LMFDB - Embedded newform 4009.2.a.c.1.61

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.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:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.61
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.99860 q^{2} -0.865127 q^{3} +1.99440 q^{4} +0.00202949 q^{5} -1.72904 q^{6} +1.41052 q^{7} -0.0111926 q^{8} -2.25155 q^{9} +O(q^{10})$	\(q+1.99860 q^{2} -0.865127 q^{3} +1.99440 q^{4} +0.00202949 q^{5} -1.72904 q^{6} +1.41052 q^{7} -0.0111926 q^{8} -2.25155 q^{9} +0.00405614 q^{10} +1.51440 q^{11} -1.72541 q^{12} +1.66068 q^{13} +2.81906 q^{14} -0.00175577 q^{15} -4.01117 q^{16} -6.12061 q^{17} -4.49996 q^{18} +1.00000 q^{19} +0.00404762 q^{20} -1.22028 q^{21} +3.02667 q^{22} +2.85561 q^{23} +0.00968299 q^{24} -5.00000 q^{25} +3.31904 q^{26} +4.54326 q^{27} +2.81314 q^{28} -3.45604 q^{29} -0.00350908 q^{30} -5.19602 q^{31} -7.99434 q^{32} -1.31015 q^{33} -12.2327 q^{34} +0.00286263 q^{35} -4.49050 q^{36} -4.70882 q^{37} +1.99860 q^{38} -1.43670 q^{39} -2.27152e-5 q^{40} -5.04603 q^{41} -2.43885 q^{42} +4.12683 q^{43} +3.02031 q^{44} -0.00456951 q^{45} +5.70722 q^{46} +5.91506 q^{47} +3.47017 q^{48} -5.01044 q^{49} -9.99299 q^{50} +5.29511 q^{51} +3.31207 q^{52} +2.87376 q^{53} +9.08016 q^{54} +0.00307345 q^{55} -0.0157873 q^{56} -0.865127 q^{57} -6.90724 q^{58} +2.35864 q^{59} -0.00350170 q^{60} -9.19319 q^{61} -10.3848 q^{62} -3.17586 q^{63} -7.95514 q^{64} +0.00337034 q^{65} -2.61846 q^{66} -8.84406 q^{67} -12.2069 q^{68} -2.47047 q^{69} +0.00572126 q^{70} +8.05124 q^{71} +0.0252007 q^{72} -8.73309 q^{73} -9.41105 q^{74} +4.32563 q^{75} +1.99440 q^{76} +2.13608 q^{77} -2.87139 q^{78} +8.32296 q^{79} -0.00814063 q^{80} +2.82416 q^{81} -10.0850 q^{82} -1.91068 q^{83} -2.43372 q^{84} -0.0124217 q^{85} +8.24787 q^{86} +2.98991 q^{87} -0.0169500 q^{88} +13.3292 q^{89} -0.00913262 q^{90} +2.34242 q^{91} +5.69523 q^{92} +4.49522 q^{93} +11.8218 q^{94} +0.00202949 q^{95} +6.91612 q^{96} -9.39658 q^{97} -10.0139 q^{98} -3.40975 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) $ 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * 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 $

$2$	1.99860	1.41322	0.706612	−	0.707602i	$-0.250223\pi$
$2$	1.99860	1.41322	0.706612	+	0.707602i	$0.250223\pi$
$3$	−0.865127	−0.499482	−0.249741	−	0.968313i	$-0.580345\pi$
$3$	−0.865127	−0.499482	−0.249741	+	0.968313i	$0.580345\pi$
$4$	1.99440	0.997200
$5$	0.00202949	0.000907616 0	0.000453808	−	1.00000i	$-0.499856\pi$
$5$	0.00202949	0.000907616 0	0.000453808		1.00000i	$0.499856\pi$
$6$	−1.72904	−0.705879
$7$	1.41052	0.533126	0.266563	−	0.963818i	$-0.414112\pi$
$7$	1.41052	0.533126	0.266563	+	0.963818i	$0.414112\pi$
$8$	−0.0111926	−0.00395717
$9$	−2.25155	−0.750518
$10$	0.00405614	0.00128266
$11$	1.51440	0.456608	0.228304	−	0.973590i	$-0.426682\pi$
$11$	1.51440	0.456608	0.228304	+	0.973590i	$0.426682\pi$
$12$	−1.72541	−0.498083
$13$	1.66068	0.460591	0.230295	−	0.973121i	$-0.426031\pi$
$13$	1.66068	0.460591	0.230295	+	0.973121i	$0.426031\pi$
$14$	2.81906	0.753426
$15$	−0.00175577	−0.000453337 0
$16$	−4.01117	−1.00279
$17$	−6.12061	−1.48447	−0.742233	−	0.670142i	$-0.766233\pi$
$17$	−6.12061	−1.48447	−0.742233	+	0.670142i	$0.766233\pi$
$18$	−4.49996	−1.06065
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	0.00404762	0.000905074 0
$21$	−1.22028	−0.266287
$22$	3.02667	0.645289
$23$	2.85561	0.595436	0.297718	−	0.954654i	$-0.403774\pi$
$23$	2.85561	0.595436	0.297718	+	0.954654i	$0.403774\pi$
$24$	0.00968299	0.00197653
$25$	−5.00000	−0.999999
$26$	3.31904	0.650918
$27$	4.54326	0.874352
$28$	2.81314	0.531633
$29$	−3.45604	−0.641770	−0.320885	−	0.947118i	$-0.603980\pi$
$29$	−3.45604	−0.641770	−0.320885	+	0.947118i	$0.603980\pi$
$30$	−0.00350908	−0.000640667 0
$31$	−5.19602	−0.933232	−0.466616	−	0.884460i	$-0.654527\pi$
$31$	−5.19602	−0.933232	−0.466616	+	0.884460i	$0.654527\pi$
$32$	−7.99434	−1.41321
$33$	−1.31015	−0.228067
$34$	−12.2327	−2.09788
$35$	0.00286263	0.000483873 0
$36$	−4.49050	−0.748417
$37$	−4.70882	−0.774125	−0.387063	−	0.922053i	$-0.626510\pi$
$37$	−4.70882	−0.774125	−0.387063	+	0.922053i	$0.626510\pi$
$38$	1.99860	0.324216
$39$	−1.43670	−0.230057
$40$	−2.27152e−5 0	−3.59159e−6 0
$41$	−5.04603	−0.788058	−0.394029	−	0.919098i	$-0.628919\pi$
$41$	−5.04603	−0.788058	−0.394029	+	0.919098i	$0.628919\pi$
$42$	−2.43885	−0.376322
$43$	4.12683	0.629335	0.314668	−	0.949202i	$-0.398107\pi$
$43$	4.12683	0.629335	0.314668	+	0.949202i	$0.398107\pi$
$44$	3.02031	0.455329
$45$	−0.00456951	−0.000681182 0
$46$	5.70722	0.841484
$47$	5.91506	0.862800	0.431400	−	0.902161i	$-0.358020\pi$
$47$	5.91506	0.862800	0.431400	+	0.902161i	$0.358020\pi$
$48$	3.47017	0.500876
$49$	−5.01044	−0.715777
$50$	−9.99299	−1.41322
$51$	5.29511	0.741464
$52$	3.31207	0.459301
$53$	2.87376	0.394741	0.197370	−	0.980329i	$-0.436760\pi$
$53$	2.87376	0.394741	0.197370	+	0.980329i	$0.436760\pi$
$54$	9.08016	1.23565
$55$	0.00307345	0.000414424 0
$56$	−0.0157873	−0.00210967
$57$	−0.865127	−0.114589
$58$	−6.90724	−0.906965
$59$	2.35864	0.307069	0.153534	−	0.988143i	$-0.450934\pi$
$59$	2.35864	0.307069	0.153534	+	0.988143i	$0.450934\pi$
$60$	−0.00350170	−0.000452068 0
$61$	−9.19319	−1.17707	−0.588533	−	0.808473i	$-0.700294\pi$
$61$	−9.19319	−1.17707	−0.588533	+	0.808473i	$0.700294\pi$
$62$	−10.3848	−1.31886
$63$	−3.17586	−0.400121
$64$	−7.95514	−0.994392
$65$	0.00337034	0.000418040 0
$66$	−2.61846	−0.322310
$67$	−8.84406	−1.08047	−0.540237	−	0.841513i	$-0.681665\pi$
$67$	−8.84406	−1.08047	−0.540237	+	0.841513i	$0.681665\pi$
$68$	−12.2069	−1.48031
$69$	−2.47047	−0.297409
$70$	0.00572126	0.000683821 0
$71$	8.05124	0.955507	0.477753	−	0.878494i	$-0.341451\pi$
$71$	8.05124	0.955507	0.477753	+	0.878494i	$0.341451\pi$
$72$	0.0252007	0.00296993
$73$	−8.73309	−1.02213	−0.511066	−	0.859542i	$-0.670749\pi$
$73$	−8.73309	−1.02213	−0.511066	+	0.859542i	$0.670749\pi$
$74$	−9.41105	−1.09401
$75$	4.32563	0.499481
$76$	1.99440	0.228773
$77$	2.13608	0.243429
$78$	−2.87139	−0.325121
$79$	8.32296	0.936407	0.468203	−	0.883621i	$-0.344902\pi$
$79$	8.32296	0.936407	0.468203	+	0.883621i	$0.344902\pi$
$80$	−0.00814063	−0.000910150 0
$81$	2.82416	0.313796
$82$	−10.0850	−1.11370
$83$	−1.91068	−0.209725	−0.104862	−	0.994487i	$-0.533440\pi$
$83$	−1.91068	−0.209725	−0.104862	+	0.994487i	$0.533440\pi$
$84$	−2.43372	−0.265541
$85$	−0.0124217	−0.00134733
$86$	8.24787	0.889391
$87$	2.98991	0.320552
$88$	−0.0169500	−0.00180687
$89$	13.3292	1.41290	0.706448	−	0.707765i	$-0.250296\pi$
$89$	13.3292	1.41290	0.706448	+	0.707765i	$0.250296\pi$
$90$	−0.00913262	−0.000962662 0
$91$	2.34242	0.245553
$92$	5.69523	0.593769
$93$	4.49522	0.466132
$94$	11.8218	1.21933
$95$	0.00202949	0.000208221 0
$96$	6.91612	0.705873
$97$	−9.39658	−0.954079	−0.477039	−	0.878882i	$-0.658290\pi$
$97$	−9.39658	−0.954079	−0.477039	+	0.878882i	$0.658290\pi$
$98$	−10.0139	−1.01155
$99$	−3.40975	−0.342692
$100$	−9.97199	−0.997199
$101$	−7.17473	−0.713912	−0.356956	−	0.934121i	$-0.616185\pi$
$101$	−7.17473	−0.713912	−0.356956	+	0.934121i	$0.616185\pi$
$102$	10.5828	1.04785
$103$	−4.01150	−0.395265	−0.197633	−	0.980276i	$-0.563325\pi$
$103$	−4.01150	−0.395265	−0.197633	+	0.980276i	$0.563325\pi$
$104$	−0.0185873	−0.00182264
$105$	−0.00247654	−0.000241686 0
$106$	5.74349	0.557857
$107$	−18.4070	−1.77947	−0.889734	−	0.456480i	$-0.849110\pi$
$107$	−18.4070	−1.77947	−0.889734	+	0.456480i	$0.849110\pi$
$108$	9.06108	0.871903
$109$	−10.9592	−1.04970	−0.524849	−	0.851195i	$-0.675878\pi$
$109$	−10.9592	−1.04970	−0.524849	+	0.851195i	$0.675878\pi$
$110$	0.00614260	0.000585674 0
$111$	4.07373	0.386661
$112$	−5.65783	−0.534614
$113$	−14.0917	−1.32564	−0.662818	−	0.748781i	$-0.730640\pi$
$113$	−14.0917	−1.32564	−0.662818	+	0.748781i	$0.730640\pi$
$114$	−1.72904	−0.161940
$115$	0.00579544	0.000540427 0
$116$	−6.89272	−0.639973
$117$	−3.73912	−0.345682
$118$	4.71397	0.433956
$119$	−8.63323	−0.791407
$120$	1.96515e−5 0	1.79393e−6 0
$121$	−8.70660	−0.791509
$122$	−18.3735	−1.66346
$123$	4.36546	0.393621
$124$	−10.3629	−0.930619
$125$	−0.0202949	−0.00181523
$126$	−6.34727	−0.565460
$127$	10.0127	0.888485	0.444243	−	0.895906i	$-0.353473\pi$
$127$	10.0127	0.888485	0.444243	+	0.895906i	$0.353473\pi$
$128$	0.0895402	0.00791431
$129$	−3.57023	−0.314341
$130$	0.00673596	0.000590783 0
$131$	−10.5639	−0.922970	−0.461485	−	0.887148i	$-0.652683\pi$
$131$	−10.5639	−0.922970	−0.461485	+	0.887148i	$0.652683\pi$
$132$	−2.61295	−0.227429
$133$	1.41052	0.122307
$134$	−17.6757	−1.52695
$135$	0.00922051	0.000793575 0
$136$	0.0685053	0.00587428
$137$	−1.89531	−0.161927	−0.0809637	−	0.996717i	$-0.525800\pi$
$137$	−1.89531	−0.161927	−0.0809637	+	0.996717i	$0.525800\pi$
$138$	−4.93748	−0.420306
$139$	−12.7161	−1.07857	−0.539284	−	0.842124i	$-0.681305\pi$
$139$	−12.7161	−1.07857	−0.539284	+	0.842124i	$0.681305\pi$
$140$	0.00570924	0.000482519 0
$141$	−5.11728	−0.430953
$142$	16.0912	1.35034
$143$	2.51493	0.210309
$144$	9.03137	0.752614
$145$	−0.00701400	−0.000582481 0
$146$	−17.4540	−1.44450
$147$	4.33467	0.357517
$148$	−9.39127	−0.771958
$149$	−8.25337	−0.676142	−0.338071	−	0.941121i	$-0.609774\pi$
$149$	−8.25337	−0.676142	−0.338071	+	0.941121i	$0.609774\pi$
$150$	8.64521	0.705878
$151$	13.1772	1.07234	0.536171	−	0.844109i	$-0.319870\pi$
$151$	13.1772	1.07234	0.536171	+	0.844109i	$0.319870\pi$
$152$	−0.0111926	−0.000907837 0
$153$	13.7809	1.11412
$154$	4.26918	0.344020
$155$	−0.0105453	−0.000847016 0
$156$	−2.86536	−0.229412
$157$	21.0781	1.68222	0.841109	−	0.540866i	$-0.181903\pi$
$157$	21.0781	1.68222	0.841109	+	0.540866i	$0.181903\pi$
$158$	16.6343	1.32335
$159$	−2.48616	−0.197166
$160$	−0.0162244	−0.00128265
$161$	4.02789	0.317442
$162$	5.64437	0.443463
$163$	7.44347	0.583018	0.291509	−	0.956568i	$-0.405843\pi$
$163$	7.44347	0.583018	0.291509	+	0.956568i	$0.405843\pi$
$164$	−10.0638	−0.785852
$165$	−0.00265893	−0.000206997 0
$166$	−3.81869	−0.296388
$167$	18.9875	1.46930	0.734650	−	0.678447i	$-0.237347\pi$
$167$	18.9875	1.46930	0.734650	+	0.678447i	$0.237347\pi$
$168$	0.0136580	0.00105374
$169$	−10.2421	−0.787856
$170$	−0.0248261	−0.00190407
$171$	−2.25155	−0.172181
$172$	8.23054	0.627573
$173$	−0.913664	−0.0694646	−0.0347323	−	0.999397i	$-0.511058\pi$
$173$	−0.913664	−0.0694646	−0.0347323	+	0.999397i	$0.511058\pi$
$174$	5.97564	0.453012
$175$	−7.05259	−0.533125
$176$	−6.07450	−0.457883
$177$	−2.04052	−0.153375
$178$	26.6398	1.99674
$179$	10.1678	0.759977	0.379988	−	0.924991i	$-0.375928\pi$
$179$	10.1678	0.759977	0.379988	+	0.924991i	$0.375928\pi$
$180$	−0.00911343	−0.000679275 0
$181$	−14.6675	−1.09023	−0.545113	−	0.838362i	$-0.683513\pi$
$181$	−14.6675	−1.09023	−0.545113	+	0.838362i	$0.683513\pi$
$182$	4.68157	0.347021
$183$	7.95328	0.587923
$184$	−0.0319616	−0.00235624
$185$	−0.00955651	−0.000702609 0
$186$	8.98413	0.658749
$187$	−9.26903	−0.677819
$188$	11.7970	0.860384
$189$	6.40836	0.466139
$190$	0.00405614	0.000294263 0
$191$	4.69892	0.340002	0.170001	−	0.985444i	$-0.445623\pi$
$191$	4.69892	0.340002	0.170001	+	0.985444i	$0.445623\pi$
$192$	6.88221	0.496680
$193$	−0.0586710	−0.00422323	−0.00211161	−	0.999998i	$-0.500672\pi$
$193$	−0.0586710	−0.00422323	−0.00211161	+	0.999998i	$0.500672\pi$
$194$	−18.7800	−1.34833
$195$	−0.00291578	−0.000208803 0
$196$	−9.99282	−0.713773
$197$	4.56810	0.325464	0.162732	−	0.986670i	$-0.447969\pi$
$197$	4.56810	0.325464	0.162732	+	0.986670i	$0.447969\pi$
$198$	−6.81472	−0.484301
$199$	15.8215	1.12156	0.560779	−	0.827965i	$-0.310502\pi$
$199$	15.8215	1.12156	0.560779	+	0.827965i	$0.310502\pi$
$200$	0.0559628	0.00395717
$201$	7.65124	0.539677
$202$	−14.3394	−1.00892
$203$	−4.87481	−0.342144
$204$	10.5606	0.739387
$205$	−0.0102409	−0.000715254 0
$206$	−8.01739	−0.558598
$207$	−6.42957	−0.446886
$208$	−6.66128	−0.461877
$209$	1.51440	0.104753
$210$	−0.00494962	−0.000341556 0
$211$	1.00000	0.0688428
$211$	1.00000	0.0688428
$212$	5.73142	0.393635
$213$	−6.96535	−0.477258
$214$	−36.7881	−2.51479
$215$	0.00837536	0.000571195 0
$216$	−0.0508508	−0.00345996
$217$	−7.32907	−0.497530
$218$	−21.9030	−1.48346
$219$	7.55524	0.510536
$220$	0.00612969	0.000413264 0
$221$	−10.1644	−0.683732
$222$	8.14176	0.546439
$223$	−20.0085	−1.33987	−0.669934	−	0.742421i	$-0.733678\pi$
$223$	−20.0085	−1.33987	−0.669934	+	0.742421i	$0.733678\pi$
$224$	−11.2762	−0.753420
$225$	11.2578	0.750518
$226$	−28.1637	−1.87342
$227$	0.529099	0.0351175	0.0175588	−	0.999846i	$-0.494411\pi$
$227$	0.529099	0.0351175	0.0175588	+	0.999846i	$0.494411\pi$
$228$	−1.72541	−0.114268
$229$	28.3818	1.87552	0.937761	−	0.347280i	$-0.112895\pi$
$229$	28.3818	1.87552	0.937761	+	0.347280i	$0.112895\pi$
$230$	0.0115828	0.000763744 0
$231$	−1.84798	−0.121588
$232$	0.0386819	0.00253959
$233$	−19.4798	−1.27617	−0.638084	−	0.769967i	$-0.720273\pi$
$233$	−19.4798	−1.27617	−0.638084	+	0.769967i	$0.720273\pi$
$234$	−7.47300	−0.488526
$235$	0.0120046	0.000783091 0
$236$	4.70407	0.306209
$237$	−7.20042	−0.467718
$238$	−17.2544	−1.11844
$239$	−19.1566	−1.23914	−0.619570	−	0.784942i	$-0.712693\pi$
$239$	−19.1566	−1.23914	−0.619570	+	0.784942i	$0.712693\pi$
$240$	0.00704268	0.000454603 0
$241$	15.7228	1.01279	0.506396	−	0.862301i	$-0.330977\pi$
$241$	15.7228	1.01279	0.506396	+	0.862301i	$0.330977\pi$
$242$	−17.4010	−1.11858
$243$	−16.0731	−1.03109
$244$	−18.3349	−1.17377
$245$	−0.0101686	−0.000649650 0
$246$	8.72481	0.556274
$247$	1.66068	0.105667
$248$	0.0581567	0.00369296
$249$	1.65298	0.104754
$250$	−0.0405614	−0.00256533
$251$	17.7020	1.11734	0.558671	−	0.829389i	$-0.311311\pi$
$251$	17.7020	1.11734	0.558671	+	0.829389i	$0.311311\pi$
$252$	−6.33393	−0.399000
$253$	4.32453	0.271881
$254$	20.0114	1.25563
$255$	0.0107464	0.000672964 0
$256$	16.0892	1.00558
$257$	−24.3166	−1.51682	−0.758412	−	0.651775i	$-0.774025\pi$
$257$	−24.3166	−1.51682	−0.758412	+	0.651775i	$0.774025\pi$
$258$	−7.13546	−0.444234
$259$	−6.64188	−0.412706
$260$	0.00672181	0.000416869 0
$261$	7.78146	0.481660
$262$	−21.1130	−1.30436
$263$	3.05559	0.188416	0.0942078	−	0.995553i	$-0.469968\pi$
$263$	3.05559	0.188416	0.0942078	+	0.995553i	$0.469968\pi$
$264$	0.0146639	0.000902500 0
$265$	0.00583226	0.000358273 0
$266$	2.81906	0.172848
$267$	−11.5315	−0.705716
$268$	−17.6386	−1.07745
$269$	21.1381	1.28881	0.644406	−	0.764683i	$-0.277105\pi$
$269$	21.1381	1.28881	0.644406	+	0.764683i	$0.277105\pi$
$270$	0.0184281	0.00112150
$271$	−7.55650	−0.459025	−0.229512	−	0.973306i	$-0.573713\pi$
$271$	−7.55650	−0.459025	−0.229512	+	0.973306i	$0.573713\pi$
$272$	24.5508	1.48861
$273$	−2.02650	−0.122649
$274$	−3.78797	−0.228840
$275$	−7.57198	−0.456607
$276$	−4.92710	−0.296577
$277$	21.1633	1.27158	0.635789	−	0.771863i	$-0.280675\pi$
$277$	21.1633	1.27158	0.635789	+	0.771863i	$0.280675\pi$
$278$	−25.4145	−1.52426
$279$	11.6991	0.700408
$280$	−3.20402e−5 0	−1.91477e−6 0
$281$	−11.4575	−0.683499	−0.341749	−	0.939791i	$-0.611019\pi$
$281$	−11.4575	−0.683499	−0.341749	+	0.939791i	$0.611019\pi$
$282$	−10.2274	−0.609032
$283$	14.7434	0.876405	0.438203	−	0.898876i	$-0.355615\pi$
$283$	14.7434	0.876405	0.438203	+	0.898876i	$0.355615\pi$
$284$	16.0574	0.952831
$285$	−0.00175577	−0.000104003 0
$286$	5.02635	0.297214
$287$	−7.11752	−0.420134
$288$	17.9997	1.06064
$289$	20.4619	1.20364
$290$	−0.0140182	−0.000823175 0
$291$	8.12924	0.476545
$292$	−17.4173	−1.01927
$293$	−11.1077	−0.648918	−0.324459	−	0.945900i	$-0.605182\pi$
$293$	−11.1077	−0.648918	−0.324459	+	0.945900i	$0.605182\pi$
$294$	8.66326	0.505252
$295$	0.00478684	0.000278700 0
$296$	0.0527038	0.00306335
$297$	6.88030	0.399236
$298$	−16.4952	−0.955540
$299$	4.74227	0.274252
$300$	8.62704	0.498083
$301$	5.82096	0.335515
$302$	26.3359	1.51546
$303$	6.20705	0.356586
$304$	−4.01117	−0.230056
$305$	−0.0186575	−0.00106832
$306$	27.5425	1.57450
$307$	5.46652	0.311991	0.155995	−	0.987758i	$-0.450142\pi$
$307$	5.46652	0.311991	0.155995	+	0.987758i	$0.450142\pi$
$308$	4.26021	0.242748
$309$	3.47046	0.197428
$310$	−0.0210758	−0.00119702
$311$	16.6242	0.942673	0.471336	−	0.881954i	$-0.343772\pi$
$311$	16.6242	0.942673	0.471336	+	0.881954i	$0.343772\pi$
$312$	0.0160804	0.000910373 0
$313$	−12.0316	−0.680066	−0.340033	−	0.940413i	$-0.610438\pi$
$313$	−12.0316	−0.680066	−0.340033	+	0.940413i	$0.610438\pi$
$314$	42.1267	2.37735
$315$	−0.00644538	−0.000363156 0
$316$	16.5993	0.933785
$317$	−24.4838	−1.37515	−0.687574	−	0.726114i	$-0.741324\pi$
$317$	−24.4838	−1.37515	−0.687574	+	0.726114i	$0.741324\pi$
$318$	−4.96885	−0.278639
$319$	−5.23381	−0.293037
$320$	−0.0161449	−0.000902526 0
$321$	15.9244	0.888811
$322$	8.05014	0.448617
$323$	−6.12061	−0.340560
$324$	5.63251	0.312917
$325$	−8.30341	−0.460590
$326$	14.8765	0.823934
$327$	9.48108	0.524305
$328$	0.0564781	0.00311848
$329$	8.34330	0.459981
$330$	−0.00531413	−0.000292533 0
$331$	25.9291	1.42519	0.712595	−	0.701576i	$-0.247520\pi$
$331$	25.9291	1.42519	0.712595	+	0.701576i	$0.247520\pi$
$332$	−3.81066	−0.209137
$333$	10.6022	0.580995
$334$	37.9485	2.07645
$335$	−0.0179489	−0.000980655 0
$336$	4.89474	0.267030
$337$	0.800565	0.0436095	0.0218048	−	0.999762i	$-0.493059\pi$
$337$	0.800565	0.0436095	0.0218048	+	0.999762i	$0.493059\pi$
$338$	−20.4699	−1.11342
$339$	12.1911	0.662131
$340$	−0.0247739	−0.00134355
$341$	−7.86883	−0.426121
$342$	−4.49996	−0.243330
$343$	−16.9409	−0.914725
$344$	−0.0461898	−0.00249039
$345$	−0.00501379	−0.000269933 0
$346$	−1.82605	−0.0981690
$347$	0.406776	0.0218369	0.0109184	−	0.999940i	$-0.496524\pi$
$347$	0.406776	0.0218369	0.0109184	+	0.999940i	$0.496524\pi$
$348$	5.96308	0.319655
$349$	−15.2671	−0.817231	−0.408615	−	0.912707i	$-0.633988\pi$
$349$	−15.2671	−0.817231	−0.408615	+	0.912707i	$0.633988\pi$
$350$	−14.0953	−0.753425
$351$	7.54492	0.402718
$352$	−12.1066	−0.645284
$353$	17.0149	0.905612	0.452806	−	0.891609i	$-0.350423\pi$
$353$	17.0149	0.905612	0.452806	+	0.891609i	$0.350423\pi$
$354$	−4.07819	−0.216753
$355$	0.0163399	0.000867233 0
$356$	26.5838	1.40894
$357$	7.46885	0.395293
$358$	20.3214	1.07402
$359$	−8.94398	−0.472045	−0.236023	−	0.971748i	$-0.575844\pi$
$359$	−8.94398	−0.472045	−0.236023	+	0.971748i	$0.575844\pi$
$360$	5.11445e−5 0	2.69555e−6 0
$361$	1.00000	0.0526316
$362$	−29.3145	−1.54073
$363$	7.53232	0.395344
$364$	4.67173	0.244865
$365$	−0.0177237	−0.000927702 0
$366$	15.8954	0.830867
$367$	7.79856	0.407081	0.203541	−	0.979066i	$-0.434755\pi$
$367$	7.79856	0.407081	0.203541	+	0.979066i	$0.434755\pi$
$368$	−11.4543	−0.597099
$369$	11.3614	0.591452
$370$	−0.0190996	−0.000992943 0
$371$	4.05348	0.210446
$372$	8.96526	0.464827
$373$	0.755831	0.0391355	0.0195677	−	0.999809i	$-0.493771\pi$
$373$	0.755831	0.0391355	0.0195677	+	0.999809i	$0.493771\pi$
$374$	−18.5251	−0.957909
$375$	0.0175577	0.000906674 0
$376$	−0.0662047	−0.00341425
$377$	−5.73939	−0.295593
$378$	12.8077	0.658759
$379$	18.4089	0.945599	0.472800	−	0.881170i	$-0.343243\pi$
$379$	18.4089	0.945599	0.472800	+	0.881170i	$0.343243\pi$
$380$	0.00404762	0.000207638 0
$381$	−8.66228	−0.443782
$382$	9.39126	0.480499
$383$	−37.4725	−1.91476	−0.957378	−	0.288838i	$-0.906731\pi$
$383$	−37.4725	−1.91476	−0.957378	+	0.288838i	$0.906731\pi$
$384$	−0.0774637	−0.00395305
$385$	0.00433516	0.000220940 0
$386$	−0.117260	−0.00596836
$387$	−9.29178	−0.472328
$388$	−18.7405	−0.951407
$389$	11.6662	0.591501	0.295751	−	0.955265i	$-0.404430\pi$
$389$	11.6662	0.591501	0.295751	+	0.955265i	$0.404430\pi$
$390$	−0.00582747	−0.000295085 0
$391$	−17.4781	−0.883905
$392$	0.0560797	0.00283245
$393$	9.13910	0.461007
$394$	9.12981	0.459953
$395$	0.0168914	0.000849897 0
$396$	−6.80040	−0.341733
$397$	2.96493	0.148805	0.0744027	−	0.997228i	$-0.476295\pi$
$397$	2.96493	0.148805	0.0744027	+	0.997228i	$0.476295\pi$
$398$	31.6209	1.58501
$399$	−1.22028	−0.0610903
$400$	20.0558	1.00279
$401$	32.5293	1.62444	0.812218	−	0.583354i	$-0.198260\pi$
$401$	32.5293	1.62444	0.812218	+	0.583354i	$0.198260\pi$
$402$	15.2918	0.762683
$403$	−8.62894	−0.429838
$404$	−14.3093	−0.711913
$405$	0.00573161	0.000284806 0
$406$	−9.74278	−0.483526
$407$	−7.13102	−0.353472
$408$	−0.0592658	−0.00293410
$409$	29.0281	1.43535	0.717673	−	0.696381i	$-0.245207\pi$
$409$	29.0281	1.43535	0.717673	+	0.696381i	$0.245207\pi$
$410$	−0.0204674	−0.00101081
$411$	1.63969	0.0808797
$412$	−8.00054	−0.394158
$413$	3.32690	0.163706
$414$	−12.8501	−0.631549
$415$	−0.00387771	−0.000190349 0
$416$	−13.2761	−0.650913
$417$	11.0011	0.538725
$418$	3.02667	0.148039
$419$	−33.1731	−1.62061	−0.810307	−	0.586006i	$-0.800700\pi$
$419$	−33.1731	−1.62061	−0.810307	+	0.586006i	$0.800700\pi$
$420$	−0.00493922	−0.000241009 0
$421$	−4.26475	−0.207851	−0.103926	−	0.994585i	$-0.533140\pi$
$421$	−4.26475	−0.207851	−0.103926	+	0.994585i	$0.533140\pi$
$422$	1.99860	0.0972903
$423$	−13.3181	−0.647547
$424$	−0.0321647	−0.00156206
$425$	30.6030	1.48447
$426$	−13.9209	−0.674472
$427$	−12.9672	−0.627525
$428$	−36.7108	−1.77449
$429$	−2.17574	−0.105046
$430$	0.0167390	0.000807225 0
$431$	36.0282	1.73542	0.867709	−	0.497073i	$-0.165592\pi$
$431$	36.0282	1.73542	0.867709	+	0.497073i	$0.165592\pi$
$432$	−18.2238	−0.876793
$433$	36.6865	1.76304	0.881521	−	0.472145i	$-0.156520\pi$
$433$	36.6865	1.76304	0.881521	+	0.472145i	$0.156520\pi$
$434$	−14.6479	−0.703121
$435$	0.00606800	0.000290938 0
$436$	−21.8570	−1.04676
$437$	2.85561	0.136602
$438$	15.0999	0.721501
$439$	18.4095	0.878640	0.439320	−	0.898331i	$-0.355219\pi$
$439$	18.4095	0.878640	0.439320	+	0.898331i	$0.355219\pi$
$440$	−3.43998e−5 0	−1.63995e−6 0
$441$	11.2813	0.537204
$442$	−20.3146	−0.966265
$443$	−20.6161	−0.979501	−0.489750	−	0.871863i	$-0.662912\pi$
$443$	−20.6161	−0.979501	−0.489750	+	0.871863i	$0.662912\pi$
$444$	8.12465	0.385579
$445$	0.0270516	0.00128237
$446$	−39.9890	−1.89353
$447$	7.14022	0.337721
$448$	−11.2209	−0.530136
$449$	−36.5225	−1.72360	−0.861801	−	0.507247i	$-0.830663\pi$
$449$	−36.5225	−1.72360	−0.861801	+	0.507247i	$0.830663\pi$
$450$	22.4998	1.06065
$451$	−7.64170	−0.359833
$452$	−28.1045	−1.32192
$453$	−11.3999	−0.535615
$454$	1.05746	0.0496289
$455$	0.00475393	0.000222868 0
$456$	0.00968299	0.000453448 0
$457$	38.6043	1.80583	0.902916	−	0.429817i	$-0.141422\pi$
$457$	38.6043	1.80583	0.902916	+	0.429817i	$0.141422\pi$
$458$	56.7239	2.65053
$459$	−27.8076	−1.29795
$460$	0.0115584	0.000538914 0
$461$	−38.1354	−1.77614	−0.888070	−	0.459707i	$-0.847954\pi$
$461$	−38.1354	−1.77614	−0.888070	+	0.459707i	$0.847954\pi$
$462$	−3.69338	−0.171832
$463$	35.8435	1.66579	0.832895	−	0.553431i	$-0.186682\pi$
$463$	35.8435	1.66579	0.832895	+	0.553431i	$0.186682\pi$
$464$	13.8628	0.643562
$465$	0.00912300	0.000423069 0
$466$	−38.9324	−1.80351
$467$	22.1975	1.02718	0.513588	−	0.858037i	$-0.328316\pi$
$467$	22.1975	1.02718	0.513588	+	0.858037i	$0.328316\pi$
$468$	−7.45730	−0.344714
$469$	−12.4747	−0.576028
$470$	0.0239923	0.00110668
$471$	−18.2353	−0.840237
$472$	−0.0263992	−0.00121512
$473$	6.24965	0.287359
$474$	−14.3908	−0.660990
$475$	−5.00000	−0.229416
$476$	−17.2181	−0.789191
$477$	−6.47042	−0.296260
$478$	−38.2864	−1.75118
$479$	9.55810	0.436721	0.218360	−	0.975868i	$-0.429929\pi$
$479$	9.55810	0.436721	0.218360	+	0.975868i	$0.429929\pi$
$480$	0.0140362	0.000640662 0
$481$	−7.81986	−0.356555
$482$	31.4235	1.43130
$483$	−3.48464	−0.158557
$484$	−17.3644	−0.789293
$485$	−0.0190703	−0.000865937 0
$486$	−32.1236	−1.45716
$487$	34.3506	1.55658	0.778288	−	0.627908i	$-0.216089\pi$
$487$	34.3506	1.55658	0.778288	+	0.627908i	$0.216089\pi$
$488$	0.102895	0.00465785
$489$	−6.43955	−0.291207
$490$	−0.0203230	−0.000918101 0
$491$	−29.7480	−1.34251	−0.671254	−	0.741227i	$-0.734244\pi$
$491$	−29.7480	−1.34251	−0.671254	+	0.741227i	$0.734244\pi$
$492$	8.70648	0.392518
$493$	21.1531	0.952686
$494$	3.31904	0.149331
$495$	−0.00692005	−0.000311033 0
$496$	20.8421	0.935838
$497$	11.3564	0.509405
$498$	3.30365	0.148040
$499$	−2.21105	−0.0989803	−0.0494902	−	0.998775i	$-0.515760\pi$
$499$	−2.21105	−0.0989803	−0.0494902	+	0.998775i	$0.515760\pi$
$500$	−0.0404761	−0.00181015
$501$	−16.4266	−0.733888
$502$	35.3793	1.57905
$503$	−11.4454	−0.510323	−0.255162	−	0.966898i	$-0.582129\pi$
$503$	−11.4454	−0.510323	−0.255162	+	0.966898i	$0.582129\pi$
$504$	0.0355460	0.00158335
$505$	−0.0145610	−0.000647958 0
$506$	8.64300	0.384228
$507$	8.86075	0.393520
$508$	19.9694	0.885998
$509$	−18.5361	−0.821598	−0.410799	−	0.911726i	$-0.634750\pi$
$509$	−18.5361	−0.821598	−0.410799	+	0.911726i	$0.634750\pi$
$510$	0.0214777	0.000951048 0
$511$	−12.3182	−0.544924
$512$	31.9768	1.41319
$513$	4.54326	0.200590
$514$	−48.5990	−2.14361
$515$	−0.00814131	−0.000358749 0
$516$	−7.12047	−0.313461
$517$	8.95774	0.393961
$518$	−13.2745	−0.583246
$519$	0.790436	0.0346963
$520$	−3.77228e−5 0	−1.65425e−6 0
$521$	30.4625	1.33459	0.667293	−	0.744795i	$-0.267453\pi$
$521$	30.4625	1.33459	0.667293	+	0.744795i	$0.267453\pi$
$522$	15.5520	0.680693
$523$	−37.4169	−1.63612	−0.818062	−	0.575130i	$-0.804952\pi$
$523$	−37.4169	−1.63612	−0.818062	+	0.575130i	$0.804952\pi$
$524$	−21.0686	−0.920386
$525$	6.10139	0.266286
$526$	6.10690	0.266273
$527$	31.8028	1.38535
$528$	5.25522	0.228704
$529$	−14.8455	−0.645456
$530$	0.0116564	0.000506320 0
$531$	−5.31060	−0.230461
$532$	2.81314	0.121965
$533$	−8.37987	−0.362972
$534$	−23.0468	−0.997334
$535$	−0.0373568	−0.00161507
$536$	0.0989877	0.00427562
$537$	−8.79644	−0.379594
$538$	42.2466	1.82138
$539$	−7.58779	−0.326829
$540$	0.0183894	0.000791353 0
$541$	3.39180	0.145825	0.0729125	−	0.997338i	$-0.476771\pi$
$541$	3.39180	0.145825	0.0729125	+	0.997338i	$0.476771\pi$
$542$	−15.1024	−0.648704
$543$	12.6893	0.544548
$544$	48.9302	2.09787
$545$	−0.0222415	−0.000952723 0
$546$	−4.05015	−0.173331
$547$	−3.88662	−0.166180	−0.0830898	−	0.996542i	$-0.526479\pi$
$547$	−3.88662	−0.166180	−0.0830898	+	0.996542i	$0.526479\pi$
$548$	−3.78001	−0.161474
$549$	20.6990	0.883410
$550$	−15.1333	−0.645288
$551$	−3.45604	−0.147232
$552$	0.0276509	0.00117690
$553$	11.7397	0.499223
$554$	42.2969	1.79702
$555$	0.00826760	0.000350940 0
$556$	−25.3611	−1.07555
$557$	−9.02011	−0.382194	−0.191097	−	0.981571i	$-0.561205\pi$
$557$	−9.02011	−0.382194	−0.191097	+	0.981571i	$0.561205\pi$
$558$	23.3818	0.989832
$559$	6.85335	0.289866
$560$	−0.0114825	−0.000485225 0
$561$	8.01889	0.338558
$562$	−22.8990	−0.965936
$563$	−20.1737	−0.850219	−0.425109	−	0.905142i	$-0.639764\pi$
$563$	−20.1737	−0.850219	−0.425109	+	0.905142i	$0.639764\pi$
$564$	−10.2059	−0.429746
$565$	−0.0285990	−0.00120317
$566$	29.4662	1.23856
$567$	3.98353	0.167293
$568$	−0.0901141	−0.00378110
$569$	−5.34787	−0.224195	−0.112097	−	0.993697i	$-0.535757\pi$
$569$	−5.34787	−0.224195	−0.112097	+	0.993697i	$0.535757\pi$
$570$	−0.00350908	−0.000146979 0
$571$	−17.7765	−0.743923	−0.371961	−	0.928248i	$-0.621315\pi$
$571$	−17.7765	−0.743923	−0.371961	+	0.928248i	$0.621315\pi$
$572$	5.01578	0.209720
$573$	−4.06516	−0.169825
$574$	−14.2251	−0.593743
$575$	−14.2780	−0.595436
$576$	17.9114	0.746309
$577$	−35.7474	−1.48819	−0.744093	−	0.668076i	$-0.767118\pi$
$577$	−35.7474	−1.48819	−0.744093	+	0.668076i	$0.767118\pi$
$578$	40.8951	1.70101
$579$	0.0507579	0.00210942
$580$	−0.0139887	−0.000580850 0
$581$	−2.69505	−0.111810
$582$	16.2471	0.673464
$583$	4.35200	0.180242
$584$	0.0977457	0.00404475
$585$	−0.00758851	−0.000313746 0
$586$	−22.1998	−0.917067
$587$	3.99876	0.165047	0.0825233	−	0.996589i	$-0.473702\pi$
$587$	3.99876	0.165047	0.0825233	+	0.996589i	$0.473702\pi$
$588$	8.64506	0.356516
$589$	−5.19602	−0.214098
$590$	0.00956697	0.000393866 0
$591$	−3.95199	−0.162563
$592$	18.8879	0.776287
$593$	2.24462	0.0921754	0.0460877	−	0.998937i	$-0.485325\pi$
$593$	2.24462	0.0921754	0.0460877	+	0.998937i	$0.485325\pi$
$594$	13.7510	0.564209
$595$	−0.0175211	−0.000718294 0
$596$	−16.4605	−0.674249
$597$	−13.6876	−0.560198
$598$	9.47789	0.387580
$599$	40.7965	1.66690	0.833450	−	0.552595i	$-0.186362\pi$
$599$	40.7965	1.66690	0.833450	+	0.552595i	$0.186362\pi$
$600$	−0.0484149	−0.00197653
$601$	−42.1479	−1.71925	−0.859624	−	0.510928i	$-0.829302\pi$
$601$	−42.1479	−1.71925	−0.859624	+	0.510928i	$0.829302\pi$
$602$	11.6338	0.474157
$603$	19.9129	0.810915
$604$	26.2805	1.06934
$605$	−0.0176700	−0.000718386 0
$606$	12.4054	0.503935
$607$	−5.33843	−0.216680	−0.108340	−	0.994114i	$-0.534554\pi$
$607$	−5.33843	−0.216680	−0.108340	+	0.994114i	$0.534554\pi$
$608$	−7.99434	−0.324213
$609$	4.21733	0.170895
$610$	−0.0372888	−0.00150978
$611$	9.82304	0.397398
$612$	27.4846	1.11100
$613$	−41.0284	−1.65712	−0.828562	−	0.559898i	$-0.810840\pi$
$613$	−41.0284	−1.65712	−0.828562	+	0.559898i	$0.810840\pi$
$614$	10.9254	0.440912
$615$	0.00885967	0.000357256 0
$616$	−0.0239083	−0.000963291 0
$617$	−8.58964	−0.345806	−0.172903	−	0.984939i	$-0.555315\pi$
$617$	−8.58964	−0.345806	−0.172903	+	0.984939i	$0.555315\pi$
$618$	6.93606	0.279009
$619$	12.2527	0.492478	0.246239	−	0.969209i	$-0.420805\pi$
$619$	12.2527	0.492478	0.246239	+	0.969209i	$0.420805\pi$
$620$	−0.0210315	−0.000844644 0
$621$	12.9738	0.520621
$622$	33.2251	1.33221
$623$	18.8011	0.753252
$624$	5.76286	0.230699
$625$	24.9999	0.999998
$626$	−24.0463	−0.961085
$627$	−1.31015	−0.0523222
$628$	42.0382	1.67751
$629$	28.8209	1.14916
$630$	−0.0128817	−0.000513220 0
$631$	18.5636	0.739007	0.369503	−	0.929229i	$-0.379528\pi$
$631$	18.5636	0.739007	0.369503	+	0.929229i	$0.379528\pi$
$632$	−0.0931553	−0.00370552
$633$	−0.865127	−0.0343857
$634$	−48.9334	−1.94339
$635$	0.0203207	0.000806403 0
$636$	−4.95841	−0.196614
$637$	−8.32075	−0.329680
$638$	−10.4603	−0.414127
$639$	−18.1278	−0.717125
$640$	0.000181721 0	7.18315e−6 0
$641$	−15.8190	−0.624812	−0.312406	−	0.949949i	$-0.601135\pi$
$641$	−15.8190	−0.624812	−0.312406	+	0.949949i	$0.601135\pi$
$642$	31.8264	1.25609
$643$	4.14733	0.163555	0.0817774	−	0.996651i	$-0.473940\pi$
$643$	4.14733	0.163555	0.0817774	+	0.996651i	$0.473940\pi$
$644$	8.03323	0.316554
$645$	−0.00724575	−0.000285301 0
$646$	−12.2327	−0.481287
$647$	20.3051	0.798277	0.399138	−	0.916891i	$-0.369309\pi$
$647$	20.3051	0.798277	0.399138	+	0.916891i	$0.369309\pi$
$648$	−0.0316096	−0.00124174
$649$	3.57191	0.140210
$650$	−16.5952	−0.650917
$651$	6.34058	0.248507
$652$	14.8453	0.581385
$653$	−17.0462	−0.667068	−0.333534	−	0.942738i	$-0.608241\pi$
$653$	−17.0462	−0.667068	−0.333534	+	0.942738i	$0.608241\pi$
$654$	18.9489	0.740960
$655$	−0.0214393	−0.000837702 0
$656$	20.2405	0.790259
$657$	19.6630	0.767128
$658$	16.6749	0.650056
$659$	−4.00366	−0.155960	−0.0779802	−	0.996955i	$-0.524847\pi$
$659$	−4.00366	−0.155960	−0.0779802	+	0.996955i	$0.524847\pi$
$660$	−0.00530297	−0.000206418 0
$661$	29.4541	1.14563	0.572817	−	0.819683i	$-0.305851\pi$
$661$	29.4541	1.14563	0.572817	+	0.819683i	$0.305851\pi$
$662$	51.8218	2.01411
$663$	8.79350	0.341511
$664$	0.0213854	0.000829916 0
$665$	0.00286263	0.000111008 0
$666$	21.1895	0.821076
$667$	−9.86910	−0.382133
$668$	37.8687	1.46518
$669$	17.3099	0.669239
$670$	−0.0358727	−0.00138588
$671$	−13.9221	−0.537458
$672$	9.75531	0.376319
$673$	−3.65867	−0.141031	−0.0705156	−	0.997511i	$-0.522464\pi$
$673$	−3.65867	−0.141031	−0.0705156	+	0.997511i	$0.522464\pi$
$674$	1.60001	0.0616300
$675$	−22.7163	−0.874351
$676$	−20.4269	−0.785650
$677$	36.9955	1.42185	0.710926	−	0.703267i	$-0.248276\pi$
$677$	36.9955	1.42185	0.710926	+	0.703267i	$0.248276\pi$
$678$	24.3652	0.935738
$679$	−13.2541	−0.508644
$680$	0.000139031 0	5.33159e−6 0
$681$	−0.457738	−0.0175405
$682$	−15.7266	−0.602204
$683$	−18.2637	−0.698841	−0.349421	−	0.936966i	$-0.613622\pi$
$683$	−18.2637	−0.698841	−0.349421	+	0.936966i	$0.613622\pi$
$684$	−4.49050	−0.171699
$685$	−0.00384652	−0.000146968 0
$686$	−33.8582	−1.29271
$687$	−24.5539	−0.936789
$688$	−16.5534	−0.631092
$689$	4.77240	0.181814
$690$	−0.0100206	−0.000381476 0
$691$	−14.3884	−0.547362	−0.273681	−	0.961821i	$-0.588241\pi$
$691$	−14.3884	−0.547362	−0.273681	+	0.961821i	$0.588241\pi$
$692$	−1.82221	−0.0692701
$693$	−4.80951	−0.182698
$694$	0.812981	0.0308604
$695$	−0.0258073	−0.000978926 0
$696$	−0.0334648	−0.00126848
$697$	30.8848	1.16985
$698$	−30.5129	−1.15493
$699$	16.8526	0.637422
$700$	−14.0657	−0.531633
$701$	−3.36935	−0.127259	−0.0636293	−	0.997974i	$-0.520268\pi$
$701$	−3.36935	−0.127259	−0.0636293	+	0.997974i	$0.520268\pi$
$702$	15.0793	0.569131
$703$	−4.70882	−0.177597
$704$	−12.0472	−0.454047
$705$	−0.0103855	−0.000391139 0
$706$	34.0060	1.27983
$707$	−10.1201	−0.380605
$708$	−4.06962	−0.152946
$709$	50.8254	1.90879	0.954395	−	0.298548i	$-0.0965024\pi$
$709$	50.8254	1.90879	0.954395	+	0.298548i	$0.0965024\pi$
$710$	0.0326570	0.00122559
$711$	−18.7396	−0.702790
$712$	−0.149188	−0.00559107
$713$	−14.8378	−0.555680
$714$	14.9272	0.558638
$715$	0.00510403	0.000190880 0
$716$	20.2786	0.757849
$717$	16.5729	0.618927
$718$	−17.8754	−0.667106
$719$	39.1049	1.45837	0.729183	−	0.684318i	$-0.239900\pi$
$719$	39.1049	1.45837	0.729183	+	0.684318i	$0.239900\pi$
$720$	0.0183291	0.000683084 0
$721$	−5.65830	−0.210726
$722$	1.99860	0.0743802
$723$	−13.6022	−0.505871
$724$	−29.2529	−1.08717
$725$	17.2802	0.641770
$726$	15.0541	0.558710
$727$	27.2621	1.01109	0.505547	−	0.862799i	$-0.331291\pi$
$727$	27.2621	1.01109	0.505547	+	0.862799i	$0.331291\pi$
$728$	−0.0262177	−0.000971694 0
$729$	5.43275	0.201213
$730$	−0.0354226	−0.00131105
$731$	−25.2587	−0.934227
$732$	15.8620	0.586277
$733$	15.3326	0.566323	0.283162	−	0.959072i	$-0.408617\pi$
$733$	15.3326	0.566323	0.283162	+	0.959072i	$0.408617\pi$
$734$	15.5862	0.575297
$735$	0.00879717	0.000324488 0
$736$	−22.8287	−0.841478
$737$	−13.3934	−0.493352
$738$	22.7069	0.835854
$739$	−1.17481	−0.0432162	−0.0216081	−	0.999767i	$-0.506879\pi$
$739$	−1.17481	−0.0432162	−0.0216081	+	0.999767i	$0.506879\pi$
$740$	−0.0190595	−0.000700641 0
$741$	−1.43670	−0.0527786
$742$	8.10129	0.297408
$743$	−49.9769	−1.83347	−0.916737	−	0.399492i	$-0.869186\pi$
$743$	−49.9769	−1.83347	−0.916737	+	0.399492i	$0.869186\pi$
$744$	−0.0503130	−0.00184456
$745$	−0.0167501	−0.000613678 0
$746$	1.51060	0.0553072
$747$	4.30200	0.157402
$748$	−18.4862	−0.675921
$749$	−25.9634	−0.948680
$750$	0.0350908	0.00128133
$751$	−2.06208	−0.0752464	−0.0376232	−	0.999292i	$-0.511979\pi$
$751$	−2.06208	−0.0752464	−0.0376232	+	0.999292i	$0.511979\pi$
$752$	−23.7263	−0.865209
$753$	−15.3145	−0.558092
$754$	−11.4707	−0.417740
$755$	0.0267429	0.000973275 0
$756$	12.7808	0.464834
$757$	−7.96453	−0.289476	−0.144738	−	0.989470i	$-0.546234\pi$
$757$	−7.96453	−0.289476	−0.144738	+	0.989470i	$0.546234\pi$
$758$	36.7919	1.33634
$759$	−3.74127	−0.135799
$760$	−2.27152e−5 0	−8.23967e−7 0
$761$	−8.12654	−0.294587	−0.147294	−	0.989093i	$-0.547056\pi$
$761$	−8.12654	−0.294587	−0.147294	+	0.989093i	$0.547056\pi$
$762$	−17.3124	−0.627163
$763$	−15.4581	−0.559622
$764$	9.37152	0.339050
$765$	0.0279682	0.00101119
$766$	−74.8926	−2.70598
$767$	3.91695	0.141433
$768$	−13.9192	−0.502267
$769$	28.7002	1.03495	0.517477	−	0.855697i	$-0.326871\pi$
$769$	28.7002	1.03495	0.517477	+	0.855697i	$0.326871\pi$
$770$	0.00866425	0.000312238 0
$771$	21.0369	0.757626
$772$	−0.117013	−0.00421140
$773$	28.5527	1.02697	0.513484	−	0.858099i	$-0.328355\pi$
$773$	28.5527	1.02697	0.513484	+	0.858099i	$0.328355\pi$
$774$	−18.5705	−0.667504
$775$	25.9801	0.933231
$776$	0.105172	0.00377545
$777$	5.74607	0.206139
$778$	23.3161	0.835923
$779$	−5.04603	−0.180793
$780$	−0.00581522	−0.000208218 0
$781$	12.1928	0.436292
$782$	−34.9317	−1.24916
$783$	−15.7017	−0.561133
$784$	20.0977	0.717775
$785$	0.0427779	0.00152681
$786$	18.2654	0.651505
$787$	22.3504	0.796707	0.398353	−	0.917232i	$-0.369582\pi$
$787$	22.3504	0.796707	0.398353	+	0.917232i	$0.369582\pi$
$788$	9.11062	0.324552
$789$	−2.64347	−0.0941101
$790$	0.0337591	0.00120109
$791$	−19.8766	−0.706731
$792$	0.0381638	0.00135609
$793$	−15.2670	−0.542146
$794$	5.92570	0.210295
$795$	−0.00504565	−0.000178951 0
$796$	31.5545	1.11842
$797$	17.2652	0.611565	0.305782	−	0.952101i	$-0.401082\pi$
$797$	17.2652	0.611565	0.305782	+	0.952101i	$0.401082\pi$
$798$	−2.43885	−0.0863342
$799$	−36.2038	−1.28080
$800$	39.9716	1.41321
$801$	−30.0115	−1.06040
$802$	65.0131	2.29569
$803$	−13.2254	−0.466713
$804$	15.2596	0.538165
$805$	0.00817457	0.000288116 0
$806$	−17.2458	−0.607457
$807$	−18.2871	−0.643738
$808$	0.0803036	0.00282507
$809$	−54.0044	−1.89869	−0.949346	−	0.314232i	$-0.898253\pi$
$809$	−54.0044	−1.89869	−0.949346	+	0.314232i	$0.898253\pi$
$810$	0.0114552	0.000402494 0
$811$	10.3579	0.363714	0.181857	−	0.983325i	$-0.441789\pi$
$811$	10.3579	0.363714	0.181857	+	0.983325i	$0.441789\pi$
$812$	−9.72231	−0.341186
$813$	6.53733	0.229274
$814$	−14.2521	−0.499534
$815$	0.0151065	0.000529156 0
$816$	−21.2396	−0.743534
$817$	4.12683	0.144379
$818$	58.0155	2.02846
$819$	−5.27410	−0.184292
$820$	−0.0204244	−0.000713251 0
$821$	−13.7628	−0.480326	−0.240163	−	0.970733i	$-0.577201\pi$
$821$	−13.7628	−0.480326	−0.240163	+	0.970733i	$0.577201\pi$
$822$	3.27707	0.114301
$823$	27.3296	0.952649	0.476325	−	0.879269i	$-0.341969\pi$
$823$	27.3296	0.952649	0.476325	+	0.879269i	$0.341969\pi$
$824$	0.0448990	0.00156413
$825$	6.55072	0.228067
$826$	6.64915	0.231353
$827$	−22.5931	−0.785638	−0.392819	−	0.919616i	$-0.628500\pi$
$827$	−22.5931	−0.785638	−0.392819	+	0.919616i	$0.628500\pi$
$828$	−12.8231	−0.445634
$829$	−30.8535	−1.07159	−0.535793	−	0.844350i	$-0.679987\pi$
$829$	−30.8535	−1.07159	−0.535793	+	0.844350i	$0.679987\pi$
$830$	−0.00774999	−0.000269006 0
$831$	−18.3089	−0.635129
$832$	−13.2110	−0.458008
$833$	30.6669	1.06255
$834$	21.9868	0.761339
$835$	0.0385350	0.00133356
$836$	3.02031	0.104460
$837$	−23.6069	−0.815973
$838$	−66.2998	−2.29029
$839$	−24.2159	−0.836027	−0.418013	−	0.908441i	$-0.637274\pi$
$839$	−24.2159	−0.836027	−0.418013	+	0.908441i	$0.637274\pi$
$840$	2.77189e−5 0	9.56392e−7 0
$841$	−17.0558	−0.588131
$842$	−8.52352	−0.293740
$843$	9.91222	0.341395
$844$	1.99440	0.0686501
$845$	−0.0207863	−0.000715071 0
$846$	−26.6175	−0.915129
$847$	−12.2808	−0.421974
$848$	−11.5271	−0.395843
$849$	−12.7549	−0.437748
$850$	61.1632	2.09788
$851$	−13.4466	−0.460942
$852$	−13.8917	−0.475922
$853$	47.5292	1.62737	0.813685	−	0.581306i	$-0.197458\pi$
$853$	47.5292	1.62737	0.813685	+	0.581306i	$0.197458\pi$
$854$	−25.9162	−0.886832
$855$	−0.00456951	−0.000156274 0
$856$	0.206021	0.00704166
$857$	35.8952	1.22616	0.613078	−	0.790022i	$-0.289931\pi$
$857$	35.8952	1.22616	0.613078	+	0.790022i	$0.289931\pi$
$858$	−4.34843	−0.148453
$859$	18.9386	0.646178	0.323089	−	0.946369i	$-0.395279\pi$
$859$	18.9386	0.646178	0.323089	+	0.946369i	$0.395279\pi$
$860$	0.0167038	0.000569595 0
$861$	6.15757	0.209849
$862$	72.0059	2.45253
$863$	−30.1979	−1.02795	−0.513974	−	0.857806i	$-0.671827\pi$
$863$	−30.1979	−1.02795	−0.513974	+	0.857806i	$0.671827\pi$
$864$	−36.3204	−1.23564
$865$	−0.00185427	−6.30472e−5 0
$866$	73.3217	2.49157
$867$	−17.7021	−0.601196
$868$	−14.6171	−0.496137
$869$	12.6043	0.427570
$870$	0.0121275	0.000411161 0
$871$	−14.6872	−0.497656
$872$	0.122661	0.00415384
$873$	21.1569	0.716053
$874$	5.70722	0.193050
$875$	−0.0286263	−0.000967746 0
$876$	15.0682	0.509106
$877$	38.0068	1.28340	0.641699	−	0.766956i	$-0.278230\pi$
$877$	38.0068	1.28340	0.641699	+	0.766956i	$0.278230\pi$
$878$	36.7933	1.24171
$879$	9.60957	0.324123
$880$	−0.0123281	−0.000415582 0
$881$	25.0615	0.844342	0.422171	−	0.906516i	$-0.361268\pi$
$881$	25.0615	0.844342	0.422171	+	0.906516i	$0.361268\pi$
$882$	22.5467	0.759189
$883$	30.5533	1.02820	0.514100	−	0.857730i	$-0.328126\pi$
$883$	30.5533	1.02820	0.514100	+	0.857730i	$0.328126\pi$
$884$	−20.2719	−0.681817
$885$	−0.00414122	−0.000139206 0
$886$	−41.2033	−1.38425
$887$	20.3629	0.683721	0.341860	−	0.939751i	$-0.388943\pi$
$887$	20.3629	0.683721	0.341860	+	0.939751i	$0.388943\pi$
$888$	−0.0455955	−0.00153008
$889$	14.1231	0.473675
$890$	0.0540653	0.00181227
$891$	4.27690	0.143282
$892$	−39.9049	−1.33612
$893$	5.91506	0.197940
$894$	14.2704	0.477275
$895$	0.0206354	0.000689767 0
$896$	0.126298	0.00421932
$897$	−4.10267	−0.136984
$898$	−72.9938	−2.43583
$899$	17.9576	0.598920
$900$	22.4525	0.748416
$901$	−17.5891	−0.585979
$902$	−15.2727	−0.508525
$903$	−5.03588	−0.167583
$904$	0.157722	0.00524577
$905$	−0.0297676	−0.000989507 0
$906$	−22.7839	−0.756944
$907$	−20.7258	−0.688190	−0.344095	−	0.938935i	$-0.611814\pi$
$907$	−20.7258	−0.688190	−0.344095	+	0.938935i	$0.611814\pi$
$908$	1.05523	0.0350192
$909$	16.1543	0.535804
$910$	0.00950120	0.000314962 0
$911$	−13.7246	−0.454716	−0.227358	−	0.973811i	$-0.573009\pi$
$911$	−13.7246	−0.454716	−0.227358	+	0.973811i	$0.573009\pi$
$912$	3.47017	0.114909
$913$	−2.89353	−0.0957619
$914$	77.1545	2.55204
$915$	0.0161411	0.000533608 0
$916$	56.6047	1.87027
$917$	−14.9005	−0.492059
$918$	−55.5762	−1.83429
$919$	−16.2878	−0.537286	−0.268643	−	0.963240i	$-0.586575\pi$
$919$	−16.2878	−0.537286	−0.268643	+	0.963240i	$0.586575\pi$
$920$	−6.48658e−5 0	−2.13856e−6 0
$921$	−4.72923	−0.155834
$922$	−76.2173	−2.51008
$923$	13.3706	0.440098
$924$	−3.68562	−0.121248
$925$	23.5441	0.774125
$926$	71.6368	2.35413
$927$	9.03212	0.296654
$928$	27.6287	0.906957
$929$	7.87707	0.258438	0.129219	−	0.991616i	$-0.458753\pi$
$929$	7.87707	0.258438	0.129219	+	0.991616i	$0.458753\pi$
$930$	0.0182332	0.000597891 0
$931$	−5.01044	−0.164210
$932$	−38.8506	−1.27259
$933$	−14.3821	−0.470848
$934$	44.3638	1.45163
$935$	−0.0188114	−0.000615199 0
$936$	0.0418503	0.00136792
$937$	−1.96561	−0.0642135	−0.0321068	−	0.999484i	$-0.510222\pi$
$937$	−1.96561	−0.0642135	−0.0321068	+	0.999484i	$0.510222\pi$
$938$	−24.9319	−0.814057
$939$	10.4089	0.339680
$940$	0.0239419	0.000780898 0
$941$	−21.1403	−0.689156	−0.344578	−	0.938758i	$-0.611978\pi$
$941$	−21.1403	−0.689156	−0.344578	+	0.938758i	$0.611978\pi$
$942$	−36.4450	−1.18744
$943$	−14.4095	−0.469238
$944$	−9.46090	−0.307926
$945$	0.0130057	0.000423075 0
$946$	12.4906	0.406103
$947$	−1.57978	−0.0513360	−0.0256680	−	0.999671i	$-0.508171\pi$
$947$	−1.57978	−0.0513360	−0.0256680	+	0.999671i	$0.508171\pi$
$948$	−14.3605	−0.466408
$949$	−14.5029	−0.470784
$950$	−9.99299	−0.324215
$951$	21.1816	0.686861
$952$	0.0966280	0.00313173
$953$	−50.5767	−1.63834	−0.819170	−	0.573551i	$-0.805566\pi$
$953$	−50.5767	−1.63834	−0.819170	+	0.573551i	$0.805566\pi$
$954$	−12.9318	−0.418682
$955$	0.00953641	0.000308591 0
$956$	−38.2060	−1.23567
$957$	4.52791	0.146367
$958$	19.1028	0.617184
$959$	−2.67337	−0.0863277
$960$	0.0139674	0.000450795 0
$961$	−4.00143	−0.129078
$962$	−15.6288	−0.503892
$963$	41.4443	1.33552
$964$	31.3575	1.00996
$965$	−0.000119072 0	−3.83307e−6 0
$966$	−6.96440	−0.224076
$967$	7.00707	0.225332	0.112666	−	0.993633i	$-0.464061\pi$
$967$	7.00707	0.225332	0.112666	+	0.993633i	$0.464061\pi$
$968$	0.0974492	0.00313214
$969$	5.29511	0.170103
$970$	−0.0381139	−0.00122376
$971$	−61.1223	−1.96151	−0.980755	−	0.195244i	$-0.937450\pi$
$971$	−61.1223	−1.96151	−0.980755	+	0.195244i	$0.937450\pi$
$972$	−32.0561	−1.02820
$973$	−17.9363	−0.575013
$974$	68.6531	2.19979
$975$	7.18351	0.230056
$976$	36.8754	1.18035
$977$	−44.5643	−1.42574	−0.712869	−	0.701297i	$-0.752605\pi$
$977$	−44.5643	−1.42574	−0.712869	+	0.701297i	$0.752605\pi$
$978$	−12.8701	−0.411540
$979$	20.1858	0.645140
$980$	−0.0202803	−0.000647831 0
$981$	24.6752	0.787818
$982$	−59.4544	−1.89726
$983$	−48.5374	−1.54810	−0.774051	−	0.633123i	$-0.781773\pi$
$983$	−48.5374	−1.54810	−0.774051	+	0.633123i	$0.781773\pi$
$984$	−0.0488607	−0.00155762
$985$	0.00927092	0.000295396 0
$986$	42.2765	1.34636
$987$	−7.21802	−0.229752
$988$	3.31207	0.105371
$989$	11.7846	0.374729
$990$	−0.0138304	−0.000439559 0
$991$	−19.0477	−0.605069	−0.302535	−	0.953138i	$-0.597833\pi$
$991$	−19.0477	−0.605069	−0.302535	+	0.953138i	$0.597833\pi$
$992$	41.5387	1.31885
$993$	−22.4319	−0.711856
$994$	22.6969	0.719903
$995$	0.0321097	0.00101794
$996$	3.29671	0.104460
$997$	−38.8964	−1.23186	−0.615931	−	0.787800i	$-0.711220\pi$
$997$	−38.8964	−1.23186	−0.615931	+	0.787800i	$0.711220\pi$
$998$	−4.41901	−0.139881
$999$	−21.3934	−0.676858

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.c.1.61	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.c.1.61	✓	71	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q+1.99860 q^{2} -0.865127 q^{3} +1.99440 q^{4} +0.00202949 q^{5} -1.72904 q^{6} +1.41052 q^{7} -0.0111926 q^{8} -2.25155 q^{9} +O(q^{10})\)	\(q+1.99860 q^{2} -0.865127 q^{3} +1.99440 q^{4} +0.00202949 q^{5} -1.72904 q^{6} +1.41052 q^{7} -0.0111926 q^{8} -2.25155 q^{9} +0.00405614 q^{10} +1.51440 q^{11} -1.72541 q^{12} +1.66068 q^{13} +2.81906 q^{14} -0.00175577 q^{15} -4.01117 q^{16} -6.12061 q^{17} -4.49996 q^{18} +1.00000 q^{19} +0.00404762 q^{20} -1.22028 q^{21} +3.02667 q^{22} +2.85561 q^{23} +0.00968299 q^{24} -5.00000 q^{25} +3.31904 q^{26} +4.54326 q^{27} +2.81314 q^{28} -3.45604 q^{29} -0.00350908 q^{30} -5.19602 q^{31} -7.99434 q^{32} -1.31015 q^{33} -12.2327 q^{34} +0.00286263 q^{35} -4.49050 q^{36} -4.70882 q^{37} +1.99860 q^{38} -1.43670 q^{39} -2.27152e-5 q^{40} -5.04603 q^{41} -2.43885 q^{42} +4.12683 q^{43} +3.02031 q^{44} -0.00456951 q^{45} +5.70722 q^{46} +5.91506 q^{47} +3.47017 q^{48} -5.01044 q^{49} -9.99299 q^{50} +5.29511 q^{51} +3.31207 q^{52} +2.87376 q^{53} +9.08016 q^{54} +0.00307345 q^{55} -0.0157873 q^{56} -0.865127 q^{57} -6.90724 q^{58} +2.35864 q^{59} -0.00350170 q^{60} -9.19319 q^{61} -10.3848 q^{62} -3.17586 q^{63} -7.95514 q^{64} +0.00337034 q^{65} -2.61846 q^{66} -8.84406 q^{67} -12.2069 q^{68} -2.47047 q^{69} +0.00572126 q^{70} +8.05124 q^{71} +0.0252007 q^{72} -8.73309 q^{73} -9.41105 q^{74} +4.32563 q^{75} +1.99440 q^{76} +2.13608 q^{77} -2.87139 q^{78} +8.32296 q^{79} -0.00814063 q^{80} +2.82416 q^{81} -10.0850 q^{82} -1.91068 q^{83} -2.43372 q^{84} -0.0124217 q^{85} +8.24787 q^{86} +2.98991 q^{87} -0.0169500 q^{88} +13.3292 q^{89} -0.00913262 q^{90} +2.34242 q^{91} +5.69523 q^{92} +4.49522 q^{93} +11.8218 q^{94} +0.00202949 q^{95} +6.91612 q^{96} -9.39658 q^{97} -10.0139 q^{98} -3.40975 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9}+O(q^{10}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9	\( 71 q - 15 q^{2} - 8 q^{3} + 69 q^{4} - 18 q^{5} - 9 q^{6} - 19 q^{7} - 39 q^{8} + 63 q^{9} - 10 q^{10} - 52 q^{11} - 9 q^{12} - 15 q^{13} - 53 q^{14} - 33 q^{15} + 53 q^{16} - 10 q^{17} - 35 q^{18} + 71 q^{19} - 33 q^{20} - 38 q^{21} - 6 q^{22} - 65 q^{23} - 30 q^{24} + 51 q^{25} - 4 q^{26} - 23 q^{27} - 29 q^{28} - 97 q^{29} - 27 q^{30} - 53 q^{31} - 78 q^{32} - 17 q^{33} - 24 q^{34} - 38 q^{35} + 24 q^{36} - 33 q^{37} - 15 q^{38} - 86 q^{39} + 25 q^{40} - 69 q^{41} + 64 q^{42} - 10 q^{43} - 94 q^{44} - 34 q^{45} - 6 q^{46} - 37 q^{47} - q^{48} + 74 q^{49} - 41 q^{50} - 46 q^{51} - 30 q^{52} - 50 q^{53} - 17 q^{54} - 30 q^{55} - 116 q^{56} - 8 q^{57} + 11 q^{58} - 93 q^{59} - 56 q^{60} - 18 q^{61} - q^{62} - 84 q^{63} + 93 q^{64} - 78 q^{65} - 53 q^{66} - 5 q^{67} - 9 q^{68} - 69 q^{69} - 10 q^{70} - 221 q^{71} - 73 q^{72} - 34 q^{73} - 58 q^{74} - 70 q^{75} + 69 q^{76} - 2 q^{77} + 7 q^{78} - 68 q^{79} - 71 q^{80} + 39 q^{81} + 26 q^{82} - 45 q^{83} - 10 q^{84} - 44 q^{85} - 80 q^{86} - 7 q^{87} - 46 q^{88} - 143 q^{89} + 41 q^{90} - 30 q^{91} - 46 q^{92} + 32 q^{93} + 41 q^{94} - 18 q^{95} - 140 q^{96} - 18 q^{97} - 97 q^{98} - 142 q^{99}+O(q^{100}) \) 71 * q - 15 * q^2 - 8 * q^3 + 69 * q^4 - 18 * q^5 - 9 * q^6 - 19 * q^7 - 39 * q^8 + 63 * q^9 - 10 * q^10 - 52 * q^11 - 9 * q^12 - 15 * q^13 - 53 * q^14 - 33 * q^15 + 53 * q^16 - 10 * q^17 - 35 * q^18 + 71 * q^19 - 33 * q^20 - 38 * q^21 - 6 * q^22 - 65 * q^23 - 30 * q^24 + 51 * q^25 - 4 * q^26 - 23 * q^27 - 29 * q^28 - 97 * q^29 - 27 * q^30 - 53 * q^31 - 78 * q^32 - 17 * q^33 - 24 * q^34 - 38 * q^35 + 24 * q^36 - 33 * q^37 - 15 * q^38 - 86 * q^39 + 25 * q^40 - 69 * q^41 + 64 * q^42 - 10 * q^43 - 94 * q^44 - 34 * q^45 - 6 * q^46 - 37 * q^47 - q^48 + 74 * q^49 - 41 * q^50 - 46 * q^51 - 30 * q^52 - 50 * q^53 - 17 * q^54 - 30 * q^55 - 116 * q^56 - 8 * q^57 + 11 * q^58 - 93 * q^59 - 56 * q^60 - 18 * q^61 - q^62 - 84 * q^63 + 93 * q^64 - 78 * q^65 - 53 * q^66 - 5 * q^67 - 9 * q^68 - 69 * q^69 - 10 * q^70 - 221 * q^71 - 73 * q^72 - 34 * q^73 - 58 * q^74 - 70 * q^75 + 69 * q^76 - 2 * q^77 + 7 * q^78 - 68 * q^79 - 71 * q^80 + 39 * q^81 + 26 * q^82 - 45 * q^83 - 10 * q^84 - 44 * q^85 - 80 * q^86 - 7 * q^87 - 46 * q^88 - 143 * q^89 + 41 * q^90 - 30 * q^91 - 46 * q^92 + 32 * q^93 + 41 * q^94 - 18 * q^95 - 140 * q^96 - 18 * q^97 - 97 * q^98 - 142 * q^99

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