LMFDB - Embedded newform 529.4.a.m.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [529,4,Mod(1,529)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(529, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("529.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 529 = 23^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	529.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:	$31.2120103930$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 23)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.46235 q^{2} +2.34669 q^{3} -1.93685 q^{4} +7.40267 q^{5} -5.77838 q^{6} -12.1855 q^{7} +24.4680 q^{8} -21.4930 q^{9} +O(q^{10})$	\(q-2.46235 q^{2} +2.34669 q^{3} -1.93685 q^{4} +7.40267 q^{5} -5.77838 q^{6} -12.1855 q^{7} +24.4680 q^{8} -21.4930 q^{9} -18.2279 q^{10} +5.10651 q^{11} -4.54520 q^{12} +24.2741 q^{13} +30.0050 q^{14} +17.3718 q^{15} -44.7538 q^{16} +64.3464 q^{17} +52.9233 q^{18} -49.5777 q^{19} -14.3379 q^{20} -28.5957 q^{21} -12.5740 q^{22} +57.4189 q^{24} -70.2005 q^{25} -59.7711 q^{26} -113.798 q^{27} +23.6016 q^{28} +172.492 q^{29} -42.7754 q^{30} -232.381 q^{31} -85.5444 q^{32} +11.9834 q^{33} -158.443 q^{34} -90.2055 q^{35} +41.6288 q^{36} +238.059 q^{37} +122.078 q^{38} +56.9638 q^{39} +181.128 q^{40} +311.679 q^{41} +70.4126 q^{42} -525.706 q^{43} -9.89055 q^{44} -159.106 q^{45} +407.467 q^{47} -105.024 q^{48} -194.513 q^{49} +172.858 q^{50} +151.001 q^{51} -47.0152 q^{52} -481.371 q^{53} +280.211 q^{54} +37.8018 q^{55} -298.155 q^{56} -116.344 q^{57} -424.734 q^{58} -42.8594 q^{59} -33.6466 q^{60} +340.245 q^{61} +572.202 q^{62} +261.904 q^{63} +568.670 q^{64} +179.693 q^{65} -29.5074 q^{66} -530.324 q^{67} -124.629 q^{68} +222.117 q^{70} -746.072 q^{71} -525.891 q^{72} -302.165 q^{73} -586.184 q^{74} -164.739 q^{75} +96.0246 q^{76} -62.2256 q^{77} -140.265 q^{78} -775.764 q^{79} -331.298 q^{80} +313.262 q^{81} -767.462 q^{82} -293.493 q^{83} +55.3857 q^{84} +476.335 q^{85} +1294.47 q^{86} +404.785 q^{87} +124.946 q^{88} -569.584 q^{89} +391.773 q^{90} -295.792 q^{91} -545.327 q^{93} -1003.32 q^{94} -367.007 q^{95} -200.746 q^{96} -1869.28 q^{97} +478.958 q^{98} -109.754 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9}+O(q^{10}) $ 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19} - 578 q^{20} - 352 q^{21} - 155 q^{22} + 803 q^{24} + 90 q^{25} - 850 q^{26} + 368 q^{27} - 459 q^{28} + 175 q^{29} - 893 q^{30} + 287 q^{31} + 164 q^{32} - 1020 q^{33} - 335 q^{34} + 462 q^{35} - 1092 q^{36} - 471 q^{37} - 810 q^{38} - 822 q^{39} - 1405 q^{40} - 73 q^{41} - 556 q^{42} - 901 q^{43} - 2073 q^{44} - 1384 q^{45} + 1452 q^{47} - 4028 q^{48} - 1092 q^{49} + 364 q^{50} - 2214 q^{51} + 1287 q^{52} - 2071 q^{53} + 2052 q^{54} + 1006 q^{55} - 4879 q^{56} - 418 q^{57} + 2796 q^{58} - 2713 q^{59} - 2805 q^{60} - 1225 q^{61} - 2852 q^{62} - 4003 q^{63} + 217 q^{64} - 2030 q^{65} - 2933 q^{66} - 767 q^{67} - 4175 q^{68} + 4851 q^{70} - 1683 q^{71} - 5265 q^{72} + 2203 q^{73} - 3089 q^{74} + 2333 q^{75} - 5252 q^{76} + 2760 q^{77} - 692 q^{78} - 5425 q^{79} - 4689 q^{80} + 1929 q^{81} - 2725 q^{82} - 5425 q^{83} - 4317 q^{84} - 912 q^{85} - 4359 q^{86} - 4404 q^{87} - 2610 q^{88} - 4933 q^{89} - 2695 q^{90} - 3619 q^{91} + 6375 q^{93} - 5117 q^{94} - 1338 q^{95} + 20 q^{96} - 2085 q^{97} + 5951 q^{98} - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.46235	−0.870571	−0.435285	−	0.900292i	$-0.643353\pi$
$2$	−2.46235	−0.870571	−0.435285	+	0.900292i	$0.643353\pi$
$3$	2.34669	0.451622	0.225811	−	0.974171i	$-0.427497\pi$
$3$	2.34669	0.451622	0.225811	+	0.974171i	$0.427497\pi$
$4$	−1.93685	−0.242106
$5$	7.40267	0.662115	0.331057	−	0.943611i	$-0.392595\pi$
$5$	7.40267	0.662115	0.331057	+	0.943611i	$0.392595\pi$
$6$	−5.77838	−0.393169
$7$	−12.1855	−0.657957	−0.328979	−	0.944337i	$-0.606704\pi$
$7$	−12.1855	−0.657957	−0.328979	+	0.944337i	$0.606704\pi$
$8$	24.4680	1.08134
$9$	−21.4930	−0.796038
$10$	−18.2279	−0.576418
$11$	5.10651	0.139970	0.0699851	−	0.997548i	$-0.477705\pi$
$11$	5.10651	0.139970	0.0699851	+	0.997548i	$0.477705\pi$
$12$	−4.54520	−0.109340
$13$	24.2741	0.517878	0.258939	−	0.965894i	$-0.416627\pi$
$13$	24.2741	0.517878	0.258939	+	0.965894i	$0.416627\pi$
$14$	30.0050	0.572798
$15$	17.3718	0.299025
$16$	−44.7538	−0.699278
$17$	64.3464	0.918017	0.459009	−	0.888432i	$-0.348205\pi$
$17$	64.3464	0.918017	0.459009	+	0.888432i	$0.348205\pi$
$18$	52.9233	0.693007
$19$	−49.5777	−0.598627	−0.299313	−	0.954155i	$-0.596758\pi$
$19$	−49.5777	−0.598627	−0.299313	+	0.954155i	$0.596758\pi$
$20$	−14.3379	−0.160302
$21$	−28.5957	−0.297148
$22$	−12.5740	−0.121854
$23$	0	0
$23$	0	0
$24$	57.4189	0.488357
$25$	−70.2005	−0.561604
$26$	−59.7711	−0.450849
$27$	−113.798	−0.811130
$28$	23.6016	0.159296
$29$	172.492	1.10451	0.552257	−	0.833674i	$-0.313767\pi$
$29$	172.492	1.10451	0.552257	+	0.833674i	$0.313767\pi$
$30$	−42.7754	−0.260323
$31$	−232.381	−1.34635	−0.673174	−	0.739484i	$-0.735070\pi$
$31$	−232.381	−1.34635	−0.673174	+	0.739484i	$0.735070\pi$
$32$	−85.5444	−0.472570
$33$	11.9834	0.0632136
$34$	−158.443	−0.799199
$35$	−90.2055	−0.435643
$36$	41.6288	0.192726
$37$	238.059	1.05775	0.528874	−	0.848701i	$-0.322615\pi$
$37$	238.059	1.05775	0.528874	+	0.848701i	$0.322615\pi$
$38$	122.078	0.521147
$39$	56.9638	0.233885
$40$	181.128	0.715972
$41$	311.679	1.18722	0.593611	−	0.804752i	$-0.297702\pi$
$41$	311.679	1.18722	0.593611	+	0.804752i	$0.297702\pi$
$42$	70.4126	0.258688
$43$	−525.706	−1.86440	−0.932202	−	0.361937i	$-0.882115\pi$
$43$	−525.706	−1.86440	−0.932202	+	0.361937i	$0.882115\pi$
$44$	−9.89055	−0.0338877
$45$	−159.106	−0.527069
$46$	0	0
$47$	407.467	1.26458	0.632289	−	0.774733i	$-0.282116\pi$
$47$	407.467	1.26458	0.632289	+	0.774733i	$0.282116\pi$
$48$	−105.024	−0.315809
$49$	−194.513	−0.567092
$50$	172.858	0.488916
$51$	151.001	0.414596
$52$	−47.0152	−0.125381
$53$	−481.371	−1.24757	−0.623786	−	0.781595i	$-0.714407\pi$
$53$	−481.371	−1.24757	−0.623786	+	0.781595i	$0.714407\pi$
$54$	280.211	0.706146
$55$	37.8018	0.0926763
$56$	−298.155	−0.711476
$57$	−116.344	−0.270353
$58$	−424.734	−0.961558
$59$	−42.8594	−0.0945732	−0.0472866	−	0.998881i	$-0.515057\pi$
$59$	−42.8594	−0.0945732	−0.0472866	+	0.998881i	$0.515057\pi$
$60$	−33.6466	−0.0723959
$61$	340.245	0.714161	0.357081	−	0.934074i	$-0.383772\pi$
$61$	340.245	0.714161	0.357081	+	0.934074i	$0.383772\pi$
$62$	572.202	1.17209
$63$	261.904	0.523759
$64$	568.670	1.11068
$65$	179.693	0.342895
$66$	−29.5074	−0.0550319
$67$	−530.324	−0.967005	−0.483503	−	0.875343i	$-0.660636\pi$
$67$	−530.324	−0.967005	−0.483503	+	0.875343i	$0.660636\pi$
$68$	−124.629	−0.222258
$69$	0	0
$70$	222.117	0.379258
$71$	−746.072	−1.24708	−0.623538	−	0.781793i	$-0.714305\pi$
$71$	−746.072	−1.24708	−0.623538	+	0.781793i	$0.714305\pi$
$72$	−525.891	−0.860789
$73$	−302.165	−0.484463	−0.242231	−	0.970219i	$-0.577879\pi$
$73$	−302.165	−0.484463	−0.242231	+	0.970219i	$0.577879\pi$
$74$	−586.184	−0.920844
$75$	−164.739	−0.253632
$76$	96.0246	0.144931
$77$	−62.2256	−0.0920944
$78$	−140.265	−0.203613
$79$	−775.764	−1.10481	−0.552407	−	0.833575i	$-0.686290\pi$
$79$	−775.764	−1.10481	−0.552407	+	0.833575i	$0.686290\pi$
$80$	−331.298	−0.463003
$81$	313.262	0.429714
$82$	−767.462	−1.03356
$83$	−293.493	−0.388133	−0.194067	−	0.980988i	$-0.562168\pi$
$83$	−293.493	−0.388133	−0.194067	+	0.980988i	$0.562168\pi$
$84$	55.3857	0.0719413
$85$	476.335	0.607833
$86$	1294.47	1.62310
$87$	404.785	0.498823
$88$	124.946	0.151356
$89$	−569.584	−0.678379	−0.339190	−	0.940718i	$-0.610153\pi$
$89$	−569.584	−0.678379	−0.339190	+	0.940718i	$0.610153\pi$
$90$	391.773	0.458851
$91$	−295.792	−0.340741
$92$	0	0
$93$	−545.327	−0.608040
$94$	−1003.32	−1.10090
$95$	−367.007	−0.396360
$96$	−200.746	−0.213423
$97$	−1869.28	−1.95667	−0.978335	−	0.207026i	$-0.933621\pi$
$97$	−1869.28	−1.95667	−0.978335	+	0.207026i	$0.933621\pi$
$98$	478.958	0.493694
$99$	−109.754	−0.111422
$100$	135.968	0.135968
$101$	1752.11	1.72615	0.863076	−	0.505073i	$-0.168535\pi$
$101$	1752.11	1.72615	0.863076	+	0.505073i	$0.168535\pi$
$102$	−371.818	−0.360936
$103$	−828.309	−0.792386	−0.396193	−	0.918167i	$-0.629669\pi$
$103$	−828.309	−0.792386	−0.396193	+	0.918167i	$0.629669\pi$
$104$	593.937	0.560003
$105$	−211.685	−0.196746
$106$	1185.30	1.08610
$107$	63.3583	0.0572437	0.0286218	−	0.999590i	$-0.490888\pi$
$107$	63.3583	0.0572437	0.0286218	+	0.999590i	$0.490888\pi$
$108$	220.410	0.196380
$109$	−1451.21	−1.27524	−0.637618	−	0.770353i	$-0.720080\pi$
$109$	−1451.21	−1.27524	−0.637618	+	0.770353i	$0.720080\pi$
$110$	−93.0812	−0.0806813
$111$	558.652	0.477701
$112$	545.349	0.460095
$113$	−756.735	−0.629979	−0.314990	−	0.949095i	$-0.602001\pi$
$113$	−756.735	−0.629979	−0.314990	+	0.949095i	$0.602001\pi$
$114$	286.479	0.235361
$115$	0	0
$116$	−334.091	−0.267410
$117$	−521.723	−0.412250
$118$	105.535	0.0823326
$119$	−784.095	−0.604016
$120$	425.053	0.323349
$121$	−1304.92	−0.980408
$122$	−837.800	−0.621728
$123$	731.416	0.536175
$124$	450.087	0.325959
$125$	−1445.00	−1.03396
$126$	−644.898	−0.455969
$127$	−1199.82	−0.838322	−0.419161	−	0.907912i	$-0.637676\pi$
$127$	−1199.82	−0.838322	−0.419161	+	0.907912i	$0.637676\pi$
$128$	−715.908	−0.494359
$129$	−1233.67	−0.842006
$130$	−442.466	−0.298514
$131$	−281.534	−0.187769	−0.0938846	−	0.995583i	$-0.529928\pi$
$131$	−281.534	−0.187769	−0.0938846	+	0.995583i	$0.529928\pi$
$132$	−23.2101	−0.0153044
$133$	604.131	0.393871
$134$	1305.84	0.841847
$135$	−842.411	−0.537061
$136$	1574.43	0.992690
$137$	−1327.07	−0.827586	−0.413793	−	0.910371i	$-0.635796\pi$
$137$	−1327.07	−0.827586	−0.413793	+	0.910371i	$0.635796\pi$
$138$	0	0
$139$	−452.323	−0.276011	−0.138006	−	0.990431i	$-0.544069\pi$
$139$	−452.323	−0.276011	−0.138006	+	0.990431i	$0.544069\pi$
$140$	174.715	0.105472
$141$	956.200	0.571111
$142$	1837.09	1.08567
$143$	123.956	0.0724874
$144$	961.895	0.556652
$145$	1276.90	0.731315
$146$	744.036	0.421759
$147$	−456.462	−0.256111
$148$	−461.084	−0.256087
$149$	−334.507	−0.183919	−0.0919593	−	0.995763i	$-0.529313\pi$
$149$	−334.507	−0.183919	−0.0919593	+	0.995763i	$0.529313\pi$
$150$	405.645	0.220805
$151$	1023.94	0.551833	0.275917	−	0.961182i	$-0.411019\pi$
$151$	1023.94	0.551833	0.275917	+	0.961182i	$0.411019\pi$
$152$	−1213.07	−0.647320
$153$	−1383.00	−0.730776
$154$	153.221	0.0801747
$155$	−1720.24	−0.891437
$156$	−110.330	−0.0566250
$157$	−2683.06	−1.36389	−0.681947	−	0.731402i	$-0.738866\pi$
$157$	−2683.06	−1.36389	−0.681947	+	0.731402i	$0.738866\pi$
$158$	1910.20	0.961819
$159$	−1129.63	−0.563431
$160$	−633.257	−0.312896
$161$	0	0
$162$	−771.359	−0.374097
$163$	2035.74	0.978230	0.489115	−	0.872219i	$-0.337320\pi$
$163$	2035.74	0.978230	0.489115	+	0.872219i	$0.337320\pi$
$164$	−603.676	−0.287434
$165$	88.7094	0.0418546
$166$	722.682	0.337898
$167$	692.265	0.320773	0.160386	−	0.987054i	$-0.448726\pi$
$167$	692.265	0.320773	0.160386	+	0.987054i	$0.448726\pi$
$168$	−699.680	−0.321318
$169$	−1607.77	−0.731803
$170$	−1172.90	−0.529162
$171$	1065.57	0.476530
$172$	1018.21	0.451384
$173$	369.411	0.162346	0.0811729	−	0.996700i	$-0.474133\pi$
$173$	369.411	0.162346	0.0811729	+	0.996700i	$0.474133\pi$
$174$	−996.722	−0.434260
$175$	855.431	0.369511
$176$	−228.536	−0.0978781
$177$	−100.578	−0.0427113
$178$	1402.51	0.590577
$179$	−1122.79	−0.468832	−0.234416	−	0.972136i	$-0.575318\pi$
$179$	−1122.79	−0.468832	−0.234416	+	0.972136i	$0.575318\pi$
$180$	308.164	0.127607
$181$	1287.93	0.528901	0.264451	−	0.964399i	$-0.414809\pi$
$181$	1287.93	0.528901	0.264451	+	0.964399i	$0.414809\pi$
$182$	728.343	0.296640
$183$	798.450	0.322531
$184$	0	0
$185$	1762.27	0.700350
$186$	1342.78	0.529342
$187$	328.586	0.128495
$188$	−789.202	−0.306162
$189$	1386.69	0.533688
$190$	903.699	0.345059
$191$	2454.05	0.929681	0.464840	−	0.885395i	$-0.346112\pi$
$191$	2454.05	0.929681	0.464840	+	0.885395i	$0.346112\pi$
$192$	1334.50	0.501609
$193$	655.493	0.244474	0.122237	−	0.992501i	$-0.460993\pi$
$193$	655.493	0.244474	0.122237	+	0.992501i	$0.460993\pi$
$194$	4602.83	1.70342
$195$	421.684	0.154859
$196$	376.742	0.137297
$197$	3423.72	1.23822	0.619112	−	0.785303i	$-0.287493\pi$
$197$	3423.72	1.23822	0.619112	+	0.785303i	$0.287493\pi$
$198$	270.253	0.0970004
$199$	3152.29	1.12292	0.561458	−	0.827506i	$-0.310241\pi$
$199$	3152.29	1.12292	0.561458	+	0.827506i	$0.310241\pi$
$200$	−1717.66	−0.607286
$201$	−1244.51	−0.436720
$202$	−4314.30	−1.50274
$203$	−2101.90	−0.726723
$204$	−292.467	−0.100376
$205$	2307.26	0.786077
$206$	2039.58	0.689828
$207$	0	0
$208$	−1086.36	−0.362141
$209$	−253.169	−0.0837899
$210$	521.241	0.171281
$211$	−1097.46	−0.358066	−0.179033	−	0.983843i	$-0.557297\pi$
$211$	−1097.46	−0.358066	−0.179033	+	0.983843i	$0.557297\pi$
$212$	932.343	0.302045
$213$	−1750.80	−0.563207
$214$	−156.010	−0.0498347
$215$	−3891.63	−1.23445
$216$	−2784.41	−0.877108
$217$	2831.68	0.885840
$218$	3573.38	1.11018
$219$	−709.090	−0.218794
$220$	−73.2165	−0.0224375
$221$	1561.95	0.475421
$222$	−1375.59	−0.415873
$223$	−3110.06	−0.933925	−0.466962	−	0.884277i	$-0.654652\pi$
$223$	−3110.06	−0.933925	−0.466962	+	0.884277i	$0.654652\pi$
$224$	1042.40	0.310931
$225$	1508.82	0.447058
$226$	1863.34	0.548442
$227$	−2954.44	−0.863847	−0.431924	−	0.901910i	$-0.642165\pi$
$227$	−2954.44	−0.863847	−0.431924	+	0.901910i	$0.642165\pi$
$228$	225.340	0.0654541
$229$	5467.66	1.57779	0.788893	−	0.614530i	$-0.210654\pi$
$229$	5467.66	1.57779	0.788893	+	0.614530i	$0.210654\pi$
$230$	0	0
$231$	−146.025	−0.0415918
$232$	4220.52	1.19436
$233$	4679.09	1.31561	0.657806	−	0.753188i	$-0.271485\pi$
$233$	4679.09	1.31561	0.657806	+	0.753188i	$0.271485\pi$
$234$	1284.66	0.358893
$235$	3016.34	0.837296
$236$	83.0122	0.0228968
$237$	−1820.48	−0.498958
$238$	1930.71	0.525839
$239$	−4701.35	−1.27241	−0.636204	−	0.771521i	$-0.719496\pi$
$239$	−4701.35	−1.27241	−0.636204	+	0.771521i	$0.719496\pi$
$240$	−777.455	−0.209102
$241$	6938.45	1.85454	0.927271	−	0.374391i	$-0.122148\pi$
$241$	6938.45	1.85454	0.927271	+	0.374391i	$0.122148\pi$
$242$	3213.17	0.853515
$243$	3807.68	1.00520
$244$	−659.003	−0.172903
$245$	−1439.91	−0.375480
$246$	−1801.00	−0.466779
$247$	−1203.45	−0.310015
$248$	−5685.88	−1.45586
$249$	−688.739	−0.175289
$250$	3558.10	0.900137
$251$	−7111.45	−1.78833	−0.894165	−	0.447737i	$-0.852230\pi$
$251$	−7111.45	−1.78833	−0.894165	+	0.447737i	$0.852230\pi$
$252$	−507.269	−0.126805
$253$	0	0
$254$	2954.38	0.729819
$255$	1117.81	0.274510
$256$	−2786.55	−0.680310
$257$	3058.05	0.742241	0.371120	−	0.928585i	$-0.378974\pi$
$257$	3058.05	0.742241	0.371120	+	0.928585i	$0.378974\pi$
$258$	3037.73	0.733026
$259$	−2900.88	−0.695952
$260$	−348.038	−0.0830169
$261$	−3707.37	−0.879235
$262$	693.235	0.163466
$263$	7287.34	1.70858	0.854290	−	0.519797i	$-0.173992\pi$
$263$	7287.34	1.70858	0.854290	+	0.519797i	$0.173992\pi$
$264$	293.210	0.0683555
$265$	−3563.43	−0.826037
$266$	−1487.58	−0.342892
$267$	−1336.64	−0.306371
$268$	1027.16	0.234118
$269$	−472.734	−0.107149	−0.0535745	−	0.998564i	$-0.517061\pi$
$269$	−472.734	−0.107149	−0.0535745	+	0.998564i	$0.517061\pi$
$270$	2074.31	0.467550
$271$	2506.38	0.561815	0.280907	−	0.959735i	$-0.409365\pi$
$271$	2506.38	0.561815	0.280907	+	0.959735i	$0.409365\pi$
$272$	−2879.75	−0.641949
$273$	−694.134	−0.153886
$274$	3267.71	0.720472
$275$	−358.480	−0.0786078
$276$	0	0
$277$	694.569	0.150659	0.0753296	−	0.997159i	$-0.475999\pi$
$277$	694.569	0.150659	0.0753296	+	0.997159i	$0.475999\pi$
$278$	1113.78	0.240287
$279$	4994.56	1.07174
$280$	−2207.15	−0.471079
$281$	979.984	0.208046	0.104023	−	0.994575i	$-0.466828\pi$
$281$	979.984	0.208046	0.104023	+	0.994575i	$0.466828\pi$
$282$	−2354.50	−0.497192
$283$	7313.03	1.53609	0.768047	−	0.640394i	$-0.221229\pi$
$283$	7313.03	1.53609	0.768047	+	0.640394i	$0.221229\pi$
$284$	1445.03	0.301925
$285$	−861.254	−0.179005
$286$	−305.222	−0.0631055
$287$	−3797.98	−0.781141
$288$	1838.61	0.376184
$289$	−772.542	−0.157244
$290$	−3144.17	−0.636662
$291$	−4386.64	−0.883675
$292$	585.249	0.117291
$293$	−5197.76	−1.03637	−0.518185	−	0.855269i	$-0.673392\pi$
$293$	−5197.76	−1.03637	−0.518185	+	0.855269i	$0.673392\pi$
$294$	1123.97	0.222963
$295$	−317.274	−0.0626183
$296$	5824.82	1.14379
$297$	−581.113	−0.113534
$298$	823.672	0.160114
$299$	0	0
$300$	319.075	0.0614060
$301$	6406.01	1.22670
$302$	−2521.29	−0.480410
$303$	4111.67	0.779568
$304$	2218.79	0.418607
$305$	2518.72	0.472857
$306$	3405.42	0.636193
$307$	−618.475	−0.114978	−0.0574890	−	0.998346i	$-0.518309\pi$
$307$	−618.475	−0.114978	−0.0574890	+	0.998346i	$0.518309\pi$
$308$	120.522	0.0222966
$309$	−1943.79	−0.357859
$310$	4235.82	0.776060
$311$	4052.28	0.738855	0.369427	−	0.929260i	$-0.379554\pi$
$311$	4052.28	0.738855	0.369427	+	0.929260i	$0.379554\pi$
$312$	1393.79	0.252909
$313$	3750.51	0.677288	0.338644	−	0.940915i	$-0.390032\pi$
$313$	3750.51	0.677288	0.338644	+	0.940915i	$0.390032\pi$
$314$	6606.62	1.18737
$315$	1938.79	0.346788
$316$	1502.54	0.267482
$317$	−2672.14	−0.473446	−0.236723	−	0.971577i	$-0.576073\pi$
$317$	−2672.14	−0.473446	−0.236723	+	0.971577i	$0.576073\pi$
$318$	2781.54	0.490507
$319$	880.832	0.154599
$320$	4209.68	0.735401
$321$	148.683	0.0258525
$322$	0	0
$323$	−3190.15	−0.549550
$324$	−606.741	−0.104037
$325$	−1704.05	−0.290842
$326$	−5012.70	−0.851619
$327$	−3405.55	−0.575924
$328$	7626.16	1.28379
$329$	−4965.20	−0.832038
$330$	−218.433	−0.0364374
$331$	7245.13	1.20311	0.601553	−	0.798833i	$-0.294549\pi$
$331$	7245.13	1.20311	0.601553	+	0.798833i	$0.294549\pi$
$332$	568.453	0.0939696
$333$	−5116.61	−0.842007
$334$	−1704.60	−0.279256
$335$	−3925.81	−0.640268
$336$	1279.77	0.207789
$337$	−2647.76	−0.427991	−0.213995	−	0.976835i	$-0.568648\pi$
$337$	−2647.76	−0.427991	−0.213995	+	0.976835i	$0.568648\pi$
$338$	3958.89	0.637086
$339$	−1775.83	−0.284512
$340$	−922.590	−0.147160
$341$	−1186.66	−0.188449
$342$	−2623.81	−0.414853
$343$	6549.88	1.03108
$344$	−12863.0	−2.01606
$345$	0	0
$346$	−909.619	−0.141334
$347$	−8159.25	−1.26228	−0.631141	−	0.775668i	$-0.717413\pi$
$347$	−8159.25	−1.26228	−0.631141	+	0.775668i	$0.717413\pi$
$348$	−784.009	−0.120768
$349$	2121.43	0.325380	0.162690	−	0.986677i	$-0.447983\pi$
$349$	2121.43	0.325380	0.162690	+	0.986677i	$0.447983\pi$
$350$	−2106.37	−0.321686
$351$	−2762.35	−0.420066
$352$	−436.833	−0.0661457
$353$	227.717	0.0343346	0.0171673	−	0.999853i	$-0.494535\pi$
$353$	227.717	0.0343346	0.0171673	+	0.999853i	$0.494535\pi$
$354$	247.658	0.0371832
$355$	−5522.92	−0.825708
$356$	1103.20	0.164240
$357$	−1840.03	−0.272787
$358$	2764.69	0.408151
$359$	−2698.04	−0.396650	−0.198325	−	0.980136i	$-0.563550\pi$
$359$	−2698.04	−0.396650	−0.198325	+	0.980136i	$0.563550\pi$
$360$	−3892.99	−0.569941
$361$	−4401.05	−0.641646
$362$	−3171.33	−0.460446
$363$	−3062.26	−0.442774
$364$	572.905	0.0824956
$365$	−2236.83	−0.320770
$366$	−1966.06	−0.280786
$367$	7082.81	1.00741	0.503705	−	0.863876i	$-0.331970\pi$
$367$	7082.81	1.00741	0.503705	+	0.863876i	$0.331970\pi$
$368$	0	0
$369$	−6698.93	−0.945074
$370$	−4339.32	−0.609704
$371$	5865.76	0.820849
$372$	1056.22	0.147210
$373$	−7996.59	−1.11005	−0.555023	−	0.831835i	$-0.687291\pi$
$373$	−7996.59	−1.11005	−0.555023	+	0.831835i	$0.687291\pi$
$374$	−809.092	−0.111864
$375$	−3390.98	−0.466959
$376$	9969.88	1.36744
$377$	4187.07	0.572003
$378$	−3414.52	−0.464614
$379$	−12189.3	−1.65204	−0.826022	−	0.563638i	$-0.809401\pi$
$379$	−12189.3	−1.65204	−0.826022	+	0.563638i	$0.809401\pi$
$380$	710.838	0.0959612
$381$	−2815.61	−0.378604
$382$	−6042.73	−0.809353
$383$	−4553.32	−0.607477	−0.303739	−	0.952755i	$-0.598235\pi$
$383$	−4553.32	−0.607477	−0.303739	+	0.952755i	$0.598235\pi$
$384$	−1680.02	−0.223263
$385$	−460.636	−0.0609771
$386$	−1614.05	−0.212832
$387$	11299.0	1.48414
$388$	3620.52	0.473722
$389$	−7879.32	−1.02698	−0.513492	−	0.858094i	$-0.671649\pi$
$389$	−7879.32	−1.02698	−0.513492	+	0.858094i	$0.671649\pi$
$390$	−1038.33	−0.134815
$391$	0	0
$392$	−4759.33	−0.613221
$393$	−660.675	−0.0848007
$394$	−8430.39	−1.07796
$395$	−5742.73	−0.731514
$396$	212.578	0.0269759
$397$	−5582.16	−0.705694	−0.352847	−	0.935681i	$-0.614786\pi$
$397$	−5582.16	−0.705694	−0.352847	+	0.935681i	$0.614786\pi$
$398$	−7762.04	−0.977577
$399$	1417.71	0.177881
$400$	3141.74	0.392717
$401$	−6288.98	−0.783184	−0.391592	−	0.920139i	$-0.628075\pi$
$401$	−6288.98	−0.783184	−0.391592	+	0.920139i	$0.628075\pi$
$402$	3064.41	0.380196
$403$	−5640.82	−0.697244
$404$	−3393.57	−0.417912
$405$	2318.97	0.284520
$406$	5175.62	0.632664
$407$	1215.65	0.148053
$408$	3694.70	0.448320
$409$	16205.5	1.95920	0.979599	−	0.200963i	$-0.0644072\pi$
$409$	16205.5	1.95920	0.979599	+	0.200963i	$0.0644072\pi$
$410$	−5681.27	−0.684336
$411$	−3114.23	−0.373756
$412$	1604.31	0.191842
$413$	522.265	0.0622251
$414$	0	0
$415$	−2172.63	−0.256989
$416$	−2076.51	−0.244734
$417$	−1061.46	−0.124653
$418$	623.391	0.0729450
$419$	−11139.6	−1.29882	−0.649411	−	0.760438i	$-0.724985\pi$
$419$	−11139.6	−1.29882	−0.649411	+	0.760438i	$0.724985\pi$
$420$	410.002	0.0476334
$421$	5182.41	0.599941	0.299971	−	0.953948i	$-0.403023\pi$
$421$	5182.41	0.599941	0.299971	+	0.953948i	$0.403023\pi$
$422$	2702.32	0.311722
$423$	−8757.69	−1.00665
$424$	−11778.2	−1.34905
$425$	−4517.15	−0.515562
$426$	4311.08	0.490311
$427$	−4146.06	−0.469888
$428$	−122.715	−0.0138591
$429$	290.886	0.0327369
$430$	9582.53	1.07468
$431$	−2395.67	−0.267739	−0.133869	−	0.990999i	$-0.542740\pi$
$431$	−2395.67	−0.267739	−0.133869	+	0.990999i	$0.542740\pi$
$432$	5092.91	0.567205
$433$	−8202.44	−0.910356	−0.455178	−	0.890400i	$-0.650424\pi$
$433$	−8202.44	−0.910356	−0.455178	+	0.890400i	$0.650424\pi$
$434$	−6972.59	−0.771186
$435$	2996.49	0.330278
$436$	2810.78	0.308743
$437$	0	0
$438$	1746.03	0.190476
$439$	−10549.6	−1.14693	−0.573466	−	0.819229i	$-0.694402\pi$
$439$	−10549.6	−1.14693	−0.573466	+	0.819229i	$0.694402\pi$
$440$	924.934	0.100215
$441$	4180.67	0.451427
$442$	−3846.06	−0.413887
$443$	8760.98	0.939609	0.469804	−	0.882771i	$-0.344324\pi$
$443$	8760.98	0.939609	0.469804	+	0.882771i	$0.344324\pi$
$444$	−1082.02	−0.115655
$445$	−4216.44	−0.449165
$446$	7658.05	0.813048
$447$	−784.986	−0.0830616
$448$	−6929.55	−0.730783
$449$	−3244.11	−0.340978	−0.170489	−	0.985360i	$-0.554535\pi$
$449$	−3244.11	−0.340978	−0.170489	+	0.985360i	$0.554535\pi$
$450$	−3715.24	−0.389196
$451$	1591.59	0.166176
$452$	1465.68	0.152522
$453$	2402.87	0.249220
$454$	7274.86	0.752040
$455$	−2189.65	−0.225610
$456$	−2846.70	−0.292344
$457$	−2975.91	−0.304611	−0.152306	−	0.988333i	$-0.548670\pi$
$457$	−2975.91	−0.304611	−0.152306	+	0.988333i	$0.548670\pi$
$458$	−13463.3	−1.37358
$459$	−7322.51	−0.744631
$460$	0	0
$461$	19088.5	1.92850	0.964252	−	0.264986i	$-0.0853672\pi$
$461$	19088.5	1.92850	0.964252	+	0.264986i	$0.0853672\pi$
$462$	359.563	0.0362086
$463$	1284.62	0.128944	0.0644722	−	0.997920i	$-0.479464\pi$
$463$	1284.62	0.128944	0.0644722	+	0.997920i	$0.479464\pi$
$464$	−7719.66	−0.772363
$465$	−4036.87	−0.402592
$466$	−11521.5	−1.14533
$467$	−5617.88	−0.556670	−0.278335	−	0.960484i	$-0.589782\pi$
$467$	−5617.88	−0.556670	−0.278335	+	0.960484i	$0.589782\pi$
$468$	1010.50	0.0998084
$469$	6462.28	0.636248
$470$	−7427.28	−0.728925
$471$	−6296.32	−0.615964
$472$	−1048.68	−0.102266
$473$	−2684.52	−0.260961
$474$	4482.66	0.434378
$475$	3480.38	0.336191
$476$	1518.68	0.146236
$477$	10346.1	0.993115
$478$	11576.4	1.10772
$479$	5975.11	0.569958	0.284979	−	0.958534i	$-0.408013\pi$
$479$	5975.11	0.569958	0.284979	+	0.958534i	$0.408013\pi$
$480$	−1486.06	−0.141311
$481$	5778.65	0.547784
$482$	−17084.9	−1.61451
$483$	0	0
$484$	2527.44	0.237363
$485$	−13837.7	−1.29554
$486$	−9375.84	−0.875096
$487$	−179.691	−0.0167198	−0.00835992	−	0.999965i	$-0.502661\pi$
$487$	−179.691	−0.0167198	−0.00835992	+	0.999965i	$0.502661\pi$
$488$	8325.09	0.772252
$489$	4777.26	0.441790
$490$	3545.57	0.326882
$491$	−4277.59	−0.393167	−0.196584	−	0.980487i	$-0.562985\pi$
$491$	−4277.59	−0.393167	−0.196584	+	0.980487i	$0.562985\pi$
$492$	−1416.64	−0.129811
$493$	11099.2	1.01396
$494$	2963.32	0.269890
$495$	−812.476	−0.0737739
$496$	10399.9	0.941472
$497$	9091.28	0.820523
$498$	1695.91	0.152602
$499$	11826.2	1.06095	0.530476	−	0.847700i	$-0.322013\pi$
$499$	11826.2	1.06095	0.530476	+	0.847700i	$0.322013\pi$
$500$	2798.76	0.250328
$501$	1624.54	0.144868
$502$	17510.9	1.55687
$503$	5870.52	0.520384	0.260192	−	0.965557i	$-0.416214\pi$
$503$	5870.52	0.520384	0.260192	+	0.965557i	$0.416214\pi$
$504$	6408.26	0.566362
$505$	12970.3	1.14291
$506$	0	0
$507$	−3772.95	−0.330498
$508$	2323.87	0.202963
$509$	−12362.2	−1.07651	−0.538256	−	0.842781i	$-0.680917\pi$
$509$	−12362.2	−1.07651	−0.538256	+	0.842781i	$0.680917\pi$
$510$	−2752.44	−0.238981
$511$	3682.05	0.318756
$512$	12588.7	1.08662
$513$	5641.86	0.485564
$514$	−7529.98	−0.646173
$515$	−6131.70	−0.524651
$516$	2389.44	0.203855
$517$	2080.73	0.177003
$518$	7142.96	0.605876
$519$	866.896	0.0733189
$520$	4396.72	0.370786
$521$	20502.2	1.72402	0.862011	−	0.506889i	$-0.169205\pi$
$521$	20502.2	1.72402	0.862011	+	0.506889i	$0.169205\pi$
$522$	9128.83	0.765437
$523$	6857.92	0.573377	0.286688	−	0.958024i	$-0.407446\pi$
$523$	6857.92	0.573377	0.286688	+	0.958024i	$0.407446\pi$
$524$	545.290	0.0454601
$525$	2007.43	0.166879
$526$	−17944.0	−1.48744
$527$	−14952.9	−1.23597
$528$	−536.304	−0.0442039
$529$	0	0
$530$	8774.40	0.719123
$531$	921.178	0.0752838
$532$	−1170.11	−0.0953586
$533$	7565.72	0.614836
$534$	3291.27	0.266717
$535$	469.020	0.0379019
$536$	−12975.9	−1.04566
$537$	−2634.83	−0.211735
$538$	1164.03	0.0932808
$539$	−993.282	−0.0793760
$540$	1631.62	0.130026
$541$	−16439.2	−1.30643	−0.653213	−	0.757174i	$-0.726579\pi$
$541$	−16439.2	−1.30643	−0.653213	+	0.757174i	$0.726579\pi$
$542$	−6171.58	−0.489100
$543$	3022.38	0.238863
$544$	−5504.47	−0.433828
$545$	−10742.8	−0.844353
$546$	1709.20	0.133969
$547$	15032.7	1.17505	0.587524	−	0.809207i	$-0.300103\pi$
$547$	15032.7	1.17505	0.587524	+	0.809207i	$0.300103\pi$
$548$	2570.34	0.200364
$549$	−7312.88	−0.568500
$550$	882.701	0.0684337
$551$	−8551.75	−0.661192
$552$	0	0
$553$	9453.10	0.726920
$554$	−1710.27	−0.131159
$555$	4135.51	0.316293
$556$	876.082	0.0668240
$557$	6056.60	0.460730	0.230365	−	0.973104i	$-0.426008\pi$
$557$	6056.60	0.460730	0.230365	+	0.973104i	$0.426008\pi$
$558$	−12298.3	−0.933030
$559$	−12761.0	−0.965534
$560$	4037.04	0.304636
$561$	771.090	0.0580311
$562$	−2413.06	−0.181119
$563$	8433.26	0.631296	0.315648	−	0.948876i	$-0.397778\pi$
$563$	8433.26	0.631296	0.315648	+	0.948876i	$0.397778\pi$
$564$	−1852.02	−0.138269
$565$	−5601.86	−0.417119
$566$	−18007.2	−1.33728
$567$	−3817.26	−0.282734
$568$	−18254.9	−1.34852
$569$	10569.3	0.778716	0.389358	−	0.921087i	$-0.372697\pi$
$569$	10569.3	0.778716	0.389358	+	0.921087i	$0.372697\pi$
$570$	2120.71	0.155836
$571$	−9582.70	−0.702318	−0.351159	−	0.936316i	$-0.614212\pi$
$571$	−9582.70	−0.702318	−0.351159	+	0.936316i	$0.614212\pi$
$572$	−240.084	−0.0175497
$573$	5758.91	0.419864
$574$	9351.94	0.680039
$575$	0	0
$576$	−12222.4	−0.884147
$577$	12781.5	0.922187	0.461094	−	0.887352i	$-0.347457\pi$
$577$	12781.5	0.922187	0.461094	+	0.887352i	$0.347457\pi$
$578$	1902.27	0.136892
$579$	1538.24	0.110410
$580$	−2473.16	−0.177056
$581$	3576.37	0.255375
$582$	10801.4	0.769302
$583$	−2458.13	−0.174623
$584$	−7393.37	−0.523870
$585$	−3862.14	−0.272957
$586$	12798.7	0.902233
$587$	15625.2	1.09867	0.549337	−	0.835601i	$-0.314880\pi$
$587$	15625.2	1.09867	0.549337	+	0.835601i	$0.314880\pi$
$588$	884.098	0.0620061
$589$	11520.9	0.805960
$590$	781.238	0.0545137
$591$	8034.43	0.559209
$592$	−10654.0	−0.739660
$593$	−21723.4	−1.50434	−0.752169	−	0.658970i	$-0.770992\pi$
$593$	−21723.4	−1.50434	−0.752169	+	0.658970i	$0.770992\pi$
$594$	1430.90	0.0988394
$595$	−5804.40	−0.399928
$596$	647.890	0.0445278
$597$	7397.47	0.507133
$598$	0	0
$599$	24421.4	1.66583	0.832915	−	0.553401i	$-0.186670\pi$
$599$	24421.4	1.66583	0.832915	+	0.553401i	$0.186670\pi$
$600$	−4030.83	−0.274263
$601$	−8003.16	−0.543188	−0.271594	−	0.962412i	$-0.587551\pi$
$601$	−8003.16	−0.543188	−0.271594	+	0.962412i	$0.587551\pi$
$602$	−15773.8	−1.06793
$603$	11398.3	0.769773
$604$	−1983.21	−0.133602
$605$	−9659.92	−0.649143
$606$	−10124.3	−0.678669
$607$	−16324.9	−1.09161	−0.545806	−	0.837911i	$-0.683777\pi$
$607$	−16324.9	−1.09161	−0.545806	+	0.837911i	$0.683777\pi$
$608$	4241.09	0.282893
$609$	−4932.53	−0.328204
$610$	−6201.96	−0.411655
$611$	9890.87	0.654897
$612$	2678.66	0.176926
$613$	−11712.0	−0.771685	−0.385842	−	0.922565i	$-0.626089\pi$
$613$	−11712.0	−0.771685	−0.385842	+	0.922565i	$0.626089\pi$
$614$	1522.90	0.100096
$615$	5414.43	0.355010
$616$	−1522.53	−0.0995855
$617$	−18170.3	−1.18559	−0.592796	−	0.805353i	$-0.701976\pi$
$617$	−18170.3	−1.18559	−0.592796	+	0.805353i	$0.701976\pi$
$618$	4786.28	0.311541
$619$	−14644.2	−0.950889	−0.475444	−	0.879746i	$-0.657713\pi$
$619$	−14644.2	−0.950889	−0.475444	+	0.879746i	$0.657713\pi$
$620$	3331.84	0.215823
$621$	0	0
$622$	−9978.12	−0.643226
$623$	6940.68	0.446345
$624$	−2549.35	−0.163551
$625$	−1921.83	−0.122997
$626$	−9235.05	−0.589628
$627$	−594.111	−0.0378413
$628$	5196.68	0.330207
$629$	15318.2	0.971030
$630$	−4773.97	−0.301904
$631$	9674.08	0.610331	0.305166	−	0.952299i	$-0.401288\pi$
$631$	9674.08	0.610331	0.305166	+	0.952299i	$0.401288\pi$
$632$	−18981.4	−1.19468
$633$	−2575.39	−0.161710
$634$	6579.73	0.412168
$635$	−8881.88	−0.555066
$636$	2187.92	0.136410
$637$	−4721.61	−0.293685
$638$	−2168.91	−0.134589
$639$	16035.3	0.992720
$640$	−5299.63	−0.327323
$641$	17653.4	1.08778	0.543890	−	0.839157i	$-0.316951\pi$
$641$	17653.4	1.08778	0.543890	+	0.839157i	$0.316951\pi$
$642$	−366.108	−0.0225064
$643$	1015.03	0.0622533	0.0311267	−	0.999515i	$-0.490090\pi$
$643$	1015.03	0.0622533	0.0311267	+	0.999515i	$0.490090\pi$
$644$	0	0
$645$	−9132.46	−0.557504
$646$	7855.25	0.478422
$647$	29920.9	1.81810	0.909051	−	0.416686i	$-0.136808\pi$
$647$	29920.9	1.81810	0.909051	+	0.416686i	$0.136808\pi$
$648$	7664.88	0.464668
$649$	−218.862	−0.0132374
$650$	4195.96	0.253199
$651$	6645.10	0.400064
$652$	−3942.93	−0.236836
$653$	1052.12	0.0630514	0.0315257	−	0.999503i	$-0.489963\pi$
$653$	1052.12	0.0630514	0.0315257	+	0.999503i	$0.489963\pi$
$654$	8385.64	0.501383
$655$	−2084.11	−0.124325
$656$	−13948.8	−0.830199
$657$	6494.45	0.385651
$658$	12226.0	0.724348
$659$	583.625	0.0344989	0.0172495	−	0.999851i	$-0.494509\pi$
$659$	583.625	0.0344989	0.0172495	+	0.999851i	$0.494509\pi$
$660$	−171.817	−0.0101333
$661$	−16133.1	−0.949326	−0.474663	−	0.880168i	$-0.657430\pi$
$661$	−16133.1	−0.949326	−0.474663	+	0.880168i	$0.657430\pi$
$662$	−17840.0	−1.04739
$663$	3665.41	0.214710
$664$	−7181.19	−0.419705
$665$	4472.18	0.260788
$666$	12598.9	0.733027
$667$	0	0
$668$	−1340.81	−0.0776612
$669$	−7298.37	−0.421781
$670$	9666.71	0.557399
$671$	1737.46	0.0999613
$672$	2446.20	0.140423
$673$	−3887.53	−0.222665	−0.111332	−	0.993783i	$-0.535512\pi$
$673$	−3887.53	−0.222665	−0.111332	+	0.993783i	$0.535512\pi$
$674$	6519.71	0.372596
$675$	7988.70	0.455534
$676$	3114.01	0.177174
$677$	2330.76	0.132317	0.0661583	−	0.997809i	$-0.478926\pi$
$677$	2330.76	0.132317	0.0661583	+	0.997809i	$0.478926\pi$
$678$	4372.70	0.247688
$679$	22778.2	1.28741
$680$	11655.0	0.657275
$681$	−6933.18	−0.390132
$682$	2921.96	0.164058
$683$	−19042.8	−1.06684	−0.533420	−	0.845850i	$-0.679094\pi$
$683$	−19042.8	−1.06684	−0.533420	+	0.845850i	$0.679094\pi$
$684$	−2063.86	−0.115371
$685$	−9823.86	−0.547957
$686$	−16128.1	−0.897628
$687$	12830.9	0.712563
$688$	23527.3	1.30374
$689$	−11684.8	−0.646090
$690$	0	0
$691$	−31012.9	−1.70736	−0.853681	−	0.520796i	$-0.825635\pi$
$691$	−31012.9	−1.70736	−0.853681	+	0.520796i	$0.825635\pi$
$692$	−715.495	−0.0393049
$693$	1337.42	0.0733106
$694$	20090.9	1.09891
$695$	−3348.40	−0.182751
$696$	9904.28	0.539398
$697$	20055.4	1.08989
$698$	−5223.70	−0.283267
$699$	10980.4	0.594158
$700$	−1656.84	−0.0894610
$701$	26575.1	1.43185	0.715926	−	0.698176i	$-0.246005\pi$
$701$	26575.1	1.43185	0.715926	+	0.698176i	$0.246005\pi$
$702$	6801.85	0.365697
$703$	−11802.4	−0.633196
$704$	2903.92	0.155463
$705$	7078.43	0.378141
$706$	−560.717	−0.0298907
$707$	−21350.4	−1.13573
$708$	194.804	0.0103407
$709$	6061.25	0.321065	0.160533	−	0.987031i	$-0.448679\pi$
$709$	6061.25	0.321065	0.160533	+	0.987031i	$0.448679\pi$
$710$	13599.3	0.718837
$711$	16673.5	0.879474
$712$	−13936.6	−0.733560
$713$	0	0
$714$	4530.80	0.237480
$715$	917.604	0.0479950
$716$	2174.67	0.113507
$717$	−11032.6	−0.574647
$718$	6643.51	0.345312
$719$	10971.4	0.569072	0.284536	−	0.958665i	$-0.408160\pi$
$719$	10971.4	0.569072	0.284536	+	0.958665i	$0.408160\pi$
$720$	7120.59	0.368568
$721$	10093.4	0.521356
$722$	10836.9	0.558598
$723$	16282.4	0.837551
$724$	−2494.53	−0.128050
$725$	−12109.0	−0.620299
$726$	7540.34	0.385466
$727$	−18746.8	−0.956368	−0.478184	−	0.878260i	$-0.658705\pi$
$727$	−18746.8	−0.956368	−0.478184	+	0.878260i	$0.658705\pi$
$728$	−7237.44	−0.368458
$729$	477.408	0.0242548
$730$	5507.85	0.279253
$731$	−33827.3	−1.71156
$732$	−1546.48	−0.0780867
$733$	33613.0	1.69376	0.846879	−	0.531786i	$-0.178479\pi$
$733$	33613.0	1.69376	0.846879	+	0.531786i	$0.178479\pi$
$734$	−17440.3	−0.877022
$735$	−3379.04	−0.169575
$736$	0	0
$737$	−2708.11	−0.135352
$738$	16495.1	0.822754
$739$	−6689.63	−0.332993	−0.166497	−	0.986042i	$-0.553246\pi$
$739$	−6689.63	−0.332993	−0.166497	+	0.986042i	$0.553246\pi$
$740$	−3413.26	−0.169559
$741$	−2824.13	−0.140010
$742$	−14443.5	−0.714608
$743$	−23093.7	−1.14028	−0.570139	−	0.821548i	$-0.693111\pi$
$743$	−23093.7	−1.14028	−0.570139	+	0.821548i	$0.693111\pi$
$744$	−13343.0	−0.657499
$745$	−2476.24	−0.121775
$746$	19690.4	0.966375
$747$	6308.06	0.308969
$748$	−636.421	−0.0311095
$749$	−772.055	−0.0376639
$750$	8349.78	0.406521
$751$	−24968.7	−1.21321	−0.606606	−	0.795003i	$-0.707469\pi$
$751$	−24968.7	−1.21321	−0.606606	+	0.795003i	$0.707469\pi$
$752$	−18235.7	−0.884292
$753$	−16688.4	−0.807649
$754$	−10310.0	−0.497969
$755$	7579.87	0.365377
$756$	−2685.82	−0.129209
$757$	14955.0	0.718031	0.359015	−	0.933332i	$-0.383113\pi$
$757$	14955.0	0.718031	0.359015	+	0.933332i	$0.383113\pi$
$758$	30014.4	1.43822
$759$	0	0
$760$	−8979.93	−0.428600
$761$	33199.3	1.58144	0.790719	−	0.612179i	$-0.209707\pi$
$761$	33199.3	1.58144	0.790719	+	0.612179i	$0.209707\pi$
$762$	6933.02	0.329602
$763$	17683.8	0.839051
$764$	−4753.13	−0.225081
$765$	−10237.9	−0.483858
$766$	11211.8	0.528852
$767$	−1040.37	−0.0489773
$768$	−6539.18	−0.307243
$769$	−34593.5	−1.62220	−0.811101	−	0.584906i	$-0.801131\pi$
$769$	−34593.5	−1.62220	−0.811101	+	0.584906i	$0.801131\pi$
$770$	1134.24	0.0530849
$771$	7176.31	0.335212
$772$	−1269.59	−0.0591886
$773$	−34411.3	−1.60115	−0.800574	−	0.599234i	$-0.795472\pi$
$773$	−34411.3	−1.60115	−0.800574	+	0.599234i	$0.795472\pi$
$774$	−27822.1	−1.29205
$775$	16313.2	0.756115
$776$	−45737.6	−2.11583
$777$	−6807.47	−0.314307
$778$	19401.6	0.894063
$779$	−15452.3	−0.710703
$780$	−816.739	−0.0374922
$781$	−3809.83	−0.174553
$782$	0	0
$783$	−19629.3	−0.895904
$784$	8705.18	0.396555
$785$	−19861.8	−0.903054
$786$	1626.81	0.0738250
$787$	40801.8	1.84806	0.924032	−	0.382314i	$-0.124873\pi$
$787$	40801.8	1.84806	0.924032	+	0.382314i	$0.124873\pi$
$788$	−6631.24	−0.299782
$789$	17101.2	0.771632
$790$	14140.6	0.636834
$791$	9221.22	0.414499
$792$	−2685.47	−0.120485
$793$	8259.11	0.369848
$794$	13745.2	0.614357
$795$	−8362.28	−0.373056
$796$	−6105.52	−0.271865
$797$	58.9683	0.00262078	0.00131039	−	0.999999i	$-0.499583\pi$
$797$	58.9683	0.00262078	0.00131039	+	0.999999i	$0.499583\pi$
$798$	−3490.90	−0.154858
$799$	26219.0	1.16090
$800$	6005.26	0.265397
$801$	12242.1	0.540016
$802$	15485.6	0.681817
$803$	−1543.01	−0.0678103
$804$	2410.43	0.105733
$805$	0	0
$806$	13889.7	0.607000
$807$	−1109.36	−0.0483908
$808$	42870.6	1.86656
$809$	−21579.8	−0.937830	−0.468915	−	0.883243i	$-0.655355\pi$
$809$	−21579.8	−0.937830	−0.468915	+	0.883243i	$0.655355\pi$
$810$	−5710.11	−0.247695
$811$	−10357.3	−0.448453	−0.224227	−	0.974537i	$-0.571986\pi$
$811$	−10357.3	−0.448453	−0.224227	+	0.974537i	$0.571986\pi$
$812$	4071.07	0.175944
$813$	5881.71	0.253728
$814$	−2993.35	−0.128891
$815$	15069.9	0.647701
$816$	−6757.89	−0.289918
$817$	26063.3	1.11608
$818$	−39903.6	−1.70562
$819$	6357.47	0.271243
$820$	−4468.81	−0.190314
$821$	−4821.44	−0.204957	−0.102478	−	0.994735i	$-0.532677\pi$
$821$	−4821.44	−0.204957	−0.102478	+	0.994735i	$0.532677\pi$
$822$	7668.31	0.325381
$823$	−35449.7	−1.50146	−0.750728	−	0.660611i	$-0.770297\pi$
$823$	−35449.7	−1.50146	−0.750728	+	0.660611i	$0.770297\pi$
$824$	−20267.0	−0.856840
$825$	−841.243	−0.0355010
$826$	−1286.00	−0.0541713
$827$	−23791.2	−1.00037	−0.500183	−	0.865920i	$-0.666734\pi$
$827$	−23791.2	−1.00037	−0.500183	+	0.865920i	$0.666734\pi$
$828$	0	0
$829$	−14874.3	−0.623167	−0.311584	−	0.950219i	$-0.600859\pi$
$829$	−14874.3	−0.623167	−0.311584	+	0.950219i	$0.600859\pi$
$830$	5349.78	0.223727
$831$	1629.94	0.0680409
$832$	13803.9	0.575199
$833$	−12516.2	−0.520601
$834$	2613.69	0.108519
$835$	5124.61	0.212389
$836$	490.351	0.0202861
$837$	26444.5	1.09206
$838$	27429.6	1.13072
$839$	11074.0	0.455682	0.227841	−	0.973698i	$-0.426833\pi$
$839$	11074.0	0.455682	0.227841	+	0.973698i	$0.426833\pi$
$840$	−5179.50	−0.212750
$841$	5364.40	0.219952
$842$	−12760.9	−0.522291
$843$	2299.72	0.0939581
$844$	2125.61	0.0866901
$845$	−11901.8	−0.484537
$846$	21564.5	0.876362
$847$	15901.2	0.645067
$848$	21543.2	0.872401
$849$	17161.4	0.693733
$850$	11122.8	0.448833
$851$	0	0
$852$	3391.04	0.136356
$853$	29164.2	1.17065	0.585325	−	0.810799i	$-0.300967\pi$
$853$	29164.2	1.17065	0.585325	+	0.810799i	$0.300967\pi$
$854$	10209.0	0.409070
$855$	7888.10	0.315517
$856$	1550.25	0.0619000
$857$	−8148.27	−0.324784	−0.162392	−	0.986726i	$-0.551921\pi$
$857$	−8148.27	−0.324784	−0.162392	+	0.986726i	$0.551921\pi$
$858$	−716.263	−0.0284998
$859$	−7345.62	−0.291769	−0.145884	−	0.989302i	$-0.546603\pi$
$859$	−7345.62	−0.291769	−0.145884	+	0.989302i	$0.546603\pi$
$860$	7537.50	0.298868
$861$	−8912.69	−0.352780
$862$	5898.97	0.233086
$863$	23871.9	0.941610	0.470805	−	0.882237i	$-0.343964\pi$
$863$	23871.9	0.941610	0.470805	+	0.882237i	$0.343964\pi$
$864$	9734.80	0.383316
$865$	2734.63	0.107492
$866$	20197.2	0.792529
$867$	−1812.92	−0.0710150
$868$	−5484.55	−0.214467
$869$	−3961.45	−0.154641
$870$	−7378.40	−0.287530
$871$	−12873.1	−0.500790
$872$	−35508.2	−1.37897
$873$	40176.6	1.55758
$874$	0	0
$875$	17608.2	0.680302
$876$	1373.40	0.0529714
$877$	−15150.3	−0.583342	−0.291671	−	0.956519i	$-0.594211\pi$
$877$	−15150.3	−0.583342	−0.291671	+	0.956519i	$0.594211\pi$
$878$	25976.7	0.998486
$879$	−12197.6	−0.468047
$880$	−1691.78	−0.0648065
$881$	8462.80	0.323631	0.161816	−	0.986821i	$-0.448265\pi$
$881$	8462.80	0.323631	0.161816	+	0.986821i	$0.448265\pi$
$882$	−10294.2	−0.392999
$883$	−49243.3	−1.87675	−0.938374	−	0.345622i	$-0.887668\pi$
$883$	−49243.3	−1.87675	−0.938374	+	0.345622i	$0.887668\pi$
$884$	−3025.26	−0.115102
$885$	−744.545	−0.0282798
$886$	−21572.6	−0.817996
$887$	28877.4	1.09313	0.546566	−	0.837416i	$-0.315935\pi$
$887$	28877.4	1.09313	0.546566	+	0.837416i	$0.315935\pi$
$888$	13669.1	0.516558
$889$	14620.5	0.551580
$890$	10382.3	0.391030
$891$	1599.68	0.0601472
$892$	6023.73	0.226109
$893$	−20201.3	−0.757010
$894$	1932.91	0.0723110
$895$	−8311.61	−0.310421
$896$	8723.73	0.325267
$897$	0	0
$898$	7988.12	0.296845
$899$	−40083.8	−1.48706
$900$	−2922.36	−0.108236
$901$	−30974.5	−1.14529
$902$	−3919.06	−0.144668
$903$	15032.9	0.554004
$904$	−18515.8	−0.681223
$905$	9534.12	0.350193
$906$	−5916.69	−0.216964
$907$	715.375	0.0261893	0.0130946	−	0.999914i	$-0.495832\pi$
$907$	715.375	0.0261893	0.0130946	+	0.999914i	$0.495832\pi$
$908$	5722.31	0.209143
$909$	−37658.1	−1.37408
$910$	5391.68	0.196409
$911$	16281.5	0.592129	0.296065	−	0.955168i	$-0.404326\pi$
$911$	16281.5	0.592129	0.296065	+	0.955168i	$0.404326\pi$
$912$	5206.83	0.189052
$913$	−1498.73	−0.0543271
$914$	7327.73	0.265186
$915$	5910.66	0.213552
$916$	−10590.0	−0.381992
$917$	3430.65	0.123544
$918$	18030.6	0.648254
$919$	−43308.7	−1.55454	−0.777270	−	0.629167i	$-0.783396\pi$
$919$	−43308.7	−1.55454	−0.777270	+	0.629167i	$0.783396\pi$
$920$	0	0
$921$	−1451.37	−0.0519265
$922$	−47002.5	−1.67890
$923$	−18110.2	−0.645833
$924$	282.828	0.0100696
$925$	−16711.9	−0.594035
$926$	−3163.17	−0.112255
$927$	17802.9	0.630769
$928$	−14755.7	−0.521961
$929$	35185.6	1.24263	0.621314	−	0.783562i	$-0.286599\pi$
$929$	35185.6	1.24263	0.621314	+	0.783562i	$0.286599\pi$
$930$	9940.18	0.350485
$931$	9643.50	0.339477
$932$	−9062.70	−0.318518
$933$	9509.47	0.333683
$934$	13833.2	0.484620
$935$	2432.41	0.0850785
$936$	−12765.5	−0.445783
$937$	30321.6	1.05717	0.528583	−	0.848882i	$-0.322724\pi$
$937$	30321.6	1.05717	0.528583	+	0.848882i	$0.322724\pi$
$938$	−15912.4	−0.553899
$939$	8801.30	0.305878
$940$	−5842.20	−0.202715
$941$	17584.1	0.609167	0.304583	−	0.952486i	$-0.401483\pi$
$941$	17584.1	0.609167	0.304583	+	0.952486i	$0.401483\pi$
$942$	15503.7	0.536240
$943$	0	0
$944$	1918.12	0.0661330
$945$	10265.2	0.353363
$946$	6610.23	0.227185
$947$	−30667.7	−1.05234	−0.526170	−	0.850379i	$-0.676372\pi$
$947$	−30667.7	−1.05234	−0.526170	+	0.850379i	$0.676372\pi$
$948$	3526.00	0.120801
$949$	−7334.78	−0.250893
$950$	−8569.90	−0.292678
$951$	−6270.70	−0.213818
$952$	−19185.2	−0.653148
$953$	23821.1	0.809697	0.404849	−	0.914384i	$-0.367324\pi$
$953$	23821.1	0.809697	0.404849	+	0.914384i	$0.367324\pi$
$954$	−25475.7	−0.864577
$955$	18166.5	0.615555
$956$	9105.82	0.308058
$957$	2067.04	0.0698203
$958$	−14712.8	−0.496189
$959$	16171.1	0.544516
$960$	9878.83	0.332123
$961$	24209.8	0.812655
$962$	−14229.0	−0.476885
$963$	−1361.76	−0.0455682
$964$	−13438.7	−0.448996
$965$	4852.40	0.161870
$966$	0	0
$967$	−3825.29	−0.127211	−0.0636055	−	0.997975i	$-0.520260\pi$
$967$	−3825.29	−0.127211	−0.0636055	+	0.997975i	$0.520260\pi$
$968$	−31928.8	−1.06016
$969$	−7486.30	−0.248188
$970$	34073.2	1.12786
$971$	36824.3	1.21704	0.608521	−	0.793538i	$-0.291763\pi$
$971$	36824.3	1.21704	0.608521	+	0.793538i	$0.291763\pi$
$972$	−7374.91	−0.243365
$973$	5511.80	0.181603
$974$	442.461	0.0145558
$975$	−3998.89	−0.131351
$976$	−15227.2	−0.499398
$977$	35837.0	1.17352	0.586759	−	0.809762i	$-0.300404\pi$
$977$	35837.0	1.17352	0.586759	+	0.809762i	$0.300404\pi$
$978$	−11763.3	−0.384610
$979$	−2908.59	−0.0949529
$980$	2788.90	0.0909061
$981$	31190.9	1.01514
$982$	10532.9	0.342280
$983$	25453.0	0.825863	0.412931	−	0.910762i	$-0.364505\pi$
$983$	25453.0	0.825863	0.412931	+	0.910762i	$0.364505\pi$
$984$	17896.3	0.579789
$985$	25344.7	0.819846
$986$	−27330.1	−0.882727
$987$	−11651.8	−0.375766
$988$	2330.91	0.0750567
$989$	0	0
$990$	2000.60	0.0642254
$991$	21122.3	0.677065	0.338533	−	0.940955i	$-0.390069\pi$
$991$	21122.3	0.677065	0.338533	+	0.940955i	$0.390069\pi$
$992$	19878.9	0.636244
$993$	17002.1	0.543349
$994$	−22385.9	−0.714323
$995$	23335.4	0.743499
$996$	1333.98	0.0424387
$997$	8006.91	0.254344	0.127172	−	0.991881i	$-0.459410\pi$
$997$	8006.91	0.254344	0.127172	+	0.991881i	$0.459410\pi$
$998$	−29120.3	−0.923634
$999$	−27090.7	−0.857970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	529.4.a.m.1.8		25
23.17	odd	22		23.4.c.a.13.4	✓	50
23.19	odd	22		23.4.c.a.16.4	yes	50
23.22	odd	2		529.4.a.n.1.8		25
69.17	even	22		207.4.i.a.82.2		50
69.65	even	22		207.4.i.a.154.2		50

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.4.c.a.13.4	✓	50	23.17	odd	22
23.4.c.a.16.4	yes	50	23.19	odd	22
207.4.i.a.82.2		50	69.17	even	22
207.4.i.a.154.2		50	69.65	even	22
529.4.a.m.1.8		25	1.1	even	1	trivial
529.4.a.n.1.8		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:	\( N \)	\(=\)	\( 529 = 23^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	529.a (trivial)

\(f(q)\)	\(=\)	\(q-2.46235 q^{2} +2.34669 q^{3} -1.93685 q^{4} +7.40267 q^{5} -5.77838 q^{6} -12.1855 q^{7} +24.4680 q^{8} -21.4930 q^{9} +O(q^{10})\)	\(q-2.46235 q^{2} +2.34669 q^{3} -1.93685 q^{4} +7.40267 q^{5} -5.77838 q^{6} -12.1855 q^{7} +24.4680 q^{8} -21.4930 q^{9} -18.2279 q^{10} +5.10651 q^{11} -4.54520 q^{12} +24.2741 q^{13} +30.0050 q^{14} +17.3718 q^{15} -44.7538 q^{16} +64.3464 q^{17} +52.9233 q^{18} -49.5777 q^{19} -14.3379 q^{20} -28.5957 q^{21} -12.5740 q^{22} +57.4189 q^{24} -70.2005 q^{25} -59.7711 q^{26} -113.798 q^{27} +23.6016 q^{28} +172.492 q^{29} -42.7754 q^{30} -232.381 q^{31} -85.5444 q^{32} +11.9834 q^{33} -158.443 q^{34} -90.2055 q^{35} +41.6288 q^{36} +238.059 q^{37} +122.078 q^{38} +56.9638 q^{39} +181.128 q^{40} +311.679 q^{41} +70.4126 q^{42} -525.706 q^{43} -9.89055 q^{44} -159.106 q^{45} +407.467 q^{47} -105.024 q^{48} -194.513 q^{49} +172.858 q^{50} +151.001 q^{51} -47.0152 q^{52} -481.371 q^{53} +280.211 q^{54} +37.8018 q^{55} -298.155 q^{56} -116.344 q^{57} -424.734 q^{58} -42.8594 q^{59} -33.6466 q^{60} +340.245 q^{61} +572.202 q^{62} +261.904 q^{63} +568.670 q^{64} +179.693 q^{65} -29.5074 q^{66} -530.324 q^{67} -124.629 q^{68} +222.117 q^{70} -746.072 q^{71} -525.891 q^{72} -302.165 q^{73} -586.184 q^{74} -164.739 q^{75} +96.0246 q^{76} -62.2256 q^{77} -140.265 q^{78} -775.764 q^{79} -331.298 q^{80} +313.262 q^{81} -767.462 q^{82} -293.493 q^{83} +55.3857 q^{84} +476.335 q^{85} +1294.47 q^{86} +404.785 q^{87} +124.946 q^{88} -569.584 q^{89} +391.773 q^{90} -295.792 q^{91} -545.327 q^{93} -1003.32 q^{94} -367.007 q^{95} -200.746 q^{96} -1869.28 q^{97} +478.958 q^{98} -109.754 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9}+O(q^{10}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9	\( 25 q - q^{3} + 80 q^{4} - 51 q^{5} + 86 q^{6} - 73 q^{7} + 3 q^{8} + 166 q^{9} - 139 q^{10} - 221 q^{11} - 191 q^{12} - 27 q^{13} - 372 q^{14} - 310 q^{15} + 152 q^{16} - 365 q^{17} - 538 q^{18} - 405 q^{19} - 578 q^{20} - 352 q^{21} - 155 q^{22} + 803 q^{24} + 90 q^{25} - 850 q^{26} + 368 q^{27} - 459 q^{28} + 175 q^{29} - 893 q^{30} + 287 q^{31} + 164 q^{32} - 1020 q^{33} - 335 q^{34} + 462 q^{35} - 1092 q^{36} - 471 q^{37} - 810 q^{38} - 822 q^{39} - 1405 q^{40} - 73 q^{41} - 556 q^{42} - 901 q^{43} - 2073 q^{44} - 1384 q^{45} + 1452 q^{47} - 4028 q^{48} - 1092 q^{49} + 364 q^{50} - 2214 q^{51} + 1287 q^{52} - 2071 q^{53} + 2052 q^{54} + 1006 q^{55} - 4879 q^{56} - 418 q^{57} + 2796 q^{58} - 2713 q^{59} - 2805 q^{60} - 1225 q^{61} - 2852 q^{62} - 4003 q^{63} + 217 q^{64} - 2030 q^{65} - 2933 q^{66} - 767 q^{67} - 4175 q^{68} + 4851 q^{70} - 1683 q^{71} - 5265 q^{72} + 2203 q^{73} - 3089 q^{74} + 2333 q^{75} - 5252 q^{76} + 2760 q^{77} - 692 q^{78} - 5425 q^{79} - 4689 q^{80} + 1929 q^{81} - 2725 q^{82} - 5425 q^{83} - 4317 q^{84} - 912 q^{85} - 4359 q^{86} - 4404 q^{87} - 2610 q^{88} - 4933 q^{89} - 2695 q^{90} - 3619 q^{91} + 6375 q^{93} - 5117 q^{94} - 1338 q^{95} + 20 q^{96} - 2085 q^{97} + 5951 q^{98} - 7317 q^{99}+O(q^{100}) \) 25 * q - q^3 + 80 * q^4 - 51 * q^5 + 86 * q^6 - 73 * q^7 + 3 * q^8 + 166 * q^9 - 139 * q^10 - 221 * q^11 - 191 * q^12 - 27 * q^13 - 372 * q^14 - 310 * q^15 + 152 * q^16 - 365 * q^17 - 538 * q^18 - 405 * q^19 - 578 * q^20 - 352 * q^21 - 155 * q^22 + 803 * q^24 + 90 * q^25 - 850 * q^26 + 368 * q^27 - 459 * q^28 + 175 * q^29 - 893 * q^30 + 287 * q^31 + 164 * q^32 - 1020 * q^33 - 335 * q^34 + 462 * q^35 - 1092 * q^36 - 471 * q^37 - 810 * q^38 - 822 * q^39 - 1405 * q^40 - 73 * q^41 - 556 * q^42 - 901 * q^43 - 2073 * q^44 - 1384 * q^45 + 1452 * q^47 - 4028 * q^48 - 1092 * q^49 + 364 * q^50 - 2214 * q^51 + 1287 * q^52 - 2071 * q^53 + 2052 * q^54 + 1006 * q^55 - 4879 * q^56 - 418 * q^57 + 2796 * q^58 - 2713 * q^59 - 2805 * q^60 - 1225 * q^61 - 2852 * q^62 - 4003 * q^63 + 217 * q^64 - 2030 * q^65 - 2933 * q^66 - 767 * q^67 - 4175 * q^68 + 4851 * q^70 - 1683 * q^71 - 5265 * q^72 + 2203 * q^73 - 3089 * q^74 + 2333 * q^75 - 5252 * q^76 + 2760 * q^77 - 692 * q^78 - 5425 * q^79 - 4689 * q^80 + 1929 * q^81 - 2725 * q^82 - 5425 * q^83 - 4317 * q^84 - 912 * q^85 - 4359 * q^86 - 4404 * q^87 - 2610 * q^88 - 4933 * q^89 - 2695 * q^90 - 3619 * q^91 + 6375 * q^93 - 5117 * q^94 - 1338 * q^95 + 20 * q^96 - 2085 * q^97 + 5951 * q^98 - 7317 * q^99

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