LMFDB - Embedded newform 81.9.f.a.8.12

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			8.12
Character	$\chi$	$=$	81.8
Dual form			81.9.f.a.71.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.46646 + 0.434904i) q^{2} +(-234.667 - 85.4118i) q^{4} +(411.949 + 490.942i) q^{5} +(243.334 - 88.5664i) q^{7} +(-1096.91 - 633.301i) q^{8} +(802.546 + 1390.05i) q^{10} +(-4355.96 + 5191.23i) q^{11} +(-733.507 - 4159.93i) q^{13} +(638.693 - 112.619i) q^{14} +(46543.3 + 39054.5i) q^{16} +(27580.9 - 15923.8i) q^{17} +(-31761.5 + 55012.5i) q^{19} +(-54738.7 - 150393. i) q^{20} +(-13001.5 + 10909.6i) q^{22} +(67576.8 - 185666. i) q^{23} +(-3490.62 + 19796.3i) q^{25} -10579.3i q^{26} -64667.1 q^{28} +(-1.01674e6 - 179279. i) q^{29} +(-1.67239e6 - 608702. i) q^{31} +(306236. + 364958. i) q^{32} +(74952.5 - 27280.5i) q^{34} +(143722. + 82978.2i) q^{35} +(-711454. - 1.23227e6i) q^{37} +(-102264. + 121873. i) q^{38} +(-140957. - 799407. i) q^{40} +(-47826.5 + 8433.11i) q^{41} +(670492. + 562610. i) q^{43} +(1.46559e6 - 846160. i) q^{44} +(247423. - 428549. i) q^{46} +(-2.11724e6 - 5.81707e6i) q^{47} +(-4.36473e6 + 3.66244e6i) q^{49} +(-17219.0 + 47308.8i) q^{50} +(-183177. + 1.03885e6i) q^{52} -9.95902e6i q^{53} -4.34303e6 q^{55} +(-323005. - 56954.4i) q^{56} +(-2.42979e6 - 884370. i) q^{58} +(-9.92151e6 - 1.18240e7i) q^{59} +(-2.00776e7 + 7.30764e6i) q^{61} +(-3.86018e6 - 2.22867e6i) q^{62} +(-7.18042e6 - 1.24369e7i) q^{64} +(1.74012e6 - 2.07379e6i) q^{65} +(2.15182e6 + 1.22036e7i) q^{67} +(-7.83240e6 + 1.38106e6i) q^{68} +(318399. + 267168. i) q^{70} +(2.36946e6 - 1.36801e6i) q^{71} +(874977. - 1.51550e6i) q^{73} +(-1.21886e6 - 3.34878e6i) q^{74} +(1.21521e7 - 1.01968e7i) q^{76} +(-600185. + 1.64900e6i) q^{77} +(7.53737e6 - 4.27466e7i) q^{79} +3.89386e7i q^{80} -121630. q^{82} +(5.86063e7 + 1.03339e7i) q^{83} +(1.91796e7 + 6.98080e6i) q^{85} +(1.40906e6 + 1.67926e6i) q^{86} +(8.06570e6 - 2.93568e6i) q^{88} +(3.32007e7 + 1.91684e7i) q^{89} +(-546917. - 947288. i) q^{91} +(-3.17161e7 + 3.77978e7i) q^{92} +(-2.69223e6 - 1.52684e7i) q^{94} +(-4.00921e7 + 7.06932e6i) q^{95} +(1.06250e8 + 8.91546e7i) q^{97} +(-1.23583e7 + 7.13504e6i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.46646	+	0.434904i	0.154154	+	0.0271815i	0.250193	−	0.968196i	$-0.419506\pi$
$2$	2.46646	+	0.434904i	0.154154	+	0.0271815i	−0.0960385	+	0.995378i	$0.530617\pi$
$3$		0			0
$3$		0			0
$4$	−234.667	−	85.4118i	−0.916668	−	0.333640i
$5$	411.949	+	490.942i	0.659119	+	0.785508i	0.987259	−	0.159122i	$-0.0508662\pi$
$5$	411.949	+	490.942i	0.659119	+	0.785508i	−0.328140	+	0.944629i	$0.606422\pi$
$6$		0			0
$7$	243.334	−	88.5664i	0.101347	−	0.0368873i	−0.290849	−	0.956769i	$-0.593938\pi$
$7$	243.334	−	88.5664i	0.101347	−	0.0368873i	0.392196	+	0.919882i	$0.371715\pi$
$8$	−1096.91	−	633.301i	−0.267800	−	0.154614i
$9$		0			0
$10$	802.546	+	1390.05i	0.0802546	+	0.139005i
$11$	−4355.96	+	5191.23i	−0.297518	+	0.354568i	−0.894007	−	0.448053i	$-0.852118\pi$
$11$	−4355.96	+	5191.23i	−0.297518	+	0.354568i	0.596489	+	0.802621i	$0.296562\pi$
$12$		0			0
$13$	−733.507	−	4159.93i	−0.0256821	−	0.145651i	0.969270	−	0.245998i	$-0.0791157\pi$
$13$	−733.507	−	4159.93i	−0.0256821	−	0.145651i	−0.994952	+	0.100347i	$0.968005\pi$
$14$	638.693	−	112.619i	0.0166257	−	0.00293156i
$15$		0			0
$16$	46543.3	+	39054.5i	0.710195	+	0.595924i
$17$	27580.9	−	15923.8i	0.330227	−	0.190656i	−0.325715	−	0.945468i	$-0.605605\pi$
$17$	27580.9	−	15923.8i	0.330227	−	0.190656i	0.655942	+	0.754812i	$0.272272\pi$
$18$		0			0
$19$	−31761.5	+	55012.5i	−0.243717	+	0.422131i	−0.961770	−	0.273858i	$-0.911700\pi$
$19$	−31761.5	+	55012.5i	−0.243717	+	0.422131i	0.718053	+	0.695989i	$0.245034\pi$
$20$	−54738.7	−	150393.i	−0.342117	−	0.939958i
$21$		0			0
$22$	−13001.5	+	10909.6i	−0.0555013	+	0.0465711i
$23$	67576.8	−	185666.i	0.241483	−	0.663469i	−0.758448	−	0.651733i	$-0.774042\pi$
$23$	67576.8	−	185666.i	0.241483	−	0.663469i	0.999931	−	0.0117355i	$-0.00373562\pi$
$24$		0			0
$25$	−3490.62	+	19796.3i	−0.00893599	+	0.0506785i
$26$		−	10579.3i		−	0.0231507i
$27$		0			0
$28$	−64667.1			−0.105209
$29$	−1.01674e6	−	179279.i	−1.43753	−	0.253476i	−0.600061	−	0.799954i	$-0.704857\pi$
$29$	−1.01674e6	−	179279.i	−1.43753	−	0.253476i	−0.837474	+	0.546478i	$0.815968\pi$
$30$		0			0
$31$	−1.67239e6	−	608702.i	−1.81089	−	0.659110i	−0.996940	−	0.0781752i	$-0.975091\pi$
$31$	−1.67239e6	−	608702.i	−1.81089	−	0.659110i	−0.813950	−	0.580935i	$-0.802687\pi$
$32$	306236.	+	364958.i	0.292050	+	0.348051i
$33$		0			0
$34$	74952.5	−	27280.5i	0.0560881	−	0.0204144i
$35$	143722.	+	82978.2i	0.0957750	+	0.0552957i
$36$		0			0
$37$	−711454.	−	1.23227e6i	−0.379612	−	0.657507i	0.611394	−	0.791327i	$-0.290609\pi$
$37$	−711454.	−	1.23227e6i	−0.379612	−	0.657507i	−0.991006	+	0.133819i	$0.957276\pi$
$38$	−102264.	+	121873.i	−0.0490442	+	0.0584486i
$39$		0			0
$40$	−140957.	−	799407.i	−0.0550613	−	0.312268i
$41$	−47826.5	+	8433.11i	−0.0169252	+	0.00298437i	−0.182104	−	0.983279i	$-0.558291\pi$
$41$	−47826.5	+	8433.11i	−0.0169252	+	0.00298437i	0.165179	+	0.986264i	$0.447180\pi$
$42$		0			0
$43$	670492.	+	562610.i	0.196119	+	0.164564i	0.735559	−	0.677461i	$-0.236920\pi$
$43$	670492.	+	562610.i	0.196119	+	0.164564i	−0.539440	+	0.842024i	$0.681364\pi$
$44$	1.46559e6	−	846160.i	0.391023	−	0.225757i
$45$		0			0
$46$	247423.	−	428549.i	0.0552597	−	0.0957125i
$47$	−2.11724e6	−	5.81707e6i	−0.433889	−	1.19210i	−0.943406	−	0.331639i	$-0.892398\pi$
$47$	−2.11724e6	−	5.81707e6i	−0.433889	−	1.19210i	0.509517	−	0.860460i	$-0.329824\pi$
$48$		0			0
$49$	−4.36473e6	+	3.66244e6i	−0.757134	+	0.635311i
$50$	−17219.0	+	47308.8i	−0.00275504	+	0.00756941i
$51$		0			0
$52$	−183177.	+	1.03885e6i	−0.0250529	+	0.142082i
$53$		−	9.95902e6i		−	1.26216i	−0.775719	−	0.631078i	$-0.782613\pi$
$53$		−	9.95902e6i		−	1.26216i	0.775719	−	0.631078i	$-0.217387\pi$
$54$		0			0
$55$	−4.34303e6			−0.474616
$56$	−323005.	−	56954.4i	−0.0328440	−	0.00579129i
$57$		0			0
$58$	−2.42979e6	−	884370.i	−0.214712	−	0.0781487i
$59$	−9.92151e6	−	1.18240e7i	−0.818785	−	0.975790i	0.181186	−	0.983449i	$-0.442006\pi$
$59$	−9.92151e6	−	1.18240e7i	−0.818785	−	0.975790i	−0.999971	+	0.00765928i	$0.997562\pi$
$60$		0			0
$61$	−2.00776e7	+	7.30764e6i	−1.45008	+	0.527786i	−0.942613	−	0.333886i	$-0.891640\pi$
$61$	−2.00776e7	+	7.30764e6i	−1.45008	+	0.527786i	−0.507466	+	0.861672i	$0.669418\pi$
$62$	−3.86018e6	−	2.22867e6i	−0.261240	−	0.150827i
$63$		0			0
$64$	−7.18042e6	−	1.24369e7i	−0.427987	−	0.741295i
$65$	1.74012e6	−	2.07379e6i	0.0974821	−	0.116175i
$66$		0			0
$67$	2.15182e6	+	1.22036e7i	0.106784	+	0.605602i	0.990493	+	0.137565i	$0.0439276\pi$
$67$	2.15182e6	+	1.22036e7i	0.106784	+	0.605602i	−0.883709	+	0.468037i	$0.844961\pi$
$68$	−7.83240e6	+	1.38106e6i	−0.366319	+	0.0645919i
$69$		0			0
$70$	318399.	+	267168.i	0.0132611	+	0.0111274i
$71$	2.36946e6	−	1.36801e6i	0.0932429	−	0.0538338i	−0.452654	−	0.891686i	$-0.649523\pi$
$71$	2.36946e6	−	1.36801e6i	0.0932429	−	0.0538338i	0.545896	+	0.837853i	$0.316189\pi$
$72$		0			0
$73$	874977.	−	1.51550e6i	0.0308109	−	0.0533661i	−0.850209	−	0.526446i	$-0.823524\pi$
$73$	874977.	−	1.51550e6i	0.0308109	−	0.0533661i	0.881020	+	0.473080i	$0.156858\pi$
$74$	−1.21886e6	−	3.34878e6i	−0.0406467	−	0.111676i
$75$		0			0
$76$	1.21521e7	−	1.01968e7i	0.364248	−	0.305640i
$77$	−600185.	+	1.64900e6i	−0.0170735	+	0.0469091i
$78$		0			0
$79$	7.53737e6	−	4.27466e7i	0.193514	−	1.09747i	−0.721006	−	0.692929i	$-0.756320\pi$
$79$	7.53737e6	−	4.27466e7i	0.193514	−	1.09747i	0.914520	−	0.404542i	$-0.132569\pi$
$80$			3.89386e7i			0.950648i
$81$		0			0
$82$	−121630.			−0.00269020
$83$	5.86063e7	+	1.03339e7i	1.23490	+	0.217746i	0.752729	−	0.658330i	$-0.228737\pi$
$83$	5.86063e7	+	1.03339e7i	1.23490	+	0.217746i	0.482172	+	0.876077i	$0.339848\pi$
$84$		0			0
$85$	1.91796e7	+	6.98080e6i	0.367421	+	0.133730i
$86$	1.40906e6	+	1.67926e6i	0.0257595	+	0.0306990i
$87$		0			0
$88$	8.06570e6	−	2.93568e6i	0.134497	−	0.0489528i
$89$	3.32007e7	+	1.91684e7i	0.529161	+	0.305511i	0.740675	−	0.671864i	$-0.234506\pi$
$89$	3.32007e7	+	1.91684e7i	0.529161	+	0.305511i	−0.211514	+	0.977375i	$0.567839\pi$
$90$		0			0
$91$	−546917.	−	947288.i	−0.00797547	−	0.0138139i
$92$	−3.17161e7	+	3.77978e7i	−0.442719	+	0.527612i
$93$		0			0
$94$	−2.69223e6	−	1.52684e7i	−0.0344826	−	0.195561i
$95$	−4.00921e7	+	7.06932e6i	−0.492226	+	0.0867927i
$96$		0			0
$97$	1.06250e8	+	8.91546e7i	1.20017	+	1.00706i	0.999625	+	0.0273787i	$0.00871601\pi$
$97$	1.06250e8	+	8.91546e7i	1.20017	+	1.00706i	0.200546	+	0.979684i	$0.435728\pi$
$98$	−1.23583e7	+	7.13504e6i	−0.133984	+	0.0773557i
$99$		0			0
$100$	2.50997e6	−	4.34740e6i	0.0250997	−	0.0434740i
$101$	−4.55685e7	−	1.25198e8i	−0.437904	−	1.20313i	−0.940853	−	0.338816i	$-0.889974\pi$
$101$	−4.55685e7	−	1.25198e8i	−0.437904	−	1.20313i	0.502949	−	0.864316i	$-0.332249\pi$
$102$		0			0
$103$	−9.13908e7	+	7.66860e7i	−0.811995	+	0.681345i	−0.951083	−	0.308935i	$-0.900027\pi$
$103$	−9.13908e7	+	7.66860e7i	−0.811995	+	0.681345i	0.139088	+	0.990280i	$0.455583\pi$
$104$	−1.82989e6	+	5.02759e6i	−0.0156420	+	0.0429761i
$105$		0			0
$106$	4.33122e6	−	2.45636e7i	0.0343073	−	0.194567i
$107$			1.15116e8i			0.878216i	0.898434	+	0.439108i	$0.144705\pi$
$107$			1.15116e8i			0.878216i	−0.898434	+	0.439108i	$0.855295\pi$
$108$		0			0
$109$	3.18734e7			0.225799			0.112900	−	0.993606i	$-0.463986\pi$
$109$	3.18734e7			0.225799			0.112900	+	0.993606i	$0.463986\pi$
$110$	−1.07119e7	−	1.88880e6i	−0.0731639	−	0.0129008i
$111$		0			0
$112$	1.47845e7	+	5.38112e6i	0.0939582	+	0.0341980i
$113$	4.45785e7	+	5.31266e7i	0.273408	+	0.325835i	0.885224	−	0.465165i	$-0.154005\pi$
$113$	4.45785e7	+	5.31266e7i	0.273408	+	0.325835i	−0.611816	+	0.791000i	$0.709561\pi$
$114$		0			0
$115$	1.18989e8	−	4.33086e7i	0.680326	−	0.247618i
$116$	2.23283e8	+	1.28913e8i	1.23317	+	0.711972i
$117$		0			0
$118$	−1.93287e7	−	3.34784e7i	−0.0996955	−	0.172678i
$119$	5.30105e6	−	6.31755e6i	0.0264347	−	0.0315036i
$120$		0			0
$121$	2.92485e7	+	1.65877e8i	0.136447	+	0.773827i
$122$	−5.26987e7	+	9.29221e6i	−0.237882	+	0.0419449i
$123$		0			0
$124$	3.40466e8	+	2.85685e8i	1.44008	+	1.20837i
$125$	2.05647e8	−	1.18730e8i	0.842331	−	0.486320i
$126$		0			0
$127$	2.33645e8	−	4.04684e8i	0.898133	−	1.55561i	0.0682548	−	0.997668i	$-0.478257\pi$
$127$	2.33645e8	−	4.04684e8i	0.898133	−	1.55561i	0.829878	−	0.557944i	$-0.188410\pi$
$128$	−5.40153e7	−	1.48406e8i	−0.201223	−	0.552855i
$129$		0			0
$130$	5.19383e6	−	4.35814e6i	0.0181851	−	0.0152591i
$131$	−1.80234e8	+	4.95187e8i	−0.611998	+	1.68145i	0.113765	+	0.993508i	$0.463709\pi$
$131$	−1.80234e8	+	4.95187e8i	−0.611998	+	1.68145i	−0.725763	+	0.687944i	$0.758513\pi$
$132$		0			0
$133$	−2.85640e6	+	1.61994e7i	−0.00912876	+	0.0517718i
$134$			3.10355e7i			0.0962586i
$135$		0			0
$136$	−4.03382e7			−0.117913
$137$	3.13130e8	+	5.52133e7i	0.888879	+	0.156733i	0.599399	−	0.800451i	$-0.295406\pi$
$137$	3.13130e8	+	5.52133e7i	0.888879	+	0.156733i	0.289480	+	0.957184i	$0.406518\pi$
$138$		0			0
$139$	−5.17739e8	−	1.88442e8i	−1.38692	−	0.504798i	−0.462652	−	0.886540i	$-0.653102\pi$
$139$	−5.17739e8	−	1.88442e8i	−1.38692	−	0.504798i	−0.924269	+	0.381742i	$0.875324\pi$
$140$	−2.66396e7	−	3.17478e7i	−0.0693450	−	0.0826422i
$141$		0			0
$142$	6.43914e6	−	2.34365e6i	0.0158370	−	0.00576421i
$143$	2.47903e7	+	1.43127e7i	0.0592839	+	0.0342276i
$144$		0			0
$145$	−3.30830e8	−	5.73015e8i	−0.748399	−	1.29627i
$146$	2.81720e6	−	3.35741e6i	0.00620020	−	0.00738912i
$147$		0			0
$148$	6.17040e7	+	3.49941e8i	0.128608	+	0.729370i
$149$	−6.98309e8	+	1.23131e8i	−1.41678	+	0.249817i	−0.829021	−	0.559218i	$-0.811101\pi$
$149$	−6.98309e8	+	1.23131e8i	−1.41678	+	0.249817i	−0.587761	+	0.809035i	$0.699990\pi$
$150$		0			0
$151$	−2.61562e8	−	2.19476e8i	−0.503114	−	0.422163i	0.355584	−	0.934644i	$-0.384282\pi$
$151$	−2.61562e8	−	2.19476e8i	−0.503114	−	0.422163i	−0.858698	+	0.512481i	$0.828726\pi$
$152$	6.96789e7	−	4.02291e7i	0.130535	−	0.0753644i
$153$		0			0
$154$	−2.19749e6	+	3.80617e6i	−0.00390701	+	0.00676714i
$155$	−3.90105e8	−	1.07180e9i	−0.675856	−	1.85690i
$156$		0			0
$157$	−6.89517e8	+	5.78573e8i	−1.13487	+	0.952269i	−0.999259	−	0.0384927i	$-0.987744\pi$
$157$	−6.89517e8	+	5.78573e8i	−1.13487	+	0.952269i	−0.135612	+	0.990762i	$0.543300\pi$
$158$	3.71813e7	−	1.02155e8i	0.0596618	−	0.163920i
$159$		0			0
$160$	−5.30195e7	+	3.00689e8i	−0.0809014	+	0.458815i
$161$		−	5.11639e7i		−	0.0761483i
$162$		0			0
$163$	−5.07912e8			−0.719512			−0.359756	−	0.933046i	$-0.617140\pi$
$163$	−5.07912e8			−0.719512			−0.359756	+	0.933046i	$0.617140\pi$
$164$	1.19436e7	+	2.10598e6i	0.0165105	+	0.00291124i
$165$		0			0
$166$	1.40056e8	+	5.09763e7i	0.184446	+	0.0671330i
$167$	−5.64103e8	−	6.72272e8i	−0.725258	−	0.864329i	0.269872	−	0.962896i	$-0.413019\pi$
$167$	−5.64103e8	−	6.72272e8i	−0.725258	−	0.864329i	−0.995130	+	0.0985671i	$0.968574\pi$
$168$		0			0
$169$	7.49769e8	−	2.72894e8i	0.919138	−	0.334539i
$170$	4.42698e7	+	2.55592e7i	0.0530044	+	0.0306021i
$171$		0			0
$172$	−1.09289e8	−	1.89294e8i	−0.124871	−	0.216283i
$173$	9.08559e8	−	1.08278e9i	1.01430	−	1.20880i	0.0364893	−	0.999334i	$-0.488383\pi$
$173$	9.08559e8	−	1.08278e9i	1.01430	−	1.20880i	0.977816	−	0.209467i	$-0.0671730\pi$
$174$		0			0
$175$	903900.	+	5.12627e6i	0.000963758	+	0.00546574i
$176$	−4.05482e8	+	7.14974e7i	−0.422591	+	0.0745143i
$177$		0			0
$178$	7.35520e7	+	6.17174e7i	0.0732680	+	0.0614792i
$179$	1.09594e8	−	6.32741e7i	0.106752	−	0.0616330i	−0.445674	−	0.895196i	$-0.647036\pi$
$179$	1.09594e8	−	6.32741e7i	0.106752	−	0.0616330i	0.552425	+	0.833562i	$0.313702\pi$
$180$		0			0
$181$	−2.30450e8	+	3.99152e8i	−0.214715	+	0.371898i	−0.953185	−	0.302389i	$-0.902216\pi$
$181$	−2.30450e8	+	3.99152e8i	−0.214715	+	0.371898i	0.738469	+	0.674287i	$0.235549\pi$
$182$	−936972.	−	2.57431e6i	−0.000853967	−	0.00234626i
$183$		0			0
$184$	−1.91708e8	+	1.60862e8i	−0.167251	+	0.140340i
$185$	3.11893e8	−	8.56918e8i	0.266268	−	0.731564i
$186$		0			0
$187$	−3.74769e7	+	2.12542e8i	−0.0306477	+	0.173811i
$188$			1.54591e9i			1.23752i
$189$		0			0
$190$	−1.01960e8			−0.0782378
$191$	−7.37923e8	−	1.30116e8i	−0.554469	−	0.0977679i	−0.110609	−	0.993864i	$-0.535280\pi$
$191$	−7.37923e8	−	1.30116e8i	−0.554469	−	0.0977679i	−0.443860	+	0.896096i	$0.646391\pi$
$192$		0			0
$193$	−1.25557e9	−	4.56992e8i	−0.904927	−	0.329366i	−0.152701	−	0.988272i	$-0.548797\pi$
$193$	−1.25557e9	−	4.56992e8i	−0.904927	−	0.329366i	−0.752225	+	0.658906i	$0.771019\pi$
$194$	2.23289e8	+	2.66105e8i	0.157638	+	0.187865i
$195$		0			0
$196$	1.33707e9	−	4.86655e8i	0.906005	−	0.329759i
$197$	8.27317e8	+	4.77652e8i	0.549297	+	0.317137i	0.748838	−	0.662753i	$-0.230612\pi$
$197$	8.27317e8	+	4.77652e8i	0.549297	+	0.317137i	−0.199541	+	0.979889i	$0.563945\pi$
$198$		0			0
$199$	−4.23487e8	−	7.33501e8i	−0.270040	−	0.467723i	0.698832	−	0.715286i	$-0.253704\pi$
$199$	−4.23487e8	−	7.33501e8i	−0.270040	−	0.467723i	−0.968872	+	0.247563i	$0.920370\pi$
$200$	1.63659e7	−	1.95041e7i	0.0102287	−	0.0121901i
$201$		0			0
$202$	−5.79438e7	−	3.28615e8i	−0.0348018	−	0.197371i
$203$	−2.63286e8	+	4.64244e7i	−0.155040	+	0.0273377i
$204$		0			0
$205$	−2.38423e7	−	2.00060e7i	−0.0135000	−	0.0113278i
$206$	−2.58763e8	+	1.49397e8i	−0.143692	+	0.0829608i
$207$		0			0
$208$	1.28324e8	−	2.22264e8i	0.0685574	−	0.118745i
$209$	−1.47231e8	−	4.04514e8i	−0.0771638	−	0.212006i
$210$		0			0
$211$	−1.74069e8	+	1.46061e8i	−0.0878195	+	0.0736893i	−0.685641	−	0.727940i	$-0.740478\pi$
$211$	−1.74069e8	+	1.46061e8i	−0.0878195	+	0.0736893i	0.597821	+	0.801630i	$0.296033\pi$
$212$	−8.50618e8	+	2.33705e9i	−0.421106	+	1.15698i
$213$		0			0
$214$	−5.00645e7	+	2.83930e8i	−0.0238712	+	0.135381i
$215$			5.60940e8i			0.262520i
$216$		0			0
$217$	−4.60861e8			−0.207841
$218$	7.86146e7	+	1.38619e7i	0.0348079	+	0.00613757i
$219$		0			0
$220$	1.01917e9	+	3.70946e8i	0.435065	+	0.158351i
$221$	−8.64727e7	−	1.03054e8i	−0.0362501	−	0.0432012i
$222$		0			0
$223$	6.09381e8	−	2.21796e8i	0.246416	−	0.0896882i	−0.215859	−	0.976424i	$-0.569255\pi$
$223$	6.09381e8	−	2.21796e8i	0.246416	−	0.0896882i	0.462276	+	0.886736i	$0.347033\pi$
$224$	1.06841e8	+	6.16846e7i	0.0424371	+	0.0245010i
$225$		0			0
$226$	8.68463e7	+	1.50422e8i	0.0332903	+	0.0576605i
$227$	6.84046e8	−	8.15215e8i	0.257622	−	0.307021i	−0.621695	−	0.783260i	$-0.713556\pi$
$227$	6.84046e8	−	8.15215e8i	0.257622	−	0.307021i	0.879316	+	0.476238i	$0.158000\pi$
$228$		0			0
$229$	3.42445e8	+	1.94210e9i	0.124523	+	0.706205i	0.981590	+	0.191000i	$0.0611731\pi$
$229$	3.42445e8	+	1.94210e9i	0.124523	+	0.706205i	−0.857067	+	0.515205i	$0.827716\pi$
$230$	3.12318e8	−	5.50701e7i	0.111606	−	0.0196791i
$231$		0			0
$232$	1.00173e9	+	8.40555e8i	0.345781	+	0.290145i
$233$	3.99283e9	−	2.30526e9i	1.35474	−	0.782161i	0.365833	−	0.930680i	$-0.380784\pi$
$233$	3.99283e9	−	2.30526e9i	1.35474	−	0.782161i	0.988910	+	0.148519i	$0.0474507\pi$
$234$		0			0
$235$	1.98365e9	−	3.43578e9i	0.650419	−	1.12656i
$236$	1.31834e9	+	3.62212e9i	0.424991	+	1.16765i
$237$		0			0
$238$	1.58224e7	−	1.32766e7i	0.00493133	−	0.00413788i
$239$	−4.79266e8	+	1.31677e9i	−0.146888	+	0.403570i	−0.991216	−	0.132256i	$-0.957778\pi$
$239$	−4.79266e8	+	1.31677e9i	−0.146888	+	0.403570i	0.844328	+	0.535827i	$0.180000\pi$
$240$		0			0
$241$	−5.55644e8	+	3.15122e9i	−0.164713	+	0.934136i	0.784646	+	0.619944i	$0.212845\pi$
$241$	−5.55644e8	+	3.15122e9i	−0.164713	+	0.934136i	−0.949359	+	0.314192i	$0.898266\pi$
$242$			4.21849e8i			0.122997i
$243$		0			0
$244$	5.33570e9			1.50533
$245$	−3.59609e9	−	6.34088e8i	−0.998083	−	0.175989i
$246$		0			0
$247$	2.52145e8	+	9.17734e7i	0.0677428	+	0.0246564i
$248$	1.44897e9	+	1.72682e9i	0.383048	+	0.456499i
$249$		0			0
$250$	5.58858e8	−	2.03408e8i	0.143068	−	0.0520723i
$251$	−2.82883e9	−	1.63323e9i	−0.712709	−	0.411483i	0.0993540	−	0.995052i	$-0.468322\pi$
$251$	−2.82883e9	−	1.63323e9i	−0.712709	−	0.411483i	−0.812063	+	0.583569i	$0.801656\pi$
$252$		0			0
$253$	6.69472e8	+	1.15956e9i	0.163399	+	0.283016i
$254$	7.52275e8	−	8.96526e8i	0.180735	−	0.215391i
$255$		0			0
$256$	5.69712e8	+	3.23100e9i	0.132646	+	0.752275i
$257$	1.01335e9	−	1.78680e8i	0.232287	−	0.0409585i	−0.0562927	−	0.998414i	$-0.517928\pi$
$257$	1.01335e9	−	1.78680e8i	0.232287	−	0.0409585i	0.288580	+	0.957456i	$0.406817\pi$
$258$		0			0
$259$	−2.82259e8	−	2.36844e8i	−0.0627262	−	0.0526336i
$260$	−5.85474e8	+	3.38023e8i	−0.128119	+	0.0739696i
$261$		0			0
$262$	−6.59899e8	+	1.14298e9i	−0.140046	+	0.242568i
$263$	1.69620e9	+	4.66027e9i	0.354531	+	0.974066i	0.980895	+	0.194536i	$0.0623200\pi$
$263$	1.69620e9	+	4.66027e9i	0.354531	+	0.974066i	−0.626364	+	0.779530i	$0.715458\pi$
$264$		0			0
$265$	4.88931e9	−	4.10261e9i	0.991434	−	0.831912i
$266$	−1.40904e7	+	3.87131e7i	−0.00281447	+	0.00773270i
$267$		0			0
$268$	5.37368e8	−	3.04756e9i	0.104168	−	0.590764i
$269$			1.08134e9i			0.206516i	0.994655	+	0.103258i	$0.0329267\pi$
$269$			1.08134e9i			0.206516i	−0.994655	+	0.103258i	$0.967073\pi$
$270$		0			0
$271$	−4.66467e9			−0.864855			−0.432428	−	0.901669i	$-0.642343\pi$
$271$	−4.66467e9			−0.864855			−0.432428	+	0.901669i	$0.642343\pi$
$272$	1.90560e9	+	3.36009e8i	0.348142	+	0.0613868i
$273$		0			0
$274$	7.48312e8	+	2.72363e8i	0.132764	+	0.0483221i
$275$	−8.75622e7	−	1.04353e8i	−0.0153104	−	0.0182462i
$276$		0			0
$277$	−8.24991e9	+	3.00272e9i	−1.40130	+	0.510030i	−0.928563	−	0.371175i	$-0.878955\pi$
$277$	−8.24991e9	+	3.00272e9i	−1.40130	+	0.510030i	−0.472734	+	0.881205i	$0.656733\pi$
$278$	−1.19503e9	−	6.89951e8i	−0.200078	−	0.115515i
$279$		0			0
$280$	−1.05100e8	−	1.82039e8i	−0.0170990	−	0.0296164i
$281$	−3.27244e9	+	3.89994e9i	−0.524864	+	0.625508i	−0.961724	−	0.274021i	$-0.911646\pi$
$281$	−3.27244e9	+	3.89994e9i	−0.524864	+	0.625508i	0.436860	+	0.899530i	$0.356091\pi$
$282$		0			0
$283$	−1.36212e9	−	7.72497e9i	−0.212359	−	1.20435i	−0.885432	−	0.464770i	$-0.846137\pi$
$283$	−1.36212e9	−	7.72497e9i	−0.212359	−	1.20435i	0.673073	−	0.739576i	$-0.264974\pi$
$284$	−6.72878e8	+	1.18646e8i	−0.103434	+	0.0182382i
$285$		0			0
$286$	5.49197e7	+	4.60831e7i	0.00820850	+	0.00688775i
$287$	−1.08909e7	+	6.28789e6i	−0.00160523	+	0.000926781i
$288$		0			0
$289$	−2.98074e9	+	5.16280e9i	−0.427300	+	0.740106i
$290$	−5.66775e8	−	1.55720e9i	−0.0801343	−	0.220167i
$291$		0			0
$292$	−3.34770e8	+	2.80905e8i	−0.0460485	+	0.0386393i
$293$	4.13715e9	−	1.13667e10i	0.561347	−	1.54229i	−0.256318	−	0.966592i	$-0.582510\pi$
$293$	4.13715e9	−	1.13667e10i	0.561347	−	1.54229i	0.817665	−	0.575695i	$-0.195268\pi$
$294$		0			0
$295$	1.71774e9	−	9.74178e9i	0.226813	−	1.28632i
$296$			1.80226e9i			0.234774i
$297$		0			0
$298$	−1.77591e9			−0.225193
$299$	−8.21924e8	−	1.44927e8i	−0.102836	−	0.0181328i
$300$		0			0
$301$	2.12982e8	+	7.75192e7i	0.0259464	+	0.00944372i
$302$	−5.49682e8	−	6.55085e8i	−0.0660820	−	0.0787535i
$303$		0			0
$304$	−3.62677e9	+	1.32004e9i	−0.424645	+	0.154558i
$305$	−1.18586e10	−	6.84655e9i	−1.37035	−	0.791175i
$306$		0			0
$307$	6.47222e9	+	1.12102e10i	0.728618	+	1.26200i	0.957467	+	0.288542i	$0.0931705\pi$
$307$	6.47222e9	+	1.12102e10i	0.728618	+	1.26200i	−0.228849	+	0.973462i	$0.573496\pi$
$308$	2.81687e8	−	3.35702e8i	0.0313015	−	0.0373036i
$309$		0			0
$310$	−4.96047e8	−	2.81322e9i	−0.0537126	−	0.304619i
$311$	1.24197e10	−	2.18993e9i	1.32761	−	0.234093i	0.535531	−	0.844516i	$-0.320112\pi$
$311$	1.24197e10	−	2.18993e9i	1.32761	−	0.234093i	0.792076	+	0.610423i	$0.209000\pi$
$312$		0			0
$313$	−6.91530e9	−	5.80262e9i	−0.720499	−	0.604571i	0.207024	−	0.978336i	$-0.433622\pi$
$313$	−6.91530e9	−	5.80262e9i	−0.720499	−	0.604571i	−0.927523	+	0.373765i	$0.878067\pi$
$314$	−1.95229e9	+	1.12716e9i	−0.200829	+	0.115949i
$315$		0			0
$316$	−5.41983e9	+	9.38743e9i	−0.543548	+	0.941452i
$317$	8.52565e8	+	2.34240e9i	0.0844287	+	0.231966i	0.974722	−	0.223422i	$-0.0717228\pi$
$317$	8.52565e8	+	2.34240e9i	0.0844287	+	0.231966i	−0.890293	+	0.455388i	$0.849501\pi$
$318$		0			0
$319$	5.35956e9	−	4.49721e9i	0.517567	−	0.434290i
$320$	3.14781e9	−	8.64853e9i	0.300198	−	0.824788i
$321$		0			0
$322$	2.22514e7	−	1.26194e8i	0.00206983	−	0.0117386i
$323$			2.02306e9i			0.185865i
$324$		0			0
$325$	8.49116e7			0.00761085
$326$	−1.25275e9	−	2.20893e8i	−0.110916	−	0.0195574i
$327$		0			0
$328$	5.78020e7	+	2.10382e7i	0.00499399	+	0.00181766i
$329$	−1.03039e9	−	1.22798e9i	−0.0879467	−	0.104811i
$330$		0			0
$331$	−1.23169e10	+	4.48300e9i	−1.02610	+	0.373471i	−0.799596	−	0.600539i	$-0.794953\pi$
$331$	−1.23169e10	+	4.48300e9i	−1.02610	+	0.373471i	−0.226507	+	0.974010i	$0.572731\pi$
$332$	−1.28703e10	−	7.43069e9i	−1.05935	−	0.611614i
$333$		0			0
$334$	−1.09897e9	−	1.90347e9i	−0.0883077	−	0.152953i
$335$	−5.10481e9	+	6.08367e9i	−0.405322	+	0.483044i
$336$		0			0
$337$	−2.91787e8	−	1.65481e9i	−0.0226228	−	0.128300i	0.971405	−	0.237430i	$-0.0763049\pi$
$337$	−2.91787e8	−	1.65481e9i	−0.0226228	−	0.128300i	−0.994028	+	0.109129i	$0.965194\pi$
$338$	1.96796e9	−	3.47005e8i	0.150782	−	0.0265870i
$339$		0			0
$340$	−3.90457e9	−	3.27633e9i	−0.292185	−	0.245172i
$341$	1.04448e10	−	6.03031e9i	0.772472	−	0.445987i
$342$		0			0
$343$	−1.48412e9	+	2.57057e9i	−0.107224	+	0.185717i
$344$	−3.79168e8	−	1.04176e9i	−0.0270768	−	0.0743930i
$345$		0			0
$346$	2.71183e9	−	2.27550e9i	0.189216	−	0.158771i
$347$	−2.77675e9	+	7.62907e9i	−0.191522	+	0.526203i	−0.997870	−	0.0652390i	$-0.979219\pi$
$347$	−2.77675e9	+	7.62907e9i	−0.191522	+	0.526203i	0.806347	+	0.591442i	$0.201441\pi$
$348$		0			0
$349$	1.80498e7	−	1.02366e8i	0.00121667	−	0.00690006i	−0.984193	−	0.177097i	$-0.943329\pi$
$349$	1.80498e7	−	1.02366e8i	0.00121667	−	0.00690006i	0.985410	+	0.170197i	$0.0544404\pi$
$350$			1.30369e7i			0.000868763i
$351$		0			0
$352$	−3.22854e9			−0.210298
$353$	9.42955e9	+	1.66268e9i	0.607285	+	0.107081i	0.468830	−	0.883288i	$-0.344676\pi$
$353$	9.42955e9	+	1.66268e9i	0.607285	+	0.107081i	0.138454	+	0.990369i	$0.455787\pi$
$354$		0			0
$355$	1.64771e9	+	5.99717e8i	0.103745	+	0.0377601i
$356$	−6.15390e9	−	7.33394e9i	−0.383134	−	0.456601i
$357$		0			0
$358$	2.97828e8	−	1.08400e8i	0.0181315	−	0.00659931i
$359$	−2.20697e10	−	1.27419e10i	−1.32867	−	0.767109i	−0.343578	−	0.939124i	$-0.611639\pi$
$359$	−2.20697e10	−	1.27419e10i	−1.32867	−	0.767109i	−0.985094	+	0.172015i	$0.944972\pi$
$360$		0			0
$361$	6.47420e9	+	1.12136e10i	0.381204	+	0.660264i
$362$	−7.41991e8	+	8.84270e8i	−0.0432080	+	0.0514933i
$363$		0			0
$364$	4.74338e7	+	2.69011e8i	0.00270198	+	0.0153237i
$365$	1.10447e9	−	1.94748e8i	0.0622276	−	0.0109724i
$366$		0			0
$367$	−4.98172e8	−	4.18016e8i	−0.0274609	−	0.0230424i	0.628954	−	0.777443i	$-0.283483\pi$
$367$	−4.98172e8	−	4.18016e8i	−0.0274609	−	0.0230424i	−0.656415	+	0.754400i	$0.727928\pi$
$368$	1.03963e10	−	6.00232e9i	0.566877	−	0.327287i
$369$		0			0
$370$	1.14195e9	−	1.97791e9i	0.0609312	−	0.105536i
$371$	−8.82035e8	−	2.42337e9i	−0.0465576	−	0.127916i
$372$		0			0
$373$	9.77422e8	−	8.20154e8i	0.0504948	−	0.0423702i	−0.617191	−	0.786813i	$-0.711729\pi$
$373$	9.77422e8	−	8.20154e8i	0.0504948	−	0.0423702i	0.667686	+	0.744443i	$0.267285\pi$
$374$	−1.84871e8	+	5.07929e8i	−0.00944892	+	0.0259607i
$375$		0			0
$376$	−1.36153e9	+	7.72164e9i	−0.0681204	+	0.386330i
$377$			4.36107e9i			0.215888i
$378$		0			0
$379$	2.22343e10			1.07762			0.538811	−	0.842427i	$-0.318874\pi$
$379$	2.22343e10			1.07762			0.538811	+	0.842427i	$0.318874\pi$
$380$	1.00121e10	+	1.76540e9i	0.480165	+	0.0846661i
$381$		0			0
$382$	−1.76347e9	−	6.41851e8i	−0.0828162	−	0.0301426i
$383$	2.13080e10	+	2.53939e10i	0.990258	+	1.18014i	0.983636	+	0.180166i	$0.0576634\pi$
$383$	2.13080e10	+	2.53939e10i	0.990258	+	1.18014i	0.00662182	+	0.999978i	$0.497892\pi$
$384$		0			0
$385$	−1.05681e9	+	3.84647e8i	−0.0481009	+	0.0175073i
$386$	−2.89808e9	−	1.67321e9i	−0.130545	−	0.0753704i
$387$		0			0
$388$	−1.73186e10	−	2.99967e10i	−0.764162	−	1.32357i
$389$	−2.54213e10	+	3.02959e10i	−1.11019	+	1.32308i	−0.168845	+	0.985643i	$0.554004\pi$
$389$	−2.54213e10	+	3.02959e10i	−1.11019	+	1.32308i	−0.941349	+	0.337435i	$0.890441\pi$
$390$		0			0
$391$	−1.09268e9	−	6.19690e9i	−0.0467505	−	0.265135i
$392$	7.10713e9	−	1.25318e9i	0.300989	−	0.0530724i
$393$		0			0
$394$	1.83282e9	+	1.53792e9i	0.0760561	+	0.0638186i
$395$	2.40911e10	−	1.39090e10i	0.989620	−	0.571357i
$396$		0			0
$397$	1.01278e10	−	1.75419e10i	0.407712	−	0.706179i	−0.586921	−	0.809645i	$-0.699660\pi$
$397$	1.01278e10	−	1.75419e10i	0.407712	−	0.706179i	0.994633	+	0.103466i	$0.0329932\pi$
$398$	−7.25513e8	−	1.99333e9i	−0.0289143	−	0.0794414i
$399$		0			0
$400$	−9.35600e8	+	7.85061e8i	−0.0365469	+	0.0306665i
$401$	−9.60582e9	+	2.63918e10i	−0.371498	+	1.02068i	0.603284	+	0.797526i	$0.293858\pi$
$401$	−9.60582e9	+	2.63918e10i	−0.371498	+	1.02068i	−0.974783	+	0.223157i	$0.928364\pi$
$402$		0			0
$403$	−1.30544e9	+	7.40353e9i	−0.0494923	+	0.280685i
$404$			3.32720e10i			1.24897i
$405$		0			0
$406$	−6.69576e8			−0.0246431
$407$	9.49609e9	+	1.67442e9i	0.346073	+	0.0610219i
$408$		0			0
$409$	2.22849e10	+	8.11103e9i	0.796374	+	0.289856i	0.707983	−	0.706229i	$-0.249605\pi$
$409$	2.22849e10	+	8.11103e9i	0.796374	+	0.289856i	0.0883910	+	0.996086i	$0.471828\pi$
$410$	−5.01054e7	−	5.97133e7i	−0.00177317	−	0.00211318i
$411$		0			0
$412$	2.79963e10	−	1.01898e10i	0.971654	−	0.353653i
$413$	−3.46145e9	−	1.99847e9i	−0.118976	−	0.0686906i
$414$		0			0
$415$	1.90695e10	+	3.30294e10i	0.642906	+	1.11355i
$416$	1.29357e9	−	1.54162e9i	0.0431934	−	0.0514759i
$417$		0			0
$418$	−1.87215e8	−	1.06175e9i	−0.00613248	−	0.0347790i
$419$	−1.55067e10	+	2.73425e9i	−0.503111	+	0.0887120i	−0.419443	−	0.907782i	$-0.637775\pi$
$419$	−1.55067e10	+	2.73425e9i	−0.503111	+	0.0887120i	−0.0836677	+	0.996494i	$0.526663\pi$
$420$		0			0
$421$	3.24333e9	+	2.72148e9i	0.103244	+	0.0866316i	0.692948	−	0.720987i	$-0.256311\pi$
$421$	3.24333e9	+	2.72148e9i	0.103244	+	0.0866316i	−0.589705	+	0.807619i	$0.700756\pi$
$422$	−4.92857e8	+	2.84551e8i	−0.0155407	+	0.00897244i
$423$		0			0
$424$	−6.30706e9	+	1.09241e10i	−0.195148	+	0.338006i
$425$	2.18958e8	+	6.01583e8i	0.00671128	+	0.0184391i
$426$		0			0
$427$	−4.23835e9	+	3.55640e9i	−0.127493	+	0.106979i
$428$	9.83228e9	−	2.70140e10i	0.293008	−	0.805033i
$429$		0			0
$430$	−2.43955e8	+	1.38354e9i	−0.00713569	+	0.0404685i
$431$			5.43801e10i			1.57591i	0.615734	+	0.787954i	$0.288860\pi$
$431$			5.43801e10i			1.57591i	−0.615734	+	0.787954i	$0.711140\pi$
$432$		0			0
$433$	1.01330e10			0.288261			0.144130	−	0.989559i	$-0.453962\pi$
$433$	1.01330e10			0.288261			0.144130	+	0.989559i	$0.453962\pi$
$434$	−1.13670e9	−	2.00431e8i	−0.0320395	−	0.00564944i
$435$		0			0
$436$	−7.47964e9	−	2.72237e9i	−0.206983	−	0.0753356i
$437$	8.06760e9	+	9.61459e9i	0.221217	+	0.263636i
$438$		0			0
$439$	4.09720e10	−	1.49126e10i	1.10314	−	0.401509i	0.274665	−	0.961540i	$-0.411433\pi$
$439$	4.09720e10	−	1.49126e10i	1.10314	−	0.401509i	0.828471	+	0.560031i	$0.189211\pi$
$440$	4.76391e9	+	2.75044e9i	0.127102	+	0.0733824i
$441$		0			0
$442$	−1.68463e8	−	2.91787e8i	−0.00441383	−	0.00764498i
$443$	2.87742e10	−	3.42918e10i	0.747117	−	0.890379i	−0.249844	−	0.968286i	$-0.580379\pi$
$443$	2.87742e10	−	3.42918e10i	0.747117	−	0.890379i	0.996961	+	0.0779071i	$0.0248238\pi$
$444$		0			0
$445$	4.26642e9	+	2.41961e10i	0.108799	+	0.617028i
$446$	1.59948e9	−	2.82031e8i	0.0404239	−	0.00712783i
$447$		0			0
$448$	−2.84873e9	−	2.39037e9i	−0.0707195	−	0.0593407i
$449$	3.94571e10	−	2.27806e10i	0.970823	−	0.560505i	0.0713360	−	0.997452i	$-0.477274\pi$
$449$	3.94571e10	−	2.27806e10i	0.970823	−	0.560505i	0.899487	+	0.436947i	$0.143940\pi$
$450$		0			0
$451$	1.64552e8	−	2.85013e8i	0.00397738	−	0.00688903i
$452$	−5.92346e9	−	1.62746e10i	−0.141913	−	0.389903i
$453$		0			0
$454$	2.04172e9	−	1.71320e9i	0.0480587	−	0.0403260i
$455$	2.39762e8	−	6.58740e8i	0.00559415	−	0.0153698i
$456$		0			0
$457$	−7.31714e9	+	4.14976e10i	−0.167755	+	0.951388i	0.778422	+	0.627741i	$0.216020\pi$
$457$	−7.31714e9	+	4.14976e10i	−0.167755	+	0.951388i	−0.946178	+	0.323647i	$0.895091\pi$
$458$			4.93906e9i			0.112249i
$459$		0			0
$460$	−3.16220e10			−0.706248
$461$	−1.81731e10	−	3.20440e9i	−0.402369	−	0.0709484i	−0.0311982	−	0.999513i	$-0.509932\pi$
$461$	−1.81731e10	−	3.20440e9i	−0.402369	−	0.0709484i	−0.371170	+	0.928565i	$0.621043\pi$
$462$		0			0
$463$	−2.73595e10	−	9.95805e9i	−0.595367	−	0.216696i	0.0267215	−	0.999643i	$-0.491493\pi$
$463$	−2.73595e10	−	9.95805e9i	−0.595367	−	0.216696i	−0.622088	+	0.782947i	$0.713715\pi$
$464$	−4.03209e10	−	4.80525e10i	−0.869877	−	1.03668i
$465$		0			0
$466$	1.08507e10	−	3.94934e9i	0.230099	−	0.0837493i
$467$	−4.63413e10	−	2.67552e10i	−0.974319	−	0.562523i	−0.0737688	−	0.997275i	$-0.523503\pi$
$467$	−4.63413e10	−	2.67552e10i	−0.974319	−	0.562523i	−0.900550	+	0.434752i	$0.856836\pi$
$468$		0			0
$469$	1.60444e9	+	2.77897e9i	0.0331613	+	0.0574370i
$470$	6.38683e9	−	7.61153e9i	0.130886	−	0.155984i
$471$		0			0
$472$	3.39485e9	+	1.92531e10i	0.0683994	+	0.387912i
$473$	−5.84128e9	+	1.02997e9i	−0.116698	+	0.0205770i
$474$		0			0
$475$	−9.78177e8	−	8.20788e8i	−0.0192151	−	0.0161234i
$476$	−1.78357e9	+	1.02975e9i	−0.0347427	+	0.0200587i
$477$		0			0
$478$	−1.75476e9	+	3.03934e9i	−0.0336130	+	0.0582194i
$479$	−9.54151e9	−	2.62151e10i	−0.181249	−	0.497977i	0.815481	−	0.578784i	$-0.196473\pi$
$479$	−9.54151e9	−	2.62151e10i	−0.181249	−	0.497977i	−0.996730	+	0.0808069i	$0.974250\pi$
$480$		0			0
$481$	−4.60432e9	+	3.86348e9i	−0.0860171	+	0.0721769i
$482$	−2.74095e9	+	7.53071e9i	−0.0507825	+	0.139524i
$483$		0			0
$484$	7.30416e9	−	4.14240e10i	0.133103	−	0.754867i
$485$			8.88899e10i			1.60652i
$486$		0			0
$487$	−5.43062e10			−0.965458			−0.482729	−	0.875770i	$-0.660354\pi$
$487$	−5.43062e10			−0.965458			−0.482729	+	0.875770i	$0.660354\pi$
$488$	2.66512e10	+	4.69932e9i	0.469934	+	0.0828621i
$489$		0			0
$490$	−8.59387e9	−	3.12791e9i	−0.149075	−	0.0542588i
$491$	−2.12598e10	−	2.53364e10i	−0.365791	−	0.435933i	0.551485	−	0.834185i	$-0.314061\pi$
$491$	−2.12598e10	−	2.53364e10i	−0.365791	−	0.435933i	−0.917276	+	0.398252i	$0.869617\pi$
$492$		0			0
$493$	−3.08974e10	+	1.12457e10i	−0.523039	+	0.190371i
$494$	5.81995e8	+	3.36015e8i	0.00977263	+	0.00564223i
$495$		0			0
$496$	−5.40663e10	−	9.36455e10i	−0.893305	−	1.54725i
$497$	4.55411e8	−	5.42737e8i	0.00746410	−	0.00889537i
$498$		0			0
$499$	−7.01014e9	−	3.97565e10i	−0.113064	−	0.641218i	−0.987691	−	0.156421i	$-0.950004\pi$
$499$	−7.01014e9	−	3.97565e10i	−0.113064	−	0.641218i	0.874626	−	0.484798i	$-0.161107\pi$
$500$	−5.83996e10	+	1.02974e10i	−0.934393	+	0.164759i
$501$		0			0
$502$	−6.26692e9	−	5.25857e9i	−0.0986823	−	0.0828043i
$503$	1.03883e11	−	5.99768e10i	1.62283	−	0.936940i	0.636668	−	0.771138i	$-0.280312\pi$
$503$	1.03883e11	−	5.99768e10i	1.62283	−	0.936940i	0.986159	−	0.165801i	$-0.0530211\pi$
$504$		0			0
$505$	4.26933e10	−	7.39469e10i	0.656438	−	1.13698i
$506$	1.14693e9	+	3.15117e9i	0.0174959	+	0.0480695i
$507$		0			0
$508$	−8.93935e10	+	7.50100e10i	−1.34230	+	1.12633i
$509$	−1.99802e10	+	5.48952e10i	−0.297666	+	0.817830i	0.697223	+	0.716854i	$0.254419\pi$
$509$	−1.99802e10	+	5.48952e10i	−0.297666	+	0.817830i	−0.994889	+	0.100976i	$0.967803\pi$
$510$		0			0
$511$	7.86890e7	−	4.46268e8i	0.00115407	−	0.00654503i
$512$			4.86471e10i			0.707908i
$513$		0			0
$514$	2.57709e9			0.0369213
$515$	−7.52968e10	−	1.32768e10i	−1.07040	−	0.188741i
$516$		0			0
$517$	3.94203e10	+	1.43478e10i	0.551770	+	0.200828i
$518$	−5.93178e8	−	7.06922e8i	−0.00823884	−	0.00981867i
$519$		0			0
$520$	−3.22208e9	+	1.17274e9i	−0.0440680	+	0.0160394i
$521$	−6.93877e9	−	4.00610e9i	−0.0941741	−	0.0543715i	0.452173	−	0.891930i	$-0.350649\pi$
$521$	−6.93877e9	−	4.00610e9i	−0.0941741	−	0.0543715i	−0.546347	+	0.837559i	$0.683982\pi$
$522$		0			0
$523$	−2.54192e10	−	4.40273e10i	−0.339746	−	0.588457i	0.644639	−	0.764487i	$-0.277008\pi$
$523$	−2.54192e10	−	4.40273e10i	−0.339746	−	0.588457i	−0.984385	+	0.176030i	$0.943674\pi$
$524$	8.45897e10	−	1.00810e11i	1.12200	−	1.33715i
$525$		0			0
$526$	2.15685e9	+	1.22321e10i	0.0281758	+	0.159793i
$527$	−5.58189e10	+	9.84238e9i	−0.723667	+	0.127602i
$528$		0			0
$529$	3.00845e10	+	2.52439e10i	0.384168	+	0.322355i
$530$	1.38435e10	−	7.99257e9i	0.175446	−	0.101294i
$531$		0			0
$532$	2.05392e9	−	3.55750e9i	0.0256412	−	0.0444118i
$533$	7.01622e7	+	1.92769e8i	0.000869349	+	0.00238852i
$534$		0			0
$535$	−5.65154e10	+	4.74221e10i	−0.689845	+	0.578849i
$536$	5.36818e9	−	1.47489e10i	0.0650381	−	0.178691i
$537$		0			0
$538$	−4.70280e8	+	2.66709e9i	−0.00561342	+	0.0318353i
$539$		−	3.86117e10i		−	0.457472i
$540$		0			0
$541$	4.99438e10			0.583032			0.291516	−	0.956566i	$-0.405840\pi$
$541$	4.99438e10			0.583032			0.291516	+	0.956566i	$0.405840\pi$
$542$	−1.15052e10	−	2.02868e9i	−0.133321	−	0.0235081i
$543$		0			0
$544$	1.42578e10	+	5.18941e9i	0.162801	+	0.0592546i
$545$	1.31302e10	+	1.56480e10i	0.148829	+	0.177367i
$546$		0			0
$547$	−2.21042e10	+	8.04528e9i	−0.246903	+	0.0898653i	−0.462507	−	0.886616i	$-0.653050\pi$
$547$	−2.21042e10	+	8.04528e9i	−0.246903	+	0.0898653i	0.215604	+	0.976481i	$0.430828\pi$
$548$	−6.87654e10	−	3.97017e10i	−0.762514	−	0.440238i
$549$		0			0
$550$	−1.70586e8	−	2.95463e8i	−0.00186420	−	0.00322888i
$551$	4.21558e10	−	5.02393e10i	0.457352	−	0.545051i
$552$		0			0
$553$	−1.95181e9	−	1.10693e10i	−0.0208707	−	0.118364i
$554$	−2.16540e10	+	3.81819e9i	−0.229879	+	0.0405339i
$555$		0			0
$556$	1.05401e11	+	8.84420e10i	1.10293	+	0.925464i
$557$	1.24286e11	−	7.17563e10i	1.29122	−	0.745486i	0.312349	−	0.949968i	$-0.398884\pi$
$557$	1.24286e11	−	7.17563e10i	1.29122	−	0.745486i	0.978870	+	0.204482i	$0.0655509\pi$
$558$		0			0
$559$	1.84861e9	−	3.20188e9i	0.0189320	−	0.0327912i
$560$	3.44865e9	+	9.47509e9i	0.0350669	+	0.0963454i
$561$		0			0
$562$	−9.76746e9	+	8.19588e9i	−0.0979121	+	0.0821580i
$563$	−1.27931e10	+	3.51488e10i	−0.127334	+	0.349846i	−0.986935	−	0.161119i	$-0.948490\pi$
$563$	−1.27931e10	+	3.51488e10i	−0.127334	+	0.349846i	0.859601	+	0.510965i	$0.170712\pi$
$564$		0			0
$565$	−7.71799e9	+	4.37709e10i	−0.0757375	+	0.429528i
$566$		−	1.96458e10i		−	0.191427i
$567$		0			0
$568$	−3.46544e9			−0.0332939
$569$	−1.61367e11	−	2.84534e10i	−1.53945	−	0.271447i	−0.661407	−	0.750028i	$-0.730040\pi$
$569$	−1.61367e11	−	2.84534e10i	−1.53945	−	0.271447i	−0.878043	+	0.478581i	$0.841151\pi$
$570$		0			0
$571$	−1.72062e11	−	6.26253e10i	−1.61860	−	0.589122i	−0.635486	−	0.772112i	$-0.719200\pi$
$571$	−1.72062e11	−	6.26253e10i	−1.61860	−	0.589122i	−0.983115	+	0.182990i	$0.941422\pi$
$572$	−4.59499e9	−	5.47609e9i	−0.0429240	−	0.0511548i
$573$		0			0
$574$	−2.95967e7	+	1.07723e7i	−0.000272644	+	9.92344e-5i
$575$	3.43961e9	+	1.98586e9i	0.0314657	+	0.0181668i
$576$		0			0
$577$	−1.38743e10	−	2.40309e10i	−0.125172	−	0.216804i	0.796628	−	0.604470i	$-0.206615\pi$
$577$	−1.38743e10	−	2.40309e10i	−0.125172	−	0.216804i	−0.921800	+	0.387665i	$0.873282\pi$
$578$	−9.59722e9	+	1.14375e10i	−0.0859873	+	0.102476i
$579$		0			0
$580$	2.86927e10	+	1.62725e11i	0.253548	+	1.43794i
$581$	1.51762e10	−	2.67597e9i	0.133186	−	0.0234842i
$582$		0			0
$583$	5.16996e10	+	4.33811e10i	0.447520	+	0.375514i
$584$	−1.91954e9	+	1.10825e9i	−0.0165023	+	0.00952763i
$585$		0			0
$586$	1.51476e10	−	2.62364e10i	0.128456	−	0.222492i
$587$	−1.84410e10	−	5.06662e10i	−0.155322	−	0.426743i	0.837487	−	0.546458i	$-0.184024\pi$
$587$	−1.84410e10	−	5.06662e10i	−0.155322	−	0.426743i	−0.992808	+	0.119715i	$0.961802\pi$
$588$		0			0
$589$	8.66040e10	−	7.26694e10i	0.719576	−	0.603796i
$590$	8.47348e9	−	2.32807e10i	0.0699284	−	0.192127i
$591$		0			0
$592$	1.50124e10	−	8.51396e10i	0.122226	−	0.693178i
$593$			1.98579e11i			1.60589i	0.596054	+	0.802945i	$0.296735\pi$
$593$			1.98579e11i			1.60589i	−0.596054	+	0.802945i	$0.703265\pi$
$594$		0			0
$595$	5.28532e9			0.0421700
$596$	1.74387e11	+	3.07491e10i	1.38207	+	0.243696i
$597$		0			0
$598$	−1.96422e9	−	7.14917e8i	−0.0153598	−	0.00559050i
$599$	1.00906e11	+	1.20255e11i	0.783808	+	0.934105i	0.999099	−	0.0424444i	$-0.0135145\pi$
$599$	1.00906e11	+	1.20255e11i	0.783808	+	0.934105i	−0.215291	+	0.976550i	$0.569070\pi$
$600$		0			0
$601$	1.23406e10	−	4.49162e9i	0.0945887	−	0.0344275i	−0.294292	−	0.955715i	$-0.595084\pi$
$601$	1.23406e10	−	4.49162e9i	0.0945887	−	0.0344275i	0.388881	+	0.921288i	$0.372862\pi$
$602$	4.91599e8	+	2.83825e8i	0.00374305	+	0.00216105i
$603$		0			0
$604$	4.26340e10	+	7.38443e10i	0.320338	+	0.554842i
$605$	−6.93870e10	+	8.26922e10i	−0.517912	+	0.617224i
$606$		0			0
$607$	−2.69000e10	−	1.52558e11i	−0.198152	−	1.12377i	−0.907858	−	0.419277i	$-0.862284\pi$
$607$	−2.69000e10	−	1.52558e11i	−0.198152	−	1.12377i	0.709706	−	0.704497i	$-0.248828\pi$
$608$	−2.98038e10	+	5.25521e9i	−0.218101	+	0.0384571i
$609$		0			0
$610$	−2.62711e10	−	2.20441e10i	−0.189740	−	0.159211i
$611$	−2.26456e10	+	1.30744e10i	−0.162487	+	0.0938118i
$612$		0			0
$613$	−6.82522e10	+	1.18216e11i	−0.483364	+	0.837212i	−0.999818	−	0.0191038i	$-0.993919\pi$
$613$	−6.82522e10	+	1.18216e11i	−0.483364	+	0.837212i	0.516453	+	0.856315i	$0.327252\pi$
$614$	1.10881e10	+	3.04644e10i	0.0780163	+	0.214348i
$615$		0			0
$616$	1.70266e9	−	1.42870e9i	0.0118251	−	0.00992244i
$617$	−1.05167e10	+	2.88945e10i	−0.0725672	+	0.199377i	−0.970673	−	0.240402i	$-0.922721\pi$
$617$	−1.05167e10	+	2.88945e10i	−0.0725672	+	0.199377i	0.898106	+	0.439778i	$0.144943\pi$
$618$		0			0
$619$	2.29396e10	−	1.30097e11i	0.156251	−	0.886143i	−0.801382	−	0.598152i	$-0.795902\pi$
$619$	2.29396e10	−	1.30097e11i	0.156251	−	0.886143i	0.957633	−	0.287991i	$-0.0929872\pi$
$620$			2.84837e11i			1.92765i
$621$		0			0
$622$	3.15852e10			0.211019
$623$	9.77655e9	+	1.72387e9i	0.0648983	+	0.0114433i
$624$		0			0
$625$	1.50385e11	+	5.47355e10i	0.985561	+	0.358715i
$626$	−1.45327e10	−	1.73195e10i	−0.0946347	−	0.112781i
$627$		0			0
$628$	2.11224e11	−	7.68792e10i	1.35801	−	0.494277i
$629$	−3.92450e10	−	2.26581e10i	−0.250716	−	0.144751i
$630$		0			0
$631$	6.47545e10	+	1.12158e11i	0.408463	+	0.707478i	0.994718	−	0.102648i	$-0.0327316\pi$
$631$	6.47545e10	+	1.12158e11i	0.408463	+	0.707478i	−0.586255	+	0.810127i	$0.699398\pi$
$632$	−3.53392e10	+	4.21157e10i	−0.221508	+	0.263983i
$633$		0			0
$634$	1.08410e9	+	6.14824e9i	0.00670984	+	0.0380534i
$635$	2.94926e11	−	5.20035e10i	1.81392	−	0.319843i
$636$		0			0
$637$	1.84370e10	+	1.54705e10i	0.111978	+	0.0939609i
$638$	1.51750e10	−	8.76130e9i	0.0915897	−	0.0528793i
$639$		0			0
$640$	5.06071e10	−	8.76541e10i	0.301642	−	0.522459i
$641$	5.46839e10	+	1.50243e11i	0.323912	+	0.889941i	0.989617	+	0.143726i	$0.0459085\pi$
$641$	5.46839e10	+	1.50243e11i	0.323912	+	0.889941i	−0.665706	+	0.746215i	$0.731869\pi$
$642$		0			0
$643$	1.61080e11	−	1.35162e11i	0.942318	−	0.790699i	−0.0356691	−	0.999364i	$-0.511356\pi$
$643$	1.61080e11	−	1.35162e11i	0.942318	−	0.790699i	0.977987	+	0.208665i	$0.0669118\pi$
$644$	−4.37000e9	+	1.20065e10i	−0.0254061	+	0.0698027i
$645$		0			0
$646$	−8.79836e8	+	4.98980e9i	−0.00505210	+	0.0286519i
$647$		−	1.78264e11i		−	1.01730i	−0.860974	−	0.508648i	$-0.830145\pi$
$647$		−	1.78264e11i		−	1.01730i	0.860974	−	0.508648i	$-0.169855\pi$
$648$		0			0
$649$	1.04599e11			0.589587
$650$	2.09431e8	+	3.69284e7i	0.00117324	+	0.000206875i
$651$		0			0
$652$	1.19190e11	+	4.33817e10i	0.659554	+	0.240058i
$653$	−6.49968e10	−	7.74602e10i	−0.357470	−	0.426016i	0.557099	−	0.830446i	$-0.311914\pi$
$653$	−6.49968e10	−	7.74602e10i	−0.357470	−	0.426016i	−0.914569	+	0.404430i	$0.867470\pi$
$654$		0			0
$655$	−3.17356e11	+	1.15508e11i	−1.72417	+	0.627548i
$656$	−2.55536e9	−	1.47534e9i	−0.0137986	−	0.00796664i
$657$		0			0
$658$	−2.00738e9	−	3.47688e9i	−0.0107084	−	0.0185475i
$659$	1.04978e9	−	1.25108e9i	0.00556616	−	0.00663349i	−0.763254	−	0.646098i	$-0.776400\pi$
$659$	1.04978e9	−	1.25108e9i	0.00556616	−	0.00663349i	0.768820	+	0.639465i	$0.220844\pi$
$660$		0			0
$661$	−1.54225e10	−	8.74653e10i	−0.0807884	−	0.458174i	−0.998186	−	0.0602023i	$-0.980825\pi$
$661$	−1.54225e10	−	8.74653e10i	−0.0807884	−	0.458174i	0.917398	−	0.397971i	$-0.130286\pi$
$662$	−3.23290e10	+	5.70047e9i	−0.168329	+	0.0296810i
$663$		0			0
$664$	−5.77414e10	−	4.84508e10i	−0.297040	−	0.249246i
$665$	−9.12968e9	+	5.27102e9i	−0.0466841	+	0.0269531i
$666$		0			0
$667$	−1.01994e11	+	1.76659e11i	−0.515314	+	0.892549i
$668$	7.49564e10	+	2.05941e11i	0.376446	+	1.03428i
$669$		0			0
$670$	−1.52366e10	+	1.27851e10i	−0.0756119	+	0.0634459i
$671$	4.95214e10	−	1.36059e11i	0.244289	−	0.671177i
$672$		0			0
$673$	−1.34793e10	+	7.64450e10i	−0.0657064	+	0.372640i	0.934169	+	0.356832i	$0.116143\pi$
$673$	−1.34793e10	+	7.64450e10i	−0.0657064	+	0.372640i	−0.999875	+	0.0158078i	$0.994968\pi$
$674$		−	4.20842e9i		−	0.0203929i
$675$		0			0
$676$	−1.99254e11			−0.954160
$677$	1.68693e11	+	2.97451e10i	0.803050	+	0.141599i	0.560084	−	0.828436i	$-0.310769\pi$
$677$	1.68693e11	+	2.97451e10i	0.803050	+	0.141599i	0.242965	+	0.970035i	$0.421880\pi$
$678$		0			0
$679$	3.37504e10	+	1.22842e10i	0.158782	+	0.0577918i
$680$	−1.66173e10	−	1.98037e10i	−0.0777187	−	0.0926215i
$681$		0			0
$682$	2.83843e10	−	1.03311e10i	0.131202	−	0.0477537i
$683$	−3.58504e11	−	2.06982e11i	−1.64744	−	0.951153i	−0.978083	−	0.208216i	$-0.933234\pi$
$683$	−3.58504e11	−	2.06982e11i	−1.64744	−	0.951153i	−0.669362	−	0.742937i	$-0.733432\pi$
$684$		0			0
$685$	1.01887e11	+	1.76474e11i	0.462762	+	0.801527i
$686$	−4.77848e9	+	5.69477e9i	−0.0215771	+	0.0257146i
$687$		0			0
$688$	9.23450e9	+	5.23715e10i	0.0412154	+	0.233744i
$689$	−4.14288e10	+	7.30502e9i	−0.183834	+	0.0324149i
$690$		0			0
$691$	−3.19102e11	−	2.67758e11i	−1.39964	−	1.17444i	−0.961258	−	0.275650i	$-0.911107\pi$
$691$	−3.19102e11	−	2.67758e11i	−1.39964	−	1.17444i	−0.438383	−	0.898788i	$-0.644449\pi$
$692$	−3.05691e11	+	1.76491e11i	−1.33309	+	0.769657i
$693$		0			0
$694$	−1.01667e10	+	1.76092e10i	−0.0438269	+	0.0759105i
$695$	−1.20768e11	−	3.31808e11i	−0.517623	−	1.42216i
$696$		0			0
$697$	−1.18481e9	+	9.94173e8i	−0.00502016	+	0.00421241i
$698$	8.90386e7	−	2.44632e8i	0.000375108	−	0.00103060i
$699$		0			0
$700$	2.25729e8	−	1.28017e9i	0.000940144	−	0.00533182i
$701$		−	4.23591e11i		−	1.75418i	−0.480326	−	0.877090i	$-0.659482\pi$
$701$		−	4.23591e11i		−	1.75418i	0.480326	−	0.877090i	$-0.340518\pi$
$702$		0			0
$703$	9.03874e10			0.370072
$704$	9.58403e10	+	1.68992e10i	0.390173	+	0.0687980i
$705$		0			0
$706$	2.25345e10	+	8.20191e9i	0.0907048	+	0.0330138i
$707$	−2.21767e10	−	2.64292e10i	−0.0887606	−	0.105781i
$708$		0			0
$709$	−1.98886e11	+	7.23886e10i	−0.787081	+	0.286474i	−0.704122	−	0.710079i	$-0.748659\pi$
$709$	−1.98886e11	+	7.23886e10i	−0.787081	+	0.286474i	−0.0829588	+	0.996553i	$0.526437\pi$
$710$	3.80320e9	+	2.19578e9i	0.0149663	+	0.00864082i
$711$		0			0
$712$	−2.42788e10	−	4.20521e10i	−0.0944728	−	0.163632i
$713$	−2.26030e11	+	2.69372e11i	−0.874598	+	1.04231i
$714$		0			0
$715$	3.18564e9	+	1.80667e10i	0.0121891	+	0.0691281i
$716$	−3.11224e10	+	5.48772e9i	−0.118419	+	0.0208805i
$717$		0			0
$718$	−4.88925e10	−	4.10257e10i	−0.183969	−	0.154368i
$719$	3.55351e11	−	2.05162e11i	1.32966	−	0.767681i	0.344415	−	0.938817i	$-0.388077\pi$
$719$	3.55351e11	−	2.05162e11i	1.32966	−	0.767681i	0.985247	+	0.171137i	$0.0547439\pi$
$720$		0			0
$721$	−1.54467e10	+	2.67545e10i	−0.0571603	+	0.0990046i
$722$	1.10915e10	+	3.04737e10i	0.0408171	+	0.112144i
$723$		0			0
$724$	8.81714e10	−	7.39846e10i	0.320903	−	0.269269i
$725$	7.09812e9	−	1.95019e10i	0.0256916	−	0.0705871i
$726$		0			0
$727$	−5.40742e10	+	3.06670e11i	−0.193576	+	1.09783i	0.720855	+	0.693086i	$0.243749\pi$
$727$	−5.40742e10	+	3.06670e11i	−0.193576	+	1.09783i	−0.914432	+	0.404741i	$0.867362\pi$
$728$			1.38545e9i			0.00493249i
$729$		0			0
$730$	2.80884e9			0.00989088
$731$	2.74517e10	+	4.84047e9i	0.0961389	+	0.0169519i
$732$		0			0
$733$	−1.43090e11	−	5.20803e10i	−0.495669	−	0.180409i	0.0820759	−	0.996626i	$-0.473845\pi$
$733$	−1.43090e11	−	5.20803e10i	−0.495669	−	0.180409i	−0.577745	+	0.816217i	$0.696067\pi$
$734$	−1.04693e9	−	1.24768e9i	−0.00360688	−	0.00429851i
$735$		0			0
$736$	8.84547e10	−	3.21949e10i	0.301446	−	0.109717i
$737$	−7.27248e10	−	4.19877e10i	−0.246497	−	0.142315i
$738$		0			0
$739$	−3.62658e10	−	6.28143e10i	−0.121596	−	0.210611i	0.798801	−	0.601595i	$-0.205468\pi$
$739$	−3.62658e10	−	6.28143e10i	−0.121596	−	0.210611i	−0.920397	+	0.390984i	$0.872135\pi$
$740$	−1.46382e11	+	1.74451e11i	−0.488158	+	0.581764i
$741$		0			0
$742$	−1.12157e9	−	6.36076e9i	−0.00370009	−	0.0209842i
$743$	2.97391e11	−	5.24380e10i	0.975826	−	0.172064i	0.337075	−	0.941478i	$-0.390562\pi$
$743$	2.97391e11	−	5.24380e10i	0.975826	−	0.172064i	0.638751	+	0.769413i	$0.279451\pi$
$744$		0			0
$745$	−3.48118e11	−	2.92106e11i	−1.13006	−	0.948234i
$746$	2.76746e9	−	1.59780e9i	0.00893566	−	0.00515901i
$747$		0			0
$748$	2.69482e10	−	4.66756e10i	0.0860842	−	0.149102i
$749$	1.01954e10	+	2.80117e10i	0.0323950	+	0.0890046i
$750$		0			0
$751$	1.35125e11	−	1.13384e11i	0.424793	−	0.356443i	−0.405190	−	0.914232i	$-0.632795\pi$
$751$	1.35125e11	−	1.13384e11i	0.424793	−	0.356443i	0.829983	+	0.557789i	$0.188350\pi$
$752$	1.28639e11	−	3.53433e11i	0.402255	−	1.10519i
$753$		0			0
$754$	−1.89665e9	+	1.07564e10i	−0.00586815	+	0.0332799i
$755$		−	2.18825e11i		−	0.673455i
$756$		0			0
$757$	1.08704e11			0.331025			0.165513	−	0.986208i	$-0.447072\pi$
$757$	1.08704e11			0.331025			0.165513	+	0.986208i	$0.447072\pi$
$758$	5.48401e10	+	9.66979e9i	0.166120	+	0.0292914i
$759$		0			0
$760$	4.84544e10	+	1.76360e10i	0.145237	+	0.0528621i
$761$	3.21895e11	+	3.83619e11i	0.959788	+	1.14383i	0.989538	+	0.144273i	$0.0460845\pi$
$761$	3.21895e11	+	3.83619e11i	0.959788	+	1.14383i	−0.0297499	+	0.999557i	$0.509471\pi$
$762$		0			0
$763$	7.75589e9	−	2.82291e9i	0.0228841	−	0.00832913i
$764$	1.62053e11	+	9.35612e10i	0.475645	+	0.274614i
$765$		0			0
$766$	4.15116e10	+	7.19002e10i	0.120574	+	0.208841i
$767$	−4.19094e10	+	4.99457e10i	−0.121096	+	0.144317i
$768$		0			0
$769$	−7.36249e10	−	4.17547e11i	−0.210533	−	1.19399i	−0.888493	−	0.458891i	$-0.848247\pi$
$769$	−7.36249e10	−	4.17547e11i	−0.210533	−	1.19399i	0.677960	−	0.735099i	$-0.262864\pi$
$770$	−2.77386e9	+	4.89107e8i	−0.00789082	+	0.00139136i
$771$		0			0
$772$	2.55609e11	+	2.14482e11i	0.719627	+	0.603839i
$773$	−2.87823e11	+	1.66175e11i	−0.806134	+	0.465422i	−0.845612	−	0.533799i	$-0.820764\pi$
$773$	−2.87823e11	+	1.66175e11i	−0.806134	+	0.465422i	0.0394773	+	0.999220i	$0.487431\pi$
$774$		0			0
$775$	1.78877e10	−	3.09825e10i	0.0495848	−	0.0858834i
$776$	−6.00852e10	−	1.65083e11i	−0.165699	−	0.455255i
$777$		0			0
$778$	−7.58765e10	+	6.36679e10i	−0.207104	+	0.173781i
$779$	1.05512e9	−	2.89891e9i	0.00286517	−	0.00787198i
$780$		0			0
$781$	−3.21962e9	+	1.82594e10i	−0.00865368	+	0.0490775i
$782$		−	1.57596e10i		−	0.0421424i
$783$		0			0
$784$	−3.46184e11			−0.916310
$785$	−5.68092e11	−	1.00170e11i	−1.49603	−	0.263790i
$786$		0			0
$787$	−4.41598e11	−	1.60728e11i	−1.15114	−	0.418980i	−0.305215	−	0.952283i	$-0.598728\pi$
$787$	−4.41598e11	−	1.60728e11i	−1.15114	−	0.418980i	−0.845924	+	0.533303i	$0.820951\pi$
$788$	−1.53347e11	−	1.82752e11i	−0.397714	−	0.473977i
$789$		0			0
$790$	6.54690e10	−	2.38288e10i	0.168084	−	0.0611777i
$791$	1.55527e10	+	8.97936e9i	0.0397283	+	0.0229371i
$792$		0			0
$793$	4.51263e10	+	7.81610e10i	0.114113	+	0.197650i
$794$	3.26090e10	−	3.88618e10i	0.0820455	−	0.0977781i
$795$		0			0
$796$	3.67288e10	+	2.08299e11i	0.0914859	+	0.518842i
$797$	4.55285e10	−	8.02790e9i	0.112837	−	0.0198961i	−0.116945	−	0.993138i	$-0.537310\pi$
$797$	4.55285e10	−	8.02790e9i	0.112837	−	0.0198961i	0.229781	+	0.973242i	$0.426199\pi$
$798$		0			0
$799$	−1.51025e11	−	1.26725e11i	−0.370563	−	0.310939i
$800$	−8.29378e9	+	4.78842e9i	−0.0202485	+	0.0116905i
$801$		0			0
$802$	−3.51703e10	+	6.09168e10i	−0.0850117	+	0.147245i
$803$	4.05597e9	+	1.11437e10i	0.00975512	+	0.0268020i
$804$		0			0
$805$	2.51185e10	−	2.10769e10i	0.0598150	−	0.0501908i
$806$	−6.43965e9	+	1.76928e10i	−0.0152589	+	0.0419234i
$807$		0			0
$808$	−2.93037e10	+	1.66190e11i	−0.0687508	+	0.389905i
$809$		−	1.18357e11i		−	0.276312i	−0.990410	−	0.138156i	$-0.955882\pi$
$809$		−	1.18357e11i		−	0.276312i	0.990410	−	0.138156i	$-0.0441175\pi$
$810$		0			0
$811$	9.39449e10			0.217165			0.108582	−	0.994087i	$-0.465369\pi$
$811$	9.39449e10			0.217165			0.108582	+	0.994087i	$0.465369\pi$
$812$	6.57497e10	+	1.15935e10i	0.151241	+	0.0266679i
$813$		0			0
$814$	2.26936e10	+	8.25978e9i	0.0516898	+	0.0188136i
$815$	−2.09234e11	−	2.49355e11i	−0.474244	−	0.565182i
$816$		0			0
$817$	−5.22464e10	+	1.90161e10i	−0.117265	+	0.0426810i
$818$	5.14373e10	+	2.96974e10i	0.114886	+	0.0663292i
$819$		0			0
$820$	3.88624e9	+	6.73117e9i	0.00859557	+	0.0148880i
$821$	−1.46122e11	+	1.74141e11i	−0.321619	+	0.383291i	−0.902494	−	0.430702i	$-0.858266\pi$
$821$	−1.46122e11	+	1.74141e11i	−0.321619	+	0.383291i	0.580875	+	0.813993i	$0.302710\pi$
$822$		0			0
$823$	6.39160e9	+	3.62485e10i	0.0139319	+	0.0790117i	0.990981	−	0.134003i	$-0.0427830\pi$
$823$	6.39160e9	+	3.62485e10i	0.0139319	+	0.0790117i	−0.977049	+	0.213014i	$0.931672\pi$
$824$	1.48813e11	−	2.62397e10i	0.322798	−	0.0569180i
$825$		0			0
$826$	−7.66841e9	−	6.43456e9i	−0.0164735	−	0.0138229i
$827$	−3.00935e11	+	1.73745e11i	−0.643354	+	0.371441i	−0.785906	−	0.618347i	$-0.787803\pi$
$827$	−3.00935e11	+	1.73745e11i	−0.643354	+	0.371441i	0.142551	+	0.989787i	$0.454469\pi$
$828$		0			0
$829$	−2.97922e11	+	5.16016e11i	−0.630790	+	1.09256i	0.356601	+	0.934257i	$0.383936\pi$
$829$	−2.97922e11	+	5.16016e11i	−0.630790	+	1.09256i	−0.987391	+	0.158303i	$0.949398\pi$
$830$	3.26697e10	+	8.97592e10i	0.0688387	+	0.189133i
$831$		0			0
$832$	−4.64695e10	+	3.89926e10i	−0.0969784	+	0.0813745i
$833$	−6.20629e10	+	1.70516e11i	−0.128900	+	0.354149i
$834$		0			0
$835$	9.76647e10	−	5.53884e11i	0.200905	−	1.13939i
$836$			1.07501e11i			0.220084i
$837$		0			0
$838$	−3.94359e10			−0.0799678
$839$	3.77521e11	+	6.65672e10i	0.761892	+	0.134342i	0.541077	−	0.840973i	$-0.318017\pi$
$839$	3.77521e11	+	6.65672e10i	0.761892	+	0.134342i	0.220816	+	0.975316i	$0.429128\pi$
$840$		0			0
$841$	5.31543e11	+	1.93466e11i	1.06256	+	0.386741i
$842$	6.81598e9	+	8.12297e9i	0.0135606	+	0.0161609i
$843$		0			0
$844$	5.33235e10	−	1.94082e10i	0.105087	−	0.0382486i
$845$	4.42842e11	+	2.55675e11i	0.868604	+	0.501489i
$846$		0			0
$847$	2.18083e10	+	3.77730e10i	0.0423729	+	0.0733919i
$848$	3.88945e11	−	4.63526e11i	0.752150	−	0.896377i
$849$		0			0
$850$	2.78422e8	+	1.57901e9i	0.000533369	+	0.00302489i
$851$	−2.76869e11	+	4.88195e10i	−0.527906	+	0.0930840i
$852$		0			0
$853$	6.58027e11	+	5.52150e11i	1.24293	+	1.04294i	0.997289	+	0.0735846i	$0.0234439\pi$
$853$	6.58027e11	+	5.52150e11i	1.24293	+	1.04294i	0.245644	+	0.969360i	$0.421001\pi$
$854$	−1.20004e10	+	6.92845e9i	−0.0225614	+	0.0130258i
$855$		0			0
$856$	7.29032e10	−	1.26272e11i	0.135785	−	0.235186i
$857$	1.21489e11	+	3.33788e11i	0.225223	+	0.618795i	0.999908	−	0.0135519i	$-0.00431385\pi$
$857$	1.21489e11	+	3.33788e11i	0.225223	+	0.618795i	−0.774685	+	0.632347i	$0.782092\pi$
$858$		0			0
$859$	3.20921e11	−	2.69285e11i	0.589421	−	0.494583i	−0.298605	−	0.954377i	$-0.596521\pi$
$859$	3.20921e11	−	2.69285e11i	0.589421	−	0.494583i	0.888026	+	0.459794i	$0.152077\pi$
$860$	4.79109e10	−	1.31634e11i	0.0875872	−	0.240644i
$861$		0			0
$862$	−2.36501e10	+	1.34127e11i	−0.0428356	+	0.242933i
$863$		−	3.69630e11i		−	0.666383i	−0.942859	−	0.333191i	$-0.891875\pi$
$863$		−	3.69630e11i		−	0.666383i	0.942859	−	0.333191i	$-0.108125\pi$
$864$		0			0
$865$	9.05862e11			1.61807
$866$	2.49926e10	+	4.40687e9i	0.0444365	+	0.00783536i
$867$		0			0
$868$	1.08149e11	+	3.93630e10i	0.190521	+	0.0693441i
$869$	1.89075e11	+	2.25331e11i	0.331554	+	0.395131i
$870$		0			0
$871$	4.91876e10	−	1.79028e10i	0.0854639	−	0.0311063i
$872$	−3.49622e10	−	2.01855e10i	−0.0604691	−	0.0349118i
$873$		0			0
$874$	1.57170e10	+	2.72227e10i	0.0269355	+	0.0466536i
$875$	3.95255e10	−	4.71046e10i	0.0674287	−	0.0803584i
$876$		0			0
$877$	1.45845e11	+	8.27127e11i	0.246543	+	1.39821i	0.816882	+	0.576805i	$0.195701\pi$
$877$	1.45845e11	+	8.27127e11i	0.246543	+	1.39821i	−0.570339	+	0.821409i	$0.693188\pi$
$878$	1.07542e11	−	1.89625e10i	0.180967	−	0.0319093i
$879$		0			0
$880$	−2.02139e11	−	1.69615e11i	−0.337070	−	0.282835i
$881$	−6.57619e11	+	3.79677e11i	−1.09162	+	0.630246i	−0.934007	−	0.357255i	$-0.883713\pi$
$881$	−6.57619e11	+	3.79677e11i	−1.09162	+	0.630246i	−0.157612	+	0.987501i	$0.550379\pi$
$882$		0			0
$883$	5.00897e11	−	8.67579e11i	0.823959	−	1.42714i	−0.0787530	−	0.996894i	$-0.525094\pi$
$883$	5.00897e11	−	8.67579e11i	0.823959	−	1.42714i	0.902712	−	0.430245i	$-0.141573\pi$
$884$	1.14902e10	+	3.15692e10i	0.0188157	+	0.0516957i
$885$		0			0
$886$	8.58842e10	−	7.20654e10i	0.139373	−	0.116948i
$887$	−2.56509e11	+	7.04753e11i	−0.414389	+	1.13853i	0.540443	+	0.841380i	$0.318257\pi$
$887$	−2.56509e11	+	7.04753e11i	−0.414389	+	1.13853i	−0.954832	+	0.297145i	$0.903966\pi$
$888$		0			0
$889$	2.10123e10	−	1.19167e11i	0.0336408	−	0.190786i
$890$			6.15342e10i			0.0980747i
$891$		0			0
$892$	−1.61946e11			−0.255805
$893$	3.87258e11	+	6.82841e10i	0.608968	+	0.107378i
$894$		0			0
$895$	7.62111e10	+	2.77386e10i	0.118775	+	0.0432306i
$896$	−2.62876e10	−	3.13283e10i	−0.0407867	−	0.0486077i
$897$		0			0
$898$	1.07227e11	−	3.90274e10i	0.164892	−	0.0600157i
$899$	1.59126e12	+	9.18717e11i	2.43615	+	1.40651i
$900$		0			0
$901$	−1.58586e11	−	2.74678e11i	−0.240638	−	0.416798i
$902$	5.29815e8	−	6.31409e8i	0.000800384	−	0.000953861i
$903$		0			0
$904$	−1.52534e10	−	8.65066e10i	−0.0228399	−	0.129532i
$905$	−2.90895e11	+	5.12925e10i	−0.433652	+	0.0764645i
$906$		0			0
$907$	1.50108e11	+	1.25956e11i	0.221807	+	0.186118i	0.746919	−	0.664915i	$-0.231532\pi$
$907$	1.50108e11	+	1.25956e11i	0.221807	+	0.186118i	−0.525112	+	0.851033i	$0.675977\pi$
$908$	−2.30152e11	+	1.32878e11i	−0.338588	+	0.195484i
$909$		0			0
$910$	8.77852e8	−	1.52049e9i	0.00128014	−	0.00221726i
$911$	2.20777e11	+	6.06578e11i	0.320538	+	0.880671i	0.990406	+	0.138190i	$0.0441285\pi$
$911$	2.20777e11	+	6.06578e11i	0.320538	+	0.880671i	−0.669868	+	0.742480i	$0.733649\pi$
$912$		0			0
$913$	−3.08932e11	+	2.59225e11i	−0.444611	+	0.373073i
$914$	−3.60949e10	+	9.91700e10i	−0.0517204	+	0.142101i
$915$		0			0
$916$	8.55180e10	−	4.84997e11i	0.121472	−	0.688901i
$917$			1.36459e11i			0.192985i
$918$		0			0
$919$	−6.41781e11			−0.899756			−0.449878	−	0.893090i	$-0.648532\pi$
$919$	−6.41781e11			−0.899756			−0.449878	+	0.893090i	$0.648532\pi$
$920$	−1.57948e11	−	2.78505e10i	−0.220477	−	0.0388760i
$921$		0			0
$922$	−4.34296e10	−	1.58071e10i	−0.0600983	−	0.0218740i
$923$	−7.42882e9	−	8.85333e9i	−0.0102356	−	0.0121983i
$924$		0			0
$925$	2.68779e10	−	9.78276e9i	0.0367137	−	0.0133627i
$926$	−6.31505e10	−	3.64600e10i	−0.0858881	−	0.0495875i
$927$		0			0
$928$	−2.45934e11	−	4.25970e11i	−0.331609	−	0.574363i
$929$	8.58049e11	−	1.02258e12i	1.15199	−	1.37289i	0.235970	−	0.971760i	$-0.424173\pi$
$929$	8.58049e11	−	1.02258e12i	1.15199	−	1.37289i	0.916021	−	0.401129i	$-0.131382\pi$
$930$		0			0
$931$	−6.28498e10	−	3.56439e11i	−0.0836576	−	0.474446i
$932$	−1.13388e12	+	1.99934e11i	−1.50281	+	0.264986i
$933$		0			0
$934$	−1.02663e11	−	8.61448e10i	−0.134905	−	0.113199i
$935$	−1.19784e11	+	6.91576e10i	−0.156731	+	0.0904885i
$936$		0			0
$937$	−2.84345e11	+	4.92500e11i	−0.368882	+	0.638922i	−0.989391	−	0.145277i	$-0.953593\pi$
$937$	−2.84345e11	+	4.92500e11i	−0.368882	+	0.638922i	0.620509	+	0.784199i	$0.286926\pi$
$938$	2.74870e9	+	7.55200e9i	0.00355072	+	0.00975552i
$939$		0			0
$940$	−7.58953e11	+	6.36837e11i	−0.972083	+	0.815675i
$941$	−1.33808e11	+	3.67635e11i	−0.170657	+	0.468876i	−0.995307	−	0.0967671i	$-0.969150\pi$
$941$	−1.33808e11	+	3.67635e11i	−0.170657	+	0.468876i	0.824650	+	0.565643i	$0.191372\pi$
$942$		0			0
$943$	−1.66622e9	+	9.44963e9i	−0.00210711	+	0.0119500i
$944$		−	9.37807e11i		−	1.18093i
$945$		0			0
$946$	−1.48552e10			−0.0185488
$947$	−1.36936e12	−	2.41455e11i	−1.70262	−	0.300218i	−0.764011	−	0.645203i	$-0.776773\pi$
$947$	−1.36936e12	−	2.41455e11i	−1.70262	−	0.300218i	−0.938608	+	0.344986i	$0.887884\pi$
$948$		0			0
$949$	−6.94619e9	−	2.52821e9i	−0.00856410	−	0.00311708i
$950$	−2.05568e9	−	2.44986e9i	−0.00252383	−	0.00300778i
$951$		0			0
$952$	−9.81568e9	+	3.57261e9i	−0.0119501	+	0.00434949i
$953$	2.09625e11	+	1.21027e11i	0.254139	+	0.146727i	0.621658	−	0.783289i	$-0.286459\pi$
$953$	2.09625e11	+	1.21027e11i	0.254139	+	0.146727i	−0.367519	+	0.930016i	$0.619793\pi$
$954$		0			0
$955$	−2.40108e11	−	4.15879e11i	−0.288664	−	0.499980i
$956$	2.24936e11	−	2.68068e11i	0.269294	−	0.320932i
$957$		0			0
$958$	−1.21327e10	−	6.88082e10i	−0.0144045	−	0.0816918i
$959$	8.10853e10	−	1.42975e10i	0.0958667	−	0.0169039i
$960$		0			0
$961$	1.77303e12	+	1.48775e12i	2.07885	+	1.74436i
$962$	−1.30366e10	+	7.52670e9i	−0.0152218	+	0.00878829i
$963$		0			0
$964$	3.99542e11	−	6.92028e11i	0.462652	−	0.801337i
$965$	−2.92877e11	−	8.04672e11i	−0.337735	−	0.927918i
$966$		0			0
$967$	−2.96716e11	+	2.48974e11i	−0.339340	+	0.284740i	−0.796492	−	0.604648i	$-0.793314\pi$
$967$	−2.96716e11	+	2.48974e11i	−0.339340	+	0.284740i	0.457153	+	0.889388i	$0.348869\pi$
$968$	7.29668e10	−	2.00475e11i	0.0831044	−	0.228328i
$969$		0			0
$970$	−3.86586e10	+	2.19244e11i	−0.0436676	+	0.247651i
$971$		−	4.12689e11i		−	0.464243i	−0.972687	−	0.232122i	$-0.925433\pi$
$971$		−	4.12689e11i		−	0.464243i	0.972687	−	0.232122i	$-0.0745668\pi$
$972$		0			0
$973$	−1.42673e11			−0.159181
$974$	−1.33944e11	−	2.36180e10i	−0.148829	−	0.0262426i
$975$		0			0
$976$	−1.21987e12	−	4.43997e11i	−1.34436	−	0.489307i
$977$	−2.63596e11	−	3.14142e11i	−0.289308	−	0.344784i	0.601741	−	0.798692i	$-0.294474\pi$
$977$	−2.63596e11	−	3.14142e11i	−0.289308	−	0.344784i	−0.891049	+	0.453907i	$0.850030\pi$
$978$		0			0
$979$	−2.44129e11	+	8.88556e10i	−0.265759	+	0.0967285i
$980$	7.89726e11	+	4.55948e11i	0.856194	+	0.494324i
$981$		0			0
$982$	−4.14176e10	−	7.17374e10i	−0.0445389	−	0.0771436i
$983$	1.47538e11	−	1.75829e11i	0.158012	−	0.188311i	−0.681230	−	0.732069i	$-0.738555\pi$
$983$	1.47538e11	−	1.75829e11i	0.158012	−	0.188311i	0.839242	+	0.543758i	$0.182999\pi$
$984$		0			0
$985$	1.06313e11	+	6.02934e11i	0.112939	+	0.640508i
$986$	−8.10981e10	+	1.42998e10i	−0.0858031	+	0.0151294i
$987$		0			0
$988$	−5.13317e10	−	4.30724e10i	−0.0538713	−	0.0452034i
$989$	1.49767e11	−	8.64681e10i	0.156542	−	0.0903797i
$990$		0			0
$991$	2.92488e11	−	5.06604e11i	0.303259	−	0.525260i	−0.673613	−	0.739084i	$-0.735259\pi$
$991$	2.92488e11	−	5.06604e11i	0.303259	−	0.525260i	0.976872	+	0.213824i	$0.0685920\pi$
$992$	−2.89997e11	−	7.96761e11i	−0.299466	−	0.822775i
$993$		0			0
$994$	1.35929e9	−	1.14058e9i	0.00139241	−	0.00116837i
$995$	1.85651e11	−	5.10073e11i	0.189411	−	0.520403i
$996$		0			0
$997$	−5.61372e10	+	3.18370e11i	−0.0568160	+	0.322219i	−0.999948	−	0.0101990i	$-0.996753\pi$
$997$	−5.61372e10	+	3.18370e11i	−0.0568160	+	0.322219i	0.943132	+	0.332418i	$0.107865\pi$
$998$		−	1.01107e11i		−	0.101920i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.8.12		138
3.2	odd	2		27.9.f.a.2.12	✓	138
27.13	even	9		27.9.f.a.14.12	yes	138
27.14	odd	18	inner	81.9.f.a.71.12		138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.12	✓	138	3.2	odd	2
27.9.f.a.14.12	yes	138	27.13	even	9
81.9.f.a.8.12		138	1.1	even	1	trivial
81.9.f.a.71.12		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)

\(f(q)\)	\(=\)	\(q+(2.46646 + 0.434904i) q^{2} +(-234.667 - 85.4118i) q^{4} +(411.949 + 490.942i) q^{5} +(243.334 - 88.5664i) q^{7} +(-1096.91 - 633.301i) q^{8} +(802.546 + 1390.05i) q^{10} +(-4355.96 + 5191.23i) q^{11} +(-733.507 - 4159.93i) q^{13} +(638.693 - 112.619i) q^{14} +(46543.3 + 39054.5i) q^{16} +(27580.9 - 15923.8i) q^{17} +(-31761.5 + 55012.5i) q^{19} +(-54738.7 - 150393. i) q^{20} +(-13001.5 + 10909.6i) q^{22} +(67576.8 - 185666. i) q^{23} +(-3490.62 + 19796.3i) q^{25} -10579.3i q^{26} -64667.1 q^{28} +(-1.01674e6 - 179279. i) q^{29} +(-1.67239e6 - 608702. i) q^{31} +(306236. + 364958. i) q^{32} +(74952.5 - 27280.5i) q^{34} +(143722. + 82978.2i) q^{35} +(-711454. - 1.23227e6i) q^{37} +(-102264. + 121873. i) q^{38} +(-140957. - 799407. i) q^{40} +(-47826.5 + 8433.11i) q^{41} +(670492. + 562610. i) q^{43} +(1.46559e6 - 846160. i) q^{44} +(247423. - 428549. i) q^{46} +(-2.11724e6 - 5.81707e6i) q^{47} +(-4.36473e6 + 3.66244e6i) q^{49} +(-17219.0 + 47308.8i) q^{50} +(-183177. + 1.03885e6i) q^{52} -9.95902e6i q^{53} -4.34303e6 q^{55} +(-323005. - 56954.4i) q^{56} +(-2.42979e6 - 884370. i) q^{58} +(-9.92151e6 - 1.18240e7i) q^{59} +(-2.00776e7 + 7.30764e6i) q^{61} +(-3.86018e6 - 2.22867e6i) q^{62} +(-7.18042e6 - 1.24369e7i) q^{64} +(1.74012e6 - 2.07379e6i) q^{65} +(2.15182e6 + 1.22036e7i) q^{67} +(-7.83240e6 + 1.38106e6i) q^{68} +(318399. + 267168. i) q^{70} +(2.36946e6 - 1.36801e6i) q^{71} +(874977. - 1.51550e6i) q^{73} +(-1.21886e6 - 3.34878e6i) q^{74} +(1.21521e7 - 1.01968e7i) q^{76} +(-600185. + 1.64900e6i) q^{77} +(7.53737e6 - 4.27466e7i) q^{79} +3.89386e7i q^{80} -121630. q^{82} +(5.86063e7 + 1.03339e7i) q^{83} +(1.91796e7 + 6.98080e6i) q^{85} +(1.40906e6 + 1.67926e6i) q^{86} +(8.06570e6 - 2.93568e6i) q^{88} +(3.32007e7 + 1.91684e7i) q^{89} +(-546917. - 947288. i) q^{91} +(-3.17161e7 + 3.77978e7i) q^{92} +(-2.69223e6 - 1.52684e7i) q^{94} +(-4.00921e7 + 7.06932e6i) q^{95} +(1.06250e8 + 8.91546e7i) q^{97} +(-1.23583e7 + 7.13504e6i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 6 q^{2} - 6 q^{4} + 447 q^{5} - 6 q^{7} + 9 q^{8} - 3 q^{10} - 28668 q^{11} - 6 q^{13} + 120975 q^{14} - 774 q^{16} + 9 q^{17} - 3 q^{19} - 137913 q^{20} - 185478 q^{22} - 68376 q^{23} + 507585 q^{25}+ \cdots - 1293135102 q^{98}+O(q^{100}) \) 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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