LMFDB - Embedded newform 98.10.c.j.79.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [98,10,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, 10); 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, 10, names="a")

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:traces = [4,32,14] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$50.4735119441$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{2305})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 577x^{2} + 576x + 331776 $ x^4 - x^3 + 577x^2 + 576x + 331776
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
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			79.1
Root			$-11.7526 - 20.3561i$ of defining polynomial
Character	$\chi$	$=$	98.79
Dual form			98.10.c.j.67.1

$q$-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} +(-116.526 - 201.829i) q^{3} +(-128.000 - 221.703i) q^{4} +(178.391 - 308.982i) q^{5} -3728.83 q^{6} -4096.00 q^{8} +(-17315.1 + 29990.7i) q^{9} +(-2854.25 - 4943.71i) q^{10} +(-36440.5 - 63116.7i) q^{11} +(-29830.7 + 51668.2i) q^{12} +39338.7 q^{13} -83148.6 q^{15} +(-32768.0 + 56755.8i) q^{16} +(255770. + 443007. i) q^{17} +(277042. + 479851. i) q^{18} +(-450184. + 779741. i) q^{19} -91336.0 q^{20} -1.16609e6 q^{22} +(-191347. + 331423. i) q^{23} +(477291. + 826692. i) q^{24} +(912916. + 1.58122e6i) q^{25} +(314709. - 545092. i) q^{26} +3.48349e6 q^{27} -4.73360e6 q^{29} +(-665189. + 1.15214e6i) q^{30} +(396942. + 687523. i) q^{31} +(524288. + 908093. i) q^{32} +(-8.49253e6 + 1.47095e7i) q^{33} +8.18465e6 q^{34} +8.86535e6 q^{36} +(8.61388e6 - 1.49197e7i) q^{37} +(7.20294e6 + 1.24759e7i) q^{38} +(-4.58398e6 - 7.93968e6i) q^{39} +(-730688. + 1.26559e6i) q^{40} -1.53558e7 q^{41} +1.87022e7 q^{43} +(-9.32876e6 + 1.61579e7i) q^{44} +(6.17772e6 + 1.07001e7i) q^{45} +(3.06155e6 + 5.30277e6i) q^{46} +(2.34470e7 - 4.06114e7i) q^{47} +1.52733e7 q^{48} +2.92133e7 q^{50} +(5.96078e7 - 1.03244e8i) q^{51} +(-5.03535e6 - 8.72148e6i) q^{52} +(-1.03410e7 - 1.79111e7i) q^{53} +(2.78679e7 - 4.82687e7i) q^{54} -2.60026e7 q^{55} +2.09832e8 q^{57} +(-3.78688e7 + 6.55907e7i) q^{58} +(6.53112e6 + 1.13122e7i) q^{59} +(1.06430e7 + 1.84343e7i) q^{60} +(-7.77439e7 + 1.34656e8i) q^{61} +1.27021e7 q^{62} +1.67772e7 q^{64} +(7.01765e6 - 1.21549e7i) q^{65} +(1.35880e8 + 2.35352e8i) q^{66} +(-1.22946e8 - 2.12949e8i) q^{67} +(6.54772e7 - 1.13410e8i) q^{68} +8.91877e7 q^{69} -3.87608e8 q^{71} +(7.09228e7 - 1.22842e8i) q^{72} +(1.56238e8 + 2.70612e8i) q^{73} +(-1.37822e8 - 2.38715e8i) q^{74} +(2.12757e8 - 3.68506e8i) q^{75} +2.30494e8 q^{76} -1.46687e8 q^{78} +(-1.20554e8 + 2.08805e8i) q^{79} +(1.16910e7 + 2.02494e7i) q^{80} +(-6.51038e7 - 1.12763e8i) q^{81} +(-1.22847e8 + 2.12776e8i) q^{82} +2.00131e8 q^{83} +1.82508e8 q^{85} +(1.49618e8 - 2.59146e8i) q^{86} +(5.51588e8 + 9.55378e8i) q^{87} +(1.49260e8 + 2.58526e8i) q^{88} +(-3.50381e7 + 6.06878e7i) q^{89} +1.97687e8 q^{90} +9.79698e7 q^{92} +(9.25081e7 - 1.60229e8i) q^{93} +(-3.75152e8 - 6.49782e8i) q^{94} +(1.60617e8 + 2.78197e8i) q^{95} +(1.22186e8 - 2.11633e8i) q^{96} +6.69566e8 q^{97} +2.52389e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 32 q^{2} + 14 q^{3} - 512 q^{4} + 2730 q^{5} + 448 q^{6} - 16384 q^{8} - 75982 q^{9} - 43680 q^{10} - 44940 q^{11} + 3584 q^{12} + 200564 q^{13} + 1006320 q^{15} - 131072 q^{16} + 870408 q^{17} + 1215712 q^{18}+ \cdots + 2736961080 q^{99}+O(q^{100}) $ 4 * q + 32 * q^2 + 14 * q^3 - 512 * q^4 + 2730 * q^5 + 448 * q^6 - 16384 * q^8 - 75982 * q^9 - 43680 * q^10 - 44940 * q^11 + 3584 * q^12 + 200564 * q^13 + 1006320 * q^15 - 131072 * q^16 + 870408 * q^17 + 1215712 * q^18 - 508774 * q^19 - 1397760 * q^20 - 1438080 * q^22 - 79800 * q^23 - 57344 * q^24 - 1853210 * q^25 + 1604512 * q^26 - 3739624 * q^27 + 4012656 * q^29 + 8050560 * q^30 - 2188732 * q^31 + 2097152 * q^32 - 23887920 * q^33 + 27853056 * q^34 + 38902784 * q^36 + 20723576 * q^37 + 8140384 * q^38 + 5888224 * q^39 - 11182080 * q^40 + 38033184 * q^41 + 8387432 * q^43 - 11504640 * q^44 + 110492130 * q^45 + 1276800 * q^46 + 74542524 * q^47 - 1835008 * q^48 - 59302720 * q^50 + 30556644 * q^51 - 25672192 * q^52 + 3239748 * q^53 - 29916992 * q^54 + 80614800 * q^55 + 613152664 * q^57 + 32101248 * q^58 + 133642362 * q^59 - 128808960 * q^60 - 227801686 * q^61 - 70039424 * q^62 + 67108864 * q^64 + 158667180 * q^65 + 382206720 * q^66 - 332930272 * q^67 + 222824448 * q^68 + 328036800 * q^69 - 335971440 * q^71 + 311222272 * q^72 + 44684276 * q^73 - 331577216 * q^74 + 1334428970 * q^75 + 260492288 * q^76 + 188423168 * q^78 - 269642776 * q^79 + 178913280 * q^80 - 638826478 * q^81 + 304265472 * q^82 - 366211524 * q^83 + 2068358040 * q^85 + 67099456 * q^86 + 2768288796 * q^87 + 184074240 * q^88 - 791657748 * q^89 + 3535748160 * q^90 + 40857600 * q^92 + 921877624 * q^93 - 1192680384 * q^94 - 608102040 * q^95 - 14680064 * q^96 - 8338960 * q^97 + 2736961080 * 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 $

$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$2$	8.00000	−	13.8564i	0.353553	−	0.612372i
$3$	−116.526	−	201.829i	−0.830572	−	1.43859i	−0.897585	−	0.440841i	$-0.854680\pi$
$3$	−116.526	−	201.829i	−0.830572	−	1.43859i	0.0670131	−	0.997752i	$-0.478653\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	178.391	−	308.982i	0.127646	−	0.221089i	−0.795118	−	0.606455i	$-0.792591\pi$
$5$	178.391	−	308.982i	0.127646	−	0.221089i	0.922764	+	0.385365i	$0.125925\pi$
$6$	−3728.83			−1.17461
$7$		0			0
$7$		0			0
$8$	−4096.00			−0.353553
$9$	−17315.1	+	29990.7i	−0.879700	+	1.52369i
$10$	−2854.25	−	4943.71i	−0.0902593	−	0.156334i
$11$	−36440.5	−	63116.7i	−0.750442	−	1.29980i	−0.947609	−	0.319433i	$-0.896508\pi$
$11$	−36440.5	−	63116.7i	−0.750442	−	1.29980i	0.197167	−	0.980370i	$-0.436826\pi$
$12$	−29830.7	+	51668.2i	−0.415286	+	0.719297i
$13$	39338.7			0.382010			0.191005	−	0.981589i	$-0.438825\pi$
$13$	39338.7			0.382010			0.191005	+	0.981589i	$0.438825\pi$
$14$		0			0
$15$	−83148.6			−0.424077
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	255770.	+	443007.i	0.742728	+	1.28644i	0.951249	+	0.308425i	$0.0998019\pi$
$17$	255770.	+	443007.i	0.742728	+	1.28644i	−0.208520	+	0.978018i	$0.566865\pi$
$18$	277042.	+	479851.i	0.622042	+	1.07741i
$19$	−450184.	+	779741.i	−0.792498	+	1.37265i	0.131917	+	0.991261i	$0.457887\pi$
$19$	−450184.	+	779741.i	−0.792498	+	1.37265i	−0.924416	+	0.381387i	$0.875447\pi$
$20$	−91336.0			−0.127646
$21$		0			0
$22$	−1.16609e6			−1.06128
$23$	−191347.	+	331423.i	−0.142576	+	0.246949i	−0.928466	−	0.371417i	$-0.878872\pi$
$23$	−191347.	+	331423.i	−0.142576	+	0.246949i	0.785890	+	0.618366i	$0.212205\pi$
$24$	477291.	+	826692.i	0.293652	+	0.508619i
$25$	912916.	+	1.58122e6i	0.467413	+	0.809583i
$26$	314709.	−	545092.i	0.135061	−	0.233932i
$27$	3.48349e6			1.26147
$28$		0			0
$29$	−4.73360e6			−1.24280			−0.621399	−	0.783494i	$-0.713435\pi$
$29$	−4.73360e6			−1.24280			−0.621399	+	0.783494i	$0.713435\pi$
$30$	−665189.	+	1.15214e6i	−0.149934	+	0.259693i
$31$	396942.	+	687523.i	0.0771968	+	0.133709i	0.902039	−	0.431654i	$-0.142070\pi$
$31$	396942.	+	687523.i	0.0771968	+	0.133709i	−0.824843	+	0.565362i	$0.808736\pi$
$32$	524288.	+	908093.i	0.0883883	+	0.153093i
$33$	−8.49253e6	+	1.47095e7i	−1.24659	+	2.15916i
$34$	8.18465e6			1.05038
$35$		0			0
$36$	8.86535e6			0.879700
$37$	8.61388e6	−	1.49197e7i	0.755598	−	1.30873i	−0.189478	−	0.981885i	$-0.560680\pi$
$37$	8.61388e6	−	1.49197e7i	0.755598	−	1.30873i	0.945076	−	0.326850i	$-0.105987\pi$
$38$	7.20294e6	+	1.24759e7i	0.560381	+	0.970608i
$39$	−4.58398e6	−	7.93968e6i	−0.317287	−	0.549557i
$40$	−730688.	+	1.26559e6i	−0.0451297	+	0.0781669i
$41$	−1.53558e7			−0.848683			−0.424342	−	0.905502i	$-0.639494\pi$
$41$	−1.53558e7			−0.848683			−0.424342	+	0.905502i	$0.639494\pi$
$42$		0			0
$43$	1.87022e7			0.834229			0.417114	−	0.908854i	$-0.363041\pi$
$43$	1.87022e7			0.834229			0.417114	+	0.908854i	$0.363041\pi$
$44$	−9.32876e6	+	1.61579e7i	−0.375221	+	0.649901i
$45$	6.17772e6	+	1.07001e7i	0.224580	+	0.388984i
$46$	3.06155e6	+	5.30277e6i	0.100817	+	0.174619i
$47$	2.34470e7	−	4.06114e7i	0.700885	−	1.21397i	−0.267271	−	0.963621i	$-0.586122\pi$
$47$	2.34470e7	−	4.06114e7i	0.700885	−	1.21397i	0.968156	−	0.250347i	$-0.0805448\pi$
$48$	1.52733e7			0.415286
$49$		0			0
$50$	2.92133e7			0.661022
$51$	5.96078e7	−	1.03244e8i	1.23378	−	2.13697i
$52$	−5.03535e6	−	8.72148e6i	−0.0955024	−	0.165415i
$53$	−1.03410e7	−	1.79111e7i	−0.180019	−	0.311803i	0.761867	−	0.647733i	$-0.224283\pi$
$53$	−1.03410e7	−	1.79111e7i	−0.180019	−	0.311803i	−0.941887	+	0.335930i	$0.890949\pi$
$54$	2.78679e7	−	4.82687e7i	0.445998	−	0.772491i
$55$	−2.60026e7			−0.383163
$56$		0			0
$57$	2.09832e8			2.63291
$58$	−3.78688e7	+	6.55907e7i	−0.439396	+	0.761055i
$59$	6.53112e6	+	1.13122e7i	0.0701703	+	0.121539i	0.898976	−	0.437998i	$-0.144312\pi$
$59$	6.53112e6	+	1.13122e7i	0.0701703	+	0.121539i	−0.828806	+	0.559537i	$0.810979\pi$
$60$	1.06430e7	+	1.84343e7i	0.106019	+	0.183631i
$61$	−7.77439e7	+	1.34656e8i	−0.718922	+	1.24521i	0.242505	+	0.970150i	$0.422031\pi$
$61$	−7.77439e7	+	1.34656e8i	−0.718922	+	1.24521i	−0.961427	+	0.275059i	$0.911302\pi$
$62$	1.27021e7			0.109173
$63$		0			0
$64$	1.67772e7			0.125000
$65$	7.01765e6	−	1.21549e7i	0.0487620	−	0.0844583i
$66$	1.35880e8	+	2.35352e8i	0.881473	+	1.52676i
$67$	−1.22946e8	−	2.12949e8i	−0.745382	−	1.29104i	−0.950016	−	0.312201i	$-0.898934\pi$
$67$	−1.22946e8	−	2.12949e8i	−0.745382	−	1.29104i	0.204634	−	0.978839i	$-0.434400\pi$
$68$	6.54772e7	−	1.13410e8i	0.371364	−	0.643222i
$69$	8.91877e7			0.473679
$70$		0			0
$71$	−3.87608e8			−1.81021			−0.905107	−	0.425184i	$-0.860210\pi$
$71$	−3.87608e8			−1.81021			−0.905107	+	0.425184i	$0.860210\pi$
$72$	7.09228e7	−	1.22842e8i	0.311021	−	0.538704i
$73$	1.56238e8	+	2.70612e8i	0.643922	+	1.11531i	0.984549	+	0.175108i	$0.0560274\pi$
$73$	1.56238e8	+	2.70612e8i	0.643922	+	1.11531i	−0.340627	+	0.940199i	$0.610639\pi$
$74$	−1.37822e8	−	2.38715e8i	−0.534289	−	0.925415i
$75$	2.12757e8	−	3.68506e8i	0.776440	−	1.34483i
$76$	2.30494e8			0.792498
$77$		0			0
$78$	−1.46687e8			−0.448711
$79$	−1.20554e8	+	2.08805e8i	−0.348225	+	0.603143i	−0.985934	−	0.167134i	$-0.946549\pi$
$79$	−1.20554e8	+	2.08805e8i	−0.348225	+	0.603143i	0.637710	+	0.770277i	$0.279882\pi$
$80$	1.16910e7	+	2.02494e7i	0.0319115	+	0.0552723i
$81$	−6.51038e7	−	1.12763e8i	−0.168044	−	0.291061i
$82$	−1.22847e8	+	2.12776e8i	−0.300055	+	0.519710i
$83$	2.00131e8			0.462875			0.231437	−	0.972850i	$-0.425657\pi$
$83$	2.00131e8			0.462875			0.231437	+	0.972850i	$0.425657\pi$
$84$		0			0
$85$	1.82508e8			0.379225
$86$	1.49618e8	−	2.59146e8i	0.294944	−	0.510859i
$87$	5.51588e8	+	9.55378e8i	1.03223	+	1.78788i
$88$	1.49260e8	+	2.58526e8i	0.265321	+	0.459550i
$89$	−3.50381e7	+	6.06878e7i	−0.0591951	+	0.102529i	−0.894104	−	0.447859i	$-0.852187\pi$
$89$	−3.50381e7	+	6.06878e7i	−0.0591951	+	0.102529i	0.834909	+	0.550388i	$0.185520\pi$
$90$	1.97687e8			0.317604
$91$		0			0
$92$	9.79698e7			0.142576
$93$	9.25081e7	−	1.60229e8i	0.128235	−	0.222110i
$94$	−3.75152e8	−	6.49782e8i	−0.495601	−	0.858405i
$95$	1.60617e8	+	2.78197e8i	0.202318	+	0.350426i
$96$	1.22186e8	−	2.11633e8i	0.146826	−	0.254310i
$97$	6.69566e8			0.767928			0.383964	−	0.923348i	$-0.374559\pi$
$97$	6.69566e8			0.767928			0.383964	+	0.923348i	$0.374559\pi$
$98$		0			0
$99$	2.52389e9			2.64065
$100$	2.33707e8	−	4.04792e8i	0.233707	−	0.404792i
$101$	4.26449e8	+	7.38631e8i	0.407775	+	0.706287i	0.994640	−	0.103398i	$-0.0329714\pi$
$101$	4.26449e8	+	7.38631e8i	0.407775	+	0.706287i	−0.586865	+	0.809685i	$0.699638\pi$
$102$	−9.53725e8	−	1.65190e9i	−0.872413	−	1.51106i
$103$	5.00991e8	−	8.67742e8i	0.438594	−	0.759667i	−0.558987	−	0.829176i	$-0.688810\pi$
$103$	5.00991e8	−	8.67742e8i	0.438594	−	0.759667i	0.997581	+	0.0695092i	$0.0221433\pi$
$104$	−1.61131e8			−0.135061
$105$		0			0
$106$	−3.30911e8			−0.254586
$107$	−2.09153e8	+	3.62263e8i	−0.154254	+	0.267176i	−0.932787	−	0.360428i	$-0.882631\pi$
$107$	−2.09153e8	+	3.62263e8i	−0.154254	+	0.267176i	0.778533	+	0.627603i	$0.215964\pi$
$108$	−4.45887e8	−	7.72299e8i	−0.315368	−	0.546234i
$109$	−2.34533e8	−	4.06223e8i	−0.159142	−	0.275642i	0.775418	−	0.631449i	$-0.217539\pi$
$109$	−2.34533e8	−	4.06223e8i	−0.159142	−	0.275642i	−0.934559	+	0.355807i	$0.884206\pi$
$110$	−2.08020e8	+	3.60302e8i	−0.135469	+	0.234639i
$111$	−4.01496e9			−2.51032
$112$		0			0
$113$	5.03772e8			0.290657			0.145329	−	0.989383i	$-0.453576\pi$
$113$	5.03772e8			0.290657			0.145329	+	0.989383i	$0.453576\pi$
$114$	1.67866e9	−	2.90752e9i	0.930874	−	1.61232i
$115$	6.82691e7	+	1.18246e8i	0.0363985	+	0.0630441i
$116$	6.05901e8	+	1.04945e9i	0.310700	+	0.538147i
$117$	−6.81154e8	+	1.17979e9i	−0.336054	+	0.582063i
$118$	2.08996e8			0.0992358
$119$		0			0
$120$	3.40577e8			0.149934
$121$	−1.47684e9	+	2.55796e9i	−0.626325	+	1.08483i
$122$	1.24390e9	+	2.15450e9i	0.508355	+	0.880496i
$123$	1.78935e9	+	3.09925e9i	0.704893	+	1.22091i
$124$	1.01617e8	−	1.76006e8i	0.0385984	−	0.0668544i
$125$	1.34826e9			0.493945
$126$		0			0
$127$	1.45724e9			0.497065			0.248532	−	0.968624i	$-0.420052\pi$
$127$	1.45724e9			0.497065			0.248532	+	0.968624i	$0.420052\pi$
$128$	1.34218e8	−	2.32472e8i	0.0441942	−	0.0765466i
$129$	−2.17930e9	−	3.77465e9i	−0.692887	−	1.20012i
$130$	−1.12282e8	−	1.94479e8i	−0.0344799	−	0.0597210i
$131$	−2.22230e9	+	3.84914e9i	−0.659299	+	1.14194i	0.321498	+	0.946910i	$0.395814\pi$
$131$	−2.22230e9	+	3.84914e9i	−0.659299	+	1.14194i	−0.980797	+	0.195030i	$0.937520\pi$
$132$	4.34817e9			1.24659
$133$		0			0
$134$	−3.93428e9			−1.05413
$135$	6.21422e8	−	1.07634e9i	0.161022	−	0.278898i
$136$	−1.04764e9	−	1.81456e9i	−0.262594	−	0.454826i
$137$	1.56628e9	+	2.71288e9i	0.379864	+	0.657944i	0.991042	−	0.133549i	$-0.0426375\pi$
$137$	1.56628e9	+	2.71288e9i	0.379864	+	0.657944i	−0.611178	+	0.791493i	$0.709304\pi$
$138$	7.13502e8	−	1.23582e9i	0.167471	−	0.290068i
$139$	1.90826e9			0.433581			0.216790	−	0.976218i	$-0.430441\pi$
$139$	1.90826e9			0.433581			0.216790	+	0.976218i	$0.430441\pi$
$140$		0			0
$141$	−1.09287e10			−2.32854
$142$	−3.10086e9	+	5.37085e9i	−0.640007	+	1.10853i
$143$	−1.43352e9	−	2.48293e9i	−0.286676	−	0.496537i
$144$	−1.13476e9	−	1.96547e9i	−0.219925	−	0.380921i
$145$	−8.44430e8	+	1.46260e9i	−0.158638	+	0.274769i
$146$	4.99961e9			0.910644
$147$		0			0
$148$	−4.41031e9			−0.755598
$149$	−3.10948e9	+	5.38578e9i	−0.516832	+	0.895179i	0.482977	+	0.875633i	$0.339556\pi$
$149$	−3.10948e9	+	5.38578e9i	−0.516832	+	0.895179i	−0.999809	+	0.0195463i	$0.993778\pi$
$150$	−3.40411e9	−	5.89609e9i	−0.549026	−	0.950941i
$151$	1.21776e8	+	2.10922e8i	0.0190619	+	0.0330162i	0.875399	−	0.483401i	$-0.160599\pi$
$151$	1.21776e8	+	2.10922e8i	0.0190619	+	0.0330162i	−0.856337	+	0.516417i	$0.827265\pi$
$152$	1.84395e9	−	3.19382e9i	0.280191	−	0.485304i
$153$	−1.77148e10			−2.61351
$154$		0			0
$155$	2.83243e8			0.0394154
$156$	−1.17350e9	+	2.03256e9i	−0.158643	+	0.274778i
$157$	2.82078e9	+	4.88574e9i	0.370528	+	0.641774i	0.989647	−	0.143524i	$-0.0458433\pi$
$157$	2.82078e9	+	4.88574e9i	0.370528	+	0.641774i	−0.619119	+	0.785297i	$0.712510\pi$
$158$	1.92886e9	+	3.34089e9i	0.246232	+	0.426486i
$159$	−2.40998e9	+	4.17421e9i	−0.299038	+	0.517950i
$160$	3.74112e8			0.0451297
$161$		0			0
$162$	−2.08332e9			−0.237650
$163$	−4.75790e8	+	8.24093e8i	−0.0527924	+	0.0914391i	−0.891214	−	0.453583i	$-0.850145\pi$
$163$	−4.75790e8	+	8.24093e8i	−0.0527924	+	0.0914391i	0.838422	+	0.545022i	$0.183479\pi$
$164$	1.96554e9	+	3.40442e9i	0.212171	+	0.367491i
$165$	3.02997e9	+	5.24807e9i	0.318245	+	0.551216i
$166$	1.60105e9	−	2.77310e9i	0.163651	−	0.283452i
$167$	−1.63986e10			−1.63149			−0.815743	−	0.578414i	$-0.803672\pi$
$167$	−1.63986e10			−1.63149			−0.815743	+	0.578414i	$0.803672\pi$
$168$		0			0
$169$	−9.05697e9			−0.854069
$170$	1.46006e9	−	2.52891e9i	0.134076	−	0.232227i
$171$	−1.55900e10	−	2.70026e10i	−1.39432	−	2.41504i
$172$	−2.39388e9	−	4.14633e9i	−0.208557	−	0.361232i
$173$	−9.36444e8	+	1.62197e9i	−0.0794830	+	0.137669i	−0.903027	−	0.429584i	$-0.858660\pi$
$173$	−9.36444e8	+	1.62197e9i	−0.0794830	+	0.137669i	0.823544	+	0.567252i	$0.191994\pi$
$174$	1.76508e10			1.45980
$175$		0			0
$176$	4.77633e9			0.375221
$177$	1.52209e9	−	2.63634e9i	0.116563	−	0.201893i
$178$	5.60610e8	+	9.71005e8i	0.0418573	+	0.0724989i
$179$	−6.03931e9	−	1.04604e10i	−0.439692	−	0.761569i	0.557973	−	0.829859i	$-0.311579\pi$
$179$	−6.03931e9	−	1.04604e10i	−0.439692	−	0.761569i	−0.997666	+	0.0682895i	$0.978246\pi$
$180$	1.58150e9	−	2.73923e9i	0.112290	−	0.194492i
$181$	−6.74447e9			−0.467083			−0.233541	−	0.972347i	$-0.575031\pi$
$181$	−6.74447e9			−0.467083			−0.233541	+	0.972347i	$0.575031\pi$
$182$		0			0
$183$	3.62367e10			2.38847
$184$	7.83758e8	−	1.35751e9i	0.0504083	−	0.0873097i
$185$	−3.07327e9	−	5.32306e9i	−0.192898	−	0.334109i
$186$	−1.48013e9	−	2.56366e9i	−0.0906758	−	0.157055i
$187$	1.86408e10	−	3.22868e10i	1.11475	−	1.93080i
$188$	−1.20049e10			−0.700885
$189$		0			0
$190$	5.13975e9			0.286121
$191$	−1.30308e10	+	2.25700e10i	−0.708468	+	1.22710i	0.256957	+	0.966423i	$0.417280\pi$
$191$	−1.30308e10	+	2.25700e10i	−0.708468	+	1.22710i	−0.965425	+	0.260680i	$0.916053\pi$
$192$	−1.95498e9	−	3.38613e9i	−0.103822	−	0.179824i
$193$	1.19542e10	+	2.07052e10i	0.620170	+	1.07417i	0.989454	+	0.144849i	$0.0462698\pi$
$193$	1.19542e10	+	2.07052e10i	0.620170	+	1.07417i	−0.369284	+	0.929317i	$0.620397\pi$
$194$	5.35653e9	−	9.27778e9i	0.271504	−	0.470258i
$195$	−3.27095e9			−0.162001
$196$		0			0
$197$	4.91068e9			0.232297			0.116149	−	0.993232i	$-0.462945\pi$
$197$	4.91068e9			0.232297			0.116149	+	0.993232i	$0.462945\pi$
$198$	2.01911e10	−	3.49720e10i	0.933612	−	1.61706i
$199$	1.16907e10	+	2.02490e10i	0.528449	+	0.915301i	0.999450	+	0.0331679i	$0.0105596\pi$
$199$	1.16907e10	+	2.02490e10i	0.528449	+	0.915301i	−0.471001	+	0.882133i	$0.656107\pi$
$200$	−3.73930e9	−	6.47666e9i	−0.165255	−	0.286231i
$201$	−2.86529e10	+	4.96283e10i	−1.23819	+	2.14460i
$202$	1.36464e10			0.576681
$203$		0			0
$204$	−3.05192e10			−1.23378
$205$	−2.73933e9	+	4.74467e9i	−0.108331	+	0.187635i
$206$	−8.01586e9	−	1.38839e10i	−0.310133	−	0.537166i
$207$	−6.62640e9	−	1.14773e10i	−0.250848	−	0.434482i
$208$	−1.28905e9	+	2.23270e9i	−0.0477512	+	0.0827075i
$209$	6.56196e10			2.37890
$210$		0			0
$211$	2.20831e10			0.766989			0.383494	−	0.923543i	$-0.374721\pi$
$211$	2.20831e10			0.766989			0.383494	+	0.923543i	$0.374721\pi$
$212$	−2.64729e9	+	4.58523e9i	−0.0900097	+	0.155901i
$213$	4.51664e10	+	7.82305e10i	1.50351	+	2.60416i
$214$	3.34644e9	+	5.79621e9i	0.109074	+	0.188922i
$215$	3.33630e9	−	5.77864e9i	0.106486	−	0.184439i
$216$	−1.42684e10			−0.445998
$217$		0			0
$218$	−7.50505e9			−0.225061
$219$	3.64116e10	−	6.30667e10i	1.06965	−	1.85268i
$220$	3.32833e9	+	5.76483e9i	0.0957908	+	0.165915i
$221$	1.00617e10	+	1.74273e10i	0.283729	+	0.491434i
$222$	−3.21197e10	+	5.56330e10i	−0.887531	+	1.53725i
$223$	−3.22102e10			−0.872211			−0.436106	−	0.899895i	$-0.643643\pi$
$223$	−3.22102e10			−0.872211			−0.436106	+	0.899895i	$0.643643\pi$
$224$		0			0
$225$	−6.32291e10			−1.64473
$226$	4.03018e9	−	6.98047e9i	0.102763	−	0.177991i
$227$	2.07667e10	+	3.59690e10i	0.519101	+	0.899109i	0.999754	+	0.0221980i	$0.00706644\pi$
$227$	2.07667e10	+	3.59690e10i	0.519101	+	0.899109i	−0.480653	+	0.876911i	$0.659600\pi$
$228$	−2.68586e10	−	4.65204e10i	−0.658227	−	1.14008i
$229$	6.65363e9	−	1.15244e10i	0.159882	−	0.276923i	−0.774944	−	0.632030i	$-0.782222\pi$
$229$	6.65363e9	−	1.15244e10i	0.159882	−	0.276923i	0.934826	+	0.355106i	$0.115555\pi$
$230$	2.18461e9			0.0514753
$231$		0			0
$232$	1.93888e10			0.439396
$233$	−4.01372e10	+	6.95197e10i	−0.892166	+	1.54528i	−0.0548936	+	0.998492i	$0.517482\pi$
$233$	−4.01372e10	+	6.95197e10i	−0.892166	+	1.54528i	−0.837273	+	0.546785i	$0.815851\pi$
$234$	1.08985e10	+	1.88767e10i	0.237626	+	0.411580i
$235$	−8.36545e9	−	1.44894e10i	−0.178930	−	0.309916i
$236$	1.67197e9	−	2.89593e9i	0.0350852	−	0.0607693i
$237$	5.61907e10			1.15690
$238$		0			0
$239$	6.27858e10			1.24472			0.622359	−	0.782732i	$-0.286174\pi$
$239$	6.27858e10			1.24472			0.622359	+	0.782732i	$0.286174\pi$
$240$	2.72461e9	−	4.71917e9i	0.0530096	−	0.0918153i
$241$	4.23466e9	+	7.33464e9i	0.0808615	+	0.140056i	0.903620	−	0.428335i	$-0.140900\pi$
$241$	4.23466e9	+	7.33464e9i	0.0808615	+	0.140056i	−0.822759	+	0.568391i	$0.807566\pi$
$242$	2.36295e10	+	4.09274e10i	0.442879	+	0.767088i
$243$	1.91102e10	−	3.30999e10i	0.351591	−	0.608973i
$244$	3.98049e10			0.718922
$245$		0			0
$246$	5.72593e10			0.996869
$247$	−1.77096e10	+	3.06740e10i	−0.302742	+	0.524365i
$248$	−1.62587e9	−	2.81610e9i	−0.0272932	−	0.0472732i
$249$	−2.33205e10	−	4.03923e10i	−0.384451	−	0.665889i
$250$	1.07861e10	−	1.86821e10i	0.174636	−	0.302479i
$251$	9.73168e6			0.000154759			7.73795e−5	−	1.00000i	$-0.499975\pi$
$251$	9.73168e6			0.000154759			7.73795e−5		1.00000i	$0.499975\pi$
$252$		0			0
$253$	2.78911e10			0.427980
$254$	1.16579e10	−	2.01921e10i	0.175739	−	0.304389i
$255$	−2.12669e10	−	3.68354e10i	−0.314974	−	0.545550i
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	8.63284e9	−	1.49525e10i	0.123440	−	0.213804i	−0.797682	−	0.603078i	$-0.793941\pi$
$257$	8.63284e9	−	1.49525e10i	0.123440	−	0.213804i	0.921122	+	0.389274i	$0.127274\pi$
$258$	−6.97375e10			−0.979890
$259$		0			0
$260$	−3.59304e9			−0.0487620
$261$	8.19629e10	−	1.41964e11i	1.09329	−	1.89363i
$262$	3.55569e10	+	6.15863e10i	0.466195	+	0.807473i
$263$	1.25707e10	+	2.17731e10i	0.162016	+	0.280621i	0.935592	−	0.353084i	$-0.114867\pi$
$263$	1.25707e10	+	2.17731e10i	0.162016	+	0.280621i	−0.773575	+	0.633704i	$0.781534\pi$
$264$	3.47854e10	−	6.02501e10i	0.440737	−	0.763378i
$265$	−7.37892e9			−0.0919150
$266$		0			0
$267$	1.63314e10			0.196663
$268$	−3.14743e10	+	5.45150e10i	−0.372691	+	0.645520i
$269$	−3.98552e10	−	6.90313e10i	−0.464087	−	0.803823i	0.535072	−	0.844806i	$-0.320284\pi$
$269$	−3.98552e10	−	6.90313e10i	−0.464087	−	0.803823i	−0.999160	+	0.0409831i	$0.986951\pi$
$270$	−9.94276e9	−	1.72214e10i	−0.113860	−	0.197211i
$271$	1.55347e10	−	2.69069e10i	0.174961	−	0.303042i	−0.765187	−	0.643808i	$-0.777353\pi$
$271$	1.55347e10	−	2.69069e10i	0.174961	−	0.303042i	0.940148	+	0.340767i	$0.110687\pi$
$272$	−3.35243e10			−0.371364
$273$		0			0
$274$	5.01211e10			0.537209
$275$	6.65342e10	−	1.15241e11i	0.701532	−	1.21509i
$276$	−1.14160e10	−	1.97731e10i	−0.118420	−	0.205109i
$277$	−8.35497e10	−	1.44712e11i	−0.852679	−	1.47688i	−0.878781	−	0.477225i	$-0.841643\pi$
$277$	−8.35497e10	−	1.44712e11i	−0.852679	−	1.47688i	0.0261018	−	0.999659i	$-0.491691\pi$
$278$	1.52660e10	−	2.64416e10i	0.153294	−	0.265513i
$279$	−2.74924e10			−0.271640
$280$		0			0
$281$	−7.05809e10			−0.675318			−0.337659	−	0.941268i	$-0.609635\pi$
$281$	−7.05809e10			−0.675318			−0.337659	+	0.941268i	$0.609635\pi$
$282$	−8.74299e10	+	1.51433e11i	−0.823264	+	1.42594i
$283$	1.28894e10	+	2.23251e10i	0.119452	+	0.206897i	0.919551	−	0.392971i	$-0.128553\pi$
$283$	1.28894e10	+	2.23251e10i	0.119452	+	0.206897i	−0.800099	+	0.599869i	$0.795220\pi$
$284$	4.96138e10	+	8.59336e10i	0.452554	+	0.783846i
$285$	3.74321e10	−	6.48344e10i	0.336080	−	0.582108i
$286$	−4.58726e10			−0.405421
$287$		0			0
$288$	−3.63125e10			−0.311021
$289$	−7.15429e10	+	1.23916e11i	−0.603290	+	1.04493i
$290$	1.35109e10	+	2.34015e10i	0.112174	+	0.194291i
$291$	−7.80219e10	−	1.35138e11i	−0.637820	−	1.10474i
$292$	3.99969e10	−	6.92767e10i	0.321961	−	0.557653i
$293$	−4.21819e10			−0.334365			−0.167183	−	0.985926i	$-0.553467\pi$
$293$	−4.21819e10			−0.334365			−0.167183	+	0.985926i	$0.553467\pi$
$294$		0			0
$295$	4.66036e9			0.0358278
$296$	−3.52824e10	+	6.11110e10i	−0.267144	+	0.462708i
$297$	−1.26940e11	−	2.19867e11i	−0.946662	−	1.63967i
$298$	4.97517e10	+	8.61724e10i	0.365455	+	0.632987i
$299$	−7.52734e9	+	1.30377e10i	−0.0544655	+	0.0943370i
$300$	−1.08932e11			−0.776440
$301$		0			0
$302$	3.89684e9			0.0269576
$303$	9.93848e10	−	1.72140e11i	0.677373	−	1.17325i
$304$	−2.95032e10	−	5.11011e10i	−0.198125	−	0.343162i
$305$	2.77376e10	+	4.80428e10i	0.183535	+	0.317892i
$306$	−1.41718e11	+	2.45463e11i	−0.924016	+	1.60044i
$307$	2.36528e11			1.51971			0.759855	−	0.650093i	$-0.225270\pi$
$307$	2.36528e11			1.51971			0.759855	+	0.650093i	$0.225270\pi$
$308$		0			0
$309$	−2.33514e11			−1.45714
$310$	2.26594e9	−	3.92473e9i	0.0139355	−	0.0241369i
$311$	−3.87665e10	−	6.71456e10i	−0.234982	−	0.407001i	0.724285	−	0.689500i	$-0.242170\pi$
$311$	−3.87665e10	−	6.71456e10i	−0.234982	−	0.407001i	−0.959268	+	0.282499i	$0.908837\pi$
$312$	1.87760e10	+	3.25209e10i	0.112178	+	0.194298i
$313$	−1.19220e11	+	2.06495e11i	−0.702101	+	1.21607i	0.265627	+	0.964076i	$0.414421\pi$
$313$	−1.19220e11	+	2.06495e11i	−0.702101	+	1.21607i	−0.967728	+	0.251998i	$0.918912\pi$
$314$	9.02651e10			0.524006
$315$		0			0
$316$	6.17236e10			0.348225
$317$	−8.22013e10	+	1.42377e11i	−0.457206	+	0.791904i	−0.998812	−	0.0487283i	$-0.984483\pi$
$317$	−8.22013e10	+	1.42377e11i	−0.457206	+	0.791904i	0.541606	+	0.840632i	$0.317817\pi$
$318$	3.85597e10	+	6.67874e10i	0.211452	+	0.366246i
$319$	1.72495e11	+	2.98769e11i	0.932647	+	1.61539i
$320$	2.99290e9	−	5.18385e9i	0.0159557	−	0.0276362i
$321$	9.74869e10			0.512476
$322$		0			0
$323$	−4.60574e11			−2.35444
$324$	−1.66666e10	+	2.88673e10i	−0.0840221	+	0.145531i
$325$	3.59129e10	+	6.22030e10i	0.178556	+	0.309269i
$326$	7.61265e9	+	1.31855e10i	0.0373299	+	0.0646572i
$327$	−5.46584e10	+	9.46711e10i	−0.264358	+	0.457881i
$328$	6.28974e10			0.300055
$329$		0			0
$330$	9.69592e10			0.450066
$331$	−2.83731e10	+	4.91436e10i	−0.129921	+	0.225030i	−0.923646	−	0.383247i	$-0.874806\pi$
$331$	−2.83731e10	+	4.91436e10i	−0.129921	+	0.225030i	0.793725	+	0.608277i	$0.208139\pi$
$332$	−2.56168e10	−	4.43696e10i	−0.115719	−	0.200431i
$333$	2.98301e11	+	5.16672e11i	1.32940	+	2.30259i
$334$	−1.31189e11	+	2.27226e11i	−0.576818	+	0.999077i
$335$	−8.77299e10			−0.380580
$336$		0			0
$337$	6.03813e10			0.255016			0.127508	−	0.991838i	$-0.459302\pi$
$337$	6.03813e10			0.255016			0.127508	+	0.991838i	$0.459302\pi$
$338$	−7.24558e10	+	1.25497e11i	−0.301959	+	0.523008i
$339$	−5.87026e10	−	1.01676e11i	−0.241412	−	0.418138i
$340$	−2.33610e10	−	4.04625e10i	−0.0948063	−	0.164209i
$341$	2.89295e10	−	5.01073e10i	0.115863	−	0.200681i
$342$	−4.98879e11			−1.97187
$343$		0			0
$344$	−7.66043e10			−0.294944
$345$	1.59103e10	−	2.75574e10i	0.0604632	−	0.104725i
$346$	1.49831e10	+	2.59515e10i	0.0562030	+	0.0973464i
$347$	−1.36982e11	−	2.37260e11i	−0.507201	−	0.878498i	−0.999965	−	0.00833542i	$-0.997347\pi$
$347$	−1.36982e11	−	2.37260e11i	−0.507201	−	0.878498i	0.492764	−	0.870163i	$-0.335987\pi$
$348$	1.41206e11	−	2.44577e11i	0.516117	−	0.893940i
$349$	−2.44394e11			−0.881814			−0.440907	−	0.897553i	$-0.645343\pi$
$349$	−2.44394e11			−0.881814			−0.440907	+	0.897553i	$0.645343\pi$
$350$		0			0
$351$	1.37036e11			0.481895
$352$	3.82106e10	−	6.61827e10i	0.132661	−	0.229775i
$353$	−9.50389e10	−	1.64612e11i	−0.325773	−	0.564255i	0.655896	−	0.754852i	$-0.272291\pi$
$353$	−9.50389e10	−	1.64612e11i	−0.325773	−	0.564255i	−0.981668	+	0.190596i	$0.938958\pi$
$354$	−2.43535e10	−	4.21814e10i	−0.0824225	−	0.142760i
$355$	−6.91456e10	+	1.19764e11i	−0.231067	+	0.400219i
$356$	1.79395e10			0.0591951
$357$		0			0
$358$	−1.93258e11			−0.621819
$359$	−2.37132e11	+	4.10724e11i	−0.753468	+	1.30504i	0.192665	+	0.981265i	$0.438287\pi$
$359$	−2.37132e11	+	4.10724e11i	−0.753468	+	1.30504i	−0.946133	+	0.323779i	$0.895046\pi$
$360$	−2.53039e10	−	4.38277e10i	−0.0794011	−	0.137527i
$361$	−2.43987e11	−	4.22597e11i	−0.756108	−	1.30962i
$362$	−5.39557e10	+	9.34541e10i	−0.165139	+	0.286029i
$363$	6.88362e11			2.08083
$364$		0			0
$365$	1.11486e11			0.328776
$366$	2.89894e11	−	5.02111e11i	0.844450	−	1.46263i
$367$	2.36860e11	+	4.10253e11i	0.681544	+	1.18047i	0.974509	+	0.224346i	$0.0720247\pi$
$367$	2.36860e11	+	4.10253e11i	0.681544	+	1.18047i	−0.292965	+	0.956123i	$0.594642\pi$
$368$	−1.25401e10	−	2.17201e10i	−0.0356440	−	0.0617373i
$369$	2.65888e11	−	4.60532e11i	0.746587	−	1.29313i
$370$	−9.83447e10			−0.272799
$371$		0			0
$372$	−4.73642e10			−0.128235
$373$	2.92040e11	−	5.05828e11i	0.781183	−	1.35305i	−0.150071	−	0.988675i	$-0.547950\pi$
$373$	2.92040e11	−	5.05828e11i	0.781183	−	1.35305i	0.931253	−	0.364373i	$-0.118717\pi$
$374$	−2.98252e11	−	5.16588e11i	−0.788246	−	1.36528i
$375$	−1.57108e11	−	2.72118e11i	−0.410257	−	0.710586i
$376$	−9.60389e10	+	1.66344e11i	−0.247800	+	0.429203i
$377$	−1.86213e11			−0.474761
$378$		0			0
$379$	5.61076e11			1.39684			0.698418	−	0.715691i	$-0.253888\pi$
$379$	5.61076e11			1.39684			0.698418	+	0.715691i	$0.253888\pi$
$380$	4.11180e10	−	7.12184e10i	0.101159	−	0.175213i
$381$	−1.69806e11	−	2.94112e11i	−0.412848	−	0.715074i
$382$	2.08492e11	+	3.61120e11i	0.500962	+	0.867692i
$383$	4.42251e10	−	7.66001e10i	0.105021	−	0.181901i	−0.808726	−	0.588185i	$-0.799843\pi$
$383$	4.42251e10	−	7.66001e10i	0.105021	−	0.181901i	0.913747	+	0.406285i	$0.133176\pi$
$384$	−6.25594e10			−0.146826
$385$		0			0
$386$	3.82533e11			0.877053
$387$	−3.23831e11	+	5.60893e11i	−0.733871	+	1.27110i
$388$	−8.57045e10	−	1.48444e11i	−0.191982	−	0.332523i
$389$	2.11736e11	+	3.66737e11i	0.468836	+	0.812048i	0.999365	−	0.0356187i	$-0.0113402\pi$
$389$	2.11736e11	+	3.66737e11i	0.468836	+	0.812048i	−0.530529	+	0.847667i	$0.678007\pi$
$390$	−2.61676e10	+	4.53237e10i	−0.0572761	+	0.0992052i
$391$	−1.95764e11			−0.423581
$392$		0			0
$393$	1.03582e12			2.19038
$394$	3.92854e10	−	6.80444e10i	0.0821294	−	0.142252i
$395$	4.30114e10	+	7.44979e10i	0.0888989	+	0.153977i
$396$	−3.23057e11	−	5.59552e11i	−0.660163	−	1.14344i
$397$	1.81536e11	−	3.14430e11i	0.366780	−	0.635281i	−0.622280	−	0.782795i	$-0.713794\pi$
$397$	1.81536e11	−	3.14430e11i	0.366780	−	0.635281i	0.989060	+	0.147513i	$0.0471269\pi$
$398$	3.74104e11			0.747340
$399$		0			0
$400$	−1.19658e11			−0.233707
$401$	2.51584e11	−	4.35757e11i	0.485885	−	0.841578i	−0.513983	−	0.857800i	$-0.671831\pi$
$401$	2.51584e11	−	4.35757e11i	0.485885	−	0.841578i	0.999868	+	0.0162223i	$0.00516395\pi$
$402$	4.58446e11	+	7.94052e11i	0.875530	+	1.51646i
$403$	1.56152e10	+	2.70462e10i	0.0294899	+	0.0510780i
$404$	1.09171e11	−	1.89090e11i	0.203888	−	0.353144i
$405$	−4.64556e10			−0.0858007
$406$		0			0
$407$	−1.25558e12			−2.26813
$408$	−2.44154e11	+	4.22886e11i	−0.436207	+	0.755532i
$409$	3.96077e10	+	6.86026e10i	0.0699882	+	0.121223i	0.898896	−	0.438162i	$-0.144370\pi$
$409$	3.96077e10	+	6.86026e10i	0.0699882	+	0.121223i	−0.828908	+	0.559385i	$0.811037\pi$
$410$	4.38293e10	+	7.59147e10i	0.0766016	+	0.132678i
$411$	3.65026e11	−	6.32243e11i	0.631009	−	1.09294i
$412$	−2.56508e11			−0.438594
$413$		0			0
$414$	−2.12045e11			−0.354753
$415$	3.57015e10	−	6.18369e10i	0.0590841	−	0.102337i
$416$	2.06248e10	+	3.57232e10i	0.0337652	+	0.0584831i
$417$	−2.22362e11	−	3.85141e11i	−0.360120	−	0.623746i
$418$	5.24957e11	−	9.09252e11i	0.841066	−	1.45677i
$419$	−3.38943e11			−0.537234			−0.268617	−	0.963247i	$-0.586567\pi$
$419$	−3.38943e11			−0.537234			−0.268617	+	0.963247i	$0.586567\pi$
$420$		0			0
$421$	−6.34126e11			−0.983799			−0.491899	−	0.870652i	$-0.663697\pi$
$421$	−6.34126e11			−0.983799			−0.491899	+	0.870652i	$0.663697\pi$
$422$	1.76665e11	−	3.05992e11i	0.271171	−	0.469683i
$423$	8.11976e11	+	1.40638e12i	1.23314	+	2.13586i
$424$	4.23566e10	+	7.33638e10i	0.0636465	+	0.110239i
$425$	−4.66994e11	+	8.08857e11i	−0.694322	+	1.20260i
$426$	1.44533e12			2.12629
$427$		0			0
$428$	1.07086e11			0.154254
$429$	−3.34085e11	+	5.78651e11i	−0.476210	+	0.824820i
$430$	−5.33808e10	−	9.24583e10i	−0.0752969	−	0.130418i
$431$	−2.06806e11	−	3.58198e11i	−0.288679	−	0.500007i	0.684816	−	0.728716i	$-0.259883\pi$
$431$	−2.06806e11	−	3.58198e11i	−0.288679	−	0.500007i	−0.973495	+	0.228710i	$0.926549\pi$
$432$	−1.14147e11	+	1.97709e11i	−0.157684	+	0.273117i
$433$	−8.78540e11			−1.20106			−0.600532	−	0.799601i	$-0.705044\pi$
$433$	−8.78540e11			−1.20106			−0.600532	+	0.799601i	$0.705044\pi$
$434$		0			0
$435$	3.93592e11			0.527042
$436$	−6.00404e10	+	1.03993e11i	−0.0795709	+	0.137821i
$437$	−1.72283e11	−	2.98402e11i	−0.225983	−	0.391414i
$438$	−5.82585e11	−	1.00907e12i	−0.756355	−	1.31005i
$439$	−7.13355e11	+	1.23557e12i	−0.916675	+	1.58773i	−0.112244	+	0.993681i	$0.535804\pi$
$439$	−7.13355e11	+	1.23557e12i	−0.916675	+	1.58773i	−0.804431	+	0.594047i	$0.797529\pi$
$440$	1.06506e11			0.135469
$441$		0			0
$442$	3.21973e11			0.401254
$443$	5.83021e11	−	1.00982e12i	0.719230	−	1.24574i	−0.242076	−	0.970257i	$-0.577828\pi$
$443$	5.83021e11	−	1.00982e12i	0.719230	−	1.24574i	0.961305	−	0.275485i	$-0.0888384\pi$
$444$	5.13915e11	+	8.90128e11i	0.627579	+	1.08700i
$445$	1.25010e10	+	2.16523e10i	0.0151120	+	0.0261748i
$446$	−2.57682e11	+	4.46318e11i	−0.308373	+	0.534118i
$447$	1.44934e12			1.71707
$448$		0			0
$449$	4.47993e11			0.520191			0.260095	−	0.965583i	$-0.416246\pi$
$449$	4.47993e11			0.520191			0.260095	+	0.965583i	$0.416246\pi$
$450$	−5.05832e11	+	8.76128e11i	−0.581501	+	1.00719i
$451$	5.59573e11	+	9.69209e11i	0.636887	+	1.10312i
$452$	−6.44828e10	−	1.11688e11i	−0.0726643	−	0.125858i
$453$	2.83802e10	−	4.91559e10i	0.0316645	−	0.0548446i
$454$	6.64535e11			0.734119
$455$		0			0
$456$	−8.59474e11			−0.930874
$457$	−2.69732e11	+	4.67190e11i	−0.289274	+	0.501038i	−0.973637	−	0.228104i	$-0.926747\pi$
$457$	−2.69732e11	+	4.67190e11i	−0.289274	+	0.501038i	0.684362	+	0.729142i	$0.260081\pi$
$458$	−1.06458e11	−	1.84391e11i	−0.113053	−	0.195814i
$459$	8.90974e11	+	1.54321e12i	0.936932	+	1.62281i
$460$	1.74769e10	−	3.02709e10i	0.0181993	−	0.0315221i
$461$	−4.24948e11			−0.438209			−0.219105	−	0.975701i	$-0.570314\pi$
$461$	−4.24948e11			−0.438209			−0.219105	+	0.975701i	$0.570314\pi$
$462$		0			0
$463$	8.61716e11			0.871465			0.435732	−	0.900076i	$-0.356489\pi$
$463$	8.61716e11			0.871465			0.435732	+	0.900076i	$0.356489\pi$
$464$	1.55111e11	−	2.68659e11i	0.155350	−	0.269074i
$465$	−3.30052e10	−	5.71666e10i	−0.0327374	−	0.0567028i
$466$	6.42196e11	+	1.11232e12i	0.630857	+	1.09268i
$467$	−3.32732e11	+	5.76308e11i	−0.323719	+	0.560698i	−0.981252	−	0.192728i	$-0.938267\pi$
$467$	−3.32732e11	+	5.76308e11i	−0.323719	+	0.560698i	0.657533	+	0.753425i	$0.271600\pi$
$468$	3.48751e11			0.336054
$469$		0			0
$470$	−2.67694e11			−0.253046
$471$	6.57389e11	−	1.13863e12i	0.615501	−	1.06608i
$472$	−2.67515e10	−	4.63349e10i	−0.0248090	−	0.0429704i
$473$	−6.81518e11	−	1.18042e12i	−0.626040	−	1.08433i
$474$	4.49525e11	−	7.78601e11i	0.409027	−	0.708455i
$475$	−1.64392e12			−1.48170
$476$		0			0
$477$	7.16221e11			0.633453
$478$	5.02286e11	−	8.69986e11i	0.440074	−	0.762231i
$479$	−4.28730e11	−	7.42582e11i	−0.372112	−	0.644517i	0.617778	−	0.786352i	$-0.288033\pi$
$479$	−4.28730e11	−	7.42582e11i	−0.372112	−	0.644517i	−0.989890	+	0.141835i	$0.954700\pi$
$480$	−4.35938e10	−	7.55067e10i	−0.0374834	−	0.0649232i
$481$	3.38858e11	−	5.86920e11i	0.288646	−	0.499949i
$482$	1.35509e11			0.114355
$483$		0			0
$484$	7.56143e11			0.626325
$485$	1.19444e11	−	2.06884e11i	0.0980229	−	0.169781i
$486$	−3.05764e11	−	5.29598e11i	−0.248612	−	0.430609i
$487$	−1.01875e12	−	1.76453e12i	−0.820708	−	1.42151i	−0.905155	−	0.425081i	$-0.860246\pi$
$487$	−1.01875e12	−	1.76453e12i	−0.820708	−	1.42151i	0.0844470	−	0.996428i	$-0.473088\pi$
$488$	3.18439e11	−	5.51552e11i	0.254177	−	0.440248i
$489$	2.21768e11			0.175392
$490$		0			0
$491$	7.85012e11			0.609550			0.304775	−	0.952424i	$-0.401419\pi$
$491$	7.85012e11			0.609550			0.304775	+	0.952424i	$0.401419\pi$
$492$	4.58074e11	−	7.93408e11i	0.352446	−	0.610455i
$493$	−1.21071e12	−	2.09702e12i	−0.923061	−	1.59879i
$494$	2.83354e11	+	4.90783e11i	0.214071	+	0.370782i
$495$	4.50238e11	−	7.79835e11i	0.337069	−	0.583820i
$496$	−5.20280e10			−0.0385984
$497$		0			0
$498$	−7.46256e11			−0.543696
$499$	1.30963e11	−	2.26835e11i	0.0945578	−	0.163779i	−0.814866	−	0.579649i	$-0.803190\pi$
$499$	1.30963e11	−	2.26835e11i	0.0945578	−	0.163779i	0.909424	+	0.415870i	$0.136523\pi$
$500$	−1.72577e11	−	2.98913e11i	−0.123486	−	0.213885i
$501$	1.91087e12	+	3.30972e12i	1.35507	+	2.34705i
$502$	7.78534e7	−	1.34846e8i	5.47156e−5	−	9.47702e-5i
$503$	8.93639e11			0.622452			0.311226	−	0.950336i	$-0.399260\pi$
$503$	8.93639e11			0.622452			0.311226	+	0.950336i	$0.399260\pi$
$504$		0			0
$505$	3.04298e11			0.208203
$506$	2.23129e11	−	3.86471e11i	0.151314	−	0.262083i
$507$	1.05537e12	+	1.82796e12i	0.709366	+	1.22866i
$508$	−1.86526e11	−	3.23073e11i	−0.124266	−	0.215235i
$509$	2.60651e11	−	4.51462e11i	0.172120	−	0.298120i	−0.767041	−	0.641598i	$-0.778272\pi$
$509$	2.60651e11	−	4.51462e11i	0.172120	−	0.298120i	0.939161	+	0.343478i	$0.111605\pi$
$510$	−6.80542e11			−0.445440
$511$		0			0
$512$	−6.87195e10			−0.0441942
$513$	−1.56821e12	+	2.71622e12i	−0.999715	+	1.73156i
$514$	−1.38125e11	−	2.39240e11i	−0.0872850	−	0.151182i
$515$	−1.78744e11	−	3.09594e11i	−0.111969	−	0.193937i
$516$	−5.57900e11	+	9.66311e11i	−0.346444	+	0.600058i
$517$	−3.41768e12			−2.10389
$518$		0			0
$519$	4.36480e11			0.264066
$520$	−2.87443e10	+	4.97866e10i	−0.0172400	+	0.0298605i
$521$	−1.20673e11	−	2.09012e11i	−0.0717530	−	0.124280i	0.827917	−	0.560851i	$-0.189526\pi$
$521$	−1.20673e11	−	2.09012e11i	−0.0717530	−	0.124280i	−0.899670	+	0.436571i	$0.856193\pi$
$522$	−1.31141e12	−	2.27142e12i	−0.773072	−	1.33900i
$523$	−1.13218e12	+	1.96099e12i	−0.661693	+	1.14609i	0.318478	+	0.947930i	$0.396828\pi$
$523$	−1.13218e12	+	1.96099e12i	−0.661693	+	1.14609i	−0.980171	+	0.198155i	$0.936505\pi$
$524$	1.13782e12			0.659299
$525$		0			0
$526$	4.02263e11			0.229126
$527$	−2.03052e11	+	3.51696e11i	−0.114672	+	0.198619i
$528$	−5.56566e11	−	9.64001e11i	−0.311648	−	0.539790i
$529$	8.27349e11	+	1.43301e12i	0.459344	+	0.795607i
$530$	−5.90314e10	+	1.02245e11i	−0.0324969	+	0.0562862i
$531$	−4.52349e11			−0.246915
$532$		0			0
$533$	−6.04077e11			−0.324205
$534$	1.30651e11	−	2.26295e11i	0.0695310	−	0.120431i
$535$	7.46217e10	+	1.29249e11i	0.0393798	+	0.0682078i
$536$	5.03588e11	+	8.72240e11i	0.263532	+	0.456451i
$537$	−1.40747e12	+	2.43782e12i	−0.730392	+	1.26508i
$538$	−1.27537e12			−0.656319
$539$		0			0
$540$	−3.18168e11			−0.161022
$541$	−1.87065e12	+	3.24005e12i	−0.938867	+	1.62616i	−0.171277	+	0.985223i	$0.554789\pi$
$541$	−1.87065e12	+	3.24005e12i	−0.938867	+	1.62616i	−0.767590	+	0.640942i	$0.778544\pi$
$542$	−2.48555e11	−	4.30511e11i	−0.123716	−	0.214283i
$543$	7.85906e11	+	1.36123e12i	0.387946	+	0.671942i
$544$	−2.68195e11	+	4.64527e11i	−0.131297	+	0.227413i
$545$	−1.67354e11			−0.0812553
$546$		0			0
$547$	−8.37063e11			−0.399775			−0.199887	−	0.979819i	$-0.564058\pi$
$547$	−8.37063e11			−0.399775			−0.199887	+	0.979819i	$0.564058\pi$
$548$	4.00969e11	−	6.94498e11i	0.189932	−	0.328972i
$549$	−2.69229e12	−	4.66318e12i	−1.26487	−	2.19082i
$550$	−1.06455e12	−	1.84385e12i	−0.496058	−	0.859198i
$551$	2.13099e12	−	3.69098e12i	0.984916	−	1.70592i
$552$	−3.65313e11			−0.167471
$553$		0			0
$554$	−2.67359e12			−1.20587
$555$	−7.16232e11	+	1.24055e12i	−0.320432	+	0.555004i
$556$	−2.44257e11	−	4.23065e11i	−0.108395	−	0.187746i
$557$	−8.22028e11	−	1.42379e12i	−0.361858	−	0.626756i	0.626409	−	0.779495i	$-0.284524\pi$
$557$	−8.22028e11	−	1.42379e12i	−0.361858	−	0.626756i	−0.988267	+	0.152738i	$0.951191\pi$
$558$	−2.19939e11	+	3.80946e11i	−0.0960393	+	0.166345i
$559$	7.35720e11			0.318683
$560$		0			0
$561$	−8.68854e12			−3.70352
$562$	−5.64647e11	+	9.77997e11i	−0.238761	+	0.413546i
$563$	6.32203e11	+	1.09501e12i	0.265197	+	0.459335i	0.967615	−	0.252429i	$-0.0812296\pi$
$563$	6.32203e11	+	1.09501e12i	0.265197	+	0.459335i	−0.702418	+	0.711765i	$0.747896\pi$
$564$	1.39888e12	+	2.42293e12i	0.582136	+	1.00829i
$565$	8.98682e10	−	1.55656e11i	0.0371012	−	0.0642612i
$566$	4.12461e11			0.168931
$567$		0			0
$568$	1.58764e12			0.640007
$569$	2.93350e11	−	5.08097e11i	0.117322	−	0.203208i	−0.801383	−	0.598151i	$-0.795902\pi$
$569$	2.93350e11	−	5.08097e11i	0.117322	−	0.203208i	0.918706	+	0.394943i	$0.129236\pi$
$570$	−5.98914e11	−	1.03735e12i	−0.237645	−	0.411612i
$571$	2.89491e11	+	5.01413e11i	0.113965	+	0.197394i	0.917366	−	0.398046i	$-0.130311\pi$
$571$	2.89491e11	+	5.01413e11i	0.113965	+	0.197394i	−0.803400	+	0.595439i	$0.796978\pi$
$572$	−3.66981e11	+	6.35630e11i	−0.143338	+	0.248269i
$573$	6.07370e12			2.35373
$574$		0			0
$575$	−6.98736e11			−0.266568
$576$	−2.90500e11	+	5.03160e11i	−0.109963	+	0.190461i
$577$	1.54947e12	+	2.68377e12i	0.581960	+	1.00798i	0.995247	+	0.0973829i	$0.0310471\pi$
$577$	1.54947e12	+	2.68377e12i	0.581960	+	1.00798i	−0.413287	+	0.910601i	$0.635620\pi$
$578$	1.14469e12	+	1.98266e12i	0.426591	+	0.738877i
$579$	2.78594e12	−	4.82539e12i	1.03019	−	1.78434i
$580$	4.32348e11			0.158638
$581$		0			0
$582$	−2.49670e12			−0.902013
$583$	−7.53659e11	+	1.30538e12i	−0.270188	+	0.467980i
$584$	−6.39950e11	−	1.10843e12i	−0.227661	−	0.394320i
$585$	2.43023e11	+	4.20928e11i	0.0857919	+	0.148596i
$586$	−3.37455e11	+	5.84489e11i	−0.118216	+	0.204756i
$587$	−1.61097e12			−0.560035			−0.280017	−	0.959995i	$-0.590340\pi$
$587$	−1.61097e12			−0.560035			−0.280017	+	0.959995i	$0.590340\pi$
$588$		0			0
$589$	−7.14787e11			−0.244713
$590$	3.72829e10	−	6.45759e10i	0.0126671	−	0.0219400i
$591$	−5.72222e11	−	9.91118e11i	−0.192939	−	0.334181i
$592$	5.64519e11	+	9.77776e11i	0.188900	+	0.327184i
$593$	−1.94134e12	+	3.36251e12i	−0.644698	+	1.11665i	0.339673	+	0.940543i	$0.389683\pi$
$593$	−1.94134e12	+	3.36251e12i	−0.644698	+	1.11665i	−0.984371	+	0.176106i	$0.943650\pi$
$594$	−4.06208e12			−1.33878
$595$		0			0
$596$	1.59205e12			0.516832
$597$	2.72455e12	−	4.71906e12i	0.877830	−	1.52045i
$598$	1.20437e11	+	2.08604e11i	0.0385129	+	0.0667063i
$599$	−1.18137e12	−	2.04619e12i	−0.374942	−	0.649419i	0.615376	−	0.788234i	$-0.289004\pi$
$599$	−1.18137e12	−	2.04619e12i	−0.374942	−	0.649419i	−0.990318	+	0.138814i	$0.955671\pi$
$600$	−8.71453e11	+	1.50940e12i	−0.274513	+	0.475471i
$601$	−1.88288e12			−0.588692			−0.294346	−	0.955699i	$-0.595102\pi$
$601$	−1.88288e12			−0.588692			−0.294346	+	0.955699i	$0.595102\pi$
$602$		0			0
$603$	8.51533e12			2.62285
$604$	3.11747e10	−	5.39961e10i	0.00953094	−	0.0165081i
$605$	5.26909e11	+	9.12634e11i	0.159896	+	0.276947i
$606$	−1.59016e12	−	2.75423e12i	−0.478975	−	0.829610i
$607$	−1.28351e12	+	2.22311e12i	−0.383753	+	0.664679i	−0.991595	−	0.129378i	$-0.958702\pi$
$607$	−1.28351e12	+	2.22311e12i	−0.383753	+	0.664679i	0.607843	+	0.794057i	$0.292035\pi$
$608$	−9.44103e11			−0.280191
$609$		0			0
$610$	8.87602e11			0.259558
$611$	9.22373e11	−	1.59760e12i	0.267745	−	0.463748i
$612$	2.26749e12	+	3.92741e12i	0.653378	+	1.13168i
$613$	3.07070e12	+	5.31861e12i	0.878345	+	1.52134i	0.853156	+	0.521655i	$0.174685\pi$
$613$	3.07070e12	+	5.31861e12i	0.878345	+	1.52134i	0.0251888	+	0.999683i	$0.491981\pi$
$614$	1.89223e12	−	3.27743e12i	0.537299	−	0.930629i
$615$	1.27682e12			0.359907
$616$		0			0
$617$	−4.36828e12			−1.21347			−0.606733	−	0.794906i	$-0.707520\pi$
$617$	−4.36828e12			−1.21347			−0.606733	+	0.794906i	$0.707520\pi$
$618$	−1.86811e12	+	3.23567e12i	−0.515175	+	0.892310i
$619$	−2.40713e12	−	4.16927e12i	−0.659009	−	1.14144i	−0.980872	−	0.194651i	$-0.937642\pi$
$619$	−2.40713e12	−	4.16927e12i	−0.659009	−	1.14144i	0.321863	−	0.946786i	$-0.395691\pi$
$620$	−3.62551e10	−	6.27956e10i	−0.00985386	−	0.0170674i
$621$	−6.66556e11	+	1.15451e12i	−0.179856	+	0.311520i
$622$	−1.24053e12			−0.332315
$623$		0			0
$624$	6.00831e11			0.158643
$625$	−1.54252e12	+	2.67173e12i	−0.404363	+	0.700377i
$626$	1.90752e12	+	3.30392e12i	0.496460	+	0.859894i
$627$	−7.64639e12	−	1.32439e13i	−1.97584	−	3.42226i
$628$	7.22121e11	−	1.25075e12i	0.185264	−	0.320887i
$629$	8.81270e12			2.24482
$630$		0			0
$631$	7.12132e12			1.78825			0.894125	−	0.447818i	$-0.147799\pi$
$631$	7.12132e12			1.78825			0.894125	+	0.447818i	$0.147799\pi$
$632$	4.93789e11	−	8.55267e11i	0.123116	−	0.213243i
$633$	−2.57326e12	−	4.45701e12i	−0.637039	−	1.10338i
$634$	1.31522e12	+	2.27803e12i	0.323294	+	0.559961i
$635$	2.59957e11	−	4.50259e11i	0.0634483	−	0.109896i
$636$	1.23391e12			0.299038
$637$		0			0
$638$	5.51983e12			1.31896
$639$	6.71148e12	−	1.16246e13i	1.59245	−	2.75820i
$640$	−4.78864e10	−	8.29416e10i	−0.0112824	−	0.0195417i
$641$	−9.29649e11	−	1.61020e12i	−0.217499	−	0.376720i	0.736543	−	0.676390i	$-0.236457\pi$
$641$	−9.29649e11	−	1.61020e12i	−0.217499	−	0.376720i	−0.954043	+	0.299670i	$0.903123\pi$
$642$	7.79895e11	−	1.35082e12i	0.181188	−	0.313826i
$643$	−6.16271e12			−1.42175			−0.710874	−	0.703320i	$-0.751700\pi$
$643$	−6.16271e12			−1.42175			−0.710874	+	0.703320i	$0.751700\pi$
$644$		0			0
$645$	−1.55506e12			−0.353777
$646$	−3.68459e12	+	6.38190e12i	−0.832422	+	1.44180i
$647$	1.81716e12	+	3.14742e12i	0.407685	+	0.706131i	0.994630	−	0.103496i	$-0.0330029\pi$
$647$	1.81716e12	+	3.14742e12i	0.407685	+	0.706131i	−0.586945	+	0.809627i	$0.699670\pi$
$648$	2.66665e11	+	4.61877e11i	0.0594126	+	0.102906i
$649$	4.75994e11	−	8.24446e11i	0.105317	−	0.182415i
$650$	1.14921e12			0.252517
$651$		0			0
$652$	2.43605e11			0.0527924
$653$	−3.34372e10	+	5.79149e10i	−0.00719649	+	0.0124647i	−0.869601	−	0.493755i	$-0.835624\pi$
$653$	−3.34372e10	+	5.79149e10i	−0.00719649	+	0.0124647i	0.862405	+	0.506219i	$0.168957\pi$
$654$	8.74534e11	+	1.51474e12i	0.186929	+	0.323771i
$655$	7.92876e11	+	1.37330e12i	0.168314	+	0.291528i
$656$	5.03179e11	−	8.71532e11i	0.106085	−	0.183745i
$657$	−1.08211e13			−2.26583
$658$		0			0
$659$	5.97503e12			1.23411			0.617057	−	0.786918i	$-0.288325\pi$
$659$	5.97503e12			1.23411			0.617057	+	0.786918i	$0.288325\pi$
$660$	7.75673e11	−	1.34351e12i	0.159122	−	0.275608i
$661$	3.11074e12	+	5.38796e12i	0.633807	+	1.09779i	0.986767	+	0.162147i	$0.0518420\pi$
$661$	3.11074e12	+	5.38796e12i	0.633807	+	1.09779i	−0.352960	+	0.935639i	$0.614825\pi$
$662$	4.53969e11	+	7.86298e11i	0.0918683	+	0.159121i
$663$	2.34489e12	−	4.06147e12i	0.471315	−	0.816342i
$664$	−8.19738e11			−0.163651
$665$		0			0
$666$	9.54563e12			1.88006
$667$	9.05761e11	−	1.56882e12i	0.177193	−	0.306908i
$668$	2.09902e12	+	3.63562e12i	0.407872	+	0.706454i
$669$	3.75333e12	+	6.50096e12i	0.724434	+	1.25476i
$670$	−7.01839e11	+	1.21562e12i	−0.134555	+	0.233057i
$671$	1.13321e13			2.15804
$672$		0			0
$673$	−4.79437e12			−0.900874			−0.450437	−	0.892808i	$-0.648732\pi$
$673$	−4.79437e12			−0.900874			−0.450437	+	0.892808i	$0.648732\pi$
$674$	4.83050e11	−	8.36667e11i	0.0901618	−	0.156165i
$675$	3.18014e12	+	5.50816e12i	0.589629	+	1.02127i
$676$	1.15929e12	+	2.00795e12i	0.213517	+	0.369823i
$677$	−2.10458e11	+	3.64523e11i	−0.0385049	+	0.0666924i	−0.884636	−	0.466283i	$-0.845593\pi$
$677$	−2.10458e11	+	3.64523e11i	−0.0385049	+	0.0666924i	0.846131	+	0.532975i	$0.178926\pi$
$678$	−1.87848e12			−0.341408
$679$		0			0
$680$	−7.47553e11			−0.134076
$681$	4.83973e12	−	8.38266e12i	0.862301	−	1.49355i
$682$	−4.62872e11	−	8.01718e11i	−0.0819278	−	0.141903i
$683$	1.15885e12	+	2.00719e12i	0.203768	+	0.352936i	0.949739	−	0.313042i	$-0.101348\pi$
$683$	1.15885e12	+	2.00719e12i	0.203768	+	0.352936i	−0.745972	+	0.665978i	$0.768015\pi$
$684$	−3.99103e12	+	6.91267e12i	−0.697161	+	1.20752i
$685$	1.11764e12			0.193952
$686$		0			0
$687$	−3.10128e12			−0.531173
$688$	−6.12834e11	+	1.06146e12i	−0.104279	+	0.180616i
$689$	−4.06800e11	−	7.04598e11i	−0.0687692	−	0.119112i
$690$	−2.54564e11	−	4.40918e11i	−0.0427539	−	0.0740520i
$691$	−1.21890e12	+	2.11120e12i	−0.203384	+	0.352272i	−0.949617	−	0.313413i	$-0.898527\pi$
$691$	−1.21890e12	+	2.11120e12i	−0.203384	+	0.352272i	0.746232	+	0.665686i	$0.231861\pi$
$692$	4.79459e11			0.0794830
$693$		0			0
$694$	−4.38342e12			−0.717291
$695$	3.40415e11	−	5.89616e11i	0.0553448	−	0.0958601i
$696$	−2.25930e12	−	3.91323e12i	−0.364950	−	0.632111i
$697$	−3.92756e12	−	6.80274e12i	−0.630341	−	1.09178i
$698$	−1.95516e12	+	3.38643e12i	−0.311768	+	0.539998i
$699$	1.87081e13			2.96403
$700$		0			0
$701$	1.26491e12			0.197846			0.0989231	−	0.995095i	$-0.468460\pi$
$701$	1.26491e12			0.197846			0.0989231	+	0.995095i	$0.468460\pi$
$702$	1.09629e12	−	1.89883e12i	0.170376	−	0.295099i
$703$	7.75565e12	+	1.34332e13i	1.19762	+	2.07434i
$704$	−6.11370e11	−	1.05892e12i	−0.0938052	−	0.162475i
$705$	−1.94959e12	+	3.37678e12i	−0.297229	+	0.514816i
$706$	−3.04124e12			−0.460713
$707$		0			0
$708$	−7.79311e11			−0.116563
$709$	−3.85471e12	+	6.67656e12i	−0.572907	+	0.992303i	0.423359	+	0.905962i	$0.360851\pi$
$709$	−3.85471e12	+	6.67656e12i	−0.572907	+	0.992303i	−0.996266	+	0.0863414i	$0.972482\pi$
$710$	1.10633e12	+	1.91622e12i	0.163389	+	0.282998i
$711$	−4.17481e12	−	7.23099e12i	−0.612666	−	1.06117i
$712$	1.43516e11	−	2.48577e11i	0.0209286	−	0.0362495i
$713$	−3.03815e11			−0.0440257
$714$		0			0
$715$	−1.02291e12			−0.146372
$716$	−1.54606e12	+	2.67786e12i	−0.219846	+	0.380785i
$717$	−7.31618e12	−	1.26720e13i	−1.03383	−	1.79064i
$718$	3.79411e12	+	6.57159e12i	0.532782	+	0.922806i
$719$	4.22559e12	−	7.31894e12i	0.589668	−	1.02134i	−0.404607	−	0.914491i	$-0.632592\pi$
$719$	4.22559e12	−	7.31894e12i	0.589668	−	1.02134i	0.994276	−	0.106845i	$-0.0340749\pi$
$720$	−8.09726e11			−0.112290
$721$		0			0
$722$	−7.80757e12			−1.06930
$723$	9.86896e11	−	1.70935e12i	0.134323	−	0.232653i
$724$	8.63292e11	+	1.49526e12i	0.116771	+	0.202253i
$725$	−4.32138e12	−	7.48485e12i	−0.580900	−	1.00615i
$726$	5.50690e12	−	9.53822e12i	0.735685	−	1.27424i
$727$	−9.21867e12			−1.22395			−0.611974	−	0.790878i	$-0.709624\pi$
$727$	−9.21867e12			−1.22395			−0.611974	+	0.790878i	$0.709624\pi$
$728$		0			0
$729$	−1.14702e13			−1.50417
$730$	8.91884e11	−	1.54479e12i	0.116240	−	0.201334i
$731$	4.78347e12	+	8.28522e12i	0.619605	+	1.07319i
$732$	−4.63830e12	−	8.03377e12i	−0.597117	−	1.03424i
$733$	2.52129e11	−	4.36701e11i	0.0322593	−	0.0558748i	−0.849445	−	0.527677i	$-0.823063\pi$
$733$	2.52129e11	−	4.36701e11i	0.0322593	−	0.0558748i	0.881704	+	0.471802i	$0.156396\pi$
$734$	7.57951e12			0.963849
$735$		0			0
$736$	−4.01284e11			−0.0504083
$737$	−8.96044e12	+	1.55199e13i	−1.11873	+	1.93770i
$738$	−4.25421e12	−	7.36851e12i	−0.527916	−	0.914378i
$739$	5.82376e12	+	1.00871e13i	0.718296	+	1.24413i	0.961674	+	0.274194i	$0.0884112\pi$
$739$	5.82376e12	+	1.00871e13i	0.718296	+	1.24413i	−0.243378	+	0.969932i	$0.578255\pi$
$740$	−7.86757e11	+	1.36270e12i	−0.0964491	+	0.167055i
$741$	8.25453e12			1.00580
$742$		0			0
$743$	−2.69366e12			−0.324260			−0.162130	−	0.986769i	$-0.551836\pi$
$743$	−2.69366e12			−0.324260			−0.162130	+	0.986769i	$0.551836\pi$
$744$	−3.78913e11	+	6.56297e11i	−0.0453379	+	0.0785276i
$745$	1.10940e12	+	1.92154e12i	0.131943	+	0.228532i
$746$	−4.67264e12	−	8.09325e12i	−0.552380	−	0.956749i
$747$	−3.46530e12	+	6.00208e12i	−0.407191	+	0.705275i
$748$	−9.54408e12			−1.11475
$749$		0			0
$750$	−5.02744e12			−0.580191
$751$	−4.10201e12	+	7.10489e12i	−0.470562	+	0.815037i	−0.999433	−	0.0336648i	$-0.989282\pi$
$751$	−4.10201e12	+	7.10489e12i	−0.470562	+	0.815037i	0.528871	+	0.848702i	$0.322615\pi$
$752$	1.53662e12	+	2.66151e12i	0.175221	+	0.303492i
$753$	−1.13399e9	−	1.96413e9i	−0.000128539	−	0.000222635i
$754$	−1.48971e12	+	2.58025e12i	−0.167853	+	0.290731i
$755$	8.68949e10			0.00973269
$756$		0			0
$757$	1.42404e13			1.57613			0.788064	−	0.615594i	$-0.211084\pi$
$757$	1.42404e13			1.57613			0.788064	+	0.615594i	$0.211084\pi$
$758$	4.48861e12	−	7.77450e12i	0.493856	−	0.855383i
$759$	−3.25004e12	−	5.62924e12i	−0.355468	−	0.615689i
$760$	−6.57888e11	−	1.13949e12i	−0.0715304	−	0.123894i
$761$	5.97436e12	−	1.03479e13i	0.645744	−	1.11846i	−0.338385	−	0.941008i	$-0.609881\pi$
$761$	5.97436e12	−	1.03479e13i	0.645744	−	1.11846i	0.984129	−	0.177454i	$-0.0567861\pi$
$762$	−5.43379e12			−0.583856
$763$		0			0
$764$	6.67176e12			0.708468
$765$	−3.16015e12	+	5.47354e12i	−0.333604	+	0.577819i
$766$	−7.07601e11	−	1.22560e12i	−0.0742607	−	0.128623i
$767$	2.56925e11	+	4.45008e11i	0.0268058	+	0.0464289i
$768$	−5.00476e11	+	8.66849e11i	−0.0519108	+	0.0899121i
$769$	−1.09236e13			−1.12641			−0.563206	−	0.826317i	$-0.690432\pi$
$769$	−1.09236e13			−1.12641			−0.563206	+	0.826317i	$0.690432\pi$
$770$		0			0
$771$	−4.02380e12			−0.410102
$772$	3.06026e12	−	5.30053e12i	0.310085	−	0.537083i
$773$	−8.69476e12	−	1.50598e13i	−0.875890	−	1.51709i	−0.855811	−	0.517288i	$-0.826942\pi$
$773$	−8.69476e12	−	1.50598e13i	−0.875890	−	1.51709i	−0.0200787	−	0.999798i	$-0.506392\pi$
$774$	5.18130e12	+	8.97428e12i	0.518925	+	0.898805i
$775$	−7.24749e11	+	1.25530e12i	−0.0721656	+	0.124994i
$776$	−2.74254e12			−0.271504
$777$		0			0
$778$	6.77554e12			0.663034
$779$	6.91294e12	−	1.19736e13i	0.672580	−	1.16494i
$780$	4.18682e11	+	7.25179e11i	0.0405004	+	0.0701487i
$781$	1.41246e13	+	2.44645e13i	1.35846	+	2.35292i
$782$	−1.56611e12	+	2.71258e12i	−0.149759	+	0.259389i
$783$	−1.64895e13			−1.56776
$784$		0			0
$785$	2.01281e12			0.189186
$786$	8.28660e12	−	1.43528e13i	0.774417	−	1.34133i
$787$	−4.34835e12	−	7.53156e12i	−0.404053	−	0.699840i	0.590158	−	0.807288i	$-0.299065\pi$
$787$	−4.34835e12	−	7.53156e12i	−0.404053	−	0.699840i	−0.994211	+	0.107448i	$0.965732\pi$
$788$	−6.28567e11	−	1.08871e12i	−0.0580743	−	0.100588i
$789$	2.92963e12	−	5.07427e12i	0.269132	−	0.466151i
$790$	1.37636e12			0.125722
$791$		0			0
$792$	−1.03378e13			−0.933612
$793$	−3.05834e12	+	5.29720e12i	−0.274635	+	0.475682i
$794$	−2.90458e12	−	5.03087e12i	−0.259353	−	0.449212i
$795$	8.59837e11	+	1.48928e12i	0.0763421	+	0.132228i
$796$	2.99283e12	−	5.18373e12i	0.264225	−	0.457650i
$797$	6.04620e12			0.530787			0.265393	−	0.964140i	$-0.414498\pi$
$797$	6.04620e12			0.530787			0.265393	+	0.964140i	$0.414498\pi$
$798$		0			0
$799$	2.39882e13			2.08227
$800$	−9.57262e11	+	1.65803e12i	−0.0826277	+	0.143115i
$801$	−1.21338e12	−	2.10164e12i	−0.104148	−	0.180390i
$802$	−4.02535e12	−	6.97211e12i	−0.343573	−	0.595085i
$803$	1.13868e13	−	1.97225e13i	0.966452	−	1.67394i
$804$	1.46703e13			1.23819
$805$		0			0
$806$	4.99685e11			0.0417051
$807$	−9.28834e12	+	1.60879e13i	−0.770916	+	1.33527i
$808$	−1.74673e12	−	3.02543e12i	−0.144170	−	0.249710i
$809$	−6.68109e12	−	1.15720e13i	−0.548377	−	0.949817i	−0.998386	−	0.0567926i	$-0.981913\pi$
$809$	−6.68109e12	−	1.15720e13i	−0.548377	−	0.949817i	0.450009	−	0.893024i	$-0.351421\pi$
$810$	−3.71645e11	+	6.43708e11i	−0.0303351	+	0.0525420i
$811$	2.55667e11			0.0207530			0.0103765	−	0.999946i	$-0.496697\pi$
$811$	2.55667e11			0.0207530			0.0103765	+	0.999946i	$0.496697\pi$
$812$		0			0
$813$	−7.24080e12			−0.581271
$814$	−1.00446e13	+	1.73978e13i	−0.801905	+	1.38894i
$815$	1.69753e11	+	2.94021e11i	0.0134775	+	0.0233437i
$816$	3.90646e12	+	6.76618e12i	0.308445	+	0.534242i
$817$	−8.41943e12	+	1.45829e13i	−0.661125	+	1.14510i
$818$	1.26745e12			0.0989783
$819$		0			0
$820$	1.40254e12			0.108331
$821$	8.40243e12	−	1.45534e13i	0.645447	−	1.11795i	−0.338751	−	0.940876i	$-0.610004\pi$
$821$	8.40243e12	−	1.45534e13i	0.645447	−	1.11795i	0.984198	−	0.177071i	$-0.0566623\pi$
$822$	−5.84041e12	−	1.01159e13i	−0.446191	−	0.772825i
$823$	7.58134e11	+	1.31313e12i	0.0576032	+	0.0997717i	0.893389	−	0.449284i	$-0.148321\pi$
$823$	7.58134e11	+	1.31313e12i	0.0576032	+	0.0997717i	−0.835786	+	0.549056i	$0.814987\pi$
$824$	−2.05206e12	+	3.55427e12i	−0.155066	+	0.268583i
$825$	−3.10119e13			−2.33069
$826$		0			0
$827$	−2.47074e13			−1.83676			−0.918380	−	0.395699i	$-0.870502\pi$
$827$	−2.47074e13			−1.83676			−0.918380	+	0.395699i	$0.870502\pi$
$828$	−1.69636e12	+	2.93818e12i	−0.125424	+	0.217241i
$829$	−9.77015e12	−	1.69224e13i	−0.718465	−	1.24442i	−0.961608	−	0.274428i	$-0.911512\pi$
$829$	−9.77015e12	−	1.69224e13i	−0.718465	−	1.24442i	0.243142	−	0.969991i	$-0.421822\pi$
$830$	−5.71225e11	−	9.89390e11i	−0.0417788	−	0.0723629i
$831$	−1.94714e13	+	3.37255e13i	−1.41642	+	2.45332i
$832$	6.59993e11			0.0477512
$833$		0			0
$834$	−7.11557e12			−0.509287
$835$	−2.92536e12	+	5.06688e12i	−0.208253	+	0.360704i
$836$	−8.39931e12	−	1.45480e13i	−0.594724	−	1.03009i
$837$	1.38274e12	+	2.39498e12i	0.0973817	+	0.168670i
$838$	−2.71154e12	+	4.69653e12i	−0.189941	+	0.328987i
$839$	−1.73255e13			−1.20714			−0.603569	−	0.797311i	$-0.706255\pi$
$839$	−1.73255e13			−1.20714			−0.603569	+	0.797311i	$0.706255\pi$
$840$		0			0
$841$	7.89983e12			0.544547
$842$	−5.07301e12	+	8.78671e12i	−0.347825	+	0.602451i
$843$	8.22451e12	+	1.42453e13i	0.560900	+	0.971508i
$844$	−2.82664e12	−	4.89588e12i	−0.191747	−	0.332116i
$845$	−1.61568e12	+	2.79844e12i	−0.109018	+	0.188825i
$846$	2.59832e13			1.74392
$847$		0			0
$848$	1.35541e12			0.0900097
$849$	3.00390e12	−	5.20291e12i	0.198427	−	0.343686i
$850$	7.47190e12	+	1.29417e13i	0.490960	+	0.850367i
$851$	3.29648e12	+	5.70968e12i	0.215461	+	0.373189i
$852$	1.15626e13	−	2.00270e13i	0.751757	−	1.30208i
$853$	−1.19537e12			−0.0773096			−0.0386548	−	0.999253i	$-0.512307\pi$
$853$	−1.19537e12			−0.0773096			−0.0386548	+	0.999253i	$0.512307\pi$
$854$		0			0
$855$	−1.11244e13			−0.711918
$856$	8.56689e11	−	1.48383e12i	0.0545370	−	0.0944608i
$857$	1.06769e13	+	1.84929e13i	0.676132	+	1.17110i	0.976137	+	0.217157i	$0.0696785\pi$
$857$	1.06769e13	+	1.84929e13i	0.676132	+	1.17110i	−0.300004	+	0.953938i	$0.596988\pi$
$858$	5.34535e12	+	9.25842e12i	0.336731	+	0.583236i
$859$	−5.31711e12	+	9.20950e12i	−0.333201	+	0.577121i	−0.983138	−	0.182867i	$-0.941462\pi$
$859$	−5.31711e12	+	9.20950e12i	−0.333201	+	0.577121i	0.649937	+	0.759989i	$0.274795\pi$
$860$	−1.70819e12			−0.106486
$861$		0			0
$862$	−6.61779e12			−0.408254
$863$	7.07090e11	−	1.22472e12i	0.0433936	−	0.0751600i	−0.843513	−	0.537109i	$-0.819516\pi$
$863$	7.07090e11	−	1.22472e12i	0.0433936	−	0.0751600i	0.886906	+	0.461949i	$0.152850\pi$
$864$	1.82635e12	+	3.16334e12i	0.111500	+	0.193123i
$865$	3.34106e11	+	5.78688e11i	0.0202914	+	0.0351457i
$866$	−7.02832e12	+	1.21734e13i	−0.424640	+	0.735498i
$867$	3.33465e13			2.00430
$868$		0			0
$869$	1.75722e13			1.04529
$870$	3.14874e12	−	5.45378e12i	0.186337	−	0.322746i
$871$	−4.83654e12	−	8.37714e12i	−0.284743	−	0.493190i
$872$	9.60647e11	+	1.66389e12i	0.0562651	+	0.0974541i
$873$	−1.15936e13	+	2.00808e13i	−0.675546	+	1.17008i
$874$	−5.51305e12			−0.319588
$875$		0			0
$876$	−1.86427e13			−1.06965
$877$	7.78878e12	−	1.34906e13i	0.444602	−	0.770073i	−0.553422	−	0.832901i	$-0.686678\pi$
$877$	7.78878e12	−	1.34906e13i	0.444602	−	0.770073i	0.998024	+	0.0628273i	$0.0200117\pi$
$878$	1.14137e13	+	1.97691e13i	0.648187	+	1.12269i
$879$	4.91529e12	+	8.51352e12i	0.277715	+	0.481016i
$880$	8.52052e11	−	1.47580e12i	0.0478954	−	0.0829573i
$881$	1.55176e13			0.867825			0.433912	−	0.900955i	$-0.357133\pi$
$881$	1.55176e13			0.867825			0.433912	+	0.900955i	$0.357133\pi$
$882$		0			0
$883$	−2.94777e13			−1.63181			−0.815906	−	0.578185i	$-0.803761\pi$
$883$	−2.94777e13			−1.63181			−0.815906	+	0.578185i	$0.803761\pi$
$884$	2.57578e12	−	4.46139e12i	0.141865	−	0.245717i
$885$	−5.43054e11	−	9.40596e11i	−0.0297576	−	0.0515417i
$886$	−9.32834e12	−	1.61572e13i	−0.508572	−	0.880873i
$887$	−3.15812e12	+	5.47002e12i	−0.171306	+	0.296710i	−0.938877	−	0.344254i	$-0.888132\pi$
$887$	−3.15812e12	+	5.47002e12i	−0.171306	+	0.296710i	0.767571	+	0.640964i	$0.221465\pi$
$888$	1.64453e13			0.887531
$889$		0			0
$890$	4.00030e11			0.0213717
$891$	−4.74482e12	+	8.21828e12i	−0.252215	+	0.436849i
$892$	4.12291e12	+	7.14109e12i	0.218053	+	0.377679i
$893$	2.11109e13	+	3.65652e13i	1.11090	+	1.92414i
$894$	1.15947e13	−	2.00827e13i	0.607074	−	1.05148i
$895$	−4.30943e12			−0.224500
$896$		0			0
$897$	3.50852e12			0.180950
$898$	3.58394e12	−	6.20757e12i	0.183915	−	0.318550i
$899$	−1.87896e12	−	3.25446e12i	−0.0959400	−	0.166173i
$900$	8.09332e12	+	1.40180e13i	0.411183	+	0.712190i
$901$	5.28982e12	−	9.16224e12i	0.267411	−	0.463170i
$902$	1.79063e13			0.900694
$903$		0			0
$904$	−2.06345e12			−0.102763
$905$	−1.20315e12	+	2.08392e12i	−0.0596212	+	0.103267i
$906$	−4.54083e11	−	7.86495e11i	−0.0223902	−	0.0387810i
$907$	−9.43632e12	−	1.63442e13i	−0.462988	−	0.801919i	0.536120	−	0.844142i	$-0.319889\pi$
$907$	−9.43632e12	−	1.63442e13i	−0.462988	−	0.801919i	−0.999108	+	0.0422226i	$0.986556\pi$
$908$	5.31628e12	−	9.20807e12i	0.259550	−	0.449555i
$909$	−2.95361e13			−1.43488
$910$		0			0
$911$	−2.40579e13			−1.15724			−0.578622	−	0.815596i	$-0.696409\pi$
$911$	−2.40579e13			−1.15724			−0.578622	+	0.815596i	$0.696409\pi$
$912$	−6.87579e12	+	1.19092e13i	−0.329114	+	0.570041i
$913$	−7.29288e12	−	1.26316e13i	−0.347360	−	0.601646i
$914$	4.31571e12	+	7.47504e12i	0.204548	+	0.354287i
$915$	6.46429e12	−	1.11965e13i	0.304878	−	0.528064i
$916$	−3.40666e12			−0.159882
$917$		0			0
$918$	2.85112e13			1.32502
$919$	−8.95336e12	+	1.55077e13i	−0.414063	+	0.717178i	−0.995330	−	0.0965354i	$-0.969224\pi$
$919$	−8.95336e12	+	1.55077e13i	−0.414063	+	0.717178i	0.581267	+	0.813713i	$0.302557\pi$
$920$	−2.79630e11	−	4.84334e11i	−0.0128688	−	0.0222895i
$921$	−2.75617e13	−	4.77383e13i	−1.26223	−	2.18624i
$922$	−3.39958e12	+	5.88825e12i	−0.154930	+	0.268347i
$923$	−1.52480e13			−0.691519
$924$		0			0
$925$	3.14550e13			1.41271
$926$	6.89373e12	−	1.19403e13i	0.308109	−	0.533661i
$927$	1.73495e13	+	3.00502e13i	0.771662	+	1.33656i
$928$	−2.48177e12	−	4.29855e12i	−0.109849	−	0.190264i
$929$	5.90070e12	−	1.02203e13i	0.259916	−	0.450187i	−0.706303	−	0.707909i	$-0.749639\pi$
$929$	5.90070e12	−	1.02203e13i	0.259916	−	0.450187i	0.966219	+	0.257722i	$0.0829719\pi$
$930$	−1.05617e12			−0.0462976
$931$		0			0
$932$	2.05503e13			0.892166
$933$	−9.03462e12	+	1.56484e13i	−0.390339	+	0.676088i
$934$	5.32371e12	+	9.22093e12i	0.228904	+	0.396473i
$935$	−6.65068e12	−	1.15193e13i	−0.284586	−	0.492918i
$936$	2.79001e12	−	4.83243e12i	0.118813	−	0.205790i
$937$	−2.93165e13			−1.24246			−0.621231	−	0.783627i	$-0.713367\pi$
$937$	−2.93165e13			−1.24246			−0.621231	+	0.783627i	$0.713367\pi$
$938$		0			0
$939$	5.55689e13			2.33258
$940$	−2.14155e12	+	3.70928e12i	−0.0894651	+	0.154958i
$941$	−2.28937e13	−	3.96531e13i	−0.951837	−	1.64863i	−0.741445	−	0.671014i	$-0.765859\pi$
$941$	−2.28937e13	−	3.96531e13i	−0.951837	−	1.64863i	−0.210393	−	0.977617i	$-0.567474\pi$
$942$	−1.05182e13	−	1.82181e13i	−0.435225	−	0.753832i
$943$	2.93829e12	−	5.08927e12i	0.121002	−	0.209582i
$944$	−8.56047e11			−0.0350852
$945$		0			0
$946$	−2.18086e13			−0.885354
$947$	9.47480e12	−	1.64108e13i	0.382820	−	0.663064i	−0.608644	−	0.793444i	$-0.708286\pi$
$947$	9.47480e12	−	1.64108e13i	0.382820	−	0.663064i	0.991464	+	0.130379i	$0.0416195\pi$
$948$	−7.19241e12	−	1.24576e13i	−0.289226	−	0.500953i
$949$	6.14619e12	+	1.06455e13i	0.245985	+	0.426058i
$950$	−1.31514e13	+	2.27788e13i	−0.523859	+	0.907350i
$951$	3.83144e13			1.51897
$952$		0			0
$953$	1.44979e13			0.569362			0.284681	−	0.958622i	$-0.408112\pi$
$953$	1.44979e13			0.569362			0.284681	+	0.958622i	$0.408112\pi$
$954$	5.72977e12	−	9.92424e12i	0.223959	−	0.387909i
$955$	4.64914e12	+	8.05254e12i	0.180866	+	0.313269i
$956$	−8.03658e12	−	1.39198e13i	−0.311179	−	0.538979i
$957$	4.02002e13	−	6.96288e13i	1.54926	−	2.68340i
$958$	−1.37194e13			−0.526246
$959$		0			0
$960$	−1.39500e12			−0.0530096
$961$	1.29047e13	−	2.23516e13i	0.488081	−	0.845382i
$962$	−5.42173e12	−	9.39072e12i	−0.204103	−	0.353518i
$963$	−7.24301e12	−	1.25453e13i	−0.271394	−	0.470069i
$964$	1.08407e12	−	1.87767e12i	0.0404307	−	0.0700281i
$965$	8.53003e12			0.316649
$966$		0			0
$967$	1.84871e13			0.679909			0.339954	−	0.940442i	$-0.389588\pi$
$967$	1.84871e13			0.679909			0.339954	+	0.940442i	$0.389588\pi$
$968$	6.04914e12	−	1.04774e13i	0.221439	−	0.383544i
$969$	5.36689e13	+	9.29573e13i	1.95554	+	3.38709i
$970$	−1.91111e12	−	3.31014e12i	−0.0693127	−	0.120053i
$971$	−2.24078e13	+	3.88114e13i	−0.808933	+	1.40111i	0.104670	+	0.994507i	$0.466621\pi$
$971$	−2.24078e13	+	3.88114e13i	−0.808933	+	1.40111i	−0.913603	+	0.406607i	$0.866712\pi$
$972$	−9.78443e12			−0.351591
$973$		0			0
$974$	−3.26001e13			−1.16066
$975$	8.36957e12	−	1.44965e13i	0.296608	−	0.513740i
$976$	−5.09502e12	−	8.82484e12i	−0.179731	−	0.311302i
$977$	−1.23981e13	−	2.14742e13i	−0.435342	−	0.754035i	0.561981	−	0.827150i	$-0.310039\pi$
$977$	−1.23981e13	−	2.14742e13i	−0.435342	−	0.754035i	−0.997324	+	0.0731151i	$0.976706\pi$
$978$	1.77414e12	−	3.07291e12i	0.0620103	−	0.107405i
$979$	5.10723e12			0.177690
$980$		0			0
$981$	1.62439e13			0.559988
$982$	6.28010e12	−	1.08774e13i	0.215509	−	0.373272i
$983$	−6.93158e12	−	1.20058e13i	−0.236778	−	0.410111i	0.723010	−	0.690838i	$-0.242758\pi$
$983$	−6.93158e12	−	1.20058e13i	−0.236778	−	0.410111i	−0.959788	+	0.280726i	$0.909425\pi$
$984$	−7.32919e12	−	1.26945e13i	−0.249217	−	0.431657i
$985$	8.76019e11	−	1.51731e12i	0.0296518	−	0.0513584i
$986$	−3.87429e13			−1.30541
$987$		0			0
$988$	9.06732e12			0.302742
$989$	−3.57862e12	+	6.19835e12i	−0.118941	+	0.206012i
$990$	−7.20380e12	−	1.24774e13i	−0.238344	−	0.412823i
$991$	3.32399e12	+	5.75732e12i	0.109478	+	0.189622i	0.915559	−	0.402184i	$-0.131749\pi$
$991$	3.32399e12	+	5.75732e12i	0.109478	+	0.189622i	−0.806081	+	0.591806i	$0.798415\pi$
$992$	−4.16224e11	+	7.20921e11i	−0.0136466	+	0.0236366i
$993$	1.32248e13			0.431636
$994$		0			0
$995$	8.34208e12			0.269818
$996$	−5.97005e12	+	1.03404e13i	−0.192225	+	0.332944i
$997$	2.92310e13	+	5.06296e13i	0.936949	+	1.62284i	0.771122	+	0.636688i	$0.219696\pi$
$997$	2.92310e13	+	5.06296e13i	0.936949	+	1.62284i	0.165827	+	0.986155i	$0.446971\pi$
$998$	−2.09541e12	−	3.62936e12i	−0.0668625	−	0.115809i
$999$	3.00064e13	−	5.19726e13i	0.953167	−	1.65093i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	98.10.c.j.79.1		4
7.2	even	3		14.10.a.c.1.2	✓	2
7.3	odd	6		98.10.c.h.67.2		4
7.4	even	3	inner	98.10.c.j.67.1		4
7.5	odd	6		98.10.a.e.1.1		2
7.6	odd	2		98.10.c.h.79.2		4
21.2	odd	6		126.10.a.o.1.1		2
28.23	odd	6		112.10.a.c.1.1		2
35.2	odd	12		350.10.c.j.99.1		4
35.9	even	6		350.10.a.j.1.1		2
35.23	odd	12		350.10.c.j.99.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.10.a.c.1.2	✓	2	7.2	even	3
98.10.a.e.1.1		2	7.5	odd	6
98.10.c.h.67.2		4	7.3	odd	6
98.10.c.h.79.2		4	7.6	odd	2
98.10.c.j.67.1		4	7.4	even	3	inner
98.10.c.j.79.1		4	1.1	even	1	trivial
112.10.a.c.1.1		2	28.23	odd	6
126.10.a.o.1.1		2	21.2	odd	6
350.10.a.j.1.1		2	35.9	even	6
350.10.c.j.99.1		4	35.2	odd	12
350.10.c.j.99.4		4	35.23	odd	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 $\F_{q}$
Belyi maps

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} +(-116.526 - 201.829i) q^{3} +(-128.000 - 221.703i) q^{4} +(178.391 - 308.982i) q^{5} -3728.83 q^{6} -4096.00 q^{8} +(-17315.1 + 29990.7i) q^{9} +(-2854.25 - 4943.71i) q^{10} +(-36440.5 - 63116.7i) q^{11} +(-29830.7 + 51668.2i) q^{12} +39338.7 q^{13} -83148.6 q^{15} +(-32768.0 + 56755.8i) q^{16} +(255770. + 443007. i) q^{17} +(277042. + 479851. i) q^{18} +(-450184. + 779741. i) q^{19} -91336.0 q^{20} -1.16609e6 q^{22} +(-191347. + 331423. i) q^{23} +(477291. + 826692. i) q^{24} +(912916. + 1.58122e6i) q^{25} +(314709. - 545092. i) q^{26} +3.48349e6 q^{27} -4.73360e6 q^{29} +(-665189. + 1.15214e6i) q^{30} +(396942. + 687523. i) q^{31} +(524288. + 908093. i) q^{32} +(-8.49253e6 + 1.47095e7i) q^{33} +8.18465e6 q^{34} +8.86535e6 q^{36} +(8.61388e6 - 1.49197e7i) q^{37} +(7.20294e6 + 1.24759e7i) q^{38} +(-4.58398e6 - 7.93968e6i) q^{39} +(-730688. + 1.26559e6i) q^{40} -1.53558e7 q^{41} +1.87022e7 q^{43} +(-9.32876e6 + 1.61579e7i) q^{44} +(6.17772e6 + 1.07001e7i) q^{45} +(3.06155e6 + 5.30277e6i) q^{46} +(2.34470e7 - 4.06114e7i) q^{47} +1.52733e7 q^{48} +2.92133e7 q^{50} +(5.96078e7 - 1.03244e8i) q^{51} +(-5.03535e6 - 8.72148e6i) q^{52} +(-1.03410e7 - 1.79111e7i) q^{53} +(2.78679e7 - 4.82687e7i) q^{54} -2.60026e7 q^{55} +2.09832e8 q^{57} +(-3.78688e7 + 6.55907e7i) q^{58} +(6.53112e6 + 1.13122e7i) q^{59} +(1.06430e7 + 1.84343e7i) q^{60} +(-7.77439e7 + 1.34656e8i) q^{61} +1.27021e7 q^{62} +1.67772e7 q^{64} +(7.01765e6 - 1.21549e7i) q^{65} +(1.35880e8 + 2.35352e8i) q^{66} +(-1.22946e8 - 2.12949e8i) q^{67} +(6.54772e7 - 1.13410e8i) q^{68} +8.91877e7 q^{69} -3.87608e8 q^{71} +(7.09228e7 - 1.22842e8i) q^{72} +(1.56238e8 + 2.70612e8i) q^{73} +(-1.37822e8 - 2.38715e8i) q^{74} +(2.12757e8 - 3.68506e8i) q^{75} +2.30494e8 q^{76} -1.46687e8 q^{78} +(-1.20554e8 + 2.08805e8i) q^{79} +(1.16910e7 + 2.02494e7i) q^{80} +(-6.51038e7 - 1.12763e8i) q^{81} +(-1.22847e8 + 2.12776e8i) q^{82} +2.00131e8 q^{83} +1.82508e8 q^{85} +(1.49618e8 - 2.59146e8i) q^{86} +(5.51588e8 + 9.55378e8i) q^{87} +(1.49260e8 + 2.58526e8i) q^{88} +(-3.50381e7 + 6.06878e7i) q^{89} +1.97687e8 q^{90} +9.79698e7 q^{92} +(9.25081e7 - 1.60229e8i) q^{93} +(-3.75152e8 - 6.49782e8i) q^{94} +(1.60617e8 + 2.78197e8i) q^{95} +(1.22186e8 - 2.11633e8i) q^{96} +6.69566e8 q^{97} +2.52389e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 32 q^{2} + 14 q^{3} - 512 q^{4} + 2730 q^{5} + 448 q^{6} - 16384 q^{8} - 75982 q^{9} - 43680 q^{10} - 44940 q^{11} + 3584 q^{12} + 200564 q^{13} + 1006320 q^{15} - 131072 q^{16} + 870408 q^{17} + 1215712 q^{18}+ \cdots + 2736961080 q^{99}+O(q^{100}) \) 4 * q + 32 * q^2 + 14 * q^3 - 512 * q^4 + 2730 * q^5 + 448 * q^6 - 16384 * q^8 - 75982 * q^9 - 43680 * q^10 - 44940 * q^11 + 3584 * q^12 + 200564 * q^13 + 1006320 * q^15 - 131072 * q^16 + 870408 * q^17 + 1215712 * q^18 - 508774 * q^19 - 1397760 * q^20 - 1438080 * q^22 - 79800 * q^23 - 57344 * q^24 - 1853210 * q^25 + 1604512 * q^26 - 3739624 * q^27 + 4012656 * q^29 + 8050560 * q^30 - 2188732 * q^31 + 2097152 * q^32 - 23887920 * q^33 + 27853056 * q^34 + 38902784 * q^36 + 20723576 * q^37 + 8140384 * q^38 + 5888224 * q^39 - 11182080 * q^40 + 38033184 * q^41 + 8387432 * q^43 - 11504640 * q^44 + 110492130 * q^45 + 1276800 * q^46 + 74542524 * q^47 - 1835008 * q^48 - 59302720 * q^50 + 30556644 * q^51 - 25672192 * q^52 + 3239748 * q^53 - 29916992 * q^54 + 80614800 * q^55 + 613152664 * q^57 + 32101248 * q^58 + 133642362 * q^59 - 128808960 * q^60 - 227801686 * q^61 - 70039424 * q^62 + 67108864 * q^64 + 158667180 * q^65 + 382206720 * q^66 - 332930272 * q^67 + 222824448 * q^68 + 328036800 * q^69 - 335971440 * q^71 + 311222272 * q^72 + 44684276 * q^73 - 331577216 * q^74 + 1334428970 * q^75 + 260492288 * q^76 + 188423168 * q^78 - 269642776 * q^79 + 178913280 * q^80 - 638826478 * q^81 + 304265472 * q^82 - 366211524 * q^83 + 2068358040 * q^85 + 67099456 * q^86 + 2768288796 * q^87 + 184074240 * q^88 - 791657748 * q^89 + 3535748160 * q^90 + 40857600 * q^92 + 921877624 * q^93 - 1192680384 * q^94 - 608102040 * q^95 - 14680064 * q^96 - 8338960 * q^97 + 2736961080 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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