LMFDB - Embedded newform 8043.2.a.s.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$64.2236783457$
Analytic rank:	$0$
Dimension:	$50$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.46962 q^{2} -1.00000 q^{3} +0.159775 q^{4} +3.40283 q^{5} +1.46962 q^{6} -1.00000 q^{7} +2.70443 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.46962 q^{2} -1.00000 q^{3} +0.159775 q^{4} +3.40283 q^{5} +1.46962 q^{6} -1.00000 q^{7} +2.70443 q^{8} +1.00000 q^{9} -5.00085 q^{10} -6.33646 q^{11} -0.159775 q^{12} +5.54685 q^{13} +1.46962 q^{14} -3.40283 q^{15} -4.29402 q^{16} +7.88057 q^{17} -1.46962 q^{18} +5.01037 q^{19} +0.543688 q^{20} +1.00000 q^{21} +9.31217 q^{22} -3.20602 q^{23} -2.70443 q^{24} +6.57922 q^{25} -8.15174 q^{26} -1.00000 q^{27} -0.159775 q^{28} +6.21983 q^{29} +5.00085 q^{30} +8.55180 q^{31} +0.901719 q^{32} +6.33646 q^{33} -11.5814 q^{34} -3.40283 q^{35} +0.159775 q^{36} +4.32497 q^{37} -7.36333 q^{38} -5.54685 q^{39} +9.20269 q^{40} +9.81825 q^{41} -1.46962 q^{42} +6.37147 q^{43} -1.01241 q^{44} +3.40283 q^{45} +4.71163 q^{46} -4.22723 q^{47} +4.29402 q^{48} +1.00000 q^{49} -9.66894 q^{50} -7.88057 q^{51} +0.886250 q^{52} -5.65948 q^{53} +1.46962 q^{54} -21.5619 q^{55} -2.70443 q^{56} -5.01037 q^{57} -9.14077 q^{58} +5.50335 q^{59} -0.543688 q^{60} -12.8935 q^{61} -12.5679 q^{62} -1.00000 q^{63} +7.26286 q^{64} +18.8750 q^{65} -9.31217 q^{66} +10.3570 q^{67} +1.25912 q^{68} +3.20602 q^{69} +5.00085 q^{70} -9.93341 q^{71} +2.70443 q^{72} -8.38480 q^{73} -6.35605 q^{74} -6.57922 q^{75} +0.800534 q^{76} +6.33646 q^{77} +8.15174 q^{78} -14.6480 q^{79} -14.6118 q^{80} +1.00000 q^{81} -14.4291 q^{82} +8.82661 q^{83} +0.159775 q^{84} +26.8162 q^{85} -9.36363 q^{86} -6.21983 q^{87} -17.1365 q^{88} +5.62398 q^{89} -5.00085 q^{90} -5.54685 q^{91} -0.512244 q^{92} -8.55180 q^{93} +6.21241 q^{94} +17.0494 q^{95} -0.901719 q^{96} +10.7345 q^{97} -1.46962 q^{98} -6.33646 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) $ 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * 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 $

$2$	−1.46962	−1.03918	−0.519588	−	0.854417i	$-0.673915\pi$
$2$	−1.46962	−1.03918	−0.519588	+	0.854417i	$0.673915\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.159775	0.0798877
$5$	3.40283	1.52179	0.760895	−	0.648875i	$-0.224760\pi$
$5$	3.40283	1.52179	0.760895	+	0.648875i	$0.224760\pi$
$6$	1.46962	0.599969
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	2.70443	0.956159
$9$	1.00000	0.333333
$10$	−5.00085	−1.58141
$11$	−6.33646	−1.91051	−0.955257	−	0.295778i	$-0.904421\pi$
$11$	−6.33646	−1.91051	−0.955257	+	0.295778i	$0.904421\pi$
$12$	−0.159775	−0.0461232
$13$	5.54685	1.53842	0.769209	−	0.638997i	$-0.220650\pi$
$13$	5.54685	1.53842	0.769209	+	0.638997i	$0.220650\pi$
$14$	1.46962	0.392772
$15$	−3.40283	−0.878606
$16$	−4.29402	−1.07351
$17$	7.88057	1.91132	0.955660	−	0.294473i	$-0.0951441\pi$
$17$	7.88057	1.91132	0.955660	+	0.294473i	$0.0951441\pi$
$18$	−1.46962	−0.346392
$19$	5.01037	1.14946	0.574729	−	0.818344i	$-0.305107\pi$
$19$	5.01037	1.14946	0.574729	+	0.818344i	$0.305107\pi$
$20$	0.543688	0.121572
$21$	1.00000	0.218218
$22$	9.31217	1.98536
$23$	−3.20602	−0.668502	−0.334251	−	0.942484i	$-0.608483\pi$
$23$	−3.20602	−0.668502	−0.334251	+	0.942484i	$0.608483\pi$
$24$	−2.70443	−0.552039
$25$	6.57922	1.31584
$26$	−8.15174	−1.59869
$27$	−1.00000	−0.192450
$28$	−0.159775	−0.0301947
$29$	6.21983	1.15499	0.577496	−	0.816393i	$-0.304030\pi$
$29$	6.21983	1.15499	0.577496	+	0.816393i	$0.304030\pi$
$30$	5.00085	0.913026
$31$	8.55180	1.53595	0.767975	−	0.640480i	$-0.221265\pi$
$31$	8.55180	1.53595	0.767975	+	0.640480i	$0.221265\pi$
$32$	0.901719	0.159403
$33$	6.33646	1.10304
$34$	−11.5814	−1.98620
$35$	−3.40283	−0.575182
$36$	0.159775	0.0266292
$37$	4.32497	0.711020	0.355510	−	0.934672i	$-0.384307\pi$
$37$	4.32497	0.711020	0.355510	+	0.934672i	$0.384307\pi$
$38$	−7.36333	−1.19449
$39$	−5.54685	−0.888207
$40$	9.20269	1.45507
$41$	9.81825	1.53335	0.766677	−	0.642033i	$-0.221909\pi$
$41$	9.81825	1.53335	0.766677	+	0.642033i	$0.221909\pi$
$42$	−1.46962	−0.226767
$43$	6.37147	0.971640	0.485820	−	0.874059i	$-0.338521\pi$
$43$	6.37147	0.971640	0.485820	+	0.874059i	$0.338521\pi$
$44$	−1.01241	−0.152627
$45$	3.40283	0.507263
$46$	4.71163	0.694692
$47$	−4.22723	−0.616605	−0.308302	−	0.951288i	$-0.599761\pi$
$47$	−4.22723	−0.616605	−0.308302	+	0.951288i	$0.599761\pi$
$48$	4.29402	0.619789
$49$	1.00000	0.142857
$50$	−9.66894	−1.36739
$51$	−7.88057	−1.10350
$52$	0.886250	0.122901
$53$	−5.65948	−0.777390	−0.388695	−	0.921367i	$-0.627074\pi$
$53$	−5.65948	−0.777390	−0.388695	+	0.921367i	$0.627074\pi$
$54$	1.46962	0.199990
$55$	−21.5619	−2.90740
$56$	−2.70443	−0.361394
$57$	−5.01037	−0.663640
$58$	−9.14077	−1.20024
$59$	5.50335	0.716476	0.358238	−	0.933630i	$-0.383378\pi$
$59$	5.50335	0.716476	0.358238	+	0.933630i	$0.383378\pi$
$60$	−0.543688	−0.0701898
$61$	−12.8935	−1.65084	−0.825422	−	0.564516i	$-0.809063\pi$
$61$	−12.8935	−1.65084	−0.825422	+	0.564516i	$0.809063\pi$
$62$	−12.5679	−1.59612
$63$	−1.00000	−0.125988
$64$	7.26286	0.907858
$65$	18.8750	2.34115
$66$	−9.31217	−1.14625
$67$	10.3570	1.26531	0.632656	−	0.774433i	$-0.281965\pi$
$67$	10.3570	1.26531	0.632656	+	0.774433i	$0.281965\pi$
$68$	1.25912	0.152691
$69$	3.20602	0.385960
$70$	5.00085	0.597716
$71$	−9.93341	−1.17888	−0.589439	−	0.807813i	$-0.700651\pi$
$71$	−9.93341	−1.17888	−0.589439	+	0.807813i	$0.700651\pi$
$72$	2.70443	0.318720
$73$	−8.38480	−0.981367	−0.490683	−	0.871338i	$-0.663253\pi$
$73$	−8.38480	−0.981367	−0.490683	+	0.871338i	$0.663253\pi$
$74$	−6.35605	−0.738876
$75$	−6.57922	−0.759703
$76$	0.800534	0.0918276
$77$	6.33646	0.722106
$78$	8.15174	0.923003
$79$	−14.6480	−1.64803	−0.824016	−	0.566566i	$-0.808272\pi$
$79$	−14.6480	−1.64803	−0.824016	+	0.566566i	$0.808272\pi$
$80$	−14.6118	−1.63365
$81$	1.00000	0.111111
$82$	−14.4291	−1.59342
$83$	8.82661	0.968846	0.484423	−	0.874834i	$-0.339030\pi$
$83$	8.82661	0.968846	0.484423	+	0.874834i	$0.339030\pi$
$84$	0.159775	0.0174329
$85$	26.8162	2.90863
$86$	−9.36363	−1.00971
$87$	−6.21983	−0.666835
$88$	−17.1365	−1.82675
$89$	5.62398	0.596141	0.298071	−	0.954544i	$-0.403657\pi$
$89$	5.62398	0.596141	0.298071	+	0.954544i	$0.403657\pi$
$90$	−5.00085	−0.527136
$91$	−5.54685	−0.581468
$92$	−0.512244	−0.0534051
$93$	−8.55180	−0.886781
$94$	6.21241	0.640761
$95$	17.0494	1.74923
$96$	−0.901719	−0.0920313
$97$	10.7345	1.08992	0.544960	−	0.838462i	$-0.316545\pi$
$97$	10.7345	1.08992	0.544960	+	0.838462i	$0.316545\pi$
$98$	−1.46962	−0.148454
$99$	−6.33646	−0.636838
$100$	1.05120	0.105120
$101$	5.54825	0.552071	0.276036	−	0.961147i	$-0.410979\pi$
$101$	5.54825	0.552071	0.276036	+	0.961147i	$0.410979\pi$
$102$	11.5814	1.14673
$103$	13.7325	1.35310	0.676552	−	0.736395i	$-0.263473\pi$
$103$	13.7325	1.35310	0.676552	+	0.736395i	$0.263473\pi$
$104$	15.0010	1.47097
$105$	3.40283	0.332082
$106$	8.31727	0.807845
$107$	4.58063	0.442826	0.221413	−	0.975180i	$-0.428933\pi$
$107$	4.58063	0.442826	0.221413	+	0.975180i	$0.428933\pi$
$108$	−0.159775	−0.0153744
$109$	−8.68422	−0.831798	−0.415899	−	0.909411i	$-0.636533\pi$
$109$	−8.68422	−0.831798	−0.415899	+	0.909411i	$0.636533\pi$
$110$	31.6877	3.02130
$111$	−4.32497	−0.410508
$112$	4.29402	0.405747
$113$	−10.7269	−1.00910	−0.504551	−	0.863382i	$-0.668342\pi$
$113$	−10.7269	−1.00910	−0.504551	+	0.863382i	$0.668342\pi$
$114$	7.36333	0.689639
$115$	−10.9095	−1.01732
$116$	0.993776	0.0922698
$117$	5.54685	0.512806
$118$	−8.08783	−0.744545
$119$	−7.88057	−0.722411
$120$	−9.20269	−0.840087
$121$	29.1507	2.65006
$122$	18.9485	1.71552
$123$	−9.81825	−0.885282
$124$	1.36637	0.122704
$125$	5.37381	0.480649
$126$	1.46962	0.130924
$127$	2.14276	0.190139	0.0950695	−	0.995471i	$-0.469693\pi$
$127$	2.14276	0.190139	0.0950695	+	0.995471i	$0.469693\pi$
$128$	−12.4771	−1.10283
$129$	−6.37147	−0.560977
$130$	−27.7390	−2.43287
$131$	13.2924	1.16137	0.580683	−	0.814130i	$-0.302786\pi$
$131$	13.2924	1.16137	0.580683	+	0.814130i	$0.302786\pi$
$132$	1.01241	0.0881190
$133$	−5.01037	−0.434454
$134$	−15.2209	−1.31488
$135$	−3.40283	−0.292869
$136$	21.3124	1.82753
$137$	−3.73497	−0.319100	−0.159550	−	0.987190i	$-0.551004\pi$
$137$	−3.73497	−0.319100	−0.159550	+	0.987190i	$0.551004\pi$
$138$	−4.71163	−0.401081
$139$	−1.33028	−0.112833	−0.0564166	−	0.998407i	$-0.517967\pi$
$139$	−1.33028	−0.112833	−0.0564166	+	0.998407i	$0.517967\pi$
$140$	−0.543688	−0.0459500
$141$	4.22723	0.355997
$142$	14.5983	1.22506
$143$	−35.1474	−2.93917
$144$	−4.29402	−0.357835
$145$	21.1650	1.75766
$146$	12.3224	1.01981
$147$	−1.00000	−0.0824786
$148$	0.691024	0.0568018
$149$	8.91467	0.730319	0.365159	−	0.930945i	$-0.381015\pi$
$149$	8.91467	0.730319	0.365159	+	0.930945i	$0.381015\pi$
$150$	9.66894	0.789466
$151$	−3.57945	−0.291291	−0.145646	−	0.989337i	$-0.546526\pi$
$151$	−3.57945	−0.291291	−0.145646	+	0.989337i	$0.546526\pi$
$152$	13.5502	1.09906
$153$	7.88057	0.637107
$154$	−9.31217	−0.750396
$155$	29.1003	2.33739
$156$	−0.886250	−0.0709568
$157$	−14.2010	−1.13336	−0.566680	−	0.823938i	$-0.691772\pi$
$157$	−14.2010	−1.13336	−0.566680	+	0.823938i	$0.691772\pi$
$158$	21.5270	1.71260
$159$	5.65948	0.448826
$160$	3.06839	0.242578
$161$	3.20602	0.252670
$162$	−1.46962	−0.115464
$163$	−16.1171	−1.26239	−0.631193	−	0.775626i	$-0.717434\pi$
$163$	−16.1171	−1.26239	−0.631193	+	0.775626i	$0.717434\pi$
$164$	1.56872	0.122496
$165$	21.5619	1.67859
$166$	−12.9717	−1.00680
$167$	−6.22754	−0.481901	−0.240951	−	0.970537i	$-0.577459\pi$
$167$	−6.22754	−0.481901	−0.240951	+	0.970537i	$0.577459\pi$
$168$	2.70443	0.208651
$169$	17.7675	1.36673
$170$	−39.4096	−3.02258
$171$	5.01037	0.383153
$172$	1.01800	0.0776222
$173$	−5.13087	−0.390093	−0.195046	−	0.980794i	$-0.562486\pi$
$173$	−5.13087	−0.390093	−0.195046	+	0.980794i	$0.562486\pi$
$174$	9.14077	0.692960
$175$	−6.57922	−0.497342
$176$	27.2089	2.05095
$177$	−5.50335	−0.413657
$178$	−8.26510	−0.619496
$179$	−14.9958	−1.12084	−0.560419	−	0.828209i	$-0.689360\pi$
$179$	−14.9958	−1.12084	−0.560419	+	0.828209i	$0.689360\pi$
$180$	0.543688	0.0405241
$181$	0.856974	0.0636984	0.0318492	−	0.999493i	$-0.489860\pi$
$181$	0.856974	0.0636984	0.0318492	+	0.999493i	$0.489860\pi$
$182$	8.15174	0.604248
$183$	12.8935	0.953116
$184$	−8.67046	−0.639195
$185$	14.7171	1.08202
$186$	12.5679	0.921522
$187$	−49.9349	−3.65160
$188$	−0.675407	−0.0492591
$189$	1.00000	0.0727393
$190$	−25.0561	−1.81776
$191$	2.96876	0.214812	0.107406	−	0.994215i	$-0.465746\pi$
$191$	2.96876	0.214812	0.107406	+	0.994215i	$0.465746\pi$
$192$	−7.26286	−0.524152
$193$	−18.2670	−1.31489	−0.657443	−	0.753504i	$-0.728362\pi$
$193$	−18.2670	−1.31489	−0.657443	+	0.753504i	$0.728362\pi$
$194$	−15.7756	−1.13262
$195$	−18.8750	−1.35166
$196$	0.159775	0.0114125
$197$	8.26653	0.588966	0.294483	−	0.955657i	$-0.404853\pi$
$197$	8.26653	0.588966	0.294483	+	0.955657i	$0.404853\pi$
$198$	9.31217	0.661787
$199$	11.2433	0.797017	0.398508	−	0.917165i	$-0.369528\pi$
$199$	11.2433	0.797017	0.398508	+	0.917165i	$0.369528\pi$
$200$	17.7930	1.25816
$201$	−10.3570	−0.730528
$202$	−8.15380	−0.573700
$203$	−6.21983	−0.436546
$204$	−1.25912	−0.0881562
$205$	33.4098	2.33344
$206$	−20.1815	−1.40611
$207$	−3.20602	−0.222834
$208$	−23.8183	−1.65150
$209$	−31.7480	−2.19606
$210$	−5.00085	−0.345092
$211$	22.7689	1.56748	0.783738	−	0.621091i	$-0.213310\pi$
$211$	22.7689	1.56748	0.783738	+	0.621091i	$0.213310\pi$
$212$	−0.904246	−0.0621039
$213$	9.93341	0.680626
$214$	−6.73177	−0.460174
$215$	21.6810	1.47863
$216$	−2.70443	−0.184013
$217$	−8.55180	−0.580534
$218$	12.7625	0.864385
$219$	8.38480	0.566592
$220$	−3.44506	−0.232266
$221$	43.7123	2.94041
$222$	6.35605	0.426590
$223$	−7.30308	−0.489050	−0.244525	−	0.969643i	$-0.578632\pi$
$223$	−7.30308	−0.489050	−0.244525	+	0.969643i	$0.578632\pi$
$224$	−0.901719	−0.0602486
$225$	6.57922	0.438615
$226$	15.7644	1.04864
$227$	−18.4013	−1.22134	−0.610669	−	0.791886i	$-0.709099\pi$
$227$	−18.4013	−1.22134	−0.610669	+	0.791886i	$0.709099\pi$
$228$	−0.800534	−0.0530167
$229$	−29.0078	−1.91689	−0.958445	−	0.285278i	$-0.907914\pi$
$229$	−29.0078	−1.91689	−0.958445	+	0.285278i	$0.907914\pi$
$230$	16.0329	1.05718
$231$	−6.33646	−0.416908
$232$	16.8211	1.10436
$233$	−5.06885	−0.332071	−0.166036	−	0.986120i	$-0.553097\pi$
$233$	−5.06885	−0.332071	−0.166036	+	0.986120i	$0.553097\pi$
$234$	−8.15174	−0.532896
$235$	−14.3845	−0.938342
$236$	0.879301	0.0572376
$237$	14.6480	0.951492
$238$	11.5814	0.750712
$239$	8.36417	0.541033	0.270516	−	0.962715i	$-0.412806\pi$
$239$	8.36417	0.541033	0.270516	+	0.962715i	$0.412806\pi$
$240$	14.6118	0.943188
$241$	3.73731	0.240741	0.120371	−	0.992729i	$-0.461592\pi$
$241$	3.73731	0.240741	0.120371	+	0.992729i	$0.461592\pi$
$242$	−42.8404	−2.75388
$243$	−1.00000	−0.0641500
$244$	−2.06007	−0.131882
$245$	3.40283	0.217399
$246$	14.4291	0.919964
$247$	27.7918	1.76835
$248$	23.1277	1.46861
$249$	−8.82661	−0.559364
$250$	−7.89745	−0.499479
$251$	−13.1618	−0.830767	−0.415384	−	0.909646i	$-0.636353\pi$
$251$	−13.1618	−0.830767	−0.415384	+	0.909646i	$0.636353\pi$
$252$	−0.159775	−0.0100649
$253$	20.3148	1.27718
$254$	−3.14903	−0.197588
$255$	−26.8162	−1.67930
$256$	3.81079	0.238174
$257$	−30.9992	−1.93368	−0.966838	−	0.255392i	$-0.917795\pi$
$257$	−30.9992	−1.93368	−0.966838	+	0.255392i	$0.917795\pi$
$258$	9.36363	0.582954
$259$	−4.32497	−0.268740
$260$	3.01575	0.187029
$261$	6.21983	0.384998
$262$	−19.5348	−1.20686
$263$	25.7664	1.58883	0.794413	−	0.607378i	$-0.207779\pi$
$263$	25.7664	1.58883	0.794413	+	0.607378i	$0.207779\pi$
$264$	17.1365	1.05468
$265$	−19.2582	−1.18302
$266$	7.36333	0.451475
$267$	−5.62398	−0.344182
$268$	1.65480	0.101083
$269$	−8.44911	−0.515151	−0.257576	−	0.966258i	$-0.582924\pi$
$269$	−8.44911	−0.515151	−0.257576	+	0.966258i	$0.582924\pi$
$270$	5.00085	0.304342
$271$	30.5855	1.85794	0.928968	−	0.370159i	$-0.120697\pi$
$271$	30.5855	1.85794	0.928968	+	0.370159i	$0.120697\pi$
$272$	−33.8394	−2.05181
$273$	5.54685	0.335711
$274$	5.48898	0.331601
$275$	−41.6890	−2.51394
$276$	0.512244	0.0308335
$277$	4.22856	0.254070	0.127035	−	0.991898i	$-0.459454\pi$
$277$	4.22856	0.254070	0.127035	+	0.991898i	$0.459454\pi$
$278$	1.95501	0.117254
$279$	8.55180	0.511983
$280$	−9.20269	−0.549966
$281$	5.52023	0.329309	0.164655	−	0.986351i	$-0.447349\pi$
$281$	5.52023	0.329309	0.164655	+	0.986351i	$0.447349\pi$
$282$	−6.21241	−0.369943
$283$	1.31373	0.0780934	0.0390467	−	0.999237i	$-0.487568\pi$
$283$	1.31373	0.0780934	0.0390467	+	0.999237i	$0.487568\pi$
$284$	−1.58711	−0.0941779
$285$	−17.0494	−1.00992
$286$	51.6532	3.05432
$287$	−9.81825	−0.579553
$288$	0.901719	0.0531343
$289$	45.1034	2.65314
$290$	−31.1044	−1.82652
$291$	−10.7345	−0.629265
$292$	−1.33969	−0.0783992
$293$	18.7375	1.09466	0.547328	−	0.836918i	$-0.315645\pi$
$293$	18.7375	1.09466	0.547328	+	0.836918i	$0.315645\pi$
$294$	1.46962	0.0857098
$295$	18.7270	1.09033
$296$	11.6966	0.679849
$297$	6.33646	0.367679
$298$	−13.1012	−0.758930
$299$	−17.7833	−1.02844
$300$	−1.05120	−0.0606909
$301$	−6.37147	−0.367246
$302$	5.26042	0.302703
$303$	−5.54825	−0.318739
$304$	−21.5146	−1.23395
$305$	−43.8744	−2.51224
$306$	−11.5814	−0.662066
$307$	−17.2387	−0.983863	−0.491931	−	0.870634i	$-0.663709\pi$
$307$	−17.2387	−0.983863	−0.491931	+	0.870634i	$0.663709\pi$
$308$	1.01241	0.0576874
$309$	−13.7325	−0.781215
$310$	−42.7663	−2.42896
$311$	−25.9794	−1.47316	−0.736578	−	0.676353i	$-0.763560\pi$
$311$	−25.9794	−1.47316	−0.736578	+	0.676353i	$0.763560\pi$
$312$	−15.0010	−0.849267
$313$	−27.7369	−1.56778	−0.783892	−	0.620897i	$-0.786768\pi$
$313$	−27.7369	−1.56778	−0.783892	+	0.620897i	$0.786768\pi$
$314$	20.8700	1.17776
$315$	−3.40283	−0.191727
$316$	−2.34040	−0.131658
$317$	−10.9184	−0.613238	−0.306619	−	0.951832i	$-0.599198\pi$
$317$	−10.9184	−0.613238	−0.306619	+	0.951832i	$0.599198\pi$
$318$	−8.31727	−0.466409
$319$	−39.4117	−2.20663
$320$	24.7143	1.38157
$321$	−4.58063	−0.255666
$322$	−4.71163	−0.262569
$323$	39.4846	2.19698
$324$	0.159775	0.00887641
$325$	36.4939	2.02432
$326$	23.6859	1.31184
$327$	8.68422	0.480239
$328$	26.5527	1.46613
$329$	4.22723	0.233055
$330$	−31.6877	−1.74435
$331$	6.13152	0.337019	0.168509	−	0.985700i	$-0.446105\pi$
$331$	6.13152	0.337019	0.168509	+	0.985700i	$0.446105\pi$
$332$	1.41028	0.0773989
$333$	4.32497	0.237007
$334$	9.15210	0.500781
$335$	35.2431	1.92554
$336$	−4.29402	−0.234258
$337$	16.9145	0.921390	0.460695	−	0.887558i	$-0.347600\pi$
$337$	16.9145	0.921390	0.460695	+	0.887558i	$0.347600\pi$
$338$	−26.1115	−1.42028
$339$	10.7269	0.582605
$340$	4.28457	0.232364
$341$	−54.1881	−2.93445
$342$	−7.36333	−0.398163
$343$	−1.00000	−0.0539949
$344$	17.2312	0.929043
$345$	10.9095	0.587350
$346$	7.54042	0.405375
$347$	−29.1836	−1.56666	−0.783329	−	0.621608i	$-0.786480\pi$
$347$	−29.1836	−1.56666	−0.783329	+	0.621608i	$0.786480\pi$
$348$	−0.993776	−0.0532720
$349$	27.4556	1.46966	0.734831	−	0.678250i	$-0.237261\pi$
$349$	27.4556	1.46966	0.734831	+	0.678250i	$0.237261\pi$
$350$	9.66894	0.516826
$351$	−5.54685	−0.296069
$352$	−5.71370	−0.304541
$353$	2.80252	0.149163	0.0745816	−	0.997215i	$-0.476238\pi$
$353$	2.80252	0.149163	0.0745816	+	0.997215i	$0.476238\pi$
$354$	8.08783	0.429863
$355$	−33.8017	−1.79401
$356$	0.898575	0.0476244
$357$	7.88057	0.417084
$358$	22.0381	1.16475
$359$	21.6830	1.14439	0.572194	−	0.820118i	$-0.306093\pi$
$359$	21.6830	1.14439	0.572194	+	0.820118i	$0.306093\pi$
$360$	9.20269	0.485024
$361$	6.10382	0.321254
$362$	−1.25942	−0.0661939
$363$	−29.1507	−1.53001
$364$	−0.886250	−0.0464521
$365$	−28.5320	−1.49343
$366$	−18.9485	−0.990455
$367$	8.36082	0.436431	0.218216	−	0.975901i	$-0.429976\pi$
$367$	8.36082	0.436431	0.218216	+	0.975901i	$0.429976\pi$
$368$	13.7667	0.717641
$369$	9.81825	0.511118
$370$	−21.6285	−1.12441
$371$	5.65948	0.293826
$372$	−1.36637	−0.0708429
$373$	−4.16426	−0.215617	−0.107809	−	0.994172i	$-0.534383\pi$
$373$	−4.16426	−0.215617	−0.107809	+	0.994172i	$0.534383\pi$
$374$	73.3852	3.79466
$375$	−5.37381	−0.277503
$376$	−11.4322	−0.589572
$377$	34.5004	1.77686
$378$	−1.46962	−0.0755890
$379$	−18.2414	−0.936998	−0.468499	−	0.883464i	$-0.655205\pi$
$379$	−18.2414	−0.936998	−0.468499	+	0.883464i	$0.655205\pi$
$380$	2.72408	0.139742
$381$	−2.14276	−0.109777
$382$	−4.36294	−0.223227
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	12.4771	0.636718
$385$	21.5619	1.09889
$386$	26.8455	1.36640
$387$	6.37147	0.323880
$388$	1.71510	0.0870712
$389$	−28.3954	−1.43971	−0.719853	−	0.694127i	$-0.755791\pi$
$389$	−28.3954	−1.43971	−0.719853	+	0.694127i	$0.755791\pi$
$390$	27.7390	1.40462
$391$	−25.2653	−1.27772
$392$	2.70443	0.136594
$393$	−13.2924	−0.670515
$394$	−12.1486	−0.612040
$395$	−49.8447	−2.50796
$396$	−1.01241	−0.0508755
$397$	21.8041	1.09431	0.547157	−	0.837030i	$-0.315710\pi$
$397$	21.8041	1.09431	0.547157	+	0.837030i	$0.315710\pi$
$398$	−16.5234	−0.828241
$399$	5.01037	0.250832
$400$	−28.2513	−1.41257
$401$	0.0921093	0.00459972	0.00229986	−	0.999997i	$-0.499268\pi$
$401$	0.0921093	0.00459972	0.00229986	+	0.999997i	$0.499268\pi$
$402$	15.2209	0.759147
$403$	47.4356	2.36293
$404$	0.886474	0.0441037
$405$	3.40283	0.169088
$406$	9.14077	0.453649
$407$	−27.4050	−1.35841
$408$	−21.3124	−1.05512
$409$	−12.3200	−0.609186	−0.304593	−	0.952483i	$-0.598520\pi$
$409$	−12.3200	−0.609186	−0.304593	+	0.952483i	$0.598520\pi$
$410$	−49.0996	−2.42486
$411$	3.73497	0.184233
$412$	2.19412	0.108096
$413$	−5.50335	−0.270802
$414$	4.71163	0.231564
$415$	30.0354	1.47438
$416$	5.00170	0.245228
$417$	1.33028	0.0651443
$418$	46.6574	2.28209
$419$	−34.8975	−1.70486	−0.852428	−	0.522845i	$-0.824871\pi$
$419$	−34.8975	−1.70486	−0.852428	+	0.522845i	$0.824871\pi$
$420$	0.543688	0.0265293
$421$	36.9122	1.79899	0.899494	−	0.436933i	$-0.143935\pi$
$421$	36.9122	1.79899	0.899494	+	0.436933i	$0.143935\pi$
$422$	−33.4616	−1.62888
$423$	−4.22723	−0.205535
$424$	−15.3056	−0.743308
$425$	51.8480	2.51500
$426$	−14.5983	−0.707290
$427$	12.8935	0.623961
$428$	0.731872	0.0353763
$429$	35.1474	1.69693
$430$	−31.8628	−1.53656
$431$	−37.8741	−1.82433	−0.912167	−	0.409819i	$-0.865592\pi$
$431$	−37.8741	−1.82433	−0.912167	+	0.409819i	$0.865592\pi$
$432$	4.29402	0.206596
$433$	14.8980	0.715950	0.357975	−	0.933731i	$-0.383467\pi$
$433$	14.8980	0.715950	0.357975	+	0.933731i	$0.383467\pi$
$434$	12.5679	0.603278
$435$	−21.1650	−1.01478
$436$	−1.38753	−0.0664504
$437$	−16.0634	−0.768415
$438$	−12.3224	−0.588789
$439$	8.80240	0.420116	0.210058	−	0.977689i	$-0.432635\pi$
$439$	8.80240	0.420116	0.210058	+	0.977689i	$0.432635\pi$
$440$	−58.3124	−2.77994
$441$	1.00000	0.0476190
$442$	−64.2404	−3.05560
$443$	−33.5177	−1.59247	−0.796237	−	0.604984i	$-0.793179\pi$
$443$	−33.5177	−1.59247	−0.796237	+	0.604984i	$0.793179\pi$
$444$	−0.691024	−0.0327945
$445$	19.1374	0.907201
$446$	10.7327	0.508210
$447$	−8.91467	−0.421650
$448$	−7.26286	−0.343138
$449$	18.9377	0.893727	0.446863	−	0.894602i	$-0.352541\pi$
$449$	18.9377	0.893727	0.446863	+	0.894602i	$0.352541\pi$
$450$	−9.66894	−0.455798
$451$	−62.2129	−2.92949
$452$	−1.71390	−0.0806149
$453$	3.57945	0.168177
$454$	27.0429	1.26918
$455$	−18.8750	−0.884872
$456$	−13.5502	−0.634545
$457$	19.4068	0.907812	0.453906	−	0.891049i	$-0.350030\pi$
$457$	19.4068	0.907812	0.453906	+	0.891049i	$0.350030\pi$
$458$	42.6304	1.99199
$459$	−7.88057	−0.367834
$460$	−1.74308	−0.0812714
$461$	−29.6299	−1.38000	−0.690000	−	0.723809i	$-0.742390\pi$
$461$	−29.6299	−1.38000	−0.690000	+	0.723809i	$0.742390\pi$
$462$	9.31217	0.433241
$463$	−35.1700	−1.63449	−0.817245	−	0.576291i	$-0.804500\pi$
$463$	−35.1700	−1.63449	−0.817245	+	0.576291i	$0.804500\pi$
$464$	−26.7081	−1.23989
$465$	−29.1003	−1.34949
$466$	7.44927	0.345081
$467$	−32.2180	−1.49087	−0.745435	−	0.666578i	$-0.767758\pi$
$467$	−32.2180	−1.49087	−0.745435	+	0.666578i	$0.767758\pi$
$468$	0.886250	0.0409669
$469$	−10.3570	−0.478243
$470$	21.1397	0.975103
$471$	14.2010	0.654346
$472$	14.8834	0.685065
$473$	−40.3726	−1.85633
$474$	−21.5270	−0.988768
$475$	32.9643	1.51251
$476$	−1.25912	−0.0577118
$477$	−5.65948	−0.259130
$478$	−12.2921	−0.562229
$479$	23.8960	1.09184	0.545918	−	0.837838i	$-0.316181\pi$
$479$	23.8960	1.09184	0.545918	+	0.837838i	$0.316181\pi$
$480$	−3.06839	−0.140052
$481$	23.9899	1.09385
$482$	−5.49241	−0.250173
$483$	−3.20602	−0.145879
$484$	4.65756	0.211707
$485$	36.5275	1.65863
$486$	1.46962	0.0666632
$487$	−31.5040	−1.42758	−0.713791	−	0.700359i	$-0.753023\pi$
$487$	−31.5040	−1.42758	−0.713791	+	0.700359i	$0.753023\pi$
$488$	−34.8695	−1.57847
$489$	16.1171	0.728838
$490$	−5.00085	−0.225915
$491$	36.0001	1.62466	0.812331	−	0.583197i	$-0.198198\pi$
$491$	36.0001	1.62466	0.812331	+	0.583197i	$0.198198\pi$
$492$	−1.56872	−0.0707232
$493$	49.0158	2.20756
$494$	−40.8433	−1.83763
$495$	−21.5619	−0.969133
$496$	−36.7216	−1.64885
$497$	9.93341	0.445574
$498$	12.9717	0.581277
$499$	9.99033	0.447228	0.223614	−	0.974678i	$-0.428214\pi$
$499$	9.99033	0.447228	0.223614	+	0.974678i	$0.428214\pi$
$500$	0.858604	0.0383979
$501$	6.22754	0.278226
$502$	19.3429	0.863314
$503$	17.2859	0.770742	0.385371	−	0.922762i	$-0.374073\pi$
$503$	17.2859	0.770742	0.385371	+	0.922762i	$0.374073\pi$
$504$	−2.70443	−0.120465
$505$	18.8797	0.840137
$506$	−29.8550	−1.32722
$507$	−17.7675	−0.789083
$508$	0.342360	0.0151898
$509$	−24.2413	−1.07448	−0.537238	−	0.843431i	$-0.680532\pi$
$509$	−24.2413	−1.07448	−0.537238	+	0.843431i	$0.680532\pi$
$510$	39.4096	1.74509
$511$	8.38480	0.370922
$512$	19.3537	0.855322
$513$	−5.01037	−0.221213
$514$	45.5569	2.00943
$515$	46.7293	2.05914
$516$	−1.01800	−0.0448152
$517$	26.7856	1.17803
$518$	6.35605	0.279269
$519$	5.13087	0.225220
$520$	51.0459	2.23851
$521$	−7.12497	−0.312151	−0.156075	−	0.987745i	$-0.549884\pi$
$521$	−7.12497	−0.312151	−0.156075	+	0.987745i	$0.549884\pi$
$522$	−9.14077	−0.400080
$523$	9.82152	0.429465	0.214732	−	0.976673i	$-0.431112\pi$
$523$	9.82152	0.429465	0.214732	+	0.976673i	$0.431112\pi$
$524$	2.12381	0.0927789
$525$	6.57922	0.287141
$526$	−37.8668	−1.65107
$527$	67.3931	2.93569
$528$	−27.2089	−1.18411
$529$	−12.7214	−0.553105
$530$	28.3022	1.22937
$531$	5.50335	0.238825
$532$	−0.800534	−0.0347076
$533$	54.4604	2.35894
$534$	8.26510	0.357666
$535$	15.5871	0.673888
$536$	28.0098	1.20984
$537$	14.9958	0.647116
$538$	12.4170	0.535333
$539$	−6.33646	−0.272931
$540$	−0.543688	−0.0233966
$541$	16.1579	0.694684	0.347342	−	0.937739i	$-0.387084\pi$
$541$	16.1579	0.694684	0.347342	+	0.937739i	$0.387084\pi$
$542$	−44.9490	−1.93072
$543$	−0.856974	−0.0367763
$544$	7.10606	0.304670
$545$	−29.5509	−1.26582
$546$	−8.15174	−0.348862
$547$	8.73030	0.373281	0.186640	−	0.982428i	$-0.440240\pi$
$547$	8.73030	0.373281	0.186640	+	0.982428i	$0.440240\pi$
$548$	−0.596757	−0.0254922
$549$	−12.8935	−0.550282
$550$	61.2668	2.61243
$551$	31.1636	1.32762
$552$	8.67046	0.369039
$553$	14.6480	0.622898
$554$	−6.21437	−0.264023
$555$	−14.7171	−0.624707
$556$	−0.212547	−0.00901398
$557$	21.7677	0.922326	0.461163	−	0.887315i	$-0.347432\pi$
$557$	21.7677	0.922326	0.461163	+	0.887315i	$0.347432\pi$
$558$	−12.5679	−0.532041
$559$	35.3416	1.49479
$560$	14.6118	0.617462
$561$	49.9349	2.10825
$562$	−8.11262	−0.342210
$563$	20.2092	0.851715	0.425858	−	0.904790i	$-0.359972\pi$
$563$	20.2092	0.851715	0.425858	+	0.904790i	$0.359972\pi$
$564$	0.675407	0.0284398
$565$	−36.5018	−1.53564
$566$	−1.93069	−0.0811528
$567$	−1.00000	−0.0419961
$568$	−26.8642	−1.12720
$569$	13.0288	0.546196	0.273098	−	0.961986i	$-0.411952\pi$
$569$	13.0288	0.546196	0.273098	+	0.961986i	$0.411952\pi$
$570$	25.0561	1.04949
$571$	24.4046	1.02130	0.510649	−	0.859789i	$-0.329405\pi$
$571$	24.4046	1.02130	0.510649	+	0.859789i	$0.329405\pi$
$572$	−5.61569	−0.234804
$573$	−2.96876	−0.124022
$574$	14.4291	0.602258
$575$	−21.0931	−0.879645
$576$	7.26286	0.302619
$577$	14.7585	0.614406	0.307203	−	0.951644i	$-0.400607\pi$
$577$	14.7585	0.614406	0.307203	+	0.951644i	$0.400607\pi$
$578$	−66.2848	−2.75708
$579$	18.2670	0.759150
$580$	3.38165	0.140415
$581$	−8.82661	−0.366189
$582$	15.7756	0.653918
$583$	35.8611	1.48521
$584$	−22.6761	−0.938343
$585$	18.8750	0.780383
$586$	−27.5369	−1.13754
$587$	6.51938	0.269084	0.134542	−	0.990908i	$-0.457044\pi$
$587$	6.51938	0.269084	0.134542	+	0.990908i	$0.457044\pi$
$588$	−0.159775	−0.00658903
$589$	42.8477	1.76551
$590$	−27.5215	−1.13304
$591$	−8.26653	−0.340040
$592$	−18.5715	−0.763284
$593$	−0.185859	−0.00763230	−0.00381615	−	0.999993i	$-0.501215\pi$
$593$	−0.185859	−0.00763230	−0.00381615	+	0.999993i	$0.501215\pi$
$594$	−9.31217	−0.382083
$595$	−26.8162	−1.09936
$596$	1.42435	0.0583435
$597$	−11.2433	−0.460158
$598$	26.1347	1.06873
$599$	3.21874	0.131514	0.0657570	−	0.997836i	$-0.479054\pi$
$599$	3.21874	0.131514	0.0657570	+	0.997836i	$0.479054\pi$
$600$	−17.7930	−0.726397
$601$	−22.4864	−0.917240	−0.458620	−	0.888632i	$-0.651656\pi$
$601$	−22.4864	−0.917240	−0.458620	+	0.888632i	$0.651656\pi$
$602$	9.36363	0.381633
$603$	10.3570	0.421770
$604$	−0.571908	−0.0232706
$605$	99.1947	4.03284
$606$	8.15380	0.331226
$607$	30.5622	1.24048	0.620241	−	0.784411i	$-0.287035\pi$
$607$	30.5622	1.24048	0.620241	+	0.784411i	$0.287035\pi$
$608$	4.51794	0.183227
$609$	6.21983	0.252040
$610$	64.4785	2.61066
$611$	−23.4478	−0.948596
$612$	1.25912	0.0508970
$613$	41.9245	1.69331	0.846657	−	0.532139i	$-0.178612\pi$
$613$	41.9245	1.69331	0.846657	+	0.532139i	$0.178612\pi$
$614$	25.3343	1.02241
$615$	−33.4098	−1.34721
$616$	17.1365	0.690448
$617$	−28.3390	−1.14089	−0.570443	−	0.821337i	$-0.693228\pi$
$617$	−28.3390	−1.14089	−0.570443	+	0.821337i	$0.693228\pi$
$618$	20.1815	0.811820
$619$	3.57793	0.143809	0.0719046	−	0.997412i	$-0.477092\pi$
$619$	3.57793	0.143809	0.0719046	+	0.997412i	$0.477092\pi$
$620$	4.64951	0.186729
$621$	3.20602	0.128653
$622$	38.1798	1.53087
$623$	−5.62398	−0.225320
$624$	23.8183	0.953495
$625$	−14.6100	−0.584398
$626$	40.7627	1.62920
$627$	31.7480	1.26789
$628$	−2.26896	−0.0905415
$629$	34.0832	1.35899
$630$	5.00085	0.199239
$631$	4.59541	0.182940	0.0914702	−	0.995808i	$-0.470843\pi$
$631$	4.59541	0.182940	0.0914702	+	0.995808i	$0.470843\pi$
$632$	−39.6145	−1.57578
$633$	−22.7689	−0.904983
$634$	16.0458	0.637262
$635$	7.29143	0.289352
$636$	0.904246	0.0358557
$637$	5.54685	0.219774
$638$	57.9201	2.29308
$639$	−9.93341	−0.392960
$640$	−42.4573	−1.67827
$641$	−12.5107	−0.494144	−0.247072	−	0.968997i	$-0.579468\pi$
$641$	−12.5107	−0.494144	−0.247072	+	0.968997i	$0.579468\pi$
$642$	6.73177	0.265682
$643$	−2.73386	−0.107813	−0.0539064	−	0.998546i	$-0.517167\pi$
$643$	−2.73386	−0.107813	−0.0539064	+	0.998546i	$0.517167\pi$
$644$	0.512244	0.0201852
$645$	−21.6810	−0.853689
$646$	−58.0273	−2.28305
$647$	18.5311	0.728533	0.364266	−	0.931295i	$-0.381320\pi$
$647$	18.5311	0.728533	0.364266	+	0.931295i	$0.381320\pi$
$648$	2.70443	0.106240
$649$	−34.8718	−1.36884
$650$	−53.6321	−2.10363
$651$	8.55180	0.335172
$652$	−2.57511	−0.100849
$653$	−4.59116	−0.179666	−0.0898330	−	0.995957i	$-0.528633\pi$
$653$	−4.59116	−0.179666	−0.0898330	+	0.995957i	$0.528633\pi$
$654$	−12.7625	−0.499053
$655$	45.2318	1.76735
$656$	−42.1598	−1.64606
$657$	−8.38480	−0.327122
$658$	−6.21241	−0.242185
$659$	28.5834	1.11345	0.556725	−	0.830697i	$-0.312058\pi$
$659$	28.5834	1.11345	0.556725	+	0.830697i	$0.312058\pi$
$660$	3.44506	0.134099
$661$	36.2730	1.41086	0.705429	−	0.708781i	$-0.250755\pi$
$661$	36.2730	1.41086	0.705429	+	0.708781i	$0.250755\pi$
$662$	−9.01099	−0.350222
$663$	−43.7123	−1.69765
$664$	23.8709	0.926371
$665$	−17.0494	−0.661148
$666$	−6.35605	−0.246292
$667$	−19.9409	−0.772115
$668$	−0.995008	−0.0384980
$669$	7.30308	0.282353
$670$	−51.7939	−2.00097
$671$	81.6992	3.15396
$672$	0.901719	0.0347845
$673$	25.2065	0.971639	0.485820	−	0.874059i	$-0.338521\pi$
$673$	25.2065	0.971639	0.485820	+	0.874059i	$0.338521\pi$
$674$	−24.8578	−0.957487
$675$	−6.57922	−0.253234
$676$	2.83881	0.109185
$677$	−16.3095	−0.626825	−0.313413	−	0.949617i	$-0.601472\pi$
$677$	−16.3095	−0.626825	−0.313413	+	0.949617i	$0.601472\pi$
$678$	−15.7644	−0.605430
$679$	−10.7345	−0.411951
$680$	72.5225	2.78111
$681$	18.4013	0.705139
$682$	79.6358	3.04941
$683$	12.4586	0.476715	0.238358	−	0.971177i	$-0.423391\pi$
$683$	12.4586	0.476715	0.238358	+	0.971177i	$0.423391\pi$
$684$	0.800534	0.0306092
$685$	−12.7095	−0.485603
$686$	1.46962	0.0561103
$687$	29.0078	1.10672
$688$	−27.3592	−1.04306
$689$	−31.3923	−1.19595
$690$	−16.0329	−0.610360
$691$	4.98180	0.189516	0.0947582	−	0.995500i	$-0.469792\pi$
$691$	4.98180	0.189516	0.0947582	+	0.995500i	$0.469792\pi$
$692$	−0.819787	−0.0311636
$693$	6.33646	0.240702
$694$	42.8887	1.62803
$695$	−4.52672	−0.171708
$696$	−16.8211	−0.637601
$697$	77.3735	2.93073
$698$	−40.3492	−1.52724
$699$	5.06885	0.191721
$700$	−1.05120	−0.0397316
$701$	−10.9740	−0.414481	−0.207240	−	0.978290i	$-0.566448\pi$
$701$	−10.9740	−0.414481	−0.207240	+	0.978290i	$0.566448\pi$
$702$	8.15174	0.307668
$703$	21.6697	0.817288
$704$	−46.0208	−1.73448
$705$	14.3845	0.541752
$706$	−4.11863	−0.155007
$707$	−5.54825	−0.208663
$708$	−0.879301	−0.0330462
$709$	13.9897	0.525396	0.262698	−	0.964878i	$-0.415388\pi$
$709$	13.9897	0.525396	0.262698	+	0.964878i	$0.415388\pi$
$710$	49.6755	1.86429
$711$	−14.6480	−0.549344
$712$	15.2096	0.570006
$713$	−27.4173	−1.02679
$714$	−11.5814	−0.433424
$715$	−119.600	−4.47280
$716$	−2.39596	−0.0895411
$717$	−8.36417	−0.312366
$718$	−31.8658	−1.18922
$719$	16.6597	0.621303	0.310652	−	0.950524i	$-0.399453\pi$
$719$	16.6597	0.621303	0.310652	+	0.950524i	$0.399453\pi$
$720$	−14.6118	−0.544550
$721$	−13.7325	−0.511425
$722$	−8.97028	−0.333839
$723$	−3.73731	−0.138992
$724$	0.136923	0.00508872
$725$	40.9216	1.51979
$726$	42.8404	1.58995
$727$	−39.6652	−1.47110	−0.735550	−	0.677471i	$-0.763076\pi$
$727$	−39.6652	−1.47110	−0.735550	+	0.677471i	$0.763076\pi$
$728$	−15.0010	−0.555976
$729$	1.00000	0.0370370
$730$	41.9311	1.55194
$731$	50.2109	1.85712
$732$	2.06007	0.0761422
$733$	−21.6562	−0.799890	−0.399945	−	0.916539i	$-0.630971\pi$
$733$	−21.6562	−0.799890	−0.399945	+	0.916539i	$0.630971\pi$
$734$	−12.2872	−0.453529
$735$	−3.40283	−0.125515
$736$	−2.89093	−0.106561
$737$	−65.6268	−2.41739
$738$	−14.4291	−0.531142
$739$	−35.6162	−1.31016	−0.655081	−	0.755558i	$-0.727366\pi$
$739$	−35.6162	−1.31016	−0.655081	+	0.755558i	$0.727366\pi$
$740$	2.35143	0.0864404
$741$	−27.7918	−1.02096
$742$	−8.31727	−0.305337
$743$	−24.8936	−0.913257	−0.456628	−	0.889658i	$-0.650943\pi$
$743$	−24.8936	−0.913257	−0.456628	+	0.889658i	$0.650943\pi$
$744$	−23.1277	−0.847903
$745$	30.3351	1.11139
$746$	6.11987	0.224064
$747$	8.82661	0.322949
$748$	−7.97837	−0.291718
$749$	−4.58063	−0.167372
$750$	7.89745	0.288374
$751$	14.5929	0.532501	0.266251	−	0.963904i	$-0.414215\pi$
$751$	14.5929	0.532501	0.266251	+	0.963904i	$0.414215\pi$
$752$	18.1518	0.661928
$753$	13.1618	0.479644
$754$	−50.7024	−1.84647
$755$	−12.1802	−0.443284
$756$	0.159775	0.00581098
$757$	43.4513	1.57927	0.789633	−	0.613579i	$-0.210271\pi$
$757$	43.4513	1.57927	0.789633	+	0.613579i	$0.210271\pi$
$758$	26.8079	0.973706
$759$	−20.3148	−0.737382
$760$	46.1089	1.67255
$761$	−3.56794	−0.129338	−0.0646688	−	0.997907i	$-0.520599\pi$
$761$	−3.56794	−0.129338	−0.0646688	+	0.997907i	$0.520599\pi$
$762$	3.14903	0.114077
$763$	8.68422	0.314390
$764$	0.474335	0.0171608
$765$	26.8162	0.969542
$766$	−1.46962	−0.0530994
$767$	30.5263	1.10224
$768$	−3.81079	−0.137510
$769$	9.28429	0.334800	0.167400	−	0.985889i	$-0.446463\pi$
$769$	9.28429	0.334800	0.167400	+	0.985889i	$0.446463\pi$
$770$	−31.6877	−1.14194
$771$	30.9992	1.11641
$772$	−2.91862	−0.105043
$773$	33.1957	1.19397	0.596984	−	0.802253i	$-0.296366\pi$
$773$	33.1957	1.19397	0.596984	+	0.802253i	$0.296366\pi$
$774$	−9.36363	−0.336569
$775$	56.2642	2.02107
$776$	29.0306	1.04214
$777$	4.32497	0.155157
$778$	41.7304	1.49611
$779$	49.1931	1.76253
$780$	−3.01575	−0.107981
$781$	62.9426	2.25226
$782$	37.1303	1.32778
$783$	−6.21983	−0.222278
$784$	−4.29402	−0.153358
$785$	−48.3234	−1.72474
$786$	19.5348	0.696783
$787$	51.8531	1.84836	0.924181	−	0.381955i	$-0.124749\pi$
$787$	51.8531	1.84836	0.924181	+	0.381955i	$0.124749\pi$
$788$	1.32079	0.0470512
$789$	−25.7664	−0.917309
$790$	73.2527	2.60621
$791$	10.7269	0.381405
$792$	−17.1365	−0.608918
$793$	−71.5183	−2.53969
$794$	−32.0436	−1.13719
$795$	19.2582	0.683019
$796$	1.79640	0.0636719
$797$	−0.745277	−0.0263991	−0.0131995	−	0.999913i	$-0.504202\pi$
$797$	−0.745277	−0.0263991	−0.0131995	+	0.999913i	$0.504202\pi$
$798$	−7.36333	−0.260659
$799$	−33.3130	−1.17853
$800$	5.93261	0.209749
$801$	5.62398	0.198714
$802$	−0.135365	−0.00477992
$803$	53.1299	1.87491
$804$	−1.65480	−0.0583602
$805$	10.9095	0.384511
$806$	−69.7121	−2.45550
$807$	8.44911	0.297423
$808$	15.0048	0.527868
$809$	13.6648	0.480430	0.240215	−	0.970720i	$-0.422782\pi$
$809$	13.6648	0.480430	0.240215	+	0.970720i	$0.422782\pi$
$810$	−5.00085	−0.175712
$811$	−5.48793	−0.192707	−0.0963536	−	0.995347i	$-0.530718\pi$
$811$	−5.48793	−0.192707	−0.0963536	+	0.995347i	$0.530718\pi$
$812$	−0.993776	−0.0348747
$813$	−30.5855	−1.07268
$814$	40.2748	1.41163
$815$	−54.8435	−1.92108
$816$	33.8394	1.18461
$817$	31.9234	1.11686
$818$	18.1057	0.633052
$819$	−5.54685	−0.193823
$820$	5.33807	0.186413
$821$	−3.01827	−0.105338	−0.0526691	−	0.998612i	$-0.516773\pi$
$821$	−3.01827	−0.105338	−0.0526691	+	0.998612i	$0.516773\pi$
$822$	−5.48898	−0.191450
$823$	−12.9296	−0.450696	−0.225348	−	0.974278i	$-0.572352\pi$
$823$	−12.9296	−0.450696	−0.225348	+	0.974278i	$0.572352\pi$
$824$	37.1386	1.29378
$825$	41.6890	1.45142
$826$	8.08783	0.281411
$827$	−23.5375	−0.818481	−0.409240	−	0.912427i	$-0.634206\pi$
$827$	−23.5375	−0.818481	−0.409240	+	0.912427i	$0.634206\pi$
$828$	−0.512244	−0.0178017
$829$	−9.92847	−0.344830	−0.172415	−	0.985024i	$-0.555157\pi$
$829$	−9.92847	−0.344830	−0.172415	+	0.985024i	$0.555157\pi$
$830$	−44.1406	−1.53214
$831$	−4.22856	−0.146687
$832$	40.2860	1.39667
$833$	7.88057	0.273046
$834$	−1.95501	−0.0676964
$835$	−21.1912	−0.733353
$836$	−5.07255	−0.175438
$837$	−8.55180	−0.295594
$838$	51.2860	1.77165
$839$	−42.4787	−1.46653	−0.733264	−	0.679944i	$-0.762004\pi$
$839$	−42.4787	−1.46653	−0.733264	+	0.679944i	$0.762004\pi$
$840$	9.20269	0.317523
$841$	9.68624	0.334008
$842$	−54.2467	−1.86947
$843$	−5.52023	−0.190127
$844$	3.63791	0.125222
$845$	60.4598	2.07988
$846$	6.21241	0.213587
$847$	−29.1507	−1.00163
$848$	24.3019	0.834532
$849$	−1.31373	−0.0450872
$850$	−76.1968	−2.61353
$851$	−13.8660	−0.475319
$852$	1.58711	0.0543737
$853$	24.1599	0.827220	0.413610	−	0.910454i	$-0.364268\pi$
$853$	24.1599	0.827220	0.413610	+	0.910454i	$0.364268\pi$
$854$	−18.9485	−0.648405
$855$	17.0494	0.583078
$856$	12.3880	0.423412
$857$	8.89068	0.303700	0.151850	−	0.988404i	$-0.451477\pi$
$857$	8.89068	0.303700	0.151850	+	0.988404i	$0.451477\pi$
$858$	−51.6532	−1.76341
$859$	−29.0312	−0.990531	−0.495266	−	0.868742i	$-0.664929\pi$
$859$	−29.0312	−0.990531	−0.495266	+	0.868742i	$0.664929\pi$
$860$	3.46409	0.118125
$861$	9.81825	0.334605
$862$	55.6605	1.89580
$863$	30.5015	1.03828	0.519142	−	0.854688i	$-0.326252\pi$
$863$	30.5015	1.03828	0.519142	+	0.854688i	$0.326252\pi$
$864$	−0.901719	−0.0306771
$865$	−17.4595	−0.593639
$866$	−21.8943	−0.743998
$867$	−45.1034	−1.53179
$868$	−1.36637	−0.0463776
$869$	92.8167	3.14859
$870$	31.1044	1.05454
$871$	57.4488	1.94658
$872$	−23.4858	−0.795331
$873$	10.7345	0.363307
$874$	23.6070	0.798519
$875$	−5.37381	−0.181668
$876$	1.33969	0.0452638
$877$	21.4501	0.724317	0.362158	−	0.932117i	$-0.382040\pi$
$877$	21.4501	0.724317	0.362158	+	0.932117i	$0.382040\pi$
$878$	−12.9362	−0.436574
$879$	−18.7375	−0.632000
$880$	92.5871	3.12111
$881$	−17.4065	−0.586441	−0.293220	−	0.956045i	$-0.594727\pi$
$881$	−17.4065	−0.586441	−0.293220	+	0.956045i	$0.594727\pi$
$882$	−1.46962	−0.0494846
$883$	29.8548	1.00470	0.502348	−	0.864666i	$-0.332470\pi$
$883$	29.8548	1.00470	0.502348	+	0.864666i	$0.332470\pi$
$884$	6.98416	0.234903
$885$	−18.7270	−0.629500
$886$	49.2582	1.65486
$887$	19.2283	0.645624	0.322812	−	0.946463i	$-0.395372\pi$
$887$	19.2283	0.645624	0.322812	+	0.946463i	$0.395372\pi$
$888$	−11.6966	−0.392511
$889$	−2.14276	−0.0718658
$890$	−28.1247	−0.942742
$891$	−6.33646	−0.212279
$892$	−1.16685	−0.0390691
$893$	−21.1800	−0.708761
$894$	13.1012	0.438168
$895$	−51.0280	−1.70568
$896$	12.4771	0.416830
$897$	17.7833	0.593768
$898$	−27.8312	−0.928740
$899$	53.1907	1.77401
$900$	1.05120	0.0350399
$901$	−44.6000	−1.48584
$902$	91.4292	3.04426
$903$	6.37147	0.212029
$904$	−29.0101	−0.964862
$905$	2.91613	0.0969356
$906$	−5.26042	−0.174766
$907$	−9.79299	−0.325171	−0.162585	−	0.986694i	$-0.551983\pi$
$907$	−9.79299	−0.325171	−0.162585	+	0.986694i	$0.551983\pi$
$908$	−2.94008	−0.0975699
$909$	5.54825	0.184024
$910$	27.7390	0.919538
$911$	−56.4327	−1.86970	−0.934850	−	0.355044i	$-0.884466\pi$
$911$	−56.4327	−1.86970	−0.934850	+	0.355044i	$0.884466\pi$
$912$	21.5146	0.712421
$913$	−55.9294	−1.85099
$914$	−28.5206	−0.943377
$915$	43.8744	1.45044
$916$	−4.63473	−0.153136
$917$	−13.2924	−0.438955
$918$	11.5814	0.382244
$919$	1.23969	0.0408936	0.0204468	−	0.999791i	$-0.493491\pi$
$919$	1.23969	0.0408936	0.0204468	+	0.999791i	$0.493491\pi$
$920$	−29.5040	−0.972720
$921$	17.2387	0.568034
$922$	43.5446	1.43406
$923$	−55.0991	−1.81361
$924$	−1.01241	−0.0333059
$925$	28.4549	0.935592
$926$	51.6865	1.69852
$927$	13.7325	0.451035
$928$	5.60853	0.184109
$929$	50.7345	1.66455	0.832273	−	0.554366i	$-0.187039\pi$
$929$	50.7345	1.66455	0.832273	+	0.554366i	$0.187039\pi$
$930$	42.7663	1.40236
$931$	5.01037	0.164208
$932$	−0.809877	−0.0265284
$933$	25.9794	0.850527
$934$	47.3481	1.54928
$935$	−169.920	−5.55697
$936$	15.0010	0.490324
$937$	18.1600	0.593260	0.296630	−	0.954992i	$-0.404137\pi$
$937$	18.1600	0.593260	0.296630	+	0.954992i	$0.404137\pi$
$938$	15.2209	0.496979
$939$	27.7369	0.905160
$940$	−2.29829	−0.0749620
$941$	−2.14825	−0.0700310	−0.0350155	−	0.999387i	$-0.511148\pi$
$941$	−2.14825	−0.0700310	−0.0350155	+	0.999387i	$0.511148\pi$
$942$	−20.8700	−0.679981
$943$	−31.4776	−1.02505
$944$	−23.6315	−0.769141
$945$	3.40283	0.110694
$946$	59.3322	1.92906
$947$	23.0412	0.748739	0.374369	−	0.927280i	$-0.377859\pi$
$947$	23.0412	0.748739	0.374369	+	0.927280i	$0.377859\pi$
$948$	2.34040	0.0760126
$949$	−46.5092	−1.50975
$950$	−48.4450	−1.57176
$951$	10.9184	0.354053
$952$	−21.3124	−0.690740
$953$	−35.5720	−1.15229	−0.576144	−	0.817348i	$-0.695443\pi$
$953$	−35.5720	−1.15229	−0.576144	+	0.817348i	$0.695443\pi$
$954$	8.31727	0.269282
$955$	10.1022	0.326898
$956$	1.33639	0.0432219
$957$	39.4117	1.27400
$958$	−35.1180	−1.13461
$959$	3.73497	0.120608
$960$	−24.7143	−0.797649
$961$	42.1334	1.35914
$962$	−35.2560	−1.13670
$963$	4.58063	0.147609
$964$	0.597130	0.0192323
$965$	−62.1594	−2.00098
$966$	4.71163	0.151594
$967$	12.1858	0.391869	0.195934	−	0.980617i	$-0.437226\pi$
$967$	12.1858	0.391869	0.195934	+	0.980617i	$0.437226\pi$
$968$	78.8359	2.53388
$969$	−39.4846	−1.26843
$970$	−53.6815	−1.72361
$971$	48.3060	1.55021	0.775106	−	0.631831i	$-0.217696\pi$
$971$	48.3060	1.55021	0.775106	+	0.631831i	$0.217696\pi$
$972$	−0.159775	−0.00512480
$973$	1.33028	0.0426469
$974$	46.2988	1.48351
$975$	−36.4939	−1.16874
$976$	55.3650	1.77219
$977$	−9.50833	−0.304198	−0.152099	−	0.988365i	$-0.548603\pi$
$977$	−9.50833	−0.304198	−0.152099	+	0.988365i	$0.548603\pi$
$978$	−23.6859	−0.757392
$979$	−35.6361	−1.13894
$980$	0.543688	0.0173675
$981$	−8.68422	−0.277266
$982$	−52.9064	−1.68831
$983$	35.7875	1.14144	0.570722	−	0.821143i	$-0.306663\pi$
$983$	35.7875	1.14144	0.570722	+	0.821143i	$0.306663\pi$
$984$	−26.5527	−0.846470
$985$	28.1296	0.896283
$986$	−72.0345	−2.29404
$987$	−4.22723	−0.134554
$988$	4.44044	0.141269
$989$	−20.4271	−0.649544
$990$	31.6877	1.00710
$991$	42.6682	1.35540	0.677700	−	0.735338i	$-0.262977\pi$
$991$	42.6682	1.35540	0.677700	+	0.735338i	$0.262977\pi$
$992$	7.71132	0.244835
$993$	−6.13152	−0.194578
$994$	−14.5983	−0.463030
$995$	38.2590	1.21289
$996$	−1.41028	−0.0446863
$997$	22.7747	0.721282	0.360641	−	0.932705i	$-0.382558\pi$
$997$	22.7747	0.721282	0.360641	+	0.932705i	$0.382558\pi$
$998$	−14.6820	−0.464749
$999$	−4.32497	−0.136836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.s.1.13	✓	50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.s.1.13	✓	50	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-1.46962 q^{2} -1.00000 q^{3} +0.159775 q^{4} +3.40283 q^{5} +1.46962 q^{6} -1.00000 q^{7} +2.70443 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.46962 q^{2} -1.00000 q^{3} +0.159775 q^{4} +3.40283 q^{5} +1.46962 q^{6} -1.00000 q^{7} +2.70443 q^{8} +1.00000 q^{9} -5.00085 q^{10} -6.33646 q^{11} -0.159775 q^{12} +5.54685 q^{13} +1.46962 q^{14} -3.40283 q^{15} -4.29402 q^{16} +7.88057 q^{17} -1.46962 q^{18} +5.01037 q^{19} +0.543688 q^{20} +1.00000 q^{21} +9.31217 q^{22} -3.20602 q^{23} -2.70443 q^{24} +6.57922 q^{25} -8.15174 q^{26} -1.00000 q^{27} -0.159775 q^{28} +6.21983 q^{29} +5.00085 q^{30} +8.55180 q^{31} +0.901719 q^{32} +6.33646 q^{33} -11.5814 q^{34} -3.40283 q^{35} +0.159775 q^{36} +4.32497 q^{37} -7.36333 q^{38} -5.54685 q^{39} +9.20269 q^{40} +9.81825 q^{41} -1.46962 q^{42} +6.37147 q^{43} -1.01241 q^{44} +3.40283 q^{45} +4.71163 q^{46} -4.22723 q^{47} +4.29402 q^{48} +1.00000 q^{49} -9.66894 q^{50} -7.88057 q^{51} +0.886250 q^{52} -5.65948 q^{53} +1.46962 q^{54} -21.5619 q^{55} -2.70443 q^{56} -5.01037 q^{57} -9.14077 q^{58} +5.50335 q^{59} -0.543688 q^{60} -12.8935 q^{61} -12.5679 q^{62} -1.00000 q^{63} +7.26286 q^{64} +18.8750 q^{65} -9.31217 q^{66} +10.3570 q^{67} +1.25912 q^{68} +3.20602 q^{69} +5.00085 q^{70} -9.93341 q^{71} +2.70443 q^{72} -8.38480 q^{73} -6.35605 q^{74} -6.57922 q^{75} +0.800534 q^{76} +6.33646 q^{77} +8.15174 q^{78} -14.6480 q^{79} -14.6118 q^{80} +1.00000 q^{81} -14.4291 q^{82} +8.82661 q^{83} +0.159775 q^{84} +26.8162 q^{85} -9.36363 q^{86} -6.21983 q^{87} -17.1365 q^{88} +5.62398 q^{89} -5.00085 q^{90} -5.54685 q^{91} -0.512244 q^{92} -8.55180 q^{93} +6.21241 q^{94} +17.0494 q^{95} -0.901719 q^{96} +10.7345 q^{97} -1.46962 q^{98} -6.33646 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9}+O(q^{10}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9	\( 50 q - q^{2} - 50 q^{3} + 53 q^{4} + 11 q^{5} + q^{6} - 50 q^{7} - 6 q^{8} + 50 q^{9} + 16 q^{10} - 31 q^{11} - 53 q^{12} + 42 q^{13} + q^{14} - 11 q^{15} + 59 q^{16} + 44 q^{17} - q^{18} + 11 q^{19} + 7 q^{20} + 50 q^{21} + 19 q^{22} - 16 q^{23} + 6 q^{24} + 71 q^{25} + q^{26} - 50 q^{27} - 53 q^{28} + 3 q^{29} - 16 q^{30} + 13 q^{31} - 23 q^{32} + 31 q^{33} + q^{34} - 11 q^{35} + 53 q^{36} + 53 q^{37} + 28 q^{38} - 42 q^{39} + 50 q^{40} + 23 q^{41} - q^{42} + 9 q^{43} - 78 q^{44} + 11 q^{45} - 8 q^{46} + 26 q^{47} - 59 q^{48} + 50 q^{49} - 38 q^{50} - 44 q^{51} + 86 q^{52} + 58 q^{53} + q^{54} + 28 q^{55} + 6 q^{56} - 11 q^{57} - 4 q^{58} + 7 q^{59} - 7 q^{60} + 51 q^{61} + 7 q^{62} - 50 q^{63} + 74 q^{64} - 14 q^{65} - 19 q^{66} + 23 q^{67} + 98 q^{68} + 16 q^{69} - 16 q^{70} - 75 q^{71} - 6 q^{72} + 34 q^{73} - 68 q^{74} - 71 q^{75} + 31 q^{76} + 31 q^{77} - q^{78} - 18 q^{79} - 21 q^{80} + 50 q^{81} + 31 q^{82} + 40 q^{83} + 53 q^{84} + 30 q^{85} - 15 q^{86} - 3 q^{87} + 70 q^{88} + 63 q^{89} + 16 q^{90} - 42 q^{91} - 38 q^{92} - 13 q^{93} + q^{94} - 77 q^{95} + 23 q^{96} + 77 q^{97} - q^{98} - 31 q^{99}+O(q^{100}) \) 50 * q - q^2 - 50 * q^3 + 53 * q^4 + 11 * q^5 + q^6 - 50 * q^7 - 6 * q^8 + 50 * q^9 + 16 * q^10 - 31 * q^11 - 53 * q^12 + 42 * q^13 + q^14 - 11 * q^15 + 59 * q^16 + 44 * q^17 - q^18 + 11 * q^19 + 7 * q^20 + 50 * q^21 + 19 * q^22 - 16 * q^23 + 6 * q^24 + 71 * q^25 + q^26 - 50 * q^27 - 53 * q^28 + 3 * q^29 - 16 * q^30 + 13 * q^31 - 23 * q^32 + 31 * q^33 + q^34 - 11 * q^35 + 53 * q^36 + 53 * q^37 + 28 * q^38 - 42 * q^39 + 50 * q^40 + 23 * q^41 - q^42 + 9 * q^43 - 78 * q^44 + 11 * q^45 - 8 * q^46 + 26 * q^47 - 59 * q^48 + 50 * q^49 - 38 * q^50 - 44 * q^51 + 86 * q^52 + 58 * q^53 + q^54 + 28 * q^55 + 6 * q^56 - 11 * q^57 - 4 * q^58 + 7 * q^59 - 7 * q^60 + 51 * q^61 + 7 * q^62 - 50 * q^63 + 74 * q^64 - 14 * q^65 - 19 * q^66 + 23 * q^67 + 98 * q^68 + 16 * q^69 - 16 * q^70 - 75 * q^71 - 6 * q^72 + 34 * q^73 - 68 * q^74 - 71 * q^75 + 31 * q^76 + 31 * q^77 - q^78 - 18 * q^79 - 21 * q^80 + 50 * q^81 + 31 * q^82 + 40 * q^83 + 53 * q^84 + 30 * q^85 - 15 * q^86 - 3 * q^87 + 70 * q^88 + 63 * q^89 + 16 * q^90 - 42 * q^91 - 38 * q^92 - 13 * q^93 + q^94 - 77 * q^95 + 23 * q^96 + 77 * q^97 - q^98 - 31 * q^99

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