LMFDB - Embedded newform 81.9.f.a.71.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("81.8");

S:= CuspForms(chi, 9);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$32.9976674150$
Analytic rank:	$0$
Dimension:	$138$
Relative dimension:	$23$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			71.19
Character	$\chi$	$=$	81.71
Dual form			81.9.f.a.8.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(21.5826 - 3.80559i) q^{2} +(210.764 - 76.7119i) q^{4} +(-129.757 + 154.639i) q^{5} +(1479.28 + 538.412i) q^{7} +(-601.827 + 347.465i) q^{8} +(-2212.01 + 3831.31i) q^{10} +(5647.40 + 6730.30i) q^{11} +(-2496.75 + 14159.8i) q^{13} +(33975.6 + 5990.81i) q^{14} +(-55651.7 + 46697.3i) q^{16} +(48327.4 + 27901.8i) q^{17} +(24124.8 + 41785.3i) q^{19} +(-15485.6 + 42546.2i) q^{20} +(147498. + 123766. i) q^{22} +(57310.9 + 157460. i) q^{23} +(60755.1 + 344560. i) q^{25} +315106. i q^{26} +353081. q^{28} +(52796.6 - 9309.47i) q^{29} +(971027. - 353425. i) q^{31} +(-909043. + 1.08336e6i) q^{32} +(1.14921e6 + 418280. i) q^{34} +(-275206. + 158890. i) q^{35} +(-932654. + 1.61540e6i) q^{37} +(679693. + 810026. i) q^{38} +(24359.9 - 138152. i) q^{40} +(4.40599e6 + 776896. i) q^{41} +(-3.96290e6 + 3.32527e6i) q^{43} +(1.70656e6 + 985285. i) q^{44} +(1.83615e6 + 3.18030e6i) q^{46} +(1.82983e6 - 5.02741e6i) q^{47} +(-2.51772e6 - 2.11262e6i) q^{49} +(2.62251e6 + 7.20528e6i) q^{50} +(559998. + 3.17591e6i) q^{52} -1.03085e7i q^{53} -1.77356e6 q^{55} +(-1.07735e6 + 189966. i) q^{56} +(1.10406e6 - 401845. i) q^{58} +(555817. - 662397. i) q^{59} +(-1.53716e7 - 5.59480e6i) q^{61} +(1.96123e7 - 1.13232e7i) q^{62} +(-6.19773e6 + 1.07348e7i) q^{64} +(-1.86568e6 - 2.22343e6i) q^{65} +(1.38317e6 - 7.84434e6i) q^{67} +(1.23261e7 + 2.17342e6i) q^{68} +(-5.33499e6 + 4.47659e6i) q^{70} +(1.63960e7 + 9.46623e6i) q^{71} +(2.49290e7 + 4.31782e7i) q^{73} +(-1.39815e7 + 3.84139e7i) q^{74} +(8.29006e6 + 6.95619e6i) q^{76} +(4.73038e6 + 1.29966e7i) q^{77} +(-2.63044e6 - 1.49180e7i) q^{79} -1.46652e7i q^{80} +9.80493e7 q^{82} +(-8.67787e7 + 1.53014e7i) q^{83} +(-1.05855e7 + 3.85282e6i) q^{85} +(-7.28750e7 + 8.68490e7i) q^{86} +(-5.73730e6 - 2.08821e6i) q^{88} +(6.02765e7 - 3.48007e7i) q^{89} +(-1.13172e7 + 1.96019e7i) q^{91} +(2.41582e7 + 2.87906e7i) q^{92} +(2.03602e7 - 1.15468e8i) q^{94} +(-9.59199e6 - 1.69133e6i) q^{95} +(-2.85952e7 + 2.39942e7i) q^{97} +(-6.23788e7 - 3.60144e7i) 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 $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	21.5826	−	3.80559i	1.34891	−	0.237850i	0.547923	−	0.836529i	$-0.315419\pi$
$2$	21.5826	−	3.80559i	1.34891	−	0.237850i	0.800989	+	0.598679i	$0.204308\pi$
$3$		0			0
$3$		0			0
$4$	210.764	−	76.7119i	0.823297	−	0.299656i
$5$	−129.757	+	154.639i	−0.207612	+	0.247422i	−0.859795	−	0.510639i	$-0.829409\pi$
$5$	−129.757	+	154.639i	−0.207612	+	0.247422i	0.652183	+	0.758061i	$0.273853\pi$
$6$		0			0
$7$	1479.28	+	538.412i	0.616108	+	0.224245i	0.631174	−	0.775641i	$-0.282573\pi$
$7$	1479.28	+	538.412i	0.616108	+	0.224245i	−0.0150656	+	0.999887i	$0.504796\pi$
$8$	−601.827	+	347.465i	−0.146930	+	0.0848304i
$9$		0			0
$10$	−2212.01	+	3831.31i	−0.221201	+	0.383131i
$11$	5647.40	+	6730.30i	0.385725	+	0.459689i	0.923612	−	0.383328i	$-0.125222\pi$
$11$	5647.40	+	6730.30i	0.385725	+	0.459689i	−0.537888	+	0.843017i	$0.680778\pi$
$12$		0			0
$13$	−2496.75	+	14159.8i	−0.0874182	+	0.495773i	0.909390	+	0.415944i	$0.136549\pi$
$13$	−2496.75	+	14159.8i	−0.0874182	+	0.495773i	−0.996809	+	0.0798295i	$0.974562\pi$
$14$	33975.6	+	5990.81i	0.884412	+	0.155946i
$15$		0			0
$16$	−55651.7	+	46697.3i	−0.849178	+	0.712545i
$17$	48327.4	+	27901.8i	0.578626	+	0.334070i	0.760587	−	0.649236i	$-0.224911\pi$
$17$	48327.4	+	27901.8i	0.578626	+	0.334070i	−0.181961	+	0.983306i	$0.558245\pi$
$18$		0			0
$19$	24124.8	+	41785.3i	0.185118	+	0.320634i	0.943616	−	0.331041i	$-0.107400\pi$
$19$	24124.8	+	41785.3i	0.185118	+	0.320634i	−0.758498	+	0.651675i	$0.774067\pi$
$20$	−15485.6	+	42546.2i	−0.0967847	+	0.265914i
$21$		0			0
$22$	147498.	+	123766.i	0.629645	+	0.528335i
$23$	57310.9	+	157460.i	0.204798	+	0.562678i	0.998987	−	0.0449922i	$-0.0143263\pi$
$23$	57310.9	+	157460.i	0.204798	+	0.562678i	−0.794189	+	0.607671i	$0.792104\pi$
$24$		0			0
$25$	60755.1	+	344560.i	0.155533	+	0.882072i
$26$			315106.i			0.689547i
$27$		0			0
$28$	353081.			0.574437
$29$	52796.6	−	9309.47i	0.0746473	−	0.0131623i	−0.136200	−	0.990681i	$-0.543489\pi$
$29$	52796.6	−	9309.47i	0.0746473	−	0.0131623i	0.210847	+	0.977519i	$0.432378\pi$
$30$		0			0
$31$	971027.	−	353425.i	1.05144	−	0.382693i	0.242234	−	0.970218i	$-0.422120\pi$
$31$	971027.	−	353425.i	1.05144	−	0.382693i	0.809206	+	0.587525i	$0.199898\pi$
$32$	−909043.	+	1.08336e6i	−0.866931	+	1.03317i
$33$		0			0
$34$	1.14921e6	+	418280.i	0.859974	+	0.313005i
$35$	−275206.	+	158890.i	−0.183394	+	0.105883i
$36$		0			0
$37$	−932654.	+	1.61540e6i	−0.497638	+	0.861935i	−0.999996	−	0.00272492i	$-0.999133\pi$
$37$	−932654.	+	1.61540e6i	−0.497638	+	0.861935i	0.502358	+	0.864660i	$0.332466\pi$
$38$	679693.	+	810026.i	0.325970	+	0.388476i
$39$		0			0
$40$	24359.9	−	138152.i	0.00951559	−	0.0539656i
$41$	4.40599e6	+	776896.i	1.55922	+	0.274933i	0.885709	−	0.464241i	$-0.153673\pi$
$41$	4.40599e6	+	776896.i	1.55922	+	0.274933i	0.673515	+	0.739174i	$0.264784\pi$
$42$		0			0
$43$	−3.96290e6	+	3.32527e6i	−1.15915	+	0.972641i	−0.999893	−	0.0145968i	$-0.995354\pi$
$43$	−3.96290e6	+	3.32527e6i	−1.15915	+	0.972641i	−0.159255	+	0.987238i	$0.550909\pi$
$44$	1.70656e6	+	985285.i	0.455315	+	0.262876i
$45$		0			0
$46$	1.83615e6	+	3.18030e6i	0.410087	+	0.710292i
$47$	1.82983e6	−	5.02741e6i	0.374990	−	1.03028i	−0.598416	−	0.801186i	$-0.704203\pi$
$47$	1.82983e6	−	5.02741e6i	0.374990	−	1.03028i	0.973405	−	0.229090i	$-0.0735749\pi$
$48$		0			0
$49$	−2.51772e6	−	2.11262e6i	−0.436741	−	0.366469i
$50$	2.62251e6	+	7.20528e6i	0.419601	+	1.15284i
$51$		0			0
$52$	559998.	+	3.17591e6i	0.0765901	+	0.434364i
$53$		−	1.03085e7i		−	1.30645i	−0.757163	−	0.653226i	$-0.773415\pi$
$53$		−	1.03085e7i		−	1.30645i	0.757163	−	0.653226i	$-0.226585\pi$
$54$		0			0
$55$	−1.77356e6			−0.193818
$56$	−1.07735e6	+	189966.i	−0.109548	+	0.0193162i
$57$		0			0
$58$	1.10406e6	−	401845.i	0.0975620	−	0.0355097i
$59$	555817.	−	662397.i	0.0458695	−	0.0546651i	−0.742622	−	0.669711i	$-0.766418\pi$
$59$	555817.	−	662397.i	0.0458695	−	0.0546651i	0.788491	+	0.615046i	$0.210862\pi$
$60$		0			0
$61$	−1.53716e7	−	5.59480e6i	−1.11020	−	0.404078i	−0.279130	−	0.960253i	$-0.590046\pi$
$61$	−1.53716e7	−	5.59480e6i	−1.11020	−	0.404078i	−0.831065	+	0.556175i	$0.812268\pi$
$62$	1.96123e7	−	1.13232e7i	1.32728	−	0.766303i
$63$		0			0
$64$	−6.19773e6	+	1.07348e7i	−0.369414	+	0.639843i
$65$	−1.86568e6	−	2.22343e6i	−0.104516	−	0.124558i
$66$		0			0
$67$	1.38317e6	−	7.84434e6i	0.0686398	−	0.389276i	−0.931062	−	0.364861i	$-0.881117\pi$
$67$	1.38317e6	−	7.84434e6i	0.0686398	−	0.389276i	0.999702	−	0.0244149i	$-0.00777228\pi$
$68$	1.23261e7	+	2.17342e6i	0.576487	+	0.101650i
$69$		0			0
$70$	−5.33499e6	+	4.47659e6i	−0.222199	+	0.186447i
$71$	1.63960e7	+	9.46623e6i	0.645215	+	0.372515i	0.786620	−	0.617437i	$-0.211829\pi$
$71$	1.63960e7	+	9.46623e6i	0.645215	+	0.372515i	−0.141406	+	0.989952i	$0.545162\pi$
$72$		0			0
$73$	2.49290e7	+	4.31782e7i	0.877835	+	1.52045i	0.853712	+	0.520745i	$0.174346\pi$
$73$	2.49290e7	+	4.31782e7i	0.877835	+	1.52045i	0.0241223	+	0.999709i	$0.492321\pi$
$74$	−1.39815e7	+	3.84139e7i	−0.466259	+	1.28104i
$75$		0			0
$76$	8.29006e6	+	6.95619e6i	0.248487	+	0.208505i
$77$	4.73038e6	+	1.29966e7i	0.134565	+	0.369715i
$78$		0			0
$79$	−2.63044e6	−	1.49180e7i	−0.0675336	−	0.383002i	−0.999776	−	0.0211675i	$-0.993262\pi$
$79$	−2.63044e6	−	1.49180e7i	−0.0675336	−	0.383002i	0.932242	−	0.361834i	$-0.117849\pi$
$80$		−	1.46652e7i		−	0.358038i
$81$		0			0
$82$	9.80493e7			2.16865
$83$	−8.67787e7	+	1.53014e7i	−1.82852	+	0.322418i	−0.978802	−	0.204811i	$-0.934342\pi$
$83$	−8.67787e7	+	1.53014e7i	−1.82852	+	0.322418i	−0.849723	+	0.527229i	$0.823231\pi$
$84$		0			0
$85$	−1.05855e7	+	3.85282e6i	−0.202786	+	0.0738080i
$86$	−7.28750e7	+	8.68490e7i	−1.33225	+	1.58771i
$87$		0			0
$88$	−5.73730e6	−	2.08821e6i	−0.0956703	−	0.0348211i
$89$	6.02765e7	−	3.48007e7i	0.960701	−	0.554661i	0.0643121	−	0.997930i	$-0.479515\pi$
$89$	6.02765e7	−	3.48007e7i	0.960701	−	0.554661i	0.896389	+	0.443269i	$0.146181\pi$
$90$		0			0
$91$	−1.13172e7	+	1.96019e7i	−0.165034	+	0.285847i
$92$	2.41582e7	+	2.87906e7i	0.337220	+	0.401883i
$93$		0			0
$94$	2.03602e7	−	1.15468e8i	0.260777	−	1.47894i
$95$	−9.59199e6	−	1.69133e6i	−0.117765	−	0.0207651i
$96$		0			0
$97$	−2.85952e7	+	2.39942e7i	−0.323003	+	0.271032i	−0.789842	−	0.613311i	$-0.789837\pi$
$97$	−2.85952e7	+	2.39942e7i	−0.323003	+	0.271032i	0.466839	+	0.884343i	$0.345393\pi$
$98$	−6.23788e7	−	3.60144e7i	−0.676289	−	0.390456i
$99$		0			0
$100$	3.92368e7	+	6.79601e7i	0.392368	+	0.679601i
$101$	4.94931e7	−	1.35981e8i	0.475619	−	1.30675i	−0.437558	−	0.899190i	$-0.644157\pi$
$101$	4.94931e7	−	1.35981e8i	0.475619	−	1.30675i	0.913177	−	0.407563i	$-0.133621\pi$
$102$		0			0
$103$	−9.02900e7	−	7.57623e7i	−0.802215	−	0.673138i	0.146521	−	0.989208i	$-0.453192\pi$
$103$	−9.02900e7	−	7.57623e7i	−0.802215	−	0.673138i	−0.948736	+	0.316069i	$0.897637\pi$
$104$	−3.41742e6	−	9.38928e6i	−0.0292122	−	0.0802599i
$105$		0			0
$106$	−3.92301e7	−	2.22485e8i	−0.310739	−	1.76229i
$107$		−	1.92244e8i		−	1.46662i	−0.679894	−	0.733311i	$-0.737974\pi$
$107$		−	1.92244e8i		−	1.46662i	0.679894	−	0.733311i	$-0.262026\pi$
$108$		0			0
$109$	−8.87094e7			−0.628440			−0.314220	−	0.949350i	$-0.601743\pi$
$109$	−8.87094e7			−0.628440			−0.314220	+	0.949350i	$0.601743\pi$
$110$	−3.82779e7	+	6.74943e6i	−0.261443	+	0.0460995i
$111$		0			0
$112$	−1.07467e8	+	3.91147e7i	−0.682970	+	0.248581i
$113$	1.98236e7	−	2.36248e7i	0.121582	−	0.144895i	−0.701820	−	0.712354i	$-0.747629\pi$
$113$	1.98236e7	−	2.36248e7i	0.121582	−	0.144895i	0.823402	+	0.567459i	$0.192073\pi$
$114$		0			0
$115$	−3.17860e7	−	1.15692e7i	−0.181738	−	0.0661470i
$116$	1.04135e7	−	6.01223e6i	0.0575128	−	0.0332050i
$117$		0			0
$118$	9.47516e6	−	1.64115e7i	0.0488718	−	0.0846485i
$119$	5.64669e7	+	6.72946e7i	0.281583	+	0.335577i
$120$		0			0
$121$	2.38191e7	−	1.35085e8i	0.111118	−	0.630181i
$122$	−3.53050e8	−	6.22523e7i	−1.59366	−	0.281006i
$123$		0			0
$124$	1.77546e8	−	1.48979e8i	0.750972	−	0.630140i
$125$	−1.29455e8	−	7.47411e7i	−0.530249	−	0.306139i
$126$		0			0
$127$	−3.00728e7	−	5.20876e7i	−0.115600	−	0.200225i	0.802419	−	0.596761i	$-0.203546\pi$
$127$	−3.00728e7	−	5.20876e7i	−0.115600	−	0.200225i	−0.918020	+	0.396535i	$0.870212\pi$
$128$	3.09142e7	−	8.49361e7i	0.115164	−	0.316412i
$129$		0			0
$130$	−4.87276e7	−	4.08874e7i	−0.170609	−	0.143158i
$131$	3.55348e7	+	9.76311e7i	0.120662	+	0.331515i	0.985288	−	0.170900i	$-0.0546674\pi$
$131$	3.55348e7	+	9.76311e7i	0.120662	+	0.331515i	−0.864627	+	0.502415i	$0.832445\pi$
$132$		0			0
$133$	1.31894e7	+	7.48011e7i	0.0421522	+	0.239057i
$134$		−	1.74565e8i		−	0.541424i
$135$		0			0
$136$	−3.87797e7			−0.113357
$137$	1.72397e8	−	3.03983e7i	0.489383	−	0.0862913i	0.0764886	−	0.997070i	$-0.475629\pi$
$137$	1.72397e8	−	3.03983e7i	0.489383	−	0.0862913i	0.412894	+	0.910779i	$0.364518\pi$
$138$		0			0
$139$	−3.82714e8	+	1.39297e8i	−1.02522	+	0.373148i	−0.799257	−	0.600989i	$-0.794774\pi$
$139$	−3.82714e8	+	1.39297e8i	−1.02522	+	0.373148i	−0.225959	+	0.974137i	$0.572551\pi$
$140$	−4.58148e7	+	5.46000e7i	−0.119260	+	0.142128i
$141$		0			0
$142$	3.89892e8	+	1.41909e8i	0.958940	+	0.349026i
$143$	−1.09400e8	+	6.31620e7i	−0.261621	+	0.151047i
$144$		0			0
$145$	−5.41114e6	+	9.37238e6i	−0.0122410	+	0.0212020i
$146$	7.02350e8	+	8.37028e8i	1.54576	+	1.84217i
$147$		0			0
$148$	−7.26494e7	+	4.12015e8i	−0.151421	+	0.858749i
$149$	−2.83527e8	−	4.99934e7i	−0.575240	−	0.101430i	−0.121543	−	0.992586i	$-0.538784\pi$
$149$	−2.83527e8	−	4.99934e7i	−0.575240	−	0.101430i	−0.453697	+	0.891156i	$0.649895\pi$
$150$		0			0
$151$	5.12960e8	−	4.30425e8i	0.986680	−	0.827922i	0.00159590	−	0.999999i	$-0.499492\pi$
$151$	5.12960e8	−	4.30425e8i	0.986680	−	0.827922i	0.985084	+	0.172076i	$0.0550476\pi$
$152$	−2.90379e7	−	1.67650e7i	−0.0543990	−	0.0314073i
$153$		0			0
$154$	1.51554e8	+	2.62498e8i	0.269453	+	0.466706i
$155$	−7.13446e7	+	1.96018e8i	−0.123605	+	0.339601i
$156$		0			0
$157$	6.50076e8	+	5.45478e8i	1.06995	+	0.897798i	0.995048	−	0.0993922i	$-0.0316898\pi$
$157$	6.50076e8	+	5.45478e8i	1.06995	+	0.897798i	0.0749061	+	0.997191i	$0.476134\pi$
$158$	−1.13543e8	−	3.11958e8i	−0.182194	−	0.500573i
$159$		0			0
$160$	−4.95737e7	−	2.81147e8i	−0.0756435	−	0.428996i
$161$			2.63784e8i			0.392596i
$162$		0			0
$163$	4.59051e8			0.650296			0.325148	−	0.945663i	$-0.394586\pi$
$163$	4.59051e8			0.650296			0.325148	+	0.945663i	$0.394586\pi$
$164$	9.88223e8	−	1.74250e8i	1.36609	−	0.240879i
$165$		0			0
$166$	−1.81468e9	+	6.60489e8i	−2.38983	+	0.869827i
$167$	−1.44585e8	+	1.72310e8i	−0.185890	+	0.221536i	−0.850939	−	0.525265i	$-0.823966\pi$
$167$	−1.44585e8	+	1.72310e8i	−0.185890	+	0.221536i	0.665049	+	0.746800i	$0.268411\pi$
$168$		0			0
$169$	5.72270e8	+	2.08289e8i	0.701543	+	0.255341i
$170$	−2.13801e8	+	1.23438e8i	−0.255985	+	0.147793i
$171$		0			0
$172$	−5.80149e8	+	1.00485e9i	−0.662866	+	1.14812i
$173$	8.39464e8	+	1.00043e9i	0.937169	+	1.11687i	0.992962	+	0.118432i	$0.0377866\pi$
$173$	8.39464e8	+	1.00043e9i	0.937169	+	1.11687i	−0.0557937	+	0.998442i	$0.517769\pi$
$174$		0			0
$175$	−9.56415e7	+	5.42410e8i	−0.101975	+	0.578330i
$176$	−6.28574e8	−	1.10835e8i	−0.655098	−	0.115511i
$177$		0			0
$178$	1.16849e9	−	9.80476e8i	1.16397	−	0.976691i
$179$	1.21670e9	+	7.02464e8i	1.18515	+	0.684245i	0.957200	−	0.289428i	$-0.0934652\pi$
$179$	1.21670e9	+	7.02464e8i	1.18515	+	0.684245i	0.227948	+	0.973673i	$0.426799\pi$
$180$		0			0
$181$	5.89616e8	+	1.02124e9i	0.549357	+	0.951514i	0.998319	+	0.0579632i	$0.0184606\pi$
$181$	5.89616e8	+	1.02124e9i	0.549357	+	0.951514i	−0.448962	+	0.893551i	$0.648206\pi$
$182$	−1.69657e8	+	4.66129e8i	−0.154627	+	0.424835i
$183$		0			0
$184$	−8.92033e7	−	7.48505e7i	−0.0778233	−	0.0653015i
$185$	−1.28785e8	−	3.53835e8i	−0.109946	−	0.302074i
$186$		0			0
$187$	8.51361e7	+	4.82831e8i	0.0696222	+	0.394847i
$188$		−	1.19997e9i		−	0.960591i
$189$		0			0
$190$	−2.13457e8			−0.163793
$191$	1.37346e9	−	2.42179e8i	1.03201	−	0.181971i	0.368102	−	0.929785i	$-0.380008\pi$
$191$	1.37346e9	−	2.42179e8i	1.03201	−	0.181971i	0.663908	+	0.747814i	$0.268897\pi$
$192$		0			0
$193$	−2.42195e9	+	8.81518e8i	−1.74557	+	0.635334i	−0.999532	−	0.0305752i	$-0.990266\pi$
$193$	−2.42195e9	+	8.81518e8i	−1.74557	+	0.635334i	−0.746033	+	0.665909i	$0.768044\pi$
$194$	−5.25847e8	+	6.26680e8i	−0.371238	+	0.442424i
$195$		0			0
$196$	−6.92709e8	−	2.52126e8i	−0.469382	−	0.170841i
$197$	1.45799e9	−	8.41768e8i	0.968029	−	0.558892i	0.0693939	−	0.997589i	$-0.477893\pi$
$197$	1.45799e9	−	8.41768e8i	0.968029	−	0.558892i	0.898635	+	0.438698i	$0.144560\pi$
$198$		0			0
$199$	3.37619e8	−	5.84773e8i	0.215285	−	0.372885i	−0.738076	−	0.674718i	$-0.764265\pi$
$199$	3.37619e8	−	5.84773e8i	0.215285	−	0.372885i	0.953361	+	0.301833i	$0.0975986\pi$
$200$	−1.56287e8	−	1.86255e8i	−0.0976791	−	0.116409i
$201$		0			0
$202$	5.50700e8	−	3.12318e9i	0.330758	−	1.87582i
$203$	8.31131e7	+	1.46551e7i	0.0489424	+	0.00862987i
$204$		0			0
$205$	−6.91848e8	+	5.80529e8i	−0.391738	+	0.328707i
$206$	−2.23701e9	−	1.29154e9i	−1.24222	−	0.717198i
$207$		0			0
$208$	−5.22275e8	−	9.04608e8i	−0.279027	−	0.483289i
$209$	−1.44986e8	+	3.98345e8i	−0.0759872	+	0.208773i
$210$		0			0
$211$	1.43470e9	+	1.20386e9i	0.723823	+	0.607359i	0.928440	−	0.371483i	$-0.121151\pi$
$211$	1.43470e9	+	1.20386e9i	0.723823	+	0.607359i	−0.204617	+	0.978842i	$0.565595\pi$
$212$	−7.90787e8	−	2.17267e9i	−0.391486	−	1.07560i
$213$		0			0
$214$	−7.31603e8	−	4.14913e9i	−0.348835	−	1.97834i
$215$		−	1.04429e9i		−	0.488730i
$216$		0			0
$217$	1.62670e9			0.733618
$218$	−1.91458e9	+	3.37592e8i	−0.847710	+	0.149474i
$219$		0			0
$220$	−3.73802e8	+	1.36053e8i	−0.159570	+	0.0580787i
$221$	−5.15746e8	+	6.14642e8i	−0.216205	+	0.257664i
$222$		0			0
$223$	−2.38952e8	−	8.69713e7i	−0.0966252	−	0.0351687i	0.293255	−	0.956034i	$-0.405261\pi$
$223$	−2.38952e8	−	8.69713e7i	−0.0966252	−	0.0351687i	−0.389880	+	0.920865i	$0.627484\pi$
$224$	−1.92802e9	+	1.11314e9i	−0.765806	+	0.442139i
$225$		0			0
$226$	3.37937e8	−	5.85325e8i	0.129540	−	0.224369i
$227$	−2.65807e9	−	3.16776e9i	−1.00106	−	1.19302i	−0.981155	−	0.193221i	$-0.938107\pi$
$227$	−2.65807e9	−	3.16776e9i	−1.00106	−	1.19302i	−0.0199095	−	0.999802i	$-0.506338\pi$
$228$		0			0
$229$	8.13979e8	−	4.61631e9i	0.295986	−	1.67862i	−0.367181	−	0.930150i	$-0.619677\pi$
$229$	8.13979e8	−	4.61631e9i	0.295986	−	1.67862i	0.663167	−	0.748472i	$-0.269212\pi$
$230$	−7.30052e8	−	1.28728e8i	−0.260881	−	0.0460003i
$231$		0			0
$232$	−2.85397e7	+	2.39477e7i	−0.00985140	+	0.00826631i
$233$	1.81802e9	+	1.04964e9i	0.616844	+	0.356135i	0.775639	−	0.631176i	$-0.217428\pi$
$233$	1.81802e9	+	1.04964e9i	0.616844	+	0.356135i	−0.158795	+	0.987312i	$0.550761\pi$
$234$		0			0
$235$	5.39999e8	+	9.35306e8i	0.177061	+	0.306678i
$236$	6.63326e7	−	1.82247e8i	0.0213835	−	0.0587507i
$237$		0			0
$238$	1.47480e9	+	1.23750e9i	0.459647	+	0.385690i
$239$	2.15785e9	+	5.92864e9i	0.661347	+	1.81704i	0.570708	+	0.821153i	$0.306669\pi$
$239$	2.15785e9	+	5.92864e9i	0.661347	+	1.81704i	0.0906399	+	0.995884i	$0.471109\pi$
$240$		0			0
$241$	1.06267e9	+	6.02671e9i	0.315015	+	1.78654i	0.572137	+	0.820158i	$0.306115\pi$
$241$	1.06267e9	+	6.02671e9i	0.315015	+	1.78654i	−0.257122	+	0.966379i	$0.582774\pi$
$242$		−	3.00613e9i		−	0.876488i
$243$		0			0
$244$	−3.66897e9			−1.03511
$245$	6.53386e8	−	1.15210e8i	0.181345	−	0.0319760i
$246$		0			0
$247$	−6.51905e8	+	2.37274e8i	−0.175144	+	0.0637473i
$248$	−4.61588e8	+	5.50099e8i	−0.122025	+	0.145423i
$249$		0			0
$250$	−3.07841e9	−	1.12045e9i	−0.788074	−	0.286836i
$251$	1.88232e9	−	1.08676e9i	0.474241	−	0.273803i	−0.243773	−	0.969832i	$-0.578385\pi$
$251$	1.88232e9	−	1.08676e9i	0.474241	−	0.273803i	0.718013	+	0.696029i	$0.245052\pi$
$252$		0			0
$253$	−7.36100e8	+	1.27496e9i	−0.179661	+	0.311182i
$254$	−8.47272e8	−	1.00974e9i	−0.203558	−	0.242591i
$255$		0			0
$256$	8.95004e8	−	5.07582e9i	0.208384	−	1.18181i
$257$	3.64585e9	+	6.42861e8i	0.835730	+	0.147362i	0.575106	−	0.818079i	$-0.304961\pi$
$257$	3.64585e9	+	6.42861e8i	0.835730	+	0.147362i	0.260624	+	0.965440i	$0.416072\pi$
$258$		0			0
$259$	−2.24941e9	+	1.88748e9i	−0.499884	+	0.419452i
$260$	−5.63782e8	−	3.25500e8i	−0.123372	−	0.0712290i
$261$		0			0
$262$	1.13848e9	+	1.97190e9i	0.241612	+	0.418485i
$263$	−1.37284e9	+	3.77183e9i	−0.286943	+	0.788369i	0.709547	+	0.704658i	$0.248900\pi$
$263$	−1.37284e9	+	3.77183e9i	−0.286943	+	0.788369i	−0.996490	+	0.0837112i	$0.973323\pi$
$264$		0			0
$265$	1.59410e9	+	1.33761e9i	0.323245	+	0.271235i
$266$	5.69325e8	+	1.56421e9i	0.113719	+	0.312441i
$267$		0			0
$268$	−3.10232e8	−	1.75941e9i	−0.0601377	−	0.341058i
$269$		−	8.40864e8i		−	0.160589i	−0.996771	−	0.0802946i	$-0.974414\pi$
$269$		−	8.40864e8i		−	0.160589i	0.996771	−	0.0802946i	$-0.0255861\pi$
$270$		0			0
$271$	7.85425e9			1.45622			0.728111	−	0.685459i	$-0.240398\pi$
$271$	7.85425e9			1.45622			0.728111	+	0.685459i	$0.240398\pi$
$272$	−3.99244e9	+	7.03976e8i	−0.729396	+	0.128612i
$273$		0			0
$274$	3.60510e9	−	1.31215e9i	0.639609	−	0.232799i
$275$	−1.97588e9	+	2.35476e9i	−0.345486	+	0.411734i
$276$		0			0
$277$	1.01728e9	+	3.70260e8i	0.172792	+	0.0628910i	0.426967	−	0.904267i	$-0.359582\pi$
$277$	1.01728e9	+	3.70260e8i	0.172792	+	0.0628910i	−0.254176	+	0.967158i	$0.581804\pi$
$278$	−7.72986e9	+	4.46283e9i	−1.29417	+	0.747191i
$279$		0			0
$280$	1.10418e8	−	1.91249e8i	0.0179642	−	0.0311148i
$281$	−6.63691e9	−	7.90956e9i	−1.06449	−	1.26861i	−0.961759	−	0.273897i	$-0.911687\pi$
$281$	−6.63691e9	−	7.90956e9i	−1.06449	−	1.26861i	−0.102728	−	0.994709i	$-0.532757\pi$
$282$		0			0
$283$	1.22974e9	−	6.97420e9i	0.191720	−	1.08730i	−0.725293	−	0.688440i	$-0.758296\pi$
$283$	1.22974e9	−	6.97420e9i	0.191720	−	1.08730i	0.917013	−	0.398858i	$-0.130593\pi$
$284$	4.18186e9	+	7.37374e8i	0.642830	+	0.113348i
$285$		0			0
$286$	−2.12076e9	+	1.77953e9i	−0.316977	+	0.265975i
$287$	6.09939e9	+	3.52148e9i	0.898998	+	0.519037i
$288$		0			0
$289$	−1.93085e9	−	3.34433e9i	−0.276795	−	0.479422i
$290$	−8.11190e7	+	2.22873e8i	−0.0114691	+	0.0315112i
$291$		0			0
$292$	8.56641e9	+	7.18807e9i	1.17833	+	0.988738i
$293$	−1.02284e9	−	2.81023e9i	−0.138783	−	0.381304i	0.850757	−	0.525559i	$-0.176144\pi$
$293$	−1.02284e9	−	2.81023e9i	−0.138783	−	0.381304i	−0.989541	+	0.144255i	$0.953922\pi$
$294$		0			0
$295$	3.03109e7	+	1.71902e8i	0.00400231	+	0.0226982i
$296$		−	1.29626e9i		−	0.168859i
$297$		0			0
$298$	−6.30950e9			−0.800073
$299$	−2.37270e9	+	4.18371e8i	−0.296864	+	0.0523451i
$300$		0			0
$301$	−7.65258e9	+	2.78531e9i	−0.932271	+	0.339319i
$302$	9.43299e9	−	1.12418e10i	1.13402	−	1.35148i
$303$		0			0
$304$	−3.29385e9	−	1.19886e9i	−0.385664	−	0.140370i
$305$	2.85975e9	−	1.65108e9i	0.330467	−	0.190795i
$306$		0			0
$307$	3.33707e9	−	5.77997e9i	0.375675	−	0.650687i	−0.614753	−	0.788720i	$-0.710744\pi$
$307$	3.33707e9	−	5.77997e9i	0.375675	−	0.650687i	0.990428	+	0.138032i	$0.0440777\pi$
$308$	1.99399e9	+	2.37634e9i	0.221574	+	0.264062i
$309$		0			0
$310$	−7.93838e8	+	4.50208e9i	−0.0859578	+	0.487491i
$311$	−3.83851e9	−	6.76833e8i	−0.410319	−	0.0723502i	−0.0353210	−	0.999376i	$-0.511245\pi$
$311$	−3.83851e9	−	6.76833e8i	−0.410319	−	0.0723502i	−0.374998	+	0.927026i	$0.622356\pi$
$312$		0			0
$313$	−9.12437e9	+	7.65626e9i	−0.950661	+	0.797699i	−0.979409	−	0.201887i	$-0.935293\pi$
$313$	−9.12437e9	+	7.65626e9i	−0.950661	+	0.797699i	0.0287476	+	0.999587i	$0.490848\pi$
$314$	1.61062e10	+	9.29891e9i	1.65681	+	0.956563i
$315$		0			0
$316$	−1.69879e9	−	2.94238e9i	−0.170369	−	0.295088i
$317$	2.42078e9	−	6.65105e9i	0.239728	−	0.658647i	−0.760232	−	0.649652i	$-0.774915\pi$
$317$	2.42078e9	−	6.65105e9i	0.239728	−	0.658647i	0.999960	−	0.00899508i	$-0.00286326\pi$
$318$		0			0
$319$	3.60819e8	+	3.02763e8i	0.0348439	+	0.0292375i
$320$	−8.55813e8	−	2.35133e9i	−0.0816167	−	0.224240i
$321$		0			0
$322$	1.00386e9	+	5.69315e9i	0.0933787	+	0.529577i
$323$			2.69250e9i			0.247369i
$324$		0			0
$325$	−5.03058e9			−0.450904
$326$	9.90752e9	−	1.74696e9i	0.877192	−	0.154673i
$327$		0			0
$328$	−2.92159e9	+	1.06337e9i	−0.252420	+	0.0918734i
$329$	5.41364e9	−	6.45173e9i	0.462068	−	0.550671i
$330$		0			0
$331$	1.33703e9	+	4.86637e8i	0.111385	+	0.0405409i	0.397112	−	0.917770i	$-0.370013\pi$
$331$	1.33703e9	+	4.86637e8i	0.111385	+	0.0405409i	−0.285726	+	0.958311i	$0.592235\pi$
$332$	−1.71160e10	+	9.88195e9i	−1.40881	+	0.813374i
$333$		0			0
$334$	−2.46478e9	+	4.26912e9i	−0.198058	+	0.343046i
$335$	1.03356e9	+	1.23175e9i	0.0820649	+	0.0978012i
$336$		0			0
$337$	−9.90440e8	+	5.61706e9i	−0.0767907	+	0.435502i	0.922037	+	0.387101i	$0.126524\pi$
$337$	−9.90440e8	+	5.61706e9i	−0.0767907	+	0.435502i	−0.998828	+	0.0484006i	$0.984588\pi$
$338$	1.31437e10	+	2.31760e9i	1.00705	+	0.177571i
$339$		0			0
$340$	−1.93550e9	+	1.62407e9i	−0.144836	+	0.121532i
$341$	7.86243e9	+	4.53938e9i	0.581486	+	0.335721i
$342$		0			0
$343$	−7.12446e9	−	1.23399e10i	−0.514725	−	0.891530i
$344$	1.22957e9	−	3.37820e9i	0.0878047	−	0.241242i
$345$		0			0
$346$	2.19250e10	+	1.83973e10i	1.52981	+	1.28366i
$347$	−1.18946e9	−	3.26801e9i	−0.0820412	−	0.225406i	0.891889	−	0.452254i	$-0.149380\pi$
$347$	−1.18946e9	−	3.26801e9i	−0.0820412	−	0.225406i	−0.973930	+	0.226848i	$0.927158\pi$
$348$		0			0
$349$	1.12421e9	+	6.37569e9i	0.0757782	+	0.429759i	0.998968	+	0.0454155i	$0.0144612\pi$
$349$	1.12421e9	+	6.37569e9i	0.0757782	+	0.429759i	−0.923190	+	0.384344i	$0.874428\pi$
$350$			1.20706e10i			0.804370i
$351$		0			0
$352$	−1.24250e10			−0.809333
$353$	−1.33418e10	+	2.35251e9i	−0.859240	+	0.151507i	−0.585873	−	0.810403i	$-0.699248\pi$
$353$	−1.33418e10	+	2.35251e9i	−0.859240	+	0.151507i	−0.273366	+	0.961910i	$0.588137\pi$
$354$		0			0
$355$	−3.59134e9	+	1.30714e9i	−0.226122	+	0.0823018i
$356$	1.00345e10	−	1.19587e10i	0.624735	−	0.744530i
$357$		0			0
$358$	2.89329e10	+	1.05307e10i	1.76141	+	0.641099i
$359$	−1.20904e10	+	6.98039e9i	−0.727885	+	0.420244i	−0.817648	−	0.575719i	$-0.804722\pi$
$359$	−1.20904e10	+	6.98039e9i	−0.727885	+	0.420244i	0.0897632	+	0.995963i	$0.471389\pi$
$360$		0			0
$361$	7.32777e9	−	1.26921e10i	0.431463	−	0.747315i
$362$	1.66119e10	+	1.97973e10i	0.967351	+	1.15284i
$363$		0			0
$364$	−8.81555e8	+	4.99955e9i	−0.0502162	+	0.284790i
$365$	−9.91174e9	−	1.74771e9i	−0.558442	−	0.0984685i
$366$		0			0
$367$	3.14341e9	−	2.63763e9i	0.173275	−	0.145395i	−0.552026	−	0.833827i	$-0.686145\pi$
$367$	3.14341e9	−	2.63763e9i	0.173275	−	0.145395i	0.725301	+	0.688432i	$0.241701\pi$
$368$	−1.05424e10	−	6.08668e9i	−0.574843	−	0.331886i
$369$		0			0
$370$	−4.12607e9	−	7.14657e9i	−0.220156	−	0.381321i
$371$	5.55024e9	−	1.52492e10i	0.292965	−	0.804916i
$372$		0			0
$373$	−7.37158e9	−	6.18549e9i	−0.380825	−	0.319550i	0.432201	−	0.901777i	$-0.357737\pi$
$373$	−7.37158e9	−	6.18549e9i	−0.380825	−	0.319550i	−0.813026	+	0.582227i	$0.802181\pi$
$374$	3.67492e9	+	1.00967e10i	0.187828	+	0.516054i
$375$		0			0
$376$	6.45610e8	+	3.66144e9i	0.0323012	+	0.183189i
$377$			7.70832e8i			0.0381588i
$378$		0			0
$379$	−1.08158e9			−0.0524205			−0.0262102	−	0.999656i	$-0.508344\pi$
$379$	−1.08158e9			−0.0524205			−0.0262102	+	0.999656i	$0.508344\pi$
$380$	−2.15139e9	+	3.79349e8i	−0.103178	+	0.0181930i
$381$		0			0
$382$	2.87213e10	−	1.04537e10i	1.34881	−	0.490926i
$383$	−9.63162e9	+	1.14785e10i	−0.447615	+	0.533446i	−0.941918	−	0.335843i	$-0.890979\pi$
$383$	−9.63162e9	+	1.14785e10i	−0.447615	+	0.533446i	0.494303	+	0.869290i	$0.335423\pi$
$384$		0			0
$385$	−2.62358e9	−	9.54905e8i	−0.119413	−	0.0434627i
$386$	−4.89173e10	+	2.82424e10i	−2.20350	+	1.27219i
$387$		0			0
$388$	−4.18621e9	+	7.25072e9i	−0.184711	+	0.319930i
$389$	−5.18750e9	−	6.18222e9i	−0.226548	−	0.269989i	0.640782	−	0.767723i	$-0.278610\pi$
$389$	−5.18750e9	−	6.18222e9i	−0.226548	−	0.269989i	−0.867330	+	0.497734i	$0.834166\pi$
$390$		0			0
$391$	−1.62375e9	+	9.20874e9i	−0.0694723	+	0.393997i
$392$	2.24930e9	+	3.96612e8i	0.0952583	+	0.0167966i
$393$		0			0
$394$	2.82637e10	−	2.37160e10i	1.17285	−	0.984140i
$395$	2.64821e9	+	1.52895e9i	0.108784	+	0.0628064i
$396$		0			0
$397$	−1.52733e10	−	2.64542e10i	−0.614854	−	1.06496i	−0.990410	−	0.138158i	$-0.955882\pi$
$397$	−1.52733e10	−	2.64542e10i	−0.614854	−	1.06496i	0.375556	−	0.926800i	$-0.377452\pi$
$398$	5.06128e9	−	1.39057e10i	0.201710	−	0.554194i
$399$		0			0
$400$	−1.94711e10	−	1.63382e10i	−0.760591	−	0.638212i
$401$	−6.89815e9	−	1.89525e10i	−0.266781	−	0.732975i	−0.998670	−	0.0515517i	$-0.983583\pi$
$401$	−6.89815e9	−	1.89525e10i	−0.266781	−	0.732975i	0.731889	−	0.681424i	$-0.238639\pi$
$402$		0			0
$403$	2.58001e9	+	1.46319e10i	0.0978139	+	0.554730i
$404$		−	3.24567e10i		−	1.21837i
$405$		0			0
$406$	1.84957e9			0.0680716
$407$	−1.61392e10	+	2.84578e9i	−0.588173	+	0.103711i
$408$		0			0
$409$	2.42731e10	−	8.83468e9i	0.867424	−	0.315717i	0.130301	−	0.991475i	$-0.458406\pi$
$409$	2.42731e10	−	8.83468e9i	0.867424	−	0.315717i	0.737124	+	0.675758i	$0.236184\pi$
$410$	−1.27226e10	+	1.51622e10i	−0.450237	+	0.536571i
$411$		0			0
$412$	−2.48418e10	−	9.04166e9i	−0.862171	−	0.313805i
$413$	1.17885e9	−	6.80609e8i	0.0405189	−	0.0233936i
$414$		0			0
$415$	8.89398e9	−	1.54048e10i	0.299850	−	0.519355i
$416$	−1.30704e10	−	1.55767e10i	−0.436432	−	0.520119i
$417$		0			0
$418$	−1.61323e9	+	9.14908e9i	−0.0528434	+	0.299690i
$419$	1.14285e10	+	2.01516e9i	0.370796	+	0.0653813i	0.355941	−	0.934508i	$-0.384160\pi$
$419$	1.14285e10	+	2.01516e9i	0.370796	+	0.0653813i	0.0148546	+	0.999890i	$0.495271\pi$
$420$		0			0
$421$	−6.33667e9	+	5.31710e9i	−0.201713	+	0.169257i	−0.738049	−	0.674748i	$-0.764252\pi$
$421$	−6.33667e9	+	5.31710e9i	−0.201713	+	0.169257i	0.536336	+	0.844005i	$0.319808\pi$
$422$	3.55460e10	+	2.05225e10i	1.12083	+	0.647113i
$423$		0			0
$424$	3.58186e9	+	6.20396e9i	0.110827	+	0.191958i
$425$	−6.67771e9	+	1.83469e10i	−0.204678	+	0.562349i
$426$		0			0
$427$	−1.97265e10	−	1.65525e10i	−0.593388	−	0.497912i
$428$	−1.47474e10	−	4.05182e10i	−0.439482	−	1.20747i
$429$		0			0
$430$	−3.97416e9	−	2.25386e10i	−0.116244	−	0.659254i
$431$		−	4.80677e10i		−	1.39298i	−0.717567	−	0.696490i	$-0.754744\pi$
$431$		−	4.80677e10i		−	1.39298i	0.717567	−	0.696490i	$-0.245256\pi$
$432$		0			0
$433$	9.18386e9			0.261260			0.130630	−	0.991431i	$-0.458300\pi$
$433$	9.18386e9			0.261260			0.130630	+	0.991431i	$0.458300\pi$
$434$	3.51085e10	−	6.19057e9i	0.989585	−	0.174491i
$435$		0			0
$436$	−1.86968e10	+	6.80507e9i	−0.517393	+	0.188316i
$437$	−5.19692e9	+	6.19345e9i	−0.142502	+	0.169827i
$438$		0			0
$439$	−5.28907e10	−	1.92506e10i	−1.42404	−	0.518307i	−0.488821	−	0.872384i	$-0.662573\pi$
$439$	−5.28907e10	−	1.92506e10i	−1.42404	−	0.518307i	−0.935216	+	0.354077i	$0.884795\pi$
$440$	1.06737e9	−	6.16249e8i	0.0284778	−	0.0164417i
$441$		0			0
$442$	−8.79205e9	+	1.52283e10i	−0.230357	+	0.398990i
$443$	−2.37382e9	−	2.82901e9i	−0.0616357	−	0.0734546i	0.734346	−	0.678776i	$-0.237489\pi$
$443$	−2.37382e9	−	2.82901e9i	−0.0616357	−	0.0734546i	−0.795981	+	0.605321i	$0.793045\pi$
$444$		0			0
$445$	−2.43979e9	+	1.38367e10i	−0.0622174	+	0.352853i
$446$	−5.48817e9	−	9.67713e8i	−0.138704	−	0.0244572i
$447$		0			0
$448$	−1.49479e10	+	1.25428e10i	−0.371081	+	0.311374i
$449$	3.11307e10	+	1.79733e10i	0.765956	+	0.442225i	0.831430	−	0.555629i	$-0.187523\pi$
$449$	3.11307e10	+	1.79733e10i	0.765956	+	0.442225i	−0.0654738	+	0.997854i	$0.520856\pi$
$450$		0			0
$451$	1.96536e10	+	3.40411e10i	0.475047	+	0.822806i
$452$	2.36579e9	−	6.49997e9i	0.0566791	−	0.155725i
$453$		0			0
$454$	−6.94231e10	−	5.82529e10i	−1.63411	−	1.37118i
$455$	−1.56273e9	−	4.29357e9i	−0.0364619	−	0.100178i
$456$		0			0
$457$	−8.23273e9	−	4.66901e10i	−0.188747	−	1.07044i	−0.921046	−	0.389453i	$-0.872664\pi$
$457$	−8.23273e9	−	4.66901e10i	−0.188747	−	1.07044i	0.732300	−	0.680982i	$-0.238447\pi$
$458$		−	1.02729e11i		−	2.33471i
$459$		0			0
$460$	−7.58684e9			−0.169445
$461$	−5.56762e10	+	9.81722e9i	−1.23272	+	0.217363i	−0.751795	−	0.659397i	$-0.770812\pi$
$461$	−5.56762e10	+	9.81722e9i	−1.23272	+	0.217363i	−0.480930	+	0.876759i	$0.659701\pi$
$462$		0			0
$463$	3.32703e10	−	1.21094e10i	0.723990	−	0.263511i	0.0463714	−	0.998924i	$-0.485234\pi$
$463$	3.32703e10	−	1.21094e10i	0.723990	−	0.263511i	0.677619	+	0.735413i	$0.263012\pi$
$464$	−2.50349e9	+	2.98355e9i	−0.0540101	+	0.0643667i
$465$		0			0
$466$	4.32321e10	+	1.57352e10i	0.916775	+	0.333679i
$467$	3.69556e10	−	2.13363e10i	0.776984	−	0.448592i	−0.0583762	−	0.998295i	$-0.518592\pi$
$467$	3.69556e10	−	2.13363e10i	0.776984	−	0.448592i	0.835360	+	0.549703i	$0.185259\pi$
$468$		0			0
$469$	6.26958e9	−	1.08592e10i	0.129583	−	0.224444i
$470$	1.52140e10	+	1.81313e10i	0.311782	+	0.371568i
$471$		0			0
$472$	−1.04346e8	+	5.91776e8i	−0.00210236	+	0.0119231i
$473$	−4.47601e10	−	7.89241e9i	−0.894224	−	0.157676i
$474$		0			0
$475$	−1.29318e10	+	1.08511e10i	−0.254030	+	0.213157i
$476$	1.70635e10	+	9.85161e9i	0.332384	+	0.191902i
$477$		0			0
$478$	6.91340e10	+	1.19744e11i	1.32428	+	2.29372i
$479$	−1.59069e10	+	4.37038e10i	−0.302164	+	0.830189i	0.691959	+	0.721936i	$0.256748\pi$
$479$	−1.59069e10	+	4.37038e10i	−0.302164	+	0.830189i	−0.994123	+	0.108252i	$0.965475\pi$
$480$		0			0
$481$	−2.05452e10	−	1.72394e10i	−0.383822	−	0.322065i
$482$	4.58704e10	+	1.26028e11i	0.849854	+	2.33495i
$483$		0			0
$484$	−5.34240e9	−	3.02983e10i	−0.0973543	−	0.552124i
$485$		−	7.53536e9i		−	0.136187i
$486$		0			0
$487$	8.34928e10			1.48434			0.742170	−	0.670212i	$-0.233797\pi$
$487$	8.34928e10			1.48434			0.742170	+	0.670212i	$0.233797\pi$
$488$	1.11950e10	−	1.97399e9i	0.197400	−	0.0348069i
$489$		0			0
$490$	1.36633e10	−	4.97304e9i	0.237013	−	0.0862657i
$491$	−1.56381e10	+	1.86368e10i	−0.269066	+	0.320660i	−0.883611	−	0.468221i	$-0.844895\pi$
$491$	−1.56381e10	+	1.86368e10i	−0.269066	+	0.320660i	0.614545	+	0.788882i	$0.289339\pi$
$492$		0			0
$493$	2.81128e9	+	1.02322e9i	0.0475900	+	0.0173213i
$494$	−1.31668e10	+	7.60187e9i	−0.221092	+	0.127648i
$495$		0			0
$496$	−3.75353e10	+	6.50130e10i	−0.620173	+	1.07417i
$497$	1.91575e10	+	2.28310e10i	0.313987	+	0.374196i
$498$		0			0
$499$	−9.77907e9	+	5.54599e10i	−0.157723	+	0.894493i	0.798531	+	0.601954i	$0.205611\pi$
$499$	−9.77907e9	+	5.54599e10i	−0.157723	+	0.894493i	−0.956254	+	0.292538i	$0.905500\pi$
$500$	−3.30181e10	−	5.82198e9i	−0.528289	−	0.0931516i
$501$		0			0
$502$	3.64896e10	−	3.06184e10i	0.574585	−	0.482134i
$503$	6.61060e10	+	3.81663e10i	1.03269	+	0.596223i	0.917754	−	0.397150i	$-0.130001\pi$
$503$	6.61060e10	+	3.81663e10i	1.03269	+	0.596223i	0.114935	+	0.993373i	$0.463334\pi$
$504$		0			0
$505$	1.46059e10	+	2.52981e10i	0.224575	+	0.388976i
$506$	−1.10349e10	+	3.03183e10i	−0.168333	+	0.462490i
$507$		0			0
$508$	−1.03340e10	−	8.67125e9i	−0.155172	−	0.130205i
$509$	2.18554e10	+	6.00473e10i	0.325603	+	0.894586i	0.989210	+	0.146505i	$0.0468024\pi$
$509$	2.18554e10	+	6.00473e10i	0.325603	+	0.894586i	−0.663607	+	0.748081i	$0.730975\pi$
$510$		0			0
$511$	1.36291e10	+	7.72946e10i	0.199887	+	1.13361i
$512$		−	8.98162e10i		−	1.30700i
$513$		0			0
$514$	8.11333e10			1.16238
$515$	2.34316e10	−	4.13162e9i	0.333098	−	0.0587342i
$516$		0			0
$517$	4.41698e10	−	1.60765e10i	0.618249	−	0.225024i
$518$	−4.13650e10	+	4.92969e10i	−0.574532	+	0.684701i
$519$		0			0
$520$	1.89538e9	+	6.89862e8i	0.0259229	+	0.00943516i
$521$	−6.91938e10	+	3.99491e10i	−0.939110	+	0.542195i	−0.889681	−	0.456582i	$-0.849073\pi$
$521$	−6.91938e10	+	3.99491e10i	−0.939110	+	0.542195i	−0.0494285	+	0.998778i	$0.515740\pi$
$522$		0			0
$523$	−2.22994e10	+	3.86237e10i	−0.298048	+	0.516235i	−0.975689	−	0.219158i	$-0.929669\pi$
$523$	−2.22994e10	+	3.86237e10i	−0.298048	+	0.516235i	0.677641	+	0.735393i	$0.263002\pi$
$524$	1.49789e10	+	1.78512e10i	0.198681	+	0.236779i
$525$		0			0
$526$	−1.52753e10	+	8.66304e10i	−0.199547	+	1.13169i
$527$	5.67884e10	+	1.00133e10i	0.736236	+	0.129818i
$528$		0			0
$529$	3.84804e10	−	3.22889e10i	0.491380	−	0.412317i
$530$	3.94952e10	+	2.28026e10i	0.500542	+	0.288988i
$531$		0			0
$532$	8.51799e9	+	1.47536e10i	0.106339	+	0.184184i
$533$	−2.20013e10	+	6.04482e10i	−0.272609	+	0.748987i
$534$		0			0
$535$	2.97284e10	+	2.49451e10i	0.362874	+	0.304488i
$536$	1.89321e9	+	5.20154e9i	0.0229371	+	0.0630192i
$537$		0			0
$538$	−3.19998e9	−	1.81480e10i	−0.0381961	−	0.216621i
$539$		−	2.88759e10i		−	0.342121i
$540$		0			0
$541$	−1.16720e11			−1.36256			−0.681282	−	0.732021i	$-0.738577\pi$
$541$	−1.16720e11			−1.36256			−0.681282	+	0.732021i	$0.738577\pi$
$542$	1.69515e11	−	2.98901e10i	1.96432	−	0.346362i
$543$		0			0
$544$	−7.41593e10	+	2.69918e10i	−0.846779	+	0.308202i
$545$	1.15107e10	−	1.37179e10i	0.130471	−	0.155490i
$546$		0			0
$547$	−3.09611e10	−	1.12689e10i	−0.345834	−	0.125873i	0.163263	−	0.986583i	$-0.447798\pi$
$547$	−3.09611e10	−	1.12689e10i	−0.345834	−	0.125873i	−0.509097	+	0.860709i	$0.670020\pi$
$548$	3.40033e10	−	1.96318e10i	0.377050	−	0.217690i
$549$		0			0
$550$	−3.36834e10	+	5.83413e10i	−0.368099	+	0.637566i
$551$	1.66271e9	+	1.98154e9i	0.0180389	+	0.0214979i
$552$		0			0
$553$	4.14087e9	−	2.34840e10i	0.0442783	−	0.251115i
$554$	2.33646e10	+	4.11982e9i	0.248039	+	0.0437360i
$555$		0			0
$556$	−6.99767e10	+	5.87175e10i	−0.732242	+	0.614424i
$557$	−1.80115e10	−	1.03990e10i	−0.187124	−	0.108036i	0.403511	−	0.914975i	$-0.367790\pi$
$557$	−1.80115e10	−	1.03990e10i	−0.187124	−	0.108036i	−0.590636	+	0.806938i	$0.701123\pi$
$558$		0			0
$559$	−3.71907e10	−	6.44161e10i	−0.380879	−	0.659701i
$560$	7.89594e9	−	2.16939e10i	0.0802882	−	0.220590i
$561$		0			0
$562$	−1.73342e11	−	1.45451e11i	−1.73764	−	1.45805i
$563$	−5.32759e10	−	1.46374e11i	−0.530270	−	1.45690i	−0.858750	−	0.512394i	$-0.828759\pi$
$563$	−5.32759e10	−	1.46374e11i	−0.530270	−	1.45690i	0.328480	−	0.944511i	$-0.393464\pi$
$564$		0			0
$565$	1.08106e9	+	6.13098e9i	0.0106085	+	0.0601639i
$566$		−	1.55201e11i		−	1.51227i
$567$		0			0
$568$	−1.31567e10			−0.126402
$569$	3.54658e10	−	6.25358e9i	0.338346	−	0.0596595i	−0.00189393	−	0.999998i	$-0.500603\pi$
$569$	3.54658e10	−	6.25358e9i	0.338346	−	0.0596595i	0.340240	+	0.940339i	$0.389492\pi$
$570$		0			0
$571$	8.81956e10	−	3.21006e10i	0.829664	−	0.301973i	0.107943	−	0.994157i	$-0.465574\pi$
$571$	8.81956e10	−	3.21006e10i	0.829664	−	0.301973i	0.721721	+	0.692184i	$0.243351\pi$
$572$	−1.82123e10	+	2.17045e10i	−0.170130	+	0.202753i
$573$		0			0
$574$	1.45042e11	+	5.27909e10i	1.33612	+	0.486309i
$575$	−5.07726e10	+	2.93136e10i	−0.464470	+	0.268162i
$576$		0			0
$577$	6.26865e10	−	1.08576e11i	0.565549	−	0.979560i	−0.431449	−	0.902137i	$-0.641998\pi$
$577$	6.26865e10	−	1.08576e11i	0.565549	−	0.979560i	0.996998	−	0.0774229i	$-0.0246692\pi$
$578$	−5.44000e10	−	6.48313e10i	−0.487402	−	0.580863i
$579$		0			0
$580$	−4.21503e8	+	2.39046e9i	−0.00372467	+	0.0211237i
$581$	−1.36608e11	−	2.40877e10i	−1.19887	−	0.211393i
$582$		0			0
$583$	6.93796e10	−	5.82164e10i	0.600562	−	0.503931i
$584$	−3.00059e10	−	1.73239e10i	−0.257961	−	0.148934i
$585$		0			0
$586$	−3.27702e10	−	5.67596e10i	−0.277900	−	0.481336i
$587$	5.98853e9	−	1.64533e10i	0.0504392	−	0.138580i	−0.911915	−	0.410379i	$-0.865396\pi$
$587$	5.98853e9	−	1.64533e10i	0.0504392	−	0.138580i	0.962354	+	0.271799i	$0.0876185\pi$
$588$		0			0
$589$	3.81938e10	+	3.20484e10i	0.317345	+	0.266284i
$590$	1.30838e9	+	3.59473e9i	0.0107975	+	0.0296660i
$591$		0			0
$592$	−2.35313e10	−	1.33452e11i	−0.191584	−	1.08653i
$593$			8.13815e10i			0.658123i	0.944309	+	0.329061i	$0.106732\pi$
$593$			8.13815e10i			0.658123i	−0.944309	+	0.329061i	$0.893268\pi$
$594$		0			0
$595$	−1.77333e10			−0.141489
$596$	−6.35924e10	+	1.12131e10i	−0.503988	+	0.0888666i
$597$		0			0
$598$	−4.96168e10	+	1.80590e10i	−0.387993	+	0.141218i
$599$	1.44379e11	−	1.72064e11i	1.12149	−	1.33654i	0.186260	−	0.982500i	$-0.440363\pi$
$599$	1.44379e11	−	1.72064e11i	1.12149	−	1.33654i	0.935230	−	0.354040i	$-0.115192\pi$
$600$		0			0
$601$	−1.43492e11	−	5.22268e10i	−1.09984	−	0.400309i	−0.272583	−	0.962132i	$-0.587878\pi$
$601$	−1.43492e11	−	5.22268e10i	−1.09984	−	0.400309i	−0.827257	+	0.561823i	$0.810100\pi$
$602$	−1.54563e11	+	8.92368e10i	−1.17684	+	0.679451i
$603$		0			0
$604$	7.50950e10	−	1.30068e11i	0.564239	−	0.977291i
$605$	1.77987e10	+	2.12116e10i	0.132851	+	0.158326i
$606$		0			0
$607$	−2.34613e10	+	1.33056e11i	−0.172821	+	0.980119i	0.767807	+	0.640681i	$0.221348\pi$
$607$	−2.34613e10	+	1.33056e11i	−0.172821	+	0.980119i	−0.940628	+	0.339438i	$0.889763\pi$
$608$	−6.71988e10	−	1.18490e10i	−0.491753	−	0.0867094i
$609$		0			0
$610$	5.54374e10	−	4.65175e10i	0.400391	−	0.335968i
$611$	6.66185e10	+	3.84622e10i	0.478002	+	0.275975i
$612$		0			0
$613$	−8.05944e10	−	1.39594e11i	−0.570772	−	0.988606i	−0.996487	−	0.0837489i	$-0.973311\pi$
$613$	−8.05944e10	−	1.39594e11i	−0.570772	−	0.988606i	0.425715	−	0.904857i	$-0.360023\pi$
$614$	5.00264e10	−	1.37446e11i	0.351986	−	0.967074i
$615$		0			0
$616$	−7.36274e9	−	6.17807e9i	−0.0511348	−	0.0429072i
$617$	−6.78498e10	−	1.86416e11i	−0.468175	−	1.28630i	−0.919201	−	0.393789i	$-0.871164\pi$
$617$	−6.78498e10	−	1.86416e11i	−0.468175	−	1.28630i	0.451026	−	0.892511i	$-0.351058\pi$
$618$		0			0
$619$	−5.42660e9	−	3.07758e10i	−0.0369628	−	0.209626i	0.960733	−	0.277475i	$-0.0894976\pi$
$619$	−5.42660e9	−	3.07758e10i	−0.0369628	−	0.209626i	−0.997696	+	0.0678486i	$0.978386\pi$
$620$			4.67865e10i			0.316631i
$621$		0			0
$622$	−8.54207e10			−0.570692
$623$	1.07903e11	−	1.90262e10i	0.716276	−	0.126299i
$624$		0			0
$625$	−1.00072e11	+	3.64232e10i	−0.655832	+	0.238703i
$626$	−1.67791e11	+	1.99966e11i	−1.09263	+	1.30214i
$627$		0			0
$628$	1.78857e11	+	6.50987e10i	1.14992	+	0.418537i
$629$	−9.01456e10	+	5.20456e10i	−0.575893	+	0.332492i
$630$		0			0
$631$	−6.49274e10	+	1.12458e11i	−0.409553	+	0.709367i	−0.994840	−	0.101460i	$-0.967649\pi$
$631$	−6.49274e10	+	1.12458e11i	−0.409553	+	0.709367i	0.585286	+	0.810827i	$0.300982\pi$
$632$	6.76654e9	+	8.06405e9i	0.0424129	+	0.0505458i
$633$		0			0
$634$	2.69356e10	−	1.52759e11i	0.166713	−	0.945476i
$635$	1.19569e10	+	2.10833e9i	0.0735401	+	0.0129671i
$636$		0			0
$637$	3.62004e10	−	3.03757e10i	0.219865	−	0.184488i
$638$	8.93960e9	+	5.16128e9i	0.0539555	+	0.0311512i
$639$		0			0
$640$	9.12307e9	+	1.58016e10i	0.0543777	+	0.0941850i
$641$	−4.87804e10	+	1.34023e11i	−0.288944	+	0.793867i	0.707271	+	0.706943i	$0.249926\pi$
$641$	−4.87804e10	+	1.34023e11i	−0.288944	+	0.793867i	−0.996215	+	0.0869244i	$0.972296\pi$
$642$		0			0
$643$	1.87640e11	+	1.57449e11i	1.09770	+	0.921076i	0.997268	−	0.0738681i	$-0.0235344\pi$
$643$	1.87640e11	+	1.57449e11i	1.09770	+	0.921076i	0.100428	+	0.994944i	$0.467979\pi$
$644$	2.02354e10	+	5.55963e10i	0.117644	+	0.323223i
$645$		0			0
$646$	1.02466e10	+	5.81112e10i	0.0588367	+	0.333679i
$647$			3.75157e9i			0.0214090i	0.999943	+	0.0107045i	$0.00340741\pi$
$647$			3.75157e9i			0.0214090i	−0.999943	+	0.0107045i	$0.996593\pi$
$648$		0			0
$649$	7.59705e9			0.0428219
$650$	−1.08573e11	+	1.91443e10i	−0.608230	+	0.107247i
$651$		0			0
$652$	9.67516e10	−	3.52147e10i	0.535387	−	0.194865i
$653$	1.12531e11	−	1.34110e11i	0.618900	−	0.737577i	−0.361981	−	0.932186i	$-0.617899\pi$
$653$	1.12531e11	−	1.34110e11i	0.618900	−	0.737577i	0.980881	+	0.194609i	$0.0623438\pi$
$654$		0			0
$655$	−1.97085e10	−	7.17329e9i	−0.107075	−	0.0389721i
$656$	−2.81480e11	+	1.62513e11i	−1.51996	+	0.877549i
$657$		0			0
$658$	9.22878e10	−	1.59847e11i	0.492312	−	0.852710i
$659$	1.07843e11	+	1.28523e11i	0.571810	+	0.681457i	0.972001	−	0.234975i	$-0.0755008\pi$
$659$	1.07843e11	+	1.28523e11i	0.571810	+	0.681457i	−0.400191	+	0.916432i	$0.631056\pi$
$660$		0			0
$661$	−3.24693e10	+	1.84143e11i	−0.170086	+	0.964603i	0.773579	+	0.633700i	$0.218465\pi$
$661$	−3.24693e10	+	1.84143e11i	−0.170086	+	0.964603i	−0.943665	+	0.330903i	$0.892647\pi$
$662$	3.07084e10	+	5.41472e9i	0.159891	+	0.0281932i
$663$		0			0
$664$	4.69091e10	−	3.93614e10i	0.241315	−	0.202487i
$665$	−1.32786e10	−	7.66639e9i	−0.0678992	−	0.0392016i
$666$		0			0
$667$	4.49170e9	+	7.77985e9i	0.0226938	+	0.0393068i
$668$	−1.72551e10	+	4.74080e10i	−0.0866587	+	0.238093i
$669$		0			0
$670$	2.69945e10	+	2.26511e10i	0.133960	+	0.112406i
$671$	−4.91547e10	−	1.35052e11i	−0.242480	−	0.666207i
$672$		0			0
$673$	−8.32962e8	−	4.72396e9i	−0.00406037	−	0.0230275i	0.982710	−	0.185150i	$-0.0592771\pi$
$673$	−8.32962e8	−	4.72396e9i	−0.00406037	−	0.0230275i	−0.986771	+	0.162123i	$0.948166\pi$
$674$			1.25000e11i			0.605718i
$675$		0			0
$676$	1.36592e11			0.654093
$677$	−1.91119e11	+	3.36994e10i	−0.909807	+	0.160423i	−0.608916	−	0.793235i	$-0.708395\pi$
$677$	−1.91119e11	+	3.36994e10i	−0.909807	+	0.160423i	−0.300891	+	0.953659i	$0.597284\pi$
$678$		0			0
$679$	−5.52190e10	+	2.00981e10i	−0.259782	+	0.0945531i
$680$	5.03195e9	−	5.99684e9i	0.0235343	−	0.0280470i
$681$		0			0
$682$	1.86967e11	+	6.80503e10i	0.864224	+	0.314552i
$683$	2.62322e11	−	1.51452e11i	1.20546	−	0.695972i	0.243695	−	0.969852i	$-0.421640\pi$
$683$	2.62322e11	−	1.51452e11i	1.20546	−	0.695972i	0.961764	+	0.273880i	$0.0883071\pi$
$684$		0			0
$685$	−1.76691e10	+	3.06037e10i	−0.0802512	+	0.138999i
$686$	−2.00725e11	−	2.39215e11i	−0.906369	−	1.08017i
$687$		0			0
$688$	6.52610e10	−	3.70113e11i	0.291273	−	1.65189i
$689$	1.45967e11	+	2.57379e10i	0.647704	+	0.114208i
$690$		0			0
$691$	−2.26657e11	+	1.90187e11i	−0.994160	+	0.834199i	−0.986165	−	0.165769i	$-0.946989\pi$
$691$	−2.26657e11	+	1.90187e11i	−0.994160	+	0.834199i	−0.00799511	+	0.999968i	$0.502545\pi$
$692$	2.53674e11	+	1.46459e11i	1.10625	+	0.638691i
$693$		0			0
$694$	−3.81083e10	−	6.60056e10i	−0.164279	−	0.284540i
$695$	2.81193e10	−	7.72572e10i	0.120522	−	0.331131i
$696$		0			0
$697$	1.91253e11	+	1.60481e11i	0.810360	+	0.679973i
$698$	4.85265e10	+	1.33326e11i	0.204436	+	0.561684i
$699$		0			0
$700$	2.14515e10	+	1.21657e11i	0.0893439	+	0.506695i
$701$			2.45235e10i			0.101557i	0.998710	+	0.0507785i	$0.0161703\pi$
$701$			2.45235e10i			0.101557i	−0.998710	+	0.0507785i	$0.983830\pi$
$702$		0			0
$703$	−9.00003e10			−0.368487
$704$	−1.07249e11	+	1.89110e10i	−0.436621	+	0.0769880i
$705$		0			0
$706$	−2.78997e11	+	1.01547e11i	−1.12300	+	0.408739i
$707$	1.46428e11	−	1.74506e11i	0.586066	−	0.698446i
$708$		0			0
$709$	−3.53052e11	−	1.28500e11i	−1.39718	−	0.508533i	−0.469843	−	0.882750i	$-0.655689\pi$
$709$	−3.53052e11	−	1.28500e11i	−1.39718	−	0.508533i	−0.927341	+	0.374217i	$0.877912\pi$
$710$	−7.25360e10	+	4.18787e10i	−0.285444	+	0.164801i
$711$		0			0
$712$	−2.41840e10	+	4.18880e10i	−0.0941042	+	0.162993i
$713$	1.11301e11	+	1.32643e11i	0.430666	+	0.513248i
$714$		0			0
$715$	4.42813e9	−	2.51132e10i	0.0169432	−	0.0960899i
$716$	3.10325e11	+	5.47186e10i	1.18077	+	0.208201i
$717$		0			0
$718$	−2.34377e11	+	1.96666e11i	−0.881897	+	0.739999i
$719$	1.30207e11	+	7.51752e10i	0.487214	+	0.281293i	0.723418	−	0.690410i	$-0.242570\pi$
$719$	1.30207e11	+	7.51752e10i	0.487214	+	0.281293i	−0.236204	+	0.971703i	$0.575903\pi$
$720$		0			0
$721$	−9.27725e10	−	1.60687e11i	−0.343303	−	0.594619i
$722$	1.09851e11	−	3.01814e11i	0.404256	−	1.11069i
$723$		0			0
$724$	2.02611e11	+	1.70011e11i	0.737411	+	0.618761i
$725$	6.41533e9	+	1.76260e10i	0.0232203	+	0.0637972i
$726$		0			0
$727$	7.72535e10	+	4.38126e11i	0.276554	+	1.56842i	0.733981	+	0.679170i	$0.237660\pi$
$727$	7.72535e10	+	4.38126e11i	0.276554	+	1.56842i	−0.457427	+	0.889247i	$0.651229\pi$
$728$		−	1.57293e10i		−	0.0559995i
$729$		0			0
$730$	−2.20572e11			−0.776710
$731$	−2.84298e11	+	5.01293e10i	−0.995643	+	0.175559i
$732$		0			0
$733$	2.01572e11	−	7.33664e10i	0.698257	−	0.254145i	0.0315904	−	0.999501i	$-0.489943\pi$
$733$	2.01572e11	−	7.33664e10i	0.698257	−	0.254145i	0.666666	+	0.745356i	$0.267721\pi$
$734$	5.78051e10	−	6.88894e10i	0.199151	−	0.237338i
$735$		0			0
$736$	−2.22684e11	−	8.10503e10i	−0.758888	−	0.276212i
$737$	6.06061e10	−	3.49909e10i	0.205422	−	0.118600i
$738$		0			0
$739$	5.48728e10	−	9.50425e10i	0.183984	−	0.318669i	−0.759250	−	0.650799i	$-0.774434\pi$
$739$	5.48728e10	−	9.50425e10i	0.183984	−	0.318669i	0.943234	+	0.332130i	$0.107767\pi$
$740$	−5.42867e10	−	6.46964e10i	−0.181037	−	0.215751i
$741$		0			0
$742$	6.17565e10	−	3.50239e11i	0.203736	−	1.15544i
$743$	3.62815e11	+	6.39740e10i	1.19050	+	0.209917i	0.733588	−	0.679594i	$-0.237844\pi$
$743$	3.62815e11	+	6.39740e10i	1.19050	+	0.209917i	0.456912	+	0.889512i	$0.348955\pi$
$744$		0			0
$745$	4.45206e10	−	3.73572e10i	0.144523	−	0.121269i
$746$	−1.82637e11	−	1.05446e11i	−0.589704	−	0.340466i
$747$		0			0
$748$	5.49825e10	+	9.52325e10i	0.175638	+	0.304214i
$749$	1.03507e11	−	2.84382e11i	0.328883	−	0.903597i
$750$		0			0
$751$	4.65384e11	+	3.90504e11i	1.46303	+	1.22762i	0.922329	+	0.386406i	$0.126284\pi$
$751$	4.65384e11	+	3.90504e11i	1.46303	+	1.22762i	0.540696	+	0.841218i	$0.318161\pi$
$752$	1.32934e11	+	3.65232e11i	0.415684	+	1.14208i
$753$		0			0
$754$	2.93347e9	+	1.66366e10i	0.00907605	+	0.0514728i
$755$			1.35174e11i			0.416013i
$756$		0			0
$757$	−7.74160e10			−0.235747			−0.117874	−	0.993029i	$-0.537608\pi$
$757$	−7.74160e10			−0.235747			−0.117874	+	0.993029i	$0.537608\pi$
$758$	−2.33432e10	+	4.11604e9i	−0.0707106	+	0.0124682i
$759$		0			0
$760$	6.36040e9	−	2.31500e9i	0.0190647	−	0.00693899i
$761$	−2.33613e11	+	2.78409e11i	−0.696560	+	0.830128i	−0.992132	−	0.125193i	$-0.960045\pi$
$761$	−2.33613e11	+	2.78409e11i	−0.696560	+	0.830128i	0.295573	+	0.955320i	$0.404490\pi$
$762$		0			0
$763$	−1.31226e11	−	4.77622e10i	−0.387187	−	0.140925i
$764$	2.70899e11	−	1.56404e11i	0.795122	−	0.459064i
$765$		0			0
$766$	−1.64193e11	+	2.84390e11i	−0.476913	+	0.826037i
$767$	7.99166e9	+	9.52409e9i	0.0230917	+	0.0275196i
$768$		0			0
$769$	1.08599e11	−	6.15897e11i	0.310543	−	1.76117i	−0.285651	−	0.958334i	$-0.592210\pi$
$769$	1.08599e11	−	6.15897e11i	0.310543	−	1.76117i	0.596193	−	0.802841i	$-0.296679\pi$
$770$	−6.02576e10	−	1.06250e10i	−0.171415	−	0.0302251i
$771$		0			0
$772$	−4.42838e11	+	3.71585e11i	−1.24674	+	1.04614i
$773$	−1.31183e11	−	7.57386e10i	−0.367418	−	0.212129i	0.304912	−	0.952381i	$-0.401373\pi$
$773$	−1.31183e11	−	7.57386e10i	−0.367418	−	0.212129i	−0.672330	+	0.740252i	$0.734706\pi$
$774$		0			0
$775$	1.80771e11	+	3.13104e11i	0.501096	+	0.867925i
$776$	8.87223e9	−	2.43762e10i	0.0244673	−	0.0672233i
$777$		0			0
$778$	−1.35487e11	−	1.13687e11i	−0.369810	−	0.310307i
$779$	7.38307e10	+	2.02848e11i	0.200488	+	0.550835i
$780$		0			0
$781$	2.88840e10	+	1.63810e11i	0.0776343	+	0.440286i
$782$			2.04928e11i			0.547991i
$783$		0			0
$784$	2.38769e11			0.631996
$785$	−1.68704e11	+	2.97471e10i	−0.444270	+	0.0783368i
$786$		0			0
$787$	2.31521e11	−	8.42667e10i	0.603520	−	0.219663i	−0.0221457	−	0.999755i	$-0.507050\pi$
$787$	2.31521e11	−	8.42667e10i	0.603520	−	0.219663i	0.625665	+	0.780092i	$0.284828\pi$
$788$	2.42717e11	−	2.89259e11i	0.629500	−	0.750209i
$789$		0			0
$790$	6.29738e10	+	2.29206e10i	0.161678	+	0.0588461i
$791$	4.20444e10	−	2.42744e10i	0.107400	−	0.0620071i
$792$		0			0
$793$	1.17600e11	−	2.03690e11i	0.297382	−	0.515081i
$794$	−4.30312e11	−	5.12826e11i	−1.08268	−	1.29029i
$795$		0			0
$796$	2.62989e10	−	1.49148e11i	0.0655066	−	0.371507i
$797$	−5.26169e10	−	9.27778e9i	−0.130404	−	0.0229938i	0.108065	−	0.994144i	$-0.465535\pi$
$797$	−5.26169e10	−	9.27778e9i	−0.130404	−	0.0229938i	−0.238469	+	0.971150i	$0.576646\pi$
$798$		0			0
$799$	2.28705e11	−	1.91906e11i	0.561163	−	0.470871i
$800$	−4.28510e11	−	2.47400e11i	−1.04617	−	0.604004i
$801$		0			0
$802$	−2.21006e11	−	3.82793e11i	−0.534202	−	0.925265i
$803$	−1.49819e11	+	4.11624e11i	−0.360333	+	0.990008i
$804$		0			0
$805$	−4.07913e10	−	3.42280e10i	−0.0971368	−	0.0815075i
$806$	1.11366e11	+	3.05977e11i	0.263885	+	0.725017i
$807$		0			0
$808$	1.74624e10	+	9.90344e10i	0.0409694	+	0.232349i
$809$			1.30189e11i			0.303935i	0.988385	+	0.151968i	$0.0485610\pi$
$809$			1.30189e11i			0.303935i	−0.988385	+	0.151968i	$0.951439\pi$
$810$		0			0
$811$	1.10741e11			0.255990			0.127995	−	0.991775i	$-0.459146\pi$
$811$	1.10741e11			0.255990			0.127995	+	0.991775i	$0.459146\pi$
$812$	1.86415e10	−	3.28700e9i	0.0428802	−	0.00756093i
$813$		0			0
$814$	−3.37496e11	+	1.22839e11i	−0.768726	+	0.279793i
$815$	−5.95653e10	+	7.09871e10i	−0.135009	+	0.160897i
$816$		0			0
$817$	−2.34551e11	−	8.53697e10i	−0.526441	−	0.191609i
$818$	4.90255e11	−	2.83049e11i	1.09499	−	0.632190i
$819$		0			0
$820$	−1.01283e11	+	1.75428e11i	−0.224018	+	0.388010i
$821$	−1.21666e11	−	1.44996e11i	−0.267792	−	0.319142i	0.615344	−	0.788258i	$-0.289017\pi$
$821$	−1.21666e11	−	1.44996e11i	−0.267792	−	0.319142i	−0.883136	+	0.469116i	$0.844572\pi$
$822$		0			0
$823$	4.72310e10	−	2.67860e11i	0.102950	−	0.583860i	−0.889069	−	0.457773i	$-0.848647\pi$
$823$	4.72310e10	−	2.67860e11i	0.102950	−	0.583860i	0.992019	−	0.126087i	$-0.0402418\pi$
$824$	8.06638e10	+	1.42232e10i	0.174972	+	0.0308524i
$825$		0			0
$826$	2.28525e10	−	1.91755e10i	0.0490923	−	0.0411933i
$827$	4.83513e11	+	2.79156e11i	1.03368	+	0.596795i	0.918037	−	0.396496i	$-0.129774\pi$
$827$	4.83513e11	+	2.79156e11i	1.03368	+	0.596795i	0.115643	+	0.993291i	$0.463107\pi$
$828$		0			0
$829$	3.05847e11	+	5.29743e11i	0.647569	+	1.12162i	0.983702	+	0.179808i	$0.0575477\pi$
$829$	3.05847e11	+	5.29743e11i	0.647569	+	1.12162i	−0.336132	+	0.941815i	$0.609119\pi$
$830$	1.33331e11	−	3.66323e11i	0.280942	−	0.771883i
$831$		0			0
$832$	−1.36528e11	−	1.14561e11i	−0.284924	−	0.239079i
$833$	−6.27291e10	−	1.72347e11i	−0.130283	−	0.357951i
$834$		0			0
$835$	−7.88478e9	−	4.47168e10i	−0.0162197	−	0.0919867i
$836$			9.50790e10i			0.194652i
$837$		0			0
$838$	2.54326e11			0.515722
$839$	9.49572e10	−	1.67435e10i	0.191637	−	0.0337908i	−0.0770056	−	0.997031i	$-0.524536\pi$
$839$	9.49572e10	−	1.67435e10i	0.191637	−	0.0337908i	0.268643	+	0.963240i	$0.413425\pi$
$840$		0			0
$841$	−4.67377e11	+	1.70111e11i	−0.934294	+	0.340055i
$842$	−1.16527e11	+	1.38872e11i	−0.231835	+	0.276290i
$843$		0			0
$844$	3.94734e11	+	1.43671e11i	0.777920	+	0.283140i
$845$	−1.06466e11	+	6.14681e10i	−0.208826	+	0.120565i
$846$		0			0
$847$	1.07966e11	−	1.87003e11i	0.209776	−	0.363342i
$848$	4.81381e11	+	5.73688e11i	0.930906	+	1.10941i
$849$		0			0
$850$	−7.43016e10	+	4.21385e11i	−0.142338	+	0.807242i
$851$	−3.07814e11	−	5.42759e10i	−0.586908	−	0.103488i
$852$		0			0
$853$	−3.15446e10	+	2.64690e10i	−0.0595839	+	0.0499968i	−0.672093	−	0.740467i	$-0.734605\pi$
$853$	−3.15446e10	+	2.64690e10i	−0.0595839	+	0.0499968i	0.612509	+	0.790463i	$0.290160\pi$
$854$	−4.88741e11	−	2.82175e11i	−0.918856	−	0.530502i
$855$		0			0
$856$	6.67981e10	+	1.15698e11i	0.124414	+	0.215491i
$857$	−3.20388e11	+	8.80260e11i	−0.593955	+	1.63188i	0.169140	+	0.985592i	$0.445901\pi$
$857$	−3.20388e11	+	8.80260e11i	−0.593955	+	1.63188i	−0.763095	+	0.646286i	$0.776321\pi$
$858$		0			0
$859$	4.21815e11	+	3.53945e11i	0.774728	+	0.650074i	0.941915	−	0.335851i	$-0.109024\pi$
$859$	4.21815e11	+	3.53945e11i	0.774728	+	0.650074i	−0.167187	+	0.985925i	$0.553468\pi$
$860$	−8.01098e10	−	2.20100e11i	−0.146451	−	0.402370i
$861$		0			0
$862$	−1.82926e11	−	1.03743e12i	−0.331319	−	1.87901i
$863$			1.57375e11i			0.283722i	0.989887	+	0.141861i	$0.0453086\pi$
$863$			1.57375e11i			0.283722i	−0.989887	+	0.141861i	$0.954691\pi$
$864$		0			0
$865$	−2.63632e11			−0.470906
$866$	1.98211e11	−	3.49500e10i	0.352417	−	0.0621407i
$867$		0			0
$868$	3.42851e11	−	1.24788e11i	0.603985	−	0.219833i
$869$	8.55473e10	−	1.01951e11i	0.150012	−	0.178778i
$870$		0			0
$871$	1.07621e11	+	3.91707e10i	0.186992	+	0.0680596i
$872$	5.33877e10	−	3.08234e10i	0.0923370	−	0.0533108i
$873$		0			0
$874$	−8.85933e10	+	1.53448e11i	−0.151829	+	0.262976i
$875$	−1.51259e11	−	1.80263e11i	−0.258041	−	0.307521i
$876$		0			0
$877$	−6.44658e10	+	3.65604e11i	−0.108976	+	0.618034i	0.880581	+	0.473895i	$0.157152\pi$
$877$	−6.44658e10	+	3.65604e11i	−0.108976	+	0.618034i	−0.989557	+	0.144139i	$0.953959\pi$
$878$	−1.21478e12	−	2.14198e11i	−2.04418	−	0.360444i
$879$		0			0
$880$	9.87015e10	−	8.28204e10i	0.164586	−	0.138104i
$881$	−3.48108e11	−	2.00980e11i	−0.577844	−	0.333618i	0.182432	−	0.983218i	$-0.441603\pi$
$881$	−3.48108e11	−	2.00980e11i	−0.577844	−	0.333618i	−0.760276	+	0.649600i	$0.774936\pi$
$882$		0			0
$883$	−3.70632e11	−	6.41954e11i	−0.609677	−	1.05599i	−0.991293	−	0.131671i	$-0.957966\pi$
$883$	−3.70632e11	−	6.41954e11i	−0.609677	−	1.05599i	0.381616	−	0.924321i	$-0.375368\pi$
$884$	−6.15504e10	+	1.69108e11i	−0.100791	+	0.276921i
$885$		0			0
$886$	−6.19992e10	−	5.20235e10i	−0.100612	−	0.0844237i
$887$	−8.13054e10	−	2.23385e11i	−0.131348	−	0.360877i	0.856532	−	0.516094i	$-0.172614\pi$
$887$	−8.13054e10	−	2.23385e11i	−0.131348	−	0.360877i	−0.987880	+	0.155217i	$0.950392\pi$
$888$		0			0
$889$	−1.64413e10	−	9.32434e10i	−0.0263227	−	0.149283i
$890$			3.07917e11i			0.490765i
$891$		0			0
$892$	−5.70342e10			−0.0900898
$893$	2.54216e11	−	4.48252e10i	0.399758	−	0.0704882i
$894$		0			0
$895$	−2.66504e11	+	9.69996e10i	−0.415348	+	0.151174i
$896$	9.14613e10	−	1.08999e11i	0.141908	−	0.169119i
$897$		0			0
$898$	7.40281e11	+	2.69440e11i	1.13839	+	0.414340i
$899$	4.79767e10	−	2.76994e10i	0.0734500	−	0.0424064i
$900$		0			0
$901$	2.87627e11	−	4.98185e11i	0.436446	−	0.755947i
$902$	5.53723e11	+	6.59902e11i	0.836501	+	0.996903i
$903$		0			0
$904$	−3.72157e9	+	2.11061e10i	−0.00557253	+	0.0316034i
$905$	−2.34431e11	−	4.13365e10i	−0.349478	−	0.0616225i
$906$		0			0
$907$	7.52329e11	−	6.31279e11i	1.11168	−	0.932807i	0.113522	−	0.993535i	$-0.463787\pi$
$907$	7.52329e11	−	6.31279e11i	1.11168	−	0.932807i	0.998154	+	0.0607281i	$0.0193423\pi$
$908$	−8.03229e11	−	4.63745e11i	−1.18167	−	0.682238i
$909$		0			0
$910$	−5.00674e10	−	8.67192e10i	−0.0730112	−	0.126459i
$911$	−1.30412e10	+	3.58304e10i	−0.0189341	+	0.0520210i	−0.948800	−	0.315879i	$-0.897701\pi$
$911$	−1.30412e10	+	3.58304e10i	−0.0189341	+	0.0520210i	0.929866	+	0.367900i	$0.119923\pi$
$912$		0			0
$913$	−5.93057e11	−	4.97634e11i	−0.853519	−	0.716188i
$914$	−3.55367e11	−	9.76364e11i	−0.509205	−	1.39903i
$915$		0			0
$916$	−1.82568e11	−	1.03539e12i	−0.259324	−	1.47070i
$917$			1.63556e11i			0.231307i
$918$		0			0
$919$	8.74067e11			1.22541			0.612707	−	0.790310i	$-0.290081\pi$
$919$	8.74067e11			1.22541			0.612707	+	0.790310i	$0.290081\pi$
$920$	2.31496e10	−	4.08189e9i	0.0323141	−	0.00569784i
$921$		0			0
$922$	−1.16428e12	+	4.23762e11i	−1.61114	+	0.586406i
$923$	−1.74976e11	+	2.08529e11i	−0.241086	+	0.287316i
$924$		0			0
$925$	−6.13267e11	−	2.23211e11i	−0.837688	−	0.304894i
$926$	6.71976e11	−	3.87965e11i	0.913923	−	0.527654i
$927$		0			0
$928$	−3.79090e10	+	6.56602e10i	−0.0511152	+	0.0885341i
$929$	−8.86492e11	−	1.05648e12i	−1.19018	−	1.41840i	−0.884675	−	0.466208i	$-0.845620\pi$
$929$	−8.86492e11	−	1.05648e12i	−1.19018	−	1.41840i	−0.305503	−	0.952191i	$-0.598825\pi$
$930$		0			0
$931$	2.75371e10	−	1.56170e11i	0.0366538	−	0.207874i
$932$	4.63693e11	+	8.17616e10i	0.614564	+	0.108364i
$933$		0			0
$934$	7.16399e11	−	6.01130e11i	0.941386	−	0.789916i
$935$	−8.57114e10	−	4.94855e10i	−0.112148	−	0.0647488i
$936$		0			0
$937$	−4.16564e11	−	7.21510e11i	−0.540410	−	0.936018i	−0.998880	−	0.0473080i	$-0.984936\pi$
$937$	−4.16564e11	−	7.21510e11i	−0.540410	−	0.936018i	0.458470	−	0.888710i	$-0.348398\pi$
$938$	9.39879e10	−	2.58230e11i	0.121412	−	0.333576i
$939$		0			0
$940$	1.85562e11	+	1.55705e11i	0.237671	+	0.199430i
$941$	−2.80549e11	−	7.70802e11i	−0.357808	−	0.983070i	−0.979788	−	0.200037i	$-0.935894\pi$
$941$	−2.80549e11	−	7.70802e11i	−0.357808	−	0.983070i	0.621980	−	0.783033i	$-0.286328\pi$
$942$		0			0
$943$	1.30181e11	+	7.38295e11i	0.164627	+	0.933647i
$944$			6.28187e10i			0.0791045i
$945$		0			0
$946$	−9.96074e11			−1.24373
$947$	9.44642e11	−	1.66566e11i	1.17454	−	0.207103i	0.447875	−	0.894096i	$-0.352181\pi$
$947$	9.44642e11	−	1.66566e11i	1.17454	−	0.207103i	0.726664	+	0.686993i	$0.241070\pi$
$948$		0			0
$949$	−6.73636e11	+	2.45183e11i	−0.830539	+	0.302292i
$950$	−2.37807e11	+	2.83408e11i	−0.291965	+	0.347950i
$951$		0			0
$952$	−5.73658e10	−	2.08795e10i	−0.0698402	−	0.0254198i
$953$	2.03870e11	−	1.17705e11i	0.247162	−	0.142699i	−0.371302	−	0.928512i	$-0.621088\pi$
$953$	2.03870e11	−	1.17705e11i	0.247162	−	0.142699i	0.618464	+	0.785813i	$0.287755\pi$
$954$		0			0
$955$	−1.40767e11	+	2.43815e11i	−0.169234	+	0.293121i
$956$	9.09595e11	+	1.08401e12i	1.08897	+	1.29779i
$957$		0			0
$958$	−1.76993e11	+	1.00378e12i	−0.210133	+	1.19172i
$959$	2.71390e11	+	4.78534e10i	0.320863	+	0.0565768i
$960$		0			0
$961$	1.64631e11	−	1.38142e11i	0.193027	−	0.161969i
$962$	−5.09024e11	−	2.93885e11i	−0.594344	−	0.343145i
$963$		0			0
$964$	6.86293e11	+	1.18869e12i	0.794697	+	1.37646i
$965$	1.77949e11	−	4.88911e11i	0.205204	−	0.563794i
$966$		0			0
$967$	−1.27323e12	−	1.06837e12i	−1.45613	−	1.22184i	−0.927948	−	0.372709i	$-0.878429\pi$
$967$	−1.27323e12	−	1.06837e12i	−1.45613	−	1.22184i	−0.528183	−	0.849130i	$-0.677127\pi$
$968$	3.26023e10	+	8.95741e10i	0.0371319	+	0.102019i
$969$		0			0
$970$	−2.86765e10	−	1.62633e11i	−0.0323921	−	0.183705i
$971$		−	7.56001e11i		−	0.850443i	−0.905089	−	0.425222i	$-0.860196\pi$
$971$		−	7.56001e11i		−	0.850443i	0.905089	−	0.425222i	$-0.139804\pi$
$972$		0			0
$973$	−6.41139e11			−0.715321
$974$	1.80199e12	−	3.17740e11i	2.00224	−	0.353049i
$975$		0			0
$976$	1.11672e12	−	4.06452e11i	1.23068	−	0.447930i
$977$	−6.91971e11	+	8.24659e11i	−0.759468	+	0.905099i	−0.997814	−	0.0660815i	$-0.978950\pi$
$977$	−6.91971e11	+	8.24659e11i	−0.759468	+	0.905099i	0.238346	+	0.971180i	$0.423395\pi$
$978$		0			0
$979$	5.74624e11	+	2.09146e11i	0.625537	+	0.227677i
$980$	1.28872e11	−	7.44046e10i	0.139719	−	0.0806669i
$981$		0			0
$982$	−2.66587e11	+	4.61743e11i	−0.286677	+	0.496540i
$983$	5.84236e11	+	6.96265e11i	0.625711	+	0.745694i	0.982041	−	0.188667i	$-0.0604165\pi$
$983$	5.84236e11	+	6.96265e11i	0.625711	+	0.745694i	−0.356330	+	0.934360i	$0.615972\pi$
$984$		0			0
$985$	−5.90143e10	+	3.34687e11i	−0.0626920	+	0.355544i
$986$	6.45686e10	+	1.13852e10i	0.0683146	+	0.0120457i
$987$		0			0
$988$	−1.19196e11	+	1.00018e11i	−0.125094	+	0.104966i
$989$	−7.50715e11	−	4.33426e11i	−0.784675	−	0.453033i
$990$		0			0
$991$	8.93401e10	+	1.54742e11i	0.0926300	+	0.160440i	0.908617	−	0.417630i	$-0.137139\pi$
$991$	8.93401e10	+	1.54742e11i	0.0926300	+	0.160440i	−0.815987	+	0.578070i	$0.803806\pi$
$992$	−4.99821e11	+	1.37325e12i	−0.516140	+	1.41808i
$993$		0			0
$994$	5.00353e11	+	4.19846e11i	0.512543	+	0.430075i
$995$	4.66200e10	+	1.28087e11i	0.0475642	+	0.130682i
$996$		0			0
$997$	1.88373e11	+	1.06831e12i	0.190650	+	1.08123i	0.918478	+	0.395471i	$0.129419\pi$
$997$	1.88373e11	+	1.06831e12i	0.190650	+	1.08123i	−0.727828	+	0.685759i	$0.759470\pi$
$998$			1.23418e12i			1.24411i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.9.f.a.71.19		138
3.2	odd	2		27.9.f.a.14.5	yes	138
27.2	odd	18	inner	81.9.f.a.8.19		138
27.25	even	9		27.9.f.a.2.5	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.9.f.a.2.5	✓	138	27.25	even	9
27.9.f.a.14.5	yes	138	3.2	odd	2
81.9.f.a.8.19		138	27.2	odd	18	inner
81.9.f.a.71.19		138	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(21.5826 - 3.80559i) q^{2} +(210.764 - 76.7119i) q^{4} +(-129.757 + 154.639i) q^{5} +(1479.28 + 538.412i) q^{7} +(-601.827 + 347.465i) q^{8} +(-2212.01 + 3831.31i) q^{10} +(5647.40 + 6730.30i) q^{11} +(-2496.75 + 14159.8i) q^{13} +(33975.6 + 5990.81i) q^{14} +(-55651.7 + 46697.3i) q^{16} +(48327.4 + 27901.8i) q^{17} +(24124.8 + 41785.3i) q^{19} +(-15485.6 + 42546.2i) q^{20} +(147498. + 123766. i) q^{22} +(57310.9 + 157460. i) q^{23} +(60755.1 + 344560. i) q^{25} +315106. i q^{26} +353081. q^{28} +(52796.6 - 9309.47i) q^{29} +(971027. - 353425. i) q^{31} +(-909043. + 1.08336e6i) q^{32} +(1.14921e6 + 418280. i) q^{34} +(-275206. + 158890. i) q^{35} +(-932654. + 1.61540e6i) q^{37} +(679693. + 810026. i) q^{38} +(24359.9 - 138152. i) q^{40} +(4.40599e6 + 776896. i) q^{41} +(-3.96290e6 + 3.32527e6i) q^{43} +(1.70656e6 + 985285. i) q^{44} +(1.83615e6 + 3.18030e6i) q^{46} +(1.82983e6 - 5.02741e6i) q^{47} +(-2.51772e6 - 2.11262e6i) q^{49} +(2.62251e6 + 7.20528e6i) q^{50} +(559998. + 3.17591e6i) q^{52} -1.03085e7i q^{53} -1.77356e6 q^{55} +(-1.07735e6 + 189966. i) q^{56} +(1.10406e6 - 401845. i) q^{58} +(555817. - 662397. i) q^{59} +(-1.53716e7 - 5.59480e6i) q^{61} +(1.96123e7 - 1.13232e7i) q^{62} +(-6.19773e6 + 1.07348e7i) q^{64} +(-1.86568e6 - 2.22343e6i) q^{65} +(1.38317e6 - 7.84434e6i) q^{67} +(1.23261e7 + 2.17342e6i) q^{68} +(-5.33499e6 + 4.47659e6i) q^{70} +(1.63960e7 + 9.46623e6i) q^{71} +(2.49290e7 + 4.31782e7i) q^{73} +(-1.39815e7 + 3.84139e7i) q^{74} +(8.29006e6 + 6.95619e6i) q^{76} +(4.73038e6 + 1.29966e7i) q^{77} +(-2.63044e6 - 1.49180e7i) q^{79} -1.46652e7i q^{80} +9.80493e7 q^{82} +(-8.67787e7 + 1.53014e7i) q^{83} +(-1.05855e7 + 3.85282e6i) q^{85} +(-7.28750e7 + 8.68490e7i) q^{86} +(-5.73730e6 - 2.08821e6i) q^{88} +(6.02765e7 - 3.48007e7i) q^{89} +(-1.13172e7 + 1.96019e7i) q^{91} +(2.41582e7 + 2.87906e7i) q^{92} +(2.03602e7 - 1.15468e8i) q^{94} +(-9.59199e6 - 1.69133e6i) q^{95} +(-2.85952e7 + 2.39942e7i) q^{97} +(-6.23788e7 - 3.60144e7i) 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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