LMFDB - Embedded newform 25.24.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,24,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, 24, names="a")

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

chi := DirichletCharacter("25.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 24 $
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:	$83.8010093363$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 5761014x^{2} - 3205061410x + 2143006857425 $ x^4 - 2x^3 - 5761014x^2 - 3205061410*x + 2143006857425
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{8}\cdot 3\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1838.47$ 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)

$f(q)$	$=$	$q-3482.94 q^{2} -517572. q^{3} +3.74229e6 q^{4} +1.80268e9 q^{6} -8.64758e9 q^{7} +1.61829e10 q^{8} +1.73738e11 q^{9} +O(q^{10})$	\(q-3482.94 q^{2} -517572. q^{3} +3.74229e6 q^{4} +1.80268e9 q^{6} -8.64758e9 q^{7} +1.61829e10 q^{8} +1.73738e11 q^{9} +4.59523e11 q^{11} -1.93690e12 q^{12} +2.79244e12 q^{13} +3.01190e13 q^{14} -8.77566e13 q^{16} +1.40467e14 q^{17} -6.05119e14 q^{18} +7.82480e14 q^{19} +4.47575e15 q^{21} -1.60049e15 q^{22} +3.06806e15 q^{23} -8.37581e15 q^{24} -9.72592e15 q^{26} -4.11960e16 q^{27} -3.23617e16 q^{28} -9.69499e16 q^{29} +1.54585e16 q^{31} +1.69899e17 q^{32} -2.37836e17 q^{33} -4.89240e17 q^{34} +6.50177e17 q^{36} +4.47673e17 q^{37} -2.72533e18 q^{38} -1.44529e18 q^{39} -4.27946e18 q^{41} -1.55888e19 q^{42} -3.50056e18 q^{43} +1.71967e18 q^{44} -1.06859e19 q^{46} +1.79769e19 q^{47} +4.54204e19 q^{48} +4.74120e19 q^{49} -7.27020e19 q^{51} +1.04501e19 q^{52} -4.84476e19 q^{53} +1.43484e20 q^{54} -1.39943e20 q^{56} -4.04990e20 q^{57} +3.37671e20 q^{58} -1.49550e20 q^{59} -1.86216e20 q^{61} -5.38410e19 q^{62} -1.50241e21 q^{63} +1.44406e20 q^{64} +8.28370e20 q^{66} +1.62625e21 q^{67} +5.25669e20 q^{68} -1.58794e21 q^{69} +1.03230e21 q^{71} +2.81158e21 q^{72} -4.50707e20 q^{73} -1.55922e21 q^{74} +2.92826e21 q^{76} -3.97376e21 q^{77} +5.03387e21 q^{78} +7.76563e21 q^{79} +4.96569e21 q^{81} +1.49051e22 q^{82} -6.10977e21 q^{83} +1.67495e22 q^{84} +1.21923e22 q^{86} +5.01786e22 q^{87} +7.43640e21 q^{88} +4.80129e22 q^{89} -2.41479e22 q^{91} +1.14815e22 q^{92} -8.00088e21 q^{93} -6.26124e22 q^{94} -8.79353e22 q^{96} -1.13004e23 q^{97} -1.65133e23 q^{98} +7.98365e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 780 q^{2} + 206680 q^{3} + 12685792 q^{4} + 1815003208 q^{6} + 1010710600 q^{7} + 90964721760 q^{8} + 235963350628 q^{9}+O(q^{10}) $ 4 * q + 780 * q^2 + 206680 * q^3 + 12685792 * q^4 + 1815003208 * q^6 + 1010710600 * q^7 + 90964721760 * q^8 + 235963350628 * q^9	$ 4 q + 780 q^{2} + 206680 q^{3} + 12685792 q^{4} + 1815003208 q^{6} + 1010710600 q^{7} + 90964721760 q^{8} + 235963350628 q^{9} + 510770963328 q^{11} + 661143479360 q^{12} + 14153856943960 q^{13} + 64982579554584 q^{14} + 113436824881024 q^{16} - 15332090016360 q^{17} - 13\!\cdots\!20 q^{18}+ \cdots + 48\!\cdots\!96 q^{99}+O(q^{100}) $ 4 * q + 780 * q^2 + 206680 * q^3 + 12685792 * q^4 + 1815003208 * q^6 + 1010710600 * q^7 + 90964721760 * q^8 + 235963350628 * q^9 + 510770963328 * q^11 + 661143479360 * q^12 + 14153856943960 * q^13 + 64982579554584 * q^14 + 113436824881024 * q^16 - 15332090016360 * q^17 - 1358606920324820 * q^18 + 1111809672255440 * q^19 + 7473099301754928 * q^21 - 10708927083459840 * q^22 + 3998020505342040 * q^23 + 20506026884128320 * q^24 - 877714925108472 * q^26 - 7075241632262960 * q^27 + 113078857801120960 * q^28 - 170274795551093640 * q^29 - 172942006080462832 * q^31 + 567511045488564480 * q^32 + 412144491766396160 * q^33 + 207151653136271304 * q^34 - 399040975966317856 * q^36 - 461695977491285480 * q^37 - 2127655695829602960 * q^38 + 6106939319789349776 * q^39 + 1746066900841990488 * q^41 - 9471713482945058160 * q^42 - 13231308551430609800 * q^43 - 21011535794344429056 * q^44 + 22929884441616610248 * q^46 + 25463181064945728360 * q^47 + 71089747411795600640 * q^48 + 27752501816433355572 * q^49 - 125606664173105019632 * q^51 + 155108839850940462400 * q^52 - 19153511824499883720 * q^53 - 134876121729061126160 * q^54 + 411860605716761453760 * q^56 - 492873713134228236320 * q^57 - 221034899302314393240 * q^58 + 217218038347313160720 * q^59 + 152379678911827122728 * q^61 + 363203697269394525360 * q^62 - 1325154150818870981880 * q^63 + 1121074796200062441472 * q^64 - 2099356427487208082944 * q^66 + 2317407910895557756840 * q^67 + 3800878923901661494080 * q^68 + 1219801147861096918416 * q^69 + 1453247054528140867248 * q^71 + 6515421665165001556320 * q^72 - 2601821824581282121160 * q^73 - 3991697886987492208056 * q^74 - 514198358053038321280 * q^76 - 7444709512703076153600 * q^77 + 1414791230076275697200 * q^78 + 22817266427547282683360 * q^79 + 23313538421946355263124 * q^81 + 25020293761756353578760 * q^82 - 49081293110242175251080 * q^83 + 45061681389793768930944 * q^84 - 37195944193834827943512 * q^86 + 58630440765630026531920 * q^87 - 7962508551211096903680 * q^88 + 50023669870473477290280 * q^89 + 55881722079510765798448 * q^91 + 239405355986426422923840 * q^92 - 48979232599473583086240 * q^93 - 34668831477450377120136 * q^94 - 102550574820923244800512 * q^96 + 141223261544238546490360 * q^97 + 8062497360198964195740 * q^98 + 486593842095233676826496 * 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 $

$2$	−3482.94	−1.20255	−0.601273	−	0.799044i	$-0.705339\pi$
$2$	−3482.94	−1.20255	−0.601273	+	0.799044i	$0.705339\pi$
$3$	−517572.	−1.68685	−0.843425	−	0.537246i	$-0.819465\pi$
$3$	−517572.	−1.68685	−0.843425	+	0.537246i	$0.819465\pi$
$4$	3.74229e6	0.446115
$5$	0	0
$5$	0	0
$6$	1.80268e9	2.02851
$7$	−8.64758e9	−1.65298	−0.826489	−	0.562952i	$-0.809666\pi$
$7$	−8.64758e9	−1.65298	−0.826489	+	0.562952i	$0.809666\pi$
$8$	1.61829e10	0.666072
$9$	1.73738e11	1.84547
$10$	0	0
$11$	4.59523e11	0.485614	0.242807	−	0.970075i	$-0.421932\pi$
$11$	4.59523e11	0.485614	0.242807	+	0.970075i	$0.421932\pi$
$12$	−1.93690e12	−0.752530
$13$	2.79244e12	0.432151	0.216076	−	0.976377i	$-0.430674\pi$
$13$	2.79244e12	0.432151	0.216076	+	0.976377i	$0.430674\pi$
$14$	3.01190e13	1.98778
$15$	0	0
$16$	−8.77566e13	−1.24710
$17$	1.40467e14	0.994060	0.497030	−	0.867733i	$-0.334424\pi$
$17$	1.40467e14	0.994060	0.497030	+	0.867733i	$0.334424\pi$
$18$	−6.05119e14	−2.21926
$19$	7.82480e14	1.54101	0.770507	−	0.637431i	$-0.220003\pi$
$19$	7.82480e14	1.54101	0.770507	+	0.637431i	$0.220003\pi$
$20$	0	0
$21$	4.47575e15	2.78833
$22$	−1.60049e15	−0.583973
$23$	3.06806e15	0.671418	0.335709	−	0.941966i	$-0.391024\pi$
$23$	3.06806e15	0.671418	0.335709	+	0.941966i	$0.391024\pi$
$24$	−8.37581e15	−1.12356
$25$	0	0
$26$	−9.72592e15	−0.519681
$27$	−4.11960e16	−1.42617
$28$	−3.23617e16	−0.737419
$29$	−9.69499e16	−1.47561	−0.737803	−	0.675016i	$-0.764137\pi$
$29$	−9.69499e16	−1.47561	−0.737803	+	0.675016i	$0.764137\pi$
$30$	0	0
$31$	1.54585e16	0.109272	0.0546358	−	0.998506i	$-0.482600\pi$
$31$	1.54585e16	0.109272	0.0546358	+	0.998506i	$0.482600\pi$
$32$	1.69899e17	0.833618
$33$	−2.37836e17	−0.819158
$34$	−4.89240e17	−1.19540
$35$	0	0
$36$	6.50177e17	0.823290
$37$	4.47673e17	0.413658	0.206829	−	0.978377i	$-0.433686\pi$
$37$	4.47673e17	0.413658	0.206829	+	0.978377i	$0.433686\pi$
$38$	−2.72533e18	−1.85314
$39$	−1.44529e18	−0.728975
$40$	0	0
$41$	−4.27946e18	−1.21444	−0.607218	−	0.794535i	$-0.707714\pi$
$41$	−4.27946e18	−1.21444	−0.607218	+	0.794535i	$0.707714\pi$
$42$	−1.55888e19	−3.35309
$43$	−3.50056e18	−0.574448	−0.287224	−	0.957863i	$-0.592732\pi$
$43$	−3.50056e18	−0.574448	−0.287224	+	0.957863i	$0.592732\pi$
$44$	1.71967e18	0.216640
$45$	0	0
$46$	−1.06859e19	−0.807411
$47$	1.79769e19	1.06069	0.530345	−	0.847782i	$-0.322062\pi$
$47$	1.79769e19	1.06069	0.530345	+	0.847782i	$0.322062\pi$
$48$	4.54204e19	2.10367
$49$	4.74120e19	1.73234
$50$	0	0
$51$	−7.27020e19	−1.67683
$52$	1.04501e19	0.192789
$53$	−4.84476e19	−0.717959	−0.358980	−	0.933345i	$-0.616875\pi$
$53$	−4.84476e19	−0.717959	−0.358980	+	0.933345i	$0.616875\pi$
$54$	1.43484e20	1.71504
$55$	0	0
$56$	−1.39943e20	−1.10100
$57$	−4.04990e20	−2.59946
$58$	3.37671e20	1.77448
$59$	−1.49550e20	−0.645639	−0.322819	−	0.946461i	$-0.604631\pi$
$59$	−1.49550e20	−0.645639	−0.322819	+	0.946461i	$0.604631\pi$
$60$	0	0
$61$	−1.86216e20	−0.547929	−0.273965	−	0.961740i	$-0.588335\pi$
$61$	−1.86216e20	−0.547929	−0.273965	+	0.961740i	$0.588335\pi$
$62$	−5.38410e19	−0.131404
$63$	−1.50241e21	−3.05051
$64$	1.44406e20	0.244632
$65$	0	0
$66$	8.28370e20	0.985075
$67$	1.62625e21	1.62677	0.813386	−	0.581725i	$-0.197622\pi$
$67$	1.62625e21	1.62677	0.813386	+	0.581725i	$0.197622\pi$
$68$	5.25669e20	0.443465
$69$	−1.58794e21	−1.13258
$70$	0	0
$71$	1.03230e21	0.530073	0.265037	−	0.964238i	$-0.414616\pi$
$71$	1.03230e21	0.530073	0.265037	+	0.964238i	$0.414616\pi$
$72$	2.81158e21	1.22921
$73$	−4.50707e20	−0.168144	−0.0840721	−	0.996460i	$-0.526793\pi$
$73$	−4.50707e20	−0.168144	−0.0840721	+	0.996460i	$0.526793\pi$
$74$	−1.55922e21	−0.497443
$75$	0	0
$76$	2.92826e21	0.687470
$77$	−3.97376e21	−0.802710
$78$	5.03387e21	0.876625
$79$	7.76563e21	1.16806	0.584030	−	0.811732i	$-0.301475\pi$
$79$	7.76563e21	1.16806	0.584030	+	0.811732i	$0.301475\pi$
$80$	0	0
$81$	4.96569e21	0.560276
$82$	1.49051e22	1.46041
$83$	−6.10977e21	−0.520747	−0.260374	−	0.965508i	$-0.583846\pi$
$83$	−6.10977e21	−0.520747	−0.260374	+	0.965508i	$0.583846\pi$
$84$	1.67495e22	1.24392
$85$	0	0
$86$	1.21923e22	0.690799
$87$	5.01786e22	2.48913
$88$	7.43640e21	0.323454
$89$	4.80129e22	1.83389	0.916943	−	0.399017i	$-0.130649\pi$
$89$	4.80129e22	1.83389	0.916943	+	0.399017i	$0.130649\pi$
$90$	0	0
$91$	−2.41479e22	−0.714337
$92$	1.14815e22	0.299530
$93$	−8.00088e21	−0.184325
$94$	−6.26124e22	−1.27553
$95$	0	0
$96$	−8.79353e22	−1.40619
$97$	−1.13004e23	−1.60405	−0.802025	−	0.597291i	$-0.796244\pi$
$97$	−1.13004e23	−1.60405	−0.802025	+	0.597291i	$0.796244\pi$
$98$	−1.65133e23	−2.08322
$99$	7.98365e22	0.896184
$100$	0	0
$101$	6.96717e22	0.621385	0.310692	−	0.950510i	$-0.399439\pi$
$101$	6.96717e22	0.621385	0.310692	+	0.950510i	$0.399439\pi$
$102$	2.53217e23	2.01647
$103$	4.66657e22	0.332177	0.166088	−	0.986111i	$-0.446886\pi$
$103$	4.66657e22	0.332177	0.166088	+	0.986111i	$0.446886\pi$
$104$	4.51898e22	0.287844
$105$	0	0
$106$	1.68740e23	0.863379
$107$	−1.36060e23	−0.624909	−0.312454	−	0.949933i	$-0.601151\pi$
$107$	−1.36060e23	−0.624909	−0.312454	+	0.949933i	$0.601151\pi$
$108$	−1.54167e23	−0.636238
$109$	2.92750e23	1.08665	0.543327	−	0.839521i	$-0.317164\pi$
$109$	2.92750e23	1.08665	0.543327	+	0.839521i	$0.317164\pi$
$110$	0	0
$111$	−2.31703e23	−0.697779
$112$	7.58883e23	2.06142
$113$	−3.58585e23	−0.879407	−0.439704	−	0.898143i	$-0.644916\pi$
$113$	−3.58585e23	−0.879407	−0.439704	+	0.898143i	$0.644916\pi$
$114$	1.41056e24	3.12597
$115$	0	0
$116$	−3.62814e23	−0.658290
$117$	4.85153e23	0.797520
$118$	5.20876e23	0.776410
$119$	−1.21470e24	−1.64316
$120$	0	0
$121$	−6.84269e23	−0.764179
$122$	6.48581e23	0.658910
$123$	2.21493e24	2.04857
$124$	5.78501e22	0.0487477
$125$	0	0
$126$	5.23282e24	3.66838
$127$	1.35565e24	0.867773	0.433887	−	0.900967i	$-0.357142\pi$
$127$	1.35565e24	0.867773	0.433887	+	0.900967i	$0.357142\pi$
$128$	−1.92818e24	−1.12780
$129$	1.81179e24	0.969007
$130$	0	0
$131$	−1.30032e24	−0.582682	−0.291341	−	0.956619i	$-0.594101\pi$
$131$	−1.30032e24	−0.582682	−0.291341	+	0.956619i	$0.594101\pi$
$132$	−8.90051e23	−0.365439
$133$	−6.76656e24	−2.54726
$134$	−5.66413e24	−1.95627
$135$	0	0
$136$	2.27317e24	0.662115
$137$	−1.67618e23	−0.0448780	−0.0224390	−	0.999748i	$-0.507143\pi$
$137$	−1.67618e23	−0.0448780	−0.0224390	+	0.999748i	$0.507143\pi$
$138$	5.53071e24	1.36198
$139$	4.85141e24	1.09951	0.549753	−	0.835327i	$-0.314722\pi$
$139$	4.85141e24	1.09951	0.549753	+	0.835327i	$0.314722\pi$
$140$	0	0
$141$	−9.30433e24	−1.78923
$142$	−3.59545e24	−0.637437
$143$	1.28319e24	0.209859
$144$	−1.52467e25	−2.30147
$145$	0	0
$146$	1.56979e24	0.202201
$147$	−2.45391e25	−2.92220
$148$	1.67532e24	0.184539
$149$	−3.22578e24	−0.328846	−0.164423	−	0.986390i	$-0.552576\pi$
$149$	−3.22578e24	−0.328846	−0.164423	+	0.986390i	$0.552576\pi$
$150$	0	0
$151$	−1.29362e25	−1.13128	−0.565640	−	0.824652i	$-0.691371\pi$
$151$	−1.29362e25	−1.13128	−0.565640	+	0.824652i	$0.691371\pi$
$152$	1.26628e25	1.02643
$153$	2.44045e25	1.83450
$154$	1.38404e25	0.965295
$155$	0	0
$156$	−5.40869e24	−0.325207
$157$	−2.60805e25	−1.45704	−0.728518	−	0.685027i	$-0.759791\pi$
$157$	−2.60805e25	−1.45704	−0.728518	+	0.685027i	$0.759791\pi$
$158$	−2.70472e25	−1.40464
$159$	2.50751e25	1.21109
$160$	0	0
$161$	−2.65313e25	−1.10984
$162$	−1.72952e25	−0.673758
$163$	1.16248e25	0.421919	0.210959	−	0.977495i	$-0.432341\pi$
$163$	1.16248e25	0.421919	0.210959	+	0.977495i	$0.432341\pi$
$164$	−1.60150e25	−0.541778
$165$	0	0
$166$	2.12800e25	0.626222
$167$	−5.88853e24	−0.161721	−0.0808607	−	0.996725i	$-0.525767\pi$
$167$	−5.88853e24	−0.161721	−0.0808607	+	0.996725i	$0.525767\pi$
$168$	7.24305e25	1.85723
$169$	−3.39562e25	−0.813245
$170$	0	0
$171$	1.35946e26	2.84389
$172$	−1.31001e25	−0.256270
$173$	−4.10418e25	−0.751097	−0.375548	−	0.926803i	$-0.622546\pi$
$173$	−4.10418e25	−0.751097	−0.375548	+	0.926803i	$0.622546\pi$
$174$	−1.74769e26	−2.99329
$175$	0	0
$176$	−4.03262e25	−0.605607
$177$	7.74032e25	1.08910
$178$	−1.67226e26	−2.20533
$179$	−3.35956e25	−0.415406	−0.207703	−	0.978192i	$-0.566599\pi$
$179$	−3.35956e25	−0.415406	−0.207703	+	0.978192i	$0.566599\pi$
$180$	0	0
$181$	−5.14467e25	−0.559827	−0.279913	−	0.960025i	$-0.590306\pi$
$181$	−5.14467e25	−0.559827	−0.279913	+	0.960025i	$0.590306\pi$
$182$	8.41057e25	0.859023
$183$	9.63804e25	0.924275
$184$	4.96500e25	0.447213
$185$	0	0
$186$	2.78666e25	0.221659
$187$	6.45479e25	0.482729
$188$	6.72746e25	0.473190
$189$	3.56246e26	2.35743
$190$	0	0
$191$	8.94888e25	0.524669	0.262334	−	0.964977i	$-0.415508\pi$
$191$	8.94888e25	0.524669	0.262334	+	0.964977i	$0.415508\pi$
$192$	−7.47403e25	−0.412658
$193$	−1.00398e26	−0.522173	−0.261087	−	0.965315i	$-0.584081\pi$
$193$	−1.00398e26	−0.522173	−0.261087	+	0.965315i	$0.584081\pi$
$194$	3.93586e26	1.92894
$195$	0	0
$196$	1.77429e26	0.772823
$197$	2.28398e26	0.938277	0.469138	−	0.883125i	$-0.344565\pi$
$197$	2.28398e26	0.938277	0.469138	+	0.883125i	$0.344565\pi$
$198$	−2.78066e26	−1.07770
$199$	3.01704e25	0.110350	0.0551748	−	0.998477i	$-0.482428\pi$
$199$	3.01704e25	0.110350	0.0551748	+	0.998477i	$0.482428\pi$
$200$	0	0
$201$	−8.41701e26	−2.74412
$202$	−2.42663e26	−0.747243
$203$	8.38382e26	2.43914
$204$	−2.72072e26	−0.748060
$205$	0	0
$206$	−1.62534e26	−0.399458
$207$	5.33038e26	1.23908
$208$	−2.45055e26	−0.538934
$209$	3.59567e26	0.748338
$210$	0	0
$211$	6.35486e26	1.18538	0.592690	−	0.805430i	$-0.298066\pi$
$211$	6.35486e26	1.18538	0.592690	+	0.805430i	$0.298066\pi$
$212$	−1.81305e26	−0.320293
$213$	−5.34291e26	−0.894155
$214$	4.73889e26	0.751481
$215$	0	0
$216$	−6.66671e26	−0.949933
$217$	−1.33679e26	−0.180624
$218$	−1.01963e27	−1.30675
$219$	2.33274e26	0.283634
$220$	0	0
$221$	3.92247e26	0.429584
$222$	8.07010e26	0.839111
$223$	−2.33487e26	−0.230546	−0.115273	−	0.993334i	$-0.536774\pi$
$223$	−2.33487e26	−0.230546	−0.115273	+	0.993334i	$0.536774\pi$
$224$	−1.46922e27	−1.37795
$225$	0	0
$226$	1.24893e27	1.05753
$227$	1.62098e27	1.30461	0.652305	−	0.757956i	$-0.273802\pi$
$227$	1.62098e27	1.30461	0.652305	+	0.757956i	$0.273802\pi$
$228$	−1.51559e27	−1.15966
$229$	−1.18775e27	−0.864203	−0.432102	−	0.901825i	$-0.642228\pi$
$229$	−1.18775e27	−0.864203	−0.432102	+	0.901825i	$0.642228\pi$
$230$	0	0
$231$	2.05671e27	1.35405
$232$	−1.56893e27	−0.982859
$233$	2.57303e27	1.53409	0.767046	−	0.641592i	$-0.221726\pi$
$233$	2.57303e27	1.53409	0.767046	+	0.641592i	$0.221726\pi$
$234$	−1.68976e27	−0.959054
$235$	0	0
$236$	−5.59661e26	−0.288029
$237$	−4.01927e27	−1.97034
$238$	4.23074e27	1.97597
$239$	2.57120e27	1.14435	0.572177	−	0.820130i	$-0.306099\pi$
$239$	2.57120e27	1.14435	0.572177	+	0.820130i	$0.306099\pi$
$240$	0	0
$241$	9.02690e26	0.365042	0.182521	−	0.983202i	$-0.441574\pi$
$241$	9.02690e26	0.365042	0.182521	+	0.983202i	$0.441574\pi$
$242$	2.38327e27	0.918960
$243$	1.30822e27	0.481071
$244$	−6.96874e26	−0.244440
$245$	0	0
$246$	−7.71447e27	−2.46350
$247$	2.18503e27	0.665951
$248$	2.50163e26	0.0727827
$249$	3.16225e27	0.878423
$250$	0	0
$251$	1.83880e27	0.465894	0.232947	−	0.972489i	$-0.425163\pi$
$251$	1.83880e27	0.465894	0.232947	+	0.972489i	$0.425163\pi$
$252$	−5.62246e27	−1.36088
$253$	1.40984e27	0.326050
$254$	−4.72167e27	−1.04354
$255$	0	0
$256$	5.50437e27	1.11160
$257$	−4.62113e27	−0.892313	−0.446157	−	0.894955i	$-0.647208\pi$
$257$	−4.62113e27	−0.892313	−0.446157	+	0.894955i	$0.647208\pi$
$258$	−6.31038e27	−1.16528
$259$	−3.87129e27	−0.683768
$260$	0	0
$261$	−1.68439e28	−2.72318
$262$	4.52896e27	0.700702
$263$	−8.97869e27	−1.32960	−0.664801	−	0.747020i	$-0.731484\pi$
$263$	−8.97869e27	−1.32960	−0.664801	+	0.747020i	$0.731484\pi$
$264$	−3.84888e27	−0.545618
$265$	0	0
$266$	2.35675e28	3.06320
$267$	−2.48501e28	−3.09349
$268$	6.08588e27	0.725728
$269$	−4.19862e27	−0.479684	−0.239842	−	0.970812i	$-0.577096\pi$
$269$	−4.19862e27	−0.479684	−0.239842	+	0.970812i	$0.577096\pi$
$270$	0	0
$271$	−1.79741e28	−1.88582	−0.942910	−	0.333048i	$-0.891923\pi$
$271$	−1.79741e28	−1.88582	−0.942910	+	0.333048i	$0.891923\pi$
$272$	−1.23269e28	−1.23969
$273$	1.24983e28	1.20498
$274$	5.83804e26	0.0539679
$275$	0	0
$276$	−5.94253e27	−0.505262
$277$	1.68639e28	1.37543	0.687717	−	0.725979i	$-0.258613\pi$
$277$	1.68639e28	1.37543	0.687717	+	0.725979i	$0.258613\pi$
$278$	−1.68972e28	−1.32221
$279$	2.68573e27	0.201657
$280$	0	0
$281$	−3.68206e27	−0.254665	−0.127332	−	0.991860i	$-0.540641\pi$
$281$	−3.68206e27	−0.254665	−0.127332	+	0.991860i	$0.540641\pi$
$282$	3.24065e28	2.15163
$283$	−1.38319e28	−0.881733	−0.440867	−	0.897573i	$-0.645329\pi$
$283$	−1.38319e28	−0.881733	−0.440867	+	0.897573i	$0.645329\pi$
$284$	3.86317e27	0.236474
$285$	0	0
$286$	−4.46928e27	−0.252365
$287$	3.70070e28	2.00744
$288$	2.95180e28	1.53841
$289$	−2.36505e26	−0.0118445
$290$	0	0
$291$	5.84876e28	2.70579
$292$	−1.68668e27	−0.0750117
$293$	1.22393e28	0.523333	0.261667	−	0.965158i	$-0.415728\pi$
$293$	1.22393e28	0.523333	0.261667	+	0.965158i	$0.415728\pi$
$294$	8.54684e28	3.51408
$295$	0	0
$296$	7.24464e27	0.275526
$297$	−1.89305e28	−0.692570
$298$	1.12352e28	0.395452
$299$	8.56737e27	0.290154
$300$	0	0
$301$	3.02714e28	0.949550
$302$	4.50559e28	1.36042
$303$	−3.60602e28	−1.04818
$304$	−6.86678e28	−1.92179
$305$	0	0
$306$	−8.49995e28	−2.20607
$307$	1.17607e28	0.293997	0.146998	−	0.989137i	$-0.453039\pi$
$307$	1.17607e28	0.293997	0.146998	+	0.989137i	$0.453039\pi$
$308$	−1.48710e28	−0.358101
$309$	−2.41529e28	−0.560333
$310$	0	0
$311$	−1.40025e28	−0.301622	−0.150811	−	0.988563i	$-0.548188\pi$
$311$	−1.40025e28	−0.301622	−0.150811	+	0.988563i	$0.548188\pi$
$312$	−2.33890e28	−0.485549
$313$	−2.95636e28	−0.591559	−0.295780	−	0.955256i	$-0.595579\pi$
$313$	−2.95636e28	−0.591559	−0.295780	+	0.955256i	$0.595579\pi$
$314$	9.08370e28	1.75215
$315$	0	0
$316$	2.90612e28	0.521089
$317$	3.09352e28	0.534898	0.267449	−	0.963572i	$-0.413819\pi$
$317$	3.09352e28	0.534898	0.267449	+	0.963572i	$0.413819\pi$
$318$	−8.73353e28	−1.45639
$319$	−4.45507e28	−0.716575
$320$	0	0
$321$	7.04208e28	1.05413
$322$	9.24069e28	1.33463
$323$	1.09913e29	1.53186
$324$	1.85830e28	0.249948
$325$	0	0
$326$	−4.04886e28	−0.507377
$327$	−1.51519e29	−1.83302
$328$	−6.92540e28	−0.808901
$329$	−1.55457e29	−1.75330
$330$	0	0
$331$	8.94811e28	0.941260	0.470630	−	0.882331i	$-0.344027\pi$
$331$	8.94811e28	0.941260	0.470630	+	0.882331i	$0.344027\pi$
$332$	−2.28645e28	−0.232313
$333$	7.77779e28	0.763391
$334$	2.05094e28	0.194477
$335$	0	0
$336$	−3.92777e29	−3.47731
$337$	1.88248e28	0.161059	0.0805297	−	0.996752i	$-0.474339\pi$
$337$	1.88248e28	0.161059	0.0805297	+	0.996752i	$0.474339\pi$
$338$	1.18267e29	0.977964
$339$	1.85594e29	1.48343
$340$	0	0
$341$	7.10353e27	0.0530638
$342$	−4.73494e29	−3.41990
$343$	−1.73325e29	−1.21054
$344$	−5.66492e28	−0.382623
$345$	0	0
$346$	1.42946e29	0.903228
$347$	−1.45249e29	−0.887818	−0.443909	−	0.896072i	$-0.646409\pi$
$347$	−1.45249e29	−0.887818	−0.443909	+	0.896072i	$0.646409\pi$
$348$	1.87783e29	1.11044
$349$	5.82508e28	0.333280	0.166640	−	0.986018i	$-0.446708\pi$
$349$	5.82508e28	0.333280	0.166640	+	0.986018i	$0.446708\pi$
$350$	0	0
$351$	−1.15038e29	−0.616323
$352$	7.80727e28	0.404817
$353$	6.95395e27	0.0348998	0.0174499	−	0.999848i	$-0.494445\pi$
$353$	6.95395e27	0.0348998	0.0174499	+	0.999848i	$0.494445\pi$
$354$	−2.69591e29	−1.30969
$355$	0	0
$356$	1.79678e29	0.818125
$357$	6.28697e29	2.77177
$358$	1.17012e29	0.499545
$359$	1.54223e29	0.637623	0.318812	−	0.947818i	$-0.396716\pi$
$359$	1.54223e29	0.637623	0.318812	+	0.947818i	$0.396716\pi$
$360$	0	0
$361$	3.54445e29	1.37472
$362$	1.79186e29	0.673217
$363$	3.54159e29	1.28906
$364$	−9.03683e28	−0.318677
$365$	0	0
$366$	−3.35687e29	−1.11148
$367$	−3.30752e29	−1.06131	−0.530656	−	0.847587i	$-0.678054\pi$
$367$	−3.30752e29	−1.06131	−0.530656	+	0.847587i	$0.678054\pi$
$368$	−2.69242e29	−0.837323
$369$	−7.43504e29	−2.24120
$370$	0	0
$371$	4.18955e29	1.18677
$372$	−2.99416e28	−0.0822302
$373$	1.41877e29	0.377799	0.188899	−	0.981996i	$-0.439508\pi$
$373$	1.41877e29	0.377799	0.188899	+	0.981996i	$0.439508\pi$
$374$	−2.24817e29	−0.580504
$375$	0	0
$376$	2.90918e29	0.706496
$377$	−2.70727e29	−0.637685
$378$	−1.24079e30	−2.83492
$379$	−3.35326e29	−0.743219	−0.371610	−	0.928389i	$-0.621194\pi$
$379$	−3.35326e29	−0.743219	−0.371610	+	0.928389i	$0.621194\pi$
$380$	0	0
$381$	−7.01649e29	−1.46380
$382$	−3.11684e29	−0.630938
$383$	6.42876e29	1.26282	0.631410	−	0.775449i	$-0.282477\pi$
$383$	6.42876e29	1.26282	0.631410	+	0.775449i	$0.282477\pi$
$384$	9.97971e29	1.90243
$385$	0	0
$386$	3.49679e29	0.627937
$387$	−6.08180e29	−1.06012
$388$	−4.22892e29	−0.715591
$389$	−1.65277e29	−0.271515	−0.135757	−	0.990742i	$-0.543347\pi$
$389$	−1.65277e29	−0.271515	−0.135757	+	0.990742i	$0.543347\pi$
$390$	0	0
$391$	4.30962e29	0.667430
$392$	7.67262e29	1.15386
$393$	6.73012e29	0.982898
$394$	−7.95498e29	−1.12832
$395$	0	0
$396$	2.98771e29	0.399801
$397$	−8.33502e28	−0.108347	−0.0541734	−	0.998532i	$-0.517252\pi$
$397$	−8.33502e28	−0.108347	−0.0541734	+	0.998532i	$0.517252\pi$
$398$	−1.05082e29	−0.132700
$399$	3.50218e30	4.29685
$400$	0	0
$401$	−1.27732e30	−1.47958	−0.739789	−	0.672839i	$-0.765075\pi$
$401$	−1.27732e30	−1.47958	−0.739789	+	0.672839i	$0.765075\pi$
$402$	2.93160e30	3.29993
$403$	4.31669e28	0.0472219
$404$	2.60731e29	0.277209
$405$	0	0
$406$	−2.92004e30	−2.93318
$407$	2.05716e29	0.200878
$408$	−1.17653e30	−1.11689
$409$	1.55049e30	1.43104	0.715519	−	0.698594i	$-0.246191\pi$
$409$	1.55049e30	1.43104	0.715519	+	0.698594i	$0.246191\pi$
$410$	0	0
$411$	8.67544e28	0.0757026
$412$	1.74636e29	0.148189
$413$	1.29325e30	1.06723
$414$	−1.85654e30	−1.49005
$415$	0	0
$416$	4.74435e29	0.360249
$417$	−2.51095e30	−1.85470
$418$	−1.25235e30	−0.899910
$419$	8.47546e29	0.592518	0.296259	−	0.955108i	$-0.404261\pi$
$419$	8.47546e29	0.592518	0.296259	+	0.955108i	$0.404261\pi$
$420$	0	0
$421$	2.82495e30	1.86968	0.934839	−	0.355072i	$-0.115544\pi$
$421$	2.82495e30	1.86968	0.934839	+	0.355072i	$0.115544\pi$
$422$	−2.21336e30	−1.42547
$423$	3.12327e30	1.95747
$424$	−7.84022e29	−0.478212
$425$	0	0
$426$	1.86091e30	1.07526
$427$	1.61032e30	0.905716
$428$	−5.09175e29	−0.278781
$429$	−6.64144e29	−0.354000
$430$	0	0
$431$	−3.23923e30	−1.63664	−0.818321	−	0.574762i	$-0.805095\pi$
$431$	−3.23923e30	−1.63664	−0.818321	+	0.574762i	$0.805095\pi$
$432$	3.61523e30	1.77858
$433$	−3.92656e30	−1.88105	−0.940527	−	0.339719i	$-0.889668\pi$
$433$	−3.92656e30	−1.88105	−0.940527	+	0.339719i	$0.889668\pi$
$434$	4.65595e29	0.217208
$435$	0	0
$436$	1.09555e30	0.484773
$437$	2.40069e30	1.03467
$438$	−8.12479e29	−0.341083
$439$	−4.50231e30	−1.84117	−0.920585	−	0.390543i	$-0.872287\pi$
$439$	−4.50231e30	−1.84117	−0.920585	+	0.390543i	$0.872287\pi$
$440$	0	0
$441$	8.23726e30	3.19697
$442$	−1.36617e30	−0.516595
$443$	−2.44230e30	−0.899820	−0.449910	−	0.893074i	$-0.648544\pi$
$443$	−2.44230e30	−0.899820	−0.449910	+	0.893074i	$0.648544\pi$
$444$	−8.67100e29	−0.311290
$445$	0	0
$446$	8.13222e29	0.277241
$447$	1.66957e30	0.554714
$448$	−1.24876e30	−0.404372
$449$	5.34123e30	1.68581	0.842904	−	0.538064i	$-0.180844\pi$
$449$	5.34123e30	1.68581	0.842904	+	0.538064i	$0.180844\pi$
$450$	0	0
$451$	−1.96651e30	−0.589747
$452$	−1.34193e30	−0.392317
$453$	6.69540e30	1.90830
$454$	−5.64579e30	−1.56885
$455$	0	0
$456$	−6.55390e30	−1.73143
$457$	−4.09268e30	−1.05432	−0.527159	−	0.849767i	$-0.676743\pi$
$457$	−4.09268e30	−1.05432	−0.527159	+	0.849767i	$0.676743\pi$
$458$	4.13686e30	1.03924
$459$	−5.78670e30	−1.41770
$460$	0	0
$461$	−4.79456e30	−1.11735	−0.558674	−	0.829388i	$-0.688690\pi$
$461$	−4.79456e30	−1.11735	−0.558674	+	0.829388i	$0.688690\pi$
$462$	−7.16340e30	−1.62831
$463$	4.18755e30	0.928493	0.464247	−	0.885706i	$-0.346325\pi$
$463$	4.18755e30	0.928493	0.464247	+	0.885706i	$0.346325\pi$
$464$	8.50799e30	1.84022
$465$	0	0
$466$	−8.96171e30	−1.84482
$467$	−3.38764e29	−0.0680382	−0.0340191	−	0.999421i	$-0.510831\pi$
$467$	−3.38764e29	−0.0680382	−0.0340191	+	0.999421i	$0.510831\pi$
$468$	1.81558e30	0.355786
$469$	−1.40631e31	−2.68902
$470$	0	0
$471$	1.34986e31	2.45780
$472$	−2.42016e30	−0.430042
$473$	−1.60859e30	−0.278960
$474$	1.39989e31	2.36943
$475$	0	0
$476$	−4.54577e30	−0.733039
$477$	−8.41719e30	−1.32497
$478$	−8.95535e30	−1.37614
$479$	1.01289e31	1.51950	0.759752	−	0.650212i	$-0.225320\pi$
$479$	1.01289e31	1.51950	0.759752	+	0.650212i	$0.225320\pi$
$480$	0	0
$481$	1.25010e30	0.178763
$482$	−3.14402e30	−0.438979
$483$	1.37319e31	1.87213
$484$	−2.56073e30	−0.340912
$485$	0	0
$486$	−4.55646e30	−0.578510
$487$	4.51035e30	0.559277	0.279638	−	0.960105i	$-0.409785\pi$
$487$	4.51035e30	0.559277	0.279638	+	0.960105i	$0.409785\pi$
$488$	−3.01351e30	−0.364960
$489$	−6.01669e30	−0.711714
$490$	0	0
$491$	9.02388e29	0.101849	0.0509244	−	0.998703i	$-0.483783\pi$
$491$	9.02388e29	0.101849	0.0509244	+	0.998703i	$0.483783\pi$
$492$	8.28890e30	0.913899
$493$	−1.36183e31	−1.46684
$494$	−7.61034e30	−0.800837
$495$	0	0
$496$	−1.35658e30	−0.136272
$497$	−8.92692e30	−0.876200
$498$	−1.10139e31	−1.05634
$499$	5.96674e30	0.559217	0.279609	−	0.960114i	$-0.409795\pi$
$499$	5.96674e30	0.559217	0.279609	+	0.960114i	$0.409795\pi$
$500$	0	0
$501$	3.04774e30	0.272800
$502$	−6.40445e30	−0.560259
$503$	1.74710e31	1.49378	0.746889	−	0.664948i	$-0.231546\pi$
$503$	1.74710e31	1.49378	0.746889	+	0.664948i	$0.231546\pi$
$504$	−2.43134e31	−2.03186
$505$	0	0
$506$	−4.91040e30	−0.392090
$507$	1.75748e31	1.37182
$508$	5.07325e30	0.387127
$509$	−1.04409e31	−0.778901	−0.389451	−	0.921047i	$-0.627335\pi$
$509$	−1.04409e31	−0.778901	−0.389451	+	0.921047i	$0.627335\pi$
$510$	0	0
$511$	3.89753e30	0.277939
$512$	−2.99668e30	−0.208947
$513$	−3.22351e31	−2.19775
$514$	1.60951e31	1.07305
$515$	0	0
$516$	6.78025e30	0.432289
$517$	8.26078e30	0.515086
$518$	1.34835e31	0.822262
$519$	2.12421e31	1.26699
$520$	0	0
$521$	1.37614e31	0.785289	0.392645	−	0.919690i	$-0.371560\pi$
$521$	1.37614e31	0.785289	0.392645	+	0.919690i	$0.371560\pi$
$522$	5.86662e31	3.27475
$523$	−8.72908e30	−0.476649	−0.238325	−	0.971186i	$-0.576598\pi$
$523$	−8.72908e30	−0.476649	−0.238325	+	0.971186i	$0.576598\pi$
$524$	−4.86619e30	−0.259943
$525$	0	0
$526$	3.12723e31	1.59891
$527$	2.17141e30	0.108623
$528$	2.08717e31	1.02157
$529$	−1.14675e31	−0.549197
$530$	0	0
$531$	−2.59826e31	−1.19150
$532$	−2.53224e31	−1.13637
$533$	−1.19501e31	−0.524820
$534$	8.65516e31	3.72007
$535$	0	0
$536$	2.63174e31	1.08355
$537$	1.73882e31	0.700728
$538$	1.46235e31	0.576842
$539$	2.17869e31	0.841248
$540$	0	0
$541$	1.86887e31	0.691529	0.345765	−	0.938321i	$-0.387620\pi$
$541$	1.86887e31	0.691529	0.345765	+	0.938321i	$0.387620\pi$
$542$	6.26028e31	2.26778
$543$	2.66274e31	0.944344
$544$	2.38653e31	0.828667
$545$	0	0
$546$	−4.35308e31	−1.44904
$547$	−4.47901e31	−1.45992	−0.729958	−	0.683492i	$-0.760460\pi$
$547$	−4.47901e31	−1.45992	−0.729958	+	0.683492i	$0.760460\pi$
$548$	−6.27274e29	−0.0200208
$549$	−3.23528e31	−1.01118
$550$	0	0
$551$	−7.58613e31	−2.27393
$552$	−2.56975e31	−0.754381
$553$	−6.71539e31	−1.93078
$554$	−5.87359e31	−1.65402
$555$	0	0
$556$	1.81553e31	0.490506
$557$	−5.47014e31	−1.44765	−0.723825	−	0.689984i	$-0.757618\pi$
$557$	−5.47014e31	−1.44765	−0.723825	+	0.689984i	$0.757618\pi$
$558$	−9.35423e30	−0.242502
$559$	−9.77512e30	−0.248248
$560$	0	0
$561$	−3.34082e31	−0.814293
$562$	1.28244e31	0.306246
$563$	4.68187e31	1.09540	0.547700	−	0.836675i	$-0.315503\pi$
$563$	4.68187e31	1.09540	0.547700	+	0.836675i	$0.315503\pi$
$564$	−3.48195e31	−0.798202
$565$	0	0
$566$	4.81757e31	1.06032
$567$	−4.29413e31	−0.926125
$568$	1.67056e31	0.353067
$569$	2.97676e31	0.616528	0.308264	−	0.951301i	$-0.400252\pi$
$569$	2.97676e31	0.616528	0.308264	+	0.951301i	$0.400252\pi$
$570$	0	0
$571$	−1.67432e31	−0.333061	−0.166531	−	0.986036i	$-0.553256\pi$
$571$	−1.67432e31	−0.333061	−0.166531	+	0.986036i	$0.553256\pi$
$572$	4.80207e30	0.0936212
$573$	−4.63169e31	−0.885037
$574$	−1.28893e32	−2.41403
$575$	0	0
$576$	2.50887e31	0.451461
$577$	1.06853e32	1.88481	0.942403	−	0.334480i	$-0.108561\pi$
$577$	1.06853e32	1.88481	0.942403	+	0.334480i	$0.108561\pi$
$578$	8.23734e29	0.0142435
$579$	5.19631e31	0.880828
$580$	0	0
$581$	5.28348e31	0.860784
$582$	−2.03709e32	−3.25384
$583$	−2.22628e31	−0.348651
$584$	−7.29374e30	−0.111996
$585$	0	0
$586$	−4.26287e31	−0.629332
$587$	2.57743e31	0.373121	0.186560	−	0.982444i	$-0.440266\pi$
$587$	2.57743e31	0.373121	0.186560	+	0.982444i	$0.440266\pi$
$588$	−9.18324e31	−1.30364
$589$	1.20959e31	0.168389
$590$	0	0
$591$	−1.18213e32	−1.58273
$592$	−3.92863e31	−0.515871
$593$	5.96138e31	0.767747	0.383874	−	0.923386i	$-0.374590\pi$
$593$	5.96138e31	0.767747	0.383874	+	0.923386i	$0.374590\pi$
$594$	6.59339e31	0.832846
$595$	0	0
$596$	−1.20718e31	−0.146703
$597$	−1.56154e31	−0.186143
$598$	−2.98397e31	−0.348924
$599$	1.18951e32	1.36446	0.682230	−	0.731138i	$-0.261010\pi$
$599$	1.18951e32	1.36446	0.682230	+	0.731138i	$0.261010\pi$
$600$	0	0
$601$	1.20295e32	1.32798	0.663988	−	0.747743i	$-0.268863\pi$
$601$	1.20295e32	1.32798	0.663988	+	0.747743i	$0.268863\pi$
$602$	−1.05434e32	−1.14188
$603$	2.82541e32	3.00215
$604$	−4.84108e31	−0.504682
$605$	0	0
$606$	1.25595e32	1.26049
$607$	1.66513e32	1.63976	0.819878	−	0.572538i	$-0.194041\pi$
$607$	1.66513e32	1.63976	0.819878	+	0.572538i	$0.194041\pi$
$608$	1.32943e32	1.28462
$609$	−4.33923e32	−4.11447
$610$	0	0
$611$	5.01994e31	0.458379
$612$	9.13286e31	0.818400
$613$	1.62167e32	1.42615	0.713077	−	0.701086i	$-0.247301\pi$
$613$	1.62167e32	1.42615	0.713077	+	0.701086i	$0.247301\pi$
$614$	−4.09619e31	−0.353544
$615$	0	0
$616$	−6.43069e31	−0.534662
$617$	9.13641e30	0.0745583	0.0372792	−	0.999305i	$-0.488131\pi$
$617$	9.13641e30	0.0745583	0.0372792	+	0.999305i	$0.488131\pi$
$618$	8.41231e31	0.673826
$619$	2.00611e32	1.57729	0.788645	−	0.614849i	$-0.210783\pi$
$619$	2.00611e32	1.57729	0.788645	+	0.614849i	$0.210783\pi$
$620$	0	0
$621$	−1.26392e32	−0.957559
$622$	4.87701e31	0.362714
$623$	−4.15195e32	−3.03138
$624$	1.26834e32	0.909102
$625$	0	0
$626$	1.02968e32	0.711377
$627$	−1.86102e32	−1.26233
$628$	−9.76008e31	−0.650006
$629$	6.28835e31	0.411201
$630$	0	0
$631$	4.21641e31	0.265831	0.132915	−	0.991127i	$-0.457566\pi$
$631$	4.21641e31	0.265831	0.132915	+	0.991127i	$0.457566\pi$
$632$	1.25670e32	0.778011
$633$	−3.28910e32	−1.99956
$634$	−1.07745e32	−0.643239
$635$	0	0
$636$	9.38384e31	0.540286
$637$	1.32395e32	0.748633
$638$	1.55167e32	0.861713
$639$	1.79350e32	0.978232
$640$	0	0
$641$	−1.52885e32	−0.804448	−0.402224	−	0.915541i	$-0.631763\pi$
$641$	−1.52885e32	−0.804448	−0.402224	+	0.915541i	$0.631763\pi$
$642$	−2.45272e32	−1.26764
$643$	−2.75547e32	−1.39884	−0.699422	−	0.714709i	$-0.746559\pi$
$643$	−2.75547e32	−1.39884	−0.699422	+	0.714709i	$0.746559\pi$
$644$	−9.92876e31	−0.495117
$645$	0	0
$646$	−3.82820e32	−1.84213
$647$	2.72847e32	1.28979	0.644896	−	0.764270i	$-0.276901\pi$
$647$	2.72847e32	1.28979	0.644896	+	0.764270i	$0.276901\pi$
$648$	8.03592e31	0.373184
$649$	−6.87218e31	−0.313531
$650$	0	0
$651$	6.91883e31	0.304685
$652$	4.35034e31	0.188224
$653$	−1.77887e32	−0.756209	−0.378105	−	0.925763i	$-0.623424\pi$
$653$	−1.77887e32	−0.756209	−0.378105	+	0.925763i	$0.623424\pi$
$654$	5.27732e32	2.20430
$655$	0	0
$656$	3.75551e32	1.51452
$657$	−7.83050e31	−0.310304
$658$	5.41446e32	2.10842
$659$	−3.66864e32	−1.40386	−0.701928	−	0.712248i	$-0.747677\pi$
$659$	−3.66864e32	−1.40386	−0.701928	+	0.712248i	$0.747677\pi$
$660$	0	0
$661$	1.42358e32	0.526094	0.263047	−	0.964783i	$-0.415273\pi$
$661$	1.42358e32	0.526094	0.263047	+	0.964783i	$0.415273\pi$
$662$	−3.11658e32	−1.13191
$663$	−2.03016e32	−0.724645
$664$	−9.88737e31	−0.346855
$665$	0	0
$666$	−2.70896e32	−0.918013
$667$	−2.97448e32	−0.990748
$668$	−2.20366e31	−0.0721464
$669$	1.20846e32	0.388896
$670$	0	0
$671$	−8.55706e31	−0.266082
$672$	7.60428e32	2.32440
$673$	4.30783e32	1.29445	0.647225	−	0.762299i	$-0.275929\pi$
$673$	4.30783e32	1.29445	0.647225	+	0.762299i	$0.275929\pi$
$674$	−6.55656e31	−0.193681
$675$	0	0
$676$	−1.27074e32	−0.362801
$677$	4.18262e32	1.17403	0.587015	−	0.809576i	$-0.300303\pi$
$677$	4.18262e32	1.17403	0.587015	+	0.809576i	$0.300303\pi$
$678$	−6.46412e32	−1.78389
$679$	9.77209e32	2.65146
$680$	0	0
$681$	−8.38975e32	−2.20068
$682$	−2.47412e31	−0.0638117
$683$	6.21337e32	1.57576	0.787878	−	0.615832i	$-0.211180\pi$
$683$	6.21337e32	1.57576	0.787878	+	0.615832i	$0.211180\pi$
$684$	5.08750e32	1.26870
$685$	0	0
$686$	6.03683e32	1.45573
$687$	6.14745e32	1.45778
$688$	3.07197e32	0.716392
$689$	−1.35287e32	−0.310267
$690$	0	0
$691$	−3.22727e32	−0.715876	−0.357938	−	0.933745i	$-0.616520\pi$
$691$	−3.22727e32	−0.715876	−0.357938	+	0.933745i	$0.616520\pi$
$692$	−1.53590e32	−0.335076
$693$	−6.90393e32	−1.48137
$694$	5.05894e32	1.06764
$695$	0	0
$696$	8.12034e32	1.65794
$697$	−6.01124e32	−1.20722
$698$	−2.02884e32	−0.400785
$699$	−1.33173e33	−2.58779
$700$	0	0
$701$	6.04008e32	1.13576	0.567879	−	0.823112i	$-0.307764\pi$
$701$	6.04008e32	1.13576	0.567879	+	0.823112i	$0.307764\pi$
$702$	4.00670e32	0.741156
$703$	3.50295e32	0.637453
$704$	6.63576e31	0.118797
$705$	0	0
$706$	−2.42202e31	−0.0419685
$707$	−6.02492e32	−1.02714
$708$	2.89665e32	0.485862
$709$	1.41695e32	0.233842	0.116921	−	0.993141i	$-0.462698\pi$
$709$	1.41695e32	0.233842	0.116921	+	0.993141i	$0.462698\pi$
$710$	0	0
$711$	1.34918e33	2.15561
$712$	7.76986e32	1.22150
$713$	4.74275e31	0.0733670
$714$	−2.18971e33	−3.33317
$715$	0	0
$716$	−1.25724e32	−0.185319
$717$	−1.33078e33	−1.93035
$718$	−5.37151e32	−0.766771
$719$	−7.99309e32	−1.12288	−0.561439	−	0.827518i	$-0.689752\pi$
$719$	−7.99309e32	−1.12288	−0.561439	+	0.827518i	$0.689752\pi$
$720$	0	0
$721$	−4.03545e32	−0.549081
$722$	−1.23451e33	−1.65317
$723$	−4.67207e32	−0.615771
$724$	−1.92528e32	−0.249747
$725$	0	0
$726$	−1.23351e33	−1.55015
$727$	5.38025e32	0.665514	0.332757	−	0.943013i	$-0.392021\pi$
$727$	5.38025e32	0.665514	0.332757	+	0.943013i	$0.392021\pi$
$728$	−3.90782e32	−0.475800
$729$	−1.14459e33	−1.37177
$730$	0	0
$731$	−4.91714e32	−0.571036
$732$	3.60683e32	0.412333
$733$	−2.14429e32	−0.241317	−0.120658	−	0.992694i	$-0.538501\pi$
$733$	−2.14429e32	−0.241317	−0.120658	+	0.992694i	$0.538501\pi$
$734$	1.15199e33	1.27628
$735$	0	0
$736$	5.21261e32	0.559707
$737$	7.47298e32	0.789983
$738$	2.58958e33	2.69514
$739$	1.13335e33	1.16132	0.580660	−	0.814146i	$-0.302795\pi$
$739$	1.13335e33	1.16132	0.580660	+	0.814146i	$0.302795\pi$
$740$	0	0
$741$	−1.13091e33	−1.12336
$742$	−1.45920e33	−1.42715
$743$	6.51220e32	0.627128	0.313564	−	0.949567i	$-0.398477\pi$
$743$	6.51220e32	0.627128	0.313564	+	0.949567i	$0.398477\pi$
$744$	−1.29477e32	−0.122774
$745$	0	0
$746$	−4.94150e32	−0.454320
$747$	−1.06150e33	−0.961021
$748$	2.41557e32	0.215353
$749$	1.17659e33	1.03296
$750$	0	0
$751$	−3.51591e32	−0.299349	−0.149675	−	0.988735i	$-0.547823\pi$
$751$	−3.51591e32	−0.299349	−0.149675	+	0.988735i	$0.547823\pi$
$752$	−1.57759e33	−1.32278
$753$	−9.51714e32	−0.785894
$754$	9.42927e32	0.766845
$755$	0	0
$756$	1.33318e33	1.05169
$757$	−6.99863e32	−0.543764	−0.271882	−	0.962331i	$-0.587646\pi$
$757$	−6.99863e32	−0.543764	−0.271882	+	0.962331i	$0.587646\pi$
$758$	1.16792e33	0.893755
$759$	−7.29695e32	−0.549998
$760$	0	0
$761$	−4.14558e32	−0.303153	−0.151576	−	0.988446i	$-0.548435\pi$
$761$	−4.14558e32	−0.303153	−0.151576	+	0.988446i	$0.548435\pi$
$762$	2.44381e33	1.76029
$763$	−2.53158e33	−1.79622
$764$	3.34893e32	0.234063
$765$	0	0
$766$	−2.23910e33	−1.51860
$767$	−4.17611e32	−0.279014
$768$	−2.84891e33	−1.87510
$769$	9.81121e32	0.636165	0.318082	−	0.948063i	$-0.396961\pi$
$769$	9.81121e32	0.636165	0.318082	+	0.948063i	$0.396961\pi$
$770$	0	0
$771$	2.39177e33	1.50520
$772$	−3.75717e32	−0.232949
$773$	2.80480e33	1.71332	0.856659	−	0.515883i	$-0.172536\pi$
$773$	2.80480e33	1.71332	0.856659	+	0.515883i	$0.172536\pi$
$774$	2.11826e33	1.27485
$775$	0	0
$776$	−1.82873e33	−1.06841
$777$	2.00367e33	1.15341
$778$	5.75652e32	0.326509
$779$	−3.34859e33	−1.87146
$780$	0	0
$781$	4.74367e32	0.257411
$782$	−1.50101e33	−0.802615
$783$	3.99395e33	2.10447
$784$	−4.16071e33	−2.16039
$785$	0	0
$786$	−2.34406e33	−1.18198
$787$	−1.29475e31	−0.00643395	−0.00321697	−	0.999995i	$-0.501024\pi$
$787$	−1.29475e31	−0.00643395	−0.00321697	+	0.999995i	$0.501024\pi$
$788$	8.54731e32	0.418580
$789$	4.64712e33	2.24284
$790$	0	0
$791$	3.10089e33	1.45364
$792$	1.29198e33	0.596922
$793$	−5.19998e32	−0.236788
$794$	2.90304e32	0.130292
$795$	0	0
$796$	1.12906e32	0.0492287
$797$	4.31035e33	1.85243	0.926214	−	0.376998i	$-0.123044\pi$
$797$	4.31035e33	1.85243	0.926214	+	0.376998i	$0.123044\pi$
$798$	−1.21979e34	−5.16716
$799$	2.52516e33	1.05439
$800$	0	0
$801$	8.34166e33	3.38437
$802$	4.44882e33	1.77926
$803$	−2.07110e32	−0.0816532
$804$	−3.14989e33	−1.22419
$805$	0	0
$806$	−1.50348e32	−0.0567864
$807$	2.17309e33	0.809155
$808$	1.12749e33	0.413887
$809$	1.38091e33	0.499754	0.249877	−	0.968278i	$-0.419610\pi$
$809$	1.38091e33	0.499754	0.249877	+	0.968278i	$0.419610\pi$
$810$	0	0
$811$	−5.31082e33	−1.86819	−0.934097	−	0.357019i	$-0.883793\pi$
$811$	−5.31082e33	−1.86819	−0.934097	+	0.357019i	$0.883793\pi$
$812$	3.13747e33	1.08814
$813$	9.30290e33	3.18110
$814$	−7.16498e32	−0.241565
$815$	0	0
$816$	6.38008e33	2.09117
$817$	−2.73912e33	−0.885232
$818$	−5.40027e33	−1.72089
$819$	−4.19540e33	−1.31828
$820$	0	0
$821$	3.74336e33	1.14371	0.571854	−	0.820355i	$-0.306224\pi$
$821$	3.74336e33	1.14371	0.571854	+	0.820355i	$0.306224\pi$
$822$	−3.02161e32	−0.0910358
$823$	−5.42555e33	−1.61193	−0.805965	−	0.591964i	$-0.798353\pi$
$823$	−5.42555e33	−1.61193	−0.805965	+	0.591964i	$0.798353\pi$
$824$	7.55185e32	0.221254
$825$	0	0
$826$	−4.50432e33	−1.28339
$827$	−4.40624e33	−1.23810	−0.619049	−	0.785352i	$-0.712482\pi$
$827$	−4.40624e33	−1.23810	−0.619049	+	0.785352i	$0.712482\pi$
$828$	1.99478e33	0.552772
$829$	−2.97522e32	−0.0813098	−0.0406549	−	0.999173i	$-0.512944\pi$
$829$	−2.97522e32	−0.0813098	−0.0406549	+	0.999173i	$0.512944\pi$
$830$	0	0
$831$	−8.72827e33	−2.32015
$832$	4.03244e32	0.105718
$833$	6.65983e33	1.72205
$834$	8.74551e33	2.23036
$835$	0	0
$836$	1.34560e33	0.333845
$837$	−6.36829e32	−0.155840
$838$	−2.95195e33	−0.712530
$839$	3.05689e33	0.727809	0.363904	−	0.931436i	$-0.381443\pi$
$839$	3.05689e33	0.727809	0.363904	+	0.931436i	$0.381443\pi$
$840$	0	0
$841$	5.08255e33	1.17741
$842$	−9.83914e33	−2.24837
$843$	1.90573e33	0.429581
$844$	2.37817e33	0.528816
$845$	0	0
$846$	−1.08782e34	−2.35394
$847$	5.91727e33	1.26317
$848$	4.25160e33	0.895365
$849$	7.15900e33	1.48735
$850$	0	0
$851$	1.37349e33	0.277738
$852$	−1.99947e33	−0.398896
$853$	2.74815e33	0.540911	0.270456	−	0.962732i	$-0.412826\pi$
$853$	2.74815e33	0.540911	0.270456	+	0.962732i	$0.412826\pi$
$854$	−5.60866e33	−1.08916
$855$	0	0
$856$	−2.20184e33	−0.416234
$857$	−7.03785e33	−1.31269	−0.656343	−	0.754463i	$-0.727897\pi$
$857$	−7.03785e33	−1.31269	−0.656343	+	0.754463i	$0.727897\pi$
$858$	2.31318e33	0.425701
$859$	−5.19873e33	−0.944009	−0.472005	−	0.881596i	$-0.656469\pi$
$859$	−5.19873e33	−0.944009	−0.472005	+	0.881596i	$0.656469\pi$
$860$	0	0
$861$	−1.91538e34	−3.38625
$862$	1.12821e34	1.96814
$863$	−4.99662e33	−0.860107	−0.430054	−	0.902803i	$-0.641505\pi$
$863$	−4.99662e33	−0.860107	−0.430054	+	0.902803i	$0.641505\pi$
$864$	−6.99919e33	−1.18888
$865$	0	0
$866$	1.36760e34	2.26205
$867$	1.22408e32	0.0199798
$868$	−5.00263e32	−0.0805790
$869$	3.56848e33	0.567226
$870$	0	0
$871$	4.54121e33	0.703011
$872$	4.73753e33	0.723790
$873$	−1.96330e34	−2.96022
$874$	−8.36147e33	−1.24423
$875$	0	0
$876$	8.72977e32	0.126534
$877$	−8.71040e33	−1.24607	−0.623035	−	0.782194i	$-0.714101\pi$
$877$	−8.71040e33	−1.24607	−0.623035	+	0.782194i	$0.714101\pi$
$878$	1.56813e34	2.21409
$879$	−6.33471e33	−0.882785
$880$	0	0
$881$	1.34397e33	0.182460	0.0912301	−	0.995830i	$-0.470920\pi$
$881$	1.34397e33	0.182460	0.0912301	+	0.995830i	$0.470920\pi$
$882$	−2.86899e34	−3.84450
$883$	9.50375e33	1.25703	0.628517	−	0.777796i	$-0.283662\pi$
$883$	9.50375e33	1.25703	0.628517	+	0.777796i	$0.283662\pi$
$884$	1.46790e33	0.191644
$885$	0	0
$886$	8.50639e33	1.08207
$887$	1.82994e33	0.229782	0.114891	−	0.993378i	$-0.463348\pi$
$887$	1.82994e33	0.229782	0.114891	+	0.993378i	$0.463348\pi$
$888$	−3.74963e33	−0.464771
$889$	−1.17231e34	−1.43441
$890$	0	0
$891$	2.28185e33	0.272078
$892$	−8.73775e32	−0.102850
$893$	1.40665e34	1.63454
$894$	−5.81503e33	−0.667069
$895$	0	0
$896$	1.66741e34	1.86423
$897$	−4.43423e33	−0.489447
$898$	−1.86032e34	−2.02726
$899$	−1.49870e33	−0.161242
$900$	0	0
$901$	−6.80531e33	−0.713695
$902$	6.84924e33	0.709197
$903$	−1.56676e34	−1.60175
$904$	−5.80294e33	−0.585748
$905$	0	0
$906$	−2.33197e34	−2.29482
$907$	−1.77973e34	−1.72930	−0.864650	−	0.502375i	$-0.832460\pi$
$907$	−1.77973e34	−1.72930	−0.864650	+	0.502375i	$0.832460\pi$
$908$	6.06618e33	0.582007
$909$	1.21046e34	1.14674
$910$	0	0
$911$	1.74322e34	1.61024	0.805119	−	0.593114i	$-0.202102\pi$
$911$	1.74322e34	1.61024	0.805119	+	0.593114i	$0.202102\pi$
$912$	3.55405e34	3.24178
$913$	−2.80758e33	−0.252882
$914$	1.42546e34	1.26787
$915$	0	0
$916$	−4.44489e33	−0.385534
$917$	1.12447e34	0.963162
$918$	2.01547e34	1.70485
$919$	−1.47114e34	−1.22893	−0.614464	−	0.788945i	$-0.710628\pi$
$919$	−1.47114e34	−1.22893	−0.614464	+	0.788945i	$0.710628\pi$
$920$	0	0
$921$	−6.08702e33	−0.495928
$922$	1.66992e34	1.34366
$923$	2.88265e33	0.229072
$924$	7.69679e33	0.604063
$925$	0	0
$926$	−1.45850e34	−1.11656
$927$	8.10760e33	0.613021
$928$	−1.64717e34	−1.23009
$929$	8.36002e33	0.616633	0.308317	−	0.951284i	$-0.400234\pi$
$929$	8.36002e33	0.616633	0.308317	+	0.951284i	$0.400234\pi$
$930$	0	0
$931$	3.70989e34	2.66956
$932$	9.62901e33	0.684382
$933$	7.24733e33	0.508791
$934$	1.17990e33	0.0818191
$935$	0	0
$936$	7.85118e33	0.531205
$937$	1.67822e34	1.12161	0.560807	−	0.827947i	$-0.310491\pi$
$937$	1.67822e34	1.12161	0.560807	+	0.827947i	$0.310491\pi$
$938$	4.89810e34	3.23367
$939$	1.53013e34	0.997872
$940$	0	0
$941$	−2.19130e34	−1.39451	−0.697254	−	0.716824i	$-0.745595\pi$
$941$	−2.19130e34	−1.39451	−0.697254	+	0.716824i	$0.745595\pi$
$942$	−4.70147e34	−2.95562
$943$	−1.31296e34	−0.815394
$944$	1.31240e34	0.805174
$945$	0	0
$946$	5.60262e33	0.335462
$947$	−1.41902e34	−0.839388	−0.419694	−	0.907666i	$-0.637863\pi$
$947$	−1.41902e34	−0.839388	−0.419694	+	0.907666i	$0.637863\pi$
$948$	−1.50413e34	−0.879000
$949$	−1.25857e33	−0.0726637
$950$	0	0
$951$	−1.60112e34	−0.902293
$952$	−1.96574e34	−1.09446
$953$	9.37154e33	0.515517	0.257758	−	0.966209i	$-0.417016\pi$
$953$	9.37154e33	0.515517	0.257758	+	0.966209i	$0.417016\pi$
$954$	2.93166e34	1.59334
$955$	0	0
$956$	9.62217e33	0.510513
$957$	2.30582e34	1.20875
$958$	−3.52782e34	−1.82727
$959$	1.44949e33	0.0741825
$960$	0	0
$961$	−1.97743e34	−0.988060
$962$	−4.35404e33	−0.214970
$963$	−2.36388e34	−1.15325
$964$	3.37812e33	0.162851
$965$	0	0
$966$	−4.78273e34	−2.25133
$967$	4.30462e33	0.200231	0.100115	−	0.994976i	$-0.468079\pi$
$967$	4.30462e33	0.200231	0.100115	+	0.994976i	$0.468079\pi$
$968$	−1.10734e34	−0.508998
$969$	−5.68878e34	−2.58402
$970$	0	0
$971$	3.14085e33	0.139324	0.0696619	−	0.997571i	$-0.477808\pi$
$971$	3.14085e33	0.139324	0.0696619	+	0.997571i	$0.477808\pi$
$972$	4.89574e33	0.214613
$973$	−4.19529e34	−1.81746
$974$	−1.57093e34	−0.672556
$975$	0	0
$976$	1.63417e34	0.683321
$977$	−1.88718e33	−0.0779877	−0.0389939	−	0.999239i	$-0.512415\pi$
$977$	−1.88718e33	−0.0779877	−0.0389939	+	0.999239i	$0.512415\pi$
$978$	2.09558e34	0.855869
$979$	2.20630e34	0.890561
$980$	0	0
$981$	5.08617e34	2.00538
$982$	−3.14297e33	−0.122478
$983$	3.74187e34	1.44120	0.720599	−	0.693352i	$-0.243867\pi$
$983$	3.74187e34	1.44120	0.720599	+	0.693352i	$0.243867\pi$
$984$	3.58439e34	1.36450
$985$	0	0
$986$	4.74317e34	1.76394
$987$	8.04600e34	2.95755
$988$	8.17701e33	0.297091
$989$	−1.07399e34	−0.385695
$990$	0	0
$991$	−3.57254e34	−1.25352	−0.626759	−	0.779213i	$-0.715619\pi$
$991$	−3.57254e34	−1.25352	−0.626759	+	0.779213i	$0.715619\pi$
$992$	2.62639e33	0.0910909
$993$	−4.63130e34	−1.58776
$994$	3.10920e34	1.05367
$995$	0	0
$996$	1.18340e34	0.391878
$997$	7.47285e33	0.244620	0.122310	−	0.992492i	$-0.460970\pi$
$997$	7.47285e33	0.244620	0.122310	+	0.992492i	$0.460970\pi$
$998$	−2.07818e34	−0.672484
$999$	−1.84424e34	−0.589948

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.24.a.c.1.1		4
5.2	odd	4		25.24.b.c.24.2		8
5.3	odd	4		25.24.b.c.24.7		8
5.4	even	2		5.24.a.b.1.4	✓	4
15.14	odd	2		45.24.a.d.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.a.b.1.4	✓	4	5.4	even	2
25.24.a.c.1.1		4	1.1	even	1	trivial
25.24.b.c.24.2		8	5.2	odd	4
25.24.b.c.24.7		8	5.3	odd	4
45.24.a.d.1.1		4	15.14	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:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

\(f(q)\)	\(=\)	\(q-3482.94 q^{2} -517572. q^{3} +3.74229e6 q^{4} +1.80268e9 q^{6} -8.64758e9 q^{7} +1.61829e10 q^{8} +1.73738e11 q^{9} +O(q^{10})\)	\(q-3482.94 q^{2} -517572. q^{3} +3.74229e6 q^{4} +1.80268e9 q^{6} -8.64758e9 q^{7} +1.61829e10 q^{8} +1.73738e11 q^{9} +4.59523e11 q^{11} -1.93690e12 q^{12} +2.79244e12 q^{13} +3.01190e13 q^{14} -8.77566e13 q^{16} +1.40467e14 q^{17} -6.05119e14 q^{18} +7.82480e14 q^{19} +4.47575e15 q^{21} -1.60049e15 q^{22} +3.06806e15 q^{23} -8.37581e15 q^{24} -9.72592e15 q^{26} -4.11960e16 q^{27} -3.23617e16 q^{28} -9.69499e16 q^{29} +1.54585e16 q^{31} +1.69899e17 q^{32} -2.37836e17 q^{33} -4.89240e17 q^{34} +6.50177e17 q^{36} +4.47673e17 q^{37} -2.72533e18 q^{38} -1.44529e18 q^{39} -4.27946e18 q^{41} -1.55888e19 q^{42} -3.50056e18 q^{43} +1.71967e18 q^{44} -1.06859e19 q^{46} +1.79769e19 q^{47} +4.54204e19 q^{48} +4.74120e19 q^{49} -7.27020e19 q^{51} +1.04501e19 q^{52} -4.84476e19 q^{53} +1.43484e20 q^{54} -1.39943e20 q^{56} -4.04990e20 q^{57} +3.37671e20 q^{58} -1.49550e20 q^{59} -1.86216e20 q^{61} -5.38410e19 q^{62} -1.50241e21 q^{63} +1.44406e20 q^{64} +8.28370e20 q^{66} +1.62625e21 q^{67} +5.25669e20 q^{68} -1.58794e21 q^{69} +1.03230e21 q^{71} +2.81158e21 q^{72} -4.50707e20 q^{73} -1.55922e21 q^{74} +2.92826e21 q^{76} -3.97376e21 q^{77} +5.03387e21 q^{78} +7.76563e21 q^{79} +4.96569e21 q^{81} +1.49051e22 q^{82} -6.10977e21 q^{83} +1.67495e22 q^{84} +1.21923e22 q^{86} +5.01786e22 q^{87} +7.43640e21 q^{88} +4.80129e22 q^{89} -2.41479e22 q^{91} +1.14815e22 q^{92} -8.00088e21 q^{93} -6.26124e22 q^{94} -8.79353e22 q^{96} -1.13004e23 q^{97} -1.65133e23 q^{98} +7.98365e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 780 q^{2} + 206680 q^{3} + 12685792 q^{4} + 1815003208 q^{6} + 1010710600 q^{7} + 90964721760 q^{8} + 235963350628 q^{9}+O(q^{10}) \) 4 * q + 780 * q^2 + 206680 * q^3 + 12685792 * q^4 + 1815003208 * q^6 + 1010710600 * q^7 + 90964721760 * q^8 + 235963350628 * q^9	\( 4 q + 780 q^{2} + 206680 q^{3} + 12685792 q^{4} + 1815003208 q^{6} + 1010710600 q^{7} + 90964721760 q^{8} + 235963350628 q^{9} + 510770963328 q^{11} + 661143479360 q^{12} + 14153856943960 q^{13} + 64982579554584 q^{14} + 113436824881024 q^{16} - 15332090016360 q^{17} - 13\!\cdots\!20 q^{18}+ \cdots + 48\!\cdots\!96 q^{99}+O(q^{100}) \) 4 * q + 780 * q^2 + 206680 * q^3 + 12685792 * q^4 + 1815003208 * q^6 + 1010710600 * q^7 + 90964721760 * q^8 + 235963350628 * q^9 + 510770963328 * q^11 + 661143479360 * q^12 + 14153856943960 * q^13 + 64982579554584 * q^14 + 113436824881024 * q^16 - 15332090016360 * q^17 - 1358606920324820 * q^18 + 1111809672255440 * q^19 + 7473099301754928 * q^21 - 10708927083459840 * q^22 + 3998020505342040 * q^23 + 20506026884128320 * q^24 - 877714925108472 * q^26 - 7075241632262960 * q^27 + 113078857801120960 * q^28 - 170274795551093640 * q^29 - 172942006080462832 * q^31 + 567511045488564480 * q^32 + 412144491766396160 * q^33 + 207151653136271304 * q^34 - 399040975966317856 * q^36 - 461695977491285480 * q^37 - 2127655695829602960 * q^38 + 6106939319789349776 * q^39 + 1746066900841990488 * q^41 - 9471713482945058160 * q^42 - 13231308551430609800 * q^43 - 21011535794344429056 * q^44 + 22929884441616610248 * q^46 + 25463181064945728360 * q^47 + 71089747411795600640 * q^48 + 27752501816433355572 * q^49 - 125606664173105019632 * q^51 + 155108839850940462400 * q^52 - 19153511824499883720 * q^53 - 134876121729061126160 * q^54 + 411860605716761453760 * q^56 - 492873713134228236320 * q^57 - 221034899302314393240 * q^58 + 217218038347313160720 * q^59 + 152379678911827122728 * q^61 + 363203697269394525360 * q^62 - 1325154150818870981880 * q^63 + 1121074796200062441472 * q^64 - 2099356427487208082944 * q^66 + 2317407910895557756840 * q^67 + 3800878923901661494080 * q^68 + 1219801147861096918416 * q^69 + 1453247054528140867248 * q^71 + 6515421665165001556320 * q^72 - 2601821824581282121160 * q^73 - 3991697886987492208056 * q^74 - 514198358053038321280 * q^76 - 7444709512703076153600 * q^77 + 1414791230076275697200 * q^78 + 22817266427547282683360 * q^79 + 23313538421946355263124 * q^81 + 25020293761756353578760 * q^82 - 49081293110242175251080 * q^83 + 45061681389793768930944 * q^84 - 37195944193834827943512 * q^86 + 58630440765630026531920 * q^87 - 7962508551211096903680 * q^88 + 50023669870473477290280 * q^89 + 55881722079510765798448 * q^91 + 239405355986426422923840 * q^92 - 48979232599473583086240 * q^93 - 34668831477450377120136 * q^94 - 102550574820923244800512 * q^96 + 141223261544238546490360 * q^97 + 8062497360198964195740 * q^98 + 486593842095233676826496 * q^99

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