LMFDB - Embedded newform 1339.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1339,2,Mod(1,1339)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1339, 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("1339.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1339 = 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1339.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:	$10.6919688306$
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} - 9 x^{18} + 13 x^{17} + 106 x^{16} - 351 x^{15} - 279 x^{14} + 2337 x^{13} - 1079 x^{12} + \cdots - 63 $ x^19 - 9x^18 + 13x^17 + 106x^16 - 351x^15 - 279x^14 + 2337x^13 - 1079x^12 - 6826x^11 + 7199x^10 + 9364x^9 - 14841x^8 - 5183x^7 + 14037x^6 - 108x^5 - 6099x^4 + 855x^3 + 1062x^2 - 135x - 63
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Root			$-2.17587$ of defining polynomial
Character	$\chi$	$=$	1339.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.17587 q^{2} -0.456273 q^{3} +2.73443 q^{4} -0.352848 q^{5} -0.992793 q^{6} -3.48073 q^{7} +1.59803 q^{8} -2.79181 q^{9} +O(q^{10})$	\(q+2.17587 q^{2} -0.456273 q^{3} +2.73443 q^{4} -0.352848 q^{5} -0.992793 q^{6} -3.48073 q^{7} +1.59803 q^{8} -2.79181 q^{9} -0.767754 q^{10} -1.91738 q^{11} -1.24765 q^{12} +1.00000 q^{13} -7.57363 q^{14} +0.160995 q^{15} -1.99175 q^{16} +0.154400 q^{17} -6.07464 q^{18} -0.270945 q^{19} -0.964839 q^{20} +1.58816 q^{21} -4.17198 q^{22} +4.69183 q^{23} -0.729138 q^{24} -4.87550 q^{25} +2.17587 q^{26} +2.64265 q^{27} -9.51781 q^{28} -0.575062 q^{29} +0.350305 q^{30} -5.73622 q^{31} -7.52986 q^{32} +0.874849 q^{33} +0.335954 q^{34} +1.22817 q^{35} -7.63403 q^{36} -10.0384 q^{37} -0.589541 q^{38} -0.456273 q^{39} -0.563862 q^{40} -5.23682 q^{41} +3.45564 q^{42} -10.9895 q^{43} -5.24295 q^{44} +0.985087 q^{45} +10.2088 q^{46} +10.3904 q^{47} +0.908781 q^{48} +5.11546 q^{49} -10.6085 q^{50} -0.0704484 q^{51} +2.73443 q^{52} +12.0387 q^{53} +5.75007 q^{54} +0.676544 q^{55} -5.56231 q^{56} +0.123625 q^{57} -1.25126 q^{58} +2.14257 q^{59} +0.440230 q^{60} +10.0996 q^{61} -12.4813 q^{62} +9.71755 q^{63} -12.4005 q^{64} -0.352848 q^{65} +1.90356 q^{66} +1.62925 q^{67} +0.422195 q^{68} -2.14075 q^{69} +2.67234 q^{70} +5.16831 q^{71} -4.46140 q^{72} +2.32413 q^{73} -21.8424 q^{74} +2.22456 q^{75} -0.740879 q^{76} +6.67388 q^{77} -0.992793 q^{78} +15.4671 q^{79} +0.702785 q^{80} +7.16968 q^{81} -11.3947 q^{82} -11.0181 q^{83} +4.34272 q^{84} -0.0544797 q^{85} -23.9118 q^{86} +0.262385 q^{87} -3.06403 q^{88} -2.09969 q^{89} +2.14343 q^{90} -3.48073 q^{91} +12.8295 q^{92} +2.61728 q^{93} +22.6081 q^{94} +0.0956023 q^{95} +3.43567 q^{96} -10.0037 q^{97} +11.1306 q^{98} +5.35297 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) $ 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * 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 $

$2$	2.17587	1.53858	0.769288	−	0.638902i	$-0.220611\pi$
$2$	2.17587	1.53858	0.769288	+	0.638902i	$0.220611\pi$
$3$	−0.456273	−0.263429	−0.131715	−	0.991288i	$-0.542048\pi$
$3$	−0.456273	−0.263429	−0.131715	+	0.991288i	$0.542048\pi$
$4$	2.73443	1.36722
$5$	−0.352848	−0.157799	−0.0788993	−	0.996883i	$-0.525141\pi$
$5$	−0.352848	−0.157799	−0.0788993	+	0.996883i	$0.525141\pi$
$6$	−0.992793	−0.405306
$7$	−3.48073	−1.31559	−0.657796	−	0.753197i	$-0.728511\pi$
$7$	−3.48073	−1.31559	−0.657796	+	0.753197i	$0.728511\pi$
$8$	1.59803	0.564989
$9$	−2.79181	−0.930605
$10$	−0.767754	−0.242785
$11$	−1.91738	−0.578112	−0.289056	−	0.957312i	$-0.593341\pi$
$11$	−1.91738	−0.578112	−0.289056	+	0.957312i	$0.593341\pi$
$12$	−1.24765	−0.360165
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−7.57363	−2.02414
$15$	0.160995	0.0415688
$16$	−1.99175	−0.497937
$17$	0.154400	0.0374474	0.0187237	−	0.999825i	$-0.494040\pi$
$17$	0.154400	0.0374474	0.0187237	+	0.999825i	$0.494040\pi$
$18$	−6.07464	−1.43181
$19$	−0.270945	−0.0621589	−0.0310795	−	0.999517i	$-0.509894\pi$
$19$	−0.270945	−0.0621589	−0.0310795	+	0.999517i	$0.509894\pi$
$20$	−0.964839	−0.215745
$21$	1.58816	0.346565
$22$	−4.17198	−0.889469
$23$	4.69183	0.978314	0.489157	−	0.872196i	$-0.337305\pi$
$23$	4.69183	0.978314	0.489157	+	0.872196i	$0.337305\pi$
$24$	−0.729138	−0.148835
$25$	−4.87550	−0.975100
$26$	2.17587	0.426724
$27$	2.64265	0.508578
$28$	−9.51781	−1.79870
$29$	−0.575062	−0.106786	−0.0533932	−	0.998574i	$-0.517004\pi$
$29$	−0.575062	−0.106786	−0.0533932	+	0.998574i	$0.517004\pi$
$30$	0.350305	0.0639567
$31$	−5.73622	−1.03025	−0.515127	−	0.857114i	$-0.672255\pi$
$31$	−5.73622	−1.03025	−0.515127	+	0.857114i	$0.672255\pi$
$32$	−7.52986	−1.33110
$33$	0.874849	0.152292
$34$	0.335954	0.0576157
$35$	1.22817	0.207598
$36$	−7.63403	−1.27234
$37$	−10.0384	−1.65031	−0.825155	−	0.564907i	$-0.808912\pi$
$37$	−10.0384	−1.65031	−0.825155	+	0.564907i	$0.808912\pi$
$38$	−0.589541	−0.0956362
$39$	−0.456273	−0.0730622
$40$	−0.563862	−0.0891545
$41$	−5.23682	−0.817854	−0.408927	−	0.912567i	$-0.634097\pi$
$41$	−5.23682	−0.817854	−0.408927	+	0.912567i	$0.634097\pi$
$42$	3.45564	0.533217
$43$	−10.9895	−1.67589	−0.837944	−	0.545757i	$-0.816242\pi$
$43$	−10.9895	−1.67589	−0.837944	+	0.545757i	$0.816242\pi$
$44$	−5.24295	−0.790404
$45$	0.985087	0.146848
$46$	10.2088	1.50521
$47$	10.3904	1.51559	0.757794	−	0.652494i	$-0.226277\pi$
$47$	10.3904	1.51559	0.757794	+	0.652494i	$0.226277\pi$
$48$	0.908781	0.131171
$49$	5.11546	0.730780
$50$	−10.6085	−1.50026
$51$	−0.0704484	−0.00986475
$52$	2.73443	0.379197
$53$	12.0387	1.65364	0.826818	−	0.562470i	$-0.190149\pi$
$53$	12.0387	1.65364	0.826818	+	0.562470i	$0.190149\pi$
$54$	5.75007	0.782486
$55$	0.676544	0.0912252
$56$	−5.56231	−0.743295
$57$	0.123625	0.0163745
$58$	−1.25126	−0.164299
$59$	2.14257	0.278939	0.139469	−	0.990226i	$-0.455460\pi$
$59$	2.14257	0.278939	0.139469	+	0.990226i	$0.455460\pi$
$60$	0.440230	0.0568335
$61$	10.0996	1.29313	0.646563	−	0.762860i	$-0.276206\pi$
$61$	10.0996	1.29313	0.646563	+	0.762860i	$0.276206\pi$
$62$	−12.4813	−1.58513
$63$	9.71755	1.22430
$64$	−12.4005	−1.55007
$65$	−0.352848	−0.0437654
$66$	1.90356	0.234312
$67$	1.62925	0.199044	0.0995222	−	0.995035i	$-0.468269\pi$
$67$	1.62925	0.199044	0.0995222	+	0.995035i	$0.468269\pi$
$68$	0.422195	0.0511987
$69$	−2.14075	−0.257717
$70$	2.67234	0.319406
$71$	5.16831	0.613366	0.306683	−	0.951812i	$-0.400781\pi$
$71$	5.16831	0.613366	0.306683	+	0.951812i	$0.400781\pi$
$72$	−4.46140	−0.525782
$73$	2.32413	0.272019	0.136010	−	0.990708i	$-0.456572\pi$
$73$	2.32413	0.272019	0.136010	+	0.990708i	$0.456572\pi$
$74$	−21.8424	−2.53913
$75$	2.22456	0.256870
$76$	−0.740879	−0.0849847
$77$	6.67388	0.760559
$78$	−0.992793	−0.112412
$79$	15.4671	1.74019	0.870095	−	0.492885i	$-0.164058\pi$
$79$	15.4671	1.74019	0.870095	+	0.492885i	$0.164058\pi$
$80$	0.702785	0.0785738
$81$	7.16968	0.796631
$82$	−11.3947	−1.25833
$83$	−11.0181	−1.20940	−0.604698	−	0.796455i	$-0.706706\pi$
$83$	−11.0181	−1.20940	−0.604698	+	0.796455i	$0.706706\pi$
$84$	4.34272	0.473829
$85$	−0.0544797	−0.00590915
$86$	−23.9118	−2.57848
$87$	0.262385	0.0281307
$88$	−3.06403	−0.326627
$89$	−2.09969	−0.222567	−0.111283	−	0.993789i	$-0.535496\pi$
$89$	−2.09969	−0.222567	−0.111283	+	0.993789i	$0.535496\pi$
$90$	2.14343	0.225937
$91$	−3.48073	−0.364879
$92$	12.8295	1.33757
$93$	2.61728	0.271399
$94$	22.6081	2.33185
$95$	0.0956023	0.00980859
$96$	3.43567	0.350652
$97$	−10.0037	−1.01572	−0.507860	−	0.861440i	$-0.669563\pi$
$97$	−10.0037	−1.01572	−0.507860	+	0.861440i	$0.669563\pi$
$98$	11.1306	1.12436
$99$	5.35297	0.537994
$100$	−13.3317	−1.33317
$101$	−11.7640	−1.17056	−0.585281	−	0.810830i	$-0.699016\pi$
$101$	−11.7640	−1.17056	−0.585281	+	0.810830i	$0.699016\pi$
$102$	−0.153287	−0.0151777
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.59803	0.156700
$105$	−0.560380	−0.0546875
$106$	26.1946	2.54424
$107$	0.500865	0.0484205	0.0242102	−	0.999707i	$-0.492293\pi$
$107$	0.500865	0.0484205	0.0242102	+	0.999707i	$0.492293\pi$
$108$	7.22614	0.695336
$109$	2.90185	0.277947	0.138973	−	0.990296i	$-0.455620\pi$
$109$	2.90185	0.277947	0.138973	+	0.990296i	$0.455620\pi$
$110$	1.47208	0.140357
$111$	4.58027	0.434740
$112$	6.93273	0.655082
$113$	−7.84658	−0.738144	−0.369072	−	0.929401i	$-0.620324\pi$
$113$	−7.84658	−0.738144	−0.369072	+	0.929401i	$0.620324\pi$
$114$	0.268992	0.0251934
$115$	−1.65550	−0.154377
$116$	−1.57247	−0.146000
$117$	−2.79181	−0.258103
$118$	4.66196	0.429168
$119$	−0.537423	−0.0492655
$120$	0.257275	0.0234859
$121$	−7.32365	−0.665787
$122$	21.9756	1.98957
$123$	2.38942	0.215447
$124$	−15.6853	−1.40858
$125$	3.48455	0.311668
$126$	21.1442	1.88367
$127$	−4.80033	−0.425960	−0.212980	−	0.977057i	$-0.568317\pi$
$127$	−4.80033	−0.425960	−0.212980	+	0.977057i	$0.568317\pi$
$128$	−11.9223	−1.05379
$129$	5.01422	0.441478
$130$	−0.767754	−0.0673365
$131$	1.25521	0.109668	0.0548342	−	0.998495i	$-0.482537\pi$
$131$	1.25521	0.109668	0.0548342	+	0.998495i	$0.482537\pi$
$132$	2.39221	0.208216
$133$	0.943084	0.0817758
$134$	3.54504	0.306245
$135$	−0.932454	−0.0802529
$136$	0.246735	0.0211574
$137$	−9.54063	−0.815111	−0.407555	−	0.913180i	$-0.633619\pi$
$137$	−9.54063	−0.815111	−0.407555	+	0.913180i	$0.633619\pi$
$138$	−4.65801	−0.396517
$139$	−9.21631	−0.781718	−0.390859	−	0.920451i	$-0.627822\pi$
$139$	−9.21631	−0.781718	−0.390859	+	0.920451i	$0.627822\pi$
$140$	3.35834	0.283832
$141$	−4.74084	−0.399250
$142$	11.2456	0.943709
$143$	−1.91738	−0.160339
$144$	5.56059	0.463383
$145$	0.202910	0.0168507
$146$	5.05702	0.418522
$147$	−2.33405	−0.192509
$148$	−27.4494	−2.25633
$149$	3.54891	0.290738	0.145369	−	0.989377i	$-0.453563\pi$
$149$	3.54891	0.290738	0.145369	+	0.989377i	$0.453563\pi$
$150$	4.84036	0.395214
$151$	2.47061	0.201056	0.100528	−	0.994934i	$-0.467947\pi$
$151$	2.47061	0.201056	0.100528	+	0.994934i	$0.467947\pi$
$152$	−0.432978	−0.0351191
$153$	−0.431055	−0.0348488
$154$	14.5215	1.17018
$155$	2.02401	0.162573
$156$	−1.24765	−0.0998917
$157$	−3.64054	−0.290547	−0.145273	−	0.989392i	$-0.546406\pi$
$157$	−3.64054	−0.290547	−0.145273	+	0.989392i	$0.546406\pi$
$158$	33.6546	2.67741
$159$	−5.49291	−0.435616
$160$	2.65690	0.210046
$161$	−16.3310	−1.28706
$162$	15.6003	1.22568
$163$	16.6598	1.30490	0.652448	−	0.757834i	$-0.273742\pi$
$163$	16.6598	1.30490	0.652448	+	0.757834i	$0.273742\pi$
$164$	−14.3197	−1.11818
$165$	−0.308689	−0.0240314
$166$	−23.9741	−1.86075
$167$	8.59562	0.665149	0.332574	−	0.943077i	$-0.392083\pi$
$167$	8.59562	0.665149	0.332574	+	0.943077i	$0.392083\pi$
$168$	2.53793	0.195806
$169$	1.00000	0.0769231
$170$	−0.118541	−0.00909168
$171$	0.756427	0.0578454
$172$	−30.0501	−2.29130
$173$	−17.4214	−1.32452	−0.662260	−	0.749274i	$-0.730403\pi$
$173$	−17.4214	−1.32452	−0.662260	+	0.749274i	$0.730403\pi$
$174$	0.570918	0.0432812
$175$	16.9703	1.28283
$176$	3.81894	0.287863
$177$	−0.977596	−0.0734806
$178$	−4.56866	−0.342436
$179$	20.1772	1.50811	0.754056	−	0.656810i	$-0.228095\pi$
$179$	20.1772	1.50811	0.754056	+	0.656810i	$0.228095\pi$
$180$	2.69365	0.200773
$181$	6.65304	0.494517	0.247258	−	0.968950i	$-0.420470\pi$
$181$	6.65304	0.494517	0.247258	+	0.968950i	$0.420470\pi$
$182$	−7.57363	−0.561395
$183$	−4.60819	−0.340648
$184$	7.49768	0.552737
$185$	3.54205	0.260417
$186$	5.69487	0.417568
$187$	−0.296043	−0.0216488
$188$	28.4117	2.07214
$189$	−9.19834	−0.669081
$190$	0.208019	0.0150913
$191$	−21.3463	−1.54456	−0.772280	−	0.635282i	$-0.780884\pi$
$191$	−21.3463	−1.54456	−0.772280	+	0.635282i	$0.780884\pi$
$192$	5.65803	0.408333
$193$	−19.1979	−1.38190	−0.690948	−	0.722904i	$-0.742807\pi$
$193$	−19.1979	−1.38190	−0.690948	+	0.722904i	$0.742807\pi$
$194$	−21.7668	−1.56276
$195$	0.160995	0.0115291
$196$	13.9879	0.999134
$197$	−12.0836	−0.860921	−0.430460	−	0.902610i	$-0.641649\pi$
$197$	−12.0836	−0.860921	−0.430460	+	0.902610i	$0.641649\pi$
$198$	11.6474	0.827744
$199$	−10.2190	−0.724404	−0.362202	−	0.932100i	$-0.617975\pi$
$199$	−10.2190	−0.724404	−0.362202	+	0.932100i	$0.617975\pi$
$200$	−7.79119	−0.550921
$201$	−0.743382	−0.0524341
$202$	−25.5970	−1.80100
$203$	2.00164	0.140487
$204$	−0.192636	−0.0134872
$205$	1.84780	0.129056
$206$	2.17587	0.151600
$207$	−13.0987	−0.910424
$208$	−1.99175	−0.138103
$209$	0.519504	0.0359348
$210$	−1.21932	−0.0841409
$211$	26.4637	1.82184	0.910919	−	0.412586i	$-0.135374\pi$
$211$	26.4637	1.82184	0.910919	+	0.412586i	$0.135374\pi$
$212$	32.9189	2.26088
$213$	−2.35816	−0.161578
$214$	1.08982	0.0744985
$215$	3.87764	0.264453
$216$	4.22303	0.287341
$217$	19.9662	1.35539
$218$	6.31406	0.427642
$219$	−1.06044	−0.0716578
$220$	1.84996	0.124725
$221$	0.154400	0.0103860
$222$	9.96609	0.668880
$223$	−15.7516	−1.05481	−0.527403	−	0.849615i	$-0.676834\pi$
$223$	−15.7516	−1.05481	−0.527403	+	0.849615i	$0.676834\pi$
$224$	26.2094	1.75119
$225$	13.6115	0.907433
$226$	−17.0732	−1.13569
$227$	−0.372870	−0.0247483	−0.0123741	−	0.999923i	$-0.503939\pi$
$227$	−0.372870	−0.0247483	−0.0123741	+	0.999923i	$0.503939\pi$
$228$	0.338043	0.0223875
$229$	−15.0086	−0.991798	−0.495899	−	0.868380i	$-0.665161\pi$
$229$	−15.0086	−0.991798	−0.495899	+	0.868380i	$0.665161\pi$
$230$	−3.60217	−0.237520
$231$	−3.04511	−0.200354
$232$	−0.918967	−0.0603332
$233$	20.1763	1.32180	0.660898	−	0.750476i	$-0.270176\pi$
$233$	20.1763	1.32180	0.660898	+	0.750476i	$0.270176\pi$
$234$	−6.07464	−0.397112
$235$	−3.66622	−0.239158
$236$	5.85870	0.381369
$237$	−7.05724	−0.458417
$238$	−1.16937	−0.0757987
$239$	−16.1233	−1.04293	−0.521466	−	0.853272i	$-0.674615\pi$
$239$	−16.1233	−1.04293	−0.521466	+	0.853272i	$0.674615\pi$
$240$	−0.320662	−0.0206986
$241$	−1.28585	−0.0828290	−0.0414145	−	0.999142i	$-0.513186\pi$
$241$	−1.28585	−0.0828290	−0.0414145	+	0.999142i	$0.513186\pi$
$242$	−15.9353	−1.02436
$243$	−11.1993	−0.718434
$244$	27.6168	1.76798
$245$	−1.80498	−0.115316
$246$	5.19908	0.331481
$247$	−0.270945	−0.0172398
$248$	−9.16665	−0.582083
$249$	5.02727	0.318591
$250$	7.58195	0.479525
$251$	26.6274	1.68071	0.840355	−	0.542037i	$-0.182347\pi$
$251$	26.6274	1.68071	0.840355	+	0.542037i	$0.182347\pi$
$252$	26.5720	1.67388
$253$	−8.99602	−0.565575
$254$	−10.4449	−0.655372
$255$	0.0248576	0.00155664
$256$	−1.14034	−0.0712712
$257$	−12.6711	−0.790404	−0.395202	−	0.918594i	$-0.629325\pi$
$257$	−12.6711	−0.790404	−0.395202	+	0.918594i	$0.629325\pi$
$258$	10.9103	0.679247
$259$	34.9411	2.17113
$260$	−0.964839	−0.0598368
$261$	1.60547	0.0993760
$262$	2.73118	0.168733
$263$	21.1522	1.30430	0.652149	−	0.758091i	$-0.273868\pi$
$263$	21.1522	1.30430	0.652149	+	0.758091i	$0.273868\pi$
$264$	1.39804	0.0860431
$265$	−4.24782	−0.260941
$266$	2.05203	0.125818
$267$	0.958032	0.0586306
$268$	4.45507	0.272137
$269$	−10.3144	−0.628878	−0.314439	−	0.949278i	$-0.601816\pi$
$269$	−10.3144	−0.628878	−0.314439	+	0.949278i	$0.601816\pi$
$270$	−2.02890	−0.123475
$271$	−13.5848	−0.825216	−0.412608	−	0.910909i	$-0.635382\pi$
$271$	−13.5848	−0.825216	−0.412608	+	0.910909i	$0.635382\pi$
$272$	−0.307525	−0.0186465
$273$	1.58816	0.0961199
$274$	−20.7592	−1.25411
$275$	9.34819	0.563717
$276$	−5.85375	−0.352354
$277$	−4.47367	−0.268796	−0.134398	−	0.990927i	$-0.542910\pi$
$277$	−4.47367	−0.268796	−0.134398	+	0.990927i	$0.542910\pi$
$278$	−20.0535	−1.20273
$279$	16.0145	0.958760
$280$	1.96265	0.117291
$281$	8.73683	0.521196	0.260598	−	0.965447i	$-0.416080\pi$
$281$	8.73683	0.521196	0.260598	+	0.965447i	$0.416080\pi$
$282$	−10.3155	−0.614277
$283$	−28.0352	−1.66652	−0.833261	−	0.552880i	$-0.813529\pi$
$283$	−28.0352	−1.66652	−0.833261	+	0.552880i	$0.813529\pi$
$284$	14.1324	0.838603
$285$	−0.0436208	−0.00258387
$286$	−4.17198	−0.246694
$287$	18.2279	1.07596
$288$	21.0220	1.23873
$289$	−16.9762	−0.998598
$290$	0.441506	0.0259261
$291$	4.56441	0.267571
$292$	6.35518	0.371909
$293$	−8.23781	−0.481258	−0.240629	−	0.970617i	$-0.577354\pi$
$293$	−8.23781	−0.481258	−0.240629	+	0.970617i	$0.577354\pi$
$294$	−5.07859	−0.296190
$295$	−0.756001	−0.0440161
$296$	−16.0417	−0.932407
$297$	−5.06696	−0.294015
$298$	7.72199	0.447323
$299$	4.69183	0.271335
$300$	6.08290	0.351196
$301$	38.2515	2.20478
$302$	5.37575	0.309340
$303$	5.36760	0.308361
$304$	0.539653	0.0309512
$305$	−3.56364	−0.204054
$306$	−0.937923	−0.0536175
$307$	0.287523	0.0164098	0.00820489	−	0.999966i	$-0.497388\pi$
$307$	0.287523	0.0164098	0.00820489	+	0.999966i	$0.497388\pi$
$308$	18.2493	1.03985
$309$	−0.456273	−0.0259565
$310$	4.40400	0.250130
$311$	−21.6485	−1.22757	−0.613787	−	0.789472i	$-0.710354\pi$
$311$	−21.6485	−1.22757	−0.613787	+	0.789472i	$0.710354\pi$
$312$	−0.729138	−0.0412793
$313$	−11.2074	−0.633479	−0.316739	−	0.948513i	$-0.602588\pi$
$313$	−11.2074	−0.633479	−0.316739	+	0.948513i	$0.602588\pi$
$314$	−7.92136	−0.447028
$315$	−3.42882	−0.193192
$316$	42.2938	2.37921
$317$	−15.7051	−0.882088	−0.441044	−	0.897486i	$-0.645392\pi$
$317$	−15.7051	−0.882088	−0.441044	+	0.897486i	$0.645392\pi$
$318$	−11.9519	−0.670229
$319$	1.10261	0.0617345
$320$	4.37550	0.244598
$321$	−0.228531	−0.0127554
$322$	−35.5342	−1.98024
$323$	−0.0418338	−0.00232769
$324$	19.6050	1.08917
$325$	−4.87550	−0.270444
$326$	36.2496	2.00768
$327$	−1.32403	−0.0732193
$328$	−8.36860	−0.462078
$329$	−36.1660	−1.99389
$330$	−0.671669	−0.0369741
$331$	−20.4068	−1.12166	−0.560830	−	0.827931i	$-0.689518\pi$
$331$	−20.4068	−1.12166	−0.560830	+	0.827931i	$0.689518\pi$
$332$	−30.1283	−1.65351
$333$	28.0255	1.53579
$334$	18.7030	1.02338
$335$	−0.574878	−0.0314089
$336$	−3.16322	−0.172568
$337$	31.9030	1.73787	0.868934	−	0.494927i	$-0.164805\pi$
$337$	31.9030	1.73787	0.868934	+	0.494927i	$0.164805\pi$
$338$	2.17587	0.118352
$339$	3.58018	0.194449
$340$	−0.148971	−0.00807908
$341$	10.9985	0.595603
$342$	1.64589	0.0889996
$343$	6.55957	0.354183
$344$	−17.5616	−0.946858
$345$	0.755362	0.0406673
$346$	−37.9067	−2.03788
$347$	9.35916	0.502426	0.251213	−	0.967932i	$-0.419171\pi$
$347$	9.35916	0.502426	0.251213	+	0.967932i	$0.419171\pi$
$348$	0.717475	0.0384607
$349$	32.1892	1.72305	0.861525	−	0.507715i	$-0.169510\pi$
$349$	32.1892	1.72305	0.861525	+	0.507715i	$0.169510\pi$
$350$	36.9252	1.97373
$351$	2.64265	0.141054
$352$	14.4376	0.769527
$353$	−6.47884	−0.344834	−0.172417	−	0.985024i	$-0.555158\pi$
$353$	−6.47884	−0.344834	−0.172417	+	0.985024i	$0.555158\pi$
$354$	−2.12713	−0.113055
$355$	−1.82363	−0.0967882
$356$	−5.74146	−0.304297
$357$	0.245212	0.0129780
$358$	43.9030	2.32034
$359$	−14.5163	−0.766143	−0.383072	−	0.923719i	$-0.625134\pi$
$359$	−14.5163	−0.766143	−0.383072	+	0.923719i	$0.625134\pi$
$360$	1.57420	0.0829676
$361$	−18.9266	−0.996136
$362$	14.4762	0.760851
$363$	3.34158	0.175388
$364$	−9.51781	−0.498869
$365$	−0.820066	−0.0429242
$366$	−10.0269	−0.524112
$367$	2.91344	0.152080	0.0760400	−	0.997105i	$-0.475772\pi$
$367$	2.91344	0.152080	0.0760400	+	0.997105i	$0.475772\pi$
$368$	−9.34494	−0.487139
$369$	14.6202	0.761099
$370$	7.70705	0.400671
$371$	−41.9033	−2.17551
$372$	7.15677	0.371061
$373$	4.87485	0.252410	0.126205	−	0.992004i	$-0.459720\pi$
$373$	4.87485	0.252410	0.126205	+	0.992004i	$0.459720\pi$
$374$	−0.644152	−0.0333083
$375$	−1.58991	−0.0821025
$376$	16.6041	0.856291
$377$	−0.575062	−0.0296172
$378$	−20.0144	−1.02943
$379$	11.8093	0.606605	0.303303	−	0.952894i	$-0.401911\pi$
$379$	11.8093	0.606605	0.303303	+	0.952894i	$0.401911\pi$
$380$	0.261418	0.0134105
$381$	2.19026	0.112210
$382$	−46.4468	−2.37642
$383$	−33.7079	−1.72239	−0.861197	−	0.508271i	$-0.830285\pi$
$383$	−33.7079	−1.72239	−0.861197	+	0.508271i	$0.830285\pi$
$384$	5.43982	0.277599
$385$	−2.35487	−0.120015
$386$	−41.7723	−2.12615
$387$	30.6807	1.55959
$388$	−27.3544	−1.38871
$389$	14.3990	0.730057	0.365029	−	0.930996i	$-0.381059\pi$
$389$	14.3990	0.730057	0.365029	+	0.930996i	$0.381059\pi$
$390$	0.350305	0.0177384
$391$	0.724417	0.0366353
$392$	8.17466	0.412883
$393$	−0.572719	−0.0288899
$394$	−26.2924	−1.32459
$395$	−5.45755	−0.274599
$396$	14.6373	0.735554
$397$	29.1210	1.46154	0.730771	−	0.682623i	$-0.239161\pi$
$397$	29.1210	1.46154	0.730771	+	0.682623i	$0.239161\pi$
$398$	−22.2352	−1.11455
$399$	−0.430304	−0.0215421
$400$	9.71077	0.485538
$401$	−22.6261	−1.12990	−0.564948	−	0.825127i	$-0.691104\pi$
$401$	−22.6261	−1.12990	−0.564948	+	0.825127i	$0.691104\pi$
$402$	−1.61751	−0.0806739
$403$	−5.73622	−0.285741
$404$	−32.1679	−1.60041
$405$	−2.52981	−0.125707
$406$	4.35531	0.216150
$407$	19.2475	0.954064
$408$	−0.112579	−0.00557348
$409$	18.0516	0.892593	0.446297	−	0.894885i	$-0.352743\pi$
$409$	18.0516	0.892593	0.446297	+	0.894885i	$0.352743\pi$
$410$	4.02059	0.198563
$411$	4.35313	0.214724
$412$	2.73443	0.134716
$413$	−7.45769	−0.366969
$414$	−28.5012	−1.40076
$415$	3.88773	0.190841
$416$	−7.52986	−0.369182
$417$	4.20516	0.205927
$418$	1.13038	0.0552885
$419$	25.7764	1.25926	0.629629	−	0.776896i	$-0.283207\pi$
$419$	25.7764	1.25926	0.629629	+	0.776896i	$0.283207\pi$
$420$	−1.53232	−0.0747696
$421$	−33.2568	−1.62084	−0.810419	−	0.585851i	$-0.800760\pi$
$421$	−33.2568	−1.62084	−0.810419	+	0.585851i	$0.800760\pi$
$422$	57.5817	2.80304
$423$	−29.0079	−1.41041
$424$	19.2381	0.934286
$425$	−0.752775	−0.0365150
$426$	−5.13106	−0.248601
$427$	−35.1541	−1.70123
$428$	1.36958	0.0662012
$429$	0.874849	0.0422381
$430$	8.43725	0.406880
$431$	6.57752	0.316828	0.158414	−	0.987373i	$-0.449362\pi$
$431$	6.57752	0.316828	0.158414	+	0.987373i	$0.449362\pi$
$432$	−5.26349	−0.253240
$433$	−30.0360	−1.44344	−0.721718	−	0.692187i	$-0.756647\pi$
$433$	−30.0360	−1.44344	−0.721718	+	0.692187i	$0.756647\pi$
$434$	43.4440	2.08538
$435$	−0.0925823	−0.00443898
$436$	7.93490	0.380013
$437$	−1.27123	−0.0608110
$438$	−2.30738	−0.110251
$439$	−13.5254	−0.645534	−0.322767	−	0.946478i	$-0.604613\pi$
$439$	−13.5254	−0.645534	−0.322767	+	0.946478i	$0.604613\pi$
$440$	1.08114	0.0515413
$441$	−14.2814	−0.680068
$442$	0.335954	0.0159797
$443$	−16.8324	−0.799730	−0.399865	−	0.916574i	$-0.630943\pi$
$443$	−16.8324	−0.799730	−0.399865	+	0.916574i	$0.630943\pi$
$444$	12.5244	0.594383
$445$	0.740872	0.0351207
$446$	−34.2735	−1.62290
$447$	−1.61927	−0.0765890
$448$	43.1628	2.03925
$449$	−33.8238	−1.59624	−0.798121	−	0.602498i	$-0.794172\pi$
$449$	−33.8238	−1.59624	−0.798121	+	0.602498i	$0.794172\pi$
$450$	29.6169	1.39615
$451$	10.0410	0.472811
$452$	−21.4559	−1.00920
$453$	−1.12727	−0.0529640
$454$	−0.811319	−0.0380771
$455$	1.22817	0.0575774
$456$	0.197556	0.00925141
$457$	27.9326	1.30663	0.653317	−	0.757084i	$-0.273377\pi$
$457$	27.9326	1.30663	0.653317	+	0.757084i	$0.273377\pi$
$458$	−32.6569	−1.52596
$459$	0.408024	0.0190449
$460$	−4.52686	−0.211066
$461$	−40.2662	−1.87539	−0.937693	−	0.347465i	$-0.887042\pi$
$461$	−40.2662	−1.87539	−0.937693	+	0.347465i	$0.887042\pi$
$462$	−6.62578	−0.308259
$463$	11.1184	0.516717	0.258359	−	0.966049i	$-0.416818\pi$
$463$	11.1184	0.516717	0.258359	+	0.966049i	$0.416818\pi$
$464$	1.14538	0.0531729
$465$	−0.923503	−0.0428264
$466$	43.9012	2.03368
$467$	−12.6052	−0.583299	−0.291649	−	0.956525i	$-0.594204\pi$
$467$	−12.6052	−0.583299	−0.291649	+	0.956525i	$0.594204\pi$
$468$	−7.63403	−0.352883
$469$	−5.67097	−0.261861
$470$	−7.97723	−0.367962
$471$	1.66108	0.0765385
$472$	3.42389	0.157597
$473$	21.0711	0.968851
$474$	−15.3557	−0.705309
$475$	1.32099	0.0606112
$476$	−1.46955	−0.0673566
$477$	−33.6097	−1.53888
$478$	−35.0824	−1.60463
$479$	3.96360	0.181102	0.0905508	−	0.995892i	$-0.471137\pi$
$479$	3.96360	0.181102	0.0905508	+	0.995892i	$0.471137\pi$
$480$	−1.21227	−0.0553323
$481$	−10.0384	−0.457714
$482$	−2.79785	−0.127439
$483$	7.45138	0.339050
$484$	−20.0260	−0.910274
$485$	3.52978	0.160279
$486$	−24.3682	−1.10536
$487$	34.1480	1.54739	0.773697	−	0.633555i	$-0.218405\pi$
$487$	34.1480	1.54739	0.773697	+	0.633555i	$0.218405\pi$
$488$	16.1395	0.730602
$489$	−7.60141	−0.343748
$490$	−3.92741	−0.177422
$491$	−17.3892	−0.784762	−0.392381	−	0.919803i	$-0.628349\pi$
$491$	−17.3892	−0.784762	−0.392381	+	0.919803i	$0.628349\pi$
$492$	6.53370	0.294562
$493$	−0.0887895	−0.00399888
$494$	−0.589541	−0.0265247
$495$	−1.88879	−0.0848947
$496$	11.4251	0.513002
$497$	−17.9895	−0.806938
$498$	10.9387	0.490176
$499$	−16.6182	−0.743931	−0.371965	−	0.928247i	$-0.621316\pi$
$499$	−16.6182	−0.743931	−0.371965	+	0.928247i	$0.621316\pi$
$500$	9.52827	0.426117
$501$	−3.92195	−0.175220
$502$	57.9380	2.58590
$503$	2.87251	0.128079	0.0640394	−	0.997947i	$-0.479602\pi$
$503$	2.87251	0.128079	0.0640394	+	0.997947i	$0.479602\pi$
$504$	15.5289	0.691714
$505$	4.15091	0.184713
$506$	−19.5742	−0.870180
$507$	−0.456273	−0.0202638
$508$	−13.1262	−0.582380
$509$	−34.7005	−1.53807	−0.769036	−	0.639205i	$-0.779263\pi$
$509$	−34.7005	−1.53807	−0.769036	+	0.639205i	$0.779263\pi$
$510$	0.0540870	0.00239501
$511$	−8.08967	−0.357866
$512$	21.3633	0.944135
$513$	−0.716011	−0.0316127
$514$	−27.5708	−1.21610
$515$	−0.352848	−0.0155484
$516$	13.7111	0.603595
$517$	−19.9223	−0.876180
$518$	76.0274	3.34045
$519$	7.94889	0.348918
$520$	−0.563862	−0.0247270
$521$	40.7164	1.78382	0.891909	−	0.452215i	$-0.149366\pi$
$521$	40.7164	1.78382	0.891909	+	0.452215i	$0.149366\pi$
$522$	3.49330	0.152897
$523$	−33.3004	−1.45613	−0.728063	−	0.685510i	$-0.759579\pi$
$523$	−33.3004	−1.45613	−0.728063	+	0.685510i	$0.759579\pi$
$524$	3.43229	0.149940
$525$	−7.74308	−0.337936
$526$	46.0245	2.00676
$527$	−0.885670	−0.0385804
$528$	−1.74248	−0.0758317
$529$	−0.986742	−0.0429018
$530$	−9.24272	−0.401478
$531$	−5.98165	−0.259582
$532$	2.57880	0.111805
$533$	−5.23682	−0.226832
$534$	2.08456	0.0902076
$535$	−0.176729	−0.00764068
$536$	2.60359	0.112458
$537$	−9.20630	−0.397281
$538$	−22.4428	−0.967577
$539$	−9.80829	−0.422473
$540$	−2.54973	−0.109723
$541$	−10.1136	−0.434818	−0.217409	−	0.976081i	$-0.569761\pi$
$541$	−10.1136	−0.434818	−0.217409	+	0.976081i	$0.569761\pi$
$542$	−29.5588	−1.26966
$543$	−3.03560	−0.130270
$544$	−1.16261	−0.0498464
$545$	−1.02391	−0.0438596
$546$	3.45564	0.147888
$547$	43.7658	1.87129	0.935646	−	0.352940i	$-0.114818\pi$
$547$	43.7658	1.87129	0.935646	+	0.352940i	$0.114818\pi$
$548$	−26.0882	−1.11443
$549$	−28.1963	−1.20339
$550$	20.3405	0.867321
$551$	0.155810	0.00663773
$552$	−3.42099	−0.145607
$553$	−53.8369	−2.28938
$554$	−9.73414	−0.413564
$555$	−1.61614	−0.0686013
$556$	−25.2014	−1.06878
$557$	7.52856	0.318995	0.159498	−	0.987198i	$-0.449013\pi$
$557$	7.52856	0.318995	0.159498	+	0.987198i	$0.449013\pi$
$558$	34.8454	1.47513
$559$	−10.9895	−0.464807
$560$	−2.44620	−0.103371
$561$	0.135076	0.00570293
$562$	19.0103	0.801899
$563$	9.78410	0.412351	0.206175	−	0.978515i	$-0.433898\pi$
$563$	9.78410	0.412351	0.206175	+	0.978515i	$0.433898\pi$
$564$	−12.9635	−0.545861
$565$	2.76865	0.116478
$566$	−61.0012	−2.56407
$567$	−24.9557	−1.04804
$568$	8.25912	0.346545
$569$	32.1781	1.34898	0.674488	−	0.738286i	$-0.264365\pi$
$569$	32.1781	1.34898	0.674488	+	0.738286i	$0.264365\pi$
$570$	−0.0949133	−0.00397548
$571$	−25.1783	−1.05368	−0.526839	−	0.849965i	$-0.676623\pi$
$571$	−25.1783	−1.05368	−0.526839	+	0.849965i	$0.676623\pi$
$572$	−5.24295	−0.219219
$573$	9.73972	0.406883
$574$	39.6617	1.65545
$575$	−22.8750	−0.953954
$576$	34.6200	1.44250
$577$	35.9562	1.49688	0.748438	−	0.663205i	$-0.230804\pi$
$577$	35.9562	1.49688	0.748438	+	0.663205i	$0.230804\pi$
$578$	−36.9380	−1.53642
$579$	8.75949	0.364032
$580$	0.554843	0.0230386
$581$	38.3511	1.59107
$582$	9.93159	0.411678
$583$	−23.0827	−0.955987
$584$	3.71403	0.153688
$585$	0.985087	0.0407283
$586$	−17.9244	−0.740452
$587$	9.13906	0.377209	0.188605	−	0.982053i	$-0.439604\pi$
$587$	9.13906	0.377209	0.188605	+	0.982053i	$0.439604\pi$
$588$	−6.38229	−0.263201
$589$	1.55420	0.0640395
$590$	−1.64496	−0.0677221
$591$	5.51342	0.226792
$592$	19.9941	0.821750
$593$	39.2542	1.61198	0.805988	−	0.591932i	$-0.201635\pi$
$593$	39.2542	1.61198	0.805988	+	0.591932i	$0.201635\pi$
$594$	−11.0251	−0.452364
$595$	0.189629	0.00777403
$596$	9.70426	0.397502
$597$	4.66264	0.190829
$598$	10.2088	0.417470
$599$	13.4250	0.548532	0.274266	−	0.961654i	$-0.411565\pi$
$599$	13.4250	0.548532	0.274266	+	0.961654i	$0.411565\pi$
$600$	3.55491	0.145129
$601$	−33.3410	−1.36001	−0.680005	−	0.733208i	$-0.738022\pi$
$601$	−33.3410	−1.36001	−0.680005	+	0.733208i	$0.738022\pi$
$602$	83.2306	3.39223
$603$	−4.54856	−0.185232
$604$	6.75573	0.274887
$605$	2.58414	0.105060
$606$	11.6792	0.474436
$607$	16.6907	0.677453	0.338726	−	0.940885i	$-0.390004\pi$
$607$	16.6907	0.677453	0.338726	+	0.940885i	$0.390004\pi$
$608$	2.04017	0.0827400
$609$	−0.913292	−0.0370085
$610$	−7.75404	−0.313952
$611$	10.3904	0.420349
$612$	−1.17869	−0.0476458
$613$	4.14469	0.167403	0.0837013	−	0.996491i	$-0.473326\pi$
$613$	4.14469	0.167403	0.0837013	+	0.996491i	$0.473326\pi$
$614$	0.625613	0.0252477
$615$	−0.843103	−0.0339972
$616$	10.6651	0.429708
$617$	10.9743	0.441810	0.220905	−	0.975295i	$-0.429099\pi$
$617$	10.9743	0.441810	0.220905	+	0.975295i	$0.429099\pi$
$618$	−0.992793	−0.0399360
$619$	37.8585	1.52166	0.760831	−	0.648950i	$-0.224792\pi$
$619$	37.8585	1.52166	0.760831	+	0.648950i	$0.224792\pi$
$620$	5.53453	0.222272
$621$	12.3989	0.497549
$622$	−47.1044	−1.88871
$623$	7.30845	0.292807
$624$	0.908781	0.0363804
$625$	23.1480	0.925919
$626$	−24.3859	−0.974655
$627$	−0.237036	−0.00946629
$628$	−9.95481	−0.397240
$629$	−1.54993	−0.0617999
$630$	−7.46068	−0.297241
$631$	−15.8291	−0.630147	−0.315074	−	0.949067i	$-0.602029\pi$
$631$	−15.8291	−0.630147	−0.315074	+	0.949067i	$0.602029\pi$
$632$	24.7170	0.983188
$633$	−12.0747	−0.479925
$634$	−34.1724	−1.35716
$635$	1.69379	0.0672159
$636$	−15.0200	−0.595581
$637$	5.11546	0.202682
$638$	2.39915	0.0949832
$639$	−14.4290	−0.570801
$640$	4.20676	0.166287
$641$	−27.5386	−1.08771	−0.543855	−	0.839179i	$-0.683036\pi$
$641$	−27.5386	−1.08771	−0.543855	+	0.839179i	$0.683036\pi$
$642$	−0.497255	−0.0196251
$643$	−10.4595	−0.412481	−0.206241	−	0.978501i	$-0.566123\pi$
$643$	−10.4595	−0.412481	−0.206241	+	0.978501i	$0.566123\pi$
$644$	−44.6559	−1.75969
$645$	−1.76926	−0.0696646
$646$	−0.0910250	−0.00358133
$647$	41.1744	1.61873	0.809366	−	0.587305i	$-0.199811\pi$
$647$	41.1744	1.61873	0.809366	+	0.587305i	$0.199811\pi$
$648$	11.4574	0.450088
$649$	−4.10812	−0.161258
$650$	−10.6085	−0.416099
$651$	−9.11004	−0.357051
$652$	45.5550	1.78407
$653$	−7.19534	−0.281576	−0.140788	−	0.990040i	$-0.544964\pi$
$653$	−7.19534	−0.281576	−0.140788	+	0.990040i	$0.544964\pi$
$654$	−2.88093	−0.112653
$655$	−0.442899	−0.0173055
$656$	10.4304	0.407240
$657$	−6.48855	−0.253142
$658$	−78.6926	−3.06776
$659$	20.5916	0.802134	0.401067	−	0.916049i	$-0.368639\pi$
$659$	20.5916	0.802134	0.401067	+	0.916049i	$0.368639\pi$
$660$	−0.844089	−0.0328561
$661$	−19.4619	−0.756980	−0.378490	−	0.925605i	$-0.623557\pi$
$661$	−19.4619	−0.756980	−0.378490	+	0.925605i	$0.623557\pi$
$662$	−44.4027	−1.72576
$663$	−0.0704484	−0.00273599
$664$	−17.6073	−0.683296
$665$	−0.332766	−0.0129041
$666$	60.9799	2.36292
$667$	−2.69809	−0.104471
$668$	23.5041	0.909402
$669$	7.18704	0.277867
$670$	−1.25086	−0.0483250
$671$	−19.3649	−0.747572
$672$	−11.9586	−0.461314
$673$	25.3652	0.977758	0.488879	−	0.872351i	$-0.337406\pi$
$673$	25.3652	0.977758	0.488879	+	0.872351i	$0.337406\pi$
$674$	69.4170	2.67384
$675$	−12.8842	−0.495914
$676$	2.73443	0.105170
$677$	−32.4836	−1.24845	−0.624223	−	0.781246i	$-0.714585\pi$
$677$	−32.4836	−1.24845	−0.624223	+	0.781246i	$0.714585\pi$
$678$	7.79003	0.299174
$679$	34.8201	1.33627
$680$	−0.0870602	−0.00333860
$681$	0.170131	0.00651942
$682$	23.9314	0.916380
$683$	35.0405	1.34079	0.670394	−	0.742006i	$-0.266125\pi$
$683$	35.0405	1.34079	0.670394	+	0.742006i	$0.266125\pi$
$684$	2.06840	0.0790872
$685$	3.36639	0.128623
$686$	14.2728	0.544938
$687$	6.84803	0.261269
$688$	21.8884	0.834486
$689$	12.0387	0.458636
$690$	1.64357	0.0625697
$691$	13.8747	0.527818	0.263909	−	0.964548i	$-0.414988\pi$
$691$	13.8747	0.527818	0.263909	+	0.964548i	$0.414988\pi$
$692$	−47.6375	−1.81091
$693$	−18.6322	−0.707780
$694$	20.3644	0.773021
$695$	3.25196	0.123354
$696$	0.419300	0.0158935
$697$	−0.808563	−0.0306265
$698$	70.0397	2.65104
$699$	−9.20591	−0.348200
$700$	46.4041	1.75391
$701$	−33.2977	−1.25764	−0.628818	−	0.777552i	$-0.716461\pi$
$701$	−33.2977	−1.25764	−0.628818	+	0.777552i	$0.716461\pi$
$702$	5.75007	0.217023
$703$	2.71986	0.102582
$704$	23.7765	0.896112
$705$	1.67280	0.0630011
$706$	−14.0972	−0.530553
$707$	40.9473	1.53998
$708$	−2.67317	−0.100464
$709$	37.3940	1.40436	0.702181	−	0.711998i	$-0.252210\pi$
$709$	37.3940	1.40436	0.702181	+	0.711998i	$0.252210\pi$
$710$	−3.96799	−0.148916
$711$	−43.1814	−1.61943
$712$	−3.35537	−0.125748
$713$	−26.9133	−1.00791
$714$	0.533550	0.0199676
$715$	0.676544	0.0253013
$716$	55.1731	2.06191
$717$	7.35664	0.274739
$718$	−31.5857	−1.17877
$719$	−11.1231	−0.414821	−0.207410	−	0.978254i	$-0.566504\pi$
$719$	−11.1231	−0.414821	−0.207410	+	0.978254i	$0.566504\pi$
$720$	−1.96205	−0.0731211
$721$	−3.48073	−0.129629
$722$	−41.1819	−1.53263
$723$	0.586699	0.0218196
$724$	18.1923	0.676111
$725$	2.80372	0.104127
$726$	7.27087	0.269847
$727$	36.1012	1.33892	0.669459	−	0.742849i	$-0.266526\pi$
$727$	36.1012	1.33892	0.669459	+	0.742849i	$0.266526\pi$
$728$	−5.56231	−0.206153
$729$	−16.3991	−0.607374
$730$	−1.78436	−0.0660422
$731$	−1.69678	−0.0627577
$732$	−12.6008	−0.465739
$733$	−4.39836	−0.162457	−0.0812285	−	0.996696i	$-0.525884\pi$
$733$	−4.39836	−0.162457	−0.0812285	+	0.996696i	$0.525884\pi$
$734$	6.33927	0.233987
$735$	0.823564	0.0303776
$736$	−35.3288	−1.30224
$737$	−3.12389	−0.115070
$738$	31.8118	1.17101
$739$	−20.7901	−0.764778	−0.382389	−	0.924001i	$-0.624899\pi$
$739$	−20.7901	−0.764778	−0.382389	+	0.924001i	$0.624899\pi$
$740$	9.68548	0.356046
$741$	0.123625	0.00454147
$742$	−91.1762	−3.34719
$743$	38.1432	1.39934	0.699668	−	0.714468i	$-0.253331\pi$
$743$	38.1432	1.39934	0.699668	+	0.714468i	$0.253331\pi$
$744$	4.18249	0.153338
$745$	−1.25223	−0.0458781
$746$	10.6071	0.388352
$747$	30.7606	1.12547
$748$	−0.809509	−0.0295986
$749$	−1.74337	−0.0637015
$750$	−3.45944	−0.126321
$751$	−0.675992	−0.0246673	−0.0123336	−	0.999924i	$-0.503926\pi$
$751$	−0.675992	−0.0246673	−0.0123336	+	0.999924i	$0.503926\pi$
$752$	−20.6950	−0.754668
$753$	−12.1494	−0.442748
$754$	−1.25126	−0.0455683
$755$	−0.871752	−0.0317263
$756$	−25.1522	−0.914778
$757$	22.2472	0.808588	0.404294	−	0.914629i	$-0.367517\pi$
$757$	22.2472	0.808588	0.404294	+	0.914629i	$0.367517\pi$
$758$	25.6957	0.933308
$759$	4.10464	0.148989
$760$	0.152775	0.00554175
$761$	−22.9460	−0.831791	−0.415895	−	0.909412i	$-0.636532\pi$
$761$	−22.9460	−0.831791	−0.415895	+	0.909412i	$0.636532\pi$
$762$	4.76573	0.172644
$763$	−10.1005	−0.365664
$764$	−58.3699	−2.11175
$765$	0.152097	0.00549908
$766$	−73.3442	−2.65003
$767$	2.14257	0.0773636
$768$	0.520306	0.0187749
$769$	−27.0999	−0.977246	−0.488623	−	0.872495i	$-0.662501\pi$
$769$	−27.0999	−0.977246	−0.488623	+	0.872495i	$0.662501\pi$
$770$	−5.12390	−0.184652
$771$	5.78150	0.208216
$772$	−52.4954	−1.88935
$773$	44.4746	1.59964	0.799820	−	0.600240i	$-0.204928\pi$
$773$	44.4746	1.59964	0.799820	+	0.600240i	$0.204928\pi$
$774$	66.7574	2.39955
$775$	27.9669	1.00460
$776$	−15.9862	−0.573871
$777$	−15.9427	−0.571940
$778$	31.3304	1.12325
$779$	1.41889	0.0508369
$780$	0.440230	0.0157628
$781$	−9.90962	−0.354594
$782$	1.57624	0.0563662
$783$	−1.51969	−0.0543092
$784$	−10.1887	−0.363883
$785$	1.28456	0.0458479
$786$	−1.24617	−0.0444492
$787$	−4.17374	−0.148778	−0.0743888	−	0.997229i	$-0.523701\pi$
$787$	−4.17374	−0.148778	−0.0743888	+	0.997229i	$0.523701\pi$
$788$	−33.0418	−1.17706
$789$	−9.65116	−0.343590
$790$	−11.8750	−0.422492
$791$	27.3118	0.971096
$792$	8.55421	0.303961
$793$	10.0996	0.358649
$794$	63.3637	2.24869
$795$	1.93816	0.0687396
$796$	−27.9431	−0.990416
$797$	−1.19064	−0.0421746	−0.0210873	−	0.999778i	$-0.506713\pi$
$797$	−1.19064	−0.0421746	−0.0210873	+	0.999778i	$0.506713\pi$
$798$	−0.936287	−0.0331442
$799$	1.60427	0.0567549
$800$	36.7118	1.29796
$801$	5.86194	0.207122
$802$	−49.2317	−1.73843
$803$	−4.45625	−0.157258
$804$	−2.03273	−0.0716888
$805$	5.76236	0.203096
$806$	−12.4813	−0.439635
$807$	4.70617	0.165665
$808$	−18.7992	−0.661355
$809$	−22.8060	−0.801817	−0.400908	−	0.916118i	$-0.631305\pi$
$809$	−22.8060	−0.801817	−0.400908	+	0.916118i	$0.631305\pi$
$810$	−5.50455	−0.193410
$811$	−5.13323	−0.180252	−0.0901261	−	0.995930i	$-0.528727\pi$
$811$	−5.13323	−0.180252	−0.0901261	+	0.995930i	$0.528727\pi$
$812$	5.47333	0.192076
$813$	6.19837	0.217386
$814$	41.8802	1.46790
$815$	−5.87838	−0.205911
$816$	0.140316	0.00491203
$817$	2.97755	0.104171
$818$	39.2780	1.37332
$819$	9.71755	0.339559
$820$	5.05269	0.176448
$821$	−9.08136	−0.316942	−0.158471	−	0.987364i	$-0.550656\pi$
$821$	−9.08136	−0.316942	−0.158471	+	0.987364i	$0.550656\pi$
$822$	9.47187	0.330369
$823$	9.27297	0.323235	0.161618	−	0.986853i	$-0.448329\pi$
$823$	9.27297	0.323235	0.161618	+	0.986853i	$0.448329\pi$
$824$	1.59803	0.0556700
$825$	−4.26532	−0.148500
$826$	−16.2270	−0.564610
$827$	−15.1315	−0.526173	−0.263086	−	0.964772i	$-0.584740\pi$
$827$	−15.1315	−0.526173	−0.263086	+	0.964772i	$0.584740\pi$
$828$	−35.8175	−1.24475
$829$	−2.19144	−0.0761118	−0.0380559	−	0.999276i	$-0.512117\pi$
$829$	−2.19144	−0.0761118	−0.0380559	+	0.999276i	$0.512117\pi$
$830$	8.45921	0.293623
$831$	2.04121	0.0708089
$832$	−12.4005	−0.429911
$833$	0.789826	0.0273658
$834$	9.14989	0.316835
$835$	−3.03295	−0.104960
$836$	1.42055	0.0491307
$837$	−15.1588	−0.523965
$838$	56.0862	1.93746
$839$	−19.3360	−0.667554	−0.333777	−	0.942652i	$-0.608323\pi$
$839$	−19.3360	−0.667554	−0.333777	+	0.942652i	$0.608323\pi$
$840$	−0.895505	−0.0308978
$841$	−28.6693	−0.988597
$842$	−72.3626	−2.49378
$843$	−3.98638	−0.137298
$844$	72.3632	2.49084
$845$	−0.352848	−0.0121384
$846$	−63.1176	−2.17003
$847$	25.4916	0.875903
$848$	−23.9780	−0.823407
$849$	12.7917	0.439011
$850$	−1.63795	−0.0561811
$851$	−47.0987	−1.61452
$852$	−6.44823	−0.220913
$853$	−9.12219	−0.312338	−0.156169	−	0.987730i	$-0.549914\pi$
$853$	−9.12219	−0.312338	−0.156169	+	0.987730i	$0.549914\pi$
$854$	−76.4909	−2.61747
$855$	−0.266904	−0.00912792
$856$	0.800398	0.0273570
$857$	13.9056	0.475006	0.237503	−	0.971387i	$-0.423671\pi$
$857$	13.9056	0.475006	0.237503	+	0.971387i	$0.423671\pi$
$858$	1.90356	0.0649865
$859$	−5.17143	−0.176447	−0.0882234	−	0.996101i	$-0.528119\pi$
$859$	−5.17143	−0.176447	−0.0882234	+	0.996101i	$0.528119\pi$
$860$	10.6031	0.361564
$861$	−8.31692	−0.283440
$862$	14.3119	0.487464
$863$	8.08506	0.275219	0.137609	−	0.990487i	$-0.456058\pi$
$863$	8.08506	0.275219	0.137609	+	0.990487i	$0.456058\pi$
$864$	−19.8988	−0.676970
$865$	6.14709	0.209007
$866$	−65.3545	−2.22084
$867$	7.74576	0.263060
$868$	54.5962	1.85312
$869$	−29.6564	−1.00602
$870$	−0.201447	−0.00682971
$871$	1.62925	0.0552050
$872$	4.63724	0.157037
$873$	27.9284	0.945234
$874$	−2.76603	−0.0935623
$875$	−12.1288	−0.410028
$876$	−2.89970	−0.0979717
$877$	−33.5313	−1.13227	−0.566136	−	0.824312i	$-0.691562\pi$
$877$	−33.5313	−1.13227	−0.566136	+	0.824312i	$0.691562\pi$
$878$	−29.4297	−0.993203
$879$	3.75869	0.126777
$880$	−1.34751	−0.0454244
$881$	50.9443	1.71636	0.858179	−	0.513351i	$-0.171596\pi$
$881$	50.9443	1.71636	0.858179	+	0.513351i	$0.171596\pi$
$882$	−31.0746	−1.04634
$883$	−45.9797	−1.54734	−0.773669	−	0.633590i	$-0.781581\pi$
$883$	−45.9797	−1.54734	−0.773669	+	0.633590i	$0.781581\pi$
$884$	0.422195	0.0142000
$885$	0.344943	0.0115951
$886$	−36.6251	−1.23045
$887$	−4.16350	−0.139797	−0.0698984	−	0.997554i	$-0.522268\pi$
$887$	−4.16350	−0.139797	−0.0698984	+	0.997554i	$0.522268\pi$
$888$	7.31941	0.245623
$889$	16.7086	0.560390
$890$	1.61204	0.0540359
$891$	−13.7470	−0.460542
$892$	−43.0717	−1.44215
$893$	−2.81521	−0.0942074
$894$	−3.52334	−0.117838
$895$	−7.11948	−0.237978
$896$	41.4982	1.38636
$897$	−2.14075	−0.0714777
$898$	−73.5962	−2.45594
$899$	3.29868	0.110017
$900$	37.2197	1.24066
$901$	1.85876	0.0619244
$902$	21.8479	0.727456
$903$	−17.4531	−0.580804
$904$	−12.5391	−0.417043
$905$	−2.34751	−0.0780340
$906$	−2.45281	−0.0814891
$907$	17.2776	0.573694	0.286847	−	0.957976i	$-0.407393\pi$
$907$	17.2776	0.573694	0.286847	+	0.957976i	$0.407393\pi$
$908$	−1.01959	−0.0338362
$909$	32.8429	1.08933
$910$	2.67234	0.0885872
$911$	−3.41659	−0.113197	−0.0565984	−	0.998397i	$-0.518025\pi$
$911$	−3.41659	−0.113197	−0.0565984	+	0.998397i	$0.518025\pi$
$912$	−0.246229	−0.00815347
$913$	21.1259	0.699167
$914$	60.7779	2.01036
$915$	1.62599	0.0537537
$916$	−41.0400	−1.35600
$917$	−4.36905	−0.144279
$918$	0.887809	0.0293021
$919$	0.206391	0.00680820	0.00340410	−	0.999994i	$-0.498916\pi$
$919$	0.206391	0.00680820	0.00340410	+	0.999994i	$0.498916\pi$
$920$	−2.64555	−0.0872210
$921$	−0.131189	−0.00432282
$922$	−87.6143	−2.88542
$923$	5.16831	0.170117
$924$	−8.32665	−0.273927
$925$	48.9424	1.60922
$926$	24.1923	0.795009
$927$	−2.79181	−0.0916952
$928$	4.33014	0.142144
$929$	0.828505	0.0271824	0.0135912	−	0.999908i	$-0.495674\pi$
$929$	0.828505	0.0271824	0.0135912	+	0.999908i	$0.495674\pi$
$930$	−2.00943	−0.0658917
$931$	−1.38601	−0.0454245
$932$	55.1708	1.80718
$933$	9.87762	0.323379
$934$	−27.4273	−0.897450
$935$	0.104458	0.00341615
$936$	−4.46140	−0.145826
$937$	−33.1401	−1.08264	−0.541320	−	0.840816i	$-0.682075\pi$
$937$	−33.1401	−1.08264	−0.541320	+	0.840816i	$0.682075\pi$
$938$	−12.3393	−0.402893
$939$	5.11363	0.166877
$940$	−10.0250	−0.326980
$941$	−46.7226	−1.52311	−0.761556	−	0.648099i	$-0.775564\pi$
$941$	−46.7226	−1.52311	−0.761556	+	0.648099i	$0.775564\pi$
$942$	3.61430	0.117760
$943$	−24.5703	−0.800118
$944$	−4.26746	−0.138894
$945$	3.24562	0.105580
$946$	45.8481	1.49065
$947$	1.43851	0.0467452	0.0233726	−	0.999727i	$-0.492560\pi$
$947$	1.43851	0.0467452	0.0233726	+	0.999727i	$0.492560\pi$
$948$	−19.2975	−0.626755
$949$	2.32413	0.0754445
$950$	2.87431	0.0932549
$951$	7.16582	0.232368
$952$	−0.858819	−0.0278345
$953$	−33.6968	−1.09155	−0.545773	−	0.837933i	$-0.683764\pi$
$953$	−33.6968	−1.09155	−0.545773	+	0.837933i	$0.683764\pi$
$954$	−73.1305	−2.36769
$955$	7.53199	0.243729
$956$	−44.0882	−1.42591
$957$	−0.503093	−0.0162627
$958$	8.62431	0.278639
$959$	33.2083	1.07235
$960$	−1.99642	−0.0644343
$961$	1.90417	0.0614249
$962$	−21.8424	−0.704227
$963$	−1.39832	−0.0450603
$964$	−3.51607	−0.113245
$965$	6.77395	0.218061
$966$	16.2133	0.521654
$967$	24.0823	0.774434	0.387217	−	0.921989i	$-0.373436\pi$
$967$	24.0823	0.774434	0.387217	+	0.921989i	$0.373436\pi$
$968$	−11.7034	−0.376162
$969$	0.0190876	0.000613182 0
$970$	7.68037	0.246602
$971$	27.2102	0.873217	0.436608	−	0.899652i	$-0.356180\pi$
$971$	27.2102	0.873217	0.436608	+	0.899652i	$0.356180\pi$
$972$	−30.6236	−0.982254
$973$	32.0795	1.02842
$974$	74.3018	2.38078
$975$	2.22456	0.0712429
$976$	−20.1159	−0.643896
$977$	7.49086	0.239654	0.119827	−	0.992795i	$-0.461766\pi$
$977$	7.49086	0.239654	0.119827	+	0.992795i	$0.461766\pi$
$978$	−16.5397	−0.528882
$979$	4.02590	0.128668
$980$	−4.93560	−0.157662
$981$	−8.10142	−0.258658
$982$	−37.8366	−1.20742
$983$	−29.0073	−0.925189	−0.462595	−	0.886570i	$-0.653081\pi$
$983$	−29.0073	−0.925189	−0.462595	+	0.886570i	$0.653081\pi$
$984$	3.81836	0.121725
$985$	4.26368	0.135852
$986$	−0.193195	−0.00615257
$987$	16.5016	0.525250
$988$	−0.740879	−0.0235705
$989$	−51.5610	−1.63954
$990$	−4.10976	−0.130617
$991$	49.3697	1.56828	0.784140	−	0.620584i	$-0.213104\pi$
$991$	49.3697	1.56828	0.784140	+	0.620584i	$0.213104\pi$
$992$	43.1929	1.37138
$993$	9.31108	0.295478
$994$	−39.1428	−1.24154
$995$	3.60575	0.114310
$996$	13.7467	0.435582
$997$	14.8914	0.471616	0.235808	−	0.971800i	$-0.424226\pi$
$997$	14.8914	0.471616	0.235808	+	0.971800i	$0.424226\pi$
$998$	−36.1590	−1.14459
$999$	−26.5281	−0.839311

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1339.2.a.d.1.18	✓	19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1339.2.a.d.1.18	✓	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:	\( N \)	\(=\)	\( 1339 = 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1339.a (trivial)

\(f(q)\)	\(=\)	\(q+2.17587 q^{2} -0.456273 q^{3} +2.73443 q^{4} -0.352848 q^{5} -0.992793 q^{6} -3.48073 q^{7} +1.59803 q^{8} -2.79181 q^{9} +O(q^{10})\)	\(q+2.17587 q^{2} -0.456273 q^{3} +2.73443 q^{4} -0.352848 q^{5} -0.992793 q^{6} -3.48073 q^{7} +1.59803 q^{8} -2.79181 q^{9} -0.767754 q^{10} -1.91738 q^{11} -1.24765 q^{12} +1.00000 q^{13} -7.57363 q^{14} +0.160995 q^{15} -1.99175 q^{16} +0.154400 q^{17} -6.07464 q^{18} -0.270945 q^{19} -0.964839 q^{20} +1.58816 q^{21} -4.17198 q^{22} +4.69183 q^{23} -0.729138 q^{24} -4.87550 q^{25} +2.17587 q^{26} +2.64265 q^{27} -9.51781 q^{28} -0.575062 q^{29} +0.350305 q^{30} -5.73622 q^{31} -7.52986 q^{32} +0.874849 q^{33} +0.335954 q^{34} +1.22817 q^{35} -7.63403 q^{36} -10.0384 q^{37} -0.589541 q^{38} -0.456273 q^{39} -0.563862 q^{40} -5.23682 q^{41} +3.45564 q^{42} -10.9895 q^{43} -5.24295 q^{44} +0.985087 q^{45} +10.2088 q^{46} +10.3904 q^{47} +0.908781 q^{48} +5.11546 q^{49} -10.6085 q^{50} -0.0704484 q^{51} +2.73443 q^{52} +12.0387 q^{53} +5.75007 q^{54} +0.676544 q^{55} -5.56231 q^{56} +0.123625 q^{57} -1.25126 q^{58} +2.14257 q^{59} +0.440230 q^{60} +10.0996 q^{61} -12.4813 q^{62} +9.71755 q^{63} -12.4005 q^{64} -0.352848 q^{65} +1.90356 q^{66} +1.62925 q^{67} +0.422195 q^{68} -2.14075 q^{69} +2.67234 q^{70} +5.16831 q^{71} -4.46140 q^{72} +2.32413 q^{73} -21.8424 q^{74} +2.22456 q^{75} -0.740879 q^{76} +6.67388 q^{77} -0.992793 q^{78} +15.4671 q^{79} +0.702785 q^{80} +7.16968 q^{81} -11.3947 q^{82} -11.0181 q^{83} +4.34272 q^{84} -0.0544797 q^{85} -23.9118 q^{86} +0.262385 q^{87} -3.06403 q^{88} -2.09969 q^{89} +2.14343 q^{90} -3.48073 q^{91} +12.8295 q^{92} +2.61728 q^{93} +22.6081 q^{94} +0.0956023 q^{95} +3.43567 q^{96} -10.0037 q^{97} +11.1306 q^{98} +5.35297 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9}+O(q^{10}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9	\( 19 q - 9 q^{2} - 2 q^{3} + 17 q^{4} - 18 q^{5} - 8 q^{6} - 8 q^{7} - 24 q^{8} + 7 q^{9} - q^{11} + 18 q^{12} + 19 q^{13} - 8 q^{14} - 11 q^{15} + 21 q^{16} - 16 q^{17} - 10 q^{19} - 20 q^{20} - 33 q^{21} + 2 q^{22} - 14 q^{23} - 9 q^{24} + 23 q^{25} - 9 q^{26} + q^{27} + 10 q^{28} - 22 q^{29} + 28 q^{30} - 3 q^{31} - 47 q^{32} - 25 q^{33} - 35 q^{34} - 3 q^{35} - 33 q^{36} - 19 q^{37} - 15 q^{38} - 2 q^{39} + 8 q^{40} - 52 q^{41} - 3 q^{42} - 2 q^{43} - 54 q^{44} - 40 q^{45} + 33 q^{46} - 24 q^{47} - 8 q^{48} + 7 q^{49} - 10 q^{50} - 7 q^{51} + 17 q^{52} - 11 q^{53} - 23 q^{54} - 29 q^{55} - 17 q^{56} - 34 q^{57} + 18 q^{58} - 52 q^{59} - 71 q^{60} - 25 q^{61} - 22 q^{62} - 19 q^{63} + 48 q^{64} - 18 q^{65} + 9 q^{66} - 2 q^{67} + 18 q^{68} - 26 q^{69} - 12 q^{70} - 44 q^{71} - 6 q^{72} - 39 q^{73} - 4 q^{74} + 17 q^{75} - 10 q^{76} - 18 q^{77} - 8 q^{78} + q^{79} - 9 q^{80} - 13 q^{81} + 47 q^{82} - 27 q^{83} - 24 q^{84} - 26 q^{85} - q^{86} + 31 q^{87} + 19 q^{88} - 86 q^{89} + 48 q^{90} - 8 q^{91} - 19 q^{92} + 32 q^{93} + 45 q^{94} + 17 q^{95} - 25 q^{96} - 20 q^{97} + 39 q^{98} + 50 q^{99}+O(q^{100}) \) 19 * q - 9 * q^2 - 2 * q^3 + 17 * q^4 - 18 * q^5 - 8 * q^6 - 8 * q^7 - 24 * q^8 + 7 * q^9 - q^11 + 18 * q^12 + 19 * q^13 - 8 * q^14 - 11 * q^15 + 21 * q^16 - 16 * q^17 - 10 * q^19 - 20 * q^20 - 33 * q^21 + 2 * q^22 - 14 * q^23 - 9 * q^24 + 23 * q^25 - 9 * q^26 + q^27 + 10 * q^28 - 22 * q^29 + 28 * q^30 - 3 * q^31 - 47 * q^32 - 25 * q^33 - 35 * q^34 - 3 * q^35 - 33 * q^36 - 19 * q^37 - 15 * q^38 - 2 * q^39 + 8 * q^40 - 52 * q^41 - 3 * q^42 - 2 * q^43 - 54 * q^44 - 40 * q^45 + 33 * q^46 - 24 * q^47 - 8 * q^48 + 7 * q^49 - 10 * q^50 - 7 * q^51 + 17 * q^52 - 11 * q^53 - 23 * q^54 - 29 * q^55 - 17 * q^56 - 34 * q^57 + 18 * q^58 - 52 * q^59 - 71 * q^60 - 25 * q^61 - 22 * q^62 - 19 * q^63 + 48 * q^64 - 18 * q^65 + 9 * q^66 - 2 * q^67 + 18 * q^68 - 26 * q^69 - 12 * q^70 - 44 * q^71 - 6 * q^72 - 39 * q^73 - 4 * q^74 + 17 * q^75 - 10 * q^76 - 18 * q^77 - 8 * q^78 + q^79 - 9 * q^80 - 13 * q^81 + 47 * q^82 - 27 * q^83 - 24 * q^84 - 26 * q^85 - q^86 + 31 * q^87 + 19 * q^88 - 86 * q^89 + 48 * q^90 - 8 * q^91 - 19 * q^92 + 32 * q^93 + 45 * q^94 + 17 * q^95 - 25 * q^96 - 20 * q^97 + 39 * q^98 + 50 * q^99

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