LMFDB - Embedded newform 325.10.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,10,Mod(1,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("325.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	325.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:	$167.386646753$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - x^{16} - 6453 x^{15} - 11965 x^{14} + 16673200 x^{13} + 68278926 x^{12} - 22023799708 x^{11} + \cdots + 22\!\cdots\!80 $ x^17 - x^16 - 6453x^15 - 11965x^14 + 16673200x^13 + 68278926x^12 - 22023799708x^11 - 125071202096x^10 + 15798589803808x^9 + 104438346864256x^8 - 6069247386513920x^7 - 42150961741219840x^6 + 1176708099630112256x^5 + 8192400410671614464x^4 - 105394686485039805440x^3 - 728872183505786896384x^2 + 3347611667766002909184*x + 22946266613430737633280
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{16}\cdot 3^{4}\cdot 5^{8} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-8.60741$ of defining polynomial
Character	$\chi$	$=$	325.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+10.6074 q^{2} +39.6173 q^{3} -399.483 q^{4} +420.237 q^{6} +7059.84 q^{7} -9668.47 q^{8} -18113.5 q^{9} +41815.8 q^{11} -15826.4 q^{12} -28561.0 q^{13} +74886.7 q^{14} +101978. q^{16} +189793. q^{17} -192137. q^{18} -901879. q^{19} +279692. q^{21} +443557. q^{22} +1.17742e6 q^{23} -383039. q^{24} -302958. q^{26} -1.49739e6 q^{27} -2.82029e6 q^{28} -1.67282e6 q^{29} +6.49608e6 q^{31} +6.03198e6 q^{32} +1.65663e6 q^{33} +2.01321e6 q^{34} +7.23602e6 q^{36} -1.15017e7 q^{37} -9.56661e6 q^{38} -1.13151e6 q^{39} +1.94859e7 q^{41} +2.96681e6 q^{42} -1.18398e7 q^{43} -1.67047e7 q^{44} +1.24893e7 q^{46} -2.11765e7 q^{47} +4.04008e6 q^{48} +9.48776e6 q^{49} +7.51907e6 q^{51} +1.14096e7 q^{52} +3.67444e7 q^{53} -1.58835e7 q^{54} -6.82579e7 q^{56} -3.57300e7 q^{57} -1.77443e7 q^{58} +1.04985e8 q^{59} -1.05980e8 q^{61} +6.89066e7 q^{62} -1.27878e8 q^{63} +1.17711e7 q^{64} +1.75725e7 q^{66} -2.54898e7 q^{67} -7.58189e7 q^{68} +4.66460e7 q^{69} +4.38520e7 q^{71} +1.75130e8 q^{72} -2.59790e8 q^{73} -1.22004e8 q^{74} +3.60285e8 q^{76} +2.95213e8 q^{77} -1.20024e7 q^{78} +3.25043e8 q^{79} +2.97205e8 q^{81} +2.06695e8 q^{82} +2.65493e8 q^{83} -1.11732e8 q^{84} -1.25589e8 q^{86} -6.62726e7 q^{87} -4.04295e8 q^{88} +3.01612e8 q^{89} -2.01636e8 q^{91} -4.70357e8 q^{92} +2.57357e8 q^{93} -2.24628e8 q^{94} +2.38971e8 q^{96} -1.38428e9 q^{97} +1.00641e8 q^{98} -7.57429e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q + 33 q^{2} - 73 q^{3} + 4267 q^{4} - 1103 q^{6} + 10670 q^{7} - 11481 q^{8} + 47590 q^{9} - 130917 q^{11} - 32239 q^{12} - 485537 q^{13} - 292206 q^{14} + 1064251 q^{16} + 193953 q^{17} + 2026286 q^{18}+ \cdots - 3023832936 q^{99}+O(q^{100}) $ 17 * q + 33 * q^2 - 73 * q^3 + 4267 * q^4 - 1103 * q^6 + 10670 * q^7 - 11481 * q^8 + 47590 * q^9 - 130917 * q^11 - 32239 * q^12 - 485537 * q^13 - 292206 * q^14 + 1064251 * q^16 + 193953 * q^17 + 2026286 * q^18 - 1244111 * q^19 - 115896 * q^21 + 786475 * q^22 + 2599170 * q^23 + 1304331 * q^24 - 942513 * q^26 - 6747967 * q^27 + 14275516 * q^28 - 2247174 * q^29 - 7948896 * q^31 - 23873169 * q^32 + 13542215 * q^33 - 5605153 * q^34 - 25196656 * q^36 - 17455504 * q^37 - 33099219 * q^38 + 2084953 * q^39 - 28253763 * q^41 - 71221836 * q^42 + 28631126 * q^43 - 123980223 * q^44 - 124743136 * q^46 + 41505678 * q^47 - 51624919 * q^48 + 88370777 * q^49 - 97297213 * q^51 - 121869787 * q^52 + 20918940 * q^53 - 279383933 * q^54 - 81987402 * q^56 + 168605047 * q^57 + 533278432 * q^58 - 242672658 * q^59 - 236730546 * q^61 - 630173268 * q^62 + 563712646 * q^63 - 8650957 * q^64 - 247702451 * q^66 - 33870225 * q^67 + 521453709 * q^68 - 16163890 * q^69 - 809145252 * q^71 - 632968230 * q^72 - 460218191 * q^73 + 540389844 * q^74 - 1067090107 * q^76 - 331946328 * q^77 + 31502783 * q^78 - 295742582 * q^79 - 1013246447 * q^81 - 436735349 * q^82 - 298090917 * q^83 - 2574679448 * q^84 - 2183241552 * q^86 - 164038106 * q^87 + 961546625 * q^88 - 448474185 * q^89 - 304745870 * q^91 - 1091742000 * q^92 - 1680564078 * q^93 - 2962970430 * q^94 + 2289126403 * q^96 + 2630881746 * q^97 + 236409993 * q^98 - 3023832936 * q^99

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 $

$2$	10.6074	0.468786	0.234393	−	0.972142i	$-0.424690\pi$
$2$	10.6074	0.468786	0.234393	+	0.972142i	$0.424690\pi$
$3$	39.6173	0.282383	0.141192	−	0.989982i	$-0.454907\pi$
$3$	39.6173	0.282383	0.141192	+	0.989982i	$0.454907\pi$
$4$	−399.483	−0.780240
$5$	0	0
$5$	0	0
$6$	420.237	0.132377
$7$	7059.84	1.11136	0.555679	−	0.831397i	$-0.312458\pi$
$7$	7059.84	1.11136	0.555679	+	0.831397i	$0.312458\pi$
$8$	−9668.47	−0.834551
$9$	−18113.5	−0.920260
$10$	0	0
$11$	41815.8	0.861139	0.430569	−	0.902558i	$-0.358313\pi$
$11$	41815.8	0.861139	0.430569	+	0.902558i	$0.358313\pi$
$12$	−15826.4	−0.220327
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	74886.7	0.520989
$15$	0	0
$16$	101978.	0.389014
$17$	189793.	0.551137	0.275568	−	0.961281i	$-0.411134\pi$
$17$	189793.	0.551137	0.275568	+	0.961281i	$0.411134\pi$
$18$	−192137.	−0.431405
$19$	−901879.	−1.58766	−0.793829	−	0.608140i	$-0.791916\pi$
$19$	−901879.	−1.58766	−0.793829	+	0.608140i	$0.791916\pi$
$20$	0	0
$21$	279692.	0.313829
$22$	443557.	0.403690
$23$	1.17742e6	0.877313	0.438657	−	0.898655i	$-0.355454\pi$
$23$	1.17742e6	0.877313	0.438657	+	0.898655i	$0.355454\pi$
$24$	−383039.	−0.235663
$25$	0	0
$26$	−302958.	−0.130018
$27$	−1.49739e6	−0.542249
$28$	−2.82029e6	−0.867125
$29$	−1.67282e6	−0.439196	−0.219598	−	0.975590i	$-0.570475\pi$
$29$	−1.67282e6	−0.439196	−0.219598	+	0.975590i	$0.570475\pi$
$30$	0	0
$31$	6.49608e6	1.26335	0.631675	−	0.775233i	$-0.282368\pi$
$31$	6.49608e6	1.26335	0.631675	+	0.775233i	$0.282368\pi$
$32$	6.03198e6	1.01692
$33$	1.65663e6	0.243171
$34$	2.01321e6	0.258365
$35$	0	0
$36$	7.23602e6	0.718023
$37$	−1.15017e7	−1.00892	−0.504459	−	0.863436i	$-0.668308\pi$
$37$	−1.15017e7	−1.00892	−0.504459	+	0.863436i	$0.668308\pi$
$38$	−9.56661e6	−0.744272
$39$	−1.13151e6	−0.0783190
$40$	0	0
$41$	1.94859e7	1.07694	0.538471	−	0.842644i	$-0.319002\pi$
$41$	1.94859e7	1.07694	0.538471	+	0.842644i	$0.319002\pi$
$42$	2.96681e6	0.147118
$43$	−1.18398e7	−0.528123	−0.264062	−	0.964506i	$-0.585062\pi$
$43$	−1.18398e7	−0.528123	−0.264062	+	0.964506i	$0.585062\pi$
$44$	−1.67047e7	−0.671895
$45$	0	0
$46$	1.24893e7	0.411272
$47$	−2.11765e7	−0.633016	−0.316508	−	0.948590i	$-0.602510\pi$
$47$	−2.11765e7	−0.633016	−0.316508	+	0.948590i	$0.602510\pi$
$48$	4.04008e6	0.109851
$49$	9.48776e6	0.235116
$50$	0	0
$51$	7.51907e6	0.155632
$52$	1.14096e7	0.216400
$53$	3.67444e7	0.639661	0.319830	−	0.947475i	$-0.396374\pi$
$53$	3.67444e7	0.639661	0.319830	+	0.947475i	$0.396374\pi$
$54$	−1.58835e7	−0.254199
$55$	0	0
$56$	−6.82579e7	−0.927485
$57$	−3.57300e7	−0.448328
$58$	−1.77443e7	−0.205889
$59$	1.04985e8	1.12796	0.563982	−	0.825787i	$-0.309269\pi$
$59$	1.04985e8	1.12796	0.563982	+	0.825787i	$0.309269\pi$
$60$	0	0
$61$	−1.05980e8	−0.980030	−0.490015	−	0.871714i	$-0.663009\pi$
$61$	−1.05980e8	−0.980030	−0.490015	+	0.871714i	$0.663009\pi$
$62$	6.89066e7	0.592241
$63$	−1.27878e8	−1.02274
$64$	1.17711e7	0.0877017
$65$	0	0
$66$	1.75725e7	0.113995
$67$	−2.54898e7	−0.154536	−0.0772680	−	0.997010i	$-0.524620\pi$
$67$	−2.54898e7	−0.154536	−0.0772680	+	0.997010i	$0.524620\pi$
$68$	−7.58189e7	−0.430019
$69$	4.66460e7	0.247739
$70$	0	0
$71$	4.38520e7	0.204799	0.102399	−	0.994743i	$-0.467348\pi$
$71$	4.38520e7	0.204799	0.102399	+	0.994743i	$0.467348\pi$
$72$	1.75130e8	0.768004
$73$	−2.59790e8	−1.07071	−0.535353	−	0.844629i	$-0.679821\pi$
$73$	−2.59790e8	−1.07071	−0.535353	+	0.844629i	$0.679821\pi$
$74$	−1.22004e8	−0.472966
$75$	0	0
$76$	3.60285e8	1.23875
$77$	2.95213e8	0.957033
$78$	−1.20024e7	−0.0367149
$79$	3.25043e8	0.938899	0.469450	−	0.882959i	$-0.344452\pi$
$79$	3.25043e8	0.938899	0.469450	+	0.882959i	$0.344452\pi$
$80$	0	0
$81$	2.97205e8	0.767138
$82$	2.06695e8	0.504855
$83$	2.65493e8	0.614048	0.307024	−	0.951702i	$-0.400667\pi$
$83$	2.65493e8	0.614048	0.307024	+	0.951702i	$0.400667\pi$
$84$	−1.11732e8	−0.244862
$85$	0	0
$86$	−1.25589e8	−0.247577
$87$	−6.62726e7	−0.124022
$88$	−4.04295e8	−0.718664
$89$	3.01612e8	0.509558	0.254779	−	0.966999i	$-0.417997\pi$
$89$	3.01612e8	0.509558	0.254779	+	0.966999i	$0.417997\pi$
$90$	0	0
$91$	−2.01636e8	−0.308235
$92$	−4.70357e8	−0.684515
$93$	2.57357e8	0.356749
$94$	−2.24628e8	−0.296749
$95$	0	0
$96$	2.38971e8	0.287160
$97$	−1.38428e9	−1.58763	−0.793817	−	0.608157i	$-0.791909\pi$
$97$	−1.38428e9	−1.58763	−0.793817	+	0.608157i	$0.791909\pi$
$98$	1.00641e8	0.110219
$99$	−7.57429e8	−0.792471
$100$	0	0
$101$	−1.03603e8	−0.0990666	−0.0495333	−	0.998772i	$-0.515773\pi$
$101$	−1.03603e8	−0.0990666	−0.0495333	+	0.998772i	$0.515773\pi$
$102$	7.97579e7	0.0729580
$103$	−1.27982e9	−1.12042	−0.560209	−	0.828351i	$-0.689279\pi$
$103$	−1.27982e9	−1.12042	−0.560209	+	0.828351i	$0.689279\pi$
$104$	2.76141e8	0.231463
$105$	0	0
$106$	3.89763e8	0.299864
$107$	−1.46144e9	−1.07784	−0.538921	−	0.842356i	$-0.681168\pi$
$107$	−1.46144e9	−1.07784	−0.538921	+	0.842356i	$0.681168\pi$
$108$	5.98183e8	0.423084
$109$	−2.22647e9	−1.51077	−0.755383	−	0.655284i	$-0.772549\pi$
$109$	−2.22647e9	−1.51077	−0.755383	+	0.655284i	$0.772549\pi$
$110$	0	0
$111$	−4.55667e8	−0.284901
$112$	7.19946e8	0.432334
$113$	8.13140e8	0.469151	0.234575	−	0.972098i	$-0.424630\pi$
$113$	8.13140e8	0.469151	0.234575	+	0.972098i	$0.424630\pi$
$114$	−3.79003e8	−0.210170
$115$	0	0
$116$	6.68263e8	0.342678
$117$	5.17339e8	0.255234
$118$	1.11362e9	0.528774
$119$	1.33991e9	0.612510
$120$	0	0
$121$	−6.09389e8	−0.258440
$122$	−1.12417e9	−0.459424
$123$	7.71977e8	0.304110
$124$	−2.59507e9	−0.985716
$125$	0	0
$126$	−1.35646e9	−0.479445
$127$	−1.51830e9	−0.517894	−0.258947	−	0.965892i	$-0.583375\pi$
$127$	−1.51830e9	−0.517894	−0.258947	+	0.965892i	$0.583375\pi$
$128$	−2.96351e9	−0.975802
$129$	−4.69060e8	−0.149133
$130$	0	0
$131$	−1.34209e9	−0.398162	−0.199081	−	0.979983i	$-0.563796\pi$
$131$	−1.34209e9	−0.398162	−0.199081	+	0.979983i	$0.563796\pi$
$132$	−6.61794e8	−0.189732
$133$	−6.36713e9	−1.76446
$134$	−2.70381e8	−0.0724443
$135$	0	0
$136$	−1.83501e9	−0.459952
$137$	−3.99500e9	−0.968889	−0.484445	−	0.874822i	$-0.660978\pi$
$137$	−3.99500e9	−0.968889	−0.484445	+	0.874822i	$0.660978\pi$
$138$	4.94794e8	0.116136
$139$	−8.16348e9	−1.85485	−0.927424	−	0.374011i	$-0.877982\pi$
$139$	−8.16348e9	−1.85485	−0.927424	+	0.374011i	$0.877982\pi$
$140$	0	0
$141$	−8.38956e8	−0.178753
$142$	4.65156e8	0.0960067
$143$	−1.19430e9	−0.238837
$144$	−1.84717e9	−0.357994
$145$	0	0
$146$	−2.75570e9	−0.501932
$147$	3.75879e8	0.0663927
$148$	4.59475e9	0.787198
$149$	5.19659e9	0.863735	0.431867	−	0.901937i	$-0.357855\pi$
$149$	5.19659e9	0.863735	0.431867	+	0.901937i	$0.357855\pi$
$150$	0	0
$151$	−2.57840e9	−0.403603	−0.201801	−	0.979426i	$-0.564680\pi$
$151$	−2.57840e9	−0.403603	−0.201801	+	0.979426i	$0.564680\pi$
$152$	8.71980e9	1.32498
$153$	−3.43781e9	−0.507189
$154$	3.13144e9	0.448643
$155$	0	0
$156$	4.52018e8	0.0611076
$157$	5.82664e9	0.765368	0.382684	−	0.923879i	$-0.375000\pi$
$157$	5.82664e9	0.765368	0.382684	+	0.923879i	$0.375000\pi$
$158$	3.44787e9	0.440143
$159$	1.45571e9	0.180630
$160$	0	0
$161$	8.31237e9	0.975009
$162$	3.15257e9	0.359623
$163$	7.97012e9	0.884343	0.442171	−	0.896931i	$-0.354208\pi$
$163$	7.97012e9	0.884343	0.442171	+	0.896931i	$0.354208\pi$
$164$	−7.78426e9	−0.840273
$165$	0	0
$166$	2.81620e9	0.287857
$167$	−4.14246e9	−0.412130	−0.206065	−	0.978538i	$-0.566066\pi$
$167$	−4.14246e9	−0.412130	−0.206065	+	0.978538i	$0.566066\pi$
$168$	−2.70419e9	−0.261906
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	1.63362e10	1.46106
$172$	4.72979e9	0.412063
$173$	−1.16240e10	−0.986612	−0.493306	−	0.869856i	$-0.664212\pi$
$173$	−1.16240e10	−0.986612	−0.493306	+	0.869856i	$0.664212\pi$
$174$	−7.02981e8	−0.0581396
$175$	0	0
$176$	4.26427e9	0.334995
$177$	4.15924e9	0.318518
$178$	3.19932e9	0.238874
$179$	−8.25443e9	−0.600964	−0.300482	−	0.953787i	$-0.597148\pi$
$179$	−8.25443e9	−0.600964	−0.300482	+	0.953787i	$0.597148\pi$
$180$	0	0
$181$	−2.01413e10	−1.39487	−0.697436	−	0.716647i	$-0.745676\pi$
$181$	−2.01413e10	−1.39487	−0.697436	+	0.716647i	$0.745676\pi$
$182$	−2.13884e9	−0.144496
$183$	−4.19864e9	−0.276744
$184$	−1.13838e10	−0.732163
$185$	0	0
$186$	2.72989e9	0.167239
$187$	7.93633e9	0.474605
$188$	8.45966e9	0.493904
$189$	−1.05714e10	−0.602633
$190$	0	0
$191$	1.73463e10	0.943098	0.471549	−	0.881840i	$-0.343695\pi$
$191$	1.73463e10	0.943098	0.471549	+	0.881840i	$0.343695\pi$
$192$	4.66340e8	0.0247655
$193$	−2.09400e10	−1.08635	−0.543175	−	0.839620i	$-0.682778\pi$
$193$	−2.09400e10	−1.08635	−0.543175	+	0.839620i	$0.682778\pi$
$194$	−1.46836e10	−0.744260
$195$	0	0
$196$	−3.79020e9	−0.183447
$197$	2.00721e10	0.949500	0.474750	−	0.880121i	$-0.342538\pi$
$197$	2.00721e10	0.949500	0.474750	+	0.880121i	$0.342538\pi$
$198$	−8.03436e9	−0.371499
$199$	−7.09798e9	−0.320846	−0.160423	−	0.987048i	$-0.551286\pi$
$199$	−7.09798e9	−0.320846	−0.160423	+	0.987048i	$0.551286\pi$
$200$	0	0
$201$	−1.00984e9	−0.0436384
$202$	−1.09896e9	−0.0464410
$203$	−1.18099e10	−0.488104
$204$	−3.00374e9	−0.121430
$205$	0	0
$206$	−1.35755e10	−0.525236
$207$	−2.13271e10	−0.807356
$208$	−2.91258e9	−0.107893
$209$	−3.77128e10	−1.36719
$210$	0	0
$211$	−4.77609e10	−1.65883	−0.829414	−	0.558635i	$-0.811325\pi$
$211$	−4.77609e10	−1.65883	−0.829414	+	0.558635i	$0.811325\pi$
$212$	−1.46788e10	−0.499089
$213$	1.73730e9	0.0578317
$214$	−1.55021e10	−0.505277
$215$	0	0
$216$	1.44775e10	0.452535
$217$	4.58613e10	1.40403
$218$	−2.36171e10	−0.708225
$219$	−1.02922e10	−0.302349
$220$	0	0
$221$	−5.42067e9	−0.152858
$222$	−4.83345e9	−0.133558
$223$	−4.50927e10	−1.22105	−0.610526	−	0.791996i	$-0.709042\pi$
$223$	−4.50927e10	−1.22105	−0.610526	+	0.791996i	$0.709042\pi$
$224$	4.25848e10	1.13016
$225$	0	0
$226$	8.62531e9	0.219931
$227$	5.14032e10	1.28491	0.642457	−	0.766322i	$-0.277915\pi$
$227$	5.14032e10	1.28491	0.642457	+	0.766322i	$0.277915\pi$
$228$	1.42735e10	0.349804
$229$	−8.65756e9	−0.208035	−0.104017	−	0.994575i	$-0.533170\pi$
$229$	−8.65756e9	−0.208035	−0.104017	+	0.994575i	$0.533170\pi$
$230$	0	0
$231$	1.16955e10	0.270250
$232$	1.61736e10	0.366532
$233$	−6.18115e10	−1.37394	−0.686970	−	0.726686i	$-0.741060\pi$
$233$	−6.18115e10	−1.37394	−0.686970	+	0.726686i	$0.741060\pi$
$234$	5.48763e9	0.119650
$235$	0	0
$236$	−4.19399e10	−0.880082
$237$	1.28773e10	0.265129
$238$	1.42129e10	0.287136
$239$	−5.77153e10	−1.14420	−0.572098	−	0.820185i	$-0.693870\pi$
$239$	−5.77153e10	−1.14420	−0.572098	+	0.820185i	$0.693870\pi$
$240$	0	0
$241$	1.45035e10	0.276947	0.138474	−	0.990366i	$-0.455780\pi$
$241$	1.45035e10	0.276947	0.138474	+	0.990366i	$0.455780\pi$
$242$	−6.46404e9	−0.121153
$243$	4.12476e10	0.758876
$244$	4.23372e10	0.764658
$245$	0	0
$246$	8.18867e9	0.142563
$247$	2.57586e10	0.440337
$248$	−6.28072e10	−1.05433
$249$	1.05181e10	0.173397
$250$	0	0
$251$	−1.19655e11	−1.90283	−0.951413	−	0.307918i	$-0.900368\pi$
$251$	−1.19655e11	−1.90283	−0.951413	+	0.307918i	$0.900368\pi$
$252$	5.10852e10	0.797981
$253$	4.92346e10	0.755488
$254$	−1.61052e10	−0.242781
$255$	0	0
$256$	−3.74620e10	−0.545144
$257$	5.16474e10	0.738497	0.369249	−	0.929331i	$-0.379615\pi$
$257$	5.16474e10	0.738497	0.369249	+	0.929331i	$0.379615\pi$
$258$	−4.97551e9	−0.0699115
$259$	−8.12004e10	−1.12127
$260$	0	0
$261$	3.03006e10	0.404175
$262$	−1.42361e10	−0.186653
$263$	4.32530e9	0.0557462	0.0278731	−	0.999611i	$-0.491127\pi$
$263$	4.32530e9	0.0557462	0.0278731	+	0.999611i	$0.491127\pi$
$264$	−1.60171e10	−0.202939
$265$	0	0
$266$	−6.75387e10	−0.827152
$267$	1.19490e10	0.143891
$268$	1.01827e10	0.120575
$269$	−2.02373e9	−0.0235649	−0.0117825	−	0.999931i	$-0.503751\pi$
$269$	−2.02373e9	−0.0235649	−0.0117825	+	0.999931i	$0.503751\pi$
$270$	0	0
$271$	−1.67526e10	−0.188678	−0.0943390	−	0.995540i	$-0.530074\pi$
$271$	−1.67526e10	−0.188678	−0.0943390	+	0.995540i	$0.530074\pi$
$272$	1.93546e10	0.214400
$273$	−7.98827e9	−0.0870404
$274$	−4.23766e10	−0.454202
$275$	0	0
$276$	−1.86343e10	−0.193295
$277$	8.72923e10	0.890875	0.445437	−	0.895313i	$-0.353048\pi$
$277$	8.72923e10	0.890875	0.445437	+	0.895313i	$0.353048\pi$
$278$	−8.65934e10	−0.869527
$279$	−1.17667e11	−1.16261
$280$	0	0
$281$	−1.33617e11	−1.27845	−0.639225	−	0.769019i	$-0.720745\pi$
$281$	−1.33617e11	−1.27845	−0.639225	+	0.769019i	$0.720745\pi$
$282$	−8.89916e9	−0.0837969
$283$	1.20149e11	1.11348	0.556740	−	0.830687i	$-0.312052\pi$
$283$	1.20149e11	1.11348	0.556740	+	0.830687i	$0.312052\pi$
$284$	−1.75181e10	−0.159792
$285$	0	0
$286$	−1.26684e10	−0.111963
$287$	1.37567e11	1.19687
$288$	−1.09260e11	−0.935826
$289$	−8.25666e10	−0.696248
$290$	0	0
$291$	−5.48413e10	−0.448321
$292$	1.03782e11	0.835407
$293$	−9.34714e10	−0.740926	−0.370463	−	0.928847i	$-0.620801\pi$
$293$	−9.34714e10	−0.740926	−0.370463	+	0.928847i	$0.620801\pi$
$294$	3.98711e9	0.0311240
$295$	0	0
$296$	1.11204e11	0.841993
$297$	−6.26146e10	−0.466952
$298$	5.51224e10	0.404907
$299$	−3.36282e10	−0.243323
$300$	0	0
$301$	−8.35869e10	−0.586934
$302$	−2.73502e10	−0.189203
$303$	−4.10448e9	−0.0279748
$304$	−9.19715e10	−0.617621
$305$	0	0
$306$	−3.64662e10	−0.237763
$307$	−1.12751e11	−0.724433	−0.362216	−	0.932094i	$-0.617980\pi$
$307$	−1.12751e11	−0.724433	−0.362216	+	0.932094i	$0.617980\pi$
$308$	−1.17932e11	−0.746715
$309$	−5.07028e10	−0.316387
$310$	0	0
$311$	1.67036e11	1.01248	0.506242	−	0.862391i	$-0.331034\pi$
$311$	1.67036e11	1.01248	0.506242	+	0.862391i	$0.331034\pi$
$312$	1.09400e10	0.0653612
$313$	1.26256e11	0.743536	0.371768	−	0.928326i	$-0.378752\pi$
$313$	1.26256e11	0.743536	0.371768	+	0.928326i	$0.378752\pi$
$314$	6.18056e10	0.358793
$315$	0	0
$316$	−1.29849e11	−0.732566
$317$	−2.34026e11	−1.30166	−0.650829	−	0.759224i	$-0.725579\pi$
$317$	−2.34026e11	−1.30166	−0.650829	+	0.759224i	$0.725579\pi$
$318$	1.54414e10	0.0846766
$319$	−6.99503e10	−0.378209
$320$	0	0
$321$	−5.78985e10	−0.304365
$322$	8.81728e10	0.457070
$323$	−1.71170e11	−0.875017
$324$	−1.18728e11	−0.598551
$325$	0	0
$326$	8.45424e10	0.414567
$327$	−8.82066e10	−0.426615
$328$	−1.88399e11	−0.898763
$329$	−1.49503e11	−0.703507
$330$	0	0
$331$	5.82842e10	0.266885	0.133443	−	0.991057i	$-0.457397\pi$
$331$	5.82842e10	0.266885	0.133443	+	0.991057i	$0.457397\pi$
$332$	−1.06060e11	−0.479105
$333$	2.08336e11	0.928466
$334$	−4.39408e10	−0.193201
$335$	0	0
$336$	2.85223e10	0.122084
$337$	8.15971e10	0.344620	0.172310	−	0.985043i	$-0.444877\pi$
$337$	8.15971e10	0.344620	0.172310	+	0.985043i	$0.444877\pi$
$338$	8.65279e9	0.0360605
$339$	3.22144e10	0.132480
$340$	0	0
$341$	2.71639e11	1.08792
$342$	1.73284e11	0.684924
$343$	−2.17908e11	−0.850060
$344$	1.14473e11	0.440746
$345$	0	0
$346$	−1.23300e11	−0.462510
$347$	−2.97245e9	−0.0110061	−0.00550303	−	0.999985i	$-0.501752\pi$
$347$	−2.97245e9	−0.0110061	−0.00550303	+	0.999985i	$0.501752\pi$
$348$	2.64748e10	0.0967667
$349$	−3.25463e11	−1.17432	−0.587161	−	0.809470i	$-0.699755\pi$
$349$	−3.25463e11	−1.17432	−0.587161	+	0.809470i	$0.699755\pi$
$350$	0	0
$351$	4.27670e10	0.150393
$352$	2.52232e11	0.875705
$353$	−3.73886e11	−1.28160	−0.640801	−	0.767707i	$-0.721398\pi$
$353$	−3.73886e11	−1.28160	−0.640801	+	0.767707i	$0.721398\pi$
$354$	4.41188e10	0.149317
$355$	0	0
$356$	−1.20489e11	−0.397577
$357$	5.30835e10	0.172963
$358$	−8.75582e10	−0.281724
$359$	5.76577e11	1.83203	0.916014	−	0.401147i	$-0.131388\pi$
$359$	5.76577e11	1.83203	0.916014	+	0.401147i	$0.131388\pi$
$360$	0	0
$361$	4.90698e11	1.52066
$362$	−2.13647e11	−0.653897
$363$	−2.41423e10	−0.0729793
$364$	8.05502e10	0.240497
$365$	0	0
$366$	−4.45367e10	−0.129734
$367$	6.04552e11	1.73955	0.869774	−	0.493451i	$-0.164265\pi$
$367$	6.04552e11	1.73955	0.869774	+	0.493451i	$0.164265\pi$
$368$	1.20070e11	0.341287
$369$	−3.52957e11	−0.991066
$370$	0	0
$371$	2.59410e11	0.710892
$372$	−1.02810e11	−0.278350
$373$	−3.90114e11	−1.04352	−0.521762	−	0.853091i	$-0.674725\pi$
$373$	−3.90114e11	−1.04352	−0.521762	+	0.853091i	$0.674725\pi$
$374$	8.41839e10	0.222488
$375$	0	0
$376$	2.04745e11	0.528284
$377$	4.77775e10	0.121811
$378$	−1.12135e11	−0.282506
$379$	6.56944e11	1.63551	0.817753	−	0.575570i	$-0.195220\pi$
$379$	6.56944e11	1.63551	0.817753	+	0.575570i	$0.195220\pi$
$380$	0	0
$381$	−6.01509e10	−0.146245
$382$	1.83999e11	0.442111
$383$	6.87899e11	1.63354	0.816771	−	0.576962i	$-0.195762\pi$
$383$	6.87899e11	1.63354	0.816771	+	0.576962i	$0.195762\pi$
$384$	−1.17406e11	−0.275550
$385$	0	0
$386$	−2.22120e11	−0.509265
$387$	2.14459e11	0.486011
$388$	5.52995e11	1.23873
$389$	−8.31135e11	−1.84034	−0.920170	−	0.391518i	$-0.871950\pi$
$389$	−8.31135e11	−1.84034	−0.920170	+	0.391518i	$0.871950\pi$
$390$	0	0
$391$	2.23465e11	0.483520
$392$	−9.17322e10	−0.196216
$393$	−5.31699e10	−0.112434
$394$	2.12913e11	0.445112
$395$	0	0
$396$	3.02580e11	0.618317
$397$	−5.53624e11	−1.11856	−0.559278	−	0.828980i	$-0.688922\pi$
$397$	−5.53624e11	−1.11856	−0.559278	+	0.828980i	$0.688922\pi$
$398$	−7.52912e10	−0.150408
$399$	−2.52248e11	−0.498253
$400$	0	0
$401$	−7.96171e11	−1.53765	−0.768824	−	0.639461i	$-0.779158\pi$
$401$	−7.96171e11	−1.53765	−0.768824	+	0.639461i	$0.779158\pi$
$402$	−1.07117e10	−0.0204571
$403$	−1.85535e11	−0.350390
$404$	4.13877e10	0.0772957
$405$	0	0
$406$	−1.25272e11	−0.228816
$407$	−4.80954e11	−0.868818
$408$	−7.26980e10	−0.129883
$409$	−3.87733e11	−0.685138	−0.342569	−	0.939493i	$-0.611297\pi$
$409$	−3.87733e11	−0.685138	−0.342569	+	0.939493i	$0.611297\pi$
$410$	0	0
$411$	−1.58271e11	−0.273598
$412$	5.11264e11	0.874194
$413$	7.41181e11	1.25357
$414$	−2.26225e11	−0.378477
$415$	0	0
$416$	−1.72279e11	−0.282042
$417$	−3.23415e11	−0.523778
$418$	−4.00035e11	−0.640921
$419$	3.33743e11	0.528991	0.264496	−	0.964387i	$-0.414795\pi$
$419$	3.33743e11	0.528991	0.264496	+	0.964387i	$0.414795\pi$
$420$	0	0
$421$	−8.16850e11	−1.26728	−0.633640	−	0.773628i	$-0.718440\pi$
$421$	−8.16850e11	−1.26728	−0.633640	+	0.773628i	$0.718440\pi$
$422$	−5.06619e11	−0.777635
$423$	3.83580e11	0.582539
$424$	−3.55262e11	−0.533830
$425$	0	0
$426$	1.84282e10	0.0271107
$427$	−7.48202e11	−1.08916
$428$	5.83822e11	0.840976
$429$	−4.73149e10	−0.0674435
$430$	0	0
$431$	1.23826e12	1.72847	0.864237	−	0.503085i	$-0.167802\pi$
$431$	1.23826e12	1.72847	0.864237	+	0.503085i	$0.167802\pi$
$432$	−1.52701e11	−0.210942
$433$	9.18106e11	1.25516	0.627578	−	0.778554i	$-0.284047\pi$
$433$	9.18106e11	1.25516	0.627578	+	0.778554i	$0.284047\pi$
$434$	4.86470e11	0.658191
$435$	0	0
$436$	8.89435e11	1.17876
$437$	−1.06189e12	−1.39287
$438$	−1.09173e11	−0.141737
$439$	8.17970e11	1.05111	0.525553	−	0.850761i	$-0.323858\pi$
$439$	8.17970e11	1.05111	0.525553	+	0.850761i	$0.323858\pi$
$440$	0	0
$441$	−1.71856e11	−0.216367
$442$	−5.74993e10	−0.0716576
$443$	−8.22578e11	−1.01475	−0.507377	−	0.861724i	$-0.669385\pi$
$443$	−8.22578e11	−1.01475	−0.507377	+	0.861724i	$0.669385\pi$
$444$	1.82031e11	0.222291
$445$	0	0
$446$	−4.78317e11	−0.572412
$447$	2.05875e11	0.243904
$448$	8.31023e10	0.0974680
$449$	1.42936e12	1.65972	0.829859	−	0.557973i	$-0.188421\pi$
$449$	1.42936e12	1.65972	0.829859	+	0.557973i	$0.188421\pi$
$450$	0	0
$451$	8.14816e11	0.927396
$452$	−3.24835e11	−0.366050
$453$	−1.02149e11	−0.113971
$454$	5.45255e11	0.602349
$455$	0	0
$456$	3.45455e11	0.374153
$457$	−1.02265e11	−0.109674	−0.0548369	−	0.998495i	$-0.517464\pi$
$457$	−1.02265e11	−0.109674	−0.0548369	+	0.998495i	$0.517464\pi$
$458$	−9.18344e10	−0.0975238
$459$	−2.84194e11	−0.298854
$460$	0	0
$461$	−7.01331e11	−0.723217	−0.361609	−	0.932330i	$-0.617772\pi$
$461$	−7.01331e11	−0.723217	−0.361609	+	0.932330i	$0.617772\pi$
$462$	1.24059e11	0.126689
$463$	−4.06102e10	−0.0410696	−0.0205348	−	0.999789i	$-0.506537\pi$
$463$	−4.06102e10	−0.0410696	−0.0205348	+	0.999789i	$0.506537\pi$
$464$	−1.70590e11	−0.170853
$465$	0	0
$466$	−6.55660e11	−0.644084
$467$	1.59339e11	0.155023	0.0775117	−	0.996991i	$-0.475302\pi$
$467$	1.59339e11	0.155023	0.0775117	+	0.996991i	$0.475302\pi$
$468$	−2.06668e11	−0.199144
$469$	−1.79954e11	−0.171745
$470$	0	0
$471$	2.30836e11	0.216127
$472$	−1.01505e12	−0.941344
$473$	−4.95089e11	−0.454787
$474$	1.36595e11	0.124289
$475$	0	0
$476$	−5.35270e11	−0.477905
$477$	−6.65569e11	−0.588654
$478$	−6.12211e11	−0.536383
$479$	1.81846e12	1.57832	0.789159	−	0.614189i	$-0.210517\pi$
$479$	1.81846e12	1.57832	0.789159	+	0.614189i	$0.210517\pi$
$480$	0	0
$481$	3.28501e11	0.279823
$482$	1.53845e11	0.129829
$483$	3.29313e11	0.275326
$484$	2.43440e11	0.201646
$485$	0	0
$486$	4.37531e11	0.355750
$487$	−2.58312e10	−0.0208097	−0.0104048	−	0.999946i	$-0.503312\pi$
$487$	−2.58312e10	−0.0208097	−0.0104048	+	0.999946i	$0.503312\pi$
$488$	1.02466e12	0.817885
$489$	3.15754e11	0.249724
$490$	0	0
$491$	3.22969e11	0.250781	0.125390	−	0.992107i	$-0.459982\pi$
$491$	3.22969e11	0.250781	0.125390	+	0.992107i	$0.459982\pi$
$492$	−3.08391e11	−0.237279
$493$	−3.17489e11	−0.242057
$494$	2.73232e11	0.206424
$495$	0	0
$496$	6.62455e11	0.491461
$497$	3.09588e11	0.227604
$498$	1.11570e11	0.0812860
$499$	2.78527e11	0.201101	0.100551	−	0.994932i	$-0.467940\pi$
$499$	2.78527e11	0.201101	0.100551	+	0.994932i	$0.467940\pi$
$500$	0	0
$501$	−1.64113e11	−0.116379
$502$	−1.26923e12	−0.892018
$503$	2.69599e12	1.87785	0.938927	−	0.344117i	$-0.111822\pi$
$503$	2.69599e12	1.87785	0.938927	+	0.344117i	$0.111822\pi$
$504$	1.23639e12	0.853527
$505$	0	0
$506$	5.22251e11	0.354162
$507$	3.23170e10	0.0217218
$508$	6.06535e11	0.404081
$509$	−1.83646e10	−0.0121269	−0.00606347	−	0.999982i	$-0.501930\pi$
$509$	−1.83646e10	−0.0121269	−0.00606347	+	0.999982i	$0.501930\pi$
$510$	0	0
$511$	−1.83408e12	−1.18994
$512$	1.11994e12	0.720246
$513$	1.35047e12	0.860907
$514$	5.47845e11	0.346197
$515$	0	0
$516$	1.87381e11	0.116360
$517$	−8.85513e11	−0.545114
$518$	−8.61327e11	−0.525635
$519$	−4.60510e11	−0.278603
$520$	0	0
$521$	5.71331e11	0.339718	0.169859	−	0.985468i	$-0.445669\pi$
$521$	5.71331e11	0.339718	0.169859	+	0.985468i	$0.445669\pi$
$522$	3.21411e11	0.189471
$523$	−4.28321e11	−0.250330	−0.125165	−	0.992136i	$-0.539946\pi$
$523$	−4.28321e11	−0.250330	−0.125165	+	0.992136i	$0.539946\pi$
$524$	5.36141e11	0.310662
$525$	0	0
$526$	4.58802e10	0.0261330
$527$	1.23291e12	0.696279
$528$	1.68939e11	0.0945969
$529$	−4.14844e11	−0.230322
$530$	0	0
$531$	−1.90165e12	−1.03802
$532$	2.54356e12	1.37670
$533$	−5.56536e11	−0.298690
$534$	1.26748e11	0.0674539
$535$	0	0
$536$	2.46447e11	0.128968
$537$	−3.27018e11	−0.169702
$538$	−2.14665e10	−0.0110469
$539$	3.96738e11	0.202467
$540$	0	0
$541$	7.96212e10	0.0399614	0.0199807	−	0.999800i	$-0.493640\pi$
$541$	7.96212e10	0.0399614	0.0199807	+	0.999800i	$0.493640\pi$
$542$	−1.77702e11	−0.0884495
$543$	−7.97945e11	−0.393889
$544$	1.14483e12	0.560460
$545$	0	0
$546$	−8.47349e10	−0.0408033
$547$	2.30263e12	1.09972	0.549860	−	0.835257i	$-0.314681\pi$
$547$	2.30263e12	1.09972	0.549860	+	0.835257i	$0.314681\pi$
$548$	1.59593e12	0.755966
$549$	1.91966e12	0.901882
$550$	0	0
$551$	1.50868e12	0.697294
$552$	−4.50996e11	−0.206751
$553$	2.29475e12	1.04345
$554$	9.25945e11	0.417630
$555$	0	0
$556$	3.26117e12	1.44723
$557$	−8.65592e11	−0.381035	−0.190517	−	0.981684i	$-0.561017\pi$
$557$	−8.65592e11	−0.381035	−0.190517	+	0.981684i	$0.561017\pi$
$558$	−1.24814e12	−0.545015
$559$	3.38156e11	0.146475
$560$	0	0
$561$	3.14416e11	0.134021
$562$	−1.41733e12	−0.599320
$563$	3.11714e12	1.30758	0.653791	−	0.756675i	$-0.273178\pi$
$563$	3.11714e12	1.30758	0.653791	+	0.756675i	$0.273178\pi$
$564$	3.35149e11	0.139470
$565$	0	0
$566$	1.27447e12	0.521984
$567$	2.09822e12	0.852564
$568$	−4.23982e11	−0.170915
$569$	4.10441e12	1.64152	0.820759	−	0.571274i	$-0.193551\pi$
$569$	4.10441e12	1.64152	0.820759	+	0.571274i	$0.193551\pi$
$570$	0	0
$571$	−1.68482e12	−0.663272	−0.331636	−	0.943407i	$-0.607601\pi$
$571$	−1.68482e12	−0.663272	−0.331636	+	0.943407i	$0.607601\pi$
$572$	4.77102e11	0.186350
$573$	6.87213e11	0.266315
$574$	1.45923e12	0.561074
$575$	0	0
$576$	−2.13216e11	−0.0807084
$577$	−2.60646e12	−0.978947	−0.489473	−	0.872018i	$-0.662811\pi$
$577$	−2.60646e12	−0.978947	−0.489473	+	0.872018i	$0.662811\pi$
$578$	−8.75818e11	−0.326391
$579$	−8.29587e11	−0.306767
$580$	0	0
$581$	1.87434e12	0.682427
$582$	−5.81724e11	−0.210167
$583$	1.53650e12	0.550837
$584$	2.51178e12	0.893558
$585$	0	0
$586$	−9.91490e11	−0.347335
$587$	2.50883e12	0.872167	0.436083	−	0.899906i	$-0.356365\pi$
$587$	2.50883e12	0.872167	0.436083	+	0.899906i	$0.356365\pi$
$588$	−1.50157e11	−0.0518022
$589$	−5.85868e12	−2.00577
$590$	0	0
$591$	7.95203e11	0.268123
$592$	−1.17292e12	−0.392483
$593$	4.12741e12	1.37067	0.685333	−	0.728230i	$-0.259657\pi$
$593$	4.12741e12	1.37067	0.685333	+	0.728230i	$0.259657\pi$
$594$	−6.64179e11	−0.218900
$595$	0	0
$596$	−2.07595e12	−0.673920
$597$	−2.81203e11	−0.0906014
$598$	−3.56708e11	−0.114066
$599$	2.27898e11	0.0723302	0.0361651	−	0.999346i	$-0.488486\pi$
$599$	2.27898e11	0.0723302	0.0361651	+	0.999346i	$0.488486\pi$
$600$	0	0
$601$	4.64556e12	1.45246	0.726228	−	0.687454i	$-0.241272\pi$
$601$	4.64556e12	1.45246	0.726228	+	0.687454i	$0.241272\pi$
$602$	−8.86641e11	−0.275146
$603$	4.61708e11	0.142213
$604$	1.03003e12	0.314907
$605$	0	0
$606$	−4.35379e10	−0.0131142
$607$	−2.24855e12	−0.672285	−0.336142	−	0.941811i	$-0.609122\pi$
$607$	−2.24855e12	−0.672285	−0.336142	+	0.941811i	$0.609122\pi$
$608$	−5.44012e12	−1.61451
$609$	−4.67874e11	−0.137832
$610$	0	0
$611$	6.04823e11	0.175567
$612$	1.37334e12	0.395729
$613$	−2.88188e12	−0.824336	−0.412168	−	0.911108i	$-0.635228\pi$
$613$	−2.88188e12	−0.824336	−0.412168	+	0.911108i	$0.635228\pi$
$614$	−1.19600e12	−0.339604
$615$	0	0
$616$	−2.85426e12	−0.798693
$617$	−4.36400e12	−1.21227	−0.606137	−	0.795360i	$-0.707282\pi$
$617$	−4.36400e12	−1.21227	−0.606137	+	0.795360i	$0.707282\pi$
$618$	−5.37826e11	−0.148318
$619$	3.23424e12	0.885450	0.442725	−	0.896658i	$-0.354012\pi$
$619$	3.23424e12	0.885450	0.442725	+	0.896658i	$0.354012\pi$
$620$	0	0
$621$	−1.76305e12	−0.475722
$622$	1.77182e12	0.474638
$623$	2.12933e12	0.566301
$624$	−1.15389e11	−0.0304672
$625$	0	0
$626$	1.33925e12	0.348559
$627$	−1.49408e12	−0.386073
$628$	−2.32764e12	−0.597170
$629$	−2.18295e12	−0.556052
$630$	0	0
$631$	−3.29382e12	−0.827118	−0.413559	−	0.910477i	$-0.635714\pi$
$631$	−3.29382e12	−0.827118	−0.413559	+	0.910477i	$0.635714\pi$
$632$	−3.14267e12	−0.783559
$633$	−1.89216e12	−0.468425
$634$	−2.48241e12	−0.610199
$635$	0	0
$636$	−5.81532e11	−0.140934
$637$	−2.70980e11	−0.0652093
$638$	−7.41992e11	−0.177299
$639$	−7.94312e11	−0.188468
$640$	0	0
$641$	4.27802e12	1.00088	0.500439	−	0.865772i	$-0.333172\pi$
$641$	4.27802e12	1.00088	0.500439	+	0.865772i	$0.333172\pi$
$642$	−6.14153e11	−0.142682
$643$	−3.33298e12	−0.768923	−0.384461	−	0.923141i	$-0.625613\pi$
$643$	−3.33298e12	−0.768923	−0.384461	+	0.923141i	$0.625613\pi$
$644$	−3.32065e12	−0.760741
$645$	0	0
$646$	−1.81567e12	−0.410196
$647$	6.18197e12	1.38694	0.693470	−	0.720485i	$-0.256081\pi$
$647$	6.18197e12	1.38694	0.693470	+	0.720485i	$0.256081\pi$
$648$	−2.87352e12	−0.640216
$649$	4.39005e12	0.971333
$650$	0	0
$651$	1.81690e12	0.396476
$652$	−3.18393e12	−0.689999
$653$	7.64064e12	1.64445	0.822224	−	0.569164i	$-0.192733\pi$
$653$	7.64064e12	1.64445	0.822224	+	0.569164i	$0.192733\pi$
$654$	−9.35643e11	−0.199991
$655$	0	0
$656$	1.98712e12	0.418945
$657$	4.70570e12	0.985327
$658$	−1.58584e12	−0.329794
$659$	1.90916e12	0.394327	0.197164	−	0.980371i	$-0.436827\pi$
$659$	1.90916e12	0.394327	0.197164	+	0.980371i	$0.436827\pi$
$660$	0	0
$661$	−1.36384e12	−0.277879	−0.138940	−	0.990301i	$-0.544369\pi$
$661$	−1.36384e12	−0.277879	−0.138940	+	0.990301i	$0.544369\pi$
$662$	6.18244e11	0.125112
$663$	−2.14752e11	−0.0431645
$664$	−2.56692e12	−0.512454
$665$	0	0
$666$	2.20991e12	0.435252
$667$	−1.96961e12	−0.385313
$668$	1.65484e12	0.321560
$669$	−1.78645e12	−0.344805
$670$	0	0
$671$	−4.43163e12	−0.843942
$672$	1.68709e12	0.319137
$673$	−2.70123e12	−0.507567	−0.253784	−	0.967261i	$-0.581675\pi$
$673$	−2.70123e12	−0.507567	−0.253784	+	0.967261i	$0.581675\pi$
$674$	8.65534e11	0.161553
$675$	0	0
$676$	−3.25870e11	−0.0600184
$677$	−6.85241e12	−1.25370	−0.626851	−	0.779139i	$-0.715656\pi$
$677$	−6.85241e12	−1.25370	−0.626851	+	0.779139i	$0.715656\pi$
$678$	3.41711e11	0.0621049
$679$	−9.77278e12	−1.76443
$680$	0	0
$681$	2.03645e12	0.362838
$682$	2.88138e12	0.510001
$683$	7.13875e12	1.25525	0.627623	−	0.778517i	$-0.284028\pi$
$683$	7.13875e12	1.25525	0.627623	+	0.778517i	$0.284028\pi$
$684$	−6.52602e12	−1.13998
$685$	0	0
$686$	−2.31144e12	−0.398496
$687$	−3.42989e11	−0.0587455
$688$	−1.20739e12	−0.205447
$689$	−1.04946e12	−0.177410
$690$	0	0
$691$	−3.78880e12	−0.632194	−0.316097	−	0.948727i	$-0.602372\pi$
$691$	−3.78880e12	−0.632194	−0.316097	+	0.948727i	$0.602372\pi$
$692$	4.64357e12	0.769794
$693$	−5.34733e12	−0.880719
$694$	−3.15300e10	−0.00515949
$695$	0	0
$696$	6.40755e11	0.103502
$697$	3.69827e12	0.593542
$698$	−3.45232e12	−0.550506
$699$	−2.44880e12	−0.387978
$700$	0	0
$701$	−2.81594e12	−0.440445	−0.220223	−	0.975450i	$-0.570678\pi$
$701$	−2.81594e12	−0.440445	−0.220223	+	0.975450i	$0.570678\pi$
$702$	4.53648e11	0.0705021
$703$	1.03732e13	1.60182
$704$	4.92219e11	0.0755233
$705$	0	0
$706$	−3.96597e12	−0.600797
$707$	−7.31423e11	−0.110098
$708$	−1.66154e12	−0.248521
$709$	−4.28790e12	−0.637290	−0.318645	−	0.947874i	$-0.603228\pi$
$709$	−4.28790e12	−0.637290	−0.318645	+	0.947874i	$0.603228\pi$
$710$	0	0
$711$	−5.88766e12	−0.864031
$712$	−2.91613e12	−0.425252
$713$	7.64859e12	1.10835
$714$	5.63078e11	0.0810824
$715$	0	0
$716$	3.29750e12	0.468896
$717$	−2.28652e12	−0.323102
$718$	6.11599e12	0.858829
$719$	8.25681e11	0.115221	0.0576106	−	0.998339i	$-0.481652\pi$
$719$	8.25681e11	0.115221	0.0576106	+	0.998339i	$0.481652\pi$
$720$	0	0
$721$	−9.03530e12	−1.24518
$722$	5.20504e12	0.712864
$723$	5.74590e11	0.0782052
$724$	8.04611e12	1.08834
$725$	0	0
$726$	−2.56088e11	−0.0342116
$727$	−5.14290e12	−0.682815	−0.341408	−	0.939915i	$-0.610904\pi$
$727$	−5.14290e12	−0.682815	−0.341408	+	0.939915i	$0.610904\pi$
$728$	1.94951e12	0.257238
$729$	−4.21576e12	−0.552844
$730$	0	0
$731$	−2.24710e12	−0.291068
$732$	1.67728e12	0.215927
$733$	−1.45460e13	−1.86113	−0.930563	−	0.366133i	$-0.880682\pi$
$733$	−1.45460e13	−1.86113	−0.930563	+	0.366133i	$0.880682\pi$
$734$	6.41273e12	0.815475
$735$	0	0
$736$	7.10215e12	0.892153
$737$	−1.06587e12	−0.133077
$738$	−3.74396e12	−0.464598
$739$	−3.02351e12	−0.372916	−0.186458	−	0.982463i	$-0.559701\pi$
$739$	−3.02351e12	−0.372916	−0.186458	+	0.982463i	$0.559701\pi$
$740$	0	0
$741$	1.02048e12	0.124344
$742$	2.75167e12	0.333256
$743$	−1.47422e13	−1.77465	−0.887325	−	0.461144i	$-0.847439\pi$
$743$	−1.47422e13	−1.77465	−0.887325	+	0.461144i	$0.847439\pi$
$744$	−2.48825e12	−0.297725
$745$	0	0
$746$	−4.13810e12	−0.489189
$747$	−4.80901e12	−0.565083
$748$	−3.17043e12	−0.370306
$749$	−1.03176e13	−1.19787
$750$	0	0
$751$	−1.40778e13	−1.61494	−0.807469	−	0.589910i	$-0.799163\pi$
$751$	−1.40778e13	−1.61494	−0.807469	+	0.589910i	$0.799163\pi$
$752$	−2.15953e12	−0.246252
$753$	−4.74040e12	−0.537326
$754$	5.06795e11	0.0571033
$755$	0	0
$756$	4.22308e12	0.470198
$757$	1.42372e13	1.57577	0.787885	−	0.615823i	$-0.211176\pi$
$757$	1.42372e13	1.57577	0.787885	+	0.615823i	$0.211176\pi$
$758$	6.96848e12	0.766702
$759$	1.95054e12	0.213337
$760$	0	0
$761$	1.00559e13	1.08690	0.543449	−	0.839442i	$-0.317118\pi$
$761$	1.00559e13	1.08690	0.543449	+	0.839442i	$0.317118\pi$
$762$	−6.38046e11	−0.0685574
$763$	−1.57185e13	−1.67900
$764$	−6.92955e12	−0.735843
$765$	0	0
$766$	7.29683e12	0.765781
$767$	−2.99849e12	−0.312841
$768$	−1.48414e12	−0.153940
$769$	−2.23252e12	−0.230212	−0.115106	−	0.993353i	$-0.536721\pi$
$769$	−2.23252e12	−0.230212	−0.115106	+	0.993353i	$0.536721\pi$
$770$	0	0
$771$	2.04613e12	0.208539
$772$	8.36518e12	0.847613
$773$	−4.87460e12	−0.491057	−0.245528	−	0.969389i	$-0.578961\pi$
$773$	−4.87460e12	−0.491057	−0.245528	+	0.969389i	$0.578961\pi$
$774$	2.27486e12	0.227835
$775$	0	0
$776$	1.33838e13	1.32496
$777$	−3.21694e12	−0.316627
$778$	−8.81619e12	−0.862726
$779$	−1.75739e13	−1.70982
$780$	0	0
$781$	1.83371e12	0.176360
$782$	2.37039e12	0.226667
$783$	2.50487e12	0.238154
$784$	9.67540e11	0.0914632
$785$	0	0
$786$	−5.63995e11	−0.0527076
$787$	3.88782e12	0.361260	0.180630	−	0.983551i	$-0.442186\pi$
$787$	3.88782e12	0.361260	0.180630	+	0.983551i	$0.442186\pi$
$788$	−8.01847e12	−0.740838
$789$	1.71356e11	0.0157418
$790$	0	0
$791$	5.74064e12	0.521394
$792$	7.32318e12	0.661358
$793$	3.02689e12	0.271811
$794$	−5.87252e12	−0.524363
$795$	0	0
$796$	2.83552e12	0.250336
$797$	7.61196e12	0.668242	0.334121	−	0.942530i	$-0.391561\pi$
$797$	7.61196e12	0.668242	0.334121	+	0.942530i	$0.391561\pi$
$798$	−2.67570e12	−0.233574
$799$	−4.01915e12	−0.348878
$800$	0	0
$801$	−5.46324e12	−0.468926
$802$	−8.44532e12	−0.720827
$803$	−1.08633e13	−0.922026
$804$	4.03412e11	0.0340484
$805$	0	0
$806$	−1.96804e12	−0.164258
$807$	−8.01745e10	−0.00665435
$808$	1.00169e12	0.0826762
$809$	−9.82054e12	−0.806059	−0.403030	−	0.915187i	$-0.632043\pi$
$809$	−9.82054e12	−0.806059	−0.403030	+	0.915187i	$0.632043\pi$
$810$	0	0
$811$	−9.15136e12	−0.742834	−0.371417	−	0.928466i	$-0.621128\pi$
$811$	−9.15136e12	−0.742834	−0.371417	+	0.928466i	$0.621128\pi$
$812$	4.71783e12	0.380838
$813$	−6.63693e11	−0.0532795
$814$	−5.10168e12	−0.407289
$815$	0	0
$816$	7.66777e11	0.0605429
$817$	1.06780e13	0.838480
$818$	−4.11285e12	−0.321183
$819$	3.65233e12	0.283656
$820$	0	0
$821$	−2.42674e13	−1.86415	−0.932073	−	0.362272i	$-0.882001\pi$
$821$	−2.42674e13	−1.86415	−0.932073	+	0.362272i	$0.882001\pi$
$822$	−1.67885e12	−0.128259
$823$	−6.09583e12	−0.463163	−0.231581	−	0.972816i	$-0.574390\pi$
$823$	−6.09583e12	−0.463163	−0.231581	+	0.972816i	$0.574390\pi$
$824$	1.23739e13	0.935046
$825$	0	0
$826$	7.86201e12	0.587657
$827$	1.05553e13	0.784684	0.392342	−	0.919819i	$-0.371665\pi$
$827$	1.05553e13	0.784684	0.392342	+	0.919819i	$0.371665\pi$
$828$	8.51981e12	0.629931
$829$	3.16763e12	0.232937	0.116469	−	0.993194i	$-0.462843\pi$
$829$	3.16763e12	0.232937	0.116469	+	0.993194i	$0.462843\pi$
$830$	0	0
$831$	3.45828e12	0.251568
$832$	−3.36195e11	−0.0243241
$833$	1.80071e12	0.129581
$834$	−3.43059e12	−0.245540
$835$	0	0
$836$	1.50656e13	1.06674
$837$	−9.72718e12	−0.685050
$838$	3.54015e12	0.247984
$839$	−1.76898e13	−1.23252	−0.616260	−	0.787543i	$-0.711353\pi$
$839$	−1.76898e13	−1.23252	−0.616260	+	0.787543i	$0.711353\pi$
$840$	0	0
$841$	−1.17088e13	−0.807107
$842$	−8.66466e12	−0.594083
$843$	−5.29355e12	−0.361013
$844$	1.90796e13	1.29428
$845$	0	0
$846$	4.06880e12	0.273086
$847$	−4.30219e12	−0.287220
$848$	3.74711e12	0.248837
$849$	4.75999e12	0.314428
$850$	0	0
$851$	−1.35423e13	−0.885137
$852$	−6.94020e11	−0.0451226
$853$	−9.95608e12	−0.643899	−0.321950	−	0.946757i	$-0.604338\pi$
$853$	−9.95608e12	−0.643899	−0.321950	+	0.946757i	$0.604338\pi$
$854$	−7.93648e12	−0.510585
$855$	0	0
$856$	1.41299e13	0.899515
$857$	−2.30894e13	−1.46217	−0.731087	−	0.682285i	$-0.760986\pi$
$857$	−2.30894e13	−1.46217	−0.731087	+	0.682285i	$0.760986\pi$
$858$	−5.01889e11	−0.0316166
$859$	5.77387e12	0.361824	0.180912	−	0.983499i	$-0.442095\pi$
$859$	5.77387e12	0.361824	0.180912	+	0.983499i	$0.442095\pi$
$860$	0	0
$861$	5.45003e12	0.337975
$862$	1.31347e13	0.810284
$863$	1.14444e13	0.702338	0.351169	−	0.936312i	$-0.385784\pi$
$863$	1.14444e13	0.702338	0.351169	+	0.936312i	$0.385784\pi$
$864$	−9.03224e12	−0.551422
$865$	0	0
$866$	9.73873e12	0.588399
$867$	−3.27106e12	−0.196609
$868$	−1.83208e13	−1.09548
$869$	1.35919e13	0.808522
$870$	0	0
$871$	7.28014e11	0.0428606
$872$	2.15265e13	1.26081
$873$	2.50741e13	1.46104
$874$	−1.12639e13	−0.652960
$875$	0	0
$876$	4.11155e12	0.235905
$877$	9.22439e12	0.526550	0.263275	−	0.964721i	$-0.415197\pi$
$877$	9.22439e12	0.526550	0.263275	+	0.964721i	$0.415197\pi$
$878$	8.67654e12	0.492744
$879$	−3.70308e12	−0.209225
$880$	0	0
$881$	−3.40228e13	−1.90274	−0.951369	−	0.308055i	$-0.900322\pi$
$881$	−3.40228e13	−1.90274	−0.951369	+	0.308055i	$0.900322\pi$
$882$	−1.82295e12	−0.101430
$883$	2.48858e13	1.37761	0.688807	−	0.724945i	$-0.258135\pi$
$883$	2.48858e13	1.37761	0.688807	+	0.724945i	$0.258135\pi$
$884$	2.16546e12	0.119266
$885$	0	0
$886$	−8.72543e12	−0.475702
$887$	6.06525e12	0.328997	0.164499	−	0.986377i	$-0.447399\pi$
$887$	6.06525e12	0.328997	0.164499	+	0.986377i	$0.447399\pi$
$888$	4.40561e12	0.237765
$889$	−1.07190e13	−0.575565
$890$	0	0
$891$	1.24278e13	0.660612
$892$	1.80138e13	0.952714
$893$	1.90987e13	1.00501
$894$	2.18380e12	0.114339
$895$	0	0
$896$	−2.09219e13	−1.08447
$897$	−1.33226e12	−0.0687103
$898$	1.51619e13	0.778053
$899$	−1.08668e13	−0.554859
$900$	0	0
$901$	6.97382e12	0.352541
$902$	8.64309e12	0.434750
$903$	−3.31149e12	−0.165740
$904$	−7.86182e12	−0.391530
$905$	0	0
$906$	−1.08354e12	−0.0534278
$907$	2.49998e13	1.22660	0.613301	−	0.789850i	$-0.289841\pi$
$907$	2.49998e13	1.22660	0.613301	+	0.789850i	$0.289841\pi$
$908$	−2.05347e13	−1.00254
$909$	1.87662e12	0.0911670
$910$	0	0
$911$	−2.82447e13	−1.35864	−0.679319	−	0.733843i	$-0.737725\pi$
$911$	−2.82447e13	−1.35864	−0.679319	+	0.733843i	$0.737725\pi$
$912$	−3.64366e12	−0.174406
$913$	1.11018e13	0.528780
$914$	−1.08476e12	−0.0514135
$915$	0	0
$916$	3.45855e12	0.162317
$917$	−9.47493e12	−0.442501
$918$	−3.01457e12	−0.140098
$919$	2.32324e13	1.07442	0.537210	−	0.843448i	$-0.319478\pi$
$919$	2.32324e13	1.07442	0.537210	+	0.843448i	$0.319478\pi$
$920$	0	0
$921$	−4.46689e12	−0.204568
$922$	−7.43930e12	−0.339034
$923$	−1.25246e12	−0.0568009
$924$	−4.67216e12	−0.210860
$925$	0	0
$926$	−4.30769e11	−0.0192529
$927$	2.31819e13	1.03108
$928$	−1.00904e13	−0.446626
$929$	3.02630e13	1.33303	0.666517	−	0.745490i	$-0.267785\pi$
$929$	3.02630e13	1.33303	0.666517	+	0.745490i	$0.267785\pi$
$930$	0	0
$931$	−8.55682e12	−0.373283
$932$	2.46926e13	1.07200
$933$	6.61751e12	0.285909
$934$	1.69018e12	0.0726728
$935$	0	0
$936$	−5.00188e12	−0.213006
$937$	−1.38314e13	−0.586191	−0.293096	−	0.956083i	$-0.594685\pi$
$937$	−1.38314e13	−0.586191	−0.293096	+	0.956083i	$0.594685\pi$
$938$	−1.90884e12	−0.0805115
$939$	5.00191e12	0.209962
$940$	0	0
$941$	−1.09092e13	−0.453566	−0.226783	−	0.973945i	$-0.572821\pi$
$941$	−1.09092e13	−0.453566	−0.226783	+	0.973945i	$0.572821\pi$
$942$	2.44857e12	0.101317
$943$	2.29430e13	0.944815
$944$	1.07062e13	0.438794
$945$	0	0
$946$	−5.25162e12	−0.213198
$947$	−2.97826e13	−1.20334	−0.601668	−	0.798746i	$-0.705497\pi$
$947$	−2.97826e13	−1.20334	−0.601668	+	0.798746i	$0.705497\pi$
$948$	−5.14427e12	−0.206864
$949$	7.41987e12	0.296960
$950$	0	0
$951$	−9.27146e12	−0.367567
$952$	−1.29549e13	−0.511171
$953$	−1.65043e13	−0.648155	−0.324078	−	0.946030i	$-0.605054\pi$
$953$	−1.65043e13	−0.648155	−0.324078	+	0.946030i	$0.605054\pi$
$954$	−7.05996e12	−0.275953
$955$	0	0
$956$	2.30563e13	0.892748
$957$	−2.77124e12	−0.106800
$958$	1.92892e13	0.739893
$959$	−2.82041e13	−1.07678
$960$	0	0
$961$	1.57594e13	0.596053
$962$	3.48455e12	0.131177
$963$	2.64718e13	0.991895
$964$	−5.79391e12	−0.216085
$965$	0	0
$966$	3.49316e12	0.129069
$967$	−2.09401e13	−0.770122	−0.385061	−	0.922891i	$-0.625820\pi$
$967$	−2.09401e13	−0.770122	−0.385061	+	0.922891i	$0.625820\pi$
$968$	5.89186e12	0.215682
$969$	−6.78129e12	−0.247090
$970$	0	0
$971$	1.50360e13	0.542806	0.271403	−	0.962466i	$-0.412512\pi$
$971$	1.50360e13	0.542806	0.271403	+	0.962466i	$0.412512\pi$
$972$	−1.64777e13	−0.592105
$973$	−5.76329e13	−2.06140
$974$	−2.74003e11	−0.00975527
$975$	0	0
$976$	−1.08076e13	−0.381245
$977$	−3.10616e13	−1.09068	−0.545341	−	0.838214i	$-0.683600\pi$
$977$	−3.10616e13	−1.09068	−0.545341	+	0.838214i	$0.683600\pi$
$978$	3.34934e12	0.117067
$979$	1.26121e13	0.438800
$980$	0	0
$981$	4.03290e13	1.39030
$982$	3.42587e12	0.117563
$983$	−6.35006e12	−0.216914	−0.108457	−	0.994101i	$-0.534591\pi$
$983$	−6.35006e12	−0.216914	−0.108457	+	0.994101i	$0.534591\pi$
$984$	−7.46384e12	−0.253796
$985$	0	0
$986$	−3.36774e12	−0.113473
$987$	−5.92290e12	−0.198659
$988$	−1.02901e13	−0.343569
$989$	−1.39403e13	−0.463330
$990$	0	0
$991$	−6.46977e12	−0.213087	−0.106544	−	0.994308i	$-0.533978\pi$
$991$	−6.46977e12	−0.213087	−0.106544	+	0.994308i	$0.533978\pi$
$992$	3.91842e13	1.28472
$993$	2.30906e12	0.0753639
$994$	3.28393e12	0.106698
$995$	0	0
$996$	−4.20181e12	−0.135291
$997$	1.35531e13	0.434421	0.217210	−	0.976125i	$-0.430304\pi$
$997$	1.35531e13	0.434421	0.217210	+	0.976125i	$0.430304\pi$
$998$	2.95445e12	0.0942733
$999$	1.72226e13	0.547085

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.h.1.10	yes	17
5.4	even	2		325.10.a.g.1.8	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.10.a.g.1.8	✓	17	5.4	even	2
325.10.a.h.1.10	yes	17	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	325.a (trivial)

\(f(q)\)	\(=\)	\(q+10.6074 q^{2} +39.6173 q^{3} -399.483 q^{4} +420.237 q^{6} +7059.84 q^{7} -9668.47 q^{8} -18113.5 q^{9} +41815.8 q^{11} -15826.4 q^{12} -28561.0 q^{13} +74886.7 q^{14} +101978. q^{16} +189793. q^{17} -192137. q^{18} -901879. q^{19} +279692. q^{21} +443557. q^{22} +1.17742e6 q^{23} -383039. q^{24} -302958. q^{26} -1.49739e6 q^{27} -2.82029e6 q^{28} -1.67282e6 q^{29} +6.49608e6 q^{31} +6.03198e6 q^{32} +1.65663e6 q^{33} +2.01321e6 q^{34} +7.23602e6 q^{36} -1.15017e7 q^{37} -9.56661e6 q^{38} -1.13151e6 q^{39} +1.94859e7 q^{41} +2.96681e6 q^{42} -1.18398e7 q^{43} -1.67047e7 q^{44} +1.24893e7 q^{46} -2.11765e7 q^{47} +4.04008e6 q^{48} +9.48776e6 q^{49} +7.51907e6 q^{51} +1.14096e7 q^{52} +3.67444e7 q^{53} -1.58835e7 q^{54} -6.82579e7 q^{56} -3.57300e7 q^{57} -1.77443e7 q^{58} +1.04985e8 q^{59} -1.05980e8 q^{61} +6.89066e7 q^{62} -1.27878e8 q^{63} +1.17711e7 q^{64} +1.75725e7 q^{66} -2.54898e7 q^{67} -7.58189e7 q^{68} +4.66460e7 q^{69} +4.38520e7 q^{71} +1.75130e8 q^{72} -2.59790e8 q^{73} -1.22004e8 q^{74} +3.60285e8 q^{76} +2.95213e8 q^{77} -1.20024e7 q^{78} +3.25043e8 q^{79} +2.97205e8 q^{81} +2.06695e8 q^{82} +2.65493e8 q^{83} -1.11732e8 q^{84} -1.25589e8 q^{86} -6.62726e7 q^{87} -4.04295e8 q^{88} +3.01612e8 q^{89} -2.01636e8 q^{91} -4.70357e8 q^{92} +2.57357e8 q^{93} -2.24628e8 q^{94} +2.38971e8 q^{96} -1.38428e9 q^{97} +1.00641e8 q^{98} -7.57429e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 33 q^{2} - 73 q^{3} + 4267 q^{4} - 1103 q^{6} + 10670 q^{7} - 11481 q^{8} + 47590 q^{9} - 130917 q^{11} - 32239 q^{12} - 485537 q^{13} - 292206 q^{14} + 1064251 q^{16} + 193953 q^{17} + 2026286 q^{18}+ \cdots - 3023832936 q^{99}+O(q^{100}) \) 17 * q + 33 * q^2 - 73 * q^3 + 4267 * q^4 - 1103 * q^6 + 10670 * q^7 - 11481 * q^8 + 47590 * q^9 - 130917 * q^11 - 32239 * q^12 - 485537 * q^13 - 292206 * q^14 + 1064251 * q^16 + 193953 * q^17 + 2026286 * q^18 - 1244111 * q^19 - 115896 * q^21 + 786475 * q^22 + 2599170 * q^23 + 1304331 * q^24 - 942513 * q^26 - 6747967 * q^27 + 14275516 * q^28 - 2247174 * q^29 - 7948896 * q^31 - 23873169 * q^32 + 13542215 * q^33 - 5605153 * q^34 - 25196656 * q^36 - 17455504 * q^37 - 33099219 * q^38 + 2084953 * q^39 - 28253763 * q^41 - 71221836 * q^42 + 28631126 * q^43 - 123980223 * q^44 - 124743136 * q^46 + 41505678 * q^47 - 51624919 * q^48 + 88370777 * q^49 - 97297213 * q^51 - 121869787 * q^52 + 20918940 * q^53 - 279383933 * q^54 - 81987402 * q^56 + 168605047 * q^57 + 533278432 * q^58 - 242672658 * q^59 - 236730546 * q^61 - 630173268 * q^62 + 563712646 * q^63 - 8650957 * q^64 - 247702451 * q^66 - 33870225 * q^67 + 521453709 * q^68 - 16163890 * q^69 - 809145252 * q^71 - 632968230 * q^72 - 460218191 * q^73 + 540389844 * q^74 - 1067090107 * q^76 - 331946328 * q^77 + 31502783 * q^78 - 295742582 * q^79 - 1013246447 * q^81 - 436735349 * q^82 - 298090917 * q^83 - 2574679448 * q^84 - 2183241552 * q^86 - 164038106 * q^87 + 961546625 * q^88 - 448474185 * q^89 - 304745870 * q^91 - 1091742000 * q^92 - 1680564078 * q^93 - 2962970430 * q^94 + 2289126403 * q^96 + 2630881746 * q^97 + 236409993 * q^98 - 3023832936 * q^99

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