LMFDB - Embedded newform 50.26.a.k.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,26,Mod(1,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("50.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	50.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:	$197.998389976$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2 x^{5} - 27590779188 x^{4} + 26487255863952 x^{3} + \cdots - 30\!\cdots\!08 $ x^6 - 2x^5 - 27590779188x^4 + 26487255863952x^3 + 180405425727179733780x^2 - 1479960352440847053525960*x - 3018239644098422083113677808
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{20}\cdot 3^{4}\cdot 5^{18} $
Twist minimal:	no (minimal twist has level 10)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$10012.7$ of defining polynomial
Character	$\chi$	$=$	50.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00 q^{2} +233693. q^{3} +1.67772e7 q^{4} -9.57206e8 q^{6} -6.39090e10 q^{7} -6.87195e10 q^{8} -7.92676e11 q^{9} +6.04007e12 q^{11} +3.92071e12 q^{12} +1.13809e14 q^{13} +2.61771e14 q^{14} +2.81475e14 q^{16} +9.52541e14 q^{17} +3.24680e15 q^{18} +8.44950e15 q^{19} -1.49351e16 q^{21} -2.47401e16 q^{22} -1.51928e16 q^{23} -1.60592e16 q^{24} -4.66162e17 q^{26} -3.83248e17 q^{27} -1.07222e18 q^{28} -1.63360e18 q^{29} -7.82464e18 q^{31} -1.15292e18 q^{32} +1.41152e18 q^{33} -3.90161e18 q^{34} -1.32989e19 q^{36} +3.53342e19 q^{37} -3.46091e19 q^{38} +2.65964e19 q^{39} -2.35937e20 q^{41} +6.11741e19 q^{42} +3.29832e19 q^{43} +1.01335e20 q^{44} +6.22296e19 q^{46} +1.82685e20 q^{47} +6.57787e19 q^{48} +2.74329e21 q^{49} +2.22602e20 q^{51} +1.90940e21 q^{52} -5.40172e21 q^{53} +1.56978e21 q^{54} +4.39179e21 q^{56} +1.97459e21 q^{57} +6.69124e21 q^{58} -1.13226e22 q^{59} -2.83642e22 q^{61} +3.20497e22 q^{62} +5.06592e22 q^{63} +4.72237e21 q^{64} -5.78158e21 q^{66} -1.16196e23 q^{67} +1.59810e22 q^{68} -3.55044e21 q^{69} +1.14601e23 q^{71} +5.44723e22 q^{72} -8.85118e21 q^{73} -1.44729e23 q^{74} +1.41759e23 q^{76} -3.86015e23 q^{77} -1.08939e23 q^{78} +2.17397e23 q^{79} +5.82063e23 q^{81} +9.66398e23 q^{82} +6.46451e22 q^{83} -2.50569e23 q^{84} -1.35099e23 q^{86} -3.81761e23 q^{87} -4.15070e23 q^{88} +3.57337e24 q^{89} -7.27343e24 q^{91} -2.54893e23 q^{92} -1.82856e24 q^{93} -7.48277e23 q^{94} -2.69429e23 q^{96} +2.49389e24 q^{97} -1.12365e25 q^{98} -4.78782e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 24576 q^{2} + 801416 q^{3} + 100663296 q^{4} - 3282599936 q^{6} + 34007705352 q^{7} - 412316860416 q^{8} + 541468782118 q^{9} + 9861544614312 q^{11} + 13445529337856 q^{12} + 30787386783696 q^{13}+ \cdots - 20\!\cdots\!64 q^{99}+O(q^{100}) $ 6 * q - 24576 * q^2 + 801416 * q^3 + 100663296 * q^4 - 3282599936 * q^6 + 34007705352 * q^7 - 412316860416 * q^8 + 541468782118 * q^9 + 9861544614312 * q^11 + 13445529337856 * q^12 + 30787386783696 * q^13 - 139295561121792 * q^14 + 1688849860263936 * q^16 + 3432836939805312 * q^17 - 2217856131555328 * q^18 + 2007656488916520 * q^19 - 28181710291014728 * q^21 - 40392886740221952 * q^22 + 135711886432707576 * q^23 - 55072888167858176 * q^24 - 126105136266018816 * q^26 + 788054364552235760 * q^27 + 570554618354860032 * q^28 - 2926032031655504820 * q^29 + 79292935777014912 * q^31 - 6917529027641081856 * q^32 - 6844843638395003168 * q^33 - 14060900105442557952 * q^34 + 9084338714850623488 * q^36 + 3345885298190974032 * q^37 - 8223360978602065920 * q^38 + 124726636622561793456 * q^39 + 103229301719876244012 * q^41 + 115432285351996325888 * q^42 + 166390524239317503336 * q^43 + 165449264087949115392 * q^44 - 555875886828370231296 * q^46 + 405906243391034677992 * q^47 + 225578549935547088896 * q^48 + 1716280748139027694542 * q^49 - 1516225893661962013568 * q^51 + 516526638145613070336 * q^52 + 9772760301640799789616 * q^53 - 3227870677205957672960 * q^54 - 2336991716781506691072 * q^56 + 26174725126915157341920 * q^57 + 11985027201660947742720 * q^58 - 12499075130880780168840 * q^59 + 3687285610311118296612 * q^61 - 324783864942653079552 * q^62 + 93007818034972665339656 * q^63 + 28334198897217871282176 * q^64 + 28036479542865932976128 * q^66 + 16759935062266648886712 * q^67 + 57593446831892717371392 * q^68 + 185125325982378999854536 * q^69 + 74568876221253661649712 * q^71 - 37209451376028153806848 * q^72 + 381797761857106829638176 * q^73 - 13704746181390229635072 * q^74 + 33682886568354062008320 * q^76 - 80271541631956375339296 * q^77 - 510880303606013105995776 * q^78 - 400850316873811624799520 * q^79 - 1432110118616113828343714 * q^81 - 422827219844613095473152 * q^82 - 2423159733509985740001144 * q^83 - 472810640801776950837248 * q^84 - 681535587284244493664256 * q^86 - 1231328665433636473947120 * q^87 - 677680185704239576645632 * q^88 + 2982172528060341024616740 * q^89 - 7001711719121019241314768 * q^91 + 2276867632449004467388416 * q^92 - 8806417055581711481018368 * q^93 - 1662591972929678041055232 * q^94 - 923969740536000876118016 * q^96 - 4960469410756873985567808 * q^97 - 7029885944377457436844032 * q^98 - 2053720289282411723573464 * 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 $

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	233693.	0.253881	0.126940	−	0.991910i	$-0.459484\pi$
$3$	233693.	0.253881	0.126940	+	0.991910i	$0.459484\pi$
$4$	1.67772e7	0.500000
$5$	0	0
$5$	0	0
$6$	−9.57206e8	−0.179521
$7$	−6.39090e10	−1.74517	−0.872583	−	0.488466i	$-0.837557\pi$
$7$	−6.39090e10	−1.74517	−0.872583	+	0.488466i	$0.837557\pi$
$8$	−6.87195e10	−0.353553
$9$	−7.92676e11	−0.935545
$10$	0	0
$11$	6.04007e12	0.580274	0.290137	−	0.956985i	$-0.406299\pi$
$11$	6.04007e12	0.580274	0.290137	+	0.956985i	$0.406299\pi$
$12$	3.92071e12	0.126940
$13$	1.13809e14	1.35483	0.677415	−	0.735601i	$-0.263100\pi$
$13$	1.13809e14	1.35483	0.677415	+	0.735601i	$0.263100\pi$
$14$	2.61771e14	1.23402
$15$	0	0
$16$	2.81475e14	0.250000
$17$	9.52541e14	0.396526	0.198263	−	0.980149i	$-0.436470\pi$
$17$	9.52541e14	0.396526	0.198263	+	0.980149i	$0.436470\pi$
$18$	3.24680e15	0.661530
$19$	8.44950e15	0.875812	0.437906	−	0.899021i	$-0.355720\pi$
$19$	8.44950e15	0.875812	0.437906	+	0.899021i	$0.355720\pi$
$20$	0	0
$21$	−1.49351e16	−0.443064
$22$	−2.47401e16	−0.410316
$23$	−1.51928e16	−0.144557	−0.0722786	−	0.997384i	$-0.523027\pi$
$23$	−1.51928e16	−0.144557	−0.0722786	+	0.997384i	$0.523027\pi$
$24$	−1.60592e16	−0.0897604
$25$	0	0
$26$	−4.66162e17	−0.958010
$27$	−3.83248e17	−0.491397
$28$	−1.07222e18	−0.872583
$29$	−1.63360e18	−0.857376	−0.428688	−	0.903452i	$-0.641024\pi$
$29$	−1.63360e18	−0.857376	−0.428688	+	0.903452i	$0.641024\pi$
$30$	0	0
$31$	−7.82464e18	−1.78420	−0.892099	−	0.451840i	$-0.850768\pi$
$31$	−7.82464e18	−1.78420	−0.892099	+	0.451840i	$0.850768\pi$
$32$	−1.15292e18	−0.176777
$33$	1.41152e18	0.147320
$34$	−3.90161e18	−0.280386
$35$	0	0
$36$	−1.32989e19	−0.467772
$37$	3.53342e19	0.882417	0.441208	−	0.897405i	$-0.354550\pi$
$37$	3.53342e19	0.882417	0.441208	+	0.897405i	$0.354550\pi$
$38$	−3.46091e19	−0.619293
$39$	2.65964e19	0.343965
$40$	0	0
$41$	−2.35937e20	−1.63304	−0.816522	−	0.577315i	$-0.804101\pi$
$41$	−2.35937e20	−1.63304	−0.816522	+	0.577315i	$0.804101\pi$
$42$	6.11741e19	0.313293
$43$	3.29832e19	0.125874	0.0629372	−	0.998017i	$-0.479953\pi$
$43$	3.29832e19	0.125874	0.0629372	+	0.998017i	$0.479953\pi$
$44$	1.01335e20	0.290137
$45$	0	0
$46$	6.22296e19	0.102217
$47$	1.82685e20	0.229340	0.114670	−	0.993404i	$-0.463419\pi$
$47$	1.82685e20	0.229340	0.114670	+	0.993404i	$0.463419\pi$
$48$	6.57787e19	0.0634702
$49$	2.74329e21	2.04560
$50$	0	0
$51$	2.22602e20	0.100670
$52$	1.90940e21	0.677415
$53$	−5.40172e21	−1.51037	−0.755186	−	0.655511i	$-0.772453\pi$
$53$	−5.40172e21	−1.51037	−0.755186	+	0.655511i	$0.772453\pi$
$54$	1.56978e21	0.347470
$55$	0	0
$56$	4.39179e21	0.617009
$57$	1.97459e21	0.222352
$58$	6.69124e21	0.606257
$59$	−1.13226e22	−0.828509	−0.414254	−	0.910161i	$-0.635958\pi$
$59$	−1.13226e22	−0.828509	−0.414254	+	0.910161i	$0.635958\pi$
$60$	0	0
$61$	−2.83642e22	−1.36820	−0.684098	−	0.729390i	$-0.739804\pi$
$61$	−2.83642e22	−1.36820	−0.684098	+	0.729390i	$0.739804\pi$
$62$	3.20497e22	1.26162
$63$	5.06592e22	1.63268
$64$	4.72237e21	0.125000
$65$	0	0
$66$	−5.78158e21	−0.104171
$67$	−1.16196e23	−1.73483	−0.867415	−	0.497586i	$-0.834220\pi$
$67$	−1.16196e23	−1.73483	−0.867415	+	0.497586i	$0.834220\pi$
$68$	1.59810e22	0.198263
$69$	−3.55044e21	−0.0367003
$70$	0	0
$71$	1.14601e23	0.828816	0.414408	−	0.910091i	$-0.363989\pi$
$71$	1.14601e23	0.828816	0.414408	+	0.910091i	$0.363989\pi$
$72$	5.44723e22	0.330765
$73$	−8.85118e21	−0.0452340	−0.0226170	−	0.999744i	$-0.507200\pi$
$73$	−8.85118e21	−0.0452340	−0.0226170	+	0.999744i	$0.507200\pi$
$74$	−1.44729e23	−0.623963
$75$	0	0
$76$	1.41759e23	0.437906
$77$	−3.86015e23	−1.01267
$78$	−1.08939e23	−0.243220
$79$	2.17397e23	0.413918	0.206959	−	0.978350i	$-0.433643\pi$
$79$	2.17397e23	0.413918	0.206959	+	0.978350i	$0.433643\pi$
$80$	0	0
$81$	5.82063e23	0.810788
$82$	9.66398e23	1.15474
$83$	6.46451e22	0.0663834	0.0331917	−	0.999449i	$-0.489433\pi$
$83$	6.46451e22	0.0663834	0.0331917	+	0.999449i	$0.489433\pi$
$84$	−2.50569e23	−0.221532
$85$	0	0
$86$	−1.35099e23	−0.0890067
$87$	−3.81761e23	−0.217671
$88$	−4.15070e23	−0.205158
$89$	3.57337e24	1.53357	0.766783	−	0.641906i	$-0.221856\pi$
$89$	3.57337e24	1.53357	0.766783	+	0.641906i	$0.221856\pi$
$90$	0	0
$91$	−7.27343e24	−2.36440
$92$	−2.54893e23	−0.0722786
$93$	−1.82856e24	−0.452973
$94$	−7.48277e23	−0.162168
$95$	0	0
$96$	−2.69429e23	−0.0448802
$97$	2.49389e24	0.364948	0.182474	−	0.983211i	$-0.441589\pi$
$97$	2.49389e24	0.364948	0.182474	+	0.983211i	$0.441589\pi$
$98$	−1.12365e25	−1.44646
$99$	−4.78782e24	−0.542872
$100$	0	0
$101$	−1.34804e25	−1.19038	−0.595192	−	0.803584i	$-0.702924\pi$
$101$	−1.34804e25	−1.19038	−0.595192	+	0.803584i	$0.702924\pi$
$102$	−9.11777e23	−0.0711847
$103$	1.98475e25	1.37164	0.685822	−	0.727769i	$-0.259443\pi$
$103$	1.98475e25	1.37164	0.685822	+	0.727769i	$0.259443\pi$
$104$	−7.82090e24	−0.479005
$105$	0	0
$106$	2.21255e25	1.06799
$107$	6.60004e24	0.283302	0.141651	−	0.989917i	$-0.454759\pi$
$107$	6.60004e24	0.283302	0.141651	+	0.989917i	$0.454759\pi$
$108$	−6.42983e24	−0.245699
$109$	−6.35443e24	−0.216394	−0.108197	−	0.994129i	$-0.534508\pi$
$109$	−6.35443e24	−0.216394	−0.108197	+	0.994129i	$0.534508\pi$
$110$	0	0
$111$	8.25735e24	0.224029
$112$	−1.79888e25	−0.436291
$113$	5.12661e25	1.11263	0.556313	−	0.830973i	$-0.312215\pi$
$113$	5.12661e25	1.11263	0.556313	+	0.830973i	$0.312215\pi$
$114$	−8.08791e24	−0.157226
$115$	0	0
$116$	−2.74073e25	−0.428688
$117$	−9.02138e25	−1.26750
$118$	4.63775e25	0.585844
$119$	−6.08759e25	−0.692004
$120$	0	0
$121$	−7.18647e25	−0.663282
$122$	1.16180e26	0.967460
$123$	−5.51368e25	−0.414598
$124$	−1.31276e26	−0.892099
$125$	0	0
$126$	−2.07500e26	−1.15448
$127$	1.52068e26	0.766462	0.383231	−	0.923653i	$-0.374811\pi$
$127$	1.52068e26	0.766462	0.383231	+	0.923653i	$0.374811\pi$
$128$	−1.93428e25	−0.0883883
$129$	7.70794e24	0.0319571
$130$	0	0
$131$	−4.54456e26	−1.55454	−0.777268	−	0.629170i	$-0.783395\pi$
$131$	−4.54456e26	−1.55454	−0.777268	+	0.629170i	$0.783395\pi$
$132$	2.36814e25	0.0736602
$133$	−5.39999e26	−1.52844
$134$	4.75940e26	1.22671
$135$	0	0
$136$	−6.54581e25	−0.140193
$137$	5.90117e25	0.115327	0.0576635	−	0.998336i	$-0.481635\pi$
$137$	5.90117e25	0.115327	0.0576635	+	0.998336i	$0.481635\pi$
$138$	1.45426e25	0.0259510
$139$	−1.48479e26	−0.242091	−0.121046	−	0.992647i	$-0.538625\pi$
$139$	−1.48479e26	−0.242091	−0.121046	+	0.992647i	$0.538625\pi$
$140$	0	0
$141$	4.26921e25	0.0582249
$142$	−4.69405e26	−0.586062
$143$	6.87414e26	0.786173
$144$	−2.23119e26	−0.233886
$145$	0	0
$146$	3.62544e25	0.0319853
$147$	6.41088e26	0.519339
$148$	5.92809e26	0.441208
$149$	−5.34888e26	−0.365961	−0.182981	−	0.983117i	$-0.558575\pi$
$149$	−5.34888e26	−0.365961	−0.182981	+	0.983117i	$0.558575\pi$
$150$	0	0
$151$	2.12275e27	1.22938	0.614691	−	0.788768i	$-0.289281\pi$
$151$	2.12275e27	1.22938	0.614691	+	0.788768i	$0.289281\pi$
$152$	−5.80645e26	−0.309646
$153$	−7.55056e26	−0.370968
$154$	1.58112e27	0.716069
$155$	0	0
$156$	4.46213e26	0.171983
$157$	1.66162e26	0.0591271	0.0295636	−	0.999563i	$-0.490588\pi$
$157$	1.66162e26	0.0591271	0.0295636	+	0.999563i	$0.490588\pi$
$158$	−8.90456e26	−0.292684
$159$	−1.26234e27	−0.383454
$160$	0	0
$161$	9.70956e26	0.252276
$162$	−2.38413e27	−0.573314
$163$	2.97944e27	0.663421	0.331710	−	0.943381i	$-0.392374\pi$
$163$	2.97944e27	0.663421	0.331710	+	0.943381i	$0.392374\pi$
$164$	−3.95837e27	−0.816522
$165$	0	0
$166$	−2.64786e26	−0.0469401
$167$	8.95870e27	1.47329	0.736647	−	0.676278i	$-0.236408\pi$
$167$	8.95870e27	1.47329	0.736647	+	0.676278i	$0.236408\pi$
$168$	1.02633e27	0.156647
$169$	5.89610e27	0.835567
$170$	0	0
$171$	−6.69772e27	−0.819361
$172$	5.53367e26	0.0629372
$173$	1.40879e28	1.49028	0.745142	−	0.666905i	$-0.232381\pi$
$173$	1.40879e28	1.49028	0.745142	+	0.666905i	$0.232381\pi$
$174$	1.56369e27	0.153917
$175$	0	0
$176$	1.70013e27	0.145068
$177$	−2.64602e27	−0.210342
$178$	−1.46365e28	−1.08440
$179$	9.19738e27	0.635333	0.317667	−	0.948202i	$-0.397101\pi$
$179$	9.19738e27	0.635333	0.317667	+	0.948202i	$0.397101\pi$
$180$	0	0
$181$	2.77373e28	1.66756	0.833782	−	0.552094i	$-0.186171\pi$
$181$	2.77373e28	1.66756	0.833782	+	0.552094i	$0.186171\pi$
$182$	2.97920e28	1.67189
$183$	−6.62852e27	−0.347358
$184$	1.04404e27	0.0511087
$185$	0	0
$186$	7.48979e27	0.320301
$187$	5.75341e27	0.230094
$188$	3.06494e27	0.114670
$189$	2.44930e28	0.857570
$190$	0	0
$191$	−1.68120e28	−0.516064	−0.258032	−	0.966136i	$-0.583074\pi$
$191$	−1.68120e28	−0.516064	−0.258032	+	0.966136i	$0.583074\pi$
$192$	1.10358e27	0.0317351
$193$	−2.97967e28	−0.802975	−0.401487	−	0.915865i	$-0.631507\pi$
$193$	−2.97967e28	−0.802975	−0.401487	+	0.915865i	$0.631507\pi$
$194$	−1.02150e28	−0.258057
$195$	0	0
$196$	4.60248e28	1.02280
$197$	−8.93281e27	−0.186277	−0.0931387	−	0.995653i	$-0.529690\pi$
$197$	−8.93281e27	−0.186277	−0.0931387	+	0.995653i	$0.529690\pi$
$198$	1.96109e28	0.383869
$199$	−9.58646e28	−1.76196	−0.880978	−	0.473157i	$-0.843114\pi$
$199$	−9.58646e28	−1.76196	−0.880978	+	0.473157i	$0.843114\pi$
$200$	0	0
$201$	−2.71542e28	−0.440440
$202$	5.52159e28	0.841728
$203$	1.04402e29	1.49626
$204$	3.73464e27	0.0503352
$205$	0	0
$206$	−8.12956e28	−0.969899
$207$	1.20430e28	0.135240
$208$	3.20344e28	0.338708
$209$	5.10355e28	0.508211
$210$	0	0
$211$	5.69613e27	0.0503558	0.0251779	−	0.999683i	$-0.491985\pi$
$211$	5.69613e27	0.0503558	0.0251779	+	0.999683i	$0.491985\pi$
$212$	−9.06259e28	−0.755186
$213$	2.67814e28	0.210420
$214$	−2.70338e28	−0.200325
$215$	0	0
$216$	2.63366e28	0.173735
$217$	5.00065e29	3.11372
$218$	2.60278e28	0.153014
$219$	−2.06846e27	−0.0114840
$220$	0	0
$221$	1.08408e29	0.537226
$222$	−3.38221e28	−0.158412
$223$	5.84548e28	0.258827	0.129413	−	0.991591i	$-0.458691\pi$
$223$	5.84548e28	0.258827	0.129413	+	0.991591i	$0.458691\pi$
$224$	7.36821e28	0.308505
$225$	0	0
$226$	−2.09986e29	−0.786746
$227$	5.52270e29	1.95807	0.979035	−	0.203691i	$-0.0652938\pi$
$227$	5.52270e29	1.95807	0.979035	+	0.203691i	$0.0652938\pi$
$228$	3.31281e28	0.111176
$229$	−5.80273e28	−0.184369	−0.0921847	−	0.995742i	$-0.529385\pi$
$229$	−5.80273e28	−0.184369	−0.0921847	+	0.995742i	$0.529385\pi$
$230$	0	0
$231$	−9.02088e28	−0.257098
$232$	1.12260e29	0.303128
$233$	−1.93762e29	−0.495816	−0.247908	−	0.968784i	$-0.579743\pi$
$233$	−1.93762e29	−0.495816	−0.247908	+	0.968784i	$0.579743\pi$
$234$	3.69516e29	0.896261
$235$	0	0
$236$	−1.89962e29	−0.414254
$237$	5.08040e28	0.105086
$238$	2.49348e29	0.489321
$239$	7.15964e28	0.133327	0.0666634	−	0.997776i	$-0.478765\pi$
$239$	7.15964e28	0.133327	0.0666634	+	0.997776i	$0.478765\pi$
$240$	0	0
$241$	−8.42045e29	−1.41293	−0.706467	−	0.707746i	$-0.749712\pi$
$241$	−8.42045e29	−1.41293	−0.706467	+	0.707746i	$0.749712\pi$
$242$	2.94358e29	0.469011
$243$	4.60746e29	0.697241
$244$	−4.75873e29	−0.684098
$245$	0	0
$246$	2.25840e29	0.293165
$247$	9.61630e29	1.18658
$248$	5.37705e29	0.630809
$249$	1.51071e28	0.0168535
$250$	0	0
$251$	−3.23321e28	−0.0326372	−0.0163186	−	0.999867i	$-0.505195\pi$
$251$	−3.23321e28	−0.0326372	−0.0163186	+	0.999867i	$0.505195\pi$
$252$	8.49920e29	0.816340
$253$	−9.17654e28	−0.0838827
$254$	−6.22869e29	−0.541970
$255$	0	0
$256$	7.92282e28	0.0625000
$257$	−2.39756e29	−0.180138	−0.0900689	−	0.995936i	$-0.528709\pi$
$257$	−2.39756e29	−0.180138	−0.0900689	+	0.995936i	$0.528709\pi$
$258$	−3.15717e28	−0.0225971
$259$	−2.25817e30	−1.53996
$260$	0	0
$261$	1.29492e30	0.802114
$262$	1.86145e30	1.09922
$263$	2.50236e30	1.40898	0.704488	−	0.709716i	$-0.251177\pi$
$263$	2.50236e30	1.40898	0.704488	+	0.709716i	$0.251177\pi$
$264$	−9.69989e28	−0.0520856
$265$	0	0
$266$	2.21184e30	1.08077
$267$	8.35070e29	0.389343
$268$	−1.94945e30	−0.867415
$269$	3.20998e30	1.36332	0.681662	−	0.731667i	$-0.261257\pi$
$269$	3.20998e30	1.36332	0.681662	+	0.731667i	$0.261257\pi$
$270$	0	0
$271$	1.88885e30	0.731277	0.365638	−	0.930757i	$-0.380851\pi$
$271$	1.88885e30	0.731277	0.365638	+	0.930757i	$0.380851\pi$
$272$	2.68116e29	0.0991316
$273$	−1.69975e30	−0.600277
$274$	−2.41712e29	−0.0815485
$275$	0	0
$276$	−5.95666e28	−0.0183501
$277$	2.14925e29	0.0632835	0.0316417	−	0.999499i	$-0.489926\pi$
$277$	2.14925e29	0.0632835	0.0316417	+	0.999499i	$0.489926\pi$
$278$	6.08169e29	0.171184
$279$	6.20241e30	1.66920
$280$	0	0
$281$	−1.34905e30	−0.332048	−0.166024	−	0.986122i	$-0.553093\pi$
$281$	−1.34905e30	−0.332048	−0.166024	+	0.986122i	$0.553093\pi$
$282$	−1.74867e29	−0.0411712
$283$	7.01801e30	1.58082	0.790412	−	0.612576i	$-0.209867\pi$
$283$	7.01801e30	1.58082	0.790412	+	0.612576i	$0.209867\pi$
$284$	1.92268e30	0.414408
$285$	0	0
$286$	−2.81565e30	−0.555908
$287$	1.50785e31	2.84993
$288$	9.13894e29	0.165382
$289$	−4.86329e30	−0.842767
$290$	0	0
$291$	5.82805e29	0.0926533
$292$	−1.48498e29	−0.0226170
$293$	−4.23132e30	−0.617491	−0.308746	−	0.951145i	$-0.599909\pi$
$293$	−4.23132e30	−0.617491	−0.308746	+	0.951145i	$0.599909\pi$
$294$	−2.62590e30	−0.367228
$295$	0	0
$296$	−2.42815e30	−0.311981
$297$	−2.31484e30	−0.285145
$298$	2.19090e30	0.258774
$299$	−1.72908e30	−0.195850
$300$	0	0
$301$	−2.10793e30	−0.219672
$302$	−8.69478e30	−0.869304
$303$	−3.15028e30	−0.302215
$304$	2.37832e30	0.218953
$305$	0	0
$306$	3.09271e30	0.262314
$307$	−3.15394e30	−0.256817	−0.128409	−	0.991721i	$-0.540987\pi$
$307$	−3.15394e30	−0.256817	−0.128409	+	0.991721i	$0.540987\pi$
$308$	−6.47625e30	−0.506337
$309$	4.63823e30	0.348234
$310$	0	0
$311$	1.98559e31	1.37526	0.687628	−	0.726063i	$-0.258652\pi$
$311$	1.98559e31	1.37526	0.687628	+	0.726063i	$0.258652\pi$
$312$	−1.82769e30	−0.121610
$313$	−5.47200e29	−0.0349818	−0.0174909	−	0.999847i	$-0.505568\pi$
$313$	−5.47200e29	−0.0349818	−0.0174909	+	0.999847i	$0.505568\pi$
$314$	−6.80601e29	−0.0418092
$315$	0	0
$316$	3.64731e30	0.206959
$317$	−2.18550e31	−1.19209	−0.596046	−	0.802950i	$-0.703263\pi$
$317$	−2.18550e31	−1.19209	−0.596046	+	0.802950i	$0.703263\pi$
$318$	5.17056e30	0.271143
$319$	−9.86707e30	−0.497513
$320$	0	0
$321$	1.54238e30	0.0719249
$322$	−3.97704e30	−0.178386
$323$	8.04849e30	0.347282
$324$	9.76540e30	0.405394
$325$	0	0
$326$	−1.22038e31	−0.469109
$327$	−1.48499e30	−0.0549383
$328$	1.62135e31	0.577368
$329$	−1.16752e31	−0.400236
$330$	0	0
$331$	−2.93057e31	−0.931325	−0.465663	−	0.884962i	$-0.654184\pi$
$331$	−2.93057e31	−0.931325	−0.465663	+	0.884962i	$0.654184\pi$
$332$	1.08456e30	0.0331917
$333$	−2.80086e31	−0.825540
$334$	−3.66949e31	−1.04178
$335$	0	0
$336$	−4.20385e30	−0.110766
$337$	−4.60143e31	−1.16821	−0.584103	−	0.811680i	$-0.698553\pi$
$337$	−4.60143e31	−1.16821	−0.584103	+	0.811680i	$0.698553\pi$
$338$	−2.41504e31	−0.590835
$339$	1.19805e31	0.282474
$340$	0	0
$341$	−4.72613e31	−1.03532
$342$	2.74338e31	0.579376
$343$	−8.96148e31	−1.82475
$344$	−2.26659e30	−0.0445033
$345$	0	0
$346$	−5.77039e31	−1.05379
$347$	−7.38077e31	−1.30012	−0.650060	−	0.759883i	$-0.725256\pi$
$347$	−7.38077e31	−1.30012	−0.650060	+	0.759883i	$0.725256\pi$
$348$	−6.40489e30	−0.108836
$349$	3.56553e31	0.584530	0.292265	−	0.956337i	$-0.405591\pi$
$349$	3.56553e31	0.584530	0.292265	+	0.956337i	$0.405591\pi$
$350$	0	0
$351$	−4.36171e31	−0.665760
$352$	−6.96372e30	−0.102579
$353$	8.69355e31	1.23599	0.617993	−	0.786184i	$-0.287946\pi$
$353$	8.69355e31	1.23599	0.617993	+	0.786184i	$0.287946\pi$
$354$	1.08381e31	0.148735
$355$	0	0
$356$	5.99512e31	0.766783
$357$	−1.42263e31	−0.175686
$358$	−3.76725e31	−0.449248
$359$	2.26294e30	0.0260611	0.0130305	−	0.999915i	$-0.495852\pi$
$359$	2.26294e30	0.0260611	0.0130305	+	0.999915i	$0.495852\pi$
$360$	0	0
$361$	−2.16825e31	−0.232954
$362$	−1.13612e32	−1.17915
$363$	−1.67943e31	−0.168395
$364$	−1.22028e32	−1.18220
$365$	0	0
$366$	2.71504e31	0.245619
$367$	−3.34192e31	−0.292193	−0.146096	−	0.989270i	$-0.546671\pi$
$367$	−3.34192e31	−0.292193	−0.146096	+	0.989270i	$0.546671\pi$
$368$	−4.27639e30	−0.0361393
$369$	1.87022e32	1.52779
$370$	0	0
$371$	3.45219e32	2.63585
$372$	−3.06782e31	−0.226487
$373$	1.79027e32	1.27808	0.639041	−	0.769172i	$-0.279331\pi$
$373$	1.79027e32	1.27808	0.639041	+	0.769172i	$0.279331\pi$
$374$	−2.35660e31	−0.162701
$375$	0	0
$376$	−1.25540e31	−0.0810839
$377$	−1.85919e32	−1.16160
$378$	−1.00323e32	−0.606393
$379$	−9.45760e31	−0.553084	−0.276542	−	0.961002i	$-0.589188\pi$
$379$	−9.45760e31	−0.553084	−0.276542	+	0.961002i	$0.589188\pi$
$380$	0	0
$381$	3.55371e31	0.194590
$382$	6.88621e31	0.364912
$383$	−2.01782e32	−1.03490	−0.517449	−	0.855714i	$-0.673118\pi$
$383$	−2.01782e32	−1.03490	−0.517449	+	0.855714i	$0.673118\pi$
$384$	−4.52028e30	−0.0224401
$385$	0	0
$386$	1.22047e32	0.567789
$387$	−2.61450e31	−0.117761
$388$	4.18406e31	0.182474
$389$	1.16247e32	0.490921	0.245460	−	0.969407i	$-0.421061\pi$
$389$	1.16247e32	0.490921	0.245460	+	0.969407i	$0.421061\pi$
$390$	0	0
$391$	−1.44717e31	−0.0573207
$392$	−1.88518e32	−0.723230
$393$	−1.06203e32	−0.394667
$394$	3.65888e31	0.131718
$395$	0	0
$396$	−8.03262e31	−0.271436
$397$	−2.03760e32	−0.667172	−0.333586	−	0.942720i	$-0.608259\pi$
$397$	−2.03760e32	−0.667172	−0.333586	+	0.942720i	$0.608259\pi$
$398$	3.92662e32	1.24589
$399$	−1.26194e32	−0.388041
$400$	0	0
$401$	−1.67418e32	−0.483613	−0.241806	−	0.970324i	$-0.577740\pi$
$401$	−1.67418e32	−0.483613	−0.241806	+	0.970324i	$0.577740\pi$
$402$	1.11224e32	0.311438
$403$	−8.90515e32	−2.41729
$404$	−2.26164e32	−0.595192
$405$	0	0
$406$	−4.27630e32	−1.05802
$407$	2.13421e32	0.512043
$408$	−1.52971e31	−0.0355924
$409$	7.52295e32	1.69765	0.848823	−	0.528678i	$-0.177312\pi$
$409$	7.52295e32	1.69765	0.848823	+	0.528678i	$0.177312\pi$
$410$	0	0
$411$	1.37906e31	0.0292793
$412$	3.32987e32	0.685822
$413$	7.23618e32	1.44589
$414$	−4.93280e31	−0.0956288
$415$	0	0
$416$	−1.31213e32	−0.239503
$417$	−3.46984e31	−0.0614623
$418$	−2.09041e32	−0.359359
$419$	−6.25496e31	−0.104364	−0.0521818	−	0.998638i	$-0.516618\pi$
$419$	−6.25496e31	−0.104364	−0.0521818	+	0.998638i	$0.516618\pi$
$420$	0	0
$421$	8.02159e32	1.26106	0.630528	−	0.776167i	$-0.282838\pi$
$421$	8.02159e32	1.26106	0.630528	+	0.776167i	$0.282838\pi$
$422$	−2.33314e31	−0.0356069
$423$	−1.44810e32	−0.214558
$424$	3.71204e32	0.533997
$425$	0	0
$426$	−1.09697e32	−0.148790
$427$	1.81273e33	2.38773
$428$	1.10730e32	0.141651
$429$	1.60644e32	0.199594
$430$	0	0
$431$	1.32299e33	1.55092	0.775460	−	0.631397i	$-0.217518\pi$
$431$	1.32299e33	1.55092	0.775460	+	0.631397i	$0.217518\pi$
$432$	−1.07875e32	−0.122849
$433$	1.44206e33	1.59546	0.797730	−	0.603015i	$-0.206034\pi$
$433$	1.44206e33	1.59546	0.797730	+	0.603015i	$0.206034\pi$
$434$	−2.04827e33	−2.20173
$435$	0	0
$436$	−1.06610e32	−0.108197
$437$	−1.28371e32	−0.126605
$438$	8.47240e30	0.00812045
$439$	9.88019e32	0.920362	0.460181	−	0.887825i	$-0.347785\pi$
$439$	9.88019e32	0.920362	0.460181	+	0.887825i	$0.347785\pi$
$440$	0	0
$441$	−2.17454e33	−1.91375
$442$	−4.44038e32	−0.379876
$443$	6.78172e32	0.564018	0.282009	−	0.959412i	$-0.408999\pi$
$443$	6.78172e32	0.564018	0.282009	+	0.959412i	$0.408999\pi$
$444$	1.38535e32	0.112014
$445$	0	0
$446$	−2.39431e32	−0.183018
$447$	−1.25000e32	−0.0929104
$448$	−3.01802e32	−0.218146
$449$	−1.40094e33	−0.984784	−0.492392	−	0.870374i	$-0.663877\pi$
$449$	−1.40094e33	−0.984784	−0.492392	+	0.870374i	$0.663877\pi$
$450$	0	0
$451$	−1.42507e33	−0.947613
$452$	8.60102e32	0.556313
$453$	4.96071e32	0.312116
$454$	−2.26210e33	−1.38456
$455$	0	0
$456$	−1.35693e32	−0.0786132
$457$	2.87797e33	1.62231	0.811156	−	0.584830i	$-0.198839\pi$
$457$	2.87797e33	1.62231	0.811156	+	0.584830i	$0.198839\pi$
$458$	2.37680e32	0.130369
$459$	−3.65059e32	−0.194852
$460$	0	0
$461$	−4.62750e32	−0.233930	−0.116965	−	0.993136i	$-0.537316\pi$
$461$	−4.62750e32	−0.233930	−0.116965	+	0.993136i	$0.537316\pi$
$462$	3.69495e32	0.181796
$463$	2.53220e32	0.121265	0.0606325	−	0.998160i	$-0.480688\pi$
$463$	2.53220e32	0.121265	0.0606325	+	0.998160i	$0.480688\pi$
$464$	−4.59818e32	−0.214344
$465$	0	0
$466$	7.93650e32	0.350595
$467$	−1.56052e33	−0.671134	−0.335567	−	0.942016i	$-0.608928\pi$
$467$	−1.56052e33	−0.671134	−0.335567	+	0.942016i	$0.608928\pi$
$468$	−1.51354e33	−0.633752
$469$	7.42598e33	3.02757
$470$	0	0
$471$	3.88309e31	0.0150112
$472$	7.78085e32	0.292922
$473$	1.99221e32	0.0730416
$474$	−2.08093e32	−0.0743068
$475$	0	0
$476$	−1.02133e33	−0.346002
$477$	4.28182e33	1.41302
$478$	−2.93259e32	−0.0942763
$479$	7.23567e32	0.226613	0.113306	−	0.993560i	$-0.463856\pi$
$479$	7.23567e32	0.226613	0.113306	+	0.993560i	$0.463856\pi$
$480$	0	0
$481$	4.02135e33	1.19553
$482$	3.44901e33	0.999096
$483$	2.26905e32	0.0640480
$484$	−1.20569e33	−0.331641
$485$	0	0
$486$	−1.88721e33	−0.493024
$487$	3.11091e33	0.792091	0.396046	−	0.918231i	$-0.370382\pi$
$487$	3.11091e33	0.792091	0.396046	+	0.918231i	$0.370382\pi$
$488$	1.94918e33	0.483730
$489$	6.96273e32	0.168430
$490$	0	0
$491$	3.51132e33	0.807146	0.403573	−	0.914948i	$-0.367768\pi$
$491$	3.51132e33	0.807146	0.403573	+	0.914948i	$0.367768\pi$
$492$	−9.25042e32	−0.207299
$493$	−1.55607e33	−0.339972
$494$	−3.93883e33	−0.839037
$495$	0	0
$496$	−2.20244e33	−0.446050
$497$	−7.32402e33	−1.44642
$498$	−6.18787e31	−0.0119172
$499$	8.78119e33	1.64929	0.824644	−	0.565652i	$-0.191376\pi$
$499$	8.78119e33	1.64929	0.824644	+	0.565652i	$0.191376\pi$
$500$	0	0
$501$	2.09358e33	0.374041
$502$	1.32432e32	0.0230780
$503$	−1.68186e33	−0.285883	−0.142942	−	0.989731i	$-0.545656\pi$
$503$	−1.68186e33	−0.285883	−0.142942	+	0.989731i	$0.545656\pi$
$504$	−3.48127e33	−0.577240
$505$	0	0
$506$	3.75871e32	0.0593140
$507$	1.37788e33	0.212134
$508$	2.55127e33	0.383231
$509$	−5.67785e33	−0.832169	−0.416084	−	0.909326i	$-0.636598\pi$
$509$	−5.67785e33	−0.832169	−0.416084	+	0.909326i	$0.636598\pi$
$510$	0	0
$511$	5.65670e32	0.0789409
$512$	−3.24519e32	−0.0441942
$513$	−3.23825e33	−0.430372
$514$	9.82039e32	0.127377
$515$	0	0
$516$	1.29318e32	0.0159785
$517$	1.10343e33	0.133080
$518$	9.24948e33	1.08892
$519$	3.29224e33	0.378355
$520$	0	0
$521$	8.57848e33	0.939591	0.469796	−	0.882775i	$-0.344328\pi$
$521$	8.57848e33	0.939591	0.469796	+	0.882775i	$0.344328\pi$
$522$	−5.30399e33	−0.567180
$523$	1.65708e34	1.73010	0.865052	−	0.501683i	$-0.167286\pi$
$523$	1.65708e34	1.73010	0.865052	+	0.501683i	$0.167286\pi$
$524$	−7.62451e33	−0.777268
$525$	0	0
$526$	−1.02497e34	−0.996296
$527$	−7.45329e33	−0.707482
$528$	3.97307e32	0.0368301
$529$	−1.08149e34	−0.979103
$530$	0	0
$531$	8.97518e33	0.775107
$532$	−9.05968e33	−0.764218
$533$	−2.68518e34	−2.21250
$534$	−3.42045e33	−0.275307
$535$	0	0
$536$	7.98494e33	0.613355
$537$	2.14936e33	0.161299
$538$	−1.31481e34	−0.964016
$539$	1.65697e34	1.18701
$540$	0	0
$541$	−4.23198e33	−0.289453	−0.144727	−	0.989472i	$-0.546230\pi$
$541$	−4.23198e33	−0.289453	−0.144727	+	0.989472i	$0.546230\pi$
$542$	−7.73674e33	−0.517091
$543$	6.48202e33	0.423362
$544$	−1.09820e33	−0.0700966
$545$	0	0
$546$	6.96217e33	0.424460
$547$	−5.57179e33	−0.332011	−0.166006	−	0.986125i	$-0.553087\pi$
$547$	−5.57179e33	−0.332011	−0.166006	+	0.986125i	$0.553087\pi$
$548$	9.90052e32	0.0576635
$549$	2.24837e34	1.28001
$550$	0	0
$551$	−1.38031e34	−0.750900
$552$	2.43985e32	0.0129755
$553$	−1.38936e34	−0.722355
$554$	−8.80334e32	−0.0447482
$555$	0	0
$556$	−2.49106e33	−0.121046
$557$	−1.51207e34	−0.718427	−0.359213	−	0.933255i	$-0.616955\pi$
$557$	−1.51207e34	−0.718427	−0.359213	+	0.933255i	$0.616955\pi$
$558$	−2.54051e34	−1.18030
$559$	3.75379e33	0.170539
$560$	0	0
$561$	1.34453e33	0.0584164
$562$	5.52573e33	0.234793
$563$	1.21471e34	0.504799	0.252400	−	0.967623i	$-0.418780\pi$
$563$	1.21471e34	0.504799	0.252400	+	0.967623i	$0.418780\pi$
$564$	7.16255e32	0.0291125
$565$	0	0
$566$	−2.87458e34	−1.11781
$567$	−3.71991e34	−1.41496
$568$	−7.87531e33	−0.293031
$569$	2.58692e34	0.941628	0.470814	−	0.882232i	$-0.343960\pi$
$569$	2.58692e34	0.941628	0.470814	+	0.882232i	$0.343960\pi$
$570$	0	0
$571$	−3.34607e34	−1.16569	−0.582846	−	0.812583i	$-0.698061\pi$
$571$	−3.34607e34	−1.16569	−0.582846	+	0.812583i	$0.698061\pi$
$572$	1.15329e34	0.393086
$573$	−3.92885e33	−0.131019
$574$	−6.17615e34	−2.01521
$575$	0	0
$576$	−3.74331e33	−0.116943
$577$	−1.34968e34	−0.412603	−0.206302	−	0.978488i	$-0.566143\pi$
$577$	−1.34968e34	−0.412603	−0.206302	+	0.978488i	$0.566143\pi$
$578$	1.99201e34	0.595926
$579$	−6.96328e33	−0.203860
$580$	0	0
$581$	−4.13140e33	−0.115850
$582$	−2.38717e33	−0.0655158
$583$	−3.26268e34	−0.876429
$584$	6.08248e32	0.0159926
$585$	0	0
$586$	1.73315e34	0.436632
$587$	−4.17737e34	−1.03021	−0.515107	−	0.857126i	$-0.672248\pi$
$587$	−4.17737e34	−1.03021	−0.515107	+	0.857126i	$0.672248\pi$
$588$	1.07557e34	0.259670
$589$	−6.61143e34	−1.56262
$590$	0	0
$591$	−2.08753e33	−0.0472923
$592$	9.94569e33	0.220604
$593$	−2.55607e33	−0.0555123	−0.0277562	−	0.999615i	$-0.508836\pi$
$593$	−2.55607e33	−0.0555123	−0.0277562	+	0.999615i	$0.508836\pi$
$594$	9.48160e33	0.201628
$595$	0	0
$596$	−8.97394e33	−0.182981
$597$	−2.24029e34	−0.447327
$598$	7.08230e33	0.138487
$599$	4.70324e34	0.900662	0.450331	−	0.892862i	$-0.351306\pi$
$599$	4.70324e34	0.900662	0.450331	+	0.892862i	$0.351306\pi$
$600$	0	0
$601$	5.96787e34	1.09620	0.548099	−	0.836414i	$-0.315352\pi$
$601$	5.96787e34	1.09620	0.548099	+	0.836414i	$0.315352\pi$
$602$	8.63406e33	0.155331
$603$	9.21060e34	1.62301
$604$	3.56138e34	0.614691
$605$	0	0
$606$	1.29036e34	0.213699
$607$	−2.92667e34	−0.474804	−0.237402	−	0.971411i	$-0.576296\pi$
$607$	−2.92667e34	−0.474804	−0.237402	+	0.971411i	$0.576296\pi$
$608$	−9.74161e33	−0.154823
$609$	2.43980e34	0.379872
$610$	0	0
$611$	2.07912e34	0.310717
$612$	−1.26677e34	−0.185484
$613$	8.48844e34	1.21779	0.608895	−	0.793251i	$-0.291613\pi$
$613$	8.48844e34	1.21779	0.608895	+	0.793251i	$0.291613\pi$
$614$	1.29186e34	0.181597
$615$	0	0
$616$	2.65267e34	0.358034
$617$	1.30414e35	1.72488	0.862442	−	0.506156i	$-0.168934\pi$
$617$	1.30414e35	1.72488	0.862442	+	0.506156i	$0.168934\pi$
$618$	−1.89982e34	−0.246239
$619$	−8.02670e34	−1.01954	−0.509770	−	0.860311i	$-0.670269\pi$
$619$	−8.02670e34	−1.01954	−0.509770	+	0.860311i	$0.670269\pi$
$620$	0	0
$621$	5.82260e33	0.0710350
$622$	−8.13296e34	−0.972453
$623$	−2.28370e35	−2.67633
$624$	7.48621e33	0.0859913
$625$	0	0
$626$	2.24133e33	0.0247359
$627$	1.19266e34	0.129025
$628$	2.78774e33	0.0295636
$629$	3.36573e34	0.349901
$630$	0	0
$631$	−3.51125e34	−0.350828	−0.175414	−	0.984495i	$-0.556126\pi$
$631$	−3.51125e34	−0.350828	−0.175414	+	0.984495i	$0.556126\pi$
$632$	−1.49394e34	−0.146342
$633$	1.33115e33	0.0127844
$634$	8.95181e34	0.842937
$635$	0	0
$636$	−2.11786e34	−0.191727
$637$	3.12212e35	2.77145
$638$	4.04155e34	0.351795
$639$	−9.08413e34	−0.775394
$640$	0	0
$641$	−1.10476e35	−0.906862	−0.453431	−	0.891291i	$-0.649800\pi$
$641$	−1.10476e35	−0.906862	−0.453431	+	0.891291i	$0.649800\pi$
$642$	−6.31760e33	−0.0508586
$643$	5.33371e34	0.421107	0.210553	−	0.977582i	$-0.432473\pi$
$643$	5.33371e34	0.421107	0.210553	+	0.977582i	$0.432473\pi$
$644$	1.62899e34	0.126138
$645$	0	0
$646$	−3.29666e34	−0.245566
$647$	2.39579e34	0.175043	0.0875216	−	0.996163i	$-0.472105\pi$
$647$	2.39579e34	0.175043	0.0875216	+	0.996163i	$0.472105\pi$
$648$	−3.99991e34	−0.286657
$649$	−6.83894e34	−0.480762
$650$	0	0
$651$	1.16862e35	0.790514
$652$	4.99866e34	0.331710
$653$	6.46858e34	0.421109	0.210554	−	0.977582i	$-0.432473\pi$
$653$	6.46858e34	0.421109	0.210554	+	0.977582i	$0.432473\pi$
$654$	6.08250e33	0.0388472
$655$	0	0
$656$	−6.64104e34	−0.408261
$657$	7.01612e33	0.0423185
$658$	4.78217e34	0.283010
$659$	1.74748e35	1.01471	0.507357	−	0.861736i	$-0.330623\pi$
$659$	1.74748e35	1.01471	0.507357	+	0.861736i	$0.330623\pi$
$660$	0	0
$661$	2.05707e35	1.15009	0.575044	−	0.818123i	$-0.304985\pi$
$661$	2.05707e35	1.15009	0.575044	+	0.818123i	$0.304985\pi$
$662$	1.20036e35	0.658547
$663$	2.53341e34	0.136391
$664$	−4.44238e33	−0.0234701
$665$	0	0
$666$	1.14723e35	0.583745
$667$	2.48190e34	0.123940
$668$	1.50302e35	0.736647
$669$	1.36605e34	0.0657112
$670$	0	0
$671$	−1.71322e35	−0.793928
$672$	1.72190e34	0.0783234
$673$	1.94000e35	0.866190	0.433095	−	0.901348i	$-0.357421\pi$
$673$	1.94000e35	0.866190	0.433095	+	0.901348i	$0.357421\pi$
$674$	1.88475e35	0.826046
$675$	0	0
$676$	9.89201e34	0.417783
$677$	−1.50061e35	−0.622172	−0.311086	−	0.950382i	$-0.600693\pi$
$677$	−1.50061e35	−0.622172	−0.311086	+	0.950382i	$0.600693\pi$
$678$	−4.90722e34	−0.199740
$679$	−1.59382e35	−0.636895
$680$	0	0
$681$	1.29062e35	0.497116
$682$	1.93582e35	0.732084
$683$	−2.23175e35	−0.828679	−0.414339	−	0.910122i	$-0.635987\pi$
$683$	−2.23175e35	−0.828679	−0.414339	+	0.910122i	$0.635987\pi$
$684$	−1.12369e35	−0.409681
$685$	0	0
$686$	3.67062e35	1.29029
$687$	−1.35606e34	−0.0468078
$688$	9.28395e33	0.0314686
$689$	−6.14765e35	−2.04630
$690$	0	0
$691$	4.24403e34	0.136240	0.0681198	−	0.997677i	$-0.478300\pi$
$691$	4.24403e34	0.136240	0.0681198	+	0.997677i	$0.478300\pi$
$692$	2.36355e35	0.745142
$693$	3.05985e35	0.947402
$694$	3.02316e35	0.919324
$695$	0	0
$696$	2.62344e34	0.0769584
$697$	−2.24740e35	−0.647545
$698$	−1.46044e35	−0.413325
$699$	−4.52808e34	−0.125878
$700$	0	0
$701$	−6.67347e35	−1.79010	−0.895048	−	0.445969i	$-0.852859\pi$
$701$	−6.67347e35	−1.79010	−0.895048	+	0.445969i	$0.852859\pi$
$702$	1.78656e35	0.470764
$703$	2.98556e35	0.772831
$704$	2.85234e34	0.0725342
$705$	0	0
$706$	−3.56088e35	−0.873974
$707$	8.61522e35	2.07742
$708$	−4.43928e34	−0.105171
$709$	5.82085e35	1.35490	0.677452	−	0.735567i	$-0.263084\pi$
$709$	5.82085e35	1.35490	0.677452	+	0.735567i	$0.263084\pi$
$710$	0	0
$711$	−1.72325e35	−0.387238
$712$	−2.45560e35	−0.542198
$713$	1.18878e35	0.257919
$714$	5.82708e34	0.124229
$715$	0	0
$716$	1.54307e35	0.317667
$717$	1.67316e34	0.0338491
$718$	−9.26900e33	−0.0184280
$719$	−4.08106e35	−0.797374	−0.398687	−	0.917087i	$-0.630534\pi$
$719$	−4.08106e35	−0.797374	−0.398687	+	0.917087i	$0.630534\pi$
$720$	0	0
$721$	−1.26844e36	−2.39375
$722$	8.88115e34	0.164723
$723$	−1.96780e35	−0.358717
$724$	4.65355e35	0.833782
$725$	0	0
$726$	6.87893e34	0.119073
$727$	7.44759e34	0.126717	0.0633586	−	0.997991i	$-0.479819\pi$
$727$	7.44759e34	0.126717	0.0633586	+	0.997991i	$0.479819\pi$
$728$	4.99826e35	0.835943
$729$	−3.85503e35	−0.633772
$730$	0	0
$731$	3.14179e34	0.0499125
$732$	−1.11208e35	−0.173679
$733$	−1.00546e36	−1.54371	−0.771853	−	0.635802i	$-0.780670\pi$
$733$	−1.00546e36	−1.54371	−0.771853	+	0.635802i	$0.780670\pi$
$734$	1.36885e35	0.206612
$735$	0	0
$736$	1.75161e34	0.0255543
$737$	−7.01833e35	−1.00668
$738$	−7.66041e35	−1.08031
$739$	−7.42029e35	−1.02888	−0.514441	−	0.857526i	$-0.672001\pi$
$739$	−7.42029e35	−1.02888	−0.514441	+	0.857526i	$0.672001\pi$
$740$	0	0
$741$	2.24726e35	0.301249
$742$	−1.41402e36	−1.86383
$743$	−4.93877e35	−0.640115	−0.320058	−	0.947398i	$-0.603702\pi$
$743$	−4.93877e35	−0.640115	−0.320058	+	0.947398i	$0.603702\pi$
$744$	1.25658e35	0.160150
$745$	0	0
$746$	−7.33296e35	−0.903741
$747$	−5.12426e34	−0.0621046
$748$	9.65262e34	0.115047
$749$	−4.21802e35	−0.494409
$750$	0	0
$751$	1.60017e36	1.81413	0.907063	−	0.420995i	$-0.138319\pi$
$751$	1.60017e36	1.81413	0.907063	+	0.420995i	$0.138319\pi$
$752$	5.14212e34	0.0573349
$753$	−7.55579e33	−0.00828595
$754$	7.61524e35	0.821375
$755$	0	0
$756$	4.10924e35	0.428785
$757$	9.77978e34	0.100376	0.0501881	−	0.998740i	$-0.484018\pi$
$757$	9.77978e34	0.100376	0.0501881	+	0.998740i	$0.484018\pi$
$758$	3.87383e35	0.391089
$759$	−2.14449e34	−0.0212962
$760$	0	0
$761$	1.42035e36	1.36485	0.682427	−	0.730954i	$-0.260924\pi$
$761$	1.42035e36	1.36485	0.682427	+	0.730954i	$0.260924\pi$
$762$	−1.45560e35	−0.137596
$763$	4.06106e35	0.377644
$764$	−2.82059e35	−0.258032
$765$	0	0
$766$	8.26499e35	0.731784
$767$	−1.28862e36	−1.12249
$768$	1.85151e34	0.0158675
$769$	4.43106e35	0.373619	0.186809	−	0.982396i	$-0.440185\pi$
$769$	4.43106e35	0.373619	0.186809	+	0.982396i	$0.440185\pi$
$770$	0	0
$771$	−5.60292e34	−0.0457335
$772$	−4.99906e35	−0.401487
$773$	1.04683e36	0.827241	0.413621	−	0.910449i	$-0.364264\pi$
$773$	1.04683e36	0.827241	0.413621	+	0.910449i	$0.364264\pi$
$774$	1.07090e35	0.0832697
$775$	0	0
$776$	−1.71379e35	−0.129029
$777$	−5.27719e35	−0.390967
$778$	−4.76147e35	−0.347133
$779$	−1.99355e36	−1.43024
$780$	0	0
$781$	6.92196e35	0.480940
$782$	5.92763e34	0.0405319
$783$	6.26075e35	0.421313
$784$	7.72169e35	0.511401
$785$	0	0
$786$	4.35008e35	0.279071
$787$	−1.02940e36	−0.649977	−0.324989	−	0.945718i	$-0.605360\pi$
$787$	−1.02940e36	−0.649977	−0.324989	+	0.945718i	$0.605360\pi$
$788$	−1.49868e35	−0.0931387
$789$	5.84784e35	0.357712
$790$	0	0
$791$	−3.27636e36	−1.94172
$792$	3.29016e35	0.191934
$793$	−3.22811e36	−1.85367
$794$	8.34601e35	0.471762
$795$	0	0
$796$	−1.60834e36	−0.880978
$797$	−2.74499e36	−1.48017	−0.740086	−	0.672512i	$-0.765215\pi$
$797$	−2.74499e36	−1.48017	−0.740086	+	0.672512i	$0.765215\pi$
$798$	5.16890e35	0.274386
$799$	1.74015e35	0.0909393
$800$	0	0
$801$	−2.83252e36	−1.43472
$802$	6.85745e35	0.341966
$803$	−5.34617e34	−0.0262481
$804$	−4.55572e35	−0.220220
$805$	0	0
$806$	3.64755e36	1.70928
$807$	7.50150e35	0.346122
$808$	9.26369e35	0.420864
$809$	2.35511e36	1.05355	0.526776	−	0.850004i	$-0.323401\pi$
$809$	2.35511e36	1.05355	0.526776	+	0.850004i	$0.323401\pi$
$810$	0	0
$811$	3.33343e36	1.44587	0.722936	−	0.690915i	$-0.242792\pi$
$811$	3.33343e36	1.44587	0.722936	+	0.690915i	$0.242792\pi$
$812$	1.75157e36	0.748132
$813$	4.41411e35	0.185657
$814$	−8.74172e35	−0.362069
$815$	0	0
$816$	6.26569e34	0.0251676
$817$	2.78692e35	0.110242
$818$	−3.08140e36	−1.20042
$819$	5.76547e36	2.21201
$820$	0	0
$821$	1.82523e36	0.679249	0.339625	−	0.940561i	$-0.389700\pi$
$821$	1.82523e36	0.679249	0.339625	+	0.940561i	$0.389700\pi$
$822$	−5.64864e34	−0.0207036
$823$	−1.63571e36	−0.590483	−0.295241	−	0.955423i	$-0.595400\pi$
$823$	−1.63571e36	−0.590483	−0.295241	+	0.955423i	$0.595400\pi$
$824$	−1.36391e36	−0.484950
$825$	0	0
$826$	−2.96394e36	−1.02240
$827$	−3.73907e36	−1.27041	−0.635206	−	0.772342i	$-0.719085\pi$
$827$	−3.73907e36	−1.27041	−0.635206	+	0.772342i	$0.719085\pi$
$828$	2.02047e35	0.0676198
$829$	−3.08664e36	−1.01755	−0.508773	−	0.860901i	$-0.669901\pi$
$829$	−3.08664e36	−1.01755	−0.508773	+	0.860901i	$0.669901\pi$
$830$	0	0
$831$	5.02265e34	0.0160665
$832$	5.37448e35	0.169354
$833$	2.61310e36	0.811135
$834$	1.42125e35	0.0434604
$835$	0	0
$836$	8.56234e35	0.254105
$837$	2.99878e36	0.876750
$838$	2.56203e35	0.0737963
$839$	−3.69450e36	−1.04841	−0.524205	−	0.851592i	$-0.675637\pi$
$839$	−3.69450e36	−1.04841	−0.524205	+	0.851592i	$0.675637\pi$
$840$	0	0
$841$	−9.61704e35	−0.264906
$842$	−3.28564e36	−0.891701
$843$	−3.15264e35	−0.0843005
$844$	9.55652e34	0.0251779
$845$	0	0
$846$	5.93142e35	0.151715
$847$	4.59280e36	1.15754
$848$	−1.52045e36	−0.377593
$849$	1.64006e36	0.401341
$850$	0	0
$851$	−5.36825e35	−0.127560
$852$	4.49317e35	0.105210
$853$	7.36060e35	0.169844	0.0849220	−	0.996388i	$-0.472936\pi$
$853$	7.36060e35	0.169844	0.0849220	+	0.996388i	$0.472936\pi$
$854$	−7.42494e36	−1.68838
$855$	0	0
$856$	−4.53551e35	−0.100162
$857$	−5.06811e35	−0.110303	−0.0551513	−	0.998478i	$-0.517564\pi$
$857$	−5.06811e35	−0.110303	−0.0551513	+	0.998478i	$0.517564\pi$
$858$	−6.57997e35	−0.141134
$859$	7.80778e33	0.00165049	0.000825245	−	1.00000i	$-0.499737\pi$
$859$	7.80778e33	0.00165049	0.000825245		1.00000i	$0.499737\pi$
$860$	0	0
$861$	3.52374e36	0.723543
$862$	−5.41895e36	−1.09667
$863$	8.60176e36	1.71574	0.857871	−	0.513864i	$-0.171787\pi$
$863$	8.60176e36	1.71574	0.857871	+	0.513864i	$0.171787\pi$
$864$	4.41855e35	0.0868676
$865$	0	0
$866$	−5.90669e36	−1.12816
$867$	−1.13652e36	−0.213962
$868$	8.38970e36	1.55686
$869$	1.31309e36	0.240186
$870$	0	0
$871$	−1.32242e37	−2.35040
$872$	4.36673e35	0.0765069
$873$	−1.97685e36	−0.341425
$874$	5.25809e35	0.0895231
$875$	0	0
$876$	−3.47029e34	−0.00574202
$877$	7.33903e36	1.19714	0.598568	−	0.801072i	$-0.295737\pi$
$877$	7.33903e36	1.19714	0.598568	+	0.801072i	$0.295737\pi$
$878$	−4.04692e36	−0.650794
$879$	−9.88829e35	−0.156769
$880$	0	0
$881$	7.73442e36	1.19187	0.595935	−	0.803032i	$-0.296781\pi$
$881$	7.73442e36	1.19187	0.595935	+	0.803032i	$0.296781\pi$
$882$	8.90693e36	1.35323
$883$	−1.11931e37	−1.67664	−0.838320	−	0.545178i	$-0.816462\pi$
$883$	−1.11931e37	−1.67664	−0.838320	+	0.545178i	$0.816462\pi$
$884$	1.81878e36	0.268613
$885$	0	0
$886$	−2.77779e36	−0.398821
$887$	9.94167e36	1.40739	0.703695	−	0.710502i	$-0.251532\pi$
$887$	9.94167e36	1.40739	0.703695	+	0.710502i	$0.251532\pi$
$888$	−5.67441e35	−0.0792060
$889$	−9.71850e36	−1.33760
$890$	0	0
$891$	3.51570e36	0.470479
$892$	9.80709e35	0.129413
$893$	1.54360e36	0.200858
$894$	5.11998e35	0.0656976
$895$	0	0
$896$	1.23618e36	0.154252
$897$	−4.04073e35	−0.0497226
$898$	5.73826e36	0.696347
$899$	1.27824e37	1.52973
$900$	0	0
$901$	−5.14536e36	−0.598902
$902$	5.83711e36	0.670063
$903$	−4.92607e35	−0.0557704
$904$	−3.52298e36	−0.393373
$905$	0	0
$906$	−2.03191e36	−0.220700
$907$	−2.49643e36	−0.267441	−0.133721	−	0.991019i	$-0.542692\pi$
$907$	−2.49643e36	−0.267441	−0.133721	+	0.991019i	$0.542692\pi$
$908$	9.26555e36	0.979035
$909$	1.06856e37	1.11366
$910$	0	0
$911$	9.34594e36	0.947640	0.473820	−	0.880622i	$-0.342875\pi$
$911$	9.34594e36	0.947640	0.473820	+	0.880622i	$0.342875\pi$
$912$	5.55797e35	0.0555879
$913$	3.90461e35	0.0385205
$914$	−1.17882e37	−1.14715
$915$	0	0
$916$	−9.73537e35	−0.0921847
$917$	2.90438e37	2.71292
$918$	1.49528e36	0.137781
$919$	2.08298e37	1.89340	0.946698	−	0.322122i	$-0.104396\pi$
$919$	2.08298e37	1.89340	0.946698	+	0.322122i	$0.104396\pi$
$920$	0	0
$921$	−7.37054e35	−0.0652010
$922$	1.89543e36	0.165413
$923$	1.30426e37	1.12291
$924$	−1.51345e36	−0.128549
$925$	0	0
$926$	−1.03719e36	−0.0857474
$927$	−1.57327e37	−1.28323
$928$	1.88342e36	0.151564
$929$	−2.93833e36	−0.233294	−0.116647	−	0.993173i	$-0.537215\pi$
$929$	−2.93833e36	−0.233294	−0.116647	+	0.993173i	$0.537215\pi$
$930$	0	0
$931$	2.31795e37	1.79156
$932$	−3.25079e36	−0.247908
$933$	4.64017e36	0.349151
$934$	6.39190e36	0.474563
$935$	0	0
$936$	6.19944e36	0.448131
$937$	−1.33465e37	−0.951968	−0.475984	−	0.879454i	$-0.657908\pi$
$937$	−1.33465e37	−0.951968	−0.475984	+	0.879454i	$0.657908\pi$
$938$	−3.04168e37	−2.14081
$939$	−1.27877e35	−0.00888120
$940$	0	0
$941$	−1.37070e37	−0.926983	−0.463492	−	0.886101i	$-0.653404\pi$
$941$	−1.37070e37	−0.926983	−0.463492	+	0.886101i	$0.653404\pi$
$942$	−1.59051e35	−0.0106145
$943$	3.58454e36	0.236068
$944$	−3.18704e36	−0.207127
$945$	0	0
$946$	−8.16009e35	−0.0516482
$947$	3.73876e36	0.233535	0.116768	−	0.993159i	$-0.462747\pi$
$947$	3.73876e36	0.233535	0.116768	+	0.993159i	$0.462747\pi$
$948$	8.52350e35	0.0525429
$949$	−1.00734e36	−0.0612845
$950$	0	0
$951$	−5.10736e36	−0.302649
$952$	4.18336e36	0.244660
$953$	−4.80715e36	−0.277477	−0.138738	−	0.990329i	$-0.544305\pi$
$953$	−4.80715e36	−0.277477	−0.138738	+	0.990329i	$0.544305\pi$
$954$	−1.75383e37	−0.999156
$955$	0	0
$956$	1.20119e36	0.0666634
$957$	−2.30586e36	−0.126309
$958$	−2.96373e36	−0.160240
$959$	−3.77138e36	−0.201265
$960$	0	0
$961$	4.19922e37	2.18336
$962$	−1.64715e37	−0.845364
$963$	−5.23170e36	−0.265042
$964$	−1.41272e37	−0.706467
$965$	0	0
$966$	−9.29405e35	−0.0452888
$967$	1.46042e37	0.702498	0.351249	−	0.936282i	$-0.385757\pi$
$967$	1.46042e37	0.702498	0.351249	+	0.936282i	$0.385757\pi$
$968$	4.93850e36	0.234506
$969$	1.88087e36	0.0881683
$970$	0	0
$971$	−3.16381e37	−1.44534	−0.722670	−	0.691193i	$-0.757085\pi$
$971$	−3.16381e37	−1.44534	−0.722670	+	0.691193i	$0.757085\pi$
$972$	7.73003e36	0.348620
$973$	9.48913e36	0.422490
$974$	−1.27423e37	−0.560093
$975$	0	0
$976$	−7.98382e36	−0.342049
$977$	−3.15815e37	−1.33583	−0.667914	−	0.744239i	$-0.732812\pi$
$977$	−3.15815e37	−1.33583	−0.667914	+	0.744239i	$0.732812\pi$
$978$	−2.85193e36	−0.119098
$979$	2.15834e37	0.889889
$980$	0	0
$981$	5.03701e36	0.202446
$982$	−1.43824e37	−0.570738
$983$	1.30026e37	0.509461	0.254731	−	0.967012i	$-0.418013\pi$
$983$	1.30026e37	0.509461	0.254731	+	0.967012i	$0.418013\pi$
$984$	3.78897e36	0.146583
$985$	0	0
$986$	6.37368e36	0.240397
$987$	−2.72841e36	−0.101612
$988$	1.61335e37	0.593288
$989$	−5.01107e35	−0.0181960
$990$	0	0
$991$	1.69845e37	0.601355	0.300677	−	0.953726i	$-0.402787\pi$
$991$	1.69845e37	0.601355	0.300677	+	0.953726i	$0.402787\pi$
$992$	9.02119e36	0.315405
$993$	−6.84852e36	−0.236446
$994$	2.99992e37	1.02277
$995$	0	0
$996$	2.53455e35	0.00842673
$997$	1.43944e37	0.472612	0.236306	−	0.971679i	$-0.424063\pi$
$997$	1.43944e37	0.472612	0.236306	+	0.971679i	$0.424063\pi$
$998$	−3.59677e37	−1.16622
$999$	−1.35418e37	−0.433617

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.26.a.k.1.4		6
5.2	odd	4		10.26.b.a.9.3	✓	12
5.3	odd	4		10.26.b.a.9.10	yes	12
5.4	even	2		50.26.a.l.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.b.a.9.3	✓	12	5.2	odd	4
10.26.b.a.9.10	yes	12	5.3	odd	4
50.26.a.k.1.4		6	1.1	even	1	trivial
50.26.a.l.1.3		6	5.4	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	50.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} +233693. q^{3} +1.67772e7 q^{4} -9.57206e8 q^{6} -6.39090e10 q^{7} -6.87195e10 q^{8} -7.92676e11 q^{9} +6.04007e12 q^{11} +3.92071e12 q^{12} +1.13809e14 q^{13} +2.61771e14 q^{14} +2.81475e14 q^{16} +9.52541e14 q^{17} +3.24680e15 q^{18} +8.44950e15 q^{19} -1.49351e16 q^{21} -2.47401e16 q^{22} -1.51928e16 q^{23} -1.60592e16 q^{24} -4.66162e17 q^{26} -3.83248e17 q^{27} -1.07222e18 q^{28} -1.63360e18 q^{29} -7.82464e18 q^{31} -1.15292e18 q^{32} +1.41152e18 q^{33} -3.90161e18 q^{34} -1.32989e19 q^{36} +3.53342e19 q^{37} -3.46091e19 q^{38} +2.65964e19 q^{39} -2.35937e20 q^{41} +6.11741e19 q^{42} +3.29832e19 q^{43} +1.01335e20 q^{44} +6.22296e19 q^{46} +1.82685e20 q^{47} +6.57787e19 q^{48} +2.74329e21 q^{49} +2.22602e20 q^{51} +1.90940e21 q^{52} -5.40172e21 q^{53} +1.56978e21 q^{54} +4.39179e21 q^{56} +1.97459e21 q^{57} +6.69124e21 q^{58} -1.13226e22 q^{59} -2.83642e22 q^{61} +3.20497e22 q^{62} +5.06592e22 q^{63} +4.72237e21 q^{64} -5.78158e21 q^{66} -1.16196e23 q^{67} +1.59810e22 q^{68} -3.55044e21 q^{69} +1.14601e23 q^{71} +5.44723e22 q^{72} -8.85118e21 q^{73} -1.44729e23 q^{74} +1.41759e23 q^{76} -3.86015e23 q^{77} -1.08939e23 q^{78} +2.17397e23 q^{79} +5.82063e23 q^{81} +9.66398e23 q^{82} +6.46451e22 q^{83} -2.50569e23 q^{84} -1.35099e23 q^{86} -3.81761e23 q^{87} -4.15070e23 q^{88} +3.57337e24 q^{89} -7.27343e24 q^{91} -2.54893e23 q^{92} -1.82856e24 q^{93} -7.48277e23 q^{94} -2.69429e23 q^{96} +2.49389e24 q^{97} -1.12365e25 q^{98} -4.78782e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 24576 q^{2} + 801416 q^{3} + 100663296 q^{4} - 3282599936 q^{6} + 34007705352 q^{7} - 412316860416 q^{8} + 541468782118 q^{9} + 9861544614312 q^{11} + 13445529337856 q^{12} + 30787386783696 q^{13}+ \cdots - 20\!\cdots\!64 q^{99}+O(q^{100}) \) 6 * q - 24576 * q^2 + 801416 * q^3 + 100663296 * q^4 - 3282599936 * q^6 + 34007705352 * q^7 - 412316860416 * q^8 + 541468782118 * q^9 + 9861544614312 * q^11 + 13445529337856 * q^12 + 30787386783696 * q^13 - 139295561121792 * q^14 + 1688849860263936 * q^16 + 3432836939805312 * q^17 - 2217856131555328 * q^18 + 2007656488916520 * q^19 - 28181710291014728 * q^21 - 40392886740221952 * q^22 + 135711886432707576 * q^23 - 55072888167858176 * q^24 - 126105136266018816 * q^26 + 788054364552235760 * q^27 + 570554618354860032 * q^28 - 2926032031655504820 * q^29 + 79292935777014912 * q^31 - 6917529027641081856 * q^32 - 6844843638395003168 * q^33 - 14060900105442557952 * q^34 + 9084338714850623488 * q^36 + 3345885298190974032 * q^37 - 8223360978602065920 * q^38 + 124726636622561793456 * q^39 + 103229301719876244012 * q^41 + 115432285351996325888 * q^42 + 166390524239317503336 * q^43 + 165449264087949115392 * q^44 - 555875886828370231296 * q^46 + 405906243391034677992 * q^47 + 225578549935547088896 * q^48 + 1716280748139027694542 * q^49 - 1516225893661962013568 * q^51 + 516526638145613070336 * q^52 + 9772760301640799789616 * q^53 - 3227870677205957672960 * q^54 - 2336991716781506691072 * q^56 + 26174725126915157341920 * q^57 + 11985027201660947742720 * q^58 - 12499075130880780168840 * q^59 + 3687285610311118296612 * q^61 - 324783864942653079552 * q^62 + 93007818034972665339656 * q^63 + 28334198897217871282176 * q^64 + 28036479542865932976128 * q^66 + 16759935062266648886712 * q^67 + 57593446831892717371392 * q^68 + 185125325982378999854536 * q^69 + 74568876221253661649712 * q^71 - 37209451376028153806848 * q^72 + 381797761857106829638176 * q^73 - 13704746181390229635072 * q^74 + 33682886568354062008320 * q^76 - 80271541631956375339296 * q^77 - 510880303606013105995776 * q^78 - 400850316873811624799520 * q^79 - 1432110118616113828343714 * q^81 - 422827219844613095473152 * q^82 - 2423159733509985740001144 * q^83 - 472810640801776950837248 * q^84 - 681535587284244493664256 * q^86 - 1231328665433636473947120 * q^87 - 677680185704239576645632 * q^88 + 2982172528060341024616740 * q^89 - 7001711719121019241314768 * q^91 + 2276867632449004467388416 * q^92 - 8806417055581711481018368 * q^93 - 1662591972929678041055232 * q^94 - 923969740536000876118016 * q^96 - 4960469410756873985567808 * q^97 - 7029885944377457436844032 * q^98 - 2053720289282411723573464 * q^99

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