LMFDB - Embedded newform 26.10.c.b.9.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,10,Mod(3,26)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 10, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("26.3"); S:= CuspForms(chi, 10); N := Newforms(S);

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$13.3909317403$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 10384 x^{10} + 120855 x^{9} + 81803040 x^{8} + 688592615 x^{7} + \cdots + 27\!\cdots\!00 $ x^12 - 3x^11 + 10384x^10 + 120855x^9 + 81803040x^8 + 688592615x^7 + 235441918375x^6 + 326685836650x^5 + 490232889649600x^4 + 270381215117000x^3 + 434580563567230000x^2 - 1152225642325800000*x + 279661605363396000000
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{7}\cdot 13^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.4
Root			$15.5034 + 26.8527i$ of defining polynomial
Character	$\chi$	$=$	26.9
Dual form			26.10.c.b.3.4

$q$-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} +(39.0102 - 67.5676i) q^{3} +(-128.000 - 221.703i) q^{4} -1338.85 q^{5} +(624.163 + 1081.08i) q^{6} +(66.0901 + 114.471i) q^{7} +4096.00 q^{8} +(6797.91 + 11774.3i) q^{9} +(10710.8 - 18551.6i) q^{10} +(12128.8 - 21007.7i) q^{11} -19973.2 q^{12} +(99851.2 - 25184.1i) q^{13} -2114.88 q^{14} +(-52228.7 + 90462.7i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(213586. + 369942. i) q^{17} -217533. q^{18} +(474552. + 821948. i) q^{19} +(171372. + 296826. i) q^{20} +10312.8 q^{21} +(194061. + 336123. i) q^{22} +(-486392. + 842456. i) q^{23} +(159786. - 276757. i) q^{24} -160614. q^{25} +(-449848. + 1.58505e6i) q^{26} +2.59643e6 q^{27} +(16919.1 - 29304.7i) q^{28} +(1.52289e6 - 2.63773e6i) q^{29} +(-835659. - 1.44740e6i) q^{30} +2.57547e6 q^{31} +(-524288. - 908093. i) q^{32} +(-946292. - 1.63903e6i) q^{33} -6.83475e6 q^{34} +(-88484.5 - 153260. i) q^{35} +(1.74026e6 - 3.01423e6i) q^{36} +(5.43712e6 - 9.41737e6i) q^{37} -1.51857e7 q^{38} +(2.19358e6 - 7.72915e6i) q^{39} -5.48392e6 q^{40} +(-6.03259e6 + 1.04488e7i) q^{41} +(-82502.0 + 142898. i) q^{42} +(1.06937e7 + 1.85221e7i) q^{43} -6.20994e6 q^{44} +(-9.10136e6 - 1.57640e7i) q^{45} +(-7.78228e6 - 1.34793e7i) q^{46} -2.69913e7 q^{47} +(2.55657e6 + 4.42811e6i) q^{48} +(2.01681e7 - 3.49321e7i) q^{49} +(1.28491e6 - 2.22553e6i) q^{50} +3.33281e7 q^{51} +(-1.83643e7 - 1.89137e7i) q^{52} +3.73277e7 q^{53} +(-2.07714e7 + 3.59771e7i) q^{54} +(-1.62386e7 + 2.81261e7i) q^{55} +(270705. + 468875. i) q^{56} +7.40495e7 q^{57} +(2.43663e7 + 4.22037e7i) q^{58} +(-1.74537e7 - 3.02308e7i) q^{59} +2.67411e7 q^{60} +(7.91644e7 + 1.37117e8i) q^{61} +(-2.06037e7 + 3.56867e7i) q^{62} +(-898549. + 1.55633e6i) q^{63} +1.67772e7 q^{64} +(-1.33685e8 + 3.37177e7i) q^{65} +3.02814e7 q^{66} +(-3.38204e7 + 5.85787e7i) q^{67} +(5.46780e7 - 9.47051e7i) q^{68} +(3.79485e7 + 6.57288e7i) q^{69} +2.83150e6 q^{70} +(-5.73905e7 - 9.94033e7i) q^{71} +(2.78442e7 + 4.82276e7i) q^{72} -1.49856e8 q^{73} +(8.69939e7 + 1.50678e8i) q^{74} +(-6.26557e6 + 1.08523e7i) q^{75} +(1.21485e8 - 2.10419e8i) q^{76} +3.20637e6 q^{77} +(8.95496e7 + 9.22283e7i) q^{78} +6.16681e7 q^{79} +(4.38713e7 - 7.59874e7i) q^{80} +(-3.25161e7 + 5.63196e7i) q^{81} +(-9.65215e7 - 1.67180e8i) q^{82} -4.82674e8 q^{83} +(-1.32003e6 - 2.28636e6i) q^{84} +(-2.85959e8 - 4.95296e8i) q^{85} -3.42200e8 q^{86} +(-1.18817e8 - 2.05797e8i) q^{87} +(4.96795e7 - 8.60474e7i) q^{88} +(9.56598e7 - 1.65688e8i) q^{89} +2.91244e8 q^{90} +(9.48204e6 + 9.76568e6i) q^{91} +2.49033e8 q^{92} +(1.00470e8 - 1.74018e8i) q^{93} +(2.15931e8 - 3.74003e8i) q^{94} +(-6.35352e8 - 1.10046e9i) q^{95} -8.18103e7 q^{96} +(5.35450e7 + 9.27427e7i) q^{97} +(3.22689e8 + 5.58914e8i) q^{98} +3.29801e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 96 q^{2} - 81 q^{3} - 1536 q^{4} + 3386 q^{5} - 1296 q^{6} - 473 q^{7} + 49152 q^{8} - 69813 q^{9} - 27088 q^{10} - 14011 q^{11} + 41472 q^{12} + 152853 q^{13} + 15136 q^{14} + 294780 q^{15} - 393216 q^{16}+ \cdots - 1763539020 q^{99}+O(q^{100}) $ 12 * q - 96 * q^2 - 81 * q^3 - 1536 * q^4 + 3386 * q^5 - 1296 * q^6 - 473 * q^7 + 49152 * q^8 - 69813 * q^9 - 27088 * q^10 - 14011 * q^11 + 41472 * q^12 + 152853 * q^13 + 15136 * q^14 + 294780 * q^15 - 393216 * q^16 + 173558 * q^17 + 2234016 * q^18 - 322367 * q^19 - 433408 * q^20 + 4513770 * q^21 - 224176 * q^22 + 1644771 * q^23 - 331776 * q^24 + 5375138 * q^25 - 4031808 * q^26 - 1845990 * q^27 - 121088 * q^28 - 10801236 * q^29 + 4716480 * q^30 + 20870244 * q^31 - 6291456 * q^32 - 26201763 * q^33 - 5553856 * q^34 - 2168950 * q^35 - 17872128 * q^36 + 15710464 * q^37 + 10315744 * q^38 - 22298325 * q^39 + 13869056 * q^40 + 1525478 * q^41 - 36110160 * q^42 - 50959661 * q^43 + 7173632 * q^44 - 18619731 * q^45 + 26316336 * q^46 + 136313996 * q^47 - 5308416 * q^48 - 162536361 * q^49 - 43001104 * q^50 - 169357962 * q^51 + 25378560 * q^52 + 144556418 * q^53 + 14767920 * q^54 + 353372330 * q^55 - 1937408 * q^56 + 35902050 * q^57 - 172819776 * q^58 + 5665291 * q^59 - 150927360 * q^60 + 353387956 * q^61 - 166961952 * q^62 + 224088894 * q^63 + 201326592 * q^64 - 205394773 * q^65 + 838456416 * q^66 - 371115369 * q^67 + 44430848 * q^68 - 280317279 * q^69 + 69406400 * q^70 - 156688763 * q^71 - 285954048 * q^72 + 932803326 * q^73 + 251367424 * q^74 - 1149481845 * q^75 - 82525952 * q^76 + 624920666 * q^77 - 420616752 * q^78 + 325086960 * q^79 - 110952448 * q^80 - 295496586 * q^81 + 24407648 * q^82 - 870229152 * q^83 - 577762560 * q^84 - 2307296767 * q^85 + 1630709152 * q^86 + 617376057 * q^87 - 57389056 * q^88 - 163315063 * q^89 + 595831392 * q^90 - 208860497 * q^91 - 842122752 * q^92 - 2056270836 * q^93 - 1090511968 * q^94 + 537110948 * q^95 + 169869312 * q^96 + 1500514705 * q^97 - 2600581776 * q^98 - 1763539020 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/26\mathbb{Z}\right)^\times$.

$n$	$15$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$2$	−8.00000	+	13.8564i	−0.353553	+	0.612372i
$3$	39.0102	−	67.5676i	0.278056	−	0.481607i	−0.692845	−	0.721086i	$-0.743643\pi$
$3$	39.0102	−	67.5676i	0.278056	−	0.481607i	0.970902	+	0.239479i	$0.0769765\pi$
$4$	−128.000	−	221.703i	−0.250000	−	0.433013i
$5$	−1338.85			−0.958001			−0.479000	−	0.877815i	$-0.659001\pi$
$5$	−1338.85			−0.958001			−0.479000	+	0.877815i	$0.659001\pi$
$6$	624.163	+	1081.08i	0.196615	+	0.340548i
$7$	66.0901	+	114.471i	0.0104039	+	0.0180200i	0.871180	−	0.490963i	$-0.163355\pi$
$7$	66.0901	+	114.471i	0.0104039	+	0.0180200i	−0.860777	+	0.508983i	$0.830022\pi$
$8$	4096.00			0.353553
$9$	6797.91	+	11774.3i	0.345370	+	0.598198i
$10$	10710.8	−	18551.6i	0.338704	−	0.586653i
$11$	12128.8	−	21007.7i	0.249776	−	0.432624i	−0.713688	−	0.700464i	$-0.752976\pi$
$11$	12128.8	−	21007.7i	0.249776	−	0.432624i	0.963463	+	0.267840i	$0.0863098\pi$
$12$	−19973.2			−0.278056
$13$	99851.2	−	25184.1i	0.969635	−	0.244558i
$13$	99851.2	−	25184.1i	0.969635	−	0.244558i
$14$	−2114.88			−0.0147133
$15$	−52228.7	+	90462.7i	−0.266378	+	0.461380i
$16$	−32768.0	+	56755.8i	−0.125000	+	0.216506i
$17$	213586.	+	369942.i	0.620230	+	1.07427i	0.989443	+	0.144925i	$0.0462941\pi$
$17$	213586.	+	369942.i	0.620230	+	1.07427i	−0.369213	+	0.929345i	$0.620373\pi$
$18$	−217533.			−0.488426
$19$	474552.	+	821948.i	0.835396	+	1.44695i	0.893707	+	0.448650i	$0.148095\pi$
$19$	474552.	+	821948.i	0.835396	+	1.44695i	−0.0583109	+	0.998298i	$0.518571\pi$
$20$	171372.	+	296826.i	0.239500	+	0.414827i
$21$	10312.8			0.0115714
$22$	194061.	+	336123.i	0.176618	+	0.305911i
$23$	−486392.	+	842456.i	−0.362419	+	0.627729i	−0.988358	−	0.152143i	$-0.951383\pi$
$23$	−486392.	+	842456.i	−0.362419	+	0.627729i	0.625939	+	0.779872i	$0.284716\pi$
$24$	159786.	−	276757.i	0.0983077	−	0.170274i
$25$	−160614.			−0.0822342
$26$	−449848.	+	1.58505e6i	−0.193057	+	0.680242i
$27$	2.59643e6			0.940241
$28$	16919.1	−	29304.7i	0.00520194	−	0.00901002i
$29$	1.52289e6	−	2.63773e6i	0.399833	−	0.692531i	−0.593872	−	0.804559i	$-0.702402\pi$
$29$	1.52289e6	−	2.63773e6i	0.399833	−	0.692531i	0.993705	+	0.112029i	$0.0357349\pi$
$30$	−835659.	−	1.44740e6i	−0.188358	−	0.326245i
$31$	2.57547e6			0.500874			0.250437	−	0.968133i	$-0.419426\pi$
$31$	2.57547e6			0.500874			0.250437	+	0.968133i	$0.419426\pi$
$32$	−524288.	−	908093.i	−0.0883883	−	0.153093i
$33$	−946292.	−	1.63903e6i	−0.138903	−	0.240588i
$34$	−6.83475e6			−0.877138
$35$	−88484.5	−	153260.i	−0.00996692	−	0.0172632i
$36$	1.74026e6	−	3.01423e6i	0.172685	−	0.299099i
$37$	5.43712e6	−	9.41737e6i	0.476937	−	0.826079i	−0.522714	−	0.852508i	$-0.675080\pi$
$37$	5.43712e6	−	9.41737e6i	0.476937	−	0.826079i	0.999651	+	0.0264290i	$0.00841360\pi$
$38$	−1.51857e7			−1.18143
$39$	2.19358e6	−	7.72915e6i	0.151832	−	0.534984i
$40$	−5.48392e6			−0.338704
$41$	−6.03259e6	+	1.04488e7i	−0.333408	+	0.577480i	−0.983178	−	0.182651i	$-0.941532\pi$
$41$	−6.03259e6	+	1.04488e7i	−0.333408	+	0.577480i	0.649769	+	0.760131i	$0.274865\pi$
$42$	−82502.0	+	142898.i	−0.00409112	+	0.00708604i
$43$	1.06937e7	+	1.85221e7i	0.477004	+	0.826195i	0.999653	−	0.0263531i	$-0.00838942\pi$
$43$	1.06937e7	+	1.85221e7i	0.477004	+	0.826195i	−0.522649	+	0.852548i	$0.675056\pi$
$44$	−6.20994e6			−0.249776
$45$	−9.10136e6	−	1.57640e7i	−0.330864	−	0.573074i
$46$	−7.78228e6	−	1.34793e7i	−0.256269	−	0.443871i
$47$	−2.69913e7			−0.806833			−0.403417	−	0.915016i	$-0.632177\pi$
$47$	−2.69913e7			−0.806833			−0.403417	+	0.915016i	$0.632177\pi$
$48$	2.55657e6	+	4.42811e6i	0.0695140	+	0.120402i
$49$	2.01681e7	−	3.49321e7i	0.499784	−	0.865650i
$50$	1.28491e6	−	2.22553e6i	0.0290742	−	0.0503580i
$51$	3.33281e7			0.689835
$52$	−1.83643e7	−	1.89137e7i	−0.348305	−	0.358725i
$53$	3.73277e7			0.649815			0.324908	−	0.945746i	$-0.394667\pi$
$53$	3.73277e7			0.649815			0.324908	+	0.945746i	$0.394667\pi$
$54$	−2.07714e7	+	3.59771e7i	−0.332425	+	0.575778i
$55$	−1.62386e7	+	2.81261e7i	−0.239285	+	0.414454i
$56$	270705.	+	468875.i	0.00367833	+	0.00637105i
$57$	7.40495e7			0.929148
$58$	2.43663e7	+	4.22037e7i	0.282724	+	0.489693i
$59$	−1.74537e7	−	3.02308e7i	−0.187523	−	0.324799i	0.756901	−	0.653530i	$-0.226713\pi$
$59$	−1.74537e7	−	3.02308e7i	−0.187523	−	0.324799i	−0.944424	+	0.328730i	$0.893379\pi$
$60$	2.67411e7			0.266378
$61$	7.91644e7	+	1.37117e8i	0.732058	+	1.26796i	0.956002	+	0.293360i	$0.0947735\pi$
$61$	7.91644e7	+	1.37117e8i	0.732058	+	1.26796i	−0.223944	+	0.974602i	$0.571893\pi$
$62$	−2.06037e7	+	3.56867e7i	−0.177086	+	0.306721i
$63$	−898549.	+	1.55633e6i	−0.00718636	+	0.0124471i
$64$	1.67772e7			0.125000
$65$	−1.33685e8	+	3.37177e7i	−0.928911	+	0.234287i
$66$	3.02814e7			0.196439
$67$	−3.38204e7	+	5.85787e7i	−0.205042	+	0.355143i	−0.950146	−	0.311805i	$-0.899066\pi$
$67$	−3.38204e7	+	5.85787e7i	−0.205042	+	0.355143i	0.745104	+	0.666948i	$0.232400\pi$
$68$	5.46780e7	−	9.47051e7i	0.310115	−	0.537135i
$69$	3.79485e7	+	6.57288e7i	0.201546	+	0.349088i
$70$	2.83150e6			0.0140954
$71$	−5.73905e7	−	9.94033e7i	−0.268026	−	0.464235i	0.700326	−	0.713823i	$-0.253038\pi$
$71$	−5.73905e7	−	9.94033e7i	−0.268026	−	0.464235i	−0.968352	+	0.249588i	$0.919705\pi$
$72$	2.78442e7	+	4.82276e7i	0.122107	+	0.211495i
$73$	−1.49856e8			−0.617620			−0.308810	−	0.951124i	$-0.599931\pi$
$73$	−1.49856e8			−0.617620			−0.308810	+	0.951124i	$0.599931\pi$
$74$	8.69939e7	+	1.50678e8i	0.337245	+	0.584126i
$75$	−6.26557e6	+	1.08523e7i	−0.0228657	+	0.0396046i
$76$	1.21485e8	−	2.10419e8i	0.417698	−	0.723474i
$77$	3.20637e6			0.0103945
$78$	8.95496e7	+	9.22283e7i	0.273929	+	0.282123i
$79$	6.16681e7			0.178131			0.0890654	−	0.996026i	$-0.471612\pi$
$79$	6.16681e7			0.178131			0.0890654	+	0.996026i	$0.471612\pi$
$80$	4.38713e7	−	7.59874e7i	0.119750	−	0.207413i
$81$	−3.25161e7	+	5.63196e7i	−0.0839298	+	0.145371i
$82$	−9.65215e7	−	1.67180e8i	−0.235755	−	0.408340i
$83$	−4.82674e8			−1.11636			−0.558178	−	0.829721i	$-0.688499\pi$
$83$	−4.82674e8			−1.11636			−0.558178	+	0.829721i	$0.688499\pi$
$84$	−1.32003e6	−	2.28636e6i	−0.00289286	−	0.00501058i
$85$	−2.85959e8	−	4.95296e8i	−0.594181	−	1.02915i
$86$	−3.42200e8			−0.674585
$87$	−1.18817e8	−	2.05797e8i	−0.222352	−	0.385125i
$88$	4.96795e7	−	8.60474e7i	0.0883090	−	0.152956i
$89$	9.56598e7	−	1.65688e8i	0.161612	−	0.279921i	−0.773835	−	0.633388i	$-0.781664\pi$
$89$	9.56598e7	−	1.65688e8i	0.161612	−	0.279921i	0.935447	+	0.353467i	$0.114997\pi$
$90$	2.91244e8			0.467913
$91$	9.48204e6	+	9.76568e6i	0.0144949	+	0.0149285i
$92$	2.49033e8			0.362419
$93$	1.00470e8	−	1.74018e8i	0.139271	−	0.241225i
$94$	2.15931e8	−	3.74003e8i	0.285259	−	0.494082i
$95$	−6.35352e8	−	1.10046e9i	−0.800310	−	1.38618i
$96$	−8.18103e7			−0.0983077
$97$	5.35450e7	+	9.27427e7i	0.0614110	+	0.106367i	0.895096	−	0.445873i	$-0.147107\pi$
$97$	5.35450e7	+	9.27427e7i	0.0614110	+	0.106367i	−0.833685	+	0.552240i	$0.813773\pi$
$98$	3.22689e8	+	5.58914e8i	0.353400	+	0.612107i
$99$	3.29801e8			0.345060
$100$	2.05586e7	+	3.56085e7i	0.0205586	+	0.0356085i
$101$	−6.85605e8	+	1.18750e9i	−0.655583	+	1.13550i	0.326164	+	0.945313i	$0.394244\pi$
$101$	−6.85605e8	+	1.18750e9i	−0.655583	+	1.13550i	−0.981747	+	0.190190i	$0.939090\pi$
$102$	−2.66625e8	+	4.61808e8i	−0.243894	+	0.422436i
$103$	1.97511e9			1.72911			0.864555	−	0.502537i	$-0.167600\pi$
$103$	1.97511e9			1.72911			0.864555	+	0.502537i	$0.167600\pi$
$104$	4.08990e8	−	1.03154e8i	0.342818	−	0.0864643i
$105$	−1.38072e7			−0.0110855
$106$	−2.98622e8	+	5.17228e8i	−0.229744	+	0.397929i
$107$	−1.12729e9	+	1.95253e9i	−0.831400	+	1.44003i	0.0655277	+	0.997851i	$0.479127\pi$
$107$	−1.12729e9	+	1.95253e9i	−0.831400	+	1.44003i	−0.896928	+	0.442177i	$0.854206\pi$
$108$	−3.32343e8	−	5.75634e8i	−0.235060	−	0.407136i
$109$	6.84819e7			0.0464683			0.0232341	−	0.999730i	$-0.492604\pi$
$109$	6.84819e7			0.0464683			0.0232341	+	0.999730i	$0.492604\pi$
$110$	−2.59817e8	−	4.50017e8i	−0.169200	−	0.293063i
$111$	−4.24206e8	−	7.34747e8i	−0.265231	−	0.459393i
$112$	−8.66256e6			−0.00520194
$113$	1.34644e9	+	2.33210e9i	0.776844	+	1.34553i	0.933752	+	0.357921i	$0.116514\pi$
$113$	1.34644e9	+	2.33210e9i	0.776844	+	1.34553i	−0.156907	+	0.987613i	$0.550152\pi$
$114$	−5.92396e8	+	1.02606e9i	−0.328504	+	0.568985i
$115$	6.51205e8	−	1.12792e9i	0.347198	−	0.601365i
$116$	−7.79721e8			−0.399833
$117$	9.75305e8	+	1.00448e9i	0.481176	+	0.495570i
$118$	5.58520e8			0.265197
$119$	−2.82318e7	+	4.88990e7i	−0.0129056	+	0.0223531i
$120$	−2.13929e8	+	3.70535e8i	−0.0941789	+	0.163123i
$121$	8.84759e8	+	1.53245e9i	0.375224	+	0.649907i
$122$	−2.53326e9			−1.03529
$123$	4.70665e8	+	8.15216e8i	0.185413	+	0.321144i
$124$	−3.29660e8	−	5.70988e8i	−0.125219	−	0.216885i
$125$	2.82997e9			1.03678
$126$	−1.43768e7	−	2.49013e7i	−0.00508153	−	0.00880146i
$127$	2.39819e9	−	4.15379e9i	0.818027	−	1.41686i	−0.0891067	−	0.996022i	$-0.528401\pi$
$127$	2.39819e9	−	4.15379e9i	0.818027	−	1.41686i	0.907134	−	0.420842i	$-0.138265\pi$
$128$	−1.34218e8	+	2.32472e8i	−0.0441942	+	0.0765466i
$129$	1.66866e9			0.530536
$130$	6.02277e8	−	2.12214e9i	0.184949	−	0.651672i
$131$	−2.25488e8			−0.0668965			−0.0334483	−	0.999440i	$-0.510649\pi$
$131$	−2.25488e8			−0.0668965			−0.0334483	+	0.999440i	$0.510649\pi$
$132$	−2.42251e8	+	4.19591e8i	−0.0694517	+	0.120294i
$133$	−6.27264e7	+	1.08645e8i	−0.0173827	+	0.0301078i
$134$	−5.41126e8	−	9.37259e8i	−0.144986	−	0.251124i
$135$	−3.47622e9			−0.900752
$136$	8.74849e8	+	1.51528e9i	0.219284	+	0.379812i
$137$	−2.94085e9	−	5.09370e9i	−0.713230	−	1.23535i	−0.963638	−	0.267211i	$-0.913898\pi$
$137$	−2.94085e9	−	5.09370e9i	−0.713230	−	1.23535i	0.250408	−	0.968141i	$-0.419435\pi$
$138$	−1.21435e9			−0.285029
$139$	−2.49285e9	−	4.31773e9i	−0.566407	−	0.981046i	−0.996917	−	0.0784602i	$-0.975000\pi$
$139$	−2.49285e9	−	4.31773e9i	−0.566407	−	0.981046i	0.430510	−	0.902586i	$-0.358334\pi$
$140$	−2.26520e7	+	3.92345e7i	−0.00498346	+	0.00863161i
$141$	−1.05294e9	+	1.82374e9i	−0.224345	+	0.388577i
$142$	1.83650e9			0.379046
$143$	6.82013e8	−	2.40309e9i	0.136389	−	0.480572i
$144$	−8.91015e8			−0.172685
$145$	−2.03892e9	+	3.53151e9i	−0.383040	+	0.663445i
$146$	1.19885e9	−	2.07647e9i	0.218362	−	0.378213i
$147$	−1.57352e9	−	2.72542e9i	−0.277936	−	0.481399i
$148$	−2.78381e9			−0.476937
$149$	2.05723e9	+	3.56322e9i	0.341935	+	0.592249i	0.984792	−	0.173737i	$-0.0555843\pi$
$149$	2.05723e9	+	3.56322e9i	0.341935	+	0.592249i	−0.642857	+	0.765986i	$0.722251\pi$
$150$	−1.00249e8	−	1.73637e8i	−0.0161685	−	0.0280047i
$151$	−4.09807e9			−0.641480			−0.320740	−	0.947167i	$-0.603932\pi$
$151$	−4.09807e9			−0.641480			−0.320740	+	0.947167i	$0.603932\pi$
$152$	1.94376e9	+	3.36670e9i	0.295357	+	0.511574i
$153$	−2.90388e9	+	5.02966e9i	−0.428417	+	0.742040i
$154$	−2.56510e7	+	4.44288e7i	−0.00367503	+	0.00636533i
$155$	−3.44816e9			−0.479838
$156$	−1.99435e9	+	5.03008e8i	−0.269613	+	0.0680009i
$157$	1.11279e10			1.46173			0.730863	−	0.682524i	$-0.239118\pi$
$157$	1.11279e10			1.46173			0.730863	+	0.682524i	$0.239118\pi$
$158$	−4.93345e8	+	8.54499e8i	−0.0629787	+	0.109082i
$159$	1.45616e9	−	2.52214e9i	0.180685	−	0.312956i
$160$	7.01941e8	+	1.21580e9i	0.0846761	+	0.146663i
$161$	−1.28583e8			−0.0150823
$162$	−5.20258e8	−	9.01113e8i	−0.0593473	−	0.102793i
$163$	−6.76532e9	−	1.17179e10i	−0.750661	−	1.30018i	−0.947503	−	0.319748i	$-0.896402\pi$
$163$	−6.76532e9	−	1.17179e10i	−0.750661	−	1.30018i	0.196842	−	0.980435i	$-0.436931\pi$
$164$	3.08869e9			0.333408
$165$	1.26694e9	+	2.19441e9i	0.133070	+	0.230483i
$166$	3.86140e9	−	6.68813e9i	0.394692	−	0.683626i
$167$	−3.80270e9	+	6.58647e9i	−0.378328	+	0.655283i	−0.990819	−	0.135194i	$-0.956834\pi$
$167$	−3.80270e9	+	6.58647e9i	−0.378328	+	0.655283i	0.612491	+	0.790477i	$0.290167\pi$
$168$	4.22410e7			0.00409112
$169$	9.33602e9	−	5.02933e9i	0.880383	−	0.474264i
$170$	9.15069e9			0.840299
$171$	−6.45192e9	+	1.11751e10i	−0.577041	+	0.999464i
$172$	2.73760e9	−	4.74166e9i	0.238502	−	0.413098i
$173$	2.28915e9	+	3.96492e9i	0.194297	+	0.336532i	0.946670	−	0.322205i	$-0.104424\pi$
$173$	2.28915e9	+	3.96492e9i	0.194297	+	0.336532i	−0.752373	+	0.658737i	$0.771091\pi$
$174$	3.80214e9			0.314453
$175$	−1.06150e7	−	1.83857e7i	−0.000855555	−	0.00148186i
$176$	7.94872e8	+	1.37676e9i	0.0624439	+	0.108156i
$177$	−2.72350e9			−0.208568
$178$	1.53056e9	+	2.65100e9i	0.114277	+	0.197934i
$179$	−1.49975e9	+	2.59765e9i	−0.109190	+	0.189122i	−0.915442	−	0.402449i	$-0.868159\pi$
$179$	−1.49975e9	+	2.59765e9i	−0.109190	+	0.189122i	0.806253	+	0.591571i	$0.201492\pi$
$180$	−2.32995e9	+	4.03559e9i	−0.165432	+	0.286537i
$181$	−9.34858e9			−0.647429			−0.323714	−	0.946155i	$-0.604932\pi$
$181$	−9.34858e9			−0.647429			−0.323714	+	0.946155i	$0.604932\pi$
$182$	−2.11174e8	+	5.32615e7i	−0.0142665	+	0.00359826i
$183$	1.23529e10			0.814213
$184$	−1.99226e9	+	3.45070e9i	−0.128135	+	0.221936i
$185$	−7.27947e9	+	1.26084e10i	−0.456906	+	0.791385i
$186$	1.60751e9	+	2.78429e9i	0.0984796	+	0.170572i
$187$	1.03622e10			0.619673
$188$	3.45489e9	+	5.98404e9i	0.201708	+	0.349369i
$189$	1.71598e8	+	2.97217e8i	0.00978215	+	0.0169432i
$190$	2.03313e10			1.13181
$191$	2.54620e9	+	4.41015e9i	0.138434	+	0.239775i	0.926904	−	0.375298i	$-0.122460\pi$
$191$	2.54620e9	+	4.41015e9i	0.138434	+	0.239775i	−0.788470	+	0.615073i	$0.789126\pi$
$192$	6.54483e8	−	1.13360e9i	0.0347570	−	0.0602009i
$193$	−6.83052e9	+	1.18308e10i	−0.354361	+	0.613771i	−0.987008	−	0.160669i	$-0.948635\pi$
$193$	−6.83052e9	+	1.18308e10i	−0.354361	+	0.613771i	0.632647	+	0.774440i	$0.281968\pi$
$194$	−1.71344e9			−0.0868483
$195$	−2.93687e9	+	1.03481e10i	−0.145455	+	0.512515i
$196$	−1.03261e10			−0.499784
$197$	1.23667e9	−	2.14198e9i	0.0585001	−	0.101325i	−0.835292	−	0.549806i	$-0.814702\pi$
$197$	1.23667e9	−	2.14198e9i	0.0585001	−	0.101325i	0.893792	+	0.448481i	$0.148035\pi$
$198$	−2.63841e9	+	4.56986e9i	−0.121997	+	0.211305i
$199$	−2.17703e10	−	3.77073e10i	−0.984071	−	1.70446i	−0.645995	−	0.763342i	$-0.723557\pi$
$199$	−2.17703e10	−	3.77073e10i	−0.984071	−	1.70446i	−0.338076	−	0.941119i	$-0.609776\pi$
$200$	−6.57874e8			−0.0290742
$201$	2.63868e9	+	4.57033e9i	0.114026	+	0.197499i
$202$	−1.09697e10	−	1.90000e10i	−0.463567	−	0.802922i
$203$	4.02593e8			0.0166392
$204$	−4.26600e9	−	7.38893e9i	−0.172459	−	0.298707i
$205$	8.07672e9	−	1.39893e10i	0.319406	−	0.553227i
$206$	−1.58008e10	+	2.73679e10i	−0.611333	+	1.05886i
$207$	−1.32258e10			−0.500674
$208$	−1.84258e9	+	6.49237e9i	−0.0682560	+	0.240502i
$209$	2.30230e10			0.834647
$210$	1.10458e8	−	1.91318e8i	0.00391930	−	0.00678843i
$211$	1.13987e10	−	1.97431e10i	0.395898	−	0.685715i	−0.597318	−	0.802005i	$-0.703767\pi$
$211$	1.13987e10	−	1.97431e10i	0.395898	−	0.685715i	0.993215	+	0.116290i	$0.0371002\pi$
$212$	−4.77795e9	−	8.27564e9i	−0.162454	−	0.281378i
$213$	−8.95526e9			−0.298105
$214$	−1.80367e10	−	3.12405e10i	−0.587889	−	1.01825i
$215$	−1.43173e10	−	2.47983e10i	−0.456970	−	0.791496i
$216$	1.06350e10			0.332425
$217$	1.70213e8	+	2.94817e8i	0.00521103	+	0.00902577i
$218$	−5.47855e8	+	9.48913e8i	−0.0164290	+	0.0284559i
$219$	−5.84591e9	+	1.01254e10i	−0.171733	+	0.297450i
$220$	8.31416e9			0.239285
$221$	3.06435e10	+	3.15602e10i	0.864118	+	0.889967i
$222$	1.35746e10			0.375093
$223$	1.57607e10	−	2.72984e10i	0.426780	−	0.739205i	−0.569804	−	0.821780i	$-0.692981\pi$
$223$	1.57607e10	−	2.72984e10i	0.426780	−	0.739205i	0.996585	+	0.0825749i	$0.0263144\pi$
$224$	6.93005e7	−	1.20032e8i	0.00183916	−	0.00318552i
$225$	−1.09184e9	−	1.89112e9i	−0.0284012	−	0.0491923i
$226$	−4.30861e10			−1.09862
$227$	−2.79988e10	−	4.84954e10i	−0.699880	−	1.21223i	−0.968508	−	0.248983i	$-0.919904\pi$
$227$	−2.79988e10	−	4.84954e10i	−0.699880	−	1.21223i	0.268628	−	0.963244i	$-0.413430\pi$
$228$	−9.47833e9	−	1.64170e10i	−0.232287	−	0.402333i
$229$	5.70932e10			1.37191			0.685953	−	0.727646i	$-0.259385\pi$
$229$	5.70932e10			1.37191			0.685953	+	0.727646i	$0.259385\pi$
$230$	1.04193e10	+	1.80467e10i	0.245506	+	0.425229i
$231$	1.25081e8	−	2.16647e8i	0.00289027	−	0.00500609i
$232$	6.23777e9	−	1.08041e10i	0.141362	−	0.244847i
$233$	−6.90380e10			−1.53457			−0.767285	−	0.641306i	$-0.778393\pi$
$233$	−6.90380e10			−1.53457			−0.767285	+	0.641306i	$0.778393\pi$
$234$	−2.17209e10	+	5.47838e9i	−0.473595	+	0.119449i
$235$	3.61372e10			0.772947
$236$	−4.46816e9	+	7.73907e9i	−0.0937615	+	0.162400i
$237$	2.40569e9	−	4.16677e9i	0.0495303	−	0.0857891i
$238$	−4.51710e8	−	7.82384e8i	−0.00912563	−	0.0158061i
$239$	1.10735e10			0.219530			0.109765	−	0.993958i	$-0.464990\pi$
$239$	1.10735e10			0.219530			0.109765	+	0.993958i	$0.464990\pi$
$240$	−3.42286e9	−	5.92857e9i	−0.0665945	−	0.115345i
$241$	1.25064e10	+	2.16617e10i	0.238812	+	0.413634i	0.960374	−	0.278716i	$-0.0899087\pi$
$241$	1.25064e10	+	2.16617e10i	0.238812	+	0.413634i	−0.721562	+	0.692350i	$0.756575\pi$
$242$	−2.83123e10			−0.530647
$243$	2.80897e10	+	4.86527e10i	0.516795	+	0.895115i
$244$	2.02661e10	−	3.51019e10i	0.366029	−	0.633981i
$245$	−2.70020e10	+	4.67688e10i	−0.478793	+	0.829294i
$246$	−1.50613e10			−0.262213
$247$	6.80846e10	+	7.01213e10i	1.16389	+	1.19871i
$248$	1.05491e10			0.177086
$249$	−1.88292e10	+	3.26132e10i	−0.310410	+	0.537646i
$250$	−2.26398e10	+	3.92133e10i	−0.366558	+	0.634896i
$251$	−5.37320e9	−	9.30665e9i	−0.0854478	−	0.148000i	0.820134	−	0.572171i	$-0.193899\pi$
$251$	−5.37320e9	−	9.30665e9i	−0.0854478	−	0.148000i	−0.905582	+	0.424171i	$0.860565\pi$
$252$	4.60057e8			0.00718636
$253$	1.17987e10	+	2.04359e10i	0.181047	+	0.313583i
$254$	3.83711e10	+	6.64607e10i	0.578432	+	1.00187i
$255$	−4.46213e10			−0.660863
$256$	−2.14748e9	−	3.71955e9i	−0.0312500	−	0.0541266i
$257$	6.57134e10	−	1.13819e11i	0.939626	−	1.62748i	0.173457	−	0.984841i	$-0.444506\pi$
$257$	6.57134e10	−	1.13819e11i	0.939626	−	1.62748i	0.766169	−	0.642639i	$-0.222160\pi$
$258$	−1.33493e10	+	2.31216e10i	−0.187573	+	0.324885i
$259$	1.43736e9			0.0198480
$260$	2.45870e10	+	2.53225e10i	0.333677	+	0.343659i
$261$	4.14100e10			0.552360
$262$	1.80391e9	−	3.12446e9i	0.0236515	−	0.0409656i
$263$	−5.79281e8	+	1.00334e9i	−0.00746600	+	0.0129315i	−0.869734	−	0.493520i	$-0.835710\pi$
$263$	−5.79281e8	+	1.00334e9i	−0.00746600	+	0.0129315i	0.862268	+	0.506452i	$0.169043\pi$
$264$	−3.87601e9	−	6.71345e9i	−0.0491097	−	0.0850606i
$265$	−4.99761e10			−0.622523
$266$	−1.00362e9	−	1.73832e9i	−0.0122914	−	0.0212894i
$267$	−7.46341e9	−	1.29270e10i	−0.0898746	−	0.155667i
$268$	1.73160e10			0.205042
$269$	1.60324e10	+	2.77689e10i	0.186687	+	0.323351i	0.944144	−	0.329534i	$-0.106892\pi$
$269$	1.60324e10	+	2.77689e10i	0.186687	+	0.323351i	−0.757457	+	0.652885i	$0.773558\pi$
$270$	2.78097e10	−	4.81679e10i	0.318464	−	0.551595i
$271$	−8.17585e10	+	1.41610e11i	−0.920812	+	1.59489i	−0.122650	+	0.992450i	$0.539139\pi$
$271$	−8.17585e10	+	1.41610e11i	−0.920812	+	1.59489i	−0.798162	+	0.602443i	$0.794194\pi$
$272$	−2.79952e10			−0.310115
$273$	1.02974e9	−	2.59718e8i	0.0112201	−	0.00282989i
$274$	9.41071e10			1.00866
$275$	−1.94805e9	+	3.37412e9i	−0.0205401	+	0.0355765i
$276$	9.71482e9	−	1.68266e10i	0.100773	−	0.174544i
$277$	−6.40663e10	−	1.10966e11i	−0.653839	−	1.13248i	−0.982183	−	0.187924i	$-0.939824\pi$
$277$	−6.40663e10	−	1.10966e11i	−0.653839	−	1.13248i	0.328344	−	0.944558i	$-0.393509\pi$
$278$	7.97710e10			0.801021
$279$	1.75078e10	+	3.03244e10i	0.172987	+	0.299622i
$280$	−3.62433e8	−	6.27752e8i	−0.00352384	−	0.00610347i
$281$	−6.67853e10			−0.639003			−0.319501	−	0.947586i	$-0.603515\pi$
$281$	−6.67853e10			−0.639003			−0.319501	+	0.947586i	$0.603515\pi$
$282$	−1.68470e10	−	2.91798e10i	−0.158636	−	0.274765i
$283$	7.90167e10	−	1.36861e11i	0.732285	−	1.26835i	−0.223620	−	0.974677i	$-0.571787\pi$
$283$	7.90167e10	−	1.36861e11i	0.732285	−	1.26835i	0.955904	−	0.293678i	$-0.0948794\pi$
$284$	−1.46920e10	+	2.54472e10i	−0.134013	+	0.232118i
$285$	−9.91409e10			−0.890125
$286$	2.78421e10	+	2.86750e10i	0.246068	+	0.253429i
$287$	−1.59478e9			−0.0138750
$288$	7.12812e9	−	1.23463e10i	0.0610533	−	0.105747i
$289$	−3.19441e10	+	5.53288e10i	−0.269370	+	0.466563i
$290$	−3.26227e10	−	5.65042e10i	−0.270850	−	0.469127i
$291$	8.35521e9			0.0683028
$292$	1.91816e10	+	3.32235e10i	0.154405	+	0.267437i
$293$	−1.17203e11	−	2.03002e11i	−0.929043	−	1.60915i	−0.784926	−	0.619589i	$-0.787299\pi$
$293$	−1.17203e11	−	2.03002e11i	−0.929043	−	1.60915i	−0.144117	−	0.989561i	$-0.546034\pi$
$294$	5.03527e10			0.393061
$295$	2.33679e10	+	4.04744e10i	0.179647	+	0.311158i
$296$	2.22704e10	−	3.85735e10i	0.168623	−	0.292063i
$297$	3.14915e10	−	5.45449e10i	0.234849	−	0.406771i
$298$	−6.58313e10			−0.483570
$299$	−2.73503e10	+	9.63696e10i	−0.197898	+	0.697300i
$300$	3.20797e9			0.0228657
$301$	−1.41350e9	+	2.44826e9i	−0.00992538	+	0.0171913i
$302$	3.27846e10	−	5.67846e10i	0.226798	−	0.392825i
$303$	5.34912e10	+	9.26494e10i	0.364578	+	0.631467i
$304$	−6.22005e10			−0.417698
$305$	−1.05989e11	−	1.83578e11i	−0.701313	−	1.21471i
$306$	−4.64620e10	−	8.04746e10i	−0.302937	−	0.524702i
$307$	−5.83393e10			−0.374833			−0.187417	−	0.982281i	$-0.560011\pi$
$307$	−5.83393e10			−0.374833			−0.187417	+	0.982281i	$0.560011\pi$
$308$	−4.10415e8	−	7.10860e8i	−0.00259864	−	0.00450097i
$309$	7.70493e10	−	1.33453e11i	0.480790	−	0.832753i
$310$	2.75853e10	−	4.77791e10i	0.169648	−	0.293839i
$311$	−6.30562e9			−0.0382213			−0.0191107	−	0.999817i	$-0.506083\pi$
$311$	−6.30562e9			−0.0382213			−0.0191107	+	0.999817i	$0.506083\pi$
$312$	8.98491e9	−	3.16586e10i	0.0536807	−	0.189145i
$313$	2.01041e10			0.118396			0.0591978	−	0.998246i	$-0.481146\pi$
$313$	2.01041e10			0.118396			0.0591978	+	0.998246i	$0.481146\pi$
$314$	−8.90234e10	+	1.54193e11i	−0.516798	+	0.895120i
$315$	1.20302e9	−	2.08369e9i	0.00688454	−	0.0119244i
$316$	−7.89352e9	−	1.36720e10i	−0.0445327	−	0.0771329i
$317$	−3.31339e9			−0.0184292			−0.00921458	−	0.999958i	$-0.502933\pi$
$317$	−3.31339e9			−0.0184292			−0.00921458	+	0.999958i	$0.502933\pi$
$318$	2.32986e10	+	4.03543e10i	0.127764	+	0.221293i
$319$	−3.69417e10	−	6.39849e10i	−0.199737	−	0.345955i
$320$	−2.24621e10			−0.119750
$321$	8.79519e10	+	1.52337e11i	0.462352	+	0.800817i
$322$	1.02866e9	−	1.78170e9i	0.00533239	−	0.00923596i
$323$	−2.02715e11	+	3.51113e11i	−1.03628	+	1.79488i
$324$	1.66483e10			0.0839298
$325$	−1.60375e10	+	4.04492e9i	−0.0797372	+	0.0201110i
$326$	2.16490e11			1.06159
$327$	2.67149e9	−	4.62716e9i	0.0129208	−	0.0223795i
$328$	−2.47095e10	+	4.27981e10i	−0.117878	+	0.204170i
$329$	−1.78386e9	−	3.08973e9i	−0.00839419	−	0.0145392i
$330$	−4.05421e10			−0.188189
$331$	7.23964e10	+	1.25394e11i	0.331506	+	0.574185i	0.982807	−	0.184634i	$-0.0591100\pi$
$331$	7.23964e10	+	1.25394e11i	0.331506	+	0.574185i	−0.651302	+	0.758819i	$0.725777\pi$
$332$	6.17823e10	+	1.07010e11i	0.279089	+	0.483397i
$333$	1.47844e11			0.658878
$334$	−6.08432e10	−	1.05384e11i	−0.267518	−	0.463355i
$335$	4.52803e10	−	7.84279e10i	0.196430	−	0.340227i
$336$	−3.37928e8	+	5.85309e8i	−0.00144643	+	0.00250529i
$337$	−2.45134e10			−0.103531			−0.0517654	−	0.998659i	$-0.516485\pi$
$337$	−2.45134e10			−0.103531			−0.0517654	+	0.998659i	$0.516485\pi$
$338$	−4.99969e9	+	1.69598e11i	−0.0208362	+	0.706800i
$339$	2.10100e11			0.864026
$340$	−7.32055e10	+	1.26796e11i	−0.297090	+	0.514576i
$341$	3.12373e10	−	5.41046e10i	0.125106	−	0.216690i
$342$	−1.03231e11	−	1.78801e11i	−0.408030	−	0.706728i
$343$	1.06656e10			0.0416065
$344$	4.38016e10	+	7.58666e10i	0.168646	+	0.292104i
$345$	−5.08073e10	−	8.80008e10i	−0.193081	−	0.334426i
$346$	−7.32527e10			−0.274777
$347$	−3.93699e10	−	6.81908e10i	−0.145775	−	0.252489i	0.783887	−	0.620904i	$-0.213234\pi$
$347$	−3.93699e10	−	6.81908e10i	−0.145775	−	0.252489i	−0.929662	+	0.368414i	$0.879901\pi$
$348$	−3.04171e10	+	5.26839e10i	−0.111176	+	0.192562i
$349$	−1.81614e11	+	3.14564e11i	−0.655290	+	1.13500i	0.326531	+	0.945187i	$0.394120\pi$
$349$	−1.81614e11	+	3.14564e11i	−0.655290	+	1.13500i	−0.981821	+	0.189810i	$0.939213\pi$
$350$	3.39679e8			0.00120994
$351$	2.59256e11	−	6.53888e10i	0.911690	−	0.229943i
$352$	−2.54359e10			−0.0883090
$353$	2.85119e11	−	4.93840e11i	0.977327	−	1.69278i	0.305294	−	0.952258i	$-0.401245\pi$
$353$	2.85119e11	−	4.93840e11i	0.977327	−	1.69278i	0.672033	−	0.740521i	$-0.265421\pi$
$354$	2.17880e10	−	3.77379e10i	0.0737398	−	0.127721i
$355$	7.68371e10	+	1.33086e11i	0.256769	+	0.444738i
$356$	−4.89778e10			−0.161612
$357$	2.20266e9	+	3.81512e9i	0.00717696	+	0.0124309i
$358$	−2.39961e10	−	4.15624e10i	−0.0772087	−	0.133729i
$359$	4.97640e11			1.58121			0.790607	−	0.612324i	$-0.209765\pi$
$359$	4.97640e11			1.58121			0.790607	+	0.612324i	$0.209765\pi$
$360$	−3.72792e10	−	6.45694e10i	−0.116978	−	0.202612i
$361$	−2.89055e11	+	5.00658e11i	−0.895774	+	1.55153i
$362$	7.47886e10	−	1.29538e11i	0.228901	−	0.396468i
$363$	1.38059e11			0.417334
$364$	9.51376e8	−	3.35220e9i	0.00284051	−	0.0100086i
$365$	2.00634e11			0.591681
$366$	−9.88230e10	+	1.71166e11i	−0.287868	+	0.498602i
$367$	9.90716e10	−	1.71597e11i	0.285070	−	0.493756i	−0.687556	−	0.726131i	$-0.741316\pi$
$367$	9.90716e10	−	1.71597e11i	0.285070	−	0.493756i	0.972626	+	0.232375i	$0.0746497\pi$
$368$	−3.18762e10	−	5.52112e10i	−0.0906049	−	0.156932i
$369$	−1.64036e11			−0.460597
$370$	−1.16472e11	−	2.01735e11i	−0.323081	−	0.559594i
$371$	2.46699e9	+	4.27295e9i	0.00676060	+	0.0117097i
$372$	−5.14404e10			−0.139271
$373$	3.07776e11	+	5.33084e11i	0.823276	+	1.42596i	0.903230	+	0.429157i	$0.141189\pi$
$373$	3.07776e11	+	5.33084e11i	0.823276	+	1.42596i	−0.0799540	+	0.996799i	$0.525477\pi$
$374$	−8.28972e10	+	1.43582e11i	−0.219088	+	0.379471i
$375$	1.10398e11	−	1.91215e11i	0.288283	−	0.499322i
$376$	−1.10556e11			−0.285259
$377$	8.56338e10	−	3.01733e11i	0.218328	−	0.769284i
$378$	−5.49114e9			−0.0138340
$379$	−3.66964e11	+	6.35601e11i	−0.913582	+	1.58237i	−0.104618	+	0.994512i	$0.533362\pi$
$379$	−3.66964e11	+	6.35601e11i	−0.913582	+	1.58237i	−0.808964	+	0.587858i	$0.799971\pi$
$380$	−1.62650e11	+	2.81718e11i	−0.400155	+	0.693089i
$381$	−1.87108e11	−	3.24081e11i	−0.454915	−	0.787936i
$382$	−8.14785e10			−0.195775
$383$	−2.29603e11	−	3.97683e11i	−0.545233	−	0.944372i	−0.998592	−	0.0530437i	$-0.983108\pi$
$383$	−2.29603e11	−	3.97683e11i	−0.545233	−	0.944372i	0.453359	−	0.891328i	$-0.350226\pi$
$384$	1.04717e10	+	1.81376e10i	0.0245769	+	0.0425685i
$385$	−4.29284e9			−0.00995798
$386$	−1.09288e11	−	1.89293e11i	−0.250571	−	0.434002i
$387$	−1.45390e11	+	2.51823e11i	−0.329485	+	0.570685i
$388$	1.37075e10	−	2.37421e10i	0.0307055	−	0.0531835i
$389$	−3.60025e11			−0.797185			−0.398593	−	0.917128i	$-0.630501\pi$
$389$	−3.60025e11			−0.797185			−0.398593	+	0.917128i	$0.630501\pi$
$390$	−1.19893e11	−	1.23480e11i	−0.262424	−	0.270274i
$391$	−4.15546e11			−0.899134
$392$	8.26084e10	−	1.43082e11i	0.176700	−	0.306054i
$393$	−8.79635e9	+	1.52357e10i	−0.0186010	+	0.0322179i
$394$	1.97868e10	+	3.42717e10i	0.0413658	+	0.0716477i
$395$	−8.25642e10			−0.170649
$396$	−4.22146e10	−	7.31178e10i	−0.0862649	−	0.149415i
$397$	−4.25763e11	−	7.37443e11i	−0.860222	−	1.48995i	−0.871714	−	0.490015i	$-0.836991\pi$
$397$	−4.25763e11	−	7.37443e11i	−0.860222	−	1.48995i	0.0114918	−	0.999934i	$-0.496342\pi$
$398$	6.96651e11			1.39169
$399$	4.89394e9	+	8.47655e9i	0.00966674	+	0.0167433i
$400$	5.26299e9	−	9.11577e9i	0.0102793	−	0.0178042i
$401$	2.09280e11	−	3.62483e11i	0.404183	−	0.700065i	−0.590043	−	0.807372i	$-0.700889\pi$
$401$	2.09280e11	−	3.62483e11i	0.404183	−	0.700065i	0.994226	+	0.107307i	$0.0342227\pi$
$402$	−8.44378e10			−0.161257
$403$	2.57164e11	−	6.48609e10i	0.485665	−	0.122493i
$404$	3.51030e11			0.655583
$405$	4.35341e10	−	7.54033e10i	0.0804048	−	0.139265i
$406$	−3.22074e9	+	5.57849e9i	−0.00588286	+	0.0101894i
$407$	−1.31891e11	−	2.28442e11i	−0.238255	−	0.412669i
$408$	1.36512e11			0.243894
$409$	2.49070e11	+	4.31402e11i	0.440116	+	0.762303i	0.997698	−	0.0678191i	$-0.0216041\pi$
$409$	2.49070e11	+	4.31402e11i	0.440116	+	0.762303i	−0.557582	+	0.830122i	$0.688271\pi$
$410$	1.29227e11	+	2.23829e11i	0.225854	+	0.391190i
$411$	−4.58892e11			−0.793273
$412$	−2.52814e11	−	4.37886e11i	−0.432278	−	0.748727i
$413$	2.30704e9	−	3.99591e9i	0.00390193	−	0.00675834i
$414$	1.05806e11	−	1.83262e11i	0.177015	−	0.306599i
$415$	6.46227e11			1.06947
$416$	−7.52203e10	−	7.74705e10i	−0.123145	−	0.126828i
$417$	−3.88986e11			−0.629972
$418$	−1.84184e11	+	3.19015e11i	−0.295092	+	0.511115i
$419$	1.64219e11	−	2.84436e11i	0.260292	−	0.450839i	−0.706027	−	0.708185i	$-0.749514\pi$
$419$	1.64219e11	−	2.84436e11i	0.260292	−	0.450839i	0.966320	+	0.257345i	$0.0828478\pi$
$420$	1.76732e9	+	3.06109e9i	0.00277136	+	0.00480014i
$421$	−1.25167e11			−0.194187			−0.0970937	−	0.995275i	$-0.530955\pi$
$421$	−1.25167e11			−0.194187			−0.0970937	+	0.995275i	$0.530955\pi$
$422$	1.82379e11	+	3.15889e11i	0.279942	+	0.484873i
$423$	−1.83484e11	−	3.17804e11i	−0.278656	−	0.482646i
$424$	1.52894e11			0.229744
$425$	−3.43049e10	−	5.94177e10i	−0.0510041	−	0.0883418i
$426$	7.16421e10	−	1.24088e11i	0.105396	−	0.182552i
$427$	−1.04640e10	+	1.81241e10i	−0.0152325	+	0.0263834i
$428$	5.77174e11			0.831400
$429$	−1.35766e11	−	1.39827e11i	−0.193523	−	0.199312i
$430$	4.58153e11			0.646253
$431$	3.38827e11	−	5.86866e11i	0.472966	−	0.819202i	−0.526555	−	0.850141i	$-0.676517\pi$
$431$	3.38827e11	−	5.86866e11i	0.472966	−	0.819202i	0.999521	+	0.0309393i	$0.00984987\pi$
$432$	−8.50797e10	+	1.47362e11i	−0.117530	+	0.203568i
$433$	3.74944e11	+	6.49422e11i	0.512591	+	0.887834i	0.999893	+	0.0146003i	$0.00464758\pi$
$433$	3.74944e11	+	6.49422e11i	0.512591	+	0.887834i	−0.487302	+	0.873233i	$0.662019\pi$
$434$	−5.44681e9			−0.00736951
$435$	1.59077e11	+	2.75530e11i	0.213013	+	0.368950i
$436$	−8.76568e9	−	1.51826e10i	−0.0116171	−	0.0201214i
$437$	−9.23274e11			−1.21106
$438$	−9.35346e10	−	1.62007e11i	−0.121434	−	0.210329i
$439$	−3.54505e11	+	6.14020e11i	−0.455545	+	0.789028i	−0.998719	−	0.0505925i	$-0.983889\pi$
$439$	−3.54505e11	+	6.14020e11i	−0.455545	+	0.789028i	0.543174	+	0.839620i	$0.317222\pi$
$440$	−6.65132e10	+	1.15204e11i	−0.0846001	+	0.146532i
$441$	5.48403e11			0.690440
$442$	−6.82458e11	+	1.72127e11i	−0.850503	+	0.214511i
$443$	−1.27698e12			−1.57532			−0.787659	−	0.616112i	$-0.788707\pi$
$443$	−1.27698e12			−1.57532			−0.787659	+	0.616112i	$0.788707\pi$
$444$	−1.08597e11	+	1.88095e11i	−0.132615	+	0.229696i
$445$	−1.28074e11	+	2.21830e11i	−0.154825	+	0.268164i
$446$	2.52172e11	+	4.36774e11i	0.301779	+	0.522697i
$447$	3.21011e11			0.380309
$448$	1.10881e9	+	1.92051e9i	0.00130048	+	0.00225251i
$449$	6.75071e11	+	1.16926e12i	0.783865	+	1.35769i	0.929675	+	0.368381i	$0.120088\pi$
$449$	6.75071e11	+	1.16926e12i	0.783865	+	1.35769i	−0.145810	+	0.989313i	$0.546579\pi$
$450$	3.49388e10			0.0401654
$451$	1.46336e11	+	2.53461e11i	0.166555	+	0.288481i
$452$	3.44689e11	−	5.97018e11i	0.388422	−	0.672767i
$453$	−1.59867e11	+	2.76897e11i	−0.178368	+	0.308942i
$454$	8.95962e11			0.989779
$455$	−1.26950e10	−	1.30748e10i	−0.0138861	−	0.0143015i
$456$	3.03307e11			0.328504
$457$	2.52954e11	−	4.38129e11i	0.271280	−	0.469871i	−0.697910	−	0.716186i	$-0.745886\pi$
$457$	2.52954e11	−	4.38129e11i	0.271280	−	0.469871i	0.969190	+	0.246315i	$0.0792197\pi$
$458$	−4.56745e11	+	7.91106e11i	−0.485042	+	0.840118i
$459$	5.54561e11	+	9.60527e11i	0.583166	+	1.01007i
$460$	−3.33417e11			−0.347198
$461$	7.92556e11	+	1.37275e12i	0.817289	+	1.41559i	0.907672	+	0.419679i	$0.137857\pi$
$461$	7.92556e11	+	1.37275e12i	0.817289	+	1.41559i	−0.0903834	+	0.995907i	$0.528809\pi$
$462$	2.00130e9	+	3.46635e9i	0.00204373	+	0.00353984i
$463$	−6.78962e11			−0.686643			−0.343321	−	0.939218i	$-0.611552\pi$
$463$	−6.78962e11			−0.686643			−0.343321	+	0.939218i	$0.611552\pi$
$464$	9.98043e10	+	1.72866e11i	0.0999582	+	0.173133i
$465$	−1.34513e11	+	2.32984e11i	−0.133422	+	0.231093i
$466$	5.52304e11	−	9.56619e11i	0.542552	−	0.939728i
$467$	−1.16699e12			−1.13538			−0.567689	−	0.823243i	$-0.692162\pi$
$467$	−1.16699e12			−1.13538			−0.567689	+	0.823243i	$0.692162\pi$
$468$	9.78568e10	−	3.44801e11i	0.0942941	−	0.332248i
$469$	−8.94077e9			−0.00853291
$470$	−2.89098e11	+	5.00732e11i	−0.273278	+	0.473331i
$471$	4.34103e11	−	7.51888e11i	0.406442	−	0.703978i
$472$	−7.14905e10	−	1.23825e11i	−0.0662994	−	0.114834i
$473$	5.18809e11			0.476576
$474$	3.84910e10	+	6.66683e10i	0.0350232	+	0.0606620i
$475$	−7.62196e10	−	1.32016e11i	−0.0686982	−	0.118989i
$476$	1.44547e10			0.0129056
$477$	2.53750e11	+	4.39508e11i	0.224426	+	0.388718i
$478$	−8.85880e10	+	1.53439e11i	−0.0776156	+	0.134434i
$479$	4.79200e11	−	8.29999e11i	0.415917	−	0.720390i	−0.579607	−	0.814896i	$-0.696794\pi$
$479$	4.79200e11	−	8.29999e11i	0.415917	−	0.720390i	0.995524	+	0.0945061i	$0.0301272\pi$
$480$	1.09531e11			0.0941789
$481$	3.05735e11	−	1.07726e12i	0.260430	−	0.917634i
$482$	−4.00205e11			−0.337731
$483$	−5.01604e9	+	8.68804e9i	−0.00419372	+	0.00726373i
$484$	2.26498e11	−	3.92307e11i	0.187612	−	0.324954i
$485$	−7.16886e10	−	1.24168e11i	−0.0588318	−	0.101900i
$486$	−8.98869e11			−0.730858
$487$	−1.08232e12	−	1.87464e12i	−0.871919	−	1.51021i	−0.860009	−	0.510279i	$-0.829542\pi$
$487$	−1.08232e12	−	1.87464e12i	−0.871919	−	1.51021i	−0.0119101	−	0.999929i	$-0.503791\pi$
$488$	3.24257e11	+	5.61630e11i	0.258822	+	0.448292i
$489$	−1.05567e12			−0.834904
$490$	−4.32031e11	−	7.48300e11i	−0.338558	−	0.586399i
$491$	1.55636e11	−	2.69569e11i	0.120849	−	0.209316i	−0.799254	−	0.600994i	$-0.794772\pi$
$491$	1.55636e11	−	2.69569e11i	0.120849	−	0.209316i	0.920103	+	0.391677i	$0.128105\pi$
$492$	1.20490e11	−	2.08695e11i	0.0927063	−	0.160572i
$493$	1.30107e12			0.991953
$494$	−1.51631e12	+	3.82438e11i	−1.14555	+	0.288928i
$495$	−4.41554e11			−0.330567
$496$	−8.43929e10	+	1.46173e11i	−0.0626093	+	0.108442i
$497$	7.58589e9	−	1.31391e10i	0.00557702	−	0.00965969i
$498$	−3.01268e11	−	5.21811e11i	−0.219493	−	0.380173i
$499$	1.41915e12			1.02465			0.512325	−	0.858792i	$-0.328784\pi$
$499$	1.41915e12			1.02465			0.512325	+	0.858792i	$0.328784\pi$
$500$	−3.62237e11	−	6.27412e11i	−0.259195	−	0.448940i
$501$	2.96688e11	+	5.13879e11i	0.210393	+	0.364411i
$502$	1.71942e11			0.120841
$503$	−2.62029e11	−	4.53848e11i	−0.182513	−	0.316122i	0.760223	−	0.649662i	$-0.225090\pi$
$503$	−2.62029e11	−	4.53848e11i	−0.182513	−	0.316122i	−0.942736	+	0.333541i	$0.891756\pi$
$504$	−3.68046e9	+	6.37474e9i	−0.00254076	+	0.00440073i
$505$	9.17920e11	−	1.58988e12i	0.628049	−	1.08781i
$506$	−3.77558e11			−0.256039
$507$	2.43799e10	−	8.27008e11i	0.0163869	−	0.555871i
$508$	−1.22788e12			−0.818027
$509$	1.01441e12	−	1.75701e12i	0.669859	−	1.16023i	−0.308084	−	0.951359i	$-0.599688\pi$
$509$	1.01441e12	−	1.75701e12i	0.669859	−	1.16023i	0.977943	−	0.208871i	$-0.0669789\pi$
$510$	3.56970e11	−	6.18291e11i	0.233650	−	0.404694i
$511$	−9.90400e9	−	1.71542e10i	−0.00642564	−	0.0111295i
$512$	6.87195e10			0.0441942
$513$	1.23214e12	+	2.13413e12i	0.785474	+	1.36048i
$514$	1.05142e12	+	1.82110e12i	0.664416	+	1.15080i
$515$	−2.64436e12			−1.65649
$516$	−2.13589e11	−	3.69946e11i	−0.132634	−	0.229729i
$517$	−3.27372e11	+	5.67025e11i	−0.201527	+	0.349055i
$518$	−1.14989e10	+	1.99166e10i	−0.00701732	+	0.0121544i
$519$	3.57200e11			0.216102
$520$	−5.47576e11	+	1.38108e11i	−0.328420	+	0.0828329i
$521$	−2.41913e12			−1.43843			−0.719216	−	0.694787i	$-0.755499\pi$
$521$	−2.41913e12			−1.43843			−0.719216	+	0.694787i	$0.755499\pi$
$522$	−3.31280e11	+	5.73793e11i	−0.195289	+	0.338250i
$523$	−9.38982e10	+	1.62636e11i	−0.0548782	+	0.0950518i	−0.892159	−	0.451721i	$-0.850810\pi$
$523$	−9.38982e10	+	1.62636e11i	−0.0548782	+	0.0950518i	0.837281	+	0.546772i	$0.184144\pi$
$524$	2.88625e10	+	4.99914e10i	0.0167241	+	0.0289670i
$525$	−1.65637e9			−0.000951569
$526$	−9.26849e9	−	1.60535e10i	−0.00527926	−	0.00914395i
$527$	5.50084e11	+	9.52774e11i	0.310657	+	0.538074i
$528$	1.24032e11			0.0694517
$529$	4.27421e11	+	7.40316e11i	0.237304	+	0.411023i
$530$	3.99809e11	−	6.92489e11i	0.220095	−	0.381216i
$531$	2.37298e11	−	4.11012e11i	0.129529	−	0.224352i
$532$	3.21159e10			0.0173827
$533$	−3.39219e11	+	1.19525e12i	−0.182057	+	0.641483i
$534$	2.38829e11			0.127102
$535$	1.50927e12	−	2.61414e12i	0.796482	−	1.37955i
$536$	−1.38528e11	+	2.39938e11i	−0.0724932	+	0.125562i
$537$	1.17011e11	+	2.02670e11i	0.0607217	+	0.105173i
$538$	−5.13037e11			−0.264015
$539$	−4.89228e11	−	8.47368e11i	−0.249668	−	0.432437i
$540$	4.44956e11	+	7.70686e11i	0.225188	+	0.390037i
$541$	2.23118e12			1.11982			0.559908	−	0.828554i	$-0.310836\pi$
$541$	2.23118e12			1.11982			0.559908	+	0.828554i	$0.310836\pi$
$542$	−1.30814e12	−	2.26576e12i	−0.651112	−	1.12776i
$543$	−3.64690e11	+	6.31662e11i	−0.180022	+	0.311807i
$544$	2.23961e11	−	3.87912e11i	0.109642	−	0.189906i
$545$	−9.16868e10			−0.0445167
$546$	−4.63917e9	+	1.63462e10i	−0.00223395	+	0.00787138i
$547$	−3.74325e12			−1.78775			−0.893874	−	0.448318i	$-0.852023\pi$
$547$	−3.74325e12			−1.78775			−0.893874	+	0.448318i	$0.852023\pi$
$548$	−7.52857e11	+	1.30399e12i	−0.356615	+	0.617676i
$549$	−1.07630e12	+	1.86421e12i	−0.505661	+	0.875831i
$550$	−3.11688e10	−	5.39859e10i	−0.0145241	−	0.0251564i
$551$	2.89077e12			1.33608
$552$	1.55437e11	+	2.69225e11i	0.0712572	+	0.123421i
$553$	4.07565e9	+	7.05924e9i	0.00185325	+	0.00320992i
$554$	2.05012e12			0.924668
$555$	5.67947e11	+	9.83714e11i	0.254091	+	0.440099i
$556$	−6.38168e11	+	1.10534e12i	−0.283204	+	0.490523i
$557$	−3.39900e10	+	5.88724e10i	−0.0149625	+	0.0259157i	−0.873410	−	0.486986i	$-0.838096\pi$
$557$	−3.39900e10	+	5.88724e10i	−0.0149625	+	0.0259157i	0.858447	+	0.512902i	$0.171430\pi$
$558$	−5.60250e11			−0.244640
$559$	1.53425e12	+	1.58014e12i	0.664572	+	0.684452i
$560$	1.15978e10			0.00498346
$561$	4.04230e11	−	7.00146e11i	0.172304	−	0.298439i
$562$	5.34283e11	−	9.25405e11i	0.225922	−	0.391308i
$563$	2.19673e12	+	3.80484e12i	0.921485	+	1.59606i	0.797119	+	0.603822i	$0.206356\pi$
$563$	2.19673e12	+	3.80484e12i	0.921485	+	1.59606i	0.124365	+	0.992237i	$0.460311\pi$
$564$	5.39104e11			0.224345
$565$	−1.80268e12	−	3.12233e12i	−0.744218	−	1.28902i
$566$	1.26427e12	+	2.18978e12i	0.517804	+	0.896862i
$567$	−8.59597e9			−0.00349278
$568$	−2.35071e11	−	4.07156e11i	−0.0947616	−	0.164132i
$569$	−2.09652e12	+	3.63127e12i	−0.838480	+	1.45229i	0.0526845	+	0.998611i	$0.483222\pi$
$569$	−2.09652e12	+	3.63127e12i	−0.838480	+	1.45229i	−0.891165	+	0.453679i	$0.850111\pi$
$570$	7.93127e11	−	1.37374e12i	0.314707	−	0.545088i
$571$	9.45651e10			0.0372279			0.0186139	−	0.999827i	$-0.494075\pi$
$571$	9.45651e10			0.0372279			0.0186139	+	0.999827i	$0.494075\pi$
$572$	−6.20070e11	+	1.56392e11i	−0.242191	+	0.0610846i
$573$	3.97312e11			0.153970
$574$	1.27582e10	−	2.20979e10i	0.00490554	−	0.00849664i
$575$	7.81213e10	−	1.35310e11i	0.0298033	−	0.0516208i
$576$	1.14050e11	+	1.97540e11i	0.0431712	+	0.0747747i
$577$	1.78911e12			0.671963			0.335981	−	0.941869i	$-0.390932\pi$
$577$	1.78911e12			0.671963			0.335981	+	0.941869i	$0.390932\pi$
$578$	−5.11105e11	−	8.85260e11i	−0.190474	−	0.329910i
$579$	5.32920e11	+	9.23045e11i	0.197065	+	0.341326i
$580$	1.04393e12			0.383040
$581$	−3.19000e10	−	5.52524e10i	−0.0116144	−	0.0201168i
$582$	−6.68417e10	+	1.15773e11i	−0.0241487	+	0.0418268i
$583$	4.52740e11	−	7.84168e11i	0.162308	−	0.281126i
$584$	−6.13810e11			−0.218362
$585$	−1.30578e12	−	1.34485e12i	−0.460967	−	0.474757i
$586$	3.75051e12			1.31387
$587$	1.36650e12	−	2.36684e12i	0.475048	−	0.822807i	−0.524544	−	0.851383i	$-0.675764\pi$
$587$	1.36650e12	−	2.36684e12i	0.475048	−	0.822807i	0.999592	+	0.0285766i	$0.00909745\pi$
$588$	−4.02821e11	+	6.97707e11i	−0.138968	+	0.240699i
$589$	1.22219e12	+	2.11690e12i	0.418428	+	0.724739i
$590$	−7.47772e11			−0.254059
$591$	−9.64856e10	−	1.67118e11i	−0.0325326	−	0.0563482i
$592$	3.56327e11	+	6.17177e11i	0.119234	+	0.206520i
$593$	5.86251e11			0.194687			0.0973436	−	0.995251i	$-0.468965\pi$
$593$	5.86251e11			0.194687			0.0973436	+	0.995251i	$0.468965\pi$
$594$	5.03864e11	+	8.72718e11i	0.166064	+	0.287630i
$595$	3.77981e10	−	6.54683e10i	0.0123636	−	0.0214143i
$596$	5.26650e11	−	9.12185e11i	0.170968	−	0.296125i
$597$	−3.39706e12			−1.09451
$598$	−1.11653e12	−	1.14993e12i	−0.357040	−	0.367720i
$599$	−3.70853e12			−1.17701			−0.588506	−	0.808493i	$-0.700284\pi$
$599$	−3.70853e12			−1.17701			−0.588506	+	0.808493i	$0.700284\pi$
$600$	−2.56638e10	+	4.44510e10i	−0.00808426	+	0.0140023i
$601$	6.51346e11	−	1.12816e12i	0.203646	−	0.352726i	−0.746054	−	0.665885i	$-0.768054\pi$
$601$	6.51346e11	−	1.12816e12i	0.203646	−	0.352726i	0.949701	+	0.313159i	$0.101387\pi$
$602$	−2.26160e10	−	3.91721e10i	−0.00701830	−	0.0121561i
$603$	−9.19632e11			−0.283261
$604$	5.24553e11	+	9.08553e11i	0.160370	+	0.277769i
$605$	−1.18456e12	−	2.05171e12i	−0.359465	−	0.622612i
$606$	−1.71172e12			−0.515591
$607$	−2.11725e12	−	3.66719e12i	−0.633029	−	1.09644i	−0.986929	−	0.161155i	$-0.948478\pi$
$607$	−2.11725e12	−	3.66719e12i	−0.633029	−	1.09644i	0.353901	−	0.935283i	$-0.384855\pi$
$608$	4.97604e11	−	8.61875e11i	0.147679	−	0.255787i
$609$	1.57052e10	−	2.72022e10i	0.00462664	−	0.00801358i
$610$	3.39165e12			0.991806
$611$	−2.69511e12	+	6.79753e11i	−0.782333	+	0.197317i
$612$	1.48679e12			0.428417
$613$	2.87157e8	−	4.97371e8i	8.21386e−5	−	0.000142268i	−0.865984	−	0.500071i	$-0.833307\pi$
$613$	2.87157e8	−	4.97371e8i	8.21386e−5	−	0.000142268i	0.866066	+	0.499929i	$0.166641\pi$
$614$	4.66714e11	−	8.08372e11i	0.132524	−	0.229538i
$615$	−6.30149e11	−	1.09145e12i	−0.177625	−	0.307656i
$616$	1.31333e10			0.00367503
$617$	3.25733e11	+	5.64186e11i	0.0904854	+	0.156725i	0.907715	−	0.419586i	$-0.137825\pi$
$617$	3.25733e11	+	5.64186e11i	0.0904854	+	0.156725i	−0.817230	+	0.576312i	$0.804491\pi$
$618$	1.23279e12	+	2.13525e12i	0.339970	+	0.588845i
$619$	−2.12694e12			−0.582301			−0.291150	−	0.956677i	$-0.594038\pi$
$619$	−2.12694e12			−0.582301			−0.291150	+	0.956677i	$0.594038\pi$
$620$	4.41364e11	+	7.64465e11i	0.119959	+	0.207776i
$621$	−1.26288e12	+	2.18738e12i	−0.340762	+	0.590216i
$622$	5.04449e10	−	8.73732e10i	0.0135133	−	0.0234057i
$623$	2.52887e10			0.00672558
$624$	3.66795e11	+	3.77767e11i	0.0968485	+	0.0997456i
$625$	−3.47520e12			−0.911003
$626$	−1.60833e11	+	2.78571e11i	−0.0418592	+	0.0725022i
$627$	8.98130e11	−	1.55561e12i	0.232079	−	0.401972i
$628$	−1.42437e12	−	2.46709e12i	−0.365431	−	0.632946i
$629$	4.64517e12			1.18324
$630$	1.92483e10	+	3.33391e10i	0.00486811	+	0.00843181i
$631$	−1.06181e12	−	1.83911e12i	−0.266634	−	0.461824i	0.701356	−	0.712811i	$-0.252578\pi$
$631$	−1.06181e12	−	1.83911e12i	−0.266634	−	0.461824i	−0.967990	+	0.250987i	$0.919245\pi$
$632$	2.52593e11			0.0629787
$633$	−8.89328e11	−	1.54036e12i	−0.220163	−	0.381334i
$634$	2.65071e10	−	4.59117e10i	0.00651570	−	0.0112855i
$635$	−3.21082e12	+	5.56130e12i	−0.783671	+	1.35736i
$636$	−7.45554e11			−0.180685
$637$	1.13407e12	−	3.99593e12i	0.272906	−	0.961591i
$638$	1.18213e12			0.282471
$639$	7.80271e11	−	1.35147e12i	0.185136	−	0.320665i
$640$	1.79697e11	−	3.11244e11i	0.0423381	−	0.0733317i
$641$	−4.44285e11	−	7.69524e11i	−0.103944	−	0.180037i	0.809362	−	0.587310i	$-0.199813\pi$
$641$	−4.44285e11	−	7.69524e11i	−0.103944	−	0.180037i	−0.913306	+	0.407273i	$0.866480\pi$
$642$	−2.81446e12			−0.653864
$643$	2.87600e12	+	4.98137e12i	0.663497	+	1.14921i	0.979691	+	0.200516i	$0.0642617\pi$
$643$	2.87600e12	+	4.98137e12i	0.663497	+	1.14921i	−0.316194	+	0.948695i	$0.602405\pi$
$644$	1.64586e10	+	2.85071e10i	0.00377057	+	0.00653081i
$645$	−2.23408e12			−0.508254
$646$	−3.24345e12	−	5.61781e12i	−0.732758	−	1.26917i
$647$	2.24297e12	−	3.88494e12i	0.503216	−	0.871595i	−0.496777	−	0.867878i	$-0.665483\pi$
$647$	2.24297e12	−	3.88494e12i	0.503216	−	0.871595i	0.999993	−	0.00371729i	$-0.00118325\pi$
$648$	−1.33186e11	+	2.30685e11i	−0.0296737	+	0.0513963i
$649$	−8.46770e11			−0.187355
$650$	7.22517e10	−	2.54581e11i	0.0158759	−	0.0559392i
$651$	2.65602e10			0.00579584
$652$	−1.73192e12	+	2.99977e12i	−0.375330	+	0.650091i
$653$	1.38296e12	−	2.39535e12i	0.297645	−	0.515537i	−0.677951	−	0.735107i	$-0.737132\pi$
$653$	1.38296e12	−	2.39535e12i	0.297645	−	0.515537i	0.975597	+	0.219570i	$0.0704653\pi$
$654$	4.27439e10	+	7.40346e10i	0.00913638	+	0.0158247i
$655$	3.01895e11			0.0640869
$656$	−3.95352e11	−	6.84770e11i	−0.0833521	−	0.144370i
$657$	−1.01871e12	−	1.76445e12i	−0.213307	−	0.369459i
$658$	5.70835e10			0.0118712
$659$	3.68725e12	+	6.38650e12i	0.761584	+	1.31910i	0.942034	+	0.335518i	$0.108911\pi$
$659$	3.68725e12	+	6.38650e12i	0.761584	+	1.31910i	−0.180450	+	0.983584i	$0.557755\pi$
$660$	3.24337e11	−	5.61768e11i	0.0665348	−	0.115242i
$661$	−3.54859e11	+	6.14634e11i	−0.0723019	+	0.125230i	−0.899910	−	0.436076i	$-0.856368\pi$
$661$	−3.54859e11	+	6.14634e11i	−0.0723019	+	0.125230i	0.827608	+	0.561307i	$0.189701\pi$
$662$	−2.31669e12			−0.468820
$663$	3.32785e12	−	8.39340e11i	0.668888	−	0.168705i
$664$	−1.97703e12			−0.394692
$665$	8.39810e10	−	1.45459e11i	0.0166527	−	0.0288433i
$666$	−1.18275e12	+	2.04859e12i	−0.232949	+	0.403479i
$667$	1.48145e12	+	2.56594e12i	0.289814	+	0.501973i
$668$	1.94698e12			0.378328
$669$	−1.22966e12	−	2.12983e12i	−0.237338	−	0.411081i
$670$	7.24486e11	+	1.25485e12i	0.138897	+	0.240577i
$671$	3.84067e12			0.731401
$672$	−5.40685e9	−	9.36494e9i	−0.00102278	−	0.00177151i
$673$	2.54891e12	−	4.41483e12i	0.478945	−	0.829558i	−0.520763	−	0.853701i	$-0.674353\pi$
$673$	2.54891e12	−	4.41483e12i	0.478945	−	0.829558i	0.999709	+	0.0241436i	$0.00768588\pi$
$674$	1.96108e11	−	3.39668e11i	0.0366037	−	0.0633994i
$675$	−4.17022e11			−0.0773200
$676$	−2.31003e12	−	1.42606e12i	−0.425458	−	0.262651i
$677$	9.32854e11			0.170673			0.0853365	−	0.996352i	$-0.472803\pi$
$677$	9.32854e11			0.170673			0.0853365	+	0.996352i	$0.472803\pi$
$678$	−1.68080e12	+	2.91123e12i	−0.305479	+	0.529105i
$679$	−7.07759e9	+	1.22587e10i	−0.00127783	+	0.00221326i
$680$	−1.17129e12	−	2.02873e12i	−0.210075	−	0.363860i
$681$	−4.36896e12			−0.778423
$682$	4.99797e11	+	8.65673e11i	0.0884634	+	0.153223i
$683$	1.42575e12	+	2.46948e12i	0.250698	+	0.434222i	0.963718	−	0.266922i	$-0.0860065\pi$
$683$	1.42575e12	+	2.46948e12i	0.250698	+	0.434222i	−0.713020	+	0.701144i	$0.752673\pi$
$684$	3.30338e12			0.577041
$685$	3.93734e12	+	6.81968e12i	0.683275	+	1.18347i
$686$	−8.53247e10	+	1.47787e11i	−0.0147101	+	0.0254787i
$687$	2.22722e12	−	3.85765e12i	0.381467	−	0.660720i
$688$	−1.40165e12			−0.238502
$689$	3.72721e12	−	9.40066e11i	0.630083	−	0.158917i
$690$	1.62583e12			0.273058
$691$	−3.86220e12	+	6.68952e12i	−0.644441	+	1.11620i	0.339989	+	0.940429i	$0.389577\pi$
$691$	−3.86220e12	+	6.68952e12i	−0.644441	+	1.11620i	−0.984430	+	0.175775i	$0.943757\pi$
$692$	5.86021e11	−	1.01502e12i	0.0971485	−	0.168266i
$693$	2.17966e10	+	3.77528e10i	0.00358996	+	0.00621799i
$694$	1.25984e12			0.206157
$695$	3.33754e12	+	5.78079e12i	0.542619	+	0.939843i
$696$	−4.86673e11	−	8.42943e11i	−0.0786133	−	0.136162i
$697$	−5.15391e12			−0.827160
$698$	−2.90582e12	−	5.03302e12i	−0.463360	−	0.802563i
$699$	−2.69319e12	+	4.66474e12i	−0.426697	+	0.739060i
$700$	−2.71743e9	+	4.70673e9i	−0.000427777	+	0.000740932i
$701$	9.46243e12			1.48003			0.740017	−	0.672588i	$-0.234817\pi$
$701$	9.46243e12			1.48003			0.740017	+	0.672588i	$0.234817\pi$
$702$	−1.16800e12	+	4.11547e12i	−0.181520	+	0.639591i
$703$	1.03208e13			1.59373
$704$	2.03487e11	−	3.52450e11i	0.0312220	−	0.0540780i
$705$	1.40972e12	−	2.44171e12i	0.214923	−	0.372257i
$706$	4.56190e12	+	7.90145e12i	0.691074	+	1.19698i
$707$	−1.81247e11			−0.0272824
$708$	3.48607e11	+	6.03806e11i	0.0521419	+	0.0903124i
$709$	−5.70237e12	−	9.87680e12i	−0.847515	−	1.46794i	−0.883419	−	0.468584i	$-0.844764\pi$
$709$	−5.70237e12	−	9.87680e12i	−0.847515	−	1.46794i	0.0359036	−	0.999355i	$-0.488569\pi$
$710$	−2.45879e12			−0.363127
$711$	4.19214e11	+	7.26100e11i	0.0615209	+	0.106557i
$712$	3.91823e11	−	6.78656e11i	0.0571386	−	0.0989669i
$713$	−1.25269e12	+	2.16972e12i	−0.181526	+	0.314413i
$714$	−7.04851e10			−0.0101498
$715$	−9.13112e11	+	3.21737e12i	−0.130661	+	0.460388i
$716$	7.67874e11			0.109190
$717$	4.31979e11	−	7.48210e11i	0.0610417	−	0.105727i
$718$	−3.98112e12	+	6.89551e12i	−0.559044	+	0.968292i
$719$	−2.24794e12	−	3.89355e12i	−0.313694	−	0.543333i	0.665465	−	0.746429i	$-0.268233\pi$
$719$	−2.24794e12	−	3.89355e12i	−0.313694	−	0.543333i	−0.979159	+	0.203096i	$0.934900\pi$
$720$	1.19293e12			0.165432
$721$	1.30535e11	+	2.26093e11i	0.0179895	+	0.0311587i
$722$	−4.62488e12	−	8.01054e12i	−0.633408	−	1.09709i
$723$	1.95151e12			0.265612
$724$	1.19662e12	+	2.07260e12i	0.161857	+	0.280345i
$725$	−2.44598e11	+	4.23655e11i	−0.0328799	+	0.0569497i
$726$	−1.10447e12	+	1.91299e12i	−0.147550	+	0.255564i
$727$	−4.49807e11			−0.0597203			−0.0298601	−	0.999554i	$-0.509506\pi$
$727$	−4.49807e11			−0.0597203			−0.0298601	+	0.999554i	$0.509506\pi$
$728$	3.88384e10	+	4.00002e10i	0.00512472	+	0.00527802i
$729$	3.10310e12			0.406932
$730$	−1.60507e12	+	2.78007e12i	−0.209191	+	0.362329i
$731$	−4.56807e12	+	7.91213e12i	−0.591704	+	1.02486i
$732$	−1.58117e12	−	2.73866e12i	−0.203553	−	0.352565i
$733$	−1.37779e13			−1.76285			−0.881424	−	0.472326i	$-0.843415\pi$
$733$	−1.37779e13			−1.76285			−0.881424	+	0.472326i	$0.843415\pi$
$734$	1.58515e12	+	2.74555e12i	0.201575	+	0.349138i
$735$	2.10670e12	+	3.64892e12i	0.266263	+	0.461181i
$736$	1.02004e12			0.128135
$737$	8.20401e11	+	1.42098e12i	0.102429	+	0.177412i
$738$	1.31229e12	−	2.27295e12i	0.162845	−	0.282057i
$739$	−6.93321e12	+	1.20087e13i	−0.855135	+	1.48114i	0.0213855	+	0.999771i	$0.493192\pi$
$739$	−6.93321e12	+	1.20087e13i	−0.855135	+	1.48114i	−0.876520	+	0.481365i	$0.840141\pi$
$740$	3.72709e12			0.456906
$741$	7.39393e12	−	1.86487e12i	0.900935	−	0.227231i
$742$	−7.89437e10			−0.00956093
$743$	5.27145e12	−	9.13042e12i	0.634571	−	1.09911i	−0.352035	−	0.935987i	$-0.614510\pi$
$743$	5.27145e12	−	9.13042e12i	0.634571	−	1.09911i	0.986606	−	0.163122i	$-0.0521565\pi$
$744$	4.11523e11	−	7.12779e11i	0.0492398	−	0.0852858i
$745$	−2.75431e12	−	4.77061e12i	−0.327574	−	0.567376i
$746$	−9.84884e12			−1.16429
$747$	−3.28118e12	−	5.68317e12i	−0.385556	−	0.667802i
$748$	−1.32636e12	−	2.29732e12i	−0.154918	−	0.268326i
$749$	−2.98012e11			−0.0345991
$750$	1.76636e12	+	3.05943e12i	0.203847	+	0.353074i
$751$	3.75741e12	−	6.50803e12i	0.431032	−	0.746569i	−0.565931	−	0.824453i	$-0.691483\pi$
$751$	3.75741e12	−	6.50803e12i	0.431032	−	0.746569i	0.996962	+	0.0778840i	$0.0248164\pi$
$752$	8.84451e11	−	1.53191e12i	0.100854	−	0.174684i
$753$	−8.38438e11			−0.0950372
$754$	3.49587e12	+	3.60044e12i	0.393898	+	0.405681i
$755$	5.48669e12			0.614539
$756$	4.39291e10	−	7.60874e10i	0.00489107	−	0.00847159i
$757$	−6.00176e11	+	1.03954e12i	−0.0664274	+	0.115056i	−0.897326	−	0.441368i	$-0.854493\pi$
$757$	−6.00176e11	+	1.03954e12i	−0.0664274	+	0.115056i	0.830899	+	0.556423i	$0.187827\pi$
$758$	−5.87143e12	−	1.01696e13i	−0.646000	−	1.11890i
$759$	1.84108e12			0.201365
$760$	−2.60240e12	−	4.50750e12i	−0.282952	−	0.490088i
$761$	−5.50082e12	−	9.52770e12i	−0.594561	−	1.02981i	−0.993609	−	0.112880i	$-0.963992\pi$
$761$	−5.50082e12	−	9.52770e12i	−0.594561	−	1.02981i	0.399047	−	0.916930i	$-0.369341\pi$
$762$	5.98746e12			0.643347
$763$	4.52598e9	+	7.83922e9i	0.000483450	+	0.000837360i
$764$	6.51828e11	−	1.12900e12i	0.0692170	−	0.119887i
$765$	3.88785e12	−	6.73395e12i	0.410424	−	0.710875i
$766$	7.34728e12			0.771076
$767$	−2.50411e12	−	2.57902e12i	−0.261261	−	0.269076i
$768$	−3.35095e11			−0.0347570
$769$	−3.02076e12	+	5.23212e12i	−0.311493	+	0.539522i	−0.978686	−	0.205363i	$-0.934162\pi$
$769$	−3.02076e12	+	5.23212e12i	−0.311493	+	0.539522i	0.667193	+	0.744885i	$0.267496\pi$
$770$	3.43427e10	−	5.94833e10i	0.00352068	−	0.00609799i
$771$	−5.12699e12	−	8.88020e12i	−0.522538	−	0.905062i
$772$	3.49723e12			0.354361
$773$	−2.06874e12	−	3.58316e12i	−0.208400	−	0.360960i	0.742810	−	0.669502i	$-0.233492\pi$
$773$	−2.06874e12	−	3.58316e12i	−0.208400	−	0.360960i	−0.951211	+	0.308542i	$0.900159\pi$
$774$	−2.32624e12	−	4.02917e12i	−0.232981	−	0.403535i
$775$	−4.13656e11			−0.0411890
$776$	2.19320e11	+	3.79874e11i	0.0217121	+	0.0376064i
$777$	5.60717e10	−	9.71190e10i	0.00551885	−	0.00955893i
$778$	2.88020e12	−	4.98865e12i	0.281848	−	0.488174i
$779$	−1.14511e13			−1.11411
$780$	2.67013e12	−	6.73451e11i	0.258289	−	0.0651449i
$781$	−2.78431e12			−0.267786
$782$	3.32437e12	−	5.75798e12i	0.317892	−	0.550605i
$783$	3.95408e12	−	6.84867e12i	0.375939	−	0.651146i
$784$	1.32173e12	+	2.28931e12i	0.124946	+	0.216413i
$785$	−1.48986e13			−1.40033
$786$	−1.40742e11	−	2.43772e11i	−0.0131529	−	0.0227815i
$787$	−2.48626e11	−	4.30634e11i	−0.0231026	−	0.0400149i	0.854243	−	0.519874i	$-0.174021\pi$
$787$	−2.48626e11	−	4.30634e11i	−0.0231026	−	0.0400149i	−0.877346	+	0.479859i	$0.840688\pi$
$788$	−6.33176e11			−0.0585001
$789$	4.51957e10	+	7.82813e10i	0.00415194	+	0.00719136i
$790$	6.60513e11	−	1.14404e12i	0.0603337	−	0.104501i
$791$	−1.77973e11	+	3.08258e11i	−0.0161644	+	0.0279975i
$792$	1.35087e12			0.121997
$793$	1.13578e13	+	1.16976e13i	1.01992	+	1.05043i
$794$	1.36244e13			1.21654
$795$	−1.94958e12	+	3.37677e12i	−0.173096	+	0.299812i
$796$	−5.57321e12	+	9.65308e12i	−0.492035	+	0.852230i
$797$	−1.28059e12	−	2.21804e12i	−0.112421	−	0.194718i	0.804325	−	0.594190i	$-0.202527\pi$
$797$	−1.28059e12	−	2.21804e12i	−0.112421	−	0.194718i	−0.916746	+	0.399471i	$0.869194\pi$
$798$	−1.56606e11			−0.0136708
$799$	−5.76497e12	−	9.98522e12i	−0.500422	−	0.866756i
$800$	8.42079e10	+	1.45852e11i	0.00726855	+	0.0125895i
$801$	2.60115e12			0.223264
$802$	3.34848e12	+	5.79973e12i	0.285800	+	0.495021i
$803$	−1.81757e12	+	3.14813e12i	−0.154266	+	0.267197i
$804$	6.75502e11	−	1.17000e12i	0.0570131	−	0.0987496i
$805$	1.72153e11			0.0144488
$806$	−1.15857e12	+	4.08225e12i	−0.0966973	+	0.340716i
$807$	2.50171e12			0.207637
$808$	−2.80824e12	+	4.86401e12i	−0.231784	+	0.401461i
$809$	2.70377e11	−	4.68307e11i	0.0221923	−	0.0384381i	−0.854716	−	0.519096i	$-0.826269\pi$
$809$	2.70377e11	−	4.68307e11i	0.0221923	−	0.0384381i	0.876908	+	0.480658i	$0.159602\pi$
$810$	6.96546e11	+	1.20645e12i	0.0568548	+	0.0984754i
$811$	−1.95940e12			−0.159048			−0.0795242	−	0.996833i	$-0.525340\pi$
$811$	−1.95940e12			−0.159048			−0.0795242	+	0.996833i	$0.525340\pi$
$812$	−5.15318e10	−	8.92558e10i	−0.00415981	−	0.00720500i
$813$	6.37883e12	+	1.10485e13i	0.512075	+	0.886940i
$814$	4.22052e12			0.336943
$815$	9.05772e12	+	1.56884e13i	0.719134	+	1.24558i
$816$	−1.09210e12	+	1.89157e12i	−0.0862294	+	0.149354i
$817$	−1.01495e13	+	1.75794e13i	−0.796975	+	1.38040i
$818$	−7.97025e12			−0.622418
$819$	−5.05263e10	+	1.78031e11i	−0.00392410	+	0.0138267i
$820$	−4.13528e12			−0.319406
$821$	−1.04876e13	+	1.81650e13i	−0.805620	+	1.39538i	0.110251	+	0.993904i	$0.464835\pi$
$821$	−1.04876e13	+	1.81650e13i	−0.805620	+	1.39538i	−0.915871	+	0.401472i	$0.868499\pi$
$822$	3.67114e12	−	6.35860e12i	0.280464	−	0.485778i
$823$	−3.78409e12	−	6.55423e12i	−0.287516	−	0.497992i	0.685700	−	0.727884i	$-0.259496\pi$
$823$	−3.78409e12	−	6.55423e12i	−0.287516	−	0.497992i	−0.973216	+	0.229892i	$0.926163\pi$
$824$	8.09003e12			0.611333
$825$	1.51988e11	+	2.63250e11i	0.0114226	+	0.0197845i
$826$	3.69126e10	+	6.39345e10i	0.00275908	+	0.00477887i
$827$	3.34596e12			0.248740			0.124370	−	0.992236i	$-0.460309\pi$
$827$	3.34596e12			0.248740			0.124370	+	0.992236i	$0.460309\pi$
$828$	1.69290e12	+	2.93219e12i	0.125169	+	0.216798i
$829$	−2.55248e12	+	4.42103e12i	−0.187701	+	0.325108i	−0.944483	−	0.328559i	$-0.893437\pi$
$829$	−2.55248e12	+	4.42103e12i	−0.187701	+	0.325108i	0.756782	+	0.653667i	$0.226770\pi$
$830$	−5.16982e12	+	8.95439e12i	−0.378115	+	0.654914i
$831$	−9.99696e12			−0.727216
$832$	1.67522e12	−	4.22520e11i	0.121204	−	0.0305698i
$833$	1.72305e13			1.23992
$834$	3.11188e12	−	5.38994e12i	0.222729	−	0.385777i
$835$	5.09124e12	−	8.81828e12i	0.362438	−	0.627762i
$836$	−2.94694e12	−	5.10425e12i	−0.208662	−	0.361413i
$837$	6.68701e12			0.470942
$838$	2.62751e12	+	4.55098e12i	0.184054	+	0.318792i
$839$	−9.81574e12	−	1.70014e13i	−0.683903	−	1.18455i	−0.973780	−	0.227490i	$-0.926948\pi$
$839$	−9.81574e12	−	1.70014e13i	−0.683903	−	1.18455i	0.289878	−	0.957064i	$-0.406385\pi$
$840$	−5.65543e10			−0.00391930
$841$	2.61517e12	+	4.52960e12i	0.180267	+	0.312232i
$842$	1.00134e12	−	1.73437e12i	0.0686556	−	0.118915i
$843$	−2.60531e12	+	4.51253e12i	−0.177679	+	0.307748i
$844$	−5.83611e12			−0.395898
$845$	−1.24995e13	+	6.73350e12i	−0.843407	+	0.454345i
$846$	5.87150e12			0.394078
$847$	−1.16948e11	+	2.02559e11i	−0.00780757	+	0.0135231i
$848$	−1.22315e12	+	2.11856e12i	−0.0812269	+	0.140689i
$849$	−6.16492e12	−	1.06779e13i	−0.407233	−	0.705348i
$850$	1.09776e12			0.0721307
$851$	5.28915e12	+	9.16107e12i	0.345703	+	0.598774i
$852$	1.14627e12	+	1.98540e12i	0.0745264	+	0.129083i
$853$	1.41852e13			0.917411			0.458706	−	0.888588i	$-0.348313\pi$
$853$	1.41852e13			0.917411			0.458706	+	0.888588i	$0.348313\pi$
$854$	−1.67423e11	−	2.89986e11i	−0.0107710	−	0.0186559i
$855$	8.63814e12	−	1.49617e13i	0.552806	−	0.957488i
$856$	−4.61740e12	+	7.99756e12i	−0.293944	+	0.509127i
$857$	3.06579e13			1.94146			0.970732	−	0.240167i	$-0.0772021\pi$
$857$	3.06579e13			1.94146			0.970732	+	0.240167i	$0.0772021\pi$
$858$	3.02363e12	−	7.62610e11i	0.190474	−	0.0480407i
$859$	1.13754e13			0.712848			0.356424	−	0.934324i	$-0.383996\pi$
$859$	1.13754e13			0.712848			0.356424	+	0.934324i	$0.383996\pi$
$860$	−3.66523e12	+	6.34836e12i	−0.228485	+	0.395748i
$861$	−6.22126e10	+	1.07755e11i	−0.00385802	+	0.00668228i
$862$	5.42123e12	+	9.38985e12i	0.334438	+	0.579263i
$863$	1.07114e13			0.657349			0.328675	−	0.944443i	$-0.393398\pi$
$863$	1.07114e13			0.657349			0.328675	+	0.944443i	$0.393398\pi$
$864$	−1.36128e12	−	2.35780e12i	−0.0831063	−	0.143944i
$865$	−3.06482e12	−	5.30842e12i	−0.186137	−	0.322398i
$866$	−1.19982e13			−0.724913
$867$	2.49229e12	+	4.31677e12i	0.149800	+	0.259462i
$868$	4.35745e10	−	7.54733e10i	0.00260552	−	0.00451289i
$869$	7.47959e11	−	1.29550e12i	0.0444927	−	0.0770636i
$870$	−5.09048e12			−0.301246
$871$	−1.90175e12	+	6.70089e12i	−0.111963	+	0.394503i
$872$	2.80502e11			0.0164290
$873$	−7.27988e11	+	1.26091e12i	−0.0424190	+	0.0734718i
$874$	7.38619e12	−	1.27933e13i	0.428173	−	0.741617i
$875$	1.87033e11	+	3.23951e11i	0.0107865	+	0.0186828i
$876$	2.99311e12			0.171733
$877$	1.85175e12	+	3.20733e12i	0.105702	+	0.183082i	0.914025	−	0.405658i	$-0.132958\pi$
$877$	1.85175e12	+	3.20733e12i	0.105702	+	0.183082i	−0.808323	+	0.588740i	$0.799624\pi$
$878$	−5.67207e12	−	9.82432e12i	−0.322119	−	0.557927i
$879$	−1.82885e13			−1.03330
$880$	−1.06421e12	−	1.84327e12i	−0.0598213	−	0.103614i
$881$	8.93063e12	−	1.54683e13i	0.499449	−	0.865070i	−0.500551	−	0.865707i	$-0.666869\pi$
$881$	8.93063e12	−	1.54683e13i	0.499449	−	0.865070i	1.00000		0.000636653i	$0.000202653\pi$
$882$	−4.38722e12	+	7.59889e12i	−0.244107	+	0.422806i
$883$	−1.97547e13			−1.09357			−0.546785	−	0.837273i	$-0.684149\pi$
$883$	−1.97547e13			−1.09357			−0.546785	+	0.837273i	$0.684149\pi$
$884$	3.07460e12	−	1.08334e13i	0.169338	−	0.596666i
$885$	3.64634e12			0.199808
$886$	1.02159e13	−	1.76944e13i	0.556959	−	0.964681i
$887$	−8.44834e12	+	1.46330e13i	−0.458263	+	0.793736i	−0.998869	−	0.0475404i	$-0.984862\pi$
$887$	−8.44834e12	+	1.46330e13i	−0.458263	+	0.793736i	0.540606	+	0.841276i	$0.318195\pi$
$888$	−1.73755e12	−	3.00952e12i	−0.0937732	−	0.162420i
$889$	6.33988e11			0.0340426
$890$	−2.04918e12	−	3.54929e12i	−0.109478	−	0.189621i
$891$	7.88762e11	+	1.36618e12i	0.0419272	+	0.0726201i
$892$	−8.06950e12			−0.426780
$893$	−1.28088e13	−	2.21855e13i	−0.674025	−	1.16745i
$894$	−2.56809e12	+	4.44806e12i	−0.134460	+	0.232891i
$895$	2.00794e12	−	3.47786e12i	0.104604	−	0.181179i
$896$	−3.54818e10			−0.00183916
$897$	5.44453e12	+	5.60739e12i	0.280798	+	0.289198i
$898$	−2.16023e13			−1.10855
$899$	3.92216e12	−	6.79338e12i	0.200266	−	0.346871i
$900$	−2.79510e11	+	4.84126e11i	−0.0142006	+	0.0245962i
$901$	7.97268e12	+	1.38091e13i	0.403035	+	0.698077i
$902$	−4.68275e12			−0.235544
$903$	1.10282e11	+	1.91014e11i	0.00551963	+	0.00956027i
$904$	5.51502e12	+	9.55229e12i	0.274656	+	0.475718i
$905$	1.25163e13			0.620237
$906$	−2.55787e12	−	4.43035e12i	−0.126125	−	0.218455i
$907$	1.32436e13	−	2.29385e13i	0.649788	−	1.12547i	−0.333385	−	0.942791i	$-0.608191\pi$
$907$	1.32436e13	−	2.29385e13i	0.649788	−	1.12547i	0.983173	−	0.182675i	$-0.0584757\pi$
$908$	−7.16770e12	+	1.24148e13i	−0.349940	+	0.606114i
$909$	−1.86427e13			−0.905673
$910$	2.82729e11	−	7.13090e10i	0.0136673	−	0.00344713i
$911$	8.31999e12			0.400212			0.200106	−	0.979774i	$-0.435871\pi$
$911$	8.31999e12			0.400212			0.200106	+	0.979774i	$0.435871\pi$
$912$	−2.42645e12	+	4.20274e12i	−0.116144	+	0.201167i
$913$	−5.85425e12	+	1.01399e13i	−0.278839	+	0.482963i
$914$	4.04726e12	+	7.01006e12i	0.191824	+	0.332249i
$915$	−1.65386e13			−0.780017
$916$	−7.30793e12	−	1.26577e13i	−0.342977	−	0.594053i
$917$	−1.49026e10	−	2.58120e10i	−0.000695983	−	0.00120548i
$918$	−1.77459e13			−0.824721
$919$	−1.60897e13	−	2.78682e13i	−0.744095	−	1.28881i	−0.950616	−	0.310368i	$-0.899548\pi$
$919$	−1.60897e13	−	2.78682e13i	−0.744095	−	1.28881i	0.206521	−	0.978442i	$-0.433786\pi$
$920$	2.66734e12	−	4.61996e12i	0.122753	−	0.212615i
$921$	−2.27583e12	+	3.94185e12i	−0.104225	+	0.180523i
$922$	−2.53618e13			−1.15582
$923$	−8.23389e12	−	8.48020e12i	−0.373420	−	0.384591i
$924$	−6.40415e10			−0.00289027
$925$	−8.73276e11	+	1.51256e12i	−0.0392206	+	0.0679320i
$926$	5.43169e12	−	9.40797e12i	0.242765	−	0.420481i
$927$	1.34266e13	+	2.32555e13i	0.597182	+	1.03435i
$928$	−3.19374e12			−0.141362
$929$	−3.89819e12	−	6.75186e12i	−0.171709	−	0.297408i	0.767309	−	0.641278i	$-0.221595\pi$
$929$	−3.89819e12	−	6.75186e12i	−0.171709	−	0.297408i	−0.939017	+	0.343870i	$0.888262\pi$
$930$	−2.15221e12	−	3.72774e12i	−0.0943435	−	0.163408i
$931$	3.82832e13			1.67007
$932$	8.83687e12	+	1.53059e13i	0.383642	+	0.664488i
$933$	−2.45983e11	+	4.26056e11i	−0.0106277	+	0.0184077i
$934$	9.33590e12	−	1.61703e13i	0.401417	−	0.695274i
$935$	−1.38733e13			−0.593648
$936$	3.99485e12	+	4.11435e12i	0.170122	+	0.175211i
$937$	1.98759e13			0.842361			0.421181	−	0.906977i	$-0.361616\pi$
$937$	1.98759e13			0.842361			0.421181	+	0.906977i	$0.361616\pi$
$938$	7.15262e10	−	1.23887e11i	0.00301684	−	0.00522532i
$939$	7.84266e11	−	1.35839e12i	0.0329206	−	0.0570202i
$940$	−4.62557e12	−	8.01172e12i	−0.193237	−	0.334696i
$941$	3.05247e13			1.26910			0.634552	−	0.772880i	$-0.281184\pi$
$941$	3.05247e13			1.26910			0.634552	+	0.772880i	$0.281184\pi$
$942$	6.94564e12	+	1.20302e13i	0.287398	+	0.497788i
$943$	−5.86841e12	−	1.01644e13i	−0.241667	−	0.418580i
$944$	2.28770e12			0.0937615
$945$	−2.29744e11	−	3.97928e11i	−0.00937131	−	0.0162316i
$946$	−4.15047e12	+	7.18882e12i	−0.168495	+	0.291842i
$947$	−6.04738e12	+	1.04744e13i	−0.244339	+	0.423207i	−0.961945	−	0.273242i	$-0.911904\pi$
$947$	−6.04738e12	+	1.04744e13i	−0.244339	+	0.423207i	0.717607	+	0.696448i	$0.245238\pi$
$948$	−1.23171e12			−0.0495303
$949$	−1.49633e13	+	3.77399e12i	−0.598866	+	0.151044i
$950$	2.43903e12			0.0971539
$951$	−1.29256e11	+	2.23878e11i	−0.00512434	+	0.00887562i
$952$	−1.15638e11	+	2.00290e11i	−0.00456282	+	0.00790303i
$953$	1.48337e12	+	2.56928e12i	0.0582548	+	0.100900i	0.893682	−	0.448701i	$-0.148113\pi$
$953$	1.48337e12	+	2.56928e12i	0.0582548	+	0.100900i	−0.835427	+	0.549601i	$0.814780\pi$
$954$	−8.12001e12			−0.317387
$955$	−3.40898e12	−	5.90452e12i	−0.132620	−	0.229705i
$956$	−1.41741e12	−	2.45502e12i	−0.0548825	−	0.0950593i
$957$	−5.76441e12			−0.222152
$958$	7.66720e12	+	1.32800e13i	0.294098	+	0.509393i
$959$	3.88722e11	−	6.73286e11i	0.0148407	−	0.0257049i
$960$	−8.76252e11	+	1.51771e12i	−0.0332973	+	0.0576725i
$961$	−1.98066e13			−0.749125
$962$	1.24811e13	+	1.28545e13i	0.469858	+	0.483913i
$963$	−3.06530e13			−1.14856
$964$	3.20164e12	−	5.54540e12i	0.119406	−	0.206817i
$965$	9.14503e12	−	1.58396e13i	0.339478	−	0.587994i
$966$	−8.02567e10	−	1.39009e11i	−0.00296541	−	0.00513623i
$967$	2.38826e13			0.878341			0.439170	−	0.898404i	$-0.355272\pi$
$967$	2.38826e13			0.878341			0.439170	+	0.898404i	$0.355272\pi$
$968$	3.62397e12	+	6.27691e12i	0.132662	+	0.229777i
$969$	1.58159e13	+	2.73940e13i	0.576286	+	0.998156i
$970$	2.29403e12			0.0832007
$971$	−1.99420e13	−	3.45405e13i	−0.719916	−	1.24693i	−0.961032	−	0.276435i	$-0.910847\pi$
$971$	−1.99420e13	−	3.45405e13i	−0.719916	−	1.24693i	0.241116	−	0.970496i	$-0.422487\pi$
$972$	7.19095e12	−	1.24551e13i	0.258397	−	0.447557i
$973$	3.29505e11	−	5.70719e11i	0.0117857	−	0.0204134i
$974$	3.46343e13			1.23308
$975$	−3.52319e11	+	1.24141e12i	−0.0124858	+	0.0439940i
$976$	−1.03762e13			−0.366029
$977$	−1.16418e13	+	2.01641e13i	−0.408783	+	0.708034i	−0.994754	−	0.102299i	$-0.967380\pi$
$977$	−1.16418e13	+	2.01641e13i	−0.408783	+	0.708034i	0.585970	+	0.810333i	$0.300714\pi$
$978$	8.44532e12	−	1.46277e13i	0.295183	−	0.511272i
$979$	−2.32047e12	−	4.01918e12i	−0.0807336	−	0.139835i
$980$	1.38250e13			0.478793
$981$	4.65534e11	+	8.06328e11i	0.0160487	+	0.0277972i
$982$	2.49017e12	+	4.31310e12i	0.0854531	+	0.148009i
$983$	−1.80946e13			−0.618099			−0.309050	−	0.951046i	$-0.600011\pi$
$983$	−1.80946e13			−0.618099			−0.309050	+	0.951046i	$0.600011\pi$
$984$	1.92784e12	+	3.33913e12i	0.0655532	+	0.113542i
$985$	−1.65571e12	+	2.86778e12i	−0.0560431	+	0.0970696i
$986$	−1.04086e13	+	1.80282e13i	−0.350708	+	0.607445i
$987$	−2.78355e11			−0.00933623
$988$	6.83124e12	−	2.40701e13i	0.228083	−	0.803657i
$989$	−2.08054e13			−0.691502
$990$	3.53243e12	−	6.11835e12i	0.116873	−	0.202430i
$991$	−1.44794e13	+	2.50790e13i	−0.476890	+	0.825998i	−0.999649	−	0.0264824i	$-0.991569\pi$
$991$	−1.44794e13	+	2.50790e13i	−0.476890	+	0.825998i	0.522759	+	0.852480i	$0.324903\pi$
$992$	−1.35029e12	−	2.33877e12i	−0.0442714	−	0.0766804i
$993$	1.12968e13			0.368709
$994$	1.21374e11	+	2.10226e11i	0.00394355	+	0.00683043i
$995$	2.91472e13	+	5.04844e13i	0.942741	+	1.63287i
$996$	9.64056e12			0.310410
$997$	1.58889e12	+	2.75204e12i	0.0509291	+	0.0882118i	0.890366	−	0.455245i	$-0.150448\pi$
$997$	1.58889e12	+	2.75204e12i	0.0509291	+	0.0882118i	−0.839437	+	0.543457i	$0.817115\pi$
$998$	−1.13532e13	+	1.96643e13i	−0.362268	+	0.627467i
$999$	1.41171e13	−	2.44515e13i	0.448436	−	0.776714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.10.c.b.9.4	yes	12
13.3	even	3	inner	26.10.c.b.3.4	✓	12
13.4	even	6		338.10.a.k.1.3		6
13.9	even	3		338.10.a.l.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.10.c.b.3.4	✓	12	13.3	even	3	inner
26.10.c.b.9.4	yes	12	1.1	even	1	trivial
338.10.a.k.1.3		6	13.4	even	6
338.10.a.l.1.3		6	13.9	even	3

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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-8.00000 + 13.8564i) q^{2} +(39.0102 - 67.5676i) q^{3} +(-128.000 - 221.703i) q^{4} -1338.85 q^{5} +(624.163 + 1081.08i) q^{6} +(66.0901 + 114.471i) q^{7} +4096.00 q^{8} +(6797.91 + 11774.3i) q^{9} +(10710.8 - 18551.6i) q^{10} +(12128.8 - 21007.7i) q^{11} -19973.2 q^{12} +(99851.2 - 25184.1i) q^{13} -2114.88 q^{14} +(-52228.7 + 90462.7i) q^{15} +(-32768.0 + 56755.8i) q^{16} +(213586. + 369942. i) q^{17} -217533. q^{18} +(474552. + 821948. i) q^{19} +(171372. + 296826. i) q^{20} +10312.8 q^{21} +(194061. + 336123. i) q^{22} +(-486392. + 842456. i) q^{23} +(159786. - 276757. i) q^{24} -160614. q^{25} +(-449848. + 1.58505e6i) q^{26} +2.59643e6 q^{27} +(16919.1 - 29304.7i) q^{28} +(1.52289e6 - 2.63773e6i) q^{29} +(-835659. - 1.44740e6i) q^{30} +2.57547e6 q^{31} +(-524288. - 908093. i) q^{32} +(-946292. - 1.63903e6i) q^{33} -6.83475e6 q^{34} +(-88484.5 - 153260. i) q^{35} +(1.74026e6 - 3.01423e6i) q^{36} +(5.43712e6 - 9.41737e6i) q^{37} -1.51857e7 q^{38} +(2.19358e6 - 7.72915e6i) q^{39} -5.48392e6 q^{40} +(-6.03259e6 + 1.04488e7i) q^{41} +(-82502.0 + 142898. i) q^{42} +(1.06937e7 + 1.85221e7i) q^{43} -6.20994e6 q^{44} +(-9.10136e6 - 1.57640e7i) q^{45} +(-7.78228e6 - 1.34793e7i) q^{46} -2.69913e7 q^{47} +(2.55657e6 + 4.42811e6i) q^{48} +(2.01681e7 - 3.49321e7i) q^{49} +(1.28491e6 - 2.22553e6i) q^{50} +3.33281e7 q^{51} +(-1.83643e7 - 1.89137e7i) q^{52} +3.73277e7 q^{53} +(-2.07714e7 + 3.59771e7i) q^{54} +(-1.62386e7 + 2.81261e7i) q^{55} +(270705. + 468875. i) q^{56} +7.40495e7 q^{57} +(2.43663e7 + 4.22037e7i) q^{58} +(-1.74537e7 - 3.02308e7i) q^{59} +2.67411e7 q^{60} +(7.91644e7 + 1.37117e8i) q^{61} +(-2.06037e7 + 3.56867e7i) q^{62} +(-898549. + 1.55633e6i) q^{63} +1.67772e7 q^{64} +(-1.33685e8 + 3.37177e7i) q^{65} +3.02814e7 q^{66} +(-3.38204e7 + 5.85787e7i) q^{67} +(5.46780e7 - 9.47051e7i) q^{68} +(3.79485e7 + 6.57288e7i) q^{69} +2.83150e6 q^{70} +(-5.73905e7 - 9.94033e7i) q^{71} +(2.78442e7 + 4.82276e7i) q^{72} -1.49856e8 q^{73} +(8.69939e7 + 1.50678e8i) q^{74} +(-6.26557e6 + 1.08523e7i) q^{75} +(1.21485e8 - 2.10419e8i) q^{76} +3.20637e6 q^{77} +(8.95496e7 + 9.22283e7i) q^{78} +6.16681e7 q^{79} +(4.38713e7 - 7.59874e7i) q^{80} +(-3.25161e7 + 5.63196e7i) q^{81} +(-9.65215e7 - 1.67180e8i) q^{82} -4.82674e8 q^{83} +(-1.32003e6 - 2.28636e6i) q^{84} +(-2.85959e8 - 4.95296e8i) q^{85} -3.42200e8 q^{86} +(-1.18817e8 - 2.05797e8i) q^{87} +(4.96795e7 - 8.60474e7i) q^{88} +(9.56598e7 - 1.65688e8i) q^{89} +2.91244e8 q^{90} +(9.48204e6 + 9.76568e6i) q^{91} +2.49033e8 q^{92} +(1.00470e8 - 1.74018e8i) q^{93} +(2.15931e8 - 3.74003e8i) q^{94} +(-6.35352e8 - 1.10046e9i) q^{95} -8.18103e7 q^{96} +(5.35450e7 + 9.27427e7i) q^{97} +(3.22689e8 + 5.58914e8i) q^{98} +3.29801e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 96 q^{2} - 81 q^{3} - 1536 q^{4} + 3386 q^{5} - 1296 q^{6} - 473 q^{7} + 49152 q^{8} - 69813 q^{9} - 27088 q^{10} - 14011 q^{11} + 41472 q^{12} + 152853 q^{13} + 15136 q^{14} + 294780 q^{15} - 393216 q^{16}+ \cdots - 1763539020 q^{99}+O(q^{100}) \) 12 * q - 96 * q^2 - 81 * q^3 - 1536 * q^4 + 3386 * q^5 - 1296 * q^6 - 473 * q^7 + 49152 * q^8 - 69813 * q^9 - 27088 * q^10 - 14011 * q^11 + 41472 * q^12 + 152853 * q^13 + 15136 * q^14 + 294780 * q^15 - 393216 * q^16 + 173558 * q^17 + 2234016 * q^18 - 322367 * q^19 - 433408 * q^20 + 4513770 * q^21 - 224176 * q^22 + 1644771 * q^23 - 331776 * q^24 + 5375138 * q^25 - 4031808 * q^26 - 1845990 * q^27 - 121088 * q^28 - 10801236 * q^29 + 4716480 * q^30 + 20870244 * q^31 - 6291456 * q^32 - 26201763 * q^33 - 5553856 * q^34 - 2168950 * q^35 - 17872128 * q^36 + 15710464 * q^37 + 10315744 * q^38 - 22298325 * q^39 + 13869056 * q^40 + 1525478 * q^41 - 36110160 * q^42 - 50959661 * q^43 + 7173632 * q^44 - 18619731 * q^45 + 26316336 * q^46 + 136313996 * q^47 - 5308416 * q^48 - 162536361 * q^49 - 43001104 * q^50 - 169357962 * q^51 + 25378560 * q^52 + 144556418 * q^53 + 14767920 * q^54 + 353372330 * q^55 - 1937408 * q^56 + 35902050 * q^57 - 172819776 * q^58 + 5665291 * q^59 - 150927360 * q^60 + 353387956 * q^61 - 166961952 * q^62 + 224088894 * q^63 + 201326592 * q^64 - 205394773 * q^65 + 838456416 * q^66 - 371115369 * q^67 + 44430848 * q^68 - 280317279 * q^69 + 69406400 * q^70 - 156688763 * q^71 - 285954048 * q^72 + 932803326 * q^73 + 251367424 * q^74 - 1149481845 * q^75 - 82525952 * q^76 + 624920666 * q^77 - 420616752 * q^78 + 325086960 * q^79 - 110952448 * q^80 - 295496586 * q^81 + 24407648 * q^82 - 870229152 * q^83 - 577762560 * q^84 - 2307296767 * q^85 + 1630709152 * q^86 + 617376057 * q^87 - 57389056 * q^88 - 163315063 * q^89 + 595831392 * q^90 - 208860497 * q^91 - 842122752 * q^92 - 2056270836 * q^93 - 1090511968 * q^94 + 537110948 * q^95 + 169869312 * q^96 + 1500514705 * q^97 - 2600581776 * q^98 - 1763539020 * q^99

Introduction

L-functions

Modular forms

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