LMFDB - Embedded newform 4017.2.a.l.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.85552 q^{2} +1.00000 q^{3} +1.44297 q^{4} +3.38665 q^{5} -1.85552 q^{6} -2.21342 q^{7} +1.03358 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.85552 q^{2} +1.00000 q^{3} +1.44297 q^{4} +3.38665 q^{5} -1.85552 q^{6} -2.21342 q^{7} +1.03358 q^{8} +1.00000 q^{9} -6.28400 q^{10} -3.17620 q^{11} +1.44297 q^{12} -1.00000 q^{13} +4.10706 q^{14} +3.38665 q^{15} -4.80378 q^{16} +2.20037 q^{17} -1.85552 q^{18} +0.991895 q^{19} +4.88683 q^{20} -2.21342 q^{21} +5.89352 q^{22} +8.85024 q^{23} +1.03358 q^{24} +6.46937 q^{25} +1.85552 q^{26} +1.00000 q^{27} -3.19391 q^{28} -3.51866 q^{29} -6.28400 q^{30} +3.53135 q^{31} +6.84636 q^{32} -3.17620 q^{33} -4.08285 q^{34} -7.49608 q^{35} +1.44297 q^{36} -11.0969 q^{37} -1.84049 q^{38} -1.00000 q^{39} +3.50038 q^{40} +2.73100 q^{41} +4.10706 q^{42} -0.852494 q^{43} -4.58317 q^{44} +3.38665 q^{45} -16.4218 q^{46} -7.14240 q^{47} -4.80378 q^{48} -2.10075 q^{49} -12.0041 q^{50} +2.20037 q^{51} -1.44297 q^{52} +9.36036 q^{53} -1.85552 q^{54} -10.7567 q^{55} -2.28776 q^{56} +0.991895 q^{57} +6.52896 q^{58} +12.1511 q^{59} +4.88683 q^{60} +8.02903 q^{61} -6.55250 q^{62} -2.21342 q^{63} -3.09603 q^{64} -3.38665 q^{65} +5.89352 q^{66} +11.7960 q^{67} +3.17507 q^{68} +8.85024 q^{69} +13.9092 q^{70} -5.39703 q^{71} +1.03358 q^{72} -13.2496 q^{73} +20.5906 q^{74} +6.46937 q^{75} +1.43128 q^{76} +7.03029 q^{77} +1.85552 q^{78} +12.1228 q^{79} -16.2687 q^{80} +1.00000 q^{81} -5.06744 q^{82} +17.1387 q^{83} -3.19391 q^{84} +7.45188 q^{85} +1.58182 q^{86} -3.51866 q^{87} -3.28287 q^{88} +2.53375 q^{89} -6.28400 q^{90} +2.21342 q^{91} +12.7706 q^{92} +3.53135 q^{93} +13.2529 q^{94} +3.35920 q^{95} +6.84636 q^{96} +10.1799 q^{97} +3.89800 q^{98} -3.17620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) $ 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.85552	−1.31205	−0.656027	−	0.754738i	$-0.727764\pi$
$2$	−1.85552	−1.31205	−0.656027	+	0.754738i	$0.727764\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.44297	0.721485
$5$	3.38665	1.51455	0.757277	−	0.653094i	$-0.226529\pi$
$5$	3.38665	1.51455	0.757277	+	0.653094i	$0.226529\pi$
$6$	−1.85552	−0.757515
$7$	−2.21342	−0.836596	−0.418298	−	0.908310i	$-0.637373\pi$
$7$	−2.21342	−0.836596	−0.418298	+	0.908310i	$0.637373\pi$
$8$	1.03358	0.365426
$9$	1.00000	0.333333
$10$	−6.28400	−1.98718
$11$	−3.17620	−0.957662	−0.478831	−	0.877907i	$-0.658939\pi$
$11$	−3.17620	−0.957662	−0.478831	+	0.877907i	$0.658939\pi$
$12$	1.44297	0.416550
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	4.10706	1.09766
$15$	3.38665	0.874428
$16$	−4.80378	−1.20094
$17$	2.20037	0.533669	0.266835	−	0.963742i	$-0.414022\pi$
$17$	2.20037	0.533669	0.266835	+	0.963742i	$0.414022\pi$
$18$	−1.85552	−0.437351
$19$	0.991895	0.227556	0.113778	−	0.993506i	$-0.463705\pi$
$19$	0.991895	0.227556	0.113778	+	0.993506i	$0.463705\pi$
$20$	4.88683	1.09273
$21$	−2.21342	−0.483009
$22$	5.89352	1.25650
$23$	8.85024	1.84540	0.922702	−	0.385515i	$-0.125976\pi$
$23$	8.85024	1.84540	0.922702	+	0.385515i	$0.125976\pi$
$24$	1.03358	0.210979
$25$	6.46937	1.29387
$26$	1.85552	0.363898
$27$	1.00000	0.192450
$28$	−3.19391	−0.603591
$29$	−3.51866	−0.653399	−0.326699	−	0.945128i	$-0.605936\pi$
$29$	−3.51866	−0.653399	−0.326699	+	0.945128i	$0.605936\pi$
$30$	−6.28400	−1.14730
$31$	3.53135	0.634249	0.317124	−	0.948384i	$-0.397283\pi$
$31$	3.53135	0.634249	0.317124	+	0.948384i	$0.397283\pi$
$32$	6.84636	1.21028
$33$	−3.17620	−0.552906
$34$	−4.08285	−0.700202
$35$	−7.49608	−1.26707
$36$	1.44297	0.240495
$37$	−11.0969	−1.82432	−0.912162	−	0.409830i	$-0.865588\pi$
$37$	−11.0969	−1.82432	−0.912162	+	0.409830i	$0.865588\pi$
$38$	−1.84049	−0.298566
$39$	−1.00000	−0.160128
$40$	3.50038	0.553458
$41$	2.73100	0.426511	0.213256	−	0.976996i	$-0.431593\pi$
$41$	2.73100	0.426511	0.213256	+	0.976996i	$0.431593\pi$
$42$	4.10706	0.633734
$43$	−0.852494	−0.130004	−0.0650020	−	0.997885i	$-0.520705\pi$
$43$	−0.852494	−0.130004	−0.0650020	+	0.997885i	$0.520705\pi$
$44$	−4.58317	−0.690939
$45$	3.38665	0.504851
$46$	−16.4218	−2.42127
$47$	−7.14240	−1.04183	−0.520913	−	0.853610i	$-0.674409\pi$
$47$	−7.14240	−1.04183	−0.520913	+	0.853610i	$0.674409\pi$
$48$	−4.80378	−0.693366
$49$	−2.10075	−0.300107
$50$	−12.0041	−1.69763
$51$	2.20037	0.308114
$52$	−1.44297	−0.200104
$53$	9.36036	1.28574	0.642872	−	0.765974i	$-0.277743\pi$
$53$	9.36036	1.28574	0.642872	+	0.765974i	$0.277743\pi$
$54$	−1.85552	−0.252505
$55$	−10.7567	−1.45043
$56$	−2.28776	−0.305714
$57$	0.991895	0.131380
$58$	6.52896	0.857294
$59$	12.1511	1.58194	0.790968	−	0.611858i	$-0.209577\pi$
$59$	12.1511	1.58194	0.790968	+	0.611858i	$0.209577\pi$
$60$	4.88683	0.630887
$61$	8.02903	1.02801	0.514006	−	0.857787i	$-0.328161\pi$
$61$	8.02903	1.02801	0.514006	+	0.857787i	$0.328161\pi$
$62$	−6.55250	−0.832168
$63$	−2.21342	−0.278865
$64$	−3.09603	−0.387004
$65$	−3.38665	−0.420062
$66$	5.89352	0.725443
$67$	11.7960	1.44111	0.720557	−	0.693395i	$-0.243886\pi$
$67$	11.7960	1.44111	0.720557	+	0.693395i	$0.243886\pi$
$68$	3.17507	0.385034
$69$	8.85024	1.06544
$70$	13.9092	1.66246
$71$	−5.39703	−0.640509	−0.320255	−	0.947331i	$-0.603768\pi$
$71$	−5.39703	−0.640509	−0.320255	+	0.947331i	$0.603768\pi$
$72$	1.03358	0.121809
$73$	−13.2496	−1.55075	−0.775375	−	0.631502i	$-0.782439\pi$
$73$	−13.2496	−1.55075	−0.775375	+	0.631502i	$0.782439\pi$
$74$	20.5906	2.39361
$75$	6.46937	0.747018
$76$	1.43128	0.164179
$77$	7.03029	0.801176
$78$	1.85552	0.210097
$79$	12.1228	1.36392	0.681960	−	0.731390i	$-0.261128\pi$
$79$	12.1228	1.36392	0.681960	+	0.731390i	$0.261128\pi$
$80$	−16.2687	−1.81889
$81$	1.00000	0.111111
$82$	−5.06744	−0.559606
$83$	17.1387	1.88122	0.940609	−	0.339491i	$-0.110255\pi$
$83$	17.1387	1.88122	0.940609	+	0.339491i	$0.110255\pi$
$84$	−3.19391	−0.348484
$85$	7.45188	0.808270
$86$	1.58182	0.170572
$87$	−3.51866	−0.377240
$88$	−3.28287	−0.349955
$89$	2.53375	0.268577	0.134289	−	0.990942i	$-0.457125\pi$
$89$	2.53375	0.268577	0.134289	+	0.990942i	$0.457125\pi$
$90$	−6.28400	−0.662392
$91$	2.21342	0.232030
$92$	12.7706	1.33143
$93$	3.53135	0.366184
$94$	13.2529	1.36693
$95$	3.35920	0.344646
$96$	6.84636	0.698754
$97$	10.1799	1.03361	0.516807	−	0.856102i	$-0.327121\pi$
$97$	10.1799	1.03361	0.516807	+	0.856102i	$0.327121\pi$
$98$	3.89800	0.393757
$99$	−3.17620	−0.319221
$100$	9.33510	0.933510
$101$	7.96012	0.792061	0.396031	−	0.918237i	$-0.370387\pi$
$101$	7.96012	0.792061	0.396031	+	0.918237i	$0.370387\pi$
$102$	−4.08285	−0.404262
$103$	−1.00000	−0.0985329
$103$	−1.00000	−0.0985329
$104$	−1.03358	−0.101351
$105$	−7.49608	−0.731543
$106$	−17.3684	−1.68696
$107$	−5.11308	−0.494300	−0.247150	−	0.968977i	$-0.579494\pi$
$107$	−5.11308	−0.494300	−0.247150	+	0.968977i	$0.579494\pi$
$108$	1.44297	0.138850
$109$	7.20429	0.690046	0.345023	−	0.938594i	$-0.387871\pi$
$109$	7.20429	0.690046	0.345023	+	0.938594i	$0.387871\pi$
$110$	19.9593	1.90304
$111$	−11.0969	−1.05327
$112$	10.6328	1.00470
$113$	−7.39021	−0.695213	−0.347606	−	0.937641i	$-0.613005\pi$
$113$	−7.39021	−0.695213	−0.347606	+	0.937641i	$0.613005\pi$
$114$	−1.84049	−0.172377
$115$	29.9726	2.79496
$116$	−5.07732	−0.471418
$117$	−1.00000	−0.0924500
$118$	−22.5466	−2.07558
$119$	−4.87036	−0.446465
$120$	3.50038	0.319539
$121$	−0.911727	−0.0828843
$122$	−14.8981	−1.34881
$123$	2.73100	0.246246
$124$	5.09563	0.457601
$125$	4.97622	0.445087
$126$	4.10706	0.365886
$127$	−0.112993	−0.0100265	−0.00501323	−	0.999987i	$-0.501596\pi$
$127$	−0.112993	−0.0100265	−0.00501323	+	0.999987i	$0.501596\pi$
$128$	−7.94796	−0.702507
$129$	−0.852494	−0.0750579
$130$	6.28400	0.551143
$131$	−10.3698	−0.906017	−0.453009	−	0.891506i	$-0.649649\pi$
$131$	−10.3698	−0.906017	−0.453009	+	0.891506i	$0.649649\pi$
$132$	−4.58317	−0.398914
$133$	−2.19549	−0.190373
$134$	−21.8878	−1.89082
$135$	3.38665	0.291476
$136$	2.27427	0.195017
$137$	5.68610	0.485796	0.242898	−	0.970052i	$-0.421902\pi$
$137$	5.68610	0.485796	0.242898	+	0.970052i	$0.421902\pi$
$138$	−16.4218	−1.39792
$139$	10.8518	0.920437	0.460218	−	0.887806i	$-0.347771\pi$
$139$	10.8518	0.920437	0.460218	+	0.887806i	$0.347771\pi$
$140$	−10.8166	−0.914172
$141$	−7.14240	−0.601499
$142$	10.0143	0.840383
$143$	3.17620	0.265608
$144$	−4.80378	−0.400315
$145$	−11.9165	−0.989608
$146$	24.5850	2.03467
$147$	−2.10075	−0.173267
$148$	−16.0125	−1.31622
$149$	−15.0345	−1.23168	−0.615839	−	0.787872i	$-0.711183\pi$
$149$	−15.0345	−1.23168	−0.615839	+	0.787872i	$0.711183\pi$
$150$	−12.0041	−0.980128
$151$	6.90990	0.562320	0.281160	−	0.959661i	$-0.409281\pi$
$151$	6.90990	0.562320	0.281160	+	0.959661i	$0.409281\pi$
$152$	1.02521	0.0831551
$153$	2.20037	0.177890
$154$	−13.0449	−1.05119
$155$	11.9594	0.960604
$156$	−1.44297	−0.115530
$157$	16.2797	1.29926	0.649632	−	0.760249i	$-0.274923\pi$
$157$	16.2797	1.29926	0.649632	+	0.760249i	$0.274923\pi$
$158$	−22.4941	−1.78954
$159$	9.36036	0.742324
$160$	23.1862	1.83303
$161$	−19.5893	−1.54386
$162$	−1.85552	−0.145784
$163$	11.1111	0.870286	0.435143	−	0.900361i	$-0.356698\pi$
$163$	11.1111	0.870286	0.435143	+	0.900361i	$0.356698\pi$
$164$	3.94076	0.307721
$165$	−10.7567	−0.837406
$166$	−31.8013	−2.46826
$167$	−20.6810	−1.60034	−0.800170	−	0.599773i	$-0.795258\pi$
$167$	−20.6810	−1.60034	−0.800170	+	0.599773i	$0.795258\pi$
$168$	−2.28776	−0.176504
$169$	1.00000	0.0769231
$170$	−13.8272	−1.06049
$171$	0.991895	0.0758521
$172$	−1.23012	−0.0937960
$173$	9.29298	0.706532	0.353266	−	0.935523i	$-0.385071\pi$
$173$	9.29298	0.706532	0.353266	+	0.935523i	$0.385071\pi$
$174$	6.52896	0.494959
$175$	−14.3195	−1.08245
$176$	15.2578	1.15010
$177$	12.1511	0.913331
$178$	−4.70144	−0.352388
$179$	12.7321	0.951640	0.475820	−	0.879543i	$-0.342151\pi$
$179$	12.7321	0.951640	0.475820	+	0.879543i	$0.342151\pi$
$180$	4.88683	0.364243
$181$	24.7935	1.84289	0.921444	−	0.388510i	$-0.127010\pi$
$181$	24.7935	1.84289	0.921444	+	0.388510i	$0.127010\pi$
$182$	−4.10706	−0.304436
$183$	8.02903	0.593523
$184$	9.14745	0.674359
$185$	−37.5814	−2.76304
$186$	−6.55250	−0.480453
$187$	−6.98884	−0.511074
$188$	−10.3063	−0.751662
$189$	−2.21342	−0.161003
$190$	−6.23307	−0.452195
$191$	7.00968	0.507202	0.253601	−	0.967309i	$-0.418385\pi$
$191$	7.00968	0.507202	0.253601	+	0.967309i	$0.418385\pi$
$192$	−3.09603	−0.223437
$193$	−6.80948	−0.490157	−0.245078	−	0.969503i	$-0.578814\pi$
$193$	−6.80948	−0.490157	−0.245078	+	0.969503i	$0.578814\pi$
$194$	−18.8891	−1.35616
$195$	−3.38665	−0.242523
$196$	−3.03132	−0.216523
$197$	−3.74469	−0.266798	−0.133399	−	0.991062i	$-0.542589\pi$
$197$	−3.74469	−0.266798	−0.133399	+	0.991062i	$0.542589\pi$
$198$	5.89352	0.418835
$199$	2.40580	0.170543	0.0852714	−	0.996358i	$-0.472824\pi$
$199$	2.40580	0.170543	0.0852714	+	0.996358i	$0.472824\pi$
$200$	6.68662	0.472815
$201$	11.7960	0.832028
$202$	−14.7702	−1.03923
$203$	7.78829	0.546631
$204$	3.17507	0.222300
$205$	9.24894	0.645974
$206$	1.85552	0.129281
$207$	8.85024	0.615134
$208$	4.80378	0.333082
$209$	−3.15046	−0.217922
$210$	13.9092	0.959824
$211$	−11.0519	−0.760841	−0.380420	−	0.924814i	$-0.624221\pi$
$211$	−11.0519	−0.760841	−0.380420	+	0.924814i	$0.624221\pi$
$212$	13.5067	0.927645
$213$	−5.39703	−0.369798
$214$	9.48744	0.648548
$215$	−2.88709	−0.196898
$216$	1.03358	0.0703264
$217$	−7.81637	−0.530610
$218$	−13.3677	−0.905377
$219$	−13.2496	−0.895325
$220$	−15.5216	−1.04646
$221$	−2.20037	−0.148013
$222$	20.5906	1.38195
$223$	8.15610	0.546173	0.273087	−	0.961989i	$-0.411955\pi$
$223$	8.15610	0.546173	0.273087	+	0.961989i	$0.411955\pi$
$224$	−15.1539	−1.01251
$225$	6.46937	0.431291
$226$	13.7127	0.912157
$227$	−21.7426	−1.44311	−0.721555	−	0.692357i	$-0.756572\pi$
$227$	−21.7426	−1.44311	−0.721555	+	0.692357i	$0.756572\pi$
$228$	1.43128	0.0947885
$229$	29.1979	1.92945	0.964726	−	0.263255i	$-0.0847962\pi$
$229$	29.1979	1.92945	0.964726	+	0.263255i	$0.0847962\pi$
$230$	−55.6149	−3.66714
$231$	7.03029	0.462559
$232$	−3.63682	−0.238769
$233$	−4.11104	−0.269323	−0.134662	−	0.990892i	$-0.542995\pi$
$233$	−4.11104	−0.269323	−0.134662	+	0.990892i	$0.542995\pi$
$234$	1.85552	0.121299
$235$	−24.1888	−1.57790
$236$	17.5336	1.14134
$237$	12.1228	0.787460
$238$	9.03707	0.585786
$239$	−12.0843	−0.781668	−0.390834	−	0.920461i	$-0.627813\pi$
$239$	−12.0843	−0.781668	−0.390834	+	0.920461i	$0.627813\pi$
$240$	−16.2687	−1.05014
$241$	−15.2517	−0.982449	−0.491224	−	0.871033i	$-0.663450\pi$
$241$	−15.2517	−0.982449	−0.491224	+	0.871033i	$0.663450\pi$
$242$	1.69173	0.108749
$243$	1.00000	0.0641500
$244$	11.5856	0.741695
$245$	−7.11450	−0.454529
$246$	−5.06744	−0.323088
$247$	−0.991895	−0.0631128
$248$	3.64994	0.231771
$249$	17.1387	1.08612
$250$	−9.23349	−0.583977
$251$	−8.70708	−0.549586	−0.274793	−	0.961503i	$-0.588609\pi$
$251$	−8.70708	−0.549586	−0.274793	+	0.961503i	$0.588609\pi$
$252$	−3.19391	−0.201197
$253$	−28.1102	−1.76727
$254$	0.209660	0.0131553
$255$	7.45188	0.466655
$256$	20.9397	1.30873
$257$	3.11347	0.194213	0.0971065	−	0.995274i	$-0.469041\pi$
$257$	3.11347	0.194213	0.0971065	+	0.995274i	$0.469041\pi$
$258$	1.58182	0.0984800
$259$	24.5622	1.52622
$260$	−4.88683	−0.303068
$261$	−3.51866	−0.217800
$262$	19.2415	1.18874
$263$	−7.67744	−0.473411	−0.236706	−	0.971581i	$-0.576068\pi$
$263$	−7.67744	−0.473411	−0.236706	+	0.971581i	$0.576068\pi$
$264$	−3.28287	−0.202047
$265$	31.7002	1.94733
$266$	4.07378	0.249779
$267$	2.53375	0.155063
$268$	17.0213	1.03974
$269$	4.19993	0.256075	0.128037	−	0.991769i	$-0.459132\pi$
$269$	4.19993	0.256075	0.128037	+	0.991769i	$0.459132\pi$
$270$	−6.28400	−0.382432
$271$	7.09594	0.431048	0.215524	−	0.976499i	$-0.430854\pi$
$271$	7.09594	0.431048	0.215524	+	0.976499i	$0.430854\pi$
$272$	−10.5701	−0.640907
$273$	2.21342	0.133963
$274$	−10.5507	−0.637391
$275$	−20.5480	−1.23909
$276$	12.7706	0.768702
$277$	−6.67179	−0.400869	−0.200434	−	0.979707i	$-0.564235\pi$
$277$	−6.67179	−0.400869	−0.200434	+	0.979707i	$0.564235\pi$
$278$	−20.1358	−1.20766
$279$	3.53135	0.211416
$280$	−7.74782	−0.463021
$281$	19.1031	1.13959	0.569797	−	0.821786i	$-0.307022\pi$
$281$	19.1031	1.13959	0.569797	+	0.821786i	$0.307022\pi$
$282$	13.2529	0.789199
$283$	15.4629	0.919177	0.459588	−	0.888132i	$-0.347997\pi$
$283$	15.4629	0.919177	0.459588	+	0.888132i	$0.347997\pi$
$284$	−7.78775	−0.462118
$285$	3.35920	0.198982
$286$	−5.89352	−0.348491
$287$	−6.04487	−0.356817
$288$	6.84636	0.403426
$289$	−12.1584	−0.715197
$290$	22.1113	1.29842
$291$	10.1799	0.596757
$292$	−19.1188	−1.11884
$293$	26.6563	1.55728	0.778638	−	0.627474i	$-0.215911\pi$
$293$	26.6563	1.55728	0.778638	+	0.627474i	$0.215911\pi$
$294$	3.89800	0.227336
$295$	41.1514	2.39593
$296$	−11.4696	−0.666656
$297$	−3.17620	−0.184302
$298$	27.8970	1.61603
$299$	−8.85024	−0.511823
$300$	9.33510	0.538962
$301$	1.88693	0.108761
$302$	−12.8215	−0.737794
$303$	7.96012	0.457297
$304$	−4.76484	−0.273283
$305$	27.1915	1.55698
$306$	−4.08285	−0.233401
$307$	9.10687	0.519756	0.259878	−	0.965641i	$-0.416318\pi$
$307$	9.10687	0.519756	0.259878	+	0.965641i	$0.416318\pi$
$308$	10.1445	0.578036
$309$	−1.00000	−0.0568880
$310$	−22.1910	−1.26036
$311$	−33.3769	−1.89263	−0.946314	−	0.323248i	$-0.895225\pi$
$311$	−33.3769	−1.89263	−0.946314	+	0.323248i	$0.895225\pi$
$312$	−1.03358	−0.0585151
$313$	−23.8795	−1.34975	−0.674875	−	0.737932i	$-0.735803\pi$
$313$	−23.8795	−1.34975	−0.674875	+	0.737932i	$0.735803\pi$
$314$	−30.2075	−1.70471
$315$	−7.49608	−0.422356
$316$	17.4928	0.984048
$317$	10.0895	0.566684	0.283342	−	0.959019i	$-0.408557\pi$
$317$	10.0895	0.566684	0.283342	+	0.959019i	$0.408557\pi$
$318$	−17.3684	−0.973970
$319$	11.1760	0.625735
$320$	−10.4852	−0.586139
$321$	−5.11308	−0.285384
$322$	36.3485	2.02562
$323$	2.18254	0.121440
$324$	1.44297	0.0801650
$325$	−6.46937	−0.358856
$326$	−20.6169	−1.14186
$327$	7.20429	0.398398
$328$	2.82272	0.155858
$329$	15.8092	0.871588
$330$	19.9593	1.09872
$331$	5.51330	0.303038	0.151519	−	0.988454i	$-0.451583\pi$
$331$	5.51330	0.303038	0.151519	+	0.988454i	$0.451583\pi$
$332$	24.7307	1.35727
$333$	−11.0969	−0.608108
$334$	38.3740	2.09973
$335$	39.9490	2.18265
$336$	10.6328	0.580067
$337$	2.08205	0.113417	0.0567083	−	0.998391i	$-0.481939\pi$
$337$	2.08205	0.113417	0.0567083	+	0.998391i	$0.481939\pi$
$338$	−1.85552	−0.100927
$339$	−7.39021	−0.401381
$340$	10.7528	0.583155
$341$	−11.2163	−0.607396
$342$	−1.84049	−0.0995221
$343$	20.1438	1.08766
$344$	−0.881122	−0.0475069
$345$	29.9726	1.61367
$346$	−17.2434	−0.927008
$347$	13.9017	0.746280	0.373140	−	0.927775i	$-0.378281\pi$
$347$	13.9017	0.746280	0.373140	+	0.927775i	$0.378281\pi$
$348$	−5.07732	−0.272173
$349$	−23.5009	−1.25797	−0.628987	−	0.777416i	$-0.716530\pi$
$349$	−23.5009	−1.25797	−0.628987	+	0.777416i	$0.716530\pi$
$350$	26.5701	1.42023
$351$	−1.00000	−0.0533761
$352$	−21.7454	−1.15904
$353$	−17.0727	−0.908689	−0.454344	−	0.890826i	$-0.650126\pi$
$353$	−17.0727	−0.908689	−0.454344	+	0.890826i	$0.650126\pi$
$354$	−22.5466	−1.19834
$355$	−18.2778	−0.970086
$356$	3.65613	0.193774
$357$	−4.87036	−0.257767
$358$	−23.6247	−1.24860
$359$	23.1909	1.22397	0.611984	−	0.790870i	$-0.290372\pi$
$359$	23.1909	1.22397	0.611984	+	0.790870i	$0.290372\pi$
$360$	3.50038	0.184486
$361$	−18.0161	−0.948218
$362$	−46.0050	−2.41797
$363$	−0.911727	−0.0478533
$364$	3.19391	0.167406
$365$	−44.8717	−2.34869
$366$	−14.8981	−0.778734
$367$	8.18820	0.427421	0.213710	−	0.976897i	$-0.431445\pi$
$367$	8.18820	0.427421	0.213710	+	0.976897i	$0.431445\pi$
$368$	−42.5146	−2.21623
$369$	2.73100	0.142170
$370$	69.7331	3.62525
$371$	−20.7184	−1.07565
$372$	5.09563	0.264196
$373$	9.69524	0.502001	0.251000	−	0.967987i	$-0.419240\pi$
$373$	9.69524	0.502001	0.251000	+	0.967987i	$0.419240\pi$
$374$	12.9680	0.670557
$375$	4.97622	0.256971
$376$	−7.38226	−0.380711
$377$	3.51866	0.181220
$378$	4.10706	0.211245
$379$	−5.01129	−0.257413	−0.128706	−	0.991683i	$-0.541082\pi$
$379$	−5.01129	−0.257413	−0.128706	+	0.991683i	$0.541082\pi$
$380$	4.84722	0.248657
$381$	−0.112993	−0.00578878
$382$	−13.0066	−0.665477
$383$	30.6698	1.56715	0.783577	−	0.621295i	$-0.213393\pi$
$383$	30.6698	1.56715	0.783577	+	0.621295i	$0.213393\pi$
$384$	−7.94796	−0.405592
$385$	23.8091	1.21342
$386$	12.6351	0.643112
$387$	−0.852494	−0.0433347
$388$	14.6893	0.745737
$389$	7.00163	0.354997	0.177498	−	0.984121i	$-0.443200\pi$
$389$	7.00163	0.354997	0.177498	+	0.984121i	$0.443200\pi$
$390$	6.28400	0.318203
$391$	19.4738	0.984835
$392$	−2.17130	−0.109667
$393$	−10.3698	−0.523089
$394$	6.94835	0.350053
$395$	41.0556	2.06573
$396$	−4.58317	−0.230313
$397$	−24.3254	−1.22086	−0.610430	−	0.792071i	$-0.709003\pi$
$397$	−24.3254	−1.22086	−0.610430	+	0.792071i	$0.709003\pi$
$398$	−4.46403	−0.223761
$399$	−2.19549	−0.109912
$400$	−31.0774	−1.55387
$401$	−18.9249	−0.945063	−0.472531	−	0.881314i	$-0.656660\pi$
$401$	−18.9249	−0.945063	−0.472531	+	0.881314i	$0.656660\pi$
$402$	−21.8878	−1.09167
$403$	−3.53135	−0.175909
$404$	11.4862	0.571461
$405$	3.38665	0.168284
$406$	−14.4514	−0.717209
$407$	35.2461	1.74709
$408$	2.27427	0.112593
$409$	−15.9933	−0.790818	−0.395409	−	0.918505i	$-0.629397\pi$
$409$	−15.9933	−0.790818	−0.395409	+	0.918505i	$0.629397\pi$
$410$	−17.1616	−0.847553
$411$	5.68610	0.280475
$412$	−1.44297	−0.0710900
$413$	−26.8955	−1.32344
$414$	−16.4218	−0.807089
$415$	58.0428	2.84921
$416$	−6.84636	−0.335670
$417$	10.8518	0.531415
$418$	5.84576	0.285925
$419$	38.2485	1.86856	0.934280	−	0.356540i	$-0.116044\pi$
$419$	38.2485	1.86856	0.934280	+	0.356540i	$0.116044\pi$
$420$	−10.8166	−0.527797
$421$	−16.8696	−0.822175	−0.411087	−	0.911596i	$-0.634851\pi$
$421$	−16.8696	−0.822175	−0.411087	+	0.911596i	$0.634851\pi$
$422$	20.5070	0.998264
$423$	−7.14240	−0.347276
$424$	9.67470	0.469845
$425$	14.2350	0.690500
$426$	10.0143	0.485195
$427$	−17.7716	−0.860030
$428$	−7.37802	−0.356630
$429$	3.17620	0.153349
$430$	5.35707	0.258341
$431$	7.90585	0.380812	0.190406	−	0.981705i	$-0.439020\pi$
$431$	7.90585	0.380812	0.190406	+	0.981705i	$0.439020\pi$
$432$	−4.80378	−0.231122
$433$	22.9605	1.10341	0.551705	−	0.834039i	$-0.313977\pi$
$433$	22.9605	1.10341	0.551705	+	0.834039i	$0.313977\pi$
$434$	14.5035	0.696189
$435$	−11.9165	−0.571350
$436$	10.3956	0.497858
$437$	8.77851	0.419933
$438$	24.5850	1.17472
$439$	25.6763	1.22546	0.612731	−	0.790291i	$-0.290071\pi$
$439$	25.6763	1.22546	0.612731	+	0.790291i	$0.290071\pi$
$440$	−11.1179	−0.530026
$441$	−2.10075	−0.100036
$442$	4.08285	0.194201
$443$	4.39923	0.209014	0.104507	−	0.994524i	$-0.466674\pi$
$443$	4.39923	0.209014	0.104507	+	0.994524i	$0.466674\pi$
$444$	−16.0125	−0.759922
$445$	8.58092	0.406775
$446$	−15.1338	−0.716608
$447$	−15.0345	−0.711110
$448$	6.85284	0.323766
$449$	36.1723	1.70708	0.853538	−	0.521030i	$-0.174452\pi$
$449$	36.1723	1.70708	0.853538	+	0.521030i	$0.174452\pi$
$450$	−12.0041	−0.565877
$451$	−8.67423	−0.408453
$452$	−10.6639	−0.501586
$453$	6.90990	0.324655
$454$	40.3440	1.89344
$455$	7.49608	0.351422
$456$	1.02521	0.0480096
$457$	17.6119	0.823849	0.411925	−	0.911218i	$-0.364857\pi$
$457$	17.6119	0.823849	0.411925	+	0.911218i	$0.364857\pi$
$458$	−54.1774	−2.53155
$459$	2.20037	0.102705
$460$	43.2496	2.01652
$461$	−24.4808	−1.14019	−0.570093	−	0.821580i	$-0.693093\pi$
$461$	−24.4808	−1.14019	−0.570093	+	0.821580i	$0.693093\pi$
$462$	−13.0449	−0.606902
$463$	−4.93579	−0.229386	−0.114693	−	0.993401i	$-0.536588\pi$
$463$	−4.93579	−0.229386	−0.114693	+	0.993401i	$0.536588\pi$
$464$	16.9029	0.784696
$465$	11.9594	0.554605
$466$	7.62814	0.353367
$467$	30.0946	1.39261	0.696307	−	0.717744i	$-0.254825\pi$
$467$	30.0946	1.39261	0.696307	+	0.717744i	$0.254825\pi$
$468$	−1.44297	−0.0667013
$469$	−26.1096	−1.20563
$470$	44.8829	2.07029
$471$	16.2797	0.750131
$472$	12.5591	0.578081
$473$	2.70769	0.124500
$474$	−22.4941	−1.03319
$475$	6.41693	0.294429
$476$	−7.02779	−0.322118
$477$	9.36036	0.428581
$478$	22.4227	1.02559
$479$	−22.3057	−1.01917	−0.509586	−	0.860420i	$-0.670201\pi$
$479$	−22.3057	−1.01917	−0.509586	+	0.860420i	$0.670201\pi$
$480$	23.1862	1.05830
$481$	11.0969	0.505976
$482$	28.2999	1.28903
$483$	−19.5893	−0.891346
$484$	−1.31560	−0.0597998
$485$	34.4757	1.56546
$486$	−1.85552	−0.0841683
$487$	−24.8828	−1.12755	−0.563773	−	0.825930i	$-0.690651\pi$
$487$	−24.8828	−1.12755	−0.563773	+	0.825930i	$0.690651\pi$
$488$	8.29866	0.375663
$489$	11.1111	0.502460
$490$	13.2011	0.596366
$491$	1.85141	0.0835530	0.0417765	−	0.999127i	$-0.486698\pi$
$491$	1.85141	0.0835530	0.0417765	+	0.999127i	$0.486698\pi$
$492$	3.94076	0.177663
$493$	−7.74237	−0.348699
$494$	1.84049	0.0828074
$495$	−10.7567	−0.483477
$496$	−16.9638	−0.761697
$497$	11.9459	0.535847
$498$	−31.8013	−1.42505
$499$	8.07321	0.361406	0.180703	−	0.983538i	$-0.442163\pi$
$499$	8.07321	0.361406	0.180703	+	0.983538i	$0.442163\pi$
$500$	7.18054	0.321123
$501$	−20.6810	−0.923957
$502$	16.1562	0.721087
$503$	7.35692	0.328029	0.164014	−	0.986458i	$-0.447556\pi$
$503$	7.35692	0.328029	0.164014	+	0.986458i	$0.447556\pi$
$504$	−2.28776	−0.101905
$505$	26.9581	1.19962
$506$	52.1591	2.31876
$507$	1.00000	0.0444116
$508$	−0.163045	−0.00723395
$509$	−21.7835	−0.965536	−0.482768	−	0.875748i	$-0.660368\pi$
$509$	−21.7835	−0.965536	−0.482768	+	0.875748i	$0.660368\pi$
$510$	−13.8272	−0.612277
$511$	29.3270	1.29735
$512$	−22.9582	−1.01462
$513$	0.991895	0.0437932
$514$	−5.77712	−0.254818
$515$	−3.38665	−0.149233
$516$	−1.23012	−0.0541532
$517$	22.6857	0.997717
$518$	−45.5758	−2.00249
$519$	9.29298	0.407917
$520$	−3.50038	−0.153502
$521$	3.31467	0.145218	0.0726092	−	0.997360i	$-0.476867\pi$
$521$	3.31467	0.145218	0.0726092	+	0.997360i	$0.476867\pi$
$522$	6.52896	0.285765
$523$	27.3571	1.19624	0.598122	−	0.801405i	$-0.295914\pi$
$523$	27.3571	1.19624	0.598122	+	0.801405i	$0.295914\pi$
$524$	−14.9634	−0.653678
$525$	−14.3195	−0.624952
$526$	14.2457	0.621141
$527$	7.77028	0.338479
$528$	15.2578	0.664010
$529$	55.3268	2.40551
$530$	−58.8205	−2.55500
$531$	12.1511	0.527312
$532$	−3.16802	−0.137351
$533$	−2.73100	−0.118293
$534$	−4.70144	−0.203451
$535$	−17.3162	−0.748643
$536$	12.1922	0.526622
$537$	12.7321	0.549430
$538$	−7.79308	−0.335984
$539$	6.67242	0.287401
$540$	4.88683	0.210296
$541$	8.65542	0.372126	0.186063	−	0.982538i	$-0.440427\pi$
$541$	8.65542	0.372126	0.186063	+	0.982538i	$0.440427\pi$
$542$	−13.1667	−0.565558
$543$	24.7935	1.06399
$544$	15.0646	0.645887
$545$	24.3984	1.04511
$546$	−4.10706	−0.175766
$547$	−13.4124	−0.573474	−0.286737	−	0.958009i	$-0.592571\pi$
$547$	−13.4124	−0.573474	−0.286737	+	0.958009i	$0.592571\pi$
$548$	8.20488	0.350495
$549$	8.02903	0.342671
$550$	38.1274	1.62576
$551$	−3.49014	−0.148685
$552$	9.14745	0.389341
$553$	−26.8329	−1.14105
$554$	12.3797	0.525961
$555$	−37.5814	−1.59524
$556$	15.6588	0.664082
$557$	−19.7344	−0.836172	−0.418086	−	0.908407i	$-0.637299\pi$
$557$	−19.7344	−0.836172	−0.418086	+	0.908407i	$0.637299\pi$
$558$	−6.55250	−0.277389
$559$	0.852494	0.0360566
$560$	36.0095	1.52168
$561$	−6.98884	−0.295069
$562$	−35.4462	−1.49521
$563$	40.5791	1.71020	0.855102	−	0.518460i	$-0.173494\pi$
$563$	40.5791	1.71020	0.855102	+	0.518460i	$0.173494\pi$
$564$	−10.3063	−0.433973
$565$	−25.0280	−1.05294
$566$	−28.6919	−1.20601
$567$	−2.21342	−0.0929551
$568$	−5.57827	−0.234059
$569$	−33.4290	−1.40142	−0.700708	−	0.713448i	$-0.747133\pi$
$569$	−33.4290	−1.40142	−0.700708	+	0.713448i	$0.747133\pi$
$570$	−6.23307	−0.261075
$571$	−19.8478	−0.830603	−0.415302	−	0.909684i	$-0.636324\pi$
$571$	−19.8478	−0.830603	−0.415302	+	0.909684i	$0.636324\pi$
$572$	4.58317	0.191632
$573$	7.00968	0.292833
$574$	11.2164	0.468164
$575$	57.2555	2.38772
$576$	−3.09603	−0.129001
$577$	3.36834	0.140226	0.0701129	−	0.997539i	$-0.477664\pi$
$577$	3.36834	0.140226	0.0701129	+	0.997539i	$0.477664\pi$
$578$	22.5601	0.938377
$579$	−6.80948	−0.282992
$580$	−17.1951	−0.713987
$581$	−37.9353	−1.57382
$582$	−18.8891	−0.782977
$583$	−29.7304	−1.23131
$584$	−13.6946	−0.566685
$585$	−3.38665	−0.140021
$586$	−49.4613	−2.04323
$587$	19.9688	0.824200	0.412100	−	0.911139i	$-0.364795\pi$
$587$	19.9688	0.824200	0.412100	+	0.911139i	$0.364795\pi$
$588$	−3.03132	−0.125010
$589$	3.50273	0.144327
$590$	−76.3574	−3.14358
$591$	−3.74469	−0.154036
$592$	53.3072	2.19091
$593$	−29.5294	−1.21263	−0.606313	−	0.795226i	$-0.707352\pi$
$593$	−29.5294	−1.21263	−0.606313	+	0.795226i	$0.707352\pi$
$594$	5.89352	0.241814
$595$	−16.4942	−0.676196
$596$	−21.6944	−0.888637
$597$	2.40580	0.0984630
$598$	16.4218	0.671539
$599$	−14.8425	−0.606447	−0.303223	−	0.952920i	$-0.598063\pi$
$599$	−14.8425	−0.606447	−0.303223	+	0.952920i	$0.598063\pi$
$600$	6.68662	0.272980
$601$	−4.00075	−0.163194	−0.0815970	−	0.996665i	$-0.526002\pi$
$601$	−4.00075	−0.163194	−0.0815970	+	0.996665i	$0.526002\pi$
$602$	−3.50125	−0.142700
$603$	11.7960	0.480372
$604$	9.97078	0.405705
$605$	−3.08770	−0.125533
$606$	−14.7702	−0.599998
$607$	44.4763	1.80524	0.902619	−	0.430441i	$-0.141642\pi$
$607$	44.4763	1.80524	0.902619	+	0.430441i	$0.141642\pi$
$608$	6.79087	0.275406
$609$	7.78829	0.315597
$610$	−50.4544	−2.04284
$611$	7.14240	0.288951
$612$	3.17507	0.128345
$613$	−14.1012	−0.569544	−0.284772	−	0.958595i	$-0.591918\pi$
$613$	−14.1012	−0.569544	−0.284772	+	0.958595i	$0.591918\pi$
$614$	−16.8980	−0.681948
$615$	9.24894	0.372953
$616$	7.26638	0.292771
$617$	47.8976	1.92829	0.964143	−	0.265383i	$-0.0854984\pi$
$617$	47.8976	1.92829	0.964143	+	0.265383i	$0.0854984\pi$
$618$	1.85552	0.0746401
$619$	30.0670	1.20850	0.604248	−	0.796796i	$-0.293474\pi$
$619$	30.0670	1.20850	0.604248	+	0.796796i	$0.293474\pi$
$620$	17.2571	0.693061
$621$	8.85024	0.355148
$622$	61.9316	2.48323
$623$	−5.60827	−0.224691
$624$	4.80378	0.192305
$625$	−15.4941	−0.619766
$626$	44.3091	1.77095
$627$	−3.15046	−0.125817
$628$	23.4912	0.937400
$629$	−24.4174	−0.973585
$630$	13.9092	0.554154
$631$	−36.0489	−1.43508	−0.717542	−	0.696516i	$-0.754733\pi$
$631$	−36.0489	−1.43508	−0.717542	+	0.696516i	$0.754733\pi$
$632$	12.5299	0.498412
$633$	−11.0519	−0.439272
$634$	−18.7213	−0.743519
$635$	−0.382666	−0.0151856
$636$	13.5067	0.535576
$637$	2.10075	0.0832348
$638$	−20.7373	−0.820998
$639$	−5.39703	−0.213503
$640$	−26.9169	−1.06398
$641$	−42.1204	−1.66365	−0.831827	−	0.555035i	$-0.812705\pi$
$641$	−42.1204	−1.66365	−0.831827	+	0.555035i	$0.812705\pi$
$642$	9.48744	0.374439
$643$	−8.53052	−0.336411	−0.168205	−	0.985752i	$-0.553797\pi$
$643$	−8.53052	−0.336411	−0.168205	+	0.985752i	$0.553797\pi$
$644$	−28.2668	−1.11387
$645$	−2.88709	−0.113679
$646$	−4.04976	−0.159336
$647$	−12.2482	−0.481525	−0.240762	−	0.970584i	$-0.577397\pi$
$647$	−12.2482	−0.481525	−0.240762	+	0.970584i	$0.577397\pi$
$648$	1.03358	0.0406029
$649$	−38.5943	−1.51496
$650$	12.0041	0.470838
$651$	−7.81637	−0.306348
$652$	16.0329	0.627898
$653$	−36.5003	−1.42837	−0.714184	−	0.699958i	$-0.753202\pi$
$653$	−36.5003	−1.42837	−0.714184	+	0.699958i	$0.753202\pi$
$654$	−13.3677	−0.522720
$655$	−35.1190	−1.37221
$656$	−13.1191	−0.512216
$657$	−13.2496	−0.516916
$658$	−29.3343	−1.14357
$659$	−3.91713	−0.152590	−0.0762948	−	0.997085i	$-0.524309\pi$
$659$	−3.91713	−0.152590	−0.0762948	+	0.997085i	$0.524309\pi$
$660$	−15.5216	−0.604176
$661$	−38.9791	−1.51611	−0.758057	−	0.652189i	$-0.773851\pi$
$661$	−38.9791	−1.51611	−0.758057	+	0.652189i	$0.773851\pi$
$662$	−10.2301	−0.397602
$663$	−2.20037	−0.0854554
$664$	17.7143	0.687447
$665$	−7.43533	−0.288330
$666$	20.5906	0.797870
$667$	−31.1410	−1.20578
$668$	−29.8420	−1.15462
$669$	8.15610	0.315333
$670$	−74.1263	−2.86375
$671$	−25.5018	−0.984487
$672$	−15.1539	−0.584575
$673$	16.0224	0.617617	0.308809	−	0.951124i	$-0.400070\pi$
$673$	16.0224	0.617617	0.308809	+	0.951124i	$0.400070\pi$
$674$	−3.86330	−0.148809
$675$	6.46937	0.249006
$676$	1.44297	0.0554989
$677$	38.6225	1.48438	0.742191	−	0.670188i	$-0.233787\pi$
$677$	38.6225	1.48438	0.742191	+	0.670188i	$0.233787\pi$
$678$	13.7127	0.526634
$679$	−22.5325	−0.864717
$680$	7.70214	0.295363
$681$	−21.7426	−0.833180
$682$	20.8121	0.796936
$683$	−26.7928	−1.02520	−0.512598	−	0.858628i	$-0.671317\pi$
$683$	−26.7928	−1.02520	−0.512598	+	0.858628i	$0.671317\pi$
$684$	1.43128	0.0547262
$685$	19.2568	0.735765
$686$	−37.3774	−1.42707
$687$	29.1979	1.11397
$688$	4.09519	0.156128
$689$	−9.36036	−0.356601
$690$	−55.6149	−2.11722
$691$	26.1652	0.995371	0.497685	−	0.867358i	$-0.334183\pi$
$691$	26.1652	0.995371	0.497685	+	0.867358i	$0.334183\pi$
$692$	13.4095	0.509753
$693$	7.03029	0.267059
$694$	−25.7949	−0.979160
$695$	36.7512	1.39405
$696$	−3.63682	−0.137853
$697$	6.00923	0.227616
$698$	43.6065	1.65053
$699$	−4.11104	−0.155494
$700$	−20.6625	−0.780971
$701$	−27.2671	−1.02986	−0.514932	−	0.857231i	$-0.672183\pi$
$701$	−27.2671	−1.02986	−0.514932	+	0.857231i	$0.672183\pi$
$702$	1.85552	0.0700323
$703$	−11.0070	−0.415137
$704$	9.83364	0.370619
$705$	−24.1888	−0.911002
$706$	31.6788	1.19225
$707$	−17.6191	−0.662635
$708$	17.5336	0.658955
$709$	11.9244	0.447829	0.223915	−	0.974609i	$-0.428116\pi$
$709$	11.9244	0.447829	0.223915	+	0.974609i	$0.428116\pi$
$710$	33.9149	1.27280
$711$	12.1228	0.454640
$712$	2.61884	0.0981452
$713$	31.2533	1.17044
$714$	9.03707	0.338204
$715$	10.7567	0.402277
$716$	18.3720	0.686594
$717$	−12.0843	−0.451296
$718$	−43.0312	−1.60591
$719$	5.78002	0.215558	0.107779	−	0.994175i	$-0.465626\pi$
$719$	5.78002	0.215558	0.107779	+	0.994175i	$0.465626\pi$
$720$	−16.2687	−0.606298
$721$	2.21342	0.0824322
$722$	33.4294	1.24411
$723$	−15.2517	−0.567217
$724$	35.7763	1.32962
$725$	−22.7635	−0.845415
$726$	1.69173	0.0627861
$727$	50.7342	1.88163	0.940814	−	0.338922i	$-0.110062\pi$
$727$	50.7342	1.88163	0.940814	+	0.338922i	$0.110062\pi$
$728$	2.28776	0.0847899
$729$	1.00000	0.0370370
$730$	83.2606	3.08161
$731$	−1.87580	−0.0693791
$732$	11.5856	0.428218
$733$	−21.4570	−0.792531	−0.396265	−	0.918136i	$-0.629694\pi$
$733$	−21.4570	−0.792531	−0.396265	+	0.918136i	$0.629694\pi$
$734$	−15.1934	−0.560799
$735$	−7.11450	−0.262422
$736$	60.5920	2.23345
$737$	−37.4666	−1.38010
$738$	−5.06744	−0.186535
$739$	0.158220	0.00582022	0.00291011	−	0.999996i	$-0.499074\pi$
$739$	0.158220	0.00582022	0.00291011	+	0.999996i	$0.499074\pi$
$740$	−54.2288	−1.99349
$741$	−0.991895	−0.0364382
$742$	38.4436	1.41131
$743$	7.97977	0.292749	0.146375	−	0.989229i	$-0.453239\pi$
$743$	7.97977	0.292749	0.146375	+	0.989229i	$0.453239\pi$
$744$	3.64994	0.133813
$745$	−50.9167	−1.86544
$746$	−17.9898	−0.658652
$747$	17.1387	0.627073
$748$	−10.0847	−0.368733
$749$	11.3174	0.413529
$750$	−9.23349	−0.337160
$751$	20.8709	0.761590	0.380795	−	0.924659i	$-0.375650\pi$
$751$	20.8709	0.761590	0.380795	+	0.924659i	$0.375650\pi$
$752$	34.3105	1.25118
$753$	−8.70708	−0.317304
$754$	−6.52896	−0.237771
$755$	23.4014	0.851663
$756$	−3.19391	−0.116161
$757$	8.87309	0.322498	0.161249	−	0.986914i	$-0.448448\pi$
$757$	8.87309	0.322498	0.161249	+	0.986914i	$0.448448\pi$
$758$	9.29858	0.337740
$759$	−28.1102	−1.02033
$760$	3.47201	0.125943
$761$	−40.0502	−1.45182	−0.725910	−	0.687790i	$-0.758581\pi$
$761$	−40.0502	−1.45182	−0.725910	+	0.687790i	$0.758581\pi$
$762$	0.209660	0.00759520
$763$	−15.9462	−0.577290
$764$	10.1148	0.365939
$765$	7.45188	0.269423
$766$	−56.9086	−2.05619
$767$	−12.1511	−0.438750
$768$	20.9397	0.755596
$769$	−9.50754	−0.342851	−0.171425	−	0.985197i	$-0.554837\pi$
$769$	−9.50754	−0.342851	−0.171425	+	0.985197i	$0.554837\pi$
$770$	−44.1783	−1.59208
$771$	3.11347	0.112129
$772$	−9.82587	−0.353641
$773$	−44.1039	−1.58631	−0.793154	−	0.609021i	$-0.791562\pi$
$773$	−44.1039	−1.58631	−0.793154	+	0.609021i	$0.791562\pi$
$774$	1.58182	0.0568574
$775$	22.8456	0.820637
$776$	10.5218	0.377710
$777$	24.5622	0.881165
$778$	−12.9917	−0.465775
$779$	2.70887	0.0970553
$780$	−4.88683	−0.174977
$781$	17.1421	0.613391
$782$	−36.1342	−1.29216
$783$	−3.51866	−0.125747
$784$	10.0915	0.360412
$785$	55.1337	1.96781
$786$	19.2415	0.686321
$787$	2.81471	0.100334	0.0501668	−	0.998741i	$-0.484025\pi$
$787$	2.81471	0.100334	0.0501668	+	0.998741i	$0.484025\pi$
$788$	−5.40347	−0.192491
$789$	−7.67744	−0.273324
$790$	−76.1796	−2.71035
$791$	16.3577	0.581612
$792$	−3.28287	−0.116652
$793$	−8.02903	−0.285119
$794$	45.1365	1.60183
$795$	31.7002	1.12429
$796$	3.47150	0.123044
$797$	−46.7866	−1.65727	−0.828633	−	0.559792i	$-0.810881\pi$
$797$	−46.7866	−1.65727	−0.828633	+	0.559792i	$0.810881\pi$
$798$	4.07378	0.144210
$799$	−15.7160	−0.555991
$800$	44.2916	1.56594
$801$	2.53375	0.0895257
$802$	35.1155	1.23997
$803$	42.0835	1.48509
$804$	17.0213	0.600296
$805$	−66.3422	−2.33825
$806$	6.55250	0.230802
$807$	4.19993	0.147845
$808$	8.22744	0.289440
$809$	30.8667	1.08522	0.542608	−	0.839986i	$-0.317437\pi$
$809$	30.8667	1.08522	0.542608	+	0.839986i	$0.317437\pi$
$810$	−6.28400	−0.220797
$811$	−47.6323	−1.67260	−0.836298	−	0.548275i	$-0.815285\pi$
$811$	−47.6323	−1.67260	−0.836298	+	0.548275i	$0.815285\pi$
$812$	11.2383	0.394386
$813$	7.09594	0.248866
$814$	−65.4000	−2.29227
$815$	37.6292	1.31809
$816$	−10.5701	−0.370028
$817$	−0.845584	−0.0295833
$818$	29.6760	1.03760
$819$	2.21342	0.0773433
$820$	13.3459	0.466061
$821$	24.4904	0.854722	0.427361	−	0.904081i	$-0.359443\pi$
$821$	24.4904	0.854722	0.427361	+	0.904081i	$0.359443\pi$
$822$	−10.5507	−0.367998
$823$	52.2135	1.82005	0.910024	−	0.414555i	$-0.136063\pi$
$823$	52.2135	1.82005	0.910024	+	0.414555i	$0.136063\pi$
$824$	−1.03358	−0.0360065
$825$	−20.5480	−0.715390
$826$	49.9052	1.73643
$827$	−36.5178	−1.26985	−0.634924	−	0.772575i	$-0.718969\pi$
$827$	−36.5178	−1.26985	−0.634924	+	0.772575i	$0.718969\pi$
$828$	12.7706	0.443810
$829$	15.1824	0.527306	0.263653	−	0.964618i	$-0.415073\pi$
$829$	15.1824	0.527306	0.263653	+	0.964618i	$0.415073\pi$
$830$	−107.700	−3.73831
$831$	−6.67179	−0.231442
$832$	3.09603	0.107336
$833$	−4.62244	−0.160158
$834$	−20.1358	−0.697244
$835$	−70.0391	−2.42380
$836$	−4.54602	−0.157227
$837$	3.53135	0.122061
$838$	−70.9710	−2.45165
$839$	−28.4895	−0.983567	−0.491783	−	0.870718i	$-0.663655\pi$
$839$	−28.4895	−0.983567	−0.491783	+	0.870718i	$0.663655\pi$
$840$	−7.74782	−0.267325
$841$	−16.6190	−0.573070
$842$	31.3020	1.07874
$843$	19.1031	0.657945
$844$	−15.9475	−0.548935
$845$	3.38665	0.116504
$846$	13.2529	0.455644
$847$	2.01804	0.0693406
$848$	−44.9651	−1.54411
$849$	15.4629	0.530687
$850$	−26.4134	−0.905973
$851$	−98.2105	−3.36661
$852$	−7.78775	−0.266804
$853$	−2.82648	−0.0967770	−0.0483885	−	0.998829i	$-0.515409\pi$
$853$	−2.82648	−0.0967770	−0.0483885	+	0.998829i	$0.515409\pi$
$854$	32.9757	1.12841
$855$	3.35920	0.114882
$856$	−5.28478	−0.180630
$857$	30.5578	1.04383	0.521917	−	0.852996i	$-0.325217\pi$
$857$	30.5578	1.04383	0.521917	+	0.852996i	$0.325217\pi$
$858$	−5.89352	−0.201202
$859$	−12.2462	−0.417836	−0.208918	−	0.977933i	$-0.566994\pi$
$859$	−12.2462	−0.417836	−0.208918	+	0.977933i	$0.566994\pi$
$860$	−4.16599	−0.142059
$861$	−6.04487	−0.206009
$862$	−14.6695	−0.499645
$863$	−19.7242	−0.671421	−0.335711	−	0.941965i	$-0.608976\pi$
$863$	−19.7242	−0.671421	−0.335711	+	0.941965i	$0.608976\pi$
$864$	6.84636	0.232918
$865$	31.4720	1.07008
$866$	−42.6037	−1.44773
$867$	−12.1584	−0.412919
$868$	−11.2788	−0.382827
$869$	−38.5044	−1.30617
$870$	22.1113	0.749642
$871$	−11.7960	−0.399693
$872$	7.44623	0.252161
$873$	10.1799	0.344538
$874$	−16.2887	−0.550975
$875$	−11.0145	−0.372358
$876$	−19.1188	−0.645964
$877$	−23.0891	−0.779663	−0.389832	−	0.920886i	$-0.627467\pi$
$877$	−23.0891	−0.779663	−0.389832	+	0.920886i	$0.627467\pi$
$878$	−47.6430	−1.60787
$879$	26.6563	0.899093
$880$	51.6727	1.74189
$881$	38.9292	1.31156	0.655780	−	0.754952i	$-0.272340\pi$
$881$	38.9292	1.31156	0.655780	+	0.754952i	$0.272340\pi$
$882$	3.89800	0.131252
$883$	37.4713	1.26101	0.630505	−	0.776186i	$-0.282848\pi$
$883$	37.4713	1.26101	0.630505	+	0.776186i	$0.282848\pi$
$884$	−3.17507	−0.106789
$885$	41.1514	1.38329
$886$	−8.16288	−0.274237
$887$	19.8750	0.667336	0.333668	−	0.942691i	$-0.391714\pi$
$887$	19.8750	0.667336	0.333668	+	0.942691i	$0.391714\pi$
$888$	−11.4696	−0.384894
$889$	0.250100	0.00838810
$890$	−15.9221	−0.533710
$891$	−3.17620	−0.106407
$892$	11.7690	0.394056
$893$	−7.08452	−0.237074
$894$	27.8970	0.933014
$895$	43.1190	1.44131
$896$	17.5922	0.587714
$897$	−8.85024	−0.295501
$898$	−67.1186	−2.23978
$899$	−12.4256	−0.414417
$900$	9.33510	0.311170
$901$	20.5963	0.686162
$902$	16.0952	0.535913
$903$	1.88693	0.0627931
$904$	−7.63839	−0.254049
$905$	83.9669	2.79115
$906$	−12.8215	−0.425965
$907$	26.8403	0.891218	0.445609	−	0.895228i	$-0.352987\pi$
$907$	26.8403	0.891218	0.445609	+	0.895228i	$0.352987\pi$
$908$	−31.3740	−1.04118
$909$	7.96012	0.264020
$910$	−13.9092	−0.461084
$911$	0.986456	0.0326828	0.0163414	−	0.999866i	$-0.494798\pi$
$911$	0.986456	0.0326828	0.0163414	+	0.999866i	$0.494798\pi$
$912$	−4.76484	−0.157780
$913$	−54.4361	−1.80157
$914$	−32.6793	−1.08093
$915$	27.1915	0.898922
$916$	42.1317	1.39207
$917$	22.9529	0.757970
$918$	−4.08285	−0.134754
$919$	−3.33166	−0.109901	−0.0549507	−	0.998489i	$-0.517500\pi$
$919$	−3.33166	−0.109901	−0.0549507	+	0.998489i	$0.517500\pi$
$920$	30.9792	1.02135
$921$	9.10687	0.300082
$922$	45.4248	1.49598
$923$	5.39703	0.177645
$924$	10.1445	0.333729
$925$	−71.7901	−2.36044
$926$	9.15847	0.300966
$927$	−1.00000	−0.0328443
$928$	−24.0900	−0.790794
$929$	−5.40583	−0.177360	−0.0886798	−	0.996060i	$-0.528265\pi$
$929$	−5.40583	−0.177360	−0.0886798	+	0.996060i	$0.528265\pi$
$930$	−22.1910	−0.727671
$931$	−2.08373	−0.0682914
$932$	−5.93212	−0.194313
$933$	−33.3769	−1.09271
$934$	−55.8413	−1.82718
$935$	−23.6687	−0.774050
$936$	−1.03358	−0.0337837
$937$	21.0448	0.687504	0.343752	−	0.939061i	$-0.388302\pi$
$937$	21.0448	0.687504	0.343752	+	0.939061i	$0.388302\pi$
$938$	48.4471	1.58185
$939$	−23.8795	−0.779279
$940$	−34.9037	−1.13843
$941$	−51.6891	−1.68502	−0.842508	−	0.538684i	$-0.818922\pi$
$941$	−51.6891	−1.68502	−0.842508	+	0.538684i	$0.818922\pi$
$942$	−30.2075	−0.984212
$943$	24.1700	0.787085
$944$	−58.3711	−1.89982
$945$	−7.49608	−0.243848
$946$	−5.02419	−0.163351
$947$	48.5670	1.57822	0.789108	−	0.614255i	$-0.210543\pi$
$947$	48.5670	1.57822	0.789108	+	0.614255i	$0.210543\pi$
$948$	17.4928	0.568140
$949$	13.2496	0.430100
$950$	−11.9068	−0.386307
$951$	10.0895	0.327175
$952$	−5.03392	−0.163150
$953$	8.22330	0.266379	0.133189	−	0.991091i	$-0.457478\pi$
$953$	8.22330	0.266379	0.133189	+	0.991091i	$0.457478\pi$
$954$	−17.3684	−0.562322
$955$	23.7393	0.768185
$956$	−17.4373	−0.563962
$957$	11.1760	0.361268
$958$	41.3887	1.33721
$959$	−12.5858	−0.406415
$960$	−10.4852	−0.338407
$961$	−18.5296	−0.597729
$962$	−20.5906	−0.663868
$963$	−5.11308	−0.164767
$964$	−22.0078	−0.708822
$965$	−23.0613	−0.742369
$966$	36.3485	1.16949
$967$	12.0203	0.386546	0.193273	−	0.981145i	$-0.438090\pi$
$967$	12.0203	0.386546	0.193273	+	0.981145i	$0.438090\pi$
$968$	−0.942345	−0.0302881
$969$	2.18254	0.0701133
$970$	−63.9706	−2.05397
$971$	38.1914	1.22562	0.612810	−	0.790230i	$-0.290039\pi$
$971$	38.1914	1.22562	0.612810	+	0.790230i	$0.290039\pi$
$972$	1.44297	0.0462833
$973$	−24.0196	−0.770034
$974$	46.1706	1.47940
$975$	−6.46937	−0.207186
$976$	−38.5697	−1.23458
$977$	−8.77560	−0.280756	−0.140378	−	0.990098i	$-0.544832\pi$
$977$	−8.77560	−0.280756	−0.140378	+	0.990098i	$0.544832\pi$
$978$	−20.6169	−0.659254
$979$	−8.04771	−0.257206
$980$	−10.2660	−0.327936
$981$	7.20429	0.230015
$982$	−3.43534	−0.109626
$983$	19.0495	0.607586	0.303793	−	0.952738i	$-0.401747\pi$
$983$	19.0495	0.607586	0.303793	+	0.952738i	$0.401747\pi$
$984$	2.82272	0.0899849
$985$	−12.6819	−0.404080
$986$	14.3662	0.457511
$987$	15.8092	0.503211
$988$	−1.43128	−0.0455349
$989$	−7.54478	−0.239910
$990$	19.9593	0.634347
$991$	12.1190	0.384971	0.192486	−	0.981300i	$-0.438345\pi$
$991$	12.1190	0.384971	0.192486	+	0.981300i	$0.438345\pi$
$992$	24.1769	0.767617
$993$	5.51330	0.174959
$994$	−22.1659	−0.703061
$995$	8.14760	0.258296
$996$	24.7307	0.783621
$997$	−24.1171	−0.763798	−0.381899	−	0.924204i	$-0.624730\pi$
$997$	−24.1171	−0.763798	−0.381899	+	0.924204i	$0.624730\pi$
$998$	−14.9800	−0.474185
$999$	−11.0969	−0.351091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.l.1.6	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.l.1.6	✓	32	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q-1.85552 q^{2} +1.00000 q^{3} +1.44297 q^{4} +3.38665 q^{5} -1.85552 q^{6} -2.21342 q^{7} +1.03358 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.85552 q^{2} +1.00000 q^{3} +1.44297 q^{4} +3.38665 q^{5} -1.85552 q^{6} -2.21342 q^{7} +1.03358 q^{8} +1.00000 q^{9} -6.28400 q^{10} -3.17620 q^{11} +1.44297 q^{12} -1.00000 q^{13} +4.10706 q^{14} +3.38665 q^{15} -4.80378 q^{16} +2.20037 q^{17} -1.85552 q^{18} +0.991895 q^{19} +4.88683 q^{20} -2.21342 q^{21} +5.89352 q^{22} +8.85024 q^{23} +1.03358 q^{24} +6.46937 q^{25} +1.85552 q^{26} +1.00000 q^{27} -3.19391 q^{28} -3.51866 q^{29} -6.28400 q^{30} +3.53135 q^{31} +6.84636 q^{32} -3.17620 q^{33} -4.08285 q^{34} -7.49608 q^{35} +1.44297 q^{36} -11.0969 q^{37} -1.84049 q^{38} -1.00000 q^{39} +3.50038 q^{40} +2.73100 q^{41} +4.10706 q^{42} -0.852494 q^{43} -4.58317 q^{44} +3.38665 q^{45} -16.4218 q^{46} -7.14240 q^{47} -4.80378 q^{48} -2.10075 q^{49} -12.0041 q^{50} +2.20037 q^{51} -1.44297 q^{52} +9.36036 q^{53} -1.85552 q^{54} -10.7567 q^{55} -2.28776 q^{56} +0.991895 q^{57} +6.52896 q^{58} +12.1511 q^{59} +4.88683 q^{60} +8.02903 q^{61} -6.55250 q^{62} -2.21342 q^{63} -3.09603 q^{64} -3.38665 q^{65} +5.89352 q^{66} +11.7960 q^{67} +3.17507 q^{68} +8.85024 q^{69} +13.9092 q^{70} -5.39703 q^{71} +1.03358 q^{72} -13.2496 q^{73} +20.5906 q^{74} +6.46937 q^{75} +1.43128 q^{76} +7.03029 q^{77} +1.85552 q^{78} +12.1228 q^{79} -16.2687 q^{80} +1.00000 q^{81} -5.06744 q^{82} +17.1387 q^{83} -3.19391 q^{84} +7.45188 q^{85} +1.58182 q^{86} -3.51866 q^{87} -3.28287 q^{88} +2.53375 q^{89} -6.28400 q^{90} +2.21342 q^{91} +12.7706 q^{92} +3.53135 q^{93} +13.2529 q^{94} +3.35920 q^{95} +6.84636 q^{96} +10.1799 q^{97} +3.89800 q^{98} -3.17620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9}+O(q^{10}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9	\( 32 q + 5 q^{2} + 32 q^{3} + 45 q^{4} + q^{5} + 5 q^{6} + 11 q^{7} + 12 q^{8} + 32 q^{9} + 16 q^{10} + 3 q^{11} + 45 q^{12} - 32 q^{13} + 12 q^{14} + q^{15} + 75 q^{16} + 10 q^{17} + 5 q^{18} + 4 q^{20} + 11 q^{21} + 27 q^{22} + 53 q^{23} + 12 q^{24} + 67 q^{25} - 5 q^{26} + 32 q^{27} + 32 q^{28} + 6 q^{29} + 16 q^{30} + 12 q^{31} + 19 q^{32} + 3 q^{33} + 25 q^{34} + 16 q^{35} + 45 q^{36} + 36 q^{37} + 8 q^{38} - 32 q^{39} + 36 q^{40} - 19 q^{41} + 12 q^{42} + 43 q^{43} - 23 q^{44} + q^{45} + 11 q^{46} + 30 q^{47} + 75 q^{48} + 75 q^{49} + 28 q^{50} + 10 q^{51} - 45 q^{52} + 22 q^{53} + 5 q^{54} + 58 q^{55} + 60 q^{56} + 33 q^{58} - 24 q^{59} + 4 q^{60} + 47 q^{61} - 25 q^{62} + 11 q^{63} + 146 q^{64} - q^{65} + 27 q^{66} + 34 q^{67} + 58 q^{68} + 53 q^{69} - 35 q^{70} + 18 q^{71} + 12 q^{72} - 2 q^{73} - 20 q^{74} + 67 q^{75} + 24 q^{76} + 39 q^{77} - 5 q^{78} + 39 q^{79} + 2 q^{80} + 32 q^{81} + 64 q^{82} + 17 q^{83} + 32 q^{84} + 35 q^{85} - 13 q^{86} + 6 q^{87} + 55 q^{88} - 48 q^{89} + 16 q^{90} - 11 q^{91} + 39 q^{92} + 12 q^{93} + 58 q^{94} + 59 q^{95} + 19 q^{96} + 42 q^{97} + 16 q^{98} + 3 q^{99}+O(q^{100}) \) 32 * q + 5 * q^2 + 32 * q^3 + 45 * q^4 + q^5 + 5 * q^6 + 11 * q^7 + 12 * q^8 + 32 * q^9 + 16 * q^10 + 3 * q^11 + 45 * q^12 - 32 * q^13 + 12 * q^14 + q^15 + 75 * q^16 + 10 * q^17 + 5 * q^18 + 4 * q^20 + 11 * q^21 + 27 * q^22 + 53 * q^23 + 12 * q^24 + 67 * q^25 - 5 * q^26 + 32 * q^27 + 32 * q^28 + 6 * q^29 + 16 * q^30 + 12 * q^31 + 19 * q^32 + 3 * q^33 + 25 * q^34 + 16 * q^35 + 45 * q^36 + 36 * q^37 + 8 * q^38 - 32 * q^39 + 36 * q^40 - 19 * q^41 + 12 * q^42 + 43 * q^43 - 23 * q^44 + q^45 + 11 * q^46 + 30 * q^47 + 75 * q^48 + 75 * q^49 + 28 * q^50 + 10 * q^51 - 45 * q^52 + 22 * q^53 + 5 * q^54 + 58 * q^55 + 60 * q^56 + 33 * q^58 - 24 * q^59 + 4 * q^60 + 47 * q^61 - 25 * q^62 + 11 * q^63 + 146 * q^64 - q^65 + 27 * q^66 + 34 * q^67 + 58 * q^68 + 53 * q^69 - 35 * q^70 + 18 * q^71 + 12 * q^72 - 2 * q^73 - 20 * q^74 + 67 * q^75 + 24 * q^76 + 39 * q^77 - 5 * q^78 + 39 * q^79 + 2 * q^80 + 32 * q^81 + 64 * q^82 + 17 * q^83 + 32 * q^84 + 35 * q^85 - 13 * q^86 + 6 * q^87 + 55 * q^88 - 48 * q^89 + 16 * q^90 - 11 * q^91 + 39 * q^92 + 12 * q^93 + 58 * q^94 + 59 * q^95 + 19 * q^96 + 42 * q^97 + 16 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more