LMFDB - Embedded newform 25.30.a.a.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,30,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, 30, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 30);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 30 $
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:	$133.195105958$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{51349}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 12837 $ x^2 - x - 12837
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2^{6}\cdot 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			$-112.802$ 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)

$f(q)$	$=$	$q+17433.9 q^{2} -9.52434e6 q^{3} -2.32930e8 q^{4} -1.66046e11 q^{6} +2.98628e12 q^{7} -1.34206e13 q^{8} +2.20826e13 q^{9} +O(q^{10})$	\(q+17433.9 q^{2} -9.52434e6 q^{3} -2.32930e8 q^{4} -1.66046e11 q^{6} +2.98628e12 q^{7} -1.34206e13 q^{8} +2.20826e13 q^{9} -1.25811e15 q^{11} +2.21850e15 q^{12} -6.09036e15 q^{13} +5.20625e16 q^{14} -1.08921e17 q^{16} -8.28952e16 q^{17} +3.84986e17 q^{18} +3.72257e18 q^{19} -2.84423e19 q^{21} -2.19338e19 q^{22} +1.69513e19 q^{23} +1.27823e20 q^{24} -1.06179e20 q^{26} +4.43337e20 q^{27} -6.95594e20 q^{28} -8.81402e20 q^{29} +3.71093e21 q^{31} +5.30623e21 q^{32} +1.19827e22 q^{33} -1.44519e21 q^{34} -5.14369e21 q^{36} -1.97746e22 q^{37} +6.48990e22 q^{38} +5.80066e22 q^{39} -1.00635e23 q^{41} -4.95861e23 q^{42} +1.61886e23 q^{43} +2.93051e23 q^{44} +2.95527e23 q^{46} +2.61745e24 q^{47} +1.03740e24 q^{48} +5.69796e24 q^{49} +7.89521e23 q^{51} +1.41863e24 q^{52} +1.44856e25 q^{53} +7.72909e24 q^{54} -4.00778e25 q^{56} -3.54550e25 q^{57} -1.53663e25 q^{58} +5.87125e24 q^{59} -6.18692e25 q^{61} +6.46960e25 q^{62} +6.59448e25 q^{63} +1.50985e26 q^{64} +2.08905e26 q^{66} -1.29243e26 q^{67} +1.93088e25 q^{68} -1.61450e26 q^{69} -3.63672e26 q^{71} -2.96362e26 q^{72} -1.45255e27 q^{73} -3.44748e26 q^{74} -8.67098e26 q^{76} -3.75707e27 q^{77} +1.01128e27 q^{78} -3.93709e27 q^{79} -5.73802e27 q^{81} -1.75447e27 q^{82} -6.61171e27 q^{83} +6.62507e27 q^{84} +2.82231e27 q^{86} +8.39477e27 q^{87} +1.68846e28 q^{88} +6.47986e27 q^{89} -1.81875e28 q^{91} -3.94847e27 q^{92} -3.53442e28 q^{93} +4.56324e28 q^{94} -5.05383e28 q^{96} -9.52029e28 q^{97} +9.93377e28 q^{98} -2.77823e28 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8640 q^{2} + 4967640 q^{3} - 89952256 q^{4} - 543908756736 q^{6} + 3020312682800 q^{7} - 3150297169920 q^{8} + 163469569523706 q^{9}+O(q^{10}) $ 2 * q - 8640 * q^2 + 4967640 * q^3 - 89952256 * q^4 - 543908756736 * q^6 + 3020312682800 * q^7 - 3150297169920 * q^8 + 163469569523706 * q^9	$ 2 q - 8640 q^{2} + 4967640 q^{3} - 89952256 q^{4} - 543908756736 q^{6} + 3020312682800 q^{7} - 3150297169920 q^{8} + 163469569523706 q^{9} - 20\!\cdots\!16 q^{11}+ \cdots - 14\!\cdots\!48 q^{99}+O(q^{100}) $ 2 * q - 8640 * q^2 + 4967640 * q^3 - 89952256 * q^4 - 543908756736 * q^6 + 3020312682800 * q^7 - 3150297169920 * q^8 + 163469569523706 * q^9 - 2055380519588616 * q^11 + 4290530276229120 * q^12 - 17139371179332220 * q^13 + 51175123348059648 * q^14 - 453469082063208448 * q^16 + 664795927907749980 * q^17 - 3301524864881760960 * q^18 + 1232169445452155080 * q^19 - 27949113476248821696 * q^21 - 1145797484912974080 * q^22 + 18588430504374379920 * q^23 + 276660084668356362240 * q^24 + 181912132597777755264 * q^26 + 1497723629507205824880 * q^27 - 690727602371844997120 * q^28 + 996096417765761595420 * q^29 - 1087258664181924030656 * q^31 + 8776107971762202869760 * q^32 + 428627571739162757280 * q^33 - 20940413403809031000192 * q^34 + 15071477561016892895232 * q^36 - 98878127759336138311660 * q^37 + 129833487351109249470720 * q^38 - 102115380027539490485328 * q^39 - 106699837259610025757676 * q^41 - 508720764303162503608320 * q^42 - 510640433114974031366200 * q^43 + 179059414424913371086848 * q^44 + 252841215606439776920064 * q^46 + 4521107671109825795039520 * q^47 - 3955787455065109907374080 * q^48 + 2479210387392854586312114 * q^49 + 11625042659032475755122384 * q^51 - 161134672249303679180800 * q^52 + 16141544629666790250663540 * q^53 - 19762893017614843677688320 * q^54 - 39728224533177935352299520 * q^56 - 71545878452212360967003040 * q^57 - 64319996083339084169992320 * q^58 - 83497291515660150276062760 * q^59 - 15876762943230179624113316 * q^61 + 189803556071494720042936320 * q^62 + 70756669640265175617870960 * q^63 + 245489542813624183222697984 * q^64 + 510163218803227073870066688 * q^66 - 24468754434128844890782120 * q^67 + 126211850011481106095677440 * q^68 - 137724750477330905859409728 * q^69 - 188428428253360067209577136 * q^71 + 1155729487872248549372067840 * q^72 - 995872721297568533052080980 * q^73 + 1717790650063115374837542528 * q^74 - 1223170019527541658110935040 * q^76 - 3784200478484579386131729600 * q^77 + 5186288053950004913991206400 * q^78 - 7218460852587735797823642080 * q^79 - 161317068789001769884865358 * q^81 - 1596346485209467674952913280 * q^82 - 2210846225248155523694669640 * q^83 + 6695585379451908015663218688 * q^84 + 20357697303796411232450244864 * q^86 + 35603430680717182696869516240 * q^87 + 8696387677835767416210063360 * q^88 + 5872964746600969363962031860 * q^89 - 18563550073842319069958420896 * q^91 - 3714393183413159199429918720 * q^92 - 104879397265778648689061310720 * q^93 - 4003342107705068447401638912 * q^94 - 253006717086360117933244416 * q^96 - 109649982219471997093227005380 * q^97 + 183262972410594366168864121920 * q^98 - 140506044809020243496724809448 * 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 $

$2$	17433.9	0.752419	0.376209	−	0.926535i	$-0.377227\pi$
$2$	17433.9	0.752419	0.376209	+	0.926535i	$0.377227\pi$
$3$	−9.52434e6	−1.14968	−0.574839	−	0.818266i	$-0.694935\pi$
$3$	−9.52434e6	−1.14968	−0.574839	+	0.818266i	$0.694935\pi$
$4$	−2.32930e8	−0.433866
$5$	0	0
$5$	0	0
$6$	−1.66046e11	−0.865040
$7$	2.98628e12	1.66421	0.832106	−	0.554616i	$-0.187135\pi$
$7$	2.98628e12	1.66421	0.832106	+	0.554616i	$0.187135\pi$
$8$	−1.34206e13	−1.07887
$9$	2.20826e13	0.321761
$10$	0	0
$11$	−1.25811e15	−0.998906	−0.499453	−	0.866341i	$-0.666466\pi$
$11$	−1.25811e15	−0.998906	−0.499453	+	0.866341i	$0.666466\pi$
$12$	2.21850e15	0.498806
$13$	−6.09036e15	−0.429007	−0.214503	−	0.976723i	$-0.568813\pi$
$13$	−6.09036e15	−0.429007	−0.214503	+	0.976723i	$0.568813\pi$
$14$	5.20625e16	1.25219
$15$	0	0
$16$	−1.08921e17	−0.377895
$17$	−8.28952e16	−0.119404	−0.0597021	−	0.998216i	$-0.519015\pi$
$17$	−8.28952e16	−0.119404	−0.0597021	+	0.998216i	$0.519015\pi$
$18$	3.84986e17	0.242099
$19$	3.72257e18	1.06885	0.534424	−	0.845217i	$-0.320529\pi$
$19$	3.72257e18	1.06885	0.534424	+	0.845217i	$0.320529\pi$
$20$	0	0
$21$	−2.84423e19	−1.91331
$22$	−2.19338e19	−0.751596
$23$	1.69513e19	0.304894	0.152447	−	0.988312i	$-0.451285\pi$
$23$	1.69513e19	0.304894	0.152447	+	0.988312i	$0.451285\pi$
$24$	1.27823e20	1.24035
$25$	0	0
$26$	−1.06179e20	−0.322793
$27$	4.43337e20	0.779757
$28$	−6.95594e20	−0.722045
$29$	−8.81402e20	−0.550051	−0.275026	−	0.961437i	$-0.588686\pi$
$29$	−8.81402e20	−0.550051	−0.275026	+	0.961437i	$0.588686\pi$
$30$	0	0
$31$	3.71093e21	0.880518	0.440259	−	0.897871i	$-0.354887\pi$
$31$	3.71093e21	0.880518	0.440259	+	0.897871i	$0.354887\pi$
$32$	5.30623e21	0.794532
$33$	1.19827e22	1.14842
$34$	−1.44519e21	−0.0898420
$35$	0	0
$36$	−5.14369e21	−0.139601
$37$	−1.97746e22	−0.360730	−0.180365	−	0.983600i	$-0.557728\pi$
$37$	−1.97746e22	−0.360730	−0.180365	+	0.983600i	$0.557728\pi$
$38$	6.48990e22	0.804221
$39$	5.80066e22	0.493220
$40$	0	0
$41$	−1.00635e23	−0.414367	−0.207183	−	0.978302i	$-0.566430\pi$
$41$	−1.00635e23	−0.414367	−0.207183	+	0.978302i	$0.566430\pi$
$42$	−4.95861e23	−1.43961
$43$	1.61886e23	0.334131	0.167066	−	0.985946i	$-0.446571\pi$
$43$	1.61886e23	0.334131	0.167066	+	0.985946i	$0.446571\pi$
$44$	2.93051e23	0.433391
$45$	0	0
$46$	2.95527e23	0.229408
$47$	2.61745e24	1.48751	0.743755	−	0.668453i	$-0.233043\pi$
$47$	2.61745e24	1.48751	0.743755	+	0.668453i	$0.233043\pi$
$48$	1.03740e24	0.434458
$49$	5.69796e24	1.76960
$50$	0	0
$51$	7.89521e23	0.137277
$52$	1.41863e24	0.186131
$53$	1.44856e25	1.44190	0.720951	−	0.692986i	$-0.243705\pi$
$53$	1.44856e25	1.44190	0.720951	+	0.692986i	$0.243705\pi$
$54$	7.72909e24	0.586704
$55$	0	0
$56$	−4.00778e25	−1.79547
$57$	−3.54550e25	−1.22883
$58$	−1.53663e25	−0.413869
$59$	5.87125e24	0.123417	0.0617087	−	0.998094i	$-0.480345\pi$
$59$	5.87125e24	0.123417	0.0617087	+	0.998094i	$0.480345\pi$
$60$	0	0
$61$	−6.18692e25	−0.802032	−0.401016	−	0.916071i	$-0.631343\pi$
$61$	−6.18692e25	−0.802032	−0.401016	+	0.916071i	$0.631343\pi$
$62$	6.46960e25	0.662519
$63$	6.59448e25	0.535479
$64$	1.50985e26	0.975716
$65$	0	0
$66$	2.08905e26	0.864094
$67$	−1.29243e26	−0.429854	−0.214927	−	0.976630i	$-0.568951\pi$
$67$	−1.29243e26	−0.429854	−0.214927	+	0.976630i	$0.568951\pi$
$68$	1.93088e25	0.0518054
$69$	−1.61450e26	−0.350531
$70$	0	0
$71$	−3.63672e26	−0.521751	−0.260876	−	0.965372i	$-0.584011\pi$
$71$	−3.63672e26	−0.521751	−0.260876	+	0.965372i	$0.584011\pi$
$72$	−2.96362e26	−0.347138
$73$	−1.45255e27	−1.39299	−0.696496	−	0.717561i	$-0.745259\pi$
$73$	−1.45255e27	−1.39299	−0.696496	+	0.717561i	$0.745259\pi$
$74$	−3.44748e26	−0.271420
$75$	0	0
$76$	−8.67098e26	−0.463736
$77$	−3.75707e27	−1.66239
$78$	1.01128e27	0.371108
$79$	−3.93709e27	−1.20111	−0.600554	−	0.799584i	$-0.705053\pi$
$79$	−3.93709e27	−1.20111	−0.600554	+	0.799584i	$0.705053\pi$
$80$	0	0
$81$	−5.73802e27	−1.21823
$82$	−1.75447e27	−0.311778
$83$	−6.61171e27	−0.985556	−0.492778	−	0.870155i	$-0.664018\pi$
$83$	−6.61171e27	−0.985556	−0.492778	+	0.870155i	$0.664018\pi$
$84$	6.62507e27	0.830120
$85$	0	0
$86$	2.82231e27	0.251407
$87$	8.39477e27	0.632382
$88$	1.68846e28	1.07769
$89$	6.47986e27	0.351084	0.175542	−	0.984472i	$-0.443832\pi$
$89$	6.47986e27	0.351084	0.175542	+	0.984472i	$0.443832\pi$
$90$	0	0
$91$	−1.81875e28	−0.713959
$92$	−3.94847e27	−0.132283
$93$	−3.53442e28	−1.01231
$94$	4.56324e28	1.11923
$95$	0	0
$96$	−5.05383e28	−0.913457
$97$	−9.52029e28	−1.48068	−0.740338	−	0.672235i	$-0.765334\pi$
$97$	−9.52029e28	−1.48068	−0.740338	+	0.672235i	$0.765334\pi$
$98$	9.93377e28	1.33148
$99$	−2.77823e28	−0.321409
$100$	0	0
$101$	4.65862e28	0.403271	0.201635	−	0.979461i	$-0.435374\pi$
$101$	4.65862e28	0.403271	0.201635	+	0.979461i	$0.435374\pi$
$102$	1.37644e28	0.103289
$103$	1.34288e29	0.874775	0.437388	−	0.899273i	$-0.355904\pi$
$103$	1.34288e29	0.874775	0.437388	+	0.899273i	$0.355904\pi$
$104$	8.17365e28	0.462842
$105$	0	0
$106$	2.52540e29	1.08491
$107$	4.69036e29	1.75850	0.879248	−	0.476364i	$-0.158045\pi$
$107$	4.69036e29	1.75850	0.879248	+	0.476364i	$0.158045\pi$
$108$	−1.03266e29	−0.338310
$109$	−5.33865e29	−1.53020	−0.765098	−	0.643913i	$-0.777310\pi$
$109$	−5.33865e29	−1.53020	−0.765098	+	0.643913i	$0.777310\pi$
$110$	0	0
$111$	1.88340e29	0.414723
$112$	−3.25268e29	−0.628897
$113$	−7.95436e29	−1.35197	−0.675987	−	0.736914i	$-0.736282\pi$
$113$	−7.95436e29	−1.35197	−0.675987	+	0.736914i	$0.736282\pi$
$114$	−6.18120e29	−0.924596
$115$	0	0
$116$	2.05305e29	0.238648
$117$	−1.34491e29	−0.138038
$118$	1.02359e29	0.0928615
$119$	−2.47548e29	−0.198714
$120$	0	0
$121$	−3.46951e27	−0.00218716
$122$	−1.07862e30	−0.603464
$123$	9.58486e29	0.476389
$124$	−8.64387e29	−0.382027
$125$	0	0
$126$	1.14968e30	0.402905
$127$	−1.93923e29	−0.0606003	−0.0303002	−	0.999541i	$-0.509646\pi$
$127$	−1.93923e29	−0.0606003	−0.0303002	+	0.999541i	$0.509646\pi$
$128$	−2.16508e29	−0.0603851
$129$	−1.54186e30	−0.384143
$130$	0	0
$131$	−2.32229e30	−0.462894	−0.231447	−	0.972847i	$-0.574346\pi$
$131$	−2.32229e30	−0.462894	−0.231447	+	0.972847i	$0.574346\pi$
$132$	−2.79112e30	−0.498260
$133$	1.11166e31	1.77879
$134$	−2.25320e30	−0.323430
$135$	0	0
$136$	1.11251e30	0.128821
$137$	−1.26990e31	−1.32228	−0.661139	−	0.750263i	$-0.729927\pi$
$137$	−1.26990e31	−1.32228	−0.661139	+	0.750263i	$0.729927\pi$
$138$	−2.81470e30	−0.263746
$139$	1.14547e31	0.966648	0.483324	−	0.875442i	$-0.339429\pi$
$139$	1.14547e31	0.966648	0.483324	+	0.875442i	$0.339429\pi$
$140$	0	0
$141$	−2.49295e31	−1.71016
$142$	−6.34022e30	−0.392575
$143$	7.66234e30	0.428538
$144$	−2.40525e30	−0.121592
$145$	0	0
$146$	−2.53236e31	−1.04811
$147$	−5.42693e31	−2.03448
$148$	4.60609e30	0.156508
$149$	−5.74280e31	−1.76979	−0.884897	−	0.465787i	$-0.845771\pi$
$149$	−5.74280e31	−1.76979	−0.884897	+	0.465787i	$0.845771\pi$
$150$	0	0
$151$	5.07974e31	1.29026	0.645128	−	0.764075i	$-0.276804\pi$
$151$	5.07974e31	1.29026	0.645128	+	0.764075i	$0.276804\pi$
$152$	−4.99593e31	−1.15315
$153$	−1.83054e30	−0.0384197
$154$	−6.55003e31	−1.25082
$155$	0	0
$156$	−1.35115e31	−0.213991
$157$	9.31373e30	0.134455	0.0672277	−	0.997738i	$-0.478585\pi$
$157$	9.31373e30	0.134455	0.0672277	+	0.997738i	$0.478585\pi$
$158$	−6.86388e31	−0.903736
$159$	−1.37965e32	−1.65772
$160$	0	0
$161$	5.06213e31	0.507409
$162$	−1.00036e32	−0.916620
$163$	4.45351e31	0.373235	0.186617	−	0.982433i	$-0.440248\pi$
$163$	4.45351e31	0.373235	0.186617	+	0.982433i	$0.440248\pi$
$164$	2.34410e31	0.179780
$165$	0	0
$166$	−1.15268e32	−0.741551
$167$	−1.74608e32	−1.02962	−0.514808	−	0.857305i	$-0.672137\pi$
$167$	−1.74608e32	−1.02962	−0.514808	+	0.857305i	$0.672137\pi$
$168$	3.81714e32	2.06421
$169$	−1.64446e32	−0.815953
$170$	0	0
$171$	8.22040e31	0.343914
$172$	−3.77081e31	−0.144968
$173$	−4.75360e31	−0.168017	−0.0840086	−	0.996465i	$-0.526772\pi$
$173$	−4.75360e31	−0.168017	−0.0840086	+	0.996465i	$0.526772\pi$
$174$	1.46354e32	0.475816
$175$	0	0
$176$	1.37034e32	0.377481
$177$	−5.59197e31	−0.141890
$178$	1.12969e32	0.264162
$179$	−6.60198e32	−1.42333	−0.711664	−	0.702520i	$-0.752058\pi$
$179$	−6.60198e32	−1.42333	−0.711664	+	0.702520i	$0.752058\pi$
$180$	0	0
$181$	5.34310e32	0.980515	0.490257	−	0.871578i	$-0.336903\pi$
$181$	5.34310e32	0.980515	0.490257	+	0.871578i	$0.336903\pi$
$182$	−3.17079e32	−0.537196
$183$	5.89263e32	0.922079
$184$	−2.27497e32	−0.328941
$185$	0	0
$186$	−6.16187e32	−0.761683
$187$	1.04291e32	0.119274
$188$	−6.09683e32	−0.645379
$189$	1.32393e33	1.29768
$190$	0	0
$191$	−9.58754e32	−0.806721	−0.403360	−	0.915041i	$-0.632158\pi$
$191$	−9.58754e32	−0.806721	−0.403360	+	0.915041i	$0.632158\pi$
$192$	−1.43803e33	−1.12176
$193$	−7.81683e31	−0.0565522	−0.0282761	−	0.999600i	$-0.509002\pi$
$193$	−7.81683e31	−0.0565522	−0.0282761	+	0.999600i	$0.509002\pi$
$194$	−1.65976e33	−1.11409
$195$	0	0
$196$	−1.32722e33	−0.767770
$197$	5.60393e32	0.301115	0.150557	−	0.988601i	$-0.451893\pi$
$197$	5.60393e32	0.301115	0.150557	+	0.988601i	$0.451893\pi$
$198$	−4.84354e32	−0.241834
$199$	8.91542e32	0.413783	0.206891	−	0.978364i	$-0.433665\pi$
$199$	8.91542e32	0.413783	0.206891	+	0.978364i	$0.433665\pi$
$200$	0	0
$201$	1.23095e33	0.494194
$202$	8.12179e32	0.303429
$203$	−2.63211e33	−0.915402
$204$	−1.83903e32	−0.0595596
$205$	0	0
$206$	2.34116e33	0.658198
$207$	3.74329e32	0.0981032
$208$	6.63367e32	0.162120
$209$	−4.68340e33	−1.06768
$210$	0	0
$211$	1.07645e33	0.213746	0.106873	−	0.994273i	$-0.465916\pi$
$211$	1.07645e33	0.213746	0.106873	+	0.994273i	$0.465916\pi$
$212$	−3.37412e33	−0.625592
$213$	3.46373e33	0.599846
$214$	8.17713e33	1.32313
$215$	0	0
$216$	−5.94986e33	−0.841254
$217$	1.10819e34	1.46537
$218$	−9.30735e33	−1.15135
$219$	1.38345e34	1.60149
$220$	0	0
$221$	5.04861e32	0.0512253
$222$	3.28350e33	0.312046
$223$	3.94073e33	0.350878	0.175439	−	0.984490i	$-0.443866\pi$
$223$	3.94073e33	0.350878	0.175439	+	0.984490i	$0.443866\pi$
$224$	1.58459e34	1.32227
$225$	0	0
$226$	−1.38676e34	−1.01725
$227$	2.60531e34	1.79260	0.896302	−	0.443445i	$-0.146244\pi$
$227$	2.60531e34	1.79260	0.896302	+	0.443445i	$0.146244\pi$
$228$	8.25853e33	0.533148
$229$	1.02479e34	0.620898	0.310449	−	0.950590i	$-0.399521\pi$
$229$	1.02479e34	0.620898	0.310449	+	0.950590i	$0.399521\pi$
$230$	0	0
$231$	3.57836e34	1.91122
$232$	1.18290e34	0.593432
$233$	−1.94574e34	−0.917113	−0.458557	−	0.888665i	$-0.651633\pi$
$233$	−1.94574e34	−0.917113	−0.458557	+	0.888665i	$0.651633\pi$
$234$	−2.34470e33	−0.103862
$235$	0	0
$236$	−1.36759e33	−0.0535465
$237$	3.74981e34	1.38089
$238$	−4.31573e33	−0.149516
$239$	−4.56285e34	−1.48753	−0.743766	−	0.668440i	$-0.766963\pi$
$239$	−4.56285e34	−1.48753	−0.743766	+	0.668440i	$0.766963\pi$
$240$	0	0
$241$	2.90791e34	0.840107	0.420053	−	0.907499i	$-0.362011\pi$
$241$	2.90791e34	0.840107	0.420053	+	0.907499i	$0.362011\pi$
$242$	−6.04870e31	−0.00164566
$243$	2.42245e34	0.620817
$244$	1.44112e34	0.347974
$245$	0	0
$246$	1.67101e34	0.358444
$247$	−2.26718e34	−0.458543
$248$	−4.98030e34	−0.949963
$249$	6.29721e34	1.13307
$250$	0	0
$251$	−1.72418e34	−0.276256	−0.138128	−	0.990414i	$-0.544109\pi$
$251$	−1.72418e34	−0.276256	−0.138128	+	0.990414i	$0.544109\pi$
$252$	−1.53605e34	−0.232326
$253$	−2.13266e34	−0.304561
$254$	−3.38083e33	−0.0455968
$255$	0	0
$256$	−8.48339e34	−1.02115
$257$	−4.22826e33	−0.0480985	−0.0240493	−	0.999711i	$-0.507656\pi$
$257$	−4.22826e33	−0.0480985	−0.0240493	+	0.999711i	$0.507656\pi$
$258$	−2.68806e34	−0.289037
$259$	−5.90524e34	−0.600331
$260$	0	0
$261$	−1.94636e34	−0.176985
$262$	−4.04865e34	−0.348290
$263$	3.28330e34	0.267271	0.133635	−	0.991031i	$-0.457335\pi$
$263$	3.28330e34	0.267271	0.133635	+	0.991031i	$0.457335\pi$
$264$	−1.60815e35	−1.23899
$265$	0	0
$266$	1.93806e35	1.33840
$267$	−6.17164e34	−0.403633
$268$	3.01045e34	0.186499
$269$	2.79966e35	1.64322	0.821612	−	0.570048i	$-0.193075\pi$
$269$	2.79966e35	1.64322	0.821612	+	0.570048i	$0.193075\pi$
$270$	0	0
$271$	−3.70768e35	−1.95455	−0.977277	−	0.211965i	$-0.932014\pi$
$271$	−3.70768e35	−1.95455	−0.977277	+	0.211965i	$0.932014\pi$
$272$	9.02901e33	0.0451223
$273$	1.73224e35	0.820823
$274$	−2.21394e35	−0.994907
$275$	0	0
$276$	3.76065e34	0.152083
$277$	−3.33125e35	−1.27835	−0.639176	−	0.769060i	$-0.720725\pi$
$277$	−3.33125e35	−1.27835	−0.639176	+	0.769060i	$0.720725\pi$
$278$	1.99700e35	0.727324
$279$	8.19470e34	0.283317
$280$	0	0
$281$	−5.19345e35	−1.61888	−0.809440	−	0.587203i	$-0.800229\pi$
$281$	−5.19345e35	−1.61888	−0.809440	+	0.587203i	$0.800229\pi$
$282$	−4.34618e35	−1.28676
$283$	1.04587e34	0.0294154	0.0147077	−	0.999892i	$-0.495318\pi$
$283$	1.04587e34	0.0294154	0.0147077	+	0.999892i	$0.495318\pi$
$284$	8.47100e34	0.226370
$285$	0	0
$286$	1.33585e35	0.322440
$287$	−3.00526e35	−0.689595
$288$	1.17175e35	0.255650
$289$	−4.75097e35	−0.985743
$290$	0	0
$291$	9.06744e35	1.70230
$292$	3.38341e35	0.604371
$293$	3.74269e35	0.636214	0.318107	−	0.948055i	$-0.396953\pi$
$293$	3.74269e35	0.636214	0.318107	+	0.948055i	$0.396953\pi$
$294$	−9.46125e35	−1.53078
$295$	0	0
$296$	2.65387e35	0.389180
$297$	−5.57766e35	−0.778904
$298$	−1.00119e36	−1.33163
$299$	−1.03240e35	−0.130802
$300$	0	0
$301$	4.83437e35	0.556065
$302$	8.85597e35	0.970813
$303$	−4.43702e35	−0.463632
$304$	−4.05465e35	−0.403912
$305$	0	0
$306$	−3.19135e34	−0.0289077
$307$	5.37563e35	0.464433	0.232217	−	0.972664i	$-0.425402\pi$
$307$	5.37563e35	0.464433	0.232217	+	0.972664i	$0.425402\pi$
$308$	8.75133e35	0.721255
$309$	−1.27900e36	−1.00571
$310$	0	0
$311$	−4.11459e35	−0.294646	−0.147323	−	0.989088i	$-0.547066\pi$
$311$	−4.11459e35	−0.294646	−0.147323	+	0.989088i	$0.547066\pi$
$312$	−7.78486e35	−0.532119
$313$	1.66582e36	1.08702	0.543508	−	0.839404i	$-0.317096\pi$
$313$	1.66582e36	1.08702	0.543508	+	0.839404i	$0.317096\pi$
$314$	1.62375e35	0.101167
$315$	0	0
$316$	9.17065e35	0.521120
$317$	−2.49069e36	−1.35195	−0.675975	−	0.736925i	$-0.736277\pi$
$317$	−2.49069e36	−1.35195	−0.675975	+	0.736925i	$0.736277\pi$
$318$	−2.40528e36	−1.24730
$319$	1.10890e36	0.549449
$320$	0	0
$321$	−4.46726e36	−2.02171
$322$	8.82527e35	0.381784
$323$	−3.08583e35	−0.127625
$324$	1.33656e36	0.528549
$325$	0	0
$326$	7.76421e35	0.280829
$327$	5.08471e36	1.75923
$328$	1.35059e36	0.447047
$329$	7.81644e36	2.47553
$330$	0	0
$331$	1.70323e36	0.494046	0.247023	−	0.969010i	$-0.420548\pi$
$331$	1.70323e36	0.494046	0.247023	+	0.969010i	$0.420548\pi$
$332$	1.54006e36	0.427599
$333$	−4.36674e35	−0.116069
$334$	−3.04410e36	−0.774703
$335$	0	0
$336$	3.09796e36	0.723030
$337$	−1.36026e36	−0.304080	−0.152040	−	0.988374i	$-0.548584\pi$
$337$	−1.36026e36	−0.304080	−0.152040	+	0.988374i	$0.548584\pi$
$338$	−2.86693e36	−0.613939
$339$	7.57600e36	1.55433
$340$	0	0
$341$	−4.66876e36	−0.879555
$342$	1.43314e36	0.258767
$343$	7.40016e36	1.28078
$344$	−2.17261e36	−0.360483
$345$	0	0
$346$	−8.28738e35	−0.126419
$347$	6.83587e36	1.00004	0.500019	−	0.866015i	$-0.333326\pi$
$347$	6.83587e36	1.00004	0.500019	+	0.866015i	$0.333326\pi$
$348$	−1.95539e36	−0.274369
$349$	4.60521e36	0.619842	0.309921	−	0.950762i	$-0.399697\pi$
$349$	4.60521e36	0.619842	0.309921	+	0.950762i	$0.399697\pi$
$350$	0	0
$351$	−2.70008e36	−0.334521
$352$	−6.67582e36	−0.793663
$353$	−1.14489e37	−1.30627	−0.653134	−	0.757243i	$-0.726546\pi$
$353$	−1.14489e37	−1.30627	−0.653134	+	0.757243i	$0.726546\pi$
$354$	−9.74899e35	−0.106761
$355$	0	0
$356$	−1.50935e36	−0.152323
$357$	2.35773e36	0.228457
$358$	−1.15098e37	−1.07094
$359$	−1.33540e37	−1.19328	−0.596638	−	0.802510i	$-0.703497\pi$
$359$	−1.33540e37	−1.19328	−0.596638	+	0.802510i	$0.703497\pi$
$360$	0	0
$361$	1.72772e36	0.142436
$362$	9.31511e36	0.737758
$363$	3.30447e34	0.00251453
$364$	4.23642e36	0.309762
$365$	0	0
$366$	1.02732e37	0.693790
$367$	1.51022e37	0.980353	0.490177	−	0.871623i	$-0.336932\pi$
$367$	1.51022e37	0.980353	0.490177	+	0.871623i	$0.336932\pi$
$368$	−1.84635e36	−0.115218
$369$	−2.22229e36	−0.133327
$370$	0	0
$371$	4.32580e37	2.39963
$372$	8.23271e36	0.439208
$373$	1.09297e36	0.0560828	0.0280414	−	0.999607i	$-0.491073\pi$
$373$	1.09297e36	0.0560828	0.0280414	+	0.999607i	$0.491073\pi$
$374$	1.81820e36	0.0897437
$375$	0	0
$376$	−3.51279e37	−1.60483
$377$	5.36806e36	0.235976
$378$	2.30812e37	0.976400
$379$	1.45750e37	0.593392	0.296696	−	0.954972i	$-0.404115\pi$
$379$	1.45750e37	0.593392	0.296696	+	0.954972i	$0.404115\pi$
$380$	0	0
$381$	1.84699e36	0.0696709
$382$	−1.67148e37	−0.606992
$383$	5.82118e36	0.203530	0.101765	−	0.994808i	$-0.467551\pi$
$383$	5.82118e36	0.203530	0.101765	+	0.994808i	$0.467551\pi$
$384$	2.06210e36	0.0694235
$385$	0	0
$386$	−1.36278e36	−0.0425510
$387$	3.57486e36	0.107510
$388$	2.21756e37	0.642414
$389$	−6.42121e36	−0.179204	−0.0896020	−	0.995978i	$-0.528560\pi$
$389$	−6.42121e36	−0.179204	−0.0896020	+	0.995978i	$0.528560\pi$
$390$	0	0
$391$	−1.40518e36	−0.0364057
$392$	−7.64702e37	−1.90917
$393$	2.21182e37	0.532180
$394$	9.76983e36	0.226564
$395$	0	0
$396$	6.47133e36	0.139448
$397$	−6.76912e37	−1.40627	−0.703137	−	0.711054i	$-0.748218\pi$
$397$	−6.76912e37	−1.40627	−0.703137	+	0.711054i	$0.748218\pi$
$398$	1.55431e37	0.311338
$399$	−1.05879e38	−2.04504
$400$	0	0
$401$	−8.28993e37	−1.48922	−0.744608	−	0.667502i	$-0.767364\pi$
$401$	−8.28993e37	−1.48922	−0.744608	+	0.667502i	$0.767364\pi$
$402$	2.14603e37	0.371841
$403$	−2.26009e37	−0.377748
$404$	−1.08513e37	−0.174965
$405$	0	0
$406$	−4.58880e37	−0.688766
$407$	2.48786e37	0.360335
$408$	−1.05959e37	−0.148103
$409$	2.19435e37	0.296018	0.148009	−	0.988986i	$-0.452714\pi$
$409$	2.19435e37	0.296018	0.148009	+	0.988986i	$0.452714\pi$
$410$	0	0
$411$	1.20950e38	1.52019
$412$	−3.12796e37	−0.379535
$413$	1.75332e37	0.205393
$414$	6.52601e36	0.0738147
$415$	0	0
$416$	−3.23169e37	−0.340860
$417$	−1.09098e38	−1.11133
$418$	−8.16500e37	−0.803341
$419$	−1.94941e37	−0.185268	−0.0926338	−	0.995700i	$-0.529529\pi$
$419$	−1.94941e37	−0.185268	−0.0926338	+	0.995700i	$0.529529\pi$
$420$	0	0
$421$	−3.14435e37	−0.278895	−0.139447	−	0.990229i	$-0.544533\pi$
$421$	−3.14435e37	−0.278895	−0.139447	+	0.990229i	$0.544533\pi$
$422$	1.87667e37	0.160827
$423$	5.78001e37	0.478623
$424$	−1.94406e38	−1.55562
$425$	0	0
$426$	6.03863e37	0.451336
$427$	−1.84759e38	−1.33475
$428$	−1.09253e38	−0.762951
$429$	−7.29787e37	−0.492680
$430$	0	0
$431$	−2.71956e38	−1.71624	−0.858120	−	0.513449i	$-0.828367\pi$
$431$	−2.71956e38	−1.71624	−0.858120	+	0.513449i	$0.828367\pi$
$432$	−4.82886e37	−0.294666
$433$	−1.20292e38	−0.709842	−0.354921	−	0.934896i	$-0.615492\pi$
$433$	−1.20292e38	−0.709842	−0.354921	+	0.934896i	$0.615492\pi$
$434$	1.93200e38	1.10257
$435$	0	0
$436$	1.24353e38	0.663900
$437$	6.31025e37	0.325886
$438$	2.41190e38	1.20499
$439$	−6.48441e37	−0.313426	−0.156713	−	0.987644i	$-0.550090\pi$
$439$	−6.48441e37	−0.313426	−0.156713	+	0.987644i	$0.550090\pi$
$440$	0	0
$441$	1.25826e38	0.569390
$442$	8.80171e36	0.0385429
$443$	1.25901e38	0.533550	0.266775	−	0.963759i	$-0.414042\pi$
$443$	1.25901e38	0.533550	0.266775	+	0.963759i	$0.414042\pi$
$444$	−4.38699e37	−0.179934
$445$	0	0
$446$	6.87022e37	0.264007
$447$	5.46963e38	2.03469
$448$	4.50883e38	1.62380
$449$	4.32701e38	1.50874	0.754372	−	0.656447i	$-0.227941\pi$
$449$	4.32701e38	1.50874	0.754372	+	0.656447i	$0.227941\pi$
$450$	0	0
$451$	1.26610e38	0.413914
$452$	1.85281e38	0.586575
$453$	−4.83812e38	−1.48338
$454$	4.54207e38	1.34879
$455$	0	0
$456$	4.75829e38	1.32575
$457$	5.34446e38	1.44251	0.721255	−	0.692670i	$-0.243566\pi$
$457$	5.34446e38	1.44251	0.721255	+	0.692670i	$0.243566\pi$
$458$	1.78661e38	0.467176
$459$	−3.67505e37	−0.0931063
$460$	0	0
$461$	−2.70831e38	−0.644220	−0.322110	−	0.946702i	$-0.604392\pi$
$461$	−2.70831e38	−0.644220	−0.322110	+	0.946702i	$0.604392\pi$
$462$	6.23847e38	1.43804
$463$	−5.36275e38	−1.19802	−0.599009	−	0.800742i	$-0.704439\pi$
$463$	−5.36275e38	−1.19802	−0.599009	+	0.800742i	$0.704439\pi$
$464$	9.60030e37	0.207862
$465$	0	0
$466$	−3.39218e38	−0.690054
$467$	−9.88390e38	−1.94910	−0.974549	−	0.224177i	$-0.928031\pi$
$467$	−9.88390e38	−1.94910	−0.974549	+	0.224177i	$0.928031\pi$
$468$	3.13270e37	0.0598899
$469$	−3.85954e38	−0.715368
$470$	0	0
$471$	−8.87071e37	−0.154581
$472$	−7.87958e37	−0.133151
$473$	−2.03670e38	−0.333765
$474$	6.53739e38	1.03901
$475$	0	0
$476$	5.76614e37	0.0862152
$477$	3.19879e38	0.463948
$478$	−7.95483e38	−1.11925
$479$	−1.66145e38	−0.226789	−0.113395	−	0.993550i	$-0.536172\pi$
$479$	−1.66145e38	−0.226789	−0.113395	+	0.993550i	$0.536172\pi$
$480$	0	0
$481$	1.20434e38	0.154756
$482$	5.06963e38	0.632112
$483$	−4.82135e38	−0.583358
$484$	8.08152e35	0.000948932 0
$485$	0	0
$486$	4.22328e38	0.467115
$487$	5.21209e38	0.559554	0.279777	−	0.960065i	$-0.409740\pi$
$487$	5.21209e38	0.559554	0.279777	+	0.960065i	$0.409740\pi$
$488$	8.30323e38	0.865286
$489$	−4.24167e38	−0.429100
$490$	0	0
$491$	−6.08070e38	−0.579791	−0.289896	−	0.957058i	$-0.593621\pi$
$491$	−6.08070e38	−0.579791	−0.289896	+	0.957058i	$0.593621\pi$
$492$	−2.23260e38	−0.206689
$493$	7.30640e37	0.0656785
$494$	−3.95258e38	−0.345017
$495$	0	0
$496$	−4.04197e38	−0.332743
$497$	−1.08602e39	−0.868305
$498$	1.09785e39	0.852545
$499$	1.92541e39	1.45233	0.726165	−	0.687521i	$-0.241301\pi$
$499$	1.92541e39	1.45233	0.726165	+	0.687521i	$0.241301\pi$
$500$	0	0
$501$	1.66303e39	1.18373
$502$	−3.00591e38	−0.207861
$503$	−1.47205e39	−0.988981	−0.494490	−	0.869183i	$-0.664645\pi$
$503$	−1.47205e39	−0.988981	−0.494490	+	0.869183i	$0.664645\pi$
$504$	−8.85021e38	−0.577711
$505$	0	0
$506$	−3.71806e38	−0.229157
$507$	1.56624e39	0.938084
$508$	4.51704e37	0.0262924
$509$	9.86933e37	0.0558316	0.0279158	−	0.999610i	$-0.491113\pi$
$509$	9.86933e37	0.0558316	0.0279158	+	0.999610i	$0.491113\pi$
$510$	0	0
$511$	−4.33771e39	−2.31823
$512$	−1.36275e39	−0.707948
$513$	1.65035e39	0.833441
$514$	−7.37152e37	−0.0361903
$515$	0	0
$516$	3.59145e38	0.166667
$517$	−3.29304e39	−1.48588
$518$	−1.02951e39	−0.451701
$519$	4.52749e38	0.193166
$520$	0	0
$521$	1.36208e39	0.549613	0.274806	−	0.961500i	$-0.411386\pi$
$521$	1.36208e39	0.549613	0.274806	+	0.961500i	$0.411386\pi$
$522$	−3.39327e38	−0.133167
$523$	3.92619e39	1.49864	0.749320	−	0.662208i	$-0.230381\pi$
$523$	3.92619e39	1.49864	0.749320	+	0.662208i	$0.230381\pi$
$524$	5.40930e38	0.200834
$525$	0	0
$526$	5.72407e38	0.201100
$527$	−3.07618e38	−0.105138
$528$	−1.30516e39	−0.433982
$529$	−2.80371e39	−0.907039
$530$	0	0
$531$	1.29652e38	0.0397109
$532$	−2.58940e39	−0.771756
$533$	6.12906e38	0.177766
$534$	−1.07596e39	−0.303701
$535$	0	0
$536$	1.73452e39	0.463756
$537$	6.28794e39	1.63637
$538$	4.88089e39	1.23639
$539$	−7.16866e39	−1.76767
$540$	0	0
$541$	3.64331e39	0.851405	0.425702	−	0.904863i	$-0.360027\pi$
$541$	3.64331e39	0.851405	0.425702	+	0.904863i	$0.360027\pi$
$542$	−6.46394e39	−1.47064
$543$	−5.08895e39	−1.12728
$544$	−4.39861e38	−0.0948706
$545$	0	0
$546$	3.01997e39	0.617603
$547$	9.64716e38	0.192125	0.0960624	−	0.995375i	$-0.469375\pi$
$547$	9.64716e38	0.192125	0.0960624	+	0.995375i	$0.469375\pi$
$548$	2.95799e39	0.573691
$549$	−1.36623e39	−0.258063
$550$	0	0
$551$	−3.28108e39	−0.587921
$552$	2.16676e39	0.378176
$553$	−1.17572e40	−1.99890
$554$	−5.80767e39	−0.961857
$555$	0	0
$556$	−2.66814e39	−0.419395
$557$	4.34857e39	0.665956	0.332978	−	0.942935i	$-0.391946\pi$
$557$	4.34857e39	0.665956	0.332978	+	0.942935i	$0.391946\pi$
$558$	1.42866e39	0.213173
$559$	−9.85944e38	−0.143345
$560$	0	0
$561$	−9.93305e38	−0.137126
$562$	−9.05422e39	−1.21808
$563$	5.22292e39	0.684765	0.342382	−	0.939561i	$-0.388766\pi$
$563$	5.22292e39	0.684765	0.342382	+	0.939561i	$0.388766\pi$
$564$	5.80682e39	0.741979
$565$	0	0
$566$	1.82336e38	0.0221327
$567$	−1.71353e40	−2.02740
$568$	4.88070e39	0.562900
$569$	8.52031e39	0.957916	0.478958	−	0.877838i	$-0.341015\pi$
$569$	8.52031e39	0.957916	0.478958	+	0.877838i	$0.341015\pi$
$570$	0	0
$571$	8.06636e38	0.0861894	0.0430947	−	0.999071i	$-0.486278\pi$
$571$	8.06636e38	0.0861894	0.0430947	+	0.999071i	$0.486278\pi$
$572$	−1.78479e39	−0.185928
$573$	9.13149e39	0.927470
$574$	−5.23933e39	−0.518864
$575$	0	0
$576$	3.33413e39	0.313948
$577$	1.60079e40	1.46989	0.734947	−	0.678125i	$-0.237207\pi$
$577$	1.60079e40	1.46989	0.734947	+	0.678125i	$0.237207\pi$
$578$	−8.28280e39	−0.741691
$579$	7.44501e38	0.0650169
$580$	0	0
$581$	−1.97444e40	−1.64017
$582$	1.58081e40	1.28084
$583$	−1.82244e40	−1.44032
$584$	1.94941e40	1.50285
$585$	0	0
$586$	6.52496e39	0.478699
$587$	7.25470e39	0.519239	0.259619	−	0.965711i	$-0.416403\pi$
$587$	7.25470e39	0.519239	0.259619	+	0.965711i	$0.416403\pi$
$588$	1.26409e40	0.882689
$589$	1.38142e40	0.941140
$590$	0	0
$591$	−5.33737e39	−0.346185
$592$	2.15386e39	0.136318
$593$	−4.67095e39	−0.288478	−0.144239	−	0.989543i	$-0.546073\pi$
$593$	−4.67095e39	−0.288478	−0.144239	+	0.989543i	$0.546073\pi$
$594$	−9.72404e39	−0.586062
$595$	0	0
$596$	1.33767e40	0.767853
$597$	−8.49135e39	−0.475717
$598$	−1.79987e39	−0.0984178
$599$	3.02320e40	1.61353	0.806766	−	0.590871i	$-0.201216\pi$
$599$	3.02320e40	1.61353	0.806766	+	0.590871i	$0.201216\pi$
$600$	0	0
$601$	−1.75696e40	−0.893476	−0.446738	−	0.894665i	$-0.647414\pi$
$601$	−1.75696e40	−0.893476	−0.446738	+	0.894665i	$0.647414\pi$
$602$	8.42819e39	0.418394
$603$	−2.85401e39	−0.138310
$604$	−1.18322e40	−0.559798
$605$	0	0
$606$	−7.73546e39	−0.348846
$607$	2.78325e40	1.22551	0.612755	−	0.790273i	$-0.290061\pi$
$607$	2.78325e40	1.22551	0.612755	+	0.790273i	$0.290061\pi$
$608$	1.97528e40	0.849234
$609$	2.50691e40	1.05242
$610$	0	0
$611$	−1.59412e40	−0.638152
$612$	4.26387e38	0.0166690
$613$	−2.63728e40	−1.00688	−0.503441	−	0.864030i	$-0.667933\pi$
$613$	−2.63728e40	−1.00688	−0.503441	+	0.864030i	$0.667933\pi$
$614$	9.37183e39	0.349448
$615$	0	0
$616$	5.04222e40	1.79350
$617$	−9.21532e38	−0.0320166	−0.0160083	−	0.999872i	$-0.505096\pi$
$617$	−9.21532e38	−0.0320166	−0.0160083	+	0.999872i	$0.505096\pi$
$618$	−2.22980e40	−0.756716
$619$	−4.42763e40	−1.46777	−0.733883	−	0.679276i	$-0.762294\pi$
$619$	−4.42763e40	−1.46777	−0.733883	+	0.679276i	$0.762294\pi$
$620$	0	0
$621$	7.51514e39	0.237744
$622$	−7.17333e39	−0.221697
$623$	1.93507e40	0.584278
$624$	−6.31813e39	−0.186385
$625$	0	0
$626$	2.90418e40	0.817891
$627$	4.46063e40	1.22749
$628$	−2.16945e39	−0.0583356
$629$	1.63922e39	0.0430727
$630$	0	0
$631$	4.23643e40	1.06310	0.531551	−	0.847026i	$-0.321609\pi$
$631$	4.23643e40	1.06310	0.531551	+	0.847026i	$0.321609\pi$
$632$	5.28382e40	1.29584
$633$	−1.02525e40	−0.245739
$634$	−4.34225e40	−1.01723
$635$	0	0
$636$	3.21363e40	0.719229
$637$	−3.47026e40	−0.759172
$638$	1.93325e40	0.413416
$639$	−8.03081e39	−0.167879
$640$	0	0
$641$	−4.13775e40	−0.826652	−0.413326	−	0.910583i	$-0.635633\pi$
$641$	−4.13775e40	−0.826652	−0.413326	+	0.910583i	$0.635633\pi$
$642$	−7.78818e40	−1.52117
$643$	−9.84722e40	−1.88042	−0.940209	−	0.340598i	$-0.889370\pi$
$643$	−9.84722e40	−1.88042	−0.940209	+	0.340598i	$0.889370\pi$
$644$	−1.17912e40	−0.220147
$645$	0	0
$646$	−5.37981e39	−0.0960275
$647$	6.78001e39	0.118336	0.0591682	−	0.998248i	$-0.481155\pi$
$647$	6.78001e39	0.118336	0.0591682	+	0.998248i	$0.481155\pi$
$648$	7.70079e40	1.31431
$649$	−7.38667e39	−0.123282
$650$	0	0
$651$	−1.05548e41	−1.68470
$652$	−1.03736e40	−0.161934
$653$	−3.23913e40	−0.494524	−0.247262	−	0.968949i	$-0.579531\pi$
$653$	−3.23913e40	−0.494524	−0.247262	+	0.968949i	$0.579531\pi$
$654$	8.86464e40	1.32368
$655$	0	0
$656$	1.09613e40	0.156587
$657$	−3.20760e40	−0.448211
$658$	1.36271e41	1.86264
$659$	−1.40926e40	−0.188431	−0.0942156	−	0.995552i	$-0.530034\pi$
$659$	−1.40926e40	−0.188431	−0.0942156	+	0.995552i	$0.530034\pi$
$660$	0	0
$661$	−9.56737e40	−1.22425	−0.612127	−	0.790759i	$-0.709686\pi$
$661$	−9.56737e40	−1.22425	−0.612127	+	0.790759i	$0.709686\pi$
$662$	2.96940e40	0.371730
$663$	−4.80847e39	−0.0588926
$664$	8.87333e40	1.06328
$665$	0	0
$666$	−7.61293e39	−0.0873324
$667$	−1.49409e40	−0.167708
$668$	4.06714e40	0.446715
$669$	−3.75328e40	−0.403397
$670$	0	0
$671$	7.78382e40	0.801154
$672$	−1.50922e41	−1.52019
$673$	1.43434e40	0.141394	0.0706972	−	0.997498i	$-0.477478\pi$
$673$	1.43434e40	0.141394	0.0706972	+	0.997498i	$0.477478\pi$
$674$	−2.37146e40	−0.228796
$675$	0	0
$676$	3.83043e40	0.354014
$677$	−8.89678e40	−0.804817	−0.402408	−	0.915460i	$-0.631827\pi$
$677$	−8.89678e40	−0.804817	−0.402408	+	0.915460i	$0.631827\pi$
$678$	1.32079e41	1.16951
$679$	−2.84302e41	−2.46416
$680$	0	0
$681$	−2.48138e41	−2.06092
$682$	−8.13947e40	−0.661794
$683$	−1.49228e41	−1.18782	−0.593910	−	0.804531i	$-0.702417\pi$
$683$	−1.49228e41	−1.18782	−0.593910	+	0.804531i	$0.702417\pi$
$684$	−1.91478e40	−0.149212
$685$	0	0
$686$	1.29014e41	0.963687
$687$	−9.76045e40	−0.713834
$688$	−1.76328e40	−0.126266
$689$	−8.82224e40	−0.618586
$690$	0	0
$691$	2.54015e41	1.70776	0.853880	−	0.520469i	$-0.174243\pi$
$691$	2.54015e41	1.70776	0.853880	+	0.520469i	$0.174243\pi$
$692$	1.10725e40	0.0728969
$693$	−8.29658e40	−0.534893
$694$	1.19176e41	0.752447
$695$	0	0
$696$	−1.12663e41	−0.682257
$697$	8.34219e39	0.0494772
$698$	8.02868e40	0.466381
$699$	1.85318e41	1.05439
$700$	0	0
$701$	−1.56415e40	−0.0853824	−0.0426912	−	0.999088i	$-0.513593\pi$
$701$	−1.56415e40	−0.0853824	−0.0426912	+	0.999088i	$0.513593\pi$
$702$	−4.70729e40	−0.251700
$703$	−7.36123e40	−0.385565
$704$	−1.89955e41	−0.974649
$705$	0	0
$706$	−1.99600e41	−0.982860
$707$	1.39119e41	0.671129
$708$	1.30254e40	0.0615613
$709$	−7.96882e40	−0.368998	−0.184499	−	0.982833i	$-0.559066\pi$
$709$	−7.96882e40	−0.368998	−0.184499	+	0.982833i	$0.559066\pi$
$710$	0	0
$711$	−8.69411e40	−0.386470
$712$	−8.69638e40	−0.378773
$713$	6.29051e40	0.268465
$714$	4.11045e40	0.171896
$715$	0	0
$716$	1.53780e41	0.617533
$717$	4.34581e41	1.71018
$718$	−2.32812e41	−0.897844
$719$	6.70217e39	0.0253306	0.0126653	−	0.999920i	$-0.495968\pi$
$719$	6.70217e39	0.0253306	0.0126653	+	0.999920i	$0.495968\pi$
$720$	0	0
$721$	4.01021e41	1.45581
$722$	3.01209e40	0.107171
$723$	−2.76960e41	−0.965853
$724$	−1.24457e41	−0.425412
$725$	0	0
$726$	5.76099e38	0.00189198
$727$	3.08325e41	0.992565	0.496283	−	0.868161i	$-0.334698\pi$
$727$	3.08325e41	0.992565	0.496283	+	0.868161i	$0.334698\pi$
$728$	2.44088e41	0.770267
$729$	1.63080e41	0.504490
$730$	0	0
$731$	−1.34196e40	−0.0398967
$732$	−1.37257e41	−0.400058
$733$	2.79480e41	0.798626	0.399313	−	0.916815i	$-0.369249\pi$
$733$	2.79480e41	0.798626	0.399313	+	0.916815i	$0.369249\pi$
$734$	2.63290e41	0.737636
$735$	0	0
$736$	8.99476e40	0.242249
$737$	1.62601e41	0.429384
$738$	−3.87432e40	−0.100318
$739$	−4.36349e41	−1.10787	−0.553936	−	0.832560i	$-0.686875\pi$
$739$	−4.36349e41	−1.10787	−0.553936	+	0.832560i	$0.686875\pi$
$740$	0	0
$741$	2.15934e41	0.527177
$742$	7.54155e41	1.80553
$743$	1.06242e41	0.249437	0.124718	−	0.992192i	$-0.460197\pi$
$743$	1.06242e41	0.249437	0.124718	+	0.992192i	$0.460197\pi$
$744$	4.74341e41	1.09215
$745$	0	0
$746$	1.90547e40	0.0421977
$747$	−1.46004e41	−0.317114
$748$	−2.42925e40	−0.0517487
$749$	1.40067e42	2.92651
$750$	0	0
$751$	−1.53315e41	−0.308181	−0.154091	−	0.988057i	$-0.549245\pi$
$751$	−1.53315e41	−0.308181	−0.154091	+	0.988057i	$0.549245\pi$
$752$	−2.85095e41	−0.562122
$753$	1.64216e41	0.317606
$754$	9.35862e40	0.177553
$755$	0	0
$756$	−3.08382e41	−0.563019
$757$	1.29063e41	0.231160	0.115580	−	0.993298i	$-0.463127\pi$
$757$	1.29063e41	0.231160	0.115580	+	0.993298i	$0.463127\pi$
$758$	2.54100e41	0.446479
$759$	2.03122e41	0.350147
$760$	0	0
$761$	−1.01002e42	−1.67592	−0.837962	−	0.545728i	$-0.816253\pi$
$761$	−1.01002e42	−1.67592	−0.837962	+	0.545728i	$0.816253\pi$
$762$	3.22002e40	0.0524217
$763$	−1.59427e42	−2.54657
$764$	2.23322e41	0.350008
$765$	0	0
$766$	1.01486e41	0.153140
$767$	−3.57580e40	−0.0529469
$768$	8.07987e41	1.17400
$769$	−8.10252e41	−1.15528	−0.577641	−	0.816291i	$-0.696027\pi$
$769$	−8.10252e41	−1.15528	−0.577641	+	0.816291i	$0.696027\pi$
$770$	0	0
$771$	4.02714e40	0.0552979
$772$	1.82077e40	0.0245361
$773$	−3.13830e41	−0.415042	−0.207521	−	0.978231i	$-0.566539\pi$
$773$	−3.13830e41	−0.415042	−0.207521	+	0.978231i	$0.566539\pi$
$774$	6.23238e40	0.0808929
$775$	0	0
$776$	1.27768e42	1.59745
$777$	5.62435e41	0.690188
$778$	−1.11947e41	−0.134836
$779$	−3.74623e41	−0.442895
$780$	0	0
$781$	4.57539e41	0.521180
$782$	−2.44978e40	−0.0273923
$783$	−3.90758e41	−0.428906
$784$	−6.20626e41	−0.668724
$785$	0	0
$786$	3.85607e41	0.400422
$787$	−8.07245e41	−0.822947	−0.411473	−	0.911422i	$-0.634986\pi$
$787$	−8.07245e41	−0.822947	−0.411473	+	0.911422i	$0.634986\pi$
$788$	−1.30532e41	−0.130643
$789$	−3.12712e41	−0.307276
$790$	0	0
$791$	−2.37540e42	−2.24997
$792$	3.72856e41	0.346758
$793$	3.76805e41	0.344077
$794$	−1.18012e42	−1.05811
$795$	0	0
$796$	−2.07667e41	−0.179526
$797$	−2.35976e41	−0.200319	−0.100160	−	0.994971i	$-0.531935\pi$
$797$	−2.35976e41	−0.200319	−0.100160	+	0.994971i	$0.531935\pi$
$798$	−1.84588e42	−1.53872
$799$	−2.16974e41	−0.177615
$800$	0	0
$801$	1.43092e41	0.112965
$802$	−1.44526e42	−1.12051
$803$	1.82746e42	1.39147
$804$	−2.86725e41	−0.214414
$805$	0	0
$806$	−3.94022e41	−0.284225
$807$	−2.66649e42	−1.88918
$808$	−6.25216e41	−0.435076
$809$	2.25512e42	1.54140	0.770700	−	0.637198i	$-0.219907\pi$
$809$	2.25512e42	1.54140	0.770700	+	0.637198i	$0.219907\pi$
$810$	0	0
$811$	8.17269e41	0.538967	0.269484	−	0.963005i	$-0.413147\pi$
$811$	8.17269e41	0.538967	0.269484	+	0.963005i	$0.413147\pi$
$812$	6.13098e41	0.397162
$813$	3.53132e42	2.24711
$814$	4.33731e41	0.271123
$815$	0	0
$816$	−8.59953e40	−0.0518761
$817$	6.02632e41	0.357135
$818$	3.82560e41	0.222729
$819$	−4.01627e41	−0.229724
$820$	0	0
$821$	8.86919e39	0.00489675	0.00244838	−	0.999997i	$-0.499221\pi$
$821$	8.86919e39	0.00489675	0.00244838	+	0.999997i	$0.499221\pi$
$822$	2.10863e42	1.14382
$823$	−4.50695e41	−0.240207	−0.120103	−	0.992761i	$-0.538323\pi$
$823$	−4.50695e41	−0.240207	−0.120103	+	0.992761i	$0.538323\pi$
$824$	−1.80223e42	−0.943767
$825$	0	0
$826$	3.05672e41	0.154541
$827$	−1.64298e42	−0.816211	−0.408106	−	0.912935i	$-0.633810\pi$
$827$	−1.64298e42	−0.816211	−0.408106	+	0.912935i	$0.633810\pi$
$828$	−8.71923e40	−0.0425636
$829$	9.28693e41	0.445483	0.222742	−	0.974878i	$-0.428499\pi$
$829$	9.28693e41	0.445483	0.222742	+	0.974878i	$0.428499\pi$
$830$	0	0
$831$	3.17280e42	1.46970
$832$	−9.19552e41	−0.418589
$833$	−4.72333e41	−0.211298
$834$	−1.90201e42	−0.836189
$835$	0	0
$836$	1.09090e42	0.463229
$837$	1.64519e42	0.686590
$838$	−3.39858e41	−0.139399
$839$	−1.59653e42	−0.643620	−0.321810	−	0.946804i	$-0.604291\pi$
$839$	−1.59653e42	−0.643620	−0.321810	+	0.946804i	$0.604291\pi$
$840$	0	0
$841$	−1.79082e42	−0.697444
$842$	−5.48183e41	−0.209846
$843$	4.94642e42	1.86119
$844$	−2.50737e41	−0.0927371
$845$	0	0
$846$	1.00768e42	0.360125
$847$	−1.03609e40	−0.00363989
$848$	−1.57778e42	−0.544887
$849$	−9.96121e40	−0.0338182
$850$	0	0
$851$	−3.35205e41	−0.109985
$852$	−8.06806e41	−0.260253
$853$	2.50802e42	0.795373	0.397686	−	0.917521i	$-0.369813\pi$
$853$	2.50802e42	0.795373	0.397686	+	0.917521i	$0.369813\pi$
$854$	−3.22106e42	−1.00429
$855$	0	0
$856$	−6.29476e42	−1.89719
$857$	−4.74569e42	−1.40630	−0.703149	−	0.711043i	$-0.748223\pi$
$857$	−4.74569e42	−1.40630	−0.703149	+	0.711043i	$0.748223\pi$
$858$	−1.27230e42	−0.370702
$859$	−1.19413e42	−0.342098	−0.171049	−	0.985263i	$-0.554716\pi$
$859$	−1.19413e42	−0.342098	−0.171049	+	0.985263i	$0.554716\pi$
$860$	0	0
$861$	2.86231e42	0.792812
$862$	−4.74125e42	−1.29133
$863$	−5.51388e42	−1.47673	−0.738364	−	0.674402i	$-0.764401\pi$
$863$	−5.51388e42	−1.47673	−0.738364	+	0.674402i	$0.764401\pi$
$864$	2.35245e42	0.619542
$865$	0	0
$866$	−2.09716e42	−0.534099
$867$	4.52498e42	1.13329
$868$	−2.58130e42	−0.635774
$869$	4.95329e42	1.19979
$870$	0	0
$871$	7.87134e41	0.184410
$872$	7.16481e42	1.65088
$873$	−2.10233e42	−0.476424
$874$	1.10012e42	0.245203
$875$	0	0
$876$	−3.22248e42	−0.694833
$877$	−3.25016e42	−0.689304	−0.344652	−	0.938731i	$-0.612003\pi$
$877$	−3.25016e42	−0.689304	−0.344652	+	0.938731i	$0.612003\pi$
$878$	−1.13049e42	−0.235828
$879$	−3.56466e42	−0.731441
$880$	0	0
$881$	1.07364e42	0.213162	0.106581	−	0.994304i	$-0.466010\pi$
$881$	1.07364e42	0.213162	0.106581	+	0.994304i	$0.466010\pi$
$882$	2.19363e42	0.428420
$883$	−4.03526e42	−0.775250	−0.387625	−	0.921817i	$-0.626704\pi$
$883$	−4.03526e42	−0.775250	−0.387625	+	0.921817i	$0.626704\pi$
$884$	−1.17597e41	−0.0222249
$885$	0	0
$886$	2.19495e42	0.401453
$887$	1.14783e42	0.206532	0.103266	−	0.994654i	$-0.467071\pi$
$887$	1.14783e42	0.206532	0.103266	+	0.994654i	$0.467071\pi$
$888$	−2.52764e42	−0.447432
$889$	−5.79108e41	−0.100852
$890$	0	0
$891$	7.21906e42	1.21690
$892$	−9.17913e41	−0.152234
$893$	9.74365e42	1.58992
$894$	9.53571e42	1.53094
$895$	0	0
$896$	−6.46554e41	−0.100494
$897$	9.83288e41	0.150380
$898$	7.54366e42	1.13521
$899$	−3.27082e42	−0.484330
$900$	0	0
$901$	−1.20078e42	−0.172169
$902$	2.20731e42	0.311436
$903$	−4.60442e42	−0.639296
$904$	1.06753e43	1.45860
$905$	0	0
$906$	−8.43472e42	−1.11612
$907$	1.34894e43	1.75666	0.878328	−	0.478058i	$-0.158659\pi$
$907$	1.34894e43	1.75666	0.878328	+	0.478058i	$0.158659\pi$
$908$	−6.06854e42	−0.777749
$909$	1.02874e42	0.129757
$910$	0	0
$911$	3.01049e42	0.367807	0.183904	−	0.982944i	$-0.441127\pi$
$911$	3.01049e42	0.367807	0.183904	+	0.982944i	$0.441127\pi$
$912$	3.86179e42	0.464369
$913$	8.31825e42	0.984477
$914$	9.31747e42	1.08537
$915$	0	0
$916$	−2.38704e42	−0.269386
$917$	−6.93499e42	−0.770355
$918$	−6.40704e41	−0.0700549
$919$	6.28761e42	0.676723	0.338361	−	0.941016i	$-0.390127\pi$
$919$	6.28761e42	0.676723	0.338361	+	0.941016i	$0.390127\pi$
$920$	0	0
$921$	−5.11993e42	−0.533949
$922$	−4.72163e42	−0.484723
$923$	2.21489e42	0.223835
$924$	−8.33506e42	−0.829211
$925$	0	0
$926$	−9.34937e42	−0.901412
$927$	2.96542e42	0.281469
$928$	−4.67692e42	−0.437034
$929$	1.66684e43	1.53344	0.766720	−	0.641982i	$-0.221888\pi$
$929$	1.66684e43	1.53344	0.766720	+	0.641982i	$0.221888\pi$
$930$	0	0
$931$	2.12111e43	1.89144
$932$	4.53220e42	0.397904
$933$	3.91887e42	0.338748
$934$	−1.72315e43	−1.46654
$935$	0	0
$936$	1.80495e42	0.148925
$937$	1.87621e43	1.52426	0.762129	−	0.647425i	$-0.224154\pi$
$937$	1.87621e43	1.52426	0.762129	+	0.647425i	$0.224154\pi$
$938$	−6.72869e42	−0.538257
$939$	−1.58659e43	−1.24972
$940$	0	0
$941$	5.14783e42	0.393165	0.196582	−	0.980487i	$-0.437016\pi$
$941$	5.14783e42	0.393165	0.196582	+	0.980487i	$0.437016\pi$
$942$	−1.54651e42	−0.116309
$943$	−1.70590e42	−0.126338
$944$	−6.39501e41	−0.0466388
$945$	0	0
$946$	−3.55077e42	−0.251131
$947$	2.96240e42	0.206333	0.103167	−	0.994664i	$-0.467103\pi$
$947$	2.96240e42	0.206333	0.103167	+	0.994664i	$0.467103\pi$
$948$	−8.73443e42	−0.599120
$949$	8.84653e42	0.597603
$950$	0	0
$951$	2.37222e43	1.55431
$952$	3.32225e42	0.214386
$953$	−1.30942e43	−0.832208	−0.416104	−	0.909317i	$-0.636605\pi$
$953$	−1.30942e43	−0.832208	−0.416104	+	0.909317i	$0.636605\pi$
$954$	5.57674e42	0.349083
$955$	0	0
$956$	1.06282e43	0.645390
$957$	−1.05615e43	−0.631690
$958$	−2.89656e42	−0.170640
$959$	−3.79229e43	−2.20055
$960$	0	0
$961$	−3.99088e42	−0.224688
$962$	2.09964e42	0.116441
$963$	1.03575e43	0.565816
$964$	−6.77340e42	−0.364493
$965$	0	0
$966$	−8.40549e42	−0.438929
$967$	−2.64169e43	−1.35894	−0.679468	−	0.733706i	$-0.737789\pi$
$967$	−2.64169e43	−1.35894	−0.679468	+	0.733706i	$0.737789\pi$
$968$	4.65630e40	0.00235965
$969$	2.93905e42	0.146728
$970$	0	0
$971$	−3.41602e43	−1.65517	−0.827583	−	0.561343i	$-0.810285\pi$
$971$	−3.41602e43	−1.65517	−0.827583	+	0.561343i	$0.810285\pi$
$972$	−5.64261e42	−0.269351
$973$	3.42069e43	1.60871
$974$	9.08670e42	0.421019
$975$	0	0
$976$	6.73884e42	0.303084
$977$	−2.06179e43	−0.913636	−0.456818	−	0.889560i	$-0.651011\pi$
$977$	−2.06179e43	−0.913636	−0.456818	+	0.889560i	$0.651011\pi$
$978$	−7.39489e42	−0.322863
$979$	−8.15238e42	−0.350700
$980$	0	0
$981$	−1.17891e43	−0.492358
$982$	−1.06010e43	−0.436246
$983$	1.21841e43	0.494047	0.247023	−	0.969009i	$-0.420548\pi$
$983$	1.21841e43	0.494047	0.247023	+	0.969009i	$0.420548\pi$
$984$	−1.28635e43	−0.513961
$985$	0	0
$986$	1.27379e42	0.0494177
$987$	−7.44464e43	−2.84607
$988$	5.28094e42	0.198946
$989$	2.74418e42	0.101875
$990$	0	0
$991$	−1.94686e43	−0.701888	−0.350944	−	0.936397i	$-0.614139\pi$
$991$	−1.94686e43	−0.701888	−0.350944	+	0.936397i	$0.614139\pi$
$992$	1.96911e43	0.699600
$993$	−1.62221e43	−0.567994
$994$	−1.89337e43	−0.653329
$995$	0	0
$996$	−1.46681e43	−0.491601
$997$	−2.12798e43	−0.702891	−0.351446	−	0.936208i	$-0.614310\pi$
$997$	−2.12798e43	−0.702891	−0.351446	+	0.936208i	$0.614310\pi$
$998$	3.35674e43	1.09276
$999$	−8.76679e42	−0.281282

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.30.a.a.1.2		2
5.2	odd	4		25.30.b.a.24.3		4
5.3	odd	4		25.30.b.a.24.2		4
5.4	even	2		1.30.a.a.1.1	✓	2
15.14	odd	2		9.30.a.a.1.2		2
20.19	odd	2		16.30.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.30.a.a.1.1	✓	2	5.4	even	2
9.30.a.a.1.2		2	15.14	odd	2
16.30.a.c.1.1		2	20.19	odd	2
25.30.a.a.1.2		2	1.1	even	1	trivial
25.30.b.a.24.2		4	5.3	odd	4
25.30.b.a.24.3		4	5.2	odd	4

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:	\( k \)	\(=\)	\( 30 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q+17433.9 q^{2} -9.52434e6 q^{3} -2.32930e8 q^{4} -1.66046e11 q^{6} +2.98628e12 q^{7} -1.34206e13 q^{8} +2.20826e13 q^{9} +O(q^{10})\)	\(q+17433.9 q^{2} -9.52434e6 q^{3} -2.32930e8 q^{4} -1.66046e11 q^{6} +2.98628e12 q^{7} -1.34206e13 q^{8} +2.20826e13 q^{9} -1.25811e15 q^{11} +2.21850e15 q^{12} -6.09036e15 q^{13} +5.20625e16 q^{14} -1.08921e17 q^{16} -8.28952e16 q^{17} +3.84986e17 q^{18} +3.72257e18 q^{19} -2.84423e19 q^{21} -2.19338e19 q^{22} +1.69513e19 q^{23} +1.27823e20 q^{24} -1.06179e20 q^{26} +4.43337e20 q^{27} -6.95594e20 q^{28} -8.81402e20 q^{29} +3.71093e21 q^{31} +5.30623e21 q^{32} +1.19827e22 q^{33} -1.44519e21 q^{34} -5.14369e21 q^{36} -1.97746e22 q^{37} +6.48990e22 q^{38} +5.80066e22 q^{39} -1.00635e23 q^{41} -4.95861e23 q^{42} +1.61886e23 q^{43} +2.93051e23 q^{44} +2.95527e23 q^{46} +2.61745e24 q^{47} +1.03740e24 q^{48} +5.69796e24 q^{49} +7.89521e23 q^{51} +1.41863e24 q^{52} +1.44856e25 q^{53} +7.72909e24 q^{54} -4.00778e25 q^{56} -3.54550e25 q^{57} -1.53663e25 q^{58} +5.87125e24 q^{59} -6.18692e25 q^{61} +6.46960e25 q^{62} +6.59448e25 q^{63} +1.50985e26 q^{64} +2.08905e26 q^{66} -1.29243e26 q^{67} +1.93088e25 q^{68} -1.61450e26 q^{69} -3.63672e26 q^{71} -2.96362e26 q^{72} -1.45255e27 q^{73} -3.44748e26 q^{74} -8.67098e26 q^{76} -3.75707e27 q^{77} +1.01128e27 q^{78} -3.93709e27 q^{79} -5.73802e27 q^{81} -1.75447e27 q^{82} -6.61171e27 q^{83} +6.62507e27 q^{84} +2.82231e27 q^{86} +8.39477e27 q^{87} +1.68846e28 q^{88} +6.47986e27 q^{89} -1.81875e28 q^{91} -3.94847e27 q^{92} -3.53442e28 q^{93} +4.56324e28 q^{94} -5.05383e28 q^{96} -9.52029e28 q^{97} +9.93377e28 q^{98} -2.77823e28 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8640 q^{2} + 4967640 q^{3} - 89952256 q^{4} - 543908756736 q^{6} + 3020312682800 q^{7} - 3150297169920 q^{8} + 163469569523706 q^{9}+O(q^{10}) \) 2 * q - 8640 * q^2 + 4967640 * q^3 - 89952256 * q^4 - 543908756736 * q^6 + 3020312682800 * q^7 - 3150297169920 * q^8 + 163469569523706 * q^9	\( 2 q - 8640 q^{2} + 4967640 q^{3} - 89952256 q^{4} - 543908756736 q^{6} + 3020312682800 q^{7} - 3150297169920 q^{8} + 163469569523706 q^{9} - 20\!\cdots\!16 q^{11}+ \cdots - 14\!\cdots\!48 q^{99}+O(q^{100}) \) 2 * q - 8640 * q^2 + 4967640 * q^3 - 89952256 * q^4 - 543908756736 * q^6 + 3020312682800 * q^7 - 3150297169920 * q^8 + 163469569523706 * q^9 - 2055380519588616 * q^11 + 4290530276229120 * q^12 - 17139371179332220 * q^13 + 51175123348059648 * q^14 - 453469082063208448 * q^16 + 664795927907749980 * q^17 - 3301524864881760960 * q^18 + 1232169445452155080 * q^19 - 27949113476248821696 * q^21 - 1145797484912974080 * q^22 + 18588430504374379920 * q^23 + 276660084668356362240 * q^24 + 181912132597777755264 * q^26 + 1497723629507205824880 * q^27 - 690727602371844997120 * q^28 + 996096417765761595420 * q^29 - 1087258664181924030656 * q^31 + 8776107971762202869760 * q^32 + 428627571739162757280 * q^33 - 20940413403809031000192 * q^34 + 15071477561016892895232 * q^36 - 98878127759336138311660 * q^37 + 129833487351109249470720 * q^38 - 102115380027539490485328 * q^39 - 106699837259610025757676 * q^41 - 508720764303162503608320 * q^42 - 510640433114974031366200 * q^43 + 179059414424913371086848 * q^44 + 252841215606439776920064 * q^46 + 4521107671109825795039520 * q^47 - 3955787455065109907374080 * q^48 + 2479210387392854586312114 * q^49 + 11625042659032475755122384 * q^51 - 161134672249303679180800 * q^52 + 16141544629666790250663540 * q^53 - 19762893017614843677688320 * q^54 - 39728224533177935352299520 * q^56 - 71545878452212360967003040 * q^57 - 64319996083339084169992320 * q^58 - 83497291515660150276062760 * q^59 - 15876762943230179624113316 * q^61 + 189803556071494720042936320 * q^62 + 70756669640265175617870960 * q^63 + 245489542813624183222697984 * q^64 + 510163218803227073870066688 * q^66 - 24468754434128844890782120 * q^67 + 126211850011481106095677440 * q^68 - 137724750477330905859409728 * q^69 - 188428428253360067209577136 * q^71 + 1155729487872248549372067840 * q^72 - 995872721297568533052080980 * q^73 + 1717790650063115374837542528 * q^74 - 1223170019527541658110935040 * q^76 - 3784200478484579386131729600 * q^77 + 5186288053950004913991206400 * q^78 - 7218460852587735797823642080 * q^79 - 161317068789001769884865358 * q^81 - 1596346485209467674952913280 * q^82 - 2210846225248155523694669640 * q^83 + 6695585379451908015663218688 * q^84 + 20357697303796411232450244864 * q^86 + 35603430680717182696869516240 * q^87 + 8696387677835767416210063360 * q^88 + 5872964746600969363962031860 * q^89 - 18563550073842319069958420896 * q^91 - 3714393183413159199429918720 * q^92 - 104879397265778648689061310720 * q^93 - 4003342107705068447401638912 * q^94 - 253006717086360117933244416 * q^96 - 109649982219471997093227005380 * q^97 + 183262972410594366168864121920 * q^98 - 140506044809020243496724809448 * q^99

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