LMFDB - Embedded newform 98.8.c.h.79.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,8,Mod(67,98)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("98.67"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(98, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 98 = 2 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	98.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,-16,-56,-128,-238,896,0,2048,-1972] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$30.6137324974$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{2389})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 598x^{2} + 597x + 356409 $ x^4 - x^3 + 598x^2 + 597x + 356409
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 14)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$-11.9693 - 20.7315i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.8.c.h.67.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-4.00000 + 6.92820i) q^{2} +(10.4387 + 18.0804i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(-108.377 + 187.715i) q^{5} -167.019 q^{6} +512.000 q^{8} +(875.567 - 1516.53i) q^{9} +(-867.019 - 1501.72i) q^{10} +(-1290.93 - 2235.95i) q^{11} +(668.077 - 1157.14i) q^{12} +8921.97 q^{13} -4525.28 q^{15} +(-2048.00 + 3547.24i) q^{16} +(-5556.44 - 9624.03i) q^{17} +(7004.54 + 12132.2i) q^{18} +(-4323.40 + 7488.34i) q^{19} +13872.3 q^{20} +20654.9 q^{22} +(33028.6 - 57207.2i) q^{23} +(5344.61 + 9257.14i) q^{24} +(15571.2 + 26970.1i) q^{25} +(-35687.9 + 61813.2i) q^{26} +82218.0 q^{27} +128836. q^{29} +(18101.1 - 31352.0i) q^{30} +(-102048. - 176752. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(26951.2 - 46680.9i) q^{33} +88903.0 q^{34} -112073. q^{36} +(-245856. + 425834. i) q^{37} +(-34587.2 - 59906.7i) q^{38} +(93133.8 + 161312. i) q^{39} +(-55489.2 + 96110.2i) q^{40} +623293. q^{41} +422919. q^{43} +(-82619.5 + 143101. i) q^{44} +(189783. + 328714. i) q^{45} +(264229. + 457657. i) q^{46} +(-602714. + 1.04393e6i) q^{47} -85513.8 q^{48} -249139. q^{50} +(116004. - 200925. i) q^{51} +(-285503. - 494506. i) q^{52} +(636483. + 1.10242e6i) q^{53} +(-328872. + 569623. i) q^{54} +559630. q^{55} -180523. q^{57} +(-515342. + 892599. i) q^{58} +(840430. + 1.45567e6i) q^{59} +(144809. + 250816. i) q^{60} +(1.06128e6 - 1.83818e6i) q^{61} +1.63276e6 q^{62} +262144. q^{64} +(-966940. + 1.67479e6i) q^{65} +(215610. + 373447. i) q^{66} +(1.67466e6 + 2.90060e6i) q^{67} +(-355612. + 615938. i) q^{68} +1.37910e6 q^{69} +2.49257e6 q^{71} +(448290. - 776462. i) q^{72} +(-1.63676e6 - 2.83496e6i) q^{73} +(-1.96684e6 - 3.40667e6i) q^{74} +(-325086. + 563065. i) q^{75} +553395. q^{76} -1.49014e6 q^{78} +(2.09920e6 - 3.63591e6i) q^{79} +(-443914. - 768881. i) q^{80} +(-1.05662e6 - 1.83011e6i) q^{81} +(-2.49317e6 + 4.31830e6i) q^{82} -3.35527e6 q^{83} +2.40877e6 q^{85} +(-1.69168e6 + 2.93007e6i) q^{86} +(1.34488e6 + 2.32939e6i) q^{87} +(-660956. - 1.14481e6i) q^{88} +(1.19979e6 - 2.07810e6i) q^{89} -3.03653e6 q^{90} -4.22766e6 q^{92} +(2.13049e6 - 3.69011e6i) q^{93} +(-4.82171e6 - 8.35145e6i) q^{94} +(-937117. - 1.62313e6i) q^{95} +(342055. - 592457. i) q^{96} -4.51506e6 q^{97} -4.52118e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 16 q^{2} - 56 q^{3} - 128 q^{4} - 238 q^{5} + 896 q^{6} + 2048 q^{8} - 1972 q^{9} - 1904 q^{10} - 5848 q^{11} - 3584 q^{12} - 2632 q^{13} - 5784 q^{15} - 8192 q^{16} - 47642 q^{17} - 15776 q^{18}+ \cdots + 15278208 q^{99}+O(q^{100}) $ 4 * q - 16 * q^2 - 56 * q^3 - 128 * q^4 - 238 * q^5 + 896 * q^6 + 2048 * q^8 - 1972 * q^9 - 1904 * q^10 - 5848 * q^11 - 3584 * q^12 - 2632 * q^13 - 5784 * q^15 - 8192 * q^16 - 47642 * q^17 - 15776 * q^18 - 41048 * q^19 + 30464 * q^20 + 93568 * q^22 + 49316 * q^23 - 28672 * q^24 + 108816 * q^25 + 10528 * q^26 + 400624 * q^27 + 345640 * q^29 + 23136 * q^30 - 70252 * q^31 - 65536 * q^32 - 197190 * q^33 + 762272 * q^34 + 252416 * q^36 + 88166 * q^37 - 328384 * q^38 + 973336 * q^39 - 121856 * q^40 + 2312520 * q^41 + 115088 * q^43 - 374272 * q^44 + 300468 * q^45 + 394528 * q^46 - 1412292 * q^47 + 458752 * q^48 - 1741056 * q^50 - 2576256 * q^51 + 84224 * q^52 + 2361174 * q^53 - 1602496 * q^54 + 1258040 * q^55 + 4620796 * q^57 - 1382560 * q^58 + 1842512 * q^59 + 185088 * q^60 + 1278242 * q^61 + 1124032 * q^62 + 1048576 * q^64 - 1716372 * q^65 - 1577520 * q^66 + 2121480 * q^67 - 3049088 * q^68 + 5332236 * q^69 + 7200320 * q^71 - 1009664 * q^72 - 1634682 * q^73 + 705328 * q^74 + 5321176 * q^75 + 5254144 * q^76 - 15573376 * q^78 + 9192604 * q^79 - 974848 * q^80 - 3049498 * q^81 - 9250080 * q^82 + 56560 * q^83 + 6369676 * q^85 - 460352 * q^86 - 691656 * q^87 - 2994176 * q^88 + 8936550 * q^89 - 4807488 * q^90 - 6312448 * q^92 + 14550490 * q^93 - 11298336 * q^94 - 2562604 * q^95 - 1835008 * q^96 - 11748408 * q^97 + 15278208 * q^99

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 $

$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$2$	−4.00000	+	6.92820i	−0.353553	+	0.612372i
$3$	10.4387	+	18.0804i	0.223214	+	0.386618i	0.955782	−	0.294075i	$-0.0950117\pi$
$3$	10.4387	+	18.0804i	0.223214	+	0.386618i	−0.732568	+	0.680694i	$0.761678\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	−108.377	+	187.715i	−0.387743	+	0.671590i	−0.992146	−	0.125089i	$-0.960078\pi$
$5$	−108.377	+	187.715i	−0.387743	+	0.671590i	0.604403	+	0.796679i	$0.293412\pi$
$6$	−167.019			−0.315673
$7$		0			0
$7$		0			0
$8$	512.000			0.353553
$9$	875.567	−	1516.53i	0.400351	−	0.693428i
$10$	−867.019	−	1501.72i	−0.274176	−	0.474886i
$11$	−1290.93	−	2235.95i	−0.292434	−	0.506511i	0.681951	−	0.731398i	$-0.261132\pi$
$11$	−1290.93	−	2235.95i	−0.292434	−	0.506511i	−0.974385	+	0.224887i	$0.927799\pi$
$12$	668.077	−	1157.14i	0.111607	−	0.193309i
$13$	8921.97			1.12631			0.563156	−	0.826350i	$-0.309587\pi$
$13$	8921.97			1.12631			0.563156	+	0.826350i	$0.309587\pi$
$14$		0			0
$15$	−4525.28			−0.346199
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	−5556.44	−	9624.03i	−0.274300	−	0.475101i	0.695659	−	0.718373i	$-0.255113\pi$
$17$	−5556.44	−	9624.03i	−0.274300	−	0.475101i	−0.969958	+	0.243272i	$0.921779\pi$
$18$	7004.54	+	12132.2i	0.283091	+	0.490328i
$19$	−4323.40	+	7488.34i	−0.144606	+	0.250466i	−0.929226	−	0.369512i	$-0.879525\pi$
$19$	−4323.40	+	7488.34i	−0.144606	+	0.250466i	0.784620	+	0.619977i	$0.212858\pi$
$20$	13872.3			0.387743
$21$		0			0
$22$	20654.9			0.413564
$23$	33028.6	−	57207.2i	0.566034	−	0.980399i	−0.430919	−	0.902391i	$-0.641810\pi$
$23$	33028.6	−	57207.2i	0.566034	−	0.980399i	0.996953	−	0.0780088i	$-0.0248562\pi$
$24$	5344.61	+	9257.14i	0.0789182	+	0.136690i
$25$	15571.2	+	26970.1i	0.199311	+	0.345217i
$26$	−35687.9	+	61813.2i	−0.398212	+	0.689723i
$27$	82218.0			0.803885
$28$		0			0
$29$	128836.			0.980941			0.490470	−	0.871458i	$-0.336825\pi$
$29$	128836.			0.980941			0.490470	+	0.871458i	$0.336825\pi$
$30$	18101.1	−	31352.0i	0.122400	−	0.212003i
$31$	−102048.	−	176752.i	−0.615229	−	1.06561i	−0.990344	−	0.138630i	$-0.955730\pi$
$31$	−102048.	−	176752.i	−0.615229	−	1.06561i	0.375115	−	0.926978i	$-0.377603\pi$
$32$	−16384.0	−	28377.9i	−0.0883883	−	0.153093i
$33$	26951.2	−	46680.9i	0.130551	−	0.226121i
$34$	88903.0			0.387918
$35$		0			0
$36$	−112073.			−0.400351
$37$	−245856.	+	425834.i	−0.797947	+	1.38208i	0.123004	+	0.992406i	$0.460747\pi$
$37$	−245856.	+	425834.i	−0.797947	+	1.38208i	−0.920951	+	0.389678i	$0.872586\pi$
$38$	−34587.2	−	59906.7i	−0.102252	−	0.177106i
$39$	93133.8	+	161312.i	0.251409	+	0.435453i
$40$	−55489.2	+	96110.2i	−0.137088	+	0.237443i
$41$	623293.			1.41237			0.706185	−	0.708027i	$-0.250415\pi$
$41$	623293.			1.41237			0.706185	+	0.708027i	$0.250415\pi$
$42$		0			0
$43$	422919.			0.811181			0.405591	−	0.914055i	$-0.367066\pi$
$43$	422919.			0.811181			0.405591	+	0.914055i	$0.367066\pi$
$44$	−82619.5	+	143101.i	−0.146217	+	0.253255i
$45$	189783.	+	328714.i	0.310466	+	0.537743i
$46$	264229.	+	457657.i	0.400246	+	0.693247i
$47$	−602714.	+	1.04393e6i	−0.846777	+	1.46666i	0.0372922	+	0.999304i	$0.488127\pi$
$47$	−602714.	+	1.04393e6i	−0.846777	+	1.46666i	−0.884069	+	0.467356i	$0.845207\pi$
$48$	−85513.8			−0.111607
$49$		0			0
$50$	−249139.			−0.281868
$51$	116004.	−	200925.i	0.122455	−	0.212099i
$52$	−285503.	−	494506.i	−0.281578	−	0.487708i
$53$	636483.	+	1.10242e6i	0.587247	+	1.01714i	0.994591	+	0.103867i	$0.0331217\pi$
$53$	636483.	+	1.10242e6i	0.587247	+	1.01714i	−0.407344	+	0.913275i	$0.633545\pi$
$54$	−328872.	+	569623.i	−0.284216	+	0.492277i
$55$	559630.			0.453557
$56$		0			0
$57$	−180523.			−0.129113
$58$	−515342.	+	892599.i	−0.346815	+	0.600701i
$59$	840430.	+	1.45567e6i	0.532745	+	0.922741i	0.999269	+	0.0382328i	$0.0121729\pi$
$59$	840430.	+	1.45567e6i	0.532745	+	0.922741i	−0.466524	+	0.884509i	$0.654494\pi$
$60$	144809.	+	250816.i	0.0865497	+	0.149909i
$61$	1.06128e6	−	1.83818e6i	0.598651	−	1.03689i	−0.394370	−	0.918952i	$-0.629037\pi$
$61$	1.06128e6	−	1.83818e6i	0.598651	−	1.03689i	0.993021	−	0.117942i	$-0.0376296\pi$
$62$	1.63276e6			0.870065
$63$		0			0
$64$	262144.			0.125000
$65$	−966940.	+	1.67479e6i	−0.436720	+	0.756421i
$66$	215610.	+	373447.i	0.0923134	+	0.159892i
$67$	1.67466e6	+	2.90060e6i	0.680245	+	1.17822i	0.974906	+	0.222618i	$0.0714602\pi$
$67$	1.67466e6	+	2.90060e6i	0.680245	+	1.17822i	−0.294660	+	0.955602i	$0.595207\pi$
$68$	−355612.	+	615938.i	−0.137150	+	0.237550i
$69$	1.37910e6			0.505387
$70$		0			0
$71$	2.49257e6			0.826502			0.413251	−	0.910617i	$-0.364393\pi$
$71$	2.49257e6			0.826502			0.413251	+	0.910617i	$0.364393\pi$
$72$	448290.	−	776462.i	0.141545	−	0.245164i
$73$	−1.63676e6	−	2.83496e6i	−0.492443	−	0.852936i	0.507519	−	0.861641i	$-0.330563\pi$
$73$	−1.63676e6	−	2.83496e6i	−0.492443	−	0.852936i	−0.999962	+	0.00870409i	$0.997229\pi$
$74$	−1.96684e6	−	3.40667e6i	−0.564234	−	0.977281i
$75$	−325086.	+	563065.i	−0.0889782	+	0.154115i
$76$	553395.			0.144606
$77$		0			0
$78$	−1.49014e6			−0.355546
$79$	2.09920e6	−	3.63591e6i	0.479025	−	0.829695i	−0.520686	−	0.853748i	$-0.674324\pi$
$79$	2.09920e6	−	3.63591e6i	0.479025	−	0.829695i	0.999711	+	0.0240529i	$0.00765703\pi$
$80$	−443914.	−	768881.i	−0.0969357	−	0.167898i
$81$	−1.05662e6	−	1.83011e6i	−0.220912	−	0.382631i
$82$	−2.49317e6	+	4.31830e6i	−0.499348	+	0.864897i
$83$	−3.35527e6			−0.644102			−0.322051	−	0.946722i	$-0.604372\pi$
$83$	−3.35527e6			−0.644102			−0.322051	+	0.946722i	$0.604372\pi$
$84$		0			0
$85$	2.40877e6			0.425431
$86$	−1.69168e6	+	2.93007e6i	−0.286796	+	0.496745i
$87$	1.34488e6	+	2.32939e6i	0.218960	+	0.379250i
$88$	−660956.	−	1.14481e6i	−0.103391	−	0.179079i
$89$	1.19979e6	−	2.07810e6i	0.180402	−	0.312466i	−0.761615	−	0.648029i	$-0.775593\pi$
$89$	1.19979e6	−	2.07810e6i	0.180402	−	0.312466i	0.942018	+	0.335564i	$0.108927\pi$
$90$	−3.03653e6			−0.439066
$91$		0			0
$92$	−4.22766e6			−0.566034
$93$	2.13049e6	−	3.69011e6i	0.274656	−	0.475718i
$94$	−4.82171e6	−	8.35145e6i	−0.598762	−	1.03709i
$95$	−937117.	−	1.62313e6i	−0.112140	−	0.194232i
$96$	342055.	−	592457.i	0.0394591	−	0.0683451i
$97$	−4.51506e6			−0.502299			−0.251150	−	0.967948i	$-0.580809\pi$
$97$	−4.51506e6			−0.502299			−0.251150	+	0.967948i	$0.580809\pi$
$98$		0			0
$99$	−4.52118e6			−0.468305
$100$	996555.	−	1.72608e6i	0.0996555	−	0.172608i
$101$	3.69997e6	+	6.40853e6i	0.357333	+	0.618919i	0.987514	−	0.157529i	$-0.0503527\pi$
$101$	3.69997e6	+	6.40853e6i	0.357333	+	0.618919i	−0.630181	+	0.776448i	$0.717019\pi$
$102$	928032.	+	1.60740e6i	0.0865889	+	0.149976i
$103$	9.22855e6	−	1.59843e7i	0.832153	−	1.44133i	−0.0641744	−	0.997939i	$-0.520441\pi$
$103$	9.22855e6	−	1.59843e7i	0.832153	−	1.44133i	0.896327	−	0.443393i	$-0.146225\pi$
$104$	4.56805e6			0.398212
$105$		0			0
$106$	−1.01837e7			−0.830493
$107$	2.49697e6	−	4.32488e6i	0.197047	−	0.341296i	−0.750523	−	0.660845i	$-0.770198\pi$
$107$	2.49697e6	−	4.32488e6i	0.197047	−	0.341296i	0.947570	+	0.319549i	$0.103531\pi$
$108$	−2.63098e6	−	4.55698e6i	−0.200971	−	0.348092i
$109$	−9.34351e6	−	1.61834e7i	−0.691062	−	1.19695i	−0.971490	−	0.237080i	$-0.923810\pi$
$109$	−9.34351e6	−	1.61834e7i	−0.691062	−	1.19695i	0.280428	−	0.959875i	$-0.409524\pi$
$110$	−2.23852e6	+	3.87723e6i	−0.160357	+	0.277746i
$111$	−1.02656e7			−0.712452
$112$		0			0
$113$	2.49534e7			1.62688			0.813438	−	0.581651i	$-0.197593\pi$
$113$	2.49534e7			1.62688			0.813438	+	0.581651i	$0.197593\pi$
$114$	722090.	−	1.25070e6i	0.0456483	−	0.0790651i
$115$	7.15910e6	+	1.23999e7i	0.438951	+	0.760286i
$116$	−4.12274e6	−	7.14079e6i	−0.245235	−	0.424760i
$117$	7.81178e6	−	1.35304e7i	0.450920	−	0.781017i
$118$	−1.34469e7			−0.753415
$119$		0			0
$120$	−2.31694e6			−0.122400
$121$	6.41059e6	−	1.11035e7i	0.328965	−	0.569783i
$122$	8.49020e6	+	1.47055e7i	0.423310	+	0.733194i
$123$	6.50636e6	+	1.12694e7i	0.315261	+	0.546048i
$124$	−6.53105e6	+	1.13121e7i	−0.307614	+	0.532804i
$125$	−2.36842e7			−1.08461
$126$		0			0
$127$	−1.72080e7			−0.745449			−0.372724	−	0.927942i	$-0.621576\pi$
$127$	−1.72080e7			−0.745449			−0.372724	+	0.927942i	$0.621576\pi$
$128$	−1.04858e6	+	1.81619e6i	−0.0441942	+	0.0765466i
$129$	4.41473e6	+	7.64653e6i	0.181067	+	0.313618i
$130$	−7.73552e6	−	1.33983e7i	−0.308807	−	0.534870i
$131$	1.34633e7	−	2.33191e7i	0.523242	−	0.906281i	−0.476392	−	0.879233i	$-0.658056\pi$
$131$	1.34633e7	−	2.33191e7i	0.523242	−	0.906281i	0.999634	−	0.0270484i	$-0.00861082\pi$
$132$	−3.44976e6			−0.130551
$133$		0			0
$134$	−2.67946e7			−0.962012
$135$	−8.91057e6	+	1.54336e7i	−0.311700	+	0.539881i
$136$	−2.84490e6	−	4.92751e6i	−0.0969796	−	0.167974i
$137$	1.36301e7	+	2.36080e7i	0.452873	+	0.784399i	0.998563	−	0.0535877i	$-0.0170657\pi$
$137$	1.36301e7	+	2.36080e7i	0.452873	+	0.784399i	−0.545690	+	0.837987i	$0.683732\pi$
$138$	−5.51641e6	+	9.55470e6i	−0.178681	+	0.309485i
$139$	1.36813e7			0.432092			0.216046	−	0.976383i	$-0.430684\pi$
$139$	1.36813e7			0.432092			0.216046	+	0.976383i	$0.430684\pi$
$140$		0			0
$141$	−2.51662e7			−0.756051
$142$	−9.97030e6	+	1.72691e7i	−0.292213	+	0.506127i
$143$	−1.15176e7	−	1.99491e7i	−0.329372	−	0.570489i
$144$	3.58632e6	+	6.21169e6i	0.100088	+	0.173357i
$145$	−1.39629e7	+	2.41844e7i	−0.380353	+	0.658790i
$146$	2.61882e7			0.696420
$147$		0			0
$148$	3.14695e7			0.797947
$149$	−1.21944e7	+	2.11214e7i	−0.302002	+	0.523083i	−0.976589	−	0.215112i	$-0.930988\pi$
$149$	−1.21944e7	+	2.11214e7i	−0.302002	+	0.523083i	0.674587	+	0.738195i	$0.264322\pi$
$150$	−2.60069e6	−	4.50452e6i	−0.0629171	−	0.108976i
$151$	−1.69013e7	−	2.92740e7i	−0.399486	−	0.691930i	0.594177	−	0.804335i	$-0.297478\pi$
$151$	−1.69013e7	−	2.92740e7i	−0.399486	−	0.691930i	−0.993663	+	0.112405i	$0.964145\pi$
$152$	−2.21358e6	+	3.83403e6i	−0.0511261	+	0.0885530i
$153$	−1.94601e7			−0.439264
$154$		0			0
$155$	4.42386e7			0.954202
$156$	5.96056e6	−	1.03240e7i	0.125705	−	0.217727i
$157$	3.97833e6	+	6.89067e6i	0.0820450	+	0.142106i	0.904128	−	0.427261i	$-0.140522\pi$
$157$	3.97833e6	+	6.89067e6i	0.0820450	+	0.142106i	−0.822083	+	0.569367i	$0.807188\pi$
$158$	1.67936e7	+	2.90873e7i	0.338722	+	0.586683i
$159$	−1.32881e7	+	2.30157e7i	−0.262164	+	0.454081i
$160$	7.10262e6			0.137088
$161$		0			0
$162$	1.69059e7			0.312417
$163$	2.68214e7	−	4.64560e7i	0.485093	−	0.840205i	−0.514761	−	0.857334i	$-0.672119\pi$
$163$	2.68214e7	−	4.64560e7i	0.485093	−	0.840205i	0.999853	+	0.0171289i	$0.00545257\pi$
$164$	−1.99454e7	−	3.45464e7i	−0.353093	−	0.611574i
$165$	5.84181e6	+	1.01183e7i	0.101240	+	0.175353i
$166$	1.34211e7	−	2.32460e7i	0.227724	−	0.394430i
$167$	8.20253e7			1.36283			0.681413	−	0.731899i	$-0.261366\pi$
$167$	8.20253e7			1.36283			0.681413	+	0.731899i	$0.261366\pi$
$168$		0			0
$169$	1.68530e7			0.268581
$170$	−9.63508e6	+	1.66884e7i	−0.150413	+	0.260522i
$171$	7.57085e6	+	1.31131e7i	0.115787	+	0.200548i
$172$	−1.35334e7	−	2.34406e7i	−0.202795	−	0.351252i
$173$	−3.39592e7	+	5.88190e7i	−0.498650	+	0.863687i	−0.999999	−	0.00155811i	$-0.999504\pi$
$173$	−3.39592e7	+	5.88190e7i	−0.498650	+	0.863687i	0.501349	+	0.865245i	$0.332837\pi$
$174$	−2.15180e7			−0.309656
$175$		0			0
$176$	1.05753e7			0.146217
$177$	−1.75460e7	+	3.03905e7i	−0.237833	+	0.411938i
$178$	9.59835e6	+	1.66248e7i	0.127564	+	0.220947i
$179$	3.04898e7	+	5.28098e7i	0.397346	+	0.688223i	0.993398	−	0.114723i	$-0.0365980\pi$
$179$	3.04898e7	+	5.28098e7i	0.397346	+	0.688223i	−0.596052	+	0.802946i	$0.703265\pi$
$180$	1.21461e7	−	2.10377e7i	0.155233	−	0.268872i
$181$	1.53894e8			1.92907			0.964533	−	0.263963i	$-0.0850295\pi$
$181$	1.53894e8			1.92907			0.964533	+	0.263963i	$0.0850295\pi$
$182$		0			0
$183$	4.43133e7			0.534510
$184$	1.69106e7	−	2.92901e7i	0.200123	−	0.346624i
$185$	−5.32904e7	−	9.23016e7i	−0.618796	−	1.07179i
$186$	1.70439e7	+	2.95209e7i	0.194211	+	0.336383i
$187$	−1.43459e7	+	2.48479e7i	−0.160429	+	0.277871i
$188$	7.71474e7			0.846777
$189$		0			0
$190$	1.49939e7			0.158590
$191$	−1.12603e7	+	1.95034e7i	−0.116932	+	0.202532i	−0.918550	−	0.395304i	$-0.870639\pi$
$191$	−1.12603e7	+	1.95034e7i	−0.116932	+	0.202532i	0.801618	+	0.597836i	$0.203973\pi$
$192$	2.73644e6	+	4.73966e6i	0.0279018	+	0.0483273i
$193$	6.76381e7	+	1.17153e8i	0.677237	+	1.17301i	0.975810	+	0.218622i	$0.0701563\pi$
$193$	6.76381e7	+	1.17153e8i	0.677237	+	1.17301i	−0.298572	+	0.954387i	$0.596510\pi$
$194$	1.80602e7	−	3.12813e7i	0.177590	−	0.307594i
$195$	−4.03744e7			−0.389928
$196$		0			0
$197$	−8.96233e7			−0.835197			−0.417598	−	0.908632i	$-0.637128\pi$
$197$	−8.96233e7			−0.835197			−0.417598	+	0.908632i	$0.637128\pi$
$198$	1.80847e7	−	3.13237e7i	0.165571	−	0.286777i
$199$	−2.74707e7	−	4.75806e7i	−0.247106	−	0.428000i	0.715616	−	0.698494i	$-0.246146\pi$
$199$	−2.74707e7	−	4.75806e7i	−0.247106	−	0.428000i	−0.962722	+	0.270494i	$0.912813\pi$
$200$	7.97244e6	+	1.38087e7i	0.0704671	+	0.122053i
$201$	−3.49626e7	+	6.05570e7i	−0.303681	+	0.525991i
$202$	−5.91995e7			−0.505345
$203$		0			0
$204$	−1.48485e7			−0.122455
$205$	−6.75508e7	+	1.17001e8i	−0.547636	+	0.948534i
$206$	7.38284e7	+	1.27875e8i	0.588421	+	1.01918i
$207$	−5.78375e7	−	1.00177e8i	−0.453224	−	0.785007i
$208$	−1.82722e7	+	3.16484e7i	−0.140789	+	0.243854i
$209$	2.23248e7			0.169151
$210$		0			0
$211$	−1.24539e8			−0.912677			−0.456338	−	0.889806i	$-0.650839\pi$
$211$	−1.24539e8			−0.912677			−0.456338	+	0.889806i	$0.650839\pi$
$212$	4.07349e7	−	7.05549e7i	0.293624	−	0.508571i
$213$	2.60192e7	+	4.50666e7i	0.184487	+	0.319541i
$214$	1.99758e7	+	3.45990e7i	0.139333	+	0.241332i
$215$	−4.58349e7	+	7.93884e7i	−0.314530	+	0.544781i
$216$	4.20956e7			0.284216
$217$		0			0
$218$	1.49496e8			0.977310
$219$	3.41714e7	−	5.91866e7i	0.219841	−	0.380775i
$220$	−1.79082e7	−	3.10179e7i	−0.113389	−	0.196396i
$221$	−4.95744e7	−	8.58653e7i	−0.308947	−	0.535112i
$222$	4.10626e7	−	7.11225e7i	0.251890	−	0.436286i
$223$	−2.85464e8			−1.72379			−0.861895	−	0.507087i	$-0.830722\pi$
$223$	−2.85464e8			−1.72379			−0.861895	+	0.507087i	$0.830722\pi$
$224$		0			0
$225$	5.45345e7			0.319177
$226$	−9.98135e7	+	1.72882e8i	−0.575188	+	0.996254i
$227$	3.37141e7	+	5.83946e7i	0.191303	+	0.331346i	0.945682	−	0.325092i	$-0.105395\pi$
$227$	3.37141e7	+	5.83946e7i	0.191303	+	0.331346i	−0.754379	+	0.656439i	$0.772062\pi$
$228$	5.77672e6	+	1.00056e7i	0.0322782	+	0.0559075i
$229$	3.58459e7	−	6.20869e7i	0.197249	−	0.341646i	−0.750386	−	0.660999i	$-0.770133\pi$
$229$	3.58459e7	−	6.20869e7i	0.197249	−	0.341646i	0.947636	+	0.319354i	$0.103466\pi$
$230$	−1.14546e8			−0.620771
$231$		0			0
$232$	6.59638e7			0.346815
$233$	−1.08990e6	+	1.88777e6i	−0.00564472	+	0.00977693i	−0.868834	−	0.495104i	$-0.835130\pi$
$233$	−1.08990e6	+	1.88777e6i	−0.00564472	+	0.00977693i	0.863189	+	0.504881i	$0.168463\pi$
$234$	6.24943e7	+	1.08243e8i	0.318849	+	0.552262i
$235$	−1.30641e8	−	2.26277e8i	−0.656663	−	1.13737i
$236$	5.37875e7	−	9.31627e7i	0.266373	−	0.461371i
$237$	8.76515e7			0.427701
$238$		0			0
$239$	−1.87131e8			−0.886654			−0.443327	−	0.896360i	$-0.646202\pi$
$239$	−1.87131e8			−0.886654			−0.443327	+	0.896360i	$0.646202\pi$
$240$	9.26777e6	−	1.60522e7i	0.0432749	−	0.0749543i
$241$	−6.26650e7	−	1.08539e8i	−0.288380	−	0.499489i	0.685043	−	0.728502i	$-0.259783\pi$
$241$	−6.26650e7	−	1.08539e8i	−0.288380	−	0.499489i	−0.973423	+	0.229014i	$0.926450\pi$
$242$	5.12847e7	+	8.88277e7i	0.232613	+	0.402898i
$243$	1.11965e8	−	1.93929e8i	0.500564	−	0.867002i
$244$	−1.35843e8			−0.598651
$245$		0			0
$246$	−1.04102e8			−0.445847
$247$	−3.85732e7	+	6.68108e7i	−0.162872	+	0.282103i
$248$	−5.22484e7	−	9.04968e7i	−0.217516	−	0.376749i
$249$	−3.50247e7	−	6.06645e7i	−0.143773	−	0.249022i
$250$	9.47369e7	−	1.64089e8i	0.383468	−	0.664186i
$251$	−3.48978e7			−0.139296			−0.0696482	−	0.997572i	$-0.522188\pi$
$251$	−3.48978e7			−0.139296			−0.0696482	+	0.997572i	$0.522188\pi$
$252$		0			0
$253$	−1.70550e8			−0.662110
$254$	6.88321e7	−	1.19221e8i	0.263556	−	0.456492i
$255$	2.51444e7	+	4.35514e7i	0.0949622	+	0.164479i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	−2.96784e7	+	5.14046e7i	−0.109062	+	0.188902i	−0.915391	−	0.402567i	$-0.868118\pi$
$257$	−2.96784e7	+	5.14046e7i	−0.109062	+	0.188902i	0.806328	+	0.591468i	$0.201452\pi$
$258$	−7.06356e7			−0.256068
$259$		0			0
$260$	1.23768e8			0.436720
$261$	1.12804e8	−	1.95383e8i	0.392720	−	0.680212i
$262$	1.07706e8	+	1.86553e8i	0.369988	+	0.640838i
$263$	1.06373e7	+	1.84243e7i	0.0360567	+	0.0624521i	0.883491	−	0.468449i	$-0.155187\pi$
$263$	1.06373e7	+	1.84243e7i	0.0360567	+	0.0624521i	−0.847434	+	0.530901i	$0.821854\pi$
$264$	1.37990e7	−	2.39006e7i	0.0461567	−	0.0799458i
$265$	−2.75921e8			−0.910804
$266$		0			0
$267$	5.00972e7			0.161073
$268$	1.07178e8	−	1.85639e8i	0.340123	−	0.589110i
$269$	5.85529e7	+	1.01417e8i	0.183407	+	0.317670i	0.943038	−	0.332684i	$-0.107954\pi$
$269$	5.85529e7	+	1.01417e8i	0.183407	+	0.317670i	−0.759632	+	0.650353i	$0.774621\pi$
$270$	−7.12846e7	−	1.23469e8i	−0.220405	−	0.381754i
$271$	−1.01385e8	+	1.75603e8i	−0.309442	+	0.535970i	−0.978240	−	0.207474i	$-0.933476\pi$
$271$	−1.01385e8	+	1.75603e8i	−0.309442	+	0.535970i	0.668798	+	0.743444i	$0.266809\pi$
$272$	4.55183e7			0.137150
$273$		0			0
$274$	−2.18081e8			−0.640459
$275$	4.02026e7	−	6.96329e7i	0.116571	−	0.201906i
$276$	−4.41312e7	−	7.64376e7i	−0.126347	−	0.218839i
$277$	−5.05757e7	−	8.75996e7i	−0.142976	−	0.247641i	0.785640	−	0.618684i	$-0.212334\pi$
$277$	−5.05757e7	−	8.75996e7i	−0.142976	−	0.247641i	−0.928616	+	0.371042i	$0.879000\pi$
$278$	−5.47253e7	+	9.47869e7i	−0.152768	+	0.264601i
$279$	−3.57398e8			−0.985230
$280$		0			0
$281$	3.69631e8			0.993793			0.496897	−	0.867810i	$-0.334473\pi$
$281$	3.69631e8			0.993793			0.496897	+	0.867810i	$0.334473\pi$
$282$	1.00665e8	−	1.74357e8i	0.267304	−	0.462985i
$283$	−1.09831e8	−	1.90232e8i	−0.288052	−	0.498921i	0.685293	−	0.728268i	$-0.259674\pi$
$283$	−1.09831e8	−	1.90232e8i	−0.288052	−	0.498921i	−0.973345	+	0.229347i	$0.926341\pi$
$284$	−7.97624e7	−	1.38153e8i	−0.206626	−	0.357886i
$285$	1.95646e7	−	3.38868e7i	0.0500626	−	0.0867109i
$286$	1.84282e8			0.465803
$287$		0			0
$288$	−5.73812e7			−0.141545
$289$	1.43421e8	−	2.48413e8i	0.349519	−	0.605385i
$290$	−1.11703e8	−	1.93475e8i	−0.268950	−	0.465835i
$291$	−4.71314e7	−	8.16339e7i	−0.112120	−	0.194198i
$292$	−1.04753e8	+	1.81437e8i	−0.246222	+	0.426468i
$293$	7.22230e8			1.67741			0.838704	−	0.544587i	$-0.183314\pi$
$293$	7.22230e8			1.67741			0.838704	+	0.544587i	$0.183314\pi$
$294$		0			0
$295$	−3.64334e8			−0.826272
$296$	−1.25878e8	+	2.18027e8i	−0.282117	+	0.488641i
$297$	−1.06138e8	−	1.83836e8i	−0.235083	−	0.407176i
$298$	−9.75555e7	−	1.68971e8i	−0.213548	−	0.369875i
$299$	2.94680e8	−	5.10401e8i	0.637531	−	1.10424i
$300$	4.16110e7			0.0889782
$301$		0			0
$302$	2.70421e8			0.564959
$303$	−7.72457e7	+	1.33794e8i	−0.159524	+	0.276303i
$304$	−1.77086e7	−	3.06722e7i	−0.0361516	−	0.0626164i
$305$	2.30036e8	+	3.98435e8i	0.464245	+	0.804096i
$306$	7.78406e7	−	1.34824e8i	0.155303	−	0.268993i
$307$	6.39545e7			0.126150			0.0630750	−	0.998009i	$-0.479909\pi$
$307$	6.39545e7			0.126150			0.0630750	+	0.998009i	$0.479909\pi$
$308$		0			0
$309$	3.85336e8			0.742994
$310$	−1.76954e8	+	3.06494e8i	−0.337361	+	0.584327i
$311$	7.73216e7	+	1.33925e8i	0.145760	+	0.252464i	0.929656	−	0.368428i	$-0.120104\pi$
$311$	7.73216e7	+	1.33925e8i	0.145760	+	0.252464i	−0.783896	+	0.620892i	$0.786771\pi$
$312$	4.76845e7	+	8.25919e7i	0.0888865	+	0.153956i
$313$	−2.46992e8	+	4.27803e8i	−0.455279	+	0.788567i	−0.998704	−	0.0508911i	$-0.983794\pi$
$313$	−2.46992e8	+	4.27803e8i	−0.455279	+	0.788567i	0.543425	+	0.839458i	$0.317127\pi$
$314$	−6.36533e7			−0.116029
$315$		0			0
$316$	−2.68697e8			−0.479025
$317$	−2.14969e8	+	3.72338e8i	−0.379026	+	0.656492i	−0.990921	−	0.134447i	$-0.957074\pi$
$317$	−2.14969e8	+	3.72338e8i	−0.379026	+	0.656492i	0.611895	+	0.790939i	$0.290408\pi$
$318$	−1.06305e8	−	1.84125e8i	−0.185378	−	0.321084i
$319$	−1.66318e8	−	2.88071e8i	−0.286861	−	0.496857i
$320$	−2.84105e7	+	4.92084e7i	−0.0484678	+	0.0839488i
$321$	1.04260e8			0.175935
$322$		0			0
$323$	9.60907e7			0.158662
$324$	−6.76235e7	+	1.17127e8i	−0.110456	+	0.191316i
$325$	1.38926e8	+	2.40626e8i	0.224487	+	0.388822i
$326$	2.14571e8	+	3.71648e8i	0.343012	+	0.594115i
$327$	1.95068e8	−	3.37868e8i	0.308510	−	0.534355i
$328$	3.19126e8			0.499348
$329$		0			0
$330$	−9.34690e7			−0.143175
$331$	1.64085e8	−	2.84203e8i	0.248697	−	0.430755i	−0.714468	−	0.699668i	$-0.753331\pi$
$331$	1.64085e8	−	2.84203e8i	0.248697	−	0.430755i	0.963164	+	0.268913i	$0.0866645\pi$
$332$	1.07369e8	+	1.85968e8i	0.161025	+	0.278904i
$333$	4.30526e8	+	7.45693e8i	0.638917	+	1.10664i
$334$	−3.28101e8	+	5.68288e8i	−0.481832	+	0.834557i
$335$	−7.25983e8			−1.05504
$336$		0			0
$337$	−1.14409e8			−0.162838			−0.0814189	−	0.996680i	$-0.525945\pi$
$337$	−1.14409e8			−0.162838			−0.0814189	+	0.996680i	$0.525945\pi$
$338$	−6.74121e7	+	1.16761e8i	−0.0949576	+	0.164471i
$339$	2.60481e8	+	4.51166e8i	0.363142	+	0.628981i
$340$	−7.70806e7	−	1.33508e8i	−0.106358	−	0.184217i
$341$	−2.63472e8	+	4.56348e8i	−0.359828	+	0.623240i
$342$	−1.21134e8			−0.163747
$343$		0			0
$344$	2.16535e8			0.286796
$345$	−1.49463e8	+	2.58878e8i	−0.195960	+	0.339413i
$346$	−2.71673e8	−	4.70552e8i	−0.352599	−	0.610719i
$347$	3.28339e8	+	5.68699e8i	0.421860	+	0.730684i	0.996121	−	0.0879887i	$-0.0280439\pi$
$347$	3.28339e8	+	5.68699e8i	0.421860	+	0.730684i	−0.574261	+	0.818672i	$0.694711\pi$
$348$	8.60721e7	−	1.49081e8i	0.109480	−	0.189625i
$349$	8.85994e8			1.11569			0.557843	−	0.829947i	$-0.311629\pi$
$349$	8.85994e8			1.11569			0.557843	+	0.829947i	$0.311629\pi$
$350$		0			0
$351$	7.33546e8			0.905426
$352$	−4.23012e7	+	7.32678e7i	−0.0516955	+	0.0895393i
$353$	3.43700e8	+	5.95305e8i	0.415880	+	0.720324i	0.995520	−	0.0945476i	$-0.0301405\pi$
$353$	3.43700e8	+	5.95305e8i	0.415880	+	0.720324i	−0.579641	+	0.814872i	$0.696807\pi$
$354$	−1.40368e8	−	2.43124e8i	−0.168173	−	0.291284i
$355$	−2.70139e8	+	4.67894e8i	−0.320470	+	0.555071i
$356$	−1.53574e8			−0.180402
$357$		0			0
$358$	−4.87836e8			−0.561932
$359$	−1.61222e7	+	2.79244e7i	−0.0183905	+	0.0318533i	−0.875074	−	0.483989i	$-0.839188\pi$
$359$	−1.61222e7	+	2.79244e7i	−0.0183905	+	0.0318533i	0.856684	+	0.515842i	$0.172521\pi$
$360$	9.71691e7	+	1.68302e8i	0.109766	+	0.190121i
$361$	4.09552e8	+	7.09365e8i	0.458178	+	0.793588i
$362$	−6.15577e8	+	1.06621e9i	−0.682028	+	1.18131i
$363$	2.67673e8			0.293718
$364$		0			0
$365$	7.09553e8			0.763765
$366$	−1.77253e8	+	3.07012e8i	−0.188978	+	0.327319i
$367$	−3.58275e8	−	6.20551e8i	−0.378343	−	0.655309i	0.612479	−	0.790487i	$-0.290173\pi$
$367$	−3.58275e8	−	6.20551e8i	−0.378343	−	0.655309i	−0.990821	+	0.135178i	$0.956839\pi$
$368$	1.35285e8	+	2.34321e8i	0.141508	+	0.245100i
$369$	5.45735e8	−	9.45240e8i	0.565444	−	0.979377i
$370$	8.52646e8			0.875110
$371$		0			0
$372$	−2.72702e8			−0.274656
$373$	−6.11134e8	+	1.05852e9i	−0.609755	+	1.05613i	0.381525	+	0.924358i	$0.375399\pi$
$373$	−6.11134e8	+	1.05852e9i	−0.609755	+	1.05613i	−0.991281	+	0.131769i	$0.957934\pi$
$374$	−1.14767e8	−	1.98783e8i	−0.113441	−	0.196485i
$375$	−2.47232e8	−	4.28219e8i	−0.242101	−	0.419331i
$376$	−3.08590e8	+	5.34493e8i	−0.299381	+	0.518543i
$377$	1.14947e9			1.10485
$378$		0			0
$379$	−6.83298e8			−0.644723			−0.322361	−	0.946617i	$-0.604477\pi$
$379$	−6.83298e8			−0.644723			−0.322361	+	0.946617i	$0.604477\pi$
$380$	−5.99755e7	+	1.03881e8i	−0.0560701	+	0.0971162i
$381$	−1.79629e8	−	3.11127e8i	−0.166395	−	0.288204i
$382$	−9.00823e7	−	1.56027e8i	−0.0826833	−	0.143212i
$383$	1.01294e9	−	1.75447e9i	0.921273	−	1.59569i	0.123826	−	0.992304i	$-0.460484\pi$
$383$	1.01294e9	−	1.75447e9i	0.921273	−	1.59569i	0.797447	−	0.603388i	$-0.206183\pi$
$384$	−4.37831e7			−0.0394591
$385$		0			0
$386$	−1.08221e9			−0.957758
$387$	3.70294e8	−	6.41368e8i	0.324757	−	0.562496i
$388$	1.44482e8	+	2.50250e8i	0.125575	+	0.217502i
$389$	3.64506e8	+	6.31342e8i	0.313965	+	0.543803i	0.979217	−	0.202816i	$-0.0650093\pi$
$389$	3.64506e8	+	6.31342e8i	0.313965	+	0.543803i	−0.665252	+	0.746619i	$0.731676\pi$
$390$	1.61498e8	−	2.79722e8i	0.137860	−	0.238781i
$391$	−7.34085e8			−0.621052
$392$		0			0
$393$	5.62158e8			0.467180
$394$	3.58493e8	−	6.20928e8i	0.295287	−	0.511452i
$395$	4.55011e8	+	7.88102e8i	0.371477	+	0.643417i
$396$	1.44678e8	+	2.50589e8i	0.117076	+	0.202782i
$397$	−6.63836e8	+	1.14980e9i	−0.532469	+	0.922263i	0.466812	+	0.884356i	$0.345402\pi$
$397$	−6.63836e8	+	1.14980e9i	−0.532469	+	0.922263i	−0.999281	+	0.0379069i	$0.987931\pi$
$398$	4.39531e8			0.349461
$399$		0			0
$400$	−1.27559e8			−0.0996555
$401$	4.28975e8	−	7.43007e8i	0.332221	−	0.575423i	−0.650726	−	0.759312i	$-0.725535\pi$
$401$	4.28975e8	−	7.43007e8i	0.332221	−	0.575423i	0.982947	+	0.183889i	$0.0588688\pi$
$402$	−2.79701e8	−	4.84456e8i	−0.214735	−	0.371932i
$403$	−9.10465e8	−	1.57697e9i	−0.692940	−	1.20021i
$404$	2.36798e8	−	4.10146e8i	0.178667	−	0.309460i
$405$	4.58053e8			0.342629
$406$		0			0
$407$	1.26953e9			0.933387
$408$	5.93940e7	−	1.02873e8i	0.0432945	−	0.0749882i
$409$	−1.05133e9	−	1.82096e9i	−0.759814	−	1.31604i	−0.942945	−	0.332948i	$-0.891956\pi$
$409$	−1.05133e9	−	1.82096e9i	−0.759814	−	1.31604i	0.183131	−	0.983089i	$-0.441377\pi$
$410$	−5.40407e8	−	9.36012e8i	−0.387237	−	0.670715i
$411$	−2.84561e8	+	4.92874e8i	−0.202176	+	0.350178i
$412$	−1.18125e9			−0.832153
$413$		0			0
$414$	9.25400e8			0.640956
$415$	3.63636e8	−	6.29835e8i	0.249746	−	0.432572i
$416$	−1.46178e8	−	2.53187e8i	−0.0995529	−	0.172431i
$417$	1.42815e8	+	2.47363e8i	0.0964490	+	0.167055i
$418$	−8.92992e7	+	1.54671e8i	−0.0598040	+	0.103584i
$419$	−2.47991e9			−1.64697			−0.823486	−	0.567336i	$-0.807974\pi$
$419$	−2.47991e9			−1.64697			−0.823486	+	0.567336i	$0.807974\pi$
$420$		0			0
$421$	−5.51855e7			−0.0360444			−0.0180222	−	0.999838i	$-0.505737\pi$
$421$	−5.51855e7			−0.0360444			−0.0180222	+	0.999838i	$0.505737\pi$
$422$	4.98156e8	−	8.62832e8i	0.322680	−	0.558898i
$423$	1.05543e9	+	1.82806e9i	0.678016	+	1.17436i
$424$	3.25879e8	+	5.64439e8i	0.207623	+	0.359614i
$425$	1.73041e8	−	2.99715e8i	0.109342	−	0.189386i
$426$	−4.16308e8			−0.260904
$427$		0			0
$428$	−3.19612e8			−0.197047
$429$	2.40458e8	−	4.16486e8i	0.147041	−	0.254683i
$430$	−3.66679e8	−	6.35107e8i	−0.222406	−	0.385219i
$431$	−8.42361e8	−	1.45901e9i	−0.506790	−	0.877786i	−0.999969	−	0.00785824i	$-0.997499\pi$
$431$	−8.42361e8	−	1.45901e9i	−0.506790	−	0.877786i	0.493179	−	0.869928i	$-0.335835\pi$
$432$	−1.68382e8	+	2.91647e8i	−0.100486	+	0.174046i
$433$	1.29692e9			0.767724			0.383862	−	0.923390i	$-0.374594\pi$
$433$	1.29692e9			0.767724			0.383862	+	0.923390i	$0.374594\pi$
$434$		0			0
$435$	−5.83017e8			−0.339601
$436$	−5.97984e8	+	1.03574e9i	−0.345531	+	0.598477i
$437$	2.85591e8	+	4.94659e8i	0.163704	+	0.283544i
$438$	2.73371e8	+	4.73492e8i	0.155451	+	0.269249i
$439$	−7.03191e7	+	1.21796e8i	−0.0396686	+	0.0687081i	−0.885178	−	0.465252i	$-0.845964\pi$
$439$	−7.03191e7	+	1.21796e8i	−0.0396686	+	0.0687081i	0.845509	+	0.533960i	$0.179297\pi$
$440$	2.86531e8			0.160357
$441$		0			0
$442$	7.93190e8			0.436917
$443$	9.24666e8	−	1.60157e9i	0.505326	−	0.875251i	−0.494655	−	0.869090i	$-0.664705\pi$
$443$	9.24666e8	−	1.60157e9i	0.505326	−	0.875251i	0.999981	−	0.00616141i	$-0.00196125\pi$
$444$	3.28501e8	+	5.68980e8i	0.178113	+	0.308501i
$445$	2.60061e8	+	4.50439e8i	0.139899	+	0.242313i
$446$	1.14186e9	−	1.97775e9i	0.609452	−	1.05560i
$447$	−5.09176e8			−0.269645
$448$		0			0
$449$	−2.91794e9			−1.52130			−0.760648	−	0.649165i	$-0.775118\pi$
$449$	−2.91794e9			−1.52130			−0.760648	+	0.649165i	$0.775118\pi$
$450$	−2.18138e8	+	3.77826e8i	−0.112846	+	0.195455i
$451$	−8.04627e8	−	1.39365e9i	−0.413025	−	0.715381i
$452$	−7.98508e8	−	1.38306e9i	−0.406719	−	0.704458i
$453$	3.52856e8	−	6.11164e8i	0.178342	−	0.308897i
$454$	−5.39426e8			−0.270543
$455$		0			0
$456$	−9.24275e7			−0.0456483
$457$	−1.42040e9	+	2.46021e9i	−0.696153	+	1.20577i	0.273638	+	0.961833i	$0.411773\pi$
$457$	−1.42040e9	+	2.46021e9i	−0.696153	+	1.20577i	−0.969791	+	0.243939i	$0.921560\pi$
$458$	2.86767e8	+	4.96695e8i	0.139476	+	0.241580i
$459$	−4.56839e8	−	7.91269e8i	−0.220505	−	0.381926i
$460$	4.58183e8	−	7.93595e8i	0.219476	−	0.380143i
$461$	−3.96057e9			−1.88280			−0.941400	−	0.337291i	$-0.890489\pi$
$461$	−3.96057e9			−1.88280			−0.941400	+	0.337291i	$0.890489\pi$
$462$		0			0
$463$	−2.19815e9			−1.02926			−0.514629	−	0.857413i	$-0.672070\pi$
$463$	−2.19815e9			−1.02926			−0.514629	+	0.857413i	$0.672070\pi$
$464$	−2.63855e8	+	4.57011e8i	−0.122618	+	0.212380i
$465$	4.61793e8	+	7.99850e8i	0.212992	+	0.368912i
$466$	−8.71922e6	−	1.51021e7i	−0.00399142	−	0.00691334i
$467$	1.56120e9	−	2.70408e9i	0.709332	−	1.22860i	−0.255773	−	0.966737i	$-0.582330\pi$
$467$	1.56120e9	−	2.70408e9i	0.709332	−	1.22860i	0.965105	−	0.261862i	$-0.0843366\pi$
$468$	−9.99908e8			−0.450920
$469$		0			0
$470$	2.09026e9			0.928662
$471$	−8.30572e7	+	1.43859e8i	−0.0366272	+	0.0634403i
$472$	4.30300e8	+	7.45302e8i	0.188354	+	0.326238i
$473$	−5.45959e8	−	9.45629e8i	−0.237217	−	0.410872i
$474$	−3.50606e8	+	6.07267e8i	−0.151215	+	0.261912i
$475$	−2.69282e8			−0.115287
$476$		0			0
$477$	2.22913e9			0.940420
$478$	7.48526e8	−	1.29648e9i	0.313479	−	0.542962i
$479$	−6.79522e8	−	1.17697e9i	−0.282507	−	0.489317i	0.689494	−	0.724291i	$-0.257833\pi$
$479$	−6.79522e8	−	1.17697e9i	−0.282507	−	0.489317i	−0.972002	+	0.234974i	$0.924499\pi$
$480$	7.41421e7	+	1.28418e8i	0.0305999	+	0.0530007i
$481$	−2.19352e9	+	3.79928e9i	−0.898738	+	1.55666i
$482$	1.00264e9			0.407831
$483$		0			0
$484$	−8.20555e8			−0.328965
$485$	4.89330e8	−	8.47545e8i	0.194763	−	0.337339i
$486$	8.95718e8	+	1.55143e9i	0.353952	+	0.613063i
$487$	−1.19733e9	−	2.07383e9i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$487$	−1.19733e9	−	2.07383e9i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$488$	5.43373e8	−	9.41149e8i	0.211655	−	0.366597i
$489$	1.11992e9			0.433118
$490$		0			0
$491$	−1.95738e9			−0.746261			−0.373130	−	0.927779i	$-0.621716\pi$
$491$	−1.95738e9			−0.746261			−0.373130	+	0.927779i	$0.621716\pi$
$492$	4.16407e8	−	7.21239e8i	0.157631	−	0.273024i
$493$	−7.15867e8	−	1.23992e9i	−0.269072	−	0.466046i
$494$	−3.08586e8	−	5.34486e8i	−0.115168	−	0.199477i
$495$	4.89994e8	−	8.48694e8i	0.181582	−	0.314509i
$496$	8.35974e8			0.307614
$497$		0			0
$498$	5.60395e8			0.203325
$499$	−1.47577e8	+	2.55611e8i	−0.0531699	+	0.0920931i	−0.891385	−	0.453246i	$-0.850266\pi$
$499$	−1.47577e8	+	2.55611e8i	−0.0531699	+	0.0920931i	0.838215	+	0.545339i	$0.183599\pi$
$500$	7.57895e8	+	1.31271e9i	0.271153	+	0.469650i
$501$	8.56238e8	+	1.48305e9i	0.304202	+	0.526893i
$502$	1.39591e8	−	2.41779e8i	0.0492487	−	0.0853013i
$503$	−2.51431e9			−0.880909			−0.440454	−	0.897775i	$-0.645183\pi$
$503$	−2.51431e9			−0.880909			−0.440454	+	0.897775i	$0.645183\pi$
$504$		0			0
$505$	−1.60397e9			−0.554213
$506$	6.82201e8	−	1.18161e9i	0.234091	−	0.405458i
$507$	1.75924e8	+	3.04709e8i	0.0599510	+	0.103838i
$508$	5.50657e8	+	9.53765e8i	0.186362	+	0.322789i
$509$	−1.11783e9	+	1.93615e9i	−0.375721	+	0.650767i	−0.990435	−	0.137983i	$-0.955938\pi$
$509$	−1.11783e9	+	1.93615e9i	−0.375721	+	0.650767i	0.614714	+	0.788750i	$0.289271\pi$
$510$	−4.02311e8			−0.134297
$511$		0			0
$512$	1.34218e8			0.0441942
$513$	−3.55461e8	+	6.15676e8i	−0.116247	+	0.201345i
$514$	−2.37427e8	−	4.11236e8i	−0.0771188	−	0.133574i
$515$	2.00033e9	+	3.46468e9i	0.645323	+	1.11773i
$516$	2.82543e8	−	4.89378e8i	0.0905336	−	0.156809i
$517$	3.11225e9			0.990506
$518$		0			0
$519$	−1.41796e9			−0.445223
$520$	−4.95073e8	+	8.57492e8i	−0.154404	+	0.267435i
$521$	1.59740e9	+	2.76677e9i	0.494858	+	0.857120i	0.999982	−	0.00592705i	$-0.00188665\pi$
$521$	1.59740e9	+	2.76677e9i	0.494858	+	0.857120i	−0.505124	+	0.863047i	$0.668553\pi$
$522$	9.02434e8	+	1.56306e9i	0.277695	+	0.480982i
$523$	−4.70741e8	+	8.15348e8i	−0.143889	+	0.249222i	−0.928958	−	0.370186i	$-0.879294\pi$
$523$	−4.70741e8	+	8.15348e8i	−0.143889	+	0.249222i	0.785069	+	0.619408i	$0.212627\pi$
$524$	−1.72330e9			−0.523242
$525$		0			0
$526$	−1.70197e8			−0.0509919
$527$	−1.13404e9	+	1.96422e9i	−0.337514	+	0.584592i
$528$	1.10392e8	+	1.91205e8i	0.0326377	+	0.0565302i
$529$	−4.79361e8	−	8.30278e8i	−0.140789	−	0.243853i
$530$	1.10369e9	−	1.91164e9i	0.322018	−	0.557751i
$531$	2.94341e9			0.853140
$532$		0			0
$533$	5.56100e9			1.59077
$534$	−2.00389e8	+	3.47083e8i	−0.0569480	+	0.0986369i
$535$	5.41230e8	+	9.37438e8i	0.152807	+	0.264670i
$536$	8.57428e8	+	1.48511e9i	0.240503	+	0.416564i
$537$	−6.36547e8	+	1.10253e9i	−0.177387	+	0.307242i
$538$	−9.36846e8			−0.259376
$539$		0			0
$540$	1.14055e9			0.311700
$541$	−1.93667e9	+	3.35441e9i	−0.525854	+	0.910806i	0.473692	+	0.880691i	$0.342921\pi$
$541$	−1.93667e9	+	3.35441e9i	−0.525854	+	0.910806i	−0.999546	+	0.0301159i	$0.990412\pi$
$542$	−8.11077e8	−	1.40483e9i	−0.218809	−	0.378988i
$543$	1.60645e9	+	2.78246e9i	0.430595	+	0.745813i
$544$	−1.82073e8	+	3.15360e8i	−0.0484898	+	0.0839868i
$545$	4.05050e9			1.07182
$546$		0			0
$547$	−1.92865e9			−0.503845			−0.251922	−	0.967747i	$-0.581063\pi$
$547$	−1.92865e9			−0.503845			−0.251922	+	0.967747i	$0.581063\pi$
$548$	8.72326e8	−	1.51091e9i	0.226437	−	0.392200i
$549$	−1.85844e9	−	3.21890e9i	−0.479341	−	0.830242i
$550$	3.21621e8	+	5.57063e8i	0.0824279	+	0.142769i
$551$	−5.57007e8	+	9.64765e8i	−0.141850	+	0.245692i
$552$	7.06100e8			0.178681
$553$		0			0
$554$	8.09210e8			0.202198
$555$	1.11256e9	−	1.92702e9i	0.276248	−	0.478476i
$556$	−4.37802e8	−	7.58295e8i	−0.108023	−	0.187101i
$557$	−1.65798e9	−	2.87170e9i	−0.406524	−	0.704120i	0.587974	−	0.808880i	$-0.299926\pi$
$557$	−1.65798e9	−	2.87170e9i	−0.406524	−	0.704120i	−0.994498	+	0.104760i	$0.966593\pi$
$558$	1.42959e9	−	2.47613e9i	0.348331	−	0.603327i
$559$	3.77327e9			0.913644
$560$		0			0
$561$	−5.99012e8			−0.143240
$562$	−1.47852e9	+	2.56088e9i	−0.351359	+	0.608572i
$563$	−9.36100e8	−	1.62137e9i	−0.221077	−	0.382916i	0.734059	−	0.679086i	$-0.237624\pi$
$563$	−9.36100e8	−	1.62137e9i	−0.221077	−	0.382916i	−0.955135	+	0.296170i	$0.904290\pi$
$564$	8.05319e8	+	1.39485e9i	0.189013	+	0.327380i
$565$	−2.70438e9	+	4.68413e9i	−0.630810	+	1.09259i
$566$	1.75729e9			0.407367
$567$		0			0
$568$	1.27620e9			0.292213
$569$	3.17886e8	−	5.50595e8i	0.0723400	−	0.125297i	−0.827586	−	0.561338i	$-0.810287\pi$
$569$	3.17886e8	−	5.50595e8i	0.0723400	−	0.125297i	0.899926	+	0.436042i	$0.143620\pi$
$570$	1.56516e8	+	2.71095e8i	0.0353996	+	0.0613139i
$571$	−2.85689e9	−	4.94828e9i	−0.642196	−	1.11232i	−0.984942	−	0.172887i	$-0.944690\pi$
$571$	−2.85689e9	−	4.94828e9i	−0.642196	−	1.11232i	0.342746	−	0.939428i	$-0.388643\pi$
$572$	−7.37128e8	+	1.27674e9i	−0.164686	+	0.285245i
$573$	−4.70171e8			−0.104403
$574$		0			0
$575$	2.05718e9			0.451267
$576$	2.29525e8	−	3.97548e8i	0.0500438	−	0.0866785i
$577$	−3.17926e9	−	5.50664e9i	−0.688986	−	1.19336i	−0.972166	−	0.234292i	$-0.924723\pi$
$577$	−3.17926e9	−	5.50664e9i	−0.688986	−	1.19336i	0.283180	−	0.959067i	$-0.408611\pi$
$578$	1.14737e9	+	1.98730e9i	0.247148	+	0.428072i
$579$	−1.41211e9	+	2.44584e9i	−0.302338	+	0.523665i
$580$	1.78725e9			0.380353
$581$		0			0
$582$	7.54102e8			0.158562
$583$	1.64331e9	−	2.84629e9i	0.343462	−	0.594894i
$584$	−8.38023e8	−	1.45150e9i	−0.174105	−	0.301559i
$585$	1.69324e9	+	2.93278e9i	0.349682	+	0.605667i
$586$	−2.88892e9	+	5.00376e9i	−0.593054	+	1.02720i
$587$	−7.71077e8			−0.157349			−0.0786745	−	0.996900i	$-0.525069\pi$
$587$	−7.71077e8			−0.157349			−0.0786745	+	0.996900i	$0.525069\pi$
$588$		0			0
$589$	1.76477e9			0.355864
$590$	1.45734e9	−	2.52418e9i	0.292131	−	0.505986i
$591$	−9.35550e8	−	1.62042e9i	−0.186428	−	0.322903i
$592$	−1.00702e9	−	1.74422e9i	−0.199487	−	0.345521i
$593$	3.20093e9	−	5.54417e9i	0.630354	−	1.09181i	−0.357125	−	0.934057i	$-0.616243\pi$
$593$	3.20093e9	−	5.54417e9i	0.630354	−	1.09181i	0.987479	−	0.157749i	$-0.0504238\pi$
$594$	1.69820e9			0.332458
$595$		0			0
$596$	1.56089e9			0.302002
$597$	5.73516e8	−	9.93359e8i	0.110315	−	0.191072i
$598$	2.35744e9	+	4.08321e9i	0.450803	+	0.780813i
$599$	6.60575e8	+	1.14415e9i	0.125582	+	0.217515i	0.921960	−	0.387284i	$-0.126587\pi$
$599$	6.60575e8	+	1.14415e9i	0.125582	+	0.217515i	−0.796378	+	0.604799i	$0.793253\pi$
$600$	−1.66444e8	+	2.88289e8i	−0.0314585	+	0.0544878i
$601$	2.93204e9			0.550947			0.275474	−	0.961309i	$-0.411165\pi$
$601$	2.93204e9			0.550947			0.275474	+	0.961309i	$0.411165\pi$
$602$		0			0
$603$	5.86512e9			1.08935
$604$	−1.08169e9	+	1.87353e9i	−0.199743	+	0.345965i
$605$	1.38953e9	+	2.40673e9i	0.255107	+	0.441859i
$606$	−6.17966e8	−	1.07035e9i	−0.112800	−	0.195376i
$607$	−2.76216e9	+	4.78420e9i	−0.501289	+	0.868258i	0.498710	+	0.866769i	$0.333807\pi$
$607$	−2.76216e9	+	4.78420e9i	−0.501289	+	0.868258i	−0.999999	+	0.00148902i	$0.999526\pi$
$608$	2.83338e8			0.0511261
$609$		0			0
$610$	−3.68058e9			−0.656542
$611$	−5.37740e9	+	9.31393e9i	−0.953736	+	1.65192i
$612$	6.22724e8	+	1.07859e9i	0.109816	+	0.190207i
$613$	3.14956e9	+	5.45520e9i	0.552253	+	0.956530i	0.998112	+	0.0614270i	$0.0195651\pi$
$613$	3.14956e9	+	5.45520e9i	0.552253	+	0.956530i	−0.445858	+	0.895103i	$0.647102\pi$
$614$	−2.55818e8	+	4.43090e8i	−0.0446007	+	0.0772507i
$615$	−2.82057e9			−0.488961
$616$		0			0
$617$	−4.76835e9			−0.817278			−0.408639	−	0.912696i	$-0.633996\pi$
$617$	−4.76835e9			−0.817278			−0.408639	+	0.912696i	$0.633996\pi$
$618$	−1.54134e9	+	2.66969e9i	−0.262688	+	0.454989i
$619$	3.93891e8	+	6.82239e8i	0.0667511	+	0.115616i	0.897469	−	0.441077i	$-0.145403\pi$
$619$	3.93891e8	+	6.82239e8i	0.0667511	+	0.115616i	−0.830718	+	0.556693i	$0.812070\pi$
$620$	−1.41564e9	−	2.45195e9i	−0.238551	−	0.413182i
$621$	2.71554e9	−	4.70346e9i	0.455026	−	0.788128i
$622$	−1.23715e9			−0.206136
$623$		0			0
$624$	−7.62952e8			−0.125705
$625$	1.35034e9	−	2.33885e9i	0.221239	−	0.383197i
$626$	−1.97594e9	−	3.42242e9i	−0.321931	−	0.557601i
$627$	2.33042e8	+	4.03640e8i	0.0377570	+	0.0653970i
$628$	2.54613e8	−	4.41003e8i	0.0410225	−	0.0710531i
$629$	5.46432e9			0.875506
$630$		0			0
$631$	−9.52407e9			−1.50911			−0.754553	−	0.656239i	$-0.772146\pi$
$631$	−9.52407e9			−1.50911			−0.754553	+	0.656239i	$0.772146\pi$
$632$	1.07479e9	−	1.86159e9i	0.169361	−	0.293342i
$633$	−1.30003e9	−	2.25171e9i	−0.203723	−	0.352858i
$634$	−1.71975e9	−	2.97870e9i	−0.268012	−	0.464210i
$635$	1.86496e9	−	3.23021e9i	0.289042	−	0.500636i
$636$	1.70088e9			0.262164
$637$		0			0
$638$	2.66108e9			0.405682
$639$	2.18242e9	−	3.78006e9i	0.330891	−	0.573120i
$640$	−2.27284e8	−	3.93667e8i	−0.0342719	−	0.0593607i
$641$	1.32160e9	+	2.28909e9i	0.198198	+	0.343288i	0.947944	−	0.318437i	$-0.103158\pi$
$641$	1.32160e9	+	2.28909e9i	0.198198	+	0.343288i	−0.749746	+	0.661725i	$0.769825\pi$
$642$	−4.17042e8	+	7.22338e8i	−0.0622024	+	0.107738i
$643$	−7.78643e9			−1.15505			−0.577524	−	0.816374i	$-0.695981\pi$
$643$	−7.78643e9			−1.15505			−0.577524	+	0.816374i	$0.695981\pi$
$644$		0			0
$645$	−1.91383e9			−0.280830
$646$	−3.84363e8	+	6.65736e8i	−0.0560955	+	0.0971602i
$647$	4.77250e9	+	8.26622e9i	0.692757	+	1.19989i	0.970931	+	0.239360i	$0.0769377\pi$
$647$	4.77250e9	+	8.26622e9i	0.692757	+	1.19989i	−0.278173	+	0.960531i	$0.589729\pi$
$648$	−5.40988e8	−	9.37018e8i	−0.0781043	−	0.135281i
$649$	2.16987e9	−	3.75833e9i	0.311586	−	0.539682i
$650$	−2.22281e9			−0.317472
$651$		0			0
$652$	−3.43314e9			−0.485093
$653$	5.15813e8	−	8.93414e8i	0.0724930	−	0.125562i	−0.827500	−	0.561465i	$-0.810238\pi$
$653$	5.15813e8	−	8.93414e8i	0.0724930	−	0.125562i	0.899993	+	0.435904i	$0.143571\pi$
$654$	1.56054e9	+	2.70294e9i	0.218149	+	0.377846i
$655$	2.91824e9	+	5.05453e9i	0.405766	+	0.702808i
$656$	−1.27650e9	+	2.21097e9i	−0.176546	+	0.305787i
$657$	−5.73239e9			−0.788600
$658$		0			0
$659$	9.97213e9			1.35734			0.678671	−	0.734443i	$-0.262556\pi$
$659$	9.97213e9			1.35734			0.678671	+	0.734443i	$0.262556\pi$
$660$	3.73876e8	−	6.47572e8i	0.0506202	−	0.0876767i
$661$	4.39852e9	+	7.61845e9i	0.592381	+	1.02603i	0.993911	+	0.110188i	$0.0351453\pi$
$661$	4.39852e9	+	7.61845e9i	0.592381	+	1.02603i	−0.401530	+	0.915846i	$0.631521\pi$
$662$	1.31268e9	+	2.27362e9i	0.175855	+	0.304590i
$663$	1.03498e9	−	1.79264e9i	0.137923	−	0.238889i
$664$	−1.71790e9			−0.227724
$665$		0			0
$666$	−6.88842e9			−0.903565
$667$	4.25526e9	−	7.37032e9i	0.555246	−	0.961714i
$668$	−2.62481e9	−	4.54630e9i	−0.340706	−	0.590121i
$669$	−2.97987e9	−	5.16129e9i	−0.384774	−	0.666449i
$670$	2.90393e9	−	5.02975e9i	0.373013	−	0.646078i
$671$	−5.48012e9			−0.700264
$672$		0			0
$673$	7.42386e9			0.938808			0.469404	−	0.882983i	$-0.344469\pi$
$673$	7.42386e9			0.938808			0.469404	+	0.882983i	$0.344469\pi$
$674$	4.57636e8	−	7.92648e8i	0.0575719	−	0.0997174i
$675$	1.28023e9	+	2.21743e9i	0.160223	+	0.277515i
$676$	−5.39297e8	−	9.34090e8i	−0.0671451	−	0.116299i
$677$	−5.72981e8	+	9.92432e8i	−0.0709708	+	0.122925i	−0.899327	−	0.437277i	$-0.855943\pi$
$677$	−5.72981e8	+	9.92432e8i	−0.0709708	+	0.122925i	0.828356	+	0.560202i	$0.189276\pi$
$678$	−4.16769e9			−0.513561
$679$		0			0
$680$	1.23329e9			0.150413
$681$	−7.03863e8	+	1.21913e9i	−0.0854030	+	0.147922i
$682$	−2.10778e9	−	3.65078e9i	−0.254437	−	0.440697i
$683$	−5.29365e9	−	9.16887e9i	−0.635745	−	1.10114i	−0.986357	−	0.164621i	$-0.947360\pi$
$683$	−5.29365e9	−	9.16887e9i	−0.635745	−	1.10114i	0.350612	−	0.936521i	$-0.385974\pi$
$684$	4.84534e8	−	8.39238e8i	0.0578933	−	0.100274i
$685$	−5.90877e9			−0.702393
$686$		0			0
$687$	1.49674e9			0.176115
$688$	−8.66139e8	+	1.50020e9i	−0.101398	+	0.175626i
$689$	5.67868e9	+	9.83576e9i	0.661424	+	1.14562i
$690$	−1.19571e9	−	2.07103e9i	−0.138565	−	0.240001i
$691$	3.78065e9	−	6.54827e9i	0.435906	−	0.755011i	−0.561463	−	0.827502i	$-0.689761\pi$
$691$	3.78065e9	−	6.54827e9i	0.435906	−	0.755011i	0.997369	+	0.0724904i	$0.0230947\pi$
$692$	4.34678e9			0.498650
$693$		0			0
$694$	−5.25342e9			−0.596601
$695$	−1.48275e9	+	2.56819e9i	−0.167540	+	0.290189i
$696$	6.88576e8	+	1.19265e9i	0.0774141	+	0.134085i
$697$	−3.46329e9	−	5.99859e9i	−0.387413	−	0.671018i
$698$	−3.54398e9	+	6.13835e9i	−0.394454	+	0.683215i
$699$	−4.55087e7			−0.00503992
$700$		0			0
$701$	−1.31100e10			−1.43744			−0.718719	−	0.695301i	$-0.755271\pi$
$701$	−1.31100e10			−1.43744			−0.718719	+	0.695301i	$0.755271\pi$
$702$	−2.93419e9	+	5.08216e9i	−0.320116	+	0.554458i
$703$	−2.12586e9	−	3.68210e9i	−0.230776	−	0.399716i
$704$	−3.38409e8	−	5.86142e8i	−0.0365543	−	0.0633138i
$705$	2.72745e9	−	4.72408e9i	0.293153	−	0.507756i
$706$	−5.49919e9			−0.588142
$707$		0			0
$708$	2.24589e9			0.237833
$709$	−1.55398e8	+	2.69157e8i	−0.0163750	+	0.0283624i	−0.874097	−	0.485752i	$-0.838546\pi$
$709$	−1.55398e8	+	2.69157e8i	−0.0163750	+	0.0283624i	0.857722	+	0.514114i	$0.171879\pi$
$710$	−2.16111e9	−	3.74315e9i	−0.226607	−	0.392494i
$711$	−3.67597e9	−	6.36697e9i	−0.383556	−	0.664338i
$712$	6.14295e8	−	1.06399e9i	0.0637818	−	0.110473i
$713$	−1.34819e10			−1.39296
$714$		0			0
$715$	4.99300e9			0.510847
$716$	1.95135e9	−	3.37983e9i	0.198673	−	0.344112i
$717$	−1.95341e9	−	3.38340e9i	−0.197914	−	0.342797i
$718$	−1.28977e8	−	2.23395e8i	−0.0130040	−	0.0225237i
$719$	2.09243e9	−	3.62420e9i	0.209943	−	0.363631i	−0.741754	−	0.670673i	$-0.766006\pi$
$719$	2.09243e9	−	3.62420e9i	0.209943	−	0.363631i	0.951696	+	0.307041i	$0.0993389\pi$
$720$	−1.55471e9			−0.155233
$721$		0			0
$722$	−6.55284e9			−0.647962
$723$	1.30828e9	−	2.26601e9i	0.128741	−	0.222986i
$724$	−4.92461e9	−	8.52968e9i	−0.482266	−	0.835310i
$725$	2.00612e9	+	3.47471e9i	0.195512	+	0.338637i
$726$	−1.07069e9	+	1.85449e9i	−0.103845	+	0.179865i
$727$	9.54370e9			0.921184			0.460592	−	0.887612i	$-0.347637\pi$
$727$	9.54370e9			0.921184			0.460592	+	0.887612i	$0.347637\pi$
$728$		0			0
$729$	5.34261e7			0.00510749
$730$	−2.83821e9	+	4.91593e9i	−0.270032	+	0.467709i
$731$	−2.34993e9	−	4.07019e9i	−0.222507	−	0.385393i
$732$	−1.41803e9	−	2.45609e9i	−0.133627	−	0.231449i
$733$	5.03140e9	−	8.71464e9i	0.471873	−	0.817307i	−0.527609	−	0.849487i	$-0.676912\pi$
$733$	5.03140e9	−	8.71464e9i	0.471873	−	0.817307i	0.999482	+	0.0321796i	$0.0102449\pi$
$734$	5.73240e9			0.535057
$735$		0			0
$736$	−2.16456e9			−0.200123
$737$	4.32374e9	−	7.48894e9i	0.397854	−	0.689103i
$738$	4.36588e9	+	7.56192e9i	0.399829	+	0.692524i
$739$	3.54880e9	+	6.14670e9i	0.323464	+	0.560256i	0.981200	−	0.192992i	$-0.0618193\pi$
$739$	3.54880e9	+	6.14670e9i	0.323464	+	0.560256i	−0.657736	+	0.753248i	$0.728486\pi$
$740$	−3.41058e9	+	5.90730e9i	−0.309398	+	0.535893i
$741$	−1.61062e9			−0.145421
$742$		0			0
$743$	3.16400e8			0.0282993			0.0141497	−	0.999900i	$-0.495496\pi$
$743$	3.16400e8			0.0282993			0.0141497	+	0.999900i	$0.495496\pi$
$744$	1.09081e9	−	1.88934e9i	0.0971055	−	0.168192i
$745$	−2.64320e9	−	4.57816e9i	−0.234198	−	0.405643i
$746$	−4.88907e9	−	8.46812e9i	−0.431162	−	0.746794i
$747$	−2.93777e9	+	5.08836e9i	−0.257867	+	0.446638i
$748$	1.83628e9			0.160429
$749$		0			0
$750$	3.95572e9			0.342382
$751$	−3.22967e9	+	5.59396e9i	−0.278240	+	0.481925i	−0.970947	−	0.239293i	$-0.923084\pi$
$751$	−3.22967e9	+	5.59396e9i	−0.278240	+	0.481925i	0.692708	+	0.721218i	$0.256418\pi$
$752$	−2.46872e9	−	4.27594e9i	−0.211694	−	0.366665i
$753$	−3.64287e8	−	6.30964e8i	−0.0310929	−	0.0538545i
$754$	−4.59787e9	+	7.96374e9i	−0.390622	+	0.676577i
$755$	7.32689e9			0.619591
$756$		0			0
$757$	1.07167e10			0.897892			0.448946	−	0.893559i	$-0.351800\pi$
$757$	1.07167e10			0.897892			0.448946	+	0.893559i	$0.351800\pi$
$758$	2.73319e9	−	4.73403e9i	0.227944	−	0.394810i
$759$	−1.78032e9	−	3.08361e9i	−0.147793	−	0.255984i
$760$	−4.79804e8	−	8.31045e8i	−0.0396475	−	0.0686715i
$761$	−4.51415e9	+	7.81874e9i	−0.371304	+	0.643117i	−0.989766	−	0.142697i	$-0.954423\pi$
$761$	−4.51415e9	+	7.81874e9i	−0.371304	+	0.643117i	0.618462	+	0.785814i	$0.287756\pi$
$762$	2.87407e9			0.235318
$763$		0			0
$764$	1.44132e9			0.116932
$765$	2.10904e9	−	3.65296e9i	0.170322	−	0.295006i
$766$	8.10353e9	+	1.40357e10i	0.651439	+	1.12832i
$767$	7.49829e9	+	1.29874e10i	0.600038	+	1.03930i
$768$	1.75132e8	−	3.03338e8i	0.0139509	−	0.0241637i
$769$	−8.30919e9			−0.658895			−0.329448	−	0.944174i	$-0.606863\pi$
$769$	−8.30919e9			−0.658895			−0.329448	+	0.944174i	$0.606863\pi$
$770$		0			0
$771$	−1.23922e9			−0.0973771
$772$	4.32884e9	−	7.49777e9i	0.338619	−	0.586505i
$773$	5.63091e9	+	9.75302e9i	0.438480	+	0.759470i	0.997573	−	0.0696352i	$-0.0221835\pi$
$773$	5.63091e9	+	9.75302e9i	0.438480	+	0.759470i	−0.559092	+	0.829106i	$0.688850\pi$
$774$	2.96235e9	+	5.13095e9i	0.229638	+	0.397745i
$775$	3.17800e9	−	5.50446e9i	0.245244	−	0.424775i
$776$	−2.31171e9			−0.177590
$777$		0			0
$778$	−5.83209e9			−0.444013
$779$	−2.69474e9	+	4.66743e9i	−0.204238	+	0.353750i
$780$	1.29198e9	+	2.23778e9i	0.0974821	+	0.168844i
$781$	−3.21774e9	−	5.57328e9i	−0.241697	−	0.418632i
$782$	2.93634e9	−	5.08589e9i	0.219575	−	0.380315i
$783$	1.05926e10			0.788563
$784$		0			0
$785$	−1.72465e9			−0.127249
$786$	−2.24863e9	+	3.89474e9i	−0.165173	+	0.286088i
$787$	−1.11102e10	−	1.92434e10i	−0.812475	−	1.40725i	−0.911127	−	0.412127i	$-0.864786\pi$
$787$	−1.11102e10	−	1.92434e10i	−0.812475	−	1.40725i	0.0986511	−	0.995122i	$-0.468547\pi$
$788$	2.86794e9	+	4.96743e9i	0.208799	+	0.361651i
$789$	−2.22079e8	+	3.84652e8i	−0.0160968	+	0.0278804i
$790$	−7.28017e9			−0.525348
$791$		0			0
$792$	−2.31484e9			−0.165571
$793$	9.46866e9	−	1.64002e10i	0.674268	−	1.16787i
$794$	−5.31069e9	−	9.19839e9i	−0.376512	−	0.652139i
$795$	−2.88026e9	−	4.98876e9i	−0.203304	−	0.352133i
$796$	−1.75812e9	+	3.04516e9i	−0.123553	+	0.214000i
$797$	6.49195e9			0.454225			0.227113	−	0.973868i	$-0.427071\pi$
$797$	6.49195e9			0.454225			0.227113	+	0.973868i	$0.427071\pi$
$798$		0			0
$799$	1.33958e10			0.929082
$800$	5.10236e8	−	8.83755e8i	0.0352336	−	0.0610263i
$801$	−2.10100e9	−	3.63904e9i	−0.144448	−	0.250192i
$802$	3.43180e9	+	5.94405e9i	0.234916	+	0.406886i
$803$	−4.22589e9	+	7.31946e9i	−0.288014	+	0.498855i
$804$	4.47521e9			0.303681
$805$		0			0
$806$	1.45674e10			0.979966
$807$	−1.22243e9	+	2.11731e9i	−0.0818780	+	0.141817i
$808$	1.89438e9	+	3.28117e9i	0.126336	+	0.218821i
$809$	5.80562e9	+	1.00556e10i	0.385504	+	0.667712i	0.991839	−	0.127497i	$-0.0406944\pi$
$809$	5.80562e9	+	1.00556e10i	0.385504	+	0.667712i	−0.606335	+	0.795209i	$0.707361\pi$
$810$	−1.83221e9	+	3.17349e9i	−0.121137	+	0.209816i
$811$	1.72427e10			1.13510			0.567548	−	0.823340i	$-0.307892\pi$
$811$	1.72427e10			1.13510			0.567548	+	0.823340i	$0.307892\pi$
$812$		0			0
$813$	−4.23329e9			−0.276288
$814$	−5.07811e9	+	8.79555e9i	−0.330002	+	0.571581i
$815$	5.81366e9	+	1.00696e10i	0.376182	+	0.651567i
$816$	4.75152e8	+	8.22988e8i	0.0306138	+	0.0530247i
$817$	−1.82845e9	+	3.16696e9i	−0.117302	+	0.203173i
$818$	1.68213e10			1.07454
$819$		0			0
$820$	8.64651e9			0.547636
$821$	−7.15770e9	+	1.23975e10i	−0.451412	+	0.781868i	−0.998474	−	0.0552240i	$-0.982413\pi$
$821$	−7.15770e9	+	1.23975e10i	−0.451412	+	0.781868i	0.547062	+	0.837092i	$0.315746\pi$
$822$	−2.27649e9	−	3.94299e9i	−0.142960	−	0.247613i
$823$	2.33905e9	+	4.05135e9i	0.146265	+	0.253338i	0.929844	−	0.367954i	$-0.119941\pi$
$823$	2.33905e9	+	4.05135e9i	0.146265	+	0.253338i	−0.783579	+	0.621292i	$0.786608\pi$
$824$	4.72502e9	−	8.18397e9i	0.294211	−	0.509588i
$825$	1.67865e9			0.104081
$826$		0			0
$827$	−1.01540e10			−0.624264			−0.312132	−	0.950039i	$-0.601043\pi$
$827$	−1.01540e10			−0.624264			−0.312132	+	0.950039i	$0.601043\pi$
$828$	−3.70160e9	+	6.41136e9i	−0.226612	+	0.392504i
$829$	5.51455e9	+	9.55148e9i	0.336178	+	0.582278i	0.983710	−	0.179760i	$-0.0575323\pi$
$829$	5.51455e9	+	9.55148e9i	0.336178	+	0.582278i	−0.647532	+	0.762038i	$0.724199\pi$
$830$	2.90909e9	+	5.03868e9i	0.176597	+	0.305875i
$831$	1.05589e9	−	1.82885e9i	0.0638284	−	0.110554i
$832$	2.33884e9			0.140789
$833$		0			0
$834$	−2.28504e9			−0.136400
$835$	−8.88969e9	+	1.53974e10i	−0.528426	+	0.915260i
$836$	−7.14393e8	−	1.23737e9i	−0.0422878	−	0.0732447i
$837$	−8.39015e9	−	1.45322e10i	−0.494573	−	0.856626i
$838$	9.91963e9	−	1.71813e10i	0.582293	−	1.00856i
$839$	1.71068e10			1.00001			0.500003	−	0.866023i	$-0.333332\pi$
$839$	1.71068e10			1.00001			0.500003	+	0.866023i	$0.333332\pi$
$840$		0			0
$841$	−6.51269e8			−0.0377550
$842$	2.20742e8	−	3.82337e8i	0.0127436	−	0.0220726i
$843$	3.85847e9	+	6.68306e9i	0.221829	+	0.384219i
$844$	3.98525e9	+	6.90266e9i	0.228169	+	0.395201i
$845$	−1.82649e9	+	3.16357e9i	−0.104140	+	0.180376i
$846$	−1.68869e10			−0.958859
$847$		0			0
$848$	−5.21407e9			−0.293624
$849$	2.29298e9	−	3.97156e9i	0.128595	−	0.222733i
$850$	1.38432e9	+	2.39772e9i	0.0773164	+	0.133916i
$851$	1.62405e10	+	2.81294e10i	0.903330	+	1.56461i
$852$	1.66523e9	−	2.88427e9i	0.0922435	−	0.159771i
$853$	2.88309e9			0.159051			0.0795256	−	0.996833i	$-0.474659\pi$
$853$	2.88309e9			0.159051			0.0795256	+	0.996833i	$0.474659\pi$
$854$		0			0
$855$	−3.28203e9			−0.179582
$856$	1.27845e9	−	2.21434e9i	0.0696667	−	0.120666i
$857$	−1.20159e10	−	2.08122e10i	−0.652116	−	1.12950i	−0.982608	−	0.185690i	$-0.940548\pi$
$857$	−1.20159e10	−	2.08122e10i	−0.652116	−	1.12950i	0.330492	−	0.943809i	$-0.392785\pi$
$858$	1.92367e9	+	3.33189e9i	0.103974	+	0.180088i
$859$	−1.70872e10	+	2.95958e10i	−0.919801	+	1.59314i	−0.120084	+	0.992764i	$0.538317\pi$
$859$	−1.70872e10	+	2.95958e10i	−0.919801	+	1.59314i	−0.799716	+	0.600378i	$0.795017\pi$
$860$	5.86687e9			0.314530
$861$		0			0
$862$	1.34778e10			0.716709
$863$	−1.48357e10	+	2.56962e10i	−0.785724	+	1.36091i	0.142841	+	0.989746i	$0.454376\pi$
$863$	−1.48357e10	+	2.56962e10i	−0.785724	+	1.36091i	−0.928566	+	0.371168i	$0.878957\pi$
$864$	−1.34706e9	−	2.33318e9i	−0.0710540	−	0.123069i
$865$	−7.36082e9	−	1.27493e10i	−0.386696	−	0.669777i
$866$	−5.18768e9	+	8.98532e9i	−0.271432	+	0.470133i
$867$	5.98853e9			0.312071
$868$		0			0
$869$	−1.08397e10			−0.560333
$870$	2.33207e9	−	4.03926e9i	0.120067	−	0.207962i
$871$	1.49413e10	+	2.58791e10i	0.766169	+	1.32704i
$872$	−4.78388e9	−	8.28592e9i	−0.244327	−	0.423187i
$873$	−3.95324e9	+	6.84721e9i	−0.201096	+	0.348308i
$874$	−4.56946e9			−0.231513
$875$		0			0
$876$	−4.37394e9			−0.219841
$877$	3.70786e9	−	6.42220e9i	0.185620	−	0.321503i	−0.758165	−	0.652062i	$-0.773904\pi$
$877$	3.70786e9	−	6.42220e9i	0.185620	−	0.321503i	0.943785	+	0.330559i	$0.107237\pi$
$878$	−5.62552e8	−	9.74369e8i	−0.0280500	−	0.0485840i
$879$	7.53914e9	+	1.30582e10i	0.374422	+	0.648517i
$880$	−1.14612e9	+	1.98514e9i	−0.0566946	+	0.0981979i
$881$	−3.89699e10			−1.92005			−0.960027	−	0.279907i	$-0.909696\pi$
$881$	−3.89699e10			−1.92005			−0.960027	+	0.279907i	$0.909696\pi$
$882$		0			0
$883$	−6.37811e9			−0.311767			−0.155883	−	0.987775i	$-0.549822\pi$
$883$	−6.37811e9			−0.311767			−0.155883	+	0.987775i	$0.549822\pi$
$884$	−3.17276e9	+	5.49538e9i	−0.154474	+	0.267556i
$885$	−3.80318e9	−	6.58730e9i	−0.184436	−	0.319452i
$886$	7.39733e9	+	1.28126e10i	0.357320	+	0.618896i
$887$	−1.84996e10	+	3.20422e10i	−0.890079	+	1.54166i	−0.0503004	+	0.998734i	$0.516018\pi$
$887$	−1.84996e10	+	3.20422e10i	−0.890079	+	1.54166i	−0.839779	+	0.542928i	$0.817315\pi$
$888$	−5.25601e9			−0.251890
$889$		0			0
$890$	−4.16098e9			−0.197847
$891$	−2.72803e9	+	4.72509e9i	−0.129205	+	0.223789i
$892$	9.13484e9	+	1.58220e10i	0.430947	+	0.746423i
$893$	−5.21155e9	−	9.02666e9i	−0.244899	−	0.424177i
$894$	2.03670e9	−	3.52768e9i	0.0953337	−	0.165123i
$895$	−1.32176e10			−0.616272
$896$		0			0
$897$	1.23043e10			0.569224
$898$	1.16717e10	−	2.02161e10i	0.537859	−	0.931599i
$899$	−1.31474e10	−	2.27719e10i	−0.603503	−	1.04530i
$900$	−1.74510e9	−	3.02261e9i	−0.0797944	−	0.138208i
$901$	7.07315e9	−	1.22511e10i	0.322163	−	0.558003i
$902$	1.28740e10			0.584106
$903$		0			0
$904$	1.27761e10			0.575188
$905$	−1.66786e10	+	2.88883e10i	−0.747981	+	1.29554i
$906$	2.82285e9	+	4.88931e9i	0.126107	+	0.218423i
$907$	3.20212e9	+	5.54623e9i	0.142499	+	0.246816i	0.928437	−	0.371490i	$-0.121153\pi$
$907$	3.20212e9	+	5.54623e9i	0.142499	+	0.246816i	−0.785938	+	0.618305i	$0.787820\pi$
$908$	2.15770e9	−	3.73725e9i	0.0956514	−	0.165673i
$909$	1.29583e10			0.572234
$910$		0			0
$911$	−2.59678e9			−0.113794			−0.0568971	−	0.998380i	$-0.518121\pi$
$911$	−2.59678e9			−0.113794			−0.0568971	+	0.998380i	$0.518121\pi$
$912$	3.69710e8	−	6.40357e8i	0.0161391	−	0.0279537i
$913$	4.33142e9	+	7.50224e9i	0.188357	+	0.326244i
$914$	−1.13632e10	−	1.96817e10i	−0.492254	−	0.852609i
$915$	−4.80256e9	+	8.31828e9i	−0.207252	+	0.358971i
$916$	−4.58827e9			−0.197249
$917$		0			0
$918$	7.30943e9			0.311842
$919$	1.87721e10	−	3.25142e10i	0.797825	−	1.38187i	−0.123205	−	0.992381i	$-0.539317\pi$
$919$	1.87721e10	−	3.25142e10i	0.797825	−	1.38187i	0.921030	−	0.389492i	$-0.127349\pi$
$920$	3.66546e9	+	6.34876e9i	0.155193	+	0.268802i
$921$	6.67602e8	+	1.15632e9i	0.0281585	+	0.0487719i
$922$	1.58423e10	−	2.74396e10i	0.665671	−	1.15298i
$923$	2.22387e10			0.930900
$924$		0			0
$925$	−1.53130e10			−0.636159
$926$	8.79260e9	−	1.52292e10i	0.363897	−	0.630289i
$927$	−1.61604e10	−	2.79907e10i	−0.666306	−	1.15408i
$928$	−2.11084e9	−	3.65609e9i	−0.0867037	−	0.150175i
$929$	1.26185e10	−	2.18559e10i	0.516361	−	0.894363i	−0.483459	−	0.875367i	$-0.660620\pi$
$929$	1.26185e10	−	2.18559e10i	0.516361	−	0.894363i	0.999820	−	0.0189960i	$-0.00604698\pi$
$930$	−7.38870e9			−0.301216
$931$		0			0
$932$	1.39508e8			0.00564472
$933$	−1.61427e9	+	2.79600e9i	−0.0650716	+	0.112707i
$934$	1.24896e10	+	2.16326e10i	0.501573	+	0.868751i
$935$	−3.10955e9	−	5.38590e9i	−0.124410	−	0.215485i
$936$	3.99963e9	−	6.92757e9i	0.159424	−	0.276131i
$937$	6.75432e9			0.268221			0.134111	−	0.990966i	$-0.457182\pi$
$937$	6.75432e9			0.268221			0.134111	+	0.990966i	$0.457182\pi$
$938$		0			0
$939$	−1.03131e10			−0.406499
$940$	−8.36104e9	+	1.44817e10i	−0.328332	+	0.568687i
$941$	−4.73345e9	−	8.19857e9i	−0.185188	−	0.320756i	0.758452	−	0.651729i	$-0.225956\pi$
$941$	−4.73345e9	−	8.19857e9i	−0.185188	−	0.320756i	−0.943640	+	0.330974i	$0.892623\pi$
$942$	−6.64458e8	−	1.15087e9i	−0.0258994	−	0.0448590i
$943$	2.05865e10	−	3.56568e10i	0.799449	−	1.38469i
$944$	−6.88480e9			−0.266373
$945$		0			0
$946$	8.73534e9			0.335476
$947$	2.51579e10	−	4.35748e10i	0.962608	−	1.66729i	0.246701	−	0.969092i	$-0.420654\pi$
$947$	2.51579e10	−	4.35748e10i	0.962608	−	1.66729i	0.715908	−	0.698195i	$-0.246013\pi$
$948$	−2.80485e9	−	4.85814e9i	−0.106925	−	0.185200i
$949$	−1.46032e10	−	2.52934e10i	−0.554645	−	0.960673i
$950$	1.07713e9	−	1.86564e9i	0.0407600	−	0.0705983i
$951$	−8.97599e9			−0.338416
$952$		0			0
$953$	−2.56329e9			−0.0959342			−0.0479671	−	0.998849i	$-0.515274\pi$
$953$	−2.56329e9			−0.0959342			−0.0479671	+	0.998849i	$0.515274\pi$
$954$	−8.91653e9	+	1.54439e10i	−0.332489	+	0.575887i
$955$	−2.44072e9	−	4.22745e9i	−0.0906790	−	0.157061i
$956$	5.98820e9	+	1.03719e10i	0.221663	+	0.383932i
$957$	3.47228e9	−	6.01416e9i	0.128063	−	0.221811i
$958$	1.08724e10			0.399525
$959$		0			0
$960$	−1.18627e9			−0.0432749
$961$	−7.07111e9	+	1.22475e10i	−0.257013	+	0.445160i
$962$	−1.75481e10	−	3.03942e10i	−0.635504	−	1.10072i
$963$	−4.37253e9	−	7.57344e9i	−0.157776	−	0.273276i
$964$	−4.01056e9	+	6.94649e9i	−0.144190	+	0.249744i
$965$	−2.93218e10			−1.05038
$966$		0			0
$967$	1.17322e10			0.417241			0.208621	−	0.977997i	$-0.433103\pi$
$967$	1.17322e10			0.417241			0.208621	+	0.977997i	$0.433103\pi$
$968$	3.28222e9	−	5.68498e9i	0.116307	−	0.201449i
$969$	1.00306e9	+	1.73735e9i	0.0354156	+	0.0613416i
$970$	3.91464e9	+	6.78036e9i	0.137718	+	0.238535i
$971$	−8.01185e9	+	1.38769e10i	−0.280844	+	0.486437i	−0.971593	−	0.236658i	$-0.923948\pi$
$971$	−8.01185e9	+	1.38769e10i	−0.280844	+	0.486437i	0.690749	+	0.723095i	$0.257281\pi$
$972$	−1.43315e10			−0.500564
$973$		0			0
$974$	1.91573e10			0.664319
$975$	−2.90040e9	+	5.02365e9i	−0.100217	+	0.173581i
$976$	4.34698e9	+	7.52919e9i	0.149663	+	0.259223i
$977$	−2.08302e10	−	3.60790e10i	−0.714601	−	1.23772i	−0.963113	−	0.269096i	$-0.913275\pi$
$977$	−2.08302e10	−	3.60790e10i	−0.714601	−	1.23772i	0.248513	−	0.968629i	$-0.420058\pi$
$978$	−4.47969e9	+	7.75904e9i	−0.153130	+	0.265230i
$979$	−6.19540e9			−0.211023
$980$		0			0
$981$	−3.27235e10			−1.10667
$982$	7.82953e9	−	1.35611e10i	0.263843	−	0.456989i
$983$	2.36038e10	+	4.08830e10i	0.792584	+	1.37280i	0.924362	+	0.381516i	$0.124598\pi$
$983$	2.36038e10	+	4.08830e10i	0.792584	+	1.37280i	−0.131778	+	0.991279i	$0.542069\pi$
$984$	3.33126e9	+	5.76991e9i	0.111462	+	0.193057i
$985$	9.71314e9	−	1.68236e10i	0.323842	−	0.560910i
$986$	1.14539e10			0.380525
$987$		0			0
$988$	4.93737e9			0.162872
$989$	1.39684e10	−	2.41940e10i	0.459156	−	0.795282i
$990$	3.91995e9	+	6.78955e9i	0.128398	+	0.222391i
$991$	3.20329e9	+	5.54826e9i	0.104553	+	0.181092i	0.913556	−	0.406714i	$-0.133325\pi$
$991$	3.20329e9	+	5.54826e9i	0.104553	+	0.181092i	−0.809002	+	0.587806i	$0.799992\pi$
$992$	−3.34390e9	+	5.79180e9i	−0.108758	+	0.188375i
$993$	6.85132e9			0.222051
$994$		0			0
$995$	1.19088e10			0.383254
$996$	−2.24158e9	+	3.88253e9i	−0.0718863	+	0.124511i
$997$	−6.01597e9	−	1.04200e10i	−0.192253	−	0.332991i	0.753744	−	0.657168i	$-0.228246\pi$
$997$	−6.01597e9	−	1.04200e10i	−0.192253	−	0.332991i	−0.945996	+	0.324177i	$0.894913\pi$
$998$	−1.18061e9	−	2.04488e9i	−0.0375968	−	0.0651196i
$999$	−2.02137e10	+	3.50112e10i	−0.641457	+	1.11104i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.8.c.h.79.2		4
7.2	even	3		98.8.a.k.1.1		2
7.3	odd	6		14.8.c.a.11.1	yes	4
7.4	even	3	inner	98.8.c.h.67.2		4
7.5	odd	6		98.8.a.h.1.2		2
7.6	odd	2		14.8.c.a.9.1	✓	4
21.17	even	6		126.8.g.e.109.1		4
21.20	even	2		126.8.g.e.37.1		4
28.3	even	6		112.8.i.a.81.2		4
28.27	even	2		112.8.i.a.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.c.a.9.1	✓	4	7.6	odd	2
14.8.c.a.11.1	yes	4	7.3	odd	6
98.8.a.h.1.2		2	7.5	odd	6
98.8.a.k.1.1		2	7.2	even	3
98.8.c.h.67.2		4	7.4	even	3	inner
98.8.c.h.79.2		4	1.1	even	1	trivial
112.8.i.a.65.2		4	28.27	even	2
112.8.i.a.81.2		4	28.3	even	6
126.8.g.e.37.1		4	21.20	even	2
126.8.g.e.109.1		4	21.17	even	6

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 98 = 2 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	98.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-4.00000 + 6.92820i) q^{2} +(10.4387 + 18.0804i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(-108.377 + 187.715i) q^{5} -167.019 q^{6} +512.000 q^{8} +(875.567 - 1516.53i) q^{9} +(-867.019 - 1501.72i) q^{10} +(-1290.93 - 2235.95i) q^{11} +(668.077 - 1157.14i) q^{12} +8921.97 q^{13} -4525.28 q^{15} +(-2048.00 + 3547.24i) q^{16} +(-5556.44 - 9624.03i) q^{17} +(7004.54 + 12132.2i) q^{18} +(-4323.40 + 7488.34i) q^{19} +13872.3 q^{20} +20654.9 q^{22} +(33028.6 - 57207.2i) q^{23} +(5344.61 + 9257.14i) q^{24} +(15571.2 + 26970.1i) q^{25} +(-35687.9 + 61813.2i) q^{26} +82218.0 q^{27} +128836. q^{29} +(18101.1 - 31352.0i) q^{30} +(-102048. - 176752. i) q^{31} +(-16384.0 - 28377.9i) q^{32} +(26951.2 - 46680.9i) q^{33} +88903.0 q^{34} -112073. q^{36} +(-245856. + 425834. i) q^{37} +(-34587.2 - 59906.7i) q^{38} +(93133.8 + 161312. i) q^{39} +(-55489.2 + 96110.2i) q^{40} +623293. q^{41} +422919. q^{43} +(-82619.5 + 143101. i) q^{44} +(189783. + 328714. i) q^{45} +(264229. + 457657. i) q^{46} +(-602714. + 1.04393e6i) q^{47} -85513.8 q^{48} -249139. q^{50} +(116004. - 200925. i) q^{51} +(-285503. - 494506. i) q^{52} +(636483. + 1.10242e6i) q^{53} +(-328872. + 569623. i) q^{54} +559630. q^{55} -180523. q^{57} +(-515342. + 892599. i) q^{58} +(840430. + 1.45567e6i) q^{59} +(144809. + 250816. i) q^{60} +(1.06128e6 - 1.83818e6i) q^{61} +1.63276e6 q^{62} +262144. q^{64} +(-966940. + 1.67479e6i) q^{65} +(215610. + 373447. i) q^{66} +(1.67466e6 + 2.90060e6i) q^{67} +(-355612. + 615938. i) q^{68} +1.37910e6 q^{69} +2.49257e6 q^{71} +(448290. - 776462. i) q^{72} +(-1.63676e6 - 2.83496e6i) q^{73} +(-1.96684e6 - 3.40667e6i) q^{74} +(-325086. + 563065. i) q^{75} +553395. q^{76} -1.49014e6 q^{78} +(2.09920e6 - 3.63591e6i) q^{79} +(-443914. - 768881. i) q^{80} +(-1.05662e6 - 1.83011e6i) q^{81} +(-2.49317e6 + 4.31830e6i) q^{82} -3.35527e6 q^{83} +2.40877e6 q^{85} +(-1.69168e6 + 2.93007e6i) q^{86} +(1.34488e6 + 2.32939e6i) q^{87} +(-660956. - 1.14481e6i) q^{88} +(1.19979e6 - 2.07810e6i) q^{89} -3.03653e6 q^{90} -4.22766e6 q^{92} +(2.13049e6 - 3.69011e6i) q^{93} +(-4.82171e6 - 8.35145e6i) q^{94} +(-937117. - 1.62313e6i) q^{95} +(342055. - 592457. i) q^{96} -4.51506e6 q^{97} -4.52118e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 16 q^{2} - 56 q^{3} - 128 q^{4} - 238 q^{5} + 896 q^{6} + 2048 q^{8} - 1972 q^{9} - 1904 q^{10} - 5848 q^{11} - 3584 q^{12} - 2632 q^{13} - 5784 q^{15} - 8192 q^{16} - 47642 q^{17} - 15776 q^{18}+ \cdots + 15278208 q^{99}+O(q^{100}) \) 4 * q - 16 * q^2 - 56 * q^3 - 128 * q^4 - 238 * q^5 + 896 * q^6 + 2048 * q^8 - 1972 * q^9 - 1904 * q^10 - 5848 * q^11 - 3584 * q^12 - 2632 * q^13 - 5784 * q^15 - 8192 * q^16 - 47642 * q^17 - 15776 * q^18 - 41048 * q^19 + 30464 * q^20 + 93568 * q^22 + 49316 * q^23 - 28672 * q^24 + 108816 * q^25 + 10528 * q^26 + 400624 * q^27 + 345640 * q^29 + 23136 * q^30 - 70252 * q^31 - 65536 * q^32 - 197190 * q^33 + 762272 * q^34 + 252416 * q^36 + 88166 * q^37 - 328384 * q^38 + 973336 * q^39 - 121856 * q^40 + 2312520 * q^41 + 115088 * q^43 - 374272 * q^44 + 300468 * q^45 + 394528 * q^46 - 1412292 * q^47 + 458752 * q^48 - 1741056 * q^50 - 2576256 * q^51 + 84224 * q^52 + 2361174 * q^53 - 1602496 * q^54 + 1258040 * q^55 + 4620796 * q^57 - 1382560 * q^58 + 1842512 * q^59 + 185088 * q^60 + 1278242 * q^61 + 1124032 * q^62 + 1048576 * q^64 - 1716372 * q^65 - 1577520 * q^66 + 2121480 * q^67 - 3049088 * q^68 + 5332236 * q^69 + 7200320 * q^71 - 1009664 * q^72 - 1634682 * q^73 + 705328 * q^74 + 5321176 * q^75 + 5254144 * q^76 - 15573376 * q^78 + 9192604 * q^79 - 974848 * q^80 - 3049498 * q^81 - 9250080 * q^82 + 56560 * q^83 + 6369676 * q^85 - 460352 * q^86 - 691656 * q^87 - 2994176 * q^88 + 8936550 * q^89 - 4807488 * q^90 - 6312448 * q^92 + 14550490 * q^93 - 11298336 * q^94 - 2562604 * q^95 - 1835008 * q^96 - 11748408 * q^97 + 15278208 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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