LMFDB - Embedded newform 1859.4.a.o.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,4,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, 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("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1859.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:	$109.684550701$
Analytic rank:	$1$
Dimension:	$39$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	1859.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.18198 q^{2} -2.60560 q^{3} -6.60292 q^{4} -7.12046 q^{5} +3.07976 q^{6} +33.7625 q^{7} +17.2604 q^{8} -20.2109 q^{9} +O(q^{10})$	\(q-1.18198 q^{2} -2.60560 q^{3} -6.60292 q^{4} -7.12046 q^{5} +3.07976 q^{6} +33.7625 q^{7} +17.2604 q^{8} -20.2109 q^{9} +8.41624 q^{10} -11.0000 q^{11} +17.2046 q^{12} -39.9066 q^{14} +18.5531 q^{15} +32.4220 q^{16} +36.4619 q^{17} +23.8888 q^{18} -97.0784 q^{19} +47.0159 q^{20} -87.9716 q^{21} +13.0018 q^{22} +31.1406 q^{23} -44.9736 q^{24} -74.2990 q^{25} +123.013 q^{27} -222.931 q^{28} +133.651 q^{29} -21.9293 q^{30} -130.533 q^{31} -176.405 q^{32} +28.6616 q^{33} -43.0972 q^{34} -240.405 q^{35} +133.451 q^{36} +22.5981 q^{37} +114.745 q^{38} -122.902 q^{40} -416.330 q^{41} +103.981 q^{42} +30.9324 q^{43} +72.6322 q^{44} +143.911 q^{45} -36.8075 q^{46} +448.067 q^{47} -84.4787 q^{48} +796.908 q^{49} +87.8199 q^{50} -95.0051 q^{51} +0.0701780 q^{53} -145.398 q^{54} +78.3251 q^{55} +582.753 q^{56} +252.947 q^{57} -157.973 q^{58} +27.1974 q^{59} -122.505 q^{60} -609.852 q^{61} +154.287 q^{62} -682.370 q^{63} -50.8690 q^{64} -33.8774 q^{66} +895.075 q^{67} -240.755 q^{68} -81.1399 q^{69} +284.154 q^{70} +215.095 q^{71} -348.847 q^{72} +784.746 q^{73} -26.7105 q^{74} +193.593 q^{75} +641.002 q^{76} -371.388 q^{77} +91.6999 q^{79} -230.860 q^{80} +225.172 q^{81} +492.093 q^{82} -818.063 q^{83} +580.870 q^{84} -259.626 q^{85} -36.5614 q^{86} -348.241 q^{87} -189.864 q^{88} -49.3172 q^{89} -170.099 q^{90} -205.619 q^{92} +340.115 q^{93} -529.607 q^{94} +691.243 q^{95} +459.641 q^{96} +186.122 q^{97} -941.929 q^{98} +222.319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) $ 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.18198	−0.417893	−0.208946	−	0.977927i	$-0.567003\pi$
$2$	−1.18198	−0.417893	−0.208946	+	0.977927i	$0.567003\pi$
$3$	−2.60560	−0.501448	−0.250724	−	0.968059i	$-0.580669\pi$
$3$	−2.60560	−0.501448	−0.250724	+	0.968059i	$0.580669\pi$
$4$	−6.60292	−0.825366
$5$	−7.12046	−0.636874	−0.318437	−	0.947944i	$-0.603158\pi$
$5$	−7.12046	−0.636874	−0.318437	+	0.947944i	$0.603158\pi$
$6$	3.07976	0.209551
$7$	33.7625	1.82300	0.911502	−	0.411295i	$-0.134923\pi$
$7$	33.7625	1.82300	0.911502	+	0.411295i	$0.134923\pi$
$8$	17.2604	0.762807
$9$	−20.2109	−0.748550
$10$	8.41624	0.266145
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	17.2046	0.413878
$13$	0	0
$13$	0	0
$14$	−39.9066	−0.761821
$15$	18.5531	0.319359
$16$	32.4220	0.506594
$17$	36.4619	0.520195	0.260098	−	0.965582i	$-0.416245\pi$
$17$	36.4619	0.520195	0.260098	+	0.965582i	$0.416245\pi$
$18$	23.8888	0.312814
$19$	−97.0784	−1.17217	−0.586087	−	0.810248i	$-0.699332\pi$
$19$	−97.0784	−1.17217	−0.586087	+	0.810248i	$0.699332\pi$
$20$	47.0159	0.525654
$21$	−87.9716	−0.914141
$22$	13.0018	0.125999
$23$	31.1406	0.282316	0.141158	−	0.989987i	$-0.454917\pi$
$23$	31.1406	0.282316	0.141158	+	0.989987i	$0.454917\pi$
$24$	−44.9736	−0.382508
$25$	−74.2990	−0.594392
$26$	0	0
$27$	123.013	0.876806
$28$	−222.931	−1.50465
$29$	133.651	0.855805	0.427903	−	0.903825i	$-0.359253\pi$
$29$	133.651	0.855805	0.427903	+	0.903825i	$0.359253\pi$
$30$	−21.9293	−0.133458
$31$	−130.533	−0.756269	−0.378134	−	0.925751i	$-0.623434\pi$
$31$	−130.533	−0.756269	−0.378134	+	0.925751i	$0.623434\pi$
$32$	−176.405	−0.974509
$33$	28.6616	0.151192
$34$	−43.0972	−0.217386
$35$	−240.405	−1.16102
$36$	133.451	0.617828
$37$	22.5981	0.100408	0.0502041	−	0.998739i	$-0.484013\pi$
$37$	22.5981	0.100408	0.0502041	+	0.998739i	$0.484013\pi$
$38$	114.745	0.489843
$39$	0	0
$40$	−122.902	−0.485812
$41$	−416.330	−1.58585	−0.792924	−	0.609320i	$-0.791442\pi$
$41$	−416.330	−1.58585	−0.792924	+	0.609320i	$0.791442\pi$
$42$	103.981	0.382013
$43$	30.9324	0.109701	0.0548505	−	0.998495i	$-0.482532\pi$
$43$	30.9324	0.109701	0.0548505	+	0.998495i	$0.482532\pi$
$44$	72.6322	0.248857
$45$	143.911	0.476732
$46$	−36.8075	−0.117978
$47$	448.067	1.39058	0.695291	−	0.718728i	$-0.255275\pi$
$47$	448.067	1.39058	0.695291	+	0.718728i	$0.255275\pi$
$48$	−84.4787	−0.254030
$49$	796.908	2.32335
$50$	87.8199	0.248392
$51$	−95.0051	−0.260851
$52$	0	0
$53$	0.0701780	0.000181881 0	9.09404e−5	−	1.00000i	$-0.499971\pi$
$53$	0.0701780	0.000181881 0	9.09404e−5		1.00000i	$0.499971\pi$
$54$	−145.398	−0.366411
$55$	78.3251	0.192025
$56$	582.753	1.39060
$57$	252.947	0.587784
$58$	−157.973	−0.357635
$59$	27.1974	0.0600136	0.0300068	−	0.999550i	$-0.490447\pi$
$59$	27.1974	0.0600136	0.0300068	+	0.999550i	$0.490447\pi$
$60$	−122.505	−0.263588
$61$	−609.852	−1.28006	−0.640029	−	0.768351i	$-0.721078\pi$
$61$	−609.852	−1.28006	−0.640029	+	0.768351i	$0.721078\pi$
$62$	154.287	0.316039
$63$	−682.370	−1.36461
$64$	−50.8690	−0.0993535
$65$	0	0
$66$	−33.8774	−0.0631821
$67$	895.075	1.63210	0.816051	−	0.577980i	$-0.196159\pi$
$67$	895.075	1.63210	0.816051	+	0.577980i	$0.196159\pi$
$68$	−240.755	−0.429351
$69$	−81.1399	−0.141567
$70$	284.154	0.485183
$71$	215.095	0.359536	0.179768	−	0.983709i	$-0.442465\pi$
$71$	215.095	0.359536	0.179768	+	0.983709i	$0.442465\pi$
$72$	−348.847	−0.571000
$73$	784.746	1.25819	0.629093	−	0.777330i	$-0.283427\pi$
$73$	784.746	1.25819	0.629093	+	0.777330i	$0.283427\pi$
$74$	−26.7105	−0.0419598
$75$	193.593	0.298056
$76$	641.002	0.967473
$77$	−371.388	−0.549657
$78$	0	0
$79$	91.6999	0.130595	0.0652977	−	0.997866i	$-0.479200\pi$
$79$	91.6999	0.130595	0.0652977	+	0.997866i	$0.479200\pi$
$80$	−230.860	−0.322636
$81$	225.172	0.308878
$82$	492.093	0.662715
$83$	−818.063	−1.08186	−0.540928	−	0.841069i	$-0.681927\pi$
$83$	−818.063	−1.08186	−0.540928	+	0.841069i	$0.681927\pi$
$84$	580.870	0.754501
$85$	−259.626	−0.331298
$86$	−36.5614	−0.0458433
$87$	−348.241	−0.429141
$88$	−189.864	−0.229995
$89$	−49.3172	−0.0587372	−0.0293686	−	0.999569i	$-0.509350\pi$
$89$	−49.3172	−0.0587372	−0.0293686	+	0.999569i	$0.509350\pi$
$90$	−170.099	−0.199223
$91$	0	0
$92$	−205.619	−0.233014
$93$	340.115	0.379229
$94$	−529.607	−0.581114
$95$	691.243	0.746527
$96$	459.641	0.488665
$97$	186.122	0.194823	0.0974114	−	0.995244i	$-0.468944\pi$
$97$	186.122	0.194823	0.0974114	+	0.995244i	$0.468944\pi$
$98$	−941.929	−0.970910
$99$	222.319	0.225696
$100$	490.591	0.490591
$101$	−1250.50	−1.23198	−0.615988	−	0.787756i	$-0.711243\pi$
$101$	−1250.50	−1.23198	−0.615988	+	0.787756i	$0.711243\pi$
$102$	112.294	0.109008
$103$	1264.71	1.20986	0.604932	−	0.796277i	$-0.293200\pi$
$103$	1264.71	1.20986	0.604932	+	0.796277i	$0.293200\pi$
$104$	0	0
$105$	626.398	0.582193
$106$	−0.0829489	−7.60067e−5 0
$107$	555.701	0.502071	0.251036	−	0.967978i	$-0.419229\pi$
$107$	555.701	0.502071	0.251036	+	0.967978i	$0.419229\pi$
$108$	−812.242	−0.723686
$109$	1680.20	1.47645	0.738227	−	0.674552i	$-0.235663\pi$
$109$	1680.20	1.47645	0.738227	+	0.674552i	$0.235663\pi$
$110$	−92.5786	−0.0802457
$111$	−58.8815	−0.0503494
$112$	1094.65	0.923523
$113$	931.769	0.775694	0.387847	−	0.921724i	$-0.373219\pi$
$113$	931.769	0.775694	0.387847	+	0.921724i	$0.373219\pi$
$114$	−298.979	−0.245631
$115$	−221.735	−0.179799
$116$	−882.487	−0.706352
$117$	0	0
$118$	−32.1468	−0.0250792
$119$	1231.05	0.948318
$120$	320.233	0.243609
$121$	121.000	0.0909091
$122$	720.833	0.534927
$123$	1084.79	0.795220
$124$	861.896	0.624198
$125$	1419.10	1.01543
$126$	806.547	0.570261
$127$	102.266	0.0714540	0.0357270	−	0.999362i	$-0.488625\pi$
$127$	102.266	0.0714540	0.0357270	+	0.999362i	$0.488625\pi$
$128$	1471.37	1.01603
$129$	−80.5973	−0.0550093
$130$	0	0
$131$	696.294	0.464393	0.232196	−	0.972669i	$-0.425409\pi$
$131$	696.294	0.464393	0.232196	+	0.972669i	$0.425409\pi$
$132$	−189.250	−0.124789
$133$	−3277.61	−2.13688
$134$	−1057.96	−0.682044
$135$	−875.906	−0.558415
$136$	629.346	0.396809
$137$	−2523.50	−1.57370	−0.786850	−	0.617145i	$-0.788289\pi$
$137$	−2523.50	−1.57370	−0.786850	+	0.617145i	$0.788289\pi$
$138$	95.9057	0.0591596
$139$	−2134.11	−1.30225	−0.651127	−	0.758969i	$-0.725703\pi$
$139$	−2134.11	−1.30225	−0.651127	+	0.758969i	$0.725703\pi$
$140$	1587.37	0.958269
$141$	−1167.48	−0.697304
$142$	−254.237	−0.150247
$143$	0	0
$144$	−655.277	−0.379211
$145$	−951.656	−0.545040
$146$	−927.553	−0.525787
$147$	−2076.42	−1.16504
$148$	−149.213	−0.0828734
$149$	1772.13	0.974354	0.487177	−	0.873303i	$-0.338027\pi$
$149$	1772.13	0.974354	0.487177	+	0.873303i	$0.338027\pi$
$150$	−228.823	−0.124556
$151$	129.652	0.0698739	0.0349370	−	0.999390i	$-0.488877\pi$
$151$	129.652	0.0698739	0.0349370	+	0.999390i	$0.488877\pi$
$152$	−1675.61	−0.894143
$153$	−736.927	−0.389392
$154$	438.973	0.229698
$155$	929.452	0.481648
$156$	0	0
$157$	2748.06	1.39694	0.698469	−	0.715641i	$-0.253865\pi$
$157$	2748.06	1.39694	0.698469	+	0.715641i	$0.253865\pi$
$158$	−108.387	−0.0545749
$159$	−0.182856	−9.12037e−5 0
$160$	1256.09	0.620639
$161$	1051.38	0.514663
$162$	−266.149	−0.129078
$163$	−2706.21	−1.30041	−0.650205	−	0.759759i	$-0.725317\pi$
$163$	−2706.21	−1.30041	−0.650205	+	0.759759i	$0.725317\pi$
$164$	2748.99	1.30890
$165$	−204.084	−0.0962903
$166$	966.933	0.452100
$167$	−1600.15	−0.741455	−0.370728	−	0.928742i	$-0.620892\pi$
$167$	−1600.15	−0.741455	−0.370728	+	0.928742i	$0.620892\pi$
$168$	−1518.42	−0.697314
$169$	0	0
$170$	306.872	0.138447
$171$	1962.04	0.877432
$172$	−204.244	−0.0905434
$173$	−3509.64	−1.54239	−0.771194	−	0.636600i	$-0.780340\pi$
$173$	−3509.64	−1.54239	−0.771194	+	0.636600i	$0.780340\pi$
$174$	411.613	0.179335
$175$	−2508.52	−1.08358
$176$	−356.642	−0.152744
$177$	−70.8655	−0.0300937
$178$	58.2919	0.0245459
$179$	1592.74	0.665069	0.332534	−	0.943091i	$-0.392096\pi$
$179$	1592.74	0.665069	0.332534	+	0.943091i	$0.392096\pi$
$180$	−950.231	−0.393478
$181$	−842.718	−0.346070	−0.173035	−	0.984916i	$-0.555357\pi$
$181$	−842.718	−0.346070	−0.173035	+	0.984916i	$0.555357\pi$
$182$	0	0
$183$	1589.03	0.641882
$184$	537.498	0.215352
$185$	−160.909	−0.0639473
$186$	−402.009	−0.158477
$187$	−401.081	−0.156845
$188$	−2958.56	−1.14774
$189$	4153.21	1.59842
$190$	−817.036	−0.311968
$191$	−309.712	−0.117330	−0.0586649	−	0.998278i	$-0.518684\pi$
$191$	−309.712	−0.117330	−0.0586649	+	0.998278i	$0.518684\pi$
$192$	132.544	0.0498206
$193$	−3072.77	−1.14603	−0.573013	−	0.819546i	$-0.694226\pi$
$193$	−3072.77	−1.14603	−0.573013	+	0.819546i	$0.694226\pi$
$194$	−219.992	−0.0814151
$195$	0	0
$196$	−5261.92	−1.91761
$197$	2846.99	1.02964	0.514822	−	0.857297i	$-0.327858\pi$
$197$	2846.99	1.02964	0.514822	+	0.857297i	$0.327858\pi$
$198$	−262.777	−0.0943169
$199$	−1499.27	−0.534073	−0.267037	−	0.963686i	$-0.586044\pi$
$199$	−1499.27	−0.534073	−0.267037	+	0.963686i	$0.586044\pi$
$200$	−1282.43	−0.453407
$201$	−2332.21	−0.818414
$202$	1478.07	0.514834
$203$	4512.39	1.56014
$204$	627.312	0.215297
$205$	2964.46	1.00998
$206$	−1494.87	−0.505593
$207$	−629.378	−0.211328
$208$	0	0
$209$	1067.86	0.353424
$210$	−740.390	−0.243294
$211$	−4623.43	−1.50848	−0.754242	−	0.656596i	$-0.771996\pi$
$211$	−4623.43	−1.50848	−0.754242	+	0.656596i	$0.771996\pi$
$212$	−0.463380	−0.000150118 0
$213$	−560.450	−0.180288
$214$	−656.827	−0.209812
$215$	−220.253	−0.0698657
$216$	2123.24	0.668834
$217$	−4407.11	−1.37868
$218$	−1985.96	−0.617000
$219$	−2044.73	−0.630914
$220$	−517.175	−0.158491
$221$	0	0
$222$	69.5967	0.0210407
$223$	−3399.76	−1.02092	−0.510458	−	0.859902i	$-0.670524\pi$
$223$	−3399.76	−1.02092	−0.510458	+	0.859902i	$0.670524\pi$
$224$	−5955.88	−1.77653
$225$	1501.65	0.444932
$226$	−1101.33	−0.324157
$227$	−6070.71	−1.77501	−0.887505	−	0.460798i	$-0.847563\pi$
$227$	−6070.71	−1.77501	−0.887505	+	0.460798i	$0.847563\pi$
$228$	−1670.19	−0.485137
$229$	−6818.90	−1.96771	−0.983856	−	0.178964i	$-0.942725\pi$
$229$	−6818.90	−1.96771	−0.983856	+	0.178964i	$0.942725\pi$
$230$	262.087	0.0751369
$231$	967.687	0.275624
$232$	2306.86	0.652814
$233$	−716.376	−0.201422	−0.100711	−	0.994916i	$-0.532112\pi$
$233$	−716.376	−0.201422	−0.100711	+	0.994916i	$0.532112\pi$
$234$	0	0
$235$	−3190.45	−0.885625
$236$	−179.582	−0.0495332
$237$	−238.933	−0.0654868
$238$	−1455.07	−0.396295
$239$	−1673.67	−0.452974	−0.226487	−	0.974014i	$-0.572724\pi$
$239$	−1673.67	−0.452974	−0.226487	+	0.974014i	$0.572724\pi$
$240$	601.528	0.161785
$241$	112.293	0.0300141	0.0150070	−	0.999887i	$-0.495223\pi$
$241$	112.293	0.0300141	0.0150070	+	0.999887i	$0.495223\pi$
$242$	−143.020	−0.0379903
$243$	−3908.05	−1.03169
$244$	4026.81	1.05652
$245$	−5674.35	−1.47968
$246$	−1282.20	−0.332317
$247$	0	0
$248$	−2253.04	−0.576887
$249$	2131.54	0.542494
$250$	−1677.35	−0.424339
$251$	−3545.08	−0.891489	−0.445744	−	0.895160i	$-0.647061\pi$
$251$	−3545.08	−0.891489	−0.445744	+	0.895160i	$0.647061\pi$
$252$	4505.63	1.12630
$253$	−342.546	−0.0851214
$254$	−120.877	−0.0298601
$255$	676.481	0.166129
$256$	−1332.17	−0.325237
$257$	4760.21	1.15538	0.577692	−	0.816255i	$-0.303953\pi$
$257$	4760.21	1.15538	0.577692	+	0.816255i	$0.303953\pi$
$258$	95.2644	0.0229880
$259$	762.968	0.183045
$260$	0	0
$261$	−2701.20	−0.640613
$262$	−823.005	−0.194066
$263$	400.784	0.0939674	0.0469837	−	0.998896i	$-0.485039\pi$
$263$	400.784	0.0939674	0.0469837	+	0.998896i	$0.485039\pi$
$264$	494.709	0.115330
$265$	−0.499700	−0.000115835 0
$266$	3874.07	0.892987
$267$	128.501	0.0294537
$268$	−5910.12	−1.34708
$269$	−3304.66	−0.749029	−0.374515	−	0.927221i	$-0.622191\pi$
$269$	−3304.66	−0.749029	−0.374515	+	0.927221i	$0.622191\pi$
$270$	1035.30	0.233358
$271$	3276.19	0.734370	0.367185	−	0.930148i	$-0.380322\pi$
$271$	3276.19	0.734370	0.367185	+	0.930148i	$0.380322\pi$
$272$	1182.17	0.263528
$273$	0	0
$274$	2982.72	0.657638
$275$	817.289	0.179216
$276$	535.760	0.116844
$277$	−6687.36	−1.45056	−0.725279	−	0.688455i	$-0.758289\pi$
$277$	−6687.36	−1.45056	−0.725279	+	0.688455i	$0.758289\pi$
$278$	2522.48	0.544202
$279$	2638.17	0.566105
$280$	−4149.47	−0.885637
$281$	7474.97	1.58690	0.793451	−	0.608635i	$-0.208282\pi$
$281$	7474.97	1.58690	0.793451	+	0.608635i	$0.208282\pi$
$282$	1379.94	0.291398
$283$	1504.56	0.316032	0.158016	−	0.987437i	$-0.449490\pi$
$283$	1504.56	0.316032	0.158016	+	0.987437i	$0.449490\pi$
$284$	−1420.25	−0.296748
$285$	−1801.10	−0.374344
$286$	0	0
$287$	−14056.3	−2.89101
$288$	3565.30	0.729469
$289$	−3583.53	−0.729397
$290$	1124.84	0.227768
$291$	−484.959	−0.0976935
$292$	−5181.62	−1.03846
$293$	−5889.56	−1.17431	−0.587154	−	0.809476i	$-0.699752\pi$
$293$	−5889.56	−1.17431	−0.587154	+	0.809476i	$0.699752\pi$
$294$	2454.29	0.486861
$295$	−193.658	−0.0382211
$296$	390.051	0.0765921
$297$	−1353.14	−0.264367
$298$	−2094.62	−0.407175
$299$	0	0
$300$	−1278.28	−0.246006
$301$	1044.35	0.199985
$302$	−153.246	−0.0291998
$303$	3258.30	0.617771
$304$	−3147.48	−0.593817
$305$	4342.43	0.815235
$306$	871.032	0.162724
$307$	−5670.03	−1.05409	−0.527045	−	0.849837i	$-0.676700\pi$
$307$	−5670.03	−1.05409	−0.527045	+	0.849837i	$0.676700\pi$
$308$	2452.25	0.453668
$309$	−3295.34	−0.606683
$310$	−1098.59	−0.201277
$311$	−8264.39	−1.50685	−0.753426	−	0.657533i	$-0.771600\pi$
$311$	−8264.39	−1.50685	−0.753426	+	0.657533i	$0.771600\pi$
$312$	0	0
$313$	10974.1	1.98176	0.990882	−	0.134735i	$-0.0430184\pi$
$313$	10974.1	1.98176	0.990882	+	0.134735i	$0.0430184\pi$
$314$	−3248.15	−0.583770
$315$	4858.79	0.869085
$316$	−605.487	−0.107789
$317$	9307.19	1.64903	0.824517	−	0.565837i	$-0.191447\pi$
$317$	9307.19	1.64903	0.824517	+	0.565837i	$0.191447\pi$
$318$	0.216132	3.81134e−5 0
$319$	−1470.16	−0.258035
$320$	362.211	0.0632756
$321$	−1447.93	−0.251763
$322$	−1242.72	−0.215074
$323$	−3539.67	−0.609760
$324$	−1486.79	−0.254937
$325$	0	0
$326$	3198.68	0.543432
$327$	−4377.91	−0.740365
$328$	−7186.00	−1.20970
$329$	15127.9	2.53504
$330$	241.223	0.0402390
$331$	7385.46	1.22641	0.613205	−	0.789924i	$-0.289880\pi$
$331$	7385.46	1.22641	0.613205	+	0.789924i	$0.289880\pi$
$332$	5401.61	0.892927
$333$	−456.727	−0.0751606
$334$	1891.34	0.309849
$335$	−6373.35	−1.03944
$336$	−2852.22	−0.463099
$337$	−12006.3	−1.94072	−0.970360	−	0.241662i	$-0.922307\pi$
$337$	−12006.3	−1.94072	−0.970360	+	0.241662i	$0.922307\pi$
$338$	0	0
$339$	−2427.82	−0.388970
$340$	1714.29	0.273442
$341$	1435.86	0.228024
$342$	−2319.09	−0.366672
$343$	15325.1	2.41247
$344$	533.904	0.0836807
$345$	577.753	0.0901600
$346$	4148.33	0.644553
$347$	−194.603	−0.0301062	−0.0150531	−	0.999887i	$-0.504792\pi$
$347$	−194.603	−0.0301062	−0.0150531	+	0.999887i	$0.504792\pi$
$348$	2299.41	0.354199
$349$	−855.223	−0.131172	−0.0655860	−	0.997847i	$-0.520892\pi$
$349$	−855.223	−0.131172	−0.0655860	+	0.997847i	$0.520892\pi$
$350$	2965.02	0.452820
$351$	0	0
$352$	1940.46	0.293826
$353$	2465.54	0.371749	0.185874	−	0.982574i	$-0.440488\pi$
$353$	2465.54	0.371749	0.185874	+	0.982574i	$0.440488\pi$
$354$	83.7616	0.0125759
$355$	−1531.57	−0.228979
$356$	325.638	0.0484797
$357$	−3207.61	−0.475532
$358$	−1882.59	−0.277928
$359$	11939.2	1.75522	0.877611	−	0.479374i	$-0.159136\pi$
$359$	11939.2	1.75522	0.877611	+	0.479374i	$0.159136\pi$
$360$	2483.95	0.363655
$361$	2565.22	0.373994
$362$	996.075	0.144620
$363$	−315.277	−0.0455861
$364$	0	0
$365$	−5587.75	−0.801305
$366$	−1878.20	−0.268238
$367$	−9638.96	−1.37098	−0.685490	−	0.728082i	$-0.740412\pi$
$367$	−9638.96	−1.37098	−0.685490	+	0.728082i	$0.740412\pi$
$368$	1009.64	0.143019
$369$	8414.38	1.18709
$370$	190.191	0.0267231
$371$	2.36939	0.000331570 0
$372$	−2245.76	−0.313003
$373$	−9207.25	−1.27811	−0.639053	−	0.769163i	$-0.720674\pi$
$373$	−9207.25	−1.27811	−0.639053	+	0.769163i	$0.720674\pi$
$374$	474.070	0.0655443
$375$	−3697.61	−0.509183
$376$	7733.80	1.06075
$377$	0	0
$378$	−4909.01	−0.667969
$379$	−1137.98	−0.154232	−0.0771161	−	0.997022i	$-0.524571\pi$
$379$	−1137.98	−0.154232	−0.0771161	+	0.997022i	$0.524571\pi$
$380$	−4564.23	−0.616158
$381$	−266.465	−0.0358304
$382$	366.073	0.0490313
$383$	14222.1	1.89743	0.948714	−	0.316137i	$-0.102386\pi$
$383$	14222.1	1.89743	0.948714	+	0.316137i	$0.102386\pi$
$384$	−3833.79	−0.509485
$385$	2644.45	0.350062
$386$	3631.95	0.478916
$387$	−625.170	−0.0821167
$388$	−1228.95	−0.160800
$389$	4259.17	0.555138	0.277569	−	0.960706i	$-0.410471\pi$
$389$	4259.17	0.555138	0.277569	+	0.960706i	$0.410471\pi$
$390$	0	0
$391$	1135.45	0.146859
$392$	13754.9	1.77227
$393$	−1814.26	−0.232869
$394$	−3365.09	−0.430281
$395$	−652.946	−0.0831728
$396$	−1467.96	−0.186282
$397$	593.419	0.0750197	0.0375099	−	0.999296i	$-0.488057\pi$
$397$	593.419	0.0750197	0.0375099	+	0.999296i	$0.488057\pi$
$398$	1772.11	0.223185
$399$	8540.14	1.07153
$400$	−2408.92	−0.301115
$401$	8874.30	1.10514	0.552570	−	0.833466i	$-0.313647\pi$
$401$	8874.30	1.10514	0.552570	+	0.833466i	$0.313647\pi$
$402$	2756.62	0.342009
$403$	0	0
$404$	8256.96	1.01683
$405$	−1603.33	−0.196716
$406$	−5333.55	−0.651970
$407$	−248.579	−0.0302742
$408$	−1639.82	−0.198979
$409$	−4592.03	−0.555161	−0.277581	−	0.960702i	$-0.589533\pi$
$409$	−4592.03	−0.555161	−0.277581	+	0.960702i	$0.589533\pi$
$410$	−3503.93	−0.422065
$411$	6575.22	0.789128
$412$	−8350.81	−0.998580
$413$	918.253	0.109405
$414$	743.912	0.0883123
$415$	5824.99	0.689006
$416$	0	0
$417$	5560.65	0.653012
$418$	−1262.19	−0.147693
$419$	−11296.8	−1.31715	−0.658574	−	0.752516i	$-0.728840\pi$
$419$	−11296.8	−1.31715	−0.658574	+	0.752516i	$0.728840\pi$
$420$	−4136.06	−0.480522
$421$	5768.10	0.667743	0.333872	−	0.942619i	$-0.391645\pi$
$421$	5768.10	0.667743	0.333872	+	0.942619i	$0.391645\pi$
$422$	5464.80	0.630385
$423$	−9055.83	−1.04092
$424$	1.21130	0.000138740 0
$425$	−2709.08	−0.309200
$426$	662.441	0.0753412
$427$	−20590.1	−2.33355
$428$	−3669.25	−0.414393
$429$	0	0
$430$	260.334	0.0291964
$431$	−13082.8	−1.46212	−0.731060	−	0.682313i	$-0.760974\pi$
$431$	−13082.8	−1.46212	−0.731060	+	0.682313i	$0.760974\pi$
$432$	3988.31	0.444185
$433$	2284.27	0.253521	0.126761	−	0.991933i	$-0.459542\pi$
$433$	2284.27	0.253521	0.126761	+	0.991933i	$0.459542\pi$
$434$	5209.11	0.576141
$435$	2479.63	0.273309
$436$	−11094.2	−1.21861
$437$	−3023.08	−0.330923
$438$	2416.83	0.263654
$439$	6903.58	0.750547	0.375273	−	0.926914i	$-0.377549\pi$
$439$	6903.58	0.750547	0.375273	+	0.926914i	$0.377549\pi$
$440$	1351.92	0.146478
$441$	−16106.2	−1.73914
$442$	0	0
$443$	−1161.28	−0.124547	−0.0622733	−	0.998059i	$-0.519835\pi$
$443$	−1161.28	−0.124547	−0.0622733	+	0.998059i	$0.519835\pi$
$444$	388.790	0.0415567
$445$	351.161	0.0374082
$446$	4018.44	0.426634
$447$	−4617.46	−0.488587
$448$	−1717.47	−0.181122
$449$	16536.1	1.73806	0.869029	−	0.494761i	$-0.164744\pi$
$449$	16536.1	1.73806	0.869029	+	0.494761i	$0.164744\pi$
$450$	−1774.92	−0.185934
$451$	4579.63	0.478151
$452$	−6152.40	−0.640231
$453$	−337.822	−0.0350381
$454$	7175.46	0.741764
$455$	0	0
$456$	4365.96	0.448366
$457$	−15979.4	−1.63564	−0.817818	−	0.575478i	$-0.804816\pi$
$457$	−15979.4	−1.63564	−0.817818	+	0.575478i	$0.804816\pi$
$458$	8059.80	0.822292
$459$	4485.27	0.456110
$460$	1464.10	0.148400
$461$	−2748.38	−0.277668	−0.138834	−	0.990316i	$-0.544335\pi$
$461$	−2748.38	−0.277668	−0.138834	+	0.990316i	$0.544335\pi$
$462$	−1143.79	−0.115181
$463$	−15367.5	−1.54253	−0.771263	−	0.636517i	$-0.780374\pi$
$463$	−15367.5	−1.54253	−0.771263	+	0.636517i	$0.780374\pi$
$464$	4333.23	0.433546
$465$	−2421.78	−0.241521
$466$	846.742	0.0841729
$467$	−8408.66	−0.833204	−0.416602	−	0.909089i	$-0.636779\pi$
$467$	−8408.66	−0.833204	−0.416602	+	0.909089i	$0.636779\pi$
$468$	0	0
$469$	30220.0	2.97533
$470$	3771.04	0.370096
$471$	−7160.35	−0.700491
$472$	469.437	0.0457788
$473$	−340.256	−0.0330761
$474$	282.414	0.0273665
$475$	7212.83	0.696731
$476$	−8128.51	−0.782709
$477$	−1.41836	−0.000136147 0
$478$	1978.24	0.189295
$479$	−7338.32	−0.699992	−0.349996	−	0.936751i	$-0.613817\pi$
$479$	−7338.32	−0.699992	−0.349996	+	0.936751i	$0.613817\pi$
$480$	−3272.85	−0.311218
$481$	0	0
$482$	−132.727	−0.0125427
$483$	−2739.49	−0.258077
$484$	−798.954	−0.0750332
$485$	−1325.27	−0.124078
$486$	4619.23	0.431137
$487$	−8048.00	−0.748850	−0.374425	−	0.927257i	$-0.622160\pi$
$487$	−8048.00	−0.748850	−0.374425	+	0.927257i	$0.622160\pi$
$488$	−10526.3	−0.976438
$489$	7051.29	0.652087
$490$	6706.97	0.618347
$491$	14832.1	1.36326	0.681632	−	0.731696i	$-0.261271\pi$
$491$	14832.1	1.36326	0.681632	+	0.731696i	$0.261271\pi$
$492$	−7162.77	−0.656347
$493$	4873.17	0.445186
$494$	0	0
$495$	−1583.02	−0.143740
$496$	−4232.13	−0.383121
$497$	7262.14	0.655436
$498$	−2519.44	−0.226704
$499$	−16236.1	−1.45657	−0.728283	−	0.685277i	$-0.759681\pi$
$499$	−16236.1	−1.45657	−0.728283	+	0.685277i	$0.759681\pi$
$500$	−9370.22	−0.838098
$501$	4169.34	0.371801
$502$	4190.22	0.372547
$503$	−4191.47	−0.371547	−0.185774	−	0.982593i	$-0.559479\pi$
$503$	−4191.47	−0.371547	−0.185774	+	0.982593i	$0.559479\pi$
$504$	−11777.9	−1.04093
$505$	8904.14	0.784612
$506$	404.883	0.0355716
$507$	0	0
$508$	−675.256	−0.0589757
$509$	6615.21	0.576059	0.288030	−	0.957622i	$-0.407000\pi$
$509$	6615.21	0.576059	0.288030	+	0.957622i	$0.407000\pi$
$510$	−799.586	−0.0694241
$511$	26495.0	2.29368
$512$	−10196.3	−0.880114
$513$	−11941.9	−1.02777
$514$	−5626.47	−0.482827
$515$	−9005.35	−0.770530
$516$	532.178	0.0454028
$517$	−4928.74	−0.419276
$518$	−901.813	−0.0764930
$519$	9144.72	0.773427
$520$	0	0
$521$	−19165.7	−1.61164	−0.805820	−	0.592161i	$-0.798275\pi$
$521$	−19165.7	−1.61164	−0.805820	+	0.592161i	$0.798275\pi$
$522$	3192.76	0.267708
$523$	17123.2	1.43164	0.715819	−	0.698285i	$-0.246053\pi$
$523$	17123.2	1.43164	0.715819	+	0.698285i	$0.246053\pi$
$524$	−4597.57	−0.383294
$525$	6536.20	0.543358
$526$	−473.719	−0.0392683
$527$	−4759.47	−0.393407
$528$	929.266	0.0765930
$529$	−11197.3	−0.920298
$530$	0.590635	4.84067e−5 0
$531$	−549.683	−0.0449232
$532$	21641.8	1.76371
$533$	0	0
$534$	−151.885	−0.0123085
$535$	−3956.85	−0.319756
$536$	15449.3	1.24498
$537$	−4150.05	−0.333497
$538$	3906.04	0.313014
$539$	−8765.99	−0.700515
$540$	5783.54	0.460896
$541$	−11747.7	−0.933591	−0.466795	−	0.884365i	$-0.654592\pi$
$541$	−11747.7	−0.933591	−0.466795	+	0.884365i	$0.654592\pi$
$542$	−3872.39	−0.306888
$543$	2195.78	0.173536
$544$	−6432.07	−0.506935
$545$	−11963.8	−0.940315
$546$	0	0
$547$	−17405.7	−1.36054	−0.680270	−	0.732962i	$-0.738137\pi$
$547$	−17405.7	−1.36054	−0.680270	+	0.732962i	$0.738137\pi$
$548$	16662.5	1.29888
$549$	12325.6	0.958188
$550$	−966.019	−0.0748931
$551$	−12974.6	−1.00315
$552$	−1400.50	−0.107988
$553$	3096.02	0.238076
$554$	7904.33	0.606178
$555$	419.264	0.0320662
$556$	14091.4	1.07484
$557$	23101.5	1.75735	0.878674	−	0.477423i	$-0.158429\pi$
$557$	23101.5	1.75735	0.878674	+	0.477423i	$0.158429\pi$
$558$	−3118.27	−0.236571
$559$	0	0
$560$	−7794.41	−0.588168
$561$	1045.06	0.0786494
$562$	−8835.26	−0.663155
$563$	−3708.12	−0.277582	−0.138791	−	0.990322i	$-0.544322\pi$
$563$	−3708.12	−0.277582	−0.138791	+	0.990322i	$0.544322\pi$
$564$	7708.81	0.575531
$565$	−6634.63	−0.494019
$566$	−1778.36	−0.132067
$567$	7602.37	0.563086
$568$	3712.61	0.274256
$569$	−16441.5	−1.21136	−0.605682	−	0.795707i	$-0.707099\pi$
$569$	−16441.5	−1.21136	−0.605682	+	0.795707i	$0.707099\pi$
$570$	2128.87	0.156436
$571$	−19030.3	−1.39473	−0.697367	−	0.716714i	$-0.745645\pi$
$571$	−19030.3	−1.39473	−0.697367	+	0.716714i	$0.745645\pi$
$572$	0	0
$573$	806.986	0.0588347
$574$	16614.3	1.20813
$575$	−2313.71	−0.167806
$576$	1028.11	0.0743711
$577$	−19437.3	−1.40240	−0.701201	−	0.712964i	$-0.747352\pi$
$577$	−19437.3	−1.40240	−0.701201	+	0.712964i	$0.747352\pi$
$578$	4235.66	0.304810
$579$	8006.41	0.574672
$580$	6283.72	0.449857
$581$	−27619.9	−1.97223
$582$	573.211	0.0408254
$583$	−0.771958	−5.48391e−5 0
$584$	13545.0	0.959753
$585$	0	0
$586$	6961.34	0.490734
$587$	−17425.8	−1.22528	−0.612639	−	0.790363i	$-0.709892\pi$
$587$	−17425.8	−1.22528	−0.612639	+	0.790363i	$0.709892\pi$
$588$	13710.5	0.961581
$589$	12671.9	0.886479
$590$	228.900	0.0159723
$591$	−7418.12	−0.516313
$592$	732.675	0.0508662
$593$	8353.34	0.578467	0.289233	−	0.957259i	$-0.406600\pi$
$593$	8353.34	0.578467	0.289233	+	0.957259i	$0.406600\pi$
$594$	1599.38	0.110477
$595$	−8765.62	−0.603959
$596$	−11701.3	−0.804198
$597$	3906.50	0.267810
$598$	0	0
$599$	12644.8	0.862528	0.431264	−	0.902226i	$-0.358068\pi$
$599$	12644.8	0.862528	0.431264	+	0.902226i	$0.358068\pi$
$600$	3341.49	0.227360
$601$	−595.168	−0.0403950	−0.0201975	−	0.999796i	$-0.506430\pi$
$601$	−595.168	−0.0403950	−0.0201975	+	0.999796i	$0.506430\pi$
$602$	−1234.41	−0.0835725
$603$	−18090.2	−1.22171
$604$	−856.085	−0.0576715
$605$	−861.576	−0.0578976
$606$	−3851.25	−0.258162
$607$	−4842.08	−0.323779	−0.161890	−	0.986809i	$-0.551759\pi$
$607$	−4842.08	−0.323779	−0.161890	+	0.986809i	$0.551759\pi$
$608$	17125.1	1.14230
$609$	−11757.5	−0.782327
$610$	−5132.66	−0.340681
$611$	0	0
$612$	4865.87	0.321391
$613$	2020.18	0.133106	0.0665532	−	0.997783i	$-0.478800\pi$
$613$	2020.18	0.133106	0.0665532	+	0.997783i	$0.478800\pi$
$614$	6701.86	0.440497
$615$	−7724.19	−0.506455
$616$	−6410.29	−0.419282
$617$	−14504.7	−0.946416	−0.473208	−	0.880951i	$-0.656904\pi$
$617$	−14504.7	−0.946416	−0.473208	+	0.880951i	$0.656904\pi$
$618$	3895.02	0.253529
$619$	−5789.88	−0.375953	−0.187977	−	0.982174i	$-0.560193\pi$
$619$	−5789.88	−0.375953	−0.187977	+	0.982174i	$0.560193\pi$
$620$	−6137.10	−0.397535
$621$	3830.68	0.247536
$622$	9768.34	0.629702
$623$	−1665.07	−0.107078
$624$	0	0
$625$	−817.282	−0.0523060
$626$	−12971.1	−0.828165
$627$	−2782.42	−0.177224
$628$	−18145.2	−1.15298
$629$	823.970	0.0522318
$630$	−5742.99	−0.363184
$631$	6669.42	0.420769	0.210385	−	0.977619i	$-0.432528\pi$
$631$	6669.42	0.420769	0.210385	+	0.977619i	$0.432528\pi$
$632$	1582.77	0.0996192
$633$	12046.8	0.756426
$634$	−11000.9	−0.689120
$635$	−728.183	−0.0455072
$636$	1.20738	7.52764e−5 0
$637$	0	0
$638$	1737.70	0.107831
$639$	−4347.25	−0.269131
$640$	−10476.8	−0.647082
$641$	−19895.0	−1.22590	−0.612952	−	0.790120i	$-0.710018\pi$
$641$	−19895.0	−1.22590	−0.612952	+	0.790120i	$0.710018\pi$
$642$	1711.43	0.105210
$643$	8162.27	0.500604	0.250302	−	0.968168i	$-0.419470\pi$
$643$	8162.27	0.500604	0.250302	+	0.968168i	$0.419470\pi$
$644$	−6942.22	−0.424785
$645$	573.890	0.0350340
$646$	4183.81	0.254814
$647$	−15588.0	−0.947186	−0.473593	−	0.880744i	$-0.657043\pi$
$647$	−15588.0	−0.947186	−0.473593	+	0.880744i	$0.657043\pi$
$648$	3886.55	0.235614
$649$	−299.172	−0.0180948
$650$	0	0
$651$	11483.1	0.691337
$652$	17868.9	1.07331
$653$	−6690.97	−0.400977	−0.200488	−	0.979696i	$-0.564253\pi$
$653$	−6690.97	−0.400977	−0.200488	+	0.979696i	$0.564253\pi$
$654$	5174.61	0.309393
$655$	−4957.93	−0.295760
$656$	−13498.2	−0.803381
$657$	−15860.4	−0.941815
$658$	−17880.9	−1.05937
$659$	19689.4	1.16387	0.581934	−	0.813236i	$-0.302296\pi$
$659$	19689.4	1.16387	0.581934	+	0.813236i	$0.302296\pi$
$660$	1347.55	0.0794747
$661$	13667.9	0.804266	0.402133	−	0.915581i	$-0.368269\pi$
$661$	13667.9	0.804266	0.402133	+	0.915581i	$0.368269\pi$
$662$	−8729.46	−0.512508
$663$	0	0
$664$	−14120.1	−0.825248
$665$	23338.1	1.36092
$666$	539.841	0.0314091
$667$	4161.97	0.241607
$668$	10565.6	0.611972
$669$	8858.40	0.511936
$670$	7533.17	0.434376
$671$	6708.37	0.385952
$672$	15518.6	0.890839
$673$	21050.5	1.20570	0.602850	−	0.797855i	$-0.294032\pi$
$673$	21050.5	1.20570	0.602850	+	0.797855i	$0.294032\pi$
$674$	14191.2	0.811013
$675$	−9139.71	−0.521167
$676$	0	0
$677$	−3051.21	−0.173217	−0.0866083	−	0.996242i	$-0.527603\pi$
$677$	−3051.21	−0.173217	−0.0866083	+	0.996242i	$0.527603\pi$
$678$	2869.63	0.162548
$679$	6283.95	0.355163
$680$	−4481.23	−0.252717
$681$	15817.8	0.890075
$682$	−1697.15	−0.0952894
$683$	−2838.16	−0.159003	−0.0795017	−	0.996835i	$-0.525333\pi$
$683$	−2838.16	−0.159003	−0.0795017	+	0.996835i	$0.525333\pi$
$684$	−12955.2	−0.724202
$685$	17968.5	1.00225
$686$	−18113.9	−1.00815
$687$	17767.3	0.986704
$688$	1002.89	0.0555738
$689$	0	0
$690$	−682.893	−0.0376772
$691$	7044.52	0.387824	0.193912	−	0.981019i	$-0.437882\pi$
$691$	7044.52	0.387824	0.193912	+	0.981019i	$0.437882\pi$
$692$	23173.9	1.27303
$693$	7506.06	0.411446
$694$	230.017	0.0125811
$695$	15195.9	0.829371
$696$	−6010.76	−0.327352
$697$	−15180.2	−0.824950
$698$	1010.86	0.0548158
$699$	1866.59	0.101003
$700$	16563.6	0.894349
$701$	8276.14	0.445914	0.222957	−	0.974828i	$-0.428429\pi$
$701$	8276.14	0.445914	0.222957	+	0.974828i	$0.428429\pi$
$702$	0	0
$703$	−2193.79	−0.117696
$704$	559.559	0.0299562
$705$	8313.03	0.444095
$706$	−2914.21	−0.155351
$707$	−42220.1	−2.24590
$708$	467.920	0.0248383
$709$	34410.0	1.82270	0.911349	−	0.411634i	$-0.135042\pi$
$709$	34410.0	1.82270	0.911349	+	0.411634i	$0.135042\pi$
$710$	1810.29	0.0956886
$711$	−1853.33	−0.0977573
$712$	−851.233	−0.0448052
$713$	−4064.86	−0.213507
$714$	3791.33	0.198721
$715$	0	0
$716$	−10516.8	−0.548925
$717$	4360.91	0.227143
$718$	−14111.8	−0.733494
$719$	9987.78	0.518055	0.259027	−	0.965870i	$-0.416598\pi$
$719$	9987.78	0.518055	0.259027	+	0.965870i	$0.416598\pi$
$720$	4665.87	0.241509
$721$	42699.9	2.20559
$722$	−3032.04	−0.156289
$723$	−292.589	−0.0150505
$724$	5564.40	0.285635
$725$	−9930.13	−0.508684
$726$	372.651	0.0190501
$727$	−320.762	−0.0163637	−0.00818186	−	0.999967i	$-0.502604\pi$
$727$	−320.762	−0.0163637	−0.00818186	+	0.999967i	$0.502604\pi$
$728$	0	0
$729$	4103.16	0.208462
$730$	6604.61	0.334860
$731$	1127.85	0.0570659
$732$	−10492.2	−0.529788
$733$	−5279.38	−0.266028	−0.133014	−	0.991114i	$-0.542466\pi$
$733$	−5279.38	−0.266028	−0.133014	+	0.991114i	$0.542466\pi$
$734$	11393.1	0.572923
$735$	14785.1	0.741981
$736$	−5493.36	−0.275119
$737$	−9845.83	−0.492097
$738$	−9945.63	−0.496075
$739$	20900.3	1.04037	0.520183	−	0.854055i	$-0.325864\pi$
$739$	20900.3	1.04037	0.520183	+	0.854055i	$0.325864\pi$
$740$	1062.47	0.0527799
$741$	0	0
$742$	−2.80056	−0.000138561 0
$743$	−30573.6	−1.50960	−0.754802	−	0.655953i	$-0.772267\pi$
$743$	−30573.6	−1.50960	−0.754802	+	0.655953i	$0.772267\pi$
$744$	5870.51	0.289279
$745$	−12618.4	−0.620540
$746$	10882.8	0.534111
$747$	16533.7	0.809824
$748$	2648.31	0.129454
$749$	18761.9	0.915279
$750$	4370.50	0.212784
$751$	−5827.55	−0.283156	−0.141578	−	0.989927i	$-0.545218\pi$
$751$	−5827.55	−0.283156	−0.141578	+	0.989927i	$0.545218\pi$
$752$	14527.2	0.704460
$753$	9237.07	0.447035
$754$	0	0
$755$	−923.185	−0.0445009
$756$	−27423.4	−1.31928
$757$	11311.5	0.543097	0.271549	−	0.962425i	$-0.412464\pi$
$757$	11311.5	0.543097	0.271549	+	0.962425i	$0.412464\pi$
$758$	1345.07	0.0644525
$759$	892.539	0.0426839
$760$	11931.1	0.569456
$761$	31865.2	1.51789	0.758944	−	0.651156i	$-0.225715\pi$
$761$	31865.2	1.51789	0.758944	+	0.651156i	$0.225715\pi$
$762$	314.956	0.0149733
$763$	56727.6	2.69158
$764$	2045.01	0.0968400
$765$	5247.26	0.247994
$766$	−16810.2	−0.792921
$767$	0	0
$768$	3471.11	0.163090
$769$	−7829.78	−0.367164	−0.183582	−	0.983004i	$-0.558769\pi$
$769$	−7829.78	−0.367164	−0.183582	+	0.983004i	$0.558769\pi$
$770$	−3125.69	−0.146288
$771$	−12403.2	−0.579365
$772$	20289.3	0.945890
$773$	19778.8	0.920302	0.460151	−	0.887841i	$-0.347795\pi$
$773$	19778.8	0.920302	0.460151	+	0.887841i	$0.347795\pi$
$774$	738.938	0.0343160
$775$	9698.44	0.449520
$776$	3212.53	0.148612
$777$	−1987.99	−0.0917873
$778$	−5034.26	−0.231988
$779$	40416.6	1.85889
$780$	0	0
$781$	−2366.04	−0.108404
$782$	−1342.07	−0.0613714
$783$	16440.7	0.750375
$784$	25837.4	1.17699
$785$	−19567.5	−0.889673
$786$	2144.42	0.0973142
$787$	−39238.2	−1.77724	−0.888622	−	0.458641i	$-0.848336\pi$
$787$	−39238.2	−1.77724	−0.888622	+	0.458641i	$0.848336\pi$
$788$	−18798.5	−0.849833
$789$	−1044.28	−0.0471197
$790$	771.768	0.0347573
$791$	31458.9	1.41409
$792$	3837.31	0.172163
$793$	0	0
$794$	−701.409	−0.0313502
$795$	1.30202	5.80852e−5 0
$796$	9899.58	0.440806
$797$	−10077.1	−0.447865	−0.223933	−	0.974605i	$-0.571890\pi$
$797$	−10077.1	−0.447865	−0.223933	+	0.974605i	$0.571890\pi$
$798$	−10094.3	−0.447786
$799$	16337.4	0.723374
$800$	13106.7	0.579240
$801$	996.743	0.0439678
$802$	−10489.2	−0.461830
$803$	−8632.20	−0.379357
$804$	15399.4	0.675491
$805$	−7486.35	−0.327775
$806$	0	0
$807$	8610.63	0.375599
$808$	−21584.1	−0.939759
$809$	−27246.2	−1.18409	−0.592044	−	0.805906i	$-0.701679\pi$
$809$	−27246.2	−1.18409	−0.592044	+	0.805906i	$0.701679\pi$
$810$	1895.10	0.0822062
$811$	−27686.8	−1.19878	−0.599392	−	0.800456i	$-0.704591\pi$
$811$	−27686.8	−1.19878	−0.599392	+	0.800456i	$0.704591\pi$
$812$	−29795.0	−1.28768
$813$	−8536.43	−0.368248
$814$	293.815	0.0126514
$815$	19269.5	0.828196
$816$	−3080.26	−0.132145
$817$	−3002.87	−0.128589
$818$	5427.68	0.231998
$819$	0	0
$820$	−19574.1	−0.833607
$821$	28352.4	1.20525	0.602623	−	0.798026i	$-0.294122\pi$
$821$	28352.4	1.20525	0.602623	+	0.798026i	$0.294122\pi$
$822$	−7771.77	−0.329771
$823$	−8540.10	−0.361712	−0.180856	−	0.983510i	$-0.557887\pi$
$823$	−8540.10	−0.361712	−0.180856	+	0.983510i	$0.557887\pi$
$824$	21829.4	0.922893
$825$	−2129.53	−0.0898674
$826$	−1085.36	−0.0457196
$827$	2208.51	0.0928625	0.0464313	−	0.998921i	$-0.485215\pi$
$827$	2208.51	0.0928625	0.0464313	+	0.998921i	$0.485215\pi$
$828$	4155.74	0.174422
$829$	−3177.16	−0.133109	−0.0665544	−	0.997783i	$-0.521201\pi$
$829$	−3177.16	−0.133109	−0.0665544	+	0.997783i	$0.521201\pi$
$830$	−6885.01	−0.287930
$831$	17424.6	0.727379
$832$	0	0
$833$	29056.8	1.20859
$834$	−6572.57	−0.272889
$835$	11393.8	0.472213
$836$	−7051.02	−0.291704
$837$	−16057.1	−0.663101
$838$	13352.6	0.550427
$839$	31076.1	1.27874	0.639371	−	0.768898i	$-0.279195\pi$
$839$	31076.1	1.27874	0.639371	+	0.768898i	$0.279195\pi$
$840$	10811.9	0.444101
$841$	−6526.44	−0.267597
$842$	−6817.77	−0.279045
$843$	−19476.8	−0.795748
$844$	30528.2	1.24505
$845$	0	0
$846$	10703.8	0.434993
$847$	4085.27	0.165728
$848$	2.27531	9.21397e−5 0
$849$	−3920.28	−0.158473
$850$	3202.08	0.129212
$851$	703.718	0.0283468
$852$	3700.61	0.148804
$853$	−28780.5	−1.15525	−0.577624	−	0.816303i	$-0.696020\pi$
$853$	−28780.5	−1.15525	−0.577624	+	0.816303i	$0.696020\pi$
$854$	24337.1	0.975175
$855$	−13970.6	−0.558813
$856$	9591.60	0.382984
$857$	29741.3	1.18546	0.592732	−	0.805400i	$-0.298049\pi$
$857$	29741.3	1.18546	0.592732	+	0.805400i	$0.298049\pi$
$858$	0	0
$859$	−43171.4	−1.71477	−0.857386	−	0.514674i	$-0.827913\pi$
$859$	−43171.4	−1.71477	−0.857386	+	0.514674i	$0.827913\pi$
$860$	1454.31	0.0576647
$861$	36625.2	1.44969
$862$	15463.5	0.611010
$863$	6948.03	0.274060	0.137030	−	0.990567i	$-0.456244\pi$
$863$	6948.03	0.274060	0.137030	+	0.990567i	$0.456244\pi$
$864$	−21700.0	−0.854456
$865$	24990.3	0.982306
$866$	−2699.95	−0.105945
$867$	9337.23	0.365754
$868$	29099.8	1.13792
$869$	−1008.70	−0.0393760
$870$	−2930.88	−0.114214
$871$	0	0
$872$	29000.8	1.12625
$873$	−3761.68	−0.145835
$874$	3573.22	0.138291
$875$	47912.4	1.85113
$876$	13501.2	0.520735
$877$	11310.0	0.435475	0.217737	−	0.976007i	$-0.430132\pi$
$877$	11310.0	0.435475	0.217737	+	0.976007i	$0.430132\pi$
$878$	−8159.89	−0.313648
$879$	15345.8	0.588853
$880$	2539.46	0.0972785
$881$	22023.3	0.842206	0.421103	−	0.907013i	$-0.361643\pi$
$881$	22023.3	0.842206	0.421103	+	0.907013i	$0.361643\pi$
$882$	19037.2	0.726775
$883$	−19786.0	−0.754080	−0.377040	−	0.926197i	$-0.623058\pi$
$883$	−19786.0	−0.754080	−0.377040	+	0.926197i	$0.623058\pi$
$884$	0	0
$885$	504.595	0.0191659
$886$	1372.61	0.0520471
$887$	−2157.27	−0.0816619	−0.0408309	−	0.999166i	$-0.513001\pi$
$887$	−2157.27	−0.0816619	−0.0408309	+	0.999166i	$0.513001\pi$
$888$	−1016.32	−0.0384069
$889$	3452.76	0.130261
$890$	−415.066	−0.0156326
$891$	−2476.89	−0.0931302
$892$	22448.3	0.842630
$893$	−43497.7	−1.63001
$894$	5457.75	0.204177
$895$	−11341.1	−0.423565
$896$	49677.0	1.85222
$897$	0	0
$898$	−19545.4	−0.726322
$899$	−17445.8	−0.647219
$900$	−9915.26	−0.367232
$901$	2.55882	9.46135e−5 0
$902$	−5413.03	−0.199816
$903$	−2721.17	−0.100282
$904$	16082.7	0.591705
$905$	6000.54	0.220403
$906$	399.299	0.0146422
$907$	−38801.6	−1.42049	−0.710246	−	0.703954i	$-0.751416\pi$
$907$	−38801.6	−1.42049	−0.710246	+	0.703954i	$0.751416\pi$
$908$	40084.5	1.46503
$909$	25273.7	0.922195
$910$	0	0
$911$	48686.3	1.77064	0.885319	−	0.464985i	$-0.153940\pi$
$911$	48686.3	1.77064	0.885319	+	0.464985i	$0.153940\pi$
$912$	8201.06	0.297768
$913$	8998.69	0.326192
$914$	18887.3	0.683520
$915$	−11314.6	−0.408798
$916$	45024.7	1.62408
$917$	23508.6	0.846590
$918$	−5301.50	−0.190605
$919$	−26065.4	−0.935601	−0.467801	−	0.883834i	$-0.654953\pi$
$919$	−26065.4	−0.935601	−0.467801	+	0.883834i	$0.654953\pi$
$920$	−3827.23	−0.137152
$921$	14773.8	0.528571
$922$	3248.53	0.116035
$923$	0	0
$924$	−6389.57	−0.227491
$925$	−1679.02	−0.0596818
$926$	18164.1	0.644610
$927$	−25560.9	−0.905644
$928$	−23576.7	−0.833990
$929$	−48674.7	−1.71902	−0.859508	−	0.511123i	$-0.829230\pi$
$929$	−48674.7	−1.71902	−0.859508	+	0.511123i	$0.829230\pi$
$930$	2862.49	0.100930
$931$	−77362.6	−2.72337
$932$	4730.18	0.166247
$933$	21533.7	0.755607
$934$	9938.86	0.348190
$935$	2855.88	0.0998903
$936$	0	0
$937$	−8963.97	−0.312530	−0.156265	−	0.987715i	$-0.549945\pi$
$937$	−8963.97	−0.312530	−0.156265	+	0.987715i	$0.549945\pi$
$938$	−35719.4	−1.24337
$939$	−28594.1	−0.993750
$940$	21066.3	0.730964
$941$	−11706.3	−0.405541	−0.202771	−	0.979226i	$-0.564995\pi$
$941$	−11706.3	−0.405541	−0.202771	+	0.979226i	$0.564995\pi$
$942$	8463.38	0.292730
$943$	−12964.8	−0.447710
$944$	881.795	0.0304025
$945$	−29572.8	−1.01799
$946$	402.176	0.0138223
$947$	6267.57	0.215067	0.107534	−	0.994201i	$-0.465705\pi$
$947$	6267.57	0.215067	0.107534	+	0.994201i	$0.465705\pi$
$948$	1577.66	0.0540506
$949$	0	0
$950$	−8525.42	−0.291159
$951$	−24250.8	−0.826905
$952$	21248.3	0.723384
$953$	−29202.8	−0.992626	−0.496313	−	0.868144i	$-0.665313\pi$
$953$	−29202.8	−0.992626	−0.496313	+	0.868144i	$0.665313\pi$
$954$	1.67647	5.68948e−5 0
$955$	2205.29	0.0747242
$956$	11051.1	0.373869
$957$	3830.65	0.129391
$958$	8673.74	0.292522
$959$	−85199.6	−2.86886
$960$	−943.776	−0.0317294
$961$	−12752.3	−0.428058
$962$	0	0
$963$	−11231.2	−0.375826
$964$	−741.459	−0.0247726
$965$	21879.6	0.729874
$966$	3238.02	0.107848
$967$	−21992.9	−0.731381	−0.365691	−	0.930737i	$-0.619167\pi$
$967$	−21992.9	−0.731381	−0.365691	+	0.930737i	$0.619167\pi$
$968$	2088.50	0.0693461
$969$	9222.95	0.305762
$970$	1566.45	0.0518511
$971$	−35150.6	−1.16173	−0.580863	−	0.814001i	$-0.697285\pi$
$971$	−35150.6	−1.16173	−0.580863	+	0.814001i	$0.697285\pi$
$972$	25804.5	0.851523
$973$	−72053.1	−2.37401
$974$	9512.57	0.312939
$975$	0	0
$976$	−19772.6	−0.648470
$977$	22263.8	0.729049	0.364525	−	0.931194i	$-0.381232\pi$
$977$	22263.8	0.729049	0.364525	+	0.931194i	$0.381232\pi$
$978$	−8334.49	−0.272503
$979$	542.489	0.0177099
$980$	37467.3	1.22128
$981$	−33958.2	−1.10520
$982$	−17531.2	−0.569698
$983$	−20818.3	−0.675484	−0.337742	−	0.941239i	$-0.609663\pi$
$983$	−20818.3	−0.675484	−0.337742	+	0.941239i	$0.609663\pi$
$984$	18723.8	0.606599
$985$	−20271.9	−0.655753
$986$	−5759.99	−0.186040
$987$	−39417.2	−1.27119
$988$	0	0
$989$	963.252	0.0309703
$990$	1871.09	0.0600679
$991$	35089.4	1.12477	0.562387	−	0.826874i	$-0.309883\pi$
$991$	35089.4	1.12477	0.562387	+	0.826874i	$0.309883\pi$
$992$	23026.6	0.736991
$993$	−19243.5	−0.614980
$994$	−8583.70	−0.273902
$995$	10675.5	0.340137
$996$	−14074.4	−0.447756
$997$	−13307.3	−0.422715	−0.211358	−	0.977409i	$-0.567788\pi$
$997$	−13307.3	−0.422715	−0.211358	+	0.977409i	$0.567788\pi$
$998$	19190.7	0.608688
$999$	2779.85	0.0880385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.o.1.16	yes	39
13.12	even	2		1859.4.a.n.1.24	✓	39

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.n.1.24	✓	39	13.12	even	2
1859.4.a.o.1.16	yes	39	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-1.18198 q^{2} -2.60560 q^{3} -6.60292 q^{4} -7.12046 q^{5} +3.07976 q^{6} +33.7625 q^{7} +17.2604 q^{8} -20.2109 q^{9} +O(q^{10})\)	\(q-1.18198 q^{2} -2.60560 q^{3} -6.60292 q^{4} -7.12046 q^{5} +3.07976 q^{6} +33.7625 q^{7} +17.2604 q^{8} -20.2109 q^{9} +8.41624 q^{10} -11.0000 q^{11} +17.2046 q^{12} -39.9066 q^{14} +18.5531 q^{15} +32.4220 q^{16} +36.4619 q^{17} +23.8888 q^{18} -97.0784 q^{19} +47.0159 q^{20} -87.9716 q^{21} +13.0018 q^{22} +31.1406 q^{23} -44.9736 q^{24} -74.2990 q^{25} +123.013 q^{27} -222.931 q^{28} +133.651 q^{29} -21.9293 q^{30} -130.533 q^{31} -176.405 q^{32} +28.6616 q^{33} -43.0972 q^{34} -240.405 q^{35} +133.451 q^{36} +22.5981 q^{37} +114.745 q^{38} -122.902 q^{40} -416.330 q^{41} +103.981 q^{42} +30.9324 q^{43} +72.6322 q^{44} +143.911 q^{45} -36.8075 q^{46} +448.067 q^{47} -84.4787 q^{48} +796.908 q^{49} +87.8199 q^{50} -95.0051 q^{51} +0.0701780 q^{53} -145.398 q^{54} +78.3251 q^{55} +582.753 q^{56} +252.947 q^{57} -157.973 q^{58} +27.1974 q^{59} -122.505 q^{60} -609.852 q^{61} +154.287 q^{62} -682.370 q^{63} -50.8690 q^{64} -33.8774 q^{66} +895.075 q^{67} -240.755 q^{68} -81.1399 q^{69} +284.154 q^{70} +215.095 q^{71} -348.847 q^{72} +784.746 q^{73} -26.7105 q^{74} +193.593 q^{75} +641.002 q^{76} -371.388 q^{77} +91.6999 q^{79} -230.860 q^{80} +225.172 q^{81} +492.093 q^{82} -818.063 q^{83} +580.870 q^{84} -259.626 q^{85} -36.5614 q^{86} -348.241 q^{87} -189.864 q^{88} -49.3172 q^{89} -170.099 q^{90} -205.619 q^{92} +340.115 q^{93} -529.607 q^{94} +691.243 q^{95} +459.641 q^{96} +186.122 q^{97} -941.929 q^{98} +222.319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9}+O(q^{10}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9	\( 39 q - 23 q^{3} + 114 q^{4} + 23 q^{5} + 77 q^{6} - 4 q^{7} - 21 q^{8} + 260 q^{9} - 158 q^{10} - 429 q^{11} - 351 q^{12} - 176 q^{14} + 30 q^{15} + 230 q^{16} - 244 q^{17} + 21 q^{18} - 70 q^{19} + 366 q^{20} - 142 q^{21} - 47 q^{23} + 846 q^{24} + 322 q^{25} - 416 q^{27} + 1131 q^{28} - 838 q^{29} - 293 q^{30} + 507 q^{31} - 1433 q^{32} + 253 q^{33} + 166 q^{34} - 498 q^{35} + 815 q^{36} + 89 q^{37} + 81 q^{38} - 2917 q^{40} + 618 q^{41} - 318 q^{42} - 1064 q^{43} - 1254 q^{44} + 238 q^{45} - 1331 q^{46} + 1499 q^{47} - 1460 q^{48} - 413 q^{49} - 2459 q^{50} - 2350 q^{51} - 2745 q^{53} - 845 q^{54} - 253 q^{55} - 2904 q^{56} + 1450 q^{57} - 2509 q^{58} + 2285 q^{59} - 3566 q^{60} - 6218 q^{61} - 911 q^{62} - 1930 q^{63} + 67 q^{64} - 847 q^{66} + 546 q^{67} - 170 q^{68} - 5254 q^{69} - 2195 q^{70} - 263 q^{71} - 2393 q^{72} - 1148 q^{73} + 775 q^{74} - 5385 q^{75} - 7247 q^{76} + 44 q^{77} - 3666 q^{79} + 5594 q^{80} - 1901 q^{81} - 4414 q^{82} + 2722 q^{83} - 9971 q^{84} + 1858 q^{85} + 2478 q^{86} - 2284 q^{87} + 231 q^{88} + 13 q^{89} - 6771 q^{90} - 2232 q^{92} - 1082 q^{93} - 7330 q^{94} - 2352 q^{95} + 5770 q^{96} - 1197 q^{97} + 6813 q^{98} - 2860 q^{99}+O(q^{100}) \) 39 * q - 23 * q^3 + 114 * q^4 + 23 * q^5 + 77 * q^6 - 4 * q^7 - 21 * q^8 + 260 * q^9 - 158 * q^10 - 429 * q^11 - 351 * q^12 - 176 * q^14 + 30 * q^15 + 230 * q^16 - 244 * q^17 + 21 * q^18 - 70 * q^19 + 366 * q^20 - 142 * q^21 - 47 * q^23 + 846 * q^24 + 322 * q^25 - 416 * q^27 + 1131 * q^28 - 838 * q^29 - 293 * q^30 + 507 * q^31 - 1433 * q^32 + 253 * q^33 + 166 * q^34 - 498 * q^35 + 815 * q^36 + 89 * q^37 + 81 * q^38 - 2917 * q^40 + 618 * q^41 - 318 * q^42 - 1064 * q^43 - 1254 * q^44 + 238 * q^45 - 1331 * q^46 + 1499 * q^47 - 1460 * q^48 - 413 * q^49 - 2459 * q^50 - 2350 * q^51 - 2745 * q^53 - 845 * q^54 - 253 * q^55 - 2904 * q^56 + 1450 * q^57 - 2509 * q^58 + 2285 * q^59 - 3566 * q^60 - 6218 * q^61 - 911 * q^62 - 1930 * q^63 + 67 * q^64 - 847 * q^66 + 546 * q^67 - 170 * q^68 - 5254 * q^69 - 2195 * q^70 - 263 * q^71 - 2393 * q^72 - 1148 * q^73 + 775 * q^74 - 5385 * q^75 - 7247 * q^76 + 44 * q^77 - 3666 * q^79 + 5594 * q^80 - 1901 * q^81 - 4414 * q^82 + 2722 * q^83 - 9971 * q^84 + 1858 * q^85 + 2478 * q^86 - 2284 * q^87 + 231 * q^88 + 13 * q^89 - 6771 * q^90 - 2232 * q^92 - 1082 * q^93 - 7330 * q^94 - 2352 * q^95 + 5770 * q^96 - 1197 * q^97 + 6813 * q^98 - 2860 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

Properties

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