LMFDB - Embedded newform 4029.2.a.i.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.94224 q^{2} -1.00000 q^{3} +1.77230 q^{4} +1.77354 q^{5} +1.94224 q^{6} -4.05542 q^{7} +0.442253 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.94224 q^{2} -1.00000 q^{3} +1.77230 q^{4} +1.77354 q^{5} +1.94224 q^{6} -4.05542 q^{7} +0.442253 q^{8} +1.00000 q^{9} -3.44464 q^{10} +5.02900 q^{11} -1.77230 q^{12} -4.49993 q^{13} +7.87661 q^{14} -1.77354 q^{15} -4.40356 q^{16} +1.00000 q^{17} -1.94224 q^{18} -4.73585 q^{19} +3.14324 q^{20} +4.05542 q^{21} -9.76753 q^{22} -3.67449 q^{23} -0.442253 q^{24} -1.85456 q^{25} +8.73995 q^{26} -1.00000 q^{27} -7.18742 q^{28} +4.05477 q^{29} +3.44464 q^{30} -0.227238 q^{31} +7.66826 q^{32} -5.02900 q^{33} -1.94224 q^{34} -7.19245 q^{35} +1.77230 q^{36} -2.78710 q^{37} +9.19816 q^{38} +4.49993 q^{39} +0.784352 q^{40} +0.691622 q^{41} -7.87661 q^{42} +9.43158 q^{43} +8.91289 q^{44} +1.77354 q^{45} +7.13675 q^{46} +3.75516 q^{47} +4.40356 q^{48} +9.44645 q^{49} +3.60200 q^{50} -1.00000 q^{51} -7.97522 q^{52} -9.51033 q^{53} +1.94224 q^{54} +8.91914 q^{55} -1.79352 q^{56} +4.73585 q^{57} -7.87534 q^{58} +9.47831 q^{59} -3.14324 q^{60} -5.98076 q^{61} +0.441350 q^{62} -4.05542 q^{63} -6.08649 q^{64} -7.98081 q^{65} +9.76753 q^{66} -9.65663 q^{67} +1.77230 q^{68} +3.67449 q^{69} +13.9695 q^{70} -5.89355 q^{71} +0.442253 q^{72} -0.250945 q^{73} +5.41322 q^{74} +1.85456 q^{75} -8.39333 q^{76} -20.3947 q^{77} -8.73995 q^{78} -1.00000 q^{79} -7.80988 q^{80} +1.00000 q^{81} -1.34330 q^{82} +10.8628 q^{83} +7.18742 q^{84} +1.77354 q^{85} -18.3184 q^{86} -4.05477 q^{87} +2.22409 q^{88} +12.1666 q^{89} -3.44464 q^{90} +18.2491 q^{91} -6.51230 q^{92} +0.227238 q^{93} -7.29343 q^{94} -8.39921 q^{95} -7.66826 q^{96} -4.25029 q^{97} -18.3473 q^{98} +5.02900 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) $ 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * 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 $

$2$	−1.94224	−1.37337	−0.686686	−	0.726954i	$-0.740935\pi$
$2$	−1.94224	−1.37337	−0.686686	+	0.726954i	$0.740935\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.77230	0.886149
$5$	1.77354	0.793151	0.396575	−	0.918002i	$-0.370199\pi$
$5$	1.77354	0.793151	0.396575	+	0.918002i	$0.370199\pi$
$6$	1.94224	0.792916
$7$	−4.05542	−1.53281	−0.766403	−	0.642360i	$-0.777955\pi$
$7$	−4.05542	−1.53281	−0.766403	+	0.642360i	$0.777955\pi$
$8$	0.442253	0.156360
$9$	1.00000	0.333333
$10$	−3.44464	−1.08929
$11$	5.02900	1.51630	0.758151	−	0.652079i	$-0.226103\pi$
$11$	5.02900	1.51630	0.758151	+	0.652079i	$0.226103\pi$
$12$	−1.77230	−0.511618
$13$	−4.49993	−1.24806	−0.624028	−	0.781402i	$-0.714505\pi$
$13$	−4.49993	−1.24806	−0.624028	+	0.781402i	$0.714505\pi$
$14$	7.87661	2.10511
$15$	−1.77354	−0.457926
$16$	−4.40356	−1.10089
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.94224	−0.457790
$19$	−4.73585	−1.08648	−0.543239	−	0.839578i	$-0.682802\pi$
$19$	−4.73585	−1.08648	−0.543239	+	0.839578i	$0.682802\pi$
$20$	3.14324	0.702850
$21$	4.05542	0.884966
$22$	−9.76753	−2.08245
$23$	−3.67449	−0.766185	−0.383092	−	0.923710i	$-0.625141\pi$
$23$	−3.67449	−0.766185	−0.383092	+	0.923710i	$0.625141\pi$
$24$	−0.442253	−0.0902744
$25$	−1.85456	−0.370912
$26$	8.73995	1.71405
$27$	−1.00000	−0.192450
$28$	−7.18742	−1.35829
$29$	4.05477	0.752952	0.376476	−	0.926426i	$-0.377136\pi$
$29$	4.05477	0.752952	0.376476	+	0.926426i	$0.377136\pi$
$30$	3.44464	0.628902
$31$	−0.227238	−0.0408131	−0.0204065	−	0.999792i	$-0.506496\pi$
$31$	−0.227238	−0.0408131	−0.0204065	+	0.999792i	$0.506496\pi$
$32$	7.66826	1.35557
$33$	−5.02900	−0.875437
$34$	−1.94224	−0.333091
$35$	−7.19245	−1.21575
$36$	1.77230	0.295383
$37$	−2.78710	−0.458196	−0.229098	−	0.973403i	$-0.573578\pi$
$37$	−2.78710	−0.458196	−0.229098	+	0.973403i	$0.573578\pi$
$38$	9.19816	1.49214
$39$	4.49993	0.720566
$40$	0.784352	0.124017
$41$	0.691622	0.108013	0.0540066	−	0.998541i	$-0.482801\pi$
$41$	0.691622	0.108013	0.0540066	+	0.998541i	$0.482801\pi$
$42$	−7.87661	−1.21539
$43$	9.43158	1.43830	0.719151	−	0.694854i	$-0.244531\pi$
$43$	9.43158	1.43830	0.719151	+	0.694854i	$0.244531\pi$
$44$	8.91289	1.34367
$45$	1.77354	0.264384
$46$	7.13675	1.05226
$47$	3.75516	0.547747	0.273873	−	0.961766i	$-0.411695\pi$
$47$	3.75516	0.547747	0.273873	+	0.961766i	$0.411695\pi$
$48$	4.40356	0.635599
$49$	9.44645	1.34949
$50$	3.60200	0.509399
$51$	−1.00000	−0.140028
$52$	−7.97522	−1.10596
$53$	−9.51033	−1.30634	−0.653172	−	0.757209i	$-0.726562\pi$
$53$	−9.51033	−1.30634	−0.653172	+	0.757209i	$0.726562\pi$
$54$	1.94224	0.264305
$55$	8.91914	1.20266
$56$	−1.79352	−0.239669
$57$	4.73585	0.627278
$58$	−7.87534	−1.03408
$59$	9.47831	1.23397	0.616985	−	0.786975i	$-0.288354\pi$
$59$	9.47831	1.23397	0.616985	+	0.786975i	$0.288354\pi$
$60$	−3.14324	−0.405790
$61$	−5.98076	−0.765758	−0.382879	−	0.923798i	$-0.625067\pi$
$61$	−5.98076	−0.765758	−0.382879	+	0.923798i	$0.625067\pi$
$62$	0.441350	0.0560515
$63$	−4.05542	−0.510935
$64$	−6.08649	−0.760811
$65$	−7.98081	−0.989897
$66$	9.76753	1.20230
$67$	−9.65663	−1.17974	−0.589872	−	0.807497i	$-0.700822\pi$
$67$	−9.65663	−1.17974	−0.589872	+	0.807497i	$0.700822\pi$
$68$	1.77230	0.214923
$69$	3.67449	0.442357
$70$	13.9695	1.66967
$71$	−5.89355	−0.699435	−0.349718	−	0.936855i	$-0.613722\pi$
$71$	−5.89355	−0.699435	−0.349718	+	0.936855i	$0.613722\pi$
$72$	0.442253	0.0521200
$73$	−0.250945	−0.0293709	−0.0146854	−	0.999892i	$-0.504675\pi$
$73$	−0.250945	−0.0293709	−0.0146854	+	0.999892i	$0.504675\pi$
$74$	5.41322	0.629274
$75$	1.85456	0.214146
$76$	−8.39333	−0.962781
$77$	−20.3947	−2.32420
$78$	−8.73995	−0.989604
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	−7.80988	−0.873171
$81$	1.00000	0.111111
$82$	−1.34330	−0.148342
$83$	10.8628	1.19235	0.596176	−	0.802854i	$-0.296686\pi$
$83$	10.8628	1.19235	0.596176	+	0.802854i	$0.296686\pi$
$84$	7.18742	0.784211
$85$	1.77354	0.192367
$86$	−18.3184	−1.97532
$87$	−4.05477	−0.434717
$88$	2.22409	0.237089
$89$	12.1666	1.28965	0.644826	−	0.764329i	$-0.276930\pi$
$89$	12.1666	1.28965	0.644826	+	0.764329i	$0.276930\pi$
$90$	−3.44464	−0.363097
$91$	18.2491	1.91303
$92$	−6.51230	−0.678954
$93$	0.227238	0.0235634
$94$	−7.29343	−0.752260
$95$	−8.39921	−0.861741
$96$	−7.66826	−0.782638
$97$	−4.25029	−0.431551	−0.215776	−	0.976443i	$-0.569228\pi$
$97$	−4.25029	−0.431551	−0.215776	+	0.976443i	$0.569228\pi$
$98$	−18.3473	−1.85336
$99$	5.02900	0.505434
$100$	−3.28683	−0.328683
$101$	−1.67318	−0.166488	−0.0832440	−	0.996529i	$-0.526528\pi$
$101$	−1.67318	−0.166488	−0.0832440	+	0.996529i	$0.526528\pi$
$102$	1.94224	0.192310
$103$	0.0939879	0.00926090	0.00463045	−	0.999989i	$-0.498526\pi$
$103$	0.0939879	0.00926090	0.00463045	+	0.999989i	$0.498526\pi$
$104$	−1.99011	−0.195146
$105$	7.19245	0.701911
$106$	18.4714	1.79410
$107$	3.47987	0.336411	0.168206	−	0.985752i	$-0.446203\pi$
$107$	3.47987	0.336411	0.168206	+	0.985752i	$0.446203\pi$
$108$	−1.77230	−0.170539
$109$	0.691770	0.0662595	0.0331298	−	0.999451i	$-0.489453\pi$
$109$	0.691770	0.0662595	0.0331298	+	0.999451i	$0.489453\pi$
$110$	−17.3231	−1.65169
$111$	2.78710	0.264540
$112$	17.8583	1.68745
$113$	5.61631	0.528338	0.264169	−	0.964476i	$-0.414902\pi$
$113$	5.61631	0.528338	0.264169	+	0.964476i	$0.414902\pi$
$114$	−9.19816	−0.861486
$115$	−6.51686	−0.607700
$116$	7.18626	0.667227
$117$	−4.49993	−0.416019
$118$	−18.4091	−1.69470
$119$	−4.05542	−0.371760
$120$	−0.784352	−0.0716012
$121$	14.2909	1.29917
$122$	11.6161	1.05167
$123$	−0.691622	−0.0623614
$124$	−0.402733	−0.0361665
$125$	−12.1568	−1.08734
$126$	7.87661	0.701704
$127$	4.67968	0.415254	0.207627	−	0.978208i	$-0.433426\pi$
$127$	4.67968	0.415254	0.207627	+	0.978208i	$0.433426\pi$
$128$	−3.51509	−0.310693
$129$	−9.43158	−0.830404
$130$	15.5006	1.35950
$131$	4.50267	0.393400	0.196700	−	0.980464i	$-0.436978\pi$
$131$	4.50267	0.393400	0.196700	+	0.980464i	$0.436978\pi$
$132$	−8.91289	−0.775768
$133$	19.2059	1.66536
$134$	18.7555	1.62023
$135$	−1.77354	−0.152642
$136$	0.442253	0.0379228
$137$	−1.69138	−0.144504	−0.0722520	−	0.997386i	$-0.523019\pi$
$137$	−1.69138	−0.144504	−0.0722520	+	0.997386i	$0.523019\pi$
$138$	−7.13675	−0.607521
$139$	14.3151	1.21419	0.607096	−	0.794629i	$-0.292334\pi$
$139$	14.3151	1.21419	0.607096	+	0.794629i	$0.292334\pi$
$140$	−12.7472	−1.07733
$141$	−3.75516	−0.316242
$142$	11.4467	0.960584
$143$	−22.6302	−1.89243
$144$	−4.40356	−0.366963
$145$	7.19129	0.597204
$146$	0.487396	0.0403371
$147$	−9.44645	−0.779130
$148$	−4.93957	−0.406030
$149$	−13.5295	−1.10838	−0.554192	−	0.832389i	$-0.686973\pi$
$149$	−13.5295	−1.10838	−0.554192	+	0.832389i	$0.686973\pi$
$150$	−3.60200	−0.294102
$151$	−21.9064	−1.78272	−0.891359	−	0.453298i	$-0.850247\pi$
$151$	−21.9064	−1.78272	−0.891359	+	0.453298i	$0.850247\pi$
$152$	−2.09444	−0.169882
$153$	1.00000	0.0808452
$154$	39.6115	3.19198
$155$	−0.403015	−0.0323709
$156$	7.97522	0.638529
$157$	−16.3018	−1.30103	−0.650514	−	0.759494i	$-0.725447\pi$
$157$	−16.3018	−1.30103	−0.650514	+	0.759494i	$0.725447\pi$
$158$	1.94224	0.154516
$159$	9.51033	0.754219
$160$	13.6000	1.07517
$161$	14.9016	1.17441
$162$	−1.94224	−0.152597
$163$	20.1839	1.58092	0.790462	−	0.612511i	$-0.209841\pi$
$163$	20.1839	1.58092	0.790462	+	0.612511i	$0.209841\pi$
$164$	1.22576	0.0957157
$165$	−8.91914	−0.694354
$166$	−21.0983	−1.63754
$167$	7.12575	0.551407	0.275704	−	0.961243i	$-0.411089\pi$
$167$	7.12575	0.551407	0.275704	+	0.961243i	$0.411089\pi$
$168$	1.79352	0.138373
$169$	7.24939	0.557645
$170$	−3.44464	−0.264192
$171$	−4.73585	−0.362159
$172$	16.7156	1.27455
$173$	−14.4344	−1.09743	−0.548715	−	0.836009i	$-0.684883\pi$
$173$	−14.4344	−1.09743	−0.548715	+	0.836009i	$0.684883\pi$
$174$	7.87534	0.597028
$175$	7.52102	0.568536
$176$	−22.1455	−1.66928
$177$	−9.47831	−0.712433
$178$	−23.6304	−1.77117
$179$	18.0199	1.34687	0.673434	−	0.739247i	$-0.264818\pi$
$179$	18.0199	1.34687	0.673434	+	0.739247i	$0.264818\pi$
$180$	3.14324	0.234283
$181$	18.2588	1.35716	0.678582	−	0.734525i	$-0.262595\pi$
$181$	18.2588	1.35716	0.678582	+	0.734525i	$0.262595\pi$
$182$	−35.4442	−2.62730
$183$	5.98076	0.442111
$184$	−1.62505	−0.119801
$185$	−4.94303	−0.363419
$186$	−0.441350	−0.0323614
$187$	5.02900	0.367757
$188$	6.65527	0.485385
$189$	4.05542	0.294989
$190$	16.3133	1.18349
$191$	−0.200006	−0.0144719	−0.00723596	−	0.999974i	$-0.502303\pi$
$191$	−0.200006	−0.0144719	−0.00723596	+	0.999974i	$0.502303\pi$
$192$	6.08649	0.439255
$193$	−18.9252	−1.36226	−0.681132	−	0.732160i	$-0.738512\pi$
$193$	−18.9252	−1.36226	−0.681132	+	0.732160i	$0.738512\pi$
$194$	8.25508	0.592680
$195$	7.98081	0.571517
$196$	16.7419	1.19585
$197$	−15.2856	−1.08905	−0.544527	−	0.838743i	$-0.683291\pi$
$197$	−15.2856	−1.08905	−0.544527	+	0.838743i	$0.683291\pi$
$198$	−9.76753	−0.694148
$199$	−11.1860	−0.792957	−0.396479	−	0.918044i	$-0.629768\pi$
$199$	−11.1860	−0.792957	−0.396479	+	0.918044i	$0.629768\pi$
$200$	−0.820183	−0.0579957
$201$	9.65663	0.681126
$202$	3.24973	0.228650
$203$	−16.4438	−1.15413
$204$	−1.77230	−0.124086
$205$	1.22662	0.0856707
$206$	−0.182547	−0.0127187
$207$	−3.67449	−0.255395
$208$	19.8157	1.37397
$209$	−23.8166	−1.64743
$210$	−13.9695	−0.963985
$211$	17.7268	1.22037	0.610183	−	0.792260i	$-0.291096\pi$
$211$	17.7268	1.22037	0.610183	+	0.792260i	$0.291096\pi$
$212$	−16.8551	−1.15762
$213$	5.89355	0.403819
$214$	−6.75873	−0.462018
$215$	16.7273	1.14079
$216$	−0.442253	−0.0300915
$217$	0.921545	0.0625585
$218$	−1.34358	−0.0909989
$219$	0.250945	0.0169573
$220$	15.8074	1.06573
$221$	−4.49993	−0.302698
$222$	−5.41322	−0.363311
$223$	−25.9490	−1.73767	−0.868836	−	0.495101i	$-0.835131\pi$
$223$	−25.9490	−1.73767	−0.868836	+	0.495101i	$0.835131\pi$
$224$	−31.0980	−2.07782
$225$	−1.85456	−0.123637
$226$	−10.9082	−0.725604
$227$	17.3806	1.15359	0.576795	−	0.816889i	$-0.304303\pi$
$227$	17.3806	1.15359	0.576795	+	0.816889i	$0.304303\pi$
$228$	8.39333	0.555862
$229$	−5.79110	−0.382687	−0.191343	−	0.981523i	$-0.561284\pi$
$229$	−5.79110	−0.382687	−0.191343	+	0.981523i	$0.561284\pi$
$230$	12.6573	0.834598
$231$	20.3947	1.34188
$232$	1.79323	0.117731
$233$	−3.81240	−0.249759	−0.124879	−	0.992172i	$-0.539854\pi$
$233$	−3.81240	−0.249759	−0.124879	+	0.992172i	$0.539854\pi$
$234$	8.73995	0.571348
$235$	6.65993	0.434446
$236$	16.7984	1.09348
$237$	1.00000	0.0649570
$238$	7.87661	0.510565
$239$	23.6885	1.53228	0.766140	−	0.642673i	$-0.222175\pi$
$239$	23.6885	1.53228	0.766140	+	0.642673i	$0.222175\pi$
$240$	7.80988	0.504126
$241$	15.0822	0.971529	0.485764	−	0.874090i	$-0.338541\pi$
$241$	15.0822	0.971529	0.485764	+	0.874090i	$0.338541\pi$
$242$	−27.7563	−1.78424
$243$	−1.00000	−0.0641500
$244$	−10.5997	−0.678576
$245$	16.7537	1.07035
$246$	1.34330	0.0856454
$247$	21.3110	1.35599
$248$	−0.100496	−0.00638153
$249$	−10.8628	−0.688405
$250$	23.6115	1.49332
$251$	−4.78626	−0.302106	−0.151053	−	0.988526i	$-0.548266\pi$
$251$	−4.78626	−0.302106	−0.151053	+	0.988526i	$0.548266\pi$
$252$	−7.18742	−0.452765
$253$	−18.4790	−1.16177
$254$	−9.08906	−0.570299
$255$	−1.77354	−0.111063
$256$	19.0001	1.18751
$257$	31.3372	1.95476	0.977379	−	0.211495i	$-0.0678331\pi$
$257$	31.3372	1.95476	0.977379	+	0.211495i	$0.0678331\pi$
$258$	18.3184	1.14045
$259$	11.3029	0.702326
$260$	−14.1444	−0.877196
$261$	4.05477	0.250984
$262$	−8.74526	−0.540284
$263$	13.0083	0.802125	0.401062	−	0.916051i	$-0.368641\pi$
$263$	13.0083	0.802125	0.401062	+	0.916051i	$0.368641\pi$
$264$	−2.22409	−0.136883
$265$	−16.8670	−1.03613
$266$	−37.3024	−2.28716
$267$	−12.1666	−0.744581
$268$	−17.1144	−1.04543
$269$	16.5998	1.01211	0.506055	−	0.862501i	$-0.331103\pi$
$269$	16.5998	1.01211	0.506055	+	0.862501i	$0.331103\pi$
$270$	3.44464	0.209634
$271$	17.8032	1.08147	0.540733	−	0.841194i	$-0.318147\pi$
$271$	17.8032	1.08147	0.540733	+	0.841194i	$0.318147\pi$
$272$	−4.40356	−0.267005
$273$	−18.2491	−1.10449
$274$	3.28506	0.198458
$275$	−9.32658	−0.562414
$276$	6.51230	0.391994
$277$	−26.2189	−1.57534	−0.787672	−	0.616095i	$-0.788714\pi$
$277$	−26.2189	−1.57534	−0.787672	+	0.616095i	$0.788714\pi$
$278$	−27.8034	−1.66754
$279$	−0.227238	−0.0136044
$280$	−3.18088	−0.190094
$281$	7.37463	0.439933	0.219967	−	0.975507i	$-0.429405\pi$
$281$	7.37463	0.439933	0.219967	+	0.975507i	$0.429405\pi$
$282$	7.29343	0.434317
$283$	−3.39597	−0.201870	−0.100935	−	0.994893i	$-0.532183\pi$
$283$	−3.39597	−0.201870	−0.100935	+	0.994893i	$0.532183\pi$
$284$	−10.4451	−0.619804
$285$	8.39921	0.497526
$286$	43.9532	2.59901
$287$	−2.80482	−0.165563
$288$	7.66826	0.451857
$289$	1.00000	0.0588235
$290$	−13.9672	−0.820183
$291$	4.25029	0.249156
$292$	−0.444749	−0.0260270
$293$	22.5779	1.31902	0.659508	−	0.751697i	$-0.270765\pi$
$293$	22.5779	1.31902	0.659508	+	0.751697i	$0.270765\pi$
$294$	18.3473	1.07004
$295$	16.8101	0.978725
$296$	−1.23260	−0.0716435
$297$	−5.02900	−0.291812
$298$	26.2776	1.52222
$299$	16.5350	0.956242
$300$	3.28683	0.189765
$301$	−38.2490	−2.20464
$302$	42.5475	2.44833
$303$	1.67318	0.0961219
$304$	20.8546	1.19609
$305$	−10.6071	−0.607362
$306$	−1.94224	−0.111030
$307$	−15.2407	−0.869831	−0.434916	−	0.900471i	$-0.643222\pi$
$307$	−15.2407	−0.869831	−0.434916	+	0.900471i	$0.643222\pi$
$308$	−36.1455	−2.05958
$309$	−0.0939879	−0.00534679
$310$	0.782752	0.0444573
$311$	−19.3425	−1.09681	−0.548406	−	0.836212i	$-0.684765\pi$
$311$	−19.3425	−1.09681	−0.548406	+	0.836212i	$0.684765\pi$
$312$	1.99011	0.112668
$313$	−14.0929	−0.796579	−0.398289	−	0.917260i	$-0.630396\pi$
$313$	−14.0929	−0.796579	−0.398289	+	0.917260i	$0.630396\pi$
$314$	31.6621	1.78679
$315$	−7.19245	−0.405249
$316$	−1.77230	−0.0996995
$317$	20.5059	1.15172	0.575862	−	0.817547i	$-0.304666\pi$
$317$	20.5059	1.15172	0.575862	+	0.817547i	$0.304666\pi$
$318$	−18.4714	−1.03582
$319$	20.3914	1.14170
$320$	−10.7946	−0.603438
$321$	−3.47987	−0.194227
$322$	−28.9425	−1.61290
$323$	−4.73585	−0.263510
$324$	1.77230	0.0984610
$325$	8.34539	0.462919
$326$	−39.2020	−2.17120
$327$	−0.691770	−0.0382550
$328$	0.305871	0.0168889
$329$	−15.2288	−0.839589
$330$	17.3231	0.953606
$331$	25.0566	1.37724	0.688619	−	0.725123i	$-0.258217\pi$
$331$	25.0566	1.37724	0.688619	+	0.725123i	$0.258217\pi$
$332$	19.2522	1.05660
$333$	−2.78710	−0.152732
$334$	−13.8399	−0.757287
$335$	−17.1264	−0.935715
$336$	−17.8583	−0.974249
$337$	22.2314	1.21102	0.605510	−	0.795838i	$-0.292969\pi$
$337$	22.2314	1.21102	0.605510	+	0.795838i	$0.292969\pi$
$338$	−14.0801	−0.765854
$339$	−5.61631	−0.305036
$340$	3.14324	0.170466
$341$	−1.14278	−0.0618849
$342$	9.19816	0.497379
$343$	−9.92140	−0.535705
$344$	4.17114	0.224893
$345$	6.51686	0.350856
$346$	28.0352	1.50718
$347$	8.52596	0.457698	0.228849	−	0.973462i	$-0.426504\pi$
$347$	8.52596	0.457698	0.228849	+	0.973462i	$0.426504\pi$
$348$	−7.18626	−0.385224
$349$	−15.3248	−0.820320	−0.410160	−	0.912014i	$-0.634527\pi$
$349$	−15.3248	−0.820320	−0.410160	+	0.912014i	$0.634527\pi$
$350$	−14.6076	−0.780810
$351$	4.49993	0.240189
$352$	38.5637	2.05545
$353$	2.14082	0.113944	0.0569722	−	0.998376i	$-0.481855\pi$
$353$	2.14082	0.113944	0.0569722	+	0.998376i	$0.481855\pi$
$354$	18.4091	0.978435
$355$	−10.4524	−0.554758
$356$	21.5628	1.14282
$357$	4.05542	0.214636
$358$	−34.9989	−1.84975
$359$	17.3997	0.918322	0.459161	−	0.888353i	$-0.348150\pi$
$359$	17.3997	0.918322	0.459161	+	0.888353i	$0.348150\pi$
$360$	0.784352	0.0413390
$361$	3.42826	0.180435
$362$	−35.4629	−1.86389
$363$	−14.2909	−0.750077
$364$	32.3429	1.69523
$365$	−0.445061	−0.0232956
$366$	−11.6161	−0.607182
$367$	9.45719	0.493661	0.246831	−	0.969059i	$-0.420611\pi$
$367$	9.45719	0.493661	0.246831	+	0.969059i	$0.420611\pi$
$368$	16.1808	0.843485
$369$	0.691622	0.0360044
$370$	9.60055	0.499109
$371$	38.5684	2.00237
$372$	0.402733	0.0208807
$373$	26.0859	1.35067	0.675337	−	0.737509i	$-0.263998\pi$
$373$	26.0859	1.35067	0.675337	+	0.737509i	$0.263998\pi$
$374$	−9.76753	−0.505067
$375$	12.1568	0.627776
$376$	1.66073	0.0856456
$377$	−18.2462	−0.939726
$378$	−7.87661	−0.405129
$379$	−2.61988	−0.134574	−0.0672872	−	0.997734i	$-0.521434\pi$
$379$	−2.61988	−0.134574	−0.0672872	+	0.997734i	$0.521434\pi$
$380$	−14.8859	−0.763631
$381$	−4.67968	−0.239747
$382$	0.388459	0.0198753
$383$	12.3240	0.629728	0.314864	−	0.949137i	$-0.398041\pi$
$383$	12.3240	0.629728	0.314864	+	0.949137i	$0.398041\pi$
$384$	3.51509	0.179379
$385$	−36.1709	−1.84344
$386$	36.7573	1.87089
$387$	9.43158	0.479434
$388$	−7.53278	−0.382419
$389$	1.53037	0.0775926	0.0387963	−	0.999247i	$-0.487648\pi$
$389$	1.53037	0.0775926	0.0387963	+	0.999247i	$0.487648\pi$
$390$	−15.5006	−0.784906
$391$	−3.67449	−0.185827
$392$	4.17772	0.211007
$393$	−4.50267	−0.227129
$394$	29.6883	1.49567
$395$	−1.77354	−0.0892364
$396$	8.91289	0.447890
$397$	20.6737	1.03758	0.518791	−	0.854901i	$-0.326382\pi$
$397$	20.6737	1.03758	0.518791	+	0.854901i	$0.326382\pi$
$398$	21.7260	1.08903
$399$	−19.2059	−0.961496
$400$	8.16665	0.408333
$401$	14.7198	0.735074	0.367537	−	0.930009i	$-0.380201\pi$
$401$	14.7198	0.735074	0.367537	+	0.930009i	$0.380201\pi$
$402$	−18.7555	−0.935439
$403$	1.02255	0.0509370
$404$	−2.96538	−0.147533
$405$	1.77354	0.0881279
$406$	31.9378	1.58505
$407$	−14.0163	−0.694764
$408$	−0.442253	−0.0218948
$409$	27.6521	1.36731	0.683653	−	0.729807i	$-0.260390\pi$
$409$	27.6521	1.36731	0.683653	+	0.729807i	$0.260390\pi$
$410$	−2.38239	−0.117658
$411$	1.69138	0.0834294
$412$	0.166575	0.00820654
$413$	−38.4385	−1.89144
$414$	7.13675	0.350752
$415$	19.2657	0.945715
$416$	−34.5066	−1.69183
$417$	−14.3151	−0.701014
$418$	46.2576	2.26253
$419$	−2.60570	−0.127297	−0.0636484	−	0.997972i	$-0.520274\pi$
$419$	−2.60570	−0.127297	−0.0636484	+	0.997972i	$0.520274\pi$
$420$	12.7472	0.621998
$421$	12.1816	0.593693	0.296847	−	0.954925i	$-0.404065\pi$
$421$	12.1816	0.593693	0.296847	+	0.954925i	$0.404065\pi$
$422$	−34.4298	−1.67602
$423$	3.75516	0.182582
$424$	−4.20597	−0.204260
$425$	−1.85456	−0.0899593
$426$	−11.4467	−0.554594
$427$	24.2545	1.17376
$428$	6.16736	0.298110
$429$	22.6302	1.09260
$430$	−32.4884	−1.56673
$431$	33.6630	1.62149	0.810745	−	0.585399i	$-0.199062\pi$
$431$	33.6630	1.62149	0.810745	+	0.585399i	$0.199062\pi$
$432$	4.40356	0.211866
$433$	6.35749	0.305521	0.152761	−	0.988263i	$-0.451184\pi$
$433$	6.35749	0.305521	0.152761	+	0.988263i	$0.451184\pi$
$434$	−1.78986	−0.0859161
$435$	−7.19129	−0.344796
$436$	1.22602	0.0587158
$437$	17.4018	0.832443
$438$	−0.487396	−0.0232887
$439$	15.0068	0.716237	0.358119	−	0.933676i	$-0.383418\pi$
$439$	15.0068	0.716237	0.358119	+	0.933676i	$0.383418\pi$
$440$	3.94451	0.188047
$441$	9.44645	0.449831
$442$	8.73995	0.415717
$443$	5.76302	0.273809	0.136905	−	0.990584i	$-0.456285\pi$
$443$	5.76302	0.273809	0.136905	+	0.990584i	$0.456285\pi$
$444$	4.93957	0.234422
$445$	21.5779	1.02289
$446$	50.3991	2.38647
$447$	13.5295	0.639925
$448$	24.6833	1.16618
$449$	35.5713	1.67871	0.839357	−	0.543580i	$-0.182932\pi$
$449$	35.5713	1.67871	0.839357	+	0.543580i	$0.182932\pi$
$450$	3.60200	0.169800
$451$	3.47817	0.163781
$452$	9.95377	0.468186
$453$	21.9064	1.02925
$454$	−33.7573	−1.58431
$455$	32.3655	1.51732
$456$	2.09444	0.0980812
$457$	−2.66428	−0.124630	−0.0623149	−	0.998057i	$-0.519848\pi$
$457$	−2.66428	−0.124630	−0.0623149	+	0.998057i	$0.519848\pi$
$458$	11.2477	0.525571
$459$	−1.00000	−0.0466760
$460$	−11.5498	−0.538513
$461$	20.5117	0.955325	0.477662	−	0.878544i	$-0.341484\pi$
$461$	20.5117	0.955325	0.477662	+	0.878544i	$0.341484\pi$
$462$	−39.6115	−1.84289
$463$	31.6383	1.47036	0.735178	−	0.677875i	$-0.237099\pi$
$463$	31.6383	1.47036	0.735178	+	0.677875i	$0.237099\pi$
$464$	−17.8554	−0.828916
$465$	0.403015	0.0186894
$466$	7.40461	0.343012
$467$	−4.53904	−0.210042	−0.105021	−	0.994470i	$-0.533491\pi$
$467$	−4.53904	−0.210042	−0.105021	+	0.994470i	$0.533491\pi$
$468$	−7.97522	−0.368655
$469$	39.1617	1.80832
$470$	−12.9352	−0.596655
$471$	16.3018	0.751149
$472$	4.19180	0.192943
$473$	47.4314	2.18090
$474$	−1.94224	−0.0892101
$475$	8.78291	0.402987
$476$	−7.18742	−0.329435
$477$	−9.51033	−0.435448
$478$	−46.0087	−2.10439
$479$	−34.6723	−1.58422	−0.792108	−	0.610381i	$-0.791017\pi$
$479$	−34.6723	−1.58422	−0.792108	+	0.610381i	$0.791017\pi$
$480$	−13.6000	−0.620750
$481$	12.5418	0.571855
$482$	−29.2932	−1.33427
$483$	−14.9016	−0.678047
$484$	25.3277	1.15126
$485$	−7.53805	−0.342285
$486$	1.94224	0.0881018
$487$	4.18890	0.189817	0.0949087	−	0.995486i	$-0.469744\pi$
$487$	4.18890	0.189817	0.0949087	+	0.995486i	$0.469744\pi$
$488$	−2.64501	−0.119734
$489$	−20.1839	−0.912747
$490$	−32.5396	−1.46999
$491$	−8.41634	−0.379824	−0.189912	−	0.981801i	$-0.560820\pi$
$491$	−8.41634	−0.379824	−0.189912	+	0.981801i	$0.560820\pi$
$492$	−1.22576	−0.0552615
$493$	4.05477	0.182618
$494$	−41.3911	−1.86227
$495$	8.91914	0.400885
$496$	1.00065	0.0449307
$497$	23.9008	1.07210
$498$	21.0983	0.945436
$499$	−25.8002	−1.15497	−0.577487	−	0.816400i	$-0.695966\pi$
$499$	−25.8002	−1.15497	−0.577487	+	0.816400i	$0.695966\pi$
$500$	−21.5455	−0.963545
$501$	−7.12575	−0.318355
$502$	9.29607	0.414904
$503$	27.1334	1.20982	0.604910	−	0.796294i	$-0.293209\pi$
$503$	27.1334	1.20982	0.604910	+	0.796294i	$0.293209\pi$
$504$	−1.79352	−0.0798898
$505$	−2.96746	−0.132050
$506$	35.8907	1.59554
$507$	−7.24939	−0.321957
$508$	8.29379	0.367977
$509$	25.1439	1.11448	0.557242	−	0.830350i	$-0.311860\pi$
$509$	25.1439	1.11448	0.557242	+	0.830350i	$0.311860\pi$
$510$	3.44464	0.152531
$511$	1.01769	0.0450199
$512$	−29.8726	−1.32020
$513$	4.73585	0.209093
$514$	−60.8643	−2.68461
$515$	0.166691	0.00734529
$516$	−16.7156	−0.735862
$517$	18.8847	0.830549
$518$	−21.9529	−0.964554
$519$	14.4344	0.633602
$520$	−3.52953	−0.154780
$521$	9.40929	0.412229	0.206114	−	0.978528i	$-0.433918\pi$
$521$	9.40929	0.412229	0.206114	+	0.978528i	$0.433918\pi$
$522$	−7.87534	−0.344694
$523$	1.60068	0.0699929	0.0349965	−	0.999387i	$-0.488858\pi$
$523$	1.60068	0.0699929	0.0349965	+	0.999387i	$0.488858\pi$
$524$	7.98006	0.348611
$525$	−7.52102	−0.328244
$526$	−25.2652	−1.10161
$527$	−0.227238	−0.00989863
$528$	22.1455	0.963759
$529$	−9.49810	−0.412961
$530$	32.7597	1.42299
$531$	9.47831	0.411323
$532$	34.0385	1.47576
$533$	−3.11225	−0.134807
$534$	23.6304	1.02259
$535$	6.17168	0.266825
$536$	−4.27067	−0.184465
$537$	−18.0199	−0.777615
$538$	−32.2408	−1.39000
$539$	47.5063	2.04624
$540$	−3.14324	−0.135263
$541$	−12.8174	−0.551062	−0.275531	−	0.961292i	$-0.588854\pi$
$541$	−12.8174	−0.551062	−0.275531	+	0.961292i	$0.588854\pi$
$542$	−34.5781	−1.48526
$543$	−18.2588	−0.783559
$544$	7.66826	0.328774
$545$	1.22688	0.0525538
$546$	35.4442	1.51687
$547$	−28.8831	−1.23495	−0.617476	−	0.786590i	$-0.711845\pi$
$547$	−28.8831	−1.23495	−0.617476	+	0.786590i	$0.711845\pi$
$548$	−2.99762	−0.128052
$549$	−5.98076	−0.255253
$550$	18.1145	0.772403
$551$	−19.2028	−0.818065
$552$	1.62505	0.0691669
$553$	4.05542	0.172454
$554$	50.9235	2.16353
$555$	4.94303	0.209820
$556$	25.3706	1.07595
$557$	18.4216	0.780546	0.390273	−	0.920699i	$-0.372381\pi$
$557$	18.4216	0.780546	0.390273	+	0.920699i	$0.372381\pi$
$558$	0.441350	0.0186838
$559$	−42.4415	−1.79508
$560$	31.6724	1.33840
$561$	−5.02900	−0.212325
$562$	−14.3233	−0.604192
$563$	−22.5519	−0.950450	−0.475225	−	0.879864i	$-0.657633\pi$
$563$	−22.5519	−0.950450	−0.475225	+	0.879864i	$0.657633\pi$
$564$	−6.65527	−0.280237
$565$	9.96074	0.419052
$566$	6.59580	0.277242
$567$	−4.05542	−0.170312
$568$	−2.60644	−0.109364
$569$	−9.29367	−0.389611	−0.194805	−	0.980842i	$-0.562408\pi$
$569$	−9.29367	−0.389611	−0.194805	+	0.980842i	$0.562408\pi$
$570$	−16.3133	−0.683289
$571$	−8.32133	−0.348237	−0.174118	−	0.984725i	$-0.555708\pi$
$571$	−8.32133	−0.348237	−0.174118	+	0.984725i	$0.555708\pi$
$572$	−40.1074	−1.67698
$573$	0.200006	0.00835536
$574$	5.44763	0.227380
$575$	6.81456	0.284187
$576$	−6.08649	−0.253604
$577$	10.3065	0.429066	0.214533	−	0.976717i	$-0.431177\pi$
$577$	10.3065	0.429066	0.214533	+	0.976717i	$0.431177\pi$
$578$	−1.94224	−0.0807866
$579$	18.9252	0.786504
$580$	12.7451	0.529212
$581$	−44.0534	−1.82764
$582$	−8.25508	−0.342184
$583$	−47.8275	−1.98081
$584$	−0.110981	−0.00459243
$585$	−7.98081	−0.329966
$586$	−43.8518	−1.81150
$587$	8.20847	0.338800	0.169400	−	0.985547i	$-0.445817\pi$
$587$	8.20847	0.338800	0.169400	+	0.985547i	$0.445817\pi$
$588$	−16.7419	−0.690425
$589$	1.07616	0.0443425
$590$	−32.6493	−1.34415
$591$	15.2856	0.628765
$592$	12.2731	0.504423
$593$	−9.62844	−0.395392	−0.197696	−	0.980263i	$-0.563346\pi$
$593$	−9.62844	−0.395392	−0.197696	+	0.980263i	$0.563346\pi$
$594$	9.76753	0.400767
$595$	−7.19245	−0.294862
$596$	−23.9784	−0.982193
$597$	11.1860	0.457814
$598$	−32.1149	−1.31328
$599$	33.0989	1.35238	0.676192	−	0.736726i	$-0.263629\pi$
$599$	33.0989	1.35238	0.676192	+	0.736726i	$0.263629\pi$
$600$	0.820183	0.0334838
$601$	−17.7218	−0.722886	−0.361443	−	0.932394i	$-0.617716\pi$
$601$	−17.7218	−0.722886	−0.361443	+	0.932394i	$0.617716\pi$
$602$	74.2888	3.02779
$603$	−9.65663	−0.393248
$604$	−38.8247	−1.57975
$605$	25.3454	1.03044
$606$	−3.24973	−0.132011
$607$	34.6518	1.40647	0.703237	−	0.710956i	$-0.251737\pi$
$607$	34.6518	1.40647	0.703237	+	0.710956i	$0.251737\pi$
$608$	−36.3157	−1.47280
$609$	16.4438	0.666336
$610$	20.6016	0.834133
$611$	−16.8980	−0.683619
$612$	1.77230	0.0716409
$613$	17.5416	0.708499	0.354249	−	0.935151i	$-0.384736\pi$
$613$	17.5416	0.708499	0.354249	+	0.935151i	$0.384736\pi$
$614$	29.6010	1.19460
$615$	−1.22662	−0.0494620
$616$	−9.01962	−0.363411
$617$	−25.5704	−1.02943	−0.514713	−	0.857363i	$-0.672101\pi$
$617$	−25.5704	−1.02943	−0.514713	+	0.857363i	$0.672101\pi$
$618$	0.182547	0.00734312
$619$	36.5624	1.46957	0.734783	−	0.678302i	$-0.237284\pi$
$619$	36.5624	1.46957	0.734783	+	0.678302i	$0.237284\pi$
$620$	−0.714262	−0.0286855
$621$	3.67449	0.147452
$622$	37.5678	1.50633
$623$	−49.3405	−1.97679
$624$	−19.8157	−0.793263
$625$	−12.2878	−0.491513
$626$	27.3718	1.09400
$627$	23.8166	0.951143
$628$	−28.8917	−1.15290
$629$	−2.78710	−0.111129
$630$	13.9695	0.556557
$631$	40.4069	1.60857	0.804287	−	0.594241i	$-0.202547\pi$
$631$	40.4069	1.60857	0.804287	+	0.594241i	$0.202547\pi$
$632$	−0.442253	−0.0175919
$633$	−17.7268	−0.704579
$634$	−39.8273	−1.58175
$635$	8.29960	0.329359
$636$	16.8551	0.668350
$637$	−42.5084	−1.68424
$638$	−39.6051	−1.56798
$639$	−5.89355	−0.233145
$640$	−6.23415	−0.246426
$641$	−44.3533	−1.75185	−0.875924	−	0.482449i	$-0.839747\pi$
$641$	−44.3533	−1.75185	−0.875924	+	0.482449i	$0.839747\pi$
$642$	6.75873	0.266746
$643$	−34.5189	−1.36129	−0.680646	−	0.732612i	$-0.738301\pi$
$643$	−34.5189	−1.36129	−0.680646	+	0.732612i	$0.738301\pi$
$644$	26.4101	1.04070
$645$	−16.7273	−0.658636
$646$	9.19816	0.361897
$647$	41.1141	1.61636	0.808181	−	0.588935i	$-0.200452\pi$
$647$	41.1141	1.61636	0.808181	+	0.588935i	$0.200452\pi$
$648$	0.442253	0.0173733
$649$	47.6664	1.87107
$650$	−16.2087	−0.635759
$651$	−0.921545	−0.0361182
$652$	35.7719	1.40093
$653$	−33.3609	−1.30551	−0.652756	−	0.757568i	$-0.726387\pi$
$653$	−33.3609	−1.30551	−0.652756	+	0.757568i	$0.726387\pi$
$654$	1.34358	0.0525383
$655$	7.98565	0.312025
$656$	−3.04559	−0.118910
$657$	−0.250945	−0.00979030
$658$	29.5779	1.15307
$659$	−1.65221	−0.0643610	−0.0321805	−	0.999482i	$-0.510245\pi$
$659$	−1.65221	−0.0643610	−0.0321805	+	0.999482i	$0.510245\pi$
$660$	−15.8074	−0.615301
$661$	−31.0060	−1.20599	−0.602996	−	0.797744i	$-0.706026\pi$
$661$	−31.0060	−1.20599	−0.602996	+	0.797744i	$0.706026\pi$
$662$	−48.6660	−1.89146
$663$	4.49993	0.174763
$664$	4.80412	0.186436
$665$	34.0624	1.32088
$666$	5.41322	0.209758
$667$	−14.8992	−0.576900
$668$	12.6289	0.488629
$669$	25.9490	1.00325
$670$	33.2636	1.28508
$671$	−30.0773	−1.16112
$672$	31.0980	1.19963
$673$	13.0474	0.502942	0.251471	−	0.967865i	$-0.419086\pi$
$673$	13.0474	0.502942	0.251471	+	0.967865i	$0.419086\pi$
$674$	−43.1787	−1.66318
$675$	1.85456	0.0713820
$676$	12.8481	0.494157
$677$	21.2396	0.816304	0.408152	−	0.912914i	$-0.366173\pi$
$677$	21.2396	0.816304	0.408152	+	0.912914i	$0.366173\pi$
$678$	10.9082	0.418928
$679$	17.2367	0.661485
$680$	0.784352	0.0300785
$681$	−17.3806	−0.666025
$682$	2.21955	0.0849910
$683$	46.1203	1.76474	0.882371	−	0.470554i	$-0.155946\pi$
$683$	46.1203	1.76474	0.882371	+	0.470554i	$0.155946\pi$
$684$	−8.39333	−0.320927
$685$	−2.99972	−0.114613
$686$	19.2698	0.735722
$687$	5.79110	0.220944
$688$	−41.5325	−1.58341
$689$	42.7959	1.63039
$690$	−12.6573	−0.481855
$691$	−12.8073	−0.487214	−0.243607	−	0.969874i	$-0.578331\pi$
$691$	−12.8073	−0.487214	−0.243607	+	0.969874i	$0.578331\pi$
$692$	−25.5821	−0.972487
$693$	−20.3947	−0.774732
$694$	−16.5595	−0.628589
$695$	25.3884	0.963037
$696$	−1.79323	−0.0679723
$697$	0.691622	0.0261970
$698$	29.7645	1.12660
$699$	3.81240	0.144198
$700$	13.3295	0.503807
$701$	−35.3685	−1.33585	−0.667925	−	0.744229i	$-0.732817\pi$
$701$	−35.3685	−1.33585	−0.667925	+	0.744229i	$0.732817\pi$
$702$	−8.73995	−0.329868
$703$	13.1993	0.497820
$704$	−30.6090	−1.15362
$705$	−6.65993	−0.250827
$706$	−4.15799	−0.156488
$707$	6.78547	0.255194
$708$	−16.7984	−0.631322
$709$	−14.1146	−0.530085	−0.265042	−	0.964237i	$-0.585386\pi$
$709$	−14.1146	−0.530085	−0.265042	+	0.964237i	$0.585386\pi$
$710$	20.3011	0.761888
$711$	−1.00000	−0.0375029
$712$	5.38069	0.201650
$713$	0.834983	0.0312704
$714$	−7.87661	−0.294775
$715$	−40.1355	−1.50098
$716$	31.9366	1.19353
$717$	−23.6885	−0.884663
$718$	−33.7944	−1.26120
$719$	−1.61551	−0.0602485	−0.0301242	−	0.999546i	$-0.509590\pi$
$719$	−1.61551	−0.0602485	−0.0301242	+	0.999546i	$0.509590\pi$
$720$	−7.80988	−0.291057
$721$	−0.381161	−0.0141952
$722$	−6.65850	−0.247804
$723$	−15.0822	−0.560912
$724$	32.3600	1.20265
$725$	−7.51981	−0.279279
$726$	27.7563	1.03013
$727$	−34.1919	−1.26811	−0.634054	−	0.773289i	$-0.718610\pi$
$727$	−34.1919	−1.26811	−0.634054	+	0.773289i	$0.718610\pi$
$728$	8.07072	0.299121
$729$	1.00000	0.0370370
$730$	0.864415	0.0319934
$731$	9.43158	0.348840
$732$	10.5997	0.391776
$733$	−40.3099	−1.48888	−0.744439	−	0.667690i	$-0.767283\pi$
$733$	−40.3099	−1.48888	−0.744439	+	0.667690i	$0.767283\pi$
$734$	−18.3681	−0.677980
$735$	−16.7537	−0.617968
$736$	−28.1770	−1.03862
$737$	−48.5632	−1.78885
$738$	−1.34330	−0.0494474
$739$	−10.3939	−0.382346	−0.191173	−	0.981556i	$-0.561229\pi$
$739$	−10.3939	−0.382346	−0.191173	+	0.981556i	$0.561229\pi$
$740$	−8.76052	−0.322043
$741$	−21.3110	−0.782879
$742$	−74.9092	−2.75000
$743$	9.45723	0.346952	0.173476	−	0.984838i	$-0.444500\pi$
$743$	9.45723	0.346952	0.173476	+	0.984838i	$0.444500\pi$
$744$	0.100496	0.00368438
$745$	−23.9952	−0.879115
$746$	−50.6650	−1.85498
$747$	10.8628	0.397451
$748$	8.91289	0.325888
$749$	−14.1123	−0.515653
$750$	−23.6115	−0.862169
$751$	−29.2999	−1.06917	−0.534584	−	0.845115i	$-0.679532\pi$
$751$	−29.2999	−1.06917	−0.534584	+	0.845115i	$0.679532\pi$
$752$	−16.5361	−0.603008
$753$	4.78626	0.174421
$754$	35.4385	1.29059
$755$	−38.8519	−1.41396
$756$	7.18742	0.261404
$757$	45.2983	1.64640	0.823198	−	0.567754i	$-0.192188\pi$
$757$	45.2983	1.64640	0.823198	+	0.567754i	$0.192188\pi$
$758$	5.08845	0.184821
$759$	18.4790	0.670747
$760$	−3.71457	−0.134742
$761$	−5.04852	−0.183009	−0.0915044	−	0.995805i	$-0.529168\pi$
$761$	−5.04852	−0.183009	−0.0915044	+	0.995805i	$0.529168\pi$
$762$	9.08906	0.329262
$763$	−2.80542	−0.101563
$764$	−0.354470	−0.0128243
$765$	1.77354	0.0641224
$766$	−23.9362	−0.864850
$767$	−42.6517	−1.54006
$768$	−19.0001	−0.685608
$769$	54.8525	1.97803	0.989016	−	0.147806i	$-0.0472212\pi$
$769$	54.8525	1.97803	0.989016	+	0.147806i	$0.0472212\pi$
$770$	70.2525	2.53173
$771$	−31.3372	−1.12858
$772$	−33.5411	−1.20717
$773$	−2.69376	−0.0968878	−0.0484439	−	0.998826i	$-0.515426\pi$
$773$	−2.69376	−0.0968878	−0.0484439	+	0.998826i	$0.515426\pi$
$774$	−18.3184	−0.658441
$775$	0.421425	0.0151380
$776$	−1.87970	−0.0674773
$777$	−11.3029	−0.405488
$778$	−2.97234	−0.106563
$779$	−3.27541	−0.117354
$780$	14.1444	0.506449
$781$	−29.6387	−1.06055
$782$	7.13675	0.255210
$783$	−4.05477	−0.144906
$784$	−41.5980	−1.48564
$785$	−28.9119	−1.03191
$786$	8.74526	0.311933
$787$	2.92869	0.104397	0.0521983	−	0.998637i	$-0.483377\pi$
$787$	2.92869	0.104397	0.0521983	+	0.998637i	$0.483377\pi$
$788$	−27.0906	−0.965064
$789$	−13.0083	−0.463107
$790$	3.44464	0.122555
$791$	−22.7765	−0.809839
$792$	2.22409	0.0790296
$793$	26.9130	0.955710
$794$	−40.1533	−1.42499
$795$	16.8670	0.598209
$796$	−19.8250	−0.702678
$797$	25.3602	0.898303	0.449151	−	0.893456i	$-0.351726\pi$
$797$	25.3602	0.898303	0.449151	+	0.893456i	$0.351726\pi$
$798$	37.3024	1.32049
$799$	3.75516	0.132848
$800$	−14.2212	−0.502797
$801$	12.1666	0.429884
$802$	−28.5895	−1.00953
$803$	−1.26200	−0.0445351
$804$	17.1144	0.603579
$805$	26.4286	0.931486
$806$	−1.98605	−0.0699555
$807$	−16.5998	−0.584341
$808$	−0.739970	−0.0260320
$809$	−10.3841	−0.365086	−0.182543	−	0.983198i	$-0.558433\pi$
$809$	−10.3841	−0.365086	−0.182543	+	0.983198i	$0.558433\pi$
$810$	−3.44464	−0.121032
$811$	−17.3349	−0.608712	−0.304356	−	0.952558i	$-0.598441\pi$
$811$	−17.3349	−0.608712	−0.304356	+	0.952558i	$0.598441\pi$
$812$	−29.1433	−1.02273
$813$	−17.8032	−0.624385
$814$	27.2231	0.954169
$815$	35.7969	1.25391
$816$	4.40356	0.154155
$817$	−44.6665	−1.56268
$818$	−53.7070	−1.87782
$819$	18.2491	0.637676
$820$	2.17393	0.0759170
$821$	20.8897	0.729054	0.364527	−	0.931193i	$-0.381231\pi$
$821$	20.8897	0.729054	0.364527	+	0.931193i	$0.381231\pi$
$822$	−3.28506	−0.114580
$823$	25.9803	0.905617	0.452808	−	0.891608i	$-0.350422\pi$
$823$	25.9803	0.905617	0.452808	+	0.891608i	$0.350422\pi$
$824$	0.0415664	0.00144803
$825$	9.32658	0.324710
$826$	74.6569	2.59765
$827$	43.0355	1.49649	0.748245	−	0.663422i	$-0.230897\pi$
$827$	43.0355	1.49649	0.748245	+	0.663422i	$0.230897\pi$
$828$	−6.51230	−0.226318
$829$	15.6038	0.541943	0.270972	−	0.962587i	$-0.412655\pi$
$829$	15.6038	0.541943	0.270972	+	0.962587i	$0.412655\pi$
$830$	−37.4186	−1.29882
$831$	26.2189	0.909525
$832$	27.3888	0.949536
$833$	9.44645	0.327300
$834$	27.8034	0.962752
$835$	12.6378	0.437349
$836$	−42.2101	−1.45987
$837$	0.227238	0.00785448
$838$	5.06090	0.174826
$839$	23.8951	0.824951	0.412475	−	0.910969i	$-0.364664\pi$
$839$	23.8951	0.824951	0.412475	+	0.910969i	$0.364664\pi$
$840$	3.18088	0.109751
$841$	−12.5589	−0.433064
$842$	−23.6595	−0.815361
$843$	−7.37463	−0.253996
$844$	31.4172	1.08143
$845$	12.8571	0.442297
$846$	−7.29343	−0.250753
$847$	−57.9556	−1.99138
$848$	41.8793	1.43814
$849$	3.39597	0.116550
$850$	3.60200	0.123548
$851$	10.2412	0.351063
$852$	10.4451	0.357844
$853$	0.0557194	0.00190779	0.000953897	−	1.00000i	$-0.499696\pi$
$853$	0.0557194	0.00190779	0.000953897		1.00000i	$0.499696\pi$
$854$	−47.1081	−1.61201
$855$	−8.39921	−0.287247
$856$	1.53898	0.0526012
$857$	−36.4088	−1.24370	−0.621851	−	0.783136i	$-0.713619\pi$
$857$	−36.4088	−1.24370	−0.621851	+	0.783136i	$0.713619\pi$
$858$	−43.9532	−1.50054
$859$	40.9838	1.39835	0.699175	−	0.714951i	$-0.253551\pi$
$859$	40.9838	1.39835	0.699175	+	0.714951i	$0.253551\pi$
$860$	29.6457	1.01091
$861$	2.80482	0.0955879
$862$	−65.3817	−2.22691
$863$	−55.1386	−1.87694	−0.938469	−	0.345363i	$-0.887756\pi$
$863$	−55.1386	−1.87694	−0.938469	+	0.345363i	$0.887756\pi$
$864$	−7.66826	−0.260879
$865$	−25.6001	−0.870428
$866$	−12.3478	−0.419594
$867$	−1.00000	−0.0339618
$868$	1.63325	0.0554362
$869$	−5.02900	−0.170597
$870$	13.9672	0.473533
$871$	43.4542	1.47239
$872$	0.305937	0.0103603
$873$	−4.25029	−0.143850
$874$	−33.7986	−1.14325
$875$	49.3011	1.66668
$876$	0.444749	0.0150267
$877$	−46.2405	−1.56143	−0.780715	−	0.624887i	$-0.785145\pi$
$877$	−46.2405	−1.56143	−0.780715	+	0.624887i	$0.785145\pi$
$878$	−29.1469	−0.983660
$879$	−22.5779	−0.761534
$880$	−39.2759	−1.32399
$881$	−12.0453	−0.405817	−0.202908	−	0.979198i	$-0.565039\pi$
$881$	−12.0453	−0.405817	−0.202908	+	0.979198i	$0.565039\pi$
$882$	−18.3473	−0.617785
$883$	−20.7682	−0.698906	−0.349453	−	0.936954i	$-0.613633\pi$
$883$	−20.7682	−0.698906	−0.349453	+	0.936954i	$0.613633\pi$
$884$	−7.97522	−0.268236
$885$	−16.8101	−0.565067
$886$	−11.1932	−0.376042
$887$	25.8004	0.866294	0.433147	−	0.901323i	$-0.357403\pi$
$887$	25.8004	0.866294	0.433147	+	0.901323i	$0.357403\pi$
$888$	1.23260	0.0413634
$889$	−18.9781	−0.636504
$890$	−41.9094	−1.40481
$891$	5.02900	0.168478
$892$	−45.9893	−1.53984
$893$	−17.7839	−0.595115
$894$	−26.2776	−0.878855
$895$	31.9590	1.06827
$896$	14.2552	0.476232
$897$	−16.5350	−0.552087
$898$	−69.0881	−2.30550
$899$	−0.921396	−0.0307303
$900$	−3.28683	−0.109561
$901$	−9.51033	−0.316835
$902$	−6.75544	−0.224931
$903$	38.2490	1.27285
$904$	2.48383	0.0826108
$905$	32.3827	1.07644
$906$	−42.5475	−1.41355
$907$	−42.5669	−1.41341	−0.706706	−	0.707507i	$-0.749820\pi$
$907$	−42.5669	−1.41341	−0.706706	+	0.707507i	$0.749820\pi$
$908$	30.8036	1.02225
$909$	−1.67318	−0.0554960
$910$	−62.8617	−2.08384
$911$	−10.9701	−0.363454	−0.181727	−	0.983349i	$-0.558169\pi$
$911$	−10.9701	−0.363454	−0.181727	+	0.983349i	$0.558169\pi$
$912$	−20.8546	−0.690564
$913$	54.6293	1.80797
$914$	5.17467	0.171163
$915$	10.6071	0.350661
$916$	−10.2636	−0.339117
$917$	−18.2602	−0.603005
$918$	1.94224	0.0641035
$919$	53.5086	1.76508	0.882542	−	0.470233i	$-0.155830\pi$
$919$	53.5086	1.76508	0.882542	+	0.470233i	$0.155830\pi$
$920$	−2.88210	−0.0950199
$921$	15.2407	0.502197
$922$	−39.8386	−1.31202
$923$	26.5206	0.872935
$924$	36.1455	1.18910
$925$	5.16884	0.169950
$926$	−61.4491	−2.01934
$927$	0.0939879	0.00308697
$928$	31.0930	1.02068
$929$	−3.49511	−0.114671	−0.0573354	−	0.998355i	$-0.518260\pi$
$929$	−3.49511	−0.114671	−0.0573354	+	0.998355i	$0.518260\pi$
$930$	−0.782752	−0.0256674
$931$	−44.7370	−1.46620
$932$	−6.75672	−0.221324
$933$	19.3425	0.633245
$934$	8.81590	0.288465
$935$	8.91914	0.291687
$936$	−1.99011	−0.0650487
$937$	38.5006	1.25776	0.628879	−	0.777503i	$-0.283514\pi$
$937$	38.5006	1.25776	0.628879	+	0.777503i	$0.283514\pi$
$938$	−76.0614	−2.48349
$939$	14.0929	0.459905
$940$	11.8034	0.384984
$941$	13.1521	0.428745	0.214373	−	0.976752i	$-0.431229\pi$
$941$	13.1521	0.428745	0.214373	+	0.976752i	$0.431229\pi$
$942$	−31.6621	−1.03161
$943$	−2.54136	−0.0827580
$944$	−41.7383	−1.35846
$945$	7.19245	0.233970
$946$	−92.1233	−2.99519
$947$	−43.9964	−1.42969	−0.714845	−	0.699283i	$-0.753503\pi$
$947$	−43.9964	−1.42969	−0.714845	+	0.699283i	$0.753503\pi$
$948$	1.77230	0.0575616
$949$	1.12924	0.0366565
$950$	−17.0585	−0.553451
$951$	−20.5059	−0.664949
$952$	−1.79352	−0.0581283
$953$	43.3294	1.40358	0.701788	−	0.712386i	$-0.252385\pi$
$953$	43.3294	1.40358	0.701788	+	0.712386i	$0.252385\pi$
$954$	18.4714	0.598032
$955$	−0.354718	−0.0114784
$956$	41.9830	1.35783
$957$	−20.3914	−0.659162
$958$	67.3419	2.17572
$959$	6.85925	0.221497
$960$	10.7946	0.348395
$961$	−30.9484	−0.998334
$962$	−24.3591	−0.785369
$963$	3.47987	0.112137
$964$	26.7301	0.860919
$965$	−33.5646	−1.08048
$966$	28.9425	0.931211
$967$	52.4064	1.68528	0.842639	−	0.538479i	$-0.181001\pi$
$967$	52.4064	1.68528	0.842639	+	0.538479i	$0.181001\pi$
$968$	6.32018	0.203138
$969$	4.73585	0.152137
$970$	14.6407	0.470085
$971$	−14.4837	−0.464805	−0.232402	−	0.972620i	$-0.574659\pi$
$971$	−14.4837	−0.464805	−0.232402	+	0.972620i	$0.574659\pi$
$972$	−1.77230	−0.0568465
$973$	−58.0538	−1.86112
$974$	−8.13586	−0.260690
$975$	−8.34539	−0.267266
$976$	26.3366	0.843015
$977$	−5.22635	−0.167206	−0.0836028	−	0.996499i	$-0.526643\pi$
$977$	−5.22635	−0.167206	−0.0836028	+	0.996499i	$0.526643\pi$
$978$	39.2020	1.25354
$979$	61.1857	1.95550
$980$	29.6925	0.948491
$981$	0.691770	0.0220865
$982$	16.3466	0.521639
$983$	−38.1284	−1.21611	−0.608054	−	0.793895i	$-0.708050\pi$
$983$	−38.1284	−1.21611	−0.608054	+	0.793895i	$0.708050\pi$
$984$	−0.305871	−0.00975082
$985$	−27.1096	−0.863784
$986$	−7.87534	−0.250802
$987$	15.2288	0.484737
$988$	37.7694	1.20161
$989$	−34.6563	−1.10201
$990$	−17.3231	−0.550564
$991$	3.42837	0.108906	0.0544529	−	0.998516i	$-0.482659\pi$
$991$	3.42837	0.108906	0.0544529	+	0.998516i	$0.482659\pi$
$992$	−1.74252	−0.0553250
$993$	−25.0566	−0.795149
$994$	−46.4211	−1.47239
$995$	−19.8389	−0.628935
$996$	−19.2522	−0.610029
$997$	32.8540	1.04050	0.520249	−	0.854015i	$-0.325839\pi$
$997$	32.8540	1.04050	0.520249	+	0.854015i	$0.325839\pi$
$998$	50.1101	1.58621
$999$	2.78710	0.0881799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.i.1.5	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.i.1.5	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-1.94224 q^{2} -1.00000 q^{3} +1.77230 q^{4} +1.77354 q^{5} +1.94224 q^{6} -4.05542 q^{7} +0.442253 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.94224 q^{2} -1.00000 q^{3} +1.77230 q^{4} +1.77354 q^{5} +1.94224 q^{6} -4.05542 q^{7} +0.442253 q^{8} +1.00000 q^{9} -3.44464 q^{10} +5.02900 q^{11} -1.77230 q^{12} -4.49993 q^{13} +7.87661 q^{14} -1.77354 q^{15} -4.40356 q^{16} +1.00000 q^{17} -1.94224 q^{18} -4.73585 q^{19} +3.14324 q^{20} +4.05542 q^{21} -9.76753 q^{22} -3.67449 q^{23} -0.442253 q^{24} -1.85456 q^{25} +8.73995 q^{26} -1.00000 q^{27} -7.18742 q^{28} +4.05477 q^{29} +3.44464 q^{30} -0.227238 q^{31} +7.66826 q^{32} -5.02900 q^{33} -1.94224 q^{34} -7.19245 q^{35} +1.77230 q^{36} -2.78710 q^{37} +9.19816 q^{38} +4.49993 q^{39} +0.784352 q^{40} +0.691622 q^{41} -7.87661 q^{42} +9.43158 q^{43} +8.91289 q^{44} +1.77354 q^{45} +7.13675 q^{46} +3.75516 q^{47} +4.40356 q^{48} +9.44645 q^{49} +3.60200 q^{50} -1.00000 q^{51} -7.97522 q^{52} -9.51033 q^{53} +1.94224 q^{54} +8.91914 q^{55} -1.79352 q^{56} +4.73585 q^{57} -7.87534 q^{58} +9.47831 q^{59} -3.14324 q^{60} -5.98076 q^{61} +0.441350 q^{62} -4.05542 q^{63} -6.08649 q^{64} -7.98081 q^{65} +9.76753 q^{66} -9.65663 q^{67} +1.77230 q^{68} +3.67449 q^{69} +13.9695 q^{70} -5.89355 q^{71} +0.442253 q^{72} -0.250945 q^{73} +5.41322 q^{74} +1.85456 q^{75} -8.39333 q^{76} -20.3947 q^{77} -8.73995 q^{78} -1.00000 q^{79} -7.80988 q^{80} +1.00000 q^{81} -1.34330 q^{82} +10.8628 q^{83} +7.18742 q^{84} +1.77354 q^{85} -18.3184 q^{86} -4.05477 q^{87} +2.22409 q^{88} +12.1666 q^{89} -3.44464 q^{90} +18.2491 q^{91} -6.51230 q^{92} +0.227238 q^{93} -7.29343 q^{94} -8.39921 q^{95} -7.66826 q^{96} -4.25029 q^{97} -18.3473 q^{98} +5.02900 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9}+O(q^{10}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9	\( 25 q - 2 q^{2} - 25 q^{3} + 26 q^{4} - 2 q^{5} + 2 q^{6} + 12 q^{7} + 25 q^{9} + 19 q^{10} + 19 q^{11} - 26 q^{12} + 4 q^{13} + 15 q^{14} + 2 q^{15} + 32 q^{16} + 25 q^{17} - 2 q^{18} + 29 q^{19} - 8 q^{20} - 12 q^{21} + 23 q^{22} + 6 q^{23} + 15 q^{25} - 8 q^{26} - 25 q^{27} + 23 q^{28} + 11 q^{29} - 19 q^{30} + 38 q^{31} - 27 q^{32} - 19 q^{33} - 2 q^{34} + 20 q^{35} + 26 q^{36} + 8 q^{37} - 25 q^{38} - 4 q^{39} + 48 q^{40} + 24 q^{41} - 15 q^{42} + 11 q^{43} + 6 q^{44} - 2 q^{45} + 25 q^{46} + 23 q^{47} - 32 q^{48} + 21 q^{49} - 21 q^{50} - 25 q^{51} + 31 q^{52} - 16 q^{53} + 2 q^{54} - 11 q^{55} + 18 q^{56} - 29 q^{57} - 5 q^{58} + 27 q^{59} + 8 q^{60} + 40 q^{61} - 34 q^{62} + 12 q^{63} + 46 q^{64} - 19 q^{65} - 23 q^{66} + 24 q^{67} + 26 q^{68} - 6 q^{69} + 17 q^{70} + 19 q^{71} + 13 q^{73} - 56 q^{74} - 15 q^{75} + 21 q^{76} - 30 q^{77} + 8 q^{78} - 25 q^{79} - 40 q^{80} + 25 q^{81} + 61 q^{82} + q^{83} - 23 q^{84} - 2 q^{85} + 62 q^{86} - 11 q^{87} - q^{88} - 10 q^{89} + 19 q^{90} + 50 q^{91} + 18 q^{92} - 38 q^{93} + 15 q^{94} + 14 q^{95} + 27 q^{96} + 19 q^{97} - 23 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q - 2 * q^2 - 25 * q^3 + 26 * q^4 - 2 * q^5 + 2 * q^6 + 12 * q^7 + 25 * q^9 + 19 * q^10 + 19 * q^11 - 26 * q^12 + 4 * q^13 + 15 * q^14 + 2 * q^15 + 32 * q^16 + 25 * q^17 - 2 * q^18 + 29 * q^19 - 8 * q^20 - 12 * q^21 + 23 * q^22 + 6 * q^23 + 15 * q^25 - 8 * q^26 - 25 * q^27 + 23 * q^28 + 11 * q^29 - 19 * q^30 + 38 * q^31 - 27 * q^32 - 19 * q^33 - 2 * q^34 + 20 * q^35 + 26 * q^36 + 8 * q^37 - 25 * q^38 - 4 * q^39 + 48 * q^40 + 24 * q^41 - 15 * q^42 + 11 * q^43 + 6 * q^44 - 2 * q^45 + 25 * q^46 + 23 * q^47 - 32 * q^48 + 21 * q^49 - 21 * q^50 - 25 * q^51 + 31 * q^52 - 16 * q^53 + 2 * q^54 - 11 * q^55 + 18 * q^56 - 29 * q^57 - 5 * q^58 + 27 * q^59 + 8 * q^60 + 40 * q^61 - 34 * q^62 + 12 * q^63 + 46 * q^64 - 19 * q^65 - 23 * q^66 + 24 * q^67 + 26 * q^68 - 6 * q^69 + 17 * q^70 + 19 * q^71 + 13 * q^73 - 56 * q^74 - 15 * q^75 + 21 * q^76 - 30 * q^77 + 8 * q^78 - 25 * q^79 - 40 * q^80 + 25 * q^81 + 61 * q^82 + q^83 - 23 * q^84 - 2 * q^85 + 62 * q^86 - 11 * q^87 - q^88 - 10 * q^89 + 19 * q^90 + 50 * q^91 + 18 * q^92 - 38 * q^93 + 15 * q^94 + 14 * q^95 + 27 * q^96 + 19 * q^97 - 23 * q^98 + 19 * q^99

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