LMFDB - Embedded newform 1859.2.a.l.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1859,2,Mod(1,1859)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.6.28561300.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 9x^{4} - x^{3} + 22x^{2} + 4x - 12 $ x^6 - 9x^4 - x^3 + 22x^2 + 4*x - 12
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 143)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$-1.08549$ 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)

$f(q)$	$=$	$q+1.82172 q^{2} +3.11527 q^{3} +1.31865 q^{4} -0.0854874 q^{5} +5.67515 q^{6} +4.51942 q^{7} -1.24122 q^{8} +6.70494 q^{9} +O(q^{10})$	\(q+1.82172 q^{2} +3.11527 q^{3} +1.31865 q^{4} -0.0854874 q^{5} +5.67515 q^{6} +4.51942 q^{7} -1.24122 q^{8} +6.70494 q^{9} -0.155734 q^{10} +1.00000 q^{11} +4.10797 q^{12} +8.23310 q^{14} -0.266317 q^{15} -4.89846 q^{16} -4.09273 q^{17} +12.2145 q^{18} -2.67659 q^{19} -0.112728 q^{20} +14.0792 q^{21} +1.82172 q^{22} -2.41220 q^{23} -3.86675 q^{24} -4.99269 q^{25} +11.5419 q^{27} +5.95954 q^{28} -8.74853 q^{29} -0.485154 q^{30} -0.664547 q^{31} -6.44117 q^{32} +3.11527 q^{33} -7.45579 q^{34} -0.386353 q^{35} +8.84149 q^{36} +0.935625 q^{37} -4.87598 q^{38} +0.106109 q^{40} +1.80729 q^{41} +25.6484 q^{42} -0.969395 q^{43} +1.31865 q^{44} -0.573188 q^{45} -4.39434 q^{46} -0.118639 q^{47} -15.2600 q^{48} +13.4251 q^{49} -9.09527 q^{50} -12.7500 q^{51} +2.80455 q^{53} +21.0261 q^{54} -0.0854874 q^{55} -5.60959 q^{56} -8.33830 q^{57} -15.9373 q^{58} -3.17927 q^{59} -0.351179 q^{60} -0.216814 q^{61} -1.21062 q^{62} +30.3024 q^{63} -1.93706 q^{64} +5.67515 q^{66} +7.51367 q^{67} -5.39689 q^{68} -7.51465 q^{69} -0.703826 q^{70} +14.5412 q^{71} -8.32231 q^{72} +4.37905 q^{73} +1.70444 q^{74} -15.5536 q^{75} -3.52949 q^{76} +4.51942 q^{77} -14.5600 q^{79} +0.418757 q^{80} +15.8414 q^{81} +3.29238 q^{82} +8.24028 q^{83} +18.5656 q^{84} +0.349877 q^{85} -1.76596 q^{86} -27.2541 q^{87} -1.24122 q^{88} -10.0440 q^{89} -1.04419 q^{90} -3.18085 q^{92} -2.07025 q^{93} -0.216126 q^{94} +0.228814 q^{95} -20.0660 q^{96} -0.407962 q^{97} +24.4568 q^{98} +6.70494 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	$ 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} - 3 q^{10} + 6 q^{11} - 17 q^{12} + 12 q^{14} - 4 q^{15} + 8 q^{16} + 2 q^{17} - 6 q^{18} + 10 q^{19} + 15 q^{20} + 12 q^{21} + 3 q^{23} + 14 q^{24} - 6 q^{25} + 10 q^{27} + 16 q^{28} + 3 q^{29} + 19 q^{30} + 5 q^{31} - q^{32} + q^{33} - 5 q^{34} - 13 q^{35} + 20 q^{36} + 25 q^{37} - 27 q^{38} - 8 q^{40} + 24 q^{41} + 13 q^{42} - 8 q^{43} + 8 q^{44} + 27 q^{45} + 18 q^{46} + 10 q^{47} - 28 q^{48} - q^{49} - 26 q^{50} - 17 q^{51} + 10 q^{53} + 47 q^{54} + 6 q^{55} + 15 q^{56} + 6 q^{58} - 4 q^{59} - 61 q^{60} - 21 q^{61} - 5 q^{62} + 6 q^{63} - 27 q^{64} + 12 q^{66} + 21 q^{67} + 14 q^{68} + 5 q^{69} + 31 q^{70} - 3 q^{71} - 50 q^{72} + 13 q^{73} - 38 q^{74} - 23 q^{75} + 8 q^{76} + 3 q^{77} - 4 q^{79} + 44 q^{80} + 34 q^{81} - 33 q^{82} + 8 q^{83} + 47 q^{84} - 13 q^{85} - 11 q^{86} - 51 q^{87} - 3 q^{88} - 9 q^{89} - 70 q^{90} + 15 q^{92} - 21 q^{93} + 10 q^{94} + 27 q^{95} - 19 q^{96} + 15 q^{97} + 21 q^{98} + 7 q^{99}+O(q^{100}) $ 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 - 3 * q^10 + 6 * q^11 - 17 * q^12 + 12 * q^14 - 4 * q^15 + 8 * q^16 + 2 * q^17 - 6 * q^18 + 10 * q^19 + 15 * q^20 + 12 * q^21 + 3 * q^23 + 14 * q^24 - 6 * q^25 + 10 * q^27 + 16 * q^28 + 3 * q^29 + 19 * q^30 + 5 * q^31 - q^32 + q^33 - 5 * q^34 - 13 * q^35 + 20 * q^36 + 25 * q^37 - 27 * q^38 - 8 * q^40 + 24 * q^41 + 13 * q^42 - 8 * q^43 + 8 * q^44 + 27 * q^45 + 18 * q^46 + 10 * q^47 - 28 * q^48 - q^49 - 26 * q^50 - 17 * q^51 + 10 * q^53 + 47 * q^54 + 6 * q^55 + 15 * q^56 + 6 * q^58 - 4 * q^59 - 61 * q^60 - 21 * q^61 - 5 * q^62 + 6 * q^63 - 27 * q^64 + 12 * q^66 + 21 * q^67 + 14 * q^68 + 5 * q^69 + 31 * q^70 - 3 * q^71 - 50 * q^72 + 13 * q^73 - 38 * q^74 - 23 * q^75 + 8 * q^76 + 3 * q^77 - 4 * q^79 + 44 * q^80 + 34 * q^81 - 33 * q^82 + 8 * q^83 + 47 * q^84 - 13 * q^85 - 11 * q^86 - 51 * q^87 - 3 * q^88 - 9 * q^89 - 70 * q^90 + 15 * q^92 - 21 * q^93 + 10 * q^94 + 27 * q^95 - 19 * q^96 + 15 * q^97 + 21 * q^98 + 7 * 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 $

$2$	1.82172	1.28815	0.644074	−	0.764963i	$-0.277243\pi$
$2$	1.82172	1.28815	0.644074	+	0.764963i	$0.277243\pi$
$3$	3.11527	1.79860	0.899302	−	0.437327i	$-0.144075\pi$
$3$	3.11527	1.79860	0.899302	+	0.437327i	$0.144075\pi$
$4$	1.31865	0.659327
$5$	−0.0854874	−0.0382311	−0.0191156	−	0.999817i	$-0.506085\pi$
$5$	−0.0854874	−0.0382311	−0.0191156	+	0.999817i	$0.506085\pi$
$6$	5.67515	2.31687
$7$	4.51942	1.70818	0.854089	−	0.520127i	$-0.174115\pi$
$7$	4.51942	1.70818	0.854089	+	0.520127i	$0.174115\pi$
$8$	−1.24122	−0.438838
$9$	6.70494	2.23498
$10$	−0.155734	−0.0492474
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	4.10797	1.18587
$13$	0	0
$13$	0	0
$14$	8.23310	2.20039
$15$	−0.266317	−0.0687627
$16$	−4.89846	−1.22462
$17$	−4.09273	−0.992632	−0.496316	−	0.868142i	$-0.665314\pi$
$17$	−4.09273	−0.992632	−0.496316	+	0.868142i	$0.665314\pi$
$18$	12.2145	2.87898
$19$	−2.67659	−0.614051	−0.307025	−	0.951701i	$-0.599334\pi$
$19$	−2.67659	−0.614051	−0.307025	+	0.951701i	$0.599334\pi$
$20$	−0.112728	−0.0252068
$21$	14.0792	3.07234
$22$	1.82172	0.388391
$23$	−2.41220	−0.502978	−0.251489	−	0.967860i	$-0.580920\pi$
$23$	−2.41220	−0.502978	−0.251489	+	0.967860i	$0.580920\pi$
$24$	−3.86675	−0.789296
$25$	−4.99269	−0.998538
$26$	0	0
$27$	11.5419	2.22124
$28$	5.95954	1.12625
$29$	−8.74853	−1.62456	−0.812280	−	0.583267i	$-0.801774\pi$
$29$	−8.74853	−1.62456	−0.812280	+	0.583267i	$0.801774\pi$
$30$	−0.485154	−0.0885766
$31$	−0.664547	−0.119356	−0.0596781	−	0.998218i	$-0.519007\pi$
$31$	−0.664547	−0.119356	−0.0596781	+	0.998218i	$0.519007\pi$
$32$	−6.44117	−1.13865
$33$	3.11527	0.542300
$34$	−7.45579	−1.27866
$35$	−0.386353	−0.0653056
$36$	8.84149	1.47358
$37$	0.935625	0.153816	0.0769079	−	0.997038i	$-0.475495\pi$
$37$	0.935625	0.153816	0.0769079	+	0.997038i	$0.475495\pi$
$38$	−4.87598	−0.790989
$39$	0	0
$40$	0.106109	0.0167773
$41$	1.80729	0.282252	0.141126	−	0.989992i	$-0.454928\pi$
$41$	1.80729	0.282252	0.141126	+	0.989992i	$0.454928\pi$
$42$	25.6484	3.95763
$43$	−0.969395	−0.147831	−0.0739157	−	0.997264i	$-0.523550\pi$
$43$	−0.969395	−0.147831	−0.0739157	+	0.997264i	$0.523550\pi$
$44$	1.31865	0.198794
$45$	−0.573188	−0.0854458
$46$	−4.39434	−0.647910
$47$	−0.118639	−0.0173052	−0.00865260	−	0.999963i	$-0.502754\pi$
$47$	−0.118639	−0.0173052	−0.00865260	+	0.999963i	$0.502754\pi$
$48$	−15.2600	−2.20260
$49$	13.4251	1.91787
$50$	−9.09527	−1.28627
$51$	−12.7500	−1.78535
$52$	0	0
$53$	2.80455	0.385234	0.192617	−	0.981274i	$-0.438302\pi$
$53$	2.80455	0.385234	0.192617	+	0.981274i	$0.438302\pi$
$54$	21.0261	2.86129
$55$	−0.0854874	−0.0115271
$56$	−5.60959	−0.749614
$57$	−8.33830	−1.10443
$58$	−15.9373	−2.09268
$59$	−3.17927	−0.413906	−0.206953	−	0.978351i	$-0.566355\pi$
$59$	−3.17927	−0.413906	−0.206953	+	0.978351i	$0.566355\pi$
$60$	−0.351179	−0.0453371
$61$	−0.216814	−0.0277602	−0.0138801	−	0.999904i	$-0.504418\pi$
$61$	−0.216814	−0.0277602	−0.0138801	+	0.999904i	$0.504418\pi$
$62$	−1.21062	−0.153748
$63$	30.3024	3.81774
$64$	−1.93706	−0.242133
$65$	0	0
$66$	5.67515	0.698563
$67$	7.51367	0.917940	0.458970	−	0.888452i	$-0.348218\pi$
$67$	7.51367	0.917940	0.458970	+	0.888452i	$0.348218\pi$
$68$	−5.39689	−0.654468
$69$	−7.51465	−0.904658
$70$	−0.703826	−0.0841233
$71$	14.5412	1.72572	0.862862	−	0.505440i	$-0.168670\pi$
$71$	14.5412	1.72572	0.862862	+	0.505440i	$0.168670\pi$
$72$	−8.32231	−0.980794
$73$	4.37905	0.512528	0.256264	−	0.966607i	$-0.417508\pi$
$73$	4.37905	0.512528	0.256264	+	0.966607i	$0.417508\pi$
$74$	1.70444	0.198138
$75$	−15.5536	−1.79598
$76$	−3.52949	−0.404860
$77$	4.51942	0.515035
$78$	0	0
$79$	−14.5600	−1.63813	−0.819063	−	0.573704i	$-0.805506\pi$
$79$	−14.5600	−1.63813	−0.819063	+	0.573704i	$0.805506\pi$
$80$	0.418757	0.0468184
$81$	15.8414	1.76015
$82$	3.29238	0.363582
$83$	8.24028	0.904488	0.452244	−	0.891894i	$-0.350624\pi$
$83$	8.24028	0.904488	0.452244	+	0.891894i	$0.350624\pi$
$84$	18.5656	2.02567
$85$	0.349877	0.0379494
$86$	−1.76596	−0.190429
$87$	−27.2541	−2.92194
$88$	−1.24122	−0.132315
$89$	−10.0440	−1.06466	−0.532332	−	0.846536i	$-0.678684\pi$
$89$	−10.0440	−1.06466	−0.532332	+	0.846536i	$0.678684\pi$
$90$	−1.04419	−0.110067
$91$	0	0
$92$	−3.18085	−0.331627
$93$	−2.07025	−0.214675
$94$	−0.216126	−0.0222917
$95$	0.228814	0.0234759
$96$	−20.0660	−2.04798
$97$	−0.407962	−0.0414223	−0.0207111	−	0.999786i	$-0.506593\pi$
$97$	−0.407962	−0.0414223	−0.0207111	+	0.999786i	$0.506593\pi$
$98$	24.4568	2.47051
$99$	6.70494	0.673871
$100$	−6.58363	−0.658363
$101$	−6.37674	−0.634509	−0.317255	−	0.948340i	$-0.602761\pi$
$101$	−6.37674	−0.634509	−0.317255	+	0.948340i	$0.602761\pi$
$102$	−23.2268	−2.29980
$103$	5.84829	0.576249	0.288125	−	0.957593i	$-0.406968\pi$
$103$	5.84829	0.576249	0.288125	+	0.957593i	$0.406968\pi$
$104$	0	0
$105$	−1.20360	−0.117459
$106$	5.10909	0.496239
$107$	12.6837	1.22618	0.613088	−	0.790015i	$-0.289927\pi$
$107$	12.6837	1.22618	0.613088	+	0.790015i	$0.289927\pi$
$108$	15.2198	1.46452
$109$	17.2073	1.64816	0.824081	−	0.566472i	$-0.191692\pi$
$109$	17.2073	1.64816	0.824081	+	0.566472i	$0.191692\pi$
$110$	−0.155734	−0.0148486
$111$	2.91473	0.276654
$112$	−22.1382	−2.09186
$113$	0.349551	0.0328830	0.0164415	−	0.999865i	$-0.494766\pi$
$113$	0.349551	0.0328830	0.0164415	+	0.999865i	$0.494766\pi$
$114$	−15.1900	−1.42268
$115$	0.206212	0.0192294
$116$	−11.5363	−1.07112
$117$	0	0
$118$	−5.79173	−0.533172
$119$	−18.4967	−1.69559
$120$	0.330558	0.0301757
$121$	1.00000	0.0909091
$122$	−0.394975	−0.0357593
$123$	5.63022	0.507659
$124$	−0.876307	−0.0786947
$125$	0.854249	0.0764064
$126$	55.2024	4.91782
$127$	15.5150	1.37674	0.688368	−	0.725362i	$-0.258328\pi$
$127$	15.5150	1.37674	0.688368	+	0.725362i	$0.258328\pi$
$128$	9.35355	0.826745
$129$	−3.01993	−0.265890
$130$	0	0
$131$	9.94205	0.868641	0.434321	−	0.900758i	$-0.356989\pi$
$131$	9.94205	0.868641	0.434321	+	0.900758i	$0.356989\pi$
$132$	4.10797	0.357553
$133$	−12.0966	−1.04891
$134$	13.6878	1.18244
$135$	−0.986687	−0.0849205
$136$	5.07998	0.435605
$137$	−7.72047	−0.659604	−0.329802	−	0.944050i	$-0.606982\pi$
$137$	−7.72047	−0.659604	−0.329802	+	0.944050i	$0.606982\pi$
$138$	−13.6896	−1.16533
$139$	−12.9610	−1.09934	−0.549670	−	0.835382i	$-0.685247\pi$
$139$	−12.9610	−1.09934	−0.549670	+	0.835382i	$0.685247\pi$
$140$	−0.509466	−0.0430577
$141$	−0.369592	−0.0311252
$142$	26.4900	2.22299
$143$	0	0
$144$	−32.8439	−2.73699
$145$	0.747889	0.0621088
$146$	7.97738	0.660213
$147$	41.8229	3.44950
$148$	1.23377	0.101415
$149$	−13.8257	−1.13264	−0.566321	−	0.824185i	$-0.691634\pi$
$149$	−13.8257	−1.13264	−0.566321	+	0.824185i	$0.691634\pi$
$150$	−28.3343	−2.31348
$151$	4.68471	0.381236	0.190618	−	0.981664i	$-0.438951\pi$
$151$	4.68471	0.381236	0.190618	+	0.981664i	$0.438951\pi$
$152$	3.32223	0.269469
$153$	−27.4415	−2.21851
$154$	8.23310	0.663442
$155$	0.0568104	0.00456312
$156$	0	0
$157$	10.9832	0.876553	0.438277	−	0.898840i	$-0.355589\pi$
$157$	10.9832	0.876553	0.438277	+	0.898840i	$0.355589\pi$
$158$	−26.5242	−2.11015
$159$	8.73694	0.692884
$160$	0.550639	0.0435318
$161$	−10.9017	−0.859176
$162$	28.8585	2.26734
$163$	7.49111	0.586749	0.293374	−	0.955998i	$-0.405222\pi$
$163$	7.49111	0.586749	0.293374	+	0.955998i	$0.405222\pi$
$164$	2.38319	0.186096
$165$	−0.266317	−0.0207327
$166$	15.0115	1.16512
$167$	7.32765	0.567031	0.283515	−	0.958968i	$-0.408499\pi$
$167$	7.32765	0.567031	0.283515	+	0.958968i	$0.408499\pi$
$168$	−17.4754	−1.34826
$169$	0	0
$170$	0.637376	0.0488845
$171$	−17.9463	−1.37239
$172$	−1.27830	−0.0974692
$173$	6.18947	0.470577	0.235288	−	0.971926i	$-0.424397\pi$
$173$	6.18947	0.470577	0.235288	+	0.971926i	$0.424397\pi$
$174$	−49.6492	−3.76390
$175$	−22.5640	−1.70568
$176$	−4.89846	−0.369235
$177$	−9.90430	−0.744453
$178$	−18.2974	−1.37144
$179$	−6.19336	−0.462914	−0.231457	−	0.972845i	$-0.574349\pi$
$179$	−6.19336	−0.462914	−0.231457	+	0.972845i	$0.574349\pi$
$180$	−0.755836	−0.0563367
$181$	−16.0308	−1.19156	−0.595778	−	0.803149i	$-0.703156\pi$
$181$	−16.0308	−1.19156	−0.595778	+	0.803149i	$0.703156\pi$
$182$	0	0
$183$	−0.675437	−0.0499297
$184$	2.99407	0.220726
$185$	−0.0799842	−0.00588056
$186$	−3.77140	−0.276533
$187$	−4.09273	−0.299290
$188$	−0.156443	−0.0114098
$189$	52.1626	3.79427
$190$	0.416835	0.0302404
$191$	−20.9284	−1.51433	−0.757164	−	0.653225i	$-0.773415\pi$
$191$	−20.9284	−1.51433	−0.757164	+	0.653225i	$0.773415\pi$
$192$	−6.03448	−0.435501
$193$	10.2262	0.736097	0.368049	−	0.929807i	$-0.380026\pi$
$193$	10.2262	0.736097	0.368049	+	0.929807i	$0.380026\pi$
$194$	−0.743191	−0.0533580
$195$	0	0
$196$	17.7031	1.26450
$197$	−14.0497	−1.00100	−0.500499	−	0.865737i	$-0.666850\pi$
$197$	−14.0497	−1.00100	−0.500499	+	0.865737i	$0.666850\pi$
$198$	12.2145	0.868047
$199$	3.84720	0.272720	0.136360	−	0.990659i	$-0.456460\pi$
$199$	3.84720	0.272720	0.136360	+	0.990659i	$0.456460\pi$
$200$	6.19704	0.438197
$201$	23.4071	1.65101
$202$	−11.6166	−0.817342
$203$	−39.5382	−2.77504
$204$	−16.8128	−1.17713
$205$	−0.154501	−0.0107908
$206$	10.6539	0.742295
$207$	−16.1736	−1.12414
$208$	0	0
$209$	−2.67659	−0.185143
$210$	−2.19261	−0.151305
$211$	−16.1699	−1.11318	−0.556592	−	0.830786i	$-0.687891\pi$
$211$	−16.1699	−1.11318	−0.556592	+	0.830786i	$0.687891\pi$
$212$	3.69823	0.253995
$213$	45.2998	3.10389
$214$	23.1060	1.57950
$215$	0.0828711	0.00565176
$216$	−14.3260	−0.974764
$217$	−3.00336	−0.203882
$218$	31.3469	2.12308
$219$	13.6419	0.921836
$220$	−0.112728	−0.00760014
$221$	0	0
$222$	5.30981	0.356371
$223$	15.3485	1.02781	0.513906	−	0.857847i	$-0.328198\pi$
$223$	15.3485	1.02781	0.513906	+	0.857847i	$0.328198\pi$
$224$	−29.1103	−1.94501
$225$	−33.4757	−2.23171
$226$	0.636782	0.0423581
$227$	−24.1479	−1.60275	−0.801376	−	0.598160i	$-0.795899\pi$
$227$	−24.1479	−1.60275	−0.801376	+	0.598160i	$0.795899\pi$
$228$	−10.9953	−0.728183
$229$	24.3619	1.60988	0.804941	−	0.593354i	$-0.202197\pi$
$229$	24.3619	1.60988	0.804941	+	0.593354i	$0.202197\pi$
$230$	0.375661	0.0247703
$231$	14.0792	0.926345
$232$	10.8589	0.712919
$233$	−2.52952	−0.165714	−0.0828570	−	0.996561i	$-0.526404\pi$
$233$	−2.52952	−0.165714	−0.0828570	+	0.996561i	$0.526404\pi$
$234$	0	0
$235$	0.0101421	0.000661598 0
$236$	−4.19235	−0.272899
$237$	−45.3583	−2.94634
$238$	−33.6958	−2.18417
$239$	0.271160	0.0175399	0.00876993	−	0.999962i	$-0.497208\pi$
$239$	0.271160	0.0175399	0.00876993	+	0.999962i	$0.497208\pi$
$240$	1.30454	0.0842078
$241$	−3.96510	−0.255415	−0.127707	−	0.991812i	$-0.540762\pi$
$241$	−3.96510	−0.255415	−0.127707	+	0.991812i	$0.540762\pi$
$242$	1.82172	0.117104
$243$	14.7245	0.944578
$244$	−0.285903	−0.0183031
$245$	−1.14768	−0.0733225
$246$	10.2567	0.653941
$247$	0	0
$248$	0.824850	0.0523780
$249$	25.6707	1.62682
$250$	1.55620	0.0984228
$251$	24.6649	1.55684	0.778419	−	0.627746i	$-0.216022\pi$
$251$	24.6649	1.55684	0.778419	+	0.627746i	$0.216022\pi$
$252$	39.9583	2.51714
$253$	−2.41220	−0.151653
$254$	28.2640	1.77344
$255$	1.08996	0.0682560
$256$	20.9137	1.30710
$257$	−23.5033	−1.46610	−0.733048	−	0.680177i	$-0.761903\pi$
$257$	−23.5033	−1.46610	−0.733048	+	0.680177i	$0.761903\pi$
$258$	−5.50146	−0.342506
$259$	4.22848	0.262745
$260$	0	0
$261$	−58.6583	−3.63086
$262$	18.1116	1.11894
$263$	−2.94763	−0.181758	−0.0908792	−	0.995862i	$-0.528968\pi$
$263$	−2.94763	−0.181758	−0.0908792	+	0.995862i	$0.528968\pi$
$264$	−3.86675	−0.237982
$265$	−0.239754	−0.0147279
$266$	−22.0366	−1.35115
$267$	−31.2899	−1.91491
$268$	9.90792	0.605222
$269$	−9.03305	−0.550755	−0.275378	−	0.961336i	$-0.588803\pi$
$269$	−9.03305	−0.550755	−0.275378	+	0.961336i	$0.588803\pi$
$270$	−1.79746	−0.109390
$271$	−28.3089	−1.71964	−0.859821	−	0.510595i	$-0.829425\pi$
$271$	−28.3089	−1.71964	−0.859821	+	0.510595i	$0.829425\pi$
$272$	20.0481	1.21559
$273$	0	0
$274$	−14.0645	−0.849668
$275$	−4.99269	−0.301071
$276$	−9.90922	−0.596465
$277$	−20.6956	−1.24348	−0.621740	−	0.783224i	$-0.713574\pi$
$277$	−20.6956	−1.24348	−0.621740	+	0.783224i	$0.713574\pi$
$278$	−23.6113	−1.41611
$279$	−4.45575	−0.266758
$280$	0.479550	0.0286586
$281$	−11.2428	−0.670688	−0.335344	−	0.942096i	$-0.608852\pi$
$281$	−11.2428	−0.670688	−0.335344	+	0.942096i	$0.608852\pi$
$282$	−0.673291	−0.0400939
$283$	32.3981	1.92587	0.962933	−	0.269740i	$-0.0869376\pi$
$283$	32.3981	1.92587	0.962933	+	0.269740i	$0.0869376\pi$
$284$	19.1748	1.13782
$285$	0.712820	0.0422238
$286$	0	0
$287$	8.16791	0.482136
$288$	−43.1876	−2.54485
$289$	−0.249597	−0.0146822
$290$	1.36244	0.0800054
$291$	−1.27091	−0.0745023
$292$	5.77444	0.337924
$293$	−21.1015	−1.23276	−0.616381	−	0.787448i	$-0.711402\pi$
$293$	−21.1015	−1.23276	−0.616381	+	0.787448i	$0.711402\pi$
$294$	76.1895	4.44346
$295$	0.271788	0.0158241
$296$	−1.16132	−0.0675003
$297$	11.5419	0.669729
$298$	−25.1864	−1.45901
$299$	0	0
$300$	−20.5098	−1.18413
$301$	−4.38110	−0.252522
$302$	8.53422	0.491089
$303$	−19.8653	−1.14123
$304$	13.1111	0.751976
$305$	0.0185349	0.00106131
$306$	−49.9906	−2.85777
$307$	−1.13214	−0.0646144	−0.0323072	−	0.999478i	$-0.510285\pi$
$307$	−1.13214	−0.0646144	−0.0323072	+	0.999478i	$0.510285\pi$
$308$	5.95954	0.339576
$309$	18.2190	1.03644
$310$	0.103492	0.00587798
$311$	26.4303	1.49873	0.749363	−	0.662159i	$-0.230360\pi$
$311$	26.4303	1.49873	0.749363	+	0.662159i	$0.230360\pi$
$312$	0	0
$313$	7.85597	0.444046	0.222023	−	0.975041i	$-0.428734\pi$
$313$	7.85597	0.444046	0.222023	+	0.975041i	$0.428734\pi$
$314$	20.0083	1.12913
$315$	−2.59047	−0.145957
$316$	−19.1996	−1.08006
$317$	−5.80743	−0.326177	−0.163089	−	0.986611i	$-0.552146\pi$
$317$	−5.80743	−0.326177	−0.163089	+	0.986611i	$0.552146\pi$
$318$	15.9162	0.892538
$319$	−8.74853	−0.489824
$320$	0.165594	0.00925701
$321$	39.5131	2.20541
$322$	−19.8598	−1.10675
$323$	10.9545	0.609526
$324$	20.8893	1.16051
$325$	0	0
$326$	13.6467	0.755820
$327$	53.6055	2.96439
$328$	−2.24325	−0.123863
$329$	−0.536177	−0.0295604
$330$	−0.485154	−0.0267068
$331$	35.9845	1.97788	0.988942	−	0.148302i	$-0.0473806\pi$
$331$	35.9845	1.97788	0.988942	+	0.148302i	$0.0473806\pi$
$332$	10.8661	0.596353
$333$	6.27331	0.343775
$334$	13.3489	0.730420
$335$	−0.642324	−0.0350939
$336$	−68.9665	−3.76243
$337$	14.1266	0.769524	0.384762	−	0.923016i	$-0.374283\pi$
$337$	14.1266	0.769524	0.384762	+	0.923016i	$0.374283\pi$
$338$	0	0
$339$	1.08895	0.0591434
$340$	0.461366	0.0250211
$341$	−0.664547	−0.0359872
$342$	−32.6931	−1.76784
$343$	29.0378	1.56789
$344$	1.20323	0.0648740
$345$	0.642408	0.0345861
$346$	11.2755	0.606173
$347$	−7.70722	−0.413745	−0.206873	−	0.978368i	$-0.566329\pi$
$347$	−7.70722	−0.413745	−0.206873	+	0.978368i	$0.566329\pi$
$348$	−35.9387	−1.92651
$349$	−4.44535	−0.237954	−0.118977	−	0.992897i	$-0.537962\pi$
$349$	−4.44535	−0.237954	−0.118977	+	0.992897i	$0.537962\pi$
$350$	−41.1053	−2.19717
$351$	0	0
$352$	−6.44117	−0.343315
$353$	−30.6598	−1.63186	−0.815928	−	0.578154i	$-0.803773\pi$
$353$	−30.6598	−1.63186	−0.815928	+	0.578154i	$0.803773\pi$
$354$	−18.0428	−0.958966
$355$	−1.24309	−0.0659764
$356$	−13.2446	−0.701961
$357$	−57.6224	−3.04970
$358$	−11.2826	−0.596302
$359$	8.40038	0.443355	0.221677	−	0.975120i	$-0.428847\pi$
$359$	8.40038	0.443355	0.221677	+	0.975120i	$0.428847\pi$
$360$	0.711453	0.0374969
$361$	−11.8359	−0.622942
$362$	−29.2035	−1.53490
$363$	3.11527	0.163510
$364$	0	0
$365$	−0.374353	−0.0195945
$366$	−1.23045	−0.0643169
$367$	30.6922	1.60212	0.801060	−	0.598584i	$-0.204270\pi$
$367$	30.6922	1.60212	0.801060	+	0.598584i	$0.204270\pi$
$368$	11.8160	0.615954
$369$	12.1178	0.630827
$370$	−0.145709	−0.00757503
$371$	12.6749	0.658049
$372$	−2.72994	−0.141541
$373$	−13.0202	−0.674158	−0.337079	−	0.941476i	$-0.609439\pi$
$373$	−13.0202	−0.674158	−0.337079	+	0.941476i	$0.609439\pi$
$374$	−7.45579	−0.385530
$375$	2.66122	0.137425
$376$	0.147257	0.00759418
$377$	0	0
$378$	95.0255	4.88759
$379$	0.261814	0.0134485	0.00672424	−	0.999977i	$-0.497860\pi$
$379$	0.261814	0.0134485	0.00672424	+	0.999977i	$0.497860\pi$
$380$	0.301727	0.0154783
$381$	48.3336	2.47620
$382$	−38.1257	−1.95068
$383$	16.0965	0.822490	0.411245	−	0.911525i	$-0.365094\pi$
$383$	16.0965	0.822490	0.411245	+	0.911525i	$0.365094\pi$
$384$	29.1389	1.48699
$385$	−0.386353	−0.0196904
$386$	18.6292	0.948202
$387$	−6.49973	−0.330400
$388$	−0.537960	−0.0273108
$389$	15.7466	0.798383	0.399192	−	0.916867i	$-0.369291\pi$
$389$	15.7466	0.798383	0.399192	+	0.916867i	$0.369291\pi$
$390$	0	0
$391$	9.87246	0.499272
$392$	−16.6635	−0.841636
$393$	30.9722	1.56234
$394$	−25.5945	−1.28943
$395$	1.24469	0.0626274
$396$	8.84149	0.444301
$397$	14.6912	0.737331	0.368666	−	0.929562i	$-0.379815\pi$
$397$	14.6912	0.737331	0.368666	+	0.929562i	$0.379815\pi$
$398$	7.00850	0.351304
$399$	−37.6842	−1.88657
$400$	24.4565	1.22283
$401$	28.1775	1.40712	0.703560	−	0.710636i	$-0.251593\pi$
$401$	28.1775	1.40712	0.703560	+	0.710636i	$0.251593\pi$
$402$	42.6412	2.12675
$403$	0	0
$404$	−8.40871	−0.418349
$405$	−1.35424	−0.0672926
$406$	−72.0275	−3.57466
$407$	0.935625	0.0463772
$408$	15.8255	0.783480
$409$	−21.9248	−1.08411	−0.542057	−	0.840342i	$-0.682354\pi$
$409$	−21.9248	−1.08411	−0.542057	+	0.840342i	$0.682354\pi$
$410$	−0.281457	−0.0139002
$411$	−24.0514	−1.18637
$412$	7.71187	0.379936
$413$	−14.3684	−0.707025
$414$	−29.4638	−1.44806
$415$	−0.704440	−0.0345796
$416$	0	0
$417$	−40.3772	−1.97728
$418$	−4.87598	−0.238492
$419$	0.885713	0.0432699	0.0216350	−	0.999766i	$-0.493113\pi$
$419$	0.885713	0.0432699	0.0216350	+	0.999766i	$0.493113\pi$
$420$	−1.58713	−0.0774438
$421$	15.4292	0.751972	0.375986	−	0.926625i	$-0.377304\pi$
$421$	15.4292	0.751972	0.375986	+	0.926625i	$0.377304\pi$
$422$	−29.4570	−1.43395
$423$	−0.795464	−0.0386768
$424$	−3.48107	−0.169055
$425$	20.4337	0.991181
$426$	82.5235	3.99828
$427$	−0.979875	−0.0474195
$428$	16.7254	0.808450
$429$	0	0
$430$	0.150968	0.00728031
$431$	10.8499	0.522621	0.261311	−	0.965255i	$-0.415845\pi$
$431$	10.8499	0.522621	0.261311	+	0.965255i	$0.415845\pi$
$432$	−56.5375	−2.72016
$433$	−25.6693	−1.23359	−0.616793	−	0.787125i	$-0.711569\pi$
$433$	−25.6693	−1.23359	−0.616793	+	0.787125i	$0.711569\pi$
$434$	−5.47128	−0.262630
$435$	2.32988	0.111709
$436$	22.6905	1.08668
$437$	6.45645	0.308854
$438$	24.8517	1.18746
$439$	9.95109	0.474939	0.237470	−	0.971395i	$-0.423682\pi$
$439$	9.95109	0.474939	0.237470	+	0.971395i	$0.423682\pi$
$440$	0.106109	0.00505854
$441$	90.0145	4.28641
$442$	0	0
$443$	16.9416	0.804918	0.402459	−	0.915438i	$-0.368156\pi$
$443$	16.9416	0.804918	0.402459	+	0.915438i	$0.368156\pi$
$444$	3.84352	0.182405
$445$	0.858637	0.0407033
$446$	27.9606	1.32397
$447$	−43.0707	−2.03717
$448$	−8.75439	−0.413606
$449$	−19.5582	−0.923008	−0.461504	−	0.887138i	$-0.652690\pi$
$449$	−19.5582	−0.923008	−0.461504	+	0.887138i	$0.652690\pi$
$450$	−60.9832	−2.87478
$451$	1.80729	0.0851021
$452$	0.460936	0.0216806
$453$	14.5942	0.685693
$454$	−43.9907	−2.06458
$455$	0	0
$456$	10.3497	0.484668
$457$	11.2470	0.526113	0.263057	−	0.964780i	$-0.415269\pi$
$457$	11.2470	0.526113	0.263057	+	0.964780i	$0.415269\pi$
$458$	44.3806	2.07377
$459$	−47.2378	−2.20487
$460$	0.271923	0.0126785
$461$	−14.8231	−0.690383	−0.345191	−	0.938532i	$-0.612186\pi$
$461$	−14.8231	−0.690383	−0.345191	+	0.938532i	$0.612186\pi$
$462$	25.6484	1.19327
$463$	37.6159	1.74816	0.874079	−	0.485784i	$-0.161466\pi$
$463$	37.6159	1.74816	0.874079	+	0.485784i	$0.161466\pi$
$464$	42.8543	1.98946
$465$	0.176980	0.00820725
$466$	−4.60806	−0.213464
$467$	−16.4512	−0.761272	−0.380636	−	0.924725i	$-0.624295\pi$
$467$	−16.4512	−0.761272	−0.380636	+	0.924725i	$0.624295\pi$
$468$	0	0
$469$	33.9574	1.56801
$470$	0.0184760	0.000852236 0
$471$	34.2156	1.57657
$472$	3.94618	0.181638
$473$	−0.969395	−0.0445728
$474$	−82.6300	−3.79532
$475$	13.3634	0.613153
$476$	−24.3908	−1.11795
$477$	18.8043	0.860991
$478$	0.493976	0.0225939
$479$	7.82896	0.357714	0.178857	−	0.983875i	$-0.442760\pi$
$479$	7.82896	0.357714	0.178857	+	0.983875i	$0.442760\pi$
$480$	1.71539	0.0782965
$481$	0	0
$482$	−7.22330	−0.329012
$483$	−33.9618	−1.54532
$484$	1.31865	0.0599388
$485$	0.0348756	0.00158362
$486$	26.8239	1.21676
$487$	−2.80510	−0.127111	−0.0635555	−	0.997978i	$-0.520244\pi$
$487$	−2.80510	−0.127111	−0.0635555	+	0.997978i	$0.520244\pi$
$488$	0.269115	0.0121823
$489$	23.3369	1.05533
$490$	−2.09075	−0.0944502
$491$	25.5509	1.15309	0.576547	−	0.817064i	$-0.304400\pi$
$491$	25.5509	1.15309	0.576547	+	0.817064i	$0.304400\pi$
$492$	7.42430	0.334713
$493$	35.8053	1.61259
$494$	0	0
$495$	−0.573188	−0.0257629
$496$	3.25526	0.146165
$497$	65.7177	2.94784
$498$	46.7648	2.09558
$499$	−38.5862	−1.72736	−0.863678	−	0.504045i	$-0.831845\pi$
$499$	−38.5862	−1.72736	−0.863678	+	0.504045i	$0.831845\pi$
$500$	1.12646	0.0503768
$501$	22.8277	1.01986
$502$	44.9325	2.00544
$503$	21.5547	0.961079	0.480539	−	0.876973i	$-0.340441\pi$
$503$	21.5547	0.961079	0.480539	+	0.876973i	$0.340441\pi$
$504$	−37.6120	−1.67537
$505$	0.545131	0.0242580
$506$	−4.39434	−0.195352
$507$	0	0
$508$	20.4589	0.907718
$509$	−19.8447	−0.879599	−0.439799	−	0.898096i	$-0.644950\pi$
$509$	−19.8447	−0.879599	−0.439799	+	0.898096i	$0.644950\pi$
$510$	1.98560	0.0879239
$511$	19.7907	0.875490
$512$	19.3916	0.856998
$513$	−30.8929	−1.36395
$514$	−42.8164	−1.88855
$515$	−0.499955	−0.0220307
$516$	−3.98224	−0.175309
$517$	−0.118639	−0.00521772
$518$	7.70309	0.338455
$519$	19.2819	0.846382
$520$	0	0
$521$	17.9303	0.785539	0.392770	−	0.919637i	$-0.371517\pi$
$521$	17.9303	0.785539	0.392770	+	0.919637i	$0.371517\pi$
$522$	−106.859	−4.67709
$523$	27.0417	1.18245	0.591226	−	0.806506i	$-0.298644\pi$
$523$	27.0417	1.18245	0.591226	+	0.806506i	$0.298644\pi$
$524$	13.1101	0.572718
$525$	−70.2932	−3.06785
$526$	−5.36974	−0.234132
$527$	2.71981	0.118477
$528$	−15.2600	−0.664108
$529$	−17.1813	−0.747013
$530$	−0.436763	−0.0189718
$531$	−21.3168	−0.925071
$532$	−15.9512	−0.691573
$533$	0	0
$534$	−57.0013	−2.46669
$535$	−1.08429	−0.0468781
$536$	−9.32612	−0.402827
$537$	−19.2940	−0.832599
$538$	−16.4557	−0.709454
$539$	13.4251	0.578261
$540$	−1.30110	−0.0559903
$541$	0.789746	0.0339538	0.0169769	−	0.999856i	$-0.494596\pi$
$541$	0.789746	0.0339538	0.0169769	+	0.999856i	$0.494596\pi$
$542$	−51.5708	−2.21515
$543$	−49.9402	−2.14314
$544$	26.3619	1.13026
$545$	−1.47101	−0.0630111
$546$	0	0
$547$	10.5588	0.451461	0.225730	−	0.974190i	$-0.427523\pi$
$547$	10.5588	0.451461	0.225730	+	0.974190i	$0.427523\pi$
$548$	−10.1806	−0.434895
$549$	−1.45373	−0.0620436
$550$	−9.09527	−0.387824
$551$	23.4162	0.997563
$552$	9.32735	0.396998
$553$	−65.8026	−2.79821
$554$	−37.7016	−1.60179
$555$	−0.249173	−0.0105768
$556$	−17.0911	−0.724824
$557$	−12.2151	−0.517571	−0.258786	−	0.965935i	$-0.583322\pi$
$557$	−12.2151	−0.517571	−0.258786	+	0.965935i	$0.583322\pi$
$558$	−8.11711	−0.343625
$559$	0	0
$560$	1.89254	0.0799742
$561$	−12.7500	−0.538304
$562$	−20.4812	−0.863945
$563$	−22.1791	−0.934738	−0.467369	−	0.884062i	$-0.654798\pi$
$563$	−22.1791	−0.934738	−0.467369	+	0.884062i	$0.654798\pi$
$564$	−0.487363	−0.0205217
$565$	−0.0298822	−0.00125715
$566$	59.0202	2.48080
$567$	71.5937	3.00665
$568$	−18.0489	−0.757313
$569$	−27.2893	−1.14403	−0.572014	−	0.820244i	$-0.693838\pi$
$569$	−27.2893	−1.14403	−0.572014	+	0.820244i	$0.693838\pi$
$570$	1.29856	0.0543905
$571$	−26.6917	−1.11701	−0.558506	−	0.829500i	$-0.688625\pi$
$571$	−26.6917	−1.11701	−0.558506	+	0.829500i	$0.688625\pi$
$572$	0	0
$573$	−65.1978	−2.72368
$574$	14.8796	0.621063
$575$	12.0434	0.502243
$576$	−12.9879	−0.541161
$577$	−13.8358	−0.575994	−0.287997	−	0.957631i	$-0.592989\pi$
$577$	−13.8358	−0.575994	−0.287997	+	0.957631i	$0.592989\pi$
$578$	−0.454695	−0.0189128
$579$	31.8574	1.32395
$580$	0.986206	0.0409500
$581$	37.2413	1.54503
$582$	−2.31525	−0.0959700
$583$	2.80455	0.116153
$584$	−5.43536	−0.224917
$585$	0	0
$586$	−38.4410	−1.58798
$587$	−15.7220	−0.648918	−0.324459	−	0.945900i	$-0.605182\pi$
$587$	−15.7220	−0.648918	−0.324459	+	0.945900i	$0.605182\pi$
$588$	55.1499	2.27434
$589$	1.77872	0.0732907
$590$	0.495120	0.0203838
$591$	−43.7686	−1.80040
$592$	−4.58312	−0.188365
$593$	−9.78144	−0.401676	−0.200838	−	0.979625i	$-0.564366\pi$
$593$	−9.78144	−0.401676	−0.200838	+	0.979625i	$0.564366\pi$
$594$	21.0261	0.862710
$595$	1.58124	0.0648244
$596$	−18.2312	−0.746781
$597$	11.9851	0.490516
$598$	0	0
$599$	30.1707	1.23274	0.616370	−	0.787456i	$-0.288602\pi$
$599$	30.1707	1.23274	0.616370	+	0.787456i	$0.288602\pi$
$600$	19.3055	0.788142
$601$	−32.6513	−1.33187	−0.665936	−	0.746008i	$-0.731968\pi$
$601$	−32.6513	−1.33187	−0.665936	+	0.746008i	$0.731968\pi$
$602$	−7.98112	−0.325286
$603$	50.3787	2.05158
$604$	6.17751	0.251359
$605$	−0.0854874	−0.00347556
$606$	−36.1889	−1.47008
$607$	−14.0501	−0.570275	−0.285137	−	0.958487i	$-0.592039\pi$
$607$	−14.0501	−0.570275	−0.285137	+	0.958487i	$0.592039\pi$
$608$	17.2403	0.699188
$609$	−123.172	−4.99120
$610$	0.0337654	0.00136712
$611$	0	0
$612$	−36.1858	−1.46272
$613$	−13.8601	−0.559804	−0.279902	−	0.960029i	$-0.590302\pi$
$613$	−13.8601	−0.559804	−0.279902	+	0.960029i	$0.590302\pi$
$614$	−2.06243	−0.0832330
$615$	−0.481313	−0.0194084
$616$	−5.60959	−0.226017
$617$	41.6777	1.67788	0.838941	−	0.544222i	$-0.183175\pi$
$617$	41.6777	1.67788	0.838941	+	0.544222i	$0.183175\pi$
$618$	33.1899	1.33509
$619$	−11.7714	−0.473134	−0.236567	−	0.971615i	$-0.576022\pi$
$619$	−11.7714	−0.473134	−0.236567	+	0.971615i	$0.576022\pi$
$620$	0.0749132	0.00300859
$621$	−27.8413	−1.11723
$622$	48.1486	1.93058
$623$	−45.3931	−1.81863
$624$	0	0
$625$	24.8904	0.995617
$626$	14.3114	0.571997
$627$	−8.33830	−0.333000
$628$	14.4830	0.577935
$629$	−3.82926	−0.152683
$630$	−4.71911	−0.188014
$631$	−36.4625	−1.45155	−0.725775	−	0.687932i	$-0.758519\pi$
$631$	−36.4625	−1.45155	−0.725775	+	0.687932i	$0.758519\pi$
$632$	18.0722	0.718872
$633$	−50.3738	−2.00218
$634$	−10.5795	−0.420165
$635$	−1.32634	−0.0526342
$636$	11.5210	0.456837
$637$	0	0
$638$	−15.9373	−0.630965
$639$	97.4979	3.85696
$640$	−0.799611	−0.0316074
$641$	6.75602	0.266847	0.133423	−	0.991059i	$-0.457403\pi$
$641$	6.75602	0.266847	0.133423	+	0.991059i	$0.457403\pi$
$642$	71.9817	2.84089
$643$	−12.1953	−0.480936	−0.240468	−	0.970657i	$-0.577301\pi$
$643$	−12.1953	−0.480936	−0.240468	+	0.970657i	$0.577301\pi$
$644$	−14.3756	−0.566477
$645$	0.258166	0.0101653
$646$	19.9561	0.785160
$647$	4.44244	0.174650	0.0873252	−	0.996180i	$-0.472168\pi$
$647$	4.44244	0.174650	0.0873252	+	0.996180i	$0.472168\pi$
$648$	−19.6626	−0.772421
$649$	−3.17927	−0.124797
$650$	0	0
$651$	−9.35630	−0.366702
$652$	9.87817	0.386859
$653$	−36.6342	−1.43361	−0.716804	−	0.697275i	$-0.754396\pi$
$653$	−36.6342	−1.43361	−0.716804	+	0.697275i	$0.754396\pi$
$654$	97.6541	3.81858
$655$	−0.849920	−0.0332091
$656$	−8.85296	−0.345650
$657$	29.3612	1.14549
$658$	−0.976762	−0.0380782
$659$	24.2296	0.943853	0.471926	−	0.881638i	$-0.343559\pi$
$659$	24.2296	0.943853	0.471926	+	0.881638i	$0.343559\pi$
$660$	−0.351179	−0.0136696
$661$	21.3719	0.831269	0.415635	−	0.909532i	$-0.363560\pi$
$661$	21.3719	0.831269	0.415635	+	0.909532i	$0.363560\pi$
$662$	65.5535	2.54781
$663$	0	0
$664$	−10.2280	−0.396924
$665$	1.03411	0.0401010
$666$	11.4282	0.442834
$667$	21.1032	0.817118
$668$	9.66263	0.373858
$669$	47.8148	1.84863
$670$	−1.17013	−0.0452062
$671$	−0.216814	−0.00837003
$672$	−90.6866	−3.49831
$673$	−30.4316	−1.17305	−0.586526	−	0.809930i	$-0.699505\pi$
$673$	−30.4316	−1.17305	−0.586526	+	0.809930i	$0.699505\pi$
$674$	25.7346	0.991261
$675$	−57.6251	−2.21799
$676$	0	0
$677$	−8.52439	−0.327619	−0.163809	−	0.986492i	$-0.552378\pi$
$677$	−8.52439	−0.327619	−0.163809	+	0.986492i	$0.552378\pi$
$678$	1.98375	0.0761855
$679$	−1.84375	−0.0707566
$680$	−0.434274	−0.0166537
$681$	−75.2274	−2.88272
$682$	−1.21062	−0.0463569
$683$	−5.00482	−0.191504	−0.0957521	−	0.995405i	$-0.530526\pi$
$683$	−5.00482	−0.191504	−0.0957521	+	0.995405i	$0.530526\pi$
$684$	−23.6650	−0.904853
$685$	0.660003	0.0252174
$686$	52.8986	2.01968
$687$	75.8941	2.89554
$688$	4.74854	0.181037
$689$	0	0
$690$	1.17029	0.0445520
$691$	21.5355	0.819250	0.409625	−	0.912254i	$-0.365660\pi$
$691$	21.5355	0.819250	0.409625	+	0.912254i	$0.365660\pi$
$692$	8.16177	0.310264
$693$	30.3024	1.15109
$694$	−14.0404	−0.532965
$695$	1.10800	0.0420290
$696$	33.8283	1.28226
$697$	−7.39676	−0.280172
$698$	−8.09818	−0.306520
$699$	−7.88014	−0.298054
$700$	−29.7542	−1.12460
$701$	7.82988	0.295731	0.147865	−	0.989008i	$-0.452760\pi$
$701$	7.82988	0.295731	0.147865	+	0.989008i	$0.452760\pi$
$702$	0	0
$703$	−2.50428	−0.0944508
$704$	−1.93706	−0.0730058
$705$	0.0315954	0.00118995
$706$	−55.8534	−2.10207
$707$	−28.8191	−1.08385
$708$	−13.0603	−0.490838
$709$	18.3833	0.690400	0.345200	−	0.938529i	$-0.387811\pi$
$709$	18.3833	0.690400	0.345200	+	0.938529i	$0.387811\pi$
$710$	−2.26456	−0.0849874
$711$	−97.6237	−3.66117
$712$	12.4668	0.467215
$713$	1.60302	0.0600335
$714$	−104.972	−3.92847
$715$	0	0
$716$	−8.16690	−0.305211
$717$	0.844737	0.0315473
$718$	15.3031	0.571107
$719$	−4.12816	−0.153955	−0.0769773	−	0.997033i	$-0.524527\pi$
$719$	−4.12816	−0.153955	−0.0769773	+	0.997033i	$0.524527\pi$
$720$	2.80774	0.104638
$721$	26.4309	0.984337
$722$	−21.5616	−0.802441
$723$	−12.3524	−0.459390
$724$	−21.1390	−0.785625
$725$	43.6787	1.62219
$726$	5.67515	0.210625
$727$	−10.5948	−0.392939	−0.196469	−	0.980510i	$-0.562948\pi$
$727$	−10.5948	−0.392939	−0.196469	+	0.980510i	$0.562948\pi$
$728$	0	0
$729$	−1.65319	−0.0612292
$730$	−0.681966	−0.0252407
$731$	3.96747	0.146742
$732$	−0.890667	−0.0329200
$733$	−7.51115	−0.277430	−0.138715	−	0.990332i	$-0.544297\pi$
$733$	−7.51115	−0.277430	−0.138715	+	0.990332i	$0.544297\pi$
$734$	55.9125	2.06377
$735$	−3.57533	−0.131878
$736$	15.5374	0.572715
$737$	7.51367	0.276769
$738$	22.0752	0.812599
$739$	−33.3962	−1.22850	−0.614249	−	0.789112i	$-0.710541\pi$
$739$	−33.3962	−1.22850	−0.614249	+	0.789112i	$0.710541\pi$
$740$	−0.105471	−0.00387721
$741$	0	0
$742$	23.0901	0.847665
$743$	−29.7052	−1.08978	−0.544889	−	0.838508i	$-0.683428\pi$
$743$	−29.7052	−1.08978	−0.544889	+	0.838508i	$0.683428\pi$
$744$	2.56963	0.0942074
$745$	1.18192	0.0433022
$746$	−23.7190	−0.868416
$747$	55.2506	2.02151
$748$	−5.39689	−0.197330
$749$	57.3227	2.09453
$750$	4.84799	0.177024
$751$	2.47413	0.0902824	0.0451412	−	0.998981i	$-0.485626\pi$
$751$	2.47413	0.0902824	0.0451412	+	0.998981i	$0.485626\pi$
$752$	0.581146	0.0211922
$753$	76.8381	2.80013
$754$	0	0
$755$	−0.400484	−0.0145751
$756$	68.7844	2.50166
$757$	10.1573	0.369172	0.184586	−	0.982816i	$-0.440906\pi$
$757$	10.1573	0.369172	0.184586	+	0.982816i	$0.440906\pi$
$758$	0.476951	0.0173237
$759$	−7.51465	−0.272765
$760$	−0.284009	−0.0103021
$761$	−26.4430	−0.958559	−0.479280	−	0.877662i	$-0.659102\pi$
$761$	−26.4430	−0.958559	−0.479280	+	0.877662i	$0.659102\pi$
$762$	88.0501	3.18972
$763$	77.7670	2.81535
$764$	−27.5973	−0.998436
$765$	2.34590	0.0848162
$766$	29.3232	1.05949
$767$	0	0
$768$	65.1518	2.35096
$769$	−20.3485	−0.733784	−0.366892	−	0.930264i	$-0.619578\pi$
$769$	−20.3485	−0.733784	−0.366892	+	0.930264i	$0.619578\pi$
$770$	−0.703826	−0.0253641
$771$	−73.2192	−2.63693
$772$	13.4848	0.485328
$773$	35.5411	1.27833	0.639163	−	0.769072i	$-0.279281\pi$
$773$	35.5411	1.27833	0.639163	+	0.769072i	$0.279281\pi$
$774$	−11.8407	−0.425604
$775$	3.31788	0.119182
$776$	0.506371	0.0181777
$777$	13.1729	0.472574
$778$	28.6858	1.02844
$779$	−4.83738	−0.173317
$780$	0	0
$781$	14.5412	0.520325
$782$	17.9848	0.643136
$783$	−100.975	−3.60854
$784$	−65.7624	−2.34866
$785$	−0.938924	−0.0335116
$786$	56.4226	2.01253
$787$	−38.3791	−1.36807	−0.684034	−	0.729450i	$-0.739776\pi$
$787$	−38.3791	−1.36807	−0.684034	+	0.729450i	$0.739776\pi$
$788$	−18.5267	−0.659985
$789$	−9.18266	−0.326911
$790$	2.26748	0.0806734
$791$	1.57976	0.0561700
$792$	−8.32231	−0.295720
$793$	0	0
$794$	26.7633	0.949792
$795$	−0.746898	−0.0264898
$796$	5.07312	0.179812
$797$	25.3079	0.896453	0.448226	−	0.893920i	$-0.352056\pi$
$797$	25.3079	0.896453	0.448226	+	0.893920i	$0.352056\pi$
$798$	−68.6500	−2.43018
$799$	0.485555	0.0171777
$800$	32.1588	1.13698
$801$	−67.3445	−2.37950
$802$	51.3315	1.81258
$803$	4.37905	0.154533
$804$	30.8659	1.08856
$805$	0.931960	0.0328473
$806$	0	0
$807$	−28.1404	−0.990591
$808$	7.91494	0.278447
$809$	−19.5139	−0.686073	−0.343037	−	0.939322i	$-0.611455\pi$
$809$	−19.5139	−0.686073	−0.343037	+	0.939322i	$0.611455\pi$
$810$	−2.46704	−0.0866828
$811$	38.5466	1.35356	0.676778	−	0.736187i	$-0.263376\pi$
$811$	38.5466	1.35356	0.676778	+	0.736187i	$0.263376\pi$
$812$	−52.1372	−1.82966
$813$	−88.1899	−3.09296
$814$	1.70444	0.0597408
$815$	−0.640395	−0.0224321
$816$	62.4552	2.18637
$817$	2.59467	0.0907760
$818$	−39.9408	−1.39650
$819$	0	0
$820$	−0.203733	−0.00711467
$821$	−25.1534	−0.877861	−0.438930	−	0.898521i	$-0.644643\pi$
$821$	−25.1534	−0.877861	−0.438930	+	0.898521i	$0.644643\pi$
$822$	−43.8148	−1.52822
$823$	56.7058	1.97664	0.988319	−	0.152398i	$-0.0486995\pi$
$823$	56.7058	1.97664	0.988319	+	0.152398i	$0.0486995\pi$
$824$	−7.25902	−0.252880
$825$	−15.5536	−0.541507
$826$	−26.1752	−0.910753
$827$	−9.99227	−0.347465	−0.173733	−	0.984793i	$-0.555583\pi$
$827$	−9.99227	−0.347465	−0.173733	+	0.984793i	$0.555583\pi$
$828$	−21.3274	−0.741178
$829$	−30.0585	−1.04397	−0.521987	−	0.852953i	$-0.674809\pi$
$829$	−30.0585	−1.04397	−0.521987	+	0.852953i	$0.674809\pi$
$830$	−1.28329	−0.0445437
$831$	−64.4726	−2.23653
$832$	0	0
$833$	−54.9453	−1.90374
$834$	−73.5558	−2.54703
$835$	−0.626422	−0.0216782
$836$	−3.52949	−0.122070
$837$	−7.67013	−0.265119
$838$	1.61352	0.0557381
$839$	−24.4598	−0.844445	−0.422222	−	0.906492i	$-0.638750\pi$
$839$	−24.4598	−0.844445	−0.422222	+	0.906492i	$0.638750\pi$
$840$	1.49393	0.0515455
$841$	47.5367	1.63920
$842$	28.1076	0.968651
$843$	−35.0243	−1.20630
$844$	−21.3225	−0.733952
$845$	0	0
$846$	−1.44911	−0.0498214
$847$	4.51942	0.155289
$848$	−13.7380	−0.471764
$849$	100.929	3.46387
$850$	37.2245	1.27679
$851$	−2.25691	−0.0773659
$852$	59.7348	2.04648
$853$	4.39228	0.150389	0.0751945	−	0.997169i	$-0.476042\pi$
$853$	4.39228	0.150389	0.0751945	+	0.997169i	$0.476042\pi$
$854$	−1.78505	−0.0610833
$855$	1.53419	0.0524680
$856$	−15.7432	−0.538093
$857$	34.1752	1.16740	0.583701	−	0.811968i	$-0.301604\pi$
$857$	34.1752	1.16740	0.583701	+	0.811968i	$0.301604\pi$
$858$	0	0
$859$	19.9981	0.682327	0.341163	−	0.940004i	$-0.389179\pi$
$859$	19.9981	0.682327	0.341163	+	0.940004i	$0.389179\pi$
$860$	0.109278	0.00372636
$861$	25.4453	0.867173
$862$	19.7655	0.673214
$863$	22.3462	0.760673	0.380337	−	0.924848i	$-0.375808\pi$
$863$	22.3462	0.760673	0.380337	+	0.924848i	$0.375808\pi$
$864$	−74.3433	−2.52921
$865$	−0.529122	−0.0179907
$866$	−46.7621	−1.58904
$867$	−0.777563	−0.0264074
$868$	−3.96040	−0.134425
$869$	−14.5600	−0.493913
$870$	4.24438	0.143898
$871$	0	0
$872$	−21.3581	−0.723276
$873$	−2.73536	−0.0925779
$874$	11.7618	0.397850
$875$	3.86071	0.130516
$876$	17.9890	0.607791
$877$	26.9172	0.908929	0.454465	−	0.890765i	$-0.349831\pi$
$877$	26.9172	0.908929	0.454465	+	0.890765i	$0.349831\pi$
$878$	18.1281	0.611793
$879$	−65.7370	−2.21725
$880$	0.418757	0.0141163
$881$	−51.7072	−1.74206	−0.871030	−	0.491230i	$-0.836547\pi$
$881$	−51.7072	−1.74206	−0.871030	+	0.491230i	$0.836547\pi$
$882$	163.981	5.52153
$883$	45.0959	1.51760	0.758799	−	0.651325i	$-0.225787\pi$
$883$	45.0959	1.51760	0.758799	+	0.651325i	$0.225787\pi$
$884$	0	0
$885$	0.846693	0.0284613
$886$	30.8627	1.03685
$887$	0.729698	0.0245008	0.0122504	−	0.999925i	$-0.496100\pi$
$887$	0.729698	0.0245008	0.0122504	+	0.999925i	$0.496100\pi$
$888$	−3.61783	−0.121406
$889$	70.1188	2.35171
$890$	1.56419	0.0524319
$891$	15.8414	0.530706
$892$	20.2393	0.677663
$893$	0.317546	0.0106263
$894$	−78.4626	−2.62418
$895$	0.529455	0.0176977
$896$	42.2726	1.41223
$897$	0	0
$898$	−35.6295	−1.18897
$899$	5.81381	0.193901
$900$	−44.1428	−1.47143
$901$	−11.4782	−0.382396
$902$	3.29238	0.109624
$903$	−13.6483	−0.454188
$904$	−0.433870	−0.0144303
$905$	1.37043	0.0455546
$906$	26.5864	0.883275
$907$	34.4565	1.14411	0.572055	−	0.820215i	$-0.306146\pi$
$907$	34.4565	1.14411	0.572055	+	0.820215i	$0.306146\pi$
$908$	−31.8427	−1.05674
$909$	−42.7556	−1.41811
$910$	0	0
$911$	14.0949	0.466984	0.233492	−	0.972359i	$-0.424985\pi$
$911$	14.0949	0.466984	0.233492	+	0.972359i	$0.424985\pi$
$912$	40.8448	1.35251
$913$	8.24028	0.272714
$914$	20.4889	0.677712
$915$	0.0577413	0.00190887
$916$	32.1250	1.06144
$917$	44.9323	1.48379
$918$	−86.0539	−2.84020
$919$	−45.3432	−1.49573	−0.747866	−	0.663849i	$-0.768922\pi$
$919$	−45.3432	−1.49573	−0.747866	+	0.663849i	$0.768922\pi$
$920$	−0.255955	−0.00843859
$921$	−3.52692	−0.116216
$922$	−27.0036	−0.889315
$923$	0	0
$924$	18.5656	0.610764
$925$	−4.67129	−0.153591
$926$	68.5255	2.25189
$927$	39.2124	1.28790
$928$	56.3507	1.84980
$929$	−14.5370	−0.476943	−0.238471	−	0.971150i	$-0.576646\pi$
$929$	−14.5370	−0.476943	−0.238471	+	0.971150i	$0.576646\pi$
$930$	0.322408	0.0105722
$931$	−35.9335	−1.17767
$932$	−3.33555	−0.109260
$933$	82.3378	2.69562
$934$	−29.9695	−0.980631
$935$	0.349877	0.0114422
$936$	0	0
$937$	43.0932	1.40779	0.703896	−	0.710303i	$-0.251442\pi$
$937$	43.0932	1.40779	0.703896	+	0.710303i	$0.251442\pi$
$938$	61.8607	2.01982
$939$	24.4735	0.798663
$940$	0.0133739	0.000436209 0
$941$	40.5816	1.32292	0.661461	−	0.749979i	$-0.269937\pi$
$941$	40.5816	1.32292	0.661461	+	0.749979i	$0.269937\pi$
$942$	62.3312	2.03086
$943$	−4.35955	−0.141966
$944$	15.5735	0.506875
$945$	−4.45925	−0.145059
$946$	−1.76596	−0.0574164
$947$	45.8045	1.48845	0.744223	−	0.667932i	$-0.232820\pi$
$947$	45.8045	1.48845	0.744223	+	0.667932i	$0.232820\pi$
$948$	−59.8119	−1.94260
$949$	0	0
$950$	24.3443	0.789832
$951$	−18.0917	−0.586664
$952$	22.9585	0.744090
$953$	−43.7134	−1.41602	−0.708009	−	0.706204i	$-0.750406\pi$
$953$	−43.7134	−1.41602	−0.708009	+	0.706204i	$0.750406\pi$
$954$	34.2561	1.10908
$955$	1.78912	0.0578944
$956$	0.357565	0.0115645
$957$	−27.2541	−0.880999
$958$	14.2621	0.460789
$959$	−34.8920	−1.12672
$960$	0.515872	0.0166497
$961$	−30.5584	−0.985754
$962$	0	0
$963$	85.0431	2.74048
$964$	−5.22860	−0.168402
$965$	−0.874210	−0.0281418
$966$	−61.8689	−1.99060
$967$	42.8421	1.37771	0.688854	−	0.724900i	$-0.258114\pi$
$967$	42.8421	1.37771	0.688854	+	0.724900i	$0.258114\pi$
$968$	−1.24122	−0.0398944
$969$	34.1264	1.09630
$970$	0.0635335	0.00203994
$971$	−16.9216	−0.543041	−0.271521	−	0.962433i	$-0.587527\pi$
$971$	−16.9216	−0.543041	−0.271521	+	0.962433i	$0.587527\pi$
$972$	19.4165	0.622785
$973$	−58.5763	−1.87787
$974$	−5.11009	−0.163738
$975$	0	0
$976$	1.06206	0.0339956
$977$	16.6274	0.531958	0.265979	−	0.963979i	$-0.414305\pi$
$977$	16.6274	0.531958	0.265979	+	0.963979i	$0.414305\pi$
$978$	42.5131	1.35942
$979$	−10.0440	−0.321008
$980$	−1.51339	−0.0483435
$981$	115.374	3.68361
$982$	46.5464	1.48536
$983$	4.64461	0.148140	0.0740701	−	0.997253i	$-0.476401\pi$
$983$	4.64461	0.148140	0.0740701	+	0.997253i	$0.476401\pi$
$984$	−6.98834	−0.222780
$985$	1.20107	0.0382693
$986$	65.2272	2.07726
$987$	−1.67034	−0.0531674
$988$	0	0
$989$	2.33837	0.0743559
$990$	−1.04419	−0.0331864
$991$	−31.8009	−1.01019	−0.505094	−	0.863064i	$-0.668542\pi$
$991$	−31.8009	−1.01019	−0.505094	+	0.863064i	$0.668542\pi$
$992$	4.28046	0.135905
$993$	112.101	3.55743
$994$	119.719	3.79726
$995$	−0.328887	−0.0104264
$996$	33.8508	1.07260
$997$	35.8549	1.13554	0.567768	−	0.823189i	$-0.307807\pi$
$997$	35.8549	1.13554	0.567768	+	0.823189i	$0.307807\pi$
$998$	−70.2931	−2.22509
$999$	10.7989	0.341662

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.l.1.5		6
13.4	even	6		143.2.e.c.133.5	yes	12
13.10	even	6		143.2.e.c.100.5	✓	12
13.12	even	2		1859.2.a.k.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.c.100.5	✓	12	13.10	even	6
143.2.e.c.133.5	yes	12	13.4	even	6
1859.2.a.k.1.2		6	13.12	even	2
1859.2.a.l.1.5		6	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1859.a (trivial)

\(f(q)\)	\(=\)	\(q+1.82172 q^{2} +3.11527 q^{3} +1.31865 q^{4} -0.0854874 q^{5} +5.67515 q^{6} +4.51942 q^{7} -1.24122 q^{8} +6.70494 q^{9} +O(q^{10})\)	\(q+1.82172 q^{2} +3.11527 q^{3} +1.31865 q^{4} -0.0854874 q^{5} +5.67515 q^{6} +4.51942 q^{7} -1.24122 q^{8} +6.70494 q^{9} -0.155734 q^{10} +1.00000 q^{11} +4.10797 q^{12} +8.23310 q^{14} -0.266317 q^{15} -4.89846 q^{16} -4.09273 q^{17} +12.2145 q^{18} -2.67659 q^{19} -0.112728 q^{20} +14.0792 q^{21} +1.82172 q^{22} -2.41220 q^{23} -3.86675 q^{24} -4.99269 q^{25} +11.5419 q^{27} +5.95954 q^{28} -8.74853 q^{29} -0.485154 q^{30} -0.664547 q^{31} -6.44117 q^{32} +3.11527 q^{33} -7.45579 q^{34} -0.386353 q^{35} +8.84149 q^{36} +0.935625 q^{37} -4.87598 q^{38} +0.106109 q^{40} +1.80729 q^{41} +25.6484 q^{42} -0.969395 q^{43} +1.31865 q^{44} -0.573188 q^{45} -4.39434 q^{46} -0.118639 q^{47} -15.2600 q^{48} +13.4251 q^{49} -9.09527 q^{50} -12.7500 q^{51} +2.80455 q^{53} +21.0261 q^{54} -0.0854874 q^{55} -5.60959 q^{56} -8.33830 q^{57} -15.9373 q^{58} -3.17927 q^{59} -0.351179 q^{60} -0.216814 q^{61} -1.21062 q^{62} +30.3024 q^{63} -1.93706 q^{64} +5.67515 q^{66} +7.51367 q^{67} -5.39689 q^{68} -7.51465 q^{69} -0.703826 q^{70} +14.5412 q^{71} -8.32231 q^{72} +4.37905 q^{73} +1.70444 q^{74} -15.5536 q^{75} -3.52949 q^{76} +4.51942 q^{77} -14.5600 q^{79} +0.418757 q^{80} +15.8414 q^{81} +3.29238 q^{82} +8.24028 q^{83} +18.5656 q^{84} +0.349877 q^{85} -1.76596 q^{86} -27.2541 q^{87} -1.24122 q^{88} -10.0440 q^{89} -1.04419 q^{90} -3.18085 q^{92} -2.07025 q^{93} -0.216126 q^{94} +0.228814 q^{95} -20.0660 q^{96} -0.407962 q^{97} +24.4568 q^{98} +6.70494 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9	\( 6 q + q^{3} + 8 q^{4} + 6 q^{5} + 12 q^{6} + 3 q^{7} - 3 q^{8} + 7 q^{9} - 3 q^{10} + 6 q^{11} - 17 q^{12} + 12 q^{14} - 4 q^{15} + 8 q^{16} + 2 q^{17} - 6 q^{18} + 10 q^{19} + 15 q^{20} + 12 q^{21} + 3 q^{23} + 14 q^{24} - 6 q^{25} + 10 q^{27} + 16 q^{28} + 3 q^{29} + 19 q^{30} + 5 q^{31} - q^{32} + q^{33} - 5 q^{34} - 13 q^{35} + 20 q^{36} + 25 q^{37} - 27 q^{38} - 8 q^{40} + 24 q^{41} + 13 q^{42} - 8 q^{43} + 8 q^{44} + 27 q^{45} + 18 q^{46} + 10 q^{47} - 28 q^{48} - q^{49} - 26 q^{50} - 17 q^{51} + 10 q^{53} + 47 q^{54} + 6 q^{55} + 15 q^{56} + 6 q^{58} - 4 q^{59} - 61 q^{60} - 21 q^{61} - 5 q^{62} + 6 q^{63} - 27 q^{64} + 12 q^{66} + 21 q^{67} + 14 q^{68} + 5 q^{69} + 31 q^{70} - 3 q^{71} - 50 q^{72} + 13 q^{73} - 38 q^{74} - 23 q^{75} + 8 q^{76} + 3 q^{77} - 4 q^{79} + 44 q^{80} + 34 q^{81} - 33 q^{82} + 8 q^{83} + 47 q^{84} - 13 q^{85} - 11 q^{86} - 51 q^{87} - 3 q^{88} - 9 q^{89} - 70 q^{90} + 15 q^{92} - 21 q^{93} + 10 q^{94} + 27 q^{95} - 19 q^{96} + 15 q^{97} + 21 q^{98} + 7 q^{99}+O(q^{100}) \) 6 * q + q^3 + 8 * q^4 + 6 * q^5 + 12 * q^6 + 3 * q^7 - 3 * q^8 + 7 * q^9 - 3 * q^10 + 6 * q^11 - 17 * q^12 + 12 * q^14 - 4 * q^15 + 8 * q^16 + 2 * q^17 - 6 * q^18 + 10 * q^19 + 15 * q^20 + 12 * q^21 + 3 * q^23 + 14 * q^24 - 6 * q^25 + 10 * q^27 + 16 * q^28 + 3 * q^29 + 19 * q^30 + 5 * q^31 - q^32 + q^33 - 5 * q^34 - 13 * q^35 + 20 * q^36 + 25 * q^37 - 27 * q^38 - 8 * q^40 + 24 * q^41 + 13 * q^42 - 8 * q^43 + 8 * q^44 + 27 * q^45 + 18 * q^46 + 10 * q^47 - 28 * q^48 - q^49 - 26 * q^50 - 17 * q^51 + 10 * q^53 + 47 * q^54 + 6 * q^55 + 15 * q^56 + 6 * q^58 - 4 * q^59 - 61 * q^60 - 21 * q^61 - 5 * q^62 + 6 * q^63 - 27 * q^64 + 12 * q^66 + 21 * q^67 + 14 * q^68 + 5 * q^69 + 31 * q^70 - 3 * q^71 - 50 * q^72 + 13 * q^73 - 38 * q^74 - 23 * q^75 + 8 * q^76 + 3 * q^77 - 4 * q^79 + 44 * q^80 + 34 * q^81 - 33 * q^82 + 8 * q^83 + 47 * q^84 - 13 * q^85 - 11 * q^86 - 51 * q^87 - 3 * q^88 - 9 * q^89 - 70 * q^90 + 15 * q^92 - 21 * q^93 + 10 * q^94 + 27 * q^95 - 19 * q^96 + 15 * q^97 + 21 * q^98 + 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more