LMFDB - Embedded newform 245.10.a.e.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [245,10,Mod(1,245)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("245.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(245, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	245.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,-19,18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$126.183779860$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 648x^{2} + 6926x - 8308 $ x^4 - x^3 - 648x^2 + 6926x - 8308
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2\cdot 3^{2}\cdot 5 $
Twist minimal:	no (minimal twist has level 35)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-29.3917$ of defining polynomial
Character	$\chi$	$=$	245.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+15.4436 q^{2} -137.736 q^{3} -273.496 q^{4} +625.000 q^{5} -2127.13 q^{6} -12130.9 q^{8} -711.820 q^{9} +9652.23 q^{10} -8060.89 q^{11} +37670.3 q^{12} +137129. q^{13} -86084.9 q^{15} -47313.7 q^{16} +23676.1 q^{17} -10993.0 q^{18} -572389. q^{19} -170935. q^{20} -124489. q^{22} -997700. q^{23} +1.67086e6 q^{24} +390625. q^{25} +2.11777e6 q^{26} +2.80910e6 q^{27} +1.97927e6 q^{29} -1.32946e6 q^{30} +8.47740e6 q^{31} +5.48031e6 q^{32} +1.11027e6 q^{33} +365643. q^{34} +194680. q^{36} -4.33062e6 q^{37} -8.83972e6 q^{38} -1.88876e7 q^{39} -7.58179e6 q^{40} +1.48554e7 q^{41} +3.14842e7 q^{43} +2.20462e6 q^{44} -444888. q^{45} -1.54081e7 q^{46} -2.31045e7 q^{47} +6.51680e6 q^{48} +6.03264e6 q^{50} -3.26104e6 q^{51} -3.75044e7 q^{52} -6.79444e6 q^{53} +4.33825e7 q^{54} -5.03805e6 q^{55} +7.88385e7 q^{57} +3.05671e7 q^{58} -8.85117e7 q^{59} +2.35439e7 q^{60} -1.24823e8 q^{61} +1.30921e8 q^{62} +1.08860e8 q^{64} +8.57059e7 q^{65} +1.71466e7 q^{66} +9.58712e7 q^{67} -6.47531e6 q^{68} +1.37419e8 q^{69} -2.16795e8 q^{71} +8.63500e6 q^{72} +1.50701e8 q^{73} -6.68803e7 q^{74} -5.38031e7 q^{75} +1.56546e8 q^{76} -2.91693e8 q^{78} -3.89487e8 q^{79} -2.95711e7 q^{80} -3.72903e8 q^{81} +2.29420e8 q^{82} +7.43467e8 q^{83} +1.47975e7 q^{85} +4.86228e8 q^{86} -2.72617e8 q^{87} +9.77855e7 q^{88} -2.64429e8 q^{89} -6.87065e6 q^{90} +2.72867e8 q^{92} -1.16764e9 q^{93} -3.56816e8 q^{94} -3.57743e8 q^{95} -7.54835e8 q^{96} -1.39343e9 q^{97} +5.73790e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 19 q^{2} + 18 q^{3} + 1729 q^{4} + 2500 q^{5} + 144 q^{6} - 30495 q^{8} + 5382 q^{9} - 11875 q^{10} + 82438 q^{11} - 41328 q^{12} + 72962 q^{13} + 11250 q^{15} + 64257 q^{16} + 357542 q^{17} - 965367 q^{18}+ \cdots + 1222369524 q^{99}+O(q^{100}) $ 4 * q - 19 * q^2 + 18 * q^3 + 1729 * q^4 + 2500 * q^5 + 144 * q^6 - 30495 * q^8 + 5382 * q^9 - 11875 * q^10 + 82438 * q^11 - 41328 * q^12 + 72962 * q^13 + 11250 * q^15 + 64257 * q^16 + 357542 * q^17 - 965367 * q^18 - 300732 * q^19 + 1080625 * q^20 - 5595068 * q^22 - 2340836 * q^23 + 7636320 * q^24 + 1562500 * q^25 - 1305666 * q^26 + 4240350 * q^27 - 1372022 * q^29 + 90000 * q^30 + 4590888 * q^31 - 10529439 * q^32 - 2000034 * q^33 + 7199478 * q^34 - 9144243 * q^36 - 38868456 * q^37 + 15477280 * q^38 - 46666242 * q^39 - 19059375 * q^40 - 57287084 * q^41 - 43403452 * q^43 + 87639348 * q^44 + 3363750 * q^45 + 28892416 * q^46 - 91822222 * q^47 - 156168864 * q^48 - 7421875 * q^50 + 86342634 * q^51 - 1953386 * q^52 - 61086884 * q^53 - 187589520 * q^54 + 51523750 * q^55 - 79928892 * q^57 + 29615390 * q^58 - 72569680 * q^59 - 25830000 * q^60 + 225681036 * q^61 - 190286472 * q^62 + 141443393 * q^64 + 45601250 * q^65 + 119673648 * q^66 - 4429720 * q^67 - 15339698 * q^68 - 348300612 * q^69 - 470468984 * q^71 + 298610685 * q^72 + 168326464 * q^73 + 927809502 * q^74 + 7031250 * q^75 + 892265344 * q^76 + 281290896 * q^78 - 598805646 * q^79 + 40160625 * q^80 - 847155996 * q^81 + 1821993318 * q^82 + 1159074304 * q^83 + 223463750 * q^85 + 706791156 * q^86 + 421480998 * q^87 - 1992103900 * q^88 + 1380153012 * q^89 - 603354375 * q^90 + 710319264 * q^92 - 1601969400 * q^93 - 2466744152 * q^94 - 187957500 * q^95 + 799321824 * q^96 - 754874082 * q^97 + 1222369524 * 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 $

$2$	15.4436	0.682516	0.341258	−	0.939970i	$-0.389147\pi$
$2$	15.4436	0.682516	0.341258	+	0.939970i	$0.389147\pi$
$3$	−137.736	−0.981751	−0.490876	−	0.871230i	$-0.663323\pi$
$3$	−137.736	−0.981751	−0.490876	+	0.871230i	$0.663323\pi$
$4$	−273.496	−0.534172
$5$	625.000	0.447214
$5$	625.000	0.447214
$6$	−2127.13	−0.670061
$7$	0	0
$7$	0	0
$8$	−12130.9	−1.04710
$9$	−711.820	−0.0361642
$10$	9652.23	0.305230
$11$	−8060.89	−0.166003	−0.0830015	−	0.996549i	$-0.526451\pi$
$11$	−8060.89	−0.166003	−0.0830015	+	0.996549i	$0.526451\pi$
$12$	37670.3	0.524424
$13$	137129.	1.33164	0.665818	−	0.746114i	$-0.268083\pi$
$13$	137129.	1.33164	0.665818	+	0.746114i	$0.268083\pi$
$14$	0	0
$15$	−86084.9	−0.439053
$16$	−47313.7	−0.180488
$17$	23676.1	0.0687526	0.0343763	−	0.999409i	$-0.489056\pi$
$17$	23676.1	0.0687526	0.0343763	+	0.999409i	$0.489056\pi$
$18$	−10993.0	−0.0246826
$19$	−572389.	−1.00763	−0.503814	−	0.863812i	$-0.668070\pi$
$19$	−572389.	−1.00763	−0.503814	+	0.863812i	$0.668070\pi$
$20$	−170935.	−0.238889
$21$	0	0
$22$	−124489.	−0.113300
$23$	−997700.	−0.743404	−0.371702	−	0.928352i	$-0.621226\pi$
$23$	−997700.	−0.743404	−0.371702	+	0.928352i	$0.621226\pi$
$24$	1.67086e6	1.02799
$25$	390625.	0.200000
$26$	2.11777e6	0.908862
$27$	2.80910e6	1.01726
$28$	0	0
$29$	1.97927e6	0.519655	0.259827	−	0.965655i	$-0.416334\pi$
$29$	1.97927e6	0.519655	0.259827	+	0.965655i	$0.416334\pi$
$30$	−1.32946e6	−0.299660
$31$	8.47740e6	1.64867	0.824337	−	0.566099i	$-0.191548\pi$
$31$	8.47740e6	1.64867	0.824337	+	0.566099i	$0.191548\pi$
$32$	5.48031e6	0.923911
$33$	1.11027e6	0.162974
$34$	365643.	0.0469247
$35$	0	0
$36$	194680.	0.0193179
$37$	−4.33062e6	−0.379877	−0.189938	−	0.981796i	$-0.560829\pi$
$37$	−4.33062e6	−0.379877	−0.189938	+	0.981796i	$0.560829\pi$
$38$	−8.83972e6	−0.687721
$39$	−1.88876e7	−1.30734
$40$	−7.58179e6	−0.468276
$41$	1.48554e7	0.821024	0.410512	−	0.911855i	$-0.365350\pi$
$41$	1.48554e7	0.821024	0.410512	+	0.911855i	$0.365350\pi$
$42$	0	0
$43$	3.14842e7	1.40438	0.702189	−	0.711991i	$-0.252206\pi$
$43$	3.14842e7	1.40438	0.702189	+	0.711991i	$0.252206\pi$
$44$	2.20462e6	0.0886742
$45$	−444888.	−0.0161731
$46$	−1.54081e7	−0.507385
$47$	−2.31045e7	−0.690647	−0.345324	−	0.938484i	$-0.612231\pi$
$47$	−2.31045e7	−0.690647	−0.345324	+	0.938484i	$0.612231\pi$
$48$	6.51680e6	0.177194
$49$	0	0
$50$	6.03264e6	0.136503
$51$	−3.26104e6	−0.0674980
$52$	−3.75044e7	−0.711323
$53$	−6.79444e6	−0.118280	−0.0591401	−	0.998250i	$-0.518836\pi$
$53$	−6.79444e6	−0.118280	−0.0591401	+	0.998250i	$0.518836\pi$
$54$	4.33825e7	0.694293
$55$	−5.03805e6	−0.0742388
$56$	0	0
$57$	7.88385e7	0.989239
$58$	3.05671e7	0.354673
$59$	−8.85117e7	−0.950969	−0.475485	−	0.879724i	$-0.657727\pi$
$59$	−8.85117e7	−0.950969	−0.475485	+	0.879724i	$0.657727\pi$
$60$	2.35439e7	0.234530
$61$	−1.24823e8	−1.15428	−0.577138	−	0.816647i	$-0.695831\pi$
$61$	−1.24823e8	−1.15428	−0.577138	+	0.816647i	$0.695831\pi$
$62$	1.30921e8	1.12525
$63$	0	0
$64$	1.08860e8	0.811071
$65$	8.57059e7	0.595526
$66$	1.71466e7	0.111232
$67$	9.58712e7	0.581235	0.290617	−	0.956839i	$-0.406139\pi$
$67$	9.58712e7	0.581235	0.290617	+	0.956839i	$0.406139\pi$
$68$	−6.47531e6	−0.0367257
$69$	1.37419e8	0.729838
$70$	0	0
$71$	−2.16795e8	−1.01248	−0.506241	−	0.862392i	$-0.668965\pi$
$71$	−2.16795e8	−1.01248	−0.506241	+	0.862392i	$0.668965\pi$
$72$	8.63500e6	0.0378674
$73$	1.50701e8	0.621101	0.310551	−	0.950557i	$-0.399487\pi$
$73$	1.50701e8	0.621101	0.310551	+	0.950557i	$0.399487\pi$
$74$	−6.68803e7	−0.259272
$75$	−5.38031e7	−0.196350
$76$	1.56546e8	0.538247
$77$	0	0
$78$	−2.91693e8	−0.892277
$79$	−3.89487e8	−1.12505	−0.562523	−	0.826781i	$-0.690169\pi$
$79$	−3.89487e8	−1.12505	−0.562523	+	0.826781i	$0.690169\pi$
$80$	−2.95711e7	−0.0807165
$81$	−3.72903e8	−0.962528
$82$	2.29420e8	0.560362
$83$	7.43467e8	1.71953	0.859766	−	0.510688i	$-0.170609\pi$
$83$	7.43467e8	1.71953	0.859766	+	0.510688i	$0.170609\pi$
$84$	0	0
$85$	1.47975e7	0.0307471
$86$	4.86228e8	0.958510
$87$	−2.72617e8	−0.510172
$88$	9.77855e7	0.173821
$89$	−2.64429e8	−0.446739	−0.223369	−	0.974734i	$-0.571706\pi$
$89$	−2.64429e8	−0.446739	−0.223369	+	0.974734i	$0.571706\pi$
$90$	−6.87065e6	−0.0110384
$91$	0	0
$92$	2.72867e8	0.397106
$93$	−1.16764e9	−1.61859
$94$	−3.56816e8	−0.471378
$95$	−3.57743e8	−0.450625
$96$	−7.54835e8	−0.907051
$97$	−1.39343e9	−1.59813	−0.799063	−	0.601248i	$-0.794671\pi$
$97$	−1.39343e9	−1.59813	−0.799063	+	0.601248i	$0.794671\pi$
$98$	0	0
$99$	5.73790e6	0.00600337
$100$	−1.06834e8	−0.106834
$101$	6.43863e8	0.615669	0.307834	−	0.951440i	$-0.400396\pi$
$101$	6.43863e8	0.615669	0.307834	+	0.951440i	$0.400396\pi$
$102$	−5.03621e7	−0.0460684
$103$	9.64216e8	0.844125	0.422063	−	0.906567i	$-0.361306\pi$
$103$	9.64216e8	0.844125	0.422063	+	0.906567i	$0.361306\pi$
$104$	−1.66350e9	−1.39435
$105$	0	0
$106$	−1.04930e8	−0.0807281
$107$	−1.97477e9	−1.45643	−0.728215	−	0.685348i	$-0.759650\pi$
$107$	−1.97477e9	−1.45643	−0.728215	+	0.685348i	$0.759650\pi$
$108$	−7.68278e8	−0.543390
$109$	1.03957e9	0.705401	0.352701	−	0.935736i	$-0.385263\pi$
$109$	1.03957e9	0.705401	0.352701	+	0.935736i	$0.385263\pi$
$110$	−7.78055e7	−0.0506691
$111$	5.96482e8	0.372944
$112$	0	0
$113$	5.48265e8	0.316328	0.158164	−	0.987413i	$-0.449443\pi$
$113$	5.48265e8	0.316328	0.158164	+	0.987413i	$0.449443\pi$
$114$	1.21755e9	0.675171
$115$	−6.23563e8	−0.332460
$116$	−5.41324e8	−0.277585
$117$	−9.76115e7	−0.0481576
$118$	−1.36694e9	−0.649052
$119$	0	0
$120$	1.04428e9	0.459730
$121$	−2.29297e9	−0.972443
$122$	−1.92771e9	−0.787811
$123$	−2.04612e9	−0.806042
$124$	−2.31854e9	−0.880676
$125$	2.44141e8	0.0894427
$126$	0	0
$127$	−5.40565e9	−1.84387	−0.921936	−	0.387341i	$-0.873394\pi$
$127$	−5.40565e9	−1.84387	−0.921936	+	0.387341i	$0.873394\pi$
$128$	−1.12473e9	−0.370342
$129$	−4.33650e9	−1.37875
$130$	1.32360e9	0.406456
$131$	1.81287e9	0.537832	0.268916	−	0.963164i	$-0.413335\pi$
$131$	1.81287e9	0.537832	0.268916	+	0.963164i	$0.413335\pi$
$132$	−3.03656e8	−0.0870560
$133$	0	0
$134$	1.48059e9	0.396702
$135$	1.75569e9	0.454931
$136$	−2.87211e8	−0.0719906
$137$	−7.50191e8	−0.181940	−0.0909702	−	0.995854i	$-0.528997\pi$
$137$	−7.50191e8	−0.181940	−0.0909702	+	0.995854i	$0.528997\pi$
$138$	2.12224e9	0.498126
$139$	−6.59090e9	−1.49754	−0.748769	−	0.662831i	$-0.769355\pi$
$139$	−6.59090e9	−1.49754	−0.748769	+	0.662831i	$0.769355\pi$
$140$	0	0
$141$	3.18232e9	0.678044
$142$	−3.34809e9	−0.691035
$143$	−1.10538e9	−0.221055
$144$	3.36789e7	0.00652719
$145$	1.23705e9	0.232397
$146$	2.32736e9	0.423911
$147$	0	0
$148$	1.18441e9	0.202920
$149$	−3.29437e9	−0.547564	−0.273782	−	0.961792i	$-0.588275\pi$
$149$	−3.29437e9	−0.547564	−0.273782	+	0.961792i	$0.588275\pi$
$150$	−8.30912e8	−0.134012
$151$	−1.04401e10	−1.63421	−0.817103	−	0.576492i	$-0.804421\pi$
$151$	−1.04401e10	−1.63421	−0.817103	+	0.576492i	$0.804421\pi$
$152$	6.94357e9	1.05508
$153$	−1.68531e7	−0.00248638
$154$	0	0
$155$	5.29837e9	0.737310
$156$	5.16570e9	0.698342
$157$	4.88247e9	0.641344	0.320672	−	0.947190i	$-0.396091\pi$
$157$	4.88247e9	0.641344	0.320672	+	0.947190i	$0.396091\pi$
$158$	−6.01506e9	−0.767862
$159$	9.35838e8	0.116122
$160$	3.42519e9	0.413186
$161$	0	0
$162$	−5.75895e9	−0.656940
$163$	−1.00685e10	−1.11717	−0.558584	−	0.829448i	$-0.688655\pi$
$163$	−1.00685e10	−1.11717	−0.558584	+	0.829448i	$0.688655\pi$
$164$	−4.06289e9	−0.438568
$165$	6.93921e8	0.0728840
$166$	1.14818e10	1.17361
$167$	−1.11826e10	−1.11255	−0.556273	−	0.831000i	$-0.687769\pi$
$167$	−1.11826e10	−1.11255	−0.556273	+	0.831000i	$0.687769\pi$
$168$	0	0
$169$	8.19997e9	0.773254
$170$	2.28527e8	0.0209854
$171$	4.07438e8	0.0364400
$172$	−8.61080e9	−0.750180
$173$	1.55595e10	1.32065	0.660325	−	0.750980i	$-0.270418\pi$
$173$	1.55595e10	1.32065	0.660325	+	0.750980i	$0.270418\pi$
$174$	−4.21018e9	−0.348200
$175$	0	0
$176$	3.81391e8	0.0299615
$177$	1.21912e10	0.933616
$178$	−4.08372e9	−0.304906
$179$	−1.14811e10	−0.835884	−0.417942	−	0.908474i	$-0.637248\pi$
$179$	−1.14811e10	−0.835884	−0.417942	+	0.908474i	$0.637248\pi$
$180$	1.21675e8	0.00863924
$181$	−1.64859e10	−1.14172	−0.570860	−	0.821047i	$-0.693390\pi$
$181$	−1.64859e10	−1.14172	−0.570860	+	0.821047i	$0.693390\pi$
$182$	0	0
$183$	1.71926e10	1.13321
$184$	1.21030e10	0.778416
$185$	−2.70664e9	−0.169886
$186$	−1.80326e10	−1.10471
$187$	−1.90850e8	−0.0114131
$188$	6.31900e9	0.368925
$189$	0	0
$190$	−5.52483e9	−0.307558
$191$	1.75186e10	0.952466	0.476233	−	0.879319i	$-0.342002\pi$
$191$	1.75186e10	0.952466	0.476233	+	0.879319i	$0.342002\pi$
$192$	−1.49940e10	−0.796270
$193$	−2.51278e10	−1.30361	−0.651805	−	0.758387i	$-0.725988\pi$
$193$	−2.51278e10	−1.30361	−0.651805	+	0.758387i	$0.725988\pi$
$194$	−2.15195e10	−1.09075
$195$	−1.18048e10	−0.584658
$196$	0	0
$197$	3.28481e10	1.55386	0.776930	−	0.629587i	$-0.216776\pi$
$197$	3.28481e10	1.55386	0.776930	+	0.629587i	$0.216776\pi$
$198$	8.86137e7	0.00409739
$199$	3.56924e9	0.161338	0.0806691	−	0.996741i	$-0.474294\pi$
$199$	3.56924e9	0.161338	0.0806691	+	0.996741i	$0.474294\pi$
$200$	−4.73862e9	−0.209419
$201$	−1.32049e10	−0.570628
$202$	9.94354e9	0.420204
$203$	0	0
$204$	8.91883e8	0.0360556
$205$	9.28460e9	0.367173
$206$	1.48909e10	0.576129
$207$	7.10183e8	0.0268846
$208$	−6.48810e9	−0.240344
$209$	4.61396e9	0.167269
$210$	0	0
$211$	−8.88255e9	−0.308508	−0.154254	−	0.988031i	$-0.549297\pi$
$211$	−8.88255e9	−0.308508	−0.154254	+	0.988031i	$0.549297\pi$
$212$	1.85825e9	0.0631820
$213$	2.98605e10	0.994006
$214$	−3.04975e10	−0.994037
$215$	1.96776e10	0.628057
$216$	−3.40768e10	−1.06517
$217$	0	0
$218$	1.60547e10	0.481447
$219$	−2.07569e10	−0.609767
$220$	1.37789e9	0.0396563
$221$	3.24668e9	0.0915534
$222$	9.21182e9	0.254540
$223$	−1.85138e10	−0.501330	−0.250665	−	0.968074i	$-0.580649\pi$
$223$	−1.85138e10	−0.501330	−0.250665	+	0.968074i	$0.580649\pi$
$224$	0	0
$225$	−2.78055e8	−0.00723284
$226$	8.46716e9	0.215899
$227$	−6.91501e10	−1.72853	−0.864265	−	0.503037i	$-0.832216\pi$
$227$	−6.91501e10	−1.72853	−0.864265	+	0.503037i	$0.832216\pi$
$228$	−2.15620e10	−0.528424
$229$	4.14990e10	0.997190	0.498595	−	0.866835i	$-0.333850\pi$
$229$	4.14990e10	0.997190	0.498595	+	0.866835i	$0.333850\pi$
$230$	−9.63003e9	−0.226909
$231$	0	0
$232$	−2.40103e10	−0.544129
$233$	1.06684e10	0.237136	0.118568	−	0.992946i	$-0.462170\pi$
$233$	1.06684e10	0.237136	0.118568	+	0.992946i	$0.462170\pi$
$234$	−1.50747e9	−0.0328683
$235$	−1.44403e10	−0.308867
$236$	2.42076e10	0.507982
$237$	5.36463e10	1.10452
$238$	0	0
$239$	6.89311e9	0.136655	0.0683274	−	0.997663i	$-0.478234\pi$
$239$	6.89311e9	0.136655	0.0683274	+	0.997663i	$0.478234\pi$
$240$	4.07300e9	0.0792435
$241$	2.72593e10	0.520520	0.260260	−	0.965539i	$-0.416192\pi$
$241$	2.72593e10	0.520520	0.260260	+	0.965539i	$0.416192\pi$
$242$	−3.54116e10	−0.663708
$243$	−3.92936e9	−0.0722925
$244$	3.41386e10	0.616582
$245$	0	0
$246$	−3.15993e10	−0.550136
$247$	−7.84913e10	−1.34179
$248$	−1.02838e11	−1.72632
$249$	−1.02402e11	−1.68815
$250$	3.77040e9	0.0610461
$251$	−1.11185e11	−1.76812	−0.884062	−	0.467370i	$-0.845202\pi$
$251$	−1.11185e11	−1.76812	−0.884062	+	0.467370i	$0.845202\pi$
$252$	0	0
$253$	8.04235e9	0.123407
$254$	−8.34825e10	−1.25847
$255$	−2.03815e9	−0.0301860
$256$	−7.31062e10	−1.06384
$257$	3.84555e10	0.549869	0.274935	−	0.961463i	$-0.411344\pi$
$257$	3.84555e10	0.549869	0.274935	+	0.961463i	$0.411344\pi$
$258$	−6.69710e10	−0.941018
$259$	0	0
$260$	−2.34402e10	−0.318113
$261$	−1.40889e9	−0.0187929
$262$	2.79972e10	0.367079
$263$	1.50225e11	1.93616	0.968082	−	0.250634i	$-0.0806390\pi$
$263$	1.50225e11	1.93616	0.968082	+	0.250634i	$0.0806390\pi$
$264$	−1.34686e10	−0.170649
$265$	−4.24653e9	−0.0528965
$266$	0	0
$267$	3.64213e10	0.438587
$268$	−2.62204e10	−0.310479
$269$	−9.22583e10	−1.07429	−0.537143	−	0.843491i	$-0.680497\pi$
$269$	−9.22583e10	−1.07429	−0.537143	+	0.843491i	$0.680497\pi$
$270$	2.71141e10	0.310497
$271$	1.10392e11	1.24330	0.621649	−	0.783296i	$-0.286463\pi$
$271$	1.10392e11	1.24330	0.621649	+	0.783296i	$0.286463\pi$
$272$	−1.12020e9	−0.0124090
$273$	0	0
$274$	−1.15856e10	−0.124177
$275$	−3.14878e9	−0.0332006
$276$	−3.75836e10	−0.389859
$277$	1.06151e11	1.08334	0.541672	−	0.840590i	$-0.317792\pi$
$277$	1.06151e11	1.08334	0.541672	+	0.840590i	$0.317792\pi$
$278$	−1.01787e11	−1.02209
$279$	−6.03438e9	−0.0596230
$280$	0	0
$281$	1.69943e11	1.62602	0.813008	−	0.582252i	$-0.197828\pi$
$281$	1.69943e11	1.62602	0.813008	+	0.582252i	$0.197828\pi$
$282$	4.91464e10	0.462776
$283$	6.63477e10	0.614875	0.307438	−	0.951568i	$-0.400528\pi$
$283$	6.63477e10	0.614875	0.307438	+	0.951568i	$0.400528\pi$
$284$	5.92927e10	0.540840
$285$	4.92740e10	0.442401
$286$	−1.70711e10	−0.150874
$287$	0	0
$288$	−3.90100e9	−0.0334125
$289$	−1.18027e11	−0.995273
$290$	1.91044e10	0.158614
$291$	1.91925e11	1.56896
$292$	−4.12161e10	−0.331775
$293$	−7.54377e9	−0.0597976	−0.0298988	−	0.999553i	$-0.509519\pi$
$293$	−7.54377e9	−0.0597976	−0.0298988	+	0.999553i	$0.509519\pi$
$294$	0	0
$295$	−5.53198e10	−0.425286
$296$	5.25342e10	0.397768
$297$	−2.26438e10	−0.168867
$298$	−5.08769e10	−0.373721
$299$	−1.36814e11	−0.989943
$300$	1.47149e10	0.104885
$301$	0	0
$302$	−1.61232e11	−1.11537
$303$	−8.86830e10	−0.604434
$304$	2.70818e10	0.181864
$305$	−7.80142e10	−0.516208
$306$	−2.60272e8	−0.00169700
$307$	9.90848e10	0.636626	0.318313	−	0.947986i	$-0.396884\pi$
$307$	9.90848e10	0.636626	0.318313	+	0.947986i	$0.396884\pi$
$308$	0	0
$309$	−1.32807e11	−0.828721
$310$	8.18258e10	0.503225
$311$	2.78000e10	0.168509	0.0842545	−	0.996444i	$-0.473149\pi$
$311$	2.78000e10	0.168509	0.0842545	+	0.996444i	$0.473149\pi$
$312$	2.29123e11	1.36891
$313$	−7.09223e10	−0.417670	−0.208835	−	0.977951i	$-0.566967\pi$
$313$	−7.09223e10	−0.417670	−0.208835	+	0.977951i	$0.566967\pi$
$314$	7.54027e10	0.437727
$315$	0	0
$316$	1.06523e11	0.600969
$317$	−3.11422e11	−1.73214	−0.866068	−	0.499926i	$-0.833360\pi$
$317$	−3.11422e11	−1.73214	−0.866068	+	0.499926i	$0.833360\pi$
$318$	1.44527e10	0.0792550
$319$	−1.59547e10	−0.0862643
$320$	6.80376e10	0.362722
$321$	2.71997e11	1.42985
$322$	0	0
$323$	−1.35519e10	−0.0692770
$324$	1.01988e11	0.514156
$325$	5.35662e10	0.266327
$326$	−1.55493e11	−0.762485
$327$	−1.43187e11	−0.692529
$328$	−1.80208e11	−0.859692
$329$	0	0
$330$	1.07166e10	0.0497445
$331$	2.94782e11	1.34982	0.674908	−	0.737902i	$-0.264183\pi$
$331$	2.94782e11	1.34982	0.674908	+	0.737902i	$0.264183\pi$
$332$	−2.03336e11	−0.918527
$333$	3.08263e9	0.0137379
$334$	−1.72699e11	−0.759330
$335$	5.99195e10	0.259936
$336$	0	0
$337$	−2.02609e11	−0.855705	−0.427852	−	0.903849i	$-0.640730\pi$
$337$	−2.02609e11	−0.855705	−0.427852	+	0.903849i	$0.640730\pi$
$338$	1.26637e11	0.527758
$339$	−7.55158e10	−0.310555
$340$	−4.04707e9	−0.0164243
$341$	−6.83353e10	−0.273685
$342$	6.29229e9	0.0248709
$343$	0	0
$344$	−3.81930e11	−1.47052
$345$	8.58870e10	0.326393
$346$	2.40294e11	0.901365
$347$	−1.52000e11	−0.562810	−0.281405	−	0.959589i	$-0.590800\pi$
$347$	−1.52000e11	−0.562810	−0.281405	+	0.959589i	$0.590800\pi$
$348$	7.45598e10	0.272520
$349$	2.82049e11	1.01768	0.508840	−	0.860861i	$-0.330075\pi$
$349$	2.82049e11	1.01768	0.508840	+	0.860861i	$0.330075\pi$
$350$	0	0
$351$	3.85210e11	1.35461
$352$	−4.41762e10	−0.153372
$353$	4.32937e11	1.48402	0.742008	−	0.670391i	$-0.233874\pi$
$353$	4.32937e11	1.48402	0.742008	+	0.670391i	$0.233874\pi$
$354$	1.88276e11	0.637207
$355$	−1.35497e11	−0.452796
$356$	7.23203e10	0.238636
$357$	0	0
$358$	−1.77310e11	−0.570504
$359$	1.35500e10	0.0430542	0.0215271	−	0.999768i	$-0.493147\pi$
$359$	1.35500e10	0.0430542	0.0215271	+	0.999768i	$0.493147\pi$
$360$	5.39687e9	0.0169348
$361$	4.94112e9	0.0153124
$362$	−2.54601e11	−0.779242
$363$	3.15824e11	0.954697
$364$	0	0
$365$	9.41879e10	0.277765
$366$	2.65515e11	0.773435
$367$	1.26149e11	0.362984	0.181492	−	0.983392i	$-0.441907\pi$
$367$	1.26149e11	0.362984	0.181492	+	0.983392i	$0.441907\pi$
$368$	4.72049e10	0.134175
$369$	−1.05744e10	−0.0296917
$370$	−4.18002e10	−0.115950
$371$	0	0
$372$	3.19346e11	0.864605
$373$	−2.45212e11	−0.655923	−0.327961	−	0.944691i	$-0.606362\pi$
$373$	−2.45212e11	−0.655923	−0.327961	+	0.944691i	$0.606362\pi$
$374$	−2.94741e9	−0.00778964
$375$	−3.36269e10	−0.0878105
$376$	2.80278e11	0.723175
$377$	2.71417e11	0.691991
$378$	0	0
$379$	3.62591e11	0.902694	0.451347	−	0.892348i	$-0.350944\pi$
$379$	3.62591e11	0.902694	0.451347	+	0.892348i	$0.350944\pi$
$380$	9.78413e10	0.240711
$381$	7.44552e11	1.81022
$382$	2.70550e11	0.650073
$383$	−7.23039e10	−0.171699	−0.0858494	−	0.996308i	$-0.527360\pi$
$383$	−7.23039e10	−0.171699	−0.0858494	+	0.996308i	$0.527360\pi$
$384$	1.54916e11	0.363584
$385$	0	0
$386$	−3.88064e11	−0.889734
$387$	−2.24111e10	−0.0507882
$388$	3.81097e11	0.853674
$389$	3.00609e11	0.665624	0.332812	−	0.942993i	$-0.392002\pi$
$389$	3.00609e11	0.665624	0.332812	+	0.942993i	$0.392002\pi$
$390$	−1.82308e11	−0.399038
$391$	−2.36216e10	−0.0511110
$392$	0	0
$393$	−2.49698e11	−0.528017
$394$	5.07291e11	1.06053
$395$	−2.43429e11	−0.503136
$396$	−1.56930e9	−0.00320683
$397$	2.86335e11	0.578518	0.289259	−	0.957251i	$-0.406591\pi$
$397$	2.86335e11	0.578518	0.289259	+	0.957251i	$0.406591\pi$
$398$	5.51219e10	0.110116
$399$	0	0
$400$	−1.84819e10	−0.0360975
$401$	8.19964e11	1.58360	0.791800	−	0.610781i	$-0.209144\pi$
$401$	8.19964e11	1.58360	0.791800	+	0.610781i	$0.209144\pi$
$402$	−2.03931e11	−0.389462
$403$	1.16250e12	2.19543
$404$	−1.76094e11	−0.328873
$405$	−2.33064e11	−0.430456
$406$	0	0
$407$	3.49087e10	0.0630607
$408$	3.95593e10	0.0706769
$409$	−9.67528e11	−1.70966	−0.854828	−	0.518911i	$-0.826337\pi$
$409$	−9.67528e11	−1.70966	−0.854828	+	0.518911i	$0.826337\pi$
$410$	1.43387e11	0.250601
$411$	1.03328e11	0.178620
$412$	−2.63710e11	−0.450908
$413$	0	0
$414$	1.09678e10	0.0183492
$415$	4.64667e11	0.768998
$416$	7.51511e11	1.23031
$417$	9.07803e11	1.47021
$418$	7.12560e10	0.114164
$419$	8.51357e10	0.134942	0.0674712	−	0.997721i	$-0.478507\pi$
$419$	8.51357e10	0.134942	0.0674712	+	0.997721i	$0.478507\pi$
$420$	0	0
$421$	5.61043e10	0.0870415	0.0435207	−	0.999053i	$-0.486143\pi$
$421$	5.61043e10	0.0870415	0.0435207	+	0.999053i	$0.486143\pi$
$422$	−1.37178e11	−0.210562
$423$	1.64463e10	0.0249767
$424$	8.24224e10	0.123851
$425$	9.24846e9	0.0137505
$426$	4.61153e11	0.678425
$427$	0	0
$428$	5.40093e11	0.777985
$429$	1.52251e11	0.217022
$430$	3.03892e11	0.428659
$431$	−1.36440e11	−0.190456	−0.0952278	−	0.995456i	$-0.530358\pi$
$431$	−1.36440e11	−0.190456	−0.0952278	+	0.995456i	$0.530358\pi$
$432$	−1.32909e11	−0.183602
$433$	−3.25710e11	−0.445282	−0.222641	−	0.974900i	$-0.571468\pi$
$433$	−3.25710e11	−0.445282	−0.222641	+	0.974900i	$0.571468\pi$
$434$	0	0
$435$	−1.70386e11	−0.228156
$436$	−2.84320e11	−0.376806
$437$	5.71072e11	0.749074
$438$	−3.20560e11	−0.416175
$439$	−1.44336e11	−0.185474	−0.0927372	−	0.995691i	$-0.529562\pi$
$439$	−1.44336e11	−0.185474	−0.0927372	+	0.995691i	$0.529562\pi$
$440$	6.11160e10	0.0777352
$441$	0	0
$442$	5.01404e10	0.0624867
$443$	−9.59823e11	−1.18406	−0.592031	−	0.805915i	$-0.701674\pi$
$443$	−9.59823e11	−1.18406	−0.592031	+	0.805915i	$0.701674\pi$
$444$	−1.63136e11	−0.199217
$445$	−1.65268e11	−0.199788
$446$	−2.85919e11	−0.342166
$447$	4.53754e11	0.537572
$448$	0	0
$449$	−1.02004e12	−1.18443	−0.592215	−	0.805780i	$-0.701747\pi$
$449$	−1.02004e12	−1.18443	−0.592215	+	0.805780i	$0.701747\pi$
$450$	−4.29416e9	−0.00493653
$451$	−1.19747e11	−0.136292
$452$	−1.49948e11	−0.168974
$453$	1.43797e12	1.60438
$454$	−1.06792e12	−1.17975
$455$	0	0
$456$	−9.56379e11	−1.03583
$457$	−6.45199e11	−0.691944	−0.345972	−	0.938245i	$-0.612451\pi$
$457$	−6.45199e11	−0.691944	−0.345972	+	0.938245i	$0.612451\pi$
$458$	6.40892e11	0.680598
$459$	6.65084e10	0.0699390
$460$	1.70542e11	0.177591
$461$	−1.04575e12	−1.07838	−0.539192	−	0.842183i	$-0.681270\pi$
$461$	−1.04575e12	−1.07838	−0.539192	+	0.842183i	$0.681270\pi$
$462$	0	0
$463$	6.01465e11	0.608269	0.304134	−	0.952629i	$-0.401633\pi$
$463$	6.01465e11	0.608269	0.304134	+	0.952629i	$0.401633\pi$
$464$	−9.36469e10	−0.0937913
$465$	−7.29776e11	−0.723855
$466$	1.64758e11	0.161849
$467$	−9.53000e11	−0.927186	−0.463593	−	0.886048i	$-0.653440\pi$
$467$	−9.53000e11	−0.927186	−0.463593	+	0.886048i	$0.653440\pi$
$468$	2.66964e10	0.0257244
$469$	0	0
$470$	−2.23010e11	−0.210806
$471$	−6.72491e11	−0.629640
$472$	1.07372e12	0.995757
$473$	−2.53790e11	−0.233131
$474$	8.28490e11	0.753850
$475$	−2.23589e11	−0.201525
$476$	0	0
$477$	4.83642e9	0.00427751
$478$	1.06454e11	0.0932690
$479$	−1.99157e12	−1.72857	−0.864283	−	0.503005i	$-0.832228\pi$
$479$	−1.99157e12	−1.72857	−0.864283	+	0.503005i	$0.832228\pi$
$480$	−4.71772e11	−0.405646
$481$	−5.93856e11	−0.505857
$482$	4.20981e11	0.355263
$483$	0	0
$484$	6.27119e11	0.519452
$485$	−8.70891e11	−0.714703
$486$	−6.06833e10	−0.0493408
$487$	−2.40847e12	−1.94027	−0.970134	−	0.242570i	$-0.922010\pi$
$487$	−2.40847e12	−1.94027	−0.970134	+	0.242570i	$0.922010\pi$
$488$	1.51421e12	1.20864
$489$	1.38679e12	1.09678
$490$	0	0
$491$	2.85374e11	0.221589	0.110794	−	0.993843i	$-0.464661\pi$
$491$	2.85374e11	0.221589	0.110794	+	0.993843i	$0.464661\pi$
$492$	5.59605e11	0.430565
$493$	4.68614e10	0.0357276
$494$	−1.21219e12	−0.915794
$495$	3.58619e9	0.00268479
$496$	−4.01097e11	−0.297565
$497$	0	0
$498$	−1.58145e12	−1.15219
$499$	2.11594e12	1.52775	0.763873	−	0.645367i	$-0.223296\pi$
$499$	2.11594e12	1.52775	0.763873	+	0.645367i	$0.223296\pi$
$500$	−6.67715e10	−0.0477778
$501$	1.54024e12	1.09224
$502$	−1.71709e12	−1.20677
$503$	−7.41865e11	−0.516736	−0.258368	−	0.966047i	$-0.583185\pi$
$503$	−7.41865e11	−0.516736	−0.258368	+	0.966047i	$0.583185\pi$
$504$	0	0
$505$	4.02414e11	0.275335
$506$	1.24203e11	0.0842274
$507$	−1.12943e12	−0.759143
$508$	1.47842e12	0.984946
$509$	−1.62377e12	−1.07225	−0.536124	−	0.844140i	$-0.680112\pi$
$509$	−1.62377e12	−1.07225	−0.536124	+	0.844140i	$0.680112\pi$
$510$	−3.14763e10	−0.0206024
$511$	0	0
$512$	−5.53160e11	−0.355742
$513$	−1.60790e12	−1.02501
$514$	5.93890e11	0.375294
$515$	6.02635e11	0.377504
$516$	1.18602e12	0.736490
$517$	1.86243e11	0.114649
$518$	0	0
$519$	−2.14310e12	−1.29655
$520$	−1.03969e12	−0.623573
$521$	−1.48817e12	−0.884877	−0.442439	−	0.896799i	$-0.645887\pi$
$521$	−1.48817e12	−0.884877	−0.442439	+	0.896799i	$0.645887\pi$
$522$	−2.17583e10	−0.0128265
$523$	−2.41360e12	−1.41061	−0.705306	−	0.708903i	$-0.749190\pi$
$523$	−2.41360e12	−1.41061	−0.705306	+	0.708903i	$0.749190\pi$
$524$	−4.95814e11	−0.287295
$525$	0	0
$526$	2.32001e12	1.32146
$527$	2.00711e11	0.113351
$528$	−5.25312e10	−0.0294147
$529$	−8.05747e11	−0.447351
$530$	−6.55815e10	−0.0361027
$531$	6.30044e10	0.0343911
$532$	0	0
$533$	2.03711e12	1.09331
$534$	5.62475e11	0.299342
$535$	−1.23423e12	−0.651336
$536$	−1.16300e12	−0.608609
$537$	1.58136e12	0.820630
$538$	−1.42480e12	−0.733218
$539$	0	0
$540$	−4.80174e11	−0.243011
$541$	−2.14334e12	−1.07573	−0.537864	−	0.843032i	$-0.680769\pi$
$541$	−2.14334e12	−1.07573	−0.537864	+	0.843032i	$0.680769\pi$
$542$	1.70484e12	0.848570
$543$	2.27070e12	1.12089
$544$	1.29752e11	0.0635213
$545$	6.49734e11	0.315465
$546$	0	0
$547$	1.02462e12	0.489349	0.244675	−	0.969605i	$-0.421319\pi$
$547$	1.02462e12	0.489349	0.244675	+	0.969605i	$0.421319\pi$
$548$	2.05174e11	0.0971875
$549$	8.88514e10	0.0417435
$550$	−4.86285e10	−0.0226599
$551$	−1.13291e12	−0.523618
$552$	−1.66701e12	−0.764211
$553$	0	0
$554$	1.63935e12	0.739399
$555$	3.72801e11	0.166786
$556$	1.80259e12	0.799944
$557$	−3.18977e12	−1.40414	−0.702070	−	0.712108i	$-0.747741\pi$
$557$	−3.18977e12	−1.40414	−0.702070	+	0.712108i	$0.747741\pi$
$558$	−9.31924e10	−0.0406936
$559$	4.31740e12	1.87012
$560$	0	0
$561$	2.62869e10	0.0112049
$562$	2.62453e12	1.10978
$563$	−1.08826e12	−0.456503	−0.228252	−	0.973602i	$-0.573301\pi$
$563$	−1.08826e12	−0.456503	−0.228252	+	0.973602i	$0.573301\pi$
$564$	−8.70353e11	−0.362192
$565$	3.42666e11	0.141466
$566$	1.02465e12	0.419662
$567$	0	0
$568$	2.62992e12	1.06017
$569$	−3.28834e12	−1.31514	−0.657569	−	0.753394i	$-0.728415\pi$
$569$	−3.28834e12	−1.31514	−0.657569	+	0.753394i	$0.728415\pi$
$570$	7.60967e11	0.301946
$571$	−1.88806e12	−0.743283	−0.371641	−	0.928376i	$-0.621205\pi$
$571$	−1.88806e12	−0.743283	−0.371641	+	0.928376i	$0.621205\pi$
$572$	3.02319e11	0.118082
$573$	−2.41294e12	−0.935084
$574$	0	0
$575$	−3.89727e11	−0.148681
$576$	−7.74889e10	−0.0293318
$577$	−1.12881e12	−0.423963	−0.211982	−	0.977274i	$-0.567992\pi$
$577$	−1.12881e12	−0.423963	−0.211982	+	0.977274i	$0.567992\pi$
$578$	−1.82276e12	−0.679289
$579$	3.46101e12	1.27982
$580$	−3.38328e11	−0.124140
$581$	0	0
$582$	2.96400e12	1.07084
$583$	5.47692e10	0.0196349
$584$	−1.82813e12	−0.650353
$585$	−6.10072e10	−0.0215367
$586$	−1.16503e11	−0.0408128
$587$	−6.31776e11	−0.219630	−0.109815	−	0.993952i	$-0.535026\pi$
$587$	−6.31776e11	−0.219630	−0.109815	+	0.993952i	$0.535026\pi$
$588$	0	0
$589$	−4.85237e12	−1.66125
$590$	−8.54335e11	−0.290265
$591$	−4.52436e12	−1.52550
$592$	2.04898e11	0.0685630
$593$	4.97504e12	1.65215	0.826077	−	0.563557i	$-0.190568\pi$
$593$	4.97504e12	1.65215	0.826077	+	0.563557i	$0.190568\pi$
$594$	−3.49702e11	−0.115255
$595$	0	0
$596$	9.00999e11	0.292493
$597$	−4.91613e11	−0.158394
$598$	−2.11290e12	−0.675652
$599$	−4.55686e12	−1.44626	−0.723128	−	0.690714i	$-0.757296\pi$
$599$	−4.55686e12	−1.44626	−0.723128	+	0.690714i	$0.757296\pi$
$600$	6.52678e11	0.205598
$601$	5.78188e12	1.80773	0.903866	−	0.427815i	$-0.140717\pi$
$601$	5.78188e12	1.80773	0.903866	+	0.427815i	$0.140717\pi$
$602$	0	0
$603$	−6.82431e10	−0.0210199
$604$	2.85532e12	0.872948
$605$	−1.43311e12	−0.434890
$606$	−1.36958e12	−0.412536
$607$	7.37332e11	0.220452	0.110226	−	0.993907i	$-0.464843\pi$
$607$	7.37332e11	0.220452	0.110226	+	0.993907i	$0.464843\pi$
$608$	−3.13687e12	−0.930958
$609$	0	0
$610$	−1.20482e12	−0.352320
$611$	−3.16831e12	−0.919691
$612$	4.60926e9	0.00132816
$613$	−3.50587e12	−1.00282	−0.501410	−	0.865210i	$-0.667185\pi$
$613$	−3.50587e12	−1.00282	−0.501410	+	0.865210i	$0.667185\pi$
$614$	1.53022e12	0.434507
$615$	−1.27882e12	−0.360473
$616$	0	0
$617$	2.47222e12	0.686759	0.343380	−	0.939197i	$-0.388428\pi$
$617$	2.47222e12	0.686759	0.343380	+	0.939197i	$0.388428\pi$
$618$	−2.05102e12	−0.565615
$619$	1.57589e12	0.431436	0.215718	−	0.976456i	$-0.430791\pi$
$619$	1.57589e12	0.431436	0.215718	+	0.976456i	$0.430791\pi$
$620$	−1.44908e12	−0.393850
$621$	−2.80264e12	−0.756232
$622$	4.29331e11	0.115010
$623$	0	0
$624$	8.93645e11	0.235958
$625$	1.52588e11	0.0400000
$626$	−1.09529e12	−0.285066
$627$	−6.35508e11	−0.164217
$628$	−1.33534e12	−0.342588
$629$	−1.02532e11	−0.0261175
$630$	0	0
$631$	4.95895e11	0.124525	0.0622627	−	0.998060i	$-0.480168\pi$
$631$	4.95895e11	0.124525	0.0622627	+	0.998060i	$0.480168\pi$
$632$	4.72481e12	1.17803
$633$	1.22345e12	0.302878
$634$	−4.80946e12	−1.18221
$635$	−3.37853e12	−0.824605
$636$	−2.55948e11	−0.0620291
$637$	0	0
$638$	−2.46398e11	−0.0588767
$639$	1.54319e11	0.0366156
$640$	−7.02956e11	−0.165622
$641$	1.72054e12	0.402535	0.201268	−	0.979536i	$-0.435494\pi$
$641$	1.72054e12	0.402535	0.201268	+	0.979536i	$0.435494\pi$
$642$	4.20060e12	0.975897
$643$	−8.19457e12	−1.89050	−0.945250	−	0.326346i	$-0.894182\pi$
$643$	−8.19457e12	−1.89050	−0.945250	+	0.326346i	$0.894182\pi$
$644$	0	0
$645$	−2.71031e12	−0.616596
$646$	−2.09290e11	−0.0472826
$647$	2.56336e12	0.575097	0.287549	−	0.957766i	$-0.407160\pi$
$647$	2.56336e12	0.575097	0.287549	+	0.957766i	$0.407160\pi$
$648$	4.52364e12	1.00786
$649$	7.13483e11	0.157864
$650$	8.27253e11	0.181772
$651$	0	0
$652$	2.75368e12	0.596760
$653$	−2.23256e12	−0.480499	−0.240250	−	0.970711i	$-0.577229\pi$
$653$	−2.23256e12	−0.480499	−0.240250	+	0.970711i	$0.577229\pi$
$654$	−2.21131e12	−0.472662
$655$	1.13305e12	0.240526
$656$	−7.02863e11	−0.148185
$657$	−1.07272e11	−0.0224616
$658$	0	0
$659$	6.47077e12	1.33651	0.668254	−	0.743933i	$-0.267042\pi$
$659$	6.47077e12	1.33651	0.668254	+	0.743933i	$0.267042\pi$
$660$	−1.89785e11	−0.0389326
$661$	2.35514e12	0.479856	0.239928	−	0.970791i	$-0.422876\pi$
$661$	2.35514e12	0.479856	0.239928	+	0.970791i	$0.422876\pi$
$662$	4.55248e12	0.921270
$663$	−4.47185e11	−0.0898827
$664$	−9.01890e12	−1.80052
$665$	0	0
$666$	4.76067e10	0.00937636
$667$	−1.97472e12	−0.386314
$668$	3.05839e12	0.594291
$669$	2.55002e12	0.492182
$670$	9.25371e11	0.177410
$671$	1.00618e12	0.191613
$672$	0	0
$673$	−1.00068e13	−1.88030	−0.940149	−	0.340764i	$-0.889314\pi$
$673$	−1.00068e13	−1.88030	−0.940149	+	0.340764i	$0.889314\pi$
$674$	−3.12900e12	−0.584032
$675$	1.09730e12	0.203451
$676$	−2.24266e12	−0.413051
$677$	4.75925e12	0.870742	0.435371	−	0.900251i	$-0.356617\pi$
$677$	4.75925e12	0.870742	0.435371	+	0.900251i	$0.356617\pi$
$678$	−1.16623e12	−0.211959
$679$	0	0
$680$	−1.79507e11	−0.0321952
$681$	9.52446e12	1.69699
$682$	−1.05534e12	−0.186794
$683$	5.44016e11	0.0956575	0.0478287	−	0.998856i	$-0.484770\pi$
$683$	5.44016e11	0.0956575	0.0478287	+	0.998856i	$0.484770\pi$
$684$	−1.11433e11	−0.0194653
$685$	−4.68869e11	−0.0813662
$686$	0	0
$687$	−5.71590e12	−0.978992
$688$	−1.48963e12	−0.253473
$689$	−9.31717e11	−0.157506
$690$	1.32640e12	0.222769
$691$	−8.57339e12	−1.43054	−0.715272	−	0.698846i	$-0.753697\pi$
$691$	−8.57339e12	−1.43054	−0.715272	+	0.698846i	$0.753697\pi$
$692$	−4.25546e12	−0.705455
$693$	0	0
$694$	−2.34743e12	−0.384127
$695$	−4.11931e12	−0.669720
$696$	3.30708e12	0.534199
$697$	3.51716e11	0.0564476
$698$	4.35585e12	0.694582
$699$	−1.46942e12	−0.232809
$700$	0	0
$701$	1.25396e13	1.96133	0.980666	−	0.195687i	$-0.0626935\pi$
$701$	1.25396e13	1.96133	0.980666	+	0.195687i	$0.0626935\pi$
$702$	5.94902e12	0.924545
$703$	2.47880e12	0.382774
$704$	−8.77510e11	−0.134640
$705$	1.98895e12	0.303230
$706$	6.68609e12	1.01286
$707$	0	0
$708$	−3.33426e12	−0.498712
$709$	4.37869e12	0.650782	0.325391	−	0.945580i	$-0.394504\pi$
$709$	4.37869e12	0.650782	0.325391	+	0.945580i	$0.394504\pi$
$710$	−2.09256e12	−0.309040
$711$	2.77244e11	0.0406864
$712$	3.20775e12	0.467779
$713$	−8.45790e12	−1.22563
$714$	0	0
$715$	−6.90865e11	−0.0988590
$716$	3.14004e12	0.446506
$717$	−9.49429e11	−0.134161
$718$	2.09261e11	0.0293852
$719$	−7.76448e12	−1.08351	−0.541754	−	0.840537i	$-0.682240\pi$
$719$	−7.76448e12	−1.08351	−0.541754	+	0.840537i	$0.682240\pi$
$720$	2.10493e10	0.00291905
$721$	0	0
$722$	7.63086e10	0.0104510
$723$	−3.75458e12	−0.511022
$724$	4.50884e12	0.609875
$725$	7.73154e11	0.103931
$726$	4.87745e12	0.651596
$727$	−7.08318e11	−0.0940423	−0.0470211	−	0.998894i	$-0.514973\pi$
$727$	−7.08318e11	−0.0940423	−0.0470211	+	0.998894i	$0.514973\pi$
$728$	0	0
$729$	7.88106e12	1.03350
$730$	1.45460e12	0.189579
$731$	7.45421e11	0.0965547
$732$	−4.70211e12	−0.605331
$733$	−6.81304e12	−0.871712	−0.435856	−	0.900017i	$-0.643554\pi$
$733$	−6.81304e12	−0.871712	−0.435856	+	0.900017i	$0.643554\pi$
$734$	1.94820e12	0.247743
$735$	0	0
$736$	−5.46771e12	−0.686839
$737$	−7.72807e11	−0.0964866
$738$	−1.63306e11	−0.0202651
$739$	9.20369e12	1.13517	0.567586	−	0.823314i	$-0.307877\pi$
$739$	9.20369e12	1.13517	0.567586	+	0.823314i	$0.307877\pi$
$740$	7.40256e11	0.0907484
$741$	1.08111e13	1.31731
$742$	0	0
$743$	−8.72196e12	−1.04994	−0.524970	−	0.851121i	$-0.675923\pi$
$743$	−8.72196e12	−1.04994	−0.524970	+	0.851121i	$0.675923\pi$
$744$	1.41645e13	1.69482
$745$	−2.05898e12	−0.244878
$746$	−3.78695e12	−0.447678
$747$	−5.29215e11	−0.0621856
$748$	5.21968e10	0.00609658
$749$	0	0
$750$	−5.19320e11	−0.0599321
$751$	−1.63201e13	−1.87216	−0.936078	−	0.351793i	$-0.885572\pi$
$751$	−1.63201e13	−1.87216	−0.936078	+	0.351793i	$0.885572\pi$
$752$	1.09316e12	0.124653
$753$	1.53141e13	1.73586
$754$	4.19164e12	0.472295
$755$	−6.52504e12	−0.730839
$756$	0	0
$757$	−3.23287e12	−0.357813	−0.178907	−	0.983866i	$-0.557256\pi$
$757$	−3.23287e12	−0.357813	−0.178907	+	0.983866i	$0.557256\pi$
$758$	5.59970e12	0.616103
$759$	−1.10772e12	−0.121155
$760$	4.33973e12	0.471847
$761$	6.46766e11	0.0699063	0.0349531	−	0.999389i	$-0.488872\pi$
$761$	6.46766e11	0.0699063	0.0349531	+	0.999389i	$0.488872\pi$
$762$	1.14985e13	1.23551
$763$	0	0
$764$	−4.79127e12	−0.508781
$765$	−1.05332e10	−0.00111195
$766$	−1.11663e12	−0.117187
$767$	−1.21376e13	−1.26634
$768$	1.00694e13	1.04442
$769$	2.42101e12	0.249648	0.124824	−	0.992179i	$-0.460163\pi$
$769$	2.42101e12	0.249648	0.124824	+	0.992179i	$0.460163\pi$
$770$	0	0
$771$	−5.29670e12	−0.539835
$772$	6.87237e12	0.696352
$773$	4.43910e12	0.447185	0.223592	−	0.974683i	$-0.428222\pi$
$773$	4.43910e12	0.447185	0.223592	+	0.974683i	$0.428222\pi$
$774$	−3.46107e11	−0.0346638
$775$	3.31148e12	0.329735
$776$	1.69035e13	1.67339
$777$	0	0
$778$	4.64248e12	0.454299
$779$	−8.50304e12	−0.827286
$780$	3.22856e12	0.312308
$781$	1.74756e12	0.168075
$782$	−3.64802e11	−0.0348840
$783$	5.55998e12	0.528622
$784$	0	0
$785$	3.05154e12	0.286818
$786$	−3.85622e12	−0.360380
$787$	1.72989e13	1.60744	0.803718	−	0.595011i	$-0.202852\pi$
$787$	1.72989e13	1.60744	0.803718	+	0.595011i	$0.202852\pi$
$788$	−8.98382e12	−0.830029
$789$	−2.06914e13	−1.90083
$790$	−3.75941e12	−0.343398
$791$	0	0
$792$	−6.96057e10	−0.00628611
$793$	−1.71169e13	−1.53708
$794$	4.42203e12	0.394848
$795$	5.84899e11	0.0519313
$796$	−9.76175e11	−0.0861825
$797$	1.37776e13	1.20951	0.604756	−	0.796410i	$-0.293270\pi$
$797$	1.37776e13	1.20951	0.604756	+	0.796410i	$0.293270\pi$
$798$	0	0
$799$	−5.47024e11	−0.0474838
$800$	2.14075e12	0.184782
$801$	1.88226e11	0.0161560
$802$	1.26632e13	1.08083
$803$	−1.21478e12	−0.103105
$804$	3.61149e12	0.304814
$805$	0	0
$806$	1.79531e13	1.49842
$807$	1.27073e13	1.05468
$808$	−7.81061e12	−0.644665
$809$	1.38369e13	1.13572	0.567860	−	0.823125i	$-0.307772\pi$
$809$	1.38369e13	1.13572	0.567860	+	0.823125i	$0.307772\pi$
$810$	−3.59935e12	−0.293793
$811$	1.96078e13	1.59161	0.795804	−	0.605555i	$-0.207049\pi$
$811$	1.96078e13	1.59161	0.795804	+	0.605555i	$0.207049\pi$
$812$	0	0
$813$	−1.52049e13	−1.22061
$814$	5.39114e11	0.0430399
$815$	−6.29278e12	−0.499613
$816$	1.54292e11	0.0121825
$817$	−1.80212e13	−1.41509
$818$	−1.49421e13	−1.16687
$819$	0	0
$820$	−2.53930e12	−0.196134
$821$	2.41017e13	1.85142	0.925708	−	0.378239i	$-0.123470\pi$
$821$	2.41017e13	1.85142	0.925708	+	0.378239i	$0.123470\pi$
$822$	1.59576e12	0.121911
$823$	8.20762e12	0.623617	0.311809	−	0.950145i	$-0.399065\pi$
$823$	8.20762e12	0.623617	0.311809	+	0.950145i	$0.399065\pi$
$824$	−1.16968e13	−0.883881
$825$	4.33701e11	0.0325947
$826$	0	0
$827$	2.84612e12	0.211582	0.105791	−	0.994388i	$-0.466263\pi$
$827$	2.84612e12	0.211582	0.105791	+	0.994388i	$0.466263\pi$
$828$	−1.94233e11	−0.0143610
$829$	5.88562e12	0.432809	0.216405	−	0.976304i	$-0.430567\pi$
$829$	5.88562e12	0.432809	0.216405	+	0.976304i	$0.430567\pi$
$830$	7.17612e12	0.524853
$831$	−1.46208e13	−1.06357
$832$	1.49279e13	1.08005
$833$	0	0
$834$	1.40197e13	1.00344
$835$	−6.98911e12	−0.497546
$836$	−1.26190e12	−0.0893505
$837$	2.38138e13	1.67712
$838$	1.31480e12	0.0921003
$839$	8.44799e12	0.588606	0.294303	−	0.955712i	$-0.404913\pi$
$839$	8.44799e12	0.588606	0.294303	+	0.955712i	$0.404913\pi$
$840$	0	0
$841$	−1.05896e13	−0.729959
$842$	8.66450e11	0.0594072
$843$	−2.34073e13	−1.59634
$844$	2.42934e12	0.164796
$845$	5.12498e12	0.345810
$846$	2.53989e11	0.0170470
$847$	0	0
$848$	3.21470e11	0.0213481
$849$	−9.13847e12	−0.603655
$850$	1.42829e11	0.00938495
$851$	4.32066e12	0.282402
$852$	−8.16674e12	−0.530970
$853$	7.17311e12	0.463913	0.231957	−	0.972726i	$-0.425487\pi$
$853$	7.17311e12	0.463913	0.231957	+	0.972726i	$0.425487\pi$
$854$	0	0
$855$	2.54649e11	0.0162965
$856$	2.39557e13	1.52502
$857$	−2.17636e13	−1.37821	−0.689107	−	0.724660i	$-0.741997\pi$
$857$	−2.17636e13	−1.37821	−0.689107	+	0.724660i	$0.741997\pi$
$858$	2.35130e12	0.148121
$859$	9.02945e12	0.565838	0.282919	−	0.959144i	$-0.408697\pi$
$859$	9.02945e12	0.565838	0.282919	+	0.959144i	$0.408697\pi$
$860$	−5.38175e12	−0.335491
$861$	0	0
$862$	−2.10712e12	−0.129989
$863$	−1.84428e13	−1.13182	−0.565910	−	0.824467i	$-0.691475\pi$
$863$	−1.84428e13	−1.13182	−0.565910	+	0.824467i	$0.691475\pi$
$864$	1.53947e13	0.939854
$865$	9.72468e12	0.590613
$866$	−5.03012e12	−0.303912
$867$	1.62566e13	0.977111
$868$	0	0
$869$	3.13961e12	0.186761
$870$	−2.63136e12	−0.155720
$871$	1.31468e13	0.773993
$872$	−1.26109e13	−0.738623
$873$	9.91868e11	0.0577950
$874$	8.81940e12	0.511255
$875$	0	0
$876$	5.67693e12	0.325721
$877$	−1.12140e13	−0.640120	−0.320060	−	0.947397i	$-0.603703\pi$
$877$	−1.12140e13	−0.640120	−0.320060	+	0.947397i	$0.603703\pi$
$878$	−2.22906e12	−0.126589
$879$	1.03905e12	0.0587064
$880$	2.38369e11	0.0133992
$881$	−3.00664e13	−1.68147	−0.840735	−	0.541446i	$-0.817877\pi$
$881$	−3.00664e13	−1.68147	−0.840735	+	0.541446i	$0.817877\pi$
$882$	0	0
$883$	−1.58968e13	−0.880007	−0.440004	−	0.897996i	$-0.645023\pi$
$883$	−1.58968e13	−0.880007	−0.440004	+	0.897996i	$0.645023\pi$
$884$	−8.87956e11	−0.0489053
$885$	7.61952e12	0.417526
$886$	−1.48231e13	−0.808141
$887$	−1.46131e13	−0.792658	−0.396329	−	0.918109i	$-0.629716\pi$
$887$	−1.46131e13	−0.792658	−0.396329	+	0.918109i	$0.629716\pi$
$888$	−7.23585e12	−0.390509
$889$	0	0
$890$	−2.55233e12	−0.136358
$891$	3.00593e12	0.159782
$892$	5.06346e12	0.267797
$893$	1.32248e13	0.695915
$894$	7.00758e12	0.366901
$895$	−7.17570e12	−0.373819
$896$	0	0
$897$	1.88442e13	0.971878
$898$	−1.57531e13	−0.808393
$899$	1.67791e13	0.856742
$900$	7.60469e10	0.00386359
$901$	−1.60866e11	−0.00813208
$902$	−1.84933e12	−0.0930217
$903$	0	0
$904$	−6.65093e12	−0.331226
$905$	−1.03037e13	−0.510593
$906$	2.22074e13	1.09502
$907$	1.41504e12	0.0694281	0.0347141	−	0.999397i	$-0.488948\pi$
$907$	1.41504e12	0.0694281	0.0347141	+	0.999397i	$0.488948\pi$
$908$	1.89123e13	0.923333
$909$	−4.58315e11	−0.0222652
$910$	0	0
$911$	−1.61901e13	−0.778784	−0.389392	−	0.921072i	$-0.627315\pi$
$911$	−1.61901e13	−0.778784	−0.389392	+	0.921072i	$0.627315\pi$
$912$	−3.73014e12	−0.178545
$913$	−5.99301e12	−0.285447
$914$	−9.96417e12	−0.472262
$915$	1.07454e13	0.506788
$916$	−1.13498e13	−0.532671
$917$	0	0
$918$	1.02713e12	0.0477345
$919$	−1.60413e13	−0.741858	−0.370929	−	0.928661i	$-0.620961\pi$
$919$	−1.60413e13	−0.741858	−0.370929	+	0.928661i	$0.620961\pi$
$920$	7.56435e12	0.348118
$921$	−1.36475e13	−0.625008
$922$	−1.61501e13	−0.736014
$923$	−2.97290e13	−1.34826
$924$	0	0
$925$	−1.69165e12	−0.0759753
$926$	9.28876e12	0.415153
$927$	−6.86349e11	−0.0305271
$928$	1.08470e13	0.480115
$929$	3.98759e13	1.75647	0.878233	−	0.478233i	$-0.158723\pi$
$929$	3.98759e13	1.75647	0.878233	+	0.478233i	$0.158723\pi$
$930$	−1.12703e13	−0.494042
$931$	0	0
$932$	−2.91777e12	−0.126672
$933$	−3.82906e12	−0.165434
$934$	−1.47177e13	−0.632819
$935$	−1.19281e11	−0.00510411
$936$	1.18411e12	0.0504256
$937$	5.95427e12	0.252348	0.126174	−	0.992008i	$-0.459730\pi$
$937$	5.95427e12	0.252348	0.126174	+	0.992008i	$0.459730\pi$
$938$	0	0
$939$	9.76855e12	0.410048
$940$	3.94937e12	0.164988
$941$	−9.86055e12	−0.409966	−0.204983	−	0.978766i	$-0.565714\pi$
$941$	−9.86055e12	−0.409966	−0.204983	+	0.978766i	$0.565714\pi$
$942$	−1.03857e13	−0.429739
$943$	−1.48212e13	−0.610353
$944$	4.18782e12	0.171638
$945$	0	0
$946$	−3.91943e12	−0.159115
$947$	−2.10061e13	−0.848732	−0.424366	−	0.905491i	$-0.639503\pi$
$947$	−2.10061e13	−0.848732	−0.424366	+	0.905491i	$0.639503\pi$
$948$	−1.46721e13	−0.590002
$949$	2.06655e13	0.827080
$950$	−3.45302e12	−0.137544
$951$	4.28939e13	1.70053
$952$	0	0
$953$	−4.25218e13	−1.66991	−0.834955	−	0.550318i	$-0.814506\pi$
$953$	−4.25218e13	−1.66991	−0.834955	+	0.550318i	$0.814506\pi$
$954$	7.46916e10	0.00291947
$955$	1.09491e13	0.425956
$956$	−1.88524e12	−0.0729972
$957$	2.19754e12	0.0846901
$958$	−3.07570e13	−1.17977
$959$	0	0
$960$	−9.37122e12	−0.356103
$961$	4.54266e13	1.71813
$962$	−9.17125e12	−0.345256
$963$	1.40568e12	0.0526707
$964$	−7.45531e12	−0.278048
$965$	−1.57049e13	−0.582992
$966$	0	0
$967$	−1.21906e13	−0.448338	−0.224169	−	0.974550i	$-0.571967\pi$
$967$	−1.21906e13	−0.448338	−0.224169	+	0.974550i	$0.571967\pi$
$968$	2.78157e13	1.01824
$969$	1.86658e12	0.0680128
$970$	−1.34497e13	−0.487796
$971$	−5.38639e12	−0.194452	−0.0972258	−	0.995262i	$-0.530997\pi$
$971$	−5.38639e12	−0.194452	−0.0972258	+	0.995262i	$0.530997\pi$
$972$	1.07466e12	0.0386167
$973$	0	0
$974$	−3.71954e13	−1.32426
$975$	−7.37798e12	−0.261467
$976$	5.90583e12	0.208332
$977$	−1.89284e13	−0.664643	−0.332321	−	0.943166i	$-0.607832\pi$
$977$	−1.89284e13	−0.664643	−0.332321	+	0.943166i	$0.607832\pi$
$978$	2.14169e13	0.748570
$979$	2.13153e12	0.0741600
$980$	0	0
$981$	−7.39990e11	−0.0255103
$982$	4.40719e12	0.151238
$983$	−3.98513e13	−1.36129	−0.680647	−	0.732612i	$-0.738301\pi$
$983$	−3.98513e13	−1.36129	−0.680647	+	0.732612i	$0.738301\pi$
$984$	2.48212e13	0.844004
$985$	2.05300e13	0.694907
$986$	7.23708e11	0.0243847
$987$	0	0
$988$	2.14671e13	0.716748
$989$	−3.14118e13	−1.04402
$990$	5.53836e10	0.00183241
$991$	−3.44424e13	−1.13439	−0.567194	−	0.823584i	$-0.691971\pi$
$991$	−3.44424e13	−1.13439	−0.567194	+	0.823584i	$0.691971\pi$
$992$	4.64588e13	1.52323
$993$	−4.06020e13	−1.32518
$994$	0	0
$995$	2.23078e12	0.0721527
$996$	2.80066e13	0.901765
$997$	−4.12406e13	−1.32189	−0.660947	−	0.750433i	$-0.729845\pi$
$997$	−4.12406e13	−1.32189	−0.660947	+	0.750433i	$0.729845\pi$
$998$	3.26777e13	1.04271
$999$	−1.21652e13	−0.386432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.10.a.e.1.3		4
7.6	odd	2		35.10.a.c.1.3	✓	4
21.20	even	2		315.10.a.g.1.2		4
35.13	even	4		175.10.b.e.99.4		8
35.27	even	4		175.10.b.e.99.5		8
35.34	odd	2		175.10.a.e.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.10.a.c.1.3	✓	4	7.6	odd	2
175.10.a.e.1.2		4	35.34	odd	2
175.10.b.e.99.4		8	35.13	even	4
175.10.b.e.99.5		8	35.27	even	4
245.10.a.e.1.3		4	1.1	even	1	trivial
315.10.a.g.1.2		4	21.20	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	245.a (trivial)

\(f(q)\)	\(=\)	\(q+15.4436 q^{2} -137.736 q^{3} -273.496 q^{4} +625.000 q^{5} -2127.13 q^{6} -12130.9 q^{8} -711.820 q^{9} +9652.23 q^{10} -8060.89 q^{11} +37670.3 q^{12} +137129. q^{13} -86084.9 q^{15} -47313.7 q^{16} +23676.1 q^{17} -10993.0 q^{18} -572389. q^{19} -170935. q^{20} -124489. q^{22} -997700. q^{23} +1.67086e6 q^{24} +390625. q^{25} +2.11777e6 q^{26} +2.80910e6 q^{27} +1.97927e6 q^{29} -1.32946e6 q^{30} +8.47740e6 q^{31} +5.48031e6 q^{32} +1.11027e6 q^{33} +365643. q^{34} +194680. q^{36} -4.33062e6 q^{37} -8.83972e6 q^{38} -1.88876e7 q^{39} -7.58179e6 q^{40} +1.48554e7 q^{41} +3.14842e7 q^{43} +2.20462e6 q^{44} -444888. q^{45} -1.54081e7 q^{46} -2.31045e7 q^{47} +6.51680e6 q^{48} +6.03264e6 q^{50} -3.26104e6 q^{51} -3.75044e7 q^{52} -6.79444e6 q^{53} +4.33825e7 q^{54} -5.03805e6 q^{55} +7.88385e7 q^{57} +3.05671e7 q^{58} -8.85117e7 q^{59} +2.35439e7 q^{60} -1.24823e8 q^{61} +1.30921e8 q^{62} +1.08860e8 q^{64} +8.57059e7 q^{65} +1.71466e7 q^{66} +9.58712e7 q^{67} -6.47531e6 q^{68} +1.37419e8 q^{69} -2.16795e8 q^{71} +8.63500e6 q^{72} +1.50701e8 q^{73} -6.68803e7 q^{74} -5.38031e7 q^{75} +1.56546e8 q^{76} -2.91693e8 q^{78} -3.89487e8 q^{79} -2.95711e7 q^{80} -3.72903e8 q^{81} +2.29420e8 q^{82} +7.43467e8 q^{83} +1.47975e7 q^{85} +4.86228e8 q^{86} -2.72617e8 q^{87} +9.77855e7 q^{88} -2.64429e8 q^{89} -6.87065e6 q^{90} +2.72867e8 q^{92} -1.16764e9 q^{93} -3.56816e8 q^{94} -3.57743e8 q^{95} -7.54835e8 q^{96} -1.39343e9 q^{97} +5.73790e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 19 q^{2} + 18 q^{3} + 1729 q^{4} + 2500 q^{5} + 144 q^{6} - 30495 q^{8} + 5382 q^{9} - 11875 q^{10} + 82438 q^{11} - 41328 q^{12} + 72962 q^{13} + 11250 q^{15} + 64257 q^{16} + 357542 q^{17} - 965367 q^{18}+ \cdots + 1222369524 q^{99}+O(q^{100}) \) 4 * q - 19 * q^2 + 18 * q^3 + 1729 * q^4 + 2500 * q^5 + 144 * q^6 - 30495 * q^8 + 5382 * q^9 - 11875 * q^10 + 82438 * q^11 - 41328 * q^12 + 72962 * q^13 + 11250 * q^15 + 64257 * q^16 + 357542 * q^17 - 965367 * q^18 - 300732 * q^19 + 1080625 * q^20 - 5595068 * q^22 - 2340836 * q^23 + 7636320 * q^24 + 1562500 * q^25 - 1305666 * q^26 + 4240350 * q^27 - 1372022 * q^29 + 90000 * q^30 + 4590888 * q^31 - 10529439 * q^32 - 2000034 * q^33 + 7199478 * q^34 - 9144243 * q^36 - 38868456 * q^37 + 15477280 * q^38 - 46666242 * q^39 - 19059375 * q^40 - 57287084 * q^41 - 43403452 * q^43 + 87639348 * q^44 + 3363750 * q^45 + 28892416 * q^46 - 91822222 * q^47 - 156168864 * q^48 - 7421875 * q^50 + 86342634 * q^51 - 1953386 * q^52 - 61086884 * q^53 - 187589520 * q^54 + 51523750 * q^55 - 79928892 * q^57 + 29615390 * q^58 - 72569680 * q^59 - 25830000 * q^60 + 225681036 * q^61 - 190286472 * q^62 + 141443393 * q^64 + 45601250 * q^65 + 119673648 * q^66 - 4429720 * q^67 - 15339698 * q^68 - 348300612 * q^69 - 470468984 * q^71 + 298610685 * q^72 + 168326464 * q^73 + 927809502 * q^74 + 7031250 * q^75 + 892265344 * q^76 + 281290896 * q^78 - 598805646 * q^79 + 40160625 * q^80 - 847155996 * q^81 + 1821993318 * q^82 + 1159074304 * q^83 + 223463750 * q^85 + 706791156 * q^86 + 421480998 * q^87 - 1992103900 * q^88 + 1380153012 * q^89 - 603354375 * q^90 + 710319264 * q^92 - 1601969400 * q^93 - 2466744152 * q^94 - 187957500 * q^95 + 799321824 * q^96 - 754874082 * q^97 + 1222369524 * q^99

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