LMFDB - Embedded newform 7935.2.a.bt.1.16

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			1.16
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)

$f(q)$	$=$	$q+0.902689 q^{2} -1.00000 q^{3} -1.18515 q^{4} -1.00000 q^{5} -0.902689 q^{6} -0.451264 q^{7} -2.87520 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.902689 q^{2} -1.00000 q^{3} -1.18515 q^{4} -1.00000 q^{5} -0.902689 q^{6} -0.451264 q^{7} -2.87520 q^{8} +1.00000 q^{9} -0.902689 q^{10} +5.51561 q^{11} +1.18515 q^{12} +5.84415 q^{13} -0.407351 q^{14} +1.00000 q^{15} -0.225111 q^{16} +5.83557 q^{17} +0.902689 q^{18} +0.208039 q^{19} +1.18515 q^{20} +0.451264 q^{21} +4.97888 q^{22} +2.87520 q^{24} +1.00000 q^{25} +5.27545 q^{26} -1.00000 q^{27} +0.534816 q^{28} +8.20051 q^{29} +0.902689 q^{30} -1.38391 q^{31} +5.54720 q^{32} -5.51561 q^{33} +5.26771 q^{34} +0.451264 q^{35} -1.18515 q^{36} +2.33183 q^{37} +0.187795 q^{38} -5.84415 q^{39} +2.87520 q^{40} -4.76213 q^{41} +0.407351 q^{42} -3.59057 q^{43} -6.53683 q^{44} -1.00000 q^{45} -11.6966 q^{47} +0.225111 q^{48} -6.79636 q^{49} +0.902689 q^{50} -5.83557 q^{51} -6.92620 q^{52} +9.73970 q^{53} -0.902689 q^{54} -5.51561 q^{55} +1.29748 q^{56} -0.208039 q^{57} +7.40251 q^{58} +5.24387 q^{59} -1.18515 q^{60} -3.07490 q^{61} -1.24924 q^{62} -0.451264 q^{63} +5.45762 q^{64} -5.84415 q^{65} -4.97888 q^{66} -12.5160 q^{67} -6.91604 q^{68} +0.407351 q^{70} -7.39966 q^{71} -2.87520 q^{72} +14.9860 q^{73} +2.10492 q^{74} -1.00000 q^{75} -0.246558 q^{76} -2.48900 q^{77} -5.27545 q^{78} -1.08864 q^{79} +0.225111 q^{80} +1.00000 q^{81} -4.29872 q^{82} +7.73458 q^{83} -0.534816 q^{84} -5.83557 q^{85} -3.24117 q^{86} -8.20051 q^{87} -15.8585 q^{88} -0.255814 q^{89} -0.902689 q^{90} -2.63725 q^{91} +1.38391 q^{93} -10.5584 q^{94} -0.208039 q^{95} -5.54720 q^{96} +1.97328 q^{97} -6.13500 q^{98} +5.51561 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.902689	0.638298	0.319149	−	0.947705i	$-0.396603\pi$
$2$	0.902689	0.638298	0.319149	+	0.947705i	$0.396603\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.18515	−0.592576
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.902689	−0.368521
$7$	−0.451264	−0.170562	−0.0852809	−	0.996357i	$-0.527179\pi$
$7$	−0.451264	−0.170562	−0.0852809	+	0.996357i	$0.527179\pi$
$8$	−2.87520	−1.01654
$9$	1.00000	0.333333
$10$	−0.902689	−0.285455
$11$	5.51561	1.66302	0.831509	−	0.555511i	$-0.187477\pi$
$11$	5.51561	1.66302	0.831509	+	0.555511i	$0.187477\pi$
$12$	1.18515	0.342124
$13$	5.84415	1.62088	0.810438	−	0.585825i	$-0.199229\pi$
$13$	5.84415	1.62088	0.810438	+	0.585825i	$0.199229\pi$
$14$	−0.407351	−0.108869
$15$	1.00000	0.258199
$16$	−0.225111	−0.0562779
$17$	5.83557	1.41533	0.707667	−	0.706546i	$-0.249748\pi$
$17$	5.83557	1.41533	0.707667	+	0.706546i	$0.249748\pi$
$18$	0.902689	0.212766
$19$	0.208039	0.0477275	0.0238637	−	0.999715i	$-0.492403\pi$
$19$	0.208039	0.0477275	0.0238637	+	0.999715i	$0.492403\pi$
$20$	1.18515	0.265008
$21$	0.451264	0.0984739
$22$	4.97888	1.06150
$23$	0	0
$23$	0	0
$24$	2.87520	0.586898
$25$	1.00000	0.200000
$26$	5.27545	1.03460
$27$	−1.00000	−0.192450
$28$	0.534816	0.101071
$29$	8.20051	1.52280	0.761398	−	0.648284i	$-0.224513\pi$
$29$	8.20051	1.52280	0.761398	+	0.648284i	$0.224513\pi$
$30$	0.902689	0.164808
$31$	−1.38391	−0.248558	−0.124279	−	0.992247i	$-0.539662\pi$
$31$	−1.38391	−0.248558	−0.124279	+	0.992247i	$0.539662\pi$
$32$	5.54720	0.980616
$33$	−5.51561	−0.960144
$34$	5.26771	0.903405
$35$	0.451264	0.0762775
$36$	−1.18515	−0.197525
$37$	2.33183	0.383351	0.191675	−	0.981458i	$-0.438608\pi$
$37$	2.33183	0.383351	0.191675	+	0.981458i	$0.438608\pi$
$38$	0.187795	0.0304643
$39$	−5.84415	−0.935813
$40$	2.87520	0.454609
$41$	−4.76213	−0.743719	−0.371860	−	0.928289i	$-0.621280\pi$
$41$	−4.76213	−0.743719	−0.371860	+	0.928289i	$0.621280\pi$
$42$	0.407351	0.0628557
$43$	−3.59057	−0.547556	−0.273778	−	0.961793i	$-0.588273\pi$
$43$	−3.59057	−0.547556	−0.273778	+	0.961793i	$0.588273\pi$
$44$	−6.53683	−0.985465
$45$	−1.00000	−0.149071
$46$	0	0
$47$	−11.6966	−1.70613	−0.853064	−	0.521806i	$-0.825259\pi$
$47$	−11.6966	−1.70613	−0.853064	+	0.521806i	$0.825259\pi$
$48$	0.225111	0.0324920
$49$	−6.79636	−0.970909
$50$	0.902689	0.127660
$51$	−5.83557	−0.817144
$52$	−6.92620	−0.960492
$53$	9.73970	1.33785	0.668926	−	0.743329i	$-0.266754\pi$
$53$	9.73970	1.33785	0.668926	+	0.743329i	$0.266754\pi$
$54$	−0.902689	−0.122840
$55$	−5.51561	−0.743725
$56$	1.29748	0.173382
$57$	−0.208039	−0.0275555
$58$	7.40251	0.971998
$59$	5.24387	0.682693	0.341347	−	0.939937i	$-0.389117\pi$
$59$	5.24387	0.682693	0.341347	+	0.939937i	$0.389117\pi$
$60$	−1.18515	−0.153002
$61$	−3.07490	−0.393700	−0.196850	−	0.980434i	$-0.563071\pi$
$61$	−3.07490	−0.393700	−0.196850	+	0.980434i	$0.563071\pi$
$62$	−1.24924	−0.158654
$63$	−0.451264	−0.0568539
$64$	5.45762	0.682203
$65$	−5.84415	−0.724877
$66$	−4.97888	−0.612858
$67$	−12.5160	−1.52908	−0.764539	−	0.644578i	$-0.777033\pi$
$67$	−12.5160	−1.52908	−0.764539	+	0.644578i	$0.777033\pi$
$68$	−6.91604	−0.838693
$69$	0	0
$70$	0.407351	0.0486878
$71$	−7.39966	−0.878178	−0.439089	−	0.898444i	$-0.644699\pi$
$71$	−7.39966	−0.878178	−0.439089	+	0.898444i	$0.644699\pi$
$72$	−2.87520	−0.338846
$73$	14.9860	1.75398	0.876992	−	0.480505i	$-0.159547\pi$
$73$	14.9860	1.75398	0.876992	+	0.480505i	$0.159547\pi$
$74$	2.10492	0.244692
$75$	−1.00000	−0.115470
$76$	−0.246558	−0.0282822
$77$	−2.48900	−0.283647
$78$	−5.27545	−0.597327
$79$	−1.08864	−0.122482	−0.0612409	−	0.998123i	$-0.519506\pi$
$79$	−1.08864	−0.122482	−0.0612409	+	0.998123i	$0.519506\pi$
$80$	0.225111	0.0251682
$81$	1.00000	0.111111
$82$	−4.29872	−0.474714
$83$	7.73458	0.848981	0.424490	−	0.905432i	$-0.360453\pi$
$83$	7.73458	0.848981	0.424490	+	0.905432i	$0.360453\pi$
$84$	−0.534816	−0.0583533
$85$	−5.83557	−0.632957
$86$	−3.24117	−0.349504
$87$	−8.20051	−0.879187
$88$	−15.8585	−1.69052
$89$	−0.255814	−0.0271163	−0.0135581	−	0.999908i	$-0.504316\pi$
$89$	−0.255814	−0.0271163	−0.0135581	+	0.999908i	$0.504316\pi$
$90$	−0.902689	−0.0951518
$91$	−2.63725	−0.276459
$92$	0	0
$93$	1.38391	0.143505
$94$	−10.5584	−1.08902
$95$	−0.208039	−0.0213444
$96$	−5.54720	−0.566159
$97$	1.97328	0.200356	0.100178	−	0.994970i	$-0.468059\pi$
$97$	1.97328	0.200356	0.100178	+	0.994970i	$0.468059\pi$
$98$	−6.13500	−0.619729
$99$	5.51561	0.554340
$100$	−1.18515	−0.118515
$101$	16.0785	1.59987	0.799933	−	0.600089i	$-0.204868\pi$
$101$	16.0785	1.59987	0.799933	+	0.600089i	$0.204868\pi$
$102$	−5.26771	−0.521581
$103$	−9.07103	−0.893796	−0.446898	−	0.894585i	$-0.647471\pi$
$103$	−9.07103	−0.893796	−0.446898	+	0.894585i	$0.647471\pi$
$104$	−16.8031	−1.64768
$105$	−0.451264	−0.0440389
$106$	8.79193	0.853947
$107$	−10.1643	−0.982621	−0.491310	−	0.870985i	$-0.663482\pi$
$107$	−10.1643	−0.982621	−0.491310	+	0.870985i	$0.663482\pi$
$108$	1.18515	0.114041
$109$	10.7237	1.02715	0.513574	−	0.858045i	$-0.328321\pi$
$109$	10.7237	1.02715	0.513574	+	0.858045i	$0.328321\pi$
$110$	−4.97888	−0.474718
$111$	−2.33183	−0.221328
$112$	0.101585	0.00959885
$113$	16.1548	1.51971	0.759857	−	0.650091i	$-0.225269\pi$
$113$	16.1548	1.51971	0.759857	+	0.650091i	$0.225269\pi$
$114$	−0.187795	−0.0175886
$115$	0	0
$116$	−9.71885	−0.902373
$117$	5.84415	0.540292
$118$	4.73358	0.435762
$119$	−2.63338	−0.241402
$120$	−2.87520	−0.262469
$121$	19.4219	1.76563
$122$	−2.77568	−0.251298
$123$	4.76213	0.429387
$124$	1.64015	0.147290
$125$	−1.00000	−0.0894427
$126$	−0.407351	−0.0362897
$127$	−2.64945	−0.235101	−0.117551	−	0.993067i	$-0.537504\pi$
$127$	−2.64945	−0.235101	−0.117551	+	0.993067i	$0.537504\pi$
$128$	−6.16786	−0.545167
$129$	3.59057	0.316132
$130$	−5.27545	−0.462688
$131$	0.352120	0.0307649	0.0153824	−	0.999882i	$-0.495103\pi$
$131$	0.352120	0.0307649	0.0153824	+	0.999882i	$0.495103\pi$
$132$	6.53683	0.568958
$133$	−0.0938806	−0.00814048
$134$	−11.2981	−0.976007
$135$	1.00000	0.0860663
$136$	−16.7785	−1.43874
$137$	−7.07002	−0.604032	−0.302016	−	0.953303i	$-0.597660\pi$
$137$	−7.07002	−0.604032	−0.302016	+	0.953303i	$0.597660\pi$
$138$	0	0
$139$	21.2336	1.80101	0.900506	−	0.434844i	$-0.143196\pi$
$139$	21.2336	1.80101	0.900506	+	0.434844i	$0.143196\pi$
$140$	−0.534816	−0.0452002
$141$	11.6966	0.985034
$142$	−6.67960	−0.560539
$143$	32.2340	2.69555
$144$	−0.225111	−0.0187593
$145$	−8.20051	−0.681015
$146$	13.5277	1.11956
$147$	6.79636	0.560554
$148$	−2.76357	−0.227164
$149$	−4.00600	−0.328184	−0.164092	−	0.986445i	$-0.552469\pi$
$149$	−4.00600	−0.328184	−0.164092	+	0.986445i	$0.552469\pi$
$150$	−0.902689	−0.0737043
$151$	−17.8347	−1.45136	−0.725682	−	0.688030i	$-0.758476\pi$
$151$	−17.8347	−1.45136	−0.725682	+	0.688030i	$0.758476\pi$
$152$	−0.598155	−0.0485168
$153$	5.83557	0.471778
$154$	−2.24679	−0.181051
$155$	1.38391	0.111159
$156$	6.92620	0.554540
$157$	−17.8855	−1.42742	−0.713711	−	0.700440i	$-0.752987\pi$
$157$	−17.8855	−1.42742	−0.713711	+	0.700440i	$0.752987\pi$
$158$	−0.982706	−0.0781799
$159$	−9.73970	−0.772409
$160$	−5.54720	−0.438545
$161$	0	0
$162$	0.902689	0.0709220
$163$	15.8412	1.24078	0.620389	−	0.784295i	$-0.286975\pi$
$163$	15.8412	1.24078	0.620389	+	0.784295i	$0.286975\pi$
$164$	5.64384	0.440710
$165$	5.51561	0.429390
$166$	6.98193	0.541902
$167$	8.82234	0.682694	0.341347	−	0.939937i	$-0.389117\pi$
$167$	8.82234	0.682694	0.341347	+	0.939937i	$0.389117\pi$
$168$	−1.29748	−0.100102
$169$	21.1541	1.62724
$170$	−5.26771	−0.404015
$171$	0.208039	0.0159092
$172$	4.25537	0.324469
$173$	11.4303	0.869028	0.434514	−	0.900665i	$-0.356920\pi$
$173$	11.4303	0.869028	0.434514	+	0.900665i	$0.356920\pi$
$174$	−7.40251	−0.561183
$175$	−0.451264	−0.0341124
$176$	−1.24163	−0.0935911
$177$	−5.24387	−0.394153
$178$	−0.230921	−0.0173082
$179$	−5.49009	−0.410348	−0.205174	−	0.978725i	$-0.565776\pi$
$179$	−5.49009	−0.410348	−0.205174	+	0.978725i	$0.565776\pi$
$180$	1.18515	0.0883360
$181$	2.49112	0.185163	0.0925817	−	0.995705i	$-0.470488\pi$
$181$	2.49112	0.185163	0.0925817	+	0.995705i	$0.470488\pi$
$182$	−2.38062	−0.176463
$183$	3.07490	0.227303
$184$	0	0
$185$	−2.33183	−0.171440
$186$	1.24924	0.0915990
$187$	32.1867	2.35373
$188$	13.8623	1.01101
$189$	0.451264	0.0328246
$190$	−0.187795	−0.0136241
$191$	−5.50019	−0.397980	−0.198990	−	0.980002i	$-0.563766\pi$
$191$	−5.50019	−0.397980	−0.198990	+	0.980002i	$0.563766\pi$
$192$	−5.45762	−0.393870
$193$	14.0631	1.01228	0.506141	−	0.862451i	$-0.331071\pi$
$193$	14.0631	1.01228	0.506141	+	0.862451i	$0.331071\pi$
$194$	1.78126	0.127887
$195$	5.84415	0.418508
$196$	8.05472	0.575337
$197$	8.67555	0.618107	0.309054	−	0.951045i	$-0.399988\pi$
$197$	8.67555	0.618107	0.309054	+	0.951045i	$0.399988\pi$
$198$	4.97888	0.353834
$199$	20.2045	1.43226	0.716129	−	0.697968i	$-0.245912\pi$
$199$	20.2045	1.43226	0.716129	+	0.697968i	$0.245912\pi$
$200$	−2.87520	−0.203308
$201$	12.5160	0.882813
$202$	14.5138	1.02119
$203$	−3.70060	−0.259731
$204$	6.91604	0.484220
$205$	4.76213	0.332601
$206$	−8.18833	−0.570508
$207$	0	0
$208$	−1.31558	−0.0912194
$209$	1.14746	0.0793717
$210$	−0.407351	−0.0281099
$211$	7.17251	0.493776	0.246888	−	0.969044i	$-0.420592\pi$
$211$	7.17251	0.493776	0.246888	+	0.969044i	$0.420592\pi$
$212$	−11.5430	−0.792778
$213$	7.39966	0.507016
$214$	−9.17521	−0.627205
$215$	3.59057	0.244875
$216$	2.87520	0.195633
$217$	0.624510	0.0423945
$218$	9.68020	0.655626
$219$	−14.9860	−1.01266
$220$	6.53683	0.440713
$221$	34.1040	2.29408
$222$	−2.10492	−0.141273
$223$	−14.5877	−0.976862	−0.488431	−	0.872603i	$-0.662431\pi$
$223$	−14.5877	−0.976862	−0.488431	+	0.872603i	$0.662431\pi$
$224$	−2.50325	−0.167256
$225$	1.00000	0.0666667
$226$	14.5827	0.970030
$227$	4.52210	0.300142	0.150071	−	0.988675i	$-0.452050\pi$
$227$	4.52210	0.300142	0.150071	+	0.988675i	$0.452050\pi$
$228$	0.246558	0.0163287
$229$	−21.6882	−1.43320	−0.716600	−	0.697485i	$-0.754303\pi$
$229$	−21.6882	−1.43320	−0.716600	+	0.697485i	$0.754303\pi$
$230$	0	0
$231$	2.48900	0.163764
$232$	−23.5781	−1.54798
$233$	−4.83658	−0.316855	−0.158428	−	0.987371i	$-0.550642\pi$
$233$	−4.83658	−0.316855	−0.158428	+	0.987371i	$0.550642\pi$
$234$	5.27545	0.344867
$235$	11.6966	0.763004
$236$	−6.21478	−0.404548
$237$	1.08864	0.0707149
$238$	−2.37713	−0.154086
$239$	−16.3127	−1.05518	−0.527592	−	0.849498i	$-0.676905\pi$
$239$	−16.3127	−1.05518	−0.527592	+	0.849498i	$0.676905\pi$
$240$	−0.225111	−0.0145309
$241$	−14.5002	−0.934037	−0.467019	−	0.884247i	$-0.654672\pi$
$241$	−14.5002	−0.934037	−0.467019	+	0.884247i	$0.654672\pi$
$242$	17.5320	1.12700
$243$	−1.00000	−0.0641500
$244$	3.64422	0.233297
$245$	6.79636	0.434204
$246$	4.29872	0.274077
$247$	1.21581	0.0773603
$248$	3.97903	0.252669
$249$	−7.73458	−0.490159
$250$	−0.902689	−0.0570911
$251$	−15.7183	−0.992132	−0.496066	−	0.868285i	$-0.665223\pi$
$251$	−15.7183	−0.992132	−0.496066	+	0.868285i	$0.665223\pi$
$252$	0.534816	0.0336903
$253$	0	0
$254$	−2.39163	−0.150065
$255$	5.83557	0.365438
$256$	−16.4829	−1.03018
$257$	−5.64056	−0.351848	−0.175924	−	0.984404i	$-0.556291\pi$
$257$	−5.64056	−0.351848	−0.175924	+	0.984404i	$0.556291\pi$
$258$	3.24117	0.201786
$259$	−1.05227	−0.0653850
$260$	6.92620	0.429545
$261$	8.20051	0.507599
$262$	0.317855	0.0196372
$263$	−12.6489	−0.779968	−0.389984	−	0.920822i	$-0.627519\pi$
$263$	−12.6489	−0.779968	−0.389984	+	0.920822i	$0.627519\pi$
$264$	15.8585	0.976023
$265$	−9.73970	−0.598305
$266$	−0.0847450	−0.00519605
$267$	0.255814	0.0156556
$268$	14.8334	0.906095
$269$	−14.1934	−0.865389	−0.432695	−	0.901541i	$-0.642437\pi$
$269$	−14.1934	−0.865389	−0.432695	+	0.901541i	$0.642437\pi$
$270$	0.902689	0.0549359
$271$	−11.8181	−0.717901	−0.358950	−	0.933357i	$-0.616865\pi$
$271$	−11.8181	−0.717901	−0.358950	+	0.933357i	$0.616865\pi$
$272$	−1.31365	−0.0796520
$273$	2.63725	0.159614
$274$	−6.38203	−0.385553
$275$	5.51561	0.332604
$276$	0	0
$277$	21.7172	1.30486	0.652431	−	0.757848i	$-0.273749\pi$
$277$	21.7172	1.30486	0.652431	+	0.757848i	$0.273749\pi$
$278$	19.1674	1.14958
$279$	−1.38391	−0.0828527
$280$	−1.29748	−0.0775390
$281$	−0.869740	−0.0518843	−0.0259422	−	0.999663i	$-0.508259\pi$
$281$	−0.869740	−0.0518843	−0.0259422	+	0.999663i	$0.508259\pi$
$282$	10.5584	0.628745
$283$	14.9108	0.886358	0.443179	−	0.896433i	$-0.353851\pi$
$283$	14.9108	0.886358	0.443179	+	0.896433i	$0.353851\pi$
$284$	8.76972	0.520387
$285$	0.208039	0.0123232
$286$	29.0973	1.72056
$287$	2.14898	0.126850
$288$	5.54720	0.326872
$289$	17.0539	1.00317
$290$	−7.40251	−0.434691
$291$	−1.97328	−0.115676
$292$	−17.7607	−1.03937
$293$	4.48484	0.262007	0.131004	−	0.991382i	$-0.458180\pi$
$293$	4.48484	0.262007	0.131004	+	0.991382i	$0.458180\pi$
$294$	6.13500	0.357801
$295$	−5.24387	−0.305310
$296$	−6.70449	−0.389690
$297$	−5.51561	−0.320048
$298$	−3.61617	−0.209479
$299$	0	0
$300$	1.18515	0.0684248
$301$	1.62029	0.0933922
$302$	−16.0992	−0.926402
$303$	−16.0785	−0.923683
$304$	−0.0468320	−0.00268600
$305$	3.07490	0.176068
$306$	5.26771	0.301135
$307$	4.65915	0.265912	0.132956	−	0.991122i	$-0.457553\pi$
$307$	4.65915	0.265912	0.132956	+	0.991122i	$0.457553\pi$
$308$	2.94984	0.168083
$309$	9.07103	0.516033
$310$	1.24924	0.0709523
$311$	27.5936	1.56469	0.782345	−	0.622845i	$-0.214023\pi$
$311$	27.5936	1.56469	0.782345	+	0.622845i	$0.214023\pi$
$312$	16.8031	0.951289
$313$	−22.4415	−1.26847	−0.634236	−	0.773140i	$-0.718685\pi$
$313$	−22.4415	−1.26847	−0.634236	+	0.773140i	$0.718685\pi$
$314$	−16.1451	−0.911120
$315$	0.451264	0.0254258
$316$	1.29021	0.0725798
$317$	15.2928	0.858927	0.429464	−	0.903084i	$-0.358703\pi$
$317$	15.2928	0.858927	0.429464	+	0.903084i	$0.358703\pi$
$318$	−8.79193	−0.493027
$319$	45.2308	2.53244
$320$	−5.45762	−0.305090
$321$	10.1643	0.567316
$322$	0	0
$323$	1.21403	0.0675503
$324$	−1.18515	−0.0658418
$325$	5.84415	0.324175
$326$	14.2997	0.791985
$327$	−10.7237	−0.593024
$328$	13.6921	0.756019
$329$	5.27827	0.291000
$330$	4.97888	0.274078
$331$	22.0539	1.21219	0.606095	−	0.795392i	$-0.292735\pi$
$331$	22.0539	1.21219	0.606095	+	0.795392i	$0.292735\pi$
$332$	−9.16665	−0.503085
$333$	2.33183	0.127784
$334$	7.96384	0.435762
$335$	12.5160	0.683824
$336$	−0.101585	−0.00554190
$337$	−10.8338	−0.590154	−0.295077	−	0.955474i	$-0.595345\pi$
$337$	−10.8338	−0.590154	−0.295077	+	0.955474i	$0.595345\pi$
$338$	19.0956	1.03866
$339$	−16.1548	−0.877407
$340$	6.91604	0.375075
$341$	−7.63312	−0.413357
$342$	0.187795	0.0101548
$343$	6.22580	0.336162
$344$	10.3236	0.556612
$345$	0	0
$346$	10.3180	0.554699
$347$	28.0721	1.50699	0.753494	−	0.657455i	$-0.228367\pi$
$347$	28.0721	1.50699	0.753494	+	0.657455i	$0.228367\pi$
$348$	9.71885	0.520985
$349$	−5.48448	−0.293578	−0.146789	−	0.989168i	$-0.546894\pi$
$349$	−5.48448	−0.293578	−0.146789	+	0.989168i	$0.546894\pi$
$350$	−0.407351	−0.0217738
$351$	−5.84415	−0.311938
$352$	30.5962	1.63078
$353$	−6.08952	−0.324113	−0.162056	−	0.986782i	$-0.551813\pi$
$353$	−6.08952	−0.324113	−0.162056	+	0.986782i	$0.551813\pi$
$354$	−4.73358	−0.251587
$355$	7.39966	0.392733
$356$	0.303179	0.0160684
$357$	2.63338	0.139373
$358$	−4.95584	−0.261924
$359$	−34.4275	−1.81701	−0.908506	−	0.417872i	$-0.862776\pi$
$359$	−34.4275	−1.81701	−0.908506	+	0.417872i	$0.862776\pi$
$360$	2.87520	0.151536
$361$	−18.9567	−0.997722
$362$	2.24871	0.118189
$363$	−19.4219	−1.01939
$364$	3.12555	0.163823
$365$	−14.9860	−0.784405
$366$	2.77568	0.145087
$367$	−7.10017	−0.370626	−0.185313	−	0.982680i	$-0.559330\pi$
$367$	−7.10017	−0.370626	−0.185313	+	0.982680i	$0.559330\pi$
$368$	0	0
$369$	−4.76213	−0.247906
$370$	−2.10492	−0.109430
$371$	−4.39518	−0.228186
$372$	−1.64015	−0.0850377
$373$	6.02480	0.311953	0.155976	−	0.987761i	$-0.450148\pi$
$373$	6.02480	0.311953	0.155976	+	0.987761i	$0.450148\pi$
$374$	29.0546	1.50238
$375$	1.00000	0.0516398
$376$	33.6302	1.73434
$377$	47.9250	2.46826
$378$	0.407351	0.0209519
$379$	38.6321	1.98440	0.992200	−	0.124659i	$-0.0397835\pi$
$379$	38.6321	1.98440	0.992200	+	0.124659i	$0.0397835\pi$
$380$	0.246558	0.0126482
$381$	2.64945	0.135736
$382$	−4.96497	−0.254030
$383$	−13.4449	−0.687000	−0.343500	−	0.939153i	$-0.611613\pi$
$383$	−13.4449	−0.687000	−0.343500	+	0.939153i	$0.611613\pi$
$384$	6.16786	0.314752
$385$	2.48900	0.126851
$386$	12.6946	0.646138
$387$	−3.59057	−0.182519
$388$	−2.33863	−0.118726
$389$	−29.4157	−1.49144	−0.745718	−	0.666262i	$-0.767893\pi$
$389$	−29.4157	−1.49144	−0.745718	+	0.666262i	$0.767893\pi$
$390$	5.27545	0.267133
$391$	0	0
$392$	19.5409	0.986965
$393$	−0.352120	−0.0177621
$394$	7.83132	0.394536
$395$	1.08864	0.0547755
$396$	−6.53683	−0.328488
$397$	9.61782	0.482704	0.241352	−	0.970438i	$-0.422409\pi$
$397$	9.61782	0.482704	0.241352	+	0.970438i	$0.422409\pi$
$398$	18.2384	0.914207
$399$	0.0938806	0.00469991
$400$	−0.225111	−0.0112556
$401$	−25.6966	−1.28323	−0.641613	−	0.767029i	$-0.721734\pi$
$401$	−25.6966	−1.28323	−0.641613	+	0.767029i	$0.721734\pi$
$402$	11.2981	0.563498
$403$	−8.08779	−0.402882
$404$	−19.0554	−0.948042
$405$	−1.00000	−0.0496904
$406$	−3.34049	−0.165786
$407$	12.8615	0.637519
$408$	16.7785	0.830657
$409$	24.4654	1.20974	0.604869	−	0.796325i	$-0.293226\pi$
$409$	24.4654	1.20974	0.604869	+	0.796325i	$0.293226\pi$
$410$	4.29872	0.212299
$411$	7.07002	0.348738
$412$	10.7506	0.529642
$413$	−2.36637	−0.116441
$414$	0	0
$415$	−7.73458	−0.379676
$416$	32.4187	1.58946
$417$	−21.2336	−1.03981
$418$	1.03580	0.0506628
$419$	18.8564	0.921196	0.460598	−	0.887609i	$-0.347635\pi$
$419$	18.8564	0.921196	0.460598	+	0.887609i	$0.347635\pi$
$420$	0.534816	0.0260964
$421$	−10.3993	−0.506832	−0.253416	−	0.967357i	$-0.581554\pi$
$421$	−10.3993	−0.506832	−0.253416	+	0.967357i	$0.581554\pi$
$422$	6.47455	0.315176
$423$	−11.6966	−0.568710
$424$	−28.0036	−1.35998
$425$	5.83557	0.283067
$426$	6.67960	0.323627
$427$	1.38759	0.0671502
$428$	12.0462	0.582277
$429$	−32.2340	−1.55627
$430$	3.24117	0.156303
$431$	24.7909	1.19414	0.597069	−	0.802190i	$-0.296332\pi$
$431$	24.7909	1.19414	0.597069	+	0.802190i	$0.296332\pi$
$432$	0.225111	0.0108307
$433$	13.5118	0.649334	0.324667	−	0.945828i	$-0.394748\pi$
$433$	13.5118	0.649334	0.324667	+	0.945828i	$0.394748\pi$
$434$	0.563739	0.0270603
$435$	8.20051	0.393184
$436$	−12.7093	−0.608663
$437$	0	0
$438$	−13.5277	−0.646381
$439$	−12.1355	−0.579195	−0.289597	−	0.957149i	$-0.593521\pi$
$439$	−12.1355	−0.579195	−0.289597	+	0.957149i	$0.593521\pi$
$440$	15.8585	0.756024
$441$	−6.79636	−0.323636
$442$	30.7853	1.46431
$443$	5.51167	0.261867	0.130934	−	0.991391i	$-0.458203\pi$
$443$	5.51167	0.261867	0.130934	+	0.991391i	$0.458203\pi$
$444$	2.76357	0.131153
$445$	0.255814	0.0121268
$446$	−13.1681	−0.623529
$447$	4.00600	0.189477
$448$	−2.46283	−0.116358
$449$	36.1197	1.70459	0.852297	−	0.523059i	$-0.175209\pi$
$449$	36.1197	1.70459	0.852297	+	0.523059i	$0.175209\pi$
$450$	0.902689	0.0425532
$451$	−26.2660	−1.23682
$452$	−19.1459	−0.900545
$453$	17.8347	0.837945
$454$	4.08205	0.191580
$455$	2.63725	0.123636
$456$	0.598155	0.0280112
$457$	−20.6656	−0.966695	−0.483347	−	0.875429i	$-0.660579\pi$
$457$	−20.6656	−0.966695	−0.483347	+	0.875429i	$0.660579\pi$
$458$	−19.5777	−0.914808
$459$	−5.83557	−0.272381
$460$	0	0
$461$	14.2672	0.664491	0.332246	−	0.943193i	$-0.392194\pi$
$461$	14.2672	0.664491	0.332246	+	0.943193i	$0.392194\pi$
$462$	2.24679	0.104530
$463$	4.04219	0.187857	0.0939283	−	0.995579i	$-0.470058\pi$
$463$	4.04219	0.187857	0.0939283	+	0.995579i	$0.470058\pi$
$464$	−1.84603	−0.0856997
$465$	−1.38391	−0.0641774
$466$	−4.36593	−0.202248
$467$	−31.0937	−1.43884	−0.719422	−	0.694574i	$-0.755593\pi$
$467$	−31.0937	−1.43884	−0.719422	+	0.694574i	$0.755593\pi$
$468$	−6.92620	−0.320164
$469$	5.64804	0.260802
$470$	10.5584	0.487024
$471$	17.8855	0.824123
$472$	−15.0772	−0.693984
$473$	−19.8042	−0.910596
$474$	0.982706	0.0451372
$475$	0.208039	0.00954550
$476$	3.12096	0.143049
$477$	9.73970	0.445950
$478$	−14.7253	−0.673522
$479$	4.40697	0.201360	0.100680	−	0.994919i	$-0.467898\pi$
$479$	4.40697	0.201360	0.100680	+	0.994919i	$0.467898\pi$
$480$	5.54720	0.253194
$481$	13.6276	0.621364
$482$	−13.0891	−0.596194
$483$	0	0
$484$	−23.0179	−1.04627
$485$	−1.97328	−0.0896019
$486$	−0.902689	−0.0409468
$487$	−16.2162	−0.734827	−0.367414	−	0.930058i	$-0.619757\pi$
$487$	−16.2162	−0.734827	−0.367414	+	0.930058i	$0.619757\pi$
$488$	8.84095	0.400211
$489$	−15.8412	−0.716363
$490$	6.13500	0.277151
$491$	−2.26919	−0.102407	−0.0512035	−	0.998688i	$-0.516306\pi$
$491$	−2.26919	−0.102407	−0.0512035	+	0.998688i	$0.516306\pi$
$492$	−5.64384	−0.254444
$493$	47.8547	2.15527
$494$	1.09750	0.0493789
$495$	−5.51561	−0.247908
$496$	0.311535	0.0139883
$497$	3.33920	0.149784
$498$	−6.98193	−0.312868
$499$	−8.29463	−0.371319	−0.185659	−	0.982614i	$-0.559442\pi$
$499$	−8.29463	−0.371319	−0.185659	+	0.982614i	$0.559442\pi$
$500$	1.18515	0.0530016
$501$	−8.82234	−0.394153
$502$	−14.1888	−0.633275
$503$	34.2829	1.52860	0.764299	−	0.644862i	$-0.223085\pi$
$503$	34.2829	1.52860	0.764299	+	0.644862i	$0.223085\pi$
$504$	1.29748	0.0577942
$505$	−16.0785	−0.715482
$506$	0	0
$507$	−21.1541	−0.939485
$508$	3.14001	0.139315
$509$	38.2259	1.69433	0.847167	−	0.531327i	$-0.178306\pi$
$509$	38.2259	1.69433	0.847167	+	0.531327i	$0.178306\pi$
$510$	5.26771	0.233258
$511$	−6.76266	−0.299163
$512$	−2.54322	−0.112396
$513$	−0.208039	−0.00918516
$514$	−5.09167	−0.224584
$515$	9.07103	0.399718
$516$	−4.25537	−0.187332
$517$	−64.5140	−2.83732
$518$	−0.949874	−0.0417351
$519$	−11.4303	−0.501734
$520$	16.8031	0.736865
$521$	4.97881	0.218125	0.109063	−	0.994035i	$-0.465215\pi$
$521$	4.97881	0.218125	0.109063	+	0.994035i	$0.465215\pi$
$522$	7.40251	0.323999
$523$	17.6252	0.770697	0.385348	−	0.922771i	$-0.374081\pi$
$523$	17.6252	0.770697	0.385348	+	0.922771i	$0.374081\pi$
$524$	−0.417316	−0.0182305
$525$	0.451264	0.0196948
$526$	−11.4181	−0.497852
$527$	−8.07593	−0.351793
$528$	1.24163	0.0540349
$529$	0	0
$530$	−8.79193	−0.381897
$531$	5.24387	0.227564
$532$	0.111263	0.00482385
$533$	−27.8306	−1.20548
$534$	0.230921	0.00999292
$535$	10.1643	0.439441
$536$	35.9862	1.55437
$537$	5.49009	0.236915
$538$	−12.8123	−0.552376
$539$	−37.4861	−1.61464
$540$	−1.18515	−0.0510008
$541$	1.30263	0.0560046	0.0280023	−	0.999608i	$-0.491085\pi$
$541$	1.30263	0.0560046	0.0280023	+	0.999608i	$0.491085\pi$
$542$	−10.6681	−0.458235
$543$	−2.49112	−0.106904
$544$	32.3711	1.38790
$545$	−10.7237	−0.459354
$546$	2.38062	0.101881
$547$	31.1879	1.33350	0.666748	−	0.745283i	$-0.267686\pi$
$547$	31.1879	1.33350	0.666748	+	0.745283i	$0.267686\pi$
$548$	8.37905	0.357935
$549$	−3.07490	−0.131233
$550$	4.97888	0.212300
$551$	1.70603	0.0726792
$552$	0	0
$553$	0.491265	0.0208907
$554$	19.6039	0.832891
$555$	2.33183	0.0989807
$556$	−25.1651	−1.06724
$557$	−5.43446	−0.230266	−0.115133	−	0.993350i	$-0.536729\pi$
$557$	−5.43446	−0.230266	−0.115133	+	0.993350i	$0.536729\pi$
$558$	−1.24924	−0.0528847
$559$	−20.9838	−0.887520
$560$	−0.101585	−0.00429274
$561$	−32.1867	−1.35893
$562$	−0.785105	−0.0331176
$563$	34.4066	1.45007	0.725033	−	0.688714i	$-0.241824\pi$
$563$	34.4066	1.45007	0.725033	+	0.688714i	$0.241824\pi$
$564$	−13.8623	−0.583707
$565$	−16.1548	−0.679636
$566$	13.4599	0.565760
$567$	−0.451264	−0.0189513
$568$	21.2755	0.892701
$569$	−36.2781	−1.52086	−0.760429	−	0.649421i	$-0.775011\pi$
$569$	−36.2781	−1.52086	−0.760429	+	0.649421i	$0.775011\pi$
$570$	0.187795	0.00786586
$571$	−31.1035	−1.30164	−0.650820	−	0.759232i	$-0.725575\pi$
$571$	−31.1035	−1.30164	−0.650820	+	0.759232i	$0.725575\pi$
$572$	−38.2022	−1.59732
$573$	5.50019	0.229774
$574$	1.93986	0.0809681
$575$	0	0
$576$	5.45762	0.227401
$577$	33.6827	1.40223	0.701115	−	0.713049i	$-0.252686\pi$
$577$	33.6827	1.40223	0.701115	+	0.713049i	$0.252686\pi$
$578$	15.3944	0.640322
$579$	−14.0631	−0.584442
$580$	9.71885	0.403553
$581$	−3.49034	−0.144804
$582$	−1.78126	−0.0738354
$583$	53.7204	2.22487
$584$	−43.0879	−1.78299
$585$	−5.84415	−0.241626
$586$	4.04842	0.167239
$587$	−15.2753	−0.630480	−0.315240	−	0.949012i	$-0.602085\pi$
$587$	−15.2753	−0.630480	−0.315240	+	0.949012i	$0.602085\pi$
$588$	−8.05472	−0.332171
$589$	−0.287908	−0.0118631
$590$	−4.73358	−0.194879
$591$	−8.67555	−0.356864
$592$	−0.524922	−0.0215742
$593$	4.71768	0.193732	0.0968660	−	0.995297i	$-0.469118\pi$
$593$	4.71768	0.193732	0.0968660	+	0.995297i	$0.469118\pi$
$594$	−4.97888	−0.204286
$595$	2.63338	0.107958
$596$	4.74771	0.194474
$597$	−20.2045	−0.826915
$598$	0	0
$599$	−31.1589	−1.27312	−0.636558	−	0.771229i	$-0.719642\pi$
$599$	−31.1589	−1.27312	−0.636558	+	0.771229i	$0.719642\pi$
$600$	2.87520	0.117380
$601$	−25.1326	−1.02518	−0.512590	−	0.858634i	$-0.671314\pi$
$601$	−25.1326	−1.02518	−0.512590	+	0.858634i	$0.671314\pi$
$602$	1.46262	0.0596120
$603$	−12.5160	−0.509693
$604$	21.1368	0.860043
$605$	−19.4219	−0.789614
$606$	−14.5138	−0.589585
$607$	−13.6489	−0.553992	−0.276996	−	0.960871i	$-0.589339\pi$
$607$	−13.6489	−0.553992	−0.276996	+	0.960871i	$0.589339\pi$
$608$	1.15404	0.0468023
$609$	3.70060	0.149956
$610$	2.77568	0.112384
$611$	−68.3568	−2.76542
$612$	−6.91604	−0.279564
$613$	−0.909738	−0.0367440	−0.0183720	−	0.999831i	$-0.505848\pi$
$613$	−0.909738	−0.0367440	−0.0183720	+	0.999831i	$0.505848\pi$
$614$	4.20576	0.169731
$615$	−4.76213	−0.192028
$616$	7.15637	0.288338
$617$	−9.04009	−0.363940	−0.181970	−	0.983304i	$-0.558247\pi$
$617$	−9.04009	−0.363940	−0.181970	+	0.983304i	$0.558247\pi$
$618$	8.18833	0.329383
$619$	−13.3945	−0.538372	−0.269186	−	0.963088i	$-0.586755\pi$
$619$	−13.3945	−0.538372	−0.269186	+	0.963088i	$0.586755\pi$
$620$	−1.64015	−0.0658699
$621$	0	0
$622$	24.9085	0.998738
$623$	0.115440	0.00462500
$624$	1.31558	0.0526655
$625$	1.00000	0.0400000
$626$	−20.2577	−0.809662
$627$	−1.14746	−0.0458253
$628$	21.1971	0.845856
$629$	13.6076	0.542569
$630$	0.407351	0.0162293
$631$	18.6711	0.743285	0.371643	−	0.928376i	$-0.378795\pi$
$631$	18.6711	0.743285	0.371643	+	0.928376i	$0.378795\pi$
$632$	3.13007	0.124507
$633$	−7.17251	−0.285082
$634$	13.8046	0.548251
$635$	2.64945	0.105140
$636$	11.5430	0.457711
$637$	−39.7189	−1.57372
$638$	40.8294	1.61645
$639$	−7.39966	−0.292726
$640$	6.16786	0.243806
$641$	−14.7690	−0.583341	−0.291671	−	0.956519i	$-0.594211\pi$
$641$	−14.7690	−0.583341	−0.291671	+	0.956519i	$0.594211\pi$
$642$	9.17521	0.362117
$643$	1.87582	0.0739750	0.0369875	−	0.999316i	$-0.488224\pi$
$643$	1.87582	0.0739750	0.0369875	+	0.999316i	$0.488224\pi$
$644$	0	0
$645$	−3.59057	−0.141378
$646$	1.09589	0.0431172
$647$	5.34867	0.210278	0.105139	−	0.994458i	$-0.466471\pi$
$647$	5.34867	0.210278	0.105139	+	0.994458i	$0.466471\pi$
$648$	−2.87520	−0.112949
$649$	28.9231	1.13533
$650$	5.27545	0.206920
$651$	−0.624510	−0.0244765
$652$	−18.7742	−0.735255
$653$	45.5457	1.78234	0.891170	−	0.453670i	$-0.149885\pi$
$653$	45.5457	1.78234	0.891170	+	0.453670i	$0.149885\pi$
$654$	−9.68020	−0.378526
$655$	−0.352120	−0.0137585
$656$	1.07201	0.0418549
$657$	14.9860	0.584661
$658$	4.76464	0.185745
$659$	−30.5338	−1.18943	−0.594714	−	0.803937i	$-0.702735\pi$
$659$	−30.5338	−1.18943	−0.594714	+	0.803937i	$0.702735\pi$
$660$	−6.53683	−0.254446
$661$	1.11403	0.0433309	0.0216655	−	0.999765i	$-0.493103\pi$
$661$	1.11403	0.0433309	0.0216655	+	0.999765i	$0.493103\pi$
$662$	19.9078	0.773738
$663$	−34.1040	−1.32449
$664$	−22.2385	−0.863021
$665$	0.0938806	0.00364053
$666$	2.10492	0.0815640
$667$	0	0
$668$	−10.4558	−0.404548
$669$	14.5877	0.563992
$670$	11.2981	0.436484
$671$	−16.9599	−0.654730
$672$	2.50325	0.0965650
$673$	−17.8536	−0.688206	−0.344103	−	0.938932i	$-0.611817\pi$
$673$	−17.8536	−0.688206	−0.344103	+	0.938932i	$0.611817\pi$
$674$	−9.77954	−0.376694
$675$	−1.00000	−0.0384900
$676$	−25.0708	−0.964261
$677$	−4.73699	−0.182057	−0.0910287	−	0.995848i	$-0.529016\pi$
$677$	−4.73699	−0.182057	−0.0910287	+	0.995848i	$0.529016\pi$
$678$	−14.5827	−0.560047
$679$	−0.890469	−0.0341731
$680$	16.7785	0.643424
$681$	−4.52210	−0.173287
$682$	−6.89034	−0.263845
$683$	−5.14675	−0.196935	−0.0984675	−	0.995140i	$-0.531394\pi$
$683$	−5.14675	−0.196935	−0.0984675	+	0.995140i	$0.531394\pi$
$684$	−0.246558	−0.00942738
$685$	7.07002	0.270132
$686$	5.61996	0.214571
$687$	21.6882	0.827458
$688$	0.808278	0.0308153
$689$	56.9203	2.16849
$690$	0	0
$691$	21.4106	0.814497	0.407249	−	0.913317i	$-0.366488\pi$
$691$	21.4106	0.814497	0.407249	+	0.913317i	$0.366488\pi$
$692$	−13.5466	−0.514965
$693$	−2.48900	−0.0945491
$694$	25.3404	0.961907
$695$	−21.2336	−0.805437
$696$	23.5781	0.893727
$697$	−27.7897	−1.05261
$698$	−4.95078	−0.187390
$699$	4.83658	0.182936
$700$	0.534816	0.0202142
$701$	−7.93840	−0.299829	−0.149915	−	0.988699i	$-0.547900\pi$
$701$	−7.93840	−0.299829	−0.149915	+	0.988699i	$0.547900\pi$
$702$	−5.27545	−0.199109
$703$	0.485112	0.0182964
$704$	30.1021	1.13452
$705$	−11.6966	−0.440520
$706$	−5.49695	−0.206880
$707$	−7.25563	−0.272876
$708$	6.21478	0.233566
$709$	41.7276	1.56711	0.783556	−	0.621321i	$-0.213404\pi$
$709$	41.7276	1.56711	0.783556	+	0.621321i	$0.213404\pi$
$710$	6.67960	0.250681
$711$	−1.08864	−0.0408273
$712$	0.735518	0.0275647
$713$	0	0
$714$	2.37713	0.0889618
$715$	−32.2340	−1.20548
$716$	6.50659	0.243163
$717$	16.3127	0.609211
$718$	−31.0773	−1.15979
$719$	−15.0039	−0.559552	−0.279776	−	0.960065i	$-0.590260\pi$
$719$	−15.0039	−0.559552	−0.279776	+	0.960065i	$0.590260\pi$
$720$	0.225111	0.00838941
$721$	4.09343	0.152447
$722$	−17.1120	−0.636844
$723$	14.5002	0.539267
$724$	−2.95235	−0.109723
$725$	8.20051	0.304559
$726$	−17.5320	−0.650673
$727$	20.3236	0.753761	0.376880	−	0.926262i	$-0.376997\pi$
$727$	20.3236	0.753761	0.376880	+	0.926262i	$0.376997\pi$
$728$	7.58264	0.281031
$729$	1.00000	0.0370370
$730$	−13.5277	−0.500684
$731$	−20.9530	−0.774975
$732$	−3.64422	−0.134694
$733$	30.4398	1.12432	0.562159	−	0.827029i	$-0.309971\pi$
$733$	30.4398	1.12432	0.562159	+	0.827029i	$0.309971\pi$
$734$	−6.40925	−0.236570
$735$	−6.79636	−0.250688
$736$	0	0
$737$	−69.0336	−2.54288
$738$	−4.29872	−0.158238
$739$	−5.99689	−0.220599	−0.110300	−	0.993898i	$-0.535181\pi$
$739$	−5.99689	−0.220599	−0.110300	+	0.993898i	$0.535181\pi$
$740$	2.76357	0.101591
$741$	−1.21581	−0.0446640
$742$	−3.96748	−0.145651
$743$	38.2154	1.40199	0.700993	−	0.713168i	$-0.252740\pi$
$743$	38.2154	1.40199	0.700993	+	0.713168i	$0.252740\pi$
$744$	−3.97903	−0.145878
$745$	4.00600	0.146768
$746$	5.43853	0.199119
$747$	7.73458	0.282994
$748$	−38.1462	−1.39476
$749$	4.58679	0.167598
$750$	0.902689	0.0329616
$751$	−7.60056	−0.277348	−0.138674	−	0.990338i	$-0.544284\pi$
$751$	−7.60056	−0.277348	−0.138674	+	0.990338i	$0.544284\pi$
$752$	2.63304	0.0960173
$753$	15.7183	0.572807
$754$	43.2614	1.57549
$755$	17.8347	0.649070
$756$	−0.534816	−0.0194511
$757$	28.9569	1.05246	0.526228	−	0.850343i	$-0.323606\pi$
$757$	28.9569	1.05246	0.526228	+	0.850343i	$0.323606\pi$
$758$	34.8728	1.26664
$759$	0	0
$760$	0.598155	0.0216974
$761$	38.0384	1.37889	0.689446	−	0.724337i	$-0.257854\pi$
$761$	38.0384	1.37889	0.689446	+	0.724337i	$0.257854\pi$
$762$	2.39163	0.0866398
$763$	−4.83923	−0.175192
$764$	6.51856	0.235833
$765$	−5.83557	−0.210986
$766$	−12.1365	−0.438511
$767$	30.6459	1.10656
$768$	16.4829	0.594776
$769$	4.43723	0.160011	0.0800053	−	0.996794i	$-0.474506\pi$
$769$	4.43723	0.160011	0.0800053	+	0.996794i	$0.474506\pi$
$770$	2.24679	0.0809687
$771$	5.64056	0.203140
$772$	−16.6669	−0.599854
$773$	−10.2798	−0.369739	−0.184870	−	0.982763i	$-0.559186\pi$
$773$	−10.2798	−0.369739	−0.184870	+	0.982763i	$0.559186\pi$
$774$	−3.24117	−0.116501
$775$	−1.38391	−0.0497116
$776$	−5.67357	−0.203669
$777$	1.05227	0.0377500
$778$	−26.5532	−0.951980
$779$	−0.990709	−0.0354959
$780$	−6.92620	−0.247998
$781$	−40.8136	−1.46043
$782$	0	0
$783$	−8.20051	−0.293062
$784$	1.52994	0.0546407
$785$	17.8855	0.638363
$786$	−0.317855	−0.0113375
$787$	1.24498	0.0443787	0.0221894	−	0.999754i	$-0.492936\pi$
$787$	1.24498	0.0443787	0.0221894	+	0.999754i	$0.492936\pi$
$788$	−10.2818	−0.366275
$789$	12.6489	0.450314
$790$	0.982706	0.0349631
$791$	−7.29007	−0.259205
$792$	−15.8585	−0.563507
$793$	−17.9701	−0.638138
$794$	8.68190	0.308109
$795$	9.73970	0.345432
$796$	−23.9454	−0.848722
$797$	29.1883	1.03390	0.516951	−	0.856015i	$-0.327067\pi$
$797$	29.1883	1.03390	0.516951	+	0.856015i	$0.327067\pi$
$798$	0.0847450	0.00299994
$799$	−68.2565	−2.41474
$800$	5.54720	0.196123
$801$	−0.255814	−0.00903875
$802$	−23.1960	−0.819080
$803$	82.6572	2.91691
$804$	−14.8334	−0.523134
$805$	0	0
$806$	−7.30077	−0.257159
$807$	14.1934	0.499633
$808$	−46.2288	−1.62632
$809$	1.79208	0.0630061	0.0315030	−	0.999504i	$-0.489971\pi$
$809$	1.79208	0.0630061	0.0315030	+	0.999504i	$0.489971\pi$
$810$	−0.902689	−0.0317173
$811$	17.8990	0.628520	0.314260	−	0.949337i	$-0.398244\pi$
$811$	17.8990	0.628520	0.314260	+	0.949337i	$0.398244\pi$
$812$	4.38577	0.153910
$813$	11.8181	0.414480
$814$	11.6099	0.406927
$815$	−15.8412	−0.554892
$816$	1.31365	0.0459871
$817$	−0.746979	−0.0261335
$818$	22.0847	0.772173
$819$	−2.63725	−0.0921531
$820$	−5.64384	−0.197092
$821$	−26.0101	−0.907760	−0.453880	−	0.891063i	$-0.649961\pi$
$821$	−26.0101	−0.907760	−0.453880	+	0.891063i	$0.649961\pi$
$822$	6.38203	0.222599
$823$	−9.64634	−0.336250	−0.168125	−	0.985766i	$-0.553771\pi$
$823$	−9.64634	−0.336250	−0.168125	+	0.985766i	$0.553771\pi$
$824$	26.0811	0.908577
$825$	−5.51561	−0.192029
$826$	−2.13610	−0.0743243
$827$	6.00020	0.208647	0.104324	−	0.994543i	$-0.466732\pi$
$827$	6.00020	0.208647	0.104324	+	0.994543i	$0.466732\pi$
$828$	0	0
$829$	40.0471	1.39089	0.695447	−	0.718578i	$-0.255207\pi$
$829$	40.0471	1.39089	0.695447	+	0.718578i	$0.255207\pi$
$830$	−6.98193	−0.242346
$831$	−21.7172	−0.753363
$832$	31.8951	1.10577
$833$	−39.6607	−1.37416
$834$	−19.1674	−0.663711
$835$	−8.82234	−0.305310
$836$	−1.35992	−0.0470337
$837$	1.38391	0.0478350
$838$	17.0215	0.587997
$839$	−20.1378	−0.695233	−0.347616	−	0.937637i	$-0.613009\pi$
$839$	−20.1378	−0.695233	−0.347616	+	0.937637i	$0.613009\pi$
$840$	1.29748	0.0447672
$841$	38.2484	1.31891
$842$	−9.38737	−0.323510
$843$	0.869740	0.0299554
$844$	−8.50051	−0.292600
$845$	−21.1541	−0.727722
$846$	−10.5584	−0.363006
$847$	−8.76442	−0.301149
$848$	−2.19252	−0.0752914
$849$	−14.9108	−0.511739
$850$	5.26771	0.180681
$851$	0	0
$852$	−8.76972	−0.300446
$853$	−36.1845	−1.23893	−0.619467	−	0.785023i	$-0.712651\pi$
$853$	−36.1845	−1.23893	−0.619467	+	0.785023i	$0.712651\pi$
$854$	1.25256	0.0428618
$855$	−0.208039	−0.00711479
$856$	29.2244	0.998871
$857$	−53.9955	−1.84445	−0.922225	−	0.386653i	$-0.873631\pi$
$857$	−53.9955	−1.84445	−0.922225	+	0.386653i	$0.873631\pi$
$858$	−29.0973	−0.993366
$859$	16.5663	0.565233	0.282617	−	0.959233i	$-0.408798\pi$
$859$	16.5663	0.565233	0.282617	+	0.959233i	$0.408798\pi$
$860$	−4.25537	−0.145107
$861$	−2.14898	−0.0732369
$862$	22.3785	0.762215
$863$	0.0644337	0.00219335	0.00109667	−	0.999999i	$-0.499651\pi$
$863$	0.0644337	0.00219335	0.00109667	+	0.999999i	$0.499651\pi$
$864$	−5.54720	−0.188720
$865$	−11.4303	−0.388641
$866$	12.1969	0.414468
$867$	−17.0539	−0.579181
$868$	−0.740139	−0.0251220
$869$	−6.00452	−0.203689
$870$	7.40251	0.250969
$871$	−73.1456	−2.47844
$872$	−30.8329	−1.04413
$873$	1.97328	0.0667853
$874$	0	0
$875$	0.451264	0.0152555
$876$	17.7607	0.600080
$877$	11.1697	0.377176	0.188588	−	0.982056i	$-0.439609\pi$
$877$	11.1697	0.377176	0.188588	+	0.982056i	$0.439609\pi$
$878$	−10.9546	−0.369699
$879$	−4.48484	−0.151270
$880$	1.24163	0.0418552
$881$	−47.4050	−1.59711	−0.798557	−	0.601919i	$-0.794403\pi$
$881$	−47.4050	−1.59711	−0.798557	+	0.601919i	$0.794403\pi$
$882$	−6.13500	−0.206576
$883$	3.16892	0.106643	0.0533214	−	0.998577i	$-0.483019\pi$
$883$	3.16892	0.106643	0.0533214	+	0.998577i	$0.483019\pi$
$884$	−40.4184	−1.35942
$885$	5.24387	0.176271
$886$	4.97532	0.167149
$887$	7.97933	0.267920	0.133960	−	0.990987i	$-0.457231\pi$
$887$	7.97933	0.267920	0.133960	+	0.990987i	$0.457231\pi$
$888$	6.70449	0.224988
$889$	1.19560	0.0400993
$890$	0.230921	0.00774048
$891$	5.51561	0.184780
$892$	17.2886	0.578865
$893$	−2.43336	−0.0814292
$894$	3.61617	0.120943
$895$	5.49009	0.183513
$896$	2.78333	0.0929847
$897$	0	0
$898$	32.6049	1.08804
$899$	−11.3488	−0.378503
$900$	−1.18515	−0.0395051
$901$	56.8368	1.89351
$902$	−23.7101	−0.789459
$903$	−1.62029	−0.0539200
$904$	−46.4482	−1.54485
$905$	−2.49112	−0.0828076
$906$	16.0992	0.534859
$907$	38.5554	1.28021	0.640105	−	0.768288i	$-0.278891\pi$
$907$	38.5554	1.28021	0.640105	+	0.768288i	$0.278891\pi$
$908$	−5.35937	−0.177857
$909$	16.0785	0.533289
$910$	2.38062	0.0789168
$911$	−30.3591	−1.00584	−0.502921	−	0.864333i	$-0.667741\pi$
$911$	−30.3591	−1.00584	−0.502921	+	0.864333i	$0.667741\pi$
$912$	0.0468320	0.00155076
$913$	42.6609	1.41187
$914$	−18.6546	−0.617039
$915$	−3.07490	−0.101653
$916$	25.7039	0.849280
$917$	−0.158899	−0.00524731
$918$	−5.26771	−0.173860
$919$	7.58946	0.250353	0.125177	−	0.992134i	$-0.460050\pi$
$919$	7.58946	0.250353	0.125177	+	0.992134i	$0.460050\pi$
$920$	0	0
$921$	−4.65915	−0.153524
$922$	12.8789	0.424143
$923$	−43.2447	−1.42342
$924$	−2.94984	−0.0970425
$925$	2.33183	0.0766702
$926$	3.64885	0.119909
$927$	−9.07103	−0.297932
$928$	45.4899	1.49328
$929$	−4.35474	−0.142874	−0.0714372	−	0.997445i	$-0.522759\pi$
$929$	−4.35474	−0.142874	−0.0714372	+	0.997445i	$0.522759\pi$
$930$	−1.24924	−0.0409643
$931$	−1.41391	−0.0463390
$932$	5.73209	0.187761
$933$	−27.5936	−0.903374
$934$	−28.0679	−0.918410
$935$	−32.1867	−1.05262
$936$	−16.8031	−0.549227
$937$	43.2848	1.41405	0.707027	−	0.707187i	$-0.250036\pi$
$937$	43.2848	1.41405	0.707027	+	0.707187i	$0.250036\pi$
$938$	5.09842	0.166469
$939$	22.4415	0.732352
$940$	−13.8623	−0.452138
$941$	31.1698	1.01611	0.508053	−	0.861326i	$-0.330365\pi$
$941$	31.1698	1.01611	0.508053	+	0.861326i	$0.330365\pi$
$942$	16.1451	0.526036
$943$	0	0
$944$	−1.18045	−0.0384205
$945$	−0.451264	−0.0146796
$946$	−17.8770	−0.581232
$947$	−15.3001	−0.497187	−0.248594	−	0.968608i	$-0.579968\pi$
$947$	−15.3001	−0.497187	−0.248594	+	0.968608i	$0.579968\pi$
$948$	−1.29021	−0.0419039
$949$	87.5807	2.84299
$950$	0.187795	0.00609287
$951$	−15.2928	−0.495902
$952$	7.57151	0.245394
$953$	52.9152	1.71409	0.857046	−	0.515239i	$-0.172297\pi$
$953$	52.9152	1.71409	0.857046	+	0.515239i	$0.172297\pi$
$954$	8.79193	0.284649
$955$	5.50019	0.177982
$956$	19.3331	0.625277
$957$	−45.2308	−1.46210
$958$	3.97813	0.128527
$959$	3.19044	0.103025
$960$	5.45762	0.176144
$961$	−29.0848	−0.938219
$962$	12.3015	0.396615
$963$	−10.1643	−0.327540
$964$	17.1849	0.553488
$965$	−14.0631	−0.452707
$966$	0	0
$967$	36.0063	1.15788	0.578942	−	0.815369i	$-0.303466\pi$
$967$	36.0063	1.15788	0.578942	+	0.815369i	$0.303466\pi$
$968$	−55.8420	−1.79483
$969$	−1.21403	−0.0390002
$970$	−1.78126	−0.0571927
$971$	41.3764	1.32783	0.663916	−	0.747807i	$-0.268893\pi$
$971$	41.3764	1.32783	0.663916	+	0.747807i	$0.268893\pi$
$972$	1.18515	0.0380138
$973$	−9.58197	−0.307184
$974$	−14.6382	−0.469039
$975$	−5.84415	−0.187163
$976$	0.692194	0.0221566
$977$	17.8917	0.572408	0.286204	−	0.958169i	$-0.407607\pi$
$977$	17.8917	0.572408	0.286204	+	0.958169i	$0.407607\pi$
$978$	−14.2997	−0.457253
$979$	−1.41097	−0.0450948
$980$	−8.05472	−0.257299
$981$	10.7237	0.342382
$982$	−2.04837	−0.0653662
$983$	30.4187	0.970206	0.485103	−	0.874457i	$-0.338782\pi$
$983$	30.4187	0.970206	0.485103	+	0.874457i	$0.338782\pi$
$984$	−13.6921	−0.436488
$985$	−8.67555	−0.276426
$986$	43.1979	1.37570
$987$	−5.27827	−0.168009
$988$	−1.44092	−0.0458418
$989$	0	0
$990$	−4.97888	−0.158239
$991$	−30.5814	−0.971451	−0.485725	−	0.874112i	$-0.661444\pi$
$991$	−30.5814	−0.971451	−0.485725	+	0.874112i	$0.661444\pi$
$992$	−7.67684	−0.243740
$993$	−22.0539	−0.699858
$994$	3.01426	0.0956066
$995$	−20.2045	−0.640525
$996$	9.16665	0.290457
$997$	−36.4988	−1.15593	−0.577965	−	0.816062i	$-0.696153\pi$
$997$	−36.4988	−1.15593	−0.577965	+	0.816062i	$0.696153\pi$
$998$	−7.48748	−0.237012
$999$	−2.33183	−0.0737759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bt.1.16		25
23.7	odd	22		345.2.m.d.256.3	yes	50
23.10	odd	22		345.2.m.d.31.3	✓	50
23.22	odd	2		7935.2.a.bu.1.16		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.31.3	✓	50	23.10	odd	22
345.2.m.d.256.3	yes	50	23.7	odd	22
7935.2.a.bt.1.16		25	1.1	even	1	trivial
7935.2.a.bu.1.16		25	23.22	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.902689 q^{2} -1.00000 q^{3} -1.18515 q^{4} -1.00000 q^{5} -0.902689 q^{6} -0.451264 q^{7} -2.87520 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.902689 q^{2} -1.00000 q^{3} -1.18515 q^{4} -1.00000 q^{5} -0.902689 q^{6} -0.451264 q^{7} -2.87520 q^{8} +1.00000 q^{9} -0.902689 q^{10} +5.51561 q^{11} +1.18515 q^{12} +5.84415 q^{13} -0.407351 q^{14} +1.00000 q^{15} -0.225111 q^{16} +5.83557 q^{17} +0.902689 q^{18} +0.208039 q^{19} +1.18515 q^{20} +0.451264 q^{21} +4.97888 q^{22} +2.87520 q^{24} +1.00000 q^{25} +5.27545 q^{26} -1.00000 q^{27} +0.534816 q^{28} +8.20051 q^{29} +0.902689 q^{30} -1.38391 q^{31} +5.54720 q^{32} -5.51561 q^{33} +5.26771 q^{34} +0.451264 q^{35} -1.18515 q^{36} +2.33183 q^{37} +0.187795 q^{38} -5.84415 q^{39} +2.87520 q^{40} -4.76213 q^{41} +0.407351 q^{42} -3.59057 q^{43} -6.53683 q^{44} -1.00000 q^{45} -11.6966 q^{47} +0.225111 q^{48} -6.79636 q^{49} +0.902689 q^{50} -5.83557 q^{51} -6.92620 q^{52} +9.73970 q^{53} -0.902689 q^{54} -5.51561 q^{55} +1.29748 q^{56} -0.208039 q^{57} +7.40251 q^{58} +5.24387 q^{59} -1.18515 q^{60} -3.07490 q^{61} -1.24924 q^{62} -0.451264 q^{63} +5.45762 q^{64} -5.84415 q^{65} -4.97888 q^{66} -12.5160 q^{67} -6.91604 q^{68} +0.407351 q^{70} -7.39966 q^{71} -2.87520 q^{72} +14.9860 q^{73} +2.10492 q^{74} -1.00000 q^{75} -0.246558 q^{76} -2.48900 q^{77} -5.27545 q^{78} -1.08864 q^{79} +0.225111 q^{80} +1.00000 q^{81} -4.29872 q^{82} +7.73458 q^{83} -0.534816 q^{84} -5.83557 q^{85} -3.24117 q^{86} -8.20051 q^{87} -15.8585 q^{88} -0.255814 q^{89} -0.902689 q^{90} -2.63725 q^{91} +1.38391 q^{93} -10.5584 q^{94} -0.208039 q^{95} -5.54720 q^{96} +1.97328 q^{97} -6.13500 q^{98} +5.51561 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} - 25 q^{5} - q^{6} + 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 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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