LMFDB - Embedded newform 1859.4.a.q.1.6

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			1.6
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)

$f(q)$	$=$	$q-4.84162 q^{2} +9.88636 q^{3} +15.4413 q^{4} -0.786780 q^{5} -47.8660 q^{6} -26.4479 q^{7} -36.0278 q^{8} +70.7402 q^{9} +O(q^{10})$	\(q-4.84162 q^{2} +9.88636 q^{3} +15.4413 q^{4} -0.786780 q^{5} -47.8660 q^{6} -26.4479 q^{7} -36.0278 q^{8} +70.7402 q^{9} +3.80929 q^{10} +11.0000 q^{11} +152.658 q^{12} +128.051 q^{14} -7.77840 q^{15} +50.9029 q^{16} -25.1694 q^{17} -342.497 q^{18} +84.1943 q^{19} -12.1489 q^{20} -261.474 q^{21} -53.2578 q^{22} +180.733 q^{23} -356.184 q^{24} -124.381 q^{25} +432.431 q^{27} -408.390 q^{28} +16.2994 q^{29} +37.6600 q^{30} +273.790 q^{31} +41.7704 q^{32} +108.750 q^{33} +121.861 q^{34} +20.8087 q^{35} +1092.32 q^{36} +69.7919 q^{37} -407.637 q^{38} +28.3460 q^{40} +242.028 q^{41} +1265.96 q^{42} -320.427 q^{43} +169.854 q^{44} -55.6570 q^{45} -875.038 q^{46} -112.044 q^{47} +503.244 q^{48} +356.494 q^{49} +602.205 q^{50} -248.834 q^{51} -467.808 q^{53} -2093.67 q^{54} -8.65459 q^{55} +952.862 q^{56} +832.376 q^{57} -78.9154 q^{58} +89.6066 q^{59} -120.108 q^{60} -564.769 q^{61} -1325.59 q^{62} -1870.93 q^{63} -609.459 q^{64} -526.526 q^{66} -762.376 q^{67} -388.648 q^{68} +1786.79 q^{69} -100.748 q^{70} +739.018 q^{71} -2548.62 q^{72} -866.598 q^{73} -337.906 q^{74} -1229.68 q^{75} +1300.07 q^{76} -290.927 q^{77} +1366.82 q^{79} -40.0494 q^{80} +2365.19 q^{81} -1171.81 q^{82} -670.194 q^{83} -4037.49 q^{84} +19.8028 q^{85} +1551.39 q^{86} +161.142 q^{87} -396.306 q^{88} -1121.54 q^{89} +269.470 q^{90} +2790.74 q^{92} +2706.79 q^{93} +542.473 q^{94} -66.2424 q^{95} +412.957 q^{96} +1811.55 q^{97} -1726.01 q^{98} +778.142 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.84162	−1.71177	−0.855885	−	0.517165i	$-0.826987\pi$
$2$	−4.84162	−1.71177	−0.855885	+	0.517165i	$0.826987\pi$
$3$	9.88636	1.90263	0.951316	−	0.308218i	$-0.0997326\pi$
$3$	9.88636	1.90263	0.951316	+	0.308218i	$0.0997326\pi$
$4$	15.4413	1.93016
$5$	−0.786780	−0.0703718	−0.0351859	−	0.999381i	$-0.511202\pi$
$5$	−0.786780	−0.0703718	−0.0351859	+	0.999381i	$0.511202\pi$
$6$	−47.8660	−3.25687
$7$	−26.4479	−1.42805	−0.714027	−	0.700118i	$-0.753131\pi$
$7$	−26.4479	−1.42805	−0.714027	+	0.700118i	$0.753131\pi$
$8$	−36.0278	−1.59222
$9$	70.7402	2.62001
$10$	3.80929	0.120460
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	152.658	3.67238
$13$	0	0
$13$	0	0
$14$	128.051	2.44450
$15$	−7.77840	−0.133892
$16$	50.9029	0.795357
$17$	−25.1694	−0.359087	−0.179544	−	0.983750i	$-0.557462\pi$
$17$	−25.1694	−0.359087	−0.179544	+	0.983750i	$0.557462\pi$
$18$	−342.497	−4.48485
$19$	84.1943	1.01661	0.508303	−	0.861179i	$-0.330273\pi$
$19$	84.1943	1.01661	0.508303	+	0.861179i	$0.330273\pi$
$20$	−12.1489	−0.135829
$21$	−261.474	−2.71706
$22$	−53.2578	−0.516118
$23$	180.733	1.63849	0.819246	−	0.573442i	$-0.194392\pi$
$23$	180.733	1.63849	0.819246	+	0.573442i	$0.194392\pi$
$24$	−356.184	−3.02941
$25$	−124.381	−0.995048
$26$	0	0
$27$	432.431	3.08228
$28$	−408.390	−2.75637
$29$	16.2994	0.104370	0.0521848	−	0.998637i	$-0.483382\pi$
$29$	16.2994	0.104370	0.0521848	+	0.998637i	$0.483382\pi$
$30$	37.6600	0.229192
$31$	273.790	1.58626	0.793132	−	0.609050i	$-0.208449\pi$
$31$	273.790	1.58626	0.793132	+	0.609050i	$0.208449\pi$
$32$	41.7704	0.230751
$33$	108.750	0.573665
$34$	121.861	0.614675
$35$	20.8087	0.100495
$36$	1092.32	5.05703
$37$	69.7919	0.310100	0.155050	−	0.987907i	$-0.450446\pi$
$37$	69.7919	0.310100	0.155050	+	0.987907i	$0.450446\pi$
$38$	−407.637	−1.74020
$39$	0	0
$40$	28.3460	0.112047
$41$	242.028	0.921913	0.460956	−	0.887423i	$-0.347506\pi$
$41$	242.028	0.921913	0.460956	+	0.887423i	$0.347506\pi$
$42$	1265.96	4.65099
$43$	−320.427	−1.13639	−0.568195	−	0.822894i	$-0.692358\pi$
$43$	−320.427	−1.13639	−0.568195	+	0.822894i	$0.692358\pi$
$44$	169.854	0.581965
$45$	−55.6570	−0.184375
$46$	−875.038	−2.80472
$47$	−112.044	−0.347729	−0.173864	−	0.984770i	$-0.555625\pi$
$47$	−112.044	−0.347729	−0.173864	+	0.984770i	$0.555625\pi$
$48$	503.244	1.51327
$49$	356.494	1.03934
$50$	602.205	1.70329
$51$	−248.834	−0.683210
$52$	0	0
$53$	−467.808	−1.21242	−0.606211	−	0.795304i	$-0.707311\pi$
$53$	−467.808	−1.21242	−0.606211	+	0.795304i	$0.707311\pi$
$54$	−2093.67	−5.27615
$55$	−8.65459	−0.0212179
$56$	952.862	2.27378
$57$	832.376	1.93423
$58$	−78.9154	−0.178657
$59$	89.6066	0.197725	0.0988626	−	0.995101i	$-0.468480\pi$
$59$	89.6066	0.197725	0.0988626	+	0.995101i	$0.468480\pi$
$60$	−120.108	−0.258432
$61$	−564.769	−1.18543	−0.592716	−	0.805412i	$-0.701944\pi$
$61$	−564.769	−1.18543	−0.592716	+	0.805412i	$0.701944\pi$
$62$	−1325.59	−2.71532
$63$	−1870.93	−3.74151
$64$	−609.459	−1.19035
$65$	0	0
$66$	−526.526	−0.981983
$67$	−762.376	−1.39013	−0.695067	−	0.718945i	$-0.744625\pi$
$67$	−762.376	−1.39013	−0.695067	+	0.718945i	$0.744625\pi$
$68$	−388.648	−0.693096
$69$	1786.79	3.11745
$70$	−100.748	−0.172024
$71$	739.018	1.23529	0.617643	−	0.786459i	$-0.288088\pi$
$71$	739.018	1.23529	0.617643	+	0.786459i	$0.288088\pi$
$72$	−2548.62	−4.17163
$73$	−866.598	−1.38942	−0.694710	−	0.719290i	$-0.744467\pi$
$73$	−866.598	−1.38942	−0.694710	+	0.719290i	$0.744467\pi$
$74$	−337.906	−0.530821
$75$	−1229.68	−1.89321
$76$	1300.07	1.96221
$77$	−290.927	−0.430575
$78$	0	0
$79$	1366.82	1.94657	0.973285	−	0.229601i	$-0.0737421\pi$
$79$	1366.82	1.94657	0.973285	+	0.229601i	$0.0737421\pi$
$80$	−40.0494	−0.0559707
$81$	2365.19	3.24443
$82$	−1171.81	−1.57810
$83$	−670.194	−0.886306	−0.443153	−	0.896446i	$-0.646140\pi$
$83$	−670.194	−0.886306	−0.443153	+	0.896446i	$0.646140\pi$
$84$	−4037.49	−5.24436
$85$	19.8028	0.0252696
$86$	1551.39	1.94524
$87$	161.142	0.198577
$88$	−396.306	−0.480073
$89$	−1121.54	−1.33576	−0.667882	−	0.744267i	$-0.732799\pi$
$89$	−1121.54	−1.33576	−0.667882	+	0.744267i	$0.732799\pi$
$90$	269.470	0.315607
$91$	0	0
$92$	2790.74	3.16255
$93$	2706.79	3.01808
$94$	542.473	0.595232
$95$	−66.2424	−0.0715403
$96$	412.957	0.439034
$97$	1811.55	1.89624	0.948118	−	0.317919i	$-0.102984\pi$
$97$	1811.55	1.89624	0.948118	+	0.317919i	$0.102984\pi$
$98$	−1726.01	−1.77911
$99$	778.142	0.789962
$100$	−1920.60	−1.92060
$101$	−801.011	−0.789145	−0.394572	−	0.918865i	$-0.629107\pi$
$101$	−801.011	−0.789145	−0.394572	+	0.918865i	$0.629107\pi$
$102$	1204.76	1.16950
$103$	365.244	0.349404	0.174702	−	0.984621i	$-0.444104\pi$
$103$	365.244	0.349404	0.174702	+	0.984621i	$0.444104\pi$
$104$	0	0
$105$	205.723	0.191205
$106$	2264.95	2.07539
$107$	335.078	0.302740	0.151370	−	0.988477i	$-0.451631\pi$
$107$	335.078	0.302740	0.151370	+	0.988477i	$0.451631\pi$
$108$	6677.29	5.94929
$109$	−241.189	−0.211943	−0.105971	−	0.994369i	$-0.533795\pi$
$109$	−241.189	−0.211943	−0.105971	+	0.994369i	$0.533795\pi$
$110$	41.9022	0.0363202
$111$	689.988	0.590007
$112$	−1346.28	−1.13581
$113$	408.803	0.340327	0.170164	−	0.985416i	$-0.445570\pi$
$113$	408.803	0.340327	0.170164	+	0.985416i	$0.445570\pi$
$114$	−4030.05	−3.31095
$115$	−142.197	−0.115304
$116$	251.683	0.201450
$117$	0	0
$118$	−433.841	−0.338460
$119$	665.679	0.512796
$120$	280.239	0.213185
$121$	121.000	0.0909091
$122$	2734.40	2.02919
$123$	2392.78	1.75406
$124$	4227.67	3.06174
$125$	196.208	0.140395
$126$	9058.34	6.40461
$127$	1381.74	0.965430	0.482715	−	0.875777i	$-0.339651\pi$
$127$	1381.74	0.965430	0.482715	+	0.875777i	$0.339651\pi$
$128$	2616.61	1.80686
$129$	−3167.86	−2.16213
$130$	0	0
$131$	1465.25	0.977250	0.488625	−	0.872494i	$-0.337499\pi$
$131$	1465.25	0.977250	0.488625	+	0.872494i	$0.337499\pi$
$132$	1679.24	1.10727
$133$	−2226.77	−1.45177
$134$	3691.13	2.37959
$135$	−340.229	−0.216905
$136$	906.800	0.571746
$137$	910.344	0.567708	0.283854	−	0.958868i	$-0.408387\pi$
$137$	910.344	0.567708	0.283854	+	0.958868i	$0.408387\pi$
$138$	−8650.94	−5.33636
$139$	2893.92	1.76590	0.882948	−	0.469471i	$-0.155555\pi$
$139$	2893.92	1.76590	0.882948	+	0.469471i	$0.155555\pi$
$140$	321.313	0.193971
$141$	−1107.71	−0.661600
$142$	−3578.04	−2.11453
$143$	0	0
$144$	3600.88	2.08384
$145$	−12.8240	−0.00734467
$146$	4195.74	2.37837
$147$	3524.43	1.97748
$148$	1077.68	0.598543
$149$	−1111.07	−0.610886	−0.305443	−	0.952210i	$-0.598805\pi$
$149$	−1111.07	−0.610886	−0.305443	+	0.952210i	$0.598805\pi$
$150$	5953.62	3.24074
$151$	1804.90	0.972720	0.486360	−	0.873758i	$-0.338324\pi$
$151$	1804.90	0.972720	0.486360	+	0.873758i	$0.338324\pi$
$152$	−3033.34	−1.61866
$153$	−1780.49	−0.940811
$154$	1408.56	0.737045
$155$	−215.413	−0.111628
$156$	0	0
$157$	−680.744	−0.346047	−0.173023	−	0.984918i	$-0.555354\pi$
$157$	−680.744	−0.346047	−0.173023	+	0.984918i	$0.555354\pi$
$158$	−6617.61	−3.33208
$159$	−4624.92	−2.30679
$160$	−32.8641	−0.0162384
$161$	−4780.00	−2.33986
$162$	−11451.3	−5.55372
$163$	2497.92	1.20032	0.600160	−	0.799880i	$-0.295103\pi$
$163$	2497.92	1.20032	0.600160	+	0.799880i	$0.295103\pi$
$164$	3737.22	1.77944
$165$	−85.5624	−0.0403698
$166$	3244.83	1.51715
$167$	2157.25	0.999600	0.499800	−	0.866141i	$-0.333407\pi$
$167$	2157.25	0.999600	0.499800	+	0.866141i	$0.333407\pi$
$168$	9420.34	4.32616
$169$	0	0
$170$	−95.8777	−0.0432558
$171$	5955.92	2.66351
$172$	−4947.81	−2.19341
$173$	2253.28	0.990254	0.495127	−	0.868821i	$-0.335122\pi$
$173$	2253.28	0.990254	0.495127	+	0.868821i	$0.335122\pi$
$174$	−780.186	−0.339918
$175$	3289.62	1.42098
$176$	559.932	0.239809
$177$	885.884	0.376198
$178$	5430.07	2.28652
$179$	−262.928	−0.109789	−0.0548944	−	0.998492i	$-0.517482\pi$
$179$	−262.928	−0.109789	−0.0548944	+	0.998492i	$0.517482\pi$
$180$	−859.415	−0.355872
$181$	−623.672	−0.256117	−0.128058	−	0.991767i	$-0.540875\pi$
$181$	−623.672	−0.256117	−0.128058	+	0.991767i	$0.540875\pi$
$182$	0	0
$183$	−5583.52	−2.25544
$184$	−6511.40	−2.60884
$185$	−54.9109	−0.0218223
$186$	−13105.2	−5.16626
$187$	−276.864	−0.108269
$188$	−1730.10	−0.671172
$189$	−11436.9	−4.40166
$190$	320.721	0.122461
$191$	4179.40	1.58330	0.791652	−	0.610972i	$-0.209221\pi$
$191$	4179.40	1.58330	0.791652	+	0.610972i	$0.209221\pi$
$192$	−6025.34	−2.26480
$193$	234.435	0.0874353	0.0437176	−	0.999044i	$-0.486080\pi$
$193$	234.435	0.0874353	0.0437176	+	0.999044i	$0.486080\pi$
$194$	−8770.83	−3.24592
$195$	0	0
$196$	5504.72	2.00609
$197$	183.685	0.0664317	0.0332159	−	0.999448i	$-0.489425\pi$
$197$	183.685	0.0664317	0.0332159	+	0.999448i	$0.489425\pi$
$198$	−3767.47	−1.35223
$199$	2447.13	0.871720	0.435860	−	0.900014i	$-0.356444\pi$
$199$	2447.13	0.871720	0.435860	+	0.900014i	$0.356444\pi$
$200$	4481.18	1.58434
$201$	−7537.12	−2.64491
$202$	3878.19	1.35083
$203$	−431.085	−0.149045
$204$	−3842.32	−1.31871
$205$	−190.423	−0.0648767
$206$	−1768.37	−0.598099
$207$	12785.1	4.29286
$208$	0	0
$209$	926.137	0.306518
$210$	−996.031	−0.327298
$211$	3198.37	1.04353	0.521765	−	0.853089i	$-0.325274\pi$
$211$	3198.37	1.04353	0.521765	+	0.853089i	$0.325274\pi$
$212$	−7223.56	−2.34017
$213$	7306.20	2.35029
$214$	−1622.32	−0.518222
$215$	252.106	0.0799697
$216$	−15579.6	−4.90766
$217$	−7241.19	−2.26527
$218$	1167.75	0.362798
$219$	−8567.50	−2.64355
$220$	−133.638	−0.0409539
$221$	0	0
$222$	−3340.66	−1.00996
$223$	886.798	0.266298	0.133149	−	0.991096i	$-0.457491\pi$
$223$	886.798	0.266298	0.133149	+	0.991096i	$0.457491\pi$
$224$	−1104.74	−0.329525
$225$	−8798.73	−2.60703
$226$	−1979.27	−0.582562
$227$	−1905.52	−0.557154	−0.278577	−	0.960414i	$-0.589863\pi$
$227$	−1905.52	−0.557154	−0.278577	+	0.960414i	$0.589863\pi$
$228$	12852.9	3.73336
$229$	−1236.89	−0.356927	−0.178464	−	0.983947i	$-0.557113\pi$
$229$	−1236.89	−0.356927	−0.178464	+	0.983947i	$0.557113\pi$
$230$	688.463	0.197373
$231$	−2876.21	−0.819225
$232$	−587.231	−0.166179
$233$	−2617.36	−0.735917	−0.367959	−	0.929842i	$-0.619943\pi$
$233$	−2617.36	−0.735917	−0.367959	+	0.929842i	$0.619943\pi$
$234$	0	0
$235$	88.1538	0.0244703
$236$	1383.64	0.381641
$237$	13512.9	3.70361
$238$	−3222.97	−0.877789
$239$	−848.203	−0.229564	−0.114782	−	0.993391i	$-0.536617\pi$
$239$	−848.203	−0.229564	−0.114782	+	0.993391i	$0.536617\pi$
$240$	−395.943	−0.106492
$241$	4589.45	1.22669	0.613346	−	0.789814i	$-0.289823\pi$
$241$	4589.45	1.22669	0.613346	+	0.789814i	$0.289823\pi$
$242$	−585.836	−0.155616
$243$	11707.5	3.09068
$244$	−8720.76	−2.28807
$245$	−280.482	−0.0731402
$246$	−11584.9	−3.00255
$247$	0	0
$248$	−9864.07	−2.52568
$249$	−6625.79	−1.68631
$250$	−949.965	−0.240324
$251$	1755.09	0.441355	0.220677	−	0.975347i	$-0.429173\pi$
$251$	1755.09	0.441355	0.220677	+	0.975347i	$0.429173\pi$
$252$	−28889.6	−7.22172
$253$	1988.06	0.494024
$254$	−6689.86	−1.65260
$255$	195.778	0.0480787
$256$	−7792.94	−1.90257
$257$	50.5818	0.0122771	0.00613854	−	0.999981i	$-0.498046\pi$
$257$	50.5818	0.0122771	0.00613854	+	0.999981i	$0.498046\pi$
$258$	15337.6	3.70107
$259$	−1845.85	−0.442840
$260$	0	0
$261$	1153.02	0.273449
$262$	−7094.20	−1.67283
$263$	784.971	0.184043	0.0920217	−	0.995757i	$-0.470667\pi$
$263$	784.971	0.184043	0.0920217	+	0.995757i	$0.470667\pi$
$264$	−3918.03	−0.913401
$265$	368.062	0.0853203
$266$	10781.2	2.48509
$267$	−11088.0	−2.54147
$268$	−11772.1	−2.68318
$269$	7246.89	1.64257	0.821284	−	0.570520i	$-0.193258\pi$
$269$	7246.89	1.64257	0.821284	+	0.570520i	$0.193258\pi$
$270$	1647.26	0.371292
$271$	−1178.96	−0.264269	−0.132134	−	0.991232i	$-0.542183\pi$
$271$	−1178.96	−0.264269	−0.132134	+	0.991232i	$0.542183\pi$
$272$	−1281.20	−0.285603
$273$	0	0
$274$	−4407.54	−0.971786
$275$	−1368.19	−0.300018
$276$	27590.3	6.01717
$277$	6448.98	1.39885	0.699425	−	0.714706i	$-0.253439\pi$
$277$	6448.98	1.39885	0.699425	+	0.714706i	$0.253439\pi$
$278$	−14011.3	−3.02281
$279$	19368.0	4.15602
$280$	−749.694	−0.160010
$281$	2313.89	0.491228	0.245614	−	0.969368i	$-0.421010\pi$
$281$	2313.89	0.491228	0.245614	+	0.969368i	$0.421010\pi$
$282$	5363.09	1.13251
$283$	1876.52	0.394161	0.197081	−	0.980387i	$-0.436854\pi$
$283$	1876.52	0.394161	0.197081	+	0.980387i	$0.436854\pi$
$284$	11411.4	2.38430
$285$	−654.897	−0.136115
$286$	0	0
$287$	−6401.14	−1.31654
$288$	2954.85	0.604569
$289$	−4279.50	−0.871056
$290$	62.0891	0.0125724
$291$	17909.6	3.60784
$292$	−13381.4	−2.68180
$293$	165.034	0.0329058	0.0164529	−	0.999865i	$-0.494763\pi$
$293$	165.034	0.0329058	0.0164529	+	0.999865i	$0.494763\pi$
$294$	−17063.9	−3.38500
$295$	−70.5007	−0.0139143
$296$	−2514.45	−0.493748
$297$	4756.75	0.929341
$298$	5379.35	1.04570
$299$	0	0
$300$	−18987.8	−3.65420
$301$	8474.65	1.62283
$302$	−8738.64	−1.66507
$303$	−7919.09	−1.50145
$304$	4285.73	0.808564
$305$	444.350	0.0834209
$306$	8620.45	1.61045
$307$	−4116.91	−0.765357	−0.382678	−	0.923882i	$-0.624998\pi$
$307$	−4116.91	−0.765357	−0.382678	+	0.923882i	$0.624998\pi$
$308$	−4492.29	−0.831078
$309$	3610.94	0.664787
$310$	1042.95	0.191082
$311$	1434.89	0.261624	0.130812	−	0.991407i	$-0.458242\pi$
$311$	1434.89	0.261624	0.130812	+	0.991407i	$0.458242\pi$
$312$	0	0
$313$	1667.94	0.301206	0.150603	−	0.988594i	$-0.451878\pi$
$313$	1667.94	0.301206	0.150603	+	0.988594i	$0.451878\pi$
$314$	3295.90	0.592352
$315$	1472.01	0.263297
$316$	21105.4	3.75719
$317$	−1199.08	−0.212452	−0.106226	−	0.994342i	$-0.533877\pi$
$317$	−1199.08	−0.212452	−0.106226	+	0.994342i	$0.533877\pi$
$318$	22392.1	3.94870
$319$	179.293	0.0314686
$320$	479.511	0.0837671
$321$	3312.70	0.576003
$322$	23143.0	4.00530
$323$	−2119.12	−0.365050
$324$	36521.5	6.26227
$325$	0	0
$326$	−12094.0	−2.05467
$327$	−2384.49	−0.403249
$328$	−8719.75	−1.46789
$329$	2963.33	0.496576
$330$	414.260	0.0691039
$331$	10263.6	1.70434	0.852172	−	0.523261i	$-0.175285\pi$
$331$	10263.6	1.70434	0.852172	+	0.523261i	$0.175285\pi$
$332$	−10348.7	−1.71071
$333$	4937.09	0.812465
$334$	−10444.6	−1.71109
$335$	599.822	0.0978262
$336$	−13309.8	−2.16104
$337$	4596.47	0.742984	0.371492	−	0.928436i	$-0.378846\pi$
$337$	4596.47	0.742984	0.371492	+	0.928436i	$0.378846\pi$
$338$	0	0
$339$	4041.58	0.647517
$340$	305.781	0.0487744
$341$	3011.69	0.478277
$342$	−28836.3	−4.55932
$343$	−356.880	−0.0561799
$344$	11544.3	1.80938
$345$	−1405.81	−0.219380
$346$	−10909.5	−1.69509
$347$	−3602.74	−0.557364	−0.278682	−	0.960383i	$-0.589898\pi$
$347$	−3602.74	−0.557364	−0.278682	+	0.960383i	$0.589898\pi$
$348$	2488.23	0.383285
$349$	−2027.47	−0.310968	−0.155484	−	0.987838i	$-0.549694\pi$
$349$	−2027.47	−0.310968	−0.155484	+	0.987838i	$0.549694\pi$
$350$	−15927.1	−2.43240
$351$	0	0
$352$	459.474	0.0695741
$353$	−4501.19	−0.678680	−0.339340	−	0.940664i	$-0.610204\pi$
$353$	−4501.19	−0.678680	−0.339340	+	0.940664i	$0.610204\pi$
$354$	−4289.11	−0.643965
$355$	−581.445	−0.0869293
$356$	−17318.0	−2.57824
$357$	6581.15	0.975662
$358$	1273.00	0.187933
$359$	3455.96	0.508074	0.254037	−	0.967195i	$-0.418242\pi$
$359$	3455.96	0.508074	0.254037	+	0.967195i	$0.418242\pi$
$360$	2005.20	0.293565
$361$	229.681	0.0334860
$362$	3019.58	0.438413
$363$	1196.25	0.172967
$364$	0	0
$365$	681.822	0.0977759
$366$	27033.3	3.86080
$367$	−8161.92	−1.16090	−0.580448	−	0.814298i	$-0.697122\pi$
$367$	−8161.92	−1.16090	−0.580448	+	0.814298i	$0.697122\pi$
$368$	9199.80	1.30319
$369$	17121.1	2.41542
$370$	265.858	0.0373548
$371$	12372.6	1.73141
$372$	41796.3	5.82537
$373$	−8396.54	−1.16557	−0.582784	−	0.812627i	$-0.698036\pi$
$373$	−8396.54	−1.16557	−0.582784	+	0.812627i	$0.698036\pi$
$374$	1340.47	0.185331
$375$	1939.78	0.267120
$376$	4036.69	0.553661
$377$	0	0
$378$	55373.2	7.53463
$379$	1514.56	0.205271	0.102636	−	0.994719i	$-0.467272\pi$
$379$	1514.56	0.205271	0.102636	+	0.994719i	$0.467272\pi$
$380$	−1022.87	−0.138084
$381$	13660.4	1.83686
$382$	−20235.1	−2.71025
$383$	−2236.24	−0.298346	−0.149173	−	0.988811i	$-0.547661\pi$
$383$	−2236.24	−0.298346	−0.149173	+	0.988811i	$0.547661\pi$
$384$	25868.7	3.43778
$385$	228.896	0.0303003
$386$	−1135.05	−0.149669
$387$	−22667.1	−2.97735
$388$	27972.6	3.66004
$389$	−15127.7	−1.97173	−0.985867	−	0.167528i	$-0.946422\pi$
$389$	−15127.7	−1.97173	−0.985867	+	0.167528i	$0.946422\pi$
$390$	0	0
$391$	−4548.93	−0.588362
$392$	−12843.7	−1.65486
$393$	14486.0	1.85935
$394$	−889.335	−0.113716
$395$	−1075.39	−0.136984
$396$	12015.5	1.52475
$397$	2602.82	0.329048	0.164524	−	0.986373i	$-0.447391\pi$
$397$	2602.82	0.329048	0.164524	+	0.986373i	$0.447391\pi$
$398$	−11848.1	−1.49219
$399$	−22014.6	−2.76218
$400$	−6331.35	−0.791419
$401$	−9212.24	−1.14723	−0.573613	−	0.819127i	$-0.694459\pi$
$401$	−9212.24	−1.14723	−0.573613	+	0.819127i	$0.694459\pi$
$402$	36491.9	4.52749
$403$	0	0
$404$	−12368.6	−1.52318
$405$	−1860.88	−0.228316
$406$	2087.15	0.255132
$407$	767.711	0.0934988
$408$	8964.95	1.08782
$409$	−12568.5	−1.51949	−0.759747	−	0.650219i	$-0.774677\pi$
$409$	−12568.5	−1.51949	−0.759747	+	0.650219i	$0.774677\pi$
$410$	921.955	0.111054
$411$	9000.00	1.08014
$412$	5639.84	0.674405
$413$	−2369.91	−0.282362
$414$	−61900.4	−7.34840
$415$	527.296	0.0623709
$416$	0	0
$417$	28610.4	3.35985
$418$	−4484.00	−0.524689
$419$	4748.02	0.553594	0.276797	−	0.960928i	$-0.410727\pi$
$419$	4748.02	0.553594	0.276797	+	0.960928i	$0.410727\pi$
$420$	3176.62	0.369055
$421$	14610.5	1.69138	0.845689	−	0.533675i	$-0.179190\pi$
$421$	14610.5	1.69138	0.845689	+	0.533675i	$0.179190\pi$
$422$	−15485.3	−1.78628
$423$	−7925.99	−0.911052
$424$	16854.1	1.93044
$425$	3130.60	0.357309
$426$	−35373.8	−4.02316
$427$	14937.0	1.69286
$428$	5174.03	0.584337
$429$	0	0
$430$	−1220.60	−0.136890
$431$	−13757.8	−1.53756	−0.768782	−	0.639511i	$-0.779137\pi$
$431$	−13757.8	−1.53756	−0.768782	+	0.639511i	$0.779137\pi$
$432$	22012.0	2.45151
$433$	−75.9256	−0.00842668	−0.00421334	−	0.999991i	$-0.501341\pi$
$433$	−75.9256	−0.00842668	−0.00421334	+	0.999991i	$0.501341\pi$
$434$	35059.1	3.87763
$435$	−126.783	−0.0139742
$436$	−3724.27	−0.409083
$437$	15216.6	1.66570
$438$	41480.6	4.52516
$439$	9974.22	1.08438	0.542191	−	0.840255i	$-0.317595\pi$
$439$	9974.22	1.08438	0.542191	+	0.840255i	$0.317595\pi$
$440$	311.806	0.0337836
$441$	25218.4	2.72308
$442$	0	0
$443$	−12635.2	−1.35512	−0.677558	−	0.735470i	$-0.736962\pi$
$443$	−12635.2	−1.35512	−0.677558	+	0.735470i	$0.736962\pi$
$444$	10654.3	1.13881
$445$	882.406	0.0940001
$446$	−4293.54	−0.455841
$447$	−10984.4	−1.16229
$448$	16118.9	1.69989
$449$	−7218.88	−0.758753	−0.379376	−	0.925242i	$-0.623861\pi$
$449$	−7218.88	−0.758753	−0.379376	+	0.925242i	$0.623861\pi$
$450$	42600.1	4.46264
$451$	2662.31	0.277967
$452$	6312.45	0.656886
$453$	17843.9	1.85073
$454$	9225.81	0.953720
$455$	0	0
$456$	−29988.7	−3.07971
$457$	6510.57	0.666415	0.333207	−	0.942854i	$-0.391869\pi$
$457$	6510.57	0.666415	0.333207	+	0.942854i	$0.391869\pi$
$458$	5988.57	0.610977
$459$	−10884.0	−1.10681
$460$	−2195.70	−0.222555
$461$	2706.53	0.273440	0.136720	−	0.990610i	$-0.456344\pi$
$461$	2706.53	0.273440	0.136720	+	0.990610i	$0.456344\pi$
$462$	13925.5	1.40233
$463$	−4770.17	−0.478809	−0.239404	−	0.970920i	$-0.576952\pi$
$463$	−4770.17	−0.478809	−0.239404	+	0.970920i	$0.576952\pi$
$464$	829.685	0.0830111
$465$	−2129.65	−0.212387
$466$	12672.2	1.25972
$467$	16825.5	1.66722	0.833608	−	0.552356i	$-0.186271\pi$
$467$	16825.5	1.66722	0.833608	+	0.552356i	$0.186271\pi$
$468$	0	0
$469$	20163.3	1.98519
$470$	−426.807	−0.0418876
$471$	−6730.09	−0.658399
$472$	−3228.33	−0.314822
$473$	−3524.70	−0.342634
$474$	−65424.1	−6.33972
$475$	−10472.2	−1.01157
$476$	10278.9	0.989778
$477$	−33092.8	−3.17656
$478$	4106.68	0.392960
$479$	19091.9	1.82115	0.910576	−	0.413343i	$-0.135639\pi$
$479$	19091.9	1.82115	0.910576	+	0.413343i	$0.135639\pi$
$480$	−324.907	−0.0308956
$481$	0	0
$482$	−22220.4	−2.09982
$483$	−47256.8	−4.45189
$484$	1868.39	0.175469
$485$	−1425.29	−0.133441
$486$	−56683.1	−5.29053
$487$	9055.73	0.842616	0.421308	−	0.906918i	$-0.361571\pi$
$487$	9055.73	0.842616	0.421308	+	0.906918i	$0.361571\pi$
$488$	20347.4	1.88747
$489$	24695.3	2.28377
$490$	1357.99	0.125199
$491$	−6322.21	−0.581094	−0.290547	−	0.956861i	$-0.593837\pi$
$491$	−6322.21	−0.581094	−0.290547	+	0.956861i	$0.593837\pi$
$492$	36947.5	3.38562
$493$	−410.246	−0.0374778
$494$	0	0
$495$	−612.227	−0.0555910
$496$	13936.7	1.26165
$497$	−19545.5	−1.76406
$498$	32079.5	2.88658
$499$	8884.07	0.797005	0.398503	−	0.917167i	$-0.369530\pi$
$499$	8884.07	0.797005	0.398503	+	0.917167i	$0.369530\pi$
$500$	3029.70	0.270985
$501$	21327.4	1.90187
$502$	−8497.45	−0.755498
$503$	−4543.52	−0.402754	−0.201377	−	0.979514i	$-0.564542\pi$
$503$	−4543.52	−0.402754	−0.201377	+	0.979514i	$0.564542\pi$
$504$	67405.7	5.95732
$505$	630.220	0.0555335
$506$	−9625.42	−0.845656
$507$	0	0
$508$	21335.8	1.86343
$509$	−14120.7	−1.22964	−0.614821	−	0.788667i	$-0.710772\pi$
$509$	−14120.7	−1.22964	−0.614821	+	0.788667i	$0.710772\pi$
$510$	−947.881	−0.0822998
$511$	22919.7	1.98417
$512$	16797.6	1.44991
$513$	36408.3	3.13346
$514$	−244.898	−0.0210155
$515$	−287.367	−0.0245882
$516$	−48915.8	−4.17326
$517$	−1232.48	−0.104844
$518$	8936.91	0.758041
$519$	22276.8	1.88409
$520$	0	0
$521$	−10766.6	−0.905361	−0.452681	−	0.891673i	$-0.649532\pi$
$521$	−10766.6	−0.905361	−0.452681	+	0.891673i	$0.649532\pi$
$522$	−5582.49	−0.468082
$523$	18187.9	1.52065	0.760327	−	0.649541i	$-0.225039\pi$
$523$	18187.9	1.52065	0.760327	+	0.649541i	$0.225039\pi$
$524$	22625.4	1.88625
$525$	32522.4	2.70361
$526$	−3800.53	−0.315040
$527$	−6891.14	−0.569607
$528$	5535.69	0.456269
$529$	20497.2	1.68466
$530$	−1782.02	−0.146049
$531$	6338.79	0.518041
$532$	−34384.1	−2.80214
$533$	0	0
$534$	53683.6	4.35041
$535$	−263.633	−0.0213044
$536$	27466.7	2.21340
$537$	−2599.41	−0.208888
$538$	−35086.7	−2.81170
$539$	3921.43	0.313373
$540$	−5253.57	−0.418662
$541$	4714.21	0.374639	0.187319	−	0.982299i	$-0.440020\pi$
$541$	4714.21	0.374639	0.187319	+	0.982299i	$0.440020\pi$
$542$	5708.09	0.452368
$543$	−6165.85	−0.487296
$544$	−1051.34	−0.0828597
$545$	189.763	0.0149148
$546$	0	0
$547$	−12253.9	−0.957841	−0.478921	−	0.877858i	$-0.658972\pi$
$547$	−12253.9	−0.957841	−0.478921	+	0.877858i	$0.658972\pi$
$548$	14056.9	1.09577
$549$	−39951.9	−3.10584
$550$	6624.26	0.513562
$551$	1372.31	0.106103
$552$	−64374.1	−4.96367
$553$	−36149.5	−2.77981
$554$	−31223.5	−2.39451
$555$	−542.869	−0.0415198
$556$	44685.9	3.40846
$557$	10069.4	0.765985	0.382993	−	0.923751i	$-0.374893\pi$
$557$	10069.4	0.765985	0.382993	+	0.923751i	$0.374893\pi$
$558$	−93772.4	−7.11416
$559$	0	0
$560$	1059.22	0.0799293
$561$	−2737.17	−0.205996
$562$	−11203.0	−0.840870
$563$	−1899.37	−0.142183	−0.0710913	−	0.997470i	$-0.522648\pi$
$563$	−1899.37	−0.142183	−0.0710913	+	0.997470i	$0.522648\pi$
$564$	−17104.4	−1.27699
$565$	−321.638	−0.0239494
$566$	−9085.40	−0.674714
$567$	−62554.4	−4.63322
$568$	−26625.2	−1.96685
$569$	7350.17	0.541538	0.270769	−	0.962644i	$-0.412722\pi$
$569$	7350.17	0.541538	0.270769	+	0.962644i	$0.412722\pi$
$570$	3170.76	0.232997
$571$	8371.62	0.613558	0.306779	−	0.951781i	$-0.400749\pi$
$571$	8371.62	0.613558	0.306779	+	0.951781i	$0.400749\pi$
$572$	0	0
$573$	41319.1	3.01244
$574$	30991.9	2.25362
$575$	−22479.7	−1.63038
$576$	−43113.3	−3.11873
$577$	1067.50	0.0770203	0.0385102	−	0.999258i	$-0.487739\pi$
$577$	1067.50	0.0770203	0.0385102	+	0.999258i	$0.487739\pi$
$578$	20719.7	1.49105
$579$	2317.71	0.166357
$580$	−198.019	−0.0141764
$581$	17725.3	1.26569
$582$	−86711.6	−6.17579
$583$	−5145.89	−0.365559
$584$	31221.6	2.21226
$585$	0	0
$586$	−799.033	−0.0563272
$587$	7129.52	0.501306	0.250653	−	0.968077i	$-0.419355\pi$
$587$	7129.52	0.501306	0.250653	+	0.968077i	$0.419355\pi$
$588$	54421.6	3.81686
$589$	23051.6	1.61260
$590$	341.338	0.0238181
$591$	1815.98	0.126395
$592$	3552.61	0.246641
$593$	864.433	0.0598617	0.0299309	−	0.999552i	$-0.490471\pi$
$593$	864.433	0.0598617	0.0299309	+	0.999552i	$0.490471\pi$
$594$	−23030.4	−1.59082
$595$	−523.744	−0.0360864
$596$	−17156.3	−1.17911
$597$	24193.2	1.65856
$598$	0	0
$599$	−9400.90	−0.641253	−0.320626	−	0.947206i	$-0.603893\pi$
$599$	−9400.90	−0.641253	−0.320626	+	0.947206i	$0.603893\pi$
$600$	44302.6	3.01441
$601$	−12501.7	−0.848511	−0.424256	−	0.905542i	$-0.639464\pi$
$601$	−12501.7	−0.848511	−0.424256	+	0.905542i	$0.639464\pi$
$602$	−41031.0	−2.77791
$603$	−53930.6	−3.64216
$604$	27870.0	1.87751
$605$	−95.2004	−0.00639744
$606$	38341.2	2.57014
$607$	−1883.36	−0.125936	−0.0629681	−	0.998016i	$-0.520057\pi$
$607$	−1883.36	−0.125936	−0.0629681	+	0.998016i	$0.520057\pi$
$608$	3516.83	0.234583
$609$	−4261.86	−0.283579
$610$	−2151.37	−0.142798
$611$	0	0
$612$	−27493.0	−1.81592
$613$	−6329.61	−0.417048	−0.208524	−	0.978017i	$-0.566866\pi$
$613$	−6329.61	−0.417048	−0.208524	+	0.978017i	$0.566866\pi$
$614$	19932.5	1.31012
$615$	−1882.59	−0.123436
$616$	10481.5	0.685570
$617$	−22158.6	−1.44582	−0.722910	−	0.690942i	$-0.757196\pi$
$617$	−22158.6	−1.44582	−0.722910	+	0.690942i	$0.757196\pi$
$618$	−17482.8	−1.13796
$619$	−7167.37	−0.465397	−0.232699	−	0.972549i	$-0.574756\pi$
$619$	−7167.37	−0.465397	−0.232699	+	0.972549i	$0.574756\pi$
$620$	−3326.25	−0.215460
$621$	78154.4	5.05029
$622$	−6947.17	−0.447840
$623$	29662.4	1.90754
$624$	0	0
$625$	15393.2	0.985168
$626$	−8075.53	−0.515596
$627$	9156.13	0.583191
$628$	−10511.6	−0.667925
$629$	−1756.62	−0.111353
$630$	−7126.93	−0.450704
$631$	26888.3	1.69636	0.848181	−	0.529707i	$-0.177698\pi$
$631$	26888.3	1.69636	0.848181	+	0.529707i	$0.177698\pi$
$632$	−49243.5	−3.09937
$633$	31620.2	1.98545
$634$	5805.51	0.363669
$635$	−1087.13	−0.0679390
$636$	−71414.7	−4.45248
$637$	0	0
$638$	−868.069	−0.0538671
$639$	52278.3	3.23646
$640$	−2058.70	−0.127152
$641$	−26367.6	−1.62474	−0.812369	−	0.583143i	$-0.801823\pi$
$641$	−26367.6	−1.62474	−0.812369	+	0.583143i	$0.801823\pi$
$642$	−16038.8	−0.985986
$643$	−21771.5	−1.33528	−0.667640	−	0.744484i	$-0.732695\pi$
$643$	−21771.5	−1.33528	−0.667640	+	0.744484i	$0.732695\pi$
$644$	−73809.4	−4.51630
$645$	2492.41	0.152153
$646$	10260.0	0.624882
$647$	1671.81	0.101585	0.0507927	−	0.998709i	$-0.483825\pi$
$647$	1671.81	0.101585	0.0507927	+	0.998709i	$0.483825\pi$
$648$	−85212.7	−5.16585
$649$	985.673	0.0596164
$650$	0	0
$651$	−71589.0	−4.30998
$652$	38571.1	2.31681
$653$	6157.13	0.368985	0.184492	−	0.982834i	$-0.440936\pi$
$653$	6157.13	0.368985	0.184492	+	0.982834i	$0.440936\pi$
$654$	11544.8	0.690270
$655$	−1152.83	−0.0687708
$656$	12319.9	0.733250
$657$	−61303.3	−3.64029
$658$	−14347.3	−0.850024
$659$	8784.33	0.519255	0.259627	−	0.965709i	$-0.416400\pi$
$659$	8784.33	0.519255	0.259627	+	0.965709i	$0.416400\pi$
$660$	−1321.19	−0.0779202
$661$	13358.4	0.786054	0.393027	−	0.919527i	$-0.371428\pi$
$661$	13358.4	0.786054	0.393027	+	0.919527i	$0.371428\pi$
$662$	−49692.4	−2.91745
$663$	0	0
$664$	24145.7	1.41119
$665$	1751.98	0.102163
$666$	−23903.5	−1.39075
$667$	2945.83	0.171009
$668$	33310.7	1.92939
$669$	8767.21	0.506667
$670$	−2904.11	−0.167456
$671$	−6212.46	−0.357421
$672$	−10921.9	−0.626965
$673$	−7725.74	−0.442504	−0.221252	−	0.975217i	$-0.571014\pi$
$673$	−7725.74	−0.442504	−0.221252	+	0.975217i	$0.571014\pi$
$674$	−22254.4	−1.27182
$675$	−53786.2	−3.06701
$676$	0	0
$677$	−9055.37	−0.514071	−0.257035	−	0.966402i	$-0.582746\pi$
$677$	−9055.37	−0.514071	−0.257035	+	0.966402i	$0.582746\pi$
$678$	−19567.8	−1.10840
$679$	−47911.7	−2.70793
$680$	−713.452	−0.0402348
$681$	−18838.7	−1.06006
$682$	−14581.5	−0.818700
$683$	−26079.5	−1.46106	−0.730531	−	0.682880i	$-0.760727\pi$
$683$	−26079.5	−1.46106	−0.730531	+	0.682880i	$0.760727\pi$
$684$	91967.0	5.14101
$685$	−716.241	−0.0399506
$686$	1727.88	0.0961671
$687$	−12228.4	−0.679101
$688$	−16310.7	−0.903835
$689$	0	0
$690$	6806.39	0.375529
$691$	−17738.8	−0.976579	−0.488290	−	0.872682i	$-0.662379\pi$
$691$	−17738.8	−0.976579	−0.488290	+	0.872682i	$0.662379\pi$
$692$	34793.6	1.91135
$693$	−20580.3	−1.12811
$694$	17443.1	0.954080
$695$	−2276.88	−0.124269
$696$	−5805.58	−0.316178
$697$	−6091.70	−0.331047
$698$	9816.24	0.532307
$699$	−25876.1	−1.40018
$700$	50796.0	2.74272
$701$	−22990.4	−1.23871	−0.619354	−	0.785112i	$-0.712606\pi$
$701$	−22990.4	−1.23871	−0.619354	+	0.785112i	$0.712606\pi$
$702$	0	0
$703$	5876.08	0.315250
$704$	−6704.05	−0.358904
$705$	871.521	0.0465580
$706$	21793.0	1.16174
$707$	21185.1	1.12694
$708$	13679.2	0.726123
$709$	−4848.18	−0.256809	−0.128404	−	0.991722i	$-0.540986\pi$
$709$	−4848.18	−0.256809	−0.128404	+	0.991722i	$0.540986\pi$
$710$	2815.13	0.148803
$711$	96688.9	5.10003
$712$	40406.7	2.12683
$713$	49482.8	2.59908
$714$	−31863.4	−1.67011
$715$	0	0
$716$	−4059.95	−0.211910
$717$	−8385.64	−0.436775
$718$	−16732.4	−0.869706
$719$	−1737.98	−0.0901470	−0.0450735	−	0.998984i	$-0.514352\pi$
$719$	−1737.98	−0.0901470	−0.0450735	+	0.998984i	$0.514352\pi$
$720$	−2833.10	−0.146644
$721$	−9659.96	−0.498968
$722$	−1112.03	−0.0573204
$723$	45373.0	2.33394
$724$	−9630.29	−0.494347
$725$	−2027.33	−0.103853
$726$	−5791.79	−0.296079
$727$	−17927.4	−0.914566	−0.457283	−	0.889321i	$-0.651177\pi$
$727$	−17927.4	−0.914566	−0.457283	+	0.889321i	$0.651177\pi$
$728$	0	0
$729$	51884.2	2.63599
$730$	−3301.12	−0.167370
$731$	8064.97	0.408063
$732$	−86216.6	−4.35336
$733$	24607.4	1.23996	0.619982	−	0.784616i	$-0.287140\pi$
$733$	24607.4	1.23996	0.619982	+	0.784616i	$0.287140\pi$
$734$	39516.9	1.98719
$735$	−2772.95	−0.139159
$736$	7549.27	0.378084
$737$	−8386.13	−0.419141
$738$	−82893.9	−4.13464
$739$	−31113.5	−1.54875	−0.774375	−	0.632726i	$-0.781936\pi$
$739$	−31113.5	−1.54875	−0.774375	+	0.632726i	$0.781936\pi$
$740$	−847.895	−0.0421206
$741$	0	0
$742$	−59903.2	−2.96377
$743$	613.655	0.0302999	0.0151499	−	0.999885i	$-0.495177\pi$
$743$	613.655	0.0302999	0.0151499	+	0.999885i	$0.495177\pi$
$744$	−97519.8	−4.80544
$745$	874.164	0.0429891
$746$	40652.9	1.99518
$747$	−47409.7	−2.32213
$748$	−4275.13	−0.208976
$749$	−8862.12	−0.432330
$750$	−9391.70	−0.457248
$751$	−4463.76	−0.216890	−0.108445	−	0.994102i	$-0.534587\pi$
$751$	−4463.76	−0.216890	−0.108445	+	0.994102i	$0.534587\pi$
$752$	−5703.35	−0.276569
$753$	17351.4	0.839735
$754$	0	0
$755$	−1420.06	−0.0684521
$756$	−176601.	−8.49591
$757$	10280.2	0.493581	0.246791	−	0.969069i	$-0.420624\pi$
$757$	10280.2	0.493581	0.246791	+	0.969069i	$0.420624\pi$
$758$	−7332.93	−0.351377
$759$	19654.7	0.939946
$760$	2386.57	0.113908
$761$	28655.5	1.36500	0.682498	−	0.730887i	$-0.260894\pi$
$761$	28655.5	1.36500	0.682498	+	0.730887i	$0.260894\pi$
$762$	−66138.4	−3.14428
$763$	6378.97	0.302666
$764$	64535.4	3.05603
$765$	1400.85	0.0662065
$766$	10827.0	0.510699
$767$	0	0
$768$	−77043.9	−3.61990
$769$	34348.5	1.61071	0.805356	−	0.592791i	$-0.201974\pi$
$769$	34348.5	1.61071	0.805356	+	0.592791i	$0.201974\pi$
$770$	−1108.23	−0.0518672
$771$	500.070	0.0233587
$772$	3619.98	0.168764
$773$	28254.0	1.31465	0.657326	−	0.753606i	$-0.271687\pi$
$773$	28254.0	1.31465	0.657326	+	0.753606i	$0.271687\pi$
$774$	109745.	5.09654
$775$	−34054.3	−1.57841
$776$	−65266.2	−3.01923
$777$	−18248.8	−0.842562
$778$	73242.6	3.37516
$779$	20377.4	0.937221
$780$	0	0
$781$	8129.20	0.372453
$782$	22024.2	1.00714
$783$	7048.36	0.321696
$784$	18146.6	0.826647
$785$	535.596	0.0243519
$786$	−70135.8	−3.18278
$787$	7619.96	0.345136	0.172568	−	0.984998i	$-0.444794\pi$
$787$	7619.96	0.345136	0.172568	+	0.984998i	$0.444794\pi$
$788$	2836.34	0.128224
$789$	7760.51	0.350167
$790$	5206.61	0.234485
$791$	−10812.0	−0.486006
$792$	−28034.8	−1.25779
$793$	0	0
$794$	−12601.9	−0.563255
$795$	3638.80	0.162333
$796$	37786.8	1.68256
$797$	−23554.9	−1.04687	−0.523436	−	0.852065i	$-0.675350\pi$
$797$	−23554.9	−1.04687	−0.523436	+	0.852065i	$0.675350\pi$
$798$	106586.	4.72822
$799$	2820.08	0.124865
$800$	−5195.44	−0.229608
$801$	−79338.0	−3.49971
$802$	44602.2	1.96379
$803$	−9532.58	−0.418926
$804$	−116383.	−5.10511
$805$	3760.81	0.164660
$806$	0	0
$807$	71645.4	3.12520
$808$	28858.7	1.25649
$809$	28517.6	1.23934	0.619670	−	0.784862i	$-0.287266\pi$
$809$	28517.6	1.23934	0.619670	+	0.784862i	$0.287266\pi$
$810$	9009.70	0.390825
$811$	−2442.23	−0.105744	−0.0528720	−	0.998601i	$-0.516838\pi$
$811$	−2442.23	−0.105744	−0.0528720	+	0.998601i	$0.516838\pi$
$812$	−6656.50	−0.287682
$813$	−11655.6	−0.502806
$814$	−3716.96	−0.160049
$815$	−1965.32	−0.0844687
$816$	−12666.4	−0.543397
$817$	−26978.2	−1.15526
$818$	60852.0	2.60103
$819$	0	0
$820$	−2940.37	−0.125222
$821$	1622.92	0.0689893	0.0344946	−	0.999405i	$-0.489018\pi$
$821$	1622.92	0.0689893	0.0344946	+	0.999405i	$0.489018\pi$
$822$	−43574.6	−1.84895
$823$	45908.6	1.94444	0.972219	−	0.234073i	$-0.0752055\pi$
$823$	45908.6	1.94444	0.972219	+	0.234073i	$0.0752055\pi$
$824$	−13159.0	−0.556328
$825$	−13526.4	−0.570824
$826$	11474.2	0.483340
$827$	−22218.5	−0.934235	−0.467118	−	0.884195i	$-0.654708\pi$
$827$	−22218.5	−0.934235	−0.467118	+	0.884195i	$0.654708\pi$
$828$	197418.	8.28591
$829$	6425.34	0.269193	0.134597	−	0.990900i	$-0.457026\pi$
$829$	6425.34	0.269193	0.134597	+	0.990900i	$0.457026\pi$
$830$	−2552.97	−0.106765
$831$	63757.0	2.66150
$832$	0	0
$833$	−8972.74	−0.373214
$834$	−138521.	−5.75129
$835$	−1697.28	−0.0703436
$836$	14300.7	0.591629
$837$	118396.	4.88930
$838$	−22988.1	−0.947626
$839$	3735.70	0.153720	0.0768598	−	0.997042i	$-0.475511\pi$
$839$	3735.70	0.153720	0.0768598	+	0.997042i	$0.475511\pi$
$840$	−7411.74	−0.304440
$841$	−24123.3	−0.989107
$842$	−70738.3	−2.89525
$843$	22875.9	0.934626
$844$	49386.9	2.01418
$845$	0	0
$846$	38374.6	1.55951
$847$	−3200.20	−0.129823
$848$	−23812.8	−0.964309
$849$	18552.0	0.749944
$850$	−15157.2	−0.611631
$851$	12613.7	0.508097
$852$	112817.	4.53644
$853$	27791.1	1.11553	0.557765	−	0.829999i	$-0.311659\pi$
$853$	27791.1	1.11553	0.557765	+	0.829999i	$0.311659\pi$
$854$	−72319.2	−2.89779
$855$	−4686.00	−0.187436
$856$	−12072.1	−0.482029
$857$	−46913.6	−1.86994	−0.934970	−	0.354726i	$-0.884574\pi$
$857$	−46913.6	−1.86994	−0.934970	+	0.354726i	$0.884574\pi$
$858$	0	0
$859$	11554.3	0.458937	0.229469	−	0.973316i	$-0.426301\pi$
$859$	11554.3	0.458937	0.229469	+	0.973316i	$0.426301\pi$
$860$	3892.84	0.154354
$861$	−63284.0	−2.50489
$862$	66610.0	2.63196
$863$	−2563.21	−0.101104	−0.0505519	−	0.998721i	$-0.516098\pi$
$863$	−2563.21	−0.101104	−0.0505519	+	0.998721i	$0.516098\pi$
$864$	18062.8	0.711238
$865$	−1772.84	−0.0696859
$866$	367.603	0.0144245
$867$	−42308.7	−1.65730
$868$	−111813.	−4.37234
$869$	15035.0	0.586913
$870$	613.835	0.0239206
$871$	0	0
$872$	8689.54	0.337460
$873$	128149.	4.96815
$874$	−73673.2	−2.85130
$875$	−5189.30	−0.200492
$876$	−132293.	−5.10248
$877$	1761.13	0.0678098	0.0339049	−	0.999425i	$-0.489206\pi$
$877$	1761.13	0.0678098	0.0339049	+	0.999425i	$0.489206\pi$
$878$	−48291.4	−1.85621
$879$	1631.59	0.0626076
$880$	−440.543	−0.0168758
$881$	−15710.6	−0.600800	−0.300400	−	0.953813i	$-0.597120\pi$
$881$	−15710.6	−0.600800	−0.300400	+	0.953813i	$0.597120\pi$
$882$	−122098.	−4.66129
$883$	36386.5	1.38675	0.693377	−	0.720575i	$-0.256122\pi$
$883$	36386.5	1.38675	0.693377	+	0.720575i	$0.256122\pi$
$884$	0	0
$885$	−696.996	−0.0264737
$886$	61174.8	2.31965
$887$	32956.7	1.24755	0.623776	−	0.781603i	$-0.285598\pi$
$887$	32956.7	1.24755	0.623776	+	0.781603i	$0.285598\pi$
$888$	−24858.8	−0.939421
$889$	−36544.2	−1.37869
$890$	−4272.27	−0.160907
$891$	26017.1	0.978232
$892$	13693.3	0.513997
$893$	−9433.44	−0.353503
$894$	53182.3	1.98958
$895$	206.867	0.00772603
$896$	−69203.9	−2.58029
$897$	0	0
$898$	34951.1	1.29881
$899$	4462.61	0.165558
$900$	−135864.	−5.03199
$901$	11774.5	0.435365
$902$	−12889.9	−0.475816
$903$	83783.4	3.08764
$904$	−14728.3	−0.541876
$905$	490.693	0.0180234
$906$	−86393.4	−3.16802
$907$	−3035.61	−0.111131	−0.0555655	−	0.998455i	$-0.517696\pi$
$907$	−3035.61	−0.111131	−0.0555655	+	0.998455i	$0.517696\pi$
$908$	−29423.7	−1.07540
$909$	−56663.7	−2.06756
$910$	0	0
$911$	−16827.6	−0.611989	−0.305995	−	0.952033i	$-0.598989\pi$
$911$	−16827.6	−0.611989	−0.305995	+	0.952033i	$0.598989\pi$
$912$	42370.3	1.53840
$913$	−7372.14	−0.267231
$914$	−31521.7	−1.14075
$915$	4393.00	0.158719
$916$	−19099.2	−0.688926
$917$	−38752.9	−1.39557
$918$	52696.4	1.89460
$919$	20591.6	0.739124	0.369562	−	0.929206i	$-0.379508\pi$
$919$	20591.6	0.739124	0.369562	+	0.929206i	$0.379508\pi$
$920$	5123.04	0.183589
$921$	−40701.3	−1.45619
$922$	−13104.0	−0.468067
$923$	0	0
$924$	−44412.4	−1.58124
$925$	−8680.78	−0.308565
$926$	23095.3	0.819611
$927$	25837.5	0.915440
$928$	680.831	0.0240834
$929$	−33226.6	−1.17344	−0.586722	−	0.809788i	$-0.699582\pi$
$929$	−33226.6	−1.17344	−0.586722	+	0.809788i	$0.699582\pi$
$930$	10311.0	0.363559
$931$	30014.7	1.05660
$932$	−40415.3	−1.42044
$933$	14185.8	0.497773
$934$	−81462.5	−2.85389
$935$	217.831	0.00761907
$936$	0	0
$937$	−29758.0	−1.03752	−0.518758	−	0.854921i	$-0.673606\pi$
$937$	−29758.0	−1.03752	−0.518758	+	0.854921i	$0.673606\pi$
$938$	−97622.9	−3.39819
$939$	16489.8	0.573084
$940$	1361.21	0.0472316
$941$	−29373.3	−1.01758	−0.508789	−	0.860891i	$-0.669907\pi$
$941$	−29373.3	−1.01758	−0.508789	+	0.860891i	$0.669907\pi$
$942$	32584.5	1.12703
$943$	43742.3	1.51055
$944$	4561.23	0.157262
$945$	8998.35	0.309753
$946$	17065.3	0.586511
$947$	26844.1	0.921138	0.460569	−	0.887624i	$-0.347645\pi$
$947$	26844.1	0.921138	0.460569	+	0.887624i	$0.347645\pi$
$948$	208656.	7.14855
$949$	0	0
$950$	50702.3	1.73158
$951$	−11854.6	−0.404218
$952$	−23983.0	−0.816484
$953$	−57580.7	−1.95721	−0.978605	−	0.205750i	$-0.934037\pi$
$953$	−57580.7	−1.95721	−0.978605	+	0.205750i	$0.934037\pi$
$954$	160223.	5.43754
$955$	−3288.27	−0.111420
$956$	−13097.3	−0.443094
$957$	1772.56	0.0598732
$958$	−92435.7	−3.11739
$959$	−24076.7	−0.810718
$960$	4740.62	0.159378
$961$	45170.1	1.51623
$962$	0	0
$963$	23703.5	0.793182
$964$	70867.0	2.36771
$965$	−184.449	−0.00615298
$966$	228800.	7.62061
$967$	−45598.3	−1.51638	−0.758192	−	0.652031i	$-0.773917\pi$
$967$	−45598.3	−1.51638	−0.758192	+	0.652031i	$0.773917\pi$
$968$	−4359.37	−0.144747
$969$	−20950.4	−0.694555
$970$	6900.72	0.228421
$971$	−6565.24	−0.216981	−0.108491	−	0.994097i	$-0.534602\pi$
$971$	−6565.24	−0.216981	−0.108491	+	0.994097i	$0.534602\pi$
$972$	180778.	5.96550
$973$	−76538.4	−2.52180
$974$	−43844.4	−1.44237
$975$	0	0
$976$	−28748.4	−0.942842
$977$	54415.4	1.78189	0.890943	−	0.454115i	$-0.150044\pi$
$977$	54415.4	1.78189	0.890943	+	0.454115i	$0.150044\pi$
$978$	−119565.	−3.90929
$979$	−12336.9	−0.402748
$980$	−4331.01	−0.141172
$981$	−17061.8	−0.555292
$982$	30609.7	0.994701
$983$	−30003.7	−0.973520	−0.486760	−	0.873536i	$-0.661821\pi$
$983$	−30003.7	−0.973520	−0.486760	+	0.873536i	$0.661821\pi$
$984$	−86206.6	−2.79285
$985$	−144.520	−0.00467492
$986$	1986.25	0.0641534
$987$	29296.5	0.944801
$988$	0	0
$989$	−57911.7	−1.86197
$990$	2964.17	0.0951591
$991$	−6723.23	−0.215510	−0.107755	−	0.994177i	$-0.534366\pi$
$991$	−6723.23	−0.215510	−0.107755	+	0.994177i	$0.534366\pi$
$992$	11436.3	0.366032
$993$	101470.	3.24274
$994$	94631.9	3.01966
$995$	−1925.35	−0.0613445
$996$	−102311.	−3.25486
$997$	45826.3	1.45570	0.727850	−	0.685737i	$-0.240520\pi$
$997$	45826.3	1.45570	0.727850	+	0.685737i	$0.240520\pi$
$998$	−43013.3	−1.36429
$999$	30180.2	0.955815

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.6	yes	51
13.12	even	2		1859.4.a.p.1.46	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.46	✓	51	13.12	even	2
1859.4.a.q.1.6	yes	51	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)

\(f(q)\)	\(=\)	\(q-4.84162 q^{2} +9.88636 q^{3} +15.4413 q^{4} -0.786780 q^{5} -47.8660 q^{6} -26.4479 q^{7} -36.0278 q^{8} +70.7402 q^{9} +O(q^{10})\)	\(q-4.84162 q^{2} +9.88636 q^{3} +15.4413 q^{4} -0.786780 q^{5} -47.8660 q^{6} -26.4479 q^{7} -36.0278 q^{8} +70.7402 q^{9} +3.80929 q^{10} +11.0000 q^{11} +152.658 q^{12} +128.051 q^{14} -7.77840 q^{15} +50.9029 q^{16} -25.1694 q^{17} -342.497 q^{18} +84.1943 q^{19} -12.1489 q^{20} -261.474 q^{21} -53.2578 q^{22} +180.733 q^{23} -356.184 q^{24} -124.381 q^{25} +432.431 q^{27} -408.390 q^{28} +16.2994 q^{29} +37.6600 q^{30} +273.790 q^{31} +41.7704 q^{32} +108.750 q^{33} +121.861 q^{34} +20.8087 q^{35} +1092.32 q^{36} +69.7919 q^{37} -407.637 q^{38} +28.3460 q^{40} +242.028 q^{41} +1265.96 q^{42} -320.427 q^{43} +169.854 q^{44} -55.6570 q^{45} -875.038 q^{46} -112.044 q^{47} +503.244 q^{48} +356.494 q^{49} +602.205 q^{50} -248.834 q^{51} -467.808 q^{53} -2093.67 q^{54} -8.65459 q^{55} +952.862 q^{56} +832.376 q^{57} -78.9154 q^{58} +89.6066 q^{59} -120.108 q^{60} -564.769 q^{61} -1325.59 q^{62} -1870.93 q^{63} -609.459 q^{64} -526.526 q^{66} -762.376 q^{67} -388.648 q^{68} +1786.79 q^{69} -100.748 q^{70} +739.018 q^{71} -2548.62 q^{72} -866.598 q^{73} -337.906 q^{74} -1229.68 q^{75} +1300.07 q^{76} -290.927 q^{77} +1366.82 q^{79} -40.0494 q^{80} +2365.19 q^{81} -1171.81 q^{82} -670.194 q^{83} -4037.49 q^{84} +19.8028 q^{85} +1551.39 q^{86} +161.142 q^{87} -396.306 q^{88} -1121.54 q^{89} +269.470 q^{90} +2790.74 q^{92} +2706.79 q^{93} +542.473 q^{94} -66.2424 q^{95} +412.957 q^{96} +1811.55 q^{97} -1726.01 q^{98} +778.142 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 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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