LMFDB - Embedded newform 26.8.c.b.3.1

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			3.1
Root			$-45.7672i$ of defining polynomial
Character	$\chi$	$=$	26.3
Dual form			26.8.c.b.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 + 6.92820i) q^{2} +(-39.6356 - 68.6509i) q^{3} +(-32.0000 + 55.4256i) q^{4} +132.638 q^{5} +(317.085 - 549.207i) q^{6} +(-754.459 + 1306.76i) q^{7} -512.000 q^{8} +(-2048.46 + 3548.04i) q^{9} +(530.551 + 918.941i) q^{10} +(1463.11 + 2534.19i) q^{11} +5073.36 q^{12} +(-7917.74 + 240.503i) q^{13} -12071.3 q^{14} +(-5257.18 - 9105.70i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(10869.5 - 18826.5i) q^{17} -32775.4 q^{18} +(-26739.1 + 46313.4i) q^{19} +(-4244.41 + 7351.53i) q^{20} +119614. q^{21} +(-11704.9 + 20273.5i) q^{22} +(14224.0 + 24636.6i) q^{23} +(20293.4 + 35149.2i) q^{24} -60532.2 q^{25} +(-33337.2 - 53893.7i) q^{26} +151402. q^{27} +(-48285.4 - 83632.7i) q^{28} +(-76324.1 - 132197. i) q^{29} +(42057.4 - 72845.6i) q^{30} +83326.6 q^{31} +(16384.0 - 28377.9i) q^{32} +(115983. - 200888. i) q^{33} +173911. q^{34} +(-100070. + 173326. i) q^{35} +(-131102. - 227075. i) q^{36} +(-56229.4 - 97392.2i) q^{37} -427825. q^{38} +(330335. + 534028. i) q^{39} -67910.5 q^{40} +(-55065.1 - 95375.6i) q^{41} +(478455. + 828708. i) q^{42} +(-52967.4 + 91742.2i) q^{43} -187279. q^{44} +(-271703. + 470604. i) q^{45} +(-113792. + 197093. i) q^{46} +413100. q^{47} +(-162347. + 281194. i) q^{48} +(-726645. - 1.25859e6i) q^{49} +(-242129. - 419380. i) q^{50} -1.72327e6 q^{51} +(240038. - 446542. i) q^{52} -889607. q^{53} +(605608. + 1.04894e6i) q^{54} +(194064. + 336129. i) q^{55} +(386283. - 669062. i) q^{56} +4.23928e6 q^{57} +(610593. - 1.05758e6i) q^{58} +(-1.20535e6 + 2.08773e6i) q^{59} +672919. q^{60} +(-1.19229e6 + 2.06512e6i) q^{61} +(333306. + 577304. i) q^{62} +(-3.09096e6 - 5.35370e6i) q^{63} +262144. q^{64} +(-1.05019e6 + 31899.8i) q^{65} +1.85573e6 q^{66} +(184882. + 320224. i) q^{67} +(695646. + 1.20489e6i) q^{68} +(1.12755e6 - 1.95298e6i) q^{69} -1.60112e6 q^{70} +(1.59359e6 - 2.76018e6i) q^{71} +(1.04881e6 - 1.81660e6i) q^{72} +5.84239e6 q^{73} +(449835. - 779138. i) q^{74} +(2.39923e6 + 4.15559e6i) q^{75} +(-1.71130e6 - 2.96406e6i) q^{76} -4.41544e6 q^{77} +(-2.37851e6 + 4.42474e6i) q^{78} +1.07694e6 q^{79} +(-271642. - 470498. i) q^{80} +(-1.52092e6 - 2.63431e6i) q^{81} +(440521. - 763005. i) q^{82} +647944. q^{83} +(-3.82764e6 + 6.62966e6i) q^{84} +(1.44170e6 - 2.49710e6i) q^{85} -847478. q^{86} +(-6.05031e6 + 1.04794e7i) q^{87} +(-749115. - 1.29750e6i) q^{88} +(5.81291e6 + 1.00682e7i) q^{89} -4.34725e6 q^{90} +(5.65933e6 - 1.05280e7i) q^{91} -1.82067e6 q^{92} +(-3.30270e6 - 5.72045e6i) q^{93} +(1.65240e6 + 2.86204e6i) q^{94} +(-3.54661e6 + 6.14291e6i) q^{95} -2.59756e6 q^{96} +(-31183.4 + 54011.2i) q^{97} +(5.81316e6 - 1.00687e7i) q^{98} -1.19885e7 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
$3$	−39.6356	−	68.6509i	−0.847542	−	1.46799i	−0.883396	−	0.468628i	$-0.844748\pi$
$3$	−39.6356	−	68.6509i	−0.847542	−	1.46799i	0.0358539	−	0.999357i	$-0.488585\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	132.638			0.474539			0.237270	−	0.971444i	$-0.423748\pi$
$5$	132.638			0.474539			0.237270	+	0.971444i	$0.423748\pi$
$6$	317.085	−	549.207i	0.599302	−	1.03802i
$7$	−754.459	+	1306.76i	−0.831366	+	1.43997i	0.0655888	+	0.997847i	$0.479107\pi$
$7$	−754.459	+	1306.76i	−0.831366	+	1.43997i	−0.896955	+	0.442122i	$0.854226\pi$
$8$	−512.000			−0.353553
$9$	−2048.46	+	3548.04i	−0.936654	+	1.62233i
$10$	530.551	+	918.941i	0.167775	+	0.290595i
$11$	1463.11	+	2534.19i	0.331439	+	0.574070i	0.982794	−	0.184703i	$-0.0591325\pi$
$11$	1463.11	+	2534.19i	0.331439	+	0.574070i	−0.651355	+	0.758773i	$0.725799\pi$
$12$	5073.36			0.847542
$13$	−7917.74	+	240.503i	−0.999539	+	0.0303612i
$13$	−7917.74	+	240.503i	−0.999539	+	0.0303612i
$14$	−12071.3			−1.17573
$15$	−5257.18	−	9105.70i	−0.402192	−	0.696617i
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	10869.5	−	18826.5i	0.536583	−	0.929389i	−0.462502	−	0.886618i	$-0.653048\pi$
$17$	10869.5	−	18826.5i	0.536583	−	0.929389i	0.999085	−	0.0427706i	$-0.0136185\pi$
$18$	−32775.4			−1.32463
$19$	−26739.1	+	46313.4i	−0.894352	+	1.54906i	−0.0597485	+	0.998213i	$0.519030\pi$
$19$	−26739.1	+	46313.4i	−0.894352	+	1.54906i	−0.834604	+	0.550850i	$0.814303\pi$
$20$	−4244.41	+	7351.53i	−0.118635	+	0.205482i
$21$	119614.			2.81847
$22$	−11704.9	+	20273.5i	−0.234363	+	0.405929i
$23$	14224.0	+	24636.6i	0.243766	+	0.422215i	0.961784	−	0.273809i	$-0.0882837\pi$
$23$	14224.0	+	24636.6i	0.243766	+	0.422215i	−0.718018	+	0.696025i	$0.754950\pi$
$24$	20293.4	+	35149.2i	0.299651	+	0.519011i
$25$	−60532.2			−0.774813
$26$	−33337.2	−	53893.7i	−0.371983	−	0.601356i
$27$	151402.			1.48033
$28$	−48285.4	−	83632.7i	−0.415683	−	0.719984i
$29$	−76324.1	−	132197.i	−0.581124	−	1.00654i	−0.995346	−	0.0963608i	$-0.969280\pi$
$29$	−76324.1	−	132197.i	−0.581124	−	1.00654i	0.414222	−	0.910176i	$-0.364054\pi$
$30$	42057.4	−	72845.6i	0.284393	−	0.492582i
$31$	83326.6			0.502363			0.251182	−	0.967940i	$-0.419181\pi$
$31$	83326.6			0.502363			0.251182	+	0.967940i	$0.419181\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	115983.	−	200888.i	0.561817	−	0.973096i
$34$	173911.			0.758843
$35$	−100070.	+	173326.i	−0.394516	+	0.683322i
$36$	−131102.	−	227075.i	−0.468327	−	0.811166i
$37$	−56229.4	−	97392.2i	−0.182498	−	0.316095i	0.760233	−	0.649651i	$-0.225085\pi$
$37$	−56229.4	−	97392.2i	−0.182498	−	0.316095i	−0.942730	+	0.333555i	$0.891752\pi$
$38$	−427825.			−1.26481
$39$	330335.	+	534028.i	0.891721	+	1.44158i
$40$	−67910.5			−0.167775
$41$	−55065.1	−	95375.6i	−0.124777	−	0.216119i	0.796869	−	0.604152i	$-0.206488\pi$
$41$	−55065.1	−	95375.6i	−0.124777	−	0.216119i	−0.921646	+	0.388033i	$0.873155\pi$
$42$	478455.	+	828708.i	0.996480	+	1.72595i
$43$	−52967.4	+	91742.2i	−0.101594	+	0.175966i	−0.912342	−	0.409430i	$-0.865728\pi$
$43$	−52967.4	+	91742.2i	−0.101594	+	0.175966i	0.810747	+	0.585396i	$0.199061\pi$
$44$	−187279.			−0.331439
$45$	−271703.	+	470604.i	−0.444479	+	0.769860i
$46$	−113792.	+	197093.i	−0.172369	+	0.298551i
$47$	413100.			0.580381			0.290190	−	0.956969i	$-0.406281\pi$
$47$	413100.			0.580381			0.290190	+	0.956969i	$0.406281\pi$
$48$	−162347.	+	281194.i	−0.211885	+	0.366996i
$49$	−726645.	−	1.25859e6i	−0.882340	−	1.52826i
$50$	−242129.	−	419380.i	−0.273938	−	0.474474i
$51$	−1.72327e6			−1.81911
$52$	240038.	−	446542.i	0.236738	−	0.440403i
$53$	−889607.			−0.820791			−0.410395	−	0.911908i	$-0.634609\pi$
$53$	−889607.			−0.820791			−0.410395	+	0.911908i	$0.634609\pi$
$54$	605608.	+	1.04894e6i	0.523375	+	0.906513i
$55$	194064.	+	336129.i	0.157281	+	0.272419i
$56$	386283.	−	669062.i	0.293932	−	0.509106i
$57$	4.23928e6			3.03200
$58$	610593.	−	1.05758e6i	0.410917	−	0.711729i
$59$	−1.20535e6	+	2.08773e6i	−0.764066	+	1.32340i	0.176673	+	0.984270i	$0.443467\pi$
$59$	−1.20535e6	+	2.08773e6i	−0.764066	+	1.32340i	−0.940739	+	0.339132i	$0.889867\pi$
$60$	672919.			0.402192
$61$	−1.19229e6	+	2.06512e6i	−0.672557	+	1.16490i	0.304619	+	0.952474i	$0.401471\pi$
$61$	−1.19229e6	+	2.06512e6i	−0.672557	+	1.16490i	−0.977176	+	0.212429i	$0.931863\pi$
$62$	333306.	+	577304.i	0.177612	+	0.307633i
$63$	−3.09096e6	−	5.35370e6i	−1.55740	−	2.69750i
$64$	262144.			0.125000
$65$	−1.05019e6	+	31899.8i	−0.474320	+	0.0144076i
$66$	1.85573e6			0.794530
$67$	184882.	+	320224.i	0.0750986	+	0.130075i	0.901129	−	0.433551i	$-0.142740\pi$
$67$	184882.	+	320224.i	0.0750986	+	0.130075i	−0.826031	+	0.563625i	$0.809406\pi$
$68$	695646.	+	1.20489e6i	0.268291	+	0.464694i
$69$	1.12755e6	−	1.95298e6i	0.413204	−	0.715690i
$70$	−1.60112e6			−0.557930
$71$	1.59359e6	−	2.76018e6i	0.528412	−	0.915236i	−0.471039	−	0.882112i	$-0.656121\pi$
$71$	1.59359e6	−	2.76018e6i	0.528412	−	0.915236i	0.999451	−	0.0331239i	$-0.0105456\pi$
$72$	1.04881e6	−	1.81660e6i	0.331157	−	0.573581i
$73$	5.84239e6			1.75776			0.878882	−	0.477038i	$-0.158290\pi$
$73$	5.84239e6			1.75776			0.878882	+	0.477038i	$0.158290\pi$
$74$	449835.	−	779138.i	0.129045	−	0.223513i
$75$	2.39923e6	+	4.15559e6i	0.656686	+	1.13741i
$76$	−1.71130e6	−	2.96406e6i	−0.447176	−	0.774532i
$77$	−4.41544e6			−1.10219
$78$	−2.37851e6	+	4.42474e6i	−0.567511	+	1.05574i
$79$	1.07694e6			0.245751			0.122876	−	0.992422i	$-0.460788\pi$
$79$	1.07694e6			0.245751			0.122876	+	0.992422i	$0.460788\pi$
$80$	−271642.	−	470498.i	−0.0593174	−	0.102741i
$81$	−1.52092e6	−	2.63431e6i	−0.317987	−	0.550769i
$82$	440521.	−	763005.i	0.0882304	−	0.152820i
$83$	647944.			0.124384			0.0621920	−	0.998064i	$-0.480191\pi$
$83$	647944.			0.124384			0.0621920	+	0.998064i	$0.480191\pi$
$84$	−3.82764e6	+	6.62966e6i	−0.704618	+	1.22043i
$85$	1.44170e6	−	2.49710e6i	0.254630	−	0.441031i
$86$	−847478.			−0.143676
$87$	−6.05031e6	+	1.04794e7i	−0.985054	+	1.70616i
$88$	−749115.	−	1.29750e6i	−0.117181	−	0.202964i
$89$	5.81291e6	+	1.00682e7i	0.874034	+	1.51387i	0.857788	+	0.514003i	$0.171838\pi$
$89$	5.81291e6	+	1.00682e7i	0.874034	+	1.51387i	0.0162455	+	0.999868i	$0.494829\pi$
$90$	−4.34725e6			−0.628588
$91$	5.65933e6	−	1.05280e7i	0.787264	−	1.46455i
$92$	−1.82067e6			−0.243766
$93$	−3.30270e6	−	5.72045e6i	−0.425774	−	0.737462i
$94$	1.65240e6	+	2.86204e6i	0.205196	+	0.355409i
$95$	−3.54661e6	+	6.14291e6i	−0.424405	+	0.735092i
$96$	−2.59756e6			−0.299651
$97$	−31183.4	+	54011.2i	−0.00346914	+	0.00600873i	−0.867755	−	0.496993i	$-0.834438\pi$
$97$	−31183.4	+	54011.2i	−0.00346914	+	0.00600873i	0.864286	+	0.503001i	$0.167771\pi$
$98$	5.81316e6	−	1.00687e7i	0.623908	−	1.08064i
$99$	−1.19885e7			−1.24178
$100$	1.93703e6	−	3.35504e6i	0.193703	−	0.335504i
$101$	7.40293e6	+	1.28222e7i	0.714955	+	1.23834i	0.962977	+	0.269584i	$0.0868862\pi$
$101$	7.40293e6	+	1.28222e7i	0.714955	+	1.23834i	−0.248022	+	0.968754i	$0.579781\pi$
$102$	−6.89308e6	−	1.19392e7i	−0.643151	−	1.11397i
$103$	−1.24059e7			−1.11866			−0.559332	−	0.828944i	$-0.688942\pi$
$103$	−1.24059e7			−1.11866			−0.559332	+	0.828944i	$0.688942\pi$
$104$	4.05389e6	−	123138.i	0.353390	−	0.0107343i
$105$	1.58653e7			1.33747
$106$	−3.55843e6	−	6.16338e6i	−0.290193	−	0.502630i
$107$	−284651.	−	493030.i	−0.0224631	−	0.0389072i	0.854575	−	0.519327i	$-0.173817\pi$
$107$	−284651.	−	493030.i	−0.0224631	−	0.0389072i	−0.877038	+	0.480420i	$0.840484\pi$
$108$	−4.84486e6	+	8.39155e6i	−0.370082	+	0.641001i
$109$	−3.87174e6			−0.286361			−0.143181	−	0.989697i	$-0.545733\pi$
$109$	−3.87174e6			−0.286361			−0.143181	+	0.989697i	$0.545733\pi$
$110$	−1.55251e6	+	2.68903e6i	−0.111214	+	0.192629i
$111$	−4.45737e6	+	7.72040e6i	−0.309349	+	0.535808i
$112$	6.18053e6			0.415683
$113$	1.39031e7	−	2.40808e7i	0.906433	−	1.56999i	0.0874519	−	0.996169i	$-0.472128\pi$
$113$	1.39031e7	−	2.40808e7i	0.906433	−	1.56999i	0.818981	−	0.573820i	$-0.194539\pi$
$114$	1.69571e7	+	2.93706e7i	1.07198	+	1.85672i
$115$	1.88664e6	+	3.26775e6i	0.115677	+	0.200358i
$116$	9.76949e6			0.581124
$117$	1.53659e7	−	2.85851e7i	0.886966	−	1.65002i
$118$	−1.92856e7			−1.08055
$119$	1.64011e7	+	2.84076e7i	0.892194	+	1.54533i
$120$	2.69167e6	+	4.66212e6i	0.142196	+	0.246291i
$121$	5.46218e6	−	9.46077e6i	0.280296	−	0.485487i
$122$	−1.90767e7			−0.951140
$123$	−4.36508e6	+	7.56054e6i	−0.211507	+	0.366341i
$124$	−2.66645e6	+	4.61843e6i	−0.125591	+	0.217530i
$125$	−1.83912e7			−0.842218
$126$	2.47277e7	−	4.28296e7i	1.10125	−	1.90742i
$127$	−8.01861e6	−	1.38886e7i	−0.347365	−	0.601654i	0.638415	−	0.769692i	$-0.279590\pi$
$127$	−8.01861e6	−	1.38886e7i	−0.347365	−	0.601654i	−0.985781	+	0.168038i	$0.946257\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	8.39757e6			0.344421
$130$	−4.42178e6	−	7.14834e6i	−0.176520	−	0.285367i
$131$	2.10431e7			0.817824			0.408912	−	0.912574i	$-0.365908\pi$
$131$	2.10431e7			0.817824			0.408912	+	0.912574i	$0.365908\pi$
$132$	7.42290e6	+	1.28568e7i	0.280909	+	0.486548i
$133$	−4.03471e7	−	6.98831e7i	−1.48707	−	2.57568i
$134$	−1.47905e6	+	2.56180e6i	−0.0531028	+	0.0919767i
$135$	2.00816e7			0.702474
$136$	−5.56516e6	+	9.63915e6i	−0.189711	+	0.328589i
$137$	−2.19368e7	+	3.79957e7i	−0.728873	+	1.26244i	0.228488	+	0.973547i	$0.426622\pi$
$137$	−2.19368e7	+	3.79957e7i	−0.728873	+	1.26244i	−0.957360	+	0.288897i	$0.906711\pi$
$138$	1.80408e7			0.584359
$139$	−6.95070e6	+	1.20390e7i	−0.219521	+	0.380222i	−0.954662	−	0.297693i	$-0.903783\pi$
$139$	−6.95070e6	+	1.20390e7i	−0.219521	+	0.380222i	0.735140	+	0.677915i	$0.237116\pi$
$140$	−6.40446e6	−	1.10929e7i	−0.197258	−	0.341661i
$141$	−1.63735e7	−	2.83597e7i	−0.491897	−	0.851991i
$142$	2.54974e7			0.747287
$143$	−1.21940e7	−	1.97132e7i	−0.348716	−	0.563742i
$144$	1.67810e7			0.468327
$145$	−1.01235e7	−	1.75343e7i	−0.275766	−	0.477641i
$146$	2.33696e7	+	4.04773e7i	0.621464	+	1.07641i
$147$	−5.76020e7	+	9.97696e7i	−1.49564	+	2.59052i
$148$	7.19737e6			0.182498
$149$	−2.03877e7	+	3.53125e7i	−0.504912	+	0.874533i	0.495072	+	0.868852i	$0.335142\pi$
$149$	−2.03877e7	+	3.53125e7i	−0.504912	+	0.874533i	−0.999984	+	0.00568086i	$0.998192\pi$
$150$	−1.91938e7	+	3.32447e7i	−0.464347	+	0.804273i
$151$	−6.68855e7			−1.58093			−0.790465	−	0.612507i	$-0.790161\pi$
$151$	−6.68855e7			−1.58093			−0.790465	+	0.612507i	$0.790161\pi$
$152$	1.36904e7	−	2.37125e7i	0.316201	−	0.547677i
$153$	4.45314e7	+	7.71306e7i	1.00518	+	1.74103i
$154$	−1.76618e7	−	3.05911e7i	−0.389683	−	0.674951i
$155$	1.10523e7			0.238391
$156$	−4.01695e7	+	1.22016e6i	−0.847151	+	0.0257324i
$157$	7.74485e7			1.59722			0.798609	−	0.601850i	$-0.205569\pi$
$157$	7.74485e7			1.59722			0.798609	+	0.601850i	$0.205569\pi$
$158$	4.30775e6	+	7.46124e6i	0.0868861	+	0.150491i
$159$	3.52601e7	+	6.10723e7i	0.695654	+	1.20491i
$160$	2.17314e6	−	3.76398e6i	0.0419437	−	0.0726487i
$161$	−4.29256e7			−0.810636
$162$	1.21674e7	−	2.10745e7i	0.224850	−	0.389452i
$163$	1.53988e7	−	2.66715e7i	0.278503	−	0.482381i	−0.692510	−	0.721408i	$-0.743495\pi$
$163$	1.53988e7	−	2.66715e7i	0.278503	−	0.482381i	0.971013	+	0.239027i	$0.0768284\pi$
$164$	7.04834e6			0.124777
$165$	1.53837e7	−	2.66454e7i	0.266604	−	0.461772i
$166$	2.59178e6	+	4.48909e6i	0.0439763	+	0.0761693i
$167$	−2.03626e7	−	3.52691e7i	−0.338318	−	0.585985i	0.645798	−	0.763508i	$-0.276525\pi$
$167$	−2.03626e7	−	3.52691e7i	−0.338318	−	0.585985i	−0.984117	+	0.177524i	$0.943191\pi$
$168$	−6.12422e7			−0.996480
$169$	6.26328e7	−	3.80849e6i	0.998156	−	0.0606945i
$170$	2.30672e7			0.360101
$171$	−1.09548e8	−	1.89743e8i	−1.67540	−	2.90187i
$172$	−3.38991e6	−	5.87150e6i	−0.0507971	−	0.0879831i
$173$	−1.47009e7	+	2.54627e7i	−0.215865	+	0.373889i	−0.953540	−	0.301267i	$-0.902590\pi$
$173$	−1.47009e7	+	2.54627e7i	−0.215865	+	0.373889i	0.737675	+	0.675156i	$0.235924\pi$
$174$	−9.68049e7			−1.39308
$175$	4.56691e7	−	7.91012e7i	0.644153	−	1.11571i
$176$	5.99292e6	−	1.03800e7i	0.0828598	−	0.143517i
$177$	1.91099e8			2.59031
$178$	−4.65032e7	+	8.05460e7i	−0.618035	+	1.07047i
$179$	−2.25181e7	−	3.90025e7i	−0.293458	−	0.508285i	0.681167	−	0.732128i	$-0.261473\pi$
$179$	−2.25181e7	−	3.90025e7i	−0.293458	−	0.508285i	−0.974625	+	0.223844i	$0.928140\pi$
$180$	−1.73890e7	−	3.01187e7i	−0.222239	−	0.384930i
$181$	−7.76931e7			−0.973885			−0.486942	−	0.873434i	$-0.661888\pi$
$181$	−7.76931e7			−0.973885			−0.486942	+	0.873434i	$0.661888\pi$
$182$	9.55778e7	−	2.90320e6i	1.17519	−	0.0356966i
$183$	1.89029e8			2.28008
$184$	−7.28267e6	−	1.26140e7i	−0.0861844	−	0.149276i
$185$	−7.45814e6	−	1.29179e7i	−0.0866024	−	0.150000i
$186$	2.64216e7	−	4.57636e7i	0.301068	−	0.521464i
$187$	6.36131e7			0.711379
$188$	−1.32192e7	+	2.28963e7i	−0.145095	+	0.251312i
$189$	−1.14226e8	+	1.97846e8i	−1.23070	+	2.13163i
$190$	−5.67458e7			−0.600200
$191$	−8.27657e6	+	1.43354e7i	−0.0859476	+	0.148866i	−0.905795	−	0.423717i	$-0.860725\pi$
$191$	−8.27657e6	+	1.43354e7i	−0.0859476	+	0.148866i	0.819847	+	0.572583i	$0.194058\pi$
$192$	−1.03902e7	−	1.79964e7i	−0.105943	−	0.183498i
$193$	2.90207e7	+	5.02653e7i	0.290574	+	0.503290i	0.973946	−	0.226781i	$-0.0728203\pi$
$193$	2.90207e7	+	5.02653e7i	0.290574	+	0.503290i	−0.683371	+	0.730071i	$0.739487\pi$
$194$	−498934.			−0.00490611
$195$	4.38149e7	+	7.08322e7i	0.423156	+	0.684084i
$196$	9.30105e7			0.882340
$197$	−1.93955e7	−	3.35940e7i	−0.180746	−	0.313062i	0.761389	−	0.648296i	$-0.224518\pi$
$197$	−1.93955e7	−	3.35940e7i	−0.180746	−	0.313062i	−0.942135	+	0.335234i	$0.891185\pi$
$198$	−4.79542e7	−	8.30590e7i	−0.439034	−	0.760429i
$199$	−1.41836e7	+	2.45667e7i	−0.127585	+	0.220984i	−0.922740	−	0.385422i	$-0.874056\pi$
$199$	−1.41836e7	+	2.45667e7i	−0.127585	+	0.220984i	0.795155	+	0.606406i	$0.207389\pi$
$200$	3.09925e7			0.273938
$201$	1.46558e7	−	2.53846e7i	0.127298	−	0.220487i
$202$	−5.92234e7	+	1.02578e8i	−0.505550	+	0.875637i
$203$	2.30334e8			1.93251
$204$	5.51447e7	−	9.55134e7i	0.454776	−	0.787696i
$205$	−7.30372e6	−	1.26504e7i	−0.0592114	−	0.102557i
$206$	−4.96238e7	−	8.59509e7i	−0.395507	−	0.685039i
$207$	−1.16549e8			−0.913298
$208$	1.70687e7	+	2.75936e7i	0.131516	+	0.212611i
$209$	−1.56489e8			−1.18569
$210$	6.34612e7	+	1.09918e8i	0.472869	+	0.819033i
$211$	3.26467e7	+	5.65457e7i	0.239249	+	0.414392i	0.960499	−	0.278283i	$-0.0897654\pi$
$211$	3.26467e7	+	5.65457e7i	0.239249	+	0.414392i	−0.721250	+	0.692675i	$0.756432\pi$
$212$	2.84674e7	−	4.93070e7i	0.205198	−	0.355413i
$213$	−2.52652e8			−1.79140
$214$	2.27721e6	−	3.94424e6i	0.0158838	−	0.0275115i
$215$	−7.02547e6	+	1.21685e7i	−0.0482104	+	0.0835029i
$216$	−7.75178e7			−0.523375
$217$	−6.28665e7	+	1.08888e8i	−0.417648	+	0.723387i
$218$	−1.54870e7	−	2.68242e7i	−0.101244	−	0.175360i
$219$	−2.31567e8	−	4.01085e8i	−1.48978	−	2.58037i
$220$	−2.48402e7			−0.157281
$221$	−8.15338e7	+	1.51677e8i	−0.508118	+	0.945252i
$222$	−7.13180e7			−0.437485
$223$	5.24401e7	+	9.08290e7i	0.316663	+	0.548476i	0.979790	−	0.200031i	$-0.0641043\pi$
$223$	5.24401e7	+	9.08290e7i	0.316663	+	0.548476i	−0.663127	+	0.748507i	$0.730771\pi$
$224$	2.47221e7	+	4.28199e7i	0.146966	+	0.254553i
$225$	1.23998e8	−	2.14771e8i	0.725731	−	1.25700i
$226$	2.22449e8			1.28189
$227$	−2.49235e7	+	4.31688e7i	−0.141423	+	0.244951i	−0.928033	−	0.372499i	$-0.878501\pi$
$227$	−2.49235e7	+	4.31688e7i	−0.141423	+	0.244951i	0.786610	+	0.617450i	$0.211834\pi$
$228$	−1.35657e8	+	2.34965e8i	−0.758001	+	1.31290i
$229$	1.15632e8			0.636287			0.318144	−	0.948043i	$-0.396941\pi$
$229$	1.15632e8			0.636287			0.318144	+	0.948043i	$0.396941\pi$
$230$	−1.50931e7	+	2.61420e7i	−0.0817957	+	0.141674i
$231$	1.75009e8	+	3.03124e8i	0.934152	+	1.61800i
$232$	3.90780e7	+	6.76850e7i	0.205458	+	0.355864i
$233$	7.04962e7			0.365107			0.182553	−	0.983196i	$-0.441564\pi$
$233$	7.04962e7			0.365107			0.182553	+	0.983196i	$0.441564\pi$
$234$	2.59507e8	−	7.88259e6i	1.32402	−	0.0402173i
$235$	5.47927e7			0.275413
$236$	−7.71424e7	−	1.33615e8i	−0.382033	−	0.661701i
$237$	−4.26850e7	−	7.39327e7i	−0.208284	−	0.360759i
$238$	−1.31209e8	+	2.27261e8i	−0.630876	+	1.09271i
$239$	−3.08705e8			−1.46269			−0.731343	−	0.682010i	$-0.761106\pi$
$239$	−3.08705e8			−1.46269			−0.731343	+	0.682010i	$0.761106\pi$
$240$	−2.15334e7	+	3.72969e7i	−0.100548	+	0.174154i
$241$	−6.18820e7	+	1.07183e8i	−0.284777	+	0.493248i	−0.972555	−	0.232673i	$-0.925253\pi$
$241$	−6.18820e7	+	1.07183e8i	−0.284777	+	0.493248i	0.687778	+	0.725921i	$0.258586\pi$
$242$	8.73948e7			0.396398
$243$	4.49928e7	−	7.79299e7i	0.201151	−	0.348403i
$244$	−7.63069e7	−	1.32167e8i	−0.336279	−	0.582452i
$245$	−9.63805e7	−	1.66936e8i	−0.418705	−	0.725218i
$246$	−6.98413e7			−0.299116
$247$	2.00575e8	−	3.73129e8i	0.846909	−	1.57550i
$248$	−4.26632e7			−0.177612
$249$	−2.56817e7	−	4.44819e7i	−0.105421	−	0.182594i
$250$	−7.35647e7	−	1.27418e8i	−0.297769	−	0.515751i
$251$	−1.68238e8	+	2.91397e8i	−0.671531	+	1.16313i	0.305939	+	0.952051i	$0.401030\pi$
$251$	−1.68238e8	+	2.91397e8i	−0.671531	+	1.16313i	−0.977470	+	0.211075i	$0.932304\pi$
$252$	3.95643e8			1.55740
$253$	−4.16226e7	+	7.20925e7i	−0.161587	+	0.279878i
$254$	6.41489e7	−	1.11109e8i	0.245624	−	0.425434i
$255$	−2.28571e8			−0.863237
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	−1.35250e8	−	2.34259e8i	−0.497016	−	0.860857i	0.502978	−	0.864299i	$-0.332238\pi$
$257$	−1.35250e8	−	2.34259e8i	−0.497016	−	0.860857i	−0.999994	+	0.00344215i	$0.998904\pi$
$258$	3.35903e7	+	5.81801e7i	0.121771	+	0.210914i
$259$	1.69691e8			0.606890
$260$	3.18381e7	−	5.92283e7i	0.112341	−	0.208989i
$261$	6.25388e8			2.17725
$262$	8.41723e7	+	1.45791e8i	0.289144	+	0.500813i
$263$	2.01493e8	+	3.48997e8i	0.682992	+	1.18298i	0.974063	+	0.226275i	$0.0726548\pi$
$263$	2.01493e8	+	3.48997e8i	0.682992	+	1.18298i	−0.291072	+	0.956701i	$0.594012\pi$
$264$	−5.93832e7	+	1.02855e8i	−0.198632	+	0.344041i
$265$	−1.17995e8			−0.389497
$266$	3.22776e8	−	5.59065e8i	1.05152	−	1.82128i
$267$	4.60796e8	−	7.98122e8i	1.48156	−	2.56614i
$268$	−2.36649e7			−0.0750986
$269$	7.27637e7	−	1.26030e8i	0.227920	−	0.394768i	−0.729272	−	0.684224i	$-0.760141\pi$
$269$	7.27637e7	−	1.26030e8i	0.227920	−	0.394768i	0.957191	+	0.289456i	$0.0934743\pi$
$270$	8.03264e7	+	1.39129e8i	0.248362	+	0.430176i
$271$	1.78039e8	+	3.08372e8i	0.543403	+	0.941202i	0.998706	+	0.0508652i	$0.0161979\pi$
$271$	1.78039e8	+	3.08372e8i	0.543403	+	0.941202i	−0.455302	+	0.890337i	$0.650469\pi$
$272$	−8.90426e7			−0.268291
$273$	−9.47071e8	+	2.87675e7i	−2.81717	+	0.0855722i
$274$	−3.50989e8			−1.03078
$275$	−8.85656e7	−	1.53400e8i	−0.256803	−	0.444796i
$276$	7.21633e7	+	1.24990e8i	0.206602	+	0.357845i
$277$	−2.43177e8	+	4.21195e8i	−0.687454	+	1.19071i	0.285205	+	0.958467i	$0.407938\pi$
$277$	−2.43177e8	+	4.21195e8i	−0.687454	+	1.19071i	−0.972659	+	0.232239i	$0.925395\pi$
$278$	−1.11211e8			−0.310450
$279$	−1.70691e8	+	2.95646e8i	−0.470540	+	0.815000i
$280$	5.12357e7	−	8.87428e7i	0.139482	−	0.241591i
$281$	−4.89344e7			−0.131566			−0.0657828	−	0.997834i	$-0.520954\pi$
$281$	−4.89344e7			−0.131566			−0.0657828	+	0.997834i	$0.520954\pi$
$282$	1.30988e8	−	2.26878e8i	0.347824	−	0.602448i
$283$	1.37703e8	+	2.38509e8i	0.361153	+	0.625535i	0.988151	−	0.153486i	$-0.0490499\pi$
$283$	1.37703e8	+	2.38509e8i	0.361153	+	0.625535i	−0.626998	+	0.779021i	$0.715717\pi$
$284$	1.01990e8	+	1.76651e8i	0.264206	+	0.457618i
$285$	5.62288e8			1.43880
$286$	8.78007e7	−	1.63336e8i	0.221930	−	0.412857i
$287$	1.66178e8			0.414940
$288$	6.71240e7	+	1.16262e8i	0.165579	+	0.286790i
$289$	−3.11211e7	−	5.39033e7i	−0.0758425	−	0.131363i
$290$	8.09877e7	−	1.40275e8i	0.194996	−	0.337743i
$291$	4.94389e6			0.0117610
$292$	−1.86957e8	+	3.23818e8i	−0.439441	+	0.761135i
$293$	1.53439e8	−	2.65765e8i	0.356369	−	0.617249i	−0.630982	−	0.775797i	$-0.717348\pi$
$293$	1.53439e8	−	2.65765e8i	0.356369	−	0.617249i	0.987351	+	0.158548i	$0.0506813\pi$
$294$	−9.21632e8			−2.11515
$295$	−1.59875e8	+	2.76911e8i	−0.362579	+	0.628006i
$296$	2.87895e7	+	4.98648e7i	0.0645227	+	0.111757i
$297$	2.21518e8	+	3.83681e8i	0.490639	+	0.849812i
$298$	−3.26203e8			−0.714053
$299$	−1.18547e8	−	1.91646e8i	−0.256473	−	0.414620i
$300$	−3.07102e8			−0.656686
$301$	−7.99234e7	−	1.38431e8i	−0.168924	−	0.292585i
$302$	−2.67542e8	−	4.63396e8i	−0.558943	−	0.968118i
$303$	5.86839e8	−	1.01643e9i	1.21191	−	2.09909i
$304$	2.19046e8			0.447176
$305$	−1.58143e8	+	2.73912e8i	−0.319155	+	0.552792i
$306$	−3.56251e8	+	6.17045e8i	−0.710773	+	1.23109i
$307$	−1.55157e8			−0.306046			−0.153023	−	0.988223i	$-0.548901\pi$
$307$	−1.55157e8			−0.306046			−0.153023	+	0.988223i	$0.548901\pi$
$308$	1.41294e8	−	2.44728e8i	0.275547	−	0.477262i
$309$	4.91717e8	+	8.51679e8i	0.948114	+	1.64218i
$310$	4.42090e7	+	7.65723e7i	0.0842840	+	0.145984i
$311$	−5.61165e8			−1.05786			−0.528931	−	0.848665i	$-0.677407\pi$
$311$	−5.61165e8			−1.05786			−0.528931	+	0.848665i	$0.677407\pi$
$312$	−1.69132e8	−	2.73422e8i	−0.315271	−	0.509674i
$313$	−3.88240e8			−0.715640			−0.357820	−	0.933791i	$-0.616480\pi$
$313$	−3.88240e8			−0.715640			−0.357820	+	0.933791i	$0.616480\pi$
$314$	3.09794e8	+	5.36579e8i	0.564702	+	0.978093i
$315$	−4.09978e8	−	7.10103e8i	−0.739050	−	1.28007i
$316$	−3.44620e7	+	5.96899e7i	−0.0614378	+	0.106413i
$317$	6.56778e7			0.115801			0.0579003	−	0.998322i	$-0.481559\pi$
$317$	6.56778e7			0.115801			0.0579003	+	0.998322i	$0.481559\pi$
$318$	−2.82081e8	+	4.88578e8i	−0.491902	+	0.851999i
$319$	2.23342e8	−	3.86840e8i	0.385215	−	0.667212i
$320$	3.47702e7			0.0593174
$321$	−2.25646e7	+	3.90831e7i	−0.0380768	+	0.0659509i
$322$	−1.71702e8	−	2.97397e8i	−0.286603	−	0.496411i
$323$	5.81279e8	+	1.00680e9i	0.959789	+	1.66240i
$324$	1.94678e8			0.317987
$325$	4.79279e8	−	1.45582e7i	0.774455	−	0.0235243i
$326$	2.46381e8			0.393863
$327$	1.53459e8	+	2.65799e8i	0.242703	+	0.420374i
$328$	2.81934e7	+	4.88323e7i	0.0441152	+	0.0764098i
$329$	−3.11667e8	+	5.39823e8i	−0.482509	+	0.835730i
$330$	2.46139e8			0.377035
$331$	−3.41087e8	+	5.90779e8i	−0.516971	+	0.895421i	0.482834	+	0.875712i	$0.339607\pi$
$331$	−3.41087e8	+	5.90779e8i	−0.516971	+	0.895421i	−0.999806	+	0.0197091i	$0.993726\pi$
$332$	−2.07342e7	+	3.59127e7i	−0.0310960	+	0.0538598i
$333$	4.60735e8			0.683749
$334$	1.62901e8	−	2.82152e8i	0.239227	−	0.414354i
$335$	2.45223e7	+	4.24738e7i	0.0356372	+	0.0617255i
$336$	−2.44969e8	−	4.24299e8i	−0.352309	−	0.610217i
$337$	5.06834e8			0.721375			0.360687	−	0.932687i	$-0.382542\pi$
$337$	5.06834e8			0.721375			0.360687	+	0.932687i	$0.382542\pi$
$338$	2.76917e8	+	4.18699e8i	0.390069	+	0.589785i
$339$	−2.20422e9			−3.07296
$340$	9.22689e7	+	1.59814e8i	0.127315	+	0.220516i
$341$	1.21916e8	+	2.11165e8i	0.166503	+	0.288392i
$342$	8.76383e8	−	1.51794e9i	1.18468	−	2.05193i
$343$	9.50235e8			1.27146
$344$	2.71193e7	−	4.69720e7i	0.0359190	−	0.0622135i
$345$	1.49556e8	−	2.59038e8i	0.196081	−	0.339623i
$346$	−2.35214e8			−0.305279
$347$	2.42354e8	−	4.19770e8i	0.311385	−	0.539334i	−0.667278	−	0.744809i	$-0.732541\pi$
$347$	2.42354e8	−	4.19770e8i	0.311385	−	0.539334i	0.978662	+	0.205475i	$0.0658738\pi$
$348$	−3.87220e8	−	6.70684e8i	−0.492527	−	0.853082i
$349$	−1.46232e8	−	2.53281e8i	−0.184142	−	0.318943i	0.759145	−	0.650921i	$-0.225617\pi$
$349$	−1.46232e8	−	2.53281e8i	−0.184142	−	0.318943i	−0.943287	+	0.331978i	$0.892284\pi$
$350$	7.30705e8			0.910970
$351$	−1.19876e9	+	3.64127e7i	−1.47965	+	0.0449446i
$352$	9.58867e7			0.117181
$353$	−3.95188e8	−	6.84485e8i	−0.478181	−	0.828233i	0.521506	−	0.853247i	$-0.325370\pi$
$353$	−3.95188e8	−	6.84485e8i	−0.478181	−	0.828233i	−0.999687	+	0.0250141i	$0.992037\pi$
$354$	7.64396e8	+	1.32397e9i	0.915813	+	1.58624i
$355$	2.11370e8	−	3.66104e8i	0.250752	−	0.434315i
$356$	−7.44052e8			−0.874034
$357$	1.30014e9	−	2.25190e9i	1.51234	−	2.61945i
$358$	1.80145e8	−	3.12020e8i	0.207506	−	0.359412i
$359$	−1.31770e8			−0.150309			−0.0751544	−	0.997172i	$-0.523945\pi$
$359$	−1.31770e8			−0.150309			−0.0751544	+	0.997172i	$0.523945\pi$
$360$	1.39112e8	−	2.40949e8i	0.157147	−	0.272187i
$361$	−9.83020e8	−	1.70264e9i	−1.09973	−	1.90479i
$362$	−3.10772e8	−	5.38274e8i	−0.344320	−	0.596380i
$363$	−8.65986e8			−0.950250
$364$	4.02425e8	+	6.50570e8i	0.437351	+	0.707032i
$365$	7.74922e8			0.834128
$366$	7.56117e8	+	1.30963e9i	0.806130	+	1.39626i
$367$	4.36649e8	+	7.56299e8i	0.461107	+	0.798661i	0.999016	−	0.0443420i	$-0.0141191\pi$
$367$	4.36649e8	+	7.56299e8i	0.461107	+	0.798661i	−0.537909	+	0.843003i	$0.680786\pi$
$368$	5.82614e7	−	1.00912e8i	0.0609415	−	0.105554i
$369$	4.51195e8			0.467490
$370$	5.96651e7	−	1.03343e8i	0.0612371	−	0.106066i
$371$	6.71172e8	−	1.16250e9i	0.682378	−	1.18191i
$372$	4.22746e8			0.425774
$373$	−6.30678e8	+	1.09237e9i	−0.629255	+	1.08990i	0.358446	+	0.933550i	$0.383307\pi$
$373$	−6.30678e8	+	1.09237e9i	−0.629255	+	1.08990i	−0.987701	+	0.156352i	$0.950027\pi$
$374$	2.54452e8	+	4.40724e8i	0.251510	+	0.435629i
$375$	7.28946e8	+	1.26257e9i	0.713815	+	1.23636i
$376$	−2.11507e8			−0.205196
$377$	6.36109e8	+	1.02835e9i	0.611416	+	0.988429i
$378$	−1.82762e9			−1.74047
$379$	−2.35511e8	−	4.07916e8i	−0.222215	−	0.384887i	0.733265	−	0.679943i	$-0.237995\pi$
$379$	−2.35511e8	−	4.07916e8i	−0.222215	−	0.384887i	−0.955480	+	0.295055i	$0.904662\pi$
$380$	−2.26983e8	−	3.93146e8i	−0.212203	−	0.367546i
$381$	−6.35645e8	+	1.10097e9i	−0.588813	+	1.01985i
$382$	−1.32425e8			−0.121548
$383$	−4.16532e8	+	7.21454e8i	−0.378837	+	0.656165i	−0.990893	−	0.134649i	$-0.957009\pi$
$383$	−4.16532e8	+	7.21454e8i	−0.378837	+	0.656165i	0.612056	+	0.790814i	$0.290343\pi$
$384$	8.31219e7	−	1.43971e8i	0.0749128	−	0.129753i
$385$	−5.85654e8			−0.523032
$386$	−2.32166e8	+	4.02123e8i	−0.205467	+	0.355880i
$387$	−2.17003e8	−	3.75861e8i	−0.190317	−	0.329639i
$388$	−1.99574e6	−	3.45671e6i	−0.00173457	−	0.00300436i
$389$	−1.21290e8			−0.104472			−0.0522362	−	0.998635i	$-0.516635\pi$
$389$	−1.21290e8			−0.104472			−0.0522362	+	0.998635i	$0.516635\pi$
$390$	−3.15480e8	+	5.86888e8i	−0.269306	+	0.500990i
$391$	6.18428e8			0.523203
$392$	3.72042e8	+	6.44396e8i	0.311954	+	0.540320i
$393$	−8.34055e8	−	1.44463e9i	−0.693140	−	1.20055i
$394$	1.55164e8	−	2.68752e8i	0.127807	−	0.221368i
$395$	1.42842e8			0.116619
$396$	3.83633e8	−	6.64472e8i	0.310444	−	0.537704i
$397$	3.95732e8	−	6.85429e8i	0.317420	−	0.549788i	−0.662529	−	0.749037i	$-0.730517\pi$
$397$	3.95732e8	−	6.85429e8i	0.317420	−	0.549788i	0.979949	+	0.199248i	$0.0638500\pi$
$398$	−2.26937e8			−0.180433
$399$	−3.19836e9	+	5.53972e9i	−2.52071	+	4.36599i
$400$	1.23970e8	+	2.14722e8i	0.0968516	+	0.167752i
$401$	7.55394e8	+	1.30838e9i	0.585017	+	1.01328i	0.994873	+	0.101129i	$0.0322453\pi$
$401$	7.55394e8	+	1.30838e9i	0.585017	+	1.01328i	−0.409857	+	0.912150i	$0.634421\pi$
$402$	2.34493e8			0.180027
$403$	−6.59759e8	+	2.00403e7i	−0.502132	+	0.0152524i
$404$	−9.47575e8			−0.714955
$405$	−2.01731e8	−	3.49409e8i	−0.150897	−	0.261361i
$406$	9.21335e8	+	1.59580e9i	0.683245	+	1.18341i
$407$	1.64540e8	−	2.84992e8i	0.120974	−	0.209533i
$408$	8.82315e8			0.643151
$409$	1.16664e9	−	2.02068e9i	0.843151	−	1.46038i	−0.0440666	−	0.999029i	$-0.514031\pi$
$409$	1.16664e9	−	2.02068e9i	0.843151	−	1.46038i	0.887217	−	0.461351i	$-0.152635\pi$
$410$	5.84297e7	−	1.01203e8i	0.0418688	−	0.0725189i
$411$	3.47792e9			2.47100
$412$	3.96990e8	−	6.87607e8i	0.279666	−	0.484396i
$413$	−1.81877e9	−	3.15021e9i	−1.27044	−	2.20046i
$414$	−4.66196e8	−	8.07475e8i	−0.322900	−	0.559279i
$415$	8.59418e7			0.0590250
$416$	−1.22899e8	+	2.28630e8i	−0.0836995	+	0.155706i
$417$	1.10198e9			0.744214
$418$	−6.25957e8	−	1.08419e9i	−0.419206	−	0.726086i
$419$	−5.09928e8	−	8.83220e8i	−0.338656	−	0.586570i	0.645524	−	0.763740i	$-0.276639\pi$
$419$	−5.09928e8	−	8.83220e8i	−0.338656	−	0.586570i	−0.984180	+	0.177170i	$0.943306\pi$
$420$	−5.07689e8	+	8.79344e8i	−0.334369	+	0.579143i
$421$	−1.73659e9			−1.13426			−0.567128	−	0.823630i	$-0.691945\pi$
$421$	−1.73659e9			−1.13426			−0.567128	+	0.823630i	$0.691945\pi$
$422$	−2.61174e8	+	4.52366e8i	−0.169175	+	0.293019i
$423$	−8.46220e8	+	1.46570e9i	−0.543616	+	0.941570i
$424$	4.55479e8			0.290193
$425$	−6.57953e8	+	1.13961e9i	−0.415751	+	0.720102i
$426$	−1.01061e9	−	1.75042e9i	−0.633357	−	1.09701i
$427$	−1.79907e9	−	3.11609e9i	−1.11828	−	1.93692i
$428$	3.64353e7			0.0224631
$429$	−8.70008e8	+	1.61848e9i	−0.532014	+	0.989705i
$430$	−1.12408e8			−0.0681798
$431$	1.20435e8	+	2.08599e8i	0.0724573	+	0.125500i	0.899978	−	0.435936i	$-0.143583\pi$
$431$	1.20435e8	+	2.08599e8i	0.0724573	+	0.125500i	−0.827520	+	0.561436i	$0.810249\pi$
$432$	−3.10071e8	−	5.37059e8i	−0.185041	−	0.320501i
$433$	1.10516e9	−	1.91420e9i	0.654212	−	1.13313i	−0.327878	−	0.944720i	$-0.606334\pi$
$433$	1.10516e9	−	1.91420e9i	0.654212	−	1.13313i	0.982091	−	0.188409i	$-0.0603330\pi$
$434$	−1.00586e9			−0.590643
$435$	−8.02499e8	+	1.38997e9i	−0.467447	+	0.809641i
$436$	1.23896e8	−	2.14594e8i	0.0715903	−	0.123998i
$437$	−1.52134e9			−0.872052
$438$	1.85253e9	−	3.20868e9i	1.05343	−	1.82460i
$439$	1.15306e9	+	1.99716e9i	0.650468	+	1.12664i	0.983010	+	0.183554i	$0.0587603\pi$
$439$	1.15306e9	+	1.99716e9i	0.650468	+	1.12664i	−0.332542	+	0.943088i	$0.607906\pi$
$440$	−9.93609e7	−	1.72098e8i	−0.0556072	−	0.0963145i
$441$	5.95401e9			3.30579
$442$	−1.37699e9	+	4.18263e7i	−0.758493	+	0.0230394i
$443$	1.10170e9			0.602073			0.301036	−	0.953613i	$-0.402667\pi$
$443$	1.10170e9			0.602073			0.301036	+	0.953613i	$0.402667\pi$
$444$	−2.85272e8	−	4.94105e8i	−0.154674	−	0.267904i
$445$	7.71011e8	+	1.33543e9i	0.414763	+	0.718391i
$446$	−4.19521e8	+	7.26632e8i	−0.223914	+	0.387831i
$447$	3.23231e9			1.71173
$448$	−1.97777e8	+	3.42560e8i	−0.103921	+	0.179996i
$449$	−9.03527e8	+	1.56495e9i	−0.471063	+	0.815905i	−0.999452	−	0.0330974i	$-0.989463\pi$
$449$	−9.03527e8	+	1.56495e9i	−0.471063	+	0.815905i	0.528389	+	0.849002i	$0.322796\pi$
$450$	1.98397e9			1.02634
$451$	1.61133e8	−	2.79091e8i	0.0827118	−	0.143261i
$452$	8.89796e8	+	1.54117e9i	0.453217	+	0.784994i
$453$	2.65105e9	+	4.59175e9i	1.33990	+	2.32078i
$454$	−3.98776e8			−0.200002
$455$	7.50641e8	−	1.39642e9i	0.373588	−	0.694985i
$456$	−2.17051e9			−1.07198
$457$	−9.01035e8	−	1.56064e9i	−0.441606	−	0.764884i	0.556203	−	0.831047i	$-0.312258\pi$
$457$	−9.01035e8	−	1.56064e9i	−0.441606	−	0.764884i	−0.997809	+	0.0661624i	$0.978924\pi$
$458$	4.62527e8	+	8.01121e8i	0.224962	+	0.389645i
$459$	1.64566e9	−	2.85036e9i	0.794319	−	1.37580i
$460$	−2.41489e8			−0.115677
$461$	3.90785e8	−	6.76859e8i	0.185774	−	0.321770i	−0.758063	−	0.652181i	$-0.773854\pi$
$461$	3.90785e8	−	6.76859e8i	0.185774	−	0.321770i	0.943837	+	0.330412i	$0.107188\pi$
$462$	−1.40007e9	+	2.42499e9i	−0.660545	+	1.14410i
$463$	−7.80510e8			−0.365464			−0.182732	−	0.983163i	$-0.558494\pi$
$463$	−7.80510e8			−0.365464			−0.182732	+	0.983163i	$0.558494\pi$
$464$	−3.12624e8	+	5.41480e8i	−0.145281	+	0.251634i
$465$	−4.38063e8	−	7.58747e8i	−0.202046	−	0.349955i
$466$	2.81985e8	+	4.88412e8i	0.129085	+	0.223581i
$467$	−2.48897e9			−1.13087			−0.565433	−	0.824794i	$-0.691291\pi$
$467$	−2.48897e9			−1.13087			−0.565433	+	0.824794i	$0.691291\pi$
$468$	1.09264e9	+	1.76639e9i	0.492739	+	0.796573i
$469$	−5.57942e8			−0.249738
$470$	2.19171e8	+	3.79615e8i	0.0973734	+	0.168656i
$471$	−3.06972e9	−	5.31691e9i	−1.35371	−	2.34469i
$472$	6.17139e8	−	1.06892e9i	0.270138	−	0.467893i
$473$	−3.09989e8			−0.134689
$474$	3.41480e8	−	5.91461e8i	0.147279	−	0.255095i
$475$	1.61858e9	−	2.80346e9i	0.692956	−	1.20023i
$476$	−2.09934e9			−0.892194
$477$	1.82233e9	−	3.15636e9i	0.768797	−	1.33160i
$478$	−1.23482e9	−	2.13877e9i	−0.517137	−	0.895708i
$479$	1.73346e9	+	3.00243e9i	0.720673	+	1.24824i	0.960730	+	0.277484i	$0.0895006\pi$
$479$	1.73346e9	+	3.00243e9i	0.720673	+	1.24824i	−0.240057	+	0.970759i	$0.577166\pi$
$480$	−3.44534e8			−0.142196
$481$	4.68633e8	+	7.57603e8i	0.192011	+	0.310409i
$482$	−9.90112e8			−0.402735
$483$	1.70138e9	+	2.94688e9i	0.687048	+	1.19000i
$484$	3.49579e8	+	6.05489e8i	0.140148	+	0.242743i
$485$	−4.13609e6	+	7.16392e6i	−0.00164624	+	0.00285138i
$486$	7.19885e8			0.284470
$487$	5.00506e8	−	8.66901e8i	0.196362	−	0.340109i	−0.750984	−	0.660320i	$-0.770421\pi$
$487$	5.00506e8	−	8.66901e8i	0.196362	−	0.340109i	0.947346	+	0.320211i	$0.103754\pi$
$488$	6.10455e8	−	1.05734e9i	0.237785	−	0.411856i
$489$	−2.44136e9			−0.944172
$490$	7.71044e8	−	1.33549e9i	0.296069	−	0.512806i
$491$	7.39363e7	+	1.28061e8i	0.0281885	+	0.0488240i	0.879776	−	0.475389i	$-0.157693\pi$
$491$	7.39363e7	+	1.28061e8i	0.0281885	+	0.0488240i	−0.851587	+	0.524213i	$0.824359\pi$
$492$	−2.79365e8	−	4.83875e8i	−0.105753	−	0.183170i
$493$	−3.31841e9			−1.24729
$494$	3.38741e9	−	1.02893e8i	1.26422	−	0.0384011i
$495$	−1.59013e9			−0.589271
$496$	−1.70653e8	−	2.95580e8i	−0.0627954	−	0.108765i
$497$	2.40460e9	+	4.16488e9i	0.878607	+	1.52179i
$498$	2.05453e8	−	3.55855e8i	0.0745436	−	0.129113i
$499$	−3.44602e9			−1.24155			−0.620777	−	0.783988i	$-0.713183\pi$
$499$	−3.44602e9			−1.24155			−0.620777	+	0.783988i	$0.713183\pi$
$500$	5.88518e8	−	1.01934e9i	0.210555	−	0.364691i
$501$	−1.61417e9	+	2.79582e9i	−0.573478	+	0.993293i
$502$	−2.69181e9			−0.949688
$503$	2.83908e9	−	4.91744e9i	0.994696	−	1.72286i	0.408267	−	0.912862i	$-0.366133\pi$
$503$	2.83908e9	−	4.91744e9i	0.994696	−	1.72286i	0.586428	−	0.810001i	$-0.300533\pi$
$504$	1.58257e9	+	2.74109e9i	0.550626	+	0.953712i
$505$	9.81908e8	+	1.70071e9i	0.339274	+	0.587640i
$506$	−6.65962e8			−0.228519
$507$	−2.74395e9	−	4.14885e9i	−0.935078	−	1.41384i
$508$	1.02638e9			0.347365
$509$	−1.82542e9	−	3.16171e9i	−0.613549	−	1.06270i	−0.990637	−	0.136521i	$-0.956408\pi$
$509$	−1.82542e9	−	3.16171e9i	−0.613549	−	1.06270i	0.377088	−	0.926177i	$-0.376925\pi$
$510$	−9.14283e8	−	1.58358e9i	−0.305200	−	0.528622i
$511$	−4.40785e9	+	7.63461e9i	−1.46135	+	2.53113i
$512$	−1.34218e8			−0.0441942
$513$	−4.04835e9	+	7.01194e9i	−1.32394	+	2.29312i
$514$	1.08200e9	−	1.87407e9i	0.351443	−	0.608718i
$515$	−1.64550e9			−0.530850
$516$	−2.68722e8	+	4.65441e8i	−0.0861053	+	0.149139i
$517$	6.04413e8	+	1.04687e9i	0.192361	+	0.333179i
$518$	6.78765e8	+	1.17565e9i	0.214568	+	0.371643i
$519$	2.33071e9			0.731819
$520$	5.37698e8	−	1.63327e7i	0.167698	−	0.00509385i
$521$	3.14626e9			0.974680			0.487340	−	0.873212i	$-0.337967\pi$
$521$	3.14626e9			0.974680			0.487340	+	0.873212i	$0.337967\pi$
$522$	2.50155e9	+	4.33282e9i	0.769774	+	1.33329i
$523$	3.21632e9	+	5.57083e9i	0.983113	+	1.70280i	0.650039	+	0.759901i	$0.274752\pi$
$523$	3.21632e9	+	5.57083e9i	0.983113	+	1.70280i	0.333074	+	0.942901i	$0.391914\pi$
$524$	−6.73379e8	+	1.16633e9i	−0.204456	+	0.354128i
$525$	−7.24048e9			−2.18379
$526$	−1.61195e9	+	2.79197e9i	−0.482948	+	0.836491i
$527$	9.05716e8	−	1.56875e9i	0.269560	−	0.466891i
$528$	−9.50132e8			−0.280909
$529$	1.29777e9	−	2.24780e9i	0.381156	−	0.660182i
$530$	−4.71982e8	−	8.17496e8i	−0.137708	−	0.238518i
$531$	−4.93822e9	−	8.55326e9i	−1.43133	−	2.47914i
$532$	5.16442e9			1.48707
$533$	4.58930e8	+	7.41917e8i	0.131281	+	0.212231i
$534$	7.37274e9			2.09524
$535$	−3.77555e7	−	6.53944e7i	−0.0106596	−	0.0184630i
$536$	−9.46594e7	−	1.63955e8i	−0.0265514	−	0.0459883i
$537$	−1.78504e9	+	3.09178e9i	−0.497436	+	0.861585i
$538$	1.16422e9			0.322327
$539$	2.12633e9	−	3.68291e9i	0.584884	−	1.01305i
$540$	−6.42611e8	+	1.11304e9i	−0.175619	+	0.304180i
$541$	1.42344e9			0.386500			0.193250	−	0.981150i	$-0.438097\pi$
$541$	1.42344e9			0.386500			0.193250	+	0.981150i	$0.438097\pi$
$542$	−1.42431e9	+	2.46698e9i	−0.384244	+	0.665530i
$543$	3.07941e9	+	5.33370e9i	0.825408	+	1.42965i
$544$	−3.56171e8	−	6.16905e8i	−0.0948554	−	0.164294i
$545$	−5.13539e8			−0.135890
$546$	−3.98759e9	−	6.44643e9i	−1.04842	−	1.69490i
$547$	−1.52035e9			−0.397181			−0.198591	−	0.980083i	$-0.563636\pi$
$547$	−1.52035e9			−0.397181			−0.198591	+	0.980083i	$0.563636\pi$
$548$	−1.40396e9	−	2.43172e9i	−0.364436	−	0.631222i
$549$	−4.88474e9	−	8.46062e9i	−1.25991	−	2.18222i
$550$	7.08525e8	−	1.22720e9i	0.181587	−	0.314519i
$551$	8.16335e9			2.07892
$552$	−5.77306e8	+	9.99924e8i	−0.146090	+	0.253035i
$553$	−8.12505e8	+	1.40730e9i	−0.204309	+	0.353874i
$554$	−3.89084e9			−0.972207
$555$	−5.91216e8	+	1.02402e9i	−0.146798	+	0.254262i
$556$	−4.44845e8	−	7.70494e8i	−0.109761	−	0.190111i
$557$	4.15106e8	+	7.18985e8i	0.101781	+	0.176290i	0.912418	−	0.409259i	$-0.134213\pi$
$557$	4.15106e8	+	7.18985e8i	0.101781	+	0.176290i	−0.810638	+	0.585548i	$0.800879\pi$
$558$	−2.73106e9			−0.665445
$559$	3.97318e8	−	7.39130e8i	0.0962048	−	0.178970i
$560$	8.19771e8			0.197258
$561$	−2.52134e9	−	4.36709e9i	−0.602923	−	1.04429i
$562$	−1.95738e8	−	3.39027e8i	−0.0465154	−	0.0805671i
$563$	1.61860e9	−	2.80351e9i	0.382262	−	0.662098i	−0.609123	−	0.793076i	$-0.708478\pi$
$563$	1.61860e9	−	2.80351e9i	0.382262	−	0.662098i	0.991385	+	0.130978i	$0.0418118\pi$
$564$	2.09581e9			0.491897
$565$	1.84407e9	−	3.19402e9i	0.430138	−	0.745021i
$566$	−1.10162e9	+	1.90807e9i	−0.255374	+	0.442320i
$567$	4.58989e9			1.05745
$568$	−8.15918e8	+	1.41321e9i	−0.186822	+	0.323585i
$569$	2.35987e9	+	4.08742e9i	0.537026	+	0.930157i	0.999062	+	0.0432957i	$0.0137857\pi$
$569$	2.35987e9	+	4.08742e9i	0.537026	+	0.930157i	−0.462036	+	0.886861i	$0.652881\pi$
$570$	2.24915e9	+	3.89565e9i	0.508694	+	0.881084i
$571$	3.95218e9			0.888403			0.444201	−	0.895927i	$-0.353487\pi$
$571$	3.95218e9			0.888403			0.444201	+	0.895927i	$0.353487\pi$
$572$	1.48282e9	−	4.50412e7i	0.331286	−	0.0100629i
$573$	1.31219e9			0.291377
$574$	6.64710e8	+	1.15131e9i	0.146704	+	0.254098i
$575$	−8.61009e8	−	1.49131e9i	−0.188873	−	0.327138i
$576$	−5.36992e8	+	9.30097e8i	−0.117082	+	0.202791i
$577$	−2.12731e9			−0.461016			−0.230508	−	0.973070i	$-0.574039\pi$
$577$	−2.12731e9			−0.461016			−0.230508	+	0.973070i	$0.574039\pi$
$578$	2.48969e8	−	4.31227e8i	0.0536287	−	0.0928877i
$579$	2.30051e9	−	3.98459e9i	0.492548	−	0.853118i
$580$	1.29580e9			0.275766
$581$	−4.88847e8	+	8.46708e8i	−0.103409	+	0.179109i
$582$	1.97755e7	+	3.42522e7i	0.00415813	+	0.00720209i
$583$	−1.30160e9	−	2.25443e9i	−0.272042	−	0.471191i
$584$	−2.99131e9			−0.621464
$585$	2.03810e9	−	3.79147e9i	0.420900	−	0.783000i
$586$	2.45503e9			0.503982
$587$	2.65059e9	+	4.59096e9i	0.540890	+	0.936850i	0.998853	+	0.0478782i	$0.0152459\pi$
$587$	2.65059e9	+	4.59096e9i	0.540890	+	0.936850i	−0.457963	+	0.888971i	$0.651421\pi$
$588$	−3.68653e9	−	6.38525e9i	−0.747820	−	1.29526i
$589$	−2.22808e9	+	3.85914e9i	−0.449290	+	0.778193i
$590$	−2.55800e9			−0.512765
$591$	−1.53750e9	+	2.66304e9i	−0.306380	+	0.530666i
$592$	−2.30316e8	+	3.98919e8i	−0.0456244	+	0.0790239i
$593$	7.20568e9			1.41900			0.709501	−	0.704704i	$-0.248920\pi$
$593$	7.20568e9			1.41900			0.709501	+	0.704704i	$0.248920\pi$
$594$	−1.77215e9	+	3.06945e9i	−0.346934	+	0.600908i
$595$	2.17541e9	+	3.76792e9i	0.423381	+	0.733317i
$596$	−1.30481e9	−	2.26000e9i	−0.252456	−	0.437266i
$597$	2.24870e9			0.432535
$598$	8.53573e8	−	1.58790e9i	0.163225	−	0.303647i
$599$	−1.75875e9			−0.334357			−0.167179	−	0.985927i	$-0.553466\pi$
$599$	−1.75875e9			−0.334357			−0.167179	+	0.985927i	$0.553466\pi$
$600$	−1.22841e9	−	2.12766e9i	−0.232174	−	0.402136i
$601$	3.50633e9	+	6.07314e9i	0.658858	+	1.14118i	0.980912	+	0.194454i	$0.0622936\pi$
$601$	3.50633e9	+	6.07314e9i	0.658858	+	1.14118i	−0.322054	+	0.946721i	$0.604373\pi$
$602$	6.39387e8	−	1.10745e9i	0.119447	−	0.206889i
$603$	−1.51489e9			−0.281366
$604$	2.14034e9	−	3.70717e9i	0.395232	−	0.684563i
$605$	7.24491e8	−	1.25485e9i	0.133011	−	0.230383i
$606$	9.38942e9			1.71390
$607$	−7.96698e8	+	1.37992e9i	−0.144588	+	0.250435i	−0.929219	−	0.369529i	$-0.879519\pi$
$607$	−7.96698e8	+	1.37992e9i	−0.144588	+	0.250435i	0.784631	+	0.619963i	$0.212852\pi$
$608$	8.76186e8	+	1.51760e9i	0.158101	+	0.273838i
$609$	−9.12941e9	−	1.58126e10i	−1.63788	−	2.83689i
$610$	−2.53029e9			−0.451353
$611$	−3.27082e9	+	9.93520e7i	−0.580113	+	0.0176211i
$612$	−5.70001e9			−1.00518
$613$	5.40201e8	+	9.35656e8i	0.0947205	+	0.164061i	0.909492	−	0.415722i	$-0.136471\pi$
$613$	5.40201e8	+	9.35656e8i	0.0947205	+	0.164061i	−0.814771	+	0.579782i	$0.803138\pi$
$614$	−6.20627e8	−	1.07496e9i	−0.108204	−	0.187414i
$615$	−5.78974e8	+	1.00281e9i	−0.100368	+	0.173843i
$616$	2.26070e9			0.389683
$617$	−3.25522e9	+	5.63820e9i	−0.557933	+	0.966368i	0.439736	+	0.898127i	$0.355072\pi$
$617$	−3.25522e9	+	5.63820e9i	−0.557933	+	0.966368i	−0.997669	+	0.0682409i	$0.978261\pi$
$618$	−3.93374e9	+	6.81343e9i	−0.670418	+	1.16120i
$619$	−2.46380e9			−0.417531			−0.208766	−	0.977966i	$-0.566945\pi$
$619$	−2.46380e9			−0.417531			−0.208766	+	0.977966i	$0.566945\pi$
$620$	−3.53672e8	+	6.12578e8i	−0.0595978	+	0.103226i
$621$	2.15354e9	+	3.73003e9i	0.360854	+	0.625018i
$622$	−2.24466e9	−	3.88787e9i	−0.374011	−	0.647806i
$623$	−1.75424e10			−2.90657
$624$	1.21780e9	−	2.26547e9i	0.200645	−	0.373260i
$625$	2.28972e9			0.375147
$626$	−1.55296e9	−	2.68980e9i	−0.253017	−	0.438238i
$627$	6.20255e9	+	1.07431e10i	1.00493	+	1.74058i
$628$	−2.47835e9	+	4.29263e9i	−0.399305	+	0.691616i
$629$	−2.44473e9			−0.391701
$630$	3.27982e9	−	5.68082e9i	0.522587	−	0.905147i
$631$	1.56214e9	−	2.70571e9i	0.247524	−	0.428725i	−0.715314	−	0.698803i	$-0.753716\pi$
$631$	1.56214e9	−	2.70571e9i	0.247524	−	0.428725i	0.962838	+	0.270078i	$0.0870496\pi$
$632$	−5.51392e8			−0.0868861
$633$	2.58794e9	−	4.48245e9i	0.405547	−	0.702429i
$634$	2.62711e8	+	4.55029e8i	0.0409417	+	0.0709131i
$635$	−1.06357e9	−	1.84216e9i	−0.164838	−	0.285509i
$636$	−4.51329e9			−0.695654
$637$	6.05608e9	+	9.79040e9i	0.928333	+	1.50076i
$638$	3.57347e9			0.544776
$639$	6.52882e9	+	1.13082e10i	0.989878	+	1.71452i
$640$	1.39081e8	+	2.40895e8i	0.0209719	+	0.0363243i
$641$	4.15064e9	−	7.18911e9i	0.622460	−	1.07813i	−0.366566	−	0.930392i	$-0.619467\pi$
$641$	4.15064e9	−	7.18911e9i	0.622460	−	1.07813i	0.989026	−	0.147741i	$-0.0472001\pi$
$642$	−3.61034e8			−0.0538487
$643$	−3.87700e9	+	6.71515e9i	−0.575118	+	0.996133i	0.420911	+	0.907102i	$0.361710\pi$
$643$	−3.87700e9	+	6.71515e9i	−0.575118	+	0.996133i	−0.996029	+	0.0890314i	$0.971623\pi$
$644$	1.37362e9	−	2.37918e9i	0.202659	−	0.351016i
$645$	1.11384e9			0.163441
$646$	−4.65023e9	+	8.05443e9i	−0.678673	+	1.17550i
$647$	−4.87730e9	−	8.44773e9i	−0.707969	−	1.22624i	−0.965609	−	0.259998i	$-0.916278\pi$
$647$	−4.87730e9	−	8.44773e9i	−0.707969	−	1.22624i	0.257640	−	0.966241i	$-0.417055\pi$
$648$	7.78711e8	+	1.34877e9i	0.112425	+	0.194726i
$649$	−7.05426e9			−1.01297
$650$	2.01798e9	+	3.26231e9i	0.288217	+	0.465938i
$651$	9.96701e9			1.41590
$652$	9.85523e8	+	1.70698e9i	0.139252	+	0.241191i
$653$	1.40039e9	+	2.42555e9i	0.196813	+	0.340890i	0.947493	−	0.319775i	$-0.103607\pi$
$653$	1.40039e9	+	2.42555e9i	0.196813	+	0.340890i	−0.750680	+	0.660666i	$0.770274\pi$
$654$	−1.22767e9	+	2.12639e9i	−0.171617	+	0.297249i
$655$	2.79111e9			0.388090
$656$	−2.25547e8	+	3.90659e8i	−0.0311942	+	0.0540299i
$657$	−1.19679e10	+	2.07290e10i	−1.64642	+	2.85168i
$658$	−4.98668e9			−0.682371
$659$	4.64679e9	−	8.04848e9i	0.632491	−	1.09551i	−0.354550	−	0.935037i	$-0.615366\pi$
$659$	4.64679e9	−	8.04848e9i	0.632491	−	1.09551i	0.987041	−	0.160469i	$-0.0513007\pi$
$660$	9.84557e8	+	1.70530e9i	0.133302	+	0.230886i
$661$	−2.38956e9	−	4.13885e9i	−0.321820	−	0.557409i	0.659043	−	0.752105i	$-0.270961\pi$
$661$	−2.38956e9	−	4.13885e9i	−0.321820	−	0.557409i	−0.980864	+	0.194696i	$0.937628\pi$
$662$	−5.45738e9			−0.731108
$663$	1.36444e10	−	4.14452e8i	1.81827	−	0.0552303i
$664$	−3.31747e8			−0.0439763
$665$	−5.35154e9	−	9.26914e9i	−0.705672	−	1.22226i
$666$	1.84294e9	+	3.19207e9i	0.241742	+	0.418709i
$667$	2.17126e9	−	3.76074e9i	0.283317	−	0.490719i
$668$	2.60641e9			0.338318
$669$	4.15699e9	−	7.20012e9i	0.536770	−	0.929712i
$670$	−1.96178e8	+	3.39791e8i	−0.0251993	+	0.0436465i
$671$	−6.97786e9			−0.891648
$672$	1.95975e9	−	3.39439e9i	0.249120	−	0.431488i
$673$	−1.48349e9	−	2.56948e9i	−0.187599	−	0.324932i	0.756850	−	0.653589i	$-0.226737\pi$
$673$	−1.48349e9	−	2.56948e9i	−0.187599	−	0.324932i	−0.944449	+	0.328657i	$0.893404\pi$
$674$	2.02734e9	+	3.51145e9i	0.255045	+	0.441750i
$675$	−9.16469e9			−1.14698
$676$	−1.79316e9	+	3.59334e9i	−0.223258	+	0.447388i
$677$	−7.59327e8			−0.0940521			−0.0470260	−	0.998894i	$-0.514974\pi$
$677$	−7.59327e8			−0.0940521			−0.0470260	+	0.998894i	$0.514974\pi$
$678$	−8.81690e9	−	1.52713e10i	−1.08646	−	1.88180i
$679$	−4.70531e7	−	8.14984e7i	−0.00576825	−	0.00999091i
$680$	−7.38151e8	+	1.27851e9i	−0.0900252	+	0.155928i
$681$	3.95143e9			0.479446
$682$	−9.75331e8	+	1.68932e9i	−0.117735	+	0.203924i
$683$	3.30422e9	−	5.72307e9i	0.396822	−	0.687316i	−0.596510	−	0.802606i	$-0.703446\pi$
$683$	3.30422e9	−	5.72307e9i	0.396822	−	0.687316i	0.993332	+	0.115290i	$0.0367797\pi$
$684$	1.40221e10			1.67540
$685$	−2.90965e9	+	5.03966e9i	−0.345879	+	0.599079i
$686$	3.80094e9	+	6.58342e9i	0.449528	+	0.778605i
$687$	−4.58314e9	−	7.93823e9i	−0.539280	−	0.934060i
$688$	4.33909e8			0.0507971
$689$	7.04368e9	−	2.13953e8i	0.820412	−	0.0249202i
$690$	2.39289e9			0.277301
$691$	−4.34206e9	−	7.52066e9i	−0.500636	−	0.867128i	−1.00000		0.000734904i	$-0.999766\pi$
$691$	−4.34206e9	−	7.52066e9i	−0.500636	−	0.867128i	0.499363	−	0.866393i	$-0.333567\pi$
$692$	−9.40857e8	−	1.62961e9i	−0.107933	−	0.186945i
$693$	9.04486e9	−	1.56662e10i	1.03237	−	1.78812i
$694$	3.87767e9			0.440365
$695$	−9.21925e8	+	1.59682e9i	−0.104171	+	0.180430i
$696$	3.09776e9	−	5.36547e9i	0.348269	−	0.603220i
$697$	−2.39411e9			−0.267812
$698$	1.16985e9	−	2.02625e9i	0.130208	−	0.225527i
$699$	−2.79416e9	−	4.83962e9i	−0.309443	−	0.535971i
$700$	2.92282e9	+	5.06247e9i	0.322076	+	0.557853i
$701$	7.50161e9			0.822510			0.411255	−	0.911520i	$-0.365091\pi$
$701$	7.50161e9			0.822510			0.411255	+	0.911520i	$0.365091\pi$
$702$	−5.04732e9	−	8.15961e9i	−0.550657	−	0.890204i
$703$	6.01409e9			0.652869
$704$	3.83547e8	+	6.64322e8i	0.0414299	+	0.0717587i
$705$	−2.17174e9	−	3.76157e9i	−0.233424	−	0.404303i
$706$	3.16150e9	−	5.47588e9i	0.338125	−	0.585649i
$707$	−2.23408e10			−2.37756
$708$	−6.11517e9	+	1.05918e10i	−0.647578	+	1.12164i
$709$	−3.60933e9	+	6.25154e9i	−0.380334	+	0.658757i	−0.991110	−	0.133046i	$-0.957524\pi$
$709$	−3.60933e9	+	6.25154e9i	−0.380334	+	0.658757i	0.610776	+	0.791803i	$0.290858\pi$
$710$	3.38192e9			0.354617
$711$	−2.20606e9	+	3.82102e9i	−0.230184	+	0.398690i
$712$	−2.97621e9	−	5.15494e9i	−0.309018	−	0.535234i
$713$	1.18524e9	+	2.05289e9i	0.122459	+	0.212106i
$714$	2.08022e10			2.13878
$715$	−1.61739e9	−	2.61471e9i	−0.165479	−	0.267518i
$716$	2.88232e9			0.293458
$717$	1.22357e10	+	2.11929e10i	1.23969	+	2.14720i
$718$	−5.27078e8	−	9.12926e8i	−0.0531422	−	0.0920450i
$719$	−7.39310e9	+	1.28052e10i	−0.741781	+	1.28480i	0.209903	+	0.977722i	$0.432685\pi$
$719$	−7.39310e9	+	1.28052e10i	−0.741781	+	1.28480i	−0.951684	+	0.307080i	$0.900648\pi$
$720$	2.22579e9			0.222239
$721$	9.35978e9	−	1.62116e10i	0.930019	−	1.61084i
$722$	7.86416e9	−	1.36211e10i	0.777628	−	1.34689i
$723$	9.81092e9			0.965441
$724$	2.48618e9	−	4.30619e9i	0.243471	−	0.421704i
$725$	4.62007e9	+	8.00220e9i	0.450262	+	0.779877i
$726$	−3.46395e9	−	5.99973e9i	−0.335964	−	0.581907i
$727$	−5.23529e9			−0.505325			−0.252662	−	0.967554i	$-0.581306\pi$
$727$	−5.23529e9			−0.505325			−0.252662	+	0.967554i	$0.581306\pi$
$728$	−2.89758e9	+	5.39036e9i	−0.278340	+	0.517795i
$729$	−1.37858e10			−1.31791
$730$	3.09969e9	+	5.36882e9i	0.294909	+	0.510797i
$731$	1.15145e9	+	1.99438e9i	0.109027	+	0.188841i
$732$	−6.04894e9	+	1.04771e10i	−0.570020	+	0.987304i
$733$	2.06458e10			1.93628			0.968138	−	0.250417i	$-0.0805676\pi$
$733$	2.06458e10			1.93628			0.968138	+	0.250417i	$0.0805676\pi$
$734$	−3.49320e9	+	6.05039e9i	−0.326052	+	0.564738i
$735$	−7.64020e9	+	1.32332e10i	−0.709739	+	1.22930i
$736$	9.32182e8			0.0861844
$737$	−5.41006e8	+	9.37050e8i	−0.0497813	+	0.0862237i
$738$	1.80478e9	+	3.12597e9i	0.165283	+	0.286278i
$739$	4.34202e9	+	7.52060e9i	0.395764	+	0.685483i	0.993198	−	0.116435i	$-0.0371465\pi$
$739$	4.34202e9	+	7.52060e9i	0.395764	+	0.685483i	−0.597434	+	0.801918i	$0.703813\pi$
$740$	9.54642e8			0.0866024
$741$	−3.35655e10	+	1.01956e9i	−3.03061	+	0.0920554i
$742$	1.07387e10			0.965028
$743$	−5.13915e9	−	8.90127e9i	−0.459653	−	0.796143i	0.539289	−	0.842121i	$-0.318693\pi$
$743$	−5.13915e9	−	8.90127e9i	−0.459653	−	0.796143i	−0.998942	+	0.0459776i	$0.985360\pi$
$744$	1.69098e9	+	2.92887e9i	0.150534	+	0.260732i
$745$	−2.70417e9	+	4.68377e9i	−0.239600	+	0.415000i
$746$	−1.00909e10			−0.889901
$747$	−1.32729e9	+	2.29893e9i	−0.116505	+	0.201792i
$748$	−2.03562e9	+	3.52579e9i	−0.177845	+	0.308036i
$749$	8.59030e8			0.0747002
$750$	−5.83156e9	+	1.01006e10i	−0.504743	+	0.874241i
$751$	−4.41272e9	−	7.64306e9i	−0.380161	−	0.658457i	0.610924	−	0.791689i	$-0.290798\pi$
$751$	−4.41272e9	−	7.64306e9i	−0.380161	−	0.658457i	−0.991085	+	0.133232i	$0.957465\pi$
$752$	−8.46030e8	−	1.46537e9i	−0.0725476	−	0.125656i
$753$	2.66729e10			2.27660
$754$	−4.58017e9	+	8.52048e9i	−0.389118	+	0.723877i
$755$	−8.87154e9			−0.750213
$756$	−7.31050e9	−	1.26622e10i	−0.615348	−	1.06581i
$757$	−8.12765e9	−	1.40775e10i	−0.680972	−	1.17948i	−0.974684	−	0.223585i	$-0.928224\pi$
$757$	−8.12765e9	−	1.40775e10i	−0.680972	−	1.17948i	0.293712	−	0.955894i	$-0.405109\pi$
$758$	1.88408e9	−	3.26333e9i	0.157130	−	0.272156i
$759$	6.59895e9			0.547808
$760$	1.81586e9	−	3.14517e9i	0.150050	−	0.259894i
$761$	1.45722e8	−	2.52398e8i	0.0119862	−	0.0207606i	−0.859970	−	0.510344i	$-0.829518\pi$
$761$	1.45722e8	−	2.52398e8i	0.0119862	−	0.0207606i	0.871956	+	0.489584i	$0.162851\pi$
$762$	−1.01703e10			−0.832707
$763$	2.92107e9	−	5.05944e9i	0.238071	−	0.412351i
$764$	−5.29700e8	−	9.17468e8i	−0.0429738	−	0.0744328i
$765$	5.90654e9	+	1.02304e10i	0.477000	+	0.826188i
$766$	−6.66451e9			−0.535756
$767$	9.04154e9	−	1.68200e10i	0.723534	−	1.34599i
$768$	1.32995e9			0.105943
$769$	−2.22330e9	−	3.85087e9i	−0.176302	−	0.305363i	0.764309	−	0.644850i	$-0.223080\pi$
$769$	−2.22330e9	−	3.85087e9i	−0.176302	−	0.305363i	−0.940611	+	0.339486i	$0.889747\pi$
$770$	−2.34262e9	−	4.05753e9i	−0.184920	−	0.320291i
$771$	−1.07214e10	+	1.85700e10i	−0.842484	+	1.45922i
$772$	−3.71465e9			−0.290574
$773$	−2.56726e9	+	4.44663e9i	−0.199913	+	0.346260i	−0.948500	−	0.316777i	$-0.897399\pi$
$773$	−2.56726e9	+	4.44663e9i	−0.199913	+	0.346260i	0.748587	+	0.663037i	$0.230733\pi$
$774$	1.73603e9	−	3.00688e9i	0.134575	−	0.233090i
$775$	−5.04395e9			−0.389237
$776$	1.59659e7	−	2.76537e7i	0.00122653	−	0.00212441i
$777$	−6.72581e9	−	1.16494e10i	−0.514365	−	0.890905i
$778$	−4.85160e8	−	8.40322e8i	−0.0369366	−	0.0639760i
$779$	5.88956e9			0.446377
$780$	−5.32800e9	+	1.61839e8i	−0.402006	+	0.0122110i
$781$	9.32642e9			0.700546
$782$	2.47371e9	+	4.28459e9i	0.184980	+	0.320395i
$783$	−1.15556e10	−	2.00149e10i	−0.860255	−	1.49000i
$784$	−2.97634e9	+	5.15517e9i	−0.220585	+	0.382064i
$785$	1.02726e10			0.757943
$786$	6.67244e9	−	1.15570e10i	0.490124	−	0.848919i
$787$	−1.07057e10	+	1.85428e10i	−0.782895	+	1.35601i	0.147353	+	0.989084i	$0.452925\pi$
$787$	−1.07057e10	+	1.85428e10i	−0.782895	+	1.35601i	−0.930248	+	0.366930i	$0.880409\pi$
$788$	2.48262e9			0.180746
$789$	1.59726e10	−	2.76654e10i	1.15773	−	2.00524i
$790$	5.71370e8	+	9.89642e8i	0.0412309	+	0.0714140i
$791$	2.09786e10	+	3.63360e10i	1.50716	+	2.61047i
$792$	6.13813e9			0.439034
$793$	8.94362e9	−	1.66378e10i	0.636879	−	1.18479i
$794$	6.33172e9			0.448900
$795$	4.67682e9	+	8.10049e9i	0.330115	+	0.571776i
$796$	−9.07749e8	−	1.57227e9i	−0.0637926	−	0.110492i
$797$	−2.24946e9	+	3.89618e9i	−0.157389	+	0.272605i	−0.933926	−	0.357466i	$-0.883641\pi$
$797$	−2.24946e9	+	3.89618e9i	−0.157389	+	0.272605i	0.776537	+	0.630071i	$0.216974\pi$
$798$	−5.11738e10			−3.56482
$799$	4.49018e9	−	7.77722e9i	0.311422	−	0.539400i
$800$	−9.91760e8	+	1.71778e9i	−0.0684844	+	0.118618i
$801$	−4.76301e10			−3.27467
$802$	−6.04315e9	+	1.04670e10i	−0.413669	+	0.716496i
$803$	8.54809e9	+	1.48057e10i	0.582592	+	1.00908i
$804$	9.37971e8	+	1.62461e9i	0.0636492	+	0.110244i
$805$	−5.69356e9			−0.384679
$806$	−2.77788e9	−	4.49078e9i	−0.186870	−	0.302099i
$807$	−1.15361e10			−0.772685
$808$	−3.79030e9	−	6.56499e9i	−0.252775	−	0.437819i
$809$	1.23533e10	+	2.13966e10i	0.820282	+	1.42077i	0.905472	+	0.424406i	$0.139517\pi$
$809$	1.23533e10	+	2.13966e10i	0.820282	+	1.42077i	−0.0851894	+	0.996365i	$0.527150\pi$
$810$	1.61385e9	−	2.79527e9i	0.106700	−	0.184810i
$811$	1.66270e9			0.109456			0.0547282	−	0.998501i	$-0.482571\pi$
$811$	1.66270e9			0.109456			0.0547282	+	0.998501i	$0.482571\pi$
$812$	−7.37068e9	+	1.27664e10i	−0.483127	+	0.836800i
$813$	1.41134e10	−	2.44450e10i	0.921114	−	1.59542i
$814$	2.63264e9			0.171083
$815$	2.04246e9	−	3.53765e9i	0.132161	−	0.228909i
$816$	3.52926e9	+	6.11285e9i	0.227388	+	0.393848i
$817$	−2.83260e9	−	4.90620e9i	−0.181722	−	0.314752i
$818$	1.86662e10			1.19240
$819$	2.57610e10	+	4.16458e10i	1.63859	+	2.64898i
$820$	9.34876e8			0.0592114
$821$	7.44317e9	+	1.28920e10i	0.469415	+	0.813051i	0.999389	−	0.0349635i	$-0.0111315\pi$
$821$	7.44317e9	+	1.28920e10i	0.469415	+	0.813051i	−0.529974	+	0.848014i	$0.677798\pi$
$822$	1.39117e10	+	2.40957e10i	0.873630	+	1.51317i
$823$	4.69118e9	−	8.12536e9i	0.293347	−	0.508093i	−0.681252	−	0.732049i	$-0.738564\pi$
$823$	4.69118e9	−	8.12536e9i	0.293347	−	0.508093i	0.974599	+	0.223957i	$0.0718974\pi$
$824$	6.35184e9			0.395507
$825$	−7.02070e9	+	1.21602e10i	−0.435303	+	0.753967i
$826$	1.45502e10	−	2.52017e10i	0.898335	−	1.55596i
$827$	−5.95599e9			−0.366172			−0.183086	−	0.983097i	$-0.558609\pi$
$827$	−5.95599e9			−0.366172			−0.183086	+	0.983097i	$0.558609\pi$
$828$	3.72957e9	−	6.45980e9i	0.228324	−	0.395470i
$829$	−1.02687e10	−	1.77859e10i	−0.626002	−	1.08427i	−0.988346	−	0.152223i	$-0.951357\pi$
$829$	−1.02687e10	−	1.77859e10i	−0.626002	−	1.08427i	0.362345	−	0.932044i	$-0.381976\pi$
$830$	3.43767e8	+	5.95422e8i	0.0208685	+	0.0361453i
$831$	3.85539e10			2.33058
$832$	−2.07559e9	+	6.30465e7i	−0.124942	+	0.00379515i
$833$	−3.15929e10			−1.89379
$834$	4.40792e9	+	7.63474e9i	0.263119	+	0.455736i
$835$	−2.70085e9	−	4.67801e9i	−0.160545	−	0.278073i
$836$	5.00766e9	−	8.67352e9i	0.296424	−	0.513421i
$837$	1.26158e10			0.743663
$838$	4.07942e9	−	7.06576e9i	0.239466	−	0.414768i
$839$	6.87493e9	−	1.19077e10i	0.401884	−	0.696084i	−0.592069	−	0.805887i	$-0.701689\pi$
$839$	6.87493e9	−	1.19077e10i	0.401884	−	0.696084i	0.993953	+	0.109803i	$0.0350220\pi$
$840$	−8.12303e9			−0.472869
$841$	−3.02581e9	+	5.24086e9i	−0.175411	+	0.303820i
$842$	−6.94637e9	−	1.20315e10i	−0.401020	−	0.694587i
$843$	1.93954e9	+	3.35939e9i	0.111507	+	0.193136i
$844$	−4.17878e9			−0.239249
$845$	8.30748e9	−	5.05149e8i	0.473664	−	0.0288019i
$846$	−1.35395e10			−0.768789
$847$	8.24197e9	+	1.42755e10i	0.466057	+	0.807235i
$848$	1.82191e9	+	3.15565e9i	0.102599	+	0.177706i
$849$	1.09159e10	−	1.89069e10i	0.612184	−	1.06033i
$850$	−1.05272e10			−0.587961
$851$	1.59961e9	−	2.77061e9i	0.0889736	−	0.154107i
$852$	8.08485e9	−	1.40034e10i	0.447851	−	0.775701i
$853$	9.49367e9			0.523736			0.261868	−	0.965104i	$-0.415661\pi$
$853$	9.49367e9			0.523736			0.261868	+	0.965104i	$0.415661\pi$
$854$	1.43926e10	−	2.49287e10i	0.790745	−	1.36961i
$855$	−1.45302e10	−	2.51670e10i	−0.795042	−	1.37705i
$856$	1.45741e8	+	2.52431e8i	0.00794190	+	0.0137558i
$857$	−1.03739e9			−0.0562998			−0.0281499	−	0.999604i	$-0.508962\pi$
$857$	−1.03739e9			−0.0562998			−0.0281499	+	0.999604i	$0.508962\pi$
$858$	−1.46932e10	+	4.46308e8i	−0.794163	+	0.0241229i
$859$	−3.21586e10			−1.73110			−0.865549	−	0.500824i	$-0.833030\pi$
$859$	−3.21586e10			−1.73110			−0.865549	+	0.500824i	$0.833030\pi$
$860$	−4.49630e8	−	7.78782e8i	−0.0241052	−	0.0417514i
$861$	−6.58655e9	−	1.14082e10i	−0.351679	−	0.609126i
$862$	−9.63480e8	+	1.66880e9i	−0.0512350	+	0.0887417i
$863$	−1.58573e10			−0.839828			−0.419914	−	0.907564i	$-0.637940\pi$
$863$	−1.58573e10			−0.839828			−0.419914	+	0.907564i	$0.637940\pi$
$864$	2.48057e9	−	4.29647e9i	0.130844	−	0.226628i
$865$	−1.94989e9	+	3.37731e9i	−0.102436	+	0.177425i
$866$	1.76826e10			0.925196
$867$	−2.46701e9	+	4.27298e9i	−0.128559	+	0.222671i
$868$	−4.02346e9	−	6.96883e9i	−0.208824	−	0.361694i
$869$	1.57568e9	+	2.72916e9i	0.0814516	+	0.141078i
$870$	−1.28400e10			−0.661069
$871$	−1.54086e9	−	2.49099e9i	−0.0790132	−	0.127735i
$872$	1.98233e9			0.101244
$873$	−1.27756e8	−	2.21280e8i	−0.00649877	−	0.0112562i
$874$	−6.08537e9	−	1.05402e10i	−0.308317	−	0.534020i
$875$	1.38754e10	−	2.40329e10i	0.700192	−	1.21277i
$876$	2.96405e10			1.48978
$877$	1.44053e10	−	2.49507e10i	0.721145	−	1.24906i	−0.239395	−	0.970922i	$-0.576949\pi$
$877$	1.44053e10	−	2.49507e10i	0.721145	−	1.24906i	0.960541	−	0.278138i	$-0.0897174\pi$
$878$	−9.22447e9	+	1.59773e10i	−0.459950	+	0.796657i
$879$	−2.43266e10			−1.20815
$880$	7.94887e8	−	1.37678e9i	0.0393202	−	0.0681046i
$881$	1.65245e10	+	2.86213e10i	0.814167	+	1.41018i	0.909925	+	0.414773i	$0.136139\pi$
$881$	1.65245e10	+	2.86213e10i	0.814167	+	1.41018i	−0.0957580	+	0.995405i	$0.530527\pi$
$882$	2.38161e10	+	4.12506e10i	1.16877	+	2.02437i
$883$	−1.91851e9			−0.0937783			−0.0468891	−	0.998900i	$-0.514931\pi$
$883$	−1.91851e9			−0.0937783			−0.0468891	+	0.998900i	$0.514931\pi$
$884$	−5.79772e9	−	9.37273e9i	−0.282276	−	0.456335i
$885$	2.53469e10			1.22920
$886$	4.40679e9	+	7.63278e9i	0.212865	+	0.368693i
$887$	−1.12577e10	−	1.94989e10i	−0.541646	−	0.938159i	−0.998810	−	0.0487763i	$-0.984468\pi$
$887$	−1.12577e10	−	1.94989e10i	−0.541646	−	0.938159i	0.457163	−	0.889383i	$-0.348865\pi$
$888$	2.28218e9	−	3.95284e9i	0.109371	−	0.189437i
$889$	2.41989e10			1.15515
$890$	−6.16809e9	+	1.06834e10i	−0.293282	+	0.507979i
$891$	4.45056e9	−	7.70860e9i	0.210786	−	0.365093i
$892$	−6.71234e9			−0.316663
$893$	−1.10459e10	+	1.91321e10i	−0.519065	+	0.899047i
$894$	1.29292e10	+	2.23941e10i	0.605190	+	1.04822i
$895$	−2.98675e9	−	5.17321e9i	−0.139257	−	0.241201i
$896$	−3.16443e9			−0.146966
$897$	−8.45797e9	+	1.57343e10i	−0.391284	+	0.727906i
$898$	−1.44564e10			−0.666184
$899$	−6.35983e9	−	1.10156e10i	−0.291935	−	0.505647i
$900$	7.93587e9	+	1.37453e10i	0.362866	+	0.628501i
$901$	−9.66955e9	+	1.67481e10i	−0.440422	+	0.762834i
$902$	2.57813e9			0.116972
$903$	−6.33562e9	+	1.09736e10i	−0.286340	+	0.495956i
$904$	−7.11837e9	+	1.23294e10i	−0.320473	+	0.555075i
$905$	−1.03050e10			−0.462146
$906$	−2.12084e10	+	3.67340e10i	−0.947455	+	1.64104i
$907$	−1.77982e10	−	3.08274e10i	−0.792047	−	1.37187i	−0.924697	−	0.380703i	$-0.875682\pi$
$907$	−1.77982e10	−	3.08274e10i	−0.792047	−	1.37187i	0.132650	−	0.991163i	$-0.457651\pi$
$908$	−1.59510e9	−	2.76280e9i	−0.0707113	−	0.122475i
$909$	−6.06585e10			−2.67866
$910$	1.26772e10	−	3.85074e8i	0.557672	−	0.0169394i
$911$	−2.01254e10			−0.881923			−0.440962	−	0.897526i	$-0.645363\pi$
$911$	−2.01254e10			−0.881923			−0.440962	+	0.897526i	$0.645363\pi$
$912$	−8.68204e9	−	1.50377e10i	−0.379000	−	0.656448i
$913$	9.48016e8	+	1.64201e9i	0.0412257	+	0.0714050i
$914$	7.20828e9	−	1.24851e10i	0.312263	−	0.540855i
$915$	2.50724e10			1.08199
$916$	−3.70022e9	+	6.40897e9i	−0.159072	+	0.275520i
$917$	−1.58761e10	+	2.74983e10i	−0.679911	+	1.17764i
$918$	2.63305e10			1.12334
$919$	−5.03019e9	+	8.71254e9i	−0.213786	+	0.370289i	−0.952896	−	0.303296i	$-0.901913\pi$
$919$	−5.03019e9	+	8.71254e9i	−0.213786	+	0.370289i	0.739110	+	0.673585i	$0.235246\pi$
$920$	−9.65957e8	−	1.67309e9i	−0.0408979	−	0.0708372i
$921$	6.14973e9	+	1.06517e10i	0.259387	+	0.449271i
$922$	6.25255e9			0.262724
$923$	−1.19538e10	+	2.22377e10i	−0.500381	+	0.930857i
$924$	−2.24011e10			−0.934152
$925$	3.40369e9	+	5.89537e9i	0.141402	+	0.244915i
$926$	−3.12204e9	−	5.40753e9i	−0.129211	−	0.223800i
$927$	2.54131e10	−	4.40168e10i	1.04780	−	1.81484i
$928$	−5.00198e9			−0.205458
$929$	−1.24643e10	+	2.15889e10i	−0.510052	+	0.883436i	0.489880	+	0.871790i	$0.337040\pi$
$929$	−1.24643e10	+	2.15889e10i	−0.510052	+	0.883436i	−0.999932	+	0.0116460i	$0.996293\pi$
$930$	3.50450e9	−	6.06998e9i	0.142868	−	0.247455i
$931$	7.77192e10			3.15649
$932$	−2.25588e9	+	3.90729e9i	−0.0912766	+	0.158096i
$933$	2.22421e10	+	3.85245e10i	0.896582	+	1.55293i
$934$	−9.95590e9	−	1.72441e10i	−0.399822	−	0.692511i
$935$	8.43750e9			0.337577
$936$	−7.86733e9	+	1.46356e10i	−0.313590	+	0.583371i
$937$	3.64214e9			0.144633			0.0723166	−	0.997382i	$-0.476961\pi$
$937$	3.64214e9			0.144633			0.0723166	+	0.997382i	$0.476961\pi$
$938$	−2.23177e9	−	3.86554e9i	−0.0882957	−	0.152933i
$939$	1.53881e10	+	2.66530e10i	0.606535	+	1.05055i
$940$	−1.75337e9	+	3.03692e9i	−0.0688534	+	0.119258i
$941$	−3.92765e10			−1.53663			−0.768314	−	0.640073i	$-0.778904\pi$
$941$	−3.92765e10			−1.53663			−0.768314	+	0.640073i	$0.778904\pi$
$942$	2.45577e10	−	4.25353e10i	0.957217	−	1.65795i
$943$	1.56649e9	−	2.71324e9i	0.0608327	−	0.105365i
$944$	9.87422e9			0.382033
$945$	−1.51507e10	+	2.62419e10i	−0.584013	+	1.01154i
$946$	−1.23996e9	−	2.14767e9i	−0.0476198	−	0.0824800i
$947$	−4.01982e9	−	6.96253e9i	−0.153809	−	0.266405i	0.778816	−	0.627253i	$-0.215821\pi$
$947$	−4.01982e9	−	6.96253e9i	−0.153809	−	0.266405i	−0.932625	+	0.360848i	$0.882487\pi$
$948$	5.46369e9			0.208284
$949$	−4.62586e10	+	1.40512e9i	−1.75695	+	0.0533679i
$950$	2.58972e10			0.979987
$951$	−2.60318e9	−	4.50884e9i	−0.0981459	−	0.169994i
$952$	−8.39738e9	−	1.45447e10i	−0.315438	−	0.546355i
$953$	7.75981e9	−	1.34404e10i	0.290420	−	0.503022i	−0.683489	−	0.729961i	$-0.739538\pi$
$953$	7.75981e9	−	1.34404e10i	0.290420	−	0.503022i	0.973909	+	0.226939i	$0.0728718\pi$
$954$	2.91572e10			1.08724
$955$	−1.09779e9	+	1.90142e9i	−0.0407855	+	0.0706425i
$956$	9.87856e9	−	1.71102e10i	0.365671	−	0.633361i
$957$	−3.54092e10			−1.30594
$958$	−1.38676e10	+	2.40195e10i	−0.509593	+	0.882641i
$959$	−3.31008e10	−	5.73323e10i	−1.21192	−	2.09911i
$960$	−1.37814e9	−	2.38700e9i	−0.0502740	−	0.0870771i
$961$	−2.05693e10			−0.747631
$962$	−3.37430e9	+	6.27720e9i	−0.122200	+	0.227328i
$963$	2.33239e9			0.0841605
$964$	−3.96045e9	−	6.85970e9i	−0.142388	−	0.246624i
$965$	3.84924e9	+	6.66708e9i	0.137889	+	0.238831i
$966$	−1.36111e10	+	2.35750e10i	−0.485816	+	0.841458i
$967$	−1.65901e10			−0.590006			−0.295003	−	0.955496i	$-0.595321\pi$
$967$	−1.65901e10			−0.590006			−0.295003	+	0.955496i	$0.595321\pi$
$968$	−2.79663e9	+	4.84391e9i	−0.0990996	+	0.171646i
$969$	4.60787e10	−	7.98106e10i	1.62692	−	2.81791i
$970$	−6.61775e7			−0.00232814
$971$	−2.75084e9	+	4.76459e9i	−0.0964268	+	0.167016i	−0.910203	−	0.414162i	$-0.864075\pi$
$971$	−2.75084e9	+	4.76459e9i	−0.0964268	+	0.167016i	0.813776	+	0.581178i	$0.197408\pi$
$972$	2.87954e9	+	4.98751e9i	0.100575	+	0.174202i
$973$	−1.04880e10	−	1.81658e10i	−0.365005	−	0.632208i
$974$	8.00809e9			0.277698
$975$	−1.99959e10	−	3.23259e10i	−0.690916	−	1.11695i
$976$	9.76728e9			0.336279
$977$	1.36203e10	+	2.35910e10i	0.467256	+	0.809312i	0.999300	−	0.0374051i	$-0.0119092\pi$
$977$	1.36203e10	+	2.35910e10i	0.467256	+	0.809312i	−0.532044	+	0.846717i	$0.678576\pi$
$978$	−9.76545e9	−	1.69142e10i	−0.333815	−	0.578185i
$979$	−1.70099e10	+	2.94620e10i	−0.579378	+	1.00351i
$980$	1.23367e10			0.418705
$981$	7.93112e9	−	1.37371e10i	0.268221	−	0.464573i
$982$	−5.91490e8	+	1.02449e9i	−0.0199323	+	0.0345238i
$983$	3.12589e10			1.04963			0.524816	−	0.851216i	$-0.324134\pi$
$983$	3.12589e10			1.04963			0.524816	+	0.851216i	$0.324134\pi$
$984$	2.23492e9	−	3.87100e9i	0.0747789	−	0.129521i
$985$	−2.57258e9	−	4.45583e9i	−0.0857712	−	0.148560i
$986$	−1.32736e10	−	2.29906e10i	−0.440982	−	0.763803i
$987$	4.94125e10			1.63579
$988$	1.42625e10	+	2.30571e10i	0.470486	+	0.760598i
$989$	−3.01363e9			−0.0990609
$990$	−6.36053e9	−	1.10168e10i	−0.208339	−	0.360853i
$991$	2.70471e10	+	4.68470e10i	0.882802	+	1.52906i	0.848213	+	0.529656i	$0.177679\pi$
$991$	2.70471e10	+	4.68470e10i	0.882802	+	1.52906i	0.0345889	+	0.999402i	$0.488988\pi$
$992$	1.36522e9	−	2.36464e9i	0.0444031	−	0.0769084i
$993$	5.40767e10			1.75262
$994$	−1.92368e10	+	3.33191e10i	−0.621269	+	1.07607i
$995$	−1.88128e9	+	3.25847e9i	−0.0605441	+	0.104866i
$996$	3.28725e9			0.105421
$997$	−1.77119e10	+	3.06779e10i	−0.566021	+	0.980377i	0.430933	+	0.902384i	$0.358184\pi$
$997$	−1.77119e10	+	3.06779e10i	−0.566021	+	0.980377i	−0.996954	+	0.0779930i	$0.975149\pi$
$998$	−1.37841e10	−	2.38747e10i	−0.438955	−	0.760293i
$999$	−8.51324e9	−	1.47454e10i	−0.270157	−	0.467925i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	26.8.c.b.3.1	✓	8
3.2	odd	2		234.8.h.b.55.2		8
4.3	odd	2		208.8.i.b.81.4		8
13.2	odd	12		338.8.b.h.337.8		8
13.3	even	3		338.8.a.i.1.4		4
13.9	even	3	inner	26.8.c.b.9.1	yes	8
13.10	even	6		338.8.a.j.1.4		4
13.11	odd	12		338.8.b.h.337.4		8
39.35	odd	6		234.8.h.b.217.2		8
52.35	odd	6		208.8.i.b.113.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.8.c.b.3.1	✓	8	1.1	even	1	trivial
26.8.c.b.9.1	yes	8	13.9	even	3	inner
208.8.i.b.81.4		8	4.3	odd	2
208.8.i.b.113.4		8	52.35	odd	6
234.8.h.b.55.2		8	3.2	odd	2
234.8.h.b.217.2		8	39.35	odd	6
338.8.a.i.1.4		4	13.3	even	3
338.8.a.j.1.4		4	13.10	even	6
338.8.b.h.337.4		8	13.11	odd	12
338.8.b.h.337.8		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} +(-39.6356 - 68.6509i) q^{3} +(-32.0000 + 55.4256i) q^{4} +132.638 q^{5} +(317.085 - 549.207i) q^{6} +(-754.459 + 1306.76i) q^{7} -512.000 q^{8} +(-2048.46 + 3548.04i) q^{9} +(530.551 + 918.941i) q^{10} +(1463.11 + 2534.19i) q^{11} +5073.36 q^{12} +(-7917.74 + 240.503i) q^{13} -12071.3 q^{14} +(-5257.18 - 9105.70i) q^{15} +(-2048.00 - 3547.24i) q^{16} +(10869.5 - 18826.5i) q^{17} -32775.4 q^{18} +(-26739.1 + 46313.4i) q^{19} +(-4244.41 + 7351.53i) q^{20} +119614. q^{21} +(-11704.9 + 20273.5i) q^{22} +(14224.0 + 24636.6i) q^{23} +(20293.4 + 35149.2i) q^{24} -60532.2 q^{25} +(-33337.2 - 53893.7i) q^{26} +151402. q^{27} +(-48285.4 - 83632.7i) q^{28} +(-76324.1 - 132197. i) q^{29} +(42057.4 - 72845.6i) q^{30} +83326.6 q^{31} +(16384.0 - 28377.9i) q^{32} +(115983. - 200888. i) q^{33} +173911. q^{34} +(-100070. + 173326. i) q^{35} +(-131102. - 227075. i) q^{36} +(-56229.4 - 97392.2i) q^{37} -427825. q^{38} +(330335. + 534028. i) q^{39} -67910.5 q^{40} +(-55065.1 - 95375.6i) q^{41} +(478455. + 828708. i) q^{42} +(-52967.4 + 91742.2i) q^{43} -187279. q^{44} +(-271703. + 470604. i) q^{45} +(-113792. + 197093. i) q^{46} +413100. q^{47} +(-162347. + 281194. i) q^{48} +(-726645. - 1.25859e6i) q^{49} +(-242129. - 419380. i) q^{50} -1.72327e6 q^{51} +(240038. - 446542. i) q^{52} -889607. q^{53} +(605608. + 1.04894e6i) q^{54} +(194064. + 336129. i) q^{55} +(386283. - 669062. i) q^{56} +4.23928e6 q^{57} +(610593. - 1.05758e6i) q^{58} +(-1.20535e6 + 2.08773e6i) q^{59} +672919. q^{60} +(-1.19229e6 + 2.06512e6i) q^{61} +(333306. + 577304. i) q^{62} +(-3.09096e6 - 5.35370e6i) q^{63} +262144. q^{64} +(-1.05019e6 + 31899.8i) q^{65} +1.85573e6 q^{66} +(184882. + 320224. i) q^{67} +(695646. + 1.20489e6i) q^{68} +(1.12755e6 - 1.95298e6i) q^{69} -1.60112e6 q^{70} +(1.59359e6 - 2.76018e6i) q^{71} +(1.04881e6 - 1.81660e6i) q^{72} +5.84239e6 q^{73} +(449835. - 779138. i) q^{74} +(2.39923e6 + 4.15559e6i) q^{75} +(-1.71130e6 - 2.96406e6i) q^{76} -4.41544e6 q^{77} +(-2.37851e6 + 4.42474e6i) q^{78} +1.07694e6 q^{79} +(-271642. - 470498. i) q^{80} +(-1.52092e6 - 2.63431e6i) q^{81} +(440521. - 763005. i) q^{82} +647944. q^{83} +(-3.82764e6 + 6.62966e6i) q^{84} +(1.44170e6 - 2.49710e6i) q^{85} -847478. q^{86} +(-6.05031e6 + 1.04794e7i) q^{87} +(-749115. - 1.29750e6i) q^{88} +(5.81291e6 + 1.00682e7i) q^{89} -4.34725e6 q^{90} +(5.65933e6 - 1.05280e7i) q^{91} -1.82067e6 q^{92} +(-3.30270e6 - 5.72045e6i) q^{93} +(1.65240e6 + 2.86204e6i) q^{94} +(-3.54661e6 + 6.14291e6i) q^{95} -2.59756e6 q^{96} +(-31183.4 + 54011.2i) q^{97} +(5.81316e6 - 1.00687e7i) q^{98} -1.19885e7 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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