LMFDB - Embedded newform 161.4.a.a.1.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [161,4,Mod(1,161)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(161, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("161.1"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	161.a (trivial)

Newform invariants

comment:select newform

sage:traces = [5] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	yes
Analytic conductor:	$9.49930751092$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 18x^{3} - 4x^{2} + 44x + 24 $ x^5 - x^4 - 18x^3 - 4x^2 + 44*x + 24
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-3.14816$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-4.14816 q^{2} -4.24155 q^{3} +9.20723 q^{4} -7.96567 q^{5} +17.5946 q^{6} +7.00000 q^{7} -5.00776 q^{8} -9.00922 q^{9} +33.0429 q^{10} +61.8101 q^{11} -39.0529 q^{12} -7.79423 q^{13} -29.0371 q^{14} +33.7868 q^{15} -52.8848 q^{16} +69.4266 q^{17} +37.3717 q^{18} +27.5368 q^{19} -73.3417 q^{20} -29.6909 q^{21} -256.398 q^{22} -23.0000 q^{23} +21.2407 q^{24} -61.5481 q^{25} +32.3317 q^{26} +152.735 q^{27} +64.4506 q^{28} -252.830 q^{29} -140.153 q^{30} -288.795 q^{31} +259.437 q^{32} -262.171 q^{33} -287.993 q^{34} -55.7597 q^{35} -82.9500 q^{36} -75.3646 q^{37} -114.227 q^{38} +33.0597 q^{39} +39.8902 q^{40} +81.1462 q^{41} +123.162 q^{42} -361.319 q^{43} +569.100 q^{44} +71.7645 q^{45} +95.4077 q^{46} +407.124 q^{47} +224.314 q^{48} +49.0000 q^{49} +255.311 q^{50} -294.477 q^{51} -71.7633 q^{52} -429.836 q^{53} -633.569 q^{54} -492.359 q^{55} -35.0543 q^{56} -116.799 q^{57} +1048.78 q^{58} +637.860 q^{59} +311.083 q^{60} -502.016 q^{61} +1197.97 q^{62} -63.0646 q^{63} -653.106 q^{64} +62.0863 q^{65} +1087.53 q^{66} +365.598 q^{67} +639.227 q^{68} +97.5557 q^{69} +231.300 q^{70} -645.350 q^{71} +45.1161 q^{72} +1043.38 q^{73} +312.624 q^{74} +261.059 q^{75} +253.537 q^{76} +432.671 q^{77} -137.137 q^{78} -563.988 q^{79} +421.263 q^{80} -404.585 q^{81} -336.607 q^{82} -513.618 q^{83} -273.371 q^{84} -553.030 q^{85} +1498.81 q^{86} +1072.39 q^{87} -309.530 q^{88} -1143.56 q^{89} -297.691 q^{90} -54.5596 q^{91} -211.766 q^{92} +1224.94 q^{93} -1688.82 q^{94} -219.349 q^{95} -1100.41 q^{96} -328.899 q^{97} -203.260 q^{98} -556.861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - 4 q^{2} - 11 q^{3} - 4 q^{5} + 35 q^{7} + 18 q^{8} + 14 q^{9} + 26 q^{10} - 36 q^{11} - 28 q^{12} - 69 q^{13} - 28 q^{14} - 88 q^{15} - 124 q^{16} - 42 q^{17} - 94 q^{18} - 140 q^{19} - 168 q^{20}+ \cdots - 990 q^{99}+O(q^{100}) $ 5 * q - 4 * q^2 - 11 * q^3 - 4 * q^5 + 35 * q^7 + 18 * q^8 + 14 * q^9 + 26 * q^10 - 36 * q^11 - 28 * q^12 - 69 * q^13 - 28 * q^14 - 88 * q^15 - 124 * q^16 - 42 * q^17 - 94 * q^18 - 140 * q^19 - 168 * q^20 - 77 * q^21 - 346 * q^22 - 115 * q^23 + 18 * q^24 - 357 * q^25 + 68 * q^26 - 35 * q^27 - 383 * q^29 + 184 * q^30 - 319 * q^31 - 50 * q^32 - 108 * q^33 - 376 * q^34 - 28 * q^35 - 180 * q^36 - 154 * q^37 + 8 * q^38 - 235 * q^39 + 90 * q^40 + 277 * q^41 - 718 * q^43 + 422 * q^44 + 470 * q^45 + 92 * q^46 + 53 * q^47 + 248 * q^48 + 245 * q^49 - 60 * q^50 + 232 * q^51 + 178 * q^52 + 450 * q^53 + 468 * q^54 - 206 * q^55 + 126 * q^56 - 560 * q^57 + 1738 * q^58 + 936 * q^59 + 944 * q^60 - 522 * q^61 + 788 * q^62 + 98 * q^63 - 252 * q^64 + 264 * q^65 + 2310 * q^66 - 810 * q^67 + 1326 * q^68 + 253 * q^69 + 182 * q^70 - 1373 * q^71 + 1590 * q^72 + 459 * q^73 + 330 * q^74 + 333 * q^75 + 1168 * q^76 - 252 * q^77 + 462 * q^78 - 728 * q^79 + 1368 * q^80 - 895 * q^81 + 1034 * q^82 - 500 * q^83 - 196 * q^84 - 1432 * q^85 + 3138 * q^86 + 1803 * q^87 - 722 * q^88 - 586 * q^89 - 1024 * q^90 - 483 * q^91 + 2149 * q^93 + 316 * q^94 - 188 * q^95 + 1210 * q^96 - 2150 * q^97 - 196 * q^98 - 990 * 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 $

$2$	−4.14816	−1.46660	−0.733298	−	0.679907i	$-0.762020\pi$
$2$	−4.14816	−1.46660	−0.733298	+	0.679907i	$0.762020\pi$
$3$	−4.24155	−0.816287	−0.408144	−	0.912918i	$-0.633824\pi$
$3$	−4.24155	−0.816287	−0.408144	+	0.912918i	$0.633824\pi$
$4$	9.20723	1.15090
$5$	−7.96567	−0.712471	−0.356236	−	0.934396i	$-0.615940\pi$
$5$	−7.96567	−0.712471	−0.356236	+	0.934396i	$0.615940\pi$
$6$	17.5946	1.19716
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−5.00776	−0.221314
$9$	−9.00922	−0.333675
$10$	33.0429	1.04491
$11$	61.8101	1.69422	0.847111	−	0.531415i	$-0.178340\pi$
$11$	61.8101	1.69422	0.847111	+	0.531415i	$0.178340\pi$
$12$	−39.0529	−0.939468
$13$	−7.79423	−0.166287	−0.0831435	−	0.996538i	$-0.526496\pi$
$13$	−7.79423	−0.166287	−0.0831435	+	0.996538i	$0.526496\pi$
$14$	−29.0371	−0.554321
$15$	33.7868	0.581581
$16$	−52.8848	−0.826325
$17$	69.4266	0.990496	0.495248	−	0.868752i	$-0.335077\pi$
$17$	69.4266	0.990496	0.495248	+	0.868752i	$0.335077\pi$
$18$	37.3717	0.489366
$19$	27.5368	0.332493	0.166246	−	0.986084i	$-0.446835\pi$
$19$	27.5368	0.332493	0.166246	+	0.986084i	$0.446835\pi$
$20$	−73.3417	−0.819986
$21$	−29.6909	−0.308528
$22$	−256.398	−2.48474
$23$	−23.0000	−0.208514
$23$	−23.0000	−0.208514
$24$	21.2407	0.180656
$25$	−61.5481	−0.492385
$26$	32.3317	0.243876
$27$	152.735	1.08866
$28$	64.4506	0.435001
$29$	−252.830	−1.61894	−0.809470	−	0.587161i	$-0.800246\pi$
$29$	−252.830	−1.61894	−0.809470	+	0.587161i	$0.800246\pi$
$30$	−140.153	−0.852945
$31$	−288.795	−1.67320	−0.836600	−	0.547815i	$-0.815460\pi$
$31$	−288.795	−1.67320	−0.836600	+	0.547815i	$0.815460\pi$
$32$	259.437	1.43320
$33$	−262.171	−1.38297
$34$	−287.993	−1.45266
$35$	−55.7597	−0.269289
$36$	−82.9500	−0.384028
$37$	−75.3646	−0.334861	−0.167431	−	0.985884i	$-0.553547\pi$
$37$	−75.3646	−0.334861	−0.167431	+	0.985884i	$0.553547\pi$
$38$	−114.227	−0.487633
$39$	33.0597	0.135738
$40$	39.8902	0.157680
$41$	81.1462	0.309095	0.154548	−	0.987985i	$-0.450608\pi$
$41$	81.1462	0.309095	0.154548	+	0.987985i	$0.450608\pi$
$42$	123.162	0.452485
$43$	−361.319	−1.28141	−0.640704	−	0.767788i	$-0.721357\pi$
$43$	−361.319	−1.28141	−0.640704	+	0.767788i	$0.721357\pi$
$44$	569.100	1.94989
$45$	71.7645	0.237734
$46$	95.4077	0.305806
$47$	407.124	1.26351	0.631757	−	0.775167i	$-0.282334\pi$
$47$	407.124	1.26351	0.631757	+	0.775167i	$0.282334\pi$
$48$	224.314	0.674519
$49$	49.0000	0.142857
$50$	255.311	0.722129
$51$	−294.477	−0.808529
$52$	−71.7633	−0.191380
$53$	−429.836	−1.11401	−0.557005	−	0.830509i	$-0.688050\pi$
$53$	−429.836	−1.11401	−0.557005	+	0.830509i	$0.688050\pi$
$54$	−633.569	−1.59663
$55$	−492.359	−1.20709
$56$	−35.0543	−0.0836488
$57$	−116.799	−0.271410
$58$	1048.78	2.37433
$59$	637.860	1.40750	0.703748	−	0.710449i	$-0.251508\pi$
$59$	637.860	1.40750	0.703748	+	0.710449i	$0.251508\pi$
$60$	311.083	0.669344
$61$	−502.016	−1.05371	−0.526857	−	0.849954i	$-0.676630\pi$
$61$	−502.016	−1.05371	−0.526857	+	0.849954i	$0.676630\pi$
$62$	1197.97	2.45391
$63$	−63.0646	−0.126117
$64$	−653.106	−1.27560
$65$	62.0863	0.118475
$66$	1087.53	2.02826
$67$	365.598	0.666640	0.333320	−	0.942814i	$-0.391831\pi$
$67$	365.598	0.666640	0.333320	+	0.942814i	$0.391831\pi$
$68$	639.227	1.13996
$69$	97.5557	0.170208
$70$	231.300	0.394938
$71$	−645.350	−1.07872	−0.539359	−	0.842076i	$-0.681333\pi$
$71$	−645.350	−1.07872	−0.539359	+	0.842076i	$0.681333\pi$
$72$	45.1161	0.0738469
$73$	1043.38	1.67286	0.836430	−	0.548074i	$-0.184639\pi$
$73$	1043.38	1.67286	0.836430	+	0.548074i	$0.184639\pi$
$74$	312.624	0.491106
$75$	261.059	0.401927
$76$	253.537	0.382667
$77$	432.671	0.640356
$78$	−137.137	−0.199073
$79$	−563.988	−0.803210	−0.401605	−	0.915813i	$-0.631548\pi$
$79$	−563.988	−0.803210	−0.401605	+	0.915813i	$0.631548\pi$
$80$	421.263	0.588733
$81$	−404.585	−0.554986
$82$	−336.607	−0.453318
$83$	−513.618	−0.679240	−0.339620	−	0.940563i	$-0.610298\pi$
$83$	−513.618	−0.679240	−0.339620	+	0.940563i	$0.610298\pi$
$84$	−273.371	−0.355085
$85$	−553.030	−0.705700
$86$	1498.81	1.87931
$87$	1072.39	1.32152
$88$	−309.530	−0.374955
$89$	−1143.56	−1.36199	−0.680993	−	0.732290i	$-0.738452\pi$
$89$	−1143.56	−1.36199	−0.680993	+	0.732290i	$0.738452\pi$
$90$	−297.691	−0.348659
$91$	−54.5596	−0.0628506
$92$	−211.766	−0.239980
$93$	1224.94	1.36581
$94$	−1688.82	−1.85306
$95$	−219.349	−0.236892
$96$	−1100.41	−1.16990
$97$	−328.899	−0.344274	−0.172137	−	0.985073i	$-0.555067\pi$
$97$	−328.899	−0.344274	−0.172137	+	0.985073i	$0.555067\pi$
$98$	−203.260	−0.209514
$99$	−556.861	−0.565320
$100$	−566.687	−0.566687
$101$	−1430.15	−1.40897	−0.704483	−	0.709721i	$-0.748821\pi$
$101$	−1430.15	−1.40897	−0.704483	+	0.709721i	$0.748821\pi$
$102$	1221.54	1.18579
$103$	−1361.77	−1.30271	−0.651355	−	0.758773i	$-0.725799\pi$
$103$	−1361.77	−1.30271	−0.651355	+	0.758773i	$0.725799\pi$
$104$	39.0317	0.0368017
$105$	236.508	0.219817
$106$	1783.03	1.63380
$107$	−1141.73	−1.03154	−0.515770	−	0.856727i	$-0.672494\pi$
$107$	−1141.73	−1.03154	−0.515770	+	0.856727i	$0.672494\pi$
$108$	1406.27	1.25294
$109$	−173.687	−0.152626	−0.0763128	−	0.997084i	$-0.524315\pi$
$109$	−173.687	−0.152626	−0.0763128	+	0.997084i	$0.524315\pi$
$110$	2042.38	1.77031
$111$	319.663	0.273343
$112$	−370.194	−0.312322
$113$	1355.42	1.12838	0.564191	−	0.825645i	$-0.309188\pi$
$113$	1355.42	1.12838	0.564191	+	0.825645i	$0.309188\pi$
$114$	484.499	0.398048
$115$	183.210	0.148561
$116$	−2327.86	−1.86324
$117$	70.2200	0.0554858
$118$	−2645.95	−2.06423
$119$	485.986	0.374372
$120$	−169.196	−0.128712
$121$	2489.49	1.87039
$122$	2082.44	1.54537
$123$	−344.186	−0.252311
$124$	−2659.00	−1.92569
$125$	1485.98	1.06328
$126$	261.602	0.184963
$127$	−1584.92	−1.10739	−0.553697	−	0.832719i	$-0.686783\pi$
$127$	−1584.92	−1.10739	−0.553697	+	0.832719i	$0.686783\pi$
$128$	633.695	0.437588
$129$	1532.55	1.04600
$130$	−257.544	−0.173755
$131$	−1613.76	−1.07630	−0.538148	−	0.842850i	$-0.680876\pi$
$131$	−1613.76	−1.07630	−0.538148	+	0.842850i	$0.680876\pi$
$132$	−2413.87	−1.59167
$133$	192.757	0.125670
$134$	−1516.56	−0.977691
$135$	−1216.64	−0.775641
$136$	−347.672	−0.219211
$137$	−350.201	−0.218392	−0.109196	−	0.994020i	$-0.534828\pi$
$137$	−350.201	−0.218392	−0.109196	+	0.994020i	$0.534828\pi$
$138$	−404.677	−0.249626
$139$	189.311	0.115519	0.0577594	−	0.998331i	$-0.481604\pi$
$139$	189.311	0.115519	0.0577594	+	0.998331i	$0.481604\pi$
$140$	−513.392	−0.309925
$141$	−1726.84	−1.03139
$142$	2677.01	1.58204
$143$	−481.763	−0.281727
$144$	476.451	0.275724
$145$	2013.96	1.15345
$146$	−4328.12	−2.45341
$147$	−207.836	−0.116612
$148$	−693.899	−0.385393
$149$	1363.77	0.749827	0.374913	−	0.927060i	$-0.377672\pi$
$149$	1363.77	0.749827	0.374913	+	0.927060i	$0.377672\pi$
$150$	−1082.92	−0.589465
$151$	−2973.95	−1.60276	−0.801380	−	0.598155i	$-0.795901\pi$
$151$	−2973.95	−1.60276	−0.801380	+	0.598155i	$0.795901\pi$
$152$	−137.898	−0.0735853
$153$	−625.480	−0.330504
$154$	−1794.79	−0.939143
$155$	2300.45	1.19211
$156$	304.388	0.156221
$157$	−963.379	−0.489720	−0.244860	−	0.969558i	$-0.578742\pi$
$157$	−963.379	−0.489720	−0.244860	+	0.969558i	$0.578742\pi$
$158$	2339.51	1.17798
$159$	1823.17	0.909352
$160$	−2066.59	−1.02111
$161$	−161.000	−0.0788110
$162$	1678.28	0.813940
$163$	−1018.40	−0.489369	−0.244684	−	0.969603i	$-0.578684\pi$
$163$	−1018.40	−0.489369	−0.244684	+	0.969603i	$0.578684\pi$
$164$	747.132	0.355739
$165$	2088.37	0.985328
$166$	2130.57	0.996170
$167$	−795.570	−0.368641	−0.184321	−	0.982866i	$-0.559008\pi$
$167$	−795.570	−0.368641	−0.184321	+	0.982866i	$0.559008\pi$
$168$	148.685	0.0682815
$169$	−2136.25	−0.972349
$170$	2294.06	1.03498
$171$	−248.085	−0.110945
$172$	−3326.74	−1.47478
$173$	1018.47	0.447590	0.223795	−	0.974636i	$-0.428155\pi$
$173$	1018.47	0.447590	0.223795	+	0.974636i	$0.428155\pi$
$174$	−4448.45	−1.93814
$175$	−430.836	−0.186104
$176$	−3268.82	−1.39998
$177$	−2705.52	−1.14892
$178$	4743.66	1.99748
$179$	3951.06	1.64981	0.824905	−	0.565271i	$-0.191228\pi$
$179$	3951.06	1.64981	0.824905	+	0.565271i	$0.191228\pi$
$180$	660.752	0.273609
$181$	1153.46	0.473681	0.236840	−	0.971549i	$-0.423888\pi$
$181$	1153.46	0.473681	0.236840	+	0.971549i	$0.423888\pi$
$182$	226.322	0.0921764
$183$	2129.33	0.860134
$184$	115.179	0.0461472
$185$	600.329	0.238579
$186$	−5081.25	−2.00309
$187$	4291.27	1.67812
$188$	3748.48	1.45418
$189$	1069.15	0.411476
$190$	909.893	0.347424
$191$	−2567.20	−0.972546	−0.486273	−	0.873807i	$-0.661644\pi$
$191$	−2567.20	−0.972546	−0.486273	+	0.873807i	$0.661644\pi$
$192$	2770.19	1.04125
$193$	801.338	0.298868	0.149434	−	0.988772i	$-0.452255\pi$
$193$	801.338	0.298868	0.149434	+	0.988772i	$0.452255\pi$
$194$	1364.32	0.504911
$195$	−263.342	−0.0967095
$196$	451.154	0.164415
$197$	5345.91	1.93340	0.966702	−	0.255906i	$-0.0823739\pi$
$197$	5345.91	1.93340	0.966702	+	0.255906i	$0.0823739\pi$
$198$	2309.95	0.829096
$199$	−838.023	−0.298522	−0.149261	−	0.988798i	$-0.547689\pi$
$199$	−838.023	−0.298522	−0.149261	+	0.988798i	$0.547689\pi$
$200$	308.218	0.108972
$201$	−1550.70	−0.544170
$202$	5932.50	2.06638
$203$	−1769.81	−0.611902
$204$	−2711.31	−0.930539
$205$	−646.384	−0.220222
$206$	5648.84	1.91055
$207$	207.212	0.0695760
$208$	412.197	0.137407
$209$	1702.05	0.563317
$210$	−981.072	−0.322383
$211$	−3161.04	−1.03135	−0.515675	−	0.856784i	$-0.672459\pi$
$211$	−3161.04	−1.03135	−0.515675	+	0.856784i	$0.672459\pi$
$212$	−3957.60	−1.28212
$213$	2737.29	0.880544
$214$	4736.06	1.51285
$215$	2878.14	0.912967
$216$	−764.861	−0.240936
$217$	−2021.57	−0.632410
$218$	720.481	0.223840
$219$	−4425.56	−1.36553
$220$	−4533.26	−1.38924
$221$	−541.127	−0.164707
$222$	−1326.01	−0.400883
$223$	6265.42	1.88145	0.940725	−	0.339171i	$-0.110147\pi$
$223$	6265.42	1.88145	0.940725	+	0.339171i	$0.110147\pi$
$224$	1816.06	0.541698
$225$	554.500	0.164296
$226$	−5622.49	−1.65488
$227$	171.936	0.0502721	0.0251361	−	0.999684i	$-0.491998\pi$
$227$	171.936	0.0502721	0.0251361	+	0.999684i	$0.491998\pi$
$228$	−1075.39	−0.312366
$229$	−139.090	−0.0401367	−0.0200683	−	0.999799i	$-0.506388\pi$
$229$	−139.090	−0.0401367	−0.0200683	+	0.999799i	$0.506388\pi$
$230$	−759.986	−0.217878
$231$	−1835.20	−0.522715
$232$	1266.11	0.358294
$233$	−1900.80	−0.534443	−0.267222	−	0.963635i	$-0.586106\pi$
$233$	−1900.80	−0.534443	−0.267222	+	0.963635i	$0.586106\pi$
$234$	−291.284	−0.0813753
$235$	−3243.02	−0.900217
$236$	5872.92	1.61989
$237$	2392.19	0.655650
$238$	−2015.95	−0.549053
$239$	−3871.53	−1.04782	−0.523908	−	0.851775i	$-0.675527\pi$
$239$	−3871.53	−1.04782	−0.523908	+	0.851775i	$0.675527\pi$
$240$	−1786.81	−0.480575
$241$	−2613.26	−0.698486	−0.349243	−	0.937032i	$-0.613561\pi$
$241$	−2613.26	−0.698486	−0.349243	+	0.937032i	$0.613561\pi$
$242$	−10326.8	−2.74311
$243$	−2407.78	−0.635634
$244$	−4622.18	−1.21272
$245$	−390.318	−0.101782
$246$	1427.74	0.370038
$247$	−214.628	−0.0552893
$248$	1446.22	0.370302
$249$	2178.54	0.554455
$250$	−6164.08	−1.55940
$251$	2205.76	0.554687	0.277344	−	0.960771i	$-0.410546\pi$
$251$	2205.76	0.554687	0.277344	+	0.960771i	$0.410546\pi$
$252$	−580.650	−0.145149
$253$	−1421.63	−0.353270
$254$	6574.50	1.62410
$255$	2345.71	0.576054
$256$	2596.18	0.633833
$257$	−1505.91	−0.365511	−0.182755	−	0.983158i	$-0.558502\pi$
$257$	−1505.91	−0.365511	−0.182755	+	0.983158i	$0.558502\pi$
$258$	−6357.27	−1.53406
$259$	−527.552	−0.126566
$260$	571.643	0.136353
$261$	2277.80	0.540200
$262$	6694.13	1.57849
$263$	−5162.98	−1.21051	−0.605253	−	0.796033i	$-0.706928\pi$
$263$	−5162.98	−1.21051	−0.605253	+	0.796033i	$0.706928\pi$
$264$	1312.89	0.306071
$265$	3423.93	0.793700
$266$	−799.588	−0.184308
$267$	4850.46	1.11177
$268$	3366.14	0.767238
$269$	895.827	0.203047	0.101523	−	0.994833i	$-0.467628\pi$
$269$	895.827	0.203047	0.101523	+	0.994833i	$0.467628\pi$
$270$	5046.81	1.13755
$271$	2854.00	0.639735	0.319868	−	0.947462i	$-0.396362\pi$
$271$	2854.00	0.639735	0.319868	+	0.947462i	$0.396362\pi$
$272$	−3671.61	−0.818472
$273$	231.418	0.0513042
$274$	1452.69	0.320293
$275$	−3804.29	−0.834209
$276$	898.218	0.195893
$277$	−1804.75	−0.391469	−0.195735	−	0.980657i	$-0.562709\pi$
$277$	−1804.75	−0.391469	−0.195735	+	0.980657i	$0.562709\pi$
$278$	−785.291	−0.169419
$279$	2601.82	0.558305
$280$	279.231	0.0595974
$281$	−2703.49	−0.573938	−0.286969	−	0.957940i	$-0.592648\pi$
$281$	−2703.49	−0.573938	−0.286969	+	0.957940i	$0.592648\pi$
$282$	7163.20	1.51263
$283$	−3279.31	−0.688815	−0.344407	−	0.938820i	$-0.611920\pi$
$283$	−3279.31	−0.688815	−0.344407	+	0.938820i	$0.611920\pi$
$284$	−5941.88	−1.24150
$285$	930.379	0.193372
$286$	1998.43	0.413180
$287$	568.024	0.116827
$288$	−2337.32	−0.478223
$289$	−92.9437	−0.0189179
$290$	−8354.22	−1.69164
$291$	1395.04	0.281027
$292$	9606.66	1.92530
$293$	6504.61	1.29694	0.648469	−	0.761241i	$-0.275409\pi$
$293$	6504.61	1.29694	0.648469	+	0.761241i	$0.275409\pi$
$294$	862.137	0.171023
$295$	−5080.98	−1.00280
$296$	377.408	0.0741094
$297$	9440.57	1.84444
$298$	−5657.13	−1.09969
$299$	179.267	0.0346732
$300$	2403.63	0.462579
$301$	−2529.23	−0.484327
$302$	12336.4	2.35060
$303$	6066.07	1.15012
$304$	−1456.28	−0.274747
$305$	3998.90	0.750742
$306$	2594.59	0.484715
$307$	1677.26	0.311811	0.155906	−	0.987772i	$-0.450170\pi$
$307$	1677.26	0.311811	0.155906	+	0.987772i	$0.450170\pi$
$308$	3983.70	0.736988
$309$	5776.02	1.06339
$310$	−9542.63	−1.74834
$311$	−8015.21	−1.46142	−0.730709	−	0.682689i	$-0.760810\pi$
$311$	−8015.21	−1.46142	−0.730709	+	0.682689i	$0.760810\pi$
$312$	−165.555	−0.0300407
$313$	3209.00	0.579500	0.289750	−	0.957102i	$-0.406428\pi$
$313$	3209.00	0.579500	0.289750	+	0.957102i	$0.406428\pi$
$314$	3996.25	0.718221
$315$	502.352	0.0898550
$316$	−5192.77	−0.924417
$317$	−5836.12	−1.03403	−0.517017	−	0.855975i	$-0.672958\pi$
$317$	−5836.12	−1.03403	−0.517017	+	0.855975i	$0.672958\pi$
$318$	−7562.81	−1.33365
$319$	−15627.4	−2.74285
$320$	5202.43	0.908827
$321$	4842.69	0.842034
$322$	667.854	0.115584
$323$	1911.78	0.329333
$324$	−3725.10	−0.638735
$325$	479.720	0.0818772
$326$	4224.48	0.717706
$327$	736.703	0.124586
$328$	−406.361	−0.0684071
$329$	2849.87	0.477563
$330$	−8662.88	−1.44508
$331$	−772.802	−0.128329	−0.0641647	−	0.997939i	$-0.520438\pi$
$331$	−772.802	−0.128329	−0.0641647	+	0.997939i	$0.520438\pi$
$332$	−4729.00	−0.781739
$333$	678.976	0.111735
$334$	3300.15	0.540647
$335$	−2912.23	−0.474962
$336$	1570.20	0.254944
$337$	−2671.61	−0.431845	−0.215923	−	0.976410i	$-0.569276\pi$
$337$	−2671.61	−0.431845	−0.215923	+	0.976410i	$0.569276\pi$
$338$	8861.50	1.42604
$339$	−5749.08	−0.921083
$340$	−5091.87	−0.812192
$341$	−17850.5	−2.83477
$342$	1029.10	0.162711
$343$	343.000	0.0539949
$344$	1809.40	0.283594
$345$	−777.097	−0.121268
$346$	−4224.79	−0.656433
$347$	6495.27	1.00485	0.502427	−	0.864620i	$-0.332441\pi$
$347$	6495.27	1.00485	0.502427	+	0.864620i	$0.332441\pi$
$348$	9873.74	1.52094
$349$	3842.03	0.589281	0.294641	−	0.955608i	$-0.404800\pi$
$349$	3842.03	0.589281	0.294641	+	0.955608i	$0.404800\pi$
$350$	1787.18	0.272939
$351$	−1190.45	−0.181030
$352$	16035.8	2.42816
$353$	−4927.37	−0.742939	−0.371469	−	0.928445i	$-0.621146\pi$
$353$	−4927.37	−0.742939	−0.371469	+	0.928445i	$0.621146\pi$
$354$	11222.9	1.68500
$355$	5140.65	0.768555
$356$	−10529.0	−1.56751
$357$	−2061.34	−0.305595
$358$	−16389.6	−2.41961
$359$	−1213.81	−0.178448	−0.0892238	−	0.996012i	$-0.528439\pi$
$359$	−1213.81	−0.178448	−0.0892238	+	0.996012i	$0.528439\pi$
$360$	−359.380	−0.0526138
$361$	−6100.73	−0.889449
$362$	−4784.75	−0.694698
$363$	−10559.3	−1.52678
$364$	−502.343	−0.0723350
$365$	−8311.24	−1.19186
$366$	−8832.80	−1.26147
$367$	8423.89	1.19816	0.599078	−	0.800691i	$-0.295534\pi$
$367$	8423.89	1.19816	0.599078	+	0.800691i	$0.295534\pi$
$368$	1216.35	0.172301
$369$	−731.065	−0.103137
$370$	−2490.26	−0.349899
$371$	−3008.85	−0.421056
$372$	11278.3	1.57192
$373$	1519.77	0.210968	0.105484	−	0.994421i	$-0.466361\pi$
$373$	1519.77	0.210968	0.105484	+	0.994421i	$0.466361\pi$
$374$	−17800.9	−2.46112
$375$	−6302.87	−0.867943
$376$	−2038.78	−0.279633
$377$	1970.61	0.269209
$378$	−4434.99	−0.603468
$379$	7201.55	0.976039	0.488020	−	0.872833i	$-0.337719\pi$
$379$	7201.55	0.976039	0.488020	+	0.872833i	$0.337719\pi$
$380$	−2019.59	−0.272639
$381$	6722.52	0.903951
$382$	10649.2	1.42633
$383$	−3478.08	−0.464025	−0.232013	−	0.972713i	$-0.574531\pi$
$383$	−3478.08	−0.464025	−0.232013	+	0.972713i	$0.574531\pi$
$384$	−2687.85	−0.357198
$385$	−3446.51	−0.456235
$386$	−3324.08	−0.438319
$387$	3255.20	0.427574
$388$	−3028.25	−0.396226
$389$	−848.484	−0.110591	−0.0552954	−	0.998470i	$-0.517610\pi$
$389$	−848.484	−0.110591	−0.0552954	+	0.998470i	$0.517610\pi$
$390$	1092.39	0.141834
$391$	−1596.81	−0.206533
$392$	−245.380	−0.0316163
$393$	6844.85	0.878567
$394$	−22175.7	−2.83552
$395$	4492.54	0.572264
$396$	−5127.15	−0.650628
$397$	11355.0	1.43549	0.717747	−	0.696304i	$-0.245174\pi$
$397$	11355.0	1.43549	0.717747	+	0.696304i	$0.245174\pi$
$398$	3476.25	0.437811
$399$	−817.590	−0.102583
$400$	3254.96	0.406870
$401$	−3590.27	−0.447106	−0.223553	−	0.974692i	$-0.571766\pi$
$401$	−3590.27	−0.447106	−0.223553	+	0.974692i	$0.571766\pi$
$402$	6432.56	0.798077
$403$	2250.94	0.278231
$404$	−13167.7	−1.62158
$405$	3222.79	0.395412
$406$	7341.44	0.897413
$407$	−4658.29	−0.567329
$408$	1474.67	0.178939
$409$	6046.66	0.731022	0.365511	−	0.930807i	$-0.380894\pi$
$409$	6046.66	0.731022	0.365511	+	0.930807i	$0.380894\pi$
$410$	2681.30	0.322976
$411$	1485.40	0.178271
$412$	−12538.1	−1.49929
$413$	4465.02	0.531984
$414$	−859.549	−0.102040
$415$	4091.31	0.483939
$416$	−2022.11	−0.238322
$417$	−802.971	−0.0942966
$418$	−7060.37	−0.826158
$419$	15974.2	1.86251	0.931254	−	0.364370i	$-0.118716\pi$
$419$	15974.2	1.86251	0.931254	+	0.364370i	$0.118716\pi$
$420$	2177.58	0.252988
$421$	17042.6	1.97294	0.986469	−	0.163949i	$-0.0524231\pi$
$421$	17042.6	1.97294	0.986469	+	0.163949i	$0.0524231\pi$
$422$	13112.5	1.51257
$423$	−3667.87	−0.421603
$424$	2152.52	0.246546
$425$	−4273.07	−0.487705
$426$	−11354.7	−1.29140
$427$	−3514.11	−0.398267
$428$	−10512.1	−1.18720
$429$	2043.42	0.229970
$430$	−11939.0	−1.33895
$431$	13516.7	1.51061	0.755307	−	0.655371i	$-0.227488\pi$
$431$	13516.7	1.51061	0.755307	+	0.655371i	$0.227488\pi$
$432$	−8077.36	−0.899589
$433$	−15003.4	−1.66516	−0.832582	−	0.553902i	$-0.813138\pi$
$433$	−15003.4	−1.66516	−0.832582	+	0.553902i	$0.813138\pi$
$434$	8385.78	0.927490
$435$	−8542.31	−0.941546
$436$	−1599.18	−0.175657
$437$	−633.345	−0.0693295
$438$	18357.9	2.00269
$439$	4217.29	0.458497	0.229248	−	0.973368i	$-0.426373\pi$
$439$	4217.29	0.458497	0.229248	+	0.973368i	$0.426373\pi$
$440$	2465.62	0.267145
$441$	−441.452	−0.0476679
$442$	2244.68	0.241558
$443$	−2547.89	−0.273259	−0.136630	−	0.990622i	$-0.543627\pi$
$443$	−2547.89	−0.273259	−0.136630	+	0.990622i	$0.543627\pi$
$444$	2943.21	0.314591
$445$	9109.20	0.970377
$446$	−25989.9	−2.75933
$447$	−5784.49	−0.612074
$448$	−4571.74	−0.482131
$449$	−5063.60	−0.532219	−0.266109	−	0.963943i	$-0.585738\pi$
$449$	−5063.60	−0.532219	−0.266109	+	0.963943i	$0.585738\pi$
$450$	−2300.16	−0.240956
$451$	5015.66	0.523676
$452$	12479.6	1.29866
$453$	12614.2	1.30831
$454$	−713.216	−0.0737289
$455$	434.604	0.0447793
$456$	584.900	0.0600668
$457$	4174.18	0.427264	0.213632	−	0.976914i	$-0.431471\pi$
$457$	4174.18	0.427264	0.213632	+	0.976914i	$0.431471\pi$
$458$	576.966	0.0588643
$459$	10603.9	1.07832
$460$	1686.86	0.170979
$461$	8836.07	0.892704	0.446352	−	0.894857i	$-0.352723\pi$
$461$	8836.07	0.892704	0.446352	+	0.894857i	$0.352723\pi$
$462$	7612.69	0.766611
$463$	9688.99	0.972539	0.486270	−	0.873809i	$-0.338357\pi$
$463$	9688.99	0.972539	0.486270	+	0.873809i	$0.338357\pi$
$464$	13370.8	1.33777
$465$	−9757.48	−0.973101
$466$	7884.80	0.783812
$467$	−1061.42	−0.105175	−0.0525876	−	0.998616i	$-0.516747\pi$
$467$	−1061.42	−0.105175	−0.0525876	+	0.998616i	$0.516747\pi$
$468$	646.531	0.0638588
$469$	2559.18	0.251966
$470$	13452.5	1.32026
$471$	4086.22	0.399752
$472$	−3194.25	−0.311499
$473$	−22333.1	−2.17099
$474$	−9923.17	−0.961574
$475$	−1694.83	−0.163714
$476$	4474.59	0.430866
$477$	3872.49	0.371717
$478$	16059.7	1.53672
$479$	−3042.48	−0.290218	−0.145109	−	0.989416i	$-0.546353\pi$
$479$	−3042.48	−0.290218	−0.145109	+	0.989416i	$0.546353\pi$
$480$	8765.54	0.833522
$481$	587.409	0.0556831
$482$	10840.2	1.02440
$483$	682.890	0.0643325
$484$	22921.3	2.15264
$485$	2619.90	0.245286
$486$	9987.85	0.932218
$487$	−2800.58	−0.260589	−0.130294	−	0.991475i	$-0.541592\pi$
$487$	−2800.58	−0.260589	−0.130294	+	0.991475i	$0.541592\pi$
$488$	2513.98	0.233202
$489$	4319.59	0.399465
$490$	1619.10	0.149273
$491$	16055.6	1.47572	0.737862	−	0.674952i	$-0.235836\pi$
$491$	16055.6	1.47572	0.737862	+	0.674952i	$0.235836\pi$
$492$	−3169.00	−0.290385
$493$	−17553.1	−1.60355
$494$	890.311	0.0810870
$495$	4435.77	0.402774
$496$	15272.9	1.38261
$497$	−4517.45	−0.407717
$498$	−9036.92	−0.813161
$499$	−10791.3	−0.968106	−0.484053	−	0.875039i	$-0.660836\pi$
$499$	−10791.3	−0.968106	−0.484053	+	0.875039i	$0.660836\pi$
$500$	13681.8	1.22373
$501$	3374.45	0.300917
$502$	−9149.86	−0.813502
$503$	−19552.1	−1.73317	−0.866587	−	0.499026i	$-0.833691\pi$
$503$	−19552.1	−1.73317	−0.866587	+	0.499026i	$0.833691\pi$
$504$	315.812	0.0279115
$505$	11392.1	1.00385
$506$	5897.16	0.518104
$507$	9061.02	0.793716
$508$	−14592.7	−1.27450
$509$	−7944.22	−0.691791	−0.345895	−	0.938273i	$-0.612425\pi$
$509$	−7944.22	−0.691791	−0.345895	+	0.938273i	$0.612425\pi$
$510$	−9730.36	−0.844838
$511$	7303.68	0.632281
$512$	−15838.9	−1.36717
$513$	4205.83	0.361972
$514$	6246.76	0.536056
$515$	10847.4	0.928143
$516$	14110.6	1.20384
$517$	25164.4	2.14067
$518$	2188.37	0.185621
$519$	−4319.91	−0.365362
$520$	−310.914	−0.0262201
$521$	−3927.08	−0.330227	−0.165114	−	0.986275i	$-0.552799\pi$
$521$	−3927.08	−0.330227	−0.165114	+	0.986275i	$0.552799\pi$
$522$	−9448.67	−0.792255
$523$	−148.545	−0.0124195	−0.00620977	−	0.999981i	$-0.501977\pi$
$523$	−148.545	−0.0124195	−0.00620977	+	0.999981i	$0.501977\pi$
$524$	−14858.2	−1.23871
$525$	1827.42	0.151914
$526$	21416.9	1.77532
$527$	−20050.1	−1.65730
$528$	13864.9	1.14278
$529$	529.000	0.0434783
$530$	−14203.0	−1.16404
$531$	−5746.62	−0.469646
$532$	1774.76	0.144635
$533$	−632.473	−0.0513986
$534$	−20120.5	−1.63052
$535$	9094.62	0.734943
$536$	−1830.83	−0.147537
$537$	−16758.6	−1.34672
$538$	−3716.03	−0.297787
$539$	3028.70	0.242032
$540$	−11201.9	−0.892687
$541$	3261.80	0.259215	0.129608	−	0.991565i	$-0.458628\pi$
$541$	3261.80	0.259215	0.129608	+	0.991565i	$0.458628\pi$
$542$	−11838.9	−0.938233
$543$	−4892.48	−0.386660
$544$	18011.8	1.41958
$545$	1383.53	0.108741
$546$	−959.957	−0.0752425
$547$	−23917.9	−1.86957	−0.934785	−	0.355213i	$-0.884408\pi$
$547$	−23917.9	−1.86957	−0.934785	+	0.355213i	$0.884408\pi$
$548$	−3224.38	−0.251348
$549$	4522.78	0.351598
$550$	15780.8	1.22345
$551$	−6962.11	−0.538286
$552$	−488.536	−0.0376693
$553$	−3947.92	−0.303585
$554$	7486.39	0.574127
$555$	−2546.33	−0.194749
$556$	1743.03	0.132951
$557$	19922.3	1.51550	0.757749	−	0.652546i	$-0.226299\pi$
$557$	19922.3	1.51550	0.757749	+	0.652546i	$0.226299\pi$
$558$	−10792.8	−0.818807
$559$	2816.20	0.213082
$560$	2948.84	0.222520
$561$	−18201.6	−1.36983
$562$	11214.5	0.841735
$563$	−11266.3	−0.843372	−0.421686	−	0.906742i	$-0.638562\pi$
$563$	−11266.3	−0.843372	−0.421686	+	0.906742i	$0.638562\pi$
$564$	−15899.4	−1.18703
$565$	−10796.8	−0.803939
$566$	13603.1	1.01021
$567$	−2832.09	−0.209765
$568$	3231.76	0.238735
$569$	−21430.9	−1.57897	−0.789483	−	0.613773i	$-0.789651\pi$
$569$	−21430.9	−1.57897	−0.789483	+	0.613773i	$0.789651\pi$
$570$	−3859.36	−0.283598
$571$	11577.3	0.848500	0.424250	−	0.905545i	$-0.360538\pi$
$571$	11577.3	0.848500	0.424250	+	0.905545i	$0.360538\pi$
$572$	−4435.70	−0.324241
$573$	10888.9	0.793877
$574$	−2356.25	−0.171338
$575$	1415.61	0.102669
$576$	5883.98	0.425635
$577$	8949.82	0.645729	0.322865	−	0.946445i	$-0.395354\pi$
$577$	8949.82	0.645729	0.322865	+	0.946445i	$0.395354\pi$
$578$	385.545	0.0277449
$579$	−3398.92	−0.243962
$580$	18543.0	1.32751
$581$	−3595.33	−0.256729
$582$	−5786.86	−0.412153
$583$	−26568.2	−1.88738
$584$	−5225.01	−0.370227
$585$	−559.350	−0.0395321
$586$	−26982.1	−1.90209
$587$	21580.3	1.51740	0.758702	−	0.651438i	$-0.225834\pi$
$587$	21580.3	1.51740	0.758702	+	0.651438i	$0.225834\pi$
$588$	−1913.59	−0.134210
$589$	−7952.48	−0.556327
$590$	21076.7	1.47070
$591$	−22675.0	−1.57821
$592$	3985.64	0.276704
$593$	−8233.64	−0.570177	−0.285089	−	0.958501i	$-0.592023\pi$
$593$	−8233.64	−0.570177	−0.285089	+	0.958501i	$0.592023\pi$
$594$	−39161.0	−2.70504
$595$	−3871.21	−0.266730
$596$	12556.5	0.862978
$597$	3554.52	0.243680
$598$	−743.630	−0.0508516
$599$	14044.2	0.957978	0.478989	−	0.877821i	$-0.341003\pi$
$599$	14044.2	0.957978	0.478989	+	0.877821i	$0.341003\pi$
$600$	−1307.32	−0.0889521
$601$	−4991.83	−0.338804	−0.169402	−	0.985547i	$-0.554184\pi$
$601$	−4991.83	−0.338804	−0.169402	+	0.985547i	$0.554184\pi$
$602$	10491.6	0.710312
$603$	−3293.75	−0.222441
$604$	−27381.8	−1.84462
$605$	−19830.5	−1.33260
$606$	−25163.0	−1.68676
$607$	−18893.1	−1.26334	−0.631670	−	0.775237i	$-0.717630\pi$
$607$	−18893.1	−1.26334	−0.631670	+	0.775237i	$0.717630\pi$
$608$	7144.04	0.476528
$609$	7506.73	0.499488
$610$	−16588.1	−1.10103
$611$	−3173.22	−0.210106
$612$	−5758.94	−0.380378
$613$	−9303.53	−0.612995	−0.306498	−	0.951871i	$-0.599157\pi$
$613$	−9303.53	−0.612995	−0.306498	+	0.951871i	$0.599157\pi$
$614$	−6957.52	−0.457301
$615$	2741.67	0.179764
$616$	−2166.71	−0.141720
$617$	24943.5	1.62754	0.813768	−	0.581190i	$-0.197413\pi$
$617$	24943.5	1.62754	0.813768	+	0.581190i	$0.197413\pi$
$618$	−23959.8	−1.55956
$619$	−5040.50	−0.327294	−0.163647	−	0.986519i	$-0.552326\pi$
$619$	−5040.50	−0.327294	−0.163647	+	0.986519i	$0.552326\pi$
$620$	21180.8	1.37200
$621$	−3512.91	−0.227002
$622$	33248.4	2.14331
$623$	−8004.90	−0.514783
$624$	−1748.35	−0.112164
$625$	−4143.33	−0.265173
$626$	−13311.4	−0.849892
$627$	−7219.34	−0.459829
$628$	−8870.05	−0.563620
$629$	−5232.31	−0.331678
$630$	−2083.83	−0.131781
$631$	−16445.3	−1.03752	−0.518761	−	0.854919i	$-0.673606\pi$
$631$	−16445.3	−1.03752	−0.518761	+	0.854919i	$0.673606\pi$
$632$	2824.32	0.177762
$633$	13407.7	0.841879
$634$	24209.1	1.51651
$635$	12625.0	0.788986
$636$	16786.4	1.04658
$637$	−381.918	−0.0237553
$638$	64825.1	4.02265
$639$	5814.10	0.359941
$640$	−5047.81	−0.311769
$641$	15725.1	0.968959	0.484480	−	0.874803i	$-0.339009\pi$
$641$	15725.1	0.968959	0.484480	+	0.874803i	$0.339009\pi$
$642$	−20088.3	−1.23492
$643$	−20048.6	−1.22961	−0.614804	−	0.788680i	$-0.710765\pi$
$643$	−20048.6	−1.22961	−0.614804	+	0.788680i	$0.710765\pi$
$644$	−1482.36	−0.0907039
$645$	−12207.8	−0.745243
$646$	−7930.38	−0.482998
$647$	4100.77	0.249177	0.124589	−	0.992208i	$-0.460239\pi$
$647$	4100.77	0.249177	0.124589	+	0.992208i	$0.460239\pi$
$648$	2026.07	0.122826
$649$	39426.2	2.38461
$650$	−1989.96	−0.120081
$651$	8574.59	0.516228
$652$	−9376.62	−0.563216
$653$	−12525.0	−0.750601	−0.375300	−	0.926903i	$-0.622460\pi$
$653$	−12525.0	−0.750601	−0.375300	+	0.926903i	$0.622460\pi$
$654$	−3055.96	−0.182718
$655$	12854.7	0.766830
$656$	−4291.40	−0.255413
$657$	−9400.07	−0.558191
$658$	−11821.7	−0.700392
$659$	2962.28	0.175105	0.0875525	−	0.996160i	$-0.472095\pi$
$659$	2962.28	0.175105	0.0875525	+	0.996160i	$0.472095\pi$
$660$	19228.1	1.13402
$661$	−21794.8	−1.28248	−0.641239	−	0.767341i	$-0.721579\pi$
$661$	−21794.8	−1.28248	−0.641239	+	0.767341i	$0.721579\pi$
$662$	3205.71	0.188207
$663$	2295.22	0.134448
$664$	2572.08	0.150325
$665$	−1535.44	−0.0895366
$666$	−2816.50	−0.163870
$667$	5815.08	0.337573
$668$	−7324.99	−0.424270
$669$	−26575.1	−1.53580
$670$	12080.4	0.696577
$671$	−31029.7	−1.78523
$672$	−7702.90	−0.442181
$673$	−23276.4	−1.33319	−0.666596	−	0.745419i	$-0.732249\pi$
$673$	−23276.4	−1.33319	−0.666596	+	0.745419i	$0.732249\pi$
$674$	11082.3	0.633343
$675$	−9400.55	−0.536040
$676$	−19668.9	−1.11908
$677$	31403.5	1.78277	0.891385	−	0.453247i	$-0.149734\pi$
$677$	31403.5	1.78277	0.891385	+	0.453247i	$0.149734\pi$
$678$	23848.1	1.35086
$679$	−2302.29	−0.130123
$680$	2769.44	0.156181
$681$	−729.274	−0.0410365
$682$	74046.6	4.15746
$683$	−25304.8	−1.41766	−0.708829	−	0.705380i	$-0.750776\pi$
$683$	−25304.8	−1.41766	−0.708829	+	0.705380i	$0.750776\pi$
$684$	−2284.17	−0.127686
$685$	2789.59	0.155598
$686$	−1422.82	−0.0791887
$687$	589.956	0.0327631
$688$	19108.3	1.05886
$689$	3350.24	0.185245
$690$	3223.52	0.177851
$691$	−24270.6	−1.33618	−0.668088	−	0.744082i	$-0.732887\pi$
$691$	−24270.6	−1.33618	−0.668088	+	0.744082i	$0.732887\pi$
$692$	9377.30	0.515132
$693$	−3898.03	−0.213671
$694$	−26943.4	−1.47371
$695$	−1507.99	−0.0823039
$696$	−5370.28	−0.292471
$697$	5633.71	0.306158
$698$	−15937.4	−0.864238
$699$	8062.33	0.436259
$700$	−3966.81	−0.214188
$701$	18969.8	1.02208	0.511041	−	0.859556i	$-0.329260\pi$
$701$	18969.8	1.02208	0.511041	+	0.859556i	$0.329260\pi$
$702$	4938.19	0.265498
$703$	−2075.30	−0.111339
$704$	−40368.6	−2.16115
$705$	13755.4	0.734836
$706$	20439.5	1.08959
$707$	−10011.1	−0.532539
$708$	−24910.3	−1.32230
$709$	−11496.0	−0.608943	−0.304472	−	0.952521i	$-0.598480\pi$
$709$	−11496.0	−0.608943	−0.304472	+	0.952521i	$0.598480\pi$
$710$	−21324.2	−1.12716
$711$	5081.10	0.268011
$712$	5726.66	0.301427
$713$	6642.29	0.348886
$714$	8550.76	0.448185
$715$	3837.56	0.200723
$716$	36378.3	1.89877
$717$	16421.3	0.855320
$718$	5035.10	0.261710
$719$	31091.3	1.61267	0.806336	−	0.591457i	$-0.201447\pi$
$719$	31091.3	1.61267	0.806336	+	0.591457i	$0.201447\pi$
$720$	−3795.25	−0.196445
$721$	−9532.38	−0.492378
$722$	25306.8	1.30446
$723$	11084.3	0.570165
$724$	10620.2	0.545161
$725$	15561.2	0.797141
$726$	43801.7	2.23916
$727$	−23915.7	−1.22006	−0.610032	−	0.792377i	$-0.708843\pi$
$727$	−23915.7	−1.22006	−0.610032	+	0.792377i	$0.708843\pi$
$728$	273.222	0.0139097
$729$	21136.5	1.07385
$730$	34476.4	1.74798
$731$	−25085.1	−1.26923
$732$	19605.2	0.989931
$733$	37215.0	1.87526	0.937632	−	0.347628i	$-0.113013\pi$
$733$	37215.0	1.87526	0.937632	+	0.347628i	$0.113013\pi$
$734$	−34943.6	−1.75721
$735$	1655.55	0.0830831
$736$	−5967.04	−0.298843
$737$	22597.6	1.12944
$738$	3032.57	0.151261
$739$	4855.18	0.241679	0.120840	−	0.992672i	$-0.461441\pi$
$739$	4855.18	0.241679	0.120840	+	0.992672i	$0.461441\pi$
$740$	5527.37	0.274581
$741$	910.356	0.0451319
$742$	12481.2	0.617519
$743$	834.561	0.0412074	0.0206037	−	0.999788i	$-0.493441\pi$
$743$	834.561	0.0412074	0.0206037	+	0.999788i	$0.493441\pi$
$744$	−6134.21	−0.302273
$745$	−10863.3	−0.534230
$746$	−6304.26	−0.309404
$747$	4627.30	0.226645
$748$	39510.7	1.93135
$749$	−7992.09	−0.389886
$750$	26145.3	1.27292
$751$	−15399.9	−0.748268	−0.374134	−	0.927375i	$-0.622060\pi$
$751$	−15399.9	−0.748268	−0.374134	+	0.927375i	$0.622060\pi$
$752$	−21530.7	−1.04407
$753$	−9355.86	−0.452784
$754$	−8174.42	−0.394821
$755$	23689.5	1.14192
$756$	9843.86	0.473569
$757$	1879.55	0.0902423	0.0451212	−	0.998982i	$-0.485633\pi$
$757$	1879.55	0.0902423	0.0451212	+	0.998982i	$0.485633\pi$
$758$	−29873.2	−1.43145
$759$	6029.93	0.288370
$760$	1098.45	0.0524274
$761$	6048.22	0.288105	0.144052	−	0.989570i	$-0.453987\pi$
$761$	6048.22	0.288105	0.144052	+	0.989570i	$0.453987\pi$
$762$	−27886.1	−1.32573
$763$	−1215.81	−0.0576871
$764$	−23636.8	−1.11931
$765$	4982.37	0.235474
$766$	14427.6	0.680537
$767$	−4971.63	−0.234049
$768$	−11011.8	−0.517390
$769$	−19068.0	−0.894160	−0.447080	−	0.894494i	$-0.647536\pi$
$769$	−19068.0	−0.894160	−0.447080	+	0.894494i	$0.647536\pi$
$770$	14296.7	0.669113
$771$	6387.41	0.298362
$772$	7378.10	0.343968
$773$	−13715.0	−0.638154	−0.319077	−	0.947729i	$-0.603373\pi$
$773$	−13715.0	−0.638154	−0.319077	+	0.947729i	$0.603373\pi$
$774$	−13503.1	−0.627078
$775$	17774.8	0.823857
$776$	1647.05	0.0761927
$777$	2237.64	0.103314
$778$	3519.65	0.162192
$779$	2234.50	0.102772
$780$	−2424.65	−0.111303
$781$	−39889.2	−1.82759
$782$	6623.83	0.302900
$783$	−38615.9	−1.76248
$784$	−2591.36	−0.118046
$785$	7673.96	0.348911
$786$	−28393.5	−1.28850
$787$	−35676.1	−1.61590	−0.807952	−	0.589248i	$-0.799424\pi$
$787$	−35676.1	−1.61590	−0.807952	+	0.589248i	$0.799424\pi$
$788$	49221.0	2.22516
$789$	21899.0	0.988120
$790$	−18635.8	−0.839281
$791$	9487.93	0.426488
$792$	2788.63	0.125113
$793$	3912.83	0.175219
$794$	−47102.3	−2.10529
$795$	−14522.8	−0.647888
$796$	−7715.86	−0.343570
$797$	−5428.65	−0.241271	−0.120635	−	0.992697i	$-0.538493\pi$
$797$	−5428.65	−0.241271	−0.120635	+	0.992697i	$0.538493\pi$
$798$	3391.49	0.150448
$799$	28265.2	1.25151
$800$	−15967.8	−0.705685
$801$	10302.6	0.454461
$802$	14893.0	0.655724
$803$	64491.6	2.83420
$804$	−14277.7	−0.626286
$805$	1282.47	0.0561506
$806$	−9337.25	−0.408053
$807$	−3799.70	−0.165744
$808$	7161.87	0.311824
$809$	−13432.1	−0.583743	−0.291871	−	0.956458i	$-0.594278\pi$
$809$	−13432.1	−0.583743	−0.291871	+	0.956458i	$0.594278\pi$
$810$	−13368.6	−0.579909
$811$	45087.0	1.95218	0.976090	−	0.217367i	$-0.0697468\pi$
$811$	45087.0	1.95218	0.976090	+	0.217367i	$0.0697468\pi$
$812$	−16295.0	−0.704240
$813$	−12105.4	−0.522208
$814$	19323.3	0.832043
$815$	8112.22	0.348661
$816$	15573.3	0.668108
$817$	−9949.54	−0.426059
$818$	−25082.5	−1.07211
$819$	491.540	0.0209717
$820$	−5951.41	−0.253454
$821$	−29491.7	−1.25368	−0.626838	−	0.779150i	$-0.715651\pi$
$821$	−29491.7	−1.25368	−0.626838	+	0.779150i	$0.715651\pi$
$822$	−6161.67	−0.261451
$823$	9.51830	0.000403143 0	0.000201572	−	1.00000i	$-0.499936\pi$
$823$	9.51830	0.000403143 0	0.000201572		1.00000i	$0.499936\pi$
$824$	6819.42	0.288308
$825$	16136.1	0.680954
$826$	−18521.6	−0.780205
$827$	−21372.1	−0.898647	−0.449323	−	0.893369i	$-0.648335\pi$
$827$	−21372.1	−0.898647	−0.449323	+	0.893369i	$0.648335\pi$
$828$	1907.85	0.0800753
$829$	28337.6	1.18722	0.593611	−	0.804752i	$-0.297702\pi$
$829$	28337.6	1.18722	0.593611	+	0.804752i	$0.297702\pi$
$830$	−16971.4	−0.709743
$831$	7654.95	0.319551
$832$	5090.46	0.212115
$833$	3401.90	0.141499
$834$	3330.85	0.138295
$835$	6337.25	0.262646
$836$	15671.2	0.648323
$837$	−44109.2	−1.82155
$838$	−66263.6	−2.73155
$839$	−47275.0	−1.94531	−0.972655	−	0.232254i	$-0.925390\pi$
$839$	−47275.0	−1.94531	−0.972655	+	0.232254i	$0.925390\pi$
$840$	−1184.38	−0.0486486
$841$	39533.8	1.62097
$842$	−70695.5	−2.89350
$843$	11467.0	0.468498
$844$	−29104.4	−1.18698
$845$	17016.7	0.692771
$846$	15214.9	0.618321
$847$	17426.4	0.706941
$848$	22731.8	0.920534
$849$	13909.4	0.562271
$850$	17725.4	0.715266
$851$	1733.38	0.0698233
$852$	25202.8	1.01342
$853$	20851.3	0.836970	0.418485	−	0.908224i	$-0.362561\pi$
$853$	20851.3	0.836970	0.418485	+	0.908224i	$0.362561\pi$
$854$	14577.1	0.584096
$855$	1976.16	0.0790448
$856$	5717.50	0.228294
$857$	−15211.2	−0.606306	−0.303153	−	0.952942i	$-0.598039\pi$
$857$	−15211.2	−0.606306	−0.303153	+	0.952942i	$0.598039\pi$
$858$	−8476.44	−0.337274
$859$	21925.0	0.870862	0.435431	−	0.900222i	$-0.356596\pi$
$859$	21925.0	0.870862	0.435431	+	0.900222i	$0.356596\pi$
$860$	26499.7	1.05074
$861$	−2409.30	−0.0953645
$862$	−56069.3	−2.21546
$863$	36509.9	1.44011	0.720053	−	0.693919i	$-0.244117\pi$
$863$	36509.9	1.44011	0.720053	+	0.693919i	$0.244117\pi$
$864$	39625.1	1.56027
$865$	−8112.82	−0.318895
$866$	62236.4	2.44212
$867$	394.226	0.0154425
$868$	−18613.0	−0.727842
$869$	−34860.2	−1.36082
$870$	35434.9	1.38087
$871$	−2849.55	−0.110854
$872$	869.783	0.0337782
$873$	2963.12	0.114876
$874$	2627.22	0.101678
$875$	10401.9	0.401883
$876$	−40747.2	−1.57160
$877$	−11035.5	−0.424904	−0.212452	−	0.977171i	$-0.568145\pi$
$877$	−11035.5	−0.424904	−0.212452	+	0.977171i	$0.568145\pi$
$878$	−17494.0	−0.672430
$879$	−27589.6	−1.05867
$880$	26038.3	0.997445
$881$	23545.6	0.900422	0.450211	−	0.892922i	$-0.351349\pi$
$881$	23545.6	0.900422	0.450211	+	0.892922i	$0.351349\pi$
$882$	1831.21	0.0699095
$883$	−12196.5	−0.464828	−0.232414	−	0.972617i	$-0.574662\pi$
$883$	−12196.5	−0.464828	−0.232414	+	0.972617i	$0.574662\pi$
$884$	−4982.28	−0.189561
$885$	21551.3	0.818574
$886$	10569.1	0.400761
$887$	34421.0	1.30298	0.651491	−	0.758656i	$-0.274144\pi$
$887$	34421.0	1.30298	0.651491	+	0.758656i	$0.274144\pi$
$888$	−1600.80	−0.0604946
$889$	−11094.4	−0.418555
$890$	−37786.4	−1.42315
$891$	−25007.4	−0.940270
$892$	57687.1	2.16537
$893$	11210.9	0.420109
$894$	23995.0	0.897665
$895$	−31472.8	−1.17544
$896$	4435.87	0.165393
$897$	−760.372	−0.0283033
$898$	21004.6	0.780550
$899$	73016.0	2.70881
$900$	5105.41	0.189089
$901$	−29842.1	−1.10342
$902$	−20805.7	−0.768022
$903$	10727.9	0.395350
$904$	−6787.62	−0.249727
$905$	−9188.11	−0.337484
$906$	−52325.6	−1.91877
$907$	870.549	0.0318700	0.0159350	−	0.999873i	$-0.494928\pi$
$907$	870.549	0.0318700	0.0159350	+	0.999873i	$0.494928\pi$
$908$	1583.05	0.0578583
$909$	12884.6	0.470137
$910$	−1802.81	−0.0656731
$911$	48709.9	1.77149	0.885747	−	0.464168i	$-0.153646\pi$
$911$	48709.9	1.77149	0.885747	+	0.464168i	$0.153646\pi$
$912$	6176.87	0.224273
$913$	−31746.8	−1.15078
$914$	−17315.1	−0.626624
$915$	−16961.5	−0.612821
$916$	−1280.63	−0.0461934
$917$	−11296.3	−0.406802
$918$	−43986.6	−1.58145
$919$	36669.8	1.31624	0.658121	−	0.752912i	$-0.271352\pi$
$919$	36669.8	1.31624	0.658121	+	0.752912i	$0.271352\pi$
$920$	−917.475	−0.0328785
$921$	−7114.17	−0.254528
$922$	−36653.4	−1.30924
$923$	5030.01	0.179377
$924$	−16897.1	−0.601594
$925$	4638.54	0.164880
$926$	−40191.5	−1.42632
$927$	12268.5	0.434682
$928$	−65593.3	−2.32026
$929$	−43182.3	−1.52504	−0.762521	−	0.646963i	$-0.776039\pi$
$929$	−43182.3	−1.52504	−0.762521	+	0.646963i	$0.776039\pi$
$930$	40475.6	1.42715
$931$	1349.30	0.0474990
$932$	−17501.1	−0.615092
$933$	33997.0	1.19294
$934$	4402.95	0.154249
$935$	−34182.8	−1.19561
$936$	−351.645	−0.0122798
$937$	21453.6	0.747980	0.373990	−	0.927433i	$-0.377989\pi$
$937$	21453.6	0.747980	0.373990	+	0.927433i	$0.377989\pi$
$938$	−10615.9	−0.369532
$939$	−13611.1	−0.473038
$940$	−29859.2	−1.03606
$941$	394.938	0.0136818	0.00684092	−	0.999977i	$-0.497822\pi$
$941$	394.938	0.0136818	0.00684092	+	0.999977i	$0.497822\pi$
$942$	−16950.3	−0.586275
$943$	−1866.36	−0.0644508
$944$	−33733.1	−1.16305
$945$	−8516.46	−0.293165
$946$	92641.4	3.18397
$947$	−11802.4	−0.404991	−0.202496	−	0.979283i	$-0.564905\pi$
$947$	−11802.4	−0.404991	−0.202496	+	0.979283i	$0.564905\pi$
$948$	22025.4	0.754590
$949$	−8132.37	−0.278175
$950$	7030.44	0.240103
$951$	24754.2	0.844070
$952$	−2433.70	−0.0828538
$953$	57313.4	1.94813	0.974063	−	0.226279i	$-0.0726560\pi$
$953$	57313.4	1.94813	0.974063	+	0.226279i	$0.0726560\pi$
$954$	−16063.7	−0.545159
$955$	20449.5	0.692911
$956$	−35646.0	−1.20594
$957$	66284.6	2.23895
$958$	12620.7	0.425633
$959$	−2451.41	−0.0825445
$960$	−22066.4	−0.741864
$961$	53611.7	1.79960
$962$	−2436.67	−0.0816645
$963$	10286.1	0.344199
$964$	−24060.9	−0.803889
$965$	−6383.20	−0.212935
$966$	−2832.74	−0.0943497
$967$	−21392.4	−0.711409	−0.355704	−	0.934599i	$-0.615759\pi$
$967$	−21392.4	−0.711409	−0.355704	+	0.934599i	$0.615759\pi$
$968$	−12466.8	−0.413944
$969$	−8108.93	−0.268830
$970$	−10867.8	−0.359735
$971$	−12646.6	−0.417968	−0.208984	−	0.977919i	$-0.567016\pi$
$971$	−12646.6	−0.417968	−0.208984	+	0.977919i	$0.567016\pi$
$972$	−22169.0	−0.731553
$973$	1325.17	0.0436620
$974$	11617.3	0.382178
$975$	−2034.76	−0.0668353
$976$	26549.0	0.870711
$977$	41893.1	1.37183	0.685915	−	0.727682i	$-0.259402\pi$
$977$	41893.1	1.37183	0.685915	+	0.727682i	$0.259402\pi$
$978$	−17918.3	−0.585854
$979$	−70683.4	−2.30751
$980$	−3593.75	−0.117141
$981$	1564.79	0.0509274
$982$	−66601.3	−2.16429
$983$	−25459.3	−0.826070	−0.413035	−	0.910715i	$-0.635531\pi$
$983$	−25459.3	−0.826070	−0.413035	+	0.910715i	$0.635531\pi$
$984$	1723.60	0.0558399
$985$	−42583.8	−1.37749
$986$	72813.1	2.35177
$987$	−12087.9	−0.389829
$988$	−1976.13	−0.0636326
$989$	8310.33	0.267192
$990$	−18400.3	−0.590707
$991$	41103.7	1.31756	0.658780	−	0.752336i	$-0.271073\pi$
$991$	41103.7	1.31756	0.658780	+	0.752336i	$0.271073\pi$
$992$	−74924.1	−2.39803
$993$	3277.88	0.104754
$994$	18739.1	0.597956
$995$	6675.41	0.212688
$996$	20058.3	0.638124
$997$	2441.28	0.0775489	0.0387744	−	0.999248i	$-0.487655\pi$
$997$	2441.28	0.0775489	0.0387744	+	0.999248i	$0.487655\pi$
$998$	44764.0	1.41982
$999$	−11510.8	−0.364550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.4.a.a.1.1	✓	5
3.2	odd	2		1449.4.a.e.1.5		5
7.6	odd	2		1127.4.a.d.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.4.a.a.1.1	✓	5	1.1	even	1	trivial
1127.4.a.d.1.1		5	7.6	odd	2
1449.4.a.e.1.5		5	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q-4.14816 q^{2} -4.24155 q^{3} +9.20723 q^{4} -7.96567 q^{5} +17.5946 q^{6} +7.00000 q^{7} -5.00776 q^{8} -9.00922 q^{9} +33.0429 q^{10} +61.8101 q^{11} -39.0529 q^{12} -7.79423 q^{13} -29.0371 q^{14} +33.7868 q^{15} -52.8848 q^{16} +69.4266 q^{17} +37.3717 q^{18} +27.5368 q^{19} -73.3417 q^{20} -29.6909 q^{21} -256.398 q^{22} -23.0000 q^{23} +21.2407 q^{24} -61.5481 q^{25} +32.3317 q^{26} +152.735 q^{27} +64.4506 q^{28} -252.830 q^{29} -140.153 q^{30} -288.795 q^{31} +259.437 q^{32} -262.171 q^{33} -287.993 q^{34} -55.7597 q^{35} -82.9500 q^{36} -75.3646 q^{37} -114.227 q^{38} +33.0597 q^{39} +39.8902 q^{40} +81.1462 q^{41} +123.162 q^{42} -361.319 q^{43} +569.100 q^{44} +71.7645 q^{45} +95.4077 q^{46} +407.124 q^{47} +224.314 q^{48} +49.0000 q^{49} +255.311 q^{50} -294.477 q^{51} -71.7633 q^{52} -429.836 q^{53} -633.569 q^{54} -492.359 q^{55} -35.0543 q^{56} -116.799 q^{57} +1048.78 q^{58} +637.860 q^{59} +311.083 q^{60} -502.016 q^{61} +1197.97 q^{62} -63.0646 q^{63} -653.106 q^{64} +62.0863 q^{65} +1087.53 q^{66} +365.598 q^{67} +639.227 q^{68} +97.5557 q^{69} +231.300 q^{70} -645.350 q^{71} +45.1161 q^{72} +1043.38 q^{73} +312.624 q^{74} +261.059 q^{75} +253.537 q^{76} +432.671 q^{77} -137.137 q^{78} -563.988 q^{79} +421.263 q^{80} -404.585 q^{81} -336.607 q^{82} -513.618 q^{83} -273.371 q^{84} -553.030 q^{85} +1498.81 q^{86} +1072.39 q^{87} -309.530 q^{88} -1143.56 q^{89} -297.691 q^{90} -54.5596 q^{91} -211.766 q^{92} +1224.94 q^{93} -1688.82 q^{94} -219.349 q^{95} -1100.41 q^{96} -328.899 q^{97} -203.260 q^{98} -556.861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - 4 q^{2} - 11 q^{3} - 4 q^{5} + 35 q^{7} + 18 q^{8} + 14 q^{9} + 26 q^{10} - 36 q^{11} - 28 q^{12} - 69 q^{13} - 28 q^{14} - 88 q^{15} - 124 q^{16} - 42 q^{17} - 94 q^{18} - 140 q^{19} - 168 q^{20}+ \cdots - 990 q^{99}+O(q^{100}) \) 5 * q - 4 * q^2 - 11 * q^3 - 4 * q^5 + 35 * q^7 + 18 * q^8 + 14 * q^9 + 26 * q^10 - 36 * q^11 - 28 * q^12 - 69 * q^13 - 28 * q^14 - 88 * q^15 - 124 * q^16 - 42 * q^17 - 94 * q^18 - 140 * q^19 - 168 * q^20 - 77 * q^21 - 346 * q^22 - 115 * q^23 + 18 * q^24 - 357 * q^25 + 68 * q^26 - 35 * q^27 - 383 * q^29 + 184 * q^30 - 319 * q^31 - 50 * q^32 - 108 * q^33 - 376 * q^34 - 28 * q^35 - 180 * q^36 - 154 * q^37 + 8 * q^38 - 235 * q^39 + 90 * q^40 + 277 * q^41 - 718 * q^43 + 422 * q^44 + 470 * q^45 + 92 * q^46 + 53 * q^47 + 248 * q^48 + 245 * q^49 - 60 * q^50 + 232 * q^51 + 178 * q^52 + 450 * q^53 + 468 * q^54 - 206 * q^55 + 126 * q^56 - 560 * q^57 + 1738 * q^58 + 936 * q^59 + 944 * q^60 - 522 * q^61 + 788 * q^62 + 98 * q^63 - 252 * q^64 + 264 * q^65 + 2310 * q^66 - 810 * q^67 + 1326 * q^68 + 253 * q^69 + 182 * q^70 - 1373 * q^71 + 1590 * q^72 + 459 * q^73 + 330 * q^74 + 333 * q^75 + 1168 * q^76 - 252 * q^77 + 462 * q^78 - 728 * q^79 + 1368 * q^80 - 895 * q^81 + 1034 * q^82 - 500 * q^83 - 196 * q^84 - 1432 * q^85 + 3138 * q^86 + 1803 * q^87 - 722 * q^88 - 586 * q^89 - 1024 * q^90 - 483 * q^91 + 2149 * q^93 + 316 * q^94 - 188 * q^95 + 1210 * q^96 - 2150 * q^97 - 196 * q^98 - 990 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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