LMFDB - Embedded newform 1859.2.a.s.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1859.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$14.8441897358$
Analytic rank:	$0$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q+0.392741 q^{2} +1.69948 q^{3} -1.84575 q^{4} -1.18432 q^{5} +0.667456 q^{6} -5.07600 q^{7} -1.51039 q^{8} -0.111771 q^{9} +O(q^{10})$	\(q+0.392741 q^{2} +1.69948 q^{3} -1.84575 q^{4} -1.18432 q^{5} +0.667456 q^{6} -5.07600 q^{7} -1.51039 q^{8} -0.111771 q^{9} -0.465133 q^{10} -1.00000 q^{11} -3.13682 q^{12} -1.99356 q^{14} -2.01273 q^{15} +3.09832 q^{16} +7.48561 q^{17} -0.0438972 q^{18} +3.99272 q^{19} +2.18597 q^{20} -8.62655 q^{21} -0.392741 q^{22} +3.36585 q^{23} -2.56687 q^{24} -3.59738 q^{25} -5.28839 q^{27} +9.36905 q^{28} +8.64322 q^{29} -0.790483 q^{30} +7.64123 q^{31} +4.23761 q^{32} -1.69948 q^{33} +2.93991 q^{34} +6.01162 q^{35} +0.206302 q^{36} +0.696141 q^{37} +1.56811 q^{38} +1.78879 q^{40} -6.07962 q^{41} -3.38800 q^{42} -9.18013 q^{43} +1.84575 q^{44} +0.132373 q^{45} +1.32191 q^{46} +3.26831 q^{47} +5.26552 q^{48} +18.7658 q^{49} -1.41284 q^{50} +12.7216 q^{51} +2.06811 q^{53} -2.07697 q^{54} +1.18432 q^{55} +7.66672 q^{56} +6.78555 q^{57} +3.39455 q^{58} +3.29281 q^{59} +3.71501 q^{60} +3.96312 q^{61} +3.00103 q^{62} +0.567351 q^{63} -4.53235 q^{64} -0.667456 q^{66} -5.18488 q^{67} -13.8166 q^{68} +5.72019 q^{69} +2.36101 q^{70} +4.07910 q^{71} +0.168818 q^{72} -4.57498 q^{73} +0.273403 q^{74} -6.11367 q^{75} -7.36958 q^{76} +5.07600 q^{77} +2.93846 q^{79} -3.66941 q^{80} -8.65219 q^{81} -2.38772 q^{82} +1.47741 q^{83} +15.9225 q^{84} -8.86538 q^{85} -3.60542 q^{86} +14.6890 q^{87} +1.51039 q^{88} +17.0055 q^{89} +0.0519884 q^{90} -6.21253 q^{92} +12.9861 q^{93} +1.28360 q^{94} -4.72867 q^{95} +7.20173 q^{96} -12.7271 q^{97} +7.37009 q^{98} +0.111771 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) $ 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	0.392741	0.277710	0.138855	−	0.990313i	$-0.455658\pi$
$2$	0.392741	0.277710	0.138855	+	0.990313i	$0.455658\pi$
$3$	1.69948	0.981195	0.490597	−	0.871386i	$-0.336779\pi$
$3$	1.69948	0.981195	0.490597	+	0.871386i	$0.336779\pi$
$4$	−1.84575	−0.922877
$5$	−1.18432	−0.529645	−0.264823	−	0.964297i	$-0.585313\pi$
$5$	−1.18432	−0.529645	−0.264823	+	0.964297i	$0.585313\pi$
$6$	0.667456	0.272488
$7$	−5.07600	−1.91855	−0.959274	−	0.282478i	$-0.908844\pi$
$7$	−5.07600	−1.91855	−0.959274	+	0.282478i	$0.908844\pi$
$8$	−1.51039	−0.534002
$9$	−0.111771	−0.0372571
$10$	−0.465133	−0.147088
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.13682	−0.905522
$13$	0	0
$13$	0	0
$14$	−1.99356	−0.532800
$15$	−2.01273	−0.519685
$16$	3.09832	0.774579
$17$	7.48561	1.81553	0.907763	−	0.419483i	$-0.137789\pi$
$17$	7.48561	1.81553	0.907763	+	0.419483i	$0.137789\pi$
$18$	−0.0438972	−0.0103467
$19$	3.99272	0.915993	0.457997	−	0.888954i	$-0.348567\pi$
$19$	3.99272	0.915993	0.457997	+	0.888954i	$0.348567\pi$
$20$	2.18597	0.488798
$21$	−8.62655	−1.88247
$22$	−0.392741	−0.0837327
$23$	3.36585	0.701828	0.350914	−	0.936408i	$-0.385871\pi$
$23$	3.36585	0.701828	0.350914	+	0.936408i	$0.385871\pi$
$24$	−2.56687	−0.523960
$25$	−3.59738	−0.719476
$26$	0	0
$27$	−5.28839	−1.01775
$28$	9.36905	1.77058
$29$	8.64322	1.60501	0.802503	−	0.596648i	$-0.203501\pi$
$29$	8.64322	1.60501	0.802503	+	0.596648i	$0.203501\pi$
$30$	−0.790483	−0.144322
$31$	7.64123	1.37240	0.686202	−	0.727411i	$-0.259276\pi$
$31$	7.64123	1.37240	0.686202	+	0.727411i	$0.259276\pi$
$32$	4.23761	0.749111
$33$	−1.69948	−0.295841
$34$	2.93991	0.504190
$35$	6.01162	1.01615
$36$	0.206302	0.0343837
$37$	0.696141	0.114445	0.0572224	−	0.998361i	$-0.481776\pi$
$37$	0.696141	0.114445	0.0572224	+	0.998361i	$0.481776\pi$
$38$	1.56811	0.254381
$39$	0	0
$40$	1.78879	0.282832
$41$	−6.07962	−0.949477	−0.474738	−	0.880127i	$-0.657457\pi$
$41$	−6.07962	−0.949477	−0.474738	+	0.880127i	$0.657457\pi$
$42$	−3.38800	−0.522781
$43$	−9.18013	−1.39996	−0.699979	−	0.714164i	$-0.746807\pi$
$43$	−9.18013	−1.39996	−0.699979	+	0.714164i	$0.746807\pi$
$44$	1.84575	0.278258
$45$	0.132373	0.0197330
$46$	1.32191	0.194905
$47$	3.26831	0.476732	0.238366	−	0.971175i	$-0.423388\pi$
$47$	3.26831	0.476732	0.238366	+	0.971175i	$0.423388\pi$
$48$	5.26552	0.760013
$49$	18.7658	2.68082
$50$	−1.41284	−0.199806
$51$	12.7216	1.78138
$52$	0	0
$53$	2.06811	0.284077	0.142039	−	0.989861i	$-0.454634\pi$
$53$	2.06811	0.284077	0.142039	+	0.989861i	$0.454634\pi$
$54$	−2.07697	−0.282640
$55$	1.18432	0.159694
$56$	7.66672	1.02451
$57$	6.78555	0.898768
$58$	3.39455	0.445726
$59$	3.29281	0.428687	0.214343	−	0.976758i	$-0.431239\pi$
$59$	3.29281	0.428687	0.214343	+	0.976758i	$0.431239\pi$
$60$	3.71501	0.479606
$61$	3.96312	0.507426	0.253713	−	0.967280i	$-0.418348\pi$
$61$	3.96312	0.507426	0.253713	+	0.967280i	$0.418348\pi$
$62$	3.00103	0.381131
$63$	0.567351	0.0714794
$64$	−4.53235	−0.566544
$65$	0	0
$66$	−0.667456	−0.0821581
$67$	−5.18488	−0.633433	−0.316717	−	0.948520i	$-0.602580\pi$
$67$	−5.18488	−0.633433	−0.316717	+	0.948520i	$0.602580\pi$
$68$	−13.8166	−1.67551
$69$	5.72019	0.688629
$70$	2.36101	0.282195
$71$	4.07910	0.484100	0.242050	−	0.970264i	$-0.422180\pi$
$71$	4.07910	0.484100	0.242050	+	0.970264i	$0.422180\pi$
$72$	0.168818	0.0198954
$73$	−4.57498	−0.535461	−0.267731	−	0.963494i	$-0.586274\pi$
$73$	−4.57498	−0.535461	−0.267731	+	0.963494i	$0.586274\pi$
$74$	0.273403	0.0317825
$75$	−6.11367	−0.705946
$76$	−7.36958	−0.845349
$77$	5.07600	0.578464
$78$	0	0
$79$	2.93846	0.330602	0.165301	−	0.986243i	$-0.447140\pi$
$79$	2.93846	0.330602	0.165301	+	0.986243i	$0.447140\pi$
$80$	−3.66941	−0.410252
$81$	−8.65219	−0.961355
$82$	−2.38772	−0.263679
$83$	1.47741	0.162167	0.0810834	−	0.996707i	$-0.474162\pi$
$83$	1.47741	0.162167	0.0810834	+	0.996707i	$0.474162\pi$
$84$	15.9225	1.73729
$85$	−8.86538	−0.961585
$86$	−3.60542	−0.388782
$87$	14.6890	1.57482
$88$	1.51039	0.161008
$89$	17.0055	1.80258	0.901289	−	0.433219i	$-0.142622\pi$
$89$	17.0055	1.80258	0.901289	+	0.433219i	$0.142622\pi$
$90$	0.0519884	0.00548006
$91$	0	0
$92$	−6.21253	−0.647701
$93$	12.9861	1.34660
$94$	1.28360	0.132393
$95$	−4.72867	−0.485152
$96$	7.20173	0.735024
$97$	−12.7271	−1.29224	−0.646120	−	0.763236i	$-0.723609\pi$
$97$	−12.7271	−1.29224	−0.646120	+	0.763236i	$0.723609\pi$
$98$	7.37009	0.744492
$99$	0.111771	0.0112334
$100$	6.63988	0.663988
$101$	−5.42290	−0.539599	−0.269799	−	0.962917i	$-0.586957\pi$
$101$	−5.42290	−0.539599	−0.269799	+	0.962917i	$0.586957\pi$
$102$	4.99631	0.494708
$103$	−10.4956	−1.03416	−0.517080	−	0.855937i	$-0.672981\pi$
$103$	−10.4956	−1.03416	−0.517080	+	0.855937i	$0.672981\pi$
$104$	0	0
$105$	10.2166	0.997041
$106$	0.812233	0.0788911
$107$	9.23601	0.892879	0.446439	−	0.894814i	$-0.352692\pi$
$107$	9.23601	0.892879	0.446439	+	0.894814i	$0.352692\pi$
$108$	9.76107	0.939259
$109$	−6.34139	−0.607395	−0.303698	−	0.952768i	$-0.598221\pi$
$109$	−6.34139	−0.607395	−0.303698	+	0.952768i	$0.598221\pi$
$110$	0.465133	0.0443487
$111$	1.18308	0.112293
$112$	−15.7271	−1.48607
$113$	2.26788	0.213344	0.106672	−	0.994294i	$-0.465980\pi$
$113$	2.26788	0.213344	0.106672	+	0.994294i	$0.465980\pi$
$114$	2.66497	0.249597
$115$	−3.98625	−0.371720
$116$	−15.9533	−1.48122
$117$	0	0
$118$	1.29322	0.119051
$119$	−37.9969	−3.48317
$120$	3.04000	0.277513
$121$	1.00000	0.0909091
$122$	1.55648	0.140917
$123$	−10.3322	−0.931622
$124$	−14.1038	−1.26656
$125$	10.1821	0.910712
$126$	0.222822	0.0198506
$127$	8.46799	0.751412	0.375706	−	0.926739i	$-0.377400\pi$
$127$	8.46799	0.751412	0.375706	+	0.926739i	$0.377400\pi$
$128$	−10.2553	−0.906446
$129$	−15.6014	−1.37363
$130$	0	0
$131$	3.07651	0.268796	0.134398	−	0.990927i	$-0.457090\pi$
$131$	3.07651	0.268796	0.134398	+	0.990927i	$0.457090\pi$
$132$	3.13682	0.273025
$133$	−20.2671	−1.75738
$134$	−2.03632	−0.175911
$135$	6.26316	0.539047
$136$	−11.3062	−0.969495
$137$	−6.42662	−0.549063	−0.274532	−	0.961578i	$-0.588523\pi$
$137$	−6.42662	−0.549063	−0.274532	+	0.961578i	$0.588523\pi$
$138$	2.24655	0.191239
$139$	11.2711	0.956001	0.478001	−	0.878359i	$-0.341362\pi$
$139$	11.2711	0.956001	0.478001	+	0.878359i	$0.341362\pi$
$140$	−11.0960	−0.937781
$141$	5.55442	0.467767
$142$	1.60203	0.134439
$143$	0	0
$144$	−0.346303	−0.0288585
$145$	−10.2364	−0.850084
$146$	−1.79678	−0.148703
$147$	31.8920	2.63041
$148$	−1.28490	−0.105619
$149$	15.9762	1.30882	0.654410	−	0.756140i	$-0.272917\pi$
$149$	15.9762	1.30882	0.654410	+	0.756140i	$0.272917\pi$
$150$	−2.40109	−0.196048
$151$	4.79638	0.390324	0.195162	−	0.980771i	$-0.437477\pi$
$151$	4.79638	0.390324	0.195162	+	0.980771i	$0.437477\pi$
$152$	−6.03056	−0.489143
$153$	−0.836675	−0.0676412
$154$	1.99356	0.160645
$155$	−9.04968	−0.726888
$156$	0	0
$157$	19.3688	1.54580	0.772898	−	0.634530i	$-0.218806\pi$
$157$	19.3688	1.54580	0.772898	+	0.634530i	$0.218806\pi$
$158$	1.15405	0.0918115
$159$	3.51471	0.278735
$160$	−5.01870	−0.396763
$161$	−17.0850	−1.34649
$162$	−3.39807	−0.266978
$163$	−9.41218	−0.737219	−0.368610	−	0.929584i	$-0.620166\pi$
$163$	−9.41218	−0.737219	−0.368610	+	0.929584i	$0.620166\pi$
$164$	11.2215	0.876251
$165$	2.01273	0.156691
$166$	0.580240	0.0450354
$167$	−0.355939	−0.0275434	−0.0137717	−	0.999905i	$-0.504384\pi$
$167$	−0.355939	−0.0275434	−0.0137717	+	0.999905i	$0.504384\pi$
$168$	13.0294	1.00524
$169$	0	0
$170$	−3.48180	−0.267042
$171$	−0.446271	−0.0341272
$172$	16.9443	1.29199
$173$	9.60710	0.730414	0.365207	−	0.930926i	$-0.380998\pi$
$173$	9.60710	0.730414	0.365207	+	0.930926i	$0.380998\pi$
$174$	5.76897	0.437344
$175$	18.2603	1.38035
$176$	−3.09832	−0.233544
$177$	5.59606	0.420625
$178$	6.67876	0.500594
$179$	−2.06020	−0.153987	−0.0769933	−	0.997032i	$-0.524532\pi$
$179$	−2.06020	−0.153987	−0.0769933	+	0.997032i	$0.524532\pi$
$180$	−0.244328	−0.0182112
$181$	16.4734	1.22446	0.612231	−	0.790679i	$-0.290272\pi$
$181$	16.4734	1.22446	0.612231	+	0.790679i	$0.290272\pi$
$182$	0	0
$183$	6.73524	0.497883
$184$	−5.08373	−0.374778
$185$	−0.824456	−0.0606152
$186$	5.10018	0.373963
$187$	−7.48561	−0.547402
$188$	−6.03249	−0.439965
$189$	26.8439	1.95260
$190$	−1.85715	−0.134732
$191$	−5.30591	−0.383922	−0.191961	−	0.981403i	$-0.561485\pi$
$191$	−5.30591	−0.383922	−0.191961	+	0.981403i	$0.561485\pi$
$192$	−7.70263	−0.555890
$193$	14.0769	1.01327	0.506637	−	0.862159i	$-0.330888\pi$
$193$	14.0769	1.01327	0.506637	+	0.862159i	$0.330888\pi$
$194$	−4.99845	−0.358868
$195$	0	0
$196$	−34.6370	−2.47407
$197$	21.9002	1.56032	0.780161	−	0.625579i	$-0.215137\pi$
$197$	21.9002	1.56032	0.780161	+	0.625579i	$0.215137\pi$
$198$	0.0438972	0.00311964
$199$	−21.3859	−1.51601	−0.758004	−	0.652250i	$-0.773825\pi$
$199$	−21.3859	−1.51601	−0.758004	+	0.652250i	$0.773825\pi$
$200$	5.43343	0.384202
$201$	−8.81159	−0.621521
$202$	−2.12980	−0.149852
$203$	−43.8730	−3.07928
$204$	−23.4810	−1.64400
$205$	7.20023	0.502886
$206$	−4.12205	−0.287197
$207$	−0.376205	−0.0261480
$208$	0	0
$209$	−3.99272	−0.276182
$210$	4.01249	0.276888
$211$	−6.02049	−0.414468	−0.207234	−	0.978291i	$-0.566446\pi$
$211$	−6.02049	−0.414468	−0.207234	+	0.978291i	$0.566446\pi$
$212$	−3.81723	−0.262168
$213$	6.93234	0.474996
$214$	3.62736	0.247961
$215$	10.8722	0.741481
$216$	7.98751	0.543482
$217$	−38.7869	−2.63302
$218$	−2.49053	−0.168680
$219$	−7.77508	−0.525391
$220$	−2.18597	−0.147378
$221$	0	0
$222$	0.464643	0.0311848
$223$	−3.83948	−0.257110	−0.128555	−	0.991702i	$-0.541034\pi$
$223$	−3.83948	−0.257110	−0.128555	+	0.991702i	$0.541034\pi$
$224$	−21.5101	−1.43720
$225$	0.402083	0.0268056
$226$	0.890690	0.0592478
$227$	2.57539	0.170935	0.0854674	−	0.996341i	$-0.472762\pi$
$227$	2.57539	0.170935	0.0854674	+	0.996341i	$0.472762\pi$
$228$	−12.5245	−0.829452
$229$	5.21467	0.344595	0.172297	−	0.985045i	$-0.444881\pi$
$229$	5.21467	0.344595	0.172297	+	0.985045i	$0.444881\pi$
$230$	−1.56557	−0.103230
$231$	8.62655	0.567586
$232$	−13.0546	−0.857077
$233$	4.87965	0.319676	0.159838	−	0.987143i	$-0.448903\pi$
$233$	4.87965	0.319676	0.159838	+	0.987143i	$0.448903\pi$
$234$	0	0
$235$	−3.87073	−0.252499
$236$	−6.07771	−0.395625
$237$	4.99384	0.324385
$238$	−14.9230	−0.967312
$239$	22.5400	1.45799	0.728997	−	0.684517i	$-0.239987\pi$
$239$	22.5400	1.45799	0.728997	+	0.684517i	$0.239987\pi$
$240$	−6.23608	−0.402537
$241$	10.5543	0.679860	0.339930	−	0.940451i	$-0.389597\pi$
$241$	10.5543	0.679860	0.339930	+	0.940451i	$0.389597\pi$
$242$	0.392741	0.0252464
$243$	1.16095	0.0744748
$244$	−7.31495	−0.468291
$245$	−22.2247	−1.41989
$246$	−4.05788	−0.258721
$247$	0	0
$248$	−11.5412	−0.732867
$249$	2.51083	0.159117
$250$	3.99892	0.252914
$251$	−7.45436	−0.470515	−0.235258	−	0.971933i	$-0.575593\pi$
$251$	−7.45436	−0.470515	−0.235258	+	0.971933i	$0.575593\pi$
$252$	−1.04719	−0.0659667
$253$	−3.36585	−0.211609
$254$	3.32573	0.208675
$255$	−15.0665	−0.943502
$256$	5.03703	0.314814
$257$	15.7723	0.983850	0.491925	−	0.870638i	$-0.336294\pi$
$257$	15.7723	0.983850	0.491925	+	0.870638i	$0.336294\pi$
$258$	−6.12733	−0.381471
$259$	−3.53361	−0.219568
$260$	0	0
$261$	−0.966063	−0.0597978
$262$	1.20827	0.0746473
$263$	−1.63664	−0.100920	−0.0504598	−	0.998726i	$-0.516069\pi$
$263$	−1.63664	−0.100920	−0.0504598	+	0.998726i	$0.516069\pi$
$264$	2.56687	0.157980
$265$	−2.44931	−0.150460
$266$	−7.95971	−0.488041
$267$	28.9005	1.76868
$268$	9.57001	0.584581
$269$	−6.30640	−0.384508	−0.192254	−	0.981345i	$-0.561580\pi$
$269$	−6.30640	−0.384508	−0.192254	+	0.981345i	$0.561580\pi$
$270$	2.45980	0.149699
$271$	2.90187	0.176276	0.0881381	−	0.996108i	$-0.471908\pi$
$271$	2.90187	0.176276	0.0881381	+	0.996108i	$0.471908\pi$
$272$	23.1928	1.40627
$273$	0	0
$274$	−2.52400	−0.152480
$275$	3.59738	0.216930
$276$	−10.5581	−0.635520
$277$	−3.44417	−0.206940	−0.103470	−	0.994633i	$-0.532995\pi$
$277$	−3.44417	−0.206940	−0.103470	+	0.994633i	$0.532995\pi$
$278$	4.42662	0.265491
$279$	−0.854069	−0.0511318
$280$	−9.07988	−0.542626
$281$	23.7653	1.41772	0.708858	−	0.705351i	$-0.249211\pi$
$281$	23.7653	1.41772	0.708858	+	0.705351i	$0.249211\pi$
$282$	2.18145	0.129904
$283$	10.7805	0.640835	0.320418	−	0.947276i	$-0.396177\pi$
$283$	10.7805	0.640835	0.320418	+	0.947276i	$0.396177\pi$
$284$	−7.52901	−0.446765
$285$	−8.03628	−0.476028
$286$	0	0
$287$	30.8601	1.82162
$288$	−0.473643	−0.0279097
$289$	39.0343	2.29614
$290$	−4.02025	−0.236077
$291$	−21.6294	−1.26794
$292$	8.44429	0.494165
$293$	4.75683	0.277897	0.138948	−	0.990300i	$-0.455628\pi$
$293$	4.75683	0.277897	0.138948	+	0.990300i	$0.455628\pi$
$294$	12.5253	0.730492
$295$	−3.89975	−0.227052
$296$	−1.05144	−0.0611138
$297$	5.28839	0.306863
$298$	6.27451	0.363473
$299$	0	0
$300$	11.2843	0.651501
$301$	46.5983	2.68588
$302$	1.88374	0.108397
$303$	−9.21610	−0.529451
$304$	12.3707	0.709509
$305$	−4.69361	−0.268756
$306$	−0.328597	−0.0187846
$307$	−8.88281	−0.506969	−0.253485	−	0.967339i	$-0.581577\pi$
$307$	−8.88281	−0.506969	−0.253485	+	0.967339i	$0.581577\pi$
$308$	−9.36905	−0.533851
$309$	−17.8370	−1.01471
$310$	−3.55418	−0.201864
$311$	−2.93727	−0.166557	−0.0832785	−	0.996526i	$-0.526539\pi$
$311$	−2.93727	−0.166557	−0.0832785	+	0.996526i	$0.526539\pi$
$312$	0	0
$313$	−33.9051	−1.91643	−0.958213	−	0.286054i	$-0.907656\pi$
$313$	−33.9051	−1.91643	−0.958213	+	0.286054i	$0.907656\pi$
$314$	7.60692	0.429283
$315$	−0.671926	−0.0378588
$316$	−5.42367	−0.305105
$317$	−16.1586	−0.907556	−0.453778	−	0.891115i	$-0.649924\pi$
$317$	−16.1586	−0.907556	−0.453778	+	0.891115i	$0.649924\pi$
$318$	1.38037	0.0774075
$319$	−8.64322	−0.483928
$320$	5.36777	0.300067
$321$	15.6964	0.876088
$322$	−6.71000	−0.373934
$323$	29.8879	1.66301
$324$	15.9698	0.887212
$325$	0	0
$326$	−3.69655	−0.204733
$327$	−10.7771	−0.595973
$328$	9.18258	0.507023
$329$	−16.5899	−0.914632
$330$	0.790483	0.0435147
$331$	33.8869	1.86259	0.931296	−	0.364264i	$-0.118679\pi$
$331$	33.8869	1.86259	0.931296	+	0.364264i	$0.118679\pi$
$332$	−2.72694	−0.149660
$333$	−0.0778085	−0.00426388
$334$	−0.139792	−0.00764907
$335$	6.14057	0.335495
$336$	−26.7278	−1.45812
$337$	25.3127	1.37887	0.689437	−	0.724346i	$-0.257858\pi$
$337$	25.3127	1.37887	0.689437	+	0.724346i	$0.257858\pi$
$338$	0	0
$339$	3.85421	0.209332
$340$	16.3633	0.887425
$341$	−7.64123	−0.413796
$342$	−0.175269	−0.00947747
$343$	−59.7230	−3.22474
$344$	13.8656	0.747580
$345$	−6.77455	−0.364729
$346$	3.77310	0.202843
$347$	9.64590	0.517819	0.258909	−	0.965902i	$-0.416637\pi$
$347$	9.64590	0.517819	0.258909	+	0.965902i	$0.416637\pi$
$348$	−27.1122	−1.45337
$349$	6.16293	0.329894	0.164947	−	0.986302i	$-0.447255\pi$
$349$	6.16293	0.329894	0.164947	+	0.986302i	$0.447255\pi$
$350$	7.17157	0.383337
$351$	0	0
$352$	−4.23761	−0.225865
$353$	15.5957	0.830077	0.415039	−	0.909804i	$-0.363768\pi$
$353$	15.5957	0.830077	0.415039	+	0.909804i	$0.363768\pi$
$354$	2.19780	0.116812
$355$	−4.83097	−0.256401
$356$	−31.3879	−1.66356
$357$	−64.5750	−3.41767
$358$	−0.809126	−0.0427636
$359$	29.8672	1.57633	0.788164	−	0.615465i	$-0.211032\pi$
$359$	29.8672	1.57633	0.788164	+	0.615465i	$0.211032\pi$
$360$	−0.199935	−0.0105375
$361$	−3.05817	−0.160956
$362$	6.46980	0.340045
$363$	1.69948	0.0891995
$364$	0	0
$365$	5.41826	0.283604
$366$	2.64521	0.138267
$367$	11.1888	0.584053	0.292026	−	0.956410i	$-0.405671\pi$
$367$	11.1888	0.584053	0.292026	+	0.956410i	$0.405671\pi$
$368$	10.4285	0.543621
$369$	0.679526	0.0353747
$370$	−0.323798	−0.0168335
$371$	−10.4977	−0.545015
$372$	−23.9692	−1.24274
$373$	−18.9915	−0.983341	−0.491670	−	0.870781i	$-0.663613\pi$
$373$	−18.9915	−0.983341	−0.491670	+	0.870781i	$0.663613\pi$
$374$	−2.93991	−0.152019
$375$	17.3042	0.893586
$376$	−4.93641	−0.254576
$377$	0	0
$378$	10.5427	0.542258
$379$	−1.95187	−0.100261	−0.0501303	−	0.998743i	$-0.515964\pi$
$379$	−1.95187	−0.100261	−0.0501303	+	0.998743i	$0.515964\pi$
$380$	8.72797	0.447735
$381$	14.3912	0.737282
$382$	−2.08385	−0.106619
$383$	−21.5371	−1.10049	−0.550247	−	0.835002i	$-0.685467\pi$
$383$	−21.5371	−1.10049	−0.550247	+	0.835002i	$0.685467\pi$
$384$	−17.4286	−0.889400
$385$	−6.01162	−0.306381
$386$	5.52856	0.281396
$387$	1.02607	0.0521583
$388$	23.4911	1.19258
$389$	−8.59364	−0.435715	−0.217858	−	0.975981i	$-0.569907\pi$
$389$	−8.59364	−0.435715	−0.217858	+	0.975981i	$0.569907\pi$
$390$	0	0
$391$	25.1954	1.27419
$392$	−28.3436	−1.43157
$393$	5.22846	0.263741
$394$	8.60110	0.433317
$395$	−3.48008	−0.175102
$396$	−0.206302	−0.0103671
$397$	17.7313	0.889911	0.444955	−	0.895553i	$-0.353220\pi$
$397$	17.7313	0.889911	0.444955	+	0.895553i	$0.353220\pi$
$398$	−8.39914	−0.421011
$399$	−34.4434	−1.72433
$400$	−11.1458	−0.557291
$401$	−0.312092	−0.0155851	−0.00779256	−	0.999970i	$-0.502480\pi$
$401$	−0.312092	−0.0155851	−0.00779256	+	0.999970i	$0.502480\pi$
$402$	−3.46067	−0.172603
$403$	0	0
$404$	10.0093	0.497983
$405$	10.2470	0.509177
$406$	−17.2307	−0.855147
$407$	−0.696141	−0.0345064
$408$	−19.2146	−0.951264
$409$	6.60890	0.326789	0.163394	−	0.986561i	$-0.447756\pi$
$409$	6.60890	0.326789	0.163394	+	0.986561i	$0.447756\pi$
$410$	2.82783	0.139657
$411$	−10.9219	−0.538738
$412$	19.3723	0.954402
$413$	−16.7143	−0.822456
$414$	−0.147751	−0.00726157
$415$	−1.74973	−0.0858909
$416$	0	0
$417$	19.1550	0.938023
$418$	−1.56811	−0.0766986
$419$	23.8929	1.16724	0.583622	−	0.812025i	$-0.301635\pi$
$419$	23.8929	1.16724	0.583622	+	0.812025i	$0.301635\pi$
$420$	−18.8574	−0.920146
$421$	−1.81207	−0.0883148	−0.0441574	−	0.999025i	$-0.514060\pi$
$421$	−1.81207	−0.0883148	−0.0441574	+	0.999025i	$0.514060\pi$
$422$	−2.36450	−0.115102
$423$	−0.365303	−0.0177616
$424$	−3.12365	−0.151698
$425$	−26.9286	−1.30623
$426$	2.72262	0.131911
$427$	−20.1168	−0.973520
$428$	−17.0474	−0.824017
$429$	0	0
$430$	4.26998	0.205917
$431$	30.9597	1.49128	0.745639	−	0.666350i	$-0.232144\pi$
$431$	30.9597	1.49128	0.745639	+	0.666350i	$0.232144\pi$
$432$	−16.3851	−0.788329
$433$	−14.4440	−0.694135	−0.347067	−	0.937840i	$-0.612823\pi$
$433$	−14.4440	−0.694135	−0.347067	+	0.937840i	$0.612823\pi$
$434$	−15.2332	−0.731217
$435$	−17.3965	−0.834098
$436$	11.7047	0.560551
$437$	13.4389	0.642869
$438$	−3.05360	−0.145907
$439$	−17.5001	−0.835234	−0.417617	−	0.908623i	$-0.637135\pi$
$439$	−17.5001	−0.835234	−0.417617	+	0.908623i	$0.637135\pi$
$440$	−1.78879	−0.0852770
$441$	−2.09747	−0.0998796
$442$	0	0
$443$	−38.1706	−1.81354	−0.906769	−	0.421627i	$-0.861459\pi$
$443$	−38.1706	−1.81354	−0.906769	+	0.421627i	$0.861459\pi$
$444$	−2.18367	−0.103632
$445$	−20.1400	−0.954727
$446$	−1.50792	−0.0714022
$447$	27.1512	1.28421
$448$	23.0062	1.08694
$449$	−15.8627	−0.748609	−0.374304	−	0.927306i	$-0.622118\pi$
$449$	−15.8627	−0.748609	−0.374304	+	0.927306i	$0.622118\pi$
$450$	0.157915	0.00744417
$451$	6.07962	0.286278
$452$	−4.18595	−0.196890
$453$	8.15135	0.382984
$454$	1.01146	0.0474703
$455$	0	0
$456$	−10.2488	−0.479944
$457$	10.1022	0.472563	0.236281	−	0.971685i	$-0.424071\pi$
$457$	10.1022	0.472563	0.236281	+	0.971685i	$0.424071\pi$
$458$	2.04801	0.0956975
$459$	−39.5868	−1.84775
$460$	7.35764	0.343052
$461$	−20.7276	−0.965380	−0.482690	−	0.875791i	$-0.660340\pi$
$461$	−20.7276	−0.965380	−0.482690	+	0.875791i	$0.660340\pi$
$462$	3.38800	0.157624
$463$	6.34630	0.294938	0.147469	−	0.989067i	$-0.452887\pi$
$463$	6.34630	0.294938	0.147469	+	0.989067i	$0.452887\pi$
$464$	26.7794	1.24320
$465$	−15.3797	−0.713218
$466$	1.91644	0.0887773
$467$	−30.6350	−1.41762	−0.708809	−	0.705401i	$-0.750767\pi$
$467$	−30.6350	−1.41762	−0.708809	+	0.705401i	$0.750767\pi$
$468$	0	0
$469$	26.3184	1.21527
$470$	−1.52020	−0.0701215
$471$	32.9168	1.51673
$472$	−4.97341	−0.228920
$473$	9.18013	0.422103
$474$	1.96129	0.0900850
$475$	−14.3633	−0.659035
$476$	70.1330	3.21454
$477$	−0.231155	−0.0105839
$478$	8.85240	0.404899
$479$	25.8557	1.18137	0.590687	−	0.806900i	$-0.298857\pi$
$479$	25.8557	1.18137	0.590687	+	0.806900i	$0.298857\pi$
$480$	−8.52918	−0.389302
$481$	0	0
$482$	4.14510	0.188804
$483$	−29.0357	−1.32117
$484$	−1.84575	−0.0838979
$485$	15.0730	0.684429
$486$	0.455952	0.0206824
$487$	15.3630	0.696165	0.348082	−	0.937464i	$-0.386833\pi$
$487$	15.3630	0.696165	0.348082	+	0.937464i	$0.386833\pi$
$488$	−5.98584	−0.270966
$489$	−15.9958	−0.723355
$490$	−8.72857	−0.394317
$491$	−21.8812	−0.987483	−0.493742	−	0.869609i	$-0.664371\pi$
$491$	−21.8812	−0.987483	−0.493742	+	0.869609i	$0.664371\pi$
$492$	19.0707	0.859772
$493$	64.6998	2.91393
$494$	0	0
$495$	−0.132373	−0.00594973
$496$	23.6749	1.06304
$497$	−20.7055	−0.928768
$498$	0.986106	0.0441885
$499$	−23.9077	−1.07026	−0.535128	−	0.844771i	$-0.679737\pi$
$499$	−23.9077	−1.07026	−0.535128	+	0.844771i	$0.679737\pi$
$500$	−18.7936	−0.840476
$501$	−0.604911	−0.0270254
$502$	−2.92764	−0.130667
$503$	−36.3671	−1.62153	−0.810764	−	0.585374i	$-0.800948\pi$
$503$	−36.3671	−1.62153	−0.810764	+	0.585374i	$0.800948\pi$
$504$	−0.856919	−0.0381702
$505$	6.42246	0.285796
$506$	−1.32191	−0.0587660
$507$	0	0
$508$	−15.6298	−0.693461
$509$	−37.9752	−1.68322	−0.841610	−	0.540086i	$-0.818392\pi$
$509$	−37.9752	−1.68322	−0.841610	+	0.540086i	$0.818392\pi$
$510$	−5.91725	−0.262020
$511$	23.2226	1.02731
$512$	22.4888	0.993873
$513$	−21.1151	−0.932253
$514$	6.19444	0.273225
$515$	12.4302	0.547738
$516$	28.7964	1.26769
$517$	−3.26831	−0.143740
$518$	−1.38780	−0.0609762
$519$	16.3271	0.716678
$520$	0	0
$521$	−35.7131	−1.56462	−0.782309	−	0.622890i	$-0.785958\pi$
$521$	−35.7131	−1.56462	−0.782309	+	0.622890i	$0.785958\pi$
$522$	−0.379413	−0.0166065
$523$	−12.4494	−0.544373	−0.272187	−	0.962244i	$-0.587747\pi$
$523$	−12.4494	−0.544373	−0.272187	+	0.962244i	$0.587747\pi$
$524$	−5.67848	−0.248065
$525$	31.0330	1.35439
$526$	−0.642776	−0.0280264
$527$	57.1992	2.49164
$528$	−5.26552	−0.229153
$529$	−11.6711	−0.507438
$530$	−0.961947	−0.0417843
$531$	−0.368041	−0.0159716
$532$	37.4080	1.62184
$533$	0	0
$534$	11.3504	0.491180
$535$	−10.9384	−0.472909
$536$	7.83117	0.338255
$537$	−3.50127	−0.151091
$538$	−2.47678	−0.106782
$539$	−18.7658	−0.808299
$540$	−11.5603	−0.497474
$541$	−32.1150	−1.38073	−0.690365	−	0.723461i	$-0.742550\pi$
$541$	−32.1150	−1.38073	−0.690365	+	0.723461i	$0.742550\pi$
$542$	1.13969	0.0489537
$543$	27.9963	1.20143
$544$	31.7211	1.36003
$545$	7.51026	0.321704
$546$	0	0
$547$	−9.83396	−0.420470	−0.210235	−	0.977651i	$-0.567423\pi$
$547$	−9.83396	−0.420470	−0.210235	+	0.977651i	$0.567423\pi$
$548$	11.8620	0.506718
$549$	−0.442963	−0.0189052
$550$	1.41284	0.0602437
$551$	34.5100	1.47018
$552$	−8.63969	−0.367730
$553$	−14.9156	−0.634276
$554$	−1.35267	−0.0574694
$555$	−1.40115	−0.0594753
$556$	−20.8037	−0.882272
$557$	17.7820	0.753448	0.376724	−	0.926326i	$-0.377050\pi$
$557$	17.7820	0.753448	0.376724	+	0.926326i	$0.377050\pi$
$558$	−0.335428	−0.0141998
$559$	0	0
$560$	18.6259	0.787089
$561$	−12.7216	−0.537108
$562$	9.33360	0.393714
$563$	−12.4588	−0.525076	−0.262538	−	0.964922i	$-0.584559\pi$
$563$	−12.4588	−0.525076	−0.262538	+	0.964922i	$0.584559\pi$
$564$	−10.2521	−0.431691
$565$	−2.68590	−0.112997
$566$	4.23395	0.177966
$567$	43.9185	1.84440
$568$	−6.16101	−0.258510
$569$	−26.1052	−1.09439	−0.547194	−	0.837006i	$-0.684304\pi$
$569$	−26.1052	−1.09439	−0.547194	+	0.837006i	$0.684304\pi$
$570$	−3.15618	−0.132198
$571$	25.9415	1.08562	0.542808	−	0.839857i	$-0.317361\pi$
$571$	25.9415	1.08562	0.542808	+	0.839857i	$0.317361\pi$
$572$	0	0
$573$	−9.01728	−0.376702
$574$	12.1201	0.505881
$575$	−12.1082	−0.504948
$576$	0.506586	0.0211078
$577$	3.87306	0.161238	0.0806188	−	0.996745i	$-0.474310\pi$
$577$	3.87306	0.161238	0.0806188	+	0.996745i	$0.474310\pi$
$578$	15.3304	0.637660
$579$	23.9233	0.994219
$580$	18.8938	0.784523
$581$	−7.49933	−0.311125
$582$	−8.49477	−0.352120
$583$	−2.06811	−0.0856525
$584$	6.90999	0.285937
$585$	0	0
$586$	1.86820	0.0771748
$587$	−25.8064	−1.06514	−0.532571	−	0.846385i	$-0.678774\pi$
$587$	−25.8064	−1.06514	−0.532571	+	0.846385i	$0.678774\pi$
$588$	−58.8649	−2.42755
$589$	30.5093	1.25711
$590$	−1.53159	−0.0630547
$591$	37.2189	1.53098
$592$	2.15687	0.0886466
$593$	−20.2687	−0.832336	−0.416168	−	0.909288i	$-0.636627\pi$
$593$	−20.2687	−0.832336	−0.416168	+	0.909288i	$0.636627\pi$
$594$	2.07697	0.0852191
$595$	45.0006	1.84485
$596$	−29.4881	−1.20788
$597$	−36.3449	−1.48750
$598$	0	0
$599$	−11.0704	−0.452324	−0.226162	−	0.974090i	$-0.572618\pi$
$599$	−11.0704	−0.452324	−0.226162	+	0.974090i	$0.572618\pi$
$600$	9.23401	0.376977
$601$	−15.0016	−0.611926	−0.305963	−	0.952043i	$-0.598978\pi$
$601$	−15.0016	−0.611926	−0.305963	+	0.952043i	$0.598978\pi$
$602$	18.3011	0.745897
$603$	0.579520	0.0235999
$604$	−8.85294	−0.360221
$605$	−1.18432	−0.0481496
$606$	−3.61954	−0.147034
$607$	−23.6370	−0.959395	−0.479697	−	0.877434i	$-0.659254\pi$
$607$	−23.6370	−0.959395	−0.479697	+	0.877434i	$0.659254\pi$
$608$	16.9196	0.686181
$609$	−74.5612	−3.02137
$610$	−1.84338	−0.0746361
$611$	0	0
$612$	1.54430	0.0624245
$613$	−18.5235	−0.748158	−0.374079	−	0.927397i	$-0.622041\pi$
$613$	−18.5235	−0.748158	−0.374079	+	0.927397i	$0.622041\pi$
$614$	−3.48865	−0.140790
$615$	12.2366	0.493429
$616$	−7.66672	−0.308901
$617$	−35.3078	−1.42144	−0.710719	−	0.703476i	$-0.751630\pi$
$617$	−35.3078	−1.42144	−0.710719	+	0.703476i	$0.751630\pi$
$618$	−7.00533	−0.281796
$619$	−9.29917	−0.373765	−0.186883	−	0.982382i	$-0.559838\pi$
$619$	−9.29917	−0.373765	−0.186883	+	0.982382i	$0.559838\pi$
$620$	16.7035	0.670828
$621$	−17.7999	−0.714286
$622$	−1.15359	−0.0462546
$623$	−86.3198	−3.45833
$624$	0	0
$625$	5.92803	0.237121
$626$	−13.3159	−0.532211
$627$	−6.78555	−0.270989
$628$	−35.7500	−1.42658
$629$	5.21104	0.207778
$630$	−0.263893	−0.0105138
$631$	40.3206	1.60514	0.802569	−	0.596559i	$-0.203466\pi$
$631$	40.3206	1.60514	0.802569	+	0.596559i	$0.203466\pi$
$632$	−4.43820	−0.176542
$633$	−10.2317	−0.406674
$634$	−6.34614	−0.252037
$635$	−10.0288	−0.397982
$636$	−6.48730	−0.257238
$637$	0	0
$638$	−3.39455	−0.134392
$639$	−0.455926	−0.0180361
$640$	12.1455	0.480095
$641$	−34.3899	−1.35832	−0.679160	−	0.733991i	$-0.737656\pi$
$641$	−34.3899	−1.35832	−0.679160	+	0.733991i	$0.737656\pi$
$642$	6.16463	0.243298
$643$	−13.2767	−0.523582	−0.261791	−	0.965125i	$-0.584313\pi$
$643$	−13.2767	−0.523582	−0.261791	+	0.965125i	$0.584313\pi$
$644$	31.5348	1.24264
$645$	18.4772	0.727537
$646$	11.7382	0.461835
$647$	49.6984	1.95385	0.976923	−	0.213594i	$-0.0685170\pi$
$647$	49.6984	1.95385	0.976923	+	0.213594i	$0.0685170\pi$
$648$	13.0682	0.513366
$649$	−3.29281	−0.129254
$650$	0	0
$651$	−65.9174	−2.58351
$652$	17.3726	0.680363
$653$	43.2439	1.69226	0.846131	−	0.532974i	$-0.178926\pi$
$653$	43.2439	1.69226	0.846131	+	0.532974i	$0.178926\pi$
$654$	−4.23260	−0.165508
$655$	−3.64358	−0.142366
$656$	−18.8366	−0.735445
$657$	0.511351	0.0199497
$658$	−6.51555	−0.254003
$659$	23.2059	0.903975	0.451987	−	0.892024i	$-0.350715\pi$
$659$	23.2059	0.903975	0.451987	+	0.892024i	$0.350715\pi$
$660$	−3.71501	−0.144607
$661$	−24.5835	−0.956188	−0.478094	−	0.878309i	$-0.658672\pi$
$661$	−24.5835	−0.956188	−0.478094	+	0.878309i	$0.658672\pi$
$662$	13.3088	0.517260
$663$	0	0
$664$	−2.23146	−0.0865975
$665$	24.0027	0.930787
$666$	−0.0305586	−0.00118412
$667$	29.0918	1.12644
$668$	0.656976	0.0254191
$669$	−6.52511	−0.252275
$670$	2.41166	0.0931704
$671$	−3.96312	−0.152995
$672$	−36.5560	−1.41018
$673$	44.6671	1.72179	0.860895	−	0.508782i	$-0.169904\pi$
$673$	44.6671	1.72179	0.860895	+	0.508782i	$0.169904\pi$
$674$	9.94136	0.382927
$675$	19.0243	0.732247
$676$	0	0
$677$	28.7385	1.10451	0.552255	−	0.833675i	$-0.313767\pi$
$677$	28.7385	1.10451	0.552255	+	0.833675i	$0.313767\pi$
$678$	1.51371	0.0581336
$679$	64.6027	2.47922
$680$	13.3901	0.513489
$681$	4.37683	0.167720
$682$	−3.00103	−0.114915
$683$	−41.4598	−1.58642	−0.793208	−	0.608951i	$-0.791590\pi$
$683$	−41.4598	−1.58642	−0.793208	+	0.608951i	$0.791590\pi$
$684$	0.823707	0.0314952
$685$	7.61120	0.290809
$686$	−23.4557	−0.895543
$687$	8.86221	0.338115
$688$	−28.4430	−1.08438
$689$	0	0
$690$	−2.66065	−0.101289
$691$	15.9472	0.606662	0.303331	−	0.952885i	$-0.401901\pi$
$691$	15.9472	0.606662	0.303331	+	0.952885i	$0.401901\pi$
$692$	−17.7323	−0.674082
$693$	−0.567351	−0.0215519
$694$	3.78834	0.143804
$695$	−13.3486	−0.506342
$696$	−22.1860	−0.840960
$697$	−45.5096	−1.72380
$698$	2.42044	0.0916150
$699$	8.29285	0.313665
$700$	−33.7040	−1.27389
$701$	−31.6321	−1.19473	−0.597364	−	0.801970i	$-0.703785\pi$
$701$	−31.6321	−1.19473	−0.597364	+	0.801970i	$0.703785\pi$
$702$	0	0
$703$	2.77950	0.104831
$704$	4.53235	0.170819
$705$	−6.57823	−0.247750
$706$	6.12509	0.230521
$707$	27.5266	1.03525
$708$	−10.3289	−0.388185
$709$	23.8506	0.895728	0.447864	−	0.894102i	$-0.352185\pi$
$709$	23.8506	0.895728	0.447864	+	0.894102i	$0.352185\pi$
$710$	−1.89732	−0.0712052
$711$	−0.328435	−0.0123173
$712$	−25.6849	−0.962580
$713$	25.7192	0.963191
$714$	−25.3613	−0.949122
$715$	0	0
$716$	3.80262	0.142111
$717$	38.3063	1.43058
$718$	11.7301	0.437762
$719$	−1.19250	−0.0444727	−0.0222363	−	0.999753i	$-0.507079\pi$
$719$	−1.19250	−0.0444727	−0.0222363	+	0.999753i	$0.507079\pi$
$720$	0.410134	0.0152848
$721$	53.2755	1.98408
$722$	−1.20107	−0.0446991
$723$	17.9368	0.667075
$724$	−30.4059	−1.13003
$725$	−31.0929	−1.15476
$726$	0.667456	0.0247716
$727$	6.56110	0.243338	0.121669	−	0.992571i	$-0.461175\pi$
$727$	6.56110	0.243338	0.121669	+	0.992571i	$0.461175\pi$
$728$	0	0
$729$	27.9296	1.03443
$730$	2.12797	0.0787598
$731$	−68.7189	−2.54166
$732$	−12.4316	−0.459485
$733$	33.7942	1.24822	0.624108	−	0.781338i	$-0.285462\pi$
$733$	33.7942	1.24822	0.624108	+	0.781338i	$0.285462\pi$
$734$	4.39432	0.162197
$735$	−37.7705	−1.39318
$736$	14.2631	0.525747
$737$	5.18488	0.190987
$738$	0.266878	0.00982392
$739$	27.5257	1.01255	0.506275	−	0.862372i	$-0.331022\pi$
$739$	27.5257	1.01255	0.506275	+	0.862372i	$0.331022\pi$
$740$	1.52174	0.0559404
$741$	0	0
$742$	−4.12290	−0.151356
$743$	−35.6938	−1.30948	−0.654740	−	0.755854i	$-0.727222\pi$
$743$	−35.6938	−1.30948	−0.654740	+	0.755854i	$0.727222\pi$
$744$	−19.6140	−0.719086
$745$	−18.9210	−0.693211
$746$	−7.45873	−0.273084
$747$	−0.165132	−0.00604186
$748$	13.8166	0.505185
$749$	−46.8820	−1.71303
$750$	6.79608	0.248158
$751$	−37.4060	−1.36496	−0.682481	−	0.730903i	$-0.739099\pi$
$751$	−37.4060	−1.36496	−0.682481	+	0.730903i	$0.739099\pi$
$752$	10.1263	0.369267
$753$	−12.6685	−0.461667
$754$	0	0
$755$	−5.68047	−0.206733
$756$	−49.5472	−1.80201
$757$	37.7065	1.37047	0.685233	−	0.728324i	$-0.259701\pi$
$757$	37.7065	1.37047	0.685233	+	0.728324i	$0.259701\pi$
$758$	−0.766579	−0.0278434
$759$	−5.72019	−0.207630
$760$	7.14213	0.259072
$761$	−8.45318	−0.306428	−0.153214	−	0.988193i	$-0.548962\pi$
$761$	−8.45318	−0.306428	−0.153214	+	0.988193i	$0.548962\pi$
$762$	5.65201	0.204751
$763$	32.1889	1.16532
$764$	9.79340	0.354313
$765$	0.990894	0.0358258
$766$	−8.45851	−0.305618
$767$	0	0
$768$	8.56033	0.308894
$769$	−6.42082	−0.231541	−0.115770	−	0.993276i	$-0.536934\pi$
$769$	−6.42082	−0.231541	−0.115770	+	0.993276i	$0.536934\pi$
$770$	−2.36101	−0.0850850
$771$	26.8047	0.965348
$772$	−25.9824	−0.935127
$773$	31.3080	1.12607	0.563035	−	0.826433i	$-0.309634\pi$
$773$	31.3080	1.12607	0.563035	+	0.826433i	$0.309634\pi$
$774$	0.402982	0.0144849
$775$	−27.4884	−0.987412
$776$	19.2228	0.690059
$777$	−6.00530	−0.215439
$778$	−3.37508	−0.121002
$779$	−24.2742	−0.869715
$780$	0	0
$781$	−4.07910	−0.145962
$782$	9.89528	0.353854
$783$	−45.7087	−1.63350
$784$	58.1423	2.07651
$785$	−22.9389	−0.818724
$786$	2.05343	0.0732435
$787$	−42.1141	−1.50121	−0.750603	−	0.660754i	$-0.770237\pi$
$787$	−42.1141	−1.50121	−0.750603	+	0.660754i	$0.770237\pi$
$788$	−40.4223	−1.43999
$789$	−2.78143	−0.0990217
$790$	−1.36677	−0.0486276
$791$	−11.5118	−0.409311
$792$	−0.168818	−0.00599868
$793$	0	0
$794$	6.96383	0.247137
$795$	−4.16256	−0.147631
$796$	39.4732	1.39909
$797$	10.5972	0.375374	0.187687	−	0.982229i	$-0.439901\pi$
$797$	10.5972	0.375374	0.187687	+	0.982229i	$0.439901\pi$
$798$	−13.5274	−0.478863
$799$	24.4653	0.865519
$800$	−15.2443	−0.538967
$801$	−1.90072	−0.0671587
$802$	−0.122571	−0.00432814
$803$	4.57498	0.161448
$804$	16.2640	0.573588
$805$	20.2342	0.713162
$806$	0	0
$807$	−10.7176	−0.377277
$808$	8.19067	0.288147
$809$	5.29034	0.185998	0.0929992	−	0.995666i	$-0.470355\pi$
$809$	5.29034	0.185998	0.0929992	+	0.995666i	$0.470355\pi$
$810$	4.02442	0.141404
$811$	−13.4655	−0.472837	−0.236419	−	0.971651i	$-0.575974\pi$
$811$	−13.4655	−0.472837	−0.236419	+	0.971651i	$0.575974\pi$
$812$	80.9788	2.84180
$813$	4.93167	0.172961
$814$	−0.273403	−0.00958278
$815$	11.1471	0.390465
$816$	39.4156	1.37982
$817$	−36.6537	−1.28235
$818$	2.59559	0.0907526
$819$	0	0
$820$	−13.2899	−0.464102
$821$	−23.1787	−0.808941	−0.404470	−	0.914551i	$-0.632544\pi$
$821$	−23.1787	−0.808941	−0.404470	+	0.914551i	$0.632544\pi$
$822$	−4.28949	−0.149613
$823$	−9.64680	−0.336266	−0.168133	−	0.985764i	$-0.553774\pi$
$823$	−9.64680	−0.336266	−0.168133	+	0.985764i	$0.553774\pi$
$824$	15.8524	0.552244
$825$	6.11367	0.212851
$826$	−6.56439	−0.228404
$827$	−20.8985	−0.726710	−0.363355	−	0.931651i	$-0.618369\pi$
$827$	−20.8985	−0.726710	−0.363355	+	0.931651i	$0.618369\pi$
$828$	0.694381	0.0241314
$829$	30.1544	1.04730	0.523652	−	0.851932i	$-0.324569\pi$
$829$	30.1544	1.04730	0.523652	+	0.851932i	$0.324569\pi$
$830$	−0.687192	−0.0238528
$831$	−5.85330	−0.203049
$832$	0	0
$833$	140.473	4.86711
$834$	7.52295	0.260499
$835$	0.421547	0.0145882
$836$	7.36958	0.254882
$837$	−40.4098	−1.39677
$838$	9.38373	0.324156
$839$	18.9148	0.653010	0.326505	−	0.945196i	$-0.394129\pi$
$839$	18.9148	0.653010	0.326505	+	0.945196i	$0.394129\pi$
$840$	−15.4311	−0.532422
$841$	45.7053	1.57605
$842$	−0.711674	−0.0245259
$843$	40.3886	1.39106
$844$	11.1123	0.382503
$845$	0	0
$846$	−0.143469	−0.00493258
$847$	−5.07600	−0.174413
$848$	6.40767	0.220040
$849$	18.3213	0.628784
$850$	−10.5760	−0.362752
$851$	2.34310	0.0803206
$852$	−12.7954	−0.438363
$853$	22.4051	0.767137	0.383568	−	0.923512i	$-0.374695\pi$
$853$	22.4051	0.767137	0.383568	+	0.923512i	$0.374695\pi$
$854$	−7.90070	−0.270356
$855$	0.528530	0.0180753
$856$	−13.9499	−0.476799
$857$	26.9098	0.919221	0.459611	−	0.888121i	$-0.347989\pi$
$857$	26.9098	0.919221	0.459611	+	0.888121i	$0.347989\pi$
$858$	0	0
$859$	−30.0689	−1.02594	−0.512969	−	0.858407i	$-0.671455\pi$
$859$	−30.0689	−1.02594	−0.512969	+	0.858407i	$0.671455\pi$
$860$	−20.0675	−0.684296
$861$	52.4462	1.78736
$862$	12.1592	0.414143
$863$	23.4958	0.799805	0.399902	−	0.916558i	$-0.369044\pi$
$863$	23.4958	0.799805	0.399902	+	0.916558i	$0.369044\pi$
$864$	−22.4101	−0.762408
$865$	−11.3779	−0.386860
$866$	−5.67276	−0.192768
$867$	66.3380	2.25296
$868$	71.5910	2.42996
$869$	−2.93846	−0.0996803
$870$	−6.83232	−0.231637
$871$	0	0
$872$	9.57796	0.324351
$873$	1.42252	0.0481451
$874$	5.27801	0.178531
$875$	−51.6842	−1.74725
$876$	14.3509	0.484872
$877$	11.2925	0.381322	0.190661	−	0.981656i	$-0.438937\pi$
$877$	11.2925	0.381322	0.190661	+	0.981656i	$0.438937\pi$
$878$	−6.87301	−0.231953
$879$	8.08413	0.272671
$880$	3.66941	0.123696
$881$	−38.5640	−1.29925	−0.649627	−	0.760253i	$-0.725075\pi$
$881$	−38.5640	−1.29925	−0.649627	+	0.760253i	$0.725075\pi$
$882$	−0.823764	−0.0277376
$883$	−7.19873	−0.242257	−0.121128	−	0.992637i	$-0.538651\pi$
$883$	−7.19873	−0.242257	−0.121128	+	0.992637i	$0.538651\pi$
$884$	0	0
$885$	−6.62754	−0.222782
$886$	−14.9912	−0.503638
$887$	15.9910	0.536925	0.268462	−	0.963290i	$-0.413485\pi$
$887$	15.9910	0.536925	0.268462	+	0.963290i	$0.413485\pi$
$888$	−1.78690	−0.0599646
$889$	−42.9835	−1.44162
$890$	−7.90980	−0.265137
$891$	8.65219	0.289859
$892$	7.08673	0.237281
$893$	13.0494	0.436683
$894$	10.6634	0.356637
$895$	2.43994	0.0815583
$896$	52.0557	1.73906
$897$	0	0
$898$	−6.22995	−0.207896
$899$	66.0448	2.20272
$900$	−0.742147	−0.0247382
$901$	15.4811	0.515749
$902$	2.38772	0.0795023
$903$	79.1929	2.63538
$904$	−3.42538	−0.113926
$905$	−19.5099	−0.648530
$906$	3.20137	0.106359
$907$	40.5290	1.34574	0.672871	−	0.739760i	$-0.265061\pi$
$907$	40.5290	1.34574	0.672871	+	0.739760i	$0.265061\pi$
$908$	−4.75354	−0.157752
$909$	0.606124	0.0201039
$910$	0	0
$911$	−40.3365	−1.33641	−0.668204	−	0.743978i	$-0.732937\pi$
$911$	−40.3365	−1.33641	−0.668204	+	0.743978i	$0.732937\pi$
$912$	21.0238	0.696167
$913$	−1.47741	−0.0488951
$914$	3.96757	0.131236
$915$	−7.97670	−0.263702
$916$	−9.62499	−0.318019
$917$	−15.6164	−0.515697
$918$	−15.5474	−0.513140
$919$	28.3729	0.935937	0.467969	−	0.883745i	$-0.344986\pi$
$919$	28.3729	0.935937	0.467969	+	0.883745i	$0.344986\pi$
$920$	6.02078	0.198499
$921$	−15.0962	−0.497435
$922$	−8.14058	−0.268096
$923$	0	0
$924$	−15.9225	−0.523812
$925$	−2.50428	−0.0823403
$926$	2.49246	0.0819072
$927$	1.17310	0.0385298
$928$	36.6266	1.20233
$929$	−41.0810	−1.34782	−0.673912	−	0.738812i	$-0.735387\pi$
$929$	−41.0810	−1.34782	−0.673912	+	0.738812i	$0.735387\pi$
$930$	−6.04026	−0.198068
$931$	74.9265	2.45562
$932$	−9.00663	−0.295022
$933$	−4.99182	−0.163425
$934$	−12.0316	−0.393687
$935$	8.86538	0.289929
$936$	0	0
$937$	−14.8078	−0.483749	−0.241875	−	0.970307i	$-0.577762\pi$
$937$	−14.8078	−0.483749	−0.241875	+	0.970307i	$0.577762\pi$
$938$	10.3363	0.337493
$939$	−57.6209	−1.88039
$940$	7.14442	0.233025
$941$	20.6634	0.673607	0.336804	−	0.941575i	$-0.390654\pi$
$941$	20.6634	0.673607	0.336804	+	0.941575i	$0.390654\pi$
$942$	12.9278	0.421211
$943$	−20.4631	−0.666369
$944$	10.2022	0.332052
$945$	−31.7918	−1.03419
$946$	3.60542	0.117222
$947$	−57.5188	−1.86911	−0.934554	−	0.355820i	$-0.884202\pi$
$947$	−57.5188	−1.86911	−0.934554	+	0.355820i	$0.884202\pi$
$948$	−9.21741	−0.299367
$949$	0	0
$950$	−5.64108	−0.183021
$951$	−27.4612	−0.890489
$952$	57.3901	1.86002
$953$	9.74354	0.315624	0.157812	−	0.987469i	$-0.449556\pi$
$953$	9.74354	0.315624	0.157812	+	0.987469i	$0.449556\pi$
$954$	−0.0907843	−0.00293925
$955$	6.28391	0.203343
$956$	−41.6034	−1.34555
$957$	−14.6890	−0.474827
$958$	10.1546	0.328080
$959$	32.6215	1.05340
$960$	9.12240	0.294424
$961$	27.3883	0.883495
$962$	0	0
$963$	−1.03232	−0.0332660
$964$	−19.4806	−0.627428
$965$	−16.6715	−0.536676
$966$	−11.4035	−0.366902
$967$	0.920789	0.0296106	0.0148053	−	0.999890i	$-0.495287\pi$
$967$	0.920789	0.0296106	0.0148053	+	0.999890i	$0.495287\pi$
$968$	−1.51039	−0.0485457
$969$	50.7939	1.63174
$970$	5.91979	0.190073
$971$	−35.6324	−1.14350	−0.571749	−	0.820429i	$-0.693735\pi$
$971$	−35.6324	−1.14350	−0.571749	+	0.820429i	$0.693735\pi$
$972$	−2.14282	−0.0687311
$973$	−57.2120	−1.83413
$974$	6.03369	0.193332
$975$	0	0
$976$	12.2790	0.393041
$977$	12.6314	0.404113	0.202056	−	0.979374i	$-0.435238\pi$
$977$	12.6314	0.404113	0.202056	+	0.979374i	$0.435238\pi$
$978$	−6.28222	−0.200883
$979$	−17.0055	−0.543497
$980$	41.0214	1.31038
$981$	0.708785	0.0226298
$982$	−8.59364	−0.274234
$983$	−15.5464	−0.495854	−0.247927	−	0.968779i	$-0.579749\pi$
$983$	−15.5464	−0.495854	−0.247927	+	0.968779i	$0.579749\pi$
$984$	15.6056	0.497488
$985$	−25.9369	−0.826418
$986$	25.4103	0.809228
$987$	−28.1942	−0.897432
$988$	0	0
$989$	−30.8989	−0.982529
$990$	−0.0519884	−0.00165230
$991$	26.1068	0.829310	0.414655	−	0.909979i	$-0.363902\pi$
$991$	26.1068	0.829310	0.414655	+	0.909979i	$0.363902\pi$
$992$	32.3805	1.02808
$993$	57.5900	1.82756
$994$	−8.13190	−0.257928
$995$	25.3279	0.802947
$996$	−4.63437	−0.146846
$997$	−14.2428	−0.451076	−0.225538	−	0.974234i	$-0.572414\pi$
$997$	−14.2428	−0.451076	−0.225538	+	0.974234i	$0.572414\pi$
$998$	−9.38955	−0.297221
$999$	−3.68146	−0.116476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1859.2.a.s.1.12	✓	21
13.12	even	2		1859.2.a.t.1.10	yes	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1859.2.a.s.1.12	✓	21	1.1	even	1	trivial
1859.2.a.t.1.10	yes	21	13.12	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.392741 q^{2} +1.69948 q^{3} -1.84575 q^{4} -1.18432 q^{5} +0.667456 q^{6} -5.07600 q^{7} -1.51039 q^{8} -0.111771 q^{9} +O(q^{10})\)	\(q+0.392741 q^{2} +1.69948 q^{3} -1.84575 q^{4} -1.18432 q^{5} +0.667456 q^{6} -5.07600 q^{7} -1.51039 q^{8} -0.111771 q^{9} -0.465133 q^{10} -1.00000 q^{11} -3.13682 q^{12} -1.99356 q^{14} -2.01273 q^{15} +3.09832 q^{16} +7.48561 q^{17} -0.0438972 q^{18} +3.99272 q^{19} +2.18597 q^{20} -8.62655 q^{21} -0.392741 q^{22} +3.36585 q^{23} -2.56687 q^{24} -3.59738 q^{25} -5.28839 q^{27} +9.36905 q^{28} +8.64322 q^{29} -0.790483 q^{30} +7.64123 q^{31} +4.23761 q^{32} -1.69948 q^{33} +2.93991 q^{34} +6.01162 q^{35} +0.206302 q^{36} +0.696141 q^{37} +1.56811 q^{38} +1.78879 q^{40} -6.07962 q^{41} -3.38800 q^{42} -9.18013 q^{43} +1.84575 q^{44} +0.132373 q^{45} +1.32191 q^{46} +3.26831 q^{47} +5.26552 q^{48} +18.7658 q^{49} -1.41284 q^{50} +12.7216 q^{51} +2.06811 q^{53} -2.07697 q^{54} +1.18432 q^{55} +7.66672 q^{56} +6.78555 q^{57} +3.39455 q^{58} +3.29281 q^{59} +3.71501 q^{60} +3.96312 q^{61} +3.00103 q^{62} +0.567351 q^{63} -4.53235 q^{64} -0.667456 q^{66} -5.18488 q^{67} -13.8166 q^{68} +5.72019 q^{69} +2.36101 q^{70} +4.07910 q^{71} +0.168818 q^{72} -4.57498 q^{73} +0.273403 q^{74} -6.11367 q^{75} -7.36958 q^{76} +5.07600 q^{77} +2.93846 q^{79} -3.66941 q^{80} -8.65219 q^{81} -2.38772 q^{82} +1.47741 q^{83} +15.9225 q^{84} -8.86538 q^{85} -3.60542 q^{86} +14.6890 q^{87} +1.51039 q^{88} +17.0055 q^{89} +0.0519884 q^{90} -6.21253 q^{92} +12.9861 q^{93} +1.28360 q^{94} -4.72867 q^{95} +7.20173 q^{96} -12.7271 q^{97} +7.37009 q^{98} +0.111771 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9}+O(q^{10}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9	\( 21 q + 6 q^{3} + 32 q^{4} - 7 q^{5} + 19 q^{6} - q^{7} + 3 q^{8} + 33 q^{9} + 18 q^{10} - 21 q^{11} + 23 q^{12} + 20 q^{14} - 16 q^{15} + 50 q^{16} + 16 q^{17} - 3 q^{18} + 11 q^{19} - 24 q^{20} + 5 q^{21} - 9 q^{23} + 54 q^{24} + 36 q^{25} + 11 q^{28} + 28 q^{29} + 21 q^{30} - 15 q^{31} + 61 q^{32} - 6 q^{33} + 6 q^{34} - 3 q^{35} + 45 q^{36} + 12 q^{37} + q^{38} + 55 q^{40} + 4 q^{41} - 34 q^{42} + 17 q^{43} - 32 q^{44} - 9 q^{45} - 11 q^{46} - 36 q^{47} + 24 q^{48} + 72 q^{49} + 9 q^{50} + 2 q^{51} + 19 q^{53} - q^{54} + 7 q^{55} + 44 q^{56} + 4 q^{57} + 33 q^{58} - 54 q^{59} - 64 q^{60} + 98 q^{61} - 29 q^{62} + 81 q^{63} + 63 q^{64} - 19 q^{66} - 25 q^{67} + 4 q^{68} + 89 q^{69} - 65 q^{70} - 37 q^{71} - 55 q^{72} - 8 q^{73} - 11 q^{74} + 24 q^{75} - 13 q^{76} + q^{77} + 24 q^{79} - 26 q^{80} + 81 q^{81} + 26 q^{82} + 34 q^{83} + 103 q^{84} + 11 q^{85} - 30 q^{86} + 32 q^{87} - 3 q^{88} - 6 q^{89} + 47 q^{90} - 80 q^{92} - 41 q^{93} + 40 q^{94} + 20 q^{95} + 98 q^{96} + 5 q^{98} - 33 q^{99}+O(q^{100}) \) 21 * q + 6 * q^3 + 32 * q^4 - 7 * q^5 + 19 * q^6 - q^7 + 3 * q^8 + 33 * q^9 + 18 * q^10 - 21 * q^11 + 23 * q^12 + 20 * q^14 - 16 * q^15 + 50 * q^16 + 16 * q^17 - 3 * q^18 + 11 * q^19 - 24 * q^20 + 5 * q^21 - 9 * q^23 + 54 * q^24 + 36 * q^25 + 11 * q^28 + 28 * q^29 + 21 * q^30 - 15 * q^31 + 61 * q^32 - 6 * q^33 + 6 * q^34 - 3 * q^35 + 45 * q^36 + 12 * q^37 + q^38 + 55 * q^40 + 4 * q^41 - 34 * q^42 + 17 * q^43 - 32 * q^44 - 9 * q^45 - 11 * q^46 - 36 * q^47 + 24 * q^48 + 72 * q^49 + 9 * q^50 + 2 * q^51 + 19 * q^53 - q^54 + 7 * q^55 + 44 * q^56 + 4 * q^57 + 33 * q^58 - 54 * q^59 - 64 * q^60 + 98 * q^61 - 29 * q^62 + 81 * q^63 + 63 * q^64 - 19 * q^66 - 25 * q^67 + 4 * q^68 + 89 * q^69 - 65 * q^70 - 37 * q^71 - 55 * q^72 - 8 * q^73 - 11 * q^74 + 24 * q^75 - 13 * q^76 + q^77 + 24 * q^79 - 26 * q^80 + 81 * q^81 + 26 * q^82 + 34 * q^83 + 103 * q^84 + 11 * q^85 - 30 * q^86 + 32 * q^87 - 3 * q^88 - 6 * q^89 + 47 * q^90 - 80 * q^92 - 41 * q^93 + 40 * q^94 + 20 * q^95 + 98 * q^96 + 5 * q^98 - 33 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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