LMFDB - Embedded newform 7935.2.a.bu.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.51687 q^{2} -1.00000 q^{3} +0.300900 q^{4} +1.00000 q^{5} +1.51687 q^{6} -3.34169 q^{7} +2.57732 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.51687 q^{2} -1.00000 q^{3} +0.300900 q^{4} +1.00000 q^{5} +1.51687 q^{6} -3.34169 q^{7} +2.57732 q^{8} +1.00000 q^{9} -1.51687 q^{10} +1.18548 q^{11} -0.300900 q^{12} +0.915669 q^{13} +5.06891 q^{14} -1.00000 q^{15} -4.51126 q^{16} -2.52173 q^{17} -1.51687 q^{18} -8.46827 q^{19} +0.300900 q^{20} +3.34169 q^{21} -1.79822 q^{22} -2.57732 q^{24} +1.00000 q^{25} -1.38895 q^{26} -1.00000 q^{27} -1.00552 q^{28} +7.86833 q^{29} +1.51687 q^{30} -5.67444 q^{31} +1.68837 q^{32} -1.18548 q^{33} +3.82515 q^{34} -3.34169 q^{35} +0.300900 q^{36} -5.68722 q^{37} +12.8453 q^{38} -0.915669 q^{39} +2.57732 q^{40} +10.1782 q^{41} -5.06891 q^{42} -8.92948 q^{43} +0.356711 q^{44} +1.00000 q^{45} -7.20823 q^{47} +4.51126 q^{48} +4.16687 q^{49} -1.51687 q^{50} +2.52173 q^{51} +0.275525 q^{52} -1.10303 q^{53} +1.51687 q^{54} +1.18548 q^{55} -8.61259 q^{56} +8.46827 q^{57} -11.9353 q^{58} -3.44898 q^{59} -0.300900 q^{60} -4.49161 q^{61} +8.60740 q^{62} -3.34169 q^{63} +6.46148 q^{64} +0.915669 q^{65} +1.79822 q^{66} +0.818172 q^{67} -0.758791 q^{68} +5.06891 q^{70} +7.34757 q^{71} +2.57732 q^{72} +13.6141 q^{73} +8.62678 q^{74} -1.00000 q^{75} -2.54811 q^{76} -3.96150 q^{77} +1.38895 q^{78} -15.6680 q^{79} -4.51126 q^{80} +1.00000 q^{81} -15.4391 q^{82} -6.60930 q^{83} +1.00552 q^{84} -2.52173 q^{85} +13.5449 q^{86} -7.86833 q^{87} +3.05536 q^{88} +9.17352 q^{89} -1.51687 q^{90} -3.05988 q^{91} +5.67444 q^{93} +10.9340 q^{94} -8.46827 q^{95} -1.68837 q^{96} +3.08867 q^{97} -6.32062 q^{98} +1.18548 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * 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 $

$2$	−1.51687	−1.07259	−0.536295	−	0.844030i	$-0.680177\pi$
$2$	−1.51687	−1.07259	−0.536295	+	0.844030i	$0.680177\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.300900	0.150450
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.51687	0.619260
$7$	−3.34169	−1.26304	−0.631520	−	0.775360i	$-0.717568\pi$
$7$	−3.34169	−1.26304	−0.631520	+	0.775360i	$0.717568\pi$
$8$	2.57732	0.911219
$9$	1.00000	0.333333
$10$	−1.51687	−0.479677
$11$	1.18548	0.357435	0.178718	−	0.983900i	$-0.442805\pi$
$11$	1.18548	0.357435	0.178718	+	0.983900i	$0.442805\pi$
$12$	−0.300900	−0.0868625
$13$	0.915669	0.253961	0.126980	−	0.991905i	$-0.459471\pi$
$13$	0.915669	0.253961	0.126980	+	0.991905i	$0.459471\pi$
$14$	5.06891	1.35472
$15$	−1.00000	−0.258199
$16$	−4.51126	−1.12781
$17$	−2.52173	−0.611610	−0.305805	−	0.952094i	$-0.598926\pi$
$17$	−2.52173	−0.611610	−0.305805	+	0.952094i	$0.598926\pi$
$18$	−1.51687	−0.357530
$19$	−8.46827	−1.94276	−0.971378	−	0.237541i	$-0.923659\pi$
$19$	−8.46827	−1.94276	−0.971378	+	0.237541i	$0.923659\pi$
$20$	0.300900	0.0672834
$21$	3.34169	0.729216
$22$	−1.79822	−0.383382
$23$	0	0
$23$	0	0
$24$	−2.57732	−0.526093
$25$	1.00000	0.200000
$26$	−1.38895	−0.272396
$27$	−1.00000	−0.192450
$28$	−1.00552	−0.190025
$29$	7.86833	1.46111	0.730556	−	0.682852i	$-0.239261\pi$
$29$	7.86833	1.46111	0.730556	+	0.682852i	$0.239261\pi$
$30$	1.51687	0.276942
$31$	−5.67444	−1.01916	−0.509580	−	0.860423i	$-0.670199\pi$
$31$	−5.67444	−1.01916	−0.509580	+	0.860423i	$0.670199\pi$
$32$	1.68837	0.298465
$33$	−1.18548	−0.206365
$34$	3.82515	0.656008
$35$	−3.34169	−0.564848
$36$	0.300900	0.0501501
$37$	−5.68722	−0.934973	−0.467487	−	0.884000i	$-0.654840\pi$
$37$	−5.68722	−0.934973	−0.467487	+	0.884000i	$0.654840\pi$
$38$	12.8453	2.08378
$39$	−0.915669	−0.146624
$40$	2.57732	0.407510
$41$	10.1782	1.58957	0.794787	−	0.606888i	$-0.207582\pi$
$41$	10.1782	1.58957	0.794787	+	0.606888i	$0.207582\pi$
$42$	−5.06891	−0.782150
$43$	−8.92948	−1.36173	−0.680866	−	0.732408i	$-0.738396\pi$
$43$	−8.92948	−1.36173	−0.680866	+	0.732408i	$0.738396\pi$
$44$	0.356711	0.0537762
$45$	1.00000	0.149071
$46$	0	0
$47$	−7.20823	−1.05143	−0.525714	−	0.850661i	$-0.676202\pi$
$47$	−7.20823	−1.05143	−0.525714	+	0.850661i	$0.676202\pi$
$48$	4.51126	0.651144
$49$	4.16687	0.595268
$50$	−1.51687	−0.214518
$51$	2.52173	0.353113
$52$	0.275525	0.0382085
$53$	−1.10303	−0.151513	−0.0757567	−	0.997126i	$-0.524137\pi$
$53$	−1.10303	−0.151513	−0.0757567	+	0.997126i	$0.524137\pi$
$54$	1.51687	0.206420
$55$	1.18548	0.159850
$56$	−8.61259	−1.15091
$57$	8.46827	1.12165
$58$	−11.9353	−1.56718
$59$	−3.44898	−0.449018	−0.224509	−	0.974472i	$-0.572078\pi$
$59$	−3.44898	−0.449018	−0.224509	+	0.974472i	$0.572078\pi$
$60$	−0.300900	−0.0388461
$61$	−4.49161	−0.575092	−0.287546	−	0.957767i	$-0.592839\pi$
$61$	−4.49161	−0.575092	−0.287546	+	0.957767i	$0.592839\pi$
$62$	8.60740	1.09314
$63$	−3.34169	−0.421013
$64$	6.46148	0.807685
$65$	0.915669	0.113575
$66$	1.79822	0.221346
$67$	0.818172	0.0999556	0.0499778	−	0.998750i	$-0.484085\pi$
$67$	0.818172	0.0999556	0.0499778	+	0.998750i	$0.484085\pi$
$68$	−0.758791	−0.0920169
$69$	0	0
$70$	5.06891	0.605851
$71$	7.34757	0.871996	0.435998	−	0.899948i	$-0.356395\pi$
$71$	7.34757	0.871996	0.435998	+	0.899948i	$0.356395\pi$
$72$	2.57732	0.303740
$73$	13.6141	1.59341	0.796703	−	0.604370i	$-0.206575\pi$
$73$	13.6141	1.59341	0.796703	+	0.604370i	$0.206575\pi$
$74$	8.62678	1.00284
$75$	−1.00000	−0.115470
$76$	−2.54811	−0.292288
$77$	−3.96150	−0.451455
$78$	1.38895	0.157268
$79$	−15.6680	−1.76279	−0.881394	−	0.472382i	$-0.843394\pi$
$79$	−15.6680	−1.76279	−0.881394	+	0.472382i	$0.843394\pi$
$80$	−4.51126	−0.504374
$81$	1.00000	0.111111
$82$	−15.4391	−1.70496
$83$	−6.60930	−0.725465	−0.362732	−	0.931893i	$-0.618156\pi$
$83$	−6.60930	−0.725465	−0.362732	+	0.931893i	$0.618156\pi$
$84$	1.00552	0.109711
$85$	−2.52173	−0.273521
$86$	13.5449	1.46058
$87$	−7.86833	−0.843574
$88$	3.05536	0.325702
$89$	9.17352	0.972391	0.486195	−	0.873850i	$-0.338384\pi$
$89$	9.17352	0.972391	0.486195	+	0.873850i	$0.338384\pi$
$90$	−1.51687	−0.159892
$91$	−3.05988	−0.320763
$92$	0	0
$93$	5.67444	0.588412
$94$	10.9340	1.12775
$95$	−8.46827	−0.868827
$96$	−1.68837	−0.172319
$97$	3.08867	0.313607	0.156804	−	0.987630i	$-0.449881\pi$
$97$	3.08867	0.313607	0.156804	+	0.987630i	$0.449881\pi$
$98$	−6.32062	−0.638479
$99$	1.18548	0.119145
$100$	0.300900	0.0300900
$101$	10.0879	1.00379	0.501894	−	0.864929i	$-0.332637\pi$
$101$	10.0879	1.00379	0.501894	+	0.864929i	$0.332637\pi$
$102$	−3.82515	−0.378746
$103$	3.01573	0.297149	0.148575	−	0.988901i	$-0.452531\pi$
$103$	3.01573	0.297149	0.148575	+	0.988901i	$0.452531\pi$
$104$	2.35997	0.231414
$105$	3.34169	0.326115
$106$	1.67316	0.162512
$107$	1.71816	0.166101	0.0830503	−	0.996545i	$-0.473534\pi$
$107$	1.71816	0.166101	0.0830503	+	0.996545i	$0.473534\pi$
$108$	−0.300900	−0.0289542
$109$	−7.24743	−0.694178	−0.347089	−	0.937832i	$-0.612830\pi$
$109$	−7.24743	−0.694178	−0.347089	+	0.937832i	$0.612830\pi$
$110$	−1.79822	−0.171454
$111$	5.68722	0.539807
$112$	15.0752	1.42447
$113$	15.8405	1.49015	0.745073	−	0.666983i	$-0.232415\pi$
$113$	15.8405	1.49015	0.745073	+	0.666983i	$0.232415\pi$
$114$	−12.8453	−1.20307
$115$	0	0
$116$	2.36758	0.219825
$117$	0.915669	0.0846537
$118$	5.23166	0.481613
$119$	8.42685	0.772488
$120$	−2.57732	−0.235276
$121$	−9.59464	−0.872240
$122$	6.81320	0.616838
$123$	−10.1782	−0.917741
$124$	−1.70744	−0.153333
$125$	1.00000	0.0894427
$126$	5.06891	0.451575
$127$	−7.50750	−0.666183	−0.333091	−	0.942895i	$-0.608092\pi$
$127$	−7.50750	−0.666183	−0.333091	+	0.942895i	$0.608092\pi$
$128$	−13.1780	−1.16478
$129$	8.92948	0.786197
$130$	−1.38895	−0.121819
$131$	−18.3185	−1.60050	−0.800248	−	0.599669i	$-0.795299\pi$
$131$	−18.3185	−1.60050	−0.800248	+	0.599669i	$0.795299\pi$
$132$	−0.356711	−0.0310477
$133$	28.2983	2.45378
$134$	−1.24106	−0.107211
$135$	−1.00000	−0.0860663
$136$	−6.49931	−0.557311
$137$	−13.4737	−1.15113	−0.575567	−	0.817754i	$-0.695219\pi$
$137$	−13.4737	−1.15113	−0.575567	+	0.817754i	$0.695219\pi$
$138$	0	0
$139$	17.2453	1.46272	0.731362	−	0.681990i	$-0.238885\pi$
$139$	17.2453	1.46272	0.731362	+	0.681990i	$0.238885\pi$
$140$	−1.00552	−0.0849815
$141$	7.20823	0.607042
$142$	−11.1453	−0.935295
$143$	1.08551	0.0907747
$144$	−4.51126	−0.375938
$145$	7.86833	0.653430
$146$	−20.6508	−1.70907
$147$	−4.16687	−0.343678
$148$	−1.71129	−0.140667
$149$	4.72490	0.387079	0.193539	−	0.981092i	$-0.438003\pi$
$149$	4.72490	0.387079	0.193539	+	0.981092i	$0.438003\pi$
$150$	1.51687	0.123852
$151$	4.22106	0.343505	0.171753	−	0.985140i	$-0.445057\pi$
$151$	4.22106	0.343505	0.171753	+	0.985140i	$0.445057\pi$
$152$	−21.8254	−1.77028
$153$	−2.52173	−0.203870
$154$	6.00909	0.484226
$155$	−5.67444	−0.455782
$156$	−0.275525	−0.0220597
$157$	−19.1706	−1.52998	−0.764991	−	0.644041i	$-0.777257\pi$
$157$	−19.1706	−1.52998	−0.764991	+	0.644041i	$0.777257\pi$
$158$	23.7664	1.89075
$159$	1.10303	0.0874763
$160$	1.68837	0.133477
$161$	0	0
$162$	−1.51687	−0.119177
$163$	−18.2402	−1.42868	−0.714341	−	0.699797i	$-0.753274\pi$
$163$	−18.2402	−1.42868	−0.714341	+	0.699797i	$0.753274\pi$
$164$	3.06264	0.239152
$165$	−1.18548	−0.0922894
$166$	10.0255	0.778126
$167$	3.94892	0.305576	0.152788	−	0.988259i	$-0.451175\pi$
$167$	3.94892	0.305576	0.152788	+	0.988259i	$0.451175\pi$
$168$	8.61259	0.664475
$169$	−12.1615	−0.935504
$170$	3.82515	0.293375
$171$	−8.46827	−0.647585
$172$	−2.68688	−0.204873
$173$	4.41696	0.335815	0.167908	−	0.985803i	$-0.446299\pi$
$173$	4.41696	0.335815	0.167908	+	0.985803i	$0.446299\pi$
$174$	11.9353	0.904809
$175$	−3.34169	−0.252608
$176$	−5.34801	−0.403121
$177$	3.44898	0.259241
$178$	−13.9151	−1.04298
$179$	−6.29312	−0.470370	−0.235185	−	0.971951i	$-0.575570\pi$
$179$	−6.29312	−0.470370	−0.235185	+	0.971951i	$0.575570\pi$
$180$	0.300900	0.0224278
$181$	−12.9253	−0.960728	−0.480364	−	0.877069i	$-0.659495\pi$
$181$	−12.9253	−0.960728	−0.480364	+	0.877069i	$0.659495\pi$
$182$	4.64145	0.344047
$183$	4.49161	0.332029
$184$	0	0
$185$	−5.68722	−0.418133
$186$	−8.60740	−0.631125
$187$	−2.98946	−0.218611
$188$	−2.16896	−0.158188
$189$	3.34169	0.243072
$190$	12.8453	0.931895
$191$	26.5082	1.91806	0.959031	−	0.283300i	$-0.0914292\pi$
$191$	26.5082	1.91806	0.959031	+	0.283300i	$0.0914292\pi$
$192$	−6.46148	−0.466317
$193$	7.46115	0.537065	0.268532	−	0.963271i	$-0.413461\pi$
$193$	7.46115	0.537065	0.268532	+	0.963271i	$0.413461\pi$
$194$	−4.68512	−0.336372
$195$	−0.915669	−0.0655724
$196$	1.25381	0.0895582
$197$	−7.88559	−0.561825	−0.280913	−	0.959733i	$-0.590637\pi$
$197$	−7.88559	−0.561825	−0.280913	+	0.959733i	$0.590637\pi$
$198$	−1.79822	−0.127794
$199$	17.7491	1.25820	0.629100	−	0.777324i	$-0.283424\pi$
$199$	17.7491	1.25820	0.629100	+	0.777324i	$0.283424\pi$
$200$	2.57732	0.182244
$201$	−0.818172	−0.0577094
$202$	−15.3021	−1.07665
$203$	−26.2935	−1.84544
$204$	0.758791	0.0531260
$205$	10.1782	0.710879
$206$	−4.57448	−0.318719
$207$	0	0
$208$	−4.13082	−0.286421
$209$	−10.0390	−0.694410
$210$	−5.06891	−0.349788
$211$	1.12533	0.0774707	0.0387353	−	0.999250i	$-0.487667\pi$
$211$	1.12533	0.0774707	0.0387353	+	0.999250i	$0.487667\pi$
$212$	−0.331903	−0.0227952
$213$	−7.34757	−0.503447
$214$	−2.60622	−0.178158
$215$	−8.92948	−0.608985
$216$	−2.57732	−0.175364
$217$	18.9622	1.28724
$218$	10.9934	0.744569
$219$	−13.6141	−0.919954
$220$	0.356711	0.0240495
$221$	−2.30907	−0.155325
$222$	−8.62678	−0.578992
$223$	−4.70094	−0.314798	−0.157399	−	0.987535i	$-0.550311\pi$
$223$	−4.70094	−0.314798	−0.157399	+	0.987535i	$0.550311\pi$
$224$	−5.64201	−0.376972
$225$	1.00000	0.0666667
$226$	−24.0280	−1.59832
$227$	−11.6840	−0.775497	−0.387748	−	0.921765i	$-0.626747\pi$
$227$	−11.6840	−0.775497	−0.387748	+	0.921765i	$0.626747\pi$
$228$	2.54811	0.168753
$229$	19.7306	1.30384	0.651918	−	0.758289i	$-0.273965\pi$
$229$	19.7306	1.30384	0.651918	+	0.758289i	$0.273965\pi$
$230$	0	0
$231$	3.96150	0.260648
$232$	20.2792	1.33139
$233$	3.50451	0.229588	0.114794	−	0.993389i	$-0.463379\pi$
$233$	3.50451	0.229588	0.114794	+	0.993389i	$0.463379\pi$
$234$	−1.38895	−0.0907987
$235$	−7.20823	−0.470213
$236$	−1.03780	−0.0675549
$237$	15.6680	1.01775
$238$	−12.7824	−0.828563
$239$	−5.64390	−0.365074	−0.182537	−	0.983199i	$-0.558431\pi$
$239$	−5.64390	−0.365074	−0.182537	+	0.983199i	$0.558431\pi$
$240$	4.51126	0.291201
$241$	−9.80570	−0.631641	−0.315820	−	0.948819i	$-0.602280\pi$
$241$	−9.80570	−0.631641	−0.315820	+	0.948819i	$0.602280\pi$
$242$	14.5538	0.935556
$243$	−1.00000	−0.0641500
$244$	−1.35153	−0.0865227
$245$	4.16687	0.266212
$246$	15.4391	0.984360
$247$	−7.75414	−0.493384
$248$	−14.6248	−0.928677
$249$	6.60930	0.418847
$250$	−1.51687	−0.0959354
$251$	15.8115	0.998013	0.499007	−	0.866598i	$-0.333698\pi$
$251$	15.8115	0.998013	0.499007	+	0.866598i	$0.333698\pi$
$252$	−1.00552	−0.0633415
$253$	0	0
$254$	11.3879	0.714541
$255$	2.52173	0.157917
$256$	7.06634	0.441647
$257$	−23.3700	−1.45778	−0.728891	−	0.684630i	$-0.759964\pi$
$257$	−23.3700	−1.45778	−0.728891	+	0.684630i	$0.759964\pi$
$258$	−13.5449	−0.843267
$259$	19.0049	1.18091
$260$	0.275525	0.0170874
$261$	7.86833	0.487038
$262$	27.7869	1.71668
$263$	−19.2160	−1.18491	−0.592455	−	0.805604i	$-0.701841\pi$
$263$	−19.2160	−1.18491	−0.592455	+	0.805604i	$0.701841\pi$
$264$	−3.05536	−0.188044
$265$	−1.10303	−0.0677589
$266$	−42.9249	−2.63190
$267$	−9.17352	−0.561410
$268$	0.246188	0.0150383
$269$	−24.7222	−1.50734	−0.753669	−	0.657254i	$-0.771718\pi$
$269$	−24.7222	−1.50734	−0.753669	+	0.657254i	$0.771718\pi$
$270$	1.51687	0.0923139
$271$	−13.6555	−0.829511	−0.414756	−	0.909933i	$-0.636133\pi$
$271$	−13.6555	−0.829511	−0.414756	+	0.909933i	$0.636133\pi$
$272$	11.3762	0.689783
$273$	3.05988	0.185192
$274$	20.4379	1.23470
$275$	1.18548	0.0714871
$276$	0	0
$277$	5.90029	0.354514	0.177257	−	0.984165i	$-0.443278\pi$
$277$	5.90029	0.354514	0.177257	+	0.984165i	$0.443278\pi$
$278$	−26.1589	−1.56890
$279$	−5.67444	−0.339720
$280$	−8.61259	−0.514700
$281$	18.6057	1.10992	0.554961	−	0.831876i	$-0.312733\pi$
$281$	18.6057	1.10992	0.554961	+	0.831876i	$0.312733\pi$
$282$	−10.9340	−0.651108
$283$	11.9011	0.707449	0.353725	−	0.935350i	$-0.384915\pi$
$283$	11.9011	0.707449	0.353725	+	0.935350i	$0.384915\pi$
$284$	2.21089	0.131192
$285$	8.46827	0.501617
$286$	−1.64658	−0.0973640
$287$	−34.0125	−2.00769
$288$	1.68837	0.0994882
$289$	−10.6409	−0.625933
$290$	−11.9353	−0.700862
$291$	−3.08867	−0.181061
$292$	4.09648	0.239728
$293$	6.70436	0.391673	0.195837	−	0.980637i	$-0.437258\pi$
$293$	6.70436	0.391673	0.195837	+	0.980637i	$0.437258\pi$
$294$	6.32062	0.368626
$295$	−3.44898	−0.200807
$296$	−14.6578	−0.851965
$297$	−1.18548	−0.0687885
$298$	−7.16707	−0.415177
$299$	0	0
$300$	−0.300900	−0.0173725
$301$	29.8395	1.71992
$302$	−6.40281	−0.368440
$303$	−10.0879	−0.579537
$304$	38.2026	2.19107
$305$	−4.49161	−0.257189
$306$	3.82515	0.218669
$307$	−6.77351	−0.386585	−0.193292	−	0.981141i	$-0.561917\pi$
$307$	−6.77351	−0.386585	−0.193292	+	0.981141i	$0.561917\pi$
$308$	−1.19202	−0.0679215
$309$	−3.01573	−0.171559
$310$	8.60740	0.488867
$311$	23.7189	1.34497	0.672487	−	0.740109i	$-0.265226\pi$
$311$	23.7189	1.34497	0.672487	+	0.740109i	$0.265226\pi$
$312$	−2.35997	−0.133607
$313$	−5.87032	−0.331810	−0.165905	−	0.986142i	$-0.553055\pi$
$313$	−5.87032	−0.331810	−0.165905	+	0.986142i	$0.553055\pi$
$314$	29.0794	1.64104
$315$	−3.34169	−0.188283
$316$	−4.71451	−0.265212
$317$	1.26758	0.0711944	0.0355972	−	0.999366i	$-0.488667\pi$
$317$	1.26758	0.0711944	0.0355972	+	0.999366i	$0.488667\pi$
$318$	−1.67316	−0.0938262
$319$	9.32775	0.522254
$320$	6.46148	0.361208
$321$	−1.71816	−0.0958982
$322$	0	0
$323$	21.3547	1.18821
$324$	0.300900	0.0167167
$325$	0.915669	0.0507922
$326$	27.6680	1.53239
$327$	7.24743	0.400784
$328$	26.2326	1.44845
$329$	24.0877	1.32800
$330$	1.79822	0.0989888
$331$	−0.0750196	−0.00412345	−0.00206172	−	0.999998i	$-0.500656\pi$
$331$	−0.0750196	−0.00412345	−0.00206172	+	0.999998i	$0.500656\pi$
$332$	−1.98874	−0.109146
$333$	−5.68722	−0.311658
$334$	−5.99000	−0.327758
$335$	0.818172	0.0447015
$336$	−15.0752	−0.822421
$337$	−5.29621	−0.288503	−0.144252	−	0.989541i	$-0.546077\pi$
$337$	−5.29621	−0.288503	−0.144252	+	0.989541i	$0.546077\pi$
$338$	18.4475	1.00341
$339$	−15.8405	−0.860336
$340$	−0.758791	−0.0411512
$341$	−6.72693	−0.364284
$342$	12.8453	0.694594
$343$	9.46742	0.511193
$344$	−23.0141	−1.24084
$345$	0	0
$346$	−6.69996	−0.360192
$347$	10.3576	0.556027	0.278013	−	0.960577i	$-0.410324\pi$
$347$	10.3576	0.556027	0.278013	+	0.960577i	$0.410324\pi$
$348$	−2.36758	−0.126916
$349$	−9.36736	−0.501424	−0.250712	−	0.968062i	$-0.580665\pi$
$349$	−9.36736	−0.501424	−0.250712	+	0.968062i	$0.580665\pi$
$350$	5.06891	0.270945
$351$	−0.915669	−0.0488748
$352$	2.00153	0.106682
$353$	0.463085	0.0246475	0.0123238	−	0.999924i	$-0.496077\pi$
$353$	0.463085	0.0246475	0.0123238	+	0.999924i	$0.496077\pi$
$354$	−5.23166	−0.278059
$355$	7.34757	0.389969
$356$	2.76032	0.146296
$357$	−8.42685	−0.445996
$358$	9.54586	0.504514
$359$	30.2683	1.59750	0.798749	−	0.601665i	$-0.205496\pi$
$359$	30.2683	1.59750	0.798749	+	0.601665i	$0.205496\pi$
$360$	2.57732	0.135837
$361$	52.7117	2.77430
$362$	19.6060	1.03047
$363$	9.59464	0.503588
$364$	−0.920719	−0.0482588
$365$	13.6141	0.712593
$366$	−6.81320	−0.356132
$367$	7.18380	0.374991	0.187496	−	0.982265i	$-0.439963\pi$
$367$	7.18380	0.374991	0.187496	+	0.982265i	$0.439963\pi$
$368$	0	0
$369$	10.1782	0.529858
$370$	8.62678	0.448485
$371$	3.68600	0.191367
$372$	1.70744	0.0885267
$373$	0.741630	0.0384001	0.0192001	−	0.999816i	$-0.493888\pi$
$373$	0.741630	0.0384001	0.0192001	+	0.999816i	$0.493888\pi$
$374$	4.53463	0.234480
$375$	−1.00000	−0.0516398
$376$	−18.5779	−0.958081
$377$	7.20479	0.371066
$378$	−5.06891	−0.260717
$379$	25.9624	1.33360	0.666800	−	0.745237i	$-0.267664\pi$
$379$	25.9624	1.33360	0.666800	+	0.745237i	$0.267664\pi$
$380$	−2.54811	−0.130715
$381$	7.50750	0.384621
$382$	−40.2095	−2.05730
$383$	−2.26902	−0.115942	−0.0579708	−	0.998318i	$-0.518463\pi$
$383$	−2.26902	−0.115942	−0.0579708	+	0.998318i	$0.518463\pi$
$384$	13.1780	0.672486
$385$	−3.96150	−0.201897
$386$	−11.3176	−0.576051
$387$	−8.92948	−0.453911
$388$	0.929383	0.0471823
$389$	−0.331625	−0.0168140	−0.00840702	−	0.999965i	$-0.502676\pi$
$389$	−0.331625	−0.0168140	−0.00840702	+	0.999965i	$0.502676\pi$
$390$	1.38895	0.0703324
$391$	0	0
$392$	10.7394	0.542419
$393$	18.3185	0.924047
$394$	11.9614	0.602608
$395$	−15.6680	−0.788343
$396$	0.356711	0.0179254
$397$	−33.6099	−1.68683	−0.843417	−	0.537260i	$-0.819459\pi$
$397$	−33.6099	−1.68683	−0.843417	+	0.537260i	$0.819459\pi$
$398$	−26.9231	−1.34953
$399$	−28.2983	−1.41669
$400$	−4.51126	−0.225563
$401$	2.75774	0.137715	0.0688576	−	0.997626i	$-0.478065\pi$
$401$	2.75774	0.137715	0.0688576	+	0.997626i	$0.478065\pi$
$402$	1.24106	0.0618985
$403$	−5.19591	−0.258827
$404$	3.03546	0.151020
$405$	1.00000	0.0496904
$406$	39.8839	1.97940
$407$	−6.74208	−0.334193
$408$	6.49931	0.321764
$409$	24.9515	1.23377	0.616886	−	0.787052i	$-0.288394\pi$
$409$	24.9515	1.23377	0.616886	+	0.787052i	$0.288394\pi$
$410$	−15.4391	−0.762482
$411$	13.4737	0.664608
$412$	0.907436	0.0447062
$413$	11.5254	0.567128
$414$	0	0
$415$	−6.60930	−0.324438
$416$	1.54599	0.0757983
$417$	−17.2453	−0.844504
$418$	15.2278	0.744817
$419$	26.2127	1.28058	0.640288	−	0.768135i	$-0.278815\pi$
$419$	26.2127	1.28058	0.640288	+	0.768135i	$0.278815\pi$
$420$	1.00552	0.0490641
$421$	−25.2032	−1.22833	−0.614164	−	0.789178i	$-0.710507\pi$
$421$	−25.2032	−1.22833	−0.614164	+	0.789178i	$0.710507\pi$
$422$	−1.70698	−0.0830943
$423$	−7.20823	−0.350476
$424$	−2.84287	−0.138062
$425$	−2.52173	−0.122322
$426$	11.1453	0.539993
$427$	15.0096	0.726364
$428$	0.516994	0.0249899
$429$	−1.08551	−0.0524088
$430$	13.5449	0.653192
$431$	−10.6296	−0.512010	−0.256005	−	0.966675i	$-0.582406\pi$
$431$	−10.6296	−0.512010	−0.256005	+	0.966675i	$0.582406\pi$
$432$	4.51126	0.217048
$433$	−4.76299	−0.228895	−0.114447	−	0.993429i	$-0.536510\pi$
$433$	−4.76299	−0.228895	−0.114447	+	0.993429i	$0.536510\pi$
$434$	−28.7632	−1.38068
$435$	−7.86833	−0.377258
$436$	−2.18076	−0.104439
$437$	0	0
$438$	20.6508	0.986734
$439$	24.9611	1.19133	0.595665	−	0.803233i	$-0.296889\pi$
$439$	24.9611	1.19133	0.595665	+	0.803233i	$0.296889\pi$
$440$	3.05536	0.145658
$441$	4.16687	0.198423
$442$	3.50257	0.166600
$443$	−11.1218	−0.528413	−0.264206	−	0.964466i	$-0.585110\pi$
$443$	−11.1218	−0.528413	−0.264206	+	0.964466i	$0.585110\pi$
$444$	1.71129	0.0812141
$445$	9.17352	0.434866
$446$	7.13073	0.337650
$447$	−4.72490	−0.223480
$448$	−21.5922	−1.02014
$449$	19.7792	0.933436	0.466718	−	0.884406i	$-0.345436\pi$
$449$	19.7792	0.933436	0.466718	+	0.884406i	$0.345436\pi$
$450$	−1.51687	−0.0715060
$451$	12.0661	0.568170
$452$	4.76640	0.224193
$453$	−4.22106	−0.198323
$454$	17.7232	0.831791
$455$	−3.05988	−0.143449
$456$	21.8254	1.02207
$457$	−4.78689	−0.223921	−0.111961	−	0.993713i	$-0.535713\pi$
$457$	−4.78689	−0.223921	−0.111961	+	0.993713i	$0.535713\pi$
$458$	−29.9288	−1.39848
$459$	2.52173	0.117704
$460$	0	0
$461$	−15.4721	−0.720607	−0.360303	−	0.932835i	$-0.617327\pi$
$461$	−15.4721	−0.720607	−0.360303	+	0.932835i	$0.617327\pi$
$462$	−6.00909	−0.279568
$463$	36.9213	1.71588	0.857940	−	0.513751i	$-0.171744\pi$
$463$	36.9213	1.71588	0.857940	+	0.513751i	$0.171744\pi$
$464$	−35.4961	−1.64786
$465$	5.67444	0.263146
$466$	−5.31590	−0.246254
$467$	−12.8660	−0.595369	−0.297685	−	0.954664i	$-0.596214\pi$
$467$	−12.8660	−0.595369	−0.297685	+	0.954664i	$0.596214\pi$
$468$	0.275525	0.0127362
$469$	−2.73407	−0.126248
$470$	10.9340	0.504346
$471$	19.1706	0.883336
$472$	−8.88910	−0.409154
$473$	−10.5857	−0.486731
$474$	−23.7664	−1.09162
$475$	−8.46827	−0.388551
$476$	2.53564	0.116221
$477$	−1.10303	−0.0505045
$478$	8.56107	0.391574
$479$	9.74079	0.445068	0.222534	−	0.974925i	$-0.428567\pi$
$479$	9.74079	0.445068	0.222534	+	0.974925i	$0.428567\pi$
$480$	−1.68837	−0.0770632
$481$	−5.20761	−0.237447
$482$	14.8740	0.677492
$483$	0	0
$484$	−2.88703	−0.131229
$485$	3.08867	0.140249
$486$	1.51687	0.0688067
$487$	39.8060	1.80378	0.901892	−	0.431962i	$-0.142179\pi$
$487$	39.8060	1.80378	0.901892	+	0.431962i	$0.142179\pi$
$488$	−11.5763	−0.524035
$489$	18.2402	0.824850
$490$	−6.32062	−0.285536
$491$	15.6081	0.704384	0.352192	−	0.935928i	$-0.385436\pi$
$491$	15.6081	0.704384	0.352192	+	0.935928i	$0.385436\pi$
$492$	−3.06264	−0.138074
$493$	−19.8418	−0.893632
$494$	11.7620	0.529199
$495$	1.18548	0.0532833
$496$	25.5989	1.14942
$497$	−24.5533	−1.10137
$498$	−10.0255	−0.449251
$499$	−34.4712	−1.54314	−0.771571	−	0.636143i	$-0.780529\pi$
$499$	−34.4712	−1.54314	−0.771571	+	0.636143i	$0.780529\pi$
$500$	0.300900	0.0134567
$501$	−3.94892	−0.176425
$502$	−23.9840	−1.07046
$503$	−32.9419	−1.46881	−0.734404	−	0.678713i	$-0.762538\pi$
$503$	−32.9419	−1.46881	−0.734404	+	0.678713i	$0.762538\pi$
$504$	−8.61259	−0.383635
$505$	10.0879	0.448907
$506$	0	0
$507$	12.1615	0.540113
$508$	−2.25901	−0.100227
$509$	19.7488	0.875352	0.437676	−	0.899133i	$-0.355802\pi$
$509$	19.7488	0.875352	0.437676	+	0.899133i	$0.355802\pi$
$510$	−3.82515	−0.169380
$511$	−45.4940	−2.01254
$512$	15.6372	0.691074
$513$	8.46827	0.373883
$514$	35.4493	1.56360
$515$	3.01573	0.132889
$516$	2.68688	0.118283
$517$	−8.54521	−0.375818
$518$	−28.8280	−1.26663
$519$	−4.41696	−0.193883
$520$	2.35997	0.103492
$521$	5.67485	0.248620	0.124310	−	0.992243i	$-0.460328\pi$
$521$	5.67485	0.248620	0.124310	+	0.992243i	$0.460328\pi$
$522$	−11.9353	−0.522392
$523$	24.2711	1.06130	0.530651	−	0.847590i	$-0.321947\pi$
$523$	24.2711	1.06130	0.530651	+	0.847590i	$0.321947\pi$
$524$	−5.51205	−0.240795
$525$	3.34169	0.145843
$526$	29.1482	1.27092
$527$	14.3094	0.623329
$528$	5.34801	0.232742
$529$	0	0
$530$	1.67316	0.0726775
$531$	−3.44898	−0.149673
$532$	8.51498	0.369171
$533$	9.31990	0.403690
$534$	13.9151	0.602163
$535$	1.71816	0.0742824
$536$	2.10869	0.0910814
$537$	6.29312	0.271568
$538$	37.5004	1.61676
$539$	4.93974	0.212770
$540$	−0.300900	−0.0129487
$541$	−24.7491	−1.06405	−0.532023	−	0.846730i	$-0.678568\pi$
$541$	−24.7491	−1.06405	−0.532023	+	0.846730i	$0.678568\pi$
$542$	20.7136	0.889726
$543$	12.9253	0.554677
$544$	−4.25762	−0.182544
$545$	−7.24743	−0.310446
$546$	−4.64145	−0.198636
$547$	10.0536	0.429860	0.214930	−	0.976629i	$-0.431048\pi$
$547$	10.0536	0.429860	0.214930	+	0.976629i	$0.431048\pi$
$548$	−4.05424	−0.173188
$549$	−4.49161	−0.191697
$550$	−1.79822	−0.0766764
$551$	−66.6312	−2.83858
$552$	0	0
$553$	52.3576	2.22647
$554$	−8.94999	−0.380249
$555$	5.68722	0.241409
$556$	5.18911	0.220067
$557$	−42.0867	−1.78327	−0.891635	−	0.452755i	$-0.850441\pi$
$557$	−42.0867	−1.78327	−0.891635	+	0.452755i	$0.850441\pi$
$558$	8.60740	0.364380
$559$	−8.17645	−0.345827
$560$	15.0752	0.637044
$561$	2.98946	0.126215
$562$	−28.2224	−1.19049
$563$	−34.0940	−1.43689	−0.718445	−	0.695584i	$-0.755146\pi$
$563$	−34.0940	−1.43689	−0.718445	+	0.695584i	$0.755146\pi$
$564$	2.16896	0.0913297
$565$	15.8405	0.666413
$566$	−18.0525	−0.758803
$567$	−3.34169	−0.140338
$568$	18.9370	0.794580
$569$	−4.73609	−0.198547	−0.0992736	−	0.995060i	$-0.531652\pi$
$569$	−4.73609	−0.198547	−0.0992736	+	0.995060i	$0.531652\pi$
$570$	−12.8453	−0.538030
$571$	10.6327	0.444966	0.222483	−	0.974937i	$-0.428584\pi$
$571$	10.6327	0.444966	0.222483	+	0.974937i	$0.428584\pi$
$572$	0.326630	0.0136571
$573$	−26.5082	−1.10739
$574$	51.5926	2.15343
$575$	0	0
$576$	6.46148	0.269228
$577$	31.3949	1.30699	0.653493	−	0.756933i	$-0.273303\pi$
$577$	31.3949	1.30699	0.653493	+	0.756933i	$0.273303\pi$
$578$	16.1408	0.671369
$579$	−7.46115	−0.310075
$580$	2.36758	0.0983086
$581$	22.0862	0.916290
$582$	4.68512	0.194204
$583$	−1.30762	−0.0541563
$584$	35.0878	1.45194
$585$	0.915669	0.0378583
$586$	−10.1697	−0.420105
$587$	37.3199	1.54036	0.770178	−	0.637829i	$-0.220167\pi$
$587$	37.3199	1.54036	0.770178	+	0.637829i	$0.220167\pi$
$588$	−1.25381	−0.0517064
$589$	48.0527	1.97998
$590$	5.23166	0.215384
$591$	7.88559	0.324370
$592$	25.6565	1.05448
$593$	−12.3873	−0.508684	−0.254342	−	0.967114i	$-0.581859\pi$
$593$	−12.3873	−0.508684	−0.254342	+	0.967114i	$0.581859\pi$
$594$	1.79822	0.0737819
$595$	8.42685	0.345467
$596$	1.42172	0.0582361
$597$	−17.7491	−0.726422
$598$	0	0
$599$	1.67194	0.0683137	0.0341569	−	0.999416i	$-0.489125\pi$
$599$	1.67194	0.0683137	0.0341569	+	0.999416i	$0.489125\pi$
$600$	−2.57732	−0.105219
$601$	40.3053	1.64409	0.822043	−	0.569425i	$-0.192834\pi$
$601$	40.3053	1.64409	0.822043	+	0.569425i	$0.192834\pi$
$602$	−45.2627	−1.84477
$603$	0.818172	0.0333185
$604$	1.27012	0.0516804
$605$	−9.59464	−0.390078
$606$	15.3021	0.621606
$607$	47.1147	1.91233	0.956163	−	0.292835i	$-0.0945988\pi$
$607$	47.1147	1.91233	0.956163	+	0.292835i	$0.0945988\pi$
$608$	−14.2976	−0.579844
$609$	26.2935	1.06547
$610$	6.81320	0.275858
$611$	−6.60035	−0.267022
$612$	−0.758791	−0.0306723
$613$	−4.11013	−0.166006	−0.0830032	−	0.996549i	$-0.526451\pi$
$613$	−4.11013	−0.166006	−0.0830032	+	0.996549i	$0.526451\pi$
$614$	10.2745	0.414647
$615$	−10.1782	−0.410426
$616$	−10.2100	−0.411374
$617$	−15.5339	−0.625370	−0.312685	−	0.949857i	$-0.601228\pi$
$617$	−15.5339	−0.625370	−0.312685	+	0.949857i	$0.601228\pi$
$618$	4.57448	0.184013
$619$	−6.49312	−0.260981	−0.130490	−	0.991450i	$-0.541655\pi$
$619$	−6.49312	−0.260981	−0.130490	+	0.991450i	$0.541655\pi$
$620$	−1.70744	−0.0685725
$621$	0	0
$622$	−35.9785	−1.44261
$623$	−30.6550	−1.22817
$624$	4.13082	0.165365
$625$	1.00000	0.0400000
$626$	8.90452	0.355896
$627$	10.0390	0.400918
$628$	−5.76845	−0.230186
$629$	14.3417	0.571839
$630$	5.06891	0.201950
$631$	−41.2351	−1.64154	−0.820772	−	0.571256i	$-0.806456\pi$
$631$	−41.2351	−1.64154	−0.820772	+	0.571256i	$0.806456\pi$
$632$	−40.3814	−1.60629
$633$	−1.12533	−0.0447277
$634$	−1.92276	−0.0763625
$635$	−7.50750	−0.297926
$636$	0.331903	0.0131608
$637$	3.81548	0.151175
$638$	−14.1490	−0.560164
$639$	7.34757	0.290665
$640$	−13.1780	−0.520905
$641$	30.8144	1.21710	0.608548	−	0.793517i	$-0.291752\pi$
$641$	30.8144	1.21710	0.608548	+	0.793517i	$0.291752\pi$
$642$	2.60622	0.102859
$643$	−4.30931	−0.169943	−0.0849713	−	0.996383i	$-0.527080\pi$
$643$	−4.30931	−0.169943	−0.0849713	+	0.996383i	$0.527080\pi$
$644$	0	0
$645$	8.92948	0.351598
$646$	−32.3924	−1.27446
$647$	−35.2005	−1.38388	−0.691938	−	0.721957i	$-0.743243\pi$
$647$	−35.2005	−1.38388	−0.691938	+	0.721957i	$0.743243\pi$
$648$	2.57732	0.101247
$649$	−4.08869	−0.160495
$650$	−1.38895	−0.0544792
$651$	−18.9622	−0.743187
$652$	−5.48848	−0.214946
$653$	−39.0783	−1.52925	−0.764625	−	0.644475i	$-0.777076\pi$
$653$	−39.0783	−1.52925	−0.764625	+	0.644475i	$0.777076\pi$
$654$	−10.9934	−0.429877
$655$	−18.3185	−0.715764
$656$	−45.9167	−1.79275
$657$	13.6141	0.531136
$658$	−36.5379	−1.42439
$659$	44.5911	1.73702	0.868512	−	0.495668i	$-0.165077\pi$
$659$	44.5911	1.73702	0.868512	+	0.495668i	$0.165077\pi$
$660$	−0.356711	−0.0138850
$661$	41.3256	1.60738	0.803690	−	0.595048i	$-0.202867\pi$
$661$	41.3256	1.60738	0.803690	+	0.595048i	$0.202867\pi$
$662$	0.113795	0.00442277
$663$	2.30907	0.0896770
$664$	−17.0342	−0.661057
$665$	28.2983	1.09736
$666$	8.62678	0.334281
$667$	0	0
$668$	1.18823	0.0459740
$669$	4.70094	0.181749
$670$	−1.24106	−0.0479464
$671$	−5.32471	−0.205558
$672$	5.64201	0.217645
$673$	−16.0980	−0.620533	−0.310267	−	0.950650i	$-0.600418\pi$
$673$	−16.0980	−0.620533	−0.310267	+	0.950650i	$0.600418\pi$
$674$	8.03368	0.309446
$675$	−1.00000	−0.0384900
$676$	−3.65942	−0.140747
$677$	18.9140	0.726924	0.363462	−	0.931609i	$-0.381595\pi$
$677$	18.9140	0.726924	0.363462	+	0.931609i	$0.381595\pi$
$678$	24.0280	0.922788
$679$	−10.3214	−0.396098
$680$	−6.49931	−0.249237
$681$	11.6840	0.447733
$682$	10.2039	0.390727
$683$	−13.1889	−0.504660	−0.252330	−	0.967641i	$-0.581197\pi$
$683$	−13.1889	−0.504660	−0.252330	+	0.967641i	$0.581197\pi$
$684$	−2.54811	−0.0974293
$685$	−13.4737	−0.514803
$686$	−14.3609	−0.548300
$687$	−19.7306	−0.752770
$688$	40.2832	1.53578
$689$	−1.01001	−0.0384785
$690$	0	0
$691$	49.2043	1.87182	0.935911	−	0.352238i	$-0.114579\pi$
$691$	49.2043	1.87182	0.935911	+	0.352238i	$0.114579\pi$
$692$	1.32907	0.0505235
$693$	−3.96150	−0.150485
$694$	−15.7112	−0.596389
$695$	17.2453	0.654150
$696$	−20.2792	−0.768681
$697$	−25.6668	−0.972200
$698$	14.2091	0.537822
$699$	−3.50451	−0.132553
$700$	−1.00552	−0.0380049
$701$	21.9082	0.827463	0.413731	−	0.910399i	$-0.364225\pi$
$701$	21.9082	0.827463	0.413731	+	0.910399i	$0.364225\pi$
$702$	1.38895	0.0524227
$703$	48.1609	1.81642
$704$	7.65995	0.288695
$705$	7.20823	0.271478
$706$	−0.702440	−0.0264367
$707$	−33.7107	−1.26782
$708$	1.03780	0.0390029
$709$	49.1126	1.84446	0.922232	−	0.386637i	$-0.126363\pi$
$709$	49.1126	1.84446	0.922232	+	0.386637i	$0.126363\pi$
$710$	−11.1453	−0.418277
$711$	−15.6680	−0.587596
$712$	23.6431	0.886061
$713$	0	0
$714$	12.7824	0.478371
$715$	1.08551	0.0405957
$716$	−1.89360	−0.0707673
$717$	5.64390	0.210775
$718$	−45.9131	−1.71346
$719$	36.9481	1.37793	0.688966	−	0.724793i	$-0.258065\pi$
$719$	36.9481	1.37793	0.688966	+	0.724793i	$0.258065\pi$
$720$	−4.51126	−0.168125
$721$	−10.0776	−0.375311
$722$	−79.9568	−2.97568
$723$	9.80570	0.364678
$724$	−3.88922	−0.144542
$725$	7.86833	0.292223
$726$	−14.5538	−0.540144
$727$	−1.56501	−0.0580429	−0.0290215	−	0.999579i	$-0.509239\pi$
$727$	−1.56501	−0.0580429	−0.0290215	+	0.999579i	$0.509239\pi$
$728$	−7.88628	−0.292285
$729$	1.00000	0.0370370
$730$	−20.6508	−0.764321
$731$	22.5178	0.832850
$732$	1.35153	0.0499539
$733$	2.95045	0.108977	0.0544886	−	0.998514i	$-0.482647\pi$
$733$	2.95045	0.108977	0.0544886	+	0.998514i	$0.482647\pi$
$734$	−10.8969	−0.402212
$735$	−4.16687	−0.153697
$736$	0	0
$737$	0.969926	0.0357277
$738$	−15.4391	−0.568321
$739$	25.2790	0.929903	0.464951	−	0.885336i	$-0.346072\pi$
$739$	25.2790	0.929903	0.464951	+	0.885336i	$0.346072\pi$
$740$	−1.71129	−0.0629082
$741$	7.75414	0.284855
$742$	−5.59118	−0.205259
$743$	37.8488	1.38854	0.694269	−	0.719716i	$-0.255728\pi$
$743$	37.8488	1.38854	0.694269	+	0.719716i	$0.255728\pi$
$744$	14.6248	0.536172
$745$	4.72490	0.173107
$746$	−1.12496	−0.0411876
$747$	−6.60930	−0.241822
$748$	−0.899531	−0.0328901
$749$	−5.74154	−0.209791
$750$	1.51687	0.0553883
$751$	23.3637	0.852553	0.426277	−	0.904593i	$-0.359825\pi$
$751$	23.3637	0.852553	0.426277	+	0.904593i	$0.359825\pi$
$752$	32.5182	1.18582
$753$	−15.8115	−0.576203
$754$	−10.9287	−0.398001
$755$	4.22106	0.153620
$756$	1.00552	0.0365702
$757$	−31.4175	−1.14189	−0.570944	−	0.820989i	$-0.693423\pi$
$757$	−31.4175	−1.14189	−0.570944	+	0.820989i	$0.693423\pi$
$758$	−39.3816	−1.43041
$759$	0	0
$760$	−21.8254	−0.791691
$761$	14.6063	0.529478	0.264739	−	0.964320i	$-0.414714\pi$
$761$	14.6063	0.529478	0.264739	+	0.964320i	$0.414714\pi$
$762$	−11.3879	−0.412541
$763$	24.2187	0.876774
$764$	7.97631	0.288573
$765$	−2.52173	−0.0911735
$766$	3.44181	0.124358
$767$	−3.15812	−0.114033
$768$	−7.06634	−0.254985
$769$	−7.09022	−0.255680	−0.127840	−	0.991795i	$-0.540804\pi$
$769$	−7.09022	−0.255680	−0.127840	+	0.991795i	$0.540804\pi$
$770$	6.00909	0.216553
$771$	23.3700	0.841651
$772$	2.24506	0.0808015
$773$	51.5235	1.85317	0.926586	−	0.376082i	$-0.122729\pi$
$773$	51.5235	1.85317	0.926586	+	0.376082i	$0.122729\pi$
$774$	13.5449	0.486860
$775$	−5.67444	−0.203832
$776$	7.96049	0.285765
$777$	−19.0049	−0.681797
$778$	0.503032	0.0180346
$779$	−86.1921	−3.08815
$780$	−0.275525	−0.00986539
$781$	8.71039	0.311682
$782$	0	0
$783$	−7.86833	−0.281191
$784$	−18.7979	−0.671352
$785$	−19.1706	−0.684229
$786$	−27.7869	−0.991124
$787$	19.5456	0.696726	0.348363	−	0.937360i	$-0.386738\pi$
$787$	19.5456	0.696726	0.348363	+	0.937360i	$0.386738\pi$
$788$	−2.37278	−0.0845267
$789$	19.2160	0.684108
$790$	23.7664	0.845569
$791$	−52.9339	−1.88211
$792$	3.05536	0.108567
$793$	−4.11283	−0.146051
$794$	50.9819	1.80928
$795$	1.10303	0.0391206
$796$	5.34071	0.189296
$797$	35.1492	1.24505	0.622525	−	0.782600i	$-0.286107\pi$
$797$	35.1492	1.24505	0.622525	+	0.782600i	$0.286107\pi$
$798$	42.9249	1.51953
$799$	18.1772	0.643065
$800$	1.68837	0.0596929
$801$	9.17352	0.324130
$802$	−4.18315	−0.147712
$803$	16.1392	0.569540
$804$	−0.246188	−0.00868239
$805$	0	0
$806$	7.88153	0.277615
$807$	24.7222	0.870262
$808$	25.9998	0.914670
$809$	7.77663	0.273412	0.136706	−	0.990612i	$-0.456348\pi$
$809$	7.77663	0.273412	0.136706	+	0.990612i	$0.456348\pi$
$810$	−1.51687	−0.0532974
$811$	27.2727	0.957675	0.478837	−	0.877904i	$-0.341058\pi$
$811$	27.2727	0.957675	0.478837	+	0.877904i	$0.341058\pi$
$812$	−7.91173	−0.277647
$813$	13.6555	0.478919
$814$	10.2269	0.358452
$815$	−18.2402	−0.638926
$816$	−11.3762	−0.398247
$817$	75.6172	2.64551
$818$	−37.8482	−1.32333
$819$	−3.05988	−0.106921
$820$	3.06264	0.106952
$821$	−9.64824	−0.336726	−0.168363	−	0.985725i	$-0.553848\pi$
$821$	−9.64824	−0.336726	−0.168363	+	0.985725i	$0.553848\pi$
$822$	−20.4379	−0.712852
$823$	5.57561	0.194353	0.0971767	−	0.995267i	$-0.469019\pi$
$823$	5.57561	0.194353	0.0971767	+	0.995267i	$0.469019\pi$
$824$	7.77250	0.270768
$825$	−1.18548	−0.0412731
$826$	−17.4826	−0.608296
$827$	9.60982	0.334166	0.167083	−	0.985943i	$-0.446565\pi$
$827$	9.60982	0.334166	0.167083	+	0.985943i	$0.446565\pi$
$828$	0	0
$829$	−50.8320	−1.76547	−0.882734	−	0.469873i	$-0.844300\pi$
$829$	−50.8320	−1.76547	−0.882734	+	0.469873i	$0.844300\pi$
$830$	10.0255	0.347989
$831$	−5.90029	−0.204679
$832$	5.91658	0.205120
$833$	−10.5078	−0.364072
$834$	26.1589	0.905807
$835$	3.94892	0.136658
$836$	−3.02073	−0.104474
$837$	5.67444	0.196137
$838$	−39.7614	−1.37353
$839$	29.6836	1.02479	0.512396	−	0.858749i	$-0.328758\pi$
$839$	29.6836	1.02479	0.512396	+	0.858749i	$0.328758\pi$
$840$	8.61259	0.297162
$841$	32.9107	1.13485
$842$	38.2300	1.31749
$843$	−18.6057	−0.640814
$844$	0.338611	0.0116555
$845$	−12.1615	−0.418370
$846$	10.9340	0.375917
$847$	32.0623	1.10167
$848$	4.97607	0.170879
$849$	−11.9011	−0.408446
$850$	3.82515	0.131202
$851$	0	0
$852$	−2.21089	−0.0757437
$853$	12.3860	0.424087	0.212044	−	0.977260i	$-0.431988\pi$
$853$	12.3860	0.424087	0.212044	+	0.977260i	$0.431988\pi$
$854$	−22.7676	−0.779091
$855$	−8.46827	−0.289609
$856$	4.42824	0.151354
$857$	29.7484	1.01618	0.508092	−	0.861303i	$-0.330351\pi$
$857$	29.7484	1.01618	0.508092	+	0.861303i	$0.330351\pi$
$858$	1.64658	0.0562132
$859$	4.56314	0.155692	0.0778461	−	0.996965i	$-0.475196\pi$
$859$	4.56314	0.155692	0.0778461	+	0.996965i	$0.475196\pi$
$860$	−2.68688	−0.0916220
$861$	34.0125	1.15914
$862$	16.1237	0.549177
$863$	25.2281	0.858775	0.429388	−	0.903120i	$-0.358729\pi$
$863$	25.2281	0.858775	0.429388	+	0.903120i	$0.358729\pi$
$864$	−1.68837	−0.0574395
$865$	4.41696	0.150181
$866$	7.22485	0.245510
$867$	10.6409	0.361382
$868$	5.70574	0.193665
$869$	−18.5741	−0.630083
$870$	11.9353	0.404643
$871$	0.749175	0.0253848
$872$	−18.6789	−0.632548
$873$	3.08867	0.104536
$874$	0	0
$875$	−3.34169	−0.112970
$876$	−4.09648	−0.138407
$877$	24.2627	0.819294	0.409647	−	0.912244i	$-0.365652\pi$
$877$	24.2627	0.819294	0.409647	+	0.912244i	$0.365652\pi$
$878$	−37.8629	−1.27781
$879$	−6.70436	−0.226133
$880$	−5.34801	−0.180281
$881$	−4.19486	−0.141328	−0.0706642	−	0.997500i	$-0.522512\pi$
$881$	−4.19486	−0.141328	−0.0706642	+	0.997500i	$0.522512\pi$
$882$	−6.32062	−0.212826
$883$	18.8715	0.635078	0.317539	−	0.948245i	$-0.397144\pi$
$883$	18.8715	0.635078	0.317539	+	0.948245i	$0.397144\pi$
$884$	−0.694802	−0.0233687
$885$	3.44898	0.115936
$886$	16.8703	0.566770
$887$	33.0470	1.10961	0.554806	−	0.831980i	$-0.312793\pi$
$887$	33.0470	1.10961	0.554806	+	0.831980i	$0.312793\pi$
$888$	14.6578	0.491882
$889$	25.0877	0.841415
$890$	−13.9151	−0.466434
$891$	1.18548	0.0397151
$892$	−1.41452	−0.0473615
$893$	61.0413	2.04267
$894$	7.16707	0.239703
$895$	−6.29312	−0.210356
$896$	44.0367	1.47116
$897$	0	0
$898$	−30.0024	−1.00119
$899$	−44.6484	−1.48911
$900$	0.300900	0.0100300
$901$	2.78156	0.0926672
$902$	−18.3027	−0.609414
$903$	−29.8395	−0.992997
$904$	40.8259	1.35785
$905$	−12.9253	−0.429651
$906$	6.40281	0.212719
$907$	59.7016	1.98236	0.991179	−	0.132532i	$-0.0423107\pi$
$907$	59.7016	1.98236	0.991179	+	0.132532i	$0.0423107\pi$
$908$	−3.51573	−0.116674
$909$	10.0879	0.334596
$910$	4.64145	0.153862
$911$	−30.7477	−1.01872	−0.509358	−	0.860554i	$-0.670117\pi$
$911$	−30.7477	−1.01872	−0.509358	+	0.860554i	$0.670117\pi$
$912$	−38.2026	−1.26501
$913$	−7.83518	−0.259307
$914$	7.26110	0.240176
$915$	4.49161	0.148488
$916$	5.93695	0.196162
$917$	61.2148	2.02149
$918$	−3.82515	−0.126249
$919$	13.9339	0.459637	0.229818	−	0.973234i	$-0.426187\pi$
$919$	13.9339	0.459637	0.229818	+	0.973234i	$0.426187\pi$
$920$	0	0
$921$	6.77351	0.223195
$922$	23.4692	0.772916
$923$	6.72795	0.221453
$924$	1.19202	0.0392145
$925$	−5.68722	−0.186995
$926$	−56.0049	−1.84044
$927$	3.01573	0.0990497
$928$	13.2847	0.436090
$929$	−36.4793	−1.19685	−0.598423	−	0.801180i	$-0.704206\pi$
$929$	−36.4793	−1.19685	−0.598423	+	0.801180i	$0.704206\pi$
$930$	−8.60740	−0.282248
$931$	−35.2862	−1.15646
$932$	1.05451	0.0345416
$933$	−23.7189	−0.776521
$934$	19.5161	0.638588
$935$	−2.98946	−0.0977659
$936$	2.35997	0.0771380
$937$	−50.1209	−1.63738	−0.818690	−	0.574236i	$-0.805299\pi$
$937$	−50.1209	−1.63738	−0.818690	+	0.574236i	$0.805299\pi$
$938$	4.14724	0.135412
$939$	5.87032	0.191571
$940$	−2.16896	−0.0707437
$941$	0.994697	0.0324262	0.0162131	−	0.999869i	$-0.494839\pi$
$941$	0.994697	0.0324262	0.0162131	+	0.999869i	$0.494839\pi$
$942$	−29.0794	−0.947458
$943$	0	0
$944$	15.5592	0.506410
$945$	3.34169	0.108705
$946$	16.0572	0.522064
$947$	41.7320	1.35611	0.678053	−	0.735013i	$-0.262824\pi$
$947$	41.7320	1.35611	0.678053	+	0.735013i	$0.262824\pi$
$948$	4.71451	0.153120
$949$	12.4660	0.404663
$950$	12.8453	0.416756
$951$	−1.26758	−0.0411041
$952$	21.7187	0.703906
$953$	−4.22759	−0.136945	−0.0684725	−	0.997653i	$-0.521813\pi$
$953$	−4.22759	−0.136945	−0.0684725	+	0.997653i	$0.521813\pi$
$954$	1.67316	0.0541706
$955$	26.5082	0.857784
$956$	−1.69825	−0.0549254
$957$	−9.32775	−0.301523
$958$	−14.7755	−0.477376
$959$	45.0249	1.45393
$960$	−6.46148	−0.208543
$961$	1.19927	0.0386860
$962$	7.89928	0.254683
$963$	1.71816	0.0553668
$964$	−2.95054	−0.0950304
$965$	7.46115	0.240183
$966$	0	0
$967$	−17.0842	−0.549392	−0.274696	−	0.961531i	$-0.588577\pi$
$967$	−17.0842	−0.549392	−0.274696	+	0.961531i	$0.588577\pi$
$968$	−24.7284	−0.794802
$969$	−21.3547	−0.686013
$970$	−4.68512	−0.150430
$971$	8.32887	0.267286	0.133643	−	0.991030i	$-0.457332\pi$
$971$	8.32887	0.267286	0.133643	+	0.991030i	$0.457332\pi$
$972$	−0.300900	−0.00965139
$973$	−57.6283	−1.84748
$974$	−60.3806	−1.93472
$975$	−0.915669	−0.0293249
$976$	20.2628	0.648597
$977$	38.1165	1.21946	0.609728	−	0.792611i	$-0.291279\pi$
$977$	38.1165	1.21946	0.609728	+	0.792611i	$0.291279\pi$
$978$	−27.6680	−0.884727
$979$	10.8750	0.347567
$980$	1.25381	0.0400516
$981$	−7.24743	−0.231393
$982$	−23.6755	−0.755516
$983$	48.0094	1.53126	0.765632	−	0.643279i	$-0.222427\pi$
$983$	48.0094	1.53126	0.765632	+	0.643279i	$0.222427\pi$
$984$	−26.2326	−0.836263
$985$	−7.88559	−0.251256
$986$	30.0975	0.958501
$987$	−24.0877	−0.766718
$988$	−2.33322	−0.0742297
$989$	0	0
$990$	−1.79822	−0.0571512
$991$	−9.13462	−0.290171	−0.145085	−	0.989419i	$-0.546346\pi$
$991$	−9.13462	−0.290171	−0.145085	+	0.989419i	$0.546346\pi$
$992$	−9.58056	−0.304183
$993$	0.0750196	0.00238067
$994$	37.2442	1.18131
$995$	17.7491	0.562684
$996$	1.98874	0.0630156
$997$	19.9123	0.630629	0.315314	−	0.948987i	$-0.397890\pi$
$997$	19.9123	0.630629	0.315314	+	0.948987i	$0.397890\pi$
$998$	52.2884	1.65516
$999$	5.68722	0.179936

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bu.1.7		25
23.9	even	11		345.2.m.d.196.2	✓	50
23.18	even	11		345.2.m.d.301.2	yes	50
23.22	odd	2		7935.2.a.bt.1.7		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.196.2	✓	50	23.9	even	11
345.2.m.d.301.2	yes	50	23.18	even	11
7935.2.a.bt.1.7		25	23.22	odd	2
7935.2.a.bu.1.7		25	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q-1.51687 q^{2} -1.00000 q^{3} +0.300900 q^{4} +1.00000 q^{5} +1.51687 q^{6} -3.34169 q^{7} +2.57732 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.51687 q^{2} -1.00000 q^{3} +0.300900 q^{4} +1.00000 q^{5} +1.51687 q^{6} -3.34169 q^{7} +2.57732 q^{8} +1.00000 q^{9} -1.51687 q^{10} +1.18548 q^{11} -0.300900 q^{12} +0.915669 q^{13} +5.06891 q^{14} -1.00000 q^{15} -4.51126 q^{16} -2.52173 q^{17} -1.51687 q^{18} -8.46827 q^{19} +0.300900 q^{20} +3.34169 q^{21} -1.79822 q^{22} -2.57732 q^{24} +1.00000 q^{25} -1.38895 q^{26} -1.00000 q^{27} -1.00552 q^{28} +7.86833 q^{29} +1.51687 q^{30} -5.67444 q^{31} +1.68837 q^{32} -1.18548 q^{33} +3.82515 q^{34} -3.34169 q^{35} +0.300900 q^{36} -5.68722 q^{37} +12.8453 q^{38} -0.915669 q^{39} +2.57732 q^{40} +10.1782 q^{41} -5.06891 q^{42} -8.92948 q^{43} +0.356711 q^{44} +1.00000 q^{45} -7.20823 q^{47} +4.51126 q^{48} +4.16687 q^{49} -1.51687 q^{50} +2.52173 q^{51} +0.275525 q^{52} -1.10303 q^{53} +1.51687 q^{54} +1.18548 q^{55} -8.61259 q^{56} +8.46827 q^{57} -11.9353 q^{58} -3.44898 q^{59} -0.300900 q^{60} -4.49161 q^{61} +8.60740 q^{62} -3.34169 q^{63} +6.46148 q^{64} +0.915669 q^{65} +1.79822 q^{66} +0.818172 q^{67} -0.758791 q^{68} +5.06891 q^{70} +7.34757 q^{71} +2.57732 q^{72} +13.6141 q^{73} +8.62678 q^{74} -1.00000 q^{75} -2.54811 q^{76} -3.96150 q^{77} +1.38895 q^{78} -15.6680 q^{79} -4.51126 q^{80} +1.00000 q^{81} -15.4391 q^{82} -6.60930 q^{83} +1.00552 q^{84} -2.52173 q^{85} +13.5449 q^{86} -7.86833 q^{87} +3.05536 q^{88} +9.17352 q^{89} -1.51687 q^{90} -3.05988 q^{91} +5.67444 q^{93} +10.9340 q^{94} -8.46827 q^{95} -1.68837 q^{96} +3.08867 q^{97} -6.32062 q^{98} +1.18548 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * q^99

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