LMFDB - Embedded newform 1003.2.a.j.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1003,2,Mod(1,1003)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1003, 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("1003.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1003 = 17 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1003.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:	$8.00899532273$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	1003.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46853 q^{2} +2.37414 q^{3} +0.156587 q^{4} +0.0990345 q^{5} -3.48650 q^{6} +4.77589 q^{7} +2.70711 q^{8} +2.63653 q^{9} +O(q^{10})$	\(q-1.46853 q^{2} +2.37414 q^{3} +0.156587 q^{4} +0.0990345 q^{5} -3.48650 q^{6} +4.77589 q^{7} +2.70711 q^{8} +2.63653 q^{9} -0.145435 q^{10} +5.90063 q^{11} +0.371758 q^{12} +5.92666 q^{13} -7.01356 q^{14} +0.235121 q^{15} -4.28865 q^{16} -1.00000 q^{17} -3.87183 q^{18} -5.54544 q^{19} +0.0155075 q^{20} +11.3386 q^{21} -8.66526 q^{22} -1.97129 q^{23} +6.42706 q^{24} -4.99019 q^{25} -8.70349 q^{26} -0.862931 q^{27} +0.747841 q^{28} -3.21347 q^{29} -0.345283 q^{30} -7.62998 q^{31} +0.883802 q^{32} +14.0089 q^{33} +1.46853 q^{34} +0.472978 q^{35} +0.412845 q^{36} -7.79376 q^{37} +8.14365 q^{38} +14.0707 q^{39} +0.268097 q^{40} +5.66055 q^{41} -16.6511 q^{42} +3.21729 q^{43} +0.923959 q^{44} +0.261107 q^{45} +2.89491 q^{46} +4.30472 q^{47} -10.1819 q^{48} +15.8092 q^{49} +7.32826 q^{50} -2.37414 q^{51} +0.928035 q^{52} +0.738589 q^{53} +1.26724 q^{54} +0.584366 q^{55} +12.9289 q^{56} -13.1656 q^{57} +4.71909 q^{58} +1.00000 q^{59} +0.0368169 q^{60} -6.63404 q^{61} +11.2049 q^{62} +12.5918 q^{63} +7.27942 q^{64} +0.586943 q^{65} -20.5725 q^{66} -5.65533 q^{67} -0.156587 q^{68} -4.68012 q^{69} -0.694584 q^{70} -1.00921 q^{71} +7.13738 q^{72} +2.29835 q^{73} +11.4454 q^{74} -11.8474 q^{75} -0.868341 q^{76} +28.1808 q^{77} -20.6633 q^{78} +2.08419 q^{79} -0.424725 q^{80} -9.95830 q^{81} -8.31271 q^{82} +4.44033 q^{83} +1.77548 q^{84} -0.0990345 q^{85} -4.72470 q^{86} -7.62923 q^{87} +15.9737 q^{88} -13.8545 q^{89} -0.383444 q^{90} +28.3051 q^{91} -0.308678 q^{92} -18.1146 q^{93} -6.32162 q^{94} -0.549189 q^{95} +2.09827 q^{96} -18.8876 q^{97} -23.2163 q^{98} +15.5572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) $ 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * 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 $

$2$	−1.46853	−1.03841	−0.519205	−	0.854650i	$-0.673772\pi$
$2$	−1.46853	−1.03841	−0.519205	+	0.854650i	$0.673772\pi$
$3$	2.37414	1.37071	0.685354	−	0.728210i	$-0.259647\pi$
$3$	2.37414	1.37071	0.685354	+	0.728210i	$0.259647\pi$
$4$	0.156587	0.0782933
$5$	0.0990345	0.0442896	0.0221448	−	0.999755i	$-0.492951\pi$
$5$	0.0990345	0.0442896	0.0221448	+	0.999755i	$0.492951\pi$
$6$	−3.48650	−1.42336
$7$	4.77589	1.80512	0.902559	−	0.430566i	$-0.141686\pi$
$7$	4.77589	1.80512	0.902559	+	0.430566i	$0.141686\pi$
$8$	2.70711	0.957109
$9$	2.63653	0.878843
$10$	−0.145435	−0.0459907
$11$	5.90063	1.77911	0.889553	−	0.456832i	$-0.151016\pi$
$11$	5.90063	1.77911	0.889553	+	0.456832i	$0.151016\pi$
$12$	0.371758	0.107317
$13$	5.92666	1.64376	0.821880	−	0.569661i	$-0.192926\pi$
$13$	5.92666	1.64376	0.821880	+	0.569661i	$0.192926\pi$
$14$	−7.01356	−1.87445
$15$	0.235121	0.0607081
$16$	−4.28865	−1.07216
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−3.87183	−0.912598
$19$	−5.54544	−1.27221	−0.636105	−	0.771602i	$-0.719456\pi$
$19$	−5.54544	−1.27221	−0.636105	+	0.771602i	$0.719456\pi$
$20$	0.0155075	0.00346758
$21$	11.3386	2.47429
$22$	−8.66526	−1.84744
$23$	−1.97129	−0.411043	−0.205522	−	0.978653i	$-0.565889\pi$
$23$	−1.97129	−0.411043	−0.205522	+	0.978653i	$0.565889\pi$
$24$	6.42706	1.31192
$25$	−4.99019	−0.998038
$26$	−8.70349	−1.70689
$27$	−0.862931	−0.166071
$28$	0.747841	0.141329
$29$	−3.21347	−0.596727	−0.298364	−	0.954452i	$-0.596441\pi$
$29$	−3.21347	−0.596727	−0.298364	+	0.954452i	$0.596441\pi$
$30$	−0.345283	−0.0630398
$31$	−7.62998	−1.37039	−0.685193	−	0.728362i	$-0.740282\pi$
$31$	−7.62998	−1.37039	−0.685193	+	0.728362i	$0.740282\pi$
$32$	0.883802	0.156236
$33$	14.0089	2.43864
$34$	1.46853	0.251851
$35$	0.472978	0.0799479
$36$	0.412845	0.0688075
$37$	−7.79376	−1.28129	−0.640643	−	0.767839i	$-0.721332\pi$
$37$	−7.79376	−1.28129	−0.640643	+	0.767839i	$0.721332\pi$
$38$	8.14365	1.32107
$39$	14.0707	2.25312
$40$	0.268097	0.0423899
$41$	5.66055	0.884030	0.442015	−	0.897008i	$-0.354264\pi$
$41$	5.66055	0.884030	0.442015	+	0.897008i	$0.354264\pi$
$42$	−16.6511	−2.56933
$43$	3.21729	0.490632	0.245316	−	0.969443i	$-0.421108\pi$
$43$	3.21729	0.490632	0.245316	+	0.969443i	$0.421108\pi$
$44$	0.923959	0.139292
$45$	0.261107	0.0389236
$46$	2.89491	0.426831
$47$	4.30472	0.627908	0.313954	−	0.949438i	$-0.398346\pi$
$47$	4.30472	0.627908	0.313954	+	0.949438i	$0.398346\pi$
$48$	−10.1819	−1.46962
$49$	15.8092	2.25845
$50$	7.32826	1.03637
$51$	−2.37414	−0.332446
$52$	0.928035	0.128695
$53$	0.738589	0.101453	0.0507265	−	0.998713i	$-0.483846\pi$
$53$	0.738589	0.101453	0.0507265	+	0.998713i	$0.483846\pi$
$54$	1.26724	0.172450
$55$	0.584366	0.0787958
$56$	12.9289	1.72769
$57$	−13.1656	−1.74383
$58$	4.71909	0.619647
$59$	1.00000	0.130189
$59$	1.00000	0.130189
$60$	0.0368169	0.00475304
$61$	−6.63404	−0.849402	−0.424701	−	0.905334i	$-0.639621\pi$
$61$	−6.63404	−0.849402	−0.424701	+	0.905334i	$0.639621\pi$
$62$	11.2049	1.42302
$63$	12.5918	1.58642
$64$	7.27942	0.909927
$65$	0.586943	0.0728014
$66$	−20.5725	−2.53230
$67$	−5.65533	−0.690908	−0.345454	−	0.938436i	$-0.612275\pi$
$67$	−5.65533	−0.690908	−0.345454	+	0.938436i	$0.612275\pi$
$68$	−0.156587	−0.0189889
$69$	−4.68012	−0.563421
$70$	−0.694584	−0.0830186
$71$	−1.00921	−0.119772	−0.0598858	−	0.998205i	$-0.519074\pi$
$71$	−1.00921	−0.119772	−0.0598858	+	0.998205i	$0.519074\pi$
$72$	7.13738	0.841148
$73$	2.29835	0.269002	0.134501	−	0.990913i	$-0.457057\pi$
$73$	2.29835	0.269002	0.134501	+	0.990913i	$0.457057\pi$
$74$	11.4454	1.33050
$75$	−11.8474	−1.36802
$76$	−0.868341	−0.0996056
$77$	28.1808	3.21150
$78$	−20.6633	−2.33966
$79$	2.08419	0.234490	0.117245	−	0.993103i	$-0.462594\pi$
$79$	2.08419	0.234490	0.117245	+	0.993103i	$0.462594\pi$
$80$	−0.424725	−0.0474856
$81$	−9.95830	−1.10648
$82$	−8.31271	−0.917985
$83$	4.44033	0.487390	0.243695	−	0.969852i	$-0.421640\pi$
$83$	4.44033	0.487390	0.243695	+	0.969852i	$0.421640\pi$
$84$	1.77548	0.193720
$85$	−0.0990345	−0.0107418
$86$	−4.72470	−0.509477
$87$	−7.62923	−0.817939
$88$	15.9737	1.70280
$89$	−13.8545	−1.46857	−0.734287	−	0.678839i	$-0.762483\pi$
$89$	−13.8545	−1.46857	−0.734287	+	0.678839i	$0.762483\pi$
$90$	−0.383444	−0.0404186
$91$	28.3051	2.96718
$92$	−0.308678	−0.0321819
$93$	−18.1146	−1.87840
$94$	−6.32162	−0.652025
$95$	−0.549189	−0.0563456
$96$	2.09827	0.214154
$97$	−18.8876	−1.91774	−0.958871	−	0.283842i	$-0.908391\pi$
$97$	−18.8876	−1.91774	−0.958871	+	0.283842i	$0.908391\pi$
$98$	−23.2163	−2.34520
$99$	15.5572	1.56355
$100$	−0.781397	−0.0781397
$101$	7.55023	0.751276	0.375638	−	0.926766i	$-0.377424\pi$
$101$	7.55023	0.751276	0.375638	+	0.926766i	$0.377424\pi$
$102$	3.48650	0.345215
$103$	−15.2493	−1.50255	−0.751277	−	0.659987i	$-0.770562\pi$
$103$	−15.2493	−1.50255	−0.751277	+	0.659987i	$0.770562\pi$
$104$	16.0441	1.57326
$105$	1.12292	0.109585
$106$	−1.08464	−0.105350
$107$	−7.44365	−0.719605	−0.359802	−	0.933029i	$-0.617156\pi$
$107$	−7.44365	−0.719605	−0.359802	+	0.933029i	$0.617156\pi$
$108$	−0.135123	−0.0130023
$109$	−11.2351	−1.07612	−0.538062	−	0.842905i	$-0.680843\pi$
$109$	−11.2351	−1.07612	−0.538062	+	0.842905i	$0.680843\pi$
$110$	−0.858160	−0.0818223
$111$	−18.5035	−1.75627
$112$	−20.4822	−1.93538
$113$	−6.93725	−0.652601	−0.326301	−	0.945266i	$-0.605802\pi$
$113$	−6.93725	−0.652601	−0.326301	+	0.945266i	$0.605802\pi$
$114$	19.3342	1.81081
$115$	−0.195226	−0.0182049
$116$	−0.503187	−0.0467197
$117$	15.6258	1.44461
$118$	−1.46853	−0.135189
$119$	−4.77589	−0.437806
$120$	0.636500	0.0581042
$121$	23.8174	2.16522
$122$	9.74230	0.882026
$123$	13.4389	1.21175
$124$	−1.19475	−0.107292
$125$	−0.989373	−0.0884922
$126$	−18.4914	−1.64735
$127$	12.1516	1.07828	0.539141	−	0.842215i	$-0.318749\pi$
$127$	12.1516	1.07828	0.539141	+	0.842215i	$0.318749\pi$
$128$	−12.4577	−1.10111
$129$	7.63829	0.672514
$130$	−0.861945	−0.0755976
$131$	21.7497	1.90028	0.950140	−	0.311822i	$-0.100939\pi$
$131$	21.7497	1.90028	0.950140	+	0.311822i	$0.100939\pi$
$132$	2.19361	0.190929
$133$	−26.4844	−2.29649
$134$	8.30503	0.717445
$135$	−0.0854599	−0.00735522
$136$	−2.70711	−0.232133
$137$	4.65977	0.398111	0.199055	−	0.979988i	$-0.436213\pi$
$137$	4.65977	0.398111	0.199055	+	0.979988i	$0.436213\pi$
$138$	6.87291	0.585061
$139$	14.9667	1.26946	0.634730	−	0.772734i	$-0.281112\pi$
$139$	14.9667	1.26946	0.634730	+	0.772734i	$0.281112\pi$
$140$	0.0740621	0.00625939
$141$	10.2200	0.860679
$142$	1.48206	0.124372
$143$	34.9710	2.92442
$144$	−11.3072	−0.942263
$145$	−0.318245	−0.0264288
$146$	−3.37520	−0.279334
$147$	37.5331	3.09568
$148$	−1.22040	−0.100316
$149$	7.50605	0.614919	0.307460	−	0.951561i	$-0.400521\pi$
$149$	7.50605	0.614919	0.307460	+	0.951561i	$0.400521\pi$
$150$	17.3983	1.42056
$151$	3.69419	0.300629	0.150315	−	0.988638i	$-0.451971\pi$
$151$	3.69419	0.300629	0.150315	+	0.988638i	$0.451971\pi$
$152$	−15.0121	−1.21764
$153$	−2.63653	−0.213151
$154$	−41.3844	−3.33485
$155$	−0.755631	−0.0606938
$156$	2.20328	0.176404
$157$	−5.09769	−0.406840	−0.203420	−	0.979092i	$-0.565206\pi$
$157$	−5.09769	−0.406840	−0.203420	+	0.979092i	$0.565206\pi$
$158$	−3.06070	−0.243496
$159$	1.75351	0.139063
$160$	0.0875269	0.00691961
$161$	−9.41469	−0.741982
$162$	14.6241	1.14898
$163$	−12.5461	−0.982686	−0.491343	−	0.870966i	$-0.663494\pi$
$163$	−12.5461	−0.982686	−0.491343	+	0.870966i	$0.663494\pi$
$164$	0.886367	0.0692136
$165$	1.38736	0.108006
$166$	−6.52077	−0.506110
$167$	−1.41914	−0.109816	−0.0549081	−	0.998491i	$-0.517487\pi$
$167$	−1.41914	−0.109816	−0.0549081	+	0.998491i	$0.517487\pi$
$168$	30.6949	2.36817
$169$	22.1253	1.70194
$170$	0.145435	0.0111544
$171$	−14.6207	−1.11807
$172$	0.503785	0.0384132
$173$	−13.3368	−1.01398	−0.506990	−	0.861952i	$-0.669242\pi$
$173$	−13.3368	−1.01398	−0.506990	+	0.861952i	$0.669242\pi$
$174$	11.2038	0.849356
$175$	−23.8326	−1.80158
$176$	−25.3058	−1.90749
$177$	2.37414	0.178451
$178$	20.3458	1.52498
$179$	−10.1738	−0.760424	−0.380212	−	0.924899i	$-0.624149\pi$
$179$	−10.1738	−0.760424	−0.380212	+	0.924899i	$0.624149\pi$
$180$	0.0408859	0.00304745
$181$	−13.9509	−1.03696	−0.518480	−	0.855090i	$-0.673502\pi$
$181$	−13.9509	−1.03696	−0.518480	+	0.855090i	$0.673502\pi$
$182$	−41.5669	−3.08115
$183$	−15.7501	−1.16428
$184$	−5.33651	−0.393413
$185$	−0.771851	−0.0567476
$186$	26.6019	1.95055
$187$	−5.90063	−0.431497
$188$	0.674061	0.0491610
$189$	−4.12127	−0.299778
$190$	0.806502	0.0585098
$191$	17.3788	1.25749	0.628745	−	0.777612i	$-0.283569\pi$
$191$	17.3788	1.25749	0.628745	+	0.777612i	$0.283569\pi$
$192$	17.2823	1.24724
$193$	7.53816	0.542609	0.271304	−	0.962494i	$-0.412545\pi$
$193$	7.53816	0.542609	0.271304	+	0.962494i	$0.412545\pi$
$194$	27.7370	1.99140
$195$	1.39348	0.0997895
$196$	2.47550	0.176822
$197$	15.6687	1.11635	0.558176	−	0.829723i	$-0.311502\pi$
$197$	15.6687	1.11635	0.558176	+	0.829723i	$0.311502\pi$
$198$	−22.8462	−1.62361
$199$	10.2737	0.728285	0.364142	−	0.931343i	$-0.381362\pi$
$199$	10.2737	0.728285	0.364142	+	0.931343i	$0.381362\pi$
$200$	−13.5090	−0.955231
$201$	−13.4265	−0.947034
$202$	−11.0878	−0.780132
$203$	−15.3472	−1.07716
$204$	−0.371758	−0.0260283
$205$	0.560590	0.0391533
$206$	22.3940	1.56027
$207$	−5.19737	−0.361242
$208$	−25.4174	−1.76238
$209$	−32.7216	−2.26340
$210$	−1.64904	−0.113794
$211$	17.8074	1.22591	0.612956	−	0.790117i	$-0.289980\pi$
$211$	17.8074	1.22591	0.612956	+	0.790117i	$0.289980\pi$
$212$	0.115653	0.00794309
$213$	−2.39601	−0.164172
$214$	10.9312	0.747244
$215$	0.318623	0.0217299
$216$	−2.33605	−0.158948
$217$	−36.4400	−2.47371
$218$	16.4990	1.11746
$219$	5.45661	0.368723
$220$	0.0915038	0.00616919
$221$	−5.92666	−0.398670
$222$	27.1729	1.82373
$223$	17.9145	1.19965	0.599823	−	0.800133i	$-0.295238\pi$
$223$	17.9145	1.19965	0.599823	+	0.800133i	$0.295238\pi$
$224$	4.22095	0.282024
$225$	−13.1568	−0.877119
$226$	10.1876	0.677667
$227$	−14.7582	−0.979535	−0.489768	−	0.871853i	$-0.662918\pi$
$227$	−14.7582	−0.979535	−0.489768	+	0.871853i	$0.662918\pi$
$228$	−2.06156	−0.136530
$229$	−20.3885	−1.34731	−0.673656	−	0.739045i	$-0.735277\pi$
$229$	−20.3885	−1.34731	−0.673656	+	0.739045i	$0.735277\pi$
$230$	0.286696	0.0189042
$231$	66.9050	4.40203
$232$	−8.69924	−0.571133
$233$	16.9962	1.11346	0.556730	−	0.830693i	$-0.312056\pi$
$233$	16.9962	1.11346	0.556730	+	0.830693i	$0.312056\pi$
$234$	−22.9470	−1.50009
$235$	0.426316	0.0278098
$236$	0.156587	0.0101929
$237$	4.94815	0.321417
$238$	7.01356	0.454621
$239$	16.2296	1.04981	0.524904	−	0.851162i	$-0.324101\pi$
$239$	16.2296	1.04981	0.524904	+	0.851162i	$0.324101\pi$
$240$	−1.00835	−0.0650890
$241$	−2.98264	−0.192129	−0.0960644	−	0.995375i	$-0.530625\pi$
$241$	−2.98264	−0.192129	−0.0960644	+	0.995375i	$0.530625\pi$
$242$	−34.9766	−2.24838
$243$	−21.0536	−1.35059
$244$	−1.03880	−0.0665025
$245$	1.56565	0.100026
$246$	−19.7355	−1.25829
$247$	−32.8659	−2.09121
$248$	−20.6552	−1.31161
$249$	10.5420	0.668069
$250$	1.45293	0.0918911
$251$	2.73073	0.172362	0.0861811	−	0.996279i	$-0.472534\pi$
$251$	2.73073	0.172362	0.0861811	+	0.996279i	$0.472534\pi$
$252$	1.97170	0.124206
$253$	−11.6319	−0.731290
$254$	−17.8450	−1.11970
$255$	−0.235121	−0.0147239
$256$	3.73564	0.233478
$257$	4.53438	0.282847	0.141423	−	0.989949i	$-0.454832\pi$
$257$	4.53438	0.282847	0.141423	+	0.989949i	$0.454832\pi$
$258$	−11.2171	−0.698345
$259$	−37.2222	−2.31287
$260$	0.0919075	0.00569986
$261$	−8.47242	−0.524429
$262$	−31.9401	−1.97327
$263$	−11.7467	−0.724332	−0.362166	−	0.932114i	$-0.617963\pi$
$263$	−11.7467	−0.724332	−0.362166	+	0.932114i	$0.617963\pi$
$264$	37.9237	2.33404
$265$	0.0731458	0.00449331
$266$	38.8932	2.38470
$267$	−32.8925	−2.01299
$268$	−0.885549	−0.0540935
$269$	28.5858	1.74291	0.871453	−	0.490479i	$-0.163178\pi$
$269$	28.5858	1.74291	0.871453	+	0.490479i	$0.163178\pi$
$270$	0.125501	0.00763773
$271$	1.25879	0.0764661	0.0382330	−	0.999269i	$-0.487827\pi$
$271$	1.25879	0.0764661	0.0382330	+	0.999269i	$0.487827\pi$
$272$	4.28865	0.260038
$273$	67.2002	4.06714
$274$	−6.84302	−0.413402
$275$	−29.4453	−1.77562
$276$	−0.732845	−0.0441121
$277$	−18.4533	−1.10875	−0.554375	−	0.832267i	$-0.687043\pi$
$277$	−18.4533	−1.10875	−0.554375	+	0.832267i	$0.687043\pi$
$278$	−21.9791	−1.31822
$279$	−20.1167	−1.20435
$280$	1.28040	0.0765188
$281$	−25.7821	−1.53803	−0.769016	−	0.639230i	$-0.779253\pi$
$281$	−25.7821	−1.53803	−0.769016	+	0.639230i	$0.779253\pi$
$282$	−15.0084	−0.893737
$283$	21.8830	1.30081	0.650405	−	0.759588i	$-0.274599\pi$
$283$	21.8830	1.30081	0.650405	+	0.759588i	$0.274599\pi$
$284$	−0.158029	−0.00937731
$285$	−1.30385	−0.0772335
$286$	−51.3560	−3.03675
$287$	27.0342	1.59578
$288$	2.33017	0.137307
$289$	1.00000	0.0588235
$290$	0.467353	0.0274439
$291$	−44.8417	−2.62867
$292$	0.359891	0.0210610
$293$	25.5380	1.49195	0.745973	−	0.665976i	$-0.231985\pi$
$293$	25.5380	1.49195	0.745973	+	0.665976i	$0.231985\pi$
$294$	−55.1186	−3.21458
$295$	0.0990345	0.00576601
$296$	−21.0986	−1.22633
$297$	−5.09184	−0.295458
$298$	−11.0229	−0.638538
$299$	−11.6832	−0.675656
$300$	−1.85514	−0.107107
$301$	15.3654	0.885650
$302$	−5.42504	−0.312176
$303$	17.9253	1.02978
$304$	23.7825	1.36402
$305$	−0.656999	−0.0376196
$306$	3.87183	0.221338
$307$	−0.966707	−0.0551729	−0.0275864	−	0.999619i	$-0.508782\pi$
$307$	−0.966707	−0.0551729	−0.0275864	+	0.999619i	$0.508782\pi$
$308$	4.41273	0.251439
$309$	−36.2039	−2.05957
$310$	1.10967	0.0630249
$311$	−6.52379	−0.369930	−0.184965	−	0.982745i	$-0.559217\pi$
$311$	−6.52379	−0.369930	−0.184965	+	0.982745i	$0.559217\pi$
$312$	38.0910	2.15648
$313$	8.80874	0.497899	0.248950	−	0.968516i	$-0.419915\pi$
$313$	8.80874	0.497899	0.248950	+	0.968516i	$0.419915\pi$
$314$	7.48612	0.422466
$315$	1.24702	0.0702617
$316$	0.326356	0.0183590
$317$	23.1787	1.30184	0.650921	−	0.759145i	$-0.274383\pi$
$317$	23.1787	1.30184	0.650921	+	0.759145i	$0.274383\pi$
$318$	−2.57509	−0.144404
$319$	−18.9615	−1.06164
$320$	0.720913	0.0403003
$321$	−17.6723	−0.986369
$322$	13.8258	0.770481
$323$	5.54544	0.308556
$324$	−1.55934	−0.0866298
$325$	−29.5752	−1.64053
$326$	18.4243	1.02043
$327$	−26.6736	−1.47505
$328$	15.3238	0.846113
$329$	20.5589	1.13345
$330$	−2.03739	−0.112155
$331$	−17.5924	−0.966967	−0.483483	−	0.875353i	$-0.660629\pi$
$331$	−17.5924	−0.966967	−0.483483	+	0.875353i	$0.660629\pi$
$332$	0.695296	0.0381593
$333$	−20.5485	−1.12605
$334$	2.08405	0.114034
$335$	−0.560072	−0.0306000
$336$	−48.6275	−2.65285
$337$	−24.7431	−1.34784	−0.673921	−	0.738804i	$-0.735391\pi$
$337$	−24.7431	−1.34784	−0.673921	+	0.738804i	$0.735391\pi$
$338$	−32.4917	−1.76731
$339$	−16.4700	−0.894526
$340$	−0.0155075	−0.000841011 0
$341$	−45.0217	−2.43806
$342$	21.4710	1.16102
$343$	42.0717	2.27166
$344$	8.70957	0.469588
$345$	−0.463494	−0.0249537
$346$	19.5855	1.05293
$347$	5.72638	0.307408	0.153704	−	0.988117i	$-0.450880\pi$
$347$	5.72638	0.307408	0.153704	+	0.988117i	$0.450880\pi$
$348$	−1.19464	−0.0640392
$349$	11.4458	0.612678	0.306339	−	0.951922i	$-0.400896\pi$
$349$	11.4458	0.612678	0.306339	+	0.951922i	$0.400896\pi$
$350$	34.9990	1.87077
$351$	−5.11430	−0.272981
$352$	5.21499	0.277960
$353$	28.5616	1.52018	0.760091	−	0.649817i	$-0.225154\pi$
$353$	28.5616	1.52018	0.760091	+	0.649817i	$0.225154\pi$
$354$	−3.48650	−0.185305
$355$	−0.0999469	−0.00530463
$356$	−2.16943	−0.114979
$357$	−11.3386	−0.600104
$358$	14.9405	0.789631
$359$	−2.13326	−0.112589	−0.0562945	−	0.998414i	$-0.517929\pi$
$359$	−2.13326	−0.112589	−0.0562945	+	0.998414i	$0.517929\pi$
$360$	0.706846	0.0372541
$361$	11.7519	0.618520
$362$	20.4873	1.07679
$363$	56.5458	2.96789
$364$	4.43220	0.232310
$365$	0.227616	0.0119140
$366$	23.1296	1.20900
$367$	8.18084	0.427036	0.213518	−	0.976939i	$-0.431508\pi$
$367$	8.18084	0.427036	0.213518	+	0.976939i	$0.431508\pi$
$368$	8.45420	0.440706
$369$	14.9242	0.776923
$370$	1.13349	0.0589272
$371$	3.52742	0.183135
$372$	−2.83651	−0.147066
$373$	−16.0112	−0.829028	−0.414514	−	0.910043i	$-0.636048\pi$
$373$	−16.0112	−0.829028	−0.414514	+	0.910043i	$0.636048\pi$
$374$	8.66526	0.448070
$375$	−2.34891	−0.121297
$376$	11.6534	0.600976
$377$	−19.0452	−0.980876
$378$	6.05222	0.311292
$379$	13.5119	0.694060	0.347030	−	0.937854i	$-0.387190\pi$
$379$	13.5119	0.694060	0.347030	+	0.937854i	$0.387190\pi$
$380$	−0.0859957	−0.00441149
$381$	28.8496	1.47801
$382$	−25.5214	−1.30579
$383$	5.18646	0.265016	0.132508	−	0.991182i	$-0.457697\pi$
$383$	5.18646	0.265016	0.132508	+	0.991182i	$0.457697\pi$
$384$	−29.5762	−1.50930
$385$	2.79087	0.142236
$386$	−11.0700	−0.563450
$387$	8.48248	0.431189
$388$	−2.95754	−0.150146
$389$	8.13255	0.412337	0.206168	−	0.978517i	$-0.433901\pi$
$389$	8.13255	0.412337	0.206168	+	0.978517i	$0.433901\pi$
$390$	−2.04638	−0.103622
$391$	1.97129	0.0996926
$392$	42.7972	2.16158
$393$	51.6368	2.60473
$394$	−23.0100	−1.15923
$395$	0.206406	0.0103854
$396$	2.43605	0.122416
$397$	3.93605	0.197545	0.0987724	−	0.995110i	$-0.468508\pi$
$397$	3.93605	0.197545	0.0987724	+	0.995110i	$0.468508\pi$
$398$	−15.0873	−0.756257
$399$	−62.8777	−3.14782
$400$	21.4012	1.07006
$401$	23.3955	1.16832	0.584159	−	0.811639i	$-0.301424\pi$
$401$	23.3955	1.16832	0.584159	+	0.811639i	$0.301424\pi$
$402$	19.7173	0.983409
$403$	−45.2203	−2.25258
$404$	1.18227	0.0588199
$405$	−0.986215	−0.0490054
$406$	22.5379	1.11854
$407$	−45.9881	−2.27954
$408$	−6.42706	−0.318187
$409$	−10.2111	−0.504905	−0.252452	−	0.967609i	$-0.581237\pi$
$409$	−10.2111	−0.504905	−0.252452	+	0.967609i	$0.581237\pi$
$410$	−0.823244	−0.0406571
$411$	11.0629	0.545694
$412$	−2.38783	−0.117640
$413$	4.77589	0.235006
$414$	7.63251	0.375117
$415$	0.439746	0.0215863
$416$	5.23799	0.256814
$417$	35.5330	1.74006
$418$	48.0527	2.35033
$419$	−24.1506	−1.17983	−0.589916	−	0.807465i	$-0.700839\pi$
$419$	−24.1506	−1.17983	−0.589916	+	0.807465i	$0.700839\pi$
$420$	0.175833	0.00857980
$421$	−20.1351	−0.981325	−0.490662	−	0.871350i	$-0.663245\pi$
$421$	−20.1351	−0.981325	−0.490662	+	0.871350i	$0.663245\pi$
$422$	−26.1507	−1.27300
$423$	11.3495	0.551832
$424$	1.99944	0.0971016
$425$	4.99019	0.242060
$426$	3.51862	0.170478
$427$	−31.6835	−1.53327
$428$	−1.16558	−0.0563402
$429$	83.0260	4.00853
$430$	−0.467908	−0.0225645
$431$	−0.731668	−0.0352432	−0.0176216	−	0.999845i	$-0.505609\pi$
$431$	−0.731668	−0.0352432	−0.0176216	+	0.999845i	$0.505609\pi$
$432$	3.70081	0.178055
$433$	15.2422	0.732491	0.366246	−	0.930518i	$-0.380643\pi$
$433$	15.2422	0.732491	0.366246	+	0.930518i	$0.380643\pi$
$434$	53.5133	2.56872
$435$	−0.755557	−0.0362262
$436$	−1.75926	−0.0842532
$437$	10.9317	0.522934
$438$	−8.01320	−0.382886
$439$	16.1207	0.769399	0.384699	−	0.923042i	$-0.374305\pi$
$439$	16.1207	0.769399	0.384699	+	0.923042i	$0.374305\pi$
$440$	1.58194	0.0754162
$441$	41.6813	1.98483
$442$	8.70349	0.413983
$443$	−12.4023	−0.589251	−0.294625	−	0.955613i	$-0.595195\pi$
$443$	−12.4023	−0.589251	−0.294625	+	0.955613i	$0.595195\pi$
$444$	−2.89739	−0.137504
$445$	−1.37207	−0.0650425
$446$	−26.3080	−1.24572
$447$	17.8204	0.842875
$448$	34.7657	1.64253
$449$	36.5908	1.72683	0.863414	−	0.504496i	$-0.168322\pi$
$449$	36.5908	1.72683	0.863414	+	0.504496i	$0.168322\pi$
$450$	19.3212	0.910808
$451$	33.4008	1.57278
$452$	−1.08628	−0.0510943
$453$	8.77052	0.412075
$454$	21.6729	1.01716
$455$	2.80318	0.131415
$456$	−35.6408	−1.66903
$457$	0.256836	0.0120143	0.00600714	−	0.999982i	$-0.498088\pi$
$457$	0.256836	0.0120143	0.00600714	+	0.999982i	$0.498088\pi$
$458$	29.9412	1.39906
$459$	0.862931	0.0402782
$460$	−0.0305698	−0.00142532
$461$	24.1969	1.12696	0.563481	−	0.826129i	$-0.309462\pi$
$461$	24.1969	1.12696	0.563481	+	0.826129i	$0.309462\pi$
$462$	−98.2522	−4.57111
$463$	15.6052	0.725237	0.362619	−	0.931938i	$-0.381883\pi$
$463$	15.6052	0.725237	0.362619	+	0.931938i	$0.381883\pi$
$464$	13.7815	0.639789
$465$	−1.79397	−0.0831935
$466$	−24.9595	−1.15623
$467$	−5.34490	−0.247333	−0.123666	−	0.992324i	$-0.539465\pi$
$467$	−5.34490	−0.247333	−0.123666	+	0.992324i	$0.539465\pi$
$468$	2.44679	0.113103
$469$	−27.0093	−1.24717
$470$	−0.626058	−0.0288779
$471$	−12.1026	−0.557659
$472$	2.70711	0.124605
$473$	18.9840	0.872887
$474$	−7.26652	−0.333762
$475$	27.6728	1.26972
$476$	−0.747841	−0.0342772
$477$	1.94731	0.0891613
$478$	−23.8337	−1.09013
$479$	−6.16884	−0.281861	−0.140931	−	0.990019i	$-0.545009\pi$
$479$	−6.16884	−0.281861	−0.140931	+	0.990019i	$0.545009\pi$
$480$	0.207801	0.00948477
$481$	−46.1909	−2.10613
$482$	4.38010	0.199508
$483$	−22.3518	−1.01704
$484$	3.72949	0.169522
$485$	−1.87052	−0.0849360
$486$	30.9179	1.40246
$487$	0.0962472	0.00436138	0.00218069	−	0.999998i	$-0.499306\pi$
$487$	0.0962472	0.00436138	0.00218069	+	0.999998i	$0.499306\pi$
$488$	−17.9591	−0.812970
$489$	−29.7861	−1.34698
$490$	−2.29921	−0.103868
$491$	10.4666	0.472353	0.236177	−	0.971710i	$-0.424106\pi$
$491$	10.4666	0.472353	0.236177	+	0.971710i	$0.424106\pi$
$492$	2.10436	0.0948717
$493$	3.21347	0.144728
$494$	48.2646	2.17153
$495$	1.54070	0.0692492
$496$	32.7224	1.46928
$497$	−4.81989	−0.216202
$498$	−15.4812	−0.693729
$499$	−18.3438	−0.821183	−0.410591	−	0.911819i	$-0.634678\pi$
$499$	−18.3438	−0.821183	−0.410591	+	0.911819i	$0.634678\pi$
$500$	−0.154923	−0.00692835
$501$	−3.36923	−0.150526
$502$	−4.01016	−0.178982
$503$	−23.1269	−1.03118	−0.515589	−	0.856836i	$-0.672427\pi$
$503$	−23.1269	−1.03118	−0.515589	+	0.856836i	$0.672427\pi$
$504$	34.0874	1.51837
$505$	0.747733	0.0332737
$506$	17.0818	0.759378
$507$	52.5284	2.33287
$508$	1.90278	0.0844223
$509$	−43.7416	−1.93881	−0.969406	−	0.245462i	$-0.921060\pi$
$509$	−43.7416	−1.93881	−0.969406	+	0.245462i	$0.921060\pi$
$510$	0.345283	0.0152894
$511$	10.9767	0.485580
$512$	19.4294	0.858667
$513$	4.78533	0.211278
$514$	−6.65888	−0.293711
$515$	−1.51020	−0.0665475
$516$	1.19605	0.0526533
$517$	25.4006	1.11712
$518$	54.6620	2.40171
$519$	−31.6634	−1.38987
$520$	1.58892	0.0696788
$521$	13.0092	0.569944	0.284972	−	0.958536i	$-0.408016\pi$
$521$	13.0092	0.569944	0.284972	+	0.958536i	$0.408016\pi$
$522$	12.4420	0.544572
$523$	−31.4883	−1.37689	−0.688444	−	0.725289i	$-0.741706\pi$
$523$	−31.4883	−1.37689	−0.688444	+	0.725289i	$0.741706\pi$
$524$	3.40571	0.148779
$525$	−56.5819	−2.46944
$526$	17.2504	0.752153
$527$	7.62998	0.332367
$528$	−60.0793	−2.61462
$529$	−19.1140	−0.831043
$530$	−0.107417	−0.00466589
$531$	2.63653	0.114416
$532$	−4.14711	−0.179800
$533$	33.5482	1.45313
$534$	48.3037	2.09030
$535$	−0.737178	−0.0318710
$536$	−15.3096	−0.661274
$537$	−24.1539	−1.04232
$538$	−41.9791	−1.80985
$539$	93.2841	4.01803
$540$	−0.0133819	−0.000575864 0
$541$	14.7931	0.636004	0.318002	−	0.948090i	$-0.396988\pi$
$541$	14.7931	0.636004	0.318002	+	0.948090i	$0.396988\pi$
$542$	−1.84857	−0.0794031
$543$	−33.1213	−1.42137
$544$	−0.883802	−0.0378927
$545$	−1.11266	−0.0476610
$546$	−98.6856	−4.22335
$547$	9.40663	0.402198	0.201099	−	0.979571i	$-0.435549\pi$
$547$	9.40663	0.402198	0.201099	+	0.979571i	$0.435549\pi$
$548$	0.729657	0.0311694
$549$	−17.4908	−0.746491
$550$	43.2413	1.84382
$551$	17.8201	0.759163
$552$	−12.6696	−0.539255
$553$	9.95386	0.423281
$554$	27.0992	1.15134
$555$	−1.83248	−0.0777844
$556$	2.34358	0.0993901
$557$	−23.4455	−0.993417	−0.496708	−	0.867917i	$-0.665458\pi$
$557$	−23.4455	−0.993417	−0.496708	+	0.867917i	$0.665458\pi$
$558$	29.5420	1.25061
$559$	19.0678	0.806481
$560$	−2.02844	−0.0857172
$561$	−14.0089	−0.591456
$562$	37.8619	1.59711
$563$	9.45651	0.398544	0.199272	−	0.979944i	$-0.436142\pi$
$563$	9.45651	0.398544	0.199272	+	0.979944i	$0.436142\pi$
$564$	1.60031	0.0673854
$565$	−0.687026	−0.0289034
$566$	−32.1359	−1.35077
$567$	−47.5598	−1.99732
$568$	−2.73205	−0.114634
$569$	−12.0746	−0.506192	−0.253096	−	0.967441i	$-0.581449\pi$
$569$	−12.0746	−0.506192	−0.253096	+	0.967441i	$0.581449\pi$
$570$	1.91475	0.0801999
$571$	−35.9914	−1.50619	−0.753097	−	0.657909i	$-0.771441\pi$
$571$	−35.9914	−1.50619	−0.753097	+	0.657909i	$0.771441\pi$
$572$	5.47599	0.228963
$573$	41.2598	1.72365
$574$	−39.7006	−1.65707
$575$	9.83714	0.410237
$576$	19.1924	0.799683
$577$	−22.5299	−0.937934	−0.468967	−	0.883216i	$-0.655374\pi$
$577$	−22.5299	−0.937934	−0.468967	+	0.883216i	$0.655374\pi$
$578$	−1.46853	−0.0610829
$579$	17.8966	0.743758
$580$	−0.0498329	−0.00206920
$581$	21.2066	0.879796
$582$	65.8515	2.72963
$583$	4.35814	0.180496
$584$	6.22190	0.257464
$585$	1.54749	0.0639810
$586$	−37.5034	−1.54925
$587$	−14.0271	−0.578959	−0.289480	−	0.957184i	$-0.593482\pi$
$587$	−14.0271	−0.578959	−0.289480	+	0.957184i	$0.593482\pi$
$588$	5.87719	0.242371
$589$	42.3116	1.74342
$590$	−0.145435	−0.00598748
$591$	37.1997	1.53019
$592$	33.4247	1.37375
$593$	−38.3335	−1.57417	−0.787083	−	0.616847i	$-0.788410\pi$
$593$	−38.3335	−1.57417	−0.787083	+	0.616847i	$0.788410\pi$
$594$	7.47752	0.306807
$595$	−0.472978	−0.0193902
$596$	1.17535	0.0481441
$597$	24.3912	0.998266
$598$	17.1571	0.701607
$599$	−18.4538	−0.754003	−0.377001	−	0.926213i	$-0.623045\pi$
$599$	−18.4538	−0.754003	−0.377001	+	0.926213i	$0.623045\pi$
$600$	−32.0722	−1.30934
$601$	1.67690	0.0684021	0.0342010	−	0.999415i	$-0.489111\pi$
$601$	1.67690	0.0684021	0.0342010	+	0.999415i	$0.489111\pi$
$602$	−22.5647	−0.919667
$603$	−14.9104	−0.607200
$604$	0.578461	0.0235372
$605$	2.35875	0.0958966
$606$	−26.3239	−1.06933
$607$	36.5267	1.48257	0.741286	−	0.671189i	$-0.234216\pi$
$607$	36.5267	1.48257	0.741286	+	0.671189i	$0.234216\pi$
$608$	−4.90107	−0.198765
$609$	−36.4364	−1.47648
$610$	0.964823	0.0390646
$611$	25.5126	1.03213
$612$	−0.412845	−0.0166883
$613$	−10.0886	−0.407474	−0.203737	−	0.979026i	$-0.565309\pi$
$613$	−10.0886	−0.407474	−0.203737	+	0.979026i	$0.565309\pi$
$614$	1.41964	0.0572920
$615$	1.33092	0.0536678
$616$	76.2885	3.07375
$617$	−39.7026	−1.59837	−0.799183	−	0.601087i	$-0.794734\pi$
$617$	−39.7026	−1.59837	−0.799183	+	0.601087i	$0.794734\pi$
$618$	53.1665	2.13867
$619$	−9.38078	−0.377045	−0.188523	−	0.982069i	$-0.560370\pi$
$619$	−9.38078	−0.377045	−0.188523	+	0.982069i	$0.560370\pi$
$620$	−0.118322	−0.00475191
$621$	1.70109	0.0682624
$622$	9.58040	0.384139
$623$	−66.1676	−2.65095
$624$	−60.3444	−2.41571
$625$	24.8530	0.994119
$626$	−12.9359	−0.517023
$627$	−77.6855	−3.10246
$628$	−0.798230	−0.0318528
$629$	7.79376	0.310758
$630$	−1.83129	−0.0729603
$631$	38.5627	1.53516	0.767579	−	0.640955i	$-0.221461\pi$
$631$	38.5627	1.53516	0.767579	+	0.640955i	$0.221461\pi$
$632$	5.64213	0.224432
$633$	42.2772	1.68037
$634$	−34.0386	−1.35185
$635$	1.20343	0.0477566
$636$	0.274576	0.0108877
$637$	93.6956	3.71235
$638$	27.8456	1.10242
$639$	−2.66082	−0.105260
$640$	−1.23374	−0.0487678
$641$	−20.6839	−0.816964	−0.408482	−	0.912766i	$-0.633942\pi$
$641$	−20.6839	−0.816964	−0.408482	+	0.912766i	$0.633942\pi$
$642$	25.9523	1.02425
$643$	42.4620	1.67454	0.837269	−	0.546792i	$-0.184151\pi$
$643$	42.4620	1.67454	0.837269	+	0.546792i	$0.184151\pi$
$644$	−1.47421	−0.0580922
$645$	0.756454	0.0297854
$646$	−8.14365	−0.320408
$647$	−5.21176	−0.204895	−0.102448	−	0.994738i	$-0.532667\pi$
$647$	−5.21176	−0.204895	−0.102448	+	0.994738i	$0.532667\pi$
$648$	−26.9582	−1.05902
$649$	5.90063	0.231620
$650$	43.4321	1.70355
$651$	−86.5136	−3.39073
$652$	−1.96455	−0.0769377
$653$	32.2524	1.26213	0.631067	−	0.775728i	$-0.282617\pi$
$653$	32.2524	1.26213	0.631067	+	0.775728i	$0.282617\pi$
$654$	39.1710	1.53171
$655$	2.15397	0.0841626
$656$	−24.2762	−0.947825
$657$	6.05967	0.236410
$658$	−30.1914	−1.17698
$659$	−17.0186	−0.662952	−0.331476	−	0.943464i	$-0.607547\pi$
$659$	−17.0186	−0.662952	−0.331476	+	0.943464i	$0.607547\pi$
$660$	0.217243	0.00845616
$661$	31.9974	1.24456	0.622278	−	0.782796i	$-0.286207\pi$
$661$	31.9974	1.24456	0.622278	+	0.782796i	$0.286207\pi$
$662$	25.8350	1.00411
$663$	−14.0707	−0.546461
$664$	12.0205	0.466485
$665$	−2.62287	−0.101711
$666$	30.1761	1.16930
$667$	6.33470	0.245281
$668$	−0.222218	−0.00859787
$669$	42.5315	1.64436
$670$	0.822484	0.0317753
$671$	−39.1450	−1.51118
$672$	10.0211	0.386573
$673$	−10.6682	−0.411228	−0.205614	−	0.978633i	$-0.565919\pi$
$673$	−10.6682	−0.411228	−0.205614	+	0.978633i	$0.565919\pi$
$674$	36.3360	1.39961
$675$	4.30619	0.165745
$676$	3.46452	0.133251
$677$	−0.128241	−0.00492872	−0.00246436	−	0.999997i	$-0.500784\pi$
$677$	−0.128241	−0.00492872	−0.00246436	+	0.999997i	$0.500784\pi$
$678$	24.1867	0.928884
$679$	−90.2050	−3.46175
$680$	−0.268097	−0.0102811
$681$	−35.0380	−1.34266
$682$	66.1158	2.53170
$683$	−30.6327	−1.17213	−0.586064	−	0.810264i	$-0.699323\pi$
$683$	−30.6327	−1.17213	−0.586064	+	0.810264i	$0.699323\pi$
$684$	−2.28941	−0.0875376
$685$	0.461478	0.0176322
$686$	−61.7836	−2.35891
$687$	−48.4051	−1.84677
$688$	−13.7978	−0.526038
$689$	4.37736	0.166764
$690$	0.680655	0.0259121
$691$	−28.9760	−1.10230	−0.551150	−	0.834406i	$-0.685811\pi$
$691$	−28.9760	−1.10230	−0.551150	+	0.834406i	$0.685811\pi$
$692$	−2.08837	−0.0793878
$693$	74.2994	2.82240
$694$	−8.40937	−0.319215
$695$	1.48222	0.0562238
$696$	−20.6532	−0.782857
$697$	−5.66055	−0.214409
$698$	−16.8085	−0.636210
$699$	40.3514	1.52623
$700$	−3.73187	−0.141051
$701$	6.50315	0.245621	0.122810	−	0.992430i	$-0.460809\pi$
$701$	6.50315	0.245621	0.122810	+	0.992430i	$0.460809\pi$
$702$	7.51051	0.283466
$703$	43.2198	1.63007
$704$	42.9531	1.61886
$705$	1.01213	0.0381191
$706$	−41.9437	−1.57857
$707$	36.0591	1.35614
$708$	0.371758	0.0139715
$709$	−10.3256	−0.387788	−0.193894	−	0.981023i	$-0.562112\pi$
$709$	−10.3256	−0.387788	−0.193894	+	0.981023i	$0.562112\pi$
$710$	0.146775	0.00550837
$711$	5.49502	0.206079
$712$	−37.5057	−1.40558
$713$	15.0409	0.563288
$714$	16.6511	0.623153
$715$	3.46333	0.129521
$716$	−1.59308	−0.0595361
$717$	38.5314	1.43898
$718$	3.13275	0.116913
$719$	−39.4592	−1.47158	−0.735790	−	0.677210i	$-0.763189\pi$
$719$	−39.4592	−1.47158	−0.735790	+	0.677210i	$0.763189\pi$
$720$	−1.11980	−0.0417324
$721$	−72.8289	−2.71229
$722$	−17.2580	−0.642276
$723$	−7.08120	−0.263353
$724$	−2.18452	−0.0811870
$725$	16.0359	0.595557
$726$	−83.0393	−3.08188
$727$	35.8216	1.32855	0.664275	−	0.747489i	$-0.268741\pi$
$727$	35.8216	1.32855	0.664275	+	0.747489i	$0.268741\pi$
$728$	76.6251	2.83991
$729$	−20.1092	−0.744785
$730$	−0.334262	−0.0123716
$731$	−3.21729	−0.118996
$732$	−2.46626	−0.0911555
$733$	−5.49754	−0.203056	−0.101528	−	0.994833i	$-0.532373\pi$
$733$	−5.49754	−0.203056	−0.101528	+	0.994833i	$0.532373\pi$
$734$	−12.0138	−0.443438
$735$	3.71708	0.137106
$736$	−1.74223	−0.0642196
$737$	−33.3700	−1.22920
$738$	−21.9167	−0.806764
$739$	35.1152	1.29173	0.645866	−	0.763451i	$-0.276496\pi$
$739$	35.1152	1.29173	0.645866	+	0.763451i	$0.276496\pi$
$740$	−0.120861	−0.00444296
$741$	−78.0282	−2.86644
$742$	−5.18014	−0.190169
$743$	−9.81346	−0.360021	−0.180011	−	0.983665i	$-0.557613\pi$
$743$	−9.81346	−0.360021	−0.180011	+	0.983665i	$0.557613\pi$
$744$	−49.0383	−1.79783
$745$	0.743357	0.0272345
$746$	23.5130	0.860870
$747$	11.7071	0.428339
$748$	−0.923959	−0.0337833
$749$	−35.5501	−1.29897
$750$	3.44945	0.125956
$751$	−44.6012	−1.62752	−0.813760	−	0.581201i	$-0.802583\pi$
$751$	−44.6012	−1.62752	−0.813760	+	0.581201i	$0.802583\pi$
$752$	−18.4615	−0.673220
$753$	6.48313	0.236258
$754$	27.9684	1.01855
$755$	0.365852	0.0133147
$756$	−0.645335	−0.0234706
$757$	10.0654	0.365834	0.182917	−	0.983128i	$-0.441446\pi$
$757$	10.0654	0.365834	0.182917	+	0.983128i	$0.441446\pi$
$758$	−19.8427	−0.720718
$759$	−27.6157	−1.00239
$760$	−1.48672	−0.0539289
$761$	−8.15356	−0.295566	−0.147783	−	0.989020i	$-0.547214\pi$
$761$	−8.15356	−0.295566	−0.147783	+	0.989020i	$0.547214\pi$
$762$	−42.3666	−1.53478
$763$	−53.6575	−1.94253
$764$	2.72129	0.0984530
$765$	−0.261107	−0.00944035
$766$	−7.61649	−0.275195
$767$	5.92666	0.213999
$768$	8.86893	0.320030
$769$	−8.18383	−0.295116	−0.147558	−	0.989053i	$-0.547141\pi$
$769$	−8.18383	−0.295116	−0.147558	+	0.989053i	$0.547141\pi$
$770$	−4.09848	−0.147699
$771$	10.7652	0.387701
$772$	1.18037	0.0424826
$773$	25.4522	0.915450	0.457725	−	0.889094i	$-0.348664\pi$
$773$	25.4522	0.915450	0.457725	+	0.889094i	$0.348664\pi$
$774$	−12.4568	−0.447750
$775$	38.0751	1.36770
$776$	−51.1308	−1.83549
$777$	−88.3706	−3.17028
$778$	−11.9429	−0.428174
$779$	−31.3902	−1.12467
$780$	0.218201	0.00781285
$781$	−5.95499	−0.213086
$782$	−2.89491	−0.103522
$783$	2.77301	0.0990992
$784$	−67.8001	−2.42143
$785$	−0.504847	−0.0180188
$786$	−75.8303	−2.70478
$787$	34.5454	1.23141	0.615704	−	0.787977i	$-0.288872\pi$
$787$	34.5454	1.23141	0.615704	+	0.787977i	$0.288872\pi$
$788$	2.45351	0.0874028
$789$	−27.8883	−0.992849
$790$	−0.303115	−0.0107843
$791$	−33.1316	−1.17802
$792$	42.1150	1.49649
$793$	−39.3177	−1.39621
$794$	−5.78022	−0.205132
$795$	0.173658	0.00615902
$796$	1.60873	0.0570198
$797$	−19.0276	−0.673991	−0.336995	−	0.941506i	$-0.609411\pi$
$797$	−19.0276	−0.673991	−0.336995	+	0.941506i	$0.609411\pi$
$798$	92.3379	3.26873
$799$	−4.30472	−0.152290
$800$	−4.41034	−0.155929
$801$	−36.5278	−1.29065
$802$	−34.3571	−1.21319
$803$	13.5617	0.478583
$804$	−2.10241	−0.0741464
$805$	−0.932379	−0.0328621
$806$	66.4075	2.33910
$807$	67.8666	2.38902
$808$	20.4393	0.719053
$809$	47.9880	1.68717	0.843584	−	0.536997i	$-0.180441\pi$
$809$	47.9880	1.68717	0.843584	+	0.536997i	$0.180441\pi$
$810$	1.44829	0.0508877
$811$	−28.6256	−1.00518	−0.502590	−	0.864525i	$-0.667619\pi$
$811$	−28.6256	−1.00518	−0.502590	+	0.864525i	$0.667619\pi$
$812$	−2.40317	−0.0843347
$813$	2.98854	0.104813
$814$	67.5350	2.36710
$815$	−1.24250	−0.0435227
$816$	10.1819	0.356436
$817$	−17.8413	−0.624188
$818$	14.9953	0.524298
$819$	74.6272	2.60769
$820$	0.0877809	0.00306544
$821$	−39.1164	−1.36517	−0.682585	−	0.730806i	$-0.739144\pi$
$821$	−39.1164	−1.36517	−0.682585	+	0.730806i	$0.739144\pi$
$822$	−16.2463	−0.566654
$823$	−47.0761	−1.64097	−0.820485	−	0.571669i	$-0.806296\pi$
$823$	−47.0761	−1.64097	−0.820485	+	0.571669i	$0.806296\pi$
$824$	−41.2815	−1.43811
$825$	−69.9071	−2.43385
$826$	−7.01356	−0.244033
$827$	4.84922	0.168624	0.0843119	−	0.996439i	$-0.473131\pi$
$827$	4.84922	0.168624	0.0843119	+	0.996439i	$0.473131\pi$
$828$	−0.813839	−0.0282829
$829$	32.6887	1.13532	0.567662	−	0.823262i	$-0.307848\pi$
$829$	32.6887	1.13532	0.567662	+	0.823262i	$0.307848\pi$
$830$	−0.645781	−0.0224154
$831$	−43.8106	−1.51977
$832$	43.1426	1.49570
$833$	−15.8092	−0.547755
$834$	−52.1814	−1.80689
$835$	−0.140544	−0.00486371
$836$	−5.12376	−0.177209
$837$	6.58415	0.227581
$838$	35.4659	1.22515
$839$	53.8937	1.86062	0.930308	−	0.366779i	$-0.119539\pi$
$839$	53.8937	1.86062	0.930308	+	0.366779i	$0.119539\pi$
$840$	3.03986	0.104885
$841$	−18.6736	−0.643917
$842$	29.5690	1.01902
$843$	−61.2103	−2.10819
$844$	2.78840	0.0959806
$845$	2.19116	0.0753783
$846$	−16.6671	−0.573028
$847$	113.749	3.90848
$848$	−3.16755	−0.108774
$849$	51.9533	1.78303
$850$	−7.32826	−0.251357
$851$	15.3638	0.526664
$852$	−0.375183	−0.0128536
$853$	53.7427	1.84011	0.920057	−	0.391784i	$-0.128142\pi$
$853$	53.7427	1.84011	0.920057	+	0.391784i	$0.128142\pi$
$854$	46.5282	1.59216
$855$	−1.44795	−0.0495190
$856$	−20.1508	−0.688740
$857$	23.5525	0.804539	0.402269	−	0.915521i	$-0.368222\pi$
$857$	23.5525	0.804539	0.402269	+	0.915521i	$0.368222\pi$
$858$	−121.926	−4.16250
$859$	−58.4389	−1.99391	−0.996955	−	0.0779784i	$-0.975153\pi$
$859$	−58.4389	−1.99391	−0.996955	+	0.0779784i	$0.975153\pi$
$860$	0.0498921	0.00170130
$861$	64.1829	2.18735
$862$	1.07448	0.0365969
$863$	54.3686	1.85073	0.925364	−	0.379079i	$-0.123759\pi$
$863$	54.3686	1.85073	0.925364	+	0.379079i	$0.123759\pi$
$864$	−0.762661	−0.0259462
$865$	−1.32080	−0.0449087
$866$	−22.3836	−0.760625
$867$	2.37414	0.0806299
$868$	−5.70601	−0.193675
$869$	12.2980	0.417182
$870$	1.10956	0.0376176
$871$	−33.5172	−1.13569
$872$	−30.4146	−1.02997
$873$	−49.7976	−1.68539
$874$	−16.0535	−0.543019
$875$	−4.72514	−0.159739
$876$	0.854431	0.0288686
$877$	13.4057	0.452680	0.226340	−	0.974048i	$-0.427324\pi$
$877$	13.4057	0.452680	0.226340	+	0.974048i	$0.427324\pi$
$878$	−23.6738	−0.798951
$879$	60.6307	2.04502
$880$	−2.50614	−0.0844820
$881$	−53.3129	−1.79616	−0.898079	−	0.439835i	$-0.855037\pi$
$881$	−53.3129	−1.79616	−0.898079	+	0.439835i	$0.855037\pi$
$882$	−61.2104	−2.06106
$883$	−20.6689	−0.695564	−0.347782	−	0.937575i	$-0.613065\pi$
$883$	−20.6689	−0.695564	−0.347782	+	0.937575i	$0.613065\pi$
$884$	−0.928035	−0.0312132
$885$	0.235121	0.00790352
$886$	18.2132	0.611883
$887$	18.3024	0.614534	0.307267	−	0.951623i	$-0.400585\pi$
$887$	18.3024	0.614534	0.307267	+	0.951623i	$0.400585\pi$
$888$	−50.0909	−1.68094
$889$	58.0349	1.94643
$890$	2.01493	0.0675407
$891$	−58.7602	−1.96854
$892$	2.80517	0.0939242
$893$	−23.8716	−0.798831
$894$	−26.1698	−0.875249
$895$	−1.00755	−0.0336788
$896$	−59.4965	−1.98764
$897$	−27.7375	−0.926128
$898$	−53.7348	−1.79315
$899$	24.5188	0.817746
$900$	−2.06018	−0.0686725
$901$	−0.738589	−0.0246060
$902$	−49.0502	−1.63319
$903$	36.4797	1.21397
$904$	−18.7799	−0.624610
$905$	−1.38162	−0.0459265
$906$	−12.8798	−0.427902
$907$	38.1688	1.26737	0.633687	−	0.773590i	$-0.281541\pi$
$907$	38.1688	1.26737	0.633687	+	0.773590i	$0.281541\pi$
$908$	−2.31093	−0.0766910
$909$	19.9064	0.660254
$910$	−4.11656	−0.136463
$911$	43.2585	1.43322	0.716609	−	0.697476i	$-0.245693\pi$
$911$	43.2585	1.43322	0.716609	+	0.697476i	$0.245693\pi$
$912$	56.4628	1.86967
$913$	26.2007	0.867118
$914$	−0.377172	−0.0124757
$915$	−1.55980	−0.0515656
$916$	−3.19257	−0.105485
$917$	103.874	3.43023
$918$	−1.26724	−0.0418252
$919$	16.4161	0.541516	0.270758	−	0.962648i	$-0.412726\pi$
$919$	16.4161	0.541516	0.270758	+	0.962648i	$0.412726\pi$
$920$	−0.528499	−0.0174241
$921$	−2.29509	−0.0756259
$922$	−35.5339	−1.17025
$923$	−5.98126	−0.196876
$924$	10.4764	0.344649
$925$	38.8924	1.27877
$926$	−22.9168	−0.753093
$927$	−40.2051	−1.32051
$928$	−2.84008	−0.0932301
$929$	7.90080	0.259217	0.129608	−	0.991565i	$-0.458628\pi$
$929$	7.90080	0.259217	0.129608	+	0.991565i	$0.458628\pi$
$930$	2.63451	0.0863889
$931$	−87.6688	−2.87323
$932$	2.66138	0.0871765
$933$	−15.4884	−0.507067
$934$	7.84916	0.256832
$935$	−0.584366	−0.0191108
$936$	42.3008	1.38264
$937$	−3.85102	−0.125807	−0.0629037	−	0.998020i	$-0.520036\pi$
$937$	−3.85102	−0.125807	−0.0629037	+	0.998020i	$0.520036\pi$
$938$	39.6640	1.29507
$939$	20.9132	0.682475
$940$	0.0667553	0.00217732
$941$	−43.7205	−1.42525	−0.712624	−	0.701546i	$-0.752494\pi$
$941$	−43.7205	−1.42525	−0.712624	+	0.701546i	$0.752494\pi$
$942$	17.7731	0.579078
$943$	−11.1586	−0.363375
$944$	−4.28865	−0.139584
$945$	−0.408148	−0.0132770
$946$	−27.8787	−0.906414
$947$	−21.7038	−0.705277	−0.352639	−	0.935760i	$-0.614716\pi$
$947$	−21.7038	−0.705277	−0.352639	+	0.935760i	$0.614716\pi$
$948$	0.774814	0.0251648
$949$	13.6215	0.442174
$950$	−40.6384	−1.31848
$951$	55.0293	1.78445
$952$	−12.9289	−0.419027
$953$	40.1166	1.29950	0.649752	−	0.760146i	$-0.274873\pi$
$953$	40.1166	1.29950	0.649752	+	0.760146i	$0.274873\pi$
$954$	−2.85969	−0.0925859
$955$	1.72110	0.0556936
$956$	2.54134	0.0821929
$957$	−45.0173	−1.45520
$958$	9.05914	0.292687
$959$	22.2546	0.718637
$960$	1.71155	0.0552399
$961$	27.2166	0.877956
$962$	67.8329	2.18702
$963$	−19.6254	−0.632420
$964$	−0.467042	−0.0150424
$965$	0.746538	0.0240319
$966$	32.8243	1.05610
$967$	−33.7396	−1.08499	−0.542497	−	0.840058i	$-0.682521\pi$
$967$	−33.7396	−1.08499	−0.542497	+	0.840058i	$0.682521\pi$
$968$	64.4764	2.07235
$969$	13.1656	0.422941
$970$	2.74692	0.0881983
$971$	20.1607	0.646987	0.323494	−	0.946230i	$-0.395143\pi$
$971$	20.1607	0.646987	0.323494	+	0.946230i	$0.395143\pi$
$972$	−3.29671	−0.105742
$973$	71.4794	2.29152
$974$	−0.141342	−0.00452889
$975$	−70.2155	−2.24870
$976$	28.4511	0.910697
$977$	−28.6990	−0.918162	−0.459081	−	0.888394i	$-0.651821\pi$
$977$	−28.6990	−0.918162	−0.459081	+	0.888394i	$0.651821\pi$
$978$	43.7419	1.39871
$979$	−81.7502	−2.61275
$980$	0.245160	0.00783136
$981$	−29.6215	−0.945743
$982$	−15.3706	−0.490496
$983$	52.3082	1.66837	0.834186	−	0.551483i	$-0.185938\pi$
$983$	52.3082	1.66837	0.834186	+	0.551483i	$0.185938\pi$
$984$	36.3807	1.15977
$985$	1.55174	0.0494427
$986$	−4.71909	−0.150286
$987$	48.8096	1.55363
$988$	−5.14636	−0.163728
$989$	−6.34223	−0.201671
$990$	−2.26256	−0.0719090
$991$	31.4040	0.997582	0.498791	−	0.866722i	$-0.333778\pi$
$991$	31.4040	0.997582	0.498791	+	0.866722i	$0.333778\pi$
$992$	−6.74340	−0.214103
$993$	−41.7668	−1.32543
$994$	7.07817	0.224506
$995$	1.01745	0.0322554
$996$	1.65073	0.0523053
$997$	−55.9995	−1.77352	−0.886761	−	0.462228i	$-0.847050\pi$
$997$	−55.9995	−1.77352	−0.886761	+	0.462228i	$0.847050\pi$
$998$	26.9385	0.852724
$999$	6.72548	0.212785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.j.1.5	✓	22
3.2	odd	2		9027.2.a.s.1.18		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.j.1.5	✓	22	1.1	even	1	trivial
9027.2.a.s.1.18		22	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:	\( N \)	\(=\)	\( 1003 = 17 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1003.a (trivial)

\(f(q)\)	\(=\)	\(q-1.46853 q^{2} +2.37414 q^{3} +0.156587 q^{4} +0.0990345 q^{5} -3.48650 q^{6} +4.77589 q^{7} +2.70711 q^{8} +2.63653 q^{9} +O(q^{10})\)	\(q-1.46853 q^{2} +2.37414 q^{3} +0.156587 q^{4} +0.0990345 q^{5} -3.48650 q^{6} +4.77589 q^{7} +2.70711 q^{8} +2.63653 q^{9} -0.145435 q^{10} +5.90063 q^{11} +0.371758 q^{12} +5.92666 q^{13} -7.01356 q^{14} +0.235121 q^{15} -4.28865 q^{16} -1.00000 q^{17} -3.87183 q^{18} -5.54544 q^{19} +0.0155075 q^{20} +11.3386 q^{21} -8.66526 q^{22} -1.97129 q^{23} +6.42706 q^{24} -4.99019 q^{25} -8.70349 q^{26} -0.862931 q^{27} +0.747841 q^{28} -3.21347 q^{29} -0.345283 q^{30} -7.62998 q^{31} +0.883802 q^{32} +14.0089 q^{33} +1.46853 q^{34} +0.472978 q^{35} +0.412845 q^{36} -7.79376 q^{37} +8.14365 q^{38} +14.0707 q^{39} +0.268097 q^{40} +5.66055 q^{41} -16.6511 q^{42} +3.21729 q^{43} +0.923959 q^{44} +0.261107 q^{45} +2.89491 q^{46} +4.30472 q^{47} -10.1819 q^{48} +15.8092 q^{49} +7.32826 q^{50} -2.37414 q^{51} +0.928035 q^{52} +0.738589 q^{53} +1.26724 q^{54} +0.584366 q^{55} +12.9289 q^{56} -13.1656 q^{57} +4.71909 q^{58} +1.00000 q^{59} +0.0368169 q^{60} -6.63404 q^{61} +11.2049 q^{62} +12.5918 q^{63} +7.27942 q^{64} +0.586943 q^{65} -20.5725 q^{66} -5.65533 q^{67} -0.156587 q^{68} -4.68012 q^{69} -0.694584 q^{70} -1.00921 q^{71} +7.13738 q^{72} +2.29835 q^{73} +11.4454 q^{74} -11.8474 q^{75} -0.868341 q^{76} +28.1808 q^{77} -20.6633 q^{78} +2.08419 q^{79} -0.424725 q^{80} -9.95830 q^{81} -8.31271 q^{82} +4.44033 q^{83} +1.77548 q^{84} -0.0990345 q^{85} -4.72470 q^{86} -7.62923 q^{87} +15.9737 q^{88} -13.8545 q^{89} -0.383444 q^{90} +28.3051 q^{91} -0.308678 q^{92} -18.1146 q^{93} -6.32162 q^{94} -0.549189 q^{95} +2.09827 q^{96} -18.8876 q^{97} -23.2163 q^{98} +15.5572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9}+O(q^{10}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9	\( 22 q + 5 q^{2} + 7 q^{3} + 25 q^{4} + 19 q^{5} + 5 q^{6} + 3 q^{7} + 21 q^{8} + 31 q^{9} + 8 q^{11} + 20 q^{12} + 14 q^{13} + 5 q^{14} + 15 q^{15} + 23 q^{16} - 22 q^{17} + 6 q^{18} + 6 q^{19} + 43 q^{20} + 8 q^{21} - 8 q^{22} + 15 q^{23} - 9 q^{24} + 33 q^{25} + 9 q^{26} + 25 q^{27} + 11 q^{28} - q^{29} - 51 q^{30} - 9 q^{31} + 37 q^{32} + 21 q^{33} - 5 q^{34} + 29 q^{35} + 30 q^{36} - 2 q^{37} + 39 q^{38} + 4 q^{39} + 4 q^{40} + 21 q^{41} - 65 q^{42} + q^{43} + 17 q^{44} + 65 q^{45} - 39 q^{46} + 37 q^{47} + 15 q^{48} + 25 q^{49} - 48 q^{50} - 7 q^{51} + 7 q^{52} + 69 q^{53} + 13 q^{54} + 10 q^{55} - 33 q^{56} - 4 q^{57} + 4 q^{58} + 22 q^{59} + 18 q^{60} - 29 q^{61} + 29 q^{62} + 7 q^{63} - 3 q^{64} + 25 q^{65} - 16 q^{66} - 10 q^{67} - 25 q^{68} + 26 q^{69} + 29 q^{70} + 3 q^{71} + 53 q^{72} - 4 q^{73} + 13 q^{74} - 8 q^{75} - 13 q^{76} + 71 q^{77} + 11 q^{78} - 20 q^{79} - 9 q^{80} + 42 q^{81} + 11 q^{82} + 24 q^{83} - 92 q^{84} - 19 q^{85} - 10 q^{86} - 4 q^{87} + 2 q^{88} + 40 q^{89} - 78 q^{90} - 31 q^{91} - 39 q^{92} + 53 q^{93} + 32 q^{94} + 42 q^{95} - 36 q^{96} + 13 q^{97} - 15 q^{98} - 64 q^{99}+O(q^{100}) \) 22 * q + 5 * q^2 + 7 * q^3 + 25 * q^4 + 19 * q^5 + 5 * q^6 + 3 * q^7 + 21 * q^8 + 31 * q^9 + 8 * q^11 + 20 * q^12 + 14 * q^13 + 5 * q^14 + 15 * q^15 + 23 * q^16 - 22 * q^17 + 6 * q^18 + 6 * q^19 + 43 * q^20 + 8 * q^21 - 8 * q^22 + 15 * q^23 - 9 * q^24 + 33 * q^25 + 9 * q^26 + 25 * q^27 + 11 * q^28 - q^29 - 51 * q^30 - 9 * q^31 + 37 * q^32 + 21 * q^33 - 5 * q^34 + 29 * q^35 + 30 * q^36 - 2 * q^37 + 39 * q^38 + 4 * q^39 + 4 * q^40 + 21 * q^41 - 65 * q^42 + q^43 + 17 * q^44 + 65 * q^45 - 39 * q^46 + 37 * q^47 + 15 * q^48 + 25 * q^49 - 48 * q^50 - 7 * q^51 + 7 * q^52 + 69 * q^53 + 13 * q^54 + 10 * q^55 - 33 * q^56 - 4 * q^57 + 4 * q^58 + 22 * q^59 + 18 * q^60 - 29 * q^61 + 29 * q^62 + 7 * q^63 - 3 * q^64 + 25 * q^65 - 16 * q^66 - 10 * q^67 - 25 * q^68 + 26 * q^69 + 29 * q^70 + 3 * q^71 + 53 * q^72 - 4 * q^73 + 13 * q^74 - 8 * q^75 - 13 * q^76 + 71 * q^77 + 11 * q^78 - 20 * q^79 - 9 * q^80 + 42 * q^81 + 11 * q^82 + 24 * q^83 - 92 * q^84 - 19 * q^85 - 10 * q^86 - 4 * q^87 + 2 * q^88 + 40 * q^89 - 78 * q^90 - 31 * q^91 - 39 * q^92 + 53 * q^93 + 32 * q^94 + 42 * q^95 - 36 * q^96 + 13 * q^97 - 15 * q^98 - 64 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more