LMFDB - Embedded newform 1859.4.a.i.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:	$0$
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} - 4 x^{16} - 99 x^{15} + 375 x^{14} + 3949 x^{13} - 13998 x^{12} - 81750 x^{11} + 267574 x^{10} + \cdots + 2596992 $ x^17 - 4x^16 - 99x^15 + 375x^14 + 3949x^13 - 13998x^12 - 81750x^11 + 267574x^10 + 941923x^9 - 2799440x^8 - 6021311x^7 + 15765187x^6 + 20197463x^5 - 42560950x^4 - 32766128x^3 + 37775816x^2 + 27375104x + 2596992
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-4.18927$ 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)

$f(q)$	$=$	$q-4.18927 q^{2} -8.20774 q^{3} +9.54998 q^{4} -18.8743 q^{5} +34.3844 q^{6} -14.8122 q^{7} -6.49330 q^{8} +40.3670 q^{9} +O(q^{10})$	\(q-4.18927 q^{2} -8.20774 q^{3} +9.54998 q^{4} -18.8743 q^{5} +34.3844 q^{6} -14.8122 q^{7} -6.49330 q^{8} +40.3670 q^{9} +79.0697 q^{10} -11.0000 q^{11} -78.3838 q^{12} +62.0522 q^{14} +154.916 q^{15} -49.1977 q^{16} -79.2843 q^{17} -169.108 q^{18} +109.830 q^{19} -180.250 q^{20} +121.574 q^{21} +46.0820 q^{22} -112.584 q^{23} +53.2953 q^{24} +231.241 q^{25} -109.713 q^{27} -141.456 q^{28} +10.2650 q^{29} -648.984 q^{30} +250.224 q^{31} +258.049 q^{32} +90.2851 q^{33} +332.143 q^{34} +279.570 q^{35} +385.504 q^{36} +336.505 q^{37} -460.108 q^{38} +122.557 q^{40} +352.679 q^{41} -509.308 q^{42} +283.721 q^{43} -105.050 q^{44} -761.900 q^{45} +471.644 q^{46} +75.5585 q^{47} +403.802 q^{48} -123.599 q^{49} -968.731 q^{50} +650.745 q^{51} +195.259 q^{53} +459.615 q^{54} +207.618 q^{55} +96.1799 q^{56} -901.458 q^{57} -43.0027 q^{58} -18.1891 q^{59} +1479.44 q^{60} -545.599 q^{61} -1048.26 q^{62} -597.923 q^{63} -687.454 q^{64} -378.229 q^{66} -754.524 q^{67} -757.164 q^{68} +924.058 q^{69} -1171.20 q^{70} -137.083 q^{71} -262.115 q^{72} +371.711 q^{73} -1409.71 q^{74} -1897.97 q^{75} +1048.88 q^{76} +162.934 q^{77} +1102.80 q^{79} +928.574 q^{80} -189.416 q^{81} -1477.47 q^{82} -753.357 q^{83} +1161.03 q^{84} +1496.44 q^{85} -1188.58 q^{86} -84.2521 q^{87} +71.4263 q^{88} +863.056 q^{89} +3191.80 q^{90} -1075.17 q^{92} -2053.77 q^{93} -316.535 q^{94} -2072.97 q^{95} -2118.00 q^{96} -445.908 q^{97} +517.791 q^{98} -444.037 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9}+O(q^{10}) $ 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19} + 98 q^{20} + 220 q^{21} - 44 q^{22} - 215 q^{23} + 26 q^{24} + 319 q^{25} - 384 q^{27} - 396 q^{28} - 7 q^{29} - 1269 q^{30} + 682 q^{31} + 813 q^{32} + 66 q^{33} + 738 q^{34} + 10 q^{35} + 560 q^{36} + 1084 q^{37} + 410 q^{38} + 95 q^{40} + 240 q^{41} + 393 q^{42} - 435 q^{43} - 858 q^{44} + 1242 q^{45} + 1671 q^{46} + 549 q^{47} + 894 q^{48} + 403 q^{49} - 651 q^{50} + 1552 q^{51} - 566 q^{53} + 311 q^{54} - 176 q^{55} - 1925 q^{56} - 534 q^{57} + 618 q^{58} + 2010 q^{59} - 411 q^{60} + 460 q^{61} - 823 q^{62} + 820 q^{63} + 3171 q^{64} - 154 q^{66} - 232 q^{67} + 1795 q^{68} - 1608 q^{69} + 207 q^{70} + 489 q^{71} + 2556 q^{72} + 290 q^{73} + 2653 q^{74} - 2852 q^{75} + 2421 q^{76} + 66 q^{77} - 732 q^{79} + 4915 q^{80} + 2393 q^{81} - 1772 q^{82} - 117 q^{83} + 4161 q^{84} + 4858 q^{85} + 1034 q^{86} + 3032 q^{87} - 693 q^{88} + 4113 q^{89} + 15145 q^{90} - 3554 q^{92} + 802 q^{93} + 2325 q^{94} - 3924 q^{95} + 2601 q^{96} + 2793 q^{97} + 533 q^{98} - 1485 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * 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 $

$2$	−4.18927	−1.48113	−0.740565	−	0.671984i	$-0.765442\pi$
$2$	−4.18927	−1.48113	−0.740565	+	0.671984i	$0.765442\pi$
$3$	−8.20774	−1.57958	−0.789790	−	0.613377i	$-0.789810\pi$
$3$	−8.20774	−1.57958	−0.789790	+	0.613377i	$0.789810\pi$
$4$	9.54998	1.19375
$5$	−18.8743	−1.68817	−0.844086	−	0.536207i	$-0.819857\pi$
$5$	−18.8743	−1.68817	−0.844086	+	0.536207i	$0.819857\pi$
$6$	34.3844	2.33956
$7$	−14.8122	−0.799783	−0.399891	−	0.916563i	$-0.630952\pi$
$7$	−14.8122	−0.799783	−0.399891	+	0.916563i	$0.630952\pi$
$8$	−6.49330	−0.286966
$9$	40.3670	1.49507
$10$	79.0697	2.50040
$11$	−11.0000	−0.301511
$11$	−11.0000	−0.301511
$12$	−78.3838	−1.88562
$13$	0	0
$13$	0	0
$14$	62.0522	1.18458
$15$	154.916	2.66660
$16$	−49.1977	−0.768714
$17$	−79.2843	−1.13113	−0.565567	−	0.824703i	$-0.691343\pi$
$17$	−79.2843	−1.13113	−0.565567	+	0.824703i	$0.691343\pi$
$18$	−169.108	−2.21440
$19$	109.830	1.32615	0.663073	−	0.748555i	$-0.269252\pi$
$19$	109.830	1.32615	0.663073	+	0.748555i	$0.269252\pi$
$20$	−180.250	−2.01525
$21$	121.574	1.26332
$22$	46.0820	0.446578
$23$	−112.584	−1.02067	−0.510333	−	0.859977i	$-0.670478\pi$
$23$	−112.584	−1.02067	−0.510333	+	0.859977i	$0.670478\pi$
$24$	53.2953	0.453285
$25$	231.241	1.84993
$26$	0	0
$27$	−109.713	−0.782007
$28$	−141.456	−0.954739
$29$	10.2650	0.0657295	0.0328647	−	0.999460i	$-0.489537\pi$
$29$	10.2650	0.0657295	0.0328647	+	0.999460i	$0.489537\pi$
$30$	−648.984	−3.94959
$31$	250.224	1.44973	0.724863	−	0.688893i	$-0.241903\pi$
$31$	250.224	1.44973	0.724863	+	0.688893i	$0.241903\pi$
$32$	258.049	1.42553
$33$	90.2851	0.476261
$34$	332.143	1.67536
$35$	279.570	1.35017
$36$	385.504	1.78474
$37$	336.505	1.49516	0.747581	−	0.664170i	$-0.231215\pi$
$37$	336.505	1.49516	0.747581	+	0.664170i	$0.231215\pi$
$38$	−460.108	−1.96420
$39$	0	0
$40$	122.557	0.484448
$41$	352.679	1.34340	0.671698	−	0.740825i	$-0.265565\pi$
$41$	352.679	1.34340	0.671698	+	0.740825i	$0.265565\pi$
$42$	−509.308	−1.87114
$43$	283.721	1.00621	0.503106	−	0.864225i	$-0.332191\pi$
$43$	283.721	1.00621	0.503106	+	0.864225i	$0.332191\pi$
$44$	−105.050	−0.359929
$45$	−761.900	−2.52394
$46$	471.644	1.51174
$47$	75.5585	0.234497	0.117248	−	0.993103i	$-0.462593\pi$
$47$	75.5585	0.234497	0.117248	+	0.993103i	$0.462593\pi$
$48$	403.802	1.21425
$49$	−123.599	−0.360348
$50$	−968.731	−2.73998
$51$	650.745	1.78672
$52$	0	0
$53$	195.259	0.506055	0.253028	−	0.967459i	$-0.418574\pi$
$53$	195.259	0.506055	0.253028	+	0.967459i	$0.418574\pi$
$54$	459.615	1.15825
$55$	207.618	0.509003
$56$	96.1799	0.229510
$57$	−901.458	−2.09475
$58$	−43.0027	−0.0973539
$59$	−18.1891	−0.0401359	−0.0200680	−	0.999799i	$-0.506388\pi$
$59$	−18.1891	−0.0401359	−0.0200680	+	0.999799i	$0.506388\pi$
$60$	1479.44	3.18325
$61$	−545.599	−1.14519	−0.572596	−	0.819837i	$-0.694064\pi$
$61$	−545.599	−1.14519	−0.572596	+	0.819837i	$0.694064\pi$
$62$	−1048.26	−2.14724
$63$	−597.923	−1.19573
$64$	−687.454	−1.34268
$65$	0	0
$66$	−378.229	−0.705405
$67$	−754.524	−1.37582	−0.687909	−	0.725797i	$-0.741471\pi$
$67$	−754.524	−1.37582	−0.687909	+	0.725797i	$0.741471\pi$
$68$	−757.164	−1.35029
$69$	924.058	1.61222
$70$	−1171.20	−1.99978
$71$	−137.083	−0.229138	−0.114569	−	0.993415i	$-0.536549\pi$
$71$	−137.083	−0.229138	−0.114569	+	0.993415i	$0.536549\pi$
$72$	−262.115	−0.429035
$73$	371.711	0.595965	0.297983	−	0.954571i	$-0.403686\pi$
$73$	371.711	0.595965	0.297983	+	0.954571i	$0.403686\pi$
$74$	−1409.71	−2.21453
$75$	−1897.97	−2.92211
$76$	1048.88	1.58308
$77$	162.934	0.241144
$78$	0	0
$79$	1102.80	1.57056	0.785281	−	0.619140i	$-0.212519\pi$
$79$	1102.80	1.57056	0.785281	+	0.619140i	$0.212519\pi$
$80$	928.574	1.29772
$81$	−189.416	−0.259830
$82$	−1477.47	−1.98975
$83$	−753.357	−0.996286	−0.498143	−	0.867095i	$-0.665984\pi$
$83$	−753.357	−0.996286	−0.498143	+	0.867095i	$0.665984\pi$
$84$	1161.03	1.50809
$85$	1496.44	1.90955
$86$	−1188.58	−1.49033
$87$	−84.2521	−0.103825
$88$	71.4263	0.0865235
$89$	863.056	1.02791	0.513954	−	0.857818i	$-0.328180\pi$
$89$	863.056	1.02791	0.513954	+	0.857818i	$0.328180\pi$
$90$	3191.80	3.73829
$91$	0	0
$92$	−1075.17	−1.21842
$93$	−2053.77	−2.28996
$94$	−316.535	−0.347320
$95$	−2072.97	−2.23876
$96$	−2118.00	−2.25174
$97$	−445.908	−0.466753	−0.233377	−	0.972386i	$-0.574977\pi$
$97$	−445.908	−0.466753	−0.233377	+	0.972386i	$0.574977\pi$
$98$	517.791	0.533722
$99$	−444.037	−0.450781
$100$	2208.35	2.20835
$101$	916.840	0.903257	0.451628	−	0.892206i	$-0.350843\pi$
$101$	916.840	0.903257	0.451628	+	0.892206i	$0.350843\pi$
$102$	−2726.15	−2.64636
$103$	487.817	0.466660	0.233330	−	0.972398i	$-0.425038\pi$
$103$	487.817	0.466660	0.233330	+	0.972398i	$0.425038\pi$
$104$	0	0
$105$	−2294.64	−2.13270
$106$	−817.994	−0.749534
$107$	−767.437	−0.693374	−0.346687	−	0.937981i	$-0.612693\pi$
$107$	−767.437	−0.693374	−0.346687	+	0.937981i	$0.612693\pi$
$108$	−1047.75	−0.933519
$109$	244.701	0.215029	0.107514	−	0.994204i	$-0.465711\pi$
$109$	244.701	0.215029	0.107514	+	0.994204i	$0.465711\pi$
$110$	−869.767	−0.753900
$111$	−2761.94	−2.36173
$112$	728.725	0.614804
$113$	−953.963	−0.794171	−0.397085	−	0.917782i	$-0.629978\pi$
$113$	−953.963	−0.794171	−0.397085	+	0.917782i	$0.629978\pi$
$114$	3776.45	3.10260
$115$	2124.94	1.72306
$116$	98.0301	0.0784644
$117$	0	0
$118$	76.1991	0.0594466
$119$	1174.37	0.904661
$120$	−1005.91	−0.765224
$121$	121.000	0.0909091
$122$	2285.66	1.69618
$123$	−2894.70	−2.12200
$124$	2389.63	1.73061
$125$	−2005.23	−1.43483
$126$	2504.86	1.77104
$127$	−938.235	−0.655551	−0.327775	−	0.944756i	$-0.606299\pi$
$127$	−938.235	−0.655551	−0.327775	+	0.944756i	$0.606299\pi$
$128$	815.542	0.563160
$129$	−2328.71	−1.58939
$130$	0	0
$131$	−679.049	−0.452892	−0.226446	−	0.974024i	$-0.572711\pi$
$131$	−679.049	−0.452892	−0.226446	+	0.974024i	$0.572711\pi$
$132$	862.221	0.568536
$133$	−1626.82	−1.06063
$134$	3160.91	2.03777
$135$	2070.75	1.32016
$136$	514.816	0.324597
$137$	−209.428	−0.130603	−0.0653015	−	0.997866i	$-0.520801\pi$
$137$	−209.428	−0.130603	−0.0653015	+	0.997866i	$0.520801\pi$
$138$	−3871.13	−2.38791
$139$	1190.77	0.726615	0.363308	−	0.931669i	$-0.381647\pi$
$139$	1190.77	0.726615	0.363308	+	0.931669i	$0.381647\pi$
$140$	2669.89	1.61176
$141$	−620.164	−0.370406
$142$	574.279	0.339383
$143$	0	0
$144$	−1985.96	−1.14928
$145$	−193.744	−0.110963
$146$	−1557.20	−0.882703
$147$	1014.47	0.569198
$148$	3213.61	1.78485
$149$	−3024.95	−1.66318	−0.831589	−	0.555391i	$-0.812569\pi$
$149$	−3024.95	−1.66318	−0.831589	+	0.555391i	$0.812569\pi$
$150$	7951.09	4.32802
$151$	−213.087	−0.114840	−0.0574198	−	0.998350i	$-0.518287\pi$
$151$	−213.087	−0.114840	−0.0574198	+	0.998350i	$0.518287\pi$
$152$	−713.160	−0.380559
$153$	−3200.47	−1.69113
$154$	−682.574	−0.357165
$155$	−4722.81	−2.44739
$156$	0	0
$157$	−2688.92	−1.36687	−0.683437	−	0.730009i	$-0.739516\pi$
$157$	−2688.92	−1.36687	−0.683437	+	0.730009i	$0.739516\pi$
$158$	−4619.92	−2.32621
$159$	−1602.64	−0.799355
$160$	−4870.50	−2.40654
$161$	1667.61	0.816311
$162$	793.517	0.384843
$163$	2537.47	1.21933	0.609663	−	0.792660i	$-0.291305\pi$
$163$	2537.47	1.21933	0.609663	+	0.792660i	$0.291305\pi$
$164$	3368.08	1.60368
$165$	−1704.07	−0.804011
$166$	3156.02	1.47563
$167$	1769.83	0.820080	0.410040	−	0.912068i	$-0.365515\pi$
$167$	1769.83	0.820080	0.410040	+	0.912068i	$0.365515\pi$
$168$	−789.419	−0.362530
$169$	0	0
$170$	−6268.99	−2.82829
$171$	4433.51	1.98268
$172$	2709.53	1.20116
$173$	−3573.67	−1.57053	−0.785264	−	0.619162i	$-0.787473\pi$
$173$	−3573.67	−1.57053	−0.785264	+	0.619162i	$0.787473\pi$
$174$	352.955	0.153778
$175$	−3425.18	−1.47954
$176$	541.175	0.231776
$177$	149.291	0.0633979
$178$	−3615.58	−1.52247
$179$	1601.06	0.668540	0.334270	−	0.942477i	$-0.391510\pi$
$179$	1601.06	0.668540	0.334270	+	0.942477i	$0.391510\pi$
$180$	−7276.13	−3.01295
$181$	2558.21	1.05055	0.525277	−	0.850931i	$-0.323962\pi$
$181$	2558.21	1.05055	0.525277	+	0.850931i	$0.323962\pi$
$182$	0	0
$183$	4478.13	1.80892
$184$	731.039	0.292896
$185$	−6351.31	−2.52409
$186$	8603.81	3.39173
$187$	872.127	0.341050
$188$	721.582	0.279930
$189$	1625.08	0.625435
$190$	8684.25	3.31590
$191$	4118.53	1.56024	0.780121	−	0.625629i	$-0.215158\pi$
$191$	4118.53	1.56024	0.780121	+	0.625629i	$0.215158\pi$
$192$	5642.45	2.12088
$193$	1334.80	0.497828	0.248914	−	0.968526i	$-0.419926\pi$
$193$	1334.80	0.497828	0.248914	+	0.968526i	$0.419926\pi$
$194$	1868.03	0.691322
$195$	0	0
$196$	−1180.37	−0.430165
$197$	4117.08	1.48898	0.744491	−	0.667632i	$-0.232692\pi$
$197$	4117.08	1.48898	0.744491	+	0.667632i	$0.232692\pi$
$198$	1860.19	0.667666
$199$	−4600.73	−1.63888	−0.819441	−	0.573164i	$-0.805716\pi$
$199$	−4600.73	−1.63888	−0.819441	+	0.573164i	$0.805716\pi$
$200$	−1501.52	−0.530866
$201$	6192.94	2.17321
$202$	−3840.89	−1.33784
$203$	−152.046	−0.0525693
$204$	6214.60	2.13289
$205$	−6656.59	−2.26789
$206$	−2043.60	−0.691185
$207$	−4544.66	−1.52597
$208$	0	0
$209$	−1208.13	−0.399848
$210$	9612.86	3.15881
$211$	−1968.34	−0.642210	−0.321105	−	0.947044i	$-0.604054\pi$
$211$	−1968.34	−0.642210	−0.321105	+	0.947044i	$0.604054\pi$
$212$	1864.72	0.604103
$213$	1125.14	0.361942
$214$	3215.00	1.02698
$215$	−5355.05	−1.69866
$216$	712.396	0.224409
$217$	−3706.36	−1.15947
$218$	−1025.12	−0.318485
$219$	−3050.91	−0.941375
$220$	1982.75	0.607622
$221$	0	0
$222$	11570.5	3.49803
$223$	2344.82	0.704129	0.352064	−	0.935976i	$-0.385480\pi$
$223$	2344.82	0.704129	0.352064	+	0.935976i	$0.385480\pi$
$224$	−3822.26	−1.14012
$225$	9334.50	2.76578
$226$	3996.41	1.17627
$227$	−975.357	−0.285184	−0.142592	−	0.989782i	$-0.545544\pi$
$227$	−975.357	−0.285184	−0.142592	+	0.989782i	$0.545544\pi$
$228$	−8608.90	−2.50061
$229$	−1963.85	−0.566703	−0.283352	−	0.959016i	$-0.591446\pi$
$229$	−1963.85	−0.566703	−0.283352	+	0.959016i	$0.591446\pi$
$230$	−8901.97	−2.55208
$231$	−1337.32	−0.380905
$232$	−66.6534	−0.0188621
$233$	−5091.60	−1.43160	−0.715798	−	0.698308i	$-0.753937\pi$
$233$	−5091.60	−1.43160	−0.715798	+	0.698308i	$0.753937\pi$
$234$	0	0
$235$	−1426.12	−0.395871
$236$	−173.706	−0.0479122
$237$	−9051.47	−2.48083
$238$	−4919.77	−1.33992
$239$	2244.17	0.607378	0.303689	−	0.952771i	$-0.401782\pi$
$239$	2244.17	0.607378	0.303689	+	0.952771i	$0.401782\pi$
$240$	−7621.49	−2.04986
$241$	261.304	0.0698425	0.0349212	−	0.999390i	$-0.488882\pi$
$241$	261.304	0.0698425	0.0349212	+	0.999390i	$0.488882\pi$
$242$	−506.902	−0.134648
$243$	4516.92	1.19243
$244$	−5210.46	−1.36707
$245$	2332.86	0.608330
$246$	12126.7	3.14296
$247$	0	0
$248$	−1624.78	−0.416022
$249$	6183.36	1.57371
$250$	8400.45	2.12516
$251$	6048.76	1.52109	0.760546	−	0.649284i	$-0.224931\pi$
$251$	6048.76	1.52109	0.760546	+	0.649284i	$0.224931\pi$
$252$	−5710.15	−1.42740
$253$	1238.42	0.307743
$254$	3930.52	0.970956
$255$	−12282.4	−3.01628
$256$	2083.11	0.508572
$257$	−558.032	−0.135444	−0.0677220	−	0.997704i	$-0.521573\pi$
$257$	−558.032	−0.135444	−0.0677220	+	0.997704i	$0.521573\pi$
$258$	9755.59	2.35410
$259$	−4984.37	−1.19581
$260$	0	0
$261$	414.365	0.0982703
$262$	2844.72	0.670792
$263$	−1276.02	−0.299174	−0.149587	−	0.988749i	$-0.547794\pi$
$263$	−1276.02	−0.299174	−0.149587	+	0.988749i	$0.547794\pi$
$264$	−586.248	−0.136671
$265$	−3685.39	−0.854309
$266$	6815.21	1.57093
$267$	−7083.74	−1.62366
$268$	−7205.69	−1.64238
$269$	4295.62	0.973637	0.486818	−	0.873503i	$-0.338157\pi$
$269$	4295.62	0.973637	0.486818	+	0.873503i	$0.338157\pi$
$270$	−8674.94	−1.95533
$271$	−6165.23	−1.38196	−0.690980	−	0.722874i	$-0.742821\pi$
$271$	−6165.23	−1.38196	−0.690980	+	0.722874i	$0.742821\pi$
$272$	3900.60	0.869518
$273$	0	0
$274$	877.349	0.193440
$275$	−2543.65	−0.557774
$276$	8824.73	1.92459
$277$	3344.61	0.725481	0.362740	−	0.931890i	$-0.381841\pi$
$277$	3344.61	0.725481	0.362740	+	0.931890i	$0.381841\pi$
$278$	−4988.44	−1.07621
$279$	10100.8	2.16745
$280$	−1815.33	−0.387453
$281$	1266.76	0.268928	0.134464	−	0.990918i	$-0.457069\pi$
$281$	1266.76	0.268928	0.134464	+	0.990918i	$0.457069\pi$
$282$	2598.04	0.548620
$283$	5767.46	1.21145	0.605724	−	0.795674i	$-0.292883\pi$
$283$	5767.46	1.21145	0.605724	+	0.795674i	$0.292883\pi$
$284$	−1309.14	−0.273533
$285$	17014.4	3.53631
$286$	0	0
$287$	−5223.95	−1.07442
$288$	10416.6	2.13127
$289$	1373.00	0.279463
$290$	811.647	0.164350
$291$	3659.89	0.737274
$292$	3549.83	0.711432
$293$	−3547.08	−0.707245	−0.353622	−	0.935388i	$-0.615050\pi$
$293$	−3547.08	−0.707245	−0.353622	+	0.935388i	$0.615050\pi$
$294$	−4249.89	−0.843057
$295$	343.308	0.0677564
$296$	−2185.02	−0.429061
$297$	1206.84	0.235784
$298$	12672.3	2.46338
$299$	0	0
$300$	−18125.5	−3.48826
$301$	−4202.53	−0.804750
$302$	892.679	0.170092
$303$	−7525.18	−1.42677
$304$	−5403.39	−1.01943
$305$	10297.8	1.93328
$306$	13407.6	2.50478
$307$	−2194.62	−0.407991	−0.203996	−	0.978972i	$-0.565393\pi$
$307$	−2194.62	−0.407991	−0.203996	+	0.978972i	$0.565393\pi$
$308$	1556.02	0.287865
$309$	−4003.87	−0.737127
$310$	19785.1	3.62490
$311$	−6523.92	−1.18951	−0.594755	−	0.803907i	$-0.702751\pi$
$311$	−6523.92	−1.18951	−0.594755	+	0.803907i	$0.702751\pi$
$312$	0	0
$313$	8801.52	1.58943	0.794715	−	0.606983i	$-0.207620\pi$
$313$	8801.52	1.58943	0.794715	+	0.606983i	$0.207620\pi$
$314$	11264.6	2.02452
$315$	11285.4	2.01860
$316$	10531.7	1.87485
$317$	1309.05	0.231935	0.115967	−	0.993253i	$-0.463003\pi$
$317$	1309.05	0.231935	0.115967	+	0.993253i	$0.463003\pi$
$318$	6713.88	1.18395
$319$	−112.915	−0.0198182
$320$	12975.3	2.26668
$321$	6298.92	1.09524
$322$	−6986.07	−1.20906
$323$	−8707.81	−1.50005
$324$	−1808.92	−0.310172
$325$	0	0
$326$	−10630.2	−1.80598
$327$	−2008.44	−0.339655
$328$	−2290.05	−0.385509
$329$	−1119.19	−0.187546
$330$	7138.82	1.19085
$331$	−8501.26	−1.41170	−0.705848	−	0.708363i	$-0.749434\pi$
$331$	−8501.26	−1.41170	−0.705848	+	0.708363i	$0.749434\pi$
$332$	−7194.55	−1.18931
$333$	13583.7	2.23538
$334$	−7414.29	−1.21465
$335$	14241.1	2.32262
$336$	−5981.18	−0.971132
$337$	−2532.52	−0.409362	−0.204681	−	0.978829i	$-0.565616\pi$
$337$	−2532.52	−0.409362	−0.204681	+	0.978829i	$0.565616\pi$
$338$	0	0
$339$	7829.88	1.25446
$340$	14291.0	2.27952
$341$	−2752.46	−0.437109
$342$	−18573.2	−2.93662
$343$	6911.35	1.08798
$344$	−1842.29	−0.288748
$345$	−17441.0	−2.72171
$346$	14971.1	2.32616
$347$	2395.36	0.370575	0.185287	−	0.982684i	$-0.440678\pi$
$347$	2395.36	0.370575	0.185287	+	0.982684i	$0.440678\pi$
$348$	−804.606	−0.123941
$349$	10397.2	1.59469	0.797346	−	0.603523i	$-0.206237\pi$
$349$	10397.2	1.59469	0.797346	+	0.603523i	$0.206237\pi$
$350$	14349.0	2.19139
$351$	0	0
$352$	−2838.54	−0.429814
$353$	−9990.35	−1.50632	−0.753162	−	0.657835i	$-0.771472\pi$
$353$	−9990.35	−1.50632	−0.753162	+	0.657835i	$0.771472\pi$
$354$	−625.422	−0.0939006
$355$	2587.36	0.386824
$356$	8242.17	1.22706
$357$	−9638.95	−1.42898
$358$	−6707.26	−0.990194
$359$	−3557.96	−0.523070	−0.261535	−	0.965194i	$-0.584229\pi$
$359$	−3557.96	−0.523070	−0.261535	+	0.965194i	$0.584229\pi$
$360$	4947.24	0.724285
$361$	5203.67	0.758664
$362$	−10717.0	−1.55601
$363$	−993.136	−0.143598
$364$	0	0
$365$	−7015.80	−1.00609
$366$	−18760.1	−2.67925
$367$	−4100.18	−0.583182	−0.291591	−	0.956543i	$-0.594185\pi$
$367$	−4100.18	−0.583182	−0.291591	+	0.956543i	$0.594185\pi$
$368$	5538.86	0.784601
$369$	14236.6	2.00848
$370$	26607.3	3.73851
$371$	−2892.22	−0.404734
$372$	−19613.5	−2.73363
$373$	−8356.67	−1.16003	−0.580016	−	0.814605i	$-0.696954\pi$
$373$	−8356.67	−1.16003	−0.580016	+	0.814605i	$0.696954\pi$
$374$	−3653.58	−0.505139
$375$	16458.4	2.26642
$376$	−490.624	−0.0672925
$377$	0	0
$378$	−6807.90	−0.926351
$379$	3966.44	0.537578	0.268789	−	0.963199i	$-0.413377\pi$
$379$	3966.44	0.537578	0.268789	+	0.963199i	$0.413377\pi$
$380$	−19796.9	−2.67252
$381$	7700.79	1.03549
$382$	−17253.6	−2.31092
$383$	−8949.58	−1.19400	−0.597000	−	0.802241i	$-0.703641\pi$
$383$	−8949.58	−1.19400	−0.597000	+	0.802241i	$0.703641\pi$
$384$	−6693.76	−0.889555
$385$	−3075.27	−0.407092
$386$	−5591.83	−0.737349
$387$	11453.0	1.50436
$388$	−4258.41	−0.557186
$389$	10120.9	1.31915	0.659574	−	0.751640i	$-0.270737\pi$
$389$	10120.9	1.31915	0.659574	+	0.751640i	$0.270737\pi$
$390$	0	0
$391$	8926.12	1.15451
$392$	802.567	0.103408
$393$	5573.46	0.715378
$394$	−17247.5	−2.20538
$395$	−20814.6	−2.65138
$396$	−4240.54	−0.538119
$397$	14140.4	1.78763	0.893814	−	0.448438i	$-0.148019\pi$
$397$	14140.4	1.78763	0.893814	+	0.448438i	$0.148019\pi$
$398$	19273.7	2.42740
$399$	13352.6	1.67535
$400$	−11376.5	−1.42207
$401$	12643.1	1.57448	0.787241	−	0.616646i	$-0.211509\pi$
$401$	12643.1	1.57448	0.787241	+	0.616646i	$0.211509\pi$
$402$	−25943.9	−3.21881
$403$	0	0
$404$	8755.80	1.07826
$405$	3575.11	0.438639
$406$	636.963	0.0778620
$407$	−3701.55	−0.450809
$408$	−4225.48	−0.512726
$409$	4026.21	0.486756	0.243378	−	0.969932i	$-0.421744\pi$
$409$	4026.21	0.486756	0.243378	+	0.969932i	$0.421744\pi$
$410$	27886.3	3.35903
$411$	1718.93	0.206298
$412$	4658.64	0.557075
$413$	269.420	0.0321000
$414$	19038.8	2.26016
$415$	14219.1	1.68190
$416$	0	0
$417$	−9773.50	−1.14775
$418$	5061.19	0.592227
$419$	−5793.21	−0.675458	−0.337729	−	0.941243i	$-0.609659\pi$
$419$	−5793.21	−0.675458	−0.337729	+	0.941243i	$0.609659\pi$
$420$	−21913.8	−2.54591
$421$	3667.48	0.424566	0.212283	−	0.977208i	$-0.431910\pi$
$421$	3667.48	0.424566	0.212283	+	0.977208i	$0.431910\pi$
$422$	8245.93	0.951198
$423$	3050.07	0.350589
$424$	−1267.88	−0.145221
$425$	−18333.8	−2.09252
$426$	−4713.53	−0.536083
$427$	8081.51	0.915905
$428$	−7329.01	−0.827713
$429$	0	0
$430$	22433.8	2.51594
$431$	−15002.1	−1.67663	−0.838314	−	0.545188i	$-0.816458\pi$
$431$	−15002.1	−1.67663	−0.838314	+	0.545188i	$0.816458\pi$
$432$	5397.60	0.601139
$433$	8161.57	0.905820	0.452910	−	0.891556i	$-0.350386\pi$
$433$	8161.57	0.905820	0.452910	+	0.891556i	$0.350386\pi$
$434$	15526.9	1.71732
$435$	1590.20	0.175274
$436$	2336.89	0.256690
$437$	−12365.1	−1.35355
$438$	12781.1	1.39430
$439$	994.847	0.108158	0.0540791	−	0.998537i	$-0.482778\pi$
$439$	994.847	0.108158	0.0540791	+	0.998537i	$0.482778\pi$
$440$	−1348.12	−0.146067
$441$	−4989.33	−0.538746
$442$	0	0
$443$	11863.5	1.27235	0.636175	−	0.771545i	$-0.280516\pi$
$443$	11863.5	1.27235	0.636175	+	0.771545i	$0.280516\pi$
$444$	−26376.5	−2.81931
$445$	−16289.6	−1.73529
$446$	−9823.08	−1.04291
$447$	24828.0	2.62712
$448$	10182.7	1.07386
$449$	13856.7	1.45643	0.728214	−	0.685349i	$-0.240350\pi$
$449$	13856.7	1.45643	0.728214	+	0.685349i	$0.240350\pi$
$450$	−39104.7	−4.09648
$451$	−3879.47	−0.405049
$452$	−9110.33	−0.948040
$453$	1748.96	0.181398
$454$	4086.03	0.422394
$455$	0	0
$456$	5853.43	0.601123
$457$	−7648.90	−0.782933	−0.391467	−	0.920192i	$-0.628032\pi$
$457$	−7648.90	−0.782933	−0.391467	+	0.920192i	$0.628032\pi$
$458$	8227.11	0.839362
$459$	8698.48	0.884554
$460$	20293.2	2.05690
$461$	4657.07	0.470502	0.235251	−	0.971935i	$-0.424409\pi$
$461$	4657.07	0.470502	0.235251	+	0.971935i	$0.424409\pi$
$462$	5602.39	0.564171
$463$	15545.9	1.56043	0.780214	−	0.625513i	$-0.215110\pi$
$463$	15545.9	1.56043	0.780214	+	0.625513i	$0.215110\pi$
$464$	−505.012	−0.0505272
$465$	38763.6	3.86585
$466$	21330.1	2.12038
$467$	−6249.15	−0.619221	−0.309610	−	0.950864i	$-0.600199\pi$
$467$	−6249.15	−0.619221	−0.309610	+	0.950864i	$0.600199\pi$
$468$	0	0
$469$	11176.1	1.10035
$470$	5974.39	0.586336
$471$	22070.0	2.15909
$472$	118.107	0.0115176
$473$	−3120.93	−0.303384
$474$	37919.1	3.67443
$475$	25397.2	2.45327
$476$	11215.2	1.07994
$477$	7882.03	0.756590
$478$	−9401.43	−0.899606
$479$	10743.5	1.02481	0.512403	−	0.858745i	$-0.328756\pi$
$479$	10743.5	1.02481	0.512403	+	0.858745i	$0.328756\pi$
$480$	39975.8	3.80133
$481$	0	0
$482$	−1094.67	−0.103446
$483$	−13687.3	−1.28943
$484$	1155.55	0.108523
$485$	8416.22	0.787960
$486$	−18922.6	−1.76614
$487$	−3426.19	−0.318799	−0.159400	−	0.987214i	$-0.550956\pi$
$487$	−3426.19	−0.318799	−0.159400	+	0.987214i	$0.550956\pi$
$488$	3542.73	0.328631
$489$	−20826.9	−1.92602
$490$	−9772.97	−0.901016
$491$	10870.1	0.999106	0.499553	−	0.866283i	$-0.333498\pi$
$491$	10870.1	0.999106	0.499553	+	0.866283i	$0.333498\pi$
$492$	−27644.3	−2.53314
$493$	−813.850	−0.0743488
$494$	0	0
$495$	8380.90	0.760997
$496$	−12310.4	−1.11443
$497$	2030.50	0.183261
$498$	−25903.8	−2.33087
$499$	−7870.01	−0.706032	−0.353016	−	0.935617i	$-0.614844\pi$
$499$	−7870.01	−0.706032	−0.353016	+	0.935617i	$0.614844\pi$
$500$	−19149.9	−1.71282
$501$	−14526.3	−1.29538
$502$	−25339.9	−2.25294
$503$	−7234.18	−0.641265	−0.320632	−	0.947204i	$-0.603895\pi$
$503$	−7234.18	−0.641265	−0.320632	+	0.947204i	$0.603895\pi$
$504$	3882.49	0.343135
$505$	−17304.8	−1.52485
$506$	−5188.08	−0.455807
$507$	0	0
$508$	−8960.13	−0.782562
$509$	7296.52	0.635388	0.317694	−	0.948193i	$-0.397091\pi$
$509$	7296.52	0.635388	0.317694	+	0.948193i	$0.397091\pi$
$510$	51454.2	4.46751
$511$	−5505.85	−0.476643
$512$	−15251.0	−1.31642
$513$	−12049.7	−1.03706
$514$	2337.75	0.200610
$515$	−9207.22	−0.787803
$516$	−22239.1	−1.89733
$517$	−831.143	−0.0707034
$518$	20880.9	1.77114
$519$	29331.8	2.48077
$520$	0	0
$521$	2117.88	0.178092	0.0890462	−	0.996027i	$-0.471618\pi$
$521$	2117.88	0.178092	0.0890462	+	0.996027i	$0.471618\pi$
$522$	−1735.89	−0.145551
$523$	7979.20	0.667124	0.333562	−	0.942728i	$-0.391749\pi$
$523$	7979.20	0.667124	0.333562	+	0.942728i	$0.391749\pi$
$524$	−6484.91	−0.540638
$525$	28113.0	2.33705
$526$	5345.58	0.443115
$527$	−19838.8	−1.63983
$528$	−4441.82	−0.366109
$529$	508.095	0.0417601
$530$	15439.1	1.26534
$531$	−734.239	−0.0600061
$532$	−15536.1	−1.26612
$533$	0	0
$534$	29675.7	2.40486
$535$	14484.9	1.17053
$536$	4899.35	0.394813
$537$	−13141.1	−1.05601
$538$	−17995.5	−1.44208
$539$	1359.59	0.108649
$540$	19775.6	1.57594
$541$	−13841.4	−1.09998	−0.549990	−	0.835171i	$-0.685368\pi$
$541$	−13841.4	−1.09998	−0.549990	+	0.835171i	$0.685368\pi$
$542$	25827.8	2.04686
$543$	−20997.1	−1.65943
$544$	−20459.2	−1.61247
$545$	−4618.57	−0.363005
$546$	0	0
$547$	5590.64	0.436999	0.218500	−	0.975837i	$-0.429884\pi$
$547$	5590.64	0.436999	0.218500	+	0.975837i	$0.429884\pi$
$548$	−2000.03	−0.155907
$549$	−22024.2	−1.71215
$550$	10656.0	0.826137
$551$	1127.40	0.0871669
$552$	−6000.18	−0.462653
$553$	−16334.8	−1.25611
$554$	−14011.5	−1.07453
$555$	52129.9	3.98701
$556$	11371.8	0.867396
$557$	−18969.1	−1.44299	−0.721496	−	0.692418i	$-0.756545\pi$
$557$	−18969.1	−1.44299	−0.721496	+	0.692418i	$0.756545\pi$
$558$	−42314.9	−3.21027
$559$	0	0
$560$	−13754.2	−1.03790
$561$	−7158.19	−0.538715
$562$	−5306.81	−0.398317
$563$	−13099.7	−0.980616	−0.490308	−	0.871549i	$-0.663116\pi$
$563$	−13099.7	−0.980616	−0.490308	+	0.871549i	$0.663116\pi$
$564$	−5922.56	−0.442171
$565$	18005.4	1.34070
$566$	−24161.5	−1.79431
$567$	2805.67	0.207808
$568$	890.122	0.0657548
$569$	−11315.6	−0.833702	−0.416851	−	0.908975i	$-0.636866\pi$
$569$	−11315.6	−0.833702	−0.416851	+	0.908975i	$0.636866\pi$
$570$	−71278.0	−5.23773
$571$	−3798.54	−0.278395	−0.139198	−	0.990265i	$-0.544452\pi$
$571$	−3798.54	−0.278395	−0.139198	+	0.990265i	$0.544452\pi$
$572$	0	0
$573$	−33803.8	−2.46453
$574$	21884.5	1.59136
$575$	−26034.0	−1.88816
$576$	−27750.4	−2.00741
$577$	−16362.1	−1.18053	−0.590263	−	0.807211i	$-0.700976\pi$
$577$	−16362.1	−1.18053	−0.590263	+	0.807211i	$0.700976\pi$
$578$	−5751.87	−0.413921
$579$	−10955.7	−0.786360
$580$	−1850.26	−0.132461
$581$	11158.9	0.796812
$582$	−15332.3	−1.09200
$583$	−2147.85	−0.152581
$584$	−2413.63	−0.171022
$585$	0	0
$586$	14859.7	1.04752
$587$	−4716.01	−0.331602	−0.165801	−	0.986159i	$-0.553021\pi$
$587$	−4716.01	−0.331602	−0.165801	+	0.986159i	$0.553021\pi$
$588$	9688.18	0.679479
$589$	27482.1	1.92255
$590$	−1438.21	−0.100356
$591$	−33791.9	−2.35197
$592$	−16555.3	−1.14935
$593$	1492.38	0.103347	0.0516733	−	0.998664i	$-0.483545\pi$
$593$	1492.38	0.103347	0.0516733	+	0.998664i	$0.483545\pi$
$594$	−5055.77	−0.349227
$595$	−22165.5	−1.52722
$596$	−28888.2	−1.98542
$597$	37761.6	2.58874
$598$	0	0
$599$	−14436.5	−0.984740	−0.492370	−	0.870386i	$-0.663869\pi$
$599$	−14436.5	−0.984740	−0.492370	+	0.870386i	$0.663869\pi$
$600$	12324.1	0.838545
$601$	6183.21	0.419665	0.209832	−	0.977737i	$-0.432708\pi$
$601$	6183.21	0.419665	0.209832	+	0.977737i	$0.432708\pi$
$602$	17605.5	1.19194
$603$	−30457.8	−2.05695
$604$	−2034.98	−0.137089
$605$	−2283.80	−0.153470
$606$	31525.0	2.11323
$607$	−6223.72	−0.416167	−0.208083	−	0.978111i	$-0.566723\pi$
$607$	−6223.72	−0.416167	−0.208083	+	0.978111i	$0.566723\pi$
$608$	28341.5	1.89046
$609$	1247.96	0.0830374
$610$	−43140.3	−2.86345
$611$	0	0
$612$	−30564.4	−2.01878
$613$	3358.28	0.221272	0.110636	−	0.993861i	$-0.464711\pi$
$613$	3358.28	0.221272	0.110636	+	0.993861i	$0.464711\pi$
$614$	9193.84	0.604288
$615$	54635.6	3.58231
$616$	−1057.98	−0.0692000
$617$	−18446.5	−1.20361	−0.601807	−	0.798642i	$-0.705552\pi$
$617$	−18446.5	−1.20361	−0.601807	+	0.798642i	$0.705552\pi$
$618$	16773.3	1.09178
$619$	19732.0	1.28125	0.640627	−	0.767852i	$-0.278674\pi$
$619$	19732.0	1.28125	0.640627	+	0.767852i	$0.278674\pi$
$620$	−45102.8	−2.92157
$621$	12351.8	0.798168
$622$	27330.5	1.76182
$623$	−12783.7	−0.822103
$624$	0	0
$625$	8942.27	0.572305
$626$	−36872.0	−2.35415
$627$	9916.03	0.631592
$628$	−25679.2	−1.63170
$629$	−26679.5	−1.69123
$630$	−47277.6	−2.98982
$631$	−6579.41	−0.415090	−0.207545	−	0.978225i	$-0.566547\pi$
$631$	−6579.41	−0.415090	−0.207545	+	0.978225i	$0.566547\pi$
$632$	−7160.79	−0.450698
$633$	16155.7	1.01442
$634$	−5483.95	−0.343526
$635$	17708.6	1.10668
$636$	−15305.2	−0.954228
$637$	0	0
$638$	473.029	0.0293533
$639$	−5533.64	−0.342578
$640$	−15392.8	−0.950711
$641$	−13382.4	−0.824609	−0.412304	−	0.911046i	$-0.635276\pi$
$641$	−13382.4	−0.824609	−0.412304	+	0.911046i	$0.635276\pi$
$642$	−26387.9	−1.62219
$643$	24649.5	1.51179	0.755894	−	0.654694i	$-0.227202\pi$
$643$	24649.5	1.51179	0.755894	+	0.654694i	$0.227202\pi$
$644$	15925.7	0.974470
$645$	43952.9	2.68317
$646$	36479.4	2.22177
$647$	−1683.20	−0.102277	−0.0511387	−	0.998692i	$-0.516285\pi$
$647$	−1683.20	−0.102277	−0.0511387	+	0.998692i	$0.516285\pi$
$648$	1229.94	0.0745625
$649$	200.080	0.0121014
$650$	0	0
$651$	30420.8	1.83147
$652$	24232.8	1.45557
$653$	−3254.79	−0.195053	−0.0975266	−	0.995233i	$-0.531093\pi$
$653$	−3254.79	−0.195053	−0.0975266	+	0.995233i	$0.531093\pi$
$654$	8413.91	0.503073
$655$	12816.6	0.764559
$656$	−17351.0	−1.03269
$657$	15004.8	0.891012
$658$	4688.57	0.277781
$659$	−30892.6	−1.82611	−0.913054	−	0.407839i	$-0.866282\pi$
$659$	−30892.6	−1.82611	−0.913054	+	0.407839i	$0.866282\pi$
$660$	−16273.9	−0.959787
$661$	31421.0	1.84892	0.924458	−	0.381283i	$-0.124518\pi$
$661$	31421.0	1.84892	0.924458	+	0.381283i	$0.124518\pi$
$662$	35614.1	2.09091
$663$	0	0
$664$	4891.77	0.285900
$665$	30705.3	1.79052
$666$	−56905.7	−3.31089
$667$	−1155.67	−0.0670879
$668$	16901.8	0.978969
$669$	−19245.7	−1.11223
$670$	−59660.0	−3.44010
$671$	6001.59	0.345289
$672$	31372.1	1.80090
$673$	12272.2	0.702913	0.351456	−	0.936204i	$-0.385687\pi$
$673$	12272.2	0.702913	0.351456	+	0.936204i	$0.385687\pi$
$674$	10609.4	0.606319
$675$	−25370.0	−1.44666
$676$	0	0
$677$	−7951.18	−0.451387	−0.225693	−	0.974198i	$-0.572465\pi$
$677$	−7951.18	−0.451387	−0.225693	+	0.974198i	$0.572465\pi$
$678$	−32801.5	−1.85801
$679$	6604.86	0.373301
$680$	−9716.82	−0.547975
$681$	8005.47	0.450470
$682$	11530.8	0.647416
$683$	6024.55	0.337516	0.168758	−	0.985658i	$-0.446024\pi$
$683$	6024.55	0.337516	0.168758	+	0.985658i	$0.446024\pi$
$684$	42340.0	2.36683
$685$	3952.81	0.220480
$686$	−28953.5	−1.61144
$687$	16118.8	0.895153
$688$	−13958.4	−0.773489
$689$	0	0
$690$	73065.0	4.03121
$691$	−22810.1	−1.25577	−0.627885	−	0.778306i	$-0.716079\pi$
$691$	−22810.1	−1.25577	−0.627885	+	0.778306i	$0.716079\pi$
$692$	−34128.5	−1.87481
$693$	6577.15	0.360527
$694$	−10034.8	−0.548870
$695$	−22475.0	−1.22665
$696$	547.074	0.0297942
$697$	−27961.9	−1.51956
$698$	−43556.5	−2.36195
$699$	41790.5	2.26132
$700$	−32710.4	−1.76620
$701$	4150.51	0.223627	0.111814	−	0.993729i	$-0.464334\pi$
$701$	4150.51	0.223627	0.111814	+	0.993729i	$0.464334\pi$
$702$	0	0
$703$	36958.4	1.98280
$704$	7562.00	0.404835
$705$	11705.2	0.625309
$706$	41852.3	2.23106
$707$	−13580.4	−0.722409
$708$	1425.73	0.0756811
$709$	11164.9	0.591406	0.295703	−	0.955280i	$-0.404446\pi$
$709$	11164.9	0.591406	0.295703	+	0.955280i	$0.404446\pi$
$710$	−10839.1	−0.572938
$711$	44516.6	2.34810
$712$	−5604.08	−0.294974
$713$	−28171.1	−1.47969
$714$	40380.2	2.11651
$715$	0	0
$716$	15290.1	0.798068
$717$	−18419.6	−0.959402
$718$	14905.3	0.774735
$719$	−30131.2	−1.56287	−0.781434	−	0.623987i	$-0.785512\pi$
$719$	−30131.2	−1.56287	−0.781434	+	0.623987i	$0.785512\pi$
$720$	37483.7	1.94019
$721$	−7225.63	−0.373227
$722$	−21799.6	−1.12368
$723$	−2144.71	−0.110322
$724$	24430.9	1.25410
$725$	2373.68	0.121595
$726$	4160.52	0.212688
$727$	−28376.9	−1.44765	−0.723824	−	0.689985i	$-0.757617\pi$
$727$	−28376.9	−1.44765	−0.723824	+	0.689985i	$0.757617\pi$
$728$	0	0
$729$	−31959.4	−1.62371
$730$	29391.1	1.49015
$731$	−22494.6	−1.13816
$732$	42766.1	2.15940
$733$	−18937.3	−0.954248	−0.477124	−	0.878836i	$-0.658321\pi$
$733$	−18937.3	−0.954248	−0.477124	+	0.878836i	$0.658321\pi$
$734$	17176.8	0.863769
$735$	−19147.5	−0.960905
$736$	−29052.1	−1.45499
$737$	8299.76	0.414825
$738$	−59640.9	−2.97481
$739$	−23479.9	−1.16877	−0.584386	−	0.811476i	$-0.698665\pi$
$739$	−23479.9	−1.16877	−0.584386	+	0.811476i	$0.698665\pi$
$740$	−60654.9	−3.01313
$741$	0	0
$742$	12116.3	0.599464
$743$	−4492.24	−0.221809	−0.110905	−	0.993831i	$-0.535375\pi$
$743$	−4492.24	−0.221809	−0.110905	+	0.993831i	$0.535375\pi$
$744$	13335.8	0.657140
$745$	57094.0	2.80773
$746$	35008.3	1.71816
$747$	−30410.7	−1.48952
$748$	8328.80	0.407127
$749$	11367.4	0.554548
$750$	−68948.7	−3.35687
$751$	−24461.4	−1.18856	−0.594279	−	0.804259i	$-0.702563\pi$
$751$	−24461.4	−1.18856	−0.594279	+	0.804259i	$0.702563\pi$
$752$	−3717.30	−0.180261
$753$	−49646.6	−2.40269
$754$	0	0
$755$	4021.88	0.193869
$756$	15519.5	0.746612
$757$	9157.36	0.439669	0.219835	−	0.975537i	$-0.429448\pi$
$757$	9157.36	0.439669	0.219835	+	0.975537i	$0.429448\pi$
$758$	−16616.5	−0.796224
$759$	−10164.6	−0.486104
$760$	13460.4	0.642449
$761$	13819.1	0.658270	0.329135	−	0.944283i	$-0.393243\pi$
$761$	13819.1	0.658270	0.329135	+	0.944283i	$0.393243\pi$
$762$	−32260.7	−1.53370
$763$	−3624.56	−0.171976
$764$	39331.9	1.86253
$765$	60406.7	2.85491
$766$	37492.2	1.76847
$767$	0	0
$768$	−17097.6	−0.803330
$769$	7435.87	0.348692	0.174346	−	0.984684i	$-0.444219\pi$
$769$	7435.87	0.348692	0.174346	+	0.984684i	$0.444219\pi$
$770$	12883.1	0.602956
$771$	4580.18	0.213945
$772$	12747.3	0.594281
$773$	18964.3	0.882406	0.441203	−	0.897407i	$-0.354552\pi$
$773$	18964.3	0.882406	0.441203	+	0.897407i	$0.354552\pi$
$774$	−47979.6	−2.22815
$775$	57862.0	2.68189
$776$	2895.41	0.133942
$777$	40910.4	1.88887
$778$	−42399.0	−1.95383
$779$	38734.8	1.78154
$780$	0	0
$781$	1507.92	0.0690877
$782$	−37393.9	−1.70998
$783$	−1126.19	−0.0514009
$784$	6080.80	0.277004
$785$	50751.6	2.30752
$786$	−23348.7	−1.05957
$787$	−27222.1	−1.23299	−0.616495	−	0.787359i	$-0.711448\pi$
$787$	−27222.1	−1.23299	−0.616495	+	0.787359i	$0.711448\pi$
$788$	39318.0	1.77747
$789$	10473.2	0.472568
$790$	87197.9	3.92704
$791$	14130.3	0.635164
$792$	2883.26	0.129359
$793$	0	0
$794$	−59238.1	−2.64771
$795$	30248.7	1.34945
$796$	−43936.9	−1.95641
$797$	−33914.7	−1.50730	−0.753650	−	0.657275i	$-0.771709\pi$
$797$	−33914.7	−1.50730	−0.753650	+	0.657275i	$0.771709\pi$
$798$	−55937.4	−2.48141
$799$	−5990.60	−0.265247
$800$	59671.5	2.63713
$801$	34839.0	1.53680
$802$	−52965.4	−2.33201
$803$	−4088.82	−0.179690
$804$	59142.4	2.59427
$805$	−31475.1	−1.37807
$806$	0	0
$807$	−35257.3	−1.53794
$808$	−5953.31	−0.259204
$809$	5249.72	0.228146	0.114073	−	0.993472i	$-0.463610\pi$
$809$	5249.72	0.228146	0.114073	+	0.993472i	$0.463610\pi$
$810$	−14977.1	−0.649681
$811$	−2127.83	−0.0921308	−0.0460654	−	0.998938i	$-0.514668\pi$
$811$	−2127.83	−0.0921308	−0.0460654	+	0.998938i	$0.514668\pi$
$812$	−1452.04	−0.0627545
$813$	50602.6	2.18291
$814$	15506.8	0.667706
$815$	−47893.2	−2.05843
$816$	−32015.1	−1.37347
$817$	31161.2	1.33438
$818$	−16866.9	−0.720949
$819$	0	0
$820$	−63570.3	−2.70728
$821$	7885.93	0.335226	0.167613	−	0.985853i	$-0.446394\pi$
$821$	7885.93	0.335226	0.167613	+	0.985853i	$0.446394\pi$
$822$	−7201.05	−0.305554
$823$	45952.2	1.94628	0.973142	−	0.230207i	$-0.0739402\pi$
$823$	45952.2	1.94628	0.973142	+	0.230207i	$0.0739402\pi$
$824$	−3167.54	−0.133916
$825$	20877.6	0.881049
$826$	−1128.67	−0.0475443
$827$	10754.8	0.452213	0.226107	−	0.974103i	$-0.427400\pi$
$827$	10754.8	0.452213	0.226107	+	0.974103i	$0.427400\pi$
$828$	−43401.5	−1.82162
$829$	23007.3	0.963906	0.481953	−	0.876197i	$-0.339928\pi$
$829$	23007.3	0.963906	0.481953	+	0.876197i	$0.339928\pi$
$830$	−59567.8	−2.49112
$831$	−27451.7	−1.14596
$832$	0	0
$833$	9799.49	0.407602
$834$	40943.8	1.69996
$835$	−33404.3	−1.38444
$836$	−11537.6	−0.477318
$837$	−27452.7	−1.13370
$838$	24269.3	1.00044
$839$	26146.5	1.07590	0.537949	−	0.842977i	$-0.319199\pi$
$839$	26146.5	1.07590	0.537949	+	0.842977i	$0.319199\pi$
$840$	14899.8	0.612013
$841$	−24283.6	−0.995680
$842$	−15364.1	−0.628837
$843$	−10397.3	−0.424793
$844$	−18797.7	−0.766637
$845$	0	0
$846$	−12777.6	−0.519269
$847$	−1792.27	−0.0727075
$848$	−9606.31	−0.389012
$849$	−47337.8	−1.91358
$850$	76805.2	3.09929
$851$	−37885.0	−1.52606
$852$	10745.1	0.432067
$853$	19146.9	0.768553	0.384277	−	0.923218i	$-0.374451\pi$
$853$	19146.9	0.768553	0.384277	+	0.923218i	$0.374451\pi$
$854$	−33855.6	−1.35658
$855$	−83679.6	−3.34711
$856$	4983.20	0.198975
$857$	30715.8	1.22431	0.612154	−	0.790739i	$-0.290303\pi$
$857$	30715.8	1.22431	0.612154	+	0.790739i	$0.290303\pi$
$858$	0	0
$859$	−1618.21	−0.0642755	−0.0321377	−	0.999483i	$-0.510232\pi$
$859$	−1618.21	−0.0642755	−0.0321377	+	0.999483i	$0.510232\pi$
$860$	−51140.7	−2.02777
$861$	42876.8	1.69714
$862$	62847.9	2.48330
$863$	−16781.8	−0.661946	−0.330973	−	0.943640i	$-0.607377\pi$
$863$	−16781.8	−0.661946	−0.330973	+	0.943640i	$0.607377\pi$
$864$	−28311.2	−1.11478
$865$	67450.7	2.65132
$866$	−34191.0	−1.34164
$867$	−11269.2	−0.441434
$868$	−35395.7	−1.38411
$869$	−12130.8	−0.473542
$870$	−6661.79	−0.259604
$871$	0	0
$872$	−1588.92	−0.0617058
$873$	−17999.9	−0.697830
$874$	51800.7	2.00479
$875$	29701.8	1.14755
$876$	−29136.1	−1.12376
$877$	−29546.8	−1.13766	−0.568828	−	0.822456i	$-0.692603\pi$
$877$	−29546.8	−1.13766	−0.568828	+	0.822456i	$0.692603\pi$
$878$	−4167.68	−0.160196
$879$	29113.5	1.11715
$880$	−10214.3	−0.391278
$881$	10618.3	0.406059	0.203030	−	0.979173i	$-0.434921\pi$
$881$	10618.3	0.406059	0.203030	+	0.979173i	$0.434921\pi$
$882$	20901.6	0.797954
$883$	28816.4	1.09824	0.549121	−	0.835743i	$-0.314962\pi$
$883$	28816.4	1.09824	0.549121	+	0.835743i	$0.314962\pi$
$884$	0	0
$885$	−2817.78	−0.107027
$886$	−49699.3	−1.88452
$887$	15642.7	0.592143	0.296072	−	0.955166i	$-0.404323\pi$
$887$	15642.7	0.592143	0.296072	+	0.955166i	$0.404323\pi$
$888$	17934.1	0.677736
$889$	13897.3	0.524298
$890$	68241.6	2.57019
$891$	2083.58	0.0783418
$892$	22393.0	0.840552
$893$	8298.60	0.310977
$894$	−104011.	−3.89111
$895$	−30218.9	−1.12861
$896$	−12080.0	−0.450405
$897$	0	0
$898$	−58049.3	−2.15716
$899$	2568.54	0.0952898
$900$	89144.3	3.30164
$901$	−15481.0	−0.572416
$902$	16252.2	0.599931
$903$	34493.3	1.27117
$904$	6194.36	0.227900
$905$	−48284.6	−1.77352
$906$	−7326.87	−0.268674
$907$	2735.38	0.100140	0.0500699	−	0.998746i	$-0.484056\pi$
$907$	2735.38	0.100140	0.0500699	+	0.998746i	$0.484056\pi$
$908$	−9314.64	−0.340437
$909$	37010.0	1.35043
$910$	0	0
$911$	−45895.4	−1.66914	−0.834568	−	0.550905i	$-0.814283\pi$
$911$	−45895.4	−1.66914	−0.834568	+	0.550905i	$0.814283\pi$
$912$	44349.6	1.61027
$913$	8286.93	0.300391
$914$	32043.3	1.15963
$915$	−84521.8	−3.05378
$916$	−18754.8	−0.676501
$917$	10058.2	0.362215
$918$	−36440.3	−1.31014
$919$	11918.2	0.427797	0.213898	−	0.976856i	$-0.431384\pi$
$919$	11918.2	0.427797	0.213898	+	0.976856i	$0.431384\pi$
$920$	−13797.9	−0.494460
$921$	18012.8	0.644455
$922$	−19509.7	−0.696875
$923$	0	0
$924$	−12771.4	−0.454705
$925$	77813.7	2.76594
$926$	−65125.8	−2.31120
$927$	19691.7	0.697691
$928$	2648.86	0.0936994
$929$	−11046.0	−0.390105	−0.195052	−	0.980793i	$-0.562488\pi$
$929$	−11046.0	−0.390105	−0.195052	+	0.980793i	$0.562488\pi$
$930$	−162391.	−5.72583
$931$	−13574.9	−0.477874
$932$	−48624.7	−1.70896
$933$	53546.6	1.87893
$934$	26179.4	0.917147
$935$	−16460.8	−0.575751
$936$	0	0
$937$	43996.1	1.53393	0.766964	−	0.641691i	$-0.221767\pi$
$937$	43996.1	1.53393	0.766964	+	0.641691i	$0.221767\pi$
$938$	−46819.9	−1.62977
$939$	−72240.6	−2.51063
$940$	−13619.4	−0.472570
$941$	54071.6	1.87320	0.936601	−	0.350397i	$-0.113953\pi$
$941$	54071.6	1.87320	0.936601	+	0.350397i	$0.113953\pi$
$942$	−92457.0	−3.19789
$943$	−39705.9	−1.37116
$944$	894.862	0.0308531
$945$	−30672.4	−1.05584
$946$	13074.4	0.449352
$947$	−13456.4	−0.461746	−0.230873	−	0.972984i	$-0.574158\pi$
$947$	−13456.4	−0.461746	−0.230873	+	0.972984i	$0.574158\pi$
$948$	−86441.4	−2.96148
$949$	0	0
$950$	−106396.	−3.63362
$951$	−10744.3	−0.366360
$952$	−7625.55	−0.259607
$953$	−16315.5	−0.554575	−0.277287	−	0.960787i	$-0.589435\pi$
$953$	−16315.5	−0.554575	−0.277287	+	0.960787i	$0.589435\pi$
$954$	−33019.9	−1.12061
$955$	−77734.5	−2.63396
$956$	21431.8	0.725056
$957$	926.773	0.0313044
$958$	−45007.3	−1.51787
$959$	3102.08	0.104454
$960$	−106497.	−3.58041
$961$	32821.0	1.10171
$962$	0	0
$963$	−30979.1	−1.03664
$964$	2495.44	0.0833743
$965$	−25193.4	−0.840420
$966$	57339.8	1.90981
$967$	9095.06	0.302458	0.151229	−	0.988499i	$-0.451677\pi$
$967$	9095.06	0.302458	0.151229	+	0.988499i	$0.451677\pi$
$968$	−785.689	−0.0260878
$969$	71471.4	2.36945
$970$	−35257.8	−1.16707
$971$	−8190.65	−0.270701	−0.135350	−	0.990798i	$-0.543216\pi$
$971$	−8190.65	−0.270701	−0.135350	+	0.990798i	$0.543216\pi$
$972$	43136.5	1.42346
$973$	−17637.9	−0.581134
$974$	14353.2	0.472183
$975$	0	0
$976$	26842.2	0.880326
$977$	−60696.6	−1.98757	−0.993786	−	0.111310i	$-0.964495\pi$
$977$	−60696.6	−1.98757	−0.993786	+	0.111310i	$0.964495\pi$
$978$	87249.6	2.85269
$979$	−9493.62	−0.309926
$980$	22278.7	0.726192
$981$	9877.84	0.321483
$982$	−45537.8	−1.47981
$983$	−42736.7	−1.38666	−0.693331	−	0.720619i	$-0.743858\pi$
$983$	−42736.7	−1.38666	−0.693331	+	0.720619i	$0.743858\pi$
$984$	18796.1	0.608942
$985$	−77707.1	−2.51366
$986$	3409.44	0.110120
$987$	9185.98	0.296244
$988$	0	0
$989$	−31942.4	−1.02701
$990$	−35109.9	−1.12714
$991$	−16959.9	−0.543643	−0.271821	−	0.962348i	$-0.587626\pi$
$991$	−16959.9	−0.543643	−0.271821	+	0.962348i	$0.587626\pi$
$992$	64570.0	2.06663
$993$	69776.1	2.22989
$994$	−8506.32	−0.271433
$995$	86835.9	2.76672
$996$	59051.0	1.87862
$997$	−44258.0	−1.40588	−0.702942	−	0.711247i	$-0.748131\pi$
$997$	−44258.0	−1.40588	−0.702942	+	0.711247i	$0.748131\pi$
$998$	32969.6	1.04573
$999$	−36918.8	−1.16923

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-4.18927 q^{2} -8.20774 q^{3} +9.54998 q^{4} -18.8743 q^{5} +34.3844 q^{6} -14.8122 q^{7} -6.49330 q^{8} +40.3670 q^{9} +O(q^{10})\)	\(q-4.18927 q^{2} -8.20774 q^{3} +9.54998 q^{4} -18.8743 q^{5} +34.3844 q^{6} -14.8122 q^{7} -6.49330 q^{8} +40.3670 q^{9} +79.0697 q^{10} -11.0000 q^{11} -78.3838 q^{12} +62.0522 q^{14} +154.916 q^{15} -49.1977 q^{16} -79.2843 q^{17} -169.108 q^{18} +109.830 q^{19} -180.250 q^{20} +121.574 q^{21} +46.0820 q^{22} -112.584 q^{23} +53.2953 q^{24} +231.241 q^{25} -109.713 q^{27} -141.456 q^{28} +10.2650 q^{29} -648.984 q^{30} +250.224 q^{31} +258.049 q^{32} +90.2851 q^{33} +332.143 q^{34} +279.570 q^{35} +385.504 q^{36} +336.505 q^{37} -460.108 q^{38} +122.557 q^{40} +352.679 q^{41} -509.308 q^{42} +283.721 q^{43} -105.050 q^{44} -761.900 q^{45} +471.644 q^{46} +75.5585 q^{47} +403.802 q^{48} -123.599 q^{49} -968.731 q^{50} +650.745 q^{51} +195.259 q^{53} +459.615 q^{54} +207.618 q^{55} +96.1799 q^{56} -901.458 q^{57} -43.0027 q^{58} -18.1891 q^{59} +1479.44 q^{60} -545.599 q^{61} -1048.26 q^{62} -597.923 q^{63} -687.454 q^{64} -378.229 q^{66} -754.524 q^{67} -757.164 q^{68} +924.058 q^{69} -1171.20 q^{70} -137.083 q^{71} -262.115 q^{72} +371.711 q^{73} -1409.71 q^{74} -1897.97 q^{75} +1048.88 q^{76} +162.934 q^{77} +1102.80 q^{79} +928.574 q^{80} -189.416 q^{81} -1477.47 q^{82} -753.357 q^{83} +1161.03 q^{84} +1496.44 q^{85} -1188.58 q^{86} -84.2521 q^{87} +71.4263 q^{88} +863.056 q^{89} +3191.80 q^{90} -1075.17 q^{92} -2053.77 q^{93} -316.535 q^{94} -2072.97 q^{95} -2118.00 q^{96} -445.908 q^{97} +517.791 q^{98} -444.037 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9}+O(q^{10}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9	\( 17 q + 4 q^{2} - 6 q^{3} + 78 q^{4} + 16 q^{5} + 14 q^{6} - 6 q^{7} + 63 q^{8} + 135 q^{9} + 2 q^{10} - 187 q^{11} - 95 q^{12} - 60 q^{14} - 28 q^{15} + 350 q^{16} + 118 q^{17} + 478 q^{18} + 403 q^{19} + 98 q^{20} + 220 q^{21} - 44 q^{22} - 215 q^{23} + 26 q^{24} + 319 q^{25} - 384 q^{27} - 396 q^{28} - 7 q^{29} - 1269 q^{30} + 682 q^{31} + 813 q^{32} + 66 q^{33} + 738 q^{34} + 10 q^{35} + 560 q^{36} + 1084 q^{37} + 410 q^{38} + 95 q^{40} + 240 q^{41} + 393 q^{42} - 435 q^{43} - 858 q^{44} + 1242 q^{45} + 1671 q^{46} + 549 q^{47} + 894 q^{48} + 403 q^{49} - 651 q^{50} + 1552 q^{51} - 566 q^{53} + 311 q^{54} - 176 q^{55} - 1925 q^{56} - 534 q^{57} + 618 q^{58} + 2010 q^{59} - 411 q^{60} + 460 q^{61} - 823 q^{62} + 820 q^{63} + 3171 q^{64} - 154 q^{66} - 232 q^{67} + 1795 q^{68} - 1608 q^{69} + 207 q^{70} + 489 q^{71} + 2556 q^{72} + 290 q^{73} + 2653 q^{74} - 2852 q^{75} + 2421 q^{76} + 66 q^{77} - 732 q^{79} + 4915 q^{80} + 2393 q^{81} - 1772 q^{82} - 117 q^{83} + 4161 q^{84} + 4858 q^{85} + 1034 q^{86} + 3032 q^{87} - 693 q^{88} + 4113 q^{89} + 15145 q^{90} - 3554 q^{92} + 802 q^{93} + 2325 q^{94} - 3924 q^{95} + 2601 q^{96} + 2793 q^{97} + 533 q^{98} - 1485 q^{99}+O(q^{100}) \) 17 * q + 4 * q^2 - 6 * q^3 + 78 * q^4 + 16 * q^5 + 14 * q^6 - 6 * q^7 + 63 * q^8 + 135 * q^9 + 2 * q^10 - 187 * q^11 - 95 * q^12 - 60 * q^14 - 28 * q^15 + 350 * q^16 + 118 * q^17 + 478 * q^18 + 403 * q^19 + 98 * q^20 + 220 * q^21 - 44 * q^22 - 215 * q^23 + 26 * q^24 + 319 * q^25 - 384 * q^27 - 396 * q^28 - 7 * q^29 - 1269 * q^30 + 682 * q^31 + 813 * q^32 + 66 * q^33 + 738 * q^34 + 10 * q^35 + 560 * q^36 + 1084 * q^37 + 410 * q^38 + 95 * q^40 + 240 * q^41 + 393 * q^42 - 435 * q^43 - 858 * q^44 + 1242 * q^45 + 1671 * q^46 + 549 * q^47 + 894 * q^48 + 403 * q^49 - 651 * q^50 + 1552 * q^51 - 566 * q^53 + 311 * q^54 - 176 * q^55 - 1925 * q^56 - 534 * q^57 + 618 * q^58 + 2010 * q^59 - 411 * q^60 + 460 * q^61 - 823 * q^62 + 820 * q^63 + 3171 * q^64 - 154 * q^66 - 232 * q^67 + 1795 * q^68 - 1608 * q^69 + 207 * q^70 + 489 * q^71 + 2556 * q^72 + 290 * q^73 + 2653 * q^74 - 2852 * q^75 + 2421 * q^76 + 66 * q^77 - 732 * q^79 + 4915 * q^80 + 2393 * q^81 - 1772 * q^82 - 117 * q^83 + 4161 * q^84 + 4858 * q^85 + 1034 * q^86 + 3032 * q^87 - 693 * q^88 + 4113 * q^89 + 15145 * q^90 - 3554 * q^92 + 802 * q^93 + 2325 * q^94 - 3924 * q^95 + 2601 * q^96 + 2793 * q^97 + 533 * q^98 - 1485 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

Properties

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