LMFDB - Embedded newform 1859.4.a.p.1.1

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:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
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)

$f(q)$	$=$	$q-5.64970 q^{2} -1.71534 q^{3} +23.9192 q^{4} +7.89488 q^{5} +9.69115 q^{6} -11.5333 q^{7} -89.9385 q^{8} -24.0576 q^{9} +O(q^{10})$	\(q-5.64970 q^{2} -1.71534 q^{3} +23.9192 q^{4} +7.89488 q^{5} +9.69115 q^{6} -11.5333 q^{7} -89.9385 q^{8} -24.0576 q^{9} -44.6038 q^{10} -11.0000 q^{11} -41.0294 q^{12} +65.1596 q^{14} -13.5424 q^{15} +316.773 q^{16} +41.7366 q^{17} +135.918 q^{18} +43.5756 q^{19} +188.839 q^{20} +19.7835 q^{21} +62.1467 q^{22} +70.7907 q^{23} +154.275 q^{24} -62.6708 q^{25} +87.5810 q^{27} -275.866 q^{28} +258.458 q^{29} +76.5105 q^{30} -272.158 q^{31} -1070.16 q^{32} +18.8687 q^{33} -235.799 q^{34} -91.0539 q^{35} -575.438 q^{36} +239.916 q^{37} -246.189 q^{38} -710.054 q^{40} +212.648 q^{41} -111.771 q^{42} -131.113 q^{43} -263.111 q^{44} -189.932 q^{45} -399.946 q^{46} -241.485 q^{47} -543.372 q^{48} -209.983 q^{49} +354.072 q^{50} -71.5923 q^{51} -110.725 q^{53} -494.807 q^{54} -86.8437 q^{55} +1037.29 q^{56} -74.7468 q^{57} -1460.21 q^{58} -870.174 q^{59} -323.922 q^{60} +518.094 q^{61} +1537.61 q^{62} +277.463 q^{63} +3511.93 q^{64} -106.603 q^{66} +242.715 q^{67} +998.304 q^{68} -121.430 q^{69} +514.427 q^{70} -221.064 q^{71} +2163.71 q^{72} -120.442 q^{73} -1355.46 q^{74} +107.502 q^{75} +1042.29 q^{76} +126.866 q^{77} +376.290 q^{79} +2500.88 q^{80} +499.325 q^{81} -1201.40 q^{82} -784.899 q^{83} +473.204 q^{84} +329.506 q^{85} +740.749 q^{86} -443.343 q^{87} +989.324 q^{88} -1396.80 q^{89} +1073.06 q^{90} +1693.25 q^{92} +466.843 q^{93} +1364.32 q^{94} +344.024 q^{95} +1835.69 q^{96} +967.420 q^{97} +1186.34 q^{98} +264.634 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9} + 212 q^{10} - 561 q^{11} + 209 q^{12} + 280 q^{14} - 284 q^{15} + 1246 q^{16} + 164 q^{17} + 189 q^{18} - 26 q^{19} - 438 q^{20} - 134 q^{21} + 373 q^{23} + 354 q^{24} + 2048 q^{25} + 1470 q^{27} + 1245 q^{28} + 898 q^{29} + 427 q^{30} - 767 q^{31} - 1127 q^{32} - 231 q^{33} - 206 q^{34} + 54 q^{35} + 3415 q^{36} - 395 q^{37} + 1577 q^{38} + 3253 q^{40} + 354 q^{41} + 942 q^{42} + 484 q^{43} - 2574 q^{44} - 1452 q^{45} + 2117 q^{46} - 1925 q^{47} + 1780 q^{48} + 4535 q^{49} + 1093 q^{50} + 230 q^{51} + 1387 q^{53} + 5271 q^{54} + 451 q^{55} + 2568 q^{56} + 5738 q^{57} - 3695 q^{58} - 1145 q^{59} + 1590 q^{60} + 5382 q^{61} - 395 q^{62} - 710 q^{63} + 9839 q^{64} - 803 q^{66} + 210 q^{67} + 1742 q^{68} + 7028 q^{69} + 6747 q^{70} - 3693 q^{71} + 12481 q^{72} - 968 q^{73} + 1735 q^{74} - 727 q^{75} + 2801 q^{76} + 44 q^{77} + 4234 q^{79} - 2390 q^{80} + 7743 q^{81} + 4770 q^{82} + 2798 q^{83} - 14821 q^{84} + 1802 q^{85} - 6558 q^{86} + 1896 q^{87} - 231 q^{88} - 3927 q^{89} + 1927 q^{90} + 1984 q^{92} + 1332 q^{93} + 7590 q^{94} + 4944 q^{95} + 7280 q^{96} - 3913 q^{97} + 15201 q^{98} - 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9 + 212 * q^10 - 561 * q^11 + 209 * q^12 + 280 * q^14 - 284 * q^15 + 1246 * q^16 + 164 * q^17 + 189 * q^18 - 26 * q^19 - 438 * q^20 - 134 * q^21 + 373 * q^23 + 354 * q^24 + 2048 * q^25 + 1470 * q^27 + 1245 * q^28 + 898 * q^29 + 427 * q^30 - 767 * q^31 - 1127 * q^32 - 231 * q^33 - 206 * q^34 + 54 * q^35 + 3415 * q^36 - 395 * q^37 + 1577 * q^38 + 3253 * q^40 + 354 * q^41 + 942 * q^42 + 484 * q^43 - 2574 * q^44 - 1452 * q^45 + 2117 * q^46 - 1925 * q^47 + 1780 * q^48 + 4535 * q^49 + 1093 * q^50 + 230 * q^51 + 1387 * q^53 + 5271 * q^54 + 451 * q^55 + 2568 * q^56 + 5738 * q^57 - 3695 * q^58 - 1145 * q^59 + 1590 * q^60 + 5382 * q^61 - 395 * q^62 - 710 * q^63 + 9839 * q^64 - 803 * q^66 + 210 * q^67 + 1742 * q^68 + 7028 * q^69 + 6747 * q^70 - 3693 * q^71 + 12481 * q^72 - 968 * q^73 + 1735 * q^74 - 727 * q^75 + 2801 * q^76 + 44 * q^77 + 4234 * q^79 - 2390 * q^80 + 7743 * q^81 + 4770 * q^82 + 2798 * q^83 - 14821 * q^84 + 1802 * q^85 - 6558 * q^86 + 1896 * q^87 - 231 * q^88 - 3927 * q^89 + 1927 * q^90 + 1984 * q^92 + 1332 * q^93 + 7590 * q^94 + 4944 * q^95 + 7280 * q^96 - 3913 * q^97 + 15201 * q^98 - 6534 * 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 $

$2$	−5.64970	−1.99747	−0.998736	−	0.0502633i	$-0.983994\pi$
$2$	−5.64970	−1.99747	−0.998736	+	0.0502633i	$0.983994\pi$
$3$	−1.71534	−0.330117	−0.165058	−	0.986284i	$-0.552781\pi$
$3$	−1.71534	−0.330117	−0.165058	+	0.986284i	$0.552781\pi$
$4$	23.9192	2.98989
$5$	7.89488	0.706140	0.353070	−	0.935597i	$-0.385138\pi$
$5$	7.89488	0.706140	0.353070	+	0.935597i	$0.385138\pi$
$6$	9.69115	0.659399
$7$	−11.5333	−0.622738	−0.311369	−	0.950289i	$-0.600788\pi$
$7$	−11.5333	−0.622738	−0.311369	+	0.950289i	$0.600788\pi$
$8$	−89.9385	−3.97476
$9$	−24.0576	−0.891023
$10$	−44.6038	−1.41049
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−41.0294	−0.987014
$13$	0	0
$13$	0	0
$14$	65.1596	1.24390
$15$	−13.5424	−0.233109
$16$	316.773	4.94957
$17$	41.7366	0.595448	0.297724	−	0.954652i	$-0.403773\pi$
$17$	41.7366	0.595448	0.297724	+	0.954652i	$0.403773\pi$
$18$	135.918	1.77979
$19$	43.5756	0.526154	0.263077	−	0.964775i	$-0.415263\pi$
$19$	43.5756	0.526154	0.263077	+	0.964775i	$0.415263\pi$
$20$	188.839	2.11128
$21$	19.7835	0.205576
$22$	62.1467	0.602260
$23$	70.7907	0.641777	0.320889	−	0.947117i	$-0.396019\pi$
$23$	70.7907	0.641777	0.320889	+	0.947117i	$0.396019\pi$
$24$	154.275	1.31213
$25$	−62.6708	−0.501367
$26$	0	0
$27$	87.5810	0.624258
$28$	−275.866	−1.86192
$29$	258.458	1.65498	0.827492	−	0.561478i	$-0.189767\pi$
$29$	258.458	1.65498	0.827492	+	0.561478i	$0.189767\pi$
$30$	76.5105	0.465628
$31$	−272.158	−1.57681	−0.788404	−	0.615158i	$-0.789092\pi$
$31$	−272.158	−1.57681	−0.788404	+	0.615158i	$0.789092\pi$
$32$	−1070.16	−5.91188
$33$	18.8687	0.0995339
$34$	−235.799	−1.18939
$35$	−91.0539	−0.439740
$36$	−575.438	−2.66406
$37$	239.916	1.06600	0.533000	−	0.846115i	$-0.321065\pi$
$37$	239.916	1.06600	0.533000	+	0.846115i	$0.321065\pi$
$38$	−246.189	−1.05098
$39$	0	0
$40$	−710.054	−2.80673
$41$	212.648	0.810000	0.405000	−	0.914317i	$-0.367272\pi$
$41$	212.648	0.810000	0.405000	+	0.914317i	$0.367272\pi$
$42$	−111.771	−0.410633
$43$	−131.113	−0.464989	−0.232494	−	0.972598i	$-0.574689\pi$
$43$	−131.113	−0.464989	−0.232494	+	0.972598i	$0.574689\pi$
$44$	−263.111	−0.901487
$45$	−189.932	−0.629187
$46$	−399.946	−1.28193
$47$	−241.485	−0.749453	−0.374726	−	0.927135i	$-0.622263\pi$
$47$	−241.485	−0.749453	−0.374726	+	0.927135i	$0.622263\pi$
$48$	−543.372	−1.63394
$49$	−209.983	−0.612197
$50$	354.072	1.00147
$51$	−71.5923	−0.196567
$52$	0	0
$53$	−110.725	−0.286968	−0.143484	−	0.989653i	$-0.545831\pi$
$53$	−110.725	−0.286968	−0.143484	+	0.989653i	$0.545831\pi$
$54$	−494.807	−1.24694
$55$	−86.8437	−0.212909
$56$	1037.29	2.47523
$57$	−74.7468	−0.173692
$58$	−1460.21	−3.30578
$59$	−870.174	−1.92012	−0.960060	−	0.279796i	$-0.909733\pi$
$59$	−870.174	−1.92012	−0.960060	+	0.279796i	$0.909733\pi$
$60$	−323.922	−0.696970
$61$	518.094	1.08746	0.543730	−	0.839260i	$-0.317011\pi$
$61$	518.094	1.08746	0.543730	+	0.839260i	$0.317011\pi$
$62$	1537.61	3.14963
$63$	277.463	0.554874
$64$	3511.93	6.85924
$65$	0	0
$66$	−106.603	−0.198816
$67$	242.715	0.442573	0.221287	−	0.975209i	$-0.428974\pi$
$67$	242.715	0.442573	0.221287	+	0.975209i	$0.428974\pi$
$68$	998.304	1.78033
$69$	−121.430	−0.211861
$70$	514.427	0.878369
$71$	−221.064	−0.369514	−0.184757	−	0.982784i	$-0.559150\pi$
$71$	−221.064	−0.369514	−0.184757	+	0.982784i	$0.559150\pi$
$72$	2163.71	3.54160
$73$	−120.442	−0.193105	−0.0965526	−	0.995328i	$-0.530782\pi$
$73$	−120.442	−0.193105	−0.0965526	+	0.995328i	$0.530782\pi$
$74$	−1355.46	−2.12931
$75$	107.502	0.165510
$76$	1042.29	1.57315
$77$	126.866	0.187763
$78$	0	0
$79$	376.290	0.535898	0.267949	−	0.963433i	$-0.413654\pi$
$79$	376.290	0.535898	0.267949	+	0.963433i	$0.413654\pi$
$80$	2500.88	3.49509
$81$	499.325	0.684945
$82$	−1201.40	−1.61795
$83$	−784.899	−1.03800	−0.518999	−	0.854775i	$-0.673695\pi$
$83$	−784.899	−1.03800	−0.518999	+	0.854775i	$0.673695\pi$
$84$	473.204	0.614652
$85$	329.506	0.420469
$86$	740.749	0.928802
$87$	−443.343	−0.546338
$88$	989.324	1.19843
$89$	−1396.80	−1.66360	−0.831802	−	0.555073i	$-0.812690\pi$
$89$	−1396.80	−1.66360	−0.831802	+	0.555073i	$0.812690\pi$
$90$	1073.06	1.25678
$91$	0	0
$92$	1693.25	1.91885
$93$	466.843	0.520531
$94$	1364.32	1.49701
$95$	344.024	0.371538
$96$	1835.69	1.95161
$97$	967.420	1.01265	0.506323	−	0.862344i	$-0.331004\pi$
$97$	967.420	1.01265	0.506323	+	0.862344i	$0.331004\pi$
$98$	1186.34	1.22285
$99$	264.634	0.268654
$100$	−1499.03	−1.49903
$101$	731.314	0.720480	0.360240	−	0.932860i	$-0.382695\pi$
$101$	731.314	0.720480	0.360240	+	0.932860i	$0.382695\pi$
$102$	404.475	0.392638
$103$	−594.079	−0.568314	−0.284157	−	0.958778i	$-0.591714\pi$
$103$	−594.079	−0.568314	−0.284157	+	0.958778i	$0.591714\pi$
$104$	0	0
$105$	156.188	0.145166
$106$	625.566	0.573210
$107$	−1320.08	−1.19268	−0.596342	−	0.802730i	$-0.703380\pi$
$107$	−1320.08	−1.19268	−0.596342	+	0.802730i	$0.703380\pi$
$108$	2094.86	1.86647
$109$	1889.02	1.65995	0.829977	−	0.557798i	$-0.188354\pi$
$109$	1889.02	1.65995	0.829977	+	0.557798i	$0.188354\pi$
$110$	490.641	0.425280
$111$	−411.537	−0.351905
$112$	−3653.43	−3.08229
$113$	−1256.06	−1.04566	−0.522832	−	0.852436i	$-0.675125\pi$
$113$	−1256.06	−1.04566	−0.522832	+	0.852436i	$0.675125\pi$
$114$	422.298	0.346946
$115$	558.884	0.453184
$116$	6182.11	4.94823
$117$	0	0
$118$	4916.23	3.83538
$119$	−481.360	−0.370808
$120$	1217.98	0.926550
$121$	121.000	0.0909091
$122$	−2927.08	−2.17217
$123$	−364.763	−0.267395
$124$	−6509.79	−4.71449
$125$	−1481.64	−1.06017
$126$	−1567.59	−1.10835
$127$	−662.292	−0.462748	−0.231374	−	0.972865i	$-0.574322\pi$
$127$	−662.292	−0.462748	−0.231374	+	0.972865i	$0.574322\pi$
$128$	−11280.0	−7.78925
$129$	224.903	0.153501
$130$	0	0
$131$	−553.678	−0.369275	−0.184638	−	0.982807i	$-0.559111\pi$
$131$	−553.678	−0.369275	−0.184638	+	0.982807i	$0.559111\pi$
$132$	451.324	0.297596
$133$	−502.570	−0.327656
$134$	−1371.27	−0.884027
$135$	691.442	0.440814
$136$	−3753.73	−2.36676
$137$	452.459	0.282162	0.141081	−	0.989998i	$-0.454942\pi$
$137$	452.459	0.282162	0.141081	+	0.989998i	$0.454942\pi$
$138$	686.043	0.423187
$139$	2489.38	1.51904	0.759520	−	0.650484i	$-0.225434\pi$
$139$	2489.38	1.51904	0.759520	+	0.650484i	$0.225434\pi$
$140$	−2177.93	−1.31478
$141$	414.229	0.247407
$142$	1248.95	0.738093
$143$	0	0
$144$	−7620.80	−4.41018
$145$	2040.50	1.16865
$146$	680.462	0.385722
$147$	360.192	0.202096
$148$	5738.60	3.18723
$149$	1759.07	0.967171	0.483586	−	0.875297i	$-0.339334\pi$
$149$	1759.07	0.967171	0.483586	+	0.875297i	$0.339334\pi$
$150$	−607.352	−0.330601
$151$	−2770.90	−1.49333	−0.746665	−	0.665200i	$-0.768346\pi$
$151$	−2770.90	−1.49333	−0.746665	+	0.665200i	$0.768346\pi$
$152$	−3919.13	−2.09134
$153$	−1004.08	−0.530558
$154$	−716.756	−0.375051
$155$	−2148.66	−1.11345
$156$	0	0
$157$	−3112.82	−1.58236	−0.791178	−	0.611586i	$-0.790532\pi$
$157$	−3112.82	−1.58236	−0.791178	+	0.611586i	$0.790532\pi$
$158$	−2125.93	−1.07044
$159$	189.931	0.0947329
$160$	−8448.82	−4.17461
$161$	−816.448	−0.399659
$162$	−2821.04	−1.36816
$163$	677.014	0.325324	0.162662	−	0.986682i	$-0.447992\pi$
$163$	677.014	0.325324	0.162662	+	0.986682i	$0.447992\pi$
$164$	5086.35	2.42181
$165$	148.966	0.0702849
$166$	4434.45	2.07337
$167$	2648.95	1.22744	0.613718	−	0.789525i	$-0.289673\pi$
$167$	2648.95	1.22744	0.613718	+	0.789525i	$0.289673\pi$
$168$	−1779.29	−0.817117
$169$	0	0
$170$	−1861.61	−0.839876
$171$	−1048.33	−0.468815
$172$	−3136.11	−1.39027
$173$	−3659.06	−1.60805	−0.804026	−	0.594594i	$-0.797313\pi$
$173$	−3659.06	−1.60805	−0.804026	+	0.594594i	$0.797313\pi$
$174$	2504.76	1.09129
$175$	722.800	0.312220
$176$	−3484.50	−1.49235
$177$	1492.64	0.633863
$178$	7891.52	3.32300
$179$	3151.32	1.31587	0.657935	−	0.753075i	$-0.271430\pi$
$179$	3151.32	1.31587	0.657935	+	0.753075i	$0.271430\pi$
$180$	−4543.01	−1.88120
$181$	1366.24	0.561059	0.280529	−	0.959845i	$-0.409490\pi$
$181$	1366.24	0.561059	0.280529	+	0.959845i	$0.409490\pi$
$182$	0	0
$183$	−888.705	−0.358989
$184$	−6366.81	−2.55091
$185$	1894.11	0.752745
$186$	−2637.52	−1.03975
$187$	−459.103	−0.179534
$188$	−5776.13	−2.24078
$189$	−1010.10	−0.388750
$190$	−1943.64	−0.742138
$191$	54.4176	0.0206153	0.0103076	−	0.999947i	$-0.496719\pi$
$191$	54.4176	0.0206153	0.0103076	+	0.999947i	$0.496719\pi$
$192$	−6024.14	−2.26435
$193$	3458.70	1.28996	0.644981	−	0.764199i	$-0.276865\pi$
$193$	3458.70	1.28996	0.644981	+	0.764199i	$0.276865\pi$
$194$	−5465.64	−2.02273
$195$	0	0
$196$	−5022.63	−1.83040
$197$	−4036.11	−1.45970	−0.729850	−	0.683607i	$-0.760410\pi$
$197$	−4036.11	−1.45970	−0.729850	+	0.683607i	$0.760410\pi$
$198$	−1495.10	−0.536628
$199$	3762.58	1.34031	0.670157	−	0.742220i	$-0.266227\pi$
$199$	3762.58	1.34031	0.670157	+	0.742220i	$0.266227\pi$
$200$	5636.52	1.99281
$201$	−416.339	−0.146101
$202$	−4131.71	−1.43914
$203$	−2980.87	−1.03062
$204$	−1712.43	−0.587715
$205$	1678.83	0.571973
$206$	3356.37	1.13519
$207$	−1703.05	−0.571838
$208$	0	0
$209$	−479.332	−0.158641
$210$	−882.416	−0.289964
$211$	1464.40	0.477790	0.238895	−	0.971045i	$-0.423215\pi$
$211$	1464.40	0.477790	0.238895	+	0.971045i	$0.423215\pi$
$212$	−2648.46	−0.858004
$213$	379.199	0.121983
$214$	7458.08	2.38235
$215$	−1035.12	−0.328347
$216$	−7876.91	−2.48128
$217$	3138.88	0.981939
$218$	−10672.4	−3.31571
$219$	206.599	0.0637473
$220$	−2077.23	−0.636576
$221$	0	0
$222$	2325.06	0.702919
$223$	−686.517	−0.206155	−0.103078	−	0.994673i	$-0.532869\pi$
$223$	−686.517	−0.206155	−0.103078	+	0.994673i	$0.532869\pi$
$224$	12342.5	3.68155
$225$	1507.71	0.446729
$226$	7096.36	2.08869
$227$	3619.48	1.05830	0.529148	−	0.848530i	$-0.322512\pi$
$227$	3619.48	1.05830	0.529148	+	0.848530i	$0.322512\pi$
$228$	−1787.88	−0.519322
$229$	1861.79	0.537250	0.268625	−	0.963245i	$-0.413431\pi$
$229$	1861.79	0.537250	0.268625	+	0.963245i	$0.413431\pi$
$230$	−3157.53	−0.905223
$231$	−217.618	−0.0619836
$232$	−23245.4	−6.57816
$233$	−516.109	−0.145113	−0.0725567	−	0.997364i	$-0.523116\pi$
$233$	−516.109	−0.145113	−0.0725567	+	0.997364i	$0.523116\pi$
$234$	0	0
$235$	−1906.50	−0.529218
$236$	−20813.8	−5.74095
$237$	−645.464	−0.176909
$238$	2719.54	0.740679
$239$	−120.230	−0.0325399	−0.0162700	−	0.999868i	$-0.505179\pi$
$239$	−120.230	−0.0325399	−0.0162700	+	0.999868i	$0.505179\pi$
$240$	−4289.86	−1.15379
$241$	5996.15	1.60268	0.801340	−	0.598209i	$-0.204121\pi$
$241$	5996.15	1.60268	0.801340	+	0.598209i	$0.204121\pi$
$242$	−683.614	−0.181588
$243$	−3221.20	−0.850370
$244$	12392.4	3.25139
$245$	−1657.80	−0.432296
$246$	2060.80	0.534113
$247$	0	0
$248$	24477.5	6.26743
$249$	1346.37	0.342661
$250$	8370.82	2.11767
$251$	1171.07	0.294491	0.147245	−	0.989100i	$-0.452959\pi$
$251$	1171.07	0.294491	0.147245	+	0.989100i	$0.452959\pi$
$252$	6636.69	1.65902
$253$	−778.697	−0.193503
$254$	3741.76	0.924325
$255$	−565.213	−0.138804
$256$	35633.5	8.69958
$257$	4958.69	1.20356	0.601780	−	0.798662i	$-0.294458\pi$
$257$	4958.69	1.20356	0.601780	+	0.798662i	$0.294458\pi$
$258$	−1270.63	−0.306613
$259$	−2767.02	−0.663839
$260$	0	0
$261$	−6217.90	−1.47463
$262$	3128.12	0.737617
$263$	−4772.68	−1.11900	−0.559498	−	0.828831i	$-0.689006\pi$
$263$	−4772.68	−1.11900	−0.559498	+	0.828831i	$0.689006\pi$
$264$	−1697.02	−0.395623
$265$	−874.164	−0.202639
$266$	2839.37	0.654485
$267$	2395.99	0.549183
$268$	5805.55	1.32325
$269$	−3314.67	−0.751298	−0.375649	−	0.926762i	$-0.622580\pi$
$269$	−3314.67	−0.751298	−0.375649	+	0.926762i	$0.622580\pi$
$270$	−3906.44	−0.880513
$271$	−928.558	−0.208140	−0.104070	−	0.994570i	$-0.533187\pi$
$271$	−928.558	−0.208140	−0.104070	+	0.994570i	$0.533187\pi$
$272$	13221.0	2.94721
$273$	0	0
$274$	−2556.26	−0.563611
$275$	689.379	0.151168
$276$	−2904.50	−0.633443
$277$	−2386.41	−0.517638	−0.258819	−	0.965926i	$-0.583333\pi$
$277$	−2386.41	−0.517638	−0.258819	+	0.965926i	$0.583333\pi$
$278$	−14064.3	−3.03424
$279$	6547.48	1.40497
$280$	8189.25	1.74786
$281$	4479.17	0.950907	0.475453	−	0.879741i	$-0.342284\pi$
$281$	4479.17	0.950907	0.475453	+	0.879741i	$0.342284\pi$
$282$	−2340.27	−0.494188
$283$	1837.52	0.385968	0.192984	−	0.981202i	$-0.438183\pi$
$283$	1837.52	0.385968	0.192984	+	0.981202i	$0.438183\pi$
$284$	−5287.66	−1.10481
$285$	−590.118	−0.122651
$286$	0	0
$287$	−2452.53	−0.504418
$288$	25745.6	5.26762
$289$	−3171.06	−0.645442
$290$	−11528.2	−2.33435
$291$	−1659.45	−0.334291
$292$	−2880.87	−0.577364
$293$	−5873.55	−1.17111	−0.585557	−	0.810631i	$-0.699124\pi$
$293$	−5873.55	−1.17111	−0.585557	+	0.810631i	$0.699124\pi$
$294$	−2034.98	−0.403682
$295$	−6869.92	−1.35587
$296$	−21577.7	−4.23709
$297$	−963.391	−0.188221
$298$	−9938.22	−1.93190
$299$	0	0
$300$	2571.35	0.494856
$301$	1512.16	0.289567
$302$	15654.8	2.98289
$303$	−1254.45	−0.237842
$304$	13803.6	2.60424
$305$	4090.29	0.767899
$306$	5672.77	1.05977
$307$	3582.60	0.666025	0.333012	−	0.942922i	$-0.391935\pi$
$307$	3582.60	0.666025	0.333012	+	0.942922i	$0.391935\pi$
$308$	3034.53	0.561391
$309$	1019.05	0.187610
$310$	12139.3	2.22408
$311$	8715.71	1.58914	0.794570	−	0.607172i	$-0.207696\pi$
$311$	8715.71	1.58914	0.794570	+	0.607172i	$0.207696\pi$
$312$	0	0
$313$	−3621.35	−0.653963	−0.326982	−	0.945031i	$-0.606032\pi$
$313$	−3621.35	−0.653963	−0.326982	+	0.945031i	$0.606032\pi$
$314$	17586.5	3.16071
$315$	2190.54	0.391819
$316$	9000.54	1.60228
$317$	5390.47	0.955076	0.477538	−	0.878611i	$-0.341529\pi$
$317$	5390.47	0.955076	0.477538	+	0.878611i	$0.341529\pi$
$318$	−1073.06	−0.189226
$319$	−2843.04	−0.498996
$320$	27726.3	4.84358
$321$	2264.39	0.393725
$322$	4612.69	0.798308
$323$	1818.70	0.313297
$324$	11943.4	2.04791
$325$	0	0
$326$	−3824.93	−0.649826
$327$	−3240.30	−0.547978
$328$	−19125.2	−3.21955
$329$	2785.12	0.466713
$330$	−841.615	−0.140392
$331$	−659.896	−0.109581	−0.0547903	−	0.998498i	$-0.517449\pi$
$331$	−659.896	−0.109581	−0.0547903	+	0.998498i	$0.517449\pi$
$332$	−18774.1	−3.10351
$333$	−5771.82	−0.949831
$334$	−14965.8	−2.45177
$335$	1916.21	0.312518
$336$	6266.86	1.01752
$337$	3705.57	0.598977	0.299488	−	0.954100i	$-0.403184\pi$
$337$	3705.57	0.598977	0.299488	+	0.954100i	$0.403184\pi$
$338$	0	0
$339$	2154.56	0.345191
$340$	7881.49	1.25716
$341$	2993.74	0.475425
$342$	5922.73	0.936446
$343$	6377.71	1.00398
$344$	11792.1	1.84822
$345$	−958.674	−0.149604
$346$	20672.6	3.21204
$347$	−354.667	−0.0548689	−0.0274345	−	0.999624i	$-0.508734\pi$
$347$	−354.667	−0.0548689	−0.0274345	+	0.999624i	$0.508734\pi$
$348$	−10604.4	−1.63349
$349$	4400.11	0.674878	0.337439	−	0.941347i	$-0.390439\pi$
$349$	4400.11	0.674878	0.337439	+	0.941347i	$0.390439\pi$
$350$	−4083.61	−0.623651
$351$	0	0
$352$	11771.8	1.78250
$353$	−5230.38	−0.788626	−0.394313	−	0.918976i	$-0.629017\pi$
$353$	−5230.38	−0.788626	−0.394313	+	0.918976i	$0.629017\pi$
$354$	−8432.98	−1.26612
$355$	−1745.27	−0.260928
$356$	−33410.3	−4.97400
$357$	825.694	0.122410
$358$	−17804.0	−2.62841
$359$	4142.00	0.608932	0.304466	−	0.952523i	$-0.401522\pi$
$359$	4142.00	0.608932	0.304466	+	0.952523i	$0.401522\pi$
$360$	17082.2	2.50087
$361$	−4960.17	−0.723162
$362$	−7718.84	−1.12070
$363$	−207.556	−0.0300106
$364$	0	0
$365$	−950.877	−0.136359
$366$	5020.92	0.717070
$367$	−156.888	−0.0223147	−0.0111574	−	0.999938i	$-0.503552\pi$
$367$	−156.888	−0.0223147	−0.0111574	+	0.999938i	$0.503552\pi$
$368$	22424.6	3.17652
$369$	−5115.80	−0.721729
$370$	−10701.2	−1.50359
$371$	1277.03	0.178706
$372$	11166.5	1.55633
$373$	−9393.12	−1.30391	−0.651954	−	0.758259i	$-0.726050\pi$
$373$	−9393.12	−1.30391	−0.651954	+	0.758259i	$0.726050\pi$
$374$	2593.79	0.358615
$375$	2541.51	0.349981
$376$	21718.8	2.97889
$377$	0	0
$378$	5706.74	0.776517
$379$	−2297.82	−0.311428	−0.155714	−	0.987802i	$-0.549768\pi$
$379$	−2297.82	−0.311428	−0.155714	+	0.987802i	$0.549768\pi$
$380$	8228.77	1.11086
$381$	1136.05	0.152761
$382$	−307.443	−0.0411784
$383$	4712.88	0.628764	0.314382	−	0.949297i	$-0.398203\pi$
$383$	4712.88	0.628764	0.314382	+	0.949297i	$0.398203\pi$
$384$	19349.1	2.57136
$385$	1001.59	0.132587
$386$	−19540.6	−2.57666
$387$	3154.26	0.414316
$388$	23139.9	3.02770
$389$	−10388.3	−1.35400	−0.677001	−	0.735982i	$-0.736721\pi$
$389$	−10388.3	−1.35400	−0.677001	+	0.735982i	$0.736721\pi$
$390$	0	0
$391$	2954.56	0.382145
$392$	18885.6	2.43333
$393$	949.744	0.121904
$394$	22802.8	2.91571
$395$	2970.77	0.378419
$396$	6329.82	0.803246
$397$	3921.27	0.495725	0.247863	−	0.968795i	$-0.420272\pi$
$397$	3921.27	0.495725	0.247863	+	0.968795i	$0.420272\pi$
$398$	−21257.5	−2.67724
$399$	862.076	0.108165
$400$	−19852.4	−2.48155
$401$	6532.54	0.813515	0.406758	−	0.913536i	$-0.366659\pi$
$401$	6532.54	0.813515	0.406758	+	0.913536i	$0.366659\pi$
$402$	2352.19	0.291832
$403$	0	0
$404$	17492.4	2.15416
$405$	3942.11	0.483667
$406$	16841.1	2.05864
$407$	−2639.08	−0.321411
$408$	6438.91	0.781307
$409$	1967.76	0.237896	0.118948	−	0.992900i	$-0.462048\pi$
$409$	1967.76	0.237896	0.118948	+	0.992900i	$0.462048\pi$
$410$	−9484.89	−1.14250
$411$	−776.120	−0.0931464
$412$	−14209.9	−1.69920
$413$	10036.0	1.19573
$414$	9621.76	1.14223
$415$	−6196.69	−0.732972
$416$	0	0
$417$	−4270.13	−0.501460
$418$	2708.08	0.316882
$419$	14394.7	1.67834	0.839172	−	0.543867i	$-0.183040\pi$
$419$	14394.7	1.67834	0.839172	+	0.543867i	$0.183040\pi$
$420$	3735.89	0.434030
$421$	7236.84	0.837772	0.418886	−	0.908039i	$-0.362421\pi$
$421$	7236.84	0.837772	0.418886	+	0.908039i	$0.362421\pi$
$422$	−8273.44	−0.954371
$423$	5809.57	0.667780
$424$	9958.47	1.14063
$425$	−2615.67	−0.298538
$426$	−2142.36	−0.243657
$427$	−5975.32	−0.677203
$428$	−31575.3	−3.56600
$429$	0	0
$430$	5848.13	0.655864
$431$	−146.193	−0.0163384	−0.00816921	−	0.999967i	$-0.502600\pi$
$431$	−146.193	−0.0163384	−0.00816921	+	0.999967i	$0.502600\pi$
$432$	27743.3	3.08981
$433$	2272.40	0.252204	0.126102	−	0.992017i	$-0.459753\pi$
$433$	2272.40	0.252204	0.126102	+	0.992017i	$0.459753\pi$
$434$	−17733.7	−1.96140
$435$	−3500.14	−0.385791
$436$	45183.7	4.96308
$437$	3084.75	0.337674
$438$	−1167.22	−0.127333
$439$	10442.7	1.13531	0.567654	−	0.823267i	$-0.307851\pi$
$439$	10442.7	1.13531	0.567654	+	0.823267i	$0.307851\pi$
$440$	7810.59	0.846262
$441$	5051.70	0.545481
$442$	0	0
$443$	9553.65	1.02462	0.512311	−	0.858800i	$-0.328790\pi$
$443$	9553.65	1.02462	0.512311	+	0.858800i	$0.328790\pi$
$444$	−9843.63	−1.05216
$445$	−11027.6	−1.17474
$446$	3878.62	0.411789
$447$	−3017.39	−0.319279
$448$	−40504.0	−4.27151
$449$	−1286.34	−0.135203	−0.0676017	−	0.997712i	$-0.521535\pi$
$449$	−1286.34	−0.135203	−0.0676017	+	0.997712i	$0.521535\pi$
$450$	−8518.12	−0.892329
$451$	−2339.13	−0.244224
$452$	−30043.9	−3.12643
$453$	4753.03	0.492974
$454$	−20449.0	−2.11392
$455$	0	0
$456$	6722.62	0.690385
$457$	−9086.60	−0.930094	−0.465047	−	0.885286i	$-0.653963\pi$
$457$	−9086.60	−0.930094	−0.465047	+	0.885286i	$0.653963\pi$
$458$	−10518.5	−1.07314
$459$	3655.33	0.371713
$460$	13368.0	1.35497
$461$	12513.6	1.26424	0.632121	−	0.774870i	$-0.282185\pi$
$461$	12513.6	1.26424	0.632121	+	0.774870i	$0.282185\pi$
$462$	1229.48	0.123811
$463$	17049.3	1.71133	0.855667	−	0.517527i	$-0.173147\pi$
$463$	17049.3	1.71133	0.855667	+	0.517527i	$0.173147\pi$
$464$	81872.6	8.19147
$465$	3685.67	0.367567
$466$	2915.86	0.289860
$467$	−16082.4	−1.59359	−0.796793	−	0.604252i	$-0.793472\pi$
$467$	−16082.4	−1.59359	−0.796793	+	0.604252i	$0.793472\pi$
$468$	0	0
$469$	−2799.30	−0.275607
$470$	10771.2	1.05710
$471$	5339.53	0.522362
$472$	78262.2	7.63201
$473$	1442.24	0.140199
$474$	3646.68	0.353371
$475$	−2730.92	−0.263796
$476$	−11513.7	−1.10868
$477$	2663.79	0.255695
$478$	679.264	0.0649975
$479$	−13498.3	−1.28759	−0.643793	−	0.765199i	$-0.722640\pi$
$479$	−13498.3	−1.28759	−0.643793	+	0.765199i	$0.722640\pi$
$480$	14492.6	1.37811
$481$	0	0
$482$	−33876.5	−3.20131
$483$	1400.48	0.131934
$484$	2894.22	0.271809
$485$	7637.67	0.715070
$486$	18198.8	1.69859
$487$	16425.4	1.52835	0.764176	−	0.645007i	$-0.223146\pi$
$487$	16425.4	1.52835	0.764176	+	0.645007i	$0.223146\pi$
$488$	−46596.6	−4.32239
$489$	−1161.31	−0.107395
$490$	9366.05	0.863500
$491$	−7706.62	−0.708340	−0.354170	−	0.935181i	$-0.615237\pi$
$491$	−7706.62	−0.708340	−0.354170	+	0.935181i	$0.615237\pi$
$492$	−8724.81	−0.799481
$493$	10787.2	0.985456
$494$	0	0
$495$	2089.25	0.189707
$496$	−86212.3	−7.80453
$497$	2549.59	0.230110
$498$	−7606.57	−0.684455
$499$	−4062.19	−0.364426	−0.182213	−	0.983259i	$-0.558326\pi$
$499$	−4062.19	−0.364426	−0.182213	+	0.983259i	$0.558326\pi$
$500$	−35439.6	−3.16981
$501$	−4543.84	−0.405197
$502$	−6616.19	−0.588237
$503$	−16362.1	−1.45040	−0.725199	−	0.688539i	$-0.758252\pi$
$503$	−16362.1	−1.45040	−0.725199	+	0.688539i	$0.758252\pi$
$504$	−24954.6	−2.20549
$505$	5773.64	0.508759
$506$	4399.41	0.386517
$507$	0	0
$508$	−15841.5	−1.38357
$509$	14601.2	1.27149	0.635744	−	0.771900i	$-0.280694\pi$
$509$	14601.2	1.27149	0.635744	+	0.771900i	$0.280694\pi$
$510$	3193.29	0.277257
$511$	1389.09	0.120254
$512$	−111078.	−9.58791
$513$	3816.40	0.328456
$514$	−28015.2	−2.40408
$515$	−4690.18	−0.401309
$516$	5379.48	0.458951
$517$	2656.34	0.225969
$518$	15632.9	1.32600
$519$	6276.52	0.530845
$520$	0	0
$521$	−4681.81	−0.393693	−0.196846	−	0.980434i	$-0.563070\pi$
$521$	−4681.81	−0.393693	−0.196846	+	0.980434i	$0.563070\pi$
$522$	35129.3	2.94553
$523$	16676.3	1.39427	0.697135	−	0.716940i	$-0.254458\pi$
$523$	16676.3	1.39427	0.697135	+	0.716940i	$0.254458\pi$
$524$	−13243.5	−1.10409
$525$	−1239.85	−0.103069
$526$	26964.2	2.23516
$527$	−11359.0	−0.938907
$528$	5977.09	0.492651
$529$	−7155.68	−0.588122
$530$	4938.77	0.404767
$531$	20934.3	1.71087
$532$	−12021.0	−0.979658
$533$	0	0
$534$	−13536.6	−1.09698
$535$	−10421.9	−0.842202
$536$	−21829.5	−1.75912
$537$	−5405.58	−0.434391
$538$	18726.9	1.50070
$539$	2309.82	0.184584
$540$	16538.7	1.31799
$541$	−2568.67	−0.204132	−0.102066	−	0.994778i	$-0.532545\pi$
$541$	−2568.67	−0.204132	−0.102066	+	0.994778i	$0.532545\pi$
$542$	5246.08	0.415754
$543$	−2343.56	−0.185215
$544$	−44665.0	−3.52021
$545$	14913.6	1.17216
$546$	0	0
$547$	−11754.3	−0.918792	−0.459396	−	0.888231i	$-0.651934\pi$
$547$	−11754.3	−0.918792	−0.459396	+	0.888231i	$0.651934\pi$
$548$	10822.4	0.843635
$549$	−12464.1	−0.968952
$550$	−3894.79	−0.301953
$551$	11262.5	0.870777
$552$	10921.2	0.842098
$553$	−4339.86	−0.333724
$554$	13482.5	1.03397
$555$	−3249.04	−0.248494
$556$	59543.9	4.54177
$557$	14690.7	1.11753	0.558767	−	0.829324i	$-0.311274\pi$
$557$	14690.7	1.11753	0.558767	+	0.829324i	$0.311274\pi$
$558$	−36991.3	−2.80639
$559$	0	0
$560$	−28843.4	−2.17653
$561$	787.516	0.0592673
$562$	−25306.0	−1.89941
$563$	1745.94	0.130697	0.0653486	−	0.997862i	$-0.479184\pi$
$563$	1745.94	0.130697	0.0653486	+	0.997862i	$0.479184\pi$
$564$	9908.01	0.739720
$565$	−9916.44	−0.738385
$566$	−10381.4	−0.770961
$567$	−5758.85	−0.426541
$568$	19882.2	1.46873
$569$	11429.1	0.842065	0.421032	−	0.907046i	$-0.361668\pi$
$569$	11429.1	0.842065	0.421032	+	0.907046i	$0.361668\pi$
$570$	3333.99	0.244992
$571$	8366.06	0.613150	0.306575	−	0.951846i	$-0.400817\pi$
$571$	8366.06	0.613150	0.306575	+	0.951846i	$0.400817\pi$
$572$	0	0
$573$	−93.3445	−0.00680545
$574$	13856.0	1.00756
$575$	−4436.51	−0.321766
$576$	−84488.6	−6.11174
$577$	5755.68	0.415272	0.207636	−	0.978206i	$-0.433423\pi$
$577$	5755.68	0.415272	0.207636	+	0.978206i	$0.433423\pi$
$578$	17915.5	1.28925
$579$	−5932.84	−0.425838
$580$	48807.0	3.49414
$581$	9052.46	0.646401
$582$	9375.41	0.667738
$583$	1217.98	0.0865241
$584$	10832.4	0.767547
$585$	0	0
$586$	33183.8	2.33927
$587$	−16000.4	−1.12505	−0.562526	−	0.826780i	$-0.690170\pi$
$587$	−16000.4	−1.12505	−0.562526	+	0.826780i	$0.690170\pi$
$588$	8615.50	0.604247
$589$	−11859.5	−0.829644
$590$	38813.0	2.70832
$591$	6923.29	0.481872
$592$	75999.0	5.27625
$593$	11551.3	0.799925	0.399962	−	0.916532i	$-0.369023\pi$
$593$	11551.3	0.799925	0.399962	+	0.916532i	$0.369023\pi$
$594$	5442.88	0.375966
$595$	−3800.28	−0.261842
$596$	42075.4	2.89174
$597$	−6454.10	−0.442460
$598$	0	0
$599$	−9381.02	−0.639897	−0.319948	−	0.947435i	$-0.603666\pi$
$599$	−9381.02	−0.639897	−0.319948	+	0.947435i	$0.603666\pi$
$600$	−9668.53	−0.657860
$601$	24827.9	1.68511	0.842556	−	0.538609i	$-0.181050\pi$
$601$	24827.9	1.68511	0.842556	+	0.538609i	$0.181050\pi$
$602$	−8543.26	−0.578401
$603$	−5839.15	−0.394343
$604$	−66277.7	−4.46490
$605$	955.281	0.0641945
$606$	7087.27	0.475084
$607$	−925.293	−0.0618723	−0.0309362	−	0.999521i	$-0.509849\pi$
$607$	−925.293	−0.0618723	−0.0309362	+	0.999521i	$0.509849\pi$
$608$	−46633.0	−3.11056
$609$	5113.20	0.340226
$610$	−23108.9	−1.53386
$611$	0	0
$612$	−24016.8	−1.58631
$613$	10381.4	0.684012	0.342006	−	0.939698i	$-0.388894\pi$
$613$	10381.4	0.684012	0.342006	+	0.939698i	$0.388894\pi$
$614$	−20240.6	−1.33037
$615$	−2879.76	−0.188818
$616$	−11410.1	−0.746311
$617$	25551.7	1.66722	0.833609	−	0.552354i	$-0.186270\pi$
$617$	25551.7	1.66722	0.833609	+	0.552354i	$0.186270\pi$
$618$	−5757.31	−0.374746
$619$	−12550.9	−0.814967	−0.407484	−	0.913213i	$-0.633594\pi$
$619$	−12550.9	−0.814967	−0.407484	+	0.913213i	$0.633594\pi$
$620$	−51394.0	−3.32909
$621$	6199.92	0.400635
$622$	−49241.2	−3.17426
$623$	16109.7	1.03599
$624$	0	0
$625$	−3863.51	−0.247265
$626$	20459.5	1.30627
$627$	822.215	0.0523702
$628$	−74456.0	−4.73108
$629$	10013.3	0.634747
$630$	−12375.9	−0.782647
$631$	3184.80	0.200927	0.100463	−	0.994941i	$-0.467967\pi$
$631$	3184.80	0.200927	0.100463	+	0.994941i	$0.467967\pi$
$632$	−33843.0	−2.13007
$633$	−2511.94	−0.157726
$634$	−30454.6	−1.90774
$635$	−5228.72	−0.326764
$636$	4543.00	0.283241
$637$	0	0
$638$	16062.4	0.996731
$639$	5318.27	0.329245
$640$	−89054.6	−5.50030
$641$	−10026.7	−0.617830	−0.308915	−	0.951090i	$-0.599966\pi$
$641$	−10026.7	−0.617830	−0.308915	+	0.951090i	$0.599966\pi$
$642$	−12793.1	−0.786455
$643$	26847.6	1.64661	0.823303	−	0.567602i	$-0.192129\pi$
$643$	26847.6	1.64661	0.823303	+	0.567602i	$0.192129\pi$
$644$	−19528.8	−1.19494
$645$	1775.58	0.108393
$646$	−10275.1	−0.625803
$647$	19618.3	1.19208	0.596041	−	0.802954i	$-0.296740\pi$
$647$	19618.3	1.19208	0.596041	+	0.802954i	$0.296740\pi$
$648$	−44908.5	−2.72249
$649$	9571.92	0.578938
$650$	0	0
$651$	−5384.23	−0.324154
$652$	16193.6	0.972685
$653$	7556.88	0.452869	0.226435	−	0.974026i	$-0.427293\pi$
$653$	7556.88	0.452869	0.226435	+	0.974026i	$0.427293\pi$
$654$	18306.7	1.09457
$655$	−4371.22	−0.260760
$656$	67361.0	4.00915
$657$	2897.55	0.172061
$658$	−15735.1	−0.932246
$659$	26497.9	1.56633	0.783166	−	0.621813i	$-0.213604\pi$
$659$	26497.9	1.56633	0.783166	+	0.621813i	$0.213604\pi$
$660$	3563.15	0.210144
$661$	10473.3	0.616286	0.308143	−	0.951340i	$-0.400293\pi$
$661$	10473.3	0.616286	0.308143	+	0.951340i	$0.400293\pi$
$662$	3728.22	0.218884
$663$	0	0
$664$	70592.6	4.12579
$665$	−3967.73	−0.231371
$666$	32609.1	1.89726
$667$	18296.4	1.06213
$668$	63360.6	3.66990
$669$	1177.61	0.0680552
$670$	−10826.0	−0.624247
$671$	−5699.03	−0.327882
$672$	−21171.5	−1.21534
$673$	12793.6	0.732774	0.366387	−	0.930462i	$-0.380595\pi$
$673$	12793.6	0.732774	0.366387	+	0.930462i	$0.380595\pi$
$674$	−20935.4	−1.19644
$675$	−5488.77	−0.312982
$676$	0	0
$677$	−3700.15	−0.210057	−0.105028	−	0.994469i	$-0.533493\pi$
$677$	−3700.15	−0.210057	−0.105028	+	0.994469i	$0.533493\pi$
$678$	−12172.7	−0.689510
$679$	−11157.5	−0.630614
$680$	−29635.2	−1.67126
$681$	−6208.62	−0.349361
$682$	−16913.7	−0.949649
$683$	3092.47	0.173251	0.0866253	−	0.996241i	$-0.472392\pi$
$683$	3092.47	0.173251	0.0866253	+	0.996241i	$0.472392\pi$
$684$	−25075.1	−1.40171
$685$	3572.11	0.199246
$686$	−36032.2	−2.00542
$687$	−3193.59	−0.177355
$688$	−41533.0	−2.30150
$689$	0	0
$690$	5416.23	0.298829
$691$	−3166.79	−0.174342	−0.0871710	−	0.996193i	$-0.527783\pi$
$691$	−3166.79	−0.174342	−0.0871710	+	0.996193i	$0.527783\pi$
$692$	−87521.6	−4.80791
$693$	−3052.10	−0.167301
$694$	2003.76	0.109599
$695$	19653.4	1.07265
$696$	39873.6	2.17156
$697$	8875.19	0.482313
$698$	−24859.3	−1.34805
$699$	885.301	0.0479044
$700$	17288.8	0.933506
$701$	5178.66	0.279023	0.139512	−	0.990220i	$-0.455447\pi$
$701$	5178.66	0.279023	0.139512	+	0.990220i	$0.455447\pi$
$702$	0	0
$703$	10454.5	0.560881
$704$	−38631.2	−2.06814
$705$	3270.29	0.174704
$706$	29550.1	1.57526
$707$	−8434.45	−0.448671
$708$	35702.7	1.89518
$709$	−13513.9	−0.715831	−0.357916	−	0.933754i	$-0.616512\pi$
$709$	−13513.9	−0.715831	−0.357916	+	0.933754i	$0.616512\pi$
$710$	9860.28	0.521197
$711$	−9052.64	−0.477497
$712$	125626.	6.61242
$713$	−19266.3	−1.01196
$714$	−4664.93	−0.244511
$715$	0	0
$716$	75376.9	3.93431
$717$	206.235	0.0107420
$718$	−23401.1	−1.21632
$719$	−16060.6	−0.833043	−0.416522	−	0.909126i	$-0.636751\pi$
$719$	−16060.6	−0.833043	−0.416522	+	0.909126i	$0.636751\pi$
$720$	−60165.3	−3.11421
$721$	6851.68	0.353911
$722$	28023.5	1.44450
$723$	−10285.4	−0.529071
$724$	32679.3	1.67751
$725$	−16197.8	−0.829754
$726$	1172.63	0.0599454
$727$	2031.79	0.103652	0.0518261	−	0.998656i	$-0.483496\pi$
$727$	2031.79	0.103652	0.0518261	+	0.998656i	$0.483496\pi$
$728$	0	0
$729$	−7956.33	−0.404223
$730$	5372.17	0.272374
$731$	−5472.20	−0.276877
$732$	−21257.1	−1.07334
$733$	29661.5	1.49464	0.747320	−	0.664464i	$-0.231340\pi$
$733$	29661.5	1.49464	0.747320	+	0.664464i	$0.231340\pi$
$734$	886.373	0.0445730
$735$	2843.68	0.142708
$736$	−75757.6	−3.79411
$737$	−2669.87	−0.133441
$738$	28902.7	1.44163
$739$	−28926.3	−1.43988	−0.719940	−	0.694037i	$-0.755831\pi$
$739$	−28926.3	−1.43988	−0.719940	+	0.694037i	$0.755831\pi$
$740$	45305.6	2.25063
$741$	0	0
$742$	−7214.82	−0.356960
$743$	8907.82	0.439833	0.219917	−	0.975519i	$-0.429421\pi$
$743$	8907.82	0.439833	0.219917	+	0.975519i	$0.429421\pi$
$744$	−41987.2	−2.06898
$745$	13887.6	0.682958
$746$	53068.4	2.60452
$747$	18882.8	0.924880
$748$	−10981.3	−0.536788
$749$	15224.9	0.742730
$750$	−14358.8	−0.699078
$751$	15743.5	0.764964	0.382482	−	0.923963i	$-0.375069\pi$
$751$	15743.5	0.764964	0.382482	+	0.923963i	$0.375069\pi$
$752$	−76496.0	−3.70947
$753$	−2008.78	−0.0972163
$754$	0	0
$755$	−21876.0	−1.05450
$756$	−24160.6	−1.16232
$757$	27251.1	1.30840	0.654199	−	0.756322i	$-0.273006\pi$
$757$	27251.1	1.30840	0.654199	+	0.756322i	$0.273006\pi$
$758$	12982.0	0.622068
$759$	1335.73	0.0638786
$760$	−30941.0	−1.47678
$761$	31054.3	1.47926	0.739631	−	0.673013i	$-0.235000\pi$
$761$	31054.3	1.47926	0.739631	+	0.673013i	$0.235000\pi$
$762$	−6418.37	−0.305135
$763$	−21786.5	−1.03372
$764$	1301.62	0.0616375
$765$	−7927.12	−0.374648
$766$	−26626.4	−1.25594
$767$	0	0
$768$	−61123.4	−2.87188
$769$	34620.6	1.62347	0.811736	−	0.584024i	$-0.198523\pi$
$769$	34620.6	1.62347	0.811736	+	0.584024i	$0.198523\pi$
$770$	−5658.70	−0.264838
$771$	−8505.83	−0.397315
$772$	82729.2	3.85685
$773$	18167.9	0.845348	0.422674	−	0.906282i	$-0.361092\pi$
$773$	18167.9	0.845348	0.422674	+	0.906282i	$0.361092\pi$
$774$	−17820.7	−0.827584
$775$	17056.4	0.790559
$776$	−87008.4	−4.02502
$777$	4746.38	0.219145
$778$	58690.7	2.70458
$779$	9266.25	0.426185
$780$	0	0
$781$	2431.70	0.111413
$782$	−16692.4	−0.763323
$783$	22636.1	1.03314
$784$	−66517.0	−3.03011
$785$	−24575.3	−1.11736
$786$	−5365.77	−0.243500
$787$	−41573.5	−1.88302	−0.941509	−	0.336988i	$-0.890592\pi$
$787$	−41573.5	−1.88302	−0.941509	+	0.336988i	$0.890592\pi$
$788$	−96540.4	−4.36435
$789$	8186.76	0.369400
$790$	−16784.0	−0.755881
$791$	14486.5	0.651176
$792$	−23800.8	−1.06783
$793$	0	0
$794$	−22154.0	−0.990197
$795$	1499.49	0.0668947
$796$	89997.8	4.00740
$797$	−18973.9	−0.843277	−0.421638	−	0.906764i	$-0.638545\pi$
$797$	−18973.9	−0.843277	−0.421638	+	0.906764i	$0.638545\pi$
$798$	−4870.48	−0.216056
$799$	−10078.8	−0.446260
$800$	67068.1	2.96402
$801$	33603.7	1.48231
$802$	−36906.9	−1.62497
$803$	1324.86	0.0582234
$804$	−9958.47	−0.436826
$805$	−6445.76	−0.282215
$806$	0	0
$807$	5685.78	0.248016
$808$	−65773.3	−2.86373
$809$	9979.22	0.433684	0.216842	−	0.976207i	$-0.430424\pi$
$809$	9979.22	0.433684	0.216842	+	0.976207i	$0.430424\pi$
$810$	−22271.8	−0.966111
$811$	−22596.7	−0.978394	−0.489197	−	0.872173i	$-0.662710\pi$
$811$	−22596.7	−0.978394	−0.489197	+	0.872173i	$0.662710\pi$
$812$	−71300.0	−3.08145
$813$	1592.79	0.0687105
$814$	14910.0	0.642010
$815$	5344.95	0.229724
$816$	−22678.5	−0.972924
$817$	−5713.32	−0.244656
$818$	−11117.3	−0.475191
$819$	0	0
$820$	40156.2	1.71014
$821$	7431.50	0.315909	0.157954	−	0.987446i	$-0.449510\pi$
$821$	7431.50	0.315909	0.157954	+	0.987446i	$0.449510\pi$
$822$	4384.85	0.186057
$823$	11779.4	0.498911	0.249455	−	0.968386i	$-0.419748\pi$
$823$	11779.4	0.498911	0.249455	+	0.968386i	$0.419748\pi$
$824$	53430.6	2.25891
$825$	−1182.52	−0.0499030
$826$	−56700.2	−2.38844
$827$	−10899.0	−0.458276	−0.229138	−	0.973394i	$-0.573591\pi$
$827$	−10899.0	−0.458276	−0.229138	+	0.973394i	$0.573591\pi$
$828$	−40735.6	−1.70974
$829$	28716.8	1.20311	0.601554	−	0.798832i	$-0.294549\pi$
$829$	28716.8	1.20311	0.601554	+	0.798832i	$0.294549\pi$
$830$	35009.4	1.46409
$831$	4093.50	0.170881
$832$	0	0
$833$	−8764.00	−0.364531
$834$	24124.9	1.00165
$835$	20913.1	0.866741
$836$	−11465.2	−0.474321
$837$	−23835.9	−0.984335
$838$	−81325.6	−3.35244
$839$	−2845.98	−0.117109	−0.0585543	−	0.998284i	$-0.518649\pi$
$839$	−2845.98	−0.117109	−0.0585543	+	0.998284i	$0.518649\pi$
$840$	−14047.3	−0.576998
$841$	42411.8	1.73897
$842$	−40886.0	−1.67343
$843$	−7683.28	−0.313910
$844$	35027.3	1.42854
$845$	0	0
$846$	−32822.3	−1.33387
$847$	−1395.53	−0.0566126
$848$	−35074.8	−1.42037
$849$	−3151.96	−0.127415
$850$	14777.7	0.596320
$851$	16983.8	0.684135
$852$	9070.13	0.364715
$853$	−296.398	−0.0118974	−0.00594870	−	0.999982i	$-0.501894\pi$
$853$	−296.398	−0.0118974	−0.00594870	+	0.999982i	$0.501894\pi$
$854$	33758.8	1.35269
$855$	−8276.41	−0.331049
$856$	118726.	4.74063
$857$	5096.98	0.203162	0.101581	−	0.994827i	$-0.467610\pi$
$857$	5096.98	0.203162	0.101581	+	0.994827i	$0.467610\pi$
$858$	0	0
$859$	−5114.06	−0.203131	−0.101566	−	0.994829i	$-0.532385\pi$
$859$	−5114.06	−0.203131	−0.101566	+	0.994829i	$0.532385\pi$
$860$	−24759.2	−0.981723
$861$	4206.91	0.166517
$862$	825.946	0.0326356
$863$	−24292.9	−0.958217	−0.479108	−	0.877756i	$-0.659040\pi$
$863$	−24292.9	−0.958217	−0.479108	+	0.877756i	$0.659040\pi$
$864$	−93726.1	−3.69054
$865$	−28887.8	−1.13551
$866$	−12838.4	−0.503771
$867$	5439.43	0.213071
$868$	75079.2	2.93589
$869$	−4139.19	−0.161579
$870$	19774.8	0.770607
$871$	0	0
$872$	−169895.	−6.59791
$873$	−23273.8	−0.902291
$874$	−17427.9	−0.674494
$875$	17088.2	0.660212
$876$	4941.67	0.190598
$877$	−16517.5	−0.635981	−0.317991	−	0.948094i	$-0.603008\pi$
$877$	−16517.5	−0.635981	−0.317991	+	0.948094i	$0.603008\pi$
$878$	−58997.9	−2.26775
$879$	10075.1	0.386604
$880$	−27509.7	−1.05381
$881$	13454.1	0.514505	0.257252	−	0.966344i	$-0.417183\pi$
$881$	13454.1	0.514505	0.257252	+	0.966344i	$0.417183\pi$
$882$	−28540.6	−1.08958
$883$	41124.1	1.56731	0.783656	−	0.621194i	$-0.213352\pi$
$883$	41124.1	1.56731	0.783656	+	0.621194i	$0.213352\pi$
$884$	0	0
$885$	11784.2	0.447596
$886$	−53975.3	−2.04665
$887$	875.772	0.0331517	0.0165758	−	0.999863i	$-0.494724\pi$
$887$	875.772	0.0331517	0.0165758	+	0.999863i	$0.494724\pi$
$888$	37013.1	1.39874
$889$	7638.40	0.288171
$890$	62302.6	2.34650
$891$	−5492.57	−0.206519
$892$	−16420.9	−0.616382
$893$	−10522.9	−0.394328
$894$	17047.4	0.637752
$895$	24879.3	0.929188
$896$	130096.	4.85067
$897$	0	0
$898$	7267.46	0.270065
$899$	−70341.6	−2.60959
$900$	36063.2	1.33567
$901$	−4621.30	−0.170874
$902$	13215.4	0.487831
$903$	−2593.87	−0.0955908
$904$	112968.	4.15626
$905$	10786.3	0.396186
$906$	−26853.2	−0.984701
$907$	−903.188	−0.0330649	−0.0165325	−	0.999863i	$-0.505263\pi$
$907$	−903.188	−0.0330649	−0.0165325	+	0.999863i	$0.505263\pi$
$908$	86574.8	3.16419
$909$	−17593.7	−0.641964
$910$	0	0
$911$	−22248.9	−0.809154	−0.404577	−	0.914504i	$-0.632581\pi$
$911$	−22248.9	−0.809154	−0.404577	+	0.914504i	$0.632581\pi$
$912$	−23677.8	−0.859703
$913$	8633.89	0.312968
$914$	51336.6	1.85784
$915$	−7016.22	−0.253496
$916$	44532.3	1.60632
$917$	6385.72	0.229962
$918$	−20651.6	−0.742487
$919$	−11584.3	−0.415811	−0.207905	−	0.978149i	$-0.566665\pi$
$919$	−11584.3	−0.415811	−0.207905	+	0.978149i	$0.566665\pi$
$920$	−50265.2	−1.80130
$921$	−6145.36	−0.219866
$922$	−70698.0	−2.52529
$923$	0	0
$924$	−5205.24	−0.185324
$925$	−15035.8	−0.534457
$926$	−96323.4	−3.41834
$927$	14292.1	0.506381
$928$	−276593.	−9.78406
$929$	−379.368	−0.0133979	−0.00669896	−	0.999978i	$-0.502132\pi$
$929$	−379.368	−0.0133979	−0.00669896	+	0.999978i	$0.502132\pi$
$930$	−20822.9	−0.734206
$931$	−9150.16	−0.322110
$932$	−12344.9	−0.433874
$933$	−14950.4	−0.524602
$934$	90860.8	3.18314
$935$	−3624.56	−0.126776
$936$	0	0
$937$	−23209.7	−0.809207	−0.404604	−	0.914492i	$-0.632590\pi$
$937$	−23209.7	−0.809207	−0.404604	+	0.914492i	$0.632590\pi$
$938$	15815.2	0.550518
$939$	6211.83	0.215884
$940$	−45601.9	−1.58231
$941$	17651.8	0.611512	0.305756	−	0.952110i	$-0.401091\pi$
$941$	17651.8	0.611512	0.305756	+	0.952110i	$0.401091\pi$
$942$	−30166.8	−1.04340
$943$	15053.5	0.519839
$944$	−275647.	−9.50377
$945$	−7974.59	−0.274512
$946$	−8148.24	−0.280044
$947$	22422.0	0.769397	0.384698	−	0.923042i	$-0.374306\pi$
$947$	22422.0	0.769397	0.384698	+	0.923042i	$0.374306\pi$
$948$	−15439.0	−0.528939
$949$	0	0
$950$	15428.9	0.526925
$951$	−9246.48	−0.315287
$952$	43292.8	1.47387
$953$	23298.9	0.791946	0.395973	−	0.918262i	$-0.370407\pi$
$953$	23298.9	0.791946	0.395973	+	0.918262i	$0.370407\pi$
$954$	−15049.6	−0.510744
$955$	429.620	0.0145573
$956$	−2875.80	−0.0972909
$957$	4876.78	0.164727
$958$	76261.5	2.57192
$959$	−5218.34	−0.175713
$960$	−47559.9	−1.59895
$961$	44279.0	1.48632
$962$	0	0
$963$	31758.0	1.06271
$964$	143423.	4.79184
$965$	27306.0	0.910893
$966$	−7912.32	−0.263535
$967$	−5415.35	−0.180089	−0.0900444	−	0.995938i	$-0.528701\pi$
$967$	−5415.35	−0.180089	−0.0900444	+	0.995938i	$0.528701\pi$
$968$	−10882.6	−0.361342
$969$	−3119.68	−0.103425
$970$	−43150.6	−1.42833
$971$	−57872.6	−1.91269	−0.956343	−	0.292245i	$-0.905598\pi$
$971$	−57872.6	−1.91269	−0.956343	+	0.292245i	$0.905598\pi$
$972$	−77048.3	−2.54252
$973$	−28710.7	−0.945964
$974$	−92798.9	−3.05284
$975$	0	0
$976$	164118.	5.38247
$977$	42752.2	1.39996	0.699982	−	0.714160i	$-0.253191\pi$
$977$	42752.2	1.39996	0.699982	+	0.714160i	$0.253191\pi$
$978$	6561.05	0.214519
$979$	15364.8	0.501595
$980$	−39653.1	−1.29252
$981$	−45445.2	−1.47906
$982$	43540.1	1.41489
$983$	−2224.31	−0.0721715	−0.0360857	−	0.999349i	$-0.511489\pi$
$983$	−2224.31	−0.0721715	−0.0360857	+	0.999349i	$0.511489\pi$
$984$	32806.2	1.06283
$985$	−31864.6	−1.03075
$986$	−60944.4	−1.96842
$987$	−4777.42	−0.154070
$988$	0	0
$989$	−9281.57	−0.298419
$990$	−11803.7	−0.378934
$991$	−3311.99	−0.106164	−0.0530822	−	0.998590i	$-0.516905\pi$
$991$	−3311.99	−0.106164	−0.0530822	+	0.998590i	$0.516905\pi$
$992$	291254.	9.32189
$993$	1131.94	0.0361744
$994$	−14404.4	−0.459639
$995$	29705.1	0.946449
$996$	32203.9	1.02452
$997$	31133.3	0.988970	0.494485	−	0.869186i	$-0.335357\pi$
$997$	31133.3	0.988970	0.494485	+	0.869186i	$0.335357\pi$
$998$	22950.2	0.727932
$999$	21012.1	0.665460

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.p.1.1	✓	51
13.12	even	2		1859.4.a.q.1.51	yes	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.1	✓	51	1.1	even	1	trivial
1859.4.a.q.1.51	yes	51	13.12	even	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:	\( N \)	\(=\)	\( 1859 = 11 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q-5.64970 q^{2} -1.71534 q^{3} +23.9192 q^{4} +7.89488 q^{5} +9.69115 q^{6} -11.5333 q^{7} -89.9385 q^{8} -24.0576 q^{9} +O(q^{10})\)	\(q-5.64970 q^{2} -1.71534 q^{3} +23.9192 q^{4} +7.89488 q^{5} +9.69115 q^{6} -11.5333 q^{7} -89.9385 q^{8} -24.0576 q^{9} -44.6038 q^{10} -11.0000 q^{11} -41.0294 q^{12} +65.1596 q^{14} -13.5424 q^{15} +316.773 q^{16} +41.7366 q^{17} +135.918 q^{18} +43.5756 q^{19} +188.839 q^{20} +19.7835 q^{21} +62.1467 q^{22} +70.7907 q^{23} +154.275 q^{24} -62.6708 q^{25} +87.5810 q^{27} -275.866 q^{28} +258.458 q^{29} +76.5105 q^{30} -272.158 q^{31} -1070.16 q^{32} +18.8687 q^{33} -235.799 q^{34} -91.0539 q^{35} -575.438 q^{36} +239.916 q^{37} -246.189 q^{38} -710.054 q^{40} +212.648 q^{41} -111.771 q^{42} -131.113 q^{43} -263.111 q^{44} -189.932 q^{45} -399.946 q^{46} -241.485 q^{47} -543.372 q^{48} -209.983 q^{49} +354.072 q^{50} -71.5923 q^{51} -110.725 q^{53} -494.807 q^{54} -86.8437 q^{55} +1037.29 q^{56} -74.7468 q^{57} -1460.21 q^{58} -870.174 q^{59} -323.922 q^{60} +518.094 q^{61} +1537.61 q^{62} +277.463 q^{63} +3511.93 q^{64} -106.603 q^{66} +242.715 q^{67} +998.304 q^{68} -121.430 q^{69} +514.427 q^{70} -221.064 q^{71} +2163.71 q^{72} -120.442 q^{73} -1355.46 q^{74} +107.502 q^{75} +1042.29 q^{76} +126.866 q^{77} +376.290 q^{79} +2500.88 q^{80} +499.325 q^{81} -1201.40 q^{82} -784.899 q^{83} +473.204 q^{84} +329.506 q^{85} +740.749 q^{86} -443.343 q^{87} +989.324 q^{88} -1396.80 q^{89} +1073.06 q^{90} +1693.25 q^{92} +466.843 q^{93} +1364.32 q^{94} +344.024 q^{95} +1835.69 q^{96} +967.420 q^{97} +1186.34 q^{98} +264.634 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} - 41 q^{5} + 73 q^{6} - 4 q^{7} + 21 q^{8} + 594 q^{9} + 212 q^{10} - 561 q^{11} + 209 q^{12} + 280 q^{14} - 284 q^{15} + 1246 q^{16} + 164 q^{17} + 189 q^{18} - 26 q^{19} - 438 q^{20} - 134 q^{21} + 373 q^{23} + 354 q^{24} + 2048 q^{25} + 1470 q^{27} + 1245 q^{28} + 898 q^{29} + 427 q^{30} - 767 q^{31} - 1127 q^{32} - 231 q^{33} - 206 q^{34} + 54 q^{35} + 3415 q^{36} - 395 q^{37} + 1577 q^{38} + 3253 q^{40} + 354 q^{41} + 942 q^{42} + 484 q^{43} - 2574 q^{44} - 1452 q^{45} + 2117 q^{46} - 1925 q^{47} + 1780 q^{48} + 4535 q^{49} + 1093 q^{50} + 230 q^{51} + 1387 q^{53} + 5271 q^{54} + 451 q^{55} + 2568 q^{56} + 5738 q^{57} - 3695 q^{58} - 1145 q^{59} + 1590 q^{60} + 5382 q^{61} - 395 q^{62} - 710 q^{63} + 9839 q^{64} - 803 q^{66} + 210 q^{67} + 1742 q^{68} + 7028 q^{69} + 6747 q^{70} - 3693 q^{71} + 12481 q^{72} - 968 q^{73} + 1735 q^{74} - 727 q^{75} + 2801 q^{76} + 44 q^{77} + 4234 q^{79} - 2390 q^{80} + 7743 q^{81} + 4770 q^{82} + 2798 q^{83} - 14821 q^{84} + 1802 q^{85} - 6558 q^{86} + 1896 q^{87} - 231 q^{88} - 3927 q^{89} + 1927 q^{90} + 1984 q^{92} + 1332 q^{93} + 7590 q^{94} + 4944 q^{95} + 7280 q^{96} - 3913 q^{97} + 15201 q^{98} - 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 - 41 * q^5 + 73 * q^6 - 4 * q^7 + 21 * q^8 + 594 * q^9 + 212 * q^10 - 561 * q^11 + 209 * q^12 + 280 * q^14 - 284 * q^15 + 1246 * q^16 + 164 * q^17 + 189 * q^18 - 26 * q^19 - 438 * q^20 - 134 * q^21 + 373 * q^23 + 354 * q^24 + 2048 * q^25 + 1470 * q^27 + 1245 * q^28 + 898 * q^29 + 427 * q^30 - 767 * q^31 - 1127 * q^32 - 231 * q^33 - 206 * q^34 + 54 * q^35 + 3415 * q^36 - 395 * q^37 + 1577 * q^38 + 3253 * q^40 + 354 * q^41 + 942 * q^42 + 484 * q^43 - 2574 * q^44 - 1452 * q^45 + 2117 * q^46 - 1925 * q^47 + 1780 * q^48 + 4535 * q^49 + 1093 * q^50 + 230 * q^51 + 1387 * q^53 + 5271 * q^54 + 451 * q^55 + 2568 * q^56 + 5738 * q^57 - 3695 * q^58 - 1145 * q^59 + 1590 * q^60 + 5382 * q^61 - 395 * q^62 - 710 * q^63 + 9839 * q^64 - 803 * q^66 + 210 * q^67 + 1742 * q^68 + 7028 * q^69 + 6747 * q^70 - 3693 * q^71 + 12481 * q^72 - 968 * q^73 + 1735 * q^74 - 727 * q^75 + 2801 * q^76 + 44 * q^77 + 4234 * q^79 - 2390 * q^80 + 7743 * q^81 + 4770 * q^82 + 2798 * q^83 - 14821 * q^84 + 1802 * q^85 - 6558 * q^86 + 1896 * q^87 - 231 * q^88 - 3927 * q^89 + 1927 * q^90 + 1984 * q^92 + 1332 * q^93 + 7590 * q^94 + 4944 * q^95 + 7280 * q^96 - 3913 * q^97 + 15201 * q^98 - 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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