LMFDB - Embedded newform 161.2.a.d.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [161,2,Mod(1,161)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(161, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("161.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 161 = 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	161.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:	$1.28559147254$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.2147108.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 9x^{3} + 17x^{2} + 16x - 27 $ x^5 - 2x^4 - 9x^3 + 17x^2 + 16x - 27
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.69017$ of defining polynomial
Character	$\chi$	$=$	161.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.69017 q^{2} -0.269842 q^{3} +5.23702 q^{4} -3.51109 q^{5} -0.725921 q^{6} +1.00000 q^{7} +8.70812 q^{8} -2.92719 q^{9} +O(q^{10})$	\(q+2.69017 q^{2} -0.269842 q^{3} +5.23702 q^{4} -3.51109 q^{5} -0.725921 q^{6} +1.00000 q^{7} +8.70812 q^{8} -2.92719 q^{9} -9.44544 q^{10} -3.78810 q^{11} -1.41317 q^{12} +1.24125 q^{13} +2.69017 q^{14} +0.947441 q^{15} +12.9523 q^{16} +5.98512 q^{17} -7.87463 q^{18} -3.38034 q^{19} -18.3877 q^{20} -0.269842 q^{21} -10.1906 q^{22} -1.00000 q^{23} -2.34982 q^{24} +7.32778 q^{25} +3.33918 q^{26} +1.59940 q^{27} +5.23702 q^{28} -7.02088 q^{29} +2.54878 q^{30} +6.26984 q^{31} +17.4276 q^{32} +1.02219 q^{33} +16.1010 q^{34} -3.51109 q^{35} -15.3297 q^{36} +4.84066 q^{37} -9.09369 q^{38} -0.334942 q^{39} -30.5750 q^{40} -1.78094 q^{41} -0.725921 q^{42} +3.02219 q^{43} -19.8383 q^{44} +10.2776 q^{45} -2.69017 q^{46} +3.90322 q^{47} -3.49508 q^{48} +1.00000 q^{49} +19.7130 q^{50} -1.61504 q^{51} +6.50046 q^{52} -2.47403 q^{53} +4.30267 q^{54} +13.3004 q^{55} +8.70812 q^{56} +0.912158 q^{57} -18.8873 q^{58} -2.89143 q^{59} +4.96176 q^{60} -10.3518 q^{61} +16.8669 q^{62} -2.92719 q^{63} +20.9787 q^{64} -4.35815 q^{65} +2.74986 q^{66} +11.4466 q^{67} +31.3442 q^{68} +0.269842 q^{69} -9.44544 q^{70} +2.70157 q^{71} -25.4903 q^{72} -14.1893 q^{73} +13.0222 q^{74} -1.97734 q^{75} -17.7029 q^{76} -3.78810 q^{77} -0.901051 q^{78} +3.31407 q^{79} -45.4767 q^{80} +8.34997 q^{81} -4.79102 q^{82} +7.02219 q^{83} -1.41317 q^{84} -21.0143 q^{85} +8.13020 q^{86} +1.89453 q^{87} -32.9872 q^{88} -1.59107 q^{89} +27.6486 q^{90} +1.24125 q^{91} -5.23702 q^{92} -1.69187 q^{93} +10.5003 q^{94} +11.8687 q^{95} -4.70271 q^{96} -11.6270 q^{97} +2.69017 q^{98} +11.0885 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) $ 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9} - 8 q^{10} - 4 q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{14} + 10 q^{15} + 10 q^{16} - 12 q^{17} - 19 q^{18} + 6 q^{19} + 14 q^{22} - 5 q^{23} - 36 q^{24} + 19 q^{25} + q^{26} + 12 q^{28} - 4 q^{29} - 48 q^{30} + 30 q^{31} + 8 q^{32} - 22 q^{33} + 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{37} - 40 q^{38} + 16 q^{39} - 50 q^{40} + 6 q^{41} - 3 q^{42} - 12 q^{43} - 26 q^{44} - 12 q^{45} - 2 q^{46} + 10 q^{47} + 25 q^{48} + 5 q^{49} - 2 q^{50} - 4 q^{51} - 21 q^{52} + 16 q^{53} + 33 q^{54} + 18 q^{55} + 3 q^{56} + 6 q^{57} + 13 q^{58} + 22 q^{59} + 30 q^{60} - 18 q^{61} + 15 q^{62} + 11 q^{63} + 25 q^{64} - 26 q^{65} + 4 q^{66} - 2 q^{67} + 12 q^{68} - 8 q^{70} + 4 q^{71} - 41 q^{72} - 2 q^{73} + 38 q^{74} - 30 q^{75} + 10 q^{76} - 4 q^{77} + 41 q^{78} + 30 q^{79} - 10 q^{80} - 3 q^{81} - 7 q^{82} + 8 q^{83} + 3 q^{84} - 12 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 20 q^{89} + 34 q^{90} - 6 q^{91} - 12 q^{92} - 26 q^{93} - 25 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9 - 8 * q^10 - 4 * q^11 + 3 * q^12 - 6 * q^13 + 2 * q^14 + 10 * q^15 + 10 * q^16 - 12 * q^17 - 19 * q^18 + 6 * q^19 + 14 * q^22 - 5 * q^23 - 36 * q^24 + 19 * q^25 + q^26 + 12 * q^28 - 4 * q^29 - 48 * q^30 + 30 * q^31 + 8 * q^32 - 22 * q^33 + 6 * q^34 - 4 * q^35 - q^36 + 4 * q^37 - 40 * q^38 + 16 * q^39 - 50 * q^40 + 6 * q^41 - 3 * q^42 - 12 * q^43 - 26 * q^44 - 12 * q^45 - 2 * q^46 + 10 * q^47 + 25 * q^48 + 5 * q^49 - 2 * q^50 - 4 * q^51 - 21 * q^52 + 16 * q^53 + 33 * q^54 + 18 * q^55 + 3 * q^56 + 6 * q^57 + 13 * q^58 + 22 * q^59 + 30 * q^60 - 18 * q^61 + 15 * q^62 + 11 * q^63 + 25 * q^64 - 26 * q^65 + 4 * q^66 - 2 * q^67 + 12 * q^68 - 8 * q^70 + 4 * q^71 - 41 * q^72 - 2 * q^73 + 38 * q^74 - 30 * q^75 + 10 * q^76 - 4 * q^77 + 41 * q^78 + 30 * q^79 - 10 * q^80 - 3 * q^81 - 7 * q^82 + 8 * q^83 + 3 * q^84 - 12 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 20 * q^89 + 34 * q^90 - 6 * q^91 - 12 * q^92 - 26 * q^93 - 25 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 2 * q^98 - 8 * 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 $

$2$	2.69017	1.90224	0.951119	−	0.308825i	$-0.0999359\pi$
$2$	2.69017	1.90224	0.951119	+	0.308825i	$0.0999359\pi$
$3$	−0.269842	−0.155793	−0.0778967	−	0.996961i	$-0.524820\pi$
$3$	−0.269842	−0.155793	−0.0778967	+	0.996961i	$0.524820\pi$
$4$	5.23702	2.61851
$5$	−3.51109	−1.57021	−0.785104	−	0.619363i	$-0.787391\pi$
$5$	−3.51109	−1.57021	−0.785104	+	0.619363i	$0.787391\pi$
$6$	−0.725921	−0.296356
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	8.70812	3.07879
$9$	−2.92719	−0.975728
$10$	−9.44544	−2.98691
$11$	−3.78810	−1.14215	−0.571077	−	0.820896i	$-0.693474\pi$
$11$	−3.78810	−1.14215	−0.571077	+	0.820896i	$0.693474\pi$
$12$	−1.41317	−0.407946
$13$	1.24125	0.344261	0.172131	−	0.985074i	$-0.444935\pi$
$13$	1.24125	0.344261	0.172131	+	0.985074i	$0.444935\pi$
$14$	2.69017	0.718978
$15$	0.947441	0.244628
$16$	12.9523	3.23807
$17$	5.98512	1.45161	0.725803	−	0.687903i	$-0.241468\pi$
$17$	5.98512	1.45161	0.725803	+	0.687903i	$0.241468\pi$
$18$	−7.87463	−1.85607
$19$	−3.38034	−0.775503	−0.387752	−	0.921764i	$-0.626748\pi$
$19$	−3.38034	−0.775503	−0.387752	+	0.921764i	$0.626748\pi$
$20$	−18.3877	−4.11160
$21$	−0.269842	−0.0588844
$22$	−10.1906	−2.17265
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.34982	−0.479655
$25$	7.32778	1.46556
$26$	3.33918	0.654867
$27$	1.59940	0.307805
$28$	5.23702	0.989703
$29$	−7.02088	−1.30374	−0.651872	−	0.758329i	$-0.726016\pi$
$29$	−7.02088	−1.30374	−0.651872	+	0.758329i	$0.726016\pi$
$30$	2.54878	0.465341
$31$	6.26984	1.12610	0.563048	−	0.826424i	$-0.309628\pi$
$31$	6.26984	1.12610	0.563048	+	0.826424i	$0.309628\pi$
$32$	17.4276	3.08080
$33$	1.02219	0.177940
$34$	16.1010	2.76130
$35$	−3.51109	−0.593483
$36$	−15.3297	−2.55495
$37$	4.84066	0.795799	0.397899	−	0.917429i	$-0.369739\pi$
$37$	4.84066	0.795799	0.397899	+	0.917429i	$0.369739\pi$
$38$	−9.09369	−1.47519
$39$	−0.334942	−0.0536336
$40$	−30.5750	−4.83434
$41$	−1.78094	−0.278135	−0.139068	−	0.990283i	$-0.544411\pi$
$41$	−1.78094	−0.278135	−0.139068	+	0.990283i	$0.544411\pi$
$42$	−0.725921	−0.112012
$43$	3.02219	0.460879	0.230440	−	0.973087i	$-0.425984\pi$
$43$	3.02219	0.460879	0.230440	+	0.973087i	$0.425984\pi$
$44$	−19.8383	−2.99074
$45$	10.2776	1.53210
$46$	−2.69017	−0.396644
$47$	3.90322	0.569343	0.284671	−	0.958625i	$-0.408116\pi$
$47$	3.90322	0.569343	0.284671	+	0.958625i	$0.408116\pi$
$48$	−3.49508	−0.504471
$49$	1.00000	0.142857
$50$	19.7130	2.78784
$51$	−1.61504	−0.226151
$52$	6.50046	0.901451
$53$	−2.47403	−0.339834	−0.169917	−	0.985458i	$-0.554350\pi$
$53$	−2.47403	−0.339834	−0.169917	+	0.985458i	$0.554350\pi$
$54$	4.30267	0.585519
$55$	13.3004	1.79342
$56$	8.70812	1.16367
$57$	0.912158	0.120818
$58$	−18.8873	−2.48003
$59$	−2.89143	−0.376433	−0.188216	−	0.982128i	$-0.560271\pi$
$59$	−2.89143	−0.376433	−0.188216	+	0.982128i	$0.560271\pi$
$60$	4.96176	0.640561
$61$	−10.3518	−1.32541	−0.662703	−	0.748882i	$-0.730591\pi$
$61$	−10.3518	−1.32541	−0.662703	+	0.748882i	$0.730591\pi$
$62$	16.8669	2.14210
$63$	−2.92719	−0.368791
$64$	20.9787	2.62234
$65$	−4.35815	−0.540562
$66$	2.74986	0.338484
$67$	11.4466	1.39843	0.699213	−	0.714913i	$-0.253534\pi$
$67$	11.4466	1.39843	0.699213	+	0.714913i	$0.253534\pi$
$68$	31.3442	3.80104
$69$	0.269842	0.0324852
$70$	−9.44544	−1.12895
$71$	2.70157	0.320617	0.160309	−	0.987067i	$-0.448751\pi$
$71$	2.70157	0.320617	0.160309	+	0.987067i	$0.448751\pi$
$72$	−25.4903	−3.00406
$73$	−14.1893	−1.66073	−0.830367	−	0.557217i	$-0.811869\pi$
$73$	−14.1893	−1.66073	−0.830367	+	0.557217i	$0.811869\pi$
$74$	13.0222	1.51380
$75$	−1.97734	−0.228324
$76$	−17.7029	−2.03066
$77$	−3.78810	−0.431694
$78$	−0.901051	−0.102024
$79$	3.31407	0.372862	0.186431	−	0.982468i	$-0.440308\pi$
$79$	3.31407	0.372862	0.186431	+	0.982468i	$0.440308\pi$
$80$	−45.4767	−5.08445
$81$	8.34997	0.927774
$82$	−4.79102	−0.529080
$83$	7.02219	0.770785	0.385393	−	0.922753i	$-0.374066\pi$
$83$	7.02219	0.770785	0.385393	+	0.922753i	$0.374066\pi$
$84$	−1.41317	−0.154189
$85$	−21.0143	−2.27932
$86$	8.13020	0.876702
$87$	1.89453	0.203115
$88$	−32.9872	−3.51645
$89$	−1.59107	−0.168653	−0.0843265	−	0.996438i	$-0.526874\pi$
$89$	−1.59107	−0.168653	−0.0843265	+	0.996438i	$0.526874\pi$
$90$	27.6486	2.91441
$91$	1.24125	0.130119
$92$	−5.23702	−0.545997
$93$	−1.69187	−0.175438
$94$	10.5003	1.08302
$95$	11.8687	1.21770
$96$	−4.70271	−0.479968
$97$	−11.6270	−1.18054	−0.590270	−	0.807206i	$-0.700979\pi$
$97$	−11.6270	−1.18054	−0.590270	+	0.807206i	$0.700979\pi$
$98$	2.69017	0.271748
$99$	11.0885	1.11443
$100$	38.3757	3.83757
$101$	−0.366626	−0.0364806	−0.0182403	−	0.999834i	$-0.505806\pi$
$101$	−0.366626	−0.0364806	−0.0182403	+	0.999834i	$0.505806\pi$
$102$	−4.34473	−0.430192
$103$	−0.474030	−0.0467076	−0.0233538	−	0.999727i	$-0.507434\pi$
$103$	−0.474030	−0.0467076	−0.0233538	+	0.999727i	$0.507434\pi$
$104$	10.8090	1.05991
$105$	0.947441	0.0924608
$106$	−6.65556	−0.646445
$107$	−5.74697	−0.555580	−0.277790	−	0.960642i	$-0.589602\pi$
$107$	−5.74697	−0.555580	−0.277790	+	0.960642i	$0.589602\pi$
$108$	8.37610	0.805991
$109$	15.4877	1.48346	0.741728	−	0.670700i	$-0.234006\pi$
$109$	15.4877	1.48346	0.741728	+	0.670700i	$0.234006\pi$
$110$	35.7802	3.41151
$111$	−1.30621	−0.123980
$112$	12.9523	1.22388
$113$	−4.48250	−0.421678	−0.210839	−	0.977521i	$-0.567620\pi$
$113$	−4.48250	−0.421678	−0.210839	+	0.977521i	$0.567620\pi$
$114$	2.45386	0.229825
$115$	3.51109	0.327411
$116$	−36.7684	−3.41386
$117$	−3.63337	−0.335906
$118$	−7.77845	−0.716064
$119$	5.98512	0.548655
$120$	8.25043	0.753158
$121$	3.34968	0.304516
$122$	−27.8480	−2.52124
$123$	0.480572	0.0433317
$124$	32.8353	2.94869
$125$	−8.17306	−0.731021
$126$	−7.87463	−0.701527
$127$	−2.13061	−0.189061	−0.0945307	−	0.995522i	$-0.530135\pi$
$127$	−2.13061	−0.189061	−0.0945307	+	0.995522i	$0.530135\pi$
$128$	21.5811	1.90751
$129$	−0.815514	−0.0718020
$130$	−11.7242	−1.02828
$131$	−18.1242	−1.58352	−0.791760	−	0.610832i	$-0.790835\pi$
$131$	−18.1242	−1.58352	−0.791760	+	0.610832i	$0.790835\pi$
$132$	5.35321	0.465937
$133$	−3.38034	−0.293113
$134$	30.7933	2.66014
$135$	−5.61566	−0.483319
$136$	52.1192	4.46918
$137$	−15.3062	−1.30770	−0.653849	−	0.756625i	$-0.726847\pi$
$137$	−15.3062	−1.30770	−0.653849	+	0.756625i	$0.726847\pi$
$138$	0.725921	0.0617945
$139$	13.5273	1.14737	0.573687	−	0.819074i	$-0.305512\pi$
$139$	13.5273	1.14737	0.573687	+	0.819074i	$0.305512\pi$
$140$	−18.3877	−1.55404
$141$	−1.05325	−0.0886998
$142$	7.26768	0.609890
$143$	−4.70198	−0.393200
$144$	−37.9138	−3.15948
$145$	24.6510	2.04715
$146$	−38.1717	−3.15911
$147$	−0.269842	−0.0222562
$148$	25.3506	2.08381
$149$	5.75773	0.471691	0.235846	−	0.971791i	$-0.424214\pi$
$149$	5.75773	0.471691	0.235846	+	0.971791i	$0.424214\pi$
$150$	−5.31939	−0.434326
$151$	−9.57813	−0.779457	−0.389728	−	0.920930i	$-0.627431\pi$
$151$	−9.57813	−0.779457	−0.389728	+	0.920930i	$0.627431\pi$
$152$	−29.4364	−2.38761
$153$	−17.5196	−1.41637
$154$	−10.1906	−0.821184
$155$	−22.0140	−1.76821
$156$	−1.75410	−0.140440
$157$	−5.03706	−0.402001	−0.201001	−	0.979591i	$-0.564419\pi$
$157$	−5.03706	−0.402001	−0.201001	+	0.979591i	$0.564419\pi$
$158$	8.91540	0.709271
$159$	0.667598	0.0529439
$160$	−61.1901	−4.83750
$161$	−1.00000	−0.0788110
$162$	22.4628	1.76485
$163$	−7.35713	−0.576255	−0.288127	−	0.957592i	$-0.593033\pi$
$163$	−7.35713	−0.576255	−0.288127	+	0.957592i	$0.593033\pi$
$164$	−9.32679	−0.728300
$165$	−3.58900	−0.279403
$166$	18.8909	1.46622
$167$	20.9904	1.62428	0.812142	−	0.583460i	$-0.198302\pi$
$167$	20.9904	1.62428	0.812142	+	0.583460i	$0.198302\pi$
$168$	−2.34982	−0.181292
$169$	−11.4593	−0.881484
$170$	−56.5321	−4.33582
$171$	9.89488	0.756681
$172$	15.8272	1.20682
$173$	−12.3369	−0.937955	−0.468978	−	0.883210i	$-0.655378\pi$
$173$	−12.3369	−0.937955	−0.468978	+	0.883210i	$0.655378\pi$
$174$	5.09660	0.386372
$175$	7.32778	0.553928
$176$	−49.0646	−3.69838
$177$	0.780231	0.0586457
$178$	−4.28025	−0.320818
$179$	−12.9082	−0.964807	−0.482404	−	0.875949i	$-0.660236\pi$
$179$	−12.9082	−0.964807	−0.482404	+	0.875949i	$0.660236\pi$
$180$	53.8241	4.01181
$181$	−5.86925	−0.436258	−0.218129	−	0.975920i	$-0.569995\pi$
$181$	−5.86925	−0.436258	−0.218129	+	0.975920i	$0.569995\pi$
$182$	3.33918	0.247516
$183$	2.79334	0.206489
$184$	−8.70812	−0.641971
$185$	−16.9960	−1.24957
$186$	−4.55141	−0.333726
$187$	−22.6722	−1.65796
$188$	20.4412	1.49083
$189$	1.59940	0.116340
$190$	31.9288	2.31636
$191$	11.9343	0.863539	0.431769	−	0.901984i	$-0.357889\pi$
$191$	11.9343	0.863539	0.431769	+	0.901984i	$0.357889\pi$
$192$	−5.66094	−0.408543
$193$	0.752900	0.0541949	0.0270975	−	0.999633i	$-0.491374\pi$
$193$	0.752900	0.0541949	0.0270975	+	0.999633i	$0.491374\pi$
$194$	−31.2785	−2.24567
$195$	1.17601	0.0842160
$196$	5.23702	0.374073
$197$	25.4074	1.81020	0.905100	−	0.425200i	$-0.139796\pi$
$197$	25.4074	1.81020	0.905100	+	0.425200i	$0.139796\pi$
$198$	29.8298	2.11991
$199$	15.1988	1.07741	0.538707	−	0.842493i	$-0.318913\pi$
$199$	15.1988	1.07741	0.538707	+	0.842493i	$0.318913\pi$
$200$	63.8112	4.51213
$201$	−3.08878	−0.217866
$202$	−0.986286	−0.0693948
$203$	−7.02088	−0.492769
$204$	−8.45798	−0.592177
$205$	6.25303	0.436731
$206$	−1.27522	−0.0888489
$207$	2.92719	0.203453
$208$	16.0771	1.11474
$209$	12.8051	0.885744
$210$	2.54878	0.175882
$211$	−24.2797	−1.67148	−0.835742	−	0.549123i	$-0.814962\pi$
$211$	−24.2797	−1.67148	−0.835742	+	0.549123i	$0.814962\pi$
$212$	−12.9565	−0.889858
$213$	−0.728997	−0.0499500
$214$	−15.4603	−1.05685
$215$	−10.6112	−0.723677
$216$	13.9278	0.947667
$217$	6.26984	0.425625
$218$	41.6647	2.82189
$219$	3.82887	0.258731
$220$	69.6542	4.69609
$221$	7.42905	0.499732
$222$	−3.51393	−0.235840
$223$	17.7344	1.18758	0.593791	−	0.804619i	$-0.297631\pi$
$223$	17.7344	1.18758	0.593791	+	0.804619i	$0.297631\pi$
$224$	17.4276	1.16443
$225$	−21.4498	−1.42998
$226$	−12.0587	−0.802133
$227$	−15.7087	−1.04263	−0.521313	−	0.853366i	$-0.674558\pi$
$227$	−15.7087	−1.04263	−0.521313	+	0.853366i	$0.674558\pi$
$228$	4.77699	0.316364
$229$	−4.51633	−0.298448	−0.149224	−	0.988803i	$-0.547678\pi$
$229$	−4.51633	−0.298448	−0.149224	+	0.988803i	$0.547678\pi$
$230$	9.44544	0.622814
$231$	1.02219	0.0672550
$232$	−61.1386	−4.01395
$233$	−16.2641	−1.06549	−0.532747	−	0.846275i	$-0.678840\pi$
$233$	−16.2641	−1.06549	−0.532747	+	0.846275i	$0.678840\pi$
$234$	−9.77439	−0.638972
$235$	−13.7046	−0.893987
$236$	−15.1425	−0.985692
$237$	−0.894275	−0.0580894
$238$	16.1010	1.04367
$239$	2.14756	0.138914	0.0694571	−	0.997585i	$-0.477873\pi$
$239$	2.14756	0.138914	0.0694571	+	0.997585i	$0.477873\pi$
$240$	12.2715	0.792124
$241$	12.4676	0.803111	0.401555	−	0.915835i	$-0.368470\pi$
$241$	12.4676	0.803111	0.401555	+	0.915835i	$0.368470\pi$
$242$	9.01121	0.579262
$243$	−7.05139	−0.452347
$244$	−54.2123	−3.47059
$245$	−3.51109	−0.224316
$246$	1.29282	0.0824271
$247$	−4.19585	−0.266976
$248$	54.5985	3.46701
$249$	−1.89488	−0.120083
$250$	−21.9869	−1.39057
$251$	4.91478	0.310218	0.155109	−	0.987897i	$-0.450427\pi$
$251$	4.91478	0.310218	0.155109	+	0.987897i	$0.450427\pi$
$252$	−15.3297	−0.965681
$253$	3.78810	0.238156
$254$	−5.73172	−0.359640
$255$	5.67055	0.355104
$256$	16.0993	1.00620
$257$	28.4782	1.77642	0.888212	−	0.459433i	$-0.151948\pi$
$257$	28.4782	1.77642	0.888212	+	0.459433i	$0.151948\pi$
$258$	−2.19387	−0.136584
$259$	4.84066	0.300784
$260$	−22.8237	−1.41547
$261$	20.5514	1.27210
$262$	−48.7572	−3.01223
$263$	1.89322	0.116741	0.0583703	−	0.998295i	$-0.481410\pi$
$263$	1.89322	0.116741	0.0583703	+	0.998295i	$0.481410\pi$
$264$	8.90134	0.547839
$265$	8.68655	0.533611
$266$	−9.09369	−0.557570
$267$	0.429338	0.0262750
$268$	59.9461	3.66179
$269$	−2.51156	−0.153133	−0.0765663	−	0.997064i	$-0.524396\pi$
$269$	−2.51156	−0.153133	−0.0765663	+	0.997064i	$0.524396\pi$
$270$	−15.1071	−0.919387
$271$	25.1098	1.52531	0.762656	−	0.646804i	$-0.223895\pi$
$271$	25.1098	1.52531	0.762656	+	0.646804i	$0.223895\pi$
$272$	77.5211	4.70041
$273$	−0.334942	−0.0202716
$274$	−41.1763	−2.48755
$275$	−27.7583	−1.67389
$276$	1.41317	0.0850627
$277$	9.48643	0.569984	0.284992	−	0.958530i	$-0.408009\pi$
$277$	9.48643	0.569984	0.284992	+	0.958530i	$0.408009\pi$
$278$	36.3909	2.18258
$279$	−18.3530	−1.09876
$280$	−30.5750	−1.82721
$281$	8.71197	0.519713	0.259856	−	0.965647i	$-0.416325\pi$
$281$	8.71197	0.519713	0.259856	+	0.965647i	$0.416325\pi$
$282$	−2.83343	−0.168728
$283$	30.5543	1.81627	0.908133	−	0.418683i	$-0.137508\pi$
$283$	30.5543	1.81627	0.908133	+	0.418683i	$0.137508\pi$
$284$	14.1482	0.839538
$285$	−3.20267	−0.189710
$286$	−12.6491	−0.747959
$287$	−1.78094	−0.105125
$288$	−51.0139	−3.00602
$289$	18.8217	1.10716
$290$	66.3153	3.89417
$291$	3.13745	0.183920
$292$	−74.3096	−4.34864
$293$	12.7063	0.742312	0.371156	−	0.928570i	$-0.378961\pi$
$293$	12.7063	0.742312	0.371156	+	0.928570i	$0.378961\pi$
$294$	−0.725921	−0.0423366
$295$	10.1521	0.591078
$296$	42.1530	2.45009
$297$	−6.05870	−0.351561
$298$	15.4893	0.897269
$299$	−1.24125	−0.0717835
$300$	−10.3554	−0.597868
$301$	3.02219	0.174196
$302$	−25.7668	−1.48271
$303$	0.0989310	0.00568344
$304$	−43.7832	−2.51114
$305$	36.3460	2.08116
$306$	−47.1306	−2.69428
$307$	22.1153	1.26219	0.631094	−	0.775706i	$-0.282606\pi$
$307$	22.1153	1.26219	0.631094	+	0.775706i	$0.282606\pi$
$308$	−19.8383	−1.13039
$309$	0.127913	0.00727673
$310$	−59.2214	−3.36355
$311$	21.3945	1.21317	0.606586	−	0.795018i	$-0.292539\pi$
$311$	21.3945	1.21317	0.606586	+	0.795018i	$0.292539\pi$
$312$	−2.91672	−0.165127
$313$	−29.9051	−1.69034	−0.845169	−	0.534498i	$-0.820501\pi$
$313$	−29.9051	−1.69034	−0.845169	+	0.534498i	$0.820501\pi$
$314$	−13.5506	−0.764702
$315$	10.2776	0.579078
$316$	17.3558	0.976341
$317$	7.06103	0.396587	0.198294	−	0.980143i	$-0.436460\pi$
$317$	7.06103	0.396587	0.198294	+	0.980143i	$0.436460\pi$
$318$	1.79595	0.100712
$319$	26.5958	1.48908
$320$	−73.6583	−4.11762
$321$	1.55077	0.0865557
$322$	−2.69017	−0.149917
$323$	−20.2318	−1.12573
$324$	43.7289	2.42938
$325$	9.09562	0.504534
$326$	−19.7919	−1.09617
$327$	−4.17925	−0.231113
$328$	−15.5086	−0.856320
$329$	3.90322	0.215191
$330$	−9.65502	−0.531491
$331$	16.2063	0.890777	0.445388	−	0.895338i	$-0.353066\pi$
$331$	16.2063	0.890777	0.445388	+	0.895338i	$0.353066\pi$
$332$	36.7753	2.01831
$333$	−14.1695	−0.776484
$334$	56.4677	3.08977
$335$	−40.1901	−2.19582
$336$	−3.49508	−0.190672
$337$	5.21804	0.284245	0.142122	−	0.989849i	$-0.454607\pi$
$337$	5.21804	0.284245	0.142122	+	0.989849i	$0.454607\pi$
$338$	−30.8274	−1.67679
$339$	1.20957	0.0656947
$340$	−110.052	−5.96843
$341$	−23.7508	−1.28618
$342$	26.6189	1.43939
$343$	1.00000	0.0539949
$344$	26.3176	1.41895
$345$	−0.947441	−0.0510085
$346$	−33.1883	−1.78421
$347$	4.19094	0.224982	0.112491	−	0.993653i	$-0.464117\pi$
$347$	4.19094	0.224982	0.112491	+	0.993653i	$0.464117\pi$
$348$	9.92167	0.531857
$349$	−18.6611	−0.998903	−0.499452	−	0.866342i	$-0.666465\pi$
$349$	−18.6611	−0.998903	−0.499452	+	0.866342i	$0.666465\pi$
$350$	19.7130	1.05370
$351$	1.98526	0.105966
$352$	−66.0176	−3.51875
$353$	−11.5781	−0.616241	−0.308121	−	0.951347i	$-0.599700\pi$
$353$	−11.5781	−0.616241	−0.308121	+	0.951347i	$0.599700\pi$
$354$	2.09895	0.111558
$355$	−9.48546	−0.503436
$356$	−8.33246	−0.441619
$357$	−1.61504	−0.0854769
$358$	−34.7254	−1.83529
$359$	29.4910	1.55647	0.778237	−	0.627970i	$-0.216114\pi$
$359$	29.4910	1.55647	0.778237	+	0.627970i	$0.216114\pi$
$360$	89.4988	4.71700
$361$	−7.57330	−0.398595
$362$	−15.7893	−0.829866
$363$	−0.903884	−0.0474416
$364$	6.50046	0.340716
$365$	49.8200	2.60770
$366$	7.51455	0.392792
$367$	−24.7858	−1.29381	−0.646903	−	0.762572i	$-0.723936\pi$
$367$	−24.7858	−1.29381	−0.646903	+	0.762572i	$0.723936\pi$
$368$	−12.9523	−0.675185
$369$	5.21313	0.271385
$370$	−45.7221	−2.37698
$371$	−2.47403	−0.128445
$372$	−8.86033	−0.459387
$373$	17.1524	0.888117	0.444058	−	0.895998i	$-0.353538\pi$
$373$	17.1524	0.888117	0.444058	+	0.895998i	$0.353538\pi$
$374$	−60.9922	−3.15383
$375$	2.20544	0.113888
$376$	33.9897	1.75288
$377$	−8.71467	−0.448829
$378$	4.30267	0.221305
$379$	32.8211	1.68591	0.842953	−	0.537986i	$-0.180815\pi$
$379$	32.8211	1.68591	0.842953	+	0.537986i	$0.180815\pi$
$380$	62.1565	3.18856
$381$	0.574930	0.0294545
$382$	32.1054	1.64266
$383$	−8.42609	−0.430553	−0.215277	−	0.976553i	$-0.569065\pi$
$383$	−8.42609	−0.430553	−0.215277	+	0.976553i	$0.569065\pi$
$384$	−5.82348	−0.297178
$385$	13.3004	0.677849
$386$	2.02543	0.103092
$387$	−8.84650	−0.449693
$388$	−60.8906	−3.09125
$389$	−25.3004	−1.28278	−0.641390	−	0.767215i	$-0.721642\pi$
$389$	−25.3004	−1.28278	−0.641390	+	0.767215i	$0.721642\pi$
$390$	3.16367	0.160199
$391$	−5.98512	−0.302681
$392$	8.70812	0.439827
$393$	4.89068	0.246702
$394$	68.3501	3.44343
$395$	−11.6360	−0.585471
$396$	58.0704	2.91815
$397$	20.3650	1.02209	0.511045	−	0.859554i	$-0.329259\pi$
$397$	20.3650	1.02209	0.511045	+	0.859554i	$0.329259\pi$
$398$	40.8874	2.04950
$399$	0.912158	0.0456650
$400$	94.9116	4.74558
$401$	4.10277	0.204883	0.102441	−	0.994739i	$-0.467335\pi$
$401$	4.10277	0.204883	0.102441	+	0.994739i	$0.467335\pi$
$402$	−8.30934	−0.414432
$403$	7.78245	0.387672
$404$	−1.92002	−0.0955248
$405$	−29.3175	−1.45680
$406$	−18.8873	−0.937363
$407$	−18.3369	−0.908925
$408$	−14.0640	−0.696269
$409$	−26.8449	−1.32739	−0.663697	−	0.748002i	$-0.731013\pi$
$409$	−26.8449	−1.32739	−0.663697	+	0.748002i	$0.731013\pi$
$410$	16.8217	0.830766
$411$	4.13026	0.203731
$412$	−2.48250	−0.122304
$413$	−2.89143	−0.142278
$414$	7.87463	0.387017
$415$	−24.6556	−1.21029
$416$	21.6321	1.06060
$417$	−3.65025	−0.178753
$418$	34.4478	1.68490
$419$	0.149494	0.00730327	0.00365163	−	0.999993i	$-0.498838\pi$
$419$	0.149494	0.00730327	0.00365163	+	0.999993i	$0.498838\pi$
$420$	4.96176	0.242109
$421$	−10.5269	−0.513049	−0.256524	−	0.966538i	$-0.582577\pi$
$421$	−10.5269	−0.513049	−0.256524	+	0.966538i	$0.582577\pi$
$422$	−65.3165	−3.17956
$423$	−11.4254	−0.555524
$424$	−21.5442	−1.04628
$425$	43.8577	2.12741
$426$	−1.96113	−0.0950168
$427$	−10.3518	−0.500956
$428$	−30.0969	−1.45479
$429$	1.26879	0.0612579
$430$	−28.5459	−1.37661
$431$	−2.28665	−0.110144	−0.0550720	−	0.998482i	$-0.517539\pi$
$431$	−2.28665	−0.110144	−0.0550720	+	0.998482i	$0.517539\pi$
$432$	20.7160	0.996697
$433$	−20.4569	−0.983094	−0.491547	−	0.870851i	$-0.663568\pi$
$433$	−20.4569	−0.983094	−0.491547	+	0.870851i	$0.663568\pi$
$434$	16.8669	0.809639
$435$	−6.65186	−0.318933
$436$	81.1096	3.88444
$437$	3.38034	0.161704
$438$	10.3003	0.492168
$439$	8.93821	0.426597	0.213299	−	0.976987i	$-0.431579\pi$
$439$	8.93821	0.426597	0.213299	+	0.976987i	$0.431579\pi$
$440$	115.821	5.52156
$441$	−2.92719	−0.139390
$442$	19.9854	0.950609
$443$	−6.71589	−0.319082	−0.159541	−	0.987191i	$-0.551001\pi$
$443$	−6.71589	−0.319082	−0.159541	+	0.987191i	$0.551001\pi$
$444$	−6.84066	−0.324643
$445$	5.58640	0.264821
$446$	47.7085	2.25906
$447$	−1.55368	−0.0734864
$448$	20.9787	0.991151
$449$	39.7178	1.87440	0.937200	−	0.348792i	$-0.113408\pi$
$449$	39.7178	1.87440	0.937200	+	0.348792i	$0.113408\pi$
$450$	−57.7035	−2.72017
$451$	6.74636	0.317674
$452$	−23.4749	−1.10417
$453$	2.58458	0.121434
$454$	−42.2592	−1.98332
$455$	−4.35815	−0.204313
$456$	7.94318	0.371974
$457$	−35.7388	−1.67179	−0.835895	−	0.548889i	$-0.815051\pi$
$457$	−35.7388	−1.67179	−0.835895	+	0.548889i	$0.815051\pi$
$458$	−12.1497	−0.567719
$459$	9.57263	0.446812
$460$	18.3877	0.857329
$461$	−18.3516	−0.854720	−0.427360	−	0.904082i	$-0.640556\pi$
$461$	−18.3516	−0.854720	−0.427360	+	0.904082i	$0.640556\pi$
$462$	2.74986	0.127935
$463$	11.1821	0.519678	0.259839	−	0.965652i	$-0.416330\pi$
$463$	11.1821	0.519678	0.259839	+	0.965652i	$0.416330\pi$
$464$	−90.9365	−4.22162
$465$	5.94031	0.275475
$466$	−43.7531	−2.02682
$467$	31.7231	1.46797	0.733984	−	0.679167i	$-0.237659\pi$
$467$	31.7231	1.46797	0.733984	+	0.679167i	$0.237659\pi$
$468$	−19.0280	−0.879571
$469$	11.4466	0.528556
$470$	−36.8676	−1.70058
$471$	1.35921	0.0626292
$472$	−25.1790	−1.15896
$473$	−11.4483	−0.526395
$474$	−2.40575	−0.110500
$475$	−24.7704	−1.13654
$476$	31.3442	1.43666
$477$	7.24194	0.331586
$478$	5.77731	0.264248
$479$	−9.81725	−0.448562	−0.224281	−	0.974525i	$-0.572003\pi$
$479$	−9.81725	−0.448562	−0.224281	+	0.974525i	$0.572003\pi$
$480$	16.5117	0.753651
$481$	6.00847	0.273963
$482$	33.5400	1.52771
$483$	0.269842	0.0122782
$484$	17.5423	0.797378
$485$	40.8234	1.85369
$486$	−18.9694	−0.860471
$487$	−36.2778	−1.64390	−0.821952	−	0.569557i	$-0.807115\pi$
$487$	−36.2778	−1.64390	−0.821952	+	0.569557i	$0.807115\pi$
$488$	−90.1443	−4.08064
$489$	1.98526	0.0897767
$490$	−9.44544	−0.426701
$491$	−17.6053	−0.794514	−0.397257	−	0.917707i	$-0.630038\pi$
$491$	−17.6053	−0.794514	−0.397257	+	0.917707i	$0.630038\pi$
$492$	2.51676	0.113464
$493$	−42.0208	−1.89252
$494$	−11.2876	−0.507851
$495$	−38.9326	−1.74989
$496$	81.2089	3.64639
$497$	2.70157	0.121182
$498$	−5.09755	−0.228427
$499$	12.1142	0.542308	0.271154	−	0.962536i	$-0.412595\pi$
$499$	12.1142	0.542308	0.271154	+	0.962536i	$0.412595\pi$
$500$	−42.8024	−1.91418
$501$	−5.66408	−0.253053
$502$	13.2216	0.590109
$503$	10.2723	0.458020	0.229010	−	0.973424i	$-0.426451\pi$
$503$	10.2723	0.458020	0.229010	+	0.973424i	$0.426451\pi$
$504$	−25.4903	−1.13543
$505$	1.28726	0.0572822
$506$	10.1906	0.453029
$507$	3.09220	0.137329
$508$	−11.1581	−0.495059
$509$	−6.45082	−0.285928	−0.142964	−	0.989728i	$-0.545663\pi$
$509$	−6.45082	−0.285928	−0.142964	+	0.989728i	$0.545663\pi$
$510$	15.2547	0.675492
$511$	−14.1893	−0.627698
$512$	0.147625	0.00652419
$513$	−5.40653	−0.238704
$514$	76.6113	3.37918
$515$	1.66436	0.0733407
$516$	−4.27086	−0.188014
$517$	−14.7858	−0.650277
$518$	13.0222	0.572162
$519$	3.32901	0.146127
$520$	−37.9513	−1.66428
$521$	34.4858	1.51085	0.755425	−	0.655235i	$-0.227430\pi$
$521$	34.4858	1.51085	0.755425	+	0.655235i	$0.227430\pi$
$522$	55.2868	2.41984
$523$	−25.7852	−1.12751	−0.563753	−	0.825943i	$-0.690643\pi$
$523$	−25.7852	−1.12751	−0.563753	+	0.825943i	$0.690643\pi$
$524$	−94.9168	−4.14646
$525$	−1.97734	−0.0862984
$526$	5.09307	0.222068
$527$	37.5258	1.63465
$528$	13.2397	0.576183
$529$	1.00000	0.0434783
$530$	23.3683	1.01505
$531$	8.46376	0.367296
$532$	−17.7029	−0.767518
$533$	−2.21059	−0.0957513
$534$	1.15499	0.0499814
$535$	20.1781	0.872377
$536$	99.6785	4.30546
$537$	3.48319	0.150311
$538$	−6.75653	−0.291295
$539$	−3.78810	−0.163165
$540$	−29.4093	−1.26557
$541$	−21.1475	−0.909203	−0.454601	−	0.890695i	$-0.650218\pi$
$541$	−21.1475	−0.909203	−0.454601	+	0.890695i	$0.650218\pi$
$542$	67.5496	2.90151
$543$	1.58377	0.0679661
$544$	104.307	4.47211
$545$	−54.3789	−2.32934
$546$	−0.901051	−0.0385614
$547$	−3.97188	−0.169825	−0.0849126	−	0.996388i	$-0.527061\pi$
$547$	−3.97188	−0.169825	−0.0849126	+	0.996388i	$0.527061\pi$
$548$	−80.1589	−3.42422
$549$	30.3015	1.29324
$550$	−74.6747	−3.18414
$551$	23.7329	1.01106
$552$	2.34982	0.100015
$553$	3.31407	0.140928
$554$	25.5201	1.08425
$555$	4.58624	0.194675
$556$	70.8429	3.00441
$557$	−13.5585	−0.574491	−0.287246	−	0.957857i	$-0.592740\pi$
$557$	−13.5585	−0.574491	−0.287246	+	0.957857i	$0.592740\pi$
$558$	−49.3727	−2.09011
$559$	3.75130	0.158663
$560$	−45.4767	−1.92174
$561$	6.11792	0.258299
$562$	23.4367	0.988617
$563$	−32.4740	−1.36862	−0.684309	−	0.729193i	$-0.739896\pi$
$563$	−32.4740	−1.36862	−0.684309	+	0.729193i	$0.739896\pi$
$564$	−5.51590	−0.232261
$565$	15.7385	0.662123
$566$	82.1963	3.45497
$567$	8.34997	0.350666
$568$	23.5256	0.987111
$569$	−26.7707	−1.12228	−0.561142	−	0.827719i	$-0.689638\pi$
$569$	−26.7707	−1.12228	−0.561142	+	0.827719i	$0.689638\pi$
$570$	−8.61573	−0.360873
$571$	5.30884	0.222168	0.111084	−	0.993811i	$-0.464568\pi$
$571$	5.30884	0.222168	0.111084	+	0.993811i	$0.464568\pi$
$572$	−24.6244	−1.02960
$573$	−3.22039	−0.134534
$574$	−4.79102	−0.199973
$575$	−7.32778	−0.305590
$576$	−61.4086	−2.55869
$577$	43.9737	1.83065	0.915325	−	0.402717i	$-0.131934\pi$
$577$	43.9737	1.83065	0.915325	+	0.402717i	$0.131934\pi$
$578$	50.6336	2.10608
$579$	−0.203164	−0.00844321
$580$	129.097	5.36048
$581$	7.02219	0.291329
$582$	8.44026	0.349860
$583$	9.37187	0.388143
$584$	−123.562	−5.11304
$585$	12.7571	0.527442
$586$	34.1822	1.41205
$587$	−34.5314	−1.42526	−0.712631	−	0.701539i	$-0.752497\pi$
$587$	−34.5314	−1.42526	−0.712631	+	0.701539i	$0.752497\pi$
$588$	−1.41317	−0.0582780
$589$	−21.1942	−0.873292
$590$	27.3109	1.12437
$591$	−6.85597	−0.282017
$592$	62.6976	2.57686
$593$	2.06074	0.0846245	0.0423123	−	0.999104i	$-0.486528\pi$
$593$	2.06074	0.0846245	0.0423123	+	0.999104i	$0.486528\pi$
$594$	−16.2989	−0.668753
$595$	−21.0143	−0.861504
$596$	30.1533	1.23513
$597$	−4.10128	−0.167854
$598$	−3.33918	−0.136549
$599$	−28.2627	−1.15478	−0.577392	−	0.816467i	$-0.695930\pi$
$599$	−28.2627	−1.15478	−0.577392	+	0.816467i	$0.695930\pi$
$600$	−17.2189	−0.702961
$601$	−25.0036	−1.01992	−0.509959	−	0.860199i	$-0.670340\pi$
$601$	−25.0036	−1.01992	−0.509959	+	0.860199i	$0.670340\pi$
$602$	8.13020	0.331362
$603$	−33.5064	−1.36448
$604$	−50.1608	−2.04101
$605$	−11.7610	−0.478154
$606$	0.266141	0.0108113
$607$	−29.0255	−1.17811	−0.589054	−	0.808093i	$-0.700500\pi$
$607$	−29.0255	−1.17811	−0.589054	+	0.808093i	$0.700500\pi$
$608$	−58.9114	−2.38917
$609$	1.89453	0.0767701
$610$	97.7768	3.95887
$611$	4.84487	0.196003
$612$	−91.7502	−3.70878
$613$	−25.2180	−1.01855	−0.509274	−	0.860605i	$-0.670086\pi$
$613$	−25.2180	−1.01855	−0.509274	+	0.860605i	$0.670086\pi$
$614$	59.4940	2.40098
$615$	−1.68733	−0.0680398
$616$	−32.9872	−1.32909
$617$	41.7462	1.68064	0.840319	−	0.542093i	$-0.182368\pi$
$617$	41.7462	1.68064	0.840319	+	0.542093i	$0.182368\pi$
$618$	0.344109	0.0138421
$619$	−0.503782	−0.0202487	−0.0101243	−	0.999949i	$-0.503223\pi$
$619$	−0.503782	−0.0202487	−0.0101243	+	0.999949i	$0.503223\pi$
$620$	−115.288	−4.63006
$621$	−1.59940	−0.0641819
$622$	57.5549	2.30774
$623$	−1.59107	−0.0637449
$624$	−4.33827	−0.173670
$625$	−7.94253	−0.317701
$626$	−80.4499	−3.21543
$627$	−3.45534	−0.137993
$628$	−26.3792	−1.05264
$629$	28.9719	1.15519
$630$	27.6486	1.10154
$631$	−17.6868	−0.704102	−0.352051	−	0.935981i	$-0.614516\pi$
$631$	−17.6868	−0.704102	−0.352051	+	0.935981i	$0.614516\pi$
$632$	28.8593	1.14796
$633$	6.55168	0.260406
$634$	18.9954	0.754403
$635$	7.48079	0.296866
$636$	3.49622	0.138634
$637$	1.24125	0.0491802
$638$	71.5471	2.83258
$639$	−7.90799	−0.312835
$640$	−75.7731	−2.99519
$641$	−37.4714	−1.48003	−0.740015	−	0.672590i	$-0.765182\pi$
$641$	−37.4714	−1.48003	−0.740015	+	0.672590i	$0.765182\pi$
$642$	4.17184	0.164650
$643$	0.178907	0.00705539	0.00352770	−	0.999994i	$-0.498877\pi$
$643$	0.178907	0.00705539	0.00352770	+	0.999994i	$0.498877\pi$
$644$	−5.23702	−0.206367
$645$	2.86334	0.112744
$646$	−54.4269	−2.14140
$647$	2.94235	0.115676	0.0578379	−	0.998326i	$-0.481579\pi$
$647$	2.94235	0.115676	0.0578379	+	0.998326i	$0.481579\pi$
$648$	72.7125	2.85642
$649$	10.9530	0.429944
$650$	24.4688	0.959744
$651$	−1.69187	−0.0663095
$652$	−38.5294	−1.50893
$653$	44.1719	1.72858	0.864290	−	0.502994i	$-0.167768\pi$
$653$	44.1719	1.72858	0.864290	+	0.502994i	$0.167768\pi$
$654$	−11.2429	−0.439631
$655$	63.6358	2.48646
$656$	−23.0672	−0.900623
$657$	41.5347	1.62042
$658$	10.5003	0.409345
$659$	13.9282	0.542564	0.271282	−	0.962500i	$-0.412552\pi$
$659$	13.9282	0.542564	0.271282	+	0.962500i	$0.412552\pi$
$660$	−18.7956	−0.731619
$661$	−2.15327	−0.0837525	−0.0418763	−	0.999123i	$-0.513334\pi$
$661$	−2.15327	−0.0837525	−0.0418763	+	0.999123i	$0.513334\pi$
$662$	43.5976	1.69447
$663$	−2.00467	−0.0778549
$664$	61.1501	2.37308
$665$	11.8687	0.460248
$666$	−38.1184	−1.47706
$667$	7.02088	0.271849
$668$	109.927	4.25320
$669$	−4.78548	−0.185017
$670$	−108.118	−4.17697
$671$	39.2134	1.51382
$672$	−4.70271	−0.181411
$673$	−2.96276	−0.114206	−0.0571030	−	0.998368i	$-0.518186\pi$
$673$	−2.96276	−0.114206	−0.0571030	+	0.998368i	$0.518186\pi$
$674$	14.0374	0.540701
$675$	11.7201	0.451106
$676$	−60.0125	−2.30817
$677$	9.59927	0.368930	0.184465	−	0.982839i	$-0.440945\pi$
$677$	9.59927	0.368930	0.184465	+	0.982839i	$0.440945\pi$
$678$	3.25394	0.124967
$679$	−11.6270	−0.446202
$680$	−182.995	−7.01755
$681$	4.23888	0.162434
$682$	−63.8936	−2.44661
$683$	−24.1908	−0.925636	−0.462818	−	0.886453i	$-0.653162\pi$
$683$	−24.1908	−0.925636	−0.462818	+	0.886453i	$0.653162\pi$
$684$	51.8196	1.98137
$685$	53.7416	2.05336
$686$	2.69017	0.102711
$687$	1.21870	0.0464962
$688$	39.1443	1.49236
$689$	−3.07089	−0.116992
$690$	−2.54878	−0.0970303
$691$	30.4784	1.15945	0.579726	−	0.814811i	$-0.303159\pi$
$691$	30.4784	1.15945	0.579726	+	0.814811i	$0.303159\pi$
$692$	−64.6084	−2.45604
$693$	11.0885	0.421216
$694$	11.2743	0.427968
$695$	−47.4958	−1.80162
$696$	16.4978	0.625347
$697$	−10.6591	−0.403743
$698$	−50.2014	−1.90015
$699$	4.38873	0.165997
$700$	38.3757	1.45047
$701$	17.4101	0.657570	0.328785	−	0.944405i	$-0.393361\pi$
$701$	17.4101	0.657570	0.328785	+	0.944405i	$0.393361\pi$
$702$	5.34070	0.201572
$703$	−16.3631	−0.617145
$704$	−79.4694	−2.99512
$705$	3.69807	0.139277
$706$	−31.1471	−1.17224
$707$	−0.366626	−0.0137884
$708$	4.08608	0.153564
$709$	13.6465	0.512504	0.256252	−	0.966610i	$-0.417512\pi$
$709$	13.6465	0.512504	0.256252	+	0.966610i	$0.417512\pi$
$710$	−25.5175	−0.957655
$711$	−9.70089	−0.363812
$712$	−13.8552	−0.519247
$713$	−6.26984	−0.234807
$714$	−4.34473	−0.162597
$715$	16.5091	0.617405
$716$	−67.6007	−2.52636
$717$	−0.579503	−0.0216419
$718$	79.3358	2.96078
$719$	−29.8264	−1.11234	−0.556169	−	0.831069i	$-0.687729\pi$
$719$	−29.8264	−1.11234	−0.556169	+	0.831069i	$0.687729\pi$
$720$	133.119	4.96105
$721$	−0.474030	−0.0176538
$722$	−20.3735	−0.758222
$723$	−3.36429	−0.125119
$724$	−30.7373	−1.14234
$725$	−51.4474	−1.91071
$726$	−2.43160	−0.0902452
$727$	6.92789	0.256941	0.128471	−	0.991713i	$-0.458993\pi$
$727$	6.92789	0.256941	0.128471	+	0.991713i	$0.458993\pi$
$728$	10.8090	0.400607
$729$	−23.1471	−0.857302
$730$	134.024	4.96046
$731$	18.0882	0.669015
$732$	14.6288	0.540694
$733$	−10.8092	−0.399246	−0.199623	−	0.979873i	$-0.563972\pi$
$733$	−10.8092	−0.399246	−0.199623	+	0.979873i	$0.563972\pi$
$734$	−66.6779	−2.46113
$735$	0.947441	0.0349469
$736$	−17.4276	−0.642391
$737$	−43.3609	−1.59722
$738$	14.0242	0.516238
$739$	34.5455	1.27078	0.635388	−	0.772193i	$-0.280840\pi$
$739$	34.5455	1.27078	0.635388	+	0.772193i	$0.280840\pi$
$740$	−89.0083	−3.27201
$741$	1.13222	0.0415931
$742$	−6.65556	−0.244333
$743$	19.7750	0.725475	0.362737	−	0.931891i	$-0.381842\pi$
$743$	19.7750	0.725475	0.362737	+	0.931891i	$0.381842\pi$
$744$	−14.7330	−0.540137
$745$	−20.2159	−0.740654
$746$	46.1428	1.68941
$747$	−20.5552	−0.752077
$748$	−118.735	−4.34137
$749$	−5.74697	−0.209990
$750$	5.93300	0.216642
$751$	−31.0704	−1.13378	−0.566888	−	0.823795i	$-0.691853\pi$
$751$	−31.0704	−1.13378	−0.566888	+	0.823795i	$0.691853\pi$
$752$	50.5556	1.84357
$753$	−1.32622	−0.0483300
$754$	−23.4440	−0.853779
$755$	33.6297	1.22391
$756$	8.37610	0.304636
$757$	8.32104	0.302433	0.151217	−	0.988501i	$-0.451681\pi$
$757$	8.32104	0.302433	0.151217	+	0.988501i	$0.451681\pi$
$758$	88.2944	3.20700
$759$	−1.02219	−0.0371031
$760$	103.354	3.74904
$761$	−3.82034	−0.138487	−0.0692436	−	0.997600i	$-0.522059\pi$
$761$	−3.82034	−0.138487	−0.0692436	+	0.997600i	$0.522059\pi$
$762$	1.54666	0.0560295
$763$	15.4877	0.560694
$764$	62.5004	2.26118
$765$	61.5128	2.22400
$766$	−22.6676	−0.819014
$767$	−3.58900	−0.129591
$768$	−4.34426	−0.156760
$769$	8.05891	0.290612	0.145306	−	0.989387i	$-0.453583\pi$
$769$	8.05891	0.290612	0.145306	+	0.989387i	$0.453583\pi$
$770$	35.7802	1.28943
$771$	−7.68463	−0.276755
$772$	3.94295	0.141910
$773$	−20.3254	−0.731054	−0.365527	−	0.930801i	$-0.619111\pi$
$773$	−20.3254	−0.731054	−0.365527	+	0.930801i	$0.619111\pi$
$774$	−23.7986	−0.855423
$775$	45.9440	1.65036
$776$	−101.249	−3.63463
$777$	−1.30621	−0.0468601
$778$	−68.0623	−2.44015
$779$	6.02017	0.215695
$780$	6.15880	0.220520
$781$	−10.2338	−0.366194
$782$	−16.1010	−0.575771
$783$	−11.2292	−0.401299
$784$	12.9523	0.462582
$785$	17.6856	0.631226
$786$	13.1567	0.469286
$787$	−47.7951	−1.70371	−0.851856	−	0.523775i	$-0.824523\pi$
$787$	−47.7951	−1.70371	−0.851856	+	0.523775i	$0.824523\pi$
$788$	133.059	4.74002
$789$	−0.510869	−0.0181874
$790$	−31.3028	−1.11370
$791$	−4.48250	−0.159379
$792$	96.5597	3.43110
$793$	−12.8491	−0.456286
$794$	54.7853	1.94426
$795$	−2.34400	−0.0831330
$796$	79.5964	2.82122
$797$	−7.57090	−0.268175	−0.134088	−	0.990969i	$-0.542810\pi$
$797$	−7.57090	−0.268175	−0.134088	+	0.990969i	$0.542810\pi$
$798$	2.45386	0.0868657
$799$	23.3612	0.826461
$800$	127.706	4.51509
$801$	4.65736	0.164560
$802$	11.0372	0.389735
$803$	53.7505	1.89681
$804$	−16.1760	−0.570483
$805$	3.51109	0.123750
$806$	20.9361	0.737444
$807$	0.677725	0.0238571
$808$	−3.19262	−0.112316
$809$	8.55279	0.300700	0.150350	−	0.988633i	$-0.451960\pi$
$809$	8.55279	0.300700	0.150350	+	0.988633i	$0.451960\pi$
$810$	−78.8691	−2.77118
$811$	−45.0023	−1.58024	−0.790122	−	0.612950i	$-0.789983\pi$
$811$	−45.0023	−1.58024	−0.790122	+	0.612950i	$0.789983\pi$
$812$	−36.7684	−1.29032
$813$	−6.77568	−0.237634
$814$	−49.3293	−1.72899
$815$	25.8316	0.904841
$816$	−20.9185	−0.732293
$817$	−10.2160	−0.357413
$818$	−72.2173	−2.52502
$819$	−3.63337	−0.126960
$820$	32.7472	1.14358
$821$	41.4358	1.44612	0.723060	−	0.690785i	$-0.242735\pi$
$821$	41.4358	1.44612	0.723060	+	0.690785i	$0.242735\pi$
$822$	11.1111	0.387544
$823$	−19.1508	−0.667553	−0.333777	−	0.942652i	$-0.608323\pi$
$823$	−19.1508	−0.667553	−0.333777	+	0.942652i	$0.608323\pi$
$824$	−4.12791	−0.143803
$825$	7.49037	0.260781
$826$	−7.77845	−0.270647
$827$	−32.2820	−1.12256	−0.561278	−	0.827627i	$-0.689690\pi$
$827$	−32.2820	−1.12256	−0.561278	+	0.827627i	$0.689690\pi$
$828$	15.3297	0.532744
$829$	9.85700	0.342348	0.171174	−	0.985241i	$-0.445244\pi$
$829$	9.85700	0.342348	0.171174	+	0.985241i	$0.445244\pi$
$830$	−66.3277	−2.30227
$831$	−2.55984	−0.0887998
$832$	26.0399	0.902770
$833$	5.98512	0.207372
$834$	−9.81979	−0.340031
$835$	−73.6991	−2.55046
$836$	67.0603	2.31933
$837$	10.0280	0.346619
$838$	0.402165	0.0138925
$839$	11.7098	0.404267	0.202133	−	0.979358i	$-0.435213\pi$
$839$	11.7098	0.404267	0.202133	+	0.979358i	$0.435213\pi$
$840$	8.25043	0.284667
$841$	20.2927	0.699748
$842$	−28.3191	−0.975941
$843$	−2.35086	−0.0809678
$844$	−127.153	−4.37679
$845$	40.2347	1.38411
$846$	−30.7364	−1.05674
$847$	3.34968	0.115096
$848$	−32.0444	−1.10041
$849$	−8.24484	−0.282962
$850$	117.985	4.04684
$851$	−4.84066	−0.165936
$852$	−3.81777	−0.130795
$853$	−29.2441	−1.00130	−0.500650	−	0.865650i	$-0.666906\pi$
$853$	−29.2441	−1.00130	−0.500650	+	0.865650i	$0.666906\pi$
$854$	−27.8480	−0.952938
$855$	−34.7419	−1.18815
$856$	−50.0453	−1.71051
$857$	38.6873	1.32153	0.660766	−	0.750592i	$-0.270232\pi$
$857$	38.6873	1.32153	0.660766	+	0.750592i	$0.270232\pi$
$858$	3.41327	0.116527
$859$	−49.3913	−1.68521	−0.842604	−	0.538534i	$-0.818979\pi$
$859$	−49.3913	−1.68521	−0.842604	+	0.538534i	$0.818979\pi$
$860$	−55.5709	−1.89495
$861$	0.480572	0.0163778
$862$	−6.15148	−0.209520
$863$	−2.32156	−0.0790267	−0.0395134	−	0.999219i	$-0.512581\pi$
$863$	−2.32156	−0.0790267	−0.0395134	+	0.999219i	$0.512581\pi$
$864$	27.8738	0.948287
$865$	43.3159	1.47279
$866$	−55.0325	−1.87008
$867$	−5.07889	−0.172488
$868$	32.8353	1.11450
$869$	−12.5540	−0.425865
$870$	−17.8946	−0.606685
$871$	14.2081	0.481424
$872$	134.869	4.56725
$873$	34.0343	1.15189
$874$	9.09369	0.307599
$875$	−8.17306	−0.276300
$876$	20.0519	0.677490
$877$	36.2775	1.22500	0.612502	−	0.790469i	$-0.290163\pi$
$877$	36.2775	1.22500	0.612502	+	0.790469i	$0.290163\pi$
$878$	24.0453	0.811490
$879$	−3.42871	−0.115647
$880$	172.270	5.80723
$881$	30.1252	1.01494	0.507472	−	0.861668i	$-0.330580\pi$
$881$	30.1252	1.01494	0.507472	+	0.861668i	$0.330580\pi$
$882$	−7.87463	−0.265152
$883$	1.94158	0.0653394	0.0326697	−	0.999466i	$-0.489599\pi$
$883$	1.94158	0.0653394	0.0326697	+	0.999466i	$0.489599\pi$
$884$	38.9060	1.30855
$885$	−2.73946	−0.0920860
$886$	−18.0669	−0.606969
$887$	52.3596	1.75806	0.879031	−	0.476765i	$-0.158191\pi$
$887$	52.3596	1.75806	0.879031	+	0.476765i	$0.158191\pi$
$888$	−11.3747	−0.381709
$889$	−2.13061	−0.0714585
$890$	15.0284	0.503752
$891$	−31.6305	−1.05966
$892$	92.8752	3.10969
$893$	−13.1942	−0.441527
$894$	−4.17965	−0.139789
$895$	45.3221	1.51495
$896$	21.5811	0.720972
$897$	0.334942	0.0111834
$898$	106.848	3.56555
$899$	−44.0198	−1.46814
$900$	−112.333	−3.74443
$901$	−14.8074	−0.493305
$902$	18.1489	0.604291
$903$	−0.815514	−0.0271386
$904$	−39.0342	−1.29826
$905$	20.6075	0.685016
$906$	6.95296	0.230997
$907$	9.62846	0.319708	0.159854	−	0.987141i	$-0.448898\pi$
$907$	9.62846	0.319708	0.159854	+	0.987141i	$0.448898\pi$
$908$	−82.2669	−2.73012
$909$	1.07318	0.0355952
$910$	−11.7242	−0.388652
$911$	−24.6036	−0.815154	−0.407577	−	0.913171i	$-0.633626\pi$
$911$	−24.6036	−0.815154	−0.407577	+	0.913171i	$0.633626\pi$
$912$	11.8145	0.391219
$913$	−26.6007	−0.880356
$914$	−96.1434	−3.18014
$915$	−9.80767	−0.324232
$916$	−23.6521	−0.781488
$917$	−18.1242	−0.598514
$918$	25.7520	0.849943
$919$	18.4685	0.609220	0.304610	−	0.952477i	$-0.401474\pi$
$919$	18.4685	0.609220	0.304610	+	0.952477i	$0.401474\pi$
$920$	30.5750	1.00803
$921$	−5.96765	−0.196641
$922$	−49.3690	−1.62588
$923$	3.35333	0.110376
$924$	5.35321	0.176108
$925$	35.4713	1.16629
$926$	30.0819	0.988551
$927$	1.38757	0.0455739
$928$	−122.357	−4.01657
$929$	21.6032	0.708778	0.354389	−	0.935098i	$-0.384689\pi$
$929$	21.6032	0.708778	0.354389	+	0.935098i	$0.384689\pi$
$930$	15.9804	0.524019
$931$	−3.38034	−0.110786
$932$	−85.1751	−2.79000
$933$	−5.77314	−0.189004
$934$	85.3404	2.79242
$935$	79.6043	2.60334
$936$	−31.6399	−1.03418
$937$	4.95446	0.161855	0.0809276	−	0.996720i	$-0.474212\pi$
$937$	4.95446	0.161855	0.0809276	+	0.996720i	$0.474212\pi$
$938$	30.7933	1.00544
$939$	8.06967	0.263344
$940$	−71.7710	−2.34091
$941$	−37.1398	−1.21072	−0.605361	−	0.795951i	$-0.706971\pi$
$941$	−37.1398	−1.21072	−0.605361	+	0.795951i	$0.706971\pi$
$942$	3.65651	0.119136
$943$	1.78094	0.0579953
$944$	−37.4507	−1.21892
$945$	−5.61566	−0.182677
$946$	−30.7980	−1.00133
$947$	−11.0644	−0.359543	−0.179772	−	0.983708i	$-0.557536\pi$
$947$	−11.0644	−0.359543	−0.179772	+	0.983708i	$0.557536\pi$
$948$	−4.68333	−0.152107
$949$	−17.6125	−0.571726
$950$	−66.6366	−2.16198
$951$	−1.90536	−0.0617857
$952$	52.1192	1.68919
$953$	19.3888	0.628065	0.314033	−	0.949412i	$-0.398320\pi$
$953$	19.3888	0.628065	0.314033	+	0.949412i	$0.398320\pi$
$954$	19.4821	0.630755
$955$	−41.9026	−1.35594
$956$	11.2468	0.363748
$957$	−7.17665	−0.231988
$958$	−26.4101	−0.853271
$959$	−15.3062	−0.494263
$960$	19.8761	0.641498
$961$	8.31092	0.268094
$962$	16.1638	0.521142
$963$	16.8224	0.542095
$964$	65.2932	2.10295
$965$	−2.64350	−0.0850974
$966$	0.725921	0.0233561
$967$	−32.5154	−1.04563	−0.522813	−	0.852448i	$-0.675117\pi$
$967$	−32.5154	−1.04563	−0.522813	+	0.852448i	$0.675117\pi$
$968$	29.1694	0.937540
$969$	5.45938	0.175381
$970$	109.822	3.52617
$971$	1.32316	0.0424622	0.0212311	−	0.999775i	$-0.493241\pi$
$971$	1.32316	0.0424622	0.0212311	+	0.999775i	$0.493241\pi$
$972$	−36.9282	−1.18447
$973$	13.5273	0.433667
$974$	−97.5934	−3.12709
$975$	−2.45438	−0.0786031
$976$	−134.079	−4.29176
$977$	−31.6195	−1.01160	−0.505799	−	0.862651i	$-0.668802\pi$
$977$	−31.6195	−1.01160	−0.505799	+	0.862651i	$0.668802\pi$
$978$	5.34070	0.170777
$979$	6.02713	0.192628
$980$	−18.3877	−0.587372
$981$	−45.3355	−1.44745
$982$	−47.3611	−1.51135
$983$	−12.1696	−0.388149	−0.194074	−	0.980987i	$-0.562170\pi$
$983$	−12.1696	−0.388149	−0.194074	+	0.980987i	$0.562170\pi$
$984$	4.18488	0.133409
$985$	−89.2076	−2.84239
$986$	−113.043	−3.60003
$987$	−1.05325	−0.0335254
$988$	−21.9737	−0.699078
$989$	−3.02219	−0.0961000
$990$	−104.735	−3.32871
$991$	2.18738	0.0694844	0.0347422	−	0.999396i	$-0.488939\pi$
$991$	2.18738	0.0694844	0.0347422	+	0.999396i	$0.488939\pi$
$992$	109.269	3.46928
$993$	−4.37313	−0.138777
$994$	7.26768	0.230517
$995$	−53.3644	−1.69177
$996$	−9.92353	−0.314439
$997$	−3.78052	−0.119730	−0.0598652	−	0.998206i	$-0.519067\pi$
$997$	−3.78052	−0.119730	−0.0598652	+	0.998206i	$0.519067\pi$
$998$	32.5894	1.03160
$999$	7.74216	0.244951

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	161.2.a.d.1.5	✓	5
3.2	odd	2		1449.2.a.r.1.1		5
4.3	odd	2		2576.2.a.bd.1.3		5
5.4	even	2		4025.2.a.p.1.1		5
7.6	odd	2		1127.2.a.h.1.5		5
23.22	odd	2		3703.2.a.j.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
161.2.a.d.1.5	✓	5	1.1	even	1	trivial
1127.2.a.h.1.5		5	7.6	odd	2
1449.2.a.r.1.1		5	3.2	odd	2
2576.2.a.bd.1.3		5	4.3	odd	2
3703.2.a.j.1.5		5	23.22	odd	2
4025.2.a.p.1.1		5	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 161 = 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	161.a (trivial)

\(f(q)\)	\(=\)	\(q+2.69017 q^{2} -0.269842 q^{3} +5.23702 q^{4} -3.51109 q^{5} -0.725921 q^{6} +1.00000 q^{7} +8.70812 q^{8} -2.92719 q^{9} +O(q^{10})\)	\(q+2.69017 q^{2} -0.269842 q^{3} +5.23702 q^{4} -3.51109 q^{5} -0.725921 q^{6} +1.00000 q^{7} +8.70812 q^{8} -2.92719 q^{9} -9.44544 q^{10} -3.78810 q^{11} -1.41317 q^{12} +1.24125 q^{13} +2.69017 q^{14} +0.947441 q^{15} +12.9523 q^{16} +5.98512 q^{17} -7.87463 q^{18} -3.38034 q^{19} -18.3877 q^{20} -0.269842 q^{21} -10.1906 q^{22} -1.00000 q^{23} -2.34982 q^{24} +7.32778 q^{25} +3.33918 q^{26} +1.59940 q^{27} +5.23702 q^{28} -7.02088 q^{29} +2.54878 q^{30} +6.26984 q^{31} +17.4276 q^{32} +1.02219 q^{33} +16.1010 q^{34} -3.51109 q^{35} -15.3297 q^{36} +4.84066 q^{37} -9.09369 q^{38} -0.334942 q^{39} -30.5750 q^{40} -1.78094 q^{41} -0.725921 q^{42} +3.02219 q^{43} -19.8383 q^{44} +10.2776 q^{45} -2.69017 q^{46} +3.90322 q^{47} -3.49508 q^{48} +1.00000 q^{49} +19.7130 q^{50} -1.61504 q^{51} +6.50046 q^{52} -2.47403 q^{53} +4.30267 q^{54} +13.3004 q^{55} +8.70812 q^{56} +0.912158 q^{57} -18.8873 q^{58} -2.89143 q^{59} +4.96176 q^{60} -10.3518 q^{61} +16.8669 q^{62} -2.92719 q^{63} +20.9787 q^{64} -4.35815 q^{65} +2.74986 q^{66} +11.4466 q^{67} +31.3442 q^{68} +0.269842 q^{69} -9.44544 q^{70} +2.70157 q^{71} -25.4903 q^{72} -14.1893 q^{73} +13.0222 q^{74} -1.97734 q^{75} -17.7029 q^{76} -3.78810 q^{77} -0.901051 q^{78} +3.31407 q^{79} -45.4767 q^{80} +8.34997 q^{81} -4.79102 q^{82} +7.02219 q^{83} -1.41317 q^{84} -21.0143 q^{85} +8.13020 q^{86} +1.89453 q^{87} -32.9872 q^{88} -1.59107 q^{89} +27.6486 q^{90} +1.24125 q^{91} -5.23702 q^{92} -1.69187 q^{93} +10.5003 q^{94} +11.8687 q^{95} -4.70271 q^{96} -11.6270 q^{97} +2.69017 q^{98} +11.0885 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9}+O(q^{10}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9	\( 5 q + 2 q^{2} + 12 q^{4} - 4 q^{5} - 3 q^{6} + 5 q^{7} + 3 q^{8} + 11 q^{9} - 8 q^{10} - 4 q^{11} + 3 q^{12} - 6 q^{13} + 2 q^{14} + 10 q^{15} + 10 q^{16} - 12 q^{17} - 19 q^{18} + 6 q^{19} + 14 q^{22} - 5 q^{23} - 36 q^{24} + 19 q^{25} + q^{26} + 12 q^{28} - 4 q^{29} - 48 q^{30} + 30 q^{31} + 8 q^{32} - 22 q^{33} + 6 q^{34} - 4 q^{35} - q^{36} + 4 q^{37} - 40 q^{38} + 16 q^{39} - 50 q^{40} + 6 q^{41} - 3 q^{42} - 12 q^{43} - 26 q^{44} - 12 q^{45} - 2 q^{46} + 10 q^{47} + 25 q^{48} + 5 q^{49} - 2 q^{50} - 4 q^{51} - 21 q^{52} + 16 q^{53} + 33 q^{54} + 18 q^{55} + 3 q^{56} + 6 q^{57} + 13 q^{58} + 22 q^{59} + 30 q^{60} - 18 q^{61} + 15 q^{62} + 11 q^{63} + 25 q^{64} - 26 q^{65} + 4 q^{66} - 2 q^{67} + 12 q^{68} - 8 q^{70} + 4 q^{71} - 41 q^{72} - 2 q^{73} + 38 q^{74} - 30 q^{75} + 10 q^{76} - 4 q^{77} + 41 q^{78} + 30 q^{79} - 10 q^{80} - 3 q^{81} - 7 q^{82} + 8 q^{83} + 3 q^{84} - 12 q^{85} + 8 q^{86} - 12 q^{87} + 4 q^{88} - 20 q^{89} + 34 q^{90} - 6 q^{91} - 12 q^{92} - 26 q^{93} - 25 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 2 q^{98} - 8 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 + 12 * q^4 - 4 * q^5 - 3 * q^6 + 5 * q^7 + 3 * q^8 + 11 * q^9 - 8 * q^10 - 4 * q^11 + 3 * q^12 - 6 * q^13 + 2 * q^14 + 10 * q^15 + 10 * q^16 - 12 * q^17 - 19 * q^18 + 6 * q^19 + 14 * q^22 - 5 * q^23 - 36 * q^24 + 19 * q^25 + q^26 + 12 * q^28 - 4 * q^29 - 48 * q^30 + 30 * q^31 + 8 * q^32 - 22 * q^33 + 6 * q^34 - 4 * q^35 - q^36 + 4 * q^37 - 40 * q^38 + 16 * q^39 - 50 * q^40 + 6 * q^41 - 3 * q^42 - 12 * q^43 - 26 * q^44 - 12 * q^45 - 2 * q^46 + 10 * q^47 + 25 * q^48 + 5 * q^49 - 2 * q^50 - 4 * q^51 - 21 * q^52 + 16 * q^53 + 33 * q^54 + 18 * q^55 + 3 * q^56 + 6 * q^57 + 13 * q^58 + 22 * q^59 + 30 * q^60 - 18 * q^61 + 15 * q^62 + 11 * q^63 + 25 * q^64 - 26 * q^65 + 4 * q^66 - 2 * q^67 + 12 * q^68 - 8 * q^70 + 4 * q^71 - 41 * q^72 - 2 * q^73 + 38 * q^74 - 30 * q^75 + 10 * q^76 - 4 * q^77 + 41 * q^78 + 30 * q^79 - 10 * q^80 - 3 * q^81 - 7 * q^82 + 8 * q^83 + 3 * q^84 - 12 * q^85 + 8 * q^86 - 12 * q^87 + 4 * q^88 - 20 * q^89 + 34 * q^90 - 6 * q^91 - 12 * q^92 - 26 * q^93 - 25 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 2 * q^98 - 8 * q^99

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