LMFDB - Embedded newform 98.10.c.m.79.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [98,10,Mod(67,98)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(98, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("98.67");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, 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:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4 x^{7} - 4806 x^{6} + 14432 x^{5} + 8678459 x^{4} - 17380976 x^{3} - 6978412850 x^{2} + \cdots + 2108388231292 $ x^8 - 4x^7 - 4806x^6 + 14432x^5 + 8678459x^4 - 17380976x^3 - 6978412850x^2 + 6987105744*x + 2108388231292
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{4}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.3
Root			$35.9094 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.10.c.m.67.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 - 13.8564i) q^{2} +(51.3408 + 88.9249i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1047.40 + 1814.15i) q^{5} +1642.91 q^{6} -4096.00 q^{8} +(4569.74 - 7915.01i) q^{9} +O(q^{10})$	\(q+(8.00000 - 13.8564i) q^{2} +(51.3408 + 88.9249i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1047.40 + 1814.15i) q^{5} +1642.91 q^{6} -4096.00 q^{8} +(4569.74 - 7915.01i) q^{9} +(16758.4 + 29026.4i) q^{10} +(-28157.2 - 48769.7i) q^{11} +(13143.3 - 22764.8i) q^{12} -124915. q^{13} -215098. q^{15} +(-32768.0 + 56755.8i) q^{16} +(194320. + 336573. i) q^{17} +(-73115.8 - 126640. i) q^{18} +(-123329. + 213611. i) q^{19} +536269. q^{20} -901030. q^{22} +(858886. - 1.48763e6i) q^{23} +(-210292. - 364237. i) q^{24} +(-1.21753e6 - 2.10883e6i) q^{25} +(-999317. + 1.73087e6i) q^{26} +2.95954e6 q^{27} +5.75179e6 q^{29} +(-1.72078e6 + 2.98048e6i) q^{30} +(-2.63393e6 - 4.56209e6i) q^{31} +(524288. + 908093. i) q^{32} +(2.89123e6 - 5.00775e6i) q^{33} +6.21825e6 q^{34} -2.33970e6 q^{36} +(6.17074e6 - 1.06880e7i) q^{37} +(1.97326e6 + 3.41778e6i) q^{38} +(-6.41322e6 - 1.11080e7i) q^{39} +(4.29015e6 - 7.43076e6i) q^{40} +5.54285e6 q^{41} -5.78833e6 q^{43} +(-7.20824e6 + 1.24850e7i) q^{44} +(9.57269e6 + 1.65804e7i) q^{45} +(-1.37422e7 - 2.38021e7i) q^{46} +(2.55966e7 - 4.43346e7i) q^{47} -6.72935e6 q^{48} -3.89611e7 q^{50} +(-1.99531e7 + 3.45599e7i) q^{51} +(1.59891e7 + 2.76939e7i) q^{52} +(4.07186e7 + 7.05267e7i) q^{53} +(2.36763e7 - 4.10086e7i) q^{54} +1.17967e8 q^{55} -2.53272e7 q^{57} +(4.60143e7 - 7.96992e7i) q^{58} +(-3.92926e7 - 6.80568e7i) q^{59} +(2.75325e7 + 4.76877e7i) q^{60} +(6.90133e6 - 1.19535e7i) q^{61} -8.42856e7 q^{62} +1.67772e7 q^{64} +(1.30836e8 - 2.26614e8i) q^{65} +(-4.62596e7 - 8.01241e7i) q^{66} +(5.08587e7 + 8.80899e7i) q^{67} +(4.97460e7 - 8.61626e7i) q^{68} +1.76384e8 q^{69} -3.75670e8 q^{71} +(-1.87176e7 + 3.24199e7i) q^{72} +(-2.22973e8 - 3.86200e8i) q^{73} +(-9.87319e7 - 1.71009e8i) q^{74} +(1.25018e8 - 2.16538e8i) q^{75} +6.31442e7 q^{76} -2.05223e8 q^{78} +(1.13312e8 - 1.96262e8i) q^{79} +(-6.86425e7 - 1.18892e8i) q^{80} +(6.19992e7 + 1.07386e8i) q^{81} +(4.43428e7 - 7.68040e7i) q^{82} -5.26823e8 q^{83} -8.14125e8 q^{85} +(-4.63066e7 + 8.02054e7i) q^{86} +(2.95302e8 + 5.11478e8i) q^{87} +(1.15332e8 + 1.99761e8i) q^{88} +(2.59691e8 - 4.49797e8i) q^{89} +3.06326e8 q^{90} -4.39750e8 q^{92} +(2.70456e8 - 4.68444e8i) q^{93} +(-4.09546e8 - 7.09354e8i) q^{94} +(-2.58349e8 - 4.47473e8i) q^{95} +(-5.38348e7 + 9.32446e7i) q^{96} +8.75899e8 q^{97} -5.14684e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9}+O(q^{10}) $ 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9	$ 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9} - 9548 q^{11} - 834624 q^{15} - 262144 q^{16} + 254592 q^{18} - 305536 q^{22} + 2836736 q^{23} - 966144 q^{25} + 33339944 q^{29} - 6676992 q^{30} + 4194304 q^{32} + 8146944 q^{36} - 3226372 q^{37} - 69110568 q^{39} - 152960408 q^{43} - 2444288 q^{44} - 45387776 q^{46} - 30916608 q^{50} + 97261596 q^{51} - 13708112 q^{53} - 743115384 q^{57} + 266719552 q^{58} + 106831872 q^{60} + 134217728 q^{64} + 515731188 q^{65} + 814420776 q^{67} - 2649337488 q^{71} + 65175552 q^{72} + 51621952 q^{74} - 2211538176 q^{78} + 668411176 q^{79} + 1111307688 q^{81} - 3318529928 q^{85} - 1223683264 q^{86} + 39108608 q^{88} - 1452408832 q^{92} + 3706577496 q^{93} - 977188688 q^{95} - 5583163320 q^{99}+O(q^{100}) $ 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9 - 9548 * q^11 - 834624 * q^15 - 262144 * q^16 + 254592 * q^18 - 305536 * q^22 + 2836736 * q^23 - 966144 * q^25 + 33339944 * q^29 - 6676992 * q^30 + 4194304 * q^32 + 8146944 * q^36 - 3226372 * q^37 - 69110568 * q^39 - 152960408 * q^43 - 2444288 * q^44 - 45387776 * q^46 - 30916608 * q^50 + 97261596 * q^51 - 13708112 * q^53 - 743115384 * q^57 + 266719552 * q^58 + 106831872 * q^60 + 134217728 * q^64 + 515731188 * q^65 + 814420776 * q^67 - 2649337488 * q^71 + 65175552 * q^72 + 51621952 * q^74 - 2211538176 * q^78 + 668411176 * q^79 + 1111307688 * q^81 - 3318529928 * q^85 - 1223683264 * q^86 + 39108608 * q^88 - 1452408832 * q^92 + 3706577496 * q^93 - 977188688 * q^95 - 5583163320 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/98\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$	51.3408	+	88.9249i	0.365946	+	0.633838i	0.988928	−	0.148399i	$-0.0474121\pi$
$3$	51.3408	+	88.9249i	0.365946	+	0.633838i	−0.622981	+	0.782237i	$0.714079\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−1047.40	+	1814.15i	−0.749459	+	1.29810i	0.198623	+	0.980076i	$0.436353\pi$
$5$	−1047.40	+	1814.15i	−0.749459	+	1.29810i	−0.948082	+	0.318025i	$0.896980\pi$
$6$	1642.91			0.517526
$7$		0			0
$7$		0			0
$8$	−4096.00			−0.353553
$9$	4569.74	−	7915.01i	0.232167	−	0.402124i
$10$	16758.4	+	29026.4i	0.529948	+	0.917896i
$11$	−28157.2	−	48769.7i	−0.579859	−	1.00434i	−0.995495	−	0.0948139i	$-0.969774\pi$
$11$	−28157.2	−	48769.7i	−0.579859	−	1.00434i	0.415636	−	0.909531i	$-0.363559\pi$
$12$	13143.3	−	22764.8i	0.182973	−	0.316919i
$13$	−124915.			−1.21302			−0.606510	−	0.795076i	$-0.707431\pi$
$13$	−124915.			−1.21302			−0.606510	+	0.795076i	$0.707431\pi$
$14$		0			0
$15$	−215098.			−1.09705
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	194320.	+	336573.i	0.564285	+	0.977369i	0.997116	+	0.0758946i	$0.0241812\pi$
$17$	194320.	+	336573.i	0.564285	+	0.977369i	−0.432831	+	0.901475i	$0.642485\pi$
$18$	−73115.8	−	126640.i	−0.164167	−	0.284345i
$19$	−123329.	+	213611.i	−0.217106	+	0.376039i	−0.953922	−	0.300054i	$-0.902995\pi$
$19$	−123329.	+	213611.i	−0.217106	+	0.376039i	0.736816	+	0.676093i	$0.236328\pi$
$20$	536269.			0.749459
$21$		0			0
$22$	−901030.			−0.820044
$23$	858886.	−	1.48763e6i	0.639971	−	1.10846i	−0.345468	−	0.938431i	$-0.612280\pi$
$23$	858886.	−	1.48763e6i	0.639971	−	1.10846i	0.985439	−	0.170031i	$-0.0543869\pi$
$24$	−210292.	−	364237.i	−0.129382	−	0.224095i
$25$	−1.21753e6	−	2.10883e6i	−0.623378	−	1.07972i
$26$	−999317.	+	1.73087e6i	−0.428868	+	0.742821i
$27$	2.95954e6			1.07173
$28$		0			0
$29$	5.75179e6			1.51012			0.755061	−	0.655654i	$-0.227607\pi$
$29$	5.75179e6			1.51012			0.755061	+	0.655654i	$0.227607\pi$
$30$	−1.72078e6	+	2.98048e6i	−0.387865	+	0.671801i
$31$	−2.63393e6	−	4.56209e6i	−0.512243	−	0.887231i	−0.999899	−	0.0141951i	$-0.995481\pi$
$31$	−2.63393e6	−	4.56209e6i	−0.512243	−	0.887231i	0.487656	−	0.873036i	$-0.337852\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$	2.89123e6	−	5.00775e6i	0.424394	−	0.735073i
$34$	6.21825e6			0.798019
$35$		0			0
$36$	−2.33970e6			−0.232167
$37$	6.17074e6	−	1.06880e7i	0.541290	−	0.937541i	−0.457541	−	0.889189i	$-0.651270\pi$
$37$	6.17074e6	−	1.06880e7i	0.541290	−	0.937541i	0.998830	−	0.0483524i	$-0.0153971\pi$
$38$	1.97326e6	+	3.41778e6i	0.153517	+	0.265900i
$39$	−6.41322e6	−	1.11080e7i	−0.443900	−	0.768858i
$40$	4.29015e6	−	7.43076e6i	0.264974	−	0.458948i
$41$	5.54285e6			0.306342			0.153171	−	0.988200i	$-0.451052\pi$
$41$	5.54285e6			0.306342			0.153171	+	0.988200i	$0.451052\pi$
$42$		0			0
$43$	−5.78833e6			−0.258193			−0.129097	−	0.991632i	$-0.541208\pi$
$43$	−5.78833e6			−0.258193			−0.129097	+	0.991632i	$0.541208\pi$
$44$	−7.20824e6	+	1.24850e7i	−0.289929	+	0.502172i
$45$	9.57269e6	+	1.65804e7i	0.347999	+	0.602751i
$46$	−1.37422e7	−	2.38021e7i	−0.452528	−	0.783801i
$47$	2.55966e7	−	4.43346e7i	0.765142	−	1.32526i	−0.175029	−	0.984563i	$-0.556002\pi$
$47$	2.55966e7	−	4.43346e7i	0.765142	−	1.32526i	0.940171	−	0.340702i	$-0.110665\pi$
$48$	−6.72935e6			−0.182973
$49$		0			0
$50$	−3.89611e7			−0.881589
$51$	−1.99531e7	+	3.45599e7i	−0.412996	+	0.715329i
$52$	1.59891e7	+	2.76939e7i	0.303255	+	0.525253i
$53$	4.07186e7	+	7.05267e7i	0.708845	+	1.22776i	0.965286	+	0.261196i	$0.0841168\pi$
$53$	4.07186e7	+	7.05267e7i	0.708845	+	1.22776i	−0.256441	+	0.966560i	$0.582550\pi$
$54$	2.36763e7	−	4.10086e7i	0.378915	−	0.656301i
$55$	1.17967e8			1.73832
$56$		0			0
$57$	−2.53272e7			−0.317797
$58$	4.60143e7	−	7.96992e7i	0.533909	−	0.924757i
$59$	−3.92926e7	−	6.80568e7i	−0.422160	−	0.731202i	0.573991	−	0.818862i	$-0.305394\pi$
$59$	−3.92926e7	−	6.80568e7i	−0.422160	−	0.731202i	−0.996150	+	0.0876598i	$0.972061\pi$
$60$	2.75325e7	+	4.76877e7i	0.274262	+	0.475035i
$61$	6.90133e6	−	1.19535e7i	0.0638188	−	0.110537i	−0.832351	−	0.554249i	$-0.813005\pi$
$61$	6.90133e6	−	1.19535e7i	0.0638188	−	0.110537i	0.896169	+	0.443712i	$0.146339\pi$
$62$	−8.42856e7			−0.724421
$63$		0			0
$64$	1.67772e7			0.125000
$65$	1.30836e8	−	2.26614e8i	0.909109	−	1.57462i
$66$	−4.62596e7	−	8.01241e7i	−0.300092	−	0.519775i
$67$	5.08587e7	+	8.80899e7i	0.308339	+	0.534059i	0.977999	−	0.208609i	$-0.0668935\pi$
$67$	5.08587e7	+	8.80899e7i	0.308339	+	0.534059i	−0.669660	+	0.742668i	$0.733560\pi$
$68$	4.97460e7	−	8.61626e7i	0.282142	−	0.488685i
$69$	1.76384e8			0.936780
$70$		0			0
$71$	−3.75670e8			−1.75446			−0.877232	−	0.480067i	$-0.840612\pi$
$71$	−3.75670e8			−1.75446			−0.877232	+	0.480067i	$0.840612\pi$
$72$	−1.87176e7	+	3.24199e7i	−0.0820833	+	0.142172i
$73$	−2.22973e8	−	3.86200e8i	−0.918964	−	1.59169i	−0.800992	−	0.598676i	$-0.795694\pi$
$73$	−2.22973e8	−	3.86200e8i	−0.918964	−	1.59169i	−0.117972	−	0.993017i	$-0.537639\pi$
$74$	−9.87319e7	−	1.71009e8i	−0.382750	−	0.662942i
$75$	1.25018e8	−	2.16538e8i	0.456245	−	0.790240i
$76$	6.31442e7			0.217106
$77$		0			0
$78$	−2.05223e8			−0.627770
$79$	1.13312e8	−	1.96262e8i	0.327306	−	0.566911i	−0.654670	−	0.755915i	$-0.727193\pi$
$79$	1.13312e8	−	1.96262e8i	0.327306	−	0.566911i	0.981976	+	0.189004i	$0.0605258\pi$
$80$	−6.86425e7	−	1.18892e8i	−0.187365	−	0.324525i
$81$	6.19992e7	+	1.07386e8i	0.160031	+	0.277181i
$82$	4.43428e7	−	7.68040e7i	0.108308	−	0.187595i
$83$	−5.26823e8			−1.21847			−0.609233	−	0.792992i	$-0.708522\pi$
$83$	−5.26823e8			−1.21847			−0.609233	+	0.792992i	$0.708522\pi$
$84$		0			0
$85$	−8.14125e8			−1.69163
$86$	−4.63066e7	+	8.02054e7i	−0.0912851	+	0.158110i
$87$	2.95302e8	+	5.11478e8i	0.552624	+	0.957172i
$88$	1.15332e8	+	1.99761e8i	0.205011	+	0.355090i
$89$	2.59691e8	−	4.49797e8i	0.438734	−	0.759910i	−0.558858	−	0.829263i	$-0.688760\pi$
$89$	2.59691e8	−	4.49797e8i	0.438734	−	0.759910i	0.997592	+	0.0693536i	$0.0220937\pi$
$90$	3.06326e8			0.492145
$91$		0			0
$92$	−4.39750e8			−0.639971
$93$	2.70456e8	−	4.68444e8i	0.374907	−	0.649358i
$94$	−4.09546e8	−	7.09354e8i	−0.541037	−	0.937104i
$95$	−2.58349e8	−	4.47473e8i	−0.325424	−	0.563652i
$96$	−5.38348e7	+	9.32446e7i	−0.0646908	+	0.112048i
$97$	8.75899e8			1.00457			0.502286	−	0.864701i	$-0.332492\pi$
$97$	8.75899e8			1.00457			0.502286	+	0.864701i	$0.332492\pi$
$98$		0			0
$99$	−5.14684e8			−0.538495
$100$	−3.11689e8	+	5.39861e8i	−0.311689	+	0.539861i
$101$	−4.36810e6	−	7.56578e6i	−0.00417683	−	0.00723448i	0.863929	−	0.503613i	$-0.167996\pi$
$101$	−4.36810e6	−	7.56578e6i	−0.00417683	−	0.00723448i	−0.868106	+	0.496378i	$0.834663\pi$
$102$	3.19250e8	+	5.52958e8i	0.292032	+	0.505814i
$103$	4.79514e8	−	8.30543e8i	0.419792	−	0.727101i	−0.576126	−	0.817361i	$-0.695436\pi$
$103$	4.79514e8	−	8.30543e8i	0.419792	−	0.727101i	0.995918	+	0.0902597i	$0.0287697\pi$
$104$	5.11650e8			0.428868
$105$		0			0
$106$	1.30299e9			1.00246
$107$	7.42353e8	−	1.28579e9i	0.547499	−	0.948297i	−0.450946	−	0.892551i	$-0.648913\pi$
$107$	7.42353e8	−	1.28579e9i	0.547499	−	0.948297i	0.998445	−	0.0557454i	$-0.0177535\pi$
$108$	−3.78821e8	−	6.56137e8i	−0.267934	−	0.464075i
$109$	7.67650e8	+	1.32961e9i	0.520888	+	0.902204i	0.999705	+	0.0242895i	$0.00773235\pi$
$109$	7.67650e8	+	1.32961e9i	0.520888	+	0.902204i	−0.478817	+	0.877915i	$0.658934\pi$
$110$	9.43740e8	−	1.63461e9i	0.614589	−	1.06450i
$111$	1.26724e9			0.792332
$112$		0			0
$113$	3.29034e9			1.89840			0.949199	−	0.314677i	$-0.101896\pi$
$113$	3.29034e9			1.89840			0.949199	+	0.314677i	$0.101896\pi$
$114$	−2.02617e8	+	3.50943e8i	−0.112358	+	0.194610i
$115$	1.79920e9	+	3.11630e9i	0.959264	+	1.66149i
$116$	−7.36229e8	−	1.27519e9i	−0.377531	−	0.653902i
$117$	−5.70827e8	+	9.88701e8i	−0.281623	+	0.487785i
$118$	−1.25736e9			−0.597024
$119$		0			0
$120$	8.81040e8			0.387865
$121$	−4.06681e8	+	7.04392e8i	−0.172472	+	0.298731i
$122$	−1.10421e8	−	1.91255e8i	−0.0451267	−	0.0781618i
$123$	2.84575e8	+	4.92898e8i	0.112105	+	0.194171i
$124$	−6.74285e8	+	1.16790e9i	−0.256121	+	0.443615i
$125$	1.00958e9			0.369866
$126$		0			0
$127$	−5.41672e9			−1.84765			−0.923826	−	0.382814i	$-0.874955\pi$
$127$	−5.41672e9			−1.84765			−0.923826	+	0.382814i	$0.874955\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$	−2.97178e8	−	5.14727e8i	−0.0944849	−	0.163653i
$130$	−2.09337e9	−	3.62583e9i	−0.642837	−	1.11343i
$131$	−1.69396e9	+	2.93402e9i	−0.502553	+	0.870447i	0.497443	+	0.867497i	$0.334273\pi$
$131$	−1.69396e9	+	2.93402e9i	−0.502553	+	0.870447i	−0.999996	+	0.00295048i	$0.999061\pi$
$132$	−1.48031e9			−0.424394
$133$		0			0
$134$	1.62748e9			0.436057
$135$	−3.09982e9	+	5.36905e9i	−0.803221	+	1.39122i
$136$	−7.95936e8	−	1.37860e9i	−0.199505	−	0.345552i
$137$	−2.37364e9	−	4.11127e9i	−0.575669	−	0.997088i	−0.995969	−	0.0897026i	$-0.971408\pi$
$137$	−2.37364e9	−	4.11127e9i	−0.575669	−	0.997088i	0.420300	−	0.907385i	$-0.361925\pi$
$138$	1.41107e9	−	2.44404e9i	0.331202	−	0.573658i
$139$	−2.17838e9			−0.494958			−0.247479	−	0.968893i	$-0.579602\pi$
$139$	−2.17838e9			−0.494958			−0.247479	+	0.968893i	$0.579602\pi$
$140$		0			0
$141$	5.25661e9			1.12000
$142$	−3.00536e9	+	5.20544e9i	−0.620297	+	1.07439i
$143$	3.51725e9	+	6.09205e9i	0.703381	+	1.21829i
$144$	2.99482e8	+	5.18718e8i	0.0580417	+	0.100531i
$145$	−6.02443e9	+	1.04346e10i	−1.13177	+	1.96029i
$146$	−7.13512e9			−1.29961
$147$		0			0
$148$	−3.15942e9			−0.541290
$149$	5.90289e9	−	1.02241e10i	0.981129	−	1.69937i	0.323116	−	0.946360i	$-0.395270\pi$
$149$	5.90289e9	−	1.02241e10i	0.981129	−	1.69937i	0.658014	−	0.753006i	$-0.271397\pi$
$150$	−2.00030e9	−	3.46461e9i	−0.322614	−	0.558784i
$151$	3.15801e9	+	5.46983e9i	0.494330	+	0.856204i	0.999979	−	0.00653506i	$-0.00208019\pi$
$151$	3.15801e9	+	5.46983e9i	0.494330	+	0.856204i	−0.505649	+	0.862739i	$0.668747\pi$
$152$	5.05154e8	−	8.74952e8i	0.0767586	−	0.132950i
$153$	3.55197e9			0.524032
$154$		0			0
$155$	1.10351e10			1.53562
$156$	−1.64179e9	+	2.84366e9i	−0.221950	+	0.384429i
$157$	−5.15129e8	−	8.92229e8i	−0.0676655	−	0.117200i	0.830208	−	0.557454i	$-0.188222\pi$
$157$	−5.15129e8	−	8.92229e8i	−0.0676655	−	0.117200i	−0.897873	+	0.440254i	$0.854888\pi$
$158$	−1.81299e9	−	3.14019e9i	−0.231440	−	0.400866i
$159$	−4.18105e9	+	7.24180e9i	−0.518798	+	0.898585i
$160$	−2.19656e9			−0.264974
$161$		0			0
$162$	1.98397e9			0.226318
$163$	1.67465e9	−	2.90057e9i	0.185814	−	0.321840i	−0.758036	−	0.652212i	$-0.773841\pi$
$163$	1.67465e9	−	2.90057e9i	0.185814	−	0.321840i	0.943851	+	0.330373i	$0.107174\pi$
$164$	−7.09485e8	−	1.22886e9i	−0.0765854	−	0.132650i
$165$	6.05655e9	+	1.04903e10i	0.636132	+	1.10181i
$166$	−4.21458e9	+	7.29987e9i	−0.430793	+	0.746155i
$167$	−1.63487e10			−1.62652			−0.813261	−	0.581899i	$-0.802310\pi$
$167$	−1.63487e10			−1.62652			−0.813261	+	0.581899i	$0.802310\pi$
$168$		0			0
$169$	4.99917e9			0.471420
$170$	−6.51300e9	+	1.12808e10i	−0.598082	+	1.03591i
$171$	1.12716e9	+	1.95229e9i	0.100810	+	0.174607i
$172$	7.40906e8	+	1.28329e9i	0.0645483	+	0.111801i
$173$	−3.73549e9	+	6.47006e9i	−0.317059	+	0.549163i	−0.979873	−	0.199621i	$-0.936029\pi$
$173$	−3.73549e9	+	6.47006e9i	−0.317059	+	0.549163i	0.662814	+	0.748784i	$0.269362\pi$
$174$	9.44966e9			0.781528
$175$		0			0
$176$	3.69062e9			0.289929
$177$	4.03463e9	−	6.98818e9i	0.308976	−	0.535161i
$178$	−4.15505e9	−	7.19676e9i	−0.310232	−	0.537337i
$179$	3.11504e9	+	5.39540e9i	0.226790	+	0.392812i	0.956855	−	0.290566i	$-0.0938434\pi$
$179$	3.11504e9	+	5.39540e9i	0.226790	+	0.392812i	−0.730065	+	0.683378i	$0.760510\pi$
$180$	2.45061e9	−	4.24458e9i	0.173999	−	0.301376i
$181$	−5.46976e9			−0.378804			−0.189402	−	0.981900i	$-0.560655\pi$
$181$	−5.46976e9			−0.378804			−0.189402	+	0.981900i	$0.560655\pi$
$182$		0			0
$183$	1.41728e9			0.0934170
$184$	−3.51800e9	+	6.09335e9i	−0.226264	+	0.391901i
$185$	1.29265e10	+	2.23893e10i	0.811349	+	1.40530i
$186$	−4.32730e9	−	7.49510e9i	−0.265099	−	0.459165i
$187$	1.09430e10	−	1.89539e10i	0.654411	−	1.13347i
$188$	−1.31055e10			−0.765142
$189$		0			0
$190$	−8.26716e9			−0.460220
$191$	−3.46742e9	+	6.00576e9i	−0.188520	+	0.326526i	−0.944757	−	0.327772i	$-0.893702\pi$
$191$	−3.46742e9	+	6.00576e9i	−0.188520	+	0.326526i	0.756237	+	0.654298i	$0.227036\pi$
$192$	8.61356e8	+	1.49191e9i	0.0457433	+	0.0792297i
$193$	−2.08666e9	−	3.61420e9i	−0.108254	−	0.187501i	0.806809	−	0.590812i	$-0.201193\pi$
$193$	−2.08666e9	−	3.61420e9i	−0.108254	−	0.187501i	−0.915063	+	0.403311i	$0.867859\pi$
$194$	7.00720e9	−	1.21368e10i	0.355170	−	0.615173i
$195$	2.68689e10			1.33074
$196$		0			0
$197$	−3.62569e10			−1.71511			−0.857556	−	0.514391i	$-0.828018\pi$
$197$	−3.62569e10			−1.71511			−0.857556	+	0.514391i	$0.828018\pi$
$198$	−4.11747e9	+	7.13167e9i	−0.190387	+	0.329760i
$199$	8.97917e9	+	1.55524e10i	0.405880	+	0.703004i	0.994423	−	0.105461i	$-0.0336319\pi$
$199$	8.97917e9	+	1.55524e10i	0.405880	+	0.703004i	−0.588544	+	0.808465i	$0.700299\pi$
$200$	4.98702e9	+	8.63777e9i	0.220397	+	0.381739i
$201$	−5.22226e9	+	9.04522e9i	−0.225671	+	0.390874i
$202$	−1.39779e8			−0.00590693
$203$		0			0
$204$	1.02160e10			0.412996
$205$	−5.80559e9	+	1.00556e10i	−0.229591	+	0.397662i
$206$	−7.67223e9	−	1.32887e10i	−0.296838	−	0.514138i
$207$	−7.84976e9	−	1.35962e10i	−0.297160	−	0.514696i
$208$	4.09320e9	−	7.08964e9i	0.151628	−	0.262627i
$209$	1.38903e10			0.503564
$210$		0			0
$211$	6.33838e9			0.220144			0.110072	−	0.993924i	$-0.464892\pi$
$211$	6.33838e9			0.220144			0.110072	+	0.993924i	$0.464892\pi$
$212$	1.04240e10	−	1.80548e10i	0.354423	−	0.613878i
$213$	−1.92872e10	−	3.34065e10i	−0.642040	−	1.11205i
$214$	−1.18777e10	−	2.05727e10i	−0.387141	−	0.670547i
$215$	6.06270e9	−	1.05009e10i	0.193505	−	0.335161i
$216$	−1.21223e10			−0.378915
$217$		0			0
$218$	2.45648e10			0.736647
$219$	2.28952e10	−	3.96556e10i	0.672583	−	1.16495i
$220$	−1.50998e10	−	2.61537e10i	−0.434580	−	0.752715i
$221$	−2.42735e10	−	4.20429e10i	−0.684489	−	1.18557i
$222$	1.01380e10	−	1.75595e10i	0.280132	−	0.485202i
$223$	4.34746e10			1.17724			0.588619	−	0.808411i	$-0.299672\pi$
$223$	4.34746e10			1.17724			0.588619	+	0.808411i	$0.299672\pi$
$224$		0			0
$225$	−2.22552e10			−0.578910
$226$	2.63227e10	−	4.55922e10i	0.671185	−	1.16253i
$227$	−9.47436e9	−	1.64101e10i	−0.236828	−	0.410199i	0.722974	−	0.690875i	$-0.242775\pi$
$227$	−9.47436e9	−	1.64101e10i	−0.236828	−	0.410199i	−0.959802	+	0.280676i	$0.909441\pi$
$228$	3.24188e9	+	5.61509e9i	0.0794492	+	0.137610i
$229$	1.86189e10	−	3.22489e10i	0.447398	−	0.774916i	−0.550818	−	0.834626i	$-0.685684\pi$
$229$	1.86189e10	−	3.22489e10i	0.447398	−	0.774916i	0.998216	+	0.0597093i	$0.0190174\pi$
$230$	5.75743e10			1.35660
$231$		0			0
$232$	−2.35593e10			−0.533909
$233$	−9.19187e9	+	1.59208e10i	−0.204316	+	0.353886i	−0.949915	−	0.312510i	$-0.898830\pi$
$233$	−9.19187e9	+	1.59208e10i	−0.204316	+	0.353886i	0.745599	+	0.666395i	$0.232164\pi$
$234$	9.13323e9	+	1.58192e10i	0.199138	+	0.344916i
$235$	5.36198e10	+	9.28722e10i	1.14689	+	1.98646i
$236$	−1.00589e10	+	1.74225e10i	−0.211080	+	0.365601i
$237$	2.32701e10			0.479106
$238$		0			0
$239$	−3.65476e10			−0.724550			−0.362275	−	0.932071i	$-0.618000\pi$
$239$	−3.65476e10			−0.724550			−0.362275	+	0.932071i	$0.618000\pi$
$240$	7.04832e9	−	1.22081e10i	0.137131	−	0.237518i
$241$	1.42953e10	+	2.47601e10i	0.272970	+	0.472799i	0.969621	−	0.244612i	$-0.0786606\pi$
$241$	1.42953e10	+	2.47601e10i	0.272970	+	0.472799i	−0.696651	+	0.717411i	$0.745327\pi$
$242$	6.50690e9	+	1.12703e10i	0.121956	+	0.211235i
$243$	2.27601e10	−	3.94217e10i	0.418742	−	0.725283i
$244$	−3.53348e9			−0.0638188
$245$		0			0
$246$	9.10639e9			0.158540
$247$	1.54055e10	−	2.66832e10i	0.263354	−	0.456143i
$248$	1.07886e10	+	1.86863e10i	0.181105	+	0.313683i
$249$	−2.70475e10	−	4.68477e10i	−0.445893	−	0.772309i
$250$	8.07661e9	−	1.39891e10i	0.130767	−	0.226496i
$251$	1.00172e10			0.159300			0.0796499	−	0.996823i	$-0.474620\pi$
$251$	1.00172e10			0.159300			0.0796499	+	0.996823i	$0.474620\pi$
$252$		0			0
$253$	−9.67353e10			−1.48437
$254$	−4.33338e10	+	7.50563e10i	−0.653243	+	1.13145i
$255$	−4.17979e10	−	7.23960e10i	−0.619047	−	1.07222i
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	−8.48406e9	+	1.46948e10i	−0.121312	+	0.210119i	−0.920285	−	0.391248i	$-0.872044\pi$
$257$	−8.48406e9	+	1.46948e10i	−0.121312	+	0.210119i	0.798973	+	0.601367i	$0.205377\pi$
$258$	−9.50968e9			−0.133622
$259$		0			0
$260$	−6.69879e10			−0.909109
$261$	2.62842e10	−	4.55255e10i	0.350600	−	0.607257i
$262$	2.71033e10	+	4.69443e10i	0.355359	+	0.615499i
$263$	−3.53596e9	−	6.12447e9i	−0.0455729	−	0.0789346i	0.842339	−	0.538948i	$-0.181178\pi$
$263$	−3.53596e9	−	6.12447e9i	−0.0455729	−	0.0789346i	−0.887912	+	0.460013i	$0.847845\pi$
$264$	−1.18425e10	+	2.05118e10i	−0.150046	+	0.259887i
$265$	−1.70595e11			−2.12500
$266$		0			0
$267$	5.33310e10			0.642212
$268$	1.30198e10	−	2.25510e10i	0.154170	−	0.267030i
$269$	−1.84977e8	−	3.20389e8i	−0.00215393	−	0.00373072i	0.864946	−	0.501864i	$-0.167352\pi$
$269$	−1.84977e8	−	3.20389e8i	−0.00215393	−	0.00373072i	−0.867100	+	0.498133i	$0.834019\pi$
$270$	4.95972e10	+	8.59049e10i	0.567963	+	0.983741i
$271$	6.21441e10	−	1.07637e11i	0.699904	−	1.21227i	−0.268595	−	0.963253i	$-0.586559\pi$
$271$	6.21441e10	−	1.07637e11i	0.699904	−	1.21227i	0.968499	−	0.249016i	$-0.0801072\pi$
$272$	−2.54700e10			−0.282142
$273$		0			0
$274$	−7.59566e10			−0.814119
$275$	−6.85647e10	+	1.18758e11i	−0.722942	+	1.25217i
$276$	−2.25771e10	−	3.91047e10i	−0.234195	−	0.405638i
$277$	−8.48065e9	−	1.46889e10i	−0.0865506	−	0.149910i	0.819500	−	0.573079i	$-0.194251\pi$
$277$	−8.48065e9	−	1.46889e10i	−0.0865506	−	0.149910i	−0.906051	+	0.423169i	$0.860918\pi$
$278$	−1.74271e10	+	3.01846e10i	−0.174994	+	0.303098i
$279$	−4.81454e10			−0.475703
$280$		0			0
$281$	1.16441e11			1.11411			0.557053	−	0.830477i	$-0.311932\pi$
$281$	1.16441e11			1.11411			0.557053	+	0.830477i	$0.311932\pi$
$282$	4.20528e10	−	7.28377e10i	0.395981	−	0.685859i
$283$	−1.32766e10	−	2.29958e10i	−0.123041	−	0.213113i	0.797925	−	0.602757i	$-0.205931\pi$
$283$	−1.32766e10	−	2.29958e10i	−0.123041	−	0.213113i	−0.920965	+	0.389644i	$0.872598\pi$
$284$	4.80858e10	+	8.32871e10i	0.438616	+	0.759705i
$285$	2.65277e10	−	4.59473e10i	0.238176	−	0.412532i
$286$	1.12552e11			0.994731
$287$		0			0
$288$	9.58343e9			0.0820833
$289$	−1.62269e10	+	2.81058e10i	−0.136834	+	0.237004i
$290$	9.63909e10	+	1.66954e11i	0.800286	+	1.38614i
$291$	4.49694e10	+	7.78893e10i	0.367620	+	0.636736i
$292$	−5.70810e10	+	9.88671e10i	−0.459482	+	0.795846i
$293$	9.43424e8			0.00747829			0.00373915	−	0.999993i	$-0.498810\pi$
$293$	9.43424e8			0.00747829			0.00373915	+	0.999993i	$0.498810\pi$
$294$		0			0
$295$	1.64620e11			1.26557
$296$	−2.52754e10	+	4.37782e10i	−0.191375	+	0.331471i
$297$	−8.33323e10	−	1.44336e11i	−0.621455	−	1.07639i
$298$	−9.44462e10	−	1.63586e11i	−0.693763	−	1.20163i
$299$	−1.07287e11	+	1.85827e11i	−0.776298	+	1.34459i
$300$	−6.40095e10			−0.456245
$301$		0			0
$302$	1.01056e11			0.699088
$303$	4.48524e8	−	7.76867e8i	0.00305699	−	0.00529486i
$304$	−8.08246e9	−	1.39992e10i	−0.0542766	−	0.0940098i
$305$	1.44569e10	+	2.50401e10i	0.0956592	+	0.165687i
$306$	2.84158e10	−	4.92175e10i	0.185273	−	0.320903i
$307$	−2.20668e10			−0.141780			−0.0708902	−	0.997484i	$-0.522584\pi$
$307$	−2.20668e10			−0.141780			−0.0708902	+	0.997484i	$0.522584\pi$
$308$		0			0
$309$	9.84747e10			0.614485
$310$	8.82809e10	−	1.52907e11i	0.542924	−	0.940372i
$311$	−1.15121e11	−	1.99396e11i	−0.697805	−	1.20863i	−0.969226	−	0.246173i	$-0.920827\pi$
$311$	−1.15121e11	−	1.99396e11i	−0.697805	−	1.20863i	0.271421	−	0.962461i	$-0.412506\pi$
$312$	2.62686e10	+	4.54985e10i	0.156943	+	0.271832i
$313$	−7.87940e10	+	1.36475e11i	−0.464027	+	0.803719i	−0.999157	−	0.0410510i	$-0.986929\pi$
$313$	−7.87940e10	+	1.36475e11i	−0.464027	+	0.803719i	0.535130	+	0.844770i	$0.320263\pi$
$314$	−1.64841e10			−0.0956935
$315$		0			0
$316$	−5.80158e10			−0.327306
$317$	−1.20750e11	+	2.09145e11i	−0.671614	+	1.16327i	0.305832	+	0.952085i	$0.401065\pi$
$317$	−1.20750e11	+	2.09145e11i	−0.671614	+	1.16327i	−0.977446	+	0.211184i	$0.932268\pi$
$318$	6.68969e10	+	1.15869e11i	0.366846	+	0.635396i
$319$	−1.61954e11	−	2.80513e11i	−0.875658	−	1.51668i
$320$	−1.75725e10	+	3.04364e10i	−0.0936824	+	0.162263i
$321$	1.52452e11			0.801422
$322$		0			0
$323$	−9.58610e10			−0.490039
$324$	1.58718e10	−	2.74907e10i	0.0800153	−	0.138591i
$325$	1.52088e11	+	2.63424e11i	0.756170	+	1.30972i
$326$	−2.67944e10	−	4.64092e10i	−0.131391	−	0.227575i
$327$	−7.88236e10	+	1.36527e11i	−0.381234	+	0.660317i
$328$	−2.27035e10			−0.108308
$329$		0			0
$330$	1.93810e11			0.899627
$331$	−7.17683e10	+	1.24306e11i	−0.328630	+	0.569203i	−0.982240	−	0.187628i	$-0.939920\pi$
$331$	−7.17683e10	+	1.24306e11i	−0.328630	+	0.569203i	0.653611	+	0.756831i	$0.273253\pi$
$332$	6.74333e10	+	1.16798e11i	0.304616	+	0.527611i
$333$	−5.63973e10	−	9.76830e10i	−0.251339	−	0.435332i
$334$	−1.30790e11	+	2.26535e11i	−0.575062	+	0.996037i
$335$	−2.13078e11			−0.924350
$336$		0			0
$337$	1.35343e11			0.571612			0.285806	−	0.958288i	$-0.407739\pi$
$337$	1.35343e11			0.571612			0.285806	+	0.958288i	$0.407739\pi$
$338$	3.99934e10	−	6.92705e10i	0.166672	−	0.288684i
$339$	1.68929e11	+	2.92593e11i	0.694712	+	1.20328i
$340$	1.04208e11	+	1.80494e11i	0.422908	+	0.732498i
$341$	−1.48328e11	+	2.56912e11i	−0.594057	+	1.02894i
$342$	3.60690e10			0.142566
$343$		0			0
$344$	2.37090e10			0.0912851
$345$	−1.84744e11	+	3.19987e11i	−0.702078	+	1.21603i
$346$	5.97679e10	+	1.03521e11i	0.224195	+	0.388317i
$347$	−1.93747e11	−	3.35579e11i	−0.717383	−	1.24254i	−0.962033	−	0.272933i	$-0.912006\pi$
$347$	−1.93747e11	−	3.35579e11i	−0.717383	−	1.24254i	0.244650	−	0.969612i	$-0.421327\pi$
$348$	7.55973e10	−	1.30938e11i	0.276312	−	0.478586i
$349$	1.02561e11			0.370056			0.185028	−	0.982733i	$-0.440762\pi$
$349$	1.02561e11			0.370056			0.185028	+	0.982733i	$0.440762\pi$
$350$		0			0
$351$	−3.69690e11			−1.30004
$352$	2.95250e10	−	5.11387e10i	0.102506	−	0.177545i
$353$	−6.50080e9	−	1.12597e10i	−0.0222834	−	0.0385959i	0.854669	−	0.519174i	$-0.173760\pi$
$353$	−6.50080e9	−	1.12597e10i	−0.0222834	−	0.0385959i	−0.876952	+	0.480578i	$0.840427\pi$
$354$	−6.45541e10	−	1.11811e11i	−0.218479	−	0.378416i
$355$	3.93477e11	−	6.81523e11i	1.31490	−	2.27747i
$356$	−1.32962e11			−0.438734
$357$		0			0
$358$	9.96812e10			0.320730
$359$	4.27763e10	−	7.40907e10i	0.135918	−	0.235418i	−0.790030	−	0.613069i	$-0.789935\pi$
$359$	4.27763e10	−	7.40907e10i	0.135918	−	0.235418i	0.925948	+	0.377651i	$0.123268\pi$
$360$	−3.92097e10	−	6.79133e10i	−0.123036	−	0.213105i
$361$	1.30924e11	+	2.26767e11i	0.405730	+	0.702745i
$362$	−4.37581e10	+	7.57912e10i	−0.133927	+	0.231969i
$363$	−8.35174e10			−0.252463
$364$		0			0
$365$	9.34166e11			2.75490
$366$	1.13383e10	−	1.96384e10i	0.0330279	−	0.0572060i
$367$	−5.65584e10	−	9.79621e10i	−0.162742	−	0.281878i	0.773109	−	0.634273i	$-0.218701\pi$
$367$	−5.65584e10	−	9.79621e10i	−0.162742	−	0.281878i	−0.935851	+	0.352395i	$0.885367\pi$
$368$	5.62879e10	+	9.74936e10i	0.159993	+	0.277116i
$369$	2.53294e10	−	4.38718e10i	0.0711223	−	0.123187i
$370$	4.13647e11			1.14742
$371$		0			0
$372$	−1.38473e11			−0.374907
$373$	9.73594e10	−	1.68631e11i	0.260428	−	0.451075i	−0.705927	−	0.708284i	$-0.749470\pi$
$373$	9.73594e10	−	1.68631e11i	0.260428	−	0.451075i	0.966356	+	0.257209i	$0.0828029\pi$
$374$	−1.75088e11	−	3.03262e11i	−0.462738	−	0.801486i
$375$	5.18325e10	+	8.97765e10i	0.135351	+	0.234435i
$376$	−1.04844e11	+	1.81595e11i	−0.270519	+	0.468552i
$377$	−7.18483e11			−1.83181
$378$		0			0
$379$	−2.22727e11			−0.554493			−0.277247	−	0.960799i	$-0.589422\pi$
$379$	−2.22727e11			−0.554493			−0.277247	+	0.960799i	$0.589422\pi$
$380$	−6.61373e10	+	1.14553e11i	−0.162712	+	0.281826i
$381$	−2.78099e11	−	4.81682e11i	−0.676141	−	1.17111i
$382$	5.54788e10	+	9.60921e10i	0.133304	+	0.230889i
$383$	−1.68297e11	+	2.91499e11i	−0.399652	+	0.692218i	−0.993683	−	0.112224i	$-0.964202\pi$
$383$	−1.68297e11	+	2.91499e11i	−0.399652	+	0.692218i	0.594031	+	0.804443i	$0.297536\pi$
$384$	2.75634e10			0.0646908
$385$		0			0
$386$	−6.67730e10			−0.153094
$387$	−2.64511e10	+	4.58147e10i	−0.0599439	+	0.103826i
$388$	−1.12115e11	−	1.94189e11i	−0.251143	−	0.434993i
$389$	1.73950e11	+	3.01290e11i	0.385169	+	0.667132i	0.991793	−	0.127857i	$-0.0408098\pi$
$389$	1.73950e11	+	3.01290e11i	0.385169	+	0.667132i	−0.606624	+	0.794989i	$0.707476\pi$
$390$	2.14951e11	−	3.72306e11i	0.470488	−	0.814909i
$391$	6.67596e11			1.44450
$392$		0			0
$393$	−3.47877e11			−0.735630
$394$	−2.90055e11	+	5.02390e11i	−0.606384	+	1.05029i
$395$	2.37366e11	+	4.11130e11i	0.490605	+	0.849753i
$396$	6.58795e10	+	1.14107e11i	0.134624	+	0.233175i
$397$	1.37755e10	−	2.38598e10i	0.0278323	−	0.0482069i	−0.851774	−	0.523910i	$-0.824473\pi$
$397$	1.37755e10	−	2.38598e10i	0.0278323	−	0.0482069i	0.879606	+	0.475703i	$0.157806\pi$
$398$	2.87333e11			0.574001
$399$		0			0
$400$	1.59585e11			0.311689
$401$	3.10585e11	−	5.37949e11i	0.599834	−	1.03894i	−0.393011	−	0.919534i	$-0.628567\pi$
$401$	3.10585e11	−	5.37949e11i	0.599834	−	1.03894i	0.992845	−	0.119409i	$-0.0381001\pi$
$402$	8.35561e10	+	1.44723e11i	0.159574	+	0.276390i
$403$	3.29016e11	+	5.69872e11i	0.621361	+	1.07623i
$404$	−1.11823e9	+	1.93684e9i	−0.00208842	+	0.00361724i
$405$	−2.59752e11			−0.479746
$406$		0			0
$407$	−6.95003e11			−1.25549
$408$	8.17281e10	−	1.41557e11i	0.146016	−	0.252907i
$409$	7.31977e9	+	1.26782e10i	0.0129343	+	0.0224029i	0.872420	−	0.488757i	$-0.162549\pi$
$409$	7.31977e9	+	1.26782e10i	0.0129343	+	0.0224029i	−0.859486	+	0.511160i	$0.829216\pi$
$410$	9.28894e10	+	1.60889e11i	0.162345	+	0.281190i
$411$	2.43730e11	−	4.22152e11i	0.421328	−	0.729761i
$412$	−2.45511e11			−0.419792
$413$		0			0
$414$	−2.51192e11			−0.420247
$415$	5.51795e11	−	9.55736e11i	0.913190	−	1.58169i
$416$	−6.54913e10	−	1.13434e11i	−0.107217	−	0.185705i
$417$	−1.11840e11	−	1.93713e11i	−0.181128	−	0.313723i
$418$	1.11123e11	−	1.92470e11i	0.178037	−	0.308369i
$419$	−1.21505e11			−0.192589			−0.0962946	−	0.995353i	$-0.530699\pi$
$419$	−1.21505e11			−0.192589			−0.0962946	+	0.995353i	$0.530699\pi$
$420$		0			0
$421$	−5.61016e11			−0.870373			−0.435187	−	0.900340i	$-0.643318\pi$
$421$	−5.61016e11			−0.870373			−0.435187	+	0.900340i	$0.643318\pi$
$422$	5.07071e10	−	8.78272e10i	0.0778328	−	0.134810i
$423$	−2.33939e11	−	4.05195e11i	−0.355281	−	0.615365i
$424$	−1.66783e11	−	2.88877e11i	−0.250615	−	0.434077i
$425$	4.73183e11	−	8.19578e11i	0.703525	−	1.21854i
$426$	−6.17192e11			−0.907981
$427$		0			0
$428$	−3.80085e11			−0.547499
$429$	−3.61157e11	+	6.25542e11i	−0.514799	+	0.891658i
$430$	−9.70032e10	−	1.68014e11i	−0.136829	−	0.236995i
$431$	−5.22159e11	−	9.04405e11i	−0.728878	−	1.26245i	−0.957358	−	0.288905i	$-0.906709\pi$
$431$	−5.22159e11	−	9.04405e11i	−0.728878	−	1.26245i	0.228480	−	0.973549i	$-0.426624\pi$
$432$	−9.69782e10	+	1.67971e11i	−0.133967	+	0.232037i
$433$	1.05446e12			1.44156			0.720781	−	0.693163i	$-0.243784\pi$
$433$	1.05446e12			1.44156			0.720781	+	0.693163i	$0.243784\pi$
$434$		0			0
$435$	−1.23720e12			−1.65668
$436$	1.96518e11	−	3.40380e11i	0.260444	−	0.451102i
$437$	2.11850e11	+	3.66935e11i	0.277883	+	0.481308i
$438$	−3.66323e11	−	6.34490e11i	−0.475588	−	0.823743i
$439$	−5.85184e11	+	1.01357e12i	−0.751973	+	1.30245i	0.194893	+	0.980825i	$0.437564\pi$
$439$	−5.85184e11	+	1.01357e12i	−0.751973	+	1.30245i	−0.946865	+	0.321630i	$0.895769\pi$
$440$	−4.83195e11			−0.614589
$441$		0			0
$442$	−7.76751e11			−0.968014
$443$	3.55330e11	−	6.15449e11i	0.438344	−	0.759234i	−0.559218	−	0.829021i	$-0.688899\pi$
$443$	3.55330e11	−	6.15449e11i	0.438344	−	0.759234i	0.997562	+	0.0697869i	$0.0222319\pi$
$444$	−1.62207e11	−	2.80951e11i	−0.198083	−	0.343090i
$445$	5.44000e11	+	9.42236e11i	0.657626	+	1.13904i
$446$	3.47797e11	−	6.02402e11i	0.416216	−	0.720908i
$447$	1.21224e12			1.43616
$448$		0			0
$449$	9.40485e11			1.09205			0.546026	−	0.837768i	$-0.316140\pi$
$449$	9.40485e11			1.09205			0.546026	+	0.837768i	$0.316140\pi$
$450$	−1.78042e11	+	3.08378e11i	−0.204676	+	0.354508i
$451$	−1.56071e11	−	2.70323e11i	−0.177635	−	0.307673i
$452$	−4.21163e11	−	7.29476e11i	−0.474599	−	0.822030i
$453$	−3.24269e11	+	5.61651e11i	−0.361796	+	0.626650i
$454$	−3.03180e11			−0.334926
$455$		0			0
$456$	1.03740e11			0.112358
$457$	5.75413e11	−	9.96644e11i	0.617102	−	1.06885i	−0.372910	−	0.927867i	$-0.621640\pi$
$457$	5.75413e11	−	9.96644e11i	0.617102	−	1.06885i	0.990012	−	0.140984i	$-0.0450266\pi$
$458$	−2.97902e11	−	5.15982e11i	−0.316358	−	0.547949i
$459$	5.75099e11	+	9.96100e11i	0.604763	+	1.04748i
$460$	4.60594e11	−	7.97772e11i	0.479632	−	0.830747i
$461$	2.66471e11			0.274786			0.137393	−	0.990517i	$-0.456128\pi$
$461$	2.66471e11			0.274786			0.137393	+	0.990517i	$0.456128\pi$
$462$		0			0
$463$	−4.48766e11			−0.453843			−0.226921	−	0.973913i	$-0.572866\pi$
$463$	−4.48766e11			−0.453843			−0.226921	+	0.973913i	$0.572866\pi$
$464$	−1.88475e11	+	3.26448e11i	−0.188765	+	0.326951i
$465$	5.66552e11	+	9.81296e11i	0.561955	+	0.973334i
$466$	1.47070e11	+	2.54733e11i	0.144473	+	0.250235i
$467$	8.89076e11	−	1.53992e12i	0.864993	−	1.49821i	−0.00206063	−	0.999998i	$-0.500656\pi$
$467$	8.89076e11	−	1.53992e12i	0.864993	−	1.49821i	0.867054	−	0.498214i	$-0.166011\pi$
$468$	2.92263e11			0.281623
$469$		0			0
$470$	1.71583e12			1.62194
$471$	5.28943e10	−	9.16156e10i	0.0495239	−	0.0857779i
$472$	1.60942e11	+	2.78761e11i	0.149256	+	0.258519i
$473$	1.62983e11	+	2.82295e11i	0.149716	+	0.259315i
$474$	1.86161e11	−	3.22441e11i	0.169389	−	0.293391i
$475$	6.00627e11			0.541357
$476$		0			0
$477$	7.44293e11			0.658281
$478$	−2.92381e11	+	5.06418e11i	−0.256167	+	0.443694i
$479$	−9.94531e11	−	1.72258e12i	−0.863194	−	1.49510i	−0.868829	−	0.495112i	$-0.835127\pi$
$479$	−9.94531e11	−	1.72258e12i	−0.863194	−	1.49510i	0.00563474	−	0.999984i	$-0.498206\pi$
$480$	−1.12773e11	−	1.95329e11i	−0.0969662	−	0.167950i
$481$	−7.70816e11	+	1.33509e12i	−0.656596	+	1.13726i
$482$	4.57448e11			0.386038
$483$		0			0
$484$	2.08221e11			0.172472
$485$	−9.17418e11	+	1.58901e12i	−0.752886	+	1.30404i
$486$	−3.64162e11	−	6.30747e11i	−0.296095	−	0.512852i
$487$	−3.44296e11	−	5.96338e11i	−0.277365	−	0.480410i	0.693364	−	0.720588i	$-0.256128\pi$
$487$	−3.44296e11	−	5.96338e11i	−0.277365	−	0.480410i	−0.970729	+	0.240177i	$0.922794\pi$
$488$	−2.82679e10	+	4.89614e10i	−0.0225634	+	0.0390809i
$489$	3.43911e11			0.271992
$490$		0			0
$491$	1.86881e12			1.45111			0.725553	−	0.688166i	$-0.241584\pi$
$491$	1.86881e12			1.45111			0.725553	+	0.688166i	$0.241584\pi$
$492$	7.28512e10	−	1.26182e11i	0.0560523	−	0.0970854i
$493$	1.11769e12	+	1.93590e12i	0.852139	+	1.47595i
$494$	−2.46489e11	−	4.26931e11i	−0.186220	−	0.322542i
$495$	5.39080e11	−	9.33714e11i	0.403580	−	0.699022i
$496$	3.45234e11			0.256121
$497$		0			0
$498$	−8.65521e11			−0.630588
$499$	4.38705e11	−	7.59860e11i	0.316753	−	0.548632i	−0.663056	−	0.748570i	$-0.730741\pi$
$499$	4.38705e11	−	7.59860e11i	0.316753	−	0.548632i	0.979809	+	0.199938i	$0.0640741\pi$
$500$	−1.29226e11	−	2.23826e11i	−0.0924664	−	0.160157i
$501$	−8.39358e11	−	1.45381e12i	−0.595220	−	1.03095i
$502$	8.01377e10	−	1.38803e11i	0.0563210	−	0.0975508i
$503$	2.12177e11			0.147789			0.0738945	−	0.997266i	$-0.476457\pi$
$503$	2.12177e11			0.147789			0.0738945	+	0.997266i	$0.476457\pi$
$504$		0			0
$505$	1.83006e10			0.0125215
$506$	−7.73882e11	+	1.34040e12i	−0.524804	+	0.908988i
$507$	2.56662e11	+	4.44551e11i	0.172514	+	0.298804i
$508$	6.93341e11	+	1.20090e12i	0.461913	+	0.800056i
$509$	−9.14357e11	+	1.58371e12i	−0.603790	+	1.04579i	0.388452	+	0.921469i	$0.373010\pi$
$509$	−9.14357e11	+	1.58371e12i	−0.603790	+	1.04579i	−0.992242	+	0.124325i	$0.960323\pi$
$510$	−1.33753e12			−0.875464
$511$		0			0
$512$	−6.87195e10			−0.0441942
$513$	−3.64996e11	+	6.32191e11i	−0.232680	+	0.403014i
$514$	1.35745e11	+	2.35117e11i	0.0857807	+	0.148577i
$515$	1.00449e12	+	1.73982e12i	0.629234	+	1.08986i
$516$	−7.60775e10	+	1.31770e11i	−0.0472424	+	0.0818263i
$517$	−2.88291e12			−1.77470
$518$		0			0
$519$	−7.67134e11			−0.464107
$520$	−5.35903e11	+	9.28211e11i	−0.321419	+	0.556714i
$521$	1.34178e12	+	2.32404e12i	0.797834	+	1.38189i	0.921024	+	0.389506i	$0.127354\pi$
$521$	1.34178e12	+	2.32404e12i	0.797834	+	1.38189i	−0.123190	+	0.992383i	$0.539312\pi$
$522$	−4.20547e11	−	7.28408e11i	−0.247912	−	0.429396i
$523$	4.53722e11	−	7.85869e11i	0.265175	−	0.459296i	−0.702435	−	0.711748i	$-0.747904\pi$
$523$	4.53722e11	−	7.85869e11i	0.265175	−	0.459296i	0.967609	+	0.252452i	$0.0812370\pi$
$524$	8.67307e11			0.502553
$525$		0			0
$526$	−1.13151e11			−0.0644498
$527$	1.02365e12	−	1.77302e12i	0.578102	−	1.00130i
$528$	1.89480e11	+	3.28188e11i	0.106099	+	0.183768i
$529$	−5.74794e11	−	9.95572e11i	−0.319125	−	0.552741i
$530$	−1.36476e12	+	2.36383e12i	−0.751301	+	1.30129i
$531$	−7.18227e11			−0.392046
$532$		0			0
$533$	−6.92384e11			−0.371599
$534$	4.26648e11	−	7.38975e11i	0.227056	−	0.393273i
$535$	1.55508e12	+	2.69348e12i	0.820657	+	1.42142i
$536$	−2.08317e11	−	3.60816e11i	−0.109014	−	0.188818i
$537$	−3.19857e11	+	5.54009e11i	−0.165986	+	0.287497i
$538$	−5.91926e9			−0.00304612
$539$		0			0
$540$	1.58711e12			0.803221
$541$	2.41567e11	−	4.18407e11i	0.121241	−	0.209996i	−0.799016	−	0.601310i	$-0.794646\pi$
$541$	2.41567e11	−	4.18407e11i	0.121241	−	0.209996i	0.920257	+	0.391314i	$0.127979\pi$
$542$	−9.94306e11	−	1.72219e12i	−0.494907	−	0.857204i
$543$	−2.80822e11	−	4.86398e11i	−0.138622	−	0.240100i
$544$	−2.03760e11	+	3.52922e11i	−0.0997524	+	0.172776i
$545$	−3.21615e12			−1.56154
$546$		0			0
$547$	2.24340e12			1.07143			0.535716	−	0.844398i	$-0.320042\pi$
$547$	2.24340e12			1.07143			0.535716	+	0.844398i	$0.320042\pi$
$548$	−6.07653e11	+	1.05249e12i	−0.287835	+	0.498544i
$549$	−6.30745e10	−	1.09248e11i	−0.0296332	−	0.0513262i
$550$	1.09704e12	+	1.90012e12i	0.511197	+	0.885419i
$551$	−7.09360e11	+	1.22865e12i	−0.327857	+	0.567865i
$552$	−7.22468e11			−0.331202
$553$		0			0
$554$	−2.71381e11			−0.122401
$555$	−1.32731e12	+	2.29897e12i	−0.593820	+	1.02853i
$556$	2.78833e11	+	4.82953e11i	0.123739	+	0.214323i
$557$	−3.62305e11	−	6.27530e11i	−0.159487	−	0.276240i	0.775197	−	0.631720i	$-0.217651\pi$
$557$	−3.62305e11	−	6.27530e11i	−0.159487	−	0.276240i	−0.934684	+	0.355480i	$0.884317\pi$
$558$	−3.85163e11	+	6.67122e11i	−0.168186	+	0.291307i
$559$	7.23047e11			0.313194
$560$		0			0
$561$	2.24730e12			0.957917
$562$	9.31526e11	−	1.61345e12i	0.393896	−	0.682248i
$563$	−2.10927e12	−	3.65336e12i	−0.884799	−	1.53252i	−0.845944	−	0.533271i	$-0.820962\pi$
$563$	−2.10927e12	−	3.65336e12i	−0.884799	−	1.53252i	−0.0388545	−	0.999245i	$-0.512371\pi$
$564$	−6.72846e11	−	1.16540e12i	−0.280001	−	0.484976i
$565$	−3.44630e12	+	5.96917e12i	−1.42277	+	2.46431i
$566$	−4.24852e11			−0.174006
$567$		0			0
$568$	1.53875e12			0.620297
$569$	−2.17405e12	+	3.76556e12i	−0.869488	+	1.50600i	−0.00696716	+	0.999976i	$0.502218\pi$
$569$	−2.17405e12	+	3.76556e12i	−0.869488	+	1.50600i	−0.862521	+	0.506022i	$0.831116\pi$
$570$	−4.24443e11	−	7.35157e11i	−0.168416	−	0.291704i
$571$	1.12302e12	+	1.94512e12i	0.442103	+	0.765745i	0.997845	−	0.0656099i	$-0.0208993\pi$
$571$	1.12302e12	+	1.94512e12i	0.442103	+	0.765745i	−0.555743	+	0.831354i	$0.687566\pi$
$572$	9.00415e11	−	1.55956e12i	0.351690	−	0.609146i
$573$	−7.12082e11			−0.275952
$574$		0			0
$575$	−4.18289e12			−1.59577
$576$	7.66674e10	−	1.32792e11i	0.0290208	−	0.0502655i
$577$	−1.32414e12	−	2.29348e12i	−0.497328	−	0.861397i	0.502668	−	0.864480i	$-0.332352\pi$
$577$	−1.32414e12	−	2.29348e12i	−0.497328	−	0.861397i	−0.999995	+	0.00308304i	$0.999019\pi$
$578$	2.59630e11	+	4.49692e11i	0.0967563	+	0.167587i
$579$	2.14261e11	−	3.71112e11i	0.0792302	−	0.137231i
$580$	3.08451e12			1.13177
$581$		0			0
$582$	1.43902e12			0.519893
$583$	2.29304e12	−	3.97167e12i	0.822060	−	1.42385i
$584$	9.13296e11	+	1.58187e12i	0.324903	+	0.562748i
$585$	−1.19577e12	−	2.07113e12i	−0.422130	−	0.731150i
$586$	7.54739e9	−	1.30725e10i	0.00264398	−	0.00457950i
$587$	2.72201e12			0.946276			0.473138	−	0.880988i	$-0.343121\pi$
$587$	2.72201e12			0.946276			0.473138	+	0.880988i	$0.343121\pi$
$588$		0			0
$589$	1.29935e12			0.444845
$590$	1.31696e12	−	2.28105e12i	0.447445	−	0.774997i
$591$	−1.86146e12	−	3.22414e12i	−0.627639	−	1.08710i
$592$	4.04406e11	+	7.00451e11i	0.135322	+	0.234385i
$593$	1.07809e11	−	1.86731e11i	0.0358023	−	0.0620114i	−0.847569	−	0.530685i	$-0.821935\pi$
$593$	1.07809e11	−	1.86731e11i	0.0358023	−	0.0620114i	0.883371	+	0.468674i	$0.155268\pi$
$594$	−2.66663e12			−0.878870
$595$		0			0
$596$	−3.02228e12			−0.981129
$597$	−9.21996e11	+	1.59694e12i	−0.297060	+	0.514524i
$598$	1.71660e12	+	2.97324e12i	0.548926	+	0.950767i
$599$	5.59513e11	+	9.69105e11i	0.177578	+	0.307574i	0.941050	−	0.338266i	$-0.109840\pi$
$599$	5.59513e11	+	9.69105e11i	0.177578	+	0.307574i	−0.763472	+	0.645841i	$0.776507\pi$
$600$	−5.12076e11	+	8.86941e11i	−0.161307	+	0.279392i
$601$	−2.89926e12			−0.906467			−0.453234	−	0.891392i	$-0.649730\pi$
$601$	−2.89926e12			−0.906467			−0.453234	+	0.891392i	$0.649730\pi$
$602$		0			0
$603$	9.29643e11			0.286344
$604$	8.08450e11	−	1.40028e12i	0.247165	−	0.428102i
$605$	−8.51916e11	−	1.47556e12i	−0.258522	−	0.447773i
$606$	−7.17639e9	−	1.24299e10i	−0.00216162	−	0.00374403i
$607$	8.83626e11	−	1.53049e12i	0.264192	−	0.457594i	−0.703160	−	0.711032i	$-0.748228\pi$
$607$	8.83626e11	−	1.53049e12i	0.264192	−	0.457594i	0.967352	+	0.253438i	$0.0815614\pi$
$608$	−2.58639e11			−0.0767586
$609$		0			0
$610$	4.62622e11			0.135283
$611$	−3.19739e12	+	5.53804e12i	−0.928133	+	1.60757i
$612$	−4.54652e11	−	7.87481e11i	−0.131008	−	0.226913i
$613$	3.97147e11	+	6.87878e11i	0.113600	+	0.196761i	0.917219	−	0.398383i	$-0.130428\pi$
$613$	3.97147e11	+	6.87878e11i	0.113600	+	0.196761i	−0.803619	+	0.595144i	$0.797095\pi$
$614$	−1.76534e11	+	3.05766e11i	−0.0501269	+	0.0868224i
$615$	−1.19226e12			−0.336071
$616$		0			0
$617$	3.17799e12			0.882815			0.441407	−	0.897307i	$-0.354479\pi$
$617$	3.17799e12			0.882815			0.441407	+	0.897307i	$0.354479\pi$
$618$	7.87797e11	−	1.36451e12i	0.217253	−	0.376294i
$619$	3.29763e12	+	5.71166e12i	0.902804	+	1.56370i	0.823838	+	0.566826i	$0.191829\pi$
$619$	3.29763e12	+	5.71166e12i	0.902804	+	1.56370i	0.0789670	+	0.996877i	$0.474838\pi$
$620$	−1.41249e12	−	2.44651e12i	−0.383905	−	0.664943i
$621$	2.54191e12	−	4.40271e12i	0.685879	−	1.18798i
$622$	−3.68388e12			−0.986845
$623$		0			0
$624$	8.40594e11			0.221950
$625$	1.32057e12	−	2.28729e12i	0.346178	−	0.599598i
$626$	1.26070e12	+	2.18360e12i	0.328117	+	0.568315i
$627$	7.13142e11	+	1.23520e12i	0.184277	+	0.319178i
$628$	−1.31873e11	+	2.28411e11i	−0.0338328	+	0.0586000i
$629$	4.79640e12			1.22177
$630$		0			0
$631$	−5.22143e12			−1.31117			−0.655583	−	0.755123i	$-0.727577\pi$
$631$	−5.22143e12			−1.31117			−0.655583	+	0.755123i	$0.727577\pi$
$632$	−4.64126e11	+	8.03890e11i	−0.115720	+	0.200433i
$633$	3.25418e11	+	5.63640e11i	0.0805610	+	0.139536i
$634$	1.93200e12	+	3.34632e12i	0.474903	+	0.822556i
$635$	5.67348e12	−	9.82676e12i	1.38474	−	2.39844i
$636$	2.14070e12			0.518798
$637$		0			0
$638$	−5.18254e12			−1.23837
$639$	−1.71671e12	+	2.97344e12i	−0.407328	+	0.705513i
$640$	2.81160e11	+	4.86983e11i	0.0662434	+	0.114737i
$641$	−1.84863e12	−	3.20193e12i	−0.432504	−	0.749119i	0.564584	−	0.825375i	$-0.309036\pi$
$641$	−1.84863e12	−	3.20193e12i	−0.432504	−	0.749119i	−0.997088	+	0.0762567i	$0.975703\pi$
$642$	1.21962e12	−	2.11244e12i	0.283345	−	0.490768i
$643$	5.23082e12			1.20676			0.603379	−	0.797455i	$-0.293821\pi$
$643$	5.23082e12			1.20676			0.603379	+	0.797455i	$0.293821\pi$
$644$		0			0
$645$	1.24506e12			0.283250
$646$	−7.66888e11	+	1.32829e12i	−0.173255	+	0.300086i
$647$	−1.46236e12	−	2.53289e12i	−0.328085	−	0.568260i	0.654047	−	0.756454i	$-0.273070\pi$
$647$	−1.46236e12	−	2.53289e12i	−0.328085	−	0.568260i	−0.982132	+	0.188194i	$0.939737\pi$
$648$	−2.53949e11	−	4.39852e11i	−0.0565794	−	0.0979984i
$649$	−2.21274e12	+	3.83258e12i	−0.489586	+	0.847988i
$650$	4.86681e12			1.06939
$651$		0			0
$652$	−8.57420e11			−0.185814
$653$	2.16021e11	−	3.74160e11i	0.0464930	−	0.0805282i	−0.841842	−	0.539723i	$-0.818529\pi$
$653$	2.16021e11	−	3.74160e11i	0.0464930	−	0.0805282i	0.888335	+	0.459195i	$0.151862\pi$
$654$	1.26118e12	+	2.18442e12i	0.269573	+	0.466914i
$655$	−3.54851e12	−	6.14619e12i	−0.753286	−	1.30473i
$656$	−1.81628e11	+	3.14589e11i	−0.0382927	+	0.0663249i
$657$	−4.07570e12			−0.853411
$658$		0			0
$659$	−6.16777e12			−1.27393			−0.636963	−	0.770894i	$-0.719810\pi$
$659$	−6.16777e12			−1.27393			−0.636963	+	0.770894i	$0.719810\pi$
$660$	1.55048e12	−	2.68550e12i	0.318066	−	0.550907i
$661$	−1.12686e12	−	1.95179e12i	−0.229596	−	0.397672i	0.728092	−	0.685479i	$-0.240407\pi$
$661$	−1.12686e12	−	1.95179e12i	−0.229596	−	0.397672i	−0.957689	+	0.287807i	$0.907074\pi$
$662$	1.14829e12	+	1.98890e12i	0.232376	+	0.402487i
$663$	2.49244e12	−	4.31703e12i	0.500972	−	0.867710i
$664$	2.15787e12			0.430793
$665$		0			0
$666$	−1.80471e12			−0.355447
$667$	4.94013e12	−	8.55656e12i	0.966434	−	1.67391i
$668$	2.09264e12	+	3.62456e12i	0.406631	+	0.704305i
$669$	2.23202e12	+	3.86598e12i	0.430806	+	0.746177i
$670$	−1.70462e12	+	2.95249e12i	−0.326807	+	0.566047i
$671$	−7.77289e11			−0.148024
$672$		0			0
$673$	4.91498e12			0.923536			0.461768	−	0.887001i	$-0.347215\pi$
$673$	4.91498e12			0.923536			0.461768	+	0.887001i	$0.347215\pi$
$674$	1.08274e12	−	1.87537e12i	0.202095	−	0.350039i
$675$	−3.60334e12	−	6.24117e12i	−0.668095	−	1.15718i
$676$	−6.39894e11	−	1.10833e12i	−0.117855	−	0.204131i
$677$	5.04615e11	−	8.74019e11i	0.0923233	−	0.159909i	−0.816165	−	0.577819i	$-0.803904\pi$
$677$	5.04615e11	−	8.74019e11i	0.0923233	−	0.159909i	0.908488	+	0.417910i	$0.137237\pi$
$678$	5.40571e12			0.982470
$679$		0			0
$680$	3.33466e12			0.598082
$681$	9.72844e11	−	1.68501e12i	0.173333	−	0.300221i
$682$	2.37325e12	+	4.11058e12i	0.420062	+	0.727569i
$683$	1.16806e12	+	2.02313e12i	0.205386	+	0.355739i	0.950256	−	0.311471i	$-0.100822\pi$
$683$	1.16806e12	+	2.02313e12i	0.205386	+	0.355739i	−0.744870	+	0.667210i	$0.767488\pi$
$684$	2.88552e11	−	4.99787e11i	0.0504048	−	0.0873037i
$685$	9.94462e12			1.72576
$686$		0			0
$687$	3.82364e12			0.654895
$688$	1.89672e11	−	3.28521e11i	0.0322742	−	0.0559005i
$689$	−5.08635e12	−	8.80981e12i	−0.859844	−	1.48929i
$690$	2.95591e12	+	5.11979e12i	0.496444	+	0.859867i
$691$	5.53942e12	−	9.59456e12i	0.924300	−	1.60094i	0.131618	−	0.991301i	$-0.457983\pi$
$691$	5.53942e12	−	9.59456e12i	0.924300	−	1.60094i	0.792683	−	0.609635i	$-0.208684\pi$
$692$	1.91257e12			0.317059
$693$		0			0
$694$	−6.19989e12			−1.01453
$695$	2.28164e12	−	3.95192e12i	0.370950	−	0.642505i
$696$	−1.20956e12	−	2.09501e12i	−0.195382	−	0.338412i
$697$	1.07709e12	+	1.86557e12i	0.172864	+	0.299409i
$698$	8.20488e11	−	1.42113e12i	0.130835	−	0.226612i
$699$	−1.88767e12			−0.299075
$700$		0			0
$701$	8.11682e11			0.126956			0.0634782	−	0.997983i	$-0.479781\pi$
$701$	8.11682e11			0.126956			0.0634782	+	0.997983i	$0.479781\pi$
$702$	−2.95752e12	+	5.12257e12i	−0.459632	+	0.796107i
$703$	1.52206e12	+	2.63628e12i	0.235035	+	0.407092i
$704$	−4.72399e11	−	8.18220e11i	−0.0724823	−	0.125543i
$705$	−5.50577e12	+	9.53628e12i	−0.839397	+	1.45388i
$706$	−2.08026e11			−0.0315134
$707$		0			0
$708$	−2.06573e12			−0.308976
$709$	−4.48490e12	+	7.76807e12i	−0.666568	+	1.15453i	0.312289	+	0.949987i	$0.398904\pi$
$709$	−4.48490e12	+	7.76807e12i	−0.666568	+	1.15453i	−0.978858	+	0.204543i	$0.934429\pi$
$710$	−6.29564e12	−	1.09044e13i	−0.929774	−	1.61042i
$711$	−1.03561e12	−	1.79373e12i	−0.151979	−	0.263236i
$712$	−1.06369e12	+	1.84237e12i	−0.155116	+	0.268669i
$713$	−9.04897e12			−1.31128
$714$		0			0
$715$	−1.47359e13			−2.10862
$716$	7.97450e11	−	1.38122e12i	0.113395	−	0.196406i
$717$	−1.87638e12	−	3.24999e12i	−0.265146	−	0.459247i
$718$	−6.84421e11	−	1.18545e12i	−0.0961088	−	0.166465i
$719$	5.27879e12	−	9.14313e12i	0.736638	−	1.27590i	−0.217362	−	0.976091i	$-0.569745\pi$
$719$	5.27879e12	−	9.14313e12i	0.736638	−	1.27590i	0.954001	−	0.299804i	$-0.0969213\pi$
$720$	−1.25471e12			−0.173999
$721$		0			0
$722$	4.18957e12			0.573789
$723$	−1.46786e12	+	2.54241e12i	−0.199785	+	0.346038i
$724$	7.00129e11	+	1.21266e12i	0.0947010	+	0.164027i
$725$	−7.00300e12	−	1.21296e13i	−0.941377	−	1.63051i
$726$	−6.68139e11	+	1.15725e12i	−0.0892590	+	0.154601i
$727$	−2.48043e12			−0.329323			−0.164661	−	0.986350i	$-0.552653\pi$
$727$	−2.48043e12			−0.329323			−0.164661	+	0.986350i	$0.552653\pi$
$728$		0			0
$729$	7.11476e12			0.933010
$730$	7.47333e12	−	1.29442e13i	0.974005	−	1.68703i
$731$	−1.12479e12	−	1.94819e12i	−0.145695	−	0.252350i
$732$	−1.81412e11	−	3.14215e11i	−0.0233543	−	0.0404508i
$733$	−4.97539e12	+	8.61763e12i	−0.636589	+	1.10260i	0.349587	+	0.936904i	$0.386322\pi$
$733$	−4.97539e12	+	8.61763e12i	−0.636589	+	1.10260i	−0.986176	+	0.165701i	$0.947011\pi$
$734$	−1.80987e12			−0.230152
$735$		0			0
$736$	1.80121e12			0.226264
$737$	2.86408e12	−	4.96073e12i	0.357586	−	0.619358i
$738$	−4.05270e11	−	7.01948e11i	−0.0502911	−	0.0871067i
$739$	1.76100e12	+	3.05015e12i	0.217200	+	0.376202i	0.953951	−	0.299963i	$-0.0969742\pi$
$739$	1.76100e12	+	3.05015e12i	0.217200	+	0.376202i	−0.736751	+	0.676164i	$0.763641\pi$
$740$	3.30918e12	−	5.73167e12i	0.405674	−	0.702649i
$741$	3.16373e12			0.385494
$742$		0			0
$743$	−1.25259e13			−1.50786			−0.753930	−	0.656955i	$-0.771844\pi$
$743$	−1.25259e13			−1.50786			−0.753930	+	0.656955i	$0.771844\pi$
$744$	−1.10779e12	+	1.91874e12i	−0.132550	+	0.229583i
$745$	1.23654e13	+	2.14175e13i	1.47063	+	2.54721i
$746$	−1.55775e12	−	2.69810e12i	−0.184151	−	0.318958i
$747$	−2.40744e12	+	4.16981e12i	−0.282887	+	0.489975i
$748$	−5.60283e12			−0.654411
$749$		0			0
$750$	1.65864e12			0.191415
$751$	−3.45930e12	+	5.99168e12i	−0.396833	+	0.687335i	−0.993333	−	0.115278i	$-0.963224\pi$
$751$	−3.45930e12	+	5.99168e12i	−0.396833	+	0.687335i	0.596500	+	0.802613i	$0.296558\pi$
$752$	1.67750e12	+	2.90551e12i	0.191286	+	0.331316i
$753$	5.14292e11	+	8.90780e11i	0.0582951	+	0.100970i
$754$	−5.74786e12	+	9.95559e12i	−0.647643	+	1.12175i
$755$	−1.32308e13			−1.48192
$756$		0			0
$757$	−2.68669e12			−0.297362			−0.148681	−	0.988885i	$-0.547503\pi$
$757$	−2.68669e12			−0.297362			−0.148681	+	0.988885i	$0.547503\pi$
$758$	−1.78182e12	+	3.08620e12i	−0.196043	+	0.339556i
$759$	−4.96647e12	−	8.60218e12i	−0.543200	−	0.940850i
$760$	1.05820e12	+	1.83285e12i	0.115055	+	0.199281i
$761$	2.27106e12	−	3.93360e12i	0.245470	−	0.425166i	−0.716794	−	0.697285i	$-0.754391\pi$
$761$	2.27106e12	−	3.93360e12i	0.245470	−	0.425166i	0.962264	+	0.272119i	$0.0877244\pi$
$762$	−8.89917e12			−0.956208
$763$		0			0
$764$	1.77532e12			0.188520
$765$	−3.72034e12	+	6.44381e12i	−0.392741	+	0.680247i
$766$	2.69276e12	+	4.66399e12i	0.282597	+	0.489472i
$767$	4.90822e12	+	8.50129e12i	0.512088	+	0.886963i
$768$	2.20507e11	−	3.81930e11i	0.0228716	−	0.0396148i
$769$	2.34852e12			0.242173			0.121087	−	0.992642i	$-0.461362\pi$
$769$	2.34852e12			0.242173			0.121087	+	0.992642i	$0.461362\pi$
$770$		0			0
$771$	−1.74232e12			−0.177575
$772$	−5.34184e11	+	9.25234e11i	−0.0541269	+	0.0937506i
$773$	1.89097e11	+	3.27525e11i	0.0190492	+	0.0329941i	0.875393	−	0.483412i	$-0.160603\pi$
$773$	1.89097e11	+	3.27525e11i	0.0190492	+	0.0329941i	−0.856344	+	0.516406i	$0.827269\pi$
$774$	4.23218e11	+	7.33035e11i	0.0423867	+	0.0734160i
$775$	−6.41379e12	+	1.11090e13i	−0.638642	+	1.10616i
$776$	−3.58768e12			−0.355170
$777$		0			0
$778$	5.56640e12			0.544711
$779$	−6.83592e11	+	1.18402e12i	−0.0665087	+	0.115196i
$780$	−3.43921e12	−	5.95689e12i	−0.332685	−	0.576228i
$781$	1.05778e13	+	1.83213e13i	1.01734	+	1.76209i
$782$	5.34077e12	−	9.25048e12i	0.510709	−	0.884574i
$783$	1.70227e13			1.61845
$784$		0			0
$785$	2.15818e12			0.202850
$786$	−2.78302e12	+	4.82032e12i	−0.260084	+	0.450479i
$787$	6.05426e12	+	1.04863e13i	0.562568	+	0.974396i	0.997271	+	0.0738222i	$0.0235197\pi$
$787$	6.05426e12	+	1.04863e13i	0.562568	+	0.974396i	−0.434704	+	0.900573i	$0.643147\pi$
$788$	4.64088e12	+	8.03824e12i	0.428778	+	0.742665i
$789$	3.63079e11	−	6.28870e11i	0.0333545	−	0.0577716i
$790$	7.59572e12			0.693820
$791$		0			0
$792$	2.10814e12			0.190387
$793$	−8.62078e11	+	1.49316e12i	−0.0774136	+	0.134084i
$794$	−2.20407e11	−	3.81757e11i	−0.0196804	−	0.0340874i
$795$	−8.75848e12	−	1.51701e13i	−0.777636	−	1.34691i
$796$	2.29867e12	−	3.98141e12i	0.202940	−	0.351502i
$797$	−2.16394e13			−1.89969			−0.949846	−	0.312719i	$-0.898760\pi$
$797$	−2.16394e13			−1.89969			−0.949846	+	0.312719i	$0.898760\pi$
$798$		0			0
$799$	1.98958e13			1.72703
$800$	1.27668e12	−	2.21127e12i	0.110199	−	0.190870i
$801$	−2.37344e12	−	4.11091e12i	−0.203719	−	0.352851i
$802$	−4.96936e12	−	8.60719e12i	−0.424147	−	0.734644i
$803$	−1.25566e13	+	2.17486e13i	−1.06574	+	1.84591i
$804$	2.67380e12			0.225671
$805$		0			0
$806$	1.05285e13			0.878738
$807$	1.89937e10	−	3.28981e10i	0.00157645	−	0.00273049i
$808$	1.78918e10	+	3.09894e10i	0.00147673	+	0.00255778i
$809$	2.18435e12	+	3.78340e12i	0.179289	+	0.310537i	0.941637	−	0.336630i	$-0.109287\pi$
$809$	2.18435e12	+	3.78340e12i	0.179289	+	0.310537i	−0.762348	+	0.647167i	$0.775954\pi$
$810$	−2.07802e12	+	3.59923e12i	−0.169616	+	0.293783i
$811$	1.39017e13			1.12843			0.564215	−	0.825628i	$-0.309179\pi$
$811$	1.39017e13			1.12843			0.564215	+	0.825628i	$0.309179\pi$
$812$		0			0
$813$	1.27621e13			1.02451
$814$	−5.56003e12	+	9.63025e12i	−0.443881	+	0.768825i
$815$	3.50805e12	+	6.07613e12i	0.278520	+	0.482412i
$816$	−1.30765e12	−	2.26491e12i	−0.103249	−	0.178832i
$817$	7.13866e11	−	1.23645e12i	0.0560554	−	0.0970908i
$818$	2.34233e11			0.0182919
$819$		0			0
$820$	2.97246e12			0.229591
$821$	−4.01964e12	+	6.96221e12i	−0.308775	+	0.534814i	−0.978095	−	0.208160i	$-0.933252\pi$
$821$	−4.01964e12	+	6.96221e12i	−0.308775	+	0.534814i	0.669319	+	0.742975i	$0.266586\pi$
$822$	−3.89968e12	−	6.75444e12i	−0.297924	−	0.516019i
$823$	9.77693e12	+	1.69341e13i	0.742854	+	1.28666i	0.951191	+	0.308603i	$0.0998615\pi$
$823$	9.77693e12	+	1.69341e13i	0.742854	+	1.28666i	−0.208337	+	0.978057i	$0.566805\pi$
$824$	−1.96409e12	+	3.40190e12i	−0.148419	+	0.257069i
$825$	−1.40807e13			−1.05823
$826$		0			0
$827$	1.31390e13			0.976760			0.488380	−	0.872631i	$-0.337588\pi$
$827$	1.31390e13			0.976760			0.488380	+	0.872631i	$0.337588\pi$
$828$	−2.00954e12	+	3.48062e12i	−0.148580	+	0.257348i
$829$	1.09174e13	+	1.89094e13i	0.802827	+	1.39054i	0.917748	+	0.397163i	$0.130005\pi$
$829$	1.09174e13	+	1.89094e13i	0.802827	+	1.39054i	−0.114920	+	0.993375i	$0.536661\pi$
$830$	−8.82871e12	−	1.52918e13i	−0.645723	−	1.11842i
$831$	8.70807e11	−	1.50828e12i	0.0633458	−	0.109718i
$832$	−2.09572e12			−0.151628
$833$		0			0
$834$	−3.57888e12			−0.256154
$835$	1.71237e13	−	2.96591e13i	1.21901	−	2.11139i
$836$	−1.77796e12	−	3.07952e12i	−0.125891	−	0.218050i
$837$	−7.79521e12	−	1.35017e13i	−0.548989	−	0.950876i
$838$	−9.72042e11	+	1.68363e12i	−0.0680906	+	0.117936i
$839$	1.23225e13			0.858561			0.429281	−	0.903171i	$-0.358767\pi$
$839$	1.23225e13			0.858561			0.429281	+	0.903171i	$0.358767\pi$
$840$		0			0
$841$	1.85760e13			1.28047
$842$	−4.48812e12	+	7.77366e12i	−0.307723	+	0.532993i
$843$	5.97817e12	+	1.03545e13i	0.407703	+	0.706162i
$844$	−8.11313e11	−	1.40524e12i	−0.0550361	−	0.0953253i
$845$	−5.23613e12	+	9.06925e12i	−0.353310	+	0.611950i
$846$	−7.48606e12			−0.502443
$847$		0			0
$848$	−5.33707e12			−0.354423
$849$	1.36327e12	−	2.36125e12i	0.0900527	−	0.155976i
$850$	−7.57093e12	−	1.31132e13i	−0.497467	−	0.861638i
$851$	−1.05999e13	−	1.83596e13i	−0.692819	−	1.20000i
$852$	−4.93753e12	+	8.55206e12i	−0.321020	+	0.556023i
$853$	9.07085e12			0.586647			0.293324	−	0.956013i	$-0.405239\pi$
$853$	9.07085e12			0.586647			0.293324	+	0.956013i	$0.405239\pi$
$854$		0			0
$855$	−4.72234e12			−0.302211
$856$	−3.04068e12	+	5.26661e12i	−0.193570	+	0.335274i
$857$	−8.32198e11	−	1.44141e12i	−0.0527003	−	0.0912795i	0.838472	−	0.544945i	$-0.183449\pi$
$857$	−8.32198e11	−	1.44141e12i	−0.0527003	−	0.0912795i	−0.891172	+	0.453665i	$0.850116\pi$
$858$	5.77851e12	+	1.00087e13i	0.364018	+	0.630498i
$859$	7.01160e11	−	1.21444e12i	0.0439388	−	0.0761042i	−0.843220	−	0.537569i	$-0.819343\pi$
$859$	7.01160e11	−	1.21444e12i	0.0439388	−	0.0761042i	0.887158	+	0.461465i	$0.152676\pi$
$860$	−3.10410e12			−0.193505
$861$		0			0
$862$	−1.67091e13			−1.03079
$863$	1.02991e12	−	1.78386e12i	0.0632049	−	0.109474i	−0.832691	−	0.553737i	$-0.813201\pi$
$863$	1.02991e12	−	1.78386e12i	0.0632049	−	0.109474i	0.895896	+	0.444263i	$0.146535\pi$
$864$	1.55165e12	+	2.68754e12i	0.0947289	+	0.164075i
$865$	−7.82512e12	−	1.35535e13i	−0.475246	−	0.823150i
$866$	8.43565e12	−	1.46110e13i	0.509669	−	0.882772i
$867$	−3.33240e12			−0.200296
$868$		0			0
$869$	−1.27622e13			−0.759165
$870$	−9.89758e12	+	1.71431e13i	−0.585723	+	1.01450i
$871$	−6.35300e12	−	1.10037e13i	−0.374022	−	0.647825i
$872$	−3.14430e12	−	5.44608e12i	−0.184162	−	0.318977i
$873$	4.00263e12	−	6.93276e12i	0.233228	−	0.403963i
$874$	6.77921e12			0.392986
$875$		0			0
$876$	−1.17223e13			−0.672583
$877$	−8.71424e12	+	1.50935e13i	−0.497429	+	0.861573i	−0.999996	−	0.00296566i	$-0.999056\pi$
$877$	−8.71424e12	+	1.50935e13i	−0.497429	+	0.861573i	0.502566	+	0.864539i	$0.332389\pi$
$878$	9.36294e12	+	1.62171e13i	0.531725	+	0.920975i
$879$	4.84362e10	+	8.38939e10i	0.00273665	+	0.00474002i
$880$	−3.86556e12	+	6.69534e12i	−0.217290	+	0.376358i
$881$	−1.33834e11			−0.00748471			−0.00374235	−	0.999993i	$-0.501191\pi$
$881$	−1.33834e11			−0.00748471			−0.00374235	+	0.999993i	$0.501191\pi$
$882$		0			0
$883$	2.44009e12			0.135077			0.0675386	−	0.997717i	$-0.478485\pi$
$883$	2.44009e12			0.135077			0.0675386	+	0.997717i	$0.478485\pi$
$884$	−6.21401e12	+	1.07630e13i	−0.342244	+	0.592785i
$885$	8.45175e12	+	1.46389e13i	0.463129	+	0.802163i
$886$	−5.68528e12	−	9.84719e12i	−0.309956	−	0.536859i
$887$	6.80159e12	−	1.17807e13i	0.368939	−	0.639021i	−0.620461	−	0.784237i	$-0.713055\pi$
$887$	6.80159e12	−	1.17807e13i	0.368939	−	0.639021i	0.989400	+	0.145217i	$0.0463879\pi$
$888$	−5.19063e12			−0.280132
$889$		0			0
$890$	1.74080e13			0.930024
$891$	3.49144e12	−	6.04736e12i	0.185590	−	0.321452i
$892$	−5.56475e12	−	9.63844e12i	−0.294309	−	0.509759i
$893$	6.31358e12	+	1.09354e13i	0.332234	+	0.575447i
$894$	9.69789e12	−	1.67972e13i	0.507760	−	0.879466i
$895$	−1.30508e13			−0.679880
$896$		0			0
$897$	−2.20329e13			−1.13633
$898$	7.52388e12	−	1.30317e13i	0.386099	−	0.668742i
$899$	−1.51498e13	−	2.62402e13i	−0.773550	−	1.33983i
$900$	2.84867e12	+	4.93404e12i	0.144727	+	0.250675i
$901$	−1.58249e13	+	2.74095e13i	−0.799981	+	1.38561i
$902$	−4.99428e12			−0.251214
$903$		0			0
$904$	−1.34772e13			−0.671185
$905$	5.72903e12	−	9.92297e12i	0.283898	−	0.491726i
$906$	5.18831e12	+	8.98642e12i	0.255829	+	0.443108i
$907$	3.36775e12	+	5.83311e12i	0.165237	+	0.286198i	0.936739	−	0.350028i	$-0.113828\pi$
$907$	3.36775e12	+	5.83311e12i	0.165237	+	0.286198i	−0.771503	+	0.636226i	$0.780495\pi$
$908$	−2.42544e12	+	4.20098e12i	−0.118414	+	0.205099i
$909$	−7.98443e10			−0.00387888
$910$		0			0
$911$	6.74134e12			0.324275			0.162137	−	0.986768i	$-0.448161\pi$
$911$	6.74134e12			0.324275			0.162137	+	0.986768i	$0.448161\pi$
$912$	8.29920e11	−	1.43746e12i	0.0397246	−	0.0688050i
$913$	1.48339e13	+	2.56930e13i	0.706538	+	1.22376i
$914$	−9.20661e12	−	1.59463e13i	−0.436357	−	0.755792i
$915$	−1.48446e12	+	2.57116e12i	−0.0700122	+	0.121265i
$916$	−9.53287e12			−0.447398
$917$		0			0
$918$	1.84032e13			0.855264
$919$	1.39722e13	−	2.42006e13i	0.646167	−	1.11919i	−0.337863	−	0.941195i	$-0.609704\pi$
$919$	1.39722e13	−	2.42006e13i	0.646167	−	1.11919i	0.984031	−	0.177999i	$-0.0569625\pi$
$920$	−7.36951e12	−	1.27644e13i	−0.339151	−	0.587427i
$921$	−1.13293e12	−	1.96229e12i	−0.0518840	−	0.0898657i
$922$	2.13177e12	−	3.69233e12i	0.0971517	−	0.168272i
$923$	4.69267e13			2.12820
$924$		0			0
$925$	−3.00524e13			−1.34971
$926$	−3.59013e12	+	6.21828e12i	−0.160458	+	0.277921i
$927$	−4.38251e12	−	7.59073e12i	−0.194923	−	0.337617i
$928$	3.01560e12	+	5.22316e12i	0.133477	+	0.231189i
$929$	5.15477e12	−	8.92833e12i	0.227059	−	0.393278i	−0.729876	−	0.683579i	$-0.760422\pi$
$929$	5.15477e12	−	8.92833e12i	0.227059	−	0.393278i	0.956935	+	0.290302i	$0.0937556\pi$
$930$	1.81297e13			0.794724
$931$		0			0
$932$	4.70624e12			0.204316
$933$	1.18209e13	−	2.04743e13i	0.510718	−	0.884590i
$934$	−1.42252e13	−	2.46388e13i	−0.611643	−	1.05940i
$935$	2.29235e13	+	3.97046e13i	0.980908	+	1.69898i
$936$	2.33811e12	−	4.04972e12i	0.0995688	−	0.172458i
$937$	2.54975e13			1.08061			0.540306	−	0.841468i	$-0.318308\pi$
$937$	2.54975e13			1.08061			0.540306	+	0.841468i	$0.318308\pi$
$938$		0			0
$939$	−1.61814e13			−0.679236
$940$	1.37267e13	−	2.37753e13i	0.573443	−	0.993232i
$941$	−8.29195e12	−	1.43621e13i	−0.344749	−	0.597123i	0.640559	−	0.767909i	$-0.278703\pi$
$941$	−8.29195e12	−	1.43621e13i	−0.344749	−	0.597123i	−0.985308	+	0.170786i	$0.945369\pi$
$942$	−8.46309e11	−	1.46585e12i	−0.0350187	−	0.0606541i
$943$	4.76068e12	−	8.24574e12i	0.196050	−	0.339568i
$944$	5.15016e12			0.211080
$945$		0			0
$946$	5.21546e12			0.211730
$947$	−1.13116e13	+	1.95922e13i	−0.457034	+	0.791606i	−0.998803	−	0.0489219i	$-0.984421\pi$
$947$	−1.13116e13	+	1.95922e13i	−0.457034	+	0.791606i	0.541769	+	0.840527i	$0.317755\pi$
$948$	−2.97858e12	−	5.15905e12i	−0.119776	−	0.207459i
$949$	2.78525e13	+	4.82420e13i	1.11472	+	1.93076i
$950$	4.80501e12	−	8.32253e12i	0.191398	−	0.331512i
$951$	−2.47976e13			−0.983099
$952$		0			0
$953$	−3.02695e11			−0.0118874			−0.00594370	−	0.999982i	$-0.501892\pi$
$953$	−3.02695e11			−0.0118874			−0.00594370	+	0.999982i	$0.501892\pi$
$954$	5.95434e12	−	1.03132e13i	0.232737	−	0.403113i
$955$	−7.26357e12	−	1.25809e13i	−0.282576	−	0.489435i
$956$	4.67809e12	+	8.10269e12i	0.181137	+	0.313739i
$957$	1.66297e13	−	2.88036e13i	0.640887	−	1.11005i
$958$	−3.18250e13			−1.22074
$959$		0			0
$960$	−3.60874e12			−0.137131
$961$	−6.55326e11	+	1.13506e12i	−0.0247857	+	0.0429302i
$962$	1.23331e13	+	2.13615e13i	0.464283	+	0.804162i
$963$	−6.78472e12	−	1.17515e13i	−0.254222	−	0.440326i
$964$	3.65959e12	−	6.33859e12i	0.136485	−	0.236399i
$965$	8.74227e12			0.324527
$966$		0			0
$967$	3.03988e12			0.111799			0.0558994	−	0.998436i	$-0.482197\pi$
$967$	3.03988e12			0.111799			0.0558994	+	0.998436i	$0.482197\pi$
$968$	1.66577e12	−	2.88519e12i	0.0609782	−	0.105617i
$969$	−4.92158e12	−	8.52443e12i	−0.179328	−	0.310605i
$970$	1.46787e13	+	2.54242e13i	0.532371	+	0.922093i
$971$	−1.07603e13	+	1.86374e13i	−0.388453	+	0.672821i	−0.992242	−	0.124324i	$-0.960324\pi$
$971$	−1.07603e13	+	1.86374e13i	−0.388453	+	0.672821i	0.603788	+	0.797145i	$0.293657\pi$
$972$	−1.16532e13			−0.418742
$973$		0			0
$974$	−1.10175e13			−0.392254
$975$	−1.56166e13	+	2.70488e13i	−0.553435	+	0.958578i
$976$	4.52286e11	+	7.83382e11i	0.0159547	+	0.0276344i
$977$	7.82269e12	+	1.35493e13i	0.274682	+	0.475763i	0.970055	−	0.242886i	$-0.0780940\pi$
$977$	7.82269e12	+	1.35493e13i	0.274682	+	0.475763i	−0.695373	+	0.718649i	$0.744761\pi$
$978$	2.75129e12	−	4.76537e12i	0.0961638	−	0.166561i
$979$	−2.92486e13			−1.01762
$980$		0			0
$981$	1.40318e13			0.483731
$982$	1.49505e13	−	2.58950e13i	0.513043	−	0.888617i
$983$	1.14381e13	+	1.98114e13i	0.390719	+	0.676745i	0.992545	−	0.121883i	$-0.0388932\pi$
$983$	1.14381e13	+	1.98114e13i	0.390719	+	0.676745i	−0.601826	+	0.798627i	$0.705560\pi$
$984$	−1.16562e12	−	2.01891e12i	−0.0396350	−	0.0686498i
$985$	3.79755e13	−	6.57755e13i	1.28541	−	2.22639i
$986$	3.57661e13			1.20511
$987$		0			0
$988$	−7.88763e12			−0.263354
$989$	−4.97151e12	+	8.61091e12i	−0.165236	+	0.286198i
$990$	−8.62528e12	−	1.49394e13i	−0.285374	−	0.494283i
$991$	−2.23678e13	−	3.87421e13i	−0.736701	−	1.27600i	−0.953973	−	0.299893i	$-0.903049\pi$
$991$	−2.23678e13	−	3.87421e13i	−0.736701	−	1.27600i	0.217272	−	0.976111i	$-0.430284\pi$
$992$	2.76187e12	−	4.78370e12i	0.0905526	−	0.156842i
$993$	−1.47386e13			−0.481043
$994$		0			0
$995$	−3.76192e13			−1.21676
$996$	−6.92417e12	+	1.19930e13i	−0.222946	+	0.386155i
$997$	−1.62282e13	−	2.81081e13i	−0.520166	−	0.900954i	−0.999725	−	0.0234445i	$-0.992537\pi$
$997$	−1.62282e13	−	2.81081e13i	−0.520166	−	0.900954i	0.479559	−	0.877510i	$-0.340797\pi$
$998$	−7.01928e12	−	1.21578e13i	−0.223978	−	0.387941i
$999$	1.82626e13	−	3.16317e13i	0.580119	−	1.00480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.m.79.3		8
7.2	even	3		98.10.a.k.1.2	✓	4
7.3	odd	6	inner	98.10.c.m.67.2		8
7.4	even	3	inner	98.10.c.m.67.3		8
7.5	odd	6		98.10.a.k.1.3	yes	4
7.6	odd	2	inner	98.10.c.m.79.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
98.10.a.k.1.2	✓	4	7.2	even	3
98.10.a.k.1.3	yes	4	7.5	odd	6
98.10.c.m.67.2		8	7.3	odd	6	inner
98.10.c.m.67.3		8	7.4	even	3	inner
98.10.c.m.79.2		8	7.6	odd	2	inner
98.10.c.m.79.3		8	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:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.00000 - 13.8564i) q^{2} +(51.3408 + 88.9249i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1047.40 + 1814.15i) q^{5} +1642.91 q^{6} -4096.00 q^{8} +(4569.74 - 7915.01i) q^{9} +O(q^{10})\)	\(q+(8.00000 - 13.8564i) q^{2} +(51.3408 + 88.9249i) q^{3} +(-128.000 - 221.703i) q^{4} +(-1047.40 + 1814.15i) q^{5} +1642.91 q^{6} -4096.00 q^{8} +(4569.74 - 7915.01i) q^{9} +(16758.4 + 29026.4i) q^{10} +(-28157.2 - 48769.7i) q^{11} +(13143.3 - 22764.8i) q^{12} -124915. q^{13} -215098. q^{15} +(-32768.0 + 56755.8i) q^{16} +(194320. + 336573. i) q^{17} +(-73115.8 - 126640. i) q^{18} +(-123329. + 213611. i) q^{19} +536269. q^{20} -901030. q^{22} +(858886. - 1.48763e6i) q^{23} +(-210292. - 364237. i) q^{24} +(-1.21753e6 - 2.10883e6i) q^{25} +(-999317. + 1.73087e6i) q^{26} +2.95954e6 q^{27} +5.75179e6 q^{29} +(-1.72078e6 + 2.98048e6i) q^{30} +(-2.63393e6 - 4.56209e6i) q^{31} +(524288. + 908093. i) q^{32} +(2.89123e6 - 5.00775e6i) q^{33} +6.21825e6 q^{34} -2.33970e6 q^{36} +(6.17074e6 - 1.06880e7i) q^{37} +(1.97326e6 + 3.41778e6i) q^{38} +(-6.41322e6 - 1.11080e7i) q^{39} +(4.29015e6 - 7.43076e6i) q^{40} +5.54285e6 q^{41} -5.78833e6 q^{43} +(-7.20824e6 + 1.24850e7i) q^{44} +(9.57269e6 + 1.65804e7i) q^{45} +(-1.37422e7 - 2.38021e7i) q^{46} +(2.55966e7 - 4.43346e7i) q^{47} -6.72935e6 q^{48} -3.89611e7 q^{50} +(-1.99531e7 + 3.45599e7i) q^{51} +(1.59891e7 + 2.76939e7i) q^{52} +(4.07186e7 + 7.05267e7i) q^{53} +(2.36763e7 - 4.10086e7i) q^{54} +1.17967e8 q^{55} -2.53272e7 q^{57} +(4.60143e7 - 7.96992e7i) q^{58} +(-3.92926e7 - 6.80568e7i) q^{59} +(2.75325e7 + 4.76877e7i) q^{60} +(6.90133e6 - 1.19535e7i) q^{61} -8.42856e7 q^{62} +1.67772e7 q^{64} +(1.30836e8 - 2.26614e8i) q^{65} +(-4.62596e7 - 8.01241e7i) q^{66} +(5.08587e7 + 8.80899e7i) q^{67} +(4.97460e7 - 8.61626e7i) q^{68} +1.76384e8 q^{69} -3.75670e8 q^{71} +(-1.87176e7 + 3.24199e7i) q^{72} +(-2.22973e8 - 3.86200e8i) q^{73} +(-9.87319e7 - 1.71009e8i) q^{74} +(1.25018e8 - 2.16538e8i) q^{75} +6.31442e7 q^{76} -2.05223e8 q^{78} +(1.13312e8 - 1.96262e8i) q^{79} +(-6.86425e7 - 1.18892e8i) q^{80} +(6.19992e7 + 1.07386e8i) q^{81} +(4.43428e7 - 7.68040e7i) q^{82} -5.26823e8 q^{83} -8.14125e8 q^{85} +(-4.63066e7 + 8.02054e7i) q^{86} +(2.95302e8 + 5.11478e8i) q^{87} +(1.15332e8 + 1.99761e8i) q^{88} +(2.59691e8 - 4.49797e8i) q^{89} +3.06326e8 q^{90} -4.39750e8 q^{92} +(2.70456e8 - 4.68444e8i) q^{93} +(-4.09546e8 - 7.09354e8i) q^{94} +(-2.58349e8 - 4.47473e8i) q^{95} +(-5.38348e7 + 9.32446e7i) q^{96} +8.75899e8 q^{97} -5.14684e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9}+O(q^{10}) \) 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9	\( 8 q + 64 q^{2} - 1024 q^{4} - 32768 q^{8} - 15912 q^{9} - 9548 q^{11} - 834624 q^{15} - 262144 q^{16} + 254592 q^{18} - 305536 q^{22} + 2836736 q^{23} - 966144 q^{25} + 33339944 q^{29} - 6676992 q^{30} + 4194304 q^{32} + 8146944 q^{36} - 3226372 q^{37} - 69110568 q^{39} - 152960408 q^{43} - 2444288 q^{44} - 45387776 q^{46} - 30916608 q^{50} + 97261596 q^{51} - 13708112 q^{53} - 743115384 q^{57} + 266719552 q^{58} + 106831872 q^{60} + 134217728 q^{64} + 515731188 q^{65} + 814420776 q^{67} - 2649337488 q^{71} + 65175552 q^{72} + 51621952 q^{74} - 2211538176 q^{78} + 668411176 q^{79} + 1111307688 q^{81} - 3318529928 q^{85} - 1223683264 q^{86} + 39108608 q^{88} - 1452408832 q^{92} + 3706577496 q^{93} - 977188688 q^{95} - 5583163320 q^{99}+O(q^{100}) \) 8 * q + 64 * q^2 - 1024 * q^4 - 32768 * q^8 - 15912 * q^9 - 9548 * q^11 - 834624 * q^15 - 262144 * q^16 + 254592 * q^18 - 305536 * q^22 + 2836736 * q^23 - 966144 * q^25 + 33339944 * q^29 - 6676992 * q^30 + 4194304 * q^32 + 8146944 * q^36 - 3226372 * q^37 - 69110568 * q^39 - 152960408 * q^43 - 2444288 * q^44 - 45387776 * q^46 - 30916608 * q^50 + 97261596 * q^51 - 13708112 * q^53 - 743115384 * q^57 + 266719552 * q^58 + 106831872 * q^60 + 134217728 * q^64 + 515731188 * q^65 + 814420776 * q^67 - 2649337488 * q^71 + 65175552 * q^72 + 51621952 * q^74 - 2211538176 * q^78 + 668411176 * q^79 + 1111307688 * q^81 - 3318529928 * q^85 - 1223683264 * q^86 + 39108608 * q^88 - 1452408832 * q^92 + 3706577496 * q^93 - 977188688 * q^95 - 5583163320 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more