LMFDB - Embedded newform 25.28.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,28,Mod(1,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 28, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	25.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:	$115.463893710$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{18209}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 4552 $ x^2 - x - 4552
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{3}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 1)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-66.9704$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+18713.6 q^{2} +3.44127e6 q^{3} +2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11 q^{7} +1.53009e12 q^{8} +4.21675e12 q^{9} +O(q^{10})$	\(q+18713.6 q^{2} +3.44127e6 q^{3} +2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11 q^{7} +1.53009e12 q^{8} +4.21675e12 q^{9} +2.06714e14 q^{11} +7.43249e14 q^{12} +1.66656e14 q^{13} +3.68421e15 q^{14} -3.55072e14 q^{16} +5.47219e15 q^{17} +7.89105e16 q^{18} +1.61471e17 q^{19} +6.77495e17 q^{21} +3.86837e18 q^{22} -2.80341e18 q^{23} +5.26544e18 q^{24} +3.11874e18 q^{26} -1.17308e19 q^{27} +4.25209e19 q^{28} -2.99842e18 q^{29} +9.09190e19 q^{31} -2.12009e20 q^{32} +7.11360e20 q^{33} +1.02404e20 q^{34} +9.10738e20 q^{36} -1.50001e21 q^{37} +3.02171e21 q^{38} +5.73510e20 q^{39} +5.47146e21 q^{41} +1.26784e22 q^{42} +6.81035e21 q^{43} +4.46463e22 q^{44} -5.24619e22 q^{46} +9.41657e21 q^{47} -1.22190e21 q^{48} -2.69532e22 q^{49} +1.88313e22 q^{51} +3.59946e22 q^{52} +5.35936e22 q^{53} -2.19525e23 q^{54} +3.01233e23 q^{56} +5.55667e23 q^{57} -5.61113e22 q^{58} +9.16258e23 q^{59} +1.47362e24 q^{61} +1.70142e24 q^{62} +8.30166e23 q^{63} -3.91980e24 q^{64} +1.33121e25 q^{66} +3.21915e24 q^{67} +1.18189e24 q^{68} -9.64729e24 q^{69} +3.38255e24 q^{71} +6.45199e24 q^{72} -1.32172e25 q^{73} -2.80705e25 q^{74} +3.48748e25 q^{76} +4.06965e25 q^{77} +1.07324e25 q^{78} +4.66230e25 q^{79} -7.25240e25 q^{81} +1.02391e26 q^{82} -7.14690e25 q^{83} +1.46326e26 q^{84} +1.27446e26 q^{86} -1.03184e25 q^{87} +3.16290e26 q^{88} -1.40708e26 q^{89} +3.28102e25 q^{91} -6.05484e26 q^{92} +3.12877e26 q^{93} +1.76218e26 q^{94} -7.29582e26 q^{96} -3.77568e26 q^{97} -5.04391e26 q^{98} +8.71662e26 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} + 86882873184 q^{6} + 175391963600 q^{7} + 3195032348160 q^{8} + 1235136554154 q^{9}+O(q^{10}) $ 2 * q + 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 + 86882873184 * q^6 + 175391963600 * q^7 + 3195032348160 * q^8 + 1235136554154 * q^9	$ 2 q + 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} + 86882873184 q^{6} + 175391963600 q^{7} + 3195032348160 q^{8} + 1235136554154 q^{9} + 138167337691944 q^{11} + 797895007176960 q^{12} + 753433801271060 q^{13} + 39\!\cdots\!12 q^{14}+ \cdots + 10\!\cdots\!88 q^{99}+O(q^{100}) $ 2 * q + 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 + 86882873184 * q^6 + 175391963600 * q^7 + 3195032348160 * q^8 + 1235136554154 * q^9 + 138167337691944 * q^11 + 797895007176960 * q^12 + 753433801271060 * q^13 + 3908340052811712 * q^14 - 14322995785166848 * q^16 + 29753620331011740 * q^17 + 110019470226337080 * q^18 + 404565810372684760 * q^19 + 723787313583184704 * q^21 + 4583556785578779360 * q^22 - 2929078923121218960 * q^23 + 1677495533792532480 * q^24 - 3003459254146640016 * q^26 + 11127665129740313040 * q^27 + 43065656535315868160 * q^28 - 15546679995448558260 * q^29 + 28544554594467385024 * q^31 - 289738949030869893120 * q^32 + 859077391009750054560 * q^33 - 150938335185934859568 * q^34 + 986344620988374211392 * q^36 - 1867697204682824566780 * q^37 + 485361223888169521440 * q^38 - 690990221801025527472 * q^39 + 9081343698046512254964 * q^41 + 12195371021026332061440 * q^42 - 5145612605801421773800 * q^43 + 46384541037574305299712 * q^44 - 51150723570313970279616 * q^46 + 1150251488862201070560 * q^47 + 28878849836569912688640 * q^48 - 92204113217840907690414 * q^49 - 33494974704727214464656 * q^51 + 21115266673184124022400 * q^52 - 106953735591470060758620 * q^53 - 458020779785618027135040 * q^54 + 265467760964859260989440 * q^56 + 31800538920577362634080 * q^57 + 74812163717162466470160 * q^58 + 2009620977624026488631880 * q^59 + 147857426692448940370444 * q^61 + 2352212714010270811080960 * q^62 + 894215232558851858338320 * q^63 - 1234057803938137445761024 * q^64 + 11770868153144268253438848 * q^66 - 3051578535738098902157560 * q^67 + 566166870324676171716480 * q^68 - 9376480489705868528695872 * q^69 - 13175198820369338598286416 * q^71 + 1487763126543110308830720 * q^72 - 5284260812951286572116660 * q^73 - 24234145145448525537787728 * q^74 + 28710432717942786872615680 * q^76 + 42169025756092787413646400 * q^77 + 23925717325436558555851200 * q^78 + 62814351035720719918179040 * q^79 - 99047155826597708238103278 * q^81 + 64726649726985190956760560 * q^82 - 171806873410054757883176280 * q^83 + 145152183633423443589998592 * q^84 + 252189883901197432712215584 * q^86 + 16722988656204557792643120 * q^87 + 202163623954874235550955520 * q^88 - 313473438761105539763494380 * q^89 + 20205365125040878536694304 * q^91 - 602296848225491467788034560 * q^92 + 447293490375807514724002560 * q^93 + 262465434750720041893579392 * q^94 - 562074901098402916384505856 * q^96 + 653202933397052842883888060 * q^97 + 176410316250092689584969240 * q^98 + 1076041779280842335610479688 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	18713.6	1.61530	0.807648	−	0.589664i	$-0.200740\pi$
$2$	18713.6	1.61530	0.807648	+	0.589664i	$0.200740\pi$
$3$	3.44127e6	1.24618	0.623092	−	0.782149i	$-0.285876\pi$
$3$	3.44127e6	1.24618	0.623092	+	0.782149i	$0.285876\pi$
$4$	2.15981e8	1.60918
$5$	0	0
$5$	0	0
$6$	6.43986e10	2.01296
$7$	1.96873e11	0.768004	0.384002	−	0.923332i	$-0.374546\pi$
$7$	1.96873e11	0.768004	0.384002	+	0.923332i	$0.374546\pi$
$8$	1.53009e12	0.984013
$9$	4.21675e12	0.552973
$10$	0	0
$11$	2.06714e14	1.80538	0.902691	−	0.430290i	$-0.141589\pi$
$11$	2.06714e14	1.80538	0.902691	+	0.430290i	$0.141589\pi$
$12$	7.43249e14	2.00534
$13$	1.66656e14	0.152611	0.0763057	−	0.997084i	$-0.475688\pi$
$13$	1.66656e14	0.152611	0.0763057	+	0.997084i	$0.475688\pi$
$14$	3.68421e15	1.24055
$15$	0	0
$16$	−3.55072e14	−0.0197105
$17$	5.47219e15	0.133999	0.0669994	−	0.997753i	$-0.478657\pi$
$17$	5.47219e15	0.133999	0.0669994	+	0.997753i	$0.478657\pi$
$18$	7.89105e16	0.893215
$19$	1.61471e17	0.880891	0.440445	−	0.897779i	$-0.354821\pi$
$19$	1.61471e17	0.880891	0.440445	+	0.897779i	$0.354821\pi$
$20$	0	0
$21$	6.77495e17	0.957074
$22$	3.86837e18	2.91623
$23$	−2.80341e18	−1.15974	−0.579870	−	0.814709i	$-0.696897\pi$
$23$	−2.80341e18	−1.15974	−0.579870	+	0.814709i	$0.696897\pi$
$24$	5.26544e18	1.22626
$25$	0	0
$26$	3.11874e18	0.246513
$27$	−1.17308e19	−0.557078
$28$	4.25209e19	1.23586
$29$	−2.99842e18	−0.0542650	−0.0271325	−	0.999632i	$-0.508638\pi$
$29$	−2.99842e18	−0.0542650	−0.0271325	+	0.999632i	$0.508638\pi$
$30$	0	0
$31$	9.09190e19	0.668763	0.334381	−	0.942438i	$-0.391473\pi$
$31$	9.09190e19	0.668763	0.334381	+	0.942438i	$0.391473\pi$
$32$	−2.12009e20	−1.01585
$33$	7.11360e20	2.24984
$34$	1.02404e20	0.216448
$35$	0	0
$36$	9.10738e20	0.889835
$37$	−1.50001e21	−1.01244	−0.506220	−	0.862404i	$-0.668958\pi$
$37$	−1.50001e21	−1.01244	−0.506220	+	0.862404i	$0.668958\pi$
$38$	3.02171e21	1.42290
$39$	5.73510e20	0.190182
$40$	0	0
$41$	5.47146e21	0.923679	0.461840	−	0.886963i	$-0.347190\pi$
$41$	5.47146e21	0.923679	0.461840	+	0.886963i	$0.347190\pi$
$42$	1.26784e22	1.54596
$43$	6.81035e21	0.604429	0.302215	−	0.953240i	$-0.402274\pi$
$43$	6.81035e21	0.604429	0.302215	+	0.953240i	$0.402274\pi$
$44$	4.46463e22	2.90519
$45$	0	0
$46$	−5.24619e22	−1.87333
$47$	9.41657e21	0.251520	0.125760	−	0.992061i	$-0.459863\pi$
$47$	9.41657e21	0.251520	0.125760	+	0.992061i	$0.459863\pi$
$48$	−1.22190e21	−0.0245628
$49$	−2.69532e22	−0.410169
$50$	0	0
$51$	1.88313e22	0.166987
$52$	3.59946e22	0.245580
$53$	5.35936e22	0.282741	0.141370	−	0.989957i	$-0.454849\pi$
$53$	5.35936e22	0.282741	0.141370	+	0.989957i	$0.454849\pi$
$54$	−2.19525e23	−0.899846
$55$	0	0
$56$	3.01233e23	0.755726
$57$	5.55667e23	1.09775
$58$	−5.61113e22	−0.0876541
$59$	9.16258e23	1.13636	0.568180	−	0.822904i	$-0.307648\pi$
$59$	9.16258e23	1.13636	0.568180	+	0.822904i	$0.307648\pi$
$60$	0	0
$61$	1.47362e24	1.16529	0.582643	−	0.812728i	$-0.302019\pi$
$61$	1.47362e24	1.16529	0.582643	+	0.812728i	$0.302019\pi$
$62$	1.70142e24	1.08025
$63$	8.30166e23	0.424685
$64$	−3.91980e24	−1.62119
$65$	0	0
$66$	1.33121e25	3.63415
$67$	3.21915e24	0.717349	0.358675	−	0.933463i	$-0.383229\pi$
$67$	3.21915e24	0.717349	0.358675	+	0.933463i	$0.383229\pi$
$68$	1.18189e24	0.215629
$69$	−9.64729e24	−1.44525
$70$	0	0
$71$	3.38255e24	0.344554	0.172277	−	0.985049i	$-0.444888\pi$
$71$	3.38255e24	0.344554	0.172277	+	0.985049i	$0.444888\pi$
$72$	6.45199e24	0.544133
$73$	−1.32172e25	−0.925295	−0.462648	−	0.886542i	$-0.653100\pi$
$73$	−1.32172e25	−0.925295	−0.462648	+	0.886542i	$0.653100\pi$
$74$	−2.80705e25	−1.63539
$75$	0	0
$76$	3.48748e25	1.41752
$77$	4.06965e25	1.38654
$78$	1.07324e25	0.307200
$79$	4.66230e25	1.12366	0.561830	−	0.827253i	$-0.310098\pi$
$79$	4.66230e25	1.12366	0.561830	+	0.827253i	$0.310098\pi$
$80$	0	0
$81$	−7.25240e25	−1.24719
$82$	1.02391e26	1.49202
$83$	−7.14690e25	−0.884226	−0.442113	−	0.896959i	$-0.645771\pi$
$83$	−7.14690e25	−0.884226	−0.442113	+	0.896959i	$0.645771\pi$
$84$	1.46326e26	1.54011
$85$	0	0
$86$	1.27446e26	0.976332
$87$	−1.03184e25	−0.0676242
$88$	3.16290e26	1.77652
$89$	−1.40708e26	−0.678504	−0.339252	−	0.940696i	$-0.610174\pi$
$89$	−1.40708e26	−0.678504	−0.339252	+	0.940696i	$0.610174\pi$
$90$	0	0
$91$	3.28102e25	0.117206
$92$	−6.05484e26	−1.86624
$93$	3.12877e26	0.833401
$94$	1.76218e26	0.406279
$95$	0	0
$96$	−7.29582e26	−1.26594
$97$	−3.77568e26	−0.569609	−0.284805	−	0.958586i	$-0.591929\pi$
$97$	−3.77568e26	−0.569609	−0.284805	+	0.958586i	$0.591929\pi$
$98$	−5.04391e26	−0.662545
$99$	8.71662e26	0.998327
$100$	0	0
$101$	−1.82546e27	−1.59600	−0.798002	−	0.602654i	$-0.794110\pi$
$101$	−1.82546e27	−1.59600	−0.798002	+	0.602654i	$0.794110\pi$
$102$	3.52401e26	0.269734
$103$	−2.87048e27	−1.92598	−0.962991	−	0.269534i	$-0.913130\pi$
$103$	−2.87048e27	−1.92598	−0.962991	+	0.269534i	$0.913130\pi$
$104$	2.54999e26	0.150172
$105$	0	0
$106$	1.00293e27	0.456710
$107$	1.31331e27	0.526849	0.263425	−	0.964680i	$-0.415148\pi$
$107$	1.31331e27	0.526849	0.263425	+	0.964680i	$0.415148\pi$
$108$	−2.53362e27	−0.896441
$109$	−3.16013e27	−0.987296	−0.493648	−	0.869662i	$-0.664337\pi$
$109$	−3.16013e27	−0.987296	−0.493648	+	0.869662i	$0.664337\pi$
$110$	0	0
$111$	−5.16192e27	−1.26169
$112$	−6.99043e25	−0.0151377
$113$	−3.68033e27	−0.706851	−0.353425	−	0.935463i	$-0.614983\pi$
$113$	−3.68033e27	−0.706851	−0.353425	+	0.935463i	$0.614983\pi$
$114$	1.03985e28	1.77319
$115$	0	0
$116$	−6.47603e26	−0.0873224
$117$	7.02748e26	0.0843899
$118$	1.71465e28	1.83556
$119$	1.07733e27	0.102912
$120$	0	0
$121$	2.96208e28	2.25940
$122$	2.75767e28	1.88228
$123$	1.88288e28	1.15107
$124$	1.96368e28	1.07616
$125$	0	0
$126$	1.55354e28	0.685993
$127$	2.69227e28	1.06849	0.534243	−	0.845331i	$-0.320597\pi$
$127$	2.69227e28	1.06849	0.534243	+	0.845331i	$0.320597\pi$
$128$	−4.48982e28	−1.60285
$129$	2.34363e28	0.753229
$130$	0	0
$131$	3.17810e28	0.829860	0.414930	−	0.909853i	$-0.363806\pi$
$131$	3.17810e28	0.829860	0.414930	+	0.909853i	$0.363806\pi$
$132$	1.53640e29	3.62040
$133$	3.17894e28	0.676528
$134$	6.02418e28	1.15873
$135$	0	0
$136$	8.37292e27	0.131857
$137$	−2.13194e28	−0.304122	−0.152061	−	0.988371i	$-0.548591\pi$
$137$	−2.13194e28	−0.304122	−0.152061	+	0.988371i	$0.548591\pi$
$138$	−1.80536e29	−2.33451
$139$	−1.15969e29	−1.36032	−0.680161	−	0.733062i	$-0.738090\pi$
$139$	−1.15969e29	−1.36032	−0.680161	+	0.733062i	$0.738090\pi$
$140$	0	0
$141$	3.24050e28	0.313439
$142$	6.32998e28	0.556557
$143$	3.44502e28	0.275522
$144$	−1.49725e27	−0.0108993
$145$	0	0
$146$	−2.47341e29	−1.49463
$147$	−9.27533e28	−0.511146
$148$	−3.23973e29	−1.62920
$149$	2.70481e29	1.24200	0.621000	−	0.783810i	$-0.286727\pi$
$149$	2.70481e29	1.24200	0.621000	+	0.783810i	$0.286727\pi$
$150$	0	0
$151$	6.43669e28	0.246873	0.123437	−	0.992352i	$-0.460608\pi$
$151$	6.43669e28	0.246873	0.123437	+	0.992352i	$0.460608\pi$
$152$	2.47065e29	0.866808
$153$	2.30748e28	0.0740977
$154$	7.61579e29	2.23968
$155$	0	0
$156$	1.23867e29	0.306037
$157$	7.36476e29	1.66922	0.834609	−	0.550842i	$-0.185693\pi$
$157$	7.36476e29	1.66922	0.834609	+	0.550842i	$0.185693\pi$
$158$	8.72484e29	1.81504
$159$	1.84430e29	0.352347
$160$	0	0
$161$	−5.51917e29	−0.890686
$162$	−1.35718e30	−2.01459
$163$	−4.91659e29	−0.671632	−0.335816	−	0.941928i	$-0.609012\pi$
$163$	−4.91659e29	−0.671632	−0.335816	+	0.941928i	$0.609012\pi$
$164$	1.18173e30	1.48637
$165$	0	0
$166$	−1.33744e30	−1.42829
$167$	−6.37427e29	−0.627709	−0.313854	−	0.949471i	$-0.601620\pi$
$167$	−6.37427e29	−0.627709	−0.313854	+	0.949471i	$0.601620\pi$
$168$	1.03663e30	0.941774
$169$	−1.16476e30	−0.976710
$170$	0	0
$171$	6.80884e29	0.487109
$172$	1.47091e30	0.972638
$173$	−2.71145e30	−1.65798	−0.828989	−	0.559265i	$-0.811083\pi$
$173$	−2.71145e30	−1.65798	−0.828989	+	0.559265i	$0.811083\pi$
$174$	−1.93094e29	−0.109233
$175$	0	0
$176$	−7.33984e28	−0.0355849
$177$	3.15309e30	1.41611
$178$	−2.63315e30	−1.09599
$179$	−1.65055e30	−0.636961	−0.318481	−	0.947929i	$-0.603173\pi$
$179$	−1.65055e30	−0.636961	−0.318481	+	0.947929i	$0.603173\pi$
$180$	0	0
$181$	4.30260e30	1.42913	0.714563	−	0.699571i	$-0.246626\pi$
$181$	4.30260e30	1.42913	0.714563	+	0.699571i	$0.246626\pi$
$182$	6.13997e29	0.189323
$183$	5.07112e30	1.45216
$184$	−4.28946e30	−1.14120
$185$	0	0
$186$	5.85506e30	1.34619
$187$	1.13118e30	0.241919
$188$	2.03380e30	0.404741
$189$	−2.30948e30	−0.427838
$190$	0	0
$191$	5.35850e30	0.861177	0.430589	−	0.902548i	$-0.358306\pi$
$191$	5.35850e30	0.861177	0.430589	+	0.902548i	$0.358306\pi$
$192$	−1.34891e31	−2.02030
$193$	−2.47114e30	−0.345044	−0.172522	−	0.985006i	$-0.555192\pi$
$193$	−2.47114e30	−0.345044	−0.172522	+	0.985006i	$0.555192\pi$
$194$	−7.06566e30	−0.920088
$195$	0	0
$196$	−5.82138e30	−0.660038
$197$	4.41349e30	0.467185	0.233592	−	0.972335i	$-0.424952\pi$
$197$	4.41349e30	0.467185	0.233592	+	0.972335i	$0.424952\pi$
$198$	1.63119e31	1.61259
$199$	−1.58034e31	−1.45960	−0.729802	−	0.683658i	$-0.760388\pi$
$199$	−1.58034e31	−1.45960	−0.729802	+	0.683658i	$0.760388\pi$
$200$	0	0
$201$	1.10780e31	0.893949
$202$	−3.41610e31	−2.57802
$203$	−5.90310e29	−0.0416758
$204$	4.06720e30	0.268713
$205$	0	0
$206$	−5.37170e31	−3.11103
$207$	−1.18213e31	−0.641305
$208$	−5.91750e28	−0.00300804
$209$	3.33784e31	1.59034
$210$	0	0
$211$	−1.50086e31	−0.628820	−0.314410	−	0.949287i	$-0.601807\pi$
$211$	−1.50086e31	−0.628820	−0.314410	+	0.949287i	$0.601807\pi$
$212$	1.15752e31	0.454982
$213$	1.16403e31	0.429377
$214$	2.45768e31	0.851018
$215$	0	0
$216$	−1.79491e31	−0.548172
$217$	1.78995e31	0.513613
$218$	−5.91374e31	−1.59478
$219$	−4.54839e31	−1.15309
$220$	0	0
$221$	9.11975e29	0.0204497
$222$	−9.65982e31	−2.03800
$223$	1.04534e31	0.207559	0.103779	−	0.994600i	$-0.466906\pi$
$223$	1.04534e31	0.207559	0.103779	+	0.994600i	$0.466906\pi$
$224$	−4.17390e31	−0.780178
$225$	0	0
$226$	−6.88722e31	−1.14177
$227$	−9.45028e31	−1.47603	−0.738016	−	0.674783i	$-0.764237\pi$
$227$	−9.45028e31	−1.47603	−0.738016	+	0.674783i	$0.764237\pi$
$228$	1.20013e32	1.76648
$229$	−6.26689e31	−0.869508	−0.434754	−	0.900549i	$-0.643165\pi$
$229$	−6.26689e31	−0.869508	−0.434754	+	0.900549i	$0.643165\pi$
$230$	0	0
$231$	1.40048e32	1.72788
$232$	−4.58785e30	−0.0533975
$233$	−7.87335e31	−0.864678	−0.432339	−	0.901711i	$-0.642312\pi$
$233$	−7.87335e31	−0.864678	−0.432339	+	0.901711i	$0.642312\pi$
$234$	1.31509e31	0.136315
$235$	0	0
$236$	1.97894e32	1.82861
$237$	1.60442e32	1.40029
$238$	2.01607e31	0.166233
$239$	−5.65108e30	−0.0440311	−0.0220156	−	0.999758i	$-0.507008\pi$
$239$	−5.65108e30	−0.0440311	−0.0220156	+	0.999758i	$0.507008\pi$
$240$	0	0
$241$	−4.42939e31	−0.308400	−0.154200	−	0.988040i	$-0.549280\pi$
$241$	−4.42939e31	−0.308400	−0.154200	+	0.988040i	$0.549280\pi$
$242$	5.54311e32	3.64961
$243$	−1.60121e32	−0.997154
$244$	3.18274e32	1.87516
$245$	0	0
$246$	3.52354e32	1.85933
$247$	2.69102e31	0.134434
$248$	1.39114e32	0.658071
$249$	−2.45944e32	−1.10191
$250$	0	0
$251$	−3.28116e32	−1.31957	−0.659785	−	0.751454i	$-0.729353\pi$
$251$	−3.28116e32	−1.31957	−0.659785	+	0.751454i	$0.729353\pi$
$252$	1.79300e32	0.683397
$253$	−5.79505e32	−2.09377
$254$	5.03822e32	1.72592
$255$	0	0
$256$	−3.14099e32	−0.967894
$257$	−3.48288e31	−0.101822	−0.0509109	−	0.998703i	$-0.516212\pi$
$257$	−3.48288e31	−0.101822	−0.0509109	+	0.998703i	$0.516212\pi$
$258$	4.38577e32	1.21669
$259$	−2.95311e32	−0.777559
$260$	0	0
$261$	−1.26436e31	−0.0300071
$262$	5.94736e32	1.34047
$263$	−3.82694e31	−0.0819311	−0.0409656	−	0.999161i	$-0.513043\pi$
$263$	−3.82694e31	−0.0819311	−0.0409656	+	0.999161i	$0.513043\pi$
$264$	1.08844e33	2.21387
$265$	0	0
$266$	5.94895e32	1.09279
$267$	−4.84213e32	−0.845541
$268$	6.95274e32	1.15435
$269$	−4.44965e31	−0.0702539	−0.0351269	−	0.999383i	$-0.511184\pi$
$269$	−4.44965e31	−0.0702539	−0.0351269	+	0.999383i	$0.511184\pi$
$270$	0	0
$271$	3.62870e32	0.518401	0.259200	−	0.965824i	$-0.416541\pi$
$271$	3.62870e32	0.518401	0.259200	+	0.965824i	$0.416541\pi$
$272$	−1.94302e30	−0.00264118
$273$	1.12909e32	0.146060
$274$	−3.98963e32	−0.491247
$275$	0	0
$276$	−2.08363e33	−2.32567
$277$	−1.40758e33	−1.49622	−0.748111	−	0.663574i	$-0.769039\pi$
$277$	−1.40758e33	−1.49622	−0.748111	+	0.663574i	$0.769039\pi$
$278$	−2.17020e33	−2.19733
$279$	3.83383e32	0.369808
$280$	0	0
$281$	3.59534e32	0.314924	0.157462	−	0.987525i	$-0.449669\pi$
$281$	3.59534e32	0.314924	0.157462	+	0.987525i	$0.449669\pi$
$282$	6.06414e32	0.506298
$283$	3.59177e32	0.285885	0.142943	−	0.989731i	$-0.454344\pi$
$283$	3.59177e32	0.285885	0.142943	+	0.989731i	$0.454344\pi$
$284$	7.30568e32	0.554451
$285$	0	0
$286$	6.44688e32	0.445049
$287$	1.07719e33	0.709390
$288$	−8.93990e32	−0.561738
$289$	−1.63777e33	−0.982044
$290$	0	0
$291$	−1.29931e33	−0.709838
$292$	−2.85466e33	−1.48897
$293$	−3.51312e32	−0.174976	−0.0874882	−	0.996166i	$-0.527884\pi$
$293$	−3.51312e32	−0.174976	−0.0874882	+	0.996166i	$0.527884\pi$
$294$	−1.73575e33	−0.825653
$295$	0	0
$296$	−2.29514e33	−0.996255
$297$	−2.42492e33	−1.00574
$298$	5.06167e33	2.00620
$299$	−4.67206e32	−0.176990
$300$	0	0
$301$	1.34078e33	0.464204
$302$	1.20454e33	0.398773
$303$	−6.28191e33	−1.98891
$304$	−5.73340e31	−0.0173628
$305$	0	0
$306$	4.31813e32	0.119690
$307$	6.75654e32	0.179208	0.0896038	−	0.995977i	$-0.471440\pi$
$307$	6.75654e32	0.179208	0.0896038	+	0.995977i	$0.471440\pi$
$308$	8.78968e33	2.23120
$309$	−9.87810e33	−2.40013
$310$	0	0
$311$	5.16690e33	1.15071	0.575354	−	0.817905i	$-0.304864\pi$
$311$	5.16690e33	1.15071	0.575354	+	0.817905i	$0.304864\pi$
$312$	8.77519e32	0.187141
$313$	1.10679e33	0.226056	0.113028	−	0.993592i	$-0.463945\pi$
$313$	1.10679e33	0.226056	0.113028	+	0.993592i	$0.463945\pi$
$314$	1.37821e34	2.69628
$315$	0	0
$316$	1.00697e34	1.80817
$317$	9.49991e33	1.63463	0.817315	−	0.576191i	$-0.195461\pi$
$317$	9.49991e33	1.63463	0.817315	+	0.576191i	$0.195461\pi$
$318$	3.45135e33	0.569145
$319$	−6.19817e32	−0.0979691
$320$	0	0
$321$	4.51946e33	0.656551
$322$	−1.03284e34	−1.43872
$323$	8.83602e32	0.118038
$324$	−1.56638e34	−2.00696
$325$	0	0
$326$	−9.20072e33	−1.08489
$327$	−1.08749e34	−1.23035
$328$	8.37180e33	0.908913
$329$	1.85387e33	0.193168
$330$	0	0
$331$	−1.25351e34	−1.20351	−0.601757	−	0.798679i	$-0.705533\pi$
$331$	−1.25351e34	−1.20351	−0.601757	+	0.798679i	$0.705533\pi$
$332$	−1.54359e34	−1.42288
$333$	−6.32514e33	−0.559852
$334$	−1.19286e34	−1.01394
$335$	0	0
$336$	−2.40560e32	−0.0188644
$337$	3.36740e33	0.253683	0.126842	−	0.991923i	$-0.459516\pi$
$337$	3.36740e33	0.253683	0.126842	+	0.991923i	$0.459516\pi$
$338$	−2.17968e34	−1.57768
$339$	−1.26650e34	−0.880865
$340$	0	0
$341$	1.87943e34	1.20737
$342$	1.27418e34	0.786825
$343$	−1.82434e34	−1.08302
$344$	1.04204e34	0.594766
$345$	0	0
$346$	−5.07409e34	−2.67813
$347$	1.91545e34	0.972353	0.486177	−	0.873861i	$-0.338391\pi$
$347$	1.91545e34	0.972353	0.486177	+	0.873861i	$0.338391\pi$
$348$	−2.22858e33	−0.108820
$349$	1.45433e34	0.683158	0.341579	−	0.939853i	$-0.389038\pi$
$349$	1.45433e34	0.683158	0.341579	+	0.939853i	$0.389038\pi$
$350$	0	0
$351$	−1.95501e33	−0.0850164
$352$	−4.38253e34	−1.83400
$353$	4.39359e33	0.176954	0.0884772	−	0.996078i	$-0.471800\pi$
$353$	4.39359e33	0.176954	0.0884772	+	0.996078i	$0.471800\pi$
$354$	5.90057e34	2.28744
$355$	0	0
$356$	−3.03902e34	−1.09184
$357$	3.70738e33	0.128247
$358$	−3.08877e34	−1.02888
$359$	2.60550e34	0.835828	0.417914	−	0.908487i	$-0.362761\pi$
$359$	2.60550e34	0.835828	0.417914	+	0.908487i	$0.362761\pi$
$360$	0	0
$361$	−7.52760e33	−0.224032
$362$	8.05172e34	2.30846
$363$	1.01933e35	2.81563
$364$	7.08639e33	0.188606
$365$	0	0
$366$	9.48990e34	2.34567
$367$	−3.50053e34	−0.833953	−0.416977	−	0.908917i	$-0.636910\pi$
$367$	−3.50053e34	−0.833953	−0.416977	+	0.908917i	$0.636910\pi$
$368$	9.95413e32	0.0228590
$369$	2.30718e34	0.510770
$370$	0	0
$371$	1.05512e34	0.217146
$372$	6.75755e34	1.34110
$373$	2.06100e34	0.394464	0.197232	−	0.980357i	$-0.436805\pi$
$373$	2.06100e34	0.394464	0.197232	+	0.980357i	$0.436805\pi$
$374$	2.11684e34	0.390771
$375$	0	0
$376$	1.44082e34	0.247499
$377$	−4.99707e32	−0.00828146
$378$	−4.32186e34	−0.691086
$379$	−3.69120e34	−0.569559	−0.284779	−	0.958593i	$-0.591920\pi$
$379$	−3.69120e34	−0.569559	−0.284779	+	0.958593i	$0.591920\pi$
$380$	0	0
$381$	9.26485e34	1.33153
$382$	1.00277e35	1.39106
$383$	−6.12833e34	−0.820652	−0.410326	−	0.911939i	$-0.634585\pi$
$383$	−6.12833e34	−0.820652	−0.410326	+	0.911939i	$0.634585\pi$
$384$	−1.54507e35	−1.99745
$385$	0	0
$386$	−4.62439e34	−0.557348
$387$	2.87175e34	0.334233
$388$	−8.15476e34	−0.916606
$389$	5.65060e34	0.613444	0.306722	−	0.951799i	$-0.400768\pi$
$389$	5.65060e34	0.613444	0.306722	+	0.951799i	$0.400768\pi$
$390$	0	0
$391$	−1.53408e34	−0.155404
$392$	−4.12407e34	−0.403612
$393$	1.09367e35	1.03416
$394$	8.25924e34	0.754642
$395$	0	0
$396$	1.88262e35	1.60649
$397$	2.20649e35	1.81983	0.909915	−	0.414794i	$-0.136146\pi$
$397$	2.20649e35	1.81983	0.909915	+	0.414794i	$0.136146\pi$
$398$	−2.95739e35	−2.35769
$399$	1.09396e35	0.843078
$400$	0	0
$401$	−1.87612e35	−1.35148	−0.675741	−	0.737139i	$-0.736176\pi$
$401$	−1.87612e35	−1.35148	−0.675741	+	0.737139i	$0.736176\pi$
$402$	2.07308e35	1.44399
$403$	1.51522e34	0.102061
$404$	−3.94265e35	−2.56827
$405$	0	0
$406$	−1.10468e34	−0.0673188
$407$	−3.10072e35	−1.82784
$408$	2.88135e34	0.164317
$409$	2.22853e35	1.22957	0.614786	−	0.788694i	$-0.289242\pi$
$409$	2.22853e35	1.22957	0.614786	+	0.788694i	$0.289242\pi$
$410$	0	0
$411$	−7.33658e34	−0.378991
$412$	−6.19970e35	−3.09926
$413$	1.80387e35	0.872729
$414$	−2.21219e35	−1.03590
$415$	0	0
$416$	−3.53327e34	−0.155030
$417$	−3.99081e35	−1.69521
$418$	6.24631e35	2.56888
$419$	−5.47879e34	−0.218170	−0.109085	−	0.994032i	$-0.534792\pi$
$419$	−5.47879e34	−0.218170	−0.109085	+	0.994032i	$0.534792\pi$
$420$	0	0
$421$	−1.97758e35	−0.738458	−0.369229	−	0.929338i	$-0.620378\pi$
$421$	−1.97758e35	−0.738458	−0.369229	+	0.929338i	$0.620378\pi$
$422$	−2.80864e35	−1.01573
$423$	3.97073e34	0.139083
$424$	8.20028e34	0.278221
$425$	0	0
$426$	2.17832e35	0.693572
$427$	2.90116e35	0.894945
$428$	2.83650e35	0.847798
$429$	1.18553e35	0.343350
$430$	0	0
$431$	−4.94928e35	−1.34617	−0.673083	−	0.739567i	$-0.735030\pi$
$431$	−4.94928e35	−1.34617	−0.673083	+	0.739567i	$0.735030\pi$
$432$	4.16527e33	0.0109803
$433$	−3.12882e35	−0.799454	−0.399727	−	0.916634i	$-0.630895\pi$
$433$	−3.12882e35	−0.799454	−0.399727	+	0.916634i	$0.630895\pi$
$434$	3.34965e35	0.829637
$435$	0	0
$436$	−6.82528e35	−1.58874
$437$	−4.52671e35	−1.02160
$438$	−8.51168e35	−1.86258
$439$	7.22790e35	1.53370	0.766852	−	0.641824i	$-0.221822\pi$
$439$	7.22790e35	1.53370	0.766852	+	0.641824i	$0.221822\pi$
$440$	0	0
$441$	−1.13655e35	−0.226813
$442$	1.70663e34	0.0330324
$443$	7.68142e35	1.44209	0.721043	−	0.692891i	$-0.243663\pi$
$443$	7.68142e35	1.44209	0.721043	+	0.692891i	$0.243663\pi$
$444$	−1.11488e36	−2.03029
$445$	0	0
$446$	1.95620e35	0.335269
$447$	9.30798e35	1.54776
$448$	−7.71705e35	−1.24508
$449$	−6.52536e35	−1.02160	−0.510798	−	0.859701i	$-0.670650\pi$
$449$	−6.52536e35	−1.02160	−0.510798	+	0.859701i	$0.670650\pi$
$450$	0	0
$451$	1.13103e36	1.66759
$452$	−7.94881e35	−1.13745
$453$	2.21504e35	0.307649
$454$	−1.76849e36	−2.38423
$455$	0	0
$456$	8.50218e35	1.08020
$457$	−6.21081e35	−0.766090	−0.383045	−	0.923730i	$-0.625125\pi$
$457$	−6.21081e35	−0.766090	−0.383045	+	0.923730i	$0.625125\pi$
$458$	−1.17276e36	−1.40451
$459$	−6.41930e34	−0.0746477
$460$	0	0
$461$	1.02161e36	1.12027	0.560133	−	0.828402i	$-0.310750\pi$
$461$	1.02161e36	1.12027	0.560133	+	0.828402i	$0.310750\pi$
$462$	2.62080e36	2.79105
$463$	1.10341e36	1.14129	0.570643	−	0.821199i	$-0.306694\pi$
$463$	1.10341e36	1.14129	0.570643	+	0.821199i	$0.306694\pi$
$464$	1.06466e33	0.00106959
$465$	0	0
$466$	−1.47339e36	−1.39671
$467$	−8.66440e35	−0.797922	−0.398961	−	0.916968i	$-0.630629\pi$
$467$	−8.66440e35	−0.797922	−0.398961	+	0.916968i	$0.630629\pi$
$468$	1.51780e35	0.135799
$469$	6.33764e35	0.550927
$470$	0	0
$471$	2.53441e36	2.08015
$472$	1.40195e36	1.11819
$473$	1.40780e36	1.09123
$474$	3.00246e36	2.26188
$475$	0	0
$476$	2.32683e35	0.165604
$477$	2.25991e35	0.156348
$478$	−1.05752e35	−0.0711234
$479$	−2.57345e36	−1.68262	−0.841311	−	0.540552i	$-0.818215\pi$
$479$	−2.57345e36	−1.68262	−0.841311	+	0.540552i	$0.818215\pi$
$480$	0	0
$481$	−2.49985e35	−0.154510
$482$	−8.28899e35	−0.498157
$483$	−1.89930e36	−1.10996
$484$	6.39752e36	3.63580
$485$	0	0
$486$	−2.99643e36	−1.61070
$487$	2.28927e36	1.19690	0.598448	−	0.801162i	$-0.295784\pi$
$487$	2.28927e36	1.19690	0.598448	+	0.801162i	$0.295784\pi$
$488$	2.25476e36	1.14666
$489$	−1.69193e36	−0.836977
$490$	0	0
$491$	1.74114e36	0.815142	0.407571	−	0.913174i	$-0.366376\pi$
$491$	1.74114e36	0.815142	0.407571	+	0.913174i	$0.366376\pi$
$492$	4.06666e36	1.85229
$493$	−1.64079e34	−0.00727145
$494$	5.03587e35	0.217151
$495$	0	0
$496$	−3.22828e34	−0.0131816
$497$	6.65935e35	0.264619
$498$	−4.60250e36	−1.77991
$499$	2.80174e36	1.05456	0.527278	−	0.849693i	$-0.323213\pi$
$499$	2.80174e36	1.05456	0.527278	+	0.849693i	$0.323213\pi$
$500$	0	0
$501$	−2.19356e36	−0.782240
$502$	−6.14024e36	−2.13150
$503$	−3.44032e36	−1.16260	−0.581301	−	0.813688i	$-0.697456\pi$
$503$	−3.44032e36	−1.16260	−0.581301	+	0.813688i	$0.697456\pi$
$504$	1.27022e36	0.417896
$505$	0	0
$506$	−1.08446e37	−3.38207
$507$	−4.00825e36	−1.21716
$508$	5.81480e36	1.71939
$509$	1.50719e35	0.0433989	0.0216995	−	0.999765i	$-0.493092\pi$
$509$	1.50719e35	0.0433989	0.0216995	+	0.999765i	$0.493092\pi$
$510$	0	0
$511$	−2.60211e36	−0.710631
$512$	1.48198e35	0.0394183
$513$	−1.89418e36	−0.490725
$514$	−6.51772e35	−0.164473
$515$	0	0
$516$	5.06179e36	1.21208
$517$	1.94654e36	0.454089
$518$	−5.52634e36	−1.25599
$519$	−9.33082e36	−2.06614
$520$	0	0
$521$	8.14778e36	1.71289	0.856446	−	0.516236i	$-0.172667\pi$
$521$	8.14778e36	1.71289	0.856446	+	0.516236i	$0.172667\pi$
$522$	−2.36607e35	−0.0484704
$523$	4.14380e36	0.827229	0.413615	−	0.910452i	$-0.364266\pi$
$523$	4.14380e36	0.827229	0.413615	+	0.910452i	$0.364266\pi$
$524$	6.86409e36	1.33540
$525$	0	0
$526$	−7.16158e35	−0.132343
$527$	4.97526e35	0.0896133
$528$	−2.52584e35	−0.0443453
$529$	2.01590e36	0.344999
$530$	0	0
$531$	3.86363e36	0.628376
$532$	6.86591e36	1.08866
$533$	9.11854e35	0.140964
$534$	−9.06137e36	−1.36580
$535$	0	0
$536$	4.92557e36	0.705881
$537$	−5.67999e36	−0.793770
$538$	−8.32690e35	−0.113481
$539$	−5.57161e36	−0.740512
$540$	0	0
$541$	1.06017e37	1.34033	0.670163	−	0.742214i	$-0.266224\pi$
$541$	1.06017e37	1.34033	0.670163	+	0.742214i	$0.266224\pi$
$542$	6.79060e36	0.837371
$543$	1.48064e37	1.78095
$544$	−1.16016e36	−0.136123
$545$	0	0
$546$	2.11293e36	0.235931
$547$	−8.42305e36	−0.917573	−0.458786	−	0.888547i	$-0.651716\pi$
$547$	−8.42305e36	−0.917573	−0.458786	+	0.888547i	$0.651716\pi$
$548$	−4.60459e36	−0.489388
$549$	6.21388e36	0.644371
$550$	0	0
$551$	−4.84160e35	−0.0478016
$552$	−1.47612e37	−1.42214
$553$	9.17883e36	0.862975
$554$	−2.63409e37	−2.41684
$555$	0	0
$556$	−2.50471e37	−2.18901
$557$	5.59363e36	0.477143	0.238571	−	0.971125i	$-0.423321\pi$
$557$	5.59363e36	0.477143	0.238571	+	0.971125i	$0.423321\pi$
$558$	7.17447e36	0.597349
$559$	1.13499e36	0.0922427
$560$	0	0
$561$	3.89269e36	0.301475
$562$	6.72818e36	0.508695
$563$	−2.06136e37	−1.52157	−0.760783	−	0.649006i	$-0.775185\pi$
$563$	−2.06136e37	−1.52157	−0.760783	+	0.649006i	$0.775185\pi$
$564$	6.99886e36	0.504382
$565$	0	0
$566$	6.72150e36	0.461790
$567$	−1.42780e37	−0.957850
$568$	5.17560e36	0.339046
$569$	4.96854e36	0.317844	0.158922	−	0.987291i	$-0.449198\pi$
$569$	4.96854e36	0.317844	0.158922	+	0.987291i	$0.449198\pi$
$570$	0	0
$571$	1.02940e36	0.0628055	0.0314028	−	0.999507i	$-0.490003\pi$
$571$	1.02940e36	0.0628055	0.0314028	+	0.999507i	$0.490003\pi$
$572$	7.44060e36	0.443365
$573$	1.84400e37	1.07318
$574$	2.01580e37	1.14587
$575$	0	0
$576$	−1.65288e37	−0.896475
$577$	4.63258e36	0.245442	0.122721	−	0.992441i	$-0.460838\pi$
$577$	4.63258e36	0.245442	0.122721	+	0.992441i	$0.460838\pi$
$578$	−3.06485e37	−1.58629
$579$	−8.50387e36	−0.429987
$580$	0	0
$581$	−1.40703e37	−0.679090
$582$	−2.43149e37	−1.14660
$583$	1.10786e37	0.510455
$584$	−2.02234e37	−0.910503
$585$	0	0
$586$	−6.57430e36	−0.282639
$587$	−2.64137e36	−0.110972	−0.0554862	−	0.998459i	$-0.517671\pi$
$587$	−2.64137e36	−0.110972	−0.0554862	+	0.998459i	$0.517671\pi$
$588$	−2.00330e37	−0.822529
$589$	1.46808e37	0.589107
$590$	0	0
$591$	1.51880e37	0.582198
$592$	5.32610e35	0.0199557
$593$	3.52090e37	1.28948	0.644741	−	0.764401i	$-0.276965\pi$
$593$	3.52090e37	1.28948	0.644741	+	0.764401i	$0.276965\pi$
$594$	−4.53789e37	−1.62457
$595$	0	0
$596$	5.84187e37	1.99861
$597$	−5.43839e37	−1.81893
$598$	−8.74311e36	−0.285891
$599$	4.76915e37	1.52468	0.762341	−	0.647176i	$-0.224050\pi$
$599$	4.76915e37	1.52468	0.762341	+	0.647176i	$0.224050\pi$
$600$	0	0
$601$	−2.39124e37	−0.730831	−0.365416	−	0.930844i	$-0.619073\pi$
$601$	−2.39124e37	−0.730831	−0.365416	+	0.930844i	$0.619073\pi$
$602$	2.50908e37	0.749827
$603$	1.35743e37	0.396675
$604$	1.39020e37	0.397264
$605$	0	0
$606$	−1.17557e38	−3.21269
$607$	−3.35424e37	−0.896493	−0.448246	−	0.893910i	$-0.647951\pi$
$607$	−3.35424e37	−0.896493	−0.448246	+	0.893910i	$0.647951\pi$
$608$	−3.42334e37	−0.894854
$609$	−2.03142e36	−0.0519357
$610$	0	0
$611$	1.56933e36	0.0383847
$612$	4.98373e36	0.119237
$613$	6.25036e37	1.46281	0.731407	−	0.681942i	$-0.238864\pi$
$613$	6.25036e37	1.46281	0.731407	+	0.681942i	$0.238864\pi$
$614$	1.26439e37	0.289474
$615$	0	0
$616$	6.22692e37	1.36437
$617$	6.57455e37	1.40934	0.704671	−	0.709534i	$-0.251094\pi$
$617$	6.57455e37	1.40934	0.704671	+	0.709534i	$0.251094\pi$
$618$	−1.84855e38	−3.87692
$619$	2.39694e37	0.491851	0.245926	−	0.969289i	$-0.420908\pi$
$619$	2.39694e37	0.491851	0.245926	+	0.969289i	$0.420908\pi$
$620$	0	0
$621$	3.28862e37	0.646066
$622$	9.66913e37	1.85873
$623$	−2.77016e37	−0.521094
$624$	−2.03637e35	−0.00374857
$625$	0	0
$626$	2.07120e37	0.365148
$627$	1.14864e38	1.98186
$628$	1.59065e38	2.68608
$629$	−8.20831e36	−0.135666
$630$	0	0
$631$	−2.72032e37	−0.430748	−0.215374	−	0.976532i	$-0.569097\pi$
$631$	−2.72032e37	−0.430748	−0.215374	+	0.976532i	$0.569097\pi$
$632$	7.13372e37	1.10570
$633$	−5.16486e37	−0.783625
$634$	1.77778e38	2.64041
$635$	0	0
$636$	3.98334e37	0.566991
$637$	−4.49192e36	−0.0625965
$638$	−1.15990e37	−0.158249
$639$	1.42634e37	0.190529
$640$	0	0
$641$	6.03099e37	0.772334	0.386167	−	0.922429i	$-0.373799\pi$
$641$	6.03099e37	0.772334	0.386167	+	0.922429i	$0.373799\pi$
$642$	8.45753e37	1.06052
$643$	1.01937e38	1.25165	0.625823	−	0.779965i	$-0.284763\pi$
$643$	1.01937e38	1.25165	0.625823	+	0.779965i	$0.284763\pi$
$644$	−1.19204e38	−1.43328
$645$	0	0
$646$	1.65354e37	0.190667
$647$	−1.38190e36	−0.0156052	−0.00780260	−	0.999970i	$-0.502484\pi$
$647$	−1.38190e36	−0.0156052	−0.00780260	+	0.999970i	$0.502484\pi$
$648$	−1.10968e38	−1.22726
$649$	1.89404e38	2.05156
$650$	0	0
$651$	6.15972e37	0.640055
$652$	−1.06189e38	−1.08078
$653$	1.67383e38	1.66872	0.834358	−	0.551224i	$-0.185839\pi$
$653$	1.67383e38	1.66872	0.834358	+	0.551224i	$0.185839\pi$
$654$	−2.03508e38	−1.98738
$655$	0	0
$656$	−1.94276e36	−0.0182061
$657$	−5.57335e37	−0.511663
$658$	3.46926e37	0.312024
$659$	−1.83021e38	−1.61268	−0.806339	−	0.591454i	$-0.798554\pi$
$659$	−1.83021e38	−1.61268	−0.806339	+	0.591454i	$0.798554\pi$
$660$	0	0
$661$	6.09366e37	0.515417	0.257708	−	0.966223i	$-0.417033\pi$
$661$	6.09366e37	0.515417	0.257708	+	0.966223i	$0.417033\pi$
$662$	−2.34578e38	−1.94403
$663$	3.13835e36	0.0254841
$664$	−1.09354e38	−0.870090
$665$	0	0
$666$	−1.18366e38	−0.904327
$667$	8.40581e36	0.0629334
$668$	−1.37672e38	−1.01010
$669$	3.59729e37	0.258656
$670$	0	0
$671$	3.04618e38	2.10379
$672$	−1.43635e38	−0.972245
$673$	6.36340e37	0.422168	0.211084	−	0.977468i	$-0.432301\pi$
$673$	6.36340e37	0.422168	0.211084	+	0.977468i	$0.432301\pi$
$674$	6.30163e37	0.409774
$675$	0	0
$676$	−2.51566e38	−1.57171
$677$	5.37104e37	0.328936	0.164468	−	0.986382i	$-0.447409\pi$
$677$	5.37104e37	0.328936	0.164468	+	0.986382i	$0.447409\pi$
$678$	−2.37008e38	−1.42286
$679$	−7.43332e37	−0.437462
$680$	0	0
$681$	−3.25210e38	−1.83941
$682$	3.51708e38	1.95026
$683$	−1.59190e38	−0.865437	−0.432718	−	0.901529i	$-0.642446\pi$
$683$	−1.59190e38	−0.865437	−0.432718	+	0.901529i	$0.642446\pi$
$684$	1.47058e38	0.783847
$685$	0	0
$686$	−3.41399e38	−1.74939
$687$	−2.15661e38	−1.08357
$688$	−2.41817e36	−0.0119136
$689$	8.93171e36	0.0431495
$690$	0	0
$691$	−1.11503e38	−0.518006	−0.259003	−	0.965877i	$-0.583394\pi$
$691$	−1.11503e38	−0.518006	−0.259003	+	0.965877i	$0.583394\pi$
$692$	−5.85621e38	−2.66799
$693$	1.71607e38	0.766719
$694$	3.58451e38	1.57064
$695$	0	0
$696$	−1.57880e37	−0.0665431
$697$	2.99409e37	0.123772
$698$	2.72158e38	1.10350
$699$	−2.70943e38	−1.07755
$700$	0	0
$701$	9.04824e37	0.346235	0.173117	−	0.984901i	$-0.444616\pi$
$701$	9.04824e37	0.346235	0.173117	+	0.984901i	$0.444616\pi$
$702$	−3.65852e37	−0.137327
$703$	−2.42208e38	−0.891849
$704$	−8.10278e38	−2.92687
$705$	0	0
$706$	8.22199e37	0.285834
$707$	−3.59385e38	−1.22574
$708$	6.81008e38	2.27879
$709$	2.52263e38	0.828190	0.414095	−	0.910234i	$-0.364098\pi$
$709$	2.52263e38	0.828190	0.414095	+	0.910234i	$0.364098\pi$
$710$	0	0
$711$	1.96598e38	0.621353
$712$	−2.15295e38	−0.667657
$713$	−2.54883e38	−0.775591
$714$	6.93784e37	0.207157
$715$	0	0
$716$	−3.56488e38	−1.02499
$717$	−1.94469e37	−0.0548709
$718$	4.87584e38	1.35011
$719$	−2.15368e38	−0.585249	−0.292624	−	0.956227i	$-0.594529\pi$
$719$	−2.15368e38	−0.585249	−0.292624	+	0.956227i	$0.594529\pi$
$720$	0	0
$721$	−5.65122e38	−1.47916
$722$	−1.40869e38	−0.361878
$723$	−1.52427e38	−0.384323
$724$	9.29280e38	2.29973
$725$	0	0
$726$	1.90753e39	4.54808
$727$	6.18554e38	1.44765	0.723824	−	0.689985i	$-0.242383\pi$
$727$	6.18554e38	1.44765	0.723824	+	0.689985i	$0.242383\pi$
$728$	5.02025e37	0.115332
$729$	2.02058e36	0.00455675
$730$	0	0
$731$	3.72675e37	0.0809927
$732$	1.09527e39	2.33679
$733$	5.13013e36	0.0107455	0.00537273	−	0.999986i	$-0.498290\pi$
$733$	5.13013e36	0.0107455	0.00537273	+	0.999986i	$0.498290\pi$
$734$	−6.55075e38	−1.34708
$735$	0	0
$736$	5.94349e38	1.17812
$737$	6.65443e38	1.29509
$738$	4.31756e38	0.825044
$739$	−5.22466e38	−0.980298	−0.490149	−	0.871639i	$-0.663058\pi$
$739$	−5.22466e38	−0.980298	−0.490149	+	0.871639i	$0.663058\pi$
$740$	0	0
$741$	9.26054e37	0.167529
$742$	1.97450e38	0.350756
$743$	−1.00984e39	−1.76158	−0.880789	−	0.473509i	$-0.842987\pi$
$743$	−1.00984e39	−1.76158	−0.880789	+	0.473509i	$0.842987\pi$
$744$	4.78729e38	0.820077
$745$	0	0
$746$	3.85686e38	0.637177
$747$	−3.01367e38	−0.488953
$748$	2.44313e38	0.389292
$749$	2.58556e38	0.404622
$750$	0	0
$751$	−4.44629e38	−0.671210	−0.335605	−	0.942003i	$-0.608941\pi$
$751$	−4.44629e38	−0.671210	−0.335605	+	0.942003i	$0.608941\pi$
$752$	−3.34356e36	−0.00495757
$753$	−1.12914e39	−1.64443
$754$	−9.35131e36	−0.0133770
$755$	0	0
$756$	−4.98803e38	−0.688470
$757$	−8.24934e38	−1.11847	−0.559235	−	0.829009i	$-0.688905\pi$
$757$	−8.24934e38	−1.11847	−0.559235	+	0.829009i	$0.688905\pi$
$758$	−6.90757e38	−0.920007
$759$	−1.99423e39	−2.60923
$760$	0	0
$761$	−5.69669e38	−0.719333	−0.359666	−	0.933081i	$-0.617109\pi$
$761$	−5.69669e38	−0.719333	−0.359666	+	0.933081i	$0.617109\pi$
$762$	1.73379e39	2.15082
$763$	−6.22146e38	−0.758248
$764$	1.15733e39	1.38579
$765$	0	0
$766$	−1.14683e39	−1.32560
$767$	1.52700e38	0.173421
$768$	−1.08090e39	−1.20617
$769$	1.47938e39	1.62209	0.811043	−	0.584986i	$-0.198900\pi$
$769$	1.47938e39	1.62209	0.811043	+	0.584986i	$0.198900\pi$
$770$	0	0
$771$	−1.19855e38	−0.126889
$772$	−5.33720e38	−0.555239
$773$	1.83758e39	1.87855	0.939277	−	0.343160i	$-0.111497\pi$
$773$	1.83758e39	1.87855	0.939277	+	0.343160i	$0.111497\pi$
$774$	5.37408e38	0.539885
$775$	0	0
$776$	−5.77712e38	−0.560503
$777$	−1.01625e39	−0.968981
$778$	1.05743e39	0.990894
$779$	8.83484e38	0.813660
$780$	0	0
$781$	6.99222e38	0.622051
$782$	−2.87081e38	−0.251023
$783$	3.51738e37	0.0302298
$784$	9.57033e36	0.00808463
$785$	0	0
$786$	2.04665e39	1.67047
$787$	3.93218e38	0.315482	0.157741	−	0.987481i	$-0.449579\pi$
$787$	3.93218e38	0.315482	0.157741	+	0.987481i	$0.449579\pi$
$788$	9.53231e38	0.751786
$789$	−1.31695e38	−0.102101
$790$	0	0
$791$	−7.24559e38	−0.542864
$792$	1.33372e39	0.982367
$793$	2.45588e38	0.177836
$794$	4.12914e39	2.93957
$795$	0	0
$796$	−3.41324e39	−2.34877
$797$	1.32458e39	0.896168	0.448084	−	0.893991i	$-0.352107\pi$
$797$	1.32458e39	0.896168	0.448084	+	0.893991i	$0.352107\pi$
$798$	2.04719e39	1.36182
$799$	5.15293e37	0.0337033
$800$	0	0
$801$	−5.93329e38	−0.375194
$802$	−3.51089e39	−2.18305
$803$	−2.73218e39	−1.67051
$804$	2.39263e39	1.43853
$805$	0	0
$806$	2.83553e38	0.164858
$807$	−1.53125e38	−0.0875492
$808$	−2.79311e39	−1.57049
$809$	−2.19258e39	−1.21241	−0.606206	−	0.795308i	$-0.707309\pi$
$809$	−2.19258e39	−1.21241	−0.606206	+	0.795308i	$0.707309\pi$
$810$	0	0
$811$	2.76373e39	1.47813	0.739066	−	0.673633i	$-0.235267\pi$
$811$	2.76373e39	1.47813	0.739066	+	0.673633i	$0.235267\pi$
$812$	−1.27496e38	−0.0670640
$813$	1.24873e39	0.646022
$814$	−5.80257e39	−2.95251
$815$	0	0
$816$	−6.68646e36	−0.00329139
$817$	1.09968e39	0.532436
$818$	4.17038e39	1.98612
$819$	1.38352e38	0.0648118
$820$	0	0
$821$	−9.42212e38	−0.427087	−0.213543	−	0.976934i	$-0.568500\pi$
$821$	−9.42212e38	−0.427087	−0.213543	+	0.976934i	$0.568500\pi$
$822$	−1.37294e39	−0.612183
$823$	−2.17900e39	−0.955782	−0.477891	−	0.878419i	$-0.658599\pi$
$823$	−2.17900e39	−0.955782	−0.477891	+	0.878419i	$0.658599\pi$
$824$	−4.39208e39	−1.89519
$825$	0	0
$826$	3.37569e39	1.40972
$827$	8.15484e38	0.335036	0.167518	−	0.985869i	$-0.446425\pi$
$827$	8.15484e38	0.335036	0.167518	+	0.985869i	$0.446425\pi$
$828$	−2.55317e39	−1.03198
$829$	1.51577e39	0.602763	0.301382	−	0.953504i	$-0.402552\pi$
$829$	1.51577e39	0.602763	0.301382	+	0.953504i	$0.402552\pi$
$830$	0	0
$831$	−4.84386e39	−1.86457
$832$	−6.53260e38	−0.247412
$833$	−1.47493e38	−0.0549622
$834$	−7.46823e39	−2.73827
$835$	0	0
$836$	7.20911e39	2.55916
$837$	−1.06655e39	−0.372553
$838$	−1.02528e39	−0.352409
$839$	3.04177e39	1.02882	0.514410	−	0.857544i	$-0.328011\pi$
$839$	3.04177e39	1.02882	0.514410	+	0.857544i	$0.328011\pi$
$840$	0	0
$841$	−3.04414e39	−0.997055
$842$	−3.70077e39	−1.19283
$843$	1.23726e39	0.392453
$844$	−3.24157e39	−1.01189
$845$	0	0
$846$	7.43067e38	0.224661
$847$	5.83154e39	1.73523
$848$	−1.90296e37	−0.00557295
$849$	1.23603e39	0.356266
$850$	0	0
$851$	4.20513e39	1.17417
$852$	2.51408e39	0.690947
$853$	9.78044e38	0.264574	0.132287	−	0.991211i	$-0.457768\pi$
$853$	9.78044e38	0.264574	0.132287	+	0.991211i	$0.457768\pi$
$854$	5.42912e39	1.44560
$855$	0	0
$856$	2.00948e39	0.518427
$857$	6.93851e39	1.76208	0.881039	−	0.473044i	$-0.156845\pi$
$857$	6.93851e39	1.76208	0.881039	+	0.473044i	$0.156845\pi$
$858$	2.21855e39	0.554613
$859$	−6.79141e39	−1.67129	−0.835646	−	0.549268i	$-0.814907\pi$
$859$	−6.79141e39	−1.67129	−0.835646	+	0.549268i	$0.814907\pi$
$860$	0	0
$861$	3.70689e39	0.884030
$862$	−9.26188e39	−2.17446
$863$	5.27048e38	0.121816	0.0609080	−	0.998143i	$-0.480600\pi$
$863$	5.27048e38	0.121816	0.0609080	+	0.998143i	$0.480600\pi$
$864$	2.48703e39	0.565908
$865$	0	0
$866$	−5.85514e39	−1.29136
$867$	−5.63600e39	−1.22381
$868$	3.86596e39	0.826497
$869$	9.63764e39	2.02863
$870$	0	0
$871$	5.36491e38	0.109476
$872$	−4.83527e39	−0.971512
$873$	−1.59211e39	−0.314978
$874$	−8.47110e39	−1.65019
$875$	0	0
$876$	−9.82366e39	−1.85553
$877$	−3.42049e39	−0.636200	−0.318100	−	0.948057i	$-0.603045\pi$
$877$	−3.42049e39	−0.636200	−0.318100	+	0.948057i	$0.603045\pi$
$878$	1.35260e40	2.47739
$879$	−1.20896e39	−0.218053
$880$	0	0
$881$	−7.31752e39	−1.27994	−0.639969	−	0.768401i	$-0.721053\pi$
$881$	−7.31752e39	−1.27994	−0.639969	+	0.768401i	$0.721053\pi$
$882$	−2.12689e39	−0.366370
$883$	2.06213e39	0.349821	0.174910	−	0.984584i	$-0.444036\pi$
$883$	2.06213e39	0.349821	0.174910	+	0.984584i	$0.444036\pi$
$884$	1.96969e38	0.0329074
$885$	0	0
$886$	1.43747e40	2.32940
$887$	−6.98969e39	−1.11555	−0.557775	−	0.829992i	$-0.688345\pi$
$887$	−6.98969e39	−1.11555	−0.557775	+	0.829992i	$0.688345\pi$
$888$	−7.89819e39	−1.24152
$889$	5.30037e39	0.820602
$890$	0	0
$891$	−1.49917e40	−2.25166
$892$	2.25773e39	0.334000
$893$	1.52051e39	0.221561
$894$	1.74186e40	2.50009
$895$	0	0
$896$	−8.83926e39	−1.23100
$897$	−1.60778e39	−0.220561
$898$	−1.22113e40	−1.65018
$899$	−2.72614e38	−0.0362904
$900$	0	0
$901$	2.93274e38	0.0378869
$902$	2.11656e40	2.69366
$903$	4.61398e39	0.578483
$904$	−5.63122e39	−0.695550
$905$	0	0
$906$	4.14514e39	0.496945
$907$	2.28488e39	0.269876	0.134938	−	0.990854i	$-0.456916\pi$
$907$	2.28488e39	0.269876	0.134938	+	0.990854i	$0.456916\pi$
$908$	−2.04108e40	−2.37521
$909$	−7.69751e39	−0.882547
$910$	0	0
$911$	7.51662e39	0.836612	0.418306	−	0.908306i	$-0.362624\pi$
$911$	7.51662e39	0.836612	0.418306	+	0.908306i	$0.362624\pi$
$912$	−1.97302e38	−0.0216372
$913$	−1.47737e40	−1.59637
$914$	−1.16227e40	−1.23746
$915$	0	0
$916$	−1.35353e40	−1.39920
$917$	6.25683e39	0.637336
$918$	−1.20128e39	−0.120578
$919$	5.26405e39	0.520668	0.260334	−	0.965519i	$-0.416167\pi$
$919$	5.26405e39	0.520668	0.260334	+	0.965519i	$0.416167\pi$
$920$	0	0
$921$	2.32511e39	0.223326
$922$	1.91179e40	1.80956
$923$	5.63724e38	0.0525828
$924$	3.02477e40	2.78048
$925$	0	0
$926$	2.06488e40	1.84351
$927$	−1.21041e40	−1.06502
$928$	6.35694e38	0.0551252
$929$	−2.48177e39	−0.212104	−0.106052	−	0.994361i	$-0.533821\pi$
$929$	−2.48177e39	−0.212104	−0.106052	+	0.994361i	$0.533821\pi$
$930$	0	0
$931$	−4.35217e39	−0.361314
$932$	−1.70049e40	−1.39143
$933$	1.77807e40	1.43399
$934$	−1.62142e40	−1.28888
$935$	0	0
$936$	1.07526e39	0.0830408
$937$	2.96211e39	0.225485	0.112742	−	0.993624i	$-0.464037\pi$
$937$	2.96211e39	0.225485	0.112742	+	0.993624i	$0.464037\pi$
$938$	1.18600e40	0.889911
$939$	3.80877e39	0.281708
$940$	0	0
$941$	1.23582e40	0.888168	0.444084	−	0.895985i	$-0.353529\pi$
$941$	1.23582e40	0.888168	0.444084	+	0.895985i	$0.353529\pi$
$942$	4.74280e40	3.36006
$943$	−1.53388e40	−1.07123
$944$	−3.25338e38	−0.0223982
$945$	0	0
$946$	2.63449e40	1.76265
$947$	−3.62546e39	−0.239132	−0.119566	−	0.992826i	$-0.538150\pi$
$947$	−3.62546e39	−0.239132	−0.119566	+	0.992826i	$0.538150\pi$
$948$	3.46525e40	2.25332
$949$	−2.20273e39	−0.141210
$950$	0	0
$951$	3.26918e40	2.03705
$952$	1.64841e39	0.101266
$953$	2.05559e40	1.24504	0.622519	−	0.782605i	$-0.286109\pi$
$953$	2.05559e40	1.24504	0.622519	+	0.782605i	$0.286109\pi$
$954$	4.22910e39	0.252548
$955$	0	0
$956$	−1.22053e39	−0.0708542
$957$	−2.13296e39	−0.122087
$958$	−4.81585e40	−2.71793
$959$	−4.19722e39	−0.233567
$960$	0	0
$961$	−1.02164e40	−0.552757
$962$	−4.67813e39	−0.249579
$963$	5.53790e39	0.291333
$964$	−9.56665e39	−0.496272
$965$	0	0
$966$	−3.55427e40	−1.79291
$967$	2.81961e40	1.40259	0.701296	−	0.712871i	$-0.252605\pi$
$967$	2.81961e40	1.40259	0.701296	+	0.712871i	$0.252605\pi$
$968$	4.53223e40	2.22328
$969$	3.04071e39	0.147097
$970$	0	0
$971$	−1.81766e40	−0.855170	−0.427585	−	0.903975i	$-0.640636\pi$
$971$	−1.81766e40	−0.855170	−0.427585	+	0.903975i	$0.640636\pi$
$972$	−3.45830e40	−1.60461
$973$	−2.28312e40	−1.04473
$974$	4.28405e40	1.93334
$975$	0	0
$976$	−5.23241e38	−0.0229683
$977$	−2.03258e40	−0.879974	−0.439987	−	0.898004i	$-0.645017\pi$
$977$	−2.03258e40	−0.879974	−0.439987	+	0.898004i	$0.645017\pi$
$978$	−3.16622e40	−1.35197
$979$	−2.90863e40	−1.22496
$980$	0	0
$981$	−1.33255e40	−0.545948
$982$	3.25830e40	1.31670
$983$	−7.72807e39	−0.308034	−0.154017	−	0.988068i	$-0.549221\pi$
$983$	−7.72807e39	−0.308034	−0.154017	+	0.988068i	$0.549221\pi$
$984$	2.88096e40	1.13267
$985$	0	0
$986$	−3.07052e38	−0.0117455
$987$	6.37968e39	0.240723
$988$	5.81210e39	0.216329
$989$	−1.90922e40	−0.700981
$990$	0	0
$991$	1.25885e40	0.449758	0.224879	−	0.974387i	$-0.427801\pi$
$991$	1.25885e40	0.449758	0.224879	+	0.974387i	$0.427801\pi$
$992$	−1.92757e40	−0.679364
$993$	−4.31368e40	−1.49980
$994$	1.24620e40	0.427438
$995$	0	0
$996$	−5.31193e40	−1.77317
$997$	−4.50833e40	−1.48467	−0.742336	−	0.670028i	$-0.766282\pi$
$997$	−4.50833e40	−1.48467	−0.742336	+	0.670028i	$0.766282\pi$
$998$	5.24306e40	1.70342
$999$	1.75962e40	0.564008

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.28.a.a.1.2		2
5.2	odd	4		25.28.b.a.24.4		4
5.3	odd	4		25.28.b.a.24.1		4
5.4	even	2		1.28.a.a.1.1	✓	2
15.14	odd	2		9.28.a.d.1.2		2
20.19	odd	2		16.28.a.d.1.2		2
35.34	odd	2		49.28.a.b.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.28.a.a.1.1	✓	2	5.4	even	2
9.28.a.d.1.2		2	15.14	odd	2
16.28.a.d.1.2		2	20.19	odd	2
25.28.a.a.1.2		2	1.1	even	1	trivial
25.28.b.a.24.1		4	5.3	odd	4
25.28.b.a.24.4		4	5.2	odd	4
49.28.a.b.1.1		2	35.34	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+18713.6 q^{2} +3.44127e6 q^{3} +2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11 q^{7} +1.53009e12 q^{8} +4.21675e12 q^{9} +O(q^{10})\)	\(q+18713.6 q^{2} +3.44127e6 q^{3} +2.15981e8 q^{4} +6.43986e10 q^{6} +1.96873e11 q^{7} +1.53009e12 q^{8} +4.21675e12 q^{9} +2.06714e14 q^{11} +7.43249e14 q^{12} +1.66656e14 q^{13} +3.68421e15 q^{14} -3.55072e14 q^{16} +5.47219e15 q^{17} +7.89105e16 q^{18} +1.61471e17 q^{19} +6.77495e17 q^{21} +3.86837e18 q^{22} -2.80341e18 q^{23} +5.26544e18 q^{24} +3.11874e18 q^{26} -1.17308e19 q^{27} +4.25209e19 q^{28} -2.99842e18 q^{29} +9.09190e19 q^{31} -2.12009e20 q^{32} +7.11360e20 q^{33} +1.02404e20 q^{34} +9.10738e20 q^{36} -1.50001e21 q^{37} +3.02171e21 q^{38} +5.73510e20 q^{39} +5.47146e21 q^{41} +1.26784e22 q^{42} +6.81035e21 q^{43} +4.46463e22 q^{44} -5.24619e22 q^{46} +9.41657e21 q^{47} -1.22190e21 q^{48} -2.69532e22 q^{49} +1.88313e22 q^{51} +3.59946e22 q^{52} +5.35936e22 q^{53} -2.19525e23 q^{54} +3.01233e23 q^{56} +5.55667e23 q^{57} -5.61113e22 q^{58} +9.16258e23 q^{59} +1.47362e24 q^{61} +1.70142e24 q^{62} +8.30166e23 q^{63} -3.91980e24 q^{64} +1.33121e25 q^{66} +3.21915e24 q^{67} +1.18189e24 q^{68} -9.64729e24 q^{69} +3.38255e24 q^{71} +6.45199e24 q^{72} -1.32172e25 q^{73} -2.80705e25 q^{74} +3.48748e25 q^{76} +4.06965e25 q^{77} +1.07324e25 q^{78} +4.66230e25 q^{79} -7.25240e25 q^{81} +1.02391e26 q^{82} -7.14690e25 q^{83} +1.46326e26 q^{84} +1.27446e26 q^{86} -1.03184e25 q^{87} +3.16290e26 q^{88} -1.40708e26 q^{89} +3.28102e25 q^{91} -6.05484e26 q^{92} +3.12877e26 q^{93} +1.76218e26 q^{94} -7.29582e26 q^{96} -3.77568e26 q^{97} -5.04391e26 q^{98} +8.71662e26 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} + 86882873184 q^{6} + 175391963600 q^{7} + 3195032348160 q^{8} + 1235136554154 q^{9}+O(q^{10}) \) 2 * q + 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 + 86882873184 * q^6 + 175391963600 * q^7 + 3195032348160 * q^8 + 1235136554154 * q^9	\( 2 q + 8280 q^{2} + 1286280 q^{3} + 190623296 q^{4} + 86882873184 q^{6} + 175391963600 q^{7} + 3195032348160 q^{8} + 1235136554154 q^{9} + 138167337691944 q^{11} + 797895007176960 q^{12} + 753433801271060 q^{13} + 39\!\cdots\!12 q^{14}+ \cdots + 10\!\cdots\!88 q^{99}+O(q^{100}) \) 2 * q + 8280 * q^2 + 1286280 * q^3 + 190623296 * q^4 + 86882873184 * q^6 + 175391963600 * q^7 + 3195032348160 * q^8 + 1235136554154 * q^9 + 138167337691944 * q^11 + 797895007176960 * q^12 + 753433801271060 * q^13 + 3908340052811712 * q^14 - 14322995785166848 * q^16 + 29753620331011740 * q^17 + 110019470226337080 * q^18 + 404565810372684760 * q^19 + 723787313583184704 * q^21 + 4583556785578779360 * q^22 - 2929078923121218960 * q^23 + 1677495533792532480 * q^24 - 3003459254146640016 * q^26 + 11127665129740313040 * q^27 + 43065656535315868160 * q^28 - 15546679995448558260 * q^29 + 28544554594467385024 * q^31 - 289738949030869893120 * q^32 + 859077391009750054560 * q^33 - 150938335185934859568 * q^34 + 986344620988374211392 * q^36 - 1867697204682824566780 * q^37 + 485361223888169521440 * q^38 - 690990221801025527472 * q^39 + 9081343698046512254964 * q^41 + 12195371021026332061440 * q^42 - 5145612605801421773800 * q^43 + 46384541037574305299712 * q^44 - 51150723570313970279616 * q^46 + 1150251488862201070560 * q^47 + 28878849836569912688640 * q^48 - 92204113217840907690414 * q^49 - 33494974704727214464656 * q^51 + 21115266673184124022400 * q^52 - 106953735591470060758620 * q^53 - 458020779785618027135040 * q^54 + 265467760964859260989440 * q^56 + 31800538920577362634080 * q^57 + 74812163717162466470160 * q^58 + 2009620977624026488631880 * q^59 + 147857426692448940370444 * q^61 + 2352212714010270811080960 * q^62 + 894215232558851858338320 * q^63 - 1234057803938137445761024 * q^64 + 11770868153144268253438848 * q^66 - 3051578535738098902157560 * q^67 + 566166870324676171716480 * q^68 - 9376480489705868528695872 * q^69 - 13175198820369338598286416 * q^71 + 1487763126543110308830720 * q^72 - 5284260812951286572116660 * q^73 - 24234145145448525537787728 * q^74 + 28710432717942786872615680 * q^76 + 42169025756092787413646400 * q^77 + 23925717325436558555851200 * q^78 + 62814351035720719918179040 * q^79 - 99047155826597708238103278 * q^81 + 64726649726985190956760560 * q^82 - 171806873410054757883176280 * q^83 + 145152183633423443589998592 * q^84 + 252189883901197432712215584 * q^86 + 16722988656204557792643120 * q^87 + 202163623954874235550955520 * q^88 - 313473438761105539763494380 * q^89 + 20205365125040878536694304 * q^91 - 602296848225491467788034560 * q^92 + 447293490375807514724002560 * q^93 + 262465434750720041893579392 * q^94 - 562074901098402916384505856 * q^96 + 653202933397052842883888060 * q^97 + 176410316250092689584969240 * q^98 + 1076041779280842335610479688 * q^99

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