LMFDB - Embedded newform 5.24.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,24,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, 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("5.1");

S:= CuspForms(chi, 24);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 24 $
Character orbit:	$[\chi]$	$=$	5.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:	$16.7602018673$
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:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-1838.47$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+3482.94 q^{2} +517572. q^{3} +3.74229e6 q^{4} -4.88281e7 q^{5} +1.80268e9 q^{6} +8.64758e9 q^{7} -1.61829e10 q^{8} +1.73738e11 q^{9} +O(q^{10})$	\(q+3482.94 q^{2} +517572. q^{3} +3.74229e6 q^{4} -4.88281e7 q^{5} +1.80268e9 q^{6} +8.64758e9 q^{7} -1.61829e10 q^{8} +1.73738e11 q^{9} -1.70066e11 q^{10} +4.59523e11 q^{11} +1.93690e12 q^{12} -2.79244e12 q^{13} +3.01190e13 q^{14} -2.52721e13 q^{15} -8.77566e13 q^{16} -1.40467e14 q^{17} +6.05119e14 q^{18} +7.82480e14 q^{19} -1.82729e14 q^{20} +4.47575e15 q^{21} +1.60049e15 q^{22} -3.06806e15 q^{23} -8.37581e15 q^{24} +2.38419e15 q^{25} -9.72592e15 q^{26} +4.11960e16 q^{27} +3.23617e16 q^{28} -9.69499e16 q^{29} -8.80212e16 q^{30} +1.54585e16 q^{31} -1.69899e17 q^{32} +2.37836e17 q^{33} -4.89240e17 q^{34} -4.22245e17 q^{35} +6.50177e17 q^{36} -4.47673e17 q^{37} +2.72533e18 q^{38} -1.44529e18 q^{39} +7.90180e17 q^{40} -4.27946e18 q^{41} +1.55888e19 q^{42} +3.50056e18 q^{43} +1.71967e18 q^{44} -8.48330e18 q^{45} -1.06859e19 q^{46} -1.79769e19 q^{47} -4.54204e19 q^{48} +4.74120e19 q^{49} +8.30398e18 q^{50} -7.27020e19 q^{51} -1.04501e19 q^{52} +4.84476e19 q^{53} +1.43484e20 q^{54} -2.24376e19 q^{55} -1.39943e20 q^{56} +4.04990e20 q^{57} -3.37671e20 q^{58} -1.49550e20 q^{59} -9.45754e19 q^{60} -1.86216e20 q^{61} +5.38410e19 q^{62} +1.50241e21 q^{63} +1.44406e20 q^{64} +1.36350e20 q^{65} +8.28370e20 q^{66} -1.62625e21 q^{67} -5.25669e20 q^{68} -1.58794e21 q^{69} -1.47066e21 q^{70} +1.03230e21 q^{71} -2.81158e21 q^{72} +4.50707e20 q^{73} -1.55922e21 q^{74} +1.23399e21 q^{75} +2.92826e21 q^{76} +3.97376e21 q^{77} -5.03387e21 q^{78} +7.76563e21 q^{79} +4.28499e21 q^{80} +4.96569e21 q^{81} -1.49051e22 q^{82} +6.10977e21 q^{83} +1.67495e22 q^{84} +6.85876e21 q^{85} +1.21923e22 q^{86} -5.01786e22 q^{87} -7.43640e21 q^{88} +4.80129e22 q^{89} -2.95468e22 q^{90} -2.41479e22 q^{91} -1.14815e22 q^{92} +8.00088e21 q^{93} -6.26124e22 q^{94} -3.82070e22 q^{95} -8.79353e22 q^{96} +1.13004e23 q^{97} +1.65133e23 q^{98} +7.98365e22 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 780 q^{2} - 206680 q^{3} + 12685792 q^{4} - 195312500 q^{5} + 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 - 195312500 * q^5 + 1815003208 * q^6 - 1010710600 * q^7 - 90964721760 * q^8 + 235963350628 * q^9	$ 4 q - 780 q^{2} - 206680 q^{3} + 12685792 q^{4} - 195312500 q^{5} + 1815003208 q^{6} - 1010710600 q^{7} - 90964721760 q^{8} + 235963350628 q^{9} + 38085937500 q^{10} + 510770963328 q^{11} - 661143479360 q^{12} - 14153856943960 q^{13} + 64982579554584 q^{14} + 10091796875000 q^{15} + 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 - 195312500 * q^5 + 1815003208 * q^6 - 1010710600 * q^7 - 90964721760 * q^8 + 235963350628 * q^9 + 38085937500 * q^10 + 510770963328 * q^11 - 661143479360 * q^12 - 14153856943960 * q^13 + 64982579554584 * q^14 + 10091796875000 * q^15 + 113436824881024 * q^16 + 15332090016360 * q^17 + 1358606920324820 * q^18 + 1111809672255440 * q^19 - 619423437500000 * q^20 + 7473099301754928 * q^21 + 10708927083459840 * q^22 - 3998020505342040 * q^23 + 20506026884128320 * q^24 + 9536743164062500 * q^25 - 877714925108472 * q^26 + 7075241632262960 * q^27 - 113078857801120960 * q^28 - 170274795551093640 * q^29 - 88623203515625000 * q^30 - 172942006080462832 * q^31 - 567511045488564480 * q^32 - 412144491766396160 * q^33 + 207151653136271304 * q^34 + 49351103515625000 * q^35 - 399040975966317856 * q^36 + 461695977491285480 * q^37 + 2127655695829602960 * q^38 + 6106939319789349776 * q^39 + 4441636804687500000 * q^40 + 1746066900841990488 * q^41 + 9471713482945058160 * q^42 + 13231308551430609800 * q^43 - 21011535794344429056 * q^44 - 11521647979882812500 * q^45 + 22929884441616610248 * q^46 - 25463181064945728360 * q^47 - 71089747411795600640 * q^48 + 27752501816433355572 * q^49 - 1859664916992187500 * q^50 - 125606664173105019632 * q^51 - 155108839850940462400 * q^52 + 19153511824499883720 * q^53 - 134876121729061126160 * q^54 - 24939988443750000000 * q^55 + 411860605716761453760 * q^56 + 492873713134228236320 * q^57 + 221034899302314393240 * q^58 + 217218038347313160720 * q^59 + 32282396453125000000 * q^60 + 152379678911827122728 * q^61 - 363203697269394525360 * q^62 + 1325154150818870981880 * q^63 + 1121074796200062441472 * q^64 + 691106296091796875000 * q^65 - 2099356427487208082944 * q^66 - 2317407910895557756840 * q^67 - 3800878923901661494080 * q^68 + 1219801147861096918416 * q^69 - 3172977517313671875000 * q^70 + 1453247054528140867248 * q^71 - 6515421665165001556320 * q^72 + 2601821824581282121160 * q^73 - 3991697886987492208056 * q^74 - 492763519287109375000 * q^75 - 514198358053038321280 * q^76 + 7444709512703076153600 * q^77 - 1414791230076275697200 * q^78 + 22817266427547282683360 * q^79 - 5538907464893750000000 * q^80 + 23313538421946355263124 * q^81 - 25020293761756353578760 * q^82 + 49081293110242175251080 * q^83 + 45061681389793768930944 * q^84 - 748637207830078125000 * q^85 - 37195944193834827943512 * q^86 - 58630440765630026531920 * q^87 + 7962508551211096903680 * q^88 + 50023669870473477290280 * q^89 - 66338228531485351562500 * q^90 + 55881722079510765798448 * q^91 - 239405355986426422923840 * q^92 + 48979232599473583086240 * q^93 - 34668831477450377120136 * q^94 - 54287581653097656250000 * q^95 - 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	$-0.294661\pi$
$2$	3482.94	1.20255	0.601273	+	0.799044i	$0.294661\pi$
$3$	517572.	1.68685	0.843425	−	0.537246i	$-0.180535\pi$
$3$	517572.	1.68685	0.843425	+	0.537246i	$0.180535\pi$
$4$	3.74229e6	0.446115
$5$	−4.88281e7	−0.447214
$5$	−4.88281e7	−0.447214
$6$	1.80268e9	2.02851
$7$	8.64758e9	1.65298	0.826489	−	0.562952i	$-0.190334\pi$
$7$	8.64758e9	1.65298	0.826489	+	0.562952i	$0.190334\pi$
$8$	−1.61829e10	−0.666072
$9$	1.73738e11	1.84547
$10$	−1.70066e11	−0.537795
$11$	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	$-0.569326\pi$
$13$	−2.79244e12	−0.432151	−0.216076	+	0.976377i	$0.569326\pi$
$14$	3.01190e13	1.98778
$15$	−2.52721e13	−0.754383
$16$	−8.77566e13	−1.24710
$17$	−1.40467e14	−0.994060	−0.497030	−	0.867733i	$-0.665576\pi$
$17$	−1.40467e14	−0.994060	−0.497030	+	0.867733i	$0.665576\pi$
$18$	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	$0.220003\pi$
$20$	−1.82729e14	−0.199509
$21$	4.47575e15	2.78833
$22$	1.60049e15	0.583973
$23$	−3.06806e15	−0.671418	−0.335709	−	0.941966i	$-0.608976\pi$
$23$	−3.06806e15	−0.671418	−0.335709	+	0.941966i	$0.608976\pi$
$24$	−8.37581e15	−1.12356
$25$	2.38419e15	0.200000
$26$	−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	$0.764137\pi$
$30$	−8.80212e16	−0.907179
$31$	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
$35$	−4.22245e17	−0.739235
$36$	6.50177e17	0.823290
$37$	−4.47673e17	−0.413658	−0.206829	−	0.978377i	$-0.566314\pi$
$37$	−4.47673e17	−0.413658	−0.206829	+	0.978377i	$0.566314\pi$
$38$	2.72533e18	1.85314
$39$	−1.44529e18	−0.728975
$40$	7.90180e17	0.297876
$41$	−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	$-0.407268\pi$
$43$	3.50056e18	0.574448	0.287224	+	0.957863i	$0.407268\pi$
$44$	1.71967e18	0.216640
$45$	−8.48330e18	−0.825317
$46$	−1.06859e19	−0.807411
$47$	−1.79769e19	−1.06069	−0.530345	−	0.847782i	$-0.677938\pi$
$47$	−1.79769e19	−1.06069	−0.530345	+	0.847782i	$0.677938\pi$
$48$	−4.54204e19	−2.10367
$49$	4.74120e19	1.73234
$50$	8.30398e18	0.240509
$51$	−7.27020e19	−1.67683
$52$	−1.04501e19	−0.192789
$53$	4.84476e19	0.717959	0.358980	−	0.933345i	$-0.383125\pi$
$53$	4.84476e19	0.717959	0.358980	+	0.933345i	$0.383125\pi$
$54$	1.43484e20	1.71504
$55$	−2.24376e19	−0.217173
$56$	−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	$0.604631\pi$
$60$	−9.45754e19	−0.336542
$61$	−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
$65$	1.36350e20	0.193264
$66$	8.28370e20	0.985075
$67$	−1.62625e21	−1.62677	−0.813386	−	0.581725i	$-0.802378\pi$
$67$	−1.62625e21	−1.62677	−0.813386	+	0.581725i	$0.802378\pi$
$68$	−5.25669e20	−0.443465
$69$	−1.58794e21	−1.13258
$70$	−1.47066e21	−0.888963
$71$	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	$-0.473207\pi$
$73$	4.50707e20	0.168144	0.0840721	+	0.996460i	$0.473207\pi$
$74$	−1.55922e21	−0.497443
$75$	1.23399e21	0.337370
$76$	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	$0.301475\pi$
$80$	4.28499e21	0.557718
$81$	4.96569e21	0.560276
$82$	−1.49051e22	−1.46041
$83$	6.10977e21	0.520747	0.260374	−	0.965508i	$-0.416154\pi$
$83$	6.10977e21	0.520747	0.260374	+	0.965508i	$0.416154\pi$
$84$	1.67495e22	1.24392
$85$	6.85876e21	0.444557
$86$	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	$0.130649\pi$
$90$	−2.95468e22	−0.992481
$91$	−2.41479e22	−0.714337
$92$	−1.14815e22	−0.299530
$93$	8.00088e21	0.184325
$94$	−6.26124e22	−1.27553
$95$	−3.82070e22	−0.689162
$96$	−8.79353e22	−1.40619
$97$	1.13004e23	1.60405	0.802025	−	0.597291i	$-0.203756\pi$
$97$	1.13004e23	1.60405	0.802025	+	0.597291i	$0.203756\pi$
$98$	1.65133e23	2.08322
$99$	7.98365e22	0.896184
$100$	8.92230e21	0.0892230
$101$	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	$-0.553114\pi$
$103$	−4.66657e22	−0.332177	−0.166088	+	0.986111i	$0.553114\pi$
$104$	4.51898e22	0.287844
$105$	−2.18542e23	−1.24698
$106$	1.68740e23	0.863379
$107$	1.36060e23	0.624909	0.312454	−	0.949933i	$-0.398849\pi$
$107$	1.36060e23	0.624909	0.312454	+	0.949933i	$0.398849\pi$
$108$	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	$0.317164\pi$
$110$	−7.81490e22	−0.261161
$111$	−2.31703e23	−0.697779
$112$	−7.58883e23	−2.06142
$113$	3.58585e23	0.879407	0.439704	−	0.898143i	$-0.355084\pi$
$113$	3.58585e23	0.879407	0.439704	+	0.898143i	$0.355084\pi$
$114$	1.41056e24	3.12597
$115$	1.49807e23	0.300267
$116$	−3.62814e23	−0.658290
$117$	−4.85153e23	−0.797520
$118$	−5.20876e23	−0.776410
$119$	−1.21470e24	−1.64316
$120$	4.08975e23	0.502473
$121$	−6.84269e23	−0.764179
$122$	−6.48581e23	−0.658910
$123$	−2.21493e24	−2.04857
$124$	5.78501e22	0.0487477
$125$	−1.16415e23	−0.0894427
$126$	5.23282e24	3.66838
$127$	−1.35565e24	−0.867773	−0.433887	−	0.900967i	$-0.642858\pi$
$127$	−1.35565e24	−0.867773	−0.433887	+	0.900967i	$0.642858\pi$
$128$	1.92818e24	1.12780
$129$	1.81179e24	0.969007
$130$	4.74899e23	0.232409
$131$	−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
$135$	−2.01153e24	−0.637804
$136$	2.27317e24	0.662115
$137$	1.67618e23	0.0448780	0.0224390	−	0.999748i	$-0.492857\pi$
$137$	1.67618e23	0.0448780	0.0224390	+	0.999748i	$0.492857\pi$
$138$	−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	$0.314722\pi$
$140$	−1.58016e24	−0.329784
$141$	−9.30433e24	−1.78923
$142$	3.59545e24	0.637437
$143$	−1.28319e24	−0.209859
$144$	−1.52467e25	−2.30147
$145$	4.73388e24	0.659911
$146$	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	$0.552576\pi$
$150$	4.29791e24	0.405703
$151$	−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
$155$	−7.54809e23	−0.0488678
$156$	−5.40869e24	−0.325207
$157$	2.60805e25	1.45704	0.728518	−	0.685027i	$-0.240209\pi$
$157$	2.60805e25	1.45704	0.728518	+	0.685027i	$0.240209\pi$
$158$	2.70472e25	1.40464
$159$	2.50751e25	1.21109
$160$	8.29587e24	0.372806
$161$	−2.65313e25	−1.10984
$162$	1.72952e25	0.673758
$163$	−1.16248e25	−0.421919	−0.210959	−	0.977495i	$-0.567659\pi$
$163$	−1.16248e25	−0.421919	−0.210959	+	0.977495i	$0.567659\pi$
$164$	−1.60150e25	−0.541778
$165$	−1.16131e25	−0.366339
$166$	2.12800e25	0.626222
$167$	5.88853e24	0.161721	0.0808607	−	0.996725i	$-0.474233\pi$
$167$	5.88853e24	0.161721	0.0808607	+	0.996725i	$0.474233\pi$
$168$	−7.24305e25	−1.85723
$169$	−3.39562e25	−0.813245
$170$	2.38887e25	0.534600
$171$	1.35946e26	2.84389
$172$	1.31001e25	0.256270
$173$	4.10418e25	0.751097	0.375548	−	0.926803i	$-0.377454\pi$
$173$	4.10418e25	0.751097	0.375548	+	0.926803i	$0.377454\pi$
$174$	−1.74769e26	−2.99329
$175$	2.06174e25	0.330596
$176$	−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	$0.566599\pi$
$180$	−3.17469e25	−0.368187
$181$	−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
$185$	2.18591e25	0.184993
$186$	2.78666e25	0.221659
$187$	−6.45479e25	−0.482729
$188$	−6.72746e25	−0.473190
$189$	3.56246e26	2.35743
$190$	−1.33073e26	−0.828749
$191$	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	$-0.415919\pi$
$193$	1.00398e26	0.522173	0.261087	+	0.965315i	$0.415919\pi$
$194$	3.93586e26	1.92894
$195$	7.05709e25	0.326007
$196$	1.77429e26	0.772823
$197$	−2.28398e26	−0.938277	−0.469138	−	0.883125i	$-0.655435\pi$
$197$	−2.28398e26	−0.938277	−0.469138	+	0.883125i	$0.655435\pi$
$198$	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	$0.482428\pi$
$200$	−3.85830e25	−0.133214
$201$	−8.41701e26	−2.74412
$202$	2.42663e26	0.747243
$203$	−8.38382e26	−2.43914
$204$	−2.72072e26	−0.748060
$205$	2.08958e26	0.543112
$206$	−1.62534e26	−0.399458
$207$	−5.33038e26	−1.23908
$208$	2.45055e26	0.538934
$209$	3.59567e26	0.748338
$210$	−7.61171e26	−1.49955
$211$	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
$215$	−1.70926e26	−0.256901
$216$	−6.66671e26	−0.949933
$217$	1.33679e26	0.180624
$218$	1.01963e27	1.30675
$219$	2.33274e26	0.283634
$220$	−8.39680e25	−0.0968843
$221$	3.92247e26	0.429584
$222$	−8.07010e26	−0.839111
$223$	2.33487e26	0.230546	0.115273	−	0.993334i	$-0.463226\pi$
$223$	2.33487e26	0.230546	0.115273	+	0.993334i	$0.463226\pi$
$224$	−1.46922e27	−1.37795
$225$	4.14224e26	0.369093
$226$	1.24893e27	1.05753
$227$	−1.62098e27	−1.30461	−0.652305	−	0.757956i	$-0.726198\pi$
$227$	−1.62098e27	−1.30461	−0.652305	+	0.757956i	$0.726198\pi$
$228$	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	$0.642228\pi$
$230$	5.21771e26	0.361085
$231$	2.05671e27	1.35405
$232$	1.56893e27	0.982859
$233$	−2.57303e27	−1.53409	−0.767046	−	0.641592i	$-0.778274\pi$
$233$	−2.57303e27	−1.53409	−0.767046	+	0.641592i	$0.778274\pi$
$234$	−1.68976e27	−0.959054
$235$	8.77777e26	0.474355
$236$	−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	$0.306099\pi$
$240$	2.21779e27	0.940788
$241$	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
$245$	−2.31504e27	−0.774726
$246$	−7.71447e27	−2.46350
$247$	−2.18503e27	−0.665951
$248$	−2.50163e26	−0.0727827
$249$	3.16225e27	0.878423
$250$	−4.05468e26	−0.107559
$251$	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
$255$	3.54990e27	0.749902
$256$	5.50437e27	1.11160
$257$	4.62113e27	0.892313	0.446157	−	0.894955i	$-0.352792\pi$
$257$	4.62113e27	0.892313	0.446157	+	0.894955i	$0.352792\pi$
$258$	6.31038e27	1.16528
$259$	−3.87129e27	−0.683768
$260$	5.10260e26	0.0862180
$261$	−1.68439e28	−2.72318
$262$	−4.52896e27	−0.700702
$263$	8.97869e27	1.32960	0.664801	−	0.747020i	$-0.268516\pi$
$263$	8.97869e27	1.32960	0.664801	+	0.747020i	$0.268516\pi$
$264$	−3.84888e27	−0.545618
$265$	−2.36561e27	−0.321081
$266$	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	$0.577096\pi$
$270$	−7.00603e27	−0.766988
$271$	−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
$275$	1.09559e27	0.0971228
$276$	−5.94253e27	−0.505262
$277$	−1.68639e28	−1.37543	−0.687717	−	0.725979i	$-0.741387\pi$
$277$	−1.68639e28	−1.37543	−0.687717	+	0.725979i	$0.741387\pi$
$278$	1.68972e28	1.32221
$279$	2.68573e27	0.201657
$280$	6.83314e27	0.492383
$281$	−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	$-0.354671\pi$
$283$	1.38319e28	0.881733	0.440867	+	0.897573i	$0.354671\pi$
$284$	3.86317e27	0.236474
$285$	−1.97749e28	−1.16251
$286$	−4.46928e27	−0.252365
$287$	−3.70070e28	−2.00744
$288$	−2.95180e28	−1.53841
$289$	−2.36505e26	−0.0118445
$290$	1.64878e28	0.793573
$291$	5.84876e28	2.70579
$292$	1.68668e27	0.0750117
$293$	−1.22393e28	−0.523333	−0.261667	−	0.965158i	$-0.584272\pi$
$293$	−1.22393e28	−0.523333	−0.261667	+	0.965158i	$0.584272\pi$
$294$	8.54684e28	3.51408
$295$	7.30227e27	0.288738
$296$	7.24464e27	0.275526
$297$	1.89305e28	0.692570
$298$	−1.12352e28	−0.395452
$299$	8.56737e27	0.290154
$300$	4.61794e27	0.150506
$301$	3.02714e28	0.949550
$302$	−4.50559e28	−1.36042
$303$	3.60602e28	1.04818
$304$	−6.86678e28	−1.92179
$305$	9.09259e27	0.245041
$306$	−8.49995e28	−2.20607
$307$	−1.17607e28	−0.293997	−0.146998	−	0.989137i	$-0.546961\pi$
$307$	−1.17607e28	−0.293997	−0.146998	+	0.989137i	$0.546961\pi$
$308$	1.48710e28	0.358101
$309$	−2.41529e28	−0.560333
$310$	−2.62896e27	−0.0587657
$311$	−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	$-0.404421\pi$
$313$	2.95636e28	0.591559	0.295780	+	0.955256i	$0.404421\pi$
$314$	9.08370e28	1.75215
$315$	−7.33600e28	−1.36423
$316$	2.90612e28	0.521089
$317$	−3.09352e28	−0.534898	−0.267449	−	0.963572i	$-0.586181\pi$
$317$	−3.09352e28	−0.534898	−0.267449	+	0.963572i	$0.586181\pi$
$318$	8.73353e28	1.45639
$319$	−4.45507e28	−0.716575
$320$	−7.05105e27	−0.109403
$321$	7.04208e28	1.05413
$322$	−9.24069e28	−1.33463
$323$	−1.09913e29	−1.53186
$324$	1.85830e28	0.249948
$325$	−6.65770e27	−0.0864303
$326$	−4.04886e28	−0.507377
$327$	1.51519e29	1.83302
$328$	6.92540e28	0.808901
$329$	−1.55457e29	−1.75330
$330$	−4.04478e28	−0.440539
$331$	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
$335$	7.94066e28	0.727514
$336$	−3.92777e29	−3.47731
$337$	−1.88248e28	−0.161059	−0.0805297	−	0.996752i	$-0.525661\pi$
$337$	−1.88248e28	−0.161059	−0.0805297	+	0.996752i	$0.525661\pi$
$338$	−1.18267e29	−0.977964
$339$	1.85594e29	1.48343
$340$	2.56674e28	0.198324
$341$	7.10353e27	0.0530638
$342$	4.73494e29	3.41990
$343$	1.73325e29	1.21054
$344$	−5.66492e28	−0.382623
$345$	7.75362e28	0.506506
$346$	1.42946e29	0.903228
$347$	1.45249e29	0.887818	0.443909	−	0.896072i	$-0.353591\pi$
$347$	1.45249e29	0.887818	0.443909	+	0.896072i	$0.353591\pi$
$348$	−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	$0.446708\pi$
$350$	7.18094e28	0.397556
$351$	−1.15038e29	−0.616323
$352$	−7.80727e28	−0.404817
$353$	−6.95395e27	−0.0348998	−0.0174499	−	0.999848i	$-0.505555\pi$
$353$	−6.95395e27	−0.0348998	−0.0174499	+	0.999848i	$0.505555\pi$
$354$	−2.69591e29	−1.30969
$355$	−5.04054e28	−0.237056
$356$	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	$0.396716\pi$
$360$	1.37284e29	0.549720
$361$	3.54445e29	1.37472
$362$	−1.79186e29	−0.673217
$363$	−3.54159e29	−1.28906
$364$	−9.03683e28	−0.318677
$365$	−2.20072e28	−0.0751964
$366$	−3.35687e29	−1.11148
$367$	3.30752e29	1.06131	0.530656	−	0.847587i	$-0.321946\pi$
$367$	3.30752e29	1.06131	0.530656	+	0.847587i	$0.321946\pi$
$368$	2.69242e29	0.837323
$369$	−7.43504e29	−2.24120
$370$	7.61338e28	0.222463
$371$	4.18955e29	1.18677
$372$	2.99416e28	0.0822302
$373$	−1.41877e29	−0.377799	−0.188899	−	0.981996i	$-0.560492\pi$
$373$	−1.41877e29	−0.377799	−0.188899	+	0.981996i	$0.560492\pi$
$374$	−2.24817e29	−0.580504
$375$	−6.02534e28	−0.150877
$376$	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	$0.621194\pi$
$380$	−1.42982e29	−0.307446
$381$	−7.01649e29	−1.46380
$382$	3.11684e29	0.630938
$383$	−6.42876e29	−1.26282	−0.631410	−	0.775449i	$-0.717523\pi$
$383$	−6.42876e29	−1.26282	−0.631410	+	0.775449i	$0.717523\pi$
$384$	9.97971e29	1.90243
$385$	−1.94031e29	−0.358983
$386$	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	$0.543347\pi$
$390$	2.45794e29	0.392039
$391$	4.30962e29	0.667430
$392$	−7.67262e29	−1.15386
$393$	−6.73012e29	−0.982898
$394$	−7.95498e29	−1.12832
$395$	−3.79181e29	−0.522372
$396$	2.98771e29	0.399801
$397$	8.33502e28	0.108347	0.0541734	−	0.998532i	$-0.482748\pi$
$397$	8.33502e28	0.108347	0.0541734	+	0.998532i	$0.482748\pi$
$398$	1.05082e29	0.132700
$399$	3.50218e30	4.29685
$400$	−2.09228e29	−0.249419
$401$	−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
$405$	−2.42465e29	−0.250563
$406$	−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	$0.246191\pi$
$410$	7.27789e29	0.653117
$411$	8.67544e28	0.0757026
$412$	−1.74636e29	−0.148189
$413$	−1.29325e30	−1.06723
$414$	−1.85654e30	−1.49005
$415$	−2.98329e29	−0.232885
$416$	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	$0.404261\pi$
$420$	−8.17848e29	−0.556296
$421$	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
$425$	−3.34900e29	−0.198812
$426$	1.86091e30	1.07526
$427$	−1.61032e30	−0.905716
$428$	5.09175e29	0.278781
$429$	−6.64144e29	−0.354000
$430$	−5.95325e29	−0.308935
$431$	−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	$-0.110332\pi$
$433$	3.92656e30	1.88105	0.940527	+	0.339719i	$0.110332\pi$
$434$	4.65595e29	0.217208
$435$	2.45013e30	1.11317
$436$	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	$0.872287\pi$
$440$	3.63105e29	0.144653
$441$	8.23726e30	3.19697
$442$	1.36617e30	0.516595
$443$	2.44230e30	0.899820	0.449910	−	0.893074i	$-0.351456\pi$
$443$	2.44230e30	0.899820	0.449910	+	0.893074i	$0.351456\pi$
$444$	−8.67100e29	−0.311290
$445$	−2.34438e30	−0.820139
$446$	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	$0.180844\pi$
$450$	1.44272e30	0.443851
$451$	−1.96651e30	−0.589747
$452$	1.34193e30	0.392317
$453$	−6.69540e30	−1.90830
$454$	−5.64579e30	−1.56885
$455$	1.17910e30	0.319461
$456$	−6.55390e30	−1.73143
$457$	4.09268e30	1.05432	0.527159	−	0.849767i	$-0.323257\pi$
$457$	4.09268e30	1.05432	0.527159	+	0.849767i	$0.323257\pi$
$458$	−4.13686e30	−1.03924
$459$	−5.78670e30	−1.41770
$460$	5.60622e29	0.133954
$461$	−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	$-0.653675\pi$
$463$	−4.18755e30	−0.928493	−0.464247	+	0.885706i	$0.653675\pi$
$464$	8.50799e30	1.84022
$465$	−3.90668e29	−0.0824326
$466$	−8.96171e30	−1.84482
$467$	3.38764e29	0.0680382	0.0340191	−	0.999421i	$-0.489169\pi$
$467$	3.38764e29	0.0680382	0.0340191	+	0.999421i	$0.489169\pi$
$468$	−1.81558e30	−0.355786
$469$	−1.40631e31	−2.68902
$470$	3.05725e30	0.570434
$471$	1.34986e31	2.45780
$472$	2.42016e30	0.430042
$473$	1.60859e30	0.278960
$474$	1.39989e31	2.36943
$475$	1.86558e30	0.308203
$476$	−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	$0.225320\pi$
$480$	4.29371e30	0.628867
$481$	1.25010e30	0.178763
$482$	3.14402e30	0.438979
$483$	−1.37319e31	−1.87213
$484$	−2.56073e30	−0.340912
$485$	−5.51776e30	−0.717353
$486$	−4.55646e30	−0.578510
$487$	−4.51035e30	−0.559277	−0.279638	−	0.960105i	$-0.590215\pi$
$487$	−4.51035e30	−0.559277	−0.279638	+	0.960105i	$0.590215\pi$
$488$	3.01351e30	0.364960
$489$	−6.01669e30	−0.711714
$490$	−8.06314e30	−0.931643
$491$	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
$495$	−3.89827e30	−0.400785
$496$	−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	$0.409795\pi$
$500$	−4.35659e29	−0.0399018
$501$	3.04774e30	0.272800
$502$	6.40445e30	0.560259
$503$	−1.74710e31	−1.49378	−0.746889	−	0.664948i	$-0.768454\pi$
$503$	−1.74710e31	−1.49378	−0.746889	+	0.664948i	$0.768454\pi$
$504$	−2.43134e31	−2.03186
$505$	−3.40194e30	−0.277892
$506$	−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	$0.627335\pi$
$510$	1.23641e31	0.901791
$511$	3.89753e30	0.277939
$512$	2.99668e30	0.208947
$513$	3.22351e31	2.19775
$514$	1.60951e31	1.07305
$515$	2.27860e30	0.148554
$516$	6.78025e30	0.432289
$517$	−8.26078e30	−0.515086
$518$	−1.34835e31	−0.822262
$519$	2.12421e31	1.26699
$520$	−2.20653e30	−0.128728
$521$	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	$-0.423402\pi$
$523$	8.72908e30	0.476649	0.238325	+	0.971186i	$0.423402\pi$
$524$	−4.86619e30	−0.259943
$525$	1.06710e31	0.557666
$526$	3.12723e31	1.59891
$527$	−2.17141e30	−0.108623
$528$	−2.08717e31	−1.02157
$529$	−1.14675e31	−0.549197
$530$	−8.23927e30	−0.386115
$531$	−2.59826e31	−1.19150
$532$	2.53224e31	1.13637
$533$	1.19501e31	0.524820
$534$	8.65516e31	3.72007
$535$	−6.64355e30	−0.279468
$536$	2.63174e31	1.08355
$537$	−1.73882e31	−0.700728
$538$	−1.46235e31	−0.576842
$539$	2.17869e31	0.841248
$540$	−7.52770e30	−0.284534
$541$	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
$545$	−1.42944e31	−0.485967
$546$	−4.35308e31	−1.44904
$547$	4.47901e31	1.45992	0.729958	−	0.683492i	$-0.239540\pi$
$547$	4.47901e31	1.45992	0.729958	+	0.683492i	$0.239540\pi$
$548$	6.27274e29	0.0200208
$549$	−3.23528e31	−1.01118
$550$	3.81587e30	0.116795
$551$	−7.58613e31	−2.27393
$552$	2.56975e31	0.754381
$553$	6.71539e31	1.93078
$554$	−5.87359e31	−1.65402
$555$	1.13136e31	0.312056
$556$	1.81553e31	0.490506
$557$	5.47014e31	1.44765	0.723825	−	0.689984i	$-0.242382\pi$
$557$	5.47014e31	1.44765	0.723825	+	0.689984i	$0.242382\pi$
$558$	9.35423e30	0.242502
$559$	−9.77512e30	−0.248248
$560$	3.70548e31	0.921897
$561$	−3.34082e31	−0.814293
$562$	−1.28244e31	−0.306246
$563$	−4.68187e31	−1.09540	−0.547700	−	0.836675i	$-0.684497\pi$
$563$	−4.68187e31	−1.09540	−0.547700	+	0.836675i	$0.684497\pi$
$564$	−3.48195e31	−0.798202
$565$	−1.75090e31	−0.393283
$566$	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	$0.400252\pi$
$570$	−6.88748e31	−1.39798
$571$	−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
$575$	−7.31482e30	−0.134284
$576$	2.50887e31	0.451461
$577$	−1.06853e32	−1.88481	−0.942403	−	0.334480i	$-0.891439\pi$
$577$	−1.06853e32	−1.88481	−0.942403	+	0.334480i	$0.891439\pi$
$578$	−8.23734e29	−0.0142435
$579$	5.19631e31	0.880828
$580$	1.77155e31	0.294396
$581$	5.28348e31	0.860784
$582$	2.03709e32	3.25384
$583$	2.22628e31	0.348651
$584$	−7.29374e30	−0.111996
$585$	2.36891e31	0.356662
$586$	−4.26287e31	−0.629332
$587$	−2.57743e31	−0.373121	−0.186560	−	0.982444i	$-0.559734\pi$
$587$	−2.57743e31	−0.373121	−0.186560	+	0.982444i	$0.559734\pi$
$588$	9.18324e31	1.30364
$589$	1.20959e31	0.168389
$590$	2.54334e31	0.347221
$591$	−1.18213e32	−1.58273
$592$	3.92863e31	0.515871
$593$	−5.96138e31	−0.767747	−0.383874	−	0.923386i	$-0.625410\pi$
$593$	−5.96138e31	−0.767747	−0.383874	+	0.923386i	$0.625410\pi$
$594$	6.59339e31	0.832846
$595$	5.93117e31	0.734844
$596$	−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	$0.261010\pi$
$600$	−1.99695e31	−0.224713
$601$	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
$605$	3.34116e31	0.341751
$606$	1.25595e32	1.26049
$607$	−1.66513e32	−1.63976	−0.819878	−	0.572538i	$-0.805959\pi$
$607$	−1.66513e32	−1.63976	−0.819878	+	0.572538i	$0.805959\pi$
$608$	−1.32943e32	−1.28462
$609$	−4.33923e32	−4.11447
$610$	3.16690e31	0.294673
$611$	5.01994e31	0.458379
$612$	−9.13286e31	−0.818400
$613$	−1.62167e32	−1.42615	−0.713077	−	0.701086i	$-0.752699\pi$
$613$	−1.62167e32	−1.42615	−0.713077	+	0.701086i	$0.752699\pi$
$614$	−4.09619e31	−0.353544
$615$	1.08151e32	0.916149
$616$	−6.43069e31	−0.534662
$617$	−9.13641e30	−0.0745583	−0.0372792	−	0.999305i	$-0.511869\pi$
$617$	−9.13641e30	−0.0745583	−0.0372792	+	0.999305i	$0.511869\pi$
$618$	−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	$0.210783\pi$
$620$	−2.82471e30	−0.0218007
$621$	−1.26392e32	−0.957559
$622$	−4.87701e31	−0.362714
$623$	4.15195e32	3.03138
$624$	1.26834e32	0.909102
$625$	5.68434e30	0.0400000
$626$	1.02968e32	0.711377
$627$	1.86102e32	1.26233
$628$	9.76008e31	0.650006
$629$	6.28835e31	0.411201
$630$	−2.55509e32	−1.64055
$631$	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
$635$	6.61941e31	0.388080
$636$	9.38384e31	0.540286
$637$	−1.32395e32	−0.748633
$638$	−1.55167e32	−0.861713
$639$	1.79350e32	0.978232
$640$	−9.41492e31	−0.504368
$641$	−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	$-0.253441\pi$
$643$	2.75547e32	1.39884	0.699422	+	0.714709i	$0.253441\pi$
$644$	−9.92876e31	−0.495117
$645$	−8.84665e31	−0.433353
$646$	−3.82820e32	−1.84213
$647$	−2.72847e32	−1.28979	−0.644896	−	0.764270i	$-0.723099\pi$
$647$	−2.72847e32	−1.28979	−0.644896	+	0.764270i	$0.723099\pi$
$648$	−8.03592e31	−0.373184
$649$	−6.87218e31	−0.313531
$650$	−2.31884e31	−0.103936
$651$	6.91883e31	0.304685
$652$	−4.35034e31	−0.188224
$653$	1.77887e32	0.756209	0.378105	−	0.925763i	$-0.376576\pi$
$653$	1.77887e32	0.756209	0.378105	+	0.925763i	$0.376576\pi$
$654$	5.27732e32	2.20430
$655$	6.34924e31	0.260583
$656$	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	$0.747677\pi$
$660$	−4.34595e31	−0.163429
$661$	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
$665$	−3.30398e32	−1.13917
$666$	−2.70896e32	−0.918013
$667$	2.97448e32	0.990748
$668$	2.20366e31	0.0721464
$669$	1.20846e32	0.388896
$670$	2.76569e32	0.874869
$671$	−8.55706e31	−0.266082
$672$	−7.60428e32	−2.32440
$673$	−4.30783e32	−1.29445	−0.647225	−	0.762299i	$-0.724071\pi$
$673$	−4.30783e32	−1.29445	−0.647225	+	0.762299i	$0.724071\pi$
$674$	−6.55656e31	−0.193681
$675$	9.82190e31	0.285235
$676$	−1.27074e32	−0.362801
$677$	−4.18262e32	−1.17403	−0.587015	−	0.809576i	$-0.699697\pi$
$677$	−4.18262e32	−1.17403	−0.587015	+	0.809576i	$0.699697\pi$
$678$	6.46412e32	1.78389
$679$	9.77209e32	2.65146
$680$	−1.10994e32	−0.296107
$681$	−8.38975e32	−2.20068
$682$	2.47412e31	0.0638117
$683$	−6.21337e32	−1.57576	−0.787878	−	0.615832i	$-0.788820\pi$
$683$	−6.21337e32	−1.57576	−0.787878	+	0.615832i	$0.788820\pi$
$684$	5.08750e32	1.26870
$685$	−8.18447e30	−0.0200701
$686$	6.03683e32	1.45573
$687$	−6.14745e32	−1.45778
$688$	−3.07197e32	−0.716392
$689$	−1.35287e32	−0.310267
$690$	2.70054e32	0.609097
$691$	−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
$695$	−2.36885e32	−0.491714
$696$	8.12034e32	1.65794
$697$	6.01124e32	1.20722
$698$	2.02884e32	0.400785
$699$	−1.33173e33	−2.58779
$700$	7.71564e31	0.147484
$701$	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
$705$	4.54313e32	0.800167
$706$	−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	$0.462698\pi$
$710$	−1.75559e32	−0.285071
$711$	1.34918e33	2.15561
$712$	−7.76986e32	−1.22150
$713$	−4.74275e31	−0.0733670
$714$	−2.18971e33	−3.33317
$715$	6.26558e31	0.0938517
$716$	−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	$0.689752\pi$
$720$	7.44465e32	1.02925
$721$	−4.03545e32	−0.549081
$722$	1.23451e33	1.65317
$723$	4.67207e32	0.615771
$724$	−1.92528e32	−0.249747
$725$	−2.31146e32	−0.295121
$726$	−1.23351e33	−1.55015
$727$	−5.38025e32	−0.665514	−0.332757	−	0.943013i	$-0.607979\pi$
$727$	−5.38025e32	−0.665514	−0.332757	+	0.943013i	$0.607979\pi$
$728$	3.90782e32	0.475800
$729$	−1.14459e33	−1.37177
$730$	−7.66498e31	−0.0904270
$731$	−4.91714e32	−0.571036
$732$	−3.60683e32	−0.412333
$733$	2.14429e32	0.241317	0.120658	−	0.992694i	$-0.461499\pi$
$733$	2.14429e32	0.241317	0.120658	+	0.992694i	$0.461499\pi$
$734$	1.15199e33	1.27628
$735$	−1.19820e33	−1.30685
$736$	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	$0.302795\pi$
$740$	8.18028e31	0.0825284
$741$	−1.13091e33	−1.12336
$742$	1.45920e33	1.42715
$743$	−6.51220e32	−0.627128	−0.313564	−	0.949567i	$-0.601523\pi$
$743$	−6.51220e32	−0.627128	−0.313564	+	0.949567i	$0.601523\pi$
$744$	−1.29477e32	−0.122774
$745$	1.57509e32	0.147064
$746$	−4.94150e32	−0.454320
$747$	1.06150e33	0.961021
$748$	−2.41557e32	−0.215353
$749$	1.17659e33	1.03296
$750$	−2.09859e32	−0.181436
$751$	−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
$755$	6.31648e32	0.505924
$756$	1.33318e33	1.05169
$757$	6.99863e32	0.543764	0.271882	−	0.962331i	$-0.412354\pi$
$757$	6.99863e32	0.543764	0.271882	+	0.962331i	$0.412354\pi$
$758$	−1.16792e33	−0.893755
$759$	−7.29695e32	−0.549998
$760$	6.18299e32	0.459031
$761$	−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
$765$	1.19163e33	0.820415
$766$	−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	$0.396961\pi$
$770$	−6.75800e32	−0.431693
$771$	2.39177e33	1.50520
$772$	3.75717e32	0.232949
$773$	−2.80480e33	−1.71332	−0.856659	−	0.515883i	$-0.827464\pi$
$773$	−2.80480e33	−1.71332	−0.856659	+	0.515883i	$0.827464\pi$
$774$	2.11826e33	1.27485
$775$	3.68559e31	0.0218543
$776$	−1.82873e33	−1.06841
$777$	−2.00367e33	−1.15341
$778$	−5.75652e32	−0.326509
$779$	−3.34859e33	−1.87146
$780$	2.64096e32	0.145437
$781$	4.74367e32	0.257411
$782$	1.50101e33	0.802615
$783$	−3.99395e33	−2.10447
$784$	−4.16071e33	−2.16039
$785$	−1.27346e33	−0.651606
$786$	−2.34406e33	−1.18198
$787$	1.29475e31	0.00643395	0.00321697	−	0.999995i	$-0.498976\pi$
$787$	1.29475e31	0.00643395	0.00321697	+	0.999995i	$0.498976\pi$
$788$	−8.54731e32	−0.418580
$789$	4.64712e33	2.24284
$790$	−1.32067e33	−0.628176
$791$	3.10089e33	1.45364
$792$	−1.29198e33	−0.596922
$793$	5.19998e32	0.236788
$794$	2.90304e32	0.130292
$795$	−1.22437e33	−0.541616
$796$	1.12906e32	0.0492287
$797$	−4.31035e33	−1.85243	−0.926214	−	0.376998i	$-0.876956\pi$
$797$	−4.31035e33	−1.85243	−0.926214	+	0.376998i	$0.876956\pi$
$798$	1.21979e34	5.16716
$799$	2.52516e33	1.05439
$800$	−4.05072e32	−0.166724
$801$	8.34166e33	3.38437
$802$	−4.44882e33	−1.77926
$803$	2.07110e32	0.0816532
$804$	−3.14989e33	−1.22419
$805$	1.29547e33	0.496336
$806$	−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	$0.419610\pi$
$810$	−8.44494e32	−0.301314
$811$	−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
$815$	5.67618e32	0.188688
$816$	6.38008e33	2.09117
$817$	2.73912e33	0.885232
$818$	5.40027e33	1.72089
$819$	−4.19540e33	−1.31828
$820$	7.81980e32	0.242291
$821$	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	$-0.201647\pi$
$823$	5.42555e33	1.61193	0.805965	+	0.591964i	$0.201647\pi$
$824$	7.55185e32	0.221254
$825$	5.67046e32	0.163832
$826$	−4.50432e33	−1.28339
$827$	4.40624e33	1.23810	0.619049	−	0.785352i	$-0.287518\pi$
$827$	4.40624e33	1.23810	0.619049	+	0.785352i	$0.287518\pi$
$828$	−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	$0.512944\pi$
$830$	−1.03906e33	−0.280055
$831$	−8.72827e33	−2.32015
$832$	−4.03244e32	−0.105718
$833$	−6.65983e33	−1.72205
$834$	8.74551e33	2.23036
$835$	−2.87526e32	−0.0723240
$836$	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	$0.381443\pi$
$840$	3.53665e33	0.830577
$841$	5.08255e33	1.17741
$842$	9.83914e33	2.24837
$843$	−1.90573e33	−0.429581
$844$	2.37817e33	0.528816
$845$	1.65802e33	0.363694
$846$	−1.08782e34	−2.35394
$847$	−5.91727e33	−1.26317
$848$	−4.25160e33	−0.895365
$849$	7.15900e33	1.48735
$850$	−1.16644e33	−0.239080
$851$	1.37349e33	0.277738
$852$	1.99947e33	0.398896
$853$	−2.74815e33	−0.540911	−0.270456	−	0.962732i	$-0.587174\pi$
$853$	−2.74815e33	−0.540911	−0.270456	+	0.962732i	$0.587174\pi$
$854$	−5.60866e33	−1.08916
$855$	−6.63801e33	−1.27183
$856$	−2.20184e33	−0.416234
$857$	7.03785e33	1.31269	0.656343	−	0.754463i	$-0.272103\pi$
$857$	7.03785e33	1.31269	0.656343	+	0.754463i	$0.272103\pi$
$858$	−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	$0.656469\pi$
$860$	−6.39653e32	−0.114607
$861$	−1.91538e34	−3.38625
$862$	−1.12821e34	−1.96814
$863$	4.99662e33	0.860107	0.430054	−	0.902803i	$-0.358495\pi$
$863$	4.99662e33	0.860107	0.430054	+	0.902803i	$0.358495\pi$
$864$	−6.99919e33	−1.18888
$865$	−2.00399e33	−0.335901
$866$	1.36760e34	2.26205
$867$	−1.22408e32	−0.0199798
$868$	5.00263e32	0.0805790
$869$	3.56848e33	0.567226
$870$	8.53365e33	1.33864
$871$	4.54121e33	0.703011
$872$	−4.73753e33	−0.723790
$873$	1.96330e34	2.96022
$874$	−8.36147e33	−1.24423
$875$	−1.00671e33	−0.147847
$876$	8.72977e32	0.126534
$877$	8.71040e33	1.24607	0.623035	−	0.782194i	$-0.285899\pi$
$877$	8.71040e33	1.24607	0.623035	+	0.782194i	$0.285899\pi$
$878$	−1.56813e34	−2.21409
$879$	−6.33471e33	−0.882785
$880$	1.96905e33	0.270836
$881$	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	$-0.716338\pi$
$883$	−9.50375e33	−1.25703	−0.628517	+	0.777796i	$0.716338\pi$
$884$	1.46790e33	0.191644
$885$	3.77945e33	0.487059
$886$	8.50639e33	1.08207
$887$	−1.82994e33	−0.229782	−0.114891	−	0.993378i	$-0.536652\pi$
$887$	−1.82994e33	−0.229782	−0.114891	+	0.993378i	$0.536652\pi$
$888$	3.74963e33	0.464771
$889$	−1.17231e34	−1.43441
$890$	−8.16534e33	−0.986254
$891$	2.28185e33	0.272078
$892$	8.73775e32	0.102850
$893$	−1.40665e34	−1.63454
$894$	−5.81503e33	−0.667069
$895$	1.64041e33	0.185775
$896$	1.66741e34	1.86423
$897$	4.43423e33	0.489447
$898$	1.86032e34	2.02726
$899$	−1.49870e33	−0.161242
$900$	1.55014e33	0.164658
$901$	−6.80531e33	−0.713695
$902$	−6.84924e33	−0.709197
$903$	1.56676e34	1.60175
$904$	−5.80294e33	−0.585748
$905$	2.51204e33	0.250362
$906$	−2.33197e34	−2.29482
$907$	1.77973e34	1.72930	0.864650	−	0.502375i	$-0.167540\pi$
$907$	1.77973e34	1.72930	0.864650	+	0.502375i	$0.167540\pi$
$908$	−6.06618e33	−0.582007
$909$	1.21046e34	1.14674
$910$	4.10672e33	0.384167
$911$	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
$915$	4.70607e33	0.413348
$916$	−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	$0.710628\pi$
$920$	−2.42431e33	−0.200000
$921$	−6.08702e33	−0.495928
$922$	−1.66992e34	−1.34366
$923$	−2.88265e33	−0.229072
$924$	7.69679e33	0.604063
$925$	−1.06734e33	−0.0827316
$926$	−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	$0.400234\pi$
$930$	−1.36068e33	−0.0991290
$931$	3.70989e34	2.66956
$932$	−9.62901e33	−0.684382
$933$	−7.24733e33	−0.508791
$934$	1.17990e33	0.0818191
$935$	3.15175e33	0.215883
$936$	7.85118e33	0.531205
$937$	−1.67822e34	−1.12161	−0.560807	−	0.827947i	$-0.689509\pi$
$937$	−1.67822e34	−1.12161	−0.560807	+	0.827947i	$0.689509\pi$
$938$	−4.89810e34	−3.23367
$939$	1.53013e34	0.997872
$940$	3.28489e33	0.211617
$941$	−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
$945$	−1.73948e34	−1.05428
$946$	5.60262e33	0.335462
$947$	1.41902e34	0.839388	0.419694	−	0.907666i	$-0.362137\pi$
$947$	1.41902e34	0.839388	0.419694	+	0.907666i	$0.362137\pi$
$948$	1.50413e34	0.879000
$949$	−1.25857e33	−0.0726637
$950$	6.49770e33	0.370628
$951$	−1.60112e34	−0.902293
$952$	1.96574e34	1.09446
$953$	−9.37154e33	−0.515517	−0.257758	−	0.966209i	$-0.582984\pi$
$953$	−9.37154e33	−0.515517	−0.257758	+	0.966209i	$0.582984\pi$
$954$	2.93166e34	1.59334
$955$	−4.36957e33	−0.234639
$956$	9.62217e33	0.510513
$957$	−2.30582e34	−1.20875
$958$	3.52782e34	1.82727
$959$	1.44949e33	0.0741825
$960$	−3.64943e33	−0.184546
$961$	−1.97743e34	−0.988060
$962$	4.35404e33	0.214970
$963$	2.36388e34	1.15325
$964$	3.37812e33	0.162851
$965$	−4.90223e33	−0.233523
$966$	−4.78273e34	−2.25133
$967$	−4.30462e33	−0.200231	−0.100115	−	0.994976i	$-0.531921\pi$
$967$	−4.30462e33	−0.200231	−0.100115	+	0.994976i	$0.531921\pi$
$968$	1.10734e34	0.508998
$969$	−5.68878e34	−2.58402
$970$	−1.92180e34	−0.862649
$971$	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
$975$	−3.44584e33	−0.145795
$976$	1.63417e34	0.683321
$977$	1.88718e33	0.0779877	0.0389939	−	0.999239i	$-0.487585\pi$
$977$	1.88718e33	0.0779877	0.0389939	+	0.999239i	$0.487585\pi$
$978$	−2.09558e34	−0.855869
$979$	2.20630e34	0.890561
$980$	−8.66353e33	−0.345617
$981$	5.08617e34	2.00538
$982$	3.14297e33	0.122478
$983$	−3.74187e34	−1.44120	−0.720599	−	0.693352i	$-0.756133\pi$
$983$	−3.74187e34	−1.44120	−0.720599	+	0.693352i	$0.756133\pi$
$984$	3.58439e34	1.36450
$985$	1.11523e34	0.419610
$986$	4.74317e34	1.76394
$987$	−8.04600e34	−2.95755
$988$	−8.17701e33	−0.297091
$989$	−1.07399e34	−0.385695
$990$	−1.35774e34	−0.481963
$991$	−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
$995$	−1.47317e33	−0.0493499
$996$	1.18340e34	0.391878
$997$	−7.47285e33	−0.244620	−0.122310	−	0.992492i	$-0.539030\pi$
$997$	−7.47285e33	−0.244620	−0.122310	+	0.992492i	$0.539030\pi$
$998$	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	5.24.a.b.1.4	✓	4
3.2	odd	2		45.24.a.d.1.1		4
5.2	odd	4		25.24.b.c.24.7		8
5.3	odd	4		25.24.b.c.24.2		8
5.4	even	2		25.24.a.c.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.24.a.b.1.4	✓	4	1.1	even	1	trivial
25.24.a.c.1.1		4	5.4	even	2
25.24.b.c.24.2		8	5.3	odd	4
25.24.b.c.24.7		8	5.2	odd	4
45.24.a.d.1.1		4	3.2	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 24 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+3482.94 q^{2} +517572. q^{3} +3.74229e6 q^{4} -4.88281e7 q^{5} +1.80268e9 q^{6} +8.64758e9 q^{7} -1.61829e10 q^{8} +1.73738e11 q^{9} +O(q^{10})\)	\(q+3482.94 q^{2} +517572. q^{3} +3.74229e6 q^{4} -4.88281e7 q^{5} +1.80268e9 q^{6} +8.64758e9 q^{7} -1.61829e10 q^{8} +1.73738e11 q^{9} -1.70066e11 q^{10} +4.59523e11 q^{11} +1.93690e12 q^{12} -2.79244e12 q^{13} +3.01190e13 q^{14} -2.52721e13 q^{15} -8.77566e13 q^{16} -1.40467e14 q^{17} +6.05119e14 q^{18} +7.82480e14 q^{19} -1.82729e14 q^{20} +4.47575e15 q^{21} +1.60049e15 q^{22} -3.06806e15 q^{23} -8.37581e15 q^{24} +2.38419e15 q^{25} -9.72592e15 q^{26} +4.11960e16 q^{27} +3.23617e16 q^{28} -9.69499e16 q^{29} -8.80212e16 q^{30} +1.54585e16 q^{31} -1.69899e17 q^{32} +2.37836e17 q^{33} -4.89240e17 q^{34} -4.22245e17 q^{35} +6.50177e17 q^{36} -4.47673e17 q^{37} +2.72533e18 q^{38} -1.44529e18 q^{39} +7.90180e17 q^{40} -4.27946e18 q^{41} +1.55888e19 q^{42} +3.50056e18 q^{43} +1.71967e18 q^{44} -8.48330e18 q^{45} -1.06859e19 q^{46} -1.79769e19 q^{47} -4.54204e19 q^{48} +4.74120e19 q^{49} +8.30398e18 q^{50} -7.27020e19 q^{51} -1.04501e19 q^{52} +4.84476e19 q^{53} +1.43484e20 q^{54} -2.24376e19 q^{55} -1.39943e20 q^{56} +4.04990e20 q^{57} -3.37671e20 q^{58} -1.49550e20 q^{59} -9.45754e19 q^{60} -1.86216e20 q^{61} +5.38410e19 q^{62} +1.50241e21 q^{63} +1.44406e20 q^{64} +1.36350e20 q^{65} +8.28370e20 q^{66} -1.62625e21 q^{67} -5.25669e20 q^{68} -1.58794e21 q^{69} -1.47066e21 q^{70} +1.03230e21 q^{71} -2.81158e21 q^{72} +4.50707e20 q^{73} -1.55922e21 q^{74} +1.23399e21 q^{75} +2.92826e21 q^{76} +3.97376e21 q^{77} -5.03387e21 q^{78} +7.76563e21 q^{79} +4.28499e21 q^{80} +4.96569e21 q^{81} -1.49051e22 q^{82} +6.10977e21 q^{83} +1.67495e22 q^{84} +6.85876e21 q^{85} +1.21923e22 q^{86} -5.01786e22 q^{87} -7.43640e21 q^{88} +4.80129e22 q^{89} -2.95468e22 q^{90} -2.41479e22 q^{91} -1.14815e22 q^{92} +8.00088e21 q^{93} -6.26124e22 q^{94} -3.82070e22 q^{95} -8.79353e22 q^{96} +1.13004e23 q^{97} +1.65133e23 q^{98} +7.98365e22 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 780 q^{2} - 206680 q^{3} + 12685792 q^{4} - 195312500 q^{5} + 1815003208 q^{6} - 1010710600 q^{7} - 90964721760 q^{8} + 235963350628 q^{9}+O(q^{10}) \) 4 * q - 780 * q^2 - 206680 * q^3 + 12685792 * q^4 - 195312500 * q^5 + 1815003208 * q^6 - 1010710600 * q^7 - 90964721760 * q^8 + 235963350628 * q^9	\( 4 q - 780 q^{2} - 206680 q^{3} + 12685792 q^{4} - 195312500 q^{5} + 1815003208 q^{6} - 1010710600 q^{7} - 90964721760 q^{8} + 235963350628 q^{9} + 38085937500 q^{10} + 510770963328 q^{11} - 661143479360 q^{12} - 14153856943960 q^{13} + 64982579554584 q^{14} + 10091796875000 q^{15} + 113436824881024 q^{16} + 15332090016360 q^{17} + 13\!\cdots\!20 q^{18}+ \cdots + 48\!\cdots\!96 q^{99}+O(q^{100}) \) 4 * q - 780 * q^2 - 206680 * q^3 + 12685792 * q^4 - 195312500 * q^5 + 1815003208 * q^6 - 1010710600 * q^7 - 90964721760 * q^8 + 235963350628 * q^9 + 38085937500 * q^10 + 510770963328 * q^11 - 661143479360 * q^12 - 14153856943960 * q^13 + 64982579554584 * q^14 + 10091796875000 * q^15 + 113436824881024 * q^16 + 15332090016360 * q^17 + 1358606920324820 * q^18 + 1111809672255440 * q^19 - 619423437500000 * q^20 + 7473099301754928 * q^21 + 10708927083459840 * q^22 - 3998020505342040 * q^23 + 20506026884128320 * q^24 + 9536743164062500 * q^25 - 877714925108472 * q^26 + 7075241632262960 * q^27 - 113078857801120960 * q^28 - 170274795551093640 * q^29 - 88623203515625000 * q^30 - 172942006080462832 * q^31 - 567511045488564480 * q^32 - 412144491766396160 * q^33 + 207151653136271304 * q^34 + 49351103515625000 * q^35 - 399040975966317856 * q^36 + 461695977491285480 * q^37 + 2127655695829602960 * q^38 + 6106939319789349776 * q^39 + 4441636804687500000 * q^40 + 1746066900841990488 * q^41 + 9471713482945058160 * q^42 + 13231308551430609800 * q^43 - 21011535794344429056 * q^44 - 11521647979882812500 * q^45 + 22929884441616610248 * q^46 - 25463181064945728360 * q^47 - 71089747411795600640 * q^48 + 27752501816433355572 * q^49 - 1859664916992187500 * q^50 - 125606664173105019632 * q^51 - 155108839850940462400 * q^52 + 19153511824499883720 * q^53 - 134876121729061126160 * q^54 - 24939988443750000000 * q^55 + 411860605716761453760 * q^56 + 492873713134228236320 * q^57 + 221034899302314393240 * q^58 + 217218038347313160720 * q^59 + 32282396453125000000 * q^60 + 152379678911827122728 * q^61 - 363203697269394525360 * q^62 + 1325154150818870981880 * q^63 + 1121074796200062441472 * q^64 + 691106296091796875000 * q^65 - 2099356427487208082944 * q^66 - 2317407910895557756840 * q^67 - 3800878923901661494080 * q^68 + 1219801147861096918416 * q^69 - 3172977517313671875000 * q^70 + 1453247054528140867248 * q^71 - 6515421665165001556320 * q^72 + 2601821824581282121160 * q^73 - 3991697886987492208056 * q^74 - 492763519287109375000 * q^75 - 514198358053038321280 * q^76 + 7444709512703076153600 * q^77 - 1414791230076275697200 * q^78 + 22817266427547282683360 * q^79 - 5538907464893750000000 * q^80 + 23313538421946355263124 * q^81 - 25020293761756353578760 * q^82 + 49081293110242175251080 * q^83 + 45061681389793768930944 * q^84 - 748637207830078125000 * q^85 - 37195944193834827943512 * q^86 - 58630440765630026531920 * q^87 + 7962508551211096903680 * q^88 + 50023669870473477290280 * q^89 - 66338228531485351562500 * q^90 + 55881722079510765798448 * q^91 - 239405355986426422923840 * q^92 + 48979232599473583086240 * q^93 - 34668831477450377120136 * q^94 - 54287581653097656250000 * q^95 - 102550574820923244800512 * q^96 - 141223261544238546490360 * q^97 - 8062497360198964195740 * q^98 + 486593842095233676826496 * q^99

Introduction

L-functions

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