LMFDB - Embedded newform 731.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [731,2,Mod(1,731)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(731, 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("731.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 731 = 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	731.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:	$5.83706438776$
Analytic rank:	$0$
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} - 30 x^{17} + 62 x^{16} + 365 x^{15} - 786 x^{14} - 2295 x^{13} + 5233 x^{12} + \cdots + 64 $ x^19 - 2x^18 - 30x^17 + 62x^16 + 365x^15 - 786x^14 - 2295x^13 + 5233x^12 + 7816x^11 - 19517x^10 - 13527x^9 + 40173x^8 + 8942x^7 - 41911x^6 + 1140x^5 + 18520x^4 - 1520x^3 - 2640x^2 - 64x + 64
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.148448$ of defining polynomial
Character	$\chi$	$=$	731.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.148448 q^{2} +0.359282 q^{3} -1.97796 q^{4} +2.35987 q^{5} +0.0533348 q^{6} -1.55967 q^{7} -0.590522 q^{8} -2.87092 q^{9} +O(q^{10})$	\(q+0.148448 q^{2} +0.359282 q^{3} -1.97796 q^{4} +2.35987 q^{5} +0.0533348 q^{6} -1.55967 q^{7} -0.590522 q^{8} -2.87092 q^{9} +0.350319 q^{10} +1.82137 q^{11} -0.710647 q^{12} +5.22938 q^{13} -0.231531 q^{14} +0.847859 q^{15} +3.86826 q^{16} +1.00000 q^{17} -0.426183 q^{18} +3.40972 q^{19} -4.66773 q^{20} -0.560363 q^{21} +0.270379 q^{22} +5.17546 q^{23} -0.212164 q^{24} +0.568981 q^{25} +0.776293 q^{26} -2.10932 q^{27} +3.08498 q^{28} +7.10361 q^{29} +0.125863 q^{30} +0.110404 q^{31} +1.75528 q^{32} +0.654386 q^{33} +0.148448 q^{34} -3.68063 q^{35} +5.67857 q^{36} -0.00648354 q^{37} +0.506166 q^{38} +1.87882 q^{39} -1.39355 q^{40} +3.74124 q^{41} -0.0831850 q^{42} -1.00000 q^{43} -3.60260 q^{44} -6.77499 q^{45} +0.768289 q^{46} -5.87549 q^{47} +1.38980 q^{48} -4.56742 q^{49} +0.0844642 q^{50} +0.359282 q^{51} -10.3435 q^{52} +7.44435 q^{53} -0.313124 q^{54} +4.29819 q^{55} +0.921022 q^{56} +1.22505 q^{57} +1.05452 q^{58} +8.85363 q^{59} -1.67703 q^{60} -9.60858 q^{61} +0.0163893 q^{62} +4.47769 q^{63} -7.47596 q^{64} +12.3407 q^{65} +0.0971425 q^{66} +7.29699 q^{67} -1.97796 q^{68} +1.85945 q^{69} -0.546383 q^{70} -7.51956 q^{71} +1.69534 q^{72} +12.3900 q^{73} -0.000962471 q^{74} +0.204425 q^{75} -6.74429 q^{76} -2.84074 q^{77} +0.278908 q^{78} -3.82360 q^{79} +9.12860 q^{80} +7.85491 q^{81} +0.555381 q^{82} -8.31990 q^{83} +1.10838 q^{84} +2.35987 q^{85} -0.148448 q^{86} +2.55220 q^{87} -1.07556 q^{88} +15.3915 q^{89} -1.00574 q^{90} -8.15613 q^{91} -10.2369 q^{92} +0.0396663 q^{93} -0.872207 q^{94} +8.04648 q^{95} +0.630641 q^{96} -3.92949 q^{97} -0.678025 q^{98} -5.22900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) $ 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * 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 $

$2$	0.148448	0.104969	0.0524844	−	0.998622i	$-0.483286\pi$
$2$	0.148448	0.104969	0.0524844	+	0.998622i	$0.483286\pi$
$3$	0.359282	0.207432	0.103716	−	0.994607i	$-0.466927\pi$
$3$	0.359282	0.207432	0.103716	+	0.994607i	$0.466927\pi$
$4$	−1.97796	−0.988982
$5$	2.35987	1.05537	0.527683	−	0.849442i	$-0.323061\pi$
$5$	2.35987	1.05537	0.527683	+	0.849442i	$0.323061\pi$
$6$	0.0533348	0.0217739
$7$	−1.55967	−0.589501	−0.294751	−	0.955574i	$-0.595237\pi$
$7$	−1.55967	−0.589501	−0.294751	+	0.955574i	$0.595237\pi$
$8$	−0.590522	−0.208781
$9$	−2.87092	−0.956972
$10$	0.350319	0.110780
$11$	1.82137	0.549164	0.274582	−	0.961564i	$-0.411461\pi$
$11$	1.82137	0.549164	0.274582	+	0.961564i	$0.411461\pi$
$12$	−0.710647	−0.205146
$13$	5.22938	1.45037	0.725185	−	0.688554i	$-0.241754\pi$
$13$	5.22938	1.45037	0.725185	+	0.688554i	$0.241754\pi$
$14$	−0.231531	−0.0618793
$15$	0.847859	0.218916
$16$	3.86826	0.967066
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.426183	−0.100452
$19$	3.40972	0.782242	0.391121	−	0.920339i	$-0.372087\pi$
$19$	3.40972	0.782242	0.391121	+	0.920339i	$0.372087\pi$
$20$	−4.66773	−1.04374
$21$	−0.560363	−0.122281
$22$	0.270379	0.0576451
$23$	5.17546	1.07916	0.539579	−	0.841935i	$-0.318583\pi$
$23$	5.17546	1.07916	0.539579	+	0.841935i	$0.318583\pi$
$24$	−0.212164	−0.0433078
$25$	0.568981	0.113796
$26$	0.776293	0.152244
$27$	−2.10932	−0.405938
$28$	3.08498	0.583006
$29$	7.10361	1.31911	0.659554	−	0.751658i	$-0.270745\pi$
$29$	7.10361	1.31911	0.659554	+	0.751658i	$0.270745\pi$
$30$	0.125863	0.0229794
$31$	0.110404	0.0198292	0.00991460	−	0.999951i	$-0.496844\pi$
$31$	0.110404	0.0198292	0.00991460	+	0.999951i	$0.496844\pi$
$32$	1.75528	0.310293
$33$	0.654386	0.113914
$34$	0.148448	0.0254587
$35$	−3.68063	−0.622139
$36$	5.67857	0.946428
$37$	−0.00648354	−0.00106589	−0.000532944	−	1.00000i	$-0.500170\pi$
$37$	−0.00648354	−0.00106589	−0.000532944		1.00000i	$0.500170\pi$
$38$	0.506166	0.0821110
$39$	1.87882	0.300853
$40$	−1.39355	−0.220340
$41$	3.74124	0.584284	0.292142	−	0.956375i	$-0.405632\pi$
$41$	3.74124	0.584284	0.292142	+	0.956375i	$0.405632\pi$
$42$	−0.0831850	−0.0128357
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	−3.60260	−0.543113
$45$	−6.77499	−1.00996
$46$	0.768289	0.113278
$47$	−5.87549	−0.857028	−0.428514	−	0.903535i	$-0.640963\pi$
$47$	−5.87549	−0.857028	−0.428514	+	0.903535i	$0.640963\pi$
$48$	1.38980	0.200600
$49$	−4.56742	−0.652488
$50$	0.0844642	0.0119450
$51$	0.359282	0.0503096
$52$	−10.3435	−1.43439
$53$	7.44435	1.02256	0.511280	−	0.859414i	$-0.329171\pi$
$53$	7.44435	1.02256	0.511280	+	0.859414i	$0.329171\pi$
$54$	−0.313124	−0.0426108
$55$	4.29819	0.579568
$56$	0.921022	0.123077
$57$	1.22505	0.162262
$58$	1.05452	0.138465
$59$	8.85363	1.15264	0.576322	−	0.817223i	$-0.304487\pi$
$59$	8.85363	1.15264	0.576322	+	0.817223i	$0.304487\pi$
$60$	−1.67703	−0.216504
$61$	−9.60858	−1.23025	−0.615126	−	0.788429i	$-0.710895\pi$
$61$	−9.60858	−1.23025	−0.615126	+	0.788429i	$0.710895\pi$
$62$	0.0163893	0.00208145
$63$	4.47769	0.564136
$64$	−7.47596	−0.934495
$65$	12.3407	1.53067
$66$	0.0971425	0.0119574
$67$	7.29699	0.891469	0.445735	−	0.895165i	$-0.352943\pi$
$67$	7.29699	0.891469	0.445735	+	0.895165i	$0.352943\pi$
$68$	−1.97796	−0.239863
$69$	1.85945	0.223852
$70$	−0.546383	−0.0653052
$71$	−7.51956	−0.892407	−0.446204	−	0.894931i	$-0.647224\pi$
$71$	−7.51956	−0.892407	−0.446204	+	0.894931i	$0.647224\pi$
$72$	1.69534	0.199798
$73$	12.3900	1.45014	0.725072	−	0.688673i	$-0.241806\pi$
$73$	12.3900	1.45014	0.725072	+	0.688673i	$0.241806\pi$
$74$	−0.000962471 0	−0.000111885 0
$75$	0.204425	0.0236049
$76$	−6.74429	−0.773623
$77$	−2.84074	−0.323733
$78$	0.278908	0.0315801
$79$	−3.82360	−0.430189	−0.215094	−	0.976593i	$-0.569006\pi$
$79$	−3.82360	−0.430189	−0.215094	+	0.976593i	$0.569006\pi$
$80$	9.12860	1.02061
$81$	7.85491	0.872768
$82$	0.555381	0.0613316
$83$	−8.31990	−0.913228	−0.456614	−	0.889665i	$-0.650938\pi$
$83$	−8.31990	−0.913228	−0.456614	+	0.889665i	$0.650938\pi$
$84$	1.10838	0.120934
$85$	2.35987	0.255964
$86$	−0.148448	−0.0160076
$87$	2.55220	0.273625
$88$	−1.07556	−0.114655
$89$	15.3915	1.63150	0.815749	−	0.578407i	$-0.196325\pi$
$89$	15.3915	1.63150	0.815749	+	0.578407i	$0.196325\pi$
$90$	−1.00574	−0.106014
$91$	−8.15613	−0.854995
$92$	−10.2369	−1.06727
$93$	0.0396663	0.00411320
$94$	−0.872207	−0.0899612
$95$	8.04648	0.825551
$96$	0.630641	0.0643646
$97$	−3.92949	−0.398979	−0.199490	−	0.979900i	$-0.563928\pi$
$97$	−3.92949	−0.398979	−0.199490	+	0.979900i	$0.563928\pi$
$98$	−0.678025	−0.0684909
$99$	−5.22900	−0.525534
$100$	−1.12542	−0.112542
$101$	5.92654	0.589712	0.294856	−	0.955542i	$-0.404728\pi$
$101$	5.92654	0.589712	0.294856	+	0.955542i	$0.404728\pi$
$102$	0.0533348	0.00528094
$103$	−6.24114	−0.614958	−0.307479	−	0.951555i	$-0.599485\pi$
$103$	−6.24114	−0.614958	−0.307479	+	0.951555i	$0.599485\pi$
$104$	−3.08806	−0.302810
$105$	−1.32238	−0.129051
$106$	1.10510	0.107337
$107$	−16.6407	−1.60872	−0.804358	−	0.594145i	$-0.797490\pi$
$107$	−16.6407	−1.60872	−0.804358	+	0.594145i	$0.797490\pi$
$108$	4.17215	0.401465
$109$	−16.0673	−1.53897	−0.769483	−	0.638668i	$-0.779486\pi$
$109$	−16.0673	−1.53897	−0.769483	+	0.638668i	$0.779486\pi$
$110$	0.638060	0.0608366
$111$	−0.00232942	−0.000221099 0
$112$	−6.03323	−0.570087
$113$	5.12138	0.481779	0.240890	−	0.970553i	$-0.422561\pi$
$113$	5.12138	0.481779	0.240890	+	0.970553i	$0.422561\pi$
$114$	0.181857	0.0170324
$115$	12.2134	1.13891
$116$	−14.0507	−1.30457
$117$	−15.0131	−1.38796
$118$	1.31431	0.120992
$119$	−1.55967	−0.142975
$120$	−0.500679	−0.0457056
$121$	−7.68261	−0.698419
$122$	−1.42638	−0.129138
$123$	1.34416	0.121199
$124$	−0.218376	−0.0196107
$125$	−10.4566	−0.935269
$126$	0.664706	0.0592167
$127$	8.78452	0.779501	0.389750	−	0.920921i	$-0.372561\pi$
$127$	8.78452	0.779501	0.389750	+	0.920921i	$0.372561\pi$
$128$	−4.62036	−0.408386
$129$	−0.359282	−0.0316330
$130$	1.83195	0.160673
$131$	−2.67715	−0.233903	−0.116952	−	0.993138i	$-0.537312\pi$
$131$	−2.67715	−0.233903	−0.116952	+	0.993138i	$0.537312\pi$
$132$	−1.29435	−0.112659
$133$	−5.31804	−0.461133
$134$	1.08323	0.0935764
$135$	−4.97771	−0.428413
$136$	−0.590522	−0.0506368
$137$	1.62427	0.138771	0.0693855	−	0.997590i	$-0.477896\pi$
$137$	1.62427	0.138771	0.0693855	+	0.997590i	$0.477896\pi$
$138$	0.276033	0.0234975
$139$	−1.36318	−0.115623	−0.0578115	−	0.998328i	$-0.518412\pi$
$139$	−1.36318	−0.115623	−0.0578115	+	0.998328i	$0.518412\pi$
$140$	7.28014	0.615284
$141$	−2.11096	−0.177775
$142$	−1.11627	−0.0936749
$143$	9.52464	0.796490
$144$	−11.1055	−0.925455
$145$	16.7636	1.39214
$146$	1.83928	0.152220
$147$	−1.64099	−0.135347
$148$	0.0128242	0.00105414
$149$	−7.41244	−0.607251	−0.303626	−	0.952791i	$-0.598197\pi$
$149$	−7.41244	−0.607251	−0.303626	+	0.952791i	$0.598197\pi$
$150$	0.0303465	0.00247778
$151$	−18.7088	−1.52250	−0.761251	−	0.648457i	$-0.775415\pi$
$151$	−18.7088	−1.52250	−0.761251	+	0.648457i	$0.775415\pi$
$152$	−2.01351	−0.163317
$153$	−2.87092	−0.232100
$154$	−0.421704	−0.0339818
$155$	0.260540	0.0209271
$156$	−3.71624	−0.297538
$157$	13.2317	1.05601	0.528004	−	0.849242i	$-0.322941\pi$
$157$	13.2317	1.05601	0.528004	+	0.849242i	$0.322941\pi$
$158$	−0.567607	−0.0451564
$159$	2.67462	0.212112
$160$	4.14223	0.327472
$161$	−8.07204	−0.636166
$162$	1.16605	0.0916134
$163$	−3.92580	−0.307492	−0.153746	−	0.988110i	$-0.549134\pi$
$163$	−3.92580	−0.307492	−0.153746	+	0.988110i	$0.549134\pi$
$164$	−7.40004	−0.577846
$165$	1.54427	0.120221
$166$	−1.23508	−0.0958604
$167$	−13.4550	−1.04118	−0.520588	−	0.853808i	$-0.674287\pi$
$167$	−13.4550	−1.04118	−0.520588	+	0.853808i	$0.674287\pi$
$168$	0.330907	0.0255300
$169$	14.3464	1.10357
$170$	0.350319	0.0268682
$171$	−9.78901	−0.748584
$172$	1.97796	0.150818
$173$	6.12118	0.465385	0.232692	−	0.972550i	$-0.425246\pi$
$173$	6.12118	0.465385	0.232692	+	0.972550i	$0.425246\pi$
$174$	0.378870	0.0287221
$175$	−0.887424	−0.0670830
$176$	7.04554	0.531078
$177$	3.18095	0.239095
$178$	2.28484	0.171256
$179$	−7.91808	−0.591825	−0.295912	−	0.955215i	$-0.595624\pi$
$179$	−7.91808	−0.591825	−0.295912	+	0.955215i	$0.595624\pi$
$180$	13.4007	0.998827
$181$	−1.60868	−0.119572	−0.0597860	−	0.998211i	$-0.519042\pi$
$181$	−1.60868	−0.119572	−0.0597860	+	0.998211i	$0.519042\pi$
$182$	−1.21076	−0.0897478
$183$	−3.45219	−0.255193
$184$	−3.05622	−0.225308
$185$	−0.0153003	−0.00112490
$186$	0.00588840	0.000431758 0
$187$	1.82137	0.133192
$188$	11.6215	0.847585
$189$	3.28985	0.239301
$190$	1.19449	0.0866572
$191$	−0.557160	−0.0403147	−0.0201573	−	0.999797i	$-0.506417\pi$
$191$	−0.557160	−0.0403147	−0.0201573	+	0.999797i	$0.506417\pi$
$192$	−2.68598	−0.193844
$193$	13.4393	0.967381	0.483690	−	0.875239i	$-0.339296\pi$
$193$	13.4393	0.967381	0.483690	+	0.875239i	$0.339296\pi$
$194$	−0.583326	−0.0418804
$195$	4.43378	0.317509
$196$	9.03418	0.645299
$197$	−15.8300	−1.12784	−0.563921	−	0.825829i	$-0.690708\pi$
$197$	−15.8300	−1.12784	−0.563921	+	0.825829i	$0.690708\pi$
$198$	−0.776236	−0.0551647
$199$	14.6842	1.04093	0.520466	−	0.853882i	$-0.325758\pi$
$199$	14.6842	1.04093	0.520466	+	0.853882i	$0.325758\pi$
$200$	−0.335996	−0.0237585
$201$	2.62168	0.184919
$202$	0.879784	0.0619014
$203$	−11.0793	−0.777616
$204$	−0.710647	−0.0497552
$205$	8.82884	0.616633
$206$	−0.926487	−0.0645514
$207$	−14.8583	−1.03272
$208$	20.2286	1.40260
$209$	6.21035	0.429579
$210$	−0.196306	−0.0135464
$211$	−14.0475	−0.967069	−0.483535	−	0.875325i	$-0.660647\pi$
$211$	−14.0475	−0.967069	−0.483535	+	0.875325i	$0.660647\pi$
$212$	−14.7247	−1.01129
$213$	−2.70164	−0.185114
$214$	−2.47028	−0.168865
$215$	−2.35987	−0.160942
$216$	1.24560	0.0847522
$217$	−0.172195	−0.0116893
$218$	−2.38516	−0.161543
$219$	4.45152	0.300806
$220$	−8.50167	−0.573183
$221$	5.22938	0.351766
$222$	−0.000345799 0	−2.32085e−5 0
$223$	−8.69701	−0.582395	−0.291197	−	0.956663i	$-0.594054\pi$
$223$	−8.69701	−0.582395	−0.291197	+	0.956663i	$0.594054\pi$
$224$	−2.73767	−0.182918
$225$	−1.63350	−0.108900
$226$	0.760261	0.0505718
$227$	4.82338	0.320139	0.160070	−	0.987106i	$-0.448828\pi$
$227$	4.82338	0.320139	0.160070	+	0.987106i	$0.448828\pi$
$228$	−2.42310	−0.160474
$229$	29.2295	1.93154	0.965768	−	0.259406i	$-0.0835266\pi$
$229$	29.2295	1.93154	0.965768	+	0.259406i	$0.0835266\pi$
$230$	1.81306	0.119550
$231$	−1.02063	−0.0671525
$232$	−4.19484	−0.275405
$233$	18.2873	1.19804	0.599021	−	0.800733i	$-0.295557\pi$
$233$	18.2873	1.19804	0.599021	+	0.800733i	$0.295557\pi$
$234$	−2.22867	−0.145693
$235$	−13.8654	−0.904478
$236$	−17.5122	−1.13994
$237$	−1.37375	−0.0892348
$238$	−0.231531	−0.0150079
$239$	−23.2879	−1.50637	−0.753184	−	0.657810i	$-0.771483\pi$
$239$	−23.2879	−1.50637	−0.753184	+	0.657810i	$0.771483\pi$
$240$	3.27974	0.211706
$241$	11.5060	0.741164	0.370582	−	0.928800i	$-0.379158\pi$
$241$	11.5060	0.741164	0.370582	+	0.928800i	$0.379158\pi$
$242$	−1.14047	−0.0733122
$243$	9.15008	0.586978
$244$	19.0054	1.21670
$245$	−10.7785	−0.688613
$246$	0.199538	0.0127221
$247$	17.8307	1.13454
$248$	−0.0651962	−0.00413996
$249$	−2.98919	−0.189432
$250$	−1.55227	−0.0981741
$251$	8.87476	0.560170	0.280085	−	0.959975i	$-0.409637\pi$
$251$	8.87476	0.560170	0.280085	+	0.959975i	$0.409637\pi$
$252$	−8.85671	−0.557920
$253$	9.42644	0.592635
$254$	1.30405	0.0818232
$255$	0.847859	0.0530950
$256$	14.2660	0.891627
$257$	−30.5496	−1.90563	−0.952816	−	0.303547i	$-0.901829\pi$
$257$	−30.5496	−1.90563	−0.952816	+	0.303547i	$0.901829\pi$
$258$	−0.0533348	−0.00332048
$259$	0.0101122	0.000628342 0
$260$	−24.4094	−1.51380
$261$	−20.3939	−1.26235
$262$	−0.397418	−0.0245526
$263$	−12.3583	−0.762042	−0.381021	−	0.924566i	$-0.624428\pi$
$263$	−12.3583	−0.762042	−0.381021	+	0.924566i	$0.624428\pi$
$264$	−0.386429	−0.0237831
$265$	17.5677	1.07918
$266$	−0.789455	−0.0484046
$267$	5.52990	0.338424
$268$	−14.4332	−0.881646
$269$	−22.5214	−1.37316	−0.686578	−	0.727057i	$-0.740888\pi$
$269$	−22.5214	−1.37316	−0.686578	+	0.727057i	$0.740888\pi$
$270$	−0.738933	−0.0449700
$271$	31.4280	1.90912	0.954558	−	0.298026i	$-0.0963282\pi$
$271$	31.4280	1.90912	0.954558	+	0.298026i	$0.0963282\pi$
$272$	3.86826	0.234548
$273$	−2.93035	−0.177353
$274$	0.241120	0.0145666
$275$	1.03632	0.0624927
$276$	−3.67793	−0.221385
$277$	7.59310	0.456225	0.228113	−	0.973635i	$-0.426745\pi$
$277$	7.59310	0.456225	0.228113	+	0.973635i	$0.426745\pi$
$278$	−0.202361	−0.0121368
$279$	−0.316962	−0.0189760
$280$	2.17349	0.129891
$281$	−15.2730	−0.911111	−0.455555	−	0.890207i	$-0.650559\pi$
$281$	−15.2730	−0.911111	−0.455555	+	0.890207i	$0.650559\pi$
$282$	−0.313368	−0.0186608
$283$	−20.4300	−1.21443	−0.607217	−	0.794536i	$-0.707714\pi$
$283$	−20.4300	−1.21443	−0.607217	+	0.794536i	$0.707714\pi$
$284$	14.8734	0.882574
$285$	2.89096	0.171246
$286$	1.41392	0.0836066
$287$	−5.83512	−0.344436
$288$	−5.03927	−0.296942
$289$	1.00000	0.0588235
$290$	2.48853	0.146131
$291$	−1.41180	−0.0827609
$292$	−24.5070	−1.43417
$293$	−4.35737	−0.254560	−0.127280	−	0.991867i	$-0.540625\pi$
$293$	−4.35737	−0.254560	−0.127280	+	0.991867i	$0.540625\pi$
$294$	−0.243602	−0.0142072
$295$	20.8934	1.21646
$296$	0.00382867	0.000222537 0
$297$	−3.84185	−0.222926
$298$	−1.10036	−0.0637424
$299$	27.0645	1.56518
$300$	−0.404344	−0.0233448
$301$	1.55967	0.0898981
$302$	−2.77729	−0.159815
$303$	2.12930	0.122325
$304$	13.1897	0.756480
$305$	−22.6750	−1.29837
$306$	−0.426183	−0.0243632
$307$	−25.1841	−1.43733	−0.718666	−	0.695355i	$-0.755247\pi$
$307$	−25.1841	−1.43733	−0.718666	+	0.695355i	$0.755247\pi$
$308$	5.61889	0.320166
$309$	−2.24233	−0.127562
$310$	0.0386767	0.00219669
$311$	28.4198	1.61154	0.805770	−	0.592228i	$-0.201752\pi$
$311$	28.4198	1.61154	0.805770	+	0.592228i	$0.201752\pi$
$312$	−1.10949	−0.0628123
$313$	−6.69962	−0.378685	−0.189342	−	0.981911i	$-0.560636\pi$
$313$	−6.69962	−0.378685	−0.189342	+	0.981911i	$0.560636\pi$
$314$	1.96423	0.110848
$315$	10.5668	0.595370
$316$	7.56294	0.425449
$317$	13.7861	0.774302	0.387151	−	0.922016i	$-0.373459\pi$
$317$	13.7861	0.774302	0.387151	+	0.922016i	$0.373459\pi$
$318$	0.397044	0.0222651
$319$	12.9383	0.724406
$320$	−17.6423	−0.986234
$321$	−5.97870	−0.333699
$322$	−1.19828	−0.0667775
$323$	3.40972	0.189722
$324$	−15.5367	−0.863151
$325$	2.97542	0.165046
$326$	−0.582778	−0.0322771
$327$	−5.77269	−0.319230
$328$	−2.20928	−0.121987
$329$	9.16385	0.505219
$330$	0.229244	0.0126194
$331$	−12.0736	−0.663625	−0.331812	−	0.943345i	$-0.607660\pi$
$331$	−12.0736	−0.663625	−0.331812	+	0.943345i	$0.607660\pi$
$332$	16.4565	0.903165
$333$	0.0186137	0.00102003
$334$	−1.99737	−0.109291
$335$	17.2199	0.940826
$336$	−2.16763	−0.118254
$337$	35.3954	1.92811	0.964055	−	0.265702i	$-0.0856036\pi$
$337$	35.3954	1.92811	0.964055	+	0.265702i	$0.0856036\pi$
$338$	2.12970	0.115841
$339$	1.84002	0.0999363
$340$	−4.66773	−0.253143
$341$	0.201087	0.0108895
$342$	−1.45316	−0.0785780
$343$	18.0414	0.974144
$344$	0.590522	0.0318388
$345$	4.38806	0.236245
$346$	0.908679	0.0488509
$347$	28.5162	1.53083	0.765415	−	0.643538i	$-0.222534\pi$
$347$	28.5162	1.53083	0.765415	+	0.643538i	$0.222534\pi$
$348$	−5.04816	−0.270610
$349$	19.4369	1.04044	0.520218	−	0.854033i	$-0.325851\pi$
$349$	19.4369	1.04044	0.520218	+	0.854033i	$0.325851\pi$
$350$	−0.131737	−0.00704162
$351$	−11.0304	−0.588760
$352$	3.19702	0.170402
$353$	3.24272	0.172592	0.0862962	−	0.996270i	$-0.472497\pi$
$353$	3.24272	0.172592	0.0862962	+	0.996270i	$0.472497\pi$
$354$	0.472207	0.0250975
$355$	−17.7452	−0.941816
$356$	−30.4438	−1.61352
$357$	−0.560363	−0.0296576
$358$	−1.17543	−0.0621231
$359$	0.406821	0.0214712	0.0107356	−	0.999942i	$-0.496583\pi$
$359$	0.406821	0.0214712	0.0107356	+	0.999942i	$0.496583\pi$
$360$	4.00078	0.210859
$361$	−7.37384	−0.388097
$362$	−0.238806	−0.0125513
$363$	−2.76023	−0.144874
$364$	16.1325	0.845574
$365$	29.2389	1.53043
$366$	−0.512472	−0.0267873
$367$	9.44798	0.493181	0.246590	−	0.969120i	$-0.420690\pi$
$367$	9.44798	0.493181	0.246590	+	0.969120i	$0.420690\pi$
$368$	20.0201	1.04362
$369$	−10.7408	−0.559143
$370$	−0.00227131	−0.000118080 0
$371$	−11.6108	−0.602801
$372$	−0.0784585	−0.00406788
$373$	−21.6842	−1.12276	−0.561382	−	0.827557i	$-0.689730\pi$
$373$	−21.6842	−1.12276	−0.561382	+	0.827557i	$0.689730\pi$
$374$	0.270379	0.0139810
$375$	−3.75688	−0.194004
$376$	3.46961	0.178931
$377$	37.1475	1.91319
$378$	0.488372	0.0251191
$379$	−2.78693	−0.143155	−0.0715774	−	0.997435i	$-0.522803\pi$
$379$	−2.78693	−0.143155	−0.0715774	+	0.997435i	$0.522803\pi$
$380$	−15.9156	−0.816455
$381$	3.15612	0.161693
$382$	−0.0827095	−0.00423179
$383$	−14.2053	−0.725857	−0.362929	−	0.931817i	$-0.618223\pi$
$383$	−14.2053	−0.725857	−0.362929	+	0.931817i	$0.618223\pi$
$384$	−1.66001	−0.0847121
$385$	−6.70378	−0.341656
$386$	1.99504	0.101545
$387$	2.87092	0.145937
$388$	7.77238	0.394583
$389$	−1.52149	−0.0771424	−0.0385712	−	0.999256i	$-0.512281\pi$
$389$	−1.52149	−0.0771424	−0.0385712	+	0.999256i	$0.512281\pi$
$390$	0.658187	0.0333286
$391$	5.17546	0.261734
$392$	2.69716	0.136227
$393$	−0.961851	−0.0485190
$394$	−2.34994	−0.118388
$395$	−9.02319	−0.454006
$396$	10.3428	0.519744
$397$	24.0268	1.20587	0.602936	−	0.797789i	$-0.293997\pi$
$397$	24.0268	1.20587	0.602936	+	0.797789i	$0.293997\pi$
$398$	2.17984	0.109265
$399$	−1.91068	−0.0956536
$400$	2.20097	0.110048
$401$	13.1392	0.656140	0.328070	−	0.944653i	$-0.393602\pi$
$401$	13.1392	0.656140	0.328070	+	0.944653i	$0.393602\pi$
$402$	0.389184	0.0194107
$403$	0.577346	0.0287597
$404$	−11.7225	−0.583215
$405$	18.5366	0.921089
$406$	−1.64471	−0.0816254
$407$	−0.0118089	−0.000585347 0
$408$	−0.212164	−0.0105037
$409$	18.0430	0.892168	0.446084	−	0.894991i	$-0.352818\pi$
$409$	18.0430	0.892168	0.446084	+	0.894991i	$0.352818\pi$
$410$	1.31063	0.0647272
$411$	0.583572	0.0287855
$412$	12.3448	0.608182
$413$	−13.8088	−0.679485
$414$	−2.20569	−0.108404
$415$	−19.6339	−0.963789
$416$	9.17903	0.450039
$417$	−0.489765	−0.0239839
$418$	0.921917	0.0450924
$419$	−18.2204	−0.890123	−0.445062	−	0.895500i	$-0.646818\pi$
$419$	−18.2204	−0.890123	−0.445062	+	0.895500i	$0.646818\pi$
$420$	2.61563	0.127629
$421$	−4.09917	−0.199781	−0.0998906	−	0.994998i	$-0.531849\pi$
$421$	−4.09917	−0.199781	−0.0998906	+	0.994998i	$0.531849\pi$
$422$	−2.08533	−0.101512
$423$	16.8680	0.820152
$424$	−4.39605	−0.213491
$425$	0.568981	0.0275996
$426$	−0.401055	−0.0194312
$427$	14.9862	0.725235
$428$	32.9147	1.59099
$429$	3.42203	0.165217
$430$	−0.350319	−0.0168939
$431$	30.2592	1.45753	0.728767	−	0.684762i	$-0.240094\pi$
$431$	30.2592	1.45753	0.728767	+	0.684762i	$0.240094\pi$
$432$	−8.15939	−0.392569
$433$	11.3796	0.546870	0.273435	−	0.961890i	$-0.411840\pi$
$433$	11.3796	0.546870	0.273435	+	0.961890i	$0.411840\pi$
$434$	−0.0255620	−0.00122702
$435$	6.02286	0.288774
$436$	31.7805	1.52201
$437$	17.6469	0.844164
$438$	0.660821	0.0315752
$439$	28.9969	1.38394	0.691972	−	0.721924i	$-0.256742\pi$
$439$	28.9969	1.38394	0.691972	+	0.721924i	$0.256742\pi$
$440$	−2.53818	−0.121003
$441$	13.1127	0.624413
$442$	0.776293	0.0369245
$443$	−27.5079	−1.30694	−0.653470	−	0.756952i	$-0.726688\pi$
$443$	−27.5079	−1.30694	−0.653470	+	0.756952i	$0.726688\pi$
$444$	0.00460751	0.000218663 0
$445$	36.3220	1.72183
$446$	−1.29106	−0.0611333
$447$	−2.66316	−0.125963
$448$	11.6601	0.550886
$449$	−28.4981	−1.34491	−0.672453	−	0.740139i	$-0.734759\pi$
$449$	−28.4981	−1.34491	−0.672453	+	0.740139i	$0.734759\pi$
$450$	−0.242490	−0.0114311
$451$	6.81418	0.320867
$452$	−10.1299	−0.476471
$453$	−6.72175	−0.315815
$454$	0.716023	0.0336046
$455$	−19.2474	−0.902332
$456$	−0.723419	−0.0338772
$457$	−23.1088	−1.08098	−0.540492	−	0.841349i	$-0.681762\pi$
$457$	−23.1088	−1.08098	−0.540492	+	0.841349i	$0.681762\pi$
$458$	4.33906	0.202751
$459$	−2.10932	−0.0984544
$460$	−24.1577	−1.12636
$461$	−24.6234	−1.14683	−0.573413	−	0.819266i	$-0.694381\pi$
$461$	−24.6234	−1.14683	−0.573413	+	0.819266i	$0.694381\pi$
$462$	−0.151511	−0.00704891
$463$	15.4455	0.717812	0.358906	−	0.933374i	$-0.383150\pi$
$463$	15.4455	0.717812	0.358906	+	0.933374i	$0.383150\pi$
$464$	27.4786	1.27566
$465$	0.0936073	0.00434093
$466$	2.71472	0.125757
$467$	−20.9050	−0.967370	−0.483685	−	0.875242i	$-0.660702\pi$
$467$	−20.9050	−0.967370	−0.483685	+	0.875242i	$0.660702\pi$
$468$	29.6954	1.37267
$469$	−11.3809	−0.525522
$470$	−2.05829	−0.0949420
$471$	4.75393	0.219050
$472$	−5.22826	−0.240650
$473$	−1.82137	−0.0837467
$474$	−0.203931	−0.00936687
$475$	1.94006	0.0890162
$476$	3.08498	0.141400
$477$	−21.3721	−0.978562
$478$	−3.45705	−0.158122
$479$	19.6574	0.898168	0.449084	−	0.893490i	$-0.351750\pi$
$479$	19.6574	0.898168	0.449084	+	0.893490i	$0.351750\pi$
$480$	1.48823	0.0679281
$481$	−0.0339049	−0.00154593
$482$	1.70804	0.0777991
$483$	−2.90014	−0.131961
$484$	15.1959	0.690724
$485$	−9.27308	−0.421069
$486$	1.35831	0.0616144
$487$	−23.3783	−1.05937	−0.529685	−	0.848194i	$-0.677690\pi$
$487$	−23.3783	−1.05937	−0.529685	+	0.848194i	$0.677690\pi$
$488$	5.67408	0.256853
$489$	−1.41047	−0.0637837
$490$	−1.60005	−0.0722829
$491$	23.0241	1.03906	0.519532	−	0.854451i	$-0.326106\pi$
$491$	23.0241	1.03906	0.519532	+	0.854451i	$0.326106\pi$
$492$	−2.65870	−0.119864
$493$	7.10361	0.319930
$494$	2.64694	0.119091
$495$	−12.3398	−0.554631
$496$	0.427073	0.0191761
$497$	11.7281	0.526075
$498$	−0.443741	−0.0198845
$499$	−40.1780	−1.79861	−0.899307	−	0.437318i	$-0.855929\pi$
$499$	−40.1780	−1.79861	−0.899307	+	0.437318i	$0.855929\pi$
$500$	20.6828	0.924964
$501$	−4.83413	−0.215973
$502$	1.31744	0.0588004
$503$	−39.5638	−1.76406	−0.882030	−	0.471193i	$-0.843824\pi$
$503$	−39.5638	−1.76406	−0.882030	+	0.471193i	$0.843824\pi$
$504$	−2.64418	−0.117781
$505$	13.9858	0.622362
$506$	1.39934	0.0622082
$507$	5.15442	0.228916
$508$	−17.3755	−0.770912
$509$	−9.18353	−0.407053	−0.203526	−	0.979069i	$-0.565240\pi$
$509$	−9.18353	−0.407053	−0.203526	+	0.979069i	$0.565240\pi$
$510$	0.125863	0.00557332
$511$	−19.3244	−0.854862
$512$	11.3585	0.501979
$513$	−7.19217	−0.317542
$514$	−4.53504	−0.200032
$515$	−14.7283	−0.649006
$516$	0.710647	0.0312845
$517$	−10.7014	−0.470649
$518$	0.00150114	6.59564e−5 0
$519$	2.19923	0.0965356
$520$	−7.28743	−0.319575
$521$	−16.0246	−0.702051	−0.351026	−	0.936366i	$-0.614167\pi$
$521$	−16.0246	−0.702051	−0.351026	+	0.936366i	$0.614167\pi$
$522$	−3.02744	−0.132507
$523$	4.42779	0.193614	0.0968068	−	0.995303i	$-0.469137\pi$
$523$	4.42779	0.193614	0.0968068	+	0.995303i	$0.469137\pi$
$524$	5.29530	0.231326
$525$	−0.318836	−0.0139151
$526$	−1.83456	−0.0799907
$527$	0.110404	0.00480929
$528$	2.53134	0.110162
$529$	3.78542	0.164584
$530$	2.60790	0.113280
$531$	−25.4180	−1.10305
$532$	10.5189	0.456052
$533$	19.5644	0.847427
$534$	0.820904	0.0355240
$535$	−39.2698	−1.69778
$536$	−4.30903	−0.186122
$537$	−2.84482	−0.122763
$538$	−3.34327	−0.144138
$539$	−8.31896	−0.358323
$540$	9.84573	0.423693
$541$	0.445617	0.0191586	0.00957929	−	0.999954i	$-0.496951\pi$
$541$	0.445617	0.0191586	0.00957929	+	0.999954i	$0.496951\pi$
$542$	4.66543	0.200398
$543$	−0.577969	−0.0248030
$544$	1.75528	0.0752571
$545$	−37.9167	−1.62417
$546$	−0.435006	−0.0186165
$547$	−21.9789	−0.939750	−0.469875	−	0.882733i	$-0.655701\pi$
$547$	−21.9789	−0.939750	−0.469875	+	0.882733i	$0.655701\pi$
$548$	−3.21275	−0.137242
$549$	27.5854	1.17732
$550$	0.153841	0.00655979
$551$	24.2213	1.03186
$552$	−1.09805	−0.0467360
$553$	5.96357	0.253597
$554$	1.12718	0.0478894
$555$	−0.00549713	−0.000233340 0
$556$	2.69631	0.114349
$557$	−41.8933	−1.77508	−0.887538	−	0.460734i	$-0.847586\pi$
$557$	−41.8933	−1.77508	−0.887538	+	0.460734i	$0.847586\pi$
$558$	−0.0470524	−0.00199189
$559$	−5.22938	−0.221179
$560$	−14.2376	−0.601650
$561$	0.654386	0.0276282
$562$	−2.26725	−0.0956382
$563$	17.5133	0.738098	0.369049	−	0.929410i	$-0.379683\pi$
$563$	17.5133	0.738098	0.369049	+	0.929410i	$0.379683\pi$
$564$	4.17540	0.175816
$565$	12.0858	0.508453
$566$	−3.03279	−0.127478
$567$	−12.2511	−0.514498
$568$	4.44046	0.186318
$569$	−14.6646	−0.614771	−0.307386	−	0.951585i	$-0.599454\pi$
$569$	−14.6646	−0.614771	−0.307386	+	0.951585i	$0.599454\pi$
$570$	0.429158	0.0179754
$571$	18.6431	0.780189	0.390094	−	0.920775i	$-0.372442\pi$
$571$	18.6431	0.780189	0.390094	+	0.920775i	$0.372442\pi$
$572$	−18.8394	−0.787714
$573$	−0.200178	−0.00836255
$574$	−0.866213	−0.0361550
$575$	2.94474	0.122804
$576$	21.4629	0.894286
$577$	25.6095	1.06614	0.533068	−	0.846072i	$-0.321039\pi$
$577$	25.6095	1.06614	0.533068	+	0.846072i	$0.321039\pi$
$578$	0.148448	0.00617464
$579$	4.82850	0.200665
$580$	−33.1578	−1.37680
$581$	12.9763	0.538349
$582$	−0.209579	−0.00868732
$583$	13.5589	0.561553
$584$	−7.31659	−0.302763
$585$	−35.4290	−1.46481
$586$	−0.646844	−0.0267209
$587$	−22.3661	−0.923147	−0.461574	−	0.887102i	$-0.652715\pi$
$587$	−22.3661	−0.923147	−0.461574	+	0.887102i	$0.652715\pi$
$588$	3.24582	0.133855
$589$	0.376447	0.0155112
$590$	3.10159	0.127690
$591$	−5.68744	−0.233950
$592$	−0.0250801	−0.00103078
$593$	19.9144	0.817788	0.408894	−	0.912582i	$-0.365915\pi$
$593$	19.9144	0.817788	0.408894	+	0.912582i	$0.365915\pi$
$594$	−0.570316	−0.0234003
$595$	−3.68063	−0.150891
$596$	14.6615	0.600560
$597$	5.27576	0.215922
$598$	4.01768	0.164295
$599$	14.2787	0.583410	0.291705	−	0.956508i	$-0.405777\pi$
$599$	14.2787	0.583410	0.291705	+	0.956508i	$0.405777\pi$
$600$	−0.120717	−0.00492826
$601$	−24.1172	−0.983763	−0.491881	−	0.870662i	$-0.663691\pi$
$601$	−24.1172	−0.983763	−0.491881	+	0.870662i	$0.663691\pi$
$602$	0.231531	0.00943650
$603$	−20.9490	−0.853111
$604$	37.0054	1.50573
$605$	−18.1300	−0.737087
$606$	0.316091	0.0128403
$607$	−41.1882	−1.67178	−0.835888	−	0.548900i	$-0.815047\pi$
$607$	−41.1882	−1.67178	−0.835888	+	0.548900i	$0.815047\pi$
$608$	5.98501	0.242724
$609$	−3.98060	−0.161302
$610$	−3.36606	−0.136288
$611$	−30.7252	−1.24301
$612$	5.67857	0.229542
$613$	−12.5798	−0.508092	−0.254046	−	0.967192i	$-0.581761\pi$
$613$	−12.5798	−0.508092	−0.254046	+	0.967192i	$0.581761\pi$
$614$	−3.73854	−0.150875
$615$	3.17204	0.127909
$616$	1.67752	0.0675893
$617$	5.61169	0.225918	0.112959	−	0.993600i	$-0.463967\pi$
$617$	5.61169	0.225918	0.112959	+	0.993600i	$0.463967\pi$
$618$	−0.332870	−0.0133900
$619$	6.41138	0.257695	0.128848	−	0.991664i	$-0.458872\pi$
$619$	6.41138	0.257695	0.128848	+	0.991664i	$0.458872\pi$
$620$	−0.515338	−0.0206965
$621$	−10.9167	−0.438072
$622$	4.21888	0.169161
$623$	−24.0057	−0.961770
$624$	7.26779	0.290944
$625$	−27.5212	−1.10085
$626$	−0.994547	−0.0397501
$627$	2.23127	0.0891083
$628$	−26.1719	−1.04437
$629$	−0.00648354	−0.000258516 0
$630$	1.56862	0.0624953
$631$	−3.56300	−0.141841	−0.0709204	−	0.997482i	$-0.522594\pi$
$631$	−3.56300	−0.141841	−0.0709204	+	0.997482i	$0.522594\pi$
$632$	2.25792	0.0898152
$633$	−5.04701	−0.200601
$634$	2.04652	0.0812775
$635$	20.7303	0.822658
$636$	−5.29031	−0.209774
$637$	−23.8848	−0.946349
$638$	1.92067	0.0760400
$639$	21.5880	0.854009
$640$	−10.9034	−0.430996
$641$	5.75720	0.227396	0.113698	−	0.993515i	$-0.463730\pi$
$641$	5.75720	0.227396	0.113698	+	0.993515i	$0.463730\pi$
$642$	−0.887528	−0.0350279
$643$	−23.1791	−0.914095	−0.457048	−	0.889442i	$-0.651093\pi$
$643$	−23.1791	−0.914095	−0.457048	+	0.889442i	$0.651093\pi$
$644$	15.9662	0.629156
$645$	−0.847859	−0.0333844
$646$	0.506166	0.0199149
$647$	−20.4525	−0.804073	−0.402036	−	0.915624i	$-0.631697\pi$
$647$	−20.4525	−0.804073	−0.402036	+	0.915624i	$0.631697\pi$
$648$	−4.63850	−0.182217
$649$	16.1257	0.632991
$650$	0.441696	0.0173247
$651$	−0.0618665	−0.00242474
$652$	7.76509	0.304104
$653$	−6.97301	−0.272875	−0.136438	−	0.990649i	$-0.543565\pi$
$653$	−6.97301	−0.272875	−0.136438	+	0.990649i	$0.543565\pi$
$654$	−0.856946	−0.0335092
$655$	−6.31772	−0.246854
$656$	14.4721	0.565041
$657$	−35.5708	−1.38775
$658$	1.36036	0.0530323
$659$	−1.65056	−0.0642967	−0.0321484	−	0.999483i	$-0.510235\pi$
$659$	−1.65056	−0.0642967	−0.0321484	+	0.999483i	$0.510235\pi$
$660$	−3.05450	−0.118896
$661$	22.7973	0.886714	0.443357	−	0.896345i	$-0.353787\pi$
$661$	22.7973	0.886714	0.443357	+	0.896345i	$0.353787\pi$
$662$	−1.79230	−0.0696599
$663$	1.87882	0.0729675
$664$	4.91308	0.190665
$665$	−12.5499	−0.486664
$666$	0.00276317	0.000107071 0
$667$	36.7645	1.42353
$668$	26.6134	1.02970
$669$	−3.12468	−0.120807
$670$	2.55627	0.0987573
$671$	−17.5008	−0.675610
$672$	−0.983595	−0.0379430
$673$	3.08647	0.118975	0.0594873	−	0.998229i	$-0.481053\pi$
$673$	3.08647	0.118975	0.0594873	+	0.998229i	$0.481053\pi$
$674$	5.25439	0.202391
$675$	−1.20016	−0.0461942
$676$	−28.3767	−1.09141
$677$	16.1683	0.621398	0.310699	−	0.950508i	$-0.399437\pi$
$677$	16.1683	0.621398	0.310699	+	0.950508i	$0.399437\pi$
$678$	0.273148	0.0104902
$679$	6.12872	0.235199
$680$	−1.39355	−0.0534404
$681$	1.73296	0.0664070
$682$	0.0298510	0.00114306
$683$	28.4303	1.08786	0.543928	−	0.839132i	$-0.316937\pi$
$683$	28.4303	1.08786	0.543928	+	0.839132i	$0.316937\pi$
$684$	19.3623	0.740336
$685$	3.83307	0.146454
$686$	2.67822	0.102255
$687$	10.5016	0.400662
$688$	−3.86826	−0.147476
$689$	38.9294	1.48309
$690$	0.651401	0.0247984
$691$	19.8498	0.755124	0.377562	−	0.925984i	$-0.376763\pi$
$691$	19.8498	0.755124	0.377562	+	0.925984i	$0.376763\pi$
$692$	−12.1075	−0.460257
$693$	8.15554	0.309803
$694$	4.23318	0.160689
$695$	−3.21692	−0.122025
$696$	−1.50713	−0.0571276
$697$	3.74124	0.141710
$698$	2.88538	0.109213
$699$	6.57031	0.248512
$700$	1.75529	0.0663438
$701$	−7.60029	−0.287059	−0.143529	−	0.989646i	$-0.545845\pi$
$701$	−7.60029	−0.287059	−0.143529	+	0.989646i	$0.545845\pi$
$702$	−1.63745	−0.0618015
$703$	−0.0221070	−0.000833783 0
$704$	−13.6165	−0.513191
$705$	−4.98159	−0.187617
$706$	0.481376	0.0181168
$707$	−9.24346	−0.347636
$708$	−6.29181	−0.236461
$709$	−8.58855	−0.322550	−0.161275	−	0.986910i	$-0.551561\pi$
$709$	−8.58855	−0.322550	−0.161275	+	0.986910i	$0.551561\pi$
$710$	−2.63424	−0.0988613
$711$	10.9772	0.411678
$712$	−9.08903	−0.340626
$713$	0.571393	0.0213989
$714$	−0.0831850	−0.00311312
$715$	22.4769	0.840588
$716$	15.6617	0.585304
$717$	−8.36692	−0.312468
$718$	0.0603918	0.00225380
$719$	−14.5240	−0.541653	−0.270827	−	0.962628i	$-0.587297\pi$
$719$	−14.5240	−0.541653	−0.270827	+	0.962628i	$0.587297\pi$
$720$	−26.2074	−0.976693
$721$	9.73415	0.362519
$722$	−1.09463	−0.0407381
$723$	4.13389	0.153741
$724$	3.18191	0.118255
$725$	4.04182	0.150109
$726$	−0.409751	−0.0152073
$727$	−39.1073	−1.45041	−0.725205	−	0.688534i	$-0.758255\pi$
$727$	−39.1073	−1.45041	−0.725205	+	0.688534i	$0.758255\pi$
$728$	4.81637	0.178507
$729$	−20.2773	−0.751010
$730$	4.34046	0.160648
$731$	−1.00000	−0.0369863
$732$	6.82831	0.252382
$733$	47.6588	1.76032	0.880158	−	0.474680i	$-0.157436\pi$
$733$	47.6588	1.76032	0.880158	+	0.474680i	$0.157436\pi$
$734$	1.40254	0.0517686
$735$	−3.87253	−0.142840
$736$	9.08439	0.334855
$737$	13.2905	0.489563
$738$	−1.59445	−0.0586926
$739$	7.41220	0.272662	0.136331	−	0.990663i	$-0.456469\pi$
$739$	7.41220	0.272662	0.136331	+	0.990663i	$0.456469\pi$
$740$	0.0302635	0.00111251
$741$	6.40625	0.235340
$742$	−1.72360	−0.0632753
$743$	8.36447	0.306863	0.153431	−	0.988159i	$-0.450968\pi$
$743$	8.36447	0.306863	0.153431	+	0.988159i	$0.450968\pi$
$744$	−0.0234238	−0.000858759 0
$745$	−17.4924	−0.640872
$746$	−3.21898	−0.117855
$747$	23.8857	0.873933
$748$	−3.60260	−0.131724
$749$	25.9540	0.948340
$750$	−0.557702	−0.0203644
$751$	−43.8467	−1.59999	−0.799995	−	0.600007i	$-0.795165\pi$
$751$	−43.8467	−1.59999	−0.799995	+	0.600007i	$0.795165\pi$
$752$	−22.7279	−0.828803
$753$	3.18854	0.116197
$754$	5.51448	0.200826
$755$	−44.1504	−1.60680
$756$	−6.50719	−0.236664
$757$	30.5980	1.11210	0.556052	−	0.831148i	$-0.312316\pi$
$757$	30.5980	1.11210	0.556052	+	0.831148i	$0.312316\pi$
$758$	−0.413715	−0.0150268
$759$	3.38675	0.122931
$760$	−4.75162	−0.172359
$761$	10.2041	0.369898	0.184949	−	0.982748i	$-0.440788\pi$
$761$	10.2041	0.369898	0.184949	+	0.982748i	$0.440788\pi$
$762$	0.468521	0.0169727
$763$	25.0597	0.907222
$764$	1.10204	0.0398705
$765$	−6.77499	−0.244950
$766$	−2.10875	−0.0761923
$767$	46.2990	1.67176
$768$	5.12553	0.184952
$769$	0.714647	0.0257708	0.0128854	−	0.999917i	$-0.495898\pi$
$769$	0.714647	0.0257708	0.0128854	+	0.999917i	$0.495898\pi$
$770$	−0.995165	−0.0358633
$771$	−10.9759	−0.395289
$772$	−26.5824	−0.956722
$773$	−11.6419	−0.418731	−0.209365	−	0.977837i	$-0.567140\pi$
$773$	−11.6419	−0.418731	−0.209365	+	0.977837i	$0.567140\pi$
$774$	0.426183	0.0153188
$775$	0.0628179	0.00225649
$776$	2.32045	0.0832993
$777$	0.00363314	0.000130338 0
$778$	−0.225862	−0.00809754
$779$	12.7566	0.457051
$780$	−8.76985	−0.314011
$781$	−13.6959	−0.490078
$782$	0.768289	0.0274740
$783$	−14.9838	−0.535476
$784$	−17.6680	−0.630999
$785$	31.2252	1.11447
$786$	−0.142785	−0.00509298
$787$	14.9976	0.534606	0.267303	−	0.963613i	$-0.413868\pi$
$787$	14.9976	0.534606	0.267303	+	0.963613i	$0.413868\pi$
$788$	31.3112	1.11541
$789$	−4.44010	−0.158072
$790$	−1.33948	−0.0476565
$791$	−7.98769	−0.284010
$792$	3.08784	0.109722
$793$	−50.2469	−1.78432
$794$	3.56674	0.126579
$795$	6.31176	0.223855
$796$	−29.0447	−1.02946
$797$	−21.4764	−0.760734	−0.380367	−	0.924836i	$-0.624202\pi$
$797$	−21.4764	−0.760734	−0.380367	+	0.924836i	$0.624202\pi$
$798$	−0.283637	−0.0100406
$799$	−5.87549	−0.207860
$800$	0.998721	0.0353101
$801$	−44.1877	−1.56130
$802$	1.95049	0.0688742
$803$	22.5668	0.796367
$804$	−5.18558	−0.182881
$805$	−19.0489	−0.671387
$806$	0.0857061	0.00301887
$807$	−8.09155	−0.284836
$808$	−3.49975	−0.123121
$809$	4.17977	0.146953	0.0734765	−	0.997297i	$-0.476591\pi$
$809$	4.17977	0.146953	0.0734765	+	0.997297i	$0.476591\pi$
$810$	2.75172	0.0966856
$811$	42.3334	1.48653	0.743263	−	0.669000i	$-0.233277\pi$
$811$	42.3334	1.48653	0.743263	+	0.669000i	$0.233277\pi$
$812$	21.9145	0.769047
$813$	11.2915	0.396011
$814$	−0.00175302	−6.14432e−5 0
$815$	−9.26437	−0.324517
$816$	1.38980	0.0486527
$817$	−3.40972	−0.119291
$818$	2.67845	0.0936498
$819$	23.4156	0.818206
$820$	−17.4631	−0.609838
$821$	28.8921	1.00834	0.504170	−	0.863604i	$-0.331799\pi$
$821$	28.8921	1.00834	0.504170	+	0.863604i	$0.331799\pi$
$822$	0.0866303	0.00302158
$823$	−44.0809	−1.53656	−0.768282	−	0.640112i	$-0.778888\pi$
$823$	−44.0809	−1.53656	−0.768282	+	0.640112i	$0.778888\pi$
$824$	3.68553	0.128392
$825$	0.372333	0.0129630
$826$	−2.04989	−0.0713248
$827$	−29.7341	−1.03396	−0.516978	−	0.855999i	$-0.672943\pi$
$827$	−29.7341	−1.03396	−0.516978	+	0.855999i	$0.672943\pi$
$828$	29.3892	1.02135
$829$	−49.0302	−1.70289	−0.851444	−	0.524446i	$-0.824273\pi$
$829$	−49.0302	−1.70289	−0.851444	+	0.524446i	$0.824273\pi$
$830$	−2.91462	−0.101168
$831$	2.72807	0.0946356
$832$	−39.0946	−1.35536
$833$	−4.56742	−0.158252
$834$	−0.0727048	−0.00251756
$835$	−31.7520	−1.09882
$836$	−12.2839	−0.424846
$837$	−0.232878	−0.00804943
$838$	−2.70478	−0.0934352
$839$	−2.23735	−0.0772418	−0.0386209	−	0.999254i	$-0.512296\pi$
$839$	−2.23735	−0.0772418	−0.0386209	+	0.999254i	$0.512296\pi$
$840$	0.780897	0.0269435
$841$	21.4613	0.740044
$842$	−0.608514	−0.0209708
$843$	−5.48732	−0.188993
$844$	27.7854	0.956413
$845$	33.8557	1.16467
$846$	2.50403	0.0860904
$847$	11.9824	0.411719
$848$	28.7967	0.988884
$849$	−7.34012	−0.251912
$850$	0.0844642	0.00289710
$851$	−0.0335553	−0.00115026
$852$	5.34375	0.183074
$853$	−26.0450	−0.891766	−0.445883	−	0.895091i	$-0.647110\pi$
$853$	−26.0450	−0.891766	−0.445883	+	0.895091i	$0.647110\pi$
$854$	2.22468	0.0761271
$855$	−23.1008	−0.790030
$856$	9.82669	0.335869
$857$	−56.3605	−1.92524	−0.962619	−	0.270861i	$-0.912692\pi$
$857$	−56.3605	−1.92524	−0.962619	+	0.270861i	$0.912692\pi$
$858$	0.507995	0.0173427
$859$	−18.6176	−0.635224	−0.317612	−	0.948221i	$-0.602881\pi$
$859$	−18.6176	−0.635224	−0.317612	+	0.948221i	$0.602881\pi$
$860$	4.66773	0.159168
$861$	−2.09645	−0.0714469
$862$	4.49192	0.152996
$863$	−21.6929	−0.738436	−0.369218	−	0.929343i	$-0.620374\pi$
$863$	−21.6929	−0.738436	−0.369218	+	0.929343i	$0.620374\pi$
$864$	−3.70244	−0.125960
$865$	14.4452	0.491151
$866$	1.68929	0.0574043
$867$	0.359282	0.0122019
$868$	0.340595	0.0115605
$869$	−6.96419	−0.236244
$870$	0.894083	0.0303123
$871$	38.1587	1.29296
$872$	9.48808	0.321307
$873$	11.2812	0.381812
$874$	2.61965	0.0886108
$875$	16.3089	0.551342
$876$	−8.80494	−0.297491
$877$	12.9658	0.437824	0.218912	−	0.975745i	$-0.429749\pi$
$877$	12.9658	0.437824	0.218912	+	0.975745i	$0.429749\pi$
$878$	4.30453	0.145271
$879$	−1.56553	−0.0528039
$880$	16.6266	0.560481
$881$	−44.6102	−1.50295	−0.751477	−	0.659759i	$-0.770658\pi$
$881$	−44.6102	−1.50295	−0.751477	+	0.659759i	$0.770658\pi$
$882$	1.94655	0.0655439
$883$	−28.8409	−0.970573	−0.485287	−	0.874355i	$-0.661285\pi$
$883$	−28.8409	−0.970573	−0.485287	+	0.874355i	$0.661285\pi$
$884$	−10.3435	−0.347890
$885$	7.50663	0.252333
$886$	−4.08350	−0.137188
$887$	−42.6809	−1.43308	−0.716542	−	0.697544i	$-0.754276\pi$
$887$	−42.6809	−1.43308	−0.716542	+	0.697544i	$0.754276\pi$
$888$	0.00137557	4.61613e−5 0
$889$	−13.7010	−0.459517
$890$	5.39193	0.180738
$891$	14.3067	0.479292
$892$	17.2024	0.575978
$893$	−20.0337	−0.670404
$894$	−0.395342	−0.0132222
$895$	−18.6856	−0.624591
$896$	7.20625	0.240744
$897$	9.72378	0.324668
$898$	−4.23049	−0.141173
$899$	0.784269	0.0261568
$900$	3.23099	0.107700
$901$	7.44435	0.248007
$902$	1.01155	0.0336811
$903$	0.560363	0.0186477
$904$	−3.02429	−0.100586
$905$	−3.79627	−0.126192
$906$	−0.997832	−0.0331507
$907$	−23.4574	−0.778890	−0.389445	−	0.921050i	$-0.627333\pi$
$907$	−23.4574	−0.778890	−0.389445	+	0.921050i	$0.627333\pi$
$908$	−9.54047	−0.316612
$909$	−17.0146	−0.564338
$910$	−2.85724	−0.0947167
$911$	55.6798	1.84476	0.922378	−	0.386289i	$-0.126243\pi$
$911$	55.6798	1.84476	0.922378	+	0.386289i	$0.126243\pi$
$912$	4.73882	0.156918
$913$	−15.1536	−0.501512
$914$	−3.43046	−0.113470
$915$	−8.14672	−0.269322
$916$	−57.8148	−1.91025
$917$	4.17548	0.137886
$918$	−0.313124	−0.0103346
$919$	−34.0713	−1.12391	−0.561955	−	0.827168i	$-0.689951\pi$
$919$	−34.0713	−1.12391	−0.561955	+	0.827168i	$0.689951\pi$
$920$	−7.21229	−0.237782
$921$	−9.04820	−0.298148
$922$	−3.65530	−0.120381
$923$	−39.3226	−1.29432
$924$	2.01877	0.0664125
$925$	−0.00368901	−0.000121294 0
$926$	2.29286	0.0753479
$927$	17.9178	0.588498
$928$	12.4688	0.409309
$929$	15.1082	0.495684	0.247842	−	0.968800i	$-0.420279\pi$
$929$	15.1082	0.495684	0.247842	+	0.968800i	$0.420279\pi$
$930$	0.0138958	0.000455663 0
$931$	−15.5736	−0.510404
$932$	−36.1716	−1.18484
$933$	10.2107	0.334285
$934$	−3.10332	−0.101544
$935$	4.29819	0.140566
$936$	8.86557	0.289780
$937$	49.7020	1.62369	0.811846	−	0.583872i	$-0.198463\pi$
$937$	49.7020	1.62369	0.811846	+	0.583872i	$0.198463\pi$
$938$	−1.68948	−0.0551634
$939$	−2.40705	−0.0785512
$940$	27.4252	0.894512
$941$	15.3482	0.500336	0.250168	−	0.968202i	$-0.419514\pi$
$941$	15.3482	0.500336	0.250168	+	0.968202i	$0.419514\pi$
$942$	0.705713	0.0229934
$943$	19.3627	0.630535
$944$	34.2482	1.11468
$945$	7.76360	0.252550
$946$	−0.270379	−0.00879079
$947$	−15.4243	−0.501222	−0.250611	−	0.968088i	$-0.580631\pi$
$947$	−15.4243	−0.501222	−0.250611	+	0.968088i	$0.580631\pi$
$948$	2.71723	0.0882515
$949$	64.7922	2.10324
$950$	0.287999	0.00934392
$951$	4.95308	0.160615
$952$	0.921022	0.0298505
$953$	−18.4839	−0.598754	−0.299377	−	0.954135i	$-0.596779\pi$
$953$	−18.4839	−0.598754	−0.299377	+	0.954135i	$0.596779\pi$
$954$	−3.17265	−0.102718
$955$	−1.31482	−0.0425467
$956$	46.0625	1.48977
$957$	4.64850	0.150265
$958$	2.91810	0.0942796
$959$	−2.53334	−0.0818057
$960$	−6.33856	−0.204576
$961$	−30.9878	−0.999607
$962$	−0.00503313	−0.000162275 0
$963$	47.7740	1.53950
$964$	−22.7584	−0.732997
$965$	31.7149	1.02094
$966$	−0.430521	−0.0138518
$967$	−1.54153	−0.0495723	−0.0247862	−	0.999693i	$-0.507890\pi$
$967$	−1.54153	−0.0495723	−0.0247862	+	0.999693i	$0.507890\pi$
$968$	4.53675	0.145817
$969$	1.22505	0.0393543
$970$	−1.37657	−0.0441991
$971$	−55.8875	−1.79352	−0.896758	−	0.442521i	$-0.854084\pi$
$971$	−55.8875	−1.79352	−0.896758	+	0.442521i	$0.854084\pi$
$972$	−18.0985	−0.580510
$973$	2.12611	0.0681600
$974$	−3.47046	−0.111201
$975$	1.06901	0.0342359
$976$	−37.1685	−1.18974
$977$	−44.3999	−1.42048	−0.710240	−	0.703960i	$-0.751413\pi$
$977$	−44.3999	−1.42048	−0.710240	+	0.703960i	$0.751413\pi$
$978$	−0.209382	−0.00669530
$979$	28.0336	0.895959
$980$	21.3195	0.681026
$981$	46.1278	1.47275
$982$	3.41789	0.109069
$983$	25.6483	0.818055	0.409027	−	0.912522i	$-0.365868\pi$
$983$	25.6483	0.818055	0.409027	+	0.912522i	$0.365868\pi$
$984$	−0.793757	−0.0253040
$985$	−37.3567	−1.19028
$986$	1.05452	0.0335827
$987$	3.29241	0.104799
$988$	−35.2685	−1.12204
$989$	−5.17546	−0.164570
$990$	−1.83182	−0.0582189
$991$	58.2360	1.84993	0.924964	−	0.380054i	$-0.124095\pi$
$991$	58.2360	1.84993	0.924964	+	0.380054i	$0.124095\pi$
$992$	0.193791	0.00615286
$993$	−4.33783	−0.137657
$994$	1.74101	0.0552215
$995$	34.6527	1.09856
$996$	5.91251	0.187345
$997$	33.1238	1.04904	0.524521	−	0.851397i	$-0.324244\pi$
$997$	33.1238	1.04904	0.524521	+	0.851397i	$0.324244\pi$
$998$	−5.96436	−0.188798
$999$	0.0136758	0.000432684 0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	731.2.a.e.1.10	✓	19
3.2	odd	2		6579.2.a.t.1.10		19

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
731.2.a.e.1.10	✓	19	1.1	even	1	trivial
6579.2.a.t.1.10		19	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 731 = 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	731.a (trivial)

\(f(q)\)	\(=\)	\(q+0.148448 q^{2} +0.359282 q^{3} -1.97796 q^{4} +2.35987 q^{5} +0.0533348 q^{6} -1.55967 q^{7} -0.590522 q^{8} -2.87092 q^{9} +O(q^{10})\)	\(q+0.148448 q^{2} +0.359282 q^{3} -1.97796 q^{4} +2.35987 q^{5} +0.0533348 q^{6} -1.55967 q^{7} -0.590522 q^{8} -2.87092 q^{9} +0.350319 q^{10} +1.82137 q^{11} -0.710647 q^{12} +5.22938 q^{13} -0.231531 q^{14} +0.847859 q^{15} +3.86826 q^{16} +1.00000 q^{17} -0.426183 q^{18} +3.40972 q^{19} -4.66773 q^{20} -0.560363 q^{21} +0.270379 q^{22} +5.17546 q^{23} -0.212164 q^{24} +0.568981 q^{25} +0.776293 q^{26} -2.10932 q^{27} +3.08498 q^{28} +7.10361 q^{29} +0.125863 q^{30} +0.110404 q^{31} +1.75528 q^{32} +0.654386 q^{33} +0.148448 q^{34} -3.68063 q^{35} +5.67857 q^{36} -0.00648354 q^{37} +0.506166 q^{38} +1.87882 q^{39} -1.39355 q^{40} +3.74124 q^{41} -0.0831850 q^{42} -1.00000 q^{43} -3.60260 q^{44} -6.77499 q^{45} +0.768289 q^{46} -5.87549 q^{47} +1.38980 q^{48} -4.56742 q^{49} +0.0844642 q^{50} +0.359282 q^{51} -10.3435 q^{52} +7.44435 q^{53} -0.313124 q^{54} +4.29819 q^{55} +0.921022 q^{56} +1.22505 q^{57} +1.05452 q^{58} +8.85363 q^{59} -1.67703 q^{60} -9.60858 q^{61} +0.0163893 q^{62} +4.47769 q^{63} -7.47596 q^{64} +12.3407 q^{65} +0.0971425 q^{66} +7.29699 q^{67} -1.97796 q^{68} +1.85945 q^{69} -0.546383 q^{70} -7.51956 q^{71} +1.69534 q^{72} +12.3900 q^{73} -0.000962471 q^{74} +0.204425 q^{75} -6.74429 q^{76} -2.84074 q^{77} +0.278908 q^{78} -3.82360 q^{79} +9.12860 q^{80} +7.85491 q^{81} +0.555381 q^{82} -8.31990 q^{83} +1.10838 q^{84} +2.35987 q^{85} -0.148448 q^{86} +2.55220 q^{87} -1.07556 q^{88} +15.3915 q^{89} -1.00574 q^{90} -8.15613 q^{91} -10.2369 q^{92} +0.0396663 q^{93} -0.872207 q^{94} +8.04648 q^{95} +0.630641 q^{96} -3.92949 q^{97} -0.678025 q^{98} -5.22900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9}+O(q^{10}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9	\( 19 q + 2 q^{2} + 5 q^{3} + 26 q^{4} + 11 q^{5} + 3 q^{6} + 7 q^{7} - 6 q^{8} + 28 q^{9} - 2 q^{10} + 4 q^{11} + 9 q^{12} + 14 q^{13} + 5 q^{14} - 7 q^{15} + 32 q^{16} + 19 q^{17} + 12 q^{18} + 12 q^{19} + 23 q^{20} + 16 q^{21} + 36 q^{22} - q^{23} - 13 q^{24} + 30 q^{25} - 21 q^{26} + 8 q^{27} + 5 q^{28} + 41 q^{29} - 26 q^{30} - 8 q^{31} - 20 q^{32} - 14 q^{33} + 2 q^{34} + 3 q^{35} - 5 q^{36} + 50 q^{37} - 29 q^{38} + 17 q^{39} - 15 q^{40} + 6 q^{41} - q^{42} - 19 q^{43} + 16 q^{44} + 24 q^{45} + 38 q^{46} - 21 q^{47} - 2 q^{48} + 46 q^{49} - 36 q^{50} + 5 q^{51} + 39 q^{52} - 9 q^{53} + 53 q^{54} + 10 q^{55} - 12 q^{56} - 5 q^{57} - 45 q^{58} - 4 q^{59} - 7 q^{60} + 68 q^{61} - 25 q^{62} + 61 q^{63} - 14 q^{64} + 22 q^{65} - 17 q^{66} + 26 q^{68} - 9 q^{69} - 37 q^{70} + 23 q^{71} - 4 q^{72} - q^{73} - 30 q^{74} - 25 q^{75} + 47 q^{76} - 19 q^{77} + 12 q^{78} + 16 q^{79} + 28 q^{80} - 21 q^{81} - 13 q^{82} - 32 q^{83} - 47 q^{84} + 11 q^{85} - 2 q^{86} - 8 q^{87} + 108 q^{88} + 11 q^{89} + 5 q^{90} + 52 q^{91} - 23 q^{92} - 23 q^{93} + 47 q^{94} - 25 q^{95} - 103 q^{96} + 36 q^{97} - 100 q^{98} - 11 q^{99}+O(q^{100}) \) 19 * q + 2 * q^2 + 5 * q^3 + 26 * q^4 + 11 * q^5 + 3 * q^6 + 7 * q^7 - 6 * q^8 + 28 * q^9 - 2 * q^10 + 4 * q^11 + 9 * q^12 + 14 * q^13 + 5 * q^14 - 7 * q^15 + 32 * q^16 + 19 * q^17 + 12 * q^18 + 12 * q^19 + 23 * q^20 + 16 * q^21 + 36 * q^22 - q^23 - 13 * q^24 + 30 * q^25 - 21 * q^26 + 8 * q^27 + 5 * q^28 + 41 * q^29 - 26 * q^30 - 8 * q^31 - 20 * q^32 - 14 * q^33 + 2 * q^34 + 3 * q^35 - 5 * q^36 + 50 * q^37 - 29 * q^38 + 17 * q^39 - 15 * q^40 + 6 * q^41 - q^42 - 19 * q^43 + 16 * q^44 + 24 * q^45 + 38 * q^46 - 21 * q^47 - 2 * q^48 + 46 * q^49 - 36 * q^50 + 5 * q^51 + 39 * q^52 - 9 * q^53 + 53 * q^54 + 10 * q^55 - 12 * q^56 - 5 * q^57 - 45 * q^58 - 4 * q^59 - 7 * q^60 + 68 * q^61 - 25 * q^62 + 61 * q^63 - 14 * q^64 + 22 * q^65 - 17 * q^66 + 26 * q^68 - 9 * q^69 - 37 * q^70 + 23 * q^71 - 4 * q^72 - q^73 - 30 * q^74 - 25 * q^75 + 47 * q^76 - 19 * q^77 + 12 * q^78 + 16 * q^79 + 28 * q^80 - 21 * q^81 - 13 * q^82 - 32 * q^83 - 47 * q^84 + 11 * q^85 - 2 * q^86 - 8 * q^87 + 108 * q^88 + 11 * q^89 + 5 * q^90 + 52 * q^91 - 23 * q^92 - 23 * q^93 + 47 * q^94 - 25 * q^95 - 103 * q^96 + 36 * q^97 - 100 * q^98 - 11 * q^99

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