LMFDB - Embedded newform 8041.2.a.i.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, 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("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.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:	$64.2077082653$
Analytic rank:	$0$
Dimension:	$78$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.53120 q^{2} -2.76336 q^{3} +4.40698 q^{4} +3.58460 q^{5} +6.99462 q^{6} -0.727911 q^{7} -6.09254 q^{8} +4.63616 q^{9} +O(q^{10})$	\(q-2.53120 q^{2} -2.76336 q^{3} +4.40698 q^{4} +3.58460 q^{5} +6.99462 q^{6} -0.727911 q^{7} -6.09254 q^{8} +4.63616 q^{9} -9.07334 q^{10} +1.00000 q^{11} -12.1781 q^{12} -1.11146 q^{13} +1.84249 q^{14} -9.90554 q^{15} +6.60750 q^{16} -1.00000 q^{17} -11.7351 q^{18} +3.30470 q^{19} +15.7973 q^{20} +2.01148 q^{21} -2.53120 q^{22} -5.19699 q^{23} +16.8359 q^{24} +7.84935 q^{25} +2.81333 q^{26} -4.52131 q^{27} -3.20789 q^{28} -1.68648 q^{29} +25.0729 q^{30} +3.36917 q^{31} -4.53982 q^{32} -2.76336 q^{33} +2.53120 q^{34} -2.60927 q^{35} +20.4315 q^{36} -8.94366 q^{37} -8.36487 q^{38} +3.07136 q^{39} -21.8393 q^{40} -5.08833 q^{41} -5.09146 q^{42} -1.00000 q^{43} +4.40698 q^{44} +16.6188 q^{45} +13.1546 q^{46} +2.08535 q^{47} -18.2589 q^{48} -6.47015 q^{49} -19.8683 q^{50} +2.76336 q^{51} -4.89818 q^{52} -0.317816 q^{53} +11.4443 q^{54} +3.58460 q^{55} +4.43483 q^{56} -9.13209 q^{57} +4.26882 q^{58} +5.62610 q^{59} -43.6535 q^{60} -11.2332 q^{61} -8.52804 q^{62} -3.37471 q^{63} -1.72381 q^{64} -3.98414 q^{65} +6.99462 q^{66} -7.90842 q^{67} -4.40698 q^{68} +14.3612 q^{69} +6.60459 q^{70} +9.16197 q^{71} -28.2460 q^{72} -10.6186 q^{73} +22.6382 q^{74} -21.6906 q^{75} +14.5638 q^{76} -0.727911 q^{77} -7.77424 q^{78} +13.4281 q^{79} +23.6852 q^{80} -1.41449 q^{81} +12.8796 q^{82} -8.85038 q^{83} +8.86455 q^{84} -3.58460 q^{85} +2.53120 q^{86} +4.66035 q^{87} -6.09254 q^{88} +7.04878 q^{89} -42.0655 q^{90} +0.809044 q^{91} -22.9030 q^{92} -9.31022 q^{93} -5.27845 q^{94} +11.8460 q^{95} +12.5452 q^{96} +12.3075 q^{97} +16.3772 q^{98} +4.63616 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) $ 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.53120	−1.78983	−0.894915	−	0.446237i	$-0.852764\pi$
$2$	−2.53120	−1.78983	−0.894915	+	0.446237i	$0.852764\pi$
$3$	−2.76336	−1.59543	−0.797714	−	0.603037i	$-0.793957\pi$
$3$	−2.76336	−1.59543	−0.797714	+	0.603037i	$0.793957\pi$
$4$	4.40698	2.20349
$5$	3.58460	1.60308	0.801541	−	0.597940i	$-0.204014\pi$
$5$	3.58460	1.60308	0.801541	+	0.597940i	$0.204014\pi$
$6$	6.99462	2.85554
$7$	−0.727911	−0.275125	−0.137562	−	0.990493i	$-0.543927\pi$
$7$	−0.727911	−0.275125	−0.137562	+	0.990493i	$0.543927\pi$
$8$	−6.09254	−2.15404
$9$	4.63616	1.54539
$10$	−9.07334	−2.86924
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−12.1781	−3.51551
$13$	−1.11146	−0.308263	−0.154132	−	0.988050i	$-0.549258\pi$
$13$	−1.11146	−0.308263	−0.154132	+	0.988050i	$0.549258\pi$
$14$	1.84249	0.492426
$15$	−9.90554	−2.55760
$16$	6.60750	1.65187
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−11.7351	−2.76598
$19$	3.30470	0.758151	0.379075	−	0.925366i	$-0.376242\pi$
$19$	3.30470	0.758151	0.379075	+	0.925366i	$0.376242\pi$
$20$	15.7973	3.53237
$21$	2.01148	0.438941
$22$	−2.53120	−0.539654
$23$	−5.19699	−1.08365	−0.541824	−	0.840492i	$-0.682266\pi$
$23$	−5.19699	−1.08365	−0.541824	+	0.840492i	$0.682266\pi$
$24$	16.8359	3.43661
$25$	7.84935	1.56987
$26$	2.81333	0.551739
$27$	−4.52131	−0.870126
$28$	−3.20789	−0.606234
$29$	−1.68648	−0.313172	−0.156586	−	0.987664i	$-0.550049\pi$
$29$	−1.68648	−0.313172	−0.156586	+	0.987664i	$0.550049\pi$
$30$	25.0729	4.57767
$31$	3.36917	0.605120	0.302560	−	0.953130i	$-0.402159\pi$
$31$	3.36917	0.605120	0.302560	+	0.953130i	$0.402159\pi$
$32$	−4.53982	−0.802534
$33$	−2.76336	−0.481039
$34$	2.53120	0.434097
$35$	−2.60927	−0.441047
$36$	20.4315	3.40524
$37$	−8.94366	−1.47033	−0.735164	−	0.677889i	$-0.762895\pi$
$37$	−8.94366	−1.47033	−0.735164	+	0.677889i	$0.762895\pi$
$38$	−8.36487	−1.35696
$39$	3.07136	0.491812
$40$	−21.8393	−3.45310
$41$	−5.08833	−0.794663	−0.397331	−	0.917675i	$-0.630064\pi$
$41$	−5.08833	−0.794663	−0.397331	+	0.917675i	$0.630064\pi$
$42$	−5.09146	−0.785630
$43$	−1.00000	−0.152499
$43$	−1.00000	−0.152499
$44$	4.40698	0.664377
$45$	16.6188	2.47738
$46$	13.1546	1.93954
$47$	2.08535	0.304180	0.152090	−	0.988367i	$-0.451400\pi$
$47$	2.08535	0.304180	0.152090	+	0.988367i	$0.451400\pi$
$48$	−18.2589	−2.63545
$49$	−6.47015	−0.924306
$50$	−19.8683	−2.80980
$51$	2.76336	0.386948
$52$	−4.89818	−0.679255
$53$	−0.317816	−0.0436554	−0.0218277	−	0.999762i	$-0.506949\pi$
$53$	−0.317816	−0.0436554	−0.0218277	+	0.999762i	$0.506949\pi$
$54$	11.4443	1.55738
$55$	3.58460	0.483347
$56$	4.43483	0.592629
$57$	−9.13209	−1.20957
$58$	4.26882	0.560524
$59$	5.62610	0.732455	0.366228	−	0.930525i	$-0.380649\pi$
$59$	5.62610	0.732455	0.366228	+	0.930525i	$0.380649\pi$
$60$	−43.6535	−5.63564
$61$	−11.2332	−1.43826	−0.719130	−	0.694875i	$-0.755459\pi$
$61$	−11.2332	−1.43826	−0.719130	+	0.694875i	$0.755459\pi$
$62$	−8.52804	−1.08306
$63$	−3.37471	−0.425174
$64$	−1.72381	−0.215476
$65$	−3.98414	−0.494171
$66$	6.99462	0.860978
$67$	−7.90842	−0.966167	−0.483084	−	0.875574i	$-0.660483\pi$
$67$	−7.90842	−0.966167	−0.483084	+	0.875574i	$0.660483\pi$
$68$	−4.40698	−0.534425
$69$	14.3612	1.72888
$70$	6.60459	0.789399
$71$	9.16197	1.08733	0.543663	−	0.839304i	$-0.317037\pi$
$71$	9.16197	1.08733	0.543663	+	0.839304i	$0.317037\pi$
$72$	−28.2460	−3.32883
$73$	−10.6186	−1.24282	−0.621408	−	0.783488i	$-0.713439\pi$
$73$	−10.6186	−1.24282	−0.621408	+	0.783488i	$0.713439\pi$
$74$	22.6382	2.63164
$75$	−21.6906	−2.50461
$76$	14.5638	1.67058
$77$	−0.727911	−0.0829532
$78$	−7.77424	−0.880259
$79$	13.4281	1.51078	0.755389	−	0.655277i	$-0.227448\pi$
$79$	13.4281	1.51078	0.755389	+	0.655277i	$0.227448\pi$
$80$	23.6852	2.64809
$81$	−1.41449	−0.157165
$82$	12.8796	1.42231
$83$	−8.85038	−0.971455	−0.485728	−	0.874110i	$-0.661445\pi$
$83$	−8.85038	−0.971455	−0.485728	+	0.874110i	$0.661445\pi$
$84$	8.86455	0.967202
$85$	−3.58460	−0.388804
$86$	2.53120	0.272946
$87$	4.66035	0.499642
$88$	−6.09254	−0.649467
$89$	7.04878	0.747169	0.373584	−	0.927596i	$-0.378129\pi$
$89$	7.04878	0.747169	0.373584	+	0.927596i	$0.378129\pi$
$90$	−42.0655	−4.43409
$91$	0.809044	0.0848109
$92$	−22.9030	−2.38781
$93$	−9.31022	−0.965425
$94$	−5.27845	−0.544431
$95$	11.8460	1.21538
$96$	12.5452	1.28038
$97$	12.3075	1.24964	0.624819	−	0.780769i	$-0.285173\pi$
$97$	12.3075	1.24964	0.624819	+	0.780769i	$0.285173\pi$
$98$	16.3772	1.65435
$99$	4.63616	0.465952
$100$	34.5919	3.45919
$101$	−15.5117	−1.54347	−0.771736	−	0.635943i	$-0.780611\pi$
$101$	−15.5117	−1.54347	−0.771736	+	0.635943i	$0.780611\pi$
$102$	−6.99462	−0.692571
$103$	1.85325	0.182606	0.0913032	−	0.995823i	$-0.470897\pi$
$103$	1.85325	0.182606	0.0913032	+	0.995823i	$0.470897\pi$
$104$	6.77162	0.664012
$105$	7.21035	0.703659
$106$	0.804456	0.0781357
$107$	−9.02054	−0.872049	−0.436024	−	0.899935i	$-0.643614\pi$
$107$	−9.02054	−0.872049	−0.436024	+	0.899935i	$0.643614\pi$
$108$	−19.9253	−1.91731
$109$	17.7576	1.70087	0.850435	−	0.526080i	$-0.176339\pi$
$109$	17.7576	1.70087	0.850435	+	0.526080i	$0.176339\pi$
$110$	−9.07334	−0.865109
$111$	24.7146	2.34580
$112$	−4.80967	−0.454471
$113$	−2.02453	−0.190452	−0.0952259	−	0.995456i	$-0.530357\pi$
$113$	−2.02453	−0.190452	−0.0952259	+	0.995456i	$0.530357\pi$
$114$	23.1151	2.16493
$115$	−18.6291	−1.73718
$116$	−7.43228	−0.690070
$117$	−5.15291	−0.476386
$118$	−14.2408	−1.31097
$119$	0.727911	0.0667275
$120$	60.3500	5.50917
$121$	1.00000	0.0909091
$122$	28.4334	2.57424
$123$	14.0609	1.26783
$124$	14.8478	1.33338
$125$	10.2138	0.913549
$126$	8.54208	0.760989
$127$	13.3695	1.18635	0.593174	−	0.805074i	$-0.297875\pi$
$127$	13.3695	1.18635	0.593174	+	0.805074i	$0.297875\pi$
$128$	13.4429	1.18820
$129$	2.76336	0.243300
$130$	10.0847	0.884483
$131$	6.46156	0.564549	0.282275	−	0.959334i	$-0.408911\pi$
$131$	6.46156	0.564549	0.282275	+	0.959334i	$0.408911\pi$
$132$	−12.1781	−1.05996
$133$	−2.40553	−0.208586
$134$	20.0178	1.72927
$135$	−16.2071	−1.39488
$136$	6.09254	0.522431
$137$	19.0000	1.62328	0.811639	−	0.584160i	$-0.198576\pi$
$137$	19.0000	1.62328	0.811639	+	0.584160i	$0.198576\pi$
$138$	−36.3510	−3.09440
$139$	7.35355	0.623720	0.311860	−	0.950128i	$-0.399048\pi$
$139$	7.35355	0.623720	0.311860	+	0.950128i	$0.399048\pi$
$140$	−11.4990	−0.971843
$141$	−5.76259	−0.485297
$142$	−23.1908	−1.94613
$143$	−1.11146	−0.0929449
$144$	30.6334	2.55279
$145$	−6.04536	−0.502040
$146$	26.8779	2.22443
$147$	17.8793	1.47466
$148$	−39.4145	−3.23985
$149$	0.0875898	0.00717564	0.00358782	−	0.999994i	$-0.498858\pi$
$149$	0.0875898	0.00717564	0.00358782	+	0.999994i	$0.498858\pi$
$150$	54.9033	4.48283
$151$	−0.931349	−0.0757921	−0.0378961	−	0.999282i	$-0.512066\pi$
$151$	−0.931349	−0.0757921	−0.0378961	+	0.999282i	$0.512066\pi$
$152$	−20.1340	−1.63309
$153$	−4.63616	−0.374811
$154$	1.84249	0.148472
$155$	12.0771	0.970057
$156$	13.5354	1.08370
$157$	12.4048	0.990009	0.495005	−	0.868890i	$-0.335166\pi$
$157$	12.4048	0.990009	0.495005	+	0.868890i	$0.335166\pi$
$158$	−33.9892	−2.70403
$159$	0.878240	0.0696490
$160$	−16.2734	−1.28653
$161$	3.78295	0.298138
$162$	3.58035	0.281299
$163$	13.3465	1.04538	0.522688	−	0.852524i	$-0.324929\pi$
$163$	13.3465	1.04538	0.522688	+	0.852524i	$0.324929\pi$
$164$	−22.4241	−1.75103
$165$	−9.90554	−0.771145
$166$	22.4021	1.73874
$167$	6.43560	0.498002	0.249001	−	0.968503i	$-0.419898\pi$
$167$	6.43560	0.498002	0.249001	+	0.968503i	$0.419898\pi$
$168$	−12.2550	−0.945497
$169$	−11.7647	−0.904974
$170$	9.07334	0.695894
$171$	15.3211	1.17164
$172$	−4.40698	−0.336029
$173$	−1.68221	−0.127896	−0.0639479	−	0.997953i	$-0.520369\pi$
$173$	−1.68221	−0.127896	−0.0639479	+	0.997953i	$0.520369\pi$
$174$	−11.7963	−0.894275
$175$	−5.71363	−0.431910
$176$	6.60750	0.498059
$177$	−15.5469	−1.16858
$178$	−17.8419	−1.33730
$179$	9.36711	0.700131	0.350065	−	0.936725i	$-0.386159\pi$
$179$	9.36711	0.700131	0.350065	+	0.936725i	$0.386159\pi$
$180$	73.2386	5.45888
$181$	10.7297	0.797533	0.398766	−	0.917053i	$-0.369438\pi$
$181$	10.7297	0.797533	0.398766	+	0.917053i	$0.369438\pi$
$182$	−2.04785	−0.151797
$183$	31.0413	2.29464
$184$	31.6629	2.33422
$185$	−32.0594	−2.35706
$186$	23.5660	1.72795
$187$	−1.00000	−0.0731272
$188$	9.19011	0.670258
$189$	3.29111	0.239393
$190$	−29.9847	−2.17532
$191$	13.4288	0.971674	0.485837	−	0.874049i	$-0.338515\pi$
$191$	13.4288	0.971674	0.485837	+	0.874049i	$0.338515\pi$
$192$	4.76351	0.343776
$193$	10.6725	0.768225	0.384112	−	0.923286i	$-0.374508\pi$
$193$	10.6725	0.768225	0.384112	+	0.923286i	$0.374508\pi$
$194$	−31.1528	−2.23664
$195$	11.0096	0.788415
$196$	−28.5138	−2.03670
$197$	15.7843	1.12458	0.562292	−	0.826938i	$-0.309920\pi$
$197$	15.7843	1.12458	0.562292	+	0.826938i	$0.309920\pi$
$198$	−11.7351	−0.833974
$199$	8.05060	0.570692	0.285346	−	0.958425i	$-0.407892\pi$
$199$	8.05060	0.570692	0.285346	+	0.958425i	$0.407892\pi$
$200$	−47.8225	−3.38156
$201$	21.8538	1.54145
$202$	39.2632	2.76255
$203$	1.22761	0.0861612
$204$	12.1781	0.852635
$205$	−18.2396	−1.27391
$206$	−4.69096	−0.326834
$207$	−24.0941	−1.67466
$208$	−7.34397	−0.509213
$209$	3.30470	0.228591
$210$	−18.2509	−1.25943
$211$	9.21320	0.634263	0.317131	−	0.948382i	$-0.397280\pi$
$211$	9.21320	0.634263	0.317131	+	0.948382i	$0.397280\pi$
$212$	−1.40061	−0.0961941
$213$	−25.3178	−1.73475
$214$	22.8328	1.56082
$215$	−3.58460	−0.244468
$216$	27.5463	1.87429
$217$	−2.45245	−0.166483
$218$	−44.9481	−3.04427
$219$	29.3431	1.98282
$220$	15.7973	1.06505
$221$	1.11146	0.0747649
$222$	−62.5575	−4.19859
$223$	11.3001	0.756710	0.378355	−	0.925661i	$-0.376490\pi$
$223$	11.3001	0.756710	0.378355	+	0.925661i	$0.376490\pi$
$224$	3.30458	0.220797
$225$	36.3909	2.42606
$226$	5.12449	0.340876
$227$	−12.4027	−0.823198	−0.411599	−	0.911365i	$-0.635030\pi$
$227$	−12.4027	−0.823198	−0.411599	+	0.911365i	$0.635030\pi$
$228$	−40.2449	−2.66528
$229$	−16.7062	−1.10397	−0.551987	−	0.833853i	$-0.686130\pi$
$229$	−16.7062	−1.10397	−0.551987	+	0.833853i	$0.686130\pi$
$230$	47.1541	3.10925
$231$	2.01148	0.132346
$232$	10.2750	0.674584
$233$	0.928042	0.0607981	0.0303990	−	0.999538i	$-0.490322\pi$
$233$	0.928042	0.0607981	0.0303990	+	0.999538i	$0.490322\pi$
$234$	13.0430	0.852650
$235$	7.47516	0.487626
$236$	24.7941	1.61396
$237$	−37.1066	−2.41033
$238$	−1.84249	−0.119431
$239$	−10.7737	−0.696891	−0.348445	−	0.937329i	$-0.613290\pi$
$239$	−10.7737	−0.696891	−0.348445	+	0.937329i	$0.613290\pi$
$240$	−65.4508	−4.22483
$241$	−16.2593	−1.04735	−0.523675	−	0.851918i	$-0.675439\pi$
$241$	−16.2593	−1.04735	−0.523675	+	0.851918i	$0.675439\pi$
$242$	−2.53120	−0.162712
$243$	17.4727	1.12087
$244$	−49.5043	−3.16919
$245$	−23.1929	−1.48174
$246$	−35.5909	−2.26919
$247$	−3.67304	−0.233710
$248$	−20.5268	−1.30345
$249$	24.4568	1.54989
$250$	−25.8532	−1.63510
$251$	−4.98582	−0.314702	−0.157351	−	0.987543i	$-0.550295\pi$
$251$	−4.98582	−0.314702	−0.157351	+	0.987543i	$0.550295\pi$
$252$	−14.8723	−0.936866
$253$	−5.19699	−0.326732
$254$	−33.8408	−2.12336
$255$	9.90554	0.620309
$256$	−30.5792	−1.91120
$257$	16.3442	1.01953	0.509763	−	0.860315i	$-0.329733\pi$
$257$	16.3442	1.01953	0.509763	+	0.860315i	$0.329733\pi$
$258$	−6.99462	−0.435466
$259$	6.51019	0.404524
$260$	−17.5580	−1.08890
$261$	−7.81880	−0.483971
$262$	−16.3555	−1.01045
$263$	9.81069	0.604953	0.302476	−	0.953157i	$-0.402187\pi$
$263$	9.81069	0.604953	0.302476	+	0.953157i	$0.402187\pi$
$264$	16.8359	1.03618
$265$	−1.13924	−0.0699831
$266$	6.08888	0.373333
$267$	−19.4783	−1.19205
$268$	−34.8522	−2.12894
$269$	1.48875	0.0907706	0.0453853	−	0.998970i	$-0.485548\pi$
$269$	1.48875	0.0907706	0.0453853	+	0.998970i	$0.485548\pi$
$270$	41.0234	2.49660
$271$	−27.7376	−1.68494	−0.842468	−	0.538746i	$-0.818898\pi$
$271$	−27.7376	−1.68494	−0.842468	+	0.538746i	$0.818898\pi$
$272$	−6.60750	−0.400638
$273$	−2.23568	−0.135310
$274$	−48.0928	−2.90539
$275$	7.84935	0.473334
$276$	63.2893	3.80957
$277$	−24.6505	−1.48110	−0.740552	−	0.671999i	$-0.765436\pi$
$277$	−24.6505	−1.48110	−0.740552	+	0.671999i	$0.765436\pi$
$278$	−18.6133	−1.11635
$279$	15.6200	0.935145
$280$	15.8971	0.950033
$281$	2.76881	0.165173	0.0825867	−	0.996584i	$-0.473682\pi$
$281$	2.76881	0.165173	0.0825867	+	0.996584i	$0.473682\pi$
$282$	14.5863	0.868599
$283$	−14.7986	−0.879685	−0.439843	−	0.898075i	$-0.644966\pi$
$283$	−14.7986	−0.879685	−0.439843	+	0.898075i	$0.644966\pi$
$284$	40.3766	2.39591
$285$	−32.7349	−1.93905
$286$	2.81333	0.166356
$287$	3.70385	0.218631
$288$	−21.0473	−1.24023
$289$	1.00000	0.0588235
$290$	15.3020	0.898565
$291$	−34.0101	−1.99371
$292$	−46.7960	−2.73853
$293$	28.3688	1.65732	0.828662	−	0.559749i	$-0.189103\pi$
$293$	28.3688	1.65732	0.828662	+	0.559749i	$0.189103\pi$
$294$	−45.2562	−2.63940
$295$	20.1673	1.17419
$296$	54.4897	3.16715
$297$	−4.52131	−0.262353
$298$	−0.221707	−0.0128432
$299$	5.77625	0.334049
$300$	−95.5900	−5.51889
$301$	0.727911	0.0419561
$302$	2.35743	0.135655
$303$	42.8644	2.46250
$304$	21.8358	1.25237
$305$	−40.2664	−2.30565
$306$	11.7351	0.670849
$307$	−9.77116	−0.557670	−0.278835	−	0.960339i	$-0.589948\pi$
$307$	−9.77116	−0.557670	−0.278835	+	0.960339i	$0.589948\pi$
$308$	−3.20789	−0.182786
$309$	−5.12121	−0.291335
$310$	−30.5696	−1.73624
$311$	−9.98449	−0.566168	−0.283084	−	0.959095i	$-0.591358\pi$
$311$	−9.98449	−0.566168	−0.283084	+	0.959095i	$0.591358\pi$
$312$	−18.7124	−1.05938
$313$	31.9647	1.80675	0.903376	−	0.428849i	$-0.141081\pi$
$313$	31.9647	1.80675	0.903376	+	0.428849i	$0.141081\pi$
$314$	−31.3990	−1.77195
$315$	−12.0970	−0.681589
$316$	59.1773	3.32898
$317$	−17.1474	−0.963092	−0.481546	−	0.876421i	$-0.659925\pi$
$317$	−17.1474	−0.963092	−0.481546	+	0.876421i	$0.659925\pi$
$318$	−2.22300	−0.124660
$319$	−1.68648	−0.0944248
$320$	−6.17916	−0.345426
$321$	24.9270	1.39129
$322$	−9.57541	−0.533616
$323$	−3.30470	−0.183879
$324$	−6.23362	−0.346312
$325$	−8.72424	−0.483934
$326$	−33.7826	−1.87105
$327$	−49.0707	−2.71361
$328$	31.0009	1.71174
$329$	−1.51795	−0.0836874
$330$	25.0729	1.38022
$331$	10.9993	0.604578	0.302289	−	0.953216i	$-0.402249\pi$
$331$	10.9993	0.604578	0.302289	+	0.953216i	$0.402249\pi$
$332$	−39.0034	−2.14059
$333$	−41.4643	−2.27223
$334$	−16.2898	−0.891338
$335$	−28.3485	−1.54884
$336$	13.2909	0.725076
$337$	−8.51147	−0.463649	−0.231825	−	0.972758i	$-0.574470\pi$
$337$	−8.51147	−0.463649	−0.231825	+	0.972758i	$0.574470\pi$
$338$	29.7787	1.61975
$339$	5.59451	0.303852
$340$	−15.7973	−0.856726
$341$	3.36917	0.182451
$342$	−38.7809	−2.09703
$343$	9.80507	0.529424
$344$	6.09254	0.328488
$345$	51.4790	2.77154
$346$	4.25800	0.228912
$347$	16.1557	0.867282	0.433641	−	0.901086i	$-0.357229\pi$
$347$	16.1557	0.867282	0.433641	+	0.901086i	$0.357229\pi$
$348$	20.5381	1.10096
$349$	17.5613	0.940034	0.470017	−	0.882657i	$-0.344248\pi$
$349$	17.5613	0.940034	0.470017	+	0.882657i	$0.344248\pi$
$350$	14.4624	0.773045
$351$	5.02525	0.268228
$352$	−4.53982	−0.241973
$353$	8.61383	0.458468	0.229234	−	0.973371i	$-0.426378\pi$
$353$	8.61383	0.458468	0.229234	+	0.973371i	$0.426378\pi$
$354$	39.3524	2.09156
$355$	32.8420	1.74307
$356$	31.0638	1.64638
$357$	−2.01148	−0.106459
$358$	−23.7100	−1.25311
$359$	8.45971	0.446486	0.223243	−	0.974763i	$-0.428336\pi$
$359$	8.45971	0.446486	0.223243	+	0.974763i	$0.428336\pi$
$360$	−101.251	−5.33638
$361$	−8.07894	−0.425207
$362$	−27.1590	−1.42745
$363$	−2.76336	−0.145039
$364$	3.56544	0.186880
$365$	−38.0635	−1.99233
$366$	−78.5718	−4.10701
$367$	−17.2297	−0.899385	−0.449692	−	0.893184i	$-0.648466\pi$
$367$	−17.2297	−0.899385	−0.449692	+	0.893184i	$0.648466\pi$
$368$	−34.3391	−1.79005
$369$	−23.5903	−1.22806
$370$	81.1489	4.21873
$371$	0.231342	0.0120107
$372$	−41.0299	−2.12730
$373$	−32.2724	−1.67100	−0.835500	−	0.549490i	$-0.814822\pi$
$373$	−32.2724	−1.67100	−0.835500	+	0.549490i	$0.814822\pi$
$374$	2.53120	0.130885
$375$	−28.2244	−1.45750
$376$	−12.7051	−0.655216
$377$	1.87446	0.0965393
$378$	−8.33046	−0.428473
$379$	−8.33140	−0.427955	−0.213978	−	0.976839i	$-0.568642\pi$
$379$	−8.33140	−0.427955	−0.213978	+	0.976839i	$0.568642\pi$
$380$	52.2052	2.67807
$381$	−36.9446	−1.89273
$382$	−33.9910	−1.73913
$383$	−19.9560	−1.01970	−0.509852	−	0.860262i	$-0.670300\pi$
$383$	−19.9560	−1.01970	−0.509852	+	0.860262i	$0.670300\pi$
$384$	−37.1477	−1.89569
$385$	−2.60927	−0.132981
$386$	−27.0143	−1.37499
$387$	−4.63616	−0.235669
$388$	54.2389	2.75356
$389$	12.2884	0.623048	0.311524	−	0.950238i	$-0.399161\pi$
$389$	12.2884	0.623048	0.311524	+	0.950238i	$0.399161\pi$
$390$	−27.8675	−1.41113
$391$	5.19699	0.262823
$392$	39.4196	1.99099
$393$	−17.8556	−0.900697
$394$	−39.9532	−2.01282
$395$	48.1343	2.42190
$396$	20.4315	1.02672
$397$	30.2991	1.52067	0.760334	−	0.649532i	$-0.225035\pi$
$397$	30.2991	1.52067	0.760334	+	0.649532i	$0.225035\pi$
$398$	−20.3777	−1.02144
$399$	6.64735	0.332784
$400$	51.8646	2.59323
$401$	26.1087	1.30381	0.651903	−	0.758302i	$-0.273971\pi$
$401$	26.1087	1.30381	0.651903	+	0.758302i	$0.273971\pi$
$402$	−55.3164	−2.75893
$403$	−3.74469	−0.186536
$404$	−68.3597	−3.40102
$405$	−5.07037	−0.251949
$406$	−3.10732	−0.154214
$407$	−8.94366	−0.443321
$408$	−16.8359	−0.833501
$409$	−19.0915	−0.944014	−0.472007	−	0.881595i	$-0.656470\pi$
$409$	−19.0915	−0.944014	−0.472007	+	0.881595i	$0.656470\pi$
$410$	46.1681	2.28008
$411$	−52.5038	−2.58982
$412$	8.16724	0.402371
$413$	−4.09530	−0.201516
$414$	60.9870	2.99735
$415$	−31.7251	−1.55732
$416$	5.04582	0.247392
$417$	−20.3205	−0.995100
$418$	−8.36487	−0.409139
$419$	25.7764	1.25926	0.629631	−	0.776894i	$-0.283206\pi$
$419$	25.7764	1.25926	0.629631	+	0.776894i	$0.283206\pi$
$420$	31.7759	1.55050
$421$	16.7687	0.817256	0.408628	−	0.912701i	$-0.366007\pi$
$421$	16.7687	0.817256	0.408628	+	0.912701i	$0.366007\pi$
$422$	−23.3205	−1.13522
$423$	9.66804	0.470076
$424$	1.93631	0.0940354
$425$	−7.84935	−0.380750
$426$	64.0845	3.10490
$427$	8.17675	0.395701
$428$	−39.7533	−1.92155
$429$	3.07136	0.148287
$430$	9.07334	0.437555
$431$	17.0944	0.823410	0.411705	−	0.911317i	$-0.364933\pi$
$431$	17.0944	0.823410	0.411705	+	0.911317i	$0.364933\pi$
$432$	−29.8745	−1.43734
$433$	−8.46890	−0.406989	−0.203495	−	0.979076i	$-0.565230\pi$
$433$	−8.46890	−0.406989	−0.203495	+	0.979076i	$0.565230\pi$
$434$	6.20765	0.297977
$435$	16.7055	0.800968
$436$	78.2574	3.74785
$437$	−17.1745	−0.821569
$438$	−74.2732	−3.54891
$439$	−2.76905	−0.132159	−0.0660797	−	0.997814i	$-0.521049\pi$
$439$	−2.76905	−0.132159	−0.0660797	+	0.997814i	$0.521049\pi$
$440$	−21.8393	−1.04115
$441$	−29.9966	−1.42841
$442$	−2.81333	−0.133816
$443$	29.2479	1.38961	0.694804	−	0.719199i	$-0.255491\pi$
$443$	29.2479	1.38961	0.694804	+	0.719199i	$0.255491\pi$
$444$	108.917	5.16895
$445$	25.2670	1.19777
$446$	−28.6028	−1.35438
$447$	−0.242042	−0.0114482
$448$	1.25478	0.0592828
$449$	−4.22147	−0.199224	−0.0996118	−	0.995026i	$-0.531760\pi$
$449$	−4.22147	−0.199224	−0.0996118	+	0.995026i	$0.531760\pi$
$450$	−92.1126	−4.34223
$451$	−5.08833	−0.239600
$452$	−8.92206	−0.419658
$453$	2.57365	0.120921
$454$	31.3938	1.47338
$455$	2.90010	0.135959
$456$	55.6376	2.60547
$457$	5.45810	0.255319	0.127659	−	0.991818i	$-0.459254\pi$
$457$	5.45810	0.255319	0.127659	+	0.991818i	$0.459254\pi$
$458$	42.2867	1.97593
$459$	4.52131	0.211036
$460$	−82.0982	−3.82785
$461$	−23.6125	−1.09974	−0.549872	−	0.835249i	$-0.685324\pi$
$461$	−23.6125	−1.09974	−0.549872	+	0.835249i	$0.685324\pi$
$462$	−5.09146	−0.236876
$463$	−9.62190	−0.447168	−0.223584	−	0.974685i	$-0.571776\pi$
$463$	−9.62190	−0.447168	−0.223584	+	0.974685i	$0.571776\pi$
$464$	−11.1434	−0.517320
$465$	−33.3734	−1.54766
$466$	−2.34906	−0.108818
$467$	28.5389	1.32062	0.660312	−	0.750992i	$-0.270424\pi$
$467$	28.5389	1.32062	0.660312	+	0.750992i	$0.270424\pi$
$468$	−22.7087	−1.04971
$469$	5.75663	0.265816
$470$	−18.9211	−0.872767
$471$	−34.2789	−1.57949
$472$	−34.2772	−1.57774
$473$	−1.00000	−0.0459800
$474$	93.9243	4.31409
$475$	25.9398	1.19020
$476$	3.20789	0.147033
$477$	−1.47345	−0.0674645
$478$	27.2703	1.24732
$479$	38.0948	1.74060	0.870298	−	0.492525i	$-0.163926\pi$
$479$	38.0948	1.74060	0.870298	+	0.492525i	$0.163926\pi$
$480$	44.9693	2.05256
$481$	9.94052	0.453249
$482$	41.1554	1.87458
$483$	−10.4537	−0.475658
$484$	4.40698	0.200317
$485$	44.1175	2.00327
$486$	−44.2268	−2.00617
$487$	21.4050	0.969955	0.484978	−	0.874527i	$-0.338828\pi$
$487$	21.4050	0.969955	0.484978	+	0.874527i	$0.338828\pi$
$488$	68.4386	3.09807
$489$	−36.8811	−1.66782
$490$	58.7058	2.65206
$491$	7.63187	0.344421	0.172211	−	0.985060i	$-0.444909\pi$
$491$	7.63187	0.344421	0.172211	+	0.985060i	$0.444909\pi$
$492$	61.9660	2.79364
$493$	1.68648	0.0759553
$494$	9.29721	0.418301
$495$	16.6188	0.746959
$496$	22.2618	0.999583
$497$	−6.66910	−0.299150
$498$	−61.9050	−2.77403
$499$	−1.11221	−0.0497895	−0.0248948	−	0.999690i	$-0.507925\pi$
$499$	−1.11221	−0.0497895	−0.0248948	+	0.999690i	$0.507925\pi$
$500$	45.0119	2.01300
$501$	−17.7839	−0.794526
$502$	12.6201	0.563263
$503$	−13.8676	−0.618325	−0.309163	−	0.951009i	$-0.600049\pi$
$503$	−13.8676	−0.618325	−0.309163	+	0.951009i	$0.600049\pi$
$504$	20.5606	0.915842
$505$	−55.6033	−2.47431
$506$	13.1546	0.584795
$507$	32.5100	1.44382
$508$	58.9189	2.61410
$509$	−15.0736	−0.668125	−0.334063	−	0.942551i	$-0.608420\pi$
$509$	−15.0736	−0.668125	−0.334063	+	0.942551i	$0.608420\pi$
$510$	−25.0729	−1.11025
$511$	7.72941	0.341929
$512$	50.5161	2.23252
$513$	−14.9416	−0.659687
$514$	−41.3706	−1.82478
$515$	6.64317	0.292733
$516$	12.1781	0.536110
$517$	2.08535	0.0917138
$518$	−16.4786	−0.724028
$519$	4.64854	0.204048
$520$	24.2735	1.06447
$521$	36.0203	1.57808	0.789040	−	0.614342i	$-0.210579\pi$
$521$	36.0203	1.57808	0.789040	+	0.614342i	$0.210579\pi$
$522$	19.7909	0.866226
$523$	3.39338	0.148382	0.0741910	−	0.997244i	$-0.476363\pi$
$523$	3.39338	0.148382	0.0741910	+	0.997244i	$0.476363\pi$
$524$	28.4760	1.24398
$525$	15.7888	0.689081
$526$	−24.8328	−1.08276
$527$	−3.36917	−0.146763
$528$	−18.2589	−0.794617
$529$	4.00874	0.174293
$530$	2.88365	0.125258
$531$	26.0835	1.13193
$532$	−10.6011	−0.459617
$533$	5.65547	0.244966
$534$	49.3035	2.13357
$535$	−32.3350	−1.39797
$536$	48.1824	2.08116
$537$	−25.8847	−1.11701
$538$	−3.76832	−0.162464
$539$	−6.47015	−0.278689
$540$	−71.4242	−3.07361
$541$	28.0282	1.20502	0.602512	−	0.798110i	$-0.294166\pi$
$541$	28.0282	1.20502	0.602512	+	0.798110i	$0.294166\pi$
$542$	70.2093	3.01575
$543$	−29.6500	−1.27240
$544$	4.53982	0.194643
$545$	63.6539	2.72663
$546$	5.65896	0.242181
$547$	−1.08127	−0.0462317	−0.0231159	−	0.999733i	$-0.507359\pi$
$547$	−1.08127	−0.0462317	−0.0231159	+	0.999733i	$0.507359\pi$
$548$	83.7325	3.57687
$549$	−52.0788	−2.22267
$550$	−19.8683	−0.847187
$551$	−5.57332	−0.237431
$552$	−87.4960	−3.72408
$553$	−9.77445	−0.415652
$554$	62.3953	2.65092
$555$	88.5918	3.76051
$556$	32.4070	1.37436
$557$	−28.3971	−1.20322	−0.601612	−	0.798788i	$-0.705475\pi$
$557$	−28.3971	−1.20322	−0.601612	+	0.798788i	$0.705475\pi$
$558$	−39.5374	−1.67375
$559$	1.11146	0.0470097
$560$	−17.2407	−0.728555
$561$	2.76336	0.116669
$562$	−7.00841	−0.295632
$563$	23.4617	0.988793	0.494396	−	0.869237i	$-0.335389\pi$
$563$	23.4617	0.988793	0.494396	+	0.869237i	$0.335389\pi$
$564$	−25.3956	−1.06935
$565$	−7.25713	−0.305310
$566$	37.4582	1.57449
$567$	1.02962	0.0432400
$568$	−55.8197	−2.34214
$569$	−28.0592	−1.17630	−0.588152	−	0.808750i	$-0.700144\pi$
$569$	−28.0592	−1.17630	−0.588152	+	0.808750i	$0.700144\pi$
$570$	82.8585	3.47056
$571$	29.8020	1.24718	0.623588	−	0.781753i	$-0.285674\pi$
$571$	29.8020	1.24718	0.623588	+	0.781753i	$0.285674\pi$
$572$	−4.89818	−0.204803
$573$	−37.1086	−1.55024
$574$	−9.37519	−0.391313
$575$	−40.7930	−1.70119
$576$	−7.99186	−0.332994
$577$	−36.2189	−1.50781	−0.753906	−	0.656982i	$-0.771833\pi$
$577$	−36.2189	−1.50781	−0.753906	+	0.656982i	$0.771833\pi$
$578$	−2.53120	−0.105284
$579$	−29.4920	−1.22565
$580$	−26.6418	−1.10624
$581$	6.44229	0.267271
$582$	86.0864	3.56840
$583$	−0.317816	−0.0131626
$584$	64.6944	2.67707
$585$	−18.4711	−0.763686
$586$	−71.8072	−2.96633
$587$	10.5470	0.435321	0.217660	−	0.976025i	$-0.430157\pi$
$587$	10.5470	0.435321	0.217660	+	0.976025i	$0.430157\pi$
$588$	78.7939	3.24940
$589$	11.1341	0.458772
$590$	−51.0475	−2.10159
$591$	−43.6177	−1.79419
$592$	−59.0952	−2.42880
$593$	−17.3195	−0.711228	−0.355614	−	0.934633i	$-0.615728\pi$
$593$	−17.3195	−0.711228	−0.355614	+	0.934633i	$0.615728\pi$
$594$	11.4443	0.469567
$595$	2.60927	0.106970
$596$	0.386006	0.0158114
$597$	−22.2467	−0.910497
$598$	−14.6208	−0.597891
$599$	14.3361	0.585756	0.292878	−	0.956150i	$-0.405387\pi$
$599$	14.3361	0.585756	0.292878	+	0.956150i	$0.405387\pi$
$600$	132.151	5.39504
$601$	−25.2401	−1.02957	−0.514783	−	0.857320i	$-0.672128\pi$
$601$	−25.2401	−1.02957	−0.514783	+	0.857320i	$0.672128\pi$
$602$	−1.84249	−0.0750943
$603$	−36.6647	−1.49310
$604$	−4.10443	−0.167007
$605$	3.58460	0.145735
$606$	−108.499	−4.40745
$607$	31.2892	1.26999	0.634994	−	0.772517i	$-0.281003\pi$
$607$	31.2892	1.26999	0.634994	+	0.772517i	$0.281003\pi$
$608$	−15.0027	−0.608442
$609$	−3.39232	−0.137464
$610$	101.922	4.12672
$611$	−2.31779	−0.0937676
$612$	−20.4315	−0.825893
$613$	−37.0168	−1.49509	−0.747547	−	0.664209i	$-0.768768\pi$
$613$	−37.0168	−1.49509	−0.747547	+	0.664209i	$0.768768\pi$
$614$	24.7328	0.998134
$615$	50.4026	2.03243
$616$	4.43483	0.178684
$617$	5.36868	0.216135	0.108067	−	0.994144i	$-0.465534\pi$
$617$	5.36868	0.216135	0.108067	+	0.994144i	$0.465534\pi$
$618$	12.9628	0.521440
$619$	24.3846	0.980100	0.490050	−	0.871694i	$-0.336979\pi$
$619$	24.3846	0.980100	0.490050	+	0.871694i	$0.336979\pi$
$620$	53.2236	2.13751
$621$	23.4972	0.942910
$622$	25.2727	1.01334
$623$	−5.13088	−0.205564
$624$	20.2940	0.812412
$625$	−2.63442	−0.105377
$626$	−80.9091	−3.23378
$627$	−9.13209	−0.364700
$628$	54.6676	2.18147
$629$	8.94366	0.356607
$630$	30.6199	1.21993
$631$	−21.7848	−0.867239	−0.433620	−	0.901096i	$-0.642764\pi$
$631$	−21.7848	−0.867239	−0.433620	+	0.901096i	$0.642764\pi$
$632$	−81.8112	−3.25427
$633$	−25.4594	−1.01192
$634$	43.4034	1.72377
$635$	47.9242	1.90181
$636$	3.87038	0.153471
$637$	7.19131	0.284930
$638$	4.26882	0.169004
$639$	42.4764	1.68034
$640$	48.1876	1.90478
$641$	28.1880	1.11336	0.556680	−	0.830727i	$-0.312075\pi$
$641$	28.1880	1.11336	0.556680	+	0.830727i	$0.312075\pi$
$642$	−63.0953	−2.49017
$643$	−0.986771	−0.0389144	−0.0194572	−	0.999811i	$-0.506194\pi$
$643$	−0.986771	−0.0389144	−0.0194572	+	0.999811i	$0.506194\pi$
$644$	16.6714	0.656944
$645$	9.90554	0.390030
$646$	8.36487	0.329111
$647$	12.6065	0.495614	0.247807	−	0.968809i	$-0.420290\pi$
$647$	12.6065	0.495614	0.247807	+	0.968809i	$0.420290\pi$
$648$	8.61783	0.338540
$649$	5.62610	0.220844
$650$	22.0828	0.866159
$651$	6.77702	0.265612
$652$	58.8176	2.30348
$653$	39.5312	1.54698	0.773488	−	0.633811i	$-0.218510\pi$
$653$	39.5312	1.54698	0.773488	+	0.633811i	$0.218510\pi$
$654$	124.208	4.85691
$655$	23.1621	0.905019
$656$	−33.6211	−1.31268
$657$	−49.2296	−1.92063
$658$	3.84224	0.149786
$659$	4.72138	0.183919	0.0919594	−	0.995763i	$-0.470687\pi$
$659$	4.72138	0.183919	0.0919594	+	0.995763i	$0.470687\pi$
$660$	−43.6535	−1.69921
$661$	−13.5522	−0.527121	−0.263561	−	0.964643i	$-0.584897\pi$
$661$	−13.5522	−0.527121	−0.263561	+	0.964643i	$0.584897\pi$
$662$	−27.8415	−1.08209
$663$	−3.07136	−0.119282
$664$	53.9213	2.09255
$665$	−8.62286	−0.334380
$666$	104.954	4.06690
$667$	8.76463	0.339368
$668$	28.3616	1.09734
$669$	−31.2262	−1.20728
$670$	71.7558	2.77217
$671$	−11.2332	−0.433652
$672$	−9.13176	−0.352265
$673$	−43.0031	−1.65765	−0.828823	−	0.559511i	$-0.810989\pi$
$673$	−43.0031	−1.65765	−0.828823	+	0.559511i	$0.810989\pi$
$674$	21.5442	0.829853
$675$	−35.4893	−1.36598
$676$	−51.8466	−1.99410
$677$	−5.30738	−0.203979	−0.101990	−	0.994785i	$-0.532521\pi$
$677$	−5.30738	−0.203979	−0.101990	+	0.994785i	$0.532521\pi$
$678$	−14.1608	−0.543843
$679$	−8.95878	−0.343806
$680$	21.8393	0.837500
$681$	34.2732	1.31335
$682$	−8.52804	−0.326555
$683$	−19.4323	−0.743555	−0.371777	−	0.928322i	$-0.621252\pi$
$683$	−19.4323	−0.743555	−0.371777	+	0.928322i	$0.621252\pi$
$684$	67.5199	2.58169
$685$	68.1073	2.60225
$686$	−24.8186	−0.947579
$687$	46.1652	1.76131
$688$	−6.60750	−0.251909
$689$	0.353240	0.0134574
$690$	−130.304	−4.96058
$691$	−19.1445	−0.728290	−0.364145	−	0.931342i	$-0.618639\pi$
$691$	−19.1445	−0.728290	−0.364145	+	0.931342i	$0.618639\pi$
$692$	−7.41344	−0.281817
$693$	−3.37471	−0.128195
$694$	−40.8933	−1.55229
$695$	26.3595	0.999875
$696$	−28.3934	−1.07625
$697$	5.08833	0.192734
$698$	−44.4511	−1.68250
$699$	−2.56452	−0.0969989
$700$	−25.1799	−0.951709
$701$	−17.8388	−0.673764	−0.336882	−	0.941547i	$-0.609372\pi$
$701$	−17.8388	−0.673764	−0.336882	+	0.941547i	$0.609372\pi$
$702$	−12.7199	−0.480082
$703$	−29.5561	−1.11473
$704$	−1.72381	−0.0649685
$705$	−20.6566	−0.777971
$706$	−21.8033	−0.820579
$707$	11.2911	0.424647
$708$	−68.5150	−2.57495
$709$	−43.9451	−1.65039	−0.825196	−	0.564847i	$-0.808935\pi$
$709$	−43.9451	−1.65039	−0.825196	+	0.564847i	$0.808935\pi$
$710$	−83.1297	−3.11980
$711$	62.2548	2.33474
$712$	−42.9450	−1.60943
$713$	−17.5095	−0.655737
$714$	5.09146	0.190543
$715$	−3.98414	−0.148998
$716$	41.2806	1.54273
$717$	29.7715	1.11184
$718$	−21.4132	−0.799135
$719$	−21.3436	−0.795983	−0.397991	−	0.917389i	$-0.630293\pi$
$719$	−21.3436	−0.795983	−0.397991	+	0.917389i	$0.630293\pi$
$720$	109.809	4.09232
$721$	−1.34900	−0.0502395
$722$	20.4494	0.761049
$723$	44.9302	1.67097
$724$	47.2856	1.75735
$725$	−13.2378	−0.491639
$726$	6.99462	0.259595
$727$	22.3115	0.827487	0.413743	−	0.910394i	$-0.364221\pi$
$727$	22.3115	0.827487	0.413743	+	0.910394i	$0.364221\pi$
$728$	−4.92914	−0.182686
$729$	−44.0398	−1.63110
$730$	96.3463	3.56594
$731$	1.00000	0.0369863
$732$	136.798	5.05621
$733$	13.4155	0.495512	0.247756	−	0.968823i	$-0.420307\pi$
$733$	13.4155	0.495512	0.247756	+	0.968823i	$0.420307\pi$
$734$	43.6119	1.60974
$735$	64.0903	2.36401
$736$	23.5934	0.869664
$737$	−7.90842	−0.291310
$738$	59.7118	2.19802
$739$	26.7037	0.982310	0.491155	−	0.871072i	$-0.336575\pi$
$739$	26.7037	0.982310	0.491155	+	0.871072i	$0.336575\pi$
$740$	−141.285	−5.19375
$741$	10.1499	0.372868
$742$	−0.585572	−0.0214970
$743$	−46.4708	−1.70485	−0.852425	−	0.522849i	$-0.824869\pi$
$743$	−46.4708	−1.70485	−0.852425	+	0.522849i	$0.824869\pi$
$744$	56.7229	2.07956
$745$	0.313974	0.0115031
$746$	81.6879	2.99081
$747$	−41.0318	−1.50127
$748$	−4.40698	−0.161135
$749$	6.56615	0.239922
$750$	71.4416	2.60868
$751$	29.2481	1.06728	0.533639	−	0.845712i	$-0.320824\pi$
$751$	29.2481	1.06728	0.533639	+	0.845712i	$0.320824\pi$
$752$	13.7790	0.502467
$753$	13.7776	0.502084
$754$	−4.74462	−0.172789
$755$	−3.33851	−0.121501
$756$	14.5038	0.527500
$757$	−47.5353	−1.72770	−0.863850	−	0.503748i	$-0.831954\pi$
$757$	−47.5353	−1.72770	−0.863850	+	0.503748i	$0.831954\pi$
$758$	21.0885	0.765967
$759$	14.3612	0.521277
$760$	−72.1725	−2.61797
$761$	8.45911	0.306642	0.153321	−	0.988176i	$-0.451003\pi$
$761$	8.45911	0.306642	0.153321	+	0.988176i	$0.451003\pi$
$762$	93.5143	3.38767
$763$	−12.9260	−0.467951
$764$	59.1804	2.14107
$765$	−16.6188	−0.600853
$766$	50.5127	1.82510
$767$	−6.25318	−0.225789
$768$	84.5013	3.04918
$769$	27.4662	0.990458	0.495229	−	0.868763i	$-0.335084\pi$
$769$	27.4662	0.990458	0.495229	+	0.868763i	$0.335084\pi$
$770$	6.60459	0.238013
$771$	−45.1650	−1.62658
$772$	47.0336	1.69277
$773$	33.8368	1.21702	0.608512	−	0.793544i	$-0.291767\pi$
$773$	33.8368	1.21702	0.608512	+	0.793544i	$0.291767\pi$
$774$	11.7351	0.421808
$775$	26.4458	0.949960
$776$	−74.9841	−2.69177
$777$	−17.9900	−0.645388
$778$	−31.1045	−1.11515
$779$	−16.8154	−0.602474
$780$	48.5191	1.73726
$781$	9.16197	0.327841
$782$	−13.1546	−0.470409
$783$	7.62509	0.272499
$784$	−42.7515	−1.52684
$785$	44.4662	1.58707
$786$	45.1962	1.61209
$787$	7.45921	0.265892	0.132946	−	0.991123i	$-0.457556\pi$
$787$	7.45921	0.265892	0.132946	+	0.991123i	$0.457556\pi$
$788$	69.5611	2.47801
$789$	−27.1105	−0.965158
$790$	−121.838	−4.33479
$791$	1.47368	0.0523980
$792$	−28.2460	−1.00368
$793$	12.4852	0.443363
$794$	−76.6931	−2.72174
$795$	3.14814	0.111653
$796$	35.4788	1.25751
$797$	49.1949	1.74257	0.871286	−	0.490775i	$-0.163286\pi$
$797$	49.1949	1.74257	0.871286	+	0.490775i	$0.163286\pi$
$798$	−16.8258	−0.595626
$799$	−2.08535	−0.0737745
$800$	−35.6346	−1.25987
$801$	32.6793	1.15467
$802$	−66.0863	−2.33359
$803$	−10.6186	−0.374723
$804$	96.3093	3.39657
$805$	13.5604	0.477940
$806$	9.47857	0.333868
$807$	−4.11395	−0.144818
$808$	94.5058	3.32470
$809$	−24.9932	−0.878713	−0.439356	−	0.898313i	$-0.644793\pi$
$809$	−24.9932	−0.878713	−0.439356	+	0.898313i	$0.644793\pi$
$810$	12.8341	0.450945
$811$	16.9689	0.595859	0.297929	−	0.954588i	$-0.403704\pi$
$811$	16.9689	0.595859	0.297929	+	0.954588i	$0.403704\pi$
$812$	5.41004	0.189855
$813$	76.6489	2.68819
$814$	22.6382	0.793469
$815$	47.8418	1.67582
$816$	18.2589	0.639189
$817$	−3.30470	−0.115617
$818$	48.3244	1.68962
$819$	3.75086	0.131066
$820$	−80.3816	−2.80705
$821$	21.2283	0.740874	0.370437	−	0.928858i	$-0.379208\pi$
$821$	21.2283	0.740874	0.370437	+	0.928858i	$0.379208\pi$
$822$	132.898	4.63534
$823$	−21.6128	−0.753375	−0.376687	−	0.926340i	$-0.622937\pi$
$823$	−21.6128	−0.753375	−0.376687	+	0.926340i	$0.622937\pi$
$824$	−11.2910	−0.393342
$825$	−21.6906	−0.755170
$826$	10.3660	0.360680
$827$	−34.6050	−1.20333	−0.601666	−	0.798747i	$-0.705496\pi$
$827$	−34.6050	−1.20333	−0.601666	+	0.798747i	$0.705496\pi$
$828$	−106.182	−3.69009
$829$	−16.8068	−0.583726	−0.291863	−	0.956460i	$-0.594275\pi$
$829$	−16.8068	−0.583726	−0.291863	+	0.956460i	$0.594275\pi$
$830$	80.3025	2.78734
$831$	68.1181	2.36299
$832$	1.91594	0.0664234
$833$	6.47015	0.224177
$834$	51.4353	1.78106
$835$	23.0691	0.798338
$836$	14.5638	0.503698
$837$	−15.2330	−0.526531
$838$	−65.2454	−2.25386
$839$	46.9449	1.62072	0.810358	−	0.585935i	$-0.199273\pi$
$839$	46.9449	1.62072	0.810358	+	0.585935i	$0.199273\pi$
$840$	−43.9294	−1.51571
$841$	−26.1558	−0.901924
$842$	−42.4449	−1.46275
$843$	−7.65122	−0.263522
$844$	40.6024	1.39759
$845$	−42.1716	−1.45075
$846$	−24.4717	−0.841356
$847$	−0.727911	−0.0250113
$848$	−2.09997	−0.0721132
$849$	40.8939	1.40347
$850$	19.8683	0.681477
$851$	46.4801	1.59332
$852$	−111.575	−3.82250
$853$	22.0380	0.754566	0.377283	−	0.926098i	$-0.376858\pi$
$853$	22.0380	0.754566	0.377283	+	0.926098i	$0.376858\pi$
$854$	−20.6970	−0.708237
$855$	54.9201	1.87823
$856$	54.9581	1.87843
$857$	49.2367	1.68189	0.840946	−	0.541119i	$-0.181999\pi$
$857$	49.2367	1.68189	0.840946	+	0.541119i	$0.181999\pi$
$858$	−7.77424	−0.265408
$859$	11.4770	0.391590	0.195795	−	0.980645i	$-0.437271\pi$
$859$	11.4770	0.391590	0.195795	+	0.980645i	$0.437271\pi$
$860$	−15.7973	−0.538682
$861$	−10.2351	−0.348810
$862$	−43.2695	−1.47376
$863$	−25.2768	−0.860434	−0.430217	−	0.902726i	$-0.641563\pi$
$863$	−25.2768	−0.860434	−0.430217	+	0.902726i	$0.641563\pi$
$864$	20.5259	0.698305
$865$	−6.03003	−0.205027
$866$	21.4365	0.728441
$867$	−2.76336	−0.0938486
$868$	−10.8079	−0.366844
$869$	13.4281	0.455516
$870$	−42.2850	−1.43360
$871$	8.78989	0.297834
$872$	−108.189	−3.66374
$873$	57.0596	1.93118
$874$	43.4722	1.47047
$875$	−7.43473	−0.251340
$876$	129.314	4.36912
$877$	−16.0833	−0.543093	−0.271546	−	0.962425i	$-0.587535\pi$
$877$	−16.0833	−0.543093	−0.271546	+	0.962425i	$0.587535\pi$
$878$	7.00902	0.236543
$879$	−78.3933	−2.64414
$880$	23.6852	0.798429
$881$	−39.9404	−1.34563	−0.672813	−	0.739812i	$-0.734914\pi$
$881$	−39.9404	−1.34563	−0.672813	+	0.739812i	$0.734914\pi$
$882$	75.9275	2.55661
$883$	−23.3355	−0.785303	−0.392651	−	0.919687i	$-0.628442\pi$
$883$	−23.3355	−0.785303	−0.392651	+	0.919687i	$0.628442\pi$
$884$	4.89818	0.164744
$885$	−55.7295	−1.87333
$886$	−74.0322	−2.48716
$887$	19.0914	0.641028	0.320514	−	0.947244i	$-0.396144\pi$
$887$	19.0914	0.641028	0.320514	+	0.947244i	$0.396144\pi$
$888$	−150.575	−5.05295
$889$	−9.73178	−0.326393
$890$	−63.9559	−2.14381
$891$	−1.41449	−0.0473871
$892$	49.7992	1.66740
$893$	6.89148	0.230614
$894$	0.612658	0.0204903
$895$	33.5773	1.12237
$896$	−9.78527	−0.326903
$897$	−15.9619	−0.532951
$898$	10.6854	0.356576
$899$	−5.68203	−0.189506
$900$	160.374	5.34579
$901$	0.317816	0.0105880
$902$	12.8796	0.428843
$903$	−2.01148	−0.0669379
$904$	12.3345	0.410241
$905$	38.4617	1.27851
$906$	−6.51443	−0.216428
$907$	6.32800	0.210118	0.105059	−	0.994466i	$-0.466497\pi$
$907$	6.32800	0.210118	0.105059	+	0.994466i	$0.466497\pi$
$908$	−54.6585	−1.81391
$909$	−71.9148	−2.38526
$910$	−7.34073	−0.243343
$911$	39.9389	1.32324	0.661618	−	0.749841i	$-0.269870\pi$
$911$	39.9389	1.32324	0.661618	+	0.749841i	$0.269870\pi$
$912$	−60.3402	−1.99807
$913$	−8.85038	−0.292905
$914$	−13.8155	−0.456977
$915$	111.271	3.67849
$916$	−73.6237	−2.43260
$917$	−4.70344	−0.155321
$918$	−11.4443	−0.377719
$919$	−11.2318	−0.370503	−0.185252	−	0.982691i	$-0.559310\pi$
$919$	−11.2318	−0.370503	−0.185252	+	0.982691i	$0.559310\pi$
$920$	113.499	3.74195
$921$	27.0013	0.889721
$922$	59.7680	1.96835
$923$	−10.1832	−0.335183
$924$	8.86455	0.291622
$925$	−70.2020	−2.30823
$926$	24.3550	0.800354
$927$	8.59198	0.282198
$928$	7.65631	0.251331
$929$	56.6387	1.85826	0.929128	−	0.369759i	$-0.120560\pi$
$929$	56.6387	1.85826	0.929128	+	0.369759i	$0.120560\pi$
$930$	84.4748	2.77004
$931$	−21.3819	−0.700764
$932$	4.08986	0.133968
$933$	27.5907	0.903280
$934$	−72.2377	−2.36369
$935$	−3.58460	−0.117229
$936$	31.3943	1.02616
$937$	−30.9539	−1.01122	−0.505610	−	0.862762i	$-0.668732\pi$
$937$	−30.9539	−1.01122	−0.505610	+	0.862762i	$0.668732\pi$
$938$	−14.5712	−0.475766
$939$	−88.3300	−2.88254
$940$	32.9429	1.07448
$941$	−9.45627	−0.308266	−0.154133	−	0.988050i	$-0.549258\pi$
$941$	−9.45627	−0.308266	−0.154133	+	0.988050i	$0.549258\pi$
$942$	86.7667	2.82701
$943$	26.4440	0.861135
$944$	37.1744	1.20992
$945$	11.7973	0.383766
$946$	2.53120	0.0822964
$947$	22.4456	0.729383	0.364692	−	0.931128i	$-0.381174\pi$
$947$	22.4456	0.729383	0.364692	+	0.931128i	$0.381174\pi$
$948$	−163.528	−5.31115
$949$	11.8022	0.383114
$950$	−65.6588	−2.13025
$951$	47.3844	1.53654
$952$	−4.43483	−0.143734
$953$	53.3749	1.72898	0.864492	−	0.502647i	$-0.167640\pi$
$953$	53.3749	1.72898	0.864492	+	0.502647i	$0.167640\pi$
$954$	3.72959	0.120750
$955$	48.1369	1.55767
$956$	−47.4793	−1.53559
$957$	4.66035	0.150648
$958$	−96.4256	−3.11537
$959$	−13.8303	−0.446604
$960$	17.0753	0.551102
$961$	−19.6487	−0.633830
$962$	−25.1615	−0.811238
$963$	−41.8207	−1.34765
$964$	−71.6542	−2.30783
$965$	38.2567	1.23153
$966$	26.4603	0.851346
$967$	46.7318	1.50279	0.751397	−	0.659851i	$-0.229381\pi$
$967$	46.7318	1.50279	0.751397	+	0.659851i	$0.229381\pi$
$968$	−6.09254	−0.195822
$969$	9.13209	0.293365
$970$	−111.670	−3.58552
$971$	18.9699	0.608775	0.304387	−	0.952548i	$-0.401548\pi$
$971$	18.9699	0.608775	0.304387	+	0.952548i	$0.401548\pi$
$972$	77.0016	2.46983
$973$	−5.35274	−0.171601
$974$	−54.1805	−1.73605
$975$	24.1082	0.772081
$976$	−74.2232	−2.37583
$977$	−12.6718	−0.405407	−0.202703	−	0.979240i	$-0.564973\pi$
$977$	−12.6718	−0.405407	−0.202703	+	0.979240i	$0.564973\pi$
$978$	93.3535	2.98512
$979$	7.04878	0.225280
$980$	−102.211	−3.26499
$981$	82.3271	2.62850
$982$	−19.3178	−0.616456
$983$	−42.1953	−1.34582	−0.672911	−	0.739723i	$-0.734956\pi$
$983$	−42.1953	−1.34582	−0.672911	+	0.739723i	$0.734956\pi$
$984$	−85.6665	−2.73095
$985$	56.5804	1.80280
$986$	−4.26882	−0.135947
$987$	4.19465	0.133517
$988$	−16.1870	−0.514978
$989$	5.19699	0.165255
$990$	−42.0655	−1.33693
$991$	−46.4445	−1.47536	−0.737679	−	0.675151i	$-0.764078\pi$
$991$	−46.4445	−1.47536	−0.737679	+	0.675151i	$0.764078\pi$
$992$	−15.2954	−0.485629
$993$	−30.3951	−0.964560
$994$	16.8808	0.535427
$995$	28.8582	0.914865
$996$	107.781	3.41516
$997$	0.465258	0.0147349	0.00736743	−	0.999973i	$-0.497655\pi$
$997$	0.465258	0.0147349	0.00736743	+	0.999973i	$0.497655\pi$
$998$	2.81524	0.0891147
$999$	40.4370	1.27937

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.i.1.6	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.i.1.6	✓	78	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:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.53120 q^{2} -2.76336 q^{3} +4.40698 q^{4} +3.58460 q^{5} +6.99462 q^{6} -0.727911 q^{7} -6.09254 q^{8} +4.63616 q^{9} +O(q^{10})\)	\(q-2.53120 q^{2} -2.76336 q^{3} +4.40698 q^{4} +3.58460 q^{5} +6.99462 q^{6} -0.727911 q^{7} -6.09254 q^{8} +4.63616 q^{9} -9.07334 q^{10} +1.00000 q^{11} -12.1781 q^{12} -1.11146 q^{13} +1.84249 q^{14} -9.90554 q^{15} +6.60750 q^{16} -1.00000 q^{17} -11.7351 q^{18} +3.30470 q^{19} +15.7973 q^{20} +2.01148 q^{21} -2.53120 q^{22} -5.19699 q^{23} +16.8359 q^{24} +7.84935 q^{25} +2.81333 q^{26} -4.52131 q^{27} -3.20789 q^{28} -1.68648 q^{29} +25.0729 q^{30} +3.36917 q^{31} -4.53982 q^{32} -2.76336 q^{33} +2.53120 q^{34} -2.60927 q^{35} +20.4315 q^{36} -8.94366 q^{37} -8.36487 q^{38} +3.07136 q^{39} -21.8393 q^{40} -5.08833 q^{41} -5.09146 q^{42} -1.00000 q^{43} +4.40698 q^{44} +16.6188 q^{45} +13.1546 q^{46} +2.08535 q^{47} -18.2589 q^{48} -6.47015 q^{49} -19.8683 q^{50} +2.76336 q^{51} -4.89818 q^{52} -0.317816 q^{53} +11.4443 q^{54} +3.58460 q^{55} +4.43483 q^{56} -9.13209 q^{57} +4.26882 q^{58} +5.62610 q^{59} -43.6535 q^{60} -11.2332 q^{61} -8.52804 q^{62} -3.37471 q^{63} -1.72381 q^{64} -3.98414 q^{65} +6.99462 q^{66} -7.90842 q^{67} -4.40698 q^{68} +14.3612 q^{69} +6.60459 q^{70} +9.16197 q^{71} -28.2460 q^{72} -10.6186 q^{73} +22.6382 q^{74} -21.6906 q^{75} +14.5638 q^{76} -0.727911 q^{77} -7.77424 q^{78} +13.4281 q^{79} +23.6852 q^{80} -1.41449 q^{81} +12.8796 q^{82} -8.85038 q^{83} +8.86455 q^{84} -3.58460 q^{85} +2.53120 q^{86} +4.66035 q^{87} -6.09254 q^{88} +7.04878 q^{89} -42.0655 q^{90} +0.809044 q^{91} -22.9030 q^{92} -9.31022 q^{93} -5.27845 q^{94} +11.8460 q^{95} +12.5452 q^{96} +12.3075 q^{97} +16.3772 q^{98} +4.63616 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9}+O(q^{10}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9	\( 78 q + 7 q^{2} + 10 q^{3} + 91 q^{4} + 17 q^{5} + 12 q^{6} + 11 q^{7} + 33 q^{8} + 102 q^{9} + 3 q^{10} + 78 q^{11} + 31 q^{12} - 16 q^{13} + 31 q^{14} + 38 q^{15} + 121 q^{16} - 78 q^{17} + 11 q^{18} + 51 q^{20} + 6 q^{21} + 7 q^{22} + 48 q^{23} + 11 q^{24} + 101 q^{25} + 18 q^{26} + 46 q^{27} + 27 q^{28} + 22 q^{29} + 14 q^{30} + 56 q^{31} + 83 q^{32} + 10 q^{33} - 7 q^{34} + 24 q^{35} + 139 q^{36} + 53 q^{37} + 10 q^{38} + 79 q^{39} - q^{40} + 23 q^{41} + 17 q^{42} - 78 q^{43} + 91 q^{44} + 76 q^{45} + 21 q^{46} + 57 q^{47} + 78 q^{48} + 115 q^{49} + 58 q^{50} - 10 q^{51} - 63 q^{52} + 22 q^{53} - 18 q^{54} + 17 q^{55} + 111 q^{56} - 11 q^{57} + 36 q^{58} + 71 q^{59} + 36 q^{60} + 4 q^{61} - 5 q^{62} + 71 q^{63} + 183 q^{64} + 47 q^{65} + 12 q^{66} + 11 q^{67} - 91 q^{68} + 31 q^{69} + 33 q^{70} + 159 q^{71} + 59 q^{72} + 2 q^{73} - 4 q^{74} + 83 q^{75} - 44 q^{76} + 11 q^{77} + 101 q^{78} + 35 q^{79} + 85 q^{80} + 170 q^{81} + 98 q^{82} - 32 q^{83} + 44 q^{84} - 17 q^{85} - 7 q^{86} - 6 q^{87} + 33 q^{88} + 50 q^{89} - 5 q^{90} + 86 q^{91} + 106 q^{92} + 68 q^{93} - q^{94} + 109 q^{95} - 50 q^{96} + 40 q^{97} + 106 q^{98} + 102 q^{99}+O(q^{100}) \) 78 * q + 7 * q^2 + 10 * q^3 + 91 * q^4 + 17 * q^5 + 12 * q^6 + 11 * q^7 + 33 * q^8 + 102 * q^9 + 3 * q^10 + 78 * q^11 + 31 * q^12 - 16 * q^13 + 31 * q^14 + 38 * q^15 + 121 * q^16 - 78 * q^17 + 11 * q^18 + 51 * q^20 + 6 * q^21 + 7 * q^22 + 48 * q^23 + 11 * q^24 + 101 * q^25 + 18 * q^26 + 46 * q^27 + 27 * q^28 + 22 * q^29 + 14 * q^30 + 56 * q^31 + 83 * q^32 + 10 * q^33 - 7 * q^34 + 24 * q^35 + 139 * q^36 + 53 * q^37 + 10 * q^38 + 79 * q^39 - q^40 + 23 * q^41 + 17 * q^42 - 78 * q^43 + 91 * q^44 + 76 * q^45 + 21 * q^46 + 57 * q^47 + 78 * q^48 + 115 * q^49 + 58 * q^50 - 10 * q^51 - 63 * q^52 + 22 * q^53 - 18 * q^54 + 17 * q^55 + 111 * q^56 - 11 * q^57 + 36 * q^58 + 71 * q^59 + 36 * q^60 + 4 * q^61 - 5 * q^62 + 71 * q^63 + 183 * q^64 + 47 * q^65 + 12 * q^66 + 11 * q^67 - 91 * q^68 + 31 * q^69 + 33 * q^70 + 159 * q^71 + 59 * q^72 + 2 * q^73 - 4 * q^74 + 83 * q^75 - 44 * q^76 + 11 * q^77 + 101 * q^78 + 35 * q^79 + 85 * q^80 + 170 * q^81 + 98 * q^82 - 32 * q^83 + 44 * q^84 - 17 * q^85 - 7 * q^86 - 6 * q^87 + 33 * q^88 + 50 * q^89 - 5 * q^90 + 86 * q^91 + 106 * q^92 + 68 * q^93 - q^94 + 109 * q^95 - 50 * q^96 + 40 * q^97 + 106 * q^98 + 102 * q^99

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