LMFDB - Embedded newform 1573.2.a.s.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1573,2,Mod(1,1573)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1573, 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("1573.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1573 = 11^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1573.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:	$12.5604682379$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 21 x^{12} + 19 x^{11} + 169 x^{10} - 136 x^{9} - 649 x^{8} + 455 x^{7} + 1207 x^{6} + \cdots - 29 $ x^14 - x^13 - 21x^12 + 19x^11 + 169x^10 - 136x^9 - 649x^8 + 455x^7 + 1207x^6 - 708x^5 - 1001x^4 + 414x^3 + 343x^2 - 67x - 29
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
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			1.3
Root			$-1.99402$ of defining polynomial
Character	$\chi$	$=$	1573.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99402 q^{2} -2.52866 q^{3} +1.97611 q^{4} -1.82638 q^{5} +5.04220 q^{6} -2.02228 q^{7} +0.0476318 q^{8} +3.39413 q^{9} +O(q^{10})$	\(q-1.99402 q^{2} -2.52866 q^{3} +1.97611 q^{4} -1.82638 q^{5} +5.04220 q^{6} -2.02228 q^{7} +0.0476318 q^{8} +3.39413 q^{9} +3.64184 q^{10} -4.99692 q^{12} +1.00000 q^{13} +4.03247 q^{14} +4.61830 q^{15} -4.04720 q^{16} -1.65909 q^{17} -6.76795 q^{18} -1.97571 q^{19} -3.60914 q^{20} +5.11366 q^{21} +3.93925 q^{23} -0.120445 q^{24} -1.66433 q^{25} -1.99402 q^{26} -0.996609 q^{27} -3.99626 q^{28} -8.67673 q^{29} -9.20898 q^{30} -2.64870 q^{31} +7.97494 q^{32} +3.30826 q^{34} +3.69346 q^{35} +6.70717 q^{36} +1.38916 q^{37} +3.93960 q^{38} -2.52866 q^{39} -0.0869938 q^{40} -9.28747 q^{41} -10.1967 q^{42} -12.8417 q^{43} -6.19897 q^{45} -7.85494 q^{46} -6.15757 q^{47} +10.2340 q^{48} -2.91038 q^{49} +3.31870 q^{50} +4.19528 q^{51} +1.97611 q^{52} +12.3472 q^{53} +1.98726 q^{54} -0.0963248 q^{56} +4.99590 q^{57} +17.3016 q^{58} -4.01237 q^{59} +9.12628 q^{60} -15.5577 q^{61} +5.28155 q^{62} -6.86388 q^{63} -7.80777 q^{64} -1.82638 q^{65} +6.46440 q^{67} -3.27855 q^{68} -9.96103 q^{69} -7.36483 q^{70} +3.56879 q^{71} +0.161668 q^{72} +0.454095 q^{73} -2.77002 q^{74} +4.20852 q^{75} -3.90422 q^{76} +5.04220 q^{78} -4.82486 q^{79} +7.39174 q^{80} -7.66229 q^{81} +18.5194 q^{82} +7.57751 q^{83} +10.1052 q^{84} +3.03013 q^{85} +25.6065 q^{86} +21.9405 q^{87} -2.42469 q^{89} +12.3609 q^{90} -2.02228 q^{91} +7.78440 q^{92} +6.69765 q^{93} +12.2783 q^{94} +3.60840 q^{95} -20.1659 q^{96} -17.1245 q^{97} +5.80335 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * q^98

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 $

$2$	−1.99402	−1.40998	−0.704992	−	0.709215i	$-0.749050\pi$
$2$	−1.99402	−1.40998	−0.704992	+	0.709215i	$0.749050\pi$
$3$	−2.52866	−1.45992	−0.729961	−	0.683488i	$-0.760462\pi$
$3$	−2.52866	−1.45992	−0.729961	+	0.683488i	$0.760462\pi$
$4$	1.97611	0.988056
$5$	−1.82638	−0.816783	−0.408391	−	0.912807i	$-0.633910\pi$
$5$	−1.82638	−0.816783	−0.408391	+	0.912807i	$0.633910\pi$
$6$	5.04220	2.05847
$7$	−2.02228	−0.764350	−0.382175	−	0.924090i	$-0.624825\pi$
$7$	−2.02228	−0.764350	−0.382175	+	0.924090i	$0.624825\pi$
$8$	0.0476318	0.0168404
$9$	3.39413	1.13138
$10$	3.64184	1.15165
$11$	0	0
$11$	0	0
$12$	−4.99692	−1.44249
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.03247	1.07772
$15$	4.61830	1.19244
$16$	−4.04720	−1.01180
$17$	−1.65909	−0.402389	−0.201194	−	0.979551i	$-0.564482\pi$
$17$	−1.65909	−0.402389	−0.201194	+	0.979551i	$0.564482\pi$
$18$	−6.76795	−1.59522
$19$	−1.97571	−0.453258	−0.226629	−	0.973981i	$-0.572771\pi$
$19$	−1.97571	−0.453258	−0.226629	+	0.973981i	$0.572771\pi$
$20$	−3.60914	−0.807027
$21$	5.11366	1.11589
$22$	0	0
$23$	3.93925	0.821390	0.410695	−	0.911773i	$-0.365286\pi$
$23$	3.93925	0.821390	0.410695	+	0.911773i	$0.365286\pi$
$24$	−0.120445	−0.0245856
$25$	−1.66433	−0.332866
$26$	−1.99402	−0.391059
$27$	−0.996609	−0.191797
$28$	−3.99626	−0.755221
$29$	−8.67673	−1.61123	−0.805614	−	0.592441i	$-0.798164\pi$
$29$	−8.67673	−1.61123	−0.805614	+	0.592441i	$0.798164\pi$
$30$	−9.20898	−1.68132
$31$	−2.64870	−0.475720	−0.237860	−	0.971299i	$-0.576446\pi$
$31$	−2.64870	−0.475720	−0.237860	+	0.971299i	$0.576446\pi$
$32$	7.97494	1.40978
$33$	0	0
$34$	3.30826	0.567362
$35$	3.69346	0.624308
$36$	6.70717	1.11786
$37$	1.38916	0.228377	0.114188	−	0.993459i	$-0.463573\pi$
$37$	1.38916	0.228377	0.114188	+	0.993459i	$0.463573\pi$
$38$	3.93960	0.639087
$39$	−2.52866	−0.404910
$40$	−0.0869938	−0.0137549
$41$	−9.28747	−1.45046	−0.725229	−	0.688508i	$-0.758266\pi$
$41$	−9.28747	−1.45046	−0.725229	+	0.688508i	$0.758266\pi$
$42$	−10.1967	−1.57339
$43$	−12.8417	−1.95834	−0.979168	−	0.203053i	$-0.934914\pi$
$43$	−12.8417	−1.95834	−0.979168	+	0.203053i	$0.934914\pi$
$44$	0	0
$45$	−6.19897	−0.924088
$46$	−7.85494	−1.15815
$47$	−6.15757	−0.898174	−0.449087	−	0.893488i	$-0.648251\pi$
$47$	−6.15757	−0.898174	−0.449087	+	0.893488i	$0.648251\pi$
$48$	10.2340	1.47715
$49$	−2.91038	−0.415768
$50$	3.31870	0.469336
$51$	4.19528	0.587457
$52$	1.97611	0.274038
$53$	12.3472	1.69602	0.848009	−	0.529982i	$-0.177801\pi$
$53$	12.3472	1.69602	0.848009	+	0.529982i	$0.177801\pi$
$54$	1.98726	0.270431
$55$	0	0
$56$	−0.0963248	−0.0128719
$57$	4.99590	0.661722
$58$	17.3016	2.27181
$59$	−4.01237	−0.522366	−0.261183	−	0.965289i	$-0.584113\pi$
$59$	−4.01237	−0.522366	−0.261183	+	0.965289i	$0.584113\pi$
$60$	9.12628	1.17820
$61$	−15.5577	−1.99196	−0.995981	−	0.0895594i	$-0.971454\pi$
$61$	−15.5577	−1.99196	−0.995981	+	0.0895594i	$0.971454\pi$
$62$	5.28155	0.670758
$63$	−6.86388	−0.864767
$64$	−7.80777	−0.975972
$65$	−1.82638	−0.226535
$66$	0	0
$67$	6.46440	0.789753	0.394876	−	0.918734i	$-0.370787\pi$
$67$	6.46440	0.789753	0.394876	+	0.918734i	$0.370787\pi$
$68$	−3.27855	−0.397583
$69$	−9.96103	−1.19917
$70$	−7.36483	−0.880265
$71$	3.56879	0.423537	0.211769	−	0.977320i	$-0.432078\pi$
$71$	3.56879	0.423537	0.211769	+	0.977320i	$0.432078\pi$
$72$	0.161668	0.0190528
$73$	0.454095	0.0531478	0.0265739	−	0.999647i	$-0.491540\pi$
$73$	0.454095	0.0531478	0.0265739	+	0.999647i	$0.491540\pi$
$74$	−2.77002	−0.322008
$75$	4.20852	0.485958
$76$	−3.90422	−0.447845
$77$	0	0
$78$	5.04220	0.570917
$79$	−4.82486	−0.542840	−0.271420	−	0.962461i	$-0.587493\pi$
$79$	−4.82486	−0.542840	−0.271420	+	0.962461i	$0.587493\pi$
$80$	7.39174	0.826422
$81$	−7.66229	−0.851366
$82$	18.5194	2.04512
$83$	7.57751	0.831740	0.415870	−	0.909424i	$-0.363477\pi$
$83$	7.57751	0.831740	0.415870	+	0.909424i	$0.363477\pi$
$84$	10.1052	1.10256
$85$	3.03013	0.328664
$86$	25.6065	2.76122
$87$	21.9405	2.35227
$88$	0	0
$89$	−2.42469	−0.257016	−0.128508	−	0.991708i	$-0.541019\pi$
$89$	−2.42469	−0.257016	−0.128508	+	0.991708i	$0.541019\pi$
$90$	12.3609	1.30295
$91$	−2.02228	−0.211993
$92$	7.78440	0.811580
$93$	6.69765	0.694514
$94$	12.2783	1.26641
$95$	3.60840	0.370214
$96$	−20.1659	−2.05818
$97$	−17.1245	−1.73873	−0.869363	−	0.494175i	$-0.835470\pi$
$97$	−17.1245	−1.73873	−0.869363	+	0.494175i	$0.835470\pi$
$98$	5.80335	0.586227
$99$	0	0
$100$	−3.28890	−0.328890
$101$	−2.47405	−0.246177	−0.123089	−	0.992396i	$-0.539280\pi$
$101$	−2.47405	−0.246177	−0.123089	+	0.992396i	$0.539280\pi$
$102$	−8.36547	−0.828305
$103$	14.1332	1.39259	0.696295	−	0.717756i	$-0.254831\pi$
$103$	14.1332	1.39259	0.696295	+	0.717756i	$0.254831\pi$
$104$	0.0476318	0.00467068
$105$	−9.33950	−0.911442
$106$	−24.6205	−2.39136
$107$	4.76541	0.460690	0.230345	−	0.973109i	$-0.426015\pi$
$107$	4.76541	0.460690	0.230345	+	0.973109i	$0.426015\pi$
$108$	−1.96941	−0.189507
$109$	3.10047	0.296972	0.148486	−	0.988915i	$-0.452560\pi$
$109$	3.10047	0.296972	0.148486	+	0.988915i	$0.452560\pi$
$110$	0	0
$111$	−3.51272	−0.333413
$112$	8.18458	0.773371
$113$	−13.6254	−1.28177	−0.640885	−	0.767637i	$-0.721432\pi$
$113$	−13.6254	−1.28177	−0.640885	+	0.767637i	$0.721432\pi$
$114$	−9.96191	−0.933018
$115$	−7.19458	−0.670898
$116$	−17.1462	−1.59198
$117$	3.39413	0.313787
$118$	8.00074	0.736528
$119$	3.35515	0.307566
$120$	0.219978	0.0200811
$121$	0	0
$122$	31.0224	2.80864
$123$	23.4848	2.11756
$124$	−5.23412	−0.470038
$125$	12.1716	1.08866
$126$	13.6867	1.21931
$127$	−10.7984	−0.958203	−0.479102	−	0.877759i	$-0.659037\pi$
$127$	−10.7984	−0.958203	−0.479102	+	0.877759i	$0.659037\pi$
$128$	−0.381027	−0.0336783
$129$	32.4722	2.85902
$130$	3.64184	0.319411
$131$	6.07019	0.530355	0.265178	−	0.964200i	$-0.414569\pi$
$131$	6.07019	0.530355	0.265178	+	0.964200i	$0.414569\pi$
$132$	0	0
$133$	3.99544	0.346448
$134$	−12.8901	−1.11354
$135$	1.82019	0.156657
$136$	−0.0790254	−0.00677637
$137$	18.2582	1.55991	0.779953	−	0.625838i	$-0.215243\pi$
$137$	18.2582	1.55991	0.779953	+	0.625838i	$0.215243\pi$
$138$	19.8625	1.69081
$139$	−6.41694	−0.544277	−0.272139	−	0.962258i	$-0.587731\pi$
$139$	−6.41694	−0.544277	−0.272139	+	0.962258i	$0.587731\pi$
$140$	7.29869	0.616852
$141$	15.5704	1.31126
$142$	−7.11623	−0.597181
$143$	0	0
$144$	−13.7367	−1.14473
$145$	15.8470	1.31602
$146$	−0.905474	−0.0749376
$147$	7.35936	0.606990
$148$	2.74514	0.225649
$149$	12.4157	1.01714	0.508568	−	0.861022i	$-0.330175\pi$
$149$	12.4157	1.01714	0.508568	+	0.861022i	$0.330175\pi$
$150$	−8.39188	−0.685194
$151$	17.8463	1.45231	0.726156	−	0.687530i	$-0.241305\pi$
$151$	17.8463	1.45231	0.726156	+	0.687530i	$0.241305\pi$
$152$	−0.0941064	−0.00763304
$153$	−5.63116	−0.455253
$154$	0	0
$155$	4.83753	0.388560
$156$	−4.99692	−0.400074
$157$	−15.4037	−1.22935	−0.614675	−	0.788780i	$-0.710713\pi$
$157$	−15.4037	−1.22935	−0.614675	+	0.788780i	$0.710713\pi$
$158$	9.62087	0.765395
$159$	−31.2219	−2.47605
$160$	−14.5653	−1.15149
$161$	−7.96627	−0.627830
$162$	15.2788	1.20041
$163$	3.32370	0.260332	0.130166	−	0.991492i	$-0.458449\pi$
$163$	3.32370	0.260332	0.130166	+	0.991492i	$0.458449\pi$
$164$	−18.3531	−1.43313
$165$	0	0
$166$	−15.1097	−1.17274
$167$	−5.00493	−0.387293	−0.193647	−	0.981071i	$-0.562032\pi$
$167$	−5.00493	−0.387293	−0.193647	+	0.981071i	$0.562032\pi$
$168$	0.243573	0.0187920
$169$	1.00000	0.0769231
$170$	−6.04215	−0.463411
$171$	−6.70580	−0.512805
$172$	−25.3766	−1.93495
$173$	16.5751	1.26018	0.630090	−	0.776522i	$-0.283018\pi$
$173$	16.5751	1.26018	0.630090	+	0.776522i	$0.283018\pi$
$174$	−43.7498	−3.31666
$175$	3.36574	0.254426
$176$	0	0
$177$	10.1459	0.762614
$178$	4.83487	0.362389
$179$	22.3794	1.67272	0.836358	−	0.548184i	$-0.184681\pi$
$179$	22.3794	1.67272	0.836358	+	0.548184i	$0.184681\pi$
$180$	−12.2499	−0.913051
$181$	4.05218	0.301196	0.150598	−	0.988595i	$-0.451880\pi$
$181$	4.05218	0.301196	0.150598	+	0.988595i	$0.451880\pi$
$182$	4.03247	0.298906
$183$	39.3402	2.90811
$184$	0.187633	0.0138325
$185$	−2.53714	−0.186534
$186$	−13.3552	−0.979254
$187$	0	0
$188$	−12.1680	−0.887446
$189$	2.01542	0.146600
$190$	−7.19521	−0.521996
$191$	2.69480	0.194989	0.0974943	−	0.995236i	$-0.468917\pi$
$191$	2.69480	0.194989	0.0974943	+	0.995236i	$0.468917\pi$
$192$	19.7432	1.42484
$193$	5.25901	0.378552	0.189276	−	0.981924i	$-0.439386\pi$
$193$	5.25901	0.378552	0.189276	+	0.981924i	$0.439386\pi$
$194$	34.1465	2.45158
$195$	4.61830	0.330723
$196$	−5.75124	−0.410803
$197$	−3.83577	−0.273287	−0.136644	−	0.990620i	$-0.543632\pi$
$197$	−3.83577	−0.273287	−0.136644	+	0.990620i	$0.543632\pi$
$198$	0	0
$199$	−9.11289	−0.645996	−0.322998	−	0.946400i	$-0.604691\pi$
$199$	−9.11289	−0.645996	−0.322998	+	0.946400i	$0.604691\pi$
$200$	−0.0792749	−0.00560558
$201$	−16.3463	−1.15298
$202$	4.93331	0.347106
$203$	17.5468	1.23154
$204$	8.29034	0.580440
$205$	16.9625	1.18471
$206$	−28.1820	−1.96353
$207$	13.3703	0.929301
$208$	−4.04720	−0.280623
$209$	0	0
$210$	18.6231	1.28512
$211$	−4.79110	−0.329833	−0.164916	−	0.986308i	$-0.552735\pi$
$211$	−4.79110	−0.329833	−0.164916	+	0.986308i	$0.552735\pi$
$212$	24.3994	1.67576
$213$	−9.02425	−0.618332
$214$	−9.50232	−0.649565
$215$	23.4538	1.59953
$216$	−0.0474702	−0.00322994
$217$	5.35641	0.363617
$218$	−6.18241	−0.418725
$219$	−1.14825	−0.0775917
$220$	0	0
$221$	−1.65909	−0.111603
$222$	7.00443	0.470107
$223$	8.29987	0.555800	0.277900	−	0.960610i	$-0.410362\pi$
$223$	8.29987	0.555800	0.277900	+	0.960610i	$0.410362\pi$
$224$	−16.1276	−1.07757
$225$	−5.64894	−0.376596
$226$	27.1693	1.80728
$227$	12.1662	0.807501	0.403751	−	0.914869i	$-0.367706\pi$
$227$	12.1662	0.807501	0.403751	+	0.914869i	$0.367706\pi$
$228$	9.87245	0.653819
$229$	−25.7481	−1.70148	−0.850741	−	0.525585i	$-0.823846\pi$
$229$	−25.7481	−1.70148	−0.850741	+	0.525585i	$0.823846\pi$
$230$	14.3461	0.945955
$231$	0	0
$232$	−0.413288	−0.0271337
$233$	−11.7327	−0.768633	−0.384317	−	0.923201i	$-0.625563\pi$
$233$	−11.7327	−0.768633	−0.384317	+	0.923201i	$0.625563\pi$
$234$	−6.76795	−0.442435
$235$	11.2461	0.733613
$236$	−7.92889	−0.516127
$237$	12.2004	0.792504
$238$	−6.69023	−0.433663
$239$	4.33771	0.280583	0.140292	−	0.990110i	$-0.455196\pi$
$239$	4.33771	0.280583	0.140292	+	0.990110i	$0.455196\pi$
$240$	−18.6912	−1.20651
$241$	19.2973	1.24305	0.621525	−	0.783394i	$-0.286513\pi$
$241$	19.2973	1.24305	0.621525	+	0.783394i	$0.286513\pi$
$242$	0	0
$243$	22.3652	1.43473
$244$	−30.7438	−1.96817
$245$	5.31546	0.339592
$246$	−46.8292	−2.98572
$247$	−1.97571	−0.125711
$248$	−0.126162	−0.00801130
$249$	−19.1610	−1.21428
$250$	−24.2704	−1.53500
$251$	8.54156	0.539138	0.269569	−	0.962981i	$-0.413119\pi$
$251$	8.54156	0.539138	0.269569	+	0.962981i	$0.413119\pi$
$252$	−13.5638	−0.854439
$253$	0	0
$254$	21.5322	1.35105
$255$	−7.66218	−0.479824
$256$	16.3753	1.02346
$257$	−17.7010	−1.10416	−0.552080	−	0.833791i	$-0.686166\pi$
$257$	−17.7010	−1.10416	−0.552080	+	0.833791i	$0.686166\pi$
$258$	−64.7502	−4.03117
$259$	−2.80928	−0.174560
$260$	−3.60914	−0.223829
$261$	−29.4499	−1.82290
$262$	−12.1041	−0.747793
$263$	−25.9704	−1.60140	−0.800701	−	0.599064i	$-0.795539\pi$
$263$	−25.9704	−1.60140	−0.800701	+	0.599064i	$0.795539\pi$
$264$	0	0
$265$	−22.5507	−1.38528
$266$	−7.96698	−0.488487
$267$	6.13121	0.375224
$268$	12.7744	0.780320
$269$	21.1121	1.28723	0.643614	−	0.765350i	$-0.277434\pi$
$269$	21.1121	1.28723	0.643614	+	0.765350i	$0.277434\pi$
$270$	−3.62949	−0.220884
$271$	−1.02181	−0.0620707	−0.0310354	−	0.999518i	$-0.509880\pi$
$271$	−1.02181	−0.0620707	−0.0310354	+	0.999518i	$0.509880\pi$
$272$	6.71468	0.407137
$273$	5.11366	0.309493
$274$	−36.4073	−2.19944
$275$	0	0
$276$	−19.6841	−1.18484
$277$	−2.02437	−0.121632	−0.0608162	−	0.998149i	$-0.519370\pi$
$277$	−2.02437	−0.121632	−0.0608162	+	0.998149i	$0.519370\pi$
$278$	12.7955	0.767423
$279$	−8.99001	−0.538218
$280$	0.175926	0.0105136
$281$	−28.3293	−1.68998	−0.844991	−	0.534780i	$-0.820394\pi$
$281$	−28.3293	−1.68998	−0.844991	+	0.534780i	$0.820394\pi$
$282$	−31.0477	−1.84886
$283$	−9.83948	−0.584897	−0.292448	−	0.956281i	$-0.594470\pi$
$283$	−9.83948	−0.584897	−0.292448	+	0.956281i	$0.594470\pi$
$284$	7.05233	0.418479
$285$	−9.12441	−0.540484
$286$	0	0
$287$	18.7819	1.10866
$288$	27.0679	1.59499
$289$	−14.2474	−0.838083
$290$	−31.5992	−1.85557
$291$	43.3019	2.53840
$292$	0.897343	0.0525130
$293$	−18.4420	−1.07739	−0.538697	−	0.842500i	$-0.681083\pi$
$293$	−18.4420	−1.07739	−0.538697	+	0.842500i	$0.681083\pi$
$294$	−14.6747	−0.855846
$295$	7.32812	0.426659
$296$	0.0661682	0.00384595
$297$	0	0
$298$	−24.7572	−1.43415
$299$	3.93925	0.227813
$300$	8.31652	0.480154
$301$	25.9695	1.49685
$302$	−35.5859	−2.04774
$303$	6.25604	0.359400
$304$	7.99609	0.458607
$305$	28.4144	1.62700
$306$	11.2286	0.641899
$307$	−16.1262	−0.920370	−0.460185	−	0.887823i	$-0.652217\pi$
$307$	−16.1262	−0.920370	−0.460185	+	0.887823i	$0.652217\pi$
$308$	0	0
$309$	−35.7382	−2.03307
$310$	−9.64613	−0.547863
$311$	21.8142	1.23697	0.618485	−	0.785796i	$-0.287747\pi$
$311$	21.8142	1.23697	0.618485	+	0.785796i	$0.287747\pi$
$312$	−0.120445	−0.00681883
$313$	−12.9254	−0.730584	−0.365292	−	0.930893i	$-0.619031\pi$
$313$	−12.9254	−0.730584	−0.365292	+	0.930893i	$0.619031\pi$
$314$	30.7153	1.73337
$315$	12.5361	0.706327
$316$	−9.53447	−0.536356
$317$	−4.69292	−0.263581	−0.131790	−	0.991278i	$-0.542073\pi$
$317$	−4.69292	−0.263581	−0.131790	+	0.991278i	$0.542073\pi$
$318$	62.2570	3.49120
$319$	0	0
$320$	14.2600	0.797157
$321$	−12.0501	−0.672572
$322$	15.8849	0.885231
$323$	3.27788	0.182386
$324$	−15.1415	−0.841197
$325$	−1.66433	−0.0923204
$326$	−6.62752	−0.367064
$327$	−7.84005	−0.433556
$328$	−0.442378	−0.0244263
$329$	12.4523	0.686519
$330$	0	0
$331$	−11.2076	−0.616027	−0.308014	−	0.951382i	$-0.599664\pi$
$331$	−11.2076	−0.616027	−0.308014	+	0.951382i	$0.599664\pi$
$332$	14.9740	0.821806
$333$	4.71499	0.258380
$334$	9.97993	0.546078
$335$	−11.8065	−0.645056
$336$	−20.6960	−1.12906
$337$	6.07587	0.330974	0.165487	−	0.986212i	$-0.447080\pi$
$337$	6.07587	0.330974	0.165487	+	0.986212i	$0.447080\pi$
$338$	−1.99402	−0.108460
$339$	34.4540	1.87128
$340$	5.98789	0.324739
$341$	0	0
$342$	13.3715	0.723048
$343$	20.0416	1.08214
$344$	−0.611671	−0.0329791
$345$	18.1926	0.979459
$346$	−33.0510	−1.77683
$347$	−7.59526	−0.407735	−0.203868	−	0.978998i	$-0.565351\pi$
$347$	−7.59526	−0.407735	−0.203868	+	0.978998i	$0.565351\pi$
$348$	43.3569	2.32417
$349$	22.4810	1.20338	0.601690	−	0.798730i	$-0.294494\pi$
$349$	22.4810	1.20338	0.601690	+	0.798730i	$0.294494\pi$
$350$	−6.71135	−0.358737
$351$	−0.996609	−0.0531950
$352$	0	0
$353$	12.4405	0.662142	0.331071	−	0.943606i	$-0.392590\pi$
$353$	12.4405	0.662142	0.331071	+	0.943606i	$0.392590\pi$
$354$	−20.2312	−1.07527
$355$	−6.51797	−0.345938
$356$	−4.79146	−0.253947
$357$	−8.48403	−0.449023
$358$	−44.6250	−2.35850
$359$	−2.02560	−0.106907	−0.0534535	−	0.998570i	$-0.517023\pi$
$359$	−2.02560	−0.106907	−0.0534535	+	0.998570i	$0.517023\pi$
$360$	−0.295268	−0.0155620
$361$	−15.0966	−0.794557
$362$	−8.08013	−0.424682
$363$	0	0
$364$	−3.99626	−0.209461
$365$	−0.829351	−0.0434102
$366$	−78.4451	−4.10039
$367$	−23.9820	−1.25185	−0.625926	−	0.779882i	$-0.715279\pi$
$367$	−23.9820	−1.25185	−0.625926	+	0.779882i	$0.715279\pi$
$368$	−15.9429	−0.831084
$369$	−31.5228	−1.64101
$370$	5.05911	0.263011
$371$	−24.9695	−1.29635
$372$	13.2353	0.686219
$373$	3.81762	0.197669	0.0988343	−	0.995104i	$-0.468489\pi$
$373$	3.81762	0.197669	0.0988343	+	0.995104i	$0.468489\pi$
$374$	0	0
$375$	−30.7779	−1.58936
$376$	−0.293296	−0.0151256
$377$	−8.67673	−0.446874
$378$	−4.01879	−0.206704
$379$	7.05057	0.362163	0.181082	−	0.983468i	$-0.442040\pi$
$379$	7.05057	0.362163	0.181082	+	0.983468i	$0.442040\pi$
$380$	7.13060	0.365792
$381$	27.3055	1.39890
$382$	−5.37347	−0.274931
$383$	28.0900	1.43533	0.717665	−	0.696389i	$-0.245211\pi$
$383$	28.0900	1.43533	0.717665	+	0.696389i	$0.245211\pi$
$384$	0.963488	0.0491678
$385$	0	0
$386$	−10.4866	−0.533752
$387$	−43.5862	−2.21561
$388$	−33.8399	−1.71796
$389$	2.86718	0.145372	0.0726859	−	0.997355i	$-0.476843\pi$
$389$	2.86718	0.145372	0.0726859	+	0.997355i	$0.476843\pi$
$390$	−9.20898	−0.466315
$391$	−6.53558	−0.330518
$392$	−0.138626	−0.00700169
$393$	−15.3495	−0.774278
$394$	7.64860	0.385331
$395$	8.81204	0.443382
$396$	0	0
$397$	−2.35269	−0.118078	−0.0590391	−	0.998256i	$-0.518804\pi$
$397$	−2.35269	−0.118078	−0.0590391	+	0.998256i	$0.518804\pi$
$398$	18.1713	0.910844
$399$	−10.1031	−0.505788
$400$	6.73588	0.336794
$401$	−39.0701	−1.95107	−0.975533	−	0.219851i	$-0.929443\pi$
$401$	−39.0701	−1.95107	−0.975533	+	0.219851i	$0.929443\pi$
$402$	32.5948	1.62568
$403$	−2.64870	−0.131941
$404$	−4.88900	−0.243237
$405$	13.9943	0.695381
$406$	−34.9886	−1.73646
$407$	0	0
$408$	0.199829	0.00989299
$409$	20.1124	0.994494	0.497247	−	0.867609i	$-0.334344\pi$
$409$	20.1124	0.994494	0.497247	+	0.867609i	$0.334344\pi$
$410$	−33.8235	−1.67042
$411$	−46.1689	−2.27734
$412$	27.9289	1.37596
$413$	8.11414	0.399271
$414$	−26.6607	−1.31030
$415$	−13.8394	−0.679351
$416$	7.97494	0.391004
$417$	16.2263	0.794603
$418$	0	0
$419$	9.20303	0.449597	0.224799	−	0.974405i	$-0.427828\pi$
$419$	9.20303	0.449597	0.224799	+	0.974405i	$0.427828\pi$
$420$	−18.4559	−0.900556
$421$	18.4462	0.899014	0.449507	−	0.893277i	$-0.351600\pi$
$421$	18.4462	0.899014	0.449507	+	0.893277i	$0.351600\pi$
$422$	9.55355	0.465059
$423$	−20.8996	−1.01617
$424$	0.588118	0.0285616
$425$	2.76127	0.133941
$426$	17.9945	0.871838
$427$	31.4621	1.52256
$428$	9.41699	0.455187
$429$	0	0
$430$	−46.7673	−2.25532
$431$	0.588645	0.0283540	0.0141770	−	0.999900i	$-0.495487\pi$
$431$	0.588645	0.0283540	0.0141770	+	0.999900i	$0.495487\pi$
$432$	4.03348	0.194061
$433$	10.5922	0.509027	0.254514	−	0.967069i	$-0.418085\pi$
$433$	10.5922	0.509027	0.254514	+	0.967069i	$0.418085\pi$
$434$	−10.6808	−0.512694
$435$	−40.0717	−1.92129
$436$	6.12689	0.293425
$437$	−7.78281	−0.372302
$438$	2.28964	0.109403
$439$	−3.40730	−0.162621	−0.0813107	−	0.996689i	$-0.525911\pi$
$439$	−3.40730	−0.162621	−0.0813107	+	0.996689i	$0.525911\pi$
$440$	0	0
$441$	−9.87819	−0.470390
$442$	3.30826	0.157358
$443$	35.0546	1.66550	0.832748	−	0.553652i	$-0.186766\pi$
$443$	35.0546	1.66550	0.832748	+	0.553652i	$0.186766\pi$
$444$	−6.94153	−0.329431
$445$	4.42841	0.209927
$446$	−16.5501	−0.783670
$447$	−31.3951	−1.48494
$448$	15.7895	0.745984
$449$	14.5795	0.688049	0.344025	−	0.938961i	$-0.388210\pi$
$449$	14.5795	0.688049	0.344025	+	0.938961i	$0.388210\pi$
$450$	11.2641	0.530995
$451$	0	0
$452$	−26.9253	−1.26646
$453$	−45.1273	−2.12026
$454$	−24.2597	−1.13856
$455$	3.69346	0.173152
$456$	0.237963	0.0111436
$457$	23.2382	1.08704	0.543519	−	0.839397i	$-0.317091\pi$
$457$	23.2382	1.08704	0.543519	+	0.839397i	$0.317091\pi$
$458$	51.3422	2.39906
$459$	1.65347	0.0771771
$460$	−14.2173	−0.662885
$461$	−30.5934	−1.42488	−0.712438	−	0.701735i	$-0.752409\pi$
$461$	−30.5934	−1.42488	−0.712438	+	0.701735i	$0.752409\pi$
$462$	0	0
$463$	5.99110	0.278430	0.139215	−	0.990262i	$-0.455542\pi$
$463$	5.99110	0.278430	0.139215	+	0.990262i	$0.455542\pi$
$464$	35.1165	1.63024
$465$	−12.2325	−0.567267
$466$	23.3952	1.08376
$467$	28.6904	1.32763	0.663816	−	0.747896i	$-0.268936\pi$
$467$	28.6904	1.32763	0.663816	+	0.747896i	$0.268936\pi$
$468$	6.70717	0.310039
$469$	−13.0728	−0.603648
$470$	−22.4249	−1.03438
$471$	38.9508	1.79476
$472$	−0.191116	−0.00879683
$473$	0	0
$474$	−24.3279	−1.11742
$475$	3.28823	0.150874
$476$	6.63015	0.303893
$477$	41.9079	1.91883
$478$	−8.64948	−0.395618
$479$	33.6966	1.53964	0.769819	−	0.638262i	$-0.220347\pi$
$479$	33.6966	1.53964	0.769819	+	0.638262i	$0.220347\pi$
$480$	36.8307	1.68108
$481$	1.38916	0.0633404
$482$	−38.4792	−1.75268
$483$	20.1440	0.916584
$484$	0	0
$485$	31.2758	1.42016
$486$	−44.5966	−2.02294
$487$	29.3958	1.33205	0.666026	−	0.745928i	$-0.267994\pi$
$487$	29.3958	1.33205	0.666026	+	0.745928i	$0.267994\pi$
$488$	−0.741042	−0.0335454
$489$	−8.40450	−0.380065
$490$	−10.5991	−0.478820
$491$	12.2154	0.551272	0.275636	−	0.961262i	$-0.411112\pi$
$491$	12.2154	0.551272	0.275636	+	0.961262i	$0.411112\pi$
$492$	46.4087	2.09227
$493$	14.3955	0.648340
$494$	3.93960	0.177251
$495$	0	0
$496$	10.7198	0.481334
$497$	−7.21709	−0.323731
$498$	38.2073	1.71211
$499$	26.6695	1.19389	0.596945	−	0.802282i	$-0.296381\pi$
$499$	26.6695	1.19389	0.596945	+	0.802282i	$0.296381\pi$
$500$	24.0525	1.07566
$501$	12.6558	0.565418
$502$	−17.0320	−0.760177
$503$	−22.2573	−0.992405	−0.496202	−	0.868207i	$-0.665273\pi$
$503$	−22.2573	−0.992405	−0.496202	+	0.868207i	$0.665273\pi$
$504$	−0.326938	−0.0145630
$505$	4.51856	0.201073
$506$	0	0
$507$	−2.52866	−0.112302
$508$	−21.3389	−0.946759
$509$	−0.244445	−0.0108348	−0.00541741	−	0.999985i	$-0.501724\pi$
$509$	−0.244445	−0.0108348	−0.00541741	+	0.999985i	$0.501724\pi$
$510$	15.2785	0.676545
$511$	−0.918308	−0.0406235
$512$	−31.8907	−1.40938
$513$	1.96901	0.0869338
$514$	35.2962	1.55685
$515$	−25.8127	−1.13744
$516$	64.1688	2.82487
$517$	0	0
$518$	5.60175	0.246127
$519$	−41.9128	−1.83977
$520$	−0.0869938	−0.00381493
$521$	−26.1451	−1.14544	−0.572718	−	0.819752i	$-0.694111\pi$
$521$	−26.1451	−1.14544	−0.572718	+	0.819752i	$0.694111\pi$
$522$	58.7236	2.57026
$523$	−17.8910	−0.782317	−0.391158	−	0.920323i	$-0.627926\pi$
$523$	−17.8910	−0.782317	−0.391158	+	0.920323i	$0.627926\pi$
$524$	11.9954	0.524021
$525$	−8.51082	−0.371443
$526$	51.7854	2.25795
$527$	4.39443	0.191424
$528$	0	0
$529$	−7.48231	−0.325318
$530$	44.9665	1.95322
$531$	−13.6185	−0.590992
$532$	7.89543	0.342310
$533$	−9.28747	−0.402285
$534$	−12.2258	−0.529060
$535$	−8.70346	−0.376283
$536$	0.307911	0.0132997
$537$	−56.5899	−2.44204
$538$	−42.0980	−1.81497
$539$	0	0
$540$	3.59690	0.154786
$541$	−10.5143	−0.452044	−0.226022	−	0.974122i	$-0.572572\pi$
$541$	−10.5143	−0.452044	−0.226022	+	0.974122i	$0.572572\pi$
$542$	2.03752	0.0875188
$543$	−10.2466	−0.439723
$544$	−13.2312	−0.567281
$545$	−5.66265	−0.242561
$546$	−10.1967	−0.436380
$547$	5.38543	0.230264	0.115132	−	0.993350i	$-0.463271\pi$
$547$	5.38543	0.230264	0.115132	+	0.993350i	$0.463271\pi$
$548$	36.0803	1.54128
$549$	−52.8049	−2.25366
$550$	0	0
$551$	17.1427	0.730302
$552$	−0.474461	−0.0201944
$553$	9.75723	0.414920
$554$	4.03663	0.171500
$555$	6.41557	0.272326
$556$	−12.6806	−0.537777
$557$	24.5214	1.03900	0.519502	−	0.854469i	$-0.326117\pi$
$557$	24.5214	1.03900	0.519502	+	0.854469i	$0.326117\pi$
$558$	17.9262	0.758878
$559$	−12.8417	−0.543145
$560$	−14.9482	−0.631676
$561$	0	0
$562$	56.4891	2.38285
$563$	13.5241	0.569972	0.284986	−	0.958532i	$-0.408011\pi$
$563$	13.5241	0.569972	0.284986	+	0.958532i	$0.408011\pi$
$564$	30.7689	1.29560
$565$	24.8852	1.04693
$566$	19.6201	0.824695
$567$	15.4953	0.650742
$568$	0.169988	0.00713252
$569$	−14.3428	−0.601283	−0.300641	−	0.953737i	$-0.597201\pi$
$569$	−14.3428	−0.601283	−0.300641	+	0.953737i	$0.597201\pi$
$570$	18.1943	0.762073
$571$	4.77684	0.199905	0.0999523	−	0.994992i	$-0.468131\pi$
$571$	4.77684	0.199905	0.0999523	+	0.994992i	$0.468131\pi$
$572$	0	0
$573$	−6.81422	−0.284668
$574$	−37.4514	−1.56319
$575$	−6.55621	−0.273413
$576$	−26.5006	−1.10419
$577$	44.2633	1.84271	0.921353	−	0.388727i	$-0.127085\pi$
$577$	44.2633	1.84271	0.921353	+	0.388727i	$0.127085\pi$
$578$	28.4096	1.18168
$579$	−13.2982	−0.552656
$580$	31.3155	1.30030
$581$	−15.3239	−0.635741
$582$	−86.3449	−3.57911
$583$	0	0
$584$	0.0216293	0.000895029 0
$585$	−6.19897	−0.256296
$586$	36.7737	1.51911
$587$	25.5356	1.05397	0.526984	−	0.849875i	$-0.323323\pi$
$587$	25.5356	1.05397	0.526984	+	0.849875i	$0.323323\pi$
$588$	14.5429	0.599740
$589$	5.23305	0.215624
$590$	−14.6124	−0.601583
$591$	9.69936	0.398978
$592$	−5.62222	−0.231072
$593$	−16.5202	−0.678404	−0.339202	−	0.940714i	$-0.610157\pi$
$593$	−16.5202	−0.678404	−0.339202	+	0.940714i	$0.610157\pi$
$594$	0	0
$595$	−6.12778	−0.251215
$596$	24.5349	1.00499
$597$	23.0434	0.943104
$598$	−7.85494	−0.321212
$599$	3.62443	0.148090	0.0740452	−	0.997255i	$-0.476409\pi$
$599$	3.62443	0.148090	0.0740452	+	0.997255i	$0.476409\pi$
$600$	0.200459	0.00818372
$601$	21.3780	0.872026	0.436013	−	0.899940i	$-0.356390\pi$
$601$	21.3780	0.872026	0.436013	+	0.899940i	$0.356390\pi$
$602$	−51.7836	−2.11054
$603$	21.9410	0.893507
$604$	35.2663	1.43497
$605$	0	0
$606$	−12.4747	−0.506748
$607$	17.4187	0.707002	0.353501	−	0.935434i	$-0.384991\pi$
$607$	17.4187	0.707002	0.353501	+	0.935434i	$0.384991\pi$
$608$	−15.7562	−0.638996
$609$	−44.3698	−1.79796
$610$	−56.6588	−2.29405
$611$	−6.15757	−0.249109
$612$	−11.1278	−0.449815
$613$	−13.4632	−0.543775	−0.271888	−	0.962329i	$-0.587648\pi$
$613$	−13.4632	−0.543775	−0.271888	+	0.962329i	$0.587648\pi$
$614$	32.1559	1.29771
$615$	−42.8923	−1.72958
$616$	0	0
$617$	37.8461	1.52363	0.761813	−	0.647797i	$-0.224310\pi$
$617$	37.8461	1.52363	0.761813	+	0.647797i	$0.224310\pi$
$618$	71.2626	2.86660
$619$	14.7323	0.592142	0.296071	−	0.955166i	$-0.404324\pi$
$619$	14.7323	0.592142	0.296071	+	0.955166i	$0.404324\pi$
$620$	9.55950	0.383919
$621$	−3.92589	−0.157541
$622$	−43.4980	−1.74411
$623$	4.90340	0.196451
$624$	10.2340	0.409688
$625$	−13.9084	−0.556335
$626$	25.7734	1.03011
$627$	0	0
$628$	−30.4395	−1.21467
$629$	−2.30475	−0.0918963
$630$	−24.9971	−0.995910
$631$	−13.7890	−0.548930	−0.274465	−	0.961597i	$-0.588501\pi$
$631$	−13.7890	−0.548930	−0.274465	+	0.961597i	$0.588501\pi$
$632$	−0.229817	−0.00914162
$633$	12.1151	0.481531
$634$	9.35777	0.371644
$635$	19.7220	0.782644
$636$	−61.6979	−2.44648
$637$	−2.91038	−0.115313
$638$	0	0
$639$	12.1129	0.479179
$640$	0.695901	0.0275079
$641$	−10.6647	−0.421231	−0.210616	−	0.977569i	$-0.567547\pi$
$641$	−10.6647	−0.421231	−0.210616	+	0.977569i	$0.567547\pi$
$642$	24.0282	0.948315
$643$	−16.3561	−0.645023	−0.322511	−	0.946566i	$-0.604527\pi$
$643$	−16.3561	−0.645023	−0.322511	+	0.946566i	$0.604527\pi$
$644$	−15.7423	−0.620332
$645$	−59.3067	−2.33520
$646$	−6.53616	−0.257162
$647$	−29.0775	−1.14316	−0.571578	−	0.820548i	$-0.693668\pi$
$647$	−29.0775	−1.14316	−0.571578	+	0.820548i	$0.693668\pi$
$648$	−0.364968	−0.0143373
$649$	0	0
$650$	3.31870	0.130170
$651$	−13.5445	−0.530852
$652$	6.56800	0.257223
$653$	6.47965	0.253568	0.126784	−	0.991930i	$-0.459534\pi$
$653$	6.47965	0.253568	0.126784	+	0.991930i	$0.459534\pi$
$654$	15.6332	0.611307
$655$	−11.0865	−0.433185
$656$	37.5883	1.46758
$657$	1.54126	0.0601301
$658$	−24.8302	−0.967982
$659$	10.0364	0.390964	0.195482	−	0.980707i	$-0.437373\pi$
$659$	10.0364	0.390964	0.195482	+	0.980707i	$0.437373\pi$
$660$	0	0
$661$	16.0229	0.623220	0.311610	−	0.950210i	$-0.399132\pi$
$661$	16.0229	0.623220	0.311610	+	0.950210i	$0.399132\pi$
$662$	22.3482	0.868589
$663$	4.19528	0.162931
$664$	0.360930	0.0140068
$665$	−7.29719	−0.282973
$666$	−9.40178	−0.364312
$667$	−34.1798	−1.32345
$668$	−9.89031	−0.382668
$669$	−20.9876	−0.811426
$670$	23.5423	0.909520
$671$	0	0
$672$	40.7812	1.57317
$673$	44.4408	1.71307	0.856534	−	0.516090i	$-0.172613\pi$
$673$	44.4408	1.71307	0.856534	+	0.516090i	$0.172613\pi$
$674$	−12.1154	−0.466668
$675$	1.65869	0.0638428
$676$	1.97611	0.0760043
$677$	28.2578	1.08604	0.543018	−	0.839721i	$-0.317281\pi$
$677$	28.2578	1.08604	0.543018	+	0.839721i	$0.317281\pi$
$678$	−68.7020	−2.63848
$679$	34.6305	1.32900
$680$	0.144331	0.00553483
$681$	−30.7643	−1.17889
$682$	0	0
$683$	6.47639	0.247812	0.123906	−	0.992294i	$-0.460458\pi$
$683$	6.47639	0.247812	0.123906	+	0.992294i	$0.460458\pi$
$684$	−13.2514	−0.506681
$685$	−33.3465	−1.27410
$686$	−39.9633	−1.52581
$687$	65.1082	2.48403
$688$	51.9728	1.98145
$689$	12.3472	0.470391
$690$	−36.2765	−1.38102
$691$	−35.6083	−1.35460	−0.677302	−	0.735705i	$-0.736851\pi$
$691$	−35.6083	−1.35460	−0.677302	+	0.735705i	$0.736851\pi$
$692$	32.7542	1.24513
$693$	0	0
$694$	15.1451	0.574900
$695$	11.7198	0.444556
$696$	1.04506	0.0396131
$697$	15.4088	0.583648
$698$	−44.8275	−1.69675
$699$	29.6680	1.12214
$700$	6.65108	0.251387
$701$	5.43694	0.205350	0.102675	−	0.994715i	$-0.467260\pi$
$701$	5.43694	0.205350	0.102675	+	0.994715i	$0.467260\pi$
$702$	1.98726	0.0750042
$703$	−2.74458	−0.103514
$704$	0	0
$705$	−28.4375	−1.07102
$706$	−24.8066	−0.933610
$707$	5.00323	0.188166
$708$	20.0495	0.753505
$709$	−5.24767	−0.197080	−0.0985401	−	0.995133i	$-0.531417\pi$
$709$	−5.24767	−0.197080	−0.0985401	+	0.995133i	$0.531417\pi$
$710$	12.9970	0.487767
$711$	−16.3762	−0.614155
$712$	−0.115492	−0.00432825
$713$	−10.4339	−0.390752
$714$	16.9173	0.633115
$715$	0	0
$716$	44.2242	1.65274
$717$	−10.9686	−0.409630
$718$	4.03908	0.150737
$719$	−37.9180	−1.41410	−0.707052	−	0.707162i	$-0.749975\pi$
$719$	−37.9180	−1.41410	−0.707052	+	0.707162i	$0.749975\pi$
$720$	25.0885	0.934993
$721$	−28.5814	−1.06443
$722$	30.1029	1.12031
$723$	−48.7964	−1.81476
$724$	8.00757	0.297599
$725$	14.4409	0.536323
$726$	0	0
$727$	−39.1558	−1.45221	−0.726104	−	0.687585i	$-0.758671\pi$
$727$	−39.1558	−1.45221	−0.726104	+	0.687585i	$0.758671\pi$
$728$	−0.0963248	−0.00357003
$729$	−33.5670	−1.24322
$730$	1.65374	0.0612077
$731$	21.3055	0.788012
$732$	77.7407	2.87338
$733$	38.3093	1.41499	0.707494	−	0.706720i	$-0.249826\pi$
$733$	38.3093	1.41499	0.707494	+	0.706720i	$0.249826\pi$
$734$	47.8207	1.76509
$735$	−13.4410	−0.495779
$736$	31.4153	1.15798
$737$	0	0
$738$	62.8571	2.31380
$739$	31.4695	1.15762	0.578812	−	0.815461i	$-0.303517\pi$
$739$	31.4695	1.15762	0.578812	+	0.815461i	$0.303517\pi$
$740$	−5.01368	−0.184306
$741$	4.99590	0.183529
$742$	49.7897	1.82784
$743$	−5.67616	−0.208238	−0.104119	−	0.994565i	$-0.533202\pi$
$743$	−5.67616	−0.208238	−0.104119	+	0.994565i	$0.533202\pi$
$744$	0.319021	0.0116959
$745$	−22.6758	−0.830779
$746$	−7.61240	−0.278710
$747$	25.7190	0.941010
$748$	0	0
$749$	−9.63700	−0.352128
$750$	61.3717	2.24098
$751$	−4.86928	−0.177682	−0.0888412	−	0.996046i	$-0.528316\pi$
$751$	−4.86928	−0.177682	−0.0888412	+	0.996046i	$0.528316\pi$
$752$	24.9209	0.908773
$753$	−21.5987	−0.787101
$754$	17.3016	0.630086
$755$	−32.5942	−1.18622
$756$	3.98270	0.144850
$757$	28.0897	1.02094	0.510469	−	0.859896i	$-0.329472\pi$
$757$	28.0897	1.02094	0.510469	+	0.859896i	$0.329472\pi$
$758$	−14.0590	−0.510645
$759$	0	0
$760$	0.171874	0.00623454
$761$	−9.72025	−0.352359	−0.176179	−	0.984358i	$-0.556374\pi$
$761$	−9.72025	−0.352359	−0.176179	+	0.984358i	$0.556374\pi$
$762$	−54.4477	−1.97243
$763$	−6.27003	−0.226990
$764$	5.32522	0.192660
$765$	10.2847	0.371843
$766$	−56.0119	−2.02379
$767$	−4.01237	−0.144878
$768$	−41.4076	−1.49417
$769$	18.3552	0.661905	0.330952	−	0.943647i	$-0.392630\pi$
$769$	18.3552	0.661905	0.330952	+	0.943647i	$0.392630\pi$
$770$	0	0
$771$	44.7599	1.61199
$772$	10.3924	0.374030
$773$	−23.8493	−0.857798	−0.428899	−	0.903352i	$-0.641098\pi$
$773$	−23.8493	−0.857798	−0.428899	+	0.903352i	$0.641098\pi$
$774$	86.9118	3.12398
$775$	4.40830	0.158351
$776$	−0.815668	−0.0292808
$777$	7.10371	0.254844
$778$	−5.71722	−0.204972
$779$	18.3493	0.657433
$780$	9.12628	0.326773
$781$	0	0
$782$	13.0321	0.466026
$783$	8.64730	0.309029
$784$	11.7789	0.420675
$785$	28.1331	1.00411
$786$	30.6071	1.09172
$787$	8.43195	0.300566	0.150283	−	0.988643i	$-0.451981\pi$
$787$	8.43195	0.300566	0.150283	+	0.988643i	$0.451981\pi$
$788$	−7.57991	−0.270023
$789$	65.6703	2.33792
$790$	−17.5714	−0.625162
$791$	27.5544	0.979721
$792$	0	0
$793$	−15.5577	−0.552471
$794$	4.69132	0.166489
$795$	57.0230	2.02240
$796$	−18.0081	−0.638280
$797$	−19.3210	−0.684385	−0.342192	−	0.939630i	$-0.611169\pi$
$797$	−19.3210	−0.684385	−0.342192	+	0.939630i	$0.611169\pi$
$798$	20.1458	0.713153
$799$	10.2160	0.361415
$800$	−13.2729	−0.469269
$801$	−8.22969	−0.290782
$802$	77.9065	2.75097
$803$	0	0
$804$	−32.3021	−1.13921
$805$	14.5495	0.512801
$806$	5.28155	0.186035
$807$	−53.3854	−1.87925
$808$	−0.117843	−0.00414572
$809$	−36.5031	−1.28338	−0.641690	−	0.766964i	$-0.721767\pi$
$809$	−36.5031	−1.28338	−0.641690	+	0.766964i	$0.721767\pi$
$810$	−27.9048	−0.980476
$811$	−31.6442	−1.11118	−0.555589	−	0.831457i	$-0.687507\pi$
$811$	−31.6442	−1.11118	−0.555589	+	0.831457i	$0.687507\pi$
$812$	34.6744	1.21683
$813$	2.58382	0.0906185
$814$	0	0
$815$	−6.07034	−0.212635
$816$	−16.9792	−0.594389
$817$	25.3714	0.887632
$818$	−40.1045	−1.40222
$819$	−6.86388	−0.239843
$820$	33.5197	1.17056
$821$	4.58487	0.160013	0.0800066	−	0.996794i	$-0.474506\pi$
$821$	4.58487	0.160013	0.0800066	+	0.996794i	$0.474506\pi$
$822$	92.0617	3.21102
$823$	−50.2782	−1.75259	−0.876294	−	0.481778i	$-0.839991\pi$
$823$	−50.2782	−1.75259	−0.876294	+	0.481778i	$0.839991\pi$
$824$	0.673191	0.0234517
$825$	0	0
$826$	−16.1797	−0.562965
$827$	43.2257	1.50311	0.751553	−	0.659673i	$-0.229305\pi$
$827$	43.2257	1.50311	0.751553	+	0.659673i	$0.229305\pi$
$828$	26.4212	0.918201
$829$	−4.85161	−0.168504	−0.0842518	−	0.996444i	$-0.526850\pi$
$829$	−4.85161	−0.168504	−0.0842518	+	0.996444i	$0.526850\pi$
$830$	27.5961	0.957875
$831$	5.11894	0.177574
$832$	−7.80777	−0.270686
$833$	4.82858	0.167301
$834$	−32.3555	−1.12038
$835$	9.14092	0.316335
$836$	0	0
$837$	2.63971	0.0912418
$838$	−18.3510	−0.633925
$839$	−12.1162	−0.418296	−0.209148	−	0.977884i	$-0.567069\pi$
$839$	−12.1162	−0.418296	−0.209148	+	0.977884i	$0.567069\pi$
$840$	−0.444857	−0.0153490
$841$	46.2856	1.59605
$842$	−36.7821	−1.26760
$843$	71.6351	2.46724
$844$	−9.46775	−0.325894
$845$	−1.82638	−0.0628294
$846$	41.6741	1.43279
$847$	0	0
$848$	−49.9716	−1.71603
$849$	24.8807	0.853904
$850$	−5.50603	−0.188855
$851$	5.47226	0.187587
$852$	−17.8329	−0.610946
$853$	20.3233	0.695856	0.347928	−	0.937521i	$-0.386885\pi$
$853$	20.3233	0.695856	0.347928	+	0.937521i	$0.386885\pi$
$854$	−62.7360	−2.14678
$855$	12.2474	0.418851
$856$	0.226985	0.00775818
$857$	5.07138	0.173235	0.0866175	−	0.996242i	$-0.472394\pi$
$857$	5.07138	0.173235	0.0866175	+	0.996242i	$0.472394\pi$
$858$	0	0
$859$	31.1183	1.06174	0.530871	−	0.847452i	$-0.321865\pi$
$859$	31.1183	1.06174	0.530871	+	0.847452i	$0.321865\pi$
$860$	46.3473	1.58043
$861$	−47.4930	−1.61856
$862$	−1.17377	−0.0399787
$863$	37.1134	1.26335	0.631677	−	0.775232i	$-0.282367\pi$
$863$	37.1134	1.26335	0.631677	+	0.775232i	$0.282367\pi$
$864$	−7.94789	−0.270393
$865$	−30.2724	−1.02929
$866$	−21.1210	−0.717721
$867$	36.0269	1.22354
$868$	10.5849	0.359274
$869$	0	0
$870$	79.9038	2.70899
$871$	6.46440	0.219038
$872$	0.147681	0.00500111
$873$	−58.1226	−1.96715
$874$	15.5191	0.524940
$875$	−24.6144	−0.832119
$876$	−2.26908	−0.0766650
$877$	−32.4837	−1.09690	−0.548448	−	0.836185i	$-0.684781\pi$
$877$	−32.4837	−1.09690	−0.548448	+	0.836185i	$0.684781\pi$
$878$	6.79422	0.229294
$879$	46.6336	1.57291
$880$	0	0
$881$	4.44712	0.149827	0.0749137	−	0.997190i	$-0.476132\pi$
$881$	4.44712	0.149827	0.0749137	+	0.997190i	$0.476132\pi$
$882$	19.6973	0.663243
$883$	25.3390	0.852725	0.426363	−	0.904552i	$-0.359795\pi$
$883$	25.3390	0.852725	0.426363	+	0.904552i	$0.359795\pi$
$884$	−3.27855	−0.110270
$885$	−18.5303	−0.622890
$886$	−69.8996	−2.34832
$887$	−35.8415	−1.20344	−0.601720	−	0.798707i	$-0.705518\pi$
$887$	−35.8415	−1.20344	−0.601720	+	0.798707i	$0.705518\pi$
$888$	−0.167317	−0.00561479
$889$	21.8374	0.732403
$890$	−8.83033	−0.295993
$891$	0	0
$892$	16.4015	0.549162
$893$	12.1656	0.407105
$894$	62.6025	2.09374
$895$	−40.8734	−1.36625
$896$	0.770543	0.0257420
$897$	−9.96103	−0.332589
$898$	−29.0718	−0.970139
$899$	22.9820	0.766493
$900$	−11.1629	−0.372098
$901$	−20.4851	−0.682458
$902$	0	0
$903$	−65.6680	−2.18529
$904$	−0.649002	−0.0215855
$905$	−7.40083	−0.246012
$906$	89.9847	2.98954
$907$	−51.9809	−1.72600	−0.862999	−	0.505205i	$-0.831417\pi$
$907$	−51.9809	−1.72600	−0.862999	+	0.505205i	$0.831417\pi$
$908$	24.0418	0.797857
$909$	−8.39724	−0.278519
$910$	−7.36483	−0.244142
$911$	−37.4961	−1.24230	−0.621150	−	0.783692i	$-0.713334\pi$
$911$	−37.4961	−1.24230	−0.621150	+	0.783692i	$0.713334\pi$
$912$	−20.2194	−0.669531
$913$	0	0
$914$	−46.3375	−1.53271
$915$	−71.8503	−2.37530
$916$	−50.8811	−1.68116
$917$	−12.2756	−0.405377
$918$	−3.29704	−0.108819
$919$	55.5781	1.83335	0.916677	−	0.399630i	$-0.130861\pi$
$919$	55.5781	1.83335	0.916677	+	0.399630i	$0.130861\pi$
$920$	−0.342690	−0.0112982
$921$	40.7776	1.34367
$922$	61.0038	2.00905
$923$	3.56879	0.117468
$924$	0	0
$925$	−2.31202	−0.0760189
$926$	−11.9464	−0.392582
$927$	47.9700	1.57554
$928$	−69.1964	−2.27148
$929$	21.5411	0.706741	0.353370	−	0.935484i	$-0.385036\pi$
$929$	21.5411	0.706741	0.353370	+	0.935484i	$0.385036\pi$
$930$	24.3918	0.799838
$931$	5.75006	0.188451
$932$	−23.1851	−0.759453
$933$	−55.1607	−1.80588
$934$	−57.2092	−1.87194
$935$	0	0
$936$	0.161668	0.00528429
$937$	−9.36552	−0.305958	−0.152979	−	0.988229i	$-0.548887\pi$
$937$	−9.36552	−0.305958	−0.152979	+	0.988229i	$0.548887\pi$
$938$	26.0675	0.851134
$939$	32.6838	1.06660
$940$	22.2235	0.724851
$941$	−13.6523	−0.445053	−0.222526	−	0.974927i	$-0.571430\pi$
$941$	−13.6523	−0.445053	−0.222526	+	0.974927i	$0.571430\pi$
$942$	−77.6686	−2.53058
$943$	−36.5857	−1.19139
$944$	16.2389	0.528530
$945$	−3.68093	−0.119741
$946$	0	0
$947$	23.0149	0.747885	0.373942	−	0.927452i	$-0.378006\pi$
$947$	23.0149	0.747885	0.373942	+	0.927452i	$0.378006\pi$
$948$	24.1095	0.783039
$949$	0.454095	0.0147405
$950$	−6.55679	−0.212730
$951$	11.8668	0.384807
$952$	0.159812	0.00517953
$953$	39.4628	1.27833	0.639163	−	0.769072i	$-0.279281\pi$
$953$	39.4628	1.27833	0.639163	+	0.769072i	$0.279281\pi$
$954$	−83.5652	−2.70552
$955$	−4.92173	−0.159263
$956$	8.57180	0.277232
$957$	0	0
$958$	−67.1917	−2.17087
$959$	−36.9233	−1.19232
$960$	−36.0586	−1.16379
$961$	−23.9844	−0.773691
$962$	−2.77002	−0.0893089
$963$	16.1744	0.521213
$964$	38.1337	1.22820
$965$	−9.60496	−0.309195
$966$	−40.1675	−1.29237
$967$	−18.3171	−0.589037	−0.294518	−	0.955646i	$-0.595159\pi$
$967$	−18.3171	−0.589037	−0.294518	+	0.955646i	$0.595159\pi$
$968$	0	0
$969$	−8.28865	−0.266270
$970$	−62.3645	−2.00240
$971$	−6.20632	−0.199170	−0.0995851	−	0.995029i	$-0.531752\pi$
$971$	−6.20632	−0.199170	−0.0995851	+	0.995029i	$0.531752\pi$
$972$	44.1961	1.41759
$973$	12.9768	0.416019
$974$	−58.6159	−1.87817
$975$	4.20852	0.134781
$976$	62.9653	2.01547
$977$	0.356184	0.0113953	0.00569767	−	0.999984i	$-0.498186\pi$
$977$	0.356184	0.0113953	0.00569767	+	0.999984i	$0.498186\pi$
$978$	16.7587	0.535885
$979$	0	0
$980$	10.5040	0.335536
$981$	10.5234	0.335986
$982$	−24.3577	−0.777284
$983$	27.0237	0.861923	0.430961	−	0.902370i	$-0.358174\pi$
$983$	27.0237	0.861923	0.430961	+	0.902370i	$0.358174\pi$
$984$	1.11862	0.0356604
$985$	7.00558	0.223216
$986$	−28.7049	−0.914149
$987$	−31.4877	−1.00227
$988$	−3.90422	−0.124210
$989$	−50.5865	−1.60856
$990$	0	0
$991$	16.0927	0.511203	0.255602	−	0.966782i	$-0.417726\pi$
$991$	16.0927	0.511203	0.255602	+	0.966782i	$0.417726\pi$
$992$	−21.1232	−0.670662
$993$	28.3403	0.899352
$994$	14.3910	0.456455
$995$	16.6436	0.527638
$996$	−37.8642	−1.19977
$997$	33.8317	1.07146	0.535731	−	0.844389i	$-0.320036\pi$
$997$	33.8317	1.07146	0.535731	+	0.844389i	$0.320036\pi$
$998$	−53.1795	−1.68337
$999$	−1.38445	−0.0438021

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1573.2.a.s.1.3		14
11.5	even	5		143.2.h.c.14.6	✓	28
11.9	even	5		143.2.h.c.92.6	yes	28
11.10	odd	2		1573.2.a.r.1.12		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.h.c.14.6	✓	28	11.5	even	5
143.2.h.c.92.6	yes	28	11.9	even	5
1573.2.a.r.1.12		14	11.10	odd	2
1573.2.a.s.1.3		14	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:	\( N \)	\(=\)	\( 1573 = 11^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1573.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99402 q^{2} -2.52866 q^{3} +1.97611 q^{4} -1.82638 q^{5} +5.04220 q^{6} -2.02228 q^{7} +0.0476318 q^{8} +3.39413 q^{9} +O(q^{10})\)	\(q-1.99402 q^{2} -2.52866 q^{3} +1.97611 q^{4} -1.82638 q^{5} +5.04220 q^{6} -2.02228 q^{7} +0.0476318 q^{8} +3.39413 q^{9} +3.64184 q^{10} -4.99692 q^{12} +1.00000 q^{13} +4.03247 q^{14} +4.61830 q^{15} -4.04720 q^{16} -1.65909 q^{17} -6.76795 q^{18} -1.97571 q^{19} -3.60914 q^{20} +5.11366 q^{21} +3.93925 q^{23} -0.120445 q^{24} -1.66433 q^{25} -1.99402 q^{26} -0.996609 q^{27} -3.99626 q^{28} -8.67673 q^{29} -9.20898 q^{30} -2.64870 q^{31} +7.97494 q^{32} +3.30826 q^{34} +3.69346 q^{35} +6.70717 q^{36} +1.38916 q^{37} +3.93960 q^{38} -2.52866 q^{39} -0.0869938 q^{40} -9.28747 q^{41} -10.1967 q^{42} -12.8417 q^{43} -6.19897 q^{45} -7.85494 q^{46} -6.15757 q^{47} +10.2340 q^{48} -2.91038 q^{49} +3.31870 q^{50} +4.19528 q^{51} +1.97611 q^{52} +12.3472 q^{53} +1.98726 q^{54} -0.0963248 q^{56} +4.99590 q^{57} +17.3016 q^{58} -4.01237 q^{59} +9.12628 q^{60} -15.5577 q^{61} +5.28155 q^{62} -6.86388 q^{63} -7.80777 q^{64} -1.82638 q^{65} +6.46440 q^{67} -3.27855 q^{68} -9.96103 q^{69} -7.36483 q^{70} +3.56879 q^{71} +0.161668 q^{72} +0.454095 q^{73} -2.77002 q^{74} +4.20852 q^{75} -3.90422 q^{76} +5.04220 q^{78} -4.82486 q^{79} +7.39174 q^{80} -7.66229 q^{81} +18.5194 q^{82} +7.57751 q^{83} +10.1052 q^{84} +3.03013 q^{85} +25.6065 q^{86} +21.9405 q^{87} -2.42469 q^{89} +12.3609 q^{90} -2.02228 q^{91} +7.78440 q^{92} +6.69765 q^{93} +12.2783 q^{94} +3.60840 q^{95} -20.1659 q^{96} -17.1245 q^{97} +5.80335 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9	\( 14 q + q^{2} + 9 q^{3} + 15 q^{4} + 9 q^{5} + 13 q^{6} - q^{7} + 3 q^{8} + 17 q^{9} - 12 q^{10} + 19 q^{12} + 14 q^{13} + 9 q^{14} + 19 q^{15} + 13 q^{16} - 4 q^{17} - 15 q^{18} + 5 q^{19} + 17 q^{20} + 25 q^{23} + 29 q^{24} + 13 q^{25} + q^{26} + 33 q^{27} + 15 q^{28} - 16 q^{29} - 8 q^{30} + 6 q^{31} + 12 q^{32} + 13 q^{34} + 8 q^{35} + 24 q^{36} + 11 q^{37} + 22 q^{38} + 9 q^{39} - 43 q^{40} + q^{41} - 5 q^{42} - 16 q^{43} + 39 q^{45} + 22 q^{46} + 38 q^{47} + 6 q^{48} + 9 q^{49} + 8 q^{50} - 24 q^{51} + 15 q^{52} + 52 q^{53} - 21 q^{54} + 17 q^{56} + 9 q^{57} - 19 q^{58} + 27 q^{59} + 13 q^{60} - 19 q^{61} - 56 q^{62} + 11 q^{63} - 29 q^{64} + 9 q^{65} + 29 q^{67} - 14 q^{68} + 21 q^{69} - 68 q^{70} + 34 q^{71} + 65 q^{72} - 18 q^{73} - 18 q^{74} + 11 q^{75} + 3 q^{76} + 13 q^{78} - 17 q^{79} - q^{80} + 18 q^{81} + 9 q^{82} + 16 q^{83} - 21 q^{84} + 2 q^{85} + 9 q^{86} - 6 q^{87} + 19 q^{89} + 13 q^{90} - q^{91} + 22 q^{92} + 2 q^{93} + 75 q^{94} - 29 q^{95} - 13 q^{96} - 20 q^{97} + 81 q^{98}+O(q^{100}) \) 14 * q + q^2 + 9 * q^3 + 15 * q^4 + 9 * q^5 + 13 * q^6 - q^7 + 3 * q^8 + 17 * q^9 - 12 * q^10 + 19 * q^12 + 14 * q^13 + 9 * q^14 + 19 * q^15 + 13 * q^16 - 4 * q^17 - 15 * q^18 + 5 * q^19 + 17 * q^20 + 25 * q^23 + 29 * q^24 + 13 * q^25 + q^26 + 33 * q^27 + 15 * q^28 - 16 * q^29 - 8 * q^30 + 6 * q^31 + 12 * q^32 + 13 * q^34 + 8 * q^35 + 24 * q^36 + 11 * q^37 + 22 * q^38 + 9 * q^39 - 43 * q^40 + q^41 - 5 * q^42 - 16 * q^43 + 39 * q^45 + 22 * q^46 + 38 * q^47 + 6 * q^48 + 9 * q^49 + 8 * q^50 - 24 * q^51 + 15 * q^52 + 52 * q^53 - 21 * q^54 + 17 * q^56 + 9 * q^57 - 19 * q^58 + 27 * q^59 + 13 * q^60 - 19 * q^61 - 56 * q^62 + 11 * q^63 - 29 * q^64 + 9 * q^65 + 29 * q^67 - 14 * q^68 + 21 * q^69 - 68 * q^70 + 34 * q^71 + 65 * q^72 - 18 * q^73 - 18 * q^74 + 11 * q^75 + 3 * q^76 + 13 * q^78 - 17 * q^79 - q^80 + 18 * q^81 + 9 * q^82 + 16 * q^83 - 21 * q^84 + 2 * q^85 + 9 * q^86 - 6 * q^87 + 19 * q^89 + 13 * q^90 - q^91 + 22 * q^92 + 2 * q^93 + 75 * q^94 - 29 * q^95 - 13 * q^96 - 20 * q^97 + 81 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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