LMFDB - Embedded newform 98.10.c.e.67.1

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:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	98.67
Dual form			98.10.c.e.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.00000 + 13.8564i) q^{2} +(-3.00000 + 5.19615i) q^{3} +(-128.000 + 221.703i) q^{4} +(280.000 + 484.974i) q^{5} -96.0000 q^{6} -4096.00 q^{8} +(9823.50 + 17014.8i) q^{9} +O(q^{10})$	\(q+(8.00000 + 13.8564i) q^{2} +(-3.00000 + 5.19615i) q^{3} +(-128.000 + 221.703i) q^{4} +(280.000 + 484.974i) q^{5} -96.0000 q^{6} -4096.00 q^{8} +(9823.50 + 17014.8i) q^{9} +(-4480.00 + 7759.59i) q^{10} +(27076.0 - 46897.0i) q^{11} +(-768.000 - 1330.22i) q^{12} +113172. q^{13} -3360.00 q^{15} +(-32768.0 - 56755.8i) q^{16} +(3131.00 - 5423.05i) q^{17} +(-157176. + 272237. i) q^{18} +(128539. + 222636. i) q^{19} -143360. q^{20} +866432. q^{22} +(133000. + 230363. i) q^{23} +(12288.0 - 21283.4i) q^{24} +(819762. - 1.41987e6i) q^{25} +(905376. + 1.56816e6i) q^{26} -235980. q^{27} +1.57471e6 q^{29} +(-26880.0 - 46557.5i) q^{30} +(-2.31874e6 + 4.01618e6i) q^{31} +(524288. - 908093. i) q^{32} +(162456. + 281382. i) q^{33} +100192. q^{34} -5.02963e6 q^{36} +(5.97312e6 + 1.03457e7i) q^{37} +(-2.05662e6 + 3.56218e6i) q^{38} +(-339516. + 588059. i) q^{39} +(-1.14688e6 - 1.98645e6i) q^{40} -2.19091e7 q^{41} +2.75206e7 q^{43} +(6.93146e6 + 1.20056e7i) q^{44} +(-5.50116e6 + 9.52829e6i) q^{45} +(-2.12800e6 + 3.68580e6i) q^{46} +(2.64639e7 + 4.58369e7i) q^{47} +393216. q^{48} +2.62324e7 q^{50} +(18786.0 + 32538.3i) q^{51} +(-1.44860e7 + 2.50905e7i) q^{52} +(-8.11061e6 + 1.40480e7i) q^{53} +(-1.88784e6 - 3.26983e6i) q^{54} +3.03251e7 q^{55} -1.54247e6 q^{57} +(1.25977e7 + 2.18199e7i) q^{58} +(-7.02548e7 + 1.21685e8i) q^{59} +(430080. - 744920. i) q^{60} +(-1.01482e8 - 1.75772e8i) q^{61} -7.41997e7 q^{62} +1.67772e7 q^{64} +(3.16882e7 + 5.48855e7i) q^{65} +(-2.59930e6 + 4.50211e6i) q^{66} +(-7.68673e7 + 1.33138e8i) q^{67} +(801536. + 1.38830e6i) q^{68} -1.59600e6 q^{69} +2.79656e8 q^{71} +(-4.02371e7 - 6.96926e7i) q^{72} +(-2.02011e8 + 3.49894e8i) q^{73} +(-9.55699e7 + 1.65532e8i) q^{74} +(4.91858e6 + 8.51922e6i) q^{75} -6.58120e7 q^{76} -1.08645e7 q^{78} +(6.53449e7 + 1.13181e8i) q^{79} +(1.83501e7 - 3.17833e7i) q^{80} +(-1.92648e8 + 3.33676e8i) q^{81} +(-1.75273e8 - 3.03582e8i) q^{82} -4.20134e8 q^{83} +3.50672e6 q^{85} +(2.20165e8 + 3.81337e8i) q^{86} +(-4.72414e6 + 8.18245e6i) q^{87} +(-1.10903e8 + 1.92090e8i) q^{88} +(-2.34771e8 - 4.06636e8i) q^{89} -1.76037e8 q^{90} -6.80960e7 q^{92} +(-1.39125e7 - 2.40971e7i) q^{93} +(-4.23423e8 + 7.33390e8i) q^{94} +(-7.19818e7 + 1.24676e8i) q^{95} +(3.14573e6 + 5.44856e6i) q^{96} +8.72502e8 q^{97} +1.06392e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 16 q^{2} - 6 q^{3} - 256 q^{4} + 560 q^{5} - 192 q^{6} - 8192 q^{8} + 19647 q^{9}+O(q^{10}) $ 2 * q + 16 * q^2 - 6 * q^3 - 256 * q^4 + 560 * q^5 - 192 * q^6 - 8192 * q^8 + 19647 * q^9	\( 2 q + 16 q^{2} - 6 q^{3} - 256 q^{4} + 560 q^{5} - 192 q^{6} - 8192 q^{8} + 19647 q^{9} - 8960 q^{10} + 54152 q^{11} - 1536 q^{12} + 226344 q^{13} - 6720 q^{15} - 65536 q^{16} + 6262 q^{17} - 314352 q^{18} + 257078 q^{19} - 286720 q^{20} + 1732864 q^{22} + 266000 q^{23} + 24576 q^{24} + 1639525 q^{25} + 1810752 q^{26} - 471960 q^{27} + 3149428 q^{29} - 53760 q^{30} - 4637484 q^{31} + 1048576 q^{32} + 324912 q^{33} + 200384 q^{34} - 10059264 q^{36} + 11946238 q^{37} - 4113248 q^{38} - 679032 q^{39} - 2293760 q^{40} - 43818252 q^{41} + 55041184 q^{43} + 13862912 q^{44} - 11002320 q^{45} - 4256000 q^{46} + 52927836 q^{47} + 786432 q^{48} + 52464800 q^{50} + 37572 q^{51} - 28972032 q^{52} - 16221222 q^{53} - 3775680 q^{54} + 60650240 q^{55} - 3084936 q^{57} + 25195424 q^{58} - 140509618 q^{59} + 860160 q^{60} - 202963560 q^{61} - 148399488 q^{62} + 33554432 q^{64} + 63376320 q^{65} - 5198592 q^{66} - 153734572 q^{67} + 1603072 q^{68} - 3192000 q^{69} + 559311872 q^{71} - 80474112 q^{72} - 404022830 q^{73} - 191139808 q^{74} + 9837150 q^{75} - 131623936 q^{76} - 21729024 q^{78} + 130689816 q^{79} + 36700160 q^{80} - 385296021 q^{81} - 350546016 q^{82} - 840268028 q^{83} + 7013440 q^{85} + 440329472 q^{86} - 9448284 q^{87} - 221806592 q^{88} - 469542390 q^{89} - 352074240 q^{90} - 136192000 q^{92} - 27824904 q^{93} - 846845376 q^{94} - 143963680 q^{95} + 6291456 q^{96} + 1745003380 q^{97} + 2127848688 q^{99}+O(q^{100}) \) 2 * q + 16 * q^2 - 6 * q^3 - 256 * q^4 + 560 * q^5 - 192 * q^6 - 8192 * q^8 + 19647 * q^9 - 8960 * q^10 + 54152 * q^11 - 1536 * q^12 + 226344 * q^13 - 6720 * q^15 - 65536 * q^16 + 6262 * q^17 - 314352 * q^18 + 257078 * q^19 - 286720 * q^20 + 1732864 * q^22 + 266000 * q^23 + 24576 * q^24 + 1639525 * q^25 + 1810752 * q^26 - 471960 * q^27 + 3149428 * q^29 - 53760 * q^30 - 4637484 * q^31 + 1048576 * q^32 + 324912 * q^33 + 200384 * q^34 - 10059264 * q^36 + 11946238 * q^37 - 4113248 * q^38 - 679032 * q^39 - 2293760 * q^40 - 43818252 * q^41 + 55041184 * q^43 + 13862912 * q^44 - 11002320 * q^45 - 4256000 * q^46 + 52927836 * q^47 + 786432 * q^48 + 52464800 * q^50 + 37572 * q^51 - 28972032 * q^52 - 16221222 * q^53 - 3775680 * q^54 + 60650240 * q^55 - 3084936 * q^57 + 25195424 * q^58 - 140509618 * q^59 + 860160 * q^60 - 202963560 * q^61 - 148399488 * q^62 + 33554432 * q^64 + 63376320 * q^65 - 5198592 * q^66 - 153734572 * q^67 + 1603072 * q^68 - 3192000 * q^69 + 559311872 * q^71 - 80474112 * q^72 - 404022830 * q^73 - 191139808 * q^74 + 9837150 * q^75 - 131623936 * q^76 - 21729024 * q^78 + 130689816 * q^79 + 36700160 * q^80 - 385296021 * q^81 - 350546016 * q^82 - 840268028 * q^83 + 7013440 * q^85 + 440329472 * q^86 - 9448284 * q^87 - 221806592 * q^88 - 469542390 * q^89 - 352074240 * q^90 - 136192000 * q^92 - 27824904 * q^93 - 846845376 * q^94 - 143963680 * q^95 + 6291456 * q^96 + 1745003380 * q^97 + 2127848688 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	−3.00000	+	5.19615i	−0.0213833	+	0.0370370i	−0.876519	−	0.481367i	$-0.840140\pi$
$3$	−3.00000	+	5.19615i	−0.0213833	+	0.0370370i	0.855136	+	0.518404i	$0.173474\pi$
$4$	−128.000	+	221.703i	−0.250000	+	0.433013i
$5$	280.000	+	484.974i	0.200352	+	0.347019i	0.948642	−	0.316352i	$-0.102458\pi$
$5$	280.000	+	484.974i	0.200352	+	0.347019i	−0.748290	+	0.663372i	$0.769125\pi$
$6$	−96.0000			−0.0302406
$7$		0			0
$7$		0			0
$8$	−4096.00			−0.353553
$9$	9823.50	+	17014.8i	0.499086	+	0.864441i
$10$	−4480.00	+	7759.59i	−0.141670	+	0.245380i
$11$	27076.0	−	46897.0i	0.557593	−	0.965780i	−0.440104	−	0.897947i	$-0.645058\pi$
$11$	27076.0	−	46897.0i	0.557593	−	0.965780i	0.997697	−	0.0678326i	$-0.0216084\pi$
$12$	−768.000	−	1330.22i	−0.0106917	−	0.0185185i
$13$	113172.			1.09899			0.549495	−	0.835497i	$-0.314820\pi$
$13$	113172.			1.09899			0.549495	+	0.835497i	$0.314820\pi$
$14$		0			0
$15$	−3360.00			−0.0171368
$16$	−32768.0	−	56755.8i	−0.125000	−	0.216506i
$17$	3131.00	−	5423.05i	0.00909207	−	0.0157479i	−0.861444	−	0.507853i	$-0.830439\pi$
$17$	3131.00	−	5423.05i	0.00909207	−	0.0157479i	0.870536	+	0.492105i	$0.163773\pi$
$18$	−157176.	+	272237.i	−0.352907	+	0.611252i
$19$	128539.	+	222636.i	0.226279	+	0.391926i	0.956702	−	0.291068i	$-0.0940107\pi$
$19$	128539.	+	222636.i	0.226279	+	0.391926i	−0.730424	+	0.682994i	$0.760677\pi$
$20$	−143360.			−0.200352
$21$		0			0
$22$	866432.			0.788556
$23$	133000.	+	230363.i	0.0991006	+	0.171647i	0.911313	−	0.411715i	$-0.135070\pi$
$23$	133000.	+	230363.i	0.0991006	+	0.171647i	−0.812212	+	0.583362i	$0.801737\pi$
$24$	12288.0	−	21283.4i	0.00756015	−	0.0130946i
$25$	819762.	−	1.41987e6i	0.419718	−	0.726974i
$26$	905376.	+	1.56816e6i	0.388552	+	0.672991i
$27$	−235980.			−0.0854552
$28$		0			0
$29$	1.57471e6			0.413438			0.206719	−	0.978400i	$-0.433721\pi$
$29$	1.57471e6			0.413438			0.206719	+	0.978400i	$0.433721\pi$
$30$	−26880.0	−	46557.5i	−0.00605876	−	0.0104941i
$31$	−2.31874e6	+	4.01618e6i	−0.450946	+	0.781062i	−0.998445	−	0.0557446i	$-0.982247\pi$
$31$	−2.31874e6	+	4.01618e6i	−0.450946	+	0.781062i	0.547499	+	0.836806i	$0.315580\pi$
$32$	524288.	−	908093.i	0.0883883	−	0.153093i
$33$	162456.	+	281382.i	0.0238464	+	0.0413032i
$34$	100192.			0.0128581
$35$		0			0
$36$	−5.02963e6			−0.499086
$37$	5.97312e6	+	1.03457e7i	0.523954	+	0.907515i	0.999611	+	0.0278845i	$0.00887708\pi$
$37$	5.97312e6	+	1.03457e7i	0.523954	+	0.907515i	−0.475657	+	0.879631i	$0.657790\pi$
$38$	−2.05662e6	+	3.56218e6i	−0.160003	+	0.277134i
$39$	−339516.	+	588059.i	−0.0235001	+	0.0407033i
$40$	−1.14688e6	−	1.98645e6i	−0.0708350	−	0.122690i
$41$	−2.19091e7			−1.21087			−0.605435	−	0.795895i	$-0.707001\pi$
$41$	−2.19091e7			−1.21087			−0.605435	+	0.795895i	$0.707001\pi$
$42$		0			0
$43$	2.75206e7			1.22758			0.613790	−	0.789469i	$-0.289644\pi$
$43$	2.75206e7			1.22758			0.613790	+	0.789469i	$0.289644\pi$
$44$	6.93146e6	+	1.20056e7i	0.278797	+	0.482890i
$45$	−5.50116e6	+	9.52829e6i	−0.199985	+	0.346385i
$46$	−2.12800e6	+	3.68580e6i	−0.0700747	+	0.121373i
$47$	2.64639e7	+	4.58369e7i	0.791068	+	1.37017i	0.925306	+	0.379221i	$0.123808\pi$
$47$	2.64639e7	+	4.58369e7i	0.791068	+	1.37017i	−0.134238	+	0.990949i	$0.542859\pi$
$48$	393216.			0.0106917
$49$		0			0
$50$	2.62324e7			0.593571
$51$	18786.0	+	32538.3i	0.000388838	+	0.000673487i
$52$	−1.44860e7	+	2.50905e7i	−0.274748	+	0.475877i
$53$	−8.11061e6	+	1.40480e7i	−0.141193	+	0.244553i	−0.927946	−	0.372715i	$-0.878427\pi$
$53$	−8.11061e6	+	1.40480e7i	−0.141193	+	0.244553i	0.786753	+	0.617268i	$0.211760\pi$
$54$	−1.88784e6	−	3.26983e6i	−0.0302130	−	0.0523304i
$55$	3.03251e7			0.446859
$56$		0			0
$57$	−1.54247e6			−0.0193544
$58$	1.25977e7	+	2.18199e7i	0.146173	+	0.253178i
$59$	−7.02548e7	+	1.21685e8i	−0.754818	+	1.30738i	0.190647	+	0.981659i	$0.438941\pi$
$59$	−7.02548e7	+	1.21685e8i	−0.754818	+	1.30738i	−0.945465	+	0.325724i	$0.894392\pi$
$60$	430080.	−	744920.i	0.00428419	−	0.00742043i
$61$	−1.01482e8	−	1.75772e8i	−0.938434	−	1.62542i	−0.768393	−	0.639979i	$-0.778943\pi$
$61$	−1.01482e8	−	1.75772e8i	−0.938434	−	1.62542i	−0.170042	−	0.985437i	$-0.554390\pi$
$62$	−7.41997e7			−0.637734
$63$		0			0
$64$	1.67772e7			0.125000
$65$	3.16882e7	+	5.48855e7i	0.220185	+	0.381371i
$66$	−2.59930e6	+	4.50211e6i	−0.0168620	+	0.0292058i
$67$	−7.68673e7	+	1.33138e8i	−0.466020	+	0.807171i	−0.999247	−	0.0388015i	$-0.987646\pi$
$67$	−7.68673e7	+	1.33138e8i	−0.466020	+	0.807171i	0.533227	+	0.845972i	$0.320979\pi$
$68$	801536.	+	1.38830e6i	0.00454604	+	0.00787397i
$69$	−1.59600e6			−0.00847641
$70$		0			0
$71$	2.79656e8			1.30606			0.653028	−	0.757334i	$-0.273499\pi$
$71$	2.79656e8			1.30606			0.653028	+	0.757334i	$0.273499\pi$
$72$	−4.02371e7	−	6.96926e7i	−0.176453	−	0.305626i
$73$	−2.02011e8	+	3.49894e8i	−0.832574	+	1.44206i	0.0634158	+	0.997987i	$0.479801\pi$
$73$	−2.02011e8	+	3.49894e8i	−0.832574	+	1.44206i	−0.895990	+	0.444074i	$0.853533\pi$
$74$	−9.55699e7	+	1.65532e8i	−0.370492	+	0.641710i
$75$	4.91858e6	+	8.51922e6i	0.0179500	+	0.0310903i
$76$	−6.58120e7			−0.226279
$77$		0			0
$78$	−1.08645e7			−0.0332341
$79$	6.53449e7	+	1.13181e8i	0.188751	+	0.326927i	0.944834	−	0.327549i	$-0.106223\pi$
$79$	6.53449e7	+	1.13181e8i	0.188751	+	0.326927i	−0.756083	+	0.654476i	$0.772889\pi$
$80$	1.83501e7	−	3.17833e7i	0.0500879	−	0.0867548i
$81$	−1.92648e8	+	3.33676e8i	−0.497258	+	0.861276i
$82$	−1.75273e8	−	3.03582e8i	−0.428107	−	0.741504i
$83$	−4.20134e8			−0.971709			−0.485855	−	0.874040i	$-0.661492\pi$
$83$	−4.20134e8			−0.971709			−0.485855	+	0.874040i	$0.661492\pi$
$84$		0			0
$85$	3.50672e6			0.00728645
$86$	2.20165e8	+	3.81337e8i	0.434015	+	0.751736i
$87$	−4.72414e6	+	8.18245e6i	−0.00884069	+	0.0153125i
$88$	−1.10903e8	+	1.92090e8i	−0.197139	+	0.341455i
$89$	−2.34771e8	−	4.06636e8i	−0.396634	−	0.686990i	0.596674	−	0.802483i	$-0.296488\pi$
$89$	−2.34771e8	−	4.06636e8i	−0.396634	−	0.686990i	−0.993308	+	0.115493i	$0.963155\pi$
$90$	−1.76037e8			−0.282822
$91$		0			0
$92$	−6.80960e7			−0.0991006
$93$	−1.39125e7	−	2.40971e7i	−0.0192855	−	0.0334034i
$94$	−4.23423e8	+	7.33390e8i	−0.559370	+	0.968856i
$95$	−7.19818e7	+	1.24676e8i	−0.0906706	+	0.157046i
$96$	3.14573e6	+	5.44856e6i	0.00378008	+	0.00654729i
$97$	8.72502e8			1.00068			0.500338	−	0.865830i	$-0.333209\pi$
$97$	8.72502e8			1.00068			0.500338	+	0.865830i	$0.333209\pi$
$98$		0			0
$99$	1.06392e9			1.11315
$100$	2.09859e8	+	3.63487e8i	0.209859	+	0.363487i
$101$	−6.04507e8	+	1.04704e9i	−0.578037	+	1.00119i	0.417668	+	0.908600i	$0.362848\pi$
$101$	−6.04507e8	+	1.04704e9i	−0.578037	+	1.00119i	−0.995704	+	0.0925891i	$0.970486\pi$
$102$	−300576.	+	520613.i	−0.000274950	+	0.000476227i
$103$	3.45281e8	+	5.98045e8i	0.302277	+	0.523560i	0.976651	−	0.214830i	$-0.0689198\pi$
$103$	3.45281e8	+	5.98045e8i	0.302277	+	0.523560i	−0.674374	+	0.738390i	$0.735586\pi$
$104$	−4.63553e8			−0.388552
$105$		0			0
$106$	−2.59540e8			−0.199677
$107$	−8.97497e7	−	1.55451e8i	−0.0661921	−	0.114648i	0.831030	−	0.556227i	$-0.187752\pi$
$107$	−8.97497e7	−	1.55451e8i	−0.0661921	−	0.114648i	−0.897222	+	0.441579i	$0.854418\pi$
$108$	3.02054e7	−	5.23174e7i	0.0213638	−	0.0370032i
$109$	8.01804e8	−	1.38877e9i	0.544063	−	0.942345i	−0.454602	−	0.890695i	$-0.650219\pi$
$109$	8.01804e8	−	1.38877e9i	0.544063	−	0.942345i	0.998665	−	0.0516501i	$-0.0164480\pi$
$110$	2.42601e8	+	4.20197e8i	0.157988	+	0.273644i
$111$	−7.16774e7			−0.0448156
$112$		0			0
$113$	1.42785e9			0.823815			0.411908	−	0.911226i	$-0.364863\pi$
$113$	1.42785e9			0.823815			0.411908	+	0.911226i	$0.364863\pi$
$114$	−1.23397e7	−	2.13731e7i	−0.00684281	−	0.0118521i
$115$	−7.44800e7	+	1.29003e8i	−0.0397100	+	0.0687797i
$116$	−2.01563e8	+	3.49118e8i	−0.103360	+	0.179024i
$117$	1.11175e9	+	1.92560e9i	0.548490	+	0.950013i
$118$	−2.24815e9			−1.06747
$119$		0			0
$120$	1.37626e7			0.00605876
$121$	−2.87246e8	−	4.97524e8i	−0.121820	−	0.210999i
$122$	1.62371e9	−	2.81235e9i	0.663573	−	1.14934i
$123$	6.57274e7	−	1.13843e8i	0.0258925	−	0.0448471i
$124$	−5.93598e8	−	1.02814e9i	−0.225473	−	0.390531i
$125$	2.01188e9			0.737069
$126$		0			0
$127$	−2.35873e9			−0.804565			−0.402282	−	0.915516i	$-0.631783\pi$
$127$	−2.35873e9			−0.804565			−0.402282	+	0.915516i	$0.631783\pi$
$128$	1.34218e8	+	2.32472e8i	0.0441942	+	0.0765466i
$129$	−8.25618e7	+	1.43001e8i	−0.0262498	+	0.0454659i
$130$	−5.07011e8	+	8.78168e8i	−0.155694	+	0.269670i
$131$	3.00833e8	+	5.21057e8i	0.0892492	+	0.154584i	0.907194	−	0.420713i	$-0.138220\pi$
$131$	3.00833e8	+	5.21057e8i	0.0892492	+	0.154584i	−0.817945	+	0.575297i	$0.804887\pi$
$132$	−8.31775e7			−0.0238464
$133$		0			0
$134$	−2.45975e9			−0.659052
$135$	−6.60744e7	−	1.14444e8i	−0.0171211	−	0.0296546i
$136$	−1.28246e7	+	2.22128e7i	−0.00321453	+	0.00556773i
$137$	2.58004e9	−	4.46877e9i	0.625726	−	1.08379i	−0.362673	−	0.931916i	$-0.618136\pi$
$137$	2.58004e9	−	4.46877e9i	0.625726	−	1.08379i	0.988400	−	0.151874i	$-0.0485307\pi$
$138$	−1.27680e7	−	2.21148e7i	−0.00299686	−	0.00519072i
$139$	7.14356e9			1.62311			0.811556	−	0.584275i	$-0.198621\pi$
$139$	7.14356e9			1.62311			0.811556	+	0.584275i	$0.198621\pi$
$140$		0			0
$141$	−3.17567e8			−0.0676627
$142$	2.23725e9	+	3.87503e9i	0.461760	+	0.799792i
$143$	3.06425e9	−	5.30743e9i	0.612790	−	1.06138i
$144$	6.43793e8	−	1.11508e9i	0.124771	−	0.216110i
$145$	4.40920e8	+	7.63696e8i	0.0828331	+	0.143471i
$146$	−6.46437e9			−1.17744
$147$		0			0
$148$	−3.05824e9			−0.523954
$149$	−4.55212e9	−	7.88450e9i	−0.756616	−	1.31050i	−0.944567	−	0.328319i	$-0.893518\pi$
$149$	−4.55212e9	−	7.88450e9i	−0.756616	−	1.31050i	0.187951	−	0.982178i	$-0.439815\pi$
$150$	−7.86972e7	+	1.36308e8i	−0.0126925	+	0.0219841i
$151$	1.44716e8	−	2.50655e8i	0.0226527	−	0.0392357i	−0.854477	−	0.519490i	$-0.826122\pi$
$151$	1.44716e8	−	2.50655e8i	0.0226527	−	0.0392357i	0.877130	+	0.480254i	$0.159455\pi$
$152$	−5.26496e8	−	9.11917e8i	−0.0800016	−	0.138567i
$153$	1.23030e8			0.0181509
$154$		0			0
$155$	−2.59699e9			−0.361391
$156$	−8.69161e7	−	1.50543e8i	−0.0117500	−	0.0203517i
$157$	6.95339e9	−	1.20436e10i	0.913373	−	1.58201i	0.104107	−	0.994566i	$-0.466802\pi$
$157$	6.95339e9	−	1.20436e10i	0.913373	−	1.58201i	0.809266	−	0.587442i	$-0.199865\pi$
$158$	−1.04552e9	+	1.81089e9i	−0.133467	+	0.231172i
$159$	−4.86637e7	−	8.42879e7i	−0.00603834	−	0.0104587i
$160$	5.87203e8			0.0708350
$161$		0			0
$162$	−6.16474e9			−0.703229
$163$	−8.31162e9	−	1.43962e10i	−0.922235	−	1.59736i	−0.795948	−	0.605364i	$-0.793027\pi$
$163$	−8.31162e9	−	1.43962e10i	−0.922235	−	1.59736i	−0.126287	−	0.991994i	$-0.540306\pi$
$164$	2.80437e9	−	4.85731e9i	0.302718	−	0.524322i
$165$	−9.09754e7	+	1.57574e8i	−0.00955534	+	0.0165503i
$166$	−3.36107e9	−	5.82155e9i	−0.343551	−	0.595048i
$167$	1.58019e10			1.57212			0.786061	−	0.618149i	$-0.212117\pi$
$167$	1.58019e10			1.57212			0.786061	+	0.618149i	$0.212117\pi$
$168$		0			0
$169$	2.20340e9			0.207780
$170$	2.80538e7	+	4.85905e7i	0.00257615	+	0.00446202i
$171$	−2.52541e9	+	4.37413e9i	−0.225865	+	0.391209i
$172$	−3.52264e9	+	6.10138e9i	−0.306895	+	0.531558i
$173$	1.61562e9	+	2.79834e9i	0.137130	+	0.237516i	0.926409	−	0.376518i	$-0.122879\pi$
$173$	1.61562e9	+	2.79834e9i	0.137130	+	0.237516i	−0.789279	+	0.614035i	$0.789545\pi$
$174$	−1.51173e8			−0.0125026
$175$		0			0
$176$	−3.54891e9			−0.278797
$177$	−4.21529e8	−	7.30109e8i	−0.0322810	−	0.0559124i
$178$	3.75634e9	−	6.50617e9i	0.280462	−	0.485775i
$179$	1.20704e10	−	2.09065e10i	0.878785	−	1.52210i	0.0261099	−	0.999659i	$-0.491688\pi$
$179$	1.20704e10	−	2.09065e10i	0.878785	−	1.52210i	0.852675	−	0.522441i	$-0.174979\pi$
$180$	−1.40830e9	−	2.43924e9i	−0.0999926	−	0.173192i
$181$	3.89332e9			0.269629			0.134814	−	0.990871i	$-0.456956\pi$
$181$	3.89332e9			0.269629			0.134814	+	0.990871i	$0.456956\pi$
$182$		0			0
$183$	1.21778e9			0.0802674
$184$	−5.44768e8	−	9.43566e8i	−0.0350374	−	0.0606865i
$185$	−3.34495e9	+	5.79362e9i	−0.209950	+	0.363645i
$186$	2.22599e8	−	3.85553e8i	0.0136369	−	0.0236198i
$187$	−1.69550e8	−	2.93669e8i	−0.0101394	−	0.0175619i
$188$	−1.35495e10			−0.791068
$189$		0			0
$190$	−2.30342e9			−0.128228
$191$	1.29494e10	+	2.24290e10i	0.704043	+	1.21944i	0.967036	+	0.254641i	$0.0819571\pi$
$191$	1.29494e10	+	2.24290e10i	0.704043	+	1.21944i	−0.262993	+	0.964798i	$0.584710\pi$
$192$	−5.03316e7	+	8.71770e7i	−0.00267292	+	0.00462963i
$193$	−7.96837e9	+	1.38016e10i	−0.413391	+	0.716015i	−0.995258	−	0.0972694i	$-0.968989\pi$
$193$	−7.96837e9	+	1.38016e10i	−0.413391	+	0.716015i	0.581867	+	0.813284i	$0.302323\pi$
$194$	6.98001e9	+	1.20897e10i	0.353792	+	0.612786i
$195$	−3.80258e8			−0.0188331
$196$		0			0
$197$	−3.34685e9			−0.158321			−0.0791604	−	0.996862i	$-0.525224\pi$
$197$	−3.34685e9			−0.158321			−0.0791604	+	0.996862i	$0.525224\pi$
$198$	8.51139e9	+	1.47422e10i	0.393557	+	0.681660i
$199$	−6.71304e9	+	1.16273e10i	−0.303445	+	0.525583i	−0.976914	−	0.213633i	$-0.931470\pi$
$199$	−6.71304e9	+	1.16273e10i	−0.303445	+	0.525583i	0.673469	+	0.739216i	$0.264804\pi$
$200$	−3.35775e9	+	5.81579e9i	−0.148393	+	0.257024i
$201$	−4.61204e8	−	7.98828e8i	−0.0199301	−	0.0345200i
$202$	−1.93442e10			−0.817467
$203$		0			0
$204$	−9.61843e6			−0.000388838
$205$	−6.13456e9	−	1.06254e10i	−0.242600	−	0.420195i
$206$	−5.52450e9	+	9.56872e9i	−0.213742	+	0.370213i
$207$	−2.61305e9	+	4.52594e9i	−0.0989194	+	0.171333i
$208$	−3.70842e9	−	6.42317e9i	−0.137374	−	0.237938i
$209$	1.39213e10			0.504686
$210$		0			0
$211$	3.01702e10			1.04787			0.523935	−	0.851759i	$-0.324464\pi$
$211$	3.01702e10			1.04787			0.523935	+	0.851759i	$0.324464\pi$
$212$	−2.07632e9	−	3.59629e9i	−0.0705963	−	0.122276i
$213$	−8.38968e8	+	1.45313e9i	−0.0279278	+	0.0483724i
$214$	1.43599e9	−	2.48722e9i	0.0468049	−	0.0810684i
$215$	7.70577e9	+	1.33468e10i	0.245948	+	0.425994i
$216$	9.66574e8			0.0302130
$217$		0			0
$218$	2.56577e10			0.769421
$219$	−1.21207e9	−	2.09936e9i	−0.0356064	−	0.0616722i
$220$	−3.88162e9	+	6.72316e9i	−0.111715	+	0.193496i
$221$	3.54342e8	−	6.13738e8i	0.00999210	−	0.0173068i
$222$	−5.73419e8	−	9.93192e8i	−0.0158447	−	0.0274438i
$223$	−5.35030e10			−1.44879			−0.724396	−	0.689384i	$-0.757881\pi$
$223$	−5.35030e10			−1.44879			−0.724396	+	0.689384i	$0.757881\pi$
$224$		0			0
$225$	3.22117e10			0.837901
$226$	1.14228e10	+	1.97849e10i	0.291263	+	0.504482i
$227$	−2.01352e10	+	3.48752e10i	−0.503315	+	0.871766i	0.496678	+	0.867935i	$0.334553\pi$
$227$	−2.01352e10	+	3.48752e10i	−0.503315	+	0.871766i	−0.999993	+	0.00383159i	$0.998780\pi$
$228$	1.97436e8	−	3.41969e8i	0.00483860	−	0.00838069i
$229$	9.51236e9	+	1.64759e10i	0.228575	+	0.395903i	0.957386	−	0.288812i	$-0.0932601\pi$
$229$	9.51236e9	+	1.64759e10i	0.228575	+	0.395903i	−0.728811	+	0.684715i	$0.759927\pi$
$230$	−2.38336e9			−0.0561584
$231$		0			0
$232$	−6.45003e9			−0.146173
$233$	1.83874e10	+	3.18479e10i	0.408713	+	0.707911i	0.994746	−	0.102376i	$-0.0326444\pi$
$233$	1.83874e10	+	3.18479e10i	0.408713	+	0.707911i	−0.586033	+	0.810287i	$0.699311\pi$
$234$	−1.77879e10	+	3.08096e10i	−0.387841	+	0.671761i
$235$	−1.48198e10	+	2.56686e10i	−0.316984	+	0.549032i
$236$	−1.79852e10	−	3.11513e10i	−0.377409	−	0.653691i
$237$	−7.84139e8			−0.0161445
$238$		0			0
$239$	6.56110e9			0.130073			0.0650363	−	0.997883i	$-0.479284\pi$
$239$	6.56110e9			0.130073			0.0650363	+	0.997883i	$0.479284\pi$
$240$	1.10100e8	+	1.90700e8i	0.00214209	+	0.00371022i
$241$	−4.48409e10	+	7.76667e10i	−0.856244	+	1.48306i	0.0192424	+	0.999815i	$0.493875\pi$
$241$	−4.48409e10	+	7.76667e10i	−0.856244	+	1.48306i	−0.875486	+	0.483243i	$0.839459\pi$
$242$	4.59593e9	−	7.96039e9i	0.0861399	−	0.149199i
$243$	−3.47829e9	−	6.02457e9i	−0.0639937	−	0.110840i
$244$	5.19587e10			0.938434
$245$		0			0
$246$	2.10328e9			0.0366175
$247$	1.45470e10	+	2.51962e10i	0.248678	+	0.430723i
$248$	9.49757e9	−	1.64503e10i	0.159434	−	0.276147i
$249$	1.26040e9	−	2.18308e9i	0.0207784	−	0.0359892i
$250$	1.60951e10	+	2.78775e10i	0.260593	+	0.451360i
$251$	−5.33703e9			−0.0848727			−0.0424363	−	0.999099i	$-0.513512\pi$
$251$	−5.33703e9			−0.0848727			−0.0424363	+	0.999099i	$0.513512\pi$
$252$		0			0
$253$	1.44044e10			0.221031
$254$	−1.88698e10	−	3.26835e10i	−0.284457	−	0.492693i
$255$	−1.05202e7	+	1.82215e7i	−0.000155809	+	0.000269868i
$256$	−2.14748e9	+	3.71955e9i	−0.0312500	+	0.0541266i
$257$	−4.17788e10	−	7.23630e10i	−0.597388	−	1.03471i	−0.993205	−	0.116377i	$-0.962872\pi$
$257$	−4.17788e10	−	7.23630e10i	−0.597388	−	1.03471i	0.395817	−	0.918329i	$-0.370461\pi$
$258$	−2.64198e9			−0.0371228
$259$		0			0
$260$	−1.62243e10			−0.220185
$261$	1.54692e10	+	2.67934e10i	0.206341	+	0.357393i
$262$	−4.81332e9	+	8.33692e9i	−0.0631087	+	0.109307i
$263$	−5.43174e10	+	9.40806e10i	−0.700065	+	1.21255i	0.268378	+	0.963314i	$0.413512\pi$
$263$	−5.43174e10	+	9.40806e10i	−0.700065	+	1.21255i	−0.968443	+	0.249235i	$0.919821\pi$
$264$	−6.65420e8	−	1.15254e9i	−0.00843098	−	0.0146029i
$265$	−9.08388e9			−0.113153
$266$		0			0
$267$	2.81725e9			0.0339254
$268$	−1.96780e10	−	3.40833e10i	−0.233010	−	0.403586i
$269$	7.07003e10	−	1.22456e11i	0.823258	−	1.42592i	−0.0799860	−	0.996796i	$-0.525488\pi$
$269$	7.07003e10	−	1.22456e11i	0.823258	−	1.42592i	0.903244	−	0.429128i	$-0.141179\pi$
$270$	1.05719e9	−	1.83111e9i	0.0121064	−	0.0209690i
$271$	−4.54176e10	−	7.86657e10i	−0.511520	−	0.885979i	−0.999911	−	0.0133539i	$-0.995749\pi$
$271$	−4.54176e10	−	7.86657e10i	−0.511520	−	0.885979i	0.488391	−	0.872625i	$-0.337584\pi$
$272$	−4.10386e8			−0.00454604
$273$		0			0
$274$	8.25614e10			0.884911
$275$	−4.43918e10	−	7.68888e10i	−0.468064	−	0.810711i
$276$	2.04288e8	−	3.53837e8i	0.00211910	−	0.00367039i
$277$	1.32538e10	−	2.29562e10i	0.135263	−	0.234283i	−0.790435	−	0.612546i	$-0.790145\pi$
$277$	1.32538e10	−	2.29562e10i	0.135263	−	0.234283i	0.925698	+	0.378263i	$0.123479\pi$
$278$	5.71485e10	+	9.89841e10i	0.573857	+	0.993949i
$279$	−9.11126e10			−0.900243
$280$		0			0
$281$	−1.86968e11			−1.78891			−0.894455	−	0.447158i	$-0.852436\pi$
$281$	−1.86968e11			−1.78891			−0.894455	+	0.447158i	$0.852436\pi$
$282$	−2.54054e9	−	4.40034e9i	−0.0239224	−	0.0414348i
$283$	−2.66706e9	+	4.61949e9i	−0.0247169	+	0.0428110i	−0.878119	−	0.478442i	$-0.841202\pi$
$283$	−2.66706e9	+	4.61949e9i	−0.0247169	+	0.0428110i	0.853402	+	0.521253i	$0.174535\pi$
$284$	−3.57960e10	+	6.20004e10i	−0.326514	+	0.565538i
$285$	−4.31891e8	−	7.48057e8i	−0.00387768	−	0.00671634i
$286$	9.80558e10			0.866615
$287$		0			0
$288$	2.06014e10			0.176453
$289$	5.92743e10	+	1.02666e11i	0.499835	+	0.865739i
$290$	−7.05472e9	+	1.22191e10i	−0.0585718	+	0.101449i
$291$	−2.61751e9	+	4.53365e9i	−0.0213978	+	0.0370621i
$292$	−5.17149e10	−	8.95729e10i	−0.416287	−	0.721031i
$293$	−7.65433e10			−0.606741			−0.303370	−	0.952873i	$-0.598112\pi$
$293$	−7.65433e10			−0.606741			−0.303370	+	0.952873i	$0.598112\pi$
$294$		0			0
$295$	−7.86854e10			−0.604916
$296$	−2.44659e10	−	4.23762e10i	−0.185246	−	0.320855i
$297$	−6.38939e9	+	1.10668e10i	−0.0476492	+	0.0825308i
$298$	7.28339e10	−	1.26152e11i	0.535008	−	0.926662i
$299$	1.50519e10	+	2.60706e10i	0.108911	+	0.188639i
$300$	−2.51831e9			−0.0179500
$301$		0			0
$302$	4.63091e9			0.0320358
$303$	−3.62704e9	−	6.28223e9i	−0.0247207	−	0.0428175i
$304$	8.42393e9	−	1.45907e10i	0.0565697	−	0.0979816i
$305$	5.68298e10	−	9.84321e10i	0.376034	−	0.651310i
$306$	9.84236e8	+	1.70475e9i	0.00641731	+	0.0111151i
$307$	7.51944e10			0.483128			0.241564	−	0.970385i	$-0.422340\pi$
$307$	7.51944e10			0.483128			0.241564	+	0.970385i	$0.422340\pi$
$308$		0			0
$309$	−4.14338e9			−0.0258548
$310$	−2.07759e10	−	3.59850e10i	−0.127771	−	0.221306i
$311$	1.07567e11	−	1.86311e11i	0.652014	−	1.12932i	−0.330619	−	0.943764i	$-0.607257\pi$
$311$	1.07567e11	−	1.86311e11i	0.652014	−	1.12932i	0.982633	−	0.185558i	$-0.0594092\pi$
$312$	1.39066e9	−	2.40869e9i	0.00830854	−	0.0143908i
$313$	4.79537e10	+	8.30583e10i	0.282405	+	0.489140i	0.971977	−	0.235077i	$-0.0755344\pi$
$313$	4.79537e10	+	8.30583e10i	0.282405	+	0.489140i	−0.689571	+	0.724218i	$0.742201\pi$
$314$	2.22508e11			1.29170
$315$		0			0
$316$	−3.34566e10			−0.188751
$317$	−8.52932e10	−	1.47732e11i	−0.474403	−	0.821691i	0.525167	−	0.850999i	$-0.324003\pi$
$317$	−8.52932e10	−	1.47732e11i	−0.474403	−	0.821691i	−0.999570	+	0.0293083i	$0.990670\pi$
$318$	7.78619e8	−	1.34861e9i	0.00426975	−	0.00739543i
$319$	4.26370e10	−	7.38494e10i	0.230530	−	0.399290i
$320$	4.69762e9	+	8.13652e9i	0.0250440	+	0.0433774i
$321$	1.07700e9			0.00566163
$322$		0			0
$323$	1.60982e9			0.00822937
$324$	−4.93179e10	−	8.54211e10i	−0.248629	−	0.430638i
$325$	9.27742e10	−	1.60690e11i	0.461266	−	0.798937i
$326$	1.32986e11	−	2.30338e11i	0.652119	−	1.12950i
$327$	4.81083e9	+	8.33259e9i	0.0232678	+	0.0403010i
$328$	8.97398e10			0.428107
$329$		0			0
$330$	−2.91121e9			−0.0135133
$331$	6.19958e10	+	1.07380e11i	0.283881	+	0.491697i	0.972337	−	0.233581i	$-0.0750445\pi$
$331$	6.19958e10	+	1.07380e11i	0.283881	+	0.491697i	−0.688456	+	0.725278i	$0.741711\pi$
$332$	5.37772e10	−	9.31448e10i	0.242927	−	0.420763i
$333$	−1.17354e11	+	2.03263e11i	−0.522996	+	0.905856i
$334$	1.26416e11	+	2.18958e11i	0.555829	+	0.962724i
$335$	−8.60914e10			−0.373472
$336$		0			0
$337$	−7.29335e10			−0.308030			−0.154015	−	0.988069i	$-0.549220\pi$
$337$	−7.29335e10			−0.308030			−0.154015	+	0.988069i	$0.549220\pi$
$338$	1.76272e10	+	3.05312e10i	0.0734613	+	0.127239i
$339$	−4.28355e9	+	7.41933e9i	−0.0176159	+	0.0305117i
$340$	−4.48860e8	+	7.77449e8i	−0.00182161	+	0.00315512i
$341$	1.25565e11	+	2.17484e11i	0.502889	+	0.871029i
$342$	−8.08130e10			−0.319421
$343$		0			0
$344$	−1.12724e11			−0.434015
$345$	−4.46880e8	−	7.74019e8i	−0.00169826	−	0.00294148i
$346$	−2.58500e10	+	4.47735e10i	−0.0969657	+	0.167949i
$347$	7.78602e10	−	1.34858e11i	0.288292	−	0.499337i	−0.685110	−	0.728440i	$-0.740246\pi$
$347$	7.78602e10	−	1.34858e11i	0.288292	−	0.499337i	0.973402	+	0.229103i	$0.0735792\pi$
$348$	−1.20938e9	−	2.09471e9i	−0.00442035	−	0.00765626i
$349$	−1.08728e11			−0.392310			−0.196155	−	0.980573i	$-0.562846\pi$
$349$	−1.08728e11			−0.392310			−0.196155	+	0.980573i	$0.562846\pi$
$350$		0			0
$351$	−2.67063e10			−0.0939144
$352$	−2.83912e10	−	4.91751e10i	−0.0985695	−	0.170727i
$353$	1.62793e11	−	2.81965e11i	0.558018	−	0.966516i	−0.439644	−	0.898172i	$-0.644895\pi$
$353$	1.62793e11	−	2.81965e11i	0.558018	−	0.966516i	0.997662	−	0.0683436i	$-0.0217714\pi$
$354$	6.74446e9	−	1.16818e10i	0.0228261	−	0.0395360i
$355$	7.83037e10	+	1.35626e11i	0.261670	+	0.453226i
$356$	1.20203e11			0.396634
$357$		0			0
$358$	3.86252e11			1.24279
$359$	1.13775e11	+	1.97064e11i	0.361511	+	0.626155i	0.988210	−	0.153106i	$-0.0489277\pi$
$359$	1.13775e11	+	1.97064e11i	0.361511	+	0.626155i	−0.626699	+	0.779261i	$0.715594\pi$
$360$	2.25328e10	−	3.90279e10i	0.0707055	−	0.122465i
$361$	1.28299e11	−	2.22221e11i	0.397596	−	0.688656i
$362$	3.11465e10	+	5.39474e10i	0.0953282	+	0.165113i
$363$	3.44695e9			0.0104197
$364$		0			0
$365$	−2.26253e11			−0.667231
$366$	9.74225e9	+	1.68741e10i	0.0283788	+	0.0491536i
$367$	−2.10996e11	+	3.65457e11i	−0.607125	+	1.05157i	0.384587	+	0.923089i	$0.374344\pi$
$367$	−2.10996e11	+	3.65457e11i	−0.607125	+	1.05157i	−0.991712	+	0.128482i	$0.958989\pi$
$368$	8.71629e9	−	1.50971e10i	0.0247752	−	0.0429118i
$369$	−2.15224e11	−	3.72779e11i	−0.604328	−	1.04673i
$370$	−1.07038e11			−0.296915
$371$		0			0
$372$	7.12318e9			0.0192855
$373$	−1.91642e11	−	3.31933e11i	−0.512625	−	0.887893i	−0.999893	−	0.0146401i	$-0.995340\pi$
$373$	−1.91642e11	−	3.31933e11i	−0.512625	−	0.887893i	0.487268	−	0.873253i	$-0.337994\pi$
$374$	2.71280e9	−	4.69870e9i	0.00716961	−	0.0124181i
$375$	−6.03565e9	+	1.04541e10i	−0.0157610	+	0.0272988i
$376$	−1.08396e11	−	1.87748e11i	−0.279685	−	0.484428i
$377$	1.78214e11			0.454365
$378$		0			0
$379$	−1.21462e11			−0.302386			−0.151193	−	0.988504i	$-0.548312\pi$
$379$	−1.21462e11			−0.302386			−0.151193	+	0.988504i	$0.548312\pi$
$380$	−1.84274e10	−	3.19171e10i	−0.0453353	−	0.0785231i
$381$	7.07618e9	−	1.22563e10i	0.0172043	−	0.0297987i
$382$	−2.07190e11	+	3.58864e11i	−0.497834	+	0.862273i
$383$	−1.98860e11	−	3.44436e11i	−0.472230	−	0.817927i	0.527265	−	0.849701i	$-0.323218\pi$
$383$	−1.98860e11	−	3.44436e11i	−0.472230	−	0.817927i	−0.999495	+	0.0317740i	$0.989884\pi$
$384$	−1.61061e9			−0.00378008
$385$		0			0
$386$	−2.54988e11			−0.584624
$387$	2.70349e11	+	4.68257e11i	0.612667	+	1.06117i
$388$	−1.11680e11	+	1.93436e11i	−0.250169	+	0.433305i
$389$	−3.37731e10	+	5.84968e10i	−0.0747821	+	0.129526i	−0.900992	−	0.433837i	$-0.857159\pi$
$389$	−3.37731e10	+	5.84968e10i	−0.0747821	+	0.129526i	0.826209	+	0.563363i	$0.190493\pi$
$390$	−3.04206e9	−	5.26901e9i	−0.00665852	−	0.0115329i
$391$	1.66569e9			0.00360412
$392$		0			0
$393$	−3.60999e9			−0.00763378
$394$	−2.67748e10	−	4.63753e10i	−0.0559748	−	0.0969512i
$395$	−3.65931e10	+	6.33812e10i	−0.0756333	+	0.131001i
$396$	−1.36182e11	+	2.35875e11i	−0.278287	+	0.482007i
$397$	6.23278e10	+	1.07955e11i	0.125929	+	0.218115i	0.922096	−	0.386962i	$-0.126476\pi$
$397$	6.23278e10	+	1.07955e11i	0.125929	+	0.218115i	−0.796167	+	0.605077i	$0.793142\pi$
$398$	−2.14817e11			−0.429136
$399$		0			0
$400$	−1.07448e11			−0.209859
$401$	−1.75598e11	−	3.04144e11i	−0.339133	−	0.587395i	0.645137	−	0.764067i	$-0.276800\pi$
$401$	−1.75598e11	−	3.04144e11i	−0.339133	−	0.587395i	−0.984270	+	0.176672i	$0.943467\pi$
$402$	7.37926e9	−	1.27813e10i	0.0140927	−	0.0244093i
$403$	−2.62417e11	+	4.54519e11i	−0.495586	+	0.858380i
$404$	−1.54754e11	−	2.68042e11i	−0.289018	−	0.500594i
$405$	−2.15766e11			−0.398506
$406$		0			0
$407$	6.46913e11			1.16861
$408$	−7.69475e7	−	1.33277e8i	−0.000137475	−	0.000238114i
$409$	−1.90978e10	+	3.30784e10i	−0.0337465	+	0.0584506i	−0.882405	−	0.470490i	$-0.844077\pi$
$409$	−1.90978e10	+	3.30784e10i	−0.0337465	+	0.0584506i	0.848659	+	0.528941i	$0.177411\pi$
$410$	9.81529e10	−	1.70006e11i	0.171544	−	0.297123i
$411$	1.54803e10	+	2.68126e10i	0.0267602	+	0.0463501i
$412$	−1.76784e11			−0.302277
$413$		0			0
$414$	−8.36176e10			−0.139893
$415$	−1.17638e11	−	2.03754e11i	−0.194684	−	0.337202i
$416$	5.93347e10	−	1.02771e11i	0.0971379	−	0.168248i
$417$	−2.14307e10	+	3.71190e10i	−0.0347075	+	0.0601152i
$418$	1.11370e11	+	1.92899e11i	0.178433	+	0.309056i
$419$	−2.15268e11			−0.341205			−0.170603	−	0.985340i	$-0.554571\pi$
$419$	−2.15268e11			−0.341205			−0.170603	+	0.985340i	$0.554571\pi$
$420$		0			0
$421$	1.19933e12			1.86066			0.930332	−	0.366718i	$-0.119519\pi$
$421$	1.19933e12			1.86066			0.930332	+	0.366718i	$0.119519\pi$
$422$	2.41362e11	+	4.18050e11i	0.370478	+	0.641686i
$423$	−5.19937e11	+	9.00557e11i	−0.789621	+	1.36766i
$424$	3.32211e10	−	5.75406e10i	0.0499191	−	0.0864625i
$425$	−5.13335e9	−	8.89123e9i	−0.00763222	−	0.0132194i
$426$	−2.68470e10			−0.0394959
$427$		0			0
$428$	4.59518e10			0.0661921
$429$	1.83855e10	+	3.18446e10i	0.0262070	+	0.0453918i
$430$	−1.23292e11	+	2.13548e11i	−0.173911	+	0.301223i
$431$	−3.95559e11	+	6.85128e11i	−0.552158	+	0.956365i	0.445961	+	0.895052i	$0.352862\pi$
$431$	−3.95559e11	+	6.85128e11i	−0.552158	+	0.956365i	−0.998119	+	0.0613129i	$0.980471\pi$
$432$	7.73259e9	+	1.33932e10i	0.0106819	+	0.0185016i
$433$	1.15451e12			1.57834			0.789170	−	0.614174i	$-0.210511\pi$
$433$	1.15451e12			1.57834			0.789170	+	0.614174i	$0.210511\pi$
$434$		0			0
$435$	−5.29104e9			−0.00708499
$436$	2.05262e11	+	3.55524e11i	0.272031	+	0.471172i
$437$	−3.41914e10	+	5.92212e10i	−0.0448487	+	0.0776803i
$438$	1.93931e10	−	3.35898e10i	0.0251776	−	0.0436088i
$439$	−1.06364e11	−	1.84228e11i	−0.136680	−	0.236737i	0.789558	−	0.613676i	$-0.210310\pi$
$439$	−1.06364e11	−	1.84228e11i	−0.136680	−	0.236737i	−0.926238	+	0.376939i	$0.876977\pi$
$440$	−1.24212e11			−0.157988
$441$		0			0
$442$	1.13389e10			0.0141310
$443$	3.24150e10	+	5.61444e10i	0.0399880	+	0.0692612i	0.885327	−	0.464969i	$-0.153935\pi$
$443$	3.24150e10	+	5.61444e10i	0.0399880	+	0.0692612i	−0.845339	+	0.534231i	$0.820601\pi$
$444$	9.17471e9	−	1.58911e10i	0.0112039	−	0.0194057i
$445$	1.31472e11	−	2.27716e11i	0.158933	−	0.275279i
$446$	−4.28024e11	−	7.41359e11i	−0.512225	−	0.887200i
$447$	5.46255e10			0.0647159
$448$		0			0
$449$	−1.08031e12			−1.25441			−0.627207	−	0.778853i	$-0.715802\pi$
$449$	−1.08031e12			−1.25441			−0.627207	+	0.778853i	$0.715802\pi$
$450$	2.57694e11	+	4.46339e11i	0.296243	+	0.513108i
$451$	−5.93211e11	+	1.02747e12i	−0.675173	+	1.16943i
$452$	−1.82765e11	+	3.16558e11i	−0.205954	+	0.356722i
$453$	8.68296e8	+	1.50393e9i	0.000968782	+	0.00167798i
$454$	−6.44326e11			−0.711794
$455$		0			0
$456$	6.31795e9			0.00684281
$457$	3.23363e10	+	5.60081e10i	0.0346790	+	0.0600658i	0.882844	−	0.469666i	$-0.155626\pi$
$457$	3.23363e10	+	5.60081e10i	0.0346790	+	0.0600658i	−0.848165	+	0.529732i	$0.822292\pi$
$458$	−1.52198e11	+	2.63614e11i	−0.161627	+	0.279946i
$459$	−7.38853e8	+	1.27973e9i	−0.000776965	+	0.00134574i
$460$	−1.90669e10	−	3.30248e10i	−0.0198550	−	0.0343898i
$461$	−4.29254e11			−0.442649			−0.221325	−	0.975200i	$-0.571038\pi$
$461$	−4.29254e11			−0.442649			−0.221325	+	0.975200i	$0.571038\pi$
$462$		0			0
$463$	1.61883e12			1.63715			0.818574	−	0.574401i	$-0.194765\pi$
$463$	1.61883e12			1.63715			0.818574	+	0.574401i	$0.194765\pi$
$464$	−5.16002e10	−	8.93742e10i	−0.0516798	−	0.0895120i
$465$	7.79097e9	−	1.34944e10i	0.00772776	−	0.0133849i
$466$	−2.94198e11	+	5.09566e11i	−0.289004	+	0.500569i
$467$	1.63661e11	+	2.83468e11i	0.159228	+	0.275790i	0.934590	−	0.355726i	$-0.115766\pi$
$467$	1.63661e11	+	2.83468e11i	0.159228	+	0.275790i	−0.775363	+	0.631516i	$0.782433\pi$
$468$	−5.69214e11			−0.548490
$469$		0			0
$470$	−4.74233e11			−0.448283
$471$	4.17203e10	+	7.22617e10i	0.0390619	+	0.0676573i
$472$	2.87764e11	−	4.98421e11i	0.266868	−	0.462229i
$473$	7.45148e11	−	1.29063e12i	0.684490	−	1.18557i
$474$	−6.27311e9	−	1.08653e10i	−0.00570795	−	0.00988647i
$475$	4.21486e11			0.379893
$476$		0			0
$477$	−3.18698e11			−0.281869
$478$	5.24888e10	+	9.09132e10i	0.0459876	+	0.0796529i
$479$	1.42406e11	−	2.46654e11i	0.123600	−	0.214081i	−0.797585	−	0.603206i	$-0.793889\pi$
$479$	1.42406e11	−	2.46654e11i	0.123600	−	0.214081i	0.921185	+	0.389126i	$0.127223\pi$
$480$	−1.76161e9	+	3.05119e9i	−0.00151469	+	0.00262352i
$481$	6.75990e11	+	1.17085e12i	0.575821	+	0.997351i
$482$	−1.43491e12			−1.21091
$483$		0			0
$484$	1.47070e11			0.121820
$485$	2.44300e11	+	4.23141e11i	0.200487	+	0.347254i
$486$	5.56526e10	−	9.63931e10i	0.0452504	−	0.0783759i
$487$	3.57388e11	−	6.19014e11i	0.287912	−	0.498678i	−0.685399	−	0.728167i	$-0.740372\pi$
$487$	3.57388e11	−	6.19014e11i	0.287912	−	0.498678i	0.973311	+	0.229490i	$0.0737057\pi$
$488$	4.15669e11	+	7.19960e11i	0.331787	+	0.574671i
$489$	9.97395e10			0.0788819
$490$		0			0
$491$	1.01506e12			0.788176			0.394088	−	0.919073i	$-0.371061\pi$
$491$	1.01506e12			0.788176			0.394088	+	0.919073i	$0.371061\pi$
$492$	1.68262e10	+	2.91438e10i	0.0129462	+	0.0224235i
$493$	4.93043e9	−	8.53975e9i	0.00375901	−	0.00651080i
$494$	−2.32752e11	+	4.03139e11i	−0.175842	+	0.304567i
$495$	2.97899e11	+	5.15976e11i	0.223021	+	0.386283i
$496$	3.03922e11			0.225473
$497$		0			0
$498$	4.03329e10			0.0293851
$499$	−6.67062e11	−	1.15539e12i	−0.481630	−	0.834208i	0.518148	−	0.855291i	$-0.326622\pi$
$499$	−6.67062e11	−	1.15539e12i	−0.481630	−	0.834208i	−0.999778	+	0.0210833i	$0.993288\pi$
$500$	−2.57521e11	+	4.46040e11i	−0.184267	+	0.319160i
$501$	−4.74058e10	+	8.21093e10i	−0.0336172	+	0.0582267i
$502$	−4.26962e10	−	7.39520e10i	−0.0300070	−	0.0519737i
$503$	5.68445e11			0.395943			0.197971	−	0.980208i	$-0.436565\pi$
$503$	5.68445e11			0.395943			0.197971	+	0.980208i	$0.436565\pi$
$504$		0			0
$505$	−6.77048e11			−0.463243
$506$	1.15235e11	+	1.99594e11i	0.0781464	+	0.135353i
$507$	−6.61021e9	+	1.14492e10i	−0.00444303	+	0.00769555i
$508$	3.01917e11	−	5.22936e11i	0.201141	−	0.348387i
$509$	1.78586e11	+	3.09321e11i	0.117928	+	0.204258i	0.918947	−	0.394382i	$-0.129041\pi$
$509$	1.78586e11	+	3.09321e11i	0.117928	+	0.204258i	−0.801018	+	0.598640i	$0.795708\pi$
$510$	−3.36645e8			−0.000220347
$511$		0			0
$512$	−6.87195e10			−0.0441942
$513$	−3.03326e10	−	5.25377e10i	−0.0193367	−	0.0334921i
$514$	6.68460e11	−	1.15781e12i	0.422417	−	0.731648i
$515$	−1.93358e11	+	3.34905e11i	−0.121124	+	0.209792i
$516$	−2.11358e10	−	3.66083e10i	−0.0131249	−	0.0227330i
$517$	2.86615e12			1.76438
$518$		0			0
$519$	−1.93875e10			−0.0117292
$520$	−1.29795e11	−	2.24811e11i	−0.0778470	−	0.134835i
$521$	1.08986e12	−	1.88770e12i	0.648040	−	1.12244i	−0.335550	−	0.942022i	$-0.608922\pi$
$521$	1.08986e12	−	1.88770e12i	0.648040	−	1.12244i	0.983590	−	0.180416i	$-0.0577444\pi$
$522$	−2.47507e11	+	4.28695e11i	−0.145905	+	0.252715i
$523$	−7.85404e11	−	1.36036e12i	−0.459024	−	0.795053i	0.539885	−	0.841738i	$-0.318468\pi$
$523$	−7.85404e11	−	1.36036e12i	−0.459024	−	0.795053i	−0.998910	+	0.0466853i	$0.985134\pi$
$524$	−1.54026e11			−0.0892492
$525$		0			0
$526$	−1.73816e12			−0.990042
$527$	1.45200e10	+	2.51493e10i	0.00820007	+	0.0142029i
$528$	1.06467e10	−	1.84407e10i	0.00596160	−	0.0103258i
$529$	8.65198e11	−	1.49857e12i	0.480358	−	0.832005i
$530$	−7.26711e10	−	1.25870e11i	−0.0400055	−	0.0692916i
$531$	−2.76059e12			−1.50687
$532$		0			0
$533$	−2.47950e12			−1.33074
$534$	2.25380e10	+	3.90370e10i	0.0119945	+	0.0207750i
$535$	5.02598e10	−	8.70526e10i	0.0265234	−	0.0459399i
$536$	3.14848e11	−	5.45333e11i	0.164763	−	0.285378i
$537$	7.24223e10	+	1.25439e11i	0.0375827	+	0.0650952i
$538$	2.26241e12			1.16426
$539$		0			0
$540$	3.38301e10			0.0171211
$541$	−1.12272e12	−	1.94460e12i	−0.563486	−	0.975986i	−0.997189	−	0.0749302i	$-0.976127\pi$
$541$	−1.12272e12	−	1.94460e12i	−0.563486	−	0.975986i	0.433703	−	0.901056i	$-0.357207\pi$
$542$	7.26682e11	−	1.25865e12i	0.361699	−	0.626482i
$543$	−1.16800e10	+	2.02303e10i	−0.00576556	+	0.00998625i
$544$	−3.28309e9	−	5.68648e9i	−0.00160727	−	0.00278387i
$545$	8.98021e11			0.436016
$546$		0			0
$547$	−3.86062e11			−0.184380			−0.0921899	−	0.995741i	$-0.529387\pi$
$547$	−3.86062e11			−0.184380			−0.0921899	+	0.995741i	$0.529387\pi$
$548$	6.60491e11	+	1.14400e12i	0.312863	+	0.541895i
$549$	1.99381e12	−	3.45338e12i	0.936718	−	1.62244i
$550$	7.10268e11	−	1.23022e12i	0.330971	−	0.573259i
$551$	2.02412e11	+	3.50588e11i	0.0935523	+	0.162037i
$552$	6.53722e9			0.00299686
$553$		0			0
$554$	4.24120e11			0.191291
$555$	−2.00697e10	−	3.47617e10i	−0.00897888	−	0.0155519i
$556$	−9.14376e11	+	1.58375e12i	−0.405778	+	0.702828i
$557$	3.97551e11	−	6.88578e11i	0.175003	−	0.303113i	−0.765160	−	0.643841i	$-0.777340\pi$
$557$	3.97551e11	−	6.88578e11i	0.175003	−	0.303113i	0.940162	+	0.340727i	$0.110673\pi$
$558$	−7.28901e11	−	1.26249e12i	−0.318284	−	0.551284i
$559$	3.11456e12			1.34910
$560$		0			0
$561$	2.03460e9			0.000867253
$562$	−1.49574e12	−	2.59070e12i	−0.632475	−	1.09548i
$563$	−1.06834e12	+	1.85041e12i	−0.448146	+	0.776212i	−0.998265	−	0.0588741i	$-0.981249\pi$
$563$	−1.06834e12	+	1.85041e12i	−0.448146	+	0.776212i	0.550119	+	0.835086i	$0.314582\pi$
$564$	4.06486e10	−	7.04054e10i	0.0169157	−	0.0292988i
$565$	3.99798e11	+	6.92471e11i	0.165053	+	0.285880i
$566$	−8.53460e10			−0.0349550
$567$		0			0
$568$	−1.14547e12			−0.461760
$569$	−1.08731e12	−	1.88327e12i	−0.434857	−	0.753194i	0.562427	−	0.826847i	$-0.309868\pi$
$569$	−1.08731e12	−	1.88327e12i	−0.434857	−	0.753194i	−0.997284	+	0.0736527i	$0.976534\pi$
$570$	6.91026e9	−	1.19689e10i	0.00274194	−	0.00474917i
$571$	−4.97538e11	+	8.61760e11i	−0.195868	+	0.339253i	−0.947185	−	0.320689i	$-0.896086\pi$
$571$	−4.97538e11	+	8.61760e11i	−0.195868	+	0.339253i	0.751317	+	0.659942i	$0.229419\pi$
$572$	7.84447e11	+	1.35870e12i	0.306395	+	0.530691i
$573$	−1.55393e11			−0.0602192
$574$		0			0
$575$	4.36114e11			0.166377
$576$	1.64811e11	+	2.85461e11i	0.0623857	+	0.108055i
$577$	2.15294e12	−	3.72900e12i	0.808614	−	1.40056i	−0.105211	−	0.994450i	$-0.533552\pi$
$577$	2.15294e12	−	3.72900e12i	0.808614	−	1.40056i	0.913824	−	0.406110i	$-0.133115\pi$
$578$	−9.48389e11	+	1.64266e12i	−0.353436	+	0.612170i
$579$	−4.78102e10	−	8.28097e10i	−0.0176794	−	0.0306216i
$580$	−2.25751e11			−0.0828331
$581$		0			0
$582$	−8.37602e10			−0.0302611
$583$	4.39206e11	+	7.60727e11i	0.157456	+	0.272722i
$584$	8.27439e11	−	1.43317e12i	0.294359	−	0.509846i
$585$	−6.22577e11	+	1.07834e12i	−0.219782	+	0.380673i
$586$	−6.12347e11	−	1.06062e12i	−0.214515	−	0.371551i
$587$	−5.05762e12			−1.75822			−0.879112	−	0.476615i	$-0.841864\pi$
$587$	−5.05762e12			−1.75822			−0.879112	+	0.476615i	$0.841864\pi$
$588$		0			0
$589$	−1.19220e12			−0.408158
$590$	−6.29483e11	−	1.09030e12i	−0.213870	−	0.370434i
$591$	1.00405e10	−	1.73907e10i	0.00338543	−	0.00586373i
$592$	3.91454e11	−	6.78019e11i	0.130989	−	0.226879i
$593$	−1.40150e12	−	2.42747e12i	−0.465422	−	0.806135i	0.533798	−	0.845612i	$-0.320764\pi$
$593$	−1.40150e12	−	2.42747e12i	−0.465422	−	0.806135i	−0.999220	+	0.0394771i	$0.987431\pi$
$594$	−2.04461e11			−0.0673862
$595$		0			0
$596$	2.33069e12			0.756616
$597$	−4.02782e10	−	6.97640e10i	−0.0129773	−	0.0224774i
$598$	−2.40830e11	+	4.17130e11i	−0.0770114	+	0.133388i
$599$	−1.60454e12	+	2.77914e12i	−0.509247	+	0.882042i	0.490696	+	0.871331i	$0.336743\pi$
$599$	−1.60454e12	+	2.77914e12i	−0.509247	+	0.882042i	−0.999943	+	0.0107108i	$0.996591\pi$
$600$	−2.01465e10	−	3.48947e10i	−0.00634627	−	0.0109921i
$601$	−7.49502e11			−0.234335			−0.117168	−	0.993112i	$-0.537381\pi$
$601$	−7.49502e11			−0.234335			−0.117168	+	0.993112i	$0.537381\pi$
$602$		0			0
$603$	−3.02042e12			−0.930336
$604$	3.70473e10	+	6.41678e10i	0.0113264	+	0.0196178i
$605$	1.60858e11	−	2.78614e11i	0.0488138	−	0.0845479i
$606$	5.80327e10	−	1.00516e11i	0.0174802	−	0.0302766i
$607$	−8.70485e11	−	1.50772e12i	−0.260263	−	0.450789i	0.706049	−	0.708163i	$-0.250476\pi$
$607$	−8.70485e11	−	1.50772e12i	−0.260263	−	0.450789i	−0.966312	+	0.257375i	$0.917143\pi$
$608$	2.69566e11			0.0800016
$609$		0			0
$610$	1.81855e12			0.531792
$611$	2.99497e12	+	5.18745e12i	0.869376	+	1.50580i
$612$	−1.57478e10	+	2.72760e10i	−0.00453772	+	0.00785956i
$613$	2.01989e12	−	3.49854e12i	0.577770	−	1.00073i	−0.417965	−	0.908463i	$-0.637257\pi$
$613$	2.01989e12	−	3.49854e12i	0.577770	−	1.00073i	0.995735	−	0.0922632i	$-0.0294101\pi$
$614$	6.01555e11	+	1.04192e12i	0.170812	+	0.295855i
$615$	7.36147e10			0.0207504
$616$		0			0
$617$	−2.93367e12			−0.814945			−0.407472	−	0.913218i	$-0.633590\pi$
$617$	−2.93367e12			−0.814945			−0.407472	+	0.913218i	$0.633590\pi$
$618$	−3.31470e10	−	5.74123e10i	−0.00914105	−	0.0158328i
$619$	−2.88846e12	+	5.00295e12i	−0.790784	+	1.36968i	0.134698	+	0.990887i	$0.456994\pi$
$619$	−2.88846e12	+	5.00295e12i	−0.790784	+	1.36968i	−0.925482	+	0.378792i	$0.876340\pi$
$620$	3.32415e11	−	5.75759e11i	0.0903478	−	0.156487i
$621$	−3.13853e10	−	5.43610e10i	−0.00846866	−	0.0146681i
$622$	3.44214e12			0.922088
$623$		0			0
$624$	4.45010e10			0.0117500
$625$	−1.03777e12	−	1.79747e12i	−0.272045	−	0.471197i
$626$	−7.67260e11	+	1.32893e12i	−0.199691	+	0.345874i
$627$	−4.17639e10	+	7.23371e10i	−0.0107919	+	0.0186921i
$628$	1.78007e12	+	3.08317e12i	0.456686	+	0.791004i
$629$	7.48073e10			0.0190553
$630$		0			0
$631$	3.99985e12			1.00441			0.502206	−	0.864748i	$-0.332522\pi$
$631$	3.99985e12			1.00441			0.502206	+	0.864748i	$0.332522\pi$
$632$	−2.67653e11	−	4.63588e11i	−0.0667336	−	0.115586i
$633$	−9.05106e10	+	1.56769e11i	−0.0224069	+	0.0388100i
$634$	1.36469e12	−	2.36372e12i	0.335454	−	0.581023i
$635$	−6.60444e11	−	1.14392e12i	−0.161196	−	0.279200i
$636$	2.49158e10			0.00603834
$637$		0			0
$638$	1.36438e12			0.326019
$639$	2.74720e12	+	4.75829e12i	0.651833	+	1.12901i
$640$	−7.51619e10	+	1.30184e11i	−0.0177088	+	0.0306725i
$641$	−2.34164e12	+	4.05584e12i	−0.547846	+	0.948898i	0.450575	+	0.892738i	$0.351219\pi$
$641$	−2.34164e12	+	4.05584e12i	−0.547846	+	0.948898i	−0.998422	+	0.0561595i	$0.982114\pi$
$642$	8.61597e9	+	1.49233e10i	0.00200169	+	0.00346703i
$643$	1.54877e12			0.357304			0.178652	−	0.983912i	$-0.442826\pi$
$643$	1.54877e12			0.357304			0.178652	+	0.983912i	$0.442826\pi$
$644$		0			0
$645$	−9.24692e10			−0.0210367
$646$	1.28786e10	+	2.23064e10i	0.00290952	+	0.00503944i
$647$	−4.07246e12	+	7.05372e12i	−0.913667	+	1.58252i	−0.104826	+	0.994491i	$0.533429\pi$
$647$	−4.07246e12	+	7.05372e12i	−0.913667	+	1.58252i	−0.808841	+	0.588028i	$0.799905\pi$
$648$	7.89086e11	−	1.36674e12i	0.175807	−	0.304507i
$649$	3.80444e12	+	6.58948e12i	0.841762	+	1.45797i
$650$	2.96877e12			0.652329
$651$		0			0
$652$	4.25555e12			0.922235
$653$	1.44463e12	+	2.50216e12i	0.310918	+	0.538526i	0.978561	−	0.205955i	$-0.0660302\pi$
$653$	1.44463e12	+	2.50216e12i	0.310918	+	0.538526i	−0.667643	+	0.744481i	$0.732697\pi$
$654$	−7.69732e10	+	1.33322e11i	−0.0164528	+	0.0284971i
$655$	−1.68466e11	+	2.91792e11i	−0.0357624	+	0.0619424i
$656$	7.17918e11	+	1.24347e12i	0.151359	+	0.262161i
$657$	−7.93784e12			−1.66210
$658$		0			0
$659$	5.20255e12			1.07456			0.537281	−	0.843403i	$-0.319451\pi$
$659$	5.20255e12			1.07456			0.537281	+	0.843403i	$0.319451\pi$
$660$	−2.32897e10	−	4.03389e10i	−0.00477767	−	0.00827517i
$661$	1.44486e12	−	2.50258e12i	0.294388	−	0.509896i	−0.680454	−	0.732791i	$-0.738217\pi$
$661$	1.44486e12	−	2.50258e12i	0.294388	−	0.509896i	0.974842	+	0.222895i	$0.0715507\pi$
$662$	−9.91933e11	+	1.71808e12i	−0.200734	+	0.347682i
$663$	2.12605e9	+	3.68243e9i	0.000427329	+	0.000740156i
$664$	1.72087e12			0.343551
$665$		0			0
$666$	−3.75532e12			−0.739628
$667$	2.09437e11	+	3.62755e11i	0.0409720	+	0.0709656i
$668$	−2.02265e12	+	3.50333e12i	−0.393031	+	0.680749i
$669$	1.60509e11	−	2.78009e11i	0.0309800	−	0.0536589i
$670$	−6.88731e11	−	1.19292e12i	−0.132042	−	0.228704i
$671$	−1.09909e13			−2.09306
$672$		0			0
$673$	9.46362e12			1.77824			0.889119	−	0.457677i	$-0.151318\pi$
$673$	9.46362e12			1.77824			0.889119	+	0.457677i	$0.151318\pi$
$674$	−5.83468e11	−	1.01060e12i	−0.108905	−	0.188629i
$675$	−1.93448e11	+	3.35061e11i	−0.0358671	+	0.0621236i
$676$	−2.82035e11	+	4.88500e11i	−0.0519450	+	0.0899714i
$677$	−3.26134e12	−	5.64881e12i	−0.596688	−	1.03349i	−0.993306	−	0.115510i	$-0.963150\pi$
$677$	−3.26134e12	−	5.64881e12i	−0.596688	−	1.03349i	0.396619	−	0.917983i	$-0.370183\pi$
$678$	−1.37074e11			−0.0249127
$679$		0			0
$680$	−1.43635e10			−0.00257615
$681$	−1.20811e11	−	2.09251e11i	−0.0215251	−	0.0372826i
$682$	−2.00903e12	+	3.47975e12i	−0.355596	+	0.615911i
$683$	−2.68620e12	+	4.65264e12i	−0.472330	+	0.818099i	−0.999499	−	0.0316613i	$-0.989920\pi$
$683$	−2.68620e12	+	4.65264e12i	−0.472330	+	0.818099i	0.527169	+	0.849761i	$0.323254\pi$
$684$	−6.46504e11	−	1.11978e12i	−0.112932	−	0.195605i
$685$	2.88965e12			0.501461
$686$		0			0
$687$	−1.14148e11			−0.0195508
$688$	−9.01795e11	−	1.56195e12i	−0.153447	−	0.265779i
$689$	−9.17894e11	+	1.58984e12i	−0.155169	+	0.268761i
$690$	7.15008e9	−	1.23843e10i	0.00120085	−	0.00207994i
$691$	1.00781e12	+	1.74559e12i	0.168163	+	0.291266i	0.937774	−	0.347246i	$-0.112883\pi$
$691$	1.00781e12	+	1.74559e12i	0.168163	+	0.291266i	−0.769611	+	0.638513i	$0.779550\pi$
$692$	−8.27200e11			−0.137130
$693$		0			0
$694$	2.49153e12			0.407707
$695$	2.00020e12	+	3.46444e12i	0.325193	+	0.563251i
$696$	1.93501e10	−	3.35153e10i	0.00312566	−	0.00541380i
$697$	−6.85975e10	+	1.18814e11i	−0.0110093	+	0.0190687i
$698$	−8.69828e11	−	1.50659e12i	−0.138702	−	0.240240i
$699$	−2.20649e11			−0.0349586
$700$		0			0
$701$	−1.06523e13			−1.66614			−0.833068	−	0.553171i	$-0.813418\pi$
$701$	−1.06523e13			−1.66614			−0.833068	+	0.553171i	$0.813418\pi$
$702$	−2.13651e11	−	3.70054e11i	−0.0332038	−	0.0575106i
$703$	−1.53556e12	+	2.65966e12i	−0.237119	+	0.410703i
$704$	4.54260e11	−	7.86801e11i	0.0696991	−	0.120722i
$705$	−8.89188e10	−	1.54012e11i	−0.0135563	−	0.0234803i
$706$	5.20936e12			0.789157
$707$		0			0
$708$	2.15823e11			0.0322810
$709$	−1.73093e12	−	2.99807e12i	−0.257260	−	0.445588i	0.708247	−	0.705965i	$-0.249486\pi$
$709$	−1.73093e12	−	2.99807e12i	−0.257260	−	0.445588i	−0.965507	+	0.260377i	$0.916153\pi$
$710$	−1.25286e12	+	2.17001e12i	−0.185029	+	0.320479i
$711$	−1.28383e12	+	2.22366e12i	−0.188406	+	0.326329i
$712$	9.61623e11	+	1.66558e12i	0.140231	+	0.242888i
$713$	−1.23357e12			−0.178756
$714$		0			0
$715$	3.43195e12			0.491094
$716$	3.09002e12	+	5.35207e12i	0.439393	+	0.761050i
$717$	−1.96833e10	+	3.40925e10i	−0.00278139	+	0.00481750i
$718$	−1.82040e12	+	3.15302e12i	−0.255627	+	0.442758i
$719$	−4.81013e12	−	8.33138e12i	−0.671238	−	1.16262i	−0.977553	−	0.210688i	$-0.932430\pi$
$719$	−4.81013e12	−	8.33138e12i	−0.671238	−	1.16262i	0.306316	−	0.951930i	$-0.400904\pi$
$720$	7.21048e11			0.0999926
$721$		0			0
$722$	4.10558e12			0.562285
$723$	−2.69045e11	−	4.66000e11i	−0.0366187	−	0.0634255i
$724$	−4.98345e11	+	8.63158e11i	−0.0674072	+	0.116753i
$725$	1.29089e12	−	2.23589e12i	0.173528	−	0.300559i
$726$	2.75756e10	+	4.77623e10i	0.00368392	+	0.00638073i
$727$	3.13479e12			0.416202			0.208101	−	0.978107i	$-0.433272\pi$
$727$	3.13479e12			0.416202			0.208101	+	0.978107i	$0.433272\pi$
$728$		0			0
$729$	−7.54204e12			−0.989043
$730$	−1.81002e12	−	3.13505e12i	−0.235902	−	0.408594i
$731$	8.61670e10	−	1.49246e11i	0.0111612	−	0.0193318i
$732$	−1.55876e11	+	2.69985e11i	−0.0200669	+	0.0347568i
$733$	3.23887e12	+	5.60989e12i	0.414406	+	0.717772i	0.995366	−	0.0961599i	$-0.0306560\pi$
$733$	3.23887e12	+	5.60989e12i	0.414406	+	0.717772i	−0.580960	+	0.813932i	$0.697323\pi$
$734$	−6.75189e12			−0.858604
$735$		0			0
$736$	2.78921e11			0.0350374
$737$	4.16252e12	+	7.20969e12i	0.519700	+	0.900146i
$738$	3.44359e12	−	5.96447e12i	0.427324	−	0.740148i
$739$	5.62550e11	−	9.74365e11i	0.0693843	−	0.120177i	−0.829246	−	0.558884i	$-0.811230\pi$
$739$	5.62550e11	−	9.74365e11i	0.0693843	−	0.120177i	0.898630	+	0.438706i	$0.144563\pi$
$740$	−8.56306e11	−	1.48317e12i	−0.104975	−	0.181822i
$741$	−1.74564e11			−0.0212703
$742$		0			0
$743$	1.65266e12			0.198945			0.0994725	−	0.995040i	$-0.468284\pi$
$743$	1.65266e12			0.198945			0.0994725	+	0.995040i	$0.468284\pi$
$744$	5.69854e10	+	9.87016e10i	0.00681845	+	0.0118099i
$745$	2.54919e12	−	4.41532e12i	0.303179	−	0.525121i
$746$	3.06626e12	−	5.31093e12i	0.362481	−	0.627835i
$747$	−4.12719e12	−	7.14850e12i	−0.484966	−	0.839986i
$748$	8.68096e10			0.0101394
$749$		0			0
$750$	−1.93141e11			−0.0222894
$751$	−3.01649e12	−	5.22472e12i	−0.346037	−	0.599354i	0.639505	−	0.768787i	$-0.279140\pi$
$751$	−3.01649e12	−	5.22472e12i	−0.346037	−	0.599354i	−0.985542	+	0.169434i	$0.945806\pi$
$752$	1.73434e12	−	3.00396e12i	0.197767	−	0.342542i
$753$	1.60111e10	−	2.77320e10i	0.00181486	−	0.00314343i
$754$	1.42571e12	+	2.46940e12i	0.160642	+	0.278240i
$755$	1.62082e11			0.0181540
$756$		0			0
$757$	−8.02798e12			−0.888535			−0.444268	−	0.895894i	$-0.646536\pi$
$757$	−8.02798e12			−0.888535			−0.444268	+	0.895894i	$0.646536\pi$
$758$	−9.71692e11	−	1.68302e12i	−0.106910	−	0.185173i
$759$	−4.32133e10	+	7.48476e10i	−0.00472639	+	0.00818634i
$760$	2.94838e11	−	5.10674e11i	0.0320569	−	0.0555242i
$761$	−3.25961e12	−	5.64582e12i	−0.352318	−	0.610233i	0.634337	−	0.773057i	$-0.281273\pi$
$761$	−3.25961e12	−	5.64582e12i	−0.352318	−	0.610233i	−0.986655	+	0.162824i	$0.947940\pi$
$762$	2.26438e11			0.0243305
$763$		0			0
$764$	−6.63009e12			−0.704043
$765$	3.44483e10	+	5.96661e10i	0.00363656	+	0.00629871i
$766$	3.18177e12	−	5.51098e12i	0.333917	−	0.578362i
$767$	−7.95088e12	+	1.37713e13i	−0.829537	+	1.43680i
$768$	−1.28849e10	−	2.23173e10i	−0.00133646	−	0.00231481i
$769$	1.34250e13			1.38435			0.692175	−	0.721730i	$-0.256653\pi$
$769$	1.34250e13			1.38435			0.692175	+	0.721730i	$0.256653\pi$
$770$		0			0
$771$	5.01345e11			0.0510966
$772$	−2.03990e12	−	3.53321e12i	−0.206696	−	0.358007i
$773$	3.92967e12	−	6.80639e12i	0.395866	−	0.685660i	−0.597345	−	0.801984i	$-0.703778\pi$
$773$	3.92967e12	−	6.80639e12i	0.395866	−	0.685660i	0.993211	+	0.116324i	$0.0371110\pi$
$774$	−4.32558e12	+	7.49212e12i	−0.433221	+	0.750361i
$775$	3.80164e12	+	6.58463e12i	0.378541	+	0.655652i
$776$	−3.57377e12			−0.353792
$777$		0			0
$778$	−1.08074e12			−0.105758
$779$	−2.81618e12	−	4.87776e12i	−0.273994	−	0.474572i
$780$	4.86730e10	−	8.43041e10i	0.00470828	−	0.00815498i
$781$	7.57196e12	−	1.31150e13i	0.728247	−	1.26136i
$782$	1.33255e10	+	2.30805e10i	0.00127425	+	0.00220706i
$783$	−3.71601e11			−0.0353304
$784$		0			0
$785$	7.78780e12			0.731983
$786$	−2.88799e10	−	5.00215e10i	−0.00269895	−	0.00467472i
$787$	−7.38601e11	+	1.27930e12i	−0.0686316	+	0.118873i	−0.898299	−	0.439384i	$-0.855197\pi$
$787$	−7.38601e11	+	1.27930e12i	−0.0686316	+	0.118873i	0.829668	+	0.558258i	$0.188530\pi$
$788$	4.28396e11	−	7.42004e11i	0.0395802	−	0.0685549i
$789$	−3.25905e11	−	5.64483e11i	−0.0299395	−	0.0518567i
$790$	−1.17098e12			−0.106962
$791$		0			0
$792$	−4.35783e12			−0.393557
$793$	−1.14849e13	−	1.98924e13i	−1.03133	−	1.78632i
$794$	−9.97245e11	+	1.72728e12i	−0.0890450	+	0.154231i
$795$	2.72517e10	−	4.72012e10i	0.00241958	−	0.00419084i
$796$	−1.71854e12	−	2.97660e12i	−0.151723	−	0.262791i
$797$	6.47327e12			0.568278			0.284139	−	0.958783i	$-0.408292\pi$
$797$	6.47327e12			0.568278			0.284139	+	0.958783i	$0.408292\pi$
$798$		0			0
$799$	3.31434e11			0.0287698
$800$	−8.59583e11	−	1.48884e12i	−0.0741964	−	0.128512i
$801$	4.61255e12	−	7.98917e12i	0.395908	−	0.685733i
$802$	2.80957e12	−	4.86631e12i	0.239803	−	0.415351i
$803$	1.09393e13	+	1.89475e13i	0.928476	+	1.60817i
$804$	2.36136e11			0.0199301
$805$		0			0
$806$	−8.39733e12			−0.700864
$807$	4.24202e11	+	7.34739e11i	0.0352080	+	0.0609820i
$808$	2.47606e12	−	4.28867e12i	0.204367	−	0.353974i
$809$	7.68155e12	−	1.33048e13i	0.630493	−	1.09205i	−0.356958	−	0.934120i	$-0.616186\pi$
$809$	7.68155e12	−	1.33048e13i	0.630493	−	1.09205i	0.987451	−	0.157925i	$-0.0504806\pi$
$810$	−1.72613e12	−	2.98974e12i	−0.140893	−	0.244034i
$811$	1.29056e13			1.04757			0.523787	−	0.851849i	$-0.324519\pi$
$811$	1.29056e13			1.04757			0.523787	+	0.851849i	$0.324519\pi$
$812$		0			0
$813$	5.45012e11			0.0437520
$814$	5.17530e12	+	8.96389e12i	0.413167	+	0.715627i
$815$	4.65451e12	−	8.06185e12i	0.369543	−	0.640067i
$816$	1.23116e9	−	2.13243e9i	9.72095e−5	−	0.000168372i
$817$	3.53747e12	+	6.12708e12i	0.277775	+	0.481121i
$818$	−6.11130e11			−0.0477247
$819$		0			0
$820$	3.14089e12			0.242600
$821$	−4.46886e11	−	7.74029e11i	−0.0343283	−	0.0594583i	0.848351	−	0.529434i	$-0.177596\pi$
$821$	−4.46886e11	−	7.74029e11i	−0.0343283	−	0.0594583i	−0.882679	+	0.469976i	$0.844263\pi$
$822$	−2.47684e11	+	4.29002e11i	−0.0189224	+	0.0327745i
$823$	1.14922e13	−	1.99051e13i	0.873182	−	1.51240i	0.0144950	−	0.999895i	$-0.495386\pi$
$823$	1.14922e13	−	1.99051e13i	0.873182	−	1.51240i	0.858687	−	0.512501i	$-0.171281\pi$
$824$	−1.41427e12	−	2.44959e12i	−0.106871	−	0.185106i
$825$	5.32701e11			0.0400351
$826$		0			0
$827$	−2.75618e12			−0.204896			−0.102448	−	0.994738i	$-0.532667\pi$
$827$	−2.75618e12			−0.204896			−0.102448	+	0.994738i	$0.532667\pi$
$828$	−6.68941e11	−	1.15864e12i	−0.0494597	−	0.0856667i
$829$	−1.57962e12	+	2.73599e12i	−0.116160	+	0.201196i	−0.918243	−	0.396017i	$-0.870392\pi$
$829$	−1.57962e12	+	2.73599e12i	−0.116160	+	0.201196i	0.802083	+	0.597213i	$0.203725\pi$
$830$	1.88220e12	−	3.26007e12i	0.137662	−	0.238438i
$831$	7.95225e10	+	1.37737e11i	0.00578476	+	0.0100195i
$832$	1.89871e12			0.137374
$833$		0			0
$834$	−6.85782e11			−0.0490839
$835$	4.42454e12	+	7.66353e12i	0.314977	+	0.545557i
$836$	−1.78192e12	+	3.08638e12i	−0.126171	+	0.218535i
$837$	5.47177e11	−	9.47738e11i	0.0385357	−	0.0667458i
$838$	−1.72214e12	−	2.98284e12i	−0.120634	−	0.208945i
$839$	−1.92403e13			−1.34055			−0.670277	−	0.742111i	$-0.733825\pi$
$839$	−1.92403e13			−1.34055			−0.670277	+	0.742111i	$0.733825\pi$
$840$		0			0
$841$	−1.20274e13			−0.829069
$842$	9.59461e12	+	1.66184e13i	0.657844	+	1.13942i
$843$	5.60904e11	−	9.71514e11i	0.0382529	−	0.0662559i
$844$	−3.86178e12	+	6.68881e12i	−0.261967	+	0.453741i
$845$	6.16953e11	+	1.06859e12i	0.0416291	+	0.0721036i
$846$	−1.66380e13			−1.11669
$847$		0			0
$848$	1.06307e12			0.0705963
$849$	−1.60024e10	−	2.77169e10i	−0.00105706	−	0.00183088i
$850$	8.21336e10	−	1.42260e11i	0.00539680	−	0.00934752i
$851$	−1.58885e12	+	2.75197e12i	−0.103848	+	0.179871i
$852$	−2.14776e11	−	3.72003e11i	−0.0139639	−	0.0241862i
$853$	2.60804e13			1.68672			0.843362	−	0.537345i	$-0.180573\pi$
$853$	2.60804e13			1.68672			0.843362	+	0.537345i	$0.180573\pi$
$854$		0			0
$855$	−2.82845e12			−0.181010
$856$	3.67615e11	+	6.36727e11i	0.0234024	+	0.0405342i
$857$	1.09588e13	−	1.89813e13i	0.693986	−	1.20202i	−0.276535	−	0.961004i	$-0.589186\pi$
$857$	1.09588e13	−	1.89813e13i	0.693986	−	1.20202i	0.970521	−	0.241015i	$-0.0774804\pi$
$858$	−2.94168e11	+	5.09513e11i	−0.0185311	+	0.0320969i
$859$	−1.77794e12	−	3.07948e12i	−0.111416	−	0.192978i	0.804925	−	0.593376i	$-0.202205\pi$
$859$	−1.77794e12	−	3.07948e12i	−0.111416	−	0.192978i	−0.916341	+	0.400398i	$0.868872\pi$
$860$	−3.94535e12			−0.245948
$861$		0			0
$862$	−1.26579e13			−0.780869
$863$	−1.11042e13	−	1.92330e13i	−0.681458	−	1.18032i	−0.974536	−	0.224231i	$-0.928013\pi$
$863$	−1.11042e13	−	1.92330e13i	−0.681458	−	1.18032i	0.293079	−	0.956088i	$-0.405320\pi$
$864$	−1.23721e11	+	2.14292e11i	−0.00755324	+	0.0130826i
$865$	−9.04750e11	+	1.56707e12i	−0.0549485	+	0.0951736i
$866$	9.23605e12	+	1.59973e13i	0.558028	+	0.966532i
$867$	−7.11292e11			−0.0427525
$868$		0			0
$869$	7.07711e12			0.420986
$870$	−4.23283e10	−	7.33148e10i	−0.00250492	−	0.00433865i
$871$	−8.69922e12	+	1.50675e13i	−0.512152	+	0.887073i
$872$	−3.28419e12	+	5.68838e12i	−0.192355	+	0.333169i
$873$	8.57102e12	+	1.48454e13i	0.499423	+	0.865026i
$874$	−1.09412e12			−0.0634257
$875$		0			0
$876$	6.20579e11			0.0356064
$877$	−1.69002e12	−	2.92720e12i	−0.0964703	−	0.167091i	0.813751	−	0.581214i	$-0.197422\pi$
$877$	−1.69002e12	−	2.92720e12i	−0.0964703	−	0.167091i	−0.910221	+	0.414122i	$0.864089\pi$
$878$	1.70183e12	−	2.94765e12i	0.0966473	−	0.167398i
$879$	2.29630e11	−	3.97731e11i	0.0129741	−	0.0224719i
$880$	−9.93694e11	−	1.72113e12i	−0.0558574	−	0.0967478i
$881$	−5.25103e11			−0.0293665			−0.0146833	−	0.999892i	$-0.504674\pi$
$881$	−5.25103e11			−0.0293665			−0.0146833	+	0.999892i	$0.504674\pi$
$882$		0			0
$883$	3.33972e13			1.84879			0.924393	−	0.381441i	$-0.124572\pi$
$883$	3.33972e13			1.84879			0.924393	+	0.381441i	$0.124572\pi$
$884$	9.07114e10	+	1.57117e11i	0.00499605	+	0.00865341i
$885$	2.36056e11	−	4.08861e11i	0.0129351	−	0.0224043i
$886$	−5.18640e11	+	8.98311e11i	−0.0282758	+	0.0489750i
$887$	−4.80982e12	−	8.33086e12i	−0.260899	−	0.451891i	0.705582	−	0.708628i	$-0.250686\pi$
$887$	−4.80982e12	−	8.33086e12i	−0.260899	−	0.451891i	−0.966481	+	0.256738i	$0.917352\pi$
$888$	2.93591e11			0.0158447
$889$		0			0
$890$	4.20710e12			0.224765
$891$	1.04323e13	+	1.80692e13i	0.554536	+	0.960484i
$892$	6.84838e12	−	1.18617e13i	0.362198	−	0.627345i
$893$	−6.80329e12	+	1.17836e13i	−0.358004	+	0.620081i
$894$	4.37004e11	+	7.56912e11i	0.0228805	+	0.0396303i
$895$	1.35188e13			0.704264
$896$		0			0
$897$	−1.80623e11			−0.00931549
$898$	−8.64250e12	−	1.49692e13i	−0.443502	−	0.768168i
$899$	−3.65136e12	+	6.32433e12i	−0.186438	+	0.322921i
$900$	−4.12310e12	+	7.14143e12i	−0.209475	+	0.362822i
$901$	5.07886e10	+	8.79685e10i	0.00256747	+	0.00444699i
$902$	−1.89828e13			−0.954839
$903$		0			0
$904$	−5.84848e12			−0.291263
$905$	1.09013e12	+	1.88816e12i	0.0540206	+	0.0935664i
$906$	−1.38927e10	+	2.40629e10i	−0.000685032	+	0.00118651i
$907$	1.04170e13	−	1.80428e13i	0.511107	−	0.885263i	−0.488811	−	0.872390i	$-0.662569\pi$
$907$	1.04170e13	−	1.80428e13i	0.511107	−	0.885263i	0.999917	−	0.0128726i	$-0.00409760\pi$
$908$	−5.15461e12	−	8.92805e12i	−0.251657	−	0.435883i
$909$	−2.37535e13			−1.15396
$910$		0			0
$911$	−1.33789e13			−0.643560			−0.321780	−	0.946814i	$-0.604281\pi$
$911$	−1.33789e13			−0.643560			−0.321780	+	0.946814i	$0.604281\pi$
$912$	5.05436e10	+	8.75441e10i	0.00241930	+	0.00419035i
$913$	−1.13755e13	+	1.97030e13i	−0.541819	+	0.938457i
$914$	−5.17380e11	+	8.96129e11i	−0.0245218	+	0.0424730i
$915$	3.40979e11	+	5.90593e11i	0.0160817	+	0.0278544i
$916$	−4.87033e12			−0.228575
$917$		0			0
$918$	−2.36433e10			−0.00109879
$919$	6.91758e12	+	1.19816e13i	0.319915	+	0.554109i	0.980470	−	0.196669i	$-0.0630123\pi$
$919$	6.91758e12	+	1.19816e13i	0.319915	+	0.554109i	−0.660555	+	0.750778i	$0.729679\pi$
$920$	3.05070e11	−	5.28397e11i	0.0140396	−	0.0243173i
$921$	−2.25583e11	+	3.90721e11i	−0.0103309	+	0.0178936i
$922$	−3.43403e12	−	5.94791e12i	−0.156500	−	0.271066i
$923$	3.16492e13			1.43534
$924$		0			0
$925$	1.95862e13			0.879653
$926$	1.29507e13	+	2.24312e13i	0.578819	+	1.00254i
$927$	−6.78374e12	+	1.17498e13i	−0.301724	+	0.522602i
$928$	8.25604e11	−	1.42999e12i	0.0365431	−	0.0632946i
$929$	−8.70364e12	−	1.50751e13i	−0.383380	−	0.664034i	0.608163	−	0.793812i	$-0.291907\pi$
$929$	−8.70364e12	−	1.50751e13i	−0.383380	−	0.664034i	−0.991543	+	0.129778i	$0.958574\pi$
$930$	2.49311e11			0.0109287
$931$		0			0
$932$	−9.41434e12			−0.408713
$933$	6.45402e11	+	1.11787e12i	0.0278845	+	0.0482974i
$934$	−2.61857e12	+	4.53549e12i	−0.112591	+	0.195013i
$935$	9.49480e10	−	1.64455e11i	0.00406287	−	0.00703710i
$936$	−4.55371e12	−	7.88725e12i	−0.193921	−	0.335880i
$937$	−1.98361e12			−0.0840676			−0.0420338	−	0.999116i	$-0.513384\pi$
$937$	−1.98361e12			−0.0840676			−0.0420338	+	0.999116i	$0.513384\pi$
$938$		0			0
$939$	−5.75445e11			−0.0241551
$940$	−3.79387e12	−	6.57117e12i	−0.158492	−	0.274516i
$941$	−1.16767e13	+	2.02246e13i	−0.485473	+	0.840864i	−0.999861	−	0.0166939i	$-0.994686\pi$
$941$	−1.16767e13	+	2.02246e13i	−0.485473	+	0.840864i	0.514388	+	0.857558i	$0.328019\pi$
$942$	−6.67525e11	+	1.15619e12i	−0.0276210	+	0.0478409i
$943$	−2.91391e12	−	5.04705e12i	−0.119998	−	0.207843i
$944$	9.20844e12			0.377409
$945$		0			0
$946$	2.38447e13			0.968015
$947$	−1.79941e13	−	3.11667e13i	−0.727035	−	1.25926i	−0.958131	−	0.286331i	$-0.907564\pi$
$947$	−1.79941e13	−	3.11667e13i	−0.727035	−	1.25926i	0.231095	−	0.972931i	$-0.425769\pi$
$948$	1.00370e11	−	1.73846e11i	0.00403613	−	0.00699079i
$949$	−2.28620e13	+	3.95982e13i	−0.914991	+	1.58481i
$950$	3.37189e12	+	5.84028e12i	0.134313	+	0.232636i
$951$	1.02352e12			0.0405773
$952$		0			0
$953$	−1.37662e13			−0.540624			−0.270312	−	0.962773i	$-0.587127\pi$
$953$	−1.37662e13			−0.540624			−0.270312	+	0.962773i	$0.587127\pi$
$954$	−2.54959e12	−	4.41601e12i	−0.0996557	−	0.172609i
$955$	−7.25166e12	+	1.25602e13i	−0.282112	+	0.488633i
$956$	−8.39820e11	+	1.45461e12i	−0.0325181	+	0.0563231i
$957$	2.55822e11	+	4.43096e11i	0.00985902	+	0.0170763i
$958$	4.55698e12			0.174796
$959$		0			0
$960$	−5.63714e10			−0.00214209
$961$	2.46668e12	+	4.27242e12i	0.0932949	+	0.161592i
$962$	−1.08158e13	+	1.87336e13i	−0.407167	+	0.705234i
$963$	1.76331e12	−	3.05415e12i	0.0660710	−	0.114438i
$964$	−1.14793e13	−	1.98827e13i	−0.428122	−	0.741529i
$965$	−8.92457e12			−0.331295
$966$		0			0
$967$	−3.02718e12			−0.111332			−0.0556659	−	0.998449i	$-0.517728\pi$
$967$	−3.02718e12			−0.111332			−0.0556659	+	0.998449i	$0.517728\pi$
$968$	1.17656e12	+	2.03786e12i	0.0430700	+	0.0745993i
$969$	−4.82947e9	+	8.36488e9i	−0.000175971	+	0.000304792i
$970$	−3.90881e12	+	6.77025e12i	−0.141766	+	0.245546i
$971$	−1.26591e13	−	2.19263e13i	−0.457002	−	0.791550i	0.541799	−	0.840508i	$-0.317743\pi$
$971$	−1.26591e13	−	2.19263e13i	−0.457002	−	0.791550i	−0.998801	+	0.0489579i	$0.984410\pi$
$972$	1.78088e12			0.0639937
$973$		0			0
$974$	1.14364e13			0.407169
$975$	5.56645e11	+	9.64137e11i	0.0197268	+	0.0341679i
$976$	−6.65071e12	+	1.15194e13i	−0.234609	+	0.406354i
$977$	−4.95365e12	+	8.57997e12i	−0.173940	+	0.301273i	−0.939794	−	0.341742i	$-0.888983\pi$
$977$	−4.95365e12	+	8.57997e12i	−0.173940	+	0.301273i	0.765854	+	0.643015i	$0.222317\pi$
$978$	7.97916e11	+	1.38203e12i	0.0278890	+	0.0483051i
$979$	−2.54267e13			−0.884641
$980$		0			0
$981$	3.15061e13			1.08614
$982$	8.12045e12	+	1.40650e13i	0.278662	+	0.482657i
$983$	1.20262e13	−	2.08299e13i	0.410805	−	0.711536i	−0.584173	−	0.811629i	$-0.698581\pi$
$983$	1.20262e13	−	2.08299e13i	0.410805	−	0.711536i	0.994978	+	0.100094i	$0.0319143\pi$
$984$	−2.69219e11	+	4.66302e11i	−0.00915437	+	0.0158558i
$985$	−9.37117e11	−	1.62313e12i	−0.0317198	−	0.0549403i
$986$	1.57774e11			0.00531604
$987$		0			0
$988$	−7.44807e12			−0.248678
$989$	3.66024e12	+	6.33972e12i	0.121654	+	0.210711i
$990$	−4.76638e12	+	8.25561e12i	−0.157700	+	0.273144i
$991$	−1.57891e13	+	2.73475e13i	−0.520027	+	0.900713i	0.479702	+	0.877431i	$0.340745\pi$
$991$	−1.57891e13	+	2.73475e13i	−0.520027	+	0.900713i	−0.999729	+	0.0232813i	$0.992589\pi$
$992$	2.43138e12	+	4.21127e12i	0.0797168	+	0.138074i
$993$	−7.43950e11			−0.0242813
$994$		0			0
$995$	−7.51860e12			−0.243183
$996$	3.22663e11	+	5.58869e11i	0.0103892	+	0.0179946i
$997$	4.66121e12	−	8.07345e12i	0.149407	−	0.258780i	−0.781602	−	0.623778i	$-0.785597\pi$
$997$	4.66121e12	−	8.07345e12i	0.149407	−	0.258780i	0.931008	+	0.364998i	$0.118930\pi$
$998$	1.06730e13	−	1.84862e13i	0.340564	−	0.589874i
$999$	−1.40954e12	−	2.44139e12i	−0.0447746	−	0.0775519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.e.67.1		2
7.2	even	3	inner	98.10.c.e.79.1		2
7.3	odd	6		14.10.a.a.1.1	✓	1
7.4	even	3		98.10.a.a.1.1		1
7.5	odd	6		98.10.c.f.79.1		2
7.6	odd	2		98.10.c.f.67.1		2
21.17	even	6		126.10.a.e.1.1		1
28.3	even	6		112.10.a.b.1.1		1
35.3	even	12		350.10.c.b.99.2		2
35.17	even	12		350.10.c.b.99.1		2
35.24	odd	6		350.10.a.c.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.a.1.1	✓	1	7.3	odd	6
98.10.a.a.1.1		1	7.4	even	3
98.10.c.e.67.1		2	1.1	even	1	trivial
98.10.c.e.79.1		2	7.2	even	3	inner
98.10.c.f.67.1		2	7.6	odd	2
98.10.c.f.79.1		2	7.5	odd	6
112.10.a.b.1.1		1	28.3	even	6
126.10.a.e.1.1		1	21.17	even	6
350.10.a.c.1.1		1	35.24	odd	6
350.10.c.b.99.1		2	35.17	even	12
350.10.c.b.99.2		2	35.3	even	12

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)

\(f(q)\)	\(=\)	\(q+(8.00000 + 13.8564i) q^{2} +(-3.00000 + 5.19615i) q^{3} +(-128.000 + 221.703i) q^{4} +(280.000 + 484.974i) q^{5} -96.0000 q^{6} -4096.00 q^{8} +(9823.50 + 17014.8i) q^{9} +O(q^{10})\)	\(q+(8.00000 + 13.8564i) q^{2} +(-3.00000 + 5.19615i) q^{3} +(-128.000 + 221.703i) q^{4} +(280.000 + 484.974i) q^{5} -96.0000 q^{6} -4096.00 q^{8} +(9823.50 + 17014.8i) q^{9} +(-4480.00 + 7759.59i) q^{10} +(27076.0 - 46897.0i) q^{11} +(-768.000 - 1330.22i) q^{12} +113172. q^{13} -3360.00 q^{15} +(-32768.0 - 56755.8i) q^{16} +(3131.00 - 5423.05i) q^{17} +(-157176. + 272237. i) q^{18} +(128539. + 222636. i) q^{19} -143360. q^{20} +866432. q^{22} +(133000. + 230363. i) q^{23} +(12288.0 - 21283.4i) q^{24} +(819762. - 1.41987e6i) q^{25} +(905376. + 1.56816e6i) q^{26} -235980. q^{27} +1.57471e6 q^{29} +(-26880.0 - 46557.5i) q^{30} +(-2.31874e6 + 4.01618e6i) q^{31} +(524288. - 908093. i) q^{32} +(162456. + 281382. i) q^{33} +100192. q^{34} -5.02963e6 q^{36} +(5.97312e6 + 1.03457e7i) q^{37} +(-2.05662e6 + 3.56218e6i) q^{38} +(-339516. + 588059. i) q^{39} +(-1.14688e6 - 1.98645e6i) q^{40} -2.19091e7 q^{41} +2.75206e7 q^{43} +(6.93146e6 + 1.20056e7i) q^{44} +(-5.50116e6 + 9.52829e6i) q^{45} +(-2.12800e6 + 3.68580e6i) q^{46} +(2.64639e7 + 4.58369e7i) q^{47} +393216. q^{48} +2.62324e7 q^{50} +(18786.0 + 32538.3i) q^{51} +(-1.44860e7 + 2.50905e7i) q^{52} +(-8.11061e6 + 1.40480e7i) q^{53} +(-1.88784e6 - 3.26983e6i) q^{54} +3.03251e7 q^{55} -1.54247e6 q^{57} +(1.25977e7 + 2.18199e7i) q^{58} +(-7.02548e7 + 1.21685e8i) q^{59} +(430080. - 744920. i) q^{60} +(-1.01482e8 - 1.75772e8i) q^{61} -7.41997e7 q^{62} +1.67772e7 q^{64} +(3.16882e7 + 5.48855e7i) q^{65} +(-2.59930e6 + 4.50211e6i) q^{66} +(-7.68673e7 + 1.33138e8i) q^{67} +(801536. + 1.38830e6i) q^{68} -1.59600e6 q^{69} +2.79656e8 q^{71} +(-4.02371e7 - 6.96926e7i) q^{72} +(-2.02011e8 + 3.49894e8i) q^{73} +(-9.55699e7 + 1.65532e8i) q^{74} +(4.91858e6 + 8.51922e6i) q^{75} -6.58120e7 q^{76} -1.08645e7 q^{78} +(6.53449e7 + 1.13181e8i) q^{79} +(1.83501e7 - 3.17833e7i) q^{80} +(-1.92648e8 + 3.33676e8i) q^{81} +(-1.75273e8 - 3.03582e8i) q^{82} -4.20134e8 q^{83} +3.50672e6 q^{85} +(2.20165e8 + 3.81337e8i) q^{86} +(-4.72414e6 + 8.18245e6i) q^{87} +(-1.10903e8 + 1.92090e8i) q^{88} +(-2.34771e8 - 4.06636e8i) q^{89} -1.76037e8 q^{90} -6.80960e7 q^{92} +(-1.39125e7 - 2.40971e7i) q^{93} +(-4.23423e8 + 7.33390e8i) q^{94} +(-7.19818e7 + 1.24676e8i) q^{95} +(3.14573e6 + 5.44856e6i) q^{96} +8.72502e8 q^{97} +1.06392e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 16 q^{2} - 6 q^{3} - 256 q^{4} + 560 q^{5} - 192 q^{6} - 8192 q^{8} + 19647 q^{9}+O(q^{10}) \) 2 * q + 16 * q^2 - 6 * q^3 - 256 * q^4 + 560 * q^5 - 192 * q^6 - 8192 * q^8 + 19647 * q^9	\( 2 q + 16 q^{2} - 6 q^{3} - 256 q^{4} + 560 q^{5} - 192 q^{6} - 8192 q^{8} + 19647 q^{9} - 8960 q^{10} + 54152 q^{11} - 1536 q^{12} + 226344 q^{13} - 6720 q^{15} - 65536 q^{16} + 6262 q^{17} - 314352 q^{18} + 257078 q^{19} - 286720 q^{20} + 1732864 q^{22} + 266000 q^{23} + 24576 q^{24} + 1639525 q^{25} + 1810752 q^{26} - 471960 q^{27} + 3149428 q^{29} - 53760 q^{30} - 4637484 q^{31} + 1048576 q^{32} + 324912 q^{33} + 200384 q^{34} - 10059264 q^{36} + 11946238 q^{37} - 4113248 q^{38} - 679032 q^{39} - 2293760 q^{40} - 43818252 q^{41} + 55041184 q^{43} + 13862912 q^{44} - 11002320 q^{45} - 4256000 q^{46} + 52927836 q^{47} + 786432 q^{48} + 52464800 q^{50} + 37572 q^{51} - 28972032 q^{52} - 16221222 q^{53} - 3775680 q^{54} + 60650240 q^{55} - 3084936 q^{57} + 25195424 q^{58} - 140509618 q^{59} + 860160 q^{60} - 202963560 q^{61} - 148399488 q^{62} + 33554432 q^{64} + 63376320 q^{65} - 5198592 q^{66} - 153734572 q^{67} + 1603072 q^{68} - 3192000 q^{69} + 559311872 q^{71} - 80474112 q^{72} - 404022830 q^{73} - 191139808 q^{74} + 9837150 q^{75} - 131623936 q^{76} - 21729024 q^{78} + 130689816 q^{79} + 36700160 q^{80} - 385296021 q^{81} - 350546016 q^{82} - 840268028 q^{83} + 7013440 q^{85} + 440329472 q^{86} - 9448284 q^{87} - 221806592 q^{88} - 469542390 q^{89} - 352074240 q^{90} - 136192000 q^{92} - 27824904 q^{93} - 846845376 q^{94} - 143963680 q^{95} + 6291456 q^{96} + 1745003380 q^{97} + 2127848688 q^{99}+O(q^{100}) \) 2 * q + 16 * q^2 - 6 * q^3 - 256 * q^4 + 560 * q^5 - 192 * q^6 - 8192 * q^8 + 19647 * q^9 - 8960 * q^10 + 54152 * q^11 - 1536 * q^12 + 226344 * q^13 - 6720 * q^15 - 65536 * q^16 + 6262 * q^17 - 314352 * q^18 + 257078 * q^19 - 286720 * q^20 + 1732864 * q^22 + 266000 * q^23 + 24576 * q^24 + 1639525 * q^25 + 1810752 * q^26 - 471960 * q^27 + 3149428 * q^29 - 53760 * q^30 - 4637484 * q^31 + 1048576 * q^32 + 324912 * q^33 + 200384 * q^34 - 10059264 * q^36 + 11946238 * q^37 - 4113248 * q^38 - 679032 * q^39 - 2293760 * q^40 - 43818252 * q^41 + 55041184 * q^43 + 13862912 * q^44 - 11002320 * q^45 - 4256000 * q^46 + 52927836 * q^47 + 786432 * q^48 + 52464800 * q^50 + 37572 * q^51 - 28972032 * q^52 - 16221222 * q^53 - 3775680 * q^54 + 60650240 * q^55 - 3084936 * q^57 + 25195424 * q^58 - 140509618 * q^59 + 860160 * q^60 - 202963560 * q^61 - 148399488 * q^62 + 33554432 * q^64 + 63376320 * q^65 - 5198592 * q^66 - 153734572 * q^67 + 1603072 * q^68 - 3192000 * q^69 + 559311872 * q^71 - 80474112 * q^72 - 404022830 * q^73 - 191139808 * q^74 + 9837150 * q^75 - 131623936 * q^76 - 21729024 * q^78 + 130689816 * q^79 + 36700160 * q^80 - 385296021 * q^81 - 350546016 * q^82 - 840268028 * q^83 + 7013440 * q^85 + 440329472 * q^86 - 9448284 * q^87 - 221806592 * q^88 - 469542390 * q^89 - 352074240 * q^90 - 136192000 * q^92 - 27824904 * q^93 - 846845376 * q^94 - 143963680 * q^95 + 6291456 * q^96 + 1745003380 * q^97 + 2127848688 * q^99

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