LMFDB - Embedded newform 1859.4.a.g.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1859, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 93 x^{15} - 7 x^{14} + 3449 x^{13} + 406 x^{12} - 65242 x^{11} - 7942 x^{10} + 669163 x^{9} + \cdots - 2210688 $ x^17 - 93x^15 - 7x^14 + 3449x^13 + 406x^12 - 65242x^11 - 7942x^10 + 669163x^9 + 59532x^8 - 3663297x^7 - 79027x^6 + 9967603x^5 - 984554x^4 - 12177120x^3 + 3207432x^2 + 5215872*x - 2210688
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$4.11212$ of defining polynomial
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)

$f(q)$	$=$	$q-4.11212 q^{2} -4.01551 q^{3} +8.90957 q^{4} -12.3424 q^{5} +16.5123 q^{6} +29.6370 q^{7} -3.74025 q^{8} -10.8757 q^{9} +O(q^{10})$	\(q-4.11212 q^{2} -4.01551 q^{3} +8.90957 q^{4} -12.3424 q^{5} +16.5123 q^{6} +29.6370 q^{7} -3.74025 q^{8} -10.8757 q^{9} +50.7537 q^{10} +11.0000 q^{11} -35.7765 q^{12} -121.871 q^{14} +49.5612 q^{15} -55.8962 q^{16} +100.067 q^{17} +44.7221 q^{18} +38.7919 q^{19} -109.966 q^{20} -119.008 q^{21} -45.2334 q^{22} -107.825 q^{23} +15.0190 q^{24} +27.3360 q^{25} +152.090 q^{27} +264.053 q^{28} +136.061 q^{29} -203.802 q^{30} -7.90141 q^{31} +259.774 q^{32} -44.1706 q^{33} -411.487 q^{34} -365.794 q^{35} -96.8976 q^{36} -415.585 q^{37} -159.517 q^{38} +46.1639 q^{40} -257.265 q^{41} +489.375 q^{42} -19.0423 q^{43} +98.0052 q^{44} +134.233 q^{45} +443.391 q^{46} +167.428 q^{47} +224.452 q^{48} +535.354 q^{49} -112.409 q^{50} -401.819 q^{51} +96.3042 q^{53} -625.414 q^{54} -135.767 q^{55} -110.850 q^{56} -155.769 q^{57} -559.498 q^{58} -520.835 q^{59} +441.569 q^{60} -702.285 q^{61} +32.4916 q^{62} -322.323 q^{63} -621.054 q^{64} +181.635 q^{66} -669.596 q^{67} +891.552 q^{68} +432.973 q^{69} +1504.19 q^{70} +517.959 q^{71} +40.6778 q^{72} -1154.37 q^{73} +1708.94 q^{74} -109.768 q^{75} +345.619 q^{76} +326.007 q^{77} +1197.20 q^{79} +689.895 q^{80} -317.076 q^{81} +1057.91 q^{82} +77.3667 q^{83} -1060.31 q^{84} -1235.07 q^{85} +78.3045 q^{86} -546.353 q^{87} -41.1428 q^{88} +545.121 q^{89} -551.981 q^{90} -960.676 q^{92} +31.7282 q^{93} -688.485 q^{94} -478.787 q^{95} -1043.12 q^{96} +663.366 q^{97} -2201.44 q^{98} -119.632 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * 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 $

$2$	−4.11212	−1.45386	−0.726928	−	0.686714i	$-0.759053\pi$
$2$	−4.11212	−1.45386	−0.726928	+	0.686714i	$0.759053\pi$
$3$	−4.01551	−0.772785	−0.386393	−	0.922334i	$-0.626279\pi$
$3$	−4.01551	−0.772785	−0.386393	+	0.922334i	$0.626279\pi$
$4$	8.90957	1.11370
$5$	−12.3424	−1.10394	−0.551971	−	0.833863i	$-0.686124\pi$
$5$	−12.3424	−1.10394	−0.551971	+	0.833863i	$0.686124\pi$
$6$	16.5123	1.12352
$7$	29.6370	1.60025	0.800125	−	0.599834i	$-0.204767\pi$
$7$	29.6370	1.60025	0.800125	+	0.599834i	$0.204767\pi$
$8$	−3.74025	−0.165297
$9$	−10.8757	−0.402803
$10$	50.7537	1.60497
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	−35.7765	−0.860648
$13$	0	0
$13$	0	0
$14$	−121.871	−2.32653
$15$	49.5612	0.853110
$16$	−55.8962	−0.873377
$17$	100.067	1.42763	0.713817	−	0.700333i	$-0.246965\pi$
$17$	100.067	1.42763	0.713817	+	0.700333i	$0.246965\pi$
$18$	44.7221	0.585617
$19$	38.7919	0.468394	0.234197	−	0.972189i	$-0.424754\pi$
$19$	38.7919	0.468394	0.234197	+	0.972189i	$0.424754\pi$
$20$	−109.966	−1.22946
$21$	−119.008	−1.23665
$22$	−45.2334	−0.438354
$23$	−107.825	−0.977527	−0.488763	−	0.872416i	$-0.662552\pi$
$23$	−107.825	−0.977527	−0.488763	+	0.872416i	$0.662552\pi$
$24$	15.0190	0.127739
$25$	27.3360	0.218688
$26$	0	0
$27$	152.090	1.08407
$28$	264.053	1.78219
$29$	136.061	0.871235	0.435618	−	0.900132i	$-0.356530\pi$
$29$	136.061	0.871235	0.435618	+	0.900132i	$0.356530\pi$
$30$	−203.802	−1.24030
$31$	−7.90141	−0.0457785	−0.0228893	−	0.999738i	$-0.507287\pi$
$31$	−7.90141	−0.0457785	−0.0228893	+	0.999738i	$0.507287\pi$
$32$	259.774	1.43506
$33$	−44.1706	−0.233004
$34$	−411.487	−2.07557
$35$	−365.794	−1.76658
$36$	−96.8976	−0.448600
$37$	−415.585	−1.84653	−0.923267	−	0.384158i	$-0.874492\pi$
$37$	−415.585	−1.84653	−0.923267	+	0.384158i	$0.874492\pi$
$38$	−159.517	−0.680977
$39$	0	0
$40$	46.1639	0.182479
$41$	−257.265	−0.979954	−0.489977	−	0.871735i	$-0.662995\pi$
$41$	−257.265	−0.979954	−0.489977	+	0.871735i	$0.662995\pi$
$42$	489.375	1.79791
$43$	−19.0423	−0.0675333	−0.0337666	−	0.999430i	$-0.510750\pi$
$43$	−19.0423	−0.0675333	−0.0337666	+	0.999430i	$0.510750\pi$
$44$	98.0052	0.335792
$45$	134.233	0.444671
$46$	443.391	1.42118
$47$	167.428	0.519615	0.259807	−	0.965660i	$-0.416341\pi$
$47$	167.428	0.519615	0.259807	+	0.965660i	$0.416341\pi$
$48$	224.452	0.674933
$49$	535.354	1.56080
$50$	−112.409	−0.317941
$51$	−401.819	−1.10325
$52$	0	0
$53$	96.3042	0.249592	0.124796	−	0.992182i	$-0.460172\pi$
$53$	96.3042	0.249592	0.124796	+	0.992182i	$0.460172\pi$
$54$	−625.414	−1.57607
$55$	−135.767	−0.332851
$56$	−110.850	−0.264517
$57$	−155.769	−0.361968
$58$	−559.498	−1.26665
$59$	−520.835	−1.14927	−0.574636	−	0.818409i	$-0.694856\pi$
$59$	−520.835	−1.14927	−0.574636	+	0.818409i	$0.694856\pi$
$60$	441.569	0.950105
$61$	−702.285	−1.47407	−0.737036	−	0.675853i	$-0.763775\pi$
$61$	−702.285	−1.47407	−0.737036	+	0.675853i	$0.763775\pi$
$62$	32.4916	0.0665554
$63$	−322.323	−0.644585
$64$	−621.054	−1.21300
$65$	0	0
$66$	181.635	0.338753
$67$	−669.596	−1.22096	−0.610479	−	0.792032i	$-0.709023\pi$
$67$	−669.596	−1.22096	−0.610479	+	0.792032i	$0.709023\pi$
$68$	891.552	1.58995
$69$	432.973	0.755418
$70$	1504.19	2.56836
$71$	517.959	0.865780	0.432890	−	0.901447i	$-0.357494\pi$
$71$	517.959	0.865780	0.432890	+	0.901447i	$0.357494\pi$
$72$	40.6778	0.0665823
$73$	−1154.37	−1.85081	−0.925406	−	0.378976i	$-0.876276\pi$
$73$	−1154.37	−1.85081	−0.925406	+	0.378976i	$0.876276\pi$
$74$	1708.94	2.68459
$75$	−109.768	−0.168999
$76$	345.619	0.521648
$77$	326.007	0.482493
$78$	0	0
$79$	1197.20	1.70500	0.852502	−	0.522723i	$-0.175084\pi$
$79$	1197.20	1.70500	0.852502	+	0.522723i	$0.175084\pi$
$80$	689.895	0.964158
$81$	−317.076	−0.434947
$82$	1057.91	1.42471
$83$	77.3667	0.102314	0.0511572	−	0.998691i	$-0.483709\pi$
$83$	77.3667	0.102314	0.0511572	+	0.998691i	$0.483709\pi$
$84$	−1060.31	−1.37725
$85$	−1235.07	−1.57602
$86$	78.3045	0.0981836
$87$	−546.353	−0.673278
$88$	−41.1428	−0.0498390
$89$	545.121	0.649244	0.324622	−	0.945844i	$-0.394763\pi$
$89$	545.121	0.649244	0.324622	+	0.945844i	$0.394763\pi$
$90$	−551.981	−0.646488
$91$	0	0
$92$	−960.676	−1.08867
$93$	31.7282	0.0353770
$94$	−688.485	−0.755445
$95$	−478.787	−0.517080
$96$	−1043.12	−1.10899
$97$	663.366	0.694377	0.347189	−	0.937795i	$-0.387136\pi$
$97$	663.366	0.694377	0.347189	+	0.937795i	$0.387136\pi$
$98$	−2201.44	−2.26918
$99$	−119.632	−0.121450
$100$	243.552	0.243552
$101$	1757.00	1.73097	0.865487	−	0.500932i	$-0.167009\pi$
$101$	1757.00	1.73097	0.865487	+	0.500932i	$0.167009\pi$
$102$	1652.33	1.60397
$103$	1224.64	1.17153	0.585765	−	0.810481i	$-0.300794\pi$
$103$	1224.64	1.17153	0.585765	+	0.810481i	$0.300794\pi$
$104$	0	0
$105$	1468.85	1.36519
$106$	−396.015	−0.362871
$107$	1166.72	1.05412	0.527060	−	0.849828i	$-0.323294\pi$
$107$	1166.72	1.05412	0.527060	+	0.849828i	$0.323294\pi$
$108$	1355.06	1.20732
$109$	678.659	0.596365	0.298182	−	0.954509i	$-0.403620\pi$
$109$	678.659	0.596365	0.298182	+	0.954509i	$0.403620\pi$
$110$	558.290	0.483917
$111$	1668.79	1.42697
$112$	−1656.60	−1.39762
$113$	−524.175	−0.436374	−0.218187	−	0.975907i	$-0.570014\pi$
$113$	−524.175	−0.436374	−0.218187	+	0.975907i	$0.570014\pi$
$114$	640.543	0.526249
$115$	1330.83	1.07913
$116$	1212.24	0.970291
$117$	0	0
$118$	2141.74	1.67087
$119$	2965.68	2.28457
$120$	−185.371	−0.141017
$121$	121.000	0.0909091
$122$	2887.88	2.14309
$123$	1033.05	0.757294
$124$	−70.3981	−0.0509834
$125$	1205.41	0.862523
$126$	1325.43	0.937134
$127$	−1678.44	−1.17273	−0.586366	−	0.810046i	$-0.699442\pi$
$127$	−1678.44	−1.17273	−0.586366	+	0.810046i	$0.699442\pi$
$128$	475.658	0.328458
$129$	76.4647	0.0521887
$130$	0	0
$131$	−2327.92	−1.55261	−0.776304	−	0.630359i	$-0.782908\pi$
$131$	−2327.92	−1.55261	−0.776304	+	0.630359i	$0.782908\pi$
$132$	−393.541	−0.259495
$133$	1149.68	0.749547
$134$	2753.46	1.77510
$135$	−1877.16	−1.19675
$136$	−374.275	−0.235984
$137$	−1467.41	−0.915107	−0.457554	−	0.889182i	$-0.651274\pi$
$137$	−1467.41	−0.915107	−0.457554	+	0.889182i	$0.651274\pi$
$138$	−1780.44	−1.09827
$139$	−999.290	−0.609775	−0.304887	−	0.952388i	$-0.598619\pi$
$139$	−999.290	−0.609775	−0.304887	+	0.952388i	$0.598619\pi$
$140$	−3259.06	−1.96744
$141$	−672.309	−0.401551
$142$	−2129.91	−1.25872
$143$	0	0
$144$	607.909	0.351799
$145$	−1679.32	−0.961793
$146$	4746.93	2.69081
$147$	−2149.72	−1.20616
$148$	−3702.68	−2.05648
$149$	722.950	0.397492	0.198746	−	0.980051i	$-0.436313\pi$
$149$	722.950	0.397492	0.198746	+	0.980051i	$0.436313\pi$
$150$	451.380	0.245700
$151$	933.009	0.502829	0.251415	−	0.967879i	$-0.419104\pi$
$151$	933.009	0.502829	0.251415	+	0.967879i	$0.419104\pi$
$152$	−145.092	−0.0774242
$153$	−1088.29	−0.575055
$154$	−1340.58	−0.701476
$155$	97.5227	0.0505368
$156$	0	0
$157$	763.894	0.388314	0.194157	−	0.980970i	$-0.437803\pi$
$157$	763.894	0.388314	0.194157	+	0.980970i	$0.437803\pi$
$158$	−4923.03	−2.47883
$159$	−386.710	−0.192881
$160$	−3206.25	−1.58423
$161$	−3195.62	−1.56429
$162$	1303.86	0.632350
$163$	−2571.26	−1.23556	−0.617780	−	0.786351i	$-0.711968\pi$
$163$	−2571.26	−1.23556	−0.617780	+	0.786351i	$0.711968\pi$
$164$	−2292.12	−1.09137
$165$	545.173	0.257222
$166$	−318.141	−0.148750
$167$	2888.22	1.33831	0.669154	−	0.743124i	$-0.266657\pi$
$167$	2888.22	1.33831	0.669154	+	0.743124i	$0.266657\pi$
$168$	445.119	0.204415
$169$	0	0
$170$	5078.76	2.29131
$171$	−421.889	−0.188670
$172$	−169.659	−0.0752115
$173$	2240.44	0.984612	0.492306	−	0.870422i	$-0.336154\pi$
$173$	2240.44	0.984612	0.492306	+	0.870422i	$0.336154\pi$
$174$	2246.67	0.978848
$175$	810.159	0.349956
$176$	−614.858	−0.263333
$177$	2091.42	0.888140
$178$	−2241.61	−0.943907
$179$	1631.15	0.681104	0.340552	−	0.940226i	$-0.389386\pi$
$179$	1631.15	0.681104	0.340552	+	0.940226i	$0.389386\pi$
$180$	1195.95	0.495228
$181$	2150.28	0.883032	0.441516	−	0.897253i	$-0.354441\pi$
$181$	2150.28	0.883032	0.441516	+	0.897253i	$0.354441\pi$
$182$	0	0
$183$	2820.03	1.13914
$184$	403.293	0.161583
$185$	5129.34	2.03847
$186$	−130.470	−0.0514330
$187$	1100.73	0.430448
$188$	1491.71	0.578693
$189$	4507.50	1.73478
$190$	1968.83	0.751759
$191$	−762.764	−0.288962	−0.144481	−	0.989508i	$-0.546151\pi$
$191$	−762.764	−0.288962	−0.144481	+	0.989508i	$0.546151\pi$
$192$	2493.85	0.937385
$193$	−1670.89	−0.623176	−0.311588	−	0.950217i	$-0.600861\pi$
$193$	−1670.89	−0.623176	−0.311588	+	0.950217i	$0.600861\pi$
$194$	−2727.84	−1.00952
$195$	0	0
$196$	4769.77	1.73825
$197$	−4202.55	−1.51989	−0.759947	−	0.649985i	$-0.774775\pi$
$197$	−4202.55	−1.51989	−0.759947	+	0.649985i	$0.774775\pi$
$198$	491.944	0.176570
$199$	691.852	0.246453	0.123226	−	0.992379i	$-0.460676\pi$
$199$	691.852	0.246453	0.123226	+	0.992379i	$0.460676\pi$
$200$	−102.244	−0.0361486
$201$	2688.77	0.943539
$202$	−7225.01	−2.51659
$203$	4032.43	1.39419
$204$	−3580.04	−1.22869
$205$	3175.28	1.08181
$206$	−5035.88	−1.70323
$207$	1172.67	0.393751
$208$	0	0
$209$	426.711	0.141226
$210$	−6040.08	−1.98479
$211$	−1081.86	−0.352978	−0.176489	−	0.984303i	$-0.556474\pi$
$211$	−1081.86	−0.352978	−0.176489	+	0.984303i	$0.556474\pi$
$212$	858.028	0.277970
$213$	−2079.87	−0.669062
$214$	−4797.69	−1.53254
$215$	235.029	0.0745528
$216$	−568.856	−0.179193
$217$	−234.174	−0.0732571
$218$	−2790.73	−0.867028
$219$	4635.40	1.43028
$220$	−1209.62	−0.370695
$221$	0	0
$222$	−6862.26	−2.07462
$223$	−1071.18	−0.321665	−0.160833	−	0.986982i	$-0.551418\pi$
$223$	−1071.18	−0.321665	−0.160833	+	0.986982i	$0.551418\pi$
$224$	7698.93	2.29646
$225$	−297.298	−0.0880882
$226$	2155.47	0.634424
$227$	1876.08	0.548545	0.274272	−	0.961652i	$-0.411563\pi$
$227$	1876.08	0.548545	0.274272	+	0.961652i	$0.411563\pi$
$228$	−1387.84	−0.403122
$229$	851.152	0.245614	0.122807	−	0.992431i	$-0.460810\pi$
$229$	851.152	0.245614	0.122807	+	0.992431i	$0.460810\pi$
$230$	−5472.53	−1.56890
$231$	−1309.09	−0.372864
$232$	−508.901	−0.144013
$233$	3288.70	0.924679	0.462339	−	0.886703i	$-0.347010\pi$
$233$	3288.70	0.924679	0.462339	+	0.886703i	$0.347010\pi$
$234$	0	0
$235$	−2066.47	−0.573625
$236$	−4640.42	−1.27994
$237$	−4807.36	−1.31760
$238$	−12195.3	−3.32143
$239$	−3945.13	−1.06774	−0.533869	−	0.845567i	$-0.679262\pi$
$239$	−3945.13	−1.06774	−0.533869	+	0.845567i	$0.679262\pi$
$240$	−2770.28	−0.745087
$241$	5275.38	1.41003	0.705015	−	0.709193i	$-0.250940\pi$
$241$	5275.38	1.41003	0.705015	+	0.709193i	$0.250940\pi$
$242$	−497.567	−0.132169
$243$	−2833.21	−0.747945
$244$	−6257.06	−1.64167
$245$	−6607.58	−1.72303
$246$	−4248.04	−1.10100
$247$	0	0
$248$	29.5532	0.00756707
$249$	−310.667	−0.0790671
$250$	−4956.81	−1.25398
$251$	−3293.95	−0.828337	−0.414168	−	0.910200i	$-0.635928\pi$
$251$	−3293.95	−0.828337	−0.414168	+	0.910200i	$0.635928\pi$
$252$	−2871.76	−0.717872
$253$	−1186.08	−0.294735
$254$	6901.93	1.70498
$255$	4959.43	1.21793
$256$	3012.46	0.735465
$257$	−86.4172	−0.0209749	−0.0104875	−	0.999945i	$-0.503338\pi$
$257$	−86.4172	−0.0209749	−0.0104875	+	0.999945i	$0.503338\pi$
$258$	−314.433	−0.0758749
$259$	−12316.7	−2.95492
$260$	0	0
$261$	−1479.75	−0.350936
$262$	9572.71	2.25727
$263$	1020.78	0.239330	0.119665	−	0.992814i	$-0.461818\pi$
$263$	1020.78	0.239330	0.119665	+	0.992814i	$0.461818\pi$
$264$	165.209	0.0385149
$265$	−1188.63	−0.275535
$266$	−4727.62	−1.08973
$267$	−2188.94	−0.501726
$268$	−5965.81	−1.35978
$269$	6128.15	1.38900	0.694498	−	0.719495i	$-0.255626\pi$
$269$	6128.15	1.38900	0.694498	+	0.719495i	$0.255626\pi$
$270$	7719.14	1.73989
$271$	−5071.96	−1.13690	−0.568450	−	0.822718i	$-0.692457\pi$
$271$	−5071.96	−1.13690	−0.568450	+	0.822718i	$0.692457\pi$
$272$	−5593.35	−1.24686
$273$	0	0
$274$	6034.19	1.33043
$275$	300.696	0.0659370
$276$	3857.60	0.841306
$277$	−1424.92	−0.309079	−0.154540	−	0.987987i	$-0.549389\pi$
$277$	−1424.92	−0.309079	−0.154540	+	0.987987i	$0.549389\pi$
$278$	4109.21	0.886525
$279$	85.9332	0.0184397
$280$	1368.16	0.292011
$281$	−4430.28	−0.940529	−0.470264	−	0.882526i	$-0.655841\pi$
$281$	−4430.28	−0.940529	−0.470264	+	0.882526i	$0.655841\pi$
$282$	2764.62	0.583796
$283$	−1413.10	−0.296819	−0.148410	−	0.988926i	$-0.547415\pi$
$283$	−1413.10	−0.296819	−0.148410	+	0.988926i	$0.547415\pi$
$284$	4614.79	0.964216
$285$	1922.58	0.399591
$286$	0	0
$287$	−7624.58	−1.56817
$288$	−2825.22	−0.578047
$289$	5100.37	1.03814
$290$	6905.58	1.39831
$291$	−2663.75	−0.536605
$292$	−10285.0	−2.06124
$293$	7077.26	1.41112	0.705559	−	0.708651i	$-0.250696\pi$
$293$	7077.26	1.41112	0.705559	+	0.708651i	$0.250696\pi$
$294$	8839.91	1.75359
$295$	6428.38	1.26873
$296$	1554.39	0.305227
$297$	1672.99	0.326858
$298$	−2972.86	−0.577896
$299$	0	0
$300$	−977.986	−0.188213
$301$	−564.359	−0.108070
$302$	−3836.65	−0.731041
$303$	−7055.26	−1.33767
$304$	−2168.32	−0.409084
$305$	8667.92	1.62729
$306$	4475.20	0.836047
$307$	−7728.94	−1.43685	−0.718426	−	0.695603i	$-0.755137\pi$
$307$	−7728.94	−1.43685	−0.718426	+	0.695603i	$0.755137\pi$
$308$	2904.58	0.537351
$309$	−4917.56	−0.905340
$310$	−401.025	−0.0734733
$311$	721.632	0.131576	0.0657878	−	0.997834i	$-0.479044\pi$
$311$	721.632	0.131576	0.0657878	+	0.997834i	$0.479044\pi$
$312$	0	0
$313$	−3856.16	−0.696367	−0.348184	−	0.937426i	$-0.613201\pi$
$313$	−3856.16	−0.696367	−0.348184	+	0.937426i	$0.613201\pi$
$314$	−3141.23	−0.564553
$315$	3978.25	0.711585
$316$	10666.5	1.89886
$317$	1180.38	0.209138	0.104569	−	0.994518i	$-0.466654\pi$
$317$	1180.38	0.209138	0.104569	+	0.994518i	$0.466654\pi$
$318$	1590.20	0.280422
$319$	1496.67	0.262687
$320$	7665.32	1.33908
$321$	−4684.97	−0.814608
$322$	13140.8	2.27425
$323$	3881.79	0.668694
$324$	−2825.01	−0.484398
$325$	0	0
$326$	10573.3	1.79633
$327$	−2725.16	−0.460862
$328$	962.237	0.161984
$329$	4962.07	0.831513
$330$	−2241.82	−0.373964
$331$	−6339.17	−1.05267	−0.526333	−	0.850279i	$-0.676433\pi$
$331$	−6339.17	−1.05267	−0.526333	+	0.850279i	$0.676433\pi$
$332$	689.304	0.113947
$333$	4519.77	0.743790
$334$	−11876.7	−1.94571
$335$	8264.46	1.34787
$336$	6652.08	1.08006
$337$	3552.56	0.574244	0.287122	−	0.957894i	$-0.407302\pi$
$337$	3552.56	0.574244	0.287122	+	0.957894i	$0.407302\pi$
$338$	0	0
$339$	2104.83	0.337223
$340$	−11003.9	−1.75521
$341$	−86.9155	−0.0138027
$342$	1734.86	0.274299
$343$	5700.80	0.897418
$344$	71.2232	0.0111631
$345$	−5343.95	−0.833938
$346$	−9212.99	−1.43148
$347$	−684.857	−0.105951	−0.0529756	−	0.998596i	$-0.516871\pi$
$347$	−684.857	−0.105951	−0.0529756	+	0.998596i	$0.516871\pi$
$348$	−4867.77	−0.749827
$349$	−8247.06	−1.26491	−0.632457	−	0.774596i	$-0.717953\pi$
$349$	−8247.06	−1.26491	−0.632457	+	0.774596i	$0.717953\pi$
$350$	−3331.47	−0.508785
$351$	0	0
$352$	2857.51	0.432687
$353$	8181.92	1.23365	0.616827	−	0.787099i	$-0.288418\pi$
$353$	8181.92	1.23365	0.616827	+	0.787099i	$0.288418\pi$
$354$	−8600.18	−1.29123
$355$	−6392.88	−0.955771
$356$	4856.79	0.723061
$357$	−11908.7	−1.76548
$358$	−6707.47	−0.990226
$359$	1224.23	0.179979	0.0899894	−	0.995943i	$-0.471317\pi$
$359$	1224.23	0.179979	0.0899894	+	0.995943i	$0.471317\pi$
$360$	−502.063	−0.0735030
$361$	−5354.19	−0.780607
$362$	−8842.21	−1.28380
$363$	−485.877	−0.0702532
$364$	0	0
$365$	14247.8	2.04319
$366$	−11596.3	−1.65615
$367$	7473.63	1.06300	0.531499	−	0.847059i	$-0.321629\pi$
$367$	7473.63	1.06300	0.531499	+	0.847059i	$0.321629\pi$
$368$	6027.02	0.853750
$369$	2797.94	0.394728
$370$	−21092.5	−2.96364
$371$	2854.17	0.399410
$372$	282.684	0.0393992
$373$	−12456.4	−1.72914	−0.864569	−	0.502514i	$-0.832408\pi$
$373$	−12456.4	−1.72914	−0.864569	+	0.502514i	$0.832408\pi$
$374$	−4526.36	−0.625809
$375$	−4840.35	−0.666545
$376$	−626.223	−0.0858909
$377$	0	0
$378$	−18535.4	−2.52211
$379$	−10104.8	−1.36952	−0.684758	−	0.728771i	$-0.740092\pi$
$379$	−10104.8	−1.36952	−0.684758	+	0.728771i	$0.740092\pi$
$380$	−4265.79	−0.575869
$381$	6739.77	0.906271
$382$	3136.58	0.420108
$383$	−12948.1	−1.72746	−0.863730	−	0.503954i	$-0.831878\pi$
$383$	−12948.1	−1.72746	−0.863730	+	0.503954i	$0.831878\pi$
$384$	−1910.01	−0.253827
$385$	−4023.73	−0.532645
$386$	6870.89	0.906008
$387$	207.098	0.0272026
$388$	5910.30	0.773325
$389$	−3176.64	−0.414041	−0.207020	−	0.978337i	$-0.566377\pi$
$389$	−3176.64	−0.414041	−0.207020	+	0.978337i	$0.566377\pi$
$390$	0	0
$391$	−10789.7	−1.39555
$392$	−2002.36	−0.257996
$393$	9347.80	1.19983
$394$	17281.4	2.20971
$395$	−14776.4	−1.88223
$396$	−1065.87	−0.135258
$397$	788.468	0.0996778	0.0498389	−	0.998757i	$-0.484129\pi$
$397$	788.468	0.0996778	0.0498389	+	0.998757i	$0.484129\pi$
$398$	−2844.98	−0.358307
$399$	−4616.54	−0.579239
$400$	−1527.98	−0.190997
$401$	−7789.14	−0.970003	−0.485001	−	0.874513i	$-0.661181\pi$
$401$	−7789.14	−0.970003	−0.485001	+	0.874513i	$0.661181\pi$
$402$	−11056.6	−1.37177
$403$	0	0
$404$	15654.1	1.92778
$405$	3913.50	0.480156
$406$	−16581.9	−2.02696
$407$	−4571.44	−0.556751
$408$	1502.91	0.182365
$409$	−3579.52	−0.432752	−0.216376	−	0.976310i	$-0.569424\pi$
$409$	−3579.52	−0.432752	−0.216376	+	0.976310i	$0.569424\pi$
$410$	−13057.2	−1.57280
$411$	5892.42	0.707181
$412$	10911.0	1.30473
$413$	−15436.0	−1.83912
$414$	−4822.18	−0.572457
$415$	−954.894	−0.112949
$416$	0	0
$417$	4012.66	0.471225
$418$	−1754.69	−0.205322
$419$	−5100.62	−0.594706	−0.297353	−	0.954768i	$-0.596104\pi$
$419$	−5100.62	−0.594706	−0.297353	+	0.954768i	$0.596104\pi$
$420$	13086.8	1.52041
$421$	−9575.43	−1.10850	−0.554250	−	0.832351i	$-0.686995\pi$
$421$	−9575.43	−1.10850	−0.554250	+	0.832351i	$0.686995\pi$
$422$	4448.75	0.513179
$423$	−1820.89	−0.209302
$424$	−360.202	−0.0412570
$425$	2735.43	0.312206
$426$	8552.68	0.972720
$427$	−20813.6	−2.35888
$428$	10394.9	1.17397
$429$	0	0
$430$	−966.469	−0.108389
$431$	8758.01	0.978790	0.489395	−	0.872062i	$-0.337218\pi$
$431$	8758.01	0.978790	0.489395	+	0.872062i	$0.337218\pi$
$432$	−8501.26	−0.946798
$433$	9186.93	1.01962	0.509810	−	0.860287i	$-0.329716\pi$
$433$	9186.93	1.01962	0.509810	+	0.860287i	$0.329716\pi$
$434$	962.954	0.106505
$435$	6743.33	0.743260
$436$	6046.56	0.664169
$437$	−4182.75	−0.457867
$438$	−19061.4	−2.07942
$439$	−2908.97	−0.316258	−0.158129	−	0.987418i	$-0.550546\pi$
$439$	−2908.97	−0.316258	−0.158129	+	0.987418i	$0.550546\pi$
$440$	507.802	0.0550194
$441$	−5822.34	−0.628694
$442$	0	0
$443$	6073.14	0.651340	0.325670	−	0.945484i	$-0.394410\pi$
$443$	6073.14	0.651340	0.325670	+	0.945484i	$0.394410\pi$
$444$	14868.2	1.58922
$445$	−6728.13	−0.716728
$446$	4404.81	0.467655
$447$	−2903.01	−0.307176
$448$	−18406.2	−1.94110
$449$	−13230.7	−1.39063	−0.695316	−	0.718704i	$-0.744736\pi$
$449$	−13230.7	−1.39063	−0.695316	+	0.718704i	$0.744736\pi$
$450$	1222.53	0.128068
$451$	−2829.92	−0.295467
$452$	−4670.17	−0.485988
$453$	−3746.51	−0.388579
$454$	−7714.66	−0.797504
$455$	0	0
$456$	582.617	0.0598323
$457$	11190.0	1.14540	0.572698	−	0.819767i	$-0.305897\pi$
$457$	11190.0	1.14540	0.572698	+	0.819767i	$0.305897\pi$
$458$	−3500.04	−0.357088
$459$	15219.2	1.54765
$460$	11857.1	1.20183
$461$	−13619.2	−1.37594	−0.687970	−	0.725739i	$-0.741498\pi$
$461$	−13619.2	−1.37594	−0.687970	+	0.725739i	$0.741498\pi$
$462$	5383.12	0.542090
$463$	4389.01	0.440550	0.220275	−	0.975438i	$-0.429305\pi$
$463$	4389.01	0.440550	0.220275	+	0.975438i	$0.429305\pi$
$464$	−7605.26	−0.760917
$465$	−391.603	−0.0390541
$466$	−13523.6	−1.34435
$467$	−17910.3	−1.77471	−0.887356	−	0.461086i	$-0.847460\pi$
$467$	−17910.3	−1.77471	−0.887356	+	0.461086i	$0.847460\pi$
$468$	0	0
$469$	−19844.9	−1.95384
$470$	8497.59	0.833967
$471$	−3067.42	−0.300084
$472$	1948.06	0.189971
$473$	−209.466	−0.0203620
$474$	19768.5	1.91560
$475$	1060.42	0.102432
$476$	26423.0	2.54432
$477$	−1047.37	−0.100537
$478$	16222.9	1.55234
$479$	945.121	0.0901538	0.0450769	−	0.998984i	$-0.485647\pi$
$479$	945.121	0.0901538	0.0450769	+	0.998984i	$0.485647\pi$
$480$	12874.7	1.22427
$481$	0	0
$482$	−21693.0	−2.04998
$483$	12832.0	1.20886
$484$	1078.06	0.101245
$485$	−8187.56	−0.766552
$486$	11650.5	1.08740
$487$	7408.49	0.689345	0.344672	−	0.938723i	$-0.387990\pi$
$487$	7408.49	0.689345	0.344672	+	0.938723i	$0.387990\pi$
$488$	2626.72	0.243660
$489$	10324.9	0.954823
$490$	27171.2	2.50504
$491$	4037.32	0.371082	0.185541	−	0.982636i	$-0.440596\pi$
$491$	4037.32	0.371082	0.185541	+	0.982636i	$0.440596\pi$
$492$	9204.04	0.843395
$493$	13615.1	1.24380
$494$	0	0
$495$	1476.56	0.134073
$496$	441.658	0.0399819
$497$	15350.8	1.38546
$498$	1277.50	0.114952
$499$	14317.5	1.28445	0.642225	−	0.766516i	$-0.278011\pi$
$499$	14317.5	1.28445	0.642225	+	0.766516i	$0.278011\pi$
$500$	10739.7	0.960588
$501$	−11597.7	−1.03422
$502$	13545.2	1.20428
$503$	−7143.66	−0.633241	−0.316621	−	0.948552i	$-0.602548\pi$
$503$	−7143.66	−0.633241	−0.316621	+	0.948552i	$0.602548\pi$
$504$	1205.57	0.106548
$505$	−21685.7	−1.91089
$506$	4877.30	0.428503
$507$	0	0
$508$	−14954.1	−1.30607
$509$	11996.3	1.04465	0.522327	−	0.852745i	$-0.325064\pi$
$509$	11996.3	1.04465	0.522327	+	0.852745i	$0.325064\pi$
$510$	−20393.8	−1.77069
$511$	−34212.2	−2.96176
$512$	−16192.9	−1.39772
$513$	5899.87	0.507769
$514$	355.358	0.0304945
$515$	−15115.1	−1.29330
$516$	681.268	0.0581224
$517$	1841.71	0.156670
$518$	50647.9	4.29602
$519$	−8996.53	−0.760894
$520$	0	0
$521$	−5399.30	−0.454027	−0.227013	−	0.973892i	$-0.572896\pi$
$521$	−5399.30	−0.454027	−0.227013	+	0.973892i	$0.572896\pi$
$522$	6084.92	0.510210
$523$	−9934.19	−0.830577	−0.415289	−	0.909690i	$-0.636319\pi$
$523$	−9934.19	−0.830577	−0.415289	+	0.909690i	$0.636319\pi$
$524$	−20740.8	−1.72913
$525$	−3253.20	−0.270441
$526$	−4197.56	−0.347951
$527$	−790.669	−0.0653550
$528$	2468.97	0.203500
$529$	−540.722	−0.0444417
$530$	4887.79	0.400589
$531$	5664.44	0.462930
$532$	10243.1	0.834767
$533$	0	0
$534$	9001.19	0.729438
$535$	−14400.1	−1.16369
$536$	2504.46	0.201821
$537$	−6549.88	−0.526347
$538$	−25199.7	−2.01940
$539$	5888.89	0.470598
$540$	−16724.7	−1.33281
$541$	21273.8	1.69063	0.845316	−	0.534267i	$-0.179412\pi$
$541$	21273.8	1.69063	0.845316	+	0.534267i	$0.179412\pi$
$542$	20856.5	1.65289
$543$	−8634.46	−0.682394
$544$	25994.7	2.04874
$545$	−8376.31	−0.658352
$546$	0	0
$547$	−18476.4	−1.44423	−0.722114	−	0.691774i	$-0.756829\pi$
$547$	−18476.4	−1.44423	−0.722114	+	0.691774i	$0.756829\pi$
$548$	−13074.0	−1.01915
$549$	7637.83	0.593761
$550$	−1236.50	−0.0958628
$551$	5278.05	0.408081
$552$	−1619.43	−0.124869
$553$	35481.4	2.72843
$554$	5859.44	0.449357
$555$	−20596.9	−1.57530
$556$	−8903.24	−0.679104
$557$	−15340.4	−1.16695	−0.583476	−	0.812131i	$-0.698308\pi$
$557$	−15340.4	−1.16695	−0.583476	+	0.812131i	$0.698308\pi$
$558$	−353.368	−0.0268087
$559$	0	0
$560$	20446.5	1.54289
$561$	−4420.01	−0.332644
$562$	18217.9	1.36739
$563$	17177.5	1.28587	0.642934	−	0.765922i	$-0.277717\pi$
$563$	17177.5	1.28587	0.642934	+	0.765922i	$0.277717\pi$
$564$	−5989.98	−0.447205
$565$	6469.60	0.481731
$566$	5810.83	0.431532
$567$	−9397.20	−0.696023
$568$	−1937.30	−0.143111
$569$	−7161.71	−0.527653	−0.263827	−	0.964570i	$-0.584985\pi$
$569$	−7161.71	−0.527653	−0.263827	+	0.964570i	$0.584985\pi$
$570$	−7905.87	−0.580948
$571$	7125.27	0.522212	0.261106	−	0.965310i	$-0.415913\pi$
$571$	7125.27	0.522212	0.261106	+	0.965310i	$0.415913\pi$
$572$	0	0
$573$	3062.89	0.223305
$574$	31353.2	2.27989
$575$	−2947.51	−0.213773
$576$	6754.38	0.488598
$577$	24023.6	1.73330	0.866651	−	0.498914i	$-0.166268\pi$
$577$	24023.6	1.73330	0.866651	+	0.498914i	$0.166268\pi$
$578$	−20973.3	−1.50930
$579$	6709.46	0.481582
$580$	−14962.0	−1.07115
$581$	2292.92	0.163729
$582$	10953.7	0.780146
$583$	1059.35	0.0752549
$584$	4317.65	0.305934
$585$	0	0
$586$	−29102.6	−2.05156
$587$	−8837.49	−0.621401	−0.310700	−	0.950508i	$-0.600564\pi$
$587$	−8837.49	−0.621401	−0.310700	+	0.950508i	$0.600564\pi$
$588$	−19153.1	−1.34330
$589$	−306.511	−0.0214424
$590$	−26434.3	−1.84455
$591$	16875.4	1.17455
$592$	23229.6	1.61272
$593$	−3054.42	−0.211518	−0.105759	−	0.994392i	$-0.533727\pi$
$593$	−3054.42	−0.211518	−0.105759	+	0.994392i	$0.533727\pi$
$594$	−6879.55	−0.475204
$595$	−36603.8	−2.52203
$596$	6441.17	0.442685
$597$	−2778.14	−0.190455
$598$	0	0
$599$	21193.1	1.44562	0.722812	−	0.691045i	$-0.242849\pi$
$599$	21193.1	1.44562	0.722812	+	0.691045i	$0.242849\pi$
$600$	410.560	0.0279351
$601$	4815.47	0.326834	0.163417	−	0.986557i	$-0.447748\pi$
$601$	4815.47	0.326834	0.163417	+	0.986557i	$0.447748\pi$
$602$	2320.71	0.157118
$603$	7282.32	0.491806
$604$	8312.71	0.559999
$605$	−1493.44	−0.100358
$606$	29012.1	1.94478
$607$	−16050.3	−1.07325	−0.536626	−	0.843821i	$-0.680301\pi$
$607$	−16050.3	−1.07325	−0.536626	+	0.843821i	$0.680301\pi$
$608$	10077.1	0.672174
$609$	−16192.3	−1.07741
$610$	−35643.6	−2.36584
$611$	0	0
$612$	−9696.23	−0.640436
$613$	848.517	0.0559075	0.0279537	−	0.999609i	$-0.491101\pi$
$613$	848.517	0.0559075	0.0279537	+	0.999609i	$0.491101\pi$
$614$	31782.4	2.08898
$615$	−12750.4	−0.836008
$616$	−1219.35	−0.0797549
$617$	6280.32	0.409783	0.204891	−	0.978785i	$-0.434316\pi$
$617$	6280.32	0.409783	0.204891	+	0.978785i	$0.434316\pi$
$618$	20221.6	1.31623
$619$	−13573.1	−0.881338	−0.440669	−	0.897670i	$-0.645259\pi$
$619$	−13573.1	−0.881338	−0.440669	+	0.897670i	$0.645259\pi$
$620$	868.885	0.0562827
$621$	−16399.2	−1.05970
$622$	−2967.44	−0.191292
$623$	16155.8	1.03895
$624$	0	0
$625$	−18294.7	−1.17086
$626$	15857.0	1.01242
$627$	−1713.46	−0.109137
$628$	6805.96	0.432464
$629$	−41586.3	−2.63617
$630$	−16359.1	−1.03454
$631$	−26508.8	−1.67242	−0.836212	−	0.548407i	$-0.815235\pi$
$631$	−26508.8	−1.67242	−0.836212	+	0.548407i	$0.815235\pi$
$632$	−4477.82	−0.281833
$633$	4344.23	0.272776
$634$	−4853.86	−0.304056
$635$	20716.0	1.29463
$636$	−3445.42	−0.214811
$637$	0	0
$638$	−6154.48	−0.381909
$639$	−5633.16	−0.348739
$640$	−5870.78	−0.362599
$641$	−7041.80	−0.433907	−0.216953	−	0.976182i	$-0.569612\pi$
$641$	−7041.80	−0.433907	−0.216953	+	0.976182i	$0.569612\pi$
$642$	19265.2	1.18432
$643$	20537.2	1.25958	0.629789	−	0.776766i	$-0.283141\pi$
$643$	20537.2	1.25958	0.629789	+	0.776766i	$0.283141\pi$
$644$	−28471.6	−1.74214
$645$	−943.762	−0.0576133
$646$	−15962.4	−0.972185
$647$	24437.3	1.48490	0.742449	−	0.669903i	$-0.233664\pi$
$647$	24437.3	1.48490	0.742449	+	0.669903i	$0.233664\pi$
$648$	1185.94	0.0718956
$649$	−5729.19	−0.346518
$650$	0	0
$651$	940.329	0.0566120
$652$	−22908.8	−1.37604
$653$	670.866	0.0402037	0.0201019	−	0.999798i	$-0.493601\pi$
$653$	670.866	0.0402037	0.0201019	+	0.999798i	$0.493601\pi$
$654$	11206.2	0.670026
$655$	28732.3	1.71399
$656$	14380.1	0.855869
$657$	12554.6	0.745513
$658$	−20404.7	−1.20890
$659$	1152.52	0.0681271	0.0340635	−	0.999420i	$-0.489155\pi$
$659$	1152.52	0.0681271	0.0340635	+	0.999420i	$0.489155\pi$
$660$	4857.26	0.286468
$661$	16069.8	0.945605	0.472802	−	0.881169i	$-0.343242\pi$
$661$	16069.8	0.945605	0.472802	+	0.881169i	$0.343242\pi$
$662$	26067.5	1.53042
$663$	0	0
$664$	−289.371	−0.0169123
$665$	−14189.8	−0.827456
$666$	−18585.9	−1.08136
$667$	−14670.8	−0.851656
$668$	25732.8	1.49047
$669$	4301.32	0.248578
$670$	−33984.5	−1.95960
$671$	−7725.14	−0.444449
$672$	−30915.1	−1.77467
$673$	21971.7	1.25847	0.629233	−	0.777217i	$-0.283369\pi$
$673$	21971.7	1.25847	0.629233	+	0.777217i	$0.283369\pi$
$674$	−14608.6	−0.834867
$675$	4157.54	0.237072
$676$	0	0
$677$	27156.2	1.54165	0.770826	−	0.637046i	$-0.219844\pi$
$677$	27156.2	1.54165	0.770826	+	0.637046i	$0.219844\pi$
$678$	−8655.32	−0.490274
$679$	19660.2	1.11118
$680$	4619.47	0.260513
$681$	−7533.41	−0.423907
$682$	357.407	0.0200672
$683$	−2629.89	−0.147335	−0.0736675	−	0.997283i	$-0.523470\pi$
$683$	−2629.89	−0.147335	−0.0736675	+	0.997283i	$0.523470\pi$
$684$	−3758.85	−0.210121
$685$	18111.5	1.01023
$686$	−23442.4	−1.30472
$687$	−3417.81	−0.189807
$688$	1064.39	0.0589820
$689$	0	0
$690$	21975.0	1.21243
$691$	−3266.25	−0.179817	−0.0899087	−	0.995950i	$-0.528658\pi$
$691$	−3266.25	−0.179817	−0.0899087	+	0.995950i	$0.528658\pi$
$692$	19961.4	1.09656
$693$	−3545.55	−0.194350
$694$	2816.22	0.154038
$695$	12333.7	0.673156
$696$	2043.50	0.111291
$697$	−25743.7	−1.39901
$698$	33912.9	1.83900
$699$	−13205.8	−0.714578
$700$	7218.16	0.389744
$701$	−6866.07	−0.369940	−0.184970	−	0.982744i	$-0.559219\pi$
$701$	−6866.07	−0.369940	−0.184970	+	0.982744i	$0.559219\pi$
$702$	0	0
$703$	−16121.4	−0.864905
$704$	−6831.59	−0.365732
$705$	8297.94	0.443289
$706$	−33645.1	−1.79355
$707$	52072.4	2.76999
$708$	18633.6	0.989118
$709$	19916.6	1.05498	0.527492	−	0.849560i	$-0.323132\pi$
$709$	19916.6	1.05498	0.527492	+	0.849560i	$0.323132\pi$
$710$	26288.3	1.38955
$711$	−13020.3	−0.686781
$712$	−2038.89	−0.107318
$713$	851.971	0.0447497
$714$	48970.2	2.56676
$715$	0	0
$716$	14532.8	0.758542
$717$	15841.7	0.825132
$718$	−5034.19	−0.261663
$719$	−27973.6	−1.45096	−0.725479	−	0.688245i	$-0.758382\pi$
$719$	−27973.6	−1.45096	−0.725479	+	0.688245i	$0.758382\pi$
$720$	−7503.08	−0.388366
$721$	36294.7	1.87474
$722$	22017.1	1.13489
$723$	−21183.3	−1.08965
$724$	19158.0	0.983429
$725$	3719.35	0.190529
$726$	1997.99	0.102138
$727$	−2847.88	−0.145285	−0.0726424	−	0.997358i	$-0.523143\pi$
$727$	−2847.88	−0.145285	−0.0726424	+	0.997358i	$0.523143\pi$
$728$	0	0
$729$	19937.8	1.01295
$730$	−58588.8	−2.97050
$731$	−1905.51	−0.0964128
$732$	25125.3	1.26866
$733$	−18147.3	−0.914443	−0.457221	−	0.889353i	$-0.651155\pi$
$733$	−18147.3	−0.914443	−0.457221	+	0.889353i	$0.651155\pi$
$734$	−30732.5	−1.54545
$735$	26532.8	1.33153
$736$	−28010.2	−1.40281
$737$	−7365.56	−0.368133
$738$	−11505.5	−0.573878
$739$	8150.35	0.405704	0.202852	−	0.979209i	$-0.434979\pi$
$739$	8150.35	0.405704	0.202852	+	0.979209i	$0.434979\pi$
$740$	45700.2	2.27023
$741$	0	0
$742$	−11736.7	−0.580684
$743$	−1826.46	−0.0901837	−0.0450918	−	0.998983i	$-0.514358\pi$
$743$	−1826.46	−0.0901837	−0.0450918	+	0.998983i	$0.514358\pi$
$744$	−118.671	−0.00584772
$745$	−8922.97	−0.438808
$746$	51222.3	2.51392
$747$	−841.415	−0.0412125
$748$	9807.07	0.479388
$749$	34578.0	1.68685
$750$	19904.1	0.969060
$751$	−29233.8	−1.42045	−0.710223	−	0.703977i	$-0.751406\pi$
$751$	−29233.8	−1.42045	−0.710223	+	0.703977i	$0.751406\pi$
$752$	−9358.58	−0.453820
$753$	13226.9	0.640127
$754$	0	0
$755$	−11515.6	−0.555094
$756$	40159.9	1.93201
$757$	−14383.7	−0.690603	−0.345301	−	0.938492i	$-0.612223\pi$
$757$	−14383.7	−0.690603	−0.345301	+	0.938492i	$0.612223\pi$
$758$	41552.0	1.99108
$759$	4762.71	0.227767
$760$	1790.79	0.0854719
$761$	−13874.1	−0.660890	−0.330445	−	0.943825i	$-0.607199\pi$
$761$	−13874.1	−0.660890	−0.330445	+	0.943825i	$0.607199\pi$
$762$	−27714.8	−1.31759
$763$	20113.4	0.954332
$764$	−6795.90	−0.321815
$765$	13432.2	0.634827
$766$	53244.2	2.51148
$767$	0	0
$768$	−12096.6	−0.568356
$769$	33760.7	1.58315	0.791576	−	0.611071i	$-0.209261\pi$
$769$	33760.7	1.58315	0.791576	+	0.611071i	$0.209261\pi$
$770$	16546.1	0.774389
$771$	347.009	0.0162091
$772$	−14886.9	−0.694029
$773$	5102.17	0.237403	0.118701	−	0.992930i	$-0.462127\pi$
$773$	5102.17	0.237403	0.118701	+	0.992930i	$0.462127\pi$
$774$	−851.615	−0.0395487
$775$	−215.993	−0.0100112
$776$	−2481.16	−0.114779
$777$	49457.9	2.28352
$778$	13062.7	0.601956
$779$	−9979.82	−0.459004
$780$	0	0
$781$	5697.55	0.261043
$782$	44368.7	2.02893
$783$	20693.5	0.944476
$784$	−29924.2	−1.36317
$785$	−9428.32	−0.428677
$786$	−38439.3	−1.74438
$787$	−37026.4	−1.67706	−0.838532	−	0.544852i	$-0.816586\pi$
$787$	−37026.4	−1.67706	−0.838532	+	0.544852i	$0.816586\pi$
$788$	−37442.9	−1.69270
$789$	−4098.94	−0.184951
$790$	60762.2	2.73649
$791$	−15535.0	−0.698307
$792$	447.456	0.0200753
$793$	0	0
$794$	−3242.28	−0.144917
$795$	4772.95	0.212930
$796$	6164.10	0.274473
$797$	−11514.8	−0.511764	−0.255882	−	0.966708i	$-0.582366\pi$
$797$	−11514.8	−0.511764	−0.255882	+	0.966708i	$0.582366\pi$
$798$	18983.8	0.842129
$799$	16754.0	0.741819
$800$	7101.19	0.313831
$801$	−5928.57	−0.261518
$802$	32029.9	1.41024
$803$	−12698.1	−0.558041
$804$	23955.8	1.05082
$805$	39441.8	1.72688
$806$	0	0
$807$	−24607.7	−1.07340
$808$	−6571.63	−0.286125
$809$	−5456.94	−0.237152	−0.118576	−	0.992945i	$-0.537833\pi$
$809$	−5456.94	−0.237152	−0.118576	+	0.992945i	$0.537833\pi$
$810$	−16092.8	−0.698078
$811$	−4694.61	−0.203268	−0.101634	−	0.994822i	$-0.532407\pi$
$811$	−4694.61	−0.203268	−0.101634	+	0.994822i	$0.532407\pi$
$812$	35927.2	1.55271
$813$	20366.5	0.878579
$814$	18798.3	0.809436
$815$	31735.6	1.36399
$816$	22460.2	0.963557
$817$	−738.690	−0.0316322
$818$	14719.4	0.629159
$819$	0	0
$820$	28290.4	1.20481
$821$	−1878.93	−0.0798724	−0.0399362	−	0.999202i	$-0.512715\pi$
$821$	−1878.93	−0.0798724	−0.0399362	+	0.999202i	$0.512715\pi$
$822$	−24230.4	−1.02814
$823$	16108.5	0.682268	0.341134	−	0.940015i	$-0.389189\pi$
$823$	16108.5	0.682268	0.341134	+	0.940015i	$0.389189\pi$
$824$	−4580.47	−0.193651
$825$	−1207.45	−0.0509551
$826$	63474.8	2.67382
$827$	−24298.9	−1.02171	−0.510857	−	0.859666i	$-0.670672\pi$
$827$	−24298.9	−1.02171	−0.510857	+	0.859666i	$0.670672\pi$
$828$	10448.0	0.438518
$829$	−9546.01	−0.399936	−0.199968	−	0.979802i	$-0.564084\pi$
$829$	−9546.01	−0.399936	−0.199968	+	0.979802i	$0.564084\pi$
$830$	3926.64	0.164212
$831$	5721.77	0.238852
$832$	0	0
$833$	53571.2	2.22825
$834$	−16500.6	−0.685093
$835$	−35647.7	−1.47741
$836$	3801.81	0.157283
$837$	−1201.73	−0.0496269
$838$	20974.4	0.864616
$839$	−26922.4	−1.10782	−0.553912	−	0.832575i	$-0.686866\pi$
$839$	−26922.4	−1.10782	−0.553912	+	0.832575i	$0.686866\pi$
$840$	−5493.86	−0.225662
$841$	−5876.51	−0.240949
$842$	39375.4	1.61160
$843$	17789.8	0.726827
$844$	−9638.92	−0.393110
$845$	0	0
$846$	7487.74	0.304295
$847$	3586.08	0.145477
$848$	−5383.03	−0.217988
$849$	5674.30	0.229377
$850$	−11248.4	−0.453903
$851$	44810.6	1.80504
$852$	−18530.7	−0.745132
$853$	35519.2	1.42574	0.712868	−	0.701298i	$-0.247396\pi$
$853$	35519.2	1.42574	0.712868	+	0.701298i	$0.247396\pi$
$854$	85588.3	3.42948
$855$	5207.14	0.208281
$856$	−4363.82	−0.174243
$857$	−35440.1	−1.41262	−0.706308	−	0.707905i	$-0.749641\pi$
$857$	−35440.1	−1.41262	−0.706308	+	0.707905i	$0.749641\pi$
$858$	0	0
$859$	5211.30	0.206993	0.103497	−	0.994630i	$-0.466997\pi$
$859$	5211.30	0.206993	0.103497	+	0.994630i	$0.466997\pi$
$860$	2094.01	0.0830292
$861$	30616.6	1.21186
$862$	−36014.0	−1.42302
$863$	−23920.1	−0.943512	−0.471756	−	0.881729i	$-0.656380\pi$
$863$	−23920.1	−0.943512	−0.471756	+	0.881729i	$0.656380\pi$
$864$	39509.1	1.55570
$865$	−27652.6	−1.08695
$866$	−37777.8	−1.48238
$867$	−20480.6	−0.802257
$868$	−2086.39	−0.0815861
$869$	13169.2	0.514078
$870$	−27729.4	−1.08059
$871$	0	0
$872$	−2538.36	−0.0985775
$873$	−7214.56	−0.279697
$874$	17200.0	0.665673
$875$	35724.9	1.38025
$876$	41299.4	1.59290
$877$	−31709.5	−1.22093	−0.610464	−	0.792044i	$-0.709017\pi$
$877$	−31709.5	−1.22093	−0.610464	+	0.792044i	$0.709017\pi$
$878$	11962.0	0.459794
$879$	−28418.8	−1.09049
$880$	7588.85	0.290705
$881$	−18304.1	−0.699976	−0.349988	−	0.936754i	$-0.613814\pi$
$881$	−18304.1	−0.699976	−0.349988	+	0.936754i	$0.613814\pi$
$882$	23942.2	0.914031
$883$	9723.16	0.370567	0.185283	−	0.982685i	$-0.440680\pi$
$883$	9723.16	0.370567	0.185283	+	0.982685i	$0.440680\pi$
$884$	0	0
$885$	−25813.2	−0.980455
$886$	−24973.5	−0.946954
$887$	−26052.7	−0.986205	−0.493103	−	0.869971i	$-0.664137\pi$
$887$	−26052.7	−0.986205	−0.493103	+	0.869971i	$0.664137\pi$
$888$	−6241.68	−0.235875
$889$	−49743.8	−1.87666
$890$	27666.9	1.04202
$891$	−3487.84	−0.131141
$892$	−9543.73	−0.358237
$893$	6494.86	0.243384
$894$	11937.5	0.446590
$895$	−20132.3	−0.751899
$896$	14097.1	0.525615
$897$	0	0
$898$	54406.2	2.02178
$899$	−1075.07	−0.0398839
$900$	−2648.79	−0.0981035
$901$	9636.85	0.356326
$902$	11637.0	0.429566
$903$	2266.19	0.0835150
$904$	1960.55	0.0721314
$905$	−26539.7	−0.974816
$906$	15406.1	0.564938
$907$	21863.5	0.800401	0.400201	−	0.916427i	$-0.368940\pi$
$907$	21863.5	0.800401	0.400201	+	0.916427i	$0.368940\pi$
$908$	16715.0	0.610912
$909$	−19108.6	−0.697241
$910$	0	0
$911$	16925.2	0.615539	0.307769	−	0.951461i	$-0.400417\pi$
$911$	16925.2	0.615539	0.307769	+	0.951461i	$0.400417\pi$
$912$	8706.91	0.316134
$913$	851.033	0.0308490
$914$	−46014.6	−1.66524
$915$	−34806.1	−1.25755
$916$	7583.40	0.273540
$917$	−68992.8	−2.48456
$918$	−62583.2	−2.25006
$919$	44034.4	1.58059	0.790294	−	0.612727i	$-0.209928\pi$
$919$	44034.4	1.58059	0.790294	+	0.612727i	$0.209928\pi$
$920$	−4977.63	−0.178378
$921$	31035.6	1.11038
$922$	56003.7	2.00042
$923$	0	0
$924$	−11663.4	−0.415257
$925$	−11360.4	−0.403815
$926$	−18048.2	−0.640496
$927$	−13318.8	−0.471895
$928$	35345.0	1.25028
$929$	−20243.5	−0.714928	−0.357464	−	0.933927i	$-0.616359\pi$
$929$	−20243.5	−0.714928	−0.357464	+	0.933927i	$0.616359\pi$
$930$	1610.32	0.0567791
$931$	20767.4	0.731068
$932$	29300.9	1.02981
$933$	−2897.72	−0.101680
$934$	73649.4	2.58017
$935$	−13585.8	−0.475189
$936$	0	0
$937$	42402.7	1.47837	0.739187	−	0.673500i	$-0.235210\pi$
$937$	42402.7	1.47837	0.739187	+	0.673500i	$0.235210\pi$
$938$	81604.5	2.84060
$939$	15484.4	0.538142
$940$	−18411.4	−0.638843
$941$	−32336.2	−1.12022	−0.560111	−	0.828418i	$-0.689242\pi$
$941$	−32336.2	−1.12022	−0.560111	+	0.828418i	$0.689242\pi$
$942$	12613.6	0.436278
$943$	27739.7	0.957931
$944$	29112.7	1.00375
$945$	−55633.6	−1.91509
$946$	861.350	0.0296035
$947$	4526.56	0.155326	0.0776628	−	0.996980i	$-0.475254\pi$
$947$	4526.56	0.155326	0.0776628	+	0.996980i	$0.475254\pi$
$948$	−42831.5	−1.46741
$949$	0	0
$950$	−4360.57	−0.148922
$951$	−4739.82	−0.161619
$952$	−11092.4	−0.377633
$953$	36521.4	1.24139	0.620694	−	0.784053i	$-0.286851\pi$
$953$	36521.4	1.24139	0.620694	+	0.784053i	$0.286851\pi$
$954$	4306.93	0.146166
$955$	9414.37	0.318997
$956$	−35149.4	−1.18913
$957$	−6009.88	−0.203001
$958$	−3886.45	−0.131071
$959$	−43489.8	−1.46440
$960$	−30780.2	−1.03482
$961$	−29728.6	−0.997904
$962$	0	0
$963$	−12688.8	−0.424603
$964$	47001.3	1.57034
$965$	20622.8	0.687951
$966$	−52767.0	−1.75750
$967$	−53292.3	−1.77225	−0.886125	−	0.463446i	$-0.846613\pi$
$967$	−53292.3	−1.77225	−0.886125	+	0.463446i	$0.846613\pi$
$968$	−452.570	−0.0150270
$969$	−15587.3	−0.516757
$970$	33668.3	1.11446
$971$	−41718.3	−1.37879	−0.689394	−	0.724386i	$-0.742123\pi$
$971$	−41718.3	−1.37879	−0.689394	+	0.724386i	$0.742123\pi$
$972$	−25242.7	−0.832983
$973$	−29616.0	−0.975792
$974$	−30464.7	−1.00221
$975$	0	0
$976$	39255.0	1.28742
$977$	42962.8	1.40686	0.703429	−	0.710765i	$-0.251651\pi$
$977$	42962.8	1.40686	0.703429	+	0.710765i	$0.251651\pi$
$978$	−42457.3	−1.38817
$979$	5996.33	0.195755
$980$	−58870.7	−1.91893
$981$	−7380.88	−0.240217
$982$	−16601.9	−0.539500
$983$	−30376.8	−0.985626	−0.492813	−	0.870135i	$-0.664031\pi$
$983$	−30376.8	−0.985626	−0.492813	+	0.870135i	$0.664031\pi$
$984$	−3863.87	−0.125179
$985$	51869.7	1.67788
$986$	−55987.2	−1.80831
$987$	−19925.2	−0.642581
$988$	0	0
$989$	2053.25	0.0660156
$990$	−6071.79	−0.194923
$991$	−31044.6	−0.995120	−0.497560	−	0.867429i	$-0.665771\pi$
$991$	−31044.6	−0.995120	−0.497560	+	0.867429i	$0.665771\pi$
$992$	−2052.58	−0.0656950
$993$	25455.0	0.813485
$994$	−63124.3	−2.01427
$995$	−8539.15	−0.272070
$996$	−2767.91	−0.0880567
$997$	−22395.1	−0.711394	−0.355697	−	0.934601i	$-0.615757\pi$
$997$	−22395.1	−0.711394	−0.355697	+	0.934601i	$0.615757\pi$
$998$	−58875.5	−1.86741
$999$	−63206.4	−2.00176

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.g.1.3		17
13.3	even	3		143.4.e.b.100.15	✓	34
13.9	even	3		143.4.e.b.133.15	yes	34
13.12	even	2		1859.4.a.h.1.15		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.4.e.b.100.15	✓	34	13.3	even	3
143.4.e.b.133.15	yes	34	13.9	even	3
1859.4.a.g.1.3		17	1.1	even	1	trivial
1859.4.a.h.1.15		17	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.11212 q^{2} -4.01551 q^{3} +8.90957 q^{4} -12.3424 q^{5} +16.5123 q^{6} +29.6370 q^{7} -3.74025 q^{8} -10.8757 q^{9} +O(q^{10})\)	\(q-4.11212 q^{2} -4.01551 q^{3} +8.90957 q^{4} -12.3424 q^{5} +16.5123 q^{6} +29.6370 q^{7} -3.74025 q^{8} -10.8757 q^{9} +50.7537 q^{10} +11.0000 q^{11} -35.7765 q^{12} -121.871 q^{14} +49.5612 q^{15} -55.8962 q^{16} +100.067 q^{17} +44.7221 q^{18} +38.7919 q^{19} -109.966 q^{20} -119.008 q^{21} -45.2334 q^{22} -107.825 q^{23} +15.0190 q^{24} +27.3360 q^{25} +152.090 q^{27} +264.053 q^{28} +136.061 q^{29} -203.802 q^{30} -7.90141 q^{31} +259.774 q^{32} -44.1706 q^{33} -411.487 q^{34} -365.794 q^{35} -96.8976 q^{36} -415.585 q^{37} -159.517 q^{38} +46.1639 q^{40} -257.265 q^{41} +489.375 q^{42} -19.0423 q^{43} +98.0052 q^{44} +134.233 q^{45} +443.391 q^{46} +167.428 q^{47} +224.452 q^{48} +535.354 q^{49} -112.409 q^{50} -401.819 q^{51} +96.3042 q^{53} -625.414 q^{54} -135.767 q^{55} -110.850 q^{56} -155.769 q^{57} -559.498 q^{58} -520.835 q^{59} +441.569 q^{60} -702.285 q^{61} +32.4916 q^{62} -322.323 q^{63} -621.054 q^{64} +181.635 q^{66} -669.596 q^{67} +891.552 q^{68} +432.973 q^{69} +1504.19 q^{70} +517.959 q^{71} +40.6778 q^{72} -1154.37 q^{73} +1708.94 q^{74} -109.768 q^{75} +345.619 q^{76} +326.007 q^{77} +1197.20 q^{79} +689.895 q^{80} -317.076 q^{81} +1057.91 q^{82} +77.3667 q^{83} -1060.31 q^{84} -1235.07 q^{85} +78.3045 q^{86} -546.353 q^{87} -41.1428 q^{88} +545.121 q^{89} -551.981 q^{90} -960.676 q^{92} +31.7282 q^{93} -688.485 q^{94} -478.787 q^{95} -1043.12 q^{96} +663.366 q^{97} -2201.44 q^{98} -119.632 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9	\( 17 q - 6 q^{3} + 50 q^{4} - 24 q^{5} + 16 q^{6} - 62 q^{7} - 21 q^{8} + 135 q^{9} + 2 q^{10} + 187 q^{11} - 127 q^{12} - 148 q^{15} + 126 q^{16} - 74 q^{17} + 90 q^{18} - 159 q^{19} - 222 q^{20} - 184 q^{21} - 215 q^{23} + 214 q^{24} + 95 q^{25} - 192 q^{27} - 358 q^{28} - 157 q^{29} + 829 q^{30} - 394 q^{31} - 553 q^{32} - 66 q^{33} - 702 q^{34} + 58 q^{35} - 700 q^{36} + 88 q^{37} - 1318 q^{38} + 733 q^{40} - 512 q^{41} + 337 q^{42} + 927 q^{43} + 550 q^{44} - 1482 q^{45} - 1361 q^{46} - 143 q^{47} - 178 q^{48} + 1835 q^{49} - 583 q^{50} - 568 q^{51} + 106 q^{53} - 67 q^{54} - 264 q^{55} + 2059 q^{56} + 1298 q^{57} - 1690 q^{58} - 266 q^{59} + 37 q^{60} - 624 q^{61} + 643 q^{62} - 2360 q^{63} - 1589 q^{64} + 176 q^{66} - 676 q^{67} - 413 q^{68} + 764 q^{69} - 1061 q^{70} - 763 q^{71} - 1366 q^{72} - 2374 q^{73} - 1649 q^{74} + 2420 q^{75} - 2101 q^{76} - 682 q^{77} + 2164 q^{79} - 1013 q^{80} + 537 q^{81} + 3152 q^{82} + 777 q^{83} - 3381 q^{84} - 1690 q^{85} + 2894 q^{86} - 4200 q^{87} - 231 q^{88} - 1687 q^{89} - 5399 q^{90} + 5542 q^{92} - 4310 q^{93} + 1777 q^{94} + 1124 q^{95} - 3465 q^{96} - 2047 q^{97} + 1553 q^{98} + 1485 q^{99}+O(q^{100}) \) 17 * q - 6 * q^3 + 50 * q^4 - 24 * q^5 + 16 * q^6 - 62 * q^7 - 21 * q^8 + 135 * q^9 + 2 * q^10 + 187 * q^11 - 127 * q^12 - 148 * q^15 + 126 * q^16 - 74 * q^17 + 90 * q^18 - 159 * q^19 - 222 * q^20 - 184 * q^21 - 215 * q^23 + 214 * q^24 + 95 * q^25 - 192 * q^27 - 358 * q^28 - 157 * q^29 + 829 * q^30 - 394 * q^31 - 553 * q^32 - 66 * q^33 - 702 * q^34 + 58 * q^35 - 700 * q^36 + 88 * q^37 - 1318 * q^38 + 733 * q^40 - 512 * q^41 + 337 * q^42 + 927 * q^43 + 550 * q^44 - 1482 * q^45 - 1361 * q^46 - 143 * q^47 - 178 * q^48 + 1835 * q^49 - 583 * q^50 - 568 * q^51 + 106 * q^53 - 67 * q^54 - 264 * q^55 + 2059 * q^56 + 1298 * q^57 - 1690 * q^58 - 266 * q^59 + 37 * q^60 - 624 * q^61 + 643 * q^62 - 2360 * q^63 - 1589 * q^64 + 176 * q^66 - 676 * q^67 - 413 * q^68 + 764 * q^69 - 1061 * q^70 - 763 * q^71 - 1366 * q^72 - 2374 * q^73 - 1649 * q^74 + 2420 * q^75 - 2101 * q^76 - 682 * q^77 + 2164 * q^79 - 1013 * q^80 + 537 * q^81 + 3152 * q^82 + 777 * q^83 - 3381 * q^84 - 1690 * q^85 + 2894 * q^86 - 4200 * q^87 - 231 * q^88 - 1687 * q^89 - 5399 * q^90 + 5542 * q^92 - 4310 * q^93 + 1777 * q^94 + 1124 * q^95 - 3465 * q^96 - 2047 * q^97 + 1553 * q^98 + 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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