LMFDB - Embedded newform 1247.2.a.b.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1247,2,Mod(1,1247)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1247, 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("1247.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1247 = 29 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1247.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:	$9.95734513205$
Analytic rank:	$1$
Dimension:	$19$
Coefficient field:	$\mathbb{Q}[x]/(x^{19} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{19} - 2 x^{18} - 23 x^{17} + 44 x^{16} + 217 x^{15} - 397 x^{14} - 1080 x^{13} + 1895 x^{12} + \cdots + 2 $ x^19 - 2x^18 - 23x^17 + 44x^16 + 217x^15 - 397x^14 - 1080x^13 + 1895x^12 + 3029x^11 - 5150x^10 - 4709x^9 + 7986x^8 + 3631x^7 - 6672x^6 - 901x^5 + 2521x^4 - 177x^3 - 219x^2 + 5x + 2
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			1.8
Root			$0.881438$ of defining polynomial
Character	$\chi$	$=$	1247.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.881438 q^{2} -1.53634 q^{3} -1.22307 q^{4} +4.24722 q^{5} +1.35418 q^{6} +2.51402 q^{7} +2.84093 q^{8} -0.639673 q^{9} +O(q^{10})$	\(q-0.881438 q^{2} -1.53634 q^{3} -1.22307 q^{4} +4.24722 q^{5} +1.35418 q^{6} +2.51402 q^{7} +2.84093 q^{8} -0.639673 q^{9} -3.74366 q^{10} -1.86563 q^{11} +1.87904 q^{12} -6.20625 q^{13} -2.21595 q^{14} -6.52515 q^{15} -0.0579703 q^{16} -4.76344 q^{17} +0.563832 q^{18} -1.90399 q^{19} -5.19464 q^{20} -3.86238 q^{21} +1.64444 q^{22} -0.229035 q^{23} -4.36463 q^{24} +13.0389 q^{25} +5.47042 q^{26} +5.59176 q^{27} -3.07482 q^{28} -1.00000 q^{29} +5.75152 q^{30} -8.44930 q^{31} -5.63077 q^{32} +2.86624 q^{33} +4.19868 q^{34} +10.6776 q^{35} +0.782364 q^{36} +1.64491 q^{37} +1.67825 q^{38} +9.53488 q^{39} +12.0661 q^{40} +0.418952 q^{41} +3.40445 q^{42} -1.00000 q^{43} +2.28180 q^{44} -2.71683 q^{45} +0.201880 q^{46} +1.50831 q^{47} +0.0890618 q^{48} -0.679701 q^{49} -11.4929 q^{50} +7.31824 q^{51} +7.59066 q^{52} -9.95033 q^{53} -4.92879 q^{54} -7.92375 q^{55} +7.14216 q^{56} +2.92517 q^{57} +0.881438 q^{58} -9.03142 q^{59} +7.98070 q^{60} +1.55246 q^{61} +7.44753 q^{62} -1.60815 q^{63} +5.07911 q^{64} -26.3593 q^{65} -2.52641 q^{66} +8.66345 q^{67} +5.82601 q^{68} +0.351874 q^{69} -9.41163 q^{70} -1.85057 q^{71} -1.81727 q^{72} -13.0370 q^{73} -1.44988 q^{74} -20.0321 q^{75} +2.32871 q^{76} -4.69024 q^{77} -8.40440 q^{78} +16.1943 q^{79} -0.246212 q^{80} -6.67180 q^{81} -0.369280 q^{82} -3.36493 q^{83} +4.72395 q^{84} -20.2314 q^{85} +0.881438 q^{86} +1.53634 q^{87} -5.30014 q^{88} -6.96155 q^{89} +2.39472 q^{90} -15.6026 q^{91} +0.280125 q^{92} +12.9810 q^{93} -1.32948 q^{94} -8.08666 q^{95} +8.65075 q^{96} -19.2782 q^{97} +0.599114 q^{98} +1.19340 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 2 q^{2} - 6 q^{3} + 12 q^{4} + 2 q^{5} - 8 q^{6} - 10 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) $ 19 * q - 2 * q^2 - 6 * q^3 + 12 * q^4 + 2 * q^5 - 8 * q^6 - 10 * q^7 - 6 * q^8 + 11 * q^9	\( 19 q - 2 q^{2} - 6 q^{3} + 12 q^{4} + 2 q^{5} - 8 q^{6} - 10 q^{7} - 6 q^{8} + 11 q^{9} - 24 q^{10} - 10 q^{11} - 7 q^{12} - 22 q^{13} + 2 q^{14} - 19 q^{15} - 2 q^{16} - 26 q^{17} - 10 q^{18} - 3 q^{19} + 7 q^{20} - 10 q^{21} - 6 q^{22} + 2 q^{23} - 12 q^{24} - 13 q^{25} - 4 q^{26} - 21 q^{27} - 38 q^{28} - 19 q^{29} + 8 q^{30} - 18 q^{31} - 29 q^{32} - 27 q^{33} + 4 q^{34} - 14 q^{35} + 8 q^{36} - 22 q^{37} - 2 q^{38} - 12 q^{39} - 17 q^{40} - 24 q^{41} + 8 q^{42} - 19 q^{43} - 21 q^{44} - 13 q^{45} + q^{46} - 9 q^{47} + 16 q^{48} - 19 q^{49} + 14 q^{50} + 18 q^{51} - 16 q^{52} - 2 q^{53} + 6 q^{54} - 14 q^{55} - q^{56} - 28 q^{57} + 2 q^{58} + 16 q^{59} + 18 q^{60} - 40 q^{61} - 16 q^{62} + 27 q^{63} - 24 q^{64} - 39 q^{65} + 16 q^{66} - 10 q^{67} - 17 q^{68} - 37 q^{69} + 5 q^{70} + 26 q^{71} + 8 q^{72} - 99 q^{73} - 15 q^{74} + 7 q^{75} - 16 q^{76} - 21 q^{77} - 18 q^{78} - q^{79} + 31 q^{80} + 23 q^{81} - 15 q^{82} - 24 q^{83} - 26 q^{84} - 32 q^{85} + 2 q^{86} + 6 q^{87} - q^{88} - 11 q^{89} - 47 q^{90} + 12 q^{92} - 38 q^{93} + 20 q^{94} - 3 q^{95} - 2 q^{96} - 96 q^{97} + 30 q^{98} - 17 q^{99}+O(q^{100}) \) 19 * q - 2 * q^2 - 6 * q^3 + 12 * q^4 + 2 * q^5 - 8 * q^6 - 10 * q^7 - 6 * q^8 + 11 * q^9 - 24 * q^10 - 10 * q^11 - 7 * q^12 - 22 * q^13 + 2 * q^14 - 19 * q^15 - 2 * q^16 - 26 * q^17 - 10 * q^18 - 3 * q^19 + 7 * q^20 - 10 * q^21 - 6 * q^22 + 2 * q^23 - 12 * q^24 - 13 * q^25 - 4 * q^26 - 21 * q^27 - 38 * q^28 - 19 * q^29 + 8 * q^30 - 18 * q^31 - 29 * q^32 - 27 * q^33 + 4 * q^34 - 14 * q^35 + 8 * q^36 - 22 * q^37 - 2 * q^38 - 12 * q^39 - 17 * q^40 - 24 * q^41 + 8 * q^42 - 19 * q^43 - 21 * q^44 - 13 * q^45 + q^46 - 9 * q^47 + 16 * q^48 - 19 * q^49 + 14 * q^50 + 18 * q^51 - 16 * q^52 - 2 * q^53 + 6 * q^54 - 14 * q^55 - q^56 - 28 * q^57 + 2 * q^58 + 16 * q^59 + 18 * q^60 - 40 * q^61 - 16 * q^62 + 27 * q^63 - 24 * q^64 - 39 * q^65 + 16 * q^66 - 10 * q^67 - 17 * q^68 - 37 * q^69 + 5 * q^70 + 26 * q^71 + 8 * q^72 - 99 * q^73 - 15 * q^74 + 7 * q^75 - 16 * q^76 - 21 * q^77 - 18 * q^78 - q^79 + 31 * q^80 + 23 * q^81 - 15 * q^82 - 24 * q^83 - 26 * q^84 - 32 * q^85 + 2 * q^86 + 6 * q^87 - q^88 - 11 * q^89 - 47 * q^90 + 12 * q^92 - 38 * q^93 + 20 * q^94 - 3 * q^95 - 2 * q^96 - 96 * q^97 + 30 * q^98 - 17 * 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 $

$2$	−0.881438	−0.623271	−0.311635	−	0.950202i	$-0.600877\pi$
$2$	−0.881438	−0.623271	−0.311635	+	0.950202i	$0.600877\pi$
$3$	−1.53634	−0.887004	−0.443502	−	0.896273i	$-0.646264\pi$
$3$	−1.53634	−0.887004	−0.443502	+	0.896273i	$0.646264\pi$
$4$	−1.22307	−0.611534
$5$	4.24722	1.89941	0.949707	−	0.313140i	$-0.101381\pi$
$5$	4.24722	1.89941	0.949707	+	0.313140i	$0.101381\pi$
$6$	1.35418	0.552843
$7$	2.51402	0.950210	0.475105	−	0.879929i	$-0.342410\pi$
$7$	2.51402	0.950210	0.475105	+	0.879929i	$0.342410\pi$
$8$	2.84093	1.00442
$9$	−0.639673	−0.213224
$10$	−3.74366	−1.18385
$11$	−1.86563	−0.562510	−0.281255	−	0.959633i	$-0.590751\pi$
$11$	−1.86563	−0.562510	−0.281255	+	0.959633i	$0.590751\pi$
$12$	1.87904	0.542433
$13$	−6.20625	−1.72130	−0.860652	−	0.509194i	$-0.829944\pi$
$13$	−6.20625	−1.72130	−0.860652	+	0.509194i	$0.829944\pi$
$14$	−2.21595	−0.592238
$15$	−6.52515	−1.68479
$16$	−0.0579703	−0.0144926
$17$	−4.76344	−1.15530	−0.577652	−	0.816283i	$-0.696031\pi$
$17$	−4.76344	−1.15530	−0.577652	+	0.816283i	$0.696031\pi$
$18$	0.563832	0.132897
$19$	−1.90399	−0.436805	−0.218403	−	0.975859i	$-0.570085\pi$
$19$	−1.90399	−0.436805	−0.218403	+	0.975859i	$0.570085\pi$
$20$	−5.19464	−1.16156
$21$	−3.86238	−0.842840
$22$	1.64444	0.350596
$23$	−0.229035	−0.0477571	−0.0238785	−	0.999715i	$-0.507601\pi$
$23$	−0.229035	−0.0477571	−0.0238785	+	0.999715i	$0.507601\pi$
$24$	−4.36463	−0.890926
$25$	13.0389	2.60777
$26$	5.47042	1.07284
$27$	5.59176	1.07613
$28$	−3.07482	−0.581086
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	5.75152	1.05008
$31$	−8.44930	−1.51754	−0.758770	−	0.651359i	$-0.774199\pi$
$31$	−8.44930	−1.51754	−0.758770	+	0.651359i	$0.774199\pi$
$32$	−5.63077	−0.995389
$33$	2.86624	0.498948
$34$	4.19868	0.720067
$35$	10.6776	1.80484
$36$	0.782364	0.130394
$37$	1.64491	0.270421	0.135210	−	0.990817i	$-0.456829\pi$
$37$	1.64491	0.270421	0.135210	+	0.990817i	$0.456829\pi$
$38$	1.67825	0.272248
$39$	9.53488	1.52680
$40$	12.0661	1.90781
$41$	0.418952	0.0654293	0.0327146	−	0.999465i	$-0.489585\pi$
$41$	0.418952	0.0654293	0.0327146	+	0.999465i	$0.489585\pi$
$42$	3.40445	0.525317
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	2.28180	0.343994
$45$	−2.71683	−0.405002
$46$	0.201880	0.0297656
$47$	1.50831	0.220009	0.110005	−	0.993931i	$-0.464913\pi$
$47$	1.50831	0.220009	0.110005	+	0.993931i	$0.464913\pi$
$48$	0.0890618	0.0128550
$49$	−0.679701	−0.0971002
$50$	−11.4929	−1.62535
$51$	7.31824	1.02476
$52$	7.59066	1.05264
$53$	−9.95033	−1.36678	−0.683391	−	0.730052i	$-0.739496\pi$
$53$	−9.95033	−1.36678	−0.683391	+	0.730052i	$0.739496\pi$
$54$	−4.92879	−0.670723
$55$	−7.92375	−1.06844
$56$	7.14216	0.954412
$57$	2.92517	0.387448
$58$	0.881438	0.115738
$59$	−9.03142	−1.17579	−0.587895	−	0.808937i	$-0.700043\pi$
$59$	−9.03142	−1.17579	−0.587895	+	0.808937i	$0.700043\pi$
$60$	7.98070	1.03030
$61$	1.55246	0.198772	0.0993860	−	0.995049i	$-0.468312\pi$
$61$	1.55246	0.198772	0.0993860	+	0.995049i	$0.468312\pi$
$62$	7.44753	0.945838
$63$	−1.60815	−0.202608
$64$	5.07911	0.634889
$65$	−26.3593	−3.26947
$66$	−2.52641	−0.310980
$67$	8.66345	1.05841	0.529204	−	0.848494i	$-0.322490\pi$
$67$	8.66345	1.05841	0.529204	+	0.848494i	$0.322490\pi$
$68$	5.82601	0.706507
$69$	0.351874	0.0423607
$70$	−9.41163	−1.12491
$71$	−1.85057	−0.219622	−0.109811	−	0.993952i	$-0.535025\pi$
$71$	−1.85057	−0.219622	−0.109811	+	0.993952i	$0.535025\pi$
$72$	−1.81727	−0.214167
$73$	−13.0370	−1.52587	−0.762935	−	0.646475i	$-0.776242\pi$
$73$	−13.0370	−1.52587	−0.762935	+	0.646475i	$0.776242\pi$
$74$	−1.44988	−0.168545
$75$	−20.0321	−2.31310
$76$	2.32871	0.267121
$77$	−4.69024	−0.534502
$78$	−8.40440	−0.951611
$79$	16.1943	1.82200	0.910999	−	0.412409i	$-0.135312\pi$
$79$	16.1943	1.82200	0.910999	+	0.412409i	$0.135312\pi$
$80$	−0.246212	−0.0275274
$81$	−6.67180	−0.741311
$82$	−0.369280	−0.0407801
$83$	−3.36493	−0.369350	−0.184675	−	0.982800i	$-0.559123\pi$
$83$	−3.36493	−0.369350	−0.184675	+	0.982800i	$0.559123\pi$
$84$	4.72395	0.515425
$85$	−20.2314	−2.19440
$86$	0.881438	0.0950479
$87$	1.53634	0.164712
$88$	−5.30014	−0.564997
$89$	−6.96155	−0.737922	−0.368961	−	0.929445i	$-0.620286\pi$
$89$	−6.96155	−0.737922	−0.368961	+	0.929445i	$0.620286\pi$
$90$	2.39472	0.252426
$91$	−15.6026	−1.63560
$92$	0.280125	0.0292051
$93$	12.9810	1.34606
$94$	−1.32948	−0.137125
$95$	−8.08666	−0.829674
$96$	8.65075	0.882914
$97$	−19.2782	−1.95741	−0.978703	−	0.205280i	$-0.934189\pi$
$97$	−19.2782	−1.95741	−0.978703	+	0.205280i	$0.934189\pi$
$98$	0.599114	0.0605197
$99$	1.19340	0.119941
$100$	−15.9474	−1.59474
$101$	−15.8556	−1.57769	−0.788846	−	0.614591i	$-0.789321\pi$
$101$	−15.8556	−1.57769	−0.788846	+	0.614591i	$0.789321\pi$
$102$	−6.45057	−0.638702
$103$	9.21043	0.907531	0.453765	−	0.891121i	$-0.350080\pi$
$103$	9.21043	0.907531	0.453765	+	0.891121i	$0.350080\pi$
$104$	−17.6315	−1.72891
$105$	−16.4044	−1.60090
$106$	8.77059	0.851875
$107$	14.0177	1.35514	0.677572	−	0.735457i	$-0.263032\pi$
$107$	14.0177	1.35514	0.677572	+	0.735457i	$0.263032\pi$
$108$	−6.83910	−0.658093
$109$	18.2547	1.74849	0.874243	−	0.485488i	$-0.161358\pi$
$109$	18.2547	1.74849	0.874243	+	0.485488i	$0.161358\pi$
$110$	6.98429	0.665926
$111$	−2.52713	−0.239864
$112$	−0.145738	−0.0137710
$113$	9.49302	0.893028	0.446514	−	0.894777i	$-0.352665\pi$
$113$	9.49302	0.893028	0.446514	+	0.894777i	$0.352665\pi$
$114$	−2.57835	−0.241485
$115$	−0.972761	−0.0907105
$116$	1.22307	0.113559
$117$	3.96997	0.367024
$118$	7.96063	0.732836
$119$	−11.9754	−1.09778
$120$	−18.5375	−1.69224
$121$	−7.51941	−0.683583
$122$	−1.36840	−0.123889
$123$	−0.643651	−0.0580360
$124$	10.3341	0.928027
$125$	34.1428	3.05383
$126$	1.41749	0.126280
$127$	−12.5523	−1.11384	−0.556920	−	0.830566i	$-0.688017\pi$
$127$	−12.5523	−1.11384	−0.556920	+	0.830566i	$0.688017\pi$
$128$	6.78462	0.599681
$129$	1.53634	0.135267
$130$	23.2341	2.03776
$131$	−20.2740	−1.77135	−0.885675	−	0.464306i	$-0.846304\pi$
$131$	−20.2740	−1.77135	−0.885675	+	0.464306i	$0.846304\pi$
$132$	−3.50560	−0.305124
$133$	−4.78667	−0.415057
$134$	−7.63629	−0.659675
$135$	23.7494	2.04402
$136$	−13.5326	−1.16041
$137$	4.76328	0.406955	0.203477	−	0.979080i	$-0.434776\pi$
$137$	4.76328	0.406955	0.203477	+	0.979080i	$0.434776\pi$
$138$	−0.310155	−0.0264022
$139$	−15.7054	−1.33211	−0.666056	−	0.745902i	$-0.732019\pi$
$139$	−15.7054	−1.33211	−0.666056	+	0.745902i	$0.732019\pi$
$140$	−13.0594	−1.10372
$141$	−2.31726	−0.195149
$142$	1.63116	0.136884
$143$	11.5786	0.968250
$144$	0.0370820	0.00309017
$145$	−4.24722	−0.352712
$146$	11.4913	0.951030
$147$	1.04425	0.0861282
$148$	−2.01183	−0.165372
$149$	−13.2944	−1.08912	−0.544559	−	0.838723i	$-0.683303\pi$
$149$	−13.2944	−1.08912	−0.544559	+	0.838723i	$0.683303\pi$
$150$	17.6570	1.44169
$151$	9.95587	0.810197	0.405098	−	0.914273i	$-0.367237\pi$
$151$	9.95587	0.810197	0.405098	+	0.914273i	$0.367237\pi$
$152$	−5.40911	−0.438737
$153$	3.04705	0.246339
$154$	4.13415	0.333140
$155$	−35.8860	−2.88244
$156$	−11.6618	−0.933692
$157$	−21.6865	−1.73077	−0.865385	−	0.501108i	$-0.832926\pi$
$157$	−21.6865	−1.73077	−0.865385	+	0.501108i	$0.832926\pi$
$158$	−14.2742	−1.13560
$159$	15.2870	1.21234
$160$	−23.9151	−1.89066
$161$	−0.575798	−0.0453793
$162$	5.88077	0.462037
$163$	7.61111	0.596148	0.298074	−	0.954543i	$-0.403656\pi$
$163$	7.61111	0.596148	0.298074	+	0.954543i	$0.403656\pi$
$164$	−0.512406	−0.0400122
$165$	12.1735	0.947709
$166$	2.96598	0.230205
$167$	8.38005	0.648468	0.324234	−	0.945977i	$-0.394893\pi$
$167$	8.38005	0.648468	0.324234	+	0.945977i	$0.394893\pi$
$168$	−10.9728	−0.846567
$169$	25.5175	1.96289
$170$	17.8327	1.36771
$171$	1.21793	0.0931376
$172$	1.22307	0.0932580
$173$	8.47355	0.644232	0.322116	−	0.946700i	$-0.395606\pi$
$173$	8.47355	0.644232	0.322116	+	0.946700i	$0.395606\pi$
$174$	−1.35418	−0.102660
$175$	32.7800	2.47793
$176$	0.108151	0.00815221
$177$	13.8753	1.04293
$178$	6.13617	0.459925
$179$	6.66048	0.497827	0.248914	−	0.968526i	$-0.419926\pi$
$179$	6.66048	0.497827	0.248914	+	0.968526i	$0.419926\pi$
$180$	3.32287	0.247672
$181$	7.80748	0.580326	0.290163	−	0.956977i	$-0.406291\pi$
$181$	7.80748	0.580326	0.290163	+	0.956977i	$0.406291\pi$
$182$	13.7528	1.01942
$183$	−2.38510	−0.176311
$184$	−0.650673	−0.0479682
$185$	6.98628	0.513641
$186$	−11.4419	−0.838962
$187$	8.88683	0.649870
$188$	−1.84476	−0.134543
$189$	14.0578	1.02255
$190$	7.12789	0.517111
$191$	−0.792100	−0.0573144	−0.0286572	−	0.999589i	$-0.509123\pi$
$191$	−0.792100	−0.0573144	−0.0286572	+	0.999589i	$0.509123\pi$
$192$	−7.80322	−0.563149
$193$	−21.5332	−1.54999	−0.774995	−	0.631967i	$-0.782248\pi$
$193$	−21.5332	−1.54999	−0.774995	+	0.631967i	$0.782248\pi$
$194$	16.9925	1.21999
$195$	40.4967	2.90003
$196$	0.831320	0.0593800
$197$	−5.61187	−0.399829	−0.199915	−	0.979813i	$-0.564066\pi$
$197$	−5.61187	−0.399829	−0.199915	+	0.979813i	$0.564066\pi$
$198$	−1.05190	−0.0747556
$199$	−11.2241	−0.795652	−0.397826	−	0.917461i	$-0.630235\pi$
$199$	−11.2241	−0.795652	−0.397826	+	0.917461i	$0.630235\pi$
$200$	37.0425	2.61930
$201$	−13.3100	−0.938813
$202$	13.9757	0.983328
$203$	−2.51402	−0.176450
$204$	−8.95070	−0.626675
$205$	1.77938	0.124277
$206$	−8.11842	−0.565637
$207$	0.146508	0.0101830
$208$	0.359778	0.0249461
$209$	3.55215	0.245707
$210$	14.4594	0.997795
$211$	12.1549	0.836776	0.418388	−	0.908268i	$-0.362595\pi$
$211$	12.1549	0.836776	0.418388	+	0.908268i	$0.362595\pi$
$212$	12.1699	0.835834
$213$	2.84310	0.194806
$214$	−12.3557	−0.844621
$215$	−4.24722	−0.289658
$216$	15.8858	1.08089
$217$	−21.2417	−1.44198
$218$	−16.0904	−1.08978
$219$	20.0293	1.35345
$220$	9.69129	0.653386
$221$	29.5631	1.98863
$222$	2.22751	0.149500
$223$	−15.1577	−1.01504	−0.507519	−	0.861641i	$-0.669437\pi$
$223$	−15.1577	−1.01504	−0.507519	+	0.861641i	$0.669437\pi$
$224$	−14.1559	−0.945829
$225$	−8.34062	−0.556041
$226$	−8.36750	−0.556598
$227$	17.6018	1.16827	0.584135	−	0.811657i	$-0.301434\pi$
$227$	17.6018	1.16827	0.584135	+	0.811657i	$0.301434\pi$
$228$	−3.57768	−0.236937
$229$	6.99467	0.462221	0.231111	−	0.972928i	$-0.425764\pi$
$229$	6.99467	0.462221	0.231111	+	0.972928i	$0.425764\pi$
$230$	0.857428	0.0565372
$231$	7.20578	0.474106
$232$	−2.84093	−0.186516
$233$	−15.3497	−1.00559	−0.502795	−	0.864406i	$-0.667695\pi$
$233$	−15.3497	−1.00559	−0.502795	+	0.864406i	$0.667695\pi$
$234$	−3.49928	−0.228755
$235$	6.40611	0.417888
$236$	11.0460	0.719036
$237$	−24.8798	−1.61612
$238$	10.5556	0.684215
$239$	−5.61376	−0.363124	−0.181562	−	0.983380i	$-0.558115\pi$
$239$	−5.61376	−0.363124	−0.181562	+	0.983380i	$0.558115\pi$
$240$	0.378265	0.0244169
$241$	−20.4755	−1.31894	−0.659472	−	0.751730i	$-0.729220\pi$
$241$	−20.4755	−1.31894	−0.659472	+	0.751730i	$0.729220\pi$
$242$	6.62789	0.426057
$243$	−6.52516	−0.418589
$244$	−1.89876	−0.121556
$245$	−2.88684	−0.184433
$246$	0.567338	0.0361721
$247$	11.8166	0.751875
$248$	−24.0039	−1.52425
$249$	5.16967	0.327614
$250$	−30.0948	−1.90336
$251$	7.54742	0.476389	0.238195	−	0.971217i	$-0.423444\pi$
$251$	7.54742	0.476389	0.238195	+	0.971217i	$0.423444\pi$
$252$	1.96688	0.123902
$253$	0.427295	0.0268638
$254$	11.0641	0.694224
$255$	31.0822	1.94644
$256$	−16.1384	−1.00865
$257$	13.5279	0.843846	0.421923	−	0.906632i	$-0.361355\pi$
$257$	13.5279	0.843846	0.421923	+	0.906632i	$0.361355\pi$
$258$	−1.35418	−0.0843078
$259$	4.13533	0.256957
$260$	32.2392	1.99939
$261$	0.639673	0.0395948
$262$	17.8703	1.10403
$263$	−12.8883	−0.794725	−0.397363	−	0.917662i	$-0.630074\pi$
$263$	−12.8883	−0.794725	−0.397363	+	0.917662i	$0.630074\pi$
$264$	8.14279	0.501154
$265$	−42.2612	−2.59609
$266$	4.21915	0.258693
$267$	10.6953	0.654540
$268$	−10.5960	−0.647253
$269$	12.2991	0.749887	0.374944	−	0.927048i	$-0.377662\pi$
$269$	12.2991	0.749887	0.374944	+	0.927048i	$0.377662\pi$
$270$	−20.9336	−1.27398
$271$	−5.55049	−0.337168	−0.168584	−	0.985687i	$-0.553920\pi$
$271$	−5.55049	−0.337168	−0.168584	+	0.985687i	$0.553920\pi$
$272$	0.276138	0.0167433
$273$	23.9709	1.45078
$274$	−4.19854	−0.253643
$275$	−24.3257	−1.46690
$276$	−0.430366	−0.0259050
$277$	−13.5597	−0.814723	−0.407361	−	0.913267i	$-0.633551\pi$
$277$	−13.5597	−0.814723	−0.407361	+	0.913267i	$0.633551\pi$
$278$	13.8433	0.830266
$279$	5.40479	0.323577
$280$	30.3343	1.81282
$281$	24.8032	1.47964	0.739818	−	0.672808i	$-0.234912\pi$
$281$	24.8032	1.47964	0.739818	+	0.672808i	$0.234912\pi$
$282$	2.04252	0.121631
$283$	−6.38218	−0.379381	−0.189690	−	0.981844i	$-0.560748\pi$
$283$	−6.38218	−0.379381	−0.189690	+	0.981844i	$0.560748\pi$
$284$	2.26337	0.134306
$285$	12.4238	0.735924
$286$	−10.2058	−0.603482
$287$	1.05325	0.0621716
$288$	3.60185	0.212241
$289$	5.69036	0.334727
$290$	3.74366	0.219835
$291$	29.6178	1.73623
$292$	15.9452	0.933121
$293$	−17.8119	−1.04058	−0.520291	−	0.853989i	$-0.674176\pi$
$293$	−17.8119	−1.04058	−0.520291	+	0.853989i	$0.674176\pi$
$294$	−0.920440	−0.0536812
$295$	−38.3584	−2.23331
$296$	4.67307	0.271617
$297$	−10.4322	−0.605336
$298$	11.7182	0.678815
$299$	1.42145	0.0822044
$300$	24.5006	1.41454
$301$	−2.51402	−0.144906
$302$	−8.77548	−0.504972
$303$	24.3595	1.39942
$304$	0.110375	0.00633043
$305$	6.59363	0.377550
$306$	−2.68578	−0.153536
$307$	−10.8591	−0.619760	−0.309880	−	0.950776i	$-0.600289\pi$
$307$	−10.8591	−0.619760	−0.309880	+	0.950776i	$0.600289\pi$
$308$	5.73648	0.326866
$309$	−14.1503	−0.804983
$310$	31.6313	1.79654
$311$	10.5093	0.595927	0.297963	−	0.954577i	$-0.403693\pi$
$311$	10.5093	0.595927	0.297963	+	0.954577i	$0.403693\pi$
$312$	27.0880	1.53355
$313$	−16.8931	−0.954852	−0.477426	−	0.878672i	$-0.658430\pi$
$313$	−16.8931	−0.954852	−0.477426	+	0.878672i	$0.658430\pi$
$314$	19.1153	1.07874
$315$	−6.83017	−0.384837
$316$	−19.8067	−1.11421
$317$	14.0675	0.790112	0.395056	−	0.918657i	$-0.370725\pi$
$317$	14.0675	0.790112	0.395056	+	0.918657i	$0.370725\pi$
$318$	−13.4746	−0.755617
$319$	1.86563	0.104455
$320$	21.5721	1.20592
$321$	−21.5359	−1.20202
$322$	0.507530	0.0282836
$323$	9.06954	0.504643
$324$	8.16006	0.453337
$325$	−80.9224	−4.48877
$326$	−6.70872	−0.371561
$327$	−28.0454	−1.55091
$328$	1.19021	0.0657186
$329$	3.79191	0.209055
$330$	−10.7302	−0.590679
$331$	6.79036	0.373232	0.186616	−	0.982433i	$-0.440248\pi$
$331$	6.79036	0.373232	0.186616	+	0.982433i	$0.440248\pi$
$332$	4.11554	0.225870
$333$	−1.05220	−0.0576604
$334$	−7.38649	−0.404171
$335$	36.7956	2.01036
$336$	0.223903	0.0122149
$337$	−15.3009	−0.833494	−0.416747	−	0.909023i	$-0.636830\pi$
$337$	−15.3009	−0.833494	−0.416747	+	0.909023i	$0.636830\pi$
$338$	−22.4921	−1.22341
$339$	−14.5845	−0.792119
$340$	24.7443	1.34195
$341$	15.7633	0.853631
$342$	−1.07353	−0.0580499
$343$	−19.3069	−1.04248
$344$	−2.84093	−0.153173
$345$	1.49449	0.0804605
$346$	−7.46891	−0.401531
$347$	16.4282	0.881910	0.440955	−	0.897529i	$-0.354640\pi$
$347$	16.4282	0.881910	0.440955	+	0.897529i	$0.354640\pi$
$348$	−1.87904	−0.100727
$349$	34.0945	1.82504	0.912519	−	0.409034i	$-0.134134\pi$
$349$	34.0945	1.82504	0.912519	+	0.409034i	$0.134134\pi$
$350$	−28.8935	−1.54442
$351$	−34.7039	−1.85235
$352$	10.5050	0.559916
$353$	12.9514	0.689332	0.344666	−	0.938725i	$-0.387992\pi$
$353$	12.9514	0.689332	0.344666	+	0.938725i	$0.387992\pi$
$354$	−12.2302	−0.650028
$355$	−7.85978	−0.417154
$356$	8.51444	0.451265
$357$	18.3982	0.973737
$358$	−5.87079	−0.310281
$359$	22.6072	1.19316	0.596582	−	0.802552i	$-0.296525\pi$
$359$	22.6072	1.19316	0.596582	+	0.802552i	$0.296525\pi$
$360$	−7.71834	−0.406792
$361$	−15.3748	−0.809201
$362$	−6.88181	−0.361700
$363$	11.5523	0.606341
$364$	19.0831	1.00023
$365$	−55.3712	−2.89826
$366$	2.10231	0.109890
$367$	3.22361	0.168271	0.0841356	−	0.996454i	$-0.473187\pi$
$367$	3.22361	0.168271	0.0841356	+	0.996454i	$0.473187\pi$
$368$	0.0132772	0.000692123 0
$369$	−0.267992	−0.0139511
$370$	−6.15797	−0.320138
$371$	−25.0153	−1.29873
$372$	−15.8766	−0.823163
$373$	−0.844815	−0.0437429	−0.0218714	−	0.999761i	$-0.506962\pi$
$373$	−0.844815	−0.0437429	−0.0218714	+	0.999761i	$0.506962\pi$
$374$	−7.83319	−0.405045
$375$	−52.4548	−2.70876
$376$	4.28500	0.220982
$377$	6.20625	0.319638
$378$	−12.3911	−0.637328
$379$	7.45686	0.383033	0.191517	−	0.981489i	$-0.438659\pi$
$379$	7.45686	0.383033	0.191517	+	0.981489i	$0.438659\pi$
$380$	9.89053	0.507374
$381$	19.2846	0.987981
$382$	0.698187	0.0357223
$383$	−16.5514	−0.845735	−0.422867	−	0.906192i	$-0.638976\pi$
$383$	−16.5514	−0.845735	−0.422867	+	0.906192i	$0.638976\pi$
$384$	−10.4234	−0.531919
$385$	−19.9205	−1.01524
$386$	18.9801	0.966063
$387$	0.639673	0.0325164
$388$	23.5786	1.19702
$389$	−3.04806	−0.154543	−0.0772713	−	0.997010i	$-0.524621\pi$
$389$	−3.04806	−0.154543	−0.0772713	+	0.997010i	$0.524621\pi$
$390$	−35.6953	−1.80750
$391$	1.09099	0.0551739
$392$	−1.93099	−0.0975295
$393$	31.1477	1.57119
$394$	4.94651	0.249202
$395$	68.7806	3.46073
$396$	−1.45960	−0.0733479
$397$	−9.82863	−0.493285	−0.246642	−	0.969107i	$-0.579327\pi$
$397$	−9.82863	−0.493285	−0.246642	+	0.969107i	$0.579327\pi$
$398$	9.89330	0.495906
$399$	7.35393	0.368157
$400$	−0.755867	−0.0377933
$401$	−7.75410	−0.387221	−0.193611	−	0.981078i	$-0.562020\pi$
$401$	−7.75410	−0.387221	−0.193611	+	0.981078i	$0.562020\pi$
$402$	11.7319	0.585134
$403$	52.4385	2.61215
$404$	19.3925	0.964811
$405$	−28.3366	−1.40806
$406$	2.21595	0.109976
$407$	−3.06879	−0.152114
$408$	20.7906	1.02929
$409$	37.3243	1.84557	0.922783	−	0.385320i	$-0.125909\pi$
$409$	37.3243	1.84557	0.922783	+	0.385320i	$0.125909\pi$
$410$	−1.56841	−0.0774584
$411$	−7.31800	−0.360970
$412$	−11.2650	−0.554986
$413$	−22.7052	−1.11725
$414$	−0.129137	−0.00634675
$415$	−14.2916	−0.701548
$416$	34.9460	1.71337
$417$	24.1287	1.18159
$418$	−3.13100	−0.153142
$419$	35.2717	1.72313	0.861567	−	0.507643i	$-0.169483\pi$
$419$	35.2717	1.72313	0.861567	+	0.507643i	$0.169483\pi$
$420$	20.0636	0.979006
$421$	10.6974	0.521359	0.260680	−	0.965425i	$-0.416053\pi$
$421$	10.6974	0.521359	0.260680	+	0.965425i	$0.416053\pi$
$422$	−10.7138	−0.521538
$423$	−0.964824	−0.0469113
$424$	−28.2682	−1.37283
$425$	−62.1099	−3.01277
$426$	−2.50601	−0.121417
$427$	3.90291	0.188875
$428$	−17.1446	−0.828716
$429$	−17.7886	−0.858841
$430$	3.74366	0.180535
$431$	28.2770	1.36205	0.681027	−	0.732259i	$-0.261534\pi$
$431$	28.2770	1.36205	0.681027	+	0.732259i	$0.261534\pi$
$432$	−0.324156	−0.0155960
$433$	5.32044	0.255684	0.127842	−	0.991795i	$-0.459195\pi$
$433$	5.32044	0.255684	0.127842	+	0.991795i	$0.459195\pi$
$434$	18.7233	0.898745
$435$	6.52515	0.312857
$436$	−22.3268	−1.06926
$437$	0.436080	0.0208605
$438$	−17.6546	−0.843567
$439$	2.21750	0.105835	0.0529177	−	0.998599i	$-0.483148\pi$
$439$	2.21750	0.105835	0.0529177	+	0.998599i	$0.483148\pi$
$440$	−22.5109	−1.07316
$441$	0.434787	0.0207041
$442$	−26.0580	−1.23945
$443$	39.7556	1.88885	0.944423	−	0.328733i	$-0.106622\pi$
$443$	39.7556	1.88885	0.944423	+	0.328733i	$0.106622\pi$
$444$	3.09085	0.146685
$445$	−29.5672	−1.40162
$446$	13.3606	0.632643
$447$	20.4246	0.966052
$448$	12.7690	0.603278
$449$	14.6422	0.691006	0.345503	−	0.938418i	$-0.387708\pi$
$449$	14.6422	0.691006	0.345503	+	0.938418i	$0.387708\pi$
$450$	7.35173	0.346564
$451$	−0.781611	−0.0368046
$452$	−11.6106	−0.546117
$453$	−15.2955	−0.718648
$454$	−15.5148	−0.728148
$455$	−66.2678	−3.10668
$456$	8.31021	0.389161
$457$	22.8690	1.06977	0.534883	−	0.844926i	$-0.320356\pi$
$457$	22.8690	1.06977	0.534883	+	0.844926i	$0.320356\pi$
$458$	−6.16537	−0.288089
$459$	−26.6360	−1.24326
$460$	1.18975	0.0554725
$461$	−15.1288	−0.704618	−0.352309	−	0.935884i	$-0.614603\pi$
$461$	−15.1288	−0.704618	−0.352309	+	0.935884i	$0.614603\pi$
$462$	−6.35145	−0.295496
$463$	8.65358	0.402166	0.201083	−	0.979574i	$-0.435554\pi$
$463$	8.65358	0.402166	0.201083	+	0.979574i	$0.435554\pi$
$464$	0.0579703	0.00269120
$465$	55.1330	2.55673
$466$	13.5298	0.626754
$467$	−0.734867	−0.0340056	−0.0170028	−	0.999855i	$-0.505412\pi$
$467$	−0.734867	−0.0340056	−0.0170028	+	0.999855i	$0.505412\pi$
$468$	−4.85555	−0.224448
$469$	21.7801	1.00571
$470$	−5.64658	−0.260458
$471$	33.3177	1.53520
$472$	−25.6577	−1.18099
$473$	1.86563	0.0857819
$474$	21.9300	1.00728
$475$	−24.8259	−1.13909
$476$	14.6467	0.671331
$477$	6.36496	0.291432
$478$	4.94818	0.226324
$479$	12.2914	0.561609	0.280804	−	0.959765i	$-0.409399\pi$
$479$	12.2914	0.561609	0.280804	+	0.959765i	$0.409399\pi$
$480$	36.7416	1.67702
$481$	−10.2087	−0.465477
$482$	18.0479	0.822058
$483$	0.884620	0.0402516
$484$	9.19675	0.418034
$485$	−81.8788	−3.71792
$486$	5.75152	0.260894
$487$	−10.8094	−0.489822	−0.244911	−	0.969546i	$-0.578759\pi$
$487$	−10.8094	−0.489822	−0.244911	+	0.969546i	$0.578759\pi$
$488$	4.41043	0.199651
$489$	−11.6932	−0.528785
$490$	2.54457	0.114952
$491$	−9.32946	−0.421032	−0.210516	−	0.977590i	$-0.567514\pi$
$491$	−9.32946	−0.421032	−0.210516	+	0.977590i	$0.567514\pi$
$492$	0.787228	0.0354910
$493$	4.76344	0.214535
$494$	−10.4156	−0.468621
$495$	5.06861	0.227817
$496$	0.489808	0.0219930
$497$	−4.65237	−0.208687
$498$	−4.55674	−0.204192
$499$	9.97029	0.446332	0.223166	−	0.974781i	$-0.428361\pi$
$499$	9.97029	0.446332	0.223166	+	0.974781i	$0.428361\pi$
$500$	−41.7590	−1.86752
$501$	−12.8746	−0.575194
$502$	−6.65258	−0.296919
$503$	−27.1865	−1.21218	−0.606092	−	0.795394i	$-0.707264\pi$
$503$	−27.1865	−1.21218	−0.606092	+	0.795394i	$0.707264\pi$
$504$	−4.56865	−0.203504
$505$	−67.3422	−2.99669
$506$	−0.376634	−0.0167434
$507$	−39.2035	−1.74109
$508$	15.3524	0.681151
$509$	10.6693	0.472909	0.236454	−	0.971643i	$-0.424015\pi$
$509$	10.6693	0.472909	0.236454	+	0.971643i	$0.424015\pi$
$510$	−27.3970	−1.21316
$511$	−32.7754	−1.44990
$512$	0.655797	0.0289824
$513$	−10.6467	−0.470061
$514$	−11.9240	−0.525944
$515$	39.1187	1.72378
$516$	−1.87904	−0.0827202
$517$	−2.81395	−0.123757
$518$	−3.64503	−0.160154
$519$	−13.0182	−0.571436
$520$	−74.8850	−3.28392
$521$	42.9363	1.88107	0.940537	−	0.339692i	$-0.110323\pi$
$521$	42.9363	1.88107	0.940537	+	0.339692i	$0.110323\pi$
$522$	−0.563832	−0.0246783
$523$	33.6341	1.47072	0.735359	−	0.677678i	$-0.237014\pi$
$523$	33.6341	1.47072	0.735359	+	0.677678i	$0.237014\pi$
$524$	24.7965	1.08324
$525$	−50.3610	−2.19794
$526$	11.3602	0.495329
$527$	40.2477	1.75322
$528$	−0.166157	−0.00723104
$529$	−22.9475	−0.997719
$530$	37.2506	1.61806
$531$	5.77716	0.250707
$532$	5.85442	0.253821
$533$	−2.60012	−0.112624
$534$	−9.42721	−0.407955
$535$	59.5363	2.57398
$536$	24.6123	1.06309
$537$	−10.2327	−0.441575
$538$	−10.8409	−0.467383
$539$	1.26807	0.0546198
$540$	−29.0472	−1.24999
$541$	−22.9504	−0.986714	−0.493357	−	0.869827i	$-0.664230\pi$
$541$	−22.9504	−0.986714	−0.493357	+	0.869827i	$0.664230\pi$
$542$	4.89241	0.210147
$543$	−11.9949	−0.514751
$544$	26.8218	1.14998
$545$	77.5318	3.32110
$546$	−21.1288	−0.904231
$547$	−29.4628	−1.25974	−0.629869	−	0.776701i	$-0.716892\pi$
$547$	−29.4628	−1.25974	−0.629869	+	0.776701i	$0.716892\pi$
$548$	−5.82582	−0.248867
$549$	−0.993067	−0.0423831
$550$	21.4416	0.914274
$551$	1.90399	0.0811127
$552$	0.999652	0.0425480
$553$	40.7127	1.73128
$554$	11.9520	0.507793
$555$	−10.7333	−0.455602
$556$	19.2087	0.814631
$557$	−39.5155	−1.67432	−0.837162	−	0.546956i	$-0.815787\pi$
$557$	−39.5155	−1.67432	−0.837162	+	0.546956i	$0.815787\pi$
$558$	−4.76399	−0.201676
$559$	6.20625	0.262496
$560$	−0.618983	−0.0261568
$561$	−13.6532	−0.576437
$562$	−21.8625	−0.922213
$563$	−15.9306	−0.671396	−0.335698	−	0.941970i	$-0.608972\pi$
$563$	−15.9306	−0.671396	−0.335698	+	0.941970i	$0.608972\pi$
$564$	2.83417	0.119340
$565$	40.3189	1.69623
$566$	5.62549	0.236457
$567$	−16.7730	−0.704401
$568$	−5.25735	−0.220593
$569$	−15.4888	−0.649326	−0.324663	−	0.945830i	$-0.605251\pi$
$569$	−15.4888	−0.649326	−0.324663	+	0.945830i	$0.605251\pi$
$570$	−10.9508	−0.458680
$571$	45.4064	1.90020	0.950099	−	0.311950i	$-0.100982\pi$
$571$	45.4064	1.90020	0.950099	+	0.311950i	$0.100982\pi$
$572$	−14.1614	−0.592118
$573$	1.21693	0.0508380
$574$	−0.928377	−0.0387497
$575$	−2.98636	−0.124540
$576$	−3.24897	−0.135374
$577$	2.18572	0.0909926	0.0454963	−	0.998965i	$-0.485513\pi$
$577$	2.18572	0.0909926	0.0454963	+	0.998965i	$0.485513\pi$
$578$	−5.01570	−0.208626
$579$	33.0822	1.37485
$580$	5.19464	0.215696
$581$	−8.45951	−0.350960
$582$	−26.1063	−1.08214
$583$	18.5637	0.768828
$584$	−37.0374	−1.53262
$585$	16.8613	0.697131
$586$	15.7001	0.648564
$587$	−10.2276	−0.422137	−0.211069	−	0.977471i	$-0.567694\pi$
$587$	−10.2276	−0.422137	−0.211069	+	0.977471i	$0.567694\pi$
$588$	−1.27719	−0.0526703
$589$	16.0874	0.662869
$590$	33.8105	1.39196
$591$	8.62171	0.354650
$592$	−0.0953557	−0.00391909
$593$	−28.7868	−1.18213	−0.591066	−	0.806623i	$-0.701293\pi$
$593$	−28.7868	−1.18213	−0.591066	+	0.806623i	$0.701293\pi$
$594$	9.19531	0.377288
$595$	−50.8621	−2.08514
$596$	16.2599	0.666032
$597$	17.2439	0.705746
$598$	−1.25292	−0.0512356
$599$	25.9913	1.06197	0.530987	−	0.847380i	$-0.321821\pi$
$599$	25.9913	1.06197	0.530987	+	0.847380i	$0.321821\pi$
$600$	−56.9098	−2.32333
$601$	−17.8609	−0.728563	−0.364282	−	0.931289i	$-0.618685\pi$
$601$	−17.8609	−0.728563	−0.364282	+	0.931289i	$0.618685\pi$
$602$	2.21595	0.0903155
$603$	−5.54178	−0.225679
$604$	−12.1767	−0.495463
$605$	−31.9366	−1.29841
$606$	−21.4714	−0.872216
$607$	20.4634	0.830584	0.415292	−	0.909688i	$-0.363679\pi$
$607$	20.4634	0.830584	0.415292	+	0.909688i	$0.363679\pi$
$608$	10.7209	0.434791
$609$	3.86238	0.156511
$610$	−5.81188	−0.235316
$611$	−9.36093	−0.378703
$612$	−3.72674	−0.150645
$613$	25.7593	1.04041	0.520204	−	0.854042i	$-0.325856\pi$
$613$	25.7593	1.04041	0.520204	+	0.854042i	$0.325856\pi$
$614$	9.57159	0.386278
$615$	−2.73372	−0.110234
$616$	−13.3247	−0.536866
$617$	18.2168	0.733381	0.366690	−	0.930343i	$-0.380491\pi$
$617$	18.2168	0.733381	0.366690	+	0.930343i	$0.380491\pi$
$618$	12.4726	0.501722
$619$	9.86431	0.396480	0.198240	−	0.980153i	$-0.436477\pi$
$619$	9.86431	0.396480	0.198240	+	0.980153i	$0.436477\pi$
$620$	43.8910	1.76271
$621$	−1.28071	−0.0513930
$622$	−9.26328	−0.371424
$623$	−17.5015	−0.701182
$624$	−0.552740	−0.0221273
$625$	79.8177	3.19271
$626$	14.8902	0.595131
$627$	−5.45729	−0.217943
$628$	26.5240	1.05842
$629$	−7.83541	−0.312418
$630$	6.02037	0.239857
$631$	11.4208	0.454655	0.227327	−	0.973818i	$-0.427001\pi$
$631$	11.4208	0.454655	0.227327	+	0.973818i	$0.427001\pi$
$632$	46.0068	1.83005
$633$	−18.6740	−0.742223
$634$	−12.3997	−0.492453
$635$	−53.3126	−2.11564
$636$	−18.6971	−0.741388
$637$	4.21839	0.167139
$638$	−1.64444	−0.0651040
$639$	1.18376	0.0468288
$640$	28.8158	1.13904
$641$	4.40678	0.174057	0.0870286	−	0.996206i	$-0.472263\pi$
$641$	4.40678	0.174057	0.0870286	+	0.996206i	$0.472263\pi$
$642$	18.9826	0.749182
$643$	−13.8538	−0.546341	−0.273171	−	0.961966i	$-0.588072\pi$
$643$	−13.8538	−0.546341	−0.273171	+	0.961966i	$0.588072\pi$
$644$	0.704240	0.0277510
$645$	6.52515	0.256928
$646$	−7.99424	−0.314529
$647$	−27.0928	−1.06513	−0.532564	−	0.846390i	$-0.678771\pi$
$647$	−27.0928	−1.06513	−0.532564	+	0.846390i	$0.678771\pi$
$648$	−18.9541	−0.744589
$649$	16.8493	0.661393
$650$	71.3281	2.79772
$651$	32.6344	1.27904
$652$	−9.30890	−0.364565
$653$	−24.0132	−0.939711	−0.469855	−	0.882743i	$-0.655694\pi$
$653$	−24.0132	−0.939711	−0.469855	+	0.882743i	$0.655694\pi$
$654$	24.7203	0.966639
$655$	−86.1082	−3.36453
$656$	−0.0242868	−0.000948238 0
$657$	8.33945	0.325353
$658$	−3.34234	−0.130298
$659$	−24.8937	−0.969721	−0.484860	−	0.874592i	$-0.661130\pi$
$659$	−24.8937	−0.969721	−0.484860	+	0.874592i	$0.661130\pi$
$660$	−14.8891	−0.579556
$661$	−2.52036	−0.0980307	−0.0490154	−	0.998798i	$-0.515608\pi$
$661$	−2.52036	−0.0980307	−0.0490154	+	0.998798i	$0.515608\pi$
$662$	−5.98528	−0.232625
$663$	−45.4188	−1.76392
$664$	−9.55956	−0.370983
$665$	−20.3300	−0.788365
$666$	0.927451	0.0359380
$667$	0.229035	0.00886827
$668$	−10.2494	−0.396560
$669$	23.2874	0.900342
$670$	−32.4330	−1.25300
$671$	−2.89632	−0.111811
$672$	21.7482	0.838954
$673$	−35.6397	−1.37381	−0.686904	−	0.726748i	$-0.741031\pi$
$673$	−35.6397	−1.37381	−0.686904	+	0.726748i	$0.741031\pi$
$674$	13.4868	0.519492
$675$	72.9102	2.80631
$676$	−31.2097	−1.20037
$677$	15.8274	0.608295	0.304148	−	0.952625i	$-0.401628\pi$
$677$	15.8274	0.608295	0.304148	+	0.952625i	$0.401628\pi$
$678$	12.8553	0.493705
$679$	−48.4658	−1.85995
$680$	−57.4760	−2.20410
$681$	−27.0422	−1.03626
$682$	−13.8944	−0.532043
$683$	40.5941	1.55329	0.776645	−	0.629939i	$-0.216920\pi$
$683$	40.5941	1.55329	0.776645	+	0.629939i	$0.216920\pi$
$684$	−1.48961	−0.0569568
$685$	20.2307	0.772976
$686$	17.0179	0.649745
$687$	−10.7462	−0.409992
$688$	0.0579703	0.00221010
$689$	61.7542	2.35265
$690$	−1.31730	−0.0501487
$691$	−28.4738	−1.08320	−0.541598	−	0.840638i	$-0.682180\pi$
$691$	−28.4738	−1.08320	−0.541598	+	0.840638i	$0.682180\pi$
$692$	−10.3637	−0.393970
$693$	3.00022	0.113969
$694$	−14.4804	−0.549668
$695$	−66.7041	−2.53023
$696$	4.36463	0.165441
$697$	−1.99565	−0.0755907
$698$	−30.0522	−1.13749
$699$	23.5822	0.891962
$700$	−40.0921	−1.51534
$701$	−5.76161	−0.217613	−0.108806	−	0.994063i	$-0.534703\pi$
$701$	−5.76161	−0.217613	−0.108806	+	0.994063i	$0.534703\pi$
$702$	30.5893	1.15452
$703$	−3.13189	−0.118121
$704$	−9.47576	−0.357131
$705$	−9.84193	−0.370669
$706$	−11.4158	−0.429640
$707$	−39.8613	−1.49914
$708$	−16.9704	−0.637787
$709$	−46.9974	−1.76502	−0.882512	−	0.470289i	$-0.844150\pi$
$709$	−46.9974	−1.76502	−0.882512	+	0.470289i	$0.844150\pi$
$710$	6.92790	0.260000
$711$	−10.3590	−0.388495
$712$	−19.7773	−0.741185
$713$	1.93519	0.0724733
$714$	−16.2169	−0.606901
$715$	49.1768	1.83911
$716$	−8.14621	−0.304438
$717$	8.62461	0.322092
$718$	−19.9269	−0.743664
$719$	29.6143	1.10443	0.552214	−	0.833702i	$-0.313783\pi$
$719$	29.6143	1.10443	0.552214	+	0.833702i	$0.313783\pi$
$720$	0.157496	0.00586951
$721$	23.1552	0.862345
$722$	13.5519	0.504351
$723$	31.4572	1.16991
$724$	−9.54908	−0.354889
$725$	−13.0389	−0.484251
$726$	−10.1827	−0.377914
$727$	5.71254	0.211867	0.105933	−	0.994373i	$-0.466217\pi$
$727$	5.71254	0.211867	0.105933	+	0.994373i	$0.466217\pi$
$728$	−44.3261	−1.64283
$729$	30.0402	1.11260
$730$	48.8062	1.80640
$731$	4.76344	0.176182
$732$	2.91714	0.107820
$733$	−21.9379	−0.810295	−0.405148	−	0.914251i	$-0.632780\pi$
$733$	−21.9379	−0.810295	−0.405148	+	0.914251i	$0.632780\pi$
$734$	−2.84141	−0.104879
$735$	4.43515	0.163593
$736$	1.28964	0.0475369
$737$	−16.1628	−0.595365
$738$	0.236219	0.00869533
$739$	−37.7394	−1.38826	−0.694132	−	0.719847i	$-0.744212\pi$
$739$	−37.7394	−1.38826	−0.694132	+	0.719847i	$0.744212\pi$
$740$	−8.54469	−0.314109
$741$	−18.1543	−0.666916
$742$	22.0495	0.809461
$743$	−8.31253	−0.304957	−0.152479	−	0.988307i	$-0.548726\pi$
$743$	−8.31253	−0.304957	−0.152479	+	0.988307i	$0.548726\pi$
$744$	36.8781	1.35201
$745$	−56.4641	−2.06869
$746$	0.744652	0.0272636
$747$	2.15246	0.0787544
$748$	−10.8692	−0.397417
$749$	35.2408	1.28767
$750$	46.2357	1.68829
$751$	−10.9437	−0.399341	−0.199670	−	0.979863i	$-0.563987\pi$
$751$	−10.9437	−0.399341	−0.199670	+	0.979863i	$0.563987\pi$
$752$	−0.0874369	−0.00318850
$753$	−11.5954	−0.422559
$754$	−5.47042	−0.199221
$755$	42.2847	1.53890
$756$	−17.1936	−0.625327
$757$	−33.7748	−1.22756	−0.613782	−	0.789475i	$-0.710353\pi$
$757$	−33.7748	−1.22756	−0.613782	+	0.789475i	$0.710353\pi$
$758$	−6.57276	−0.238733
$759$	−0.656469	−0.0238283
$760$	−22.9737	−0.833342
$761$	0.570200	0.0206697	0.0103349	−	0.999947i	$-0.496710\pi$
$761$	0.570200	0.0206697	0.0103349	+	0.999947i	$0.496710\pi$
$762$	−16.9982	−0.615779
$763$	45.8928	1.66143
$764$	0.968792	0.0350497
$765$	12.9415	0.467900
$766$	14.5890	0.527122
$767$	56.0512	2.02389
$768$	24.7941	0.894679
$769$	49.9286	1.80047	0.900235	−	0.435404i	$-0.143395\pi$
$769$	49.9286	1.80047	0.900235	+	0.435404i	$0.143395\pi$
$770$	17.5587	0.632770
$771$	−20.7834	−0.748494
$772$	26.3365	0.947872
$773$	6.84945	0.246358	0.123179	−	0.992384i	$-0.460691\pi$
$773$	6.84945	0.246358	0.123179	+	0.992384i	$0.460691\pi$
$774$	−0.563832	−0.0202665
$775$	−110.169	−3.95740
$776$	−54.7681	−1.96606
$777$	−6.35325	−0.227922
$778$	2.68667	0.0963218
$779$	−0.797680	−0.0285799
$780$	−49.5302	−1.77347
$781$	3.45249	0.123540
$782$	−0.961643	−0.0343883
$783$	−5.59176	−0.199833
$784$	0.0394025	0.00140723
$785$	−92.1072	−3.28745
$786$	−27.4548	−0.979279
$787$	−4.90230	−0.174748	−0.0873740	−	0.996176i	$-0.527848\pi$
$787$	−4.90230	−0.174748	−0.0873740	+	0.996176i	$0.527848\pi$
$788$	6.86370	0.244509
$789$	19.8007	0.704924
$790$	−60.6258	−2.15697
$791$	23.8656	0.848565
$792$	3.39036	0.120471
$793$	−9.63495	−0.342147
$794$	8.66332	0.307450
$795$	64.9274	2.30274
$796$	13.7278	0.486568
$797$	22.3348	0.791140	0.395570	−	0.918436i	$-0.370547\pi$
$797$	22.3348	0.791140	0.395570	+	0.918436i	$0.370547\pi$
$798$	−6.48203	−0.229461
$799$	−7.18473	−0.254177
$800$	−73.4188	−2.59575
$801$	4.45312	0.157343
$802$	6.83476	0.241344
$803$	24.3223	0.858317
$804$	16.2790	0.574116
$805$	−2.44554	−0.0861940
$806$	−46.2213	−1.62807
$807$	−18.8955	−0.665153
$808$	−45.0447	−1.58467
$809$	−27.5532	−0.968720	−0.484360	−	0.874869i	$-0.660947\pi$
$809$	−27.5532	−0.968720	−0.484360	+	0.874869i	$0.660947\pi$
$810$	24.9769	0.877600
$811$	−48.2171	−1.69313	−0.846566	−	0.532284i	$-0.821334\pi$
$811$	−48.2171	−1.69313	−0.846566	+	0.532284i	$0.821334\pi$
$812$	3.07482	0.107905
$813$	8.52742	0.299070
$814$	2.70495	0.0948084
$815$	32.3260	1.13233
$816$	−0.424240	−0.0148514
$817$	1.90399	0.0666122
$818$	−32.8990	−1.15029
$819$	9.98059	0.348750
$820$	−2.17630	−0.0759998
$821$	−19.3272	−0.674523	−0.337262	−	0.941411i	$-0.609501\pi$
$821$	−19.3272	−0.674523	−0.337262	+	0.941411i	$0.609501\pi$
$822$	6.45036	0.224982
$823$	−28.1301	−0.980555	−0.490278	−	0.871566i	$-0.663105\pi$
$823$	−28.1301	−0.980555	−0.490278	+	0.871566i	$0.663105\pi$
$824$	26.1662	0.911543
$825$	37.3725	1.30114
$826$	20.0132	0.696348
$827$	3.87254	0.134662	0.0673308	−	0.997731i	$-0.478552\pi$
$827$	3.87254	0.134662	0.0673308	+	0.997731i	$0.478552\pi$
$828$	−0.179189	−0.00622724
$829$	29.5832	1.02747	0.513733	−	0.857950i	$-0.328262\pi$
$829$	29.5832	1.02747	0.513733	+	0.857950i	$0.328262\pi$
$830$	12.5972	0.437254
$831$	20.8322	0.722662
$832$	−31.5222	−1.09284
$833$	3.23772	0.112180
$834$	−21.2680	−0.736449
$835$	35.5919	1.23171
$836$	−4.34452	−0.150258
$837$	−47.2465	−1.63308
$838$	−31.0898	−1.07398
$839$	−17.5010	−0.604202	−0.302101	−	0.953276i	$-0.597688\pi$
$839$	−17.5010	−0.604202	−0.302101	+	0.953276i	$0.597688\pi$
$840$	−46.6037	−1.60798
$841$	1.00000	0.0344828
$842$	−9.42909	−0.324948
$843$	−38.1060	−1.31244
$844$	−14.8662	−0.511717
$845$	108.379	3.72833
$846$	0.850432	0.0292385
$847$	−18.9040	−0.649548
$848$	0.576823	0.0198082
$849$	9.80516	0.336512
$850$	54.7460	1.87777
$851$	−0.376741	−0.0129145
$852$	−3.47730	−0.119130
$853$	35.5262	1.21639	0.608196	−	0.793787i	$-0.291893\pi$
$853$	35.5262	1.21639	0.608196	+	0.793787i	$0.291893\pi$
$854$	−3.44017	−0.117720
$855$	5.17282	0.176907
$856$	39.8234	1.36114
$857$	−20.1031	−0.686709	−0.343354	−	0.939206i	$-0.611563\pi$
$857$	−20.1031	−0.686709	−0.343354	+	0.939206i	$0.611563\pi$
$858$	15.6795	0.535290
$859$	−0.921099	−0.0314275	−0.0157137	−	0.999877i	$-0.505002\pi$
$859$	−0.921099	−0.0314275	−0.0157137	+	0.999877i	$0.505002\pi$
$860$	5.19464	0.177136
$861$	−1.61815	−0.0551464
$862$	−24.9244	−0.848928
$863$	−35.6710	−1.21425	−0.607127	−	0.794604i	$-0.707678\pi$
$863$	−35.6710	−1.21425	−0.607127	+	0.794604i	$0.707678\pi$
$864$	−31.4859	−1.07117
$865$	35.9890	1.22366
$866$	−4.68964	−0.159360
$867$	−8.74230	−0.296904
$868$	25.9801	0.881821
$869$	−30.2126	−1.02489
$870$	−5.75152	−0.194995
$871$	−53.7675	−1.82184
$872$	51.8605	1.75622
$873$	12.3318	0.417367
$874$	−0.384377	−0.0130018
$875$	85.8357	2.90178
$876$	−24.4972	−0.827682
$877$	21.4334	0.723756	0.361878	−	0.932226i	$-0.382136\pi$
$877$	21.4334	0.723756	0.361878	+	0.932226i	$0.382136\pi$
$878$	−1.95458	−0.0659640
$879$	27.3650	0.923000
$880$	0.459342	0.0154844
$881$	25.6182	0.863098	0.431549	−	0.902089i	$-0.357967\pi$
$881$	25.6182	0.863098	0.431549	+	0.902089i	$0.357967\pi$
$882$	−0.383237	−0.0129043
$883$	−39.4130	−1.32635	−0.663177	−	0.748462i	$-0.730792\pi$
$883$	−39.4130	−1.32635	−0.663177	+	0.748462i	$0.730792\pi$
$884$	−36.1577	−1.21611
$885$	58.9314	1.98096
$886$	−35.0421	−1.17726
$887$	50.9934	1.71219	0.856096	−	0.516817i	$-0.172883\pi$
$887$	50.9934	1.71219	0.856096	+	0.516817i	$0.172883\pi$
$888$	−7.17940	−0.240925
$889$	−31.5569	−1.05838
$890$	26.0617	0.873589
$891$	12.4471	0.416994
$892$	18.5390	0.620730
$893$	−2.87180	−0.0961011
$894$	−18.0030	−0.602111
$895$	28.2885	0.945580
$896$	17.0567	0.569823
$897$	−2.18382	−0.0729156
$898$	−12.9061	−0.430684
$899$	8.44930	0.281800
$900$	10.2011	0.340038
$901$	47.3978	1.57905
$902$	0.688941	0.0229392
$903$	3.86238	0.128532
$904$	26.9690	0.896977
$905$	33.1601	1.10228
$906$	13.4821	0.447912
$907$	27.0466	0.898069	0.449034	−	0.893515i	$-0.351768\pi$
$907$	27.0466	0.898069	0.449034	+	0.893515i	$0.351768\pi$
$908$	−21.5281	−0.714436
$909$	10.1424	0.336402
$910$	58.4109	1.93630
$911$	−10.5703	−0.350210	−0.175105	−	0.984550i	$-0.556027\pi$
$911$	−10.5703	−0.350210	−0.175105	+	0.984550i	$0.556027\pi$
$912$	−0.169573	−0.00561511
$913$	6.27773	0.207763
$914$	−20.1576	−0.666753
$915$	−10.1300	−0.334888
$916$	−8.55496	−0.282664
$917$	−50.9693	−1.68315
$918$	23.4780	0.774889
$919$	6.77572	0.223510	0.111755	−	0.993736i	$-0.464353\pi$
$919$	6.77572	0.223510	0.111755	+	0.993736i	$0.464353\pi$
$920$	−2.76355	−0.0911115
$921$	16.6832	0.549729
$922$	13.3351	0.439167
$923$	11.4851	0.378037
$924$	−8.81316	−0.289932
$925$	21.4477	0.705197
$926$	−7.62759	−0.250658
$927$	−5.89167	−0.193508
$928$	5.63077	0.184839
$929$	49.5640	1.62614	0.813070	−	0.582165i	$-0.197794\pi$
$929$	49.5640	1.62614	0.813070	+	0.582165i	$0.197794\pi$
$930$	−48.5963	−1.59354
$931$	1.29414	0.0424139
$932$	18.7737	0.614952
$933$	−16.1458	−0.528589
$934$	0.647739	0.0211947
$935$	37.7443	1.23437
$936$	11.2784	0.368647
$937$	−15.3888	−0.502731	−0.251366	−	0.967892i	$-0.580880\pi$
$937$	−15.3888	−0.502731	−0.251366	+	0.967892i	$0.580880\pi$
$938$	−19.1978	−0.626830
$939$	25.9534	0.846957
$940$	−7.83510	−0.255553
$941$	−15.0416	−0.490341	−0.245171	−	0.969480i	$-0.578844\pi$
$941$	−15.0416	−0.490341	−0.245171	+	0.969480i	$0.578844\pi$
$942$	−29.3675	−0.956844
$943$	−0.0959546	−0.00312471
$944$	0.523554	0.0170402
$945$	59.7065	1.94225
$946$	−1.64444	−0.0534653
$947$	−34.5514	−1.12277	−0.561385	−	0.827555i	$-0.689731\pi$
$947$	−34.5514	−1.12277	−0.561385	+	0.827555i	$0.689731\pi$
$948$	30.4297	0.988311
$949$	80.9111	2.62649
$950$	21.8825	0.709961
$951$	−21.6125	−0.700832
$952$	−34.0213	−1.10264
$953$	−7.10531	−0.230164	−0.115082	−	0.993356i	$-0.536713\pi$
$953$	−7.10531	−0.230164	−0.115082	+	0.993356i	$0.536713\pi$
$954$	−5.61032	−0.181641
$955$	−3.36422	−0.108864
$956$	6.86600	0.222062
$957$	−2.86624	−0.0926523
$958$	−10.8341	−0.350034
$959$	11.9750	0.386693
$960$	−33.1420	−1.06965
$961$	40.3907	1.30293
$962$	8.99833	0.290118
$963$	−8.96676	−0.288950
$964$	25.0429	0.806578
$965$	−91.4560	−2.94407
$966$	−0.779737	−0.0250876
$967$	−1.45858	−0.0469048	−0.0234524	−	0.999725i	$-0.507466\pi$
$967$	−1.45858	−0.0469048	−0.0234524	+	0.999725i	$0.507466\pi$
$968$	−21.3621	−0.686605
$969$	−13.9339	−0.447620
$970$	72.1711	2.31727
$971$	−10.0495	−0.322505	−0.161253	−	0.986913i	$-0.551553\pi$
$971$	−10.0495	−0.322505	−0.161253	+	0.986913i	$0.551553\pi$
$972$	7.98071	0.255981
$973$	−39.4836	−1.26579
$974$	9.52784	0.305292
$975$	124.324	3.98156
$976$	−0.0899965	−0.00288072
$977$	−22.0045	−0.703987	−0.351994	−	0.936002i	$-0.614496\pi$
$977$	−22.0045	−0.703987	−0.351994	+	0.936002i	$0.614496\pi$
$978$	10.3068	0.329576
$979$	12.9877	0.415088
$980$	3.53080	0.112787
$981$	−11.6771	−0.372820
$982$	8.22333	0.262417
$983$	−1.04107	−0.0332050	−0.0166025	−	0.999862i	$-0.505285\pi$
$983$	−1.04107	−0.0332050	−0.0166025	+	0.999862i	$0.505285\pi$
$984$	−1.82857	−0.0582926
$985$	−23.8348	−0.759441
$986$	−4.19868	−0.133713
$987$	−5.82565	−0.185433
$988$	−14.4525	−0.459797
$989$	0.229035	0.00728289
$990$	−4.46767	−0.141992
$991$	60.1547	1.91088	0.955438	−	0.295192i	$-0.0953836\pi$
$991$	60.1547	1.91088	0.955438	+	0.295192i	$0.0953836\pi$
$992$	47.5761	1.51054
$993$	−10.4323	−0.331058
$994$	4.10078	0.130069
$995$	−47.6710	−1.51127
$996$	−6.32285	−0.200347
$997$	−7.09506	−0.224703	−0.112351	−	0.993669i	$-0.535838\pi$
$997$	−7.09506	−0.224703	−0.112351	+	0.993669i	$0.535838\pi$
$998$	−8.78819	−0.278185
$999$	9.19792	0.291009

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1247.2.a.b.1.8	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1247.2.a.b.1.8	✓	19	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1247 = 29 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1247.a (trivial)

\(f(q)\)	\(=\)	\(q-0.881438 q^{2} -1.53634 q^{3} -1.22307 q^{4} +4.24722 q^{5} +1.35418 q^{6} +2.51402 q^{7} +2.84093 q^{8} -0.639673 q^{9} +O(q^{10})\)	\(q-0.881438 q^{2} -1.53634 q^{3} -1.22307 q^{4} +4.24722 q^{5} +1.35418 q^{6} +2.51402 q^{7} +2.84093 q^{8} -0.639673 q^{9} -3.74366 q^{10} -1.86563 q^{11} +1.87904 q^{12} -6.20625 q^{13} -2.21595 q^{14} -6.52515 q^{15} -0.0579703 q^{16} -4.76344 q^{17} +0.563832 q^{18} -1.90399 q^{19} -5.19464 q^{20} -3.86238 q^{21} +1.64444 q^{22} -0.229035 q^{23} -4.36463 q^{24} +13.0389 q^{25} +5.47042 q^{26} +5.59176 q^{27} -3.07482 q^{28} -1.00000 q^{29} +5.75152 q^{30} -8.44930 q^{31} -5.63077 q^{32} +2.86624 q^{33} +4.19868 q^{34} +10.6776 q^{35} +0.782364 q^{36} +1.64491 q^{37} +1.67825 q^{38} +9.53488 q^{39} +12.0661 q^{40} +0.418952 q^{41} +3.40445 q^{42} -1.00000 q^{43} +2.28180 q^{44} -2.71683 q^{45} +0.201880 q^{46} +1.50831 q^{47} +0.0890618 q^{48} -0.679701 q^{49} -11.4929 q^{50} +7.31824 q^{51} +7.59066 q^{52} -9.95033 q^{53} -4.92879 q^{54} -7.92375 q^{55} +7.14216 q^{56} +2.92517 q^{57} +0.881438 q^{58} -9.03142 q^{59} +7.98070 q^{60} +1.55246 q^{61} +7.44753 q^{62} -1.60815 q^{63} +5.07911 q^{64} -26.3593 q^{65} -2.52641 q^{66} +8.66345 q^{67} +5.82601 q^{68} +0.351874 q^{69} -9.41163 q^{70} -1.85057 q^{71} -1.81727 q^{72} -13.0370 q^{73} -1.44988 q^{74} -20.0321 q^{75} +2.32871 q^{76} -4.69024 q^{77} -8.40440 q^{78} +16.1943 q^{79} -0.246212 q^{80} -6.67180 q^{81} -0.369280 q^{82} -3.36493 q^{83} +4.72395 q^{84} -20.2314 q^{85} +0.881438 q^{86} +1.53634 q^{87} -5.30014 q^{88} -6.96155 q^{89} +2.39472 q^{90} -15.6026 q^{91} +0.280125 q^{92} +12.9810 q^{93} -1.32948 q^{94} -8.08666 q^{95} +8.65075 q^{96} -19.2782 q^{97} +0.599114 q^{98} +1.19340 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 2 q^{2} - 6 q^{3} + 12 q^{4} + 2 q^{5} - 8 q^{6} - 10 q^{7} - 6 q^{8} + 11 q^{9}+O(q^{10}) \) 19 * q - 2 * q^2 - 6 * q^3 + 12 * q^4 + 2 * q^5 - 8 * q^6 - 10 * q^7 - 6 * q^8 + 11 * q^9	\( 19 q - 2 q^{2} - 6 q^{3} + 12 q^{4} + 2 q^{5} - 8 q^{6} - 10 q^{7} - 6 q^{8} + 11 q^{9} - 24 q^{10} - 10 q^{11} - 7 q^{12} - 22 q^{13} + 2 q^{14} - 19 q^{15} - 2 q^{16} - 26 q^{17} - 10 q^{18} - 3 q^{19} + 7 q^{20} - 10 q^{21} - 6 q^{22} + 2 q^{23} - 12 q^{24} - 13 q^{25} - 4 q^{26} - 21 q^{27} - 38 q^{28} - 19 q^{29} + 8 q^{30} - 18 q^{31} - 29 q^{32} - 27 q^{33} + 4 q^{34} - 14 q^{35} + 8 q^{36} - 22 q^{37} - 2 q^{38} - 12 q^{39} - 17 q^{40} - 24 q^{41} + 8 q^{42} - 19 q^{43} - 21 q^{44} - 13 q^{45} + q^{46} - 9 q^{47} + 16 q^{48} - 19 q^{49} + 14 q^{50} + 18 q^{51} - 16 q^{52} - 2 q^{53} + 6 q^{54} - 14 q^{55} - q^{56} - 28 q^{57} + 2 q^{58} + 16 q^{59} + 18 q^{60} - 40 q^{61} - 16 q^{62} + 27 q^{63} - 24 q^{64} - 39 q^{65} + 16 q^{66} - 10 q^{67} - 17 q^{68} - 37 q^{69} + 5 q^{70} + 26 q^{71} + 8 q^{72} - 99 q^{73} - 15 q^{74} + 7 q^{75} - 16 q^{76} - 21 q^{77} - 18 q^{78} - q^{79} + 31 q^{80} + 23 q^{81} - 15 q^{82} - 24 q^{83} - 26 q^{84} - 32 q^{85} + 2 q^{86} + 6 q^{87} - q^{88} - 11 q^{89} - 47 q^{90} + 12 q^{92} - 38 q^{93} + 20 q^{94} - 3 q^{95} - 2 q^{96} - 96 q^{97} + 30 q^{98} - 17 q^{99}+O(q^{100}) \) 19 * q - 2 * q^2 - 6 * q^3 + 12 * q^4 + 2 * q^5 - 8 * q^6 - 10 * q^7 - 6 * q^8 + 11 * q^9 - 24 * q^10 - 10 * q^11 - 7 * q^12 - 22 * q^13 + 2 * q^14 - 19 * q^15 - 2 * q^16 - 26 * q^17 - 10 * q^18 - 3 * q^19 + 7 * q^20 - 10 * q^21 - 6 * q^22 + 2 * q^23 - 12 * q^24 - 13 * q^25 - 4 * q^26 - 21 * q^27 - 38 * q^28 - 19 * q^29 + 8 * q^30 - 18 * q^31 - 29 * q^32 - 27 * q^33 + 4 * q^34 - 14 * q^35 + 8 * q^36 - 22 * q^37 - 2 * q^38 - 12 * q^39 - 17 * q^40 - 24 * q^41 + 8 * q^42 - 19 * q^43 - 21 * q^44 - 13 * q^45 + q^46 - 9 * q^47 + 16 * q^48 - 19 * q^49 + 14 * q^50 + 18 * q^51 - 16 * q^52 - 2 * q^53 + 6 * q^54 - 14 * q^55 - q^56 - 28 * q^57 + 2 * q^58 + 16 * q^59 + 18 * q^60 - 40 * q^61 - 16 * q^62 + 27 * q^63 - 24 * q^64 - 39 * q^65 + 16 * q^66 - 10 * q^67 - 17 * q^68 - 37 * q^69 + 5 * q^70 + 26 * q^71 + 8 * q^72 - 99 * q^73 - 15 * q^74 + 7 * q^75 - 16 * q^76 - 21 * q^77 - 18 * q^78 - q^79 + 31 * q^80 + 23 * q^81 - 15 * q^82 - 24 * q^83 - 26 * q^84 - 32 * q^85 + 2 * q^86 + 6 * q^87 - q^88 - 11 * q^89 - 47 * q^90 + 12 * q^92 - 38 * q^93 + 20 * q^94 - 3 * q^95 - 2 * q^96 - 96 * q^97 + 30 * q^98 - 17 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more