LMFDB - Embedded newform 1859.2.a.s.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,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, 2, names="a")

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1859 = 11 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
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:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
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)

$f(q)$	$=$	$q+2.76912 q^{2} -0.0832308 q^{3} +5.66800 q^{4} +1.06756 q^{5} -0.230476 q^{6} +3.59787 q^{7} +10.1571 q^{8} -2.99307 q^{9} +O(q^{10})$	\(q+2.76912 q^{2} -0.0832308 q^{3} +5.66800 q^{4} +1.06756 q^{5} -0.230476 q^{6} +3.59787 q^{7} +10.1571 q^{8} -2.99307 q^{9} +2.95619 q^{10} -1.00000 q^{11} -0.471752 q^{12} +9.96293 q^{14} -0.0888538 q^{15} +16.7902 q^{16} -7.39916 q^{17} -8.28816 q^{18} +4.02839 q^{19} +6.05092 q^{20} -0.299454 q^{21} -2.76912 q^{22} +0.0759617 q^{23} -0.845385 q^{24} -3.86032 q^{25} +0.498808 q^{27} +20.3928 q^{28} -4.74746 q^{29} -0.246046 q^{30} +0.177026 q^{31} +26.1799 q^{32} +0.0832308 q^{33} -20.4891 q^{34} +3.84094 q^{35} -16.9647 q^{36} -4.15643 q^{37} +11.1551 q^{38} +10.8433 q^{40} -3.24661 q^{41} -0.829223 q^{42} -1.63410 q^{43} -5.66800 q^{44} -3.19528 q^{45} +0.210347 q^{46} +7.85313 q^{47} -1.39747 q^{48} +5.94470 q^{49} -10.6897 q^{50} +0.615838 q^{51} -4.66525 q^{53} +1.38126 q^{54} -1.06756 q^{55} +36.5440 q^{56} -0.335287 q^{57} -13.1463 q^{58} -6.77125 q^{59} -0.503623 q^{60} +2.93743 q^{61} +0.490206 q^{62} -10.7687 q^{63} +38.9146 q^{64} +0.230476 q^{66} -6.14511 q^{67} -41.9385 q^{68} -0.00632236 q^{69} +10.6360 q^{70} +7.85704 q^{71} -30.4010 q^{72} -12.3455 q^{73} -11.5096 q^{74} +0.321298 q^{75} +22.8329 q^{76} -3.59787 q^{77} +13.7084 q^{79} +17.9246 q^{80} +8.93770 q^{81} -8.99024 q^{82} +13.3856 q^{83} -1.69731 q^{84} -7.89904 q^{85} -4.52500 q^{86} +0.395135 q^{87} -10.1571 q^{88} +3.95646 q^{89} -8.84810 q^{90} +0.430551 q^{92} -0.0147340 q^{93} +21.7462 q^{94} +4.30055 q^{95} -2.17897 q^{96} +9.04232 q^{97} +16.4616 q^{98} +2.99307 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * 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 $

$2$	2.76912	1.95806	0.979030	−	0.203715i	$-0.0653016\pi$
$2$	2.76912	1.95806	0.979030	+	0.203715i	$0.0653016\pi$
$3$	−0.0832308	−0.0480533	−0.0240267	−	0.999711i	$-0.507649\pi$
$3$	−0.0832308	−0.0480533	−0.0240267	+	0.999711i	$0.507649\pi$
$4$	5.66800	2.83400
$5$	1.06756	0.477427	0.238713	−	0.971090i	$-0.423274\pi$
$5$	1.06756	0.477427	0.238713	+	0.971090i	$0.423274\pi$
$6$	−0.230476	−0.0940913
$7$	3.59787	1.35987	0.679934	−	0.733273i	$-0.262008\pi$
$7$	3.59787	1.35987	0.679934	+	0.733273i	$0.262008\pi$
$8$	10.1571	3.59108
$9$	−2.99307	−0.997691
$10$	2.95619	0.934830
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−0.471752	−0.136183
$13$	0	0
$13$	0	0
$14$	9.96293	2.66271
$15$	−0.0888538	−0.0229419
$16$	16.7902	4.19756
$17$	−7.39916	−1.79456	−0.897280	−	0.441461i	$-0.854460\pi$
$17$	−7.39916	−1.79456	−0.897280	+	0.441461i	$0.854460\pi$
$18$	−8.28816	−1.95354
$19$	4.02839	0.924177	0.462088	−	0.886834i	$-0.347100\pi$
$19$	4.02839	0.924177	0.462088	+	0.886834i	$0.347100\pi$
$20$	6.05092	1.35303
$21$	−0.299454	−0.0653462
$22$	−2.76912	−0.590377
$23$	0.0759617	0.0158391	0.00791956	−	0.999969i	$-0.497479\pi$
$23$	0.0759617	0.0158391	0.00791956	+	0.999969i	$0.497479\pi$
$24$	−0.845385	−0.172564
$25$	−3.86032	−0.772064
$26$	0	0
$27$	0.498808	0.0959957
$28$	20.3928	3.85387
$29$	−4.74746	−0.881581	−0.440791	−	0.897610i	$-0.645302\pi$
$29$	−4.74746	−0.881581	−0.440791	+	0.897610i	$0.645302\pi$
$30$	−0.246046	−0.0449217
$31$	0.177026	0.0317948	0.0158974	−	0.999874i	$-0.494939\pi$
$31$	0.177026	0.0317948	0.0158974	+	0.999874i	$0.494939\pi$
$32$	26.1799	4.62799
$33$	0.0832308	0.0144886
$34$	−20.4891	−3.51386
$35$	3.84094	0.649237
$36$	−16.9647	−2.82746
$37$	−4.15643	−0.683312	−0.341656	−	0.939825i	$-0.610988\pi$
$37$	−4.15643	−0.683312	−0.341656	+	0.939825i	$0.610988\pi$
$38$	11.1551	1.80959
$39$	0	0
$40$	10.8433	1.71448
$41$	−3.24661	−0.507035	−0.253518	−	0.967331i	$-0.581588\pi$
$41$	−3.24661	−0.507035	−0.253518	+	0.967331i	$0.581588\pi$
$42$	−0.829223	−0.127952
$43$	−1.63410	−0.249197	−0.124599	−	0.992207i	$-0.539764\pi$
$43$	−1.63410	−0.249197	−0.124599	+	0.992207i	$0.539764\pi$
$44$	−5.66800	−0.854483
$45$	−3.19528	−0.476324
$46$	0.210347	0.0310139
$47$	7.85313	1.14550	0.572748	−	0.819731i	$-0.305877\pi$
$47$	7.85313	1.14550	0.572748	+	0.819731i	$0.305877\pi$
$48$	−1.39747	−0.201707
$49$	5.94470	0.849243
$50$	−10.6897	−1.51175
$51$	0.615838	0.0862346
$52$	0	0
$53$	−4.66525	−0.640821	−0.320411	−	0.947279i	$-0.603821\pi$
$53$	−4.66525	−0.640821	−0.320411	+	0.947279i	$0.603821\pi$
$54$	1.38126	0.187965
$55$	−1.06756	−0.143950
$56$	36.5440	4.88340
$57$	−0.335287	−0.0444098
$58$	−13.1463	−1.72619
$59$	−6.77125	−0.881542	−0.440771	−	0.897620i	$-0.645295\pi$
$59$	−6.77125	−0.881542	−0.440771	+	0.897620i	$0.645295\pi$
$60$	−0.503623	−0.0650175
$61$	2.93743	0.376099	0.188050	−	0.982160i	$-0.439783\pi$
$61$	2.93743	0.376099	0.188050	+	0.982160i	$0.439783\pi$
$62$	0.490206	0.0622562
$63$	−10.7687	−1.35673
$64$	38.9146	4.86433
$65$	0	0
$66$	0.230476	0.0283696
$67$	−6.14511	−0.750745	−0.375372	−	0.926874i	$-0.622485\pi$
$67$	−6.14511	−0.750745	−0.375372	+	0.926874i	$0.622485\pi$
$68$	−41.9385	−5.08579
$69$	−0.00632236	−0.000761122 0
$70$	10.6360	1.27125
$71$	7.85704	0.932459	0.466230	−	0.884664i	$-0.345612\pi$
$71$	7.85704	0.932459	0.466230	+	0.884664i	$0.345612\pi$
$72$	−30.4010	−3.58279
$73$	−12.3455	−1.44493	−0.722464	−	0.691409i	$-0.756990\pi$
$73$	−12.3455	−1.44493	−0.722464	+	0.691409i	$0.756990\pi$
$74$	−11.5096	−1.33797
$75$	0.321298	0.0371002
$76$	22.8329	2.61912
$77$	−3.59787	−0.410016
$78$	0	0
$79$	13.7084	1.54232	0.771158	−	0.636644i	$-0.219678\pi$
$79$	13.7084	1.54232	0.771158	+	0.636644i	$0.219678\pi$
$80$	17.9246	2.00403
$81$	8.93770	0.993078
$82$	−8.99024	−0.992806
$83$	13.3856	1.46926	0.734632	−	0.678466i	$-0.237355\pi$
$83$	13.3856	1.46926	0.734632	+	0.678466i	$0.237355\pi$
$84$	−1.69731	−0.185191
$85$	−7.89904	−0.856771
$86$	−4.52500	−0.487943
$87$	0.395135	0.0423629
$88$	−10.1571	−1.08275
$89$	3.95646	0.419384	0.209692	−	0.977768i	$-0.432754\pi$
$89$	3.95646	0.419384	0.209692	+	0.977768i	$0.432754\pi$
$90$	−8.84810	−0.932672
$91$	0	0
$92$	0.430551	0.0448881
$93$	−0.0147340	−0.00152785
$94$	21.7462	2.24295
$95$	4.30055	0.441227
$96$	−2.17897	−0.222390
$97$	9.04232	0.918108	0.459054	−	0.888408i	$-0.348188\pi$
$97$	9.04232	0.918108	0.459054	+	0.888408i	$0.348188\pi$
$98$	16.4616	1.66287
$99$	2.99307	0.300815
$100$	−21.8803	−2.18803
$101$	−14.7658	−1.46925	−0.734624	−	0.678475i	$-0.762641\pi$
$101$	−14.7658	−1.46925	−0.734624	+	0.678475i	$0.762641\pi$
$102$	1.70533	0.168853
$103$	4.61089	0.454325	0.227162	−	0.973857i	$-0.427055\pi$
$103$	4.61089	0.454325	0.227162	+	0.973857i	$0.427055\pi$
$104$	0	0
$105$	−0.319685	−0.0311980
$106$	−12.9186	−1.25477
$107$	−5.71764	−0.552745	−0.276373	−	0.961051i	$-0.589132\pi$
$107$	−5.71764	−0.552745	−0.276373	+	0.961051i	$0.589132\pi$
$108$	2.82725	0.272052
$109$	15.4449	1.47935	0.739676	−	0.672963i	$-0.234979\pi$
$109$	15.4449	1.47935	0.739676	+	0.672963i	$0.234979\pi$
$110$	−2.95619	−0.281862
$111$	0.345943	0.0328354
$112$	60.4092	5.70813
$113$	−14.1429	−1.33045	−0.665227	−	0.746641i	$-0.731665\pi$
$113$	−14.1429	−1.33045	−0.665227	+	0.746641i	$0.731665\pi$
$114$	−0.928447	−0.0869570
$115$	0.0810936	0.00756202
$116$	−26.9086	−2.49840
$117$	0	0
$118$	−18.7504	−1.72611
$119$	−26.6213	−2.44037
$120$	−0.902498	−0.0823864
$121$	1.00000	0.0909091
$122$	8.13408	0.736425
$123$	0.270218	0.0243647
$124$	1.00338	0.0901065
$125$	−9.45891	−0.846030
$126$	−29.8198	−2.65656
$127$	−10.3241	−0.916116	−0.458058	−	0.888922i	$-0.651455\pi$
$127$	−10.3241	−0.916116	−0.458058	+	0.888922i	$0.651455\pi$
$128$	55.3993	4.89665
$129$	0.136007	0.0119748
$130$	0	0
$131$	16.5969	1.45008	0.725039	−	0.688707i	$-0.241822\pi$
$131$	16.5969	1.45008	0.725039	+	0.688707i	$0.241822\pi$
$132$	0.471752	0.0410608
$133$	14.4937	1.25676
$134$	−17.0165	−1.47000
$135$	0.532507	0.0458309
$136$	−75.1542	−6.44442
$137$	−11.6276	−0.993412	−0.496706	−	0.867919i	$-0.665457\pi$
$137$	−11.6276	−0.993412	−0.496706	+	0.867919i	$0.665457\pi$
$138$	−0.0175073	−0.00149032
$139$	16.1863	1.37291	0.686454	−	0.727173i	$-0.259166\pi$
$139$	16.1863	1.37291	0.686454	+	0.727173i	$0.259166\pi$
$140$	21.7705	1.83994
$141$	−0.653622	−0.0550449
$142$	21.7571	1.82581
$143$	0	0
$144$	−50.2544	−4.18787
$145$	−5.06819	−0.420890
$146$	−34.1860	−2.82926
$147$	−0.494782	−0.0408089
$148$	−23.5586	−1.93651
$149$	−6.28767	−0.515106	−0.257553	−	0.966264i	$-0.582916\pi$
$149$	−6.28767	−0.515106	−0.257553	+	0.966264i	$0.582916\pi$
$150$	0.889710	0.0726445
$151$	−0.938333	−0.0763605	−0.0381802	−	0.999271i	$-0.512156\pi$
$151$	−0.938333	−0.0763605	−0.0381802	+	0.999271i	$0.512156\pi$
$152$	40.9169	3.31880
$153$	22.1462	1.79042
$154$	−9.96293	−0.802836
$155$	0.188986	0.0151797
$156$	0	0
$157$	18.5627	1.48146	0.740732	−	0.671800i	$-0.234479\pi$
$157$	18.5627	1.48146	0.740732	+	0.671800i	$0.234479\pi$
$158$	37.9601	3.01995
$159$	0.388293	0.0307936
$160$	27.9485	2.20953
$161$	0.273301	0.0215391
$162$	24.7495	1.94451
$163$	8.94537	0.700655	0.350328	−	0.936627i	$-0.386070\pi$
$163$	8.94537	0.700655	0.350328	+	0.936627i	$0.386070\pi$
$164$	−18.4018	−1.43694
$165$	0.0888538	0.00691726
$166$	37.0663	2.87691
$167$	−1.59550	−0.123464	−0.0617319	−	0.998093i	$-0.519662\pi$
$167$	−1.59550	−0.123464	−0.0617319	+	0.998093i	$0.519662\pi$
$168$	−3.04159	−0.234664
$169$	0	0
$170$	−21.8733	−1.67761
$171$	−12.0573	−0.922043
$172$	−9.26206	−0.706225
$173$	4.86380	0.369788	0.184894	−	0.982758i	$-0.440806\pi$
$173$	4.86380	0.369788	0.184894	+	0.982758i	$0.440806\pi$
$174$	1.09417	0.0829492
$175$	−13.8889	−1.04991
$176$	−16.7902	−1.26561
$177$	0.563577	0.0423610
$178$	10.9559	0.821179
$179$	7.69662	0.575272	0.287636	−	0.957740i	$-0.407131\pi$
$179$	7.69662	0.575272	0.287636	+	0.957740i	$0.407131\pi$
$180$	−18.1108	−1.34990
$181$	−14.4747	−1.07589	−0.537946	−	0.842979i	$-0.680800\pi$
$181$	−14.4747	−1.07589	−0.537946	+	0.842979i	$0.680800\pi$
$182$	0	0
$183$	−0.244485	−0.0180728
$184$	0.771552	0.0568796
$185$	−4.43723	−0.326231
$186$	−0.0408002	−0.00299162
$187$	7.39916	0.541080
$188$	44.5115	3.24634
$189$	1.79465	0.130542
$190$	11.9087	0.863949
$191$	11.7232	0.848263	0.424132	−	0.905601i	$-0.360579\pi$
$191$	11.7232	0.848263	0.424132	+	0.905601i	$0.360579\pi$
$192$	−3.23889	−0.233747
$193$	−9.03444	−0.650313	−0.325157	−	0.945660i	$-0.605417\pi$
$193$	−9.03444	−0.650313	−0.325157	+	0.945660i	$0.605417\pi$
$194$	25.0392	1.79771
$195$	0	0
$196$	33.6946	2.40675
$197$	−12.5092	−0.891241	−0.445621	−	0.895222i	$-0.647017\pi$
$197$	−12.5092	−0.891241	−0.445621	+	0.895222i	$0.647017\pi$
$198$	8.28816	0.589014
$199$	−9.29242	−0.658722	−0.329361	−	0.944204i	$-0.606833\pi$
$199$	−9.29242	−0.658722	−0.329361	+	0.944204i	$0.606833\pi$
$200$	−39.2097	−2.77255
$201$	0.511463	0.0360758
$202$	−40.8881	−2.87687
$203$	−17.0808	−1.19884
$204$	3.49057	0.244389
$205$	−3.46595	−0.242072
$206$	12.7681	0.889595
$207$	−0.227359	−0.0158025
$208$	0	0
$209$	−4.02839	−0.278650
$210$	−0.885244	−0.0610876
$211$	−17.5910	−1.21101	−0.605506	−	0.795841i	$-0.707029\pi$
$211$	−17.5910	−1.21101	−0.605506	+	0.795841i	$0.707029\pi$
$212$	−26.4426	−1.81609
$213$	−0.653948	−0.0448078
$214$	−15.8328	−1.08231
$215$	−1.74449	−0.118973
$216$	5.06646	0.344729
$217$	0.636917	0.0432368
$218$	42.7687	2.89666
$219$	1.02752	0.0694336
$220$	−6.05092	−0.407953
$221$	0	0
$222$	0.957955	0.0642938
$223$	3.52807	0.236257	0.118128	−	0.992998i	$-0.462311\pi$
$223$	3.52807	0.236257	0.118128	+	0.992998i	$0.462311\pi$
$224$	94.1919	6.29346
$225$	11.5542	0.770281
$226$	−39.1634	−2.60511
$227$	11.9612	0.793894	0.396947	−	0.917841i	$-0.370070\pi$
$227$	11.9612	0.793894	0.396947	+	0.917841i	$0.370070\pi$
$228$	−1.90040	−0.125857
$229$	−2.51261	−0.166038	−0.0830189	−	0.996548i	$-0.526456\pi$
$229$	−2.51261	−0.166038	−0.0830189	+	0.996548i	$0.526456\pi$
$230$	0.224558	0.0148069
$231$	0.299454	0.0197026
$232$	−48.2205	−3.16583
$233$	5.75858	0.377257	0.188629	−	0.982049i	$-0.439596\pi$
$233$	5.75858	0.377257	0.188629	+	0.982049i	$0.439596\pi$
$234$	0	0
$235$	8.38367	0.546890
$236$	−38.3795	−2.49829
$237$	−1.14096	−0.0741134
$238$	−73.7173	−4.77839
$239$	−21.8495	−1.41332	−0.706662	−	0.707551i	$-0.749800\pi$
$239$	−21.8495	−1.41332	−0.706662	+	0.707551i	$0.749800\pi$
$240$	−1.49188	−0.0963002
$241$	11.9547	0.770073	0.385036	−	0.922901i	$-0.374189\pi$
$241$	11.9547	0.770073	0.385036	+	0.922901i	$0.374189\pi$
$242$	2.76912	0.178005
$243$	−2.24032	−0.143716
$244$	16.6493	1.06587
$245$	6.34631	0.405451
$246$	0.748265	0.0477076
$247$	0	0
$248$	1.79807	0.114178
$249$	−1.11410	−0.0706030
$250$	−26.1928	−1.65658
$251$	−9.13942	−0.576875	−0.288437	−	0.957499i	$-0.593136\pi$
$251$	−9.13942	−0.576875	−0.288437	+	0.957499i	$0.593136\pi$
$252$	−61.0370	−3.84497
$253$	−0.0759617	−0.00477567
$254$	−28.5886	−1.79381
$255$	0.657443	0.0411707
$256$	75.5779	4.72362
$257$	5.49334	0.342665	0.171333	−	0.985213i	$-0.445193\pi$
$257$	5.49334	0.342665	0.171333	+	0.985213i	$0.445193\pi$
$258$	0.376620	0.0234473
$259$	−14.9543	−0.929215
$260$	0	0
$261$	14.2095	0.879546
$262$	45.9588	2.83934
$263$	−4.72227	−0.291188	−0.145594	−	0.989344i	$-0.546509\pi$
$263$	−4.72227	−0.291188	−0.145594	+	0.989344i	$0.546509\pi$
$264$	0.845385	0.0520299
$265$	−4.98043	−0.305945
$266$	40.1346	2.46081
$267$	−0.329299	−0.0201528
$268$	−34.8305	−2.12761
$269$	7.18076	0.437818	0.218909	−	0.975745i	$-0.429750\pi$
$269$	7.18076	0.437818	0.218909	+	0.975745i	$0.429750\pi$
$270$	1.47457	0.0897397
$271$	0.0615331	0.00373787	0.00186893	−	0.999998i	$-0.499405\pi$
$271$	0.0615331	0.00373787	0.00186893	+	0.999998i	$0.499405\pi$
$272$	−124.234	−7.53277
$273$	0	0
$274$	−32.1981	−1.94516
$275$	3.86032	0.232786
$276$	−0.0358351	−0.00215702
$277$	−10.2546	−0.616141	−0.308070	−	0.951364i	$-0.599683\pi$
$277$	−10.2546	−0.616141	−0.308070	+	0.951364i	$0.599683\pi$
$278$	44.8219	2.68824
$279$	−0.529852	−0.0317214
$280$	39.0129	2.33147
$281$	−27.5362	−1.64267	−0.821336	−	0.570444i	$-0.806771\pi$
$281$	−27.5362	−1.64267	−0.821336	+	0.570444i	$0.806771\pi$
$282$	−1.80996	−0.107781
$283$	−8.61317	−0.512000	−0.256000	−	0.966677i	$-0.582405\pi$
$283$	−8.61317	−0.512000	−0.256000	+	0.966677i	$0.582405\pi$
$284$	44.5337	2.64259
$285$	−0.357938	−0.0212024
$286$	0	0
$287$	−11.6809	−0.689502
$288$	−78.3582	−4.61730
$289$	37.7476	2.22045
$290$	−14.0344	−0.824129
$291$	−0.752600	−0.0441182
$292$	−69.9741	−4.09493
$293$	−20.8257	−1.21665	−0.608325	−	0.793688i	$-0.708158\pi$
$293$	−20.8257	−1.21665	−0.608325	+	0.793688i	$0.708158\pi$
$294$	−1.37011	−0.0799064
$295$	−7.22871	−0.420872
$296$	−42.2173	−2.45383
$297$	−0.498808	−0.0289438
$298$	−17.4113	−1.00861
$299$	0	0
$300$	1.82111	0.105142
$301$	−5.87927	−0.338876
$302$	−2.59835	−0.149518
$303$	1.22897	0.0706022
$304$	67.6377	3.87929
$305$	3.13588	0.179560
$306$	61.3255	3.50574
$307$	23.2876	1.32909	0.664546	−	0.747247i	$-0.268625\pi$
$307$	23.2876	1.32909	0.664546	+	0.747247i	$0.268625\pi$
$308$	−20.3928	−1.16199
$309$	−0.383768	−0.0218318
$310$	0.523323	0.0297228
$311$	10.1504	0.575579	0.287789	−	0.957694i	$-0.407080\pi$
$311$	10.1504	0.575579	0.287789	+	0.957694i	$0.407080\pi$
$312$	0	0
$313$	26.8824	1.51948	0.759741	−	0.650226i	$-0.225326\pi$
$313$	26.8824	1.51948	0.759741	+	0.650226i	$0.225326\pi$
$314$	51.4023	2.90080
$315$	−11.4962	−0.647738
$316$	77.6992	4.37092
$317$	12.6709	0.711667	0.355834	−	0.934549i	$-0.384197\pi$
$317$	12.6709	0.711667	0.355834	+	0.934549i	$0.384197\pi$
$318$	1.07523	0.0602957
$319$	4.74746	0.265807
$320$	41.5436	2.32236
$321$	0.475884	0.0265612
$322$	0.756801	0.0421749
$323$	−29.8067	−1.65849
$324$	50.6589	2.81438
$325$	0	0
$326$	24.7708	1.37193
$327$	−1.28549	−0.0710878
$328$	−32.9762	−1.82081
$329$	28.2546	1.55772
$330$	0.246046	0.0135444
$331$	−1.82373	−0.100241	−0.0501205	−	0.998743i	$-0.515961\pi$
$331$	−1.82373	−0.100241	−0.0501205	+	0.998743i	$0.515961\pi$
$332$	75.8697	4.16389
$333$	12.4405	0.681734
$334$	−4.41813	−0.241750
$335$	−6.56027	−0.358426
$336$	−5.02790	−0.274295
$337$	3.80255	0.207138	0.103569	−	0.994622i	$-0.466974\pi$
$337$	3.80255	0.207138	0.103569	+	0.994622i	$0.466974\pi$
$338$	0	0
$339$	1.17713	0.0639327
$340$	−44.7718	−2.42809
$341$	−0.177026	−0.00958650
$342$	−33.3880	−1.80542
$343$	−3.79684	−0.205010
$344$	−16.5977	−0.894889
$345$	−0.00674949	−0.000363380 0
$346$	13.4684	0.724067
$347$	−32.1531	−1.72607	−0.863034	−	0.505146i	$-0.831439\pi$
$347$	−32.1531	−1.72607	−0.863034	+	0.505146i	$0.831439\pi$
$348$	2.23963	0.120057
$349$	−19.6322	−1.05089	−0.525444	−	0.850828i	$-0.676101\pi$
$349$	−19.6322	−1.05089	−0.525444	+	0.850828i	$0.676101\pi$
$350$	−38.4601	−2.05578
$351$	0	0
$352$	−26.1799	−1.39539
$353$	1.45809	0.0776064	0.0388032	−	0.999247i	$-0.487645\pi$
$353$	1.45809	0.0776064	0.0388032	+	0.999247i	$0.487645\pi$
$354$	1.56061	0.0829455
$355$	8.38785	0.445181
$356$	22.4252	1.18853
$357$	2.21571	0.117268
$358$	21.3128	1.12642
$359$	16.4893	0.870273	0.435136	−	0.900365i	$-0.356700\pi$
$359$	16.4893	0.870273	0.435136	+	0.900365i	$0.356700\pi$
$360$	−32.4548	−1.71052
$361$	−2.77204	−0.145897
$362$	−40.0820	−2.10666
$363$	−0.0832308	−0.00436849
$364$	0	0
$365$	−13.1795	−0.689847
$366$	−0.677006	−0.0353877
$367$	0.508181	0.0265269	0.0132634	−	0.999912i	$-0.495778\pi$
$367$	0.508181	0.0265269	0.0132634	+	0.999912i	$0.495778\pi$
$368$	1.27542	0.0664856
$369$	9.71734	0.505865
$370$	−12.2872	−0.638781
$371$	−16.7850	−0.871433
$372$	−0.0835125	−0.00432992
$373$	−10.6038	−0.549044	−0.274522	−	0.961581i	$-0.588520\pi$
$373$	−10.6038	−0.549044	−0.274522	+	0.961581i	$0.588520\pi$
$374$	20.4891	1.05947
$375$	0.787273	0.0406546
$376$	79.7652	4.11357
$377$	0	0
$378$	4.96959	0.255608
$379$	−0.217213	−0.0111575	−0.00557873	−	0.999984i	$-0.501776\pi$
$379$	−0.217213	−0.0111575	−0.00557873	+	0.999984i	$0.501776\pi$
$380$	24.3755	1.25044
$381$	0.859284	0.0440225
$382$	32.4630	1.66095
$383$	−32.6070	−1.66614	−0.833070	−	0.553168i	$-0.813419\pi$
$383$	−32.6070	−1.66614	−0.833070	+	0.553168i	$0.813419\pi$
$384$	−4.61093	−0.235300
$385$	−3.84094	−0.195752
$386$	−25.0174	−1.27335
$387$	4.89097	0.248622
$388$	51.2519	2.60192
$389$	−0.457808	−0.0232118	−0.0116059	−	0.999933i	$-0.503694\pi$
$389$	−0.457808	−0.0232118	−0.0116059	+	0.999933i	$0.503694\pi$
$390$	0	0
$391$	−0.562053	−0.0284243
$392$	60.3810	3.04970
$393$	−1.38137	−0.0696811
$394$	−34.6393	−1.74510
$395$	14.6345	0.736342
$396$	16.9647	0.852510
$397$	−16.8626	−0.846309	−0.423155	−	0.906057i	$-0.639077\pi$
$397$	−16.8626	−0.846309	−0.423155	+	0.906057i	$0.639077\pi$
$398$	−25.7318	−1.28982
$399$	−1.20632	−0.0603915
$400$	−64.8157	−3.24078
$401$	31.2746	1.56178	0.780889	−	0.624670i	$-0.214767\pi$
$401$	31.2746	1.56178	0.780889	+	0.624670i	$0.214767\pi$
$402$	1.41630	0.0706386
$403$	0	0
$404$	−83.6923	−4.16385
$405$	9.54152	0.474122
$406$	−47.2986	−2.34739
$407$	4.15643	0.206026
$408$	6.25514	0.309676
$409$	32.4052	1.60233	0.801166	−	0.598442i	$-0.204213\pi$
$409$	32.4052	1.60233	0.801166	+	0.598442i	$0.204213\pi$
$410$	−9.59761	−0.473992
$411$	0.967774	0.0477368
$412$	26.1345	1.28756
$413$	−24.3621	−1.19878
$414$	−0.629583	−0.0309423
$415$	14.2899	0.701465
$416$	0	0
$417$	−1.34720	−0.0659728
$418$	−11.1551	−0.545613
$419$	−2.47724	−0.121021	−0.0605105	−	0.998168i	$-0.519273\pi$
$419$	−2.47724	−0.121021	−0.0605105	+	0.998168i	$0.519273\pi$
$420$	−1.81197	−0.0884152
$421$	0.302840	0.0147595	0.00737975	−	0.999973i	$-0.497651\pi$
$421$	0.302840	0.0147595	0.00737975	+	0.999973i	$0.497651\pi$
$422$	−48.7114	−2.37123
$423$	−23.5050	−1.14285
$424$	−47.3855	−2.30124
$425$	28.5631	1.38552
$426$	−1.81086	−0.0877363
$427$	10.5685	0.511445
$428$	−32.4076	−1.56648
$429$	0	0
$430$	−4.83070	−0.232957
$431$	8.14677	0.392416	0.196208	−	0.980562i	$-0.437137\pi$
$431$	8.14677	0.392416	0.196208	+	0.980562i	$0.437137\pi$
$432$	8.37511	0.402948
$433$	38.5372	1.85198	0.925989	−	0.377549i	$-0.123233\pi$
$433$	38.5372	1.85198	0.925989	+	0.377549i	$0.123233\pi$
$434$	1.76370	0.0846602
$435$	0.421830	0.0202252
$436$	87.5416	4.19248
$437$	0.306004	0.0146381
$438$	2.84533	0.135955
$439$	11.9879	0.572151	0.286075	−	0.958207i	$-0.407649\pi$
$439$	11.9879	0.572151	0.286075	+	0.958207i	$0.407649\pi$
$440$	−10.8433	−0.516935
$441$	−17.7929	−0.847282
$442$	0	0
$443$	19.4876	0.925885	0.462942	−	0.886388i	$-0.346794\pi$
$443$	19.4876	0.925885	0.462942	+	0.886388i	$0.346794\pi$
$444$	1.96080	0.0930556
$445$	4.22375	0.200225
$446$	9.76962	0.462605
$447$	0.523328	0.0247525
$448$	140.010	6.61484
$449$	−30.0643	−1.41882	−0.709412	−	0.704794i	$-0.751039\pi$
$449$	−30.0643	−1.41882	−0.709412	+	0.704794i	$0.751039\pi$
$450$	31.9950	1.50826
$451$	3.24661	0.152877
$452$	−80.1621	−3.77051
$453$	0.0780982	0.00366938
$454$	33.1220	1.55449
$455$	0	0
$456$	−3.40555	−0.159479
$457$	−32.6615	−1.52784	−0.763919	−	0.645312i	$-0.776727\pi$
$457$	−32.6615	−1.52784	−0.763919	+	0.645312i	$0.776727\pi$
$458$	−6.95770	−0.325112
$459$	−3.69076	−0.172270
$460$	0.459639	0.0214308
$461$	19.8261	0.923394	0.461697	−	0.887038i	$-0.347241\pi$
$461$	19.8261	0.923394	0.461697	+	0.887038i	$0.347241\pi$
$462$	0.829223	0.0385789
$463$	34.1267	1.58600	0.793002	−	0.609219i	$-0.208517\pi$
$463$	34.1267	1.58600	0.793002	+	0.609219i	$0.208517\pi$
$464$	−79.7110	−3.70049
$465$	−0.0157294	−0.000729435 0
$466$	15.9462	0.738692
$467$	−25.7139	−1.18990	−0.594950	−	0.803763i	$-0.702828\pi$
$467$	−25.7139	−1.18990	−0.594950	+	0.803763i	$0.702828\pi$
$468$	0	0
$469$	−22.1093	−1.02091
$470$	23.2154	1.07084
$471$	−1.54499	−0.0711893
$472$	−68.7764	−3.16569
$473$	1.63410	0.0751358
$474$	−3.15945	−0.145118
$475$	−15.5509	−0.713524
$476$	−150.889	−6.91600
$477$	13.9634	0.639342
$478$	−60.5037	−2.76738
$479$	11.4684	0.524006	0.262003	−	0.965067i	$-0.415617\pi$
$479$	11.4684	0.524006	0.262003	+	0.965067i	$0.415617\pi$
$480$	−2.32618	−0.106175
$481$	0	0
$482$	33.1041	1.50785
$483$	−0.0227470	−0.00103503
$484$	5.66800	0.257636
$485$	9.65320	0.438329
$486$	−6.20370	−0.281405
$487$	20.0757	0.909716	0.454858	−	0.890564i	$-0.349690\pi$
$487$	20.0757	0.909716	0.454858	+	0.890564i	$0.349690\pi$
$488$	29.8358	1.35060
$489$	−0.744530	−0.0336688
$490$	17.5737	0.793898
$491$	−15.9592	−0.720229	−0.360115	−	0.932908i	$-0.617262\pi$
$491$	−15.9592	−0.720229	−0.360115	+	0.932908i	$0.617262\pi$
$492$	1.53160	0.0690497
$493$	35.1272	1.58205
$494$	0	0
$495$	3.19528	0.143617
$496$	2.97231	0.133461
$497$	28.2686	1.26802
$498$	−3.08506	−0.138245
$499$	−8.09336	−0.362308	−0.181154	−	0.983455i	$-0.557983\pi$
$499$	−8.09336	−0.362308	−0.181154	+	0.983455i	$0.557983\pi$
$500$	−53.6131	−2.39765
$501$	0.132795	0.00593285
$502$	−25.3081	−1.12956
$503$	42.9784	1.91631	0.958156	−	0.286246i	$-0.0924076\pi$
$503$	42.9784	1.91631	0.958156	+	0.286246i	$0.0924076\pi$
$504$	−109.379	−4.87213
$505$	−15.7633	−0.701458
$506$	−0.210347	−0.00935106
$507$	0	0
$508$	−58.5171	−2.59627
$509$	−8.50105	−0.376802	−0.188401	−	0.982092i	$-0.560330\pi$
$509$	−8.50105	−0.376802	−0.188401	+	0.982092i	$0.560330\pi$
$510$	1.82054	0.0806147
$511$	−44.4174	−1.96491
$512$	98.4852	4.35247
$513$	2.00940	0.0887170
$514$	15.2117	0.670959
$515$	4.92240	0.216907
$516$	0.770889	0.0339365
$517$	−7.85313	−0.345380
$518$	−41.4102	−1.81946
$519$	−0.404818	−0.0177695
$520$	0	0
$521$	−24.8637	−1.08930	−0.544650	−	0.838664i	$-0.683337\pi$
$521$	−24.8637	−1.08930	−0.544650	+	0.838664i	$0.683337\pi$
$522$	39.3477	1.72220
$523$	23.2138	1.01507	0.507534	−	0.861631i	$-0.330557\pi$
$523$	23.2138	1.01507	0.507534	+	0.861631i	$0.330557\pi$
$524$	94.0713	4.10952
$525$	1.15599	0.0504515
$526$	−13.0765	−0.570163
$527$	−1.30984	−0.0570577
$528$	1.39747	0.0608169
$529$	−22.9942	−0.999749
$530$	−13.7914	−0.599059
$531$	20.2669	0.879507
$532$	82.1501	3.56166
$533$	0	0
$534$	−0.911868	−0.0394604
$535$	−6.10391	−0.263895
$536$	−62.4166	−2.69599
$537$	−0.640596	−0.0276437
$538$	19.8843	0.857275
$539$	−5.94470	−0.256056
$540$	3.01825	0.129885
$541$	−5.86746	−0.252262	−0.126131	−	0.992014i	$-0.540256\pi$
$541$	−5.86746	−0.252262	−0.126131	+	0.992014i	$0.540256\pi$
$542$	0.170392	0.00731897
$543$	1.20474	0.0517002
$544$	−193.709	−8.30521
$545$	16.4883	0.706282
$546$	0	0
$547$	1.40934	0.0602590	0.0301295	−	0.999546i	$-0.490408\pi$
$547$	1.40934	0.0602590	0.0301295	+	0.999546i	$0.490408\pi$
$548$	−65.9052	−2.81533
$549$	−8.79194	−0.375231
$550$	10.6897	0.455809
$551$	−19.1246	−0.814737
$552$	−0.0642169	−0.00273325
$553$	49.3211	2.09735
$554$	−28.3963	−1.20644
$555$	0.369314	0.0156765
$556$	91.7442	3.89082
$557$	14.5323	0.615752	0.307876	−	0.951426i	$-0.400382\pi$
$557$	14.5323	0.615752	0.307876	+	0.951426i	$0.400382\pi$
$558$	−1.46722	−0.0621124
$559$	0	0
$560$	64.4903	2.72521
$561$	−0.615838	−0.0260007
$562$	−76.2510	−3.21645
$563$	43.1530	1.81868	0.909340	−	0.416053i	$-0.136587\pi$
$563$	43.1530	1.81868	0.909340	+	0.416053i	$0.136587\pi$
$564$	−3.70473	−0.155997
$565$	−15.0984	−0.635194
$566$	−23.8509	−1.00253
$567$	32.1567	1.35046
$568$	79.8049	3.34854
$569$	21.1516	0.886723	0.443361	−	0.896343i	$-0.353786\pi$
$569$	21.1516	0.886723	0.443361	+	0.896343i	$0.353786\pi$
$570$	−0.991172	−0.0415156
$571$	−17.8433	−0.746718	−0.373359	−	0.927687i	$-0.621794\pi$
$571$	−17.8433	−0.746718	−0.373359	+	0.927687i	$0.621794\pi$
$572$	0	0
$573$	−0.975734	−0.0407619
$574$	−32.3458	−1.35009
$575$	−0.293237	−0.0122288
$576$	−116.474	−4.85309
$577$	−12.9238	−0.538025	−0.269013	−	0.963137i	$-0.586697\pi$
$577$	−12.9238	−0.538025	−0.269013	+	0.963137i	$0.586697\pi$
$578$	104.527	4.34777
$579$	0.751944	0.0312497
$580$	−28.7265	−1.19280
$581$	48.1598	1.99800
$582$	−2.08404	−0.0863860
$583$	4.66525	0.193215
$584$	−125.394	−5.18886
$585$	0	0
$586$	−57.6688	−2.38228
$587$	35.4448	1.46296	0.731482	−	0.681861i	$-0.238829\pi$
$587$	35.4448	1.46296	0.731482	+	0.681861i	$0.238829\pi$
$588$	−2.80443	−0.115653
$589$	0.713131	0.0293840
$590$	−20.0171	−0.824092
$591$	1.04115	0.0428271
$592$	−69.7874	−2.86824
$593$	32.1072	1.31848	0.659242	−	0.751931i	$-0.270877\pi$
$593$	32.1072	1.31848	0.659242	+	0.751931i	$0.270877\pi$
$594$	−1.38126	−0.0566737
$595$	−28.4197	−1.16510
$596$	−35.6385	−1.45981
$597$	0.773416	0.0316538
$598$	0	0
$599$	−1.44295	−0.0589574	−0.0294787	−	0.999565i	$-0.509385\pi$
$599$	−1.44295	−0.0589574	−0.0294787	+	0.999565i	$0.509385\pi$
$600$	3.26346	0.133230
$601$	20.1961	0.823817	0.411909	−	0.911225i	$-0.364862\pi$
$601$	20.1961	0.823817	0.411909	+	0.911225i	$0.364862\pi$
$602$	−16.2804	−0.663539
$603$	18.3928	0.749011
$604$	−5.31847	−0.216406
$605$	1.06756	0.0434024
$606$	3.40315	0.138243
$607$	−27.8276	−1.12949	−0.564744	−	0.825266i	$-0.691025\pi$
$607$	−27.8276	−1.12949	−0.564744	+	0.825266i	$0.691025\pi$
$608$	105.463	4.27708
$609$	1.42165	0.0576080
$610$	8.68360	0.351589
$611$	0	0
$612$	125.525	5.07404
$613$	−9.69450	−0.391557	−0.195779	−	0.980648i	$-0.562723\pi$
$613$	−9.69450	−0.391557	−0.195779	+	0.980648i	$0.562723\pi$
$614$	64.4860	2.60244
$615$	0.288474	0.0116324
$616$	−36.5440	−1.47240
$617$	3.06092	0.123228	0.0616141	−	0.998100i	$-0.480375\pi$
$617$	3.06092	0.123228	0.0616141	+	0.998100i	$0.480375\pi$
$618$	−1.06270	−0.0427480
$619$	−11.9387	−0.479858	−0.239929	−	0.970790i	$-0.577124\pi$
$619$	−11.9387	−0.479858	−0.239929	+	0.970790i	$0.577124\pi$
$620$	1.07117	0.0430193
$621$	0.0378903	0.00152049
$622$	28.1077	1.12702
$623$	14.2348	0.570307
$624$	0	0
$625$	9.20366	0.368146
$626$	74.4404	2.97524
$627$	0.335287	0.0133901
$628$	105.213	4.19847
$629$	30.7541	1.22625
$630$	−31.8343	−1.26831
$631$	26.8571	1.06917	0.534583	−	0.845116i	$-0.320469\pi$
$631$	26.8571	1.06917	0.534583	+	0.845116i	$0.320469\pi$
$632$	139.238	5.53858
$633$	1.46411	0.0581931
$634$	35.0871	1.39349
$635$	−11.0216	−0.437378
$636$	2.20084	0.0872691
$637$	0	0
$638$	13.1463	0.520466
$639$	−23.5167	−0.930306
$640$	59.1420	2.33779
$641$	−17.7268	−0.700166	−0.350083	−	0.936719i	$-0.613847\pi$
$641$	−17.7268	−0.700166	−0.350083	+	0.936719i	$0.613847\pi$
$642$	1.31778	0.0520085
$643$	26.3650	1.03974	0.519868	−	0.854247i	$-0.325981\pi$
$643$	26.3650	1.03974	0.519868	+	0.854247i	$0.325981\pi$
$644$	1.54907	0.0610419
$645$	0.145196	0.00571707
$646$	−82.5383	−3.24743
$647$	−19.9925	−0.785986	−0.392993	−	0.919542i	$-0.628560\pi$
$647$	−19.9925	−0.785986	−0.392993	+	0.919542i	$0.628560\pi$
$648$	90.7813	3.56623
$649$	6.77125	0.265795
$650$	0	0
$651$	−0.0530112	−0.00207767
$652$	50.7024	1.98566
$653$	−17.9579	−0.702747	−0.351373	−	0.936235i	$-0.614285\pi$
$653$	−17.9579	−0.702747	−0.351373	+	0.936235i	$0.614285\pi$
$654$	−3.55967	−0.139194
$655$	17.7182	0.692306
$656$	−54.5114	−2.12831
$657$	36.9509	1.44159
$658$	78.2402	3.05012
$659$	21.1859	0.825284	0.412642	−	0.910893i	$-0.364606\pi$
$659$	21.1859	0.825284	0.412642	+	0.910893i	$0.364606\pi$
$660$	0.503623	0.0196035
$661$	44.2078	1.71949	0.859743	−	0.510727i	$-0.170624\pi$
$661$	44.2078	1.71949	0.859743	+	0.510727i	$0.170624\pi$
$662$	−5.05011	−0.196278
$663$	0	0
$664$	135.959	5.27625
$665$	15.4728	0.600010
$666$	34.4491	1.33488
$667$	−0.360625	−0.0139635
$668$	−9.04332	−0.349896
$669$	−0.293644	−0.0113529
$670$	−18.1661	−0.701819
$671$	−2.93743	−0.113398
$672$	−7.83967	−0.302422
$673$	40.0351	1.54324	0.771620	−	0.636084i	$-0.219447\pi$
$673$	40.0351	1.54324	0.771620	+	0.636084i	$0.219447\pi$
$674$	10.5297	0.405589
$675$	−1.92556	−0.0741148
$676$	0	0
$677$	−18.3099	−0.703706	−0.351853	−	0.936055i	$-0.614448\pi$
$677$	−18.3099	−0.703706	−0.351853	+	0.936055i	$0.614448\pi$
$678$	3.25960	0.125184
$679$	32.5331	1.24851
$680$	−80.2315	−3.07674
$681$	−0.995542	−0.0381493
$682$	−0.490206	−0.0187709
$683$	28.7058	1.09840	0.549199	−	0.835692i	$-0.314933\pi$
$683$	28.7058	1.09840	0.549199	+	0.835692i	$0.314933\pi$
$684$	−68.3407	−2.61307
$685$	−12.4131	−0.474281
$686$	−10.5139	−0.401422
$687$	0.209126	0.00797867
$688$	−27.4369	−1.04602
$689$	0	0
$690$	−0.0186901	−0.000711520 0
$691$	36.8448	1.40164	0.700822	−	0.713336i	$-0.252817\pi$
$691$	36.8448	1.40164	0.700822	+	0.713336i	$0.252817\pi$
$692$	27.5680	1.04798
$693$	10.7687	0.409069
$694$	−89.0356	−3.37975
$695$	17.2799	0.655463
$696$	4.01343	0.152129
$697$	24.0222	0.909906
$698$	−54.3639	−2.05770
$699$	−0.479291	−0.0181285
$700$	−78.7225	−2.97543
$701$	27.8483	1.05182	0.525908	−	0.850542i	$-0.323726\pi$
$701$	27.8483	1.05182	0.525908	+	0.850542i	$0.323726\pi$
$702$	0	0
$703$	−16.7437	−0.631501
$704$	−38.9146	−1.46665
$705$	−0.697780	−0.0262799
$706$	4.03762	0.151958
$707$	−53.1253	−1.99798
$708$	3.19436	0.120051
$709$	24.0443	0.903004	0.451502	−	0.892270i	$-0.350888\pi$
$709$	24.0443	0.903004	0.451502	+	0.892270i	$0.350888\pi$
$710$	23.2269	0.871691
$711$	−41.0302	−1.53875
$712$	40.1862	1.50604
$713$	0.0134472	0.000503602 0
$714$	6.13555	0.229617
$715$	0	0
$716$	43.6244	1.63032
$717$	1.81855	0.0679150
$718$	45.6608	1.70405
$719$	−13.0734	−0.487557	−0.243778	−	0.969831i	$-0.578387\pi$
$719$	−13.0734	−0.487557	−0.243778	+	0.969831i	$0.578387\pi$
$720$	−53.6495	−1.99940
$721$	16.5894	0.617822
$722$	−7.67610	−0.285675
$723$	−0.995003	−0.0370046
$724$	−82.0423	−3.04908
$725$	18.3267	0.680637
$726$	−0.230476	−0.00855376
$727$	−35.0957	−1.30163	−0.650814	−	0.759238i	$-0.725572\pi$
$727$	−35.0957	−1.30163	−0.650814	+	0.759238i	$0.725572\pi$
$728$	0	0
$729$	−26.6266	−0.986172
$730$	−36.4956	−1.35076
$731$	12.0909	0.447200
$732$	−1.38574	−0.0512184
$733$	−16.9099	−0.624580	−0.312290	−	0.949987i	$-0.601096\pi$
$733$	−16.9099	−0.624580	−0.312290	+	0.949987i	$0.601096\pi$
$734$	1.40721	0.0519412
$735$	−0.528209	−0.0194833
$736$	1.98867	0.0733033
$737$	6.14511	0.226358
$738$	26.9084	0.990513
$739$	40.1331	1.47632	0.738159	−	0.674626i	$-0.235695\pi$
$739$	40.1331	1.47632	0.738159	+	0.674626i	$0.235695\pi$
$740$	−25.1502	−0.924540
$741$	0	0
$742$	−46.4796	−1.70632
$743$	16.1379	0.592043	0.296022	−	0.955181i	$-0.404340\pi$
$743$	16.1379	0.592043	0.296022	+	0.955181i	$0.404340\pi$
$744$	−0.149655	−0.00548663
$745$	−6.71245	−0.245925
$746$	−29.3632	−1.07506
$747$	−40.0641	−1.46587
$748$	41.9385	1.53342
$749$	−20.5713	−0.751661
$750$	2.18005	0.0796041
$751$	−42.9030	−1.56555	−0.782777	−	0.622303i	$-0.786197\pi$
$751$	−42.9030	−1.56555	−0.782777	+	0.622303i	$0.786197\pi$
$752$	131.856	4.80829
$753$	0.760681	0.0277208
$754$	0	0
$755$	−1.00173	−0.0364565
$756$	10.1721	0.369955
$757$	−16.5187	−0.600383	−0.300191	−	0.953879i	$-0.597051\pi$
$757$	−16.5187	−0.600383	−0.300191	+	0.953879i	$0.597051\pi$
$758$	−0.601487	−0.0218470
$759$	0.00632236	0.000229487 0
$760$	43.6812	1.58448
$761$	16.8904	0.612276	0.306138	−	0.951987i	$-0.400963\pi$
$761$	16.8904	0.612276	0.306138	+	0.951987i	$0.400963\pi$
$762$	2.37946	0.0861986
$763$	55.5688	2.01172
$764$	66.4473	2.40398
$765$	23.6424	0.854793
$766$	−90.2925	−3.26240
$767$	0	0
$768$	−6.29041	−0.226986
$769$	27.1130	0.977721	0.488861	−	0.872362i	$-0.337413\pi$
$769$	27.1130	0.977721	0.488861	+	0.872362i	$0.337413\pi$
$770$	−10.6360	−0.383295
$771$	−0.457215	−0.0164662
$772$	−51.2072	−1.84299
$773$	−5.18388	−0.186451	−0.0932255	−	0.995645i	$-0.529718\pi$
$773$	−5.18388	−0.186451	−0.0932255	+	0.995645i	$0.529718\pi$
$774$	13.5437	0.486817
$775$	−0.683377	−0.0245476
$776$	91.8439	3.29700
$777$	1.24466	0.0446519
$778$	−1.26772	−0.0454500
$779$	−13.0786	−0.468590
$780$	0	0
$781$	−7.85704	−0.281147
$782$	−1.55639	−0.0556564
$783$	−2.36807	−0.0846280
$784$	99.8129	3.56475
$785$	19.8168	0.707291
$786$	−3.82519	−0.136440
$787$	−27.2338	−0.970780	−0.485390	−	0.874298i	$-0.661322\pi$
$787$	−27.2338	−0.970780	−0.485390	+	0.874298i	$0.661322\pi$
$788$	−70.9020	−2.52578
$789$	0.393038	0.0139925
$790$	40.5247	1.44180
$791$	−50.8844	−1.80924
$792$	30.4010	1.08025
$793$	0	0
$794$	−46.6945	−1.65713
$795$	0.414525	0.0147017
$796$	−52.6695	−1.86682
$797$	−24.5981	−0.871308	−0.435654	−	0.900114i	$-0.643483\pi$
$797$	−24.5981	−0.871308	−0.435654	+	0.900114i	$0.643483\pi$
$798$	−3.34044	−0.118250
$799$	−58.1066	−2.05566
$800$	−101.063	−3.57310
$801$	−11.8420	−0.418415
$802$	86.6029	3.05805
$803$	12.3455	0.435662
$804$	2.89897	0.102239
$805$	0.291765	0.0102833
$806$	0	0
$807$	−0.597660	−0.0210386
$808$	−149.978	−5.27619
$809$	−25.7953	−0.906914	−0.453457	−	0.891278i	$-0.649809\pi$
$809$	−25.7953	−0.906914	−0.453457	+	0.891278i	$0.649809\pi$
$810$	26.4216	0.928359
$811$	14.3539	0.504035	0.252017	−	0.967723i	$-0.418906\pi$
$811$	14.3539	0.504035	0.252017	+	0.967723i	$0.418906\pi$
$812$	−96.8138	−3.39750
$813$	−0.00512145	−0.000179617 0
$814$	11.5096	0.403412
$815$	9.54970	0.334511
$816$	10.3401	0.361975
$817$	−6.58278	−0.230302
$818$	89.7336	3.13746
$819$	0	0
$820$	−19.6450	−0.686033
$821$	18.0028	0.628302	0.314151	−	0.949373i	$-0.398280\pi$
$821$	18.0028	0.628302	0.314151	+	0.949373i	$0.398280\pi$
$822$	2.67988	0.0934715
$823$	36.4575	1.27083	0.635415	−	0.772171i	$-0.280829\pi$
$823$	36.4575	1.27083	0.635415	+	0.772171i	$0.280829\pi$
$824$	46.8334	1.63152
$825$	−0.321298	−0.0111861
$826$	−67.4615	−2.34729
$827$	3.73303	0.129810	0.0649051	−	0.997891i	$-0.479326\pi$
$827$	3.73303	0.129810	0.0649051	+	0.997891i	$0.479326\pi$
$828$	−1.28867	−0.0447844
$829$	48.5365	1.68574	0.842872	−	0.538115i	$-0.180863\pi$
$829$	48.5365	1.68574	0.842872	+	0.538115i	$0.180863\pi$
$830$	39.5705	1.37351
$831$	0.853501	0.0296076
$832$	0	0
$833$	−43.9858	−1.52402
$834$	−3.73056	−0.129179
$835$	−1.70329	−0.0589449
$836$	−22.8329	−0.789694
$837$	0.0883021	0.00305217
$838$	−6.85976	−0.236966
$839$	−45.6319	−1.57539	−0.787694	−	0.616067i	$-0.788725\pi$
$839$	−45.6319	−1.57539	−0.787694	+	0.616067i	$0.788725\pi$
$840$	−3.24708	−0.112035
$841$	−6.46161	−0.222814
$842$	0.838598	0.0289000
$843$	2.29186	0.0789359
$844$	−99.7056	−3.43201
$845$	0	0
$846$	−65.0880	−2.23777
$847$	3.59787	0.123624
$848$	−78.3306	−2.68989
$849$	0.716881	0.0246033
$850$	79.0946	2.71292
$851$	−0.315729	−0.0108231
$852$	−3.70658	−0.126985
$853$	−26.8405	−0.919000	−0.459500	−	0.888178i	$-0.651971\pi$
$853$	−26.8405	−0.919000	−0.459500	+	0.888178i	$0.651971\pi$
$854$	29.2654	1.00144
$855$	−12.8718	−0.440208
$856$	−58.0748	−1.98495
$857$	25.5969	0.874375	0.437187	−	0.899370i	$-0.355975\pi$
$857$	25.5969	0.874375	0.437187	+	0.899370i	$0.355975\pi$
$858$	0	0
$859$	−10.7407	−0.366468	−0.183234	−	0.983069i	$-0.558657\pi$
$859$	−10.7407	−0.366468	−0.183234	+	0.983069i	$0.558657\pi$
$860$	−9.88779	−0.337171
$861$	0.972211	0.0331328
$862$	22.5593	0.768374
$863$	−39.9441	−1.35971	−0.679857	−	0.733345i	$-0.737958\pi$
$863$	−39.9441	−1.35971	−0.679857	+	0.733345i	$0.737958\pi$
$864$	13.0587	0.444267
$865$	5.19239	0.176547
$866$	106.714	3.62629
$867$	−3.14176	−0.106700
$868$	3.61005	0.122533
$869$	−13.7084	−0.465026
$870$	1.16810	0.0396021
$871$	0	0
$872$	156.876	5.31248
$873$	−27.0643	−0.915988
$874$	0.847360	0.0286624
$875$	−34.0320	−1.15049
$876$	5.82400	0.196775
$877$	−7.22726	−0.244047	−0.122024	−	0.992527i	$-0.538938\pi$
$877$	−7.22726	−0.244047	−0.122024	+	0.992527i	$0.538938\pi$
$878$	33.1959	1.12031
$879$	1.73334	0.0584641
$880$	−17.9246	−0.604237
$881$	8.06588	0.271747	0.135873	−	0.990726i	$-0.456616\pi$
$881$	8.06588	0.271747	0.135873	+	0.990726i	$0.456616\pi$
$882$	−49.2706	−1.65903
$883$	−23.9866	−0.807214	−0.403607	−	0.914932i	$-0.632244\pi$
$883$	−23.9866	−0.807214	−0.403607	+	0.914932i	$0.632244\pi$
$884$	0	0
$885$	0.601651	0.0202243
$886$	53.9635	1.81294
$887$	8.68123	0.291487	0.145744	−	0.989322i	$-0.453443\pi$
$887$	8.68123	0.291487	0.145744	+	0.989322i	$0.453443\pi$
$888$	3.51378	0.117915
$889$	−37.1448	−1.24580
$890$	11.6961	0.392053
$891$	−8.93770	−0.299424
$892$	19.9971	0.669552
$893$	31.6355	1.05864
$894$	1.44915	0.0484670
$895$	8.21659	0.274650
$896$	199.320	6.65880
$897$	0	0
$898$	−83.2516	−2.77814
$899$	−0.840424	−0.0280297
$900$	65.4893	2.18298
$901$	34.5189	1.14999
$902$	8.99024	0.299342
$903$	0.489337	0.0162841
$904$	−143.651	−4.77777
$905$	−15.4525	−0.513660
$906$	0.216263	0.00718486
$907$	−42.2401	−1.40256	−0.701279	−	0.712887i	$-0.747387\pi$
$907$	−42.2401	−1.40256	−0.701279	+	0.712887i	$0.747387\pi$
$908$	67.7962	2.24990
$909$	44.1950	1.46585
$910$	0	0
$911$	−21.4429	−0.710434	−0.355217	−	0.934784i	$-0.615593\pi$
$911$	−21.4429	−0.710434	−0.355217	+	0.934784i	$0.615593\pi$
$912$	−5.62954	−0.186413
$913$	−13.3856	−0.442999
$914$	−90.4433	−2.99160
$915$	−0.261002	−0.00862844
$916$	−14.2415	−0.470551
$917$	59.7136	1.97192
$918$	−10.2202	−0.337315
$919$	−50.6078	−1.66940	−0.834699	−	0.550706i	$-0.814358\pi$
$919$	−50.6078	−1.66940	−0.834699	+	0.550706i	$0.814358\pi$
$920$	0.823677	0.0271558
$921$	−1.93824	−0.0638673
$922$	54.9008	1.80806
$923$	0	0
$924$	1.69731	0.0558373
$925$	16.0451	0.527561
$926$	94.5009	3.10549
$927$	−13.8007	−0.453275
$928$	−124.288	−4.07995
$929$	5.98422	0.196336	0.0981679	−	0.995170i	$-0.468702\pi$
$929$	5.98422	0.196336	0.0981679	+	0.995170i	$0.468702\pi$
$930$	−0.0435566	−0.00142828
$931$	23.9476	0.784851
$932$	32.6396	1.06915
$933$	−0.844829	−0.0276585
$934$	−71.2049	−2.32989
$935$	7.89904	0.258326
$936$	0	0
$937$	−12.3851	−0.404605	−0.202302	−	0.979323i	$-0.564842\pi$
$937$	−12.3851	−0.404605	−0.202302	+	0.979323i	$0.564842\pi$
$938$	−61.2233	−1.99901
$939$	−2.23744	−0.0730162
$940$	47.5187	1.54989
$941$	−50.8259	−1.65688	−0.828439	−	0.560079i	$-0.810771\pi$
$941$	−50.8259	−1.65688	−0.828439	+	0.560079i	$0.810771\pi$
$942$	−4.27825	−0.139393
$943$	−0.246618	−0.00803099
$944$	−113.691	−3.70033
$945$	1.91589	0.0623240
$946$	4.52500	0.147120
$947$	16.6969	0.542575	0.271288	−	0.962498i	$-0.412551\pi$
$947$	16.6969	0.542575	0.271288	+	0.962498i	$0.412551\pi$
$948$	−6.46697	−0.210037
$949$	0	0
$950$	−43.0622	−1.39712
$951$	−1.05461	−0.0341980
$952$	−270.395	−8.76356
$953$	10.5606	0.342092	0.171046	−	0.985263i	$-0.445285\pi$
$953$	10.5606	0.342092	0.171046	+	0.985263i	$0.445285\pi$
$954$	38.6664	1.25187
$955$	12.5152	0.404983
$956$	−123.843	−4.00536
$957$	−0.395135	−0.0127729
$958$	31.7574	1.02604
$959$	−41.8346	−1.35091
$960$	−3.45771	−0.111597
$961$	−30.9687	−0.998989
$962$	0	0
$963$	17.1133	0.551469
$964$	67.7595	2.18239
$965$	−9.64479	−0.310477
$966$	−0.0629892	−0.00202664
$967$	−10.8624	−0.349310	−0.174655	−	0.984630i	$-0.555881\pi$
$967$	−10.8624	−0.349310	−0.174655	+	0.984630i	$0.555881\pi$
$968$	10.1571	0.326462
$969$	2.48084	0.0796961
$970$	26.7308	0.858275
$971$	50.5037	1.62074	0.810371	−	0.585918i	$-0.199266\pi$
$971$	50.5037	1.62074	0.810371	+	0.585918i	$0.199266\pi$
$972$	−12.6981	−0.407292
$973$	58.2364	1.86697
$974$	55.5919	1.78128
$975$	0	0
$976$	49.3201	1.57870
$977$	−8.04995	−0.257541	−0.128770	−	0.991674i	$-0.541103\pi$
$977$	−8.04995	−0.257541	−0.128770	+	0.991674i	$0.541103\pi$
$978$	−2.06169	−0.0659256
$979$	−3.95646	−0.126449
$980$	35.9709	1.14905
$981$	−46.2277	−1.47594
$982$	−44.1929	−1.41025
$983$	29.9305	0.954636	0.477318	−	0.878731i	$-0.341609\pi$
$983$	29.9305	0.954636	0.477318	+	0.878731i	$0.341609\pi$
$984$	2.74464	0.0874958
$985$	−13.3543	−0.425502
$986$	97.2714	3.09775
$987$	−2.35165	−0.0748539
$988$	0	0
$989$	−0.124129	−0.00394707
$990$	8.84810	0.281211
$991$	14.9437	0.474701	0.237351	−	0.971424i	$-0.423721\pi$
$991$	14.9437	0.474701	0.237351	+	0.971424i	$0.423721\pi$
$992$	4.63452	0.147146
$993$	0.151790	0.00481692
$994$	78.2791	2.48286
$995$	−9.92020	−0.314492
$996$	−6.31470	−0.200089
$997$	−52.1103	−1.65035	−0.825174	−	0.564878i	$-0.808923\pi$
$997$	−52.1103	−1.65035	−0.825174	+	0.564878i	$0.808923\pi$
$998$	−22.4114	−0.709422
$999$	−2.07326	−0.0655950

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.21	✓	21
13.12	even	2		1859.2.a.t.1.1	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.21	✓	21	1.1	even	1	trivial
1859.2.a.t.1.1	yes	21	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+2.76912 q^{2} -0.0832308 q^{3} +5.66800 q^{4} +1.06756 q^{5} -0.230476 q^{6} +3.59787 q^{7} +10.1571 q^{8} -2.99307 q^{9} +O(q^{10})\)	\(q+2.76912 q^{2} -0.0832308 q^{3} +5.66800 q^{4} +1.06756 q^{5} -0.230476 q^{6} +3.59787 q^{7} +10.1571 q^{8} -2.99307 q^{9} +2.95619 q^{10} -1.00000 q^{11} -0.471752 q^{12} +9.96293 q^{14} -0.0888538 q^{15} +16.7902 q^{16} -7.39916 q^{17} -8.28816 q^{18} +4.02839 q^{19} +6.05092 q^{20} -0.299454 q^{21} -2.76912 q^{22} +0.0759617 q^{23} -0.845385 q^{24} -3.86032 q^{25} +0.498808 q^{27} +20.3928 q^{28} -4.74746 q^{29} -0.246046 q^{30} +0.177026 q^{31} +26.1799 q^{32} +0.0832308 q^{33} -20.4891 q^{34} +3.84094 q^{35} -16.9647 q^{36} -4.15643 q^{37} +11.1551 q^{38} +10.8433 q^{40} -3.24661 q^{41} -0.829223 q^{42} -1.63410 q^{43} -5.66800 q^{44} -3.19528 q^{45} +0.210347 q^{46} +7.85313 q^{47} -1.39747 q^{48} +5.94470 q^{49} -10.6897 q^{50} +0.615838 q^{51} -4.66525 q^{53} +1.38126 q^{54} -1.06756 q^{55} +36.5440 q^{56} -0.335287 q^{57} -13.1463 q^{58} -6.77125 q^{59} -0.503623 q^{60} +2.93743 q^{61} +0.490206 q^{62} -10.7687 q^{63} +38.9146 q^{64} +0.230476 q^{66} -6.14511 q^{67} -41.9385 q^{68} -0.00632236 q^{69} +10.6360 q^{70} +7.85704 q^{71} -30.4010 q^{72} -12.3455 q^{73} -11.5096 q^{74} +0.321298 q^{75} +22.8329 q^{76} -3.59787 q^{77} +13.7084 q^{79} +17.9246 q^{80} +8.93770 q^{81} -8.99024 q^{82} +13.3856 q^{83} -1.69731 q^{84} -7.89904 q^{85} -4.52500 q^{86} +0.395135 q^{87} -10.1571 q^{88} +3.95646 q^{89} -8.84810 q^{90} +0.430551 q^{92} -0.0147340 q^{93} +21.7462 q^{94} +4.30055 q^{95} -2.17897 q^{96} +9.04232 q^{97} +16.4616 q^{98} +2.99307 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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