LMFDB - Embedded newform 81.9.f.a.35.3

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			35.3
Character	$\chi$	$=$	81.35
Dual form			81.9.f.a.44.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-17.4759 + 20.8269i) q^{2} +(-83.9009 - 475.826i) q^{4} +(-146.369 + 402.146i) q^{5} +(410.817 - 2329.86i) q^{7} +(5348.66 + 3088.05i) q^{8} +O(q^{10})$	\(q+(-17.4759 + 20.8269i) q^{2} +(-83.9009 - 475.826i) q^{4} +(-146.369 + 402.146i) q^{5} +(410.817 - 2329.86i) q^{7} +(5348.66 + 3088.05i) q^{8} +(-5817.54 - 10076.3i) q^{10} +(4863.70 + 13362.9i) q^{11} +(17844.9 - 14973.6i) q^{13} +(41344.4 + 49272.4i) q^{14} +(-41555.9 + 15125.1i) q^{16} +(44464.6 - 25671.7i) q^{17} +(-81453.1 + 141081. i) q^{19} +(203632. + 35905.8i) q^{20} +(-363305. - 132232. i) q^{22} +(-442093. + 77952.8i) q^{23} +(158939. + 133365. i) q^{25} +633330. i q^{26} -1.14308e6 q^{28} +(-88250.5 + 105173. i) q^{29} +(258769. + 1.46755e6i) q^{31} +(-129546. + 355925. i) q^{32} +(-242396. + 1.37470e6i) q^{34} +(876814. + 506229. i) q^{35} +(-1.55840e6 - 2.69922e6i) q^{37} +(-1.51482e6 - 4.16193e6i) q^{38} +(-2.02473e6 + 1.69895e6i) q^{40} +(-1.59797e6 - 1.90439e6i) q^{41} +(2.87246e6 - 1.04549e6i) q^{43} +(5.95034e6 - 3.43543e6i) q^{44} +(6.10243e6 - 1.05697e7i) q^{46} +(1.80024e6 + 317432. i) q^{47} +(157658. + 57382.9i) q^{49} +(-5.55517e6 + 979527. i) q^{50} +(-8.62202e6 - 7.23474e6i) q^{52} -1.34261e7i q^{53} -6.08573e6 q^{55} +(9.39205e6 - 1.11930e7i) q^{56} +(-648173. - 3.67597e6i) q^{58} +(-4.22385e6 + 1.16049e7i) q^{59} +(-2.36887e6 + 1.34345e7i) q^{61} +(-3.50868e7 - 2.02574e7i) q^{62} +(-1.08094e7 - 1.87225e7i) q^{64} +(3.40964e6 + 9.36791e6i) q^{65} +(-2.90051e6 + 2.43382e6i) q^{67} +(-1.59459e7 - 1.90035e7i) q^{68} +(-2.58663e7 + 9.41455e6i) q^{70} +(-2.48872e6 + 1.43686e6i) q^{71} +(-4.21902e6 + 7.30756e6i) q^{73} +(8.34508e7 + 1.47146e7i) q^{74} +(7.39639e7 + 2.69207e7i) q^{76} +(3.31318e7 - 5.84203e6i) q^{77} +(-5.57564e7 - 4.67852e7i) q^{79} -1.89254e7i q^{80} +6.75885e7 q^{82} +(-3.10234e7 + 3.69722e7i) q^{83} +(3.81551e6 + 2.16388e7i) q^{85} +(-2.84244e7 + 7.80953e7i) q^{86} +(-1.52510e7 + 8.64929e7i) q^{88} +(-6.29044e7 - 3.63179e7i) q^{89} +(-2.75555e7 - 4.77274e7i) q^{91} +(7.41839e7 + 2.03819e8i) q^{92} +(-3.80719e7 + 3.19461e7i) q^{94} +(-4.48129e7 - 5.34060e7i) q^{95} +(-1.34464e8 + 4.89407e7i) q^{97} +(-3.95032e6 + 2.28072e6i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{13}{18}\right)$

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 $

$2$	−17.4759	+	20.8269i	−1.09224	+	1.30168i	−0.142103	+	0.989852i	$0.545387\pi$
$2$	−17.4759	+	20.8269i	−1.09224	+	1.30168i	−0.950138	+	0.311830i	$0.899058\pi$
$3$		0			0
$3$		0			0
$4$	−83.9009	−	475.826i	−0.327738	−	1.85869i
$5$	−146.369	+	402.146i	−0.234191	+	0.643434i	0.765809	+	0.643068i	$0.222339\pi$
$5$	−146.369	+	402.146i	−0.234191	+	0.643434i	−1.00000		0.000365976i	$0.999884\pi$
$6$		0			0
$7$	410.817	−	2329.86i	0.171103	−	0.970371i	−0.771444	−	0.636297i	$-0.780465\pi$
$7$	410.817	−	2329.86i	0.171103	−	0.970371i	0.942547	−	0.334074i	$-0.108424\pi$
$8$	5348.66	+	3088.05i	1.30582	+	0.753918i
$9$		0			0
$10$	−5817.54	−	10076.3i	−0.581754	−	1.00763i
$11$	4863.70	+	13362.9i	0.332197	+	0.912704i	0.987539	+	0.157372i	$0.0503021\pi$
$11$	4863.70	+	13362.9i	0.332197	+	0.912704i	−0.655342	+	0.755332i	$0.727476\pi$
$12$		0			0
$13$	17844.9	−	14973.6i	0.624798	−	0.524268i	−0.274510	−	0.961584i	$-0.588516\pi$
$13$	17844.9	−	14973.6i	0.624798	−	0.524268i	0.899308	+	0.437317i	$0.144071\pi$
$14$	41344.4	+	49272.4i	1.07623	+	1.28260i
$15$		0			0
$16$	−41555.9	+	15125.1i	−0.634093	+	0.230791i
$17$	44464.6	−	25671.7i	0.532376	−	0.307368i	−0.209607	−	0.977786i	$-0.567219\pi$
$17$	44464.6	−	25671.7i	0.532376	−	0.307368i	0.741984	+	0.670418i	$0.233885\pi$
$18$		0			0
$19$	−81453.1	+	141081.i	−0.625019	+	1.08257i	0.363518	+	0.931587i	$0.381576\pi$
$19$	−81453.1	+	141081.i	−0.625019	+	1.08257i	−0.988537	+	0.150978i	$0.951758\pi$
$20$	203632.	+	35905.8i	1.27270	+	0.224411i
$21$		0			0
$22$	−363305.	−	132232.i	−1.55089	−	0.564478i
$23$	−442093.	+	77952.8i	−1.57980	+	0.278561i	−0.893604	−	0.448856i	$-0.851831\pi$
$23$	−442093.	+	77952.8i	−1.57980	+	0.278561i	−0.686195	+	0.727418i	$0.740720\pi$
$24$		0			0
$25$	158939.	+	133365.i	0.406883	+	0.341415i
$26$			633330.i			1.38591i
$27$		0			0
$28$	−1.14308e6			−1.85970
$29$	−88250.5	+	105173.i	−0.124774	+	0.148700i	−0.824815	−	0.565403i	$-0.808721\pi$
$29$	−88250.5	+	105173.i	−0.124774	+	0.148700i	0.700041	+	0.714103i	$0.253165\pi$
$30$		0			0
$31$	258769.	+	1.46755e6i	0.280199	+	1.58909i	0.721948	+	0.691947i	$0.243247\pi$
$31$	258769.	+	1.46755e6i	0.280199	+	1.58909i	−0.441750	+	0.897138i	$0.645642\pi$
$32$	−129546.	+	355925.i	−0.123545	+	0.339437i
$33$		0			0
$34$	−242396.	+	1.37470e6i	−0.181388	+	1.02870i
$35$	876814.	+	506229.i	0.584299	+	0.337345i
$36$		0			0
$37$	−1.55840e6	−	2.69922e6i	−0.831518	−	1.44023i	−0.896835	−	0.442366i	$-0.854139\pi$
$37$	−1.55840e6	−	2.69922e6i	−0.831518	−	1.44023i	0.0653170	−	0.997865i	$-0.479194\pi$
$38$	−1.51482e6	−	4.16193e6i	−0.726484	−	1.99600i
$39$		0			0
$40$	−2.02473e6	+	1.69895e6i	−0.790909	+	0.663651i
$41$	−1.59797e6	−	1.90439e6i	−0.565501	−	0.673938i	0.405200	−	0.914228i	$-0.367202\pi$
$41$	−1.59797e6	−	1.90439e6i	−0.565501	−	0.673938i	−0.970701	+	0.240290i	$0.922758\pi$
$42$		0			0
$43$	2.87246e6	−	1.04549e6i	0.840195	−	0.305806i	0.114159	−	0.993463i	$-0.463583\pi$
$43$	2.87246e6	−	1.04549e6i	0.840195	−	0.305806i	0.726036	+	0.687657i	$0.241360\pi$
$44$	5.95034e6	−	3.43543e6i	1.58756	−	0.916580i
$45$		0			0
$46$	6.10243e6	−	1.05697e7i	1.36292	−	2.36065i
$47$	1.80024e6	+	317432.i	0.368927	+	0.0650517i	0.355038	−	0.934852i	$-0.384468\pi$
$47$	1.80024e6	+	317432.i	0.368927	+	0.0650517i	0.0138885	+	0.999904i	$0.495579\pi$
$48$		0			0
$49$	157658.	+	57382.9i	0.0273484	+	0.00995402i
$50$	−5.55517e6	+	979527.i	−0.888828	+	0.156724i
$51$		0			0
$52$	−8.62202e6	−	7.23474e6i	−1.17922	−	0.989485i
$53$		−	1.34261e7i		−	1.70156i	−0.525525	−	0.850778i	$-0.676131\pi$
$53$		−	1.34261e7i		−	1.70156i	0.525525	−	0.850778i	$-0.323869\pi$
$54$		0			0
$55$	−6.08573e6			−0.665062
$56$	9.39205e6	−	1.11930e7i	0.955011	−	1.13814i
$57$		0			0
$58$	−648173.	−	3.67597e6i	−0.0572769	−	0.324833i
$59$	−4.22385e6	+	1.16049e7i	−0.348578	+	0.957710i	0.634240	+	0.773136i	$0.281313\pi$
$59$	−4.22385e6	+	1.16049e7i	−0.348578	+	0.957710i	−0.982819	+	0.184574i	$0.940909\pi$
$60$		0			0
$61$	−2.36887e6	+	1.34345e7i	−0.171089	+	0.970295i	0.771473	+	0.636263i	$0.219520\pi$
$61$	−2.36887e6	+	1.34345e7i	−0.171089	+	0.970295i	−0.942562	+	0.334032i	$0.891591\pi$
$62$	−3.50868e7	−	2.02574e7i	−2.37453	−	1.37093i
$63$		0			0
$64$	−1.08094e7	−	1.87225e7i	−0.644292	−	1.11595i
$65$	3.40964e6	+	9.36791e6i	0.191010	+	0.524795i
$66$		0			0
$67$	−2.90051e6	+	2.43382e6i	−0.143938	+	0.120778i	−0.711914	−	0.702267i	$-0.752171\pi$
$67$	−2.90051e6	+	2.43382e6i	−0.143938	+	0.120778i	0.567976	+	0.823045i	$0.307727\pi$
$68$	−1.59459e7	−	1.90035e7i	−0.745782	−	0.888789i
$69$		0			0
$70$	−2.58663e7	+	9.41455e6i	−1.07731	+	0.392109i
$71$	−2.48872e6	+	1.43686e6i	−0.0979360	+	0.0565434i	−0.548168	−	0.836368i	$-0.684675\pi$
$71$	−2.48872e6	+	1.43686e6i	−0.0979360	+	0.0565434i	0.450232	+	0.892912i	$0.351341\pi$
$72$		0			0
$73$	−4.21902e6	+	7.30756e6i	−0.148566	+	0.257324i	−0.930698	−	0.365789i	$-0.880799\pi$
$73$	−4.21902e6	+	7.30756e6i	−0.148566	+	0.257324i	0.782132	+	0.623113i	$0.214132\pi$
$74$	8.34508e7	+	1.47146e7i	2.78294	+	0.490707i
$75$		0			0
$76$	7.39639e7	+	2.69207e7i	2.21700	+	0.806922i
$77$	3.31318e7	−	5.84203e6i	0.942501	−	0.166188i
$78$		0			0
$79$	−5.57564e7	−	4.67852e7i	−1.43148	−	1.20116i	−0.944830	−	0.327561i	$-0.893773\pi$
$79$	−5.57564e7	−	4.67852e7i	−1.43148	−	1.20116i	−0.486653	−	0.873595i	$-0.661782\pi$
$80$		−	1.89254e7i		−	0.462046i
$81$		0			0
$82$	6.75885e7			1.49492
$83$	−3.10234e7	+	3.69722e7i	−0.653698	+	0.779047i	−0.986467	−	0.163962i	$-0.947573\pi$
$83$	−3.10234e7	+	3.69722e7i	−0.653698	+	0.779047i	0.332769	+	0.943008i	$0.392017\pi$
$84$		0			0
$85$	3.81551e6	+	2.16388e7i	0.0730931	+	0.414532i
$86$	−2.84244e7	+	7.80953e7i	−0.519633	+	1.42768i
$87$		0			0
$88$	−1.52510e7	+	8.64929e7i	−0.254313	+	1.44228i
$89$	−6.29044e7	−	3.63179e7i	−1.00258	−	0.578842i	−0.0935725	−	0.995612i	$-0.529829\pi$
$89$	−6.29044e7	−	3.63179e7i	−1.00258	−	0.578842i	−0.909012	+	0.416770i	$0.863162\pi$
$90$		0			0
$91$	−2.75555e7	−	4.77274e7i	−0.401830	−	0.695989i
$92$	7.41839e7	+	2.03819e8i	1.03552	+	2.84507i
$93$		0			0
$94$	−3.80719e7	+	3.19461e7i	−0.487633	+	0.409173i
$95$	−4.48129e7	−	5.34060e7i	−0.550185	−	0.655685i
$96$		0			0
$97$	−1.34464e8	+	4.89407e7i	−1.51886	+	0.552820i	−0.960863	−	0.277024i	$-0.910652\pi$
$97$	−1.34464e8	+	4.89407e7i	−1.51886	+	0.552820i	−0.557997	+	0.829843i	$0.688430\pi$
$98$	−3.95032e6	+	2.28072e6i	−0.0428281	+	0.0247268i
$99$		0			0
$100$	5.01235e7	−	8.68165e7i	0.501235	−	0.868165i
$101$	−9.22377e7	−	1.62640e7i	−0.886386	−	0.156294i	−0.288123	−	0.957593i	$-0.593031\pi$
$101$	−9.22377e7	−	1.62640e7i	−0.886386	−	0.156294i	−0.598263	+	0.801300i	$0.704142\pi$
$102$		0			0
$103$	3.01887e7	+	1.09878e7i	0.268222	+	0.0976249i	0.472630	−	0.881261i	$-0.343305\pi$
$103$	3.01887e7	+	1.09878e7i	0.268222	+	0.0976249i	−0.204408	+	0.978886i	$0.565527\pi$
$104$	1.41685e8	−	2.49829e7i	1.21113	−	0.213555i
$105$		0			0
$106$	2.79624e8	+	2.34633e8i	2.21489	+	1.85851i
$107$			5.19889e7i			0.396621i	0.980139	+	0.198311i	$0.0635454\pi$
$107$			5.19889e7i			0.396621i	−0.980139	+	0.198311i	$0.936455\pi$
$108$		0			0
$109$	−1.08913e7			−0.0771566			−0.0385783	−	0.999256i	$-0.512283\pi$
$109$	−1.08913e7			−0.0771566			−0.0385783	+	0.999256i	$0.512283\pi$
$110$	1.06353e8	−	1.26747e8i	0.726408	−	0.865699i
$111$		0			0
$112$	1.81675e7	+	1.03033e8i	0.115458	+	0.654794i
$113$	−8.53686e7	+	2.34548e8i	−0.523581	+	1.43853i	0.342925	+	0.939363i	$0.388582\pi$
$113$	−8.53686e7	+	2.34548e8i	−0.523581	+	1.43853i	−0.866507	+	0.499166i	$0.833640\pi$
$114$		0			0
$115$	3.33603e7	−	1.89196e8i	0.190739	−	1.08173i
$116$	5.74483e7	+	3.31678e7i	0.317282	+	0.183183i
$117$		0			0
$118$	−1.67879e8	−	2.90776e8i	−0.865903	−	1.49979i
$119$	−4.15446e7	−	1.14143e8i	−0.207170	−	0.569194i
$120$		0			0
$121$	9.29703e6	−	7.80114e6i	0.0433713	−	0.0363929i
$122$	−2.38402e8	−	2.84116e8i	−1.07614	−	1.28250i
$123$		0			0
$124$	6.76589e8	−	2.46258e8i	2.86179	−	1.04161i
$125$	−2.21669e8	+	1.27981e8i	−0.907958	+	0.524210i
$126$		0			0
$127$	7.07945e7	−	1.22620e8i	0.272135	−	0.471352i	−0.697273	−	0.716806i	$-0.745604\pi$
$127$	7.07945e7	−	1.22620e8i	0.272135	−	0.471352i	0.969408	+	0.245453i	$0.0789368\pi$
$128$	4.83344e8	+	8.52265e7i	1.80060	+	0.317493i
$129$		0			0
$130$	−2.54691e8	−	9.27000e7i	−0.891745	−	0.324568i
$131$	2.34887e7	−	4.14169e6i	0.0797580	−	0.0140635i	−0.133627	−	0.991032i	$-0.542662\pi$
$131$	2.34887e7	−	4.14169e6i	0.0797580	−	0.0140635i	0.213385	+	0.976968i	$0.431551\pi$
$132$		0			0
$133$	2.95237e8	+	2.47733e8i	0.943548	+	0.791730i
$134$		−	1.02942e8i		−	0.319281i
$135$		0			0
$136$	3.17101e8			0.926921
$137$	−1.14832e8	+	1.36852e8i	−0.325973	+	0.388480i	−0.903996	−	0.427541i	$-0.859380\pi$
$137$	−1.14832e8	+	1.36852e8i	−0.325973	+	0.388480i	0.578023	+	0.816021i	$0.303824\pi$
$138$		0			0
$139$	2.09878e7	+	1.19028e8i	0.0562221	+	0.318852i	0.999929	−	0.0119319i	$-0.00379813\pi$
$139$	2.09878e7	+	1.19028e8i	0.0562221	+	0.318852i	−0.943707	+	0.330783i	$0.892687\pi$
$140$	1.67311e8	−	4.59683e8i	0.435525	−	1.19659i
$141$		0			0
$142$	1.35671e7	−	7.69427e7i	0.0333682	−	0.189241i
$143$	2.86883e8	+	1.65632e8i	0.686057	+	0.396095i
$144$		0			0
$145$	−2.93777e7	−	5.08837e7i	−0.0664578	−	0.115108i
$146$	−7.84629e7	−	2.15575e8i	−0.172684	−	0.474446i
$147$		0			0
$148$	−1.15361e9	+	9.67993e8i	−2.40443	+	2.01755i
$149$	−3.59853e8	−	4.28856e8i	−0.730096	−	0.870094i	0.265474	−	0.964118i	$-0.414471\pi$
$149$	−3.59853e8	−	4.28856e8i	−0.730096	−	0.870094i	−0.995570	+	0.0940239i	$0.970027\pi$
$150$		0			0
$151$	−5.16608e8	+	1.88030e8i	−0.993696	+	0.361676i	−0.787150	−	0.616761i	$-0.788444\pi$
$151$	−5.16608e8	+	1.88030e8i	−0.993696	+	0.361676i	−0.206546	+	0.978437i	$0.566222\pi$
$152$	−8.71330e8	+	5.03063e8i	−1.63233	+	0.942427i
$153$		0			0
$154$	−4.57335e8	+	7.92127e8i	−0.813114	+	1.40835i
$155$	−6.28047e8	−	1.10742e8i	−1.08809	−	0.191860i
$156$		0			0
$157$	−5.46135e8	−	1.98777e8i	−0.898879	−	0.327165i	−0.149076	−	0.988826i	$-0.547630\pi$
$157$	−5.46135e8	−	1.98777e8i	−0.898879	−	0.327165i	−0.749803	+	0.661661i	$0.769852\pi$
$158$	1.94878e9	−	3.43623e8i	3.12705	−	0.551383i
$159$		0			0
$160$	−1.24172e8	−	1.04193e8i	−0.189472	−	0.158986i
$161$			1.06204e9i			1.58065i
$162$		0			0
$163$	−8.61408e7			−0.122028			−0.0610138	−	0.998137i	$-0.519433\pi$
$163$	−8.61408e7			−0.122028			−0.0610138	+	0.998137i	$0.519433\pi$
$164$	−7.72086e8	+	9.20136e8i	−1.06731	+	1.27197i
$165$		0			0
$166$	−2.27857e8	−	1.29224e9i	−0.300076	−	1.70181i
$167$	1.22116e8	−	3.35510e8i	0.157002	−	0.431360i	−0.836105	−	0.548570i	$-0.815173\pi$
$167$	1.22116e8	−	3.35510e8i	0.157002	−	0.431360i	0.993107	+	0.117209i	$0.0373948\pi$
$168$		0			0
$169$	−4.74204e7	+	2.68934e8i	−0.0581324	+	0.329685i
$170$	−5.17349e8	−	2.98692e8i	−0.619424	−	0.357625i
$171$		0			0
$172$	−7.38473e8	−	1.27907e9i	−0.843763	−	1.46144i
$173$	1.45190e8	+	3.98907e8i	0.162089	+	0.445336i	0.993975	−	0.109612i	$-0.0349607\pi$
$173$	1.45190e8	+	3.98907e8i	0.162089	+	0.445336i	−0.831886	+	0.554947i	$0.812738\pi$
$174$		0			0
$175$	3.76017e8	−	3.15516e8i	0.400918	−	0.336410i
$176$	−4.04230e8	−	4.81743e8i	−0.421287	−	0.502071i
$177$		0			0
$178$	1.85570e9	−	6.75419e8i	1.84853	−	0.672811i
$179$	2.16698e8	−	1.25111e8i	0.211078	−	0.121866i	−0.390734	−	0.920504i	$-0.627779\pi$
$179$	2.16698e8	−	1.25111e8i	0.211078	−	0.121866i	0.601812	+	0.798638i	$0.294446\pi$
$180$		0			0
$181$	−7.77144e8	+	1.34605e9i	−0.724081	+	1.25414i	0.235270	+	0.971930i	$0.424402\pi$
$181$	−7.77144e8	+	1.34605e9i	−0.724081	+	1.25414i	−0.959351	+	0.282215i	$0.908931\pi$
$182$	1.47557e9	+	2.60183e8i	1.34485	+	0.237134i
$183$		0			0
$184$	−2.60532e9	−	9.48260e8i	−2.27295	−	0.827287i
$185$	1.31358e9	−	2.31620e8i	1.12143	−	0.197738i
$186$		0			0
$187$	5.59310e8	+	4.69317e8i	0.457389	+	0.383795i
$188$		−	8.83235e8i		−	0.707042i
$189$		0			0
$190$	1.89543e9			1.45443
$191$	4.90410e8	−	5.84448e8i	0.368490	−	0.439150i	−0.549656	−	0.835391i	$-0.685241\pi$
$191$	4.90410e8	−	5.84448e8i	0.368490	−	0.439150i	0.918146	+	0.396241i	$0.129686\pi$
$192$		0			0
$193$	1.92284e8	+	1.09049e9i	0.138584	+	0.785949i	0.972297	+	0.233750i	$0.0750999\pi$
$193$	1.92284e8	+	1.09049e9i	0.138584	+	0.785949i	−0.833713	+	0.552199i	$0.813789\pi$
$194$	1.33058e9	−	3.65574e9i	0.939365	−	2.58088i
$195$		0			0
$196$	1.40766e7	−	7.98324e7i	0.00953835	−	0.0540947i
$197$	−2.01905e9	−	1.16570e9i	−1.34055	−	0.773965i	−0.353660	−	0.935374i	$-0.615063\pi$
$197$	−2.01905e9	−	1.16570e9i	−1.34055	−	0.773965i	−0.986888	+	0.161409i	$0.948396\pi$
$198$		0			0
$199$	−5.42051e8	−	9.38861e8i	−0.345643	−	0.598672i	0.639827	−	0.768519i	$-0.279006\pi$
$199$	−5.42051e8	−	9.38861e8i	−0.345643	−	0.598672i	−0.985470	+	0.169847i	$0.945673\pi$
$200$	4.38269e8	+	1.20414e9i	0.273918	+	0.752584i
$201$		0			0
$202$	1.95066e9	−	1.63680e9i	1.17159	−	0.983082i
$203$	2.08783e8	+	2.48818e8i	0.122945	+	0.146520i
$204$		0			0
$205$	9.99737e8	−	3.63874e8i	0.566070	−	0.206033i
$206$	−7.56414e8	+	4.36716e8i	−0.420040	+	0.242510i
$207$		0			0
$208$	−5.15081e8	+	8.92147e8i	−0.275183	+	0.476632i
$209$	−2.28141e9	−	4.02275e8i	−1.19569	−	0.210833i
$210$		0			0
$211$	1.40239e9	+	5.10429e8i	0.707522	+	0.257517i	0.670619	−	0.741802i	$-0.266029\pi$
$211$	1.40239e9	+	5.10429e8i	0.707522	+	0.257517i	0.0369029	+	0.999319i	$0.488251\pi$
$212$	−6.38848e9	+	1.12646e9i	−3.16267	+	0.557665i
$213$		0			0
$214$	−1.08277e9	−	9.08551e8i	−0.516275	−	0.433206i
$215$			1.30818e9i			0.612227i
$216$		0			0
$217$	3.52550e9			1.58995
$218$	1.90335e8	−	2.26832e8i	0.0842736	−	0.100433i
$219$		0			0
$220$	5.10598e8	+	2.89575e9i	0.217966	+	1.23615i
$221$	4.09067e8	−	1.12390e9i	0.171485	−	0.471150i
$222$		0			0
$223$	−7.16817e8	+	4.06527e9i	−0.289860	+	1.64388i	0.397529	+	0.917590i	$0.369868\pi$
$223$	−7.16817e8	+	4.06527e9i	−0.289860	+	1.64388i	−0.687389	+	0.726290i	$0.741243\pi$
$224$	7.76037e8	+	4.48045e8i	0.308241	+	0.177963i
$225$		0			0
$226$	−3.39303e9	−	5.87690e9i	−1.30063	−	2.25276i
$227$	−6.08759e8	−	1.67255e9i	−0.229267	−	0.629906i	0.770706	−	0.637191i	$-0.219904\pi$
$227$	−6.08759e8	−	1.67255e9i	−0.229267	−	0.629906i	−0.999973	+	0.00728418i	$0.997681\pi$
$228$		0			0
$229$	−1.39326e9	+	1.16908e9i	−0.506629	+	0.425112i	−0.859941	−	0.510393i	$-0.829500\pi$
$229$	−1.39326e9	+	1.16908e9i	−0.506629	+	0.425112i	0.353312	+	0.935505i	$0.385055\pi$
$230$	3.35736e9	+	4.00115e9i	1.19974	+	1.42979i
$231$		0			0
$232$	−7.96801e8	+	2.90012e8i	−0.275041	+	0.100107i
$233$	1.28942e9	−	7.44445e8i	0.437491	−	0.252586i	−0.265042	−	0.964237i	$-0.585386\pi$
$233$	1.28942e9	−	7.44445e8i	0.437491	−	0.252586i	0.702533	+	0.711651i	$0.252052\pi$
$234$		0			0
$235$	−3.91154e8	+	6.77499e8i	−0.128256	+	0.222145i
$236$	5.87630e9	+	1.03615e9i	1.89433	+	0.334022i
$237$		0			0
$238$	3.10327e9	+	1.12950e9i	0.967189	+	0.352028i
$239$	−1.54918e9	+	2.73162e8i	−0.474799	+	0.0837199i	−0.405927	−	0.913906i	$-0.633051\pi$
$239$	−1.54918e9	+	2.73162e8i	−0.474799	+	0.0837199i	−0.0688723	+	0.997625i	$0.521940\pi$
$240$		0			0
$241$	2.22777e9	+	1.86932e9i	0.660393	+	0.554135i	0.910204	−	0.414159i	$-0.135924\pi$
$241$	2.22777e9	+	1.86932e9i	0.660393	+	0.554135i	−0.249812	+	0.968294i	$0.580369\pi$
$242$			3.29960e8i			0.0962055i
$243$		0			0
$244$	6.59125e9			1.85955
$245$	−4.61527e7	+	5.50026e7i	−0.0128095	+	0.0152658i
$246$		0			0
$247$	6.58972e8	+	3.73722e9i	0.177043	+	1.00406i
$248$	−3.14781e9	+	8.64854e9i	−0.832150	+	2.28631i
$249$		0			0
$250$	1.20842e9	−	6.85327e9i	0.309354	−	1.75444i
$251$	2.54704e9	+	1.47053e9i	0.641712	+	0.370493i	0.785274	−	0.619149i	$-0.212522\pi$
$251$	2.54704e9	+	1.47053e9i	0.641712	+	0.370493i	−0.143562	+	0.989641i	$0.545856\pi$
$252$		0			0
$253$	−3.19188e9	−	5.52850e9i	−0.779048	−	1.34935i
$254$	1.31660e9	+	3.61732e9i	0.316313	+	0.869064i
$255$		0			0
$256$	−5.98223e9	+	5.01969e9i	−1.39285	+	1.16874i
$257$	3.08052e9	+	3.67123e9i	0.706142	+	0.841547i	0.993207	−	0.116364i	$-0.0371238\pi$
$257$	3.08052e9	+	3.67123e9i	0.706142	+	0.841547i	−0.287064	+	0.957911i	$0.592679\pi$
$258$		0			0
$259$	−6.92903e9	+	2.52196e9i	−1.53983	+	0.560453i
$260$	4.17142e9	−	2.40837e9i	0.912832	−	0.527024i
$261$		0			0
$262$	−3.24227e8	+	5.61577e8i	−0.0688087	+	0.119180i
$263$	5.95215e9	+	1.04952e9i	1.24409	+	0.219366i	0.756666	−	0.653801i	$-0.226827\pi$
$263$	5.95215e9	+	1.04952e9i	1.24409	+	0.219366i	0.487421	+	0.873167i	$0.337938\pi$
$264$		0			0
$265$	5.39926e9	+	1.96517e9i	1.09484	+	0.398489i
$266$	−1.03190e10	+	1.81952e9i	−2.06116	+	0.363439i
$267$		0			0
$268$	1.40143e9	+	1.17594e9i	0.271664	+	0.227953i
$269$		−	1.10877e9i		−	0.211754i	−0.994379	−	0.105877i	$-0.966235\pi$
$269$		−	1.10877e9i		−	0.211754i	0.994379	−	0.105877i	$-0.0337650\pi$
$270$		0			0
$271$	−5.94869e9			−1.10292			−0.551461	−	0.834201i	$-0.685929\pi$
$271$	−5.94869e9			−1.10292			−0.551461	+	0.834201i	$0.685929\pi$
$272$	−1.45948e9	+	1.73934e9i	−0.266638	+	0.317767i
$273$		0			0
$274$	−8.43408e8	−	4.78321e9i	−0.149636	−	0.848627i
$275$	−1.00912e9	+	2.77253e9i	−0.176446	+	0.484780i
$276$		0			0
$277$	−1.12861e9	+	6.40069e9i	−0.191702	+	1.08720i	0.725336	+	0.688395i	$0.241685\pi$
$277$	−1.12861e9	+	6.40069e9i	−0.191702	+	1.08720i	−0.917038	+	0.398801i	$0.869427\pi$
$278$	−2.84576e9	−	1.64300e9i	−0.476452	−	0.275079i
$279$		0			0
$280$	3.12652e9	+	5.41529e9i	0.508661	+	0.881027i
$281$	−3.08205e9	−	8.46786e9i	−0.494327	−	1.35815i	−0.896685	−	0.442670i	$-0.854031\pi$
$281$	−3.08205e9	−	8.46786e9i	−0.494327	−	1.35815i	0.402357	−	0.915483i	$-0.368191\pi$
$282$		0			0
$283$	7.99693e9	−	6.71022e9i	1.24674	−	1.04614i	0.249778	−	0.968303i	$-0.419642\pi$
$283$	7.99693e9	−	6.71022e9i	1.24674	−	1.04614i	0.996966	−	0.0778397i	$-0.0248022\pi$
$284$	8.92502e8	+	1.06364e9i	0.137194	+	0.163502i
$285$		0			0
$286$	−8.46312e9	+	3.08032e9i	−1.26493	+	0.460397i
$287$	−5.09344e9	+	2.94070e9i	−0.750729	+	0.433434i
$288$		0			0
$289$	−2.16981e9	+	3.75822e9i	−0.311050	+	0.538755i
$290$	1.57315e9	+	2.77389e8i	0.222422	+	0.0392191i
$291$		0			0
$292$	3.83110e9	+	1.39441e9i	0.526978	+	0.191804i
$293$	2.91859e9	−	5.14625e8i	0.396006	−	0.0698266i	0.0279009	−	0.999611i	$-0.491118\pi$
$293$	2.91859e9	−	5.14625e8i	0.396006	−	0.0698266i	0.368105	+	0.929784i	$0.380007\pi$
$294$		0			0
$295$	−4.04863e9	−	3.39721e9i	−0.534590	−	0.448574i
$296$		−	1.92496e10i		−	2.50759i
$297$		0			0
$298$	1.52205e10			1.93003
$299$	−6.72184e9	+	8.01078e9i	−0.841014	+	1.00228i
$300$		0			0
$301$	−1.25579e9	−	7.12194e9i	−0.152986	−	0.867625i
$302$	5.11209e9	−	1.40453e10i	0.614569	−	1.68851i
$303$		0			0
$304$	1.25099e9	−	7.09473e9i	0.146474	−	0.830695i
$305$	−5.05592e9	−	2.91904e9i	−0.584253	−	0.337319i
$306$		0			0
$307$	−3.09148e9	−	5.35460e9i	−0.348027	−	0.602800i	0.637872	−	0.770142i	$-0.279815\pi$
$307$	−3.09148e9	−	5.35460e9i	−0.348027	−	0.602800i	−0.985899	+	0.167342i	$0.946482\pi$
$308$	−5.55957e9	−	1.52748e10i	−0.617787	−	1.69735i
$309$		0			0
$310$	1.32821e10	−	1.11450e10i	1.43820	−	1.20679i
$311$	−3.72364e9	−	4.43766e9i	−0.398039	−	0.474365i	0.529382	−	0.848384i	$-0.322424\pi$
$311$	−3.72364e9	−	4.43766e9i	−0.398039	−	0.474365i	−0.927421	+	0.374019i	$0.877980\pi$
$312$		0			0
$313$	8.15753e8	−	2.96910e8i	0.0849927	−	0.0309348i	−0.299174	−	0.954199i	$-0.596711\pi$
$313$	8.15753e8	−	2.96910e8i	0.0849927	−	0.0309348i	0.384167	+	0.923264i	$0.374489\pi$
$314$	1.36841e10	−	7.90051e9i	1.40766	−	0.812712i
$315$		0			0
$316$	−1.75836e10	+	3.04556e10i	−1.76343	+	3.05435i
$317$	−1.72408e10	−	3.04002e9i	−1.70734	−	0.301050i	−0.767093	−	0.641536i	$-0.778297\pi$
$317$	−1.72408e10	−	3.04002e9i	−1.70734	−	0.301050i	−0.940250	+	0.340486i	$0.889408\pi$
$318$		0			0
$319$	−1.83464e9	−	6.67754e8i	−0.177169	−	0.0644842i
$320$	9.11133e9	−	1.60657e9i	0.868924	−	0.153215i
$321$		0			0
$322$	−2.21190e10	−	1.85600e10i	−2.05751	−	1.72646i
$323$			8.36415e9i			0.768443i
$324$		0			0
$325$	4.83319e9			0.433212
$326$	1.50538e9	−	1.79405e9i	0.133284	−	0.158841i
$327$		0			0
$328$	−2.66616e9	−	1.51205e10i	−0.230351	−	1.30639i
$329$	1.47914e9	−	4.06391e9i	0.126249	−	0.346865i
$330$		0			0
$331$	1.49031e9	−	8.45199e9i	0.124155	−	0.704120i	−0.857651	−	0.514233i	$-0.828077\pi$
$331$	1.49031e9	−	8.45199e9i	0.124155	−	0.704120i	0.981806	−	0.189887i	$-0.0608122\pi$
$332$	2.01952e10	+	1.16597e10i	1.66225	+	0.959701i
$333$		0			0
$334$	4.85357e9	+	8.40663e9i	0.390010	+	0.675517i
$335$	−5.54205e8	−	1.52267e9i	−0.0440039	−	0.120900i
$336$		0			0
$337$	4.21204e8	−	3.53432e8i	0.0326568	−	0.0274023i	−0.626313	−	0.779572i	$-0.715437\pi$
$337$	4.21204e8	−	3.53432e8i	0.0326568	−	0.0274023i	0.658970	+	0.752169i	$0.270992\pi$
$338$	−4.77236e9	−	5.68748e9i	−0.365651	−	0.435766i
$339$		0			0
$340$	9.97618e9	−	3.63103e9i	0.746532	−	0.271715i
$341$	−1.83522e10	+	1.05956e10i	−1.35728	+	0.783628i
$342$		0			0
$343$	7.01766e9	−	1.21549e10i	0.507009	−	0.878165i
$344$	1.85923e10	+	3.27833e9i	1.32770	+	0.234109i
$345$		0			0
$346$	−1.08453e10	−	3.94738e9i	−0.756726	−	0.275426i
$347$	2.70136e10	−	4.76322e9i	1.86322	−	0.328536i	0.875309	−	0.483563i	$-0.160658\pi$
$347$	2.70136e10	−	4.76322e9i	1.86322	−	0.328536i	0.987910	+	0.155027i	$0.0495465\pi$
$348$		0			0
$349$	4.36177e9	+	3.65996e9i	0.294009	+	0.246703i	0.777846	−	0.628455i	$-0.216313\pi$
$349$	4.36177e9	+	3.65996e9i	0.294009	+	0.246703i	−0.483836	+	0.875159i	$0.660757\pi$
$350$			1.33452e10i			0.889309i
$351$		0			0
$352$	−5.38626e9			−0.350846
$353$	−6.18947e9	+	7.37633e9i	−0.398616	+	0.475052i	−0.927597	−	0.373581i	$-0.878130\pi$
$353$	−6.18947e9	+	7.37633e9i	−0.398616	+	0.475052i	0.528981	+	0.848633i	$0.322574\pi$
$354$		0			0
$355$	−2.13557e8	−	1.21114e9i	−0.0134462	−	0.0762573i
$356$	−1.20032e10	+	3.29786e10i	−0.747306	+	2.05321i
$357$		0			0
$358$	−1.18132e9	+	6.69957e9i	−0.0719173	+	0.407864i
$359$	2.37829e10	+	1.37311e10i	1.43181	+	0.826659i	0.997259	−	0.0739862i	$-0.0235721\pi$
$359$	2.37829e10	+	1.37311e10i	1.43181	+	0.826659i	0.434556	+	0.900645i	$0.356905\pi$
$360$		0			0
$361$	−4.77745e9	−	8.27478e9i	−0.281298	−	0.487223i
$362$	−1.44529e10	−	3.97089e10i	−0.841627	−	2.31235i
$363$		0			0
$364$	−2.03980e10	+	1.71160e10i	−1.16194	+	0.974980i
$365$	−2.32117e9	−	2.76626e9i	−0.130778	−	0.155856i
$366$		0			0
$367$	1.05571e9	−	3.84249e8i	0.0581945	−	0.0211811i	−0.312759	−	0.949833i	$-0.601253\pi$
$367$	1.05571e9	−	3.84249e8i	0.0581945	−	0.0211811i	0.370953	+	0.928651i	$0.379031\pi$
$368$	1.71925e10	−	9.92610e9i	0.937449	−	0.541237i
$369$		0			0
$370$	−1.81321e10	+	3.14057e10i	−0.967477	+	1.67572i
$371$	−3.12810e10	−	5.51568e9i	−1.65114	−	0.291141i
$372$		0			0
$373$	−8.40694e9	−	3.05988e9i	−0.434313	−	0.158077i	0.115606	−	0.993295i	$-0.463119\pi$
$373$	−8.40694e9	−	3.05988e9i	−0.434313	−	0.158077i	−0.549919	+	0.835218i	$0.685341\pi$
$374$	−1.95488e10	+	3.44699e9i	−0.999159	+	0.176179i
$375$		0			0
$376$	8.64865e9	+	7.25708e9i	0.432710	+	0.363087i
$377$			3.19822e9i			0.158323i
$378$		0			0
$379$	−2.43102e10			−1.17824			−0.589118	−	0.808047i	$-0.700525\pi$
$379$	−2.43102e10			−1.17824			−0.589118	+	0.808047i	$0.700525\pi$
$380$	−2.16521e10	+	2.58040e10i	−1.03840	+	1.23752i
$381$		0			0
$382$	3.60191e9	+	2.04275e10i	0.169153	+	0.959314i
$383$	−9.92893e9	+	2.72795e10i	−0.461432	+	1.26777i	0.462977	+	0.886370i	$0.346781\pi$
$383$	−9.92893e9	+	2.72795e10i	−0.461432	+	1.26777i	−0.924409	+	0.381403i	$0.875441\pi$
$384$		0			0
$385$	−2.50012e9	+	1.41789e10i	−0.113794	+	0.645357i
$386$	−2.60720e10	−	1.50527e10i	−1.17442	−	0.678053i
$387$		0			0
$388$	3.45689e10	+	5.98750e10i	1.52531	+	2.64191i
$389$	−4.24401e9	−	1.16603e10i	−0.185344	−	0.509228i	0.811869	−	0.583840i	$-0.198450\pi$
$389$	−4.24401e9	−	1.16603e10i	−0.185344	−	0.509228i	−0.997213	+	0.0746117i	$0.976228\pi$
$390$		0			0
$391$	−1.76563e10	+	1.48154e10i	−0.755427	+	0.633879i
$392$	6.66059e8	+	7.93779e8i	0.0282078	+	0.0336167i
$393$		0			0
$394$	5.95625e10	−	2.16790e10i	2.47166	−	0.899610i
$395$	2.69755e10	−	1.55743e10i	1.10811	−	0.639765i
$396$		0			0
$397$	1.54599e10	−	2.67773e10i	0.622364	−	1.07797i	−0.366680	−	0.930347i	$-0.619506\pi$
$397$	1.54599e10	−	2.67773e10i	0.622364	−	1.07797i	0.989044	−	0.147619i	$-0.0471610\pi$
$398$	2.90264e10	+	5.11813e9i	1.15681	+	0.203976i
$399$		0			0
$400$	−8.62199e9	−	3.13815e9i	−0.336797	−	0.122584i
$401$	1.92737e10	−	3.39848e9i	0.745398	−	0.131434i	0.211966	−	0.977277i	$-0.432013\pi$
$401$	1.92737e10	−	3.39848e9i	0.745398	−	0.131434i	0.533432	+	0.845843i	$0.320902\pi$
$402$		0			0
$403$	2.65923e10	+	2.23136e10i	1.00817	+	0.845958i
$404$			4.52536e10i			1.69874i
$405$		0			0
$406$	−8.83079e9			−0.325009
$407$	2.84899e10	−	3.39529e10i	1.03828	−	1.23737i
$408$		0			0
$409$	−2.29139e9	−	1.29951e10i	−0.0818854	−	0.464395i	−0.997985	−	0.0634450i	$-0.979791\pi$
$409$	−2.29139e9	−	1.29951e10i	−0.0818854	−	0.464395i	0.916100	−	0.400950i	$-0.131320\pi$
$410$	−9.89287e9	+	2.71804e10i	−0.350096	+	0.961881i
$411$		0			0
$412$	2.69541e9	−	1.52864e10i	0.0935482	−	0.530538i
$413$	2.53026e10	+	1.46085e10i	0.869692	+	0.502117i
$414$		0			0
$415$	−1.03274e10	−	1.78875e10i	−0.348175	−	0.603057i
$416$	3.01775e9	+	8.29121e9i	0.100765	+	0.276850i
$417$		0			0
$418$	4.82478e10	−	4.04847e10i	1.58042	−	1.32613i
$419$	5.98832e9	+	7.13660e9i	0.194289	+	0.231545i	0.854390	−	0.519632i	$-0.173931\pi$
$419$	5.98832e9	+	7.13660e9i	0.194289	+	0.231545i	−0.660101	+	0.751177i	$0.729487\pi$
$420$		0			0
$421$	−3.65695e10	+	1.33102e10i	−1.16410	+	0.423698i	−0.850561	−	0.525876i	$-0.823738\pi$
$421$	−3.65695e10	+	1.33102e10i	−1.16410	+	0.423698i	−0.313541	+	0.949575i	$0.601515\pi$
$422$	−3.51387e10	+	2.02873e10i	−1.10799	+	0.639698i
$423$		0			0
$424$	4.14605e10	−	7.18116e10i	1.28283	−	2.22193i
$425$	1.04908e10	+	1.84982e9i	0.321555	+	0.0566988i
$426$		0			0
$427$	3.03275e10	+	1.10383e10i	0.912272	+	0.332040i
$428$	2.47377e10	−	4.36192e9i	0.737197	−	0.129988i
$429$		0			0
$430$	−2.72453e10	−	2.28615e10i	−0.796925	−	0.668699i
$431$		−	3.21269e9i		−	0.0931021i	−0.998916	−	0.0465510i	$-0.985177\pi$
$431$		−	3.21269e9i		−	0.0931021i	0.998916	−	0.0465510i	$-0.0148230\pi$
$432$		0			0
$433$	8.03804e9			0.228664			0.114332	−	0.993443i	$-0.463527\pi$
$433$	8.03804e9			0.228664			0.114332	+	0.993443i	$0.463527\pi$
$434$	−6.16112e10	+	7.34254e10i	−1.73660	+	2.06960i
$435$		0			0
$436$	9.13789e8	+	5.18235e9i	0.0252871	+	0.143411i
$437$	2.50122e10	−	6.87203e10i	0.685844	−	1.88434i
$438$		0			0
$439$	4.80696e9	−	2.72616e10i	0.129423	−	0.733996i	−0.849159	−	0.528138i	$-0.822890\pi$
$439$	4.80696e9	−	2.72616e10i	0.129423	−	0.733996i	0.978582	−	0.205858i	$-0.0659985\pi$
$440$	−3.25505e10	−	1.87930e10i	−0.868454	−	0.501402i
$441$		0			0
$442$	1.62586e10	+	2.81608e10i	0.425985	+	0.737828i
$443$	−8.25554e8	−	2.26819e9i	−0.0214354	−	0.0588932i	0.928513	−	0.371299i	$-0.121087\pi$
$443$	−8.25554e8	−	2.26819e9i	−0.0214354	−	0.0588932i	−0.949949	+	0.312406i	$0.898865\pi$
$444$		0			0
$445$	2.38124e10	−	1.99809e10i	0.607243	−	0.509537i
$446$	−7.21400e10	−	8.59732e10i	−1.82321	−	2.17282i
$447$		0			0
$448$	−4.80614e10	+	1.74929e10i	−1.19312	+	0.434261i
$449$	1.26932e10	−	7.32842e9i	0.312310	−	0.180312i	−0.335650	−	0.941987i	$-0.608956\pi$
$449$	1.26932e10	−	7.32842e9i	0.312310	−	0.180312i	0.647960	+	0.761675i	$0.275623\pi$
$450$		0			0
$451$	1.76761e10	−	3.06159e10i	0.427248	−	0.740015i
$452$	1.18767e11	+	2.09417e10i	2.84538	+	0.501717i
$453$		0			0
$454$	4.54727e10	+	1.65507e10i	1.07035	+	0.389577i
$455$	2.32267e10	−	4.09549e9i	0.541928	−	0.0955565i
$456$		0			0
$457$	2.84863e10	+	2.39028e10i	0.653087	+	0.548005i	0.908006	−	0.418957i	$-0.137604\pi$
$457$	2.84863e10	+	2.39028e10i	0.653087	+	0.548005i	−0.254919	+	0.966962i	$0.582049\pi$
$458$		−	4.94480e10i		−	1.12379i
$459$		0			0
$460$	−9.28231e10			−2.07312
$461$	−1.37884e10	+	1.64324e10i	−0.305288	+	0.363828i	−0.896775	−	0.442486i	$-0.854097\pi$
$461$	−1.37884e10	+	1.64324e10i	−0.305288	+	0.363828i	0.591487	+	0.806314i	$0.298541\pi$
$462$		0			0
$463$	1.14522e10	+	6.49489e10i	0.249211	+	1.41334i	0.810507	+	0.585729i	$0.199192\pi$
$463$	1.14522e10	+	6.49489e10i	0.249211	+	1.41334i	−0.561296	+	0.827615i	$0.689697\pi$
$464$	2.07658e9	−	5.70535e9i	0.0447998	−	0.123087i
$465$		0			0
$466$	−7.02916e9	+	3.98644e10i	−0.149060	+	0.845359i
$467$	−6.31019e10	−	3.64319e10i	−1.32671	−	0.765974i	−0.341918	−	0.939730i	$-0.611076\pi$
$467$	−6.31019e10	−	3.64319e10i	−1.32671	−	0.765974i	−0.984789	+	0.173756i	$0.944410\pi$
$468$		0			0
$469$	4.47888e9	+	7.75765e9i	0.0925716	+	0.160339i
$470$	−7.27446e9	−	1.99864e10i	−0.149077	−	0.409584i
$471$		0			0
$472$	−5.84285e10	+	4.90273e10i	−1.17722	+	0.987802i
$473$	2.79415e10	+	3.32994e10i	0.558220	+	0.665261i
$474$		0			0
$475$	−3.17613e10	+	1.15602e10i	−0.623913	+	0.227086i
$476$	−5.08264e10	+	2.93446e10i	−0.990060	+	0.571612i
$477$		0			0
$478$	2.13841e10	−	3.70383e10i	0.409618	−	0.709480i
$479$	6.89820e10	+	1.21634e10i	1.31037	+	0.231053i	0.784827	−	0.619715i	$-0.212752\pi$
$479$	6.89820e10	+	1.21634e10i	1.31037	+	0.231053i	0.525541	+	0.850768i	$0.323863\pi$
$480$		0			0
$481$	−6.82265e10	−	2.48324e10i	−1.27460	−	0.463915i
$482$	−7.78644e10	+	1.37296e10i	−1.44262	+	0.254372i
$483$		0			0
$484$	−4.49201e9	−	3.76924e9i	−0.0818576	−	0.0686867i
$485$		−	6.12374e10i		−	1.10675i
$486$		0			0
$487$	4.79151e10			0.851837			0.425919	−	0.904761i	$-0.359951\pi$
$487$	4.79151e10			0.851837			0.425919	+	0.904761i	$0.359951\pi$
$488$	−5.41568e10	+	6.45416e10i	−0.954935	+	1.13805i
$489$		0			0
$490$	−3.38977e8	−	1.92244e9i	−0.00588012	−	0.0333478i
$491$	−2.04354e10	+	5.61457e10i	−0.351606	+	0.966030i	0.630248	+	0.776394i	$0.282953\pi$
$491$	−2.04354e10	+	5.61457e10i	−0.351606	+	0.966030i	−0.981854	+	0.189637i	$0.939269\pi$
$492$		0			0
$493$	−1.22406e9	+	6.94201e9i	−0.0207213	+	0.117516i
$494$	−8.93508e10	−	5.15867e10i	−1.50034	−	0.866223i
$495$		0			0
$496$	−3.29503e10	−	5.70716e10i	−0.544418	−	0.942960i
$497$	2.32528e9	+	6.38866e9i	0.0381110	+	0.104709i
$498$		0			0
$499$	6.99959e10	−	5.87335e10i	1.12894	−	0.947292i	0.129917	−	0.991525i	$-0.458529\pi$
$499$	6.99959e10	−	5.87335e10i	1.12894	−	0.947292i	0.999021	+	0.0442327i	$0.0140843\pi$
$500$	7.94949e10	+	9.47383e10i	1.27192	+	1.51581i
$501$		0			0
$502$	−7.51383e10	+	2.73481e10i	−1.18317	+	0.430638i
$503$	3.20362e10	−	1.84961e10i	0.500460	−	0.288941i	−0.228444	−	0.973557i	$-0.573364\pi$
$503$	3.20362e10	−	1.84961e10i	0.500460	−	0.288941i	0.728903	+	0.684617i	$0.240030\pi$
$504$		0			0
$505$	2.00413e10	−	3.47125e10i	0.308148	−	0.533728i
$506$	1.70922e11	+	3.01382e10i	2.60733	+	0.459743i
$507$		0			0
$508$	−6.42853e10	−	2.33979e10i	−0.965288	−	0.351336i
$509$	−6.17528e10	+	1.08887e10i	−0.919995	+	0.162220i	−0.613539	−	0.789665i	$-0.710255\pi$
$509$	−6.17528e10	+	1.08887e10i	−0.919995	+	0.162220i	−0.306457	+	0.951885i	$0.599143\pi$
$510$		0			0
$511$	1.52923e10	+	1.28318e10i	0.224280	+	0.188193i
$512$		−	8.66701e10i		−	1.26122i
$513$		0			0
$514$	−1.30295e11			−1.86670
$515$	−8.83738e9	+	1.05320e10i	−0.125630	+	0.149720i
$516$		0			0
$517$	4.51403e9	+	2.56004e10i	0.0631834	+	0.358331i
$518$	6.85661e10	−	1.88384e11i	0.952337	−	2.61652i
$519$		0			0
$520$	−1.06916e10	+	6.06349e10i	−0.146227	+	0.829296i
$521$	9.20253e10	+	5.31308e10i	1.24898	+	0.721100i	0.970907	−	0.239459i	$-0.0769700\pi$
$521$	9.20253e10	+	5.31308e10i	1.24898	+	0.721100i	0.278076	+	0.960559i	$0.410303\pi$
$522$		0			0
$523$	3.33261e10	+	5.77225e10i	0.445428	+	0.771505i	0.998082	−	0.0619065i	$-0.0197181\pi$
$523$	3.33261e10	+	5.77225e10i	0.445428	+	0.771505i	−0.552654	+	0.833411i	$0.686385\pi$
$524$	−3.94145e9	−	1.08290e10i	−0.0522794	−	0.143636i
$525$		0			0
$526$	−1.25877e11	+	1.05624e11i	−1.64439	+	1.37981i
$527$	4.91806e10	+	5.86112e10i	0.637605	+	0.759868i
$528$		0			0
$529$	1.15781e11	−	4.21408e10i	1.47848	−	0.538121i
$530$	−1.35285e11	+	7.81068e10i	−1.71453	+	0.989887i
$531$		0			0
$532$	9.31071e10	−	1.61266e11i	1.16235	−	2.01325i
$533$	−5.70311e10	−	1.00561e10i	−0.706648	−	0.124601i
$534$		0			0
$535$	−2.09071e10	−	7.60958e9i	−0.255199	−	0.0928850i
$536$	−2.30296e10	+	4.06074e9i	−0.279015	+	0.0491978i
$537$		0			0
$538$	2.30922e10	+	1.93767e10i	0.275637	+	0.231287i
$539$			2.38587e9i			0.0282677i
$540$		0			0
$541$	−7.29623e10			−0.851744			−0.425872	−	0.904783i	$-0.640033\pi$
$541$	−7.29623e10			−0.851744			−0.425872	+	0.904783i	$0.640033\pi$
$542$	1.03959e11	−	1.23893e11i	1.20466	−	1.43565i
$543$		0			0
$544$	3.37697e9	+	1.91517e10i	0.0385595	+	0.218682i
$545$	1.59415e9	−	4.37989e9i	0.0180694	−	0.0496452i
$546$		0			0
$547$	−5.20084e9	+	2.94954e10i	−0.0580931	+	0.329462i	−0.999979	−	0.00647054i	$-0.997940\pi$
$547$	−5.20084e9	+	2.94954e10i	−0.0580931	+	0.329462i	0.941886	+	0.335933i	$0.109051\pi$
$548$	7.47522e10	+	4.31582e10i	0.828899	+	0.478565i
$549$		0			0
$550$	−4.01080e10	−	6.94691e10i	−0.438309	−	0.759173i
$551$	−7.64961e9	−	2.10171e10i	−0.0829914	−	0.228017i
$552$		0			0
$553$	−1.31909e11	+	1.10684e11i	−1.41050	+	1.18355i
$554$	−1.13583e11	−	1.35363e11i	−1.20580	−	1.43702i
$555$		0			0
$556$	5.48755e10	−	1.99730e10i	0.574221	−	0.208999i
$557$	8.14596e10	−	4.70307e10i	0.846295	−	0.488609i	−0.0131041	−	0.999914i	$-0.504171\pi$
$557$	8.14596e10	−	4.70307e10i	0.846295	−	0.488609i	0.859399	+	0.511306i	$0.170838\pi$
$558$		0			0
$559$	3.56039e10	−	6.16677e10i	0.364628	−	0.631554i
$560$	−4.40935e10	−	7.77488e9i	−0.448356	−	0.0790572i
$561$		0			0
$562$	2.30221e11	+	8.37936e10i	2.30781	+	0.839973i
$563$	−1.62115e11	+	2.85852e10i	−1.61357	+	0.284516i	−0.906367	−	0.422492i	$-0.861156\pi$
$563$	−1.62115e11	+	2.85852e10i	−1.61357	+	0.284516i	−0.707205	+	0.707008i	$0.750044\pi$
$564$		0			0
$565$	−8.18273e10	−	6.86613e10i	−0.802980	−	0.673780i
$566$			2.83818e11i			2.76550i
$567$		0			0
$568$	−1.77484e10			−0.170516
$569$	−1.00450e10	+	1.19712e10i	−0.0958302	+	0.114206i	−0.811828	−	0.583896i	$-0.801527\pi$
$569$	−1.00450e10	+	1.19712e10i	−0.0958302	+	0.114206i	0.715998	+	0.698102i	$0.245972\pi$
$570$		0			0
$571$	−2.30280e9	−	1.30598e10i	−0.0216627	−	0.122855i	0.972059	−	0.234738i	$-0.0754231\pi$
$571$	−2.30280e9	−	1.30598e10i	−0.0216627	−	0.122855i	−0.993721	+	0.111883i	$0.964312\pi$
$572$	5.47421e10	−	1.50403e11i	0.511373	−	1.40498i
$573$		0			0
$574$	2.77665e10	−	1.57472e11i	0.255784	−	1.45062i
$575$	−8.06617e10	−	4.65701e10i	−0.737898	−	0.426025i
$576$		0			0
$577$	−1.75359e10	−	3.03731e10i	−0.158207	−	0.274023i	0.776015	−	0.630714i	$-0.217238\pi$
$577$	−1.75359e10	−	3.03731e10i	−0.158207	−	0.274023i	−0.934222	+	0.356692i	$0.883905\pi$
$578$	−4.03529e10	−	1.10869e11i	−0.361546	−	0.993339i
$579$		0			0
$580$	−2.17469e10	+	1.82479e10i	−0.192170	+	0.161250i
$581$	7.33952e10	+	8.74691e10i	0.644115	+	0.767626i
$582$		0			0
$583$	1.79412e11	−	6.53005e10i	1.55302	−	0.565252i
$584$	−4.51322e10	+	2.60571e10i	−0.388003	+	0.224014i
$585$		0			0
$586$	−4.02867e10	+	6.97786e10i	−0.341642	+	0.591742i
$587$	−8.93599e10	−	1.57566e10i	−0.752645	−	0.132712i	−0.215853	−	0.976426i	$-0.569253\pi$
$587$	−8.93599e10	−	1.57566e10i	−0.752645	−	0.132712i	−0.536792	+	0.843714i	$0.680364\pi$
$588$		0			0
$589$	−2.28121e11	−	8.30294e10i	−1.89542	−	0.689876i
$590$	1.41507e11	−	2.49514e10i	1.16780	−	0.205915i
$591$		0			0
$592$	1.05587e11	+	8.85977e10i	0.859651	+	0.721333i
$593$		−	1.72918e11i		−	1.39836i	−0.714943	−	0.699182i	$-0.753548\pi$
$593$		−	1.72918e11i		−	1.39836i	0.714943	−	0.699182i	$-0.246452\pi$
$594$		0			0
$595$	5.19829e10			0.414756
$596$	−1.73869e11	+	2.07209e11i	−1.37796	+	1.64219i
$597$		0			0
$598$	−4.93699e10	−	2.79990e11i	−0.386062	−	2.18947i
$599$	3.14840e9	−	8.65017e9i	0.0244559	−	0.0671920i	−0.926864	−	0.375397i	$-0.877506\pi$
$599$	3.14840e9	−	8.65017e9i	0.0244559	−	0.0671920i	0.951320	+	0.308206i	$0.0997284\pi$
$600$		0			0
$601$	2.38506e9	−	1.35263e10i	0.0182810	−	0.103677i	−0.974302	−	0.225246i	$-0.927681\pi$
$601$	2.38506e9	−	1.35263e10i	0.0182810	−	0.103677i	0.992583	+	0.121569i	$0.0387926\pi$
$602$	1.70274e11	+	9.83077e10i	1.29647	+	0.748517i
$603$		0			0
$604$	1.32813e11	+	2.30040e11i	0.997916	+	1.72844i
$605$	1.77640e9	+	4.88061e9i	0.0132592	+	0.0364295i
$606$		0			0
$607$	7.12166e9	−	5.97578e9i	0.0524598	−	0.0440190i	−0.616181	−	0.787605i	$-0.711321\pi$
$607$	7.12166e9	−	5.97578e9i	0.0524598	−	0.0440190i	0.668641	+	0.743586i	$0.266876\pi$
$608$	−3.96623e10	−	4.72677e10i	−0.290244	−	0.345900i
$609$		0			0
$610$	1.49151e11	−	5.42866e10i	1.07723	−	0.392078i
$611$	3.68782e10	−	2.12916e10i	0.264609	−	0.152772i
$612$		0			0
$613$	−9.81187e10	+	1.69947e11i	−0.694880	+	1.20357i	0.275341	+	0.961347i	$0.411209\pi$
$613$	−9.81187e10	+	1.69947e11i	−0.694880	+	1.20357i	−0.970221	+	0.242221i	$0.922124\pi$
$614$	1.65546e11	+	2.91902e10i	1.16478	+	0.205383i
$615$		0			0
$616$	1.95251e11	+	7.10656e10i	1.35603	+	0.493556i
$617$	3.82689e10	−	6.74784e9i	0.264062	−	0.0465612i	−0.0400496	−	0.999198i	$-0.512752\pi$
$617$	3.82689e10	−	6.74784e9i	0.264062	−	0.0465612i	0.304111	+	0.952636i	$0.401640\pi$
$618$		0			0
$619$	1.64932e11	+	1.38394e11i	1.12342	+	0.942659i	0.998772	−	0.0495421i	$-0.0157762\pi$
$619$	1.64932e11	+	1.38394e11i	1.12342	+	0.942659i	0.124646	+	0.992201i	$0.460221\pi$
$620$			3.08132e11i			2.08531i
$621$		0			0
$622$	1.57497e11			1.05223
$623$	−1.10458e11	+	1.31639e11i	−0.733237	+	0.873838i
$624$		0			0
$625$	−4.94784e9	−	2.80606e10i	−0.0324262	−	0.183898i
$626$	−8.07227e9	+	2.21784e10i	−0.0525652	+	0.144422i
$627$		0			0
$628$	−4.87619e10	+	2.76542e11i	−0.313503	+	1.77797i
$629$	−1.38587e11	−	8.00133e10i	−0.885361	−	0.511163i
$630$		0			0
$631$	7.84064e10	+	1.35804e11i	0.494577	+	0.856633i	0.999980	−	0.00625049i	$-0.00198961\pi$
$631$	7.84064e10	+	1.35804e11i	0.494577	+	0.856633i	−0.505403	+	0.862883i	$0.668656\pi$
$632$	−1.53747e11	−	4.22416e11i	−0.963692	−	2.64772i
$633$		0			0
$634$	3.64612e11	−	3.05946e11i	2.25670	−	1.89360i
$635$	3.89489e10	+	4.64175e10i	0.239552	+	0.285487i
$636$		0			0
$637$	3.67262e9	−	1.33672e9i	0.0223058	−	0.00811866i
$638$	4.59691e10	−	2.65403e10i	0.277449	−	0.160185i
$639$		0			0
$640$	−1.05020e11	+	1.81900e11i	−0.625969	+	1.08421i
$641$	−6.02438e9	−	1.06226e9i	−0.0356845	−	0.00629215i	0.155777	−	0.987792i	$-0.450212\pi$
$641$	−6.02438e9	−	1.06226e9i	−0.0356845	−	0.00629215i	−0.191462	+	0.981500i	$0.561323\pi$
$642$		0			0
$643$	−3.09805e11	−	1.12760e11i	−1.81236	−	0.659645i	−0.996706	−	0.0811048i	$-0.974155\pi$
$643$	−3.09805e11	−	1.12760e11i	−1.81236	−	0.659645i	−0.815654	−	0.578540i	$-0.803623\pi$
$644$	5.05345e11	−	8.91060e10i	2.93795	−	0.518040i
$645$		0			0
$646$	−1.74199e11	−	1.46171e11i	−1.00027	−	0.839325i
$647$		−	4.23154e10i		−	0.241480i	−0.992684	−	0.120740i	$-0.961473\pi$
$647$		−	4.23154e10i		−	0.241480i	0.992684	−	0.120740i	$-0.0385267\pi$
$648$		0			0
$649$	−1.75619e11			−0.989902
$650$	−8.44642e10	+	1.00660e11i	−0.473172	+	0.563905i
$651$		0			0
$652$	7.22729e9	+	4.09880e10i	0.0399931	+	0.226812i
$653$	−7.09527e10	+	1.94941e11i	−0.390226	+	1.07214i	0.576672	+	0.816976i	$0.304351\pi$
$653$	−7.09527e10	+	1.94941e11i	−0.390226	+	1.07214i	−0.966898	+	0.255162i	$0.917871\pi$
$654$		0			0
$655$	−1.77246e9	+	1.00521e10i	−0.00962966	+	0.0546125i
$656$	9.52092e10	+	5.49691e10i	0.514119	+	0.296827i
$657$		0			0
$658$	5.87895e10	+	1.01826e11i	0.313614	+	0.543196i
$659$	1.18912e11	+	3.26709e11i	0.630501	+	1.73229i	0.679692	+	0.733497i	$0.262113\pi$
$659$	1.18912e11	+	3.26709e11i	0.630501	+	1.73229i	−0.0491916	+	0.998789i	$0.515664\pi$
$660$		0			0
$661$	−6.81142e9	+	5.71546e9i	−0.0356806	+	0.0299396i	−0.660454	−	0.750867i	$-0.729636\pi$
$661$	−6.81142e9	+	5.71546e9i	−0.0356806	+	0.0299396i	0.624773	+	0.780806i	$0.285192\pi$
$662$	1.49984e11	+	1.78744e11i	0.780933	+	0.930680i
$663$		0			0
$664$	−2.80106e11	+	1.01950e11i	−1.44095	+	0.524464i
$665$	−1.42838e11	+	8.24678e10i	−0.730396	+	0.421695i
$666$		0			0
$667$	3.08164e10	−	5.33755e10i	0.155696	−	0.269674i
$668$	−1.69890e11	−	2.99562e10i	−0.853222	−	0.150446i
$669$		0			0
$670$	4.13976e10	+	1.50675e10i	0.205436	+	0.0747726i
$671$	−1.91046e11	+	3.36865e10i	−0.942427	+	0.166175i
$672$		0			0
$673$	−9.15917e10	−	7.68545e10i	−0.446474	−	0.374636i	0.391652	−	0.920114i	$-0.371904\pi$
$673$	−9.15917e10	−	7.68545e10i	−0.446474	−	0.374636i	−0.838125	+	0.545478i	$0.816348\pi$
$674$			1.49489e10i			0.0724386i
$675$		0			0
$676$	1.31944e11			0.631836
$677$	−7.73973e10	+	9.22385e10i	−0.368444	+	0.439094i	−0.918131	−	0.396276i	$-0.870302\pi$
$677$	−7.73973e10	+	9.22385e10i	−0.368444	+	0.439094i	0.549688	+	0.835370i	$0.314747\pi$
$678$		0			0
$679$	5.87851e10	+	3.33387e11i	0.276559	+	1.56845i
$680$	−4.64139e10	+	1.27521e11i	−0.217076	+	0.596412i
$681$		0			0
$682$	1.00046e11	−	5.67387e11i	0.462446	−	2.62266i
$683$	4.11925e9	+	2.37825e9i	0.0189294	+	0.0109289i	0.509435	−	0.860509i	$-0.329854\pi$
$683$	4.11925e9	+	2.37825e9i	0.0189294	+	0.0109289i	−0.490505	+	0.871438i	$0.663188\pi$
$684$		0			0
$685$	−3.82265e10	−	6.62103e10i	−0.173621	−	0.300721i
$686$	1.30510e11	+	3.58574e11i	0.589316	+	1.61913i
$687$		0			0
$688$	−1.03554e11	+	8.68925e10i	−0.462184	+	0.387819i
$689$	−2.01037e11	−	2.39587e11i	−0.892071	−	1.06313i
$690$		0			0
$691$	−2.23426e11	+	8.13202e10i	−0.979988	+	0.356686i	−0.781835	−	0.623485i	$-0.785716\pi$
$691$	−2.23426e11	+	8.13202e10i	−0.979988	+	0.356686i	−0.198152	+	0.980171i	$0.563494\pi$
$692$	1.77629e11	−	1.02554e11i	0.774620	−	0.447227i
$693$		0			0
$694$	−3.72882e11	+	6.45851e11i	−1.60744	+	2.78416i
$695$	−5.09385e10	−	8.98183e9i	−0.218327	−	0.0384969i
$696$		0			0
$697$	−1.19942e11	−	4.36553e10i	−0.508207	−	0.184972i
$698$	−1.52451e11	+	2.68813e10i	−0.642258	+	0.113247i
$699$		0			0
$700$	−1.81679e11	−	1.52447e11i	−0.756679	−	0.634929i
$701$			3.66408e10i			0.151738i	0.997118	+	0.0758688i	$0.0241730\pi$
$701$			3.66408e10i			0.151738i	−0.997118	+	0.0758688i	$0.975827\pi$
$702$		0			0
$703$	5.07746e11			2.07886
$704$	1.97613e11	−	2.35505e11i	0.804496	−	0.958761i
$705$		0			0
$706$	−4.54598e10	−	2.57815e11i	−0.182982	−	1.03774i
$707$	−7.57857e10	+	2.08219e11i	−0.303326	+	0.833381i
$708$		0			0
$709$	−6.93204e9	+	3.93136e10i	−0.0274332	+	0.155581i	−0.995447	−	0.0953149i	$-0.969614\pi$
$709$	−6.93204e9	+	3.93136e10i	−0.0274332	+	0.155581i	0.968014	+	0.250896i	$0.0807253\pi$
$710$	2.89564e10	+	1.67180e10i	0.113949	+	0.0657886i
$711$		0			0
$712$	−2.24303e11	−	3.88504e11i	−0.872800	−	1.51173i
$713$	−2.28800e11	−	6.28623e11i	−0.885315	−	2.43238i
$714$		0			0
$715$	−1.08599e11	+	9.11254e10i	−0.415529	+	0.348670i
$716$	−7.77120e10	−	9.26136e10i	−0.295690	−	0.352389i
$717$		0			0
$718$	−7.01602e11	+	2.55362e11i	−2.63993	+	0.960857i
$719$	2.70888e11	−	1.56397e11i	1.01362	−	0.585213i	0.101369	−	0.994849i	$-0.467678\pi$
$719$	2.70888e11	−	1.56397e11i	1.01362	−	0.585213i	0.912249	+	0.409636i	$0.134344\pi$
$720$		0			0
$721$	3.80020e10	−	6.58214e10i	0.140626	−	0.243571i
$722$	2.55828e11	+	4.51094e10i	0.941455	+	0.166004i
$723$		0			0
$724$	7.05689e11	+	2.56850e11i	2.56838	+	0.934814i
$725$	−2.80528e10	+	4.94647e9i	−0.101537	+	0.0179037i
$726$		0			0
$727$	1.04453e11	+	8.76467e10i	0.373925	+	0.313760i	0.810312	−	0.585999i	$-0.199298\pi$
$727$	1.04453e11	+	8.76467e10i	0.373925	+	0.313760i	−0.436387	+	0.899759i	$0.643742\pi$
$728$		−	3.40370e11i		−	1.21179i
$729$		0			0
$730$	9.81772e10			0.345716
$731$	1.00883e11	−	1.20228e11i	0.353305	−	0.421053i
$732$		0			0
$733$	3.48971e10	+	1.97911e11i	0.120885	+	0.685575i	0.983667	+	0.179998i	$0.0576091\pi$
$733$	3.48971e10	+	1.97911e11i	0.120885	+	0.685575i	−0.862782	+	0.505577i	$0.831280\pi$
$734$	−1.04468e10	+	2.87023e10i	−0.0359914	+	0.0988856i
$735$		0			0
$736$	2.95260e10	−	1.67450e11i	0.100622	−	0.570657i
$737$	−4.66301e10	−	2.69219e10i	−0.158051	−	0.0912505i
$738$		0			0
$739$	−2.34984e11	−	4.07005e11i	−0.787882	−	1.36465i	−0.927262	−	0.374412i	$-0.877845\pi$
$739$	−2.34984e11	−	4.07005e11i	−0.787882	−	1.36465i	0.139381	−	0.990239i	$-0.455489\pi$
$740$	−2.20422e11	−	6.05604e11i	−0.735068	−	2.01958i
$741$		0			0
$742$	6.61536e11	−	5.55095e11i	2.18242	−	1.83127i
$743$	−3.64562e10	−	4.34469e10i	−0.119624	−	0.142562i	0.702909	−	0.711280i	$-0.251884\pi$
$743$	−3.64562e10	−	4.34469e10i	−0.119624	−	0.142562i	−0.822533	+	0.568718i	$0.807440\pi$
$744$		0			0
$745$	2.25134e11	−	8.19421e10i	0.730830	−	0.266000i
$746$	2.10646e11	−	1.21617e11i	0.680140	−	0.392679i
$747$		0			0
$748$	1.76386e11	−	3.05510e11i	0.563454	−	0.975931i
$749$	1.21127e11	+	2.13580e10i	0.384870	+	0.0678629i
$750$		0			0
$751$	−1.29164e11	−	4.70119e10i	−0.406053	−	0.147791i	0.130915	−	0.991394i	$-0.458208\pi$
$751$	−1.29164e11	−	4.70119e10i	−0.406053	−	0.147791i	−0.536968	+	0.843602i	$0.680431\pi$
$752$	−7.96119e10	+	1.40377e10i	−0.248947	+	0.0438961i
$753$		0			0
$754$	−6.66091e10	−	5.58917e10i	−0.206086	−	0.172927i
$755$		−	2.35274e11i		−	0.724079i
$756$		0			0
$757$	2.46089e11			0.749392			0.374696	−	0.927148i	$-0.377747\pi$
$757$	2.46089e11			0.749392			0.374696	+	0.927148i	$0.377747\pi$
$758$	4.24842e11	−	5.06307e11i	1.28692	−	1.53369i
$759$		0			0
$760$	−7.47688e10	−	4.24035e11i	−0.224112	−	1.27100i
$761$	−1.85094e11	+	5.08540e11i	−0.551890	+	1.51631i	0.279236	+	0.960222i	$0.409919\pi$
$761$	−1.85094e11	+	5.08540e11i	−0.551890	+	1.51631i	−0.831126	+	0.556084i	$0.812303\pi$
$762$		0			0
$763$	−4.47433e9	+	2.53752e10i	−0.0132017	+	0.0748706i
$764$	−3.19241e11	−	1.84314e11i	−0.937013	−	0.540985i
$765$		0			0
$766$	−3.94632e11	−	6.83522e11i	−1.14624	−	1.98535i
$767$	9.83936e10	+	2.70334e11i	0.284306	+	0.781124i
$768$		0			0
$769$	−2.19230e11	+	1.83955e11i	−0.626894	+	0.526026i	−0.899962	−	0.435968i	$-0.856406\pi$
$769$	−2.19230e11	+	1.83955e11i	−0.626894	+	0.526026i	0.273068	+	0.961995i	$0.411961\pi$
$770$	−2.51611e11	−	2.99859e11i	−0.715759	−	0.853009i
$771$		0			0
$772$	5.02753e11	−	1.82987e11i	1.41542	−	0.515170i
$773$	2.05793e11	−	1.18815e11i	0.576385	−	0.332776i	−0.183311	−	0.983055i	$-0.558681\pi$
$773$	2.05793e11	−	1.18815e11i	0.576385	−	0.332776i	0.759695	+	0.650279i	$0.225348\pi$
$774$		0			0
$775$	−1.54592e11	+	2.67762e11i	−0.428530	+	0.742235i
$776$	−8.70331e11	−	1.53463e11i	−2.40015	−	0.423210i
$777$		0			0
$778$	3.17017e11	+	1.15385e11i	0.865294	+	0.314941i
$779$	3.98833e11	−	7.03250e10i	1.08303	−	0.190968i
$780$		0			0
$781$	−3.13050e10	−	2.62680e10i	−0.0841414	−	0.0706030i
$782$		−	6.26638e11i		−	1.67567i
$783$		0			0
$784$	−7.41956e9			−0.0196387
$785$	1.59875e11	−	1.90531e11i	0.421018	−	0.501750i
$786$		0			0
$787$	1.74915e9	+	9.91991e9i	0.00455961	+	0.0258588i	0.987003	−	0.160704i	$-0.0513764\pi$
$787$	1.74915e9	+	9.91991e9i	0.00455961	+	0.0258588i	−0.982443	+	0.186563i	$0.940265\pi$
$788$	−3.85269e11	+	1.05852e12i	−0.999216	+	2.74532i
$789$		0			0
$790$	−1.47055e11	+	8.33991e11i	−0.377547	+	2.14118i
$791$	5.11394e11	+	2.95253e11i	1.30632	+	0.754204i
$792$		0			0
$793$	1.58891e11	+	2.75208e11i	0.401798	+	0.695934i
$794$	2.87514e11	+	7.89939e11i	0.723398	+	1.98752i
$795$		0			0
$796$	−4.01255e11	+	3.36693e11i	−0.999467	+	0.838652i
$797$	−2.00895e11	−	2.39417e11i	−0.497892	−	0.593364i	0.457315	−	0.889305i	$-0.348811\pi$
$797$	−2.00895e11	−	2.39417e11i	−0.497892	−	0.593364i	−0.955206	+	0.295941i	$0.904367\pi$
$798$		0			0
$799$	8.81962e10	−	3.21008e10i	0.216403	−	0.0787641i
$800$	−6.80579e10	+	3.92933e10i	−0.166157	+	0.0959308i
$801$		0			0
$802$	−2.66045e11	+	4.60803e11i	−0.643069	+	1.11383i
$803$	−1.18170e11	−	2.08366e10i	−0.284214	−	0.0501146i
$804$		0			0
$805$	−4.27095e11	−	1.55450e11i	−1.01705	−	0.370175i
$806$	−9.29445e11	+	1.63886e11i	−2.20234	+	0.388331i
$807$		0			0
$808$	−4.43124e11	−	3.71825e11i	−1.03963	−	0.872355i
$809$		−	4.01887e11i		−	0.938231i	−0.883137	−	0.469115i	$-0.844573\pi$
$809$		−	4.01887e11i		−	0.938231i	0.883137	−	0.469115i	$-0.155427\pi$
$810$		0			0
$811$	1.72635e11			0.399066			0.199533	−	0.979891i	$-0.436058\pi$
$811$	1.72635e11			0.399066			0.199533	+	0.979891i	$0.436058\pi$
$812$	1.00877e11	−	1.20221e11i	0.232043	−	0.276538i
$813$		0			0
$814$	2.09249e11	+	1.18671e12i	0.476614	+	2.70301i
$815$	1.26084e10	−	3.46412e10i	0.0285778	−	0.0785168i
$816$		0			0
$817$	−8.64721e10	+	4.90408e11i	−0.194083	+	1.10070i
$818$	3.10693e11	+	1.79378e11i	0.693933	+	0.400643i
$819$		0			0
$820$	−2.57020e11	−	4.45171e11i	−0.568474	−	0.984626i
$821$	3.52564e10	+	9.68661e10i	0.0776006	+	0.213206i	0.972427	−	0.233209i	$-0.0749227\pi$
$821$	3.52564e10	+	9.68661e10i	0.0776006	+	0.213206i	−0.894826	+	0.446415i	$0.852700\pi$
$822$		0			0
$823$	4.97744e11	−	4.17657e11i	1.08494	−	0.910375i	0.0886209	−	0.996065i	$-0.471754\pi$
$823$	4.97744e11	−	4.17657e11i	1.08494	−	0.910375i	0.996322	+	0.0856904i	$0.0273096\pi$
$824$	1.27538e11	+	1.51994e11i	0.276650	+	0.329699i
$825$		0			0
$826$	−7.46435e11	+	2.71680e11i	−1.60351	+	0.583630i
$827$	−2.88537e11	+	1.66587e11i	−0.616849	+	0.356138i	−0.775641	−	0.631174i	$-0.782573\pi$
$827$	−2.88537e11	+	1.66587e11i	−0.616849	+	0.356138i	0.158792	+	0.987312i	$0.449240\pi$
$828$		0			0
$829$	1.58888e11	−	2.75201e11i	0.336412	−	0.582683i	−0.647343	−	0.762199i	$-0.724120\pi$
$829$	1.58888e11	−	2.75201e11i	0.336412	−	0.582683i	0.983755	+	0.179516i	$0.0574531\pi$
$830$	5.53022e11	+	9.75127e10i	1.16528	+	0.205470i
$831$		0			0
$832$	−4.73235e11	−	1.72244e11i	−0.987606	−	0.359459i
$833$	8.48333e9	−	1.49584e9i	0.0176192	−	0.00310674i
$834$		0			0
$835$	1.17050e11	+	9.82168e10i	0.240783	+	0.202041i
$836$			1.11931e12i			2.29152i
$837$		0			0
$838$	−2.53284e11			−0.513608
$839$	−3.70120e11	+	4.41092e11i	−0.746956	+	0.890187i	−0.996949	−	0.0780605i	$-0.975127\pi$
$839$	−3.70120e11	+	4.41092e11i	−0.746956	+	0.890187i	0.249993	+	0.968248i	$0.419572\pi$
$840$		0			0
$841$	8.35937e10	+	4.74083e11i	0.167105	+	0.947700i
$842$	3.61873e11	−	9.94238e11i	0.719959	−	1.97807i
$843$		0			0
$844$	1.25213e11	−	7.10120e11i	0.246763	−	1.39946i
$845$	−1.01210e11	−	5.84336e10i	−0.198517	−	0.114614i
$846$		0			0
$847$	−1.43562e10	−	2.48656e10i	−0.0278937	−	0.0483132i
$848$	2.03071e11	+	5.57934e11i	0.392704	+	1.07894i
$849$		0			0
$850$	−2.21863e11	+	1.86165e11i	−0.425019	+	0.356633i
$851$	8.99368e11	+	1.07183e12i	1.71482	+	2.04365i
$852$		0			0
$853$	1.83293e11	−	6.67134e10i	0.346219	−	0.126013i	−0.163057	−	0.986617i	$-0.552135\pi$
$853$	1.83293e11	−	6.67134e10i	0.346219	−	0.126013i	0.509276	+	0.860603i	$0.329913\pi$
$854$	−7.59892e11	+	4.38724e11i	−1.42863	+	0.824821i
$855$		0			0
$856$	−1.60544e11	+	2.78071e11i	−0.299020	+	0.517918i
$857$	−2.11556e10	−	3.73031e9i	−0.0392195	−	0.00691546i	0.154004	−	0.988070i	$-0.450783\pi$
$857$	−2.11556e10	−	3.73031e9i	−0.0392195	−	0.00691546i	−0.193224	+	0.981155i	$0.561894\pi$
$858$		0			0
$859$	8.71300e11	+	3.17127e11i	1.60028	+	0.582453i	0.979484	−	0.201522i	$-0.0645886\pi$
$859$	8.71300e11	+	3.17127e11i	1.60028	+	0.582453i	0.620793	+	0.783975i	$0.286811\pi$
$860$	6.22464e11	−	1.09757e11i	1.13794	−	0.200650i
$861$		0			0
$862$	6.69104e10	+	5.61445e10i	0.121189	+	0.101690i
$863$		−	2.87460e9i		−	0.00518244i	−0.999997	−	0.00259122i	$-0.999175\pi$
$863$		−	2.87460e9i		−	0.00518244i	0.999997	−	0.00259122i	$-0.000824813\pi$
$864$		0			0
$865$	−1.81670e11			−0.324504
$866$	−1.40472e11	+	1.67408e11i	−0.249757	+	0.297648i
$867$		0			0
$868$	−2.95793e11	−	1.67752e12i	−0.521085	−	2.95522i
$869$	3.54003e11	−	9.72615e11i	0.620766	−	1.70554i
$870$		0			0
$871$	−1.53162e10	+	8.68623e10i	−0.0266120	+	0.150924i
$872$	−5.82538e10	−	3.36328e10i	−0.100753	−	0.0581698i
$873$		0			0
$874$	9.94124e11	+	1.72187e12i	1.70371	+	2.95091i
$875$	2.07112e11	+	5.69036e11i	0.353324	+	0.970750i
$876$		0			0
$877$	8.31838e11	−	6.97995e11i	1.40618	−	1.17992i	0.447901	−	0.894083i	$-0.352172\pi$
$877$	8.31838e11	−	6.97995e11i	1.40618	−	1.17992i	0.958277	−	0.285840i	$-0.0922726\pi$
$878$	4.83770e11	+	5.76534e11i	0.814068	+	0.970169i
$879$		0			0
$880$	2.52898e11	−	9.20473e10i	0.421711	−	0.153490i
$881$	2.65946e11	−	1.53544e11i	0.441458	−	0.254876i	−0.262758	−	0.964862i	$-0.584632\pi$
$881$	2.65946e11	−	1.53544e11i	0.441458	−	0.254876i	0.704216	+	0.709986i	$0.251299\pi$
$882$		0			0
$883$	2.24768e11	−	3.89309e11i	0.369736	−	0.640401i	−0.619788	−	0.784769i	$-0.712782\pi$
$883$	2.24768e11	−	3.89309e11i	0.369736	−	0.640401i	0.989524	+	0.144368i	$0.0461149\pi$
$884$	−5.69103e11	−	1.00348e11i	−0.931926	−	0.164324i
$885$		0			0
$886$	6.16667e10	+	2.24449e10i	0.100073	+	0.0364235i
$887$	6.48617e11	−	1.14369e11i	1.04784	−	0.184762i	0.376883	−	0.926261i	$-0.376996\pi$
$887$	6.48617e11	−	1.14369e11i	1.04784	−	0.184762i	0.670954	+	0.741499i	$0.265885\pi$
$888$		0			0
$889$	−2.56603e11	−	2.15316e11i	−0.410824	−	0.344722i
$890$			8.45122e11i			1.34697i
$891$		0			0
$892$	1.99450e12			3.15047
$893$	−1.91419e11	+	2.28124e11i	−0.301009	+	0.358729i
$894$		0			0
$895$	1.85949e10	+	1.05457e11i	0.0289802	+	0.164355i
$896$	3.97132e11	−	1.09111e12i	0.616173	−	1.69292i
$897$		0			0
$898$	−6.91961e10	+	3.92431e11i	−0.106408	+	0.603472i
$899$	−1.77183e11	−	1.02297e11i	−0.271259	−	0.156612i
$900$		0			0
$901$	−3.44670e11	−	5.96986e11i	−0.523004	−	0.905869i
$902$	3.28730e11	+	9.03178e11i	0.496607	+	1.36442i
$903$		0			0
$904$	−1.18090e12	+	9.90896e11i	−1.76824	+	1.48373i
$905$	−4.27560e11	−	5.09546e11i	−0.637386	−	0.759607i
$906$		0			0
$907$	4.96826e11	−	1.80830e11i	0.734133	−	0.267203i	0.0522199	−	0.998636i	$-0.483370\pi$
$907$	4.96826e11	−	1.80830e11i	0.734133	−	0.267203i	0.681913	+	0.731433i	$0.261148\pi$
$908$	−7.44767e11	+	4.29992e11i	−1.09566	+	0.632582i
$909$		0			0
$910$	−3.20610e11	+	5.55312e11i	−0.467532	+	0.809789i
$911$	−5.30787e11	−	9.35921e10i	−0.770632	−	0.135883i	−0.225511	−	0.974241i	$-0.572405\pi$
$911$	−5.30787e11	−	9.35921e10i	−0.770632	−	0.135883i	−0.545121	+	0.838357i	$0.683516\pi$
$912$		0			0
$913$	−6.44945e11	−	2.34741e11i	−0.928195	−	0.337835i
$914$	−9.95645e11	+	1.75559e11i	−1.42666	+	0.251558i
$915$		0			0
$916$	6.73175e11	+	5.64861e11i	0.956195	+	0.802343i
$917$		−	5.64269e10i		−	0.0798011i
$918$		0			0
$919$	−5.49365e11			−0.770193			−0.385096	−	0.922876i	$-0.625832\pi$
$919$	−5.49365e11			−0.770193			−0.385096	+	0.922876i	$0.625832\pi$
$920$	7.62679e11	−	9.08925e11i	1.06461	−	1.26875i
$921$		0			0
$922$	−1.01272e11	−	5.74340e11i	−0.140141	−	0.794777i
$923$	−2.28958e10	+	6.29057e10i	−0.0315463	+	0.0866729i
$924$		0			0
$925$	1.12293e11	−	6.36847e11i	0.153386	−	0.869897i
$926$	−1.55282e12	−	8.96523e11i	−2.11192	−	1.21932i
$927$		0			0
$928$	−2.60012e10	−	4.50353e10i	−0.0350591	−	0.0607242i
$929$	−3.96994e11	−	1.09073e12i	−0.532993	−	1.46439i	−0.855492	−	0.517815i	$-0.826745\pi$
$929$	−3.96994e11	−	1.09073e12i	−0.532993	−	1.46439i	0.322500	−	0.946570i	$-0.395477\pi$
$930$		0			0
$931$	−2.09374e10	+	1.75686e10i	−0.0278692	+	0.0233850i
$932$	−4.62409e11	−	5.51078e11i	−0.612862	−	0.730380i
$933$		0			0
$934$	1.86152e12	−	6.77539e11i	2.44614	−	0.890321i
$935$	−2.70600e11	+	1.56231e11i	−0.354063	+	0.204419i
$936$		0			0
$937$	−5.75641e11	+	9.97040e11i	−0.746781	+	1.29346i	0.202577	+	0.979266i	$0.435069\pi$
$937$	−5.75641e11	+	9.97040e11i	−0.746781	+	1.29346i	−0.949358	+	0.314197i	$0.898265\pi$
$938$	−2.39840e11	−	4.22903e10i	−0.309821	−	0.0546297i
$939$		0			0
$940$	3.55190e11	+	1.29278e11i	0.454934	+	0.165583i
$941$	−3.55574e11	+	6.26973e10i	−0.453494	+	0.0799633i	−0.395730	−	0.918367i	$-0.629508\pi$
$941$	−3.55574e11	+	6.26973e10i	−0.453494	+	0.0799633i	−0.0577644	+	0.998330i	$0.518397\pi$
$942$		0			0
$943$	8.54904e11	+	7.17350e11i	1.08111	+	0.907160i
$944$		−	5.46139e11i		−	0.687726i
$945$		0			0
$946$	−1.18183e12			−1.47567
$947$	6.87693e11	−	8.19561e11i	0.855056	−	1.01902i	−0.144508	−	0.989504i	$-0.546160\pi$
$947$	6.87693e11	−	8.19561e11i	0.855056	−	1.01902i	0.999564	−	0.0295127i	$-0.00939555\pi$
$948$		0			0
$949$	3.41327e10	+	1.93576e11i	0.0420829	+	0.238664i
$950$	3.14294e11	−	8.63515e11i	0.385870	−	1.06017i
$951$		0			0
$952$	1.30271e11	−	7.38802e11i	0.158599	−	0.899457i
$953$	5.39472e11	+	3.11464e11i	0.654029	+	0.377604i	0.789998	−	0.613109i	$-0.210081\pi$
$953$	5.39472e11	+	3.11464e11i	0.654029	+	0.377604i	−0.135969	+	0.990713i	$0.543415\pi$
$954$		0			0
$955$	1.63253e11	+	2.82762e11i	0.196267	+	0.339944i
$956$	2.59955e11	+	7.14220e11i	0.311219	+	0.855068i
$957$		0			0
$958$	−1.45884e12	+	1.22412e12i	−1.73200	+	1.45332i
$959$	2.71671e11	+	3.23765e11i	0.321195	+	0.382785i
$960$		0			0
$961$	−1.28530e12	+	4.67810e11i	−1.50699	+	0.548499i
$962$	1.70950e12	−	9.86980e11i	1.99604	−	1.15241i
$963$		0			0
$964$	7.02559e11	−	1.21687e12i	0.813532	−	1.40908i
$965$	−4.66683e11	−	8.22888e10i	−0.538161	−	0.0948924i
$966$		0			0
$967$	−1.56812e12	−	5.70747e11i	−1.79338	−	0.652737i	−0.998971	−	0.0453525i	$-0.985559\pi$
$967$	−1.56812e12	−	5.70747e11i	−1.79338	−	0.652737i	−0.794408	−	0.607384i	$-0.792219\pi$
$968$	7.38169e10	−	1.30159e10i	0.0840726	−	0.0148243i
$969$		0			0
$970$	1.27539e12	+	1.07018e12i	1.44064	+	1.20884i
$971$			7.30127e11i			0.821337i	0.911785	+	0.410669i	$0.134705\pi$
$971$			7.30127e11i			0.821337i	−0.911785	+	0.410669i	$0.865295\pi$
$972$		0			0
$973$	2.85940e11			0.319024
$974$	−8.37358e11	+	9.97924e11i	−0.930412	+	1.10882i
$975$		0			0
$976$	−1.04758e11	−	5.94114e11i	−0.115449	−	0.654742i
$977$	2.08200e11	−	5.72026e11i	0.228509	−	0.627823i	−0.771455	−	0.636284i	$-0.780471\pi$
$977$	2.08200e11	−	5.72026e11i	0.228509	−	0.627823i	0.999964	+	0.00846046i	$0.00269308\pi$
$978$		0			0
$979$	1.79364e11	−	1.01722e12i	0.195256	−	1.10735i
$980$	3.00439e10	+	1.73459e10i	0.0325726	+	0.0188058i
$981$		0			0
$982$	−8.12217e11	−	1.40680e12i	−0.873426	−	1.51282i
$983$	−3.00010e11	−	8.24270e11i	−0.321308	−	0.882785i	−0.990229	−	0.139452i	$-0.955466\pi$
$983$	−3.00010e11	−	8.24270e11i	−0.321308	−	0.882785i	0.668921	−	0.743333i	$-0.266756\pi$
$984$		0			0
$985$	7.64308e11	−	6.41331e11i	0.811939	−	0.681298i
$986$	−1.23189e11	−	1.46811e11i	−0.130336	−	0.155328i
$987$		0			0
$988$	1.72297e12	−	6.27112e11i	1.80822	−	0.658138i
$989$	−1.18839e12	+	6.86120e11i	−1.24215	+	0.717158i
$990$		0			0
$991$	8.34558e11	−	1.44550e12i	0.865290	−	1.49873i	−0.00146857	−	0.999999i	$-0.500467\pi$
$991$	8.34558e11	−	1.44550e12i	0.865290	−	1.49873i	0.866759	−	0.498728i	$-0.166199\pi$
$992$	−5.55862e11	−	9.80135e10i	−0.574011	−	0.101214i
$993$		0			0
$994$	−1.73692e11	−	6.32188e10i	−0.177924	−	0.0647591i
$995$	4.56899e11	−	8.05636e10i	0.466152	−	0.0821952i
$996$		0			0
$997$	−2.52060e11	−	2.11503e11i	−0.255107	−	0.214060i	0.506261	−	0.862381i	$-0.331027\pi$
$997$	−2.52060e11	−	2.11503e11i	−0.255107	−	0.214060i	−0.761368	+	0.648320i	$0.775472\pi$
$998$			2.48422e12i			2.50419i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.35.3		138
3.2	odd	2		27.9.f.a.11.21	yes	138
27.5	odd	18	inner	81.9.f.a.44.3		138
27.22	even	9		27.9.f.a.5.21	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.5.21	✓	138	27.22	even	9
27.9.f.a.11.21	yes	138	3.2	odd	2
81.9.f.a.35.3		138	1.1	even	1	trivial
81.9.f.a.44.3		138	27.5	odd	18	inner

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)

\(f(q)\)	\(=\)	\(q+(-17.4759 + 20.8269i) q^{2} +(-83.9009 - 475.826i) q^{4} +(-146.369 + 402.146i) q^{5} +(410.817 - 2329.86i) q^{7} +(5348.66 + 3088.05i) q^{8} +O(q^{10})\)	\(q+(-17.4759 + 20.8269i) q^{2} +(-83.9009 - 475.826i) q^{4} +(-146.369 + 402.146i) q^{5} +(410.817 - 2329.86i) q^{7} +(5348.66 + 3088.05i) q^{8} +(-5817.54 - 10076.3i) q^{10} +(4863.70 + 13362.9i) q^{11} +(17844.9 - 14973.6i) q^{13} +(41344.4 + 49272.4i) q^{14} +(-41555.9 + 15125.1i) q^{16} +(44464.6 - 25671.7i) q^{17} +(-81453.1 + 141081. i) q^{19} +(203632. + 35905.8i) q^{20} +(-363305. - 132232. i) q^{22} +(-442093. + 77952.8i) q^{23} +(158939. + 133365. i) q^{25} +633330. i q^{26} -1.14308e6 q^{28} +(-88250.5 + 105173. i) q^{29} +(258769. + 1.46755e6i) q^{31} +(-129546. + 355925. i) q^{32} +(-242396. + 1.37470e6i) q^{34} +(876814. + 506229. i) q^{35} +(-1.55840e6 - 2.69922e6i) q^{37} +(-1.51482e6 - 4.16193e6i) q^{38} +(-2.02473e6 + 1.69895e6i) q^{40} +(-1.59797e6 - 1.90439e6i) q^{41} +(2.87246e6 - 1.04549e6i) q^{43} +(5.95034e6 - 3.43543e6i) q^{44} +(6.10243e6 - 1.05697e7i) q^{46} +(1.80024e6 + 317432. i) q^{47} +(157658. + 57382.9i) q^{49} +(-5.55517e6 + 979527. i) q^{50} +(-8.62202e6 - 7.23474e6i) q^{52} -1.34261e7i q^{53} -6.08573e6 q^{55} +(9.39205e6 - 1.11930e7i) q^{56} +(-648173. - 3.67597e6i) q^{58} +(-4.22385e6 + 1.16049e7i) q^{59} +(-2.36887e6 + 1.34345e7i) q^{61} +(-3.50868e7 - 2.02574e7i) q^{62} +(-1.08094e7 - 1.87225e7i) q^{64} +(3.40964e6 + 9.36791e6i) q^{65} +(-2.90051e6 + 2.43382e6i) q^{67} +(-1.59459e7 - 1.90035e7i) q^{68} +(-2.58663e7 + 9.41455e6i) q^{70} +(-2.48872e6 + 1.43686e6i) q^{71} +(-4.21902e6 + 7.30756e6i) q^{73} +(8.34508e7 + 1.47146e7i) q^{74} +(7.39639e7 + 2.69207e7i) q^{76} +(3.31318e7 - 5.84203e6i) q^{77} +(-5.57564e7 - 4.67852e7i) q^{79} -1.89254e7i q^{80} +6.75885e7 q^{82} +(-3.10234e7 + 3.69722e7i) q^{83} +(3.81551e6 + 2.16388e7i) q^{85} +(-2.84244e7 + 7.80953e7i) q^{86} +(-1.52510e7 + 8.64929e7i) q^{88} +(-6.29044e7 - 3.63179e7i) q^{89} +(-2.75555e7 - 4.77274e7i) q^{91} +(7.41839e7 + 2.03819e8i) q^{92} +(-3.80719e7 + 3.19461e7i) q^{94} +(-4.48129e7 - 5.34060e7i) q^{95} +(-1.34464e8 + 4.89407e7i) q^{97} +(-3.95032e6 + 2.28072e6i) 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

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Database

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