LMFDB - Embedded newform 1003.2.a.g.1.9

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:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3x^{9} - 10x^{8} + 34x^{7} + 28x^{6} - 129x^{5} - 3x^{4} + 178x^{3} - 56x^{2} - 56x + 15 $ x^10 - 3x^9 - 10x^8 + 34x^7 + 28x^6 - 129x^5 - 3x^4 + 178x^3 - 56x^2 - 56*x + 15
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$0.252877$ of defining polynomial
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)

$f(q)$	$=$	$q+2.03516 q^{2} -0.747123 q^{3} +2.14188 q^{4} -1.25900 q^{5} -1.52052 q^{6} +0.391654 q^{7} +0.288756 q^{8} -2.44181 q^{9} +O(q^{10})$	\(q+2.03516 q^{2} -0.747123 q^{3} +2.14188 q^{4} -1.25900 q^{5} -1.52052 q^{6} +0.391654 q^{7} +0.288756 q^{8} -2.44181 q^{9} -2.56227 q^{10} -4.83256 q^{11} -1.60025 q^{12} -1.03108 q^{13} +0.797079 q^{14} +0.940629 q^{15} -3.69610 q^{16} -1.00000 q^{17} -4.96947 q^{18} +0.340142 q^{19} -2.69663 q^{20} -0.292614 q^{21} -9.83504 q^{22} -5.15302 q^{23} -0.215736 q^{24} -3.41492 q^{25} -2.09841 q^{26} +4.06570 q^{27} +0.838877 q^{28} +7.62344 q^{29} +1.91433 q^{30} +9.77155 q^{31} -8.09968 q^{32} +3.61052 q^{33} -2.03516 q^{34} -0.493092 q^{35} -5.23006 q^{36} +7.73716 q^{37} +0.692244 q^{38} +0.770341 q^{39} -0.363543 q^{40} -6.03800 q^{41} -0.595516 q^{42} -7.56365 q^{43} -10.3508 q^{44} +3.07424 q^{45} -10.4872 q^{46} -2.04453 q^{47} +2.76144 q^{48} -6.84661 q^{49} -6.94991 q^{50} +0.747123 q^{51} -2.20844 q^{52} -0.809105 q^{53} +8.27436 q^{54} +6.08419 q^{55} +0.113092 q^{56} -0.254128 q^{57} +15.5149 q^{58} -1.00000 q^{59} +2.01472 q^{60} -9.58988 q^{61} +19.8867 q^{62} -0.956343 q^{63} -9.09195 q^{64} +1.29813 q^{65} +7.34799 q^{66} +4.05372 q^{67} -2.14188 q^{68} +3.84994 q^{69} -1.00352 q^{70} +2.93943 q^{71} -0.705085 q^{72} -5.82102 q^{73} +15.7464 q^{74} +2.55136 q^{75} +0.728544 q^{76} -1.89269 q^{77} +1.56777 q^{78} +6.90744 q^{79} +4.65340 q^{80} +4.28784 q^{81} -12.2883 q^{82} +0.141211 q^{83} -0.626744 q^{84} +1.25900 q^{85} -15.3932 q^{86} -5.69565 q^{87} -1.39543 q^{88} -10.8692 q^{89} +6.25657 q^{90} -0.403825 q^{91} -11.0372 q^{92} -7.30055 q^{93} -4.16095 q^{94} -0.428239 q^{95} +6.05146 q^{96} +11.2025 q^{97} -13.9340 q^{98} +11.8002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) $ 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * 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 $

$2$	2.03516	1.43908	0.719538	−	0.694453i	$-0.244353\pi$
$2$	2.03516	1.43908	0.719538	+	0.694453i	$0.244353\pi$
$3$	−0.747123	−0.431352	−0.215676	−	0.976465i	$-0.569195\pi$
$3$	−0.747123	−0.431352	−0.215676	+	0.976465i	$0.569195\pi$
$4$	2.14188	1.07094
$5$	−1.25900	−0.563042	−0.281521	−	0.959555i	$-0.590839\pi$
$5$	−1.25900	−0.563042	−0.281521	+	0.959555i	$0.590839\pi$
$6$	−1.52052	−0.620748
$7$	0.391654	0.148031	0.0740156	−	0.997257i	$-0.476419\pi$
$7$	0.391654	0.148031	0.0740156	+	0.997257i	$0.476419\pi$
$8$	0.288756	0.102090
$9$	−2.44181	−0.813936
$10$	−2.56227	−0.810261
$11$	−4.83256	−1.45707	−0.728535	−	0.685008i	$-0.759799\pi$
$11$	−4.83256	−1.45707	−0.728535	+	0.685008i	$0.759799\pi$
$12$	−1.60025	−0.461953
$13$	−1.03108	−0.285969	−0.142984	−	0.989725i	$-0.545670\pi$
$13$	−1.03108	−0.285969	−0.142984	+	0.989725i	$0.545670\pi$
$14$	0.797079	0.213028
$15$	0.940629	0.242869
$16$	−3.69610	−0.924026
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−4.96947	−1.17132
$19$	0.340142	0.0780339	0.0390170	−	0.999239i	$-0.487577\pi$
$19$	0.340142	0.0780339	0.0390170	+	0.999239i	$0.487577\pi$
$20$	−2.69663	−0.602985
$21$	−0.292614	−0.0638535
$22$	−9.83504	−2.09684
$23$	−5.15302	−1.07448	−0.537240	−	0.843430i	$-0.680533\pi$
$23$	−5.15302	−1.07448	−0.537240	+	0.843430i	$0.680533\pi$
$24$	−0.215736	−0.0440369
$25$	−3.41492	−0.682984
$26$	−2.09841	−0.411531
$27$	4.06570	0.782445
$28$	0.838877	0.158533
$29$	7.62344	1.41564	0.707819	−	0.706394i	$-0.249679\pi$
$29$	7.62344	1.41564	0.707819	+	0.706394i	$0.249679\pi$
$30$	1.91433	0.349508
$31$	9.77155	1.75502	0.877511	−	0.479556i	$-0.159202\pi$
$31$	9.77155	1.75502	0.877511	+	0.479556i	$0.159202\pi$
$32$	−8.09968	−1.43183
$33$	3.61052	0.628510
$34$	−2.03516	−0.349027
$35$	−0.493092	−0.0833478
$36$	−5.23006	−0.871677
$37$	7.73716	1.27198	0.635991	−	0.771697i	$-0.280592\pi$
$37$	7.73716	1.27198	0.635991	+	0.771697i	$0.280592\pi$
$38$	0.692244	0.112297
$39$	0.770341	0.123353
$40$	−0.363543	−0.0574813
$41$	−6.03800	−0.942977	−0.471488	−	0.881872i	$-0.656283\pi$
$41$	−6.03800	−0.942977	−0.471488	+	0.881872i	$0.656283\pi$
$42$	−0.595516	−0.0918901
$43$	−7.56365	−1.15345	−0.576723	−	0.816940i	$-0.695669\pi$
$43$	−7.56365	−1.15345	−0.576723	+	0.816940i	$0.695669\pi$
$44$	−10.3508	−1.56044
$45$	3.07424	0.458280
$46$	−10.4872	−1.54626
$47$	−2.04453	−0.298225	−0.149113	−	0.988820i	$-0.547642\pi$
$47$	−2.04453	−0.298225	−0.149113	+	0.988820i	$0.547642\pi$
$48$	2.76144	0.398580
$49$	−6.84661	−0.978087
$50$	−6.94991	−0.982866
$51$	0.747123	0.104618
$52$	−2.20844	−0.306256
$53$	−0.809105	−0.111139	−0.0555696	−	0.998455i	$-0.517697\pi$
$53$	−0.809105	−0.111139	−0.0555696	+	0.998455i	$0.517697\pi$
$54$	8.27436	1.12600
$55$	6.08419	0.820392
$56$	0.113092	0.0151126
$57$	−0.254128	−0.0336601
$58$	15.5149	2.03721
$59$	−1.00000	−0.130189
$59$	−1.00000	−0.130189
$60$	2.01472	0.260099
$61$	−9.58988	−1.22786	−0.613929	−	0.789361i	$-0.710412\pi$
$61$	−9.58988	−1.22786	−0.613929	+	0.789361i	$0.710412\pi$
$62$	19.8867	2.52561
$63$	−0.956343	−0.120488
$64$	−9.09195	−1.13649
$65$	1.29813	0.161013
$66$	7.34799	0.904475
$67$	4.05372	0.495241	0.247621	−	0.968857i	$-0.420351\pi$
$67$	4.05372	0.495241	0.247621	+	0.968857i	$0.420351\pi$
$68$	−2.14188	−0.259742
$69$	3.84994	0.463479
$70$	−1.00352	−0.119944
$71$	2.93943	0.348846	0.174423	−	0.984671i	$-0.444194\pi$
$71$	2.93943	0.348846	0.174423	+	0.984671i	$0.444194\pi$
$72$	−0.705085	−0.0830951
$73$	−5.82102	−0.681299	−0.340649	−	0.940190i	$-0.610647\pi$
$73$	−5.82102	−0.681299	−0.340649	+	0.940190i	$0.610647\pi$
$74$	15.7464	1.83048
$75$	2.55136	0.294606
$76$	0.728544	0.0835698
$77$	−1.89269	−0.215692
$78$	1.56777	0.177515
$79$	6.90744	0.777148	0.388574	−	0.921417i	$-0.372968\pi$
$79$	6.90744	0.777148	0.388574	+	0.921417i	$0.372968\pi$
$80$	4.65340	0.520265
$81$	4.28784	0.476427
$82$	−12.2883	−1.35702
$83$	0.141211	0.0154999	0.00774995	−	0.999970i	$-0.497533\pi$
$83$	0.141211	0.0154999	0.00774995	+	0.999970i	$0.497533\pi$
$84$	−0.626744	−0.0683834
$85$	1.25900	0.136558
$86$	−15.3932	−1.65990
$87$	−5.69565	−0.610638
$88$	−1.39543	−0.148753
$89$	−10.8692	−1.15213	−0.576066	−	0.817403i	$-0.695413\pi$
$89$	−10.8692	−1.15213	−0.576066	+	0.817403i	$0.695413\pi$
$90$	6.25657	0.659500
$91$	−0.403825	−0.0423323
$92$	−11.0372	−1.15070
$93$	−7.30055	−0.757032
$94$	−4.16095	−0.429169
$95$	−0.428239	−0.0439364
$96$	6.05146	0.617624
$97$	11.2025	1.13744	0.568722	−	0.822530i	$-0.307438\pi$
$97$	11.2025	1.13744	0.568722	+	0.822530i	$0.307438\pi$
$98$	−13.9340	−1.40754
$99$	11.8002	1.18596
$100$	−7.31436	−0.731436
$101$	−0.749402	−0.0745682	−0.0372841	−	0.999305i	$-0.511871\pi$
$101$	−0.749402	−0.0745682	−0.0372841	+	0.999305i	$0.511871\pi$
$102$	1.52052	0.150554
$103$	−2.25909	−0.222595	−0.111297	−	0.993787i	$-0.535501\pi$
$103$	−2.25909	−0.222595	−0.111297	+	0.993787i	$0.535501\pi$
$104$	−0.297729	−0.0291947
$105$	0.368401	0.0359522
$106$	−1.64666	−0.159938
$107$	−12.5235	−1.21069	−0.605347	−	0.795962i	$-0.706966\pi$
$107$	−12.5235	−1.21069	−0.605347	+	0.795962i	$0.706966\pi$
$108$	8.70826	0.837952
$109$	18.1900	1.74228	0.871142	−	0.491031i	$-0.163380\pi$
$109$	18.1900	1.74228	0.871142	+	0.491031i	$0.163380\pi$
$110$	12.3823	1.18061
$111$	−5.78062	−0.548672
$112$	−1.44759	−0.136785
$113$	−6.90981	−0.650020	−0.325010	−	0.945711i	$-0.605368\pi$
$113$	−6.90981	−0.650020	−0.325010	+	0.945711i	$0.605368\pi$
$114$	−0.517192	−0.0484394
$115$	6.48766	0.604977
$116$	16.3285	1.51606
$117$	2.51769	0.232760
$118$	−2.03516	−0.187352
$119$	−0.391654	−0.0359028
$120$	0.271612	0.0247946
$121$	12.3536	1.12306
$122$	−19.5169	−1.76698
$123$	4.51113	0.406755
$124$	20.9295	1.87953
$125$	10.5944	0.947591
$126$	−1.94631	−0.173391
$127$	−4.39637	−0.390115	−0.195057	−	0.980792i	$-0.562489\pi$
$127$	−4.39637	−0.390115	−0.195057	+	0.980792i	$0.562489\pi$
$128$	−2.30423	−0.203667
$129$	5.65098	0.497541
$130$	2.64189	0.231709
$131$	−12.2220	−1.06784	−0.533922	−	0.845533i	$-0.679283\pi$
$131$	−12.2220	−1.06784	−0.533922	+	0.845533i	$0.679283\pi$
$132$	7.73331	0.673098
$133$	0.133218	0.0115515
$134$	8.24998	0.712690
$135$	−5.11872	−0.440549
$136$	−0.288756	−0.0247606
$137$	3.84564	0.328555	0.164278	−	0.986414i	$-0.447471\pi$
$137$	3.84564	0.328555	0.164278	+	0.986414i	$0.447471\pi$
$138$	7.83526	0.666982
$139$	−9.95666	−0.844513	−0.422256	−	0.906476i	$-0.638762\pi$
$139$	−9.95666	−0.844513	−0.422256	+	0.906476i	$0.638762\pi$
$140$	−1.05615	−0.0892606
$141$	1.52752	0.128640
$142$	5.98222	0.502017
$143$	4.98273	0.416677
$144$	9.02517	0.752097
$145$	−9.59791	−0.797063
$146$	−11.8467	−0.980441
$147$	5.11526	0.421900
$148$	16.5721	1.36222
$149$	2.04523	0.167551	0.0837757	−	0.996485i	$-0.473302\pi$
$149$	2.04523	0.167551	0.0837757	+	0.996485i	$0.473302\pi$
$150$	5.19244	0.423961
$151$	21.2968	1.73311	0.866553	−	0.499085i	$-0.166331\pi$
$151$	21.2968	1.73311	0.866553	+	0.499085i	$0.166331\pi$
$152$	0.0982179	0.00796652
$153$	2.44181	0.197408
$154$	−3.85193	−0.310397
$155$	−12.3024	−0.988152
$156$	1.64998	0.132104
$157$	1.56679	0.125044	0.0625219	−	0.998044i	$-0.480086\pi$
$157$	1.56679	0.125044	0.0625219	+	0.998044i	$0.480086\pi$
$158$	14.0578	1.11838
$159$	0.604501	0.0479401
$160$	10.1975	0.806183
$161$	−2.01820	−0.159057
$162$	8.72645	0.685614
$163$	−3.80832	−0.298290	−0.149145	−	0.988815i	$-0.547652\pi$
$163$	−3.80832	−0.298290	−0.149145	+	0.988815i	$0.547652\pi$
$164$	−12.9327	−1.00987
$165$	−4.54564	−0.353878
$166$	0.287387	0.0223056
$167$	20.1450	1.55886	0.779432	−	0.626487i	$-0.215508\pi$
$167$	20.1450	1.55886	0.779432	+	0.626487i	$0.215508\pi$
$168$	−0.0844938	−0.00651884
$169$	−11.9369	−0.918222
$170$	2.56227	0.196517
$171$	−0.830561	−0.0635146
$172$	−16.2005	−1.23527
$173$	4.03689	0.306919	0.153460	−	0.988155i	$-0.450959\pi$
$173$	4.03689	0.306919	0.153460	+	0.988155i	$0.450959\pi$
$174$	−11.5916	−0.878755
$175$	−1.33747	−0.101103
$176$	17.8616	1.34637
$177$	0.747123	0.0561572
$178$	−22.1206	−1.65801
$179$	−2.08535	−0.155867	−0.0779333	−	0.996959i	$-0.524832\pi$
$179$	−2.08535	−0.155867	−0.0779333	+	0.996959i	$0.524832\pi$
$180$	6.58465	0.490791
$181$	−24.0658	−1.78880	−0.894398	−	0.447272i	$-0.852396\pi$
$181$	−24.0658	−1.78880	−0.894398	+	0.447272i	$0.852396\pi$
$182$	−0.821849	−0.0609195
$183$	7.16482	0.529639
$184$	−1.48796	−0.109694
$185$	−9.74109	−0.716179
$186$	−14.8578	−1.08943
$187$	4.83256	0.353392
$188$	−4.37915	−0.319382
$189$	1.59235	0.115826
$190$	−0.871536	−0.0632278
$191$	−20.7125	−1.49870	−0.749352	−	0.662171i	$-0.769635\pi$
$191$	−20.7125	−1.49870	−0.749352	+	0.662171i	$0.769635\pi$
$192$	6.79281	0.490229
$193$	−6.92129	−0.498206	−0.249103	−	0.968477i	$-0.580136\pi$
$193$	−6.92129	−0.498206	−0.249103	+	0.968477i	$0.580136\pi$
$194$	22.7990	1.63687
$195$	−0.969860	−0.0694531
$196$	−14.6646	−1.04747
$197$	−22.4032	−1.59616	−0.798080	−	0.602551i	$-0.794151\pi$
$197$	−22.4032	−1.59616	−0.798080	+	0.602551i	$0.794151\pi$
$198$	24.0153	1.70669
$199$	27.1936	1.92770	0.963852	−	0.266437i	$-0.0858465\pi$
$199$	27.1936	1.92770	0.963852	+	0.266437i	$0.0858465\pi$
$200$	−0.986076	−0.0697261
$201$	−3.02863	−0.213623
$202$	−1.52515	−0.107309
$203$	2.98575	0.209558
$204$	1.60025	0.112040
$205$	7.60184	0.530936
$206$	−4.59761	−0.320331
$207$	12.5827	0.874557
$208$	3.81096	0.264243
$209$	−1.64376	−0.113701
$210$	0.749755	0.0517380
$211$	3.54351	0.243945	0.121973	−	0.992533i	$-0.461078\pi$
$211$	3.54351	0.243945	0.121973	+	0.992533i	$0.461078\pi$
$212$	−1.73301	−0.119024
$213$	−2.19612	−0.150476
$214$	−25.4874	−1.74228
$215$	9.52264	0.649439
$216$	1.17399	0.0798802
$217$	3.82706	0.259798
$218$	37.0195	2.50728
$219$	4.34902	0.293880
$220$	13.0316	0.878592
$221$	1.03108	0.0693577
$222$	−11.7645	−0.789581
$223$	−1.20713	−0.0808352	−0.0404176	−	0.999183i	$-0.512869\pi$
$223$	−1.20713	−0.0808352	−0.0404176	+	0.999183i	$0.512869\pi$
$224$	−3.17227	−0.211956
$225$	8.33857	0.555905
$226$	−14.0626	−0.935428
$227$	−10.0767	−0.668813	−0.334406	−	0.942429i	$-0.608536\pi$
$227$	−10.0767	−0.668813	−0.334406	+	0.942429i	$0.608536\pi$
$228$	−0.544313	−0.0360480
$229$	−16.7336	−1.10579	−0.552894	−	0.833252i	$-0.686476\pi$
$229$	−16.7336	−1.10579	−0.552894	+	0.833252i	$0.686476\pi$
$230$	13.2034	0.870609
$231$	1.41407	0.0930391
$232$	2.20131	0.144523
$233$	18.9582	1.24199	0.620995	−	0.783815i	$-0.286729\pi$
$233$	18.9582	1.24199	0.620995	+	0.783815i	$0.286729\pi$
$234$	5.12390	0.334960
$235$	2.57407	0.167914
$236$	−2.14188	−0.139425
$237$	−5.16071	−0.335224
$238$	−0.797079	−0.0516669
$239$	−9.35087	−0.604858	−0.302429	−	0.953172i	$-0.597797\pi$
$239$	−9.35087	−0.604858	−0.302429	+	0.953172i	$0.597797\pi$
$240$	−3.47666	−0.224417
$241$	−23.5224	−1.51521	−0.757606	−	0.652712i	$-0.773631\pi$
$241$	−23.5224	−1.51521	−0.757606	+	0.652712i	$0.773631\pi$
$242$	25.1416	1.61616
$243$	−15.4006	−0.987952
$244$	−20.5404	−1.31496
$245$	8.61988	0.550704
$246$	9.18088	0.585351
$247$	−0.350712	−0.0223153
$248$	2.82159	0.179171
$249$	−0.105502	−0.00668591
$250$	21.5613	1.36366
$251$	−18.6832	−1.17927	−0.589637	−	0.807668i	$-0.700729\pi$
$251$	−18.6832	−1.17927	−0.589637	+	0.807668i	$0.700729\pi$
$252$	−2.04837	−0.129035
$253$	24.9023	1.56559
$254$	−8.94733	−0.561405
$255$	−0.940629	−0.0589045
$256$	13.4944	0.843401
$257$	−13.3586	−0.833286	−0.416643	−	0.909070i	$-0.636793\pi$
$257$	−13.3586	−0.833286	−0.416643	+	0.909070i	$0.636793\pi$
$258$	11.5007	0.716000
$259$	3.03029	0.188293
$260$	2.78043	0.172435
$261$	−18.6150	−1.15224
$262$	−24.8738	−1.53671
$263$	8.17866	0.504318	0.252159	−	0.967686i	$-0.418859\pi$
$263$	8.17866	0.504318	0.252159	+	0.967686i	$0.418859\pi$
$264$	1.04256	0.0641649
$265$	1.01866	0.0625760
$266$	0.271120	0.0166234
$267$	8.12063	0.496975
$268$	8.68260	0.530374
$269$	−29.3192	−1.78762	−0.893812	−	0.448442i	$-0.851979\pi$
$269$	−29.3192	−1.78762	−0.893812	+	0.448442i	$0.851979\pi$
$270$	−10.4174	−0.633984
$271$	0.641330	0.0389580	0.0194790	−	0.999810i	$-0.493799\pi$
$271$	0.641330	0.0389580	0.0194790	+	0.999810i	$0.493799\pi$
$272$	3.69610	0.224109
$273$	0.301707	0.0182601
$274$	7.82650	0.472816
$275$	16.5028	0.995155
$276$	8.24613	0.496359
$277$	9.86637	0.592813	0.296406	−	0.955062i	$-0.404212\pi$
$277$	9.86637	0.592813	0.296406	+	0.955062i	$0.404212\pi$
$278$	−20.2634	−1.21532
$279$	−23.8602	−1.42847
$280$	−0.142383	−0.00850902
$281$	23.9147	1.42663	0.713316	−	0.700843i	$-0.247192\pi$
$281$	23.9147	1.42663	0.713316	+	0.700843i	$0.247192\pi$
$282$	3.10874	0.185123
$283$	15.7711	0.937493	0.468746	−	0.883333i	$-0.344706\pi$
$283$	15.7711	0.937493	0.468746	+	0.883333i	$0.344706\pi$
$284$	6.29592	0.373594
$285$	0.319947	0.0189520
$286$	10.1407	0.599630
$287$	−2.36480	−0.139590
$288$	19.7778	1.16542
$289$	1.00000	0.0588235
$290$	−19.5333	−1.14704
$291$	−8.36967	−0.490639
$292$	−12.4679	−0.729631
$293$	−9.13655	−0.533763	−0.266882	−	0.963729i	$-0.585993\pi$
$293$	−9.13655	−0.533763	−0.266882	+	0.963729i	$0.585993\pi$
$294$	10.4104	0.607146
$295$	1.25900	0.0733018
$296$	2.23415	0.129857
$297$	−19.6477	−1.14008
$298$	4.16237	0.241119
$299$	5.31316	0.307268
$300$	5.46473	0.315506
$301$	−2.96233	−0.170746
$302$	43.3423	2.49407
$303$	0.559895	0.0321652
$304$	−1.25720	−0.0721053
$305$	12.0737	0.691336
$306$	4.96947	0.284086
$307$	0.294677	0.0168181	0.00840906	−	0.999965i	$-0.497323\pi$
$307$	0.294677	0.0168181	0.00840906	+	0.999965i	$0.497323\pi$
$308$	−4.05392	−0.230993
$309$	1.68782	0.0960167
$310$	−25.0373	−1.42203
$311$	−4.42959	−0.251179	−0.125589	−	0.992082i	$-0.540082\pi$
$311$	−4.42959	−0.251179	−0.125589	+	0.992082i	$0.540082\pi$
$312$	0.222440	0.0125932
$313$	5.78925	0.327228	0.163614	−	0.986524i	$-0.447685\pi$
$313$	5.78925	0.327228	0.163614	+	0.986524i	$0.447685\pi$
$314$	3.18868	0.179948
$315$	1.20404	0.0678397
$316$	14.7949	0.832280
$317$	28.0074	1.57305	0.786525	−	0.617558i	$-0.211878\pi$
$317$	28.0074	1.57305	0.786525	+	0.617558i	$0.211878\pi$
$318$	1.23026	0.0689895
$319$	−36.8407	−2.06268
$320$	11.4468	0.639894
$321$	9.35661	0.522235
$322$	−4.10736	−0.228895
$323$	−0.340142	−0.0189260
$324$	9.18405	0.510225
$325$	3.52104	0.195312
$326$	−7.75054	−0.429263
$327$	−13.5902	−0.751538
$328$	−1.74351	−0.0962690
$329$	−0.800748	−0.0441467
$330$	−9.25112	−0.509257
$331$	18.4494	1.01407	0.507035	−	0.861926i	$-0.330742\pi$
$331$	18.4494	1.01407	0.507035	+	0.861926i	$0.330742\pi$
$332$	0.302457	0.0165995
$333$	−18.8927	−1.03531
$334$	40.9983	2.24332
$335$	−5.10364	−0.278842
$336$	1.08153	0.0590023
$337$	−18.7499	−1.02137	−0.510686	−	0.859767i	$-0.670609\pi$
$337$	−18.7499	−1.02137	−0.510686	+	0.859767i	$0.670609\pi$
$338$	−24.2935	−1.32139
$339$	5.16248	0.280387
$340$	2.69663	0.146245
$341$	−47.2216	−2.55719
$342$	−1.69033	−0.0914024
$343$	−5.42308	−0.292819
$344$	−2.18405	−0.117756
$345$	−4.84708	−0.260958
$346$	8.21573	0.441680
$347$	−27.9158	−1.49860	−0.749298	−	0.662232i	$-0.769609\pi$
$347$	−27.9158	−1.49860	−0.749298	+	0.662232i	$0.769609\pi$
$348$	−12.1994	−0.653957
$349$	−26.6941	−1.42890	−0.714452	−	0.699685i	$-0.753324\pi$
$349$	−26.6941	−1.42890	−0.714452	+	0.699685i	$0.753324\pi$
$350$	−2.72196	−0.145495
$351$	−4.19205	−0.223755
$352$	39.1422	2.08628
$353$	−16.7324	−0.890578	−0.445289	−	0.895387i	$-0.646899\pi$
$353$	−16.7324	−0.890578	−0.445289	+	0.895387i	$0.646899\pi$
$354$	1.52052	0.0808146
$355$	−3.70075	−0.196415
$356$	−23.2806	−1.23387
$357$	0.292614	0.0154868
$358$	−4.24403	−0.224304
$359$	36.8045	1.94247	0.971235	−	0.238124i	$-0.0765325\pi$
$359$	36.8045	1.94247	0.971235	+	0.238124i	$0.0765325\pi$
$360$	0.887703	0.0467860
$361$	−18.8843	−0.993911
$362$	−48.9778	−2.57421
$363$	−9.22967	−0.484432
$364$	−0.864945	−0.0453355
$365$	7.32867	0.383600
$366$	14.5816	0.762191
$367$	4.81752	0.251472	0.125736	−	0.992064i	$-0.459871\pi$
$367$	4.81752	0.251472	0.125736	+	0.992064i	$0.459871\pi$
$368$	19.0461	0.992847
$369$	14.7436	0.767522
$370$	−19.8247	−1.03064
$371$	−0.316889	−0.0164521
$372$	−15.6369	−0.810737
$373$	−32.9819	−1.70774	−0.853868	−	0.520490i	$-0.825749\pi$
$373$	−32.9819	−1.70774	−0.853868	+	0.520490i	$0.825749\pi$
$374$	9.83504	0.508558
$375$	−7.91531	−0.408745
$376$	−0.590370	−0.0304460
$377$	−7.86034	−0.404828
$378$	3.24068	0.166683
$379$	−14.7757	−0.758978	−0.379489	−	0.925196i	$-0.623900\pi$
$379$	−14.7757	−0.758978	−0.379489	+	0.925196i	$0.623900\pi$
$380$	−0.917238	−0.0470533
$381$	3.28463	0.168277
$382$	−42.1533	−2.15675
$383$	−13.6549	−0.697734	−0.348867	−	0.937172i	$-0.613433\pi$
$383$	−13.6549	−0.697734	−0.348867	+	0.937172i	$0.613433\pi$
$384$	1.72155	0.0878522
$385$	2.38290	0.121444
$386$	−14.0859	−0.716956
$387$	18.4690	0.938830
$388$	23.9945	1.21814
$389$	20.9463	1.06202	0.531010	−	0.847365i	$-0.321813\pi$
$389$	20.9463	1.06202	0.531010	+	0.847365i	$0.321813\pi$
$390$	−1.97382	−0.0999483
$391$	5.15302	0.260600
$392$	−1.97700	−0.0998534
$393$	9.13137	0.460617
$394$	−45.5941	−2.29700
$395$	−8.69648	−0.437567
$396$	25.2746	1.27010
$397$	−28.0387	−1.40722	−0.703611	−	0.710585i	$-0.748430\pi$
$397$	−28.0387	−1.40722	−0.703611	+	0.710585i	$0.748430\pi$
$398$	55.3434	2.77411
$399$	−0.0995302	−0.00498274
$400$	12.6219	0.631094
$401$	−12.2877	−0.613620	−0.306810	−	0.951771i	$-0.599262\pi$
$401$	−12.2877	−0.613620	−0.306810	+	0.951771i	$0.599262\pi$
$402$	−6.16376	−0.307420
$403$	−10.0752	−0.501882
$404$	−1.60513	−0.0798582
$405$	−5.39839	−0.268248
$406$	6.07648	0.301571
$407$	−37.3903	−1.85337
$408$	0.215736	0.0106805
$409$	−2.09302	−0.103493	−0.0517465	−	0.998660i	$-0.516479\pi$
$409$	−2.09302	−0.103493	−0.0517465	+	0.998660i	$0.516479\pi$
$410$	15.4710	0.764057
$411$	−2.87317	−0.141723
$412$	−4.83871	−0.238386
$413$	−0.391654	−0.0192720
$414$	25.6078	1.25855
$415$	−0.177785	−0.00872710
$416$	8.35138	0.409460
$417$	7.43885	0.364282
$418$	−3.34531	−0.163624
$419$	21.6835	1.05931	0.529654	−	0.848214i	$-0.322322\pi$
$419$	21.6835	1.05931	0.529654	+	0.848214i	$0.322322\pi$
$420$	0.789072	0.0385027
$421$	−20.3395	−0.991287	−0.495644	−	0.868526i	$-0.665068\pi$
$421$	−20.3395	−0.991287	−0.495644	+	0.868526i	$0.665068\pi$
$422$	7.21162	0.351056
$423$	4.99235	0.242736
$424$	−0.233634	−0.0113463
$425$	3.41492	0.165648
$426$	−4.46946	−0.216546
$427$	−3.75591	−0.181761
$428$	−26.8239	−1.29658
$429$	−3.72272	−0.179734
$430$	19.3801	0.934592
$431$	38.7328	1.86569	0.932846	−	0.360274i	$-0.117317\pi$
$431$	38.7328	1.86569	0.932846	+	0.360274i	$0.117317\pi$
$432$	−15.0272	−0.722999
$433$	13.7637	0.661443	0.330721	−	0.943728i	$-0.392708\pi$
$433$	13.7637	0.661443	0.330721	+	0.943728i	$0.392708\pi$
$434$	7.78869	0.373869
$435$	7.17083	0.343815
$436$	38.9608	1.86588
$437$	−1.75276	−0.0838459
$438$	8.85096	0.422915
$439$	6.55775	0.312984	0.156492	−	0.987679i	$-0.449981\pi$
$439$	6.55775	0.312984	0.156492	+	0.987679i	$0.449981\pi$
$440$	1.75684	0.0837543
$441$	16.7181	0.796100
$442$	2.09841	0.0998110
$443$	−9.45949	−0.449434	−0.224717	−	0.974424i	$-0.572146\pi$
$443$	−9.45949	−0.449434	−0.224717	+	0.974424i	$0.572146\pi$
$444$	−12.3814	−0.587595
$445$	13.6843	0.648699
$446$	−2.45670	−0.116328
$447$	−1.52804	−0.0722736
$448$	−3.56090	−0.168237
$449$	−4.50884	−0.212785	−0.106393	−	0.994324i	$-0.533930\pi$
$449$	−4.50884	−0.212785	−0.106393	+	0.994324i	$0.533930\pi$
$450$	16.9703	0.799989
$451$	29.1790	1.37398
$452$	−14.8000	−0.696133
$453$	−15.9113	−0.747578
$454$	−20.5077	−0.962473
$455$	0.508416	0.0238349
$456$	−0.0733809	−0.00343637
$457$	33.1061	1.54864	0.774319	−	0.632795i	$-0.218093\pi$
$457$	33.1061	1.54864	0.774319	+	0.632795i	$0.218093\pi$
$458$	−34.0556	−1.59131
$459$	−4.06570	−0.189771
$460$	13.8958	0.647895
$461$	−6.96586	−0.324432	−0.162216	−	0.986755i	$-0.551864\pi$
$461$	−6.96586	−0.324432	−0.162216	+	0.986755i	$0.551864\pi$
$462$	2.87787	0.133890
$463$	27.3832	1.27260	0.636302	−	0.771440i	$-0.280463\pi$
$463$	27.3832	1.27260	0.636302	+	0.771440i	$0.280463\pi$
$464$	−28.1770	−1.30808
$465$	9.19140	0.426241
$466$	38.5829	1.78732
$467$	−38.9705	−1.80334	−0.901669	−	0.432427i	$-0.857657\pi$
$467$	−38.9705	−1.80334	−0.901669	+	0.432427i	$0.857657\pi$
$468$	5.39259	0.249273
$469$	1.58766	0.0733111
$470$	5.23864	0.241640
$471$	−1.17059	−0.0539379
$472$	−0.288756	−0.0132911
$473$	36.5518	1.68065
$474$	−10.5029	−0.482414
$475$	−1.16156	−0.0532959
$476$	−0.838877	−0.0384498
$477$	1.97568	0.0904601
$478$	−19.0305	−0.870436
$479$	13.5125	0.617402	0.308701	−	0.951159i	$-0.400106\pi$
$479$	13.5125	0.617402	0.308701	+	0.951159i	$0.400106\pi$
$480$	−7.61879	−0.347749
$481$	−7.97760	−0.363747
$482$	−47.8719	−2.18051
$483$	1.50785	0.0686093
$484$	26.4600	1.20273
$485$	−14.1040	−0.640429
$486$	−31.3428	−1.42174
$487$	40.3129	1.82675	0.913376	−	0.407118i	$-0.133466\pi$
$487$	40.3129	1.82675	0.913376	+	0.407118i	$0.133466\pi$
$488$	−2.76913	−0.125353
$489$	2.84528	0.128668
$490$	17.5429	0.792505
$491$	−1.81312	−0.0818251	−0.0409126	−	0.999163i	$-0.513027\pi$
$491$	−1.81312	−0.0818251	−0.0409126	+	0.999163i	$0.513027\pi$
$492$	9.66231	0.435611
$493$	−7.62344	−0.343342
$494$	−0.713756	−0.0321134
$495$	−14.8564	−0.667746
$496$	−36.1167	−1.62169
$497$	1.15124	0.0516401
$498$	−0.214714	−0.00962154
$499$	11.1383	0.498621	0.249310	−	0.968424i	$-0.419796\pi$
$499$	11.1383	0.498621	0.249310	+	0.968424i	$0.419796\pi$
$500$	22.6919	1.01481
$501$	−15.0508	−0.672419
$502$	−38.0234	−1.69707
$503$	39.6064	1.76596	0.882981	−	0.469409i	$-0.155533\pi$
$503$	39.6064	1.76596	0.882981	+	0.469409i	$0.155533\pi$
$504$	−0.276149	−0.0123007
$505$	0.943497	0.0419851
$506$	50.6802	2.25301
$507$	8.91832	0.396077
$508$	−9.41651	−0.417790
$509$	15.3266	0.679339	0.339670	−	0.940545i	$-0.389685\pi$
$509$	15.3266	0.679339	0.339670	+	0.940545i	$0.389685\pi$
$510$	−1.91433	−0.0847680
$511$	−2.27982	−0.100853
$512$	32.0718	1.41739
$513$	1.38292	0.0610572
$514$	−27.1869	−1.19916
$515$	2.84419	0.125330
$516$	12.1037	0.532837
$517$	9.88031	0.434536
$518$	6.16713	0.270968
$519$	−3.01606	−0.132390
$520$	0.374841	0.0164379
$521$	20.4810	0.897287	0.448644	−	0.893711i	$-0.351907\pi$
$521$	20.4810	0.897287	0.448644	+	0.893711i	$0.351907\pi$
$522$	−37.8845	−1.65816
$523$	33.5780	1.46826	0.734131	−	0.679008i	$-0.237590\pi$
$523$	33.5780	1.46826	0.734131	+	0.679008i	$0.237590\pi$
$524$	−26.1782	−1.14360
$525$	0.999252	0.0436109
$526$	16.6449	0.725752
$527$	−9.77155	−0.425655
$528$	−13.3448	−0.580760
$529$	3.55365	0.154506
$530$	2.07315	0.0900517
$531$	2.44181	0.105965
$532$	0.285337	0.0123709
$533$	6.22563	0.269662
$534$	16.5268	0.715185
$535$	15.7671	0.681672
$536$	1.17054	0.0505594
$537$	1.55802	0.0672333
$538$	−59.6694	−2.57253
$539$	33.0866	1.42514
$540$	−10.9637	−0.471803
$541$	−5.58027	−0.239915	−0.119957	−	0.992779i	$-0.538276\pi$
$541$	−5.58027	−0.239915	−0.119957	+	0.992779i	$0.538276\pi$
$542$	1.30521	0.0560636
$543$	17.9801	0.771601
$544$	8.09968	0.347271
$545$	−22.9012	−0.980979
$546$	0.614022	0.0262777
$547$	−8.72675	−0.373129	−0.186564	−	0.982443i	$-0.559735\pi$
$547$	−8.72675	−0.373129	−0.186564	+	0.982443i	$0.559735\pi$
$548$	8.23691	0.351863
$549$	23.4166	0.999397
$550$	33.5858	1.43210
$551$	2.59305	0.110468
$552$	1.11169	0.0473168
$553$	2.70533	0.115042
$554$	20.0797	0.853103
$555$	7.27780	0.308925
$556$	−21.3260	−0.904424
$557$	−39.7299	−1.68341	−0.841705	−	0.539938i	$-0.818448\pi$
$557$	−39.7299	−1.68341	−0.841705	+	0.539938i	$0.818448\pi$
$558$	−48.5594	−2.05568
$559$	7.79870	0.329850
$560$	1.82252	0.0770155
$561$	−3.61052	−0.152436
$562$	48.6703	2.05303
$563$	−26.0543	−1.09806	−0.549028	−	0.835804i	$-0.685002\pi$
$563$	−26.0543	−1.09806	−0.549028	+	0.835804i	$0.685002\pi$
$564$	3.27176	0.137766
$565$	8.69945	0.365989
$566$	32.0967	1.34912
$567$	1.67935	0.0705260
$568$	0.848777	0.0356139
$569$	−45.7444	−1.91770	−0.958852	−	0.283905i	$-0.908370\pi$
$569$	−45.7444	−1.91770	−0.958852	+	0.283905i	$0.908370\pi$
$570$	0.651145	0.0272734
$571$	−30.2118	−1.26433	−0.632163	−	0.774836i	$-0.717833\pi$
$571$	−30.2118	−1.26433	−0.632163	+	0.774836i	$0.717833\pi$
$572$	10.6724	0.446237
$573$	15.4748	0.646469
$574$	−4.81276	−0.200881
$575$	17.5971	0.733852
$576$	22.2008	0.925033
$577$	−33.0234	−1.37478	−0.687392	−	0.726287i	$-0.741245\pi$
$577$	−33.0234	−1.37478	−0.687392	+	0.726287i	$0.741245\pi$
$578$	2.03516	0.0846516
$579$	5.17106	0.214902
$580$	−20.5576	−0.853608
$581$	0.0553058	0.00229447
$582$	−17.0336	−0.706067
$583$	3.91005	0.161938
$584$	−1.68085	−0.0695541
$585$	−3.16977	−0.131054
$586$	−18.5944	−0.768126
$587$	−22.9782	−0.948412	−0.474206	−	0.880414i	$-0.657265\pi$
$587$	−22.9782	−0.948412	−0.474206	+	0.880414i	$0.657265\pi$
$588$	10.9563	0.451830
$589$	3.32371	0.136951
$590$	2.56227	0.105487
$591$	16.7379	0.688507
$592$	−28.5973	−1.17534
$593$	27.1535	1.11506	0.557530	−	0.830157i	$-0.311749\pi$
$593$	27.1535	1.11506	0.557530	+	0.830157i	$0.311749\pi$
$594$	−39.9863	−1.64066
$595$	0.493092	0.0202148
$596$	4.38064	0.179438
$597$	−20.3170	−0.831519
$598$	10.8131	0.442182
$599$	16.8177	0.687152	0.343576	−	0.939125i	$-0.388362\pi$
$599$	16.8177	0.687152	0.343576	+	0.939125i	$0.388362\pi$
$600$	0.736721	0.0300765
$601$	−6.60289	−0.269338	−0.134669	−	0.990891i	$-0.542997\pi$
$601$	−6.60289	−0.269338	−0.134669	+	0.990891i	$0.542997\pi$
$602$	−6.02882	−0.245717
$603$	−9.89841	−0.403094
$604$	45.6152	1.85605
$605$	−15.5532	−0.632328
$606$	1.13948	0.0462881
$607$	−11.3726	−0.461599	−0.230799	−	0.973001i	$-0.574134\pi$
$607$	−11.3726	−0.461599	−0.230799	+	0.973001i	$0.574134\pi$
$608$	−2.75504	−0.111732
$609$	−2.23072	−0.0903934
$610$	24.5718	0.994885
$611$	2.10807	0.0852832
$612$	5.23006	0.211413
$613$	1.45424	0.0587364	0.0293682	−	0.999569i	$-0.490650\pi$
$613$	1.45424	0.0587364	0.0293682	+	0.999569i	$0.490650\pi$
$614$	0.599716	0.0242026
$615$	−5.67951	−0.229020
$616$	−0.546524	−0.0220201
$617$	7.56250	0.304455	0.152227	−	0.988345i	$-0.451355\pi$
$617$	7.56250	0.304455	0.152227	+	0.988345i	$0.451355\pi$
$618$	3.43498	0.138175
$619$	4.24879	0.170773	0.0853867	−	0.996348i	$-0.472787\pi$
$619$	4.24879	0.170773	0.0853867	+	0.996348i	$0.472787\pi$
$620$	−26.3503	−1.05825
$621$	−20.9507	−0.840721
$622$	−9.01493	−0.361466
$623$	−4.25696	−0.170552
$624$	−2.84726	−0.113982
$625$	3.73625	0.149450
$626$	11.7821	0.470906
$627$	1.22809	0.0490451
$628$	3.35589	0.133915
$629$	−7.73716	−0.308501
$630$	2.45041	0.0976266
$631$	−26.3219	−1.04786	−0.523929	−	0.851762i	$-0.675534\pi$
$631$	−26.3219	−1.04786	−0.523929	+	0.851762i	$0.675534\pi$
$632$	1.99456	0.0793394
$633$	−2.64744	−0.105226
$634$	56.9995	2.26374
$635$	5.53503	0.219651
$636$	1.29477	0.0513410
$637$	7.05937	0.279702
$638$	−74.9768	−2.96836
$639$	−7.17752	−0.283938
$640$	2.90103	0.114673
$641$	5.93632	0.234471	0.117235	−	0.993104i	$-0.462597\pi$
$641$	5.93632	0.234471	0.117235	+	0.993104i	$0.462597\pi$
$642$	19.0422	0.751537
$643$	13.0899	0.516217	0.258108	−	0.966116i	$-0.416901\pi$
$643$	13.0899	0.516217	0.258108	+	0.966116i	$0.416901\pi$
$644$	−4.32275	−0.170340
$645$	−7.11459	−0.280137
$646$	−0.692244	−0.0272360
$647$	−2.81411	−0.110634	−0.0553170	−	0.998469i	$-0.517617\pi$
$647$	−2.81411	−0.110634	−0.0553170	+	0.998469i	$0.517617\pi$
$648$	1.23814	0.0486386
$649$	4.83256	0.189694
$650$	7.16588	0.281069
$651$	−2.85929	−0.112064
$652$	−8.15697	−0.319452
$653$	−24.8143	−0.971057	−0.485529	−	0.874221i	$-0.661373\pi$
$653$	−24.8143	−0.971057	−0.485529	+	0.874221i	$0.661373\pi$
$654$	−27.6582	−1.08152
$655$	15.3876	0.601242
$656$	22.3171	0.871335
$657$	14.2138	0.554533
$658$	−1.62965	−0.0635304
$659$	27.5082	1.07157	0.535785	−	0.844355i	$-0.320016\pi$
$659$	27.5082	1.07157	0.535785	+	0.844355i	$0.320016\pi$
$660$	−9.73624	−0.378982
$661$	33.9468	1.32038	0.660189	−	0.751100i	$-0.270476\pi$
$661$	33.9468	1.32038	0.660189	+	0.751100i	$0.270476\pi$
$662$	37.5475	1.45932
$663$	−0.770341	−0.0299176
$664$	0.0407754	0.00158239
$665$	−0.167721	−0.00650396
$666$	−38.4496	−1.48989
$667$	−39.2838	−1.52107
$668$	43.1482	1.66945
$669$	0.901872	0.0348684
$670$	−10.3867	−0.401275
$671$	46.3436	1.78908
$672$	2.37008	0.0914277
$673$	−32.8979	−1.26812	−0.634060	−	0.773284i	$-0.718613\pi$
$673$	−32.8979	−1.26812	−0.634060	+	0.773284i	$0.718613\pi$
$674$	−38.1591	−1.46983
$675$	−13.8840	−0.534397
$676$	−25.5674	−0.983362
$677$	−33.1896	−1.27558	−0.637790	−	0.770210i	$-0.720151\pi$
$677$	−33.1896	−1.27558	−0.637790	+	0.770210i	$0.720151\pi$
$678$	10.5065	0.403499
$679$	4.38751	0.168377
$680$	0.363543	0.0139413
$681$	7.52852	0.288494
$682$	−96.1035	−3.67999
$683$	−3.18537	−0.121885	−0.0609424	−	0.998141i	$-0.519411\pi$
$683$	−3.18537	−0.121885	−0.0609424	+	0.998141i	$0.519411\pi$
$684$	−1.77896	−0.0680204
$685$	−4.84166	−0.184990
$686$	−11.0368	−0.421388
$687$	12.5021	0.476984
$688$	27.9560	1.06581
$689$	0.834249	0.0317824
$690$	−9.86460	−0.375539
$691$	35.3681	1.34547	0.672733	−	0.739885i	$-0.265120\pi$
$691$	35.3681	1.34547	0.672733	+	0.739885i	$0.265120\pi$
$692$	8.64655	0.328693
$693$	4.62158	0.175559
$694$	−56.8131	−2.15660
$695$	12.5354	0.475496
$696$	−1.64465	−0.0623403
$697$	6.03800	0.228705
$698$	−54.3268	−2.05630
$699$	−14.1641	−0.535735
$700$	−2.86469	−0.108275
$701$	−34.2160	−1.29232	−0.646160	−	0.763202i	$-0.723626\pi$
$701$	−34.2160	−1.29232	−0.646160	+	0.763202i	$0.723626\pi$
$702$	−8.53149	−0.322000
$703$	2.63173	0.0992577
$704$	43.9374	1.65595
$705$	−1.92314	−0.0724298
$706$	−34.0532	−1.28161
$707$	−0.293506	−0.0110384
$708$	1.60025	0.0601411
$709$	−18.0742	−0.678791	−0.339395	−	0.940644i	$-0.610222\pi$
$709$	−18.0742	−0.678791	−0.339395	+	0.940644i	$0.610222\pi$
$710$	−7.53162	−0.282657
$711$	−16.8666	−0.632549
$712$	−3.13854	−0.117622
$713$	−50.3530	−1.88574
$714$	0.595516	0.0222866
$715$	−6.27326	−0.234607
$716$	−4.46658	−0.166924
$717$	6.98625	0.260906
$718$	74.9032	2.79536
$719$	19.5346	0.728518	0.364259	−	0.931298i	$-0.381322\pi$
$719$	19.5346	0.728518	0.364259	+	0.931298i	$0.381322\pi$
$720$	−11.3627	−0.423462
$721$	−0.884781	−0.0329510
$722$	−38.4326	−1.43031
$723$	17.5742	0.653590
$724$	−51.5461	−1.91570
$725$	−26.0334	−0.966857
$726$	−18.7839	−0.697135
$727$	−8.66484	−0.321361	−0.160681	−	0.987006i	$-0.551369\pi$
$727$	−8.66484	−0.321361	−0.160681	+	0.987006i	$0.551369\pi$
$728$	−0.116607	−0.00432173
$729$	−1.35733	−0.0502715
$730$	14.9150	0.552030
$731$	7.56365	0.279752
$732$	15.3462	0.567212
$733$	−0.811741	−0.0299823	−0.0149912	−	0.999888i	$-0.504772\pi$
$733$	−0.811741	−0.0299823	−0.0149912	+	0.999888i	$0.504772\pi$
$734$	9.80443	0.361888
$735$	−6.44012	−0.237547
$736$	41.7378	1.53848
$737$	−19.5899	−0.721601
$738$	30.0057	1.10452
$739$	11.2167	0.412614	0.206307	−	0.978487i	$-0.433855\pi$
$739$	11.2167	0.412614	0.206307	+	0.978487i	$0.433855\pi$
$740$	−20.8643	−0.766986
$741$	0.262025	0.00962574
$742$	−0.644921	−0.0236758
$743$	−7.04158	−0.258330	−0.129165	−	0.991623i	$-0.541230\pi$
$743$	−7.04158	−0.258330	−0.129165	+	0.991623i	$0.541230\pi$
$744$	−2.10808	−0.0772858
$745$	−2.57494	−0.0943385
$746$	−67.1234	−2.45756
$747$	−0.344810	−0.0126159
$748$	10.3508	0.378462
$749$	−4.90488	−0.179221
$750$	−16.1089	−0.588215
$751$	13.7074	0.500191	0.250096	−	0.968221i	$-0.419538\pi$
$751$	13.7074	0.500191	0.250096	+	0.968221i	$0.419538\pi$
$752$	7.55680	0.275568
$753$	13.9587	0.508682
$754$	−15.9971	−0.582579
$755$	−26.8126	−0.975812
$756$	3.41062	0.124043
$757$	36.3926	1.32271	0.661356	−	0.750072i	$-0.269981\pi$
$757$	36.3926	1.32271	0.661356	+	0.750072i	$0.269981\pi$
$758$	−30.0710	−1.09223
$759$	−18.6051	−0.675321
$760$	−0.123656	−0.00448549
$761$	−7.76813	−0.281594	−0.140797	−	0.990038i	$-0.544967\pi$
$761$	−7.76813	−0.281594	−0.140797	+	0.990038i	$0.544967\pi$
$762$	6.68476	0.242163
$763$	7.12417	0.257912
$764$	−44.3638	−1.60503
$765$	−3.07424	−0.111149
$766$	−27.7900	−1.00409
$767$	1.03108	0.0372300
$768$	−10.0820	−0.363803
$769$	28.9154	1.04272	0.521358	−	0.853338i	$-0.325426\pi$
$769$	28.9154	1.04272	0.521358	+	0.853338i	$0.325426\pi$
$770$	4.84958	0.174767
$771$	9.98051	0.359439
$772$	−14.8246	−0.533549
$773$	42.9153	1.54356	0.771778	−	0.635892i	$-0.219368\pi$
$773$	42.9153	1.54356	0.771778	+	0.635892i	$0.219368\pi$
$774$	37.5873	1.35105
$775$	−33.3690	−1.19865
$776$	3.23479	0.116122
$777$	−2.26400	−0.0812205
$778$	42.6292	1.52833
$779$	−2.05378	−0.0735842
$780$	−2.07733	−0.0743802
$781$	−14.2050	−0.508294
$782$	10.4872	0.375023
$783$	30.9946	1.10766
$784$	25.3058	0.903777
$785$	−1.97260	−0.0704049
$786$	18.5838	0.662863
$787$	−25.5214	−0.909740	−0.454870	−	0.890558i	$-0.650314\pi$
$787$	−25.5214	−0.909740	−0.454870	+	0.890558i	$0.650314\pi$
$788$	−47.9850	−1.70940
$789$	−6.11047	−0.217538
$790$	−17.6987	−0.629693
$791$	−2.70625	−0.0962232
$792$	3.40736	0.121075
$793$	9.88789	0.351129
$794$	−57.0633	−2.02510
$795$	−0.761068	−0.0269923
$796$	58.2456	2.06446
$797$	−18.7688	−0.664824	−0.332412	−	0.943134i	$-0.607863\pi$
$797$	−18.7688	−0.664824	−0.332412	+	0.943134i	$0.607863\pi$
$798$	−0.202560	−0.00717055
$799$	2.04453	0.0723303
$800$	27.6597	0.977919
$801$	26.5405	0.937762
$802$	−25.0075	−0.883047
$803$	28.1304	0.992701
$804$	−6.48698	−0.228778
$805$	2.54092	0.0895555
$806$	−20.5047	−0.722247
$807$	21.9051	0.771095
$808$	−0.216394	−0.00761271
$809$	15.8201	0.556205	0.278103	−	0.960551i	$-0.410294\pi$
$809$	15.8201	0.556205	0.278103	+	0.960551i	$0.410294\pi$
$810$	−10.9866	−0.386030
$811$	27.9786	0.982463	0.491231	−	0.871029i	$-0.336547\pi$
$811$	27.9786	0.982463	0.491231	+	0.871029i	$0.336547\pi$
$812$	6.39513	0.224425
$813$	−0.479153	−0.0168046
$814$	−76.0953	−2.66714
$815$	4.79467	0.167950
$816$	−2.76144	−0.0966699
$817$	−2.57271	−0.0900079
$818$	−4.25963	−0.148934
$819$	0.986062	0.0344558
$820$	16.2823	0.568601
$821$	23.5589	0.822212	0.411106	−	0.911588i	$-0.365143\pi$
$821$	23.5589	0.822212	0.411106	+	0.911588i	$0.365143\pi$
$822$	−5.84736	−0.203950
$823$	44.7329	1.55929	0.779646	−	0.626221i	$-0.215399\pi$
$823$	44.7329	1.55929	0.779646	+	0.626221i	$0.215399\pi$
$824$	−0.652325	−0.0227248
$825$	−12.3296	−0.429262
$826$	−0.797079	−0.0277339
$827$	−31.8575	−1.10779	−0.553897	−	0.832585i	$-0.686860\pi$
$827$	−31.8575	−1.10779	−0.553897	+	0.832585i	$0.686860\pi$
$828$	26.9506	0.936600
$829$	52.4609	1.82204	0.911021	−	0.412360i	$-0.135295\pi$
$829$	52.4609	1.82204	0.911021	+	0.412360i	$0.135295\pi$
$830$	−0.361820	−0.0125590
$831$	−7.37140	−0.255711
$832$	9.37449	0.325002
$833$	6.84661	0.237221
$834$	15.1393	0.524230
$835$	−25.3625	−0.877706
$836$	−3.52073	−0.121767
$837$	39.7282	1.37321
$838$	44.1294	1.52442
$839$	−9.64274	−0.332904	−0.166452	−	0.986050i	$-0.553231\pi$
$839$	−9.64274	−0.332904	−0.166452	+	0.986050i	$0.553231\pi$
$840$	0.106378	0.00367038
$841$	29.1168	1.00403
$842$	−41.3942	−1.42654
$843$	−17.8672	−0.615380
$844$	7.58979	0.261251
$845$	15.0285	0.516998
$846$	10.1602	0.349316
$847$	4.83834	0.166247
$848$	2.99054	0.102695
$849$	−11.7829	−0.404389
$850$	6.94991	0.238380
$851$	−39.8698	−1.36672
$852$	−4.70383	−0.161151
$853$	−39.1614	−1.34086	−0.670431	−	0.741972i	$-0.733891\pi$
$853$	−39.1614	−1.34086	−0.670431	+	0.741972i	$0.733891\pi$
$854$	−7.64389	−0.261568
$855$	1.04568	0.0357614
$856$	−3.61624	−0.123600
$857$	−32.3082	−1.10363	−0.551814	−	0.833967i	$-0.686064\pi$
$857$	−32.3082	−1.10363	−0.551814	+	0.833967i	$0.686064\pi$
$858$	−7.57633	−0.258652
$859$	−1.76459	−0.0602071	−0.0301035	−	0.999547i	$-0.509584\pi$
$859$	−1.76459	−0.0602071	−0.0301035	+	0.999547i	$0.509584\pi$
$860$	20.3964	0.695511
$861$	1.76680	0.0602124
$862$	78.8275	2.68488
$863$	3.32567	0.113207	0.0566035	−	0.998397i	$-0.481973\pi$
$863$	3.32567	0.113207	0.0566035	+	0.998397i	$0.481973\pi$
$864$	−32.9309	−1.12033
$865$	−5.08245	−0.172808
$866$	28.0114	0.951867
$867$	−0.747123	−0.0253736
$868$	8.19712	0.278229
$869$	−33.3806	−1.13236
$870$	14.5938	0.494776
$871$	−4.17970	−0.141624
$872$	5.25246	0.177871
$873$	−27.3544	−0.925806
$874$	−3.56715	−0.120661
$875$	4.14933	0.140273
$876$	9.31510	0.314728
$877$	35.9336	1.21339	0.606695	−	0.794934i	$-0.292495\pi$
$877$	35.9336	1.21339	0.606695	+	0.794934i	$0.292495\pi$
$878$	13.3461	0.450408
$879$	6.82613	0.230240
$880$	−22.4878	−0.758064
$881$	8.43811	0.284287	0.142144	−	0.989846i	$-0.454601\pi$
$881$	8.43811	0.284287	0.142144	+	0.989846i	$0.454601\pi$
$882$	34.0240	1.14565
$883$	27.0929	0.911749	0.455875	−	0.890044i	$-0.349327\pi$
$883$	27.0929	0.911749	0.455875	+	0.890044i	$0.349327\pi$
$884$	2.20844	0.0742780
$885$	−0.940629	−0.0316189
$886$	−19.2516	−0.646770
$887$	−49.7335	−1.66989	−0.834944	−	0.550335i	$-0.814500\pi$
$887$	−49.7335	−1.66989	−0.834944	+	0.550335i	$0.814500\pi$
$888$	−1.66918	−0.0560142
$889$	−1.72186	−0.0577492
$890$	27.8498	0.933528
$891$	−20.7212	−0.694187
$892$	−2.58552	−0.0865698
$893$	−0.695431	−0.0232717
$894$	−3.10980	−0.104007
$895$	2.62546	0.0877594
$896$	−0.902461	−0.0301491
$897$	−3.96958	−0.132541
$898$	−9.17623	−0.306215
$899$	74.4928	2.48447
$900$	17.8602	0.595341
$901$	0.809105	0.0269552
$902$	59.3839	1.97727
$903$	2.21323	0.0736516
$904$	−1.99524	−0.0663609
$905$	30.2988	1.00717
$906$	−32.3821	−1.07582
$907$	45.6267	1.51501	0.757506	−	0.652829i	$-0.226418\pi$
$907$	45.6267	1.51501	0.757506	+	0.652829i	$0.226418\pi$
$908$	−21.5831	−0.716259
$909$	1.82989	0.0606937
$910$	1.03471	0.0343002
$911$	−16.6818	−0.552693	−0.276346	−	0.961058i	$-0.589124\pi$
$911$	−16.6818	−0.552693	−0.276346	+	0.961058i	$0.589124\pi$
$912$	0.939283	0.0311028
$913$	−0.682410	−0.0225845
$914$	67.3763	2.22861
$915$	−9.02051	−0.298209
$916$	−35.8414	−1.18423
$917$	−4.78681	−0.158074
$918$	−8.27436	−0.273095
$919$	47.9275	1.58098	0.790492	−	0.612473i	$-0.209825\pi$
$919$	47.9275	1.58098	0.790492	+	0.612473i	$0.209825\pi$
$920$	1.87335	0.0617624
$921$	−0.220160	−0.00725453
$922$	−14.1766	−0.466883
$923$	−3.03078	−0.0997592
$924$	3.02878	0.0996395
$925$	−26.4218	−0.868742
$926$	55.7292	1.83138
$927$	5.51626	0.181178
$928$	−61.7474	−2.02696
$929$	−37.1417	−1.21858	−0.609290	−	0.792947i	$-0.708546\pi$
$929$	−37.1417	−1.21858	−0.609290	+	0.792947i	$0.708546\pi$
$930$	18.7060	0.613394
$931$	−2.32882	−0.0763239
$932$	40.6062	1.33010
$933$	3.30945	0.108346
$934$	−79.3112	−2.59514
$935$	−6.08419	−0.198974
$936$	0.726996	0.0237626
$937$	−10.9472	−0.357630	−0.178815	−	0.983883i	$-0.557226\pi$
$937$	−10.9472	−0.357630	−0.178815	+	0.983883i	$0.557226\pi$
$938$	3.23114	0.105500
$939$	−4.32528	−0.141150
$940$	5.51335	0.179826
$941$	−20.5889	−0.671179	−0.335589	−	0.942008i	$-0.608935\pi$
$941$	−20.5889	−0.671179	−0.335589	+	0.942008i	$0.608935\pi$
$942$	−2.38234	−0.0776208
$943$	31.1139	1.01321
$944$	3.69610	0.120298
$945$	−2.00477	−0.0652150
$946$	74.3888	2.41859
$947$	33.2412	1.08019	0.540096	−	0.841603i	$-0.318388\pi$
$947$	33.2412	1.08019	0.540096	+	0.841603i	$0.318388\pi$
$948$	−11.0536	−0.359006
$949$	6.00191	0.194830
$950$	−2.36396	−0.0766969
$951$	−20.9250	−0.678538
$952$	−0.113092	−0.00366534
$953$	30.5024	0.988070	0.494035	−	0.869442i	$-0.335521\pi$
$953$	30.5024	0.988070	0.494035	+	0.869442i	$0.335521\pi$
$954$	4.02083	0.130179
$955$	26.0771	0.843834
$956$	−20.0285	−0.647767
$957$	27.5246	0.889743
$958$	27.5001	0.888488
$959$	1.50616	0.0486364
$960$	−8.55215	−0.276019
$961$	64.4832	2.08010
$962$	−16.2357	−0.523460
$963$	30.5800	0.985427
$964$	−50.3823	−1.62270
$965$	8.71391	0.280511
$966$	3.06871	0.0987341
$967$	5.03800	0.162011	0.0810056	−	0.996714i	$-0.474187\pi$
$967$	5.03800	0.162011	0.0810056	+	0.996714i	$0.474187\pi$
$968$	3.56717	0.114653
$969$	0.254128	0.00816377
$970$	−28.7039	−0.921627
$971$	11.8666	0.380817	0.190409	−	0.981705i	$-0.439019\pi$
$971$	11.8666	0.380817	0.190409	+	0.981705i	$0.439019\pi$
$972$	−32.9864	−1.05804
$973$	−3.89956	−0.125014
$974$	82.0432	2.62883
$975$	−2.63065	−0.0842483
$976$	35.4452	1.13457
$977$	−10.6741	−0.341494	−0.170747	−	0.985315i	$-0.554618\pi$
$977$	−10.6741	−0.341494	−0.170747	+	0.985315i	$0.554618\pi$
$978$	5.79061	0.185163
$979$	52.5260	1.67874
$980$	18.4628	0.589772
$981$	−44.4164	−1.41811
$982$	−3.69000	−0.117753
$983$	21.8317	0.696322	0.348161	−	0.937435i	$-0.386806\pi$
$983$	21.8317	0.696322	0.348161	+	0.937435i	$0.386806\pi$
$984$	1.30261	0.0415258
$985$	28.2056	0.898706
$986$	−15.5149	−0.494096
$987$	0.598258	0.0190428
$988$	−0.751185	−0.0238984
$989$	38.9757	1.23935
$990$	−30.2352	−0.960938
$991$	−43.9526	−1.39620	−0.698100	−	0.716000i	$-0.745971\pi$
$991$	−43.9526	−1.39620	−0.698100	+	0.716000i	$0.745971\pi$
$992$	−79.1464	−2.51290
$993$	−13.7840	−0.437421
$994$	2.34296	0.0743141
$995$	−34.2368	−1.08538
$996$	−0.225973	−0.00716022
$997$	19.9524	0.631899	0.315949	−	0.948776i	$-0.397677\pi$
$997$	19.9524	0.631899	0.315949	+	0.948776i	$0.397677\pi$
$998$	22.6683	0.717553
$999$	31.4570	0.995255

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1003.2.a.g.1.9	✓	10
3.2	odd	2		9027.2.a.j.1.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1003.2.a.g.1.9	✓	10	1.1	even	1	trivial
9027.2.a.j.1.2		10	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)

\(f(q)\)	\(=\)	\(q+2.03516 q^{2} -0.747123 q^{3} +2.14188 q^{4} -1.25900 q^{5} -1.52052 q^{6} +0.391654 q^{7} +0.288756 q^{8} -2.44181 q^{9} +O(q^{10})\)	\(q+2.03516 q^{2} -0.747123 q^{3} +2.14188 q^{4} -1.25900 q^{5} -1.52052 q^{6} +0.391654 q^{7} +0.288756 q^{8} -2.44181 q^{9} -2.56227 q^{10} -4.83256 q^{11} -1.60025 q^{12} -1.03108 q^{13} +0.797079 q^{14} +0.940629 q^{15} -3.69610 q^{16} -1.00000 q^{17} -4.96947 q^{18} +0.340142 q^{19} -2.69663 q^{20} -0.292614 q^{21} -9.83504 q^{22} -5.15302 q^{23} -0.215736 q^{24} -3.41492 q^{25} -2.09841 q^{26} +4.06570 q^{27} +0.838877 q^{28} +7.62344 q^{29} +1.91433 q^{30} +9.77155 q^{31} -8.09968 q^{32} +3.61052 q^{33} -2.03516 q^{34} -0.493092 q^{35} -5.23006 q^{36} +7.73716 q^{37} +0.692244 q^{38} +0.770341 q^{39} -0.363543 q^{40} -6.03800 q^{41} -0.595516 q^{42} -7.56365 q^{43} -10.3508 q^{44} +3.07424 q^{45} -10.4872 q^{46} -2.04453 q^{47} +2.76144 q^{48} -6.84661 q^{49} -6.94991 q^{50} +0.747123 q^{51} -2.20844 q^{52} -0.809105 q^{53} +8.27436 q^{54} +6.08419 q^{55} +0.113092 q^{56} -0.254128 q^{57} +15.5149 q^{58} -1.00000 q^{59} +2.01472 q^{60} -9.58988 q^{61} +19.8867 q^{62} -0.956343 q^{63} -9.09195 q^{64} +1.29813 q^{65} +7.34799 q^{66} +4.05372 q^{67} -2.14188 q^{68} +3.84994 q^{69} -1.00352 q^{70} +2.93943 q^{71} -0.705085 q^{72} -5.82102 q^{73} +15.7464 q^{74} +2.55136 q^{75} +0.728544 q^{76} -1.89269 q^{77} +1.56777 q^{78} +6.90744 q^{79} +4.65340 q^{80} +4.28784 q^{81} -12.2883 q^{82} +0.141211 q^{83} -0.626744 q^{84} +1.25900 q^{85} -15.3932 q^{86} -5.69565 q^{87} -1.39543 q^{88} -10.8692 q^{89} +6.25657 q^{90} -0.403825 q^{91} -11.0372 q^{92} -7.30055 q^{93} -4.16095 q^{94} -0.428239 q^{95} +6.05146 q^{96} +11.2025 q^{97} -13.9340 q^{98} +11.8002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9}+O(q^{10}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9	\( 10 q - q^{2} - 7 q^{3} + 15 q^{4} - 12 q^{5} + 5 q^{6} - 9 q^{7} - 12 q^{8} + 3 q^{9} + 4 q^{10} + 12 q^{11} - 24 q^{12} - 11 q^{13} - 12 q^{14} + 9 q^{15} - 3 q^{16} - 10 q^{17} - 22 q^{18} - 5 q^{19} - 36 q^{20} - 10 q^{21} + 6 q^{22} - 7 q^{23} + 35 q^{24} + 2 q^{25} + q^{26} - 31 q^{27} - 4 q^{28} + 10 q^{29} - 9 q^{30} + 13 q^{31} - 15 q^{32} - 9 q^{33} + q^{34} - 8 q^{35} + 40 q^{36} + 12 q^{37} - 50 q^{38} + 24 q^{39} + 5 q^{40} - 29 q^{41} - 17 q^{42} - 18 q^{43} - 6 q^{44} - 14 q^{45} + 11 q^{46} - 18 q^{47} - 43 q^{48} - 9 q^{49} - 31 q^{50} + 7 q^{51} - 68 q^{52} + 19 q^{54} - 27 q^{55} - 7 q^{56} + 20 q^{57} + 23 q^{58} - 10 q^{59} + 38 q^{60} + 8 q^{61} - 46 q^{62} + 39 q^{63} - 20 q^{64} + 58 q^{65} - 34 q^{66} - 6 q^{67} - 15 q^{68} + 6 q^{69} + 73 q^{70} + 8 q^{71} - 70 q^{72} - 41 q^{73} - 10 q^{74} + 10 q^{75} + 12 q^{76} - 22 q^{77} - 43 q^{78} + 3 q^{79} - 15 q^{80} + 26 q^{81} + 8 q^{82} - 22 q^{84} + 12 q^{85} - 29 q^{86} - 28 q^{87} + 33 q^{88} - 45 q^{89} + 56 q^{90} - 14 q^{91} + 36 q^{92} - 19 q^{93} + 15 q^{94} - 17 q^{95} + 90 q^{96} - 5 q^{97} + 30 q^{98} + 14 q^{99}+O(q^{100}) \) 10 * q - q^2 - 7 * q^3 + 15 * q^4 - 12 * q^5 + 5 * q^6 - 9 * q^7 - 12 * q^8 + 3 * q^9 + 4 * q^10 + 12 * q^11 - 24 * q^12 - 11 * q^13 - 12 * q^14 + 9 * q^15 - 3 * q^16 - 10 * q^17 - 22 * q^18 - 5 * q^19 - 36 * q^20 - 10 * q^21 + 6 * q^22 - 7 * q^23 + 35 * q^24 + 2 * q^25 + q^26 - 31 * q^27 - 4 * q^28 + 10 * q^29 - 9 * q^30 + 13 * q^31 - 15 * q^32 - 9 * q^33 + q^34 - 8 * q^35 + 40 * q^36 + 12 * q^37 - 50 * q^38 + 24 * q^39 + 5 * q^40 - 29 * q^41 - 17 * q^42 - 18 * q^43 - 6 * q^44 - 14 * q^45 + 11 * q^46 - 18 * q^47 - 43 * q^48 - 9 * q^49 - 31 * q^50 + 7 * q^51 - 68 * q^52 + 19 * q^54 - 27 * q^55 - 7 * q^56 + 20 * q^57 + 23 * q^58 - 10 * q^59 + 38 * q^60 + 8 * q^61 - 46 * q^62 + 39 * q^63 - 20 * q^64 + 58 * q^65 - 34 * q^66 - 6 * q^67 - 15 * q^68 + 6 * q^69 + 73 * q^70 + 8 * q^71 - 70 * q^72 - 41 * q^73 - 10 * q^74 + 10 * q^75 + 12 * q^76 - 22 * q^77 - 43 * q^78 + 3 * q^79 - 15 * q^80 + 26 * q^81 + 8 * q^82 - 22 * q^84 + 12 * q^85 - 29 * q^86 - 28 * q^87 + 33 * q^88 - 45 * q^89 + 56 * q^90 - 14 * q^91 + 36 * q^92 - 19 * q^93 + 15 * q^94 - 17 * q^95 + 90 * q^96 - 5 * q^97 + 30 * q^98 + 14 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more