LMFDB - Embedded newform 722.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(1,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("722.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.53209$ of defining polynomial
Character	$\chi$	$=$	722.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.53209 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.53209 q^{6} +2.69459 q^{7} -1.00000 q^{8} -0.652704 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.53209 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.53209 q^{6} +2.69459 q^{7} -1.00000 q^{8} -0.652704 q^{9} -2.00000 q^{10} +3.18479 q^{11} -1.53209 q^{12} +5.75877 q^{13} -2.69459 q^{14} -3.06418 q^{15} +1.00000 q^{16} -6.51754 q^{17} +0.652704 q^{18} +2.00000 q^{20} -4.12836 q^{21} -3.18479 q^{22} -0.694593 q^{23} +1.53209 q^{24} -1.00000 q^{25} -5.75877 q^{26} +5.59627 q^{27} +2.69459 q^{28} +2.82295 q^{29} +3.06418 q^{30} -2.45336 q^{31} -1.00000 q^{32} -4.87939 q^{33} +6.51754 q^{34} +5.38919 q^{35} -0.652704 q^{36} +4.36959 q^{37} -8.82295 q^{39} -2.00000 q^{40} +0.347296 q^{41} +4.12836 q^{42} +6.06418 q^{43} +3.18479 q^{44} -1.30541 q^{45} +0.694593 q^{46} +7.88713 q^{47} -1.53209 q^{48} +0.260830 q^{49} +1.00000 q^{50} +9.98545 q^{51} +5.75877 q^{52} -8.21213 q^{53} -5.59627 q^{54} +6.36959 q^{55} -2.69459 q^{56} -2.82295 q^{58} -0.573978 q^{59} -3.06418 q^{60} +2.93582 q^{61} +2.45336 q^{62} -1.75877 q^{63} +1.00000 q^{64} +11.5175 q^{65} +4.87939 q^{66} +4.95811 q^{67} -6.51754 q^{68} +1.06418 q^{69} -5.38919 q^{70} +8.45336 q^{71} +0.652704 q^{72} +15.7665 q^{73} -4.36959 q^{74} +1.53209 q^{75} +8.58172 q^{77} +8.82295 q^{78} +9.06418 q^{79} +2.00000 q^{80} -6.61587 q^{81} -0.347296 q^{82} +8.47565 q^{83} -4.12836 q^{84} -13.0351 q^{85} -6.06418 q^{86} -4.32501 q^{87} -3.18479 q^{88} -7.73917 q^{89} +1.30541 q^{90} +15.5175 q^{91} -0.694593 q^{92} +3.75877 q^{93} -7.88713 q^{94} +1.53209 q^{96} +0.347296 q^{97} -0.260830 q^{98} -2.07873 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 - 3 * q^9	$ 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{10} + 6 q^{11} + 6 q^{13} - 6 q^{14} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{20} + 6 q^{21} - 6 q^{22} - 3 q^{25} - 6 q^{26} + 3 q^{27} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 3 q^{32} - 9 q^{33} - 3 q^{34} + 12 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{39} - 6 q^{40} - 6 q^{42} + 9 q^{43} + 6 q^{44} - 6 q^{45} - 6 q^{47} + 15 q^{49} + 3 q^{50} + 12 q^{51} + 6 q^{52} - 3 q^{54} + 12 q^{55} - 6 q^{56} + 12 q^{58} + 6 q^{59} + 18 q^{61} - 6 q^{62} + 6 q^{63} + 3 q^{64} + 12 q^{65} + 9 q^{66} + 18 q^{67} + 3 q^{68} - 6 q^{69} - 12 q^{70} + 12 q^{71} + 3 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{77} + 6 q^{78} + 18 q^{79} + 6 q^{80} - 9 q^{81} + 6 q^{83} + 6 q^{84} + 6 q^{85} - 9 q^{86} - 18 q^{87} - 6 q^{88} - 9 q^{89} + 6 q^{90} + 24 q^{91} + 6 q^{94} - 15 q^{98} - 15 q^{99}+O(q^{100}) $ 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 - 3 * q^9 - 6 * q^10 + 6 * q^11 + 6 * q^13 - 6 * q^14 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^20 + 6 * q^21 - 6 * q^22 - 3 * q^25 - 6 * q^26 + 3 * q^27 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 3 * q^32 - 9 * q^33 - 3 * q^34 + 12 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^39 - 6 * q^40 - 6 * q^42 + 9 * q^43 + 6 * q^44 - 6 * q^45 - 6 * q^47 + 15 * q^49 + 3 * q^50 + 12 * q^51 + 6 * q^52 - 3 * q^54 + 12 * q^55 - 6 * q^56 + 12 * q^58 + 6 * q^59 + 18 * q^61 - 6 * q^62 + 6 * q^63 + 3 * q^64 + 12 * q^65 + 9 * q^66 + 18 * q^67 + 3 * q^68 - 6 * q^69 - 12 * q^70 + 12 * q^71 + 3 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^77 + 6 * q^78 + 18 * q^79 + 6 * q^80 - 9 * q^81 + 6 * q^83 + 6 * q^84 + 6 * q^85 - 9 * q^86 - 18 * q^87 - 6 * q^88 - 9 * q^89 + 6 * q^90 + 24 * q^91 + 6 * q^94 - 15 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.53209	−0.884552	−0.442276	−	0.896879i	$-0.645829\pi$
$3$	−1.53209	−0.884552	−0.442276	+	0.896879i	$0.645829\pi$
$4$	1.00000	0.500000
$5$	2.00000	0.894427	0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000	0.894427	0.447214	+	0.894427i	$0.352416\pi$
$6$	1.53209	0.625473
$7$	2.69459	1.01846	0.509230	−	0.860630i	$-0.329930\pi$
$7$	2.69459	1.01846	0.509230	+	0.860630i	$0.329930\pi$
$8$	−1.00000	−0.353553
$9$	−0.652704	−0.217568
$10$	−2.00000	−0.632456
$11$	3.18479	0.960251	0.480126	−	0.877200i	$-0.340591\pi$
$11$	3.18479	0.960251	0.480126	+	0.877200i	$0.340591\pi$
$12$	−1.53209	−0.442276
$13$	5.75877	1.59720	0.798598	−	0.601865i	$-0.205576\pi$
$13$	5.75877	1.59720	0.798598	+	0.601865i	$0.205576\pi$
$14$	−2.69459	−0.720160
$15$	−3.06418	−0.791167
$16$	1.00000	0.250000
$17$	−6.51754	−1.58074	−0.790368	−	0.612632i	$-0.790111\pi$
$17$	−6.51754	−1.58074	−0.790368	+	0.612632i	$0.790111\pi$
$18$	0.652704	0.153844
$19$	0	0
$19$	0	0
$20$	2.00000	0.447214
$21$	−4.12836	−0.900881
$22$	−3.18479	−0.679000
$23$	−0.694593	−0.144833	−0.0724163	−	0.997374i	$-0.523071\pi$
$23$	−0.694593	−0.144833	−0.0724163	+	0.997374i	$0.523071\pi$
$24$	1.53209	0.312736
$25$	−1.00000	−0.200000
$26$	−5.75877	−1.12939
$27$	5.59627	1.07700
$28$	2.69459	0.509230
$29$	2.82295	0.524208	0.262104	−	0.965040i	$-0.415584\pi$
$29$	2.82295	0.524208	0.262104	+	0.965040i	$0.415584\pi$
$30$	3.06418	0.559440
$31$	−2.45336	−0.440637	−0.220319	−	0.975428i	$-0.570710\pi$
$31$	−2.45336	−0.440637	−0.220319	+	0.975428i	$0.570710\pi$
$32$	−1.00000	−0.176777
$33$	−4.87939	−0.849392
$34$	6.51754	1.11775
$35$	5.38919	0.910939
$36$	−0.652704	−0.108784
$37$	4.36959	0.718355	0.359178	−	0.933269i	$-0.383057\pi$
$37$	4.36959	0.718355	0.359178	+	0.933269i	$0.383057\pi$
$38$	0	0
$39$	−8.82295	−1.41280
$40$	−2.00000	−0.316228
$41$	0.347296	0.0542386	0.0271193	−	0.999632i	$-0.491367\pi$
$41$	0.347296	0.0542386	0.0271193	+	0.999632i	$0.491367\pi$
$42$	4.12836	0.637019
$43$	6.06418	0.924778	0.462389	−	0.886677i	$-0.346992\pi$
$43$	6.06418	0.924778	0.462389	+	0.886677i	$0.346992\pi$
$44$	3.18479	0.480126
$45$	−1.30541	−0.194599
$46$	0.694593	0.102412
$47$	7.88713	1.15046	0.575228	−	0.817993i	$-0.304913\pi$
$47$	7.88713	1.15046	0.575228	+	0.817993i	$0.304913\pi$
$48$	−1.53209	−0.221138
$49$	0.260830	0.0372614
$50$	1.00000	0.141421
$51$	9.98545	1.39824
$52$	5.75877	0.798598
$53$	−8.21213	−1.12802	−0.564012	−	0.825767i	$-0.690743\pi$
$53$	−8.21213	−1.12802	−0.564012	+	0.825767i	$0.690743\pi$
$54$	−5.59627	−0.761555
$55$	6.36959	0.858875
$56$	−2.69459	−0.360080
$57$	0	0
$58$	−2.82295	−0.370671
$59$	−0.573978	−0.0747256	−0.0373628	−	0.999302i	$-0.511896\pi$
$59$	−0.573978	−0.0747256	−0.0373628	+	0.999302i	$0.511896\pi$
$60$	−3.06418	−0.395584
$61$	2.93582	0.375894	0.187947	−	0.982179i	$-0.439817\pi$
$61$	2.93582	0.375894	0.187947	+	0.982179i	$0.439817\pi$
$62$	2.45336	0.311577
$63$	−1.75877	−0.221584
$64$	1.00000	0.125000
$65$	11.5175	1.42858
$66$	4.87939	0.600611
$67$	4.95811	0.605730	0.302865	−	0.953034i	$-0.402057\pi$
$67$	4.95811	0.605730	0.302865	+	0.953034i	$0.402057\pi$
$68$	−6.51754	−0.790368
$69$	1.06418	0.128112
$70$	−5.38919	−0.644131
$71$	8.45336	1.00323	0.501615	−	0.865091i	$-0.332739\pi$
$71$	8.45336	1.00323	0.501615	+	0.865091i	$0.332739\pi$
$72$	0.652704	0.0769219
$73$	15.7665	1.84533	0.922665	−	0.385602i	$-0.126006\pi$
$73$	15.7665	1.84533	0.922665	+	0.385602i	$0.126006\pi$
$74$	−4.36959	−0.507954
$75$	1.53209	0.176910
$76$	0	0
$77$	8.58172	0.977978
$78$	8.82295	0.999002
$79$	9.06418	1.01980	0.509900	−	0.860234i	$-0.329682\pi$
$79$	9.06418	1.01980	0.509900	+	0.860234i	$0.329682\pi$
$80$	2.00000	0.223607
$81$	−6.61587	−0.735096
$82$	−0.347296	−0.0383525
$83$	8.47565	0.930324	0.465162	−	0.885226i	$-0.345996\pi$
$83$	8.47565	0.930324	0.465162	+	0.885226i	$0.345996\pi$
$84$	−4.12836	−0.450441
$85$	−13.0351	−1.41385
$86$	−6.06418	−0.653917
$87$	−4.32501	−0.463689
$88$	−3.18479	−0.339500
$89$	−7.73917	−0.820350	−0.410175	−	0.912007i	$-0.634532\pi$
$89$	−7.73917	−0.820350	−0.410175	+	0.912007i	$0.634532\pi$
$90$	1.30541	0.137602
$91$	15.5175	1.62668
$92$	−0.694593	−0.0724163
$93$	3.75877	0.389766
$94$	−7.88713	−0.813495
$95$	0	0
$96$	1.53209	0.156368
$97$	0.347296	0.0352626	0.0176313	−	0.999845i	$-0.494387\pi$
$97$	0.347296	0.0352626	0.0176313	+	0.999845i	$0.494387\pi$
$98$	−0.260830	−0.0263478
$99$	−2.07873	−0.208920
$100$	−1.00000	−0.100000
$101$	−0.369585	−0.0367751	−0.0183875	−	0.999831i	$-0.505853\pi$
$101$	−0.369585	−0.0367751	−0.0183875	+	0.999831i	$0.505853\pi$
$102$	−9.98545	−0.988707
$103$	−8.58172	−0.845582	−0.422791	−	0.906227i	$-0.638950\pi$
$103$	−8.58172	−0.845582	−0.422791	+	0.906227i	$0.638950\pi$
$104$	−5.75877	−0.564694
$105$	−8.25671	−0.805772
$106$	8.21213	0.797633
$107$	11.4534	1.10724	0.553619	−	0.832770i	$-0.313246\pi$
$107$	11.4534	1.10724	0.553619	+	0.832770i	$0.313246\pi$
$108$	5.59627	0.538501
$109$	−8.69459	−0.832791	−0.416395	−	0.909184i	$-0.636707\pi$
$109$	−8.69459	−0.832791	−0.416395	+	0.909184i	$0.636707\pi$
$110$	−6.36959	−0.607316
$111$	−6.69459	−0.635423
$112$	2.69459	0.254615
$113$	−2.85978	−0.269026	−0.134513	−	0.990912i	$-0.542947\pi$
$113$	−2.85978	−0.269026	−0.134513	+	0.990912i	$0.542947\pi$
$114$	0	0
$115$	−1.38919	−0.129542
$116$	2.82295	0.262104
$117$	−3.75877	−0.347498
$118$	0.573978	0.0528390
$119$	−17.5621	−1.60992
$120$	3.06418	0.279720
$121$	−0.857097	−0.0779179
$122$	−2.93582	−0.265797
$123$	−0.532089	−0.0479768
$124$	−2.45336	−0.220319
$125$	−12.0000	−1.07331
$126$	1.75877	0.156684
$127$	−9.72967	−0.863369	−0.431685	−	0.902025i	$-0.642081\pi$
$127$	−9.72967	−0.863369	−0.431685	+	0.902025i	$0.642081\pi$
$128$	−1.00000	−0.0883883
$129$	−9.29086	−0.818015
$130$	−11.5175	−1.01016
$131$	−6.46791	−0.565104	−0.282552	−	0.959252i	$-0.591181\pi$
$131$	−6.46791	−0.565104	−0.282552	+	0.959252i	$0.591181\pi$
$132$	−4.87939	−0.424696
$133$	0	0
$134$	−4.95811	−0.428316
$135$	11.1925	0.963300
$136$	6.51754	0.558875
$137$	−11.6604	−0.996219	−0.498109	−	0.867114i	$-0.665972\pi$
$137$	−11.6604	−0.996219	−0.498109	+	0.867114i	$0.665972\pi$
$138$	−1.06418	−0.0905888
$139$	−8.26352	−0.700902	−0.350451	−	0.936581i	$-0.613972\pi$
$139$	−8.26352	−0.700902	−0.350451	+	0.936581i	$0.613972\pi$
$140$	5.38919	0.455469
$141$	−12.0838	−1.01764
$142$	−8.45336	−0.709390
$143$	18.3405	1.53371
$144$	−0.652704	−0.0543920
$145$	5.64590	0.468866
$146$	−15.7665	−1.30485
$147$	−0.399615	−0.0329597
$148$	4.36959	0.359178
$149$	−16.4534	−1.34791	−0.673956	−	0.738771i	$-0.735406\pi$
$149$	−16.4534	−1.34791	−0.673956	+	0.738771i	$0.735406\pi$
$150$	−1.53209	−0.125095
$151$	−4.65539	−0.378850	−0.189425	−	0.981895i	$-0.560662\pi$
$151$	−4.65539	−0.378850	−0.189425	+	0.981895i	$0.560662\pi$
$152$	0	0
$153$	4.25402	0.343917
$154$	−8.58172	−0.691535
$155$	−4.90673	−0.394118
$156$	−8.82295	−0.706401
$157$	8.45336	0.674652	0.337326	−	0.941388i	$-0.390478\pi$
$157$	8.45336	0.674652	0.337326	+	0.941388i	$0.390478\pi$
$158$	−9.06418	−0.721107
$159$	12.5817	0.997795
$160$	−2.00000	−0.158114
$161$	−1.87164	−0.147506
$162$	6.61587	0.519792
$163$	17.0496	1.33543	0.667715	−	0.744417i	$-0.267272\pi$
$163$	17.0496	1.33543	0.667715	+	0.744417i	$0.267272\pi$
$164$	0.347296	0.0271193
$165$	−9.75877	−0.759719
$166$	−8.47565	−0.657838
$167$	3.19253	0.247046	0.123523	−	0.992342i	$-0.460581\pi$
$167$	3.19253	0.247046	0.123523	+	0.992342i	$0.460581\pi$
$168$	4.12836	0.318510
$169$	20.1634	1.55103
$170$	13.0351	0.999745
$171$	0	0
$172$	6.06418	0.462389
$173$	−9.63041	−0.732187	−0.366093	−	0.930578i	$-0.619305\pi$
$173$	−9.63041	−0.732187	−0.366093	+	0.930578i	$0.619305\pi$
$174$	4.32501	0.327878
$175$	−2.69459	−0.203692
$176$	3.18479	0.240063
$177$	0.879385	0.0660986
$178$	7.73917	0.580075
$179$	−18.8161	−1.40638	−0.703192	−	0.711000i	$-0.748243\pi$
$179$	−18.8161	−1.40638	−0.703192	+	0.711000i	$0.748243\pi$
$180$	−1.30541	−0.0972993
$181$	−2.77837	−0.206515	−0.103257	−	0.994655i	$-0.532927\pi$
$181$	−2.77837	−0.206515	−0.103257	+	0.994655i	$0.532927\pi$
$182$	−15.5175	−1.15024
$183$	−4.49794	−0.332497
$184$	0.694593	0.0512061
$185$	8.73917	0.642517
$186$	−3.75877	−0.275606
$187$	−20.7570	−1.51790
$188$	7.88713	0.575228
$189$	15.0797	1.09688
$190$	0	0
$191$	9.56212	0.691891	0.345945	−	0.938255i	$-0.387558\pi$
$191$	9.56212	0.691891	0.345945	+	0.938255i	$0.387558\pi$
$192$	−1.53209	−0.110569
$193$	23.6810	1.70459	0.852297	−	0.523058i	$-0.175209\pi$
$193$	23.6810	1.70459	0.852297	+	0.523058i	$0.175209\pi$
$194$	−0.347296	−0.0249344
$195$	−17.6459	−1.26365
$196$	0.260830	0.0186307
$197$	−22.9222	−1.63314	−0.816570	−	0.577247i	$-0.804127\pi$
$197$	−22.9222	−1.63314	−0.816570	+	0.577247i	$0.804127\pi$
$198$	2.07873	0.147729
$199$	10.0838	0.714820	0.357410	−	0.933948i	$-0.383660\pi$
$199$	10.0838	0.714820	0.357410	+	0.933948i	$0.383660\pi$
$200$	1.00000	0.0707107
$201$	−7.59627	−0.535799
$202$	0.369585	0.0260039
$203$	7.60670	0.533885
$204$	9.98545	0.699121
$205$	0.694593	0.0485125
$206$	8.58172	0.597917
$207$	0.453363	0.0315109
$208$	5.75877	0.399299
$209$	0	0
$210$	8.25671	0.569767
$211$	22.3601	1.53933	0.769666	−	0.638447i	$-0.220423\pi$
$211$	22.3601	1.53933	0.769666	+	0.638447i	$0.220423\pi$
$212$	−8.21213	−0.564012
$213$	−12.9513	−0.887409
$214$	−11.4534	−0.782936
$215$	12.1284	0.827147
$216$	−5.59627	−0.380778
$217$	−6.61081	−0.448771
$218$	8.69459	0.588872
$219$	−24.1557	−1.63229
$220$	6.36959	0.429437
$221$	−37.5330	−2.52474
$222$	6.69459	0.449312
$223$	9.27631	0.621188	0.310594	−	0.950543i	$-0.399472\pi$
$223$	9.27631	0.621188	0.310594	+	0.950543i	$0.399472\pi$
$224$	−2.69459	−0.180040
$225$	0.652704	0.0435136
$226$	2.85978	0.190230
$227$	−7.73648	−0.513488	−0.256744	−	0.966479i	$-0.582650\pi$
$227$	−7.73648	−0.513488	−0.256744	+	0.966479i	$0.582650\pi$
$228$	0	0
$229$	−23.0351	−1.52220	−0.761101	−	0.648634i	$-0.775341\pi$
$229$	−23.0351	−1.52220	−0.761101	+	0.648634i	$0.775341\pi$
$230$	1.38919	0.0916002
$231$	−13.1480	−0.865072
$232$	−2.82295	−0.185336
$233$	8.39961	0.550277	0.275139	−	0.961405i	$-0.411276\pi$
$233$	8.39961	0.550277	0.275139	+	0.961405i	$0.411276\pi$
$234$	3.75877	0.245719
$235$	15.7743	1.02900
$236$	−0.573978	−0.0373628
$237$	−13.8871	−0.902066
$238$	17.5621	1.13838
$239$	−15.7297	−1.01747	−0.508734	−	0.860924i	$-0.669886\pi$
$239$	−15.7297	−1.01747	−0.508734	+	0.860924i	$0.669886\pi$
$240$	−3.06418	−0.197792
$241$	−17.5030	−1.12747	−0.563733	−	0.825957i	$-0.690635\pi$
$241$	−17.5030	−1.12747	−0.563733	+	0.825957i	$0.690635\pi$
$242$	0.857097	0.0550963
$243$	−6.65270	−0.426771
$244$	2.93582	0.187947
$245$	0.521660	0.0333276
$246$	0.532089	0.0339247
$247$	0	0
$248$	2.45336	0.155789
$249$	−12.9855	−0.822920
$250$	12.0000	0.758947
$251$	8.56717	0.540755	0.270378	−	0.962754i	$-0.412851\pi$
$251$	8.56717	0.540755	0.270378	+	0.962754i	$0.412851\pi$
$252$	−1.75877	−0.110792
$253$	−2.21213	−0.139076
$254$	9.72967	0.610494
$255$	19.9709	1.25063
$256$	1.00000	0.0625000
$257$	8.02465	0.500564	0.250282	−	0.968173i	$-0.419477\pi$
$257$	8.02465	0.500564	0.250282	+	0.968173i	$0.419477\pi$
$258$	9.29086	0.578424
$259$	11.7743	0.731616
$260$	11.5175	0.714288
$261$	−1.84255	−0.114051
$262$	6.46791	0.399589
$263$	−5.96080	−0.367559	−0.183779	−	0.982968i	$-0.558833\pi$
$263$	−5.96080	−0.367559	−0.183779	+	0.982968i	$0.558833\pi$
$264$	4.87939	0.300305
$265$	−16.4243	−1.00893
$266$	0	0
$267$	11.8571	0.725643
$268$	4.95811	0.302865
$269$	1.14796	0.0699921	0.0349961	−	0.999387i	$-0.488858\pi$
$269$	1.14796	0.0699921	0.0349961	+	0.999387i	$0.488858\pi$
$270$	−11.1925	−0.681156
$271$	20.0547	1.21824	0.609118	−	0.793080i	$-0.291524\pi$
$271$	20.0547	1.21824	0.609118	+	0.793080i	$0.291524\pi$
$272$	−6.51754	−0.395184
$273$	−23.7743	−1.43888
$274$	11.6604	0.704433
$275$	−3.18479	−0.192050
$276$	1.06418	0.0640560
$277$	17.3601	1.04307	0.521533	−	0.853231i	$-0.325360\pi$
$277$	17.3601	1.04307	0.521533	+	0.853231i	$0.325360\pi$
$278$	8.26352	0.495613
$279$	1.60132	0.0958685
$280$	−5.38919	−0.322065
$281$	−2.92127	−0.174269	−0.0871343	−	0.996197i	$-0.527771\pi$
$281$	−2.92127	−0.174269	−0.0871343	+	0.996197i	$0.527771\pi$
$282$	12.0838	0.719579
$283$	−9.48070	−0.563569	−0.281785	−	0.959478i	$-0.590926\pi$
$283$	−9.48070	−0.563569	−0.281785	+	0.959478i	$0.590926\pi$
$284$	8.45336	0.501615
$285$	0	0
$286$	−18.3405	−1.08450
$287$	0.935822	0.0552398
$288$	0.652704	0.0384609
$289$	25.4783	1.49873
$290$	−5.64590	−0.331538
$291$	−0.532089	−0.0311916
$292$	15.7665	0.922665
$293$	27.2918	1.59440	0.797202	−	0.603713i	$-0.206313\pi$
$293$	27.2918	1.59440	0.797202	+	0.603713i	$0.206313\pi$
$294$	0.399615	0.0233060
$295$	−1.14796	−0.0668366
$296$	−4.36959	−0.253977
$297$	17.8229	1.03419
$298$	16.4534	0.953118
$299$	−4.00000	−0.231326
$300$	1.53209	0.0884552
$301$	16.3405	0.941850
$302$	4.65539	0.267888
$303$	0.566237	0.0325295
$304$	0	0
$305$	5.87164	0.336209
$306$	−4.25402	−0.243186
$307$	−21.3286	−1.21729	−0.608645	−	0.793443i	$-0.708286\pi$
$307$	−21.3286	−1.21729	−0.608645	+	0.793443i	$0.708286\pi$
$308$	8.58172	0.488989
$309$	13.1480	0.747961
$310$	4.90673	0.278683
$311$	−29.2918	−1.66099	−0.830493	−	0.557030i	$-0.811941\pi$
$311$	−29.2918	−1.66099	−0.830493	+	0.557030i	$0.811941\pi$
$312$	8.82295	0.499501
$313$	5.56118	0.314337	0.157168	−	0.987572i	$-0.449763\pi$
$313$	5.56118	0.314337	0.157168	+	0.987572i	$0.449763\pi$
$314$	−8.45336	−0.477051
$315$	−3.51754	−0.198191
$316$	9.06418	0.509900
$317$	−3.80335	−0.213617	−0.106809	−	0.994280i	$-0.534063\pi$
$317$	−3.80335	−0.213617	−0.106809	+	0.994280i	$0.534063\pi$
$318$	−12.5817	−0.705548
$319$	8.99050	0.503372
$320$	2.00000	0.111803
$321$	−17.5476	−0.979410
$322$	1.87164	0.104303
$323$	0	0
$324$	−6.61587	−0.367548
$325$	−5.75877	−0.319439
$326$	−17.0496	−0.944292
$327$	13.3209	0.736647
$328$	−0.347296	−0.0191762
$329$	21.2526	1.17169
$330$	9.75877	0.537203
$331$	−20.4219	−1.12249	−0.561245	−	0.827650i	$-0.689677\pi$
$331$	−20.4219	−1.12249	−0.561245	+	0.827650i	$0.689677\pi$
$332$	8.47565	0.465162
$333$	−2.85204	−0.156291
$334$	−3.19253	−0.174688
$335$	9.91622	0.541781
$336$	−4.12836	−0.225220
$337$	−20.3105	−1.10638	−0.553191	−	0.833055i	$-0.686590\pi$
$337$	−20.3105	−1.10638	−0.553191	+	0.833055i	$0.686590\pi$
$338$	−20.1634	−1.09675
$339$	4.38144	0.237967
$340$	−13.0351	−0.706927
$341$	−7.81345	−0.423122
$342$	0	0
$343$	−18.1593	−0.980511
$344$	−6.06418	−0.326959
$345$	2.12836	0.114587
$346$	9.63041	0.517734
$347$	5.21482	0.279946	0.139973	−	0.990155i	$-0.455298\pi$
$347$	5.21482	0.279946	0.139973	+	0.990155i	$0.455298\pi$
$348$	−4.32501	−0.231845
$349$	14.3405	0.767629	0.383814	−	0.923410i	$-0.374610\pi$
$349$	14.3405	0.767629	0.383814	+	0.923410i	$0.374610\pi$
$350$	2.69459	0.144032
$351$	32.2276	1.72018
$352$	−3.18479	−0.169750
$353$	26.2499	1.39714	0.698571	−	0.715541i	$-0.253820\pi$
$353$	26.2499	1.39714	0.698571	+	0.715541i	$0.253820\pi$
$354$	−0.879385	−0.0467388
$355$	16.9067	0.897316
$356$	−7.73917	−0.410175
$357$	26.9067	1.42405
$358$	18.8161	0.994464
$359$	−33.6905	−1.77812	−0.889058	−	0.457795i	$-0.848639\pi$
$359$	−33.6905	−1.77812	−0.889058	+	0.457795i	$0.848639\pi$
$360$	1.30541	0.0688010
$361$	0	0
$362$	2.77837	0.146028
$363$	1.31315	0.0689224
$364$	15.5175	0.813340
$365$	31.5330	1.65051
$366$	4.49794	0.235111
$367$	−10.4688	−0.546469	−0.273235	−	0.961947i	$-0.588094\pi$
$367$	−10.4688	−0.546469	−0.273235	+	0.961947i	$0.588094\pi$
$368$	−0.694593	−0.0362081
$369$	−0.226682	−0.0118006
$370$	−8.73917	−0.454328
$371$	−22.1284	−1.14885
$372$	3.75877	0.194883
$373$	−23.9026	−1.23763	−0.618815	−	0.785537i	$-0.712387\pi$
$373$	−23.9026	−1.23763	−0.618815	+	0.785537i	$0.712387\pi$
$374$	20.7570	1.07332
$375$	18.3851	0.949401
$376$	−7.88713	−0.406747
$377$	16.2567	0.837263
$378$	−15.0797	−0.775614
$379$	−17.8135	−0.915016	−0.457508	−	0.889206i	$-0.651258\pi$
$379$	−17.8135	−0.915016	−0.457508	+	0.889206i	$0.651258\pi$
$380$	0	0
$381$	14.9067	0.763695
$382$	−9.56212	−0.489241
$383$	−25.0797	−1.28151	−0.640755	−	0.767745i	$-0.721379\pi$
$383$	−25.0797	−1.28151	−0.640755	+	0.767745i	$0.721379\pi$
$384$	1.53209	0.0781841
$385$	17.1634	0.874730
$386$	−23.6810	−1.20533
$387$	−3.95811	−0.201202
$388$	0.347296	0.0176313
$389$	−9.41828	−0.477526	−0.238763	−	0.971078i	$-0.576742\pi$
$389$	−9.41828	−0.477526	−0.238763	+	0.971078i	$0.576742\pi$
$390$	17.6459	0.893535
$391$	4.52704	0.228942
$392$	−0.260830	−0.0131739
$393$	9.90941	0.499864
$394$	22.9222	1.15480
$395$	18.1284	0.912137
$396$	−2.07873	−0.104460
$397$	6.85204	0.343894	0.171947	−	0.985106i	$-0.444994\pi$
$397$	6.85204	0.343894	0.171947	+	0.985106i	$0.444994\pi$
$398$	−10.0838	−0.505454
$399$	0	0
$400$	−1.00000	−0.0500000
$401$	−4.74691	−0.237049	−0.118525	−	0.992951i	$-0.537816\pi$
$401$	−4.74691	−0.237049	−0.118525	+	0.992951i	$0.537816\pi$
$402$	7.59627	0.378867
$403$	−14.1284	−0.703784
$404$	−0.369585	−0.0183875
$405$	−13.2317	−0.657490
$406$	−7.60670	−0.377514
$407$	13.9162	0.689802
$408$	−9.98545	−0.494354
$409$	−31.6928	−1.56711	−0.783555	−	0.621322i	$-0.786596\pi$
$409$	−31.6928	−1.56711	−0.783555	+	0.621322i	$0.786596\pi$
$410$	−0.694593	−0.0343035
$411$	17.8648	0.881207
$412$	−8.58172	−0.422791
$413$	−1.54664	−0.0761050
$414$	−0.453363	−0.0222816
$415$	16.9513	0.832107
$416$	−5.75877	−0.282347
$417$	12.6604	0.619985
$418$	0	0
$419$	−11.0101	−0.537879	−0.268939	−	0.963157i	$-0.586673\pi$
$419$	−11.0101	−0.537879	−0.268939	+	0.963157i	$0.586673\pi$
$420$	−8.25671	−0.402886
$421$	8.66550	0.422330	0.211165	−	0.977450i	$-0.432274\pi$
$421$	8.66550	0.422330	0.211165	+	0.977450i	$0.432274\pi$
$422$	−22.3601	−1.08847
$423$	−5.14796	−0.250302
$424$	8.21213	0.398816
$425$	6.51754	0.316147
$426$	12.9513	0.627493
$427$	7.91085	0.382833
$428$	11.4534	0.553619
$429$	−28.0993	−1.35665
$430$	−12.1284	−0.584881
$431$	29.8871	1.43961	0.719806	−	0.694175i	$-0.244231\pi$
$431$	29.8871	1.43961	0.719806	+	0.694175i	$0.244231\pi$
$432$	5.59627	0.269251
$433$	−9.26083	−0.445047	−0.222524	−	0.974927i	$-0.571429\pi$
$433$	−9.26083	−0.445047	−0.222524	+	0.974927i	$0.571429\pi$
$434$	6.61081	0.317329
$435$	−8.65002	−0.414736
$436$	−8.69459	−0.416395
$437$	0	0
$438$	24.1557	1.15420
$439$	−20.8621	−0.995696	−0.497848	−	0.867264i	$-0.665876\pi$
$439$	−20.8621	−0.995696	−0.497848	+	0.867264i	$0.665876\pi$
$440$	−6.36959	−0.303658
$441$	−0.170245	−0.00810689
$442$	37.5330	1.78526
$443$	23.8280	1.13210	0.566051	−	0.824370i	$-0.308470\pi$
$443$	23.8280	1.13210	0.566051	+	0.824370i	$0.308470\pi$
$444$	−6.69459	−0.317711
$445$	−15.4783	−0.733744
$446$	−9.27631	−0.439246
$447$	25.2080	1.19230
$448$	2.69459	0.127308
$449$	2.18210	0.102980	0.0514899	−	0.998674i	$-0.483603\pi$
$449$	2.18210	0.102980	0.0514899	+	0.998674i	$0.483603\pi$
$450$	−0.652704	−0.0307687
$451$	1.10607	0.0520827
$452$	−2.85978	−0.134513
$453$	7.13247	0.335113
$454$	7.73648	0.363091
$455$	31.0351	1.45495
$456$	0	0
$457$	1.78106	0.0833144	0.0416572	−	0.999132i	$-0.486736\pi$
$457$	1.78106	0.0833144	0.0416572	+	0.999132i	$0.486736\pi$
$458$	23.0351	1.07636
$459$	−36.4739	−1.70246
$460$	−1.38919	−0.0647711
$461$	−15.4884	−0.721369	−0.360684	−	0.932688i	$-0.617457\pi$
$461$	−15.4884	−0.721369	−0.360684	+	0.932688i	$0.617457\pi$
$462$	13.1480	0.611698
$463$	−2.71007	−0.125948	−0.0629739	−	0.998015i	$-0.520058\pi$
$463$	−2.71007	−0.125948	−0.0629739	+	0.998015i	$0.520058\pi$
$464$	2.82295	0.131052
$465$	7.51754	0.348618
$466$	−8.39961	−0.389105
$467$	12.9135	0.597567	0.298784	−	0.954321i	$-0.403419\pi$
$467$	12.9135	0.597567	0.298784	+	0.954321i	$0.403419\pi$
$468$	−3.75877	−0.173749
$469$	13.3601	0.616912
$470$	−15.7743	−0.727612
$471$	−12.9513	−0.596765
$472$	0.573978	0.0264195
$473$	19.3131	0.888019
$474$	13.8871	0.637857
$475$	0	0
$476$	−17.5621	−0.804958
$477$	5.36009	0.245422
$478$	15.7297	0.719459
$479$	−18.5526	−0.847691	−0.423845	−	0.905735i	$-0.639320\pi$
$479$	−18.5526	−0.847691	−0.423845	+	0.905735i	$0.639320\pi$
$480$	3.06418	0.139860
$481$	25.1634	1.14735
$482$	17.5030	0.797239
$483$	2.86753	0.130477
$484$	−0.857097	−0.0389589
$485$	0.694593	0.0315398
$486$	6.65270	0.301773
$487$	−41.1735	−1.86575	−0.932876	−	0.360199i	$-0.882709\pi$
$487$	−41.1735	−1.86575	−0.932876	+	0.360199i	$0.882709\pi$
$488$	−2.93582	−0.132898
$489$	−26.1215	−1.18126
$490$	−0.521660	−0.0235662
$491$	−22.5776	−1.01891	−0.509456	−	0.860496i	$-0.670153\pi$
$491$	−22.5776	−1.01891	−0.509456	+	0.860496i	$0.670153\pi$
$492$	−0.532089	−0.0239884
$493$	−18.3987	−0.828635
$494$	0	0
$495$	−4.15745	−0.186864
$496$	−2.45336	−0.110159
$497$	22.7784	1.02175
$498$	12.9855	0.581892
$499$	−29.3286	−1.31293	−0.656465	−	0.754357i	$-0.727949\pi$
$499$	−29.3286	−1.31293	−0.656465	+	0.754357i	$0.727949\pi$
$500$	−12.0000	−0.536656
$501$	−4.89124	−0.218525
$502$	−8.56717	−0.382372
$503$	33.6168	1.49890	0.749450	−	0.662061i	$-0.230318\pi$
$503$	33.6168	1.49890	0.749450	+	0.662061i	$0.230318\pi$
$504$	1.75877	0.0783419
$505$	−0.739170	−0.0328926
$506$	2.21213	0.0983413
$507$	−30.8922	−1.37197
$508$	−9.72967	−0.431685
$509$	−4.02910	−0.178587	−0.0892933	−	0.996005i	$-0.528461\pi$
$509$	−4.02910	−0.178587	−0.0892933	+	0.996005i	$0.528461\pi$
$510$	−19.9709	−0.884327
$511$	42.4843	1.87940
$512$	−1.00000	−0.0441942
$513$	0	0
$514$	−8.02465	−0.353952
$515$	−17.1634	−0.756311
$516$	−9.29086	−0.409007
$517$	25.1189	1.10473
$518$	−11.7743	−0.517331
$519$	14.7547	0.647657
$520$	−11.5175	−0.505078
$521$	−4.98957	−0.218597	−0.109299	−	0.994009i	$-0.534860\pi$
$521$	−4.98957	−0.218597	−0.109299	+	0.994009i	$0.534860\pi$
$522$	1.84255	0.0806462
$523$	26.5526	1.16107	0.580533	−	0.814237i	$-0.302844\pi$
$523$	26.5526	1.16107	0.580533	+	0.814237i	$0.302844\pi$
$524$	−6.46791	−0.282552
$525$	4.12836	0.180176
$526$	5.96080	0.259903
$527$	15.9899	0.696531
$528$	−4.87939	−0.212348
$529$	−22.5175	−0.979024
$530$	16.4243	0.713425
$531$	0.374638	0.0162579
$532$	0	0
$533$	2.00000	0.0866296
$534$	−11.8571	−0.513107
$535$	22.9067	0.990344
$536$	−4.95811	−0.214158
$537$	28.8280	1.24402
$538$	−1.14796	−0.0494919
$539$	0.830689	0.0357803
$540$	11.1925	0.481650
$541$	−11.9709	−0.514669	−0.257335	−	0.966322i	$-0.582844\pi$
$541$	−11.9709	−0.514669	−0.257335	+	0.966322i	$0.582844\pi$
$542$	−20.0547	−0.861422
$543$	4.25671	0.182673
$544$	6.51754	0.279437
$545$	−17.3892	−0.744871
$546$	23.7743	1.01744
$547$	−3.19665	−0.136679	−0.0683395	−	0.997662i	$-0.521770\pi$
$547$	−3.19665	−0.136679	−0.0683395	+	0.997662i	$0.521770\pi$
$548$	−11.6604	−0.498109
$549$	−1.91622	−0.0817824
$550$	3.18479	0.135800
$551$	0	0
$552$	−1.06418	−0.0452944
$553$	24.4243	1.03863
$554$	−17.3601	−0.737560
$555$	−13.3892	−0.568339
$556$	−8.26352	−0.350451
$557$	−23.9763	−1.01591	−0.507954	−	0.861384i	$-0.669598\pi$
$557$	−23.9763	−1.01591	−0.507954	+	0.861384i	$0.669598\pi$
$558$	−1.60132	−0.0677892
$559$	34.9222	1.47705
$560$	5.38919	0.227735
$561$	31.8016	1.34266
$562$	2.92127	0.123227
$563$	8.75702	0.369064	0.184532	−	0.982826i	$-0.440923\pi$
$563$	8.75702	0.369064	0.184532	+	0.982826i	$0.440923\pi$
$564$	−12.0838	−0.508819
$565$	−5.71957	−0.240624
$566$	9.48070	0.398504
$567$	−17.8271	−0.748666
$568$	−8.45336	−0.354695
$569$	36.4201	1.52681	0.763406	−	0.645919i	$-0.223526\pi$
$569$	36.4201	1.52681	0.763406	+	0.645919i	$0.223526\pi$
$570$	0	0
$571$	34.2131	1.43177	0.715886	−	0.698217i	$-0.246023\pi$
$571$	34.2131	1.43177	0.715886	+	0.698217i	$0.246023\pi$
$572$	18.3405	0.766854
$573$	−14.6500	−0.612013
$574$	−0.935822	−0.0390605
$575$	0.694593	0.0289665
$576$	−0.652704	−0.0271960
$577$	15.5098	0.645681	0.322841	−	0.946453i	$-0.395362\pi$
$577$	15.5098	0.645681	0.322841	+	0.946453i	$0.395362\pi$
$578$	−25.4783	−1.05976
$579$	−36.2814	−1.50780
$580$	5.64590	0.234433
$581$	22.8384	0.947498
$582$	0.532089	0.0220558
$583$	−26.1539	−1.08319
$584$	−15.7665	−0.652423
$585$	−7.51754	−0.310812
$586$	−27.2918	−1.12741
$587$	−11.5817	−0.478029	−0.239014	−	0.971016i	$-0.576824\pi$
$587$	−11.5817	−0.478029	−0.239014	+	0.971016i	$0.576824\pi$
$588$	−0.399615	−0.0164798
$589$	0	0
$590$	1.14796	0.0472606
$591$	35.1189	1.44460
$592$	4.36959	0.179589
$593$	−46.3928	−1.90512	−0.952562	−	0.304344i	$-0.901563\pi$
$593$	−46.3928	−1.90512	−0.952562	+	0.304344i	$0.901563\pi$
$594$	−17.8229	−0.731284
$595$	−35.1242	−1.43995
$596$	−16.4534	−0.673956
$597$	−15.4492	−0.632295
$598$	4.00000	0.163572
$599$	−25.6323	−1.04731	−0.523653	−	0.851931i	$-0.675431\pi$
$599$	−25.6323	−1.04731	−0.523653	+	0.851931i	$0.675431\pi$
$600$	−1.53209	−0.0625473
$601$	−7.99226	−0.326011	−0.163006	−	0.986625i	$-0.552119\pi$
$601$	−7.99226	−0.326011	−0.163006	+	0.986625i	$0.552119\pi$
$602$	−16.3405	−0.665989
$603$	−3.23618	−0.131787
$604$	−4.65539	−0.189425
$605$	−1.71419	−0.0696919
$606$	−0.566237	−0.0230018
$607$	26.9905	1.09551	0.547755	−	0.836639i	$-0.315482\pi$
$607$	26.9905	1.09551	0.547755	+	0.836639i	$0.315482\pi$
$608$	0	0
$609$	−11.6541	−0.472249
$610$	−5.87164	−0.237736
$611$	45.4201	1.83750
$612$	4.25402	0.171959
$613$	−14.2513	−0.575606	−0.287803	−	0.957690i	$-0.592925\pi$
$613$	−14.2513	−0.575606	−0.287803	+	0.957690i	$0.592925\pi$
$614$	21.3286	0.860753
$615$	−1.06418	−0.0429118
$616$	−8.58172	−0.345767
$617$	−30.5604	−1.23031	−0.615157	−	0.788405i	$-0.710907\pi$
$617$	−30.5604	−1.23031	−0.615157	+	0.788405i	$0.710907\pi$
$618$	−13.1480	−0.528888
$619$	−28.6750	−1.15255	−0.576273	−	0.817258i	$-0.695493\pi$
$619$	−28.6750	−1.15255	−0.576273	+	0.817258i	$0.695493\pi$
$620$	−4.90673	−0.197059
$621$	−3.88713	−0.155985
$622$	29.2918	1.17449
$623$	−20.8539	−0.835494
$624$	−8.82295	−0.353201
$625$	−19.0000	−0.760000
$626$	−5.56118	−0.222270
$627$	0	0
$628$	8.45336	0.337326
$629$	−28.4789	−1.13553
$630$	3.51754	0.140142
$631$	−4.49794	−0.179060	−0.0895301	−	0.995984i	$-0.528537\pi$
$631$	−4.49794	−0.179060	−0.0895301	+	0.995984i	$0.528537\pi$
$632$	−9.06418	−0.360554
$633$	−34.2576	−1.36162
$634$	3.80335	0.151050
$635$	−19.4593	−0.772221
$636$	12.5817	0.498898
$637$	1.50206	0.0595138
$638$	−8.99050	−0.355937
$639$	−5.51754	−0.218271
$640$	−2.00000	−0.0790569
$641$	11.6081	0.458493	0.229247	−	0.973368i	$-0.426374\pi$
$641$	11.6081	0.458493	0.229247	+	0.973368i	$0.426374\pi$
$642$	17.5476	0.692547
$643$	26.0455	1.02713	0.513567	−	0.858049i	$-0.328324\pi$
$643$	26.0455	1.02713	0.513567	+	0.858049i	$0.328324\pi$
$644$	−1.87164	−0.0737531
$645$	−18.5817	−0.731654
$646$	0	0
$647$	−2.31490	−0.0910082	−0.0455041	−	0.998964i	$-0.514489\pi$
$647$	−2.31490	−0.0910082	−0.0455041	+	0.998964i	$0.514489\pi$
$648$	6.61587	0.259896
$649$	−1.82800	−0.0717553
$650$	5.75877	0.225878
$651$	10.1284	0.396962
$652$	17.0496	0.667715
$653$	3.30541	0.129351	0.0646753	−	0.997906i	$-0.479399\pi$
$653$	3.30541	0.129351	0.0646753	+	0.997906i	$0.479399\pi$
$654$	−13.3209	−0.520888
$655$	−12.9358	−0.505444
$656$	0.347296	0.0135596
$657$	−10.2909	−0.401485
$658$	−21.2526	−0.828512
$659$	13.7493	0.535596	0.267798	−	0.963475i	$-0.413704\pi$
$659$	13.7493	0.535596	0.267798	+	0.963475i	$0.413704\pi$
$660$	−9.75877	−0.379860
$661$	3.33450	0.129697	0.0648486	−	0.997895i	$-0.479344\pi$
$661$	3.33450	0.129697	0.0648486	+	0.997895i	$0.479344\pi$
$662$	20.4219	0.793720
$663$	57.5039	2.23327
$664$	−8.47565	−0.328919
$665$	0	0
$666$	2.85204	0.110514
$667$	−1.96080	−0.0759225
$668$	3.19253	0.123523
$669$	−14.2121	−0.549473
$670$	−9.91622	−0.383097
$671$	9.34998	0.360952
$672$	4.12836	0.159255
$673$	−38.9810	−1.50261	−0.751304	−	0.659957i	$-0.770575\pi$
$673$	−38.9810	−1.50261	−0.751304	+	0.659957i	$0.770575\pi$
$674$	20.3105	0.782330
$675$	−5.59627	−0.215400
$676$	20.1634	0.775517
$677$	43.5877	1.67521	0.837606	−	0.546275i	$-0.183955\pi$
$677$	43.5877	1.67521	0.837606	+	0.546275i	$0.183955\pi$
$678$	−4.38144	−0.168268
$679$	0.935822	0.0359136
$680$	13.0351	0.499873
$681$	11.8530	0.454207
$682$	7.81345	0.299193
$683$	−32.9317	−1.26010	−0.630048	−	0.776556i	$-0.716965\pi$
$683$	−32.9317	−1.26010	−0.630048	+	0.776556i	$0.716965\pi$
$684$	0	0
$685$	−23.3209	−0.891045
$686$	18.1593	0.693326
$687$	35.2918	1.34647
$688$	6.06418	0.231195
$689$	−47.2918	−1.80167
$690$	−2.12836	−0.0810251
$691$	34.3209	1.30563	0.652814	−	0.757518i	$-0.273588\pi$
$691$	34.3209	1.30563	0.652814	+	0.757518i	$0.273588\pi$
$692$	−9.63041	−0.366093
$693$	−5.60132	−0.212777
$694$	−5.21482	−0.197952
$695$	−16.5270	−0.626906
$696$	4.32501	0.163939
$697$	−2.26352	−0.0857369
$698$	−14.3405	−0.542796
$699$	−12.8690	−0.486749
$700$	−2.69459	−0.101846
$701$	6.45336	0.243740	0.121870	−	0.992546i	$-0.461111\pi$
$701$	6.45336	0.243740	0.121870	+	0.992546i	$0.461111\pi$
$702$	−32.2276	−1.21635
$703$	0	0
$704$	3.18479	0.120031
$705$	−24.1676	−0.910203
$706$	−26.2499	−0.987928
$707$	−0.995881	−0.0374540
$708$	0.879385	0.0330493
$709$	−3.37908	−0.126904	−0.0634520	−	0.997985i	$-0.520211\pi$
$709$	−3.37908	−0.126904	−0.0634520	+	0.997985i	$0.520211\pi$
$710$	−16.9067	−0.634498
$711$	−5.91622	−0.221876
$712$	7.73917	0.290038
$713$	1.70409	0.0638186
$714$	−26.9067	−1.00696
$715$	36.6810	1.37179
$716$	−18.8161	−0.703192
$717$	24.0993	0.900003
$718$	33.6905	1.25732
$719$	−31.2026	−1.16366	−0.581831	−	0.813310i	$-0.697664\pi$
$719$	−31.2026	−1.16366	−0.581831	+	0.813310i	$0.697664\pi$
$720$	−1.30541	−0.0486497
$721$	−23.1242	−0.861192
$722$	0	0
$723$	26.8161	0.997303
$724$	−2.77837	−0.103257
$725$	−2.82295	−0.104842
$726$	−1.31315	−0.0487355
$727$	−25.6614	−0.951728	−0.475864	−	0.879519i	$-0.657865\pi$
$727$	−25.6614	−0.951728	−0.475864	+	0.879519i	$0.657865\pi$
$728$	−15.5175	−0.575118
$729$	30.0401	1.11260
$730$	−31.5330	−1.16709
$731$	−39.5235	−1.46183
$732$	−4.49794	−0.166249
$733$	−23.8735	−0.881788	−0.440894	−	0.897559i	$-0.645339\pi$
$733$	−23.8735	−0.881788	−0.440894	+	0.897559i	$0.645339\pi$
$734$	10.4688	0.386412
$735$	−0.799229	−0.0294800
$736$	0.694593	0.0256030
$737$	15.7906	0.581653
$738$	0.226682	0.00834426
$739$	−45.9404	−1.68994	−0.844972	−	0.534810i	$-0.820383\pi$
$739$	−45.9404	−1.68994	−0.844972	+	0.534810i	$0.820383\pi$
$740$	8.73917	0.321258
$741$	0	0
$742$	22.1284	0.812357
$743$	51.0114	1.87143	0.935713	−	0.352763i	$-0.114758\pi$
$743$	51.0114	1.87143	0.935713	+	0.352763i	$0.114758\pi$
$744$	−3.75877	−0.137803
$745$	−32.9067	−1.20561
$746$	23.9026	0.875137
$747$	−5.53209	−0.202409
$748$	−20.7570	−0.758952
$749$	30.8621	1.12768
$750$	−18.3851	−0.671328
$751$	36.3696	1.32715	0.663573	−	0.748112i	$-0.269039\pi$
$751$	36.3696	1.32715	0.663573	+	0.748112i	$0.269039\pi$
$752$	7.88713	0.287614
$753$	−13.1257	−0.478326
$754$	−16.2567	−0.592034
$755$	−9.31078	−0.338854
$756$	15.0797	0.548442
$757$	−5.80335	−0.210926	−0.105463	−	0.994423i	$-0.533633\pi$
$757$	−5.80335	−0.210926	−0.105463	+	0.994423i	$0.533633\pi$
$758$	17.8135	0.647014
$759$	3.38919	0.123020
$760$	0	0
$761$	22.6355	0.820535	0.410268	−	0.911965i	$-0.365435\pi$
$761$	22.6355	0.820535	0.410268	+	0.911965i	$0.365435\pi$
$762$	−14.9067	−0.540014
$763$	−23.4284	−0.848165
$764$	9.56212	0.345945
$765$	8.50805	0.307609
$766$	25.0797	0.906165
$767$	−3.30541	−0.119351
$768$	−1.53209	−0.0552845
$769$	10.9026	0.393158	0.196579	−	0.980488i	$-0.437017\pi$
$769$	10.9026	0.393158	0.196579	+	0.980488i	$0.437017\pi$
$770$	−17.1634	−0.618527
$771$	−12.2945	−0.442775
$772$	23.6810	0.852297
$773$	5.25072	0.188855	0.0944277	−	0.995532i	$-0.469898\pi$
$773$	5.25072	0.188855	0.0944277	+	0.995532i	$0.469898\pi$
$774$	3.95811	0.142271
$775$	2.45336	0.0881274
$776$	−0.347296	−0.0124672
$777$	−18.0392	−0.647153
$778$	9.41828	0.337662
$779$	0	0
$780$	−17.6459	−0.631824
$781$	26.9222	0.963352
$782$	−4.52704	−0.161886
$783$	15.7980	0.564573
$784$	0.260830	0.00931535
$785$	16.9067	0.603427
$786$	−9.90941	−0.353457
$787$	2.38743	0.0851027	0.0425514	−	0.999094i	$-0.486451\pi$
$787$	2.38743	0.0851027	0.0425514	+	0.999094i	$0.486451\pi$
$788$	−22.9222	−0.816570
$789$	9.13247	0.325125
$790$	−18.1284	−0.644978
$791$	−7.70596	−0.273992
$792$	2.07873	0.0738643
$793$	16.9067	0.600375
$794$	−6.85204	−0.243170
$795$	25.1634	0.892455
$796$	10.0838	0.357410
$797$	−31.0951	−1.10145	−0.550723	−	0.834688i	$-0.685648\pi$
$797$	−31.0951	−1.10145	−0.550723	+	0.834688i	$0.685648\pi$
$798$	0	0
$799$	−51.4047	−1.81857
$800$	1.00000	0.0353553
$801$	5.05138	0.178482
$802$	4.74691	0.167619
$803$	50.2131	1.77198
$804$	−7.59627	−0.267900
$805$	−3.74329	−0.131934
$806$	14.1284	0.497650
$807$	−1.75877	−0.0619117
$808$	0.369585	0.0130020
$809$	22.3037	0.784155	0.392077	−	0.919932i	$-0.371757\pi$
$809$	22.3037	0.784155	0.392077	+	0.919932i	$0.371757\pi$
$810$	13.2317	0.464916
$811$	−3.31902	−0.116547	−0.0582733	−	0.998301i	$-0.518559\pi$
$811$	−3.31902	−0.116547	−0.0582733	+	0.998301i	$0.518559\pi$
$812$	7.60670	0.266943
$813$	−30.7256	−1.07759
$814$	−13.9162	−0.487763
$815$	34.0993	1.19444
$816$	9.98545	0.349561
$817$	0	0
$818$	31.6928	1.10811
$819$	−10.1284	−0.353913
$820$	0.694593	0.0242562
$821$	−1.83244	−0.0639527	−0.0319764	−	0.999489i	$-0.510180\pi$
$821$	−1.83244	−0.0639527	−0.0319764	+	0.999489i	$0.510180\pi$
$822$	−17.8648	−0.623108
$823$	−34.2377	−1.19345	−0.596726	−	0.802445i	$-0.703532\pi$
$823$	−34.2377	−1.19345	−0.596726	+	0.802445i	$0.703532\pi$
$824$	8.58172	0.298958
$825$	4.87939	0.169878
$826$	1.54664	0.0538144
$827$	19.8658	0.690801	0.345400	−	0.938455i	$-0.387743\pi$
$827$	19.8658	0.690801	0.345400	+	0.938455i	$0.387743\pi$
$828$	0.453363	0.0157555
$829$	35.7351	1.24113	0.620565	−	0.784155i	$-0.286903\pi$
$829$	35.7351	1.24113	0.620565	+	0.784155i	$0.286903\pi$
$830$	−16.9513	−0.588388
$831$	−26.5972	−0.922647
$832$	5.75877	0.199649
$833$	−1.69997	−0.0589004
$834$	−12.6604	−0.438395
$835$	6.38507	0.220964
$836$	0	0
$837$	−13.7297	−0.474567
$838$	11.0101	0.380338
$839$	54.3952	1.87793	0.938965	−	0.344013i	$-0.111786\pi$
$839$	54.3952	1.87793	0.938965	+	0.344013i	$0.111786\pi$
$840$	8.25671	0.284884
$841$	−21.0310	−0.725206
$842$	−8.66550	−0.298633
$843$	4.47565	0.154150
$844$	22.3601	0.769666
$845$	40.3269	1.38729
$846$	5.14796	0.176990
$847$	−2.30953	−0.0793563
$848$	−8.21213	−0.282006
$849$	14.5253	0.498506
$850$	−6.51754	−0.223550
$851$	−3.03508	−0.104041
$852$	−12.9513	−0.443704
$853$	15.9763	0.547017	0.273509	−	0.961870i	$-0.411816\pi$
$853$	15.9763	0.547017	0.273509	+	0.961870i	$0.411816\pi$
$854$	−7.91085	−0.270704
$855$	0	0
$856$	−11.4534	−0.391468
$857$	26.0145	0.888640	0.444320	−	0.895868i	$-0.353445\pi$
$857$	26.0145	0.888640	0.444320	+	0.895868i	$0.353445\pi$
$858$	28.0993	0.959293
$859$	53.2704	1.81756	0.908782	−	0.417271i	$-0.137014\pi$
$859$	53.2704	1.81756	0.908782	+	0.417271i	$0.137014\pi$
$860$	12.1284	0.413573
$861$	−1.43376	−0.0488625
$862$	−29.8871	−1.01796
$863$	−3.23173	−0.110010	−0.0550048	−	0.998486i	$-0.517517\pi$
$863$	−3.23173	−0.110010	−0.0550048	+	0.998486i	$0.517517\pi$
$864$	−5.59627	−0.190389
$865$	−19.2608	−0.654888
$866$	9.26083	0.314696
$867$	−39.0351	−1.32570
$868$	−6.61081	−0.224386
$869$	28.8675	0.979264
$870$	8.65002	0.293263
$871$	28.5526	0.967469
$872$	8.69459	0.294436
$873$	−0.226682	−0.00767201
$874$	0	0
$875$	−32.3351	−1.09313
$876$	−24.1557	−0.816145
$877$	−11.7243	−0.395901	−0.197951	−	0.980212i	$-0.563429\pi$
$877$	−11.7243	−0.395901	−0.197951	+	0.980212i	$0.563429\pi$
$878$	20.8621	0.704063
$879$	−41.8135	−1.41033
$880$	6.36959	0.214719
$881$	27.0473	0.911246	0.455623	−	0.890173i	$-0.349417\pi$
$881$	27.0473	0.911246	0.455623	+	0.890173i	$0.349417\pi$
$882$	0.170245	0.00573243
$883$	14.4810	0.487325	0.243663	−	0.969860i	$-0.421651\pi$
$883$	14.4810	0.487325	0.243663	+	0.969860i	$0.421651\pi$
$884$	−37.5330	−1.26237
$885$	1.75877	0.0591204
$886$	−23.8280	−0.800517
$887$	11.5912	0.389195	0.194597	−	0.980883i	$-0.437660\pi$
$887$	11.5912	0.389195	0.194597	+	0.980883i	$0.437660\pi$
$888$	6.69459	0.224656
$889$	−26.2175	−0.879307
$890$	15.4783	0.518835
$891$	−21.0702	−0.705877
$892$	9.27631	0.310594
$893$	0	0
$894$	−25.2080	−0.843082
$895$	−37.6323	−1.25791
$896$	−2.69459	−0.0900200
$897$	6.12836	0.204620
$898$	−2.18210	−0.0728178
$899$	−6.92572	−0.230986
$900$	0.652704	0.0217568
$901$	53.5229	1.78311
$902$	−1.10607	−0.0368280
$903$	−25.0351	−0.833115
$904$	2.85978	0.0951150
$905$	−5.55674	−0.184712
$906$	−7.13247	−0.236961
$907$	−41.9786	−1.39388	−0.696939	−	0.717130i	$-0.745455\pi$
$907$	−41.9786	−1.39388	−0.696939	+	0.717130i	$0.745455\pi$
$908$	−7.73648	−0.256744
$909$	0.241230	0.00800108
$910$	−31.0351	−1.02880
$911$	44.8675	1.48653	0.743264	−	0.668999i	$-0.233277\pi$
$911$	44.8675	1.48653	0.743264	+	0.668999i	$0.233277\pi$
$912$	0	0
$913$	26.9932	0.893344
$914$	−1.78106	−0.0589122
$915$	−8.99588	−0.297395
$916$	−23.0351	−0.761101
$917$	−17.4284	−0.575536
$918$	36.4739	1.20382
$919$	−32.5270	−1.07297	−0.536484	−	0.843911i	$-0.680248\pi$
$919$	−32.5270	−1.07297	−0.536484	+	0.843911i	$0.680248\pi$
$920$	1.38919	0.0458001
$921$	32.6774	1.07676
$922$	15.4884	0.510085
$923$	48.6810	1.60235
$924$	−13.1480	−0.432536
$925$	−4.36959	−0.143671
$926$	2.71007	0.0890586
$927$	5.60132	0.183971
$928$	−2.82295	−0.0926678
$929$	11.8402	0.388464	0.194232	−	0.980956i	$-0.437779\pi$
$929$	11.8402	0.388464	0.194232	+	0.980956i	$0.437779\pi$
$930$	−7.51754	−0.246510
$931$	0	0
$932$	8.39961	0.275139
$933$	44.8776	1.46923
$934$	−12.9135	−0.422544
$935$	−41.5140	−1.35765
$936$	3.75877	0.122859
$937$	−0.763823	−0.0249530	−0.0124765	−	0.999922i	$-0.503971\pi$
$937$	−0.763823	−0.0249530	−0.0124765	+	0.999922i	$0.503971\pi$
$938$	−13.3601	−0.436222
$939$	−8.52023	−0.278047
$940$	15.7743	0.514499
$941$	21.4938	0.700679	0.350339	−	0.936623i	$-0.386066\pi$
$941$	21.4938	0.700679	0.350339	+	0.936623i	$0.386066\pi$
$942$	12.9513	0.421976
$943$	−0.241230	−0.00785551
$944$	−0.573978	−0.0186814
$945$	30.1593	0.981083
$946$	−19.3131	−0.627925
$947$	31.6851	1.02963	0.514814	−	0.857302i	$-0.327861\pi$
$947$	31.6851	1.02963	0.514814	+	0.857302i	$0.327861\pi$
$948$	−13.8871	−0.451033
$949$	90.7957	2.94735
$950$	0	0
$951$	5.82707	0.188956
$952$	17.5621	0.569192
$953$	−55.8711	−1.80984	−0.904922	−	0.425577i	$-0.860071\pi$
$953$	−55.8711	−1.80984	−0.904922	+	0.425577i	$0.860071\pi$
$954$	−5.36009	−0.173539
$955$	19.1242	0.618846
$956$	−15.7297	−0.508734
$957$	−13.7743	−0.445258
$958$	18.5526	0.599408
$959$	−31.4201	−1.01461
$960$	−3.06418	−0.0988959
$961$	−24.9810	−0.805839
$962$	−25.1634	−0.811302
$963$	−7.47565	−0.240900
$964$	−17.5030	−0.563733
$965$	47.3620	1.52464
$966$	−2.86753	−0.0922611
$967$	21.5567	0.693218	0.346609	−	0.938010i	$-0.387333\pi$
$967$	21.5567	0.693218	0.346609	+	0.938010i	$0.387333\pi$
$968$	0.857097	0.0275481
$969$	0	0
$970$	−0.694593	−0.0223020
$971$	−48.6563	−1.56146	−0.780728	−	0.624871i	$-0.785151\pi$
$971$	−48.6563	−1.56146	−0.780728	+	0.624871i	$0.785151\pi$
$972$	−6.65270	−0.213386
$973$	−22.2668	−0.713841
$974$	41.1735	1.31929
$975$	8.82295	0.282560
$976$	2.93582	0.0939734
$977$	50.5482	1.61718	0.808590	−	0.588373i	$-0.200231\pi$
$977$	50.5482	1.61718	0.808590	+	0.588373i	$0.200231\pi$
$978$	26.1215	0.835275
$979$	−24.6477	−0.787742
$980$	0.521660	0.0166638
$981$	5.67499	0.181189
$982$	22.5776	0.720480
$983$	30.0601	0.958767	0.479383	−	0.877606i	$-0.340860\pi$
$983$	30.0601	0.958767	0.479383	+	0.877606i	$0.340860\pi$
$984$	0.532089	0.0169624
$985$	−45.8444	−1.46072
$986$	18.3987	0.585933
$987$	−32.5609	−1.03642
$988$	0	0
$989$	−4.21213	−0.133938
$990$	4.15745	0.132132
$991$	−2.75278	−0.0874451	−0.0437225	−	0.999044i	$-0.513922\pi$
$991$	−2.75278	−0.0874451	−0.0437225	+	0.999044i	$0.513922\pi$
$992$	2.45336	0.0778944
$993$	31.2882	0.992900
$994$	−22.7784	−0.722486
$995$	20.1676	0.639355
$996$	−12.9855	−0.411460
$997$	8.70470	0.275681	0.137840	−	0.990454i	$-0.455984\pi$
$997$	8.70470	0.275681	0.137840	+	0.990454i	$0.455984\pi$
$998$	29.3286	0.928382
$999$	24.4534	0.773670

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.a.k.1.1		3
3.2	odd	2		6498.2.a.bq.1.2		3
4.3	odd	2		5776.2.a.bo.1.3		3
19.2	odd	18		722.2.e.b.99.1		6
19.3	odd	18		722.2.e.m.389.1		6
19.4	even	9		722.2.e.k.415.1		6
19.5	even	9		722.2.e.k.595.1		6
19.6	even	9		722.2.e.a.245.1		6
19.7	even	3		722.2.c.l.429.3		6
19.8	odd	6		722.2.c.k.653.1		6
19.9	even	9		722.2.e.l.423.1		6
19.10	odd	18		722.2.e.b.423.1		6
19.11	even	3		722.2.c.l.653.3		6
19.12	odd	6		722.2.c.k.429.1		6
19.13	odd	18		722.2.e.m.245.1		6
19.14	odd	18		38.2.e.a.25.1	✓	6
19.15	odd	18		38.2.e.a.35.1	yes	6
19.16	even	9		722.2.e.a.389.1		6
19.17	even	9		722.2.e.l.99.1		6
19.18	odd	2		722.2.a.l.1.3		3
57.14	even	18		342.2.u.c.253.1		6
57.53	even	18		342.2.u.c.73.1		6
57.56	even	2		6498.2.a.bl.1.2		3
76.15	even	18		304.2.u.c.225.1		6
76.71	even	18		304.2.u.c.177.1		6
76.75	even	2		5776.2.a.bn.1.1		3
95.14	odd	18		950.2.l.d.101.1		6
95.33	even	36		950.2.u.b.899.1		12
95.34	odd	18		950.2.l.d.301.1		6
95.52	even	36		950.2.u.b.899.2		12
95.53	even	36		950.2.u.b.149.2		12
95.72	even	36		950.2.u.b.149.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.e.a.25.1	✓	6	19.14	odd	18
38.2.e.a.35.1	yes	6	19.15	odd	18
304.2.u.c.177.1		6	76.71	even	18
304.2.u.c.225.1		6	76.15	even	18
342.2.u.c.73.1		6	57.53	even	18
342.2.u.c.253.1		6	57.14	even	18
722.2.a.k.1.1		3	1.1	even	1	trivial
722.2.a.l.1.3		3	19.18	odd	2
722.2.c.k.429.1		6	19.12	odd	6
722.2.c.k.653.1		6	19.8	odd	6
722.2.c.l.429.3		6	19.7	even	3
722.2.c.l.653.3		6	19.11	even	3
722.2.e.a.245.1		6	19.6	even	9
722.2.e.a.389.1		6	19.16	even	9
722.2.e.b.99.1		6	19.2	odd	18
722.2.e.b.423.1		6	19.10	odd	18
722.2.e.k.415.1		6	19.4	even	9
722.2.e.k.595.1		6	19.5	even	9
722.2.e.l.99.1		6	19.17	even	9
722.2.e.l.423.1		6	19.9	even	9
722.2.e.m.245.1		6	19.13	odd	18
722.2.e.m.389.1		6	19.3	odd	18
950.2.l.d.101.1		6	95.14	odd	18
950.2.l.d.301.1		6	95.34	odd	18
950.2.u.b.149.1		12	95.72	even	36
950.2.u.b.149.2		12	95.53	even	36
950.2.u.b.899.1		12	95.33	even	36
950.2.u.b.899.2		12	95.52	even	36
5776.2.a.bn.1.1		3	76.75	even	2
5776.2.a.bo.1.3		3	4.3	odd	2
6498.2.a.bl.1.2		3	57.56	even	2
6498.2.a.bq.1.2		3	3.2	odd	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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.53209 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.53209 q^{6} +2.69459 q^{7} -1.00000 q^{8} -0.652704 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.53209 q^{3} +1.00000 q^{4} +2.00000 q^{5} +1.53209 q^{6} +2.69459 q^{7} -1.00000 q^{8} -0.652704 q^{9} -2.00000 q^{10} +3.18479 q^{11} -1.53209 q^{12} +5.75877 q^{13} -2.69459 q^{14} -3.06418 q^{15} +1.00000 q^{16} -6.51754 q^{17} +0.652704 q^{18} +2.00000 q^{20} -4.12836 q^{21} -3.18479 q^{22} -0.694593 q^{23} +1.53209 q^{24} -1.00000 q^{25} -5.75877 q^{26} +5.59627 q^{27} +2.69459 q^{28} +2.82295 q^{29} +3.06418 q^{30} -2.45336 q^{31} -1.00000 q^{32} -4.87939 q^{33} +6.51754 q^{34} +5.38919 q^{35} -0.652704 q^{36} +4.36959 q^{37} -8.82295 q^{39} -2.00000 q^{40} +0.347296 q^{41} +4.12836 q^{42} +6.06418 q^{43} +3.18479 q^{44} -1.30541 q^{45} +0.694593 q^{46} +7.88713 q^{47} -1.53209 q^{48} +0.260830 q^{49} +1.00000 q^{50} +9.98545 q^{51} +5.75877 q^{52} -8.21213 q^{53} -5.59627 q^{54} +6.36959 q^{55} -2.69459 q^{56} -2.82295 q^{58} -0.573978 q^{59} -3.06418 q^{60} +2.93582 q^{61} +2.45336 q^{62} -1.75877 q^{63} +1.00000 q^{64} +11.5175 q^{65} +4.87939 q^{66} +4.95811 q^{67} -6.51754 q^{68} +1.06418 q^{69} -5.38919 q^{70} +8.45336 q^{71} +0.652704 q^{72} +15.7665 q^{73} -4.36959 q^{74} +1.53209 q^{75} +8.58172 q^{77} +8.82295 q^{78} +9.06418 q^{79} +2.00000 q^{80} -6.61587 q^{81} -0.347296 q^{82} +8.47565 q^{83} -4.12836 q^{84} -13.0351 q^{85} -6.06418 q^{86} -4.32501 q^{87} -3.18479 q^{88} -7.73917 q^{89} +1.30541 q^{90} +15.5175 q^{91} -0.694593 q^{92} +3.75877 q^{93} -7.88713 q^{94} +1.53209 q^{96} +0.347296 q^{97} -0.260830 q^{98} -2.07873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 - 3 * q^9	\( 3 q - 3 q^{2} + 3 q^{4} + 6 q^{5} + 6 q^{7} - 3 q^{8} - 3 q^{9} - 6 q^{10} + 6 q^{11} + 6 q^{13} - 6 q^{14} + 3 q^{16} + 3 q^{17} + 3 q^{18} + 6 q^{20} + 6 q^{21} - 6 q^{22} - 3 q^{25} - 6 q^{26} + 3 q^{27} + 6 q^{28} - 12 q^{29} + 6 q^{31} - 3 q^{32} - 9 q^{33} - 3 q^{34} + 12 q^{35} - 3 q^{36} + 6 q^{37} - 6 q^{39} - 6 q^{40} - 6 q^{42} + 9 q^{43} + 6 q^{44} - 6 q^{45} - 6 q^{47} + 15 q^{49} + 3 q^{50} + 12 q^{51} + 6 q^{52} - 3 q^{54} + 12 q^{55} - 6 q^{56} + 12 q^{58} + 6 q^{59} + 18 q^{61} - 6 q^{62} + 6 q^{63} + 3 q^{64} + 12 q^{65} + 9 q^{66} + 18 q^{67} + 3 q^{68} - 6 q^{69} - 12 q^{70} + 12 q^{71} + 3 q^{72} + 12 q^{73} - 6 q^{74} - 6 q^{77} + 6 q^{78} + 18 q^{79} + 6 q^{80} - 9 q^{81} + 6 q^{83} + 6 q^{84} + 6 q^{85} - 9 q^{86} - 18 q^{87} - 6 q^{88} - 9 q^{89} + 6 q^{90} + 24 q^{91} + 6 q^{94} - 15 q^{98} - 15 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 + 6 * q^7 - 3 * q^8 - 3 * q^9 - 6 * q^10 + 6 * q^11 + 6 * q^13 - 6 * q^14 + 3 * q^16 + 3 * q^17 + 3 * q^18 + 6 * q^20 + 6 * q^21 - 6 * q^22 - 3 * q^25 - 6 * q^26 + 3 * q^27 + 6 * q^28 - 12 * q^29 + 6 * q^31 - 3 * q^32 - 9 * q^33 - 3 * q^34 + 12 * q^35 - 3 * q^36 + 6 * q^37 - 6 * q^39 - 6 * q^40 - 6 * q^42 + 9 * q^43 + 6 * q^44 - 6 * q^45 - 6 * q^47 + 15 * q^49 + 3 * q^50 + 12 * q^51 + 6 * q^52 - 3 * q^54 + 12 * q^55 - 6 * q^56 + 12 * q^58 + 6 * q^59 + 18 * q^61 - 6 * q^62 + 6 * q^63 + 3 * q^64 + 12 * q^65 + 9 * q^66 + 18 * q^67 + 3 * q^68 - 6 * q^69 - 12 * q^70 + 12 * q^71 + 3 * q^72 + 12 * q^73 - 6 * q^74 - 6 * q^77 + 6 * q^78 + 18 * q^79 + 6 * q^80 - 9 * q^81 + 6 * q^83 + 6 * q^84 + 6 * q^85 - 9 * q^86 - 18 * q^87 - 6 * q^88 - 9 * q^89 + 6 * q^90 + 24 * q^91 + 6 * q^94 - 15 * q^98 - 15 * q^99

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