LMFDB - Embedded newform 983.2.a.a.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,2,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	983.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:	$7.84929451869$
Analytic rank:	$1$
Dimension:	$28$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.21759 q^{2} +0.931642 q^{3} +2.91773 q^{4} +0.396530 q^{5} -2.06600 q^{6} +2.27074 q^{7} -2.03515 q^{8} -2.13204 q^{9} +O(q^{10})$	\(q-2.21759 q^{2} +0.931642 q^{3} +2.91773 q^{4} +0.396530 q^{5} -2.06600 q^{6} +2.27074 q^{7} -2.03515 q^{8} -2.13204 q^{9} -0.879344 q^{10} +0.794208 q^{11} +2.71828 q^{12} -5.19322 q^{13} -5.03559 q^{14} +0.369424 q^{15} -1.32232 q^{16} -0.949276 q^{17} +4.72801 q^{18} -2.80589 q^{19} +1.15697 q^{20} +2.11552 q^{21} -1.76123 q^{22} -5.61608 q^{23} -1.89603 q^{24} -4.84276 q^{25} +11.5165 q^{26} -4.78123 q^{27} +6.62541 q^{28} +3.20877 q^{29} -0.819233 q^{30} -6.86425 q^{31} +7.00267 q^{32} +0.739918 q^{33} +2.10511 q^{34} +0.900419 q^{35} -6.22072 q^{36} -2.34183 q^{37} +6.22234 q^{38} -4.83822 q^{39} -0.806997 q^{40} +3.61926 q^{41} -4.69136 q^{42} +2.22212 q^{43} +2.31728 q^{44} -0.845420 q^{45} +12.4542 q^{46} +2.77338 q^{47} -1.23193 q^{48} -1.84373 q^{49} +10.7393 q^{50} -0.884386 q^{51} -15.1524 q^{52} +1.27975 q^{53} +10.6028 q^{54} +0.314928 q^{55} -4.62129 q^{56} -2.61409 q^{57} -7.11576 q^{58} -4.10676 q^{59} +1.07788 q^{60} -0.814060 q^{61} +15.2221 q^{62} -4.84132 q^{63} -12.8844 q^{64} -2.05927 q^{65} -1.64084 q^{66} +0.504666 q^{67} -2.76973 q^{68} -5.23218 q^{69} -1.99676 q^{70} +7.75245 q^{71} +4.33902 q^{72} +5.86353 q^{73} +5.19323 q^{74} -4.51172 q^{75} -8.18683 q^{76} +1.80344 q^{77} +10.7292 q^{78} -3.72219 q^{79} -0.524342 q^{80} +1.94174 q^{81} -8.02605 q^{82} -3.33848 q^{83} +6.17251 q^{84} -0.376417 q^{85} -4.92777 q^{86} +2.98943 q^{87} -1.61633 q^{88} +4.59051 q^{89} +1.87480 q^{90} -11.7925 q^{91} -16.3862 q^{92} -6.39502 q^{93} -6.15024 q^{94} -1.11262 q^{95} +6.52398 q^{96} +0.550161 q^{97} +4.08864 q^{98} -1.69329 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) $ 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.21759	−1.56808	−0.784038	−	0.620713i	$-0.786843\pi$
$2$	−2.21759	−1.56808	−0.784038	+	0.620713i	$0.786843\pi$
$3$	0.931642	0.537884	0.268942	−	0.963156i	$-0.413326\pi$
$3$	0.931642	0.537884	0.268942	+	0.963156i	$0.413326\pi$
$4$	2.91773	1.45886
$5$	0.396530	0.177334	0.0886669	−	0.996061i	$-0.471739\pi$
$5$	0.396530	0.177334	0.0886669	+	0.996061i	$0.471739\pi$
$6$	−2.06600	−0.843443
$7$	2.27074	0.858260	0.429130	−	0.903243i	$-0.358820\pi$
$7$	2.27074	0.858260	0.429130	+	0.903243i	$0.358820\pi$
$8$	−2.03515	−0.719533
$9$	−2.13204	−0.710681
$10$	−0.879344	−0.278073
$11$	0.794208	0.239463	0.119731	−	0.992806i	$-0.461797\pi$
$11$	0.794208	0.239463	0.119731	+	0.992806i	$0.461797\pi$
$12$	2.71828	0.784699
$13$	−5.19322	−1.44034	−0.720170	−	0.693798i	$-0.755936\pi$
$13$	−5.19322	−1.44034	−0.720170	+	0.693798i	$0.755936\pi$
$14$	−5.03559	−1.34582
$15$	0.369424	0.0953849
$16$	−1.32232	−0.330581
$17$	−0.949276	−0.230233	−0.115117	−	0.993352i	$-0.536724\pi$
$17$	−0.949276	−0.230233	−0.115117	+	0.993352i	$0.536724\pi$
$18$	4.72801	1.11440
$19$	−2.80589	−0.643716	−0.321858	−	0.946788i	$-0.604307\pi$
$19$	−2.80589	−0.643716	−0.321858	+	0.946788i	$0.604307\pi$
$20$	1.15697	0.258706
$21$	2.11552	0.461644
$22$	−1.76123	−0.375496
$23$	−5.61608	−1.17103	−0.585517	−	0.810660i	$-0.699108\pi$
$23$	−5.61608	−1.17103	−0.585517	+	0.810660i	$0.699108\pi$
$24$	−1.89603	−0.387025
$25$	−4.84276	−0.968553
$26$	11.5165	2.25856
$27$	−4.78123	−0.920147
$28$	6.62541	1.25208
$29$	3.20877	0.595854	0.297927	−	0.954589i	$-0.403705\pi$
$29$	3.20877	0.595854	0.297927	+	0.954589i	$0.403705\pi$
$30$	−0.819233	−0.149571
$31$	−6.86425	−1.23285	−0.616427	−	0.787412i	$-0.711421\pi$
$31$	−6.86425	−1.23285	−0.616427	+	0.787412i	$0.711421\pi$
$32$	7.00267	1.23791
$33$	0.739918	0.128803
$34$	2.10511	0.361023
$35$	0.900419	0.152199
$36$	−6.22072	−1.03679
$37$	−2.34183	−0.384994	−0.192497	−	0.981298i	$-0.561659\pi$
$37$	−2.34183	−0.384994	−0.192497	+	0.981298i	$0.561659\pi$
$38$	6.22234	1.00940
$39$	−4.83822	−0.774735
$40$	−0.806997	−0.127598
$41$	3.61926	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$41$	3.61926	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$42$	−4.69136	−0.723893
$43$	2.22212	0.338870	0.169435	−	0.985541i	$-0.445806\pi$
$43$	2.22212	0.338870	0.169435	+	0.985541i	$0.445806\pi$
$44$	2.31728	0.349344
$45$	−0.845420	−0.126028
$46$	12.4542	1.83627
$47$	2.77338	0.404540	0.202270	−	0.979330i	$-0.435168\pi$
$47$	2.77338	0.404540	0.202270	+	0.979330i	$0.435168\pi$
$48$	−1.23193	−0.177814
$49$	−1.84373	−0.263390
$50$	10.7393	1.51876
$51$	−0.884386	−0.123839
$52$	−15.1524	−2.10126
$53$	1.27975	0.175788	0.0878939	−	0.996130i	$-0.471986\pi$
$53$	1.27975	0.175788	0.0878939	+	0.996130i	$0.471986\pi$
$54$	10.6028	1.44286
$55$	0.314928	0.0424648
$56$	−4.62129	−0.617546
$57$	−2.61409	−0.346244
$58$	−7.11576	−0.934345
$59$	−4.10676	−0.534654	−0.267327	−	0.963606i	$-0.586140\pi$
$59$	−4.10676	−0.534654	−0.267327	+	0.963606i	$0.586140\pi$
$60$	1.07788	0.139154
$61$	−0.814060	−0.104230	−0.0521149	−	0.998641i	$-0.516596\pi$
$61$	−0.814060	−0.104230	−0.0521149	+	0.998641i	$0.516596\pi$
$62$	15.2221	1.93321
$63$	−4.84132	−0.609949
$64$	−12.8844	−1.61055
$65$	−2.05927	−0.255421
$66$	−1.64084	−0.201973
$67$	0.504666	0.0616548	0.0308274	−	0.999525i	$-0.490186\pi$
$67$	0.504666	0.0616548	0.0308274	+	0.999525i	$0.490186\pi$
$68$	−2.76973	−0.335879
$69$	−5.23218	−0.629880
$70$	−1.99676	−0.238659
$71$	7.75245	0.920047	0.460023	−	0.887907i	$-0.347841\pi$
$71$	7.75245	0.920047	0.460023	+	0.887907i	$0.347841\pi$
$72$	4.33902	0.511359
$73$	5.86353	0.686274	0.343137	−	0.939285i	$-0.388511\pi$
$73$	5.86353	0.686274	0.343137	+	0.939285i	$0.388511\pi$
$74$	5.19323	0.603700
$75$	−4.51172	−0.520969
$76$	−8.18683	−0.939094
$77$	1.80344	0.205521
$78$	10.7292	1.21484
$79$	−3.72219	−0.418779	−0.209390	−	0.977832i	$-0.567148\pi$
$79$	−3.72219	−0.418779	−0.209390	+	0.977832i	$0.567148\pi$
$80$	−0.524342	−0.0586232
$81$	1.94174	0.215749
$82$	−8.02605	−0.886329
$83$	−3.33848	−0.366446	−0.183223	−	0.983071i	$-0.558653\pi$
$83$	−3.33848	−0.366446	−0.183223	+	0.983071i	$0.558653\pi$
$84$	6.17251	0.673476
$85$	−0.376417	−0.0408282
$86$	−4.92777	−0.531375
$87$	2.98943	0.320500
$88$	−1.61633	−0.172301
$89$	4.59051	0.486593	0.243296	−	0.969952i	$-0.421771\pi$
$89$	4.59051	0.486593	0.243296	+	0.969952i	$0.421771\pi$
$90$	1.87480	0.197621
$91$	−11.7925	−1.23619
$92$	−16.3862	−1.70838
$93$	−6.39502	−0.663132
$94$	−6.15024	−0.634349
$95$	−1.11262	−0.114153
$96$	6.52398	0.665851
$97$	0.550161	0.0558604	0.0279302	−	0.999610i	$-0.491108\pi$
$97$	0.550161	0.0558604	0.0279302	+	0.999610i	$0.491108\pi$
$98$	4.08864	0.413015
$99$	−1.69329	−0.170182
$100$	−14.1299	−1.41299
$101$	−0.435331	−0.0433170	−0.0216585	−	0.999765i	$-0.506895\pi$
$101$	−0.435331	−0.0433170	−0.0216585	+	0.999765i	$0.506895\pi$
$102$	1.96121	0.194189
$103$	−7.64638	−0.753420	−0.376710	−	0.926331i	$-0.622945\pi$
$103$	−7.64638	−0.753420	−0.376710	+	0.926331i	$0.622945\pi$
$104$	10.5690	1.03637
$105$	0.838868	0.0818651
$106$	−2.83798	−0.275649
$107$	−13.4043	−1.29584	−0.647920	−	0.761708i	$-0.724361\pi$
$107$	−13.4043	−1.29584	−0.647920	+	0.761708i	$0.724361\pi$
$108$	−13.9503	−1.34237
$109$	1.73472	0.166156	0.0830779	−	0.996543i	$-0.473525\pi$
$109$	1.73472	0.166156	0.0830779	+	0.996543i	$0.473525\pi$
$110$	−0.698382	−0.0665881
$111$	−2.18175	−0.207082
$112$	−3.00266	−0.283724
$113$	−2.65932	−0.250167	−0.125084	−	0.992146i	$-0.539920\pi$
$113$	−2.65932	−0.250167	−0.125084	+	0.992146i	$0.539920\pi$
$114$	5.79699	0.542938
$115$	−2.22695	−0.207664
$116$	9.36233	0.869270
$117$	11.0722	1.02362
$118$	9.10712	0.838378
$119$	−2.15556	−0.197600
$120$	−0.751833	−0.0686326
$121$	−10.3692	−0.942658
$122$	1.80526	0.163440
$123$	3.37185	0.304030
$124$	−20.0280	−1.79857
$125$	−3.90296	−0.349091
$126$	10.7361	0.956447
$127$	−8.26394	−0.733306	−0.366653	−	0.930358i	$-0.619496\pi$
$127$	−8.26394	−0.733306	−0.366653	+	0.930358i	$0.619496\pi$
$128$	14.5671	1.28756
$129$	2.07022	0.182273
$130$	4.56663	0.400520
$131$	−6.84827	−0.598336	−0.299168	−	0.954200i	$-0.596709\pi$
$131$	−6.84827	−0.598336	−0.299168	+	0.954200i	$0.596709\pi$
$132$	2.15888	0.187906
$133$	−6.37146	−0.552476
$134$	−1.11915	−0.0966794
$135$	−1.89590	−0.163173
$136$	1.93192	0.165660
$137$	−3.53860	−0.302323	−0.151162	−	0.988509i	$-0.548301\pi$
$137$	−3.53860	−0.302323	−0.151162	+	0.988509i	$0.548301\pi$
$138$	11.6028	0.987700
$139$	−6.27731	−0.532434	−0.266217	−	0.963913i	$-0.585774\pi$
$139$	−6.27731	−0.532434	−0.266217	+	0.963913i	$0.585774\pi$
$140$	2.62718	0.222037
$141$	2.58380	0.217595
$142$	−17.1918	−1.44270
$143$	−4.12450	−0.344908
$144$	2.81925	0.234938
$145$	1.27238	0.105665
$146$	−13.0029	−1.07613
$147$	−1.71769	−0.141673
$148$	−6.83282	−0.561654
$149$	1.84618	0.151245	0.0756224	−	0.997137i	$-0.475906\pi$
$149$	1.84618	0.151245	0.0756224	+	0.997137i	$0.475906\pi$
$150$	10.0052	0.816919
$151$	−12.6168	−1.02674	−0.513370	−	0.858168i	$-0.671603\pi$
$151$	−12.6168	−1.02674	−0.513370	+	0.858168i	$0.671603\pi$
$152$	5.71040	0.463175
$153$	2.02390	0.163623
$154$	−3.99930	−0.322273
$155$	−2.72188	−0.218627
$156$	−14.1166	−1.13023
$157$	5.08202	0.405589	0.202795	−	0.979221i	$-0.434998\pi$
$157$	5.08202	0.405589	0.202795	+	0.979221i	$0.434998\pi$
$158$	8.25432	0.656678
$159$	1.19227	0.0945534
$160$	2.77677	0.219523
$161$	−12.7527	−1.00505
$162$	−4.30599	−0.338311
$163$	−9.66205	−0.756790	−0.378395	−	0.925644i	$-0.623524\pi$
$163$	−9.66205	−0.756790	−0.378395	+	0.925644i	$0.623524\pi$
$164$	10.5600	0.824598
$165$	0.293400	0.0228411
$166$	7.40339	0.574615
$167$	−0.802885	−0.0621291	−0.0310646	−	0.999517i	$-0.509890\pi$
$167$	−0.802885	−0.0621291	−0.0310646	+	0.999517i	$0.509890\pi$
$168$	−4.30539	−0.332168
$169$	13.9695	1.07458
$170$	0.834740	0.0640217
$171$	5.98229	0.457477
$172$	6.48355	0.494366
$173$	−20.1899	−1.53501	−0.767507	−	0.641041i	$-0.778503\pi$
$173$	−20.1899	−1.53501	−0.767507	+	0.641041i	$0.778503\pi$
$174$	−6.62934	−0.502569
$175$	−10.9967	−0.831270
$176$	−1.05020	−0.0791618
$177$	−3.82603	−0.287582
$178$	−10.1799	−0.763014
$179$	23.0164	1.72032	0.860162	−	0.510021i	$-0.170362\pi$
$179$	23.0164	1.72032	0.860162	+	0.510021i	$0.170362\pi$
$180$	−2.46671	−0.183857
$181$	7.56666	0.562426	0.281213	−	0.959645i	$-0.409263\pi$
$181$	7.56666	0.562426	0.281213	+	0.959645i	$0.409263\pi$
$182$	26.1509	1.93843
$183$	−0.758413	−0.0560635
$184$	11.4295	0.842597
$185$	−0.928606	−0.0682725
$186$	14.1816	1.03984
$187$	−0.753923	−0.0551323
$188$	8.09198	0.590168
$189$	−10.8569	−0.789726
$190$	2.46735	0.179000
$191$	26.6004	1.92474	0.962368	−	0.271750i	$-0.0876025\pi$
$191$	26.6004	1.92474	0.962368	+	0.271750i	$0.0876025\pi$
$192$	−12.0037	−0.866291
$193$	19.7567	1.42212	0.711059	−	0.703132i	$-0.248216\pi$
$193$	19.7567	1.42212	0.711059	+	0.703132i	$0.248216\pi$
$194$	−1.22004	−0.0875934
$195$	−1.91850	−0.137387
$196$	−5.37950	−0.384250
$197$	2.04512	0.145709	0.0728544	−	0.997343i	$-0.476789\pi$
$197$	2.04512	0.145709	0.0728544	+	0.997343i	$0.476789\pi$
$198$	3.75502	0.266858
$199$	25.1822	1.78512	0.892558	−	0.450932i	$-0.148908\pi$
$199$	25.1822	1.78512	0.892558	+	0.450932i	$0.148908\pi$
$200$	9.85573	0.696906
$201$	0.470168	0.0331631
$202$	0.965387	0.0679244
$203$	7.28630	0.511398
$204$	−2.58040	−0.180664
$205$	1.43515	0.100235
$206$	16.9566	1.18142
$207$	11.9737	0.832232
$208$	6.86712	0.476149
$209$	−2.22846	−0.154146
$210$	−1.86027	−0.128371
$211$	−10.1508	−0.698813	−0.349407	−	0.936971i	$-0.613617\pi$
$211$	−10.1508	−0.698813	−0.349407	+	0.936971i	$0.613617\pi$
$212$	3.73397	0.256450
$213$	7.22251	0.494878
$214$	29.7252	2.03198
$215$	0.881139	0.0600932
$216$	9.73050	0.662076
$217$	−15.5869	−1.05811
$218$	−3.84690	−0.260545
$219$	5.46271	0.369135
$220$	0.918873	0.0619504
$221$	4.92980	0.331614
$222$	4.83823	0.324721
$223$	5.79943	0.388359	0.194179	−	0.980966i	$-0.437796\pi$
$223$	5.79943	0.388359	0.194179	+	0.980966i	$0.437796\pi$
$224$	15.9013	1.06245
$225$	10.3250	0.688332
$226$	5.89728	0.392282
$227$	6.19116	0.410922	0.205461	−	0.978665i	$-0.434131\pi$
$227$	6.19116	0.410922	0.205461	+	0.978665i	$0.434131\pi$
$228$	−7.62719	−0.505123
$229$	13.9593	0.922456	0.461228	−	0.887282i	$-0.347409\pi$
$229$	13.9593	0.922456	0.461228	+	0.887282i	$0.347409\pi$
$230$	4.93847	0.325633
$231$	1.68016	0.110547
$232$	−6.53032	−0.428737
$233$	−13.0703	−0.856265	−0.428132	−	0.903716i	$-0.640828\pi$
$233$	−13.0703	−0.856265	−0.428132	+	0.903716i	$0.640828\pi$
$234$	−24.5536	−1.60512
$235$	1.09973	0.0717386
$236$	−11.9824	−0.779987
$237$	−3.46775	−0.225255
$238$	4.78016	0.309852
$239$	−3.90721	−0.252736	−0.126368	−	0.991983i	$-0.540332\pi$
$239$	−3.90721	−0.252736	−0.126368	+	0.991983i	$0.540332\pi$
$240$	−0.488499	−0.0315324
$241$	2.45200	0.157947	0.0789736	−	0.996877i	$-0.474836\pi$
$241$	2.45200	0.157947	0.0789736	+	0.996877i	$0.474836\pi$
$242$	22.9948	1.47816
$243$	16.1527	1.03620
$244$	−2.37521	−0.152057
$245$	−0.731094	−0.0467079
$246$	−7.47740	−0.476742
$247$	14.5716	0.927170
$248$	13.9697	0.887080
$249$	−3.11027	−0.197105
$250$	8.65517	0.547401
$251$	15.7145	0.991888	0.495944	−	0.868354i	$-0.334822\pi$
$251$	15.7145	0.991888	0.495944	+	0.868354i	$0.334822\pi$
$252$	−14.1257	−0.889833
$253$	−4.46034	−0.280419
$254$	18.3261	1.14988
$255$	−0.350686	−0.0219608
$256$	−6.53510	−0.408444
$257$	13.4038	0.836106	0.418053	−	0.908423i	$-0.362713\pi$
$257$	13.4038	0.836106	0.418053	+	0.908423i	$0.362713\pi$
$258$	−4.59091	−0.285818
$259$	−5.31769	−0.330425
$260$	−6.00839	−0.372624
$261$	−6.84125	−0.423462
$262$	15.1867	0.938237
$263$	−12.7334	−0.785173	−0.392587	−	0.919715i	$-0.628420\pi$
$263$	−12.7334	−0.785173	−0.392587	+	0.919715i	$0.628420\pi$
$264$	−1.50584	−0.0926781
$265$	0.507462	0.0311731
$266$	14.1293	0.866324
$267$	4.27671	0.261730
$268$	1.47248	0.0899459
$269$	−10.8345	−0.660594	−0.330297	−	0.943877i	$-0.607149\pi$
$269$	−10.8345	−0.660594	−0.330297	+	0.943877i	$0.607149\pi$
$270$	4.20434	0.255868
$271$	−10.6649	−0.647846	−0.323923	−	0.946084i	$-0.605002\pi$
$271$	−10.6649	−0.647846	−0.323923	+	0.946084i	$0.605002\pi$
$272$	1.25525	0.0761108
$273$	−10.9864	−0.664924
$274$	7.84719	0.474066
$275$	−3.84616	−0.231932
$276$	−15.2661	−0.918909
$277$	−20.8246	−1.25123	−0.625616	−	0.780131i	$-0.715152\pi$
$277$	−20.8246	−1.25123	−0.625616	+	0.780131i	$0.715152\pi$
$278$	13.9205	0.834898
$279$	14.6349	0.876167
$280$	−1.83248	−0.109512
$281$	21.8206	1.30171	0.650854	−	0.759203i	$-0.274411\pi$
$281$	21.8206	1.30171	0.650854	+	0.759203i	$0.274411\pi$
$282$	−5.72982	−0.341206
$283$	−6.26316	−0.372306	−0.186153	−	0.982521i	$-0.559602\pi$
$283$	−6.26316	−0.372306	−0.186153	+	0.982521i	$0.559602\pi$
$284$	22.6195	1.34222
$285$	−1.03657	−0.0614008
$286$	9.14646	0.540842
$287$	8.21840	0.485117
$288$	−14.9300	−0.879759
$289$	−16.0989	−0.946993
$290$	−2.82162	−0.165691
$291$	0.512553	0.0300464
$292$	17.1082	1.00118
$293$	−26.6665	−1.55787	−0.778937	−	0.627102i	$-0.784241\pi$
$293$	−26.6665	−1.55787	−0.778937	+	0.627102i	$0.784241\pi$
$294$	3.80915	0.222154
$295$	−1.62845	−0.0948122
$296$	4.76596	0.277016
$297$	−3.79729	−0.220341
$298$	−4.09408	−0.237163
$299$	29.1655	1.68669
$300$	−13.1640	−0.760022
$301$	5.04587	0.290839
$302$	27.9789	1.61001
$303$	−0.405572	−0.0232995
$304$	3.71030	0.212800
$305$	−0.322800	−0.0184835
$306$	−4.48819	−0.256573
$307$	23.8218	1.35958	0.679791	−	0.733405i	$-0.262070\pi$
$307$	23.8218	1.35958	0.679791	+	0.733405i	$0.262070\pi$
$308$	5.26195	0.299828
$309$	−7.12369	−0.405253
$310$	6.03603	0.342824
$311$	16.6477	0.944004	0.472002	−	0.881597i	$-0.343531\pi$
$311$	16.6477	0.944004	0.472002	+	0.881597i	$0.343531\pi$
$312$	9.84649	0.557448
$313$	−30.0141	−1.69650	−0.848249	−	0.529598i	$-0.822343\pi$
$313$	−30.0141	−1.69650	−0.848249	+	0.529598i	$0.822343\pi$
$314$	−11.2699	−0.635995
$315$	−1.91973	−0.108165
$316$	−10.8603	−0.610942
$317$	0.397721	0.0223382	0.0111691	−	0.999938i	$-0.496445\pi$
$317$	0.397721	0.0223382	0.0111691	+	0.999938i	$0.496445\pi$
$318$	−2.64398	−0.148267
$319$	2.54843	0.142685
$320$	−5.10907	−0.285606
$321$	−12.4880	−0.697011
$322$	28.2803	1.57600
$323$	2.66357	0.148205
$324$	5.66547	0.314748
$325$	25.1495	1.39505
$326$	21.4265	1.18670
$327$	1.61614	0.0893725
$328$	−7.36572	−0.406704
$329$	6.29764	0.347200
$330$	−0.650642	−0.0358167
$331$	15.2987	0.840895	0.420447	−	0.907317i	$-0.361873\pi$
$331$	15.2987	0.840895	0.420447	+	0.907317i	$0.361873\pi$
$332$	−9.74077	−0.534594
$333$	4.99288	0.273608
$334$	1.78047	0.0974232
$335$	0.200116	0.0109335
$336$	−2.79740	−0.152611
$337$	2.35403	0.128232	0.0641160	−	0.997942i	$-0.479577\pi$
$337$	2.35403	0.128232	0.0641160	+	0.997942i	$0.479577\pi$
$338$	−30.9788	−1.68502
$339$	−2.47753	−0.134561
$340$	−1.09828	−0.0595627
$341$	−5.45164	−0.295223
$342$	−13.2663	−0.717359
$343$	−20.0818	−1.08432
$344$	−4.52234	−0.243828
$345$	−2.07472	−0.111699
$346$	44.7731	2.40702
$347$	5.42325	0.291135	0.145568	−	0.989348i	$-0.453499\pi$
$347$	5.42325	0.291135	0.145568	+	0.989348i	$0.453499\pi$
$348$	8.72233	0.467566
$349$	12.3629	0.661769	0.330884	−	0.943671i	$-0.392653\pi$
$349$	12.3629	0.661769	0.330884	+	0.943671i	$0.392653\pi$
$350$	24.3862	1.30349
$351$	24.8300	1.32533
$352$	5.56158	0.296433
$353$	−14.6122	−0.777729	−0.388865	−	0.921295i	$-0.627133\pi$
$353$	−14.6122	−0.777729	−0.388865	+	0.921295i	$0.627133\pi$
$354$	8.48457	0.450950
$355$	3.07408	0.163155
$356$	13.3938	0.709872
$357$	−2.00821	−0.106286
$358$	−51.0410	−2.69760
$359$	−25.2559	−1.33296	−0.666479	−	0.745524i	$-0.732199\pi$
$359$	−25.2559	−1.33296	−0.666479	+	0.745524i	$0.732199\pi$
$360$	1.72055	0.0906811
$361$	−11.1270	−0.585630
$362$	−16.7798	−0.881927
$363$	−9.66041	−0.507040
$364$	−34.4072	−1.80343
$365$	2.32507	0.121700
$366$	1.68185	0.0879118
$367$	16.8781	0.881030	0.440515	−	0.897745i	$-0.354796\pi$
$367$	16.8781	0.881030	0.440515	+	0.897745i	$0.354796\pi$
$368$	7.42628	0.387121
$369$	−7.71642	−0.401701
$370$	2.05927	0.107056
$371$	2.90599	0.150872
$372$	−18.6589	−0.967420
$373$	−34.1635	−1.76892	−0.884458	−	0.466619i	$-0.845472\pi$
$373$	−34.1635	−1.76892	−0.884458	+	0.466619i	$0.845472\pi$
$374$	1.67190	0.0864517
$375$	−3.63616	−0.187770
$376$	−5.64424	−0.291080
$377$	−16.6639	−0.858233
$378$	24.0763	1.23835
$379$	−19.8560	−1.01993	−0.509967	−	0.860194i	$-0.670343\pi$
$379$	−19.8560	−1.01993	−0.509967	+	0.860194i	$0.670343\pi$
$380$	−3.24633	−0.166533
$381$	−7.69903	−0.394433
$382$	−58.9889	−3.01813
$383$	−21.1244	−1.07941	−0.539703	−	0.841855i	$-0.681464\pi$
$383$	−21.1244	−1.07941	−0.539703	+	0.841855i	$0.681464\pi$
$384$	13.5713	0.692560
$385$	0.715120	0.0364459
$386$	−43.8123	−2.22999
$387$	−4.73766	−0.240829
$388$	1.60522	0.0814927
$389$	31.2164	1.58274	0.791368	−	0.611340i	$-0.209369\pi$
$389$	31.2164	1.58274	0.791368	+	0.611340i	$0.209369\pi$
$390$	4.25446	0.215433
$391$	5.33121	0.269611
$392$	3.75226	0.189518
$393$	−6.38013	−0.321835
$394$	−4.53525	−0.228483
$395$	−1.47596	−0.0742637
$396$	−4.94055	−0.248272
$397$	5.44771	0.273413	0.136706	−	0.990612i	$-0.456348\pi$
$397$	5.44771	0.273413	0.136706	+	0.990612i	$0.456348\pi$
$398$	−55.8438	−2.79920
$399$	−5.93592	−0.297168
$400$	6.40370	0.320185
$401$	1.19245	0.0595480	0.0297740	−	0.999557i	$-0.490521\pi$
$401$	1.19245	0.0595480	0.0297740	+	0.999557i	$0.490521\pi$
$402$	−1.04264	−0.0520023
$403$	35.6475	1.77573
$404$	−1.27018	−0.0631936
$405$	0.769959	0.0382596
$406$	−16.1581	−0.801911
$407$	−1.85990	−0.0921918
$408$	1.79985	0.0891061
$409$	6.54358	0.323559	0.161780	−	0.986827i	$-0.448277\pi$
$409$	6.54358	0.323559	0.161780	+	0.986827i	$0.448277\pi$
$410$	−3.18257	−0.157176
$411$	−3.29671	−0.162615
$412$	−22.3101	−1.09914
$413$	−9.32538	−0.458872
$414$	−26.5529	−1.30500
$415$	−1.32381	−0.0649832
$416$	−36.3664	−1.78301
$417$	−5.84820	−0.286388
$418$	4.94183	0.241713
$419$	26.0278	1.27154	0.635771	−	0.771878i	$-0.280682\pi$
$419$	26.0278	1.27154	0.635771	+	0.771878i	$0.280682\pi$
$420$	2.44759	0.119430
$421$	22.5183	1.09747	0.548737	−	0.835995i	$-0.315109\pi$
$421$	22.5183	1.09747	0.548737	+	0.835995i	$0.315109\pi$
$422$	22.5105	1.09579
$423$	−5.91298	−0.287499
$424$	−2.60449	−0.126485
$425$	4.59712	0.222993
$426$	−16.0166	−0.776006
$427$	−1.84852	−0.0894562
$428$	−39.1100	−1.89045
$429$	−3.84255	−0.185520
$430$	−1.95401	−0.0942307
$431$	−29.7833	−1.43461	−0.717306	−	0.696758i	$-0.754625\pi$
$431$	−29.7833	−1.43461	−0.717306	+	0.696758i	$0.754625\pi$
$432$	6.32233	0.304183
$433$	−28.7830	−1.38322	−0.691610	−	0.722271i	$-0.743098\pi$
$433$	−28.7830	−1.38322	−0.691610	+	0.722271i	$0.743098\pi$
$434$	34.5655	1.65920
$435$	1.18540	0.0568355
$436$	5.06143	0.242399
$437$	15.7581	0.753813
$438$	−12.1141	−0.578833
$439$	10.5634	0.504165	0.252083	−	0.967706i	$-0.418884\pi$
$439$	10.5634	0.504165	0.252083	+	0.967706i	$0.418884\pi$
$440$	−0.640924	−0.0305549
$441$	3.93091	0.187186
$442$	−10.9323	−0.519997
$443$	−21.4524	−1.01924	−0.509618	−	0.860401i	$-0.670213\pi$
$443$	−21.4524	−1.01924	−0.509618	+	0.860401i	$0.670213\pi$
$444$	−6.36574	−0.302104
$445$	1.82028	0.0862893
$446$	−12.8608	−0.608976
$447$	1.71998	0.0813521
$448$	−29.2572	−1.38227
$449$	−22.6507	−1.06895	−0.534475	−	0.845184i	$-0.679491\pi$
$449$	−22.6507	−1.06895	−0.534475	+	0.845184i	$0.679491\pi$
$450$	−22.8966	−1.07936
$451$	2.87444	0.135352
$452$	−7.75916	−0.364960
$453$	−11.7543	−0.552266
$454$	−13.7295	−0.644357
$455$	−4.67607	−0.219218
$456$	5.32005	0.249134
$457$	3.73852	0.174881	0.0874403	−	0.996170i	$-0.472131\pi$
$457$	3.73852	0.174881	0.0874403	+	0.996170i	$0.472131\pi$
$458$	−30.9561	−1.44648
$459$	4.53871	0.211849
$460$	−6.49762	−0.302953
$461$	−5.56922	−0.259385	−0.129692	−	0.991554i	$-0.541399\pi$
$461$	−5.56922	−0.259385	−0.129692	+	0.991554i	$0.541399\pi$
$462$	−3.72592	−0.173345
$463$	−6.66870	−0.309921	−0.154960	−	0.987921i	$-0.549525\pi$
$463$	−6.66870	−0.309921	−0.154960	+	0.987921i	$0.549525\pi$
$464$	−4.24304	−0.196978
$465$	−2.53582	−0.117596
$466$	28.9847	1.34269
$467$	27.1669	1.25713	0.628567	−	0.777756i	$-0.283642\pi$
$467$	27.1669	1.25713	0.628567	+	0.777756i	$0.283642\pi$
$468$	32.3056	1.49333
$469$	1.14597	0.0529158
$470$	−2.43876	−0.112492
$471$	4.73462	0.218160
$472$	8.35785	0.384701
$473$	1.76483	0.0811469
$474$	7.69007	0.353216
$475$	13.5883	0.623473
$476$	−6.28934	−0.288272
$477$	−2.72849	−0.124929
$478$	8.66460	0.396309
$479$	22.6892	1.03670	0.518348	−	0.855170i	$-0.326547\pi$
$479$	22.6892	1.03670	0.518348	+	0.855170i	$0.326547\pi$
$480$	2.58696	0.118078
$481$	12.1616	0.554523
$482$	−5.43754	−0.247673
$483$	−11.8809	−0.540601
$484$	−30.2546	−1.37521
$485$	0.218156	0.00990594
$486$	−35.8201	−1.62483
$487$	20.6398	0.935278	0.467639	−	0.883919i	$-0.345105\pi$
$487$	20.6398	0.935278	0.467639	+	0.883919i	$0.345105\pi$
$488$	1.65673	0.0749967
$489$	−9.00157	−0.407065
$490$	1.62127	0.0732416
$491$	24.6811	1.11384	0.556921	−	0.830566i	$-0.311983\pi$
$491$	24.6811	1.11384	0.556921	+	0.830566i	$0.311983\pi$
$492$	9.83814	0.443538
$493$	−3.04601	−0.137186
$494$	−32.3140	−1.45387
$495$	−0.671440	−0.0301790
$496$	9.07675	0.407558
$497$	17.6038	0.789639
$498$	6.89731	0.309076
$499$	−37.4677	−1.67728	−0.838642	−	0.544683i	$-0.816650\pi$
$499$	−37.4677	−1.67728	−0.838642	+	0.544683i	$0.816650\pi$
$500$	−11.3878	−0.509276
$501$	−0.748002	−0.0334182
$502$	−34.8483	−1.55536
$503$	−15.7997	−0.704473	−0.352236	−	0.935911i	$-0.614579\pi$
$503$	−15.7997	−0.704473	−0.352236	+	0.935911i	$0.614579\pi$
$504$	9.85280	0.438879
$505$	−0.172622	−0.00768157
$506$	9.89122	0.439718
$507$	13.0146	0.577999
$508$	−24.1119	−1.06979
$509$	−4.02881	−0.178574	−0.0892870	−	0.996006i	$-0.528459\pi$
$509$	−4.02881	−0.178574	−0.0892870	+	0.996006i	$0.528459\pi$
$510$	0.777679	0.0344362
$511$	13.3146	0.589001
$512$	−14.6420	−0.647093
$513$	13.4156	0.592314
$514$	−29.7242	−1.31108
$515$	−3.03202	−0.133607
$516$	6.04034	0.265911
$517$	2.20264	0.0968722
$518$	11.7925	0.518132
$519$	−18.8098	−0.825659
$520$	4.19092	0.183784
$521$	−11.8602	−0.519607	−0.259803	−	0.965662i	$-0.583658\pi$
$521$	−11.8602	−0.519607	−0.259803	+	0.965662i	$0.583658\pi$
$522$	15.1711	0.664021
$523$	36.4494	1.59382	0.796911	−	0.604097i	$-0.206466\pi$
$523$	36.4494	1.59382	0.796911	+	0.604097i	$0.206466\pi$
$524$	−19.9814	−0.872891
$525$	−10.2450	−0.447127
$526$	28.2375	1.23121
$527$	6.51607	0.283844
$528$	−0.978411	−0.0425799
$529$	8.54036	0.371320
$530$	−1.12534	−0.0488818
$531$	8.75578	0.379969
$532$	−18.5902	−0.805987
$533$	−18.7956	−0.814128
$534$	−9.48400	−0.410413
$535$	−5.31520	−0.229796
$536$	−1.02707	−0.0443627
$537$	21.4430	0.925334
$538$	24.0266	1.03586
$539$	−1.46430	−0.0630721
$540$	−5.53172	−0.238047
$541$	42.3881	1.82241	0.911204	−	0.411956i	$-0.135154\pi$
$541$	42.3881	1.82241	0.911204	+	0.411956i	$0.135154\pi$
$542$	23.6504	1.01587
$543$	7.04942	0.302520
$544$	−6.64747	−0.285008
$545$	0.687868	0.0294650
$546$	24.3633	1.04265
$547$	21.7525	0.930068	0.465034	−	0.885293i	$-0.346042\pi$
$547$	21.7525	0.930068	0.465034	+	0.885293i	$0.346042\pi$
$548$	−10.3247	−0.441049
$549$	1.73561	0.0740741
$550$	8.52923	0.363688
$551$	−9.00348	−0.383561
$552$	10.6482	0.453219
$553$	−8.45214	−0.359422
$554$	46.1806	1.96203
$555$	−0.865128	−0.0367227
$556$	−18.3155	−0.776749
$557$	12.3938	0.525140	0.262570	−	0.964913i	$-0.415430\pi$
$557$	12.3938	0.525140	0.262570	+	0.964913i	$0.415430\pi$
$558$	−32.4542	−1.37390
$559$	−11.5400	−0.488089
$560$	−1.19064	−0.0503139
$561$	−0.702386	−0.0296548
$562$	−48.3893	−2.04118
$563$	13.7304	0.578665	0.289333	−	0.957229i	$-0.406567\pi$
$563$	13.7304	0.578665	0.289333	+	0.957229i	$0.406567\pi$
$564$	7.53883	0.317442
$565$	−1.05450	−0.0443631
$566$	13.8892	0.583805
$567$	4.40919	0.185169
$568$	−15.7774	−0.662004
$569$	15.4970	0.649668	0.324834	−	0.945771i	$-0.394691\pi$
$569$	15.4970	0.649668	0.324834	+	0.945771i	$0.394691\pi$
$570$	2.29868	0.0962812
$571$	−21.9817	−0.919907	−0.459953	−	0.887943i	$-0.652134\pi$
$571$	−21.9817	−0.919907	−0.459953	+	0.887943i	$0.652134\pi$
$572$	−12.0342	−0.503173
$573$	24.7820	1.03528
$574$	−18.2251	−0.760700
$575$	27.1974	1.13421
$576$	27.4702	1.14459
$577$	−15.4334	−0.642503	−0.321251	−	0.946994i	$-0.604103\pi$
$577$	−15.4334	−0.642503	−0.321251	+	0.946994i	$0.604103\pi$
$578$	35.7008	1.48496
$579$	18.4062	0.764934
$580$	3.71245	0.154151
$581$	−7.58082	−0.314506
$582$	−1.13664	−0.0471151
$583$	1.01639	0.0420946
$584$	−11.9331	−0.493797
$585$	4.39045	0.181523
$586$	59.1355	2.44286
$587$	−47.4178	−1.95714	−0.978571	−	0.205910i	$-0.933985\pi$
$587$	−47.4178	−1.95714	−0.978571	+	0.205910i	$0.933985\pi$
$588$	−5.01176	−0.206682
$589$	19.2603	0.793609
$590$	3.61125	0.148673
$591$	1.90532	0.0783744
$592$	3.09665	0.127272
$593$	−20.3300	−0.834854	−0.417427	−	0.908711i	$-0.637068\pi$
$593$	−20.3300	−0.834854	−0.417427	+	0.908711i	$0.637068\pi$
$594$	8.42085	0.345512
$595$	−0.854746	−0.0350412
$596$	5.38665	0.220646
$597$	23.4608	0.960185
$598$	−64.6774	−2.64485
$599$	29.5307	1.20659	0.603295	−	0.797518i	$-0.293854\pi$
$599$	29.5307	1.20659	0.603295	+	0.797518i	$0.293854\pi$
$600$	9.18201	0.374854
$601$	5.39336	0.220000	0.110000	−	0.993932i	$-0.464915\pi$
$601$	5.39336	0.220000	0.110000	+	0.993932i	$0.464915\pi$
$602$	−11.1897	−0.456058
$603$	−1.07597	−0.0438169
$604$	−36.8123	−1.49787
$605$	−4.11172	−0.167165
$606$	0.899395	0.0365354
$607$	2.56078	0.103939	0.0519694	−	0.998649i	$-0.483450\pi$
$607$	2.56078	0.103939	0.0519694	+	0.998649i	$0.483450\pi$
$608$	−19.6487	−0.796862
$609$	6.78822	0.275073
$610$	0.715839	0.0289835
$611$	−14.4028	−0.582675
$612$	5.90518	0.238703
$613$	−17.7631	−0.717444	−0.358722	−	0.933444i	$-0.616787\pi$
$613$	−17.7631	−0.717444	−0.358722	+	0.933444i	$0.616787\pi$
$614$	−52.8271	−2.13193
$615$	1.33704	0.0539147
$616$	−3.67027	−0.147879
$617$	−35.2769	−1.42019	−0.710097	−	0.704104i	$-0.751349\pi$
$617$	−35.2769	−1.42019	−0.710097	+	0.704104i	$0.751349\pi$
$618$	15.7975	0.635467
$619$	−15.6525	−0.629127	−0.314564	−	0.949236i	$-0.601858\pi$
$619$	−15.6525	−0.629127	−0.314564	+	0.949236i	$0.601858\pi$
$620$	−7.94171	−0.318947
$621$	26.8518	1.07752
$622$	−36.9179	−1.48027
$623$	10.4239	0.417623
$624$	6.39769	0.256113
$625$	22.6662	0.906647
$626$	66.5591	2.66024
$627$	−2.07613	−0.0829126
$628$	14.8279	0.591699
$629$	2.22304	0.0886385
$630$	4.25719	0.169610
$631$	−10.1616	−0.404528	−0.202264	−	0.979331i	$-0.564830\pi$
$631$	−10.1616	−0.404528	−0.202264	+	0.979331i	$0.564830\pi$
$632$	7.57521	0.301326
$633$	−9.45695	−0.375880
$634$	−0.881984	−0.0350281
$635$	−3.27690	−0.130040
$636$	3.47873	0.137940
$637$	9.57489	0.379371
$638$	−5.65140	−0.223741
$639$	−16.5286	−0.653860
$640$	5.77631	0.228329
$641$	0.999867	0.0394924	0.0197462	−	0.999805i	$-0.493714\pi$
$641$	0.999867	0.0394924	0.0197462	+	0.999805i	$0.493714\pi$
$642$	27.6933	1.09297
$643$	−9.22542	−0.363815	−0.181908	−	0.983316i	$-0.558227\pi$
$643$	−9.22542	−0.363815	−0.181908	+	0.983316i	$0.558227\pi$
$644$	−37.2088	−1.46623
$645$	0.820906	0.0323231
$646$	−5.90672	−0.232397
$647$	30.5106	1.19949	0.599747	−	0.800189i	$-0.295268\pi$
$647$	30.5106	1.19949	0.599747	+	0.800189i	$0.295268\pi$
$648$	−3.95173	−0.155238
$649$	−3.26162	−0.128030
$650$	−55.7715	−2.18754
$651$	−14.5214	−0.569140
$652$	−28.1912	−1.10405
$653$	−20.1771	−0.789593	−0.394796	−	0.918769i	$-0.629185\pi$
$653$	−20.1771	−0.789593	−0.394796	+	0.918769i	$0.629185\pi$
$654$	−3.58393	−0.140143
$655$	−2.71555	−0.106105
$656$	−4.78583	−0.186855
$657$	−12.5013	−0.487722
$658$	−13.9656	−0.544437
$659$	34.6422	1.34947	0.674734	−	0.738061i	$-0.264258\pi$
$659$	34.6422	1.34947	0.674734	+	0.738061i	$0.264258\pi$
$660$	0.856061	0.0333221
$661$	−3.10717	−0.120855	−0.0604275	−	0.998173i	$-0.519246\pi$
$661$	−3.10717	−0.120855	−0.0604275	+	0.998173i	$0.519246\pi$
$662$	−33.9264	−1.31859
$663$	4.59281	0.178370
$664$	6.79429	0.263670
$665$	−2.52648	−0.0979726
$666$	−11.0722	−0.429038
$667$	−18.0207	−0.697766
$668$	−2.34260	−0.0906379
$669$	5.40299	0.208892
$670$	−0.443775	−0.0171445
$671$	−0.646534	−0.0249591
$672$	14.8143	0.571473
$673$	−18.8504	−0.726628	−0.363314	−	0.931667i	$-0.618355\pi$
$673$	−18.8504	−0.726628	−0.363314	+	0.931667i	$0.618355\pi$
$674$	−5.22028	−0.201078
$675$	23.1543	0.891211
$676$	40.7593	1.56766
$677$	21.3959	0.822311	0.411155	−	0.911565i	$-0.365125\pi$
$677$	21.3959	0.822311	0.411155	+	0.911565i	$0.365125\pi$
$678$	5.49416	0.211002
$679$	1.24927	0.0479428
$680$	0.766064	0.0293772
$681$	5.76794	0.221028
$682$	12.0895	0.462932
$683$	−30.0417	−1.14951	−0.574757	−	0.818324i	$-0.694903\pi$
$683$	−30.0417	−1.14951	−0.574757	+	0.818324i	$0.694903\pi$
$684$	17.4547	0.667396
$685$	−1.40316	−0.0536122
$686$	44.5334	1.70029
$687$	13.0051	0.496174
$688$	−2.93836	−0.112024
$689$	−6.64605	−0.253194
$690$	4.60088	0.175153
$691$	−0.0715222	−0.00272083	−0.00136042	−	0.999999i	$-0.500433\pi$
$691$	−0.0715222	−0.00272083	−0.00136042	+	0.999999i	$0.500433\pi$
$692$	−58.9088	−2.23937
$693$	−3.84502	−0.146060
$694$	−12.0266	−0.456523
$695$	−2.48914	−0.0944186
$696$	−6.08392	−0.230611
$697$	−3.43568	−0.130136
$698$	−27.4158	−1.03770
$699$	−12.1769	−0.460571
$700$	−32.0853	−1.21271
$701$	25.5723	0.965853	0.482926	−	0.875661i	$-0.339574\pi$
$701$	25.5723	0.965853	0.482926	+	0.875661i	$0.339574\pi$
$702$	−55.0628	−2.07821
$703$	6.57092	0.247827
$704$	−10.2329	−0.385668
$705$	1.02456	0.0385870
$706$	32.4039	1.21954
$707$	−0.988524	−0.0371773
$708$	−11.1633	−0.419542
$709$	22.3619	0.839818	0.419909	−	0.907566i	$-0.362062\pi$
$709$	22.3619	0.839818	0.419909	+	0.907566i	$0.362062\pi$
$710$	−6.81707	−0.255840
$711$	7.93588	0.297619
$712$	−9.34235	−0.350119
$713$	38.5502	1.44371
$714$	4.45340	0.166664
$715$	−1.63549	−0.0611638
$716$	67.1555	2.50972
$717$	−3.64012	−0.135943
$718$	56.0074	2.09018
$719$	13.9786	0.521315	0.260658	−	0.965431i	$-0.416061\pi$
$719$	13.9786	0.521315	0.260658	+	0.965431i	$0.416061\pi$
$720$	1.11792	0.0416624
$721$	−17.3630	−0.646631
$722$	24.6751	0.918312
$723$	2.28438	0.0849572
$724$	22.0775	0.820502
$725$	−15.5393	−0.577116
$726$	21.4229	0.795078
$727$	16.6230	0.616515	0.308257	−	0.951303i	$-0.400254\pi$
$727$	16.6230	0.616515	0.308257	+	0.951303i	$0.400254\pi$
$728$	23.9994	0.889477
$729$	9.22329	0.341604
$730$	−5.15606	−0.190834
$731$	−2.10941	−0.0780193
$732$	−2.21284	−0.0817890
$733$	−31.9673	−1.18074	−0.590369	−	0.807134i	$-0.701018\pi$
$733$	−31.9673	−1.18074	−0.590369	+	0.807134i	$0.701018\pi$
$734$	−37.4288	−1.38152
$735$	−0.681118	−0.0251234
$736$	−39.3276	−1.44963
$737$	0.400810	0.0147640
$738$	17.1119	0.629897
$739$	17.5242	0.644640	0.322320	−	0.946631i	$-0.395537\pi$
$739$	17.5242	0.644640	0.322320	+	0.946631i	$0.395537\pi$
$740$	−2.70942	−0.0996002
$741$	13.5755	0.498710
$742$	−6.44432	−0.236578
$743$	−22.8982	−0.840054	−0.420027	−	0.907512i	$-0.637979\pi$
$743$	−22.8982	−0.840054	−0.420027	+	0.907512i	$0.637979\pi$
$744$	13.0148	0.477146
$745$	0.732066	0.0268208
$746$	75.7607	2.77380
$747$	7.11778	0.260426
$748$	−2.19974	−0.0804305
$749$	−30.4377	−1.11217
$750$	8.06352	0.294438
$751$	16.8908	0.616356	0.308178	−	0.951329i	$-0.400281\pi$
$751$	16.8908	0.616356	0.308178	+	0.951329i	$0.400281\pi$
$752$	−3.66731	−0.133733
$753$	14.6403	0.533520
$754$	36.9537	1.34577
$755$	−5.00294	−0.182076
$756$	−31.6776	−1.15210
$757$	−31.5322	−1.14606	−0.573028	−	0.819536i	$-0.694231\pi$
$757$	−31.5322	−1.14606	−0.573028	+	0.819536i	$0.694231\pi$
$758$	44.0326	1.59934
$759$	−4.15544	−0.150833
$760$	2.26435	0.0821366
$761$	29.1804	1.05779	0.528895	−	0.848688i	$-0.322607\pi$
$761$	29.1804	1.05779	0.528895	+	0.848688i	$0.322607\pi$
$762$	17.0733	0.618502
$763$	3.93910	0.142605
$764$	77.6126	2.80793
$765$	0.802537	0.0290158
$766$	46.8454	1.69259
$767$	21.3273	0.770084
$768$	−6.08837	−0.219695
$769$	25.6440	0.924747	0.462373	−	0.886685i	$-0.346998\pi$
$769$	25.6440	0.924747	0.462373	+	0.886685i	$0.346998\pi$
$770$	−1.58585	−0.0571499
$771$	12.4875	0.449728
$772$	57.6446	2.07468
$773$	−12.0575	−0.433677	−0.216839	−	0.976207i	$-0.569575\pi$
$773$	−12.0575	−0.433677	−0.216839	+	0.976207i	$0.569575\pi$
$774$	10.5062	0.377638
$775$	33.2419	1.19408
$776$	−1.11966	−0.0401934
$777$	−4.95418	−0.177730
$778$	−69.2254	−2.48185
$779$	−10.1553	−0.363850
$780$	−5.59766	−0.200429
$781$	6.15706	0.220317
$782$	−11.8225	−0.422771
$783$	−15.3419	−0.548274
$784$	2.43801	0.0870716
$785$	2.01518	0.0719247
$786$	14.1486	0.504662
$787$	0.894357	0.0318804	0.0159402	−	0.999873i	$-0.494926\pi$
$787$	0.894357	0.0318804	0.0159402	+	0.999873i	$0.494926\pi$
$788$	5.96711	0.212569
$789$	−11.8629	−0.422332
$790$	3.27309	0.116451
$791$	−6.03862	−0.214709
$792$	3.44609	0.122451
$793$	4.22759	0.150126
$794$	−12.0808	−0.428732
$795$	0.472773	0.0167675
$796$	73.4747	2.60424
$797$	11.1140	0.393678	0.196839	−	0.980436i	$-0.436932\pi$
$797$	11.1140	0.393678	0.196839	+	0.980436i	$0.436932\pi$
$798$	13.1635	0.465982
$799$	−2.63271	−0.0931385
$800$	−33.9123	−1.19898
$801$	−9.78716	−0.345812
$802$	−2.64437	−0.0933759
$803$	4.65686	0.164337
$804$	1.37182	0.0483804
$805$	−5.05682	−0.178230
$806$	−79.0518	−2.78448
$807$	−10.0939	−0.355323
$808$	0.885962	0.0311680
$809$	−22.7743	−0.800700	−0.400350	−	0.916362i	$-0.631111\pi$
$809$	−22.7743	−0.800700	−0.400350	+	0.916362i	$0.631111\pi$
$810$	−1.70746	−0.0599939
$811$	−21.1198	−0.741616	−0.370808	−	0.928710i	$-0.620919\pi$
$811$	−21.1198	−0.741616	−0.370808	+	0.928710i	$0.620919\pi$
$812$	21.2594	0.746060
$813$	−9.93585	−0.348466
$814$	4.12450	0.144564
$815$	−3.83130	−0.134204
$816$	1.16944	0.0409387
$817$	−6.23504	−0.218136
$818$	−14.5110	−0.507365
$819$	25.1420	0.878534
$820$	4.18736	0.146229
$821$	−42.0467	−1.46744	−0.733720	−	0.679452i	$-0.762217\pi$
$821$	−42.0467	−1.46744	−0.733720	+	0.679452i	$0.762217\pi$
$822$	7.31077	0.254992
$823$	−0.181963	−0.00634283	−0.00317141	−	0.999995i	$-0.501009\pi$
$823$	−0.181963	−0.00634283	−0.00317141	+	0.999995i	$0.501009\pi$
$824$	15.5615	0.542111
$825$	−3.58325	−0.124753
$826$	20.6799	0.719547
$827$	4.59130	0.159655	0.0798276	−	0.996809i	$-0.474563\pi$
$827$	4.59130	0.159655	0.0798276	+	0.996809i	$0.474563\pi$
$828$	34.9361	1.21411
$829$	−16.7905	−0.583158	−0.291579	−	0.956547i	$-0.594181\pi$
$829$	−16.7905	−0.583158	−0.291579	+	0.956547i	$0.594181\pi$
$830$	2.93567	0.101899
$831$	−19.4011	−0.673017
$832$	66.9117	2.31975
$833$	1.75021	0.0606411
$834$	12.9689	0.449078
$835$	−0.318368	−0.0110176
$836$	−6.50205	−0.224878
$837$	32.8195	1.13441
$838$	−57.7192	−1.99387
$839$	53.5758	1.84964	0.924821	−	0.380403i	$-0.124215\pi$
$839$	53.5758	1.84964	0.924821	+	0.380403i	$0.124215\pi$
$840$	−1.70722	−0.0589046
$841$	−18.7038	−0.644958
$842$	−49.9365	−1.72092
$843$	20.3290	0.700168
$844$	−29.6174	−1.01947
$845$	5.53934	0.190559
$846$	13.1126	0.450820
$847$	−23.5459	−0.809045
$848$	−1.69225	−0.0581121
$849$	−5.83502	−0.200258
$850$	−10.1946	−0.349670
$851$	13.1519	0.450841
$852$	21.0733	0.721959
$853$	27.2026	0.931399	0.465699	−	0.884943i	$-0.345803\pi$
$853$	27.2026	0.931399	0.465699	+	0.884943i	$0.345803\pi$
$854$	4.09927	0.140274
$855$	2.37216	0.0811261
$856$	27.2797	0.932399
$857$	3.69955	0.126374	0.0631870	−	0.998002i	$-0.479874\pi$
$857$	3.69955	0.126374	0.0631870	+	0.998002i	$0.479874\pi$
$858$	8.52123	0.290910
$859$	−32.2394	−1.09999	−0.549997	−	0.835167i	$-0.685371\pi$
$859$	−32.2394	−1.09999	−0.549997	+	0.835167i	$0.685371\pi$
$860$	2.57092	0.0876678
$861$	7.65661	0.260936
$862$	66.0474	2.24958
$863$	46.2075	1.57292	0.786462	−	0.617639i	$-0.211911\pi$
$863$	46.2075	1.57292	0.786462	+	0.617639i	$0.211911\pi$
$864$	−33.4814	−1.13906
$865$	−8.00593	−0.272210
$866$	63.8289	2.16900
$867$	−14.9984	−0.509372
$868$	−45.4784	−1.54364
$869$	−2.95620	−0.100282
$870$	−2.62873	−0.0891225
$871$	−2.62084	−0.0888039
$872$	−3.53040	−0.119555
$873$	−1.17297	−0.0396990
$874$	−34.9451	−1.18204
$875$	−8.86261	−0.299611
$876$	15.9387	0.538518
$877$	20.9664	0.707987	0.353993	−	0.935248i	$-0.384824\pi$
$877$	20.9664	0.707987	0.353993	+	0.935248i	$0.384824\pi$
$878$	−23.4254	−0.790570
$879$	−24.8436	−0.837955
$880$	−0.416436	−0.0140381
$881$	−18.5601	−0.625307	−0.312653	−	0.949867i	$-0.601218\pi$
$881$	−18.5601	−0.625307	−0.312653	+	0.949867i	$0.601218\pi$
$882$	−8.71716	−0.293522
$883$	−5.73989	−0.193163	−0.0965814	−	0.995325i	$-0.530791\pi$
$883$	−5.73989	−0.193163	−0.0965814	+	0.995325i	$0.530791\pi$
$884$	14.3838	0.483780
$885$	−1.51714	−0.0509979
$886$	47.5728	1.59824
$887$	4.99316	0.167654	0.0838269	−	0.996480i	$-0.473286\pi$
$887$	4.99316	0.167654	0.0838269	+	0.996480i	$0.473286\pi$
$888$	4.44017	0.149002
$889$	−18.7653	−0.629367
$890$	−4.03663	−0.135308
$891$	1.54215	0.0516638
$892$	16.9212	0.566562
$893$	−7.78182	−0.260409
$894$	−3.81421	−0.127566
$895$	9.12669	0.305072
$896$	33.0782	1.10506
$897$	27.1718	0.907241
$898$	50.2300	1.67620
$899$	−22.0258	−0.734602
$900$	30.1255	1.00418
$901$	−1.21484	−0.0404722
$902$	−6.37435	−0.212243
$903$	4.70094	0.156438
$904$	5.41210	0.180004
$905$	3.00041	0.0997371
$906$	26.0663	0.865996
$907$	40.7437	1.35287	0.676436	−	0.736502i	$-0.263524\pi$
$907$	40.7437	1.35287	0.676436	+	0.736502i	$0.263524\pi$
$908$	18.0641	0.599479
$909$	0.928144	0.0307846
$910$	10.3696	0.343750
$911$	−25.0635	−0.830392	−0.415196	−	0.909732i	$-0.636287\pi$
$911$	−25.0635	−0.830392	−0.415196	+	0.909732i	$0.636287\pi$
$912$	3.45667	0.114462
$913$	−2.65145	−0.0877501
$914$	−8.29052	−0.274226
$915$	−0.300734	−0.00994195
$916$	40.7294	1.34574
$917$	−15.5507	−0.513528
$918$	−10.0650	−0.332195
$919$	−8.01264	−0.264312	−0.132156	−	0.991229i	$-0.542190\pi$
$919$	−8.01264	−0.264312	−0.132156	+	0.991229i	$0.542190\pi$
$920$	4.53216	0.149421
$921$	22.1934	0.731297
$922$	12.3503	0.406735
$923$	−40.2602	−1.32518
$924$	4.90225	0.161272
$925$	11.3409	0.372887
$926$	14.7885	0.485979
$927$	16.3024	0.535442
$928$	22.4700	0.737613
$929$	14.8141	0.486034	0.243017	−	0.970022i	$-0.421863\pi$
$929$	14.8141	0.486034	0.243017	+	0.970022i	$0.421863\pi$
$930$	5.62342	0.184399
$931$	5.17331	0.169548
$932$	−38.1356	−1.24917
$933$	15.5097	0.507765
$934$	−60.2451	−1.97128
$935$	−0.298953	−0.00977682
$936$	−22.5335	−0.736530
$937$	−18.9441	−0.618877	−0.309438	−	0.950920i	$-0.600141\pi$
$937$	−18.9441	−0.618877	−0.309438	+	0.950920i	$0.600141\pi$
$938$	−2.54129	−0.0829761
$939$	−27.9624	−0.912518
$940$	3.20872	0.104657
$941$	7.69890	0.250977	0.125488	−	0.992095i	$-0.459950\pi$
$941$	7.69890	0.250977	0.125488	+	0.992095i	$0.459950\pi$
$942$	−10.4995	−0.342091
$943$	−20.3260	−0.661907
$944$	5.43046	0.176746
$945$	−4.30510	−0.140045
$946$	−3.91367	−0.127244
$947$	14.9265	0.485047	0.242523	−	0.970146i	$-0.422025\pi$
$947$	14.9265	0.485047	0.242523	+	0.970146i	$0.422025\pi$
$948$	−10.1179	−0.328616
$949$	−30.4506	−0.988468
$950$	−30.1333	−0.977653
$951$	0.370533	0.0120154
$952$	4.38688	0.142180
$953$	−34.5187	−1.11817	−0.559085	−	0.829110i	$-0.688848\pi$
$953$	−34.5187	−1.11817	−0.559085	+	0.829110i	$0.688848\pi$
$954$	6.05069	0.195898
$955$	10.5479	0.341321
$956$	−11.4002	−0.368707
$957$	2.37423	0.0767479
$958$	−50.3154	−1.62562
$959$	−8.03526	−0.259472
$960$	−4.75983	−0.153623
$961$	16.1179	0.519931
$962$	−26.9696	−0.869534
$963$	28.5785	0.920929
$964$	7.15426	0.230423
$965$	7.83413	0.252190
$966$	26.3471	0.847703
$967$	−20.5625	−0.661246	−0.330623	−	0.943763i	$-0.607259\pi$
$967$	−20.5625	−0.661246	−0.330623	+	0.943763i	$0.607259\pi$
$968$	21.1029	0.678273
$969$	2.48149	0.0797170
$970$	−0.483781	−0.0155333
$971$	−47.6519	−1.52922	−0.764611	−	0.644492i	$-0.777069\pi$
$971$	−47.6519	−1.52922	−0.764611	+	0.644492i	$0.777069\pi$
$972$	47.1291	1.51167
$973$	−14.2541	−0.456967
$974$	−45.7707	−1.46659
$975$	23.4304	0.750372
$976$	1.07645	0.0344564
$977$	−24.1330	−0.772083	−0.386042	−	0.922481i	$-0.626158\pi$
$977$	−24.1330	−0.772083	−0.386042	+	0.922481i	$0.626158\pi$
$978$	19.9618	0.638309
$979$	3.64582	0.116521
$980$	−2.13313	−0.0681405
$981$	−3.69849	−0.118084
$982$	−54.7327	−1.74659
$983$	−1.00000	−0.0318950
$983$	−1.00000	−0.0318950
$984$	−6.86221	−0.218759
$985$	0.810953	0.0258391
$986$	6.75482	0.215117
$987$	5.86715	0.186753
$988$	42.5160	1.35261
$989$	−12.4796	−0.396829
$990$	1.48898	0.0473229
$991$	−10.9152	−0.346732	−0.173366	−	0.984857i	$-0.555464\pi$
$991$	−10.9152	−0.346732	−0.173366	+	0.984857i	$0.555464\pi$
$992$	−48.0681	−1.52616
$993$	14.2529	0.452304
$994$	−39.0381	−1.23821
$995$	9.98549	0.316561
$996$	−9.07491	−0.287549
$997$	0.157070	0.00497447	0.00248723	−	0.999997i	$-0.499208\pi$
$997$	0.157070	0.00497447	0.00248723	+	0.999997i	$0.499208\pi$
$998$	83.0881	2.63011
$999$	11.1968	0.354251

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.2.a.a.1.4	✓	28
3.2	odd	2		8847.2.a.b.1.25		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.2.a.a.1.4	✓	28	1.1	even	1	trivial
8847.2.a.b.1.25		28	3.2	odd	2

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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-2.21759 q^{2} +0.931642 q^{3} +2.91773 q^{4} +0.396530 q^{5} -2.06600 q^{6} +2.27074 q^{7} -2.03515 q^{8} -2.13204 q^{9} +O(q^{10})\)	\(q-2.21759 q^{2} +0.931642 q^{3} +2.91773 q^{4} +0.396530 q^{5} -2.06600 q^{6} +2.27074 q^{7} -2.03515 q^{8} -2.13204 q^{9} -0.879344 q^{10} +0.794208 q^{11} +2.71828 q^{12} -5.19322 q^{13} -5.03559 q^{14} +0.369424 q^{15} -1.32232 q^{16} -0.949276 q^{17} +4.72801 q^{18} -2.80589 q^{19} +1.15697 q^{20} +2.11552 q^{21} -1.76123 q^{22} -5.61608 q^{23} -1.89603 q^{24} -4.84276 q^{25} +11.5165 q^{26} -4.78123 q^{27} +6.62541 q^{28} +3.20877 q^{29} -0.819233 q^{30} -6.86425 q^{31} +7.00267 q^{32} +0.739918 q^{33} +2.10511 q^{34} +0.900419 q^{35} -6.22072 q^{36} -2.34183 q^{37} +6.22234 q^{38} -4.83822 q^{39} -0.806997 q^{40} +3.61926 q^{41} -4.69136 q^{42} +2.22212 q^{43} +2.31728 q^{44} -0.845420 q^{45} +12.4542 q^{46} +2.77338 q^{47} -1.23193 q^{48} -1.84373 q^{49} +10.7393 q^{50} -0.884386 q^{51} -15.1524 q^{52} +1.27975 q^{53} +10.6028 q^{54} +0.314928 q^{55} -4.62129 q^{56} -2.61409 q^{57} -7.11576 q^{58} -4.10676 q^{59} +1.07788 q^{60} -0.814060 q^{61} +15.2221 q^{62} -4.84132 q^{63} -12.8844 q^{64} -2.05927 q^{65} -1.64084 q^{66} +0.504666 q^{67} -2.76973 q^{68} -5.23218 q^{69} -1.99676 q^{70} +7.75245 q^{71} +4.33902 q^{72} +5.86353 q^{73} +5.19323 q^{74} -4.51172 q^{75} -8.18683 q^{76} +1.80344 q^{77} +10.7292 q^{78} -3.72219 q^{79} -0.524342 q^{80} +1.94174 q^{81} -8.02605 q^{82} -3.33848 q^{83} +6.17251 q^{84} -0.376417 q^{85} -4.92777 q^{86} +2.98943 q^{87} -1.61633 q^{88} +4.59051 q^{89} +1.87480 q^{90} -11.7925 q^{91} -16.3862 q^{92} -6.39502 q^{93} -6.15024 q^{94} -1.11262 q^{95} +6.52398 q^{96} +0.550161 q^{97} +4.08864 q^{98} -1.69329 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9}+O(q^{10}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9	\( 28 q - 7 q^{2} - 6 q^{3} + 17 q^{4} - 7 q^{5} - 7 q^{6} - 25 q^{7} - 15 q^{8} + 6 q^{9} - 17 q^{10} - 10 q^{11} - 10 q^{12} - 28 q^{13} + 5 q^{14} - 9 q^{15} + 3 q^{16} - 24 q^{17} - 23 q^{18} - 13 q^{19} - 4 q^{20} - 21 q^{21} - 21 q^{22} - 9 q^{23} - 19 q^{24} - 33 q^{25} + 2 q^{26} - 12 q^{27} - 58 q^{28} - 14 q^{29} - 8 q^{30} - 16 q^{31} - 27 q^{32} - 34 q^{33} - 6 q^{34} - 2 q^{35} - 6 q^{36} - 58 q^{37} + 6 q^{38} - 12 q^{39} - 24 q^{40} - 24 q^{41} + 22 q^{42} - 43 q^{43} - 19 q^{45} - 28 q^{46} + 2 q^{47} + 19 q^{48} - 21 q^{49} + 17 q^{50} - 6 q^{51} - 47 q^{52} - 16 q^{53} + 16 q^{54} - 16 q^{55} + 30 q^{56} - 70 q^{57} - 31 q^{58} + 12 q^{59} - q^{60} - 22 q^{61} - 15 q^{63} - 3 q^{64} - 24 q^{65} + 41 q^{66} - 38 q^{67} + 11 q^{68} + 2 q^{69} + 19 q^{70} + 2 q^{71} - 15 q^{72} - 124 q^{73} + 14 q^{74} + 8 q^{75} + 3 q^{76} - 20 q^{77} + 21 q^{78} - 16 q^{79} + 10 q^{80} - 36 q^{81} + 2 q^{82} + 12 q^{83} + 6 q^{84} - 73 q^{85} + 41 q^{86} - 15 q^{87} - 61 q^{88} - 3 q^{89} + 39 q^{90} + 5 q^{91} + 44 q^{92} - 21 q^{93} + 9 q^{94} + 17 q^{95} - 3 q^{96} - 105 q^{97} + 16 q^{98} - 15 q^{99}+O(q^{100}) \) 28 * q - 7 * q^2 - 6 * q^3 + 17 * q^4 - 7 * q^5 - 7 * q^6 - 25 * q^7 - 15 * q^8 + 6 * q^9 - 17 * q^10 - 10 * q^11 - 10 * q^12 - 28 * q^13 + 5 * q^14 - 9 * q^15 + 3 * q^16 - 24 * q^17 - 23 * q^18 - 13 * q^19 - 4 * q^20 - 21 * q^21 - 21 * q^22 - 9 * q^23 - 19 * q^24 - 33 * q^25 + 2 * q^26 - 12 * q^27 - 58 * q^28 - 14 * q^29 - 8 * q^30 - 16 * q^31 - 27 * q^32 - 34 * q^33 - 6 * q^34 - 2 * q^35 - 6 * q^36 - 58 * q^37 + 6 * q^38 - 12 * q^39 - 24 * q^40 - 24 * q^41 + 22 * q^42 - 43 * q^43 - 19 * q^45 - 28 * q^46 + 2 * q^47 + 19 * q^48 - 21 * q^49 + 17 * q^50 - 6 * q^51 - 47 * q^52 - 16 * q^53 + 16 * q^54 - 16 * q^55 + 30 * q^56 - 70 * q^57 - 31 * q^58 + 12 * q^59 - q^60 - 22 * q^61 - 15 * q^63 - 3 * q^64 - 24 * q^65 + 41 * q^66 - 38 * q^67 + 11 * q^68 + 2 * q^69 + 19 * q^70 + 2 * q^71 - 15 * q^72 - 124 * q^73 + 14 * q^74 + 8 * q^75 + 3 * q^76 - 20 * q^77 + 21 * q^78 - 16 * q^79 + 10 * q^80 - 36 * q^81 + 2 * q^82 + 12 * q^83 + 6 * q^84 - 73 * q^85 + 41 * q^86 - 15 * q^87 - 61 * q^88 - 3 * q^89 + 39 * q^90 + 5 * q^91 + 44 * q^92 - 21 * q^93 + 9 * q^94 + 17 * q^95 - 3 * q^96 - 105 * q^97 + 16 * q^98 - 15 * q^99

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