LMFDB - Embedded newform 8026.2.a.a.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.0879326623$
Analytic rank:	$1$
Dimension:	$71$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.95374 q^{3} +1.00000 q^{4} +0.792660 q^{5} -1.95374 q^{6} +2.85182 q^{7} +1.00000 q^{8} +0.817104 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.95374 q^{3} +1.00000 q^{4} +0.792660 q^{5} -1.95374 q^{6} +2.85182 q^{7} +1.00000 q^{8} +0.817104 q^{9} +0.792660 q^{10} -1.70879 q^{11} -1.95374 q^{12} -5.22711 q^{13} +2.85182 q^{14} -1.54865 q^{15} +1.00000 q^{16} +3.24079 q^{17} +0.817104 q^{18} -1.45720 q^{19} +0.792660 q^{20} -5.57172 q^{21} -1.70879 q^{22} -5.00995 q^{23} -1.95374 q^{24} -4.37169 q^{25} -5.22711 q^{26} +4.26481 q^{27} +2.85182 q^{28} +8.47772 q^{29} -1.54865 q^{30} +5.25114 q^{31} +1.00000 q^{32} +3.33853 q^{33} +3.24079 q^{34} +2.26052 q^{35} +0.817104 q^{36} -9.72210 q^{37} -1.45720 q^{38} +10.2124 q^{39} +0.792660 q^{40} +7.87812 q^{41} -5.57172 q^{42} +9.45730 q^{43} -1.70879 q^{44} +0.647685 q^{45} -5.00995 q^{46} -9.89718 q^{47} -1.95374 q^{48} +1.13288 q^{49} -4.37169 q^{50} -6.33167 q^{51} -5.22711 q^{52} -1.51534 q^{53} +4.26481 q^{54} -1.35449 q^{55} +2.85182 q^{56} +2.84698 q^{57} +8.47772 q^{58} -8.27437 q^{59} -1.54865 q^{60} +7.27518 q^{61} +5.25114 q^{62} +2.33023 q^{63} +1.00000 q^{64} -4.14332 q^{65} +3.33853 q^{66} -7.53248 q^{67} +3.24079 q^{68} +9.78815 q^{69} +2.26052 q^{70} -9.29323 q^{71} +0.817104 q^{72} -14.7726 q^{73} -9.72210 q^{74} +8.54115 q^{75} -1.45720 q^{76} -4.87316 q^{77} +10.2124 q^{78} -12.1996 q^{79} +0.792660 q^{80} -10.7837 q^{81} +7.87812 q^{82} +5.91547 q^{83} -5.57172 q^{84} +2.56885 q^{85} +9.45730 q^{86} -16.5633 q^{87} -1.70879 q^{88} +1.60891 q^{89} +0.647685 q^{90} -14.9068 q^{91} -5.00995 q^{92} -10.2594 q^{93} -9.89718 q^{94} -1.15506 q^{95} -1.95374 q^{96} +5.17053 q^{97} +1.13288 q^{98} -1.39626 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) $ 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.95374	−1.12799	−0.563996	−	0.825777i	$-0.690737\pi$
$3$	−1.95374	−1.12799	−0.563996	+	0.825777i	$0.690737\pi$
$4$	1.00000	0.500000
$5$	0.792660	0.354488	0.177244	−	0.984167i	$-0.443282\pi$
$5$	0.792660	0.354488	0.177244	+	0.984167i	$0.443282\pi$
$6$	−1.95374	−0.797611
$7$	2.85182	1.07789	0.538943	−	0.842342i	$-0.318824\pi$
$7$	2.85182	1.07789	0.538943	+	0.842342i	$0.318824\pi$
$8$	1.00000	0.353553
$9$	0.817104	0.272368
$10$	0.792660	0.250661
$11$	−1.70879	−0.515220	−0.257610	−	0.966249i	$-0.582935\pi$
$11$	−1.70879	−0.515220	−0.257610	+	0.966249i	$0.582935\pi$
$12$	−1.95374	−0.563996
$13$	−5.22711	−1.44974	−0.724870	−	0.688886i	$-0.758100\pi$
$13$	−5.22711	−1.44974	−0.724870	+	0.688886i	$0.758100\pi$
$14$	2.85182	0.762181
$15$	−1.54865	−0.399860
$16$	1.00000	0.250000
$17$	3.24079	0.786008	0.393004	−	0.919537i	$-0.371436\pi$
$17$	3.24079	0.786008	0.393004	+	0.919537i	$0.371436\pi$
$18$	0.817104	0.192593
$19$	−1.45720	−0.334304	−0.167152	−	0.985931i	$-0.553457\pi$
$19$	−1.45720	−0.334304	−0.167152	+	0.985931i	$0.553457\pi$
$20$	0.792660	0.177244
$21$	−5.57172	−1.21585
$22$	−1.70879	−0.364315
$23$	−5.00995	−1.04465	−0.522324	−	0.852747i	$-0.674935\pi$
$23$	−5.00995	−1.04465	−0.522324	+	0.852747i	$0.674935\pi$
$24$	−1.95374	−0.398806
$25$	−4.37169	−0.874338
$26$	−5.22711	−1.02512
$27$	4.26481	0.820764
$28$	2.85182	0.538943
$29$	8.47772	1.57427	0.787136	−	0.616779i	$-0.211563\pi$
$29$	8.47772	1.57427	0.787136	+	0.616779i	$0.211563\pi$
$30$	−1.54865	−0.282744
$31$	5.25114	0.943133	0.471566	−	0.881831i	$-0.343689\pi$
$31$	5.25114	0.943133	0.471566	+	0.881831i	$0.343689\pi$
$32$	1.00000	0.176777
$33$	3.33853	0.581164
$34$	3.24079	0.555792
$35$	2.26052	0.382098
$36$	0.817104	0.136184
$37$	−9.72210	−1.59830	−0.799151	−	0.601130i	$-0.794717\pi$
$37$	−9.72210	−1.59830	−0.799151	+	0.601130i	$0.794717\pi$
$38$	−1.45720	−0.236388
$39$	10.2124	1.63530
$40$	0.792660	0.125330
$41$	7.87812	1.23036	0.615178	−	0.788388i	$-0.289084\pi$
$41$	7.87812	1.23036	0.615178	+	0.788388i	$0.289084\pi$
$42$	−5.57172	−0.859735
$43$	9.45730	1.44222	0.721112	−	0.692818i	$-0.243631\pi$
$43$	9.45730	1.44222	0.721112	+	0.692818i	$0.243631\pi$
$44$	−1.70879	−0.257610
$45$	0.647685	0.0965512
$46$	−5.00995	−0.738678
$47$	−9.89718	−1.44365	−0.721826	−	0.692075i	$-0.756697\pi$
$47$	−9.89718	−1.44365	−0.721826	+	0.692075i	$0.756697\pi$
$48$	−1.95374	−0.281998
$49$	1.13288	0.161840
$50$	−4.37169	−0.618250
$51$	−6.33167	−0.886612
$52$	−5.22711	−0.724870
$53$	−1.51534	−0.208149	−0.104074	−	0.994570i	$-0.533188\pi$
$53$	−1.51534	−0.208149	−0.104074	+	0.994570i	$0.533188\pi$
$54$	4.26481	0.580368
$55$	−1.35449	−0.182639
$56$	2.85182	0.381090
$57$	2.84698	0.377092
$58$	8.47772	1.11318
$59$	−8.27437	−1.07723	−0.538615	−	0.842552i	$-0.681052\pi$
$59$	−8.27437	−1.07723	−0.538615	+	0.842552i	$0.681052\pi$
$60$	−1.54865	−0.199930
$61$	7.27518	0.931491	0.465746	−	0.884919i	$-0.345786\pi$
$61$	7.27518	0.931491	0.465746	+	0.884919i	$0.345786\pi$
$62$	5.25114	0.666895
$63$	2.33023	0.293582
$64$	1.00000	0.125000
$65$	−4.14332	−0.513915
$66$	3.33853	0.410945
$67$	−7.53248	−0.920239	−0.460119	−	0.887857i	$-0.652193\pi$
$67$	−7.53248	−0.920239	−0.460119	+	0.887857i	$0.652193\pi$
$68$	3.24079	0.393004
$69$	9.78815	1.17836
$70$	2.26052	0.270184
$71$	−9.29323	−1.10290	−0.551452	−	0.834207i	$-0.685926\pi$
$71$	−9.29323	−1.10290	−0.551452	+	0.834207i	$0.685926\pi$
$72$	0.817104	0.0962966
$73$	−14.7726	−1.72900	−0.864499	−	0.502634i	$-0.832364\pi$
$73$	−14.7726	−1.72900	−0.864499	+	0.502634i	$0.832364\pi$
$74$	−9.72210	−1.13017
$75$	8.54115	0.986247
$76$	−1.45720	−0.167152
$77$	−4.87316	−0.555348
$78$	10.2124	1.15633
$79$	−12.1996	−1.37257	−0.686283	−	0.727335i	$-0.740759\pi$
$79$	−12.1996	−1.37257	−0.686283	+	0.727335i	$0.740759\pi$
$80$	0.792660	0.0886220
$81$	−10.7837	−1.19818
$82$	7.87812	0.869993
$83$	5.91547	0.649308	0.324654	−	0.945833i	$-0.394752\pi$
$83$	5.91547	0.649308	0.324654	+	0.945833i	$0.394752\pi$
$84$	−5.57172	−0.607924
$85$	2.56885	0.278631
$86$	9.45730	1.01981
$87$	−16.5633	−1.77577
$88$	−1.70879	−0.182158
$89$	1.60891	0.170544	0.0852721	−	0.996358i	$-0.472824\pi$
$89$	1.60891	0.170544	0.0852721	+	0.996358i	$0.472824\pi$
$90$	0.647685	0.0682720
$91$	−14.9068	−1.56265
$92$	−5.00995	−0.522324
$93$	−10.2594	−1.06385
$94$	−9.89718	−1.02082
$95$	−1.15506	−0.118507
$96$	−1.95374	−0.199403
$97$	5.17053	0.524988	0.262494	−	0.964934i	$-0.415455\pi$
$97$	5.17053	0.524988	0.262494	+	0.964934i	$0.415455\pi$
$98$	1.13288	0.114438
$99$	−1.39626	−0.140329
$100$	−4.37169	−0.437169
$101$	−4.37234	−0.435064	−0.217532	−	0.976053i	$-0.569801\pi$
$101$	−4.37234	−0.435064	−0.217532	+	0.976053i	$0.569801\pi$
$102$	−6.33167	−0.626929
$103$	−1.71154	−0.168643	−0.0843213	−	0.996439i	$-0.526872\pi$
$103$	−1.71154	−0.168643	−0.0843213	+	0.996439i	$0.526872\pi$
$104$	−5.22711	−0.512560
$105$	−4.41648	−0.431004
$106$	−1.51534	−0.147183
$107$	17.0057	1.64401	0.822004	−	0.569482i	$-0.192856\pi$
$107$	17.0057	1.64401	0.822004	+	0.569482i	$0.192856\pi$
$108$	4.26481	0.410382
$109$	−11.1687	−1.06977	−0.534885	−	0.844925i	$-0.679645\pi$
$109$	−11.1687	−1.06977	−0.534885	+	0.844925i	$0.679645\pi$
$110$	−1.35449	−0.129145
$111$	18.9945	1.80287
$112$	2.85182	0.269472
$113$	2.76857	0.260445	0.130223	−	0.991485i	$-0.458431\pi$
$113$	2.76857	0.260445	0.130223	+	0.991485i	$0.458431\pi$
$114$	2.84698	0.266644
$115$	−3.97119	−0.370315
$116$	8.47772	0.787136
$117$	−4.27109	−0.394862
$118$	−8.27437	−0.761717
$119$	9.24216	0.847228
$120$	−1.54865	−0.141372
$121$	−8.08004	−0.734549
$122$	7.27518	0.658664
$123$	−15.3918	−1.38783
$124$	5.25114	0.471566
$125$	−7.42856	−0.664431
$126$	2.33023	0.207594
$127$	4.63613	0.411390	0.205695	−	0.978616i	$-0.434054\pi$
$127$	4.63613	0.411390	0.205695	+	0.978616i	$0.434054\pi$
$128$	1.00000	0.0883883
$129$	−18.4771	−1.62682
$130$	−4.14332	−0.363393
$131$	−17.3313	−1.51424	−0.757122	−	0.653273i	$-0.773395\pi$
$131$	−17.3313	−1.51424	−0.757122	+	0.653273i	$0.773395\pi$
$132$	3.33853	0.290582
$133$	−4.15566	−0.360341
$134$	−7.53248	−0.650707
$135$	3.38055	0.290951
$136$	3.24079	0.277896
$137$	−1.69990	−0.145232	−0.0726160	−	0.997360i	$-0.523135\pi$
$137$	−1.69990	−0.145232	−0.0726160	+	0.997360i	$0.523135\pi$
$138$	9.78815	0.833223
$139$	9.07178	0.769459	0.384729	−	0.923029i	$-0.374295\pi$
$139$	9.07178	0.769459	0.384729	+	0.923029i	$0.374295\pi$
$140$	2.26052	0.191049
$141$	19.3365	1.62843
$142$	−9.29323	−0.779870
$143$	8.93203	0.746934
$144$	0.817104	0.0680920
$145$	6.71994	0.558061
$146$	−14.7726	−1.22259
$147$	−2.21335	−0.182554
$148$	−9.72210	−0.799151
$149$	−9.82669	−0.805034	−0.402517	−	0.915413i	$-0.631865\pi$
$149$	−9.82669	−0.805034	−0.402517	+	0.915413i	$0.631865\pi$
$150$	8.54115	0.697382
$151$	−3.47436	−0.282739	−0.141370	−	0.989957i	$-0.545151\pi$
$151$	−3.47436	−0.282739	−0.141370	+	0.989957i	$0.545151\pi$
$152$	−1.45720	−0.118194
$153$	2.64806	0.214083
$154$	−4.87316	−0.392691
$155$	4.16237	0.334329
$156$	10.2124	0.817648
$157$	7.84642	0.626213	0.313106	−	0.949718i	$-0.398630\pi$
$157$	7.84642	0.626213	0.313106	+	0.949718i	$0.398630\pi$
$158$	−12.1996	−0.970551
$159$	2.96059	0.234790
$160$	0.792660	0.0626652
$161$	−14.2875	−1.12601
$162$	−10.7837	−0.847244
$163$	18.9279	1.48255	0.741273	−	0.671204i	$-0.234222\pi$
$163$	18.9279	1.48255	0.741273	+	0.671204i	$0.234222\pi$
$164$	7.87812	0.615178
$165$	2.64632	0.206016
$166$	5.91547	0.459130
$167$	2.40725	0.186279	0.0931395	−	0.995653i	$-0.470310\pi$
$167$	2.40725	0.186279	0.0931395	+	0.995653i	$0.470310\pi$
$168$	−5.57172	−0.429867
$169$	14.3227	1.10174
$170$	2.56885	0.197022
$171$	−1.19068	−0.0910536
$172$	9.45730	0.721112
$173$	9.27366	0.705063	0.352532	−	0.935800i	$-0.385321\pi$
$173$	9.27366	0.705063	0.352532	+	0.935800i	$0.385321\pi$
$174$	−16.5633	−1.25566
$175$	−12.4673	−0.942437
$176$	−1.70879	−0.128805
$177$	16.1660	1.21511
$178$	1.60891	0.120593
$179$	−3.58076	−0.267639	−0.133819	−	0.991006i	$-0.542724\pi$
$179$	−3.58076	−0.267639	−0.133819	+	0.991006i	$0.542724\pi$
$180$	0.647685	0.0482756
$181$	−20.0305	−1.48885	−0.744427	−	0.667704i	$-0.767277\pi$
$181$	−20.0305	−1.48885	−0.744427	+	0.667704i	$0.767277\pi$
$182$	−14.9068	−1.10496
$183$	−14.2138	−1.05072
$184$	−5.00995	−0.369339
$185$	−7.70631	−0.566579
$186$	−10.2594	−0.752253
$187$	−5.53784	−0.404967
$188$	−9.89718	−0.721826
$189$	12.1625	0.884690
$190$	−1.15506	−0.0837969
$191$	−22.3719	−1.61877	−0.809386	−	0.587277i	$-0.800200\pi$
$191$	−22.3719	−1.61877	−0.809386	+	0.587277i	$0.800200\pi$
$192$	−1.95374	−0.140999
$193$	−3.85278	−0.277329	−0.138665	−	0.990339i	$-0.544281\pi$
$193$	−3.85278	−0.277329	−0.138665	+	0.990339i	$0.544281\pi$
$194$	5.17053	0.371222
$195$	8.09497	0.579693
$196$	1.13288	0.0809198
$197$	−6.92681	−0.493515	−0.246757	−	0.969077i	$-0.579365\pi$
$197$	−6.92681	−0.493515	−0.246757	+	0.969077i	$0.579365\pi$
$198$	−1.39626	−0.0992278
$199$	17.7696	1.25966	0.629828	−	0.776735i	$-0.283125\pi$
$199$	17.7696	1.25966	0.629828	+	0.776735i	$0.283125\pi$
$200$	−4.37169	−0.309125
$201$	14.7165	1.03802
$202$	−4.37234	−0.307637
$203$	24.1769	1.69689
$204$	−6.33167	−0.443306
$205$	6.24467	0.436147
$206$	−1.71154	−0.119248
$207$	−4.09365	−0.284528
$208$	−5.22711	−0.362435
$209$	2.49004	0.172240
$210$	−4.41648	−0.304766
$211$	1.28630	0.0885523	0.0442762	−	0.999019i	$-0.485902\pi$
$211$	1.28630	0.0885523	0.0442762	+	0.999019i	$0.485902\pi$
$212$	−1.51534	−0.104074
$213$	18.1566	1.24407
$214$	17.0057	1.16249
$215$	7.49642	0.511252
$216$	4.26481	0.290184
$217$	14.9753	1.01659
$218$	−11.1687	−0.756441
$219$	28.8618	1.95030
$220$	−1.35449	−0.0913196
$221$	−16.9400	−1.13951
$222$	18.9945	1.27482
$223$	−21.5202	−1.44110	−0.720549	−	0.693404i	$-0.756110\pi$
$223$	−21.5202	−1.44110	−0.720549	+	0.693404i	$0.756110\pi$
$224$	2.85182	0.190545
$225$	−3.57212	−0.238142
$226$	2.76857	0.184163
$227$	−7.12872	−0.473150	−0.236575	−	0.971613i	$-0.576025\pi$
$227$	−7.12872	−0.473150	−0.236575	+	0.971613i	$0.576025\pi$
$228$	2.84698	0.188546
$229$	14.3725	0.949760	0.474880	−	0.880051i	$-0.342491\pi$
$229$	14.3725	0.949760	0.474880	+	0.880051i	$0.342491\pi$
$230$	−3.97119	−0.261852
$231$	9.52089	0.626429
$232$	8.47772	0.556589
$233$	19.4865	1.27660	0.638302	−	0.769786i	$-0.279637\pi$
$233$	19.4865	1.27660	0.638302	+	0.769786i	$0.279637\pi$
$234$	−4.27109	−0.279210
$235$	−7.84509	−0.511758
$236$	−8.27437	−0.538615
$237$	23.8349	1.54824
$238$	9.24216	0.599080
$239$	−3.39799	−0.219798	−0.109899	−	0.993943i	$-0.535053\pi$
$239$	−3.39799	−0.219798	−0.109899	+	0.993943i	$0.535053\pi$
$240$	−1.54865	−0.0999650
$241$	0.424483	0.0273434	0.0136717	−	0.999907i	$-0.495648\pi$
$241$	0.424483	0.0273434	0.0136717	+	0.999907i	$0.495648\pi$
$242$	−8.08004	−0.519404
$243$	8.27402	0.530779
$244$	7.27518	0.465746
$245$	0.897986	0.0573702
$246$	−15.3918	−0.981346
$247$	7.61692	0.484653
$248$	5.25114	0.333448
$249$	−11.5573	−0.732414
$250$	−7.42856	−0.469823
$251$	0.616945	0.0389412	0.0194706	−	0.999810i	$-0.493802\pi$
$251$	0.616945	0.0389412	0.0194706	+	0.999810i	$0.493802\pi$
$252$	2.33023	0.146791
$253$	8.56096	0.538223
$254$	4.63613	0.290897
$255$	−5.01886	−0.314293
$256$	1.00000	0.0625000
$257$	−3.16242	−0.197266	−0.0986332	−	0.995124i	$-0.531447\pi$
$257$	−3.16242	−0.197266	−0.0986332	+	0.995124i	$0.531447\pi$
$258$	−18.4771	−1.15033
$259$	−27.7257	−1.72279
$260$	−4.14332	−0.256958
$261$	6.92717	0.428781
$262$	−17.3313	−1.07073
$263$	3.22845	0.199075	0.0995373	−	0.995034i	$-0.468264\pi$
$263$	3.22845	0.199075	0.0995373	+	0.995034i	$0.468264\pi$
$264$	3.33853	0.205472
$265$	−1.20115	−0.0737862
$266$	−4.15566	−0.254800
$267$	−3.14340	−0.192373
$268$	−7.53248	−0.460119
$269$	−13.2431	−0.807447	−0.403723	−	0.914881i	$-0.632284\pi$
$269$	−13.2431	−0.807447	−0.403723	+	0.914881i	$0.632284\pi$
$270$	3.38055	0.205733
$271$	−12.8681	−0.781682	−0.390841	−	0.920458i	$-0.627816\pi$
$271$	−12.8681	−0.781682	−0.390841	+	0.920458i	$0.627816\pi$
$272$	3.24079	0.196502
$273$	29.1240	1.76266
$274$	−1.69990	−0.102695
$275$	7.47030	0.450476
$276$	9.78815	0.589178
$277$	−31.7870	−1.90990	−0.954949	−	0.296771i	$-0.904090\pi$
$277$	−31.7870	−1.90990	−0.954949	+	0.296771i	$0.904090\pi$
$278$	9.07178	0.544089
$279$	4.29073	0.256879
$280$	2.26052	0.135092
$281$	8.28966	0.494519	0.247260	−	0.968949i	$-0.420470\pi$
$281$	8.28966	0.494519	0.247260	+	0.968949i	$0.420470\pi$
$282$	19.3365	1.15147
$283$	−14.1023	−0.838296	−0.419148	−	0.907918i	$-0.637671\pi$
$283$	−14.1023	−0.838296	−0.419148	+	0.907918i	$0.637671\pi$
$284$	−9.29323	−0.551452
$285$	2.25669	0.133675
$286$	8.93203	0.528162
$287$	22.4670	1.32618
$288$	0.817104	0.0481483
$289$	−6.49725	−0.382191
$290$	6.71994	0.394609
$291$	−10.1019	−0.592182
$292$	−14.7726	−0.864499
$293$	7.81002	0.456266	0.228133	−	0.973630i	$-0.426738\pi$
$293$	7.81002	0.456266	0.228133	+	0.973630i	$0.426738\pi$
$294$	−2.21335	−0.129085
$295$	−6.55876	−0.381866
$296$	−9.72210	−0.565085
$297$	−7.28767	−0.422874
$298$	−9.82669	−0.569245
$299$	26.1876	1.51447
$300$	8.54115	0.493124
$301$	26.9705	1.55455
$302$	−3.47436	−0.199927
$303$	8.54241	0.490749
$304$	−1.45720	−0.0835759
$305$	5.76674	0.330203
$306$	2.64806	0.151380
$307$	6.35677	0.362800	0.181400	−	0.983409i	$-0.441937\pi$
$307$	6.35677	0.362800	0.181400	+	0.983409i	$0.441937\pi$
$308$	−4.87316	−0.277674
$309$	3.34390	0.190228
$310$	4.16237	0.236407
$311$	−28.7519	−1.63037	−0.815186	−	0.579199i	$-0.803365\pi$
$311$	−28.7519	−1.63037	−0.815186	+	0.579199i	$0.803365\pi$
$312$	10.2124	0.578164
$313$	−27.3280	−1.54467	−0.772335	−	0.635215i	$-0.780912\pi$
$313$	−27.3280	−1.54467	−0.772335	+	0.635215i	$0.780912\pi$
$314$	7.84642	0.442799
$315$	1.84708	0.104071
$316$	−12.1996	−0.686283
$317$	−13.1435	−0.738211	−0.369105	−	0.929388i	$-0.620336\pi$
$317$	−13.1435	−0.738211	−0.369105	+	0.929388i	$0.620336\pi$
$318$	2.96059	0.166022
$319$	−14.4866	−0.811096
$320$	0.792660	0.0443110
$321$	−33.2248	−1.85443
$322$	−14.2875	−0.796211
$323$	−4.72247	−0.262765
$324$	−10.7837	−0.599092
$325$	22.8513	1.26756
$326$	18.9279	1.04832
$327$	21.8208	1.20669
$328$	7.87812	0.434997
$329$	−28.2250	−1.55609
$330$	2.64632	0.145675
$331$	6.46591	0.355398	0.177699	−	0.984085i	$-0.443135\pi$
$331$	6.46591	0.355398	0.177699	+	0.984085i	$0.443135\pi$
$332$	5.91547	0.324654
$333$	−7.94396	−0.435326
$334$	2.40725	0.131719
$335$	−5.97069	−0.326214
$336$	−5.57172	−0.303962
$337$	−9.75693	−0.531494	−0.265747	−	0.964043i	$-0.585619\pi$
$337$	−9.75693	−0.531494	−0.265747	+	0.964043i	$0.585619\pi$
$338$	14.3227	0.779050
$339$	−5.40907	−0.293780
$340$	2.56885	0.139315
$341$	−8.97310	−0.485920
$342$	−1.19068	−0.0643846
$343$	−16.7320	−0.903442
$344$	9.45730	0.509903
$345$	7.75867	0.417713
$346$	9.27366	0.498555
$347$	−9.80320	−0.526263	−0.263132	−	0.964760i	$-0.584755\pi$
$347$	−9.80320	−0.526263	−0.263132	+	0.964760i	$0.584755\pi$
$348$	−16.5633	−0.887884
$349$	−31.5365	−1.68811	−0.844055	−	0.536257i	$-0.819838\pi$
$349$	−31.5365	−1.68811	−0.844055	+	0.536257i	$0.819838\pi$
$350$	−12.4673	−0.666404
$351$	−22.2926	−1.18989
$352$	−1.70879	−0.0910788
$353$	34.2990	1.82555	0.912775	−	0.408462i	$-0.133935\pi$
$353$	34.2990	1.82555	0.912775	+	0.408462i	$0.133935\pi$
$354$	16.1660	0.859212
$355$	−7.36637	−0.390966
$356$	1.60891	0.0852721
$357$	−18.0568	−0.955667
$358$	−3.58076	−0.189249
$359$	9.61930	0.507687	0.253844	−	0.967245i	$-0.418305\pi$
$359$	9.61930	0.507687	0.253844	+	0.967245i	$0.418305\pi$
$360$	0.647685	0.0341360
$361$	−16.8766	−0.888241
$362$	−20.0305	−1.05278
$363$	15.7863	0.828566
$364$	−14.9068	−0.781327
$365$	−11.7096	−0.612909
$366$	−14.2138	−0.742968
$367$	−32.3044	−1.68628	−0.843138	−	0.537697i	$-0.819294\pi$
$367$	−32.3044	−1.68628	−0.843138	+	0.537697i	$0.819294\pi$
$368$	−5.00995	−0.261162
$369$	6.43724	0.335109
$370$	−7.70631	−0.400632
$371$	−4.32149	−0.224361
$372$	−10.2594	−0.531923
$373$	25.0204	1.29551	0.647753	−	0.761850i	$-0.275709\pi$
$373$	25.0204	1.29551	0.647753	+	0.761850i	$0.275709\pi$
$374$	−5.53784	−0.286355
$375$	14.5135	0.749473
$376$	−9.89718	−0.510408
$377$	−44.3139	−2.28228
$378$	12.1625	0.625571
$379$	−29.6568	−1.52337	−0.761684	−	0.647949i	$-0.775627\pi$
$379$	−29.6568	−1.52337	−0.761684	+	0.647949i	$0.775627\pi$
$380$	−1.15506	−0.0592534
$381$	−9.05780	−0.464045
$382$	−22.3719	−1.14464
$383$	−21.3579	−1.09134	−0.545670	−	0.838000i	$-0.683725\pi$
$383$	−21.3579	−1.09134	−0.545670	+	0.838000i	$0.683725\pi$
$384$	−1.95374	−0.0997014
$385$	−3.86276	−0.196864
$386$	−3.85278	−0.196101
$387$	7.72759	0.392816
$388$	5.17053	0.262494
$389$	−11.6274	−0.589534	−0.294767	−	0.955569i	$-0.595242\pi$
$389$	−11.6274	−0.589534	−0.294767	+	0.955569i	$0.595242\pi$
$390$	8.09497	0.409905
$391$	−16.2362	−0.821102
$392$	1.13288	0.0572189
$393$	33.8609	1.70806
$394$	−6.92681	−0.348968
$395$	−9.67016	−0.486558
$396$	−1.39626	−0.0701646
$397$	−27.2502	−1.36765	−0.683824	−	0.729647i	$-0.739684\pi$
$397$	−27.2502	−1.36765	−0.683824	+	0.729647i	$0.739684\pi$
$398$	17.7696	0.890711
$399$	8.11908	0.406463
$400$	−4.37169	−0.218585
$401$	−0.791800	−0.0395406	−0.0197703	−	0.999805i	$-0.506293\pi$
$401$	−0.791800	−0.0395406	−0.0197703	+	0.999805i	$0.506293\pi$
$402$	14.7165	0.733993
$403$	−27.4483	−1.36730
$404$	−4.37234	−0.217532
$405$	−8.54777	−0.424742
$406$	24.1769	1.19988
$407$	16.6130	0.823477
$408$	−6.33167	−0.313465
$409$	−17.7702	−0.878680	−0.439340	−	0.898321i	$-0.644788\pi$
$409$	−17.7702	−0.878680	−0.439340	+	0.898321i	$0.644788\pi$
$410$	6.24467	0.308402
$411$	3.32116	0.163821
$412$	−1.71154	−0.0843213
$413$	−23.5970	−1.16113
$414$	−4.09365	−0.201192
$415$	4.68896	0.230172
$416$	−5.22711	−0.256280
$417$	−17.7239	−0.867944
$418$	2.49004	0.121792
$419$	33.9071	1.65647	0.828235	−	0.560380i	$-0.189345\pi$
$419$	33.9071	1.65647	0.828235	+	0.560380i	$0.189345\pi$
$420$	−4.41648	−0.215502
$421$	22.1938	1.08166	0.540831	−	0.841131i	$-0.318110\pi$
$421$	22.1938	1.08166	0.540831	+	0.841131i	$0.318110\pi$
$422$	1.28630	0.0626159
$423$	−8.08702	−0.393204
$424$	−1.51534	−0.0735916
$425$	−14.1678	−0.687237
$426$	18.1566	0.879688
$427$	20.7475	1.00404
$428$	17.0057	0.822004
$429$	−17.4509	−0.842536
$430$	7.49642	0.361509
$431$	29.3438	1.41344	0.706720	−	0.707493i	$-0.250174\pi$
$431$	29.3438	1.41344	0.706720	+	0.707493i	$0.250174\pi$
$432$	4.26481	0.205191
$433$	−13.7259	−0.659625	−0.329813	−	0.944046i	$-0.606986\pi$
$433$	−13.7259	−0.659625	−0.329813	+	0.944046i	$0.606986\pi$
$434$	14.9753	0.718838
$435$	−13.1290	−0.629489
$436$	−11.1687	−0.534885
$437$	7.30049	0.349230
$438$	28.8618	1.37907
$439$	31.9661	1.52566	0.762829	−	0.646600i	$-0.223810\pi$
$439$	31.9661	1.52566	0.762829	+	0.646600i	$0.223810\pi$
$440$	−1.35449	−0.0645727
$441$	0.925678	0.0440799
$442$	−16.9400	−0.805753
$443$	39.7776	1.88989	0.944945	−	0.327230i	$-0.106115\pi$
$443$	39.7776	1.88989	0.944945	+	0.327230i	$0.106115\pi$
$444$	18.9945	0.901437
$445$	1.27532	0.0604559
$446$	−21.5202	−1.01901
$447$	19.1988	0.908073
$448$	2.85182	0.134736
$449$	−3.56162	−0.168083	−0.0840416	−	0.996462i	$-0.526783\pi$
$449$	−3.56162	−0.168083	−0.0840416	+	0.996462i	$0.526783\pi$
$450$	−3.57212	−0.168392
$451$	−13.4621	−0.633904
$452$	2.76857	0.130223
$453$	6.78799	0.318928
$454$	−7.12872	−0.334567
$455$	−11.8160	−0.553943
$456$	2.84698	0.133322
$457$	27.1871	1.27176	0.635879	−	0.771789i	$-0.280638\pi$
$457$	27.1871	1.27176	0.635879	+	0.771789i	$0.280638\pi$
$458$	14.3725	0.671582
$459$	13.8214	0.645127
$460$	−3.97119	−0.185158
$461$	−36.1372	−1.68308	−0.841538	−	0.540198i	$-0.818349\pi$
$461$	−36.1372	−1.68308	−0.841538	+	0.540198i	$0.818349\pi$
$462$	9.52089	0.442952
$463$	26.7767	1.24442	0.622210	−	0.782850i	$-0.286235\pi$
$463$	26.7767	1.24442	0.622210	+	0.782850i	$0.286235\pi$
$464$	8.47772	0.393568
$465$	−8.13219	−0.377121
$466$	19.4865	0.902696
$467$	−16.9531	−0.784495	−0.392248	−	0.919860i	$-0.628302\pi$
$467$	−16.9531	−0.784495	−0.392248	+	0.919860i	$0.628302\pi$
$468$	−4.27109	−0.197431
$469$	−21.4813	−0.991913
$470$	−7.84509	−0.361867
$471$	−15.3299	−0.706363
$472$	−8.27437	−0.380859
$473$	−16.1605	−0.743062
$474$	23.8349	1.09477
$475$	6.37041	0.292294
$476$	9.24216	0.423614
$477$	−1.23819	−0.0566930
$478$	−3.39799	−0.155421
$479$	4.00495	0.182991	0.0914953	−	0.995806i	$-0.470835\pi$
$479$	4.00495	0.182991	0.0914953	+	0.995806i	$0.470835\pi$
$480$	−1.54865	−0.0706859
$481$	50.8185	2.31712
$482$	0.424483	0.0193347
$483$	27.9141	1.27013
$484$	−8.08004	−0.367274
$485$	4.09847	0.186102
$486$	8.27402	0.375317
$487$	−9.36989	−0.424590	−0.212295	−	0.977206i	$-0.568094\pi$
$487$	−9.36989	−0.424590	−0.212295	+	0.977206i	$0.568094\pi$
$488$	7.27518	0.329332
$489$	−36.9802	−1.67230
$490$	0.897986	0.0405669
$491$	25.1494	1.13498	0.567488	−	0.823381i	$-0.307915\pi$
$491$	25.1494	1.13498	0.567488	+	0.823381i	$0.307915\pi$
$492$	−15.3918	−0.693917
$493$	27.4745	1.23739
$494$	7.61692	0.342702
$495$	−1.10676	−0.0497451
$496$	5.25114	0.235783
$497$	−26.5026	−1.18880
$498$	−11.5573	−0.517895
$499$	21.7144	0.972071	0.486036	−	0.873939i	$-0.338442\pi$
$499$	21.7144	0.972071	0.486036	+	0.873939i	$0.338442\pi$
$500$	−7.42856	−0.332215
$501$	−4.70315	−0.210121
$502$	0.616945	0.0275356
$503$	−15.8415	−0.706336	−0.353168	−	0.935560i	$-0.614896\pi$
$503$	−15.8415	−0.706336	−0.353168	+	0.935560i	$0.614896\pi$
$504$	2.33023	0.103797
$505$	−3.46578	−0.154225
$506$	8.56096	0.380581
$507$	−27.9828	−1.24276
$508$	4.63613	0.205695
$509$	5.30005	0.234921	0.117460	−	0.993078i	$-0.462525\pi$
$509$	5.30005	0.234921	0.117460	+	0.993078i	$0.462525\pi$
$510$	−5.01886	−0.222239
$511$	−42.1287	−1.86366
$512$	1.00000	0.0441942
$513$	−6.21467	−0.274384
$514$	−3.16242	−0.139488
$515$	−1.35667	−0.0597818
$516$	−18.4771	−0.813409
$517$	16.9122	0.743798
$518$	−27.7257	−1.21820
$519$	−18.1183	−0.795306
$520$	−4.14332	−0.181697
$521$	−13.5484	−0.593568	−0.296784	−	0.954945i	$-0.595914\pi$
$521$	−13.5484	−0.593568	−0.296784	+	0.954945i	$0.595914\pi$
$522$	6.92717	0.303194
$523$	32.3457	1.41438	0.707190	−	0.707024i	$-0.249963\pi$
$523$	32.3457	1.41438	0.707190	+	0.707024i	$0.249963\pi$
$524$	−17.3313	−0.757122
$525$	24.3578	1.06306
$526$	3.22845	0.140767
$527$	17.0179	0.741310
$528$	3.33853	0.145291
$529$	2.09965	0.0912890
$530$	−1.20115	−0.0521747
$531$	−6.76101	−0.293403
$532$	−4.15566	−0.180171
$533$	−41.1798	−1.78370
$534$	−3.14340	−0.136028
$535$	13.4798	0.582781
$536$	−7.53248	−0.325354
$537$	6.99589	0.301895
$538$	−13.2431	−0.570951
$539$	−1.93585	−0.0833829
$540$	3.38055	0.145476
$541$	5.60948	0.241170	0.120585	−	0.992703i	$-0.461523\pi$
$541$	5.60948	0.241170	0.120585	+	0.992703i	$0.461523\pi$
$542$	−12.8681	−0.552732
$543$	39.1344	1.67942
$544$	3.24079	0.138948
$545$	−8.85299	−0.379220
$546$	29.1240	1.24639
$547$	12.1907	0.521238	0.260619	−	0.965442i	$-0.416073\pi$
$547$	12.1907	0.521238	0.260619	+	0.965442i	$0.416073\pi$
$548$	−1.69990	−0.0726160
$549$	5.94458	0.253708
$550$	7.47030	0.318535
$551$	−12.3537	−0.526285
$552$	9.78815	0.416611
$553$	−34.7912	−1.47947
$554$	−31.7870	−1.35050
$555$	15.0561	0.639097
$556$	9.07178	0.384729
$557$	−26.5405	−1.12456	−0.562279	−	0.826948i	$-0.690075\pi$
$557$	−26.5405	−1.12456	−0.562279	+	0.826948i	$0.690075\pi$
$558$	4.29073	0.181641
$559$	−49.4343	−2.09085
$560$	2.26052	0.0955245
$561$	10.8195	0.456800
$562$	8.28966	0.349678
$563$	8.49010	0.357815	0.178908	−	0.983866i	$-0.442744\pi$
$563$	8.49010	0.357815	0.178908	+	0.983866i	$0.442744\pi$
$564$	19.3365	0.814215
$565$	2.19453	0.0923248
$566$	−14.1023	−0.592765
$567$	−30.7530	−1.29151
$568$	−9.29323	−0.389935
$569$	−8.45931	−0.354633	−0.177316	−	0.984154i	$-0.556742\pi$
$569$	−8.45931	−0.354633	−0.177316	+	0.984154i	$0.556742\pi$
$570$	2.25669	0.0945223
$571$	7.71762	0.322972	0.161486	−	0.986875i	$-0.448371\pi$
$571$	7.71762	0.322972	0.161486	+	0.986875i	$0.448371\pi$
$572$	8.93203	0.373467
$573$	43.7088	1.82596
$574$	22.4670	0.937754
$575$	21.9020	0.913375
$576$	0.817104	0.0340460
$577$	−4.49575	−0.187161	−0.0935803	−	0.995612i	$-0.529831\pi$
$577$	−4.49575	−0.187161	−0.0935803	+	0.995612i	$0.529831\pi$
$578$	−6.49725	−0.270250
$579$	7.52734	0.312826
$580$	6.71994	0.279030
$581$	16.8699	0.699880
$582$	−10.1019	−0.418736
$583$	2.58941	0.107242
$584$	−14.7726	−0.611293
$585$	−3.38552	−0.139974
$586$	7.81002	0.322629
$587$	22.6149	0.933417	0.466709	−	0.884411i	$-0.345440\pi$
$587$	22.6149	0.933417	0.466709	+	0.884411i	$0.345440\pi$
$588$	−2.21335	−0.0912769
$589$	−7.65194	−0.315293
$590$	−6.55876	−0.270020
$591$	13.5332	0.556681
$592$	−9.72210	−0.399576
$593$	29.9127	1.22837	0.614184	−	0.789163i	$-0.289485\pi$
$593$	29.9127	1.22837	0.614184	+	0.789163i	$0.289485\pi$
$594$	−7.28767	−0.299017
$595$	7.32589	0.300332
$596$	−9.82669	−0.402517
$597$	−34.7172	−1.42088
$598$	26.1876	1.07089
$599$	−22.5746	−0.922371	−0.461186	−	0.887304i	$-0.652576\pi$
$599$	−22.5746	−0.922371	−0.461186	+	0.887304i	$0.652576\pi$
$600$	8.54115	0.348691
$601$	−22.1459	−0.903350	−0.451675	−	0.892182i	$-0.649173\pi$
$601$	−22.1459	−0.903350	−0.451675	+	0.892182i	$0.649173\pi$
$602$	26.9705	1.09924
$603$	−6.15482	−0.250643
$604$	−3.47436	−0.141370
$605$	−6.40472	−0.260389
$606$	8.54241	0.347012
$607$	−23.3338	−0.947091	−0.473546	−	0.880769i	$-0.657026\pi$
$607$	−23.3338	−0.947091	−0.473546	+	0.880769i	$0.657026\pi$
$608$	−1.45720	−0.0590971
$609$	−47.2354	−1.91408
$610$	5.76674	0.233489
$611$	51.7336	2.09292
$612$	2.64806	0.107042
$613$	−8.63041	−0.348579	−0.174290	−	0.984694i	$-0.555763\pi$
$613$	−8.63041	−0.348579	−0.174290	+	0.984694i	$0.555763\pi$
$614$	6.35677	0.256538
$615$	−12.2005	−0.491970
$616$	−4.87316	−0.196345
$617$	−32.9913	−1.32818	−0.664090	−	0.747653i	$-0.731181\pi$
$617$	−32.9913	−1.32818	−0.664090	+	0.747653i	$0.731181\pi$
$618$	3.34390	0.134511
$619$	17.3594	0.697735	0.348867	−	0.937172i	$-0.386566\pi$
$619$	17.3594	0.697735	0.348867	+	0.937172i	$0.386566\pi$
$620$	4.16237	0.167165
$621$	−21.3665	−0.857409
$622$	−28.7519	−1.15285
$623$	4.58833	0.183827
$624$	10.2124	0.408824
$625$	15.9701	0.638805
$626$	−27.3280	−1.09225
$627$	−4.86490	−0.194285
$628$	7.84642	0.313106
$629$	−31.5073	−1.25628
$630$	1.84708	0.0735895
$631$	23.7414	0.945130	0.472565	−	0.881296i	$-0.343328\pi$
$631$	23.7414	0.945130	0.472565	+	0.881296i	$0.343328\pi$
$632$	−12.1996	−0.485275
$633$	−2.51309	−0.0998864
$634$	−13.1435	−0.521994
$635$	3.67488	0.145833
$636$	2.96059	0.117395
$637$	−5.92167	−0.234625
$638$	−14.4866	−0.573531
$639$	−7.59353	−0.300395
$640$	0.792660	0.0313326
$641$	−43.8836	−1.73330	−0.866650	−	0.498917i	$-0.833731\pi$
$641$	−43.8836	−1.73330	−0.866650	+	0.498917i	$0.833731\pi$
$642$	−33.2248	−1.31128
$643$	28.3799	1.11919	0.559597	−	0.828765i	$-0.310956\pi$
$643$	28.3799	1.11919	0.559597	+	0.828765i	$0.310956\pi$
$644$	−14.2875	−0.563006
$645$	−14.6461	−0.576688
$646$	−4.72247	−0.185803
$647$	−22.6770	−0.891524	−0.445762	−	0.895152i	$-0.647067\pi$
$647$	−22.6770	−0.891524	−0.445762	+	0.895152i	$0.647067\pi$
$648$	−10.7837	−0.423622
$649$	14.1392	0.555010
$650$	22.8513	0.896302
$651$	−29.2579	−1.14671
$652$	18.9279	0.741273
$653$	22.0786	0.864001	0.432000	−	0.901873i	$-0.357808\pi$
$653$	22.0786	0.864001	0.432000	+	0.901873i	$0.357808\pi$
$654$	21.8208	0.853260
$655$	−13.7378	−0.536782
$656$	7.87812	0.307589
$657$	−12.0707	−0.470924
$658$	−28.2250	−1.10032
$659$	−17.3201	−0.674696	−0.337348	−	0.941380i	$-0.609530\pi$
$659$	−17.3201	−0.674696	−0.337348	+	0.941380i	$0.609530\pi$
$660$	2.64632	0.103008
$661$	2.63901	0.102646	0.0513228	−	0.998682i	$-0.483656\pi$
$661$	2.63901	0.102646	0.0513228	+	0.998682i	$0.483656\pi$
$662$	6.46591	0.251305
$663$	33.0963	1.28536
$664$	5.91547	0.229565
$665$	−3.29402	−0.127737
$666$	−7.94396	−0.307822
$667$	−42.4730	−1.64456
$668$	2.40725	0.0931395
$669$	42.0449	1.62555
$670$	−5.97069	−0.230668
$671$	−12.4318	−0.479923
$672$	−5.57172	−0.214934
$673$	42.4650	1.63690	0.818452	−	0.574575i	$-0.194833\pi$
$673$	42.4650	1.63690	0.818452	+	0.574575i	$0.194833\pi$
$674$	−9.75693	−0.375823
$675$	−18.6444	−0.717625
$676$	14.3227	0.550872
$677$	−46.3996	−1.78328	−0.891641	−	0.452743i	$-0.850445\pi$
$677$	−46.3996	−1.78328	−0.891641	+	0.452743i	$0.850445\pi$
$678$	−5.40907	−0.207734
$679$	14.7454	0.565877
$680$	2.56885	0.0985108
$681$	13.9277	0.533709
$682$	−8.97310	−0.343598
$683$	4.77429	0.182683	0.0913416	−	0.995820i	$-0.470884\pi$
$683$	4.77429	0.182683	0.0913416	+	0.995820i	$0.470884\pi$
$684$	−1.19068	−0.0455268
$685$	−1.34744	−0.0514831
$686$	−16.7320	−0.638830
$687$	−28.0801	−1.07132
$688$	9.45730	0.360556
$689$	7.92087	0.301761
$690$	7.75867	0.295368
$691$	7.35681	0.279866	0.139933	−	0.990161i	$-0.455311\pi$
$691$	7.35681	0.279866	0.139933	+	0.990161i	$0.455311\pi$
$692$	9.27366	0.352532
$693$	−3.98188	−0.151259
$694$	−9.80320	−0.372124
$695$	7.19084	0.272764
$696$	−16.5633	−0.627829
$697$	25.5314	0.967070
$698$	−31.5365	−1.19367
$699$	−38.0716	−1.44000
$700$	−12.4673	−0.471219
$701$	−6.15745	−0.232564	−0.116282	−	0.993216i	$-0.537098\pi$
$701$	−6.15745	−0.232564	−0.116282	+	0.993216i	$0.537098\pi$
$702$	−22.2926	−0.841382
$703$	14.1670	0.534318
$704$	−1.70879	−0.0644024
$705$	15.3273	0.577259
$706$	34.2990	1.29086
$707$	−12.4691	−0.468949
$708$	16.1660	0.607554
$709$	−18.1776	−0.682674	−0.341337	−	0.939941i	$-0.610880\pi$
$709$	−18.1776	−0.682674	−0.341337	+	0.939941i	$0.610880\pi$
$710$	−7.36637	−0.276455
$711$	−9.96836	−0.373843
$712$	1.60891	0.0602965
$713$	−26.3080	−0.985241
$714$	−18.0568	−0.675758
$715$	7.08006	0.264779
$716$	−3.58076	−0.133819
$717$	6.63880	0.247930
$718$	9.61930	0.358989
$719$	−50.1034	−1.86854	−0.934271	−	0.356564i	$-0.883948\pi$
$719$	−50.1034	−1.86854	−0.934271	+	0.356564i	$0.883948\pi$
$720$	0.647685	0.0241378
$721$	−4.88099	−0.181778
$722$	−16.8766	−0.628081
$723$	−0.829330	−0.0308431
$724$	−20.0305	−0.744427
$725$	−37.0619	−1.37645
$726$	15.7863	0.585884
$727$	33.2224	1.23215	0.616076	−	0.787687i	$-0.288722\pi$
$727$	33.2224	1.23215	0.616076	+	0.787687i	$0.288722\pi$
$728$	−14.9068	−0.552482
$729$	16.1857	0.599469
$730$	−11.7096	−0.433392
$731$	30.6492	1.13360
$732$	−14.2138	−0.525358
$733$	−2.60750	−0.0963101	−0.0481551	−	0.998840i	$-0.515334\pi$
$733$	−2.60750	−0.0963101	−0.0481551	+	0.998840i	$0.515334\pi$
$734$	−32.3044	−1.19238
$735$	−1.75443	−0.0647132
$736$	−5.00995	−0.184669
$737$	12.8714	0.474125
$738$	6.43724	0.236958
$739$	27.9557	1.02837	0.514183	−	0.857681i	$-0.328095\pi$
$739$	27.9557	1.02837	0.514183	+	0.857681i	$0.328095\pi$
$740$	−7.70631	−0.283290
$741$	−14.8815	−0.546685
$742$	−4.32149	−0.158647
$743$	−9.73294	−0.357067	−0.178534	−	0.983934i	$-0.557135\pi$
$743$	−9.73294	−0.357067	−0.178534	+	0.983934i	$0.557135\pi$
$744$	−10.2594	−0.376127
$745$	−7.78922	−0.285375
$746$	25.0204	0.916061
$747$	4.83355	0.176850
$748$	−5.53784	−0.202483
$749$	48.4973	1.77205
$750$	14.5135	0.529957
$751$	−7.89661	−0.288151	−0.144076	−	0.989567i	$-0.546021\pi$
$751$	−7.89661	−0.288151	−0.144076	+	0.989567i	$0.546021\pi$
$752$	−9.89718	−0.360913
$753$	−1.20535	−0.0439254
$754$	−44.3139	−1.61382
$755$	−2.75398	−0.100228
$756$	12.1625	0.442345
$757$	20.9026	0.759719	0.379860	−	0.925044i	$-0.375972\pi$
$757$	20.9026	0.759719	0.379860	+	0.925044i	$0.375972\pi$
$758$	−29.6568	−1.07718
$759$	−16.7259	−0.607112
$760$	−1.15506	−0.0418984
$761$	6.63319	0.240453	0.120227	−	0.992746i	$-0.461638\pi$
$761$	6.63319	0.240453	0.120227	+	0.992746i	$0.461638\pi$
$762$	−9.05780	−0.328130
$763$	−31.8512	−1.15309
$764$	−22.3719	−0.809386
$765$	2.09901	0.0758900
$766$	−21.3579	−0.771694
$767$	43.2510	1.56170
$768$	−1.95374	−0.0704996
$769$	20.9963	0.757147	0.378574	−	0.925571i	$-0.376415\pi$
$769$	20.9963	0.757147	0.378574	+	0.925571i	$0.376415\pi$
$770$	−3.86276	−0.139204
$771$	6.17855	0.222515
$772$	−3.85278	−0.138665
$773$	−24.5310	−0.882319	−0.441160	−	0.897429i	$-0.645433\pi$
$773$	−24.5310	−0.882319	−0.441160	+	0.897429i	$0.645433\pi$
$774$	7.72759	0.277763
$775$	−22.9564	−0.824617
$776$	5.17053	0.185611
$777$	54.1688	1.94329
$778$	−11.6274	−0.416864
$779$	−11.4800	−0.411313
$780$	8.09497	0.289846
$781$	15.8802	0.568237
$782$	−16.2362	−0.580607
$783$	36.1559	1.29211
$784$	1.13288	0.0404599
$785$	6.21954	0.221985
$786$	33.8609	1.20778
$787$	12.1451	0.432927	0.216464	−	0.976291i	$-0.430548\pi$
$787$	12.1451	0.432927	0.216464	+	0.976291i	$0.430548\pi$
$788$	−6.92681	−0.246757
$789$	−6.30755	−0.224555
$790$	−9.67016	−0.344049
$791$	7.89547	0.280730
$792$	−1.39626	−0.0496139
$793$	−38.0282	−1.35042
$794$	−27.2502	−0.967073
$795$	2.34674	0.0832303
$796$	17.7696	0.629828
$797$	25.5706	0.905757	0.452878	−	0.891572i	$-0.350397\pi$
$797$	25.5706	0.905757	0.452878	+	0.891572i	$0.350397\pi$
$798$	8.11908	0.287412
$799$	−32.0747	−1.13472
$800$	−4.37169	−0.154563
$801$	1.31465	0.0464508
$802$	−0.791800	−0.0279594
$803$	25.2432	0.890814
$804$	14.7165	0.519011
$805$	−11.3251	−0.399158
$806$	−27.4483	−0.966825
$807$	25.8736	0.910794
$808$	−4.37234	−0.153818
$809$	−17.3554	−0.610182	−0.305091	−	0.952323i	$-0.598687\pi$
$809$	−17.3554	−0.610182	−0.305091	+	0.952323i	$0.598687\pi$
$810$	−8.54777	−0.300338
$811$	−4.13845	−0.145321	−0.0726603	−	0.997357i	$-0.523149\pi$
$811$	−4.13845	−0.145321	−0.0726603	+	0.997357i	$0.523149\pi$
$812$	24.1769	0.848443
$813$	25.1409	0.881731
$814$	16.6130	0.582286
$815$	15.0034	0.525545
$816$	−6.33167	−0.221653
$817$	−13.7811	−0.482141
$818$	−17.7702	−0.621320
$819$	−12.1804	−0.425617
$820$	6.24467	0.218073
$821$	41.7228	1.45613	0.728067	−	0.685506i	$-0.240419\pi$
$821$	41.7228	1.45613	0.728067	+	0.685506i	$0.240419\pi$
$822$	3.32116	0.115839
$823$	36.0956	1.25821	0.629106	−	0.777319i	$-0.283421\pi$
$823$	36.0956	1.25821	0.629106	+	0.777319i	$0.283421\pi$
$824$	−1.71154	−0.0596242
$825$	−14.5950	−0.508134
$826$	−23.5970	−0.821045
$827$	−21.4802	−0.746940	−0.373470	−	0.927642i	$-0.621832\pi$
$827$	−21.4802	−0.746940	−0.373470	+	0.927642i	$0.621832\pi$
$828$	−4.09365	−0.142264
$829$	14.9143	0.517996	0.258998	−	0.965878i	$-0.416608\pi$
$829$	14.9143	0.517996	0.258998	+	0.965878i	$0.416608\pi$
$830$	4.68896	0.162756
$831$	62.1036	2.15435
$832$	−5.22711	−0.181217
$833$	3.67142	0.127207
$834$	−17.7239	−0.613729
$835$	1.90813	0.0660337
$836$	2.49004	0.0861199
$837$	22.3951	0.774089
$838$	33.9071	1.17130
$839$	−26.2431	−0.906013	−0.453006	−	0.891507i	$-0.649649\pi$
$839$	−26.2431	−0.906013	−0.453006	+	0.891507i	$0.649649\pi$
$840$	−4.41648	−0.152383
$841$	42.8717	1.47833
$842$	22.1938	0.764850
$843$	−16.1958	−0.557814
$844$	1.28630	0.0442762
$845$	11.3530	0.390555
$846$	−8.08702	−0.278037
$847$	−23.0428	−0.791760
$848$	−1.51534	−0.0520371
$849$	27.5523	0.945592
$850$	−14.1678	−0.485950
$851$	48.7073	1.66966
$852$	18.1566	0.622033
$853$	−27.3329	−0.935861	−0.467931	−	0.883765i	$-0.655000\pi$
$853$	−27.3329	−0.935861	−0.467931	+	0.883765i	$0.655000\pi$
$854$	20.7475	0.709965
$855$	−0.943804	−0.0322774
$856$	17.0057	0.581244
$857$	−19.8797	−0.679078	−0.339539	−	0.940592i	$-0.610271\pi$
$857$	−19.8797	−0.679078	−0.339539	+	0.940592i	$0.610271\pi$
$858$	−17.4509	−0.595763
$859$	−21.3980	−0.730090	−0.365045	−	0.930990i	$-0.618946\pi$
$859$	−21.3980	−0.730090	−0.365045	+	0.930990i	$0.618946\pi$
$860$	7.49642	0.255626
$861$	−43.8947	−1.49593
$862$	29.3438	0.999454
$863$	−30.0089	−1.02151	−0.510757	−	0.859725i	$-0.670635\pi$
$863$	−30.0089	−1.02151	−0.510757	+	0.859725i	$0.670635\pi$
$864$	4.26481	0.145092
$865$	7.35085	0.249937
$866$	−13.7259	−0.466425
$867$	12.6939	0.431109
$868$	14.9753	0.508295
$869$	20.8466	0.707173
$870$	−13.1290	−0.445116
$871$	39.3731	1.33411
$872$	−11.1687	−0.378220
$873$	4.22486	0.142990
$874$	7.30049	0.246943
$875$	−21.1849	−0.716181
$876$	28.8618	0.975149
$877$	−10.8639	−0.366849	−0.183424	−	0.983034i	$-0.558718\pi$
$877$	−10.8639	−0.366849	−0.183424	+	0.983034i	$0.558718\pi$
$878$	31.9661	1.07880
$879$	−15.2588	−0.514665
$880$	−1.35449	−0.0456598
$881$	1.65983	0.0559211	0.0279605	−	0.999609i	$-0.491099\pi$
$881$	1.65983	0.0559211	0.0279605	+	0.999609i	$0.491099\pi$
$882$	0.925678	0.0311692
$883$	32.4160	1.09088	0.545442	−	0.838149i	$-0.316362\pi$
$883$	32.4160	1.09088	0.545442	+	0.838149i	$0.316362\pi$
$884$	−16.9400	−0.569753
$885$	12.8141	0.430742
$886$	39.7776	1.33635
$887$	7.82597	0.262770	0.131385	−	0.991331i	$-0.458058\pi$
$887$	7.82597	0.262770	0.131385	+	0.991331i	$0.458058\pi$
$888$	18.9945	0.637412
$889$	13.2214	0.443432
$890$	1.27532	0.0427488
$891$	18.4270	0.617328
$892$	−21.5202	−0.720549
$893$	14.4221	0.482618
$894$	19.1988	0.642104
$895$	−2.83833	−0.0948748
$896$	2.85182	0.0952726
$897$	−51.1637	−1.70831
$898$	−3.56162	−0.118853
$899$	44.5177	1.48475
$900$	−3.57212	−0.119071
$901$	−4.91092	−0.163606
$902$	−13.4621	−0.448238
$903$	−52.6934	−1.75353
$904$	2.76857	0.0920813
$905$	−15.8774	−0.527781
$906$	6.78799	0.225516
$907$	−19.7984	−0.657394	−0.328697	−	0.944435i	$-0.606610\pi$
$907$	−19.7984	−0.657394	−0.328697	+	0.944435i	$0.606610\pi$
$908$	−7.12872	−0.236575
$909$	−3.57265	−0.118497
$910$	−11.8160	−0.391697
$911$	6.68105	0.221353	0.110677	−	0.993856i	$-0.464698\pi$
$911$	6.68105	0.221353	0.110677	+	0.993856i	$0.464698\pi$
$912$	2.84698	0.0942730
$913$	−10.1083	−0.334536
$914$	27.1871	0.899268
$915$	−11.2667	−0.372466
$916$	14.3725	0.474880
$917$	−49.4258	−1.63218
$918$	13.8214	0.456174
$919$	0.0896418	0.00295701	0.00147850	−	0.999999i	$-0.499529\pi$
$919$	0.0896418	0.00295701	0.00147850	+	0.999999i	$0.499529\pi$
$920$	−3.97119	−0.130926
$921$	−12.4195	−0.409236
$922$	−36.1372	−1.19011
$923$	48.5767	1.59892
$924$	9.52089	0.313214
$925$	42.5020	1.39746
$926$	26.7767	0.879938
$927$	−1.39850	−0.0459328
$928$	8.47772	0.278295
$929$	15.2405	0.500024	0.250012	−	0.968243i	$-0.419565\pi$
$929$	15.2405	0.500024	0.250012	+	0.968243i	$0.419565\pi$
$930$	−8.13219	−0.266665
$931$	−1.65082	−0.0541036
$932$	19.4865	0.638302
$933$	56.1738	1.83905
$934$	−16.9531	−0.554722
$935$	−4.38962	−0.143556
$936$	−4.27109	−0.139605
$937$	−14.3501	−0.468799	−0.234399	−	0.972140i	$-0.575312\pi$
$937$	−14.3501	−0.468799	−0.234399	+	0.972140i	$0.575312\pi$
$938$	−21.4813	−0.701389
$939$	53.3919	1.74238
$940$	−7.84509	−0.255879
$941$	12.0731	0.393573	0.196787	−	0.980446i	$-0.436949\pi$
$941$	12.0731	0.393573	0.196787	+	0.980446i	$0.436949\pi$
$942$	−15.3299	−0.499474
$943$	−39.4690	−1.28529
$944$	−8.27437	−0.269308
$945$	9.64071	0.313612
$946$	−16.1605	−0.525424
$947$	−3.94985	−0.128353	−0.0641764	−	0.997939i	$-0.520442\pi$
$947$	−3.94985	−0.128353	−0.0641764	+	0.997939i	$0.520442\pi$
$948$	23.8349	0.774122
$949$	77.2178	2.50660
$950$	6.37041	0.206683
$951$	25.6789	0.832696
$952$	9.24216	0.299540
$953$	−44.0695	−1.42755	−0.713776	−	0.700374i	$-0.753017\pi$
$953$	−44.0695	−1.42755	−0.713776	+	0.700374i	$0.753017\pi$
$954$	−1.23819	−0.0400880
$955$	−17.7333	−0.573835
$956$	−3.39799	−0.109899
$957$	28.3031	0.914910
$958$	4.00495	0.129394
$959$	−4.84780	−0.156544
$960$	−1.54865	−0.0499825
$961$	−3.42553	−0.110501
$962$	50.8185	1.63845
$963$	13.8955	0.447775
$964$	0.424483	0.0136717
$965$	−3.05395	−0.0983100
$966$	27.9141	0.898120
$967$	−24.9523	−0.802411	−0.401206	−	0.915988i	$-0.631409\pi$
$967$	−24.9523	−0.802411	−0.401206	+	0.915988i	$0.631409\pi$
$968$	−8.08004	−0.259702
$969$	9.22649	0.296398
$970$	4.09847	0.131594
$971$	51.5974	1.65584	0.827920	−	0.560847i	$-0.189524\pi$
$971$	51.5974	1.65584	0.827920	+	0.560847i	$0.189524\pi$
$972$	8.27402	0.265389
$973$	25.8711	0.829389
$974$	−9.36989	−0.300231
$975$	−44.6455	−1.42980
$976$	7.27518	0.232873
$977$	−36.2042	−1.15828	−0.579138	−	0.815230i	$-0.696611\pi$
$977$	−36.2042	−1.15828	−0.579138	+	0.815230i	$0.696611\pi$
$978$	−36.9802	−1.18250
$979$	−2.74929	−0.0878678
$980$	0.897986	0.0286851
$981$	−9.12600	−0.291371
$982$	25.1494	0.802550
$983$	30.5263	0.973639	0.486820	−	0.873503i	$-0.338157\pi$
$983$	30.5263	0.973639	0.486820	+	0.873503i	$0.338157\pi$
$984$	−15.3918	−0.490673
$985$	−5.49060	−0.174945
$986$	27.4745	0.874968
$987$	55.1443	1.75526
$988$	7.61692	0.242327
$989$	−47.3806	−1.50662
$990$	−1.10676	−0.0351751
$991$	−6.15216	−0.195430	−0.0977149	−	0.995214i	$-0.531153\pi$
$991$	−6.15216	−0.195430	−0.0977149	+	0.995214i	$0.531153\pi$
$992$	5.25114	0.166724
$993$	−12.6327	−0.400887
$994$	−26.5026	−0.840612
$995$	14.0853	0.446533
$996$	−11.5573	−0.366207
$997$	29.9539	0.948649	0.474325	−	0.880350i	$-0.342692\pi$
$997$	29.9539	0.948649	0.474325	+	0.880350i	$0.342692\pi$
$998$	21.7144	0.687358
$999$	−41.4629	−1.31183

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.a.1.17	✓	71

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.a.1.17	✓	71	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.95374 q^{3} +1.00000 q^{4} +0.792660 q^{5} -1.95374 q^{6} +2.85182 q^{7} +1.00000 q^{8} +0.817104 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.95374 q^{3} +1.00000 q^{4} +0.792660 q^{5} -1.95374 q^{6} +2.85182 q^{7} +1.00000 q^{8} +0.817104 q^{9} +0.792660 q^{10} -1.70879 q^{11} -1.95374 q^{12} -5.22711 q^{13} +2.85182 q^{14} -1.54865 q^{15} +1.00000 q^{16} +3.24079 q^{17} +0.817104 q^{18} -1.45720 q^{19} +0.792660 q^{20} -5.57172 q^{21} -1.70879 q^{22} -5.00995 q^{23} -1.95374 q^{24} -4.37169 q^{25} -5.22711 q^{26} +4.26481 q^{27} +2.85182 q^{28} +8.47772 q^{29} -1.54865 q^{30} +5.25114 q^{31} +1.00000 q^{32} +3.33853 q^{33} +3.24079 q^{34} +2.26052 q^{35} +0.817104 q^{36} -9.72210 q^{37} -1.45720 q^{38} +10.2124 q^{39} +0.792660 q^{40} +7.87812 q^{41} -5.57172 q^{42} +9.45730 q^{43} -1.70879 q^{44} +0.647685 q^{45} -5.00995 q^{46} -9.89718 q^{47} -1.95374 q^{48} +1.13288 q^{49} -4.37169 q^{50} -6.33167 q^{51} -5.22711 q^{52} -1.51534 q^{53} +4.26481 q^{54} -1.35449 q^{55} +2.85182 q^{56} +2.84698 q^{57} +8.47772 q^{58} -8.27437 q^{59} -1.54865 q^{60} +7.27518 q^{61} +5.25114 q^{62} +2.33023 q^{63} +1.00000 q^{64} -4.14332 q^{65} +3.33853 q^{66} -7.53248 q^{67} +3.24079 q^{68} +9.78815 q^{69} +2.26052 q^{70} -9.29323 q^{71} +0.817104 q^{72} -14.7726 q^{73} -9.72210 q^{74} +8.54115 q^{75} -1.45720 q^{76} -4.87316 q^{77} +10.2124 q^{78} -12.1996 q^{79} +0.792660 q^{80} -10.7837 q^{81} +7.87812 q^{82} +5.91547 q^{83} -5.57172 q^{84} +2.56885 q^{85} +9.45730 q^{86} -16.5633 q^{87} -1.70879 q^{88} +1.60891 q^{89} +0.647685 q^{90} -14.9068 q^{91} -5.00995 q^{92} -10.2594 q^{93} -9.89718 q^{94} -1.15506 q^{95} -1.95374 q^{96} +5.17053 q^{97} +1.13288 q^{98} -1.39626 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9}+O(q^{10}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9	\( 71 q + 71 q^{2} - 9 q^{3} + 71 q^{4} - 34 q^{5} - 9 q^{6} - 19 q^{7} + 71 q^{8} + 34 q^{9} - 34 q^{10} - 37 q^{11} - 9 q^{12} - 62 q^{13} - 19 q^{14} - 29 q^{15} + 71 q^{16} - 52 q^{17} + 34 q^{18} - 30 q^{19} - 34 q^{20} - 51 q^{21} - 37 q^{22} - 45 q^{23} - 9 q^{24} + 27 q^{25} - 62 q^{26} - 27 q^{27} - 19 q^{28} - 55 q^{29} - 29 q^{30} - 61 q^{31} + 71 q^{32} - 73 q^{33} - 52 q^{34} - 33 q^{35} + 34 q^{36} - 43 q^{37} - 30 q^{38} - 40 q^{39} - 34 q^{40} - 87 q^{41} - 51 q^{42} - 4 q^{43} - 37 q^{44} - 81 q^{45} - 45 q^{46} - 89 q^{47} - 9 q^{48} - 2 q^{49} + 27 q^{50} - 19 q^{51} - 62 q^{52} - 50 q^{53} - 27 q^{54} - 66 q^{55} - 19 q^{56} - 45 q^{57} - 55 q^{58} - 118 q^{59} - 29 q^{60} - 92 q^{61} - 61 q^{62} - 54 q^{63} + 71 q^{64} - 51 q^{65} - 73 q^{66} - 17 q^{67} - 52 q^{68} - 89 q^{69} - 33 q^{70} - 95 q^{71} + 34 q^{72} - 114 q^{73} - 43 q^{74} - 38 q^{75} - 30 q^{76} - 73 q^{77} - 40 q^{78} - 47 q^{79} - 34 q^{80} - 57 q^{81} - 87 q^{82} - 68 q^{83} - 51 q^{84} - 67 q^{85} - 4 q^{86} - 55 q^{87} - 37 q^{88} - 150 q^{89} - 81 q^{90} - 23 q^{91} - 45 q^{92} - 59 q^{93} - 89 q^{94} - 47 q^{95} - 9 q^{96} - 97 q^{97} - 2 q^{98} - 57 q^{99}+O(q^{100}) \) 71 * q + 71 * q^2 - 9 * q^3 + 71 * q^4 - 34 * q^5 - 9 * q^6 - 19 * q^7 + 71 * q^8 + 34 * q^9 - 34 * q^10 - 37 * q^11 - 9 * q^12 - 62 * q^13 - 19 * q^14 - 29 * q^15 + 71 * q^16 - 52 * q^17 + 34 * q^18 - 30 * q^19 - 34 * q^20 - 51 * q^21 - 37 * q^22 - 45 * q^23 - 9 * q^24 + 27 * q^25 - 62 * q^26 - 27 * q^27 - 19 * q^28 - 55 * q^29 - 29 * q^30 - 61 * q^31 + 71 * q^32 - 73 * q^33 - 52 * q^34 - 33 * q^35 + 34 * q^36 - 43 * q^37 - 30 * q^38 - 40 * q^39 - 34 * q^40 - 87 * q^41 - 51 * q^42 - 4 * q^43 - 37 * q^44 - 81 * q^45 - 45 * q^46 - 89 * q^47 - 9 * q^48 - 2 * q^49 + 27 * q^50 - 19 * q^51 - 62 * q^52 - 50 * q^53 - 27 * q^54 - 66 * q^55 - 19 * q^56 - 45 * q^57 - 55 * q^58 - 118 * q^59 - 29 * q^60 - 92 * q^61 - 61 * q^62 - 54 * q^63 + 71 * q^64 - 51 * q^65 - 73 * q^66 - 17 * q^67 - 52 * q^68 - 89 * q^69 - 33 * q^70 - 95 * q^71 + 34 * q^72 - 114 * q^73 - 43 * q^74 - 38 * q^75 - 30 * q^76 - 73 * q^77 - 40 * q^78 - 47 * q^79 - 34 * q^80 - 57 * q^81 - 87 * q^82 - 68 * q^83 - 51 * q^84 - 67 * q^85 - 4 * q^86 - 55 * q^87 - 37 * q^88 - 150 * q^89 - 81 * q^90 - 23 * q^91 - 45 * q^92 - 59 * q^93 - 89 * q^94 - 47 * q^95 - 9 * q^96 - 97 * q^97 - 2 * q^98 - 57 * q^99

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