LMFDB - Embedded newform 325.10.a.h.1.14

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			1.14
Root			$-30.4531$ 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)

$f(q)$	$=$	\(q+32.4531 q^{2} -140.165 q^{3} +541.204 q^{4} -4548.78 q^{6} -1977.44 q^{7} +947.752 q^{8} -36.8521 q^{9} +45933.0 q^{11} -75857.7 q^{12} -28561.0 q^{13} -64174.0 q^{14} -246339. q^{16} +112081. q^{17} -1195.97 q^{18} +577238. q^{19} +277167. q^{21} +1.49067e6 q^{22} +1.93424e6 q^{23} -132841. q^{24} -926893. q^{26} +2.76403e6 q^{27} -1.07020e6 q^{28} -163389. q^{29} +1.17335e6 q^{31} -8.47971e6 q^{32} -6.43818e6 q^{33} +3.63739e6 q^{34} -19944.5 q^{36} -1.66402e7 q^{37} +1.87332e7 q^{38} +4.00324e6 q^{39} -2.70676e7 q^{41} +8.99493e6 q^{42} +2.49967e7 q^{43} +2.48591e7 q^{44} +6.27720e7 q^{46} -4.14926e7 q^{47} +3.45280e7 q^{48} -3.64433e7 q^{49} -1.57098e7 q^{51} -1.54573e7 q^{52} +5.20775e7 q^{53} +8.97013e7 q^{54} -1.87412e6 q^{56} -8.09084e7 q^{57} -5.30248e6 q^{58} -3.12427e7 q^{59} +5.72870e7 q^{61} +3.80790e7 q^{62} +72872.8 q^{63} -1.49067e8 q^{64} -2.08939e8 q^{66} +1.62760e8 q^{67} +6.06588e7 q^{68} -2.71112e8 q^{69} -1.52286e8 q^{71} -34926.7 q^{72} +1.46423e8 q^{73} -5.40025e8 q^{74} +3.12403e8 q^{76} -9.08296e7 q^{77} +1.29918e8 q^{78} -2.80971e8 q^{79} -3.86694e8 q^{81} -8.78429e8 q^{82} -1.67132e7 q^{83} +1.50004e8 q^{84} +8.11221e8 q^{86} +2.29014e7 q^{87} +4.35331e7 q^{88} -3.31895e8 q^{89} +5.64776e7 q^{91} +1.04682e9 q^{92} -1.64463e8 q^{93} -1.34656e9 q^{94} +1.18856e9 q^{96} -1.22720e9 q^{97} -1.18270e9 q^{98} -1.69273e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	32.4531	1.43424	0.717119	−	0.696951i	$-0.245460\pi$
$2$	32.4531	1.43424	0.717119	+	0.696951i	$0.245460\pi$
$3$	−140.165	−0.999063	−0.499532	−	0.866296i	$-0.666495\pi$
$3$	−140.165	−0.999063	−0.499532	+	0.866296i	$0.666495\pi$
$4$	541.204	1.05704
$5$	0	0
$5$	0	0
$6$	−4548.78	−1.43289
$7$	−1977.44	−0.311287	−0.155644	−	0.987813i	$-0.549745\pi$
$7$	−1977.44	−0.311287	−0.155644	+	0.987813i	$0.549745\pi$
$8$	947.752	0.0818069
$9$	−36.8521	−0.00187228
$10$	0	0
$11$	45933.0	0.945927	0.472964	−	0.881082i	$-0.343184\pi$
$11$	45933.0	0.945927	0.472964	+	0.881082i	$0.343184\pi$
$12$	−75857.7	−1.05605
$13$	−28561.0	−0.277350
$13$	−28561.0	−0.277350
$14$	−64174.0	−0.446460
$15$	0	0
$16$	−246339.	−0.939708
$17$	112081.	0.325471	0.162736	−	0.986670i	$-0.447968\pi$
$17$	112081.	0.325471	0.162736	+	0.986670i	$0.447968\pi$
$18$	−1195.97	−0.00268530
$19$	577238.	1.01616	0.508082	−	0.861309i	$-0.330355\pi$
$19$	577238.	1.01616	0.508082	+	0.861309i	$0.330355\pi$
$20$	0	0
$21$	277167.	0.310996
$22$	1.49067e6	1.35668
$23$	1.93424e6	1.44123	0.720617	−	0.693334i	$-0.243859\pi$
$23$	1.93424e6	1.44123	0.720617	+	0.693334i	$0.243859\pi$
$24$	−132841.	−0.0817302
$25$	0	0
$26$	−926893.	−0.397786
$27$	2.76403e6	1.00093
$28$	−1.07020e6	−0.329043
$29$	−163389.	−0.0428975	−0.0214487	−	0.999770i	$-0.506828\pi$
$29$	−163389.	−0.0428975	−0.0214487	+	0.999770i	$0.506828\pi$
$30$	0	0
$31$	1.17335e6	0.228192	0.114096	−	0.993470i	$-0.463603\pi$
$31$	1.17335e6	0.228192	0.114096	+	0.993470i	$0.463603\pi$
$32$	−8.47971e6	−1.42957
$33$	−6.43818e6	−0.945041
$34$	3.63739e6	0.466804
$35$	0	0
$36$	−19944.5	−0.00197907
$37$	−1.66402e7	−1.45965	−0.729827	−	0.683632i	$-0.760399\pi$
$37$	−1.66402e7	−1.45965	−0.729827	+	0.683632i	$0.760399\pi$
$38$	1.87332e7	1.45742
$39$	4.00324e6	0.277090
$40$	0	0
$41$	−2.70676e7	−1.49597	−0.747985	−	0.663715i	$-0.768979\pi$
$41$	−2.70676e7	−1.49597	−0.747985	+	0.663715i	$0.768979\pi$
$42$	8.99493e6	0.446042
$43$	2.49967e7	1.11500	0.557500	−	0.830177i	$-0.311761\pi$
$43$	2.49967e7	1.11500	0.557500	+	0.830177i	$0.311761\pi$
$44$	2.48591e7	0.999881
$45$	0	0
$46$	6.27720e7	2.06707
$47$	−4.14926e7	−1.24031	−0.620155	−	0.784479i	$-0.712930\pi$
$47$	−4.14926e7	−1.24031	−0.620155	+	0.784479i	$0.712930\pi$
$48$	3.45280e7	0.938828
$49$	−3.64433e7	−0.903100
$50$	0	0
$51$	−1.57098e7	−0.325167
$52$	−1.54573e7	−0.293170
$53$	5.20775e7	0.906585	0.453292	−	0.891362i	$-0.350249\pi$
$53$	5.20775e7	0.906585	0.453292	+	0.891362i	$0.350249\pi$
$54$	8.97013e7	1.43558
$55$	0	0
$56$	−1.87412e6	−0.0254654
$57$	−8.09084e7	−1.01521
$58$	−5.30248e6	−0.0615252
$59$	−3.12427e7	−0.335672	−0.167836	−	0.985815i	$-0.553678\pi$
$59$	−3.12427e7	−0.335672	−0.167836	+	0.985815i	$0.553678\pi$
$60$	0	0
$61$	5.72870e7	0.529751	0.264876	−	0.964283i	$-0.414669\pi$
$61$	5.72870e7	0.529751	0.264876	+	0.964283i	$0.414669\pi$
$62$	3.80790e7	0.327282
$63$	72872.8	0.000582818 0
$64$	−1.49067e8	−1.11064
$65$	0	0
$66$	−2.08939e8	−1.35541
$67$	1.62760e8	0.986759	0.493380	−	0.869814i	$-0.335761\pi$
$67$	1.62760e8	0.986759	0.493380	+	0.869814i	$0.335761\pi$
$68$	6.06588e7	0.344036
$69$	−2.71112e8	−1.43988
$70$	0	0
$71$	−1.52286e8	−0.711207	−0.355604	−	0.934637i	$-0.615725\pi$
$71$	−1.52286e8	−0.711207	−0.355604	+	0.934637i	$0.615725\pi$
$72$	−34926.7	−0.000153166 0
$73$	1.46423e8	0.603472	0.301736	−	0.953392i	$-0.402434\pi$
$73$	1.46423e8	0.603472	0.301736	+	0.953392i	$0.402434\pi$
$74$	−5.40025e8	−2.09349
$75$	0	0
$76$	3.12403e8	1.07412
$77$	−9.08296e7	−0.294455
$78$	1.29918e8	0.397413
$79$	−2.80971e8	−0.811595	−0.405797	−	0.913963i	$-0.633006\pi$
$79$	−2.80971e8	−0.811595	−0.405797	+	0.913963i	$0.633006\pi$
$80$	0	0
$81$	−3.86694e8	−0.998124
$82$	−8.78429e8	−2.14558
$83$	−1.67132e7	−0.0386552	−0.0193276	−	0.999813i	$-0.506153\pi$
$83$	−1.67132e7	−0.0386552	−0.0193276	+	0.999813i	$0.506153\pi$
$84$	1.50004e8	0.328735
$85$	0	0
$86$	8.11221e8	1.59918
$87$	2.29014e7	0.0428573
$88$	4.35331e7	0.0773833
$89$	−3.31895e8	−0.560719	−0.280359	−	0.959895i	$-0.590454\pi$
$89$	−3.31895e8	−0.560719	−0.280359	+	0.959895i	$0.590454\pi$
$90$	0	0
$91$	5.64776e7	0.0863356
$92$	1.04682e9	1.52344
$93$	−1.64463e8	−0.227979
$94$	−1.34656e9	−1.77890
$95$	0	0
$96$	1.18856e9	1.42823
$97$	−1.22720e9	−1.40748	−0.703738	−	0.710459i	$-0.748487\pi$
$97$	−1.22720e9	−1.40748	−0.703738	+	0.710459i	$0.748487\pi$
$98$	−1.18270e9	−1.29526
$99$	−1.69273e6	−0.00177104
$100$	0	0
$101$	−7.86930e8	−0.752471	−0.376236	−	0.926524i	$-0.622782\pi$
$101$	−7.86930e8	−0.752471	−0.376236	+	0.926524i	$0.622782\pi$
$102$	−5.09833e8	−0.466366
$103$	1.27000e9	1.11182	0.555912	−	0.831241i	$-0.312369\pi$
$103$	1.27000e9	1.11182	0.555912	+	0.831241i	$0.312369\pi$
$104$	−2.70687e7	−0.0226891
$105$	0	0
$106$	1.69008e9	1.30026
$107$	−6.30085e8	−0.464699	−0.232350	−	0.972632i	$-0.574641\pi$
$107$	−6.30085e8	−0.464699	−0.232350	+	0.972632i	$0.574641\pi$
$108$	1.49590e9	1.05803
$109$	6.31111e8	0.428239	0.214119	−	0.976807i	$-0.431312\pi$
$109$	6.31111e8	0.428239	0.214119	+	0.976807i	$0.431312\pi$
$110$	0	0
$111$	2.33236e9	1.45829
$112$	4.87120e8	0.292519
$113$	−3.41718e9	−1.97158	−0.985792	−	0.167973i	$-0.946278\pi$
$113$	−3.41718e9	−1.97158	−0.985792	+	0.167973i	$0.946278\pi$
$114$	−2.62573e9	−1.45606
$115$	0	0
$116$	−8.84267e7	−0.0453443
$117$	1.05253e6	0.000519278 0
$118$	−1.01392e9	−0.481433
$119$	−2.21634e8	−0.101315
$120$	0	0
$121$	−2.48108e8	−0.105222
$122$	1.85914e9	0.759790
$123$	3.79393e9	1.49457
$124$	6.35023e8	0.241208
$125$	0	0
$126$	2.36495e6	0.000835900 0
$127$	−2.94756e9	−1.00542	−0.502709	−	0.864456i	$-0.667663\pi$
$127$	−2.94756e9	−1.00542	−0.502709	+	0.864456i	$0.667663\pi$
$128$	−4.96087e8	−0.163348
$129$	−3.50366e9	−1.11396
$130$	0	0
$131$	4.81398e9	1.42818	0.714090	−	0.700054i	$-0.246841\pi$
$131$	4.81398e9	1.42818	0.714090	+	0.700054i	$0.246841\pi$
$132$	−3.48437e9	−0.998945
$133$	−1.14145e9	−0.316319
$134$	5.28207e9	1.41525
$135$	0	0
$136$	1.06225e8	0.0266258
$137$	−5.35617e9	−1.29901	−0.649504	−	0.760358i	$-0.725024\pi$
$137$	−5.35617e9	−1.29901	−0.649504	+	0.760358i	$0.725024\pi$
$138$	−8.79841e9	−2.06514
$139$	−9.24945e8	−0.210160	−0.105080	−	0.994464i	$-0.533510\pi$
$139$	−9.24945e8	−0.210160	−0.105080	+	0.994464i	$0.533510\pi$
$140$	0	0
$141$	5.81580e9	1.23915
$142$	−4.94214e9	−1.02004
$143$	−1.31189e9	−0.262353
$144$	9.07811e6	0.00175940
$145$	0	0
$146$	4.75188e9	0.865522
$147$	5.10807e9	0.902254
$148$	−9.00571e9	−1.54291
$149$	−4.25279e9	−0.706864	−0.353432	−	0.935460i	$-0.614985\pi$
$149$	−4.25279e9	−0.706864	−0.353432	+	0.935460i	$0.614985\pi$
$150$	0	0
$151$	−5.14018e9	−0.804603	−0.402302	−	0.915507i	$-0.631790\pi$
$151$	−5.14018e9	−0.804603	−0.402302	+	0.915507i	$0.631790\pi$
$152$	5.47079e8	0.0831292
$153$	−4.13044e6	−0.000609375 0
$154$	−2.94770e9	−0.422319
$155$	0	0
$156$	2.16657e9	0.292895
$157$	−1.11024e10	−1.45837	−0.729183	−	0.684319i	$-0.760100\pi$
$157$	−1.11024e10	−1.45837	−0.729183	+	0.684319i	$0.760100\pi$
$158$	−9.11837e9	−1.16402
$159$	−7.29942e9	−0.905736
$160$	0	0
$161$	−3.82483e9	−0.448638
$162$	−1.25494e10	−1.43155
$163$	3.94647e9	0.437890	0.218945	−	0.975737i	$-0.429739\pi$
$163$	3.94647e9	0.437890	0.218945	+	0.975737i	$0.429739\pi$
$164$	−1.46491e10	−1.58130
$165$	0	0
$166$	−5.42395e8	−0.0554408
$167$	3.16550e9	0.314933	0.157466	−	0.987524i	$-0.449667\pi$
$167$	3.16550e9	0.314933	0.157466	+	0.987524i	$0.449667\pi$
$168$	2.62686e8	0.0254416
$169$	8.15731e8	0.0769231
$170$	0	0
$171$	−2.12725e7	−0.00190255
$172$	1.35283e10	1.17860
$173$	1.43846e8	0.0122093	0.00610465	−	0.999981i	$-0.498057\pi$
$173$	1.43846e8	0.0122093	0.00610465	+	0.999981i	$0.498057\pi$
$174$	7.43221e8	0.0614676
$175$	0	0
$176$	−1.13151e10	−0.888895
$177$	4.37913e9	0.335357
$178$	−1.07710e10	−0.804204
$179$	−1.79850e9	−0.130940	−0.0654699	−	0.997855i	$-0.520855\pi$
$179$	−1.79850e9	−0.130940	−0.0654699	+	0.997855i	$0.520855\pi$
$180$	0	0
$181$	−2.44006e10	−1.68984	−0.844921	−	0.534891i	$-0.820353\pi$
$181$	−2.44006e10	−1.68984	−0.844921	+	0.534891i	$0.820353\pi$
$182$	1.83287e9	0.123826
$183$	−8.02962e9	−0.529255
$184$	1.83318e9	0.117903
$185$	0	0
$186$	−5.33733e9	−0.326976
$187$	5.14823e9	0.307872
$188$	−2.24560e10	−1.31106
$189$	−5.46569e9	−0.311578
$190$	0	0
$191$	−2.12939e10	−1.15772	−0.578862	−	0.815425i	$-0.696503\pi$
$191$	−2.12939e10	−1.15772	−0.578862	+	0.815425i	$0.696503\pi$
$192$	2.08940e10	1.10960
$193$	−1.08184e10	−0.561251	−0.280625	−	0.959817i	$-0.590542\pi$
$193$	−1.08184e10	−0.561251	−0.280625	+	0.959817i	$0.590542\pi$
$194$	−3.98263e10	−2.01866
$195$	0	0
$196$	−1.97233e10	−0.954612
$197$	−1.12826e9	−0.0533718	−0.0266859	−	0.999644i	$-0.508495\pi$
$197$	−1.12826e9	−0.0533718	−0.0266859	+	0.999644i	$0.508495\pi$
$198$	−5.49343e7	−0.00254010
$199$	−9.79834e9	−0.442908	−0.221454	−	0.975171i	$-0.571080\pi$
$199$	−9.79834e9	−0.442908	−0.221454	+	0.975171i	$0.571080\pi$
$200$	0	0
$201$	−2.28132e10	−0.985835
$202$	−2.55383e10	−1.07922
$203$	3.23092e8	0.0133534
$204$	−8.50222e9	−0.343714
$205$	0	0
$206$	4.12154e10	1.59462
$207$	−7.12807e7	−0.00269840
$208$	7.03568e9	0.260628
$209$	2.65143e10	0.961217
$210$	0	0
$211$	4.90016e9	0.170192	0.0850960	−	0.996373i	$-0.472880\pi$
$211$	4.90016e9	0.170192	0.0850960	+	0.996373i	$0.472880\pi$
$212$	2.81845e10	0.958295
$213$	2.13451e10	0.710541
$214$	−2.04482e10	−0.666490
$215$	0	0
$216$	2.61961e9	0.0818833
$217$	−2.32023e9	−0.0710334
$218$	2.04815e10	0.614197
$219$	−2.05234e10	−0.602906
$220$	0	0
$221$	−3.20115e9	−0.0902695
$222$	7.56924e10	2.09153
$223$	2.00710e10	0.543498	0.271749	−	0.962368i	$-0.412398\pi$
$223$	2.00710e10	0.543498	0.271749	+	0.962368i	$0.412398\pi$
$224$	1.67681e10	0.445008
$225$	0	0
$226$	−1.10898e11	−2.82772
$227$	4.85778e10	1.21429	0.607144	−	0.794592i	$-0.292315\pi$
$227$	4.85778e10	1.21429	0.607144	+	0.794592i	$0.292315\pi$
$228$	−4.37879e10	−1.07312
$229$	−1.58719e10	−0.381391	−0.190696	−	0.981649i	$-0.561074\pi$
$229$	−1.58719e10	−0.381391	−0.190696	+	0.981649i	$0.561074\pi$
$230$	0	0
$231$	1.27311e10	0.294179
$232$	−1.54852e8	−0.00350931
$233$	2.95883e10	0.657685	0.328843	−	0.944385i	$-0.393341\pi$
$233$	2.95883e10	0.657685	0.328843	+	0.944385i	$0.393341\pi$
$234$	3.41580e7	0.000744768 0
$235$	0	0
$236$	−1.69087e10	−0.354818
$237$	3.93822e10	0.810834
$238$	−7.19270e9	−0.145310
$239$	2.67710e10	0.530730	0.265365	−	0.964148i	$-0.414508\pi$
$239$	2.67710e10	0.530730	0.265365	+	0.964148i	$0.414508\pi$
$240$	0	0
$241$	−7.76202e9	−0.148217	−0.0741085	−	0.997250i	$-0.523611\pi$
$241$	−7.76202e9	−0.148217	−0.0741085	+	0.997250i	$0.523611\pi$
$242$	−8.05187e9	−0.150913
$243$	−2.03530e8	−0.00374456
$244$	3.10040e10	0.559968
$245$	0	0
$246$	1.23125e11	2.14357
$247$	−1.64865e10	−0.281833
$248$	1.11205e9	0.0186677
$249$	2.34260e9	0.0386190
$250$	0	0
$251$	−1.89491e10	−0.301341	−0.150670	−	0.988584i	$-0.548143\pi$
$251$	−1.89491e10	−0.301341	−0.150670	+	0.988584i	$0.548143\pi$
$252$	3.94390e7	0.000616061 0
$253$	8.88453e10	1.36330
$254$	−9.56576e10	−1.44201
$255$	0	0
$256$	6.02229e10	0.876359
$257$	8.59419e10	1.22887	0.614435	−	0.788967i	$-0.289384\pi$
$257$	8.59419e10	1.22887	0.614435	+	0.788967i	$0.289384\pi$
$258$	−1.13705e11	−1.59768
$259$	3.29049e10	0.454372
$260$	0	0
$261$	6.02123e6	8.03162e−5 0
$262$	1.56228e11	2.04835
$263$	4.87750e10	0.628631	0.314316	−	0.949319i	$-0.398225\pi$
$263$	4.87750e10	0.628631	0.314316	+	0.949319i	$0.398225\pi$
$264$	−6.10180e9	−0.0773108
$265$	0	0
$266$	−3.70437e10	−0.453677
$267$	4.65199e10	0.560194
$268$	8.80863e10	1.04304
$269$	6.64637e10	0.773925	0.386963	−	0.922095i	$-0.373524\pi$
$269$	6.64637e10	0.773925	0.386963	+	0.922095i	$0.373524\pi$
$270$	0	0
$271$	7.94709e10	0.895048	0.447524	−	0.894272i	$-0.352306\pi$
$271$	7.94709e10	0.895048	0.447524	+	0.894272i	$0.352306\pi$
$272$	−2.76100e10	−0.305848
$273$	−7.91617e9	−0.0862547
$274$	−1.73824e11	−1.86309
$275$	0	0
$276$	−1.46727e11	−1.52201
$277$	1.93237e11	1.97211	0.986054	−	0.166426i	$-0.0532226\pi$
$277$	1.93237e11	1.97211	0.986054	+	0.166426i	$0.0532226\pi$
$278$	−3.00173e10	−0.301419
$279$	−4.32406e7	−0.000427241 0
$280$	0	0
$281$	−2.02998e11	−1.94229	−0.971145	−	0.238491i	$-0.923347\pi$
$281$	−2.02998e11	−1.94229	−0.971145	+	0.238491i	$0.923347\pi$
$282$	1.88741e11	1.77723
$283$	−1.39960e11	−1.29707	−0.648537	−	0.761183i	$-0.724619\pi$
$283$	−1.39960e11	−1.29707	−0.648537	+	0.761183i	$0.724619\pi$
$284$	−8.24175e10	−0.751773
$285$	0	0
$286$	−4.25750e10	−0.376277
$287$	5.35246e10	0.465677
$288$	3.12495e8	0.00267656
$289$	−1.06026e11	−0.894068
$290$	0	0
$291$	1.72010e11	1.40616
$292$	7.92447e10	0.637893
$293$	−5.84561e10	−0.463367	−0.231684	−	0.972791i	$-0.574423\pi$
$293$	−5.84561e10	−0.463367	−0.231684	+	0.972791i	$0.574423\pi$
$294$	1.65773e11	1.29405
$295$	0	0
$296$	−1.57707e10	−0.119410
$297$	1.26960e11	0.946811
$298$	−1.38016e11	−1.01381
$299$	−5.52437e10	−0.399726
$300$	0	0
$301$	−4.94294e10	−0.347086
$302$	−1.66815e11	−1.15399
$303$	1.10300e11	0.751766
$304$	−1.42196e11	−0.954898
$305$	0	0
$306$	−1.34045e8	−0.000873988 0
$307$	−4.39290e10	−0.282246	−0.141123	−	0.989992i	$-0.545071\pi$
$307$	−4.39290e10	−0.282246	−0.141123	+	0.989992i	$0.545071\pi$
$308$	−4.91573e10	−0.311251
$309$	−1.78009e11	−1.11078
$310$	0	0
$311$	−1.35107e11	−0.818948	−0.409474	−	0.912322i	$-0.634288\pi$
$311$	−1.35107e11	−0.818948	−0.409474	+	0.912322i	$0.634288\pi$
$312$	3.79408e9	0.0226679
$313$	−2.34571e11	−1.38141	−0.690707	−	0.723135i	$-0.742701\pi$
$313$	−2.34571e11	−1.38141	−0.690707	+	0.723135i	$0.742701\pi$
$314$	−3.60306e11	−2.09164
$315$	0	0
$316$	−1.52062e11	−0.857887
$317$	2.09782e11	1.16681	0.583406	−	0.812180i	$-0.301720\pi$
$317$	2.09782e11	1.16681	0.583406	+	0.812180i	$0.301720\pi$
$318$	−2.36889e11	−1.29904
$319$	−7.50495e9	−0.0405779
$320$	0	0
$321$	8.83157e10	0.464264
$322$	−1.24128e11	−0.643453
$323$	6.46976e10	0.330732
$324$	−2.09280e11	−1.05506
$325$	0	0
$326$	1.28075e11	0.628038
$327$	−8.84594e10	−0.427838
$328$	−2.56534e10	−0.122381
$329$	8.20490e10	0.386093
$330$	0	0
$331$	−3.35795e10	−0.153762	−0.0768809	−	0.997040i	$-0.524496\pi$
$331$	−3.35795e10	−0.153762	−0.0768809	+	0.997040i	$0.524496\pi$
$332$	−9.04525e9	−0.0408601
$333$	6.13225e8	0.00273288
$334$	1.02730e11	0.451688
$335$	0	0
$336$	−6.82770e10	−0.292245
$337$	−4.08385e11	−1.72479	−0.862394	−	0.506238i	$-0.831036\pi$
$337$	−4.08385e11	−1.72479	−0.862394	+	0.506238i	$0.831036\pi$
$338$	2.64730e10	0.110326
$339$	4.78968e11	1.96974
$340$	0	0
$341$	5.38956e10	0.215853
$342$	−6.90357e8	−0.00272870
$343$	1.51861e11	0.592411
$344$	2.36907e10	0.0912147
$345$	0	0
$346$	4.66826e9	0.0175111
$347$	3.18055e11	1.17766	0.588830	−	0.808257i	$-0.299589\pi$
$347$	3.18055e11	1.17766	0.588830	+	0.808257i	$0.299589\pi$
$348$	1.23943e10	0.0453018
$349$	−4.42266e10	−0.159577	−0.0797883	−	0.996812i	$-0.525424\pi$
$349$	−4.42266e10	−0.159577	−0.0797883	+	0.996812i	$0.525424\pi$
$350$	0	0
$351$	−7.89434e10	−0.277609
$352$	−3.89498e11	−1.35227
$353$	1.20263e11	0.412237	0.206119	−	0.978527i	$-0.433917\pi$
$353$	1.20263e11	0.412237	0.206119	+	0.978527i	$0.433917\pi$
$354$	1.42116e11	0.480982
$355$	0	0
$356$	−1.79623e11	−0.592701
$357$	3.10652e10	0.101220
$358$	−5.83669e10	−0.187799
$359$	−4.49351e11	−1.42778	−0.713889	−	0.700259i	$-0.753068\pi$
$359$	−4.49351e11	−1.42778	−0.713889	+	0.700259i	$0.753068\pi$
$360$	0	0
$361$	1.05162e10	0.0325894
$362$	−7.91874e11	−2.42364
$363$	3.47760e10	0.105123
$364$	3.05659e10	0.0912601
$365$	0	0
$366$	−2.60586e11	−0.759078
$367$	−1.09613e11	−0.315403	−0.157702	−	0.987487i	$-0.550408\pi$
$367$	−1.09613e11	−0.315403	−0.157702	+	0.987487i	$0.550408\pi$
$368$	−4.76477e11	−1.35434
$369$	9.97500e8	0.00280088
$370$	0	0
$371$	−1.02980e11	−0.282208
$372$	−8.90079e10	−0.240982
$373$	5.85392e11	1.56588	0.782938	−	0.622100i	$-0.213720\pi$
$373$	5.85392e11	1.56588	0.782938	+	0.622100i	$0.213720\pi$
$374$	1.67076e11	0.441562
$375$	0	0
$376$	−3.93247e10	−0.101466
$377$	4.66655e9	0.0118976
$378$	−1.77379e11	−0.446877
$379$	4.33758e11	1.07987	0.539934	−	0.841707i	$-0.318449\pi$
$379$	4.33758e11	1.07987	0.539934	+	0.841707i	$0.318449\pi$
$380$	0	0
$381$	4.13144e11	1.00448
$382$	−6.91053e11	−1.66045
$383$	1.91121e11	0.453851	0.226926	−	0.973912i	$-0.427133\pi$
$383$	1.91121e11	0.453851	0.226926	+	0.973912i	$0.427133\pi$
$384$	6.95338e10	0.163195
$385$	0	0
$386$	−3.51092e11	−0.804967
$387$	−9.21182e8	−0.00208760
$388$	−6.64163e11	−1.48776
$389$	−7.67434e11	−1.69929	−0.849645	−	0.527355i	$-0.823184\pi$
$389$	−7.67434e11	−1.69929	−0.849645	+	0.527355i	$0.823184\pi$
$390$	0	0
$391$	2.16792e11	0.469080
$392$	−3.45393e10	−0.0738798
$393$	−6.74750e11	−1.42684
$394$	−3.66156e10	−0.0765478
$395$	0	0
$396$	−9.16111e8	−0.00187206
$397$	−1.29691e11	−0.262031	−0.131015	−	0.991380i	$-0.541824\pi$
$397$	−1.29691e11	−0.262031	−0.131015	+	0.991380i	$0.541824\pi$
$398$	−3.17986e11	−0.635235
$399$	1.59991e11	0.316023
$400$	0	0
$401$	7.69168e11	1.48550	0.742748	−	0.669571i	$-0.233522\pi$
$401$	7.69168e11	1.48550	0.742748	+	0.669571i	$0.233522\pi$
$402$	−7.40359e11	−1.41392
$403$	−3.35122e10	−0.0632892
$404$	−4.25889e11	−0.795391
$405$	0	0
$406$	1.04853e10	0.0191520
$407$	−7.64332e11	−1.38073
$408$	−1.48890e10	−0.0266009
$409$	−1.25462e11	−0.221696	−0.110848	−	0.993837i	$-0.535357\pi$
$409$	−1.25462e11	−0.221696	−0.110848	+	0.993837i	$0.535357\pi$
$410$	0	0
$411$	7.50747e11	1.29779
$412$	6.87329e11	1.17524
$413$	6.17805e10	0.104490
$414$	−2.31328e9	−0.00387014
$415$	0	0
$416$	2.42189e11	0.396492
$417$	1.29645e11	0.209963
$418$	8.60470e11	1.37861
$419$	−2.65984e11	−0.421593	−0.210796	−	0.977530i	$-0.567606\pi$
$419$	−2.65984e11	−0.421593	−0.210796	+	0.977530i	$0.567606\pi$
$420$	0	0
$421$	2.82647e11	0.438505	0.219252	−	0.975668i	$-0.429638\pi$
$421$	2.82647e11	0.438505	0.219252	+	0.975668i	$0.429638\pi$
$422$	1.59025e11	0.244096
$423$	1.52909e9	0.00232221
$424$	4.93565e10	0.0741649
$425$	0	0
$426$	6.92713e11	1.01909
$427$	−1.13282e11	−0.164905
$428$	−3.41004e11	−0.491205
$429$	1.83881e11	0.262107
$430$	0	0
$431$	−2.29614e11	−0.320517	−0.160258	−	0.987075i	$-0.551233\pi$
$431$	−2.29614e11	−0.320517	−0.160258	+	0.987075i	$0.551233\pi$
$432$	−6.80887e11	−0.940586
$433$	1.31434e11	0.179686	0.0898428	−	0.995956i	$-0.471364\pi$
$433$	1.31434e11	0.179686	0.0898428	+	0.995956i	$0.471364\pi$
$434$	−7.52988e10	−0.101879
$435$	0	0
$436$	3.41559e11	0.452665
$437$	1.11651e12	1.46453
$438$	−6.66047e11	−0.864711
$439$	−9.34953e11	−1.20143	−0.600717	−	0.799462i	$-0.705118\pi$
$439$	−9.34953e11	−1.20143	−0.600717	+	0.799462i	$0.705118\pi$
$440$	0	0
$441$	1.34302e9	0.00169086
$442$	−1.03887e11	−0.129468
$443$	1.32453e12	1.63398	0.816989	−	0.576653i	$-0.195642\pi$
$443$	1.32453e12	1.63398	0.816989	+	0.576653i	$0.195642\pi$
$444$	1.26228e12	1.54146
$445$	0	0
$446$	6.51367e11	0.779505
$447$	5.96091e11	0.706202
$448$	2.94771e11	0.345728
$449$	3.24134e11	0.376371	0.188185	−	0.982134i	$-0.439739\pi$
$449$	3.24134e11	0.376371	0.188185	+	0.982134i	$0.439739\pi$
$450$	0	0
$451$	−1.24330e12	−1.41508
$452$	−1.84939e12	−2.08404
$453$	7.20471e11	0.803850
$454$	1.57650e12	1.74158
$455$	0	0
$456$	−7.66811e10	−0.0830513
$457$	1.34314e12	1.44045	0.720226	−	0.693739i	$-0.244038\pi$
$457$	1.34314e12	1.44045	0.720226	+	0.693739i	$0.244038\pi$
$458$	−5.15094e11	−0.547005
$459$	3.09796e11	0.325775
$460$	0	0
$461$	−6.79766e11	−0.700979	−0.350490	−	0.936567i	$-0.613985\pi$
$461$	−6.79766e11	−0.700979	−0.350490	+	0.936567i	$0.613985\pi$
$462$	4.13164e11	0.421923
$463$	−1.68324e11	−0.170228	−0.0851142	−	0.996371i	$-0.527125\pi$
$463$	−1.68324e11	−0.170228	−0.0851142	+	0.996371i	$0.527125\pi$
$464$	4.02491e10	0.0403111
$465$	0	0
$466$	9.60232e11	0.943277
$467$	6.99834e11	0.680878	0.340439	−	0.940267i	$-0.389424\pi$
$467$	6.99834e11	0.680878	0.340439	+	0.940267i	$0.389424\pi$
$468$	5.69635e8	0.000548897 0
$469$	−3.21848e11	−0.307166
$470$	0	0
$471$	1.55616e12	1.45700
$472$	−2.96104e10	−0.0274603
$473$	1.14817e12	1.05471
$474$	1.27807e12	1.16293
$475$	0	0
$476$	−1.19949e11	−0.107094
$477$	−1.91917e9	−0.00169738
$478$	8.68800e11	0.761192
$479$	−1.18268e12	−1.02650	−0.513250	−	0.858239i	$-0.671559\pi$
$479$	−1.18268e12	−1.02650	−0.513250	+	0.858239i	$0.671559\pi$
$480$	0	0
$481$	4.75259e11	0.404835
$482$	−2.51902e11	−0.212578
$483$	5.36106e11	0.448218
$484$	−1.34277e11	−0.111224
$485$	0	0
$486$	−6.60519e9	−0.00537059
$487$	−5.39148e11	−0.434338	−0.217169	−	0.976134i	$-0.569682\pi$
$487$	−5.39148e11	−0.434338	−0.217169	+	0.976134i	$0.569682\pi$
$488$	5.42939e10	0.0433373
$489$	−5.53156e11	−0.437480
$490$	0	0
$491$	−1.19524e11	−0.0928084	−0.0464042	−	0.998923i	$-0.514776\pi$
$491$	−1.19524e11	−0.0928084	−0.0464042	+	0.998923i	$0.514776\pi$
$492$	2.05329e12	1.57982
$493$	−1.83128e10	−0.0139619
$494$	−5.35038e11	−0.404216
$495$	0	0
$496$	−2.89043e11	−0.214434
$497$	3.01135e11	0.221390
$498$	7.60247e10	0.0553889
$499$	2.50379e12	1.80778	0.903888	−	0.427769i	$-0.140700\pi$
$499$	2.50379e12	1.80778	0.903888	+	0.427769i	$0.140700\pi$
$500$	0	0
$501$	−4.43691e11	−0.314638
$502$	−6.14958e11	−0.432194
$503$	1.99793e12	1.39163	0.695817	−	0.718219i	$-0.255043\pi$
$503$	1.99793e12	1.39163	0.695817	+	0.718219i	$0.255043\pi$
$504$	6.90653e7	4.76785e−5 0
$505$	0	0
$506$	2.88330e12	1.95530
$507$	−1.14337e11	−0.0768510
$508$	−1.59523e12	−1.06277
$509$	4.19816e9	0.00277223	0.00138611	−	0.999999i	$-0.499559\pi$
$509$	4.19816e9	0.00277223	0.00138611	+	0.999999i	$0.499559\pi$
$510$	0	0
$511$	−2.89543e11	−0.187853
$512$	2.20842e12	1.42025
$513$	1.59550e12	1.01711
$514$	2.78908e12	1.76249
$515$	0	0
$516$	−1.89619e12	−1.17749
$517$	−1.90588e12	−1.17324
$518$	1.06787e12	0.651677
$519$	−2.01622e10	−0.0121979
$520$	0	0
$521$	−2.61613e12	−1.55557	−0.777786	−	0.628530i	$-0.783657\pi$
$521$	−2.61613e12	−1.55557	−0.777786	+	0.628530i	$0.783657\pi$
$522$	1.95408e8	0.000115193 0
$523$	−5.21399e11	−0.304728	−0.152364	−	0.988324i	$-0.548689\pi$
$523$	−5.21399e11	−0.304728	−0.152364	+	0.988324i	$0.548689\pi$
$524$	2.60534e12	1.50964
$525$	0	0
$526$	1.58290e12	0.901607
$527$	1.31511e11	0.0742701
$528$	1.58597e12	0.888063
$529$	1.94012e12	1.07715
$530$	0	0
$531$	1.15136e9	0.000628473 0
$532$	−6.17758e11	−0.334361
$533$	7.73079e11	0.414908
$534$	1.50972e12	0.803451
$535$	0	0
$536$	1.54256e11	0.0807237
$537$	2.52086e11	0.130817
$538$	2.15695e12	1.10999
$539$	−1.67395e12	−0.854267
$540$	0	0
$541$	−3.20666e11	−0.160940	−0.0804702	−	0.996757i	$-0.525642\pi$
$541$	−3.20666e11	−0.160940	−0.0804702	+	0.996757i	$0.525642\pi$
$542$	2.57908e12	1.28371
$543$	3.42010e12	1.68826
$544$	−9.50417e11	−0.465285
$545$	0	0
$546$	−2.56904e11	−0.123710
$547$	−3.84616e12	−1.83689	−0.918447	−	0.395543i	$-0.870556\pi$
$547$	−3.84616e12	−1.83689	−0.918447	+	0.395543i	$0.870556\pi$
$548$	−2.89878e12	−1.37310
$549$	−2.11115e9	−0.000991844 0
$550$	0	0
$551$	−9.43144e10	−0.0435909
$552$	−2.56947e11	−0.117792
$553$	5.55602e11	0.252639
$554$	6.27113e12	2.82847
$555$	0	0
$556$	−5.00584e11	−0.222147
$557$	−4.35058e12	−1.91513	−0.957565	−	0.288217i	$-0.906938\pi$
$557$	−4.35058e12	−1.91513	−0.957565	+	0.288217i	$0.906938\pi$
$558$	−1.40329e9	−0.000612765 0
$559$	−7.13931e11	−0.309245
$560$	0	0
$561$	−7.21600e11	−0.307584
$562$	−6.58792e12	−2.78571
$563$	1.12913e12	0.473648	0.236824	−	0.971553i	$-0.423894\pi$
$563$	1.12913e12	0.473648	0.236824	+	0.971553i	$0.423894\pi$
$564$	3.14753e12	1.30983
$565$	0	0
$566$	−4.54213e12	−1.86031
$567$	7.64663e11	0.310704
$568$	−1.44329e11	−0.0581816
$569$	−2.81599e12	−1.12623	−0.563114	−	0.826379i	$-0.690397\pi$
$569$	−2.81599e12	−1.12623	−0.563114	+	0.826379i	$0.690397\pi$
$570$	0	0
$571$	−8.52974e11	−0.335794	−0.167897	−	0.985805i	$-0.553698\pi$
$571$	−8.52974e11	−0.335794	−0.167897	+	0.985805i	$0.553698\pi$
$572$	−7.10001e11	−0.277317
$573$	2.98465e12	1.15664
$574$	1.73704e12	0.667891
$575$	0	0
$576$	5.49345e9	0.00207943
$577$	2.51069e12	0.942979	0.471490	−	0.881872i	$-0.343717\pi$
$577$	2.51069e12	0.942979	0.471490	+	0.881872i	$0.343717\pi$
$578$	−3.44086e12	−1.28231
$579$	1.51636e12	0.560725
$580$	0	0
$581$	3.30493e10	0.0120329
$582$	5.58224e12	2.01677
$583$	2.39207e12	0.857563
$584$	1.38773e11	0.0493681
$585$	0	0
$586$	−1.89708e12	−0.664579
$587$	5.00003e12	1.73821	0.869103	−	0.494631i	$-0.164697\pi$
$587$	5.00003e12	1.73821	0.869103	+	0.494631i	$0.164697\pi$
$588$	2.76451e12	0.953718
$589$	6.77304e11	0.231881
$590$	0	0
$591$	1.58142e11	0.0533218
$592$	4.09912e12	1.37165
$593$	−2.18751e12	−0.726448	−0.363224	−	0.931702i	$-0.618324\pi$
$593$	−2.18751e12	−0.726448	−0.363224	+	0.931702i	$0.618324\pi$
$594$	4.12025e12	1.35795
$595$	0	0
$596$	−2.30163e12	−0.747182
$597$	1.37338e12	0.442493
$598$	−1.79283e12	−0.573302
$599$	4.00554e10	0.0127128	0.00635639	−	0.999980i	$-0.497977\pi$
$599$	4.00554e10	0.0127128	0.00635639	+	0.999980i	$0.497977\pi$
$600$	0	0
$601$	−2.05272e12	−0.641794	−0.320897	−	0.947114i	$-0.603984\pi$
$601$	−2.05272e12	−0.641794	−0.320897	+	0.947114i	$0.603984\pi$
$602$	−1.60414e12	−0.497803
$603$	−5.99805e9	−0.00184749
$604$	−2.78188e12	−0.850496
$605$	0	0
$606$	3.57957e12	1.07821
$607$	2.40562e12	0.719246	0.359623	−	0.933098i	$-0.382905\pi$
$607$	2.40562e12	0.719246	0.359623	+	0.933098i	$0.382905\pi$
$608$	−4.89481e12	−1.45268
$609$	−4.52860e10	−0.0133409
$610$	0	0
$611$	1.18507e12	0.344000
$612$	−2.23541e9	−0.000644132 0
$613$	3.88281e12	1.11064	0.555320	−	0.831636i	$-0.312596\pi$
$613$	3.88281e12	1.11064	0.555320	+	0.831636i	$0.312596\pi$
$614$	−1.42563e12	−0.404808
$615$	0	0
$616$	−8.60839e10	−0.0240885
$617$	−1.16917e12	−0.324784	−0.162392	−	0.986726i	$-0.551921\pi$
$617$	−1.16917e12	−0.324784	−0.162392	+	0.986726i	$0.551921\pi$
$618$	−5.77695e12	−1.59313
$619$	−5.67461e12	−1.55356	−0.776780	−	0.629772i	$-0.783148\pi$
$619$	−5.67461e12	−1.55356	−0.776780	+	0.629772i	$0.783148\pi$
$620$	0	0
$621$	5.34628e12	1.44258
$622$	−4.38464e12	−1.17457
$623$	6.56301e11	0.174545
$624$	−9.86155e11	−0.260384
$625$	0	0
$626$	−7.61254e12	−1.98128
$627$	−3.71637e12	−0.960317
$628$	−6.00863e12	−1.54155
$629$	−1.86505e12	−0.475075
$630$	0	0
$631$	−2.45580e12	−0.616680	−0.308340	−	0.951276i	$-0.599773\pi$
$631$	−2.45580e12	−0.616680	−0.308340	+	0.951276i	$0.599773\pi$
$632$	−2.66291e11	−0.0663940
$633$	−6.86830e11	−0.170033
$634$	6.80807e12	1.67349
$635$	0	0
$636$	−3.95048e12	−0.957398
$637$	1.04086e12	0.250475
$638$	−2.43559e11	−0.0581983
$639$	5.61205e9	0.00133158
$640$	0	0
$641$	1.77359e12	0.414947	0.207473	−	0.978241i	$-0.433476\pi$
$641$	1.77359e12	0.414947	0.207473	+	0.978241i	$0.433476\pi$
$642$	2.86612e12	0.665865
$643$	−8.05907e12	−1.85924	−0.929621	−	0.368518i	$-0.879865\pi$
$643$	−8.05907e12	−1.85924	−0.929621	+	0.368518i	$0.879865\pi$
$644$	−2.07001e12	−0.474227
$645$	0	0
$646$	2.09964e12	0.474349
$647$	−5.30499e12	−1.19019	−0.595093	−	0.803657i	$-0.702885\pi$
$647$	−5.30499e12	−1.19019	−0.595093	+	0.803657i	$0.702885\pi$
$648$	−3.66490e11	−0.0816534
$649$	−1.43507e12	−0.317521
$650$	0	0
$651$	3.25215e11	0.0709669
$652$	2.13584e12	0.462866
$653$	−7.57246e12	−1.62978	−0.814888	−	0.579619i	$-0.803202\pi$
$653$	−7.57246e12	−1.62978	−0.814888	+	0.579619i	$0.803202\pi$
$654$	−2.87078e12	−0.613621
$655$	0	0
$656$	6.66781e12	1.40578
$657$	−5.39601e9	−0.00112987
$658$	2.66275e12	0.553749
$659$	−2.34944e12	−0.485267	−0.242633	−	0.970118i	$-0.578011\pi$
$659$	−2.34944e12	−0.485267	−0.242633	+	0.970118i	$0.578011\pi$
$660$	0	0
$661$	7.60177e12	1.54885	0.774423	−	0.632669i	$-0.218040\pi$
$661$	7.60177e12	1.54885	0.774423	+	0.632669i	$0.218040\pi$
$662$	−1.08976e12	−0.220531
$663$	4.48689e11	0.0901850
$664$	−1.58400e10	−0.00316226
$665$	0	0
$666$	1.99011e10	0.00391960
$667$	−3.16033e11	−0.0618253
$668$	1.71318e12	0.332896
$669$	−2.81325e12	−0.542989
$670$	0	0
$671$	2.63137e12	0.501106
$672$	−2.35029e12	−0.444591
$673$	7.92100e12	1.48837	0.744187	−	0.667971i	$-0.232837\pi$
$673$	7.92100e12	1.48837	0.744187	+	0.667971i	$0.232837\pi$
$674$	−1.32534e13	−2.47376
$675$	0	0
$676$	4.41477e11	0.0813107
$677$	−1.41521e11	−0.0258924	−0.0129462	−	0.999916i	$-0.504121\pi$
$677$	−1.41521e11	−0.0258924	−0.0129462	+	0.999916i	$0.504121\pi$
$678$	1.55440e13	2.82507
$679$	2.42670e12	0.438130
$680$	0	0
$681$	−6.80890e12	−1.21315
$682$	1.74908e12	0.309585
$683$	−9.56533e12	−1.68193	−0.840963	−	0.541093i	$-0.818011\pi$
$683$	−9.56533e12	−1.68193	−0.840963	+	0.541093i	$0.818011\pi$
$684$	−1.15127e10	−0.00201106
$685$	0	0
$686$	4.92837e12	0.849659
$687$	2.22469e12	0.381034
$688$	−6.15766e12	−1.04777
$689$	−1.48738e12	−0.251441
$690$	0	0
$691$	6.71434e12	1.12035	0.560173	−	0.828376i	$-0.310735\pi$
$691$	6.71434e12	1.12035	0.560173	+	0.828376i	$0.310735\pi$
$692$	7.78501e10	0.0129057
$693$	3.34727e9	0.000551303 0
$694$	1.03219e13	1.68905
$695$	0	0
$696$	2.17048e10	0.00350602
$697$	−3.03378e12	−0.486896
$698$	−1.43529e12	−0.228871
$699$	−4.14723e12	−0.657069
$700$	0	0
$701$	7.92662e12	1.23981	0.619907	−	0.784675i	$-0.287170\pi$
$701$	7.92662e12	1.23981	0.619907	+	0.784675i	$0.287170\pi$
$702$	−2.56196e12	−0.398158
$703$	−9.60533e12	−1.48325
$704$	−6.84711e12	−1.05058
$705$	0	0
$706$	3.90292e12	0.591246
$707$	1.55610e12	0.234235
$708$	2.37000e12	0.354486
$709$	1.04486e12	0.155292	0.0776459	−	0.996981i	$-0.475260\pi$
$709$	1.04486e12	0.155292	0.0776459	+	0.996981i	$0.475260\pi$
$710$	0	0
$711$	1.03544e10	0.00151953
$712$	−3.14554e11	−0.0458706
$713$	2.26954e12	0.328879
$714$	1.00816e12	0.145174
$715$	0	0
$716$	−9.73355e11	−0.138408
$717$	−3.75234e12	−0.530232
$718$	−1.45828e13	−2.04777
$719$	−5.62070e11	−0.0784351	−0.0392175	−	0.999231i	$-0.512487\pi$
$719$	−5.62070e11	−0.0784351	−0.0392175	+	0.999231i	$0.512487\pi$
$720$	0	0
$721$	−2.51135e12	−0.346097
$722$	3.41284e11	0.0467410
$723$	1.08796e12	0.148078
$724$	−1.32057e13	−1.78623
$725$	0	0
$726$	1.12859e12	0.150772
$727$	−8.11852e12	−1.07788	−0.538942	−	0.842343i	$-0.681176\pi$
$727$	−8.11852e12	−1.07788	−0.538942	+	0.842343i	$0.681176\pi$
$728$	5.35267e10	0.00706284
$729$	7.63982e12	1.00187
$730$	0	0
$731$	2.80166e12	0.362901
$732$	−4.34566e12	−0.559443
$733$	1.25990e13	1.61201	0.806003	−	0.591912i	$-0.201627\pi$
$733$	1.25990e13	1.61201	0.806003	+	0.591912i	$0.201627\pi$
$734$	−3.55729e12	−0.452363
$735$	0	0
$736$	−1.64018e13	−2.06035
$737$	7.47605e12	0.933402
$738$	3.23720e10	0.00401713
$739$	1.29835e12	0.160137	0.0800687	−	0.996789i	$-0.474486\pi$
$739$	1.29835e12	0.160137	0.0800687	+	0.996789i	$0.474486\pi$
$740$	0	0
$741$	2.31083e12	0.281569
$742$	−3.34202e12	−0.404754
$743$	−1.67442e12	−0.201565	−0.100783	−	0.994908i	$-0.532135\pi$
$743$	−1.67442e12	−0.201565	−0.100783	+	0.994908i	$0.532135\pi$
$744$	−1.55870e11	−0.0186502
$745$	0	0
$746$	1.89978e13	2.24584
$747$	6.15917e8	7.23735e−5 0
$748$	2.78624e12	0.325433
$749$	1.24595e12	0.144655
$750$	0	0
$751$	8.04908e12	0.923350	0.461675	−	0.887049i	$-0.347249\pi$
$751$	8.04908e12	0.923350	0.461675	+	0.887049i	$0.347249\pi$
$752$	1.02212e13	1.16553
$753$	2.65600e12	0.301058
$754$	1.51444e11	0.0170640
$755$	0	0
$756$	−2.95805e12	−0.329350
$757$	−1.56188e13	−1.72869	−0.864345	−	0.502899i	$-0.832267\pi$
$757$	−1.56188e13	−1.72869	−0.864345	+	0.502899i	$0.832267\pi$
$758$	1.40768e13	1.54879
$759$	−1.24530e13	−1.36202
$760$	0	0
$761$	−1.39186e12	−0.150440	−0.0752202	−	0.997167i	$-0.523966\pi$
$761$	−1.39186e12	−0.150440	−0.0752202	+	0.997167i	$0.523966\pi$
$762$	1.34078e13	1.44066
$763$	−1.24798e12	−0.133305
$764$	−1.15243e13	−1.22376
$765$	0	0
$766$	6.20246e12	0.650931
$767$	8.92324e11	0.0930986
$768$	−8.44113e12	−0.875538
$769$	−1.17551e13	−1.21215	−0.606077	−	0.795406i	$-0.707258\pi$
$769$	−1.17551e13	−1.21215	−0.606077	+	0.795406i	$0.707258\pi$
$770$	0	0
$771$	−1.20460e13	−1.22772
$772$	−5.85498e12	−0.593264
$773$	1.62652e13	1.63852	0.819259	−	0.573424i	$-0.194385\pi$
$773$	1.62652e13	1.63852	0.819259	+	0.573424i	$0.194385\pi$
$774$	−2.98952e10	−0.00299411
$775$	0	0
$776$	−1.16308e12	−0.115141
$777$	−4.61210e12	−0.453946
$778$	−2.49056e13	−2.43719
$779$	−1.56245e13	−1.52015
$780$	0	0
$781$	−6.99493e12	−0.672750
$782$	7.03556e12	0.672773
$783$	−4.51612e11	−0.0429375
$784$	8.97741e12	0.848650
$785$	0	0
$786$	−2.18977e13	−2.04643
$787$	−6.27938e12	−0.583486	−0.291743	−	0.956497i	$-0.594235\pi$
$787$	−6.27938e12	−0.583486	−0.291743	+	0.956497i	$0.594235\pi$
$788$	−6.10619e11	−0.0564160
$789$	−6.83653e12	−0.628043
$790$	0	0
$791$	6.75726e12	0.613729
$792$	−1.60429e9	−0.000144883 0
$793$	−1.63618e12	−0.146927
$794$	−4.20887e12	−0.375815
$795$	0	0
$796$	−5.30290e12	−0.468171
$797$	−1.68270e11	−0.0147721	−0.00738607	−	0.999973i	$-0.502351\pi$
$797$	−1.68270e11	−0.0147721	−0.00738607	+	0.999973i	$0.502351\pi$
$798$	5.19222e12	0.453252
$799$	−4.65055e12	−0.403686
$800$	0	0
$801$	1.22310e10	0.00104982
$802$	2.49619e13	2.13056
$803$	6.72565e12	0.570840
$804$	−1.23466e13	−1.04207
$805$	0	0
$806$	−1.08757e12	−0.0907718
$807$	−9.31586e12	−0.773200
$808$	−7.45814e11	−0.0615573
$809$	−1.16770e13	−0.958432	−0.479216	−	0.877697i	$-0.659079\pi$
$809$	−1.16770e13	−0.958432	−0.479216	+	0.877697i	$0.659079\pi$
$810$	0	0
$811$	−3.15287e12	−0.255924	−0.127962	−	0.991779i	$-0.540844\pi$
$811$	−3.15287e12	−0.255924	−0.127962	+	0.991779i	$0.540844\pi$
$812$	1.74858e11	0.0141151
$813$	−1.11390e13	−0.894209
$814$	−2.48049e13	−1.98029
$815$	0	0
$816$	3.86994e12	0.305562
$817$	1.44291e13	1.13302
$818$	−4.07164e12	−0.317965
$819$	−2.08132e9	−0.000161645 0
$820$	0	0
$821$	−5.17107e12	−0.397225	−0.198612	−	0.980078i	$-0.563643\pi$
$821$	−5.17107e12	−0.397225	−0.198612	+	0.980078i	$0.563643\pi$
$822$	2.43641e13	1.86134
$823$	−1.86301e13	−1.41552	−0.707759	−	0.706454i	$-0.750294\pi$
$823$	−1.86301e13	−1.41552	−0.707759	+	0.706454i	$0.750294\pi$
$824$	1.20364e12	0.0909548
$825$	0	0
$826$	2.00497e12	0.149864
$827$	−2.11656e13	−1.57346	−0.786732	−	0.617295i	$-0.788229\pi$
$827$	−2.11656e13	−1.57346	−0.786732	+	0.617295i	$0.788229\pi$
$828$	−3.85774e10	−0.00285231
$829$	2.77298e12	0.203916	0.101958	−	0.994789i	$-0.467489\pi$
$829$	2.77298e12	0.203916	0.101958	+	0.994789i	$0.467489\pi$
$830$	0	0
$831$	−2.70850e13	−1.97026
$832$	4.25751e12	0.308036
$833$	−4.08462e12	−0.293933
$834$	4.20737e12	0.301137
$835$	0	0
$836$	1.43496e13	1.01604
$837$	3.24318e12	0.228406
$838$	−8.63202e12	−0.604664
$839$	2.22549e13	1.55059	0.775295	−	0.631599i	$-0.217601\pi$
$839$	2.22549e13	1.55059	0.775295	+	0.631599i	$0.217601\pi$
$840$	0	0
$841$	−1.44805e13	−0.998160
$842$	9.17276e12	0.628920
$843$	2.84532e13	1.94047
$844$	2.65199e12	0.179900
$845$	0	0
$846$	4.96238e10	0.00333060
$847$	4.90618e11	0.0327543
$848$	−1.28287e13	−0.851925
$849$	1.96174e13	1.29586
$850$	0	0
$851$	−3.21860e13	−2.10370
$852$	1.15520e13	0.751069
$853$	−4.23195e12	−0.273697	−0.136848	−	0.990592i	$-0.543697\pi$
$853$	−4.23195e12	−0.273697	−0.136848	+	0.990592i	$0.543697\pi$
$854$	−3.67634e12	−0.236513
$855$	0	0
$856$	−5.97164e11	−0.0380156
$857$	1.68023e13	1.06403	0.532017	−	0.846733i	$-0.321434\pi$
$857$	1.68023e13	1.06403	0.532017	+	0.846733i	$0.321434\pi$
$858$	5.96751e12	0.375924
$859$	3.21001e12	0.201158	0.100579	−	0.994929i	$-0.467931\pi$
$859$	3.21001e12	0.201158	0.100579	+	0.994929i	$0.467931\pi$
$860$	0	0
$861$	−7.50226e12	−0.465241
$862$	−7.45169e12	−0.459697
$863$	1.26590e13	0.776877	0.388438	−	0.921475i	$-0.373015\pi$
$863$	1.26590e13	0.776877	0.388438	+	0.921475i	$0.373015\pi$
$864$	−2.34381e13	−1.43091
$865$	0	0
$866$	4.26545e12	0.257712
$867$	1.48611e13	0.893231
$868$	−1.25572e12	−0.0750851
$869$	−1.29058e13	−0.767709
$870$	0	0
$871$	−4.64859e12	−0.273678
$872$	5.98136e11	0.0350329
$873$	4.52248e10	0.00263519
$874$	3.62344e13	2.10048
$875$	0	0
$876$	−1.11073e13	−0.637295
$877$	−1.27935e13	−0.730282	−0.365141	−	0.930952i	$-0.618979\pi$
$877$	−1.27935e13	−0.730282	−0.365141	+	0.930952i	$0.618979\pi$
$878$	−3.03421e13	−1.72314
$879$	8.19348e12	0.462933
$880$	0	0
$881$	−1.11000e13	−0.620773	−0.310387	−	0.950610i	$-0.600459\pi$
$881$	−1.11000e13	−0.620773	−0.310387	+	0.950610i	$0.600459\pi$
$882$	4.35850e10	0.00242509
$883$	−6.70423e12	−0.371130	−0.185565	−	0.982632i	$-0.559412\pi$
$883$	−6.70423e12	−0.371130	−0.185565	+	0.982632i	$0.559412\pi$
$884$	−1.73248e12	−0.0954184
$885$	0	0
$886$	4.29852e13	2.34351
$887$	1.42437e13	0.772624	0.386312	−	0.922368i	$-0.373749\pi$
$887$	1.42437e13	0.772624	0.386312	+	0.922368i	$0.373749\pi$
$888$	2.21050e12	0.119298
$889$	5.82862e12	0.312974
$890$	0	0
$891$	−1.77620e13	−0.944153
$892$	1.08625e13	0.574498
$893$	−2.39511e13	−1.26036
$894$	1.93450e13	1.01286
$895$	0	0
$896$	9.80980e11	0.0508480
$897$	7.74322e12	0.399352
$898$	1.05191e13	0.539805
$899$	−1.91713e11	−0.00978888
$900$	0	0
$901$	5.83691e12	0.295067
$902$	−4.03489e13	−2.02956
$903$	6.92826e12	0.346760
$904$	−3.23864e12	−0.161289
$905$	0	0
$906$	2.33815e13	1.15291
$907$	1.67991e13	0.824241	0.412120	−	0.911129i	$-0.364788\pi$
$907$	1.67991e13	0.824241	0.412120	+	0.911129i	$0.364788\pi$
$908$	2.62905e13	1.28355
$909$	2.90001e10	0.00140884
$910$	0	0
$911$	−1.56750e13	−0.754005	−0.377003	−	0.926212i	$-0.623045\pi$
$911$	−1.56750e13	−0.754005	−0.377003	+	0.926212i	$0.623045\pi$
$912$	1.99309e13	0.954003
$913$	−7.67688e11	−0.0365650
$914$	4.35891e13	2.06595
$915$	0	0
$916$	−8.58996e12	−0.403145
$917$	−9.51934e12	−0.444575
$918$	1.00538e13	0.467240
$919$	2.05037e13	0.948228	0.474114	−	0.880464i	$-0.342769\pi$
$919$	2.05037e13	0.948228	0.474114	+	0.880464i	$0.342769\pi$
$920$	0	0
$921$	6.15729e12	0.281982
$922$	−2.20605e13	−1.00537
$923$	4.34943e12	0.197253
$924$	6.89012e12	0.310959
$925$	0	0
$926$	−5.46264e12	−0.244148
$927$	−4.68022e10	−0.00208165
$928$	1.38549e12	0.0613250
$929$	−2.19601e12	−0.0967307	−0.0483653	−	0.998830i	$-0.515401\pi$
$929$	−2.19601e12	−0.0967307	−0.0483653	+	0.998830i	$0.515401\pi$
$930$	0	0
$931$	−2.10365e13	−0.917698
$932$	1.60133e13	0.695199
$933$	1.89372e13	0.818181
$934$	2.27118e13	0.976541
$935$	0	0
$936$	9.97541e8	4.24805e−5 0
$937$	7.12914e12	0.302141	0.151070	−	0.988523i	$-0.451728\pi$
$937$	7.12914e12	0.302141	0.151070	+	0.988523i	$0.451728\pi$
$938$	−1.04450e13	−0.440549
$939$	3.28785e13	1.38012
$940$	0	0
$941$	2.63088e13	1.09382	0.546912	−	0.837190i	$-0.315803\pi$
$941$	2.63088e13	1.09382	0.546912	+	0.837190i	$0.315803\pi$
$942$	5.05021e13	2.08968
$943$	−5.23552e13	−2.15604
$944$	7.69630e12	0.315434
$945$	0	0
$946$	3.72618e13	1.51270
$947$	−9.27952e12	−0.374930	−0.187465	−	0.982271i	$-0.560027\pi$
$947$	−9.27952e12	−0.374930	−0.187465	+	0.982271i	$0.560027\pi$
$948$	2.13138e13	0.857083
$949$	−4.18199e12	−0.167373
$950$	0	0
$951$	−2.94040e13	−1.16572
$952$	−2.10054e11	−0.00828828
$953$	1.22837e13	0.482403	0.241201	−	0.970475i	$-0.422459\pi$
$953$	1.22837e13	0.482403	0.241201	+	0.970475i	$0.422459\pi$
$954$	−6.22829e10	−0.00243445
$955$	0	0
$956$	1.44885e13	0.561002
$957$	1.05193e12	0.0405399
$958$	−3.83818e13	−1.47225
$959$	1.05915e13	0.404365
$960$	0	0
$961$	−2.50629e13	−0.947928
$962$	1.54236e13	0.580630
$963$	2.32200e10	0.000870049 0
$964$	−4.20083e12	−0.156671
$965$	0	0
$966$	1.73983e13	0.642851
$967$	−9.86879e12	−0.362948	−0.181474	−	0.983396i	$-0.558087\pi$
$967$	−9.86879e12	−0.362948	−0.181474	+	0.983396i	$0.558087\pi$
$968$	−2.35145e11	−0.00860788
$969$	−9.06832e12	−0.330423
$970$	0	0
$971$	3.16958e13	1.14424	0.572118	−	0.820172i	$-0.306122\pi$
$971$	3.16958e13	1.14424	0.572118	+	0.820172i	$0.306122\pi$
$972$	−1.10151e11	−0.00395814
$973$	1.82902e12	0.0654200
$974$	−1.74970e13	−0.622944
$975$	0	0
$976$	−1.41120e13	−0.497812
$977$	−3.23312e13	−1.13526	−0.567631	−	0.823283i	$-0.692140\pi$
$977$	−3.23312e13	−1.13526	−0.567631	+	0.823283i	$0.692140\pi$
$978$	−1.79516e13	−0.627450
$979$	−1.52449e13	−0.530399
$980$	0	0
$981$	−2.32578e10	−0.000801784 0
$982$	−3.87891e12	−0.133109
$983$	3.93183e13	1.34309	0.671543	−	0.740965i	$-0.265632\pi$
$983$	3.93183e13	1.34309	0.671543	+	0.740965i	$0.265632\pi$
$984$	3.59570e12	0.122266
$985$	0	0
$986$	−5.94309e11	−0.0200247
$987$	−1.15004e13	−0.385731
$988$	−8.92256e12	−0.297909
$989$	4.83496e13	1.60698
$990$	0	0
$991$	−5.00414e13	−1.64816	−0.824078	−	0.566476i	$-0.808306\pi$
$991$	−5.00414e13	−1.64816	−0.824078	+	0.566476i	$0.808306\pi$
$992$	−9.94970e12	−0.326218
$993$	4.70666e12	0.153618
$994$	9.77277e12	0.317526
$995$	0	0
$996$	1.26782e12	0.0408218
$997$	−5.09356e13	−1.63265	−0.816326	−	0.577592i	$-0.803993\pi$
$997$	−5.09356e13	−1.63265	−0.816326	+	0.577592i	$0.803993\pi$
$998$	8.12556e13	2.59278
$999$	−4.59938e13	−1.46102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.10.a.h.1.14	yes	17
5.4	even	2		325.10.a.g.1.4	✓	17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
325.10.a.g.1.4	✓	17	5.4	even	2
325.10.a.h.1.14	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)

\(f(q)\)	\(=\)	\(q+32.4531 q^{2} -140.165 q^{3} +541.204 q^{4} -4548.78 q^{6} -1977.44 q^{7} +947.752 q^{8} -36.8521 q^{9} +45933.0 q^{11} -75857.7 q^{12} -28561.0 q^{13} -64174.0 q^{14} -246339. q^{16} +112081. q^{17} -1195.97 q^{18} +577238. q^{19} +277167. q^{21} +1.49067e6 q^{22} +1.93424e6 q^{23} -132841. q^{24} -926893. q^{26} +2.76403e6 q^{27} -1.07020e6 q^{28} -163389. q^{29} +1.17335e6 q^{31} -8.47971e6 q^{32} -6.43818e6 q^{33} +3.63739e6 q^{34} -19944.5 q^{36} -1.66402e7 q^{37} +1.87332e7 q^{38} +4.00324e6 q^{39} -2.70676e7 q^{41} +8.99493e6 q^{42} +2.49967e7 q^{43} +2.48591e7 q^{44} +6.27720e7 q^{46} -4.14926e7 q^{47} +3.45280e7 q^{48} -3.64433e7 q^{49} -1.57098e7 q^{51} -1.54573e7 q^{52} +5.20775e7 q^{53} +8.97013e7 q^{54} -1.87412e6 q^{56} -8.09084e7 q^{57} -5.30248e6 q^{58} -3.12427e7 q^{59} +5.72870e7 q^{61} +3.80790e7 q^{62} +72872.8 q^{63} -1.49067e8 q^{64} -2.08939e8 q^{66} +1.62760e8 q^{67} +6.06588e7 q^{68} -2.71112e8 q^{69} -1.52286e8 q^{71} -34926.7 q^{72} +1.46423e8 q^{73} -5.40025e8 q^{74} +3.12403e8 q^{76} -9.08296e7 q^{77} +1.29918e8 q^{78} -2.80971e8 q^{79} -3.86694e8 q^{81} -8.78429e8 q^{82} -1.67132e7 q^{83} +1.50004e8 q^{84} +8.11221e8 q^{86} +2.29014e7 q^{87} +4.35331e7 q^{88} -3.31895e8 q^{89} +5.64776e7 q^{91} +1.04682e9 q^{92} -1.64463e8 q^{93} -1.34656e9 q^{94} +1.18856e9 q^{96} -1.22720e9 q^{97} -1.18270e9 q^{98} -1.69273e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q + 33 q^{2} - 73 q^{3} + 4267 q^{4} - 1103 q^{6} + 10670 q^{7} - 11481 q^{8} + 47590 q^{9} - 130917 q^{11} - 32239 q^{12} - 485537 q^{13} - 292206 q^{14} + 1064251 q^{16} + 193953 q^{17} + 2026286 q^{18}+ \cdots - 3023832936 q^{99}+O(q^{100}) \) 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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