LMFDB - Embedded newform 5929.2.a.bb.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5929,2,Mod(1,5929)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5929, 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("5929.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5929 = 7^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5929.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:	$47.3433033584$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 77)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-0.777484$ of defining polynomial
Character	$\chi$	$=$	5929.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.777484 q^{2} -0.618034 q^{3} -1.39552 q^{4} +0.222516 q^{5} -0.480512 q^{6} -2.63996 q^{8} -2.61803 q^{9} +O(q^{10})$	\(q+0.777484 q^{2} -0.618034 q^{3} -1.39552 q^{4} +0.222516 q^{5} -0.480512 q^{6} -2.63996 q^{8} -2.61803 q^{9} +0.173002 q^{10} +0.862478 q^{12} +6.52954 q^{13} -0.137522 q^{15} +0.738508 q^{16} -4.33461 q^{17} -2.03548 q^{18} +2.91501 q^{19} -0.310525 q^{20} -3.89796 q^{23} +1.63159 q^{24} -4.95049 q^{25} +5.07662 q^{26} +3.47214 q^{27} +3.77399 q^{29} -0.106921 q^{30} +6.88958 q^{31} +5.85410 q^{32} -3.37009 q^{34} +3.65351 q^{36} -5.65351 q^{37} +2.26637 q^{38} -4.03548 q^{39} -0.587433 q^{40} +1.33811 q^{41} +4.70820 q^{43} -0.582554 q^{45} -3.03060 q^{46} -6.04554 q^{47} -0.456423 q^{48} -3.84893 q^{50} +2.67894 q^{51} -9.11210 q^{52} -1.71792 q^{53} +2.69953 q^{54} -1.80157 q^{57} +2.93422 q^{58} +9.53304 q^{59} +0.191915 q^{60} -9.62943 q^{61} +5.35654 q^{62} +3.07446 q^{64} +1.45293 q^{65} +1.27155 q^{67} +6.04903 q^{68} +2.40907 q^{69} -9.30919 q^{71} +6.91151 q^{72} +5.58911 q^{73} -4.39552 q^{74} +3.05957 q^{75} -4.06794 q^{76} -3.13752 q^{78} +4.52954 q^{79} +0.164330 q^{80} +5.70820 q^{81} +1.04036 q^{82} +11.2838 q^{83} -0.964520 q^{85} +3.66055 q^{86} -2.33245 q^{87} -7.92157 q^{89} -0.452926 q^{90} +5.43967 q^{92} -4.25800 q^{93} -4.70031 q^{94} +0.648635 q^{95} -3.61803 q^{96} +9.05391 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} - q^{6} - 9 q^{8} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 - q^6 - 9 * q^8 - 6 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} - q^{6} - 9 q^{8} - 6 q^{9} - 14 q^{10} + 7 q^{12} + 3 q^{15} - 4 q^{16} - 3 q^{17} + 3 q^{18} + 3 q^{19} + 17 q^{20} - 8 q^{23} - 12 q^{24} + 12 q^{26} - 4 q^{27} - 3 q^{29} - 12 q^{30} + 3 q^{31} + 10 q^{32} + 12 q^{34} - q^{36} - 7 q^{37} + 20 q^{38} - 5 q^{39} - 13 q^{40} + 4 q^{41} - 8 q^{43} - 9 q^{45} + 3 q^{46} + 14 q^{47} + 3 q^{48} - 33 q^{50} + 11 q^{51} - 17 q^{52} - 9 q^{53} + 2 q^{54} - 6 q^{57} + 3 q^{58} + 25 q^{59} + 21 q^{60} - 19 q^{61} + 10 q^{62} + 3 q^{64} - 12 q^{65} - 15 q^{67} - q^{68} - 14 q^{69} - 7 q^{71} + 6 q^{72} - 11 q^{73} - 8 q^{74} + 5 q^{75} - 26 q^{76} - 9 q^{78} - 8 q^{79} + 4 q^{80} - 4 q^{81} - 3 q^{82} - q^{83} - 15 q^{85} + 4 q^{86} + 6 q^{87} + 17 q^{89} + 16 q^{90} - 17 q^{92} - 11 q^{93} - 20 q^{94} - 17 q^{95} - 10 q^{96} + 15 q^{97}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 - q^6 - 9 * q^8 - 6 * q^9 - 14 * q^10 + 7 * q^12 + 3 * q^15 - 4 * q^16 - 3 * q^17 + 3 * q^18 + 3 * q^19 + 17 * q^20 - 8 * q^23 - 12 * q^24 + 12 * q^26 - 4 * q^27 - 3 * q^29 - 12 * q^30 + 3 * q^31 + 10 * q^32 + 12 * q^34 - q^36 - 7 * q^37 + 20 * q^38 - 5 * q^39 - 13 * q^40 + 4 * q^41 - 8 * q^43 - 9 * q^45 + 3 * q^46 + 14 * q^47 + 3 * q^48 - 33 * q^50 + 11 * q^51 - 17 * q^52 - 9 * q^53 + 2 * q^54 - 6 * q^57 + 3 * q^58 + 25 * q^59 + 21 * q^60 - 19 * q^61 + 10 * q^62 + 3 * q^64 - 12 * q^65 - 15 * q^67 - q^68 - 14 * q^69 - 7 * q^71 + 6 * q^72 - 11 * q^73 - 8 * q^74 + 5 * q^75 - 26 * q^76 - 9 * q^78 - 8 * q^79 + 4 * q^80 - 4 * q^81 - 3 * q^82 - q^83 - 15 * q^85 + 4 * q^86 + 6 * q^87 + 17 * q^89 + 16 * q^90 - 17 * q^92 - 11 * q^93 - 20 * q^94 - 17 * q^95 - 10 * q^96 + 15 * q^97

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 $

$2$	0.777484	0.549764	0.274882	−	0.961478i	$-0.411361\pi$
$2$	0.777484	0.549764	0.274882	+	0.961478i	$0.411361\pi$
$3$	−0.618034	−0.356822	−0.178411	−	0.983956i	$-0.557096\pi$
$3$	−0.618034	−0.356822	−0.178411	+	0.983956i	$0.557096\pi$
$4$	−1.39552	−0.697759
$5$	0.222516	0.0995121	0.0497560	−	0.998761i	$-0.484156\pi$
$5$	0.222516	0.0995121	0.0497560	+	0.998761i	$0.484156\pi$
$6$	−0.480512	−0.196168
$7$	0	0
$7$	0	0
$8$	−2.63996	−0.933368
$9$	−2.61803	−0.872678
$10$	0.173002	0.0547082
$11$	0	0
$11$	0	0
$12$	0.862478	0.248976
$13$	6.52954	1.81097	0.905485	−	0.424379i	$-0.139507\pi$
$13$	6.52954	1.81097	0.905485	+	0.424379i	$0.139507\pi$
$14$	0	0
$15$	−0.137522	−0.0355081
$16$	0.738508	0.184627
$17$	−4.33461	−1.05130	−0.525649	−	0.850701i	$-0.676178\pi$
$17$	−4.33461	−1.05130	−0.525649	+	0.850701i	$0.676178\pi$
$18$	−2.03548	−0.479767
$19$	2.91501	0.668748	0.334374	−	0.942440i	$-0.391475\pi$
$19$	2.91501	0.668748	0.334374	+	0.942440i	$0.391475\pi$
$20$	−0.310525	−0.0694355
$21$	0	0
$22$	0	0
$23$	−3.89796	−0.812780	−0.406390	−	0.913700i	$-0.633213\pi$
$23$	−3.89796	−0.812780	−0.406390	+	0.913700i	$0.633213\pi$
$24$	1.63159	0.333046
$25$	−4.95049	−0.990097
$26$	5.07662	0.995607
$27$	3.47214	0.668213
$28$	0	0
$29$	3.77399	0.700812	0.350406	−	0.936598i	$-0.386044\pi$
$29$	3.77399	0.700812	0.350406	+	0.936598i	$0.386044\pi$
$30$	−0.106921	−0.0195211
$31$	6.88958	1.23741	0.618703	−	0.785625i	$-0.287659\pi$
$31$	6.88958	1.23741	0.618703	+	0.785625i	$0.287659\pi$
$32$	5.85410	1.03487
$33$	0	0
$34$	−3.37009	−0.577966
$35$	0	0
$36$	3.65351	0.608919
$37$	−5.65351	−0.929432	−0.464716	−	0.885460i	$-0.653844\pi$
$37$	−5.65351	−0.929432	−0.464716	+	0.885460i	$0.653844\pi$
$38$	2.26637	0.367654
$39$	−4.03548	−0.646194
$40$	−0.587433	−0.0928813
$41$	1.33811	0.208978	0.104489	−	0.994526i	$-0.466679\pi$
$41$	1.33811	0.208978	0.104489	+	0.994526i	$0.466679\pi$
$42$	0	0
$43$	4.70820	0.717994	0.358997	−	0.933339i	$-0.383119\pi$
$43$	4.70820	0.717994	0.358997	+	0.933339i	$0.383119\pi$
$44$	0	0
$45$	−0.582554	−0.0868420
$46$	−3.03060	−0.446838
$47$	−6.04554	−0.881832	−0.440916	−	0.897548i	$-0.645346\pi$
$47$	−6.04554	−0.881832	−0.440916	+	0.897548i	$0.645346\pi$
$48$	−0.456423	−0.0658790
$49$	0	0
$50$	−3.84893	−0.544320
$51$	2.67894	0.375126
$52$	−9.11210	−1.26362
$53$	−1.71792	−0.235974	−0.117987	−	0.993015i	$-0.537644\pi$
$53$	−1.71792	−0.235974	−0.117987	+	0.993015i	$0.537644\pi$
$54$	2.69953	0.367360
$55$	0	0
$56$	0	0
$57$	−1.80157	−0.238624
$58$	2.93422	0.385281
$59$	9.53304	1.24110	0.620548	−	0.784168i	$-0.286910\pi$
$59$	9.53304	1.24110	0.620548	+	0.784168i	$0.286910\pi$
$60$	0.191915	0.0247761
$61$	−9.62943	−1.23292	−0.616461	−	0.787386i	$-0.711434\pi$
$61$	−9.62943	−1.23292	−0.616461	+	0.787386i	$0.711434\pi$
$62$	5.35654	0.680281
$63$	0	0
$64$	3.07446	0.384307
$65$	1.45293	0.180213
$66$	0	0
$67$	1.27155	0.155344	0.0776722	−	0.996979i	$-0.475251\pi$
$67$	1.27155	0.155344	0.0776722	+	0.996979i	$0.475251\pi$
$68$	6.04903	0.733553
$69$	2.40907	0.290018
$70$	0	0
$71$	−9.30919	−1.10480	−0.552399	−	0.833580i	$-0.686287\pi$
$71$	−9.30919	−1.10480	−0.552399	+	0.833580i	$0.686287\pi$
$72$	6.91151	0.814529
$73$	5.58911	0.654156	0.327078	−	0.944997i	$-0.393936\pi$
$73$	5.58911	0.654156	0.327078	+	0.944997i	$0.393936\pi$
$74$	−4.39552	−0.510969
$75$	3.05957	0.353289
$76$	−4.06794	−0.466625
$77$	0	0
$78$	−3.13752	−0.355254
$79$	4.52954	0.509614	0.254807	−	0.966992i	$-0.417988\pi$
$79$	4.52954	0.509614	0.254807	+	0.966992i	$0.417988\pi$
$80$	0.164330	0.0183726
$81$	5.70820	0.634245
$82$	1.04036	0.114888
$83$	11.2838	1.23855	0.619277	−	0.785173i	$-0.287426\pi$
$83$	11.2838	1.23855	0.619277	+	0.785173i	$0.287426\pi$
$84$	0	0
$85$	−0.964520	−0.104617
$86$	3.66055	0.394728
$87$	−2.33245	−0.250065
$88$	0	0
$89$	−7.92157	−0.839684	−0.419842	−	0.907597i	$-0.637915\pi$
$89$	−7.92157	−0.839684	−0.419842	+	0.907597i	$0.637915\pi$
$90$	−0.452926	−0.0477426
$91$	0	0
$92$	5.43967	0.567125
$93$	−4.25800	−0.441534
$94$	−4.70031	−0.484800
$95$	0.648635	0.0665485
$96$	−3.61803	−0.369264
$97$	9.05391	0.919285	0.459643	−	0.888104i	$-0.347977\pi$
$97$	9.05391	0.919285	0.459643	+	0.888104i	$0.347977\pi$
$98$	0	0
$99$	0	0
$100$	6.90849	0.690849
$101$	−19.2102	−1.91148	−0.955741	−	0.294208i	$-0.904944\pi$
$101$	−19.2102	−1.91148	−0.955741	+	0.294208i	$0.904944\pi$
$102$	2.08283	0.206231
$103$	−16.2383	−1.60001	−0.800004	−	0.599995i	$-0.795169\pi$
$103$	−16.2383	−1.60001	−0.800004	+	0.599995i	$0.795169\pi$
$104$	−17.2377	−1.69030
$105$	0	0
$106$	−1.33565	−0.129730
$107$	5.39336	0.521396	0.260698	−	0.965420i	$-0.416047\pi$
$107$	5.39336	0.521396	0.260698	+	0.965420i	$0.416047\pi$
$108$	−4.84543	−0.466252
$109$	−5.39901	−0.517132	−0.258566	−	0.965994i	$-0.583250\pi$
$109$	−5.39901	−0.517132	−0.258566	+	0.965994i	$0.583250\pi$
$110$	0	0
$111$	3.49406	0.331642
$112$	0	0
$113$	−16.4962	−1.55183	−0.775917	−	0.630835i	$-0.782713\pi$
$113$	−16.4962	−1.55183	−0.775917	+	0.630835i	$0.782713\pi$
$114$	−1.40069	−0.131187
$115$	−0.867357	−0.0808815
$116$	−5.26667	−0.488998
$117$	−17.0946	−1.58039
$118$	7.41179	0.682310
$119$	0	0
$120$	0.363054	0.0331421
$121$	0	0
$122$	−7.48673	−0.677816
$123$	−0.826998	−0.0745679
$124$	−9.61454	−0.863411
$125$	−2.21414	−0.198039
$126$	0	0
$127$	−1.99728	−0.177230	−0.0886150	−	0.996066i	$-0.528244\pi$
$127$	−1.99728	−0.177230	−0.0886150	+	0.996066i	$0.528244\pi$
$128$	−9.31786	−0.823590
$129$	−2.90983	−0.256196
$130$	1.12963	0.0990749
$131$	1.37009	0.119706	0.0598528	−	0.998207i	$-0.480937\pi$
$131$	1.37009	0.119706	0.0598528	+	0.998207i	$0.480937\pi$
$132$	0	0
$133$	0	0
$134$	0.988609	0.0854028
$135$	0.772605	0.0664952
$136$	11.4432	0.981248
$137$	2.49924	0.213525	0.106762	−	0.994285i	$-0.465952\pi$
$137$	2.49924	0.213525	0.106762	+	0.994285i	$0.465952\pi$
$138$	1.87301	0.159442
$139$	−4.76260	−0.403958	−0.201979	−	0.979390i	$-0.564737\pi$
$139$	−4.76260	−0.403958	−0.201979	+	0.979390i	$0.564737\pi$
$140$	0	0
$141$	3.73635	0.314657
$142$	−7.23775	−0.607378
$143$	0	0
$144$	−1.93344	−0.161120
$145$	0.839772	0.0697392
$146$	4.34545	0.359632
$147$	0	0
$148$	7.88958	0.648520
$149$	7.22985	0.592293	0.296146	−	0.955143i	$-0.404298\pi$
$149$	7.22985	0.592293	0.296146	+	0.955143i	$0.404298\pi$
$150$	2.37877	0.194225
$151$	−8.13968	−0.662398	−0.331199	−	0.943561i	$-0.607453\pi$
$151$	−8.13968	−0.662398	−0.331199	+	0.943561i	$0.607453\pi$
$152$	−7.69551	−0.624188
$153$	11.3482	0.917445
$154$	0	0
$155$	1.53304	0.123137
$156$	5.63159	0.450888
$157$	−20.1514	−1.60826	−0.804129	−	0.594455i	$-0.797368\pi$
$157$	−20.1514	−1.60826	−0.804129	+	0.594455i	$0.797368\pi$
$158$	3.52165	0.280167
$159$	1.06173	0.0842007
$160$	1.30263	0.102982
$161$	0	0
$162$	4.43804	0.348685
$163$	7.43449	0.582315	0.291157	−	0.956675i	$-0.405960\pi$
$163$	7.43449	0.582315	0.291157	+	0.956675i	$0.405960\pi$
$164$	−1.86736	−0.145816
$165$	0	0
$166$	8.77295	0.680913
$167$	−2.21112	−0.171102	−0.0855510	−	0.996334i	$-0.527265\pi$
$167$	−2.21112	−0.171102	−0.0855510	+	0.996334i	$0.527265\pi$
$168$	0	0
$169$	29.6349	2.27961
$170$	−0.749899	−0.0575146
$171$	−7.63159	−0.583602
$172$	−6.57038	−0.500987
$173$	−10.3622	−0.787823	−0.393912	−	0.919148i	$-0.628878\pi$
$173$	−10.3622	−0.787823	−0.393912	+	0.919148i	$0.628878\pi$
$174$	−1.81345	−0.137477
$175$	0	0
$176$	0	0
$177$	−5.89174	−0.442851
$178$	−6.15889	−0.461629
$179$	−23.4094	−1.74970	−0.874851	−	0.484392i	$-0.839041\pi$
$179$	−23.4094	−1.74970	−0.874851	+	0.484392i	$0.839041\pi$
$180$	0.812964	0.0605948
$181$	13.7161	1.01951	0.509755	−	0.860320i	$-0.329736\pi$
$181$	13.7161	1.01951	0.509755	+	0.860320i	$0.329736\pi$
$182$	0	0
$183$	5.95131	0.439934
$184$	10.2905	0.758623
$185$	−1.25800	−0.0924897
$186$	−3.31052	−0.242739
$187$	0	0
$188$	8.43666	0.615306
$189$	0	0
$190$	0.504303	0.0365860
$191$	−12.0249	−0.870094	−0.435047	−	0.900408i	$-0.643268\pi$
$191$	−12.0249	−0.870094	−0.435047	+	0.900408i	$0.643268\pi$
$192$	−1.90012	−0.137129
$193$	−15.8839	−1.14335	−0.571675	−	0.820480i	$-0.693706\pi$
$193$	−15.8839	−1.14335	−0.571675	+	0.820480i	$0.693706\pi$
$194$	7.03927	0.505390
$195$	−0.897958	−0.0643041
$196$	0	0
$197$	−12.3035	−0.876590	−0.438295	−	0.898831i	$-0.644418\pi$
$197$	−12.3035	−0.876590	−0.438295	+	0.898831i	$0.644418\pi$
$198$	0	0
$199$	−15.2615	−1.08186	−0.540929	−	0.841068i	$-0.681927\pi$
$199$	−15.2615	−1.08186	−0.540929	+	0.841068i	$0.681927\pi$
$200$	13.0691	0.924125
$201$	−0.785860	−0.0554303
$202$	−14.9356	−1.05087
$203$	0	0
$204$	−3.73851	−0.261748
$205$	0.297751	0.0207958
$206$	−12.6250	−0.879627
$207$	10.2050	0.709296
$208$	4.82212	0.334354
$209$	0	0
$210$	0	0
$211$	−8.93344	−0.615003	−0.307502	−	0.951548i	$-0.599493\pi$
$211$	−8.93344	−0.615003	−0.307502	+	0.951548i	$0.599493\pi$
$212$	2.39738	0.164653
$213$	5.75340	0.394216
$214$	4.19325	0.286645
$215$	1.04765	0.0714491
$216$	−9.16631	−0.623688
$217$	0	0
$218$	−4.19765	−0.284301
$219$	−3.45426	−0.233417
$220$	0	0
$221$	−28.3031	−1.90387
$222$	2.71658	0.182325
$223$	−0.715244	−0.0478963	−0.0239481	−	0.999713i	$-0.507624\pi$
$223$	−0.715244	−0.0478963	−0.0239481	+	0.999713i	$0.507624\pi$
$224$	0	0
$225$	12.9605	0.864036
$226$	−12.8256	−0.853143
$227$	−5.32162	−0.353208	−0.176604	−	0.984282i	$-0.556511\pi$
$227$	−5.32162	−0.353208	−0.176604	+	0.984282i	$0.556511\pi$
$228$	2.51413	0.166502
$229$	6.60832	0.436690	0.218345	−	0.975872i	$-0.429934\pi$
$229$	6.60832	0.436690	0.218345	+	0.975872i	$0.429934\pi$
$230$	−0.674356	−0.0444657
$231$	0	0
$232$	−9.96318	−0.654115
$233$	9.55713	0.626108	0.313054	−	0.949735i	$-0.398648\pi$
$233$	9.55713	0.626108	0.313054	+	0.949735i	$0.398648\pi$
$234$	−13.2908	−0.868844
$235$	−1.34523	−0.0877529
$236$	−13.3035	−0.865986
$237$	−2.79941	−0.181841
$238$	0	0
$239$	−26.8466	−1.73656	−0.868282	−	0.496071i	$-0.834776\pi$
$239$	−26.8466	−1.73656	−0.868282	+	0.496071i	$0.834776\pi$
$240$	−0.101561	−0.00655575
$241$	18.8663	1.21529	0.607643	−	0.794210i	$-0.292115\pi$
$241$	18.8663	1.21529	0.607643	+	0.794210i	$0.292115\pi$
$242$	0	0
$243$	−13.9443	−0.894525
$244$	13.4380	0.860282
$245$	0	0
$246$	−0.642978	−0.0409948
$247$	19.0337	1.21108
$248$	−18.1882	−1.15495
$249$	−6.97375	−0.441943
$250$	−1.72146	−0.108875
$251$	−29.3732	−1.85402	−0.927009	−	0.375040i	$-0.877629\pi$
$251$	−29.3732	−1.85402	−0.927009	+	0.375040i	$0.877629\pi$
$252$	0	0
$253$	0	0
$254$	−1.55285	−0.0974348
$255$	0.596106	0.0373296
$256$	−13.3934	−0.837088
$257$	16.9164	1.05522	0.527608	−	0.849488i	$-0.323089\pi$
$257$	16.9164	1.05522	0.527608	+	0.849488i	$0.323089\pi$
$258$	−2.26235	−0.140848
$259$	0	0
$260$	−2.02759	−0.125746
$261$	−9.88043	−0.611583
$262$	1.06523	0.0658099
$263$	8.18034	0.504421	0.252211	−	0.967672i	$-0.418842\pi$
$263$	8.18034	0.504421	0.252211	+	0.967672i	$0.418842\pi$
$264$	0	0
$265$	−0.382263	−0.0234822
$266$	0	0
$267$	4.89580	0.299618
$268$	−1.77447	−0.108393
$269$	6.24716	0.380896	0.190448	−	0.981697i	$-0.439006\pi$
$269$	6.24716	0.380896	0.190448	+	0.981697i	$0.439006\pi$
$270$	0.600688	0.0365567
$271$	7.86688	0.477879	0.238939	−	0.971034i	$-0.423200\pi$
$271$	7.86688	0.477879	0.238939	+	0.971034i	$0.423200\pi$
$272$	−3.20115	−0.194098
$273$	0	0
$274$	1.94312	0.117388
$275$	0	0
$276$	−3.36190	−0.202363
$277$	−12.0476	−0.723873	−0.361937	−	0.932203i	$-0.617884\pi$
$277$	−12.0476	−0.723873	−0.361937	+	0.932203i	$0.617884\pi$
$278$	−3.70284	−0.222082
$279$	−18.0372	−1.07986
$280$	0	0
$281$	−21.1549	−1.26200	−0.630998	−	0.775784i	$-0.717354\pi$
$281$	−21.1549	−1.26200	−0.630998	+	0.775784i	$0.717354\pi$
$282$	2.90495	0.172987
$283$	−25.0034	−1.48630	−0.743148	−	0.669127i	$-0.766668\pi$
$283$	−25.0034	−1.48630	−0.743148	+	0.669127i	$0.766668\pi$
$284$	12.9911	0.770883
$285$	−0.400878	−0.0237460
$286$	0	0
$287$	0	0
$288$	−15.3262	−0.903107
$289$	1.78888	0.105228
$290$	0.652909	0.0383402
$291$	−5.59563	−0.328021
$292$	−7.79971	−0.456443
$293$	−0.455087	−0.0265865	−0.0132932	−	0.999912i	$-0.504231\pi$
$293$	−0.455087	−0.0265865	−0.0132932	+	0.999912i	$0.504231\pi$
$294$	0	0
$295$	2.12125	0.123504
$296$	14.9251	0.867502
$297$	0	0
$298$	5.62110	0.325621
$299$	−25.4519	−1.47192
$300$	−4.26968	−0.246510
$301$	0	0
$302$	−6.32848	−0.364163
$303$	11.8725	0.682059
$304$	2.15275	0.123469
$305$	−2.14270	−0.122691
$306$	8.82302	0.504378
$307$	−8.03578	−0.458626	−0.229313	−	0.973353i	$-0.573648\pi$
$307$	−8.03578	−0.458626	−0.229313	+	0.973353i	$0.573648\pi$
$308$	0	0
$309$	10.0358	0.570918
$310$	1.19191	0.0676962
$311$	−0.136965	−0.00776656	−0.00388328	−	0.999992i	$-0.501236\pi$
$311$	−0.136965	−0.00776656	−0.00388328	+	0.999992i	$0.501236\pi$
$312$	10.6535	0.603136
$313$	15.2899	0.864238	0.432119	−	0.901817i	$-0.357766\pi$
$313$	15.2899	0.864238	0.432119	+	0.901817i	$0.357766\pi$
$314$	−15.6674	−0.884163
$315$	0	0
$316$	−6.32106	−0.355587
$317$	−32.9925	−1.85304	−0.926522	−	0.376239i	$-0.877217\pi$
$317$	−32.9925	−1.85304	−0.926522	+	0.376239i	$0.877217\pi$
$318$	0.825478	0.0462905
$319$	0	0
$320$	0.684115	0.0382432
$321$	−3.33328	−0.186045
$322$	0	0
$323$	−12.6354	−0.703054
$324$	−7.96590	−0.442550
$325$	−32.3244	−1.79304
$326$	5.78020	0.320136
$327$	3.33677	0.184524
$328$	−3.53256	−0.195053
$329$	0	0
$330$	0	0
$331$	29.5335	1.62331	0.811653	−	0.584140i	$-0.198568\pi$
$331$	29.5335	1.62331	0.811653	+	0.584140i	$0.198568\pi$
$332$	−15.7467	−0.864212
$333$	14.8011	0.811095
$334$	−1.71911	−0.0940658
$335$	0.282939	0.0154586
$336$	0	0
$337$	−5.63025	−0.306699	−0.153350	−	0.988172i	$-0.549006\pi$
$337$	−5.63025	−0.306699	−0.153350	+	0.988172i	$0.549006\pi$
$338$	23.0407	1.25325
$339$	10.1952	0.553729
$340$	1.34600	0.0729974
$341$	0	0
$342$	−5.93344	−0.320844
$343$	0	0
$344$	−12.4295	−0.670153
$345$	0.536056	0.0288603
$346$	−8.05645	−0.433117
$347$	−8.73061	−0.468684	−0.234342	−	0.972154i	$-0.575294\pi$
$347$	−8.73061	−0.468684	−0.234342	+	0.972154i	$0.575294\pi$
$348$	3.25498	0.174485
$349$	18.4670	0.988514	0.494257	−	0.869316i	$-0.335440\pi$
$349$	18.4670	0.988514	0.494257	+	0.869316i	$0.335440\pi$
$350$	0	0
$351$	22.6715	1.21011
$352$	0	0
$353$	23.4857	1.25002	0.625009	−	0.780618i	$-0.285095\pi$
$353$	23.4857	1.25002	0.625009	+	0.780618i	$0.285095\pi$
$354$	−4.58074	−0.243463
$355$	−2.07144	−0.109941
$356$	11.0547	0.585897
$357$	0	0
$358$	−18.2005	−0.961924
$359$	−14.8812	−0.785400	−0.392700	−	0.919667i	$-0.628459\pi$
$359$	−14.8812	−0.785400	−0.392700	+	0.919667i	$0.628459\pi$
$360$	1.53792	0.0810555
$361$	−10.5027	−0.552776
$362$	10.6641	0.560490
$363$	0	0
$364$	0	0
$365$	1.24367	0.0650964
$366$	4.62705	0.241860
$367$	34.2259	1.78658	0.893289	−	0.449482i	$-0.148391\pi$
$367$	34.2259	1.78658	0.893289	+	0.449482i	$0.148391\pi$
$368$	−2.87867	−0.150061
$369$	−3.50322	−0.182370
$370$	−0.978072	−0.0508475
$371$	0	0
$372$	5.94211	0.308084
$373$	−3.01739	−0.156235	−0.0781173	−	0.996944i	$-0.524891\pi$
$373$	−3.01739	−0.156235	−0.0781173	+	0.996944i	$0.524891\pi$
$374$	0	0
$375$	1.36841	0.0706646
$376$	15.9600	0.823073
$377$	24.6424	1.26915
$378$	0	0
$379$	−6.12431	−0.314585	−0.157292	−	0.987552i	$-0.550277\pi$
$379$	−6.12431	−0.314585	−0.157292	+	0.987552i	$0.550277\pi$
$380$	−0.905182	−0.0464348
$381$	1.23439	0.0632396
$382$	−9.34920	−0.478347
$383$	−4.39098	−0.224369	−0.112184	−	0.993687i	$-0.535785\pi$
$383$	−4.39098	−0.224369	−0.112184	+	0.993687i	$0.535785\pi$
$384$	5.75876	0.293875
$385$	0	0
$386$	−12.3495	−0.628573
$387$	−12.3262	−0.626578
$388$	−12.6349	−0.641440
$389$	10.4960	0.532169	0.266084	−	0.963950i	$-0.414270\pi$
$389$	10.4960	0.532169	0.266084	+	0.963950i	$0.414270\pi$
$390$	−0.698148	−0.0353521
$391$	16.8961	0.854475
$392$	0	0
$393$	−0.846765	−0.0427136
$394$	−9.56580	−0.481918
$395$	1.00789	0.0507127
$396$	0	0
$397$	−11.3888	−0.571589	−0.285794	−	0.958291i	$-0.592257\pi$
$397$	−11.3888	−0.571589	−0.285794	+	0.958291i	$0.592257\pi$
$398$	−11.8656	−0.594767
$399$	0	0
$400$	−3.65597	−0.182799
$401$	−4.72496	−0.235953	−0.117977	−	0.993016i	$-0.537641\pi$
$401$	−4.72496	−0.235953	−0.117977	+	0.993016i	$0.537641\pi$
$402$	−0.610994	−0.0304736
$403$	44.9858	2.24090
$404$	26.8081	1.33375
$405$	1.27017	0.0631150
$406$	0	0
$407$	0	0
$408$	−7.07230	−0.350131
$409$	2.46544	0.121908	0.0609541	−	0.998141i	$-0.480586\pi$
$409$	2.46544	0.121908	0.0609541	+	0.998141i	$0.480586\pi$
$410$	0.231496	0.0114328
$411$	−1.54462	−0.0761903
$412$	22.6609	1.11642
$413$	0	0
$414$	7.93422	0.389945
$415$	2.51082	0.123251
$416$	38.2246	1.87412
$417$	2.94345	0.144141
$418$	0	0
$419$	14.3399	0.700548	0.350274	−	0.936647i	$-0.386088\pi$
$419$	14.3399	0.700548	0.350274	+	0.936647i	$0.386088\pi$
$420$	0	0
$421$	−17.3157	−0.843918	−0.421959	−	0.906615i	$-0.638657\pi$
$421$	−17.3157	−0.843918	−0.421959	+	0.906615i	$0.638657\pi$
$422$	−6.94561	−0.338107
$423$	15.8274	0.769555
$424$	4.53523	0.220250
$425$	21.4584	1.04089
$426$	4.47317	0.216726
$427$	0	0
$428$	−7.52653	−0.363808
$429$	0	0
$430$	0.814531	0.0392802
$431$	−27.8923	−1.34352	−0.671762	−	0.740767i	$-0.734462\pi$
$431$	−27.8923	−1.34352	−0.671762	+	0.740767i	$0.734462\pi$
$432$	2.56420	0.123370
$433$	29.5470	1.41994	0.709969	−	0.704232i	$-0.248709\pi$
$433$	29.5470	1.41994	0.709969	+	0.704232i	$0.248709\pi$
$434$	0	0
$435$	−0.519007	−0.0248845
$436$	7.53442	0.360833
$437$	−11.3626	−0.543546
$438$	−2.68563	−0.128325
$439$	−33.6655	−1.60677	−0.803384	−	0.595461i	$-0.796970\pi$
$439$	−33.6655	−1.60677	−0.803384	+	0.595461i	$0.796970\pi$
$440$	0	0
$441$	0	0
$442$	−22.0052	−1.04668
$443$	10.3267	0.490637	0.245319	−	0.969443i	$-0.421107\pi$
$443$	10.3267	0.490637	0.245319	+	0.969443i	$0.421107\pi$
$444$	−4.87603	−0.231406
$445$	−1.76267	−0.0835587
$446$	−0.556091	−0.0263317
$447$	−4.46829	−0.211343
$448$	0	0
$449$	−2.75785	−0.130151	−0.0650756	−	0.997880i	$-0.520729\pi$
$449$	−2.75785	−0.130151	−0.0650756	+	0.997880i	$0.520729\pi$
$450$	10.0766	0.475016
$451$	0	0
$452$	23.0208	1.08281
$453$	5.03060	0.236358
$454$	−4.13747	−0.194181
$455$	0	0
$456$	4.75608	0.222724
$457$	40.3305	1.88658	0.943291	−	0.331968i	$-0.107713\pi$
$457$	40.3305	1.88658	0.943291	+	0.331968i	$0.107713\pi$
$458$	5.13787	0.240077
$459$	−15.0504	−0.702491
$460$	1.21041	0.0564358
$461$	−34.2251	−1.59402	−0.797011	−	0.603965i	$-0.793587\pi$
$461$	−34.2251	−1.59402	−0.797011	+	0.603965i	$0.793587\pi$
$462$	0	0
$463$	0.707349	0.0328733	0.0164367	−	0.999865i	$-0.494768\pi$
$463$	0.707349	0.0328733	0.0164367	+	0.999865i	$0.494768\pi$
$464$	2.78712	0.129389
$465$	−0.947471	−0.0439379
$466$	7.43052	0.344212
$467$	28.5924	1.32310	0.661550	−	0.749901i	$-0.269899\pi$
$467$	28.5924	1.32310	0.661550	+	0.749901i	$0.269899\pi$
$468$	23.8558	1.10273
$469$	0	0
$470$	−1.04589	−0.0482434
$471$	12.4543	0.573862
$472$	−25.1669	−1.15840
$473$	0	0
$474$	−2.17650	−0.0999699
$475$	−14.4307	−0.662126
$476$	0	0
$477$	4.49756	0.205929
$478$	−20.8728	−0.954701
$479$	−5.09716	−0.232895	−0.116448	−	0.993197i	$-0.537151\pi$
$479$	−5.09716	−0.232895	−0.116448	+	0.993197i	$0.537151\pi$
$480$	−0.805070	−0.0367462
$481$	−36.9149	−1.68317
$482$	14.6683	0.668121
$483$	0	0
$484$	0	0
$485$	2.01464	0.0914800
$486$	−10.8415	−0.491778
$487$	29.1883	1.32265	0.661324	−	0.750101i	$-0.269995\pi$
$487$	29.1883	1.32265	0.661324	+	0.750101i	$0.269995\pi$
$488$	25.4213	1.15077
$489$	−4.59477	−0.207783
$490$	0	0
$491$	−30.1439	−1.36038	−0.680189	−	0.733037i	$-0.738102\pi$
$491$	−30.1439	−1.36038	−0.680189	+	0.733037i	$0.738102\pi$
$492$	1.15409	0.0520304
$493$	−16.3588	−0.736762
$494$	14.7984	0.665810
$495$	0	0
$496$	5.08801	0.228458
$497$	0	0
$498$	−5.42198	−0.242965
$499$	5.95104	0.266405	0.133203	−	0.991089i	$-0.457474\pi$
$499$	5.95104	0.266405	0.133203	+	0.991089i	$0.457474\pi$
$500$	3.08987	0.138183
$501$	1.36655	0.0610530
$502$	−22.8372	−1.01927
$503$	−4.97855	−0.221983	−0.110991	−	0.993821i	$-0.535403\pi$
$503$	−4.97855	−0.221983	−0.110991	+	0.993821i	$0.535403\pi$
$504$	0	0
$505$	−4.27456	−0.190216
$506$	0	0
$507$	−18.3154	−0.813416
$508$	2.78724	0.123664
$509$	21.3285	0.945370	0.472685	−	0.881231i	$-0.343285\pi$
$509$	21.3285	0.945370	0.472685	+	0.881231i	$0.343285\pi$
$510$	0.463463	0.0205225
$511$	0	0
$512$	8.22256	0.363389
$513$	10.1213	0.446866
$514$	13.1522	0.580120
$515$	−3.61328	−0.159220
$516$	4.06072	0.178763
$517$	0	0
$518$	0	0
$519$	6.40419	0.281113
$520$	−3.83567	−0.168205
$521$	22.1383	0.969899	0.484949	−	0.874542i	$-0.338838\pi$
$521$	22.1383	0.969899	0.484949	+	0.874542i	$0.338838\pi$
$522$	−7.68188	−0.336227
$523$	4.91146	0.214763	0.107382	−	0.994218i	$-0.465753\pi$
$523$	4.91146	0.214763	0.107382	+	0.994218i	$0.465753\pi$
$524$	−1.91199	−0.0835257
$525$	0	0
$526$	6.36009	0.277313
$527$	−29.8637	−1.30088
$528$	0	0
$529$	−7.80592	−0.339388
$530$	−0.297204	−0.0129097
$531$	−24.9578	−1.08308
$532$	0	0
$533$	8.73725	0.378452
$534$	3.80641	0.164719
$535$	1.20011	0.0518851
$536$	−3.35684	−0.144993
$537$	14.4678	0.624332
$538$	4.85707	0.209403
$539$	0	0
$540$	−1.07818	−0.0463977
$541$	−19.3845	−0.833404	−0.416702	−	0.909043i	$-0.636814\pi$
$541$	−19.3845	−0.833404	−0.416702	+	0.909043i	$0.636814\pi$
$542$	6.11637	0.262721
$543$	−8.47702	−0.363784
$544$	−25.3753	−1.08796
$545$	−1.20137	−0.0514609
$546$	0	0
$547$	−14.4501	−0.617840	−0.308920	−	0.951088i	$-0.599968\pi$
$547$	−14.4501	−0.617840	−0.308920	+	0.951088i	$0.599968\pi$
$548$	−3.48774	−0.148989
$549$	25.2102	1.07594
$550$	0	0
$551$	11.0012	0.468667
$552$	−6.35985	−0.270693
$553$	0	0
$554$	−9.36686	−0.397960
$555$	0.777484	0.0330024
$556$	6.64629	0.281865
$557$	−18.4708	−0.782634	−0.391317	−	0.920256i	$-0.627980\pi$
$557$	−18.4708	−0.782634	−0.391317	+	0.920256i	$0.627980\pi$
$558$	−14.0236	−0.593667
$559$	30.7424	1.30027
$560$	0	0
$561$	0	0
$562$	−16.4476	−0.693801
$563$	31.2838	1.31846	0.659228	−	0.751943i	$-0.270883\pi$
$563$	31.2838	1.31846	0.659228	+	0.751943i	$0.270883\pi$
$564$	−5.21414	−0.219555
$565$	−3.67067	−0.154426
$566$	−19.4397	−0.817112
$567$	0	0
$568$	24.5759	1.03118
$569$	−1.73605	−0.0727790	−0.0363895	−	0.999338i	$-0.511586\pi$
$569$	−1.73605	−0.0727790	−0.0363895	+	0.999338i	$0.511586\pi$
$570$	−0.311677	−0.0130547
$571$	−12.5309	−0.524403	−0.262201	−	0.965013i	$-0.584449\pi$
$571$	−12.5309	−0.524403	−0.262201	+	0.965013i	$0.584449\pi$
$572$	0	0
$573$	7.43182	0.310469
$574$	0	0
$575$	19.2968	0.804732
$576$	−8.04903	−0.335376
$577$	−20.1896	−0.840505	−0.420252	−	0.907407i	$-0.638058\pi$
$577$	−20.1896	−0.840505	−0.420252	+	0.907407i	$0.638058\pi$
$578$	1.39082	0.0578506
$579$	9.81681	0.407973
$580$	−1.17192	−0.0486612
$581$	0	0
$582$	−4.35051	−0.180334
$583$	0	0
$584$	−14.7550	−0.610568
$585$	−3.80381	−0.157268
$586$	−0.353823	−0.0146163
$587$	0.00837574	0.000345704 0	0.000172852	−	1.00000i	$-0.499945\pi$
$587$	0.00837574	0.000345704 0	0.000172852		1.00000i	$0.499945\pi$
$588$	0	0
$589$	20.0832	0.827513
$590$	1.64924	0.0678981
$591$	7.60400	0.312787
$592$	−4.17516	−0.171598
$593$	−0.439298	−0.0180398	−0.00901989	−	0.999959i	$-0.502871\pi$
$593$	−0.439298	−0.0180398	−0.00901989	+	0.999959i	$0.502871\pi$
$594$	0	0
$595$	0	0
$596$	−10.0894	−0.413278
$597$	9.43212	0.386031
$598$	−19.7884	−0.809210
$599$	45.1664	1.84545	0.922724	−	0.385462i	$-0.125958\pi$
$599$	45.1664	1.84545	0.922724	+	0.385462i	$0.125958\pi$
$600$	−8.07715	−0.329748
$601$	11.1437	0.454559	0.227280	−	0.973830i	$-0.427017\pi$
$601$	11.1437	0.454559	0.227280	+	0.973830i	$0.427017\pi$
$602$	0	0
$603$	−3.32896	−0.135566
$604$	11.3591	0.462194
$605$	0	0
$606$	9.23071	0.374972
$607$	−35.6998	−1.44901	−0.724504	−	0.689270i	$-0.757931\pi$
$607$	−35.6998	−1.44901	−0.724504	+	0.689270i	$0.757931\pi$
$608$	17.0647	0.692067
$609$	0	0
$610$	−1.66591	−0.0674509
$611$	−39.4746	−1.59697
$612$	−15.8366	−0.640156
$613$	−17.1980	−0.694620	−0.347310	−	0.937750i	$-0.612905\pi$
$613$	−17.1980	−0.694620	−0.347310	+	0.937750i	$0.612905\pi$
$614$	−6.24769	−0.252136
$615$	−0.184020	−0.00742040
$616$	0	0
$617$	−16.8852	−0.679774	−0.339887	−	0.940466i	$-0.610389\pi$
$617$	−16.8852	−0.679774	−0.339887	+	0.940466i	$0.610389\pi$
$618$	7.80270	0.313870
$619$	−31.0692	−1.24878	−0.624389	−	0.781114i	$-0.714652\pi$
$619$	−31.0692	−1.24878	−0.624389	+	0.781114i	$0.714652\pi$
$620$	−2.13939	−0.0859198
$621$	−13.5342	−0.543110
$622$	−0.106488	−0.00426978
$623$	0	0
$624$	−2.98023	−0.119305
$625$	24.2598	0.970390
$626$	11.8877	0.475127
$627$	0	0
$628$	28.1217	1.12218
$629$	24.5058	0.977110
$630$	0	0
$631$	7.25364	0.288763	0.144382	−	0.989522i	$-0.453881\pi$
$631$	7.25364	0.288763	0.144382	+	0.989522i	$0.453881\pi$
$632$	−11.9578	−0.475657
$633$	5.52117	0.219447
$634$	−25.6512	−1.01874
$635$	−0.444427	−0.0176365
$636$	−1.48166	−0.0587518
$637$	0	0
$638$	0	0
$639$	24.3718	0.964132
$640$	−2.07337	−0.0819572
$641$	−20.7499	−0.819572	−0.409786	−	0.912182i	$-0.634397\pi$
$641$	−20.7499	−0.819572	−0.409786	+	0.912182i	$0.634397\pi$
$642$	−2.59157	−0.102281
$643$	−7.11127	−0.280441	−0.140221	−	0.990120i	$-0.544781\pi$
$643$	−7.11127	−0.280441	−0.140221	+	0.990120i	$0.544781\pi$
$644$	0	0
$645$	−0.647483	−0.0254946
$646$	−9.82385	−0.386514
$647$	−27.5789	−1.08424	−0.542119	−	0.840302i	$-0.682378\pi$
$647$	−27.5789	−1.08424	−0.542119	+	0.840302i	$0.682378\pi$
$648$	−15.0694	−0.591984
$649$	0	0
$650$	−25.1317	−0.985748
$651$	0	0
$652$	−10.3750	−0.406315
$653$	16.1541	0.632160	0.316080	−	0.948732i	$-0.397633\pi$
$653$	16.1541	0.632160	0.316080	+	0.948732i	$0.397633\pi$
$654$	2.59429	0.101445
$655$	0.304867	0.0119122
$656$	0.988205	0.0385829
$657$	−14.6325	−0.570868
$658$	0	0
$659$	13.2085	0.514531	0.257266	−	0.966341i	$-0.417178\pi$
$659$	13.2085	0.514531	0.257266	+	0.966341i	$0.417178\pi$
$660$	0	0
$661$	4.90660	0.190845	0.0954223	−	0.995437i	$-0.469580\pi$
$661$	4.90660	0.190845	0.0954223	+	0.995437i	$0.469580\pi$
$662$	22.9618	0.892436
$663$	17.4922	0.679343
$664$	−29.7887	−1.15603
$665$	0	0
$666$	11.5076	0.445911
$667$	−14.7108	−0.569606
$668$	3.08566	0.119388
$669$	0.442045	0.0170905
$670$	0.219981	0.00849861
$671$	0	0
$672$	0	0
$673$	29.9872	1.15592	0.577960	−	0.816065i	$-0.303849\pi$
$673$	29.9872	1.15592	0.577960	+	0.816065i	$0.303849\pi$
$674$	−4.37743	−0.168612
$675$	−17.1888	−0.661596
$676$	−41.3561	−1.59062
$677$	12.5889	0.483832	0.241916	−	0.970297i	$-0.422224\pi$
$677$	12.5889	0.483832	0.241916	+	0.970297i	$0.422224\pi$
$678$	7.92663	0.304420
$679$	0	0
$680$	2.54630	0.0976460
$681$	3.28894	0.126033
$682$	0	0
$683$	−28.5342	−1.09183	−0.545916	−	0.837840i	$-0.683818\pi$
$683$	−28.5342	−1.09183	−0.545916	+	0.837840i	$0.683818\pi$
$684$	10.6500	0.407214
$685$	0.556120	0.0212483
$686$	0	0
$687$	−4.08417	−0.155821
$688$	3.47704	0.132561
$689$	−11.2172	−0.427341
$690$	0.416775	0.0158664
$691$	−25.3742	−0.965281	−0.482641	−	0.875818i	$-0.660322\pi$
$691$	−25.3742	−0.965281	−0.482641	+	0.875818i	$0.660322\pi$
$692$	14.4606	0.549711
$693$	0	0
$694$	−6.78791	−0.257666
$695$	−1.05975	−0.0401987
$696$	6.15759	0.233403
$697$	−5.80019	−0.219698
$698$	14.3578	0.543450
$699$	−5.90663	−0.223409
$700$	0	0
$701$	45.7021	1.72615	0.863073	−	0.505079i	$-0.168537\pi$
$701$	45.7021	1.72615	0.863073	+	0.505079i	$0.168537\pi$
$702$	17.6267	0.665277
$703$	−16.4800	−0.621556
$704$	0	0
$705$	0.831396	0.0313122
$706$	18.2598	0.687215
$707$	0	0
$708$	8.22203	0.309003
$709$	38.5304	1.44704	0.723520	−	0.690304i	$-0.242523\pi$
$709$	38.5304	1.44704	0.723520	+	0.690304i	$0.242523\pi$
$710$	−1.61051	−0.0604415
$711$	−11.8585	−0.444729
$712$	20.9126	0.783734
$713$	−26.8553	−1.00574
$714$	0	0
$715$	0	0
$716$	32.6683	1.22087
$717$	16.5921	0.619644
$718$	−11.5699	−0.431785
$719$	−5.70213	−0.212653	−0.106327	−	0.994331i	$-0.533909\pi$
$719$	−5.70213	−0.212653	−0.106327	+	0.994331i	$0.533909\pi$
$720$	−0.430220	−0.0160334
$721$	0	0
$722$	−8.16571	−0.303896
$723$	−11.6600	−0.433641
$724$	−19.1411	−0.711372
$725$	−18.6831	−0.693872
$726$	0	0
$727$	−11.8221	−0.438458	−0.219229	−	0.975673i	$-0.570354\pi$
$727$	−11.8221	−0.438458	−0.219229	+	0.975673i	$0.570354\pi$
$728$	0	0
$729$	−8.50658	−0.315058
$730$	0.966931	0.0357877
$731$	−20.4082	−0.754826
$732$	−8.30516	−0.306968
$733$	8.81193	0.325476	0.162738	−	0.986669i	$-0.447967\pi$
$733$	8.81193	0.325476	0.162738	+	0.986669i	$0.447967\pi$
$734$	26.6101	0.982197
$735$	0	0
$736$	−22.8190	−0.841121
$737$	0	0
$738$	−2.72370	−0.100261
$739$	−0.480809	−0.0176868	−0.00884342	−	0.999961i	$-0.502815\pi$
$739$	−0.480809	−0.0176868	−0.00884342	+	0.999961i	$0.502815\pi$
$740$	1.75556	0.0645355
$741$	−11.7635	−0.432141
$742$	0	0
$743$	−33.2443	−1.21961	−0.609807	−	0.792550i	$-0.708753\pi$
$743$	−33.2443	−1.21961	−0.609807	+	0.792550i	$0.708753\pi$
$744$	11.2409	0.412113
$745$	1.60876	0.0589403
$746$	−2.34598	−0.0858923
$747$	−29.5413	−1.08086
$748$	0	0
$749$	0	0
$750$	1.06392	0.0388489
$751$	28.0066	1.02198	0.510988	−	0.859588i	$-0.329280\pi$
$751$	28.0066	1.02198	0.510988	+	0.859588i	$0.329280\pi$
$752$	−4.46467	−0.162810
$753$	18.1536	0.661554
$754$	19.1591	0.697733
$755$	−1.81121	−0.0659166
$756$	0	0
$757$	−22.2468	−0.808575	−0.404288	−	0.914632i	$-0.632481\pi$
$757$	−22.2468	−0.808575	−0.404288	+	0.914632i	$0.632481\pi$
$758$	−4.76156	−0.172948
$759$	0	0
$760$	−1.71237	−0.0621142
$761$	−48.2254	−1.74817	−0.874085	−	0.485774i	$-0.838538\pi$
$761$	−48.2254	−1.74817	−0.874085	+	0.485774i	$0.838538\pi$
$762$	0.959717	0.0347669
$763$	0	0
$764$	16.7810	0.607116
$765$	2.52515	0.0912968
$766$	−3.41392	−0.123350
$767$	62.2464	2.24759
$768$	8.27758	0.298691
$769$	43.6883	1.57544	0.787721	−	0.616032i	$-0.211261\pi$
$769$	43.6883	1.57544	0.787721	+	0.616032i	$0.211261\pi$
$770$	0	0
$771$	−10.4549	−0.376524
$772$	22.1663	0.797783
$773$	0.585569	0.0210615	0.0105307	−	0.999945i	$-0.496648\pi$
$773$	0.585569	0.0210615	0.0105307	+	0.999945i	$0.496648\pi$
$774$	−9.58346	−0.344470
$775$	−34.1068	−1.22515
$776$	−23.9020	−0.858031
$777$	0	0
$778$	8.16048	0.292567
$779$	3.90060	0.139753
$780$	1.25312	0.0448688
$781$	0	0
$782$	13.1365	0.469760
$783$	13.1038	0.468292
$784$	0	0
$785$	−4.48401	−0.160041
$786$	−0.658346	−0.0234824
$787$	30.7166	1.09493	0.547464	−	0.836829i	$-0.315593\pi$
$787$	30.7166	1.09493	0.547464	+	0.836829i	$0.315593\pi$
$788$	17.1698	0.611649
$789$	−5.05573	−0.179989
$790$	0.783622	0.0278800
$791$	0	0
$792$	0	0
$793$	−62.8758	−2.23278
$794$	−8.85463	−0.314239
$795$	0.236252	0.00837898
$796$	21.2977	0.754877
$797$	10.8333	0.383735	0.191867	−	0.981421i	$-0.438546\pi$
$797$	10.8333	0.383735	0.191867	+	0.981421i	$0.438546\pi$
$798$	0	0
$799$	26.2051	0.927068
$800$	−28.9807	−1.02462
$801$	20.7389	0.732774
$802$	−3.67358	−0.129719
$803$	0	0
$804$	1.09668	0.0386770
$805$	0	0
$806$	34.9758	1.23197
$807$	−3.86096	−0.135912
$808$	50.7141	1.78412
$809$	38.5901	1.35675	0.678377	−	0.734714i	$-0.262684\pi$
$809$	38.5901	1.35675	0.678377	+	0.734714i	$0.262684\pi$
$810$	0.987533	0.0346984
$811$	−50.8935	−1.78711	−0.893556	−	0.448951i	$-0.851798\pi$
$811$	−50.8935	−1.78711	−0.893556	+	0.448951i	$0.851798\pi$
$812$	0	0
$813$	−4.86200	−0.170518
$814$	0	0
$815$	1.65429	0.0579473
$816$	1.97842	0.0692584
$817$	13.7244	0.480158
$818$	1.91684	0.0670208
$819$	0	0
$820$	−0.415516	−0.0145105
$821$	40.3094	1.40681	0.703404	−	0.710790i	$-0.251662\pi$
$821$	40.3094	1.40681	0.703404	+	0.710790i	$0.251662\pi$
$822$	−1.20091	−0.0418867
$823$	25.6817	0.895209	0.447605	−	0.894232i	$-0.352277\pi$
$823$	25.6817	0.895209	0.447605	+	0.894232i	$0.352277\pi$
$824$	42.8685	1.49340
$825$	0	0
$826$	0	0
$827$	31.9557	1.11121	0.555604	−	0.831447i	$-0.312487\pi$
$827$	31.9557	1.11121	0.555604	+	0.831447i	$0.312487\pi$
$828$	−14.2412	−0.494917
$829$	−48.4002	−1.68101	−0.840504	−	0.541805i	$-0.817741\pi$
$829$	−48.4002	−1.68101	−0.840504	+	0.541805i	$0.817741\pi$
$830$	1.95212	0.0677591
$831$	7.44586	0.258294
$832$	20.0748	0.695969
$833$	0	0
$834$	2.28848	0.0792437
$835$	−0.492010	−0.0170267
$836$	0	0
$837$	23.9216	0.826850
$838$	11.1490	0.385137
$839$	37.7165	1.30212	0.651059	−	0.759027i	$-0.274325\pi$
$839$	37.7165	1.30212	0.651059	+	0.759027i	$0.274325\pi$
$840$	0	0
$841$	−14.7570	−0.508863
$842$	−13.4627	−0.463956
$843$	13.0745	0.450308
$844$	12.4668	0.429124
$845$	6.59424	0.226849
$846$	12.3056	0.423074
$847$	0	0
$848$	−1.26869	−0.0435671
$849$	15.4529	0.530343
$850$	16.6836	0.572243
$851$	22.0372	0.755424
$852$	−8.02897	−0.275068
$853$	9.28864	0.318037	0.159019	−	0.987276i	$-0.449167\pi$
$853$	9.28864	0.318037	0.159019	+	0.987276i	$0.449167\pi$
$854$	0	0
$855$	−1.69815	−0.0580754
$856$	−14.2383	−0.486654
$857$	−29.7644	−1.01673	−0.508365	−	0.861141i	$-0.669750\pi$
$857$	−29.7644	−1.01673	−0.508365	+	0.861141i	$0.669750\pi$
$858$	0	0
$859$	−33.2611	−1.13485	−0.567427	−	0.823424i	$-0.692061\pi$
$859$	−33.2611	−1.13485	−0.567427	+	0.823424i	$0.692061\pi$
$860$	−1.46201	−0.0498543
$861$	0	0
$862$	−21.6858	−0.738622
$863$	−18.5677	−0.632051	−0.316025	−	0.948751i	$-0.602348\pi$
$863$	−18.5677	−0.632051	−0.316025	+	0.948751i	$0.602348\pi$
$864$	20.3262	0.691513
$865$	−2.30575	−0.0783979
$866$	22.9723	0.780632
$867$	−1.10559	−0.0375477
$868$	0	0
$869$	0	0
$870$	−0.403520	−0.0136806
$871$	8.30263	0.281324
$872$	14.2532	0.482674
$873$	−23.7034	−0.802240
$874$	−8.83422	−0.298822
$875$	0	0
$876$	4.82049	0.162869
$877$	22.4921	0.759505	0.379752	−	0.925088i	$-0.376009\pi$
$877$	22.4921	0.759505	0.379752	+	0.925088i	$0.376009\pi$
$878$	−26.1744	−0.883344
$879$	0.281259	0.00948664
$880$	0	0
$881$	−7.06565	−0.238048	−0.119024	−	0.992891i	$-0.537977\pi$
$881$	−7.06565	−0.238048	−0.119024	+	0.992891i	$0.537977\pi$
$882$	0	0
$883$	−19.9382	−0.670974	−0.335487	−	0.942045i	$-0.608901\pi$
$883$	−19.9382	−0.670974	−0.335487	+	0.942045i	$0.608901\pi$
$884$	39.4974	1.32844
$885$	−1.31101	−0.0440690
$886$	8.02886	0.269735
$887$	6.95481	0.233520	0.116760	−	0.993160i	$-0.462749\pi$
$887$	6.95481	0.233520	0.116760	+	0.993160i	$0.462749\pi$
$888$	−9.22420	−0.309544
$889$	0	0
$890$	−1.37045	−0.0459376
$891$	0	0
$892$	0.998136	0.0334201
$893$	−17.6228	−0.589724
$894$	−3.47403	−0.116189
$895$	−5.20896	−0.174116
$896$	0	0
$897$	15.7301	0.525214
$898$	−2.14419	−0.0715525
$899$	26.0012	0.867189
$900$	−18.0867	−0.602889
$901$	7.44650	0.248079
$902$	0	0
$903$	0	0
$904$	43.5494	1.44843
$905$	3.05205	0.101454
$906$	3.91121	0.129941
$907$	−23.4401	−0.778317	−0.389159	−	0.921171i	$-0.627234\pi$
$907$	−23.4401	−0.778317	−0.389159	+	0.921171i	$0.627234\pi$
$908$	7.42642	0.246454
$909$	50.2929	1.66811
$910$	0	0
$911$	46.8096	1.55087	0.775436	−	0.631426i	$-0.217530\pi$
$911$	46.8096	1.55087	0.775436	+	0.631426i	$0.217530\pi$
$912$	−1.33048	−0.0440564
$913$	0	0
$914$	31.3563	1.03718
$915$	1.32426	0.0437787
$916$	−9.22203	−0.304705
$917$	0	0
$918$	−11.7014	−0.386205
$919$	−10.6273	−0.350563	−0.175281	−	0.984518i	$-0.556084\pi$
$919$	−10.6273	−0.350563	−0.175281	+	0.984518i	$0.556084\pi$
$920$	2.28979	0.0754921
$921$	4.96638	0.163648
$922$	−26.6095	−0.876336
$923$	−60.7848	−2.00075
$924$	0	0
$925$	27.9876	0.920228
$926$	0.549953	0.0180726
$927$	42.5124	1.39629
$928$	22.0933	0.725248
$929$	36.6710	1.20313	0.601567	−	0.798822i	$-0.294543\pi$
$929$	36.6710	1.20313	0.601567	+	0.798822i	$0.294543\pi$
$930$	−0.736644	−0.0241555
$931$	0	0
$932$	−13.3371	−0.436873
$933$	0.0846489	0.00277128
$934$	22.2302	0.727393
$935$	0	0
$936$	45.1290	1.47509
$937$	−40.2174	−1.31384	−0.656922	−	0.753959i	$-0.728142\pi$
$937$	−40.2174	−1.31384	−0.656922	+	0.753959i	$0.728142\pi$
$938$	0	0
$939$	−9.44970	−0.308379
$940$	1.87729	0.0612304
$941$	24.9097	0.812032	0.406016	−	0.913866i	$-0.366918\pi$
$941$	24.9097	0.812032	0.406016	+	0.913866i	$0.366918\pi$
$942$	9.68299	0.315489
$943$	−5.21590	−0.169853
$944$	7.04022	0.229140
$945$	0	0
$946$	0	0
$947$	−32.2061	−1.04656	−0.523279	−	0.852161i	$-0.675292\pi$
$947$	−32.2061	−1.04656	−0.523279	+	0.852161i	$0.675292\pi$
$948$	3.90663	0.126881
$949$	36.4944	1.18466
$950$	−11.2196	−0.364013
$951$	20.3905	0.661207
$952$	0	0
$953$	−45.0611	−1.45967	−0.729837	−	0.683621i	$-0.760404\pi$
$953$	−45.0611	−1.45967	−0.729837	+	0.683621i	$0.760404\pi$
$954$	3.49678	0.113213
$955$	−2.67574	−0.0865849
$956$	37.4650	1.21170
$957$	0	0
$958$	−3.96296	−0.128038
$959$	0	0
$960$	−0.422806	−0.0136460
$961$	16.4663	0.531172
$962$	−28.7007	−0.925349
$963$	−14.1200	−0.455010
$964$	−26.3283	−0.847977
$965$	−3.53442	−0.113777
$966$	0	0
$967$	−1.81387	−0.0583300	−0.0291650	−	0.999575i	$-0.509285\pi$
$967$	−1.81387	−0.0583300	−0.0291650	+	0.999575i	$0.509285\pi$
$968$	0	0
$969$	7.80912	0.250865
$970$	1.56635	0.0502924
$971$	−23.0539	−0.739835	−0.369918	−	0.929065i	$-0.620614\pi$
$971$	−23.0539	−0.739835	−0.369918	+	0.929065i	$0.620614\pi$
$972$	19.4595	0.624163
$973$	0	0
$974$	22.6934	0.727144
$975$	19.9776	0.639795
$976$	−7.11140	−0.227630
$977$	−7.09449	−0.226973	−0.113486	−	0.993540i	$-0.536202\pi$
$977$	−7.09449	−0.226973	−0.113486	+	0.993540i	$0.536202\pi$
$978$	−3.57236	−0.114232
$979$	0	0
$980$	0	0
$981$	14.1348	0.451290
$982$	−23.4364	−0.747887
$983$	−38.3502	−1.22318	−0.611591	−	0.791174i	$-0.709470\pi$
$983$	−38.3502	−1.22318	−0.611591	+	0.791174i	$0.709470\pi$
$984$	2.18324	0.0695992
$985$	−2.73773	−0.0872313
$986$	−12.7187	−0.405046
$987$	0	0
$988$	−26.5618	−0.845044
$989$	−18.3524	−0.583572
$990$	0	0
$991$	20.2722	0.643967	0.321984	−	0.946745i	$-0.395650\pi$
$991$	20.2722	0.643967	0.321984	+	0.946745i	$0.395650\pi$
$992$	40.3323	1.28055
$993$	−18.2527	−0.579231
$994$	0	0
$995$	−3.39592	−0.107658
$996$	9.73200	0.308370
$997$	15.4107	0.488062	0.244031	−	0.969767i	$-0.421530\pi$
$997$	15.4107	0.488062	0.244031	+	0.969767i	$0.421530\pi$
$998$	4.62684	0.146460
$999$	−19.6298	−0.621058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5929.2.a.bb.1.3		4
7.6	odd	2		847.2.a.k.1.3		4
11.7	odd	10		539.2.f.d.148.1		8
11.8	odd	10		539.2.f.d.295.1		8
11.10	odd	2		5929.2.a.bi.1.2		4
21.20	even	2		7623.2.a.co.1.2		4
77.6	even	10		847.2.f.p.729.2		8
77.13	even	10		847.2.f.p.323.2		8
77.18	odd	30		539.2.q.b.324.2		16
77.19	even	30		539.2.q.c.361.2		16
77.20	odd	10		847.2.f.s.323.1		8
77.27	odd	10		847.2.f.s.729.1		8
77.30	odd	30		539.2.q.b.361.2		16
77.40	even	30		539.2.q.c.214.1		16
77.41	even	10		77.2.f.a.64.1	✓	8
77.48	odd	10		847.2.f.q.148.2		8
77.51	odd	30		539.2.q.b.214.1		16
77.52	even	30		539.2.q.c.471.1		16
77.62	even	10		77.2.f.a.71.1	yes	8
77.69	odd	10		847.2.f.q.372.2		8
77.73	even	30		539.2.q.c.324.2		16
77.74	odd	30		539.2.q.b.471.1		16
77.76	even	2		847.2.a.l.1.2		4
231.41	odd	10		693.2.m.g.64.2		8
231.62	odd	10		693.2.m.g.379.2		8
231.230	odd	2		7623.2.a.ch.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
77.2.f.a.64.1	✓	8	77.41	even	10
77.2.f.a.71.1	yes	8	77.62	even	10
539.2.f.d.148.1		8	11.7	odd	10
539.2.f.d.295.1		8	11.8	odd	10
539.2.q.b.214.1		16	77.51	odd	30
539.2.q.b.324.2		16	77.18	odd	30
539.2.q.b.361.2		16	77.30	odd	30
539.2.q.b.471.1		16	77.74	odd	30
539.2.q.c.214.1		16	77.40	even	30
539.2.q.c.324.2		16	77.73	even	30
539.2.q.c.361.2		16	77.19	even	30
539.2.q.c.471.1		16	77.52	even	30
693.2.m.g.64.2		8	231.41	odd	10
693.2.m.g.379.2		8	231.62	odd	10
847.2.a.k.1.3		4	7.6	odd	2
847.2.a.l.1.2		4	77.76	even	2
847.2.f.p.323.2		8	77.13	even	10
847.2.f.p.729.2		8	77.6	even	10
847.2.f.q.148.2		8	77.48	odd	10
847.2.f.q.372.2		8	77.69	odd	10
847.2.f.s.323.1		8	77.20	odd	10
847.2.f.s.729.1		8	77.27	odd	10
5929.2.a.bb.1.3		4	1.1	even	1	trivial
5929.2.a.bi.1.2		4	11.10	odd	2
7623.2.a.ch.1.3		4	231.230	odd	2
7623.2.a.co.1.2		4	21.20	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:	\( N \)	\(=\)	\( 5929 = 7^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5929.a (trivial)

\(f(q)\)	\(=\)	\(q+0.777484 q^{2} -0.618034 q^{3} -1.39552 q^{4} +0.222516 q^{5} -0.480512 q^{6} -2.63996 q^{8} -2.61803 q^{9} +O(q^{10})\)	\(q+0.777484 q^{2} -0.618034 q^{3} -1.39552 q^{4} +0.222516 q^{5} -0.480512 q^{6} -2.63996 q^{8} -2.61803 q^{9} +0.173002 q^{10} +0.862478 q^{12} +6.52954 q^{13} -0.137522 q^{15} +0.738508 q^{16} -4.33461 q^{17} -2.03548 q^{18} +2.91501 q^{19} -0.310525 q^{20} -3.89796 q^{23} +1.63159 q^{24} -4.95049 q^{25} +5.07662 q^{26} +3.47214 q^{27} +3.77399 q^{29} -0.106921 q^{30} +6.88958 q^{31} +5.85410 q^{32} -3.37009 q^{34} +3.65351 q^{36} -5.65351 q^{37} +2.26637 q^{38} -4.03548 q^{39} -0.587433 q^{40} +1.33811 q^{41} +4.70820 q^{43} -0.582554 q^{45} -3.03060 q^{46} -6.04554 q^{47} -0.456423 q^{48} -3.84893 q^{50} +2.67894 q^{51} -9.11210 q^{52} -1.71792 q^{53} +2.69953 q^{54} -1.80157 q^{57} +2.93422 q^{58} +9.53304 q^{59} +0.191915 q^{60} -9.62943 q^{61} +5.35654 q^{62} +3.07446 q^{64} +1.45293 q^{65} +1.27155 q^{67} +6.04903 q^{68} +2.40907 q^{69} -9.30919 q^{71} +6.91151 q^{72} +5.58911 q^{73} -4.39552 q^{74} +3.05957 q^{75} -4.06794 q^{76} -3.13752 q^{78} +4.52954 q^{79} +0.164330 q^{80} +5.70820 q^{81} +1.04036 q^{82} +11.2838 q^{83} -0.964520 q^{85} +3.66055 q^{86} -2.33245 q^{87} -7.92157 q^{89} -0.452926 q^{90} +5.43967 q^{92} -4.25800 q^{93} -4.70031 q^{94} +0.648635 q^{95} -3.61803 q^{96} +9.05391 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} - q^{6} - 9 q^{8} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 - q^6 - 9 * q^8 - 6 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} + 4 q^{4} + 6 q^{5} - q^{6} - 9 q^{8} - 6 q^{9} - 14 q^{10} + 7 q^{12} + 3 q^{15} - 4 q^{16} - 3 q^{17} + 3 q^{18} + 3 q^{19} + 17 q^{20} - 8 q^{23} - 12 q^{24} + 12 q^{26} - 4 q^{27} - 3 q^{29} - 12 q^{30} + 3 q^{31} + 10 q^{32} + 12 q^{34} - q^{36} - 7 q^{37} + 20 q^{38} - 5 q^{39} - 13 q^{40} + 4 q^{41} - 8 q^{43} - 9 q^{45} + 3 q^{46} + 14 q^{47} + 3 q^{48} - 33 q^{50} + 11 q^{51} - 17 q^{52} - 9 q^{53} + 2 q^{54} - 6 q^{57} + 3 q^{58} + 25 q^{59} + 21 q^{60} - 19 q^{61} + 10 q^{62} + 3 q^{64} - 12 q^{65} - 15 q^{67} - q^{68} - 14 q^{69} - 7 q^{71} + 6 q^{72} - 11 q^{73} - 8 q^{74} + 5 q^{75} - 26 q^{76} - 9 q^{78} - 8 q^{79} + 4 q^{80} - 4 q^{81} - 3 q^{82} - q^{83} - 15 q^{85} + 4 q^{86} + 6 q^{87} + 17 q^{89} + 16 q^{90} - 17 q^{92} - 11 q^{93} - 20 q^{94} - 17 q^{95} - 10 q^{96} + 15 q^{97}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 + 4 * q^4 + 6 * q^5 - q^6 - 9 * q^8 - 6 * q^9 - 14 * q^10 + 7 * q^12 + 3 * q^15 - 4 * q^16 - 3 * q^17 + 3 * q^18 + 3 * q^19 + 17 * q^20 - 8 * q^23 - 12 * q^24 + 12 * q^26 - 4 * q^27 - 3 * q^29 - 12 * q^30 + 3 * q^31 + 10 * q^32 + 12 * q^34 - q^36 - 7 * q^37 + 20 * q^38 - 5 * q^39 - 13 * q^40 + 4 * q^41 - 8 * q^43 - 9 * q^45 + 3 * q^46 + 14 * q^47 + 3 * q^48 - 33 * q^50 + 11 * q^51 - 17 * q^52 - 9 * q^53 + 2 * q^54 - 6 * q^57 + 3 * q^58 + 25 * q^59 + 21 * q^60 - 19 * q^61 + 10 * q^62 + 3 * q^64 - 12 * q^65 - 15 * q^67 - q^68 - 14 * q^69 - 7 * q^71 + 6 * q^72 - 11 * q^73 - 8 * q^74 + 5 * q^75 - 26 * q^76 - 9 * q^78 - 8 * q^79 + 4 * q^80 - 4 * q^81 - 3 * q^82 - q^83 - 15 * q^85 + 4 * q^86 + 6 * q^87 + 17 * q^89 + 16 * q^90 - 17 * q^92 - 11 * q^93 - 20 * q^94 - 17 * q^95 - 10 * q^96 + 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more