LMFDB - Embedded newform 10.28.b.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,28,Mod(9,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("10.9");

S:= CuspForms(chi, 28);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 28 $
Character orbit:	$[\chi]$	$=$	10.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$46.1855574838$
Analytic rank:	$0$
Dimension:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 18355117238047 x^{12} + \cdots + 11\!\cdots\!41 $ x^14 + 18355117238047x^12 + 125274446634307160014536861x^10 + 401389369749104114101796700939183433635x^8 + 632065688202840694920128473317234526554975576656835x^6 + 476296377525812542516575301312041660487369515289425409358166621x^4 + 146987616132604884440971730417666446806282040776693346217295545219398841247x^2 + 11163323583881596915368223973024442099655511628899004049829010231627814378440771196641
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{121}\cdot 3^{18}\cdot 5^{39}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			9.1
Root			$-2.18023e6i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.28.b.a.9.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-8192.00i q^{2} -4.36047e6i q^{3} -6.71089e7 q^{4} +(-1.84162e9 + 2.01470e9i) q^{5} -3.57210e10 q^{6} +1.94048e10i q^{7} +5.49756e11i q^{8} -1.13881e13 q^{9} +(1.65044e13 + 1.50865e13i) q^{10} -1.73755e14 q^{11} +2.92626e14i q^{12} -6.75010e14i q^{13} +1.58964e14 q^{14} +(8.78505e15 + 8.03032e15i) q^{15} +4.50360e15 q^{16} +4.72808e16i q^{17} +9.32913e16i q^{18} +2.99649e17 q^{19} +(1.23589e17 - 1.35204e17i) q^{20} +8.46139e16 q^{21} +1.42340e18i q^{22} +1.42626e18i q^{23} +2.39719e18 q^{24} +(-6.67471e17 - 7.42062e18i) q^{25} -5.52968e18 q^{26} +1.64063e19i q^{27} -1.30223e18i q^{28} -4.14340e19 q^{29} +(6.57844e19 - 7.19671e19i) q^{30} +1.01475e20 q^{31} -3.68935e19i q^{32} +7.57655e20i q^{33} +3.87324e20 q^{34} +(-3.90949e19 - 3.57362e19i) q^{35} +7.64242e20 q^{36} -4.31315e20i q^{37} -2.45473e21i q^{38} -2.94336e21 q^{39} +(-1.10759e21 - 1.01244e21i) q^{40} -6.35676e21 q^{41} -6.93157e20i q^{42} -1.92277e22i q^{43} +1.16605e22 q^{44} +(2.09725e22 - 2.29436e22i) q^{45} +1.16839e22 q^{46} +6.41268e22i q^{47} -1.96378e22i q^{48} +6.53358e22 q^{49} +(-6.07897e22 + 5.46792e21i) q^{50} +2.06166e23 q^{51} +4.52991e22i q^{52} -7.01449e22i q^{53} +1.34400e23 q^{54} +(3.19991e23 - 3.50065e23i) q^{55} -1.06679e22 q^{56} -1.30661e24i q^{57} +3.39428e23i q^{58} +7.97207e23 q^{59} +(-5.89555e23 - 5.38905e23i) q^{60} -7.03947e23 q^{61} -8.31280e23i q^{62} -2.20984e23i q^{63} -3.02231e23 q^{64} +(1.35994e24 + 1.24311e24i) q^{65} +6.20671e24 q^{66} +1.48454e24i q^{67} -3.17296e24i q^{68} +6.21915e24 q^{69} +(-2.92751e23 + 3.20265e23i) q^{70} -1.17498e25 q^{71} -6.26067e24i q^{72} +1.70047e25i q^{73} -3.53333e24 q^{74} +(-3.23574e25 + 2.91049e24i) q^{75} -2.01091e25 q^{76} -3.37168e24i q^{77} +2.41120e25i q^{78} +6.04850e25 q^{79} +(-8.29391e24 + 9.07341e24i) q^{80} -1.53020e25 q^{81} +5.20746e25i q^{82} +8.94591e25i q^{83} -5.67835e24 q^{84} +(-9.52567e25 - 8.70731e25i) q^{85} -1.57513e26 q^{86} +1.80672e26i q^{87} -9.55230e25i q^{88} +1.26789e26 q^{89} +(-1.87954e26 - 1.71807e26i) q^{90} +1.30984e25 q^{91} -9.57145e25i q^{92} -4.42477e26i q^{93} +5.25326e26 q^{94} +(-5.51840e26 + 6.03704e26i) q^{95} -1.60873e26 q^{96} +1.36952e26i q^{97} -5.35231e26i q^{98} +1.97874e27 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 939524096 q^{4} - 73643590 q^{5} + 16071950336 q^{6} - 40082573114558 q^{9} - 33017385943040 q^{10} - 158204810172872 q^{11} - 21\!\cdots\!48 q^{14} + 20\!\cdots\!40 q^{15} + 63\!\cdots\!44 q^{16}+ \cdots - 39\!\cdots\!16 q^{99}+O(q^{100}) $ 14 * q - 939524096 * q^4 - 73643590 * q^5 + 16071950336 * q^6 - 40082573114558 * q^9 - 33017385943040 * q^10 - 158204810172872 * q^11 - 2183598452277248 * q^14 + 20024144989158440 * q^15 + 63050394783186944 * q^16 - 140406399769275000 * q^19 + 4942137665781760 * q^20 + 457109656482968 * q^21 - 1078570329313378304 * q^24 + 6519283342722349350 * q^25 + 12210591275993726976 * q^26 - 259270857362526368940 * q^29 + 87647312900713840640 * q^30 + 101745690421209310208 * q^31 - 168898558224119103488 * q^34 + 1378811920964523641080 * q^35 + 2689895947914929242112 * q^36 - 18485576517782584068816 * q^39 + 2215759262886983106560 * q^40 - 1896584587803054469892 * q^41 + 10616945090037083537408 * q^44 - 29442738837757383895370 * q^45 + 1728449771947095719936 * q^46 + 192038716356487330909578 * q^49 - 263092763203302557286400 * q^50 - 456935745972115783739392 * q^51 - 331656187868266799759360 * q^54 + 350630587149946820863720 * q^55 + 146538811564484326326272 * q^56 - 2045452754502768653597480 * q^59 - 1343797622793715224412160 * q^60 - 4292410952783704571694812 * q^61 - 4231240368651202111471616 * q^64 + 7080387802173324288729840 * q^65 + 13458699699704954185449472 * q^66 - 7561881285185794836127976 * q^69 - 2658452801760660242923520 * q^70 - 10349408366862708776842032 * q^71 + 4825936898350986471473152 * q^74 - 32265585350433832322099600 * q^75 + 9422513986845907353600000 * q^76 + 171195367329681711405798240 * q^79 - 331661244482225585520640 * q^80 + 218412595435081152290268614 * q^81 - 30676109770002217828352 * q^84 + 49996632095782610955681280 * q^85 - 233050420171472482535440384 * q^86 - 920119011432929778337961140 * q^89 + 338023638508635646110433280 * q^90 + 1218965825148727758344415888 * q^91 + 55077388646346071267704832 * q^94 - 643974213982984055905842600 * q^95 + 72381629544326717983686656 * q^96 - 3930714930503120441731386616 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/10\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$-1$

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 $

$2$		−	8192.00i		−	0.707107i
$2$		−	8192.00i		−	0.707107i
$3$		−	4.36047e6i		−	1.57905i	−0.613717	−	0.789526i	$-0.710327\pi$
$3$		−	4.36047e6i		−	1.57905i	0.613717	−	0.789526i	$-0.289673\pi$
$4$	−6.71089e7			−0.500000
$5$	−1.84162e9	+	2.01470e9i	−0.674690	+	0.738101i
$5$	−1.84162e9	+	2.01470e9i	−0.674690	+	0.738101i
$6$	−3.57210e10			−1.11656
$7$			1.94048e10i			0.0756981i	0.999283	+	0.0378491i	$0.0120506\pi$
$7$			1.94048e10i			0.0756981i	−0.999283	+	0.0378491i	$0.987949\pi$
$8$			5.49756e11i			0.353553i
$9$	−1.13881e13			−1.49340
$10$	1.65044e13	+	1.50865e13i	0.521916	+	0.477078i
$11$	−1.73755e14			−1.51753			−0.758764	−	0.651366i	$-0.774196\pi$
$11$	−1.73755e14			−1.51753			−0.758764	+	0.651366i	$0.774196\pi$
$12$			2.92626e14i			0.789526i
$13$		−	6.75010e14i		−	0.618123i	−0.951042	−	0.309061i	$-0.899985\pi$
$13$		−	6.75010e14i		−	0.618123i	0.951042	−	0.309061i	$-0.100015\pi$
$14$	1.58964e14			0.0535267
$15$	8.78505e15	+	8.03032e15i	1.16550	+	1.06537i
$16$	4.50360e15			0.250000
$17$			4.72808e16i			1.15778i	0.815407	+	0.578888i	$0.196513\pi$
$17$			4.72808e16i			1.15778i	−0.815407	+	0.578888i	$0.803487\pi$
$18$			9.32913e16i			1.05600i
$19$	2.99649e17			1.63471			0.817353	−	0.576137i	$-0.195440\pi$
$19$	2.99649e17			1.63471			0.817353	+	0.576137i	$0.195440\pi$
$20$	1.23589e17	−	1.35204e17i	0.337345	−	0.369051i
$21$	8.46139e16			0.119531
$22$			1.42340e18i			1.07305i
$23$			1.42626e18i			0.590027i	0.955493	+	0.295014i	$0.0953242\pi$
$23$			1.42626e18i			0.590027i	−0.955493	+	0.295014i	$0.904676\pi$
$24$	2.39719e18			0.558279
$25$	−6.67471e17	−	7.42062e18i	−0.0895865	−	0.995979i
$26$	−5.52968e18			−0.437079
$27$			1.64063e19i			0.779111i
$28$		−	1.30223e18i		−	0.0378491i
$29$	−4.14340e19			−0.749867			−0.374933	−	0.927052i	$-0.622334\pi$
$29$	−4.14340e19			−0.749867			−0.374933	+	0.927052i	$0.622334\pi$
$30$	6.57844e19	−	7.19671e19i	0.753331	−	0.824133i
$31$	1.01475e20			0.746405			0.373202	−	0.927750i	$-0.378260\pi$
$31$	1.01475e20			0.746405			0.373202	+	0.927750i	$0.378260\pi$
$32$		−	3.68935e19i		−	0.176777i
$33$			7.57655e20i			2.39626i
$34$	3.87324e20			0.818671
$35$	−3.90949e19	−	3.57362e19i	−0.0558729	−	0.0510728i
$36$	7.64242e20			0.746702
$37$		−	4.31315e20i		−	0.291119i	−0.989349	−	0.145560i	$-0.953502\pi$
$37$		−	4.31315e20i		−	0.291119i	0.989349	−	0.145560i	$-0.0464983\pi$
$38$		−	2.45473e21i		−	1.15591i
$39$	−2.94336e21			−0.976048
$40$	−1.10759e21	−	1.01244e21i	−0.260958	−	0.238539i
$41$	−6.35676e21			−1.07313			−0.536567	−	0.843858i	$-0.680279\pi$
$41$	−6.35676e21			−1.07313			−0.536567	+	0.843858i	$0.680279\pi$
$42$		−	6.93157e20i		−	0.0845214i
$43$		−	1.92277e22i		−	1.70648i	−0.521515	−	0.853242i	$-0.674633\pi$
$43$		−	1.92277e22i		−	1.70648i	0.521515	−	0.853242i	$-0.325367\pi$
$44$	1.16605e22			0.758764
$45$	2.09725e22	−	2.29436e22i	1.00759	−	1.10228i
$46$	1.16839e22			0.417212
$47$			6.41268e22i			1.71285i	0.516275	+	0.856423i	$0.327318\pi$
$47$			6.41268e22i			1.71285i	−0.516275	+	0.856423i	$0.672682\pi$
$48$		−	1.96378e22i		−	0.394763i
$49$	6.53358e22			0.994270
$50$	−6.07897e22	+	5.46792e21i	−0.704264	+	0.0633472i
$51$	2.06166e23			1.82819
$52$			4.52991e22i			0.309061i
$53$		−	7.01449e22i		−	0.370060i	−0.982733	−	0.185030i	$-0.940762\pi$
$53$		−	7.01449e22i		−	0.370060i	0.982733	−	0.185030i	$-0.0592382\pi$
$54$	1.34400e23			0.550914
$55$	3.19991e23	−	3.50065e23i	1.02386	−	1.12009i
$56$	−1.06679e22			−0.0267633
$57$		−	1.30661e24i		−	2.58129i
$58$			3.39428e23i			0.530236i
$59$	7.97207e23			0.988710			0.494355	−	0.869260i	$-0.335404\pi$
$59$	7.97207e23			0.988710			0.494355	+	0.869260i	$0.335404\pi$
$60$	−5.89555e23	−	5.38905e23i	−0.582750	−	0.532685i
$61$	−7.03947e23			−0.556656			−0.278328	−	0.960486i	$-0.589780\pi$
$61$	−7.03947e23			−0.556656			−0.278328	+	0.960486i	$0.589780\pi$
$62$		−	8.31280e23i		−	0.527788i
$63$		−	2.20984e23i		−	0.113048i
$64$	−3.02231e23			−0.125000
$65$	1.35994e24	+	1.24311e24i	0.456237	+	0.417041i
$66$	6.20671e24			1.69441
$67$			1.48454e24i			0.330813i	0.986226	+	0.165406i	$0.0528936\pi$
$67$			1.48454e24i			0.330813i	−0.986226	+	0.165406i	$0.947106\pi$
$68$		−	3.17296e24i		−	0.578888i
$69$	6.21915e24			0.931683
$70$	−2.92751e23	+	3.20265e23i	−0.0361139	+	0.0395081i
$71$	−1.17498e25			−1.19685			−0.598427	−	0.801177i	$-0.704207\pi$
$71$	−1.17498e25			−1.19685			−0.598427	+	0.801177i	$0.704207\pi$
$72$		−	6.26067e24i		−	0.527998i
$73$			1.70047e25i			1.19045i	0.803560	+	0.595224i	$0.202937\pi$
$73$			1.70047e25i			1.19045i	−0.803560	+	0.595224i	$0.797063\pi$
$74$	−3.53333e24			−0.205852
$75$	−3.23574e25	+	2.91049e24i	−1.57270	+	0.141462i
$76$	−2.01091e25			−0.817353
$77$		−	3.37168e24i		−	0.114874i
$78$			2.41120e25i			0.690170i
$79$	6.04850e25			1.45775			0.728874	−	0.684648i	$-0.240044\pi$
$79$	6.04850e25			1.45775			0.728874	+	0.684648i	$0.240044\pi$
$80$	−8.29391e24	+	9.07341e24i	−0.168673	+	0.184525i
$81$	−1.53020e25			−0.263148
$82$			5.20746e25i			0.758820i
$83$			8.94591e25i			1.10680i	0.832915	+	0.553402i	$0.186671\pi$
$83$			8.94591e25i			1.10680i	−0.832915	+	0.553402i	$0.813329\pi$
$84$	−5.67835e24			−0.0597656
$85$	−9.52567e25	−	8.70731e25i	−0.854555	−	0.781140i
$86$	−1.57513e26			−1.20667
$87$			1.80672e26i			1.18408i
$88$		−	9.55230e25i		−	0.536527i
$89$	1.26789e26			0.611388			0.305694	−	0.952130i	$-0.401111\pi$
$89$	1.26789e26			0.611388			0.305694	+	0.952130i	$0.401111\pi$
$90$	−1.87954e26	−	1.71807e26i	−0.779432	−	0.712470i
$91$	1.30984e25			0.0467907
$92$		−	9.57145e25i		−	0.295014i
$93$		−	4.42477e26i		−	1.17861i
$94$	5.25326e26			1.21116
$95$	−5.51840e26	+	6.03704e26i	−1.10292	+	1.20658i
$96$	−1.60873e26			−0.279140
$97$			1.36952e26i			0.206610i	0.994650	+	0.103305i	$0.0329417\pi$
$97$			1.36952e26i			0.206610i	−0.994650	+	0.103305i	$0.967058\pi$
$98$		−	5.35231e26i		−	0.703055i
$99$	1.97874e27			2.26628
$100$	4.47932e25	+	4.97990e26i	0.0447932	+	0.497990i
$101$	1.34962e27			1.17998			0.589989	−	0.807411i	$-0.299132\pi$
$101$	1.34962e27			1.17998			0.589989	+	0.807411i	$0.299132\pi$
$102$		−	1.68892e27i		−	1.29272i
$103$			1.33478e27i			0.895588i	0.894137	+	0.447794i	$0.147790\pi$
$103$			1.33478e27i			0.895588i	−0.894137	+	0.447794i	$0.852210\pi$
$104$	3.71090e26			0.218539
$105$	−1.55827e26	+	1.70472e26i	−0.0806466	+	0.0882261i
$106$	−5.74627e26			−0.261672
$107$		−	1.89206e27i		−	0.759021i	−0.925187	−	0.379511i	$-0.876092\pi$
$107$		−	1.89206e27i		−	0.759021i	0.925187	−	0.379511i	$-0.123908\pi$
$108$		−	1.10101e27i		−	0.389555i
$109$	5.06052e27			1.58102			0.790510	−	0.612449i	$-0.209816\pi$
$109$	5.06052e27			1.58102			0.790510	+	0.612449i	$0.209816\pi$
$110$	−2.86773e27	−	2.62136e27i	−0.792023	−	0.723979i
$111$	−1.88073e27			−0.459692
$112$			8.73913e25i			0.0189245i
$113$		−	1.42472e27i		−	0.273635i	−0.990596	−	0.136817i	$-0.956313\pi$
$113$		−	1.42472e27i		−	0.273635i	0.990596	−	0.136817i	$-0.0436873\pi$
$114$	−1.07038e28			−1.82524
$115$	−2.87348e27	−	2.62662e27i	−0.435500	−	0.398085i
$116$	2.78059e27			0.374933
$117$			7.68708e27i			0.923107i
$118$		−	6.53072e27i		−	0.699123i
$119$	−9.17473e26			−0.0876414
$120$	−4.41471e27	+	4.82963e27i	−0.376665	+	0.412066i
$121$	1.70809e28			1.30289
$122$			5.76673e27i			0.393616i
$123$			2.77185e28i			1.69453i
$124$	−6.80984e27			−0.373202
$125$	1.61796e28	+	1.23212e28i	0.795576	+	0.605853i
$126$	−1.81030e27			−0.0799369
$127$			3.83086e28i			1.52036i	0.649712	+	0.760180i	$0.274889\pi$
$127$			3.83086e28i			1.52036i	−0.649712	+	0.760180i	$0.725111\pi$
$128$			2.47588e27i			0.0883883i
$129$	−8.38417e28			−2.69463
$130$	1.01836e28	−	1.11407e28i	0.294893	−	0.322608i
$131$	2.32350e28			0.606708			0.303354	−	0.952878i	$-0.401894\pi$
$131$	2.32350e28			0.606708			0.303354	+	0.952878i	$0.401894\pi$
$132$		−	5.08453e28i		−	1.19813i
$133$			5.81463e27i			0.123744i
$134$	1.21614e28			0.233920
$135$	−3.30538e28	−	3.02141e28i	−0.575062	−	0.525658i
$136$	−2.59929e28			−0.409335
$137$		−	7.49761e28i		−	1.06954i	−0.844999	−	0.534768i	$-0.820399\pi$
$137$		−	7.49761e28i		−	1.06954i	0.844999	−	0.534768i	$-0.179601\pi$
$138$		−	5.09473e28i		−	0.658800i
$139$	−1.33981e29			−1.57160			−0.785801	−	0.618479i	$-0.787749\pi$
$139$	−1.33981e29			−1.57160			−0.785801	+	0.618479i	$0.787749\pi$
$140$	2.62361e27	+	2.39821e27i	0.0279364	+	0.0255364i
$141$	2.79623e29			2.70467
$142$			9.62540e28i			0.846303i
$143$			1.17286e29i			0.938018i
$144$	−5.12874e28			−0.373351
$145$	7.63056e28	−	8.34772e28i	0.505928	−	0.553478i
$146$	1.39302e29			0.841773
$147$		−	2.84895e29i		−	1.57000i
$148$			2.89450e28i			0.145560i
$149$	2.64445e29			1.21428			0.607142	−	0.794593i	$-0.292316\pi$
$149$	2.64445e29			1.21428			0.607142	+	0.794593i	$0.292316\pi$
$150$	2.38427e28	+	2.65072e29i	0.100028	+	1.11207i
$151$	−5.47706e28			−0.210068			−0.105034	−	0.994469i	$-0.533495\pi$
$151$	−5.47706e28			−0.210068			−0.105034	+	0.994469i	$0.533495\pi$
$152$			1.64734e29i			0.577956i
$153$		−	5.38438e29i		−	1.72903i
$154$	−2.76208e28			−0.0812282
$155$	−1.86877e29	+	2.04441e29i	−0.503592	+	0.550922i
$156$	1.97525e29			0.488024
$157$		−	6.14799e28i		−	0.139344i	−0.997570	−	0.0696720i	$-0.977805\pi$
$157$		−	6.14799e28i		−	0.139344i	0.997570	−	0.0696720i	$-0.0221953\pi$
$158$		−	4.95493e29i		−	1.03078i
$159$	−3.05865e29			−0.584344
$160$	7.43294e28	+	6.79437e28i	0.130479	+	0.119269i
$161$	−2.76762e28			−0.0446639
$162$			1.25354e29i			0.186074i
$163$			9.30839e29i			1.27157i	0.771864	+	0.635787i	$0.219324\pi$
$163$			9.30839e29i			1.27157i	−0.771864	+	0.635787i	$0.780676\pi$
$164$	4.26595e29			0.536567
$165$	−1.52645e30	−	1.39531e30i	−1.76868	−	1.61673i
$166$	7.32849e29			0.782628
$167$			1.19924e30i			1.18096i	0.807053	+	0.590479i	$0.201061\pi$
$167$			1.19924e30i			1.18096i	−0.807053	+	0.590479i	$0.798939\pi$
$168$			4.65170e28i			0.0422607i
$169$	7.36895e29			0.617924
$170$	−7.13303e29	+	7.80343e29i	−0.552349	+	0.604262i
$171$	−3.41244e30			−2.44128
$172$			1.29035e30i			0.853242i
$173$			1.81586e30i			1.11035i	0.831733	+	0.555176i	$0.187349\pi$
$173$			1.81586e30i			1.11035i	−0.831733	+	0.555176i	$0.812651\pi$
$174$	1.48006e30			0.837270
$175$	1.43996e29	−	1.29521e28i	0.0753937	−	0.00678153i
$176$	−7.82524e29			−0.379382
$177$		−	3.47620e30i		−	1.56122i
$178$		−	1.03866e30i		−	0.432317i
$179$	1.24772e30			0.481504			0.240752	−	0.970587i	$-0.422606\pi$
$179$	1.24772e30			0.481504			0.240752	+	0.970587i	$0.422606\pi$
$180$	−1.40744e30	+	1.53972e30i	−0.503793	+	0.551142i
$181$	1.77785e30			0.590519			0.295260	−	0.955417i	$-0.404594\pi$
$181$	1.77785e30			0.590519			0.295260	+	0.955417i	$0.404594\pi$
$182$		−	1.07302e29i		−	0.0330860i
$183$			3.06954e30i			0.878989i
$184$	−7.84093e29			−0.208606
$185$	8.68971e29	+	7.94317e29i	0.214875	+	0.196415i
$186$	−3.62477e30			−0.833404
$187$		−	8.21529e30i		−	1.75696i
$188$		−	4.30347e30i		−	0.856423i
$189$	−3.18360e29			−0.0589772
$190$	4.94555e30	+	4.52067e30i	0.853180	+	0.779882i
$191$	4.40099e30			0.707293			0.353647	−	0.935379i	$-0.384942\pi$
$191$	4.40099e30			0.707293			0.353647	+	0.935379i	$0.384942\pi$
$192$			1.31787e30i			0.197381i
$193$			8.90239e30i			1.24303i	0.783401	+	0.621517i	$0.213483\pi$
$193$			8.90239e30i			1.24303i	−0.783401	+	0.621517i	$0.786517\pi$
$194$	1.12191e30			0.146095
$195$	5.42054e30	−	5.92999e30i	0.658530	−	0.720422i
$196$	−4.38461e30			−0.497135
$197$			9.39056e30i			0.994025i	0.867743	+	0.497013i	$0.165570\pi$
$197$			9.39056e30i			0.994025i	−0.867743	+	0.497013i	$0.834430\pi$
$198$		−	1.62099e31i		−	1.60250i
$199$	1.30788e31			1.20795			0.603976	−	0.797002i	$-0.293582\pi$
$199$	1.30788e31			1.20795			0.603976	+	0.797002i	$0.293582\pi$
$200$	4.07953e30	−	3.66946e29i	0.352132	−	0.0316736i
$201$	6.47329e30			0.522370
$202$		−	1.10561e31i		−	0.834370i
$203$		−	8.04018e29i		−	0.0567635i
$204$	−1.38356e31			−0.914094
$205$	1.17067e31	−	1.28070e31i	0.724032	−	0.792081i
$206$	1.09345e31			0.633276
$207$		−	1.62424e31i		−	0.881149i
$208$		−	3.03997e30i		−	0.154531i
$209$	−5.20657e31			−2.48071
$210$	1.39651e30	+	1.27653e30i	0.0623853	+	0.0570257i
$211$	−4.40738e31			−1.84658			−0.923288	−	0.384109i	$-0.874509\pi$
$211$	−4.40738e31			−1.84658			−0.923288	+	0.384109i	$0.874509\pi$
$212$			4.70735e30i			0.185030i
$213$			5.12345e31i			1.88989i
$214$	−1.54998e31			−0.536709
$215$	3.87380e31	+	3.54100e31i	1.25956	+	1.15135i
$216$	−9.01944e30			−0.275457
$217$			1.96909e30i			0.0565014i
$218$		−	4.14558e31i		−	1.11795i
$219$	7.41484e31			1.87978
$220$	−2.14742e31	+	2.34925e31i	−0.511931	+	0.560045i
$221$	3.19150e31			0.715647
$222$			1.54070e31i			0.325052i
$223$		−	4.82839e30i		−	0.0958709i	−0.998850	−	0.0479354i	$-0.984736\pi$
$223$		−	4.82839e30i		−	0.0958709i	0.998850	−	0.0479354i	$-0.0152642\pi$
$224$	7.15910e29			0.0133817
$225$	7.60123e30	+	8.45068e31i	0.133789	+	1.48740i
$226$	−1.16713e31			−0.193489
$227$		−	1.50227e31i		−	0.234638i	−0.993094	−	0.117319i	$-0.962570\pi$
$227$		−	1.50227e31i		−	0.234638i	0.993094	−	0.117319i	$-0.0374301\pi$
$228$			8.76853e31i			1.29064i
$229$	−1.35922e32			−1.88586			−0.942931	−	0.332989i	$-0.891943\pi$
$229$	−1.35922e32			−1.88586			−0.942931	+	0.332989i	$0.891943\pi$
$230$	−2.15173e31	+	2.35396e31i	−0.281489	+	0.307945i
$231$	−1.47021e31			−0.181392
$232$		−	2.27786e31i		−	0.265118i
$233$		−	3.79891e31i		−	0.417209i	−0.978000	−	0.208604i	$-0.933108\pi$
$233$		−	3.79891e31i		−	0.417209i	0.978000	−	0.208604i	$-0.0668921\pi$
$234$	6.29725e31			0.652735
$235$	−1.29196e32	−	1.18097e32i	−1.26425	−	1.15564i
$236$	−5.34996e31			−0.494355
$237$		−	2.63743e32i		−	2.30186i
$238$			7.51594e30i			0.0619718i
$239$	1.00391e32			0.782213			0.391107	−	0.920345i	$-0.372092\pi$
$239$	1.00391e32			0.782213			0.391107	+	0.920345i	$0.372092\pi$
$240$	3.95643e31	+	3.61653e31i	0.291375	+	0.266343i
$241$	−1.53727e31			−0.107033			−0.0535166	−	0.998567i	$-0.517043\pi$
$241$	−1.53727e31			−0.107033			−0.0535166	+	0.998567i	$0.517043\pi$
$242$		−	1.39927e32i		−	0.921283i
$243$			1.91832e32i			1.19464i
$244$	4.72411e31			0.278328
$245$	−1.20324e32	+	1.31632e32i	−0.670824	+	0.733872i
$246$	2.27070e32			1.19822
$247$		−	2.02266e32i		−	1.01045i
$248$			5.57862e31i			0.263894i
$249$	3.90084e32			1.74770
$250$	1.00935e32	−	1.32543e32i	0.428403	−	0.562557i
$251$	3.03502e31			0.122058			0.0610290	−	0.998136i	$-0.480562\pi$
$251$	3.03502e31			0.122058			0.0610290	+	0.998136i	$0.480562\pi$
$252$			1.48300e31i			0.0565239i
$253$		−	2.47820e32i		−	0.895383i
$254$	3.13824e32			1.07506
$255$	−3.79680e32	+	4.15364e32i	−1.23346	+	1.34939i
$256$	2.02824e31			0.0625000
$257$		−	3.12991e31i		−	0.0915028i	−0.998953	−	0.0457514i	$-0.985432\pi$
$257$		−	3.12991e31i		−	0.0915028i	0.998953	−	0.0457514i	$-0.0145682\pi$
$258$			6.86831e32i			1.90539i
$259$	8.36956e30			0.0220372
$260$	−9.12643e31	−	8.34237e31i	−0.228119	−	0.208521i
$261$	4.71855e32			1.11985
$262$		−	1.90341e32i		−	0.429007i
$263$		−	7.09398e32i		−	1.51875i	−0.650651	−	0.759377i	$-0.725504\pi$
$263$		−	7.09398e32i		−	1.51875i	0.650651	−	0.759377i	$-0.274496\pi$
$264$	−4.16525e32			−0.847204
$265$	1.41321e32	+	1.29180e32i	0.273142	+	0.249676i
$266$	4.76334e31			0.0875004
$267$		−	5.52861e32i		−	0.965414i
$268$		−	9.96258e31i		−	0.165406i
$269$	−8.86054e32			−1.39896			−0.699479	−	0.714653i	$-0.746584\pi$
$269$	−8.86054e32			−1.39896			−0.699479	+	0.714653i	$0.746584\pi$
$270$	−2.47514e32	+	2.70776e32i	−0.371697	+	0.406631i
$271$	−2.90104e32			−0.414446			−0.207223	−	0.978294i	$-0.566443\pi$
$271$	−2.90104e32			−0.414446			−0.207223	+	0.978294i	$0.566443\pi$
$272$			2.12934e32i			0.289444i
$273$		−	5.71152e31i		−	0.0738850i
$274$	−6.14204e32			−0.756276
$275$	1.15977e32	+	1.28937e33i	0.135950	+	1.51143i
$276$	−4.17360e32			−0.465842
$277$		−	1.11039e33i		−	1.18032i	−0.807288	−	0.590158i	$-0.799066\pi$
$277$		−	1.11039e33i		−	1.18032i	0.807288	−	0.590158i	$-0.200934\pi$
$278$			1.09757e33i			1.11129i
$279$	−1.15560e33			−1.11468
$280$	1.96462e31	−	2.14926e31i	0.0180570	−	0.0197540i
$281$	−2.23578e32			−0.195836			−0.0979181	−	0.995194i	$-0.531218\pi$
$281$	−2.23578e32			−0.195836			−0.0979181	+	0.995194i	$0.531218\pi$
$282$		−	2.29067e33i		−	1.91249i
$283$			2.15606e33i			1.71610i	0.513565	+	0.858051i	$0.328325\pi$
$283$			2.15606e33i			1.71610i	−0.513565	+	0.858051i	$0.671675\pi$
$284$	7.88513e32			0.598427
$285$	2.63243e33	+	2.40628e33i	1.90525	+	1.74157i
$286$	9.60811e32			0.663279
$287$		−	1.23351e32i		−	0.0812342i
$288$			4.20147e32i			0.263999i
$289$	−5.67762e32			−0.340444
$290$	−6.83846e32	−	6.25096e32i	−0.391368	−	0.357745i
$291$	5.97176e32			0.326247
$292$		−	1.14117e33i		−	0.595224i
$293$			2.16621e33i			1.07892i	0.842012	+	0.539458i	$0.181371\pi$
$293$			2.16621e33i			1.07892i	−0.842012	+	0.539458i	$0.818629\pi$
$294$	−2.33386e33			−1.11016
$295$	−1.46815e33	+	1.60613e33i	−0.667073	+	0.729768i
$296$	2.37118e32			0.102926
$297$		−	2.85068e33i		−	1.18232i
$298$		−	2.16633e33i		−	0.858629i
$299$	9.62737e32			0.364709
$300$	2.17147e33	−	1.95320e32i	0.786351	−	0.0707308i
$301$	3.73109e32			0.129178
$302$			4.48681e32i			0.148540i
$303$		−	5.88499e33i		−	1.86325i
$304$	1.34950e33			0.408677
$305$	1.29640e33	−	1.41824e33i	0.375571	−	0.410869i
$306$	−4.41089e33			−1.22261
$307$		−	1.46581e33i		−	0.388786i	−0.980924	−	0.194393i	$-0.937726\pi$
$307$		−	1.46581e33i		−	0.388786i	0.980924	−	0.194393i	$-0.0622737\pi$
$308$			2.26270e32i			0.0574370i
$309$	5.82028e33			1.41418
$310$	1.67478e33	+	1.53090e33i	0.389561	+	0.356093i
$311$	2.92959e33			0.652442			0.326221	−	0.945294i	$-0.394225\pi$
$311$	2.92959e33			0.652442			0.326221	+	0.945294i	$0.394225\pi$
$312$		−	1.61813e33i		−	0.345085i
$313$			3.19877e33i			0.653332i	0.945140	+	0.326666i	$0.105925\pi$
$313$			3.19877e33i			0.653332i	−0.945140	+	0.326666i	$0.894075\pi$
$314$	−5.03643e32			−0.0985310
$315$	4.45216e32	+	4.06967e32i	0.0834408	+	0.0762723i
$316$	−4.05908e33			−0.728874
$317$		−	2.65764e33i		−	0.457294i	−0.973509	−	0.228647i	$-0.926570\pi$
$317$		−	2.65764e33i		−	0.457294i	0.973509	−	0.228647i	$-0.0734302\pi$
$318$			2.50564e33i			0.413193i
$319$	7.19938e33			1.13794
$320$	5.56595e32	−	6.08906e32i	0.0843363	−	0.0922626i
$321$	−8.25027e33			−1.19853
$322$			2.26723e32i			0.0315822i
$323$			1.41677e34i			1.89262i
$324$	1.02690e33			0.131574
$325$	−5.00899e33	+	4.50549e32i	−0.615637	+	0.0553754i
$326$	7.62543e33			0.899139
$327$		−	2.20662e34i		−	2.49651i
$328$		−	3.49466e33i		−	0.379410i
$329$	−1.24437e33			−0.129659
$330$	−1.14304e34	+	1.25047e34i	−1.14320	+	1.25064i
$331$	−1.16167e34			−1.11533			−0.557666	−	0.830066i	$-0.688303\pi$
$331$	−1.16167e34			−1.11533			−0.557666	+	0.830066i	$0.688303\pi$
$332$		−	6.00350e33i		−	0.553402i
$333$			4.91185e33i			0.434759i
$334$	9.82419e33			0.835063
$335$	−2.99091e33	−	2.73396e33i	−0.244173	−	0.223196i
$336$	3.81067e32			0.0298828
$337$			1.49223e34i			1.12417i	0.827080	+	0.562084i	$0.190000\pi$
$337$			1.49223e34i			1.12417i	−0.827080	+	0.562084i	$0.810000\pi$
$338$		−	6.03665e33i		−	0.436938i
$339$	−6.21246e33			−0.432083
$340$	6.39257e33	+	5.84338e33i	0.427278	+	0.390570i
$341$	−1.76317e34			−1.13269
$342$			2.79547e34i			1.72624i
$343$			2.54296e33i			0.150962i
$344$	1.05705e34			0.603333
$345$	−1.14533e34	+	1.25297e34i	−0.628598	+	0.687676i
$346$	1.48756e34			0.785138
$347$		−	6.22064e33i		−	0.315782i	−0.987457	−	0.157891i	$-0.949531\pi$
$347$		−	6.22064e33i		−	0.315782i	0.987457	−	0.157891i	$-0.0504694\pi$
$348$		−	1.21247e34i		−	0.592039i
$349$	−4.04231e32			−0.0189883			−0.00949415	−	0.999955i	$-0.503022\pi$
$349$	−4.04231e32			−0.0189883			−0.00949415	+	0.999955i	$0.503022\pi$
$350$	−1.06104e32	−	1.17961e33i	−0.00479526	−	0.0533114i
$351$	1.10744e34			0.481586
$352$			6.41044e33i			0.268264i
$353$			1.06569e34i			0.429212i	0.976701	+	0.214606i	$0.0688468\pi$
$353$			1.06569e34i			0.429212i	−0.976701	+	0.214606i	$0.931153\pi$
$354$	−2.84770e34			−1.10395
$355$	2.16386e34	−	2.36723e34i	0.807505	−	0.883399i
$356$	−8.50868e33			−0.305694
$357$			4.00061e33i			0.138390i
$358$		−	1.02213e34i		−	0.340475i
$359$	−5.00144e34			−1.60443			−0.802213	−	0.597038i	$-0.796344\pi$
$359$	−5.00144e34			−1.60443			−0.802213	+	0.597038i	$0.796344\pi$
$360$	1.26134e34	+	1.15298e34i	0.389716	+	0.356235i
$361$	5.61891e34			1.67227
$362$		−	1.45641e34i		−	0.417560i
$363$		−	7.44807e34i		−	2.05733i
$364$	−8.79019e32			−0.0233954
$365$	−3.42594e34	−	3.13161e34i	−0.878670	−	0.803183i
$366$	2.51457e34			0.621539
$367$		−	5.65777e33i		−	0.134789i	−0.997726	−	0.0673944i	$-0.978531\pi$
$367$		−	5.65777e33i		−	0.134789i	0.997726	−	0.0673944i	$-0.0214686\pi$
$368$			6.42329e33i			0.147507i
$369$	7.23914e34			1.60262
$370$	6.50704e33	−	7.11861e33i	0.138887	−	0.151940i
$371$	1.36115e33			0.0280128
$372$			2.96941e34i			0.589306i
$373$			4.37195e34i			0.836769i	0.908270	+	0.418385i	$0.137404\pi$
$373$			4.37195e34i			0.836769i	−0.908270	+	0.418385i	$0.862596\pi$
$374$	−6.72996e34			−1.24236
$375$	5.37262e34	−	7.05505e34i	0.956674	−	1.25626i
$376$	−3.52541e34			−0.605582
$377$			2.79684e34i			0.463510i
$378$			2.60801e33i			0.0417032i
$379$	−9.27986e34			−1.43190			−0.715949	−	0.698152i	$-0.754006\pi$
$379$	−9.27986e34			−1.43190			−0.715949	+	0.698152i	$0.754006\pi$
$380$	3.70333e34	−	4.05139e34i	0.551460	−	0.603289i
$381$	1.67044e35			2.40073
$382$		−	3.60529e34i		−	0.500132i
$383$			6.54839e34i			0.876902i	0.898755	+	0.438451i	$0.144473\pi$
$383$			6.54839e34i			0.876902i	−0.898755	+	0.438451i	$0.855527\pi$
$384$	1.07960e34			0.139570
$385$	6.79294e33	+	6.20935e33i	0.0847886	+	0.0775044i
$386$	7.29284e34			0.878958
$387$			2.18967e35i			2.54847i
$388$		−	9.19071e33i		−	0.103305i
$389$	1.03818e34			0.112707			0.0563537	−	0.998411i	$-0.482053\pi$
$389$	1.03818e34			0.112707			0.0563537	+	0.998411i	$0.482053\pi$
$390$	−4.85785e34	−	4.44051e34i	−0.509415	−	0.465651i
$391$	−6.74346e34			−0.683119
$392$			3.59187e34i			0.351527i
$393$		−	1.01315e35i		−	0.958023i
$394$	7.69274e34			0.702882
$395$	−1.11390e35	+	1.21859e35i	−0.983528	+	1.07596i
$396$	−1.32791e35			−1.13314
$397$			1.03095e34i			0.0850285i	0.999096	+	0.0425143i	$0.0135368\pi$
$397$			1.03095e34i			0.0850285i	−0.999096	+	0.0425143i	$0.986463\pi$
$398$		−	1.07141e35i		−	0.854152i
$399$	2.53545e34			0.195398
$400$	−3.00602e33	−	3.34195e34i	−0.0223966	−	0.248995i
$401$	−1.99642e35			−1.43815			−0.719074	−	0.694933i	$-0.755434\pi$
$401$	−1.99642e35			−1.43815			−0.719074	+	0.694933i	$0.755434\pi$
$402$		−	5.30292e34i		−	0.369372i
$403$		−	6.84963e34i		−	0.461370i
$404$	−9.05717e34			−0.589989
$405$	2.81804e34	−	3.08290e34i	0.177543	−	0.194230i
$406$	−6.58652e33			−0.0401379
$407$			7.49432e34i			0.441782i
$408$			1.13341e35i			0.646362i
$409$	1.72738e35			0.953064			0.476532	−	0.879157i	$-0.341894\pi$
$409$	1.72738e35			0.953064			0.476532	+	0.879157i	$0.341894\pi$
$410$	−1.04915e35	−	9.59014e34i	−0.560086	−	0.511968i
$411$	−3.26931e35			−1.68885
$412$		−	8.95758e34i		−	0.447794i
$413$			1.54696e34i			0.0748435i
$414$	−1.33057e35			−0.623066
$415$	−1.80234e35	−	1.64749e35i	−0.816933	−	0.746749i
$416$	−2.49035e34			−0.109270
$417$			5.84219e35i			2.48164i
$418$			4.26522e35i			1.75413i
$419$	3.87612e35			1.54351			0.771753	−	0.635922i	$-0.219380\pi$
$419$	3.87612e35			1.54351			0.771753	+	0.635922i	$0.219380\pi$
$420$	1.04573e34	−	1.14402e34i	0.0403233	−	0.0441131i
$421$	3.72898e35			1.39246			0.696229	−	0.717820i	$-0.254860\pi$
$421$	3.72898e35			1.39246			0.696229	+	0.717820i	$0.254860\pi$
$422$			3.61052e35i			1.30573i
$423$		−	7.30282e35i		−	2.55797i
$424$	3.85626e34			0.130836
$425$	3.50853e35	−	3.15586e34i	1.15312	−	0.103721i
$426$	4.19713e35			1.33636
$427$		−	1.36599e34i		−	0.0421378i
$428$			1.26974e35i			0.379511i
$429$	5.11424e35			1.48118
$430$	2.90079e35	−	3.17342e35i	0.814126	−	0.890642i
$431$	−4.50905e35			−1.22643			−0.613214	−	0.789917i	$-0.710124\pi$
$431$	−4.50905e35			−1.22643			−0.613214	+	0.789917i	$0.710124\pi$
$432$			7.38873e34i			0.194778i
$433$		−	1.12870e35i		−	0.288399i	−0.989549	−	0.144200i	$-0.953939\pi$
$433$		−	1.12870e35i		−	0.288399i	0.989549	−	0.144200i	$-0.0460607\pi$
$434$	1.61308e34			0.0399525
$435$	−3.64000e35	−	3.32728e35i	−0.873970	−	0.798886i
$436$	−3.39606e35			−0.790510
$437$			4.27377e35i			0.964521i
$438$		−	6.07424e35i		−	1.32920i
$439$	7.99108e34			0.169564			0.0847822	−	0.996400i	$-0.472981\pi$
$439$	7.99108e34			0.169564			0.0847822	+	0.996400i	$0.472981\pi$
$440$	1.92450e35	+	1.75917e35i	0.396011	+	0.361990i
$441$	−7.44051e35			−1.48485
$442$		−	2.61448e35i		−	0.506039i
$443$		−	3.46606e35i		−	0.650707i	−0.945592	−	0.325354i	$-0.894517\pi$
$443$		−	3.46606e35i		−	0.650707i	0.945592	−	0.325354i	$-0.105483\pi$
$444$	1.26214e35			0.229846
$445$	−2.33497e35	+	2.55443e35i	−0.412498	+	0.451267i
$446$	−3.95542e34			−0.0677910
$447$		−	1.15310e36i		−	1.91742i
$448$		−	5.86473e33i		−	0.00946227i
$449$	−9.92797e35			−1.55430			−0.777150	−	0.629316i	$-0.783335\pi$
$449$	−9.92797e35			−1.55430			−0.777150	+	0.629316i	$0.783335\pi$
$450$	6.92280e35	−	6.22692e34i	1.05175	−	0.0946030i
$451$	1.10452e36			1.62851
$452$			9.56115e34i			0.136817i
$453$			2.38826e35i			0.331707i
$454$	−1.23066e35			−0.165914
$455$	−2.41223e34	+	2.63894e34i	−0.0315692	+	0.0345363i
$456$	7.18318e35			0.912622
$457$		−	2.92520e35i		−	0.360816i	−0.983592	−	0.180408i	$-0.942258\pi$
$457$		−	2.92520e35i		−	0.360816i	0.983592	−	0.180408i	$-0.0577419\pi$
$458$			1.11347e36i			1.33351i
$459$	−7.75702e35			−0.902035
$460$	1.92836e35	+	1.76269e35i	0.217750	+	0.199043i
$461$	3.02221e35			0.331408			0.165704	−	0.986176i	$-0.447010\pi$
$461$	3.02221e35			0.331408			0.165704	+	0.986176i	$0.447010\pi$
$462$			1.20440e35i			0.128264i
$463$			3.51002e35i			0.363049i	0.983386	+	0.181525i	$0.0581032\pi$
$463$			3.51002e35i			0.363049i	−0.983386	+	0.181525i	$0.941897\pi$
$464$	−1.86602e35			−0.187467
$465$	8.91459e35	+	8.14873e35i	0.869934	+	0.795198i
$466$	−3.11206e35			−0.295011
$467$		−	1.29826e35i		−	0.119559i	−0.998212	−	0.0597797i	$-0.980960\pi$
$467$		−	1.29826e35i		−	0.119559i	0.998212	−	0.0597797i	$-0.0190398\pi$
$468$		−	5.15871e35i		−	0.461554i
$469$	−2.88072e34			−0.0250419
$470$	−9.67450e35	+	1.05838e36i	−0.817161	+	0.893962i
$471$	−2.68081e35			−0.220031
$472$			4.38269e35i			0.349562i
$473$			3.34091e36i			2.58964i
$474$	−2.16058e36			−1.62766
$475$	−2.00007e35	−	2.22358e36i	−0.146448	−	1.62813i
$476$	6.15706e34			0.0438207
$477$			7.98817e35i			0.552649i
$478$		−	8.22407e35i		−	0.553108i
$479$	−8.02386e35			−0.524631			−0.262316	−	0.964982i	$-0.584486\pi$
$479$	−8.02386e35			−0.524631			−0.262316	+	0.964982i	$0.584486\pi$
$480$	2.96266e35	−	3.24111e35i	0.188333	−	0.206033i
$481$	−2.91142e35			−0.179947
$482$			1.25933e35i			0.0756840i
$483$			1.20681e35i			0.0705267i
$484$	−1.14628e36			−0.651446
$485$	−2.75918e35	−	2.52214e35i	−0.152499	−	0.139397i
$486$	1.57148e36			0.844735
$487$		−	1.61367e36i		−	0.843672i	−0.906672	−	0.421836i	$-0.861386\pi$
$487$		−	1.61367e36i		−	0.843672i	0.906672	−	0.421836i	$-0.138614\pi$
$488$		−	3.86999e35i		−	0.196808i
$489$	4.05889e36			2.00788
$490$	1.07833e36	+	9.85691e35i	0.518926	+	0.474344i
$491$	−2.14990e36			−1.00651			−0.503255	−	0.864138i	$-0.667864\pi$
$491$	−2.14990e36			−1.00651			−0.503255	+	0.864138i	$0.667864\pi$
$492$		−	1.86015e36i		−	0.847266i
$493$		−	1.95903e36i		−	0.868178i
$494$	−1.65696e36			−0.714495
$495$	−3.64409e36	+	3.98658e36i	−1.52904	+	1.67275i
$496$	4.57001e35			0.186601
$497$		−	2.28001e35i		−	0.0905996i
$498$		−	3.19557e36i		−	1.23581i
$499$	3.21120e36			1.20868			0.604339	−	0.796728i	$-0.293437\pi$
$499$	3.21120e36			1.20868			0.604339	+	0.796728i	$0.293437\pi$
$500$	−1.08579e36	−	8.26861e35i	−0.397788	−	0.302927i
$501$	5.22926e36			1.86479
$502$		−	2.48629e35i		−	0.0863080i
$503$			2.50486e36i			0.846478i	0.906018	+	0.423239i	$0.139107\pi$
$503$			2.50486e36i			0.846478i	−0.906018	+	0.423239i	$0.860893\pi$
$504$	1.21487e35			0.0399685
$505$	−2.48549e36	+	2.71909e36i	−0.796119	+	0.870943i
$506$	−2.03014e36			−0.633131
$507$		−	3.21321e36i		−	0.975734i
$508$		−	2.57085e36i		−	0.760180i
$509$	3.14700e36			0.906164			0.453082	−	0.891469i	$-0.350324\pi$
$509$	3.14700e36			0.906164			0.453082	+	0.891469i	$0.350324\pi$
$510$	3.40266e36	+	3.11034e36i	0.954161	+	0.872188i
$511$	−3.29972e35			−0.0901146
$512$		−	1.66153e35i		−	0.0441942i
$513$			4.91613e36i			1.27362i
$514$	−2.56402e35			−0.0647023
$515$	−2.68919e36	−	2.45816e36i	−0.661034	−	0.604244i
$516$	5.62652e36			1.34731
$517$		−	1.11424e37i		−	2.59929i
$518$		−	6.85635e34i		−	0.0155826i
$519$	7.91802e36			1.75330
$520$	−6.83407e35	+	7.47637e35i	−0.147446	+	0.161304i
$521$	−2.61163e36			−0.549039			−0.274519	−	0.961582i	$-0.588519\pi$
$521$	−2.61163e36			−0.549039			−0.274519	+	0.961582i	$0.588519\pi$
$522$		−	3.86544e36i		−	0.791857i
$523$		−	1.29754e35i		−	0.0259030i	−0.999916	−	0.0129515i	$-0.995877\pi$
$523$		−	1.29754e35i		−	0.0259030i	0.999916	−	0.0129515i	$-0.00412270\pi$
$524$	−1.55927e36			−0.303354
$525$	−5.64774e34	−	6.27888e35i	−0.0107084	−	0.119051i
$526$	−5.81139e36			−1.07392
$527$			4.79780e36i			0.864169i
$528$			3.41217e36i			0.599064i
$529$	3.80900e36			0.651868
$530$	1.05824e36	−	1.15770e36i	0.176547	−	0.193140i
$531$	−9.07867e36			−1.47654
$532$		−	3.90213e35i		−	0.0618721i
$533$			4.29087e36i			0.663328i
$534$	−4.52903e36			−0.682651
$535$	3.81194e36	+	3.48445e36i	0.560235	+	0.512104i
$536$	−8.16135e35			−0.116960
$537$		−	5.44063e36i		−	0.760319i
$538$			7.25856e36i			0.989212i
$539$	−1.13524e37			−1.50883
$540$	2.21820e36	+	2.02763e36i	0.287531	+	0.262829i
$541$	1.26803e37			1.60312			0.801561	−	0.597913i	$-0.204003\pi$
$541$	1.26803e37			1.60312			0.801561	+	0.597913i	$0.204003\pi$
$542$			2.37653e36i			0.293058i
$543$		−	7.75225e36i		−	0.932460i
$544$	1.74435e36			0.204668
$545$	−9.31954e36	+	1.01954e37i	−1.06670	+	1.16695i
$546$	−4.67888e35			−0.0522446
$547$		−	1.92461e36i		−	0.209659i	−0.994490	−	0.104830i	$-0.966570\pi$
$547$		−	1.92461e36i		−	0.209659i	0.994490	−	0.104830i	$-0.0334297\pi$
$548$			5.03156e36i			0.534768i
$549$	8.01662e36			0.831313
$550$	1.05625e37	−	9.50080e35i	1.06874	−	0.0961311i
$551$	−1.24157e37			−1.22581
$552$			3.41901e36i			0.329400i
$553$			1.17370e36i			0.110349i
$554$	−9.09630e36			−0.834609
$555$	3.46359e36	−	3.78912e36i	0.310150	−	0.339299i
$556$	8.99130e36			0.785801
$557$			2.79644e36i			0.238539i	0.992862	+	0.119270i	$0.0380553\pi$
$557$			2.79644e36i			0.238539i	−0.992862	+	0.119270i	$0.961945\pi$
$558$			9.46669e36i			0.788200i
$559$	−1.29789e37			−1.05482
$560$	−1.76068e35	−	1.60941e35i	−0.0139682	−	0.0127682i
$561$	−3.58225e37			−2.77433
$562$			1.83155e36i			0.138477i
$563$		−	1.25906e37i		−	0.929355i	−0.885480	−	0.464677i	$-0.846170\pi$
$563$		−	1.25906e37i		−	0.929355i	0.885480	−	0.464677i	$-0.153830\pi$
$564$	−1.87652e37			−1.35234
$565$	2.87039e36	+	2.62379e36i	0.201970	+	0.184619i
$566$	1.76624e37			1.21347
$567$		−	2.96932e35i		−	0.0199198i
$568$		−	6.45950e36i		−	0.423152i
$569$	−3.17815e36			−0.203310			−0.101655	−	0.994820i	$-0.532414\pi$
$569$	−3.17815e36			−0.203310			−0.101655	+	0.994820i	$0.532414\pi$
$570$	1.97122e37	−	2.15649e37i	1.23147	−	1.34722i
$571$	7.58646e36			0.462862			0.231431	−	0.972851i	$-0.425659\pi$
$571$	7.58646e36			0.462862			0.231431	+	0.972851i	$0.425659\pi$
$572$		−	7.87096e36i		−	0.469009i
$573$		−	1.91904e37i		−	1.11685i
$574$	−1.01050e36			−0.0574412
$575$	1.05837e37	−	9.51985e35i	0.587655	−	0.0528584i
$576$	3.44184e36			0.186676
$577$			2.14649e37i			1.13725i	0.822597	+	0.568625i	$0.192525\pi$
$577$			2.14649e37i			1.13725i	−0.822597	+	0.568625i	$0.807475\pi$
$578$			4.65111e36i			0.240730i
$579$	3.88186e37			1.96282
$580$	−5.12078e36	+	5.60206e36i	−0.252964	+	0.276739i
$581$	−1.73593e36			−0.0837829
$582$		−	4.89207e36i		−	0.230692i
$583$			1.21880e37i			0.561576i
$584$	−9.34843e36			−0.420887
$585$	−1.54872e37	−	1.41567e37i	−0.681346	−	0.622811i
$586$	1.77456e37			0.762909
$587$			3.16979e37i			1.33173i	0.746073	+	0.665864i	$0.231937\pi$
$587$			3.16979e37i			1.33173i	−0.746073	+	0.665864i	$0.768063\pi$
$588$			1.91190e37i			0.785002i
$589$	3.04068e37			1.22015
$590$	1.31575e37	+	1.20271e37i	0.516024	+	0.471692i
$591$	4.09472e37			1.56962
$592$		−	1.94247e36i		−	0.0727798i
$593$		−	1.93797e37i		−	0.709755i	−0.934913	−	0.354877i	$-0.884523\pi$
$593$		−	1.93797e37i		−	0.709755i	0.934913	−	0.354877i	$-0.115477\pi$
$594$	−2.33527e37			−0.836028
$595$	1.68963e36	−	1.84844e36i	0.0591308	−	0.0646882i
$596$	−1.77466e37			−0.607142
$597$		−	5.70295e37i		−	1.90742i
$598$		−	7.88674e36i		−	0.257888i
$599$	1.37034e37			0.438093			0.219047	−	0.975714i	$-0.429705\pi$
$599$	1.37034e37			0.438093			0.219047	+	0.975714i	$0.429705\pi$
$600$	−1.60006e36	−	1.77887e37i	−0.0500142	−	0.556034i
$601$	−1.68546e37			−0.515124			−0.257562	−	0.966262i	$-0.582919\pi$
$601$	−1.68546e37			−0.515124			−0.257562	+	0.966262i	$0.582919\pi$
$602$		−	3.05651e36i		−	0.0913424i
$603$		−	1.69061e37i		−	0.494037i
$604$	3.67559e36			0.105034
$605$	−3.14565e37	+	3.44129e37i	−0.879048	+	0.961665i
$606$	−4.82098e37			−1.31751
$607$			7.97302e36i			0.213096i	0.994308	+	0.106548i	$0.0339798\pi$
$607$			7.97302e36i			0.213096i	−0.994308	+	0.106548i	$0.966020\pi$
$608$		−	1.10551e37i		−	0.288978i
$609$	−3.50590e36			−0.0896325
$610$	−1.16183e37	−	1.06201e37i	−0.290528	−	0.265569i
$611$	4.32862e37			1.05875
$612$			3.61340e37i			0.864513i
$613$		−	4.15420e37i		−	0.972235i	−0.873893	−	0.486118i	$-0.838413\pi$
$613$		−	4.15420e37i		−	0.972235i	0.873893	−	0.486118i	$-0.161587\pi$
$614$	−1.20079e37			−0.274913
$615$	−5.58444e37	−	5.10468e37i	−1.25074	−	1.14328i
$616$	1.85360e36			0.0406141
$617$			7.07582e37i			1.51680i	0.651792	+	0.758398i	$0.274018\pi$
$617$			7.07582e37i			1.51680i	−0.651792	+	0.758398i	$0.725982\pi$
$618$		−	4.76797e37i		−	0.999976i
$619$	4.56703e37			0.937152			0.468576	−	0.883423i	$-0.344767\pi$
$619$	4.56703e37			0.937152			0.468576	+	0.883423i	$0.344767\pi$
$620$	1.25411e37	−	1.37198e37i	0.251796	−	0.275461i
$621$	−2.33996e37			−0.459696
$622$		−	2.39992e37i		−	0.461346i
$623$			2.46032e36i			0.0462810i
$624$	−1.32557e37			−0.244012
$625$	−5.46201e37	+	9.90610e36i	−0.983949	+	0.178452i
$626$	2.62043e37			0.461976
$627$			2.27031e38i			3.91717i
$628$			4.12585e36i			0.0696720i
$629$	2.03929e37			0.337051
$630$	3.33387e36	−	3.64721e36i	0.0539327	−	0.0590015i
$631$	−5.55203e37			−0.879134			−0.439567	−	0.898210i	$-0.644868\pi$
$631$	−5.55203e37			−0.879134			−0.439567	+	0.898210i	$0.644868\pi$
$632$			3.32520e37i			0.515391i
$633$			1.92182e38i			2.91584i
$634$	−2.17714e37			−0.323356
$635$	−7.71805e37	−	7.05499e37i	−1.12218	−	1.02577i
$636$	2.05262e37			0.292172
$637$		−	4.41023e37i		−	0.614581i
$638$		−	5.89773e37i		−	0.804648i
$639$	1.33807e38			1.78739
$640$	−4.98816e36	−	4.55962e36i	−0.0652395	−	0.0596347i
$641$	−1.67814e37			−0.214905			−0.107452	−	0.994210i	$-0.534269\pi$
$641$	−1.67814e37			−0.214905			−0.107452	+	0.994210i	$0.534269\pi$
$642$			6.75862e37i			0.847492i
$643$			7.08690e37i			0.870178i	0.900387	+	0.435089i	$0.143283\pi$
$643$			7.08690e37i			0.870178i	−0.900387	+	0.435089i	$0.856717\pi$
$644$	1.85732e36			0.0223320
$645$	1.54404e38	−	1.68916e38i	1.81804	−	1.98891i
$646$	1.16061e38			1.33829
$647$			3.12596e36i			0.0353001i	0.999844	+	0.0176500i	$0.00561847\pi$
$647$			3.12596e36i			0.0353001i	−0.999844	+	0.0176500i	$0.994382\pi$
$648$		−	8.41236e36i		−	0.0930369i
$649$	−1.38519e38			−1.50039
$650$	3.69090e36	+	4.10337e37i	0.0391563	+	0.435321i
$651$	8.58616e36			0.0892187
$652$		−	6.24675e37i		−	0.635787i
$653$		−	1.01275e38i		−	1.00966i	−0.863219	−	0.504829i	$-0.831555\pi$
$653$		−	1.01275e38i		−	1.00966i	0.863219	−	0.504829i	$-0.168445\pi$
$654$	−1.80767e38			−1.76530
$655$	−4.27899e37	+	4.68115e37i	−0.409340	+	0.447812i
$656$	−2.86283e37			−0.268283
$657$		−	1.93651e38i		−	1.77782i
$658$			1.01938e37i			0.0916829i
$659$	−3.03753e37			−0.267650			−0.133825	−	0.991005i	$-0.542726\pi$
$659$	−3.03753e37			−0.267650			−0.133825	+	0.991005i	$0.542726\pi$
$660$	1.02438e38	+	9.36377e37i	0.884339	+	0.808365i
$661$	4.07211e36			0.0344429			0.0172215	−	0.999852i	$-0.494518\pi$
$661$	4.07211e36			0.0344429			0.0172215	+	0.999852i	$0.494518\pi$
$662$			9.51638e37i			0.788658i
$663$		−	1.39164e38i		−	1.13004i
$664$	−4.91807e37			−0.391314
$665$	−1.17147e37	−	1.07083e37i	−0.0913357	−	0.0834890i
$666$	4.02379e37			0.307421
$667$		−	5.90956e37i		−	0.442442i
$668$		−	8.04798e37i		−	0.590479i
$669$	−2.10541e37			−0.151385
$670$	−2.23966e37	+	2.45015e37i	−0.157823	+	0.172657i
$671$	1.22315e38			0.844742
$672$		−	3.12170e36i		−	0.0211303i
$673$		−	1.51200e38i		−	1.00311i	−0.865125	−	0.501556i	$-0.832761\pi$
$673$		−	1.51200e38i		−	1.00311i	0.865125	−	0.501556i	$-0.167239\pi$
$674$	1.22243e38			0.794907
$675$	1.21745e38	−	1.09507e37i	0.775978	−	0.0697978i
$676$	−4.94522e37			−0.308962
$677$		−	2.92994e38i		−	1.79437i	−0.441656	−	0.897185i	$-0.645609\pi$
$677$		−	2.92994e38i		−	1.79437i	0.441656	−	0.897185i	$-0.354391\pi$
$678$			5.08924e37i			0.305529i
$679$	−2.65753e36			−0.0156400
$680$	4.78690e37	−	5.23679e37i	0.276175	−	0.302131i
$681$	−6.55061e37			−0.370506
$682$			1.44439e38i			0.800933i
$683$			2.53936e38i			1.38053i	0.723558	+	0.690263i	$0.242505\pi$
$683$			2.53936e38i			1.38053i	−0.723558	+	0.690263i	$0.757495\pi$
$684$	2.29005e38			1.22064
$685$	1.51055e38	+	1.38077e38i	0.789425	+	0.721605i
$686$	2.08319e37			0.106747
$687$			5.92683e38i			2.97787i
$688$		−	8.65937e37i		−	0.426621i
$689$	−4.73485e37			−0.228742
$690$	1.02644e38	+	9.38254e37i	0.486261	+	0.444486i
$691$	−1.97722e38			−0.918548			−0.459274	−	0.888295i	$-0.651890\pi$
$691$	−1.97722e38			−0.918548			−0.459274	+	0.888295i	$0.651890\pi$
$692$		−	1.21861e38i		−	0.555176i
$693$			3.83970e37i			0.171553i
$694$	−5.09595e37			−0.223291
$695$	2.46741e38	−	2.69931e38i	1.06035	−	1.16000i
$696$	−9.93254e37			−0.418635
$697$		−	3.00553e38i		−	1.24245i
$698$			3.31146e36i			0.0134267i
$699$	−1.65650e38			−0.658794
$700$	−9.66338e36	+	8.69203e35i	−0.0376969	+	0.00339076i
$701$	2.19385e38			0.839486			0.419743	−	0.907643i	$-0.362120\pi$
$701$	2.19385e38			0.839486			0.419743	+	0.907643i	$0.362120\pi$
$702$		−	9.07214e37i		−	0.340533i
$703$		−	1.29243e38i		−	0.475894i
$704$	5.25143e37			0.189691
$705$	−5.14958e38	+	5.63357e38i	−1.82482	+	1.99632i
$706$	8.73013e37			0.303499
$707$			2.61891e37i			0.0893221i
$708$			2.33284e38i			0.780612i
$709$	−2.79060e38			−0.916166			−0.458083	−	0.888910i	$-0.651464\pi$
$709$	−2.79060e38			−0.916166			−0.458083	+	0.888910i	$0.651464\pi$
$710$	−1.93923e38	−	1.77263e38i	−0.624657	−	0.570993i
$711$	−6.88809e38			−2.17701
$712$			6.97031e37i			0.216158i
$713$			1.44729e38i			0.440399i
$714$	3.27730e37			0.0978568
$715$	−2.36297e38	−	2.15997e38i	−0.692352	−	0.632872i
$716$	−8.37328e37			−0.240752
$717$		−	4.37754e38i		−	1.23515i
$718$			4.09718e38i			1.13450i
$719$	3.99399e38			1.08534			0.542671	−	0.839945i	$-0.317413\pi$
$719$	3.99399e38			1.08534			0.542671	+	0.839945i	$0.317413\pi$
$720$	9.44518e37	−	1.03329e38i	0.251896	−	0.275571i
$721$	−2.59012e37			−0.0677943
$722$		−	4.60301e38i		−	1.18247i
$723$			6.70320e37i			0.169011i
$724$	−1.19309e38			−0.295260
$725$	2.76560e37	+	3.07466e38i	0.0671779	+	0.746852i
$726$	−6.10146e38			−1.45475
$727$			3.88482e38i			0.909194i	0.890697	+	0.454597i	$0.150217\pi$
$727$			3.88482e38i			0.909194i	−0.890697	+	0.454597i	$0.849783\pi$
$728$			7.20093e36i			0.0165430i
$729$	7.19789e38			1.62324
$730$	−2.56542e38	+	2.80653e38i	−0.567936	+	0.621314i
$731$	9.09099e38			1.97573
$732$		−	2.05993e38i		−	0.439495i
$733$			5.85492e38i			1.22636i	0.789944	+	0.613179i	$0.210109\pi$
$733$			5.85492e38i			1.22636i	−0.789944	+	0.613179i	$0.789891\pi$
$734$	−4.63485e37			−0.0953100
$735$	5.73978e38	+	5.24667e38i	1.15882	+	1.05927i
$736$	5.26196e37			0.104303
$737$		−	2.57947e38i		−	0.502017i
$738$		−	5.93030e38i		−	1.13322i
$739$	4.22327e38			0.792407			0.396204	−	0.918163i	$-0.370327\pi$
$739$	4.22327e38			0.792407			0.396204	+	0.918163i	$0.370327\pi$
$740$	−5.83156e37	−	5.33057e37i	−0.107438	−	0.0982076i
$741$	−8.81976e38			−1.59555
$742$		−	1.11505e37i		−	0.0198081i
$743$		−	8.90331e38i		−	1.55311i	−0.630048	−	0.776556i	$-0.716965\pi$
$743$		−	8.90331e38i		−	1.55311i	0.630048	−	0.776556i	$-0.283035\pi$
$744$	2.43254e38			0.416702
$745$	−4.87006e38	+	5.32778e38i	−0.819266	+	0.896265i
$746$	3.58150e38			0.591685
$747$		−	1.01877e39i		−	1.65290i
$748$			5.51319e38i			0.878478i
$749$	3.67150e37			0.0574565
$750$	−5.77950e38	−	4.40125e38i	−0.888307	−	0.676471i
$751$	8.05646e38			1.21620			0.608100	−	0.793860i	$-0.291932\pi$
$751$	8.05646e38			1.21620			0.608100	+	0.793860i	$0.291932\pi$
$752$			2.88801e38i			0.428211i
$753$		−	1.32341e38i		−	0.192736i
$754$	2.29117e38			0.327751
$755$	1.00867e38	−	1.10347e38i	0.141730	−	0.155051i
$756$	2.13648e37			0.0294886
$757$		−	2.23991e38i		−	0.303693i	−0.988404	−	0.151847i	$-0.951478\pi$
$757$		−	2.23991e38i		−	0.303693i	0.988404	−	0.151847i	$-0.0485220\pi$
$758$			7.60206e38i			1.01251i
$759$	−1.08061e39			−1.41386
$760$	−3.31890e38	−	3.03377e38i	−0.426590	−	0.389941i
$761$	8.58805e38			1.08443			0.542215	−	0.840240i	$-0.317586\pi$
$761$	8.58805e38			1.08443			0.542215	+	0.840240i	$0.317586\pi$
$762$		−	1.36842e39i		−	1.69757i
$763$			9.81982e37i			0.119680i
$764$	−2.95345e38			−0.353647
$765$	1.08479e39	+	9.91598e38i	1.27620	+	1.16656i
$766$	5.36444e38			0.620064
$767$		−	5.38122e38i		−	0.611144i
$768$		−	8.84408e37i		−	0.0986907i
$769$	−1.37790e38			−0.151082			−0.0755409	−	0.997143i	$-0.524068\pi$
$769$	−1.37790e38			−0.151082			−0.0755409	+	0.997143i	$0.524068\pi$
$770$	5.08670e37	−	5.56477e37i	0.0548039	−	0.0599546i
$771$	−1.36479e38			−0.144488
$772$		−	5.97429e38i		−	0.621517i
$773$			7.94523e38i			0.812238i	0.913820	+	0.406119i	$0.133118\pi$
$773$			7.94523e38i			0.812238i	−0.913820	+	0.406119i	$0.866882\pi$
$774$	1.79377e39			1.80204
$775$	−6.77313e37	−	7.53004e38i	−0.0668677	−	0.743403i
$776$	−7.52903e37			−0.0730475
$777$		−	3.64952e37i		−	0.0347978i
$778$		−	8.50476e37i		−	0.0796961i
$779$	−1.90480e39			−1.75426
$780$	−3.63766e38	+	3.97955e38i	−0.329265	+	0.360211i
$781$	2.04158e39			1.81626
$782$			5.52424e38i			0.483038i
$783$		−	6.79778e38i		−	0.584229i
$784$	2.94246e38			0.248567
$785$	1.23864e38	+	1.13222e38i	0.102850	+	0.0940140i
$786$	−8.29975e38			−0.677424
$787$			1.76811e39i			1.41857i	0.704924	+	0.709283i	$0.250981\pi$
$787$			1.76811e39i			1.41857i	−0.704924	+	0.709283i	$0.749019\pi$
$788$		−	6.30190e38i		−	0.497013i
$789$	−3.09331e39			−2.39819
$790$	9.98272e38	+	9.12509e38i	0.760822	+	0.695459i
$791$	2.76464e37			0.0207136
$792$			1.08782e39i			0.801252i
$793$			4.75171e38i			0.344082i
$794$	8.44552e37			0.0601242
$795$	5.63286e38	−	6.16227e38i	0.394251	−	0.431305i
$796$	−8.77701e38			−0.603976
$797$		−	6.95381e38i		−	0.470474i	−0.971938	−	0.235237i	$-0.924413\pi$
$797$		−	6.95381e38i		−	0.470474i	0.971938	−	0.235237i	$-0.0755866\pi$
$798$		−	2.07704e38i		−	0.138168i
$799$	−3.03196e39			−1.98309
$800$	−2.73773e38	+	2.46253e37i	−0.176066	+	0.0158368i
$801$	−1.44389e39			−0.913050
$802$			1.63547e39i			1.01692i
$803$		−	2.95465e39i		−	1.80654i
$804$	−4.34415e38			−0.261185
$805$	5.09690e37	−	5.57593e37i	0.0301343	−	0.0329665i
$806$	−5.61122e38			−0.326238
$807$			3.86361e39i			2.20903i
$808$			7.41963e38i			0.417185i
$809$	2.97781e39			1.64661			0.823307	−	0.567597i	$-0.192127\pi$
$809$	2.97781e39			1.64661			0.823307	+	0.567597i	$0.192127\pi$
$810$	−2.52551e38	−	2.30854e38i	−0.137341	−	0.125542i
$811$	5.40399e38			0.289024			0.144512	−	0.989503i	$-0.453839\pi$
$811$	5.40399e38			0.289024			0.144512	+	0.989503i	$0.453839\pi$
$812$			5.39567e37i			0.0283818i
$813$			1.26499e39i			0.654432i
$814$	6.13935e38			0.312387
$815$	−1.87536e39	−	1.71425e39i	−0.938551	−	0.857919i
$816$	9.28491e38			0.457047
$817$		−	5.76156e39i		−	2.78960i
$818$		−	1.41507e39i		−	0.673918i
$819$	−1.49166e38			−0.0698775
$820$	−7.85624e38	+	8.59462e38i	−0.362016	+	0.396040i
$821$	1.07054e39			0.485255			0.242627	−	0.970120i	$-0.421991\pi$
$821$	1.07054e39			0.485255			0.242627	+	0.970120i	$0.421991\pi$
$822$			2.67822e39i			1.19420i
$823$			2.68082e39i			1.17590i	0.808899	+	0.587948i	$0.200064\pi$
$823$			2.68082e39i			1.17590i	−0.808899	+	0.587948i	$0.799936\pi$
$824$	−7.33805e38			−0.316638
$825$	5.62227e39	−	5.05713e38i	2.38662	−	0.214672i
$826$	1.26727e38			0.0529223
$827$			3.25409e38i			0.133692i	0.997763	+	0.0668460i	$0.0212936\pi$
$827$			3.25409e38i			0.133692i	−0.997763	+	0.0668460i	$0.978706\pi$
$828$			1.09001e39i			0.440574i
$829$	−1.02457e39			−0.407432			−0.203716	−	0.979030i	$-0.565302\pi$
$829$	−1.02457e39			−0.407432			−0.203716	+	0.979030i	$0.565302\pi$
$830$	−1.34963e39	+	1.47647e39i	−0.528031	+	0.577659i
$831$	−4.84181e39			−1.86378
$832$			2.04009e38i			0.0772653i
$833$			3.08913e39i			1.15114i
$834$	4.78592e39			1.75479
$835$	−2.41612e39	−	2.20854e39i	−0.871666	−	0.796781i
$836$	3.49407e39			1.24036
$837$			1.66482e39i			0.581532i
$838$		−	3.17532e39i		−	1.09142i
$839$	1.39142e39			0.470623			0.235311	−	0.971920i	$-0.424389\pi$
$839$	1.39142e39			0.470623			0.235311	+	0.971920i	$0.424389\pi$
$840$	−9.37179e37	−	8.56665e37i	−0.0311927	−	0.0285129i
$841$	−1.33636e39			−0.437699
$842$		−	3.05478e39i		−	0.984617i
$843$			9.74903e38i			0.309235i
$844$	2.95774e39			0.923288
$845$	−1.35708e39	+	1.48462e39i	−0.416907	+	0.456091i
$846$	−5.98247e39			−1.80876
$847$			3.31451e38i			0.0986264i
$848$		−	3.15905e38i		−	0.0925150i
$849$	9.40141e39			2.70981
$850$	−2.58528e38	−	2.87419e39i	−0.0733418	−	0.815379i
$851$	6.15165e38			0.171768
$852$		−	3.43829e39i		−	0.944947i
$853$		−	3.58348e39i		−	0.969379i	−0.874686	−	0.484690i	$-0.838933\pi$
$853$		−	3.58348e39i		−	0.969379i	0.874686	−	0.484690i	$-0.161067\pi$
$854$	−1.11902e38			−0.0297960
$855$	6.28440e39	−	6.87504e39i	1.64711	−	1.80191i
$856$	1.04017e39			0.268355
$857$			5.11180e39i			1.29817i	0.760714	+	0.649087i	$0.224849\pi$
$857$			5.11180e39i			1.29817i	−0.760714	+	0.649087i	$0.775151\pi$
$858$		−	4.18959e39i		−	1.04735i
$859$	−3.35610e39			−0.825900			−0.412950	−	0.910754i	$-0.635502\pi$
$859$	−3.35610e39			−0.825900			−0.412950	+	0.910754i	$0.635502\pi$
$860$	−2.59966e39	−	2.37633e39i	−0.629779	−	0.575674i
$861$	−5.37870e38			−0.128273
$862$			3.69381e39i			0.867215i
$863$		−	2.67309e39i		−	0.617829i	−0.951090	−	0.308914i	$-0.900034\pi$
$863$		−	2.67309e39i		−	0.617829i	0.951090	−	0.308914i	$-0.0999656\pi$
$864$	6.05285e38			0.137729
$865$	−3.65842e39	−	3.34413e39i	−0.819552	−	0.749144i
$866$	−9.24635e38			−0.203929
$867$			2.47571e39i			0.537579i
$868$		−	1.32143e38i		−	0.0282507i
$869$	−1.05096e40			−2.21217
$870$	−2.72571e39	+	2.98189e39i	−0.564898	+	0.617990i
$871$	1.00208e39			0.204483
$872$			2.78205e39i			0.558975i
$873$		−	1.55963e39i		−	0.308552i
$874$	3.50107e39			0.682019
$875$	−2.39090e38	+	3.13961e38i	−0.0458620	+	0.0602236i
$876$	−4.97602e39			−0.939889
$877$			8.13055e39i			1.51226i	0.654424	+	0.756128i	$0.272911\pi$
$877$			8.13055e39i			1.51226i	−0.654424	+	0.756128i	$0.727089\pi$
$878$		−	6.54629e38i		−	0.119900i
$879$	9.44570e39			1.70367
$880$	1.44111e39	−	1.57655e39i	0.255965	−	0.280022i
$881$	8.64905e39			1.51284			0.756421	−	0.654085i	$-0.226946\pi$
$881$	8.64905e39			1.51284			0.756421	+	0.654085i	$0.226946\pi$
$882$			6.09526e39i			1.04995i
$883$		−	1.02943e40i		−	1.74634i	−0.487415	−	0.873171i	$-0.662060\pi$
$883$		−	1.02943e40i		−	1.74634i	0.487415	−	0.873171i	$-0.337940\pi$
$884$	−2.14178e39			−0.357824
$885$	7.00350e39	+	6.40182e39i	1.15234	+	1.05334i
$886$	−2.83940e39			−0.460120
$887$			6.43727e39i			1.02738i	0.857975	+	0.513692i	$0.171723\pi$
$887$			6.43727e39i			1.02738i	−0.857975	+	0.513692i	$0.828277\pi$
$888$		−	1.03394e39i		−	0.162526i
$889$	−7.43371e38			−0.115088
$890$	2.09259e39	+	1.91281e39i	0.319094	+	0.291680i
$891$	2.65880e39			0.399335
$892$			3.24028e38i			0.0479354i
$893$			1.92155e40i			2.80000i
$894$	−9.44623e39			−1.35582
$895$	−2.29782e39	+	2.51378e39i	−0.324866	+	0.355399i
$896$	−4.80439e37			−0.00669083
$897$		−	4.19799e39i		−	0.575895i
$898$			8.13299e39i			1.09906i
$899$	−4.20450e39			−0.559704
$900$	−5.10110e38	−	5.67115e39i	−0.0668944	−	0.743700i
$901$	3.31651e39			0.428446
$902$		−	9.04823e39i		−	1.15153i
$903$		−	1.62693e39i		−	0.203978i
$904$	7.83249e38			0.0967445
$905$	−3.27412e39	+	3.58184e39i	−0.398417	+	0.435863i
$906$	1.95646e39			0.234553
$907$			6.37921e38i			0.0753474i	0.999290	+	0.0376737i	$0.0119948\pi$
$907$			6.37921e38i			0.0753474i	−0.999290	+	0.0376737i	$0.988005\pi$
$908$			1.00816e39i			0.117319i
$909$	−1.53696e40			−1.76218
$910$	2.16182e38	+	1.97610e38i	0.0244208	+	0.0223228i
$911$	−1.11286e40			−1.23864			−0.619319	−	0.785140i	$-0.712591\pi$
$911$	−1.11286e40			−1.23864			−0.619319	+	0.785140i	$0.712591\pi$
$912$		−	5.88446e39i		−	0.645321i
$913$		−	1.55440e40i		−	1.67960i
$914$	−2.39632e39			−0.255136
$915$	−6.18421e39	−	5.65292e39i	−0.648783	−	0.593045i
$916$	9.12155e39			0.942931
$917$			4.50869e38i			0.0459266i
$918$			6.35455e39i			0.637835i
$919$	1.97672e38			0.0195517			0.00977587	−	0.999952i	$-0.496888\pi$
$919$	1.97672e38			0.0195517			0.00977587	+	0.999952i	$0.496888\pi$
$920$	1.44400e39	−	1.57971e39i	0.140744	−	0.153972i
$921$	−6.39164e39			−0.613913
$922$		−	2.47580e39i		−	0.234341i
$923$			7.93120e39i			0.739802i
$924$	9.86642e38			0.0906960
$925$	−3.20062e39	+	2.87890e38i	−0.289949	+	0.0260803i
$926$	2.87540e39			0.256715
$927$		−	1.52006e40i		−	1.33747i
$928$			1.52865e39i			0.132559i
$929$	−2.03410e40			−1.73844			−0.869222	−	0.494422i	$-0.835380\pi$
$929$	−2.03410e40			−1.73844			−0.869222	+	0.494422i	$0.835380\pi$
$930$	6.67544e39	−	7.30283e39i	0.562290	−	0.615137i
$931$	1.95778e40			1.62534
$932$			2.54940e39i			0.208604i
$933$		−	1.27744e40i		−	1.03024i
$934$	−1.06353e39			−0.0845413
$935$	1.65514e40	+	1.51294e40i	1.29681	+	1.18540i
$936$	−4.22601e39			−0.326368
$937$		−	1.54398e39i		−	0.117532i	−0.998272	−	0.0587661i	$-0.981283\pi$
$937$		−	1.54398e39i		−	0.117532i	0.998272	−	0.0587661i	$-0.0187166\pi$
$938$			2.35988e38i			0.0177073i
$939$	1.39481e40			1.03165
$940$	8.67022e39	+	7.92535e39i	0.632127	+	0.577820i
$941$	1.44267e40			1.03683			0.518415	−	0.855129i	$-0.326522\pi$
$941$	1.44267e40			1.03683			0.518415	+	0.855129i	$0.326522\pi$
$942$			2.19612e39i			0.155586i
$943$		−	9.06637e39i		−	0.633178i
$944$	3.59030e39			0.247177
$945$	5.86297e38	−	6.41401e38i	0.0397913	−	0.0435311i
$946$	2.73687e40			1.83115
$947$			1.57938e40i			1.04174i	0.853635	+	0.520872i	$0.174393\pi$
$947$			1.57938e40i			1.04174i	−0.853635	+	0.520872i	$0.825607\pi$
$948$			1.76995e40i			1.15093i
$949$	1.14783e40			0.735842
$950$	−1.82156e40	+	1.63846e39i	−1.15126	+	0.103554i
$951$	−1.15885e40			−0.722091
$952$		−	5.04386e38i		−	0.0309859i
$953$		−	1.36142e40i		−	0.824592i	−0.911050	−	0.412296i	$-0.864727\pi$
$953$		−	1.36142e40i		−	0.824592i	0.911050	−	0.412296i	$-0.135273\pi$
$954$	6.54391e39			0.390782
$955$	−8.10493e39	+	8.86668e39i	−0.477204	+	0.522054i
$956$	−6.73716e39			−0.391107
$957$		−	3.13927e40i		−	1.79687i
$958$			6.57315e39i			0.370970i
$959$	1.45489e39			0.0809618
$960$	−2.65512e39	−	2.42701e39i	−0.145687	−	0.133171i
$961$	−8.18563e39			−0.442880
$962$			2.38503e39i			0.127242i
$963$			2.15470e40i			1.13353i
$964$	1.03164e39			0.0535166
$965$	−1.79357e40	−	1.63948e40i	−0.917485	−	0.838663i
$966$	9.88621e38			0.0498699
$967$		−	3.45840e40i		−	1.72035i	−0.509995	−	0.860177i	$-0.670353\pi$
$967$		−	3.45840e40i		−	1.72035i	0.509995	−	0.860177i	$-0.329647\pi$
$968$			9.39032e39i			0.460642i
$969$	6.17777e40			2.98855
$970$	−2.06613e39	+	2.26032e39i	−0.0985689	+	0.107833i
$971$	6.44257e39			0.303110			0.151555	−	0.988449i	$-0.451572\pi$
$971$	6.44257e39			0.303110			0.151555	+	0.988449i	$0.451572\pi$
$972$		−	1.28736e40i		−	0.597318i
$973$		−	2.59987e39i		−	0.118967i
$974$	−1.32192e40			−0.596566
$975$	1.96461e39	+	2.18416e40i	0.0874406	+	0.972123i
$976$	−3.17030e39			−0.139164
$977$		−	1.23545e40i		−	0.534870i	−0.963576	−	0.267435i	$-0.913824\pi$
$977$		−	1.23545e40i		−	0.534870i	0.963576	−	0.267435i	$-0.0861760\pi$
$978$		−	3.32505e40i		−	1.41979i
$979$	−2.20303e40			−0.927799
$980$	8.07478e39	−	8.83369e39i	0.335412	−	0.366936i
$981$	−5.76297e40			−2.36110
$982$			1.76120e40i			0.711710i
$983$			1.03659e40i			0.413175i	0.978428	+	0.206587i	$0.0662358\pi$
$983$			1.03659e40i			0.413175i	−0.978428	+	0.206587i	$0.933764\pi$
$984$	−1.52384e40			−0.599108
$985$	−1.89192e40	−	1.72938e40i	−0.733691	−	0.670659i
$986$	−1.60484e40			−0.613894
$987$			5.42602e39i			0.204739i
$988$			1.35739e40i			0.505225i
$989$	2.74236e40			1.00687
$990$	3.26580e40	+	2.98524e40i	1.18281	+	1.08119i
$991$	−2.33398e40			−0.833880			−0.416940	−	0.908934i	$-0.636897\pi$
$991$	−2.33398e40			−0.833880			−0.416940	+	0.908934i	$0.636897\pi$
$992$		−	3.74375e39i		−	0.131947i
$993$			5.06541e40i			1.76117i
$994$	−1.86779e39			−0.0640636
$995$	−2.40861e40	+	2.63498e40i	−0.814994	+	0.891591i
$996$	−2.61781e40			−0.873850
$997$			2.44018e40i			0.803596i	0.915728	+	0.401798i	$0.131615\pi$
$997$			2.44018e40i			0.803596i	−0.915728	+	0.401798i	$0.868385\pi$
$998$		−	2.63062e40i		−	0.854664i
$999$	7.07627e39			0.226814

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.b.a.9.1	✓	14
5.2	odd	4		50.28.a.l.1.1		7
5.3	odd	4		50.28.a.k.1.7		7
5.4	even	2	inner	10.28.b.a.9.14	yes	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.b.a.9.1	✓	14	1.1	even	1	trivial
10.28.b.a.9.14	yes	14	5.4	even	2	inner
50.28.a.k.1.7		7	5.3	odd	4
50.28.a.l.1.1		7	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 28 \)
Character orbit:	\([\chi]\)	\(=\)	10.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-8192.00i q^{2} -4.36047e6i q^{3} -6.71089e7 q^{4} +(-1.84162e9 + 2.01470e9i) q^{5} -3.57210e10 q^{6} +1.94048e10i q^{7} +5.49756e11i q^{8} -1.13881e13 q^{9} +(1.65044e13 + 1.50865e13i) q^{10} -1.73755e14 q^{11} +2.92626e14i q^{12} -6.75010e14i q^{13} +1.58964e14 q^{14} +(8.78505e15 + 8.03032e15i) q^{15} +4.50360e15 q^{16} +4.72808e16i q^{17} +9.32913e16i q^{18} +2.99649e17 q^{19} +(1.23589e17 - 1.35204e17i) q^{20} +8.46139e16 q^{21} +1.42340e18i q^{22} +1.42626e18i q^{23} +2.39719e18 q^{24} +(-6.67471e17 - 7.42062e18i) q^{25} -5.52968e18 q^{26} +1.64063e19i q^{27} -1.30223e18i q^{28} -4.14340e19 q^{29} +(6.57844e19 - 7.19671e19i) q^{30} +1.01475e20 q^{31} -3.68935e19i q^{32} +7.57655e20i q^{33} +3.87324e20 q^{34} +(-3.90949e19 - 3.57362e19i) q^{35} +7.64242e20 q^{36} -4.31315e20i q^{37} -2.45473e21i q^{38} -2.94336e21 q^{39} +(-1.10759e21 - 1.01244e21i) q^{40} -6.35676e21 q^{41} -6.93157e20i q^{42} -1.92277e22i q^{43} +1.16605e22 q^{44} +(2.09725e22 - 2.29436e22i) q^{45} +1.16839e22 q^{46} +6.41268e22i q^{47} -1.96378e22i q^{48} +6.53358e22 q^{49} +(-6.07897e22 + 5.46792e21i) q^{50} +2.06166e23 q^{51} +4.52991e22i q^{52} -7.01449e22i q^{53} +1.34400e23 q^{54} +(3.19991e23 - 3.50065e23i) q^{55} -1.06679e22 q^{56} -1.30661e24i q^{57} +3.39428e23i q^{58} +7.97207e23 q^{59} +(-5.89555e23 - 5.38905e23i) q^{60} -7.03947e23 q^{61} -8.31280e23i q^{62} -2.20984e23i q^{63} -3.02231e23 q^{64} +(1.35994e24 + 1.24311e24i) q^{65} +6.20671e24 q^{66} +1.48454e24i q^{67} -3.17296e24i q^{68} +6.21915e24 q^{69} +(-2.92751e23 + 3.20265e23i) q^{70} -1.17498e25 q^{71} -6.26067e24i q^{72} +1.70047e25i q^{73} -3.53333e24 q^{74} +(-3.23574e25 + 2.91049e24i) q^{75} -2.01091e25 q^{76} -3.37168e24i q^{77} +2.41120e25i q^{78} +6.04850e25 q^{79} +(-8.29391e24 + 9.07341e24i) q^{80} -1.53020e25 q^{81} +5.20746e25i q^{82} +8.94591e25i q^{83} -5.67835e24 q^{84} +(-9.52567e25 - 8.70731e25i) q^{85} -1.57513e26 q^{86} +1.80672e26i q^{87} -9.55230e25i q^{88} +1.26789e26 q^{89} +(-1.87954e26 - 1.71807e26i) q^{90} +1.30984e25 q^{91} -9.57145e25i q^{92} -4.42477e26i q^{93} +5.25326e26 q^{94} +(-5.51840e26 + 6.03704e26i) q^{95} -1.60873e26 q^{96} +1.36952e26i q^{97} -5.35231e26i q^{98} +1.97874e27 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 939524096 q^{4} - 73643590 q^{5} + 16071950336 q^{6} - 40082573114558 q^{9} - 33017385943040 q^{10} - 158204810172872 q^{11} - 21\!\cdots\!48 q^{14} + 20\!\cdots\!40 q^{15} + 63\!\cdots\!44 q^{16}+ \cdots - 39\!\cdots\!16 q^{99}+O(q^{100}) \) 14 * q - 939524096 * q^4 - 73643590 * q^5 + 16071950336 * q^6 - 40082573114558 * q^9 - 33017385943040 * q^10 - 158204810172872 * q^11 - 2183598452277248 * q^14 + 20024144989158440 * q^15 + 63050394783186944 * q^16 - 140406399769275000 * q^19 + 4942137665781760 * q^20 + 457109656482968 * q^21 - 1078570329313378304 * q^24 + 6519283342722349350 * q^25 + 12210591275993726976 * q^26 - 259270857362526368940 * q^29 + 87647312900713840640 * q^30 + 101745690421209310208 * q^31 - 168898558224119103488 * q^34 + 1378811920964523641080 * q^35 + 2689895947914929242112 * q^36 - 18485576517782584068816 * q^39 + 2215759262886983106560 * q^40 - 1896584587803054469892 * q^41 + 10616945090037083537408 * q^44 - 29442738837757383895370 * q^45 + 1728449771947095719936 * q^46 + 192038716356487330909578 * q^49 - 263092763203302557286400 * q^50 - 456935745972115783739392 * q^51 - 331656187868266799759360 * q^54 + 350630587149946820863720 * q^55 + 146538811564484326326272 * q^56 - 2045452754502768653597480 * q^59 - 1343797622793715224412160 * q^60 - 4292410952783704571694812 * q^61 - 4231240368651202111471616 * q^64 + 7080387802173324288729840 * q^65 + 13458699699704954185449472 * q^66 - 7561881285185794836127976 * q^69 - 2658452801760660242923520 * q^70 - 10349408366862708776842032 * q^71 + 4825936898350986471473152 * q^74 - 32265585350433832322099600 * q^75 + 9422513986845907353600000 * q^76 + 171195367329681711405798240 * q^79 - 331661244482225585520640 * q^80 + 218412595435081152290268614 * q^81 - 30676109770002217828352 * q^84 + 49996632095782610955681280 * q^85 - 233050420171472482535440384 * q^86 - 920119011432929778337961140 * q^89 + 338023638508635646110433280 * q^90 + 1218965825148727758344415888 * q^91 + 55077388646346071267704832 * q^94 - 643974213982984055905842600 * q^95 + 72381629544326717983686656 * q^96 - 3930714930503120441731386616 * q^99

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