LMFDB - Embedded newform 209.4.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [209,4,Mod(1,209)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(209, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("209.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 209 = 11 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	209.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$12.3313991912$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 2 x^{12} - 91 x^{11} + 176 x^{10} + 3117 x^{9} - 5786 x^{8} - 49725 x^{7} + 87196 x^{6} + \cdots - 86016 $ x^13 - 2x^12 - 91x^11 + 176x^10 + 3117x^9 - 5786x^8 - 49725x^7 + 87196x^6 + 366602x^5 - 590896x^4 - 1017888x^3 + 1444096x^2 + 115200x - 86016
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$1.33472$ of defining polynomial
Character	$\chi$	$=$	209.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.33472 q^{2} +8.27114 q^{3} -6.21852 q^{4} +12.3033 q^{5} -11.0397 q^{6} +31.4819 q^{7} +18.9777 q^{8} +41.4117 q^{9} -16.4215 q^{10} -11.0000 q^{11} -51.4342 q^{12} -82.5704 q^{13} -42.0195 q^{14} +101.763 q^{15} +24.4182 q^{16} +56.4729 q^{17} -55.2730 q^{18} -19.0000 q^{19} -76.5086 q^{20} +260.391 q^{21} +14.6819 q^{22} +4.15831 q^{23} +156.968 q^{24} +26.3720 q^{25} +110.208 q^{26} +119.201 q^{27} -195.771 q^{28} -22.9131 q^{29} -135.825 q^{30} +214.217 q^{31} -184.413 q^{32} -90.9825 q^{33} -75.3756 q^{34} +387.332 q^{35} -257.519 q^{36} +15.8859 q^{37} +25.3597 q^{38} -682.951 q^{39} +233.490 q^{40} +238.905 q^{41} -347.549 q^{42} -232.734 q^{43} +68.4037 q^{44} +509.502 q^{45} -5.55018 q^{46} -217.809 q^{47} +201.966 q^{48} +648.109 q^{49} -35.1993 q^{50} +467.095 q^{51} +513.466 q^{52} +675.520 q^{53} -159.100 q^{54} -135.337 q^{55} +597.455 q^{56} -157.152 q^{57} +30.5826 q^{58} +45.3345 q^{59} -632.813 q^{60} -811.571 q^{61} -285.920 q^{62} +1303.72 q^{63} +50.7947 q^{64} -1015.89 q^{65} +121.436 q^{66} -26.5741 q^{67} -351.178 q^{68} +34.3940 q^{69} -516.980 q^{70} -642.839 q^{71} +785.900 q^{72} -943.969 q^{73} -21.2033 q^{74} +218.127 q^{75} +118.152 q^{76} -346.301 q^{77} +911.548 q^{78} +1212.88 q^{79} +300.425 q^{80} -132.188 q^{81} -318.871 q^{82} -307.975 q^{83} -1619.25 q^{84} +694.805 q^{85} +310.635 q^{86} -189.517 q^{87} -208.755 q^{88} +138.983 q^{89} -680.042 q^{90} -2599.47 q^{91} -25.8586 q^{92} +1771.82 q^{93} +290.714 q^{94} -233.763 q^{95} -1525.31 q^{96} +1530.30 q^{97} -865.044 q^{98} -455.528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 2 q^{2} + 11 q^{3} + 82 q^{4} + 8 q^{5} + 13 q^{6} + 39 q^{7} + 6 q^{8} + 156 q^{9} + 124 q^{10} - 143 q^{11} + 247 q^{12} - 23 q^{13} + 47 q^{14} + 278 q^{15} + 526 q^{16} + 73 q^{17} - 165 q^{18}+ \cdots - 1716 q^{99}+O(q^{100}) $ 13 * q - 2 * q^2 + 11 * q^3 + 82 * q^4 + 8 * q^5 + 13 * q^6 + 39 * q^7 + 6 * q^8 + 156 * q^9 + 124 * q^10 - 143 * q^11 + 247 * q^12 - 23 * q^13 + 47 * q^14 + 278 * q^15 + 526 * q^16 + 73 * q^17 - 165 * q^18 - 247 * q^19 + 142 * q^20 + 77 * q^21 + 22 * q^22 + 185 * q^23 - 251 * q^24 + 641 * q^25 - 47 * q^26 + 1109 * q^27 + 289 * q^28 - 41 * q^29 + 520 * q^30 + 930 * q^31 - 194 * q^32 - 121 * q^33 - 333 * q^34 + 122 * q^35 + 1469 * q^36 + 1094 * q^37 + 38 * q^38 + 543 * q^39 + 2084 * q^40 - 766 * q^41 - 1277 * q^42 + 1024 * q^43 - 902 * q^44 - 348 * q^45 + 1927 * q^46 + 516 * q^47 + 3067 * q^48 + 1966 * q^49 + 3066 * q^50 + 1975 * q^51 - 553 * q^52 + 1017 * q^53 - 2231 * q^54 - 88 * q^55 - 1793 * q^56 - 209 * q^57 - 159 * q^58 + 15 * q^59 - 3158 * q^60 - 862 * q^61 - 3298 * q^62 + 552 * q^63 + 3694 * q^64 - 1640 * q^65 - 143 * q^66 + 621 * q^67 - 1533 * q^68 + 335 * q^69 - 3250 * q^70 + 632 * q^71 - 8349 * q^72 - 629 * q^73 - 4086 * q^74 - 2759 * q^75 - 1558 * q^76 - 429 * q^77 - 5813 * q^78 + 2444 * q^79 + 2810 * q^80 + 2265 * q^81 - 846 * q^82 + 732 * q^83 - 761 * q^84 - 3786 * q^85 - 4664 * q^86 - 1185 * q^87 - 66 * q^88 + 3178 * q^89 - 6174 * q^90 + 1349 * q^91 - 1677 * q^92 + 1328 * q^93 + 3156 * q^94 - 152 * q^95 - 13811 * q^96 + 1410 * q^97 - 6273 * q^98 - 1716 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$	−1.33472	−0.471895	−0.235947	−	0.971766i	$-0.575819\pi$
$2$	−1.33472	−0.471895	−0.235947	+	0.971766i	$0.575819\pi$
$3$	8.27114	1.59178	0.795890	−	0.605441i	$-0.207003\pi$
$3$	8.27114	1.59178	0.795890	+	0.605441i	$0.207003\pi$
$4$	−6.21852	−0.777315
$5$	12.3033	1.10044	0.550222	−	0.835019i	$-0.314543\pi$
$5$	12.3033	1.10044	0.550222	+	0.835019i	$0.314543\pi$
$6$	−11.0397	−0.751153
$7$	31.4819	1.69986	0.849931	−	0.526894i	$-0.176644\pi$
$7$	31.4819	1.69986	0.849931	+	0.526894i	$0.176644\pi$
$8$	18.9777	0.838706
$9$	41.4117	1.53377
$10$	−16.4215	−0.519294
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−51.4342	−1.23732
$13$	−82.5704	−1.76161	−0.880804	−	0.473481i	$-0.842997\pi$
$13$	−82.5704	−1.76161	−0.880804	+	0.473481i	$0.842997\pi$
$14$	−42.0195	−0.802156
$15$	101.763	1.75166
$16$	24.4182	0.381534
$17$	56.4729	0.805688	0.402844	−	0.915269i	$-0.368022\pi$
$17$	56.4729	0.805688	0.402844	+	0.915269i	$0.368022\pi$
$18$	−55.2730	−0.723776
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−76.5086	−0.855392
$21$	260.391	2.70581
$22$	14.6819	0.142282
$23$	4.15831	0.0376986	0.0188493	−	0.999822i	$-0.494000\pi$
$23$	4.15831	0.0376986	0.0188493	+	0.999822i	$0.494000\pi$
$24$	156.968	1.33504
$25$	26.3720	0.210976
$26$	110.208	0.831293
$27$	119.201	0.849638
$28$	−195.771	−1.32133
$29$	−22.9131	−0.146719	−0.0733596	−	0.997306i	$-0.523372\pi$
$29$	−22.9131	−0.146719	−0.0733596	+	0.997306i	$0.523372\pi$
$30$	−135.825	−0.826602
$31$	214.217	1.24111	0.620557	−	0.784161i	$-0.286906\pi$
$31$	214.217	1.24111	0.620557	+	0.784161i	$0.286906\pi$
$32$	−184.413	−1.01875
$33$	−90.9825	−0.479940
$34$	−75.3756	−0.380200
$35$	387.332	1.87060
$36$	−257.519	−1.19222
$37$	15.8859	0.0705846	0.0352923	−	0.999377i	$-0.488764\pi$
$37$	15.8859	0.0705846	0.0352923	+	0.999377i	$0.488764\pi$
$38$	25.3597	0.108260
$39$	−682.951	−2.80409
$40$	233.490	0.922949
$41$	238.905	0.910017	0.455008	−	0.890487i	$-0.349636\pi$
$41$	238.905	0.910017	0.455008	+	0.890487i	$0.349636\pi$
$42$	−347.549	−1.27686
$43$	−232.734	−0.825386	−0.412693	−	0.910870i	$-0.635412\pi$
$43$	−232.734	−0.825386	−0.412693	+	0.910870i	$0.635412\pi$
$44$	68.4037	0.234369
$45$	509.502	1.68782
$46$	−5.55018	−0.0177898
$47$	−217.809	−0.675973	−0.337986	−	0.941151i	$-0.609746\pi$
$47$	−217.809	−0.675973	−0.337986	+	0.941151i	$0.609746\pi$
$48$	201.966	0.607319
$49$	648.109	1.88953
$50$	−35.1993	−0.0995586
$51$	467.095	1.28248
$52$	513.466	1.36932
$53$	675.520	1.75075	0.875375	−	0.483445i	$-0.160615\pi$
$53$	675.520	1.75075	0.875375	+	0.483445i	$0.160615\pi$
$54$	−159.100	−0.400940
$55$	−135.337	−0.331796
$56$	597.455	1.42568
$57$	−157.152	−0.365180
$58$	30.5826	0.0692361
$59$	45.3345	0.100035	0.0500173	−	0.998748i	$-0.484072\pi$
$59$	45.3345	0.100035	0.0500173	+	0.998748i	$0.484072\pi$
$60$	−632.813	−1.36160
$61$	−811.571	−1.70346	−0.851730	−	0.523982i	$-0.824446\pi$
$61$	−811.571	−1.70346	−0.851730	+	0.523982i	$0.824446\pi$
$62$	−285.920	−0.585675
$63$	1303.72	2.60719
$64$	50.7947	0.0992084
$65$	−1015.89	−1.93855
$66$	121.436	0.226481
$67$	−26.5741	−0.0484559	−0.0242280	−	0.999706i	$-0.507713\pi$
$67$	−26.5741	−0.0484559	−0.0242280	+	0.999706i	$0.507713\pi$
$68$	−351.178	−0.626274
$69$	34.3940	0.0600079
$70$	−516.980	−0.882727
$71$	−642.839	−1.07452	−0.537261	−	0.843416i	$-0.680541\pi$
$71$	−642.839	−1.07452	−0.537261	+	0.843416i	$0.680541\pi$
$72$	785.900	1.28638
$73$	−943.969	−1.51347	−0.756735	−	0.653722i	$-0.773206\pi$
$73$	−943.969	−1.51347	−0.756735	+	0.653722i	$0.773206\pi$
$74$	−21.2033	−0.0333085
$75$	218.127	0.335828
$76$	118.152	0.178328
$77$	−346.301	−0.512528
$78$	911.548	1.32324
$79$	1212.88	1.72733	0.863666	−	0.504065i	$-0.168163\pi$
$79$	1212.88	1.72733	0.863666	+	0.504065i	$0.168163\pi$
$80$	300.425	0.419857
$81$	−132.188	−0.181328
$82$	−318.871	−0.429432
$83$	−307.975	−0.407285	−0.203643	−	0.979045i	$-0.565278\pi$
$83$	−307.975	−0.407285	−0.203643	+	0.979045i	$0.565278\pi$
$84$	−1619.25	−2.10327
$85$	694.805	0.886614
$86$	310.635	0.389495
$87$	−189.517	−0.233545
$88$	−208.755	−0.252879
$89$	138.983	0.165530	0.0827649	−	0.996569i	$-0.473625\pi$
$89$	138.983	0.165530	0.0827649	+	0.996569i	$0.473625\pi$
$90$	−680.042	−0.796475
$91$	−2599.47	−2.99449
$92$	−25.8586	−0.0293037
$93$	1771.82	1.97558
$94$	290.714	0.318988
$95$	−233.763	−0.252459
$96$	−1525.31	−1.62163
$97$	1530.30	1.60184	0.800922	−	0.598769i	$-0.204343\pi$
$97$	1530.30	1.60184	0.800922	+	0.598769i	$0.204343\pi$
$98$	−865.044	−0.891660
$99$	−455.528	−0.462448
$100$	−163.995	−0.163995
$101$	−1380.49	−1.36004	−0.680021	−	0.733192i	$-0.738029\pi$
$101$	−1380.49	−1.36004	−0.680021	+	0.733192i	$0.738029\pi$
$102$	−623.441	−0.605195
$103$	−1929.11	−1.84545	−0.922724	−	0.385462i	$-0.874042\pi$
$103$	−1929.11	−1.84545	−0.922724	+	0.385462i	$0.874042\pi$
$104$	−1567.00	−1.47747
$105$	3203.68	2.97759
$106$	−901.630	−0.826170
$107$	−1258.37	−1.13693	−0.568465	−	0.822707i	$-0.692463\pi$
$107$	−1258.37	−1.13693	−0.568465	+	0.822707i	$0.692463\pi$
$108$	−741.254	−0.660437
$109$	−271.913	−0.238940	−0.119470	−	0.992838i	$-0.538120\pi$
$109$	−271.913	−0.238940	−0.119470	+	0.992838i	$0.538120\pi$
$110$	180.637	0.156573
$111$	131.395	0.112355
$112$	768.731	0.648556
$113$	917.608	0.763905	0.381953	−	0.924182i	$-0.375252\pi$
$113$	917.608	0.763905	0.381953	+	0.924182i	$0.375252\pi$
$114$	209.753	0.172326
$115$	51.1611	0.0414852
$116$	142.486	0.114047
$117$	−3419.38	−2.70189
$118$	−60.5088	−0.0472059
$119$	1777.87	1.36956
$120$	1931.22	1.46913
$121$	121.000	0.0909091
$122$	1083.22	0.803854
$123$	1976.01	1.44855
$124$	−1332.11	−0.964737
$125$	−1213.45	−0.868276
$126$	−1740.10	−1.23032
$127$	219.902	0.153647	0.0768234	−	0.997045i	$-0.475522\pi$
$127$	219.902	0.153647	0.0768234	+	0.997045i	$0.475522\pi$
$128$	1407.51	0.971934
$129$	−1924.97	−1.31383
$130$	1355.93	0.914792
$131$	−2607.35	−1.73897	−0.869484	−	0.493961i	$-0.835548\pi$
$131$	−2607.35	−1.73897	−0.869484	+	0.493961i	$0.835548\pi$
$132$	565.777	0.373065
$133$	−598.156	−0.389975
$134$	35.4690	0.0228661
$135$	1466.57	0.934979
$136$	1071.73	0.675735
$137$	819.736	0.511203	0.255601	−	0.966782i	$-0.417727\pi$
$137$	819.736	0.511203	0.255601	+	0.966782i	$0.417727\pi$
$138$	−45.9063	−0.0283174
$139$	−500.781	−0.305581	−0.152790	−	0.988259i	$-0.548826\pi$
$139$	−500.781	−0.305581	−0.152790	+	0.988259i	$0.548826\pi$
$140$	−2408.63	−1.45405
$141$	−1801.53	−1.07600
$142$	858.011	0.507061
$143$	908.274	0.531145
$144$	1011.20	0.585184
$145$	−281.908	−0.161456
$146$	1259.93	0.714198
$147$	5360.60	3.00772
$148$	−98.7870	−0.0548665
$149$	−2290.13	−1.25916	−0.629581	−	0.776935i	$-0.716773\pi$
$149$	−2290.13	−1.25916	−0.629581	+	0.776935i	$0.716773\pi$
$150$	−291.138	−0.158475
$151$	167.288	0.0901570	0.0450785	−	0.998983i	$-0.485646\pi$
$151$	167.288	0.0901570	0.0450785	+	0.998983i	$0.485646\pi$
$152$	−360.577	−0.192412
$153$	2338.64	1.23574
$154$	462.215	0.241859
$155$	2635.59	1.36578
$156$	4246.94	2.17966
$157$	2415.73	1.22800	0.614001	−	0.789305i	$-0.289559\pi$
$157$	2415.73	1.22800	0.614001	+	0.789305i	$0.289559\pi$
$158$	−1618.85	−0.815119
$159$	5587.31	2.78681
$160$	−2268.90	−1.12108
$161$	130.912	0.0640824
$162$	176.434	0.0855677
$163$	1949.28	0.936682	0.468341	−	0.883548i	$-0.344852\pi$
$163$	1949.28	0.936682	0.468341	+	0.883548i	$0.344852\pi$
$164$	−1485.64	−0.707370
$165$	−1119.39	−0.528147
$166$	411.061	0.192196
$167$	−2313.86	−1.07217	−0.536084	−	0.844165i	$-0.680097\pi$
$167$	−2313.86	−1.07217	−0.536084	+	0.844165i	$0.680097\pi$
$168$	4941.63	2.26938
$169$	4620.87	2.10326
$170$	−927.371	−0.418389
$171$	−786.822	−0.351870
$172$	1447.26	0.641585
$173$	14.6757	0.00644957	0.00322478	−	0.999995i	$-0.498974\pi$
$173$	14.6757	0.00644957	0.00322478	+	0.999995i	$0.498974\pi$
$174$	252.953	0.110209
$175$	830.241	0.358630
$176$	−268.600	−0.115037
$177$	374.968	0.159233
$178$	−185.503	−0.0781127
$179$	−2099.68	−0.876744	−0.438372	−	0.898794i	$-0.644445\pi$
$179$	−2099.68	−0.876744	−0.438372	+	0.898794i	$0.644445\pi$
$180$	−3168.35	−1.31197
$181$	−1770.79	−0.727194	−0.363597	−	0.931556i	$-0.618451\pi$
$181$	−1770.79	−0.727194	−0.363597	+	0.931556i	$0.618451\pi$
$182$	3469.57	1.41308
$183$	−6712.61	−2.71153
$184$	78.9154	0.0316180
$185$	195.450	0.0776744
$186$	−2364.88	−0.932267
$187$	−621.202	−0.242924
$188$	1354.45	0.525444
$189$	3752.67	1.44427
$190$	312.009	0.119134
$191$	508.629	0.192686	0.0963432	−	0.995348i	$-0.469285\pi$
$191$	508.629	0.192686	0.0963432	+	0.995348i	$0.469285\pi$
$192$	420.130	0.157918
$193$	2185.03	0.814932	0.407466	−	0.913220i	$-0.366413\pi$
$193$	2185.03	0.814932	0.407466	+	0.913220i	$0.366413\pi$
$194$	−2042.53	−0.755902
$195$	−8402.57	−3.08575
$196$	−4030.28	−1.46876
$197$	538.713	0.194831	0.0974155	−	0.995244i	$-0.468942\pi$
$197$	538.713	0.194831	0.0974155	+	0.995244i	$0.468942\pi$
$198$	608.003	0.218227
$199$	1263.97	0.450253	0.225127	−	0.974330i	$-0.427720\pi$
$199$	1263.97	0.450253	0.225127	+	0.974330i	$0.427720\pi$
$200$	500.482	0.176947
$201$	−219.798	−0.0771312
$202$	1842.57	0.641797
$203$	−721.348	−0.249402
$204$	−2904.64	−0.996890
$205$	2939.33	1.00142
$206$	2574.82	0.870857
$207$	172.203	0.0578208
$208$	−2016.22	−0.672114
$209$	209.000	0.0691714
$210$	−4276.01	−1.40511
$211$	4820.83	1.57289	0.786445	−	0.617660i	$-0.211919\pi$
$211$	4820.83	1.57289	0.786445	+	0.617660i	$0.211919\pi$
$212$	−4200.73	−1.36088
$213$	−5317.01	−1.71040
$214$	1679.58	0.536511
$215$	−2863.40	−0.908291
$216$	2262.17	0.712597
$217$	6743.96	2.10972
$218$	362.927	0.112755
$219$	−7807.70	−2.40911
$220$	841.594	0.257910
$221$	−4662.99	−1.41931
$222$	−175.375	−0.0530199
$223$	2460.87	0.738977	0.369489	−	0.929235i	$-0.379533\pi$
$223$	2460.87	0.738977	0.369489	+	0.929235i	$0.379533\pi$
$224$	−5805.68	−1.73173
$225$	1092.11	0.323588
$226$	−1224.75	−0.360483
$227$	865.102	0.252946	0.126473	−	0.991970i	$-0.459634\pi$
$227$	865.102	0.252946	0.126473	+	0.991970i	$0.459634\pi$
$228$	977.251	0.283860
$229$	1563.38	0.451141	0.225571	−	0.974227i	$-0.427575\pi$
$229$	1563.38	0.451141	0.225571	+	0.974227i	$0.427575\pi$
$230$	−68.2858	−0.0195766
$231$	−2864.30	−0.815832
$232$	−434.839	−0.123054
$233$	−6475.61	−1.82074	−0.910368	−	0.413800i	$-0.864201\pi$
$233$	−6475.61	−1.82074	−0.910368	+	0.413800i	$0.864201\pi$
$234$	4563.91	1.27501
$235$	−2679.78	−0.743870
$236$	−281.913	−0.0777585
$237$	10031.9	2.74953
$238$	−2372.96	−0.646288
$239$	1253.64	0.339294	0.169647	−	0.985505i	$-0.445737\pi$
$239$	1253.64	0.339294	0.169647	+	0.985505i	$0.445737\pi$
$240$	2484.86	0.668320
$241$	6223.27	1.66339	0.831693	−	0.555235i	$-0.187372\pi$
$241$	6223.27	1.66339	0.831693	+	0.555235i	$0.187372\pi$
$242$	−161.501	−0.0428995
$243$	−4311.77	−1.13827
$244$	5046.77	1.32412
$245$	7973.90	2.07932
$246$	−2637.43	−0.683562
$247$	1568.84	0.404141
$248$	4065.36	1.04093
$249$	−2547.31	−0.648309
$250$	1619.62	0.409735
$251$	−5884.69	−1.47983	−0.739917	−	0.672698i	$-0.765135\pi$
$251$	−5884.69	−1.47983	−0.739917	+	0.672698i	$0.765135\pi$
$252$	−8107.20	−2.02661
$253$	−45.7414	−0.0113666
$254$	−293.507	−0.0725051
$255$	5746.83	1.41130
$256$	−2284.99	−0.557859
$257$	2168.60	0.526357	0.263179	−	0.964747i	$-0.415229\pi$
$257$	2168.60	0.526357	0.263179	+	0.964747i	$0.415229\pi$
$258$	2569.30	0.619991
$259$	500.119	0.119984
$260$	6317.34	1.50686
$261$	−948.870	−0.225033
$262$	3480.08	0.820610
$263$	2145.02	0.502918	0.251459	−	0.967868i	$-0.419090\pi$
$263$	2145.02	0.502918	0.251459	+	0.967868i	$0.419090\pi$
$264$	−1726.64	−0.402528
$265$	8311.14	1.92660
$266$	798.371	0.184027
$267$	1149.55	0.263487
$268$	165.252	0.0376655
$269$	−1673.73	−0.379366	−0.189683	−	0.981845i	$-0.560746\pi$
$269$	−1673.73	−0.379366	−0.189683	+	0.981845i	$0.560746\pi$
$270$	−1957.46	−0.441212
$271$	3402.76	0.762742	0.381371	−	0.924422i	$-0.375452\pi$
$271$	3402.76	0.762742	0.381371	+	0.924422i	$0.375452\pi$
$272$	1378.97	0.307398
$273$	−21500.6	−4.76657
$274$	−1094.12	−0.241234
$275$	−290.092	−0.0636117
$276$	−213.880	−0.0466451
$277$	−2128.78	−0.461756	−0.230878	−	0.972983i	$-0.574160\pi$
$277$	−2128.78	−0.461756	−0.230878	+	0.972983i	$0.574160\pi$
$278$	668.403	0.144202
$279$	8871.09	1.90358
$280$	7350.69	1.56889
$281$	−544.611	−0.115618	−0.0578092	−	0.998328i	$-0.518412\pi$
$281$	−544.611	−0.115618	−0.0578092	+	0.998328i	$0.518412\pi$
$282$	2404.54	0.507759
$283$	−3474.36	−0.729786	−0.364893	−	0.931050i	$-0.618894\pi$
$283$	−3474.36	−0.729786	−0.364893	+	0.931050i	$0.618894\pi$
$284$	3997.51	0.835242
$285$	−1933.49	−0.401860
$286$	−1212.29	−0.250644
$287$	7521.18	1.54690
$288$	−7636.87	−1.56252
$289$	−1723.81	−0.350867
$290$	376.268	0.0761904
$291$	12657.4	2.54978
$292$	5870.09	1.17644
$293$	2397.73	0.478079	0.239039	−	0.971010i	$-0.423168\pi$
$293$	2397.73	0.478079	0.239039	+	0.971010i	$0.423168\pi$
$294$	−7154.90	−1.41933
$295$	557.765	0.110083
$296$	301.479	0.0591997
$297$	−1311.21	−0.256176
$298$	3056.69	0.594192
$299$	−343.353	−0.0664102
$300$	−1356.43	−0.261044
$301$	−7326.90	−1.40304
$302$	−223.283	−0.0425446
$303$	−11418.3	−2.16489
$304$	−463.946	−0.0875300
$305$	−9985.03	−1.87456
$306$	−3121.43	−0.583138
$307$	−7546.79	−1.40299	−0.701495	−	0.712675i	$-0.747484\pi$
$307$	−7546.79	−1.40299	−0.701495	+	0.712675i	$0.747484\pi$
$308$	2153.48	0.398396
$309$	−15955.9	−2.93755
$310$	−3517.77	−0.644503
$311$	−2174.40	−0.396459	−0.198229	−	0.980156i	$-0.563519\pi$
$311$	−2174.40	−0.396459	−0.198229	+	0.980156i	$0.563519\pi$
$312$	−12960.9	−2.35181
$313$	753.096	0.135998	0.0679992	−	0.997685i	$-0.478338\pi$
$313$	753.096	0.135998	0.0679992	+	0.997685i	$0.478338\pi$
$314$	−3224.32	−0.579488
$315$	16040.1	2.86907
$316$	−7542.30	−1.34268
$317$	9331.70	1.65338	0.826688	−	0.562660i	$-0.190222\pi$
$317$	9331.70	1.65338	0.826688	+	0.562660i	$0.190222\pi$
$318$	−7457.50	−1.31508
$319$	252.044	0.0442375
$320$	624.944	0.109173
$321$	−10408.2	−1.80974
$322$	−174.730	−0.0302402
$323$	−1072.99	−0.184838
$324$	822.015	0.140949
$325$	−2177.55	−0.371657
$326$	−2601.74	−0.442016
$327$	−2249.03	−0.380341
$328$	4533.88	0.763236
$329$	−6857.04	−1.14906
$330$	1494.07	0.249230
$331$	−5752.17	−0.955190	−0.477595	−	0.878580i	$-0.658491\pi$
$331$	−5752.17	−0.955190	−0.477595	+	0.878580i	$0.658491\pi$
$332$	1915.15	0.316589
$333$	657.863	0.108260
$334$	3088.36	0.505950
$335$	−326.950	−0.0533230
$336$	6358.28	1.03236
$337$	2314.88	0.374183	0.187092	−	0.982342i	$-0.440094\pi$
$337$	2314.88	0.374183	0.187092	+	0.982342i	$0.440094\pi$
$338$	−6167.56	−0.992518
$339$	7589.66	1.21597
$340$	−4320.66	−0.689179
$341$	−2356.39	−0.374210
$342$	1050.19	0.166046
$343$	9605.41	1.51208
$344$	−4416.77	−0.692256
$345$	423.160	0.0660353
$346$	−19.5880	−0.00304352
$347$	3884.46	0.600947	0.300473	−	0.953790i	$-0.402855\pi$
$347$	3884.46	0.600947	0.300473	+	0.953790i	$0.402855\pi$
$348$	1178.52	0.181538
$349$	−472.017	−0.0723969	−0.0361984	−	0.999345i	$-0.511525\pi$
$349$	−472.017	−0.0723969	−0.0361984	+	0.999345i	$0.511525\pi$
$350$	−1108.14	−0.169236
$351$	−9842.47	−1.49673
$352$	2028.55	0.307165
$353$	−6866.16	−1.03527	−0.517633	−	0.855603i	$-0.673187\pi$
$353$	−6866.16	−1.03527	−0.517633	+	0.855603i	$0.673187\pi$
$354$	−500.477	−0.0751414
$355$	−7909.07	−1.18245
$356$	−864.268	−0.128669
$357$	14705.0	2.18004
$358$	2802.48	0.413731
$359$	8895.93	1.30782	0.653912	−	0.756570i	$-0.273127\pi$
$359$	8895.93	1.30782	0.653912	+	0.756570i	$0.273127\pi$
$360$	9669.19	1.41559
$361$	361.000	0.0526316
$362$	2363.52	0.343159
$363$	1000.81	0.144707
$364$	16164.9	2.32766
$365$	−11614.0	−1.66549
$366$	8959.46	1.27956
$367$	−4026.00	−0.572630	−0.286315	−	0.958136i	$-0.592430\pi$
$367$	−4026.00	−0.572630	−0.286315	+	0.958136i	$0.592430\pi$
$368$	101.538	0.0143833
$369$	9893.45	1.39575
$370$	−260.871	−0.0366541
$371$	21266.6	2.97603
$372$	−11018.1	−1.53565
$373$	3970.48	0.551163	0.275581	−	0.961278i	$-0.411130\pi$
$373$	3970.48	0.551163	0.275581	+	0.961278i	$0.411130\pi$
$374$	829.131	0.114635
$375$	−10036.6	−1.38211
$376$	−4133.53	−0.566942
$377$	1891.94	0.258462
$378$	−5008.76	−0.681542
$379$	9080.19	1.23065	0.615327	−	0.788272i	$-0.289024\pi$
$379$	9080.19	1.23065	0.615327	+	0.788272i	$0.289024\pi$
$380$	1453.66	0.196240
$381$	1818.84	0.244572
$382$	−678.878	−0.0909278
$383$	224.191	0.0299102	0.0149551	−	0.999888i	$-0.495239\pi$
$383$	224.191	0.0299102	0.0149551	+	0.999888i	$0.495239\pi$
$384$	11641.7	1.54711
$385$	−4260.65	−0.564008
$386$	−2916.40	−0.384562
$387$	−9637.90	−1.26595
$388$	−9516.23	−1.24514
$389$	−2340.12	−0.305009	−0.152505	−	0.988303i	$-0.548734\pi$
$389$	−2340.12	−0.305009	−0.152505	+	0.988303i	$0.548734\pi$
$390$	11215.1	1.45615
$391$	234.832	0.0303733
$392$	12299.6	1.58476
$393$	−21565.7	−2.76806
$394$	−719.031	−0.0919397
$395$	14922.4	1.90083
$396$	2832.71	0.359468
$397$	−9516.76	−1.20310	−0.601552	−	0.798833i	$-0.705451\pi$
$397$	−9516.76	−1.20310	−0.601552	+	0.798833i	$0.705451\pi$
$398$	−1687.05	−0.212472
$399$	−4947.43	−0.620755
$400$	643.957	0.0804947
$401$	−8861.82	−1.10359	−0.551793	−	0.833981i	$-0.686056\pi$
$401$	−8861.82	−1.10359	−0.551793	+	0.833981i	$0.686056\pi$
$402$	293.369	0.0363978
$403$	−17688.0	−2.18636
$404$	8584.63	1.05718
$405$	−1626.35	−0.199541
$406$	962.798	0.117692
$407$	−174.745	−0.0212821
$408$	8864.42	1.07562
$409$	11128.2	1.34537	0.672684	−	0.739930i	$-0.265141\pi$
$409$	11128.2	1.34537	0.672684	+	0.739930i	$0.265141\pi$
$410$	−3923.18	−0.472566
$411$	6780.15	0.813723
$412$	11996.2	1.43449
$413$	1427.21	0.170045
$414$	−229.842	−0.0272854
$415$	−3789.12	−0.448195
$416$	15227.1	1.79464
$417$	−4142.03	−0.486418
$418$	−278.956	−0.0326416
$419$	12444.5	1.45096	0.725481	−	0.688242i	$-0.241617\pi$
$419$	12444.5	1.45096	0.725481	+	0.688242i	$0.241617\pi$
$420$	−19922.1	−2.31453
$421$	−4029.16	−0.466435	−0.233217	−	0.972425i	$-0.574925\pi$
$421$	−4029.16	−0.466435	−0.233217	+	0.972425i	$0.574925\pi$
$422$	−6434.46	−0.742239
$423$	−9019.84	−1.03678
$424$	12819.8	1.46836
$425$	1489.31	0.169981
$426$	7096.72	0.807130
$427$	−25549.8	−2.89565
$428$	7825.22	0.883753
$429$	7512.46	0.845466
$430$	3821.84	0.428618
$431$	9642.70	1.07766	0.538831	−	0.842414i	$-0.318866\pi$
$431$	9642.70	1.07766	0.538831	+	0.842414i	$0.318866\pi$
$432$	2910.67	0.324166
$433$	−14351.1	−1.59277	−0.796383	−	0.604793i	$-0.793256\pi$
$433$	−14351.1	−1.59277	−0.796383	+	0.604793i	$0.793256\pi$
$434$	−9001.30	−0.995567
$435$	−2331.70	−0.257003
$436$	1690.89	0.185732
$437$	−79.0079	−0.00864865
$438$	10421.1	1.13685
$439$	6146.97	0.668288	0.334144	−	0.942522i	$-0.391553\pi$
$439$	6146.97	0.668288	0.334144	+	0.942522i	$0.391553\pi$
$440$	−2568.39	−0.278279
$441$	26839.3	2.89810
$442$	6223.79	0.669763
$443$	16627.2	1.78325	0.891626	−	0.452772i	$-0.149565\pi$
$443$	16627.2	1.78325	0.891626	+	0.452772i	$0.149565\pi$
$444$	−817.081	−0.0873355
$445$	1709.95	0.182156
$446$	−3284.57	−0.348719
$447$	−18942.0	−2.00431
$448$	1599.11	0.168641
$449$	−10601.5	−1.11428	−0.557142	−	0.830417i	$-0.688102\pi$
$449$	−10601.5	−1.11428	−0.557142	+	0.830417i	$0.688102\pi$
$450$	−1457.66	−0.152700
$451$	−2627.95	−0.274380
$452$	−5706.16	−0.593795
$453$	1383.66	0.143510
$454$	−1154.67	−0.119364
$455$	−31982.2	−3.29527
$456$	−2982.38	−0.306278
$457$	−3753.20	−0.384174	−0.192087	−	0.981378i	$-0.561526\pi$
$457$	−3753.20	−0.384174	−0.192087	+	0.981378i	$0.561526\pi$
$458$	−2086.68	−0.212891
$459$	6731.63	0.684544
$460$	−318.146	−0.0322471
$461$	−11783.3	−1.19046	−0.595231	−	0.803554i	$-0.702940\pi$
$461$	−11783.3	−1.19046	−0.595231	+	0.803554i	$0.702940\pi$
$462$	3823.04	0.384987
$463$	5188.50	0.520800	0.260400	−	0.965501i	$-0.416146\pi$
$463$	5188.50	0.520800	0.260400	+	0.965501i	$0.416146\pi$
$464$	−559.497	−0.0559784
$465$	21799.3	2.17402
$466$	8643.13	0.859196
$467$	13786.2	1.36605	0.683027	−	0.730393i	$-0.260663\pi$
$467$	13786.2	1.36605	0.683027	+	0.730393i	$0.260663\pi$
$468$	21263.5	2.10022
$469$	−836.604	−0.0823684
$470$	3576.75	0.351028
$471$	19980.8	1.95471
$472$	860.346	0.0838997
$473$	2560.07	0.248863
$474$	−13389.7	−1.29749
$475$	−501.068	−0.0484013
$476$	−11055.8	−1.06458
$477$	27974.4	2.68524
$478$	−1673.26	−0.160111
$479$	17797.6	1.69769	0.848845	−	0.528641i	$-0.177298\pi$
$479$	17797.6	1.69769	0.848845	+	0.528641i	$0.177298\pi$
$480$	−18766.4	−1.78451
$481$	−1311.71	−0.124342
$482$	−8306.33	−0.784944
$483$	1082.79	0.102005
$484$	−752.441	−0.0706650
$485$	18827.8	1.76274
$486$	5755.01	0.537145
$487$	13447.3	1.25125	0.625623	−	0.780126i	$-0.284845\pi$
$487$	13447.3	1.25125	0.625623	+	0.780126i	$0.284845\pi$
$488$	−15401.8	−1.42870
$489$	16122.7	1.49099
$490$	−10642.9	−0.981221
$491$	−10995.7	−1.01065	−0.505324	−	0.862929i	$-0.668627\pi$
$491$	−10995.7	−1.01065	−0.505324	+	0.862929i	$0.668627\pi$
$492$	−12287.9	−1.12598
$493$	−1293.97	−0.118210
$494$	−2093.96	−0.190712
$495$	−5604.52	−0.508898
$496$	5230.80	0.473528
$497$	−20237.8	−1.82654
$498$	3399.94	0.305934
$499$	10057.1	0.902241	0.451121	−	0.892463i	$-0.351024\pi$
$499$	10057.1	0.902241	0.451121	+	0.892463i	$0.351024\pi$
$500$	7545.88	0.674924
$501$	−19138.3	−1.70666
$502$	7854.42	0.698326
$503$	4459.44	0.395302	0.197651	−	0.980272i	$-0.436669\pi$
$503$	4459.44	0.395302	0.197651	+	0.980272i	$0.436669\pi$
$504$	24741.6	2.18667
$505$	−16984.7	−1.49665
$506$	61.0520	0.00536382
$507$	38219.8	3.34793
$508$	−1367.46	−0.119432
$509$	17264.3	1.50339	0.751696	−	0.659510i	$-0.229236\pi$
$509$	17264.3	1.50339	0.751696	+	0.659510i	$0.229236\pi$
$510$	−7670.41	−0.665983
$511$	−29717.9	−2.57269
$512$	−8210.26	−0.708683
$513$	−2264.82	−0.194920
$514$	−2894.48	−0.248385
$515$	−23734.5	−2.03081
$516$	11970.5	1.02126
$517$	2395.90	0.203813
$518$	−667.519	−0.0566199
$519$	121.385	0.0102663
$520$	−19279.3	−1.62587
$521$	−20504.6	−1.72423	−0.862115	−	0.506713i	$-0.830861\pi$
$521$	−20504.6	−1.72423	−0.862115	+	0.506713i	$0.830861\pi$
$522$	1266.48	0.106192
$523$	−13064.2	−1.09227	−0.546135	−	0.837697i	$-0.683901\pi$
$523$	−13064.2	−1.09227	−0.546135	+	0.837697i	$0.683901\pi$
$524$	16213.8	1.35173
$525$	6867.04	0.570861
$526$	−2863.00	−0.237325
$527$	12097.5	0.999951
$528$	−2221.63	−0.183114
$529$	−12149.7	−0.998579
$530$	−11093.0	−0.909153
$531$	1877.38	0.153430
$532$	3719.65	0.303134
$533$	−19726.5	−1.60309
$534$	−1534.32	−0.124338
$535$	−15482.2	−1.25113
$536$	−504.317	−0.0406403
$537$	−17366.7	−1.39558
$538$	2233.97	0.179021
$539$	−7129.20	−0.569715
$540$	−9119.89	−0.726774
$541$	19870.7	1.57913	0.789564	−	0.613669i	$-0.210307\pi$
$541$	19870.7	1.57913	0.789564	+	0.613669i	$0.210307\pi$
$542$	−4541.73	−0.359934
$543$	−14646.5	−1.15753
$544$	−10414.4	−0.820795
$545$	−3345.43	−0.262940
$546$	28697.2	2.24932
$547$	18949.8	1.48123	0.740615	−	0.671929i	$-0.234534\pi$
$547$	18949.8	1.48123	0.740615	+	0.671929i	$0.234534\pi$
$548$	−5097.55	−0.397366
$549$	−33608.5	−2.61271
$550$	387.192	0.0300180
$551$	435.349	0.0336597
$552$	652.720	0.0503290
$553$	38183.6	2.93623
$554$	2841.33	0.217900
$555$	1616.59	0.123641
$556$	3114.12	0.237533
$557$	−5171.91	−0.393431	−0.196715	−	0.980461i	$-0.563027\pi$
$557$	−5171.91	−0.393431	−0.196715	+	0.980461i	$0.563027\pi$
$558$	−11840.4	−0.898289
$559$	19216.9	1.45401
$560$	9457.95	0.713699
$561$	−5138.05	−0.386682
$562$	726.904	0.0545597
$563$	15002.5	1.12306	0.561529	−	0.827457i	$-0.310213\pi$
$563$	15002.5	1.12306	0.561529	+	0.827457i	$0.310213\pi$
$564$	11202.8	0.836392
$565$	11289.6	0.840634
$566$	4637.30	0.344382
$567$	−4161.53	−0.308233
$568$	−12199.6	−0.901207
$569$	−10119.4	−0.745567	−0.372783	−	0.927918i	$-0.621597\pi$
$569$	−10119.4	−0.745567	−0.372783	+	0.927918i	$0.621597\pi$
$570$	2580.67	0.189635
$571$	9281.92	0.680273	0.340137	−	0.940376i	$-0.389527\pi$
$571$	9281.92	0.680273	0.340137	+	0.940376i	$0.389527\pi$
$572$	−5648.12	−0.412867
$573$	4206.94	0.306715
$574$	−10038.7	−0.729975
$575$	109.663	0.00795351
$576$	2103.49	0.152163
$577$	7829.03	0.564865	0.282432	−	0.959287i	$-0.408859\pi$
$577$	7829.03	0.564865	0.282432	+	0.959287i	$0.408859\pi$
$578$	2300.80	0.165572
$579$	18072.7	1.29719
$580$	1753.05	0.125502
$581$	−9695.64	−0.692329
$582$	−16894.0	−1.20323
$583$	−7430.72	−0.527871
$584$	−17914.4	−1.26936
$585$	−42069.7	−2.97328
$586$	−3200.30	−0.225603
$587$	−384.079	−0.0270062	−0.0135031	−	0.999909i	$-0.504298\pi$
$587$	−384.079	−0.0270062	−0.0135031	+	0.999909i	$0.504298\pi$
$588$	−33335.0	−2.33795
$589$	−4070.13	−0.284731
$590$	−744.460	−0.0519474
$591$	4455.77	0.310128
$592$	387.906	0.0269305
$593$	345.333	0.0239142	0.0119571	−	0.999929i	$-0.496194\pi$
$593$	345.333	0.0239142	0.0119571	+	0.999929i	$0.496194\pi$
$594$	1750.10	0.120888
$595$	21873.8	1.50712
$596$	14241.2	0.978765
$597$	10454.5	0.716705
$598$	458.281	0.0313386
$599$	−19074.7	−1.30112	−0.650560	−	0.759455i	$-0.725466\pi$
$599$	−19074.7	−1.30112	−0.650560	+	0.759455i	$0.725466\pi$
$600$	4139.55	0.281661
$601$	635.475	0.0431308	0.0215654	−	0.999767i	$-0.493135\pi$
$601$	635.475	0.0431308	0.0215654	+	0.999767i	$0.493135\pi$
$602$	9779.36	0.662088
$603$	−1100.48	−0.0743200
$604$	−1040.28	−0.0700804
$605$	1488.70	0.100040
$606$	15240.2	1.02160
$607$	13556.6	0.906500	0.453250	−	0.891383i	$-0.350264\pi$
$607$	13556.6	0.906500	0.453250	+	0.891383i	$0.350264\pi$
$608$	3503.86	0.233717
$609$	−5966.37	−0.396994
$610$	13327.2	0.884596
$611$	17984.6	1.19080
$612$	−14542.9	−0.960557
$613$	−1098.47	−0.0723762	−0.0361881	−	0.999345i	$-0.511522\pi$
$613$	−1098.47	−0.0723762	−0.0361881	+	0.999345i	$0.511522\pi$
$614$	10072.8	0.662064
$615$	24311.6	1.59404
$616$	−6572.01	−0.429860
$617$	−14728.1	−0.960993	−0.480496	−	0.876997i	$-0.659543\pi$
$617$	−14728.1	−0.960993	−0.480496	+	0.876997i	$0.659543\pi$
$618$	21296.7	1.38621
$619$	6365.05	0.413300	0.206650	−	0.978415i	$-0.433744\pi$
$619$	6365.05	0.413300	0.206650	+	0.978415i	$0.433744\pi$
$620$	−16389.4	−1.06164
$621$	495.675	0.0320302
$622$	2902.21	0.187087
$623$	4375.44	0.281378
$624$	−16676.4	−1.06986
$625$	−18226.0	−1.16647
$626$	−1005.17	−0.0641770
$627$	1728.67	0.110106
$628$	−15022.3	−0.954545
$629$	897.125	0.0568692
$630$	−21409.0	−1.35390
$631$	14354.9	0.905641	0.452820	−	0.891602i	$-0.350418\pi$
$631$	14354.9	0.905641	0.452820	+	0.891602i	$0.350418\pi$
$632$	23017.7	1.44872
$633$	39873.8	2.50370
$634$	−12455.2	−0.780220
$635$	2705.53	0.169080
$636$	−34744.8	−2.16623
$637$	−53514.6	−3.32861
$638$	−336.409	−0.0208755
$639$	−26621.1	−1.64806
$640$	17317.1	1.06956
$641$	−7077.48	−0.436106	−0.218053	−	0.975937i	$-0.569970\pi$
$641$	−7077.48	−0.436106	−0.218053	+	0.975937i	$0.569970\pi$
$642$	13892.0	0.854008
$643$	−10741.8	−0.658812	−0.329406	−	0.944188i	$-0.606848\pi$
$643$	−10741.8	−0.658812	−0.329406	+	0.944188i	$0.606848\pi$
$644$	−814.076	−0.0498123
$645$	−23683.6	−1.44580
$646$	1432.14	0.0872239
$647$	−6658.44	−0.404591	−0.202295	−	0.979325i	$-0.564840\pi$
$647$	−6658.44	−0.404591	−0.202295	+	0.979325i	$0.564840\pi$
$648$	−2508.63	−0.152081
$649$	−498.679	−0.0301616
$650$	2906.42	0.175383
$651$	55780.2	3.35822
$652$	−12121.6	−0.728098
$653$	31954.0	1.91494	0.957472	−	0.288527i	$-0.0931655\pi$
$653$	31954.0	1.91494	0.957472	+	0.288527i	$0.0931655\pi$
$654$	3001.82	0.179481
$655$	−32079.0	−1.91364
$656$	5833.63	0.347203
$657$	−39091.4	−2.32131
$658$	9152.23	0.542236
$659$	−5835.87	−0.344967	−0.172484	−	0.985012i	$-0.555179\pi$
$659$	−5835.87	−0.344967	−0.172484	+	0.985012i	$0.555179\pi$
$660$	6960.94	0.410537
$661$	−1447.02	−0.0851478	−0.0425739	−	0.999093i	$-0.513556\pi$
$661$	−1447.02	−0.0851478	−0.0425739	+	0.999093i	$0.513556\pi$
$662$	7677.54	0.450749
$663$	−38568.2	−2.25922
$664$	−5844.68	−0.341593
$665$	−7359.31	−0.429146
$666$	−878.063	−0.0510875
$667$	−95.2799	−0.00553111
$668$	14388.8	0.833412
$669$	20354.2	1.17629
$670$	436.387	0.0251628
$671$	8927.28	0.513612
$672$	−48019.6	−2.75654
$673$	23138.7	1.32531	0.662654	−	0.748925i	$-0.269430\pi$
$673$	23138.7	1.32531	0.662654	+	0.748925i	$0.269430\pi$
$674$	−3089.72	−0.176575
$675$	3143.57	0.179253
$676$	−28735.0	−1.63490
$677$	18424.6	1.04596	0.522980	−	0.852345i	$-0.324820\pi$
$677$	18424.6	1.04596	0.522980	+	0.852345i	$0.324820\pi$
$678$	−10130.1	−0.573810
$679$	48176.9	2.72291
$680$	13185.8	0.743609
$681$	7155.38	0.402635
$682$	3145.12	0.176588
$683$	23120.8	1.29530	0.647651	−	0.761937i	$-0.275751\pi$
$683$	23120.8	1.29530	0.647651	+	0.761937i	$0.275751\pi$
$684$	4892.87	0.273514
$685$	10085.5	0.562550
$686$	−12820.5	−0.713542
$687$	12931.0	0.718118
$688$	−5682.94	−0.314913
$689$	−55777.9	−3.08413
$690$	−564.801	−0.0311617
$691$	34555.5	1.90239	0.951197	−	0.308586i	$-0.0998556\pi$
$691$	34555.5	1.90239	0.951197	+	0.308586i	$0.0998556\pi$
$692$	−91.2614	−0.00501335
$693$	−14340.9	−0.786097
$694$	−5184.66	−0.283584
$695$	−6161.28	−0.336274
$696$	−3596.61	−0.195875
$697$	13491.7	0.733190
$698$	630.011	0.0341637
$699$	−53560.7	−2.89821
$700$	−5162.87	−0.278769
$701$	2348.34	0.126527	0.0632635	−	0.997997i	$-0.479849\pi$
$701$	2348.34	0.126527	0.0632635	+	0.997997i	$0.479849\pi$
$702$	13136.9	0.706299
$703$	−301.833	−0.0161932
$704$	−558.742	−0.0299125
$705$	−22164.8	−1.18408
$706$	9164.40	0.488536
$707$	−43460.5	−2.31188
$708$	−2331.74	−0.123774
$709$	23636.5	1.25203	0.626013	−	0.779813i	$-0.284686\pi$
$709$	23636.5	1.25203	0.626013	+	0.779813i	$0.284686\pi$
$710$	10556.4	0.557992
$711$	50227.2	2.64932
$712$	2637.58	0.138831
$713$	890.782	0.0467883
$714$	−19627.1	−1.02875
$715$	11174.8	0.584495
$716$	13056.9	0.681506
$717$	10369.0	0.540082
$718$	−11873.6	−0.617156
$719$	26804.1	1.39030	0.695149	−	0.718865i	$-0.255338\pi$
$719$	26804.1	1.39030	0.695149	+	0.718865i	$0.255338\pi$
$720$	12441.1	0.643962
$721$	−60732.1	−3.13701
$722$	−481.834	−0.0248366
$723$	51473.5	2.64775
$724$	11011.7	0.565259
$725$	−604.265	−0.0309543
$726$	−1335.80	−0.0682866
$727$	5826.15	0.297221	0.148611	−	0.988896i	$-0.452520\pi$
$727$	5826.15	0.297221	0.148611	+	0.988896i	$0.452520\pi$
$728$	−49332.1	−2.51150
$729$	−32094.2	−1.63055
$730$	15501.4	0.785935
$731$	−13143.2	−0.665004
$732$	41742.5	2.10772
$733$	−9322.98	−0.469784	−0.234892	−	0.972021i	$-0.575474\pi$
$733$	−9322.98	−0.469784	−0.234892	+	0.972021i	$0.575474\pi$
$734$	5373.58	0.270221
$735$	65953.2	3.30982
$736$	−766.849	−0.0384055
$737$	292.315	0.0146100
$738$	−13205.0	−0.658648
$739$	−35683.3	−1.77623	−0.888113	−	0.459626i	$-0.847984\pi$
$739$	−35683.3	−1.77623	−0.888113	+	0.459626i	$0.847984\pi$
$740$	−1215.41	−0.0603775
$741$	12976.1	0.643303
$742$	−28385.0	−1.40437
$743$	17598.6	0.868948	0.434474	−	0.900684i	$-0.356934\pi$
$743$	17598.6	0.868948	0.434474	+	0.900684i	$0.356934\pi$
$744$	33625.1	1.65693
$745$	−28176.3	−1.38564
$746$	−5299.48	−0.260091
$747$	−12753.8	−0.624680
$748$	3862.96	0.188829
$749$	−39615.9	−1.93262
$750$	13396.1	0.652208
$751$	12295.0	0.597404	0.298702	−	0.954346i	$-0.403446\pi$
$751$	12295.0	0.597404	0.298702	+	0.954346i	$0.403446\pi$
$752$	−5318.51	−0.257907
$753$	−48673.1	−2.35557
$754$	−2525.22	−0.121967
$755$	2058.20	0.0992127
$756$	−23336.1	−1.12265
$757$	3925.94	0.188495	0.0942475	−	0.995549i	$-0.469955\pi$
$757$	3925.94	0.188495	0.0942475	+	0.995549i	$0.469955\pi$
$758$	−12119.5	−0.580739
$759$	−378.334	−0.0180931
$760$	−4436.30	−0.211739
$761$	34351.8	1.63634	0.818169	−	0.574978i	$-0.194989\pi$
$761$	34351.8	1.63634	0.818169	+	0.574978i	$0.194989\pi$
$762$	−2427.64	−0.115412
$763$	−8560.32	−0.406166
$764$	−3162.92	−0.149778
$765$	28773.1	1.35986
$766$	−299.232	−0.0141145
$767$	−3743.28	−0.176222
$768$	−18899.5	−0.887989
$769$	−452.819	−0.0212342	−0.0106171	−	0.999944i	$-0.503380\pi$
$769$	−452.819	−0.0212342	−0.0106171	+	0.999944i	$0.503380\pi$
$770$	5686.78	0.266152
$771$	17936.8	0.837845
$772$	−13587.6	−0.633459
$773$	−35034.0	−1.63012	−0.815062	−	0.579373i	$-0.803297\pi$
$773$	−35034.0	−1.63012	−0.815062	+	0.579373i	$0.803297\pi$
$774$	12863.9	0.597395
$775$	5649.34	0.261846
$776$	29041.7	1.34348
$777$	4136.55	0.190988
$778$	3123.40	0.143932
$779$	−4539.19	−0.208772
$780$	52251.6	2.39860
$781$	7071.23	0.323980
$782$	−313.435	−0.0143330
$783$	−2731.26	−0.124658
$784$	15825.7	0.720921
$785$	29721.5	1.35135
$786$	28784.2	1.30623
$787$	9289.03	0.420734	0.210367	−	0.977622i	$-0.432534\pi$
$787$	9289.03	0.420734	0.210367	+	0.977622i	$0.432534\pi$
$788$	−3350.00	−0.151445
$789$	17741.7	0.800536
$790$	−19917.3	−0.896992
$791$	28888.0	1.29853
$792$	−8644.90	−0.387858
$793$	67011.7	3.00083
$794$	12702.2	0.567739
$795$	68742.6	3.06673
$796$	−7860.02	−0.349989
$797$	17541.7	0.779623	0.389812	−	0.920895i	$-0.372540\pi$
$797$	17541.7	0.779623	0.389812	+	0.920895i	$0.372540\pi$
$798$	6603.43	0.292931
$799$	−12300.3	−0.544623
$800$	−4863.36	−0.214932
$801$	5755.51	0.253884
$802$	11828.1	0.520777
$803$	10383.7	0.456328
$804$	1366.82	0.0599553
$805$	1610.65	0.0705191
$806$	23608.5	1.03173
$807$	−13843.7	−0.603867
$808$	−26198.7	−1.14068
$809$	10022.9	0.435583	0.217792	−	0.975995i	$-0.430115\pi$
$809$	10022.9	0.435583	0.217792	+	0.975995i	$0.430115\pi$
$810$	2170.73	0.0941625
$811$	−25395.3	−1.09957	−0.549784	−	0.835307i	$-0.685290\pi$
$811$	−25395.3	−1.09957	−0.549784	+	0.835307i	$0.685290\pi$
$812$	4485.72	0.193864
$813$	28144.7	1.21412
$814$	233.236	0.0100429
$815$	23982.6	1.03077
$816$	11405.6	0.489310
$817$	4421.94	0.189356
$818$	−14853.1	−0.634873
$819$	−107648.	−4.59285
$820$	−18278.3	−0.778421
$821$	−14533.5	−0.617809	−0.308904	−	0.951093i	$-0.599962\pi$
$821$	−14533.5	−0.617809	−0.308904	+	0.951093i	$0.599962\pi$
$822$	−9049.60	−0.383992
$823$	−20129.1	−0.852561	−0.426281	−	0.904591i	$-0.640176\pi$
$823$	−20129.1	−0.852561	−0.426281	+	0.904591i	$0.640176\pi$
$824$	−36610.2	−1.54779
$825$	−2399.39	−0.101256
$826$	−1904.93	−0.0802434
$827$	−9726.57	−0.408979	−0.204490	−	0.978869i	$-0.565553\pi$
$827$	−9726.57	−0.408979	−0.204490	+	0.978869i	$0.565553\pi$
$828$	−1070.85	−0.0449450
$829$	18762.2	0.786054	0.393027	−	0.919527i	$-0.371428\pi$
$829$	18762.2	0.786054	0.393027	+	0.919527i	$0.371428\pi$
$830$	5057.42	0.211501
$831$	−17607.5	−0.735014
$832$	−4194.14	−0.174766
$833$	36600.6	1.52237
$834$	5528.45	0.229538
$835$	−28468.2	−1.17986
$836$	−1299.67	−0.0537680
$837$	25534.9	1.05450
$838$	−16609.9	−0.684702
$839$	−5250.80	−0.216064	−0.108032	−	0.994147i	$-0.534455\pi$
$839$	−5250.80	−0.216064	−0.108032	+	0.994147i	$0.534455\pi$
$840$	60798.6	2.49732
$841$	−23864.0	−0.978473
$842$	5377.79	0.220108
$843$	−4504.55	−0.184039
$844$	−29978.5	−1.22263
$845$	56852.0	2.31452
$846$	12039.0	0.489253
$847$	3809.31	0.154533
$848$	16495.0	0.667971
$849$	−28736.9	−1.16166
$850$	−1987.81	−0.0802132
$851$	66.0587	0.00266094
$852$	33064.0	1.32952
$853$	−10044.8	−0.403199	−0.201599	−	0.979468i	$-0.564614\pi$
$853$	−10044.8	−0.403199	−0.201599	+	0.979468i	$0.564614\pi$
$854$	34101.8	1.36644
$855$	−9680.53	−0.387213
$856$	−23881.1	−0.953550
$857$	18120.1	0.722251	0.361126	−	0.932517i	$-0.382393\pi$
$857$	18120.1	0.722251	0.361126	+	0.932517i	$0.382393\pi$
$858$	−10027.0	−0.398971
$859$	10220.5	0.405960	0.202980	−	0.979183i	$-0.434937\pi$
$859$	10220.5	0.405960	0.202980	+	0.979183i	$0.434937\pi$
$860$	17806.1	0.706028
$861$	62208.7	2.46233
$862$	−12870.3	−0.508543
$863$	−29222.2	−1.15265	−0.576324	−	0.817221i	$-0.695513\pi$
$863$	−29222.2	−1.15265	−0.576324	+	0.817221i	$0.695513\pi$
$864$	−21982.3	−0.865569
$865$	180.560	0.00709739
$866$	19154.6	0.751618
$867$	−14257.8	−0.558503
$868$	−41937.5	−1.63992
$869$	−13341.6	−0.520810
$870$	3112.16	0.121278
$871$	2194.24	0.0853603
$872$	−5160.29	−0.200401
$873$	63372.5	2.45685
$874$	105.453	0.00408126
$875$	−38201.8	−1.47595
$876$	48552.3	1.87264
$877$	1889.82	0.0727649	0.0363824	−	0.999338i	$-0.488417\pi$
$877$	1889.82	0.0727649	0.0363824	+	0.999338i	$0.488417\pi$
$878$	−8204.48	−0.315362
$879$	19832.0	0.760996
$880$	−3304.68	−0.126592
$881$	5440.27	0.208045	0.104022	−	0.994575i	$-0.466829\pi$
$881$	5440.27	0.208045	0.104022	+	0.994575i	$0.466829\pi$
$882$	−35822.9	−1.36760
$883$	−16159.0	−0.615850	−0.307925	−	0.951411i	$-0.599635\pi$
$883$	−16159.0	−0.615850	−0.307925	+	0.951411i	$0.599635\pi$
$884$	28996.9	1.10325
$885$	4613.35	0.175227
$886$	−22192.6	−0.841507
$887$	47494.4	1.79786	0.898932	−	0.438087i	$-0.144344\pi$
$887$	47494.4	1.79786	0.898932	+	0.438087i	$0.144344\pi$
$888$	2493.58	0.0942330
$889$	6922.92	0.261178
$890$	−2282.31	−0.0859586
$891$	1454.07	0.0546725
$892$	−15303.0	−0.574418
$893$	4138.37	0.155079
$894$	25282.3	0.945823
$895$	−25833.0	−0.964807
$896$	44311.1	1.65215
$897$	−2839.92	−0.105710
$898$	14150.0	0.525825
$899$	−4908.38	−0.182095
$900$	−6791.31	−0.251530
$901$	38148.6	1.41056
$902$	3507.58	0.129479
$903$	−60601.8	−2.23334
$904$	17414.1	0.640692
$905$	−21786.7	−0.800236
$906$	−1846.80	−0.0677217
$907$	9806.28	0.358999	0.179499	−	0.983758i	$-0.442552\pi$
$907$	9806.28	0.358999	0.179499	+	0.983758i	$0.442552\pi$
$908$	−5379.66	−0.196619
$909$	−57168.6	−2.08599
$910$	42687.2	1.55502
$911$	25239.2	0.917906	0.458953	−	0.888461i	$-0.348225\pi$
$911$	25239.2	0.917906	0.458953	+	0.888461i	$0.348225\pi$
$912$	−3837.36	−0.139329
$913$	3387.73	0.122801
$914$	5009.48	0.181290
$915$	−82587.5	−2.98389
$916$	−9721.94	−0.350679
$917$	−82084.1	−2.95601
$918$	−8984.84	−0.323033
$919$	15752.4	0.565423	0.282712	−	0.959205i	$-0.408766\pi$
$919$	15752.4	0.565423	0.282712	+	0.959205i	$0.408766\pi$
$920$	970.922	0.0347939
$921$	−62420.5	−2.23325
$922$	15727.4	0.561773
$923$	53079.5	1.89288
$924$	17811.7	0.634158
$925$	418.944	0.0148917
$926$	−6925.20	−0.245763
$927$	−79887.8	−2.83048
$928$	4225.49	0.149470
$929$	30241.1	1.06801	0.534004	−	0.845482i	$-0.320687\pi$
$929$	30241.1	1.06801	0.534004	+	0.845482i	$0.320687\pi$
$930$	−29095.9	−1.02591
$931$	−12314.1	−0.433488
$932$	40268.7	1.41529
$933$	−17984.7	−0.631075
$934$	−18400.7	−0.644634
$935$	−7642.86	−0.267324
$936$	−64892.1	−2.26609
$937$	13939.9	0.486017	0.243008	−	0.970024i	$-0.421866\pi$
$937$	13939.9	0.486017	0.243008	+	0.970024i	$0.421866\pi$
$938$	1116.63	0.0388692
$939$	6228.96	0.216480
$940$	16664.3	0.578222
$941$	1933.94	0.0669976	0.0334988	−	0.999439i	$-0.489335\pi$
$941$	1933.94	0.0669976	0.0334988	+	0.999439i	$0.489335\pi$
$942$	−26668.8	−0.922417
$943$	993.441	0.0343064
$944$	1106.99	0.0381667
$945$	46170.4	1.58934
$946$	−3416.98	−0.117437
$947$	−41240.8	−1.41515	−0.707575	−	0.706639i	$-0.750211\pi$
$947$	−41240.8	−1.41515	−0.707575	+	0.706639i	$0.750211\pi$
$948$	−62383.4	−2.13725
$949$	77943.9	2.66614
$950$	668.786	0.0228403
$951$	77183.7	2.63181
$952$	33740.0	1.14866
$953$	−40558.3	−1.37861	−0.689304	−	0.724473i	$-0.742083\pi$
$953$	−40558.3	−1.37861	−0.689304	+	0.724473i	$0.742083\pi$
$954$	−37338.0	−1.26715
$955$	6257.84	0.212041
$956$	−7795.79	−0.263738
$957$	2084.69	0.0704164
$958$	−23754.8	−0.801131
$959$	25806.8	0.868974
$960$	5169.00	0.173780
$961$	16098.0	0.540365
$962$	1750.76	0.0586765
$963$	−52111.3	−1.74378
$964$	−38699.6	−1.29298
$965$	26883.1	0.896786
$966$	−1445.22	−0.0481357
$967$	40390.6	1.34320	0.671599	−	0.740915i	$-0.265608\pi$
$967$	40390.6	1.34320	0.671599	+	0.740915i	$0.265608\pi$
$968$	2296.31	0.0762460
$969$	−8874.81	−0.294221
$970$	−25129.9	−0.831827
$971$	−26912.8	−0.889469	−0.444735	−	0.895662i	$-0.646702\pi$
$971$	−26912.8	−0.889469	−0.444735	+	0.895662i	$0.646702\pi$
$972$	26812.8	0.884797
$973$	−15765.5	−0.519445
$974$	−17948.4	−0.590456
$975$	−18010.8	−0.591597
$976$	−19817.1	−0.649928
$977$	−1343.43	−0.0439921	−0.0219960	−	0.999758i	$-0.507002\pi$
$977$	−1343.43	−0.0439921	−0.0219960	+	0.999758i	$0.507002\pi$
$978$	−21519.3	−0.703592
$979$	−1528.81	−0.0499091
$980$	−49585.9	−1.61629
$981$	−11260.4	−0.366479
$982$	14676.2	0.476920
$983$	1898.54	0.0616013	0.0308007	−	0.999526i	$-0.490194\pi$
$983$	1898.54	0.0616013	0.0308007	+	0.999526i	$0.490194\pi$
$984$	37500.3	1.21490
$985$	6627.96	0.214400
$986$	1727.09	0.0557827
$987$	−56715.5	−1.82905
$988$	−9755.85	−0.314145
$989$	−967.780	−0.0311159
$990$	7480.46	0.240146
$991$	−14623.4	−0.468747	−0.234373	−	0.972147i	$-0.575304\pi$
$991$	−14623.4	−0.468747	−0.234373	+	0.972147i	$0.575304\pi$
$992$	−39504.5	−1.26439
$993$	−47577.0	−1.52045
$994$	27011.8	0.861934
$995$	15551.0	0.495478
$996$	15840.5	0.503941
$997$	32748.0	1.04026	0.520130	−	0.854087i	$-0.325884\pi$
$997$	32748.0	1.04026	0.520130	+	0.854087i	$0.325884\pi$
$998$	−13423.4	−0.425763
$999$	1893.62	0.0599714

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	209.4.a.c.1.6	✓	13
3.2	odd	2		1881.4.a.k.1.8		13
11.10	odd	2		2299.4.a.k.1.8		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
209.4.a.c.1.6	✓	13	1.1	even	1	trivial
1881.4.a.k.1.8		13	3.2	odd	2
2299.4.a.k.1.8		13	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 209 = 11 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	209.a (trivial)

\(f(q)\)	\(=\)	\(q-1.33472 q^{2} +8.27114 q^{3} -6.21852 q^{4} +12.3033 q^{5} -11.0397 q^{6} +31.4819 q^{7} +18.9777 q^{8} +41.4117 q^{9} -16.4215 q^{10} -11.0000 q^{11} -51.4342 q^{12} -82.5704 q^{13} -42.0195 q^{14} +101.763 q^{15} +24.4182 q^{16} +56.4729 q^{17} -55.2730 q^{18} -19.0000 q^{19} -76.5086 q^{20} +260.391 q^{21} +14.6819 q^{22} +4.15831 q^{23} +156.968 q^{24} +26.3720 q^{25} +110.208 q^{26} +119.201 q^{27} -195.771 q^{28} -22.9131 q^{29} -135.825 q^{30} +214.217 q^{31} -184.413 q^{32} -90.9825 q^{33} -75.3756 q^{34} +387.332 q^{35} -257.519 q^{36} +15.8859 q^{37} +25.3597 q^{38} -682.951 q^{39} +233.490 q^{40} +238.905 q^{41} -347.549 q^{42} -232.734 q^{43} +68.4037 q^{44} +509.502 q^{45} -5.55018 q^{46} -217.809 q^{47} +201.966 q^{48} +648.109 q^{49} -35.1993 q^{50} +467.095 q^{51} +513.466 q^{52} +675.520 q^{53} -159.100 q^{54} -135.337 q^{55} +597.455 q^{56} -157.152 q^{57} +30.5826 q^{58} +45.3345 q^{59} -632.813 q^{60} -811.571 q^{61} -285.920 q^{62} +1303.72 q^{63} +50.7947 q^{64} -1015.89 q^{65} +121.436 q^{66} -26.5741 q^{67} -351.178 q^{68} +34.3940 q^{69} -516.980 q^{70} -642.839 q^{71} +785.900 q^{72} -943.969 q^{73} -21.2033 q^{74} +218.127 q^{75} +118.152 q^{76} -346.301 q^{77} +911.548 q^{78} +1212.88 q^{79} +300.425 q^{80} -132.188 q^{81} -318.871 q^{82} -307.975 q^{83} -1619.25 q^{84} +694.805 q^{85} +310.635 q^{86} -189.517 q^{87} -208.755 q^{88} +138.983 q^{89} -680.042 q^{90} -2599.47 q^{91} -25.8586 q^{92} +1771.82 q^{93} +290.714 q^{94} -233.763 q^{95} -1525.31 q^{96} +1530.30 q^{97} -865.044 q^{98} -455.528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 2 q^{2} + 11 q^{3} + 82 q^{4} + 8 q^{5} + 13 q^{6} + 39 q^{7} + 6 q^{8} + 156 q^{9} + 124 q^{10} - 143 q^{11} + 247 q^{12} - 23 q^{13} + 47 q^{14} + 278 q^{15} + 526 q^{16} + 73 q^{17} - 165 q^{18}+ \cdots - 1716 q^{99}+O(q^{100}) \) 13 * q - 2 * q^2 + 11 * q^3 + 82 * q^4 + 8 * q^5 + 13 * q^6 + 39 * q^7 + 6 * q^8 + 156 * q^9 + 124 * q^10 - 143 * q^11 + 247 * q^12 - 23 * q^13 + 47 * q^14 + 278 * q^15 + 526 * q^16 + 73 * q^17 - 165 * q^18 - 247 * q^19 + 142 * q^20 + 77 * q^21 + 22 * q^22 + 185 * q^23 - 251 * q^24 + 641 * q^25 - 47 * q^26 + 1109 * q^27 + 289 * q^28 - 41 * q^29 + 520 * q^30 + 930 * q^31 - 194 * q^32 - 121 * q^33 - 333 * q^34 + 122 * q^35 + 1469 * q^36 + 1094 * q^37 + 38 * q^38 + 543 * q^39 + 2084 * q^40 - 766 * q^41 - 1277 * q^42 + 1024 * q^43 - 902 * q^44 - 348 * q^45 + 1927 * q^46 + 516 * q^47 + 3067 * q^48 + 1966 * q^49 + 3066 * q^50 + 1975 * q^51 - 553 * q^52 + 1017 * q^53 - 2231 * q^54 - 88 * q^55 - 1793 * q^56 - 209 * q^57 - 159 * q^58 + 15 * q^59 - 3158 * q^60 - 862 * q^61 - 3298 * q^62 + 552 * q^63 + 3694 * q^64 - 1640 * q^65 - 143 * q^66 + 621 * q^67 - 1533 * q^68 + 335 * q^69 - 3250 * q^70 + 632 * q^71 - 8349 * q^72 - 629 * q^73 - 4086 * q^74 - 2759 * q^75 - 1558 * q^76 - 429 * q^77 - 5813 * q^78 + 2444 * q^79 + 2810 * q^80 + 2265 * q^81 - 846 * q^82 + 732 * q^83 - 761 * q^84 - 3786 * q^85 - 4664 * q^86 - 1185 * q^87 - 66 * q^88 + 3178 * q^89 - 6174 * q^90 + 1349 * q^91 - 1677 * q^92 + 1328 * q^93 + 3156 * q^94 - 152 * q^95 - 13811 * q^96 + 1410 * q^97 - 6273 * q^98 - 1716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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