LMFDB - Embedded newform 7935.2.a.bu.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.21553 q^{2} -1.00000 q^{3} -0.522493 q^{4} +1.00000 q^{5} +1.21553 q^{6} +3.08881 q^{7} +3.06616 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.21553 q^{2} -1.00000 q^{3} -0.522493 q^{4} +1.00000 q^{5} +1.21553 q^{6} +3.08881 q^{7} +3.06616 q^{8} +1.00000 q^{9} -1.21553 q^{10} +4.01380 q^{11} +0.522493 q^{12} +1.19054 q^{13} -3.75453 q^{14} -1.00000 q^{15} -2.68202 q^{16} -2.35101 q^{17} -1.21553 q^{18} +3.32407 q^{19} -0.522493 q^{20} -3.08881 q^{21} -4.87888 q^{22} -3.06616 q^{24} +1.00000 q^{25} -1.44713 q^{26} -1.00000 q^{27} -1.61388 q^{28} +5.62894 q^{29} +1.21553 q^{30} +4.99808 q^{31} -2.87226 q^{32} -4.01380 q^{33} +2.85771 q^{34} +3.08881 q^{35} -0.522493 q^{36} +2.34927 q^{37} -4.04050 q^{38} -1.19054 q^{39} +3.06616 q^{40} -6.02290 q^{41} +3.75453 q^{42} +9.78307 q^{43} -2.09718 q^{44} +1.00000 q^{45} +3.51641 q^{47} +2.68202 q^{48} +2.54072 q^{49} -1.21553 q^{50} +2.35101 q^{51} -0.622048 q^{52} -0.158885 q^{53} +1.21553 q^{54} +4.01380 q^{55} +9.47077 q^{56} -3.32407 q^{57} -6.84213 q^{58} +2.12951 q^{59} +0.522493 q^{60} +2.60525 q^{61} -6.07531 q^{62} +3.08881 q^{63} +8.85534 q^{64} +1.19054 q^{65} +4.87888 q^{66} +3.86196 q^{67} +1.22838 q^{68} -3.75453 q^{70} +1.86463 q^{71} +3.06616 q^{72} -10.3825 q^{73} -2.85561 q^{74} -1.00000 q^{75} -1.73680 q^{76} +12.3978 q^{77} +1.44713 q^{78} -1.91663 q^{79} -2.68202 q^{80} +1.00000 q^{81} +7.32100 q^{82} +10.1496 q^{83} +1.61388 q^{84} -2.35101 q^{85} -11.8916 q^{86} -5.62894 q^{87} +12.3070 q^{88} +17.0223 q^{89} -1.21553 q^{90} +3.67734 q^{91} -4.99808 q^{93} -4.27430 q^{94} +3.32407 q^{95} +2.87226 q^{96} -17.8701 q^{97} -3.08831 q^{98} +4.01380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.21553	−0.859508	−0.429754	−	0.902946i	$-0.641400\pi$
$2$	−1.21553	−0.859508	−0.429754	+	0.902946i	$0.641400\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−0.522493	−0.261246
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.21553	0.496237
$7$	3.08881	1.16746	0.583729	−	0.811948i	$-0.301593\pi$
$7$	3.08881	1.16746	0.583729	+	0.811948i	$0.301593\pi$
$8$	3.06616	1.08405
$9$	1.00000	0.333333
$10$	−1.21553	−0.384384
$11$	4.01380	1.21021	0.605103	−	0.796147i	$-0.293132\pi$
$11$	4.01380	1.21021	0.605103	+	0.796147i	$0.293132\pi$
$12$	0.522493	0.150831
$13$	1.19054	0.330196	0.165098	−	0.986277i	$-0.447206\pi$
$13$	1.19054	0.330196	0.165098	+	0.986277i	$0.447206\pi$
$14$	−3.75453	−1.00344
$15$	−1.00000	−0.258199
$16$	−2.68202	−0.670504
$17$	−2.35101	−0.570203	−0.285101	−	0.958497i	$-0.592027\pi$
$17$	−2.35101	−0.570203	−0.285101	+	0.958497i	$0.592027\pi$
$18$	−1.21553	−0.286503
$19$	3.32407	0.762594	0.381297	−	0.924453i	$-0.375478\pi$
$19$	3.32407	0.762594	0.381297	+	0.924453i	$0.375478\pi$
$20$	−0.522493	−0.116833
$21$	−3.08881	−0.674033
$22$	−4.87888	−1.04018
$23$	0	0
$23$	0	0
$24$	−3.06616	−0.625877
$25$	1.00000	0.200000
$26$	−1.44713	−0.283806
$27$	−1.00000	−0.192450
$28$	−1.61388	−0.304994
$29$	5.62894	1.04527	0.522634	−	0.852557i	$-0.324949\pi$
$29$	5.62894	1.04527	0.522634	+	0.852557i	$0.324949\pi$
$30$	1.21553	0.221924
$31$	4.99808	0.897682	0.448841	−	0.893612i	$-0.351837\pi$
$31$	4.99808	0.897682	0.448841	+	0.893612i	$0.351837\pi$
$32$	−2.87226	−0.507748
$33$	−4.01380	−0.698713
$34$	2.85771	0.490094
$35$	3.08881	0.522103
$36$	−0.522493	−0.0870822
$37$	2.34927	0.386218	0.193109	−	0.981177i	$-0.438143\pi$
$37$	2.34927	0.386218	0.193109	+	0.981177i	$0.438143\pi$
$38$	−4.04050	−0.655456
$39$	−1.19054	−0.190639
$40$	3.06616	0.484802
$41$	−6.02290	−0.940618	−0.470309	−	0.882502i	$-0.655858\pi$
$41$	−6.02290	−0.940618	−0.470309	+	0.882502i	$0.655858\pi$
$42$	3.75453	0.579336
$43$	9.78307	1.49190	0.745952	−	0.666000i	$-0.231995\pi$
$43$	9.78307	1.49190	0.745952	+	0.666000i	$0.231995\pi$
$44$	−2.09718	−0.316162
$45$	1.00000	0.149071
$46$	0	0
$47$	3.51641	0.512921	0.256461	−	0.966555i	$-0.417444\pi$
$47$	3.51641	0.512921	0.256461	+	0.966555i	$0.417444\pi$
$48$	2.68202	0.387116
$49$	2.54072	0.362960
$50$	−1.21553	−0.171902
$51$	2.35101	0.329207
$52$	−0.622048	−0.0862625
$53$	−0.158885	−0.0218245	−0.0109123	−	0.999940i	$-0.503474\pi$
$53$	−0.158885	−0.0218245	−0.0109123	+	0.999940i	$0.503474\pi$
$54$	1.21553	0.165412
$55$	4.01380	0.541221
$56$	9.47077	1.26558
$57$	−3.32407	−0.440284
$58$	−6.84213	−0.898416
$59$	2.12951	0.277238	0.138619	−	0.990346i	$-0.455734\pi$
$59$	2.12951	0.277238	0.138619	+	0.990346i	$0.455734\pi$
$60$	0.522493	0.0674536
$61$	2.60525	0.333567	0.166784	−	0.985994i	$-0.446662\pi$
$61$	2.60525	0.333567	0.166784	+	0.985994i	$0.446662\pi$
$62$	−6.07531	−0.771565
$63$	3.08881	0.389153
$64$	8.85534	1.10692
$65$	1.19054	0.147668
$66$	4.87888	0.600549
$67$	3.86196	0.471814	0.235907	−	0.971776i	$-0.424194\pi$
$67$	3.86196	0.471814	0.235907	+	0.971776i	$0.424194\pi$
$68$	1.22838	0.148963
$69$	0	0
$70$	−3.75453	−0.448752
$71$	1.86463	0.221291	0.110645	−	0.993860i	$-0.464708\pi$
$71$	1.86463	0.221291	0.110645	+	0.993860i	$0.464708\pi$
$72$	3.06616	0.361350
$73$	−10.3825	−1.21518	−0.607591	−	0.794250i	$-0.707864\pi$
$73$	−10.3825	−1.21518	−0.607591	+	0.794250i	$0.707864\pi$
$74$	−2.85561	−0.331958
$75$	−1.00000	−0.115470
$76$	−1.73680	−0.199225
$77$	12.3978	1.41287
$78$	1.44713	0.163855
$79$	−1.91663	−0.215638	−0.107819	−	0.994171i	$-0.534387\pi$
$79$	−1.91663	−0.215638	−0.107819	+	0.994171i	$0.534387\pi$
$80$	−2.68202	−0.299858
$81$	1.00000	0.111111
$82$	7.32100	0.808469
$83$	10.1496	1.11406	0.557030	−	0.830492i	$-0.311941\pi$
$83$	10.1496	1.11406	0.557030	+	0.830492i	$0.311941\pi$
$84$	1.61388	0.176089
$85$	−2.35101	−0.255002
$86$	−11.8916	−1.28230
$87$	−5.62894	−0.603486
$88$	12.3070	1.31193
$89$	17.0223	1.80436	0.902182	−	0.431356i	$-0.141965\pi$
$89$	17.0223	1.80436	0.902182	+	0.431356i	$0.141965\pi$
$90$	−1.21553	−0.128128
$91$	3.67734	0.385490
$92$	0	0
$93$	−4.99808	−0.518277
$94$	−4.27430	−0.440860
$95$	3.32407	0.341042
$96$	2.87226	0.293148
$97$	−17.8701	−1.81443	−0.907216	−	0.420664i	$-0.861797\pi$
$97$	−17.8701	−1.81443	−0.907216	+	0.420664i	$0.861797\pi$
$98$	−3.08831	−0.311967
$99$	4.01380	0.403402
$100$	−0.522493	−0.0522493
$101$	1.69600	0.168759	0.0843794	−	0.996434i	$-0.473109\pi$
$101$	1.69600	0.168759	0.0843794	+	0.996434i	$0.473109\pi$
$102$	−2.85771	−0.282956
$103$	−5.75129	−0.566691	−0.283346	−	0.959018i	$-0.591444\pi$
$103$	−5.75129	−0.566691	−0.283346	+	0.959018i	$0.591444\pi$
$104$	3.65038	0.357949
$105$	−3.08881	−0.301437
$106$	0.193129	0.0187584
$107$	19.1203	1.84843	0.924214	−	0.381876i	$-0.124722\pi$
$107$	19.1203	1.84843	0.924214	+	0.381876i	$0.124722\pi$
$108$	0.522493	0.0502769
$109$	20.3151	1.94583	0.972915	−	0.231162i	$-0.0742528\pi$
$109$	20.3151	1.94583	0.972915	+	0.231162i	$0.0742528\pi$
$110$	−4.87888	−0.465183
$111$	−2.34927	−0.222983
$112$	−8.28422	−0.782785
$113$	8.90008	0.837249	0.418625	−	0.908159i	$-0.362512\pi$
$113$	8.90008	0.837249	0.418625	+	0.908159i	$0.362512\pi$
$114$	4.04050	0.378427
$115$	0	0
$116$	−2.94108	−0.273073
$117$	1.19054	0.110065
$118$	−2.58847	−0.238288
$119$	−7.26180	−0.665688
$120$	−3.06616	−0.279901
$121$	5.11060	0.464600
$122$	−3.16675	−0.286704
$123$	6.02290	0.543066
$124$	−2.61146	−0.234516
$125$	1.00000	0.0894427
$126$	−3.75453	−0.334480
$127$	15.5113	1.37641	0.688204	−	0.725517i	$-0.258399\pi$
$127$	15.5113	1.37641	0.688204	+	0.725517i	$0.258399\pi$
$128$	−5.01939	−0.443656
$129$	−9.78307	−0.861351
$130$	−1.44713	−0.126922
$131$	−18.1134	−1.58257	−0.791286	−	0.611446i	$-0.790588\pi$
$131$	−18.1134	−1.58257	−0.791286	+	0.611446i	$0.790588\pi$
$132$	2.09718	0.182536
$133$	10.2674	0.890297
$134$	−4.69432	−0.405528
$135$	−1.00000	−0.0860663
$136$	−7.20856	−0.618129
$137$	−14.6849	−1.25461	−0.627307	−	0.778772i	$-0.715843\pi$
$137$	−14.6849	−1.25461	−0.627307	+	0.778772i	$0.715843\pi$
$138$	0	0
$139$	−3.13987	−0.266321	−0.133160	−	0.991095i	$-0.542512\pi$
$139$	−3.13987	−0.266321	−0.133160	+	0.991095i	$0.542512\pi$
$140$	−1.61388	−0.136398
$141$	−3.51641	−0.296135
$142$	−2.26651	−0.190201
$143$	4.77858	0.399605
$144$	−2.68202	−0.223501
$145$	5.62894	0.467458
$146$	12.6202	1.04446
$147$	−2.54072	−0.209555
$148$	−1.22748	−0.100898
$149$	−18.1830	−1.48961	−0.744806	−	0.667282i	$-0.767458\pi$
$149$	−18.1830	−1.48961	−0.744806	+	0.667282i	$0.767458\pi$
$150$	1.21553	0.0992474
$151$	1.38458	0.112676	0.0563378	−	0.998412i	$-0.482058\pi$
$151$	1.38458	0.112676	0.0563378	+	0.998412i	$0.482058\pi$
$152$	10.1921	0.826691
$153$	−2.35101	−0.190068
$154$	−15.0699	−1.21437
$155$	4.99808	0.401456
$156$	0.622048	0.0498037
$157$	4.18595	0.334075	0.167038	−	0.985951i	$-0.446580\pi$
$157$	4.18595	0.334075	0.167038	+	0.985951i	$0.446580\pi$
$158$	2.32971	0.185342
$159$	0.158885	0.0126004
$160$	−2.87226	−0.227072
$161$	0	0
$162$	−1.21553	−0.0955009
$163$	−15.0145	−1.17602	−0.588012	−	0.808852i	$-0.700089\pi$
$163$	−15.0145	−1.17602	−0.588012	+	0.808852i	$0.700089\pi$
$164$	3.14692	0.245733
$165$	−4.01380	−0.312474
$166$	−12.3371	−0.957543
$167$	−2.89687	−0.224166	−0.112083	−	0.993699i	$-0.535752\pi$
$167$	−2.89687	−0.224166	−0.112083	+	0.993699i	$0.535752\pi$
$168$	−9.47077	−0.730686
$169$	−11.5826	−0.890971
$170$	2.85771	0.219177
$171$	3.32407	0.254198
$172$	−5.11159	−0.389755
$173$	0.395846	0.0300956	0.0150478	−	0.999887i	$-0.495210\pi$
$173$	0.395846	0.0300956	0.0150478	+	0.999887i	$0.495210\pi$
$174$	6.84213	0.518701
$175$	3.08881	0.233492
$176$	−10.7651	−0.811448
$177$	−2.12951	−0.160063
$178$	−20.6911	−1.55086
$179$	10.7201	0.801255	0.400627	−	0.916241i	$-0.368792\pi$
$179$	10.7201	0.801255	0.400627	+	0.916241i	$0.368792\pi$
$180$	−0.522493	−0.0389443
$181$	−10.6133	−0.788880	−0.394440	−	0.918922i	$-0.629061\pi$
$181$	−10.6133	−0.788880	−0.394440	+	0.918922i	$0.629061\pi$
$182$	−4.46991	−0.331332
$183$	−2.60525	−0.192585
$184$	0	0
$185$	2.34927	0.172722
$186$	6.07531	0.445463
$187$	−9.43647	−0.690063
$188$	−1.83730	−0.133999
$189$	−3.08881	−0.224678
$190$	−4.04050	−0.293129
$191$	−16.9111	−1.22364	−0.611821	−	0.790996i	$-0.709563\pi$
$191$	−16.9111	−1.22364	−0.611821	+	0.790996i	$0.709563\pi$
$192$	−8.85534	−0.639079
$193$	11.2308	0.808410	0.404205	−	0.914668i	$-0.367548\pi$
$193$	11.2308	0.808410	0.404205	+	0.914668i	$0.367548\pi$
$194$	21.7216	1.55952
$195$	−1.19054	−0.0852562
$196$	−1.32751	−0.0948219
$197$	−22.1637	−1.57910	−0.789551	−	0.613685i	$-0.789686\pi$
$197$	−22.1637	−1.57910	−0.789551	+	0.613685i	$0.789686\pi$
$198$	−4.87888	−0.346727
$199$	26.2402	1.86012	0.930059	−	0.367411i	$-0.119756\pi$
$199$	26.2402	1.86012	0.930059	+	0.367411i	$0.119756\pi$
$200$	3.06616	0.216810
$201$	−3.86196	−0.272402
$202$	−2.06154	−0.145049
$203$	17.3867	1.22031
$204$	−1.22838	−0.0860041
$205$	−6.02290	−0.420657
$206$	6.99085	0.487076
$207$	0	0
$208$	−3.19304	−0.221398
$209$	13.3422	0.922896
$210$	3.75453	0.259087
$211$	−22.7744	−1.56786	−0.783928	−	0.620852i	$-0.786787\pi$
$211$	−22.7744	−1.56786	−0.783928	+	0.620852i	$0.786787\pi$
$212$	0.0830163	0.00570159
$213$	−1.86463	−0.127762
$214$	−23.2412	−1.58874
$215$	9.78307	0.667200
$216$	−3.06616	−0.208626
$217$	15.4381	1.04801
$218$	−24.6935	−1.67246
$219$	10.3825	0.701586
$220$	−2.09718	−0.141392
$221$	−2.79896	−0.188279
$222$	2.85561	0.191656
$223$	−3.07167	−0.205694	−0.102847	−	0.994697i	$-0.532795\pi$
$223$	−3.07167	−0.205694	−0.102847	+	0.994697i	$0.532795\pi$
$224$	−8.87184	−0.592775
$225$	1.00000	0.0666667
$226$	−10.8183	−0.719622
$227$	−11.3943	−0.756266	−0.378133	−	0.925751i	$-0.623434\pi$
$227$	−11.3943	−0.756266	−0.378133	+	0.925751i	$0.623434\pi$
$228$	1.73680	0.115023
$229$	8.96396	0.592355	0.296177	−	0.955133i	$-0.404288\pi$
$229$	8.96396	0.592355	0.296177	+	0.955133i	$0.404288\pi$
$230$	0	0
$231$	−12.3978	−0.815719
$232$	17.2592	1.13312
$233$	−25.0223	−1.63927	−0.819633	−	0.572888i	$-0.805823\pi$
$233$	−25.0223	−1.63927	−0.819633	+	0.572888i	$0.805823\pi$
$234$	−1.44713	−0.0946020
$235$	3.51641	0.229385
$236$	−1.11265	−0.0724275
$237$	1.91663	0.124498
$238$	8.82692	0.572164
$239$	−17.0746	−1.10446	−0.552231	−	0.833691i	$-0.686223\pi$
$239$	−17.0746	−1.10446	−0.552231	+	0.833691i	$0.686223\pi$
$240$	2.68202	0.173123
$241$	0.0512173	0.00329920	0.00164960	−	0.999999i	$-0.499475\pi$
$241$	0.0512173	0.00329920	0.00164960	+	0.999999i	$0.499475\pi$
$242$	−6.21207	−0.399327
$243$	−1.00000	−0.0641500
$244$	−1.36122	−0.0871433
$245$	2.54072	0.162320
$246$	−7.32100	−0.466770
$247$	3.95743	0.251805
$248$	15.3249	0.973133
$249$	−10.1496	−0.643203
$250$	−1.21553	−0.0768767
$251$	21.3645	1.34852	0.674258	−	0.738496i	$-0.264464\pi$
$251$	21.3645	1.34852	0.674258	+	0.738496i	$0.264464\pi$
$252$	−1.61388	−0.101665
$253$	0	0
$254$	−18.8544	−1.18303
$255$	2.35101	0.147226
$256$	−11.6095	−0.725591
$257$	−24.3633	−1.51974	−0.759871	−	0.650074i	$-0.774738\pi$
$257$	−24.3633	−1.51974	−0.759871	+	0.650074i	$0.774738\pi$
$258$	11.8916	0.740338
$259$	7.25645	0.450894
$260$	−0.622048	−0.0385778
$261$	5.62894	0.348423
$262$	22.0173	1.36023
$263$	−29.5159	−1.82003	−0.910015	−	0.414575i	$-0.863930\pi$
$263$	−29.5159	−1.82003	−0.910015	+	0.414575i	$0.863930\pi$
$264$	−12.3070	−0.757441
$265$	−0.158885	−0.00976023
$266$	−12.4803	−0.765217
$267$	−17.0223	−1.04175
$268$	−2.01785	−0.123260
$269$	−9.82519	−0.599052	−0.299526	−	0.954088i	$-0.596829\pi$
$269$	−9.82519	−0.599052	−0.299526	+	0.954088i	$0.596829\pi$
$270$	1.21553	0.0739746
$271$	11.7984	0.716702	0.358351	−	0.933587i	$-0.383339\pi$
$271$	11.7984	0.716702	0.358351	+	0.933587i	$0.383339\pi$
$272$	6.30543	0.382323
$273$	−3.67734	−0.222563
$274$	17.8499	1.07835
$275$	4.01380	0.242041
$276$	0	0
$277$	22.8141	1.37076	0.685382	−	0.728184i	$-0.259635\pi$
$277$	22.8141	1.37076	0.685382	+	0.728184i	$0.259635\pi$
$278$	3.81660	0.228905
$279$	4.99808	0.299227
$280$	9.47077	0.565987
$281$	−4.50017	−0.268458	−0.134229	−	0.990950i	$-0.542856\pi$
$281$	−4.50017	−0.268458	−0.134229	+	0.990950i	$0.542856\pi$
$282$	4.27430	0.254531
$283$	13.9746	0.830702	0.415351	−	0.909661i	$-0.363659\pi$
$283$	13.9746	0.830702	0.415351	+	0.909661i	$0.363659\pi$
$284$	−0.974255	−0.0578114
$285$	−3.32407	−0.196901
$286$	−5.80850	−0.343464
$287$	−18.6036	−1.09813
$288$	−2.87226	−0.169249
$289$	−11.4728	−0.674869
$290$	−6.84213	−0.401784
$291$	17.8701	1.04756
$292$	5.42479	0.317462
$293$	−20.1093	−1.17480	−0.587400	−	0.809297i	$-0.699848\pi$
$293$	−20.1093	−1.17480	−0.587400	+	0.809297i	$0.699848\pi$
$294$	3.08831	0.180114
$295$	2.12951	0.123985
$296$	7.20325	0.418680
$297$	−4.01380	−0.232904
$298$	22.1020	1.28033
$299$	0	0
$300$	0.522493	0.0301661
$301$	30.2180	1.74174
$302$	−1.68300	−0.0968455
$303$	−1.69600	−0.0974329
$304$	−8.91521	−0.511322
$305$	2.60525	0.149176
$306$	2.85771	0.163365
$307$	34.8460	1.98877	0.994384	−	0.105833i	$-0.0337507\pi$
$307$	34.8460	1.98877	0.994384	+	0.105833i	$0.0337507\pi$
$308$	−6.47779	−0.369106
$309$	5.75129	0.327179
$310$	−6.07531	−0.345054
$311$	−17.5248	−0.993737	−0.496869	−	0.867826i	$-0.665517\pi$
$311$	−17.5248	−0.993737	−0.496869	+	0.867826i	$0.665517\pi$
$312$	−3.65038	−0.206662
$313$	−18.6188	−1.05240	−0.526198	−	0.850362i	$-0.676383\pi$
$313$	−18.6188	−1.05240	−0.526198	+	0.850362i	$0.676383\pi$
$314$	−5.08814	−0.287140
$315$	3.08881	0.174034
$316$	1.00142	0.0563346
$317$	−11.7113	−0.657773	−0.328886	−	0.944369i	$-0.606673\pi$
$317$	−11.7113	−0.657773	−0.328886	+	0.944369i	$0.606673\pi$
$318$	−0.193129	−0.0108301
$319$	22.5934	1.26499
$320$	8.85534	0.495028
$321$	−19.1203	−1.06719
$322$	0	0
$323$	−7.81491	−0.434833
$324$	−0.522493	−0.0290274
$325$	1.19054	0.0660392
$326$	18.2505	1.01080
$327$	−20.3151	−1.12343
$328$	−18.4672	−1.01968
$329$	10.8615	0.598815
$330$	4.87888	0.268574
$331$	−15.1478	−0.832600	−0.416300	−	0.909227i	$-0.636673\pi$
$331$	−15.1478	−0.832600	−0.416300	+	0.909227i	$0.636673\pi$
$332$	−5.30308	−0.291044
$333$	2.34927	0.128739
$334$	3.52122	0.192673
$335$	3.86196	0.211002
$336$	8.28422	0.451941
$337$	−23.2871	−1.26853	−0.634265	−	0.773116i	$-0.718697\pi$
$337$	−23.2871	−1.26853	−0.634265	+	0.773116i	$0.718697\pi$
$338$	14.0790	0.765796
$339$	−8.90008	−0.483386
$340$	1.22838	0.0666185
$341$	20.0613	1.08638
$342$	−4.04050	−0.218485
$343$	−13.7739	−0.743718
$344$	29.9965	1.61730
$345$	0	0
$346$	−0.481162	−0.0258674
$347$	10.9016	0.585226	0.292613	−	0.956231i	$-0.405475\pi$
$347$	10.9016	0.585226	0.292613	+	0.956231i	$0.405475\pi$
$348$	2.94108	0.157659
$349$	28.1373	1.50616	0.753078	−	0.657931i	$-0.228568\pi$
$349$	28.1373	1.50616	0.753078	+	0.657931i	$0.228568\pi$
$350$	−3.75453	−0.200688
$351$	−1.19054	−0.0635462
$352$	−11.5287	−0.614480
$353$	26.1617	1.39245	0.696223	−	0.717826i	$-0.254862\pi$
$353$	26.1617	1.39245	0.696223	+	0.717826i	$0.254862\pi$
$354$	2.58847	0.137576
$355$	1.86463	0.0989641
$356$	−8.89405	−0.471384
$357$	7.26180	0.384335
$358$	−13.0305	−0.688685
$359$	26.6560	1.40685	0.703425	−	0.710769i	$-0.251653\pi$
$359$	26.6560	1.40685	0.703425	+	0.710769i	$0.251653\pi$
$360$	3.06616	0.161601
$361$	−7.95055	−0.418450
$362$	12.9007	0.678048
$363$	−5.11060	−0.268237
$364$	−1.92138	−0.100708
$365$	−10.3825	−0.543446
$366$	3.16675	0.165529
$367$	−2.22036	−0.115902	−0.0579509	−	0.998319i	$-0.518457\pi$
$367$	−2.22036	−0.115902	−0.0579509	+	0.998319i	$0.518457\pi$
$368$	0	0
$369$	−6.02290	−0.313539
$370$	−2.85561	−0.148456
$371$	−0.490765	−0.0254793
$372$	2.61146	0.135398
$373$	−17.2400	−0.892656	−0.446328	−	0.894870i	$-0.647268\pi$
$373$	−17.2400	−0.892656	−0.446328	+	0.894870i	$0.647268\pi$
$374$	11.4703	0.593115
$375$	−1.00000	−0.0516398
$376$	10.7819	0.556033
$377$	6.70147	0.345143
$378$	3.75453	0.193112
$379$	11.5395	0.592745	0.296372	−	0.955072i	$-0.404223\pi$
$379$	11.5395	0.592745	0.296372	+	0.955072i	$0.404223\pi$
$380$	−1.73680	−0.0890961
$381$	−15.5113	−0.794669
$382$	20.5559	1.05173
$383$	13.9951	0.715116	0.357558	−	0.933891i	$-0.383610\pi$
$383$	13.9951	0.715116	0.357558	+	0.933891i	$0.383610\pi$
$384$	5.01939	0.256145
$385$	12.3978	0.631853
$386$	−13.6513	−0.694835
$387$	9.78307	0.497301
$388$	9.33700	0.474014
$389$	−4.73196	−0.239920	−0.119960	−	0.992779i	$-0.538277\pi$
$389$	−4.73196	−0.239920	−0.119960	+	0.992779i	$0.538277\pi$
$390$	1.44713	0.0732784
$391$	0	0
$392$	7.79024	0.393467
$393$	18.1134	0.913698
$394$	26.9406	1.35725
$395$	−1.91663	−0.0964360
$396$	−2.09718	−0.105387
$397$	35.4296	1.77816	0.889080	−	0.457751i	$-0.151345\pi$
$397$	35.4296	1.77816	0.889080	+	0.457751i	$0.151345\pi$
$398$	−31.8957	−1.59879
$399$	−10.2674	−0.514013
$400$	−2.68202	−0.134101
$401$	−5.29202	−0.264271	−0.132135	−	0.991232i	$-0.542183\pi$
$401$	−5.29202	−0.264271	−0.132135	+	0.991232i	$0.542183\pi$
$402$	4.69432	0.234132
$403$	5.95041	0.296411
$404$	−0.886151	−0.0440876
$405$	1.00000	0.0496904
$406$	−21.1340	−1.04886
$407$	9.42952	0.467404
$408$	7.20856	0.356877
$409$	29.1021	1.43901	0.719503	−	0.694489i	$-0.244370\pi$
$409$	29.1021	1.43901	0.719503	+	0.694489i	$0.244370\pi$
$410$	7.32100	0.361558
$411$	14.6849	0.724352
$412$	3.00501	0.148046
$413$	6.57763	0.323664
$414$	0	0
$415$	10.1496	0.498223
$416$	−3.41953	−0.167656
$417$	3.13987	0.153760
$418$	−16.2178	−0.793236
$419$	13.7305	0.670777	0.335389	−	0.942080i	$-0.391132\pi$
$419$	13.7305	0.670777	0.335389	+	0.942080i	$0.391132\pi$
$420$	1.61388	0.0787492
$421$	20.4681	0.997552	0.498776	−	0.866731i	$-0.333783\pi$
$421$	20.4681	0.997552	0.498776	+	0.866731i	$0.333783\pi$
$422$	27.6829	1.34758
$423$	3.51641	0.170974
$424$	−0.487167	−0.0236589
$425$	−2.35101	−0.114041
$426$	2.26651	0.109813
$427$	8.04709	0.389426
$428$	−9.99021	−0.482895
$429$	−4.77858	−0.230712
$430$	−11.8916	−0.573463
$431$	−20.8831	−1.00590	−0.502951	−	0.864315i	$-0.667752\pi$
$431$	−20.8831	−1.00590	−0.502951	+	0.864315i	$0.667752\pi$
$432$	2.68202	0.129039
$433$	4.80604	0.230964	0.115482	−	0.993310i	$-0.463159\pi$
$433$	4.80604	0.230964	0.115482	+	0.993310i	$0.463159\pi$
$434$	−18.7654	−0.900770
$435$	−5.62894	−0.269887
$436$	−10.6145	−0.508341
$437$	0	0
$438$	−12.6202	−0.603018
$439$	−11.9232	−0.569065	−0.284533	−	0.958666i	$-0.591838\pi$
$439$	−11.9232	−0.569065	−0.284533	+	0.958666i	$0.591838\pi$
$440$	12.3070	0.586711
$441$	2.54072	0.120987
$442$	3.40222	0.161827
$443$	−15.7944	−0.750413	−0.375207	−	0.926941i	$-0.622428\pi$
$443$	−15.7944	−0.750413	−0.375207	+	0.926941i	$0.622428\pi$
$444$	1.22748	0.0582536
$445$	17.0223	0.806936
$446$	3.73370	0.176796
$447$	18.1830	0.860027
$448$	27.3524	1.29228
$449$	5.06181	0.238882	0.119441	−	0.992841i	$-0.461890\pi$
$449$	5.06181	0.238882	0.119441	+	0.992841i	$0.461890\pi$
$450$	−1.21553	−0.0573005
$451$	−24.1747	−1.13834
$452$	−4.65023	−0.218728
$453$	−1.38458	−0.0650533
$454$	13.8501	0.650016
$455$	3.67734	0.172396
$456$	−10.1921	−0.477290
$457$	−21.6789	−1.01410	−0.507048	−	0.861918i	$-0.669263\pi$
$457$	−21.6789	−1.01410	−0.507048	+	0.861918i	$0.669263\pi$
$458$	−10.8959	−0.509134
$459$	2.35101	0.109736
$460$	0	0
$461$	16.8451	0.784554	0.392277	−	0.919847i	$-0.371687\pi$
$461$	16.8451	0.784554	0.392277	+	0.919847i	$0.371687\pi$
$462$	15.0699	0.701116
$463$	14.1305	0.656702	0.328351	−	0.944556i	$-0.393507\pi$
$463$	14.1305	0.656702	0.328351	+	0.944556i	$0.393507\pi$
$464$	−15.0969	−0.700856
$465$	−4.99808	−0.231780
$466$	30.4153	1.40896
$467$	12.2974	0.569057	0.284528	−	0.958668i	$-0.408163\pi$
$467$	12.2974	0.569057	0.284528	+	0.958668i	$0.408163\pi$
$468$	−0.622048	−0.0287542
$469$	11.9289	0.550823
$470$	−4.27430	−0.197159
$471$	−4.18595	−0.192878
$472$	6.52941	0.300540
$473$	39.2673	1.80551
$474$	−2.32971	−0.107007
$475$	3.32407	0.152519
$476$	3.79424	0.173909
$477$	−0.158885	−0.00727485
$478$	20.7546	0.949294
$479$	31.3222	1.43115	0.715574	−	0.698537i	$-0.246165\pi$
$479$	31.3222	1.43115	0.715574	+	0.698537i	$0.246165\pi$
$480$	2.87226	0.131100
$481$	2.79690	0.127528
$482$	−0.0622560	−0.00283568
$483$	0	0
$484$	−2.67025	−0.121375
$485$	−17.8701	−0.811439
$486$	1.21553	0.0551374
$487$	38.3353	1.73714	0.868570	−	0.495567i	$-0.165040\pi$
$487$	38.3353	1.73714	0.868570	+	0.495567i	$0.165040\pi$
$488$	7.98810	0.361604
$489$	15.0145	0.678978
$490$	−3.08831	−0.139516
$491$	−20.9498	−0.945450	−0.472725	−	0.881210i	$-0.656730\pi$
$491$	−20.9498	−0.945450	−0.472725	+	0.881210i	$0.656730\pi$
$492$	−3.14692	−0.141874
$493$	−13.2337	−0.596015
$494$	−4.81037	−0.216429
$495$	4.01380	0.180407
$496$	−13.4049	−0.601899
$497$	5.75947	0.258348
$498$	12.3371	0.552838
$499$	−25.4111	−1.13756	−0.568780	−	0.822490i	$-0.692584\pi$
$499$	−25.4111	−1.13756	−0.568780	+	0.822490i	$0.692584\pi$
$500$	−0.522493	−0.0233666
$501$	2.89687	0.129422
$502$	−25.9691	−1.15906
$503$	−6.60397	−0.294456	−0.147228	−	0.989103i	$-0.547035\pi$
$503$	−6.60397	−0.294456	−0.147228	+	0.989103i	$0.547035\pi$
$504$	9.47077	0.421862
$505$	1.69600	0.0754712
$506$	0	0
$507$	11.5826	0.514402
$508$	−8.10456	−0.359582
$509$	3.87159	0.171605	0.0858027	−	0.996312i	$-0.472655\pi$
$509$	3.87159	0.171605	0.0858027	+	0.996312i	$0.472655\pi$
$510$	−2.85771	−0.126542
$511$	−32.0696	−1.41867
$512$	24.1504	1.06731
$513$	−3.32407	−0.146761
$514$	29.6143	1.30623
$515$	−5.75129	−0.253432
$516$	5.11159	0.225025
$517$	14.1142	0.620741
$518$	−8.82042	−0.387547
$519$	−0.395846	−0.0173757
$520$	3.65038	0.160080
$521$	27.2253	1.19276	0.596381	−	0.802702i	$-0.296605\pi$
$521$	27.2253	1.19276	0.596381	+	0.802702i	$0.296605\pi$
$522$	−6.84213	−0.299472
$523$	−14.5728	−0.637224	−0.318612	−	0.947885i	$-0.603217\pi$
$523$	−14.5728	−0.637224	−0.318612	+	0.947885i	$0.603217\pi$
$524$	9.46411	0.413441
$525$	−3.08881	−0.134807
$526$	35.8774	1.56433
$527$	−11.7505	−0.511861
$528$	10.7651	0.468490
$529$	0	0
$530$	0.193129	0.00838900
$531$	2.12951	0.0924127
$532$	−5.36465	−0.232587
$533$	−7.17049	−0.310588
$534$	20.6911	0.895392
$535$	19.1203	0.826642
$536$	11.8414	0.511471
$537$	−10.7201	−0.462605
$538$	11.9428	0.514890
$539$	10.1979	0.439256
$540$	0.522493	0.0224845
$541$	42.4600	1.82550	0.912750	−	0.408519i	$-0.133955\pi$
$541$	42.4600	1.82550	0.912750	+	0.408519i	$0.133955\pi$
$542$	−14.3413	−0.616011
$543$	10.6133	0.455460
$544$	6.75269	0.289519
$545$	20.3151	0.870202
$546$	4.46991	0.191294
$547$	−5.21527	−0.222989	−0.111495	−	0.993765i	$-0.535564\pi$
$547$	−5.21527	−0.222989	−0.111495	+	0.993765i	$0.535564\pi$
$548$	7.67274	0.327763
$549$	2.60525	0.111189
$550$	−4.87888	−0.208036
$551$	18.7110	0.797115
$552$	0	0
$553$	−5.92009	−0.251748
$554$	−27.7311	−1.17818
$555$	−2.34927	−0.0997211
$556$	1.64056	0.0695753
$557$	−12.7161	−0.538799	−0.269399	−	0.963029i	$-0.586825\pi$
$557$	−12.7161	−0.538799	−0.269399	+	0.963029i	$0.586825\pi$
$558$	−6.07531	−0.257188
$559$	11.6471	0.492621
$560$	−8.28422	−0.350072
$561$	9.43647	0.398408
$562$	5.47008	0.230741
$563$	16.5917	0.699255	0.349628	−	0.936889i	$-0.386308\pi$
$563$	16.5917	0.699255	0.349628	+	0.936889i	$0.386308\pi$
$564$	1.83730	0.0773643
$565$	8.90008	0.374429
$566$	−16.9865	−0.713995
$567$	3.08881	0.129718
$568$	5.71724	0.239890
$569$	−26.4741	−1.10985	−0.554927	−	0.831899i	$-0.687254\pi$
$569$	−26.4741	−1.10985	−0.554927	+	0.831899i	$0.687254\pi$
$570$	4.04050	0.169238
$571$	−0.266702	−0.0111611	−0.00558056	−	0.999984i	$-0.501776\pi$
$571$	−0.266702	−0.0111611	−0.00558056	+	0.999984i	$0.501776\pi$
$572$	−2.49678	−0.104395
$573$	16.9111	0.706471
$574$	22.6131	0.943854
$575$	0	0
$576$	8.85534	0.368972
$577$	−23.3118	−0.970483	−0.485241	−	0.874380i	$-0.661268\pi$
$577$	−23.3118	−0.970483	−0.485241	+	0.874380i	$0.661268\pi$
$578$	13.9455	0.580055
$579$	−11.2308	−0.466736
$580$	−2.94108	−0.122122
$581$	31.3500	1.30062
$582$	−21.7216	−0.900389
$583$	−0.637733	−0.0264122
$584$	−31.8345	−1.31732
$585$	1.19054	0.0492227
$586$	24.4435	1.00975
$587$	−23.9975	−0.990482	−0.495241	−	0.868756i	$-0.664920\pi$
$587$	−23.9975	−0.990482	−0.495241	+	0.868756i	$0.664920\pi$
$588$	1.32751	0.0547455
$589$	16.6140	0.684567
$590$	−2.58847	−0.106566
$591$	22.1637	0.911695
$592$	−6.30079	−0.258961
$593$	−25.0326	−1.02797	−0.513984	−	0.857800i	$-0.671831\pi$
$593$	−25.0326	−1.02797	−0.513984	+	0.857800i	$0.671831\pi$
$594$	4.87888	0.200183
$595$	−7.26180	−0.297705
$596$	9.50050	0.389156
$597$	−26.2402	−1.07394
$598$	0	0
$599$	−5.89870	−0.241014	−0.120507	−	0.992712i	$-0.538452\pi$
$599$	−5.89870	−0.241014	−0.120507	+	0.992712i	$0.538452\pi$
$600$	−3.06616	−0.125175
$601$	35.5450	1.44991	0.724955	−	0.688796i	$-0.241860\pi$
$601$	35.5450	1.44991	0.724955	+	0.688796i	$0.241860\pi$
$602$	−36.7308	−1.49704
$603$	3.86196	0.157271
$604$	−0.723433	−0.0294361
$605$	5.11060	0.207775
$606$	2.06154	0.0837444
$607$	9.06862	0.368084	0.184042	−	0.982918i	$-0.441082\pi$
$607$	9.06862	0.368084	0.184042	+	0.982918i	$0.441082\pi$
$608$	−9.54758	−0.387206
$609$	−17.3867	−0.704545
$610$	−3.16675	−0.128218
$611$	4.18642	0.169365
$612$	1.22838	0.0496545
$613$	−30.7521	−1.24207	−0.621033	−	0.783784i	$-0.713287\pi$
$613$	−30.7521	−1.24207	−0.621033	+	0.783784i	$0.713287\pi$
$614$	−42.3563	−1.70936
$615$	6.02290	0.242867
$616$	38.0138	1.53162
$617$	−4.84722	−0.195142	−0.0975708	−	0.995229i	$-0.531107\pi$
$617$	−4.84722	−0.195142	−0.0975708	+	0.995229i	$0.531107\pi$
$618$	−6.99085	−0.281213
$619$	28.7197	1.15434	0.577171	−	0.816623i	$-0.304157\pi$
$619$	28.7197	1.15434	0.577171	+	0.816623i	$0.304157\pi$
$620$	−2.61146	−0.104879
$621$	0	0
$622$	21.3018	0.854125
$623$	52.5787	2.10652
$624$	3.19304	0.127824
$625$	1.00000	0.0400000
$626$	22.6317	0.904543
$627$	−13.3422	−0.532834
$628$	−2.18713	−0.0872760
$629$	−5.52316	−0.220223
$630$	−3.75453	−0.149584
$631$	−43.7386	−1.74120	−0.870602	−	0.491987i	$-0.836271\pi$
$631$	−43.7386	−1.74120	−0.870602	+	0.491987i	$0.836271\pi$
$632$	−5.87669	−0.233762
$633$	22.7744	0.905202
$634$	14.2354	0.565361
$635$	15.5113	0.615548
$636$	−0.0830163	−0.00329181
$637$	3.02482	0.119848
$638$	−27.4629	−1.08727
$639$	1.86463	0.0737635
$640$	−5.01939	−0.198409
$641$	−34.4521	−1.36078	−0.680388	−	0.732853i	$-0.738189\pi$
$641$	−34.4521	−1.36078	−0.680388	+	0.732853i	$0.738189\pi$
$642$	23.2412	0.917258
$643$	−45.0719	−1.77746	−0.888731	−	0.458430i	$-0.848412\pi$
$643$	−45.0719	−1.77746	−0.888731	+	0.458430i	$0.848412\pi$
$644$	0	0
$645$	−9.78307	−0.385208
$646$	9.49924	0.373743
$647$	−22.7928	−0.896076	−0.448038	−	0.894015i	$-0.647877\pi$
$647$	−22.7928	−0.896076	−0.448038	+	0.894015i	$0.647877\pi$
$648$	3.06616	0.120450
$649$	8.54741	0.335515
$650$	−1.44713	−0.0567612
$651$	−15.4381	−0.605067
$652$	7.84496	0.307232
$653$	5.14496	0.201338	0.100669	−	0.994920i	$-0.467902\pi$
$653$	5.14496	0.201338	0.100669	+	0.994920i	$0.467902\pi$
$654$	24.6935	0.965593
$655$	−18.1134	−0.707748
$656$	16.1535	0.630688
$657$	−10.3825	−0.405061
$658$	−13.2025	−0.514686
$659$	39.6982	1.54642	0.773210	−	0.634150i	$-0.218650\pi$
$659$	39.6982	1.54642	0.773210	+	0.634150i	$0.218650\pi$
$660$	2.09718	0.0816327
$661$	−2.41954	−0.0941094	−0.0470547	−	0.998892i	$-0.514984\pi$
$661$	−2.41954	−0.0941094	−0.0470547	+	0.998892i	$0.514984\pi$
$662$	18.4126	0.715626
$663$	2.79896	0.108703
$664$	31.1202	1.20770
$665$	10.2674	0.398153
$666$	−2.85561	−0.110653
$667$	0	0
$668$	1.51359	0.0585626
$669$	3.07167	0.118758
$670$	−4.69432	−0.181358
$671$	10.4569	0.403685
$672$	8.87184	0.342239
$673$	39.8399	1.53572	0.767858	−	0.640621i	$-0.221323\pi$
$673$	39.8399	1.53572	0.767858	+	0.640621i	$0.221323\pi$
$674$	28.3061	1.09031
$675$	−1.00000	−0.0384900
$676$	6.05184	0.232763
$677$	−17.6343	−0.677742	−0.338871	−	0.940833i	$-0.610045\pi$
$677$	−17.6343	−0.677742	−0.338871	+	0.940833i	$0.610045\pi$
$678$	10.8183	0.415474
$679$	−55.1972	−2.11828
$680$	−7.20856	−0.276436
$681$	11.3943	0.436630
$682$	−24.3851	−0.933752
$683$	−21.9434	−0.839639	−0.419820	−	0.907608i	$-0.637907\pi$
$683$	−21.9434	−0.839639	−0.419820	+	0.907608i	$0.637907\pi$
$684$	−1.73680	−0.0664083
$685$	−14.6849	−0.561080
$686$	16.7425	0.639232
$687$	−8.96396	−0.341996
$688$	−26.2383	−1.00033
$689$	−0.189159	−0.00720637
$690$	0	0
$691$	46.9699	1.78682	0.893409	−	0.449244i	$-0.148306\pi$
$691$	46.9699	1.78682	0.893409	+	0.449244i	$0.148306\pi$
$692$	−0.206827	−0.00786238
$693$	12.3978	0.470955
$694$	−13.2511	−0.503006
$695$	−3.13987	−0.119102
$696$	−17.2592	−0.654209
$697$	14.1599	0.536343
$698$	−34.2017	−1.29455
$699$	25.0223	0.946431
$700$	−1.61388	−0.0609989
$701$	13.0775	0.493929	0.246964	−	0.969025i	$-0.420567\pi$
$701$	13.0775	0.493929	0.246964	+	0.969025i	$0.420567\pi$
$702$	1.44713	0.0546185
$703$	7.80915	0.294528
$704$	35.5436	1.33960
$705$	−3.51641	−0.132436
$706$	−31.8002	−1.19682
$707$	5.23863	0.197019
$708$	1.11265	0.0418160
$709$	10.1907	0.382721	0.191361	−	0.981520i	$-0.438710\pi$
$709$	10.1907	0.382721	0.191361	+	0.981520i	$0.438710\pi$
$710$	−2.26651	−0.0850604
$711$	−1.91663	−0.0718792
$712$	52.1932	1.95602
$713$	0	0
$714$	−8.82692	−0.330339
$715$	4.77858	0.178709
$716$	−5.60115	−0.209325
$717$	17.0746	0.637661
$718$	−32.4011	−1.20920
$719$	8.46122	0.315550	0.157775	−	0.987475i	$-0.449568\pi$
$719$	8.46122	0.315550	0.157775	+	0.987475i	$0.449568\pi$
$720$	−2.68202	−0.0999528
$721$	−17.7646	−0.661589
$722$	9.66412	0.359661
$723$	−0.0512173	−0.00190479
$724$	5.54537	0.206092
$725$	5.62894	0.209054
$726$	6.21207	0.230552
$727$	0.0113322	0.000420287 0	0.000210144	−	1.00000i	$-0.499933\pi$
$727$	0.0113322	0.000420287 0	0.000210144		1.00000i	$0.499933\pi$
$728$	11.2753	0.417891
$729$	1.00000	0.0370370
$730$	12.6202	0.467096
$731$	−23.0001	−0.850688
$732$	1.36122	0.0503122
$733$	18.7932	0.694142	0.347071	−	0.937839i	$-0.387176\pi$
$733$	18.7932	0.694142	0.347071	+	0.937839i	$0.387176\pi$
$734$	2.69891	0.0996184
$735$	−2.54072	−0.0937158
$736$	0	0
$737$	15.5012	0.570992
$738$	7.32100	0.269490
$739$	51.8055	1.90569	0.952847	−	0.303450i	$-0.0981387\pi$
$739$	51.8055	1.90569	0.952847	+	0.303450i	$0.0981387\pi$
$740$	−1.22748	−0.0451230
$741$	−3.95743	−0.145380
$742$	0.596538	0.0218996
$743$	−24.6532	−0.904437	−0.452219	−	0.891907i	$-0.649367\pi$
$743$	−24.6532	−0.904437	−0.452219	+	0.891907i	$0.649367\pi$
$744$	−15.3249	−0.561839
$745$	−18.1830	−0.666174
$746$	20.9557	0.767244
$747$	10.1496	0.371353
$748$	4.93049	0.180277
$749$	59.0588	2.15796
$750$	1.21553	0.0443848
$751$	19.2238	0.701485	0.350742	−	0.936472i	$-0.385929\pi$
$751$	19.2238	0.701485	0.350742	+	0.936472i	$0.385929\pi$
$752$	−9.43107	−0.343916
$753$	−21.3645	−0.778566
$754$	−8.14582	−0.296653
$755$	1.38458	0.0503900
$756$	1.61388	0.0586962
$757$	18.9269	0.687912	0.343956	−	0.938986i	$-0.388233\pi$
$757$	18.9269	0.687912	0.343956	+	0.938986i	$0.388233\pi$
$758$	−14.0266	−0.509469
$759$	0	0
$760$	10.1921	0.369707
$761$	25.5267	0.925343	0.462671	−	0.886530i	$-0.346891\pi$
$761$	25.5267	0.925343	0.462671	+	0.886530i	$0.346891\pi$
$762$	18.8544	0.683024
$763$	62.7493	2.27168
$764$	8.83592	0.319672
$765$	−2.35101	−0.0850008
$766$	−17.0114	−0.614647
$767$	2.53526	0.0915429
$768$	11.6095	0.418920
$769$	−23.9437	−0.863431	−0.431715	−	0.902010i	$-0.642091\pi$
$769$	−23.9437	−0.863431	−0.431715	+	0.902010i	$0.642091\pi$
$770$	−15.0699	−0.543082
$771$	24.3633	0.877424
$772$	−5.86801	−0.211194
$773$	8.67572	0.312044	0.156022	−	0.987754i	$-0.450133\pi$
$773$	8.67572	0.312044	0.156022	+	0.987754i	$0.450133\pi$
$774$	−11.8916	−0.427434
$775$	4.99808	0.179536
$776$	−54.7925	−1.96694
$777$	−7.25645	−0.260324
$778$	5.75183	0.206213
$779$	−20.0205	−0.717310
$780$	0.622048	0.0222729
$781$	7.48424	0.267807
$782$	0	0
$783$	−5.62894	−0.201162
$784$	−6.81424	−0.243366
$785$	4.18595	0.149403
$786$	−22.0173	−0.785331
$787$	−37.9329	−1.35216	−0.676081	−	0.736827i	$-0.736323\pi$
$787$	−37.9329	−1.35216	−0.676081	+	0.736827i	$0.736323\pi$
$788$	11.5804	0.412535
$789$	29.5159	1.05080
$790$	2.32971	0.0828875
$791$	27.4906	0.977454
$792$	12.3070	0.437309
$793$	3.10164	0.110143
$794$	−43.0657	−1.52834
$795$	0.158885	0.00563507
$796$	−13.7103	−0.485949
$797$	−26.8583	−0.951371	−0.475685	−	0.879616i	$-0.657800\pi$
$797$	−26.8583	−0.951371	−0.475685	+	0.879616i	$0.657800\pi$
$798$	12.4803	0.441798
$799$	−8.26711	−0.292469
$800$	−2.87226	−0.101550
$801$	17.0223	0.601454
$802$	6.43259	0.227143
$803$	−41.6734	−1.47062
$804$	2.01785	0.0711641
$805$	0	0
$806$	−7.23288	−0.254767
$807$	9.82519	0.345863
$808$	5.20022	0.182943
$809$	9.76257	0.343234	0.171617	−	0.985164i	$-0.445101\pi$
$809$	9.76257	0.343234	0.171617	+	0.985164i	$0.445101\pi$
$810$	−1.21553	−0.0427093
$811$	−40.6021	−1.42573	−0.712866	−	0.701300i	$-0.752603\pi$
$811$	−40.6021	−1.42573	−0.712866	+	0.701300i	$0.752603\pi$
$812$	−9.08443	−0.318801
$813$	−11.7984	−0.413788
$814$	−11.4618	−0.401737
$815$	−15.0145	−0.525934
$816$	−6.30543	−0.220734
$817$	32.5196	1.13772
$818$	−35.3744	−1.23684
$819$	3.67734	0.128497
$820$	3.14692	0.109895
$821$	51.4265	1.79480	0.897399	−	0.441219i	$-0.145454\pi$
$821$	51.4265	1.79480	0.897399	+	0.441219i	$0.145454\pi$
$822$	−17.8499	−0.622586
$823$	−20.8272	−0.725990	−0.362995	−	0.931791i	$-0.618246\pi$
$823$	−20.8272	−0.725990	−0.362995	+	0.931791i	$0.618246\pi$
$824$	−17.6344	−0.614322
$825$	−4.01380	−0.139743
$826$	−7.99529	−0.278192
$827$	−22.0801	−0.767799	−0.383899	−	0.923375i	$-0.625419\pi$
$827$	−22.0801	−0.767799	−0.383899	+	0.923375i	$0.625419\pi$
$828$	0	0
$829$	38.1111	1.32365	0.661826	−	0.749658i	$-0.269782\pi$
$829$	38.1111	1.32365	0.661826	+	0.749658i	$0.269782\pi$
$830$	−12.3371	−0.428226
$831$	−22.8141	−0.791411
$832$	10.5426	0.365499
$833$	−5.97324	−0.206961
$834$	−3.81660	−0.132158
$835$	−2.89687	−0.100250
$836$	−6.97118	−0.241103
$837$	−4.99808	−0.172759
$838$	−16.6898	−0.576538
$839$	−26.6189	−0.918987	−0.459493	−	0.888181i	$-0.651969\pi$
$839$	−26.6189	−0.918987	−0.459493	+	0.888181i	$0.651969\pi$
$840$	−9.47077	−0.326773
$841$	2.68496	0.0925848
$842$	−24.8795	−0.857403
$843$	4.50017	0.154994
$844$	11.8995	0.409597
$845$	−11.5826	−0.398454
$846$	−4.27430	−0.146953
$847$	15.7856	0.542401
$848$	0.426132	0.0146334
$849$	−13.9746	−0.479606
$850$	2.85771	0.0980187
$851$	0	0
$852$	0.974255	0.0333774
$853$	−9.01898	−0.308804	−0.154402	−	0.988008i	$-0.549345\pi$
$853$	−9.01898	−0.308804	−0.154402	+	0.988008i	$0.549345\pi$
$854$	−9.78146	−0.334715
$855$	3.32407	0.113681
$856$	58.6258	2.00379
$857$	−45.8031	−1.56461	−0.782303	−	0.622898i	$-0.785955\pi$
$857$	−45.8031	−1.56461	−0.782303	+	0.622898i	$0.785955\pi$
$858$	5.80850	0.198299
$859$	22.3607	0.762939	0.381469	−	0.924381i	$-0.375418\pi$
$859$	22.3607	0.762939	0.381469	+	0.924381i	$0.375418\pi$
$860$	−5.11159	−0.174304
$861$	18.6036	0.634007
$862$	25.3839	0.864580
$863$	−16.5845	−0.564543	−0.282272	−	0.959335i	$-0.591088\pi$
$863$	−16.5845	−0.564543	−0.282272	+	0.959335i	$0.591088\pi$
$864$	2.87226	0.0977161
$865$	0.395846	0.0134592
$866$	−5.84188	−0.198515
$867$	11.4728	0.389636
$868$	−8.06630	−0.273788
$869$	−7.69296	−0.260966
$870$	6.84213	0.231970
$871$	4.59782	0.155791
$872$	62.2892	2.10938
$873$	−17.8701	−0.604811
$874$	0	0
$875$	3.08881	0.104421
$876$	−5.42479	−0.183287
$877$	−7.63762	−0.257904	−0.128952	−	0.991651i	$-0.541161\pi$
$877$	−7.63762	−0.257904	−0.128952	+	0.991651i	$0.541161\pi$
$878$	14.4930	0.489116
$879$	20.1093	0.678271
$880$	−10.7651	−0.362891
$881$	−11.2489	−0.378985	−0.189493	−	0.981882i	$-0.560684\pi$
$881$	−11.2489	−0.378985	−0.189493	+	0.981882i	$0.560684\pi$
$882$	−3.08831	−0.103989
$883$	54.8451	1.84569	0.922843	−	0.385177i	$-0.125860\pi$
$883$	54.8451	1.84569	0.922843	+	0.385177i	$0.125860\pi$
$884$	1.46244	0.0491871
$885$	−2.12951	−0.0715826
$886$	19.1985	0.644986
$887$	−45.6628	−1.53321	−0.766603	−	0.642121i	$-0.778054\pi$
$887$	−45.6628	−1.53321	−0.766603	+	0.642121i	$0.778054\pi$
$888$	−7.20325	−0.241725
$889$	47.9115	1.60690
$890$	−20.6911	−0.693568
$891$	4.01380	0.134467
$892$	1.60493	0.0537369
$893$	11.6888	0.391151
$894$	−22.1020	−0.739200
$895$	10.7201	0.358332
$896$	−15.5039	−0.517950
$897$	0	0
$898$	−6.15277	−0.205321
$899$	28.1339	0.938318
$900$	−0.522493	−0.0174164
$901$	0.373540	0.0124444
$902$	29.3850	0.978414
$903$	−30.2180	−1.00559
$904$	27.2891	0.907621
$905$	−10.6133	−0.352798
$906$	1.68300	0.0559138
$907$	−6.23617	−0.207068	−0.103534	−	0.994626i	$-0.533015\pi$
$907$	−6.23617	−0.207068	−0.103534	+	0.994626i	$0.533015\pi$
$908$	5.95344	0.197572
$909$	1.69600	0.0562529
$910$	−4.46991	−0.148176
$911$	−5.28888	−0.175229	−0.0876143	−	0.996154i	$-0.527924\pi$
$911$	−5.28888	−0.175229	−0.0876143	+	0.996154i	$0.527924\pi$
$912$	8.91521	0.295212
$913$	40.7384	1.34824
$914$	26.3513	0.871623
$915$	−2.60525	−0.0861267
$916$	−4.68360	−0.154751
$917$	−55.9487	−1.84759
$918$	−2.85771	−0.0943186
$919$	55.2883	1.82379	0.911897	−	0.410419i	$-0.134618\pi$
$919$	55.2883	1.82379	0.911897	+	0.410419i	$0.134618\pi$
$920$	0	0
$921$	−34.8460	−1.14822
$922$	−20.4757	−0.674330
$923$	2.21991	0.0730692
$924$	6.47779	0.213104
$925$	2.34927	0.0772437
$926$	−17.1761	−0.564441
$927$	−5.75129	−0.188897
$928$	−16.1678	−0.530733
$929$	−4.48014	−0.146989	−0.0734943	−	0.997296i	$-0.523415\pi$
$929$	−4.48014	−0.146989	−0.0734943	+	0.997296i	$0.523415\pi$
$930$	6.07531	0.199217
$931$	8.44552	0.276791
$932$	13.0740	0.428253
$933$	17.5248	0.573735
$934$	−14.9478	−0.489108
$935$	−9.43647	−0.308606
$936$	3.65038	0.119316
$937$	4.60595	0.150470	0.0752350	−	0.997166i	$-0.476029\pi$
$937$	4.60595	0.150470	0.0752350	+	0.997166i	$0.476029\pi$
$938$	−14.4999	−0.473437
$939$	18.6188	0.607601
$940$	−1.83730	−0.0599261
$941$	17.0305	0.555177	0.277589	−	0.960700i	$-0.410465\pi$
$941$	17.0305	0.555177	0.277589	+	0.960700i	$0.410465\pi$
$942$	5.08814	0.165780
$943$	0	0
$944$	−5.71137	−0.185889
$945$	−3.08881	−0.100479
$946$	−47.7305	−1.55185
$947$	−41.8897	−1.36123	−0.680617	−	0.732640i	$-0.738288\pi$
$947$	−41.8897	−1.36123	−0.680617	+	0.732640i	$0.738288\pi$
$948$	−1.00142	−0.0325248
$949$	−12.3608	−0.401248
$950$	−4.04050	−0.131091
$951$	11.7113	0.379765
$952$	−22.2658	−0.721640
$953$	43.5617	1.41110	0.705550	−	0.708660i	$-0.250700\pi$
$953$	43.5617	1.41110	0.705550	+	0.708660i	$0.250700\pi$
$954$	0.193129	0.00625279
$955$	−16.9111	−0.547230
$956$	8.92134	0.288537
$957$	−22.5934	−0.730342
$958$	−38.0730	−1.23008
$959$	−45.3587	−1.46471
$960$	−8.85534	−0.285805
$961$	−6.01918	−0.194167
$962$	−3.39971	−0.109611
$963$	19.1203	0.616142
$964$	−0.0267607	−0.000861903 0
$965$	11.2308	0.361532
$966$	0	0
$967$	−25.9998	−0.836096	−0.418048	−	0.908425i	$-0.637286\pi$
$967$	−25.9998	−0.836096	−0.418048	+	0.908425i	$0.637286\pi$
$968$	15.6699	0.503650
$969$	7.81491	0.251051
$970$	21.7216	0.697438
$971$	21.6404	0.694473	0.347236	−	0.937778i	$-0.387120\pi$
$971$	21.6404	0.694473	0.347236	+	0.937778i	$0.387120\pi$
$972$	0.522493	0.0167590
$973$	−9.69845	−0.310918
$974$	−46.5976	−1.49308
$975$	−1.19054	−0.0381277
$976$	−6.98731	−0.223658
$977$	−26.6129	−0.851421	−0.425711	−	0.904859i	$-0.639976\pi$
$977$	−26.6129	−0.851421	−0.425711	+	0.904859i	$0.639976\pi$
$978$	−18.2505	−0.583587
$979$	68.3242	2.18365
$980$	−1.32751	−0.0424057
$981$	20.3151	0.648610
$982$	25.4650	0.812622
$983$	−21.8115	−0.695678	−0.347839	−	0.937554i	$-0.613084\pi$
$983$	−21.8115	−0.695678	−0.347839	+	0.937554i	$0.613084\pi$
$984$	18.4672	0.588712
$985$	−22.1637	−0.706196
$986$	16.0859	0.512279
$987$	−10.8615	−0.345726
$988$	−2.06773	−0.0657833
$989$	0	0
$990$	−4.87888	−0.155061
$991$	−40.4656	−1.28543	−0.642715	−	0.766105i	$-0.722192\pi$
$991$	−40.4656	−1.28543	−0.642715	+	0.766105i	$0.722192\pi$
$992$	−14.3558	−0.455796
$993$	15.1478	0.480702
$994$	−7.00079	−0.222052
$995$	26.2402	0.831870
$996$	5.30308	0.168035
$997$	−8.97321	−0.284184	−0.142092	−	0.989853i	$-0.545383\pi$
$997$	−8.97321	−0.284184	−0.142092	+	0.989853i	$0.545383\pi$
$998$	30.8879	0.977741
$999$	−2.34927	−0.0743278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bu.1.9		25
23.13	even	11		345.2.m.d.31.4	✓	50
23.16	even	11		345.2.m.d.256.4	yes	50
23.22	odd	2		7935.2.a.bt.1.9		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.31.4	✓	50	23.13	even	11
345.2.m.d.256.4	yes	50	23.16	even	11
7935.2.a.bt.1.9		25	23.22	odd	2
7935.2.a.bu.1.9		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)

\(f(q)\)	\(=\)	\(q-1.21553 q^{2} -1.00000 q^{3} -0.522493 q^{4} +1.00000 q^{5} +1.21553 q^{6} +3.08881 q^{7} +3.06616 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.21553 q^{2} -1.00000 q^{3} -0.522493 q^{4} +1.00000 q^{5} +1.21553 q^{6} +3.08881 q^{7} +3.06616 q^{8} +1.00000 q^{9} -1.21553 q^{10} +4.01380 q^{11} +0.522493 q^{12} +1.19054 q^{13} -3.75453 q^{14} -1.00000 q^{15} -2.68202 q^{16} -2.35101 q^{17} -1.21553 q^{18} +3.32407 q^{19} -0.522493 q^{20} -3.08881 q^{21} -4.87888 q^{22} -3.06616 q^{24} +1.00000 q^{25} -1.44713 q^{26} -1.00000 q^{27} -1.61388 q^{28} +5.62894 q^{29} +1.21553 q^{30} +4.99808 q^{31} -2.87226 q^{32} -4.01380 q^{33} +2.85771 q^{34} +3.08881 q^{35} -0.522493 q^{36} +2.34927 q^{37} -4.04050 q^{38} -1.19054 q^{39} +3.06616 q^{40} -6.02290 q^{41} +3.75453 q^{42} +9.78307 q^{43} -2.09718 q^{44} +1.00000 q^{45} +3.51641 q^{47} +2.68202 q^{48} +2.54072 q^{49} -1.21553 q^{50} +2.35101 q^{51} -0.622048 q^{52} -0.158885 q^{53} +1.21553 q^{54} +4.01380 q^{55} +9.47077 q^{56} -3.32407 q^{57} -6.84213 q^{58} +2.12951 q^{59} +0.522493 q^{60} +2.60525 q^{61} -6.07531 q^{62} +3.08881 q^{63} +8.85534 q^{64} +1.19054 q^{65} +4.87888 q^{66} +3.86196 q^{67} +1.22838 q^{68} -3.75453 q^{70} +1.86463 q^{71} +3.06616 q^{72} -10.3825 q^{73} -2.85561 q^{74} -1.00000 q^{75} -1.73680 q^{76} +12.3978 q^{77} +1.44713 q^{78} -1.91663 q^{79} -2.68202 q^{80} +1.00000 q^{81} +7.32100 q^{82} +10.1496 q^{83} +1.61388 q^{84} -2.35101 q^{85} -11.8916 q^{86} -5.62894 q^{87} +12.3070 q^{88} +17.0223 q^{89} -1.21553 q^{90} +3.67734 q^{91} -4.99808 q^{93} -4.27430 q^{94} +3.32407 q^{95} +2.87226 q^{96} -17.8701 q^{97} -3.08831 q^{98} +4.01380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 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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