LMFDB - Embedded newform 1859.4.a.q.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$109.684550701$
Analytic rank:	$0$
Dimension:	$51$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q-3.26686 q^{2} +5.88118 q^{3} +2.67240 q^{4} +20.5347 q^{5} -19.2130 q^{6} +32.9664 q^{7} +17.4046 q^{8} +7.58824 q^{9} +O(q^{10})$	\(q-3.26686 q^{2} +5.88118 q^{3} +2.67240 q^{4} +20.5347 q^{5} -19.2130 q^{6} +32.9664 q^{7} +17.4046 q^{8} +7.58824 q^{9} -67.0842 q^{10} +11.0000 q^{11} +15.7168 q^{12} -107.697 q^{14} +120.768 q^{15} -78.2375 q^{16} +54.9146 q^{17} -24.7897 q^{18} +36.1177 q^{19} +54.8769 q^{20} +193.881 q^{21} -35.9355 q^{22} -5.83311 q^{23} +102.359 q^{24} +296.675 q^{25} -114.164 q^{27} +88.0994 q^{28} -168.370 q^{29} -394.534 q^{30} -70.2506 q^{31} +116.355 q^{32} +64.6929 q^{33} -179.398 q^{34} +676.957 q^{35} +20.2788 q^{36} -406.694 q^{37} -117.992 q^{38} +357.398 q^{40} +253.648 q^{41} -633.384 q^{42} +90.6310 q^{43} +29.3964 q^{44} +155.822 q^{45} +19.0560 q^{46} -519.847 q^{47} -460.128 q^{48} +743.786 q^{49} -969.198 q^{50} +322.962 q^{51} +66.8554 q^{53} +372.958 q^{54} +225.882 q^{55} +573.766 q^{56} +212.415 q^{57} +550.042 q^{58} +676.976 q^{59} +322.741 q^{60} +82.5939 q^{61} +229.499 q^{62} +250.157 q^{63} +245.785 q^{64} -211.343 q^{66} +477.306 q^{67} +146.754 q^{68} -34.3056 q^{69} -2211.53 q^{70} +1159.89 q^{71} +132.070 q^{72} -198.161 q^{73} +1328.61 q^{74} +1744.80 q^{75} +96.5209 q^{76} +362.631 q^{77} +1153.12 q^{79} -1606.59 q^{80} -876.301 q^{81} -828.634 q^{82} -242.067 q^{83} +518.128 q^{84} +1127.66 q^{85} -296.079 q^{86} -990.215 q^{87} +191.450 q^{88} +1355.95 q^{89} -509.051 q^{90} -15.5884 q^{92} -413.156 q^{93} +1698.27 q^{94} +741.668 q^{95} +684.302 q^{96} -791.838 q^{97} -2429.85 q^{98} +83.4706 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) $ 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.26686	−1.15501	−0.577505	−	0.816387i	$-0.695974\pi$
$2$	−3.26686	−1.15501	−0.577505	+	0.816387i	$0.695974\pi$
$3$	5.88118	1.13183	0.565916	−	0.824463i	$-0.308522\pi$
$3$	5.88118	1.13183	0.565916	+	0.824463i	$0.308522\pi$
$4$	2.67240	0.334050
$5$	20.5347	1.83668	0.918341	−	0.395790i	$-0.129529\pi$
$5$	20.5347	1.83668	0.918341	+	0.395790i	$0.129529\pi$
$6$	−19.2130	−1.30728
$7$	32.9664	1.78002	0.890010	−	0.455941i	$-0.150697\pi$
$7$	32.9664	1.78002	0.890010	+	0.455941i	$0.150697\pi$
$8$	17.4046	0.769180
$9$	7.58824	0.281046
$10$	−67.0842	−2.12139
$11$	11.0000	0.301511
$11$	11.0000	0.301511
$12$	15.7168	0.378088
$13$	0	0
$13$	0	0
$14$	−107.697	−2.05594
$15$	120.768	2.07882
$16$	−78.2375	−1.22246
$17$	54.9146	0.783456	0.391728	−	0.920081i	$-0.371877\pi$
$17$	54.9146	0.783456	0.391728	+	0.920081i	$0.371877\pi$
$18$	−24.7897	−0.324611
$19$	36.1177	0.436104	0.218052	−	0.975937i	$-0.430030\pi$
$19$	36.1177	0.436104	0.218052	+	0.975937i	$0.430030\pi$
$20$	54.8769	0.613543
$21$	193.881	2.01469
$22$	−35.9355	−0.348249
$23$	−5.83311	−0.0528821	−0.0264410	−	0.999650i	$-0.508417\pi$
$23$	−5.83311	−0.0528821	−0.0264410	+	0.999650i	$0.508417\pi$
$24$	102.359	0.870583
$25$	296.675	2.37340
$26$	0	0
$27$	−114.164	−0.813736
$28$	88.0994	0.594615
$29$	−168.370	−1.07812	−0.539061	−	0.842266i	$-0.681221\pi$
$29$	−168.370	−1.07812	−0.539061	+	0.842266i	$0.681221\pi$
$30$	−394.534	−2.40106
$31$	−70.2506	−0.407012	−0.203506	−	0.979074i	$-0.565234\pi$
$31$	−70.2506	−0.407012	−0.203506	+	0.979074i	$0.565234\pi$
$32$	116.355	0.642775
$33$	64.6929	0.341260
$34$	−179.398	−0.904900
$35$	676.957	3.26933
$36$	20.2788	0.0938832
$37$	−406.694	−1.80703	−0.903514	−	0.428558i	$-0.859022\pi$
$37$	−406.694	−1.80703	−0.903514	+	0.428558i	$0.859022\pi$
$38$	−117.992	−0.503705
$39$	0	0
$40$	357.398	1.41274
$41$	253.648	0.966176	0.483088	−	0.875572i	$-0.339515\pi$
$41$	253.648	0.966176	0.483088	+	0.875572i	$0.339515\pi$
$42$	−633.384	−2.32698
$43$	90.6310	0.321421	0.160710	−	0.987002i	$-0.448621\pi$
$43$	90.6310	0.321421	0.160710	+	0.987002i	$0.448621\pi$
$44$	29.3964	0.100720
$45$	155.822	0.516192
$46$	19.0560	0.0610794
$47$	−519.847	−1.61335	−0.806676	−	0.590994i	$-0.798736\pi$
$47$	−519.847	−1.61335	−0.806676	+	0.590994i	$0.798736\pi$
$48$	−460.128	−1.38362
$49$	743.786	2.16847
$50$	−969.198	−2.74130
$51$	322.962	0.886741
$52$	0	0
$53$	66.8554	0.173270	0.0866348	−	0.996240i	$-0.472389\pi$
$53$	66.8554	0.173270	0.0866348	+	0.996240i	$0.472389\pi$
$54$	372.958	0.939874
$55$	225.882	0.553781
$56$	573.766	1.36916
$57$	212.415	0.493597
$58$	550.042	1.24524
$59$	676.976	1.49381	0.746905	−	0.664930i	$-0.231539\pi$
$59$	676.976	1.49381	0.746905	+	0.664930i	$0.231539\pi$
$60$	322.741	0.694428
$61$	82.5939	0.173362	0.0866808	−	0.996236i	$-0.472374\pi$
$61$	82.5939	0.173362	0.0866808	+	0.996236i	$0.472374\pi$
$62$	229.499	0.470103
$63$	250.157	0.500267
$64$	245.785	0.480049
$65$	0	0
$66$	−211.343	−0.394159
$67$	477.306	0.870331	0.435165	−	0.900350i	$-0.356690\pi$
$67$	477.306	0.870331	0.435165	+	0.900350i	$0.356690\pi$
$68$	146.754	0.261713
$69$	−34.3056	−0.0598537
$70$	−2211.53	−3.77611
$71$	1159.89	1.93879	0.969396	−	0.245503i	$-0.0789531\pi$
$71$	1159.89	1.93879	0.969396	+	0.245503i	$0.0789531\pi$
$72$	132.070	0.216175
$73$	−198.161	−0.317712	−0.158856	−	0.987302i	$-0.550781\pi$
$73$	−198.161	−0.317712	−0.158856	+	0.987302i	$0.550781\pi$
$74$	1328.61	2.08714
$75$	1744.80	2.68630
$76$	96.5209	0.145680
$77$	362.631	0.536696
$78$	0	0
$79$	1153.12	1.64223	0.821117	−	0.570760i	$-0.193351\pi$
$79$	1153.12	1.64223	0.821117	+	0.570760i	$0.193351\pi$
$80$	−1606.59	−2.24527
$81$	−876.301	−1.20206
$82$	−828.634	−1.11594
$83$	−242.067	−0.320124	−0.160062	−	0.987107i	$-0.551169\pi$
$83$	−242.067	−0.320124	−0.160062	+	0.987107i	$0.551169\pi$
$84$	518.128	0.673005
$85$	1127.66	1.43896
$86$	−296.079	−0.371244
$87$	−990.215	−1.22025
$88$	191.450	0.231916
$89$	1355.95	1.61495	0.807474	−	0.589903i	$-0.200834\pi$
$89$	1355.95	1.61495	0.807474	+	0.589903i	$0.200834\pi$
$90$	−509.051	−0.596207
$91$	0	0
$92$	−15.5884	−0.0176652
$93$	−413.156	−0.460670
$94$	1698.27	1.86344
$95$	741.668	0.800984
$96$	684.302	0.727514
$97$	−791.838	−0.828855	−0.414427	−	0.910082i	$-0.636018\pi$
$97$	−791.838	−0.828855	−0.414427	+	0.910082i	$0.636018\pi$
$98$	−2429.85	−2.50461
$99$	83.4706	0.0847385
$100$	792.834	0.792834
$101$	−597.476	−0.588624	−0.294312	−	0.955709i	$-0.595091\pi$
$101$	−597.476	−0.588624	−0.294312	+	0.955709i	$0.595091\pi$
$102$	−1055.07	−1.02420
$103$	343.897	0.328982	0.164491	−	0.986379i	$-0.447402\pi$
$103$	343.897	0.328982	0.164491	+	0.986379i	$0.447402\pi$
$104$	0	0
$105$	3981.30	3.70034
$106$	−218.407	−0.200128
$107$	−985.963	−0.890810	−0.445405	−	0.895329i	$-0.646940\pi$
$107$	−985.963	−0.890810	−0.445405	+	0.895329i	$0.646940\pi$
$108$	−305.091	−0.271828
$109$	96.8097	0.0850705	0.0425353	−	0.999095i	$-0.486457\pi$
$109$	96.8097	0.0850705	0.0425353	+	0.999095i	$0.486457\pi$
$110$	−737.926	−0.639622
$111$	−2391.84	−2.04525
$112$	−2579.21	−2.17600
$113$	−923.603	−0.768896	−0.384448	−	0.923147i	$-0.625608\pi$
$113$	−923.603	−0.768896	−0.384448	+	0.923147i	$0.625608\pi$
$114$	−693.930	−0.570109
$115$	−119.781	−0.0971276
$116$	−449.952	−0.360146
$117$	0	0
$118$	−2211.59	−1.72537
$119$	1810.34	1.39457
$120$	2101.92	1.59898
$121$	121.000	0.0909091
$122$	−269.823	−0.200235
$123$	1491.75	1.09355
$124$	−187.737	−0.135962
$125$	3525.31	2.52250
$126$	−817.229	−0.577814
$127$	−921.525	−0.643875	−0.321937	−	0.946761i	$-0.604334\pi$
$127$	−921.525	−0.643875	−0.321937	+	0.946761i	$0.604334\pi$
$128$	−1733.78	−1.19724
$129$	533.017	0.363795
$130$	0	0
$131$	778.336	0.519111	0.259555	−	0.965728i	$-0.416424\pi$
$131$	778.336	0.519111	0.259555	+	0.965728i	$0.416424\pi$
$132$	172.885	0.113998
$133$	1190.67	0.776274
$134$	−1559.29	−1.00524
$135$	−2344.33	−1.49457
$136$	955.764	0.602618
$137$	1598.90	0.997105	0.498552	−	0.866860i	$-0.333865\pi$
$137$	1598.90	0.997105	0.498552	+	0.866860i	$0.333865\pi$
$138$	112.072	0.0691316
$139$	−2193.04	−1.33821	−0.669104	−	0.743168i	$-0.733322\pi$
$139$	−2193.04	−1.33821	−0.669104	+	0.743168i	$0.733322\pi$
$140$	1809.10	1.09212
$141$	−3057.31	−1.82604
$142$	−3789.22	−2.23932
$143$	0	0
$144$	−593.685	−0.343567
$145$	−3457.44	−1.98017
$146$	647.365	0.366961
$147$	4374.33	2.45435
$148$	−1086.85	−0.603637
$149$	−2071.66	−1.13904	−0.569520	−	0.821978i	$-0.692871\pi$
$149$	−2071.66	−1.13904	−0.569520	+	0.821978i	$0.692871\pi$
$150$	−5700.02	−3.10270
$151$	−1269.98	−0.684433	−0.342217	−	0.939621i	$-0.611178\pi$
$151$	−1269.98	−0.684433	−0.342217	+	0.939621i	$0.611178\pi$
$152$	628.613	0.335442
$153$	416.705	0.220187
$154$	−1184.67	−0.619890
$155$	−1442.58	−0.747552
$156$	0	0
$157$	−1546.99	−0.786389	−0.393194	−	0.919455i	$-0.628630\pi$
$157$	−1546.99	−0.786389	−0.393194	+	0.919455i	$0.628630\pi$
$158$	−3767.10	−1.89680
$159$	393.188	0.196112
$160$	2389.31	1.18057
$161$	−192.297	−0.0941312
$162$	2862.76	1.38839
$163$	−149.168	−0.0716796	−0.0358398	−	0.999358i	$-0.511411\pi$
$163$	−149.168	−0.0716796	−0.0358398	+	0.999358i	$0.511411\pi$
$164$	677.848	0.322750
$165$	1328.45	0.626787
$166$	790.799	0.369746
$167$	−551.865	−0.255716	−0.127858	−	0.991792i	$-0.540810\pi$
$167$	−551.865	−0.255716	−0.127858	+	0.991792i	$0.540810\pi$
$168$	3374.42	1.54966
$169$	0	0
$170$	−3683.90	−1.66201
$171$	274.070	0.122565
$172$	242.202	0.107370
$173$	3947.69	1.73490	0.867448	−	0.497527i	$-0.165759\pi$
$173$	3947.69	1.73490	0.867448	+	0.497527i	$0.165759\pi$
$174$	3234.90	1.40941
$175$	9780.33	4.22470
$176$	−860.612	−0.368586
$177$	3981.42	1.69074
$178$	−4429.70	−1.86528
$179$	552.905	0.230872	0.115436	−	0.993315i	$-0.463174\pi$
$179$	552.905	0.230872	0.115436	+	0.993315i	$0.463174\pi$
$180$	416.419	0.172434
$181$	2974.65	1.22157	0.610784	−	0.791797i	$-0.290854\pi$
$181$	2974.65	1.22157	0.610784	+	0.791797i	$0.290854\pi$
$182$	0	0
$183$	485.749	0.196216
$184$	−101.523	−0.0406758
$185$	−8351.35	−3.31894
$186$	1349.72	0.532078
$187$	604.061	0.236221
$188$	−1389.24	−0.538939
$189$	−3763.58	−1.44847
$190$	−2422.93	−0.925145
$191$	4162.38	1.57685	0.788427	−	0.615128i	$-0.210896\pi$
$191$	4162.38	1.57685	0.788427	+	0.615128i	$0.210896\pi$
$192$	1445.50	0.543335
$193$	−4342.22	−1.61948	−0.809741	−	0.586787i	$-0.800393\pi$
$193$	−4342.22	−1.61948	−0.809741	+	0.586787i	$0.800393\pi$
$194$	2586.83	0.957336
$195$	0	0
$196$	1987.69	0.724377
$197$	552.360	0.199767	0.0998833	−	0.994999i	$-0.468153\pi$
$197$	552.360	0.199767	0.0998833	+	0.994999i	$0.468153\pi$
$198$	−272.687	−0.0978739
$199$	1688.28	0.601402	0.300701	−	0.953718i	$-0.402779\pi$
$199$	1688.28	0.601402	0.300701	+	0.953718i	$0.402779\pi$
$200$	5163.50	1.82557
$201$	2807.12	0.985069
$202$	1951.87	0.679867
$203$	−5550.56	−1.91908
$204$	863.083	0.296215
$205$	5208.60	1.77456
$206$	−1123.46	−0.379978
$207$	−44.2630	−0.0148623
$208$	0	0
$209$	397.295	0.131490
$210$	−13006.4	−4.27393
$211$	−3401.98	−1.10996	−0.554981	−	0.831863i	$-0.687275\pi$
$211$	−3401.98	−1.10996	−0.554981	+	0.831863i	$0.687275\pi$
$212$	178.664	0.0578806
$213$	6821.55	2.19439
$214$	3221.01	1.02890
$215$	1861.08	0.590348
$216$	−1986.97	−0.625909
$217$	−2315.91	−0.724490
$218$	−316.264	−0.0982574
$219$	−1165.42	−0.359597
$220$	603.646	0.184990
$221$	0	0
$222$	7813.81	2.36229
$223$	2174.79	0.653071	0.326536	−	0.945185i	$-0.394119\pi$
$223$	2174.79	0.653071	0.326536	+	0.945185i	$0.394119\pi$
$224$	3835.80	1.14415
$225$	2251.24	0.667035
$226$	3017.28	0.888083
$227$	−6163.15	−1.80204	−0.901020	−	0.433778i	$-0.857180\pi$
$227$	−6163.15	−1.80204	−0.901020	+	0.433778i	$0.857180\pi$
$228$	567.656	0.164886
$229$	−3986.15	−1.15027	−0.575136	−	0.818058i	$-0.695051\pi$
$229$	−3986.15	−1.15027	−0.575136	+	0.818058i	$0.695051\pi$
$230$	391.309	0.112183
$231$	2132.70	0.607450
$232$	−2930.41	−0.829270
$233$	152.867	0.0429813	0.0214906	−	0.999769i	$-0.493159\pi$
$233$	152.867	0.0429813	0.0214906	+	0.999769i	$0.493159\pi$
$234$	0	0
$235$	−10674.9	−2.96322
$236$	1809.15	0.499007
$237$	6781.72	1.85873
$238$	−5914.13	−1.61074
$239$	−3071.44	−0.831275	−0.415637	−	0.909530i	$-0.636441\pi$
$239$	−3071.44	−0.831275	−0.415637	+	0.909530i	$0.636441\pi$
$240$	−9448.61	−2.54127
$241$	1492.17	0.398835	0.199418	−	0.979915i	$-0.436095\pi$
$241$	1492.17	0.398835	0.199418	+	0.979915i	$0.436095\pi$
$242$	−395.290	−0.105001
$243$	−2071.25	−0.546794
$244$	220.724	0.0579114
$245$	15273.4	3.98279
$246$	−4873.34	−1.26306
$247$	0	0
$248$	−1222.68	−0.313066
$249$	−1423.64	−0.362327
$250$	−11516.7	−2.91352
$251$	−5050.49	−1.27006	−0.635028	−	0.772489i	$-0.719011\pi$
$251$	−5050.49	−1.27006	−0.635028	+	0.772489i	$0.719011\pi$
$252$	668.519	0.167114
$253$	−64.1642	−0.0159445
$254$	3010.50	0.743682
$255$	6631.95	1.62866
$256$	3697.75	0.902772
$257$	818.005	0.198544	0.0992719	−	0.995060i	$-0.468349\pi$
$257$	818.005	0.198544	0.0992719	+	0.995060i	$0.468349\pi$
$258$	−1741.29	−0.420187
$259$	−13407.2	−3.21655
$260$	0	0
$261$	−1277.63	−0.303002
$262$	−2542.72	−0.599578
$263$	−6332.82	−1.48478	−0.742392	−	0.669966i	$-0.766309\pi$
$263$	−6332.82	−1.48478	−0.742392	+	0.669966i	$0.766309\pi$
$264$	1125.95	0.262491
$265$	1372.86	0.318241
$266$	−3889.76	−0.896604
$267$	7974.58	1.82785
$268$	1275.55	0.290734
$269$	3046.58	0.690534	0.345267	−	0.938505i	$-0.387788\pi$
$269$	3046.58	0.690534	0.345267	+	0.938505i	$0.387788\pi$
$270$	7658.60	1.72625
$271$	1227.31	0.275107	0.137553	−	0.990494i	$-0.456076\pi$
$271$	1227.31	0.275107	0.137553	+	0.990494i	$0.456076\pi$
$272$	−4296.38	−0.957743
$273$	0	0
$274$	−5223.39	−1.15167
$275$	3263.43	0.715608
$276$	−91.6781	−0.0199941
$277$	2622.73	0.568897	0.284448	−	0.958691i	$-0.408190\pi$
$277$	2622.73	0.568897	0.284448	+	0.958691i	$0.408190\pi$
$278$	7164.36	1.54565
$279$	−533.078	−0.114389
$280$	11782.1	2.51470
$281$	572.185	0.121472	0.0607361	−	0.998154i	$-0.480655\pi$
$281$	572.185	0.121472	0.0607361	+	0.998154i	$0.480655\pi$
$282$	9987.83	2.10910
$283$	−1086.32	−0.228180	−0.114090	−	0.993470i	$-0.536395\pi$
$283$	−1086.32	−0.228180	−0.114090	+	0.993470i	$0.536395\pi$
$284$	3099.70	0.647652
$285$	4361.88	0.906580
$286$	0	0
$287$	8361.88	1.71981
$288$	882.927	0.180649
$289$	−1897.39	−0.386197
$290$	11295.0	2.28712
$291$	−4656.94	−0.938125
$292$	−529.565	−0.106132
$293$	−5003.82	−0.997700	−0.498850	−	0.866688i	$-0.666244\pi$
$293$	−5003.82	−0.997700	−0.498850	+	0.866688i	$0.666244\pi$
$294$	−14290.4	−2.83480
$295$	13901.5	2.74366
$296$	−7078.32	−1.38993
$297$	−1255.80	−0.245351
$298$	6767.82	1.31560
$299$	0	0
$300$	4662.80	0.897356
$301$	2987.78	0.572136
$302$	4148.85	0.790528
$303$	−3513.86	−0.666224
$304$	−2825.76	−0.533120
$305$	1696.04	0.318410
$306$	−1361.32	−0.254318
$307$	1959.81	0.364339	0.182170	−	0.983267i	$-0.441688\pi$
$307$	1959.81	0.364339	0.182170	+	0.983267i	$0.441688\pi$
$308$	969.093	0.179283
$309$	2022.52	0.372353
$310$	4712.70	0.863431
$311$	702.616	0.128108	0.0640542	−	0.997946i	$-0.479597\pi$
$311$	702.616	0.128108	0.0640542	+	0.997946i	$0.479597\pi$
$312$	0	0
$313$	4866.33	0.878790	0.439395	−	0.898294i	$-0.355193\pi$
$313$	4866.33	0.878790	0.439395	+	0.898294i	$0.355193\pi$
$314$	5053.80	0.908287
$315$	5136.91	0.918832
$316$	3081.60	0.548588
$317$	−6305.80	−1.11725	−0.558626	−	0.829419i	$-0.688671\pi$
$317$	−6305.80	−1.11725	−0.558626	+	0.829419i	$0.688671\pi$
$318$	−1284.49	−0.226512
$319$	−1852.07	−0.325066
$320$	5047.13	0.881697
$321$	−5798.63	−1.00825
$322$	628.208	0.108723
$323$	1983.39	0.341668
$324$	−2341.82	−0.401547
$325$	0	0
$326$	487.313	0.0827907
$327$	569.355	0.0962856
$328$	4414.63	0.743163
$329$	−17137.5	−2.87180
$330$	−4339.87	−0.723946
$331$	4153.61	0.689738	0.344869	−	0.938651i	$-0.387923\pi$
$331$	4153.61	0.689738	0.344869	+	0.938651i	$0.387923\pi$
$332$	−646.898	−0.106937
$333$	−3086.09	−0.507858
$334$	1802.87	0.295355
$335$	9801.35	1.59852
$336$	−15168.8	−2.46287
$337$	6165.21	0.996560	0.498280	−	0.867016i	$-0.333965\pi$
$337$	6165.21	0.996560	0.498280	+	0.867016i	$0.333965\pi$
$338$	0	0
$339$	−5431.87	−0.870262
$340$	3013.54	0.480684
$341$	−772.756	−0.122719
$342$	−895.349	−0.141564
$343$	13212.5	2.07990
$344$	1577.39	0.247230
$345$	−704.456	−0.109932
$346$	−12896.6	−2.00382
$347$	11208.9	1.73408	0.867042	−	0.498235i	$-0.166018\pi$
$347$	11208.9	1.73408	0.867042	+	0.498235i	$0.166018\pi$
$348$	−2646.25	−0.407626
$349$	1110.09	0.170263	0.0851316	−	0.996370i	$-0.472869\pi$
$349$	1110.09	0.170263	0.0851316	+	0.996370i	$0.472869\pi$
$350$	−31951.0	−4.87958
$351$	0	0
$352$	1279.90	0.193804
$353$	−11769.1	−1.77452	−0.887260	−	0.461270i	$-0.847394\pi$
$353$	−11769.1	−1.77452	−0.887260	+	0.461270i	$0.847394\pi$
$354$	−13006.7	−1.95283
$355$	23818.1	3.56094
$356$	3623.63	0.539472
$357$	10646.9	1.57842
$358$	−1806.26	−0.266659
$359$	7835.09	1.15187	0.575934	−	0.817496i	$-0.304639\pi$
$359$	7835.09	1.15187	0.575934	+	0.817496i	$0.304639\pi$
$360$	2712.02	0.397045
$361$	−5554.51	−0.809813
$362$	−9717.77	−1.41092
$363$	711.622	0.102894
$364$	0	0
$365$	−4069.18	−0.583536
$366$	−1586.88	−0.226632
$367$	−12023.5	−1.71014	−0.855070	−	0.518512i	$-0.826486\pi$
$367$	−12023.5	−1.71014	−0.855070	+	0.518512i	$0.826486\pi$
$368$	456.368	0.0646463
$369$	1924.74	0.271540
$370$	27282.7	3.83341
$371$	2203.98	0.308423
$372$	−1104.12	−0.153887
$373$	−6320.70	−0.877408	−0.438704	−	0.898632i	$-0.644562\pi$
$373$	−6320.70	−0.877408	−0.438704	+	0.898632i	$0.644562\pi$
$374$	−1973.38	−0.272837
$375$	20733.0	2.85505
$376$	−9047.71	−1.24096
$377$	0	0
$378$	12295.1	1.67299
$379$	8394.47	1.13772	0.568859	−	0.822435i	$-0.307385\pi$
$379$	8394.47	1.13772	0.568859	+	0.822435i	$0.307385\pi$
$380$	1982.03	0.267568
$381$	−5419.65	−0.728759
$382$	−13597.9	−1.82128
$383$	−7892.26	−1.05294	−0.526470	−	0.850194i	$-0.676485\pi$
$383$	−7892.26	−1.05294	−0.526470	+	0.850194i	$0.676485\pi$
$384$	−10196.7	−1.35507
$385$	7446.53	0.985741
$386$	14185.5	1.87052
$387$	687.730	0.0903340
$388$	−2116.10	−0.276879
$389$	9121.63	1.18891	0.594454	−	0.804130i	$-0.297368\pi$
$389$	9121.63	1.18891	0.594454	+	0.804130i	$0.297368\pi$
$390$	0	0
$391$	−320.323	−0.0414308
$392$	12945.3	1.66794
$393$	4577.53	0.587547
$394$	−1804.48	−0.230733
$395$	23679.1	3.01626
$396$	223.067	0.0283069
$397$	−6803.36	−0.860077	−0.430039	−	0.902810i	$-0.641500\pi$
$397$	−6803.36	−0.860077	−0.430039	+	0.902810i	$0.641500\pi$
$398$	−5515.38	−0.694626
$399$	7002.55	0.878612
$400$	−23211.1	−2.90139
$401$	8164.30	1.01672	0.508361	−	0.861144i	$-0.330251\pi$
$401$	8164.30	1.01672	0.508361	+	0.861144i	$0.330251\pi$
$402$	−9170.48	−1.13777
$403$	0	0
$404$	−1596.69	−0.196630
$405$	−17994.6	−2.20780
$406$	18132.9	2.21656
$407$	−4473.63	−0.544840
$408$	5621.02	0.682063
$409$	−6570.46	−0.794348	−0.397174	−	0.917743i	$-0.630009\pi$
$409$	−6570.46	−0.794348	−0.397174	+	0.917743i	$0.630009\pi$
$410$	−17015.8	−2.04963
$411$	9403.42	1.12856
$412$	919.029	0.109896
$413$	22317.5	2.65901
$414$	144.601	0.0171661
$415$	−4970.78	−0.587966
$416$	0	0
$417$	−12897.6	−1.51463
$418$	−1297.91	−0.151873
$419$	−13231.3	−1.54270	−0.771351	−	0.636410i	$-0.780419\pi$
$419$	−13231.3	−1.54270	−0.771351	+	0.636410i	$0.780419\pi$
$420$	10639.6	1.23610
$421$	3851.62	0.445883	0.222941	−	0.974832i	$-0.428434\pi$
$421$	3851.62	0.445883	0.222941	+	0.974832i	$0.428434\pi$
$422$	11113.8	1.28202
$423$	−3944.73	−0.453426
$424$	1163.59	0.133275
$425$	16291.8	1.85946
$426$	−22285.1	−2.53454
$427$	2722.83	0.308587
$428$	−2634.88	−0.297575
$429$	0	0
$430$	−6079.90	−0.681858
$431$	669.327	0.0748036	0.0374018	−	0.999300i	$-0.488092\pi$
$431$	669.327	0.0748036	0.0374018	+	0.999300i	$0.488092\pi$
$432$	8931.90	0.994760
$433$	−91.8885	−0.0101983	−0.00509917	−	0.999987i	$-0.501623\pi$
$433$	−91.8885	−0.0101983	−0.00509917	+	0.999987i	$0.501623\pi$
$434$	7565.76	0.836793
$435$	−20333.8	−2.24122
$436$	258.714	0.0284178
$437$	−210.679	−0.0230621
$438$	3807.27	0.415338
$439$	−798.805	−0.0868449	−0.0434224	−	0.999057i	$-0.513826\pi$
$439$	−798.805	−0.0868449	−0.0434224	+	0.999057i	$0.513826\pi$
$440$	3931.38	0.425957
$441$	5644.02	0.609440
$442$	0	0
$443$	5562.20	0.596542	0.298271	−	0.954481i	$-0.403590\pi$
$443$	5562.20	0.596542	0.298271	+	0.954481i	$0.403590\pi$
$444$	−6391.94	−0.683216
$445$	27844.1	2.96615
$446$	−7104.75	−0.754304
$447$	−12183.8	−1.28920
$448$	8102.65	0.854496
$449$	5935.09	0.623817	0.311909	−	0.950112i	$-0.399032\pi$
$449$	5935.09	0.623817	0.311909	+	0.950112i	$0.399032\pi$
$450$	−7354.50	−0.770432
$451$	2790.13	0.291313
$452$	−2468.23	−0.256849
$453$	−7468.97	−0.774664
$454$	20134.2	2.08137
$455$	0	0
$456$	3696.98	0.379665
$457$	−10466.8	−1.07137	−0.535685	−	0.844418i	$-0.679946\pi$
$457$	−10466.8	−1.07137	−0.535685	+	0.844418i	$0.679946\pi$
$458$	13022.2	1.32858
$459$	−6269.27	−0.637526
$460$	−320.103	−0.0324454
$461$	2538.56	0.256470	0.128235	−	0.991744i	$-0.459069\pi$
$461$	2538.56	0.256470	0.128235	+	0.991744i	$0.459069\pi$
$462$	−6967.22	−0.701612
$463$	1880.51	0.188757	0.0943787	−	0.995536i	$-0.469914\pi$
$463$	1880.51	0.188757	0.0943787	+	0.995536i	$0.469914\pi$
$464$	13172.9	1.31796
$465$	−8484.05	−0.846104
$466$	−499.395	−0.0496438
$467$	2848.09	0.282214	0.141107	−	0.989994i	$-0.454934\pi$
$467$	2848.09	0.282214	0.141107	+	0.989994i	$0.454934\pi$
$468$	0	0
$469$	15735.1	1.54921
$470$	34873.5	3.42254
$471$	−9098.11	−0.890061
$472$	11782.5	1.14901
$473$	996.941	0.0969120
$474$	−22155.0	−2.14686
$475$	10715.2	1.03505
$476$	4837.94	0.465854
$477$	507.314	0.0486967
$478$	10034.0	0.960131
$479$	14298.6	1.36393	0.681963	−	0.731387i	$-0.261127\pi$
$479$	14298.6	1.36393	0.681963	+	0.731387i	$0.261127\pi$
$480$	14052.0	1.33621
$481$	0	0
$482$	−4874.72	−0.460659
$483$	−1130.93	−0.106541
$484$	323.360	0.0303681
$485$	−16260.2	−1.52234
$486$	6766.50	0.631553
$487$	−6063.24	−0.564172	−0.282086	−	0.959389i	$-0.591026\pi$
$487$	−6063.24	−0.564172	−0.282086	+	0.959389i	$0.591026\pi$
$488$	1437.51	0.133346
$489$	−877.286	−0.0811293
$490$	−49896.2	−4.60017
$491$	21128.9	1.94202	0.971012	−	0.239029i	$-0.0768292\pi$
$491$	21128.9	1.94202	0.971012	+	0.239029i	$0.0768292\pi$
$492$	3986.55	0.365300
$493$	−9245.98	−0.844661
$494$	0	0
$495$	1714.05	0.155638
$496$	5496.23	0.497556
$497$	38237.6	3.45109
$498$	4650.83	0.418491
$499$	−6814.05	−0.611300	−0.305650	−	0.952144i	$-0.598874\pi$
$499$	−6814.05	−0.611300	−0.305650	+	0.952144i	$0.598874\pi$
$500$	9421.02	0.842641
$501$	−3245.62	−0.289428
$502$	16499.3	1.46693
$503$	−2506.36	−0.222173	−0.111087	−	0.993811i	$-0.535433\pi$
$503$	−2506.36	−0.222173	−0.111087	+	0.993811i	$0.535433\pi$
$504$	4353.87	0.384796
$505$	−12269.0	−1.08112
$506$	209.616	0.0184161
$507$	0	0
$508$	−2462.68	−0.215086
$509$	2632.02	0.229199	0.114600	−	0.993412i	$-0.463442\pi$
$509$	2632.02	0.229199	0.114600	+	0.993412i	$0.463442\pi$
$510$	−21665.7	−1.88112
$511$	−6532.66	−0.565534
$512$	1790.21	0.154525
$513$	−4123.34	−0.354873
$514$	−2672.31	−0.229320
$515$	7061.83	0.604236
$516$	1424.43	0.121525
$517$	−5718.32	−0.486444
$518$	43799.6	3.71515
$519$	23217.0	1.96361
$520$	0	0
$521$	−17757.8	−1.49325	−0.746623	−	0.665247i	$-0.768326\pi$
$521$	−17757.8	−1.49325	−0.746623	+	0.665247i	$0.768326\pi$
$522$	4173.85	0.349971
$523$	11779.9	0.984892	0.492446	−	0.870343i	$-0.336103\pi$
$523$	11779.9	0.984892	0.492446	+	0.870343i	$0.336103\pi$
$524$	2080.02	0.173409
$525$	57519.8	4.78166
$526$	20688.5	1.71494
$527$	−3857.78	−0.318876
$528$	−5061.41	−0.417177
$529$	−12133.0	−0.997203
$530$	−4484.94	−0.367572
$531$	5137.06	0.419829
$532$	3181.95	0.259314
$533$	0	0
$534$	−26051.9	−2.11119
$535$	−20246.5	−1.63614
$536$	8307.29	0.669441
$537$	3251.73	0.261308
$538$	−9952.78	−0.797574
$539$	8181.64	0.653819
$540$	−6264.97	−0.499262
$541$	−5324.57	−0.423144	−0.211572	−	0.977362i	$-0.567858\pi$
$541$	−5324.57	−0.423144	−0.211572	+	0.977362i	$0.567858\pi$
$542$	−4009.46	−0.317751
$543$	17494.4	1.38261
$544$	6389.57	0.503586
$545$	1987.96	0.156248
$546$	0	0
$547$	916.469	0.0716369	0.0358184	−	0.999358i	$-0.488596\pi$
$547$	916.469	0.0716369	0.0358184	+	0.999358i	$0.488596\pi$
$548$	4272.90	0.333082
$549$	626.742	0.0487226
$550$	−10661.2	−0.826535
$551$	−6081.15	−0.470174
$552$	−597.073	−0.0460383
$553$	38014.4	2.92321
$554$	−8568.09	−0.657082
$555$	−49115.8	−3.75648
$556$	−5860.67	−0.447028
$557$	−18202.5	−1.38468	−0.692339	−	0.721572i	$-0.743420\pi$
$557$	−18202.5	−1.38468	−0.692339	+	0.721572i	$0.743420\pi$
$558$	1741.49	0.132121
$559$	0	0
$560$	−52963.4	−3.99663
$561$	3552.59	0.267362
$562$	−1869.25	−0.140302
$563$	−22316.5	−1.67056	−0.835281	−	0.549823i	$-0.814695\pi$
$563$	−22316.5	−1.67056	−0.835281	+	0.549823i	$0.814695\pi$
$564$	−8170.35	−0.609989
$565$	−18965.9	−1.41222
$566$	3548.85	0.263550
$567$	−28888.5	−2.13969
$568$	20187.5	1.49128
$569$	−4793.05	−0.353137	−0.176569	−	0.984288i	$-0.556500\pi$
$569$	−4793.05	−0.353137	−0.176569	+	0.984288i	$0.556500\pi$
$570$	−14249.7	−1.04711
$571$	19503.1	1.42939	0.714695	−	0.699437i	$-0.246566\pi$
$571$	19503.1	1.42939	0.714695	+	0.699437i	$0.246566\pi$
$572$	0	0
$573$	24479.7	1.78474
$574$	−27317.1	−1.98640
$575$	−1730.54	−0.125510
$576$	1865.07	0.134916
$577$	−5008.45	−0.361359	−0.180680	−	0.983542i	$-0.557830\pi$
$577$	−5008.45	−0.361359	−0.180680	+	0.983542i	$0.557830\pi$
$578$	6198.51	0.446062
$579$	−25537.4	−1.83298
$580$	−9239.64	−0.661475
$581$	−7980.08	−0.569827
$582$	15213.6	1.08354
$583$	735.409	0.0522428
$584$	−3448.90	−0.244378
$585$	0	0
$586$	16346.8	1.15235
$587$	1731.74	0.121766	0.0608830	−	0.998145i	$-0.480608\pi$
$587$	1731.74	0.121766	0.0608830	+	0.998145i	$0.480608\pi$
$588$	11690.0	0.819873
$589$	−2537.29	−0.177500
$590$	−45414.4	−3.16895
$591$	3248.53	0.226102
$592$	31818.7	2.20902
$593$	−14137.7	−0.979029	−0.489515	−	0.871995i	$-0.662826\pi$
$593$	−14137.7	−0.979029	−0.489515	+	0.871995i	$0.662826\pi$
$594$	4102.54	0.283383
$595$	37174.8	2.56138
$596$	−5536.29	−0.380495
$597$	9929.08	0.680687
$598$	0	0
$599$	3575.41	0.243885	0.121943	−	0.992537i	$-0.461088\pi$
$599$	3575.41	0.243885	0.121943	+	0.992537i	$0.461088\pi$
$600$	30367.5	2.06624
$601$	8337.04	0.565849	0.282924	−	0.959142i	$-0.408695\pi$
$601$	8337.04	0.565849	0.282924	+	0.959142i	$0.408695\pi$
$602$	−9760.67	−0.660823
$603$	3621.91	0.244603
$604$	−3393.89	−0.228635
$605$	2484.70	0.166971
$606$	11479.3	0.769496
$607$	23747.6	1.58795	0.793975	−	0.607950i	$-0.208008\pi$
$607$	23747.6	1.58795	0.793975	+	0.607950i	$0.208008\pi$
$608$	4202.47	0.280317
$609$	−32643.9	−2.17208
$610$	−5540.74	−0.367767
$611$	0	0
$612$	1113.60	0.0735533
$613$	−10159.9	−0.669422	−0.334711	−	0.942321i	$-0.608639\pi$
$613$	−10159.9	−0.669422	−0.334711	+	0.942321i	$0.608639\pi$
$614$	−6402.43	−0.420816
$615$	30632.7	2.00850
$616$	6311.43	0.412816
$617$	−15680.0	−1.02310	−0.511550	−	0.859253i	$-0.670929\pi$
$617$	−15680.0	−1.02310	−0.511550	+	0.859253i	$0.670929\pi$
$618$	−6607.29	−0.430072
$619$	−862.708	−0.0560180	−0.0280090	−	0.999608i	$-0.508917\pi$
$619$	−862.708	−0.0560180	−0.0280090	+	0.999608i	$0.508917\pi$
$620$	−3855.14	−0.249719
$621$	665.931	0.0430321
$622$	−2295.35	−0.147966
$623$	44700.8	2.87464
$624$	0	0
$625$	35306.8	2.25964
$626$	−15897.6	−1.01501
$627$	2336.56	0.148825
$628$	−4134.16	−0.262693
$629$	−22333.4	−1.41573
$630$	−16781.6	−1.06126
$631$	−26759.5	−1.68824	−0.844121	−	0.536153i	$-0.819877\pi$
$631$	−26759.5	−1.68824	−0.844121	+	0.536153i	$0.819877\pi$
$632$	20069.6	1.26317
$633$	−20007.7	−1.25629
$634$	20600.2	1.29044
$635$	−18923.3	−1.18259
$636$	1050.75	0.0655112
$637$	0	0
$638$	6050.47	0.375455
$639$	8801.56	0.544889
$640$	−35602.8	−2.19894
$641$	−9043.01	−0.557219	−0.278610	−	0.960404i	$-0.589874\pi$
$641$	−9043.01	−0.557219	−0.278610	+	0.960404i	$0.589874\pi$
$642$	18943.3	1.16454
$643$	6566.54	0.402736	0.201368	−	0.979516i	$-0.435461\pi$
$643$	6566.54	0.402736	0.201368	+	0.979516i	$0.435461\pi$
$644$	−513.893	−0.0314445
$645$	10945.4	0.668175
$646$	−6479.46	−0.394630
$647$	−3837.35	−0.233171	−0.116586	−	0.993181i	$-0.537195\pi$
$647$	−3837.35	−0.233171	−0.116586	+	0.993181i	$0.537195\pi$
$648$	−15251.6	−0.924600
$649$	7446.74	0.450401
$650$	0	0
$651$	−13620.3	−0.820001
$652$	−398.637	−0.0239445
$653$	11021.0	0.660470	0.330235	−	0.943899i	$-0.392872\pi$
$653$	11021.0	0.660470	0.330235	+	0.943899i	$0.392872\pi$
$654$	−1860.00	−0.111211
$655$	15982.9	0.953442
$656$	−19844.8	−1.18111
$657$	−1503.69	−0.0892917
$658$	55985.9	3.31696
$659$	682.385	0.0403368	0.0201684	−	0.999797i	$-0.493580\pi$
$659$	682.385	0.0403368	0.0201684	+	0.999797i	$0.493580\pi$
$660$	3550.15	0.209378
$661$	11983.0	0.705118	0.352559	−	0.935790i	$-0.385312\pi$
$661$	11983.0	0.705118	0.352559	+	0.935790i	$0.385312\pi$
$662$	−13569.3	−0.796654
$663$	0	0
$664$	−4213.06	−0.246233
$665$	24450.1	1.42577
$666$	10081.8	0.586581
$667$	982.122	0.0570134
$668$	−1474.80	−0.0854219
$669$	12790.3	0.739168
$670$	−32019.7	−1.84631
$671$	908.533	0.0522705
$672$	22559.0	1.29499
$673$	−23842.2	−1.36560	−0.682800	−	0.730605i	$-0.739238\pi$
$673$	−23842.2	−1.36560	−0.682800	+	0.730605i	$0.739238\pi$
$674$	−20140.9	−1.15104
$675$	−33869.6	−1.93132
$676$	0	0
$677$	−18091.8	−1.02706	−0.513532	−	0.858070i	$-0.671663\pi$
$677$	−18091.8	−1.02706	−0.513532	+	0.858070i	$0.671663\pi$
$678$	17745.2	1.00516
$679$	−26104.1	−1.47538
$680$	19626.4	1.10682
$681$	−36246.6	−2.03961
$682$	2524.49	0.141741
$683$	−14409.5	−0.807271	−0.403635	−	0.914920i	$-0.632254\pi$
$683$	−14409.5	−0.807271	−0.403635	+	0.914920i	$0.632254\pi$
$684$	732.423	0.0409428
$685$	32833.0	1.83137
$686$	−43163.3	−2.40231
$687$	−23443.3	−1.30192
$688$	−7090.74	−0.392924
$689$	0	0
$690$	2301.36	0.126973
$691$	12587.8	0.693000	0.346500	−	0.938050i	$-0.387370\pi$
$691$	12587.8	0.693000	0.346500	+	0.938050i	$0.387370\pi$
$692$	10549.8	0.579541
$693$	2751.73	0.150836
$694$	−36618.1	−2.00289
$695$	−45033.5	−2.45786
$696$	−17234.2	−0.938596
$697$	13929.0	0.756956
$698$	−3626.52	−0.196656
$699$	899.037	0.0486476
$700$	26136.9	1.41126
$701$	−21413.6	−1.15375	−0.576876	−	0.816832i	$-0.695728\pi$
$701$	−21413.6	−1.15375	−0.576876	+	0.816832i	$0.695728\pi$
$702$	0	0
$703$	−14688.9	−0.788052
$704$	2703.63	0.144740
$705$	−62781.1	−3.35386
$706$	38448.0	2.04959
$707$	−19696.6	−1.04776
$708$	10639.9	0.564792
$709$	3810.81	0.201859	0.100929	−	0.994894i	$-0.467818\pi$
$709$	3810.81	0.201859	0.100929	+	0.994894i	$0.467818\pi$
$710$	−77810.6	−4.11293
$711$	8750.18	0.461543
$712$	23599.7	1.24219
$713$	409.780	0.0215237
$714$	−34782.0	−1.82309
$715$	0	0
$716$	1477.58	0.0771226
$717$	−18063.7	−0.940864
$718$	−25596.2	−1.33042
$719$	−12185.7	−0.632059	−0.316029	−	0.948749i	$-0.602350\pi$
$719$	−12185.7	−0.632059	−0.316029	+	0.948749i	$0.602350\pi$
$720$	−12191.2	−0.631024
$721$	11337.1	0.585595
$722$	18145.8	0.935343
$723$	8775.73	0.451415
$724$	7949.44	0.408064
$725$	−49951.3	−2.55882
$726$	−2324.77	−0.118844
$727$	13433.5	0.685312	0.342656	−	0.939461i	$-0.388673\pi$
$727$	13433.5	0.685312	0.342656	+	0.939461i	$0.388673\pi$
$728$	0	0
$729$	11478.7	0.583179
$730$	13293.5	0.673991
$731$	4976.96	0.251819
$732$	1298.11	0.0655460
$733$	14927.8	0.752211	0.376105	−	0.926577i	$-0.377263\pi$
$733$	14927.8	0.752211	0.376105	+	0.926577i	$0.377263\pi$
$734$	39279.1	1.97523
$735$	89825.8	4.50786
$736$	−678.710	−0.0339913
$737$	5250.36	0.262415
$738$	−6287.87	−0.313631
$739$	14090.8	0.701403	0.350702	−	0.936487i	$-0.385943\pi$
$739$	14090.8	0.701403	0.350702	+	0.936487i	$0.385943\pi$
$740$	−22318.1	−1.10869
$741$	0	0
$742$	−7200.11	−0.356232
$743$	−10465.8	−0.516760	−0.258380	−	0.966043i	$-0.583189\pi$
$743$	−10465.8	−0.516760	−0.258380	+	0.966043i	$0.583189\pi$
$744$	−7190.80	−0.354338
$745$	−42540.9	−2.09205
$746$	20648.9	1.01342
$747$	−1836.86	−0.0899695
$748$	1614.29	0.0789094
$749$	−32503.7	−1.58566
$750$	−67731.7	−3.29762
$751$	14026.0	0.681512	0.340756	−	0.940152i	$-0.389317\pi$
$751$	14026.0	0.681512	0.340756	+	0.940152i	$0.389317\pi$
$752$	40671.5	1.97226
$753$	−29702.8	−1.43749
$754$	0	0
$755$	−26078.7	−1.25709
$756$	−10057.8	−0.483859
$757$	32829.4	1.57623	0.788113	−	0.615530i	$-0.211058\pi$
$757$	32829.4	1.57623	0.788113	+	0.615530i	$0.211058\pi$
$758$	−27423.6	−1.31408
$759$	−377.361	−0.0180466
$760$	12908.4	0.616101
$761$	−16381.3	−0.780320	−0.390160	−	0.920747i	$-0.627580\pi$
$761$	−16381.3	−0.780320	−0.390160	+	0.920747i	$0.627580\pi$
$762$	17705.3	0.841724
$763$	3191.47	0.151427
$764$	11123.5	0.526747
$765$	8556.93	0.404414
$766$	25782.9	1.21616
$767$	0	0
$768$	21747.1	1.02179
$769$	38231.4	1.79279	0.896397	−	0.443252i	$-0.146175\pi$
$769$	38231.4	1.79279	0.896397	+	0.443252i	$0.146175\pi$
$770$	−24326.8	−1.13854
$771$	4810.83	0.224719
$772$	−11604.1	−0.540987
$773$	−7685.33	−0.357596	−0.178798	−	0.983886i	$-0.557221\pi$
$773$	−7685.33	−0.357596	−0.178798	+	0.983886i	$0.557221\pi$
$774$	−2246.72	−0.104337
$775$	−20841.6	−0.966004
$776$	−13781.6	−0.637539
$777$	−78850.4	−3.64059
$778$	−29799.1	−1.37320
$779$	9161.20	0.421353
$780$	0	0
$781$	12758.8	0.584568
$782$	1046.45	0.0478530
$783$	19221.8	0.877307
$784$	−58191.9	−2.65087
$785$	−31767.0	−1.44435
$786$	−14954.2	−0.678623
$787$	−3108.09	−0.140777	−0.0703885	−	0.997520i	$-0.522424\pi$
$787$	−3108.09	−0.140777	−0.0703885	+	0.997520i	$0.522424\pi$
$788$	1476.12	0.0667319
$789$	−37244.4	−1.68053
$790$	−77356.3	−3.48382
$791$	−30447.9	−1.36865
$792$	1452.77	0.0651792
$793$	0	0
$794$	22225.6	0.993398
$795$	8074.01	0.360196
$796$	4511.75	0.200898
$797$	−17563.7	−0.780600	−0.390300	−	0.920688i	$-0.627629\pi$
$797$	−17563.7	−0.780600	−0.390300	+	0.920688i	$0.627629\pi$
$798$	−22876.4	−1.01481
$799$	−28547.2	−1.26399
$800$	34519.6	1.52556
$801$	10289.3	0.453874
$802$	−26671.7	−1.17433
$803$	−2179.77	−0.0957938
$804$	7501.73	0.329062
$805$	−3948.77	−0.172889
$806$	0	0
$807$	17917.5	0.781569
$808$	−10398.8	−0.452758
$809$	−36449.3	−1.58404	−0.792020	−	0.610495i	$-0.790970\pi$
$809$	−36449.3	−1.58404	−0.792020	+	0.610495i	$0.790970\pi$
$810$	58785.9	2.55003
$811$	−44928.6	−1.94532	−0.972661	−	0.232231i	$-0.925397\pi$
$811$	−44928.6	−1.94532	−0.972661	+	0.232231i	$0.925397\pi$
$812$	−14833.3	−0.641068
$813$	7218.04	0.311375
$814$	14614.7	0.629295
$815$	−3063.13	−0.131653
$816$	−25267.8	−1.08401
$817$	3273.38	0.140173
$818$	21464.8	0.917481
$819$	0	0
$820$	13919.4	0.592790
$821$	−8389.16	−0.356618	−0.178309	−	0.983974i	$-0.557063\pi$
$821$	−8389.16	−0.356618	−0.178309	+	0.983974i	$0.557063\pi$
$822$	−30719.7	−1.30349
$823$	−8689.62	−0.368045	−0.184023	−	0.982922i	$-0.558912\pi$
$823$	−8689.62	−0.368045	−0.184023	+	0.982922i	$0.558912\pi$
$824$	5985.38	0.253047
$825$	19192.8	0.809948
$826$	−72908.2	−3.07119
$827$	−34654.3	−1.45713	−0.728567	−	0.684975i	$-0.759813\pi$
$827$	−34654.3	−1.45713	−0.728567	+	0.684975i	$0.759813\pi$
$828$	−118.288	−0.00496474
$829$	27800.8	1.16473	0.582366	−	0.812927i	$-0.302127\pi$
$829$	27800.8	1.16473	0.582366	+	0.812927i	$0.302127\pi$
$830$	16238.8	0.679107
$831$	15424.7	0.643896
$832$	0	0
$833$	40844.7	1.69890
$834$	42134.8	1.74941
$835$	−11332.4	−0.469670
$836$	1061.73	0.0439243
$837$	8020.09	0.331200
$838$	43224.9	1.78184
$839$	44602.0	1.83532	0.917659	−	0.397370i	$-0.130077\pi$
$839$	44602.0	1.83532	0.917659	+	0.397370i	$0.130077\pi$
$840$	69292.8	2.84622
$841$	3959.53	0.162349
$842$	−12582.7	−0.514999
$843$	3365.12	0.137486
$844$	−9091.44	−0.370783
$845$	0	0
$846$	12886.9	0.523712
$847$	3988.94	0.161820
$848$	−5230.59	−0.211815
$849$	−6388.82	−0.258261
$850$	−53223.1	−2.14769
$851$	2372.29	0.0955594
$852$	18229.9	0.733034
$853$	43423.2	1.74300	0.871501	−	0.490394i	$-0.163147\pi$
$853$	43423.2	1.74300	0.871501	+	0.490394i	$0.163147\pi$
$854$	−8895.10	−0.356422
$855$	5627.95	0.225113
$856$	−17160.3	−0.685193
$857$	−2236.80	−0.0891570	−0.0445785	−	0.999006i	$-0.514194\pi$
$857$	−2236.80	−0.0891570	−0.0445785	+	0.999006i	$0.514194\pi$
$858$	0	0
$859$	30040.9	1.19323	0.596613	−	0.802529i	$-0.296513\pi$
$859$	30040.9	1.19323	0.596613	+	0.802529i	$0.296513\pi$
$860$	4973.55	0.197205
$861$	49177.7	1.94654
$862$	−2186.60	−0.0863990
$863$	30278.1	1.19430	0.597149	−	0.802130i	$-0.296300\pi$
$863$	30278.1	1.19430	0.597149	+	0.802130i	$0.296300\pi$
$864$	−13283.5	−0.523049
$865$	81064.7	3.18645
$866$	300.187	0.0117792
$867$	−11158.9	−0.437111
$868$	−6189.03	−0.242015
$869$	12684.4	0.495152
$870$	66427.7	2.58863
$871$	0	0
$872$	1684.93	0.0654345
$873$	−6008.65	−0.232946
$874$	688.259	0.0266369
$875$	116217.	4.49011
$876$	−3114.46	−0.120123
$877$	−29546.2	−1.13763	−0.568816	−	0.822464i	$-0.692599\pi$
$877$	−29546.2	−1.13763	−0.568816	+	0.822464i	$0.692599\pi$
$878$	2609.59	0.100307
$879$	−29428.3	−1.12923
$880$	−17672.4	−0.676975
$881$	−17222.8	−0.658627	−0.329313	−	0.944221i	$-0.606817\pi$
$881$	−17222.8	−0.658627	−0.329313	+	0.944221i	$0.606817\pi$
$882$	−18438.3	−0.703910
$883$	−16324.2	−0.622143	−0.311071	−	0.950387i	$-0.600688\pi$
$883$	−16324.2	−0.622143	−0.311071	+	0.950387i	$0.600688\pi$
$884$	0	0
$885$	81757.4	3.10536
$886$	−18171.0	−0.689013
$887$	−17826.0	−0.674789	−0.337395	−	0.941363i	$-0.609546\pi$
$887$	−17826.0	−0.674789	−0.337395	+	0.941363i	$0.609546\pi$
$888$	−41628.9	−1.57317
$889$	−30379.4	−1.14611
$890$	−90962.7	−3.42593
$891$	−9639.31	−0.362434
$892$	5811.91	0.218158
$893$	−18775.7	−0.703589
$894$	39802.8	1.48904
$895$	11353.8	0.424038
$896$	−57156.6	−2.13110
$897$	0	0
$898$	−19389.1	−0.720516
$899$	11828.1	0.438809
$900$	6016.21	0.222823
$901$	3671.33	0.135749
$902$	−9114.97	−0.336469
$903$	17571.7	0.647562
$904$	−16074.9	−0.591419
$905$	61083.6	2.24363
$906$	24400.1	0.894745
$907$	47400.3	1.73528	0.867642	−	0.497189i	$-0.165635\pi$
$907$	47400.3	1.73528	0.867642	+	0.497189i	$0.165635\pi$
$908$	−16470.4	−0.601970
$909$	−4533.79	−0.165430
$910$	0	0
$911$	−21468.7	−0.780778	−0.390389	−	0.920650i	$-0.627660\pi$
$911$	−21468.7	−0.780778	−0.390389	+	0.920650i	$0.627660\pi$
$912$	−16618.8	−0.603402
$913$	−2662.73	−0.0965210
$914$	34193.6	1.23744
$915$	9974.73	0.360387
$916$	−10652.6	−0.384248
$917$	25659.0	0.924028
$918$	20480.8	0.736349
$919$	−20695.2	−0.742842	−0.371421	−	0.928465i	$-0.621129\pi$
$919$	−20695.2	−0.742842	−0.371421	+	0.928465i	$0.621129\pi$
$920$	−2084.74	−0.0747086
$921$	11526.0	0.412371
$922$	−8293.13	−0.296225
$923$	0	0
$924$	5699.41	0.202919
$925$	−120656.	−4.28881
$926$	−6143.37	−0.218017
$927$	2609.57	0.0924591
$928$	−19590.7	−0.692990
$929$	28703.0	1.01369	0.506843	−	0.862039i	$-0.330812\pi$
$929$	28703.0	1.01369	0.506843	+	0.862039i	$0.330812\pi$
$930$	27716.2	0.977259
$931$	26863.8	0.945679
$932$	408.521	0.0143579
$933$	4132.21	0.144997
$934$	−9304.31	−0.325960
$935$	12404.2	0.433862
$936$	0	0
$937$	14823.9	0.516838	0.258419	−	0.966033i	$-0.416799\pi$
$937$	14823.9	0.516838	0.258419	+	0.966033i	$0.416799\pi$
$938$	−51404.3	−1.78935
$939$	28619.8	0.994644
$940$	−28527.6	−0.989861
$941$	27759.2	0.961662	0.480831	−	0.876813i	$-0.340335\pi$
$941$	27759.2	0.961662	0.480831	+	0.876813i	$0.340335\pi$
$942$	29722.3	1.02803
$943$	−1479.56	−0.0510934
$944$	−52964.9	−1.82612
$945$	−77284.1	−2.66037
$946$	−3256.87	−0.111934
$947$	−16784.8	−0.575958	−0.287979	−	0.957637i	$-0.592983\pi$
$947$	−16784.8	−0.575958	−0.287979	+	0.957637i	$0.592983\pi$
$948$	18123.4	0.620910
$949$	0	0
$950$	−35005.2	−1.19549
$951$	−37085.5	−1.26454
$952$	31508.1	1.07267
$953$	−54932.1	−1.86718	−0.933591	−	0.358339i	$-0.883343\pi$
$953$	−54932.1	−1.86718	−0.933591	+	0.358339i	$0.883343\pi$
$954$	−1657.33	−0.0562452
$955$	85473.3	2.89618
$956$	−8208.09	−0.277687
$957$	−10892.4	−0.367921
$958$	−46711.6	−1.57535
$959$	52710.1	1.77487
$960$	29683.0	0.997934
$961$	−24855.9	−0.834341
$962$	0	0
$963$	−7481.73	−0.250359
$964$	3987.68	0.133231
$965$	−89166.4	−2.97447
$966$	3694.60	0.123056
$967$	−12581.4	−0.418398	−0.209199	−	0.977873i	$-0.567086\pi$
$967$	−12581.4	−0.418398	−0.209199	+	0.977873i	$0.567086\pi$
$968$	2105.95	0.0699254
$969$	11664.7	0.386711
$970$	53119.8	1.75832
$971$	−8364.28	−0.276439	−0.138220	−	0.990402i	$-0.544138\pi$
$971$	−8364.28	−0.276439	−0.138220	+	0.990402i	$0.544138\pi$
$972$	−5535.21	−0.182656
$973$	−72296.6	−2.38204
$974$	19807.8	0.651625
$975$	0	0
$976$	−6461.94	−0.211928
$977$	−19836.3	−0.649561	−0.324780	−	0.945789i	$-0.605290\pi$
$977$	−19836.3	−0.649561	−0.324780	+	0.945789i	$0.605290\pi$
$978$	2865.97	0.0937052
$979$	14915.4	0.486925
$980$	40816.7	1.33045
$981$	734.615	0.0239087
$982$	−69025.2	−2.24306
$983$	−4510.70	−0.146357	−0.0731785	−	0.997319i	$-0.523314\pi$
$983$	−4510.70	−0.146357	−0.0731785	+	0.997319i	$0.523314\pi$
$984$	25963.2	0.841136
$985$	11342.6	0.366908
$986$	30205.4	0.975593
$987$	−100789.	−3.25040
$988$	0	0
$989$	−528.661	−0.0169974
$990$	−5599.56	−0.179763
$991$	5974.97	0.191525	0.0957624	−	0.995404i	$-0.469471\pi$
$991$	5974.97	0.191525	0.0957624	+	0.995404i	$0.469471\pi$
$992$	−8173.98	−0.261617
$993$	24428.1	0.780668
$994$	−124917.	−3.98604
$995$	34668.4	1.10458
$996$	−3804.52	−0.121035
$997$	26463.6	0.840633	0.420317	−	0.907378i	$-0.361919\pi$
$997$	26463.6	0.840633	0.420317	+	0.907378i	$0.361919\pi$
$998$	22260.6	0.706058
$999$	46429.8	1.47044

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.4.a.q.1.14	yes	51
13.12	even	2		1859.4.a.p.1.38	✓	51

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.4.a.p.1.38	✓	51	13.12	even	2
1859.4.a.q.1.14	yes	51	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-3.26686 q^{2} +5.88118 q^{3} +2.67240 q^{4} +20.5347 q^{5} -19.2130 q^{6} +32.9664 q^{7} +17.4046 q^{8} +7.58824 q^{9} +O(q^{10})\)	\(q-3.26686 q^{2} +5.88118 q^{3} +2.67240 q^{4} +20.5347 q^{5} -19.2130 q^{6} +32.9664 q^{7} +17.4046 q^{8} +7.58824 q^{9} -67.0842 q^{10} +11.0000 q^{11} +15.7168 q^{12} -107.697 q^{14} +120.768 q^{15} -78.2375 q^{16} +54.9146 q^{17} -24.7897 q^{18} +36.1177 q^{19} +54.8769 q^{20} +193.881 q^{21} -35.9355 q^{22} -5.83311 q^{23} +102.359 q^{24} +296.675 q^{25} -114.164 q^{27} +88.0994 q^{28} -168.370 q^{29} -394.534 q^{30} -70.2506 q^{31} +116.355 q^{32} +64.6929 q^{33} -179.398 q^{34} +676.957 q^{35} +20.2788 q^{36} -406.694 q^{37} -117.992 q^{38} +357.398 q^{40} +253.648 q^{41} -633.384 q^{42} +90.6310 q^{43} +29.3964 q^{44} +155.822 q^{45} +19.0560 q^{46} -519.847 q^{47} -460.128 q^{48} +743.786 q^{49} -969.198 q^{50} +322.962 q^{51} +66.8554 q^{53} +372.958 q^{54} +225.882 q^{55} +573.766 q^{56} +212.415 q^{57} +550.042 q^{58} +676.976 q^{59} +322.741 q^{60} +82.5939 q^{61} +229.499 q^{62} +250.157 q^{63} +245.785 q^{64} -211.343 q^{66} +477.306 q^{67} +146.754 q^{68} -34.3056 q^{69} -2211.53 q^{70} +1159.89 q^{71} +132.070 q^{72} -198.161 q^{73} +1328.61 q^{74} +1744.80 q^{75} +96.5209 q^{76} +362.631 q^{77} +1153.12 q^{79} -1606.59 q^{80} -876.301 q^{81} -828.634 q^{82} -242.067 q^{83} +518.128 q^{84} +1127.66 q^{85} -296.079 q^{86} -990.215 q^{87} +191.450 q^{88} +1355.95 q^{89} -509.051 q^{90} -15.5884 q^{92} -413.156 q^{93} +1698.27 q^{94} +741.668 q^{95} +684.302 q^{96} -791.838 q^{97} -2429.85 q^{98} +83.4706 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9}+O(q^{10}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9	\( 51 q + 21 q^{3} + 234 q^{4} + 41 q^{5} - 73 q^{6} + 4 q^{7} - 21 q^{8} + 594 q^{9} + 212 q^{10} + 561 q^{11} + 209 q^{12} + 280 q^{14} + 284 q^{15} + 1246 q^{16} + 164 q^{17} - 189 q^{18} + 26 q^{19} + 438 q^{20} + 134 q^{21} + 373 q^{23} - 354 q^{24} + 2048 q^{25} + 1470 q^{27} - 1245 q^{28} + 898 q^{29} + 427 q^{30} + 767 q^{31} + 1127 q^{32} + 231 q^{33} + 206 q^{34} + 54 q^{35} + 3415 q^{36} + 395 q^{37} + 1577 q^{38} + 3253 q^{40} - 354 q^{41} + 942 q^{42} + 484 q^{43} + 2574 q^{44} + 1452 q^{45} - 2117 q^{46} + 1925 q^{47} + 1780 q^{48} + 4535 q^{49} - 1093 q^{50} + 230 q^{51} + 1387 q^{53} - 5271 q^{54} + 451 q^{55} + 2568 q^{56} - 5738 q^{57} + 3695 q^{58} + 1145 q^{59} - 1590 q^{60} + 5382 q^{61} - 395 q^{62} + 710 q^{63} + 9839 q^{64} - 803 q^{66} - 210 q^{67} + 1742 q^{68} + 7028 q^{69} - 6747 q^{70} + 3693 q^{71} - 12481 q^{72} + 968 q^{73} + 1735 q^{74} - 727 q^{75} - 2801 q^{76} + 44 q^{77} + 4234 q^{79} + 2390 q^{80} + 7743 q^{81} + 4770 q^{82} - 2798 q^{83} + 14821 q^{84} - 1802 q^{85} + 6558 q^{86} + 1896 q^{87} - 231 q^{88} + 3927 q^{89} + 1927 q^{90} + 1984 q^{92} - 1332 q^{93} + 7590 q^{94} + 4944 q^{95} - 7280 q^{96} + 3913 q^{97} - 15201 q^{98} + 6534 q^{99}+O(q^{100}) \) 51 * q + 21 * q^3 + 234 * q^4 + 41 * q^5 - 73 * q^6 + 4 * q^7 - 21 * q^8 + 594 * q^9 + 212 * q^10 + 561 * q^11 + 209 * q^12 + 280 * q^14 + 284 * q^15 + 1246 * q^16 + 164 * q^17 - 189 * q^18 + 26 * q^19 + 438 * q^20 + 134 * q^21 + 373 * q^23 - 354 * q^24 + 2048 * q^25 + 1470 * q^27 - 1245 * q^28 + 898 * q^29 + 427 * q^30 + 767 * q^31 + 1127 * q^32 + 231 * q^33 + 206 * q^34 + 54 * q^35 + 3415 * q^36 + 395 * q^37 + 1577 * q^38 + 3253 * q^40 - 354 * q^41 + 942 * q^42 + 484 * q^43 + 2574 * q^44 + 1452 * q^45 - 2117 * q^46 + 1925 * q^47 + 1780 * q^48 + 4535 * q^49 - 1093 * q^50 + 230 * q^51 + 1387 * q^53 - 5271 * q^54 + 451 * q^55 + 2568 * q^56 - 5738 * q^57 + 3695 * q^58 + 1145 * q^59 - 1590 * q^60 + 5382 * q^61 - 395 * q^62 + 710 * q^63 + 9839 * q^64 - 803 * q^66 - 210 * q^67 + 1742 * q^68 + 7028 * q^69 - 6747 * q^70 + 3693 * q^71 - 12481 * q^72 + 968 * q^73 + 1735 * q^74 - 727 * q^75 - 2801 * q^76 + 44 * q^77 + 4234 * q^79 + 2390 * q^80 + 7743 * q^81 + 4770 * q^82 - 2798 * q^83 + 14821 * q^84 - 1802 * q^85 + 6558 * q^86 + 1896 * q^87 - 231 * q^88 + 3927 * q^89 + 1927 * q^90 + 1984 * q^92 - 1332 * q^93 + 7590 * q^94 + 4944 * q^95 - 7280 * q^96 + 3913 * q^97 - 15201 * q^98 + 6534 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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