LMFDB - Embedded newform 81.9.f.a.71.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,9,Mod(8,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(18))

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

N = Newforms(chi, 9, names="a")

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 9 $
Character orbit:	$[\chi]$	$=$	81.f (of order $18$, degree $6$, not 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:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.10
Character	$\chi$	$=$	81.71
Dual form			81.9.f.a.8.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.08460 + 1.24921i) q^{2} +(-191.930 + 69.8569i) q^{4} +(-349.559 + 416.588i) q^{5} +(22.4234 + 8.16143i) q^{7} +(2867.39 - 1655.49i) q^{8} +O(q^{10})$	\(q+(-7.08460 + 1.24921i) q^{2} +(-191.930 + 69.8569i) q^{4} +(-349.559 + 416.588i) q^{5} +(22.4234 + 8.16143i) q^{7} +(2867.39 - 1655.49i) q^{8} +(1956.08 - 3388.03i) q^{10} +(15469.2 + 18435.5i) q^{11} +(-8798.06 + 49896.3i) q^{13} +(-169.056 - 29.8091i) q^{14} +(21808.2 - 18299.3i) q^{16} +(37540.0 + 21673.7i) q^{17} +(-75167.3 - 130194. i) q^{19} +(37989.4 - 104375. i) q^{20} +(-132623. - 111284. i) q^{22} +(108972. + 299398. i) q^{23} +(16477.1 + 93446.3i) q^{25} -364486. i q^{26} -4873.85 q^{28} +(-945594. + 166734. i) q^{29} +(736394. - 268025. i) q^{31} +(-676476. + 806193. i) q^{32} +(-293031. - 106655. i) q^{34} +(-11238.2 + 6488.40i) q^{35} +(1.21793e6 - 2.10952e6i) q^{37} +(695170. + 828471. i) q^{38} +(-312665. + 1.77321e6i) q^{40} +(-2.52414e6 - 445074. i) q^{41} +(-2.24939e6 + 1.88746e6i) q^{43} +(-4.25687e6 - 2.45770e6i) q^{44} +(-1.14603e6 - 1.98499e6i) q^{46} +(569539. - 1.56479e6i) q^{47} +(-4.41566e6 - 3.70518e6i) q^{49} +(-233468. - 641447. i) q^{50} +(-1.79699e6 - 1.01912e7i) q^{52} +3.88995e6i q^{53} -1.30874e7 q^{55} +(77807.6 - 13719.6i) q^{56} +(6.49088e6 - 2.36249e6i) q^{58} +(-6.87370e6 + 8.19175e6i) q^{59} +(-1.49222e7 - 5.43124e6i) q^{61} +(-4.88224e6 + 2.81876e6i) q^{62} +(141478. - 245047. i) q^{64} +(-1.77108e7 - 2.11069e7i) q^{65} +(1.45408e6 - 8.24651e6i) q^{67} +(-8.71913e6 - 1.53742e6i) q^{68} +(71513.1 - 60006.6i) q^{70} +(9.42132e6 + 5.43940e6i) q^{71} +(1.18791e7 + 2.05752e7i) q^{73} +(-5.99334e6 + 1.64666e7i) q^{74} +(2.35218e7 + 1.97371e7i) q^{76} +(196412. + 539638. i) q^{77} +(-7.07994e6 - 4.01523e7i) q^{79} +1.54817e7i q^{80} +1.84385e7 q^{82} +(5.20151e7 - 9.17167e6i) q^{83} +(-2.21515e7 + 8.06248e6i) q^{85} +(1.35782e7 - 1.61819e7i) q^{86} +(7.48761e7 + 2.72527e7i) q^{88} +(-3.60266e7 + 2.07999e7i) q^{89} +(-604507. + 1.04704e6i) q^{91} +(-4.18301e7 - 4.98511e7i) q^{92} +(-2.08020e6 + 1.17974e7i) q^{94} +(8.05126e7 + 1.41965e7i) q^{95} +(-7.44489e7 + 6.24700e7i) q^{97} +(3.59117e7 + 2.07336e7i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8	$ 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25} - 12 q^{28} + 943980 q^{29} + 920739 q^{31} + 3005136 q^{32} + 660474 q^{34} - 6225408 q^{35} - 3 q^{37} + 23716884 q^{38} - 975273 q^{40} - 16694382 q^{41} + 4412514 q^{43} - 17341119 q^{44} - 3 q^{46} + 11341869 q^{47} + 11347482 q^{49} + 40948977 q^{50} + 14465511 q^{52} - 12 q^{55} - 52215771 q^{56} - 19078611 q^{58} - 76116738 q^{59} + 34059450 q^{61} + 223709616 q^{62} + 100663293 q^{64} - 20396037 q^{65} - 103603884 q^{67} - 101921427 q^{68} + 135373629 q^{70} - 125718795 q^{71} - 7632642 q^{73} + 66643887 q^{74} - 203790342 q^{76} + 343269159 q^{77} - 68767890 q^{79} - 12 q^{82} - 383244663 q^{83} + 170435619 q^{85} - 71426730 q^{86} - 192774918 q^{88} - 135692730 q^{89} + 77546796 q^{91} + 1343159175 q^{92} - 44451609 q^{94} - 881099997 q^{95} + 31339344 q^{97} - 1293135102 q^{98}+O(q^{100}) $ 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{17}{18}\right)$

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 $

$2$	−7.08460	+	1.24921i	−0.442788	+	0.0780754i	−0.390597	−	0.920562i	$-0.627731\pi$
$2$	−7.08460	+	1.24921i	−0.442788	+	0.0780754i	−0.0521906	+	0.998637i	$0.516620\pi$
$3$		0			0
$3$		0			0
$4$	−191.930	+	69.8569i	−0.749727	+	0.272878i
$5$	−349.559	+	416.588i	−0.559294	+	0.666541i	−0.969397	−	0.245498i	$-0.921048\pi$
$5$	−349.559	+	416.588i	−0.559294	+	0.666541i	0.410103	+	0.912039i	$0.365493\pi$
$6$		0			0
$7$	22.4234	+	8.16143i	0.00933917	+	0.00339918i	0.346686	−	0.937981i	$-0.387307\pi$
$7$	22.4234	+	8.16143i	0.00933917	+	0.00339918i	−0.337346	+	0.941381i	$0.609529\pi$
$8$	2867.39	−	1655.49i	0.700046	−	0.404172i
$9$		0			0
$10$	1956.08	−	3388.03i	0.195608	−	0.338803i
$11$	15469.2	+	18435.5i	1.05657	+	1.25917i	0.964686	+	0.263402i	$0.0848446\pi$
$11$	15469.2	+	18435.5i	1.05657	+	1.25917i	0.0918844	+	0.995770i	$0.470711\pi$
$12$		0			0
$13$	−8798.06	+	49896.3i	−0.308045	+	1.74701i	0.300771	+	0.953696i	$0.402756\pi$
$13$	−8798.06	+	49896.3i	−0.308045	+	1.74701i	−0.608815	+	0.793312i	$0.708355\pi$
$14$	−169.056	−	29.8091i	−0.00440066	−	0.000775956i
$15$		0			0
$16$	21808.2	−	18299.3i	0.332767	−	0.279225i
$17$	37540.0	+	21673.7i	0.449468	+	0.259501i	0.707606	−	0.706608i	$-0.249775\pi$
$17$	37540.0	+	21673.7i	0.449468	+	0.259501i	−0.258137	+	0.966108i	$0.583109\pi$
$18$		0			0
$19$	−75167.3	−	130194.i	−0.576786	−	0.999023i	−0.995845	−	0.0910639i	$-0.970973\pi$
$19$	−75167.3	−	130194.i	−0.576786	−	0.999023i	0.419059	−	0.907959i	$-0.362360\pi$
$20$	37989.4	−	104375.i	0.237434	−	0.652343i
$21$		0			0
$22$	−132623.	−	111284.i	−0.566147	−	0.475054i
$23$	108972.	+	299398.i	0.389407	+	1.06989i	0.967269	+	0.253753i	$0.0816649\pi$
$23$	108972.	+	299398.i	0.389407	+	1.06989i	−0.577862	+	0.816134i	$0.696113\pi$
$24$		0			0
$25$	16477.1	+	93446.3i	0.0421814	+	0.239223i
$26$		−	364486.i		−	0.797605i
$27$		0			0
$28$	−4873.85			−0.00792940
$29$	−945594.	+	166734.i	−1.33694	+	0.235739i	−0.795988	−	0.605312i	$-0.793048\pi$
$29$	−945594.	+	166734.i	−1.33694	+	0.235739i	−0.540955	+	0.841052i	$0.681937\pi$
$30$		0			0
$31$	736394.	−	268025.i	0.797376	−	0.290221i	0.0889773	−	0.996034i	$-0.471640\pi$
$31$	736394.	−	268025.i	0.797376	−	0.290221i	0.708399	+	0.705813i	$0.249418\pi$
$32$	−676476.	+	806193.i	−0.645138	+	0.768845i
$33$		0			0
$34$	−293031.	−	106655.i	−0.219280	−	0.0798113i
$35$	−11238.2	+	6488.40i	−0.00748904	+	0.00432380i
$36$		0			0
$37$	1.21793e6	−	2.10952e6i	0.649855	−	1.12558i	−0.333303	−	0.942820i	$-0.608163\pi$
$37$	1.21793e6	−	2.10952e6i	0.649855	−	1.12558i	0.983157	−	0.182761i	$-0.0585035\pi$
$38$	695170.	+	828471.i	0.333393	+	0.397322i
$39$		0			0
$40$	−312665.	+	1.77321e6i	−0.122135	+	0.692660i
$41$	−2.52414e6	−	445074.i	−0.893261	−	0.157506i	−0.291867	−	0.956459i	$-0.594277\pi$
$41$	−2.52414e6	−	445074.i	−0.893261	−	0.157506i	−0.601394	+	0.798953i	$0.705388\pi$
$42$		0			0
$43$	−2.24939e6	+	1.88746e6i	−0.657948	+	0.552084i	−0.909471	−	0.415768i	$-0.863513\pi$
$43$	−2.24939e6	+	1.88746e6i	−0.657948	+	0.552084i	0.251523	+	0.967851i	$0.419068\pi$
$44$	−4.25687e6	−	2.45770e6i	−1.13574	−	0.655720i
$45$		0			0
$46$	−1.14603e6	−	1.98499e6i	−0.255957	−	0.443330i
$47$	569539.	−	1.56479e6i	0.116716	−	0.320676i	−0.867554	−	0.497342i	$-0.834309\pi$
$47$	569539.	−	1.56479e6i	0.116716	−	0.320676i	0.984271	+	0.176667i	$0.0565315\pi$
$48$		0			0
$49$	−4.41566e6	−	3.70518e6i	−0.765969	−	0.642724i
$50$	−233468.	−	641447.i	−0.0373548	−	0.102631i
$51$		0			0
$52$	−1.79699e6	−	1.01912e7i	−0.245771	−	1.39384i
$53$			3.88995e6i			0.492993i	0.969144	+	0.246496i	$0.0792793\pi$
$53$			3.88995e6i			0.492993i	−0.969144	+	0.246496i	$0.920721\pi$
$54$		0			0
$55$	−1.30874e7			−1.43022
$56$	77807.6	−	13719.6i	0.00791170	−	0.00139505i
$57$		0			0
$58$	6.49088e6	−	2.36249e6i	0.573577	−	0.208765i
$59$	−6.87370e6	+	8.19175e6i	−0.567260	+	0.676034i	−0.971066	−	0.238810i	$-0.923243\pi$
$59$	−6.87370e6	+	8.19175e6i	−0.567260	+	0.676034i	0.403806	+	0.914845i	$0.367687\pi$
$60$		0			0
$61$	−1.49222e7	−	5.43124e6i	−1.07774	−	0.392265i	−0.258673	−	0.965965i	$-0.583285\pi$
$61$	−1.49222e7	−	5.43124e6i	−1.07774	−	0.392265i	−0.819065	+	0.573700i	$0.805508\pi$
$62$	−4.88224e6	+	2.81876e6i	−0.330409	+	0.190762i
$63$		0			0
$64$	141478.	−	245047.i	0.00843275	−	0.0146060i
$65$	−1.77108e7	−	2.11069e7i	−0.992165	−	1.18242i
$66$		0			0
$67$	1.45408e6	−	8.24651e6i	0.0721588	−	0.409233i	−0.927237	−	0.374475i	$-0.877823\pi$
$67$	1.45408e6	−	8.24651e6i	0.0721588	−	0.409233i	0.999396	−	0.0347579i	$-0.0110660\pi$
$68$	−8.71913e6	−	1.53742e6i	−0.407791	−	0.0719045i
$69$		0			0
$70$	71513.1	−	60006.6i	0.00297847	−	0.00249924i
$71$	9.42132e6	+	5.43940e6i	0.370747	+	0.214051i	0.673785	−	0.738927i	$-0.264667\pi$
$71$	9.42132e6	+	5.43940e6i	0.370747	+	0.214051i	−0.303037	+	0.952979i	$0.598001\pi$
$72$		0			0
$73$	1.18791e7	+	2.05752e7i	0.418305	+	0.724525i	0.995769	−	0.0918908i	$-0.0292911\pi$
$73$	1.18791e7	+	2.05752e7i	0.418305	+	0.724525i	−0.577464	+	0.816416i	$0.695958\pi$
$74$	−5.99334e6	+	1.64666e7i	−0.199867	+	0.549131i
$75$		0			0
$76$	2.35218e7	+	1.97371e7i	0.705044	+	0.591602i
$77$	196412.	+	539638.i	0.00558734	+	0.0153511i
$78$		0			0
$79$	−7.07994e6	−	4.01523e7i	−0.181770	−	1.03087i	−0.930036	−	0.367468i	$-0.880225\pi$
$79$	−7.07994e6	−	4.01523e7i	−0.181770	−	1.03087i	0.748266	−	0.663398i	$-0.230886\pi$
$80$			1.54817e7i			0.377972i
$81$		0			0
$82$	1.84385e7			0.407822
$83$	5.20151e7	−	9.17167e6i	1.09602	−	0.193257i	0.403729	−	0.914879i	$-0.367714\pi$
$83$	5.20151e7	−	9.17167e6i	1.09602	−	0.193257i	0.692288	+	0.721621i	$0.256603\pi$
$84$		0			0
$85$	−2.21515e7	+	8.06248e6i	−0.424353	+	0.154452i
$86$	1.35782e7	−	1.61819e7i	0.248227	−	0.295825i
$87$		0			0
$88$	7.48761e7	+	2.72527e7i	1.24857	+	0.454442i
$89$	−3.60266e7	+	2.07999e7i	−0.574199	+	0.331514i	−0.758825	−	0.651295i	$-0.774226\pi$
$89$	−3.60266e7	+	2.07999e7i	−0.574199	+	0.331514i	0.184625	+	0.982809i	$0.440893\pi$
$90$		0			0
$91$	−604507.	+	1.04704e6i	−0.00881528	+	0.0152685i
$92$	−4.18301e7	−	4.98511e7i	−0.583898	−	0.695863i
$93$		0			0
$94$	−2.08020e6	+	1.17974e7i	−0.0266437	+	0.151104i
$95$	8.05126e7	+	1.41965e7i	0.988483	+	0.174296i
$96$		0			0
$97$	−7.44489e7	+	6.24700e7i	−0.840952	+	0.705642i	−0.957778	−	0.287510i	$-0.907172\pi$
$97$	−7.44489e7	+	6.24700e7i	−0.840952	+	0.705642i	0.116826	+	0.993152i	$0.462728\pi$
$98$	3.59117e7	+	2.07336e7i	0.389343	+	0.224787i
$99$		0			0
$100$	−9.69032e6	−	1.67841e7i	−0.0969032	−	0.167841i
$101$	2.31756e7	−	6.36744e7i	0.222713	−	0.611898i	−0.777135	−	0.629334i	$-0.783328\pi$
$101$	2.31756e7	−	6.36744e7i	0.222713	−	0.611898i	0.999848	+	0.0174353i	$0.00555010\pi$
$102$		0			0
$103$	8.20157e7	+	6.88194e7i	0.728699	+	0.611451i	0.929777	−	0.368124i	$-0.120000\pi$
$103$	8.20157e7	+	6.88194e7i	0.728699	+	0.611451i	−0.201077	+	0.979575i	$0.564444\pi$
$104$	5.73752e7	+	1.57637e8i	0.490446	+	1.34749i
$105$		0			0
$106$	−4.85935e6	−	2.75588e7i	−0.0384906	−	0.218291i
$107$		−	6.59985e7i		−	0.503499i	−0.967792	−	0.251750i	$-0.918994\pi$
$107$		−	6.59985e7i		−	0.503499i	0.967792	−	0.251750i	$-0.0810060\pi$
$108$		0			0
$109$	1.44628e8			1.02458			0.512290	−	0.858813i	$-0.328797\pi$
$109$	1.44628e8			1.02458			0.512290	+	0.858813i	$0.328797\pi$
$110$	9.27193e7	−	1.63489e7i	0.633285	−	0.111665i
$111$		0			0
$112$	638362.	−	232345.i	0.00405691	−	0.00147659i
$113$	−4.25133e7	+	5.06654e7i	−0.260742	+	0.310740i	−0.880494	−	0.474058i	$-0.842789\pi$
$113$	−4.25133e7	+	5.06654e7i	−0.260742	+	0.310740i	0.619752	+	0.784798i	$0.287233\pi$
$114$		0			0
$115$	−1.62818e8	−	5.92609e7i	−0.930917	−	0.338826i
$116$	1.69841e8	−	9.80575e7i	0.938015	−	0.541563i
$117$		0			0
$118$	3.84642e7	−	6.66220e7i	0.198394	−	0.343629i
$119$	664884.	+	792378.i	0.00331557	+	0.00395134i
$120$		0			0
$121$	−6.33482e7	+	3.59265e8i	−0.295524	+	1.67600i
$122$	1.12503e8	+	1.98372e7i	0.507836	+	0.0895451i
$123$		0			0
$124$	−1.22613e8	+	1.02884e8i	−0.518620	+	0.435173i
$125$	−2.28657e8	−	1.32015e8i	−0.936579	−	0.540734i
$126$		0			0
$127$	−8.82421e7	−	1.52840e8i	−0.339204	−	0.587519i	0.645079	−	0.764116i	$-0.276824\pi$
$127$	−8.82421e7	−	1.52840e8i	−0.339204	−	0.587519i	−0.984283	+	0.176597i	$0.943491\pi$
$128$	9.14498e7	−	2.51256e8i	0.340677	−	0.936003i
$129$		0			0
$130$	1.51841e8	+	1.27409e8i	0.531636	+	0.446096i
$131$	1.40625e7	+	3.86363e7i	0.0477503	+	0.131193i	0.961275	−	0.275589i	$-0.0888730\pi$
$131$	1.40625e7	+	3.86363e7i	0.0477503	+	0.131193i	−0.913525	+	0.406782i	$0.866651\pi$
$132$		0			0
$133$	−622937.	−	3.53285e6i	−0.00199085	−	0.0112906i
$134$			6.02397e7i			0.186837i
$135$		0			0
$136$	1.43522e8			0.419531
$137$	3.79891e8	−	6.69850e7i	1.07839	−	0.190150i	0.393888	−	0.919159i	$-0.371130\pi$
$137$	3.79891e8	−	6.69850e7i	1.07839	−	0.190150i	0.684504	+	0.729009i	$0.260019\pi$
$138$		0			0
$139$	4.70756e8	−	1.71341e8i	1.26106	−	0.458989i	0.376938	−	0.926239i	$-0.376977\pi$
$139$	4.70756e8	−	1.71341e8i	1.26106	−	0.458989i	0.884126	+	0.467249i	$0.154755\pi$
$140$	1.70370e6	−	2.03039e6i	0.00443487	−	0.00528527i
$141$		0			0
$142$	−7.35412e7	−	2.67668e7i	−0.180875	−	0.0658330i
$143$	−1.05596e9	+	6.09661e8i	−2.52525	+	1.45796i
$144$		0			0
$145$	2.61082e8	−	4.52207e8i	0.590615	−	1.02297i
$146$	−1.09862e8	−	1.30928e8i	−0.241788	−	0.288152i
$147$		0			0
$148$	−8.63934e7	+	4.89962e8i	−0.180067	+	1.02121i
$149$	1.35585e8	+	2.39072e7i	0.275084	+	0.0485048i	0.309488	−	0.950903i	$-0.399842\pi$
$149$	1.35585e8	+	2.39072e7i	0.275084	+	0.0485048i	−0.0344041	+	0.999408i	$0.510953\pi$
$150$		0			0
$151$	−2.29217e8	+	1.92336e8i	−0.440900	+	0.369959i	−0.836046	−	0.548659i	$-0.815138\pi$
$151$	−2.29217e8	+	1.92336e8i	−0.440900	+	0.369959i	0.395146	+	0.918618i	$0.370694\pi$
$152$	−4.31068e8	−	2.48877e8i	−0.807554	−	0.466241i
$153$		0			0
$154$	−2.06562e6	−	3.57776e6i	−0.00367255	−	0.00636104i
$155$	−1.45757e8	+	4.00463e8i	−0.252524	+	0.693803i
$156$		0			0
$157$	−6.09281e8	−	5.11248e8i	−1.00281	−	0.841459i	−0.0154401	−	0.999881i	$-0.504915\pi$
$157$	−6.09281e8	−	5.11248e8i	−1.00281	−	0.841459i	−0.987372	+	0.158422i	$0.949359\pi$
$158$	1.00317e8	+	2.75619e8i	0.160971	+	0.442263i
$159$		0			0
$160$	−9.93821e7	−	5.63624e8i	−0.151645	−	0.860022i
$161$			7.60288e6i			0.0113155i
$162$		0			0
$163$	5.37083e8			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$163$	5.37083e8			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$164$	5.15551e8	−	9.09055e7i	0.712682	−	0.125665i
$165$		0			0
$166$	−3.57049e8	+	1.29955e8i	−0.470214	+	0.171144i
$167$	−1.24169e8	+	1.47979e8i	−0.159642	+	0.190254i	−0.839936	−	0.542685i	$-0.817408\pi$
$167$	−1.24169e8	+	1.47979e8i	−0.159642	+	0.190254i	0.680294	+	0.732939i	$0.261852\pi$
$168$		0			0
$169$	−1.64570e9	−	5.98985e8i	−2.01745	−	0.734293i
$170$	1.46863e8	−	8.47913e7i	0.175839	−	0.101521i
$171$		0			0
$172$	2.99874e8	−	5.19397e8i	0.342630	−	0.593452i
$173$	−8.68042e8	−	1.03449e9i	−0.969072	−	1.15490i	−0.987903	−	0.155073i	$-0.950439\pi$
$173$	−8.68042e8	−	1.03449e9i	−0.969072	−	1.15490i	0.0188306	−	0.999823i	$-0.494006\pi$
$174$		0			0
$175$	−393184.	+	2.22986e6i	−0.000419221	+	0.00237752i
$176$	6.74714e8	+	1.18970e8i	0.703184	+	0.123990i
$177$		0			0
$178$	2.29250e8	−	1.92364e8i	0.228365	−	0.191621i
$179$	−2.84475e8	−	1.64242e8i	−0.277097	−	0.159982i	0.355011	−	0.934862i	$-0.384477\pi$
$179$	−2.84475e8	−	1.64242e8i	−0.277097	−	0.159982i	−0.632109	+	0.774880i	$0.717810\pi$
$180$		0			0
$181$	−4.80709e8	−	8.32613e8i	−0.447887	−	0.775762i	0.550362	−	0.834926i	$-0.314490\pi$
$181$	−4.80709e8	−	8.32613e8i	−0.447887	−	0.775762i	−0.998248	+	0.0591641i	$0.981156\pi$
$182$	2.97473e6	−	8.17300e6i	0.00271120	−	0.00744897i
$183$		0			0
$184$	8.08115e8	+	6.78089e8i	0.705021	+	0.591583i
$185$	4.53062e8	+	1.24478e9i	0.386786	+	1.06269i
$186$		0			0
$187$	1.81149e8	+	1.02735e9i	0.148139	+	0.840138i
$188$			3.40117e8i			0.272269i
$189$		0			0
$190$	−5.88134e8			−0.451296
$191$	−1.19301e9	+	2.10360e8i	−0.896419	+	0.158063i	−0.602831	−	0.797869i	$-0.705961\pi$
$191$	−1.19301e9	+	2.10360e8i	−0.896419	+	0.158063i	−0.293588	+	0.955932i	$0.594850\pi$
$192$		0			0
$193$	−1.71398e9	+	6.23836e8i	−1.23531	+	0.449615i	−0.875412	−	0.483377i	$-0.839410\pi$
$193$	−1.71398e9	+	6.23836e8i	−1.23531	+	0.449615i	−0.359896	+	0.932992i	$0.617188\pi$
$194$	4.49403e8	−	5.35577e8i	0.317270	−	0.378107i
$195$		0			0
$196$	1.10633e9	+	4.02671e8i	0.749653	+	0.272851i
$197$	−1.52700e9	+	8.81617e8i	−1.01385	+	0.585349i	−0.912318	−	0.409483i	$-0.865709\pi$
$197$	−1.52700e9	+	8.81617e8i	−1.01385	+	0.585349i	−0.101536	+	0.994832i	$0.532376\pi$
$198$		0			0
$199$	7.74048e8	−	1.34069e9i	0.493578	−	0.854902i	−0.506395	−	0.862302i	$-0.669022\pi$
$199$	7.74048e8	−	1.34069e9i	0.493578	−	0.854902i	0.999973	+	0.00739959i	$0.00235539\pi$
$200$	2.01945e8	+	2.40669e8i	0.126216	+	0.150418i
$201$		0			0
$202$	−8.46474e7	+	4.80059e8i	−0.0508403	+	0.288330i
$203$	−2.25642e7	−	3.97867e6i	−0.0132873	−	0.00234290i
$204$		0			0
$205$	1.06775e9	−	8.95948e8i	0.604580	−	0.507303i
$206$	−6.67019e8	−	3.85103e8i	−0.370398	−	0.213850i
$207$		0			0
$208$	7.21197e8	+	1.24915e9i	0.385301	+	0.667361i
$209$	1.23741e9	−	3.39975e9i	0.648526	−	1.78181i
$210$		0			0
$211$	2.15590e8	+	1.80902e8i	0.108768	+	0.0912668i	0.695549	−	0.718478i	$-0.255161\pi$
$211$	2.15590e8	+	1.80902e8i	0.108768	+	0.0912668i	−0.586782	+	0.809745i	$0.699605\pi$
$212$	−2.71740e8	−	7.46599e8i	−0.134527	−	0.369610i
$213$		0			0
$214$	8.24458e7	+	4.67573e8i	0.0393109	+	0.222943i
$215$		−	1.59685e9i		−	0.747326i
$216$		0			0
$217$	1.86999e7			0.00843335
$218$	−1.02463e9	+	1.80670e8i	−0.453671	+	0.0799945i
$219$		0			0
$220$	2.51187e9	−	9.14248e8i	1.07228	−	0.390277i
$221$	−1.41172e9	+	1.68242e9i	−0.591806	+	0.705287i
$222$		0			0
$223$	−3.57572e9	−	1.30146e9i	−1.44592	−	0.526272i	−0.504472	−	0.863428i	$-0.668313\pi$
$223$	−3.57572e9	−	1.30146e9i	−1.44592	−	0.526272i	−0.941449	+	0.337156i	$0.890535\pi$
$224$	−2.17486e7	+	1.25565e7i	−0.00863850	+	0.00498744i
$225$		0			0
$226$	2.37898e8	−	4.12052e8i	0.0911922	−	0.157950i
$227$	2.91521e9	+	3.47421e9i	1.09791	+	1.30844i	0.947479	+	0.319818i	$0.103622\pi$
$227$	2.91521e9	+	3.47421e9i	1.09791	+	1.30844i	0.150431	+	0.988621i	$0.451934\pi$
$228$		0			0
$229$	−4.94015e8	+	2.80170e9i	−0.179638	+	1.01878i	0.753015	+	0.658004i	$0.228599\pi$
$229$	−4.94015e8	+	2.80170e9i	−0.179638	+	1.01878i	−0.932653	+	0.360775i	$0.882512\pi$
$230$	1.22753e9	+	2.16447e8i	0.438652	+	0.0773463i
$231$		0			0
$232$	−2.43536e9	+	2.04351e9i	−0.840643	+	0.705383i
$233$	3.07386e9	+	1.77469e9i	1.04294	+	0.602143i	0.920665	−	0.390353i	$-0.127647\pi$
$233$	3.07386e9	+	1.77469e9i	1.04294	+	0.602143i	0.122277	+	0.992496i	$0.460980\pi$
$234$		0			0
$235$	4.52787e8	+	7.84251e8i	0.148465	+	0.257148i
$236$	7.47020e8	−	2.05242e9i	0.240815	−	0.661635i
$237$		0			0
$238$	−5.70029e6	−	4.78311e6i	−0.00177660	−	0.00149074i
$239$	2.51801e8	+	6.91818e8i	0.0771731	+	0.212031i	0.972280	−	0.233821i	$-0.0751229\pi$
$239$	2.51801e8	+	6.91818e8i	0.0771731	+	0.212031i	−0.895107	+	0.445852i	$0.852901\pi$
$240$		0			0
$241$	−2.07614e8	−	1.17744e9i	−0.0615445	−	0.349036i	−0.999993	−	0.00361833i	$-0.998848\pi$
$241$	−2.07614e8	−	1.17744e9i	−0.0615445	−	0.349036i	0.938449	−	0.345418i	$-0.112263\pi$
$242$		−	2.62439e9i		−	0.765185i
$243$		0			0
$244$	3.24343e9			0.915051
$245$	3.08707e9	−	5.44333e8i	0.856804	−	0.151078i
$246$		0			0
$247$	7.15751e9	−	2.60512e9i	1.92298	−	0.699906i
$248$	1.66781e9	−	1.98762e9i	0.440901	−	0.525445i
$249$		0			0
$250$	1.78486e9	+	6.49635e8i	0.456924	+	0.166307i
$251$	1.64288e9	−	9.48514e8i	0.413914	−	0.238973i	−0.278556	−	0.960420i	$-0.589856\pi$
$251$	1.64288e9	−	9.48514e8i	0.413914	−	0.238973i	0.692470	+	0.721447i	$0.256523\pi$
$252$		0			0
$253$	−3.83385e9	+	6.64042e9i	−0.935735	+	1.62074i
$254$	8.16089e8	+	9.72577e8i	0.196066	+	0.233663i
$255$		0			0
$256$	−3.46593e8	+	1.96563e9i	−0.0806975	+	0.457658i
$257$	−1.74694e9	−	3.08032e8i	−0.400447	−	0.0706095i	−0.0302019	−	0.999544i	$-0.509615\pi$
$257$	−1.74694e9	−	3.08032e8i	−0.400447	−	0.0706095i	−0.370245	+	0.928934i	$0.620726\pi$
$258$		0			0
$259$	4.45268e7	−	3.73624e7i	0.00989516	−	0.00830302i
$260$	4.87369e9	+	2.81383e9i	1.06651	+	0.615749i
$261$		0			0
$262$	−1.47892e8	−	2.56156e8i	−0.0313862	−	0.0543624i
$263$	−9.56007e8	+	2.62661e9i	−0.199819	+	0.549000i	−0.998616	−	0.0526024i	$-0.983248\pi$
$263$	−9.56007e8	+	2.62661e9i	−0.199819	+	0.549000i	0.798796	+	0.601602i	$0.205471\pi$
$264$		0			0
$265$	−1.62051e9	−	1.35977e9i	−0.328600	−	0.275728i
$266$	8.82653e6	+	2.42507e7i	0.00176304	+	0.00484392i
$267$		0			0
$268$	2.96993e8	+	1.68433e9i	0.0575714	+	0.326504i
$269$			3.73774e9i			0.713839i	0.934135	+	0.356919i	$0.116173\pi$
$269$			3.73774e9i			0.713839i	−0.934135	+	0.356919i	$0.883827\pi$
$270$		0			0
$271$	−4.23327e9			−0.784873			−0.392436	−	0.919779i	$-0.628368\pi$
$271$	−4.23327e9			−0.784873			−0.392436	+	0.919779i	$0.628368\pi$
$272$	1.21530e9	−	2.14290e8i	0.222027	−	0.0391494i
$273$		0			0
$274$	−2.60770e9	+	9.49124e8i	−0.462653	+	0.168392i
$275$	−1.46784e9	+	1.74931e9i	−0.256655	+	0.305869i
$276$		0			0
$277$	9.61877e9	+	3.50095e9i	1.63381	+	0.594657i	0.985940	−	0.167097i	$-0.0534394\pi$
$277$	9.61877e9	+	3.50095e9i	1.63381	+	0.594657i	0.647866	+	0.761754i	$0.275662\pi$
$278$	−3.12108e9	+	1.80196e9i	−0.522548	+	0.301693i
$279$		0			0
$280$	−2.14829e7	+	3.72095e7i	−0.00349512	+	0.00605372i
$281$	−3.70155e9	−	4.41134e9i	−0.593688	−	0.707530i	0.382622	−	0.923905i	$-0.375021\pi$
$281$	−3.70155e9	−	4.41134e9i	−0.593688	−	0.707530i	−0.976310	+	0.216375i	$0.930577\pi$
$282$		0			0
$283$	5.45231e8	−	3.09216e9i	0.0850031	−	0.482077i	−0.912353	−	0.409405i	$-0.865736\pi$
$283$	5.45231e8	−	3.09216e9i	0.0850031	−	0.482077i	0.997356	−	0.0726717i	$-0.0231525\pi$
$284$	−2.18821e9	−	3.85841e8i	−0.336369	−	0.0593110i
$285$		0			0
$286$	6.71950e9	−	5.63833e9i	1.00432	−	0.842726i
$287$	−5.29673e7	−	3.05807e7i	−0.00780693	−	0.00450733i
$288$		0			0
$289$	−2.54838e9	−	4.41392e9i	−0.365319	−	0.632751i
$290$	−1.28476e9	+	3.52985e9i	−0.181648	+	0.499073i
$291$		0			0
$292$	−3.71728e9	−	3.11917e9i	−0.511322	−	0.429050i
$293$	−2.74172e9	−	7.53280e9i	−0.372008	−	1.02208i	−0.974584	−	0.224022i	$-0.928081\pi$
$293$	−2.74172e9	−	7.53280e9i	−0.372008	−	1.02208i	0.602576	−	0.798061i	$-0.294141\pi$
$294$		0			0
$295$	−1.00982e9	−	5.72700e9i	−0.133339	−	0.756204i
$296$		−	8.06509e9i		−	1.05061i
$297$		0			0
$298$	−9.90429e8			−0.125591
$299$	−1.58976e10	+	2.80318e9i	−1.98906	+	0.350724i
$300$		0			0
$301$	−6.58433e7	+	2.39650e7i	−0.00802132	+	0.00291952i
$302$	1.38365e9	−	1.64897e9i	0.166340	−	0.198237i
$303$		0			0
$304$	−4.02172e9	−	1.46379e9i	−0.470888	−	0.171389i
$305$	7.47878e9	−	4.31787e9i	0.864234	−	0.498966i
$306$		0			0
$307$	−2.44162e9	+	4.22901e9i	−0.274868	+	0.476086i	−0.970102	−	0.242698i	$-0.921968\pi$
$307$	−2.44162e9	+	4.22901e9i	−0.274868	+	0.476086i	0.695234	+	0.718784i	$0.255301\pi$
$308$	−7.53948e7	−	8.98520e7i	−0.00837797	−	0.00998447i
$309$		0			0
$310$	5.32367e8	−	3.01921e9i	0.0576454	−	0.326923i
$311$	−1.23151e10	−	2.17148e9i	−1.31643	−	0.232121i	−0.529048	−	0.848592i	$-0.677451\pi$
$311$	−1.23151e10	−	2.17148e9i	−1.31643	−	0.232121i	−0.787378	+	0.616471i	$0.788562\pi$
$312$		0			0
$313$	−7.17480e9	+	6.02037e9i	−0.747536	+	0.627258i	−0.934850	−	0.355043i	$-0.884466\pi$
$313$	−7.17480e9	+	6.02037e9i	−0.747536	+	0.627258i	0.187314	+	0.982300i	$0.440022\pi$
$314$	4.95517e9	+	2.86087e9i	0.509730	+	0.294293i
$315$		0			0
$316$	4.16377e9	+	7.21186e9i	0.417579	+	0.723268i
$317$	−3.76140e9	+	1.03344e10i	−0.372488	+	1.02340i	0.601908	+	0.798565i	$0.294407\pi$
$317$	−3.76140e9	+	1.03344e10i	−0.372488	+	1.02340i	−0.974396	+	0.224838i	$0.927815\pi$
$318$		0			0
$319$	−1.77015e10	−	1.48533e10i	−1.70941	−	1.43437i
$320$	5.26288e7	+	1.44597e8i	0.00501908	+	0.0137898i
$321$		0			0
$322$	−9.49757e6	−	5.38634e7i	−0.000883464	−	0.00501038i
$323$		−	6.51663e9i		−	0.598705i
$324$		0			0
$325$	−4.80759e9			−0.430917
$326$	−3.80502e9	+	6.70928e8i	−0.336889	+	0.0594026i
$327$		0			0
$328$	−7.97451e9	+	2.90248e9i	−0.688983	+	0.250769i
$329$	2.55419e7	−	3.04397e7i	0.00218007	−	0.00259810i
$330$		0			0
$331$	1.70860e10	+	6.21880e9i	1.42341	+	0.518077i	0.935034	−	0.354559i	$-0.115369\pi$
$331$	1.70860e10	+	6.21880e9i	1.42341	+	0.518077i	0.488371	+	0.872636i	$0.337591\pi$
$332$	−9.34257e9	+	5.39393e9i	−0.768978	+	0.443970i
$333$		0			0
$334$	6.94831e8	−	1.20348e9i	0.0558333	−	0.0967061i
$335$	2.92711e9	+	3.48839e9i	0.232413	+	0.276979i
$336$		0			0
$337$	3.85980e9	−	2.18900e10i	0.299257	−	1.69717i	−0.350118	−	0.936705i	$-0.613859\pi$
$337$	3.85980e9	−	2.18900e10i	0.299257	−	1.69717i	0.649376	−	0.760468i	$-0.275030\pi$
$338$	1.24074e10	+	2.18776e9i	0.950634	+	0.167622i
$339$		0			0
$340$	3.68832e9	−	3.09487e9i	0.276002	−	0.231593i
$341$	1.63326e10	+	9.42966e9i	1.20792	+	0.697394i
$342$		0			0
$343$	−1.37555e8	−	2.38253e8i	−0.00993805	−	0.0172132i
$344$	−3.32521e9	+	9.13593e9i	−0.237457	+	0.652408i
$345$		0			0
$346$	7.44203e9	+	6.24460e9i	0.519262	+	0.435713i
$347$	−5.16122e9	−	1.41803e10i	−0.355987	−	0.978067i	−0.980408	−	0.196979i	$-0.936887\pi$
$347$	−5.16122e9	−	1.41803e10i	−0.355987	−	0.978067i	0.624421	−	0.781088i	$-0.285335\pi$
$348$		0			0
$349$	9.91134e8	+	5.62100e9i	0.0668083	+	0.378889i	0.999819	+	0.0190395i	$0.00606082\pi$
$349$	9.91134e8	+	5.62100e9i	0.0668083	+	0.378889i	−0.933010	+	0.359849i	$0.882828\pi$
$350$		−	1.62888e7i		−	0.00108547i
$351$		0			0
$352$	−2.53272e10			−1.64974
$353$	1.45465e10	−	2.56494e9i	0.936827	−	0.165188i	0.315666	−	0.948870i	$-0.397772\pi$
$353$	1.45465e10	−	2.56494e9i	0.936827	−	0.165188i	0.621162	+	0.783683i	$0.286661\pi$
$354$		0			0
$355$	−5.55930e9	+	2.02342e9i	−0.350031	+	0.127401i
$356$	5.46157e9	−	6.50884e9i	0.340030	−	0.405232i
$357$		0			0
$358$	2.22057e9	+	8.08220e8i	0.135186	+	0.0492037i
$359$	−2.51153e10	+	1.45003e10i	−1.51203	+	0.872972i	−0.512131	+	0.858907i	$0.671144\pi$
$359$	−2.51153e10	+	1.45003e10i	−1.51203	+	0.872972i	−0.999901	+	0.0140646i	$0.995523\pi$
$360$		0			0
$361$	−2.80848e9	+	4.86443e9i	−0.165365	+	0.286420i
$362$	4.44574e9	+	5.29823e9i	0.258887	+	0.308529i
$363$		0			0
$364$	4.28805e7	−	2.43187e8i	0.00244261	−	0.0138527i
$365$	−1.27239e10	−	2.24356e9i	−0.716881	−	0.126405i
$366$		0			0
$367$	1.36601e9	−	1.14621e9i	0.0752988	−	0.0631832i	−0.604361	−	0.796710i	$-0.706572\pi$
$367$	1.36601e9	−	1.14621e9i	0.0752988	−	0.0631832i	0.679660	+	0.733527i	$0.262127\pi$
$368$	7.85526e9	+	4.53524e9i	0.428321	+	0.247291i
$369$		0			0
$370$	−4.76475e9	−	8.25279e9i	−0.254234	−	0.440346i
$371$	−3.17476e7	+	8.72257e7i	−0.00167577	+	0.00460414i
$372$		0			0
$373$	9.68547e9	+	8.12708e9i	0.500363	+	0.419855i	0.857723	−	0.514112i	$-0.171878\pi$
$373$	9.68547e9	+	8.12708e9i	0.500363	+	0.419855i	−0.357360	+	0.933967i	$0.616323\pi$
$374$	−2.56674e9	−	7.05205e9i	−0.131188	−	0.360437i
$375$		0			0
$376$	−9.57409e8	−	5.42974e9i	−0.0479012	−	0.271661i
$377$		−	4.86486e10i		−	2.40827i
$378$		0			0
$379$	2.90826e10			1.40954			0.704768	−	0.709438i	$-0.251051\pi$
$379$	2.90826e10			1.40954			0.704768	+	0.709438i	$0.251051\pi$
$380$	−1.64445e10	+	2.89961e9i	−0.788654	+	0.139061i
$381$		0			0
$382$	8.18923e9	−	2.98064e9i	0.384583	−	0.139977i
$383$	−3.45256e9	+	4.11460e9i	−0.160452	+	0.191220i	−0.840281	−	0.542152i	$-0.817610\pi$
$383$	−3.45256e9	+	4.11460e9i	−0.160452	+	0.191220i	0.679828	+	0.733371i	$0.262054\pi$
$384$		0			0
$385$	−2.93464e8	−	1.06812e8i	−0.0133571	−	0.00486159i
$386$	1.13635e10	−	6.56074e9i	0.511876	−	0.295531i
$387$		0			0
$388$	9.92502e9	−	1.71906e10i	0.437930	−	0.758517i
$389$	1.48272e10	+	1.76703e10i	0.647530	+	0.771697i	0.985539	−	0.169446i	$-0.0541979\pi$
$389$	1.48272e10	+	1.76703e10i	0.647530	+	0.771697i	−0.338009	+	0.941143i	$0.609753\pi$
$390$		0			0
$391$	−2.39827e9	+	1.36013e10i	−0.102610	+	0.581931i
$392$	−1.87953e10	−	3.31412e9i	−0.795984	−	0.140354i
$393$		0			0
$394$	9.71690e9	−	8.15345e9i	0.403221	−	0.338342i
$395$	1.92018e10	+	1.10862e10i	0.788778	+	0.455401i
$396$		0			0
$397$	1.33126e10	+	2.30581e10i	0.535921	+	0.928242i	0.999118	+	0.0419866i	$0.0133687\pi$
$397$	1.33126e10	+	2.30581e10i	0.535921	+	0.928242i	−0.463198	+	0.886255i	$0.653298\pi$
$398$	−3.80903e9	+	1.04652e10i	−0.151803	+	0.417077i
$399$		0			0
$400$	2.06934e9	+	1.73638e9i	0.0808335	+	0.0678274i
$401$	6.68098e9	+	1.83559e10i	0.258382	+	0.709900i	0.999268	+	0.0382681i	$0.0121841\pi$
$401$	6.68098e9	+	1.83559e10i	0.258382	+	0.709900i	−0.740885	+	0.671632i	$0.765594\pi$
$402$		0			0
$403$	6.89464e9	+	3.91014e10i	0.261391	+	1.48242i
$404$			1.38400e10i			0.519531i
$405$		0			0
$406$	1.64829e8			0.00606636
$407$	5.77306e10	−	1.01795e10i	2.10392	−	0.370977i
$408$		0			0
$409$	2.91511e10	−	1.06101e10i	1.04174	−	0.379164i	0.236203	−	0.971704i	$-0.424097\pi$
$409$	2.91511e10	−	1.06101e10i	1.04174	−	0.379164i	0.805541	+	0.592539i	$0.201875\pi$
$410$	−6.44536e9	+	7.68128e9i	−0.228093	+	0.271830i
$411$		0			0
$412$	−2.05488e10	−	7.47915e9i	−0.713178	−	0.259575i
$413$	−2.20988e8	+	1.27587e8i	−0.00759570	+	0.00438538i
$414$		0			0
$415$	−1.43615e10	+	2.48749e10i	−0.484182	+	0.838628i
$416$	−3.42744e10	−	4.08466e10i	−1.14445	−	1.36390i
$417$		0			0
$418$	−4.51955e9	+	2.56317e10i	−0.148044	+	0.839598i
$419$	5.06009e10	+	8.92230e9i	1.64173	+	0.289481i	0.916802	−	0.399342i	$-0.130761\pi$
$419$	5.06009e10	+	8.92230e9i	1.64173	+	0.289481i	0.724929	+	0.688824i	$0.241873\pi$
$420$		0			0
$421$	−4.57824e9	+	3.84160e9i	−0.145737	+	0.122288i	−0.712741	−	0.701427i	$-0.752547\pi$
$421$	−4.57824e9	+	3.84160e9i	−0.145737	+	0.122288i	0.567004	+	0.823715i	$0.308102\pi$
$422$	−1.75335e9	−	1.01230e9i	−0.0552866	−	0.0319197i
$423$		0			0
$424$	6.43976e9	+	1.11540e10i	0.199254	+	0.345118i
$425$	−1.40678e9	+	3.86510e9i	−0.0431192	+	0.118469i
$426$		0			0
$427$	−2.90279e8	−	2.43573e8i	−0.00873181	−	0.00732686i
$428$	4.61045e9	+	1.26671e10i	0.137394	+	0.377487i
$429$		0			0
$430$	1.99480e9	+	1.13130e10i	0.0583478	+	0.330907i
$431$		−	2.95889e10i		−	0.857473i	−0.903430	−	0.428736i	$-0.858959\pi$
$431$		−	2.95889e10i		−	0.857473i	0.903430	−	0.428736i	$-0.141041\pi$
$432$		0			0
$433$	−6.02354e9			−0.171356			−0.0856782	−	0.996323i	$-0.527306\pi$
$433$	−6.02354e9			−0.171356			−0.0856782	+	0.996323i	$0.527306\pi$
$434$	−1.32481e8	+	2.33600e7i	−0.00373418	+	0.000658437i
$435$		0			0
$436$	−2.77584e10	+	1.01032e10i	−0.768155	+	0.279586i
$437$	3.07886e10	−	3.66924e10i	0.844237	−	1.00612i
$438$		0			0
$439$	3.27196e9	+	1.19090e9i	0.0880948	+	0.0320639i	0.385692	−	0.922628i	$-0.373963\pi$
$439$	3.27196e9	+	1.19090e9i	0.0880948	+	0.0320639i	−0.297597	+	0.954692i	$0.596185\pi$
$440$	−3.75268e10	+	2.16661e10i	−1.00122	+	0.578056i
$441$		0			0
$442$	7.89978e9	−	1.36828e10i	0.206979	−	0.358498i
$443$	−9.32868e9	−	1.11175e10i	−0.242217	−	0.288664i	0.631216	−	0.775607i	$-0.282556\pi$
$443$	−9.32868e9	−	1.11175e10i	−0.242217	−	0.288664i	−0.873433	+	0.486944i	$0.838112\pi$
$444$		0			0
$445$	3.92840e9	−	2.22790e10i	0.100179	−	0.568141i
$446$	2.69584e10	+	4.75349e9i	0.681325	+	0.120136i
$447$		0			0
$448$	5.17235e6	−	4.34012e6i	0.000128403	−	0.000107743i
$449$	5.23161e10	+	3.02047e10i	1.28721	+	0.743171i	0.978156	−	0.207873i	$-0.0666540\pi$
$449$	5.23161e10	+	3.02047e10i	1.28721	+	0.743171i	0.309055	+	0.951044i	$0.399987\pi$
$450$		0			0
$451$	−3.08414e10	−	5.34189e10i	−0.745466	−	1.29119i
$452$	4.62026e9	−	1.26941e10i	0.110691	−	0.304121i
$453$		0			0
$454$	−2.49931e10	−	2.09717e10i	−0.588298	−	0.493641i
$455$	−2.24872e8	−	6.17832e8i	−0.00524675	−	0.0144153i
$456$		0			0
$457$	−2.85275e9	−	1.61788e10i	−0.0654033	−	0.370920i	−0.999889	−	0.0149190i	$-0.995251\pi$
$457$	−2.85275e9	−	1.61788e10i	−0.0654033	−	0.370920i	0.934485	−	0.356001i	$-0.115860\pi$
$458$		−	2.04661e10i		−	0.465128i
$459$		0			0
$460$	3.53895e10			0.790392
$461$	1.19496e9	−	2.10704e8i	0.0264576	−	0.00466519i	−0.160404	−	0.987051i	$-0.551280\pi$
$461$	1.19496e9	−	2.10704e8i	0.0264576	−	0.00466519i	0.186861	+	0.982386i	$0.440168\pi$
$462$		0			0
$463$	−3.29010e10	+	1.19750e10i	−0.715953	+	0.260586i	−0.674207	−	0.738543i	$-0.735514\pi$
$463$	−3.29010e10	+	1.19750e10i	−0.715953	+	0.260586i	−0.0417465	+	0.999128i	$0.513292\pi$
$464$	−1.75706e10	+	2.09399e10i	−0.379067	+	0.451754i
$465$		0			0
$466$	−2.39940e10	−	8.73312e9i	−0.508815	−	0.185193i
$467$	−5.50338e10	+	3.17738e10i	−1.15708	+	0.668039i	−0.950602	−	0.310413i	$-0.899533\pi$
$467$	−5.50338e10	+	3.17738e10i	−1.15708	+	0.668039i	−0.206475	+	0.978452i	$0.566199\pi$
$468$		0			0
$469$	9.99087e7	−	1.73047e8i	0.00206496	−	0.00357662i
$470$	−4.18751e9	−	4.99048e9i	−0.0858153	−	0.102271i
$471$		0			0
$472$	−6.14822e9	+	3.48683e10i	−0.123874	+	0.702526i
$473$	−6.95928e10	−	1.22711e10i	−1.39034	−	0.245154i
$474$		0			0
$475$	1.09276e10	−	9.16932e9i	0.214659	−	0.180120i
$476$	−1.82965e8	−	1.05635e8i	−0.00356401	−	0.00205768i
$477$		0			0
$478$	−2.64814e9	−	4.58671e9i	−0.0507258	−	0.0878596i
$479$	1.69332e10	−	4.65236e10i	0.321660	−	0.883754i	−0.668487	−	0.743724i	$-0.733058\pi$
$479$	1.69332e10	−	4.65236e10i	0.321660	−	0.883754i	0.990147	−	0.140030i	$-0.0447199\pi$
$480$		0			0
$481$	9.45418e10	+	7.93300e10i	1.76622	+	1.48203i
$482$	2.94173e9	+	8.08234e9i	0.0545023	+	0.149744i
$483$		0			0
$484$	−1.29387e10	−	7.33792e10i	−0.235782	−	1.33719i
$485$		−	5.28515e10i		−	0.955191i
$486$		0			0
$487$	8.96707e9			0.159417			0.0797085	−	0.996818i	$-0.474601\pi$
$487$	8.96707e9			0.159417			0.0797085	+	0.996818i	$0.474601\pi$
$488$	−5.17791e10	+	9.13005e9i	−0.913009	+	0.160988i
$489$		0			0
$490$	−2.11907e10	+	7.71277e9i	−0.367587	+	0.133791i
$491$	−4.41641e10	+	5.26328e10i	−0.759878	+	0.905587i	−0.997840	−	0.0656873i	$-0.979076\pi$
$491$	−4.41641e10	+	5.26328e10i	−0.759878	+	0.905587i	0.237962	+	0.971274i	$0.423520\pi$
$492$		0			0
$493$	−3.91114e10	−	1.42354e10i	−0.662088	−	0.240980i
$494$	−4.74538e10	+	2.73975e10i	−0.796825	+	0.460047i
$495$		0			0
$496$	1.11548e10	−	1.93206e10i	0.184304	−	0.319223i
$497$	1.66864e8	+	1.98861e8i	0.00273488	+	0.00325930i
$498$		0			0
$499$	1.11840e10	−	6.34274e10i	0.180382	−	1.02300i	−0.751364	−	0.659888i	$-0.770604\pi$
$499$	1.11840e10	−	6.34274e10i	0.180382	−	1.02300i	0.931746	−	0.363110i	$-0.118285\pi$
$500$	5.31083e10	+	9.36443e9i	0.849733	+	0.149831i
$501$		0			0
$502$	−1.04542e10	+	8.77214e9i	−0.164618	+	0.138131i
$503$	1.39660e10	+	8.06327e9i	0.218173	+	0.125962i	0.605104	−	0.796147i	$-0.293132\pi$
$503$	1.39660e10	+	8.06327e9i	0.218173	+	0.125962i	−0.386931	+	0.922109i	$0.626465\pi$
$504$		0			0
$505$	1.84248e10	+	3.19126e10i	0.283293	+	0.490679i
$506$	1.88660e10	−	5.18340e10i	0.287792	−	0.790702i
$507$		0			0
$508$	2.76132e10	+	2.31703e10i	0.414632	+	0.347917i
$509$	2.93576e10	+	8.06594e10i	0.437371	+	1.20167i	0.941196	+	0.337861i	$0.109703\pi$
$509$	2.93576e10	+	8.06594e10i	0.437371	+	1.20167i	−0.503825	+	0.863806i	$0.668074\pi$
$510$		0			0
$511$	9.84463e7	+	5.58316e8i	0.00144383	+	0.00818836i
$512$			5.40910e10i			0.787127i
$513$		0			0
$514$	1.27611e10			0.182826
$515$	−5.73387e10	+	1.01104e10i	−0.815115	+	0.143727i
$516$		0			0
$517$	3.76581e10	−	1.37064e10i	0.527105	−	0.191850i
$518$	−2.68782e8	+	3.20321e8i	−0.00373319	+	0.00444905i
$519$		0			0
$520$	−8.57258e10	−	3.12016e10i	−1.17246	−	0.426741i
$521$	−1.02555e11	+	5.92104e10i	−1.39190	+	0.803614i	−0.993526	−	0.113609i	$-0.963759\pi$
$521$	−1.02555e11	+	5.92104e10i	−1.39190	+	0.803614i	−0.398374	+	0.917223i	$0.630426\pi$
$522$		0			0
$523$	1.60296e10	−	2.77642e10i	0.214248	−	0.371089i	−0.738792	−	0.673934i	$-0.764603\pi$
$523$	1.60296e10	−	2.77642e10i	0.214248	−	0.371089i	0.953040	+	0.302845i	$0.0979365\pi$
$524$	−5.39802e9	−	6.43311e9i	−0.0715994	−	0.0853288i
$525$		0			0
$526$	3.49175e9	−	1.98027e10i	0.0456143	−	0.258691i
$527$	3.34533e10	+	5.89873e9i	0.433708	+	0.0764744i
$528$		0			0
$529$	−1.77747e10	+	1.49147e10i	−0.226976	+	0.190455i
$530$	1.31793e10	+	7.60906e9i	0.167028	+	0.0964334i
$531$		0			0
$532$	3.66354e8	+	6.34545e8i	0.00457357	+	0.00792165i
$533$	4.44151e10	−	1.22030e11i	0.550329	−	1.51202i
$534$		0			0
$535$	2.74942e10	+	2.30704e10i	0.335603	+	0.281604i
$536$	−9.48257e9	−	2.60532e10i	−0.114886	−	0.315647i
$537$		0			0
$538$	−4.66921e9	−	2.64804e10i	−0.0557333	−	0.316079i
$539$		−	1.38721e11i		−	1.64357i
$540$		0			0
$541$	−4.07582e10			−0.475801			−0.237901	−	0.971290i	$-0.576459\pi$
$541$	−4.07582e10			−0.475801			−0.237901	+	0.971290i	$0.576459\pi$
$542$	2.99911e10	−	5.28824e9i	0.347532	−	0.0612793i
$543$		0			0
$544$	−4.28682e10	+	1.56027e10i	−0.489485	+	0.178158i
$545$	−5.05559e10	+	6.02502e10i	−0.573041	+	0.682924i
$546$		0			0
$547$	−3.74514e8	−	1.36312e8i	−0.00418330	−	0.00152260i	0.339928	−	0.940452i	$-0.389597\pi$
$547$	−3.74514e8	−	1.36312e8i	−0.00418330	−	0.00152260i	−0.344111	+	0.938929i	$0.611820\pi$
$548$	−6.82332e10	+	3.93944e10i	−0.756612	+	0.436830i
$549$		0			0
$550$	8.21385e9	−	1.42268e10i	0.0897627	−	0.155473i
$551$	9.27855e10	+	1.10577e11i	1.00664	+	1.19967i
$552$		0			0
$553$	1.68945e8	−	9.58133e8i	0.00180652	−	0.0102453i
$554$	−7.25186e10	−	1.27870e10i	−0.769858	−	0.135747i
$555$		0			0
$556$	−7.83830e10	+	6.57711e10i	−0.820205	+	0.688234i
$557$	−4.33094e10	−	2.50047e10i	−0.449947	−	0.259777i	0.257861	−	0.966182i	$-0.416982\pi$
$557$	−4.33094e10	−	2.50047e10i	−0.449947	−	0.259777i	−0.707808	+	0.706405i	$0.750316\pi$
$558$		0			0
$559$	−7.43872e10	−	1.28842e11i	−0.761817	−	1.31951i
$560$	−1.26353e8	+	3.47152e8i	−0.00128480	+	0.00352995i
$561$		0			0
$562$	3.17347e10	+	2.66286e10i	0.318119	+	0.266933i
$563$	−4.03175e9	−	1.10771e10i	−0.0401292	−	0.110254i	0.918010	−	0.396558i	$-0.129795\pi$
$563$	−4.03175e9	−	1.10771e10i	−0.0401292	−	0.110254i	−0.958139	+	0.286304i	$0.907573\pi$
$564$		0			0
$565$	−6.24569e9	−	3.54211e10i	−0.0612896	−	0.347590i
$566$			2.25878e10i			0.220094i
$567$		0			0
$568$	3.60194e10			0.346054
$569$	1.00783e11	−	1.77708e10i	0.961476	−	0.169534i	0.329185	−	0.944265i	$-0.393226\pi$
$569$	1.00783e11	−	1.77708e10i	0.961476	−	0.169534i	0.632291	+	0.774731i	$0.282115\pi$
$570$		0			0
$571$	−7.58711e10	+	2.76148e10i	−0.713726	+	0.259775i	−0.673260	−	0.739406i	$-0.735107\pi$
$571$	−7.58711e10	+	2.76148e10i	−0.713726	+	0.259775i	−0.0404663	+	0.999181i	$0.512884\pi$
$572$	1.60082e11	−	1.90779e11i	1.49541	−	1.78216i
$573$		0			0
$574$	4.13454e8	+	1.50485e8i	0.00380872	+	0.00138626i
$575$	−2.61821e10	+	1.51162e10i	−0.239515	+	0.138284i
$576$		0			0
$577$	6.69536e10	−	1.15967e11i	0.604047	−	1.04624i	−0.388154	−	0.921594i	$-0.626887\pi$
$577$	6.69536e10	−	1.15967e11i	0.604047	−	1.04624i	0.992201	−	0.124646i	$-0.0397794\pi$
$578$	2.35681e10	+	2.80874e10i	0.211161	+	0.251652i
$579$		0			0
$580$	−1.85197e10	+	1.05030e11i	−0.163652	+	0.928118i
$581$	1.24121e9	+	2.18858e8i	0.0108928	+	0.00192070i
$582$		0			0
$583$	−7.17133e10	+	6.01746e10i	−0.620763	+	0.520882i
$584$	6.81241e10	+	3.93315e10i	0.585665	+	0.338134i
$585$		0			0
$586$	2.88340e10	+	4.99420e10i	0.244520	+	0.423521i
$587$	−4.47539e10	+	1.22960e11i	−0.376946	+	1.03565i	0.595670	+	0.803229i	$0.296887\pi$
$587$	−4.47539e10	+	1.22960e11i	−0.376946	+	1.03565i	−0.972615	+	0.232420i	$0.925335\pi$
$588$		0			0
$589$	−9.02479e10	−	7.57270e10i	−0.749853	−	0.629201i
$590$	1.43084e10	+	3.93121e10i	0.118082	+	0.324428i
$591$		0			0
$592$	−1.20418e10	−	6.82922e10i	−0.0980400	−	0.556012i
$593$		−	1.64843e11i		−	1.33307i	−0.745474	−	0.666535i	$-0.767777\pi$
$593$		−	1.64843e11i		−	1.33307i	0.745474	−	0.666535i	$-0.232223\pi$
$594$		0			0
$595$	−5.62512e8			−0.00448811
$596$	−2.76929e10	+	4.88300e9i	−0.219474	+	0.0386992i
$597$		0			0
$598$	1.09127e11	−	3.97188e10i	0.853347	−	0.310593i
$599$	−1.35576e11	+	1.61573e11i	−1.05311	+	1.25505i	−0.0871995	+	0.996191i	$0.527792\pi$
$599$	−1.35576e11	+	1.61573e11i	−1.05311	+	1.25505i	−0.965914	+	0.258861i	$0.916653\pi$
$600$		0			0
$601$	2.01380e11	+	7.32965e10i	1.54355	+	0.561805i	0.966892	−	0.255185i	$-0.0821363\pi$
$601$	2.01380e11	+	7.32965e10i	1.54355	+	0.561805i	0.576653	+	0.816989i	$0.304358\pi$
$602$	4.36537e8	−	2.52035e8i	0.00332380	−	0.00191900i
$603$		0			0
$604$	3.05577e10	−	5.29275e10i	0.229601	−	0.397680i
$605$	−1.27522e11	−	1.51975e11i	−0.951838	−	1.13436i
$606$		0			0
$607$	−2.96670e10	+	1.68250e11i	−0.218534	+	1.23937i	0.656135	+	0.754644i	$0.272190\pi$
$607$	−2.96670e10	+	1.68250e11i	−0.218534	+	1.23937i	−0.874668	+	0.484722i	$0.838921\pi$
$608$	1.55810e11	+	2.74735e10i	1.14020	+	0.201048i
$609$		0			0
$610$	−4.75903e10	+	3.99330e10i	−0.343715	+	0.288411i
$611$	7.30666e10	+	4.21850e10i	0.524269	+	0.302687i
$612$		0			0
$613$	8.94848e10	+	1.54992e11i	0.633734	+	1.09766i	0.986782	+	0.162055i	$0.0518121\pi$
$613$	8.94848e10	+	1.54992e11i	0.633734	+	1.09766i	−0.353047	+	0.935605i	$0.614855\pi$
$614$	1.20150e10	−	3.30109e10i	0.0845377	−	0.232265i
$615$		0			0
$616$	1.45655e9	+	1.22219e9i	0.0101159	+	0.00848823i
$617$	2.07969e10	+	5.71390e10i	0.143502	+	0.394268i	0.990533	−	0.137275i	$-0.0438345\pi$
$617$	2.07969e10	+	5.71390e10i	0.143502	+	0.394268i	−0.847031	+	0.531543i	$0.821612\pi$
$618$		0			0
$619$	3.90616e10	+	2.21529e11i	0.266065	+	1.50893i	0.765985	+	0.642858i	$0.222251\pi$
$619$	3.90616e10	+	2.21529e11i	0.266065	+	1.50893i	−0.499921	+	0.866071i	$0.666637\pi$
$620$		−	8.70431e10i		−	0.589071i
$621$		0			0
$622$	8.99602e10			0.601020
$623$	−9.77593e8	+	1.72376e8i	−0.00648942	+	0.00114426i
$624$		0			0
$625$	1.00095e11	−	3.64315e10i	0.655981	−	0.238758i
$626$	4.33099e10	−	5.16148e10i	0.282027	−	0.336106i
$627$		0			0
$628$	1.52654e11	+	5.55614e10i	0.981451	+	0.357219i
$629$	9.14424e10	−	5.27943e10i	0.584178	−	0.337275i
$630$		0			0
$631$	−1.08103e11	+	1.87240e11i	−0.681901	+	1.18109i	0.292499	+	0.956266i	$0.405513\pi$
$631$	−1.08103e11	+	1.87240e11i	−0.681901	+	1.18109i	−0.974400	+	0.224821i	$0.927820\pi$
$632$	−8.67726e10	−	1.03412e11i	−0.543894	−	0.648188i
$633$		0			0
$634$	1.37383e10	−	7.79137e10i	0.0850306	−	0.482233i
$635$	9.45171e10	+	1.66659e10i	0.581320	+	0.102502i
$636$		0			0
$637$	2.23724e11	−	1.87727e11i	1.35880	−	1.14017i
$638$	1.43963e11	+	8.31169e10i	0.868895	+	0.501657i
$639$		0			0
$640$	7.27033e10	+	1.25926e11i	0.433345	+	0.750576i
$641$	−5.67063e10	+	1.55799e11i	−0.335892	+	0.922854i	0.650655	+	0.759373i	$0.274494\pi$
$641$	−5.67063e10	+	1.55799e11i	−0.335892	+	0.922854i	−0.986547	+	0.163481i	$0.947728\pi$
$642$		0			0
$643$	−9.87208e10	−	8.28366e10i	−0.577517	−	0.484594i	0.306614	−	0.951834i	$-0.400804\pi$
$643$	−9.87208e10	−	8.28366e10i	−0.577517	−	0.484594i	−0.884131	+	0.467240i	$0.845249\pi$
$644$	−5.31113e8	−	1.45922e9i	−0.00308776	−	0.00848356i
$645$		0			0
$646$	8.14062e9	+	4.61678e10i	0.0467442	+	0.265099i
$647$		−	8.44054e8i		−	0.00481674i	−0.999997	−	0.00240837i	$-0.999233\pi$
$647$		−	8.44054e8i		−	0.00481674i	0.999997	−	0.00240837i	$-0.000766609\pi$
$648$		0			0
$649$	−2.57350e11			−1.45059
$650$	3.40599e10	−	6.00568e9i	0.190805	−	0.0336441i
$651$		0			0
$652$	−1.03083e11	+	3.75190e10i	−0.570420	+	0.207616i
$653$	1.57212e11	−	1.87359e11i	0.864638	−	1.03044i	−0.134580	−	0.990903i	$-0.542969\pi$
$653$	1.57212e11	−	1.87359e11i	0.864638	−	1.03044i	0.999218	−	0.0395325i	$-0.0125869\pi$
$654$		0			0
$655$	−2.10111e10	−	7.64740e9i	−0.114152	−	0.0415479i
$656$	−6.31917e10	+	3.64837e10i	−0.341228	+	0.197008i
$657$		0			0
$658$	−1.42929e8	+	2.47560e8i	−0.000762459	+	0.00132062i
$659$	2.08795e11	+	2.48832e11i	1.10708	+	1.31936i	0.942954	+	0.332922i	$0.108035\pi$
$659$	2.08795e11	+	2.48832e11i	1.10708	+	1.31936i	0.164122	+	0.986440i	$0.447521\pi$
$660$		0			0
$661$	2.43729e10	−	1.38226e11i	0.127674	−	0.724074i	−0.852010	−	0.523526i	$-0.824616\pi$
$661$	2.43729e10	−	1.38226e11i	0.127674	−	0.724074i	0.979684	−	0.200548i	$-0.0642724\pi$
$662$	−1.28816e11	−	2.27138e10i	−0.670715	−	0.118265i
$663$		0			0
$664$	1.33964e11	−	1.12409e11i	0.689153	−	0.578268i
$665$	1.68950e9	+	9.75432e8i	0.00863915	+	0.00498781i
$666$		0			0
$667$	−1.52963e11	−	2.64940e11i	−0.772829	−	1.33858i
$668$	1.34944e10	−	3.70756e10i	0.0677717	−	0.186201i
$669$		0			0
$670$	−2.50951e10	−	2.10573e10i	−0.124535	−	0.104497i
$671$	−1.30707e11	−	3.59116e11i	−0.644778	−	1.77151i
$672$		0			0
$673$	5.61098e9	+	3.18215e10i	0.0273513	+	0.155117i	0.995425	−	0.0955502i	$-0.0304611\pi$
$673$	5.61098e9	+	3.18215e10i	0.0273513	+	0.155117i	−0.968073	+	0.250667i	$0.919350\pi$
$674$			1.59904e11i			0.774852i
$675$		0			0
$676$	3.57703e11			1.71291
$677$	−9.66599e10	+	1.70437e10i	−0.460142	+	0.0811354i	−0.398914	−	0.916988i	$-0.630613\pi$
$677$	−9.66599e10	+	1.70437e10i	−0.460142	+	0.0811354i	−0.0612279	+	0.998124i	$0.519502\pi$
$678$		0			0
$679$	−2.17924e9	+	7.93178e8i	−0.0102524	+	0.00373157i
$680$	−5.01696e10	+	5.97898e10i	−0.234641	+	0.279635i
$681$		0			0
$682$	−1.27490e11	−	4.64025e10i	−0.589303	−	0.214489i
$683$	6.47335e10	−	3.73739e10i	0.297472	−	0.171746i	−0.343835	−	0.939030i	$-0.611726\pi$
$683$	6.47335e10	−	3.73739e10i	0.297472	−	0.171746i	0.641307	+	0.767285i	$0.278393\pi$
$684$		0			0
$685$	−1.04889e11	+	1.81673e11i	−0.476396	+	0.825142i
$686$	1.27215e9	+	1.51609e9i	0.00574437	+	0.00684588i
$687$		0			0
$688$	−1.45160e10	+	8.23245e10i	−0.0647880	+	0.367431i
$689$	−1.94094e11	−	3.42240e10i	−0.861262	−	0.151864i
$690$		0			0
$691$	−1.56712e11	+	1.31497e11i	−0.687371	+	0.576772i	−0.918150	−	0.396234i	$-0.870317\pi$
$691$	−1.56712e11	+	1.31497e11i	−0.687371	+	0.576772i	0.230779	+	0.973006i	$0.425873\pi$
$692$	2.38870e11	+	1.37912e11i	1.04169	+	0.601418i
$693$		0			0
$694$	5.42794e10	+	9.40146e10i	0.233990	+	0.405282i
$695$	−9.31783e10	+	2.56005e11i	−0.399370	+	1.09726i
$696$		0			0
$697$	−8.51099e10	−	7.14157e10i	−0.360619	−	0.302596i
$698$	−1.40436e10	−	3.85844e10i	−0.0591638	−	0.162551i
$699$		0			0
$700$	−8.03069e7	−	4.55443e8i	−0.000334473	−	0.00189689i
$701$			1.17559e11i			0.486835i	0.969922	+	0.243418i	$0.0782686\pi$
$701$			1.17559e11i			0.486835i	−0.969922	+	0.243418i	$0.921731\pi$
$702$		0			0
$703$	−3.66195e11			−1.49931
$704$	6.70613e9	−	1.18247e9i	0.0273012	−	0.00481394i
$705$		0			0
$706$	−9.98520e10	+	3.63432e10i	−0.401919	+	0.146286i
$707$	1.03935e9	−	1.23865e9i	0.00415991	−	0.00495758i
$708$		0			0
$709$	2.17824e11	+	7.92814e10i	0.862026	+	0.313752i	0.734934	−	0.678139i	$-0.237213\pi$
$709$	2.17824e11	+	7.92814e10i	0.862026	+	0.313752i	0.127092	+	0.991891i	$0.459436\pi$
$710$	3.68577e10	−	2.12798e10i	0.145043	−	0.0837403i
$711$		0			0
$712$	−6.88681e10	+	1.19283e11i	−0.267977	+	0.464150i
$713$	1.60493e11	+	1.91268e11i	0.621008	+	0.740088i
$714$		0			0
$715$	1.15144e11	−	6.53015e11i	0.440573	−	2.49861i
$716$	6.60728e10	+	1.16504e10i	0.251403	+	0.0443292i
$717$		0			0
$718$	1.59818e11	−	1.34103e11i	0.601352	−	0.504594i
$719$	−3.61669e11	−	2.08810e11i	−1.35331	−	0.781332i	−0.364595	−	0.931166i	$-0.618793\pi$
$719$	−3.61669e11	−	2.08810e11i	−1.35331	−	0.781332i	−0.988711	+	0.149835i	$0.952126\pi$
$720$		0			0
$721$	1.27740e9	+	2.21253e9i	0.00472701	+	0.00818743i
$722$	1.38203e10	−	3.79709e10i	0.0508590	−	0.139734i
$723$		0			0
$724$	1.50426e11	+	1.26223e11i	0.547482	+	0.459392i
$725$	−3.11613e10	−	8.56150e10i	−0.112788	−	0.309883i
$726$		0			0
$727$	−5.38552e10	−	3.05428e11i	−0.192792	−	1.09338i	−0.915528	−	0.402255i	$-0.868226\pi$
$727$	−5.38552e10	−	3.05428e11i	−0.192792	−	1.09338i	0.722735	−	0.691125i	$-0.242885\pi$
$728$			4.00302e9i			0.0142515i
$729$		0			0
$730$	9.29461e10			0.327295
$731$	−1.25351e11	+	2.21027e10i	−0.438992	+	0.0774062i
$732$		0			0
$733$	9.20818e10	−	3.35150e10i	0.318976	−	0.116098i	−0.177570	−	0.984108i	$-0.556824\pi$
$733$	9.20818e10	−	3.35150e10i	0.318976	−	0.116098i	0.496546	+	0.868010i	$0.334601\pi$
$734$	−8.24575e9	+	9.82690e9i	−0.0284083	+	0.0338558i
$735$		0			0
$736$	−3.15090e11	−	1.14683e11i	−1.07380	−	0.390831i
$737$	1.74522e11	−	1.00760e11i	0.591536	−	0.341523i
$738$		0			0
$739$	−1.88472e11	+	3.26443e11i	−0.631931	+	1.09454i	0.355226	+	0.934780i	$0.384404\pi$
$739$	−1.88472e11	+	3.26443e11i	−0.631931	+	1.09454i	−0.987157	+	0.159755i	$0.948929\pi$
$740$	−1.73913e11	−	2.07261e11i	−0.579968	−	0.691179i
$741$		0			0
$742$	1.15956e8	−	6.57619e8i	0.000382541	−	0.00216950i
$743$	−5.58247e11	−	9.84340e10i	−1.83177	−	0.322991i	−0.852066	−	0.523434i	$-0.824651\pi$
$743$	−5.58247e11	−	9.84340e10i	−1.83177	−	0.322991i	−0.979705	+	0.200443i	$0.935762\pi$
$744$		0			0
$745$	−5.73543e10	+	4.81260e10i	−0.186183	+	0.156227i
$746$	−7.87701e10	−	4.54780e10i	−0.254335	−	0.146840i
$747$		0			0
$748$	−1.06535e11	−	1.84524e11i	−0.340320	−	0.589451i
$749$	5.38642e8	−	1.47991e9i	0.00171149	−	0.00470227i
$750$		0			0
$751$	−3.50924e11	−	2.94460e11i	−1.10320	−	0.925692i	−0.105560	−	0.994413i	$-0.533664\pi$
$751$	−3.50924e11	−	2.94460e11i	−1.10320	−	0.925692i	−0.997636	+	0.0687214i	$0.978108\pi$
$752$	−1.62140e10	−	4.45476e10i	−0.0507012	−	0.139300i
$753$		0			0
$754$	6.07722e10	+	3.44656e11i	0.188027	+	1.06635i
$755$		−	1.62722e11i		−	0.500794i
$756$		0			0
$757$	−2.66800e11			−0.812460			−0.406230	−	0.913771i	$-0.633157\pi$
$757$	−2.66800e11			−0.812460			−0.406230	+	0.913771i	$0.633157\pi$
$758$	−2.06039e11	+	3.63302e10i	−0.624125	+	0.110050i
$759$		0			0
$760$	2.54363e11	−	9.25806e10i	0.762429	−	0.277502i
$761$	−3.48504e11	+	4.15330e11i	−1.03913	+	1.23838i	−0.0685361	+	0.997649i	$0.521833\pi$
$761$	−3.48504e11	+	4.15330e11i	−1.03913	+	1.23838i	−0.970591	+	0.240735i	$0.922612\pi$
$762$		0			0
$763$	3.24304e9	+	1.18037e9i	0.00956872	+	0.00348273i
$764$	2.14280e11	−	1.23715e11i	0.628938	−	0.363118i
$765$		0			0
$766$	1.93200e10	−	3.34633e10i	0.0561167	−	0.0971971i
$767$	−3.48263e11	−	4.15044e11i	−1.00630	−	1.19926i
$768$		0			0
$769$	−5.95729e10	+	3.37855e11i	−0.170351	+	0.966106i	0.773024	+	0.634377i	$0.218743\pi$
$769$	−5.95729e10	+	3.37855e11i	−0.170351	+	0.966106i	−0.943375	+	0.331729i	$0.892368\pi$
$770$	2.21251e9	+	3.90125e8i	0.00629393	+	0.00110979i
$771$		0			0
$772$	2.85384e11	−	2.39466e11i	0.803454	−	0.674178i
$773$	3.94669e11	+	2.27862e11i	1.10539	+	0.638197i	0.937631	−	0.347631i	$-0.113014\pi$
$773$	3.94669e11	+	2.27862e11i	1.10539	+	0.638197i	0.167758	+	0.985828i	$0.446347\pi$
$774$		0			0
$775$	3.71796e10	+	6.43970e10i	0.103062	+	0.178508i
$776$	−1.10055e11	+	3.02375e11i	−0.303504	+	0.833871i
$777$		0			0
$778$	−1.27119e11	−	1.06665e11i	−0.346969	−	0.291142i
$779$	1.31787e11	+	3.62082e11i	0.357868	+	0.983235i
$780$		0			0
$781$	4.54625e10	+	2.57830e11i	0.122194	+	0.692995i
$782$		−	9.93554e10i		−	0.265683i
$783$		0			0
$784$	−1.64100e11			−0.434354
$785$	4.25960e11	−	7.51082e10i	1.12173	−	0.197792i
$786$		0			0
$787$	3.14201e11	−	1.14360e11i	0.819048	−	0.298109i	0.101692	−	0.994816i	$-0.467574\pi$
$787$	3.14201e11	−	1.14360e11i	0.819048	−	0.298109i	0.717356	+	0.696707i	$0.245352\pi$
$788$	2.31491e11	−	2.75881e11i	0.600385	−	0.715511i
$789$		0			0
$790$	−1.49886e11	−	5.45542e10i	−0.384817	−	0.140062i
$791$	−1.36679e9	+	7.89118e8i	−0.00349138	+	0.00201575i
$792$		0			0
$793$	4.02285e11	−	6.96778e11i	1.01728	−	1.76198i
$794$	−1.23119e11	−	1.46727e11i	−0.309772	−	0.369172i
$795$		0			0
$796$	−5.49068e10	+	3.11392e11i	−0.136765	+	0.775630i
$797$	−2.18436e11	−	3.85161e10i	−0.541365	−	0.0954573i	−0.103722	−	0.994606i	$-0.533075\pi$
$797$	−2.18436e11	−	3.85161e10i	−0.541365	−	0.0954573i	−0.437643	+	0.899149i	$0.644186\pi$
$798$		0			0
$799$	5.52954e10	−	4.63984e10i	0.135676	−	0.113845i
$800$	−8.64821e10	−	4.99305e10i	−0.211138	−	0.121901i
$801$		0			0
$802$	−7.02624e10	−	1.21698e11i	−0.169834	−	0.294162i
$803$	−1.95554e11	+	5.37281e11i	−0.470333	+	1.29223i
$804$		0			0
$805$	−3.16727e9	−	2.65765e9i	−0.00754226	−	0.00632871i
$806$	−9.76915e10	−	2.68405e11i	−0.231482	−	0.635991i
$807$		0			0
$808$	−3.89588e10	−	2.20946e11i	−0.0914029	−	0.518371i
$809$		−	2.04827e11i		−	0.478181i	−0.970997	−	0.239091i	$-0.923151\pi$
$809$		−	2.04827e11i		−	0.478181i	0.970997	−	0.239091i	$-0.0768493\pi$
$810$		0			0
$811$	−5.70557e9			−0.0131891			−0.00659456	−	0.999978i	$-0.502099\pi$
$811$	−5.70557e9			−0.0131891			−0.00659456	+	0.999978i	$0.502099\pi$
$812$	4.60869e9	−	8.12636e8i	0.0106012	−	0.00186927i
$813$		0			0
$814$	−3.96282e11	+	1.44235e11i	−0.902625	+	0.328528i
$815$	−1.87742e11	+	2.23743e11i	−0.425532	+	0.507129i
$816$		0			0
$817$	4.14817e11	+	1.50981e11i	0.931039	+	0.338871i
$818$	−1.93270e11	+	1.11584e11i	−0.431668	+	0.249224i
$819$		0			0
$820$	−1.42345e11	+	2.46549e11i	−0.314838	+	0.545316i
$821$	3.53407e11	+	4.21174e11i	0.777861	+	0.927019i	0.998835	−	0.0482606i	$-0.0153678\pi$
$821$	3.53407e11	+	4.21174e11i	0.777861	+	0.927019i	−0.220973	+	0.975280i	$0.570923\pi$
$822$		0			0
$823$	−3.62341e10	+	2.05494e11i	−0.0789802	+	0.447919i	0.919514	+	0.393058i	$0.128583\pi$
$823$	−3.62341e10	+	2.05494e11i	−0.0789802	+	0.447919i	−0.998494	+	0.0548611i	$0.982528\pi$
$824$	3.49101e11	+	6.15559e10i	0.757254	+	0.133524i
$825$		0			0
$826$	1.40623e9	−	1.17997e9i	0.00302089	−	0.00253483i
$827$	−2.10222e11	−	1.21372e11i	−0.449424	−	0.259475i	0.258163	−	0.966101i	$-0.416883\pi$
$827$	−2.10222e11	−	1.21372e11i	−0.449424	−	0.259475i	−0.707587	+	0.706626i	$0.750216\pi$
$828$		0			0
$829$	3.10954e11	+	5.38589e11i	0.658383	+	1.14035i	0.981034	+	0.193835i	$0.0620926\pi$
$829$	3.10954e11	+	5.38589e11i	0.658383	+	1.14035i	−0.322651	+	0.946518i	$0.604574\pi$
$830$	7.06719e10	−	1.94169e11i	0.148914	−	0.409137i
$831$		0			0
$832$	1.09822e10	+	9.21517e9i	0.0229191	+	0.0192314i
$833$	−8.54589e10	−	2.34796e11i	−0.177491	−	0.487653i
$834$		0			0
$835$	−1.82418e10	−	1.03455e11i	−0.0375251	−	0.212816i
$836$			7.38956e11i			1.51284i
$837$		0			0
$838$	−3.69633e11			−0.749540
$839$	9.66564e10	−	1.70431e10i	0.195066	−	0.0343955i	−0.0752612	−	0.997164i	$-0.523979\pi$
$839$	9.66564e10	−	1.70431e10i	0.195066	−	0.0343955i	0.270328	+	0.962768i	$0.412868\pi$
$840$		0			0
$841$	3.96271e11	−	1.44231e11i	0.792151	−	0.288319i
$842$	2.76361e10	−	3.29354e10i	0.0549829	−	0.0655261i
$843$		0			0
$844$	−5.40155e10	−	1.96600e10i	−0.106451	−	0.0387449i
$845$	8.24799e11	−	4.76198e11i	1.61779	−	0.934030i
$846$		0			0
$847$	−4.35260e9	+	7.53892e9i	−0.00845698	+	0.0146479i
$848$	7.11833e10	+	8.48330e10i	0.137656	+	0.164052i
$849$		0			0
$850$	5.13818e9	−	2.91400e10i	0.00984313	−	0.0558232i
$851$	7.64307e11	+	1.34768e11i	1.45730	+	0.256962i
$852$		0			0
$853$	−2.23404e11	+	1.87458e11i	−0.421982	+	0.354085i	−0.828916	−	0.559372i	$-0.811042\pi$
$853$	−2.23404e11	+	1.87458e11i	−0.421982	+	0.354085i	0.406934	+	0.913457i	$0.366598\pi$
$854$	2.36079e9	+	1.36300e9i	0.00443839	+	0.00256250i
$855$		0			0
$856$	−1.09260e11	−	1.89243e11i	−0.203500	−	0.352473i
$857$	2.91419e11	−	8.00668e11i	0.540250	−	1.48433i	−0.306257	−	0.951949i	$-0.599077\pi$
$857$	2.91419e11	−	8.00668e11i	0.540250	−	1.48433i	0.846508	−	0.532377i	$-0.178701\pi$
$858$		0			0
$859$	−1.76996e11	−	1.48517e11i	−0.325081	−	0.272775i	0.465611	−	0.884989i	$-0.345835\pi$
$859$	−1.76996e11	−	1.48517e11i	−0.325081	−	0.272775i	−0.790692	+	0.612214i	$0.790279\pi$
$860$	1.11551e11	+	3.06484e11i	0.203929	+	0.560291i
$861$		0			0
$862$	3.69627e10	+	2.09626e11i	0.0669475	+	0.379678i
$863$			9.48191e11i			1.70944i	0.519093	+	0.854718i	$0.326270\pi$
$863$			9.48191e11i			1.70944i	−0.519093	+	0.854718i	$0.673730\pi$
$864$		0			0
$865$	7.34389e11			1.31178
$866$	4.26744e10	−	7.52465e9i	0.0758745	−	0.0133787i
$867$		0			0
$868$	−3.58907e9	+	1.30632e9i	−0.00632271	+	0.00230128i
$869$	6.30708e11	−	7.51649e11i	1.10599	−	1.31806i
$870$		0			0
$871$	3.98677e11	+	1.45107e11i	0.692706	+	0.252124i
$872$	4.14704e11	−	2.39429e11i	0.717253	−	0.414106i
$873$		0			0
$874$	−1.72289e11	+	2.98413e11i	−0.295264	+	0.511413i
$875$	−4.04982e9	−	4.82639e9i	−0.00690882	−	0.00823361i
$876$		0			0
$877$	3.40749e10	−	1.93249e11i	0.0576019	−	0.326677i	−0.942367	−	0.334581i	$-0.891405\pi$
$877$	3.40749e10	−	1.93249e11i	0.0576019	−	0.326677i	0.999969	+	0.00790482i	$0.00251621\pi$
$878$	−2.46682e10	−	4.34968e9i	−0.0415107	−	0.00731946i
$879$		0			0
$880$	−2.85414e11	+	2.39491e11i	−0.475932	+	0.399354i
$881$	−5.35098e11	−	3.08939e11i	−0.888238	−	0.512825i	−0.0148725	−	0.999889i	$-0.504734\pi$
$881$	−5.35098e11	−	3.08939e11i	−0.888238	−	0.512825i	−0.873366	+	0.487065i	$0.838068\pi$
$882$		0			0
$883$	4.02882e11	+	6.97813e11i	0.662728	+	1.14788i	0.979896	+	0.199509i	$0.0639348\pi$
$883$	4.02882e11	+	6.97813e11i	0.662728	+	1.14788i	−0.317168	+	0.948369i	$0.602732\pi$
$884$	1.53423e11	−	4.21526e11i	0.251236	−	0.690264i
$885$		0			0
$886$	7.99781e10	+	6.71096e10i	0.129788	+	0.108905i
$887$	1.44487e11	+	3.96974e11i	0.233418	+	0.641310i	1.00000		0.000836512i	$-0.000266270\pi$
$887$	1.44487e11	+	3.96974e11i	0.233418	+	0.641310i	−0.766582	+	0.642147i	$0.778044\pi$
$888$		0			0
$889$	−7.31292e8	−	4.14736e9i	−0.00117080	−	0.00663995i
$890$			1.62746e11i			0.259388i
$891$		0			0
$892$	7.77205e11			1.22765
$893$	−2.46537e11	+	4.34711e10i	−0.387683	+	0.0683589i
$894$		0			0
$895$	1.67862e11	−	6.10968e10i	0.261614	−	0.0952196i
$896$	4.10122e9	−	4.88765e9i	0.00636329	−	0.00758347i
$897$		0			0
$898$	−4.08370e11	−	1.48635e11i	−0.627985	−	0.228568i
$899$	−6.51641e11	+	3.76225e11i	−0.997630	+	0.575982i
$900$		0			0
$901$	−8.43098e10	+	1.46029e11i	−0.127932	+	0.221585i
$902$	2.85230e11	+	3.39924e11i	0.430893	+	0.513518i
$903$		0			0
$904$	−3.80262e10	+	2.15658e11i	−0.0569390	+	0.322917i
$905$	5.14893e11	+	9.07895e10i	0.767578	+	0.135345i
$906$		0			0
$907$	−4.22135e11	+	3.54213e11i	−0.623767	+	0.523402i	−0.898985	−	0.437979i	$-0.855694\pi$
$907$	−4.22135e11	+	3.54213e11i	−0.623767	+	0.523402i	0.275218	+	0.961382i	$0.411250\pi$
$908$	−8.02215e11	−	4.63159e11i	−1.18018	−	0.681376i
$909$		0			0
$910$	2.36493e9	+	4.09618e9i	0.00344868	+	0.00597329i
$911$	1.83317e11	−	5.03660e11i	0.266152	−	0.731247i	−0.732569	−	0.680693i	$-0.761679\pi$
$911$	1.83317e11	−	5.03660e11i	0.266152	−	0.731247i	0.998721	−	0.0505544i	$-0.0160988\pi$
$912$		0			0
$913$	9.73719e11	+	8.17047e11i	1.40136	+	1.17588i
$914$	4.04213e10	+	1.11057e11i	0.0579195	+	0.159133i
$915$		0			0
$916$	−1.00902e11	−	5.72241e11i	−0.143323	−	0.812825i
$917$			9.81125e8i			0.00138754i
$918$		0			0
$919$	−4.66590e11			−0.654144			−0.327072	−	0.944999i	$-0.606062\pi$
$919$	−4.66590e11			−0.654144			−0.327072	+	0.944999i	$0.606062\pi$
$920$	−5.64968e11	+	9.96191e10i	−0.788628	+	0.139056i
$921$		0			0
$922$	−8.20262e9	+	2.98551e9i	−0.0113509	+	0.00413138i
$923$	−3.54295e11	+	4.22233e11i	−0.488156	+	0.581762i
$924$		0			0
$925$	2.17195e11	+	7.90525e10i	0.296676	+	0.107981i
$926$	2.18131e11	−	1.25938e11i	0.296670	−	0.171283i
$927$		0			0
$928$	5.05252e11	−	8.75123e11i	0.681266	−	1.17999i
$929$	2.51335e11	+	2.99530e11i	0.337435	+	0.402140i	0.907903	−	0.419180i	$-0.137682\pi$
$929$	2.51335e11	+	2.99530e11i	0.337435	+	0.402140i	−0.570468	+	0.821320i	$0.693238\pi$
$930$		0			0
$931$	−1.50477e11	+	8.53399e11i	−0.200296	+	1.13593i
$932$	−7.13941e11	−	1.25887e11i	−0.946235	−	0.166847i
$933$		0			0
$934$	3.50201e11	−	2.93853e11i	0.460182	−	0.386139i
$935$	−4.91303e11	−	2.83654e11i	−0.642840	−	0.371144i
$936$		0			0
$937$	−6.00089e11	−	1.03938e12i	−0.778497	−	1.34840i	−0.932808	−	0.360374i	$-0.882649\pi$
$937$	−6.00089e11	−	1.03938e12i	−0.778497	−	1.34840i	0.154311	−	0.988022i	$-0.450684\pi$
$938$	−4.91642e8	+	1.35078e9i	−0.000635094	+	0.00174491i
$939$		0			0
$940$	−1.41689e11	−	1.18891e11i	−0.181478	−	0.152278i
$941$	−2.70127e11	−	7.42169e11i	−0.344517	−	0.946551i	−0.984066	−	0.177802i	$-0.943101\pi$
$941$	−2.70127e11	−	7.42169e11i	−0.344517	−	0.946551i	0.639550	−	0.768750i	$-0.279121\pi$
$942$		0			0
$943$	−1.41806e11	−	8.04224e11i	−0.179328	−	1.01702i
$944$			3.04432e11i			0.383355i
$945$		0			0
$946$	5.08367e11			0.634764
$947$	5.11065e11	−	9.01145e10i	0.635442	−	0.112046i	0.153358	−	0.988171i	$-0.450991\pi$
$947$	5.11065e11	−	9.01145e10i	0.635442	−	0.112046i	0.482084	+	0.876125i	$0.339880\pi$
$948$		0			0
$949$	−1.13114e12	+	4.11702e11i	−1.39461	+	0.507596i
$950$	−6.59632e10	+	7.86118e10i	−0.0809855	+	0.0965147i
$951$		0			0
$952$	3.21825e9	+	1.17135e9i	0.00391807	+	0.00142606i
$953$	3.61729e11	−	2.08844e11i	0.438543	−	0.253193i	−0.264437	−	0.964403i	$-0.585186\pi$
$953$	3.61729e11	−	2.08844e11i	0.438543	−	0.253193i	0.702979	+	0.711210i	$0.251853\pi$
$954$		0			0
$955$	3.29394e11	−	5.70528e11i	0.396007	−	0.685904i
$956$	−9.66565e10	−	1.15191e11i	−0.115718	−	0.137907i
$957$		0			0
$958$	−6.18474e10	+	3.50754e11i	−0.0734277	+	0.416429i
$959$	9.06512e9	+	1.59842e9i	0.0107176	+	0.00188981i
$960$		0			0
$961$	−1.82915e11	+	1.53484e11i	−0.214464	+	0.179957i
$962$	−7.68891e11	−	4.43919e11i	−0.897769	−	0.518327i
$963$		0			0
$964$	1.22100e11	+	2.11483e11i	0.141386	+	0.244888i
$965$	3.39253e11	−	9.32089e11i	0.391214	−	1.07485i
$966$		0			0
$967$	4.30878e11	+	3.61550e11i	0.492775	+	0.413487i	0.855020	−	0.518596i	$-0.173545\pi$
$967$	4.30878e11	+	3.61550e11i	0.492775	+	0.413487i	−0.362245	+	0.932083i	$0.617990\pi$
$968$	4.13116e11	+	1.13503e12i	0.470511	+	1.29272i
$969$		0			0
$970$	6.60224e10	+	3.74432e11i	0.0745769	+	0.422947i
$971$			4.33654e11i			0.487828i	0.969797	+	0.243914i	$0.0784315\pi$
$971$			4.33654e11i			0.487828i	−0.969797	+	0.243914i	$0.921569\pi$
$972$		0			0
$973$	1.19543e10			0.0133375
$974$	−6.35282e10	+	1.12017e10i	−0.0705879	+	0.0124466i
$975$		0			0
$976$	−4.24815e11	+	1.54620e11i	−0.468166	+	0.170399i
$977$	2.82117e11	−	3.36214e11i	0.309636	−	0.369010i	−0.588675	−	0.808370i	$-0.700350\pi$
$977$	2.82117e11	−	3.36214e11i	0.309636	−	0.369010i	0.898311	+	0.439360i	$0.144795\pi$
$978$		0			0
$979$	−9.40762e11	−	3.42409e11i	−1.02412	−	0.372748i
$980$	−5.54476e11	+	3.20127e11i	−0.601144	+	0.347070i
$981$		0			0
$982$	2.47136e11	−	4.28052e11i	0.265760	−	0.460311i
$983$	−1.59758e11	−	1.90392e11i	−0.171100	−	0.203909i	0.673680	−	0.739023i	$-0.264713\pi$
$983$	−1.59758e11	−	1.90392e11i	−0.171100	−	0.203909i	−0.844779	+	0.535115i	$0.820268\pi$
$984$		0			0
$985$	1.66507e11	−	9.44309e11i	0.176884	−	1.00316i
$986$	2.94872e11	+	5.19938e10i	0.311979	+	0.0550103i
$987$		0			0
$988$	−1.19176e12	+	1.00000e12i	−1.25072	+	1.04948i
$989$	−8.10224e11	−	4.67783e11i	−0.846876	−	0.488944i
$990$		0			0
$991$	−9.46761e11	−	1.63984e12i	−0.981625	−	1.70022i	−0.656068	−	0.754702i	$-0.727782\pi$
$991$	−9.46761e11	−	1.63984e12i	−0.981625	−	1.70022i	−0.325557	−	0.945522i	$-0.605552\pi$
$992$	−2.82073e11	+	7.74988e11i	−0.291282	+	0.800292i
$993$		0			0
$994$	−1.43059e9	−	1.20040e9i	−0.00146544	−	0.00122965i
$995$	2.87941e11	+	7.91110e11i	0.293772	+	0.807132i
$996$		0			0
$997$	1.58879e11	+	9.01049e11i	0.160800	+	0.911943i	0.953290	+	0.302058i	$0.0976735\pi$
$997$	1.58879e11	+	9.01049e11i	0.160800	+	0.911943i	−0.792489	+	0.609886i	$0.791215\pi$
$998$			4.63329e11i			0.467054i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.71.10		138
3.2	odd	2		27.9.f.a.14.14	yes	138
27.2	odd	18	inner	81.9.f.a.8.10		138
27.25	even	9		27.9.f.a.2.14	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.14	✓	138	27.25	even	9
27.9.f.a.14.14	yes	138	3.2	odd	2
81.9.f.a.8.10		138	27.2	odd	18	inner
81.9.f.a.71.10		138	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.f (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-7.08460 + 1.24921i) q^{2} +(-191.930 + 69.8569i) q^{4} +(-349.559 + 416.588i) q^{5} +(22.4234 + 8.16143i) q^{7} +(2867.39 - 1655.49i) q^{8} +O(q^{10})\)	\(q+(-7.08460 + 1.24921i) q^{2} +(-191.930 + 69.8569i) q^{4} +(-349.559 + 416.588i) q^{5} +(22.4234 + 8.16143i) q^{7} +(2867.39 - 1655.49i) q^{8} +(1956.08 - 3388.03i) q^{10} +(15469.2 + 18435.5i) q^{11} +(-8798.06 + 49896.3i) q^{13} +(-169.056 - 29.8091i) q^{14} +(21808.2 - 18299.3i) q^{16} +(37540.0 + 21673.7i) q^{17} +(-75167.3 - 130194. i) q^{19} +(37989.4 - 104375. i) q^{20} +(-132623. - 111284. i) q^{22} +(108972. + 299398. i) q^{23} +(16477.1 + 93446.3i) q^{25} -364486. i q^{26} -4873.85 q^{28} +(-945594. + 166734. i) q^{29} +(736394. - 268025. i) q^{31} +(-676476. + 806193. i) q^{32} +(-293031. - 106655. i) q^{34} +(-11238.2 + 6488.40i) q^{35} +(1.21793e6 - 2.10952e6i) q^{37} +(695170. + 828471. i) q^{38} +(-312665. + 1.77321e6i) q^{40} +(-2.52414e6 - 445074. i) q^{41} +(-2.24939e6 + 1.88746e6i) q^{43} +(-4.25687e6 - 2.45770e6i) q^{44} +(-1.14603e6 - 1.98499e6i) q^{46} +(569539. - 1.56479e6i) q^{47} +(-4.41566e6 - 3.70518e6i) q^{49} +(-233468. - 641447. i) q^{50} +(-1.79699e6 - 1.01912e7i) q^{52} +3.88995e6i q^{53} -1.30874e7 q^{55} +(77807.6 - 13719.6i) q^{56} +(6.49088e6 - 2.36249e6i) q^{58} +(-6.87370e6 + 8.19175e6i) q^{59} +(-1.49222e7 - 5.43124e6i) q^{61} +(-4.88224e6 + 2.81876e6i) q^{62} +(141478. - 245047. i) q^{64} +(-1.77108e7 - 2.11069e7i) q^{65} +(1.45408e6 - 8.24651e6i) q^{67} +(-8.71913e6 - 1.53742e6i) q^{68} +(71513.1 - 60006.6i) q^{70} +(9.42132e6 + 5.43940e6i) q^{71} +(1.18791e7 + 2.05752e7i) q^{73} +(-5.99334e6 + 1.64666e7i) q^{74} +(2.35218e7 + 1.97371e7i) q^{76} +(196412. + 539638. i) q^{77} +(-7.07994e6 - 4.01523e7i) q^{79} +1.54817e7i q^{80} +1.84385e7 q^{82} +(5.20151e7 - 9.17167e6i) q^{83} +(-2.21515e7 + 8.06248e6i) q^{85} +(1.35782e7 - 1.61819e7i) q^{86} +(7.48761e7 + 2.72527e7i) q^{88} +(-3.60266e7 + 2.07999e7i) q^{89} +(-604507. + 1.04704e6i) q^{91} +(-4.18301e7 - 4.98511e7i) q^{92} +(-2.08020e6 + 1.17974e7i) q^{94} +(8.05126e7 + 1.41965e7i) q^{95} +(-7.44489e7 + 6.24700e7i) q^{97} +(3.59117e7 + 2.07336e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8}+O(q^{10}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25} - 12 q^{28} + 943980 q^{29} + 920739 q^{31} + 3005136 q^{32} + 660474 q^{34} - 6225408 q^{35} - 3 q^{37} + 23716884 q^{38} - 975273 q^{40} - 16694382 q^{41} + 4412514 q^{43} - 17341119 q^{44} - 3 q^{46} + 11341869 q^{47} + 11347482 q^{49} + 40948977 q^{50} + 14465511 q^{52} - 12 q^{55} - 52215771 q^{56} - 19078611 q^{58} - 76116738 q^{59} + 34059450 q^{61} + 223709616 q^{62} + 100663293 q^{64} - 20396037 q^{65} - 103603884 q^{67} - 101921427 q^{68} + 135373629 q^{70} - 125718795 q^{71} - 7632642 q^{73} + 66643887 q^{74} - 203790342 q^{76} + 343269159 q^{77} - 68767890 q^{79} - 12 q^{82} - 383244663 q^{83} + 170435619 q^{85} - 71426730 q^{86} - 192774918 q^{88} - 135692730 q^{89} + 77546796 q^{91} + 1343159175 q^{92} - 44451609 q^{94} - 881099997 q^{95} + 31339344 q^{97} - 1293135102 q^{98}+O(q^{100}) \) 138 * q + 6 * q^2 - 6 * q^4 + 447 * q^5 - 6 * q^7 + 9 * q^8 - 3 * q^10 - 28668 * q^11 - 6 * q^13 + 120975 * q^14 - 774 * q^16 + 9 * q^17 - 3 * q^19 - 137913 * q^20 - 185478 * q^22 - 68376 * q^23 + 507585 * q^25 - 12 * q^28 + 943980 * q^29 + 920739 * q^31 + 3005136 * q^32 + 660474 * q^34 - 6225408 * q^35 - 3 * q^37 + 23716884 * q^38 - 975273 * q^40 - 16694382 * q^41 + 4412514 * q^43 - 17341119 * q^44 - 3 * q^46 + 11341869 * q^47 + 11347482 * q^49 + 40948977 * q^50 + 14465511 * q^52 - 12 * q^55 - 52215771 * q^56 - 19078611 * q^58 - 76116738 * q^59 + 34059450 * q^61 + 223709616 * q^62 + 100663293 * q^64 - 20396037 * q^65 - 103603884 * q^67 - 101921427 * q^68 + 135373629 * q^70 - 125718795 * q^71 - 7632642 * q^73 + 66643887 * q^74 - 203790342 * q^76 + 343269159 * q^77 - 68767890 * q^79 - 12 * q^82 - 383244663 * q^83 + 170435619 * q^85 - 71426730 * q^86 - 192774918 * q^88 - 135692730 * q^89 + 77546796 * q^91 + 1343159175 * q^92 - 44451609 * q^94 - 881099997 * q^95 + 31339344 * q^97 - 1293135102 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

Properties

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