LMFDB - Embedded newform 185.2.a.d.1.5

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			1.5
Root			$1.17837$ 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)

$f(q)$	$=$	$q+2.27092 q^{2} -0.518894 q^{3} +3.15709 q^{4} +1.00000 q^{5} -1.17837 q^{6} -1.33546 q^{7} +2.62766 q^{8} -2.73075 q^{9} +2.27092 q^{10} +5.55161 q^{11} -1.63819 q^{12} -2.96818 q^{13} -3.03272 q^{14} -0.518894 q^{15} -0.346968 q^{16} -0.426340 q^{17} -6.20132 q^{18} -5.57456 q^{19} +3.15709 q^{20} +0.692961 q^{21} +12.6073 q^{22} -3.50406 q^{23} -1.36348 q^{24} +1.00000 q^{25} -6.74052 q^{26} +2.97365 q^{27} -4.21616 q^{28} +8.06544 q^{29} -1.17837 q^{30} +4.57289 q^{31} -6.04326 q^{32} -2.88070 q^{33} -0.968185 q^{34} -1.33546 q^{35} -8.62122 q^{36} -1.00000 q^{37} -12.6594 q^{38} +1.54017 q^{39} +2.62766 q^{40} -6.87056 q^{41} +1.57366 q^{42} +7.35197 q^{43} +17.5269 q^{44} -2.73075 q^{45} -7.95744 q^{46} +3.16383 q^{47} +0.180040 q^{48} -5.21655 q^{49} +2.27092 q^{50} +0.221225 q^{51} -9.37082 q^{52} -6.51383 q^{53} +6.75293 q^{54} +5.55161 q^{55} -3.50913 q^{56} +2.89261 q^{57} +18.3160 q^{58} +8.51080 q^{59} -1.63819 q^{60} +3.31895 q^{61} +10.3847 q^{62} +3.64680 q^{63} -13.0298 q^{64} -2.96818 q^{65} -6.54184 q^{66} +9.68410 q^{67} -1.34599 q^{68} +1.81823 q^{69} -3.03272 q^{70} +7.81324 q^{71} -7.17548 q^{72} -0.762564 q^{73} -2.27092 q^{74} -0.518894 q^{75} -17.5994 q^{76} -7.41394 q^{77} +3.49761 q^{78} +17.0722 q^{79} -0.346968 q^{80} +6.64924 q^{81} -15.6025 q^{82} -2.74656 q^{83} +2.18774 q^{84} -0.426340 q^{85} +16.6957 q^{86} -4.18511 q^{87} +14.5877 q^{88} +0.0865103 q^{89} -6.20132 q^{90} +3.96388 q^{91} -11.0626 q^{92} -2.37285 q^{93} +7.18481 q^{94} -5.57456 q^{95} +3.13581 q^{96} -17.8411 q^{97} -11.8464 q^{98} -15.1601 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$5 q - q^{3} + 6 q^{4} + 5 q^{5} - 2 q^{6} + 7 q^{7} - 6 q^{8} + 2 q^{9} + 7 q^{11} + 2 q^{13} + 4 q^{14} - q^{15} + 8 q^{16} - 8 q^{17} - 6 q^{18} + 14 q^{19} + 6 q^{20} - 9 q^{21} + 2 q^{22} + 2 q^{23}+ \cdots + 18 q^{99}+O(q^{100})$ 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

)

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

$2$	2.27092	1.60578	0.802892	−	0.596124i	$-0.203293\pi$
$2$	2.27092	1.60578	0.802892	+	0.596124i	$0.203293\pi$
$3$	−0.518894	−0.299584	−0.149792	−	0.988718i	$-0.547860\pi$
$3$	−0.518894	−0.299584	−0.149792	+	0.988718i	$0.547860\pi$
$4$	3.15709	1.57854
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.17837	−0.481067
$7$	−1.33546	−0.504755	−0.252378	−	0.967629i	$-0.581213\pi$
$7$	−1.33546	−0.504755	−0.252378	+	0.967629i	$0.581213\pi$
$8$	2.62766	0.929018
$9$	−2.73075	−0.910250
$10$	2.27092	0.718129
$11$	5.55161	1.67387	0.836937	−	0.547299i	$-0.184344\pi$
$11$	5.55161	1.67387	0.836937	+	0.547299i	$0.184344\pi$
$12$	−1.63819	−0.472906
$13$	−2.96818	−0.823226	−0.411613	−	0.911359i	$-0.635035\pi$
$13$	−2.96818	−0.823226	−0.411613	+	0.911359i	$0.635035\pi$
$14$	−3.03272	−0.810528
$15$	−0.518894	−0.133978
$16$	−0.346968	−0.0867420
$17$	−0.426340	−0.103403	−0.0517013	−	0.998663i	$-0.516464\pi$
$17$	−0.426340	−0.103403	−0.0517013	+	0.998663i	$0.516464\pi$
$18$	−6.20132	−1.46166
$19$	−5.57456	−1.27889	−0.639446	−	0.768836i	$-0.720836\pi$
$19$	−5.57456	−1.27889	−0.639446	+	0.768836i	$0.720836\pi$
$20$	3.15709	0.705947
$21$	0.692961	0.151216
$22$	12.6073	2.68788
$23$	−3.50406	−0.730646	−0.365323	−	0.930881i	$-0.619042\pi$
$23$	−3.50406	−0.730646	−0.365323	+	0.930881i	$0.619042\pi$
$24$	−1.36348	−0.278319
$25$	1.00000	0.200000
$26$	−6.74052	−1.32192
$27$	2.97365	0.572280
$28$	−4.21616	−0.796779
$29$	8.06544	1.49771	0.748857	−	0.662731i	$-0.230603\pi$
$29$	8.06544	1.49771	0.748857	+	0.662731i	$0.230603\pi$
$30$	−1.17837	−0.215140
$31$	4.57289	0.821316	0.410658	−	0.911789i	$-0.365299\pi$
$31$	4.57289	0.821316	0.410658	+	0.911789i	$0.365299\pi$
$32$	−6.04326	−1.06831
$33$	−2.88070	−0.501465
$34$	−0.968185	−0.166042
$35$	−1.33546	−0.225733
$36$	−8.62122	−1.43687
$37$	−1.00000	−0.164399
$37$	−1.00000	−0.164399
$38$	−12.6594	−2.05363
$39$	1.54017	0.246625
$40$	2.62766	0.415469
$41$	−6.87056	−1.07300	−0.536501	−	0.843900i	$-0.680254\pi$
$41$	−6.87056	−1.07300	−0.536501	+	0.843900i	$0.680254\pi$
$42$	1.57366	0.242821
$43$	7.35197	1.12116	0.560582	−	0.828099i	$-0.310577\pi$
$43$	7.35197	1.12116	0.560582	+	0.828099i	$0.310577\pi$
$44$	17.5269	2.64229
$45$	−2.73075	−0.407076
$46$	−7.95744	−1.17326
$47$	3.16383	0.461492	0.230746	−	0.973014i	$-0.425883\pi$
$47$	3.16383	0.461492	0.230746	+	0.973014i	$0.425883\pi$
$48$	0.180040	0.0259865
$49$	−5.21655	−0.745222
$50$	2.27092	0.321157
$51$	0.221225	0.0309777
$52$	−9.37082	−1.29950
$53$	−6.51383	−0.894743	−0.447371	−	0.894348i	$-0.647640\pi$
$53$	−6.51383	−0.894743	−0.447371	+	0.894348i	$0.647640\pi$
$54$	6.75293	0.918958
$55$	5.55161	0.748579
$56$	−3.50913	−0.468927
$57$	2.89261	0.383135
$58$	18.3160	2.40501
$59$	8.51080	1.10801	0.554006	−	0.832513i	$-0.313099\pi$
$59$	8.51080	1.10801	0.554006	+	0.832513i	$0.313099\pi$
$60$	−1.63819	−0.211490
$61$	3.31895	0.424948	0.212474	−	0.977167i	$-0.431848\pi$
$61$	3.31895	0.424948	0.212474	+	0.977167i	$0.431848\pi$
$62$	10.3847	1.31886
$63$	3.64680	0.459453
$64$	−13.0298	−1.62873
$65$	−2.96818	−0.368158
$66$	−6.54184	−0.805245
$67$	9.68410	1.18310	0.591550	−	0.806268i	$-0.298516\pi$
$67$	9.68410	1.18310	0.591550	+	0.806268i	$0.298516\pi$
$68$	−1.34599	−0.163226
$69$	1.81823	0.218890
$70$	−3.03272	−0.362479
$71$	7.81324	0.927261	0.463630	−	0.886029i	$-0.346547\pi$
$71$	7.81324	0.927261	0.463630	+	0.886029i	$0.346547\pi$
$72$	−7.17548	−0.845638
$73$	−0.762564	−0.0892514	−0.0446257	−	0.999004i	$-0.514210\pi$
$73$	−0.762564	−0.0892514	−0.0446257	+	0.999004i	$0.514210\pi$
$74$	−2.27092	−0.263989
$75$	−0.518894	−0.0599167
$76$	−17.5994	−2.01879
$77$	−7.41394	−0.844897
$78$	3.49761	0.396027
$79$	17.0722	1.92077	0.960385	−	0.278676i	$-0.0898956\pi$
$79$	17.0722	1.92077	0.960385	+	0.278676i	$0.0898956\pi$
$80$	−0.346968	−0.0387922
$81$	6.64924	0.738804
$82$	−15.6025	−1.72301
$83$	−2.74656	−0.301474	−0.150737	−	0.988574i	$-0.548165\pi$
$83$	−2.74656	−0.301474	−0.150737	+	0.988574i	$0.548165\pi$
$84$	2.18774	0.238702
$85$	−0.426340	−0.0462431
$86$	16.6957	1.80035
$87$	−4.18511	−0.448691
$88$	14.5877	1.55506
$89$	0.0865103	0.00917007	0.00458503	−	0.999989i	$-0.498541\pi$
$89$	0.0865103	0.00917007	0.00458503	+	0.999989i	$0.498541\pi$
$90$	−6.20132	−0.653676
$91$	3.96388	0.415528
$92$	−11.0626	−1.15336
$93$	−2.37285	−0.246053
$94$	7.18481	0.741057
$95$	−5.57456	−0.571938
$96$	3.13581	0.320047
$97$	−17.8411	−1.81149	−0.905745	−	0.423822i	$-0.860688\pi$
$97$	−17.8411	−1.81149	−0.905745	+	0.423822i	$0.860688\pi$
$98$	−11.8464	−1.19667
$99$	−15.1601	−1.52364
$100$	3.15709	0.315709
$101$	10.7584	1.07050	0.535250	−	0.844693i	$-0.320217\pi$
$101$	10.7584	1.07050	0.535250	+	0.844693i	$0.320217\pi$
$102$	0.502385	0.0497436
$103$	−8.19451	−0.807429	−0.403714	−	0.914885i	$-0.632281\pi$
$103$	−8.19451	−0.807429	−0.403714	+	0.914885i	$0.632281\pi$
$104$	−7.79938	−0.764792
$105$	0.692961	0.0676260
$106$	−14.7924	−1.43676
$107$	−5.61222	−0.542553	−0.271277	−	0.962501i	$-0.587446\pi$
$107$	−5.61222	−0.542553	−0.271277	+	0.962501i	$0.587446\pi$
$108$	9.38808	0.903369
$109$	−0.377808	−0.0361874	−0.0180937	−	0.999836i	$-0.505760\pi$
$109$	−0.377808	−0.0361874	−0.0180937	+	0.999836i	$0.505760\pi$
$110$	12.6073	1.20206
$111$	0.518894	0.0492512
$112$	0.463361	0.0437835
$113$	−4.54935	−0.427967	−0.213984	−	0.976837i	$-0.568644\pi$
$113$	−4.54935	−0.427967	−0.213984	+	0.976837i	$0.568644\pi$
$114$	6.56889	0.615233
$115$	−3.50406	−0.326755
$116$	25.4633	2.36421
$117$	8.10537	0.749341
$118$	19.3274	1.77923
$119$	0.569359	0.0521930
$120$	−1.36348	−0.124468
$121$	19.8204	1.80186
$122$	7.53707	0.682375
$123$	3.56509	0.321454
$124$	14.4370	1.29648
$125$	1.00000	0.0894427
$126$	8.28160	0.737783
$127$	12.7560	1.13191	0.565954	−	0.824437i	$-0.308508\pi$
$127$	12.7560	1.13191	0.565954	+	0.824437i	$0.308508\pi$
$128$	−17.5032	−1.54708
$129$	−3.81489	−0.335882
$130$	−6.74052	−0.591182
$131$	−14.4960	−1.26652	−0.633262	−	0.773938i	$-0.718284\pi$
$131$	−14.4960	−1.26652	−0.633262	+	0.773938i	$0.718284\pi$
$132$	−9.09462	−0.791585
$133$	7.44459	0.645528
$134$	21.9918	1.89980
$135$	2.97365	0.255931
$136$	−1.12028	−0.0960629
$137$	−10.8425	−0.926341	−0.463170	−	0.886269i	$-0.653288\pi$
$137$	−10.8425	−0.926341	−0.463170	+	0.886269i	$0.653288\pi$
$138$	4.12907	0.351490
$139$	1.56615	0.132839	0.0664197	−	0.997792i	$-0.478842\pi$
$139$	1.56615	0.132839	0.0664197	+	0.997792i	$0.478842\pi$
$140$	−4.21616	−0.356330
$141$	−1.64169	−0.138255
$142$	17.7433	1.48898
$143$	−16.4782	−1.37798
$144$	0.947482	0.0789569
$145$	8.06544	0.669798
$146$	−1.73172	−0.143319
$147$	2.70684	0.223256
$148$	−3.15709	−0.259511
$149$	−8.09762	−0.663383	−0.331692	−	0.943388i	$-0.607619\pi$
$149$	−8.09762	−0.663383	−0.331692	+	0.943388i	$0.607619\pi$
$150$	−1.17837	−0.0962134
$151$	−12.0018	−0.976693	−0.488347	−	0.872650i	$-0.662400\pi$
$151$	−12.0018	−0.976693	−0.488347	+	0.872650i	$0.662400\pi$
$152$	−14.6481	−1.18811
$153$	1.16423	0.0941222
$154$	−16.8365	−1.35672
$155$	4.57289	0.367304
$156$	4.86246	0.389309
$157$	−19.2732	−1.53817	−0.769084	−	0.639147i	$-0.779287\pi$
$157$	−19.2732	−1.53817	−0.769084	+	0.639147i	$0.779287\pi$
$158$	38.7696	3.08434
$159$	3.37999	0.268050
$160$	−6.04326	−0.477761
$161$	4.67952	0.368798
$162$	15.0999	1.18636
$163$	−0.995229	−0.0779524	−0.0389762	−	0.999240i	$-0.512410\pi$
$163$	−0.995229	−0.0779524	−0.0389762	+	0.999240i	$0.512410\pi$
$164$	−21.6910	−1.69378
$165$	−2.88070	−0.224262
$166$	−6.23723	−0.484103
$167$	−24.2625	−1.87749	−0.938744	−	0.344615i	$-0.888009\pi$
$167$	−24.2625	−1.87749	−0.938744	+	0.344615i	$0.888009\pi$
$168$	1.82086	0.140483
$169$	−4.18988	−0.322298
$170$	−0.968185	−0.0742564
$171$	15.2227	1.16411
$172$	23.2108	1.76981
$173$	−11.4556	−0.870950	−0.435475	−	0.900201i	$-0.643420\pi$
$173$	−11.4556	−0.870950	−0.435475	+	0.900201i	$0.643420\pi$
$174$	−9.50406	−0.720501
$175$	−1.33546	−0.100951
$176$	−1.92623	−0.145195
$177$	−4.41620	−0.331942
$178$	0.196458	0.0147252
$179$	−11.8233	−0.883715	−0.441858	−	0.897085i	$-0.645680\pi$
$179$	−11.8233	−0.883715	−0.441858	+	0.897085i	$0.645680\pi$
$180$	−8.62122	−0.642588
$181$	−14.8035	−1.10034	−0.550168	−	0.835054i	$-0.685436\pi$
$181$	−14.8035	−1.10034	−0.550168	+	0.835054i	$0.685436\pi$
$182$	9.00167	0.667248
$183$	−1.72218	−0.127307
$184$	−9.20747	−0.678783
$185$	−1.00000	−0.0735215
$186$	−5.38855	−0.395108
$187$	−2.36687	−0.173083
$188$	9.98849	0.728485
$189$	−3.97118	−0.288861
$190$	−12.6594	−0.918410
$191$	−7.71008	−0.557881	−0.278941	−	0.960308i	$-0.589983\pi$
$191$	−7.71008	−0.557881	−0.278941	+	0.960308i	$0.589983\pi$
$192$	6.76110	0.487940
$193$	26.0067	1.87200	0.936001	−	0.351997i	$-0.114497\pi$
$193$	26.0067	1.87200	0.936001	+	0.351997i	$0.114497\pi$
$194$	−40.5158	−2.90886
$195$	1.54017	0.110294
$196$	−16.4691	−1.17637
$197$	13.0887	0.932530	0.466265	−	0.884645i	$-0.345599\pi$
$197$	13.0887	0.932530	0.466265	+	0.884645i	$0.345599\pi$
$198$	−34.4273	−2.44664
$199$	18.2990	1.29718	0.648590	−	0.761138i	$-0.275359\pi$
$199$	18.2990	1.29718	0.648590	+	0.761138i	$0.275359\pi$
$200$	2.62766	0.185804
$201$	−5.02502	−0.354438
$202$	24.4315	1.71899
$203$	−10.7710	−0.755979
$204$	0.698428	0.0488997
$205$	−6.87056	−0.479861
$206$	−18.6091	−1.29656
$207$	9.56870	0.665071
$208$	1.02986	0.0714083
$209$	−30.9478	−2.14071
$210$	1.57366	0.108593
$211$	2.89163	0.199068	0.0995341	−	0.995034i	$-0.468265\pi$
$211$	2.89163	0.199068	0.0995341	+	0.995034i	$0.468265\pi$
$212$	−20.5647	−1.41239
$213$	−4.05424	−0.277792
$214$	−12.7449	−0.871224
$215$	7.35197	0.501400
$216$	7.81374	0.531658
$217$	−6.10690	−0.414564
$218$	−0.857973	−0.0581092
$219$	0.395690	0.0267383
$220$	17.5269	1.18167
$221$	1.26546	0.0851237
$222$	1.17837	0.0790869
$223$	25.8004	1.72772	0.863862	−	0.503728i	$-0.168039\pi$
$223$	25.8004	1.72772	0.863862	+	0.503728i	$0.168039\pi$
$224$	8.07051	0.539233
$225$	−2.73075	−0.182050
$226$	−10.3312	−0.687223
$227$	−6.01093	−0.398960	−0.199480	−	0.979902i	$-0.563925\pi$
$227$	−6.01093	−0.398960	−0.199480	+	0.979902i	$0.563925\pi$
$228$	9.13222	0.604796
$229$	5.22124	0.345029	0.172515	−	0.985007i	$-0.444811\pi$
$229$	5.22124	0.345029	0.172515	+	0.985007i	$0.444811\pi$
$230$	−7.95744	−0.524698
$231$	3.84705	0.253117
$232$	21.1932	1.39140
$233$	−15.2256	−0.997465	−0.498733	−	0.866756i	$-0.666201\pi$
$233$	−15.2256	−0.997465	−0.498733	+	0.866756i	$0.666201\pi$
$234$	18.4067	1.20328
$235$	3.16383	0.206385
$236$	26.8693	1.74905
$237$	−8.85865	−0.575431
$238$	1.29297	0.0838107
$239$	−12.1164	−0.783745	−0.391873	−	0.920019i	$-0.628173\pi$
$239$	−12.1164	−0.783745	−0.391873	+	0.920019i	$0.628173\pi$
$240$	0.180040	0.0116215
$241$	20.7909	1.33926	0.669628	−	0.742696i	$-0.266453\pi$
$241$	20.7909	1.33926	0.669628	+	0.742696i	$0.266453\pi$
$242$	45.0106	2.89339
$243$	−12.3712	−0.793613
$244$	10.4782	0.670799
$245$	−5.21655	−0.333273
$246$	8.09605	0.516185
$247$	16.5463	1.05282
$248$	12.0160	0.763017
$249$	1.42517	0.0903168
$250$	2.27092	0.143626
$251$	9.67062	0.610404	0.305202	−	0.952288i	$-0.401276\pi$
$251$	9.67062	0.610404	0.305202	+	0.952288i	$0.401276\pi$
$252$	11.5133	0.725267
$253$	−19.4532	−1.22301
$254$	28.9678	1.81760
$255$	0.221225	0.0138537
$256$	−13.6888	−0.855550
$257$	31.6442	1.97391	0.986957	−	0.160984i	$-0.0514667\pi$
$257$	31.6442	1.97391	0.986957	+	0.160984i	$0.0514667\pi$
$258$	−8.66332	−0.539355
$259$	1.33546	0.0829813
$260$	−9.37082	−0.581154
$261$	−22.0247	−1.36329
$262$	−32.9193	−2.03376
$263$	14.3161	0.882766	0.441383	−	0.897319i	$-0.354488\pi$
$263$	14.3161	0.882766	0.441383	+	0.897319i	$0.354488\pi$
$264$	−7.56950	−0.465870
$265$	−6.51383	−0.400141
$266$	16.9061	1.03658
$267$	−0.0448897	−0.00274720
$268$	30.5736	1.86758
$269$	−28.8212	−1.75726	−0.878631	−	0.477501i	$-0.841543\pi$
$269$	−28.8212	−1.75726	−0.878631	+	0.477501i	$0.841543\pi$
$270$	6.75293	0.410970
$271$	10.4382	0.634078	0.317039	−	0.948412i	$-0.397311\pi$
$271$	10.4382	0.634078	0.317039	+	0.948412i	$0.397311\pi$
$272$	0.147926	0.00896935
$273$	−2.05684	−0.124485
$274$	−24.6226	−1.48750
$275$	5.55161	0.334775
$276$	5.74033	0.345527
$277$	16.2020	0.973485	0.486742	−	0.873546i	$-0.338185\pi$
$277$	16.2020	0.973485	0.486742	+	0.873546i	$0.338185\pi$
$278$	3.55661	0.213311
$279$	−12.4874	−0.747602
$280$	−3.50913	−0.209710
$281$	8.10953	0.483774	0.241887	−	0.970304i	$-0.422234\pi$
$281$	8.10953	0.483774	0.241887	+	0.970304i	$0.422234\pi$
$282$	−3.72816	−0.222008
$283$	−0.429766	−0.0255470	−0.0127735	−	0.999918i	$-0.504066\pi$
$283$	−0.429766	−0.0255470	−0.0127735	+	0.999918i	$0.504066\pi$
$284$	24.6671	1.46372
$285$	2.89261	0.171343
$286$	−37.4207	−2.21274
$287$	9.17534	0.541603
$288$	16.5026	0.972426
$289$	−16.8182	−0.989308
$290$	18.3160	1.07555
$291$	9.25765	0.542693
$292$	−2.40748	−0.140887
$293$	14.3831	0.840270	0.420135	−	0.907462i	$-0.361983\pi$
$293$	14.3831	0.840270	0.420135	+	0.907462i	$0.361983\pi$
$294$	6.14702	0.358502
$295$	8.51080	0.495518
$296$	−2.62766	−0.152730
$297$	16.5086	0.957924
$298$	−18.3891	−1.06525
$299$	10.4007	0.601487
$300$	−1.63819	−0.0945812
$301$	−9.81823	−0.565914
$302$	−27.2552	−1.56836
$303$	−5.58247	−0.320705
$304$	1.93420	0.110934
$305$	3.31895	0.190042
$306$	2.64387	0.151140
$307$	−24.8429	−1.41786	−0.708928	−	0.705281i	$-0.750821\pi$
$307$	−24.8429	−1.41786	−0.708928	+	0.705281i	$0.750821\pi$
$308$	−23.4065	−1.33371
$309$	4.25208	0.241892
$310$	10.3847	0.589810
$311$	−13.3533	−0.757198	−0.378599	−	0.925561i	$-0.623594\pi$
$311$	−13.3533	−0.757198	−0.378599	+	0.925561i	$0.623594\pi$
$312$	4.04705	0.229119
$313$	26.1131	1.47600	0.738001	−	0.674799i	$-0.235770\pi$
$313$	26.1131	1.47600	0.738001	+	0.674799i	$0.235770\pi$
$314$	−43.7679	−2.46997
$315$	3.64680	0.205474
$316$	53.8984	3.03202
$317$	27.5077	1.54498	0.772492	−	0.635024i	$-0.219010\pi$
$317$	27.5077	1.54498	0.772492	+	0.635024i	$0.219010\pi$
$318$	7.67568	0.430431
$319$	44.7762	2.50699
$320$	−13.0298	−0.728390
$321$	2.91215	0.162540
$322$	10.6268	0.592210
$323$	2.37666	0.132241
$324$	20.9922	1.16623
$325$	−2.96818	−0.164645
$326$	−2.26009	−0.125175
$327$	0.196042	0.0108412
$328$	−18.0535	−0.996837
$329$	−4.22516	−0.232940
$330$	−6.54184	−0.360117
$331$	−33.4582	−1.83903	−0.919516	−	0.393054i	$-0.871419\pi$
$331$	−33.4582	−1.83903	−0.919516	+	0.393054i	$0.871419\pi$
$332$	−8.67114	−0.475891
$333$	2.73075	0.149644
$334$	−55.0982	−3.01484
$335$	9.68410	0.529099
$336$	−0.240435	−0.0131168
$337$	−23.0022	−1.25301	−0.626504	−	0.779418i	$-0.715515\pi$
$337$	−23.0022	−1.25301	−0.626504	+	0.779418i	$0.715515\pi$
$338$	−9.51489	−0.517542
$339$	2.36063	0.128212
$340$	−1.34599	−0.0729967
$341$	25.3869	1.37478
$342$	34.5697	1.86931
$343$	16.3147	0.880910
$344$	19.3185	1.04158
$345$	1.81823	0.0978904
$346$	−26.0147	−1.39856
$347$	−21.1611	−1.13599	−0.567993	−	0.823033i	$-0.692280\pi$
$347$	−21.1611	−1.13599	−0.567993	+	0.823033i	$0.692280\pi$
$348$	−13.2128	−0.708278
$349$	−15.9769	−0.855224	−0.427612	−	0.903962i	$-0.640645\pi$
$349$	−15.9769	−0.855224	−0.427612	+	0.903962i	$0.640645\pi$
$350$	−3.03272	−0.162106
$351$	−8.82635	−0.471116
$352$	−33.5498	−1.78821
$353$	18.8153	1.00144	0.500718	−	0.865611i	$-0.333069\pi$
$353$	18.8153	1.00144	0.500718	+	0.865611i	$0.333069\pi$
$354$	−10.0289	−0.533028
$355$	7.81324	0.414684
$356$	0.273121	0.0144754
$357$	−0.295437	−0.0156362
$358$	−26.8498	−1.41906
$359$	33.7385	1.78065	0.890326	−	0.455324i	$-0.150477\pi$
$359$	33.7385	1.78065	0.890326	+	0.455324i	$0.150477\pi$
$360$	−7.17548	−0.378181
$361$	12.0758	0.635567
$362$	−33.6176	−1.76690
$363$	−10.2847	−0.539806
$364$	12.5143	0.655929
$365$	−0.762564	−0.0399144
$366$	−3.91094	−0.204428
$367$	−18.0331	−0.941320	−0.470660	−	0.882315i	$-0.655984\pi$
$367$	−18.0331	−0.941320	−0.470660	+	0.882315i	$0.655984\pi$
$368$	1.21580	0.0633777
$369$	18.7618	0.976699
$370$	−2.27092	−0.118060
$371$	8.69893	0.451626
$372$	−7.49129	−0.388405
$373$	27.0210	1.39909	0.699547	−	0.714587i	$-0.253385\pi$
$373$	27.0210	1.39909	0.699547	+	0.714587i	$0.253385\pi$
$374$	−5.37499	−0.277934
$375$	−0.518894	−0.0267956
$376$	8.31346	0.428734
$377$	−23.9397	−1.23296
$378$	−9.01825	−0.463849
$379$	−34.0246	−1.74772	−0.873862	−	0.486173i	$-0.838392\pi$
$379$	−34.0246	−1.74772	−0.873862	+	0.486173i	$0.838392\pi$
$380$	−17.5994	−0.902830
$381$	−6.61899	−0.339101
$382$	−17.5090	−0.895838
$383$	2.74649	0.140339	0.0701696	−	0.997535i	$-0.477646\pi$
$383$	2.74649	0.140339	0.0701696	+	0.997535i	$0.477646\pi$
$384$	9.08232	0.463480
$385$	−7.41394	−0.377849
$386$	59.0592	3.00603
$387$	−20.0764	−1.02054
$388$	−56.3260	−2.85952
$389$	2.23432	0.113285	0.0566423	−	0.998395i	$-0.481961\pi$
$389$	2.23432	0.113285	0.0566423	+	0.998395i	$0.481961\pi$
$390$	3.49761	0.177109
$391$	1.49392	0.0755507
$392$	−13.7073	−0.692325
$393$	7.52190	0.379430
$394$	29.7234	1.49744
$395$	17.0722	0.858995
$396$	−47.8617	−2.40514
$397$	5.74533	0.288350	0.144175	−	0.989552i	$-0.453947\pi$
$397$	5.74533	0.288350	0.144175	+	0.989552i	$0.453947\pi$
$398$	41.5555	2.08299
$399$	−3.86295	−0.193390
$400$	−0.346968	−0.0173484
$401$	−16.4458	−0.821264	−0.410632	−	0.911801i	$-0.634692\pi$
$401$	−16.4458	−0.821264	−0.410632	+	0.911801i	$0.634692\pi$
$402$	−11.4114	−0.569150
$403$	−13.5732	−0.676129
$404$	33.9652	1.68983
$405$	6.64924	0.330403
$406$	−24.4602	−1.21394
$407$	−5.55161	−0.275183
$408$	0.581304	0.0287789
$409$	32.5835	1.61115	0.805575	−	0.592494i	$-0.201856\pi$
$409$	32.5835	1.61115	0.805575	+	0.592494i	$0.201856\pi$
$410$	−15.6025	−0.770553
$411$	5.62613	0.277517
$412$	−25.8708	−1.27456
$413$	−11.3658	−0.559275
$414$	21.7298	1.06796
$415$	−2.74656	−0.134823
$416$	17.9375	0.879458
$417$	−0.812667	−0.0397965
$418$	−70.2801	−3.43751
$419$	26.6150	1.30023	0.650115	−	0.759836i	$-0.274721\pi$
$419$	26.6150	1.30023	0.650115	+	0.759836i	$0.274721\pi$
$420$	2.18774	0.106751
$421$	−13.6775	−0.666600	−0.333300	−	0.942821i	$-0.608162\pi$
$421$	−13.6775	−0.666600	−0.333300	+	0.942821i	$0.608162\pi$
$422$	6.56667	0.319661
$423$	−8.63962	−0.420073
$424$	−17.1161	−0.831232
$425$	−0.426340	−0.0206805
$426$	−9.20687	−0.446074
$427$	−4.43231	−0.214495
$428$	−17.7183	−0.856445
$429$	8.55045	0.412820
$430$	16.6957	0.805140
$431$	11.2668	0.542704	0.271352	−	0.962480i	$-0.412529\pi$
$431$	11.2668	0.542704	0.271352	+	0.962480i	$0.412529\pi$
$432$	−1.03176	−0.0496407
$433$	19.9228	0.957427	0.478714	−	0.877971i	$-0.341103\pi$
$433$	19.9228	0.957427	0.478714	+	0.877971i	$0.341103\pi$
$434$	−13.8683	−0.665700
$435$	−4.18511	−0.200661
$436$	−1.19277	−0.0571235
$437$	19.5336	0.934418
$438$	0.898581	0.0429359
$439$	18.4321	0.879717	0.439859	−	0.898067i	$-0.355029\pi$
$439$	18.4321	0.879717	0.439859	+	0.898067i	$0.355029\pi$
$440$	14.5877	0.695444
$441$	14.2451	0.678338
$442$	2.87375	0.136690
$443$	−22.1719	−1.05342	−0.526710	−	0.850045i	$-0.676575\pi$
$443$	−22.1719	−1.05342	−0.526710	+	0.850045i	$0.676575\pi$
$444$	1.63819	0.0777453
$445$	0.0865103	0.00410098
$446$	58.5908	2.77435
$447$	4.20181	0.198739
$448$	17.4008	0.822109
$449$	−4.70999	−0.222278	−0.111139	−	0.993805i	$-0.535450\pi$
$449$	−4.70999	−0.222278	−0.111139	+	0.993805i	$0.535450\pi$
$450$	−6.20132	−0.292333
$451$	−38.1427	−1.79607
$452$	−14.3627	−0.675565
$453$	6.22767	0.292601
$454$	−13.6504	−0.640643
$455$	3.96388	0.185830
$456$	7.60079	0.355940
$457$	−12.9225	−0.604488	−0.302244	−	0.953231i	$-0.597736\pi$
$457$	−12.9225	−0.604488	−0.302244	+	0.953231i	$0.597736\pi$
$458$	11.8570	0.554043
$459$	−1.26779	−0.0591752
$460$	−11.0626	−0.515797
$461$	−11.7403	−0.546802	−0.273401	−	0.961900i	$-0.588149\pi$
$461$	−11.7403	−0.546802	−0.273401	+	0.961900i	$0.588149\pi$
$462$	8.73635	0.406452
$463$	0.377012	0.0175212	0.00876061	−	0.999962i	$-0.497211\pi$
$463$	0.377012	0.0175212	0.00876061	+	0.999962i	$0.497211\pi$
$464$	−2.79845	−0.129915
$465$	−2.37285	−0.110038
$466$	−34.5763	−1.60171
$467$	−7.22290	−0.334236	−0.167118	−	0.985937i	$-0.553446\pi$
$467$	−7.22290	−0.334236	−0.167118	+	0.985937i	$0.553446\pi$
$468$	25.5894	1.18287
$469$	−12.9327	−0.597176
$470$	7.18481	0.331411
$471$	10.0007	0.460810
$472$	22.3635	1.02936
$473$	40.8153	1.87669
$474$	−20.1173	−0.924019
$475$	−5.57456	−0.255779
$476$	1.79752	0.0823890
$477$	17.7876	0.814439
$478$	−27.5154	−1.25853
$479$	29.5805	1.35157	0.675783	−	0.737101i	$-0.263806\pi$
$479$	29.5805	1.35157	0.675783	+	0.737101i	$0.263806\pi$
$480$	3.13581	0.143129
$481$	2.96818	0.135338
$482$	47.2144	2.15056
$483$	−2.42817	−0.110486
$484$	62.5748	2.84431
$485$	−17.8411	−0.810123
$486$	−28.0940	−1.27437
$487$	3.98732	0.180683	0.0903413	−	0.995911i	$-0.471204\pi$
$487$	3.98732	0.180683	0.0903413	+	0.995911i	$0.471204\pi$
$488$	8.72106	0.394784
$489$	0.516419	0.0233533
$490$	−11.8464	−0.535165
$491$	4.67346	0.210910	0.105455	−	0.994424i	$-0.466370\pi$
$491$	4.67346	0.210910	0.105455	+	0.994424i	$0.466370\pi$
$492$	11.2553	0.507429
$493$	−3.43862	−0.154868
$494$	37.5754	1.69060
$495$	−15.1601	−0.681394
$496$	−1.58665	−0.0712426
$497$	−10.4342	−0.468040
$498$	3.23646	0.145029
$499$	2.75874	0.123498	0.0617491	−	0.998092i	$-0.480332\pi$
$499$	2.75874	0.123498	0.0617491	+	0.998092i	$0.480332\pi$
$500$	3.15709	0.141189
$501$	12.5897	0.562465
$502$	21.9612	0.980177
$503$	5.38439	0.240078	0.120039	−	0.992769i	$-0.461698\pi$
$503$	5.38439	0.240078	0.120039	+	0.992769i	$0.461698\pi$
$504$	9.58254	0.426840
$505$	10.7584	0.478742
$506$	−44.1766	−1.96389
$507$	2.17410	0.0965553
$508$	40.2717	1.78677
$509$	16.0712	0.712342	0.356171	−	0.934421i	$-0.384082\pi$
$509$	16.0712	0.712342	0.356171	+	0.934421i	$0.384082\pi$
$510$	0.502385	0.0222460
$511$	1.01837	0.0450501
$512$	3.92024	0.173252
$513$	−16.5768	−0.731884
$514$	71.8616	3.16968
$515$	−8.19451	−0.361093
$516$	−12.0440	−0.530205
$517$	17.5644	0.772479
$518$	3.03272	0.133250
$519$	5.94422	0.260922
$520$	−7.79938	−0.342025
$521$	−26.9444	−1.18045	−0.590227	−	0.807237i	$-0.700962\pi$
$521$	−26.9444	−1.18045	−0.590227	+	0.807237i	$0.700962\pi$
$522$	−50.0164	−2.18916
$523$	8.47473	0.370574	0.185287	−	0.982684i	$-0.440679\pi$
$523$	8.47473	0.370574	0.185287	+	0.982684i	$0.440679\pi$
$524$	−45.7652	−1.99926
$525$	0.692961	0.0302433
$526$	32.5107	1.41753
$527$	−1.94961	−0.0849262
$528$	0.999510	0.0434981
$529$	−10.7216	−0.466156
$530$	−14.7924	−0.642540
$531$	−23.2408	−1.00857
$532$	23.5032	1.01899
$533$	20.3931	0.883323
$534$	−0.101941	−0.00441142
$535$	−5.61222	−0.242637
$536$	25.4465	1.09912
$537$	6.13504	0.264747
$538$	−65.4508	−2.82178
$539$	−28.9603	−1.24741
$540$	9.38808	0.403999
$541$	18.8254	0.809368	0.404684	−	0.914457i	$-0.367382\pi$
$541$	18.8254	0.809368	0.404684	+	0.914457i	$0.367382\pi$
$542$	23.7045	1.01819
$543$	7.68145	0.329643
$544$	2.57648	0.110466
$545$	−0.377808	−0.0161835
$546$	−4.67091	−0.199897
$547$	17.8907	0.764953	0.382476	−	0.923965i	$-0.375071\pi$
$547$	17.8907	0.764953	0.382476	+	0.923965i	$0.375071\pi$
$548$	−34.2309	−1.46227
$549$	−9.06321	−0.386809
$550$	12.6073	0.537576
$551$	−44.9613	−1.91542
$552$	4.77770	0.203352
$553$	−22.7992	−0.969519
$554$	36.7935	1.56321
$555$	0.518894	0.0220258
$556$	4.94448	0.209693
$557$	−19.5753	−0.829433	−0.414717	−	0.909951i	$-0.636119\pi$
$557$	−19.5753	−0.829433	−0.414717	+	0.909951i	$0.636119\pi$
$558$	−28.3580	−1.20049
$559$	−21.8220	−0.922972
$560$	0.463361	0.0195806
$561$	1.22816	0.0518528
$562$	18.4161	0.776837
$563$	20.0503	0.845018	0.422509	−	0.906359i	$-0.361150\pi$
$563$	20.0503	0.845018	0.422509	+	0.906359i	$0.361150\pi$
$564$	−5.18297	−0.218242
$565$	−4.54935	−0.191393
$566$	−0.975966	−0.0410229
$567$	−8.87977	−0.372915
$568$	20.5305	0.861442
$569$	−34.7651	−1.45743	−0.728715	−	0.684817i	$-0.759882\pi$
$569$	−34.7651	−1.45743	−0.728715	+	0.684817i	$0.759882\pi$
$570$	6.56889	0.275141
$571$	1.04707	0.0438184	0.0219092	−	0.999760i	$-0.493026\pi$
$571$	1.04707	0.0438184	0.0219092	+	0.999760i	$0.493026\pi$
$572$	−52.0232	−2.17520
$573$	4.00071	0.167132
$574$	20.8365	0.869698
$575$	−3.50406	−0.146129
$576$	35.5812	1.48255
$577$	−28.6481	−1.19264	−0.596318	−	0.802749i	$-0.703370\pi$
$577$	−28.6481	−1.19264	−0.596318	+	0.802749i	$0.703370\pi$
$578$	−38.1929	−1.58862
$579$	−13.4947	−0.560821
$580$	25.4633	1.05731
$581$	3.66791	0.152171
$582$	21.0234	0.871448
$583$	−36.1622	−1.49769
$584$	−2.00376	−0.0829161
$585$	8.10537	0.335116
$586$	32.6629	1.34929
$587$	−26.6924	−1.10171	−0.550857	−	0.834600i	$-0.685699\pi$
$587$	−26.6924	−1.10171	−0.550857	+	0.834600i	$0.685699\pi$
$588$	8.54573	0.352420
$589$	−25.4919	−1.05037
$590$	19.3274	0.795695
$591$	−6.79164	−0.279371
$592$	0.346968	0.0142603
$593$	−10.0943	−0.414521	−0.207261	−	0.978286i	$-0.566455\pi$
$593$	−10.0943	−0.414521	−0.207261	+	0.978286i	$0.566455\pi$
$594$	37.4897	1.53822
$595$	0.569359	0.0233414
$596$	−25.5649	−1.04718
$597$	−9.49523	−0.388614
$598$	23.6192	0.965859
$599$	−9.37239	−0.382946	−0.191473	−	0.981498i	$-0.561326\pi$
$599$	−9.37239	−0.382946	−0.191473	+	0.981498i	$0.561326\pi$
$600$	−1.36348	−0.0556637
$601$	−41.6868	−1.70044	−0.850220	−	0.526427i	$-0.823531\pi$
$601$	−41.6868	−1.70044	−0.850220	+	0.526427i	$0.823531\pi$
$602$	−22.2964	−0.908735
$603$	−26.4448	−1.07692
$604$	−37.8908	−1.54175
$605$	19.8204	0.805814
$606$	−12.6774	−0.514982
$607$	20.4257	0.829052	0.414526	−	0.910037i	$-0.363947\pi$
$607$	20.4257	0.829052	0.414526	+	0.910037i	$0.363947\pi$
$608$	33.6885	1.36625
$609$	5.58903	0.226479
$610$	7.53707	0.305167
$611$	−9.39083	−0.379912
$612$	3.67557	0.148576
$613$	39.0819	1.57850	0.789251	−	0.614070i	$-0.210469\pi$
$613$	39.0819	1.57850	0.789251	+	0.614070i	$0.210469\pi$
$614$	−56.4162	−2.27677
$615$	3.56509	0.143758
$616$	−19.4813	−0.784924
$617$	24.7773	0.997495	0.498747	−	0.866747i	$-0.333794\pi$
$617$	24.7773	0.997495	0.498747	+	0.866747i	$0.333794\pi$
$618$	9.65615	0.388427
$619$	27.7629	1.11589	0.557943	−	0.829879i	$-0.311591\pi$
$619$	27.7629	1.11589	0.557943	+	0.829879i	$0.311591\pi$
$620$	14.4370	0.579805
$621$	−10.4198	−0.418134
$622$	−30.3244	−1.21590
$623$	−0.115531	−0.00462864
$624$	−0.534391	−0.0213928
$625$	1.00000	0.0400000
$626$	59.3009	2.37014
$627$	16.0586	0.641320
$628$	−60.8472	−2.42807
$629$	0.426340	0.0169993
$630$	8.28160	0.329947
$631$	20.6678	0.822772	0.411386	−	0.911461i	$-0.365045\pi$
$631$	20.6678	0.822772	0.411386	+	0.911461i	$0.365045\pi$
$632$	44.8599	1.78443
$633$	−1.50045	−0.0596376
$634$	62.4678	2.48091
$635$	12.7560	0.506205
$636$	10.6709	0.423129
$637$	15.4837	0.613486
$638$	101.683	4.02568
$639$	−21.3360	−0.844039
$640$	−17.5032	−0.691875
$641$	−23.3208	−0.921116	−0.460558	−	0.887630i	$-0.652351\pi$
$641$	−23.3208	−0.921116	−0.460558	+	0.887630i	$0.652351\pi$
$642$	6.61326	0.261004
$643$	8.04242	0.317162	0.158581	−	0.987346i	$-0.449308\pi$
$643$	8.04242	0.317162	0.158581	+	0.987346i	$0.449308\pi$
$644$	14.7737	0.582163
$645$	−3.81489	−0.150211
$646$	5.39721	0.212350
$647$	49.3437	1.93990	0.969950	−	0.243305i	$-0.0782315\pi$
$647$	49.3437	1.93990	0.969950	+	0.243305i	$0.0782315\pi$
$648$	17.4719	0.686362
$649$	47.2487	1.85467
$650$	−6.74052	−0.264385
$651$	3.16884	0.124196
$652$	−3.14203	−0.123051
$653$	24.9760	0.977385	0.488693	−	0.872456i	$-0.337474\pi$
$653$	24.9760	0.977385	0.488693	+	0.872456i	$0.337474\pi$
$654$	0.445197	0.0174086
$655$	−14.4960	−0.566407
$656$	2.38386	0.0930743
$657$	2.08237	0.0812410
$658$	−9.59501	−0.374052
$659$	−32.3446	−1.25997	−0.629983	−	0.776609i	$-0.716938\pi$
$659$	−32.3446	−1.25997	−0.629983	+	0.776609i	$0.716938\pi$
$660$	−9.09462	−0.354008
$661$	−1.85884	−0.0723006	−0.0361503	−	0.999346i	$-0.511510\pi$
$661$	−1.85884	−0.0723006	−0.0361503	+	0.999346i	$0.511510\pi$
$662$	−75.9811	−2.95309
$663$	−0.656637	−0.0255017
$664$	−7.21703	−0.280075
$665$	7.44459	0.288689
$666$	6.20132	0.240296
$667$	−28.2618	−1.09430
$668$	−76.5988	−2.96370
$669$	−13.3877	−0.517598
$670$	21.9918	0.849619
$671$	18.4255	0.711309
$672$	−4.18774	−0.161546
$673$	−44.3587	−1.70990	−0.854951	−	0.518709i	$-0.826413\pi$
$673$	−44.3587	−1.70990	−0.854951	+	0.518709i	$0.826413\pi$
$674$	−52.2362	−2.01206
$675$	2.97365	0.114456
$676$	−13.2278	−0.508762
$677$	8.33112	0.320191	0.160096	−	0.987102i	$-0.448820\pi$
$677$	8.33112	0.320191	0.160096	+	0.987102i	$0.448820\pi$
$678$	5.36081	0.205881
$679$	23.8260	0.914360
$680$	−1.12028	−0.0429606
$681$	3.11904	0.119522
$682$	57.6518	2.20760
$683$	−24.2726	−0.928764	−0.464382	−	0.885635i	$-0.653723\pi$
$683$	−24.2726	−0.928764	−0.464382	+	0.885635i	$0.653723\pi$
$684$	48.0595	1.83760
$685$	−10.8425	−0.414272
$686$	37.0494	1.41455
$687$	−2.70927	−0.103365
$688$	−2.55090	−0.0972520
$689$	19.3342	0.736576
$690$	4.12907	0.157191
$691$	29.0133	1.10372	0.551858	−	0.833938i	$-0.313919\pi$
$691$	29.0133	1.10372	0.551858	+	0.833938i	$0.313919\pi$
$692$	−36.1662	−1.37483
$693$	20.2456	0.769067
$694$	−48.0552	−1.82415
$695$	1.56615	0.0594076
$696$	−10.9970	−0.416842
$697$	2.92919	0.110951
$698$	−36.2823	−1.37330
$699$	7.90050	0.298824
$700$	−4.21616	−0.159356
$701$	33.0887	1.24974	0.624871	−	0.780728i	$-0.285151\pi$
$701$	33.0887	1.24974	0.624871	+	0.780728i	$0.285151\pi$
$702$	−20.0440	−0.756510
$703$	5.57456	0.210249
$704$	−72.3366	−2.72629
$705$	−1.64169	−0.0618297
$706$	42.7280	1.60809
$707$	−14.3674	−0.540341
$708$	−13.9423	−0.523985
$709$	−31.3446	−1.17717	−0.588586	−	0.808434i	$-0.700315\pi$
$709$	−31.3446	−1.17717	−0.588586	+	0.808434i	$0.700315\pi$
$710$	17.7433	0.665892
$711$	−46.6198	−1.74838
$712$	0.227319	0.00851916
$713$	−16.0237	−0.600091
$714$	−0.670914	−0.0251083
$715$	−16.4782	−0.616250
$716$	−37.3272	−1.39498
$717$	6.28713	0.234797
$718$	76.6176	2.85934
$719$	−19.2288	−0.717114	−0.358557	−	0.933508i	$-0.616731\pi$
$719$	−19.2288	−0.717114	−0.358557	+	0.933508i	$0.616731\pi$
$720$	0.947482	0.0353106
$721$	10.9434	0.407554
$722$	27.4231	1.02058
$723$	−10.7883	−0.401219
$724$	−46.7360	−1.73693
$725$	8.06544	0.299543
$726$	−23.3557	−0.866813
$727$	51.4657	1.90876	0.954379	−	0.298599i	$-0.0965192\pi$
$727$	51.4657	1.90876	0.954379	+	0.298599i	$0.0965192\pi$
$728$	10.4157	0.386033
$729$	−13.5284	−0.501051
$730$	−1.73172	−0.0640940
$731$	−3.13444	−0.115931
$732$	−5.43708	−0.200960
$733$	8.23113	0.304024	0.152012	−	0.988379i	$-0.451425\pi$
$733$	8.23113	0.304024	0.152012	+	0.988379i	$0.451425\pi$
$734$	−40.9518	−1.51156
$735$	2.70684	0.0998433
$736$	21.1759	0.780554
$737$	53.7624	1.98036
$738$	42.6065	1.56837
$739$	−11.7725	−0.433057	−0.216528	−	0.976276i	$-0.569473\pi$
$739$	−11.7725	−0.433057	−0.216528	+	0.976276i	$0.569473\pi$
$740$	−3.15709	−0.116057
$741$	−8.58580	−0.315407
$742$	19.7546	0.725214
$743$	−29.3902	−1.07822	−0.539112	−	0.842234i	$-0.681240\pi$
$743$	−29.3902	−1.07822	−0.539112	+	0.842234i	$0.681240\pi$
$744$	−6.23503	−0.228587
$745$	−8.09762	−0.296674
$746$	61.3625	2.24664
$747$	7.50017	0.274417
$748$	−7.47243	−0.273219
$749$	7.49487	0.273857
$750$	−1.17837	−0.0430279
$751$	−9.66463	−0.352667	−0.176334	−	0.984330i	$-0.556424\pi$
$751$	−9.66463	−0.352667	−0.176334	+	0.984330i	$0.556424\pi$
$752$	−1.09775	−0.0400307
$753$	−5.01803	−0.182867
$754$	−54.3652	−1.97986
$755$	−12.0018	−0.436791
$756$	−12.5374	−0.455980
$757$	3.21095	0.116704	0.0583520	−	0.998296i	$-0.481415\pi$
$757$	3.21095	0.116704	0.0583520	+	0.998296i	$0.481415\pi$
$758$	−77.2672	−2.80647
$759$	10.0941	0.366394
$760$	−14.6481	−0.531341
$761$	−3.78248	−0.137115	−0.0685574	−	0.997647i	$-0.521840\pi$
$761$	−3.78248	−0.137115	−0.0685574	+	0.997647i	$0.521840\pi$
$762$	−15.0312	−0.544524
$763$	0.504546	0.0182658
$764$	−24.3414	−0.880641
$765$	1.16423	0.0420927
$766$	6.23707	0.225354
$767$	−25.2616	−0.912144
$768$	7.10304	0.256309
$769$	7.39888	0.266810	0.133405	−	0.991062i	$-0.457409\pi$
$769$	7.39888	0.266810	0.133405	+	0.991062i	$0.457409\pi$
$770$	−16.8365	−0.606745
$771$	−16.4200	−0.591352
$772$	82.1054	2.95504
$773$	−12.8663	−0.462769	−0.231385	−	0.972862i	$-0.574326\pi$
$773$	−12.8663	−0.462769	−0.231385	+	0.972862i	$0.574326\pi$
$774$	−45.5919	−1.63877
$775$	4.57289	0.164263
$776$	−46.8804	−1.68291
$777$	−0.692961	−0.0248598
$778$	5.07397	0.181911
$779$	38.3004	1.37225
$780$	4.86246	0.174104
$781$	43.3761	1.55212
$782$	3.39257	0.121318
$783$	23.9838	0.857111
$784$	1.80998	0.0646420
$785$	−19.2732	−0.687890
$786$	17.0817	0.609282
$787$	−3.19598	−0.113924	−0.0569621	−	0.998376i	$-0.518141\pi$
$787$	−3.19598	−0.113924	−0.0569621	+	0.998376i	$0.518141\pi$
$788$	41.3221	1.47204
$789$	−7.42852	−0.264462
$790$	38.7696	1.37936
$791$	6.07546	0.216019
$792$	−39.8355	−1.41549
$793$	−9.85125	−0.349828
$794$	13.0472	0.463027
$795$	3.37999	0.119876
$796$	57.7715	2.04766
$797$	−33.4964	−1.18650	−0.593252	−	0.805017i	$-0.702156\pi$
$797$	−33.4964	−1.18650	−0.593252	+	0.805017i	$0.702156\pi$
$798$	−8.77247	−0.310542
$799$	−1.34887	−0.0477195
$800$	−6.04326	−0.213661
$801$	−0.236238	−0.00834705
$802$	−37.3471	−1.31877
$803$	−4.23346	−0.149396
$804$	−15.8644	−0.559495
$805$	4.67952	0.164931
$806$	−30.8237	−1.08572
$807$	14.9552	0.526447
$808$	28.2694	0.994514
$809$	3.02505	0.106355	0.0531775	−	0.998585i	$-0.483065\pi$
$809$	3.02505	0.106355	0.0531775	+	0.998585i	$0.483065\pi$
$810$	15.0999	0.530556
$811$	−15.5601	−0.546388	−0.273194	−	0.961959i	$-0.588080\pi$
$811$	−15.5601	−0.546388	−0.273194	+	0.961959i	$0.588080\pi$
$812$	−34.0052	−1.19335
$813$	−5.41635	−0.189960
$814$	−12.6073	−0.441885
$815$	−0.995229	−0.0348614
$816$	−0.0767581	−0.00268707
$817$	−40.9840	−1.43385
$818$	73.9946	2.58716
$819$	−10.8244	−0.378234
$820$	−21.6910	−0.757482
$821$	−21.2585	−0.741928	−0.370964	−	0.928647i	$-0.620973\pi$
$821$	−21.2585	−0.741928	−0.370964	+	0.928647i	$0.620973\pi$
$822$	12.7765	0.445632
$823$	−21.0705	−0.734472	−0.367236	−	0.930128i	$-0.619696\pi$
$823$	−21.0705	−0.734472	−0.367236	+	0.930128i	$0.619696\pi$
$824$	−21.5324	−0.750116
$825$	−2.88070	−0.100293
$826$	−25.8109	−0.898075
$827$	−11.8965	−0.413683	−0.206841	−	0.978374i	$-0.566318\pi$
$827$	−11.8965	−0.413683	−0.206841	+	0.978374i	$0.566318\pi$
$828$	30.2092	1.04984
$829$	3.76808	0.130871	0.0654355	−	0.997857i	$-0.479156\pi$
$829$	3.76808	0.130871	0.0654355	+	0.997857i	$0.479156\pi$
$830$	−6.23723	−0.216497
$831$	−8.40713	−0.291640
$832$	38.6749	1.34081
$833$	2.22403	0.0770579
$834$	−1.84550	−0.0639046
$835$	−24.2625	−0.839638
$836$	−97.7050	−3.37920
$837$	13.5982	0.470022
$838$	60.4407	2.08789
$839$	27.0741	0.934703	0.467352	−	0.884071i	$-0.345208\pi$
$839$	27.0741	0.934703	0.467352	+	0.884071i	$0.345208\pi$
$840$	1.82086	0.0628258
$841$	36.0513	1.24315
$842$	−31.0605	−1.07042
$843$	−4.20799	−0.144931
$844$	9.12914	0.314238
$845$	−4.18988	−0.144136
$846$	−19.6199	−0.674547
$847$	−26.4693	−0.909496
$848$	2.26009	0.0776118
$849$	0.223003	0.00765345
$850$	−0.968185	−0.0332085
$851$	3.50406	0.120118
$852$	−12.7996	−0.438507
$853$	−5.26211	−0.180171	−0.0900857	−	0.995934i	$-0.528714\pi$
$853$	−5.26211	−0.180171	−0.0900857	+	0.995934i	$0.528714\pi$
$854$	−10.0654	−0.344432
$855$	15.2227	0.520607
$856$	−14.7470	−0.504042
$857$	43.5043	1.48608	0.743040	−	0.669247i	$-0.233383\pi$
$857$	43.5043	1.48608	0.743040	+	0.669247i	$0.233383\pi$
$858$	19.4174	0.662899
$859$	12.2666	0.418530	0.209265	−	0.977859i	$-0.432893\pi$
$859$	12.2666	0.418530	0.209265	+	0.977859i	$0.432893\pi$
$860$	23.2108	0.791482
$861$	−4.76103	−0.162255
$862$	25.5861	0.871466
$863$	−25.5488	−0.869692	−0.434846	−	0.900505i	$-0.643197\pi$
$863$	−25.5488	−0.869692	−0.434846	+	0.900505i	$0.643197\pi$
$864$	−17.9705	−0.611370
$865$	−11.4556	−0.389501
$866$	45.2431	1.53742
$867$	8.72688	0.296380
$868$	−19.2800	−0.654407
$869$	94.7781	3.21513
$870$	−9.50406	−0.322218
$871$	−28.7442	−0.973960
$872$	−0.992751	−0.0336188
$873$	48.7196	1.64891
$874$	44.3593	1.50047
$875$	−1.33546	−0.0451467
$876$	1.24923	0.0422075
$877$	−5.42848	−0.183307	−0.0916534	−	0.995791i	$-0.529215\pi$
$877$	−5.42848	−0.183307	−0.0916534	+	0.995791i	$0.529215\pi$
$878$	41.8579	1.41264
$879$	−7.46331	−0.251731
$880$	−1.92623	−0.0649333
$881$	−1.60640	−0.0541211	−0.0270606	−	0.999634i	$-0.508615\pi$
$881$	−1.60640	−0.0541211	−0.0270606	+	0.999634i	$0.508615\pi$
$882$	32.3495	1.08926
$883$	−27.0365	−0.909850	−0.454925	−	0.890530i	$-0.650334\pi$
$883$	−27.0365	−0.909850	−0.454925	+	0.890530i	$0.650334\pi$
$884$	3.99516	0.134372
$885$	−4.41620	−0.148449
$886$	−50.3508	−1.69157
$887$	5.22338	0.175384	0.0876919	−	0.996148i	$-0.472051\pi$
$887$	5.22338	0.175384	0.0876919	+	0.996148i	$0.472051\pi$
$888$	1.36348	0.0457553
$889$	−17.0350	−0.571337
$890$	0.196458	0.00658529
$891$	36.9140	1.23667
$892$	81.4543	2.72729
$893$	−17.6370	−0.590199
$894$	9.54198	0.319132
$895$	−11.8233	−0.395209
$896$	23.3748	0.780897
$897$	−5.39686	−0.180196
$898$	−10.6960	−0.356931
$899$	36.8824	1.23010
$900$	−8.62122	−0.287374
$901$	2.77710	0.0925187
$902$	−86.6191	−2.88410
$903$	5.09462	0.169538
$904$	−11.9541	−0.397589
$905$	−14.8035	−0.492085
$906$	14.1425	0.469855
$907$	35.8601	1.19071	0.595357	−	0.803461i	$-0.297011\pi$
$907$	35.8601	1.19071	0.595357	+	0.803461i	$0.297011\pi$
$908$	−18.9771	−0.629776
$909$	−29.3785	−0.974423
$910$	9.00167	0.298403
$911$	−37.2761	−1.23501	−0.617506	−	0.786566i	$-0.711857\pi$
$911$	−37.2761	−1.23501	−0.617506	+	0.786566i	$0.711857\pi$
$912$	−1.00364	−0.0332339
$913$	−15.2478	−0.504630
$914$	−29.3459	−0.970677
$915$	−1.72218	−0.0569336
$916$	16.4839	0.544644
$917$	19.3588	0.639285
$918$	−2.87904	−0.0950226
$919$	20.7180	0.683423	0.341712	−	0.939805i	$-0.388993\pi$
$919$	20.7180	0.683423	0.341712	+	0.939805i	$0.388993\pi$
$920$	−9.20747	−0.303561
$921$	12.8908	0.424767
$922$	−26.6614	−0.878046
$923$	−23.1911	−0.763345
$924$	12.1455	0.399557
$925$	−1.00000	−0.0328798
$926$	0.856165	0.0281353
$927$	22.3771	0.734962
$928$	−48.7415	−1.60002
$929$	4.73148	0.155235	0.0776173	−	0.996983i	$-0.475269\pi$
$929$	4.73148	0.155235	0.0776173	+	0.996983i	$0.475269\pi$
$930$	−5.38855	−0.176698
$931$	29.0800	0.953059
$932$	−48.0687	−1.57454
$933$	6.92897	0.226844
$934$	−16.4026	−0.536711
$935$	−2.36687	−0.0774051
$936$	21.2981	0.696152
$937$	−9.43501	−0.308228	−0.154114	−	0.988053i	$-0.549252\pi$
$937$	−9.43501	−0.308228	−0.154114	+	0.988053i	$0.549252\pi$
$938$	−29.3691	−0.958937
$939$	−13.5500	−0.442186
$940$	9.98849	0.325789
$941$	41.6919	1.35912	0.679559	−	0.733621i	$-0.262171\pi$
$941$	41.6919	1.35912	0.679559	+	0.733621i	$0.262171\pi$
$942$	22.7109	0.739962
$943$	24.0748	0.783985
$944$	−2.95297	−0.0961111
$945$	−3.97118	−0.129183
$946$	92.6883	3.01356
$947$	40.4822	1.31550	0.657748	−	0.753238i	$-0.271509\pi$
$947$	40.4822	1.31550	0.657748	+	0.753238i	$0.271509\pi$
$948$	−27.9676	−0.908344
$949$	2.26343	0.0734741
$950$	−12.6594	−0.410725
$951$	−14.2736	−0.462852
$952$	1.49608	0.0484882
$953$	57.3835	1.85883	0.929416	−	0.369033i	$-0.120311\pi$
$953$	57.3835	1.85883	0.929416	+	0.369033i	$0.120311\pi$
$954$	40.3943	1.30781
$955$	−7.71008	−0.249492
$956$	−38.2526	−1.23718
$957$	−23.2341	−0.751052
$958$	67.1749	2.17032
$959$	14.4797	0.467575
$960$	6.76110	0.218214
$961$	−10.0887	−0.325440
$962$	6.74052	0.217323
$963$	15.3256	0.493859
$964$	65.6386	2.11408
$965$	26.0067	0.837185
$966$	−5.51419	−0.177416
$967$	−5.51447	−0.177333	−0.0886667	−	0.996061i	$-0.528261\pi$
$967$	−5.51447	−0.177333	−0.0886667	+	0.996061i	$0.528261\pi$
$968$	52.0813	1.67396
$969$	−1.23323	−0.0396172
$970$	−40.5158	−1.30088
$971$	−29.5277	−0.947590	−0.473795	−	0.880635i	$-0.657116\pi$
$971$	−29.5277	−0.947590	−0.473795	+	0.880635i	$0.657116\pi$
$972$	−39.0570	−1.25275
$973$	−2.09153	−0.0670514
$974$	9.05489	0.290137
$975$	1.54017	0.0493250
$976$	−1.15157	−0.0368608
$977$	45.5206	1.45633	0.728166	−	0.685401i	$-0.240373\pi$
$977$	45.5206	1.45633	0.728166	+	0.685401i	$0.240373\pi$
$978$	1.17275	0.0375003
$979$	0.480272	0.0153495
$980$	−16.4691	−0.526087
$981$	1.03170	0.0329396
$982$	10.6131	0.338677
$983$	−11.2739	−0.359582	−0.179791	−	0.983705i	$-0.557542\pi$
$983$	−11.2739	−0.359582	−0.179791	+	0.983705i	$0.557542\pi$
$984$	9.36785	0.298636
$985$	13.0887	0.417040
$986$	−7.80883	−0.248684
$987$	2.19241	0.0697852
$988$	52.2383	1.66192
$989$	−25.7617	−0.819175
$990$	−34.4273	−1.09417
$991$	−12.4139	−0.394341	−0.197170	−	0.980369i	$-0.563175\pi$
$991$	−12.4139	−0.394341	−0.197170	+	0.980369i	$0.563175\pi$
$992$	−27.6352	−0.877417
$993$	17.3613	0.550944
$994$	−23.6954	−0.751571
$995$	18.2990	0.580116
$996$	4.49940	0.142569
$997$	−38.6932	−1.22543	−0.612713	−	0.790306i	$-0.709922\pi$
$997$	−38.6932	−1.22543	−0.612713	+	0.790306i	$0.709922\pi$
$998$	6.26488	0.198311
$999$	−2.97365	−0.0940822

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.1.5	✓	5
3.2	odd	2		1665.2.a.q.1.1		5
4.3	odd	2		2960.2.a.ba.1.3		5
5.2	odd	4		925.2.b.g.149.9		10
5.3	odd	4		925.2.b.g.149.2		10
5.4	even	2		925.2.a.h.1.1		5
7.6	odd	2		9065.2.a.j.1.5		5
15.14	odd	2		8325.2.a.cc.1.5		5
37.36	even	2		6845.2.a.g.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.a.d.1.5	✓	5	1.1	even	1	trivial
925.2.a.h.1.1		5	5.4	even	2
925.2.b.g.149.2		10	5.3	odd	4
925.2.b.g.149.9		10	5.2	odd	4
1665.2.a.q.1.1		5	3.2	odd	2
2960.2.a.ba.1.3		5	4.3	odd	2
6845.2.a.g.1.1		5	37.36	even	2
8325.2.a.cc.1.5		5	15.14	odd	2
9065.2.a.j.1.5		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.1.5

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