LMFDB - Embedded newform 10.28.b.a.9.11

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			9.11
Root			$-331027. i$ of defining polynomial
Character	$\chi$	$=$	10.9
Dual form			10.28.b.a.9.4

$q$-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} -662054. i q^{3} -6.71089e7 q^{4} +(1.91210e9 + 1.94793e9i) q^{5} +5.42355e9 q^{6} -4.26692e11i q^{7} -5.49756e11i q^{8} +7.18728e12 q^{9} +(-1.59575e13 + 1.56640e13i) q^{10} -1.91294e14 q^{11} +4.44297e13i q^{12} +4.60623e14i q^{13} +3.49546e15 q^{14} +(1.28964e15 - 1.26592e15i) q^{15} +4.50360e15 q^{16} -1.54158e16i q^{17} +5.88782e16i q^{18} -2.35947e16 q^{19} +(-1.28319e17 - 1.30723e17i) q^{20} -2.82493e17 q^{21} -1.56708e18i q^{22} +3.52325e18i q^{23} -3.63968e17 q^{24} +(-1.38296e17 + 7.44930e18i) q^{25} -3.77343e18 q^{26} -9.80693e18i q^{27} +2.86348e19i q^{28} -4.39110e19 q^{29} +(1.03704e19 + 1.05647e19i) q^{30} -1.69201e20 q^{31} +3.68935e19i q^{32} +1.26647e20i q^{33} +1.26286e20 q^{34} +(8.31167e20 - 8.15879e20i) q^{35} -4.82330e20 q^{36} +4.30417e20i q^{37} -1.93288e20i q^{38} +3.04958e20 q^{39} +(1.07089e21 - 1.05119e21i) q^{40} -8.39419e21 q^{41} -2.31418e21i q^{42} -1.86223e22i q^{43} +1.28375e22 q^{44} +(1.37428e22 + 1.40003e22i) q^{45} -2.88625e22 q^{46} -2.62713e22i q^{47} -2.98163e21i q^{48} -1.16354e23 q^{49} +(-6.10246e22 - 1.13292e21i) q^{50} -1.02061e22 q^{51} -3.09119e22i q^{52} -8.54982e22i q^{53} +8.03383e22 q^{54} +(-3.65774e23 - 3.72628e23i) q^{55} -2.34576e23 q^{56} +1.56210e22i q^{57} -3.59719e23i q^{58} -1.36807e24 q^{59} +(-8.65460e22 + 8.49542e22i) q^{60} +1.36692e24 q^{61} -1.38609e24i q^{62} -3.06676e24i q^{63} -3.02231e23 q^{64} +(-8.97263e23 + 8.80760e23i) q^{65} -1.03749e24 q^{66} -1.05453e24i q^{67} +1.03454e24i q^{68} +2.33258e24 q^{69} +(6.68368e24 + 6.80892e24i) q^{70} -1.23132e25 q^{71} -3.95125e24i q^{72} -1.04841e24i q^{73} -3.52598e24 q^{74} +(4.93184e24 + 9.15597e22i) q^{75} +1.58341e24 q^{76} +8.16236e25i q^{77} +2.49821e24i q^{78} +4.63172e25 q^{79} +(8.61135e24 + 8.77271e24i) q^{80} +4.83146e25 q^{81} -6.87652e25i q^{82} +1.64989e25i q^{83} +1.89578e25 q^{84} +(3.00290e25 - 2.94766e25i) q^{85} +1.52554e26 q^{86} +2.90715e25i q^{87} +1.05165e26i q^{88} -2.60810e26 q^{89} +(-1.14691e26 + 1.12581e26i) q^{90} +1.96544e26 q^{91} -2.36442e26i q^{92} +1.12020e26i q^{93} +2.15215e26 q^{94} +(-4.51156e25 - 4.59609e25i) q^{95} +2.44255e25 q^{96} +4.72707e26i q^{97} -9.53169e26i q^{98} -1.37488e27 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
$3$		−	662054.i		−	0.239749i	−0.992789	−	0.119874i	$-0.961751\pi$
$3$		−	662054.i		−	0.239749i	0.992789	−	0.119874i	$-0.0382492\pi$
$4$	−6.71089e7			−0.500000
$5$	1.91210e9	+	1.94793e9i	0.700513	+	0.713639i
$5$	1.91210e9	+	1.94793e9i	0.700513	+	0.713639i
$6$	5.42355e9			0.169528
$7$		−	4.26692e11i		−	1.66453i	−0.554380	−	0.832264i	$-0.687045\pi$
$7$		−	4.26692e11i		−	1.66453i	0.554380	−	0.832264i	$-0.312955\pi$
$8$		−	5.49756e11i		−	0.353553i
$9$	7.18728e12			0.942521
$10$	−1.59575e13	+	1.56640e13i	−0.504619	+	0.495338i
$11$	−1.91294e14			−1.67071			−0.835354	−	0.549713i	$-0.814737\pi$
$11$	−1.91294e14			−1.67071			−0.835354	+	0.549713i	$0.814737\pi$
$12$			4.44297e13i			0.119874i
$13$			4.60623e14i			0.421804i	0.977507	+	0.210902i	$0.0676401\pi$
$13$			4.60623e14i			0.421804i	−0.977507	+	0.210902i	$0.932360\pi$
$14$	3.49546e15			1.17700
$15$	1.28964e15	−	1.26592e15i	0.171094	−	0.167947i
$16$	4.50360e15			0.250000
$17$		−	1.54158e16i		−	0.377491i	−0.982026	−	0.188745i	$-0.939558\pi$
$17$		−	1.54158e16i		−	0.377491i	0.982026	−	0.188745i	$-0.0604421\pi$
$18$			5.88782e16i			0.666463i
$19$	−2.35947e16			−0.128719			−0.0643593	−	0.997927i	$-0.520500\pi$
$19$	−2.35947e16			−0.128719			−0.0643593	+	0.997927i	$0.520500\pi$
$20$	−1.28319e17	−	1.30723e17i	−0.350257	−	0.356820i
$21$	−2.82493e17			−0.399068
$22$		−	1.56708e18i		−	1.18137i
$23$			3.52325e18i			1.45753i	0.684763	+	0.728766i	$0.259906\pi$
$23$			3.52325e18i			1.45753i	−0.684763	+	0.728766i	$0.740094\pi$
$24$	−3.63968e17			−0.0847640
$25$	−1.38296e17	+	7.44930e18i	−0.0185618	+	0.999828i
$26$	−3.77343e18			−0.298261
$27$		−	9.80693e18i		−	0.465717i
$28$			2.86348e19i			0.832264i
$29$	−4.39110e19			−0.794696			−0.397348	−	0.917668i	$-0.630069\pi$
$29$	−4.39110e19			−0.794696			−0.397348	+	0.917668i	$0.630069\pi$
$30$	1.03704e19	+	1.05647e19i	0.118757	+	0.120982i
$31$	−1.69201e20			−1.24457			−0.622285	−	0.782791i	$-0.713795\pi$
$31$	−1.69201e20			−1.24457			−0.622285	+	0.782791i	$0.713795\pi$
$32$			3.68935e19i			0.176777i
$33$			1.26647e20i			0.400550i
$34$	1.26286e20			0.266926
$35$	8.31167e20	−	8.15879e20i	1.18787	−	1.16602i
$36$	−4.82330e20			−0.471260
$37$			4.30417e20i			0.290514i	0.989394	+	0.145257i	$0.0464008\pi$
$37$			4.30417e20i			0.290514i	−0.989394	+	0.145257i	$0.953599\pi$
$38$		−	1.93288e20i		−	0.0910178i
$39$	3.04958e20			0.101127
$40$	1.07089e21	−	1.05119e21i	0.252310	−	0.247669i
$41$	−8.39419e21			−1.41709			−0.708544	−	0.705667i	$-0.750648\pi$
$41$	−8.39419e21			−1.41709			−0.708544	+	0.705667i	$0.750648\pi$
$42$		−	2.31418e21i		−	0.282184i
$43$		−	1.86223e22i		−	1.65276i	−0.563111	−	0.826381i	$-0.690396\pi$
$43$		−	1.86223e22i		−	1.65276i	0.563111	−	0.826381i	$-0.309604\pi$
$44$	1.28375e22			0.835354
$45$	1.37428e22	+	1.40003e22i	0.660248	+	0.672620i
$46$	−2.88625e22			−1.03063
$47$		−	2.62713e22i		−	0.701715i	−0.936429	−	0.350858i	$-0.885890\pi$
$47$		−	2.62713e22i		−	0.701715i	0.936429	−	0.350858i	$-0.114110\pi$
$48$		−	2.98163e21i		−	0.0599372i
$49$	−1.16354e23			−1.77065
$50$	−6.10246e22	−	1.13292e21i	−0.706985	−	0.0131252i
$51$	−1.02061e22			−0.0905029
$52$		−	3.09119e22i		−	0.210902i
$53$		−	8.54982e22i		−	0.451058i	−0.974236	−	0.225529i	$-0.927589\pi$
$53$		−	8.54982e22i		−	0.451058i	0.974236	−	0.225529i	$-0.0724111\pi$
$54$	8.03383e22			0.329312
$55$	−3.65774e23	−	3.72628e23i	−1.17035	−	1.19228i
$56$	−2.34576e23			−0.588499
$57$			1.56210e22i			0.0308601i
$58$		−	3.59719e23i		−	0.561935i
$59$	−1.36807e24			−1.69670			−0.848351	−	0.529434i	$-0.822404\pi$
$59$	−1.36807e24			−1.69670			−0.848351	+	0.529434i	$0.822404\pi$
$60$	−8.65460e22	+	8.49542e22i	−0.0855471	+	0.0839736i
$61$	1.36692e24			1.08091			0.540456	−	0.841372i	$-0.318252\pi$
$61$	1.36692e24			1.08091			0.540456	+	0.841372i	$0.318252\pi$
$62$		−	1.38609e24i		−	0.880044i
$63$		−	3.06676e24i		−	1.56885i
$64$	−3.02231e23			−0.125000
$65$	−8.97263e23	+	8.80760e23i	−0.301016	+	0.295479i
$66$	−1.03749e24			−0.283232
$67$		−	1.05453e24i		−	0.234989i	−0.993074	−	0.117495i	$-0.962514\pi$
$67$		−	1.05453e24i		−	0.234989i	0.993074	−	0.117495i	$-0.0374863\pi$
$68$			1.03454e24i			0.188745i
$69$	2.33258e24			0.349442
$70$	6.68368e24	+	6.80892e24i	0.824503	+	0.839952i
$71$	−1.23132e25			−1.25424			−0.627122	−	0.778921i	$-0.715767\pi$
$71$	−1.23132e25			−1.25424			−0.627122	+	0.778921i	$0.715767\pi$
$72$		−	3.95125e24i		−	0.333231i
$73$		−	1.04841e24i		−	0.0733964i	−0.999326	−	0.0366982i	$-0.988316\pi$
$73$		−	1.04841e24i		−	0.0733964i	0.999326	−	0.0366982i	$-0.0116840\pi$
$74$	−3.52598e24			−0.205424
$75$	4.93184e24	+	9.15597e22i	0.239708	+	0.00445018i
$76$	1.58341e24			0.0643593
$77$			8.16236e25i			2.78094i
$78$			2.49821e24i			0.0715076i
$79$	4.63172e25			1.11629			0.558145	−	0.829743i	$-0.311513\pi$
$79$	4.63172e25			1.11629			0.558145	+	0.829743i	$0.311513\pi$
$80$	8.61135e24	+	8.77271e24i	0.175128	+	0.178410i
$81$	4.83146e25			0.830865
$82$		−	6.87652e25i		−	1.00203i
$83$			1.64989e25i			0.204127i	0.994778	+	0.102064i	$0.0325446\pi$
$83$			1.64989e25i			0.204127i	−0.994778	+	0.102064i	$0.967455\pi$
$84$	1.89578e25			0.199534
$85$	3.00290e25	−	2.94766e25i	0.269392	−	0.264437i
$86$	1.52554e26			1.16868
$87$			2.90715e25i			0.190527i
$88$			1.05165e26i			0.590684i
$89$	−2.60810e26			−1.25765			−0.628823	−	0.777548i	$-0.716463\pi$
$89$	−2.60810e26			−1.25765			−0.628823	+	0.777548i	$0.716463\pi$
$90$	−1.14691e26	+	1.12581e26i	−0.475614	+	0.466866i
$91$	1.96544e26			0.702104
$92$		−	2.36442e26i		−	0.728766i
$93$			1.12020e26i			0.298384i
$94$	2.15215e26			0.496187
$95$	−4.51156e25	−	4.59609e25i	−0.0901691	−	0.0918586i
$96$	2.44255e25			0.0423820
$97$			4.72707e26i			0.713138i	0.934269	+	0.356569i	$0.116054\pi$
$97$			4.72707e26i			0.713138i	−0.934269	+	0.356569i	$0.883946\pi$
$98$		−	9.53169e26i		−	1.25204i
$99$	−1.37488e27			−1.57468
$100$	9.28092e24	−	4.99914e26i	0.00928092	−	0.499914i
$101$	−1.99889e27			−1.74763			−0.873815	−	0.486258i	$-0.838361\pi$
$101$	−1.99889e27			−1.74763			−0.873815	+	0.486258i	$0.838361\pi$
$102$		−	8.36084e25i		−	0.0639952i
$103$			4.56445e26i			0.306257i	0.988206	+	0.153129i	$0.0489349\pi$
$103$			4.56445e26i			0.306257i	−0.988206	+	0.153129i	$0.951065\pi$
$104$	2.53230e26			0.149130
$105$	−5.40156e26	−	5.50277e26i	−0.279553	−	0.284791i
$106$	7.00401e26			0.318946
$107$		−	3.34765e27i		−	1.34295i	−0.741029	−	0.671473i	$-0.765662\pi$
$107$		−	3.34765e27i		−	1.34295i	0.741029	−	0.671473i	$-0.234338\pi$
$108$			6.58132e26i			0.232858i
$109$	6.61020e26			0.206517			0.103259	−	0.994655i	$-0.467073\pi$
$109$	6.61020e26			0.206517			0.103259	+	0.994655i	$0.467073\pi$
$110$	3.05257e27	−	2.99642e27i	0.843071	−	0.827564i
$111$	2.84960e26			0.0696503
$112$		−	1.92165e27i		−	0.416132i
$113$			4.88462e27i			0.938150i	0.883158	+	0.469075i	$0.155413\pi$
$113$			4.88462e27i			0.938150i	−0.883158	+	0.469075i	$0.844587\pi$
$114$	−1.27967e26			−0.0218214
$115$	−6.86306e27	+	6.73683e27i	−1.04015	+	1.02102i
$116$	2.94682e27			0.397348
$117$			3.31063e27i			0.397559i
$118$		−	1.12072e28i		−	1.19975i
$119$	−6.57780e27			−0.628343
$120$	−6.95945e26	−	7.08985e26i	−0.0593783	−	0.0604909i
$121$	2.34834e28			1.79126
$122$			1.11978e28i			0.764320i
$123$			5.55741e27i			0.339745i
$124$	1.13549e28			0.622285
$125$	−1.47752e28	+	1.39744e28i	−0.726519	+	0.687146i
$126$	2.51229e28			1.10935
$127$			4.01385e28i			1.59298i	0.604652	+	0.796490i	$0.293312\pi$
$127$			4.01385e28i			1.59298i	−0.604652	+	0.796490i	$0.706688\pi$
$128$		−	2.47588e27i		−	0.0883883i
$129$	−1.23290e28			−0.396248
$130$	−7.21519e27	−	7.35038e27i	−0.208936	−	0.212850i
$131$	6.96817e27			0.181952			0.0909758	−	0.995853i	$-0.471001\pi$
$131$	6.96817e27			0.181952			0.0909758	+	0.995853i	$0.471001\pi$
$132$		−	8.49914e27i		−	0.200275i
$133$			1.00677e28i			0.214256i
$134$	8.63870e27			0.166163
$135$	1.91032e28	−	1.87519e28i	0.332354	−	0.326241i
$136$	−8.47494e27			−0.133463
$137$		−	7.83239e28i		−	1.11729i	−0.829406	−	0.558646i	$-0.811321\pi$
$137$		−	7.83239e28i		−	1.11729i	0.829406	−	0.558646i	$-0.188679\pi$
$138$			1.91085e28i			0.247093i
$139$	1.83598e28			0.215361			0.107681	−	0.994186i	$-0.465658\pi$
$139$	1.83598e28			0.215361			0.107681	+	0.994186i	$0.465658\pi$
$140$	−5.57787e28	+	5.47527e28i	−0.593936	+	0.583012i
$141$	−1.73930e28			−0.168235
$142$		−	1.00869e29i		−	0.886884i
$143$		−	8.81145e28i		−	0.704711i
$144$	3.23686e28			0.235630
$145$	−8.39625e28	−	8.55357e28i	−0.556695	−	0.567126i
$146$	8.58861e27			0.0518991
$147$			7.70324e28i			0.424511i
$148$		−	2.88848e28i		−	0.145257i
$149$	−1.02655e29			−0.471373			−0.235687	−	0.971829i	$-0.575734\pi$
$149$	−1.02655e29			−0.471373			−0.235687	+	0.971829i	$0.575734\pi$
$150$	−7.50057e26	+	4.04016e28i	−0.00314675	+	0.169499i
$151$	8.05542e28			0.308958			0.154479	−	0.987996i	$-0.450630\pi$
$151$	8.05542e28			0.308958			0.154479	+	0.987996i	$0.450630\pi$
$152$			1.29713e28i			0.0455089i
$153$		−	1.10798e29i		−	0.355793i
$154$	−6.68661e29			−1.96642
$155$	−3.23529e29	−	3.29591e29i	−0.871838	−	0.888174i
$156$	−2.04654e28			−0.0505635
$157$			1.35908e29i			0.308036i	0.988068	+	0.154018i	$0.0492214\pi$
$157$			1.35908e29i			0.308036i	−0.988068	+	0.154018i	$0.950779\pi$
$158$			3.79431e29i			0.789336i
$159$	−5.66044e28			−0.108141
$160$	−7.18660e28	+	7.05442e28i	−0.126155	+	0.123834i
$161$	1.50334e30			2.42610
$162$			3.95793e29i			0.587511i
$163$		−	9.47527e28i		−	0.129437i	−0.997904	−	0.0647186i	$-0.979385\pi$
$163$		−	9.47527e28i		−	0.129437i	0.997904	−	0.0647186i	$-0.0206150\pi$
$164$	5.63325e29			0.708544
$165$	−2.46700e29	+	2.42162e29i	−0.285848	+	0.280591i
$166$	−1.35159e29			−0.144340
$167$		−	1.31565e30i		−	1.29560i	−0.761812	−	0.647798i	$-0.775690\pi$
$167$		−	1.31565e30i		−	1.29560i	0.761812	−	0.647798i	$-0.224310\pi$
$168$			1.55302e29i			0.141092i
$169$	9.80359e29			0.822081
$170$	2.41473e29	+	2.45997e29i	0.186985	+	0.190489i
$171$	−1.69582e29			−0.121320
$172$			1.24972e30i			0.826381i
$173$			1.79114e30i			1.09523i	0.836730	+	0.547616i	$0.184465\pi$
$173$			1.79114e30i			1.09523i	−0.836730	+	0.547616i	$0.815535\pi$
$174$	−2.38154e29			−0.134723
$175$	3.17855e30	+	5.90100e28i	1.66424	+	0.0308967i
$176$	−8.61512e29			−0.417677
$177$			9.05735e29i			0.406782i
$178$		−	2.13655e30i		−	0.889290i
$179$	3.49328e28			0.0134808			0.00674042	−	0.999977i	$-0.497854\pi$
$179$	3.49328e28			0.0134808			0.00674042	+	0.999977i	$0.497854\pi$
$180$	−9.22266e29	−	9.39547e29i	−0.330124	−	0.336310i
$181$	−1.05143e30			−0.349238			−0.174619	−	0.984636i	$-0.555869\pi$
$181$	−1.05143e30			−0.349238			−0.174619	+	0.984636i	$0.555869\pi$
$182$			1.61009e30i			0.496463i
$183$		−	9.04975e29i		−	0.259147i
$184$	1.93693e30			0.515315
$185$	−8.38424e29	+	8.23003e29i	−0.207322	+	0.203509i
$186$	−9.17668e29			−0.210989
$187$			2.94896e30i			0.630676i
$188$			1.76304e30i			0.350858i
$189$	−4.18454e30			−0.775199
$190$	3.76512e29	−	3.69587e29i	0.0649538	−	0.0637592i
$191$	−9.80549e30			−1.57586			−0.787932	−	0.615762i	$-0.788848\pi$
$191$	−9.80549e30			−1.57586			−0.787932	+	0.615762i	$0.788848\pi$
$192$			2.00094e29i			0.0299686i
$193$		−	1.00156e31i		−	1.39847i	−0.714892	−	0.699235i	$-0.753524\pi$
$193$		−	1.00156e31i		−	1.39847i	0.714892	−	0.699235i	$-0.246476\pi$
$194$	−3.87242e30			−0.504265
$195$	5.83111e29	+	5.94037e29i	0.0708408	+	0.0721682i
$196$	7.80836e30			0.885325
$197$		−	8.01664e30i		−	0.848591i	−0.905524	−	0.424296i	$-0.860522\pi$
$197$		−	8.01664e30i		−	0.848591i	0.905524	−	0.424296i	$-0.139478\pi$
$198$		−	1.12631e31i		−	1.11346i
$199$	4.69136e30			0.433294			0.216647	−	0.976250i	$-0.430488\pi$
$199$	4.69136e30			0.433294			0.216647	+	0.976250i	$0.430488\pi$
$200$	4.09529e30	+	7.60293e28i	0.353492	+	0.00656260i
$201$	−6.98155e29			−0.0563384
$202$		−	1.63749e31i		−	1.23576i
$203$			1.87365e31i			1.32279i
$204$	6.84920e29			0.0452515
$205$	−1.60506e31	−	1.63513e31i	−0.992689	−	1.01129i
$206$	−3.73920e30			−0.216557
$207$			2.53226e31i			1.37375i
$208$			2.07446e30i			0.105451i
$209$	4.51353e30			0.215051
$210$	4.50787e30	−	4.42496e30i	0.201378	−	0.197674i
$211$	−3.15257e31			−1.32084			−0.660421	−	0.750895i	$-0.729622\pi$
$211$	−3.15257e31			−1.32084			−0.660421	+	0.750895i	$0.729622\pi$
$212$			5.73769e30i			0.225529i
$213$			8.15198e30i			0.300703i
$214$	2.74239e31			0.949607
$215$	3.62751e31	−	3.56079e31i	1.17948	−	1.15778i
$216$	−5.39141e30			−0.164656
$217$			7.21966e31i			2.07162i
$218$			5.41507e30i			0.146030i
$219$	−6.94107e29			−0.0175967
$220$	2.45467e31	+	2.50066e31i	0.585176	+	0.596141i
$221$	7.10089e30			0.159227
$222$			2.33439e30i			0.0492502i
$223$		−	2.70597e31i		−	0.537289i	−0.963239	−	0.268644i	$-0.913424\pi$
$223$		−	2.70597e31i		−	0.537289i	0.963239	−	0.268644i	$-0.0865756\pi$
$224$	1.57422e31			0.294250
$225$	−9.93976e29	+	5.35402e31i	−0.0174949	+	0.942358i
$226$	−4.00148e31			−0.663372
$227$			1.65230e31i			0.258071i	0.991640	+	0.129036i	$0.0411882\pi$
$227$			1.65230e31i			0.258071i	−0.991640	+	0.129036i	$0.958812\pi$
$228$		−	1.04831e30i		−	0.0154301i
$229$	4.03443e31			0.559762			0.279881	−	0.960035i	$-0.409705\pi$
$229$	4.03443e31			0.559762			0.279881	+	0.960035i	$0.409705\pi$
$230$	−5.51881e31	−	5.62222e31i	−0.721971	−	0.735499i
$231$	5.40393e31			0.666726
$232$			2.41404e31i			0.280967i
$233$			1.50624e31i			0.165420i	0.996574	+	0.0827100i	$0.0263575\pi$
$233$			1.50624e31i			0.165420i	−0.996574	+	0.0827100i	$0.973642\pi$
$234$	−2.71207e31			−0.281117
$235$	5.11747e31	−	5.02335e31i	0.500771	−	0.491561i
$236$	9.18095e31			0.848351
$237$		−	3.06645e31i		−	0.267629i
$238$		−	5.38854e31i		−	0.444306i
$239$	−1.32816e32			−1.03485			−0.517427	−	0.855727i	$-0.673110\pi$
$239$	−1.32816e32			−1.03485			−0.517427	+	0.855727i	$0.673110\pi$
$240$	5.80800e30	−	5.70118e30i	0.0427735	−	0.0419868i
$241$	1.56243e32			1.08786			0.543928	−	0.839132i	$-0.316937\pi$
$241$	1.56243e32			1.08786			0.543928	+	0.839132i	$0.316937\pi$
$242$			1.92376e32i			1.26661i
$243$		−	1.06771e32i		−	0.664916i
$244$	−9.17324e31			−0.540456
$245$	−2.22480e32	−	2.26649e32i	−1.24036	−	1.26361i
$246$	−4.55263e31			−0.240236
$247$		−	1.08683e31i		−	0.0542940i
$248$			9.30191e31i			0.440022i
$249$	1.09232e31			0.0489393
$250$	−1.14479e32	−	1.21038e32i	−0.485886	−	0.513727i
$251$	−3.39238e31			−0.136430			−0.0682149	−	0.997671i	$-0.521730\pi$
$251$	−3.39238e31			−0.136430			−0.0682149	+	0.997671i	$0.521730\pi$
$252$			2.05806e32i			0.784425i
$253$		−	6.73978e32i		−	2.43511i
$254$	−3.28814e32			−1.12641
$255$	−1.95151e31	−	1.98808e31i	−0.0633985	−	0.0645864i
$256$	2.02824e31			0.0625000
$257$			6.11323e32i			1.78720i	0.448864	+	0.893600i	$0.351829\pi$
$257$			6.11323e32i			1.78720i	−0.448864	+	0.893600i	$0.648171\pi$
$258$		−	1.00999e32i		−	0.280189i
$259$	1.83656e32			0.483568
$260$	6.02143e31	−	5.91068e31i	0.150508	−	0.147740i
$261$	−3.15601e32			−0.749017
$262$			5.70832e31i			0.128659i
$263$			3.30264e32i			0.707064i	0.935422	+	0.353532i	$0.115019\pi$
$263$			3.30264e32i			0.707064i	−0.935422	+	0.353532i	$0.884981\pi$
$264$	6.96249e31			0.141616
$265$	1.66545e32	−	1.63481e32i	0.321893	−	0.315972i
$266$	−8.24744e31			−0.151502
$267$			1.72670e32i			0.301519i
$268$			7.07682e31i			0.117495i
$269$	2.17030e32			0.342660			0.171330	−	0.985214i	$-0.445194\pi$
$269$	2.17030e32			0.342660			0.171330	+	0.985214i	$0.445194\pi$
$270$	1.53615e32	+	1.56494e32i	0.230687	+	0.235010i
$271$	1.16022e33			1.65751			0.828756	−	0.559610i	$-0.189049\pi$
$271$	1.16022e33			1.65751			0.828756	+	0.559610i	$0.189049\pi$
$272$		−	6.94267e31i		−	0.0943727i
$273$		−	1.30123e32i		−	0.168329i
$274$	6.41630e32			0.790045
$275$	2.64553e31	−	1.42501e33i	0.0310114	−	1.67042i
$276$	−1.56537e32			−0.174721
$277$			1.84954e33i			1.96601i	0.183575	+	0.983006i	$0.441233\pi$
$277$			1.84954e33i			1.96601i	−0.183575	+	0.983006i	$0.558767\pi$
$278$			1.50403e32i			0.152283i
$279$	−1.21609e33			−1.17303
$280$	−4.48534e32	−	4.56939e32i	−0.412252	−	0.419976i
$281$	4.98154e32			0.436343			0.218172	−	0.975910i	$-0.429991\pi$
$281$	4.98154e32			0.436343			0.218172	+	0.975910i	$0.429991\pi$
$282$		−	1.42484e32i		−	0.118960i
$283$			2.19736e32i			0.174898i	0.996169	+	0.0874491i	$0.0278715\pi$
$283$			2.19736e32i			0.174898i	−0.996169	+	0.0874491i	$0.972129\pi$
$284$	8.26322e32			0.627122
$285$	−3.04286e31	+	2.98689e31i	−0.0220230	+	0.0216179i
$286$	7.21834e32			0.498306
$287$			3.58173e33i			2.35878i
$288$			2.65164e32i			0.166616i
$289$	1.43006e33			0.857501
$290$	7.00709e32	−	6.87821e32i	0.401019	−	0.393643i
$291$	3.12958e32			0.170974
$292$			7.03579e31i			0.0366982i
$293$		−	2.17581e33i		−	1.08370i	−0.840475	−	0.541850i	$-0.817724\pi$
$293$		−	2.17581e33i		−	1.08370i	0.840475	−	0.541850i	$-0.182276\pi$
$294$	−6.31049e32			−0.300175
$295$	−2.61589e33	−	2.66490e33i	−1.18856	−	1.21083i
$296$	2.36624e32			0.102712
$297$			1.87601e33i			0.778077i
$298$		−	8.40949e32i		−	0.333311i
$299$	−1.62289e33			−0.614793
$300$	−3.30970e32	−	6.14447e30i	−0.119854	−	0.00222509i
$301$	−7.94601e33			−2.75107
$302$			6.59900e32i			0.218466i
$303$			1.32337e33i			0.418992i
$304$	−1.06261e32			−0.0321796
$305$	2.61369e33	+	2.66267e33i	0.757193	+	0.771381i
$306$	9.07656e32			0.251583
$307$		−	1.96986e33i		−	0.522477i	−0.965274	−	0.261239i	$-0.915869\pi$
$307$		−	1.96986e33i		−	0.522477i	0.965274	−	0.261239i	$-0.0841310\pi$
$308$		−	5.47767e33i		−	1.39047i
$309$	3.02191e32			0.0734248
$310$	2.70001e33	−	2.65035e33i	0.628034	−	0.616482i
$311$	−2.40018e33			−0.534537			−0.267269	−	0.963622i	$-0.586121\pi$
$311$	−2.40018e33			−0.534537			−0.267269	+	0.963622i	$0.586121\pi$
$312$		−	1.67652e32i		−	0.0357538i
$313$		−	6.37316e33i		−	1.30169i	−0.759212	−	0.650843i	$-0.774416\pi$
$313$		−	6.37316e33i		−	1.30169i	0.759212	−	0.650843i	$-0.225584\pi$
$314$	−1.11336e33			−0.217814
$315$	5.97383e33	−	5.86395e33i	1.11959	−	1.09900i
$316$	−3.10830e33			−0.558145
$317$			5.24658e33i			0.902769i	0.892330	+	0.451384i	$0.149070\pi$
$317$			5.24658e33i			0.902769i	−0.892330	+	0.451384i	$0.850930\pi$
$318$		−	4.63703e32i		−	0.0764670i
$319$	8.39992e33			1.32770
$320$	−5.77898e32	−	5.88726e32i	−0.0875642	−	0.0892049i
$321$	−2.21632e33			−0.321970
$322$			1.23154e34i			1.71551i
$323$			3.63732e32i			0.0485900i
$324$	−3.24234e33			−0.415433
$325$	−3.43132e33	−	6.37026e31i	−0.421731	−	0.00782946i
$326$	7.76214e32			0.0915259
$327$		−	4.37631e32i		−	0.0495123i
$328$			4.61475e33i			0.501016i
$329$	−1.12098e34			−1.16802
$330$	−1.98379e33	−	2.02096e33i	−0.198408	−	0.202125i
$331$	6.23306e33			0.598444			0.299222	−	0.954184i	$-0.403273\pi$
$331$	6.23306e33			0.598444			0.299222	+	0.954184i	$0.403273\pi$
$332$		−	1.10722e33i		−	0.102064i
$333$			3.09353e33i			0.273815i
$334$	1.07778e34			0.916124
$335$	2.05415e33	−	2.01637e33i	0.167698	−	0.164613i
$336$	−1.27224e33			−0.0997671
$337$			8.87322e33i			0.668463i	0.942491	+	0.334232i	$0.108477\pi$
$337$			8.87322e33i			0.668463i	−0.942491	+	0.334232i	$0.891523\pi$
$338$			8.03110e33i			0.581299i
$339$	3.23389e33			0.224920
$340$	−2.01521e33	+	1.97814e33i	−0.134696	+	0.132219i
$341$	3.23671e34			2.07931
$342$		−	1.38921e33i		−	0.0857861i
$343$			2.16082e34i			1.28277i
$344$	−1.02377e34			−0.584340
$345$	4.46014e33	+	4.54372e33i	0.244789	+	0.249375i
$346$	−1.46730e34			−0.774446
$347$		−	1.26226e34i		−	0.640767i	−0.947288	−	0.320383i	$-0.896188\pi$
$347$		−	1.26226e34i		−	0.640767i	0.947288	−	0.320383i	$-0.103812\pi$
$348$		−	1.95095e33i		−	0.0952637i
$349$	9.31129e33			0.437388			0.218694	−	0.975794i	$-0.429820\pi$
$349$	9.31129e33			0.437388			0.218694	+	0.975794i	$0.429820\pi$
$350$	−4.83410e32	+	2.60387e34i	−0.0218473	+	1.17680i
$351$	4.51730e33			0.196441
$352$		−	7.05751e33i		−	0.295342i
$353$		−	3.68557e34i		−	1.48438i	−0.670188	−	0.742191i	$-0.733787\pi$
$353$		−	3.68557e34i		−	1.48438i	0.670188	−	0.742191i	$-0.266213\pi$
$354$	−7.41978e33			−0.287639
$355$	−2.35440e34	−	2.39852e34i	−0.878614	−	0.895077i
$356$	1.75026e34			0.628823
$357$			4.35486e33i			0.150645i
$358$			2.86169e32i			0.00953239i
$359$	3.22285e34			1.03387			0.516933	−	0.856026i	$-0.327074\pi$
$359$	3.22285e34			1.03387			0.516933	+	0.856026i	$0.327074\pi$
$360$	7.69677e33	−	7.55520e33i	0.237807	−	0.233433i
$361$	−3.30439e34			−0.983432
$362$		−	8.61334e33i		−	0.246948i
$363$		−	1.55473e34i		−	0.429453i
$364$	−1.31899e34			−0.351052
$365$	2.04224e33	−	2.00468e33i	0.0523785	−	0.0514151i
$366$	7.41355e33			0.183245
$367$		−	2.83402e34i		−	0.675166i	−0.941296	−	0.337583i	$-0.890391\pi$
$367$		−	2.83402e34i		−	0.675166i	0.941296	−	0.337583i	$-0.109609\pi$
$368$			1.58673e34i			0.364383i
$369$	−6.03314e34			−1.33563
$370$	−6.74204e33	−	6.86837e33i	−0.143902	−	0.146599i
$371$	−3.64814e34			−0.750799
$372$		−	7.51753e33i		−	0.149192i
$373$			5.10362e34i			0.976807i	0.872618	+	0.488404i	$0.162421\pi$
$373$			5.10362e34i			0.976807i	−0.872618	+	0.488404i	$0.837579\pi$
$374$	−2.41578e34			−0.445955
$375$	9.25183e33	+	9.78195e33i	0.164743	+	0.174182i
$376$	−1.44428e34			−0.248094
$377$		−	2.02265e34i		−	0.335206i
$378$		−	3.42797e34i		−	0.548148i
$379$	4.70109e34			0.725385			0.362693	−	0.931909i	$-0.381857\pi$
$379$	4.70109e34			0.725385			0.362693	+	0.931909i	$0.381857\pi$
$380$	3.02765e33	+	3.08438e33i	0.0450845	+	0.0459293i
$381$	2.65738e34			0.381915
$382$		−	8.03266e34i		−	1.11430i
$383$			5.53570e34i			0.741292i	0.928774	+	0.370646i	$0.120864\pi$
$383$			5.53570e34i			0.741292i	−0.928774	+	0.370646i	$0.879136\pi$
$384$	−1.63917e33			−0.0211910
$385$	−1.58997e35	+	1.56073e35i	−1.98459	+	1.94808i
$386$	8.20478e34			0.988868
$387$		−	1.33844e35i		−	1.55776i
$388$		−	3.17228e34i		−	0.356569i
$389$	−7.61420e34			−0.826617			−0.413309	−	0.910591i	$-0.635627\pi$
$389$	−7.61420e34			−0.826617			−0.413309	+	0.910591i	$0.635627\pi$
$390$	−4.86635e33	+	4.77684e33i	−0.0510306	+	0.0500920i
$391$	5.43138e34			0.550205
$392$			6.39661e34i			0.626019i
$393$		−	4.61330e33i		−	0.0436227i
$394$	6.56723e34			0.600045
$395$	8.85634e34	+	9.02228e34i	0.781976	+	0.796628i
$396$	9.22669e34			0.787338
$397$		−	2.96941e34i		−	0.244905i	−0.992474	−	0.122453i	$-0.960924\pi$
$397$		−	2.96941e34i		−	0.244905i	0.992474	−	0.122453i	$-0.0390759\pi$
$398$			3.84316e34i			0.306385i
$399$	6.66534e33			0.0513675
$400$	−6.22832e32	+	3.35487e34i	−0.00464046	+	0.249957i
$401$	7.62057e34			0.548957			0.274479	−	0.961593i	$-0.411495\pi$
$401$	7.62057e34			0.548957			0.274479	+	0.961593i	$0.411495\pi$
$402$		−	5.71928e33i		−	0.0398373i
$403$		−	7.79378e34i		−	0.524965i
$404$	1.34143e35			0.873815
$405$	9.23826e34	+	9.41136e34i	0.582032	+	0.592938i
$406$	−1.53489e35			−0.935355
$407$		−	8.23363e34i		−	0.485363i
$408$			5.61087e33i			0.0319976i
$409$	7.19744e34			0.397113			0.198556	−	0.980089i	$-0.436375\pi$
$409$	7.19744e34			0.397113			0.198556	+	0.980089i	$0.436375\pi$
$410$	1.33950e35	−	1.31486e35i	0.715089	−	0.701937i
$411$	−5.18547e34			−0.267870
$412$		−	3.06315e34i		−	0.153129i
$413$			5.83744e35i			2.82421i
$414$	−2.07443e35			−0.971391
$415$	−3.21388e34	+	3.15477e34i	−0.145673	+	0.142994i
$416$	−1.69940e34			−0.0745651
$417$		−	1.21551e34i		−	0.0516325i
$418$			3.69748e34i			0.152064i
$419$	2.37543e35			0.945915			0.472958	−	0.881085i	$-0.343186\pi$
$419$	2.37543e35			0.945915			0.472958	+	0.881085i	$0.343186\pi$
$420$	3.62493e34	+	3.69285e34i	0.139776	+	0.142395i
$421$	−4.42357e35			−1.65183			−0.825913	−	0.563797i	$-0.809340\pi$
$421$	−4.42357e35			−1.65183			−0.825913	+	0.563797i	$0.809340\pi$
$422$		−	2.58258e35i		−	0.933976i
$423$		−	1.88819e35i		−	0.661381i
$424$	−4.70031e34			−0.159473
$425$	1.14837e35	+	2.13195e33i	0.377426	+	0.00700692i
$426$	−6.67810e34			−0.212629
$427$		−	5.83254e35i		−	1.79921i
$428$			2.24657e35i			0.671473i
$429$	−5.83366e34			−0.168954
$430$	2.91700e35	+	2.97165e35i	0.818676	+	0.834015i
$431$	−7.54161e33			−0.0205126			−0.0102563	−	0.999947i	$-0.503265\pi$
$431$	−7.54161e33			−0.0205126			−0.0102563	+	0.999947i	$0.503265\pi$
$432$		−	4.41665e34i		−	0.116429i
$433$		−	1.55356e35i		−	0.396955i	−0.980105	−	0.198478i	$-0.936400\pi$
$433$		−	1.55356e35i		−	0.396955i	0.980105	−	0.198478i	$-0.0635997\pi$
$434$	−5.91434e35			−1.46486
$435$	−5.66293e34	+	5.55877e34i	−0.135968	+	0.133467i
$436$	−4.43603e34			−0.103259
$437$		−	8.31302e34i		−	0.187611i
$438$		−	5.68613e33i		−	0.0124427i
$439$	2.02198e35			0.429048			0.214524	−	0.976719i	$-0.431180\pi$
$439$	2.02198e35			0.429048			0.214524	+	0.976719i	$0.431180\pi$
$440$	−2.04854e35	+	2.01087e35i	−0.421535	+	0.413782i
$441$	−8.36266e35			−1.66887
$442$			5.81705e34i			0.112591i
$443$		−	6.45681e35i		−	1.21218i	−0.795396	−	0.606090i	$-0.792737\pi$
$443$		−	6.45681e35i		−	1.21218i	0.795396	−	0.606090i	$-0.207263\pi$
$444$	−1.91233e34			−0.0348251
$445$	−4.98695e35	−	5.08039e35i	−0.880998	−	0.897506i
$446$	2.21673e35			0.379920
$447$			6.79631e34i			0.113011i
$448$			1.28960e35i			0.208066i
$449$	8.16996e35			1.27907			0.639535	−	0.768762i	$-0.279127\pi$
$449$	8.16996e35			1.27907			0.639535	+	0.768762i	$0.279127\pi$
$450$	−4.38601e35	−	8.14265e33i	−0.666348	−	0.0123708i
$451$	1.60576e36			2.36754
$452$		−	3.27802e35i		−	0.469075i
$453$		−	5.33312e34i		−	0.0740723i
$454$	−1.35356e35			−0.182484
$455$	3.75813e35	+	3.82855e35i	0.491834	+	0.501049i
$456$	8.58772e33			0.0109107
$457$		−	1.81378e34i		−	0.0223726i	−0.999937	−	0.0111863i	$-0.996439\pi$
$457$		−	1.81378e34i		−	0.0223726i	0.999937	−	0.0111863i	$-0.00356078\pi$
$458$			3.30501e35i			0.395811i
$459$	−1.51182e35			−0.175804
$460$	4.60572e35	−	4.52101e35i	0.520076	−	0.510510i
$461$	−6.71578e35			−0.736435			−0.368217	−	0.929740i	$-0.620032\pi$
$461$	−6.71578e35			−0.736435			−0.368217	+	0.929740i	$0.620032\pi$
$462$			4.42690e35i			0.471447i
$463$		−	1.04910e36i		−	1.08510i	−0.840022	−	0.542552i	$-0.817458\pi$
$463$		−	1.04910e36i		−	1.08510i	0.840022	−	0.542552i	$-0.182542\pi$
$464$	−1.97758e35			−0.198674
$465$	−2.18207e35	+	2.14194e35i	−0.212939	+	0.209022i
$466$	−1.23391e35			−0.116970
$467$			1.29627e36i			1.19377i	0.802329	+	0.596883i	$0.203594\pi$
$467$			1.29627e36i			1.19377i	−0.802329	+	0.596883i	$0.796406\pi$
$468$		−	2.22173e35i		−	0.198780i
$469$	−4.49959e35			−0.391146
$470$	4.11513e35	+	4.19223e35i	0.347586	+	0.354099i
$471$	8.99788e34			0.0738512
$472$			7.52103e35i			0.599875i
$473$			3.56235e36i			2.76128i
$474$	2.51204e35			0.189242
$475$	3.26307e33	−	1.75764e35i	0.00238925	−	0.128696i
$476$	4.41429e35			0.314172
$477$		−	6.14500e35i		−	0.425132i
$478$		−	1.08803e36i		−	0.731752i
$479$	2.73126e36			1.78580			0.892901	−	0.450253i	$-0.148666\pi$
$479$	2.73126e36			1.78580			0.892901	+	0.450253i	$0.148666\pi$
$480$	4.67041e34	+	4.75792e34i	0.0296892	+	0.0302455i
$481$	−1.98260e35			−0.122540
$482$			1.27994e36i			0.769230i
$483$		−	9.95295e35i		−	0.581655i
$484$	−1.57595e36			−0.895631
$485$	−9.20801e35	+	9.03865e35i	−0.508923	+	0.499563i
$486$	8.74664e35			0.470167
$487$		−	1.61452e35i		−	0.0844119i	−0.999109	−	0.0422059i	$-0.986561\pi$
$487$		−	1.61452e35i		−	0.0844119i	0.999109	−	0.0422059i	$-0.0134386\pi$
$488$		−	7.51472e35i		−	0.382160i
$489$	−6.27314e34			−0.0310324
$490$	1.85671e36	−	1.82256e36i	0.893504	−	0.877070i
$491$	9.92034e35			0.464436			0.232218	−	0.972664i	$-0.425402\pi$
$491$	9.92034e35			0.464436			0.232218	+	0.972664i	$0.425402\pi$
$492$		−	3.72951e35i		−	0.169873i
$493$			6.76925e35i			0.299990i
$494$	8.90330e34			0.0383917
$495$	−2.62892e36	−	2.67818e36i	−1.10308	−	1.12375i
$496$	−7.62012e35			−0.311142
$497$			5.25392e36i			2.08772i
$498$			8.94827e34i			0.0346053i
$499$	−1.94279e36			−0.731255			−0.365627	−	0.930761i	$-0.619146\pi$
$499$	−1.94279e36			−0.731255			−0.365627	+	0.930761i	$0.619146\pi$
$500$	9.91544e35	−	9.37809e35i	0.363260	−	0.343573i
$501$	−8.71034e35			−0.310617
$502$		−	2.77904e35i		−	0.0964705i
$503$		−	4.87342e36i		−	1.64690i	−0.567391	−	0.823448i	$-0.692047\pi$
$503$		−	4.87342e36i		−	1.64690i	0.567391	−	0.823448i	$-0.307953\pi$
$504$	−1.68597e36			−0.554673
$505$	−3.82208e36	−	3.89369e36i	−1.22424	−	1.24718i
$506$	5.52123e36			1.72188
$507$		−	6.49051e35i		−	0.197093i
$508$		−	2.69365e36i		−	0.796490i
$509$	1.72204e36			0.495854			0.247927	−	0.968779i	$-0.420251\pi$
$509$	1.72204e36			0.495854			0.247927	+	0.968779i	$0.420251\pi$
$510$	1.62863e35	−	1.59868e35i	0.0456695	−	0.0448295i
$511$	−4.47350e35			−0.122170
$512$			1.66153e35i			0.0441942i
$513$			2.31392e35i			0.0599464i
$514$	−5.00795e36			−1.26374
$515$	−8.89124e35	+	8.72771e35i	−0.218557	+	0.214537i
$516$	8.27385e35			0.198124
$517$			5.02555e36i			1.17236i
$518$			1.50451e36i			0.341934i
$519$	1.18583e36			0.262581
$520$	4.84203e35	+	4.93276e35i	0.104468	+	0.106425i
$521$	1.08521e35			0.0228142			0.0114071	−	0.999935i	$-0.496369\pi$
$521$	1.08521e35			0.0228142			0.0114071	+	0.999935i	$0.496369\pi$
$522$		−	2.58540e36i		−	0.529635i
$523$			3.25539e36i			0.649876i	0.945735	+	0.324938i	$0.105343\pi$
$523$			3.25539e36i			0.649876i	−0.945735	+	0.324938i	$0.894657\pi$
$524$	−4.67626e35			−0.0909758
$525$	3.90678e34	−	2.10437e36i	0.00740744	−	0.399000i
$526$	−2.70552e36			−0.499970
$527$			2.60837e36i			0.469813i
$528$			5.70367e35i			0.100138i
$529$	−6.57011e36			−1.12440
$530$	1.33924e36	+	1.36433e36i	0.223426	+	0.227613i
$531$	−9.83269e36			−1.59918
$532$		−	6.75630e35i		−	0.107128i
$533$		−	3.86656e36i		−	0.597733i
$534$	−1.41451e36			−0.213206
$535$	6.52099e36	−	6.40105e36i	0.958380	−	0.940752i
$536$	−5.79733e35			−0.0830813
$537$		−	2.31274e34i		−	0.00323201i
$538$			1.77791e36i			0.242297i
$539$	2.22578e37			2.95824
$540$	−1.28200e36	+	1.25842e36i	−0.166177	+	0.163121i
$541$	1.21809e36			0.153999			0.0769993	−	0.997031i	$-0.475466\pi$
$541$	1.21809e36			0.153999			0.0769993	+	0.997031i	$0.475466\pi$
$542$			9.50456e36i			1.17204i
$543$			6.96106e35i			0.0837293i
$544$	5.68743e35			0.0667315
$545$	1.26394e36	+	1.28762e36i	0.144668	+	0.147379i
$546$	1.06597e36			0.119026
$547$			1.25584e37i			1.36807i	0.729451	+	0.684033i	$0.239775\pi$
$547$			1.25584e37i			1.36807i	−0.729451	+	0.684033i	$0.760225\pi$
$548$			5.25623e36i			0.558646i
$549$	9.82444e36			1.01878
$550$	1.16737e37	+	2.16722e35i	1.18116	+	0.0219284i
$551$	1.03607e36			0.102292
$552$		−	1.28235e36i		−	0.123546i
$553$		−	1.97632e37i		−	1.85809i
$554$	−1.51514e37			−1.39018
$555$	5.44872e35	+	5.55082e35i	0.0487910	+	0.0497052i
$556$	−1.23210e36			−0.107681
$557$			1.14672e37i			0.978167i	0.872237	+	0.489084i	$0.162669\pi$
$557$			1.14672e37i			0.978167i	−0.872237	+	0.489084i	$0.837331\pi$
$558$		−	9.96223e36i		−	0.829459i
$559$	8.57789e36			0.697142
$560$	3.74324e36	−	3.67439e36i	0.296968	−	0.291506i
$561$	1.95237e36			0.151204
$562$			4.08088e36i			0.308541i
$563$			6.17709e36i			0.455953i	0.973667	+	0.227977i	$0.0732110\pi$
$563$			6.17709e36i			0.455953i	−0.973667	+	0.227977i	$0.926789\pi$
$564$	1.16723e36			0.0841177
$565$	−9.51492e36	+	9.33991e36i	−0.669500	+	0.657187i
$566$	−1.80008e36			−0.123672
$567$		−	2.06155e37i		−	1.38300i
$568$			6.76923e36i			0.443442i
$569$	1.75768e37			1.12441			0.562203	−	0.826999i	$-0.309954\pi$
$569$	1.75768e37			1.12441			0.562203	+	0.826999i	$0.309954\pi$
$570$	−2.44686e35	−	2.49271e35i	−0.0152862	−	0.0155726i
$571$	−1.54072e37			−0.940018			−0.470009	−	0.882661i	$-0.655749\pi$
$571$	−1.54072e37			−0.940018			−0.470009	+	0.882661i	$0.655749\pi$
$572$			5.91327e36i			0.352356i
$573$			6.49177e36i			0.377812i
$574$	−2.93416e37			−1.66791
$575$	−2.62458e37	−	4.87254e35i	−1.45728	−	0.0270545i
$576$	−2.17222e36			−0.117815
$577$		−	3.45415e37i		−	1.83007i	−0.403373	−	0.915036i	$-0.632162\pi$
$577$		−	3.45415e37i		−	1.83007i	0.403373	−	0.915036i	$-0.367838\pi$
$578$			1.17151e37i			0.606345i
$579$	−6.63087e36			−0.335282
$580$	5.63463e36	+	5.74020e36i	0.278347	+	0.283563i
$581$	7.03996e36			0.339776
$582$			2.56375e36i			0.120897i
$583$			1.63553e37i			0.753586i
$584$	−5.76372e35			−0.0259495
$585$	−6.44888e36	+	6.33027e36i	−0.283714	+	0.278495i
$586$	1.78243e37			0.766292
$587$		−	2.82262e37i		−	1.18587i	−0.805249	−	0.592936i	$-0.797969\pi$
$587$		−	2.82262e37i		−	1.18587i	0.805249	−	0.592936i	$-0.202031\pi$
$588$		−	5.16956e36i		−	0.212256i
$589$	3.99224e36			0.160199
$590$	2.18309e37	−	2.14294e37i	0.856188	−	0.840441i
$591$	−5.30745e36			−0.203449
$592$			1.93843e36i			0.0726284i
$593$			8.68891e36i			0.318220i	0.987261	+	0.159110i	$0.0508624\pi$
$593$			8.68891e36i			0.318220i	−0.987261	+	0.159110i	$0.949138\pi$
$594$	−1.53683e37			−0.550183
$595$	−1.25774e37	−	1.28131e37i	−0.440163	−	0.448410i
$596$	6.88905e36			0.235687
$597$		−	3.10594e36i		−	0.103882i
$598$		−	1.32947e37i		−	0.434724i
$599$	−8.94892e36			−0.286094			−0.143047	−	0.989716i	$-0.545690\pi$
$599$	−8.94892e36			−0.286094			−0.143047	+	0.989716i	$0.545690\pi$
$600$	5.03355e34	−	2.71131e36i	0.00157338	−	0.0847494i
$601$	−5.28715e37			−1.61591			−0.807953	−	0.589247i	$-0.799425\pi$
$601$	−5.28715e37			−1.61591			−0.807953	+	0.589247i	$0.799425\pi$
$602$		−	6.50937e37i		−	1.94530i
$603$		−	7.57919e36i		−	0.221482i
$604$	−5.40590e36			−0.154479
$605$	4.49028e37	+	4.57441e37i	1.25480	+	1.27832i
$606$	−1.08411e37			−0.296272
$607$			5.10982e37i			1.36571i	0.730554	+	0.682855i	$0.239262\pi$
$607$			5.10982e37i			1.36571i	−0.730554	+	0.682855i	$0.760738\pi$
$608$		−	8.70491e35i		−	0.0227544i
$609$	1.24046e37			0.317138
$610$	−2.18126e37	+	2.14114e37i	−0.545449	+	0.535416i
$611$	1.21012e37			0.295986
$612$			7.43552e36i			0.177896i
$613$		−	3.53419e37i		−	0.827130i	−0.910475	−	0.413565i	$-0.864284\pi$
$613$		−	3.53419e37i		−	0.827130i	0.910475	−	0.413565i	$-0.135716\pi$
$614$	1.61371e37			0.369447
$615$	−1.08254e37	+	1.06263e37i	−0.242455	+	0.237996i
$616$	4.48731e37			0.983210
$617$		−	4.41129e37i		−	0.945619i	−0.881165	−	0.472810i	$-0.843240\pi$
$617$		−	4.41129e37i		−	0.945619i	0.881165	−	0.472810i	$-0.156760\pi$
$618$			2.47555e36i			0.0519192i
$619$	3.44688e37			0.707298			0.353649	−	0.935378i	$-0.384941\pi$
$619$	3.44688e37			0.707298			0.353649	+	0.935378i	$0.384941\pi$
$620$	2.17117e37	+	2.21185e37i	0.435919	+	0.444087i
$621$	3.45523e37			0.678797
$622$		−	1.96622e37i		−	0.377975i
$623$			1.11285e38i			2.09339i
$624$	1.37341e36			0.0252818
$625$	−5.54729e37	−	2.06042e36i	−0.999311	−	0.0371173i
$626$	5.22089e37			0.920431
$627$		−	2.98820e36i		−	0.0515582i
$628$		−	9.12066e36i		−	0.154018i
$629$	6.63524e36			0.109666
$630$	4.80375e37	+	4.89376e37i	0.777111	+	0.791672i
$631$	3.02550e37			0.479072			0.239536	−	0.970887i	$-0.423005\pi$
$631$	3.02550e37			0.479072			0.239536	+	0.970887i	$0.423005\pi$
$632$		−	2.54632e37i		−	0.394668i
$633$			2.08717e37i			0.316670i
$634$	−4.29800e37			−0.638354
$635$	−7.81870e37	+	7.67489e37i	−1.13681	+	1.11590i
$636$	3.79866e36			0.0540703
$637$		−	5.35952e37i		−	0.746868i
$638$			6.88122e37i			0.938828i
$639$	−8.84981e37			−1.18215
$640$	4.82285e36	−	4.73414e36i	0.0630774	−	0.0619172i
$641$	2.89374e37			0.370576			0.185288	−	0.982684i	$-0.440678\pi$
$641$	2.89374e37			0.370576			0.185288	+	0.982684i	$0.440678\pi$
$642$		−	1.81561e37i		−	0.227667i
$643$			7.07599e37i			0.868839i	0.900711	+	0.434420i	$0.143046\pi$
$643$			7.07599e37i			0.868839i	−0.900711	+	0.434420i	$0.856954\pi$
$644$	−1.00888e38			−1.21305
$645$	−2.35743e37	−	2.40161e37i	−0.277577	−	0.282778i
$646$	−2.97969e36			−0.0343584
$647$			7.99228e36i			0.0902533i	0.998981	+	0.0451267i	$0.0143691\pi$
$647$			7.99228e36i			0.0902533i	−0.998981	+	0.0451267i	$0.985631\pi$
$648$		−	2.65612e37i		−	0.293755i
$649$	2.61703e38			2.83469
$650$	5.21852e35	−	2.81094e37i	0.00553626	−	0.298209i
$651$	4.77980e37			0.496668
$652$			6.35874e36i			0.0647186i
$653$		−	1.83027e38i		−	1.82468i	−0.409433	−	0.912340i	$-0.634273\pi$
$653$		−	1.83027e38i		−	1.82468i	0.409433	−	0.912340i	$-0.365727\pi$
$654$	3.58507e36			0.0350105
$655$	1.33239e37	+	1.35735e37i	0.127460	+	0.129848i
$656$	−3.78041e37			−0.354272
$657$		−	7.53525e36i		−	0.0691776i
$658$		−	9.18303e37i		−	0.825917i
$659$	−1.43428e38			−1.26380			−0.631902	−	0.775048i	$-0.717726\pi$
$659$	−1.43428e38			−1.26380			−0.631902	+	0.775048i	$0.717726\pi$
$660$	1.65557e37	−	1.62512e37i	0.142924	−	0.140295i
$661$	−3.88857e36			−0.0328905			−0.0164452	−	0.999865i	$-0.505235\pi$
$661$	−3.88857e36			−0.0328905			−0.0164452	+	0.999865i	$0.505235\pi$
$662$			5.10612e37i			0.423164i
$663$		−	4.70117e36i		−	0.0381745i
$664$	9.07038e36			0.0721700
$665$	−1.96111e37	+	1.92504e37i	−0.152901	+	0.150089i
$666$	−2.53422e37			−0.193616
$667$		−	1.54710e38i		−	1.15829i
$668$			8.82921e37i			0.647798i
$669$	−1.79150e37			−0.128814
$670$	1.65181e37	+	1.68276e37i	0.116399	+	0.118580i
$671$	−2.61484e38			−1.80589
$672$		−	1.04222e37i		−	0.0705460i
$673$			9.16322e37i			0.607917i	0.952685	+	0.303959i	$0.0983085\pi$
$673$			9.16322e37i			0.607917i	−0.952685	+	0.303959i	$0.901692\pi$
$674$	−7.26894e37			−0.472675
$675$	7.30547e37	+	1.35626e36i	0.465637	+	0.00864456i
$676$	−6.57908e37			−0.411041
$677$		−	2.82935e38i		−	1.73277i	−0.499379	−	0.866384i	$-0.666439\pi$
$677$		−	2.82935e38i		−	1.73277i	0.499379	−	0.866384i	$-0.333561\pi$
$678$			2.64920e37i			0.159043i
$679$	2.01700e38			1.18704
$680$	−1.62050e37	−	1.65086e37i	−0.0934927	−	0.0952445i
$681$	1.09391e37			0.0618723
$682$			2.65151e38i			1.47030i
$683$		−	3.12775e38i		−	1.70041i	−0.526455	−	0.850203i	$-0.676479\pi$
$683$		−	3.12775e38i		−	1.70041i	0.526455	−	0.850203i	$-0.323521\pi$
$684$	1.13804e37			0.0606599
$685$	1.52570e38	−	1.49764e38i	0.797344	−	0.782678i
$686$	−1.77015e38			−0.907054
$687$		−	2.67101e37i		−	0.134202i
$688$		−	8.38676e37i		−	0.413191i
$689$	3.93825e37			0.190258
$690$	−3.72221e37	+	3.65375e37i	−0.176335	+	0.173092i
$691$	−2.39079e38			−1.11068			−0.555338	−	0.831625i	$-0.687411\pi$
$691$	−2.39079e38			−1.11068			−0.555338	+	0.831625i	$0.687411\pi$
$692$		−	1.20201e38i		−	0.547616i
$693$			5.86652e38i			2.62109i
$694$	1.03404e38			0.453090
$695$	3.51058e37	+	3.57636e37i	0.150863	+	0.153690i
$696$	1.59822e37			0.0673616
$697$			1.29403e38i			0.534937i
$698$			7.62781e37i			0.309280i
$699$	9.97209e36			0.0396592
$700$	−2.13309e38	−	3.96009e36i	−0.832120	−	0.0154483i
$701$	1.19950e38			0.458996			0.229498	−	0.973309i	$-0.426292\pi$
$701$	1.19950e38			0.458996			0.229498	+	0.973309i	$0.426292\pi$
$702$			3.70057e37i			0.138905i
$703$		−	1.01556e37i		−	0.0373945i
$704$	5.78151e37			0.208838
$705$	−3.32573e37	−	3.38804e37i	−0.117851	−	0.120059i
$706$	3.01922e38			1.04962
$707$			8.52909e38i			2.90898i
$708$		−	6.07828e37i		−	0.203391i
$709$	−2.18695e38			−0.717982			−0.358991	−	0.933341i	$-0.616879\pi$
$709$	−2.18695e38			−0.717982			−0.358991	+	0.933341i	$0.616879\pi$
$710$	1.96487e38	−	1.92873e38i	0.632915	−	0.621274i
$711$	3.32895e38			1.05213
$712$			1.43382e38i			0.444645i
$713$		−	5.96137e38i		−	1.81400i
$714$	−3.56750e37			−0.106522
$715$	1.71641e38	−	1.68484e38i	0.502909	−	0.493660i
$716$	−2.34430e36			−0.00674042
$717$			8.79314e37i			0.248105i
$718$			2.64016e38i			0.731054i
$719$	−1.04263e38			−0.283329			−0.141665	−	0.989915i	$-0.545245\pi$
$719$	−1.04263e38			−0.283329			−0.141665	+	0.989915i	$0.545245\pi$
$720$	6.18922e37	+	6.30519e37i	0.165062	+	0.168155i
$721$	1.94762e38			0.509773
$722$		−	2.70696e38i		−	0.695391i
$723$		−	1.03441e38i		−	0.260812i
$724$	7.05605e37			0.174619
$725$	6.07274e36	−	3.27106e38i	0.0147510	−	0.794559i
$726$	1.27364e38			0.303669
$727$			6.05646e38i			1.41744i	0.705490	+	0.708720i	$0.250727\pi$
$727$			6.05646e38i			1.41744i	−0.705490	+	0.708720i	$0.749273\pi$
$728$		−	1.08051e38i		−	0.248231i
$729$	2.97740e38			0.671453
$730$	1.64223e37	+	1.67300e37i	0.0363560	+	0.0370372i
$731$	−2.87079e38			−0.623902
$732$			6.07318e37i			0.129574i
$733$			2.81638e38i			0.589913i	0.955511	+	0.294956i	$0.0953051\pi$
$733$			2.81638e38i			0.589913i	−0.955511	+	0.294956i	$0.904695\pi$
$734$	2.32163e38			0.477414
$735$	−1.50054e38	+	1.47294e38i	−0.302948	+	0.297376i
$736$	−1.29985e38			−0.257658
$737$			2.01725e38i			0.392599i
$738$		−	4.94235e38i		−	0.944436i
$739$	7.75639e37			0.145532			0.0727662	−	0.997349i	$-0.476817\pi$
$739$	7.75639e37			0.145532			0.0727662	+	0.997349i	$0.476817\pi$
$740$	5.62657e37	−	5.52308e37i	0.103661	−	0.101754i
$741$	−7.19539e36			−0.0130169
$742$		−	2.98855e38i		−	0.530895i
$743$		−	6.68728e38i		−	1.16654i	−0.812277	−	0.583271i	$-0.801772\pi$
$743$		−	6.68728e38i		−	1.16654i	0.812277	−	0.583271i	$-0.198228\pi$
$744$	6.15836e37			0.105495
$745$	−1.96287e38	−	1.99965e38i	−0.330203	−	0.336391i
$746$	−4.18088e38			−0.690707
$747$			1.18582e38i			0.192394i
$748$		−	1.97901e38i		−	0.315338i
$749$	−1.42841e39			−2.23537
$750$	−8.01338e37	+	7.57910e37i	−0.123165	+	0.116491i
$751$	−1.45586e38			−0.219776			−0.109888	−	0.993944i	$-0.535049\pi$
$751$	−1.45586e38			−0.219776			−0.109888	+	0.993944i	$0.535049\pi$
$752$		−	1.18315e38i		−	0.175429i
$753$			2.24594e37i			0.0327089i
$754$	1.65695e38			0.237026
$755$	1.54028e38	+	1.56914e38i	0.216429	+	0.220485i
$756$	2.80819e38			0.387599
$757$			8.78000e38i			1.19042i	0.803570	+	0.595210i	$0.202931\pi$
$757$			8.78000e38i			1.19042i	−0.803570	+	0.595210i	$0.797069\pi$
$758$			3.85113e38i			0.512925i
$759$	−4.46210e38			−0.583815
$760$	−2.52673e37	+	2.48025e37i	−0.0324769	+	0.0318796i
$761$	−5.31239e38			−0.670807			−0.335403	−	0.942075i	$-0.608873\pi$
$761$	−5.31239e38			−0.670807			−0.335403	+	0.942075i	$0.608873\pi$
$762$			2.17693e38i			0.270055i
$763$		−	2.82052e38i		−	0.343754i
$764$	6.58035e38			0.787932
$765$	2.15827e38	−	2.11857e38i	0.253908	−	0.249238i
$766$	−4.53484e38			−0.524172
$767$		−	6.30164e38i		−	0.715676i
$768$		−	1.34281e37i		−	0.0149843i
$769$	−9.89710e38			−1.08518			−0.542591	−	0.839997i	$-0.682556\pi$
$769$	−9.89710e38			−1.08518			−0.542591	+	0.839997i	$0.682556\pi$
$770$	−1.27855e39	−	1.30251e39i	−1.37750	−	1.40331i
$771$	4.04729e38			0.428479
$772$			6.72135e38i			0.699235i
$773$			1.64539e38i			0.168208i	0.996457	+	0.0841039i	$0.0268028\pi$
$773$			1.64539e38i			0.168208i	−0.996457	+	0.0841039i	$0.973197\pi$
$774$	1.09645e39			1.10150
$775$	2.33999e37	−	1.26043e39i	0.0231015	−	1.24436i
$776$	2.59873e38			0.252132
$777$		−	1.21590e38i		−	0.115935i
$778$		−	6.23755e38i		−	0.584507i
$779$	1.98059e38			0.182405
$780$	−3.91319e37	−	3.98651e37i	−0.0354204	−	0.0360841i
$781$	2.35543e39			2.09547
$782$			4.44939e38i			0.389053i
$783$			4.30632e38i			0.370103i
$784$	−5.24010e38			−0.442663
$785$	−2.64740e38	+	2.59871e38i	−0.219826	+	0.215783i
$786$	3.77922e37			0.0308459
$787$		−	3.39327e38i		−	0.272245i	−0.990692	−	0.136122i	$-0.956536\pi$
$787$		−	3.39327e38i		−	0.272245i	0.990692	−	0.136122i	$-0.0434640\pi$
$788$			5.37988e38i			0.424296i
$789$	2.18653e38			0.169518
$790$	−7.39105e38	+	7.25511e38i	−0.563301	+	0.552941i
$791$	2.08423e39			1.56158
$792$			7.55851e38i			0.556732i
$793$			6.29635e38i			0.455933i
$794$	2.43254e38			0.173174
$795$	−1.08234e38	−	1.10262e38i	−0.0757540	−	0.0771734i
$796$	−3.14832e38			−0.216647
$797$		−	1.32619e39i		−	0.897259i	−0.893718	−	0.448629i	$-0.851912\pi$
$797$		−	1.32619e39i		−	0.897259i	0.893718	−	0.448629i	$-0.148088\pi$
$798$			5.46025e37i			0.0363223i
$799$	−4.04994e38			−0.264891
$800$	−2.74831e38	−	5.10224e36i	−0.176746	−	0.00328130i
$801$	−1.87451e39			−1.18536
$802$			6.24277e38i			0.388172i
$803$			2.00556e38i			0.122624i
$804$	4.68524e37			0.0281692
$805$	2.87455e39	+	2.92841e39i	1.69952	+	1.73136i
$806$	6.38466e38			0.371206
$807$		−	1.43685e38i		−	0.0821523i
$808$			1.09890e39i			0.617881i
$809$	9.81767e38			0.542880			0.271440	−	0.962455i	$-0.412500\pi$
$809$	9.81767e38			0.542880			0.271440	+	0.962455i	$0.412500\pi$
$810$	−7.70978e38	+	7.56798e38i	−0.419271	+	0.411559i
$811$	1.86354e39			0.996684			0.498342	−	0.866981i	$-0.333942\pi$
$811$	1.86354e39			0.996684			0.498342	+	0.866981i	$0.333942\pi$
$812$		−	1.25738e39i		−	0.661396i
$813$		−	7.68132e38i		−	0.397387i
$814$	6.74499e38			0.343204
$815$	1.84572e38	−	1.81177e38i	0.0923714	−	0.0906724i
$816$	−4.59642e37			−0.0226257
$817$			4.39389e38i			0.212741i
$818$			5.89615e38i			0.280801i
$819$	1.41262e39			0.661748
$820$	1.07714e39	+	1.09732e39i	0.496344	+	0.505645i
$821$	−4.22643e39			−1.91576			−0.957881	−	0.287167i	$-0.907287\pi$
$821$	−4.22643e39			−1.91576			−0.957881	+	0.287167i	$0.907287\pi$
$822$		−	4.24794e38i		−	0.189412i
$823$		−	3.58910e38i		−	0.157430i	−0.996897	−	0.0787150i	$-0.974918\pi$
$823$		−	3.58910e38i		−	0.157430i	0.996897	−	0.0787150i	$-0.0250817\pi$
$824$	2.50933e38			0.108278
$825$	−9.43431e38	−	1.75148e37i	−0.400481	−	0.00743495i
$826$	−4.78203e39			−1.99702
$827$		−	9.52564e37i		−	0.0391354i	−0.999809	−	0.0195677i	$-0.993771\pi$
$827$		−	9.52564e37i		−	0.0391354i	0.999809	−	0.0195677i	$-0.00622899\pi$
$828$		−	1.69937e39i		−	0.686877i
$829$	−3.09619e39			−1.23123			−0.615617	−	0.788045i	$-0.711093\pi$
$829$	−3.09619e39			−1.23123			−0.615617	+	0.788045i	$0.711093\pi$
$830$	−2.58438e38	−	2.63281e38i	−0.101112	−	0.103007i
$831$	1.22449e39			0.471349
$832$		−	1.39215e38i		−	0.0527255i
$833$			1.79369e39i			0.668404i
$834$	9.95750e37			0.0365097
$835$	2.56280e39	−	2.51567e39i	0.924588	−	0.907582i
$836$	−3.02898e38			−0.107526
$837$			1.65934e39i			0.579617i
$838$			1.94595e39i			0.668863i
$839$	−2.60400e38			−0.0880753			−0.0440377	−	0.999030i	$-0.514022\pi$
$839$	−2.60400e38			−0.0880753			−0.0440377	+	0.999030i	$0.514022\pi$
$840$	−3.02518e38	+	2.96954e38i	−0.100689	+	0.0988368i
$841$	−1.12495e39			−0.368459
$842$		−	3.62379e39i		−	1.16802i
$843$		−	3.29805e38i		−	0.104613i
$844$	2.11565e39			0.660421
$845$	1.87455e39	+	1.90967e39i	0.575879	+	0.586669i
$846$	1.54681e39			0.467667
$847$		−	1.00202e40i		−	2.98160i
$848$		−	3.85050e38i		−	0.112765i
$849$	1.45477e38			0.0419316
$850$	−1.74650e37	+	9.40745e38i	−0.00495464	+	0.266880i
$851$	−1.51647e39			−0.423433
$852$		−	5.47070e38i		−	0.150352i
$853$		−	3.02315e39i		−	0.817802i	−0.912579	−	0.408901i	$-0.865912\pi$
$853$		−	3.02315e39i		−	0.817802i	0.912579	−	0.408901i	$-0.134088\pi$
$854$	4.77801e39			1.27223
$855$	−3.24258e38	−	3.30334e38i	−0.0849862	−	0.0865786i
$856$	−1.84039e39			−0.474803
$857$			3.38170e37i			0.00858803i	0.999991	+	0.00429402i	$0.00136683\pi$
$857$			3.38170e37i			0.00858803i	−0.999991	+	0.00429402i	$0.998633\pi$
$858$		−	4.77893e38i		−	0.119468i
$859$	−7.23756e39			−1.78108			−0.890542	−	0.454902i	$-0.849674\pi$
$859$	−7.23756e39			−1.78108			−0.890542	+	0.454902i	$0.849674\pi$
$860$	−2.43438e39	+	2.38960e39i	−0.589738	+	0.578891i
$861$	2.37130e39			0.565515
$862$		−	6.17809e37i		−	0.0145046i
$863$			1.91878e39i			0.443485i	0.975105	+	0.221742i	$0.0711744\pi$
$863$			1.91878e39i			0.443485i	−0.975105	+	0.221742i	$0.928826\pi$
$864$	3.61812e38			0.0823279
$865$	−3.48901e39	+	3.42484e39i	−0.781601	+	0.767225i
$866$	1.27268e39			0.280690
$867$		−	9.46779e38i		−	0.205585i
$868$		−	4.84503e39i		−	1.03581i
$869$	−8.86022e39			−1.86499
$870$	−4.55374e38	−	4.63907e38i	−0.0943754	−	0.0961437i
$871$	4.85740e38			0.0991195
$872$		−	3.63399e38i		−	0.0730149i
$873$			3.39748e39i			0.672147i
$874$	6.81002e38			0.132661
$875$	5.96278e39	+	6.30444e39i	1.14377	+	1.20931i
$876$	4.65807e37			0.00879835
$877$		−	4.76343e39i		−	0.885983i	−0.896526	−	0.442991i	$-0.853917\pi$
$877$		−	4.76343e39i		−	0.885983i	0.896526	−	0.442991i	$-0.146083\pi$
$878$			1.65641e39i			0.303383i
$879$	−1.44051e39			−0.259816
$880$	−1.64730e39	−	1.67817e39i	−0.292588	−	0.298071i
$881$	3.85203e39			0.673775			0.336888	−	0.941545i	$-0.390626\pi$
$881$	3.85203e39			0.673775			0.336888	+	0.941545i	$0.390626\pi$
$882$		−	6.85069e39i		−	1.18007i
$883$			7.75251e39i			1.31514i	0.753392	+	0.657572i	$0.228416\pi$
$883$			7.75251e39i			1.31514i	−0.753392	+	0.657572i	$0.771584\pi$
$884$	−4.76532e38			−0.0796135
$885$	−1.76431e39	+	1.73186e39i	−0.290296	+	0.284956i
$886$	5.28942e39			0.857141
$887$			1.02617e40i			1.63775i	0.573968	+	0.818877i	$0.305403\pi$
$887$			1.02617e40i			1.63775i	−0.573968	+	0.818877i	$0.694597\pi$
$888$		−	1.56658e38i		−	0.0246251i
$889$	1.71268e40			2.65156
$890$	4.16186e39	−	4.08531e39i	0.634632	−	0.622960i
$891$	−9.24230e39			−1.38813
$892$			1.81595e39i			0.268644i
$893$			6.19864e38i			0.0903237i
$894$	−5.56754e38			−0.0799110
$895$	6.67951e37	+	6.80466e37i	0.00944351	+	0.00962045i
$896$	−1.05644e39			−0.147125
$897$			1.07444e39i			0.147396i
$898$			6.69283e39i			0.904439i
$899$	7.42978e39			0.989054
$900$	6.67046e37	−	3.59302e39i	0.00874746	−	0.471179i
$901$	−1.31802e39			−0.170270
$902$			1.31544e40i			1.67410i
$903$			5.26068e39i			0.659565i
$904$	2.68535e39			0.331686
$905$	−2.01045e39	−	2.04812e39i	−0.244646	−	0.249230i
$906$	4.36889e38			0.0523770
$907$		−	1.44604e40i		−	1.70797i	−0.520295	−	0.853986i	$-0.674178\pi$
$907$		−	1.44604e40i		−	1.70797i	0.520295	−	0.853986i	$-0.325822\pi$
$908$		−	1.10884e39i		−	0.129036i
$909$	−1.43666e40			−1.64718
$910$	−3.13635e39	+	3.07866e39i	−0.354295	+	0.347779i
$911$	9.39433e39			1.04561			0.522803	−	0.852454i	$-0.324886\pi$
$911$	9.39433e39			1.04561			0.522803	+	0.852454i	$0.324886\pi$
$912$			7.03506e37i			0.00771503i
$913$		−	3.15615e39i		−	0.341037i
$914$	1.48585e38			0.0158198
$915$	1.76283e39	−	1.73041e39i	0.184938	−	0.181536i
$916$	−2.70746e39			−0.279881
$917$		−	2.97326e39i		−	0.302864i
$918$		−	1.23848e39i		−	0.124312i
$919$	8.70113e39			0.860630			0.430315	−	0.902679i	$-0.358403\pi$
$919$	8.70113e39			0.860630			0.430315	+	0.902679i	$0.358403\pi$
$920$	3.70361e39	+	3.77301e39i	0.360985	+	0.367749i
$921$	−1.30415e39			−0.125263
$922$		−	5.50157e39i		−	0.520738i
$923$		−	5.67173e39i		−	0.529045i
$924$	−3.62651e39			−0.333363
$925$	−3.20631e39	−	5.95252e37i	−0.290464	−	0.00539247i
$926$	8.59419e39			0.767285
$927$			3.28060e39i			0.288654i
$928$		−	1.62003e39i		−	0.140484i
$929$	3.28721e39			0.280941			0.140471	−	0.990085i	$-0.455138\pi$
$929$	3.28721e39			0.280941			0.140471	+	0.990085i	$0.455138\pi$
$930$	−1.75468e39	−	1.78755e39i	−0.147801	−	0.150570i
$931$	2.74533e39			0.227916
$932$		−	1.01082e39i		−	0.0827100i
$933$			1.58905e39i			0.128155i
$934$	−1.06191e40			−0.844119
$935$	−5.74436e39	+	5.63871e39i	−0.450075	+	0.441797i
$936$	1.82004e39			0.140558
$937$			2.36225e39i			0.179822i	0.995950	+	0.0899108i	$0.0286582\pi$
$937$			2.36225e39i			0.179822i	−0.995950	+	0.0899108i	$0.971342\pi$
$938$		−	3.68606e39i		−	0.276582i
$939$	−4.21938e39			−0.312078
$940$	−3.43428e39	+	3.37111e39i	−0.250386	+	0.245780i
$941$	1.68672e40			1.21223			0.606113	−	0.795378i	$-0.292728\pi$
$941$	1.68672e40			1.21223			0.606113	+	0.795378i	$0.292728\pi$
$942$			7.37106e38i			0.0522207i
$943$		−	2.95749e40i		−	2.06545i
$944$	−6.16123e39			−0.424175
$945$	−8.00127e39	−	8.15119e39i	−0.543037	−	0.553212i
$946$	−2.91827e40			−1.95252
$947$			2.10988e40i			1.39166i	0.718206	+	0.695831i	$0.244964\pi$
$947$			2.10988e40i			1.39166i	−0.718206	+	0.695831i	$0.755036\pi$
$948$			2.05786e39i			0.133815i
$949$	4.82924e38			0.0309589
$950$	1.43986e39	+	2.67310e37i	0.0910021	+	0.00168946i
$951$	3.47352e39			0.216438
$952$			3.61619e39i			0.222153i
$953$		−	1.89573e39i		−	0.114822i	−0.998351	−	0.0574108i	$-0.981716\pi$
$953$		−	1.89573e39i		−	0.114822i	0.998351	−	0.0574108i	$-0.0182845\pi$
$954$	5.03398e39			0.300613
$955$	−1.87491e40	−	1.91004e40i	−1.10391	−	1.12460i
$956$	8.91314e39			0.517427
$957$		−	5.56120e39i		−	0.318315i
$958$			2.23745e40i			1.26275i
$959$	−3.34202e40			−1.85976
$960$	−3.89769e38	+	3.82600e38i	−0.0213868	+	0.0209934i
$961$	1.01462e40			0.548954
$962$		−	1.62415e39i		−	0.0866488i
$963$		−	2.40605e40i		−	1.26576i
$964$	−1.04853e40			−0.543928
$965$	1.95097e40	−	1.91509e40i	0.998003	−	0.979647i
$966$	8.15346e39			0.411292
$967$			3.67291e40i			1.82706i	0.406771	+	0.913530i	$0.366655\pi$
$967$			3.67291e40i			1.82706i	−0.406771	+	0.913530i	$0.633345\pi$
$968$		−	1.29102e40i		−	0.633307i
$969$	2.40810e38			0.0116494
$970$	−7.40446e39	−	7.54320e39i	−0.353244	−	0.359863i
$971$	−3.15382e40			−1.48381			−0.741903	−	0.670508i	$-0.766076\pi$
$971$	−3.15382e40			−1.48381			−0.741903	+	0.670508i	$0.766076\pi$
$972$			7.16525e39i			0.332458i
$973$		−	7.83396e39i		−	0.358474i
$974$	1.32262e39			0.0596882
$975$	−4.21746e37	+	2.27172e39i	−0.00187710	+	0.101110i
$976$	6.15606e39			0.270228
$977$			1.89630e40i			0.820975i	0.911866	+	0.410488i	$0.134641\pi$
$977$			1.89630e40i			0.820975i	−0.911866	+	0.410488i	$0.865359\pi$
$978$		−	5.13896e38i		−	0.0219432i
$979$	4.98913e40			2.10116
$980$	1.49304e40	+	1.52102e40i	0.620182	+	0.631803i
$981$	4.75094e39			0.194647
$982$			8.12674e39i			0.328406i
$983$			3.69535e40i			1.47293i	0.676474	+	0.736466i	$0.263507\pi$
$983$			3.69535e40i			1.47293i	−0.676474	+	0.736466i	$0.736493\pi$
$984$	3.05522e39			0.120118
$985$	1.56159e40	−	1.53287e40i	0.605588	−	0.594450i
$986$	−5.54537e39			−0.212125
$987$			7.42147e39i			0.280032i
$988$			7.29358e38i			0.0271470i
$989$	6.56113e40			2.40895
$990$	2.19397e40	−	2.15361e40i	0.794611	−	0.779996i
$991$	−2.78228e40			−0.994046			−0.497023	−	0.867737i	$-0.665573\pi$
$991$	−2.78228e40			−0.994046			−0.497023	+	0.867737i	$0.665573\pi$
$992$		−	6.24240e39i		−	0.220011i
$993$		−	4.12662e39i		−	0.143476i
$994$	−4.30402e40			−1.47624
$995$	8.97037e39	+	9.13846e39i	0.303528	+	0.309215i
$996$	−7.33042e38			−0.0244697
$997$		−	1.80597e40i		−	0.594740i	−0.954762	−	0.297370i	$-0.903891\pi$
$997$		−	1.80597e40i		−	0.594740i	0.954762	−	0.297370i	$-0.0961094\pi$
$998$		−	1.59153e40i		−	0.517075i
$999$	4.22107e39			0.135297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.28.b.a.9.11	yes	14
5.2	odd	4		50.28.a.k.1.4		7
5.3	odd	4		50.28.a.l.1.4		7
5.4	even	2	inner	10.28.b.a.9.4	✓	14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.28.b.a.9.4	✓	14	5.4	even	2	inner
10.28.b.a.9.11	yes	14	1.1	even	1	trivial
50.28.a.k.1.4		7	5.2	odd	4
50.28.a.l.1.4		7	5.3	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} -662054. i q^{3} -6.71089e7 q^{4} +(1.91210e9 + 1.94793e9i) q^{5} +5.42355e9 q^{6} -4.26692e11i q^{7} -5.49756e11i q^{8} +7.18728e12 q^{9} +(-1.59575e13 + 1.56640e13i) q^{10} -1.91294e14 q^{11} +4.44297e13i q^{12} +4.60623e14i q^{13} +3.49546e15 q^{14} +(1.28964e15 - 1.26592e15i) q^{15} +4.50360e15 q^{16} -1.54158e16i q^{17} +5.88782e16i q^{18} -2.35947e16 q^{19} +(-1.28319e17 - 1.30723e17i) q^{20} -2.82493e17 q^{21} -1.56708e18i q^{22} +3.52325e18i q^{23} -3.63968e17 q^{24} +(-1.38296e17 + 7.44930e18i) q^{25} -3.77343e18 q^{26} -9.80693e18i q^{27} +2.86348e19i q^{28} -4.39110e19 q^{29} +(1.03704e19 + 1.05647e19i) q^{30} -1.69201e20 q^{31} +3.68935e19i q^{32} +1.26647e20i q^{33} +1.26286e20 q^{34} +(8.31167e20 - 8.15879e20i) q^{35} -4.82330e20 q^{36} +4.30417e20i q^{37} -1.93288e20i q^{38} +3.04958e20 q^{39} +(1.07089e21 - 1.05119e21i) q^{40} -8.39419e21 q^{41} -2.31418e21i q^{42} -1.86223e22i q^{43} +1.28375e22 q^{44} +(1.37428e22 + 1.40003e22i) q^{45} -2.88625e22 q^{46} -2.62713e22i q^{47} -2.98163e21i q^{48} -1.16354e23 q^{49} +(-6.10246e22 - 1.13292e21i) q^{50} -1.02061e22 q^{51} -3.09119e22i q^{52} -8.54982e22i q^{53} +8.03383e22 q^{54} +(-3.65774e23 - 3.72628e23i) q^{55} -2.34576e23 q^{56} +1.56210e22i q^{57} -3.59719e23i q^{58} -1.36807e24 q^{59} +(-8.65460e22 + 8.49542e22i) q^{60} +1.36692e24 q^{61} -1.38609e24i q^{62} -3.06676e24i q^{63} -3.02231e23 q^{64} +(-8.97263e23 + 8.80760e23i) q^{65} -1.03749e24 q^{66} -1.05453e24i q^{67} +1.03454e24i q^{68} +2.33258e24 q^{69} +(6.68368e24 + 6.80892e24i) q^{70} -1.23132e25 q^{71} -3.95125e24i q^{72} -1.04841e24i q^{73} -3.52598e24 q^{74} +(4.93184e24 + 9.15597e22i) q^{75} +1.58341e24 q^{76} +8.16236e25i q^{77} +2.49821e24i q^{78} +4.63172e25 q^{79} +(8.61135e24 + 8.77271e24i) q^{80} +4.83146e25 q^{81} -6.87652e25i q^{82} +1.64989e25i q^{83} +1.89578e25 q^{84} +(3.00290e25 - 2.94766e25i) q^{85} +1.52554e26 q^{86} +2.90715e25i q^{87} +1.05165e26i q^{88} -2.60810e26 q^{89} +(-1.14691e26 + 1.12581e26i) q^{90} +1.96544e26 q^{91} -2.36442e26i q^{92} +1.12020e26i q^{93} +2.15215e26 q^{94} +(-4.51156e25 - 4.59609e25i) q^{95} +2.44255e25 q^{96} +4.72707e26i q^{97} -9.53169e26i q^{98} -1.37488e27 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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