LMFDB - Embedded newform 4009.2.a.d.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4009,2,Mod(1,4009)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4009, 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("4009.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4009 = 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4009.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$32.0120261703$
Analytic rank:	$1$
Dimension:	$75$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4009.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.33282 q^{2} -0.629609 q^{3} +3.44205 q^{4} +3.06029 q^{5} +1.46876 q^{6} +3.36015 q^{7} -3.36405 q^{8} -2.60359 q^{9} +O(q^{10})$	\(q-2.33282 q^{2} -0.629609 q^{3} +3.44205 q^{4} +3.06029 q^{5} +1.46876 q^{6} +3.36015 q^{7} -3.36405 q^{8} -2.60359 q^{9} -7.13912 q^{10} -4.24759 q^{11} -2.16715 q^{12} -0.920594 q^{13} -7.83864 q^{14} -1.92679 q^{15} +0.963624 q^{16} -7.33506 q^{17} +6.07372 q^{18} -1.00000 q^{19} +10.5337 q^{20} -2.11558 q^{21} +9.90888 q^{22} +2.51405 q^{23} +2.11804 q^{24} +4.36540 q^{25} +2.14758 q^{26} +3.52807 q^{27} +11.5658 q^{28} -0.703673 q^{29} +4.49485 q^{30} +10.0549 q^{31} +4.48014 q^{32} +2.67432 q^{33} +17.1114 q^{34} +10.2831 q^{35} -8.96171 q^{36} -4.12031 q^{37} +2.33282 q^{38} +0.579614 q^{39} -10.2950 q^{40} +0.195331 q^{41} +4.93527 q^{42} +8.05442 q^{43} -14.6204 q^{44} -7.96776 q^{45} -5.86484 q^{46} -6.53923 q^{47} -0.606706 q^{48} +4.29064 q^{49} -10.1837 q^{50} +4.61822 q^{51} -3.16873 q^{52} -0.286675 q^{53} -8.23036 q^{54} -12.9989 q^{55} -11.3037 q^{56} +0.629609 q^{57} +1.64154 q^{58} -8.39101 q^{59} -6.63210 q^{60} +10.8508 q^{61} -23.4563 q^{62} -8.74848 q^{63} -12.3786 q^{64} -2.81729 q^{65} -6.23871 q^{66} +4.52408 q^{67} -25.2477 q^{68} -1.58287 q^{69} -23.9885 q^{70} +7.27351 q^{71} +8.75862 q^{72} -7.01271 q^{73} +9.61196 q^{74} -2.74849 q^{75} -3.44205 q^{76} -14.2726 q^{77} -1.35214 q^{78} -8.88819 q^{79} +2.94897 q^{80} +5.58948 q^{81} -0.455673 q^{82} -12.3307 q^{83} -7.28195 q^{84} -22.4474 q^{85} -18.7895 q^{86} +0.443039 q^{87} +14.2891 q^{88} +17.7284 q^{89} +18.5874 q^{90} -3.09334 q^{91} +8.65350 q^{92} -6.33067 q^{93} +15.2549 q^{94} -3.06029 q^{95} -2.82073 q^{96} -1.92030 q^{97} -10.0093 q^{98} +11.0590 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9}+O(q^{10}) $ 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9	\( 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9} - 48 q^{11} - 14 q^{12} - 3 q^{13} - 4 q^{14} - 39 q^{15} + 59 q^{16} - 23 q^{17} - 24 q^{18} - 75 q^{19} - 62 q^{20} - 3 q^{21} - 6 q^{22} - 73 q^{23} - 64 q^{24} + 57 q^{25} - 46 q^{26} - 22 q^{27} - 26 q^{28} - 39 q^{29} - 14 q^{30} - 44 q^{31} - 71 q^{32} - 3 q^{33} - 9 q^{34} - 49 q^{35} + 20 q^{36} - 12 q^{37} + 11 q^{38} - 90 q^{39} - 8 q^{40} - 42 q^{41} - 45 q^{42} - 24 q^{43} - 120 q^{44} - 63 q^{45} - 39 q^{46} - 59 q^{47} - 4 q^{48} + 48 q^{49} - 100 q^{50} - 55 q^{51} + 2 q^{52} + 13 q^{53} - 87 q^{54} - 36 q^{55} - 12 q^{56} + 4 q^{57} - 17 q^{58} - 47 q^{59} - 45 q^{60} - 35 q^{61} - 40 q^{62} - 69 q^{63} + 26 q^{64} - 44 q^{65} + 33 q^{66} - 39 q^{67} - 63 q^{68} + 42 q^{69} + 40 q^{70} - 154 q^{71} - 51 q^{72} - 29 q^{73} - 95 q^{74} + 37 q^{75} - 67 q^{76} - 24 q^{77} - 19 q^{78} - 95 q^{79} - 146 q^{80} + 23 q^{81} + 7 q^{82} - 52 q^{83} - 72 q^{84} - 36 q^{85} - 44 q^{86} - 103 q^{87} + 67 q^{88} + q^{89} - 2 q^{90} - 64 q^{91} - 183 q^{92} - 49 q^{93} + 5 q^{94} + 18 q^{95} - 69 q^{96} - 7 q^{97} - 23 q^{98} - 100 q^{99}+O(q^{100}) \) 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9 - 48 * q^11 - 14 * q^12 - 3 * q^13 - 4 * q^14 - 39 * q^15 + 59 * q^16 - 23 * q^17 - 24 * q^18 - 75 * q^19 - 62 * q^20 - 3 * q^21 - 6 * q^22 - 73 * q^23 - 64 * q^24 + 57 * q^25 - 46 * q^26 - 22 * q^27 - 26 * q^28 - 39 * q^29 - 14 * q^30 - 44 * q^31 - 71 * q^32 - 3 * q^33 - 9 * q^34 - 49 * q^35 + 20 * q^36 - 12 * q^37 + 11 * q^38 - 90 * q^39 - 8 * q^40 - 42 * q^41 - 45 * q^42 - 24 * q^43 - 120 * q^44 - 63 * q^45 - 39 * q^46 - 59 * q^47 - 4 * q^48 + 48 * q^49 - 100 * q^50 - 55 * q^51 + 2 * q^52 + 13 * q^53 - 87 * q^54 - 36 * q^55 - 12 * q^56 + 4 * q^57 - 17 * q^58 - 47 * q^59 - 45 * q^60 - 35 * q^61 - 40 * q^62 - 69 * q^63 + 26 * q^64 - 44 * q^65 + 33 * q^66 - 39 * q^67 - 63 * q^68 + 42 * q^69 + 40 * q^70 - 154 * q^71 - 51 * q^72 - 29 * q^73 - 95 * q^74 + 37 * q^75 - 67 * q^76 - 24 * q^77 - 19 * q^78 - 95 * q^79 - 146 * q^80 + 23 * q^81 + 7 * q^82 - 52 * q^83 - 72 * q^84 - 36 * q^85 - 44 * q^86 - 103 * q^87 + 67 * q^88 + q^89 - 2 * q^90 - 64 * q^91 - 183 * q^92 - 49 * q^93 + 5 * q^94 + 18 * q^95 - 69 * q^96 - 7 * q^97 - 23 * q^98 - 100 * 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 $

$2$	−2.33282	−1.64955	−0.824777	−	0.565459i	$-0.808699\pi$
$2$	−2.33282	−1.64955	−0.824777	+	0.565459i	$0.808699\pi$
$3$	−0.629609	−0.363505	−0.181752	−	0.983344i	$-0.558177\pi$
$3$	−0.629609	−0.363505	−0.181752	+	0.983344i	$0.558177\pi$
$4$	3.44205	1.72103
$5$	3.06029	1.36861	0.684303	−	0.729198i	$-0.260107\pi$
$5$	3.06029	1.36861	0.684303	+	0.729198i	$0.260107\pi$
$6$	1.46876	0.599620
$7$	3.36015	1.27002	0.635010	−	0.772504i	$-0.280996\pi$
$7$	3.36015	1.27002	0.635010	+	0.772504i	$0.280996\pi$
$8$	−3.36405	−1.18937
$9$	−2.60359	−0.867864
$10$	−7.13912	−2.25759
$11$	−4.24759	−1.28070	−0.640349	−	0.768084i	$-0.721210\pi$
$11$	−4.24759	−1.28070	−0.640349	+	0.768084i	$0.721210\pi$
$12$	−2.16715	−0.625601
$13$	−0.920594	−0.255327	−0.127663	−	0.991818i	$-0.540748\pi$
$13$	−0.920594	−0.255327	−0.127663	+	0.991818i	$0.540748\pi$
$14$	−7.83864	−2.09496
$15$	−1.92679	−0.497494
$16$	0.963624	0.240906
$17$	−7.33506	−1.77901	−0.889507	−	0.456922i	$-0.848952\pi$
$17$	−7.33506	−1.77901	−0.889507	+	0.456922i	$0.848952\pi$
$18$	6.07372	1.43159
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	10.5337	2.35541
$21$	−2.11558	−0.461658
$22$	9.90888	2.11258
$23$	2.51405	0.524216	0.262108	−	0.965039i	$-0.415582\pi$
$23$	2.51405	0.524216	0.262108	+	0.965039i	$0.415582\pi$
$24$	2.11804	0.432342
$25$	4.36540	0.873080
$26$	2.14758	0.421175
$27$	3.52807	0.678977
$28$	11.5658	2.18574
$29$	−0.703673	−0.130669	−0.0653344	−	0.997863i	$-0.520811\pi$
$29$	−0.703673	−0.130669	−0.0653344	+	0.997863i	$0.520811\pi$
$30$	4.49485	0.820644
$31$	10.0549	1.80592	0.902959	−	0.429726i	$-0.141390\pi$
$31$	10.0549	1.80592	0.902959	+	0.429726i	$0.141390\pi$
$32$	4.48014	0.791985
$33$	2.67432	0.465540
$34$	17.1114	2.93458
$35$	10.2831	1.73815
$36$	−8.96171	−1.49362
$37$	−4.12031	−0.677376	−0.338688	−	0.940899i	$-0.609983\pi$
$37$	−4.12031	−0.677376	−0.338688	+	0.940899i	$0.609983\pi$
$38$	2.33282	0.378434
$39$	0.579614	0.0928125
$40$	−10.2950	−1.62778
$41$	0.195331	0.0305056	0.0152528	−	0.999884i	$-0.495145\pi$
$41$	0.195331	0.0305056	0.0152528	+	0.999884i	$0.495145\pi$
$42$	4.93527	0.761529
$43$	8.05442	1.22829	0.614144	−	0.789194i	$-0.289502\pi$
$43$	8.05442	1.22829	0.614144	+	0.789194i	$0.289502\pi$
$44$	−14.6204	−2.20412
$45$	−7.96776	−1.18776
$46$	−5.86484	−0.864723
$47$	−6.53923	−0.953845	−0.476923	−	0.878945i	$-0.658248\pi$
$47$	−6.53923	−0.953845	−0.476923	+	0.878945i	$0.658248\pi$
$48$	−0.606706	−0.0875705
$49$	4.29064	0.612948
$50$	−10.1837	−1.44019
$51$	4.61822	0.646680
$52$	−3.16873	−0.439424
$53$	−0.286675	−0.0393779	−0.0196889	−	0.999806i	$-0.506268\pi$
$53$	−0.286675	−0.0393779	−0.0196889	+	0.999806i	$0.506268\pi$
$54$	−8.23036	−1.12001
$55$	−12.9989	−1.75277
$56$	−11.3037	−1.51053
$57$	0.629609	0.0833937
$58$	1.64154	0.215545
$59$	−8.39101	−1.09242	−0.546208	−	0.837650i	$-0.683929\pi$
$59$	−8.39101	−1.09242	−0.546208	+	0.837650i	$0.683929\pi$
$60$	−6.63210	−0.856201
$61$	10.8508	1.38931	0.694653	−	0.719345i	$-0.255558\pi$
$61$	10.8508	1.38931	0.694653	+	0.719345i	$0.255558\pi$
$62$	−23.4563	−2.97896
$63$	−8.74848	−1.10220
$64$	−12.3786	−1.54733
$65$	−2.81729	−0.349442
$66$	−6.23871	−0.767932
$67$	4.52408	0.552705	0.276352	−	0.961056i	$-0.410874\pi$
$67$	4.52408	0.552705	0.276352	+	0.961056i	$0.410874\pi$
$68$	−25.2477	−3.06173
$69$	−1.58287	−0.190555
$70$	−23.9885	−2.86718
$71$	7.27351	0.863207	0.431603	−	0.902063i	$-0.357948\pi$
$71$	7.27351	0.863207	0.431603	+	0.902063i	$0.357948\pi$
$72$	8.75862	1.03221
$73$	−7.01271	−0.820775	−0.410388	−	0.911911i	$-0.634607\pi$
$73$	−7.01271	−0.820775	−0.410388	+	0.911911i	$0.634607\pi$
$74$	9.61196	1.11737
$75$	−2.74849	−0.317369
$76$	−3.44205	−0.394831
$77$	−14.2726	−1.62651
$78$	−1.35214	−0.153099
$79$	−8.88819	−1.00000	−0.500000	−	0.866025i	$-0.666667\pi$
$79$	−8.88819	−1.00000	−0.500000	+	0.866025i	$0.666667\pi$
$80$	2.94897	0.329705
$81$	5.58948	0.621053
$82$	−0.455673	−0.0503207
$83$	−12.3307	−1.35348	−0.676738	−	0.736224i	$-0.736607\pi$
$83$	−12.3307	−1.35348	−0.676738	+	0.736224i	$0.736607\pi$
$84$	−7.28195	−0.794525
$85$	−22.4474	−2.43477
$86$	−18.7895	−2.02613
$87$	0.443039	0.0474987
$88$	14.2891	1.52323
$89$	17.7284	1.87920	0.939602	−	0.342270i	$-0.111196\pi$
$89$	17.7284	1.87920	0.939602	+	0.342270i	$0.111196\pi$
$90$	18.5874	1.95928
$91$	−3.09334	−0.324270
$92$	8.65350	0.902190
$93$	−6.33067	−0.656460
$94$	15.2549	1.57342
$95$	−3.06029	−0.313980
$96$	−2.82073	−0.287890
$97$	−1.92030	−0.194977	−0.0974887	−	0.995237i	$-0.531081\pi$
$97$	−1.92030	−0.194977	−0.0974887	+	0.995237i	$0.531081\pi$
$98$	−10.0093	−1.01109
$99$	11.0590	1.11147
$100$	15.0259	1.50259
$101$	2.43576	0.242367	0.121184	−	0.992630i	$-0.461331\pi$
$101$	2.43576	0.242367	0.121184	+	0.992630i	$0.461331\pi$
$102$	−10.7735	−1.06673
$103$	−12.8514	−1.26629	−0.633145	−	0.774033i	$-0.718236\pi$
$103$	−12.8514	−1.26629	−0.633145	+	0.774033i	$0.718236\pi$
$104$	3.09693	0.303679
$105$	−6.47430	−0.631827
$106$	0.668762	0.0649559
$107$	7.56218	0.731063	0.365532	−	0.930799i	$-0.380887\pi$
$107$	7.56218	0.731063	0.365532	+	0.930799i	$0.380887\pi$
$108$	12.1438	1.16854
$109$	−10.9213	−1.04607	−0.523036	−	0.852311i	$-0.675201\pi$
$109$	−10.9213	−1.04607	−0.523036	+	0.852311i	$0.675201\pi$
$110$	30.3241	2.89129
$111$	2.59418	0.246229
$112$	3.23793	0.305955
$113$	−5.58792	−0.525667	−0.262834	−	0.964841i	$-0.584657\pi$
$113$	−5.58792	−0.525667	−0.262834	+	0.964841i	$0.584657\pi$
$114$	−1.46876	−0.137562
$115$	7.69374	0.717445
$116$	−2.42208	−0.224885
$117$	2.39685	0.221589
$118$	19.5747	1.80200
$119$	−24.6469	−2.25938
$120$	6.48181	0.591706
$121$	7.04206	0.640187
$122$	−25.3130	−2.29173
$123$	−0.122982	−0.0110889
$124$	34.6096	3.10803
$125$	−1.94206	−0.173703
$126$	20.4086	1.81814
$127$	14.5337	1.28965	0.644827	−	0.764329i	$-0.276929\pi$
$127$	14.5337	1.28965	0.644827	+	0.764329i	$0.276929\pi$
$128$	19.9168	1.76041
$129$	−5.07113	−0.446488
$130$	6.57223	0.576423
$131$	−8.91966	−0.779315	−0.389657	−	0.920960i	$-0.627407\pi$
$131$	−8.91966	−0.779315	−0.389657	+	0.920960i	$0.627407\pi$
$132$	9.20516	0.801206
$133$	−3.36015	−0.291362
$134$	−10.5539	−0.911716
$135$	10.7969	0.929252
$136$	24.6755	2.11591
$137$	−16.1757	−1.38198	−0.690991	−	0.722863i	$-0.742826\pi$
$137$	−16.1757	−1.38198	−0.690991	+	0.722863i	$0.742826\pi$
$138$	3.69255	0.314331
$139$	−7.13480	−0.605166	−0.302583	−	0.953123i	$-0.597849\pi$
$139$	−7.13480	−0.605166	−0.302583	+	0.953123i	$0.597849\pi$
$140$	35.3948	2.99141
$141$	4.11716	0.346727
$142$	−16.9678	−1.42391
$143$	3.91031	0.326997
$144$	−2.50889	−0.209074
$145$	−2.15345	−0.178834
$146$	16.3594	1.35391
$147$	−2.70142	−0.222810
$148$	−14.1823	−1.16578
$149$	−7.02965	−0.575892	−0.287946	−	0.957647i	$-0.592972\pi$
$149$	−7.02965	−0.575892	−0.287946	+	0.957647i	$0.592972\pi$
$150$	6.41174	0.523517
$151$	−20.4097	−1.66092	−0.830458	−	0.557082i	$-0.811921\pi$
$151$	−20.4097	−1.66092	−0.830458	+	0.557082i	$0.811921\pi$
$152$	3.36405	0.272861
$153$	19.0975	1.54394
$154$	33.2954	2.68302
$155$	30.7710	2.47159
$156$	1.99506	0.159733
$157$	−8.12214	−0.648217	−0.324109	−	0.946020i	$-0.605064\pi$
$157$	−8.12214	−0.648217	−0.324109	+	0.946020i	$0.605064\pi$
$158$	20.7346	1.64955
$159$	0.180493	0.0143140
$160$	13.7105	1.08391
$161$	8.44761	0.665765
$162$	−13.0392	−1.02446
$163$	1.64336	0.128718	0.0643589	−	0.997927i	$-0.479500\pi$
$163$	1.64336	0.128718	0.0643589	+	0.997927i	$0.479500\pi$
$164$	0.672341	0.0525010
$165$	8.18421	0.637140
$166$	28.7654	2.23263
$167$	−15.6483	−1.21090	−0.605450	−	0.795883i	$-0.707007\pi$
$167$	−15.6483	−1.21090	−0.605450	+	0.795883i	$0.707007\pi$
$168$	7.11693	0.549083
$169$	−12.1525	−0.934808
$170$	52.3659	4.01628
$171$	2.60359	0.199102
$172$	27.7237	2.11392
$173$	−12.2860	−0.934089	−0.467044	−	0.884234i	$-0.654681\pi$
$173$	−12.2860	−0.934089	−0.467044	+	0.884234i	$0.654681\pi$
$174$	−1.03353	−0.0783517
$175$	14.6684	1.10883
$176$	−4.09309	−0.308528
$177$	5.28305	0.397098
$178$	−41.3571	−3.09985
$179$	0.512148	0.0382797	0.0191399	−	0.999817i	$-0.493907\pi$
$179$	0.512148	0.0382797	0.0191399	+	0.999817i	$0.493907\pi$
$180$	−27.4255	−2.04417
$181$	3.79541	0.282110	0.141055	−	0.990002i	$-0.454951\pi$
$181$	3.79541	0.282110	0.141055	+	0.990002i	$0.454951\pi$
$182$	7.21620	0.534901
$183$	−6.83177	−0.505019
$184$	−8.45741	−0.623488
$185$	−12.6094	−0.927060
$186$	14.7683	1.08287
$187$	31.1564	2.27838
$188$	−22.5084	−1.64159
$189$	11.8549	0.862314
$190$	7.13912	0.517926
$191$	−12.5372	−0.907160	−0.453580	−	0.891215i	$-0.649853\pi$
$191$	−12.5372	−0.907160	−0.453580	+	0.891215i	$0.649853\pi$
$192$	7.79368	0.562461
$193$	4.61070	0.331886	0.165943	−	0.986135i	$-0.446933\pi$
$193$	4.61070	0.331886	0.165943	+	0.986135i	$0.446933\pi$
$194$	4.47972	0.321626
$195$	1.77379	0.127024
$196$	14.7686	1.05490
$197$	−21.3221	−1.51914	−0.759569	−	0.650426i	$-0.774590\pi$
$197$	−21.3221	−1.51914	−0.759569	+	0.650426i	$0.774590\pi$
$198$	−25.7987	−1.83343
$199$	−8.97789	−0.636425	−0.318213	−	0.948019i	$-0.603083\pi$
$199$	−8.97789	−0.636425	−0.318213	+	0.948019i	$0.603083\pi$
$200$	−14.6854	−1.03842
$201$	−2.84840	−0.200911
$202$	−5.68219	−0.399798
$203$	−2.36445	−0.165952
$204$	15.8961	1.11295
$205$	0.597771	0.0417502
$206$	29.9801	2.08881
$207$	−6.54557	−0.454949
$208$	−0.887107	−0.0615098
$209$	4.24759	0.293812
$210$	15.1034	1.04223
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−0.986751	−0.0677703
$213$	−4.57946	−0.313780
$214$	−17.6412	−1.20593
$215$	24.6489	1.68104
$216$	−11.8686	−0.807557
$217$	33.7861	2.29355
$218$	25.4774	1.72555
$219$	4.41526	0.298356
$220$	−44.7429	−3.01656
$221$	6.75261	0.454230
$222$	−6.05177	−0.406168
$223$	17.0099	1.13907	0.569534	−	0.821968i	$-0.307124\pi$
$223$	17.0099	1.13907	0.569534	+	0.821968i	$0.307124\pi$
$224$	15.0540	1.00584
$225$	−11.3657	−0.757715
$226$	13.0356	0.867116
$227$	6.18429	0.410466	0.205233	−	0.978713i	$-0.434205\pi$
$227$	6.18429	0.410466	0.205233	+	0.978713i	$0.434205\pi$
$228$	2.16715	0.143523
$229$	−15.6463	−1.03394	−0.516970	−	0.856004i	$-0.672940\pi$
$229$	−15.6463	−1.03394	−0.516970	+	0.856004i	$0.672940\pi$
$230$	−17.9481	−1.18346
$231$	8.98613	0.591244
$232$	2.36719	0.155414
$233$	−25.6337	−1.67932	−0.839660	−	0.543113i	$-0.817246\pi$
$233$	−25.6337	−1.67932	−0.839660	+	0.543113i	$0.817246\pi$
$234$	−5.59143	−0.365523
$235$	−20.0120	−1.30544
$236$	−28.8823	−1.88008
$237$	5.59608	0.363505
$238$	57.4969	3.72697
$239$	−12.5889	−0.814308	−0.407154	−	0.913360i	$-0.633479\pi$
$239$	−12.5889	−0.814308	−0.407154	+	0.913360i	$0.633479\pi$
$240$	−1.85670	−0.119849
$241$	−26.7272	−1.72165	−0.860827	−	0.508898i	$-0.830053\pi$
$241$	−26.7272	−1.72165	−0.860827	+	0.508898i	$0.830053\pi$
$242$	−16.4279	−1.05602
$243$	−14.1034	−0.904733
$244$	37.3491	2.39103
$245$	13.1306	0.838884
$246$	0.286896	0.0182918
$247$	0.920594	0.0585760
$248$	−33.8253	−2.14791
$249$	7.76354	0.491995
$250$	4.53048	0.286533
$251$	3.21659	0.203029	0.101515	−	0.994834i	$-0.467631\pi$
$251$	3.21659	0.203029	0.101515	+	0.994834i	$0.467631\pi$
$252$	−30.1127	−1.89692
$253$	−10.6787	−0.671363
$254$	−33.9044	−2.12735
$255$	14.1331	0.885049
$256$	−21.7051	−1.35657
$257$	3.31360	0.206697	0.103348	−	0.994645i	$-0.467044\pi$
$257$	3.31360	0.206697	0.103348	+	0.994645i	$0.467044\pi$
$258$	11.8300	0.736506
$259$	−13.8449	−0.860280
$260$	−9.69726	−0.601398
$261$	1.83208	0.113403
$262$	20.8080	1.28552
$263$	24.9438	1.53810	0.769049	−	0.639190i	$-0.220730\pi$
$263$	24.9438	1.53810	0.769049	+	0.639190i	$0.220730\pi$
$264$	−8.99656	−0.553700
$265$	−0.877310	−0.0538927
$266$	7.83864	0.480618
$267$	−11.1619	−0.683099
$268$	15.5721	0.951220
$269$	−5.31055	−0.323790	−0.161895	−	0.986808i	$-0.551761\pi$
$269$	−5.31055	−0.323790	−0.161895	+	0.986808i	$0.551761\pi$
$270$	−25.1873	−1.53285
$271$	16.3638	0.994028	0.497014	−	0.867743i	$-0.334430\pi$
$271$	16.3638	0.994028	0.497014	+	0.867743i	$0.334430\pi$
$272$	−7.06824	−0.428575
$273$	1.94759	0.117874
$274$	37.7350	2.27965
$275$	−18.5425	−1.11815
$276$	−5.44832	−0.327950
$277$	−12.5343	−0.753111	−0.376556	−	0.926394i	$-0.622892\pi$
$277$	−12.5343	−0.753111	−0.376556	+	0.926394i	$0.622892\pi$
$278$	16.6442	0.998254
$279$	−26.1789	−1.56729
$280$	−34.5928	−2.06731
$281$	−4.68579	−0.279531	−0.139766	−	0.990185i	$-0.544635\pi$
$281$	−4.68579	−0.279531	−0.139766	+	0.990185i	$0.544635\pi$
$282$	−9.60459	−0.571945
$283$	−15.6262	−0.928878	−0.464439	−	0.885605i	$-0.653744\pi$
$283$	−15.6262	−0.928878	−0.464439	+	0.885605i	$0.653744\pi$
$284$	25.0358	1.48560
$285$	1.92679	0.114133
$286$	−9.12205	−0.539398
$287$	0.656344	0.0387427
$288$	−11.6645	−0.687335
$289$	36.8031	2.16489
$290$	5.02361	0.294996
$291$	1.20904	0.0708752
$292$	−24.1381	−1.41258
$293$	31.9813	1.86837	0.934183	−	0.356793i	$-0.116130\pi$
$293$	31.9813	1.86837	0.934183	+	0.356793i	$0.116130\pi$
$294$	6.30193	0.367536
$295$	−25.6789	−1.49509
$296$	13.8610	0.805651
$297$	−14.9858	−0.869565
$298$	16.3989	0.949964
$299$	−2.31442	−0.133846
$300$	−9.46046	−0.546200
$301$	27.0641	1.55995
$302$	47.6121	2.73977
$303$	−1.53357	−0.0881016
$304$	−0.963624	−0.0552677
$305$	33.2067	1.90141
$306$	−44.5511	−2.54682
$307$	33.1252	1.89056	0.945278	−	0.326265i	$-0.105790\pi$
$307$	33.1252	1.89056	0.945278	+	0.326265i	$0.105790\pi$
$308$	−49.1270	−2.79927
$309$	8.09138	0.460302
$310$	−71.7833	−4.07702
$311$	−21.7795	−1.23500	−0.617501	−	0.786570i	$-0.711855\pi$
$311$	−21.7795	−1.23500	−0.617501	+	0.786570i	$0.711855\pi$
$312$	−1.94985	−0.110389
$313$	2.00479	0.113317	0.0566587	−	0.998394i	$-0.481955\pi$
$313$	2.00479	0.113317	0.0566587	+	0.998394i	$0.481955\pi$
$314$	18.9475	1.06927
$315$	−26.7729	−1.50848
$316$	−30.5936	−1.72103
$317$	−15.0153	−0.843342	−0.421671	−	0.906749i	$-0.638556\pi$
$317$	−15.0153	−0.843342	−0.421671	+	0.906749i	$0.638556\pi$
$318$	−0.421058	−0.0236118
$319$	2.98892	0.167347
$320$	−37.8822	−2.11768
$321$	−4.76121	−0.265745
$322$	−19.7068	−1.09821
$323$	7.33506	0.408134
$324$	19.2393	1.06885
$325$	−4.01876	−0.222921
$326$	−3.83366	−0.212327
$327$	6.87615	0.380252
$328$	−0.657105	−0.0362825
$329$	−21.9728	−1.21140
$330$	−19.0923	−1.05100
$331$	−24.6909	−1.35713	−0.678566	−	0.734539i	$-0.737398\pi$
$331$	−24.6909	−1.35713	−0.678566	+	0.734539i	$0.737398\pi$
$332$	−42.4431	−2.32937
$333$	10.7276	0.587870
$334$	36.5046	1.99744
$335$	13.8450	0.756435
$336$	−2.03863	−0.111216
$337$	10.7791	0.587173	0.293587	−	0.955932i	$-0.405151\pi$
$337$	10.7791	0.587173	0.293587	+	0.955932i	$0.405151\pi$
$338$	28.3496	1.54202
$339$	3.51820	0.191082
$340$	−77.2653	−4.19030
$341$	−42.7093	−2.31284
$342$	−6.07372	−0.328429
$343$	−9.10387	−0.491563
$344$	−27.0955	−1.46089
$345$	−4.84405	−0.260795
$346$	28.6611	1.54083
$347$	−35.3275	−1.89648	−0.948239	−	0.317557i	$-0.897137\pi$
$347$	−35.3275	−1.89648	−0.948239	+	0.317557i	$0.897137\pi$
$348$	1.52496	0.0817466
$349$	−0.0435438	−0.00233084	−0.00116542	−	0.999999i	$-0.500371\pi$
$349$	−0.0435438	−0.00233084	−0.00116542	+	0.999999i	$0.500371\pi$
$350$	−34.2188	−1.82907
$351$	−3.24792	−0.173361
$352$	−19.0298	−1.01429
$353$	−1.89108	−0.100652	−0.0503260	−	0.998733i	$-0.516026\pi$
$353$	−1.89108	−0.100652	−0.0503260	+	0.998733i	$0.516026\pi$
$354$	−12.3244	−0.655035
$355$	22.2591	1.18139
$356$	61.0220	3.23416
$357$	15.5179	0.821296
$358$	−1.19475	−0.0631445
$359$	−26.7873	−1.41378	−0.706891	−	0.707322i	$-0.749903\pi$
$359$	−26.7873	−1.41378	−0.706891	+	0.707322i	$0.749903\pi$
$360$	26.8040	1.41269
$361$	1.00000	0.0526316
$362$	−8.85400	−0.465356
$363$	−4.43374	−0.232711
$364$	−10.6474	−0.558077
$365$	−21.4610	−1.12332
$366$	15.9373	0.833056
$367$	−10.0390	−0.524034	−0.262017	−	0.965063i	$-0.584388\pi$
$367$	−10.0390	−0.524034	−0.262017	+	0.965063i	$0.584388\pi$
$368$	2.42260	0.126287
$369$	−0.508563	−0.0264748
$370$	29.4154	1.52923
$371$	−0.963273	−0.0500106
$372$	−21.7905	−1.12978
$373$	19.3871	1.00382	0.501912	−	0.864919i	$-0.332630\pi$
$373$	19.3871	1.00382	0.501912	+	0.864919i	$0.332630\pi$
$374$	−72.6822	−3.75831
$375$	1.22274	0.0631419
$376$	21.9983	1.13448
$377$	0.647797	0.0333633
$378$	−27.6553	−1.42243
$379$	−33.2555	−1.70822	−0.854109	−	0.520094i	$-0.825897\pi$
$379$	−33.2555	−1.70822	−0.854109	+	0.520094i	$0.825897\pi$
$380$	−10.5337	−0.540367
$381$	−9.15052	−0.468795
$382$	29.2471	1.49641
$383$	2.91882	0.149145	0.0745724	−	0.997216i	$-0.476241\pi$
$383$	2.91882	0.149145	0.0745724	+	0.997216i	$0.476241\pi$
$384$	−12.5398	−0.639919
$385$	−43.6783	−2.22605
$386$	−10.7559	−0.547463
$387$	−20.9704	−1.06599
$388$	−6.60979	−0.335561
$389$	16.9178	0.857767	0.428883	−	0.903360i	$-0.358907\pi$
$389$	16.9178	0.857767	0.428883	+	0.903360i	$0.358907\pi$
$390$	−4.13793	−0.209532
$391$	−18.4407	−0.932588
$392$	−14.4339	−0.729024
$393$	5.61590	0.283284
$394$	49.7407	2.50590
$395$	−27.2005	−1.36861
$396$	38.0657	1.91287
$397$	25.9684	1.30332	0.651659	−	0.758512i	$-0.274074\pi$
$397$	25.9684	1.30332	0.651659	+	0.758512i	$0.274074\pi$
$398$	20.9438	1.04982
$399$	2.11558	0.105912
$400$	4.20661	0.210330
$401$	−7.28531	−0.363811	−0.181906	−	0.983316i	$-0.558227\pi$
$401$	−7.28531	−0.363811	−0.181906	+	0.983316i	$0.558227\pi$
$402$	6.64481	0.331413
$403$	−9.25651	−0.461099
$404$	8.38401	0.417120
$405$	17.1054	0.849976
$406$	5.51584	0.273747
$407$	17.5014	0.867513
$408$	−15.5359	−0.769143
$409$	−16.0959	−0.795889	−0.397945	−	0.917409i	$-0.630276\pi$
$409$	−16.0959	−0.795889	−0.397945	+	0.917409i	$0.630276\pi$
$410$	−1.39449	−0.0688691
$411$	10.1844	0.502357
$412$	−44.2353	−2.17932
$413$	−28.1951	−1.38739
$414$	15.2696	0.750462
$415$	−37.7357	−1.85237
$416$	−4.12439	−0.202215
$417$	4.49213	0.219981
$418$	−9.90888	−0.484659
$419$	14.9091	0.728357	0.364179	−	0.931329i	$-0.381350\pi$
$419$	14.9091	0.728357	0.364179	+	0.931329i	$0.381350\pi$
$420$	−22.2849	−1.08739
$421$	0.326248	0.0159004	0.00795018	−	0.999968i	$-0.497469\pi$
$421$	0.326248	0.0159004	0.00795018	+	0.999968i	$0.497469\pi$
$422$	2.33282	0.113560
$423$	17.0255	0.827808
$424$	0.964390	0.0468349
$425$	−32.0205	−1.55322
$426$	10.6831	0.517596
$427$	36.4605	1.76445
$428$	26.0294	1.25818
$429$	−2.46196	−0.118865
$430$	−57.5014	−2.77297
$431$	−13.2204	−0.636805	−0.318402	−	0.947956i	$-0.603146\pi$
$431$	−13.2204	−0.636805	−0.318402	+	0.947956i	$0.603146\pi$
$432$	3.39973	0.163570
$433$	12.4237	0.597043	0.298521	−	0.954403i	$-0.403507\pi$
$433$	12.4237	0.597043	0.298521	+	0.954403i	$0.403507\pi$
$434$	−78.8169	−3.78333
$435$	1.35583	0.0650070
$436$	−37.5917	−1.80032
$437$	−2.51405	−0.120263
$438$	−10.3000	−0.492154
$439$	−15.1523	−0.723180	−0.361590	−	0.932337i	$-0.617766\pi$
$439$	−15.1523	−0.723180	−0.361590	+	0.932337i	$0.617766\pi$
$440$	43.7289	2.08470
$441$	−11.1711	−0.531956
$442$	−15.7526	−0.749277
$443$	−6.18926	−0.294061	−0.147030	−	0.989132i	$-0.546971\pi$
$443$	−6.18926	−0.294061	−0.147030	+	0.989132i	$0.546971\pi$
$444$	8.92932	0.423767
$445$	54.2540	2.57189
$446$	−39.6811	−1.87895
$447$	4.42593	0.209339
$448$	−41.5941	−1.96513
$449$	−2.46717	−0.116433	−0.0582166	−	0.998304i	$-0.518541\pi$
$449$	−2.46717	−0.116433	−0.0582166	+	0.998304i	$0.518541\pi$
$450$	26.5142	1.24989
$451$	−0.829688	−0.0390685
$452$	−19.2339	−0.904687
$453$	12.8501	0.603750
$454$	−14.4268	−0.677085
$455$	−9.46652	−0.443798
$456$	−2.11804	−0.0991861
$457$	23.8944	1.11773	0.558866	−	0.829258i	$-0.311236\pi$
$457$	23.8944	1.11773	0.558866	+	0.829258i	$0.311236\pi$
$458$	36.5001	1.70554
$459$	−25.8786	−1.20791
$460$	26.4823	1.23474
$461$	−4.55000	−0.211915	−0.105957	−	0.994371i	$-0.533791\pi$
$461$	−4.55000	−0.211915	−0.105957	+	0.994371i	$0.533791\pi$
$462$	−20.9630	−0.975289
$463$	37.8917	1.76098	0.880489	−	0.474067i	$-0.157215\pi$
$463$	37.8917	1.76098	0.880489	+	0.474067i	$0.157215\pi$
$464$	−0.678077	−0.0314789
$465$	−19.3737	−0.898434
$466$	59.7988	2.77013
$467$	26.8680	1.24330	0.621652	−	0.783294i	$-0.286462\pi$
$467$	26.8680	1.24330	0.621652	+	0.783294i	$0.286462\pi$
$468$	8.25009	0.381361
$469$	15.2016	0.701946
$470$	46.6844	2.15339
$471$	5.11377	0.235630
$472$	28.2278	1.29929
$473$	−34.2119	−1.57306
$474$	−13.0547	−0.599620
$475$	−4.36540	−0.200298
$476$	−84.8361	−3.88846
$477$	0.746385	0.0341746
$478$	29.3676	1.34324
$479$	−7.96465	−0.363914	−0.181957	−	0.983306i	$-0.558243\pi$
$479$	−7.96465	−0.363914	−0.181957	+	0.983306i	$0.558243\pi$
$480$	−8.63228	−0.394008
$481$	3.79314	0.172952
$482$	62.3499	2.83996
$483$	−5.31868	−0.242009
$484$	24.2391	1.10178
$485$	−5.87669	−0.266847
$486$	32.9007	1.49241
$487$	17.2272	0.780639	0.390320	−	0.920679i	$-0.372364\pi$
$487$	17.2272	0.780639	0.390320	+	0.920679i	$0.372364\pi$
$488$	−36.5027	−1.65240
$489$	−1.03467	−0.0467895
$490$	−30.6314	−1.38378
$491$	−18.5286	−0.836182	−0.418091	−	0.908405i	$-0.637301\pi$
$491$	−18.5286	−0.836182	−0.418091	+	0.908405i	$0.637301\pi$
$492$	−0.423312	−0.0190844
$493$	5.16149	0.232462
$494$	−2.14758	−0.0966242
$495$	33.8438	1.52117
$496$	9.68917	0.435057
$497$	24.4401	1.09629
$498$	−18.1110	−0.811571
$499$	−20.3063	−0.909036	−0.454518	−	0.890737i	$-0.650189\pi$
$499$	−20.3063	−0.909036	−0.454518	+	0.890737i	$0.650189\pi$
$500$	−6.68467	−0.298948
$501$	9.85229	0.440168
$502$	−7.50372	−0.334907
$503$	−25.0543	−1.11712	−0.558559	−	0.829465i	$-0.688646\pi$
$503$	−25.0543	−1.11712	−0.558559	+	0.829465i	$0.688646\pi$
$504$	29.4303	1.31093
$505$	7.45414	0.331705
$506$	24.9114	1.10745
$507$	7.65132	0.339807
$508$	50.0256	2.21953
$509$	39.3804	1.74551	0.872753	−	0.488162i	$-0.162332\pi$
$509$	39.3804	1.74551	0.872753	+	0.488162i	$0.162332\pi$
$510$	−32.9700	−1.45994
$511$	−23.5638	−1.04240
$512$	10.8005	0.477321
$513$	−3.52807	−0.155768
$514$	−7.73005	−0.340958
$515$	−39.3292	−1.73305
$516$	−17.4551	−0.768418
$517$	27.7760	1.22159
$518$	32.2977	1.41908
$519$	7.73538	0.339546
$520$	9.47751	0.415616
$521$	29.5576	1.29494	0.647472	−	0.762089i	$-0.275826\pi$
$521$	29.5576	1.29494	0.647472	+	0.762089i	$0.275826\pi$
$522$	−4.27391	−0.187064
$523$	16.6421	0.727710	0.363855	−	0.931456i	$-0.381460\pi$
$523$	16.6421	0.727710	0.363855	+	0.931456i	$0.381460\pi$
$524$	−30.7020	−1.34122
$525$	−9.23536	−0.403064
$526$	−58.1893	−2.53717
$527$	−73.7535	−3.21275
$528$	2.57704	0.112151
$529$	−16.6795	−0.725197
$530$	2.04661	0.0888990
$531$	21.8468	0.948069
$532$	−11.5658	−0.501442
$533$	−0.179821	−0.00778891
$534$	26.0388	1.12681
$535$	23.1425	1.00054
$536$	−15.2193	−0.657372
$537$	−0.322453	−0.0139149
$538$	12.3886	0.534109
$539$	−18.2249	−0.785002
$540$	37.1636	1.59927
$541$	34.2342	1.47184	0.735922	−	0.677066i	$-0.236749\pi$
$541$	34.2342	1.47184	0.735922	+	0.677066i	$0.236749\pi$
$542$	−38.1737	−1.63970
$543$	−2.38962	−0.102548
$544$	−32.8621	−1.40895
$545$	−33.4224	−1.43166
$546$	−4.54338	−0.194439
$547$	−22.6275	−0.967484	−0.483742	−	0.875211i	$-0.660723\pi$
$547$	−22.6275	−0.967484	−0.483742	+	0.875211i	$0.660723\pi$
$548$	−55.6776	−2.37843
$549$	−28.2511	−1.20573
$550$	43.2562	1.84445
$551$	0.703673	0.0299775
$552$	5.32485	0.226641
$553$	−29.8657	−1.27002
$554$	29.2402	1.24230
$555$	7.93897	0.336990
$556$	−24.5584	−1.04151
$557$	32.8613	1.39238	0.696189	−	0.717859i	$-0.254878\pi$
$557$	32.8613	1.39238	0.696189	+	0.717859i	$0.254878\pi$
$558$	61.0708	2.58533
$559$	−7.41485	−0.313615
$560$	9.90901	0.418732
$561$	−19.6163	−0.828201
$562$	10.9311	0.461101
$563$	−15.2591	−0.643093	−0.321546	−	0.946894i	$-0.604203\pi$
$563$	−15.2591	−0.643093	−0.321546	+	0.946894i	$0.604203\pi$
$564$	14.1715	0.596727
$565$	−17.1007	−0.719431
$566$	36.4530	1.53223
$567$	18.7815	0.788749
$568$	−24.4685	−1.02667
$569$	33.4025	1.40030	0.700152	−	0.713994i	$-0.253116\pi$
$569$	33.4025	1.40030	0.700152	+	0.713994i	$0.253116\pi$
$570$	−4.49485	−0.188269
$571$	18.8304	0.788027	0.394014	−	0.919105i	$-0.371086\pi$
$571$	18.8304	0.788027	0.394014	+	0.919105i	$0.371086\pi$
$572$	13.4595	0.562770
$573$	7.89353	0.329757
$574$	−1.53113	−0.0639082
$575$	10.9748	0.457683
$576$	32.2289	1.34287
$577$	27.4648	1.14338	0.571688	−	0.820471i	$-0.306289\pi$
$577$	27.4648	1.14338	0.571688	+	0.820471i	$0.306289\pi$
$578$	−85.8551	−3.57110
$579$	−2.90294	−0.120642
$580$	−7.41228	−0.307778
$581$	−41.4332	−1.71894
$582$	−2.82047	−0.116912
$583$	1.21768	0.0504311
$584$	23.5911	0.976207
$585$	7.33507	0.303268
$586$	−74.6066	−3.08197
$587$	−32.1226	−1.32584	−0.662920	−	0.748690i	$-0.730683\pi$
$587$	−32.1226	−1.32584	−0.662920	+	0.748690i	$0.730683\pi$
$588$	−9.29844	−0.383461
$589$	−10.0549	−0.414306
$590$	59.9044	2.46622
$591$	13.4246	0.552214
$592$	−3.97044	−0.163184
$593$	−6.34287	−0.260470	−0.130235	−	0.991483i	$-0.541573\pi$
$593$	−6.34287	−0.260470	−0.130235	+	0.991483i	$0.541573\pi$
$594$	34.9592	1.43439
$595$	−75.4269	−3.09220
$596$	−24.1964	−0.991125
$597$	5.65255	0.231344
$598$	5.39913	0.220787
$599$	10.1804	0.415959	0.207980	−	0.978133i	$-0.433311\pi$
$599$	10.1804	0.415959	0.207980	+	0.978133i	$0.433311\pi$
$600$	9.24608	0.377469
$601$	23.6110	0.963112	0.481556	−	0.876415i	$-0.340072\pi$
$601$	23.6110	0.963112	0.481556	+	0.876415i	$0.340072\pi$
$602$	−63.1357	−2.57322
$603$	−11.7789	−0.479673
$604$	−70.2512	−2.85848
$605$	21.5508	0.876163
$606$	3.57756	0.145328
$607$	−45.2264	−1.83568	−0.917841	−	0.396947i	$-0.870070\pi$
$607$	−45.2264	−1.83568	−0.917841	+	0.396947i	$0.870070\pi$
$608$	−4.48014	−0.181694
$609$	1.48868	0.0603243
$610$	−77.4653	−3.13648
$611$	6.01998	0.243542
$612$	65.7347	2.65717
$613$	16.6913	0.674156	0.337078	−	0.941477i	$-0.390561\pi$
$613$	16.6913	0.674156	0.337078	+	0.941477i	$0.390561\pi$
$614$	−77.2752	−3.11857
$615$	−0.376362	−0.0151764
$616$	48.0137	1.93453
$617$	49.0209	1.97351	0.986755	−	0.162221i	$-0.0518656\pi$
$617$	49.0209	1.97351	0.986755	+	0.162221i	$0.0518656\pi$
$618$	−18.8757	−0.759293
$619$	−46.8336	−1.88240	−0.941201	−	0.337847i	$-0.890301\pi$
$619$	−46.8336	−1.88240	−0.941201	+	0.337847i	$0.890301\pi$
$620$	105.916	4.25367
$621$	8.86975	0.355931
$622$	50.8077	2.03720
$623$	59.5701	2.38662
$624$	0.558530	0.0223591
$625$	−27.7703	−1.11081
$626$	−4.67682	−0.186923
$627$	−2.67432	−0.106802
$628$	−27.9568	−1.11560
$629$	30.2228	1.20506
$630$	62.4564	2.48832
$631$	15.1727	0.604017	0.302008	−	0.953305i	$-0.402343\pi$
$631$	15.1727	0.604017	0.302008	+	0.953305i	$0.402343\pi$
$632$	29.9003	1.18937
$633$	0.629609	0.0250247
$634$	35.0279	1.39114
$635$	44.4773	1.76503
$636$	0.621267	0.0246348
$637$	−3.94994	−0.156502
$638$	−6.97261	−0.276048
$639$	−18.9373	−0.749146
$640$	60.9513	2.40931
$641$	−21.1618	−0.835839	−0.417919	−	0.908484i	$-0.637241\pi$
$641$	−21.1618	−0.835839	−0.417919	+	0.908484i	$0.637241\pi$
$642$	11.1071	0.438360
$643$	11.3777	0.448692	0.224346	−	0.974510i	$-0.427975\pi$
$643$	11.3777	0.448692	0.224346	+	0.974510i	$0.427975\pi$
$644$	29.0771	1.14580
$645$	−15.5192	−0.611066
$646$	−17.1114	−0.673238
$647$	−15.0628	−0.592178	−0.296089	−	0.955160i	$-0.595683\pi$
$647$	−15.0628	−0.592178	−0.296089	+	0.955160i	$0.595683\pi$
$648$	−18.8033	−0.738663
$649$	35.6416	1.39905
$650$	9.37505	0.367720
$651$	−21.2720	−0.833716
$652$	5.65653	0.221527
$653$	−36.9123	−1.44449	−0.722246	−	0.691637i	$-0.756890\pi$
$653$	−36.9123	−1.44449	−0.722246	+	0.691637i	$0.756890\pi$
$654$	−16.0408	−0.627246
$655$	−27.2968	−1.06657
$656$	0.188226	0.00734899
$657$	18.2582	0.712322
$658$	51.2587	1.99827
$659$	−4.25490	−0.165747	−0.0828736	−	0.996560i	$-0.526410\pi$
$659$	−4.25490	−0.165747	−0.0828736	+	0.996560i	$0.526410\pi$
$660$	28.1705	1.09653
$661$	−8.00936	−0.311528	−0.155764	−	0.987794i	$-0.549784\pi$
$661$	−8.00936	−0.311528	−0.155764	+	0.987794i	$0.549784\pi$
$662$	57.5994	2.23866
$663$	−4.25150	−0.165115
$664$	41.4813	1.60979
$665$	−10.2831	−0.398760
$666$	−25.0256	−0.969723
$667$	−1.76907	−0.0684987
$668$	−53.8622	−2.08399
$669$	−10.7096	−0.414056
$670$	−32.2980	−1.24778
$671$	−46.0899	−1.77928
$672$	−9.47811	−0.365626
$673$	−26.7381	−1.03068	−0.515340	−	0.856986i	$-0.672334\pi$
$673$	−26.7381	−1.03068	−0.515340	+	0.856986i	$0.672334\pi$
$674$	−25.1456	−0.968574
$675$	15.4014	0.592802
$676$	−41.8296	−1.60883
$677$	21.3731	0.821434	0.410717	−	0.911763i	$-0.365278\pi$
$677$	21.3731	0.821434	0.410717	+	0.911763i	$0.365278\pi$
$678$	−8.20733	−0.315201
$679$	−6.45252	−0.247625
$680$	75.5144	2.89584
$681$	−3.89368	−0.149206
$682$	99.6330	3.81515
$683$	47.2666	1.80860	0.904302	−	0.426893i	$-0.140392\pi$
$683$	47.2666	1.80860	0.904302	+	0.426893i	$0.140392\pi$
$684$	8.96171	0.342659
$685$	−49.5024	−1.89139
$686$	21.2377	0.810859
$687$	9.85107	0.375842
$688$	7.76143	0.295902
$689$	0.263911	0.0100542
$690$	11.3003	0.430195
$691$	−43.9883	−1.67339	−0.836697	−	0.547667i	$-0.815516\pi$
$691$	−43.9883	−1.67339	−0.836697	+	0.547667i	$0.815516\pi$
$692$	−42.2891	−1.60759
$693$	37.1600	1.41159
$694$	82.4127	3.12834
$695$	−21.8346	−0.828233
$696$	−1.49040	−0.0564937
$697$	−1.43277	−0.0542699
$698$	0.101580	0.00384485
$699$	16.1392	0.610441
$700$	50.4895	1.90832
$701$	39.4059	1.48834	0.744171	−	0.667989i	$-0.232845\pi$
$701$	39.4059	1.48834	0.744171	+	0.667989i	$0.232845\pi$
$702$	7.57682	0.285968
$703$	4.12031	0.155401
$704$	52.5793	1.98166
$705$	12.5997	0.474533
$706$	4.41155	0.166031
$707$	8.18453	0.307811
$708$	18.1845	0.683417
$709$	41.6281	1.56338	0.781688	−	0.623670i	$-0.214359\pi$
$709$	41.6281	1.56338	0.781688	+	0.623670i	$0.214359\pi$
$710$	−51.9264	−1.94876
$711$	23.1412	0.867864
$712$	−59.6392	−2.23507
$713$	25.2786	0.946692
$714$	−36.2005	−1.35477
$715$	11.9667	0.447529
$716$	1.76284	0.0658805
$717$	7.92607	0.296005
$718$	62.4901	2.33211
$719$	−21.7593	−0.811484	−0.405742	−	0.913988i	$-0.632987\pi$
$719$	−21.7593	−0.811484	−0.405742	+	0.913988i	$0.632987\pi$
$720$	−7.67793	−0.286140
$721$	−43.1828	−1.60821
$722$	−2.33282	−0.0868186
$723$	16.8277	0.625829
$724$	13.0640	0.485519
$725$	−3.07182	−0.114084
$726$	10.3431	0.383869
$727$	28.5213	1.05779	0.528897	−	0.848686i	$-0.322606\pi$
$727$	28.5213	1.05779	0.528897	+	0.848686i	$0.322606\pi$
$728$	10.4062	0.385678
$729$	−7.88881	−0.292178
$730$	50.0646	1.85297
$731$	−59.0796	−2.18514
$732$	−23.5153	−0.869151
$733$	−5.48795	−0.202702	−0.101351	−	0.994851i	$-0.532317\pi$
$733$	−5.48795	−0.202702	−0.101351	+	0.994851i	$0.532317\pi$
$734$	23.4193	0.864422
$735$	−8.26715	−0.304938
$736$	11.2633	0.415171
$737$	−19.2165	−0.707848
$738$	1.18639	0.0436715
$739$	7.62886	0.280632	0.140316	−	0.990107i	$-0.455188\pi$
$739$	7.62886	0.280632	0.140316	+	0.990107i	$0.455188\pi$
$740$	−43.4021	−1.59549
$741$	−0.579614	−0.0212926
$742$	2.24714	0.0824952
$743$	−35.3617	−1.29729	−0.648647	−	0.761089i	$-0.724665\pi$
$743$	−35.3617	−1.29729	−0.648647	+	0.761089i	$0.724665\pi$
$744$	21.2967	0.780775
$745$	−21.5128	−0.788168
$746$	−45.2265	−1.65586
$747$	32.1043	1.17463
$748$	107.242	3.92115
$749$	25.4101	0.928464
$750$	−2.85243	−0.104156
$751$	13.0104	0.474756	0.237378	−	0.971417i	$-0.423712\pi$
$751$	13.0104	0.474756	0.237378	+	0.971417i	$0.423712\pi$
$752$	−6.30136	−0.229787
$753$	−2.02519	−0.0738020
$754$	−1.51119	−0.0550345
$755$	−62.4596	−2.27314
$756$	40.8051	1.48407
$757$	4.13523	0.150297	0.0751487	−	0.997172i	$-0.476057\pi$
$757$	4.13523	0.150297	0.0751487	+	0.997172i	$0.476057\pi$
$758$	77.5790	2.81780
$759$	6.72339	0.244043
$760$	10.2950	0.373439
$761$	−16.0630	−0.582284	−0.291142	−	0.956680i	$-0.594035\pi$
$761$	−16.0630	−0.582284	−0.291142	+	0.956680i	$0.594035\pi$
$762$	21.3465	0.773303
$763$	−36.6973	−1.32853
$764$	−43.1537	−1.56125
$765$	58.4440	2.11305
$766$	−6.80909	−0.246022
$767$	7.72471	0.278923
$768$	13.6657	0.493120
$769$	5.07876	0.183145	0.0915723	−	0.995798i	$-0.470811\pi$
$769$	5.07876	0.183145	0.0915723	+	0.995798i	$0.470811\pi$
$770$	101.894	3.67199
$771$	−2.08627	−0.0751353
$772$	15.8703	0.571184
$773$	35.4217	1.27403	0.637015	−	0.770851i	$-0.280169\pi$
$773$	35.4217	1.27403	0.637015	+	0.770851i	$0.280169\pi$
$774$	48.9203	1.75840
$775$	43.8938	1.57671
$776$	6.46000	0.231901
$777$	8.71686	0.312716
$778$	−39.4662	−1.41493
$779$	−0.195331	−0.00699847
$780$	6.10548	0.218611
$781$	−30.8949	−1.10551
$782$	43.0189	1.53835
$783$	−2.48261	−0.0887212
$784$	4.13456	0.147663
$785$	−24.8561	−0.887153
$786$	−13.1009	−0.467293
$787$	−0.551597	−0.0196623	−0.00983116	−	0.999952i	$-0.503129\pi$
$787$	−0.551597	−0.0196623	−0.00983116	+	0.999952i	$0.503129\pi$
$788$	−73.3919	−2.61448
$789$	−15.7048	−0.559106
$790$	63.4539	2.25759
$791$	−18.7763	−0.667607
$792$	−37.2031	−1.32195
$793$	−9.98921	−0.354727
$794$	−60.5796	−2.14989
$795$	0.552362	0.0195903
$796$	−30.9024	−1.09531
$797$	−47.1917	−1.67162	−0.835808	−	0.549022i	$-0.815000\pi$
$797$	−47.1917	−1.67162	−0.835808	+	0.549022i	$0.815000\pi$
$798$	−4.93527	−0.174707
$799$	47.9657	1.69690
$800$	19.5576	0.691466
$801$	−46.1575	−1.63089
$802$	16.9953	0.600126
$803$	29.7871	1.05117
$804$	−9.80435	−0.345773
$805$	25.8522	0.911169
$806$	21.5938	0.760608
$807$	3.34357	0.117699
$808$	−8.19402	−0.288265
$809$	53.0384	1.86473	0.932366	−	0.361517i	$-0.117741\pi$
$809$	53.0384	1.86473	0.932366	+	0.361517i	$0.117741\pi$
$810$	−39.9039	−1.40208
$811$	−15.6938	−0.551082	−0.275541	−	0.961289i	$-0.588857\pi$
$811$	−15.6938	−0.551082	−0.275541	+	0.961289i	$0.588857\pi$
$812$	−8.13856	−0.285608
$813$	−10.3028	−0.361334
$814$	−40.8277	−1.43101
$815$	5.02916	0.176164
$816$	4.45023	0.155789
$817$	−8.05442	−0.281788
$818$	37.5488	1.31286
$819$	8.05379	0.281422
$820$	2.05756	0.0718531
$821$	−48.9361	−1.70788	−0.853941	−	0.520371i	$-0.825794\pi$
$821$	−48.9361	−1.70788	−0.853941	+	0.520371i	$0.825794\pi$
$822$	−23.7583	−0.828665
$823$	46.8660	1.63365	0.816824	−	0.576887i	$-0.195733\pi$
$823$	46.8660	1.63365	0.816824	+	0.576887i	$0.195733\pi$
$824$	43.2329	1.50609
$825$	11.6745	0.406453
$826$	65.7741	2.28857
$827$	22.8301	0.793881	0.396940	−	0.917844i	$-0.370072\pi$
$827$	22.8301	0.793881	0.396940	+	0.917844i	$0.370072\pi$
$828$	−22.5302	−0.782979
$829$	−13.5694	−0.471286	−0.235643	−	0.971840i	$-0.575720\pi$
$829$	−13.5694	−0.471286	−0.235643	+	0.971840i	$0.575720\pi$
$830$	88.0307	3.05559
$831$	7.89168	0.273759
$832$	11.3957	0.395074
$833$	−31.4721	−1.09044
$834$	−10.4793	−0.362870
$835$	−47.8883	−1.65724
$836$	14.6204	0.505659
$837$	35.4745	1.22618
$838$	−34.7803	−1.20146
$839$	1.96243	0.0677505	0.0338753	−	0.999426i	$-0.489215\pi$
$839$	1.96243	0.0677505	0.0338753	+	0.999426i	$0.489215\pi$
$840$	21.7799	0.751478
$841$	−28.5048	−0.982926
$842$	−0.761079	−0.0262285
$843$	2.95022	0.101611
$844$	−3.44205	−0.118480
$845$	−37.1902	−1.27938
$846$	−39.7174	−1.36551
$847$	23.6624	0.813050
$848$	−0.276247	−0.00948637
$849$	9.83836	0.337652
$850$	74.6981	2.56212
$851$	−10.3587	−0.355091
$852$	−15.7628	−0.540023
$853$	−0.315285	−0.0107952	−0.00539758	−	0.999985i	$-0.501718\pi$
$853$	−0.315285	−0.0107952	−0.00539758	+	0.999985i	$0.501718\pi$
$854$	−85.0557	−2.91055
$855$	7.96776	0.272492
$856$	−25.4396	−0.869506
$857$	−8.80328	−0.300714	−0.150357	−	0.988632i	$-0.548042\pi$
$857$	−8.80328	−0.300714	−0.150357	+	0.988632i	$0.548042\pi$
$858$	5.74332	0.196074
$859$	−1.26992	−0.0433292	−0.0216646	−	0.999765i	$-0.506897\pi$
$859$	−1.26992	−0.0433292	−0.0216646	+	0.999765i	$0.506897\pi$
$860$	84.8428	2.89312
$861$	−0.413239	−0.0140832
$862$	30.8408	1.05044
$863$	11.0308	0.375492	0.187746	−	0.982218i	$-0.439882\pi$
$863$	11.0308	0.375492	0.187746	+	0.982218i	$0.439882\pi$
$864$	15.8063	0.537740
$865$	−37.5988	−1.27840
$866$	−28.9822	−0.984854
$867$	−23.1716	−0.786947
$868$	116.294	3.94726
$869$	37.7534	1.28070
$870$	−3.16290	−0.107233
$871$	−4.16484	−0.141120
$872$	36.7398	1.24417
$873$	4.99969	0.169214
$874$	5.86484	0.198381
$875$	−6.52562	−0.220606
$876$	15.1976	0.513478
$877$	−27.8385	−0.940041	−0.470020	−	0.882656i	$-0.655753\pi$
$877$	−27.8385	−0.940041	−0.470020	+	0.882656i	$0.655753\pi$
$878$	35.3476	1.19292
$879$	−20.1357	−0.679160
$880$	−12.5260	−0.422253
$881$	−6.04510	−0.203665	−0.101832	−	0.994802i	$-0.532471\pi$
$881$	−6.04510	−0.203665	−0.101832	+	0.994802i	$0.532471\pi$
$882$	26.0601	0.877490
$883$	50.1449	1.68751	0.843755	−	0.536728i	$-0.180340\pi$
$883$	50.1449	1.68751	0.843755	+	0.536728i	$0.180340\pi$
$884$	23.2429	0.781742
$885$	16.1677	0.543471
$886$	14.4384	0.485069
$887$	12.4052	0.416526	0.208263	−	0.978073i	$-0.433219\pi$
$887$	12.4052	0.416526	0.208263	+	0.978073i	$0.433219\pi$
$888$	−8.72697	−0.292858
$889$	48.8353	1.63788
$890$	−126.565	−4.24247
$891$	−23.7418	−0.795381
$892$	58.5490	1.96037
$893$	6.53923	0.218827
$894$	−10.3249	−0.345316
$895$	1.56732	0.0523899
$896$	66.9236	2.23576
$897$	1.45718	0.0486538
$898$	5.75548	0.192063
$899$	−7.07538	−0.235977
$900$	−39.1214	−1.30405
$901$	2.10278	0.0700537
$902$	1.93551	0.0644456
$903$	−17.0398	−0.567048
$904$	18.7980	0.625214
$905$	11.6151	0.386098
$906$	−29.9770	−0.995918
$907$	12.7379	0.422955	0.211477	−	0.977383i	$-0.432173\pi$
$907$	12.7379	0.422955	0.211477	+	0.977383i	$0.432173\pi$
$908$	21.2866	0.706422
$909$	−6.34173	−0.210342
$910$	22.0837	0.732068
$911$	−0.364002	−0.0120599	−0.00602997	−	0.999982i	$-0.501919\pi$
$911$	−0.364002	−0.0120599	−0.00602997	+	0.999982i	$0.501919\pi$
$912$	0.606706	0.0200900
$913$	52.3760	1.73339
$914$	−55.7413	−1.84376
$915$	−20.9072	−0.691172
$916$	−53.8555	−1.77944
$917$	−29.9714	−0.989744
$918$	60.3702	1.99251
$919$	−27.9295	−0.921308	−0.460654	−	0.887580i	$-0.652385\pi$
$919$	−27.9295	−0.921308	−0.460654	+	0.887580i	$0.652385\pi$
$920$	−25.8821	−0.853309
$921$	−20.8559	−0.687226
$922$	10.6143	0.349564
$923$	−6.69595	−0.220400
$924$	30.9308	1.01755
$925$	−17.9868	−0.591403
$926$	−88.3946	−2.90483
$927$	33.4599	1.09897
$928$	−3.15255	−0.103488
$929$	5.01642	0.164583	0.0822917	−	0.996608i	$-0.473776\pi$
$929$	5.01642	0.164583	0.0822917	+	0.996608i	$0.473776\pi$
$930$	45.1954	1.48202
$931$	−4.29064	−0.140620
$932$	−88.2326	−2.89015
$933$	13.7126	0.448929
$934$	−62.6783	−2.05090
$935$	95.3476	3.11820
$936$	−8.06314	−0.263552
$937$	−29.2656	−0.956067	−0.478033	−	0.878342i	$-0.658650\pi$
$937$	−29.2656	−0.956067	−0.478033	+	0.878342i	$0.658650\pi$
$938$	−35.4627	−1.15790
$939$	−1.26223	−0.0411914
$940$	−68.8823	−2.24669
$941$	−12.8221	−0.417988	−0.208994	−	0.977917i	$-0.567019\pi$
$941$	−12.8221	−0.417988	−0.208994	+	0.977917i	$0.567019\pi$
$942$	−11.9295	−0.388684
$943$	0.491073	0.0159915
$944$	−8.08578	−0.263170
$945$	36.2794	1.18017
$946$	79.8102	2.59485
$947$	30.5589	0.993031	0.496515	−	0.868028i	$-0.334613\pi$
$947$	30.5589	0.993031	0.496515	+	0.868028i	$0.334613\pi$
$948$	19.2620	0.625601
$949$	6.45586	0.209566
$950$	10.1837	0.330403
$951$	9.45374	0.306559
$952$	82.9136	2.68724
$953$	−30.0933	−0.974818	−0.487409	−	0.873174i	$-0.662058\pi$
$953$	−30.0933	−0.974818	−0.487409	+	0.873174i	$0.662058\pi$
$954$	−1.74118	−0.0563729
$955$	−38.3675	−1.24154
$956$	−43.3316	−1.40145
$957$	−1.88185	−0.0608315
$958$	18.5801	0.600296
$959$	−54.3528	−1.75514
$960$	23.8510	0.769786
$961$	70.1016	2.26134
$962$	−8.84871	−0.285294
$963$	−19.6888	−0.634464
$964$	−91.9966	−2.96301
$965$	14.1101	0.454220
$966$	12.4075	0.399206
$967$	5.90595	0.189923	0.0949613	−	0.995481i	$-0.469727\pi$
$967$	5.90595	0.189923	0.0949613	+	0.995481i	$0.469727\pi$
$968$	−23.6898	−0.761421
$969$	−4.61822	−0.148359
$970$	13.7093	0.440178
$971$	−5.56527	−0.178598	−0.0892990	−	0.996005i	$-0.528463\pi$
$971$	−5.56527	−0.178598	−0.0892990	+	0.996005i	$0.528463\pi$
$972$	−48.5446	−1.55707
$973$	−23.9740	−0.768572
$974$	−40.1880	−1.28771
$975$	2.53025	0.0810327
$976$	10.4561	0.334692
$977$	−15.4106	−0.493027	−0.246514	−	0.969139i	$-0.579285\pi$
$977$	−15.4106	−0.493027	−0.246514	+	0.969139i	$0.579285\pi$
$978$	2.41371	0.0771818
$979$	−75.3029	−2.40669
$980$	45.1963	1.44374
$981$	28.4346	0.907848
$982$	43.2238	1.37933
$983$	−33.4379	−1.06650	−0.533252	−	0.845956i	$-0.679030\pi$
$983$	−33.4379	−1.06650	−0.533252	+	0.845956i	$0.679030\pi$
$984$	0.413719	0.0131889
$985$	−65.2520	−2.07910
$986$	−12.0408	−0.383458
$987$	13.8343	0.440350
$988$	3.16873	0.100811
$989$	20.2492	0.643888
$990$	−78.9516	−2.50925
$991$	10.5418	0.334872	0.167436	−	0.985883i	$-0.446451\pi$
$991$	10.5418	0.334872	0.167436	+	0.985883i	$0.446451\pi$
$992$	45.0475	1.43026
$993$	15.5456	0.493324
$994$	−57.0144	−1.80839
$995$	−27.4750	−0.871015
$996$	26.7225	0.846736
$997$	46.9516	1.48697	0.743486	−	0.668752i	$-0.233171\pi$
$997$	46.9516	1.48697	0.743486	+	0.668752i	$0.233171\pi$
$998$	47.3710	1.49950
$999$	−14.5368	−0.459923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4009.2.a.d.1.10	✓	75

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4009.2.a.d.1.10	✓	75	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:	\( N \)	\(=\)	\( 4009 = 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4009.a (trivial)

\(f(q)\)	\(=\)	\(q-2.33282 q^{2} -0.629609 q^{3} +3.44205 q^{4} +3.06029 q^{5} +1.46876 q^{6} +3.36015 q^{7} -3.36405 q^{8} -2.60359 q^{9} +O(q^{10})\)	\(q-2.33282 q^{2} -0.629609 q^{3} +3.44205 q^{4} +3.06029 q^{5} +1.46876 q^{6} +3.36015 q^{7} -3.36405 q^{8} -2.60359 q^{9} -7.13912 q^{10} -4.24759 q^{11} -2.16715 q^{12} -0.920594 q^{13} -7.83864 q^{14} -1.92679 q^{15} +0.963624 q^{16} -7.33506 q^{17} +6.07372 q^{18} -1.00000 q^{19} +10.5337 q^{20} -2.11558 q^{21} +9.90888 q^{22} +2.51405 q^{23} +2.11804 q^{24} +4.36540 q^{25} +2.14758 q^{26} +3.52807 q^{27} +11.5658 q^{28} -0.703673 q^{29} +4.49485 q^{30} +10.0549 q^{31} +4.48014 q^{32} +2.67432 q^{33} +17.1114 q^{34} +10.2831 q^{35} -8.96171 q^{36} -4.12031 q^{37} +2.33282 q^{38} +0.579614 q^{39} -10.2950 q^{40} +0.195331 q^{41} +4.93527 q^{42} +8.05442 q^{43} -14.6204 q^{44} -7.96776 q^{45} -5.86484 q^{46} -6.53923 q^{47} -0.606706 q^{48} +4.29064 q^{49} -10.1837 q^{50} +4.61822 q^{51} -3.16873 q^{52} -0.286675 q^{53} -8.23036 q^{54} -12.9989 q^{55} -11.3037 q^{56} +0.629609 q^{57} +1.64154 q^{58} -8.39101 q^{59} -6.63210 q^{60} +10.8508 q^{61} -23.4563 q^{62} -8.74848 q^{63} -12.3786 q^{64} -2.81729 q^{65} -6.23871 q^{66} +4.52408 q^{67} -25.2477 q^{68} -1.58287 q^{69} -23.9885 q^{70} +7.27351 q^{71} +8.75862 q^{72} -7.01271 q^{73} +9.61196 q^{74} -2.74849 q^{75} -3.44205 q^{76} -14.2726 q^{77} -1.35214 q^{78} -8.88819 q^{79} +2.94897 q^{80} +5.58948 q^{81} -0.455673 q^{82} -12.3307 q^{83} -7.28195 q^{84} -22.4474 q^{85} -18.7895 q^{86} +0.443039 q^{87} +14.2891 q^{88} +17.7284 q^{89} +18.5874 q^{90} -3.09334 q^{91} +8.65350 q^{92} -6.33067 q^{93} +15.2549 q^{94} -3.06029 q^{95} -2.82073 q^{96} -1.92030 q^{97} -10.0093 q^{98} +11.0590 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9}+O(q^{10}) \) 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9	\( 75 q - 11 q^{2} - 4 q^{3} + 67 q^{4} - 18 q^{5} - 15 q^{6} - 19 q^{7} - 30 q^{8} + 57 q^{9} - 48 q^{11} - 14 q^{12} - 3 q^{13} - 4 q^{14} - 39 q^{15} + 59 q^{16} - 23 q^{17} - 24 q^{18} - 75 q^{19} - 62 q^{20} - 3 q^{21} - 6 q^{22} - 73 q^{23} - 64 q^{24} + 57 q^{25} - 46 q^{26} - 22 q^{27} - 26 q^{28} - 39 q^{29} - 14 q^{30} - 44 q^{31} - 71 q^{32} - 3 q^{33} - 9 q^{34} - 49 q^{35} + 20 q^{36} - 12 q^{37} + 11 q^{38} - 90 q^{39} - 8 q^{40} - 42 q^{41} - 45 q^{42} - 24 q^{43} - 120 q^{44} - 63 q^{45} - 39 q^{46} - 59 q^{47} - 4 q^{48} + 48 q^{49} - 100 q^{50} - 55 q^{51} + 2 q^{52} + 13 q^{53} - 87 q^{54} - 36 q^{55} - 12 q^{56} + 4 q^{57} - 17 q^{58} - 47 q^{59} - 45 q^{60} - 35 q^{61} - 40 q^{62} - 69 q^{63} + 26 q^{64} - 44 q^{65} + 33 q^{66} - 39 q^{67} - 63 q^{68} + 42 q^{69} + 40 q^{70} - 154 q^{71} - 51 q^{72} - 29 q^{73} - 95 q^{74} + 37 q^{75} - 67 q^{76} - 24 q^{77} - 19 q^{78} - 95 q^{79} - 146 q^{80} + 23 q^{81} + 7 q^{82} - 52 q^{83} - 72 q^{84} - 36 q^{85} - 44 q^{86} - 103 q^{87} + 67 q^{88} + q^{89} - 2 q^{90} - 64 q^{91} - 183 q^{92} - 49 q^{93} + 5 q^{94} + 18 q^{95} - 69 q^{96} - 7 q^{97} - 23 q^{98} - 100 q^{99}+O(q^{100}) \) 75 * q - 11 * q^2 - 4 * q^3 + 67 * q^4 - 18 * q^5 - 15 * q^6 - 19 * q^7 - 30 * q^8 + 57 * q^9 - 48 * q^11 - 14 * q^12 - 3 * q^13 - 4 * q^14 - 39 * q^15 + 59 * q^16 - 23 * q^17 - 24 * q^18 - 75 * q^19 - 62 * q^20 - 3 * q^21 - 6 * q^22 - 73 * q^23 - 64 * q^24 + 57 * q^25 - 46 * q^26 - 22 * q^27 - 26 * q^28 - 39 * q^29 - 14 * q^30 - 44 * q^31 - 71 * q^32 - 3 * q^33 - 9 * q^34 - 49 * q^35 + 20 * q^36 - 12 * q^37 + 11 * q^38 - 90 * q^39 - 8 * q^40 - 42 * q^41 - 45 * q^42 - 24 * q^43 - 120 * q^44 - 63 * q^45 - 39 * q^46 - 59 * q^47 - 4 * q^48 + 48 * q^49 - 100 * q^50 - 55 * q^51 + 2 * q^52 + 13 * q^53 - 87 * q^54 - 36 * q^55 - 12 * q^56 + 4 * q^57 - 17 * q^58 - 47 * q^59 - 45 * q^60 - 35 * q^61 - 40 * q^62 - 69 * q^63 + 26 * q^64 - 44 * q^65 + 33 * q^66 - 39 * q^67 - 63 * q^68 + 42 * q^69 + 40 * q^70 - 154 * q^71 - 51 * q^72 - 29 * q^73 - 95 * q^74 + 37 * q^75 - 67 * q^76 - 24 * q^77 - 19 * q^78 - 95 * q^79 - 146 * q^80 + 23 * q^81 + 7 * q^82 - 52 * q^83 - 72 * q^84 - 36 * q^85 - 44 * q^86 - 103 * q^87 + 67 * q^88 + q^89 - 2 * q^90 - 64 * q^91 - 183 * q^92 - 49 * q^93 + 5 * q^94 + 18 * q^95 - 69 * q^96 - 7 * q^97 - 23 * q^98 - 100 * q^99

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