LMFDB - Embedded newform 4017.2.a.h.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4017,2,Mod(1,4017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4017, 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("4017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4017 = 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4017.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:	$32.0759064919$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.81336 q^{2} -1.00000 q^{3} +1.28829 q^{4} +3.11371 q^{5} -1.81336 q^{6} -0.776263 q^{7} -1.29059 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.81336 q^{2} -1.00000 q^{3} +1.28829 q^{4} +3.11371 q^{5} -1.81336 q^{6} -0.776263 q^{7} -1.29059 q^{8} +1.00000 q^{9} +5.64629 q^{10} -4.28916 q^{11} -1.28829 q^{12} +1.00000 q^{13} -1.40765 q^{14} -3.11371 q^{15} -4.91689 q^{16} -0.617094 q^{17} +1.81336 q^{18} -5.45007 q^{19} +4.01137 q^{20} +0.776263 q^{21} -7.77782 q^{22} +0.00624294 q^{23} +1.29059 q^{24} +4.69519 q^{25} +1.81336 q^{26} -1.00000 q^{27} -1.00005 q^{28} +7.37560 q^{29} -5.64629 q^{30} -8.71686 q^{31} -6.33494 q^{32} +4.28916 q^{33} -1.11902 q^{34} -2.41706 q^{35} +1.28829 q^{36} -0.950225 q^{37} -9.88297 q^{38} -1.00000 q^{39} -4.01851 q^{40} +0.751908 q^{41} +1.40765 q^{42} -5.99268 q^{43} -5.52569 q^{44} +3.11371 q^{45} +0.0113207 q^{46} -9.94236 q^{47} +4.91689 q^{48} -6.39742 q^{49} +8.51410 q^{50} +0.617094 q^{51} +1.28829 q^{52} -7.44063 q^{53} -1.81336 q^{54} -13.3552 q^{55} +1.00183 q^{56} +5.45007 q^{57} +13.3746 q^{58} +9.27534 q^{59} -4.01137 q^{60} +4.90831 q^{61} -15.8068 q^{62} -0.776263 q^{63} -1.65378 q^{64} +3.11371 q^{65} +7.77782 q^{66} +1.70063 q^{67} -0.794997 q^{68} -0.00624294 q^{69} -4.38301 q^{70} -15.4995 q^{71} -1.29059 q^{72} +8.14492 q^{73} -1.72310 q^{74} -4.69519 q^{75} -7.02128 q^{76} +3.32952 q^{77} -1.81336 q^{78} -0.578934 q^{79} -15.3098 q^{80} +1.00000 q^{81} +1.36348 q^{82} +9.55897 q^{83} +1.00005 q^{84} -1.92145 q^{85} -10.8669 q^{86} -7.37560 q^{87} +5.53553 q^{88} -2.14035 q^{89} +5.64629 q^{90} -0.776263 q^{91} +0.00804272 q^{92} +8.71686 q^{93} -18.0291 q^{94} -16.9699 q^{95} +6.33494 q^{96} +3.34907 q^{97} -11.6008 q^{98} -4.28916 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * 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 $

$2$	1.81336	1.28224	0.641121	−	0.767440i	$-0.278470\pi$
$2$	1.81336	1.28224	0.641121	+	0.767440i	$0.278470\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.28829	0.644146
$5$	3.11371	1.39249	0.696247	−	0.717802i	$-0.254852\pi$
$5$	3.11371	1.39249	0.696247	+	0.717802i	$0.254852\pi$
$6$	−1.81336	−0.740303
$7$	−0.776263	−0.293400	−0.146700	−	0.989181i	$-0.546865\pi$
$7$	−0.776263	−0.293400	−0.146700	+	0.989181i	$0.546865\pi$
$8$	−1.29059	−0.456291
$9$	1.00000	0.333333
$10$	5.64629	1.78551
$11$	−4.28916	−1.29323	−0.646616	−	0.762816i	$-0.723816\pi$
$11$	−4.28916	−1.29323	−0.646616	+	0.762816i	$0.723816\pi$
$12$	−1.28829	−0.371898
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.40765	−0.376210
$15$	−3.11371	−0.803957
$16$	−4.91689	−1.22922
$17$	−0.617094	−0.149667	−0.0748336	−	0.997196i	$-0.523843\pi$
$17$	−0.617094	−0.149667	−0.0748336	+	0.997196i	$0.523843\pi$
$18$	1.81336	0.427414
$19$	−5.45007	−1.25033	−0.625166	−	0.780492i	$-0.714969\pi$
$19$	−5.45007	−1.25033	−0.625166	+	0.780492i	$0.714969\pi$
$20$	4.01137	0.896969
$21$	0.776263	0.169394
$22$	−7.77782	−1.65824
$23$	0.00624294	0.00130174	0.000650871	−	1.00000i	$-0.499793\pi$
$23$	0.00624294	0.00130174	0.000650871		1.00000i	$0.499793\pi$
$24$	1.29059	0.263440
$25$	4.69519	0.939038
$26$	1.81336	0.355630
$27$	−1.00000	−0.192450
$28$	−1.00005	−0.188992
$29$	7.37560	1.36961	0.684807	−	0.728724i	$-0.259886\pi$
$29$	7.37560	1.36961	0.684807	+	0.728724i	$0.259886\pi$
$30$	−5.64629	−1.03087
$31$	−8.71686	−1.56559	−0.782797	−	0.622277i	$-0.786208\pi$
$31$	−8.71686	−1.56559	−0.782797	+	0.622277i	$0.786208\pi$
$32$	−6.33494	−1.11987
$33$	4.28916	0.746647
$34$	−1.11902	−0.191910
$35$	−2.41706	−0.408557
$36$	1.28829	0.214715
$37$	−0.950225	−0.156216	−0.0781080	−	0.996945i	$-0.524888\pi$
$37$	−0.950225	−0.156216	−0.0781080	+	0.996945i	$0.524888\pi$
$38$	−9.88297	−1.60323
$39$	−1.00000	−0.160128
$40$	−4.01851	−0.635383
$41$	0.751908	0.117428	0.0587142	−	0.998275i	$-0.481300\pi$
$41$	0.751908	0.117428	0.0587142	+	0.998275i	$0.481300\pi$
$42$	1.40765	0.217205
$43$	−5.99268	−0.913876	−0.456938	−	0.889499i	$-0.651054\pi$
$43$	−5.99268	−0.913876	−0.456938	+	0.889499i	$0.651054\pi$
$44$	−5.52569	−0.833030
$45$	3.11371	0.464165
$46$	0.0113207	0.00166915
$47$	−9.94236	−1.45024	−0.725121	−	0.688622i	$-0.758216\pi$
$47$	−9.94236	−1.45024	−0.725121	+	0.688622i	$0.758216\pi$
$48$	4.91689	0.709692
$49$	−6.39742	−0.913917
$50$	8.51410	1.20407
$51$	0.617094	0.0864104
$52$	1.28829	0.178654
$53$	−7.44063	−1.02205	−0.511025	−	0.859566i	$-0.670734\pi$
$53$	−7.44063	−1.02205	−0.511025	+	0.859566i	$0.670734\pi$
$54$	−1.81336	−0.246768
$55$	−13.3552	−1.80082
$56$	1.00183	0.133876
$57$	5.45007	0.721880
$58$	13.3746	1.75618
$59$	9.27534	1.20755	0.603773	−	0.797156i	$-0.293663\pi$
$59$	9.27534	1.20755	0.603773	+	0.797156i	$0.293663\pi$
$60$	−4.01137	−0.517865
$61$	4.90831	0.628444	0.314222	−	0.949349i	$-0.398256\pi$
$61$	4.90831	0.628444	0.314222	+	0.949349i	$0.398256\pi$
$62$	−15.8068	−2.00747
$63$	−0.776263	−0.0977999
$64$	−1.65378	−0.206722
$65$	3.11371	0.386208
$66$	7.77782	0.957383
$67$	1.70063	0.207765	0.103883	−	0.994590i	$-0.466873\pi$
$67$	1.70063	0.207765	0.103883	+	0.994590i	$0.466873\pi$
$68$	−0.794997	−0.0964075
$69$	−0.00624294	−0.000751561 0
$70$	−4.38301	−0.523870
$71$	−15.4995	−1.83945	−0.919724	−	0.392566i	$-0.871588\pi$
$71$	−15.4995	−1.83945	−0.919724	+	0.392566i	$0.871588\pi$
$72$	−1.29059	−0.152097
$73$	8.14492	0.953291	0.476645	−	0.879096i	$-0.341853\pi$
$73$	8.14492	0.953291	0.476645	+	0.879096i	$0.341853\pi$
$74$	−1.72310	−0.200307
$75$	−4.69519	−0.542154
$76$	−7.02128	−0.805397
$77$	3.32952	0.379434
$78$	−1.81336	−0.205323
$79$	−0.578934	−0.0651352	−0.0325676	−	0.999470i	$-0.510368\pi$
$79$	−0.578934	−0.0651352	−0.0325676	+	0.999470i	$0.510368\pi$
$80$	−15.3098	−1.71168
$81$	1.00000	0.111111
$82$	1.36348	0.150572
$83$	9.55897	1.04923	0.524616	−	0.851339i	$-0.324209\pi$
$83$	9.55897	1.04923	0.524616	+	0.851339i	$0.324209\pi$
$84$	1.00005	0.109115
$85$	−1.92145	−0.208411
$86$	−10.8669	−1.17181
$87$	−7.37560	−0.790747
$88$	5.53553	0.590090
$89$	−2.14035	−0.226877	−0.113438	−	0.993545i	$-0.536186\pi$
$89$	−2.14035	−0.226877	−0.113438	+	0.993545i	$0.536186\pi$
$90$	5.64629	0.595171
$91$	−0.776263	−0.0813745
$92$	0.00804272	0.000838512 0
$93$	8.71686	0.903896
$94$	−18.0291	−1.85956
$95$	−16.9699	−1.74108
$96$	6.33494	0.646557
$97$	3.34907	0.340046	0.170023	−	0.985440i	$-0.445616\pi$
$97$	3.34907	0.340046	0.170023	+	0.985440i	$0.445616\pi$
$98$	−11.6008	−1.17186
$99$	−4.28916	−0.431077
$100$	6.04878	0.604878
$101$	−4.01128	−0.399138	−0.199569	−	0.979884i	$-0.563954\pi$
$101$	−4.01128	−0.399138	−0.199569	+	0.979884i	$0.563954\pi$
$102$	1.11902	0.110799
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.29059	−0.126552
$105$	2.41706	0.235881
$106$	−13.4926	−1.31051
$107$	−1.40875	−0.136189	−0.0680944	−	0.997679i	$-0.521692\pi$
$107$	−1.40875	−0.136189	−0.0680944	+	0.997679i	$0.521692\pi$
$108$	−1.28829	−0.123966
$109$	−18.4877	−1.77080	−0.885399	−	0.464832i	$-0.846115\pi$
$109$	−18.4877	−1.77080	−0.885399	+	0.464832i	$0.846115\pi$
$110$	−24.2179	−2.30908
$111$	0.950225	0.0901913
$112$	3.81680	0.360653
$113$	10.8945	1.02487	0.512433	−	0.858727i	$-0.328744\pi$
$113$	10.8945	1.02487	0.512433	+	0.858727i	$0.328744\pi$
$114$	9.88297	0.925625
$115$	0.0194387	0.00181267
$116$	9.50192	0.882231
$117$	1.00000	0.0924500
$118$	16.8196	1.54837
$119$	0.479027	0.0439123
$120$	4.01851	0.366838
$121$	7.39691	0.672447
$122$	8.90055	0.805818
$123$	−0.751908	−0.0677973
$124$	−11.2299	−1.00847
$125$	−0.949085	−0.0848888
$126$	−1.40765	−0.125403
$127$	−6.65369	−0.590419	−0.295210	−	0.955433i	$-0.595389\pi$
$127$	−6.65369	−0.590419	−0.295210	+	0.955433i	$0.595389\pi$
$128$	9.67097	0.854801
$129$	5.99268	0.527626
$130$	5.64629	0.495213
$131$	−14.3245	−1.25153	−0.625767	−	0.780010i	$-0.715214\pi$
$131$	−14.3245	−1.25153	−0.625767	+	0.780010i	$0.715214\pi$
$132$	5.52569	0.480950
$133$	4.23069	0.366847
$134$	3.08387	0.266405
$135$	−3.11371	−0.267986
$136$	0.796413	0.0682918
$137$	18.8875	1.61367	0.806835	−	0.590777i	$-0.201179\pi$
$137$	18.8875	1.61367	0.806835	+	0.590777i	$0.201179\pi$
$138$	−0.0113207	−0.000963684 0
$139$	12.9199	1.09585	0.547924	−	0.836528i	$-0.315418\pi$
$139$	12.9199	1.09585	0.547924	+	0.836528i	$0.315418\pi$
$140$	−3.11388	−0.263171
$141$	9.94236	0.837297
$142$	−28.1062	−2.35862
$143$	−4.28916	−0.358678
$144$	−4.91689	−0.409741
$145$	22.9655	1.90718
$146$	14.7697	1.22235
$147$	6.39742	0.527650
$148$	−1.22417	−0.100626
$149$	−11.8743	−0.972777	−0.486389	−	0.873743i	$-0.661686\pi$
$149$	−11.8743	−0.972777	−0.486389	+	0.873743i	$0.661686\pi$
$150$	−8.51410	−0.695173
$151$	−12.2117	−0.993776	−0.496888	−	0.867815i	$-0.665524\pi$
$151$	−12.2117	−0.993776	−0.496888	+	0.867815i	$0.665524\pi$
$152$	7.03379	0.570516
$153$	−0.617094	−0.0498891
$154$	6.03763	0.486526
$155$	−27.1418	−2.18008
$156$	−1.28829	−0.103146
$157$	−9.95535	−0.794524	−0.397262	−	0.917705i	$-0.630040\pi$
$157$	−9.95535	−0.794524	−0.397262	+	0.917705i	$0.630040\pi$
$158$	−1.04982	−0.0835191
$159$	7.44063	0.590080
$160$	−19.7252	−1.55941
$161$	−0.00484616	−0.000381931 0
$162$	1.81336	0.142471
$163$	7.52744	0.589594	0.294797	−	0.955560i	$-0.404748\pi$
$163$	7.52744	0.589594	0.294797	+	0.955560i	$0.404748\pi$
$164$	0.968677	0.0756410
$165$	13.3552	1.03970
$166$	17.3339	1.34537
$167$	9.65725	0.747300	0.373650	−	0.927570i	$-0.378106\pi$
$167$	9.65725	0.747300	0.373650	+	0.927570i	$0.378106\pi$
$168$	−1.00183	−0.0772932
$169$	1.00000	0.0769231
$170$	−3.48429	−0.267233
$171$	−5.45007	−0.416777
$172$	−7.72033	−0.588669
$173$	−13.2230	−1.00532	−0.502662	−	0.864483i	$-0.667646\pi$
$173$	−13.2230	−1.00532	−0.502662	+	0.864483i	$0.667646\pi$
$174$	−13.3746	−1.01393
$175$	−3.64470	−0.275514
$176$	21.0893	1.58967
$177$	−9.27534	−0.697177
$178$	−3.88124	−0.290911
$179$	26.0432	1.94656	0.973280	−	0.229619i	$-0.0737482\pi$
$179$	26.0432	1.94656	0.973280	+	0.229619i	$0.0737482\pi$
$180$	4.01137	0.298990
$181$	−2.38806	−0.177503	−0.0887517	−	0.996054i	$-0.528288\pi$
$181$	−2.38806	−0.177503	−0.0887517	+	0.996054i	$0.528288\pi$
$182$	−1.40765	−0.104342
$183$	−4.90831	−0.362833
$184$	−0.00805705	−0.000593974 0
$185$	−2.95872	−0.217530
$186$	15.8068	1.15901
$187$	2.64681	0.193554
$188$	−12.8087	−0.934167
$189$	0.776263	0.0564648
$190$	−30.7727	−2.23249
$191$	27.0016	1.95377	0.976885	−	0.213768i	$-0.0685736\pi$
$191$	27.0016	1.95377	0.976885	+	0.213768i	$0.0685736\pi$
$192$	1.65378	0.119351
$193$	15.8649	1.14198	0.570991	−	0.820957i	$-0.306559\pi$
$193$	15.8649	1.14198	0.570991	+	0.820957i	$0.306559\pi$
$194$	6.07308	0.436022
$195$	−3.11371	−0.222977
$196$	−8.24174	−0.588696
$197$	−17.7635	−1.26560	−0.632799	−	0.774316i	$-0.718094\pi$
$197$	−17.7635	−1.26560	−0.632799	+	0.774316i	$0.718094\pi$
$198$	−7.77782	−0.552745
$199$	9.18815	0.651331	0.325665	−	0.945485i	$-0.394412\pi$
$199$	9.18815	0.651331	0.325665	+	0.945485i	$0.394412\pi$
$200$	−6.05955	−0.428475
$201$	−1.70063	−0.119953
$202$	−7.27392	−0.511791
$203$	−5.72540	−0.401844
$204$	0.794997	0.0556609
$205$	2.34122	0.163518
$206$	1.81336	0.126343
$207$	0.00624294	0.000433914 0
$208$	−4.91689	−0.340925
$209$	23.3762	1.61697
$210$	4.38301	0.302456
$211$	−6.15247	−0.423553	−0.211777	−	0.977318i	$-0.567925\pi$
$211$	−6.15247	−0.423553	−0.211777	+	0.977318i	$0.567925\pi$
$212$	−9.58570	−0.658349
$213$	15.4995	1.06201
$214$	−2.55457	−0.174627
$215$	−18.6595	−1.27257
$216$	1.29059	0.0878133
$217$	6.76657	0.459345
$218$	−33.5249	−2.27059
$219$	−8.14492	−0.550383
$220$	−17.2054	−1.15999
$221$	−0.617094	−0.0415102
$222$	1.72310	0.115647
$223$	−25.2617	−1.69165	−0.845823	−	0.533464i	$-0.820890\pi$
$223$	−25.2617	−1.69165	−0.845823	+	0.533464i	$0.820890\pi$
$224$	4.91758	0.328569
$225$	4.69519	0.313013
$226$	19.7556	1.31413
$227$	−10.8563	−0.720555	−0.360277	−	0.932845i	$-0.617318\pi$
$227$	−10.8563	−0.720555	−0.360277	+	0.932845i	$0.617318\pi$
$228$	7.02128	0.464996
$229$	−28.2592	−1.86742	−0.933710	−	0.358031i	$-0.883448\pi$
$229$	−28.2592	−1.86742	−0.933710	+	0.358031i	$0.883448\pi$
$230$	0.0352494	0.00232428
$231$	−3.32952	−0.219066
$232$	−9.51885	−0.624943
$233$	−1.82486	−0.119551	−0.0597754	−	0.998212i	$-0.519038\pi$
$233$	−1.82486	−0.119551	−0.0597754	+	0.998212i	$0.519038\pi$
$234$	1.81336	0.118543
$235$	−30.9576	−2.01945
$236$	11.9493	0.777836
$237$	0.578934	0.0376058
$238$	0.868650	0.0563062
$239$	13.9091	0.899703	0.449852	−	0.893103i	$-0.351477\pi$
$239$	13.9091	0.899703	0.449852	+	0.893103i	$0.351477\pi$
$240$	15.3098	0.988241
$241$	−3.25877	−0.209916	−0.104958	−	0.994477i	$-0.533471\pi$
$241$	−3.25877	−0.209916	−0.104958	+	0.994477i	$0.533471\pi$
$242$	13.4133	0.862240
$243$	−1.00000	−0.0641500
$244$	6.32333	0.404810
$245$	−19.9197	−1.27262
$246$	−1.36348	−0.0869326
$247$	−5.45007	−0.346780
$248$	11.2499	0.714367
$249$	−9.55897	−0.605775
$250$	−1.72104	−0.108848
$251$	−7.70031	−0.486039	−0.243020	−	0.970021i	$-0.578138\pi$
$251$	−7.70031	−0.486039	−0.243020	+	0.970021i	$0.578138\pi$
$252$	−1.00005	−0.0629974
$253$	−0.0267770	−0.00168345
$254$	−12.0656	−0.757061
$255$	1.92145	0.120326
$256$	20.8446	1.30278
$257$	−6.68712	−0.417131	−0.208566	−	0.978008i	$-0.566880\pi$
$257$	−6.68712	−0.417131	−0.208566	+	0.978008i	$0.566880\pi$
$258$	10.8669	0.676545
$259$	0.737624	0.0458337
$260$	4.01137	0.248774
$261$	7.37560	0.456538
$262$	−25.9755	−1.60477
$263$	4.42005	0.272552	0.136276	−	0.990671i	$-0.456487\pi$
$263$	4.42005	0.272552	0.136276	+	0.990671i	$0.456487\pi$
$264$	−5.53553	−0.340689
$265$	−23.1680	−1.42320
$266$	7.67178	0.470387
$267$	2.14035	0.130987
$268$	2.19091	0.133831
$269$	17.5716	1.07136	0.535680	−	0.844421i	$-0.320056\pi$
$269$	17.5716	1.07136	0.535680	+	0.844421i	$0.320056\pi$
$270$	−5.64629	−0.343622
$271$	−12.0732	−0.733397	−0.366698	−	0.930340i	$-0.619512\pi$
$271$	−12.0732	−0.733397	−0.366698	+	0.930340i	$0.619512\pi$
$272$	3.03418	0.183974
$273$	0.776263	0.0469816
$274$	34.2500	2.06912
$275$	−20.1384	−1.21439
$276$	−0.00804272	−0.000484115 0
$277$	3.52993	0.212093	0.106046	−	0.994361i	$-0.466181\pi$
$277$	3.52993	0.212093	0.106046	+	0.994361i	$0.466181\pi$
$278$	23.4284	1.40514
$279$	−8.71686	−0.521865
$280$	3.11942	0.186421
$281$	27.4237	1.63596	0.817982	−	0.575244i	$-0.195093\pi$
$281$	27.4237	1.63596	0.817982	+	0.575244i	$0.195093\pi$
$282$	18.0291	1.07362
$283$	−20.6503	−1.22753	−0.613766	−	0.789488i	$-0.710346\pi$
$283$	−20.6503	−1.22753	−0.613766	+	0.789488i	$0.710346\pi$
$284$	−19.9678	−1.18487
$285$	16.9699	1.00521
$286$	−7.77782	−0.459912
$287$	−0.583678	−0.0344534
$288$	−6.33494	−0.373290
$289$	−16.6192	−0.977600
$290$	41.6448	2.44547
$291$	−3.34907	−0.196326
$292$	10.4930	0.614058
$293$	−5.01783	−0.293145	−0.146572	−	0.989200i	$-0.546824\pi$
$293$	−5.01783	−0.293145	−0.146572	+	0.989200i	$0.546824\pi$
$294$	11.6008	0.676575
$295$	28.8807	1.68150
$296$	1.22635	0.0712800
$297$	4.28916	0.248882
$298$	−21.5324	−1.24734
$299$	0.00624294	0.000361038 0
$300$	−6.04878	−0.349226
$301$	4.65190	0.268131
$302$	−22.1443	−1.27426
$303$	4.01128	0.230442
$304$	26.7974	1.53694
$305$	15.2830	0.875105
$306$	−1.11902	−0.0639699
$307$	−4.04686	−0.230967	−0.115483	−	0.993309i	$-0.536842\pi$
$307$	−4.04686	−0.230967	−0.115483	+	0.993309i	$0.536842\pi$
$308$	4.28939	0.244411
$309$	−1.00000	−0.0568880
$310$	−49.2179	−2.79539
$311$	−7.52401	−0.426648	−0.213324	−	0.976982i	$-0.568429\pi$
$311$	−7.52401	−0.426648	−0.213324	+	0.976982i	$0.568429\pi$
$312$	1.29059	0.0730651
$313$	10.9990	0.621698	0.310849	−	0.950459i	$-0.399387\pi$
$313$	10.9990	0.621698	0.310849	+	0.950459i	$0.399387\pi$
$314$	−18.0527	−1.01877
$315$	−2.41706	−0.136186
$316$	−0.745836	−0.0419566
$317$	−20.6769	−1.16133	−0.580665	−	0.814143i	$-0.697207\pi$
$317$	−20.6769	−1.16133	−0.580665	+	0.814143i	$0.697207\pi$
$318$	13.4926	0.756626
$319$	−31.6351	−1.77123
$320$	−5.14939	−0.287859
$321$	1.40875	0.0786286
$322$	−0.00878785	−0.000489728 0
$323$	3.36321	0.187134
$324$	1.28829	0.0715718
$325$	4.69519	0.260442
$326$	13.6500	0.756003
$327$	18.4877	1.02237
$328$	−0.970403	−0.0535815
$329$	7.71788	0.425501
$330$	24.2179	1.33315
$331$	11.5853	0.636788	0.318394	−	0.947958i	$-0.396856\pi$
$331$	11.5853	0.636788	0.318394	+	0.947958i	$0.396856\pi$
$332$	12.3147	0.675859
$333$	−0.950225	−0.0520720
$334$	17.5121	0.958220
$335$	5.29527	0.289312
$336$	−3.81680	−0.208223
$337$	−23.0443	−1.25530	−0.627652	−	0.778494i	$-0.715984\pi$
$337$	−23.0443	−1.25530	−0.627652	+	0.778494i	$0.715984\pi$
$338$	1.81336	0.0986340
$339$	−10.8945	−0.591706
$340$	−2.47539	−0.134247
$341$	37.3880	2.02468
$342$	−9.88297	−0.534410
$343$	10.3999	0.561543
$344$	7.73408	0.416993
$345$	−0.0194387	−0.00104654
$346$	−23.9781	−1.28907
$347$	22.9043	1.22957	0.614783	−	0.788696i	$-0.289244\pi$
$347$	22.9043	1.22957	0.614783	+	0.788696i	$0.289244\pi$
$348$	−9.50192	−0.509357
$349$	−13.0253	−0.697227	−0.348614	−	0.937267i	$-0.613347\pi$
$349$	−13.0253	−0.697227	−0.348614	+	0.937267i	$0.613347\pi$
$350$	−6.60918	−0.353275
$351$	−1.00000	−0.0533761
$352$	27.1716	1.44825
$353$	−30.5708	−1.62712	−0.813560	−	0.581481i	$-0.802473\pi$
$353$	−30.5708	−1.62712	−0.813560	+	0.581481i	$0.802473\pi$
$354$	−16.8196	−0.893950
$355$	−48.2608	−2.56142
$356$	−2.75740	−0.146142
$357$	−0.479027	−0.0253528
$358$	47.2258	2.49596
$359$	−8.44163	−0.445532	−0.222766	−	0.974872i	$-0.571509\pi$
$359$	−8.44163	−0.445532	−0.222766	+	0.974872i	$0.571509\pi$
$360$	−4.01851	−0.211794
$361$	10.7033	0.563331
$362$	−4.33043	−0.227602
$363$	−7.39691	−0.388237
$364$	−1.00005	−0.0524170
$365$	25.3609	1.32745
$366$	−8.90055	−0.465239
$367$	9.82828	0.513032	0.256516	−	0.966540i	$-0.417425\pi$
$367$	9.82828	0.513032	0.256516	+	0.966540i	$0.417425\pi$
$368$	−0.0306958	−0.00160013
$369$	0.751908	0.0391428
$370$	−5.36525	−0.278926
$371$	5.77588	0.299869
$372$	11.2299	0.582241
$373$	−3.00695	−0.155694	−0.0778470	−	0.996965i	$-0.524805\pi$
$373$	−3.00695	−0.155694	−0.0778470	+	0.996965i	$0.524805\pi$
$374$	4.79964	0.248183
$375$	0.949085	0.0490105
$376$	12.8315	0.661733
$377$	7.37560	0.379863
$378$	1.40765	0.0724016
$379$	28.0910	1.44294	0.721469	−	0.692447i	$-0.243467\pi$
$379$	28.0910	1.44294	0.721469	+	0.692447i	$0.243467\pi$
$380$	−21.8622	−1.12151
$381$	6.65369	0.340879
$382$	48.9638	2.50521
$383$	0.244691	0.0125031	0.00625156	−	0.999980i	$-0.498010\pi$
$383$	0.244691	0.0125031	0.00625156	+	0.999980i	$0.498010\pi$
$384$	−9.67097	−0.493520
$385$	10.3672	0.528359
$386$	28.7689	1.46430
$387$	−5.99268	−0.304625
$388$	4.31457	0.219039
$389$	−23.3128	−1.18201	−0.591003	−	0.806669i	$-0.701268\pi$
$389$	−23.3128	−1.18201	−0.591003	+	0.806669i	$0.701268\pi$
$390$	−5.64629	−0.285911
$391$	−0.00385248	−0.000194828 0
$392$	8.25642	0.417012
$393$	14.3245	0.722573
$394$	−32.2117	−1.62280
$395$	−1.80263	−0.0907003
$396$	−5.52569	−0.277677
$397$	31.6151	1.58672	0.793358	−	0.608756i	$-0.208331\pi$
$397$	31.6151	1.58672	0.793358	+	0.608756i	$0.208331\pi$
$398$	16.6615	0.835164
$399$	−4.23069	−0.211799
$400$	−23.0857	−1.15429
$401$	−13.1628	−0.657320	−0.328660	−	0.944448i	$-0.606597\pi$
$401$	−13.1628	−0.657320	−0.328660	+	0.944448i	$0.606597\pi$
$402$	−3.08387	−0.153809
$403$	−8.71686	−0.434218
$404$	−5.16771	−0.257103
$405$	3.11371	0.154722
$406$	−10.3822	−0.515262
$407$	4.07567	0.202023
$408$	−0.796413	−0.0394283
$409$	−1.52063	−0.0751901	−0.0375951	−	0.999293i	$-0.511970\pi$
$409$	−1.52063	−0.0751901	−0.0375951	+	0.999293i	$0.511970\pi$
$410$	4.24549	0.209670
$411$	−18.8875	−0.931653
$412$	1.28829	0.0634696
$413$	−7.20010	−0.354294
$414$	0.0113207	0.000556383 0
$415$	29.7639	1.46105
$416$	−6.33494	−0.310596
$417$	−12.9199	−0.632688
$418$	42.3897	2.07335
$419$	25.5886	1.25008	0.625042	−	0.780591i	$-0.285082\pi$
$419$	25.5886	1.25008	0.625042	+	0.780591i	$0.285082\pi$
$420$	3.11388	0.151942
$421$	24.5900	1.19845	0.599223	−	0.800582i	$-0.295476\pi$
$421$	24.5900	1.19845	0.599223	+	0.800582i	$0.295476\pi$
$422$	−11.1567	−0.543098
$423$	−9.94236	−0.483414
$424$	9.60278	0.466352
$425$	−2.89737	−0.140543
$426$	28.1062	1.36175
$427$	−3.81014	−0.184385
$428$	−1.81488	−0.0877255
$429$	4.28916	0.207083
$430$	−33.8364	−1.63174
$431$	−8.13034	−0.391625	−0.195812	−	0.980641i	$-0.562734\pi$
$431$	−8.13034	−0.391625	−0.195812	+	0.980641i	$0.562734\pi$
$432$	4.91689	0.236564
$433$	19.8763	0.955194	0.477597	−	0.878579i	$-0.341508\pi$
$433$	19.8763	0.955194	0.477597	+	0.878579i	$0.341508\pi$
$434$	12.2703	0.588992
$435$	−22.9655	−1.10111
$436$	−23.8175	−1.14065
$437$	−0.0340245	−0.00162761
$438$	−14.7697	−0.705724
$439$	32.4040	1.54656	0.773280	−	0.634065i	$-0.218615\pi$
$439$	32.4040	1.54656	0.773280	+	0.634065i	$0.218615\pi$
$440$	17.2361	0.821697
$441$	−6.39742	−0.304639
$442$	−1.11902	−0.0532262
$443$	27.4011	1.30186	0.650932	−	0.759136i	$-0.274378\pi$
$443$	27.4011	1.30186	0.650932	+	0.759136i	$0.274378\pi$
$444$	1.22417	0.0580964
$445$	−6.66443	−0.315924
$446$	−45.8086	−2.16910
$447$	11.8743	0.561633
$448$	1.28377	0.0606523
$449$	−23.8439	−1.12526	−0.562632	−	0.826707i	$-0.690211\pi$
$449$	−23.8439	−1.12526	−0.562632	+	0.826707i	$0.690211\pi$
$450$	8.51410	0.401358
$451$	−3.22506	−0.151862
$452$	14.0353	0.660163
$453$	12.2117	0.573757
$454$	−19.6863	−0.923926
$455$	−2.41706	−0.113313
$456$	−7.03379	−0.329387
$457$	22.6970	1.06172	0.530861	−	0.847459i	$-0.321868\pi$
$457$	22.6970	1.06172	0.530861	+	0.847459i	$0.321868\pi$
$458$	−51.2442	−2.39448
$459$	0.617094	0.0288035
$460$	0.0250427	0.00116762
$461$	2.12039	0.0987564	0.0493782	−	0.998780i	$-0.484276\pi$
$461$	2.12039	0.0987564	0.0493782	+	0.998780i	$0.484276\pi$
$462$	−6.03763	−0.280896
$463$	13.5864	0.631413	0.315707	−	0.948857i	$-0.397758\pi$
$463$	13.5864	0.631413	0.315707	+	0.948857i	$0.397758\pi$
$464$	−36.2650	−1.68356
$465$	27.1418	1.25867
$466$	−3.30914	−0.153293
$467$	−6.05489	−0.280187	−0.140094	−	0.990138i	$-0.544740\pi$
$467$	−6.05489	−0.280187	−0.140094	+	0.990138i	$0.544740\pi$
$468$	1.28829	0.0595513
$469$	−1.32014	−0.0609583
$470$	−56.1374	−2.58943
$471$	9.95535	0.458718
$472$	−11.9706	−0.550993
$473$	25.7036	1.18185
$474$	1.04982	0.0482198
$475$	−25.5891	−1.17411
$476$	0.617126	0.0282859
$477$	−7.44063	−0.340683
$478$	25.2222	1.15364
$479$	−24.6761	−1.12748	−0.563740	−	0.825953i	$-0.690638\pi$
$479$	−24.6761	−1.12748	−0.563740	+	0.825953i	$0.690638\pi$
$480$	19.7252	0.900326
$481$	−0.950225	−0.0433265
$482$	−5.90934	−0.269163
$483$	0.00484616	0.000220508 0
$484$	9.52938	0.433154
$485$	10.4280	0.473512
$486$	−1.81336	−0.0822559
$487$	35.9047	1.62700	0.813499	−	0.581566i	$-0.197560\pi$
$487$	35.9047	1.62700	0.813499	+	0.581566i	$0.197560\pi$
$488$	−6.33460	−0.286754
$489$	−7.52744	−0.340402
$490$	−36.1217	−1.63181
$491$	−24.3980	−1.10107	−0.550534	−	0.834813i	$-0.685576\pi$
$491$	−24.3980	−1.10107	−0.550534	+	0.834813i	$0.685576\pi$
$492$	−0.968677	−0.0436713
$493$	−4.55143	−0.204986
$494$	−9.88297	−0.444656
$495$	−13.3552	−0.600272
$496$	42.8598	1.92446
$497$	12.0317	0.539694
$498$	−17.3339	−0.776750
$499$	11.8397	0.530018	0.265009	−	0.964246i	$-0.414625\pi$
$499$	11.8397	0.530018	0.265009	+	0.964246i	$0.414625\pi$
$500$	−1.22270	−0.0546807
$501$	−9.65725	−0.431454
$502$	−13.9635	−0.623220
$503$	38.6595	1.72374	0.861871	−	0.507128i	$-0.169293\pi$
$503$	38.6595	1.72374	0.861871	+	0.507128i	$0.169293\pi$
$504$	1.00183	0.0446252
$505$	−12.4900	−0.555797
$506$	−0.0485564	−0.00215860
$507$	−1.00000	−0.0444116
$508$	−8.57189	−0.380316
$509$	−1.71198	−0.0758820	−0.0379410	−	0.999280i	$-0.512080\pi$
$509$	−1.71198	−0.0758820	−0.0379410	+	0.999280i	$0.512080\pi$
$510$	3.48429	0.154287
$511$	−6.32260	−0.279695
$512$	18.4568	0.815685
$513$	5.45007	0.240627
$514$	−12.1262	−0.534864
$515$	3.11371	0.137206
$516$	7.72033	0.339868
$517$	42.6444	1.87550
$518$	1.33758	0.0587700
$519$	13.2230	0.580424
$520$	−4.01851	−0.176223
$521$	10.9793	0.481014	0.240507	−	0.970647i	$-0.422686\pi$
$521$	10.9793	0.481014	0.240507	+	0.970647i	$0.422686\pi$
$522$	13.3746	0.585393
$523$	−1.79001	−0.0782718	−0.0391359	−	0.999234i	$-0.512461\pi$
$523$	−1.79001	−0.0782718	−0.0391359	+	0.999234i	$0.512461\pi$
$524$	−18.4541	−0.806170
$525$	3.64470	0.159068
$526$	8.01516	0.349477
$527$	5.37912	0.234318
$528$	−21.0893	−0.917795
$529$	−23.0000	−0.999998
$530$	−42.0120	−1.82488
$531$	9.27534	0.402515
$532$	5.45036	0.236303
$533$	0.751908	0.0325688
$534$	3.88124	0.167958
$535$	−4.38643	−0.189642
$536$	−2.19481	−0.0948015
$537$	−26.0432	−1.12385
$538$	31.8637	1.37374
$539$	27.4396	1.18191
$540$	−4.01137	−0.172622
$541$	−3.88223	−0.166910	−0.0834550	−	0.996512i	$-0.526595\pi$
$541$	−3.88223	−0.166910	−0.0834550	+	0.996512i	$0.526595\pi$
$542$	−21.8932	−0.940392
$543$	2.38806	0.102482
$544$	3.90925	0.167608
$545$	−57.5653	−2.46582
$546$	1.40765	0.0602418
$547$	17.8574	0.763529	0.381765	−	0.924260i	$-0.375316\pi$
$547$	17.8574	0.763529	0.381765	+	0.924260i	$0.375316\pi$
$548$	24.3326	1.03944
$549$	4.90831	0.209481
$550$	−36.5183	−1.55715
$551$	−40.1975	−1.71247
$552$	0.00805705	0.000342931 0
$553$	0.449405	0.0191107
$554$	6.40105	0.271954
$555$	2.95872	0.125591
$556$	16.6445	0.705886
$557$	−7.56677	−0.320614	−0.160307	−	0.987067i	$-0.551248\pi$
$557$	−7.56677	−0.320614	−0.160307	+	0.987067i	$0.551248\pi$
$558$	−15.8068	−0.669157
$559$	−5.99268	−0.253463
$560$	11.8844	0.502208
$561$	−2.64681	−0.111749
$562$	49.7293	2.09770
$563$	29.5624	1.24591	0.622954	−	0.782258i	$-0.285932\pi$
$563$	29.5624	1.24591	0.622954	+	0.782258i	$0.285932\pi$
$564$	12.8087	0.539342
$565$	33.9222	1.42712
$566$	−37.4465	−1.57399
$567$	−0.776263	−0.0326000
$568$	20.0034	0.839324
$569$	−15.1851	−0.636594	−0.318297	−	0.947991i	$-0.603111\pi$
$569$	−15.1851	−0.636594	−0.318297	+	0.947991i	$0.603111\pi$
$570$	30.7727	1.28893
$571$	22.6297	0.947022	0.473511	−	0.880788i	$-0.342986\pi$
$571$	22.6297	0.947022	0.473511	+	0.880788i	$0.342986\pi$
$572$	−5.52569	−0.231041
$573$	−27.0016	−1.12801
$574$	−1.05842	−0.0441777
$575$	0.0293118	0.00122239
$576$	−1.65378	−0.0689074
$577$	0.158444	0.00659613	0.00329806	−	0.999995i	$-0.498950\pi$
$577$	0.158444	0.00659613	0.00329806	+	0.999995i	$0.498950\pi$
$578$	−30.1367	−1.25352
$579$	−15.8649	−0.659323
$580$	29.5862	1.22850
$581$	−7.42027	−0.307845
$582$	−6.07308	−0.251737
$583$	31.9141	1.32175
$584$	−10.5117	−0.434978
$585$	3.11371	0.128736
$586$	−9.09915	−0.375882
$587$	−33.7365	−1.39245	−0.696227	−	0.717822i	$-0.745139\pi$
$587$	−33.7365	−1.39245	−0.696227	+	0.717822i	$0.745139\pi$
$588$	8.24174	0.339884
$589$	47.5075	1.95751
$590$	52.3713	2.15609
$591$	17.7635	0.730693
$592$	4.67215	0.192024
$593$	17.3549	0.712680	0.356340	−	0.934356i	$-0.384025\pi$
$593$	17.3549	0.712680	0.356340	+	0.934356i	$0.384025\pi$
$594$	7.77782	0.319128
$595$	1.49155	0.0611476
$596$	−15.2975	−0.626611
$597$	−9.18815	−0.376046
$598$	0.0113207	0.000462939 0
$599$	−21.8066	−0.890994	−0.445497	−	0.895283i	$-0.646973\pi$
$599$	−21.8066	−0.890994	−0.445497	+	0.895283i	$0.646973\pi$
$600$	6.05955	0.247380
$601$	28.6125	1.16713	0.583564	−	0.812067i	$-0.301658\pi$
$601$	28.6125	1.16713	0.583564	+	0.812067i	$0.301658\pi$
$602$	8.43559	0.343809
$603$	1.70063	0.0692551
$604$	−15.7323	−0.640137
$605$	23.0318	0.936378
$606$	7.27392	0.295483
$607$	−8.40841	−0.341287	−0.170643	−	0.985333i	$-0.554585\pi$
$607$	−8.40841	−0.341287	−0.170643	+	0.985333i	$0.554585\pi$
$608$	34.5259	1.40021
$609$	5.72540	0.232005
$610$	27.7137	1.12210
$611$	−9.94236	−0.402225
$612$	−0.794997	−0.0321358
$613$	−19.1559	−0.773698	−0.386849	−	0.922143i	$-0.626436\pi$
$613$	−19.1559	−0.773698	−0.386849	+	0.922143i	$0.626436\pi$
$614$	−7.33844	−0.296155
$615$	−2.34122	−0.0944073
$616$	−4.29703	−0.173132
$617$	−43.4079	−1.74754	−0.873769	−	0.486341i	$-0.838331\pi$
$617$	−43.4079	−1.74754	−0.873769	+	0.486341i	$0.838331\pi$
$618$	−1.81336	−0.0729442
$619$	−4.85086	−0.194973	−0.0974863	−	0.995237i	$-0.531080\pi$
$619$	−4.85086	−0.194973	−0.0974863	+	0.995237i	$0.531080\pi$
$620$	−34.9665	−1.40429
$621$	−0.00624294	−0.000250520 0
$622$	−13.6438	−0.547066
$623$	1.66147	0.0665656
$624$	4.91689	0.196833
$625$	−26.4311	−1.05725
$626$	19.9451	0.797168
$627$	−23.3762	−0.933557
$628$	−12.8254	−0.511789
$629$	0.586378	0.0233804
$630$	−4.38301	−0.174623
$631$	−2.53153	−0.100779	−0.0503893	−	0.998730i	$-0.516046\pi$
$631$	−2.53153	−0.100779	−0.0503893	+	0.998730i	$0.516046\pi$
$632$	0.747165	0.0297206
$633$	6.15247	0.244539
$634$	−37.4947	−1.48911
$635$	−20.7176	−0.822155
$636$	9.58570	0.380098
$637$	−6.39742	−0.253475
$638$	−57.3660	−2.27114
$639$	−15.4995	−0.613149
$640$	30.1126	1.19031
$641$	19.1872	0.757848	0.378924	−	0.925428i	$-0.376294\pi$
$641$	19.1872	0.757848	0.378924	+	0.925428i	$0.376294\pi$
$642$	2.55457	0.100821
$643$	20.1203	0.793469	0.396735	−	0.917933i	$-0.370143\pi$
$643$	20.1203	0.793469	0.396735	+	0.917933i	$0.370143\pi$
$644$	−0.00624327	−0.000246019 0
$645$	18.6595	0.734716
$646$	6.09872	0.239951
$647$	40.4818	1.59150	0.795752	−	0.605623i	$-0.207076\pi$
$647$	40.4818	1.59150	0.795752	+	0.605623i	$0.207076\pi$
$648$	−1.29059	−0.0506990
$649$	−39.7834	−1.56164
$650$	8.51410	0.333950
$651$	−6.76657	−0.265203
$652$	9.69754	0.379785
$653$	16.4973	0.645587	0.322794	−	0.946469i	$-0.395378\pi$
$653$	16.4973	0.645587	0.322794	+	0.946469i	$0.395378\pi$
$654$	33.5249	1.31093
$655$	−44.6022	−1.74275
$656$	−3.69705	−0.144345
$657$	8.14492	0.317764
$658$	13.9953	0.545595
$659$	−0.899532	−0.0350408	−0.0175204	−	0.999847i	$-0.505577\pi$
$659$	−0.899532	−0.0350408	−0.0175204	+	0.999847i	$0.505577\pi$
$660$	17.2054	0.669720
$661$	−17.9084	−0.696555	−0.348278	−	0.937391i	$-0.613233\pi$
$661$	−17.9084	−0.696555	−0.348278	+	0.937391i	$0.613233\pi$
$662$	21.0085	0.816517
$663$	0.617094	0.0239659
$664$	−12.3367	−0.478756
$665$	13.1731	0.510832
$666$	−1.72310	−0.0667689
$667$	0.0460454	0.00178288
$668$	12.4414	0.481370
$669$	25.2617	0.976672
$670$	9.60226	0.370968
$671$	−21.0525	−0.812724
$672$	−4.91758	−0.189700
$673$	−8.19595	−0.315931	−0.157965	−	0.987445i	$-0.550493\pi$
$673$	−8.19595	−0.315931	−0.157965	+	0.987445i	$0.550493\pi$
$674$	−41.7878	−1.60961
$675$	−4.69519	−0.180718
$676$	1.28829	0.0495497
$677$	−5.46054	−0.209865	−0.104933	−	0.994479i	$-0.533463\pi$
$677$	−5.46054	−0.209865	−0.104933	+	0.994479i	$0.533463\pi$
$678$	−19.7556	−0.758711
$679$	−2.59975	−0.0997694
$680$	2.47980	0.0950959
$681$	10.8563	0.416013
$682$	67.7981	2.59612
$683$	−9.07326	−0.347179	−0.173589	−	0.984818i	$-0.555537\pi$
$683$	−9.07326	−0.347179	−0.173589	+	0.984818i	$0.555537\pi$
$684$	−7.02128	−0.268466
$685$	58.8103	2.24702
$686$	18.8588	0.720034
$687$	28.2592	1.07815
$688$	29.4654	1.12336
$689$	−7.44063	−0.283465
$690$	−0.0352494	−0.00134192
$691$	32.0636	1.21976	0.609879	−	0.792494i	$-0.291218\pi$
$691$	32.0636	1.21976	0.609879	+	0.792494i	$0.291218\pi$
$692$	−17.0350	−0.647575
$693$	3.32952	0.126478
$694$	41.5338	1.57660
$695$	40.2287	1.52596
$696$	9.51885	0.360811
$697$	−0.463998	−0.0175752
$698$	−23.6196	−0.894014
$699$	1.82486	0.0690227
$700$	−4.69544	−0.177471
$701$	45.6033	1.72241	0.861207	−	0.508254i	$-0.169709\pi$
$701$	45.6033	1.72241	0.861207	+	0.508254i	$0.169709\pi$
$702$	−1.81336	−0.0684410
$703$	5.17879	0.195322
$704$	7.09332	0.267340
$705$	30.9576	1.16593
$706$	−55.4360	−2.08636
$707$	3.11381	0.117107
$708$	−11.9493	−0.449084
$709$	6.07286	0.228071	0.114035	−	0.993477i	$-0.463622\pi$
$709$	6.07286	0.228071	0.114035	+	0.993477i	$0.463622\pi$
$710$	−87.5145	−3.28436
$711$	−0.578934	−0.0217117
$712$	2.76231	0.103522
$713$	−0.0544188	−0.00203800
$714$	−0.868650	−0.0325084
$715$	−13.3552	−0.499456
$716$	33.5513	1.25387
$717$	−13.9091	−0.519444
$718$	−15.3078	−0.571280
$719$	−28.7556	−1.07240	−0.536201	−	0.844090i	$-0.680141\pi$
$719$	−28.7556	−1.07240	−0.536201	+	0.844090i	$0.680141\pi$
$720$	−15.3098	−0.570561
$721$	−0.776263	−0.0289095
$722$	19.4090	0.722327
$723$	3.25877	0.121195
$724$	−3.07652	−0.114338
$725$	34.6298	1.28612
$726$	−13.4133	−0.497814
$727$	−41.1707	−1.52694	−0.763468	−	0.645846i	$-0.776505\pi$
$727$	−41.1707	−1.52694	−0.763468	+	0.645846i	$0.776505\pi$
$728$	1.00183	0.0371304
$729$	1.00000	0.0370370
$730$	45.9886	1.70211
$731$	3.69805	0.136777
$732$	−6.32333	−0.233717
$733$	−40.8246	−1.50789	−0.753945	−	0.656938i	$-0.771851\pi$
$733$	−40.8246	−1.50789	−0.753945	+	0.656938i	$0.771851\pi$
$734$	17.8223	0.657831
$735$	19.9197	0.734749
$736$	−0.0395486	−0.00145778
$737$	−7.29429	−0.268688
$738$	1.36348	0.0501905
$739$	−22.7565	−0.837110	−0.418555	−	0.908191i	$-0.637463\pi$
$739$	−22.7565	−0.837110	−0.418555	+	0.908191i	$0.637463\pi$
$740$	−3.81170	−0.140121
$741$	5.45007	0.200213
$742$	10.4738	0.384505
$743$	−7.64330	−0.280405	−0.140203	−	0.990123i	$-0.544775\pi$
$743$	−7.64330	−0.280405	−0.140203	+	0.990123i	$0.544775\pi$
$744$	−11.2499	−0.412440
$745$	−36.9730	−1.35459
$746$	−5.45270	−0.199637
$747$	9.55897	0.349744
$748$	3.40987	0.124677
$749$	1.09356	0.0399578
$750$	1.72104	0.0628434
$751$	8.51648	0.310771	0.155385	−	0.987854i	$-0.450338\pi$
$751$	8.51648	0.310771	0.155385	+	0.987854i	$0.450338\pi$
$752$	48.8854	1.78267
$753$	7.70031	0.280615
$754$	13.3746	0.487076
$755$	−38.0238	−1.38383
$756$	1.00005	0.0363716
$757$	13.5092	0.490999	0.245499	−	0.969397i	$-0.421048\pi$
$757$	13.5092	0.490999	0.245499	+	0.969397i	$0.421048\pi$
$758$	50.9392	1.85020
$759$	0.0267770	0.000971942 0
$760$	21.9012	0.794439
$761$	13.6261	0.493945	0.246972	−	0.969022i	$-0.420564\pi$
$761$	13.6261	0.493945	0.246972	+	0.969022i	$0.420564\pi$
$762$	12.0656	0.437089
$763$	14.3513	0.519552
$764$	34.7860	1.25851
$765$	−1.92145	−0.0694702
$766$	0.443714	0.0160320
$767$	9.27534	0.334913
$768$	−20.8446	−0.752163
$769$	−22.8087	−0.822502	−0.411251	−	0.911522i	$-0.634908\pi$
$769$	−22.8087	−0.822502	−0.411251	+	0.911522i	$0.634908\pi$
$770$	18.7994	0.677484
$771$	6.68712	0.240831
$772$	20.4386	0.735602
$773$	−39.9879	−1.43826	−0.719132	−	0.694873i	$-0.755460\pi$
$773$	−39.9879	−1.43826	−0.719132	+	0.694873i	$0.755460\pi$
$774$	−10.8669	−0.390603
$775$	−40.9273	−1.47015
$776$	−4.32226	−0.155160
$777$	−0.737624	−0.0264621
$778$	−42.2746	−1.51562
$779$	−4.09795	−0.146824
$780$	−4.01137	−0.143630
$781$	66.4797	2.37883
$782$	−0.00698594	−0.000249817 0
$783$	−7.37560	−0.263582
$784$	31.4554	1.12341
$785$	−30.9981	−1.10637
$786$	25.9755	0.926514
$787$	15.6352	0.557333	0.278666	−	0.960388i	$-0.410108\pi$
$787$	15.6352	0.557333	0.278666	+	0.960388i	$0.410108\pi$
$788$	−22.8846	−0.815229
$789$	−4.42005	−0.157358
$790$	−3.26883	−0.116300
$791$	−8.45697	−0.300695
$792$	5.53553	0.196697
$793$	4.90831	0.174299
$794$	57.3297	2.03455
$795$	23.1680	0.821683
$796$	11.8370	0.419552
$797$	12.5015	0.442825	0.221412	−	0.975180i	$-0.428933\pi$
$797$	12.5015	0.442825	0.221412	+	0.975180i	$0.428933\pi$
$798$	−7.67178	−0.271578
$799$	6.13536	0.217054
$800$	−29.7437	−1.05160
$801$	−2.14035	−0.0756256
$802$	−23.8690	−0.842844
$803$	−34.9349	−1.23283
$804$	−2.19091	−0.0772674
$805$	−0.0150895	−0.000531836 0
$806$	−15.8068	−0.556772
$807$	−17.5716	−0.618549
$808$	5.17691	0.182123
$809$	34.0544	1.19729	0.598644	−	0.801015i	$-0.295706\pi$
$809$	34.0544	1.19729	0.598644	+	0.801015i	$0.295706\pi$
$810$	5.64629	0.198390
$811$	24.4921	0.860033	0.430016	−	0.902821i	$-0.358508\pi$
$811$	24.4921	0.860033	0.430016	+	0.902821i	$0.358508\pi$
$812$	−7.37599	−0.258846
$813$	12.0732	0.423427
$814$	7.39067	0.259043
$815$	23.4383	0.821006
$816$	−3.03418	−0.106218
$817$	32.6606	1.14265
$818$	−2.75745	−0.0964120
$819$	−0.776263	−0.0271248
$820$	3.01618	0.105330
$821$	−46.4645	−1.62162	−0.810811	−	0.585308i	$-0.800974\pi$
$821$	−46.4645	−1.62162	−0.810811	+	0.585308i	$0.800974\pi$
$822$	−34.2500	−1.19460
$823$	−46.9528	−1.63667	−0.818337	−	0.574739i	$-0.805104\pi$
$823$	−46.9528	−1.63667	−0.818337	+	0.574739i	$0.805104\pi$
$824$	−1.29059	−0.0449597
$825$	20.1384	0.701130
$826$	−13.0564	−0.454290
$827$	−31.5176	−1.09597	−0.547987	−	0.836487i	$-0.684606\pi$
$827$	−31.5176	−1.09597	−0.547987	+	0.836487i	$0.684606\pi$
$828$	0.00804272	0.000279504 0
$829$	28.3738	0.985463	0.492731	−	0.870181i	$-0.335999\pi$
$829$	28.3738	0.985463	0.492731	+	0.870181i	$0.335999\pi$
$830$	53.9727	1.87342
$831$	−3.52993	−0.122452
$832$	−1.65378	−0.0573344
$833$	3.94780	0.136783
$834$	−23.4284	−0.811259
$835$	30.0699	1.04061
$836$	30.1154	1.04156
$837$	8.71686	0.301299
$838$	46.4014	1.60291
$839$	34.5407	1.19248	0.596238	−	0.802808i	$-0.296661\pi$
$839$	34.5407	1.19248	0.596238	+	0.802808i	$0.296661\pi$
$840$	−3.11942	−0.107630
$841$	25.3994	0.875843
$842$	44.5907	1.53670
$843$	−27.4237	−0.944524
$844$	−7.92617	−0.272830
$845$	3.11371	0.107115
$846$	−18.0291	−0.619854
$847$	−5.74195	−0.197296
$848$	36.5847	1.25633
$849$	20.6503	0.708715
$850$	−5.25399	−0.180210
$851$	−0.00593219	−0.000203353 0
$852$	19.9678	0.684087
$853$	42.6215	1.45933	0.729667	−	0.683803i	$-0.239675\pi$
$853$	42.6215	1.45933	0.729667	+	0.683803i	$0.239675\pi$
$854$	−6.90917	−0.236427
$855$	−16.9699	−0.580360
$856$	1.81811	0.0621418
$857$	3.09315	0.105660	0.0528300	−	0.998604i	$-0.483176\pi$
$857$	3.09315	0.105660	0.0528300	+	0.998604i	$0.483176\pi$
$858$	7.77782	0.265530
$859$	32.8008	1.11915	0.559574	−	0.828780i	$-0.310965\pi$
$859$	32.8008	1.11915	0.559574	+	0.828780i	$0.310965\pi$
$860$	−24.0389	−0.819718
$861$	0.583678	0.0198917
$862$	−14.7433	−0.502158
$863$	−20.1307	−0.685257	−0.342628	−	0.939471i	$-0.611317\pi$
$863$	−20.1307	−0.685257	−0.342628	+	0.939471i	$0.611317\pi$
$864$	6.33494	0.215519
$865$	−41.1725	−1.39991
$866$	36.0430	1.22479
$867$	16.6192	0.564417
$868$	8.71732	0.295885
$869$	2.48314	0.0842349
$870$	−41.6448	−1.41189
$871$	1.70063	0.0576237
$872$	23.8599	0.808000
$873$	3.34907	0.113349
$874$	−0.0616988	−0.00208699
$875$	0.736740	0.0249063
$876$	−10.4930	−0.354527
$877$	−31.8163	−1.07436	−0.537180	−	0.843468i	$-0.680510\pi$
$877$	−31.8163	−1.07436	−0.537180	+	0.843468i	$0.680510\pi$
$878$	58.7603	1.98307
$879$	5.01783	0.169247
$880$	65.6661	2.21360
$881$	−40.8266	−1.37548	−0.687742	−	0.725955i	$-0.741398\pi$
$881$	−40.8266	−1.37548	−0.687742	+	0.725955i	$0.741398\pi$
$882$	−11.6008	−0.390621
$883$	39.3076	1.32281	0.661403	−	0.750031i	$-0.269961\pi$
$883$	39.3076	1.32281	0.661403	+	0.750031i	$0.269961\pi$
$884$	−0.794997	−0.0267386
$885$	−28.8807	−0.970814
$886$	49.6881	1.66931
$887$	−2.52070	−0.0846367	−0.0423183	−	0.999104i	$-0.513474\pi$
$887$	−2.52070	−0.0846367	−0.0423183	+	0.999104i	$0.513474\pi$
$888$	−1.22635	−0.0411535
$889$	5.16501	0.173229
$890$	−12.0850	−0.405092
$891$	−4.28916	−0.143692
$892$	−32.5444	−1.08967
$893$	54.1866	1.81328
$894$	21.5324	0.720150
$895$	81.0910	2.71057
$896$	−7.50722	−0.250799
$897$	−0.00624294	−0.000208446 0
$898$	−43.2377	−1.44286
$899$	−64.2921	−2.14426
$900$	6.04878	0.201626
$901$	4.59156	0.152967
$902$	−5.84820	−0.194724
$903$	−4.65190	−0.154805
$904$	−14.0603	−0.467637
$905$	−7.43574	−0.247172
$906$	22.1443	0.735695
$907$	−16.6200	−0.551859	−0.275930	−	0.961178i	$-0.588986\pi$
$907$	−16.6200	−0.551859	−0.275930	+	0.961178i	$0.588986\pi$
$908$	−13.9860	−0.464142
$909$	−4.01128	−0.133046
$910$	−4.38301	−0.145295
$911$	−5.58188	−0.184936	−0.0924680	−	0.995716i	$-0.529476\pi$
$911$	−5.58188	−0.184936	−0.0924680	+	0.995716i	$0.529476\pi$
$912$	−26.7974	−0.887350
$913$	−41.0000	−1.35690
$914$	41.1580	1.36139
$915$	−15.2830	−0.505242
$916$	−36.4061	−1.20289
$917$	11.1195	0.367199
$918$	1.11902	0.0369330
$919$	−30.6358	−1.01058	−0.505291	−	0.862949i	$-0.668615\pi$
$919$	−30.6358	−1.01058	−0.505291	+	0.862949i	$0.668615\pi$
$920$	−0.0250873	−0.000827104 0
$921$	4.04686	0.133349
$922$	3.84504	0.126630
$923$	−15.4995	−0.510171
$924$	−4.28939	−0.141111
$925$	−4.46149	−0.146693
$926$	24.6371	0.809625
$927$	1.00000	0.0328443
$928$	−46.7240	−1.53379
$929$	31.5857	1.03629	0.518147	−	0.855292i	$-0.326622\pi$
$929$	31.5857	1.03629	0.518147	+	0.855292i	$0.326622\pi$
$930$	49.2179	1.61392
$931$	34.8664	1.14270
$932$	−2.35096	−0.0770081
$933$	7.52401	0.246325
$934$	−10.9797	−0.359268
$935$	8.24141	0.269523
$936$	−1.29059	−0.0421841
$937$	−53.9571	−1.76270	−0.881351	−	0.472462i	$-0.843365\pi$
$937$	−53.9571	−1.76270	−0.881351	+	0.472462i	$0.843365\pi$
$938$	−2.39389	−0.0781633
$939$	−10.9990	−0.358938
$940$	−39.8824	−1.30082
$941$	18.6764	0.608832	0.304416	−	0.952539i	$-0.401539\pi$
$941$	18.6764	0.608832	0.304416	+	0.952539i	$0.401539\pi$
$942$	18.0527	0.588188
$943$	0.00469411	0.000152861 0
$944$	−45.6058	−1.48434
$945$	2.41706	0.0786269
$946$	46.6100	1.51542
$947$	44.7871	1.45539	0.727693	−	0.685903i	$-0.240592\pi$
$947$	44.7871	1.45539	0.727693	+	0.685903i	$0.240592\pi$
$948$	0.745836	0.0242236
$949$	8.14492	0.264395
$950$	−46.4024	−1.50549
$951$	20.6769	0.670494
$952$	−0.618226	−0.0200368
$953$	−17.0417	−0.552035	−0.276017	−	0.961153i	$-0.589015\pi$
$953$	−17.0417	−0.552035	−0.276017	+	0.961153i	$0.589015\pi$
$954$	−13.4926	−0.436838
$955$	84.0752	2.72061
$956$	17.9189	0.579540
$957$	31.6351	1.02262
$958$	−44.7467	−1.44570
$959$	−14.6617	−0.473450
$960$	5.14939	0.166196
$961$	44.9837	1.45109
$962$	−1.72310	−0.0555551
$963$	−1.40875	−0.0453963
$964$	−4.19825	−0.135217
$965$	49.3987	1.59020
$966$	0.00878785	0.000282745 0
$967$	45.3560	1.45855	0.729275	−	0.684220i	$-0.239857\pi$
$967$	45.3560	1.45855	0.729275	+	0.684220i	$0.239857\pi$
$968$	−9.54636	−0.306832
$969$	−3.36321	−0.108042
$970$	18.9098	0.607157
$971$	−16.4925	−0.529269	−0.264635	−	0.964349i	$-0.585251\pi$
$971$	−16.4925	−0.529269	−0.264635	+	0.964349i	$0.585251\pi$
$972$	−1.28829	−0.0413220
$973$	−10.0292	−0.321521
$974$	65.1083	2.08621
$975$	−4.69519	−0.150366
$976$	−24.1336	−0.772498
$977$	53.6633	1.71684	0.858420	−	0.512947i	$-0.171446\pi$
$977$	53.6633	1.71684	0.858420	+	0.512947i	$0.171446\pi$
$978$	−13.6500	−0.436479
$979$	9.18031	0.293404
$980$	−25.6624	−0.819755
$981$	−18.4877	−0.590266
$982$	−44.2425	−1.41184
$983$	−40.2106	−1.28252	−0.641260	−	0.767324i	$-0.721588\pi$
$983$	−40.2106	−1.28252	−0.641260	+	0.767324i	$0.721588\pi$
$984$	0.970403	0.0309353
$985$	−55.3104	−1.76234
$986$	−8.25341	−0.262842
$987$	−7.71788	−0.245663
$988$	−7.02128	−0.223377
$989$	−0.0374119	−0.00118963
$990$	−24.2179	−0.769694
$991$	−14.3566	−0.456052	−0.228026	−	0.973655i	$-0.573227\pi$
$991$	−14.3566	−0.456052	−0.228026	+	0.973655i	$0.573227\pi$
$992$	55.2208	1.75326
$993$	−11.5853	−0.367650
$994$	21.8178	0.692018
$995$	28.6092	0.906974
$996$	−12.3147	−0.390207
$997$	10.8016	0.342089	0.171044	−	0.985263i	$-0.445286\pi$
$997$	10.8016	0.342089	0.171044	+	0.985263i	$0.445286\pi$
$998$	21.4697	0.679612
$999$	0.950225	0.0300638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4017.2.a.h.1.20	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4017.2.a.h.1.20	✓	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:	\( N \)	\(=\)	\( 4017 = 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4017.a (trivial)

\(f(q)\)	\(=\)	\(q+1.81336 q^{2} -1.00000 q^{3} +1.28829 q^{4} +3.11371 q^{5} -1.81336 q^{6} -0.776263 q^{7} -1.29059 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.81336 q^{2} -1.00000 q^{3} +1.28829 q^{4} +3.11371 q^{5} -1.81336 q^{6} -0.776263 q^{7} -1.29059 q^{8} +1.00000 q^{9} +5.64629 q^{10} -4.28916 q^{11} -1.28829 q^{12} +1.00000 q^{13} -1.40765 q^{14} -3.11371 q^{15} -4.91689 q^{16} -0.617094 q^{17} +1.81336 q^{18} -5.45007 q^{19} +4.01137 q^{20} +0.776263 q^{21} -7.77782 q^{22} +0.00624294 q^{23} +1.29059 q^{24} +4.69519 q^{25} +1.81336 q^{26} -1.00000 q^{27} -1.00005 q^{28} +7.37560 q^{29} -5.64629 q^{30} -8.71686 q^{31} -6.33494 q^{32} +4.28916 q^{33} -1.11902 q^{34} -2.41706 q^{35} +1.28829 q^{36} -0.950225 q^{37} -9.88297 q^{38} -1.00000 q^{39} -4.01851 q^{40} +0.751908 q^{41} +1.40765 q^{42} -5.99268 q^{43} -5.52569 q^{44} +3.11371 q^{45} +0.0113207 q^{46} -9.94236 q^{47} +4.91689 q^{48} -6.39742 q^{49} +8.51410 q^{50} +0.617094 q^{51} +1.28829 q^{52} -7.44063 q^{53} -1.81336 q^{54} -13.3552 q^{55} +1.00183 q^{56} +5.45007 q^{57} +13.3746 q^{58} +9.27534 q^{59} -4.01137 q^{60} +4.90831 q^{61} -15.8068 q^{62} -0.776263 q^{63} -1.65378 q^{64} +3.11371 q^{65} +7.77782 q^{66} +1.70063 q^{67} -0.794997 q^{68} -0.00624294 q^{69} -4.38301 q^{70} -15.4995 q^{71} -1.29059 q^{72} +8.14492 q^{73} -1.72310 q^{74} -4.69519 q^{75} -7.02128 q^{76} +3.32952 q^{77} -1.81336 q^{78} -0.578934 q^{79} -15.3098 q^{80} +1.00000 q^{81} +1.36348 q^{82} +9.55897 q^{83} +1.00005 q^{84} -1.92145 q^{85} -10.8669 q^{86} -7.37560 q^{87} +5.53553 q^{88} -2.14035 q^{89} +5.64629 q^{90} -0.776263 q^{91} +0.00804272 q^{92} +8.71686 q^{93} -18.0291 q^{94} -16.9699 q^{95} +6.33494 q^{96} +3.34907 q^{97} -11.6008 q^{98} -4.28916 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9	\( 25 q - 4 q^{2} - 25 q^{3} + 28 q^{4} - 5 q^{5} + 4 q^{6} - 7 q^{7} - 9 q^{8} + 25 q^{9} - 12 q^{10} - 23 q^{11} - 28 q^{12} + 25 q^{13} + 5 q^{15} + 26 q^{16} - 14 q^{17} - 4 q^{18} - 4 q^{19} - 12 q^{20} + 7 q^{21} - 7 q^{22} - 47 q^{23} + 9 q^{24} + 26 q^{25} - 4 q^{26} - 25 q^{27} - 38 q^{28} + 6 q^{29} + 12 q^{30} - 8 q^{31} - 62 q^{32} + 23 q^{33} + 25 q^{34} + 28 q^{36} - 20 q^{37} - 2 q^{38} - 25 q^{39} - 8 q^{40} - 33 q^{41} - 13 q^{43} - 13 q^{44} - 5 q^{45} - 21 q^{46} - 48 q^{47} - 26 q^{48} + 40 q^{49} - 9 q^{50} + 14 q^{51} + 28 q^{52} - 24 q^{53} + 4 q^{54} - 2 q^{55} - 14 q^{56} + 4 q^{57} - 31 q^{58} - 36 q^{59} + 12 q^{60} + 25 q^{61} - 7 q^{62} - 7 q^{63} + 45 q^{64} - 5 q^{65} + 7 q^{66} - 2 q^{67} - 32 q^{68} + 47 q^{69} - 13 q^{70} - 60 q^{71} - 9 q^{72} + 28 q^{73} - 16 q^{74} - 26 q^{75} - 12 q^{76} - 17 q^{77} + 4 q^{78} - 29 q^{79} - 88 q^{80} + 25 q^{81} - 22 q^{82} - 71 q^{83} + 38 q^{84} + 3 q^{85} - 3 q^{86} - 6 q^{87} + 23 q^{88} - 46 q^{89} - 12 q^{90} - 7 q^{91} - 69 q^{92} + 8 q^{93} + 4 q^{94} - 47 q^{95} + 62 q^{96} - 14 q^{97} - 71 q^{98} - 23 q^{99}+O(q^{100}) \) 25 * q - 4 * q^2 - 25 * q^3 + 28 * q^4 - 5 * q^5 + 4 * q^6 - 7 * q^7 - 9 * q^8 + 25 * q^9 - 12 * q^10 - 23 * q^11 - 28 * q^12 + 25 * q^13 + 5 * q^15 + 26 * q^16 - 14 * q^17 - 4 * q^18 - 4 * q^19 - 12 * q^20 + 7 * q^21 - 7 * q^22 - 47 * q^23 + 9 * q^24 + 26 * q^25 - 4 * q^26 - 25 * q^27 - 38 * q^28 + 6 * q^29 + 12 * q^30 - 8 * q^31 - 62 * q^32 + 23 * q^33 + 25 * q^34 + 28 * q^36 - 20 * q^37 - 2 * q^38 - 25 * q^39 - 8 * q^40 - 33 * q^41 - 13 * q^43 - 13 * q^44 - 5 * q^45 - 21 * q^46 - 48 * q^47 - 26 * q^48 + 40 * q^49 - 9 * q^50 + 14 * q^51 + 28 * q^52 - 24 * q^53 + 4 * q^54 - 2 * q^55 - 14 * q^56 + 4 * q^57 - 31 * q^58 - 36 * q^59 + 12 * q^60 + 25 * q^61 - 7 * q^62 - 7 * q^63 + 45 * q^64 - 5 * q^65 + 7 * q^66 - 2 * q^67 - 32 * q^68 + 47 * q^69 - 13 * q^70 - 60 * q^71 - 9 * q^72 + 28 * q^73 - 16 * q^74 - 26 * q^75 - 12 * q^76 - 17 * q^77 + 4 * q^78 - 29 * q^79 - 88 * q^80 + 25 * q^81 - 22 * q^82 - 71 * q^83 + 38 * q^84 + 3 * q^85 - 3 * q^86 - 6 * q^87 + 23 * q^88 - 46 * q^89 - 12 * q^90 - 7 * q^91 - 69 * q^92 + 8 * q^93 + 4 * q^94 - 47 * q^95 + 62 * q^96 - 14 * q^97 - 71 * q^98 - 23 * q^99

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