.58641	−0.178817
$977$	−0.318781	−0.0101987	−0.00509935	−	0.999987i	$-0.501623\pi$
$977$	−0.318781	−0.0101987	−0.00509935	+	0.999987i	$0.501623\pi$
$978$	3.28642	0.105088
$979$	46.7744	1.49492
$980$	1.25457	0.0400757
$981$	7.41681	0.236801
$982$	14.4789	0.462042
$983$	−10.7688	−0.343473	−0.171736	−	0.985143i	$-0.554938\pi$
$983$	−10.7688	−0.343473	−0.171736	+	0.985143i	$0.554938\pi$
$984$	−10.5362	−0.335881
$985$	−2.60609	−0.0830368
$986$	−32.1963	−1.02534
$987$	15.6934	0.499527
$988$	0.973756	0.0309793
$989$	5.27957	0.167881
$990$	16.2081	0.515126
$991$	−23.6638	−0.751706	−0.375853	−	0.926679i	$-0.622650\pi$
$991$	−23.6638	−0.751706	−0.375853	+	0.926679i	$0.622650\pi$
$992$	3.94167	0.125148
$993$	−0.229491	−0.00728267
$994$	87.7023	2.78175
$995$	−6.57573	−0.208465
$996$	−0.643294	−0.0203835
$997$	−4.48006	−0.141885	−0.0709425	−	0.997480i	$-0.522601\pi$
$997$	−4.48006	−0.141885	−0.0709425	+	0.997480i	$0.522601\pi$
$998$	56.2850	1.78167
$999$	4.05274	0.128223

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.a.d.1.4	✓	5
3.2	odd	2		1665.2.a.q.1.2		5
4.3	odd	2		2960.2.a.ba.1.2		5
5.2	odd	4		925.2.b.g.149.8		10
5.3	odd	4		925.2.b.g.149.3		10
5.4	even	2		925.2.a.h.1.2		5
7.6	odd	2		9065.2.a.j.1.4		5
15.14	odd	2		8325.2.a.cc.1.4		5
37.36	even	2		6845.2.a.g.1.2		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.d.1.4	✓	5	1.1	even	1	trivial
925.2.a.h.1.2		5	5.4	even	2
925.2.b.g.149.3		10	5.3	odd	4
925.2.b.g.149.8		10	5.2	odd	4
1665.2.a.q.1.2		5	3.2	odd	2
2960.2.a.ba.1.2		5	4.3	odd	2
6845.2.a.g.1.2		5	37.36	even	2
8325.2.a.cc.1.4		5	15.14	odd	2
9065.2.a.j.1.4		5	7.6	odd	2

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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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	185.2.a.d.1.4

Level	$185$
Weight	$2$
Character	185.1
Self dual	yes
Analytic conductor	$1.477$
Analytic rank	$0$
Dimension	$5$
CM	no
Inner twists	$1$