LMFDB - Embedded newform 81.9.f.a.8.5

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			8.5
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-21.0020 - 3.70323i) q^{2} +(186.811 + 67.9935i) q^{4} +(-674.968 - 804.395i) q^{5} +(-2905.52 + 1057.52i) q^{7} +(1056.43 + 609.927i) q^{8} +(11196.8 + 19393.5i) q^{10} +(-10222.7 + 12182.9i) q^{11} +(-2471.50 - 14016.6i) q^{13} +(64938.1 - 11450.3i) q^{14} +(-58914.5 - 49435.1i) q^{16} +(-51541.5 + 29757.5i) q^{17} +(-57614.1 + 99790.5i) q^{19} +(-71397.5 - 196163. i) q^{20} +(259814. - 218010. i) q^{22} +(-134153. + 368583. i) q^{23} +(-123639. + 701192. i) q^{25} +303529. i q^{26} -614687. q^{28} +(-537040. - 94694.6i) q^{29} +(-1.32290e6 - 481496. i) q^{31} +(853524. + 1.01719e6i) q^{32} +(1.19268e6 - 434098. i) q^{34} +(2.81180e6 + 1.62339e6i) q^{35} +(-288762. - 500150. i) q^{37} +(1.57956e6 - 1.88245e6i) q^{38} +(-222430. - 1.26146e6i) q^{40} +(1.84569e6 - 325445. i) q^{41} +(-2.02555e6 - 1.69964e6i) q^{43} +(-2.73807e6 + 1.58082e6i) q^{44} +(4.18244e6 - 7.24419e6i) q^{46} +(-93440.3 - 256725. i) q^{47} +(2.90760e6 - 2.43977e6i) q^{49} +(5.19335e6 - 1.42686e7i) q^{50} +(491334. - 2.78649e6i) q^{52} -1.42090e7i q^{53} +1.66999e7 q^{55} +(-3.71448e6 - 654963. i) q^{56} +(1.09283e7 + 3.97756e6i) q^{58} +(1.70695e6 + 2.03426e6i) q^{59} +(17548.6 - 6387.15i) q^{61} +(2.60005e7 + 1.50114e7i) q^{62} +(-4.31471e6 - 7.47329e6i) q^{64} +(-9.60669e6 + 1.14488e7i) q^{65} +(5.50666e6 + 3.12298e7i) q^{67} +(-1.16518e7 + 2.05453e6i) q^{68} +(-5.30418e7 - 4.45073e7i) q^{70} +(3.18584e7 - 1.83935e7i) q^{71} +(1.44422e7 - 2.50147e7i) q^{73} +(4.21241e6 + 1.15735e7i) q^{74} +(-1.75480e7 + 1.47245e7i) q^{76} +(1.68185e7 - 4.62085e7i) q^{77} +(1.46028e6 - 8.28165e6i) q^{79} +8.07577e7i q^{80} -3.99685e7 q^{82} +(-6.33917e7 - 1.11777e7i) q^{83} +(5.87257e7 + 2.13744e7i) q^{85} +(3.62466e7 + 4.31970e7i) q^{86} +(-1.82302e7 + 6.63526e6i) q^{88} +(-7.86470e7 - 4.54069e7i) q^{89} +(2.20039e7 + 3.81118e7i) q^{91} +(-5.01225e7 + 5.97336e7i) q^{92} +(1.01173e6 + 5.73778e6i) q^{94} +(1.19159e8 - 2.10109e7i) q^{95} +(-8.25735e7 - 6.92874e7i) q^{97} +(-7.01007e7 + 4.04726e7i) 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} - 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}+ \cdots - 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

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{18}\right)$

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 $

$2$	−21.0020	−	3.70323i	−1.31263	−	0.231452i	−0.526849	−	0.849959i	$-0.676627\pi$
$2$	−21.0020	−	3.70323i	−1.31263	−	0.231452i	−0.785779	+	0.618507i	$0.787738\pi$
$3$		0			0
$3$		0			0
$4$	186.811	+	67.9935i	0.729729	+	0.265600i
$5$	−674.968	−	804.395i	−1.07995	−	1.28703i	−0.955559	−	0.294799i	$-0.904747\pi$
$5$	−674.968	−	804.395i	−1.07995	−	1.28703i	−0.124390	−	0.992233i	$-0.539697\pi$
$6$		0			0
$7$	−2905.52	+	1057.52i	−1.21013	+	0.440451i	−0.866749	−	0.498745i	$-0.833794\pi$
$7$	−2905.52	+	1057.52i	−1.21013	+	0.440451i	−0.343381	+	0.939196i	$0.611572\pi$
$8$	1056.43	+	609.927i	0.257916	+	0.148908i
$9$		0			0
$10$	11196.8	+	19393.5i	1.11968	+	1.93935i
$11$	−10222.7	+	12182.9i	−0.698224	+	0.832111i	−0.992324	−	0.123664i	$-0.960536\pi$
$11$	−10222.7	+	12182.9i	−0.698224	+	0.832111i	0.294100	+	0.955775i	$0.404980\pi$
$12$		0			0
$13$	−2471.50	−	14016.6i	−0.0865341	−	0.490759i	−0.997015	−	0.0772082i	$-0.975399\pi$
$13$	−2471.50	−	14016.6i	−0.0865341	−	0.490759i	0.910481	−	0.413551i	$-0.135712\pi$
$14$	64938.1	−	11450.3i	1.69039	−	0.298062i
$15$		0			0
$16$	−58914.5	−	49435.1i	−0.898964	−	0.754320i
$17$	−51541.5	+	29757.5i	−0.617108	+	0.356288i	−0.775742	−	0.631050i	$-0.782624\pi$
$17$	−51541.5	+	29757.5i	−0.617108	+	0.356288i	0.158634	+	0.987337i	$0.449291\pi$
$18$		0			0
$19$	−57614.1	+	99790.5i	−0.442094	+	0.765728i	−0.997845	−	0.0656202i	$-0.979097\pi$
$19$	−57614.1	+	99790.5i	−0.442094	+	0.765728i	0.555751	+	0.831349i	$0.312431\pi$
$20$	−71397.5	−	196163.i	−0.446235	−	1.22602i
$21$		0			0
$22$	259814.	−	218010.i	1.10910	−	0.930647i
$23$	−134153.	+	368583.i	−0.479391	+	1.31711i	0.430621	+	0.902533i	$0.358294\pi$
$23$	−134153.	+	368583.i	−0.479391	+	1.31711i	−0.910012	+	0.414582i	$0.863928\pi$
$24$		0			0
$25$	−123639.	+	701192.i	−0.316516	+	1.79505i
$26$			303529.i			0.664213i
$27$		0			0
$28$	−614687.			−1.00005
$29$	−537040.	−	94694.6i	−0.759302	−	0.133885i	−0.219425	−	0.975629i	$-0.570418\pi$
$29$	−537040.	−	94694.6i	−0.759302	−	0.133885i	−0.539877	+	0.841744i	$0.681529\pi$
$30$		0			0
$31$	−1.32290e6	−	481496.i	−1.43245	−	0.521370i	−0.494819	−	0.868996i	$-0.664766\pi$
$31$	−1.32290e6	−	481496.i	−1.43245	−	0.521370i	−0.937633	+	0.347626i	$0.886988\pi$
$32$	853524.	+	1.01719e6i	0.813984	+	0.970068i
$33$		0			0
$34$	1.19268e6	−	434098.i	0.892497	−	0.324842i
$35$	2.81180e6	+	1.62339e6i	1.87375	+	1.08181i
$36$		0			0
$37$	−288762.	−	500150.i	−0.154075	−	0.266866i	0.778647	−	0.627463i	$-0.215906\pi$
$37$	−288762.	−	500150.i	−0.154075	−	0.266866i	−0.932722	+	0.360597i	$0.882573\pi$
$38$	1.57956e6	−	1.88245e6i	0.757533	−	0.902793i
$39$		0			0
$40$	−222430.	−	1.26146e6i	−0.0868868	−	0.492760i
$41$	1.84569e6	−	325445.i	0.653167	−	0.115171i	0.162761	−	0.986665i	$-0.447960\pi$
$41$	1.84569e6	−	325445.i	0.653167	−	0.115171i	0.490405	+	0.871495i	$0.336849\pi$
$42$		0			0
$43$	−2.02555e6	−	1.69964e6i	−0.592475	−	0.497145i	0.296542	−	0.955020i	$-0.404166\pi$
$43$	−2.02555e6	−	1.69964e6i	−0.592475	−	0.497145i	−0.889017	+	0.457874i	$0.848611\pi$
$44$	−2.73807e6	+	1.58082e6i	−0.730523	+	0.421767i
$45$		0			0
$46$	4.18244e6	−	7.24419e6i	0.934110	−	1.61793i
$47$	−93440.3	−	256725.i	−0.0191488	−	0.0526110i	0.929750	−	0.368192i	$-0.120023\pi$
$47$	−93440.3	−	256725.i	−0.0191488	−	0.0526110i	−0.948899	+	0.315581i	$0.897801\pi$
$48$		0			0
$49$	2.90760e6	−	2.43977e6i	0.504372	−	0.423218i
$50$	5.19335e6	−	1.42686e7i	0.830935	−	2.28298i
$51$		0			0
$52$	491334.	−	2.78649e6i	0.0671991	−	0.381105i
$53$		−	1.42090e7i		−	1.80077i	−0.435092	−	0.900386i	$-0.643284\pi$
$53$		−	1.42090e7i		−	1.80077i	0.435092	−	0.900386i	$-0.356716\pi$
$54$		0			0
$55$	1.66999e7			1.82500
$56$	−3.71448e6	−	654963.i	−0.377699	−	0.0665985i
$57$		0			0
$58$	1.09283e7	+	3.97756e6i	0.965693	+	0.351484i
$59$	1.70695e6	+	2.03426e6i	0.140868	+	0.167880i	0.831866	−	0.554977i	$-0.187273\pi$
$59$	1.70695e6	+	2.03426e6i	0.140868	+	0.167880i	−0.690998	+	0.722857i	$0.742829\pi$
$60$		0			0
$61$	17548.6	−	6387.15i	0.00126742	−	0.000461305i	−0.341386	−	0.939923i	$-0.610896\pi$
$61$	17548.6	−	6387.15i	0.00126742	−	0.000461305i	0.342654	+	0.939462i	$0.388674\pi$
$62$	2.60005e7	+	1.50114e7i	1.75960	+	1.01591i
$63$		0			0
$64$	−4.31471e6	−	7.47329e6i	−0.257177	−	0.445443i
$65$	−9.60669e6	+	1.14488e7i	−0.538171	+	0.641367i
$66$		0			0
$67$	5.50666e6	+	3.12298e7i	0.273268	+	1.54978i	0.744410	+	0.667722i	$0.232731\pi$
$67$	5.50666e6	+	3.12298e7i	0.273268	+	1.54978i	−0.471143	+	0.882057i	$0.656158\pi$
$68$	−1.16518e7	+	2.05453e6i	−0.544952	+	0.0960897i
$69$		0			0
$70$	−5.30418e7	−	4.45073e7i	−2.20915	−	1.85370i
$71$	3.18584e7	−	1.83935e7i	1.25369	−	0.723819i	0.281851	−	0.959458i	$-0.409052\pi$
$71$	3.18584e7	−	1.83935e7i	1.25369	−	0.723819i	0.971841	+	0.235639i	$0.0757184\pi$
$72$		0			0
$73$	1.44422e7	−	2.50147e7i	0.508561	−	0.880853i	−0.491390	−	0.870939i	$-0.663511\pi$
$73$	1.44422e7	−	2.50147e7i	0.508561	−	0.880853i	0.999951	−	0.00991319i	$-0.00315552\pi$
$74$	4.21241e6	+	1.15735e7i	0.140477	+	0.385957i
$75$		0			0
$76$	−1.75480e7	+	1.47245e7i	−0.525986	+	0.441354i
$77$	1.68185e7	−	4.62085e7i	0.478437	−	1.31450i
$78$		0			0
$79$	1.46028e6	−	8.28165e6i	0.0374910	−	0.212622i	−0.960307	−	0.278944i	$-0.910015\pi$
$79$	1.46028e6	−	8.28165e6i	0.0374910	−	0.212622i	0.997798	+	0.0663224i	$0.0211266\pi$
$80$			8.07577e7i			1.97162i
$81$		0			0
$82$	−3.99685e7			−0.884021
$83$	−6.33917e7	−	1.11777e7i	−1.33573	−	0.235526i	−0.540252	−	0.841503i	$-0.681671\pi$
$83$	−6.33917e7	−	1.11777e7i	−1.33573	−	0.235526i	−0.795482	+	0.605977i	$0.792782\pi$
$84$		0			0
$85$	5.87257e7	+	2.13744e7i	1.12500	+	0.409466i
$86$	3.62466e7	+	4.31970e7i	0.662634	+	0.789696i
$87$		0			0
$88$	−1.82302e7	+	6.63526e6i	−0.303991	+	0.110644i
$89$	−7.86470e7	−	4.54069e7i	−1.25349	−	0.723705i	−0.281693	−	0.959505i	$-0.590896\pi$
$89$	−7.86470e7	−	4.54069e7i	−1.25349	−	0.723705i	−0.971802	+	0.235799i	$0.924229\pi$
$90$		0			0
$91$	2.20039e7	+	3.81118e7i	0.320873	+	0.555768i
$92$	−5.01225e7	+	5.97336e7i	−0.699650	+	0.833811i
$93$		0			0
$94$	1.01173e6	+	5.73778e6i	0.0129584	+	0.0734907i
$95$	1.19159e8	−	2.10109e7i	1.46296	−	0.257959i
$96$		0			0
$97$	−8.25735e7	−	6.92874e7i	−0.932725	−	0.782650i	0.0435792	−	0.999050i	$-0.486124\pi$
$97$	−8.25735e7	−	6.92874e7i	−0.932725	−	0.782650i	−0.976305	+	0.216400i	$0.930568\pi$
$98$	−7.01007e7	+	4.04726e7i	−0.760007	+	0.438791i
$99$		0			0
$100$	−7.07736e7	+	1.22583e8i	−0.707736	+	1.22583i
$101$	2.61672e7	+	7.18939e7i	0.251462	+	0.690886i	0.999625	+	0.0273717i	$0.00871377\pi$
$101$	2.61672e7	+	7.18939e7i	0.251462	+	0.690886i	−0.748163	+	0.663515i	$0.769064\pi$
$102$		0			0
$103$	−6.94734e7	+	5.82951e7i	−0.617262	+	0.517944i	−0.896942	−	0.442149i	$-0.854216\pi$
$103$	−6.94734e7	+	5.82951e7i	−0.617262	+	0.517944i	0.279680	+	0.960093i	$0.409772\pi$
$104$	5.93814e6	−	1.63149e7i	0.0507595	−	0.139460i
$105$		0			0
$106$	−5.26190e7	+	2.98417e8i	−0.416792	+	2.36374i
$107$			2.72990e7i			0.208263i	0.994564	+	0.104131i	$0.0332062\pi$
$107$			2.72990e7i			0.208263i	−0.994564	+	0.104131i	$0.966794\pi$
$108$		0			0
$109$	3.17690e7			0.225060			0.112530	−	0.993648i	$-0.464105\pi$
$109$	3.17690e7			0.225060			0.112530	+	0.993648i	$0.464105\pi$
$110$	−3.50732e8	−	6.18435e7i	−2.39555	−	0.422399i
$111$		0			0
$112$	2.23456e8	+	8.13314e7i	1.42010	+	0.516876i
$113$	−9.72358e7	−	1.15881e8i	−0.596365	−	0.710720i	0.380451	−	0.924801i	$-0.375769\pi$
$113$	−9.72358e7	−	1.15881e8i	−0.596365	−	0.710720i	−0.976816	+	0.214081i	$0.931324\pi$
$114$		0			0
$115$	3.87035e8	−	1.40869e8i	2.21289	−	0.805425i
$116$	−9.38862e7	−	5.42052e7i	−0.518525	−	0.299371i
$117$		0			0
$118$	−2.83161e7	−	4.90449e7i	−0.146051	−	0.252968i
$119$	1.18286e8	−	1.40967e8i	0.589854	−	0.702960i
$120$		0			0
$121$	−6.69735e6	−	3.79826e7i	−0.0312437	−	0.177192i
$122$	−392209.	+	69157.0i	−0.00177043	+	0.000312174i
$123$		0			0
$124$	−2.14393e8	−	1.79897e8i	−0.906826	−	0.760918i
$125$	2.92261e8	−	1.68737e8i	1.19710	−	0.691146i
$126$		0			0
$127$	−2.92514e7	+	5.06648e7i	−0.112443	+	0.194756i	−0.916755	−	0.399451i	$-0.869201\pi$
$127$	−2.92514e7	+	5.06648e7i	−0.112443	+	0.194756i	0.804312	+	0.594207i	$0.202534\pi$
$128$	−5.33201e7	−	1.46496e8i	−0.198633	−	0.545739i
$129$		0			0
$130$	2.44158e8	−	2.04873e8i	0.854864	−	0.717316i
$131$	−1.70510e8	+	4.68473e8i	−0.578983	+	1.59074i	0.210916	+	0.977504i	$0.432355\pi$
$131$	−1.70510e8	+	4.68473e8i	−0.578983	+	1.59074i	−0.789898	+	0.613238i	$0.789867\pi$
$132$		0			0
$133$	6.18681e7	−	3.50872e8i	0.197725	−	1.12135i
$134$		−	6.76282e8i		−	2.09753i
$135$		0			0
$136$	−7.25996e7			−0.212216
$137$	9.32438e7	+	1.64414e7i	0.264690	+	0.0466720i	0.304418	−	0.952539i	$-0.401538\pi$
$137$	9.32438e7	+	1.64414e7i	0.264690	+	0.0466720i	−0.0397280	+	0.999211i	$0.512649\pi$
$138$		0			0
$139$	−9.96628e7	−	3.62743e7i	−0.266977	−	0.0971717i	0.205063	−	0.978749i	$-0.434260\pi$
$139$	−9.96628e7	−	3.62743e7i	−0.266977	−	0.0971717i	−0.472040	+	0.881577i	$0.656482\pi$
$140$	4.14894e8	+	4.94452e8i	1.08000	+	1.28710i
$141$		0			0
$142$	−7.37207e8	+	2.68321e8i	−1.81316	+	0.659936i
$143$	1.96028e8	+	1.13177e8i	0.468786	+	0.270654i
$144$		0			0
$145$	2.86313e8	+	4.95908e8i	0.647692	+	1.12184i
$146$	−3.95951e8	+	4.71876e8i	−0.871425	+	1.03852i
$147$		0			0
$148$	−1.99368e7	−	1.13067e8i	−0.0415536	−	0.235662i
$149$	1.86930e8	−	3.29607e7i	0.379256	−	0.0668731i	0.0192296	−	0.999815i	$-0.493879\pi$
$149$	1.86930e8	−	3.29607e7i	0.379256	−	0.0668731i	0.360027	+	0.932942i	$0.382768\pi$
$150$		0			0
$151$	−7.60027e7	−	6.37738e7i	−0.146191	−	0.122669i	0.566759	−	0.823884i	$-0.308197\pi$
$151$	−7.60027e7	−	6.37738e7i	−0.146191	−	0.122669i	−0.712950	+	0.701215i	$0.752641\pi$
$152$	−1.21730e8	+	7.02808e7i	−0.228046	+	0.131663i
$153$		0			0
$154$	−5.24344e8	+	9.08190e8i	−0.932252	+	1.61471i
$155$	5.05602e8	+	1.38913e9i	0.875955	+	2.40667i
$156$		0			0
$157$	−3.32177e7	+	2.78730e7i	−0.0546727	+	0.0458759i	−0.669715	−	0.742619i	$-0.733584\pi$
$157$	−3.32177e7	+	2.78730e7i	−0.0546727	+	0.0458759i	0.615042	+	0.788494i	$0.289139\pi$
$158$	−6.13376e7	+	1.68524e8i	−0.0984235	+	0.270416i
$159$		0			0
$160$	2.42122e8	−	1.37314e9i	0.369449	−	2.09525i
$161$		−	1.21279e9i		−	1.80503i
$162$		0			0
$163$	−7.51766e8			−1.06496			−0.532478	−	0.846444i	$-0.678739\pi$
$163$	−7.51766e8			−1.06496			−0.532478	+	0.846444i	$0.678739\pi$
$164$	3.66923e8	+	6.46985e7i	0.507224	+	0.0894373i
$165$		0			0
$166$	1.28996e9	+	4.69508e8i	1.69881	+	0.618316i
$167$	−1.17974e8	−	1.40597e8i	−0.151678	−	0.180763i	0.684855	−	0.728679i	$-0.259866\pi$
$167$	−1.17974e8	−	1.40597e8i	−0.151678	−	0.180763i	−0.836533	+	0.547917i	$0.815421\pi$
$168$		0			0
$169$	5.76180e8	−	2.09712e8i	0.706336	−	0.257085i
$170$	−1.15420e9	−	6.66380e8i	−1.38193	−	0.797860i
$171$		0			0
$172$	−2.62830e8	−	4.55236e8i	−0.300304	−	0.520143i
$173$	5.72682e8	−	6.82496e8i	0.639336	−	0.761931i	−0.344929	−	0.938629i	$-0.612097\pi$
$173$	5.72682e8	−	6.82496e8i	0.639336	−	0.761931i	0.984265	+	0.176698i	$0.0565415\pi$
$174$		0			0
$175$	−3.82291e8	−	2.16808e9i	−0.407607	−	2.31165i
$176$	1.20453e9	−	2.12391e8i	1.25536	−	0.221353i
$177$		0			0
$178$	1.48360e9	+	1.24489e9i	1.47787	+	1.24008i
$179$	−1.02095e8	+	5.89445e7i	−0.0994471	+	0.0574158i	−0.548899	−	0.835889i	$-0.684953\pi$
$179$	−1.02095e8	+	5.89445e7i	−0.0994471	+	0.0574158i	0.449452	+	0.893305i	$0.351619\pi$
$180$		0			0
$181$	−8.36215e7	+	1.44837e8i	−0.0779119	+	0.134947i	−0.902349	−	0.431006i	$-0.858159\pi$
$181$	−8.36215e7	+	1.44837e8i	−0.0779119	+	0.134947i	0.824437	+	0.565954i	$0.191492\pi$
$182$	−3.20989e8	−	8.81911e8i	−0.292553	−	0.803784i
$183$		0			0
$184$	−3.66531e8	+	3.07556e8i	−0.319772	+	0.268320i
$185$	−2.07413e8	+	5.69863e8i	−0.177072	+	0.486501i
$186$		0			0
$187$	1.64359e8	−	9.32129e8i	0.134409	−	0.762271i
$188$		−	5.43123e7i		−	0.0434777i
$189$		0			0
$190$	−2.58038e9			−1.98002
$191$	−6.68879e7	−	1.17941e7i	−0.0502590	−	0.00886202i	0.148462	−	0.988918i	$-0.452568\pi$
$191$	−6.68879e7	−	1.17941e7i	−0.0502590	−	0.00886202i	−0.198721	+	0.980056i	$0.563679\pi$
$192$		0			0
$193$	1.98206e9	+	7.21409e8i	1.42852	+	0.519939i	0.936507	−	0.350649i	$-0.114039\pi$
$193$	1.98206e9	+	7.21409e8i	1.42852	+	0.519939i	0.492014	+	0.870588i	$0.336261\pi$
$194$	1.47763e9	+	1.76097e9i	1.04318	+	1.24321i
$195$		0			0
$196$	7.09060e8	−	2.58077e8i	0.480462	−	0.174874i
$197$	−3.26541e8	−	1.88529e8i	−0.216807	−	0.125174i	0.387664	−	0.921801i	$-0.373282\pi$
$197$	−3.26541e8	−	1.88529e8i	−0.216807	−	0.125174i	−0.604471	+	0.796627i	$0.706615\pi$
$198$		0			0
$199$	1.40761e8	+	2.43804e8i	0.0897571	+	0.155464i	0.907408	−	0.420250i	$-0.138058\pi$
$199$	1.40761e8	+	2.43804e8i	0.0897571	+	0.155464i	−0.817651	+	0.575714i	$0.804724\pi$
$200$	−5.58291e8	+	6.65346e8i	−0.348932	+	0.415841i
$201$		0			0
$202$	−2.83326e8	−	1.60682e9i	−0.170169	−	0.965078i
$203$	1.66052e9	−	2.92795e8i	0.977824	−	0.172417i
$204$		0			0
$205$	−1.50757e9	−	1.26500e9i	−0.853615	−	0.716268i
$206$	1.67496e9	−	9.67040e8i	0.930114	−	0.537002i
$207$		0			0
$208$	−5.47304e8	+	9.47958e8i	−0.292399	+	0.506449i
$209$	−6.26770e8	−	1.72204e9i	−0.328491	−	0.902521i
$210$		0			0
$211$	−7.13150e8	+	5.98404e8i	−0.359791	+	0.301901i	−0.804708	−	0.593671i	$-0.797678\pi$
$211$	−7.13150e8	+	5.98404e8i	−0.359791	+	0.301901i	0.444916	+	0.895572i	$0.353233\pi$
$212$	9.66117e8	−	2.65438e9i	0.478284	−	1.31408i
$213$		0			0
$214$	1.01094e8	−	5.73334e8i	0.0482027	−	0.273371i
$215$			2.77655e9i			1.29943i
$216$		0			0
$217$	4.35291e9			1.96309
$218$	−6.67214e8	−	1.17648e8i	−0.295420	−	0.0520904i
$219$		0			0
$220$	3.11972e9	+	1.13548e9i	1.33176	+	0.484719i
$221$	5.44483e8	+	6.48890e8i	0.228252	+	0.272021i
$222$		0			0
$223$	−3.49114e9	+	1.27067e9i	−1.41172	+	0.513823i	−0.931633	−	0.363400i	$-0.881616\pi$
$223$	−3.49114e9	+	1.27067e9i	−1.41172	+	0.513823i	−0.480084	+	0.877223i	$0.659394\pi$
$224$	−3.55563e9	−	2.05285e9i	−1.41229	−	0.815388i
$225$		0			0
$226$	1.61302e9	+	2.79383e9i	0.618308	+	1.07094i
$227$	−3.19033e9	+	3.80209e9i	−1.20152	+	1.43192i	−0.328317	+	0.944568i	$0.606481\pi$
$227$	−3.19033e9	+	3.80209e9i	−1.20152	+	1.43192i	−0.873206	+	0.487352i	$0.837963\pi$
$228$		0			0
$229$	−3.85206e7	−	2.18461e8i	−0.0140072	−	0.0794387i	0.977003	−	0.213226i	$-0.0683971\pi$
$229$	−3.85206e7	−	2.18461e8i	−0.0140072	−	0.0794387i	−0.991010	+	0.133788i	$0.957286\pi$
$230$	−8.65020e9	+	1.52526e9i	−3.09111	+	0.545047i
$231$		0			0
$232$	−5.09586e8	−	4.27593e8i	−0.175900	−	0.147597i
$233$	3.33983e9	−	1.92825e9i	1.13319	−	0.654245i	0.188451	−	0.982083i	$-0.439653\pi$
$233$	3.33983e9	−	1.92825e9i	1.13319	−	0.654245i	0.944734	+	0.327838i	$0.106320\pi$
$234$		0			0
$235$	−1.43439e8	+	2.48444e8i	−0.0470323	+	0.0814624i
$236$	1.80560e8	+	4.96083e8i	0.0582066	+	0.159921i
$237$		0			0
$238$	−3.00628e9	+	2.52256e9i	−0.936960	+	0.786202i
$239$	8.10901e8	−	2.22793e9i	0.248529	−	0.682827i	−0.751212	−	0.660061i	$-0.770531\pi$
$239$	8.10901e8	−	2.22793e9i	0.248529	−	0.682827i	0.999741	−	0.0227658i	$-0.00724722\pi$
$240$		0			0
$241$	−1.10549e8	+	6.26955e8i	−0.0327708	+	0.185853i	−0.996799	−	0.0799471i	$-0.974525\pi$
$241$	−1.10549e8	+	6.26955e8i	−0.0327708	+	0.185853i	0.964028	+	0.265800i	$0.0856360\pi$
$242$			8.22514e8i			0.239818i
$243$		0			0
$244$	3.71254e6			0.00104740
$245$	−3.92508e9	−	6.92098e8i	−1.08939	−	0.192089i
$246$		0			0
$247$	1.54111e9	+	5.60920e8i	0.414045	+	0.150700i
$248$	−1.10387e9	−	1.31554e9i	−0.291817	−	0.347773i
$249$		0			0
$250$	−6.76294e9	+	2.46151e9i	−1.73131	+	0.630146i
$251$	5.54517e9	+	3.20150e9i	1.39707	+	0.806601i	0.994085	−	0.108603i	$-0.0346378\pi$
$251$	5.54517e9	+	3.20150e9i	1.39707	+	0.806601i	0.402990	+	0.915205i	$0.367971\pi$
$252$		0			0
$253$	−3.11901e9	−	5.40229e9i	−0.761263	−	1.31855i
$254$	8.01962e8	−	9.55741e8i	0.192672	−	0.229618i
$255$		0			0
$256$	9.60936e8	+	5.44974e9i	0.223735	+	1.26887i
$257$	3.54271e9	−	6.24675e8i	0.812088	−	0.143193i	0.247843	−	0.968800i	$-0.420278\pi$
$257$	3.54271e9	−	6.24675e8i	0.812088	−	0.143193i	0.564245	+	0.825607i	$0.309167\pi$
$258$		0			0
$259$	1.36792e9	+	1.14782e9i	0.303992	+	0.255080i
$260$	−2.57308e9	+	1.48557e9i	−0.563066	+	0.325086i
$261$		0			0
$262$	5.31593e9	−	9.20746e9i	1.12817	−	1.95405i
$263$	5.42885e8	+	1.49157e9i	0.113471	+	0.311759i	0.983409	−	0.181402i	$-0.0580635\pi$
$263$	5.42885e8	+	1.49157e9i	0.113471	+	0.311759i	−0.869938	+	0.493161i	$0.835841\pi$
$264$		0			0
$265$	−1.14296e10	+	9.59059e9i	−2.31765	+	1.94474i
$266$	−2.59871e9	+	7.13991e9i	−0.519077	+	1.42615i
$267$		0			0
$268$	−1.09472e9	+	6.20847e9i	−0.212209	+	1.20350i
$269$			9.64634e9i			1.84227i	0.389243	+	0.921135i	$0.372737\pi$
$269$			9.64634e9i			1.84227i	−0.389243	+	0.921135i	$0.627263\pi$
$270$		0			0
$271$	4.23418e9			0.785041			0.392520	−	0.919743i	$-0.371603\pi$
$271$	4.23418e9			0.785041			0.392520	+	0.919743i	$0.371603\pi$
$272$	4.50761e9	+	7.94813e8i	0.823513	+	0.145208i
$273$		0			0
$274$	−1.89742e9	−	6.90606e8i	−0.336637	−	0.122526i
$275$	−7.27865e9	−	8.67436e9i	−1.27268	−	1.51672i
$276$		0			0
$277$	8.21243e9	−	2.98908e9i	1.39493	−	0.507713i	0.468261	−	0.883590i	$-0.344881\pi$
$277$	8.21243e9	−	2.98908e9i	1.39493	−	0.507713i	0.926669	+	0.375877i	$0.122659\pi$
$278$	1.95879e9	+	1.13091e9i	0.327951	+	0.189343i
$279$		0			0
$280$	1.98030e9	+	3.42999e9i	0.322181	+	0.558034i
$281$	−2.77147e9	+	3.30292e9i	−0.444514	+	0.529751i	−0.941051	−	0.338264i	$-0.890160\pi$
$281$	−2.77147e9	+	3.30292e9i	−0.444514	+	0.529751i	0.496537	+	0.868016i	$0.334605\pi$
$282$		0			0
$283$	−7.35796e8	−	4.17291e9i	−0.114713	−	0.650568i	−0.986892	−	0.161382i	$-0.948405\pi$
$283$	−7.35796e8	−	4.17291e9i	−0.114713	−	0.650568i	0.872179	−	0.489186i	$-0.162706\pi$
$284$	7.20213e9	−	1.26993e9i	1.10710	−	0.195212i
$285$		0			0
$286$	−3.69788e9	−	3.10289e9i	−0.552699	−	0.463769i
$287$	−5.01853e9	+	2.89745e9i	−0.739689	+	0.427060i
$288$		0			0
$289$	−1.71686e9	+	2.97369e9i	−0.246118	+	0.426289i
$290$	−4.17669e9	−	1.14754e10i	−0.590528	−	1.62246i
$291$		0			0
$292$	4.39880e9	−	3.69103e9i	0.605066	−	0.507710i
$293$	4.29662e9	−	1.18049e10i	0.582984	−	1.60174i	−0.200070	−	0.979782i	$-0.564117\pi$
$293$	4.29662e9	−	1.18049e10i	0.582984	−	1.60174i	0.783054	−	0.621954i	$-0.213661\pi$
$294$		0			0
$295$	4.84216e8	−	2.74612e9i	0.0639368	−	0.362603i
$296$		−	7.04494e8i		−	0.0917721i
$297$		0			0
$298$	−4.04796e9			−0.513300
$299$	5.49783e9	+	9.69415e8i	0.687870	+	0.121290i
$300$		0			0
$301$	7.68270e9	+	2.79627e9i	0.935940	+	0.340654i
$302$	1.36004e9	+	1.62084e9i	0.163503	+	0.194855i
$303$		0			0
$304$	8.32746e9	−	3.03095e9i	0.975030	−	0.354882i
$305$	−1.69825e7	−	9.80486e6i	−0.00196247	−	0.00113303i
$306$		0			0
$307$	−5.43731e9	−	9.41771e9i	−0.612112	−	1.06021i	−0.990884	−	0.134719i	$-0.956987\pi$
$307$	−5.43731e9	−	9.41771e9i	−0.612112	−	1.06021i	0.378772	−	0.925490i	$-0.376347\pi$
$308$	6.28376e9	−	7.48869e9i	0.698259	−	0.832153i
$309$		0			0
$310$	−5.47441e9	−	3.10469e10i	−0.592776	−	3.36180i
$311$	4.61142e9	−	8.13118e8i	0.492939	−	0.0869184i	0.0783476	−	0.996926i	$-0.475036\pi$
$311$	4.61142e9	−	8.13118e8i	0.492939	−	0.0869184i	0.414591	+	0.910008i	$0.363924\pi$
$312$		0			0
$313$	−3.32589e9	−	2.79075e9i	−0.346521	−	0.290766i	0.452870	−	0.891577i	$-0.350400\pi$
$313$	−3.32589e9	−	2.79075e9i	−0.346521	−	0.290766i	−0.799391	+	0.600811i	$0.794845\pi$
$314$	8.00859e8	−	4.62376e8i	0.0823830	−	0.0475639i
$315$		0			0
$316$	8.35894e8	−	1.44781e9i	0.0838306	−	0.145199i
$317$	2.07900e9	+	5.71200e9i	0.205881	+	0.565655i	0.999061	−	0.0433336i	$-0.0137978\pi$
$317$	2.07900e9	+	5.71200e9i	0.205881	+	0.565655i	−0.793179	+	0.608988i	$0.791576\pi$
$318$		0			0
$319$	6.64366e9	−	5.57469e9i	0.641570	−	0.538342i
$320$	−3.09919e9	+	8.51497e9i	−0.295562	+	0.812051i
$321$		0			0
$322$	−4.49126e9	+	2.54712e10i	−0.417777	+	2.36933i
$323$		−	6.85780e9i		−	0.630050i
$324$		0			0
$325$	1.01339e10			0.908328
$326$	1.57886e10	+	2.78396e9i	1.39789	+	0.246486i
$327$		0			0
$328$	2.14833e9	+	7.81930e8i	0.185612	+	0.0675573i
$329$	5.42985e8	+	6.47105e8i	0.0463452	+	0.0552320i
$330$		0			0
$331$	2.20063e10	−	8.00962e9i	1.83330	−	0.667268i	0.841377	−	0.540448i	$-0.181745\pi$
$331$	2.20063e10	−	8.00962e9i	1.83330	−	0.667268i	0.991926	−	0.126820i	$-0.0404769\pi$
$332$	−1.10822e10	−	6.39833e9i	−0.912169	−	0.526641i
$333$		0			0
$334$	1.95704e9	+	3.38970e9i	0.157259	+	0.272380i
$335$	2.14043e10	−	2.55086e10i	1.69950	−	2.02539i
$336$		0			0
$337$	1.28715e9	+	7.29981e9i	0.0997954	+	0.565968i	0.993172	+	0.116659i	$0.0372186\pi$
$337$	1.28715e9	+	7.29981e9i	0.0997954	+	0.565968i	−0.893377	+	0.449309i	$0.851670\pi$
$338$	−1.28776e10	+	2.27066e9i	−0.986659	+	0.173975i
$339$		0			0
$340$	9.51726e9	+	7.98593e9i	0.712190	+	0.597599i
$341$	1.93896e10	−	1.11946e10i	1.43401	−	0.827926i
$342$		0			0
$343$	3.04436e9	−	5.27299e9i	0.219948	−	0.380961i
$344$	−1.10319e9	−	3.03098e9i	−0.0787800	−	0.216446i
$345$		0			0
$346$	−1.45549e10	+	1.22130e10i	−1.01556	+	0.852156i
$347$	−2.27175e9	+	6.24158e9i	−0.156691	+	0.430504i	−0.993052	−	0.117674i	$-0.962456\pi$
$347$	−2.27175e9	+	6.24158e9i	−0.156691	+	0.430504i	0.836362	+	0.548178i	$0.184678\pi$
$348$		0			0
$349$	1.68105e9	−	9.53368e9i	0.113313	−	0.642627i	−0.874259	−	0.485459i	$-0.838652\pi$
$349$	1.68105e9	−	9.53368e9i	0.113313	−	0.642627i	0.987572	−	0.157168i	$-0.0502364\pi$
$350$			4.69498e10i			3.12868i
$351$		0			0
$352$	−2.11177e10			−1.37555
$353$	−1.84985e10	−	3.26178e9i	−1.19134	−	0.210066i	−0.457391	−	0.889266i	$-0.651216\pi$
$353$	−1.84985e10	−	3.26178e9i	−1.19134	−	0.210066i	−0.733953	+	0.679200i	$0.762327\pi$
$354$		0			0
$355$	−3.62990e10	−	1.32118e10i	−2.28550	−	0.831854i
$356$	−1.16047e10	−	1.38300e10i	−0.722495	−	0.861037i
$357$		0			0
$358$	2.36249e9	−	8.59875e8i	0.143826	−	0.0523484i
$359$	−1.34240e10	−	7.75036e9i	−0.808173	−	0.466599i	0.0381478	−	0.999272i	$-0.487854\pi$
$359$	−1.34240e10	−	7.75036e9i	−0.808173	−	0.466599i	−0.846321	+	0.532673i	$0.821188\pi$
$360$		0			0
$361$	1.85302e9	+	3.20952e9i	0.109107	+	0.188978i
$362$	2.29259e9	−	2.73220e9i	0.133503	−	0.159103i
$363$		0			0
$364$	1.51920e9	+	8.61581e9i	0.0865385	+	0.490784i
$365$	−2.98697e10	+	5.26684e9i	−1.68291	+	0.296742i
$366$		0			0
$367$	1.31435e10	+	1.10287e10i	0.724515	+	0.607940i	0.928630	−	0.371007i	$-0.120987\pi$
$367$	1.31435e10	+	1.10287e10i	0.724515	+	0.607940i	−0.204116	+	0.978947i	$0.565432\pi$
$368$	2.61245e10	−	1.50830e10i	1.42448	−	0.822424i
$369$		0			0
$370$	6.46644e9	−	1.12002e10i	0.345031	−	0.597611i
$371$	1.50263e10	+	4.12844e10i	0.793152	+	2.17917i
$372$		0			0
$373$	−2.06095e10	+	1.72934e10i	−1.06471	+	0.893399i	−0.994563	−	0.104138i	$-0.966792\pi$
$373$	−2.06095e10	+	1.72934e10i	−1.06471	+	0.893399i	−0.0701485	+	0.997537i	$0.522347\pi$
$374$	−6.90377e9	+	1.89679e10i	−0.352858	+	0.969469i
$375$		0			0
$376$	5.78710e7	−	3.28203e8i	0.00289540	−	0.0164207i
$377$			7.76150e9i			0.384220i
$378$		0			0
$379$	3.45307e10			1.67359			0.836793	−	0.547519i	$-0.184428\pi$
$379$	3.45307e10			1.67359			0.836793	+	0.547519i	$0.184428\pi$
$380$	2.36887e10	+	4.17696e9i	1.13608	+	0.200321i
$381$		0			0
$382$	1.36111e9	+	4.95402e8i	0.0639203	+	0.0232651i
$383$	5.67412e9	+	6.76215e9i	0.263696	+	0.314260i	0.881604	−	0.471990i	$-0.156464\pi$
$383$	5.67412e9	+	6.76215e9i	0.263696	+	0.314260i	−0.617908	+	0.786250i	$0.712020\pi$
$384$		0			0
$385$	−4.85219e10	+	1.76605e10i	−2.20849	+	0.803823i
$386$	−3.89557e10	−	2.24911e10i	−1.75478	−	1.01312i
$387$		0			0
$388$	−1.07145e10	−	1.85581e10i	−0.472765	−	0.818854i
$389$	−1.23362e10	+	1.47017e10i	−0.538746	+	0.642052i	−0.964906	−	0.262596i	$-0.915421\pi$
$389$	−1.23362e10	+	1.47017e10i	−0.538746	+	0.642052i	0.426160	+	0.904648i	$0.359866\pi$
$390$		0			0
$391$	−4.05365e9	−	2.29894e10i	−0.173436	−	0.983603i
$392$	4.55975e9	−	8.04007e8i	0.193106	−	0.0340499i
$393$		0			0
$394$	6.15987e9	+	5.16875e9i	0.255615	+	0.214487i
$395$	−7.64736e9	+	4.41521e9i	−0.314140	+	0.181369i
$396$		0			0
$397$	−1.65088e10	+	2.85940e10i	−0.664589	+	1.15110i	0.314808	+	0.949155i	$0.398060\pi$
$397$	−1.65088e10	+	2.85940e10i	−0.664589	+	1.15110i	−0.979397	+	0.201946i	$0.935273\pi$
$398$	−2.05340e9	−	5.64166e9i	−0.0818353	−	0.224841i
$399$		0			0
$400$	4.19476e10	−	3.51982e10i	1.63858	−	1.37493i
$401$	7.96101e9	−	2.18727e10i	0.307887	−	0.845912i	−0.685182	−	0.728372i	$-0.740277\pi$
$401$	7.96101e9	−	2.18727e10i	0.307887	−	0.845912i	0.993068	−	0.117539i	$-0.0375006\pi$
$402$		0			0
$403$	−3.47938e9	+	1.97325e10i	−0.131911	+	0.748106i
$404$			1.52098e10i			0.570948i
$405$		0			0
$406$	−3.59587e10			−1.32343
$407$	9.04521e9	+	1.59491e9i	0.329641	+	0.0581246i
$408$		0			0
$409$	−1.42070e10	−	5.17093e9i	−0.507703	−	0.184789i	0.0754527	−	0.997149i	$-0.475960\pi$
$409$	−1.42070e10	−	5.17093e9i	−0.507703	−	0.184789i	−0.583155	+	0.812361i	$0.698182\pi$
$410$	2.69775e10	+	3.21505e10i	0.954697	+	1.13776i
$411$		0			0
$412$	−1.69421e10	+	6.16640e9i	−0.588000	+	0.214014i
$413$	−7.11085e9	−	4.10545e9i	−0.244411	−	0.141111i
$414$		0			0
$415$	3.37961e10	+	5.85366e10i	1.13939	+	1.97349i
$416$	1.21480e10	−	1.44775e10i	0.405633	−	0.483414i
$417$		0			0
$418$	6.78636e9	+	3.84874e10i	0.222296	+	1.26070i
$419$	−4.82910e10	+	8.51500e9i	−1.56679	+	0.276267i	−0.888621	−	0.458642i	$-0.848336\pi$
$419$	−4.82910e10	+	8.51500e9i	−1.56679	+	0.276267i	−0.678166	+	0.734909i	$0.737225\pi$
$420$		0			0
$421$	2.19607e10	+	1.84272e10i	0.699064	+	0.586584i	0.921507	−	0.388361i	$-0.126959\pi$
$421$	2.19607e10	+	1.84272e10i	0.699064	+	0.586584i	−0.222443	+	0.974946i	$0.571403\pi$
$422$	1.71936e10	−	9.92674e9i	0.542148	−	0.313009i
$423$		0			0
$424$	8.66643e9	−	1.50107e10i	0.268149	−	0.464448i
$425$	−1.44932e10	−	3.98197e10i	−0.444230	−	1.22051i
$426$		0			0
$427$	−4.42331e7	+	3.71160e7i	−0.00133057	+	0.00111648i
$428$	−1.85615e9	+	5.09974e9i	−0.0553145	+	0.151975i
$429$		0			0
$430$	1.02822e10	−	5.83132e10i	0.300754	−	1.70566i
$431$		−	1.31614e10i		−	0.381410i	−0.981647	−	0.190705i	$-0.938923\pi$
$431$		−	1.31614e10i		−	0.381410i	0.981647	−	0.190705i	$-0.0610774\pi$
$432$		0			0
$433$	−2.07765e10			−0.591046			−0.295523	−	0.955336i	$-0.595494\pi$
$433$	−2.07765e10			−0.591046			−0.295523	+	0.955336i	$0.595494\pi$
$434$	−9.14199e10	−	1.61198e10i	−2.57681	−	0.454361i
$435$		0			0
$436$	5.93479e9	+	2.16009e9i	0.164233	+	0.0597758i
$437$	−2.90519e10	−	3.46228e10i	−0.796617	−	0.949371i
$438$		0			0
$439$	3.91698e10	−	1.42567e10i	1.05461	−	0.383848i	0.244212	−	0.969722i	$-0.421471\pi$
$439$	3.91698e10	−	1.42567e10i	1.05461	−	0.383848i	0.810402	+	0.585874i	$0.199249\pi$
$440$	1.76422e10	+	1.01857e10i	0.470697	+	0.271757i
$441$		0			0
$442$	−9.03227e9	−	1.56444e10i	−0.236651	−	0.409891i
$443$	−2.09396e10	+	2.49549e10i	−0.543694	+	0.647949i	−0.966012	−	0.258499i	$-0.916772\pi$
$443$	−2.09396e10	+	2.49549e10i	−0.543694	+	0.647949i	0.422318	+	0.906448i	$0.361217\pi$
$444$		0			0
$445$	1.65591e10	+	9.39115e10i	0.422277	+	2.39485i
$446$	7.80266e10	−	1.37582e10i	1.97198	−	0.347714i
$447$		0			0
$448$	2.04397e10	+	1.71509e10i	0.507413	+	0.425770i
$449$	−3.70290e9	+	2.13787e9i	−0.0911081	+	0.0526013i	−0.544862	−	0.838526i	$-0.683418\pi$
$449$	−3.70290e9	+	2.13787e9i	−0.0911081	+	0.0526013i	0.453754	+	0.891127i	$0.350085\pi$
$450$		0			0
$451$	−1.49031e10	+	2.58129e10i	−0.360222	+	0.623922i
$452$	−1.02855e10	−	2.82592e10i	−0.246418	−	0.677028i
$453$		0			0
$454$	8.10834e10	−	6.80371e10i	1.90857	−	1.60148i
$455$	1.58051e10	−	4.34240e10i	0.368766	−	1.01318i
$456$		0			0
$457$	9.68440e9	−	5.49230e10i	0.222028	−	1.25918i	−0.646257	−	0.763120i	$-0.723667\pi$
$457$	9.68440e9	−	5.49230e10i	0.222028	−	1.25918i	0.868285	−	0.496065i	$-0.165222\pi$
$458$			4.73078e9i			0.107515i
$459$		0			0
$460$	8.18805e10			1.82873
$461$	−9.55938e9	−	1.68558e9i	−0.211654	−	0.0373203i	0.0668158	−	0.997765i	$-0.478716\pi$
$461$	−9.55938e9	−	1.68558e9i	−0.211654	−	0.0373203i	−0.278470	+	0.960445i	$0.589827\pi$
$462$		0			0
$463$	−4.17602e10	−	1.51995e10i	−0.908738	−	0.330753i	−0.154989	−	0.987916i	$-0.549534\pi$
$463$	−4.17602e10	−	1.51995e10i	−0.908738	−	0.330753i	−0.753749	+	0.657163i	$0.771756\pi$
$464$	2.69582e10	+	3.21275e10i	0.581593	+	0.693115i
$465$		0			0
$466$	−7.72841e10	+	2.81291e10i	−1.63888	+	0.596502i
$467$	−3.56397e10	−	2.05766e10i	−0.749318	−	0.432619i	0.0761293	−	0.997098i	$-0.475744\pi$
$467$	−3.56397e10	−	2.05766e10i	−0.749318	−	0.432619i	−0.825448	+	0.564479i	$0.809077\pi$
$468$		0			0
$469$	−4.90259e10	−	8.49154e10i	−1.01329	−	1.75507i
$470$	3.93256e9	−	4.68665e9i	0.0805906	−	0.0960441i
$471$		0			0
$472$	5.62511e8	+	3.19016e9i	0.0113335	+	0.0642753i
$473$	4.14132e10	−	7.30227e9i	0.827360	−	0.145886i
$474$		0			0
$475$	−6.28489e10	−	5.27365e10i	−1.23459	−	1.03595i
$476$	3.16819e10	−	1.82915e10i	0.617139	−	0.356306i
$477$		0			0
$478$	−2.52811e10	+	4.37882e10i	−0.484267	+	0.838775i
$479$	9.13357e9	+	2.50943e10i	0.173500	+	0.476686i	0.995713	−	0.0924926i	$-0.0294835\pi$
$479$	9.13357e9	+	2.50943e10i	0.173500	+	0.476686i	−0.822214	+	0.569179i	$0.807261\pi$
$480$		0			0
$481$	−6.29671e9	+	5.28357e9i	−0.117634	+	0.0987068i
$482$	4.64352e9	−	1.27580e10i	0.0860318	−	0.236370i
$483$		0			0
$484$	1.33143e9	−	7.55093e9i	0.0242626	−	0.137600i
$485$			1.13189e11i			2.04567i
$486$		0			0
$487$	−4.68571e10			−0.833028			−0.416514	−	0.909129i	$-0.636748\pi$
$487$	−4.68571e10			−0.833028			−0.416514	+	0.909129i	$0.636748\pi$
$488$	2.24344e7	+	3.95580e6i	0.000395581	+	6.97517e-5i
$489$		0			0
$490$	7.98717e10	+	2.90709e10i	1.38551	+	0.504283i
$491$	2.58778e10	+	3.08400e10i	0.445247	+	0.530625i	0.941257	−	0.337692i	$-0.109646\pi$
$491$	2.58778e10	+	3.08400e10i	0.445247	+	0.530625i	−0.496009	+	0.868317i	$0.665202\pi$
$492$		0			0
$493$	3.04977e10	−	1.11003e10i	0.516273	−	0.187908i
$494$	−3.02893e10	−	1.74876e10i	−0.508607	−	0.293644i
$495$		0			0
$496$	5.41351e10	+	9.37648e10i	0.894443	+	1.54922i
$497$	−7.31138e10	+	8.71336e10i	−1.19832	+	1.42810i
$498$		0			0
$499$	1.39014e10	+	7.88387e10i	0.224211	+	1.27156i	0.864189	+	0.503168i	$0.167832\pi$
$499$	1.39014e10	+	7.88387e10i	0.224211	+	1.27156i	−0.639978	+	0.768393i	$0.721057\pi$
$500$	6.60704e10	−	1.16500e10i	1.05713	−	0.186400i
$501$		0			0
$502$	−1.04604e11	−	8.77731e10i	−1.64715	−	1.38212i
$503$	6.85658e8	−	3.95865e8i	0.0107111	−	0.00618408i	−0.494635	−	0.869101i	$-0.664698\pi$
$503$	6.85658e8	−	3.95865e8i	0.0107111	−	0.00618408i	0.505346	+	0.862917i	$0.331365\pi$
$504$		0			0
$505$	4.01691e10	−	6.95749e10i	0.617627	−	1.06976i
$506$	4.54997e10	+	1.25009e11i	0.694076	+	1.90696i
$507$		0			0
$508$	−8.90934e9	+	7.47583e9i	−0.133780	+	0.112255i
$509$	1.10097e10	−	3.02490e10i	0.164024	−	0.450651i	−0.830266	−	0.557367i	$-0.811811\pi$
$509$	1.10097e10	−	3.02490e10i	0.164024	−	0.450651i	0.994289	+	0.106716i	$0.0340337\pi$
$510$		0			0
$511$	−1.55086e10	+	8.79536e10i	−0.227452	+	1.28994i
$512$		−	7.81044e10i		−	1.13657i
$513$		0			0
$514$	−7.67175e10			−1.09911
$515$	9.37846e10	+	1.65368e10i	1.33322	+	0.235083i
$516$		0			0
$517$	4.08288e9	+	1.48605e9i	0.0571484	+	0.0208003i
$518$	−2.44785e10	−	2.91724e10i	−0.339990	−	0.405184i
$519$		0			0
$520$	−1.71317e10	+	6.23542e9i	−0.234308	+	0.0852811i
$521$	−2.96909e10	−	1.71420e10i	−0.402970	−	0.232655i	0.284795	−	0.958588i	$-0.408074\pi$
$521$	−2.96909e10	−	1.71420e10i	−0.402970	−	0.232655i	−0.687764	+	0.725934i	$0.741408\pi$
$522$		0			0
$523$	−6.73885e10	−	1.16720e11i	−0.900697	−	1.56005i	−0.826591	−	0.562803i	$-0.809723\pi$
$523$	−6.73885e10	−	1.16720e11i	−0.900697	−	1.56005i	−0.0741061	−	0.997250i	$-0.523610\pi$
$524$	−6.37063e10	+	7.59222e10i	−0.845001	+	1.00703i
$525$		0			0
$526$	−5.87810e9	−	3.33363e10i	−0.0767881	−	0.435487i
$527$	8.25123e10	−	1.45492e10i	1.06974	−	0.188623i
$528$		0			0
$529$	−5.78665e10	−	4.85557e10i	−0.738931	−	0.620037i
$530$	2.75562e11	−	1.59096e11i	3.49233	−	2.01630i
$531$		0			0
$532$	3.54146e10	−	6.13399e10i	0.442116	−	0.765767i
$533$	−9.12326e9	−	2.50660e10i	−0.113042	−	0.310581i
$534$		0			0
$535$	2.19592e10	−	1.84259e10i	0.268041	−	0.224913i
$536$	−1.32305e10	+	3.63506e10i	−0.160294	+	0.440405i
$537$		0			0
$538$	3.57226e10	−	2.02593e11i	0.426397	−	2.41822i
$539$			6.03642e10i			0.715195i
$540$		0			0
$541$	1.03786e11			1.21158			0.605789	−	0.795626i	$-0.292858\pi$
$541$	1.03786e11			1.21158			0.605789	+	0.795626i	$0.292858\pi$
$542$	−8.89265e10	−	1.56801e10i	−1.03047	−	0.181699i
$543$		0			0
$544$	−7.42609e10	−	2.70288e10i	−0.847939	−	0.308625i
$545$	−2.14431e10	−	2.55548e10i	−0.243053	−	0.289659i
$546$		0			0
$547$	2.28611e10	−	8.32078e9i	0.255358	−	0.0929425i	−0.211170	−	0.977449i	$-0.567727\pi$
$547$	2.28611e10	−	8.32078e9i	0.255358	−	0.0929425i	0.466527	+	0.884507i	$0.345505\pi$
$548$	1.63010e10	+	9.41140e9i	0.180756	+	0.104359i
$549$		0			0
$550$	1.20743e11	+	2.09134e11i	1.31951	+	2.28546i
$551$	4.03907e10	−	4.81357e10i	0.438202	−	0.522229i
$552$		0			0
$553$	4.51517e9	+	2.56068e10i	0.0482807	+	0.273813i
$554$	−1.83547e11	+	3.23643e10i	−1.94854	+	0.343579i
$555$		0			0
$556$	−1.61517e10	−	1.35529e10i	−0.169012	−	0.141818i
$557$	3.57690e9	−	2.06513e9i	0.0371609	−	0.0214549i	−0.481304	−	0.876553i	$-0.659837\pi$
$557$	3.57690e9	−	2.06513e9i	0.0371609	−	0.0214549i	0.518465	+	0.855099i	$0.326504\pi$
$558$		0			0
$559$	−1.88170e10	+	3.25920e10i	−0.192709	+	0.333783i
$560$	−8.54031e10	−	2.34643e11i	−0.868404	−	2.38592i
$561$		0			0
$562$	7.04381e10	−	5.91046e10i	0.706094	−	0.592483i
$563$	−6.02715e10	+	1.65595e11i	−0.599899	+	1.64821i	0.151573	+	0.988446i	$0.451566\pi$
$563$	−6.02715e10	+	1.65595e11i	−0.599899	+	1.64821i	−0.751473	+	0.659764i	$0.770656\pi$
$564$		0			0
$565$	−2.75832e10	+	1.56432e11i	−0.270677	+	1.53508i
$566$			9.03644e10i			0.880504i
$567$		0			0
$568$	4.48747e10			0.431130
$569$	−1.58452e10	−	2.79394e9i	−0.151164	−	0.0266543i	0.0975539	−	0.995230i	$-0.468898\pi$
$569$	−1.58452e10	−	2.79394e9i	−0.151164	−	0.0266543i	−0.248718	+	0.968576i	$0.580009\pi$
$570$		0			0
$571$	3.83780e10	+	1.39684e10i	0.361025	+	0.131402i	0.516163	−	0.856490i	$-0.327360\pi$
$571$	3.83780e10	+	1.39684e10i	0.361025	+	0.131402i	−0.155138	+	0.987893i	$0.549582\pi$
$572$	2.89249e10	+	3.44714e10i	0.270201	+	0.322014i
$573$		0			0
$574$	1.16129e11	−	4.22676e10i	1.06978	−	0.389368i
$575$	−2.41861e11	−	1.39638e11i	−2.21255	−	1.27742i
$576$		0			0
$577$	−3.96800e10	−	6.87278e10i	−0.357988	−	0.620053i	0.629637	−	0.776890i	$-0.283204\pi$
$577$	−3.96800e10	−	6.87278e10i	−0.357988	−	0.620053i	−0.987625	+	0.156836i	$0.949870\pi$
$578$	4.70699e10	−	5.60957e10i	0.421727	−	0.502595i
$579$		0			0
$580$	1.97677e10	+	1.12108e11i	0.174681	+	0.990663i
$581$	1.96007e11	−	3.45613e10i	1.72015	−	0.303309i
$582$		0			0
$583$	1.73107e11	+	1.45254e11i	1.49844	+	1.25734i
$584$	3.05143e10	−	1.76174e10i	0.262332	−	0.151457i
$585$		0			0
$586$	−1.33954e11	+	2.32015e11i	−1.13597	+	1.96755i
$587$	−2.83387e10	−	7.78600e10i	−0.238686	−	0.655786i	−0.999973	−	0.00736984i	$-0.997654\pi$
$587$	−2.83387e10	−	7.78600e10i	−0.238686	−	0.655786i	0.761286	−	0.648416i	$-0.224568\pi$
$588$		0			0
$589$	1.24266e11	−	1.04272e11i	1.03251	−	0.866375i
$590$	−2.03390e10	+	5.58810e10i	−0.167850	+	0.461165i
$591$		0			0
$592$	−7.71272e9	+	4.37410e10i	−0.0627944	+	0.356125i
$593$		−	1.19236e11i		−	0.964248i	−0.876103	−	0.482124i	$-0.839865\pi$
$593$		−	1.19236e11i		−	0.964248i	0.876103	−	0.482124i	$-0.160135\pi$
$594$		0			0
$595$	−1.93233e11			−1.54174
$596$	3.71616e10	+	6.55258e9i	0.294516	+	0.0519311i
$597$		0			0
$598$	−1.11876e11	−	4.07194e10i	−0.874845	−	0.318417i
$599$	8.67739e9	+	1.03413e10i	0.0674034	+	0.0803282i	0.798693	−	0.601739i	$-0.205525\pi$
$599$	8.67739e9	+	1.03413e10i	0.0674034	+	0.0803282i	−0.731289	+	0.682068i	$0.761081\pi$
$600$		0			0
$601$	3.13759e10	−	1.14199e10i	0.240491	−	0.0875316i	−0.218963	−	0.975733i	$-0.570267\pi$
$601$	3.13759e10	−	1.14199e10i	0.240491	−	0.0875316i	0.459454	+	0.888202i	$0.348045\pi$
$602$	−1.50997e11	−	8.71782e10i	−1.14970	−	0.663777i
$603$		0			0
$604$	−9.86190e9	−	1.70813e10i	−0.0740991	−	0.128343i
$605$	−2.60325e10	+	3.10244e10i	−0.194310	+	0.231569i
$606$		0			0
$607$	−3.27685e10	−	1.85839e11i	−0.241380	−	1.36894i	−0.828751	−	0.559618i	$-0.810948\pi$
$607$	−3.27685e10	−	1.85839e11i	−0.241380	−	1.36894i	0.587370	−	0.809318i	$-0.300163\pi$
$608$	−1.50681e11	+	2.65691e10i	−1.10267	+	0.194430i
$609$		0			0
$610$	3.20358e8	+	2.68812e8i	0.00231375	+	0.00194146i
$611$	−3.36747e9	+	1.94421e9i	−0.0241623	+	0.0139501i
$612$		0			0
$613$	1.37242e10	−	2.37710e10i	0.0971953	−	0.168347i	−0.813327	−	0.581806i	$-0.802346\pi$
$613$	1.37242e10	−	2.37710e10i	0.0971953	−	0.168347i	0.910523	+	0.413459i	$0.135680\pi$
$614$	7.93188e10	+	2.17927e11i	0.558088	+	1.53333i
$615$		0			0
$616$	4.59513e10	−	3.85578e10i	0.319136	−	0.267787i
$617$	9.20533e9	−	2.52914e10i	0.0635183	−	0.174515i	−0.903873	−	0.427800i	$-0.859289\pi$
$617$	9.20533e9	−	2.52914e10i	0.0635183	−	0.174515i	0.967392	+	0.253285i	$0.0815110\pi$
$618$		0			0
$619$	−2.15242e10	+	1.22070e11i	−0.146611	+	0.831470i	0.819449	+	0.573152i	$0.194279\pi$
$619$	−2.15242e10	+	1.22070e11i	−0.146611	+	0.831470i	−0.966060	+	0.258318i	$0.916832\pi$
$620$			2.93882e11i			1.98887i
$621$		0			0
$622$	−9.98604e10			−0.667163
$623$	2.76530e11	+	4.87596e10i	1.83565	+	0.323674i
$624$		0			0
$625$	−7.16424e10	−	2.60757e10i	−0.469516	−	0.170890i
$626$	5.95156e10	+	7.09280e10i	0.387555	+	0.461870i
$627$		0			0
$628$	−8.10060e9	+	2.94838e9i	−0.0520809	+	0.0189559i
$629$	2.97664e10	+	1.71856e10i	0.190162	+	0.109790i
$630$		0			0
$631$	2.34383e10	+	4.05963e10i	0.147846	+	0.256076i	0.930431	−	0.366467i	$-0.119433\pi$
$631$	2.34383e10	+	4.05963e10i	0.147846	+	0.256076i	−0.782585	+	0.622543i	$0.786099\pi$
$632$	6.59388e9	−	7.85828e9i	0.0413307	−	0.0492560i
$633$		0			0
$634$	−2.25104e10	−	1.27663e11i	−0.139324	−	0.790146i
$635$	6.04983e10	−	1.06675e10i	0.372090	−	0.0656095i
$636$		0			0
$637$	−4.13834e10	−	3.47248e10i	−0.251344	−	0.210903i
$638$	−1.60175e11	+	9.24769e10i	−0.966743	+	0.558149i
$639$		0			0
$640$	−8.18512e10	+	1.41770e11i	−0.487871	+	0.845018i
$641$	4.32352e10	+	1.18788e11i	0.256098	+	0.703622i	0.999399	+	0.0346656i	$0.0110366\pi$
$641$	4.32352e10	+	1.18788e11i	0.256098	+	0.703622i	−0.743301	+	0.668957i	$0.766741\pi$
$642$		0			0
$643$	−6.88388e10	+	5.77626e10i	−0.402707	+	0.337911i	−0.821539	−	0.570153i	$-0.806884\pi$
$643$	−6.88388e10	+	5.77626e10i	−0.402707	+	0.337911i	0.418832	+	0.908064i	$0.362440\pi$
$644$	8.24622e10	−	2.26563e11i	0.479415	−	1.31718i
$645$		0			0
$646$	−2.53960e10	+	1.44028e11i	−0.145826	+	0.827021i
$647$		−	1.31839e11i		−	0.752361i	−0.926546	−	0.376181i	$-0.877237\pi$
$647$		−	1.31839e11i		−	0.752361i	0.926546	−	0.376181i	$-0.122763\pi$
$648$		0			0
$649$	−4.22329e10			−0.238052
$650$	−2.12832e11	−	3.75281e10i	−1.19230	−	0.210234i
$651$		0			0
$652$	−1.40438e11	−	5.11152e10i	−0.777130	−	0.282852i
$653$	9.44194e9	+	1.12525e10i	0.0519288	+	0.0618864i	0.791384	−	0.611320i	$-0.209361\pi$
$653$	9.44194e9	+	1.12525e10i	0.0519288	+	0.0618864i	−0.739455	+	0.673206i	$0.764917\pi$
$654$		0			0
$655$	4.91927e11	−	1.79047e11i	2.67261	−	0.972750i
$656$	−1.24826e11	−	7.20686e10i	−0.674049	−	0.389162i
$657$		0			0
$658$	−9.00743e9	−	1.56013e10i	−0.0480504	−	0.0832258i
$659$	1.20129e11	−	1.43164e11i	0.636950	−	0.759088i	−0.346935	−	0.937889i	$-0.612777\pi$
$659$	1.20129e11	−	1.43164e11i	0.636950	−	0.759088i	0.983885	+	0.178801i	$0.0572219\pi$
$660$		0			0
$661$	−4.11329e9	−	2.33276e10i	−0.0215468	−	0.122198i	0.972137	−	0.234413i	$-0.0753167\pi$
$661$	−4.11329e9	−	2.33276e10i	−0.0215468	−	0.122198i	−0.993684	+	0.112215i	$0.964206\pi$
$662$	−4.91838e11	+	8.67243e10i	−2.56088	+	0.451553i
$663$		0			0
$664$	−6.01510e10	−	5.04727e10i	−0.309436	−	0.259648i
$665$	−3.23999e11	+	1.87061e11i	−1.65675	+	0.956524i
$666$		0			0
$667$	1.06948e11	−	1.85240e11i	0.540345	−	0.935905i
$668$	−1.24792e10	−	3.42864e10i	−0.0626733	−	0.172193i
$669$		0			0
$670$	−5.43998e11	+	4.56469e11i	−2.69959	+	2.26523i
$671$	−1.01579e8	+	2.79087e8i	−0.000501089	+	0.00137673i
$672$		0			0
$673$	−4.73277e10	+	2.68409e11i	−0.230704	+	1.30839i	0.620771	+	0.783992i	$0.286820\pi$
$673$	−4.73277e10	+	2.68409e11i	−0.230704	+	1.30839i	−0.851475	+	0.524395i	$0.824292\pi$
$674$		−	1.58078e11i		−	0.766003i
$675$		0			0
$676$	1.21896e11			0.583716
$677$	4.48783e10	+	7.91326e9i	0.213640	+	0.0376704i	0.279443	−	0.960162i	$-0.409850\pi$
$677$	4.48783e10	+	7.91326e9i	0.213640	+	0.0376704i	−0.0658038	+	0.997833i	$0.520961\pi$
$678$		0			0
$679$	3.13192e11	+	1.13993e11i	1.47344	+	0.536287i
$680$	4.90024e10	+	5.83988e10i	0.229183	+	0.273129i
$681$		0			0
$682$	−4.48678e11	+	1.63306e11i	−2.07395	+	0.754855i
$683$	2.77661e11	+	1.60308e11i	1.27595	+	0.736668i	0.976101	−	0.217319i	$-0.0697313\pi$
$683$	2.77661e11	+	1.60308e11i	1.27595	+	0.736668i	0.299846	+	0.953988i	$0.403065\pi$
$684$		0			0
$685$	−4.97112e10	−	8.61023e10i	−0.225783	−	0.391068i
$686$	−8.34649e10	+	9.94696e10i	−0.376884	+	0.449153i
$687$		0			0
$688$	3.53125e10	+	2.00267e11i	0.157607	+	0.893831i
$689$	−1.99161e11	+	3.51174e10i	−0.883746	+	0.155828i
$690$		0			0
$691$	2.00811e11	+	1.68501e11i	0.880797	+	0.739076i	0.966343	−	0.257258i	$-0.0828191\pi$
$691$	2.00811e11	+	1.68501e11i	0.880797	+	0.739076i	−0.0855462	+	0.996334i	$0.527264\pi$
$692$	1.53388e11	−	8.85588e10i	0.668911	−	0.386196i
$693$		0			0
$694$	7.08254e10	−	1.22673e11i	0.305317	−	0.528825i
$695$	3.80903e10	+	1.04652e11i	0.163258	+	0.448549i
$696$		0			0
$697$	−8.54453e10	+	7.16971e10i	−0.362041	+	0.303788i
$698$	−7.06108e10	+	1.94002e11i	−0.297474	+	0.817304i
$699$		0			0
$700$	7.59993e10	−	4.31014e11i	0.316532	−	1.79514i
$701$			1.88359e11i			0.780034i	0.920808	+	0.390017i	$0.127531\pi$
$701$			1.88359e11i			0.780034i	−0.920808	+	0.390017i	$0.872469\pi$
$702$		0			0
$703$	6.65469e10			0.272462
$704$	1.35155e11	+	2.38314e10i	0.550225	+	0.0970195i
$705$		0			0
$706$	3.76427e11	+	1.37008e11i	1.51517	+	0.551477i
$707$	−1.52059e11	−	1.81217e11i	−0.608603	−	0.725305i
$708$		0			0
$709$	−2.24239e11	+	8.16164e10i	−0.887414	+	0.322992i	−0.745198	−	0.666843i	$-0.767645\pi$
$709$	−2.24239e11	+	8.16164e10i	−0.887414	+	0.322992i	−0.142216	+	0.989836i	$0.545423\pi$
$710$	7.13427e11	+	4.11898e11i	2.80748	+	1.62090i
$711$		0			0
$712$	−5.53898e10	−	9.59380e10i	−0.215531	−	0.373311i
$713$	3.54942e11	−	4.23004e11i	1.37341	−	1.63676i
$714$		0			0
$715$	−4.12738e10	−	2.34075e11i	−0.157925	−	0.895636i
$716$	−2.30803e10	+	4.06967e9i	−0.0878191	+	0.0154849i
$717$		0			0
$718$	2.53230e11	+	2.12485e11i	0.952836	+	0.799524i
$719$	9.71827e10	−	5.61085e10i	0.363642	−	0.209949i	−0.307035	−	0.951698i	$-0.599337\pi$
$719$	9.71827e10	−	5.61085e10i	0.363642	−	0.209949i	0.670677	+	0.741750i	$0.266004\pi$
$720$		0			0
$721$	1.40208e11	−	2.42847e11i	0.518838	−	0.898654i
$722$	−2.70316e10	−	7.42687e10i	−0.0994770	−	0.273311i
$723$		0			0
$724$	−2.54693e10	+	2.13713e10i	−0.0926965	+	0.0777816i
$725$	1.32798e11	−	3.64860e11i	0.480662	−	1.32061i
$726$		0			0
$727$	9.51410e10	−	5.39571e11i	0.340589	−	1.93157i	−0.0223252	−	0.999751i	$-0.507107\pi$
$727$	9.51410e10	−	5.39571e11i	0.340589	−	1.93157i	0.362914	−	0.931823i	$-0.381782\pi$
$728$			5.36830e10i			0.191122i
$729$		0			0
$730$	6.46830e11			2.27771
$731$	1.54977e11	+	2.73266e10i	0.542748	+	0.0957011i
$732$		0			0
$733$	−3.47099e11	−	1.26334e11i	−1.20237	−	0.437627i	−0.338319	−	0.941032i	$-0.609858\pi$
$733$	−3.47099e11	−	1.26334e11i	−1.20237	−	0.437627i	−0.864051	+	0.503405i	$0.832080\pi$
$734$	−2.35199e11	−	2.80299e11i	−0.810309	−	0.965689i
$735$		0			0
$736$	−4.89421e11	+	1.78135e11i	−1.66791	+	0.607068i
$737$	−4.36763e11	−	2.52165e11i	−1.48039	−	0.854704i
$738$		0			0
$739$	1.90562e10	+	3.30063e10i	0.0638938	+	0.110667i	0.896203	−	0.443645i	$-0.146315\pi$
$739$	1.90562e10	+	3.30063e10i	0.0638938	+	0.110667i	−0.832309	+	0.554312i	$0.812981\pi$
$740$	−7.74940e10	+	9.23538e10i	−0.258429	+	0.307984i
$741$		0			0
$742$	−1.62697e11	−	9.22703e11i	−0.536741	−	3.04401i
$743$	3.97983e11	−	7.01751e10i	1.30590	−	0.230265i	0.522955	−	0.852360i	$-0.324829\pi$
$743$	3.97983e11	−	7.01751e10i	1.30590	−	0.230265i	0.782942	+	0.622095i	$0.213718\pi$
$744$		0			0
$745$	−1.52685e11	−	1.28118e11i	−0.495645	−	0.415896i
$746$	4.96883e11	−	2.86875e11i	1.60435	−	0.926271i
$747$		0			0
$748$	9.40828e10	−	1.62956e11i	0.300541	−	0.520552i
$749$	−2.88693e10	−	7.93178e10i	−0.0917295	−	0.252025i
$750$		0			0
$751$	−4.46206e10	+	3.74412e10i	−0.140274	+	0.117704i	−0.710225	−	0.703975i	$-0.751407\pi$
$751$	−4.46206e10	+	3.74412e10i	−0.140274	+	0.117704i	0.569951	+	0.821679i	$0.306962\pi$
$752$	−7.18625e9	+	1.97441e10i	−0.0224714	+	0.0617398i
$753$		0			0
$754$	2.87426e10	−	1.63007e11i	0.0889284	−	0.504338i
$755$			1.04181e11i			0.320629i
$756$		0			0
$757$	2.39258e11			0.728590			0.364295	−	0.931284i	$-0.381310\pi$
$757$	2.39258e11			0.728590			0.364295	+	0.931284i	$0.381310\pi$
$758$	−7.25215e11	−	1.27875e11i	−2.19680	−	0.387354i
$759$		0			0
$760$	1.38697e11	+	5.04817e10i	0.415732	+	0.151314i
$761$	−2.35987e11	−	2.81238e11i	−0.703637	−	0.838562i	0.289296	−	0.957240i	$-0.406579\pi$
$761$	−2.35987e11	−	2.81238e11i	−0.703637	−	0.838562i	−0.992933	+	0.118678i	$0.962134\pi$
$762$		0			0
$763$	−9.23055e10	+	3.35965e10i	−0.272351	+	0.0991278i
$764$	−1.16934e10	−	6.75122e9i	−0.0343217	−	0.0198157i
$765$		0			0
$766$	−9.41263e10	−	1.63031e11i	−0.273398	−	0.473540i
$767$	2.42947e10	−	2.89533e10i	0.0701988	−	0.0836596i
$768$		0			0
$769$	6.09232e10	+	3.45513e11i	0.174212	+	0.988004i	0.939050	+	0.343781i	$0.111708\pi$
$769$	6.09232e10	+	3.45513e11i	0.174212	+	0.988004i	−0.764838	+	0.644223i	$0.777181\pi$
$770$	1.08446e12	−	1.91220e11i	3.08497	−	0.543963i
$771$		0			0
$772$	3.21218e11	+	2.69534e11i	0.904338	+	0.758829i
$773$	3.68474e9	−	2.12739e9i	0.0103202	−	0.00595838i	−0.494831	−	0.868989i	$-0.664770\pi$
$773$	3.68474e9	−	2.12739e9i	0.0103202	−	0.00595838i	0.505151	+	0.863031i	$0.331437\pi$
$774$		0			0
$775$	5.01183e11	−	8.68075e11i	1.38928	−	2.40630i
$776$	−4.49725e10	−	1.23561e11i	−0.124022	−	0.340748i
$777$		0			0
$778$	3.13530e11	−	2.63083e11i	0.855776	−	0.718082i
$779$	−7.38615e10	+	2.02933e11i	−0.200571	+	0.551065i
$780$		0			0
$781$	−1.01592e11	+	5.76160e11i	−0.273060	+	1.54860i
$782$			4.97835e11i			1.33125i
$783$		0			0
$784$	−2.91910e11			−0.772654
$785$	4.48418e10	+	7.90681e9i	0.118088	+	0.0208220i
$786$		0			0
$787$	3.91760e11	+	1.42589e11i	1.02122	+	0.371695i	0.797733	−	0.603011i	$-0.206033\pi$
$787$	3.91760e11	+	1.42589e11i	1.02122	+	0.371695i	0.223491	+	0.974706i	$0.428255\pi$
$788$	−4.81827e10	−	5.74219e10i	−0.124964	−	0.148927i
$789$		0			0
$790$	1.76961e11	−	6.44084e10i	0.454327	−	0.165362i
$791$	4.05068e11	+	2.33866e11i	1.03472	+	0.597394i
$792$		0			0
$793$	−1.32897e8	−	2.30185e8i	−0.000336065	−	0.000582082i
$794$	4.52608e11	−	5.39398e11i	1.13878	−	1.35715i
$795$		0			0
$796$	9.71845e9	+	5.51161e10i	0.0242072	+	0.137286i
$797$	−7.60682e11	+	1.34129e11i	−1.88525	+	0.332421i	−0.992903	−	0.118923i	$-0.962056\pi$
$797$	−7.60682e11	+	1.34129e11i	−1.88525	+	0.332421i	−0.892350	+	0.451344i	$0.850945\pi$
$798$		0			0
$799$	1.24555e10	+	1.04514e10i	0.0305616	+	0.0256442i
$800$	−8.18774e11	+	4.72719e11i	−1.99896	+	1.15410i
$801$		0			0
$802$	−2.48197e11	+	4.29890e11i	−0.599928	+	1.03911i
$803$	1.57114e11	+	4.31666e11i	0.377878	+	1.03821i
$804$		0			0
$805$	−9.75567e11	+	8.18598e11i	−2.32313	+	1.94934i
$806$	1.46148e11	−	4.01539e11i	0.346301	−	0.951453i
$807$		0			0
$808$	−1.62063e10	+	9.19107e10i	−0.0380224	+	0.215636i
$809$			6.64914e11i			1.55229i	0.630557	+	0.776143i	$0.282826\pi$
$809$			6.64914e11i			1.55229i	−0.630557	+	0.776143i	$0.717174\pi$
$810$		0			0
$811$	−6.83765e11			−1.58061			−0.790303	−	0.612716i	$-0.790077\pi$
$811$	−6.83765e11			−1.58061			−0.790303	+	0.612716i	$0.790077\pi$
$812$	3.30112e11	+	5.82076e10i	0.759341	+	0.133892i
$813$		0			0
$814$	−1.84062e11	−	6.69929e10i	−0.419243	−	0.152592i
$815$	5.07418e11	+	6.04717e11i	1.15010	+	1.37063i
$816$		0			0
$817$	2.86308e11	−	1.04208e11i	0.642608	−	0.233890i
$818$	2.79227e11	+	1.61212e11i	0.623655	+	0.360067i
$819$		0			0
$820$	−1.95618e11	−	3.38821e11i	−0.432667	−	0.749402i
$821$	−2.00545e11	+	2.39000e11i	−0.441407	+	0.526048i	−0.940177	−	0.340686i	$-0.889341\pi$
$821$	−2.00545e11	+	2.39000e11i	−0.441407	+	0.526048i	0.498770	+	0.866734i	$0.333785\pi$
$822$		0			0
$823$	−6.01936e10	−	3.41375e11i	−0.131205	−	0.744101i	−0.977427	−	0.211271i	$-0.932240\pi$
$823$	−6.01936e10	−	3.41375e11i	−0.131205	−	0.744101i	0.846222	−	0.532830i	$-0.178871\pi$
$824$	−1.08949e11	+	1.92107e10i	−0.236328	+	0.0416710i
$825$		0			0
$826$	1.34139e11	+	1.12556e11i	0.288161	+	0.241796i
$827$	−1.78104e11	+	1.02829e11i	−0.380761	+	0.219833i	−0.678149	−	0.734924i	$-0.737218\pi$
$827$	−1.78104e11	+	1.02829e11i	−0.380761	+	0.219833i	0.297388	+	0.954757i	$0.403884\pi$
$828$		0			0
$829$	−4.09057e11	+	7.08507e11i	−0.866095	+	1.50012i	−0.000139858		1.00000i	$0.500045\pi$
$829$	−4.09057e11	+	7.08507e11i	−0.866095	+	1.50012i	−0.865955	+	0.500121i	$0.833289\pi$
$830$	−4.93013e11	−	1.35454e12i	−1.03883	−	2.85417i
$831$		0			0
$832$	−9.40862e10	+	7.89477e10i	−0.196351	+	0.164758i
$833$	−7.72609e10	+	2.12272e11i	−0.160465	+	0.440873i
$834$		0			0
$835$	−3.34662e10	+	1.89796e11i	−0.0688431	+	0.390429i
$836$		−	3.64311e11i		−	0.745843i
$837$		0			0
$838$	1.04574e12			2.12055
$839$	−3.27420e11	−	5.77329e10i	−0.660780	−	0.116513i	−0.166806	−	0.985990i	$-0.553345\pi$
$839$	−3.27420e11	−	5.77329e10i	−0.660780	−	0.116513i	−0.493975	+	0.869476i	$0.664456\pi$
$840$		0			0
$841$	−1.90633e11	−	6.93847e10i	−0.381078	−	0.138701i
$842$	−3.92979e11	−	4.68334e11i	−0.781845	−	0.931766i
$843$		0			0
$844$	−1.73912e11	+	6.32986e10i	−0.342735	+	0.124745i
$845$	−5.57595e11	−	3.21927e11i	−1.09368	−	0.631439i
$846$		0			0
$847$	5.96268e10	+	1.03277e11i	0.115853	+	0.200663i
$848$	−7.02421e11	+	8.37113e11i	−1.35836	+	1.61883i
$849$		0			0
$850$	1.56925e11	+	8.89966e11i	0.300619	+	1.70490i
$851$	2.23085e11	−	3.93359e10i	0.425355	−	0.0750016i
$852$		0			0
$853$	−2.99121e11	−	2.50992e11i	−0.565003	−	0.474094i	0.314980	−	0.949098i	$-0.398002\pi$
$853$	−2.99121e11	−	2.50992e11i	−0.565003	−	0.474094i	−0.879984	+	0.475004i	$0.842447\pi$
$854$	1.06644e9	−	6.15707e8i	0.00200495	−	0.00115756i
$855$		0			0
$856$	−1.66504e10	+	2.88393e10i	−0.0310120	+	0.0537143i
$857$	3.66157e11	+	1.00601e12i	0.678804	+	1.86500i	0.455451	+	0.890261i	$0.349478\pi$
$857$	3.66157e11	+	1.00601e12i	0.678804	+	1.86500i	0.223353	+	0.974738i	$0.428300\pi$
$858$		0			0
$859$	−7.67174e10	+	6.43735e10i	−0.140903	+	0.118232i	−0.710515	−	0.703682i	$-0.751538\pi$
$859$	−7.67174e10	+	6.43735e10i	−0.140903	+	0.118232i	0.569612	+	0.821914i	$0.307094\pi$
$860$	−1.88787e11	+	5.18689e11i	−0.345127	+	0.948229i
$861$		0			0
$862$	−4.87396e10	+	2.76416e11i	−0.0882780	+	0.500650i
$863$		−	8.42245e11i		−	1.51843i	−0.650839	−	0.759216i	$-0.725583\pi$
$863$		−	8.42245e11i		−	1.51843i	0.650839	−	0.759216i	$-0.274417\pi$
$864$		0			0
$865$	−9.35539e11			−1.67108
$866$	4.36349e11	+	7.69402e10i	0.775823	+	0.136799i
$867$		0			0
$868$	8.13169e11	+	2.95969e11i	1.43252	+	0.521396i
$869$	8.59668e10	+	1.02451e11i	0.150748	+	0.179655i
$870$		0			0
$871$	4.24125e11	−	1.54369e11i	0.736922	−	0.268218i
$872$	3.35616e10	+	1.93768e10i	0.0580465	+	0.0335132i
$873$		0			0
$874$	4.81934e11	+	8.34735e11i	0.825928	+	1.43055i
$875$	−6.70726e11	+	7.99341e11i	−1.14423	+	1.36364i
$876$		0			0
$877$	−8.60938e10	−	4.88262e11i	−0.145537	−	0.825382i	−0.966934	−	0.255025i	$-0.917916\pi$
$877$	−8.60938e10	−	4.88262e11i	−0.145537	−	0.825382i	0.821397	−	0.570357i	$-0.193195\pi$
$878$	−8.75442e11	+	1.54364e11i	−1.47316	+	0.259758i
$879$		0			0
$880$	−9.83865e11	−	8.25561e11i	−1.64061	−	1.37663i
$881$	−8.77120e10	+	5.06405e10i	−0.145598	+	0.0840610i	−0.571029	−	0.820930i	$-0.693456\pi$
$881$	−8.77120e10	+	5.06405e10i	−0.145598	+	0.0840610i	0.425431	+	0.904991i	$0.360122\pi$
$882$		0			0
$883$	4.94259e10	−	8.56082e10i	0.0813040	−	0.140823i	−0.822506	−	0.568756i	$-0.807425\pi$
$883$	4.94259e10	−	8.56082e10i	0.0813040	−	0.140823i	0.903810	+	0.427933i	$0.140758\pi$
$884$	5.75950e10	+	1.58241e11i	0.0943138	+	0.259125i
$885$		0			0
$886$	5.32189e11	−	4.46560e11i	0.863636	−	0.724677i
$887$	2.00750e11	−	5.51556e11i	0.324310	−	0.891035i	−0.665212	−	0.746655i	$-0.731659\pi$
$887$	2.00750e11	−	5.51556e11i	0.324310	−	0.891035i	0.989522	−	0.144381i	$-0.0461190\pi$
$888$		0			0
$889$	3.14112e10	−	1.78142e11i	0.0502895	−	0.285206i
$890$		−	2.03366e12i		−	3.24129i
$891$		0			0
$892$	−7.38579e11			−1.16664
$893$	3.10022e10	+	5.46652e9i	0.0487513	+	0.00859618i
$894$		0			0
$895$	1.16326e11	+	4.23390e10i	0.181294	+	0.0659855i
$896$	3.09845e11	+	3.69259e11i	0.480743	+	0.572927i
$897$		0			0
$898$	8.56856e10	−	3.11870e10i	0.131766	−	0.0479588i
$899$	6.64855e11	+	3.83854e11i	1.01786	+	0.587662i
$900$		0			0
$901$	4.22823e11	+	7.32351e11i	0.641593	+	1.11127i
$902$	4.08586e11	−	4.86934e11i	0.617245	−	0.735604i
$903$		0			0
$904$	−3.20433e10	−	1.81726e11i	−0.0479803	−	0.272110i
$905$	1.72948e11	−	3.04954e10i	0.257822	−	0.0454610i
$906$		0			0
$907$	−8.15618e11	−	6.84385e11i	−1.20520	−	1.01128i	−0.999466	−	0.0326706i	$-0.989599\pi$
$907$	−8.15618e11	−	6.84385e11i	−1.20520	−	1.01128i	−0.205730	−	0.978609i	$-0.565957\pi$
$908$	−8.54505e11	+	4.93349e11i	−1.25710	+	0.725789i
$909$		0			0
$910$	−4.92748e11	+	8.53464e11i	−0.718553	+	1.24457i
$911$	−7.67476e10	−	2.10862e11i	−0.111427	−	0.306144i	0.871428	−	0.490524i	$-0.163195\pi$
$911$	−7.67476e10	−	2.10862e11i	−0.111427	−	0.306144i	−0.982855	+	0.184380i	$0.940972\pi$
$912$		0			0
$913$	7.84211e11	−	6.58031e11i	1.12863	−	0.947029i
$914$	−4.06785e11	+	1.11763e12i	−0.582881	+	1.60145i
$915$		0			0
$916$	7.65788e9	−	4.34300e10i	0.0108774	−	0.0616890i
$917$		−	1.54148e12i		−	2.18002i
$918$		0			0
$919$	6.59304e11			0.924322			0.462161	−	0.886796i	$-0.347074\pi$
$919$	6.59304e11			0.924322			0.462161	+	0.886796i	$0.347074\pi$
$920$	4.94794e11	+	8.72455e10i	0.690674	+	0.121784i
$921$		0			0
$922$	1.94524e11	+	7.08011e10i	0.269185	+	0.0979753i
$923$	−3.36551e11	−	4.01086e11i	−0.463708	−	0.552626i
$924$		0			0
$925$	3.86403e11	−	1.40639e11i	0.527805	−	0.192105i
$926$	8.20762e11	+	4.73867e11i	1.11628	+	0.644485i
$927$		0			0
$928$	−3.62054e11	−	6.27096e11i	−0.488181	−	0.845555i
$929$	1.80370e11	−	2.14956e11i	0.242159	−	0.288594i	−0.631252	−	0.775578i	$-0.717459\pi$
$929$	1.80370e11	−	2.14956e11i	0.242159	−	0.288594i	0.873411	+	0.486984i	$0.161903\pi$
$930$		0			0
$931$	7.59469e10	+	4.30716e11i	0.101091	+	0.573314i
$932$	7.55025e11	−	1.33131e11i	1.00069	−	0.176448i
$933$		0			0
$934$	6.72306e11	+	5.64132e11i	0.883446	+	0.741299i
$935$	−8.60737e11	+	4.96947e11i	−1.12622	+	0.650225i
$936$		0			0
$937$	−2.27693e11	+	3.94376e11i	−0.295387	+	0.511626i	−0.975075	−	0.221876i	$-0.928782\pi$
$937$	−2.27693e11	+	3.94376e11i	−0.295387	+	0.511626i	0.679688	+	0.733502i	$0.262115\pi$
$938$	7.15184e11	+	1.96495e12i	0.923860	+	2.53829i
$939$		0			0
$940$	−4.36886e10	+	3.66591e10i	−0.0559573	+	0.0469537i
$941$	1.04418e11	−	2.86886e11i	0.133173	−	0.365891i	−0.855125	−	0.518421i	$-0.826520\pi$
$941$	1.04418e11	−	2.86886e11i	0.133173	−	0.365891i	0.988299	+	0.152530i	$0.0487422\pi$
$942$		0			0
$943$	−1.27652e11	+	7.23950e11i	−0.161429	+	0.915507i
$944$		−	2.04231e11i		−	0.257177i
$945$		0			0
$946$	−8.96805e11			−1.11978
$947$	−9.28838e11	−	1.63779e11i	−1.15489	−	0.203638i	−0.436780	−	0.899568i	$-0.643881\pi$
$947$	−9.28838e11	−	1.63779e11i	−1.15489	−	0.203638i	−0.718109	+	0.695930i	$0.754992\pi$
$948$		0			0
$949$	−3.86314e11	−	1.40607e11i	−0.476295	−	0.173357i
$950$	1.12466e12	+	1.34032e12i	1.38079	+	1.64556i
$951$		0			0
$952$	2.10940e11	−	7.67758e10i	0.256809	−	0.0934709i
$953$	−6.71587e11	−	3.87741e11i	−0.814199	−	0.470078i	0.0342127	−	0.999415i	$-0.489108\pi$
$953$	−6.71587e11	−	3.87741e11i	−0.814199	−	0.470078i	−0.848412	+	0.529336i	$0.822441\pi$
$954$		0			0
$955$	3.56600e10	+	6.17650e10i	0.0428715	+	0.0742556i
$956$	3.02970e11	−	3.61065e11i	0.362717	−	0.432269i
$957$		0			0
$958$	−9.88938e10	−	5.60855e11i	−0.117411	−	0.665868i
$959$	−2.88309e11	+	5.08366e10i	−0.340866	+	0.0601039i
$960$		0			0
$961$	8.64873e11	+	7.25714e11i	1.01405	+	0.850887i
$962$	1.51810e11	−	8.76476e10i	0.177256	−	0.102339i
$963$		0			0
$964$	−6.32807e10	+	1.09605e11i	−0.0732762	+	0.126918i
$965$	−7.57526e11	−	2.08128e12i	−0.873551	−	2.40006i
$966$		0			0
$967$	−8.78671e11	+	7.37293e11i	−1.00489	+	0.843207i	−0.987655	−	0.156644i	$-0.949932\pi$
$967$	−8.78671e11	+	7.37293e11i	−1.00489	+	0.843207i	−0.0172398	+	0.999851i	$0.505488\pi$
$968$	1.60914e10	−	4.42107e10i	0.0183270	−	0.0503530i
$969$		0			0
$970$	4.19163e11	−	2.37719e12i	0.473474	−	2.68520i
$971$			3.23593e10i			0.0364017i	0.999834	+	0.0182009i	$0.00579384\pi$
$971$			3.23593e10i			0.0364017i	−0.999834	+	0.0182009i	$0.994206\pi$
$972$		0			0
$973$	3.27933e11			0.365876
$974$	9.84095e11	+	1.73522e11i	1.09346	+	0.192806i
$975$		0			0
$976$	−1.34961e9	−	4.91219e8i	−0.00148734	−	0.000541348i
$977$	−1.08116e11	−	1.28847e11i	−0.118662	−	0.141415i	0.703443	−	0.710751i	$-0.251645\pi$
$977$	−1.08116e11	−	1.28847e11i	−0.118662	−	0.141415i	−0.822105	+	0.569336i	$0.807200\pi$
$978$		0			0
$979$	1.35717e12	−	4.93971e11i	1.47742	−	0.537738i
$980$	−6.86189e11	−	3.96171e11i	−0.743942	−	0.429515i
$981$		0			0
$982$	−4.29279e11	−	7.43533e11i	−0.461630	−	0.799566i
$983$	1.23843e10	−	1.47590e10i	0.0132634	−	0.0158068i	−0.759372	−	0.650657i	$-0.774494\pi$
$983$	1.23843e10	−	1.47590e10i	0.0132634	−	0.0158068i	0.772635	+	0.634850i	$0.218938\pi$
$984$		0			0
$985$	6.87533e10	+	3.89919e11i	0.0730380	+	0.414219i
$986$	−6.81621e11	+	1.20188e11i	−0.721166	+	0.127161i
$987$		0			0
$988$	2.49758e11	+	2.09572e11i	0.262115	+	0.219940i
$989$	8.98193e11	−	5.18572e11i	0.938824	−	0.542031i
$990$		0			0
$991$	2.13512e11	−	3.69813e11i	0.221374	−	0.383432i	−0.733851	−	0.679310i	$-0.762279\pi$
$991$	2.13512e11	−	3.69813e11i	0.221374	−	0.383432i	0.955226	+	0.295879i	$0.0956124\pi$
$992$	−6.39353e11	−	1.75661e12i	−0.660228	−	1.81396i
$993$		0			0
$994$	1.85821e12	−	1.55923e12i	1.90349	−	1.59722i
$995$	1.01106e11	−	2.77787e11i	0.103154	−	0.283413i
$996$		0			0
$997$	−2.60983e11	+	1.48011e12i	−0.264138	+	1.49800i	0.507340	+	0.861746i	$0.330629\pi$
$997$	−2.60983e11	+	1.48011e12i	−0.264138	+	1.49800i	−0.771478	+	0.636256i	$0.780482\pi$
$998$		−	1.70725e12i		−	1.72098i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.5		138
3.2	odd	2		27.9.f.a.2.19	✓	138
27.13	even	9		27.9.f.a.14.19	yes	138
27.14	odd	18	inner	81.9.f.a.71.5		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.19	✓	138	3.2	odd	2
27.9.f.a.14.19	yes	138	27.13	even	9
81.9.f.a.8.5		138	1.1	even	1	trivial
81.9.f.a.71.5		138	27.14	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+(-21.0020 - 3.70323i) q^{2} +(186.811 + 67.9935i) q^{4} +(-674.968 - 804.395i) q^{5} +(-2905.52 + 1057.52i) q^{7} +(1056.43 + 609.927i) q^{8} +(11196.8 + 19393.5i) q^{10} +(-10222.7 + 12182.9i) q^{11} +(-2471.50 - 14016.6i) q^{13} +(64938.1 - 11450.3i) q^{14} +(-58914.5 - 49435.1i) q^{16} +(-51541.5 + 29757.5i) q^{17} +(-57614.1 + 99790.5i) q^{19} +(-71397.5 - 196163. i) q^{20} +(259814. - 218010. i) q^{22} +(-134153. + 368583. i) q^{23} +(-123639. + 701192. i) q^{25} +303529. i q^{26} -614687. q^{28} +(-537040. - 94694.6i) q^{29} +(-1.32290e6 - 481496. i) q^{31} +(853524. + 1.01719e6i) q^{32} +(1.19268e6 - 434098. i) q^{34} +(2.81180e6 + 1.62339e6i) q^{35} +(-288762. - 500150. i) q^{37} +(1.57956e6 - 1.88245e6i) q^{38} +(-222430. - 1.26146e6i) q^{40} +(1.84569e6 - 325445. i) q^{41} +(-2.02555e6 - 1.69964e6i) q^{43} +(-2.73807e6 + 1.58082e6i) q^{44} +(4.18244e6 - 7.24419e6i) q^{46} +(-93440.3 - 256725. i) q^{47} +(2.90760e6 - 2.43977e6i) q^{49} +(5.19335e6 - 1.42686e7i) q^{50} +(491334. - 2.78649e6i) q^{52} -1.42090e7i q^{53} +1.66999e7 q^{55} +(-3.71448e6 - 654963. i) q^{56} +(1.09283e7 + 3.97756e6i) q^{58} +(1.70695e6 + 2.03426e6i) q^{59} +(17548.6 - 6387.15i) q^{61} +(2.60005e7 + 1.50114e7i) q^{62} +(-4.31471e6 - 7.47329e6i) q^{64} +(-9.60669e6 + 1.14488e7i) q^{65} +(5.50666e6 + 3.12298e7i) q^{67} +(-1.16518e7 + 2.05453e6i) q^{68} +(-5.30418e7 - 4.45073e7i) q^{70} +(3.18584e7 - 1.83935e7i) q^{71} +(1.44422e7 - 2.50147e7i) q^{73} +(4.21241e6 + 1.15735e7i) q^{74} +(-1.75480e7 + 1.47245e7i) q^{76} +(1.68185e7 - 4.62085e7i) q^{77} +(1.46028e6 - 8.28165e6i) q^{79} +8.07577e7i q^{80} -3.99685e7 q^{82} +(-6.33917e7 - 1.11777e7i) q^{83} +(5.87257e7 + 2.13744e7i) q^{85} +(3.62466e7 + 4.31970e7i) q^{86} +(-1.82302e7 + 6.63526e6i) q^{88} +(-7.86470e7 - 4.54069e7i) q^{89} +(2.20039e7 + 3.81118e7i) q^{91} +(-5.01225e7 + 5.97336e7i) q^{92} +(1.01173e6 + 5.73778e6i) q^{94} +(1.19159e8 - 2.10109e7i) q^{95} +(-8.25735e7 - 6.92874e7i) q^{97} +(-7.01007e7 + 4.04726e7i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 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

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