LMFDB - Embedded newform 1205.2.a.e.1.23

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1205,2,Mod(1,1205)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1205, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("1205.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1205 = 5 \cdot 241 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1205.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:	$9.62197344356$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.23
Character	$\chi$	$=$	1205.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52189 q^{2} -2.20014 q^{3} +4.35995 q^{4} +1.00000 q^{5} -5.54852 q^{6} -1.38484 q^{7} +5.95156 q^{8} +1.84062 q^{9} +O(q^{10})$	\(q+2.52189 q^{2} -2.20014 q^{3} +4.35995 q^{4} +1.00000 q^{5} -5.54852 q^{6} -1.38484 q^{7} +5.95156 q^{8} +1.84062 q^{9} +2.52189 q^{10} +1.13965 q^{11} -9.59251 q^{12} -1.42729 q^{13} -3.49243 q^{14} -2.20014 q^{15} +6.28929 q^{16} +8.05325 q^{17} +4.64185 q^{18} +8.18254 q^{19} +4.35995 q^{20} +3.04685 q^{21} +2.87409 q^{22} +6.39018 q^{23} -13.0943 q^{24} +1.00000 q^{25} -3.59948 q^{26} +2.55080 q^{27} -6.03785 q^{28} -1.29066 q^{29} -5.54852 q^{30} -5.90487 q^{31} +3.95782 q^{32} -2.50740 q^{33} +20.3095 q^{34} -1.38484 q^{35} +8.02502 q^{36} -10.2623 q^{37} +20.6355 q^{38} +3.14024 q^{39} +5.95156 q^{40} -7.16948 q^{41} +7.68383 q^{42} +6.20729 q^{43} +4.96884 q^{44} +1.84062 q^{45} +16.1154 q^{46} +11.4217 q^{47} -13.8373 q^{48} -5.08221 q^{49} +2.52189 q^{50} -17.7183 q^{51} -6.22293 q^{52} +3.60717 q^{53} +6.43285 q^{54} +1.13965 q^{55} -8.24196 q^{56} -18.0027 q^{57} -3.25492 q^{58} -3.38677 q^{59} -9.59251 q^{60} +3.02994 q^{61} -14.8915 q^{62} -2.54897 q^{63} -2.59738 q^{64} -1.42729 q^{65} -6.32340 q^{66} -6.78050 q^{67} +35.1118 q^{68} -14.0593 q^{69} -3.49243 q^{70} -5.74234 q^{71} +10.9546 q^{72} +10.5460 q^{73} -25.8804 q^{74} -2.20014 q^{75} +35.6755 q^{76} -1.57824 q^{77} +7.91937 q^{78} -11.9895 q^{79} +6.28929 q^{80} -11.1340 q^{81} -18.0807 q^{82} -2.05382 q^{83} +13.2841 q^{84} +8.05325 q^{85} +15.6541 q^{86} +2.83964 q^{87} +6.78272 q^{88} +15.5874 q^{89} +4.64185 q^{90} +1.97657 q^{91} +27.8609 q^{92} +12.9915 q^{93} +28.8043 q^{94} +8.18254 q^{95} -8.70775 q^{96} -13.7395 q^{97} -12.8168 q^{98} +2.09767 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * 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 $

$2$	2.52189	1.78325	0.891624	−	0.452776i	$-0.149566\pi$
$2$	2.52189	1.78325	0.891624	+	0.452776i	$0.149566\pi$
$3$	−2.20014	−1.27025	−0.635126	−	0.772409i	$-0.719052\pi$
$3$	−2.20014	−1.27025	−0.635126	+	0.772409i	$0.719052\pi$
$4$	4.35995	2.17998
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−5.54852	−2.26518
$7$	−1.38484	−0.523421	−0.261711	−	0.965146i	$-0.584287\pi$
$7$	−1.38484	−0.523421	−0.261711	+	0.965146i	$0.584287\pi$
$8$	5.95156	2.10419
$9$	1.84062	0.613540
$10$	2.52189	0.797493
$11$	1.13965	0.343619	0.171809	−	0.985130i	$-0.445039\pi$
$11$	1.13965	0.343619	0.171809	+	0.985130i	$0.445039\pi$
$12$	−9.59251	−2.76912
$13$	−1.42729	−0.395860	−0.197930	−	0.980216i	$-0.563422\pi$
$13$	−1.42729	−0.395860	−0.197930	+	0.980216i	$0.563422\pi$
$14$	−3.49243	−0.933390
$15$	−2.20014	−0.568074
$16$	6.28929	1.57232
$17$	8.05325	1.95320	0.976600	−	0.215063i	$-0.0689958\pi$
$17$	8.05325	1.95320	0.976600	+	0.215063i	$0.0689958\pi$
$18$	4.64185	1.09409
$19$	8.18254	1.87720	0.938602	−	0.345003i	$-0.112122\pi$
$19$	8.18254	1.87720	0.938602	+	0.345003i	$0.112122\pi$
$20$	4.35995	0.974915
$21$	3.04685	0.664877
$22$	2.87409	0.612758
$23$	6.39018	1.33244	0.666222	−	0.745753i	$-0.267910\pi$
$23$	6.39018	1.33244	0.666222	+	0.745753i	$0.267910\pi$
$24$	−13.0943	−2.67285
$25$	1.00000	0.200000
$26$	−3.59948	−0.705916
$27$	2.55080	0.490902
$28$	−6.03785	−1.14105
$29$	−1.29066	−0.239670	−0.119835	−	0.992794i	$-0.538237\pi$
$29$	−1.29066	−0.239670	−0.119835	+	0.992794i	$0.538237\pi$
$30$	−5.54852	−1.01302
$31$	−5.90487	−1.06055	−0.530273	−	0.847827i	$-0.677910\pi$
$31$	−5.90487	−1.06055	−0.530273	+	0.847827i	$0.677910\pi$
$32$	3.95782	0.699650
$33$	−2.50740	−0.436482
$34$	20.3095	3.48304
$35$	−1.38484	−0.234081
$36$	8.02502	1.33750
$37$	−10.2623	−1.68711	−0.843555	−	0.537043i	$-0.819541\pi$
$37$	−10.2623	−1.68711	−0.843555	+	0.537043i	$0.819541\pi$
$38$	20.6355	3.34752
$39$	3.14024	0.502842
$40$	5.95156	0.941024
$41$	−7.16948	−1.11968	−0.559842	−	0.828599i	$-0.689138\pi$
$41$	−7.16948	−1.11968	−0.559842	+	0.828599i	$0.689138\pi$
$42$	7.68383	1.18564
$43$	6.20729	0.946602	0.473301	−	0.880901i	$-0.343062\pi$
$43$	6.20729	0.946602	0.473301	+	0.880901i	$0.343062\pi$
$44$	4.96884	0.749081
$45$	1.84062	0.274383
$46$	16.1154	2.37608
$47$	11.4217	1.66602	0.833012	−	0.553255i	$-0.186615\pi$
$47$	11.4217	1.66602	0.833012	+	0.553255i	$0.186615\pi$
$48$	−13.8373	−1.99725
$49$	−5.08221	−0.726030
$50$	2.52189	0.356650
$51$	−17.7183	−2.48106
$52$	−6.22293	−0.862965
$53$	3.60717	0.495483	0.247741	−	0.968826i	$-0.420312\pi$
$53$	3.60717	0.495483	0.247741	+	0.968826i	$0.420312\pi$
$54$	6.43285	0.875400
$55$	1.13965	0.153671
$56$	−8.24196	−1.10138
$57$	−18.0027	−2.38452
$58$	−3.25492	−0.427392
$59$	−3.38677	−0.440919	−0.220460	−	0.975396i	$-0.570756\pi$
$59$	−3.38677	−0.440919	−0.220460	+	0.975396i	$0.570756\pi$
$60$	−9.59251	−1.23839
$61$	3.02994	0.387944	0.193972	−	0.981007i	$-0.437863\pi$
$61$	3.02994	0.387944	0.193972	+	0.981007i	$0.437863\pi$
$62$	−14.8915	−1.89122
$63$	−2.54897	−0.321140
$64$	−2.59738	−0.324673
$65$	−1.42729	−0.177034
$66$	−6.32340	−0.778357
$67$	−6.78050	−0.828370	−0.414185	−	0.910193i	$-0.635933\pi$
$67$	−6.78050	−0.828370	−0.414185	+	0.910193i	$0.635933\pi$
$68$	35.1118	4.25793
$69$	−14.0593	−1.69254
$70$	−3.49243	−0.417425
$71$	−5.74234	−0.681491	−0.340745	−	0.940156i	$-0.610679\pi$
$71$	−5.74234	−0.681491	−0.340745	+	0.940156i	$0.610679\pi$
$72$	10.9546	1.29101
$73$	10.5460	1.23432	0.617159	−	0.786838i	$-0.288283\pi$
$73$	10.5460	1.23432	0.617159	+	0.786838i	$0.288283\pi$
$74$	−25.8804	−3.00854
$75$	−2.20014	−0.254050
$76$	35.6755	4.09226
$77$	−1.57824	−0.179857
$78$	7.91937	0.896692
$79$	−11.9895	−1.34892	−0.674462	−	0.738310i	$-0.735624\pi$
$79$	−11.9895	−1.34892	−0.674462	+	0.738310i	$0.735624\pi$
$80$	6.28929	0.703164
$81$	−11.1340	−1.23711
$82$	−18.0807	−1.99668
$83$	−2.05382	−0.225436	−0.112718	−	0.993627i	$-0.535956\pi$
$83$	−2.05382	−0.225436	−0.112718	+	0.993627i	$0.535956\pi$
$84$	13.2841	1.44942
$85$	8.05325	0.873498
$86$	15.6541	1.68803
$87$	2.83964	0.304442
$88$	6.78272	0.723040
$89$	15.5874	1.65227	0.826133	−	0.563475i	$-0.190536\pi$
$89$	15.5874	1.65227	0.826133	+	0.563475i	$0.190536\pi$
$90$	4.64185	0.489294
$91$	1.97657	0.207201
$92$	27.8609	2.90470
$93$	12.9915	1.34716
$94$	28.8043	2.97093
$95$	8.18254	0.839511
$96$	−8.70775	−0.888732
$97$	−13.7395	−1.39504	−0.697520	−	0.716565i	$-0.745713\pi$
$97$	−13.7395	−1.39504	−0.697520	+	0.716565i	$0.745713\pi$
$98$	−12.8168	−1.29469
$99$	2.09767	0.210824
$100$	4.35995	0.435995
$101$	−6.30180	−0.627052	−0.313526	−	0.949580i	$-0.601510\pi$
$101$	−6.30180	−0.627052	−0.313526	+	0.949580i	$0.601510\pi$
$102$	−44.6837	−4.42434
$103$	7.71667	0.760346	0.380173	−	0.924915i	$-0.375864\pi$
$103$	7.71667	0.760346	0.380173	+	0.924915i	$0.375864\pi$
$104$	−8.49461	−0.832965
$105$	3.04685	0.297342
$106$	9.09690	0.883569
$107$	13.1175	1.26812	0.634058	−	0.773286i	$-0.281388\pi$
$107$	13.1175	1.26812	0.634058	+	0.773286i	$0.281388\pi$
$108$	11.1214	1.07015
$109$	−9.57548	−0.917165	−0.458582	−	0.888652i	$-0.651643\pi$
$109$	−9.57548	−0.917165	−0.458582	+	0.888652i	$0.651643\pi$
$110$	2.87409	0.274034
$111$	22.5785	2.14305
$112$	−8.70967	−0.822987
$113$	−12.9509	−1.21832	−0.609161	−	0.793046i	$-0.708494\pi$
$113$	−12.9509	−1.21832	−0.609161	+	0.793046i	$0.708494\pi$
$114$	−45.4010	−4.25219
$115$	6.39018	0.595887
$116$	−5.62723	−0.522476
$117$	−2.62710	−0.242876
$118$	−8.54107	−0.786269
$119$	−11.1525	−1.02235
$120$	−13.0943	−1.19534
$121$	−9.70119	−0.881926
$122$	7.64120	0.691801
$123$	15.7739	1.42228
$124$	−25.7449	−2.31196
$125$	1.00000	0.0894427
$126$	−6.42823	−0.572672
$127$	6.20409	0.550524	0.275262	−	0.961369i	$-0.411235\pi$
$127$	6.20409	0.550524	0.275262	+	0.961369i	$0.411235\pi$
$128$	−14.4660	−1.27862
$129$	−13.6569	−1.20242
$130$	−3.59948	−0.315695
$131$	18.8375	1.64584	0.822921	−	0.568155i	$-0.192343\pi$
$131$	18.8375	1.64584	0.822921	+	0.568155i	$0.192343\pi$
$132$	−10.9322	−0.951522
$133$	−11.3315	−0.982568
$134$	−17.0997	−1.47719
$135$	2.55080	0.219538
$136$	47.9294	4.10991
$137$	−17.2690	−1.47539	−0.737694	−	0.675135i	$-0.764085\pi$
$137$	−17.2690	−1.47539	−0.737694	+	0.675135i	$0.764085\pi$
$138$	−35.4561	−3.01822
$139$	−5.32826	−0.451937	−0.225968	−	0.974135i	$-0.572555\pi$
$139$	−5.32826	−0.451937	−0.225968	+	0.974135i	$0.572555\pi$
$140$	−6.03785	−0.510291
$141$	−25.1293	−2.11627
$142$	−14.4816	−1.21527
$143$	−1.62662	−0.136025
$144$	11.5762	0.964683
$145$	−1.29066	−0.107184
$146$	26.5960	2.20110
$147$	11.1816	0.922241
$148$	−44.7431	−3.67786
$149$	8.41324	0.689240	0.344620	−	0.938742i	$-0.388008\pi$
$149$	8.41324	0.689240	0.344620	+	0.938742i	$0.388008\pi$
$150$	−5.54852	−0.453035
$151$	−10.0201	−0.815428	−0.407714	−	0.913110i	$-0.633674\pi$
$151$	−10.0201	−0.815428	−0.407714	+	0.913110i	$0.633674\pi$
$152$	48.6988	3.95000
$153$	14.8230	1.19837
$154$	−3.98016	−0.320730
$155$	−5.90487	−0.474290
$156$	13.6913	1.09618
$157$	−5.88674	−0.469813	−0.234907	−	0.972018i	$-0.575478\pi$
$157$	−5.88674	−0.469813	−0.234907	+	0.972018i	$0.575478\pi$
$158$	−30.2362	−2.40547
$159$	−7.93628	−0.629388
$160$	3.95782	0.312893
$161$	−8.84939	−0.697429
$162$	−28.0787	−2.20607
$163$	10.2530	0.803075	0.401538	−	0.915842i	$-0.368476\pi$
$163$	10.2530	0.803075	0.401538	+	0.915842i	$0.368476\pi$
$164$	−31.2586	−2.44089
$165$	−2.50740	−0.195201
$166$	−5.17953	−0.402009
$167$	−3.87429	−0.299802	−0.149901	−	0.988701i	$-0.547895\pi$
$167$	−3.87429	−0.299802	−0.149901	+	0.988701i	$0.547895\pi$
$168$	18.1335	1.39903
$169$	−10.9628	−0.843295
$170$	20.3095	1.55766
$171$	15.0609	1.15174
$172$	27.0635	2.06357
$173$	−9.89842	−0.752563	−0.376282	−	0.926505i	$-0.622797\pi$
$173$	−9.89842	−0.752563	−0.376282	+	0.926505i	$0.622797\pi$
$174$	7.16128	0.542895
$175$	−1.38484	−0.104684
$176$	7.16762	0.540280
$177$	7.45136	0.560079
$178$	39.3099	2.94640
$179$	3.39770	0.253956	0.126978	−	0.991906i	$-0.459472\pi$
$179$	3.39770	0.253956	0.126978	+	0.991906i	$0.459472\pi$
$180$	8.02502	0.598150
$181$	−4.68117	−0.347948	−0.173974	−	0.984750i	$-0.555661\pi$
$181$	−4.68117	−0.347948	−0.173974	+	0.984750i	$0.555661\pi$
$182$	4.98471	0.369492
$183$	−6.66630	−0.492787
$184$	38.0315	2.80372
$185$	−10.2623	−0.754498
$186$	32.7633	2.40232
$187$	9.17793	0.671156
$188$	49.7980	3.63189
$189$	−3.53245	−0.256948
$190$	20.6355	1.49706
$191$	−8.93173	−0.646278	−0.323139	−	0.946352i	$-0.604738\pi$
$191$	−8.93173	−0.646278	−0.323139	+	0.946352i	$0.604738\pi$
$192$	5.71461	0.412416
$193$	23.6016	1.69888	0.849442	−	0.527682i	$-0.176939\pi$
$193$	23.6016	1.69888	0.849442	+	0.527682i	$0.176939\pi$
$194$	−34.6497	−2.48770
$195$	3.14024	0.224878
$196$	−22.1582	−1.58273
$197$	−4.74611	−0.338147	−0.169073	−	0.985603i	$-0.554077\pi$
$197$	−4.74611	−0.338147	−0.169073	+	0.985603i	$0.554077\pi$
$198$	5.29011	0.375952
$199$	−24.4324	−1.73196	−0.865982	−	0.500075i	$-0.833306\pi$
$199$	−24.4324	−1.73196	−0.865982	+	0.500075i	$0.833306\pi$
$200$	5.95156	0.420839
$201$	14.9181	1.05224
$202$	−15.8925	−1.11819
$203$	1.78737	0.125448
$204$	−77.2509	−5.40865
$205$	−7.16948	−0.500738
$206$	19.4606	1.35589
$207$	11.7619	0.817508
$208$	−8.97666	−0.622419
$209$	9.32527	0.645042
$210$	7.68383	0.530235
$211$	8.52132	0.586632	0.293316	−	0.956016i	$-0.405241\pi$
$211$	8.52132	0.586632	0.293316	+	0.956016i	$0.405241\pi$
$212$	15.7271	1.08014
$213$	12.6340	0.865665
$214$	33.0809	2.26137
$215$	6.20729	0.423333
$216$	15.1812	1.03295
$217$	8.17731	0.555112
$218$	−24.1484	−1.63553
$219$	−23.2027	−1.56790
$220$	4.96884	0.334999
$221$	−11.4943	−0.773193
$222$	56.9405	3.82160
$223$	−20.1520	−1.34948	−0.674739	−	0.738056i	$-0.735744\pi$
$223$	−20.1520	−1.34948	−0.674739	+	0.738056i	$0.735744\pi$
$224$	−5.48095	−0.366211
$225$	1.84062	0.122708
$226$	−32.6609	−2.17257
$227$	10.7950	0.716491	0.358245	−	0.933627i	$-0.383375\pi$
$227$	10.7950	0.716491	0.358245	+	0.933627i	$0.383375\pi$
$228$	−78.4911	−5.19820
$229$	−9.12280	−0.602851	−0.301426	−	0.953490i	$-0.597463\pi$
$229$	−9.12280	−0.602851	−0.301426	+	0.953490i	$0.597463\pi$
$230$	16.1154	1.06262
$231$	3.47235	0.228464
$232$	−7.68146	−0.504312
$233$	6.89404	0.451643	0.225822	−	0.974169i	$-0.427493\pi$
$233$	6.89404	0.451643	0.225822	+	0.974169i	$0.427493\pi$
$234$	−6.62528	−0.433108
$235$	11.4217	0.745068
$236$	−14.7661	−0.961194
$237$	26.3786	1.71347
$238$	−28.1254	−1.82310
$239$	22.6675	1.46624	0.733118	−	0.680101i	$-0.238064\pi$
$239$	22.6675	1.46624	0.733118	+	0.680101i	$0.238064\pi$
$240$	−13.8373	−0.893195
$241$	−1.00000	−0.0644157
$241$	−1.00000	−0.0644157
$242$	−24.4654	−1.57269
$243$	16.8439	1.08054
$244$	13.2104	0.845710
$245$	−5.08221	−0.324691
$246$	39.7800	2.53628
$247$	−11.6789	−0.743109
$248$	−35.1431	−2.23159
$249$	4.51870	0.286361
$250$	2.52189	0.159499
$251$	−22.9808	−1.45053	−0.725266	−	0.688468i	$-0.758283\pi$
$251$	−22.9808	−1.45053	−0.725266	+	0.688468i	$0.758283\pi$
$252$	−11.1134	−0.700077
$253$	7.28260	0.457853
$254$	15.6461	0.981721
$255$	−17.7183	−1.10956
$256$	−31.2869	−1.95543
$257$	11.4379	0.713477	0.356739	−	0.934204i	$-0.383889\pi$
$257$	11.4379	0.713477	0.356739	+	0.934204i	$0.383889\pi$
$258$	−34.4413	−2.14422
$259$	14.2116	0.883069
$260$	−6.22293	−0.385930
$261$	−2.37562	−0.147047
$262$	47.5063	2.93495
$263$	−16.7937	−1.03554	−0.517771	−	0.855519i	$-0.673238\pi$
$263$	−16.7937	−1.03554	−0.517771	+	0.855519i	$0.673238\pi$
$264$	−14.9229	−0.918443
$265$	3.60717	0.221587
$266$	−28.5769	−1.75216
$267$	−34.2946	−2.09879
$268$	−29.5627	−1.80583
$269$	−23.0436	−1.40499	−0.702496	−	0.711688i	$-0.747931\pi$
$269$	−23.0436	−1.40499	−0.702496	+	0.711688i	$0.747931\pi$
$270$	6.43285	0.391491
$271$	28.3337	1.72115	0.860576	−	0.509323i	$-0.170104\pi$
$271$	28.3337	1.72115	0.860576	+	0.509323i	$0.170104\pi$
$272$	50.6492	3.07106
$273$	−4.34874	−0.263198
$274$	−43.5505	−2.63098
$275$	1.13965	0.0687238
$276$	−61.2979	−3.68970
$277$	−18.4873	−1.11079	−0.555397	−	0.831585i	$-0.687434\pi$
$277$	−18.4873	−1.11079	−0.555397	+	0.831585i	$0.687434\pi$
$278$	−13.4373	−0.805916
$279$	−10.8686	−0.650687
$280$	−8.24196	−0.492552
$281$	3.87071	0.230907	0.115453	−	0.993313i	$-0.463168\pi$
$281$	3.87071	0.230907	0.115453	+	0.993313i	$0.463168\pi$
$282$	−63.3735	−3.77384
$283$	−8.93525	−0.531146	−0.265573	−	0.964091i	$-0.585561\pi$
$283$	−8.93525	−0.531146	−0.265573	+	0.964091i	$0.585561\pi$
$284$	−25.0363	−1.48563
$285$	−18.0027	−1.06639
$286$	−4.10217	−0.242566
$287$	9.92859	0.586066
$288$	7.28484	0.429263
$289$	47.8548	2.81499
$290$	−3.25492	−0.191135
$291$	30.2289	1.77205
$292$	45.9802	2.69079
$293$	20.3985	1.19169	0.595845	−	0.803099i	$-0.296817\pi$
$293$	20.3985	1.19169	0.595845	+	0.803099i	$0.296817\pi$
$294$	28.1988	1.64459
$295$	−3.38677	−0.197185
$296$	−61.0766	−3.55000
$297$	2.90703	0.168683
$298$	21.2173	1.22909
$299$	−9.12065	−0.527461
$300$	−9.59251	−0.553824
$301$	−8.59611	−0.495472
$302$	−25.2698	−1.45411
$303$	13.8648	0.796514
$304$	51.4624	2.95157
$305$	3.02994	0.173494
$306$	37.3820	2.13699
$307$	−3.43535	−0.196066	−0.0980328	−	0.995183i	$-0.531255\pi$
$307$	−3.43535	−0.196066	−0.0980328	+	0.995183i	$0.531255\pi$
$308$	−6.88106	−0.392085
$309$	−16.9778	−0.965832
$310$	−14.8915	−0.845778
$311$	2.13570	0.121105	0.0605523	−	0.998165i	$-0.480714\pi$
$311$	2.13570	0.121105	0.0605523	+	0.998165i	$0.480714\pi$
$312$	18.6893	1.05808
$313$	18.6990	1.05693	0.528465	−	0.848955i	$-0.322768\pi$
$313$	18.6990	1.05693	0.528465	+	0.848955i	$0.322768\pi$
$314$	−14.8457	−0.837794
$315$	−2.54897	−0.143618
$316$	−52.2736	−2.94062
$317$	8.05338	0.452323	0.226162	−	0.974090i	$-0.427382\pi$
$317$	8.05338	0.452323	0.226162	+	0.974090i	$0.427382\pi$
$318$	−20.0145	−1.12236
$319$	−1.47091	−0.0823552
$320$	−2.59738	−0.145198
$321$	−28.8603	−1.61083
$322$	−22.3172	−1.24369
$323$	65.8960	3.66655
$324$	−48.5436	−2.69687
$325$	−1.42729	−0.0791719
$326$	25.8569	1.43208
$327$	21.0674	1.16503
$328$	−42.6695	−2.35603
$329$	−15.8172	−0.872032
$330$	−6.32340	−0.348092
$331$	5.65478	0.310815	0.155407	−	0.987850i	$-0.450331\pi$
$331$	5.65478	0.310815	0.155407	+	0.987850i	$0.450331\pi$
$332$	−8.95458	−0.491446
$333$	−18.8890	−1.03511
$334$	−9.77056	−0.534621
$335$	−6.78050	−0.370458
$336$	19.1625	1.04540
$337$	−9.89177	−0.538839	−0.269419	−	0.963023i	$-0.586832\pi$
$337$	−9.89177	−0.538839	−0.269419	+	0.963023i	$0.586832\pi$
$338$	−27.6471	−1.50381
$339$	28.4939	1.54758
$340$	35.1118	1.90420
$341$	−6.72951	−0.364423
$342$	37.9821	2.05384
$343$	16.7320	0.903441
$344$	36.9430	1.99183
$345$	−14.0593	−0.756927
$346$	−24.9628	−1.34201
$347$	−20.5780	−1.10468	−0.552342	−	0.833618i	$-0.686266\pi$
$347$	−20.5780	−1.10468	−0.552342	+	0.833618i	$0.686266\pi$
$348$	12.3807	0.663676
$349$	29.8468	1.59766	0.798830	−	0.601556i	$-0.205452\pi$
$349$	29.8468	1.59766	0.798830	+	0.601556i	$0.205452\pi$
$350$	−3.49243	−0.186678
$351$	−3.64074	−0.194328
$352$	4.51054	0.240413
$353$	−5.70884	−0.303851	−0.151925	−	0.988392i	$-0.548547\pi$
$353$	−5.70884	−0.303851	−0.151925	+	0.988392i	$0.548547\pi$
$354$	18.7916	0.998760
$355$	−5.74234	−0.304772
$356$	67.9606	3.60190
$357$	24.5370	1.29864
$358$	8.56865	0.452867
$359$	8.98249	0.474078	0.237039	−	0.971500i	$-0.423823\pi$
$359$	8.98249	0.474078	0.237039	+	0.971500i	$0.423823\pi$
$360$	10.9546	0.577356
$361$	47.9539	2.52389
$362$	−11.8054	−0.620478
$363$	21.3440	1.12027
$364$	8.61777	0.451694
$365$	10.5460	0.552004
$366$	−16.8117	−0.878762
$367$	7.29412	0.380750	0.190375	−	0.981711i	$-0.439030\pi$
$367$	7.29412	0.380750	0.190375	+	0.981711i	$0.439030\pi$
$368$	40.1897	2.09503
$369$	−13.1963	−0.686971
$370$	−25.8804	−1.34546
$371$	−4.99536	−0.259346
$372$	56.6425	2.93678
$373$	−25.8105	−1.33642	−0.668209	−	0.743973i	$-0.732939\pi$
$373$	−25.8105	−1.33642	−0.668209	+	0.743973i	$0.732939\pi$
$374$	23.1458	1.19684
$375$	−2.20014	−0.113615
$376$	67.9768	3.50563
$377$	1.84215	0.0948758
$378$	−8.90848	−0.458203
$379$	13.8964	0.713811	0.356905	−	0.934141i	$-0.383832\pi$
$379$	13.8964	0.713811	0.356905	+	0.934141i	$0.383832\pi$
$380$	35.6755	1.83011
$381$	−13.6499	−0.699304
$382$	−22.5249	−1.15247
$383$	−13.1635	−0.672622	−0.336311	−	0.941751i	$-0.609179\pi$
$383$	−13.1635	−0.672622	−0.336311	+	0.941751i	$0.609179\pi$
$384$	31.8271	1.62417
$385$	−1.57824	−0.0804346
$386$	59.5209	3.02953
$387$	11.4253	0.580778
$388$	−59.9038	−3.04115
$389$	27.3219	1.38528	0.692638	−	0.721285i	$-0.256448\pi$
$389$	27.3219	1.38528	0.692638	+	0.721285i	$0.256448\pi$
$390$	7.91937	0.401013
$391$	51.4617	2.60253
$392$	−30.2471	−1.52771
$393$	−41.4452	−2.09063
$394$	−11.9692	−0.603000
$395$	−11.9895	−0.603257
$396$	9.14575	0.459591
$397$	−7.34888	−0.368830	−0.184415	−	0.982848i	$-0.559039\pi$
$397$	−7.34888	−0.368830	−0.184415	+	0.982848i	$0.559039\pi$
$398$	−61.6159	−3.08852
$399$	24.9309	1.24811
$400$	6.28929	0.314464
$401$	−14.1955	−0.708892	−0.354446	−	0.935077i	$-0.615330\pi$
$401$	−14.1955	−0.708892	−0.354446	+	0.935077i	$0.615330\pi$
$402$	37.6218	1.87640
$403$	8.42797	0.419827
$404$	−27.4755	−1.36696
$405$	−11.1340	−0.553252
$406$	4.50755	0.223706
$407$	−11.6955	−0.579722
$408$	−105.451	−5.22062
$409$	6.50944	0.321871	0.160935	−	0.986965i	$-0.448549\pi$
$409$	6.50944	0.321871	0.160935	+	0.986965i	$0.448549\pi$
$410$	−18.0807	−0.892941
$411$	37.9942	1.87411
$412$	33.6443	1.65754
$413$	4.69014	0.230787
$414$	29.6623	1.45782
$415$	−2.05382	−0.100818
$416$	−5.64896	−0.276963
$417$	11.7229	0.574074
$418$	23.5173	1.15027
$419$	13.4568	0.657405	0.328703	−	0.944433i	$-0.393389\pi$
$419$	13.4568	0.657405	0.328703	+	0.944433i	$0.393389\pi$
$420$	13.2841	0.648198
$421$	−7.23863	−0.352789	−0.176395	−	0.984320i	$-0.556443\pi$
$421$	−7.23863	−0.352789	−0.176395	+	0.984320i	$0.556443\pi$
$422$	21.4899	1.04611
$423$	21.0230	1.02217
$424$	21.4683	1.04259
$425$	8.05325	0.390640
$426$	31.8615	1.54370
$427$	−4.19599	−0.203058
$428$	57.1917	2.76446
$429$	3.57879	0.172786
$430$	15.6541	0.754909
$431$	−25.4909	−1.22786	−0.613928	−	0.789362i	$-0.710411\pi$
$431$	−25.4909	−1.22786	−0.613928	+	0.789362i	$0.710411\pi$
$432$	16.0427	0.771856
$433$	29.4527	1.41541	0.707704	−	0.706509i	$-0.249731\pi$
$433$	29.4527	1.41541	0.707704	+	0.706509i	$0.249731\pi$
$434$	20.6223	0.989903
$435$	2.83964	0.136150
$436$	−41.7487	−1.99940
$437$	52.2879	2.50127
$438$	−58.5148	−2.79595
$439$	−15.4308	−0.736471	−0.368235	−	0.929733i	$-0.620038\pi$
$439$	−15.4308	−0.736471	−0.368235	+	0.929733i	$0.620038\pi$
$440$	6.78272	0.323353
$441$	−9.35442	−0.445449
$442$	−28.9875	−1.37880
$443$	3.93299	0.186862	0.0934310	−	0.995626i	$-0.470217\pi$
$443$	3.93299	0.186862	0.0934310	+	0.995626i	$0.470217\pi$
$444$	98.4411	4.67181
$445$	15.5874	0.738916
$446$	−50.8212	−2.40646
$447$	−18.5103	−0.875508
$448$	3.59696	0.169941
$449$	−18.6895	−0.882011	−0.441005	−	0.897504i	$-0.645378\pi$
$449$	−18.6895	−0.882011	−0.441005	+	0.897504i	$0.645378\pi$
$450$	4.64185	0.218819
$451$	−8.17073	−0.384745
$452$	−56.4655	−2.65591
$453$	22.0457	1.03580
$454$	27.2239	1.27768
$455$	1.97657	0.0926633
$456$	−107.144	−5.01749
$457$	−23.0884	−1.08003	−0.540015	−	0.841655i	$-0.681582\pi$
$457$	−23.0884	−1.08003	−0.540015	+	0.841655i	$0.681582\pi$
$458$	−23.0067	−1.07503
$459$	20.5422	0.958829
$460$	27.8609	1.29902
$461$	−20.5071	−0.955110	−0.477555	−	0.878602i	$-0.658477\pi$
$461$	−20.5071	−0.955110	−0.477555	+	0.878602i	$0.658477\pi$
$462$	8.75691	0.407408
$463$	4.89653	0.227561	0.113781	−	0.993506i	$-0.463704\pi$
$463$	4.89653	0.227561	0.113781	+	0.993506i	$0.463704\pi$
$464$	−8.11736	−0.376839
$465$	12.9915	0.602468
$466$	17.3860	0.805392
$467$	−9.22557	−0.426908	−0.213454	−	0.976953i	$-0.568471\pi$
$467$	−9.22557	−0.426908	−0.213454	+	0.976953i	$0.568471\pi$
$468$	−11.4540	−0.529464
$469$	9.38992	0.433586
$470$	28.8043	1.32864
$471$	12.9517	0.596781
$472$	−20.1565	−0.927779
$473$	7.07416	0.325270
$474$	66.5240	3.05555
$475$	8.18254	0.375441
$476$	−48.6243	−2.22869
$477$	6.63943	0.303998
$478$	57.1650	2.61467
$479$	23.0205	1.05183	0.525916	−	0.850536i	$-0.323723\pi$
$479$	23.0205	1.05183	0.525916	+	0.850536i	$0.323723\pi$
$480$	−8.70775	−0.397453
$481$	14.6473	0.667859
$482$	−2.52189	−0.114869
$483$	19.4699	0.885911
$484$	−42.2967	−1.92258
$485$	−13.7395	−0.623881
$486$	42.4786	1.92687
$487$	−13.8048	−0.625554	−0.312777	−	0.949827i	$-0.601259\pi$
$487$	−13.8048	−0.625554	−0.312777	+	0.949827i	$0.601259\pi$
$488$	18.0329	0.816310
$489$	−22.5580	−1.02011
$490$	−12.8168	−0.579004
$491$	12.0008	0.541589	0.270795	−	0.962637i	$-0.412714\pi$
$491$	12.0008	0.541589	0.270795	+	0.962637i	$0.412714\pi$
$492$	68.7733	3.10054
$493$	−10.3940	−0.468124
$494$	−29.4529	−1.32515
$495$	2.09767	0.0942833
$496$	−37.1374	−1.66752
$497$	7.95224	0.356707
$498$	11.3957	0.510653
$499$	−24.5084	−1.09715	−0.548574	−	0.836102i	$-0.684829\pi$
$499$	−24.5084	−1.09715	−0.548574	+	0.836102i	$0.684829\pi$
$500$	4.35995	0.194983
$501$	8.52399	0.380824
$502$	−57.9551	−2.58666
$503$	−0.513066	−0.0228765	−0.0114382	−	0.999935i	$-0.503641\pi$
$503$	−0.513066	−0.0228765	−0.0114382	+	0.999935i	$0.503641\pi$
$504$	−15.1703	−0.675740
$505$	−6.30180	−0.280426
$506$	18.3659	0.816466
$507$	24.1198	1.07120
$508$	27.0495	1.20013
$509$	−8.15378	−0.361410	−0.180705	−	0.983537i	$-0.557838\pi$
$509$	−8.15378	−0.361410	−0.180705	+	0.983537i	$0.557838\pi$
$510$	−44.6837	−1.97863
$511$	−14.6046	−0.646068
$512$	−49.9703	−2.20839
$513$	20.8720	0.921522
$514$	28.8452	1.27231
$515$	7.71667	0.340037
$516$	−59.5435	−2.62125
$517$	13.0168	0.572477
$518$	35.8403	1.57473
$519$	21.7779	0.955945
$520$	−8.49461	−0.372513
$521$	21.4295	0.938844	0.469422	−	0.882974i	$-0.344462\pi$
$521$	21.4295	0.938844	0.469422	+	0.882974i	$0.344462\pi$
$522$	−5.99107	−0.262222
$523$	−16.4748	−0.720392	−0.360196	−	0.932877i	$-0.617290\pi$
$523$	−16.4748	−0.720392	−0.360196	+	0.932877i	$0.617290\pi$
$524$	82.1308	3.58790
$525$	3.04685	0.132975
$526$	−42.3519	−1.84663
$527$	−47.5534	−2.07146
$528$	−15.7698	−0.686291
$529$	17.8344	0.775408
$530$	9.09690	0.395144
$531$	−6.23375	−0.270522
$532$	−49.4049	−2.14197
$533$	10.2329	0.443238
$534$	−86.4873	−3.74267
$535$	13.1175	0.567119
$536$	−40.3545	−1.74305
$537$	−7.47543	−0.322588
$538$	−58.1135	−2.50545
$539$	−5.79197	−0.249478
$540$	11.1214	0.478587
$541$	4.96140	0.213307	0.106654	−	0.994296i	$-0.465986\pi$
$541$	4.96140	0.213307	0.106654	+	0.994296i	$0.465986\pi$
$542$	71.4547	3.06924
$543$	10.2992	0.441982
$544$	31.8733	1.36656
$545$	−9.57548	−0.410169
$546$	−10.9671	−0.469347
$547$	9.35721	0.400085	0.200043	−	0.979787i	$-0.435892\pi$
$547$	9.35721	0.400085	0.200043	+	0.979787i	$0.435892\pi$
$548$	−75.2919	−3.21631
$549$	5.57697	0.238019
$550$	2.87409	0.122552
$551$	−10.5609	−0.449910
$552$	−83.6747	−3.56143
$553$	16.6036	0.706055
$554$	−46.6231	−1.98082
$555$	22.5785	0.958403
$556$	−23.2310	−0.985212
$557$	−15.3622	−0.650919	−0.325459	−	0.945556i	$-0.605519\pi$
$557$	−15.3622	−0.650919	−0.325459	+	0.945556i	$0.605519\pi$
$558$	−27.4095	−1.16034
$559$	−8.85961	−0.374722
$560$	−8.70967	−0.368051
$561$	−20.1927	−0.852538
$562$	9.76151	0.411765
$563$	36.4407	1.53579	0.767895	−	0.640576i	$-0.221304\pi$
$563$	36.4407	1.53579	0.767895	+	0.640576i	$0.221304\pi$
$564$	−109.563	−4.61342
$565$	−12.9509	−0.544850
$566$	−22.5338	−0.947165
$567$	15.4188	0.647529
$568$	−34.1759	−1.43399
$569$	−26.4918	−1.11060	−0.555298	−	0.831652i	$-0.687396\pi$
$569$	−26.4918	−1.11060	−0.555298	+	0.831652i	$0.687396\pi$
$570$	−45.4010	−1.90164
$571$	4.90909	0.205439	0.102719	−	0.994710i	$-0.467246\pi$
$571$	4.90909	0.205439	0.102719	+	0.994710i	$0.467246\pi$
$572$	−7.09199	−0.296531
$573$	19.6511	0.820935
$574$	25.0389	1.04510
$575$	6.39018	0.266489
$576$	−4.78079	−0.199200
$577$	−9.46096	−0.393865	−0.196932	−	0.980417i	$-0.563098\pi$
$577$	−9.46096	−0.393865	−0.196932	+	0.980417i	$0.563098\pi$
$578$	120.685	5.01983
$579$	−51.9270	−2.15801
$580$	−5.62723	−0.233658
$581$	2.84422	0.117998
$582$	76.2342	3.16001
$583$	4.11093	0.170257
$584$	62.7652	2.59724
$585$	−2.62710	−0.108617
$586$	51.4428	2.12508
$587$	−17.4974	−0.722193	−0.361097	−	0.932528i	$-0.617598\pi$
$587$	−17.4974	−0.722193	−0.361097	+	0.932528i	$0.617598\pi$
$588$	48.7512	2.01047
$589$	−48.3168	−1.99086
$590$	−8.54107	−0.351630
$591$	10.4421	0.429531
$592$	−64.5425	−2.65268
$593$	−15.2293	−0.625394	−0.312697	−	0.949853i	$-0.601232\pi$
$593$	−15.2293	−0.625394	−0.312697	+	0.949853i	$0.601232\pi$
$594$	7.33122	0.300804
$595$	−11.1525	−0.457207
$596$	36.6814	1.50253
$597$	53.7547	2.20003
$598$	−23.0013	−0.940594
$599$	29.4256	1.20230	0.601150	−	0.799136i	$-0.294710\pi$
$599$	29.4256	1.20230	0.601150	+	0.799136i	$0.294710\pi$
$600$	−13.0943	−0.534571
$601$	−42.0225	−1.71413	−0.857067	−	0.515204i	$-0.827716\pi$
$601$	−42.0225	−1.71413	−0.857067	+	0.515204i	$0.827716\pi$
$602$	−21.6785	−0.883549
$603$	−12.4803	−0.508238
$604$	−43.6874	−1.77761
$605$	−9.70119	−0.394409
$606$	34.9657	1.42038
$607$	8.69293	0.352835	0.176418	−	0.984315i	$-0.443549\pi$
$607$	8.69293	0.352835	0.176418	+	0.984315i	$0.443549\pi$
$608$	32.3850	1.31338
$609$	−3.93246	−0.159351
$610$	7.64120	0.309383
$611$	−16.3021	−0.659512
$612$	64.6275	2.61241
$613$	40.8705	1.65074	0.825372	−	0.564589i	$-0.190965\pi$
$613$	40.8705	1.65074	0.825372	+	0.564589i	$0.190965\pi$
$614$	−8.66359	−0.349634
$615$	15.7739	0.636063
$616$	−9.39299	−0.378454
$617$	5.52161	0.222292	0.111146	−	0.993804i	$-0.464548\pi$
$617$	5.52161	0.222292	0.111146	+	0.993804i	$0.464548\pi$
$618$	−42.8161	−1.72232
$619$	4.62907	0.186058	0.0930290	−	0.995663i	$-0.470345\pi$
$619$	4.62907	0.186058	0.0930290	+	0.995663i	$0.470345\pi$
$620$	−25.7449	−1.03394
$621$	16.3001	0.654099
$622$	5.38602	0.215960
$623$	−21.5862	−0.864831
$624$	19.7499	0.790629
$625$	1.00000	0.0400000
$626$	47.1569	1.88477
$627$	−20.5169	−0.819366
$628$	−25.6659	−1.02418
$629$	−82.6448	−3.29526
$630$	−6.42823	−0.256107
$631$	−50.2094	−1.99880	−0.999402	−	0.0345676i	$-0.988995\pi$
$631$	−50.2094	−1.99880	−0.999402	+	0.0345676i	$0.988995\pi$
$632$	−71.3561	−2.83839
$633$	−18.7481	−0.745171
$634$	20.3098	0.806605
$635$	6.20409	0.246202
$636$	−34.6018	−1.37205
$637$	7.25380	0.287406
$638$	−3.70948	−0.146860
$639$	−10.5695	−0.418122
$640$	−14.4660	−0.571817
$641$	−26.5824	−1.04994	−0.524970	−	0.851120i	$-0.675924\pi$
$641$	−26.5824	−1.04994	−0.524970	+	0.851120i	$0.675924\pi$
$642$	−72.7827	−2.87250
$643$	−32.8597	−1.29586	−0.647930	−	0.761700i	$-0.724365\pi$
$643$	−32.8597	−1.29586	−0.647930	+	0.761700i	$0.724365\pi$
$644$	−38.5829	−1.52038
$645$	−13.6569	−0.537740
$646$	166.183	6.53838
$647$	15.3934	0.605178	0.302589	−	0.953121i	$-0.402149\pi$
$647$	15.3934	0.605178	0.302589	+	0.953121i	$0.402149\pi$
$648$	−66.2645	−2.60311
$649$	−3.85974	−0.151508
$650$	−3.59948	−0.141183
$651$	−17.9912	−0.705132
$652$	44.7025	1.75069
$653$	11.3351	0.443578	0.221789	−	0.975095i	$-0.428810\pi$
$653$	11.3351	0.443578	0.221789	+	0.975095i	$0.428810\pi$
$654$	53.1298	2.07754
$655$	18.8375	0.736043
$656$	−45.0909	−1.76050
$657$	19.4112	0.757304
$658$	−39.8894	−1.55505
$659$	12.4953	0.486746	0.243373	−	0.969933i	$-0.421746\pi$
$659$	12.4953	0.486746	0.243373	+	0.969933i	$0.421746\pi$
$660$	−10.9322	−0.425533
$661$	−6.21773	−0.241842	−0.120921	−	0.992662i	$-0.538585\pi$
$661$	−6.21773	−0.241842	−0.120921	+	0.992662i	$0.538585\pi$
$662$	14.2608	0.554260
$663$	25.2892	0.982150
$664$	−12.2234	−0.474362
$665$	−11.3315	−0.439418
$666$	−47.6360	−1.84586
$667$	−8.24757	−0.319347
$668$	−16.8917	−0.653561
$669$	44.3373	1.71418
$670$	−17.0997	−0.660619
$671$	3.45309	0.133305
$672$	12.0589	0.465181
$673$	12.1184	0.467129	0.233564	−	0.972341i	$-0.424961\pi$
$673$	12.1184	0.467129	0.233564	+	0.972341i	$0.424961\pi$
$674$	−24.9460	−0.960884
$675$	2.55080	0.0981803
$676$	−47.7975	−1.83836
$677$	6.38521	0.245404	0.122702	−	0.992444i	$-0.460844\pi$
$677$	6.38521	0.245404	0.122702	+	0.992444i	$0.460844\pi$
$678$	71.8586	2.75971
$679$	19.0271	0.730193
$680$	47.9294	1.83801
$681$	−23.7506	−0.910124
$682$	−16.9711	−0.649858
$683$	7.33754	0.280763	0.140382	−	0.990097i	$-0.455167\pi$
$683$	7.33754	0.280763	0.140382	+	0.990097i	$0.455167\pi$
$684$	65.6650	2.51077
$685$	−17.2690	−0.659814
$686$	42.1962	1.61106
$687$	20.0714	0.765773
$688$	39.0394	1.48836
$689$	−5.14848	−0.196142
$690$	−35.4561	−1.34979
$691$	−11.9785	−0.455683	−0.227841	−	0.973698i	$-0.573167\pi$
$691$	−11.9785	−0.455683	−0.227841	+	0.973698i	$0.573167\pi$
$692$	−43.1567	−1.64057
$693$	−2.90494	−0.110350
$694$	−51.8955	−1.96993
$695$	−5.32826	−0.202112
$696$	16.9003	0.640604
$697$	−57.7376	−2.18697
$698$	75.2704	2.84903
$699$	−15.1678	−0.573701
$700$	−6.03785	−0.228209
$701$	7.74613	0.292567	0.146284	−	0.989243i	$-0.453269\pi$
$701$	7.74613	0.292567	0.146284	+	0.989243i	$0.453269\pi$
$702$	−9.18156	−0.346535
$703$	−83.9715	−3.16705
$704$	−2.96012	−0.111564
$705$	−25.1293	−0.946424
$706$	−14.3971	−0.541842
$707$	8.72699	0.328212
$708$	32.4876	1.22096
$709$	−37.7901	−1.41924	−0.709619	−	0.704586i	$-0.751133\pi$
$709$	−37.7901	−1.41924	−0.709619	+	0.704586i	$0.751133\pi$
$710$	−14.4816	−0.543484
$711$	−22.0681	−0.827619
$712$	92.7696	3.47669
$713$	−37.7332	−1.41312
$714$	61.8798	2.31579
$715$	−1.62662	−0.0608322
$716$	14.8138	0.553619
$717$	−49.8716	−1.86249
$718$	22.6529	0.845398
$719$	−0.727448	−0.0271292	−0.0135646	−	0.999908i	$-0.504318\pi$
$719$	−0.727448	−0.0271292	−0.0135646	+	0.999908i	$0.504318\pi$
$720$	11.5762	0.431419
$721$	−10.6864	−0.397981
$722$	120.935	4.50073
$723$	2.20014	0.0818241
$724$	−20.4097	−0.758519
$725$	−1.29066	−0.0479340
$726$	53.8273	1.99772
$727$	4.10672	0.152310	0.0761550	−	0.997096i	$-0.475736\pi$
$727$	4.10672	0.152310	0.0761550	+	0.997096i	$0.475736\pi$
$728$	11.7637	0.435992
$729$	−3.65707	−0.135447
$730$	26.5960	0.984360
$731$	49.9888	1.84890
$732$	−29.0648	−1.07426
$733$	1.57001	0.0579895	0.0289948	−	0.999580i	$-0.490769\pi$
$733$	1.57001	0.0579895	0.0289948	+	0.999580i	$0.490769\pi$
$734$	18.3950	0.678972
$735$	11.1816	0.412439
$736$	25.2912	0.932244
$737$	−7.72743	−0.284643
$738$	−33.2796	−1.22504
$739$	35.5217	1.30669	0.653343	−	0.757062i	$-0.273366\pi$
$739$	35.5217	1.30669	0.653343	+	0.757062i	$0.273366\pi$
$740$	−44.7431	−1.64479
$741$	25.6952	0.943936
$742$	−12.5978	−0.462479
$743$	−24.6878	−0.905706	−0.452853	−	0.891585i	$-0.649594\pi$
$743$	−24.6878	−0.905706	−0.452853	+	0.891585i	$0.649594\pi$
$744$	77.3199	2.83468
$745$	8.41324	0.308237
$746$	−65.0914	−2.38317
$747$	−3.78031	−0.138314
$748$	40.0153	1.46311
$749$	−18.1657	−0.663759
$750$	−5.54852	−0.202603
$751$	−43.7460	−1.59631	−0.798156	−	0.602450i	$-0.794191\pi$
$751$	−43.7460	−1.59631	−0.798156	+	0.602450i	$0.794191\pi$
$752$	71.8343	2.61953
$753$	50.5609	1.84254
$754$	4.64572	0.169187
$755$	−10.0201	−0.364671
$756$	−15.4013	−0.560141
$757$	32.9074	1.19604	0.598021	−	0.801481i	$-0.295954\pi$
$757$	32.9074	1.19604	0.598021	+	0.801481i	$0.295954\pi$
$758$	35.0453	1.27290
$759$	−16.0227	−0.581589
$760$	48.6988	1.76649
$761$	47.5274	1.72287	0.861433	−	0.507871i	$-0.169567\pi$
$761$	47.5274	1.72287	0.861433	+	0.507871i	$0.169567\pi$
$762$	−34.4235	−1.24703
$763$	13.2605	0.480063
$764$	−38.9419	−1.40887
$765$	14.8230	0.535926
$766$	−33.1969	−1.19945
$767$	4.83391	0.174542
$768$	68.8355	2.48389
$769$	8.08301	0.291481	0.145740	−	0.989323i	$-0.453444\pi$
$769$	8.08301	0.291481	0.145740	+	0.989323i	$0.453444\pi$
$770$	−3.98016	−0.143435
$771$	−25.1650	−0.906296
$772$	102.902	3.70353
$773$	5.96163	0.214425	0.107212	−	0.994236i	$-0.465808\pi$
$773$	5.96163	0.214425	0.107212	+	0.994236i	$0.465808\pi$
$774$	28.8133	1.03567
$775$	−5.90487	−0.212109
$776$	−81.7717	−2.93543
$777$	−31.2676	−1.12172
$778$	68.9030	2.47029
$779$	−58.6645	−2.10187
$780$	13.6913	0.490228
$781$	−6.54429	−0.234173
$782$	129.781	4.64096
$783$	−3.29222	−0.117654
$784$	−31.9635	−1.14155
$785$	−5.88674	−0.210107
$786$	−104.520	−3.72812
$787$	41.0604	1.46365	0.731823	−	0.681495i	$-0.238670\pi$
$787$	41.0604	1.46365	0.731823	+	0.681495i	$0.238670\pi$
$788$	−20.6928	−0.737152
$789$	36.9484	1.31540
$790$	−30.2362	−1.07576
$791$	17.9350	0.637696
$792$	12.4844	0.443614
$793$	−4.32461	−0.153572
$794$	−18.5331	−0.657716
$795$	−7.93628	−0.281471
$796$	−106.524	−3.77564
$797$	28.0693	0.994267	0.497134	−	0.867674i	$-0.334386\pi$
$797$	28.0693	0.994267	0.497134	+	0.867674i	$0.334386\pi$
$798$	62.8732	2.22569
$799$	91.9817	3.25408
$800$	3.95782	0.139930
$801$	28.6906	1.01373
$802$	−35.7997	−1.26413
$803$	12.0188	0.424135
$804$	65.0420	2.29386
$805$	−8.84939	−0.311900
$806$	21.2545	0.748657
$807$	50.6991	1.78469
$808$	−37.5055	−1.31944
$809$	−14.7074	−0.517084	−0.258542	−	0.966000i	$-0.583242\pi$
$809$	−14.7074	−0.517084	−0.258542	+	0.966000i	$0.583242\pi$
$810$	−28.0787	−0.986586
$811$	7.85078	0.275678	0.137839	−	0.990455i	$-0.455984\pi$
$811$	7.85078	0.275678	0.137839	+	0.990455i	$0.455984\pi$
$812$	7.79283	0.273475
$813$	−62.3382	−2.18630
$814$	−29.4947	−1.03379
$815$	10.2530	0.359146
$816$	−111.435	−3.90102
$817$	50.7914	1.77696
$818$	16.4161	0.573976
$819$	3.63812	0.127126
$820$	−31.2586	−1.09160
$821$	43.0789	1.50346	0.751732	−	0.659469i	$-0.229219\pi$
$821$	43.0789	1.50346	0.751732	+	0.659469i	$0.229219\pi$
$822$	95.8173	3.34201
$823$	−32.2924	−1.12564	−0.562821	−	0.826579i	$-0.690284\pi$
$823$	−32.2924	−1.12564	−0.562821	+	0.826579i	$0.690284\pi$
$824$	45.9262	1.59992
$825$	−2.50740	−0.0872965
$826$	11.8280	0.411550
$827$	23.8083	0.827896	0.413948	−	0.910301i	$-0.364150\pi$
$827$	23.8083	0.827896	0.413948	+	0.910301i	$0.364150\pi$
$828$	51.2813	1.78215
$829$	53.1130	1.84469	0.922346	−	0.386365i	$-0.126269\pi$
$829$	53.1130	1.84469	0.922346	+	0.386365i	$0.126269\pi$
$830$	−5.17953	−0.179784
$831$	40.6747	1.41099
$832$	3.70722	0.128525
$833$	−40.9283	−1.41808
$834$	29.5640	1.02372
$835$	−3.87429	−0.134075
$836$	40.6577	1.40618
$837$	−15.0621	−0.520623
$838$	33.9365	1.17232
$839$	−42.5530	−1.46909	−0.734546	−	0.678559i	$-0.762605\pi$
$839$	−42.5530	−1.46909	−0.734546	+	0.678559i	$0.762605\pi$
$840$	18.1335	0.625665
$841$	−27.3342	−0.942558
$842$	−18.2551	−0.629111
$843$	−8.51610	−0.293310
$844$	37.1526	1.27884
$845$	−10.9628	−0.377133
$846$	53.0177	1.82279
$847$	13.4346	0.461619
$848$	22.6865	0.779058
$849$	19.6588	0.674689
$850$	20.3095	0.696608
$851$	−65.5778	−2.24798
$852$	55.0835	1.88713
$853$	44.3489	1.51848	0.759239	−	0.650812i	$-0.225571\pi$
$853$	44.3489	1.51848	0.759239	+	0.650812i	$0.225571\pi$
$854$	−10.5818	−0.362103
$855$	15.0609	0.515073
$856$	78.0695	2.66836
$857$	−5.45726	−0.186416	−0.0932081	−	0.995647i	$-0.529712\pi$
$857$	−5.45726	−0.186416	−0.0932081	+	0.995647i	$0.529712\pi$
$858$	9.02534	0.308120
$859$	−6.88876	−0.235042	−0.117521	−	0.993070i	$-0.537495\pi$
$859$	−6.88876	−0.235042	−0.117521	+	0.993070i	$0.537495\pi$
$860$	27.0635	0.922857
$861$	−21.8443	−0.744452
$862$	−64.2855	−2.18957
$863$	−19.1904	−0.653250	−0.326625	−	0.945154i	$-0.605911\pi$
$863$	−19.1904	−0.653250	−0.326625	+	0.945154i	$0.605911\pi$
$864$	10.0956	0.343459
$865$	−9.89842	−0.336557
$866$	74.2767	2.52403
$867$	−105.287	−3.57575
$868$	35.6527	1.21013
$869$	−13.6639	−0.463515
$870$	7.16128	0.242790
$871$	9.67776	0.327918
$872$	−56.9890	−1.92989
$873$	−25.2893	−0.855913
$874$	131.865	4.46038
$875$	−1.38484	−0.0468162
$876$	−101.163	−3.41798
$877$	1.45458	0.0491178	0.0245589	−	0.999698i	$-0.492182\pi$
$877$	1.45458	0.0491178	0.0245589	+	0.999698i	$0.492182\pi$
$878$	−38.9148	−1.31331
$879$	−44.8795	−1.51375
$880$	7.16762	0.241620
$881$	−14.3480	−0.483395	−0.241698	−	0.970352i	$-0.577704\pi$
$881$	−14.3480	−0.483395	−0.241698	+	0.970352i	$0.577704\pi$
$882$	−23.5909	−0.794346
$883$	43.1586	1.45240	0.726201	−	0.687483i	$-0.241284\pi$
$883$	43.1586	1.45240	0.726201	+	0.687483i	$0.241284\pi$
$884$	−50.1148	−1.68554
$885$	7.45136	0.250475
$886$	9.91859	0.333221
$887$	−6.42117	−0.215602	−0.107801	−	0.994173i	$-0.534381\pi$
$887$	−6.42117	−0.215602	−0.107801	+	0.994173i	$0.534381\pi$
$888$	134.377	4.50940
$889$	−8.59168	−0.288156
$890$	39.3099	1.31767
$891$	−12.6889	−0.425094
$892$	−87.8618	−2.94183
$893$	93.4583	3.12746
$894$	−46.6811	−1.56125
$895$	3.39770	0.113573
$896$	20.0331	0.669258
$897$	20.0667	0.670008
$898$	−47.1329	−1.57284
$899$	7.62120	0.254181
$900$	8.02502	0.267501
$901$	29.0494	0.967777
$902$	−20.6057	−0.686095
$903$	18.9127	0.629374
$904$	−77.0783	−2.56358
$905$	−4.68117	−0.155607
$906$	55.5970	1.84709
$907$	14.7496	0.489751	0.244876	−	0.969555i	$-0.421253\pi$
$907$	14.7496	0.489751	0.244876	+	0.969555i	$0.421253\pi$
$908$	47.0658	1.56193
$909$	−11.5992	−0.384722
$910$	4.98471	0.165242
$911$	−54.0147	−1.78959	−0.894794	−	0.446480i	$-0.852678\pi$
$911$	−54.0147	−1.78959	−0.894794	+	0.446480i	$0.852678\pi$
$912$	−113.224	−3.74924
$913$	−2.34065	−0.0774642
$914$	−58.2266	−1.92596
$915$	−6.66630	−0.220381
$916$	−39.7750	−1.31420
$917$	−26.0870	−0.861469
$918$	51.8053	1.70983
$919$	41.0257	1.35331	0.676657	−	0.736298i	$-0.263428\pi$
$919$	41.0257	1.35331	0.676657	+	0.736298i	$0.263428\pi$
$920$	38.0315	1.25386
$921$	7.55825	0.249053
$922$	−51.7167	−1.70320
$923$	8.19600	0.269775
$924$	15.1393	0.498047
$925$	−10.2623	−0.337422
$926$	12.3485	0.405798
$927$	14.2035	0.466503
$928$	−5.10821	−0.167685
$929$	−37.1426	−1.21861	−0.609305	−	0.792936i	$-0.708551\pi$
$929$	−37.1426	−1.21861	−0.609305	+	0.792936i	$0.708551\pi$
$930$	32.7633	1.07435
$931$	−41.5854	−1.36291
$932$	30.0577	0.984572
$933$	−4.69885	−0.153833
$934$	−23.2659	−0.761284
$935$	9.17793	0.300150
$936$	−15.6354	−0.511057
$937$	−38.6617	−1.26302	−0.631512	−	0.775366i	$-0.717565\pi$
$937$	−38.6617	−1.26302	−0.631512	+	0.775366i	$0.717565\pi$
$938$	23.6804	0.773192
$939$	−41.1405	−1.34257
$940$	49.7980	1.62423
$941$	−26.0170	−0.848129	−0.424064	−	0.905632i	$-0.639397\pi$
$941$	−26.0170	−0.848129	−0.424064	+	0.905632i	$0.639397\pi$
$942$	32.6627	1.06421
$943$	−45.8142	−1.49192
$944$	−21.3004	−0.693268
$945$	−3.53245	−0.114911
$946$	17.8403	0.580038
$947$	54.4228	1.76850	0.884252	−	0.467010i	$-0.154669\pi$
$947$	54.4228	1.76850	0.884252	+	0.467010i	$0.154669\pi$
$948$	115.009	3.73533
$949$	−15.0523	−0.488617
$950$	20.6355	0.669504
$951$	−17.7186	−0.574564
$952$	−66.3746	−2.15121
$953$	−45.7428	−1.48176	−0.740878	−	0.671640i	$-0.765590\pi$
$953$	−45.7428	−1.48176	−0.740878	+	0.671640i	$0.765590\pi$
$954$	16.7439	0.542105
$955$	−8.93173	−0.289024
$956$	98.8291	3.19636
$957$	3.23621	0.104612
$958$	58.0552	1.87568
$959$	23.9148	0.772249
$960$	5.71461	0.184438
$961$	3.86746	0.124757
$962$	36.9389	1.19096
$963$	24.1443	0.778040
$964$	−4.35995	−0.140425
$965$	23.6016	0.759764
$966$	49.1010	1.57980
$967$	51.7953	1.66563	0.832813	−	0.553555i	$-0.186729\pi$
$967$	51.7953	1.66563	0.832813	+	0.553555i	$0.186729\pi$
$968$	−57.7372	−1.85574
$969$	−144.981	−4.65745
$970$	−34.6497	−1.11253
$971$	−41.5931	−1.33479	−0.667393	−	0.744705i	$-0.732590\pi$
$971$	−41.5931	−1.33479	−0.667393	+	0.744705i	$0.732590\pi$
$972$	73.4387	2.35555
$973$	7.37880	0.236553
$974$	−34.8142	−1.11552
$975$	3.14024	0.100568
$976$	19.0562	0.609974
$977$	−57.7962	−1.84906	−0.924532	−	0.381104i	$-0.875544\pi$
$977$	−57.7962	−1.84906	−0.924532	+	0.381104i	$0.875544\pi$
$978$	−56.8889	−1.81911
$979$	17.7643	0.567750
$980$	−22.1582	−0.707818
$981$	−17.6248	−0.562717
$982$	30.2648	0.965788
$983$	51.4042	1.63954	0.819769	−	0.572694i	$-0.194102\pi$
$983$	51.4042	1.63954	0.819769	+	0.572694i	$0.194102\pi$
$984$	93.8790	2.99275
$985$	−4.74611	−0.151224
$986$	−26.2127	−0.834782
$987$	34.8001	1.10770
$988$	−50.9194	−1.61996
$989$	39.6657	1.26129
$990$	5.29011	0.168131
$991$	−9.56285	−0.303774	−0.151887	−	0.988398i	$-0.548535\pi$
$991$	−9.56285	−0.303774	−0.151887	+	0.988398i	$0.548535\pi$
$992$	−23.3704	−0.742010
$993$	−12.4413	−0.394813
$994$	20.0547	0.636097
$995$	−24.4324	−0.774558
$996$	19.7013	0.624261
$997$	−0.936304	−0.0296530	−0.0148265	−	0.999890i	$-0.504720\pi$
$997$	−0.936304	−0.0296530	−0.0148265	+	0.999890i	$0.504720\pi$
$998$	−61.8077	−1.95649
$999$	−26.1770	−0.828205

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1205.2.a.e.1.23	✓	25
5.4	even	2		6025.2.a.j.1.3		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1205.2.a.e.1.23	✓	25	1.1	even	1	trivial
6025.2.a.j.1.3		25	5.4	even	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:	\( N \)	\(=\)	\( 1205 = 5 \cdot 241 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1205.a (trivial)

\(f(q)\)	\(=\)	\(q+2.52189 q^{2} -2.20014 q^{3} +4.35995 q^{4} +1.00000 q^{5} -5.54852 q^{6} -1.38484 q^{7} +5.95156 q^{8} +1.84062 q^{9} +O(q^{10})\)	\(q+2.52189 q^{2} -2.20014 q^{3} +4.35995 q^{4} +1.00000 q^{5} -5.54852 q^{6} -1.38484 q^{7} +5.95156 q^{8} +1.84062 q^{9} +2.52189 q^{10} +1.13965 q^{11} -9.59251 q^{12} -1.42729 q^{13} -3.49243 q^{14} -2.20014 q^{15} +6.28929 q^{16} +8.05325 q^{17} +4.64185 q^{18} +8.18254 q^{19} +4.35995 q^{20} +3.04685 q^{21} +2.87409 q^{22} +6.39018 q^{23} -13.0943 q^{24} +1.00000 q^{25} -3.59948 q^{26} +2.55080 q^{27} -6.03785 q^{28} -1.29066 q^{29} -5.54852 q^{30} -5.90487 q^{31} +3.95782 q^{32} -2.50740 q^{33} +20.3095 q^{34} -1.38484 q^{35} +8.02502 q^{36} -10.2623 q^{37} +20.6355 q^{38} +3.14024 q^{39} +5.95156 q^{40} -7.16948 q^{41} +7.68383 q^{42} +6.20729 q^{43} +4.96884 q^{44} +1.84062 q^{45} +16.1154 q^{46} +11.4217 q^{47} -13.8373 q^{48} -5.08221 q^{49} +2.52189 q^{50} -17.7183 q^{51} -6.22293 q^{52} +3.60717 q^{53} +6.43285 q^{54} +1.13965 q^{55} -8.24196 q^{56} -18.0027 q^{57} -3.25492 q^{58} -3.38677 q^{59} -9.59251 q^{60} +3.02994 q^{61} -14.8915 q^{62} -2.54897 q^{63} -2.59738 q^{64} -1.42729 q^{65} -6.32340 q^{66} -6.78050 q^{67} +35.1118 q^{68} -14.0593 q^{69} -3.49243 q^{70} -5.74234 q^{71} +10.9546 q^{72} +10.5460 q^{73} -25.8804 q^{74} -2.20014 q^{75} +35.6755 q^{76} -1.57824 q^{77} +7.91937 q^{78} -11.9895 q^{79} +6.28929 q^{80} -11.1340 q^{81} -18.0807 q^{82} -2.05382 q^{83} +13.2841 q^{84} +8.05325 q^{85} +15.6541 q^{86} +2.83964 q^{87} +6.78272 q^{88} +15.5874 q^{89} +4.64185 q^{90} +1.97657 q^{91} +27.8609 q^{92} +12.9915 q^{93} +28.8043 q^{94} +8.18254 q^{95} -8.70775 q^{96} -13.7395 q^{97} -12.8168 q^{98} +2.09767 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9	\( 25 q + 6 q^{2} + 15 q^{3} + 32 q^{4} + 25 q^{5} - q^{6} + 19 q^{7} + 15 q^{8} + 32 q^{9} + 6 q^{10} + 2 q^{11} + 20 q^{12} + 14 q^{13} - 5 q^{14} + 15 q^{15} + 38 q^{16} + 7 q^{17} + 9 q^{18} + 30 q^{19} + 32 q^{20} + q^{21} + q^{22} + 43 q^{23} - 6 q^{24} + 25 q^{25} - 22 q^{26} + 42 q^{27} + 32 q^{28} - 4 q^{29} - q^{30} + 14 q^{31} + 26 q^{32} + 4 q^{33} + 7 q^{34} + 19 q^{35} + 15 q^{36} + 16 q^{37} + 14 q^{38} - 21 q^{39} + 15 q^{40} - q^{41} - 25 q^{42} + 35 q^{43} - 52 q^{44} + 32 q^{45} - 27 q^{46} + 50 q^{47} + 26 q^{48} + 46 q^{49} + 6 q^{50} - 7 q^{51} + 3 q^{52} + 4 q^{53} - 31 q^{54} + 2 q^{55} - 51 q^{56} + 2 q^{58} + 6 q^{59} + 20 q^{60} + 19 q^{61} + 28 q^{63} + 49 q^{64} + 14 q^{65} - 27 q^{66} + 65 q^{67} - 25 q^{68} + 2 q^{69} - 5 q^{70} - 34 q^{71} - 10 q^{72} + 8 q^{73} - 42 q^{74} + 15 q^{75} + 71 q^{76} + q^{77} - 59 q^{78} - 12 q^{79} + 38 q^{80} + 29 q^{81} + 11 q^{82} + 41 q^{83} - 10 q^{84} + 7 q^{85} - 13 q^{86} + 40 q^{87} - 52 q^{88} - 24 q^{89} + 9 q^{90} + 46 q^{91} + 85 q^{92} - 30 q^{93} + 14 q^{94} + 30 q^{95} - 30 q^{96} + 9 q^{97} - 64 q^{98} + 2 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 15 * q^3 + 32 * q^4 + 25 * q^5 - q^6 + 19 * q^7 + 15 * q^8 + 32 * q^9 + 6 * q^10 + 2 * q^11 + 20 * q^12 + 14 * q^13 - 5 * q^14 + 15 * q^15 + 38 * q^16 + 7 * q^17 + 9 * q^18 + 30 * q^19 + 32 * q^20 + q^21 + q^22 + 43 * q^23 - 6 * q^24 + 25 * q^25 - 22 * q^26 + 42 * q^27 + 32 * q^28 - 4 * q^29 - q^30 + 14 * q^31 + 26 * q^32 + 4 * q^33 + 7 * q^34 + 19 * q^35 + 15 * q^36 + 16 * q^37 + 14 * q^38 - 21 * q^39 + 15 * q^40 - q^41 - 25 * q^42 + 35 * q^43 - 52 * q^44 + 32 * q^45 - 27 * q^46 + 50 * q^47 + 26 * q^48 + 46 * q^49 + 6 * q^50 - 7 * q^51 + 3 * q^52 + 4 * q^53 - 31 * q^54 + 2 * q^55 - 51 * q^56 + 2 * q^58 + 6 * q^59 + 20 * q^60 + 19 * q^61 + 28 * q^63 + 49 * q^64 + 14 * q^65 - 27 * q^66 + 65 * q^67 - 25 * q^68 + 2 * q^69 - 5 * q^70 - 34 * q^71 - 10 * q^72 + 8 * q^73 - 42 * q^74 + 15 * q^75 + 71 * q^76 + q^77 - 59 * q^78 - 12 * q^79 + 38 * q^80 + 29 * q^81 + 11 * q^82 + 41 * q^83 - 10 * q^84 + 7 * q^85 - 13 * q^86 + 40 * q^87 - 52 * q^88 - 24 * q^89 + 9 * q^90 + 46 * q^91 + 85 * q^92 - 30 * q^93 + 14 * q^94 + 30 * q^95 - 30 * q^96 + 9 * q^97 - 64 * q^98 + 2 * q^99

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