LMFDB - Embedded newform 26.8.c.b.3.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [26,8,Mod(3,26)] 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("26.3"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(26, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 26 = 2 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	26.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8] 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:	$8.12201066259$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4654x^{6} + 7012369x^{4} + 3763719168x^{2} + 637953638400 $ x^8 + 4654x^6 + 7012369x^4 + 3763719168*x^2 + 637953638400
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			3.4
Root			$41.0833i$ of defining polynomial
Character	$\chi$	$=$	26.3
Dual form			26.8.c.b.9.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 + 6.92820i) q^{2} +(35.5792 + 61.6250i) q^{3} +(-32.0000 + 55.4256i) q^{4} +523.489 q^{5} +(-284.634 + 493.000i) q^{6} +(208.401 - 360.960i) q^{7} -512.000 q^{8} +(-1438.26 + 2491.14i) q^{9} +(2093.96 + 3626.84i) q^{10} +(-1711.39 - 2964.21i) q^{11} -4554.14 q^{12} +(-6741.24 - 4159.83i) q^{13} +3334.41 q^{14} +(18625.3 + 32260.0i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(3269.02 - 5662.11i) q^{17} -23012.2 q^{18} +(-13990.2 + 24231.8i) q^{19} +(-16751.7 + 29014.7i) q^{20} +29658.9 q^{21} +(13691.1 - 23713.7i) q^{22} +(-53089.0 - 91952.9i) q^{23} +(-18216.6 - 31552.0i) q^{24} +195916. q^{25} +(1855.20 - 63344.0i) q^{26} -49065.2 q^{27} +(13337.6 + 23101.5i) q^{28} +(-34273.0 - 59362.6i) q^{29} +(-149003. + 258080. i) q^{30} +51572.8 q^{31} +(16384.0 - 28377.9i) q^{32} +(121780. - 210929. i) q^{33} +52304.3 q^{34} +(109095. - 188959. i) q^{35} +(-92048.7 - 159433. i) q^{36} +(-24067.7 - 41686.5i) q^{37} -223844. q^{38} +(16501.7 - 563432. i) q^{39} -268026. q^{40} +(301049. + 521432. i) q^{41} +(118636. + 205483. i) q^{42} +(-458126. + 793497. i) q^{43} +219058. q^{44} +(-752914. + 1.30409e6i) q^{45} +(424712. - 735623. i) q^{46} -326201. q^{47} +(145732. - 252416. i) q^{48} +(324910. + 562760. i) q^{49} +(783664. + 1.35735e6i) q^{50} +465237. q^{51} +(446281. - 240523. i) q^{52} +934068. q^{53} +(-196261. - 339934. i) q^{54} +(-895894. - 1.55173e6i) q^{55} +(-106701. + 184812. i) q^{56} -1.99105e6 q^{57} +(274184. - 474900. i) q^{58} +(-587217. + 1.01709e6i) q^{59} -2.38404e6 q^{60} +(1.44545e6 - 2.50359e6i) q^{61} +(206291. + 357307. i) q^{62} +(599469. + 1.03831e6i) q^{63} +262144. q^{64} +(-3.52897e6 - 2.17763e6i) q^{65} +1.94848e6 q^{66} +(-159079. - 275533. i) q^{67} +(209217. + 362375. i) q^{68} +(3.77773e6 - 6.54322e6i) q^{69} +1.74553e6 q^{70} +(-641869. + 1.11175e6i) q^{71} +(736389. - 1.27546e6i) q^{72} -1.67209e6 q^{73} +(192542. - 333492. i) q^{74} +(6.97054e6 + 1.20733e7i) q^{75} +(-895376. - 1.55084e6i) q^{76} -1.42662e6 q^{77} +(3.96958e6 - 2.13940e6i) q^{78} -8.09160e6 q^{79} +(-1.07211e6 - 1.85694e6i) q^{80} +(1.39977e6 + 2.42448e6i) q^{81} +(-2.40839e6 + 4.17146e6i) q^{82} +5.57141e6 q^{83} +(-949085. + 1.64386e6i) q^{84} +(1.71130e6 - 2.96405e6i) q^{85} -7.33001e6 q^{86} +(2.43881e6 - 4.22415e6i) q^{87} +(876231. + 1.51768e6i) q^{88} +(-3.93786e6 - 6.82057e6i) q^{89} -1.20466e7 q^{90} +(-2.90641e6 + 1.56641e6i) q^{91} +6.79540e6 q^{92} +(1.83492e6 + 3.17817e6i) q^{93} +(-1.30480e6 - 2.25999e6i) q^{94} +(-7.32374e6 + 1.26851e7i) q^{95} +2.33172e6 q^{96} +(3.40424e6 - 5.89631e6i) q^{97} +(-2.59928e6 + 4.50208e6i) q^{98} +9.84569e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9} + 2224 q^{10} - 7392 q^{11} - 25818 q^{13} - 8768 q^{14} + 15528 q^{15} - 16384 q^{16} + 28316 q^{17} - 83424 q^{18} - 99888 q^{19}+ \cdots - 20715312 q^{99}+O(q^{100}) $ 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9 + 2224 * q^10 - 7392 * q^11 - 25818 * q^13 - 8768 * q^14 + 15528 * q^15 - 16384 * q^16 + 28316 * q^17 - 83424 * q^18 - 99888 * q^19 - 17792 * q^20 + 182148 * q^21 + 59136 * q^22 - 33388 * q^23 + 173756 * q^25 - 156000 * q^26 + 212544 * q^27 - 35072 * q^28 + 93140 * q^29 - 124224 * q^30 + 622320 * q^31 + 131072 * q^32 + 238638 * q^33 + 453056 * q^34 + 141544 * q^35 - 333696 * q^36 - 9636 * q^37 - 1598208 * q^38 - 22932 * q^39 - 284672 * q^40 + 82892 * q^41 + 728592 * q^42 - 569264 * q^43 + 946176 * q^44 - 2303394 * q^45 + 267104 * q^46 - 1148400 * q^47 - 717798 * q^49 + 695024 * q^50 - 5459856 * q^51 + 404352 * q^52 + 2470700 * q^53 + 850176 * q^54 - 1092512 * q^55 + 280576 * q^56 + 7056924 * q^57 - 745120 * q^58 + 231504 * q^59 - 1987584 * q^60 + 685684 * q^61 + 2489280 * q^62 - 5951712 * q^63 + 2097152 * q^64 - 6216678 * q^65 + 3818208 * q^66 + 3271056 * q^67 + 1812224 * q^68 + 5600034 * q^69 + 2264704 * q^70 - 175012 * q^71 + 2669568 * q^72 + 14275780 * q^73 + 77088 * q^74 + 22200960 * q^75 - 6392832 * q^76 - 27830412 * q^77 + 5028192 * q^78 - 14107904 * q^79 - 1138688 * q^80 + 3758004 * q^81 - 663136 * q^82 + 1314576 * q^83 - 5828736 * q^84 + 11814998 * q^85 - 9108224 * q^86 - 7182900 * q^87 + 3784704 * q^88 - 11452234 * q^89 - 36854304 * q^90 + 16457168 * q^91 + 4273664 * q^92 + 2984688 * q^93 - 4593600 * q^94 - 23334088 * q^95 - 428002 * q^97 + 5742384 * q^98 - 20715312 * q^99

Character values

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

$n$	$15$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	35.5792	+	61.6250i	0.760802	+	1.31775i	0.942437	+	0.334383i	$0.108528\pi$
$3$	35.5792	+	61.6250i	0.760802	+	1.31775i	−0.181635	+	0.983366i	$0.558139\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	523.489			1.87289			0.936446	−	0.350812i	$-0.114094\pi$
$5$	523.489			1.87289			0.936446	+	0.350812i	$0.114094\pi$
$6$	−284.634	+	493.000i	−0.537969	+	0.931789i
$7$	208.401	−	360.960i	0.229644	−	0.397756i	−0.728058	−	0.685515i	$-0.759577\pi$
$7$	208.401	−	360.960i	0.229644	−	0.397756i	0.957703	+	0.287759i	$0.0929104\pi$
$8$	−512.000			−0.353553
$9$	−1438.26	+	2491.14i	−0.657641	+	1.13907i
$10$	2093.96	+	3626.84i	0.662167	+	1.14691i
$11$	−1711.39	−	2964.21i	−0.387681	−	0.671483i	0.604456	−	0.796638i	$-0.293390\pi$
$11$	−1711.39	−	2964.21i	−0.387681	−	0.671483i	−0.992137	+	0.125155i	$0.960057\pi$
$12$	−4554.14			−0.760802
$13$	−6741.24	−	4159.83i	−0.851017	−	0.525139i
$13$	−6741.24	−	4159.83i	−0.851017	−	0.525139i
$14$	3334.41			0.324766
$15$	18625.3	+	32260.0i	1.42490	+	2.46800i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	3269.02	−	5662.11i	0.161379	−	0.279516i	−0.773985	−	0.633204i	$-0.781739\pi$
$17$	3269.02	−	5662.11i	0.161379	−	0.279516i	0.935363	+	0.353688i	$0.115073\pi$
$18$	−23012.2			−0.930045
$19$	−13990.2	+	24231.8i	−0.467937	+	0.810491i	−0.999329	−	0.0366351i	$-0.988336\pi$
$19$	−13990.2	+	24231.8i	−0.467937	+	0.810491i	0.531391	+	0.847127i	$0.321669\pi$
$20$	−16751.7	+	29014.7i	−0.468223	+	0.810986i
$21$	29658.9			0.698856
$22$	13691.1	−	23713.7i	0.274132	−	0.474810i
$23$	−53089.0	−	91952.9i	−0.909824	−	1.57586i	−0.814308	−	0.580433i	$-0.802883\pi$
$23$	−53089.0	−	91952.9i	−0.909824	−	1.57586i	−0.0955160	−	0.995428i	$-0.530450\pi$
$24$	−18216.6	−	31552.0i	−0.268984	−	0.465894i
$25$	195916.			2.50772
$26$	1855.20	−	63344.0i	0.0207007	−	0.706804i
$27$	−49065.2			−0.479734
$28$	13337.6	+	23101.5i	0.114822	+	0.198878i
$29$	−34273.0	−	59362.6i	−0.260951	−	0.451980i	0.705544	−	0.708666i	$-0.250703\pi$
$29$	−34273.0	−	59362.6i	−0.260951	−	0.451980i	−0.966495	+	0.256686i	$0.917369\pi$
$30$	−149003.	+	258080.i	−1.00756	+	1.74514i
$31$	51572.8			0.310924			0.155462	−	0.987842i	$-0.450313\pi$
$31$	51572.8			0.310924			0.155462	+	0.987842i	$0.450313\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	121780.	−	210929.i	0.589897	−	1.02173i
$34$	52304.3			0.228224
$35$	109095.	−	188959.i	0.430099	−	0.744954i
$36$	−92048.7	−	159433.i	−0.328820	−	0.569534i
$37$	−24067.7	−	41686.5i	−0.0781140	−	0.135297i	0.824322	−	0.566121i	$-0.191556\pi$
$37$	−24067.7	−	41686.5i	−0.0781140	−	0.135297i	−0.902436	+	0.430824i	$0.858223\pi$
$38$	−223844.			−0.661763
$39$	16501.7	−	563432.i	0.0445452	−	1.52095i
$40$	−268026.			−0.662167
$41$	301049.	+	521432.i	0.682172	+	1.18156i	0.974317	+	0.225182i	$0.0722976\pi$
$41$	301049.	+	521432.i	0.682172	+	1.18156i	−0.292145	+	0.956374i	$0.594369\pi$
$42$	118636.	+	205483.i	0.247083	+	0.427960i
$43$	−458126.	+	793497.i	−0.878709	+	1.52197i	−0.0259511	+	0.999663i	$0.508261\pi$
$43$	−458126.	+	793497.i	−0.878709	+	1.52197i	−0.852758	+	0.522306i	$0.825072\pi$
$44$	219058.			0.387681
$45$	−752914.	+	1.30409e6i	−1.23169	+	2.13335i
$46$	424712.	−	735623.i	0.643343	−	1.11430i
$47$	−326201.			−0.458293			−0.229146	−	0.973392i	$-0.573593\pi$
$47$	−326201.			−0.458293			−0.229146	+	0.973392i	$0.573593\pi$
$48$	145732.	−	252416.i	0.190201	−	0.329437i
$49$	324910.	+	562760.i	0.394527	+	0.683341i
$50$	783664.	+	1.35735e6i	0.886615	+	1.53566i
$51$	465237.			0.491110
$52$	446281.	−	240523.i	0.440146	−	0.237216i
$53$	934068.			0.861813			0.430907	−	0.902397i	$-0.358194\pi$
$53$	934068.			0.861813			0.430907	+	0.902397i	$0.358194\pi$
$54$	−196261.	−	339934.i	−0.169612	−	0.293776i
$55$	−895894.	−	1.55173e6i	−0.726085	−	1.25762i
$56$	−106701.	+	184812.i	−0.0811915	+	0.140628i
$57$	−1.99105e6			−1.42403
$58$	274184.	−	474900.i	0.184520	−	0.319598i
$59$	−587217.	+	1.01709e6i	−0.372235	+	0.644729i	−0.989909	−	0.141705i	$-0.954742\pi$
$59$	−587217.	+	1.01709e6i	−0.372235	+	0.644729i	0.617674	+	0.786434i	$0.288075\pi$
$60$	−2.38404e6			−1.42490
$61$	1.44545e6	−	2.50359e6i	0.815358	−	1.41224i	−0.0937130	−	0.995599i	$-0.529874\pi$
$61$	1.44545e6	−	2.50359e6i	0.815358	−	1.41224i	0.909071	−	0.416642i	$-0.136793\pi$
$62$	206291.	+	357307.i	0.109928	+	0.190401i
$63$	599469.	+	1.03831e6i	0.302047	+	0.523161i
$64$	262144.			0.125000
$65$	−3.52897e6	−	2.17763e6i	−1.59386	−	0.983528i
$66$	1.94848e6			0.834241
$67$	−159079.	−	275533.i	−0.0646176	−	0.111921i	0.831907	−	0.554916i	$-0.187249\pi$
$67$	−159079.	−	275533.i	−0.0646176	−	0.111921i	−0.896524	+	0.442995i	$0.853916\pi$
$68$	209217.	+	362375.i	0.0806894	+	0.139758i
$69$	3.77773e6	−	6.54322e6i	1.38439	−	2.39784i
$70$	1.74553e6			0.608252
$71$	−641869.	+	1.11175e6i	−0.212834	+	0.368640i	−0.952600	−	0.304224i	$-0.901603\pi$
$71$	−641869.	+	1.11175e6i	−0.212834	+	0.368640i	0.739766	+	0.672864i	$0.234936\pi$
$72$	736389.	−	1.27546e6i	0.232511	−	0.402721i
$73$	−1.67209e6			−0.503070			−0.251535	−	0.967848i	$-0.580935\pi$
$73$	−1.67209e6			−0.503070			−0.251535	+	0.967848i	$0.580935\pi$
$74$	192542.	−	333492.i	0.0552349	−	0.0956697i
$75$	6.97054e6	+	1.20733e7i	1.90788	+	3.30455i
$76$	−895376.	−	1.55084e6i	−0.233969	−	0.405246i
$77$	−1.42662e6			−0.356115
$78$	3.96958e6	−	2.13940e6i	0.947139	−	0.510460i
$79$	−8.09160e6			−1.84646			−0.923229	−	0.384250i	$-0.874460\pi$
$79$	−8.09160e6			−1.84646			−0.923229	+	0.384250i	$0.874460\pi$
$80$	−1.07211e6	−	1.85694e6i	−0.234112	−	0.405493i
$81$	1.39977e6	+	2.42448e6i	0.292658	+	0.506899i
$82$	−2.40839e6	+	4.17146e6i	−0.482368	+	0.835486i
$83$	5.57141e6			1.06953			0.534764	−	0.845002i	$-0.320401\pi$
$83$	5.57141e6			1.06953			0.534764	+	0.845002i	$0.320401\pi$
$84$	−949085.	+	1.64386e6i	−0.174714	+	0.302614i
$85$	1.71130e6	−	2.96405e6i	0.302245	−	0.523504i
$86$	−7.33001e6			−1.24268
$87$	2.43881e6	−	4.22415e6i	0.397064	−	0.687736i
$88$	876231.	+	1.51768e6i	0.137066	+	0.237405i
$89$	−3.93786e6	−	6.82057e6i	−0.592100	−	1.02555i	−0.993949	−	0.109842i	$-0.964966\pi$
$89$	−3.93786e6	−	6.82057e6i	−0.592100	−	1.02555i	0.401849	−	0.915706i	$-0.368368\pi$
$90$	−1.20466e7			−1.74187
$91$	−2.90641e6	+	1.56641e6i	−0.404308	+	0.217902i
$92$	6.79540e6			0.909824
$93$	1.83492e6	+	3.17817e6i	0.236552	+	0.409720i
$94$	−1.30480e6	−	2.25999e6i	−0.162031	−	0.280646i
$95$	−7.32374e6	+	1.26851e7i	−0.876396	+	1.51796i
$96$	2.33172e6			0.268984
$97$	3.40424e6	−	5.89631e6i	0.378720	−	0.655963i	−0.612156	−	0.790737i	$-0.709698\pi$
$97$	3.40424e6	−	5.89631e6i	0.378720	−	0.655963i	0.990876	+	0.134774i	$0.0430309\pi$
$98$	−2.59928e6	+	4.50208e6i	−0.278973	+	0.483195i
$99$	9.84569e6			1.01982
$100$	−6.26931e6	+	1.08588e7i	−0.626931	+	1.08588i
$101$	−805060.	−	1.39441e6i	−0.0777506	−	0.134668i	0.824529	−	0.565820i	$-0.191440\pi$
$101$	−805060.	−	1.39441e6i	−0.0777506	−	0.134668i	−0.902279	+	0.431152i	$0.858107\pi$
$102$	1.86095e6	+	3.22326e6i	0.173633	+	0.300742i
$103$	4.93664e6			0.445145			0.222572	−	0.974916i	$-0.428555\pi$
$103$	4.93664e6			0.445145			0.222572	+	0.974916i	$0.428555\pi$
$104$	3.45151e6	+	2.12983e6i	0.300880	+	0.185665i
$105$	1.55261e7			1.30888
$106$	3.73627e6	+	6.47142e6i	0.304697	+	0.527751i
$107$	6.13515e6	+	1.06264e7i	0.484152	+	0.838576i	0.999834	−	0.0182040i	$-0.00579483\pi$
$107$	6.13515e6	+	1.06264e7i	0.484152	+	0.838576i	−0.515682	+	0.856780i	$0.672461\pi$
$108$	1.57009e6	−	2.71947e6i	0.119933	−	0.207731i
$109$	−1.65278e7			−1.22243			−0.611213	−	0.791467i	$-0.709318\pi$
$109$	−1.65278e7			−1.22243			−0.611213	+	0.791467i	$0.709318\pi$
$110$	7.16715e6	−	1.24139e7i	0.513419	−	0.889268i
$111$	1.71262e6	−	2.96634e6i	0.118859	−	0.205869i
$112$	−1.70722e6			−0.114822
$113$	−6.64380e6	+	1.15074e7i	−0.433154	+	0.750244i	−0.997143	−	0.0755379i	$-0.975933\pi$
$113$	−6.64380e6	+	1.15074e7i	−0.433154	+	0.750244i	0.563989	+	0.825782i	$0.309266\pi$
$114$	−7.96419e6	−	1.37944e7i	−0.503471	−	0.872038i
$115$	−2.77915e7	−	4.81363e7i	−1.70400	−	2.95142i
$116$	4.38694e6			0.260951
$117$	2.00584e7	−	1.08105e7i	1.15783	−	0.624013i
$118$	−9.39547e6			−0.526419
$119$	−1.36253e6	−	2.35997e6i	−0.0741195	−	0.128379i
$120$	−9.53617e6	−	1.65171e7i	−0.503779	−	0.872570i
$121$	3.88588e6	−	6.73054e6i	0.199407	−	0.345383i
$122$	2.31272e7			1.15309
$123$	−2.14222e7	+	3.71043e7i	−1.03800	+	1.79786i
$124$	−1.65033e6	+	2.85845e6i	−0.0777311	+	0.134634i
$125$	6.16623e7			2.82381
$126$	−4.79575e6	+	8.30648e6i	−0.213579	+	0.369931i
$127$	−1.36436e6	−	2.36314e6i	−0.0591040	−	0.102371i	0.834959	−	0.550311i	$-0.185491\pi$
$127$	−1.36436e6	−	2.36314e6i	−0.0591040	−	0.102371i	−0.894063	+	0.447940i	$0.852158\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	−6.51990e7			−2.67410
$130$	971178.	−	3.31599e7i	0.0387701	−	1.32377i
$131$	1.96041e7			0.761898			0.380949	−	0.924596i	$-0.375597\pi$
$131$	1.96041e7			0.761898			0.380949	+	0.924596i	$0.375597\pi$
$132$	7.79391e6	+	1.34994e7i	0.294949	+	0.510866i
$133$	5.83115e6	+	1.00999e7i	0.214918	+	0.372250i
$134$	1.27263e6	−	2.20426e6i	0.0456916	−	0.0791401i
$135$	−2.56851e7			−0.898490
$136$	−1.67374e6	+	2.89900e6i	−0.0570560	+	0.0988240i
$137$	−326199.	+	564993.i	−0.0108383	+	0.0187724i	−0.871394	−	0.490584i	$-0.836783\pi$
$137$	−326199.	+	564993.i	−0.0108383	+	0.0187724i	0.860555	+	0.509357i	$0.170117\pi$
$138$	6.04437e7			1.95783
$139$	−4.60831e6	+	7.98182e6i	−0.145542	+	0.252087i	−0.929575	−	0.368633i	$-0.879826\pi$
$139$	−4.60831e6	+	7.98182e6i	−0.145542	+	0.252087i	0.784033	+	0.620719i	$0.213159\pi$
$140$	6.98211e6	+	1.20934e7i	0.215050	+	0.372477i
$141$	−1.16060e7	−	2.01021e7i	−0.348670	−	0.603915i
$142$	−1.02699e7			−0.300993
$143$	−793743.	+	2.71016e7i	−0.0226988	+	0.775030i
$144$	1.17822e7			0.328820
$145$	−1.79415e7	−	3.10757e7i	−0.488733	−	0.846510i
$146$	−6.68835e6	−	1.15846e7i	−0.177862	−	0.308066i
$147$	−2.31201e7	+	4.00451e7i	−0.600314	+	1.03977i
$148$	3.08067e6			0.0781140
$149$	1.22231e6	−	2.11710e6i	0.0302712	−	0.0524312i	−0.850493	−	0.525986i	$-0.823696\pi$
$149$	1.22231e6	−	2.11710e6i	0.0302712	−	0.0524312i	0.880764	+	0.473555i	$0.157030\pi$
$150$	−5.57643e7	+	9.65866e7i	−1.34908	+	2.33667i
$151$	−2.73196e7			−0.645736			−0.322868	−	0.946444i	$-0.604647\pi$
$151$	−2.73196e7			−0.645736			−0.322868	+	0.946444i	$0.604647\pi$
$152$	7.16301e6	−	1.24067e7i	0.165441	−	0.286552i
$153$	9.40341e6	+	1.62872e7i	0.212259	+	0.367643i
$154$	−5.70647e6	−	9.88390e6i	−0.125906	−	0.218075i
$155$	2.69978e7			0.582328
$156$	3.07005e7	+	1.89445e7i	0.647456	+	0.399527i
$157$	5.54490e7			1.14352			0.571761	−	0.820420i	$-0.306260\pi$
$157$	5.54490e7			1.14352			0.571761	+	0.820420i	$0.306260\pi$
$158$	−3.23664e7	−	5.60602e7i	−0.652821	−	1.13072i
$159$	3.32334e7	+	5.75620e7i	0.655670	+	1.13565i
$160$	8.57685e6	−	1.48555e7i	0.165542	−	0.286727i
$161$	−4.42551e7			−0.835744
$162$	−1.11982e7	+	1.93958e7i	−0.206940	+	0.358431i
$163$	−1.60007e7	+	2.77139e7i	−0.289388	+	0.501235i	−0.973664	−	0.227988i	$-0.926785\pi$
$163$	−1.60007e7	+	2.77139e7i	−0.289388	+	0.501235i	0.684275	+	0.729224i	$0.260119\pi$
$164$	−3.85343e7			−0.682172
$165$	6.37504e7	−	1.10419e8i	1.10481	−	1.91359i
$166$	2.22856e7	+	3.85999e7i	0.378135	+	0.654949i
$167$	9.67304e6	+	1.67542e7i	0.160715	+	0.278366i	0.935125	−	0.354318i	$-0.115287\pi$
$167$	9.67304e6	+	1.67542e7i	0.160715	+	0.278366i	−0.774411	+	0.632683i	$0.781953\pi$
$168$	−1.51854e7			−0.247083
$169$	2.81401e7	+	5.60848e7i	0.448459	+	0.893804i
$170$	2.73808e7			0.427439
$171$	−4.02432e7	−	6.97033e7i	−0.615469	−	1.06602i
$172$	−2.93201e7	−	5.07838e7i	−0.439355	−	0.760985i
$173$	−2.06874e7	+	3.58317e7i	−0.303770	+	0.526145i	−0.976987	−	0.213300i	$-0.931579\pi$
$173$	−2.06874e7	+	3.58317e7i	−0.303770	+	0.526145i	0.673217	+	0.739445i	$0.264912\pi$
$174$	3.90210e7			0.561534
$175$	4.08290e7	−	7.07179e7i	0.575885	−	0.997462i
$176$	−7.00985e6	+	1.21414e7i	−0.0969202	+	0.167871i
$177$	−8.35709e7			−1.13279
$178$	3.15029e7	−	5.45646e7i	0.418678	−	0.725172i
$179$	1.61438e7	+	2.79619e7i	0.210388	+	0.364403i	0.951836	−	0.306608i	$-0.0991940\pi$
$179$	1.61438e7	+	2.79619e7i	0.210388	+	0.364403i	−0.741448	+	0.671010i	$0.765861\pi$
$180$	−4.81865e7	−	8.34614e7i	−0.615845	−	1.06667i
$181$	−8.08975e7			−1.01405			−0.507026	−	0.861931i	$-0.669255\pi$
$181$	−8.08975e7			−1.01405			−0.507026	+	0.861931i	$0.669255\pi$
$182$	−2.24781e7	−	1.38706e7i	−0.276381	−	0.170547i
$183$	2.05712e8			2.48130
$184$	2.71816e7	+	4.70799e7i	0.321671	+	0.557151i
$185$	−1.25992e7	−	2.18224e7i	−0.146299	−	0.253397i
$186$	−1.46793e7	+	2.54254e7i	−0.167267	+	0.289716i
$187$	−2.23783e7			−0.250254
$188$	1.04384e7	−	1.80799e7i	0.114573	−	0.198447i
$189$	−1.02252e7	+	1.77106e7i	−0.110168	+	0.190817i
$190$	−1.17180e8			−1.23941
$191$	6.81711e6	−	1.18076e7i	0.0707919	−	0.122615i	−0.828457	−	0.560053i	$-0.810781\pi$
$191$	6.81711e6	−	1.18076e7i	0.0707919	−	0.122615i	0.899249	+	0.437438i	$0.144114\pi$
$192$	9.32688e6	+	1.61546e7i	0.0951003	+	0.164719i
$193$	−8.66220e6	−	1.50034e7i	−0.0867316	−	0.150224i	0.819396	−	0.573228i	$-0.194309\pi$
$193$	−8.66220e6	−	1.50034e7i	−0.0867316	−	0.150224i	−0.906128	+	0.423004i	$0.860976\pi$
$194$	5.44678e7			0.535591
$195$	8.63844e6	−	2.94951e8i	0.0834284	−	2.84858i
$196$	−4.15885e7			−0.394527
$197$	−3.11874e7	−	5.40181e7i	−0.290634	−	0.503393i	0.683326	−	0.730114i	$-0.260533\pi$
$197$	−3.11874e7	−	5.40181e7i	−0.290634	−	0.503393i	−0.973960	+	0.226720i	$0.927200\pi$
$198$	3.93828e7	+	6.82130e7i	0.360561	+	0.624509i
$199$	1.20854e6	−	2.09325e6i	0.0108711	−	0.0188293i	−0.860539	−	0.509385i	$-0.829873\pi$
$199$	1.20854e6	−	2.09325e6i	0.0108711	−	0.0188293i	0.871410	+	0.490556i	$0.163206\pi$
$200$	−1.00309e8			−0.886615
$201$	1.13198e7	−	1.96065e7i	0.0983225	−	0.170300i
$202$	6.44048e6	−	1.11552e7i	0.0549780	−	0.0952246i
$203$	−2.85700e7			−0.239704
$204$	−1.48876e7	+	2.57860e7i	−0.122777	+	0.212657i
$205$	1.57596e8	+	2.72964e8i	1.27763	+	2.21293i
$206$	1.97466e7	+	3.42021e7i	0.157382	+	0.272594i
$207$	3.05423e8			2.39335
$208$	−949863.	+	3.24321e7i	−0.00731879	+	0.249893i
$209$	9.57711e7			0.725642
$210$	6.21045e7	+	1.07568e8i	0.462760	+	0.801523i
$211$	−4.86339e7	−	8.42364e7i	−0.356411	−	0.617321i	0.630948	−	0.775825i	$-0.282666\pi$
$211$	−4.86339e7	−	8.42364e7i	−0.356411	−	0.617321i	−0.987358	+	0.158504i	$0.949333\pi$
$212$	−2.98902e7	+	5.17713e7i	−0.215453	+	0.373176i
$213$	−9.13487e7			−0.647700
$214$	−4.90812e7	+	8.50111e7i	−0.342347	+	0.592963i
$215$	−2.39824e8	+	4.15387e8i	−1.64573	+	2.85048i
$216$	2.51214e7			0.169612
$217$	1.07478e7	−	1.86157e7i	0.0714020	−	0.123672i
$218$	−6.61112e7	−	1.14508e8i	−0.432193	−	0.748579i
$219$	−5.94915e7	−	1.03042e8i	−0.382737	−	0.662920i
$220$	1.14674e8			0.726085
$221$	−4.55907e7	+	2.45711e7i	−0.284121	+	0.153127i
$222$	2.74019e7			0.168091
$223$	−8.35602e7	−	1.44730e8i	−0.504583	−	0.873963i	−0.999986	−	0.00529982i	$-0.998313\pi$
$223$	−8.35602e7	−	1.44730e8i	−0.504583	−	0.873963i	0.495403	−	0.868663i	$-0.335020\pi$
$224$	−6.82887e6	−	1.18280e7i	−0.0405958	−	0.0703139i
$225$	−2.81778e8	+	4.88054e8i	−1.64918	+	2.85647i
$226$	−1.06301e8			−0.612572
$227$	−2.85340e7	+	4.94223e7i	−0.161909	+	0.280435i	−0.935553	−	0.353185i	$-0.885098\pi$
$227$	−2.85340e7	+	4.94223e7i	−0.161909	+	0.280435i	0.773644	+	0.633620i	$0.218432\pi$
$228$	6.37135e7	−	1.10355e8i	0.356008	−	0.616624i
$229$	2.68753e8			1.47886			0.739432	−	0.673231i	$-0.235094\pi$
$229$	2.68753e8			1.47886			0.739432	+	0.673231i	$0.235094\pi$
$230$	2.22332e8	−	3.85091e8i	1.20491	−	2.08697i
$231$	−5.07580e7	−	8.79154e7i	−0.270933	−	0.469270i
$232$	1.75478e7	+	3.03936e7i	0.0922601	+	0.159799i
$233$	−6.53750e7			−0.338584			−0.169292	−	0.985566i	$-0.554148\pi$
$233$	−6.53750e7			−0.338584			−0.169292	+	0.985566i	$0.554148\pi$
$234$	1.55131e8	+	9.57267e7i	0.791483	+	0.488402i
$235$	−1.70763e8			−0.858333
$236$	−3.75819e7	−	6.50938e7i	−0.186117	−	0.322365i
$237$	−2.87893e8	−	4.98645e8i	−1.40479	−	2.43317i
$238$	1.09003e7	−	1.88798e7i	0.0524104	−	0.0907775i
$239$	−2.06797e8			−0.979832			−0.489916	−	0.871770i	$-0.662973\pi$
$239$	−2.06797e8			−0.979832			−0.489916	+	0.871770i	$0.662973\pi$
$240$	7.62894e7	−	1.32137e8i	0.356225	−	0.617000i
$241$	1.40238e8	−	2.42899e8i	0.645365	−	1.11780i	−0.338852	−	0.940840i	$-0.610039\pi$
$241$	1.40238e8	−	2.42899e8i	0.645365	−	1.11780i	0.984217	−	0.176965i	$-0.0566280\pi$
$242$	6.21740e7			0.282004
$243$	−1.53259e8	+	2.65452e8i	−0.685177	+	1.18676i
$244$	9.25087e7	+	1.60230e8i	0.407679	+	0.706121i
$245$	1.70087e8	+	2.94599e8i	0.738906	+	1.27982i
$246$	−3.42755e8			−1.46795
$247$	1.95112e8	−	1.05155e8i	0.823843	−	0.444010i
$248$	−2.64053e7			−0.109928
$249$	1.98226e8	+	3.43338e8i	0.813699	+	1.40937i
$250$	2.46649e8	+	4.27209e8i	0.998366	+	1.72922i
$251$	1.55974e8	−	2.70156e8i	0.622580	−	1.07834i	−0.366423	−	0.930448i	$-0.619418\pi$
$251$	1.55974e8	−	2.70156e8i	0.622580	−	1.07834i	0.989004	−	0.147892i	$-0.0472488\pi$
$252$	−7.67320e7			−0.302047
$253$	−1.81712e8	+	3.14734e8i	−0.705443	+	1.22186i
$254$	1.09149e7	−	1.89052e7i	0.0417928	−	0.0723873i
$255$	2.43546e8			0.919795
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−1.07145e8	−	1.85580e8i	−0.393736	−	0.681970i	0.599203	−	0.800597i	$-0.295484\pi$
$257$	−1.07145e8	−	1.85580e8i	−0.393736	−	0.681970i	−0.992939	+	0.118627i	$0.962151\pi$
$258$	−2.60796e8	−	4.51712e8i	−0.945436	−	1.63754i
$259$	−2.00629e7			−0.0717537
$260$	2.33623e8	−	1.25911e8i	0.824346	−	0.444281i
$261$	1.97174e8			0.686448
$262$	7.84163e7	+	1.35821e8i	0.269372	+	0.466565i
$263$	−8.74186e7	−	1.51413e8i	−0.296318	−	0.513239i	0.678972	−	0.734164i	$-0.262426\pi$
$263$	−8.74186e7	−	1.51413e8i	−0.296318	−	0.513239i	−0.975291	+	0.220925i	$0.929092\pi$
$264$	−6.23512e7	+	1.07996e8i	−0.208560	+	0.361237i
$265$	4.88975e8			1.61408
$266$	−4.66492e7	+	8.07988e7i	−0.151970	+	0.263220i
$267$	2.80212e8	−	4.85341e8i	0.900943	−	1.56048i
$268$	2.03621e7			0.0646176
$269$	−1.41548e8	+	2.45168e8i	−0.443374	+	0.767947i	−0.997937	−	0.0641947i	$-0.979552\pi$
$269$	−1.41548e8	+	2.45168e8i	−0.443374	+	0.767947i	0.554563	+	0.832142i	$0.312885\pi$
$270$	−1.02740e8	−	1.77952e8i	−0.317664	−	0.550210i
$271$	−1.08878e8	−	1.88582e8i	−0.332312	−	0.575581i	0.650653	−	0.759375i	$-0.274495\pi$
$271$	−1.08878e8	−	1.88582e8i	−0.332312	−	0.575581i	−0.982965	+	0.183794i	$0.941162\pi$
$272$	−2.67798e7			−0.0806894
$273$	−1.99938e8	−	1.23376e8i	−0.594738	−	0.366996i
$274$	−5.21918e6			−0.0153276
$275$	−3.35289e8	−	5.80737e8i	−0.972197	−	1.68389i
$276$	2.41775e8	+	4.18766e8i	0.692196	+	1.19892i
$277$	2.75129e8	−	4.76538e8i	0.777782	−	1.34716i	−0.155436	−	0.987846i	$-0.549678\pi$
$277$	2.75129e8	−	4.76538e8i	0.777782	−	1.34716i	0.933218	−	0.359312i	$-0.116988\pi$
$278$	−7.37329e7			−0.205828
$279$	−7.41751e7	+	1.28475e8i	−0.204476	+	0.354164i
$280$	−5.58569e7	+	9.67470e7i	−0.152063	+	0.263381i
$281$	−1.42673e8			−0.383591			−0.191796	−	0.981435i	$-0.561431\pi$
$281$	−1.42673e8			−0.383591			−0.191796	+	0.981435i	$0.561431\pi$
$282$	9.28479e7	−	1.60817e8i	0.246547	−	0.427032i
$283$	1.29624e7	+	2.24515e7i	0.0339963	+	0.0588833i	0.882523	−	0.470269i	$-0.155843\pi$
$283$	1.29624e7	+	2.24515e7i	0.0339963	+	0.0588833i	−0.848527	+	0.529153i	$0.822510\pi$
$284$	−4.10796e7	−	7.11519e7i	−0.106417	−	0.184320i
$285$	−1.04229e9			−2.66706
$286$	−1.90940e8	+	1.02907e8i	−0.482632	+	0.260114i
$287$	2.50955e8			0.626627
$288$	4.71289e7	+	8.16297e7i	0.116256	+	0.201361i
$289$	1.83796e8	+	3.18345e8i	0.447914	+	0.775809i
$290$	1.43532e8	−	2.48605e8i	0.345586	−	0.598573i
$291$	4.84480e8			1.15253
$292$	5.35068e7	−	9.26764e7i	0.125768	−	0.217836i
$293$	−3.71932e8	+	6.44205e8i	−0.863827	+	1.49619i	0.00437957	+	0.999990i	$0.498606\pi$
$293$	−3.71932e8	+	6.44205e8i	−0.863827	+	1.49619i	−0.868207	+	0.496202i	$0.834727\pi$
$294$	−3.69921e8			−0.848972
$295$	−3.07402e8	+	5.32436e8i	−0.697155	+	1.20751i
$296$	1.23227e7	+	2.13435e7i	0.0276175	+	0.0478348i
$297$	8.39697e7	+	1.45440e8i	0.185984	+	0.322133i
$298$	1.95570e7			0.0428099
$299$	−2.46227e7	+	8.40718e8i	−0.0532705	+	1.81887i
$300$	−8.92229e8			−1.90788
$301$	1.90947e8	+	3.30731e8i	0.403581	+	0.699023i
$302$	−1.09278e8	−	1.89276e8i	−0.228302	−	0.395431i
$303$	5.72868e7	−	9.92237e7i	0.118306	−	0.204911i
$304$	1.14608e8			0.233969
$305$	7.56677e8	−	1.31060e9i	1.52708	−	2.64497i
$306$	−7.52273e7	+	1.30297e8i	−0.150090	+	0.259963i
$307$	2.86830e8			0.565771			0.282886	−	0.959154i	$-0.408708\pi$
$307$	2.86830e8			0.565771			0.282886	+	0.959154i	$0.408708\pi$
$308$	4.56518e7	−	7.90712e7i	0.0890288	−	0.154202i
$309$	1.75642e8	+	3.04221e8i	0.338667	+	0.586589i
$310$	1.07991e8	+	1.87046e8i	0.205884	+	0.356601i
$311$	7.18890e8			1.35519			0.677596	−	0.735434i	$-0.263022\pi$
$311$	7.18890e8			1.35519			0.677596	+	0.735434i	$0.263022\pi$
$312$	−8.44885e6	+	2.88477e8i	−0.0157491	+	0.537738i
$313$	6.20382e8			1.14355			0.571774	−	0.820411i	$-0.306255\pi$
$313$	6.20382e8			1.14355			0.571774	+	0.820411i	$0.306255\pi$
$314$	2.21796e8	+	3.84162e8i	0.404296	+	0.700262i
$315$	3.13815e8	+	5.43544e8i	0.565701	+	0.979824i
$316$	2.58931e8	−	4.48482e8i	0.461614	−	0.799540i
$317$	1.67254e8			0.294897			0.147448	−	0.989070i	$-0.452894\pi$
$317$	1.67254e8			0.294897			0.147448	+	0.989070i	$0.452894\pi$
$318$	−2.65867e8	+	4.60496e8i	−0.463628	+	0.803028i
$319$	−1.17309e8	+	2.03185e8i	−0.202331	+	0.350448i
$320$	1.37230e8			0.234112
$321$	−4.36567e8	+	7.56157e8i	−0.736688	+	1.27598i
$322$	−1.77021e8	−	3.06609e8i	−0.295480	−	0.511786i
$323$	9.14688e7	+	1.58429e8i	0.151030	+	0.261592i
$324$	−1.79171e8			−0.292658
$325$	−1.32072e9	−	8.14978e8i	−2.13412	−	1.31690i
$326$	−2.56010e8			−0.409257
$327$	−5.88046e8	−	1.01853e9i	−0.930024	−	1.61085i
$328$	−1.54137e8	−	2.66973e8i	−0.241184	−	0.417743i
$329$	−6.79805e7	+	1.17746e8i	−0.105244	+	0.182289i
$330$	1.02001e9			1.56244
$331$	−3.94643e8	+	6.83541e8i	−0.598144	+	1.03602i	0.394950	+	0.918702i	$0.370762\pi$
$331$	−3.94643e8	+	6.83541e8i	−0.598144	+	1.03602i	−0.993095	+	0.117314i	$0.962572\pi$
$332$	−1.78285e8	+	3.08799e8i	−0.267382	+	0.463119i
$333$	1.38463e8			0.205484
$334$	−7.73843e7	+	1.34034e8i	−0.113642	+	0.196834i
$335$	−8.32761e7	−	1.44238e8i	−0.121022	−	0.209616i
$336$	−6.07415e7	−	1.05207e8i	−0.0873570	−	0.151307i
$337$	−6.94195e8			−0.988046			−0.494023	−	0.869449i	$-0.664474\pi$
$337$	−6.94195e8			−0.988046			−0.494023	+	0.869449i	$0.664474\pi$
$338$	−2.76007e8	+	4.19300e8i	−0.388787	+	0.590631i
$339$	−9.45525e8			−1.31818
$340$	1.09523e8	+	1.89699e8i	0.151123	+	0.261752i
$341$	−8.82611e7	−	1.52873e8i	−0.120539	−	0.208780i
$342$	3.21946e8	−	5.57627e8i	0.435203	−	0.753793i
$343$	6.14099e8			0.821692
$344$	2.34560e8	−	4.06271e8i	0.310671	−	0.538097i
$345$	1.97760e9	−	3.42531e9i	2.59282	−	4.49089i
$346$	−3.30999e8			−0.429596
$347$	1.32264e7	−	2.29088e7i	0.0169937	−	0.0294340i	−0.857403	−	0.514645i	$-0.827924\pi$
$347$	1.32264e7	−	2.29088e7i	0.0169937	−	0.0294340i	0.874397	+	0.485211i	$0.161257\pi$
$348$	1.56084e8	+	2.70345e8i	0.198532	+	0.343868i
$349$	−3.89696e8	−	6.74973e8i	−0.490723	−	0.849957i	0.509220	−	0.860636i	$-0.329934\pi$
$349$	−3.89696e8	−	6.74973e8i	−0.490723	−	0.849957i	−0.999943	+	0.0106791i	$0.996601\pi$
$350$	6.53264e8			0.814424
$351$	3.30760e8	+	2.04103e8i	0.408262	+	0.251927i
$352$	−1.12158e8			−0.137066
$353$	3.64706e8	+	6.31689e8i	0.441297	+	0.764349i	0.997786	−	0.0665058i	$-0.0211851\pi$
$353$	3.64706e8	+	6.31689e8i	0.441297	+	0.764349i	−0.556489	+	0.830855i	$0.687852\pi$
$354$	−3.34284e8	−	5.78996e8i	−0.400501	−	0.693688i
$355$	−3.36011e8	+	5.81989e8i	−0.398616	+	0.690423i
$356$	5.04046e8			0.592100
$357$	9.69556e7	−	1.67932e8i	0.112781	−	0.195342i
$358$	−1.29151e8	+	2.23695e8i	−0.148767	+	0.257672i
$359$	−5.70058e8			−0.650262			−0.325131	−	0.945669i	$-0.605408\pi$
$359$	−5.70058e8			−0.650262			−0.325131	+	0.945669i	$0.605408\pi$
$360$	3.85492e8	−	6.67692e8i	0.435468	−	0.754253i
$361$	5.54818e7	+	9.60973e7i	0.0620691	+	0.107507i
$362$	−3.23590e8	−	5.60474e8i	−0.358521	−	0.620977i
$363$	5.53026e8			0.606837
$364$	6.18600e6	−	2.11215e8i	0.00672288	−	0.229546i
$365$	−8.75319e8			−0.942196
$366$	8.22847e8	+	1.42521e9i	0.877274	+	1.51948i
$367$	2.41067e8	+	4.17540e8i	0.254569	+	0.440927i	0.964778	−	0.263064i	$-0.0847330\pi$
$367$	2.41067e8	+	4.17540e8i	0.254569	+	0.440927i	−0.710209	+	0.703991i	$0.751400\pi$
$368$	−2.17453e8	+	3.76639e8i	−0.227456	+	0.393965i
$369$	−1.73195e9			−1.79450
$370$	1.00793e8	−	1.74579e8i	0.103449	−	0.179179i
$371$	1.94660e8	−	3.37162e8i	0.197911	−	0.342791i
$372$	−2.34870e8			−0.236552
$373$	1.49680e8	−	2.59253e8i	0.149342	−	0.258668i	−0.781642	−	0.623727i	$-0.785618\pi$
$373$	1.49680e8	−	2.59253e8i	0.149342	−	0.258668i	0.930984	+	0.365059i	$0.118951\pi$
$374$	−8.95131e7	−	1.55041e8i	−0.0884782	−	0.153249i
$375$	2.19390e9	+	3.79994e9i	2.14836	+	3.72107i
$376$	1.67015e8			0.162031
$377$	−1.58958e7	+	5.42747e8i	−0.0152788	+	0.521678i
$378$	−1.63604e8			−0.155801
$379$	−5.05321e8	−	8.75242e8i	−0.476793	−	0.825830i	0.522853	−	0.852423i	$-0.324868\pi$
$379$	−5.05321e8	−	8.75242e8i	−0.476793	−	0.825830i	−0.999646	+	0.0265924i	$0.991534\pi$
$380$	−4.68720e8	−	8.11846e8i	−0.438198	−	0.758981i
$381$	9.70858e7	−	1.68158e8i	0.0899329	−	0.155768i
$382$	1.09074e8			0.100115
$383$	−4.42877e8	+	7.67085e8i	−0.402798	+	0.697667i	−0.994062	−	0.108811i	$-0.965296\pi$
$383$	−4.42877e8	+	7.67085e8i	−0.402798	+	0.697667i	0.591264	+	0.806478i	$0.298629\pi$
$384$	−7.46150e7	+	1.29237e8i	−0.0672461	+	0.116474i
$385$	−7.46819e8			−0.666965
$386$	6.92976e7	−	1.20027e8i	0.0613285	−	0.106224i
$387$	−1.31781e9	−	2.28251e9i	−1.15575	−	2.00182i
$388$	2.17871e8	+	3.77364e8i	0.189360	+	0.327981i
$389$	2.15563e9			1.85674			0.928370	−	0.371656i	$-0.121210\pi$
$389$	2.15563e9			1.85674			0.928370	+	0.371656i	$0.121210\pi$
$390$	2.07803e9	−	1.11995e9i	1.77389	−	0.956036i
$391$	−6.94197e8			−0.587305
$392$	−1.66354e8	−	2.88133e8i	−0.139486	−	0.241597i
$393$	6.97498e8	+	1.20810e9i	0.579654	+	1.00399i
$394$	2.49499e8	−	4.32145e8i	0.205509	−	0.355953i
$395$	−4.23586e9			−3.45822
$396$	−3.15062e8	+	5.45704e8i	−0.254955	+	0.441595i
$397$	4.73536e8	−	8.20188e8i	0.379827	−	0.657880i	−0.611210	−	0.791469i	$-0.709317\pi$
$397$	4.73536e8	−	8.20188e8i	0.379827	−	0.657880i	0.991037	+	0.133589i	$0.0426501\pi$
$398$	1.93366e7			0.0153741
$399$	−4.14936e8	+	7.18689e8i	−0.327021	+	0.566417i
$400$	−4.01236e8	−	6.94961e8i	−0.313466	−	0.542938i
$401$	7.68784e8	+	1.33157e9i	0.595386	+	1.03124i	0.993492	+	0.113900i	$0.0363343\pi$
$401$	7.68784e8	+	1.33157e9i	0.595386	+	1.03124i	−0.398106	+	0.917339i	$0.630332\pi$
$402$	1.81117e8			0.139049
$403$	−3.47664e8	−	2.14534e8i	−0.264602	−	0.163278i
$404$	1.03048e8			0.0777506
$405$	7.32767e8	+	1.26919e9i	0.548117	+	0.949366i
$406$	−1.14280e8	−	1.97939e8i	−0.0847481	−	0.146788i
$407$	−8.23784e7	+	1.42684e8i	−0.0605666	+	0.104904i
$408$	−2.38201e8			−0.173633
$409$	−4.78055e8	+	8.28015e8i	−0.345498	+	0.598421i	−0.985444	−	0.169999i	$-0.945623\pi$
$409$	−4.78055e8	+	8.28015e8i	−0.345498	+	0.598421i	0.639946	+	0.768420i	$0.278957\pi$
$410$	−1.26077e9	+	2.18371e9i	−0.903423	+	1.56478i
$411$	−4.64236e7			−0.0329831
$412$	−1.57973e8	+	2.73617e8i	−0.111286	+	0.192753i
$413$	2.44753e8	+	4.23924e8i	0.170963	+	0.296117i
$414$	1.22169e9	+	2.11604e9i	0.846177	+	1.46562i
$415$	2.91657e9			2.00311
$416$	−2.28496e8	+	1.23148e8i	−0.155615	+	0.0838686i
$417$	−6.55839e8			−0.442916
$418$	3.83084e8	+	6.63521e8i	0.256553	+	0.444363i
$419$	−1.00065e9	−	1.73318e9i	−0.664559	−	1.15105i	−0.979405	−	0.201907i	$-0.935286\pi$
$419$	−1.00065e9	−	1.73318e9i	−0.664559	−	1.15105i	0.314846	−	0.949143i	$-0.398047\pi$
$420$	−4.96836e8	+	8.60545e8i	−0.327220	+	0.566763i
$421$	2.08228e9			1.36004			0.680020	−	0.733194i	$-0.261971\pi$
$421$	2.08228e9			1.36004			0.680020	+	0.733194i	$0.261971\pi$
$422$	3.89071e8	−	6.73891e8i	0.252020	−	0.436512i
$423$	4.69162e8	−	8.12613e8i	0.301392	−	0.522026i
$424$	−4.78243e8			−0.304697
$425$	6.40454e8	−	1.10930e9i	0.404694	−	0.700950i
$426$	−3.65395e8	−	6.32882e8i	−0.228996	−	0.396634i
$427$	−6.02465e8	−	1.04350e9i	−0.374485	−	0.648626i
$428$	−7.85299e8			−0.484152
$429$	−1.69837e9	+	9.15338e8i	−1.03856	+	0.559733i
$430$	−3.83718e9			−2.32741
$431$	3.68644e8	+	6.38511e8i	0.221788	+	0.384147i	0.955351	−	0.295474i	$-0.0954775\pi$
$431$	3.68644e8	+	6.38511e8i	0.221788	+	0.384147i	−0.733563	+	0.679621i	$0.762144\pi$
$432$	1.00486e8	+	1.74046e8i	0.0599667	+	0.103865i
$433$	2.20052e8	−	3.81141e8i	0.130262	−	0.225620i	−0.793516	−	0.608550i	$-0.791751\pi$
$433$	2.20052e8	−	3.81141e8i	0.130262	−	0.225620i	0.923778	+	0.382930i	$0.125085\pi$
$434$	1.71965e8			0.100978
$435$	1.27669e9	−	2.21129e9i	0.743659	−	1.28805i
$436$	5.28890e8	−	9.16064e8i	0.305606	−	0.529326i
$437$	2.97091e9			1.70296
$438$	4.75932e8	−	8.24339e8i	0.270636	−	0.468755i
$439$	1.08879e9	+	1.88584e9i	0.614212	+	1.06385i	0.990522	+	0.137353i	$0.0438595\pi$
$439$	1.08879e9	+	1.88584e9i	0.614212	+	1.06385i	−0.376310	+	0.926494i	$0.622807\pi$
$440$	4.58698e8	+	7.94488e8i	0.256710	+	0.444634i
$441$	−1.86922e9			−1.03783
$442$	−3.52596e8	−	2.17577e8i	−0.194223	−	0.119849i
$443$	1.78526e9			0.975639			0.487819	−	0.872945i	$-0.337793\pi$
$443$	1.78526e9			0.975639			0.487819	+	0.872945i	$0.337793\pi$
$444$	1.09608e8	+	1.89846e8i	0.0594293	+	0.102935i
$445$	−2.06143e9	−	3.57050e9i	−1.10894	−	1.92074i
$446$	6.68482e8	−	1.15784e9i	0.356794	−	0.617985i
$447$	1.73955e8			0.0921216
$448$	5.46310e7	−	9.46236e7i	0.0287055	−	0.0497195i
$449$	4.68771e8	−	8.11935e8i	0.244398	−	0.423310i	−0.717564	−	0.696493i	$-0.754743\pi$
$449$	4.68771e8	−	8.11935e8i	0.244398	−	0.423310i	0.961962	+	0.273182i	$0.0880762\pi$
$450$	−4.50845e9			−2.33230
$451$	1.03042e9	−	1.78475e9i	0.528930	−	0.916133i
$452$	−4.25203e8	−	7.36474e8i	−0.216577	−	0.375122i
$453$	−9.72010e8	−	1.68357e9i	−0.491278	−	0.850918i
$454$	−4.56543e8			−0.228974
$455$	−1.52148e9	+	8.19998e8i	−0.757225	+	0.408106i
$456$	1.01942e9			0.503471
$457$	−1.53717e9	−	2.66245e9i	−0.753381	−	1.30489i	−0.946175	−	0.323655i	$-0.895088\pi$
$457$	−1.53717e9	−	2.66245e9i	−0.753381	−	1.30489i	0.192794	−	0.981239i	$-0.438245\pi$
$458$	1.07501e9	+	1.86197e9i	0.522858	+	0.905616i
$459$	−1.60395e8	+	2.77813e8i	−0.0774189	+	0.134093i
$460$	3.55732e9			1.70400
$461$	−1.64378e9	+	2.84710e9i	−0.781428	+	1.35347i	0.149681	+	0.988734i	$0.452175\pi$
$461$	−1.64378e9	+	2.84710e9i	−0.781428	+	1.35347i	−0.931110	+	0.364739i	$0.881158\pi$
$462$	4.06064e8	−	7.03323e8i	0.191579	−	0.331824i
$463$	8.40096e7			0.0393365			0.0196682	−	0.999807i	$-0.493739\pi$
$463$	8.40096e7			0.0393365			0.0196682	+	0.999807i	$0.493739\pi$
$464$	−1.40382e8	+	2.43149e8i	−0.0652377	+	0.112995i
$465$	9.60560e8	+	1.66374e9i	0.443036	+	0.767361i
$466$	−2.61500e8	−	4.52932e8i	−0.119707	−	0.207339i
$467$	3.33082e9			1.51336			0.756681	−	0.653785i	$-0.226820\pi$
$467$	3.33082e9			1.51336			0.756681	+	0.653785i	$0.226820\pi$
$468$	−4.26922e7	+	1.45768e9i	−0.0192525	+	0.657359i
$469$	−1.32609e8			−0.0593563
$470$	−6.83051e8	−	1.18308e9i	−0.303467	−	0.525619i
$471$	1.97283e9	+	3.41704e9i	0.869995	+	1.50688i
$472$	3.00655e8	−	5.20750e8i	0.131605	−	0.227946i
$473$	3.13613e9			1.36264
$474$	2.30314e9	−	3.98916e9i	0.993336	−	1.72051i
$475$	−2.74091e9	+	4.74740e9i	−1.17346	+	2.03249i
$476$	1.74404e8			0.0741195
$477$	−1.34343e9	+	2.32690e9i	−0.566764	+	0.981663i
$478$	−8.27188e8	−	1.43273e9i	−0.346423	−	0.600022i
$479$	4.49485e8	+	7.78532e8i	0.186871	+	0.323670i	0.944205	−	0.329357i	$-0.106832\pi$
$479$	4.49485e8	+	7.78532e8i	0.186871	+	0.323670i	−0.757335	+	0.653027i	$0.773499\pi$
$480$	1.22063e9			0.503779
$481$	−1.11626e7	+	3.81136e8i	−0.00457360	+	0.156161i
$482$	2.24380e9			0.912684
$483$	−1.57456e9	−	2.72722e9i	−0.635836	−	1.10130i
$484$	2.48696e8	+	4.30754e8i	0.0997035	+	0.172691i
$485$	1.78208e9	−	3.08666e9i	0.709302	−	1.22855i
$486$	−2.45214e9			−0.968986
$487$	1.33482e9	−	2.31197e9i	0.523685	−	0.907048i	−0.475935	−	0.879480i	$-0.657890\pi$
$487$	1.33482e9	−	2.31197e9i	0.523685	−	0.907048i	0.999620	−	0.0275680i	$-0.00877627\pi$
$488$	−7.40070e8	+	1.28184e9i	−0.288272	+	0.499303i
$489$	−2.27716e9			−0.880670
$490$	−1.36069e9	+	2.35679e9i	−0.522486	+	0.904972i
$491$	−1.70549e9	−	2.95399e9i	−0.650225	−	1.12622i	−0.983068	−	0.183241i	$-0.941341\pi$
$491$	−1.70549e9	−	2.95399e9i	−0.650225	−	1.12622i	0.332843	−	0.942982i	$-0.391992\pi$
$492$	−1.37102e9	−	2.37467e9i	−0.518998	−	0.898931i
$493$	−4.48157e8			−0.168448
$494$	1.50899e9	+	9.31153e8i	0.563172	+	0.347518i
$495$	5.15412e9			1.91001
$496$	−1.05621e8	−	1.82941e8i	−0.0388655	−	0.0673171i
$497$	2.67532e8	+	4.63378e8i	0.0977525	+	0.169312i
$498$	−1.58581e9	+	2.74670e9i	−0.575372	+	0.996573i
$499$	−5.43259e9			−1.95729			−0.978645	−	0.205559i	$-0.934099\pi$
$499$	−5.43259e9			−1.95729			−0.978645	+	0.205559i	$0.934099\pi$
$500$	−1.97319e9	+	3.41767e9i	−0.705951	+	1.22274i
$501$	−6.88318e8	+	1.19220e9i	−0.244544	+	0.423563i
$502$	2.49559e9			0.880461
$503$	−5.84567e8	+	1.01250e9i	−0.204808	+	0.354737i	−0.950071	−	0.312032i	$-0.898990\pi$
$503$	−5.84567e8	+	1.01250e9i	−0.204808	+	0.354737i	0.745264	+	0.666770i	$0.232324\pi$
$504$	−3.06928e8	−	5.31615e8i	−0.106790	−	0.184965i
$505$	−4.21440e8	−	7.29956e8i	−0.145618	−	0.252219i
$506$	−2.90739e9			−0.997647
$507$	−2.45503e9	+	3.72959e9i	−0.836620	+	1.27096i
$508$	1.74638e8			0.0591040
$509$	−1.08501e9	−	1.87929e9i	−0.364688	−	0.631658i	0.624038	−	0.781394i	$-0.285491\pi$
$509$	−1.08501e9	−	1.87929e9i	−0.364688	−	0.631658i	−0.988726	+	0.149736i	$0.952158\pi$
$510$	9.74186e8	+	1.68734e9i	0.325197	+	0.563257i
$511$	−3.48464e8	+	6.03557e8i	−0.115527	+	0.200099i
$512$	−1.34218e8			−0.0441942
$513$	6.86434e8	−	1.18894e9i	0.224485	−	0.388820i
$514$	8.57158e8	−	1.48464e9i	0.278413	−	0.482226i
$515$	2.58428e9			0.833708
$516$	2.08637e9	−	3.61370e9i	0.668524	−	1.15792i
$517$	5.58257e8	+	9.66930e8i	0.177671	+	0.307736i
$518$	−8.02516e7	−	1.39000e8i	−0.0253688	−	0.0439400i
$519$	−2.94417e9			−0.924436
$520$	1.80683e9	+	1.11495e9i	0.563515	+	0.347730i
$521$	−5.57218e9			−1.72621			−0.863103	−	0.505027i	$-0.831482\pi$
$521$	−5.57218e9			−1.72621			−0.863103	+	0.505027i	$0.831482\pi$
$522$	7.88696e8	+	1.36606e9i	0.242696	+	0.420362i
$523$	3.33759e8	+	5.78087e8i	0.102018	+	0.176700i	0.912516	−	0.409041i	$-0.134137\pi$
$523$	3.33759e8	+	5.78087e8i	0.102018	+	0.176700i	−0.810498	+	0.585741i	$0.800803\pi$
$524$	−6.27331e8	+	1.08657e9i	−0.190475	+	0.329912i
$525$	5.81066e9			1.75254
$526$	6.99349e8	−	1.21131e9i	0.209529	−	0.362914i
$527$	1.68593e8	−	2.92011e8i	0.0501766	−	0.0869084i
$528$	−9.97620e8			−0.294949
$529$	−3.93448e9	+	6.81471e9i	−1.15556	+	2.00149i
$530$	1.95590e9	+	3.38772e9i	0.570665	+	0.988420i
$531$	−1.68914e9	−	2.92568e9i	−0.489593	−	0.848000i
$532$	−7.46387e8			−0.214918
$533$	1.39627e8	−	4.76741e9i	0.0399414	−	1.36376i
$534$	4.48339e9			1.27413
$535$	3.21168e9	+	5.56280e9i	0.906764	+	1.57056i
$536$	8.14484e7	+	1.41073e8i	0.0228458	+	0.0395701i
$537$	−1.14877e9	+	1.98973e9i	−0.320127	+	0.554477i
$538$	−2.26477e9			−0.627026
$539$	1.11209e9	−	1.92620e9i	0.305901	−	0.529836i
$540$	8.21923e8	−	1.42361e9i	0.224622	−	0.389058i
$541$	4.87524e9			1.32375			0.661875	−	0.749614i	$-0.269761\pi$
$541$	4.87524e9			1.32375			0.661875	+	0.749614i	$0.269761\pi$
$542$	8.71021e8	−	1.50865e9i	0.234980	−	0.406997i
$543$	−2.87827e9	−	4.98531e9i	−0.771493	−	1.33626i
$544$	−1.07119e8	−	1.85536e8i	−0.0285280	−	0.0494120i
$545$	−8.65212e9			−2.28947
$546$	5.50233e7	−	1.87871e9i	0.0144668	−	0.493954i
$547$	6.55899e8			0.171349			0.0856744	−	0.996323i	$-0.472696\pi$
$547$	6.55899e8			0.171349			0.0856744	+	0.996323i	$0.472696\pi$
$548$	−2.08767e7	−	3.61595e7i	−0.00541914	−	0.00938622i
$549$	4.15786e9	+	7.20163e9i	1.07242	+	1.85749i
$550$	2.68231e9	−	4.64589e9i	0.687447	−	1.19069i
$551$	1.91795e9			0.488435
$552$	−1.93420e9	+	3.35013e9i	−0.489457	+	0.847764i
$553$	−1.68629e9	+	2.92075e9i	−0.424029	+	0.734439i
$554$	4.40207e9			1.09995
$555$	8.96538e8	−	1.55285e9i	0.222609	−	0.385571i
$556$	−2.94932e8	−	5.10836e8i	−0.0727712	−	0.126043i
$557$	7.33190e8	+	1.26992e9i	0.179773	+	0.311375i	0.941803	−	0.336167i	$-0.109130\pi$
$557$	7.33190e8	+	1.26992e9i	0.179773	+	0.311375i	−0.762030	+	0.647542i	$0.775797\pi$
$558$	−1.18680e9			−0.289173
$559$	6.38915e9	−	3.44343e9i	1.54704	−	0.833777i
$560$	−8.93710e8			−0.215050
$561$	−7.96201e8	−	1.37906e9i	−0.190394	−	0.329772i
$562$	−5.70690e8	−	9.88465e8i	−0.135620	−	0.234901i
$563$	1.50686e9	−	2.60996e9i	0.355872	−	0.616388i	−0.631395	−	0.775461i	$-0.717517\pi$
$563$	1.50686e9	−	2.60996e9i	0.355872	−	0.616388i	0.987267	+	0.159074i	$0.0508507\pi$
$564$	1.48557e9			0.348670
$565$	−3.47796e9	+	6.02400e9i	−0.811250	+	1.40513i
$566$	−1.03699e8	+	1.79612e8i	−0.0240390	+	0.0416368i
$567$	1.16686e9			0.268829
$568$	3.28637e8	−	5.69216e8i	0.0752483	−	0.130334i
$569$	3.75097e9	+	6.49687e9i	0.853592	+	1.47847i	0.877945	+	0.478762i	$0.158914\pi$
$569$	3.75097e9	+	6.49687e9i	0.853592	+	1.47847i	−0.0243527	+	0.999703i	$0.507752\pi$
$570$	−4.16917e9	−	7.22121e9i	−0.942947	−	1.63323i
$571$	−1.19452e9			−0.268514			−0.134257	−	0.990947i	$-0.542865\pi$
$571$	−1.19452e9			−0.268514			−0.134257	+	0.990947i	$0.542865\pi$
$572$	−1.47672e9	−	9.11244e8i	−0.329923	−	0.203586i
$573$	9.70190e8			0.215435
$574$	1.00382e9	+	1.73867e9i	0.221546	+	0.383729i
$575$	−1.04010e10	−	1.80150e10i	−2.28159	−	3.95183i
$576$	−3.77031e8	+	6.53037e8i	−0.0822051	+	0.142383i
$577$	−4.85637e9			−1.05244			−0.526219	−	0.850349i	$-0.676391\pi$
$577$	−4.85637e9			−1.05244			−0.526219	+	0.850349i	$0.676391\pi$
$578$	−1.47037e9	+	2.54676e9i	−0.316723	+	0.548580i
$579$	6.16388e8	−	1.06762e9i	0.131971	−	0.228581i
$580$	2.29652e9			0.488733
$581$	1.16109e9	−	2.01106e9i	0.245611	−	0.425411i
$582$	1.93792e9	+	3.35658e9i	0.407479	+	0.705775i
$583$	−1.59856e9	−	2.76878e9i	−0.334109	−	0.578693i
$584$	8.56108e8			0.177862
$585$	1.05003e10	−	5.65915e9i	2.16849	−	1.16871i
$586$	−5.95091e9			−1.22164
$587$	1.01242e9	+	1.75356e9i	0.206598	+	0.357839i	0.950641	−	0.310294i	$-0.100427\pi$
$587$	1.01242e9	+	1.75356e9i	0.206598	+	0.357839i	−0.744043	+	0.668132i	$0.767094\pi$
$588$	−1.47968e9	−	2.56289e9i	−0.300157	−	0.519887i
$589$	−7.21516e8	+	1.24970e9i	−0.145493	+	0.252001i
$590$	−4.91843e9			−0.985926
$591$	2.21924e9	−	3.84384e9i	0.442231	−	0.765966i
$592$	−9.85813e7	+	1.70748e8i	−0.0195285	+	0.0338243i
$593$	9.30040e8			0.183151			0.0915757	−	0.995798i	$-0.470810\pi$
$593$	9.30040e8			0.183151			0.0915757	+	0.995798i	$0.470810\pi$
$594$	−6.71757e8	+	1.16352e9i	−0.131510	+	0.227783i
$595$	−7.13271e8	−	1.23542e9i	−0.138818	−	0.240439i
$596$	7.82278e7	+	1.35495e8i	0.0151356	+	0.0262156i
$597$	1.71995e8			0.0330831
$598$	−5.92316e9	+	3.19228e9i	−1.13266	+	0.610445i
$599$	2.25978e9			0.429608			0.214804	−	0.976657i	$-0.431089\pi$
$599$	2.25978e9			0.429608			0.214804	+	0.976657i	$0.431089\pi$
$600$	−3.56891e9	−	6.18154e9i	−0.674539	−	1.16834i
$601$	−7.28350e8	−	1.26154e9i	−0.136861	−	0.237050i	0.789446	−	0.613820i	$-0.210368\pi$
$601$	−7.28350e8	−	1.26154e9i	−0.136861	−	0.237050i	−0.926307	+	0.376770i	$0.877035\pi$
$602$	−1.52758e9	+	2.64584e9i	−0.285375	+	0.494284i
$603$	9.15188e8			0.169981
$604$	8.74228e8	−	1.51421e9i	0.161434	−	0.279612i
$605$	2.03422e9	−	3.52336e9i	0.373468	−	0.646865i
$606$	9.16589e8			0.167309
$607$	2.64143e9	−	4.57510e9i	0.479379	−	0.830309i	−0.520341	−	0.853958i	$-0.674195\pi$
$607$	2.64143e9	−	4.57510e9i	0.479379	−	0.830309i	0.999720	+	0.0236495i	$0.00752856\pi$
$608$	4.58432e8	+	7.94028e8i	0.0827204	+	0.143276i
$609$	−1.01650e9	−	1.76063e9i	−0.182367	−	0.315869i
$610$	1.21068e10			2.15961
$611$	2.19900e9	+	1.35694e9i	0.390015	+	0.240667i
$612$	−1.20364e9			−0.212259
$613$	1.20643e9	+	2.08960e9i	0.211540	+	0.366397i	0.952197	−	0.305486i	$-0.0988190\pi$
$613$	1.20643e9	+	2.08960e9i	0.211540	+	0.366397i	−0.740657	+	0.671883i	$0.765486\pi$
$614$	1.14732e9	+	1.98722e9i	0.200030	+	0.346463i
$615$	−1.12143e10	+	1.94237e10i	−1.94405	+	3.36720i
$616$	7.30429e8			0.125906
$617$	−4.68931e9	+	8.12213e9i	−0.803732	+	1.39210i	0.113412	+	0.993548i	$0.463822\pi$
$617$	−4.68931e9	+	8.12213e9i	−0.803732	+	1.39210i	−0.917144	+	0.398556i	$0.869511\pi$
$618$	−1.40513e9	+	2.43376e9i	−0.239474	+	0.414781i
$619$	2.73222e9			0.463019			0.231510	−	0.972833i	$-0.425634\pi$
$619$	2.73222e9			0.463019			0.231510	+	0.972833i	$0.425634\pi$
$620$	−8.63929e8	+	1.49637e9i	−0.145582	+	0.252155i
$621$	2.60482e9	+	4.51169e9i	0.436473	+	0.755994i
$622$	2.87556e9	+	4.98061e9i	0.479133	+	0.829882i
$623$	−3.28261e9			−0.543890
$624$	−2.03243e9	+	1.09537e9i	−0.334864	+	0.180475i
$625$	1.69736e10			2.78096
$626$	2.48153e9	+	4.29814e9i	0.404305	+	0.700277i
$627$	3.40746e9	+	5.90189e9i	0.552070	+	0.956213i
$628$	−1.77437e9	+	3.07329e9i	−0.285881	+	0.495160i
$629$	−3.14711e8			−0.0504238
$630$	−2.51052e9	+	4.34835e9i	−0.400011	+	0.692840i
$631$	−4.52633e9	+	7.83984e9i	−0.717205	+	1.24224i	0.244897	+	0.969549i	$0.421246\pi$
$631$	−4.52633e9	+	7.83984e9i	−0.717205	+	1.24224i	−0.962103	+	0.272687i	$0.912088\pi$
$632$	4.14290e9			0.652821
$633$	3.46071e9	−	5.99413e9i	0.542316	−	0.939319i
$634$	6.69017e8	+	1.15877e9i	0.104262	+	0.180587i
$635$	−7.14229e8	−	1.23708e9i	−0.110695	−	0.191730i
$636$	−4.25388e9			−0.655670
$637$	1.50693e8	−	5.14527e9i	0.0230997	−	0.788716i
$638$	−1.87694e9			−0.286140
$639$	−1.84635e9	−	3.19797e9i	−0.279937	−	0.484866i
$640$	5.48918e8	+	9.50754e8i	0.0827709	+	0.143363i
$641$	5.18052e9	−	8.97293e9i	0.776910	−	1.34565i	−0.156805	−	0.987630i	$-0.550119\pi$
$641$	5.18052e9	−	8.97293e9i	0.776910	−	1.34565i	0.933715	−	0.358018i	$-0.116547\pi$
$642$	−6.98508e9			−1.04183
$643$	1.96400e9	−	3.40175e9i	0.291342	−	0.504619i	−0.682785	−	0.730619i	$-0.739232\pi$
$643$	1.96400e9	−	3.40175e9i	0.291342	−	0.504619i	0.974127	+	0.226000i	$0.0725648\pi$
$644$	1.41616e9	−	2.45287e9i	0.208936	−	0.361888i
$645$	−3.41310e10			−5.00829
$646$	−7.31751e8	+	1.26743e9i	−0.106795	+	0.184974i
$647$	5.63673e9	+	9.76311e9i	0.818206	+	1.41717i	0.907003	+	0.421124i	$0.138364\pi$
$647$	5.63673e9	+	9.76311e9i	0.818206	+	1.41717i	−0.0887973	+	0.996050i	$0.528302\pi$
$648$	−7.16684e8	−	1.24133e9i	−0.103470	−	0.179216i
$649$	4.01983e9			0.577233
$650$	3.63464e8	−	1.24101e10i	0.0519116	−	1.77247i
$651$	1.52959e9			0.217291
$652$	−1.02404e9	−	1.77369e9i	−0.144694	−	0.250618i
$653$	6.93321e9	+	1.20087e10i	0.974401	+	1.68771i	0.681896	+	0.731449i	$0.261156\pi$
$653$	6.93321e9	+	1.20087e10i	0.974401	+	1.68771i	0.292505	+	0.956264i	$0.405511\pi$
$654$	4.70437e9	−	8.14820e9i	0.657626	−	1.13904i
$655$	1.02625e10			1.42695
$656$	1.23310e9	−	2.13579e9i	0.170543	−	0.295389i
$657$	2.40490e9	−	4.16540e9i	0.330840	−	0.573031i
$658$	−1.08769e9			−0.148838
$659$	7.94245e7	−	1.37567e8i	0.0108107	−	0.0187248i	−0.860569	−	0.509333i	$-0.829892\pi$
$659$	7.94245e7	−	1.37567e8i	0.0108107	−	0.0187248i	0.871380	+	0.490608i	$0.163225\pi$
$660$	4.08003e9	+	7.06681e9i	0.552407	+	0.956797i
$661$	−5.58771e9	−	9.67820e9i	−0.752539	−	1.30344i	−0.946589	−	0.322443i	$-0.895496\pi$
$661$	−5.58771e9	−	9.67820e9i	−0.752539	−	1.30344i	0.194050	−	0.980992i	$-0.437838\pi$
$662$	−6.31428e9			−0.845904
$663$	−3.13627e9	−	1.93531e9i	−0.417942	−	0.257901i
$664$	−2.85256e9			−0.378135
$665$	3.05255e9	+	5.28716e9i	0.402519	+	0.697183i
$666$	5.53850e8	+	9.59296e8i	0.0726495	+	0.125833i
$667$	−3.63904e9	+	6.30300e9i	−0.474839	+	0.822445i
$668$	−1.23815e9			−0.160715
$669$	5.94601e9	−	1.02988e10i	0.767776	−	1.32983i
$670$	6.66209e8	−	1.15391e9i	0.0855754	−	0.148221i
$671$	−9.89490e9			−1.26439
$672$	4.85932e8	−	8.41658e8i	0.0617707	−	0.106990i
$673$	2.69956e9	+	4.67577e9i	0.341381	+	0.591289i	0.984689	−	0.174318i	$-0.0557720\pi$
$673$	2.69956e9	+	4.67577e9i	0.341381	+	0.591289i	−0.643308	+	0.765607i	$0.722439\pi$
$674$	−2.77678e9	−	4.80953e9i	−0.349327	−	0.605052i
$675$	−9.61266e9			−1.20304
$676$	−4.00902e9	−	2.35032e8i	−0.499143	−	0.0292626i
$677$	−7.69486e9			−0.953104			−0.476552	−	0.879146i	$-0.658114\pi$
$677$	−7.69486e9			−0.953104			−0.476552	+	0.879146i	$0.658114\pi$
$678$	−3.78210e9	−	6.55079e9i	−0.466046	−	0.807216i
$679$	−1.41889e9	−	2.45759e9i	−0.173942	−	0.301276i
$680$	−8.76184e8	+	1.51760e9i	−0.106860	+	0.185087i
$681$	−4.06086e9			−0.492724
$682$	7.06089e8	−	1.22298e9i	0.0852342	−	0.147630i
$683$	2.54926e9	−	4.41544e9i	0.306155	−	0.530275i	−0.671363	−	0.741129i	$-0.734291\pi$
$683$	2.54926e9	−	4.41544e9i	0.306155	−	0.530275i	0.977518	+	0.210853i	$0.0676242\pi$
$684$	5.15113e9			0.615469
$685$	−1.70761e8	+	2.95768e8i	−0.0202989	+	0.0351588i
$686$	2.45640e9	+	4.25461e9i	0.290512	+	0.503182i
$687$	9.56200e9	+	1.65619e10i	1.12512	+	1.94877i
$688$	3.75297e9			0.439355
$689$	−6.29678e9	−	3.88557e9i	−0.733417	−	0.452572i
$690$	3.16416e10			3.66680
$691$	1.53611e8	+	2.66062e8i	0.0177112	+	0.0306768i	0.874745	−	0.484583i	$-0.161029\pi$
$691$	1.53611e8	+	2.66062e8i	0.0177112	+	0.0306768i	−0.857034	+	0.515260i	$0.827695\pi$
$692$	−1.32400e9	−	2.29323e9i	−0.151885	−	0.263073i
$693$	2.05185e9	−	3.55391e9i	0.234196	−	0.405639i
$694$	2.11623e8			0.0240328
$695$	−2.41240e9	+	4.17840e9i	−0.272585	+	0.472131i
$696$	−1.24867e9	+	2.16276e9i	−0.140383	+	0.243151i
$697$	3.93654e9			0.440352
$698$	3.11757e9	−	5.39978e9i	0.346994	−	0.601011i
$699$	−2.32599e9	−	4.02874e9i	−0.257595	−	0.446168i
$700$	2.61306e9	+	4.52595e9i	0.287942	+	0.498731i
$701$	1.35330e9			0.148382			0.0741910	−	0.997244i	$-0.476363\pi$
$701$	1.35330e9			0.148382			0.0741910	+	0.997244i	$0.476363\pi$
$702$	−9.10259e7	+	3.10799e9i	−0.00993081	+	0.339078i
$703$	1.34685e9			0.146210
$704$	−4.48630e8	−	7.77051e8i	−0.0484601	−	0.0839354i
$705$	−6.07561e9	−	1.05233e10i	−0.653022	−	1.13107i
$706$	−2.91765e9	+	5.05351e9i	−0.312044	+	0.540477i
$707$	−6.71100e8			−0.0714199
$708$	2.67427e9	−	4.63197e9i	0.283197	−	0.490512i
$709$	−5.45562e9	+	9.44942e9i	−0.574887	+	0.995734i	0.421167	+	0.906983i	$0.361621\pi$
$709$	−5.45562e9	+	9.44942e9i	−0.574887	+	0.995734i	−0.996054	+	0.0887504i	$0.971713\pi$
$710$	−5.37618e9			−0.563728
$711$	1.16378e10	−	2.01573e10i	1.21431	−	2.10324i
$712$	2.01618e9	+	3.49213e9i	0.209339	+	0.362586i
$713$	−2.73795e9	−	4.74227e9i	−0.282886	−	0.489973i
$714$	1.55129e9			0.159496
$715$	−4.15516e8	+	1.41874e10i	−0.0425125	+	1.45155i
$716$	−2.06641e9			−0.210388
$717$	−7.35768e9	−	1.27439e10i	−0.745459	−	1.29117i
$718$	−2.28023e9	−	3.94948e9i	−0.229902	−	0.398203i
$719$	5.14659e9	−	8.91415e9i	0.516379	−	0.894394i	−0.483440	−	0.875377i	$-0.660613\pi$
$719$	5.14659e9	−	8.91415e9i	0.516379	−	0.894394i	0.999819	−	0.0190170i	$-0.00605368\pi$
$720$	6.16787e9			0.615845
$721$	1.02880e9	−	1.78193e9i	0.102225	−	0.177059i
$722$	−4.43854e8	+	7.68779e8i	−0.0438895	+	0.0760188i
$723$	1.99582e10			1.96398
$724$	2.58872e9	−	4.48379e9i	0.253513	−	0.439097i
$725$	−6.71463e9	−	1.16301e10i	−0.654393	−	1.13344i
$726$	2.21210e9	+	3.83148e9i	0.214549	+	0.371610i
$727$	7.61641e9			0.735156			0.367578	−	0.929993i	$-0.380187\pi$
$727$	7.61641e9			0.735156			0.367578	+	0.929993i	$0.380187\pi$
$728$	1.48808e9	−	8.02002e8i	0.142945	−	0.0770398i
$729$	−1.56887e10			−1.49982
$730$	−3.50128e9	−	6.06439e9i	−0.333117	−	0.576975i
$731$	2.99525e9	+	5.18792e9i	0.283610	+	0.491227i
$732$	−6.58277e9	+	1.14017e10i	−0.620326	+	1.07444i
$733$	5.63920e9			0.528875			0.264438	−	0.964403i	$-0.414814\pi$
$733$	5.63920e9			0.528875			0.264438	+	0.964403i	$0.414814\pi$
$734$	−1.92853e9	+	3.34032e9i	−0.180008	+	0.311782i
$735$	−1.21031e10	+	2.09632e10i	−1.12432	+	1.94739i
$736$	−3.47924e9			−0.321671
$737$	−5.44492e8	+	9.43088e8i	−0.0501020	+	0.0867793i
$738$	−6.92779e9	−	1.19993e10i	−0.634450	−	1.09890i
$739$	−1.09173e10	−	1.89093e10i	−0.995083	−	1.72353i	−0.583317	−	0.812245i	$-0.698245\pi$
$739$	−1.09173e10	−	1.89093e10i	−0.995083	−	1.72353i	−0.411766	−	0.911289i	$-0.635088\pi$
$740$	1.61270e9			0.146299
$741$	1.34221e10	+	8.28242e9i	1.21187	+	0.747814i
$742$	3.11457e9			0.279888
$743$	5.74324e9	+	9.94759e9i	0.513684	+	0.889728i	0.999874	+	0.0158742i	$0.00505313\pi$
$743$	5.74324e9	+	9.94759e9i	0.513684	+	0.889728i	−0.486190	+	0.873853i	$0.661614\pi$
$744$	−9.39478e8	−	1.62722e9i	−0.0836337	−	0.144858i
$745$	6.39866e8	−	1.10828e9i	0.0566947	−	0.0981980i
$746$	2.39487e9			0.211201
$747$	−8.01314e9	+	1.38792e10i	−0.703365	+	1.21826i
$748$	7.16105e8	−	1.24033e9i	0.0625635	−	0.108363i
$749$	5.11427e9			0.444731
$750$	−1.75512e10	+	3.03995e10i	−1.51912	+	2.63119i
$751$	−3.48748e9	−	6.04050e9i	−0.300450	−	0.520395i	0.675788	−	0.737096i	$-0.263804\pi$
$751$	−3.48748e9	−	6.04050e9i	−0.300450	−	0.520395i	−0.976238	+	0.216701i	$0.930470\pi$
$752$	6.68060e8	+	1.15711e9i	0.0572866	+	0.0992233i
$753$	2.21978e10			1.89464
$754$	−3.82385e9	+	2.06086e9i	−0.324863	+	0.175085i
$755$	−1.43015e10			−1.20939
$756$	−6.54414e8	−	1.13348e9i	−0.0550841	−	0.0954085i
$757$	1.58758e9	+	2.74977e9i	0.133015	+	0.230389i	0.924837	−	0.380363i	$-0.124201\pi$
$757$	1.58758e9	+	2.74977e9i	0.133015	+	0.230389i	−0.791822	+	0.610751i	$0.790867\pi$
$758$	4.04257e9	−	7.00194e9i	0.337144	−	0.583950i
$759$	−2.58607e10			−2.14681
$760$	3.74976e9	−	6.49477e9i	0.309853	−	0.536681i
$761$	−7.65367e9	+	1.32565e10i	−0.629540	+	1.09040i	0.358104	+	0.933682i	$0.383423\pi$
$761$	−7.65367e9	+	1.32565e10i	−0.629540	+	1.09040i	−0.987644	+	0.156714i	$0.949910\pi$
$762$	1.55337e9			0.127184
$763$	−3.44440e9	+	5.96588e9i	−0.280723	+	0.486227i
$764$	4.36295e8	+	7.55685e8i	0.0353959	+	0.0613076i
$765$	4.92258e9	+	8.52616e9i	0.397537	+	0.688555i
$766$	−7.08603e9			−0.569642
$767$	8.18950e9	−	4.41372e9i	0.655350	−	0.353200i
$768$	−1.19384e9			−0.0951003
$769$	−1.47679e9	−	2.55788e9i	−0.117105	−	0.202833i	0.801514	−	0.597976i	$-0.204028\pi$
$769$	−1.47679e9	−	2.55788e9i	−0.117105	−	0.202833i	−0.918619	+	0.395143i	$0.870695\pi$
$770$	−2.98728e9	−	5.17412e9i	−0.235808	−	0.408431i
$771$	7.62425e9	−	1.32056e10i	0.599110	−	1.03769i
$772$	1.10876e9			0.0867316
$773$	−4.92294e9	+	8.52678e9i	−0.383351	+	0.663983i	−0.991539	−	0.129810i	$-0.958563\pi$
$773$	−4.92294e9	+	8.52678e9i	−0.383351	+	0.663983i	0.608188	+	0.793793i	$0.291897\pi$
$774$	1.05425e10	−	1.82601e10i	0.817239	−	1.41550i
$775$	1.01039e10			0.779712
$776$	−1.74297e9	+	3.01891e9i	−0.133898	+	0.231918i
$777$	−7.13822e8	−	1.23638e9i	−0.0545904	−	0.0945534i
$778$	8.62253e9	+	1.49347e10i	0.656457	+	1.13702i
$779$	−1.68470e10			−1.27685
$780$	1.60714e10	+	9.91722e9i	1.21261	+	0.748271i
$781$	4.39395e9			0.330047
$782$	−2.77679e9	−	4.80954e9i	−0.207644	−	0.359650i
$783$	1.68161e9	+	2.91264e9i	0.125187	+	0.216830i
$784$	1.33083e9	−	2.30507e9i	0.0986317	−	0.170835i
$785$	2.90269e10			2.14169
$786$	−5.57998e9	+	9.66481e9i	−0.409877	+	0.709928i
$787$	2.60565e9	−	4.51312e9i	0.190548	−	0.330039i	−0.754884	−	0.655858i	$-0.772307\pi$
$787$	2.60565e9	−	4.51312e9i	0.190548	−	0.330039i	0.945432	+	0.325820i	$0.105640\pi$
$788$	3.99198e9			0.290634
$789$	6.22057e9	−	1.07743e10i	0.450880	−	0.780946i
$790$	−1.69435e10	−	2.93469e10i	−1.22266	−	2.11772i
$791$	2.76914e9	+	4.79630e9i	0.198943	+	0.344579i
$792$	−5.04100e9			−0.360561
$793$	−2.01586e10	+	1.08645e10i	−1.43551	+	0.773665i
$794$	7.57657e9			0.537157
$795$	1.73973e10	+	3.01331e10i	1.22800	+	2.12696i
$796$	7.73464e7	+	1.33968e8i	0.00543556	+	0.00941466i
$797$	−3.92980e9	+	6.80662e9i	−0.274958	+	0.476241i	−0.970125	−	0.242607i	$-0.921997\pi$
$797$	−3.92980e9	+	6.80662e9i	−0.274958	+	0.476241i	0.695166	+	0.718849i	$0.255331\pi$
$798$	−6.63897e9			−0.462477
$799$	−1.06636e9	+	1.84699e9i	−0.0739588	+	0.128100i
$800$	3.20989e9	−	5.55969e9i	0.221654	−	0.383915i
$801$	2.26547e10			1.55756
$802$	−6.15027e9	+	1.06526e10i	−0.421002	+	0.729196i
$803$	2.86159e9	+	4.95642e9i	0.195031	+	0.337803i
$804$	7.24468e8	+	1.25481e9i	0.0491612	+	0.0851498i
$805$	−2.31671e10			−1.56526
$806$	9.56779e7	−	3.26683e9i	0.00643634	−	0.219762i
$807$	−2.01447e10			−1.34928
$808$	4.12191e8	+	7.13935e8i	0.0274890	+	0.0476123i
$809$	3.22934e9	+	5.59338e9i	0.214434	+	0.371411i	0.953097	−	0.302664i	$-0.0978760\pi$
$809$	3.22934e9	+	5.59338e9i	0.214434	+	0.371411i	−0.738663	+	0.674075i	$0.764543\pi$
$810$	−5.86213e9	+	1.01535e10i	−0.387577	+	0.671303i
$811$	−2.35320e10			−1.54912			−0.774562	−	0.632498i	$-0.782030\pi$
$811$	−2.35320e10			−1.54912			−0.774562	+	0.632498i	$0.782030\pi$
$812$	9.14241e8	−	1.58351e9i	0.0599259	−	0.103795i
$813$	7.74756e9	−	1.34192e10i	0.505648	−	0.875807i
$814$	−1.31806e9			−0.0856541
$815$	−8.37617e9	+	1.45080e10i	−0.541993	+	0.938760i
$816$	−9.52805e8	−	1.65031e9i	−0.0613887	−	0.106328i
$817$	−1.28186e10	−	2.22024e10i	−0.822362	−	1.42437i
$818$	−7.64887e9			−0.488608
$819$	2.78034e8	−	9.49319e9i	0.0176850	−	0.603835i
$820$	−2.01723e10			−1.27763
$821$	1.26199e9	+	2.18583e9i	0.0795894	+	0.137853i	0.903073	−	0.429487i	$-0.141306\pi$
$821$	1.26199e9	+	2.18583e9i	0.0795894	+	0.137853i	−0.823483	+	0.567340i	$0.807972\pi$
$822$	−1.85694e8	−	3.21632e8i	−0.0116613	−	0.0201980i
$823$	8.68821e9	−	1.50484e10i	0.543289	−	0.941004i	−0.455423	−	0.890275i	$-0.650512\pi$
$823$	8.68821e9	−	1.50484e10i	0.543289	−	0.941004i	0.998712	−	0.0507293i	$-0.0161546\pi$
$824$	−2.52756e9			−0.157382
$825$	2.38586e10	−	4.13243e10i	1.47930	−	2.56222i
$826$	−1.95802e9	+	3.39139e9i	−0.120889	+	0.209386i
$827$	1.96660e10			1.20906			0.604530	−	0.796583i	$-0.293361\pi$
$827$	1.96660e10			1.20906			0.604530	+	0.796583i	$0.293361\pi$
$828$	−9.77355e9	+	1.69283e10i	−0.598337	+	1.03635i
$829$	−1.53344e10	−	2.65600e10i	−0.934817	−	1.61915i	−0.774960	−	0.632010i	$-0.782230\pi$
$829$	−1.53344e10	−	2.65600e10i	−0.934817	−	1.61915i	−0.159857	−	0.987140i	$-0.551103\pi$
$830$	1.16663e10	+	2.02066e10i	0.708206	+	1.22665i
$831$	3.91555e10			2.36695
$832$	−1.76718e9	−	1.09047e9i	−0.106377	−	0.0656423i
$833$	4.24855e9			0.254673
$834$	−2.62336e9	−	4.54379e9i	−0.156594	−	0.271230i
$835$	5.06373e9	+	8.77064e9i	0.301001	+	0.521349i
$836$	−3.06467e9	+	5.30817e9i	−0.181410	+	0.314212i
$837$	−2.53043e9			−0.149161
$838$	8.00520e9	−	1.38654e10i	0.469914	−	0.813915i
$839$	1.50419e10	−	2.60533e10i	0.879297	−	1.52299i	0.0271823	−	0.999630i	$-0.491347\pi$
$839$	1.50419e10	−	2.60533e10i	0.879297	−	1.52299i	0.852114	−	0.523356i	$-0.175320\pi$
$840$	−7.94937e9			−0.462760
$841$	6.27566e9	−	1.08698e10i	0.363809	−	0.630136i
$842$	8.32911e9	+	1.44264e10i	0.480846	+	0.832850i
$843$	−5.07618e9	−	8.79220e9i	−0.291837	−	0.505477i
$844$	6.22514e9			0.356411
$845$	1.47310e10	+	2.93598e10i	0.839915	+	1.67400i
$846$	7.50660e9			0.426233
$847$	−1.61964e9	−	2.80530e9i	−0.0915854	−	0.158631i
$848$	−1.91297e9	−	3.31337e9i	−0.107727	−	0.186588i
$849$	−9.22381e8	+	1.59761e9i	−0.0517289	+	0.0895971i
$850$	1.02473e10			0.572323
$851$	−2.55546e9	+	4.42619e9i	−0.142140	+	0.246194i
$852$	2.92316e9	−	5.06306e9i	0.161925	−	0.280462i
$853$	−8.80922e9			−0.485977			−0.242989	−	0.970029i	$-0.578128\pi$
$853$	−8.80922e9			−0.485977			−0.242989	+	0.970029i	$0.578128\pi$
$854$	4.81972e9	−	8.34800e9i	0.264801	−	0.458648i
$855$	−2.10669e10	−	3.64889e10i	−1.15271	−	1.99655i
$856$	−3.14120e9	−	5.44071e9i	−0.171174	−	0.296481i
$857$	1.71306e10			0.929696			0.464848	−	0.885391i	$-0.346109\pi$
$857$	1.71306e10			0.929696			0.464848	+	0.885391i	$0.346109\pi$
$858$	−1.31351e10	−	8.10533e9i	−0.709953	−	0.438092i
$859$	9.23130e9			0.496921			0.248460	−	0.968642i	$-0.420075\pi$
$859$	9.23130e9			0.496921			0.248460	+	0.968642i	$0.420075\pi$
$860$	−1.53487e10	−	2.65848e10i	−0.822864	−	1.42524i
$861$	8.92879e9	+	1.54651e10i	0.476740	+	0.825737i
$862$	−2.94916e9	+	5.10809e9i	−0.156827	+	0.271633i
$863$	−2.02167e10			−1.07071			−0.535356	−	0.844627i	$-0.679822\pi$
$863$	−2.02167e10			−1.07071			−0.535356	+	0.844627i	$0.679822\pi$
$864$	−8.03884e8	+	1.39237e9i	−0.0424029	+	0.0734440i
$865$	−1.08296e10	+	1.87575e10i	−0.568929	+	0.985414i
$866$	3.52083e9			0.184218
$867$	−1.30787e10	+	2.26529e10i	−0.681548	+	1.18048i
$868$	6.87859e8	+	1.19141e9i	0.0357010	+	0.0618359i
$869$	1.38479e10	+	2.39852e10i	0.715837	+	1.23987i
$870$	2.04271e10			1.05169
$871$	−7.37809e7	+	2.51918e9i	−0.00378338	+	0.129180i
$872$	8.46223e9			0.432193
$873$	9.79236e9	+	1.69609e10i	0.498124	+	0.862776i
$874$	1.18837e10	+	2.05831e10i	0.602088	+	1.04285i
$875$	1.28505e10	−	2.22577e10i	0.648471	−	1.12318i
$876$	7.61491e9			0.382737
$877$	7.10449e9	−	1.23053e10i	0.355659	−	0.616020i	−0.631571	−	0.775318i	$-0.717590\pi$
$877$	7.10449e9	−	1.23053e10i	0.355659	−	0.616020i	0.987231	+	0.159298i	$0.0509230\pi$
$878$	−8.71033e9	+	1.50867e10i	−0.434314	+	0.752253i
$879$	−5.29322e10			−2.62881
$880$	−3.66958e9	+	6.35590e9i	−0.181521	+	0.314404i
$881$	7.59598e9	+	1.31566e10i	0.374256	+	0.648230i	0.990215	−	0.139548i	$-0.0445649\pi$
$881$	7.59598e9	+	1.31566e10i	0.374256	+	0.648230i	−0.615960	+	0.787778i	$0.711232\pi$
$882$	−7.47688e9	−	1.29503e10i	−0.366928	−	0.635537i
$883$	5.15139e8			0.0251803			0.0125902	−	0.999921i	$-0.495992\pi$
$883$	5.15139e8			0.0251803			0.0125902	+	0.999921i	$0.495992\pi$
$884$	9.70351e7	−	3.31317e9i	0.00472439	−	0.161310i
$885$	−4.37485e10			−2.12159
$886$	7.14105e9	+	1.23687e10i	0.344940	+	0.597454i
$887$	−1.37994e10	−	2.39012e10i	−0.663936	−	1.14997i	−0.979573	−	0.201091i	$-0.935551\pi$
$887$	−1.37994e10	−	2.39012e10i	−0.663936	−	1.14997i	0.315636	−	0.948880i	$-0.397782\pi$
$888$	−8.76861e8	+	1.51877e9i	−0.0420229	+	0.0727857i
$889$	−1.13734e9			−0.0542916
$890$	1.64914e10	−	2.85640e10i	0.784139	−	1.35817i
$891$	4.79112e9	−	8.29846e9i	0.226916	−	0.393030i
$892$	1.06957e10			0.504583
$893$	4.56364e9	−	7.90445e9i	0.214452	−	0.371442i
$894$	6.95821e8	+	1.20520e9i	0.0325699	+	0.0564127i
$895$	8.45112e9	+	1.46378e10i	0.394034	+	0.682487i
$896$	8.74095e8			0.0405958
$897$	−5.26853e10	+	2.83947e10i	−2.43734	+	1.31360i
$898$	7.50033e9			0.345632
$899$	−1.76755e9	−	3.06149e9i	−0.0811360	−	0.140532i
$900$	−1.80338e10	−	3.12355e10i	−0.824591	−	1.42823i
$901$	3.05349e9	−	5.28880e9i	0.139078	−	0.240891i
$902$	1.64868e10			0.748020
$903$	−1.35875e10	+	2.35343e10i	−0.614091	+	1.06364i
$904$	3.40163e9	−	5.89179e9i	0.153143	−	0.265251i
$905$	−4.23489e10			−1.89921
$906$	7.77608e9	−	1.34686e10i	0.347386	−	0.601690i
$907$	1.19671e10	+	2.07277e10i	0.532555	+	0.922412i	0.999277	+	0.0380081i	$0.0121013\pi$
$907$	1.19671e10	+	2.07277e10i	0.532555	+	0.922412i	−0.466723	+	0.884404i	$0.654565\pi$
$908$	−1.82617e9	−	3.16302e9i	−0.0809546	−	0.140217i
$909$	4.63155e9			0.204528
$910$	−1.17670e10	−	7.26110e9i	−0.517633	−	0.319417i
$911$	−2.98472e10			−1.30794			−0.653972	−	0.756519i	$-0.726898\pi$
$911$	−2.98472e10			−1.30794			−0.653972	+	0.756519i	$0.726898\pi$
$912$	4.07767e9	+	7.06272e9i	0.178004	+	0.308312i
$913$	−9.53485e9	−	1.65148e10i	−0.414635	−	0.718169i
$914$	1.22973e10	−	2.12996e10i	0.532721	−	0.922700i
$915$	1.07688e11			4.64722
$916$	−8.60008e9	+	1.48958e10i	−0.369716	+	0.640367i
$917$	4.08550e9	−	7.07630e9i	0.174966	−	0.303049i
$918$	−2.56632e9			−0.109487
$919$	4.11876e9	−	7.13390e9i	0.175050	−	0.303196i	−0.765129	−	0.643878i	$-0.777325\pi$
$919$	4.11876e9	−	7.13390e9i	0.175050	−	0.303196i	0.940179	+	0.340682i	$0.110658\pi$
$920$	1.42293e10	+	2.46458e10i	0.602456	+	1.04348i
$921$	1.02052e10	+	1.76759e10i	0.430440	+	0.745544i
$922$	−2.63004e10			−1.10511
$923$	8.95168e9	−	4.82450e9i	0.374713	−	0.201951i
$924$	6.49702e9			0.270933
$925$	−4.71525e9	−	8.16705e9i	−0.195888	−	0.339289i
$926$	3.36038e8	+	5.82035e8i	0.0139075	+	0.0240886i
$927$	−7.10018e9	+	1.22979e10i	−0.292745	+	0.507050i
$928$	−2.24611e9			−0.0922601
$929$	−1.65384e10	+	2.86454e10i	−0.676767	+	1.17219i	0.299182	+	0.954196i	$0.403286\pi$
$929$	−1.65384e10	+	2.86454e10i	−0.676767	+	1.17219i	−0.975949	+	0.217999i	$0.930047\pi$
$930$	−7.68448e9	+	1.33099e10i	−0.313274	+	0.542606i
$931$	−1.81823e10			−0.738456
$932$	2.09200e9	−	3.62345e9i	0.0846460	−	0.146611i
$933$	2.55775e10	+	4.43016e10i	1.03103	+	1.78580i
$934$	1.33233e10	+	2.30766e10i	0.535054	+	0.926741i
$935$	−1.17148e10			−0.468699
$936$	−1.02699e10	+	5.53495e9i	−0.409355	+	0.220622i
$937$	6.86759e9			0.272719			0.136360	−	0.990659i	$-0.456460\pi$
$937$	6.86759e9			0.272719			0.136360	+	0.990659i	$0.456460\pi$
$938$	−5.30434e8	−	9.18739e8i	−0.0209856	−	0.0363482i
$939$	2.20727e10	+	3.82311e10i	0.870014	+	1.50691i
$940$	5.46441e9	−	9.46464e9i	0.214583	−	0.371669i
$941$	−3.10041e10			−1.21298			−0.606492	−	0.795090i	$-0.707424\pi$
$941$	−3.10041e10			−1.21298			−0.606492	+	0.795090i	$0.707424\pi$
$942$	−1.57826e10	+	2.73363e10i	−0.615179	+	1.06552i
$943$	3.19648e10	−	5.53646e10i	1.24131	−	2.15002i
$944$	4.81048e9			0.186117
$945$	−5.35279e9	+	9.27131e9i	−0.206333	+	0.357380i
$946$	1.25445e10	+	2.17277e10i	0.481764	+	0.834440i
$947$	1.08273e10	+	1.87534e10i	0.414280	+	0.717555i	0.995353	−	0.0962973i	$-0.0307000\pi$
$947$	1.08273e10	+	1.87534e10i	0.414280	+	0.717555i	−0.581072	+	0.813852i	$0.697367\pi$
$948$	3.68503e10			1.40479
$949$	1.12719e10	+	6.95560e9i	0.428121	+	0.264182i
$950$	−4.38546e10			−1.65952
$951$	5.95078e9	+	1.03070e10i	0.224358	+	0.388600i
$952$	6.97616e8	+	1.20831e9i	0.0262052	+	0.0453887i
$953$	6.18367e9	−	1.07104e10i	0.231431	−	0.400850i	−0.726799	−	0.686851i	$-0.758993\pi$
$953$	6.18367e9	−	1.07104e10i	0.231431	−	0.400850i	0.958229	+	0.286001i	$0.0923260\pi$
$954$	−2.14949e10			−0.801525
$955$	3.56868e9	−	6.18114e9i	0.132586	−	0.229645i
$956$	6.61751e9	−	1.14619e10i	0.244958	−	0.424280i
$957$	−1.66950e10			−0.615737
$958$	−3.59588e9	+	6.22825e9i	−0.132138	+	0.228869i
$959$	1.35960e8	+	2.35490e8i	0.00497790	+	0.00862197i
$960$	4.88252e9	+	8.45677e9i	0.178113	+	0.308500i
$961$	−2.48529e10			−0.903326
$962$	−2.68524e9	+	1.44721e9i	−0.0972457	+	0.0524105i
$963$	−3.52958e10			−1.27359
$964$	8.97522e9	+	1.55455e10i	0.322682	+	0.558902i
$965$	−4.53457e9	−	7.85410e9i	−0.162439	−	0.281353i
$966$	1.25965e10	−	2.18178e10i	0.449604	−	0.778737i
$967$	3.71093e10			1.31974			0.659872	−	0.751378i	$-0.270610\pi$
$967$	3.71093e10			1.31974			0.659872	+	0.751378i	$0.270610\pi$
$968$	−1.98957e9	+	3.44604e9i	−0.0705010	+	0.122111i
$969$	−6.50878e9	+	1.12735e10i	−0.229809	+	0.398040i
$970$	2.85133e10			1.00310
$971$	1.35012e10	−	2.33848e10i	0.473267	−	0.819723i	−0.526265	−	0.850321i	$-0.676408\pi$
$971$	1.35012e10	−	2.33848e10i	0.473267	−	0.819723i	0.999532	+	0.0305981i	$0.00974119\pi$
$972$	−9.80855e9	−	1.69889e10i	−0.342588	−	0.593381i
$973$	1.92075e9	+	3.32683e9i	0.0668460	+	0.115781i
$974$	2.13570e10			0.740602
$975$	3.23294e9	−	1.10385e11i	0.111707	−	3.81413i
$976$	−1.18411e10			−0.407679
$977$	−1.50462e10	−	2.60608e10i	−0.516175	−	0.894041i	−0.999824	−	0.0187788i	$-0.994022\pi$
$977$	−1.50462e10	−	2.60608e10i	−0.516175	−	0.894041i	0.483649	−	0.875262i	$-0.339311\pi$
$978$	−9.10865e9	−	1.57766e10i	−0.311364	−	0.539298i
$979$	−1.34784e10	+	2.33453e10i	−0.459092	+	0.795171i
$980$	−2.17711e10			−0.738906
$981$	2.37713e10	−	4.11731e10i	0.803917	−	1.39242i
$982$	1.36439e10	−	2.36320e10i	0.459779	−	0.796360i
$983$	−5.51343e10			−1.85133			−0.925667	−	0.378340i	$-0.876495\pi$
$983$	−5.51343e10			−1.85133			−0.925667	+	0.378340i	$0.876495\pi$
$984$	1.09682e10	−	1.89974e10i	0.366987	−	0.635640i
$985$	−1.63262e10	−	2.82779e10i	−0.544327	−	0.942801i
$986$	−1.79263e9	−	3.10492e9i	−0.0595553	−	0.103153i
$987$	−9.67477e9			−0.320281
$988$	−4.15276e8	+	1.41792e10i	−0.0136989	+	0.467737i
$989$	9.72858e10			3.19788
$990$	2.06165e10	+	3.57088e10i	0.675291	+	1.16964i
$991$	7.69281e9	+	1.33243e10i	0.251089	+	0.434898i	0.963826	−	0.266533i	$-0.0858781\pi$
$991$	7.69281e9	+	1.33243e10i	0.251089	+	0.434898i	−0.712737	+	0.701431i	$0.752545\pi$
$992$	8.44968e8	−	1.46353e9i	0.0274821	−	0.0476004i
$993$	−5.61643e10			−1.82028
$994$	−2.14025e9	+	3.70703e9i	−0.0691214	+	0.119722i
$995$	6.32656e8	−	1.09579e9i	0.0203604	−	0.0352653i
$996$	−2.53730e10			−0.813699
$997$	1.39828e10	−	2.42190e10i	0.446850	−	0.773967i	−0.551329	−	0.834288i	$-0.685879\pi$
$997$	1.39828e10	−	2.42190e10i	0.446850	−	0.773967i	0.998179	+	0.0603210i	$0.0192124\pi$
$998$	−2.17304e10	−	3.76381e10i	−0.692006	−	1.19859i
$999$	1.18089e9	+	2.04536e9i	0.0374739	+	0.0649067i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.c.b.3.4	✓	8
3.2	odd	2		234.8.h.b.55.1		8
4.3	odd	2		208.8.i.b.81.1		8
13.2	odd	12		338.8.b.h.337.5		8
13.3	even	3		338.8.a.i.1.1		4
13.9	even	3	inner	26.8.c.b.9.4	yes	8
13.10	even	6		338.8.a.j.1.1		4
13.11	odd	12		338.8.b.h.337.1		8
39.35	odd	6		234.8.h.b.217.1		8
52.35	odd	6		208.8.i.b.113.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.c.b.3.4	✓	8	1.1	even	1	trivial
26.8.c.b.9.4	yes	8	13.9	even	3	inner
208.8.i.b.81.1		8	4.3	odd	2
208.8.i.b.113.1		8	52.35	odd	6
234.8.h.b.55.1		8	3.2	odd	2
234.8.h.b.217.1		8	39.35	odd	6
338.8.a.i.1.1		4	13.3	even	3
338.8.a.j.1.1		4	13.10	even	6
338.8.b.h.337.1		8	13.11	odd	12
338.8.b.h.337.5		8	13.2	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:	\( N \)	\(=\)	\( 26 = 2 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	26.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 + 6.92820i) q^{2} +(35.5792 + 61.6250i) q^{3} +(-32.0000 + 55.4256i) q^{4} +523.489 q^{5} +(-284.634 + 493.000i) q^{6} +(208.401 - 360.960i) q^{7} -512.000 q^{8} +(-1438.26 + 2491.14i) q^{9} +(2093.96 + 3626.84i) q^{10} +(-1711.39 - 2964.21i) q^{11} -4554.14 q^{12} +(-6741.24 - 4159.83i) q^{13} +3334.41 q^{14} +(18625.3 + 32260.0i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(3269.02 - 5662.11i) q^{17} -23012.2 q^{18} +(-13990.2 + 24231.8i) q^{19} +(-16751.7 + 29014.7i) q^{20} +29658.9 q^{21} +(13691.1 - 23713.7i) q^{22} +(-53089.0 - 91952.9i) q^{23} +(-18216.6 - 31552.0i) q^{24} +195916. q^{25} +(1855.20 - 63344.0i) q^{26} -49065.2 q^{27} +(13337.6 + 23101.5i) q^{28} +(-34273.0 - 59362.6i) q^{29} +(-149003. + 258080. i) q^{30} +51572.8 q^{31} +(16384.0 - 28377.9i) q^{32} +(121780. - 210929. i) q^{33} +52304.3 q^{34} +(109095. - 188959. i) q^{35} +(-92048.7 - 159433. i) q^{36} +(-24067.7 - 41686.5i) q^{37} -223844. q^{38} +(16501.7 - 563432. i) q^{39} -268026. q^{40} +(301049. + 521432. i) q^{41} +(118636. + 205483. i) q^{42} +(-458126. + 793497. i) q^{43} +219058. q^{44} +(-752914. + 1.30409e6i) q^{45} +(424712. - 735623. i) q^{46} -326201. q^{47} +(145732. - 252416. i) q^{48} +(324910. + 562760. i) q^{49} +(783664. + 1.35735e6i) q^{50} +465237. q^{51} +(446281. - 240523. i) q^{52} +934068. q^{53} +(-196261. - 339934. i) q^{54} +(-895894. - 1.55173e6i) q^{55} +(-106701. + 184812. i) q^{56} -1.99105e6 q^{57} +(274184. - 474900. i) q^{58} +(-587217. + 1.01709e6i) q^{59} -2.38404e6 q^{60} +(1.44545e6 - 2.50359e6i) q^{61} +(206291. + 357307. i) q^{62} +(599469. + 1.03831e6i) q^{63} +262144. q^{64} +(-3.52897e6 - 2.17763e6i) q^{65} +1.94848e6 q^{66} +(-159079. - 275533. i) q^{67} +(209217. + 362375. i) q^{68} +(3.77773e6 - 6.54322e6i) q^{69} +1.74553e6 q^{70} +(-641869. + 1.11175e6i) q^{71} +(736389. - 1.27546e6i) q^{72} -1.67209e6 q^{73} +(192542. - 333492. i) q^{74} +(6.97054e6 + 1.20733e7i) q^{75} +(-895376. - 1.55084e6i) q^{76} -1.42662e6 q^{77} +(3.96958e6 - 2.13940e6i) q^{78} -8.09160e6 q^{79} +(-1.07211e6 - 1.85694e6i) q^{80} +(1.39977e6 + 2.42448e6i) q^{81} +(-2.40839e6 + 4.17146e6i) q^{82} +5.57141e6 q^{83} +(-949085. + 1.64386e6i) q^{84} +(1.71130e6 - 2.96405e6i) q^{85} -7.33001e6 q^{86} +(2.43881e6 - 4.22415e6i) q^{87} +(876231. + 1.51768e6i) q^{88} +(-3.93786e6 - 6.82057e6i) q^{89} -1.20466e7 q^{90} +(-2.90641e6 + 1.56641e6i) q^{91} +6.79540e6 q^{92} +(1.83492e6 + 3.17817e6i) q^{93} +(-1.30480e6 - 2.25999e6i) q^{94} +(-7.32374e6 + 1.26851e7i) q^{95} +2.33172e6 q^{96} +(3.40424e6 - 5.89631e6i) q^{97} +(-2.59928e6 + 4.50208e6i) q^{98} +9.84569e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 32 q^{2} - 256 q^{4} + 556 q^{5} - 548 q^{7} - 4096 q^{8} - 5214 q^{9} + 2224 q^{10} - 7392 q^{11} - 25818 q^{13} - 8768 q^{14} + 15528 q^{15} - 16384 q^{16} + 28316 q^{17} - 83424 q^{18} - 99888 q^{19}+ \cdots - 20715312 q^{99}+O(q^{100}) \) 8 * q + 32 * q^2 - 256 * q^4 + 556 * q^5 - 548 * q^7 - 4096 * q^8 - 5214 * q^9 + 2224 * q^10 - 7392 * q^11 - 25818 * q^13 - 8768 * q^14 + 15528 * q^15 - 16384 * q^16 + 28316 * q^17 - 83424 * q^18 - 99888 * q^19 - 17792 * q^20 + 182148 * q^21 + 59136 * q^22 - 33388 * q^23 + 173756 * q^25 - 156000 * q^26 + 212544 * q^27 - 35072 * q^28 + 93140 * q^29 - 124224 * q^30 + 622320 * q^31 + 131072 * q^32 + 238638 * q^33 + 453056 * q^34 + 141544 * q^35 - 333696 * q^36 - 9636 * q^37 - 1598208 * q^38 - 22932 * q^39 - 284672 * q^40 + 82892 * q^41 + 728592 * q^42 - 569264 * q^43 + 946176 * q^44 - 2303394 * q^45 + 267104 * q^46 - 1148400 * q^47 - 717798 * q^49 + 695024 * q^50 - 5459856 * q^51 + 404352 * q^52 + 2470700 * q^53 + 850176 * q^54 - 1092512 * q^55 + 280576 * q^56 + 7056924 * q^57 - 745120 * q^58 + 231504 * q^59 - 1987584 * q^60 + 685684 * q^61 + 2489280 * q^62 - 5951712 * q^63 + 2097152 * q^64 - 6216678 * q^65 + 3818208 * q^66 + 3271056 * q^67 + 1812224 * q^68 + 5600034 * q^69 + 2264704 * q^70 - 175012 * q^71 + 2669568 * q^72 + 14275780 * q^73 + 77088 * q^74 + 22200960 * q^75 - 6392832 * q^76 - 27830412 * q^77 + 5028192 * q^78 - 14107904 * q^79 - 1138688 * q^80 + 3758004 * q^81 - 663136 * q^82 + 1314576 * q^83 - 5828736 * q^84 + 11814998 * q^85 - 9108224 * q^86 - 7182900 * q^87 + 3784704 * q^88 - 11452234 * q^89 - 36854304 * q^90 + 16457168 * q^91 + 4273664 * q^92 + 2984688 * q^93 - 4593600 * q^94 - 23334088 * q^95 - 428002 * q^97 + 5742384 * q^98 - 20715312 * q^99

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