LMFDB - Embedded newform 4031.2.a.c.1.39

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, 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("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$61$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.39
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.794348 q^{2} +1.86655 q^{3} -1.36901 q^{4} +0.394566 q^{5} +1.48269 q^{6} +1.07098 q^{7} -2.67617 q^{8} +0.484010 q^{9} +O(q^{10})$	\(q+0.794348 q^{2} +1.86655 q^{3} -1.36901 q^{4} +0.394566 q^{5} +1.48269 q^{6} +1.07098 q^{7} -2.67617 q^{8} +0.484010 q^{9} +0.313423 q^{10} -4.46028 q^{11} -2.55533 q^{12} +0.742897 q^{13} +0.850728 q^{14} +0.736478 q^{15} +0.612211 q^{16} +6.65711 q^{17} +0.384473 q^{18} -7.39117 q^{19} -0.540165 q^{20} +1.99903 q^{21} -3.54302 q^{22} +3.99265 q^{23} -4.99520 q^{24} -4.84432 q^{25} +0.590119 q^{26} -4.69622 q^{27} -1.46618 q^{28} -1.00000 q^{29} +0.585020 q^{30} -0.599936 q^{31} +5.83865 q^{32} -8.32534 q^{33} +5.28806 q^{34} +0.422571 q^{35} -0.662615 q^{36} -1.58553 q^{37} -5.87116 q^{38} +1.38665 q^{39} -1.05593 q^{40} +0.183886 q^{41} +1.58793 q^{42} -7.34164 q^{43} +6.10617 q^{44} +0.190974 q^{45} +3.17155 q^{46} -7.74848 q^{47} +1.14272 q^{48} -5.85301 q^{49} -3.84808 q^{50} +12.4258 q^{51} -1.01703 q^{52} -9.69374 q^{53} -3.73044 q^{54} -1.75988 q^{55} -2.86611 q^{56} -13.7960 q^{57} -0.794348 q^{58} +4.02564 q^{59} -1.00825 q^{60} +7.64125 q^{61} -0.476558 q^{62} +0.518363 q^{63} +3.41350 q^{64} +0.293122 q^{65} -6.61322 q^{66} +6.20563 q^{67} -9.11365 q^{68} +7.45248 q^{69} +0.335669 q^{70} -10.4718 q^{71} -1.29529 q^{72} +12.5575 q^{73} -1.25946 q^{74} -9.04216 q^{75} +10.1186 q^{76} -4.77685 q^{77} +1.10149 q^{78} -6.34166 q^{79} +0.241558 q^{80} -10.2178 q^{81} +0.146069 q^{82} -2.18323 q^{83} -2.73669 q^{84} +2.62667 q^{85} -5.83182 q^{86} -1.86655 q^{87} +11.9365 q^{88} -13.2533 q^{89} +0.151700 q^{90} +0.795624 q^{91} -5.46597 q^{92} -1.11981 q^{93} -6.15499 q^{94} -2.91631 q^{95} +10.8981 q^{96} +0.174843 q^{97} -4.64933 q^{98} -2.15882 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) $ 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * 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 $

$2$	0.794348	0.561689	0.280845	−	0.959753i	$-0.409385\pi$
$2$	0.794348	0.561689	0.280845	+	0.959753i	$0.409385\pi$
$3$	1.86655	1.07765	0.538827	−	0.842417i	$-0.318868\pi$
$3$	1.86655	1.07765	0.538827	+	0.842417i	$0.318868\pi$
$4$	−1.36901	−0.684505
$5$	0.394566	0.176455	0.0882277	−	0.996100i	$-0.471880\pi$
$5$	0.394566	0.176455	0.0882277	+	0.996100i	$0.471880\pi$
$6$	1.48269	0.605306
$7$	1.07098	0.404791	0.202395	−	0.979304i	$-0.435127\pi$
$7$	1.07098	0.404791	0.202395	+	0.979304i	$0.435127\pi$
$8$	−2.67617	−0.946168
$9$	0.484010	0.161337
$10$	0.313423	0.0991131
$11$	−4.46028	−1.34482	−0.672412	−	0.740177i	$-0.734742\pi$
$11$	−4.46028	−1.34482	−0.672412	+	0.740177i	$0.734742\pi$
$12$	−2.55533	−0.737659
$13$	0.742897	0.206042	0.103021	−	0.994679i	$-0.467149\pi$
$13$	0.742897	0.206042	0.103021	+	0.994679i	$0.467149\pi$
$14$	0.850728	0.227367
$15$	0.736478	0.190158
$16$	0.612211	0.153053
$17$	6.65711	1.61459	0.807293	−	0.590151i	$-0.200932\pi$
$17$	6.65711	1.61459	0.807293	+	0.590151i	$0.200932\pi$
$18$	0.384473	0.0906211
$19$	−7.39117	−1.69565	−0.847825	−	0.530276i	$-0.822088\pi$
$19$	−7.39117	−1.69565	−0.847825	+	0.530276i	$0.822088\pi$
$20$	−0.540165	−0.120785
$21$	1.99903	0.436224
$22$	−3.54302	−0.755374
$23$	3.99265	0.832524	0.416262	−	0.909245i	$-0.363340\pi$
$23$	3.99265	0.832524	0.416262	+	0.909245i	$0.363340\pi$
$24$	−4.99520	−1.01964
$25$	−4.84432	−0.968863
$26$	0.590119	0.115732
$27$	−4.69622	−0.903788
$28$	−1.46618	−0.277082
$29$	−1.00000	−0.185695
$29$	−1.00000	−0.185695
$30$	0.585020	0.106810
$31$	−0.599936	−0.107752	−0.0538759	−	0.998548i	$-0.517158\pi$
$31$	−0.599936	−0.107752	−0.0538759	+	0.998548i	$0.517158\pi$
$32$	5.83865	1.03214
$33$	−8.32534	−1.44926
$34$	5.28806	0.906896
$35$	0.422571	0.0714276
$36$	−0.662615	−0.110436
$37$	−1.58553	−0.260660	−0.130330	−	0.991471i	$-0.541604\pi$
$37$	−1.58553	−0.260660	−0.130330	+	0.991471i	$0.541604\pi$
$38$	−5.87116	−0.952429
$39$	1.38665	0.222042
$40$	−1.05593	−0.166957
$41$	0.183886	0.0287181	0.0143591	−	0.999897i	$-0.495429\pi$
$41$	0.183886	0.0287181	0.0143591	+	0.999897i	$0.495429\pi$
$42$	1.58793	0.245022
$43$	−7.34164	−1.11959	−0.559795	−	0.828631i	$-0.689120\pi$
$43$	−7.34164	−1.11959	−0.559795	+	0.828631i	$0.689120\pi$
$44$	6.10617	0.920540
$45$	0.190974	0.0284687
$46$	3.17155	0.467620
$47$	−7.74848	−1.13023	−0.565116	−	0.825011i	$-0.691169\pi$
$47$	−7.74848	−1.13023	−0.565116	+	0.825011i	$0.691169\pi$
$48$	1.14272	0.164938
$49$	−5.85301	−0.836144
$50$	−3.84808	−0.544200
$51$	12.4258	1.73996
$52$	−1.01703	−0.141037
$53$	−9.69374	−1.33154	−0.665769	−	0.746158i	$-0.731896\pi$
$53$	−9.69374	−1.33154	−0.665769	+	0.746158i	$0.731896\pi$
$54$	−3.73044	−0.507648
$55$	−1.75988	−0.237302
$56$	−2.86611	−0.383000
$57$	−13.7960	−1.82732
$58$	−0.794348	−0.104303
$59$	4.02564	0.524094	0.262047	−	0.965055i	$-0.415602\pi$
$59$	4.02564	0.524094	0.262047	+	0.965055i	$0.415602\pi$
$60$	−1.00825	−0.130164
$61$	7.64125	0.978362	0.489181	−	0.872182i	$-0.337296\pi$
$61$	7.64125	0.978362	0.489181	+	0.872182i	$0.337296\pi$
$62$	−0.476558	−0.0605230
$63$	0.518363	0.0653076
$64$	3.41350	0.426687
$65$	0.293122	0.0363573
$66$	−6.61322	−0.814031
$67$	6.20563	0.758138	0.379069	−	0.925368i	$-0.376244\pi$
$67$	6.20563	0.758138	0.379069	+	0.925368i	$0.376244\pi$
$68$	−9.11365	−1.10519
$69$	7.45248	0.897173
$70$	0.335669	0.0401201
$71$	−10.4718	−1.24277	−0.621386	−	0.783504i	$-0.713430\pi$
$71$	−10.4718	−1.24277	−0.621386	+	0.783504i	$0.713430\pi$
$72$	−1.29529	−0.152652
$73$	12.5575	1.46975	0.734875	−	0.678203i	$-0.237241\pi$
$73$	12.5575	1.46975	0.734875	+	0.678203i	$0.237241\pi$
$74$	−1.25946	−0.146410
$75$	−9.04216	−1.04410
$76$	10.1186	1.16068
$77$	−4.77685	−0.544373
$78$	1.10149	0.124719
$79$	−6.34166	−0.713492	−0.356746	−	0.934201i	$-0.616114\pi$
$79$	−6.34166	−0.713492	−0.356746	+	0.934201i	$0.616114\pi$
$80$	0.241558	0.0270070
$81$	−10.2178	−1.13531
$82$	0.146069	0.0161307
$83$	−2.18323	−0.239641	−0.119821	−	0.992796i	$-0.538232\pi$
$83$	−2.18323	−0.239641	−0.119821	+	0.992796i	$0.538232\pi$
$84$	−2.73669	−0.298598
$85$	2.62667	0.284902
$86$	−5.83182	−0.628861
$87$	−1.86655	−0.200115
$88$	11.9365	1.27243
$89$	−13.2533	−1.40485	−0.702425	−	0.711758i	$-0.747899\pi$
$89$	−13.2533	−1.40485	−0.702425	+	0.711758i	$0.747899\pi$
$90$	0.151700	0.0159906
$91$	0.795624	0.0834041
$92$	−5.46597	−0.569867
$93$	−1.11981	−0.116119
$94$	−6.15499	−0.634839
$95$	−2.91631	−0.299207
$96$	10.8981	1.11229
$97$	0.174843	0.0177526	0.00887629	−	0.999961i	$-0.497175\pi$
$97$	0.174843	0.0177526	0.00887629	+	0.999961i	$0.497175\pi$
$98$	−4.64933	−0.469653
$99$	−2.15882	−0.216970
$100$	6.63192	0.663192
$101$	−15.9714	−1.58921	−0.794605	−	0.607127i	$-0.792322\pi$
$101$	−15.9714	−1.58921	−0.794605	+	0.607127i	$0.792322\pi$
$102$	9.87044	0.977319
$103$	−5.57369	−0.549192	−0.274596	−	0.961560i	$-0.588544\pi$
$103$	−5.57369	−0.549192	−0.274596	+	0.961560i	$0.588544\pi$
$104$	−1.98812	−0.194951
$105$	0.788750	0.0769741
$106$	−7.70021	−0.747910
$107$	7.68852	0.743277	0.371638	−	0.928378i	$-0.378796\pi$
$107$	7.68852	0.743277	0.371638	+	0.928378i	$0.378796\pi$
$108$	6.42918	0.618648
$109$	−7.87765	−0.754542	−0.377271	−	0.926103i	$-0.623138\pi$
$109$	−7.87765	−0.754542	−0.377271	+	0.926103i	$0.623138\pi$
$110$	−1.39795	−0.133290
$111$	−2.95947	−0.280901
$112$	0.655663	0.0619543
$113$	−9.38063	−0.882455	−0.441228	−	0.897395i	$-0.645457\pi$
$113$	−9.38063	−0.882455	−0.441228	+	0.897395i	$0.645457\pi$
$114$	−10.9588	−1.02639
$115$	1.57536	0.146903
$116$	1.36901	0.127109
$117$	0.359570	0.0332422
$118$	3.19776	0.294378
$119$	7.12960	0.653570
$120$	−1.97094	−0.179921
$121$	8.89409	0.808554
$122$	6.06982	0.549535
$123$	0.343232	0.0309482
$124$	0.821319	0.0737566
$125$	−3.88424	−0.347417
$126$	0.411761	0.0366826
$127$	9.04138	0.802293	0.401146	−	0.916014i	$-0.368612\pi$
$127$	9.04138	0.802293	0.401146	+	0.916014i	$0.368612\pi$
$128$	−8.96578	−0.792471
$129$	−13.7035	−1.20653
$130$	0.232841	0.0204215
$131$	−1.99581	−0.174375	−0.0871874	−	0.996192i	$-0.527788\pi$
$131$	−1.99581	−0.174375	−0.0871874	+	0.996192i	$0.527788\pi$
$132$	11.3975	0.992023
$133$	−7.91577	−0.686384
$134$	4.92943	0.425838
$135$	−1.85297	−0.159478
$136$	−17.8155	−1.52767
$137$	−2.48411	−0.212232	−0.106116	−	0.994354i	$-0.533841\pi$
$137$	−2.48411	−0.212232	−0.106116	+	0.994354i	$0.533841\pi$
$138$	5.91986	0.503932
$139$	−1.00000	−0.0848189
$139$	−1.00000	−0.0848189
$140$	−0.578504	−0.0488925
$141$	−14.4629	−1.21800
$142$	−8.31825	−0.698052
$143$	−3.31353	−0.277091
$144$	0.296316	0.0246930
$145$	−0.394566	−0.0327669
$146$	9.97507	0.825543
$147$	−10.9249	−0.901074
$148$	2.17061	0.178423
$149$	−9.72889	−0.797022	−0.398511	−	0.917164i	$-0.630473\pi$
$149$	−9.72889	−0.797022	−0.398511	+	0.917164i	$0.630473\pi$
$150$	−7.18263	−0.586459
$151$	6.74266	0.548710	0.274355	−	0.961628i	$-0.411536\pi$
$151$	6.74266	0.548710	0.274355	+	0.961628i	$0.411536\pi$
$152$	19.7800	1.60437
$153$	3.22211	0.260492
$154$	−3.79449	−0.305768
$155$	−0.236715	−0.0190134
$156$	−1.89834	−0.151989
$157$	2.21795	0.177011	0.0885056	−	0.996076i	$-0.471791\pi$
$157$	2.21795	0.177011	0.0885056	+	0.996076i	$0.471791\pi$
$158$	−5.03748	−0.400761
$159$	−18.0939	−1.43494
$160$	2.30373	0.182126
$161$	4.27603	0.336998
$162$	−8.11647	−0.637690
$163$	22.0296	1.72550	0.862748	−	0.505635i	$-0.168742\pi$
$163$	22.0296	1.72550	0.862748	+	0.505635i	$0.168742\pi$
$164$	−0.251742	−0.0196577
$165$	−3.28490	−0.255729
$166$	−1.73425	−0.134604
$167$	14.2992	1.10650	0.553251	−	0.833015i	$-0.313387\pi$
$167$	14.2992	1.10650	0.553251	+	0.833015i	$0.313387\pi$
$168$	−5.34974	−0.412742
$169$	−12.4481	−0.957547
$170$	2.08649	0.160027
$171$	−3.57740	−0.273571
$172$	10.0508	0.766365
$173$	15.3883	1.16995	0.584976	−	0.811051i	$-0.301104\pi$
$173$	15.3883	1.16995	0.584976	+	0.811051i	$0.301104\pi$
$174$	−1.48269	−0.112403
$175$	−5.18815	−0.392187
$176$	−2.73063	−0.205829
$177$	7.51406	0.564791
$178$	−10.5278	−0.789089
$179$	−19.0876	−1.42667	−0.713336	−	0.700823i	$-0.752816\pi$
$179$	−19.0876	−1.42667	−0.713336	+	0.700823i	$0.752816\pi$
$180$	−0.261446	−0.0194870
$181$	−2.90099	−0.215629	−0.107814	−	0.994171i	$-0.534385\pi$
$181$	−2.90099	−0.215629	−0.107814	+	0.994171i	$0.534385\pi$
$182$	0.632003	0.0468472
$183$	14.2628	1.05434
$184$	−10.6850	−0.787708
$185$	−0.625597	−0.0459948
$186$	−0.889520	−0.0652228
$187$	−29.6926	−2.17134
$188$	10.6078	0.773650
$189$	−5.02954	−0.365845
$190$	−2.31656	−0.168061
$191$	−14.5621	−1.05368	−0.526838	−	0.849965i	$-0.676623\pi$
$191$	−14.5621	−1.05368	−0.526838	+	0.849965i	$0.676623\pi$
$192$	6.37146	0.459821
$193$	8.81600	0.634590	0.317295	−	0.948327i	$-0.397226\pi$
$193$	8.81600	0.634590	0.317295	+	0.948327i	$0.397226\pi$
$194$	0.138886	0.00997143
$195$	0.547127	0.0391806
$196$	8.01283	0.572345
$197$	−3.74271	−0.266657	−0.133329	−	0.991072i	$-0.542567\pi$
$197$	−3.74271	−0.266657	−0.133329	+	0.991072i	$0.542567\pi$
$198$	−1.71486	−0.121870
$199$	−4.33061	−0.306989	−0.153494	−	0.988150i	$-0.549053\pi$
$199$	−4.33061	−0.306989	−0.153494	+	0.988150i	$0.549053\pi$
$200$	12.9642	0.916708
$201$	11.5831	0.817010
$202$	−12.6868	−0.892642
$203$	−1.07098	−0.0751678
$204$	−17.0111	−1.19101
$205$	0.0725551	0.00506747
$206$	−4.42746	−0.308475
$207$	1.93248	0.134317
$208$	0.454809	0.0315353
$209$	32.9667	2.28035
$210$	0.626543	0.0432355
$211$	22.9299	1.57856	0.789280	−	0.614033i	$-0.210454\pi$
$211$	22.9299	1.57856	0.789280	+	0.614033i	$0.210454\pi$
$212$	13.2708	0.911444
$213$	−19.5461	−1.33928
$214$	6.10736	0.417491
$215$	−2.89676	−0.197558
$216$	12.5679	0.855136
$217$	−0.642517	−0.0436169
$218$	−6.25760	−0.423818
$219$	23.4393	1.58388
$220$	2.40929	0.162434
$221$	4.94554	0.332673
$222$	−2.35085	−0.157779
$223$	27.3500	1.83149	0.915747	−	0.401755i	$-0.131600\pi$
$223$	27.3500	1.83149	0.915747	+	0.401755i	$0.131600\pi$
$224$	6.25305	0.417799
$225$	−2.34470	−0.156313
$226$	−7.45149	−0.495665
$227$	19.2556	1.27804	0.639018	−	0.769192i	$-0.279341\pi$
$227$	19.2556	1.27804	0.639018	+	0.769192i	$0.279341\pi$
$228$	18.8869	1.25081
$229$	0.162405	0.0107320	0.00536602	−	0.999986i	$-0.498292\pi$
$229$	0.162405	0.0107320	0.00536602	+	0.999986i	$0.498292\pi$
$230$	1.25139	0.0825141
$231$	−8.91624	−0.586645
$232$	2.67617	0.175699
$233$	6.29827	0.412614	0.206307	−	0.978487i	$-0.433856\pi$
$233$	6.29827	0.412614	0.206307	+	0.978487i	$0.433856\pi$
$234$	0.285623	0.0186718
$235$	−3.05729	−0.199436
$236$	−5.51115	−0.358745
$237$	−11.8370	−0.768897
$238$	5.66339	0.367103
$239$	28.3688	1.83503	0.917513	−	0.397706i	$-0.130194\pi$
$239$	28.3688	1.83503	0.917513	+	0.397706i	$0.130194\pi$
$240$	0.450880	0.0291042
$241$	−29.5973	−1.90653	−0.953266	−	0.302131i	$-0.902302\pi$
$241$	−29.5973	−1.90653	−0.953266	+	0.302131i	$0.902302\pi$
$242$	7.06501	0.454156
$243$	−4.98331	−0.319679
$244$	−10.4610	−0.669694
$245$	−2.30940	−0.147542
$246$	0.272646	0.0173833
$247$	−5.49087	−0.349376
$248$	1.60553	0.101951
$249$	−4.07512	−0.258250
$250$	−3.08544	−0.195140
$251$	14.6133	0.922381	0.461190	−	0.887301i	$-0.347423\pi$
$251$	14.6133	0.922381	0.461190	+	0.887301i	$0.347423\pi$
$252$	−0.709645	−0.0447034
$253$	−17.8083	−1.11960
$254$	7.18201	0.450639
$255$	4.90281	0.307026
$256$	−13.9490	−0.871809
$257$	−2.85780	−0.178265	−0.0891323	−	0.996020i	$-0.528409\pi$
$257$	−2.85780	−0.178265	−0.0891323	+	0.996020i	$0.528409\pi$
$258$	−10.8854	−0.677694
$259$	−1.69807	−0.105513
$260$	−0.401287	−0.0248868
$261$	−0.484010	−0.0299595
$262$	−1.58537	−0.0979444
$263$	−3.08196	−0.190042	−0.0950210	−	0.995475i	$-0.530292\pi$
$263$	−3.08196	−0.190042	−0.0950210	+	0.995475i	$0.530292\pi$
$264$	22.2800	1.37124
$265$	−3.82482	−0.234957
$266$	−6.28788	−0.385534
$267$	−24.7380	−1.51394
$268$	−8.49557	−0.518949
$269$	5.97566	0.364342	0.182171	−	0.983267i	$-0.441688\pi$
$269$	5.97566	0.364342	0.182171	+	0.983267i	$0.441688\pi$
$270$	−1.47190	−0.0895773
$271$	22.3596	1.35825	0.679124	−	0.734024i	$-0.262360\pi$
$271$	22.3596	1.35825	0.679124	+	0.734024i	$0.262360\pi$
$272$	4.07555	0.247117
$273$	1.48507	0.0898807
$274$	−1.97325	−0.119208
$275$	21.6070	1.30295
$276$	−10.2025	−0.614119
$277$	−12.7746	−0.767554	−0.383777	−	0.923426i	$-0.625377\pi$
$277$	−12.7746	−0.767554	−0.383777	+	0.923426i	$0.625377\pi$
$278$	−0.794348	−0.0476419
$279$	−0.290375	−0.0173843
$280$	−1.13087	−0.0675825
$281$	24.0609	1.43535	0.717676	−	0.696377i	$-0.245206\pi$
$281$	24.0609	1.43535	0.717676	+	0.696377i	$0.245206\pi$
$282$	−11.4886	−0.684136
$283$	10.8780	0.646631	0.323315	−	0.946291i	$-0.395202\pi$
$283$	10.8780	0.646631	0.323315	+	0.946291i	$0.395202\pi$
$284$	14.3360	0.850684
$285$	−5.44343	−0.322441
$286$	−2.63209	−0.155639
$287$	0.196937	0.0116248
$288$	2.82596	0.166522
$289$	27.3171	1.60689
$290$	−0.313423	−0.0184048
$291$	0.326352	0.0191311
$292$	−17.1914	−1.00605
$293$	−18.6118	−1.08731	−0.543657	−	0.839307i	$-0.682961\pi$
$293$	−18.6118	−1.08731	−0.543657	+	0.839307i	$0.682961\pi$
$294$	−8.67821	−0.506123
$295$	1.58838	0.0924792
$296$	4.24315	0.246628
$297$	20.9465	1.21544
$298$	−7.72813	−0.447678
$299$	2.96612	0.171535
$300$	12.3788	0.714691
$301$	−7.86272	−0.453199
$302$	5.35602	0.308205
$303$	−29.8113	−1.71262
$304$	−4.52495	−0.259524
$305$	3.01498	0.172637
$306$	2.55948	0.146316
$307$	11.7423	0.670171	0.335085	−	0.942188i	$-0.391235\pi$
$307$	11.7423	0.670171	0.335085	+	0.942188i	$0.391235\pi$
$308$	6.53956	0.372626
$309$	−10.4036	−0.591839
$310$	−0.188034	−0.0106796
$311$	−6.29413	−0.356907	−0.178454	−	0.983948i	$-0.557109\pi$
$311$	−6.29413	−0.356907	−0.178454	+	0.983948i	$0.557109\pi$
$312$	−3.71092	−0.210089
$313$	−31.0177	−1.75322	−0.876611	−	0.481200i	$-0.840201\pi$
$313$	−31.0177	−1.75322	−0.876611	+	0.481200i	$0.840201\pi$
$314$	1.76182	0.0994253
$315$	0.204529	0.0115239
$316$	8.68179	0.488389
$317$	5.58916	0.313918	0.156959	−	0.987605i	$-0.449831\pi$
$317$	5.58916	0.313918	0.156959	+	0.987605i	$0.449831\pi$
$318$	−14.3728	−0.805988
$319$	4.46028	0.249728
$320$	1.34685	0.0752913
$321$	14.3510	0.800995
$322$	3.39666	0.189288
$323$	−49.2038	−2.73777
$324$	13.9882	0.777124
$325$	−3.59883	−0.199627
$326$	17.4992	0.969192
$327$	−14.7040	−0.813135
$328$	−0.492109	−0.0271722
$329$	−8.29844	−0.457508
$330$	−2.60935	−0.143640
$331$	−17.9774	−0.988130	−0.494065	−	0.869425i	$-0.664490\pi$
$331$	−17.9774	−0.988130	−0.494065	+	0.869425i	$0.664490\pi$
$332$	2.98887	0.164036
$333$	−0.767413	−0.0420540
$334$	11.3585	0.621510
$335$	2.44853	0.133778
$336$	1.22383	0.0667653
$337$	−28.0662	−1.52887	−0.764433	−	0.644703i	$-0.776981\pi$
$337$	−28.0662	−1.52887	−0.764433	+	0.644703i	$0.776981\pi$
$338$	−9.88813	−0.537844
$339$	−17.5094	−0.950981
$340$	−3.59594	−0.195017
$341$	2.67588	0.144907
$342$	−2.84170	−0.153662
$343$	−13.7653	−0.743255
$344$	19.6475	1.05932
$345$	2.94050	0.158311
$346$	12.2237	0.657150
$347$	25.9822	1.39480	0.697399	−	0.716683i	$-0.254341\pi$
$347$	25.9822	1.39480	0.697399	+	0.716683i	$0.254341\pi$
$348$	2.55533	0.136980
$349$	−13.4053	−0.717568	−0.358784	−	0.933421i	$-0.616809\pi$
$349$	−13.4053	−0.717568	−0.358784	+	0.933421i	$0.616809\pi$
$350$	−4.12120	−0.220287
$351$	−3.48881	−0.186219
$352$	−26.0420	−1.38804
$353$	−19.3184	−1.02822	−0.514108	−	0.857725i	$-0.671877\pi$
$353$	−19.3184	−1.02822	−0.514108	+	0.857725i	$0.671877\pi$
$354$	5.96878	0.317237
$355$	−4.13181	−0.219294
$356$	18.1439	0.961627
$357$	13.3078	0.704322
$358$	−15.1622	−0.801346
$359$	−17.7327	−0.935896	−0.467948	−	0.883756i	$-0.655007\pi$
$359$	−17.7327	−0.935896	−0.467948	+	0.883756i	$0.655007\pi$
$360$	−0.511079	−0.0269362
$361$	35.6294	1.87523
$362$	−2.30440	−0.121116
$363$	16.6013	0.871341
$364$	−1.08922	−0.0570905
$365$	4.95479	0.259345
$366$	11.3296	0.592209
$367$	−1.02909	−0.0537178	−0.0268589	−	0.999639i	$-0.508550\pi$
$367$	−1.02909	−0.0537178	−0.0268589	+	0.999639i	$0.508550\pi$
$368$	2.44434	0.127420
$369$	0.0890026	0.00463329
$370$	−0.496942	−0.0258348
$371$	−10.3818	−0.538994
$372$	1.53303	0.0794841
$373$	−7.84271	−0.406080	−0.203040	−	0.979170i	$-0.565082\pi$
$373$	−7.84271	−0.406080	−0.203040	+	0.979170i	$0.565082\pi$
$374$	−23.5862	−1.21962
$375$	−7.25012	−0.374395
$376$	20.7362	1.06939
$377$	−0.742897	−0.0382611
$378$	−3.99521	−0.205491
$379$	25.1339	1.29104	0.645520	−	0.763743i	$-0.276641\pi$
$379$	25.1339	1.29104	0.645520	+	0.763743i	$0.276641\pi$
$380$	3.99245	0.204809
$381$	16.8762	0.864594
$382$	−11.5674	−0.591839
$383$	−11.7157	−0.598646	−0.299323	−	0.954152i	$-0.596761\pi$
$383$	−11.7157	−0.598646	−0.299323	+	0.954152i	$0.596761\pi$
$384$	−16.7351	−0.854009
$385$	−1.88479	−0.0960575
$386$	7.00298	0.356442
$387$	−3.55343	−0.180631
$388$	−0.239361	−0.0121517
$389$	−3.37198	−0.170966	−0.0854830	−	0.996340i	$-0.527243\pi$
$389$	−3.37198	−0.170966	−0.0854830	+	0.996340i	$0.527243\pi$
$390$	0.434609	0.0220073
$391$	26.5795	1.34418
$392$	15.6636	0.791133
$393$	−3.72528	−0.187916
$394$	−2.97302	−0.149778
$395$	−2.50220	−0.125900
$396$	2.95545	0.148517
$397$	1.15502	0.0579690	0.0289845	−	0.999580i	$-0.490773\pi$
$397$	1.15502	0.0579690	0.0289845	+	0.999580i	$0.490773\pi$
$398$	−3.44001	−0.172432
$399$	−14.7752	−0.739684
$400$	−2.96574	−0.148287
$401$	−5.84455	−0.291863	−0.145931	−	0.989295i	$-0.546618\pi$
$401$	−5.84455	−0.291863	−0.145931	+	0.989295i	$0.546618\pi$
$402$	9.20103	0.458906
$403$	−0.445691	−0.0222014
$404$	21.8650	1.08782
$405$	−4.03159	−0.200331
$406$	−0.850728	−0.0422209
$407$	7.07191	0.350542
$408$	−33.2536	−1.64630
$409$	−22.4931	−1.11221	−0.556107	−	0.831111i	$-0.687706\pi$
$409$	−22.4931	−1.11221	−0.556107	+	0.831111i	$0.687706\pi$
$410$	0.0576341	0.00284634
$411$	−4.63672	−0.228712
$412$	7.63045	0.375925
$413$	4.31137	0.212148
$414$	1.53506	0.0754443
$415$	−0.861431	−0.0422860
$416$	4.33751	0.212664
$417$	−1.86655	−0.0914054
$418$	26.1870	1.28085
$419$	−6.39250	−0.312294	−0.156147	−	0.987734i	$-0.549907\pi$
$419$	−6.39250	−0.312294	−0.156147	+	0.987734i	$0.549907\pi$
$420$	−1.07981	−0.0526892
$421$	−19.4120	−0.946082	−0.473041	−	0.881040i	$-0.656844\pi$
$421$	−19.4120	−0.946082	−0.473041	+	0.881040i	$0.656844\pi$
$422$	18.2143	0.886660
$423$	−3.75034	−0.182348
$424$	25.9421	1.25986
$425$	−32.2492	−1.56431
$426$	−15.5264	−0.752258
$427$	8.18360	0.396032
$428$	−10.5257	−0.508777
$429$	−6.18486	−0.298608
$430$	−2.30104	−0.110966
$431$	−2.21818	−0.106846	−0.0534231	−	0.998572i	$-0.517013\pi$
$431$	−2.21818	−0.106846	−0.0534231	+	0.998572i	$0.517013\pi$
$432$	−2.87508	−0.138327
$433$	21.6507	1.04047	0.520234	−	0.854024i	$-0.325845\pi$
$433$	21.6507	1.04047	0.520234	+	0.854024i	$0.325845\pi$
$434$	−0.510383	−0.0244992
$435$	−0.736478	−0.0353114
$436$	10.7846	0.516488
$437$	−29.5103	−1.41167
$438$	18.6190	0.889649
$439$	8.28791	0.395560	0.197780	−	0.980246i	$-0.436627\pi$
$439$	8.28791	0.395560	0.197780	+	0.980246i	$0.436627\pi$
$440$	4.70972	0.224527
$441$	−2.83292	−0.134901
$442$	3.92848	0.186859
$443$	−5.66984	−0.269382	−0.134691	−	0.990888i	$-0.543004\pi$
$443$	−5.66984	−0.269382	−0.134691	+	0.990888i	$0.543004\pi$
$444$	4.05155	0.192278
$445$	−5.22932	−0.247893
$446$	21.7255	1.02873
$447$	−18.1595	−0.858913
$448$	3.65577	0.172719
$449$	−39.4188	−1.86029	−0.930144	−	0.367195i	$-0.880318\pi$
$449$	−39.4188	−1.86029	−0.930144	+	0.367195i	$0.880318\pi$
$450$	−1.86251	−0.0877995
$451$	−0.820182	−0.0386209
$452$	12.8422	0.604045
$453$	12.5855	0.591319
$454$	15.2956	0.717859
$455$	0.313927	0.0147171
$456$	36.9204	1.72896
$457$	−21.6549	−1.01297	−0.506486	−	0.862248i	$-0.669056\pi$
$457$	−21.6549	−1.01297	−0.506486	+	0.862248i	$0.669056\pi$
$458$	0.129006	0.00602807
$459$	−31.2633	−1.45924
$460$	−2.15669	−0.100556
$461$	22.4345	1.04488	0.522439	−	0.852677i	$-0.325022\pi$
$461$	22.4345	1.04488	0.522439	+	0.852677i	$0.325022\pi$
$462$	−7.08260	−0.329512
$463$	−36.9533	−1.71736	−0.858682	−	0.512509i	$-0.828716\pi$
$463$	−36.9533	−1.71736	−0.858682	+	0.512509i	$0.828716\pi$
$464$	−0.612211	−0.0284212
$465$	−0.441840	−0.0204898
$466$	5.00302	0.231761
$467$	31.5592	1.46039	0.730194	−	0.683240i	$-0.239430\pi$
$467$	31.5592	1.46039	0.730194	+	0.683240i	$0.239430\pi$
$468$	−0.492254	−0.0227545
$469$	6.64608	0.306887
$470$	−2.42855	−0.112021
$471$	4.13991	0.190757
$472$	−10.7733	−0.495881
$473$	32.7458	1.50565
$474$	−9.40272	−0.431881
$475$	35.8052	1.64285
$476$	−9.76050	−0.447372
$477$	−4.69187	−0.214826
$478$	22.5347	1.03071
$479$	26.1610	1.19533	0.597663	−	0.801748i	$-0.296096\pi$
$479$	26.1610	1.19533	0.597663	+	0.801748i	$0.296096\pi$
$480$	4.30003	0.196269
$481$	−1.17789	−0.0537069
$482$	−23.5106	−1.07088
$483$	7.98142	0.363167
$484$	−12.1761	−0.553459
$485$	0.0689870	0.00313254
$486$	−3.95848	−0.179560
$487$	−40.9560	−1.85590	−0.927948	−	0.372711i	$-0.878428\pi$
$487$	−40.9560	−1.85590	−0.927948	+	0.372711i	$0.878428\pi$
$488$	−20.4493	−0.925695
$489$	41.1194	1.85949
$490$	−1.83447	−0.0828729
$491$	36.5031	1.64736	0.823680	−	0.567055i	$-0.191917\pi$
$491$	36.5031	1.64736	0.823680	+	0.567055i	$0.191917\pi$
$492$	−0.469888	−0.0211842
$493$	−6.65711	−0.299821
$494$	−4.36167	−0.196241
$495$	−0.851798	−0.0382855
$496$	−0.367287	−0.0164917
$497$	−11.2150	−0.503063
$498$	−3.23706	−0.145056
$499$	34.7957	1.55767	0.778835	−	0.627229i	$-0.215811\pi$
$499$	34.7957	1.55767	0.778835	+	0.627229i	$0.215811\pi$
$500$	5.31756	0.237809
$501$	26.6901	1.19243
$502$	11.6080	0.518091
$503$	1.15175	0.0513542	0.0256771	−	0.999670i	$-0.491826\pi$
$503$	1.15175	0.0513542	0.0256771	+	0.999670i	$0.491826\pi$
$504$	−1.38723	−0.0617920
$505$	−6.30176	−0.280425
$506$	−14.1460	−0.628867
$507$	−23.2350	−1.03190
$508$	−12.3777	−0.549174
$509$	22.3770	0.991845	0.495923	−	0.868367i	$-0.334830\pi$
$509$	22.3770	0.991845	0.495923	+	0.868367i	$0.334830\pi$
$510$	3.89454	0.172453
$511$	13.4488	0.594941
$512$	6.85124	0.302785
$513$	34.7106	1.53251
$514$	−2.27009	−0.100129
$515$	−2.19919	−0.0969080
$516$	18.7603	0.825875
$517$	34.5604	1.51996
$518$	−1.34886	−0.0592653
$519$	28.7231	1.26080
$520$	−0.784444	−0.0344001
$521$	24.9171	1.09164	0.545818	−	0.837904i	$-0.316219\pi$
$521$	24.9171	1.09164	0.545818	+	0.837904i	$0.316219\pi$
$522$	−0.384473	−0.0168279
$523$	24.0474	1.05152	0.525760	−	0.850633i	$-0.323781\pi$
$523$	24.0474	1.05152	0.525760	+	0.850633i	$0.323781\pi$
$524$	2.73229	0.119360
$525$	−9.68394	−0.422642
$526$	−2.44815	−0.106745
$527$	−3.99384	−0.173974
$528$	−5.09686	−0.221812
$529$	−7.05878	−0.306903
$530$	−3.03824	−0.131973
$531$	1.94845	0.0845556
$532$	10.8368	0.469833
$533$	0.136608	0.00591715
$534$	−19.6506	−0.850365
$535$	3.03363	0.131155
$536$	−16.6073	−0.717326
$537$	−35.6279	−1.53746
$538$	4.74675	0.204647
$539$	26.1061	1.12447
$540$	2.53674	0.109164
$541$	15.4486	0.664188	0.332094	−	0.943246i	$-0.392245\pi$
$541$	15.4486	0.664188	0.332094	+	0.943246i	$0.392245\pi$
$542$	17.7613	0.762913
$543$	−5.41484	−0.232373
$544$	38.8685	1.66647
$545$	−3.10826	−0.133143
$546$	1.17967	0.0504850
$547$	7.83610	0.335048	0.167524	−	0.985868i	$-0.446423\pi$
$547$	7.83610	0.335048	0.167524	+	0.985868i	$0.446423\pi$
$548$	3.40077	0.145274
$549$	3.69844	0.157846
$550$	17.1635	0.731854
$551$	7.39117	0.314874
$552$	−19.9441	−0.848876
$553$	−6.79176	−0.288815
$554$	−10.1475	−0.431127
$555$	−1.16771	−0.0495665
$556$	1.36901	0.0580590
$557$	36.4821	1.54580	0.772898	−	0.634531i	$-0.218807\pi$
$557$	36.4821	1.54580	0.772898	+	0.634531i	$0.218807\pi$
$558$	−0.230659	−0.00976458
$559$	−5.45408	−0.230683
$560$	0.258703	0.0109322
$561$	−55.4227	−2.33995
$562$	19.1127	0.806221
$563$	21.5802	0.909497	0.454749	−	0.890620i	$-0.349729\pi$
$563$	21.5802	0.909497	0.454749	+	0.890620i	$0.349729\pi$
$564$	19.7999	0.833726
$565$	−3.70128	−0.155714
$566$	8.64094	0.363206
$567$	−10.9430	−0.459562
$568$	28.0243	1.17587
$569$	−9.44383	−0.395906	−0.197953	−	0.980212i	$-0.563429\pi$
$569$	−9.44383	−0.395906	−0.197953	+	0.980212i	$0.563429\pi$
$570$	−4.32398	−0.181112
$571$	−15.6362	−0.654356	−0.327178	−	0.944963i	$-0.606098\pi$
$571$	−15.6362	−0.654356	−0.327178	+	0.944963i	$0.606098\pi$
$572$	4.53625	0.189670
$573$	−27.1809	−1.13550
$574$	0.156437	0.00652955
$575$	−19.3416	−0.806602
$576$	1.65217	0.0688403
$577$	22.8689	0.952046	0.476023	−	0.879433i	$-0.342078\pi$
$577$	22.8689	0.952046	0.476023	+	0.879433i	$0.342078\pi$
$578$	21.6993	0.902572
$579$	16.4555	0.683868
$580$	0.540165	0.0224291
$581$	−2.33819	−0.0970045
$582$	0.259238	0.0107457
$583$	43.2368	1.79068
$584$	−33.6061	−1.39063
$585$	0.141874	0.00586577
$586$	−14.7843	−0.610733
$587$	−14.8879	−0.614487	−0.307244	−	0.951631i	$-0.599407\pi$
$587$	−14.8879	−0.614487	−0.307244	+	0.951631i	$0.599407\pi$
$588$	14.9564	0.616790
$589$	4.43423	0.182709
$590$	1.26173	0.0519446
$591$	−6.98596	−0.287364
$592$	−0.970679	−0.0398947
$593$	−34.2054	−1.40465	−0.702323	−	0.711858i	$-0.747854\pi$
$593$	−34.2054	−1.40465	−0.702323	+	0.711858i	$0.747854\pi$
$594$	16.6388	0.682698
$595$	2.81310	0.115326
$596$	13.3190	0.545565
$597$	−8.08330	−0.330828
$598$	2.35614	0.0963495
$599$	34.9928	1.42977	0.714883	−	0.699244i	$-0.246480\pi$
$599$	34.9928	1.42977	0.714883	+	0.699244i	$0.246480\pi$
$600$	24.1983	0.987893
$601$	−25.1562	−1.02614	−0.513072	−	0.858345i	$-0.671493\pi$
$601$	−25.1562	−1.02614	−0.513072	+	0.858345i	$0.671493\pi$
$602$	−6.24574	−0.254557
$603$	3.00359	0.122315
$604$	−9.23078	−0.375595
$605$	3.50931	0.142674
$606$	−23.6806	−0.961958
$607$	−40.1969	−1.63154	−0.815771	−	0.578375i	$-0.803687\pi$
$607$	−40.1969	−1.63154	−0.815771	+	0.578375i	$0.803687\pi$
$608$	−43.1544	−1.75014
$609$	−1.99903	−0.0810048
$610$	2.39495	0.0969685
$611$	−5.75632	−0.232876
$612$	−4.41110	−0.178308
$613$	0.229773	0.00928043	0.00464022	−	0.999989i	$-0.498523\pi$
$613$	0.229773	0.00928043	0.00464022	+	0.999989i	$0.498523\pi$
$614$	9.32751	0.376428
$615$	0.135428	0.00546098
$616$	12.7837	0.515068
$617$	38.4614	1.54840	0.774198	−	0.632944i	$-0.218154\pi$
$617$	38.4614	1.54840	0.774198	+	0.632944i	$0.218154\pi$
$618$	−8.26407	−0.332430
$619$	33.4394	1.34404	0.672022	−	0.740531i	$-0.265426\pi$
$619$	33.4394	1.34404	0.672022	+	0.740531i	$0.265426\pi$
$620$	0.324065	0.0130148
$621$	−18.7504	−0.752426
$622$	−4.99973	−0.200471
$623$	−14.1940	−0.568671
$624$	0.848924	0.0339842
$625$	22.6890	0.907560
$626$	−24.6388	−0.984766
$627$	61.5340	2.45743
$628$	−3.03639	−0.121165
$629$	−10.5551	−0.420857
$630$	0.162467	0.00647284
$631$	−36.4275	−1.45015	−0.725077	−	0.688667i	$-0.758196\pi$
$631$	−36.4275	−1.45015	−0.725077	+	0.688667i	$0.758196\pi$
$632$	16.9713	0.675084
$633$	42.7998	1.70114
$634$	4.43974	0.176325
$635$	3.56742	0.141569
$636$	24.7707	0.982221
$637$	−4.34818	−0.172281
$638$	3.54302	0.140269
$639$	−5.06845	−0.200505
$640$	−3.53760	−0.139836
$641$	17.0030	0.671578	0.335789	−	0.941937i	$-0.390997\pi$
$641$	17.0030	0.671578	0.335789	+	0.941937i	$0.390997\pi$
$642$	11.3997	0.449910
$643$	−29.3333	−1.15679	−0.578396	−	0.815756i	$-0.696321\pi$
$643$	−29.3333	−1.15679	−0.578396	+	0.815756i	$0.696321\pi$
$644$	−5.85393	−0.230677
$645$	−5.40695	−0.212899
$646$	−39.0850	−1.53778
$647$	−29.8446	−1.17331	−0.586656	−	0.809836i	$-0.699556\pi$
$647$	−29.8446	−1.17331	−0.586656	+	0.809836i	$0.699556\pi$
$648$	27.3445	1.07419
$649$	−17.9555	−0.704814
$650$	−2.85872	−0.112128
$651$	−1.19929	−0.0470039
$652$	−30.1588	−1.18111
$653$	42.5611	1.66555	0.832773	−	0.553614i	$-0.186752\pi$
$653$	42.5611	1.66555	0.832773	+	0.553614i	$0.186752\pi$
$654$	−11.6801	−0.456729
$655$	−0.787480	−0.0307694
$656$	0.112577	0.00439539
$657$	6.07798	0.237125
$658$	−6.59185	−0.256977
$659$	17.0405	0.663805	0.331902	−	0.943314i	$-0.392310\pi$
$659$	17.0405	0.663805	0.331902	+	0.943314i	$0.392310\pi$
$660$	4.49706	0.175048
$661$	−14.1956	−0.552147	−0.276073	−	0.961137i	$-0.589033\pi$
$661$	−14.1956	−0.552147	−0.276073	+	0.961137i	$0.589033\pi$
$662$	−14.2804	−0.555022
$663$	9.23111	0.358506
$664$	5.84270	0.226741
$665$	−3.12329	−0.121116
$666$	−0.609593	−0.0236213
$667$	−3.99265	−0.154596
$668$	−19.5757	−0.757406
$669$	51.0502	1.97372
$670$	1.94499	0.0751414
$671$	−34.0821	−1.31573
$672$	11.6716	0.450243
$673$	−26.2269	−1.01097	−0.505486	−	0.862835i	$-0.668687\pi$
$673$	−26.2269	−1.01097	−0.505486	+	0.862835i	$0.668687\pi$
$674$	−22.2944	−0.858747
$675$	22.7500	0.875647
$676$	17.0416	0.655446
$677$	2.72356	0.104675	0.0523374	−	0.998629i	$-0.483333\pi$
$677$	2.72356	0.104675	0.0523374	+	0.998629i	$0.483333\pi$
$678$	−13.9086	−0.534156
$679$	0.187252	0.00718608
$680$	−7.02941	−0.269566
$681$	35.9415	1.37728
$682$	2.12558	0.0813928
$683$	−43.8082	−1.67627	−0.838137	−	0.545460i	$-0.816355\pi$
$683$	−43.8082	−1.67627	−0.838137	+	0.545460i	$0.816355\pi$
$684$	4.89750	0.187261
$685$	−0.980146	−0.0374495
$686$	−10.9344	−0.417478
$687$	0.303138	0.0115654
$688$	−4.49463	−0.171356
$689$	−7.20144	−0.274353
$690$	2.33578	0.0889216
$691$	20.6543	0.785727	0.392864	−	0.919597i	$-0.371484\pi$
$691$	20.6543	0.785727	0.392864	+	0.919597i	$0.371484\pi$
$692$	−21.0668	−0.800838
$693$	−2.31205	−0.0878273
$694$	20.6389	0.783443
$695$	−0.394566	−0.0149668
$696$	4.99520	0.189343
$697$	1.22415	0.0463679
$698$	−10.6485	−0.403050
$699$	11.7560	0.444654
$700$	7.10263	0.268454
$701$	23.0379	0.870129	0.435065	−	0.900399i	$-0.356726\pi$
$701$	23.0379	0.870129	0.435065	+	0.900399i	$0.356726\pi$
$702$	−2.77133	−0.104597
$703$	11.7189	0.441988
$704$	−15.2252	−0.573820
$705$	−5.70658	−0.214922
$706$	−15.3456	−0.577538
$707$	−17.1049	−0.643298
$708$	−10.2868	−0.386603
$709$	−20.0926	−0.754593	−0.377297	−	0.926093i	$-0.623146\pi$
$709$	−20.0926	−0.754593	−0.377297	+	0.926093i	$0.623146\pi$
$710$	−3.28210	−0.123175
$711$	−3.06943	−0.115112
$712$	35.4681	1.32922
$713$	−2.39533	−0.0897059
$714$	10.5710	0.395610
$715$	−1.30741	−0.0488942
$716$	26.1311	0.976564
$717$	52.9518	1.97752
$718$	−14.0859	−0.525683
$719$	7.82872	0.291962	0.145981	−	0.989287i	$-0.453366\pi$
$719$	7.82872	0.291962	0.145981	+	0.989287i	$0.453366\pi$
$720$	0.116916	0.00435722
$721$	−5.96929	−0.222308
$722$	28.3021	1.05330
$723$	−55.2449	−2.05458
$724$	3.97148	0.147599
$725$	4.84432	0.179913
$726$	13.1872	0.489423
$727$	−27.7264	−1.02831	−0.514157	−	0.857696i	$-0.671895\pi$
$727$	−27.7264	−1.02831	−0.514157	+	0.857696i	$0.671895\pi$
$728$	−2.12922	−0.0789143
$729$	21.3517	0.790804
$730$	3.93583	0.145671
$731$	−48.8741	−1.80767
$732$	−19.5259	−0.721698
$733$	−31.0121	−1.14546	−0.572729	−	0.819745i	$-0.694115\pi$
$733$	−31.0121	−1.14546	−0.572729	+	0.819745i	$0.694115\pi$
$734$	−0.817452	−0.0301727
$735$	−4.31061	−0.158999
$736$	23.3116	0.859279
$737$	−27.6788	−1.01956
$738$	0.0706991	0.00260247
$739$	−10.9270	−0.401956	−0.200978	−	0.979596i	$-0.564412\pi$
$739$	−10.9270	−0.401956	−0.200978	+	0.979596i	$0.564412\pi$
$740$	0.856449	0.0314837
$741$	−10.2490	−0.376506
$742$	−8.24674	−0.302747
$743$	−44.1398	−1.61933	−0.809667	−	0.586890i	$-0.800352\pi$
$743$	−44.1398	−1.61933	−0.809667	+	0.586890i	$0.800352\pi$
$744$	2.99680	0.109868
$745$	−3.83869	−0.140639
$746$	−6.22985	−0.228091
$747$	−1.05671	−0.0386629
$748$	40.6494	1.48629
$749$	8.23422	0.300872
$750$	−5.75912	−0.210293
$751$	6.28714	0.229421	0.114711	−	0.993399i	$-0.463406\pi$
$751$	6.28714	0.229421	0.114711	+	0.993399i	$0.463406\pi$
$752$	−4.74370	−0.172985
$753$	27.2764	0.994006
$754$	−0.590119	−0.0214909
$755$	2.66043	0.0968229
$756$	6.88549	0.250423
$757$	24.7096	0.898086	0.449043	−	0.893510i	$-0.351765\pi$
$757$	24.7096	0.898086	0.449043	+	0.893510i	$0.351765\pi$
$758$	19.9651	0.725163
$759$	−33.2401	−1.20654
$760$	7.80453	0.283100
$761$	−17.5700	−0.636912	−0.318456	−	0.947938i	$-0.603164\pi$
$761$	−17.5700	−0.636912	−0.318456	+	0.947938i	$0.603164\pi$
$762$	13.4056	0.485633
$763$	−8.43678	−0.305432
$764$	19.9357	0.721247
$765$	1.27134	0.0459652
$766$	−9.30638	−0.336253
$767$	2.99063	0.107986
$768$	−26.0364	−0.939508
$769$	36.0735	1.30084	0.650422	−	0.759573i	$-0.274592\pi$
$769$	36.0735	1.30084	0.650422	+	0.759573i	$0.274592\pi$
$770$	−1.49718	−0.0539545
$771$	−5.33423	−0.192107
$772$	−12.0692	−0.434380
$773$	52.1422	1.87542	0.937712	−	0.347413i	$-0.112940\pi$
$773$	52.1422	1.87542	0.937712	+	0.347413i	$0.112940\pi$
$774$	−2.82266	−0.101458
$775$	2.90628	0.104397
$776$	−0.467908	−0.0167969
$777$	−3.16952	−0.113706
$778$	−2.67852	−0.0960297
$779$	−1.35913	−0.0486959
$780$	−0.749022	−0.0268193
$781$	46.7071	1.67131
$782$	21.1134	0.755013
$783$	4.69622	0.167829
$784$	−3.58328	−0.127974
$785$	0.875126	0.0312346
$786$	−2.95917	−0.105550
$787$	−20.0689	−0.715378	−0.357689	−	0.933841i	$-0.616435\pi$
$787$	−20.0689	−0.715378	−0.357689	+	0.933841i	$0.616435\pi$
$788$	5.12381	0.182528
$789$	−5.75264	−0.204799
$790$	−1.98762	−0.0707164
$791$	−10.0464	−0.357210
$792$	5.77737	0.205290
$793$	5.67666	0.201584
$794$	0.917492	0.0325606
$795$	−7.13922	−0.253202
$796$	5.92865	0.210135
$797$	−54.5430	−1.93201	−0.966006	−	0.258520i	$-0.916765\pi$
$797$	−54.5430	−1.93201	−0.966006	+	0.258520i	$0.916765\pi$
$798$	−11.7366	−0.415472
$799$	−51.5825	−1.82486
$800$	−28.2843	−0.999999
$801$	−6.41475	−0.226654
$802$	−4.64261	−0.163936
$803$	−56.0102	−1.97656
$804$	−15.8574	−0.559248
$805$	1.68718	0.0594652
$806$	−0.354034	−0.0124703
$807$	11.1539	0.392635
$808$	42.7420	1.50366
$809$	17.7037	0.622430	0.311215	−	0.950340i	$-0.399264\pi$
$809$	17.7037	0.622430	0.311215	+	0.950340i	$0.399264\pi$
$810$	−3.20248	−0.112524
$811$	12.5054	0.439123	0.219561	−	0.975599i	$-0.429537\pi$
$811$	12.5054	0.439123	0.219561	+	0.975599i	$0.429537\pi$
$812$	1.46618	0.0514527
$813$	41.7353	1.46372
$814$	5.61756	0.196895
$815$	8.69216	0.304473
$816$	7.60723	0.266306
$817$	54.2633	1.89843
$818$	−17.8674	−0.624719
$819$	0.385090	0.0134561
$820$	−0.0993288	−0.00346871
$821$	24.4825	0.854446	0.427223	−	0.904146i	$-0.359492\pi$
$821$	24.4825	0.854446	0.427223	+	0.904146i	$0.359492\pi$
$822$	−3.68317	−0.128465
$823$	−33.5383	−1.16907	−0.584536	−	0.811368i	$-0.698723\pi$
$823$	−33.5383	−1.16907	−0.584536	+	0.811368i	$0.698723\pi$
$824$	14.9161	0.519629
$825$	40.3306	1.40413
$826$	3.42473	0.119161
$827$	39.7528	1.38234	0.691171	−	0.722691i	$-0.257095\pi$
$827$	39.7528	1.38234	0.691171	+	0.722691i	$0.257095\pi$
$828$	−2.64559	−0.0919405
$829$	43.8871	1.52426	0.762131	−	0.647423i	$-0.224153\pi$
$829$	43.8871	1.52426	0.762131	+	0.647423i	$0.224153\pi$
$830$	−0.684276	−0.0237516
$831$	−23.8445	−0.827157
$832$	2.53588	0.0879157
$833$	−38.9641	−1.35003
$834$	−1.48269	−0.0513414
$835$	5.64197	0.195248
$836$	−45.1317	−1.56091
$837$	2.81743	0.0973847
$838$	−5.07788	−0.175412
$839$	−44.7362	−1.54447	−0.772233	−	0.635339i	$-0.780860\pi$
$839$	−44.7362	−1.54447	−0.772233	+	0.635339i	$0.780860\pi$
$840$	−2.11083	−0.0728305
$841$	1.00000	0.0344828
$842$	−15.4199	−0.531404
$843$	44.9108	1.54681
$844$	−31.3913	−1.08053
$845$	−4.91160	−0.168964
$846$	−2.97908	−0.102423
$847$	9.52536	0.327295
$848$	−5.93461	−0.203795
$849$	20.3044	0.696844
$850$	−25.6171	−0.878658
$851$	−6.33046	−0.217005
$852$	26.7588	0.916743
$853$	−27.6086	−0.945300	−0.472650	−	0.881250i	$-0.656702\pi$
$853$	−27.6086	−0.945300	−0.472650	+	0.881250i	$0.656702\pi$
$854$	6.50063	0.222447
$855$	−1.41152	−0.0482730
$856$	−20.5758	−0.703265
$857$	−40.5948	−1.38669	−0.693346	−	0.720605i	$-0.743864\pi$
$857$	−40.5948	−1.38669	−0.693346	+	0.720605i	$0.743864\pi$
$858$	−4.91294	−0.167725
$859$	−18.4261	−0.628691	−0.314346	−	0.949309i	$-0.601785\pi$
$859$	−18.4261	−0.628691	−0.314346	+	0.949309i	$0.601785\pi$
$860$	3.96570	0.135229
$861$	0.367593	0.0125275
$862$	−1.76201	−0.0600143
$863$	−17.8867	−0.608872	−0.304436	−	0.952533i	$-0.598468\pi$
$863$	−17.8867	−0.608872	−0.304436	+	0.952533i	$0.598468\pi$
$864$	−27.4196	−0.932833
$865$	6.07171	0.206444
$866$	17.1982	0.584420
$867$	50.9888	1.73167
$868$	0.879613	0.0298560
$869$	28.2856	0.959522
$870$	−0.585020	−0.0198340
$871$	4.61014	0.156209
$872$	21.0819	0.713924
$873$	0.0846256	0.00286414
$874$	−23.4415	−0.792920
$875$	−4.15992	−0.140631
$876$	−32.0886	−1.08417
$877$	7.55258	0.255033	0.127516	−	0.991836i	$-0.459299\pi$
$877$	7.55258	0.255033	0.127516	+	0.991836i	$0.459299\pi$
$878$	6.58349	0.222182
$879$	−34.7399	−1.17175
$880$	−1.07742	−0.0363197
$881$	−25.3460	−0.853930	−0.426965	−	0.904268i	$-0.640417\pi$
$881$	−25.3460	−0.853930	−0.426965	+	0.904268i	$0.640417\pi$
$882$	−2.25032	−0.0757723
$883$	31.3999	1.05669	0.528345	−	0.849030i	$-0.322813\pi$
$883$	31.3999	1.05669	0.528345	+	0.849030i	$0.322813\pi$
$884$	−6.77050	−0.227717
$885$	2.96480	0.0996605
$886$	−4.50383	−0.151309
$887$	−1.87770	−0.0630470	−0.0315235	−	0.999503i	$-0.510036\pi$
$887$	−1.87770	−0.0630470	−0.0315235	+	0.999503i	$0.510036\pi$
$888$	7.92005	0.265779
$889$	9.68310	0.324761
$890$	−4.15390	−0.139239
$891$	45.5741	1.52679
$892$	−37.4425	−1.25367
$893$	57.2703	1.91648
$894$	−14.4249	−0.482442
$895$	−7.53131	−0.251744
$896$	−9.60214	−0.320785
$897$	5.53642	0.184856
$898$	−31.3123	−1.04490
$899$	0.599936	0.0200090
$900$	3.20992	0.106997
$901$	−64.5323	−2.14988
$902$	−0.651510	−0.0216929
$903$	−14.6762	−0.488392
$904$	25.1041	0.834951
$905$	−1.14463	−0.0380489
$906$	9.99729	0.332138
$907$	−42.5362	−1.41239	−0.706195	−	0.708017i	$-0.749590\pi$
$907$	−42.5362	−1.41239	−0.706195	+	0.708017i	$0.749590\pi$
$908$	−26.3611	−0.874823
$909$	−7.73030	−0.256398
$910$	0.249367	0.00826644
$911$	36.6912	1.21563	0.607817	−	0.794077i	$-0.292045\pi$
$911$	36.6912	1.21563	0.607817	+	0.794077i	$0.292045\pi$
$912$	−8.44605	−0.279677
$913$	9.73784	0.322275
$914$	−17.2015	−0.568975
$915$	5.62761	0.186043
$916$	−0.222335	−0.00734614
$917$	−2.13747	−0.0705853
$918$	−24.8339	−0.819642
$919$	−26.1608	−0.862966	−0.431483	−	0.902121i	$-0.642010\pi$
$919$	−26.1608	−0.862966	−0.431483	+	0.902121i	$0.642010\pi$
$920$	−4.21594	−0.138995
$921$	21.9177	0.722212
$922$	17.8208	0.586897
$923$	−7.77945	−0.256064
$924$	12.2064	0.401562
$925$	7.68081	0.252544
$926$	−29.3538	−0.964625
$927$	−2.69773	−0.0886049
$928$	−5.83865	−0.191663
$929$	7.09976	0.232935	0.116468	−	0.993194i	$-0.462843\pi$
$929$	7.09976	0.232935	0.116468	+	0.993194i	$0.462843\pi$
$930$	−0.350975	−0.0115089
$931$	43.2606	1.41781
$932$	−8.62240	−0.282436
$933$	−11.7483	−0.384622
$934$	25.0690	0.820284
$935$	−11.7157	−0.383144
$936$	−0.962269	−0.0314527
$937$	10.9234	0.356852	0.178426	−	0.983953i	$-0.442900\pi$
$937$	10.9234	0.356852	0.178426	+	0.983953i	$0.442900\pi$
$938$	5.27930	0.172375
$939$	−57.8960	−1.88937
$940$	4.18546	0.136515
$941$	8.65522	0.282152	0.141076	−	0.989999i	$-0.454944\pi$
$941$	8.65522	0.282152	0.141076	+	0.989999i	$0.454944\pi$
$942$	3.28853	0.107146
$943$	0.734191	0.0239085
$944$	2.46454	0.0802140
$945$	−1.98449	−0.0645554
$946$	26.0115	0.845708
$947$	−0.570697	−0.0185452	−0.00927258	−	0.999957i	$-0.502952\pi$
$947$	−0.570697	−0.0185452	−0.00927258	+	0.999957i	$0.502952\pi$
$948$	16.2050	0.526314
$949$	9.32896	0.302831
$950$	28.4418	0.922773
$951$	10.4324	0.338295
$952$	−19.0800	−0.618387
$953$	10.2219	0.331120	0.165560	−	0.986200i	$-0.447057\pi$
$953$	10.2219	0.331120	0.165560	+	0.986200i	$0.447057\pi$
$954$	−3.72698	−0.120665
$955$	−5.74572	−0.185927
$956$	−38.8372	−1.25608
$957$	8.32534	0.269120
$958$	20.7809	0.671401
$959$	−2.66042	−0.0859095
$960$	2.51397	0.0811379
$961$	−30.6401	−0.988390
$962$	−0.935651	−0.0301666
$963$	3.72132	0.119918
$964$	40.5191	1.30503
$965$	3.47850	0.111977
$966$	6.34003	0.203987
$967$	22.2021	0.713972	0.356986	−	0.934110i	$-0.383804\pi$
$967$	22.2021	0.713972	0.356986	+	0.934110i	$0.383804\pi$
$968$	−23.8021	−0.765028
$969$	−91.8414	−2.95037
$970$	0.0547997	0.00175951
$971$	21.1017	0.677185	0.338593	−	0.940933i	$-0.390049\pi$
$971$	21.1017	0.677185	0.338593	+	0.940933i	$0.390049\pi$
$972$	6.82220	0.218822
$973$	−1.07098	−0.0343339
$974$	−32.5334	−1.04244
$975$	−6.71739	−0.215129
$976$	4.67806	0.149741
$977$	23.8134	0.761858	0.380929	−	0.924604i	$-0.375604\pi$
$977$	23.8134	0.761858	0.380929	+	0.924604i	$0.375604\pi$
$978$	32.6632	1.04445
$979$	59.1136	1.88928
$980$	3.16159	0.100993
$981$	−3.81286	−0.121735
$982$	28.9961	0.925304
$983$	20.4025	0.650738	0.325369	−	0.945587i	$-0.394511\pi$
$983$	20.4025	0.650738	0.325369	+	0.945587i	$0.394511\pi$
$984$	−0.918547	−0.0292822
$985$	−1.47675	−0.0470531
$986$	−5.28806	−0.168406
$987$	−15.4895	−0.493035
$988$	7.51706	0.239150
$989$	−29.3126	−0.932085
$990$	−0.676624	−0.0215045
$991$	7.52367	0.238997	0.119499	−	0.992834i	$-0.461871\pi$
$991$	7.52367	0.238997	0.119499	+	0.992834i	$0.461871\pi$
$992$	−3.50281	−0.111214
$993$	−33.5558	−1.06486
$994$	−8.90865	−0.282565
$995$	−1.70871	−0.0541699
$996$	5.57888	0.176773
$997$	−31.0264	−0.982617	−0.491309	−	0.870986i	$-0.663481\pi$
$997$	−31.0264	−0.982617	−0.491309	+	0.870986i	$0.663481\pi$
$998$	27.6399	0.874926
$999$	7.44600	0.235581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.c.1.39	✓	61

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.c.1.39	✓	61	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q+0.794348 q^{2} +1.86655 q^{3} -1.36901 q^{4} +0.394566 q^{5} +1.48269 q^{6} +1.07098 q^{7} -2.67617 q^{8} +0.484010 q^{9} +O(q^{10})\)	\(q+0.794348 q^{2} +1.86655 q^{3} -1.36901 q^{4} +0.394566 q^{5} +1.48269 q^{6} +1.07098 q^{7} -2.67617 q^{8} +0.484010 q^{9} +0.313423 q^{10} -4.46028 q^{11} -2.55533 q^{12} +0.742897 q^{13} +0.850728 q^{14} +0.736478 q^{15} +0.612211 q^{16} +6.65711 q^{17} +0.384473 q^{18} -7.39117 q^{19} -0.540165 q^{20} +1.99903 q^{21} -3.54302 q^{22} +3.99265 q^{23} -4.99520 q^{24} -4.84432 q^{25} +0.590119 q^{26} -4.69622 q^{27} -1.46618 q^{28} -1.00000 q^{29} +0.585020 q^{30} -0.599936 q^{31} +5.83865 q^{32} -8.32534 q^{33} +5.28806 q^{34} +0.422571 q^{35} -0.662615 q^{36} -1.58553 q^{37} -5.87116 q^{38} +1.38665 q^{39} -1.05593 q^{40} +0.183886 q^{41} +1.58793 q^{42} -7.34164 q^{43} +6.10617 q^{44} +0.190974 q^{45} +3.17155 q^{46} -7.74848 q^{47} +1.14272 q^{48} -5.85301 q^{49} -3.84808 q^{50} +12.4258 q^{51} -1.01703 q^{52} -9.69374 q^{53} -3.73044 q^{54} -1.75988 q^{55} -2.86611 q^{56} -13.7960 q^{57} -0.794348 q^{58} +4.02564 q^{59} -1.00825 q^{60} +7.64125 q^{61} -0.476558 q^{62} +0.518363 q^{63} +3.41350 q^{64} +0.293122 q^{65} -6.61322 q^{66} +6.20563 q^{67} -9.11365 q^{68} +7.45248 q^{69} +0.335669 q^{70} -10.4718 q^{71} -1.29529 q^{72} +12.5575 q^{73} -1.25946 q^{74} -9.04216 q^{75} +10.1186 q^{76} -4.77685 q^{77} +1.10149 q^{78} -6.34166 q^{79} +0.241558 q^{80} -10.2178 q^{81} +0.146069 q^{82} -2.18323 q^{83} -2.73669 q^{84} +2.62667 q^{85} -5.83182 q^{86} -1.86655 q^{87} +11.9365 q^{88} -13.2533 q^{89} +0.151700 q^{90} +0.795624 q^{91} -5.46597 q^{92} -1.11981 q^{93} -6.15499 q^{94} -2.91631 q^{95} +10.8981 q^{96} +0.174843 q^{97} -4.64933 q^{98} -2.15882 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9}+O(q^{10}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9	\( 61 q - q^{2} - 4 q^{3} + 43 q^{4} - 7 q^{5} - 13 q^{6} - 10 q^{7} - 6 q^{8} + 23 q^{9} - 16 q^{10} - 3 q^{11} - 18 q^{12} - 28 q^{13} - 14 q^{14} - 12 q^{15} + 11 q^{16} - 21 q^{17} - 17 q^{18} - 36 q^{19} - 16 q^{20} - 12 q^{21} - 42 q^{22} - 15 q^{23} - 28 q^{24} - 16 q^{25} - 13 q^{26} - 10 q^{27} - 25 q^{28} - 61 q^{29} - 12 q^{30} - 18 q^{31} - 3 q^{32} - 42 q^{33} - 22 q^{34} - 29 q^{35} - 38 q^{36} - 30 q^{37} - 27 q^{38} - 31 q^{39} - 22 q^{40} - 28 q^{41} - 9 q^{42} - 58 q^{43} - 2 q^{44} - 31 q^{45} - 40 q^{46} - 6 q^{47} - 37 q^{48} - 37 q^{49} - 15 q^{50} - 44 q^{51} - 43 q^{52} - 27 q^{53} - 18 q^{54} - 38 q^{55} - 22 q^{56} - 50 q^{57} + q^{58} - 24 q^{59} + 6 q^{60} - 76 q^{61} - 17 q^{62} - 6 q^{63} - 60 q^{64} - 65 q^{65} - 7 q^{66} - 45 q^{67} - 31 q^{68} - 16 q^{69} - 48 q^{70} - 28 q^{71} - 40 q^{72} - 50 q^{73} - 17 q^{74} - 35 q^{75} - 100 q^{76} + q^{77} - 6 q^{78} - 66 q^{79} - 10 q^{80} - 63 q^{81} - 5 q^{82} - 9 q^{83} - 24 q^{84} - 77 q^{85} + 29 q^{86} + 4 q^{87} - 62 q^{88} - 30 q^{89} + 50 q^{90} - 52 q^{91} - 53 q^{92} - 42 q^{93} - 92 q^{94} - 20 q^{95} - 47 q^{96} - 34 q^{97} + 36 q^{98} - 29 q^{99}+O(q^{100}) \) 61 * q - q^2 - 4 * q^3 + 43 * q^4 - 7 * q^5 - 13 * q^6 - 10 * q^7 - 6 * q^8 + 23 * q^9 - 16 * q^10 - 3 * q^11 - 18 * q^12 - 28 * q^13 - 14 * q^14 - 12 * q^15 + 11 * q^16 - 21 * q^17 - 17 * q^18 - 36 * q^19 - 16 * q^20 - 12 * q^21 - 42 * q^22 - 15 * q^23 - 28 * q^24 - 16 * q^25 - 13 * q^26 - 10 * q^27 - 25 * q^28 - 61 * q^29 - 12 * q^30 - 18 * q^31 - 3 * q^32 - 42 * q^33 - 22 * q^34 - 29 * q^35 - 38 * q^36 - 30 * q^37 - 27 * q^38 - 31 * q^39 - 22 * q^40 - 28 * q^41 - 9 * q^42 - 58 * q^43 - 2 * q^44 - 31 * q^45 - 40 * q^46 - 6 * q^47 - 37 * q^48 - 37 * q^49 - 15 * q^50 - 44 * q^51 - 43 * q^52 - 27 * q^53 - 18 * q^54 - 38 * q^55 - 22 * q^56 - 50 * q^57 + q^58 - 24 * q^59 + 6 * q^60 - 76 * q^61 - 17 * q^62 - 6 * q^63 - 60 * q^64 - 65 * q^65 - 7 * q^66 - 45 * q^67 - 31 * q^68 - 16 * q^69 - 48 * q^70 - 28 * q^71 - 40 * q^72 - 50 * q^73 - 17 * q^74 - 35 * q^75 - 100 * q^76 + q^77 - 6 * q^78 - 66 * q^79 - 10 * q^80 - 63 * q^81 - 5 * q^82 - 9 * q^83 - 24 * q^84 - 77 * q^85 + 29 * q^86 + 4 * q^87 - 62 * q^88 - 30 * q^89 + 50 * q^90 - 52 * q^91 - 53 * q^92 - 42 * q^93 - 92 * q^94 - 20 * q^95 - 47 * q^96 - 34 * q^97 + 36 * q^98 - 29 * q^99

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