LMFDB - Embedded newform 14.8.c.b.9.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [14,8,Mod(9,14)] 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("14.9"); S:= CuspForms(chi, 8); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(14, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2])) N = Newforms(chi, 8, names="a")

Level:	$ N $	$=$	$ 14 = 2 \cdot 7 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	14.c (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.37339035678$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{949})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 238x^{2} + 237x + 56169 $ x^4 - x^3 + 238x^2 + 237x + 56169
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			9.2
Root			$7.95146 - 13.7723i$ of defining polynomial
Character	$\chi$	$=$	14.9
Dual form			14.8.c.b.11.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(4.00000 - 6.92820i) q^{2} +(1.40292 + 2.42993i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(219.141 - 379.563i) q^{5} +22.4467 q^{6} +(-893.282 - 159.971i) q^{7} -512.000 q^{8} +(1089.56 - 1887.18i) q^{9} +(-1753.13 - 3036.51i) q^{10} +(2740.43 + 4746.57i) q^{11} +(89.7870 - 155.516i) q^{12} +4006.54 q^{13} +(-4681.44 + 5548.96i) q^{14} +1229.75 q^{15} +(-2048.00 + 3547.24i) q^{16} +(14011.5 + 24268.6i) q^{17} +(-8716.51 - 15097.4i) q^{18} +(-11920.6 + 20647.0i) q^{19} -28050.0 q^{20} +(-864.487 - 2395.04i) q^{21} +43846.9 q^{22} +(36877.3 - 63873.3i) q^{23} +(-718.296 - 1244.13i) q^{24} +(-56983.0 - 98697.4i) q^{25} +(16026.2 - 27758.1i) q^{26} +12250.7 q^{27} +(19718.5 + 54629.8i) q^{28} -98721.3 q^{29} +(4919.00 - 8519.96i) q^{30} +(23743.4 + 41124.8i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-7689.23 + 13318.1i) q^{33} +224184. q^{34} +(-256474. + 304001. i) q^{35} -139464. q^{36} +(50031.2 - 86656.7i) q^{37} +(95364.6 + 165176. i) q^{38} +(5620.87 + 9735.63i) q^{39} +(-112200. + 194336. i) q^{40} +489123. q^{41} +(-20051.3 - 3590.82i) q^{42} +299600. q^{43} +(175388. - 303781. i) q^{44} +(-477536. - 827116. i) q^{45} +(-295018. - 510986. i) q^{46} +(-481369. + 833756. i) q^{47} -11492.7 q^{48} +(772362. + 285798. i) q^{49} -911728. q^{50} +(-39314.1 + 68093.9i) q^{51} +(-128209. - 222065. i) q^{52} +(-918933. - 1.59164e6i) q^{53} +(49002.7 - 84875.1i) q^{54} +2.40216e6 q^{55} +(457360. + 81905.0i) q^{56} -66894.5 q^{57} +(-394885. + 683961. i) q^{58} +(7255.29 + 12566.5i) q^{59} +(-39352.0 - 68159.7i) q^{60} +(-1.01469e6 + 1.75749e6i) q^{61} +379895. q^{62} +(-1.27518e6 + 1.51148e6i) q^{63} +262144. q^{64} +(877997. - 1.52074e6i) q^{65} +(61513.8 + 106545. i) q^{66} +(1.48449e6 + 2.57121e6i) q^{67} +(896736. - 1.55319e6i) q^{68} +206944. q^{69} +(1.08028e6 + 2.99290e6i) q^{70} -4.34296e6 q^{71} +(-557857. + 966236. i) q^{72} +(-750529. - 1.29995e6i) q^{73} +(-400250. - 693253. i) q^{74} +(159885. - 276929. i) q^{75} +1.52583e6 q^{76} +(-1.68867e6 - 4.67841e6i) q^{77} +89933.9 q^{78} +(886182. - 1.53491e6i) q^{79} +(897601. + 1.55469e6i) q^{80} +(-2.36569e6 - 4.09749e6i) q^{81} +(1.95649e6 - 3.38874e6i) q^{82} -1.57509e6 q^{83} +(-105083. + 124556. i) q^{84} +1.22820e7 q^{85} +(1.19840e6 - 2.07569e6i) q^{86} +(-138498. - 239886. i) q^{87} +(-1.40310e6 - 2.43024e6i) q^{88} +(-4.39727e6 + 7.61629e6i) q^{89} -7.64057e6 q^{90} +(-3.57897e6 - 640929. i) q^{91} -4.72029e6 q^{92} +(-66620.4 + 115390. i) q^{93} +(3.85096e6 + 6.67005e6i) q^{94} +(5.22457e6 + 9.04922e6i) q^{95} +(-45970.9 + 79624.0i) q^{96} -1.03493e7 q^{97} +(5.06951e6 - 4.20789e6i) q^{98} +1.19435e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 16 q^{2} - 56 q^{3} - 128 q^{4} + 14 q^{5} - 896 q^{6} - 1848 q^{7} - 2048 q^{8} + 908 q^{9} - 112 q^{10} - 2408 q^{11} - 3584 q^{12} + 21448 q^{13} - 22176 q^{14} + 52360 q^{15} - 8192 q^{16} + 35098 q^{17}+ \cdots + 43942528 q^{99}+O(q^{100}) $ 4 * q + 16 * q^2 - 56 * q^3 - 128 * q^4 + 14 * q^5 - 896 * q^6 - 1848 * q^7 - 2048 * q^8 + 908 * q^9 - 112 * q^10 - 2408 * q^11 - 3584 * q^12 + 21448 * q^13 - 22176 * q^14 + 52360 * q^15 - 8192 * q^16 + 35098 * q^17 - 7264 * q^18 + 2408 * q^19 - 1792 * q^20 - 92302 * q^21 - 38528 * q^22 + 61684 * q^23 + 28672 * q^24 - 215856 * q^25 + 85792 * q^26 - 83216 * q^27 - 59136 * q^28 - 191320 * q^29 + 209440 * q^30 + 166012 * q^31 + 65536 * q^32 - 479290 * q^33 + 561568 * q^34 + 166600 * q^35 - 116224 * q^36 + 559814 * q^37 - 19264 * q^38 - 383784 * q^39 - 7168 * q^40 + 1611960 * q^41 - 11200 * q^42 + 535952 * q^43 - 154112 * q^44 - 1494388 * q^45 - 493472 * q^46 - 1769292 * q^47 + 458752 * q^48 - 98588 * q^49 - 3453696 * q^50 + 337424 * q^51 - 686336 * q^52 - 2317194 * q^53 - 332864 * q^54 + 11498536 * q^55 + 946176 * q^56 - 3220996 * q^57 - 765280 * q^58 - 660352 * q^59 - 1675520 * q^60 - 1463042 * q^61 + 2656192 * q^62 - 514472 * q^63 + 1048576 * q^64 - 1094100 * q^65 + 3834320 * q^66 + 1784280 * q^67 + 2246272 * q^68 + 1833524 * q^69 + 7388416 * q^70 + 548800 * q^71 - 464896 * q^72 - 4549062 * q^73 - 4478512 * q^74 - 5671960 * q^75 - 308224 * q^76 - 15527806 * q^77 - 6140544 * q^78 + 8673964 * q^79 + 57344 * q^80 + 1215782 * q^81 + 6447840 * q^82 - 21188720 * q^83 + 5817728 * q^84 + 18560332 * q^85 + 2143808 * q^86 - 457016 * q^87 + 1232896 * q^88 - 1779750 * q^89 - 23910208 * q^90 - 7570640 * q^91 - 7895552 * q^92 + 6836730 * q^93 + 14154336 * q^94 + 21586180 * q^95 + 1835008 * q^96 - 3497928 * q^97 + 4337872 * q^98 + 43942528 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$2$	4.00000	−	6.92820i	0.353553	−	0.612372i
$3$	1.40292	+	2.42993i	0.0299992	+	0.0519601i	0.880635	−	0.473795i	$-0.157116\pi$
$3$	1.40292	+	2.42993i	0.0299992	+	0.0519601i	−0.850636	+	0.525755i	$0.823783\pi$
$4$	−32.0000	−	55.4256i	−0.250000	−	0.433013i
$5$	219.141	−	379.563i	0.784022	−	1.35797i	−0.145559	−	0.989350i	$-0.546498\pi$
$5$	219.141	−	379.563i	0.784022	−	1.35797i	0.929581	−	0.368617i	$-0.120169\pi$
$6$	22.4467			0.0424252
$7$	−893.282	−	159.971i	−0.984340	−	0.176278i
$7$	−893.282	−	159.971i	−0.984340	−	0.176278i
$8$	−512.000			−0.353553
$9$	1089.56	−	1887.18i	0.498200	−	0.862908i
$10$	−1753.13	−	3036.51i	−0.554388	−	0.960227i
$11$	2740.43	+	4746.57i	0.620790	+	1.07524i	0.989339	+	0.145632i	$0.0465215\pi$
$11$	2740.43	+	4746.57i	0.620790	+	1.07524i	−0.368549	+	0.929609i	$0.620145\pi$
$12$	89.7870	−	155.516i	0.0149996	−	0.0259800i
$13$	4006.54			0.505787			0.252894	−	0.967494i	$-0.418618\pi$
$13$	4006.54			0.505787			0.252894	+	0.967494i	$0.418618\pi$
$14$	−4681.44	+	5548.96i	−0.455964	+	0.540459i
$15$	1229.75			0.0940800
$16$	−2048.00	+	3547.24i	−0.125000	+	0.216506i
$17$	14011.5	+	24268.6i	0.691693	+	1.19805i	0.971283	+	0.237927i	$0.0764681\pi$
$17$	14011.5	+	24268.6i	0.691693	+	1.19805i	−0.279590	+	0.960119i	$0.590199\pi$
$18$	−8716.51	−	15097.4i	−0.352281	−	0.610168i
$19$	−11920.6	+	20647.0i	−0.398712	+	0.690590i	−0.993567	−	0.113243i	$-0.963876\pi$
$19$	−11920.6	+	20647.0i	−0.398712	+	0.690590i	0.594855	+	0.803833i	$0.297209\pi$
$20$	−28050.0			−0.784022
$21$	−864.487	−	2395.04i	−0.0203700	−	0.0564346i
$22$	43846.9			0.877930
$23$	36877.3	−	63873.3i	0.631992	−	1.09464i	−0.355152	−	0.934808i	$-0.615571\pi$
$23$	36877.3	−	63873.3i	0.631992	−	1.09464i	0.987144	−	0.159833i	$-0.0510956\pi$
$24$	−718.296	−	1244.13i	−0.0106063	−	0.0183707i
$25$	−56983.0	−	98697.4i	−0.729382	−	1.26333i
$26$	16026.2	−	27758.1i	0.178823	−	0.309730i
$27$	12250.7			0.119781
$28$	19718.5	+	54629.8i	0.169755	+	0.470301i
$29$	−98721.3			−0.751653			−0.375827	−	0.926690i	$-0.622641\pi$
$29$	−98721.3			−0.751653			−0.375827	+	0.926690i	$0.622641\pi$
$30$	4919.00	−	8519.96i	0.0332623	−	0.0576120i
$31$	23743.4	+	41124.8i	0.143145	+	0.247935i	0.928680	−	0.370883i	$-0.120945\pi$
$31$	23743.4	+	41124.8i	0.143145	+	0.247935i	−0.785534	+	0.618818i	$0.787612\pi$
$32$	16384.0	+	28377.9i	0.0883883	+	0.153093i
$33$	−7689.23	+	13318.1i	−0.0372464	+	0.0645126i
$34$	224184.			0.978201
$35$	−256474.	+	304001.i	−1.01112	+	1.19850i
$36$	−139464.			−0.498200
$37$	50031.2	−	86656.7i	0.162381	−	0.281252i	−0.773341	−	0.633990i	$-0.781416\pi$
$37$	50031.2	−	86656.7i	0.162381	−	0.281252i	0.935722	+	0.352738i	$0.114749\pi$
$38$	95364.6	+	165176.i	0.281932	+	0.488321i
$39$	5620.87	+	9735.63i	0.0151732	+	0.0262808i
$40$	−112200.	+	194336.i	−0.277194	+	0.480114i
$41$	489123.			1.10834			0.554172	−	0.832402i	$-0.313035\pi$
$41$	489123.			1.10834			0.554172	+	0.832402i	$0.313035\pi$
$42$	−20051.3	−	3590.82i	−0.0417609	−	0.00747862i
$43$	299600.			0.574649			0.287324	−	0.957833i	$-0.407234\pi$
$43$	299600.			0.574649			0.287324	+	0.957833i	$0.407234\pi$
$44$	175388.	−	303781.i	0.310395	−	0.537620i
$45$	−477536.	−	827116.i	−0.781200	−	1.35308i
$46$	−295018.	−	510986.i	−0.446886	−	0.774029i
$47$	−481369.	+	833756.i	−0.676295	+	1.17138i	0.299794	+	0.954004i	$0.403082\pi$
$47$	−481369.	+	833756.i	−0.676295	+	1.17138i	−0.976089	+	0.217373i	$0.930251\pi$
$48$	−11492.7			−0.0149996
$49$	772362.	+	285798.i	0.937852	+	0.347034i
$50$	−911728.			−1.03150
$51$	−39314.1	+	68093.9i	−0.0415004	+	0.0718808i
$52$	−128209.	−	222065.i	−0.126447	−	0.219012i
$53$	−918933.	−	1.59164e6i	−0.847849	−	1.46852i	−0.883124	−	0.469139i	$-0.844564\pi$
$53$	−918933.	−	1.59164e6i	−0.847849	−	1.46852i	0.0352758	−	0.999378i	$-0.488769\pi$
$54$	49002.7	−	84875.1i	0.0423489	−	0.0733504i
$55$	2.40216e6			1.94685
$56$	457360.	+	81905.0i	0.348017	+	0.0623235i
$57$	−66894.5			−0.0478441
$58$	−394885.	+	683961.i	−0.265750	+	0.460292i
$59$	7255.29	+	12566.5i	0.00459910	+	0.00796587i	0.868316	−	0.496012i	$-0.165203\pi$
$59$	7255.29	+	12566.5i	0.00459910	+	0.00796587i	−0.863717	+	0.503978i	$0.831869\pi$
$60$	−39352.0	−	68159.7i	−0.0235200	−	0.0407379i
$61$	−1.01469e6	+	1.75749e6i	−0.572370	+	0.991374i	0.423952	+	0.905685i	$0.360643\pi$
$61$	−1.01469e6	+	1.75749e6i	−0.572370	+	0.991374i	−0.996322	+	0.0856896i	$0.972691\pi$
$62$	379895.			0.202438
$63$	−1.27518e6	+	1.51148e6i	−0.642510	+	0.761574i
$64$	262144.			0.125000
$65$	877997.	−	1.52074e6i	0.396549	−	0.686842i
$66$	61513.8	+	106545.i	0.0263372	+	0.0456173i
$67$	1.48449e6	+	2.57121e6i	0.602997	+	1.04442i	0.992365	+	0.123339i	$0.0393602\pi$
$67$	1.48449e6	+	2.57121e6i	0.602997	+	1.04442i	−0.389368	+	0.921082i	$0.627306\pi$
$68$	896736.	−	1.55319e6i	0.345846	−	0.599023i
$69$	206944.			0.0758369
$70$	1.08028e6	+	2.99290e6i	0.376439	+	1.04292i
$71$	−4.34296e6			−1.44006			−0.720031	−	0.693942i	$-0.755872\pi$
$71$	−4.34296e6			−1.44006			−0.720031	+	0.693942i	$0.755872\pi$
$72$	−557857.	+	966236.i	−0.176140	+	0.305084i
$73$	−750529.	−	1.29995e6i	−0.225807	−	0.391109i	0.730754	−	0.682641i	$-0.239169\pi$
$73$	−750529.	−	1.29995e6i	−0.225807	−	0.391109i	−0.956561	+	0.291531i	$0.905835\pi$
$74$	−400250.	−	693253.i	−0.114821	−	0.198875i
$75$	159885.	−	276929.i	0.0437617	−	0.0757975i
$76$	1.52583e6			0.398712
$77$	−1.68867e6	−	4.67841e6i	−0.421528	−	1.16783i
$78$	89933.9			0.0214581
$79$	886182.	−	1.53491e6i	0.202222	−	0.350259i	−0.747022	−	0.664799i	$-0.768517\pi$
$79$	886182.	−	1.53491e6i	0.202222	−	0.350259i	0.949244	+	0.314541i	$0.101850\pi$
$80$	897601.	+	1.55469e6i	0.196006	+	0.339492i
$81$	−2.36569e6	−	4.09749e6i	−0.494607	−	0.856684i
$82$	1.95649e6	−	3.38874e6i	0.391859	−	0.678720i
$83$	−1.57509e6			−0.302366			−0.151183	−	0.988506i	$-0.548308\pi$
$83$	−1.57509e6			−0.302366			−0.151183	+	0.988506i	$0.548308\pi$
$84$	−105083.	+	124556.i	−0.0193444	+	0.0229291i
$85$	1.22820e7			2.16921
$86$	1.19840e6	−	2.07569e6i	0.203169	−	0.351899i
$87$	−138498.	−	239886.i	−0.0225490	−	0.0390560i
$88$	−1.40310e6	−	2.43024e6i	−0.219483	−	0.380155i
$89$	−4.39727e6	+	7.61629e6i	−0.661177	+	1.14519i	0.319130	+	0.947711i	$0.396609\pi$
$89$	−4.39727e6	+	7.61629e6i	−0.661177	+	1.14519i	−0.980307	+	0.197481i	$0.936724\pi$
$90$	−7.64057e6			−1.10478
$91$	−3.57897e6	−	640929.i	−0.497867	−	0.0891590i
$92$	−4.72029e6			−0.631992
$93$	−66620.4	+	115390.i	−0.00858849	+	0.0148757i
$94$	3.85096e6	+	6.67005e6i	0.478213	+	0.828288i
$95$	5.22457e6	+	9.04922e6i	0.625199	+	1.08288i
$96$	−45970.9	+	79624.0i	−0.00530315	+	0.00918533i
$97$	−1.03493e7			−1.15135			−0.575676	−	0.817678i	$-0.695261\pi$
$97$	−1.03493e7			−1.15135			−0.575676	+	0.817678i	$0.695261\pi$
$98$	5.06951e6	−	4.20789e6i	0.544095	−	0.451620i
$99$	1.19435e7			1.23711
$100$	−3.64691e6	+	6.31663e6i	−0.364691	+	0.631663i
$101$	4.45048e6	+	7.70846e6i	0.429815	+	0.744462i	0.996857	−	0.0792273i	$-0.0252453\pi$
$101$	4.45048e6	+	7.70846e6i	0.429815	+	0.744462i	−0.567041	+	0.823689i	$0.691912\pi$
$102$	314512.	+	544752.i	0.0293452	+	0.0508274i
$103$	5.21151e6	−	9.02660e6i	0.469930	−	0.813943i	−0.529479	−	0.848323i	$-0.677612\pi$
$103$	5.21151e6	−	9.02660e6i	0.469930	−	0.813943i	0.999409	+	0.0343802i	$0.0109457\pi$
$104$	−2.05135e6			−0.178823
$105$	−1.09851e6	−	196724.i	−0.0926068	−	0.0165842i
$106$	−1.47029e7			−1.19904
$107$	−1.95481e6	+	3.38582e6i	−0.154263	+	0.267191i	−0.932790	−	0.360420i	$-0.882633\pi$
$107$	−1.95481e6	+	3.38582e6i	−0.154263	+	0.267191i	0.778528	+	0.627610i	$0.215967\pi$
$108$	−392021.	−	679001.i	−0.0299452	−	0.0518665i
$109$	9.24073e6	+	1.60054e7i	0.683461	+	1.18379i	0.973918	+	0.226901i	$0.0728593\pi$
$109$	9.24073e6	+	1.60054e7i	0.683461	+	1.18379i	−0.290457	+	0.956888i	$0.593807\pi$
$110$	9.60866e6	−	1.66427e7i	0.688317	−	1.19220i
$111$	280760.			0.0194852
$112$	2.39690e6	−	2.84107e6i	0.161208	−	0.191081i
$113$	906133.			0.0590769			0.0295384	−	0.999564i	$-0.490596\pi$
$113$	906133.			0.0590769			0.0295384	+	0.999564i	$0.490596\pi$
$114$	−267578.	+	463459.i	−0.0169155	+	0.0292984i
$115$	−1.61626e7	−	2.79945e7i	−0.990991	−	1.71645i
$116$	3.15908e6	+	5.47169e6i	0.187913	+	0.325476i
$117$	4.36538e6	−	7.56107e6i	0.251983	−	0.436448i
$118$	116085.			0.00650411
$119$	−8.63395e6	−	2.39201e7i	−0.469672	−	1.30122i
$120$	−629632.			−0.0332623
$121$	−5.27637e6	+	9.13894e6i	−0.270761	+	0.468972i
$122$	8.11748e6	+	1.40599e7i	0.404727	+	0.701008i
$123$	686202.	+	1.18854e6i	0.0332494	+	0.0575896i
$124$	1.51958e6	−	2.63199e6i	0.0715727	−	0.123968i
$125$	−1.57084e7			−0.719363
$126$	5.37115e6	+	1.48807e7i	0.239205	+	0.662712i
$127$	−3.93401e6			−0.170421			−0.0852103	−	0.996363i	$-0.527156\pi$
$127$	−3.93401e6			−0.170421			−0.0852103	+	0.996363i	$0.527156\pi$
$128$	1.04858e6	−	1.81619e6i	0.0441942	−	0.0765466i
$129$	420316.	+	728008.i	0.0172390	+	0.0298588i
$130$	−7.02398e6	−	1.21659e7i	−0.280402	−	0.485671i
$131$	−1.22880e7	+	2.12834e7i	−0.477563	+	0.827164i	−0.999669	−	0.0257168i	$-0.991813\pi$
$131$	−1.22880e7	+	2.12834e7i	−0.477563	+	0.827164i	0.522106	+	0.852881i	$0.325147\pi$
$132$	984221.			0.0372464
$133$	1.39514e7	−	1.65367e7i	0.514204	−	0.609492i
$134$	2.37518e7			0.852766
$135$	2.68462e6	−	4.64990e6i	0.0939107	−	0.162658i
$136$	−7.17388e6	−	1.24255e7i	−0.244550	−	0.423574i
$137$	1.07113e7	+	1.85525e7i	0.355893	+	0.616424i	0.987270	−	0.159051i	$-0.0508435\pi$
$137$	1.07113e7	+	1.85525e7i	0.355893	+	0.616424i	−0.631378	+	0.775476i	$0.717510\pi$
$138$	827775.	−	1.43375e6i	0.0268124	−	0.0464404i
$139$	2.70116e6			0.0853096			0.0426548	−	0.999090i	$-0.486418\pi$
$139$	2.70116e6			0.0853096			0.0426548	+	0.999090i	$0.486418\pi$
$140$	2.50566e7	+	4.48718e6i	0.771745	+	0.138206i
$141$	−2.70129e6			−0.0811531
$142$	−1.73718e7	+	3.00889e7i	−0.509139	+	0.881854i
$143$	1.09797e7	+	1.90173e7i	0.313988	+	0.543843i
$144$	4.46285e6	+	7.72989e6i	0.124550	+	0.215727i
$145$	−2.16339e7	+	3.74710e7i	−0.589313	+	1.02072i
$146$	−1.20085e7			−0.319339
$147$	389094.	+	2.27774e6i	0.0101029	+	0.0591416i
$148$	−6.40400e6			−0.162381
$149$	−4.07159e6	+	7.05220e6i	−0.100835	+	0.174652i	−0.912029	−	0.410126i	$-0.865485\pi$
$149$	−4.07159e6	+	7.05220e6i	−0.100835	+	0.174652i	0.811194	+	0.584777i	$0.198818\pi$
$150$	−1.27908e6	−	2.21544e6i	−0.0309442	−	0.0535969i
$151$	−2.50810e7	−	4.34416e7i	−0.592824	−	1.02680i	−0.993850	−	0.110734i	$-0.964680\pi$
$151$	−2.50810e7	−	4.34416e7i	−0.592824	−	1.02680i	0.401026	−	0.916067i	$-0.368654\pi$
$152$	6.10333e6	−	1.05713e7i	0.140966	−	0.244160i
$153$	6.10657e7			1.37841
$154$	−3.91677e7	−	7.01422e6i	−0.864182	−	0.154759i
$155$	2.08126e7			0.448917
$156$	359735.	−	623080.i	0.00758660	−	0.0131404i
$157$	−1.21775e7	−	2.10921e7i	−0.251137	−	0.434981i	0.712702	−	0.701466i	$-0.247471\pi$
$157$	−1.21775e7	−	2.10921e7i	−0.251137	−	0.434981i	−0.963839	+	0.266485i	$0.914138\pi$
$158$	−7.08946e6	−	1.22793e7i	−0.142993	−	0.247670i
$159$	2.57838e6	−	4.46589e6i	0.0508695	−	0.0881085i
$160$	1.43616e7			0.277194
$161$	−4.31596e7	+	5.11576e7i	−0.815056	+	0.966094i
$162$	−3.78510e7			−0.699480
$163$	4.62153e7	−	8.00472e7i	0.835852	−	1.44774i	−0.0574837	−	0.998346i	$-0.518308\pi$
$163$	4.62153e7	−	8.00472e7i	0.835852	−	1.44774i	0.893335	−	0.449391i	$-0.148359\pi$
$164$	−1.56519e7	−	2.71100e7i	−0.277086	−	0.479927i
$165$	3.37005e6	+	5.83710e6i	0.0584040	+	0.101159i
$166$	−6.30038e6	+	1.09126e7i	−0.106903	+	0.185161i
$167$	7.35041e6			0.122125			0.0610624	−	0.998134i	$-0.480551\pi$
$167$	7.35041e6			0.122125			0.0610624	+	0.998134i	$0.480551\pi$
$168$	442617.	+	1.22626e6i	0.00720188	+	0.0199526i
$169$	−4.66961e7			−0.744179
$170$	4.91279e7	−	8.50920e7i	0.766932	−	1.32836i
$171$	2.59765e7	+	4.49925e7i	0.397277	+	0.688104i
$172$	−9.58721e6	−	1.66055e7i	−0.143662	−	0.248830i
$173$	6.28549e7	−	1.08868e8i	0.922950	−	1.59860i	0.128123	−	0.991758i	$-0.459105\pi$
$173$	6.28549e7	−	1.08868e8i	0.922950	−	1.59860i	0.794826	−	0.606837i	$-0.207562\pi$
$174$	−2.21597e6			−0.0318891
$175$	3.51132e7	+	9.72802e7i	0.495264	+	1.37212i
$176$	−2.24496e7			−0.310395
$177$	−20357.2	+	35259.7i	−0.000275938	+	0.000477939i
$178$	3.51781e7	+	6.09303e7i	0.467523	+	0.809773i
$179$	−3.90512e7	−	6.76386e7i	−0.508919	−	0.881473i	−0.999947	−	0.0103294i	$-0.996712\pi$
$179$	−3.90512e7	−	6.76386e7i	−0.508919	−	0.881473i	0.491028	−	0.871144i	$-0.336621\pi$
$180$	−3.05623e7	+	5.29355e7i	−0.390600	+	0.676539i
$181$	2.22134e7			0.278445			0.139223	−	0.990261i	$-0.455540\pi$
$181$	2.22134e7			0.278445			0.139223	+	0.990261i	$0.455540\pi$
$182$	−1.87564e7	+	2.22321e7i	−0.230621	+	0.273358i
$183$	−5.69410e6			−0.0686825
$184$	−1.88812e7	+	3.27031e7i	−0.223443	+	0.387014i
$185$	−2.19278e7	−	3.79800e7i	−0.254621	−	0.441016i
$186$	532963.	+	923119.i	0.00607298	+	0.0105187i
$187$	−7.67951e7	+	1.33013e8i	−0.858792	+	1.48747i
$188$	6.16153e7			0.676295
$189$	−1.09433e7	−	1.95975e6i	−0.117905	−	0.0211146i
$190$	8.35931e7			0.884164
$191$	−9.17563e7	+	1.58927e8i	−0.952838	+	1.65036i	−0.213597	+	0.976922i	$0.568518\pi$
$191$	−9.17563e7	+	1.58927e8i	−0.952838	+	1.65036i	−0.739240	+	0.673442i	$0.764815\pi$
$192$	367768.	+	636992.i	0.00374989	+	0.00649501i
$193$	−2.48516e7	−	4.30442e7i	−0.248830	−	0.430987i	0.714371	−	0.699767i	$-0.246713\pi$
$193$	−2.48516e7	−	4.30442e7i	−0.248830	−	0.430987i	−0.963202	+	0.268780i	$0.913379\pi$
$194$	−4.13970e7	+	7.17017e7i	−0.407064	+	0.705056i
$195$	4.92705e6			0.0475845
$196$	−8.87506e6	−	5.19542e7i	−0.0841928	−	0.492861i
$197$	2.65068e7			0.247016			0.123508	−	0.992344i	$-0.460585\pi$
$197$	2.65068e7			0.247016			0.123508	+	0.992344i	$0.460585\pi$
$198$	4.77740e7	−	8.27471e7i	0.437385	−	0.757573i
$199$	2.64675e7	+	4.58430e7i	0.238082	+	0.412370i	0.960164	−	0.279438i	$-0.0901480\pi$
$199$	2.64675e7	+	4.58430e7i	0.238082	+	0.412370i	−0.722082	+	0.691808i	$0.756815\pi$
$200$	2.91753e7	+	5.05331e7i	0.257875	+	0.446653i
$201$	−4.16524e6	+	7.21441e6i	−0.0361788	+	0.0626635i
$202$	7.12077e7			0.607851
$203$	8.81859e7	+	1.57925e7i	0.739883	+	0.132500i
$204$	5.03220e6			0.0415004
$205$	1.07187e8	−	1.85653e8i	0.868967	−	1.50509i
$206$	−4.16921e7	−	7.22128e7i	−0.332291	−	0.575545i
$207$	−8.03603e7	−	1.39188e8i	−0.629717	−	1.09070i
$208$	−8.20540e6	+	1.42122e7i	−0.0632234	+	0.109506i
$209$	−1.30670e8			−0.990067
$210$	−5.75700e6	+	6.82383e6i	−0.0428972	+	0.0508464i
$211$	−1.03691e8			−0.759892			−0.379946	−	0.925009i	$-0.624057\pi$
$211$	−1.03691e8			−0.759892			−0.379946	+	0.925009i	$0.624057\pi$
$212$	−5.88117e7	+	1.01865e8i	−0.423924	+	0.734258i
$213$	−6.09283e6	−	1.05531e7i	−0.0432006	−	0.0748257i
$214$	1.56384e7	+	2.70866e7i	0.109080	+	0.188932i
$215$	6.56547e7	−	1.13717e8i	0.450538	−	0.780354i
$216$	−6.27234e6			−0.0423489
$217$	−1.46308e7	−	4.05343e7i	−0.0971984	−	0.269286i
$218$	1.47852e8			0.966559
$219$	2.10587e6	−	3.64747e6i	0.0135480	−	0.0234659i
$220$	−7.68693e7	−	1.33141e8i	−0.486713	−	0.843013i
$221$	5.61376e7	+	9.72333e7i	0.349850	+	0.605957i
$222$	1.12304e6	−	1.94516e6i	0.00688905	−	0.0119322i
$223$	2.45465e8			1.48225			0.741126	−	0.671366i	$-0.234292\pi$
$223$	2.45465e8			1.48225			0.741126	+	0.671366i	$0.234292\pi$
$224$	−1.00959e7	−	2.79704e7i	−0.0600173	−	0.166277i
$225$	−2.48346e8			−1.45351
$226$	3.62453e6	−	6.27787e6i	0.0208868	−	0.0361770i
$227$	−2.11146e7	−	3.65716e7i	−0.119810	−	0.207517i	0.799882	−	0.600157i	$-0.204895\pi$
$227$	−2.11146e7	−	3.65716e7i	−0.119810	−	0.207517i	−0.919692	+	0.392640i	$0.871562\pi$
$228$	2.14063e6	+	3.70767e6i	0.0119610	+	0.0207171i
$229$	9.47285e7	−	1.64075e8i	0.521263	−	0.902853i	−0.478432	−	0.878125i	$-0.658795\pi$
$229$	9.47285e7	−	1.64075e8i	0.521263	−	0.902853i	0.999694	−	0.0247286i	$-0.00787216\pi$
$230$	−2.58602e8			−1.40147
$231$	8.99916e6	−	1.06668e7i	0.0480352	−	0.0569367i
$232$	5.05453e7			0.265750
$233$	−1.51963e8	+	2.63207e8i	−0.787031	+	1.36318i	0.140748	+	0.990045i	$0.455049\pi$
$233$	−1.51963e8	+	2.63207e8i	−0.787031	+	1.36318i	−0.927778	+	0.373131i	$0.878284\pi$
$234$	−3.49231e7	−	6.04885e7i	−0.178179	−	0.308615i
$235$	2.10975e8	+	3.65420e8i	1.06046	+	1.83677i
$236$	464339.	−	804258.i	0.00229955	−	0.00398294i
$237$	4.97298e6			0.0242660
$238$	−2.00259e8	−	3.58628e7i	−0.962883	−	0.172435i
$239$	−6.75930e7			−0.320265			−0.160132	−	0.987096i	$-0.551192\pi$
$239$	−6.75930e7			−0.320265			−0.160132	+	0.987096i	$0.551192\pi$
$240$	−2.51853e6	+	4.36222e6i	−0.0117600	+	0.0203689i
$241$	1.22094e8	+	2.11473e8i	0.561868	+	0.973183i	0.997334	+	0.0729780i	$0.0232503\pi$
$241$	1.22094e8	+	2.11473e8i	0.561868	+	0.973183i	−0.435466	+	0.900205i	$0.643416\pi$
$242$	4.22110e7	+	7.31116e7i	0.191457	+	0.331614i
$243$	2.00339e7	−	3.46997e7i	0.0895659	−	0.155133i
$244$	1.29880e8			0.572370
$245$	2.77734e8	−	2.30530e8i	1.20656	−	1.00149i
$246$	1.09792e7			0.0470217
$247$	−4.77603e7	+	8.27233e7i	−0.201664	+	0.349292i
$248$	−1.21566e7	−	2.10559e7i	−0.0506096	−	0.0876583i
$249$	−2.20973e6	−	3.82737e6i	−0.00907073	−	0.0157110i
$250$	−6.28337e7	+	1.08831e8i	−0.254333	+	0.440518i
$251$	−2.63151e8			−1.05038			−0.525190	−	0.850985i	$-0.676006\pi$
$251$	−2.63151e8			−1.05038			−0.525190	+	0.850985i	$0.676006\pi$
$252$	1.24581e8	+	2.23102e7i	0.490399	+	0.0878215i
$253$	4.04239e8			1.56934
$254$	−1.57360e7	+	2.72556e7i	−0.0602528	+	0.104361i
$255$	1.72306e7	+	2.98443e7i	0.0650745	+	0.112712i
$256$	−8.38861e6	−	1.45295e7i	−0.0312500	−	0.0541266i
$257$	1.28609e8	−	2.22757e8i	0.472611	−	0.818587i	−0.526897	−	0.849929i	$-0.676645\pi$
$257$	1.28609e8	−	2.22757e8i	0.472611	−	0.818587i	0.999509	+	0.0313421i	$0.00997814\pi$
$258$	6.72505e6			0.0243796
$259$	−5.85545e7	+	6.94053e7i	−0.209417	+	0.248224i
$260$	−1.12384e8			−0.396549
$261$	−1.07563e8	+	1.86305e8i	−0.374474	+	0.648608i
$262$	9.83038e7	+	1.70267e8i	0.337688	+	0.584893i
$263$	−1.03651e8	−	1.79529e8i	−0.351342	−	0.608541i	0.635143	−	0.772394i	$-0.280941\pi$
$263$	−1.03651e8	−	1.79529e8i	−0.351342	−	0.608541i	−0.986485	+	0.163853i	$0.947608\pi$
$264$	3.93689e6	−	6.81889e6i	0.0131686	−	0.0228087i
$265$	−8.05503e8			−2.65893
$266$	−5.87641e7	−	1.62805e8i	−0.191437	−	0.530372i
$267$	−2.46761e7			−0.0793390
$268$	9.50073e7	−	1.64557e8i	0.301498	−	0.522211i
$269$	1.38213e8	+	2.39392e8i	0.432929	+	0.749854i	0.997124	−	0.0757870i	$-0.0241469\pi$
$269$	1.38213e8	+	2.39392e8i	0.432929	+	0.749854i	−0.564195	+	0.825641i	$0.690814\pi$
$270$	−2.14770e7	−	3.71992e7i	−0.0664049	−	0.115017i
$271$	7.53645e6	−	1.30535e7i	0.0230025	−	0.0398414i	−0.854295	−	0.519788i	$-0.826011\pi$
$271$	7.53645e6	−	1.30535e7i	0.0230025	−	0.0398414i	0.877297	+	0.479947i	$0.159344\pi$
$272$	−1.14782e8			−0.345846
$273$	−3.46360e6	−	9.59583e6i	−0.0103029	−	0.0285439i
$274$	1.71380e8			0.503308
$275$	3.12316e8	−	5.40947e8i	0.905587	−	1.56852i
$276$	−6.62220e6	−	1.14700e7i	−0.0189592	−	0.0328383i
$277$	−7.72341e7	−	1.33773e8i	−0.218338	−	0.378173i	0.735962	−	0.677023i	$-0.236730\pi$
$277$	−7.72341e7	−	1.33773e8i	−0.218338	−	0.378173i	−0.954300	+	0.298850i	$0.903397\pi$
$278$	1.08046e7	−	1.87142e7i	0.0301615	−	0.0522412i
$279$	1.03480e8			0.285260
$280$	1.31314e8	−	1.55648e8i	0.357486	−	0.423732i
$281$	2.33653e8			0.628203			0.314102	−	0.949389i	$-0.398297\pi$
$281$	2.33653e8			0.628203			0.314102	+	0.949389i	$0.398297\pi$
$282$	−1.08052e7	+	1.87151e7i	−0.0286919	+	0.0496959i
$283$	−3.00200e8	−	5.19961e8i	−0.787331	−	1.36370i	−0.927596	−	0.373584i	$-0.878129\pi$
$283$	−3.00200e8	−	5.19961e8i	−0.787331	−	1.36370i	0.140265	−	0.990114i	$-0.455205\pi$
$284$	1.38975e8	+	2.40711e8i	0.360015	+	0.623565i
$285$	−1.46593e7	+	2.53907e7i	−0.0375109	+	0.0649707i
$286$	1.75675e8			0.444046
$287$	−4.36925e8	−	7.82453e7i	−1.09099	−	0.195376i
$288$	7.14056e7			0.176140
$289$	−1.87475e8	+	3.24715e8i	−0.456878	+	0.791335i
$290$	1.73071e8	+	2.99768e8i	0.416707	+	0.721758i
$291$	−1.45192e7	−	2.51480e7i	−0.0345396	−	0.0598243i
$292$	−4.80339e7	+	8.31971e7i	−0.112904	+	0.195555i
$293$	1.34114e8			0.311484			0.155742	−	0.987798i	$-0.450223\pi$
$293$	1.34114e8			0.311484			0.155742	+	0.987798i	$0.450223\pi$
$294$	1.73370e7	+	6.41523e6i	0.0397886	+	0.0147230i
$295$	6.35973e6			0.0144232
$296$	−2.56160e7	+	4.43682e7i	−0.0574104	+	0.0994377i
$297$	3.35722e7	+	5.81487e7i	0.0743587	+	0.128793i
$298$	3.25727e7	+	5.64176e7i	0.0713012	+	0.123497i
$299$	1.47750e8	−	2.55911e8i	0.319653	−	0.553656i
$300$	−2.04653e7			−0.0437617
$301$	−2.67627e8	−	4.79272e7i	−0.565650	−	0.101298i
$302$	−4.01296e8			−0.838380
$303$	−1.24873e7	+	2.16287e7i	−0.0257882	+	0.0446665i
$304$	−4.88267e7	−	8.45703e7i	−0.0996781	−	0.172647i
$305$	4.44718e8	+	7.70275e8i	0.897502	+	1.55452i
$306$	2.44263e8	−	4.23075e8i	0.487340	−	0.844098i
$307$	4.28333e8			0.844884			0.422442	−	0.906390i	$-0.361173\pi$
$307$	4.28333e8			0.844884			0.422442	+	0.906390i	$0.361173\pi$
$308$	−2.05267e8	+	2.43305e8i	−0.400305	+	0.474486i
$309$	2.92454e7			0.0563901
$310$	8.32505e7	−	1.44194e8i	0.158716	−	0.274904i
$311$	2.10065e8	+	3.63842e8i	0.395996	+	0.685886i	0.993228	−	0.116183i	$-0.0370659\pi$
$311$	2.10065e8	+	3.63842e8i	0.395996	+	0.685886i	−0.597231	+	0.802069i	$0.703733\pi$
$312$	−2.87788e6	−	4.98464e6i	−0.00536454	−	0.00929165i
$313$	−5.08856e8	+	8.81365e8i	−0.937972	+	1.62461i	−0.168725	+	0.985663i	$0.553965\pi$
$313$	−5.08856e8	+	8.81365e8i	−0.937972	+	1.62461i	−0.769247	+	0.638952i	$0.779368\pi$
$314$	−1.94840e8			−0.355161
$315$	2.94260e8	+	8.15240e8i	0.530449	+	1.46960i
$316$	−1.13431e8			−0.202222
$317$	1.00954e8	−	1.74857e8i	0.177998	−	0.308302i	−0.763197	−	0.646166i	$-0.776371\pi$
$317$	1.00954e8	−	1.74857e8i	0.177998	−	0.308302i	0.941195	+	0.337864i	$0.109705\pi$
$318$	−2.06271e7	−	3.57271e7i	−0.0359702	−	0.0623021i
$319$	−2.70539e8	−	4.68587e8i	−0.466619	−	0.808208i
$320$	5.74465e7	−	9.95002e7i	0.0980028	−	0.169746i
$321$	−1.09698e7			−0.0185110
$322$	1.81792e8	+	5.03649e8i	0.303444	+	0.840684i
$323$	−6.68100e8			−1.10315
$324$	−1.51404e8	+	2.62240e8i	−0.247303	+	0.428342i
$325$	−2.28305e8	−	3.95435e8i	−0.368912	−	0.638975i
$326$	−3.69722e8	−	6.40378e8i	−0.591036	−	1.02370i
$327$	−2.59280e7	+	4.49087e7i	−0.0410065	+	0.0710253i
$328$	−2.50431e8			−0.391859
$329$	5.63375e8	−	6.67774e8i	0.872192	−	1.03382i
$330$	5.39208e7			0.0825957
$331$	3.40869e8	−	5.90403e8i	0.516642	−	0.894850i	−0.483171	−	0.875526i	$-0.660515\pi$
$331$	3.40869e8	−	5.90403e8i	0.516642	−	0.894850i	0.999813	−	0.0193244i	$-0.00615153\pi$
$332$	5.04030e7	+	8.73006e7i	0.0755916	+	0.130928i
$333$	−1.09024e8	−	1.88836e8i	−0.161796	−	0.280240i
$334$	2.94016e7	−	5.09251e7i	0.0431776	−	0.0747858i
$335$	1.30125e9			1.89105
$336$	1.02663e7	+	1.83850e6i	0.0147647	+	0.00264409i
$337$	6.40766e8			0.912000			0.456000	−	0.889980i	$-0.349282\pi$
$337$	6.40766e8			0.912000			0.456000	+	0.889980i	$0.349282\pi$
$338$	−1.86785e8	+	3.23520e8i	−0.263107	+	0.455715i
$339$	1.27123e6	+	2.20184e6i	0.00177226	+	0.00306964i
$340$	−3.93023e8	−	6.80736e8i	−0.542303	−	0.939296i
$341$	−1.30135e8	+	2.25400e8i	−0.177727	+	0.307832i
$342$	4.15623e8			0.561835
$343$	−6.44217e8	−	3.78853e8i	−0.861992	−	0.506922i
$344$	−1.53395e8			−0.203169
$345$	4.53498e7	−	7.85482e7i	0.0594578	−	0.102984i
$346$	−5.02839e8	−	8.70943e8i	−0.652624	−	1.13038i
$347$	−4.05232e8	−	7.01883e8i	−0.520656	−	0.901802i	−0.999712	−	0.0240179i	$-0.992354\pi$
$347$	−4.05232e8	−	7.01883e8i	−0.520656	−	0.901802i	0.479056	−	0.877785i	$-0.340979\pi$
$348$	−8.86388e6	+	1.53527e7i	−0.0112745	+	0.0195280i
$349$	3.65334e8			0.460046			0.230023	−	0.973185i	$-0.426120\pi$
$349$	3.65334e8			0.460046			0.230023	+	0.973185i	$0.426120\pi$
$350$	8.14430e8	+	1.45850e8i	1.01535	+	0.181831i
$351$	4.90828e7			0.0605836
$352$	−8.97985e7	+	1.55536e8i	−0.109741	+	0.190077i
$353$	−1.83219e8	−	3.17344e8i	−0.221696	−	0.383989i	0.733627	−	0.679553i	$-0.237826\pi$
$353$	−1.83219e8	−	3.17344e8i	−0.221696	−	0.383989i	−0.955323	+	0.295563i	$0.904493\pi$
$354$	162858.	+	282078.i	0.000195118	+	0.000337954i
$355$	−9.51719e8	+	1.64843e9i	−1.12904	+	1.95556i
$356$	5.62850e8			0.661177
$357$	4.60116e7	−	5.45380e7i	0.0535215	−	0.0634396i
$358$	−6.24819e8			−0.719720
$359$	−1.98637e8	+	3.44049e8i	−0.226584	+	0.392455i	−0.956793	−	0.290768i	$-0.906089\pi$
$359$	−1.98637e8	+	3.44049e8i	−0.226584	+	0.392455i	0.730210	+	0.683223i	$0.239422\pi$
$360$	2.44498e8	+	4.23484e8i	0.276196	+	0.478385i
$361$	1.62736e8	+	2.81866e8i	0.182057	+	0.315332i
$362$	8.88536e7	−	1.53899e8i	0.0984453	−	0.170512i
$363$	−2.96093e7			−0.0324904
$364$	7.90032e7	+	2.18876e8i	0.0858598	+	0.237873i
$365$	−6.57886e8			−0.708151
$366$	−2.27764e7	+	3.94499e7i	−0.0242829	+	0.0420593i
$367$	−5.29869e8	−	9.17760e8i	−0.559548	−	0.969166i	−0.997534	−	0.0701840i	$-0.977641\pi$
$367$	−5.29869e8	−	9.17760e8i	−0.559548	−	0.969166i	0.437986	−	0.898982i	$-0.355692\pi$
$368$	1.51049e8	+	2.61625e8i	0.157998	+	0.273660i
$369$	5.32931e8	−	9.23063e8i	0.552177	−	0.956399i
$370$	−3.50845e8			−0.360088
$371$	5.66251e8	+	1.56878e9i	0.575705	+	1.59498i
$372$	8.52741e6			0.00858849
$373$	3.00696e7	−	5.20822e7i	0.0300018	−	0.0519647i	−0.850635	−	0.525757i	$-0.823782\pi$
$373$	3.00696e7	−	5.20822e7i	0.0300018	−	0.0519647i	0.880636	+	0.473793i	$0.157115\pi$
$374$	6.14361e8	+	1.06410e9i	0.607258	+	1.05180i
$375$	−2.20377e7	−	3.81704e7i	−0.0215803	−	0.0373781i
$376$	2.46461e8	−	4.26883e8i	0.239106	−	0.414144i
$377$	−3.95531e8			−0.380177
$378$	−5.73507e7	+	6.79784e7i	−0.0546157	+	0.0647366i
$379$	7.43622e8			0.701641			0.350821	−	0.936443i	$-0.385903\pi$
$379$	7.43622e8			0.701641			0.350821	+	0.936443i	$0.385903\pi$
$380$	3.34373e8	−	5.79150e8i	0.312599	−	0.541438i
$381$	−5.51910e6	−	9.55937e6i	−0.00511247	−	0.00885506i
$382$	7.34050e8	+	1.27141e9i	0.673758	+	1.16698i
$383$	−9.01703e8	+	1.56180e9i	−0.820102	+	1.42046i	0.0855038	+	0.996338i	$0.472750\pi$
$383$	−9.01703e8	+	1.56180e9i	−0.820102	+	1.42046i	−0.905606	+	0.424120i	$0.860583\pi$
$384$	5.88428e6			0.00530315
$385$	−2.14581e9	−	3.84276e8i	−1.91637	−	0.343187i
$386$	−3.97625e8			−0.351899
$387$	3.26433e8	−	5.65399e8i	0.286290	−	0.495869i
$388$	3.31176e8	+	5.73614e8i	0.287838	+	0.498550i
$389$	3.44292e8	+	5.96331e8i	0.296554	+	0.513646i	0.975345	−	0.220685i	$-0.0708293\pi$
$389$	3.44292e8	+	5.96331e8i	0.296554	+	0.513646i	−0.678791	+	0.734331i	$0.737496\pi$
$390$	1.97082e7	−	3.41356e7i	0.0168237	−	0.0291394i
$391$	2.06682e9			1.74858
$392$	−3.95449e8	−	1.46328e8i	−0.331581	−	0.122695i
$393$	−6.89563e7			−0.0573060
$394$	1.06027e8	−	1.83645e8i	0.0873335	−	0.151266i
$395$	−3.88398e8	−	6.72724e8i	−0.317093	−	0.549221i
$396$	−3.82192e8	−	6.61976e8i	−0.309278	−	0.535685i
$397$	7.06564e8	−	1.22380e9i	0.566741	−	0.981624i	−0.430144	−	0.902760i	$-0.641537\pi$
$397$	7.06564e8	−	1.22380e9i	0.566741	−	0.981624i	0.996885	−	0.0788641i	$-0.0251293\pi$
$398$	4.23479e8			0.336699
$399$	5.97557e7	+	1.07012e7i	0.0470949	+	0.00843385i
$400$	4.66805e8			0.364691
$401$	1.12026e8	−	1.94035e8i	0.0867590	−	0.150271i	−0.819380	−	0.573250i	$-0.805682\pi$
$401$	1.12026e8	−	1.94035e8i	0.0867590	−	0.150271i	0.906139	+	0.422979i	$0.139016\pi$
$402$	3.33219e7	+	5.77153e7i	0.0255823	+	0.0443098i
$403$	9.51291e7	+	1.64768e8i	0.0724012	+	0.125403i
$404$	2.84831e8	−	4.93341e8i	0.214908	−	0.372231i
$405$	−2.07368e9			−1.55113
$406$	4.62157e8	−	5.47800e8i	0.342727	−	0.406238i
$407$	5.48429e8			0.403218
$408$	2.01288e7	−	3.48641e7i	0.0146726	−	0.0254137i
$409$	−1.71435e8	−	2.96934e8i	−0.123899	−	0.214599i	0.797403	−	0.603447i	$-0.206207\pi$
$409$	−1.71435e8	−	2.96934e8i	−0.123899	−	0.214599i	−0.921302	+	0.388848i	$0.872873\pi$
$410$	−8.57495e8	−	1.48523e9i	−0.614452	−	1.06426i
$411$	−3.00542e7	+	5.20553e7i	−0.0213530	+	0.0369844i
$412$	−6.67074e8			−0.469930
$413$	−4.47074e6	−	1.23861e7i	−0.00312287	−	0.00865185i
$414$	−1.28576e9			−0.890554
$415$	−3.45168e8	+	5.97848e8i	−0.237062	+	0.410603i
$416$	6.56432e7	+	1.13697e8i	0.0447057	+	0.0774326i
$417$	3.78951e6	+	6.56362e6i	0.00255922	+	0.00443269i
$418$	−5.22681e8	+	9.05310e8i	−0.350042	+	0.606290i
$419$	−2.04851e9			−1.36047			−0.680234	−	0.732995i	$-0.738122\pi$
$419$	−2.04851e9			−1.36047			−0.680234	+	0.732995i	$0.738122\pi$
$420$	2.42489e7	+	6.71810e7i	0.0159705	+	0.0442460i
$421$	1.83448e9			1.19819			0.599096	−	0.800677i	$-0.295527\pi$
$421$	1.83448e9			1.19819			0.599096	+	0.800677i	$0.295527\pi$
$422$	−4.14763e8	+	7.18391e8i	−0.268662	+	0.465337i
$423$	1.04897e9	+	1.81686e9i	0.673860	+	1.16716i
$424$	4.70494e8	+	8.14919e8i	0.299760	+	0.519199i
$425$	1.59683e9	−	2.76580e9i	1.00902	−	1.74767i
$426$	−9.74852e7			−0.0610949
$427$	1.18755e9	−	1.40761e9i	0.738164	−	0.874954i
$428$	2.50215e8			0.154263
$429$	−3.08072e7	+	5.33597e7i	−0.0188388	+	0.0326297i
$430$	−5.25237e8	−	9.09738e8i	−0.318578	−	0.551794i
$431$	−1.05668e9	−	1.83023e9i	−0.635732	−	1.10112i	−0.986359	−	0.164605i	$-0.947365\pi$
$431$	−1.05668e9	−	1.83023e9i	−0.635732	−	1.10112i	0.350627	−	0.936515i	$-0.385968\pi$
$432$	−2.50894e7	+	4.34561e7i	−0.0149726	+	0.0259333i
$433$	−8.48688e8			−0.502389			−0.251195	−	0.967937i	$-0.580823\pi$
$433$	−8.48688e8			−0.502389			−0.251195	+	0.967937i	$0.580823\pi$
$434$	−3.39353e8	−	6.07720e7i	−0.199268	−	0.0356853i
$435$	−1.21402e8			−0.0707156
$436$	5.91407e8	−	1.02435e9i	0.341730	−	0.591894i
$437$	8.79197e8	+	1.52281e9i	0.503966	+	0.872894i
$438$	−1.68469e7	−	2.91797e7i	−0.00957991	−	0.0165929i
$439$	−9.68945e8	+	1.67826e9i	−0.546605	+	0.946747i	0.451899	+	0.892069i	$0.350747\pi$
$439$	−9.68945e8	+	1.67826e9i	−0.546605	+	0.946747i	−0.998504	+	0.0546781i	$0.982587\pi$
$440$	−1.22991e9			−0.688317
$441$	1.38089e9	−	1.14619e9i	0.766697	−	0.636388i
$442$	8.98202e8			0.494762
$443$	−1.56059e8	+	2.70302e8i	−0.0852855	+	0.147719i	−0.905513	−	0.424319i	$-0.860514\pi$
$443$	−1.56059e8	+	2.70302e8i	−0.0852855	+	0.147719i	0.820227	+	0.572038i	$0.193847\pi$
$444$	−8.98431e6	−	1.55613e7i	−0.00487129	−	0.00843733i
$445$	1.92724e9	+	3.33808e9i	1.03675	+	1.79571i
$446$	9.81859e8	−	1.70063e9i	0.524055	−	0.907691i
$447$	−2.28485e7			−0.0120999
$448$	−2.34168e8	−	4.19353e7i	−0.123043	−	0.0220347i
$449$	−2.16559e8			−0.112905			−0.0564525	−	0.998405i	$-0.517979\pi$
$449$	−2.16559e8			−0.112905			−0.0564525	+	0.998405i	$0.517979\pi$
$450$	−9.93385e8	+	1.72059e9i	−0.513894	+	0.890091i
$451$	1.34041e9	+	2.32166e9i	0.688049	+	1.19174i
$452$	−2.89963e7	−	5.02230e7i	−0.0147692	−	0.0255810i
$453$	7.03734e7	−	1.21890e8i	0.0355684	−	0.0616063i
$454$	−3.37834e8			−0.169437
$455$	−1.02757e9	+	1.21799e9i	−0.511414	+	0.606184i
$456$	3.42500e7			0.0169155
$457$	−4.57054e7	+	7.91641e7i	−0.0224007	+	0.0387991i	−0.877008	−	0.480475i	$-0.840464\pi$
$457$	−4.57054e7	+	7.91641e7i	−0.0224007	+	0.0387991i	0.854608	+	0.519274i	$0.173798\pi$
$458$	−7.57828e8	−	1.31260e9i	−0.368588	−	0.638414i
$459$	1.71650e8	+	2.97307e8i	0.0828514	+	0.143503i
$460$	−1.03441e9	+	1.79165e9i	−0.495496	+	0.858223i
$461$	−2.01437e9			−0.957605			−0.478802	−	0.877923i	$-0.658929\pi$
$461$	−2.01437e9			−0.957605			−0.478802	+	0.877923i	$0.658929\pi$
$462$	−3.79051e7	−	1.05015e8i	−0.0178834	−	0.0495456i
$463$	2.53769e8			0.118824			0.0594121	−	0.998234i	$-0.481077\pi$
$463$	2.53769e8			0.118824			0.0594121	+	0.998234i	$0.481077\pi$
$464$	2.02181e8	−	3.50188e8i	0.0939567	−	0.162738i
$465$	2.91985e7	+	5.05733e7i	0.0134671	+	0.0233258i
$466$	1.21570e9	+	2.10566e9i	0.556515	+	0.963912i
$467$	7.27005e8	−	1.25921e9i	0.330315	−	0.572123i	−0.652258	−	0.757997i	$-0.726178\pi$
$467$	7.27005e8	−	1.25921e9i	0.330315	−	0.572123i	0.982574	+	0.185874i	$0.0595116\pi$
$468$	−5.58769e8			−0.251983
$469$	−9.14749e8	−	2.53429e9i	−0.409446	−	1.13436i
$470$	3.37561e9			1.49972
$471$	3.41682e7	−	5.91811e7i	0.0150678	−	0.0260981i
$472$	−3.71471e6	−	6.43407e6i	−0.00162603	−	0.00281636i
$473$	8.21035e8	+	1.42207e9i	0.356736	+	0.617886i
$474$	1.98919e7	−	3.44538e7i	0.00857931	−	0.0148598i
$475$	2.71708e9			1.16325
$476$	−1.04950e9	+	1.24399e9i	−0.446025	+	0.528678i
$477$	−4.00494e9			−1.68959
$478$	−2.70372e8	+	4.68298e8i	−0.113231	+	0.196121i
$479$	−2.20005e9	−	3.81060e9i	−0.914656	−	1.58423i	−0.807404	−	0.589999i	$-0.799128\pi$
$479$	−2.20005e9	−	3.81060e9i	−0.914656	−	1.58423i	−0.107253	−	0.994232i	$-0.534205\pi$
$480$	2.01482e7	+	3.48978e7i	0.00831558	+	0.0144030i
$481$	2.00452e8	−	3.47194e8i	0.0821303	−	0.142254i
$482$	1.95350e9			0.794601
$483$	−1.84859e8	−	3.31049e7i	−0.0746493	−	0.0133683i
$484$	6.75376e8			0.270761
$485$	−2.26794e9	+	3.92819e9i	−0.902685	+	1.56350i
$486$	−1.60271e8	−	2.77597e8i	−0.0633327	−	0.109695i
$487$	−3.40716e8	−	5.90137e8i	−0.133672	−	0.231527i	0.791417	−	0.611276i	$-0.209344\pi$
$487$	−3.40716e8	−	5.90137e8i	−0.133672	−	0.231527i	−0.925089	+	0.379749i	$0.876010\pi$
$488$	5.19519e8	−	8.99833e8i	0.202363	−	0.350504i
$489$	2.59346e8			0.100299
$490$	−4.86222e8	−	2.84632e9i	−0.186702	−	1.09294i
$491$	−4.49295e9			−1.71296			−0.856478	−	0.516184i	$-0.827352\pi$
$491$	−4.49295e9			−1.71296			−0.856478	+	0.516184i	$0.827352\pi$
$492$	4.39169e7	−	7.60663e7i	0.0166247	−	0.0287948i
$493$	−1.38323e9	−	2.39583e9i	−0.519913	−	0.900516i
$494$	3.82082e8	+	6.61786e8i	0.142598	+	0.246987i
$495$	2.61731e9	−	4.53332e9i	0.969923	−	1.67996i
$496$	−1.94506e8			−0.0715727
$497$	3.87948e9	+	6.94745e8i	1.41751	+	0.253851i
$498$	−3.53558e7			−0.0128280
$499$	1.56243e9	−	2.70620e9i	0.562921	−	0.975008i	−0.434319	−	0.900759i	$-0.643011\pi$
$499$	1.56243e9	−	2.70620e9i	0.562921	−	0.975008i	0.997240	−	0.0742487i	$-0.0236559\pi$
$500$	5.02670e8	+	8.70650e8i	0.179841	+	0.311493i
$501$	1.03120e7	+	1.78610e7i	0.00366364	+	0.00634561i
$502$	−1.05260e9	+	1.82316e9i	−0.371365	+	0.643224i
$503$	4.08890e8			0.143258			0.0716290	−	0.997431i	$-0.477180\pi$
$503$	4.08890e8			0.143258			0.0716290	+	0.997431i	$0.477180\pi$
$504$	6.52893e8	−	7.73880e8i	0.227162	−	0.269257i
$505$	3.90113e9			1.34794
$506$	1.61696e9	−	2.80065e9i	0.554845	−	0.961019i
$507$	−6.55110e7	−	1.13468e8i	−0.0223247	−	0.0386676i
$508$	1.25888e8	+	2.18045e8i	0.0426051	+	0.0737943i
$509$	−1.47071e9	+	2.54734e9i	−0.494327	+	0.856199i	−0.999979	−	0.00653832i	$-0.997919\pi$
$509$	−1.47071e9	+	2.54734e9i	−0.494327	+	0.856199i	0.505652	+	0.862738i	$0.331252\pi$
$510$	2.75690e8			0.0920292
$511$	4.62479e8	+	1.28129e9i	0.153327	+	0.424789i
$512$	−1.34218e8			−0.0441942
$513$	−1.46035e8	+	2.52940e8i	−0.0477580	+	0.0827193i
$514$	−1.02887e9	−	1.78205e9i	−0.334187	−	0.578828i
$515$	−2.28411e9	−	3.95620e9i	−0.736872	−	1.27630i
$516$	2.69002e7	−	4.65925e7i	0.00861949	−	0.0149294i
$517$	−5.27664e9			−1.67935
$518$	2.46636e8	+	6.83299e8i	0.0779654	+	0.216001i
$519$	3.52722e8			0.110751
$520$	−4.49535e8	+	7.78617e8i	−0.140201	+	0.242835i
$521$	2.28708e9	+	3.96135e9i	0.708517	+	1.22719i	0.965407	+	0.260746i	$0.0839686\pi$
$521$	2.28708e9	+	3.96135e9i	0.708517	+	1.22719i	−0.256891	+	0.966440i	$0.582698\pi$
$522$	8.60505e8	+	1.49044e9i	0.264793	+	0.458635i
$523$	−9.05286e8	+	1.56800e9i	−0.276713	+	0.479281i	−0.970566	−	0.240836i	$-0.922578\pi$
$523$	−9.05286e8	+	1.56800e9i	−0.276713	+	0.479281i	0.693853	+	0.720117i	$0.255912\pi$
$524$	1.57286e9			0.477563
$525$	−1.87123e8	+	2.21799e8i	−0.0564378	+	0.0668963i
$526$	−1.65842e9			−0.496872
$527$	−6.65362e8	+	1.15244e9i	−0.198025	+	0.342990i
$528$	−3.14951e7	−	5.45511e7i	−0.00931159	−	0.0161282i
$529$	−1.01745e9	−	1.76228e9i	−0.298827	−	0.517583i
$530$	−3.22201e9	+	5.58069e9i	−0.940073	+	1.62825i
$531$	3.16204e7			0.00916509
$532$	−1.36300e9	−	2.44089e8i	−0.392469	−	0.0702840i
$533$	1.95969e9			0.560587
$534$	−9.87043e7	+	1.70961e8i	−0.0280506	+	0.0485850i
$535$	8.56756e8	+	1.48394e9i	0.241891	+	0.418967i
$536$	−7.60058e8	−	1.31646e9i	−0.213192	−	0.369259i
$537$	1.09571e8	−	1.89783e8i	0.0305343	−	0.0528869i
$538$	2.21141e9			0.612253
$539$	7.60047e8	+	4.44928e9i	0.209064	+	1.22385i
$540$	−3.43632e8			−0.0939107
$541$	−1.28887e9	+	2.23240e9i	−0.349961	+	0.606151i	−0.986242	−	0.165307i	$-0.947139\pi$
$541$	−1.28887e9	+	2.23240e9i	−0.349961	+	0.606151i	0.636281	+	0.771458i	$0.280472\pi$
$542$	−6.02916e7	−	1.04428e8i	−0.0162652	−	0.0281721i
$543$	3.11637e7	+	5.39770e7i	0.00835312	+	0.0144680i
$544$	−4.59129e8	+	7.95234e8i	−0.122275	+	0.211787i
$545$	8.10009e9			2.14339
$546$	−8.03363e7	−	1.43868e7i	−0.0211221	−	0.00378259i
$547$	−3.43757e8			−0.0898039			−0.0449020	−	0.998991i	$-0.514298\pi$
$547$	−3.43757e8			−0.0898039			−0.0449020	+	0.998991i	$0.514298\pi$
$548$	6.85522e8	−	1.18736e9i	0.177946	−	0.308212i
$549$	2.21113e9	+	3.82979e9i	0.570310	+	0.987806i
$550$	−2.49853e9	−	4.32758e9i	−0.640346	−	1.10911i
$551$	1.17681e9	−	2.03830e9i	0.299693	−	0.519084i
$552$	−1.05955e8			−0.0268124
$553$	−1.03715e9	+	1.22935e9i	−0.260798	+	0.309127i
$554$	−1.23574e9			−0.308777
$555$	6.15259e7	−	1.06566e8i	0.0152768	−	0.0264602i
$556$	−8.64370e7	−	1.49713e8i	−0.0213274	−	0.0369401i
$557$	−9.15003e8	−	1.58483e9i	−0.224352	−	0.388588i	0.731773	−	0.681548i	$-0.238693\pi$
$557$	−9.15003e8	−	1.58483e9i	−0.224352	−	0.388588i	−0.956125	+	0.292960i	$0.905360\pi$
$558$	4.13920e8	−	7.16930e8i	0.100855	−	0.174686i
$559$	1.20036e9			0.290650
$560$	−5.53106e8	−	1.53237e9i	−0.133091	−	0.368727i
$561$	−4.30950e8			−0.103052
$562$	9.34614e8	−	1.61880e9i	0.222103	−	0.384694i
$563$	−1.65201e9	−	2.86136e9i	−0.390151	−	0.675761i	0.602319	−	0.798256i	$-0.294244\pi$
$563$	−1.65201e9	−	2.86136e9i	−0.390151	−	0.675761i	−0.992469	+	0.122495i	$0.960910\pi$
$564$	8.64414e7	+	1.49721e8i	0.0202883	+	0.0351403i
$565$	1.98571e8	−	3.43935e8i	0.0463176	−	0.0802244i
$566$	−4.80319e9			−1.11345
$567$	1.45775e9	+	4.03866e9i	0.335847	+	0.930457i
$568$	2.22359e9			0.509139
$569$	2.11764e9	−	3.66786e9i	0.481903	−	0.834680i	−0.517881	−	0.855452i	$-0.673279\pi$
$569$	2.11764e9	−	3.66786e9i	0.481903	−	0.834680i	0.999784	+	0.0207723i	$0.00661252\pi$
$570$	1.17275e8	+	2.03126e8i	0.0265242	+	0.0459412i
$571$	4.81565e8	+	8.34094e8i	0.108250	+	0.187495i	0.915061	−	0.403315i	$-0.132142\pi$
$571$	4.81565e8	+	8.34094e8i	0.108250	+	0.187495i	−0.806811	+	0.590809i	$0.798809\pi$
$572$	7.02699e8	−	1.21711e9i	0.156994	−	0.271922i
$573$	−5.14907e8			−0.114337
$574$	−2.28980e9	+	2.71412e9i	−0.505366	+	0.599015i
$575$	−8.40551e9			−1.84385
$576$	2.85623e8	−	4.94713e8i	0.0622750	−	0.107863i
$577$	−2.48025e9	−	4.29592e9i	−0.537502	−	0.930980i	−0.999038	−	0.0438590i	$-0.986035\pi$
$577$	−2.48025e9	−	4.29592e9i	−0.537502	−	0.930980i	0.461536	−	0.887122i	$-0.347299\pi$
$578$	1.49980e9	+	2.59772e9i	0.323061	+	0.559559i
$579$	6.97296e7	−	1.20775e8i	0.0149294	−	0.0258585i
$580$	2.76913e9			0.589313
$581$	1.40700e9	+	2.51969e8i	0.297631	+	0.0533004i
$582$	−2.32307e8			−0.0488463
$583$	5.03655e9	−	8.72356e9i	1.05267	−	1.82328i
$584$	3.84271e8	+	6.65577e8i	0.0798348	+	0.138278i
$585$	−1.91327e9	−	3.31388e9i	−0.395121	−	0.684370i
$586$	5.36454e8	−	9.29166e8i	0.110126	−	0.190744i
$587$	9.33658e9			1.90526			0.952630	−	0.304130i	$-0.0983658\pi$
$587$	9.33658e9			1.90526			0.952630	+	0.304130i	$0.0983658\pi$
$588$	1.13794e8	−	9.44534e7i	0.0230834	−	0.0191601i
$589$	−1.13214e9			−0.228295
$590$	2.54389e7	−	4.40615e7i	0.00509937	−	0.00883236i
$591$	3.71870e7	+	6.44098e7i	0.00741028	+	0.0128350i
$592$	2.04928e8	+	3.54946e8i	0.0405953	+	0.0703130i
$593$	−5.22179e8	+	9.04440e8i	−0.102832	+	0.178110i	−0.912850	−	0.408294i	$-0.866124\pi$
$593$	−5.22179e8	+	9.04440e8i	−0.102832	+	0.178110i	0.810018	+	0.586404i	$0.199457\pi$
$594$	5.37154e8			0.105159
$595$	−1.09713e10	−	1.96475e9i	−2.13524	−	0.382383i
$596$	5.21163e8			0.100835
$597$	−7.42635e7	+	1.28628e8i	−0.0142845	+	0.0247415i
$598$	−1.18200e9	−	2.04729e9i	−0.226029	−	0.391494i
$599$	6.12748e8	+	1.06131e9i	0.116490	+	0.201766i	0.918374	−	0.395713i	$-0.129502\pi$
$599$	6.12748e8	+	1.06131e9i	0.116490	+	0.201766i	−0.801885	+	0.597479i	$0.796169\pi$
$600$	−8.18613e7	+	1.41788e8i	−0.0154721	+	0.0267985i
$601$	−9.11718e9			−1.71317			−0.856584	−	0.516008i	$-0.827418\pi$
$601$	−9.11718e9			−1.71317			−0.856584	+	0.516008i	$0.827418\pi$
$602$	−1.40256e9	+	1.66247e9i	−0.262019	+	0.310574i
$603$	6.46978e9			1.20165
$604$	−1.60518e9	+	2.78026e9i	−0.296412	+	0.513401i
$605$	2.31254e9	+	4.00543e9i	0.424566	+	0.735370i
$606$	9.98988e7	+	1.73030e8i	0.0182350	+	0.0315840i
$607$	−4.68752e9	+	8.11903e9i	−0.850713	+	1.47348i	0.0298530	+	0.999554i	$0.490496\pi$
$607$	−4.68752e9	+	8.11903e9i	−0.850713	+	1.47348i	−0.880566	+	0.473924i	$0.842837\pi$
$608$	−7.81227e8			−0.140966
$609$	8.53432e7	+	2.36441e8i	0.0153112	+	0.0424192i
$610$	7.11549e9			1.26926
$611$	−1.92863e9	+	3.34048e9i	−0.342061	+	0.592468i
$612$	−1.95410e9	−	3.38460e9i	−0.344601	−	0.596867i
$613$	−1.22631e9	−	2.12403e9i	−0.215025	−	0.372434i	0.738256	−	0.674521i	$-0.235650\pi$
$613$	−1.22631e9	−	2.12403e9i	−0.215025	−	0.372434i	−0.953280	+	0.302087i	$0.902317\pi$
$614$	1.71333e9	−	2.96758e9i	0.298712	−	0.517384i
$615$	6.01499e8			0.104273
$616$	8.64598e8	+	2.39535e9i	0.149033	+	0.412892i
$617$	−2.98428e9			−0.511495			−0.255747	−	0.966744i	$-0.582322\pi$
$617$	−2.98428e9			−0.511495			−0.255747	+	0.966744i	$0.582322\pi$
$618$	1.16982e8	−	2.02618e8i	0.0199369	−	0.0345317i
$619$	1.59754e9	+	2.76702e9i	0.270728	+	0.468915i	0.969049	−	0.246870i	$-0.0794022\pi$
$619$	1.59754e9	+	2.76702e9i	0.270728	+	0.468915i	−0.698320	+	0.715786i	$0.746069\pi$
$620$	−6.66004e8	−	1.15355e9i	−0.112229	−	0.194387i
$621$	4.51771e8	−	7.82491e8i	0.0757004	−	0.131117i
$622$	3.36103e9			0.560024
$623$	5.14638e9	−	6.10006e9i	0.852695	−	1.01071i
$624$	−4.60461e7			−0.00758660
$625$	1.00943e9	−	1.74839e9i	0.165386	−	0.286456i
$626$	4.07085e9	+	7.05092e9i	0.663246	+	1.14878i
$627$	−1.83320e8	−	3.17520e8i	−0.0297012	−	0.0514439i
$628$	−7.79361e8	+	1.34989e9i	−0.125568	+	0.217491i
$629$	2.80405e9			0.449271
$630$	6.82519e9	+	1.22227e9i	1.08748	+	0.194749i
$631$	−7.26845e8			−0.115170			−0.0575850	−	0.998341i	$-0.518340\pi$
$631$	−7.26845e8			−0.115170			−0.0575850	+	0.998341i	$0.518340\pi$
$632$	−4.53725e8	+	7.85875e8i	−0.0714963	+	0.123835i
$633$	−1.45470e8	−	2.51962e8i	−0.0227961	−	0.0394840i
$634$	−8.07631e8	−	1.39886e9i	−0.125864	−	0.218002i
$635$	−8.62102e8	+	1.49320e9i	−0.133614	+	0.231425i
$636$	−3.30033e8			−0.0508695
$637$	3.09450e9	+	1.14506e9i	0.474354	+	0.175526i
$638$	−4.32863e9			−0.659899
$639$	−4.73193e9	+	8.19594e9i	−0.717439	+	1.24264i
$640$	−4.59572e8	−	7.96002e8i	−0.0692984	−	0.120028i
$641$	−1.21877e7	−	2.11097e7i	−0.00182775	−	0.00316576i	0.865110	−	0.501582i	$-0.167248\pi$
$641$	−1.21877e7	−	2.11097e7i	−0.00182775	−	0.00316576i	−0.866938	+	0.498416i	$0.833915\pi$
$642$	−4.38790e7	+	7.60007e7i	−0.00654462	+	0.0113356i
$643$	−2.62875e9			−0.389952			−0.194976	−	0.980808i	$-0.562463\pi$
$643$	−2.62875e9			−0.389952			−0.194976	+	0.980808i	$0.562463\pi$
$644$	4.21655e9	+	7.55108e8i	0.622095	+	0.111406i
$645$	3.68433e8			0.0540630
$646$	−2.67240e9	+	4.62873e9i	−0.390021	+	0.675536i
$647$	−1.60942e9	−	2.78760e9i	−0.233617	−	0.404637i	0.725253	−	0.688483i	$-0.241723\pi$
$647$	−1.60942e9	−	2.78760e9i	−0.233617	−	0.404637i	−0.958870	+	0.283846i	$0.908390\pi$
$648$	1.21123e9	+	2.09792e9i	0.174870	+	0.302884i
$649$	−3.97653e7	+	6.88755e7i	−0.00571015	+	0.00989028i
$650$	−3.65288e9			−0.521721
$651$	7.79697e7	−	9.24183e7i	0.0110762	−	0.0131288i
$652$	−5.91556e9			−0.835852
$653$	2.10281e9	−	3.64217e9i	0.295531	−	0.511875i	−0.679577	−	0.733604i	$-0.737837\pi$
$653$	2.10281e9	−	3.64217e9i	0.295531	−	0.511875i	0.975108	+	0.221729i	$0.0711701\pi$
$654$	2.07424e8	+	3.59270e8i	0.0289960	+	0.0502225i
$655$	5.38560e9	+	9.32813e9i	0.748841	+	1.29703i
$656$	−1.00172e9	+	1.73504e9i	−0.138543	+	0.239964i
$657$	−3.27100e9			−0.449988
$658$	−2.37298e9	−	6.57427e9i	−0.324715	−	0.899616i
$659$	5.67904e9			0.772994			0.386497	−	0.922291i	$-0.373685\pi$
$659$	5.67904e9			0.772994			0.386497	+	0.922291i	$0.373685\pi$
$660$	2.15683e8	−	3.73574e8i	0.0292020	−	0.0505793i
$661$	−4.71978e9	−	8.17490e9i	−0.635648	−	1.10097i	−0.986377	−	0.164498i	$-0.947400\pi$
$661$	−4.71978e9	−	8.17490e9i	−0.635648	−	1.10097i	0.350729	−	0.936477i	$-0.385934\pi$
$662$	−2.72695e9	−	4.72322e9i	−0.365321	−	0.632755i
$663$	−1.57513e8	+	2.72821e8i	−0.0209904	+	0.0363564i
$664$	8.06449e8			0.106903
$665$	−3.21940e9	−	8.91928e9i	−0.424522	−	1.17613i
$666$	−1.74439e9			−0.228815
$667$	−3.64057e9	+	6.30565e9i	−0.475039	+	0.822791i
$668$	−2.35213e8	−	4.07401e8i	−0.0305312	−	0.0528816i
$669$	3.44368e8	+	5.96463e8i	0.0444663	+	0.0770179i
$670$	5.20500e9	−	9.01532e9i	0.668588	−	1.15803i
$671$	−1.11227e10			−1.42129
$672$	5.38025e7	−	6.37727e7i	0.00683928	−	0.00810666i
$673$	1.03784e10			1.31243			0.656214	−	0.754575i	$-0.272157\pi$
$673$	1.03784e10			1.31243			0.656214	+	0.754575i	$0.272157\pi$
$674$	2.56306e9	−	4.43936e9i	0.322441	−	0.558483i
$675$	−6.98080e8	−	1.20911e9i	−0.0873659	−	0.151322i
$676$	1.49428e9	+	2.58816e9i	0.186045	+	0.322239i
$677$	4.23685e9	−	7.33843e9i	0.524786	−	0.908956i	−0.474797	−	0.880095i	$-0.657479\pi$
$677$	4.23685e9	−	7.33843e9i	0.524786	−	0.908956i	0.999583	−	0.0288609i	$-0.00918800\pi$
$678$	2.03397e7			0.00250635
$679$	9.24480e9	+	1.65558e9i	1.13332	+	0.202957i
$680$	−6.28837e9			−0.766932
$681$	5.92443e7	−	1.02614e8i	0.00718839	−	0.0124507i
$682$	1.04108e9	+	1.80320e9i	0.125672	+	0.217670i
$683$	3.01846e9	+	5.22813e9i	0.362505	+	0.627876i	0.988372	−	0.152053i	$-0.0485884\pi$
$683$	3.01846e9	+	5.22813e9i	0.362505	+	0.627876i	−0.625868	+	0.779929i	$0.715255\pi$
$684$	1.66249e9	−	2.87952e9i	0.198639	−	0.344052i
$685$	9.38911e9			1.11611
$686$	−5.20164e9	+	2.94786e9i	−0.615185	+	0.348636i
$687$	5.31587e8			0.0625498
$688$	−6.13581e8	+	1.06275e9i	−0.0718311	+	0.124415i
$689$	−3.68174e9	−	6.37697e9i	−0.428831	−	0.742757i
$690$	−3.62799e8	−	6.28386e8i	−0.0420430	−	0.0728206i
$691$	3.22605e9	−	5.58767e9i	0.371961	−	0.644255i	−0.617906	−	0.786252i	$-0.712019\pi$
$691$	3.22605e9	−	5.58767e9i	0.371961	−	0.644255i	0.989867	+	0.141997i	$0.0453522\pi$
$692$	−8.04543e9			−0.922950
$693$	−1.06689e10	−	1.91061e9i	−1.21774	−	0.218075i
$694$	−6.48372e9			−0.736319
$695$	5.91934e8	−	1.02526e9i	0.0668846	−	0.115848i
$696$	7.09111e7	+	1.22822e8i	0.00797227	+	0.0138084i
$697$	6.85335e9	+	1.18703e10i	0.766634	+	1.32785i
$698$	1.46134e9	−	2.53111e9i	0.162651	−	0.281719i
$699$	−8.52768e8			−0.0944410
$700$	4.26819e9	−	5.05914e9i	0.470328	−	0.557485i
$701$	9.23417e8			0.101248			0.0506238	−	0.998718i	$-0.483879\pi$
$701$	9.23417e8			0.101248			0.0506238	+	0.998718i	$0.483879\pi$
$702$	1.96331e8	−	3.40056e8i	0.0214195	−	0.0370997i
$703$	1.19280e9	+	2.06599e9i	0.129487	+	0.224277i
$704$	7.18388e8	+	1.24429e9i	0.0775988	+	0.134405i
$705$	−5.91964e8	+	1.02531e9i	−0.0636258	+	0.110203i
$706$	−2.93150e9			−0.313526
$707$	−2.74241e9	−	7.59777e9i	−0.291853	−	0.808571i
$708$	2.60572e6			0.000275938
$709$	−3.95369e8	+	6.84799e8i	−0.0416621	+	0.0721608i	−0.886105	−	0.463485i	$-0.846599\pi$
$709$	−3.95369e8	+	6.84799e8i	−0.0416621	+	0.0721608i	0.844442	+	0.535646i	$0.179932\pi$
$710$	7.61375e9	+	1.31874e10i	0.798352	+	1.38279i
$711$	−1.93110e9	−	3.34477e9i	−0.201494	−	0.348998i
$712$	2.25140e9	−	3.89954e9i	0.233761	−	0.404887i
$713$	3.50237e9			0.361867
$714$	−1.93804e8	−	5.36929e8i	−0.0199259	−	0.0552044i
$715$	9.62438e9			0.984694
$716$	−2.49928e9	+	4.32887e9i	−0.254459	+	0.440737i
$717$	−9.48278e7	−	1.64246e8i	−0.00960768	−	0.0166410i
$718$	1.58909e9	+	2.75239e9i	0.160219	+	0.277508i
$719$	−1.78175e9	+	3.08608e9i	−0.178770	+	0.309639i	−0.941460	−	0.337126i	$-0.890545\pi$
$719$	−1.78175e9	+	3.08608e9i	−0.178770	+	0.309639i	0.762689	+	0.646765i	$0.223879\pi$
$720$	3.91197e9			0.390600
$721$	−6.09934e9	+	7.22961e9i	−0.606051	+	0.718359i
$722$	2.60377e9			0.257468
$723$	−3.42576e8	+	5.93359e8i	−0.0337111	+	0.0583894i
$724$	−7.10829e8	−	1.23119e9i	−0.0696113	−	0.120570i
$725$	5.62543e9	+	9.74353e9i	0.548243	+	0.949584i
$726$	−1.18437e8	+	2.05140e8i	−0.0114871	+	0.0198963i
$727$	−9.69075e9			−0.935378			−0.467689	−	0.883893i	$-0.654913\pi$
$727$	−9.69075e9			−0.935378			−0.467689	+	0.883893i	$0.654913\pi$
$728$	1.83243e9	+	3.28156e8i	0.176023	+	0.0315225i
$729$	−1.02351e10			−0.978466
$730$	−2.63155e9	+	4.55797e9i	−0.250369	+	0.433652i
$731$	4.19785e9	+	7.27088e9i	0.397480	+	0.688456i
$732$	1.82211e8	+	3.15599e8i	0.0171706	+	0.0297404i
$733$	−7.33230e9	+	1.26999e10i	−0.687664	+	1.19107i	0.284928	+	0.958549i	$0.408030\pi$
$733$	−7.33230e9	+	1.26999e10i	−0.687664	+	1.19107i	−0.972592	+	0.232520i	$0.925303\pi$
$734$	−8.47791e9			−0.791321
$735$	9.49812e8	+	3.51460e8i	0.0882332	+	0.0326490i
$736$	2.41679e9			0.223443
$737$	−8.13629e9	+	1.40925e10i	−0.748669	+	1.29673i
$738$	−4.26345e9	−	7.38451e9i	−0.390448	−	0.676276i
$739$	−6.91055e9	−	1.19694e10i	−0.629879	−	1.09098i	−0.987576	−	0.157145i	$-0.949771\pi$
$739$	−6.91055e9	−	1.19694e10i	−0.629879	−	1.09098i	0.357697	−	0.933838i	$-0.383562\pi$
$740$	−1.40338e9	+	2.43072e9i	−0.127310	+	0.220508i
$741$	−2.68016e8			−0.0241990
$742$	1.31339e10	+	2.35204e9i	1.18026	+	0.211364i
$743$	1.45009e10			1.29699			0.648493	−	0.761221i	$-0.275400\pi$
$743$	1.45009e10			1.29699			0.648493	+	0.761221i	$0.275400\pi$
$744$	3.41096e7	−	5.90796e7i	0.00303649	−	0.00525935i
$745$	1.78450e9	+	3.09085e9i	0.158114	+	0.273862i
$746$	−2.40557e8	−	4.16657e8i	−0.0212145	−	0.0367446i
$747$	−1.71617e9	+	2.97249e9i	−0.150639	+	0.260914i
$748$	9.82978e9			0.858792
$749$	2.28782e9	−	2.71178e9i	0.198947	−	0.235813i
$750$	−3.52603e8			−0.0305191
$751$	1.12527e10	−	1.94903e10i	0.969433	−	1.67911i	0.272233	−	0.962231i	$-0.412238\pi$
$751$	1.12527e10	−	1.94903e10i	0.969433	−	1.67911i	0.697200	−	0.716876i	$-0.254429\pi$
$752$	−1.97169e9	−	3.41507e9i	−0.169074	−	0.292844i
$753$	−3.69180e8	−	6.39438e8i	−0.0315105	−	0.0545778i
$754$	−1.58212e9	+	2.74032e9i	−0.134413	+	0.232810i
$755$	−2.19851e10			−1.85915
$756$	2.41565e8	+	6.69251e8i	0.0203333	+	0.0563330i
$757$	−9.76692e7			−0.00818318			−0.00409159	−	0.999992i	$-0.501302\pi$
$757$	−9.76692e7			−0.00818318			−0.00409159	+	0.999992i	$0.501302\pi$
$758$	2.97449e9	−	5.15196e9i	0.248068	−	0.429666i
$759$	5.67116e8	+	9.82273e8i	0.0470788	+	0.0815429i
$760$	−2.67498e9	−	4.63320e9i	−0.221041	−	0.382854i
$761$	−2.31336e8	+	4.00686e8i	−0.0190282	+	0.0329577i	−0.875383	−	0.483431i	$-0.839391\pi$
$761$	−2.31336e8	+	4.00686e8i	−0.0190282	+	0.0329577i	0.856355	+	0.516388i	$0.172724\pi$
$762$	−8.83057e7			−0.00723013
$763$	−5.69418e9	−	1.57756e10i	−0.464083	−	1.28573i
$764$	1.17448e10			0.952838
$765$	1.33820e10	−	2.31783e10i	1.08070	−	1.87183i
$766$	7.21362e9	+	1.24944e10i	0.579900	+	1.00442i
$767$	2.90686e7	+	5.03484e7i	0.00232617	+	0.00402904i
$768$	2.35371e7	−	4.07675e7i	0.00187495	−	0.00324750i
$769$	5.59414e9			0.443600			0.221800	−	0.975092i	$-0.428807\pi$
$769$	5.59414e9			0.443600			0.221800	+	0.975092i	$0.428807\pi$
$770$	−1.12456e10	+	1.33295e10i	−0.887696	+	1.05220i
$771$	7.21711e8			0.0567118
$772$	−1.59050e9	+	2.75483e9i	−0.124415	+	0.215493i
$773$	−4.82308e9	−	8.35381e9i	−0.375574	−	0.650514i	0.614838	−	0.788653i	$-0.289221\pi$
$773$	−4.82308e9	−	8.35381e9i	−0.375574	−	0.650514i	−0.990413	+	0.138139i	$0.955888\pi$
$774$	−2.61147e9	−	4.52320e9i	−0.202438	−	0.350632i
$775$	2.70594e9	−	4.68683e9i	0.208815	−	0.361679i
$776$	5.29882e9			0.407064
$777$	−2.50798e8	−	4.49133e7i	−0.0191800	−	0.00343480i
$778$	5.50867e9			0.419390
$779$	−5.83063e9	+	1.00989e10i	−0.441911	+	0.765411i
$780$	−1.57666e8	−	2.73085e8i	−0.0118961	−	0.0206047i
$781$	−1.19016e10	−	2.06141e10i	−0.893977	−	1.54841i
$782$	8.26729e9	−	1.43194e10i	0.618215	−	1.07078i
$783$	−1.20940e9			−0.0900335
$784$	−2.59559e9	+	2.15444e9i	−0.192367	+	0.159672i
$785$	−1.06744e10			−0.787587
$786$	−2.75825e8	+	4.77743e8i	−0.0202607	+	0.0350926i
$787$	8.23168e9	+	1.42577e10i	0.601973	+	1.04265i	0.992522	+	0.122065i	$0.0389517\pi$
$787$	8.23168e9	+	1.42577e10i	0.601973	+	1.04265i	−0.390549	+	0.920582i	$0.627715\pi$
$788$	−8.48218e8	−	1.46916e9i	−0.0617541	−	0.106961i
$789$	2.90829e8	−	5.03731e8i	0.0210799	−	0.0365115i
$790$	−6.21436e9			−0.448437
$791$	−8.09432e8	−	1.44955e8i	−0.0581517	−	0.0104139i
$792$	−6.11508e9			−0.437385
$793$	−4.06538e9	+	7.04145e9i	−0.289498	+	0.501425i
$794$	−5.65251e9	−	9.79044e9i	−0.400746	−	0.694113i
$795$	−1.13006e9	−	1.95732e9i	−0.0797656	−	0.138158i
$796$	1.69392e9	−	2.93395e9i	0.119041	−	0.206185i
$797$	2.24857e10			1.57327			0.786634	−	0.617419i	$-0.211822\pi$
$797$	2.24857e10			1.57327			0.786634	+	0.617419i	$0.211822\pi$
$798$	3.13163e8	−	3.71195e8i	0.0218152	−	0.0258578i
$799$	−2.69788e10			−1.87115
$800$	1.86722e9	−	3.23412e9i	0.128938	−	0.223327i
$801$	9.58220e9	+	1.65969e10i	0.658797	+	1.14107i
$802$	−8.96210e8	−	1.55228e9i	−0.0613479	−	0.106258i
$803$	4.11355e9	−	7.12488e9i	0.280358	−	0.485594i
$804$	5.33151e8			0.0361788
$805$	9.95949e9	+	2.75925e10i	0.672902	+	1.86426i
$806$	1.52207e9			0.102391
$807$	−3.87804e8	+	6.71697e8i	−0.0259750	+	0.0449900i
$808$	−2.27865e9	−	3.94673e9i	−0.151963	−	0.263207i
$809$	3.88266e9	+	6.72496e9i	0.257816	+	0.446550i	0.965656	−	0.259822i	$-0.0836640\pi$
$809$	3.88266e9	+	6.72496e9i	0.257816	+	0.446550i	−0.707841	+	0.706372i	$0.750331\pi$
$810$	−8.29471e9	+	1.43669e10i	−0.548408	+	0.949870i
$811$	2.20730e10			1.45308			0.726539	−	0.687125i	$-0.241127\pi$
$811$	2.20730e10			1.45308			0.726539	+	0.687125i	$0.241127\pi$
$812$	−1.94664e9	−	5.39312e9i	−0.127597	−	0.353504i
$813$	4.22922e7			0.00276022
$814$	2.19372e9	−	3.79963e9i	0.142559	−	0.246920i
$815$	−2.02553e10	−	3.50833e10i	−1.31065	−	2.27012i
$816$	−1.61030e8	−	2.78913e8i	−0.0103751	−	0.0179702i
$817$	−3.57141e9	+	6.18586e9i	−0.229120	+	0.396847i
$818$	−2.74296e9			−0.175220
$819$	−5.10907e9	+	6.05583e9i	−0.324973	+	0.385194i
$820$	−1.37199e10			−0.868967
$821$	3.16187e9	−	5.47651e9i	0.199408	−	0.345385i	−0.748929	−	0.662651i	$-0.769431\pi$
$821$	3.16187e9	−	5.47651e9i	0.199408	−	0.345385i	0.948337	+	0.317266i	$0.102765\pi$
$822$	2.40433e8	+	4.16443e8i	0.0150988	+	0.0261519i
$823$	1.08179e10	+	1.87372e10i	0.676462	+	1.17167i	0.976039	+	0.217595i	$0.0698211\pi$
$823$	1.08179e10	+	1.87372e10i	0.676462	+	1.17167i	−0.299577	+	0.954072i	$0.596846\pi$
$824$	−2.66829e9	+	4.62162e9i	−0.166145	+	0.287772i
$825$	1.75262e9			0.108667
$826$	−1.03696e8	−	1.85701e7i	−0.00640226	−	0.00114653i
$827$	3.87809e9			0.238423			0.119211	−	0.992869i	$-0.461963\pi$
$827$	3.87809e9			0.238423			0.119211	+	0.992869i	$0.461963\pi$
$828$	−5.14306e9	+	8.90804e9i	−0.314858	+	0.545351i
$829$	1.81890e9	+	3.15044e9i	0.110884	+	0.192057i	0.916127	−	0.400888i	$-0.131298\pi$
$829$	1.81890e9	+	3.15044e9i	0.110884	+	0.192057i	−0.805243	+	0.592945i	$0.797965\pi$
$830$	2.76134e9	+	4.78278e9i	0.167628	+	0.290340i
$831$	2.16707e8	−	3.75347e8i	0.0130999	−	0.0226897i
$832$	1.05029e9			0.0632234
$833$	3.88603e9	+	2.27486e10i	0.232942	+	1.36363i
$834$	6.06322e7			0.00361928
$835$	1.61077e9	−	2.78994e9i	0.0957485	−	0.165841i
$836$	4.18145e9	+	7.24248e9i	0.247517	+	0.428712i
$837$	2.90873e8	+	5.03807e8i	0.0171461	+	0.0296978i
$838$	−8.19403e9	+	1.41925e10i	−0.480998	+	0.833113i
$839$	1.60241e10			0.936713			0.468357	−	0.883540i	$-0.344846\pi$
$839$	1.60241e10			0.936713			0.468357	+	0.883540i	$0.344846\pi$
$840$	5.62439e8	+	1.00723e8i	0.0327414	+	0.00586340i
$841$	−7.50399e9			−0.435017
$842$	7.33793e9	−	1.27097e10i	0.423625	−	0.733740i
$843$	3.27798e8	+	5.67762e8i	0.0188456	+	0.0326415i
$844$	3.31811e9	+	5.74713e9i	0.189973	+	0.329043i
$845$	−1.02330e10	+	1.77241e10i	−0.583453	+	1.01057i
$846$	1.67834e10			0.952982
$847$	6.17525e9	−	7.31959e9i	0.349191	−	0.413899i
$848$	7.52790e9			0.423924
$849$	8.42313e8	−	1.45893e9i	0.0472386	−	0.0818196i
$850$	−1.27747e10	−	2.21264e10i	−0.713482	−	1.23579i
$851$	−3.69003e9	−	6.39132e9i	−0.205247	−	0.355498i
$852$	−3.89941e8	+	6.75397e8i	−0.0216003	+	0.0374129i
$853$	1.36378e10			0.752357			0.376178	−	0.926547i	$-0.377238\pi$
$853$	1.36378e10			0.752357			0.376178	+	0.926547i	$0.377238\pi$
$854$	−5.00203e9	−	1.38580e10i	−0.274817	−	0.761374i
$855$	2.27700e10			1.24590
$856$	1.00086e9	−	1.73354e9i	0.0545400	−	0.0944661i
$857$	−3.30853e9	−	5.73054e9i	−0.179557	−	0.311002i	0.762172	−	0.647375i	$-0.224133\pi$
$857$	−3.30853e9	−	5.73054e9i	−0.179557	−	0.311002i	−0.941729	+	0.336373i	$0.890800\pi$
$858$	2.46458e8	+	4.26877e8i	0.0133210	+	0.0230727i
$859$	1.02440e10	−	1.77432e10i	0.551435	−	0.955114i	−0.446736	−	0.894666i	$-0.647414\pi$
$859$	1.02440e10	−	1.77432e10i	0.551435	−	0.955114i	0.998171	−	0.0604481i	$-0.0192530\pi$
$860$	−8.40380e9			−0.450538
$861$	−4.22840e8	−	1.17147e9i	−0.0225770	−	0.0625489i
$862$	−1.69069e10			−0.899061
$863$	−1.43901e10	+	2.49244e10i	−0.762125	+	1.32004i	0.179628	+	0.983735i	$0.442511\pi$
$863$	−1.43901e10	+	2.49244e10i	−0.762125	+	1.32004i	−0.941753	+	0.336305i	$0.890823\pi$
$864$	2.00715e8	+	3.47649e8i	0.0105872	+	0.0183376i
$865$	−2.75482e10	−	4.77148e10i	−1.44723	−	2.50667i
$866$	−3.39475e9	+	5.87988e9i	−0.177622	+	0.307649i
$867$	−1.05205e9			−0.0548238
$868$	−1.77845e9	+	2.10802e9i	−0.0923046	+	0.109410i
$869$	9.71410e9			0.502150
$870$	−4.85610e8	+	8.41101e8i	−0.0250017	+	0.0433043i
$871$	5.94767e9	+	1.03017e10i	0.304988	+	0.528255i
$872$	−4.73125e9	−	8.19477e9i	−0.241640	−	0.418532i
$873$	−1.12762e10	+	1.95309e10i	−0.573603	+	0.993510i
$874$	1.40671e10			0.712715
$875$	1.40321e10	+	2.51289e9i	0.708098	+	0.126808i
$876$	−2.69551e8			−0.0135480
$877$	−5.32139e9	+	9.21692e9i	−0.266395	+	0.461410i	−0.967928	−	0.251227i	$-0.919166\pi$
$877$	−5.32139e9	+	9.21692e9i	−0.266395	+	0.461410i	0.701533	+	0.712637i	$0.252499\pi$
$878$	7.75156e9	+	1.34261e10i	0.386508	+	0.669451i
$879$	1.88151e8	+	3.25887e8i	0.00934427	+	0.0161847i
$880$	−4.91963e9	+	8.52106e9i	−0.243357	+	0.421506i
$881$	−1.92301e10			−0.947472			−0.473736	−	0.880667i	$-0.657095\pi$
$881$	−1.92301e10			−0.947472			−0.473736	+	0.880667i	$0.657095\pi$
$882$	−2.41749e9	−	1.41518e10i	−0.118638	−	0.694501i
$883$	−3.35009e10			−1.63755			−0.818774	−	0.574116i	$-0.805346\pi$
$883$	−3.35009e10			−1.63755			−0.818774	+	0.574116i	$0.805346\pi$
$884$	3.59281e9	−	6.22293e9i	0.174925	−	0.302979i
$885$	8.92220e6	+	1.54537e7i	0.000432684	+	0.000749430i
$886$	1.24847e9	+	2.16241e9i	0.0603059	+	0.104453i
$887$	3.47742e8	−	6.02306e8i	0.0167311	−	0.0289791i	−0.857539	−	0.514420i	$-0.828007\pi$
$887$	3.47742e8	−	6.02306e8i	0.0167311	−	0.0289791i	0.874270	+	0.485440i	$0.161341\pi$
$888$	−1.43749e8			−0.00688905
$889$	3.51418e9	+	6.29326e8i	0.167752	+	0.0300413i
$890$	3.08359e10			1.46619
$891$	1.29660e10	−	2.24578e10i	0.614094	−	1.06364i
$892$	−7.85487e9	−	1.36050e10i	−0.370563	−	0.641834i
$893$	−1.14764e10	−	1.98777e10i	−0.539294	−	0.934085i
$894$	−9.13940e7	+	1.58299e8i	−0.00427795	+	0.00740963i
$895$	−3.42308e10			−1.59601
$896$	−1.22721e9	+	1.45463e9i	−0.0569956	+	0.0675574i
$897$	8.29129e8			0.0383573
$898$	−8.66235e8	+	1.50036e9i	−0.0399180	+	0.0691399i
$899$	−2.34398e9	−	4.05989e9i	−0.107596	−	0.186361i
$900$	7.94708e9	+	1.37647e10i	0.363378	+	0.629390i
$901$	2.57512e10	−	4.46025e10i	1.17290	−	2.03152i
$902$	2.14466e10			0.973049
$903$	−2.59000e8	−	7.17555e8i	−0.0117056	−	0.0324301i
$904$	−4.63940e8			−0.0208868
$905$	4.86786e9	−	8.43139e9i	0.218307	−	0.378119i
$906$	−5.62987e8	−	9.75122e8i	−0.0251507	−	0.0435623i
$907$	7.45722e9	+	1.29163e10i	0.331857	+	0.574794i	0.982876	−	0.184268i	$-0.0589914\pi$
$907$	7.45722e9	+	1.29163e10i	0.331857	+	0.574794i	−0.651019	+	0.759062i	$0.725658\pi$
$908$	−1.35134e9	+	2.34058e9i	−0.0599050	+	0.103758i
$909$	1.93963e10			0.856536
$910$	4.32821e9	+	1.19912e10i	0.190398	+	0.527494i
$911$	4.82224e7			0.00211317			0.00105659	−	0.999999i	$-0.499664\pi$
$911$	4.82224e7			0.00211317			0.00105659	+	0.999999i	$0.499664\pi$
$912$	1.37000e8	−	2.37291e8i	0.00598052	−	0.0103586i
$913$	−4.31644e9	−	7.47630e9i	−0.187706	−	0.325116i
$914$	3.65643e8	+	6.33313e8i	0.0158397	+	0.0274351i
$915$	−1.24781e9	+	2.16127e9i	−0.0538486	+	0.0932685i
$916$	−1.21253e10			−0.521263
$917$	1.43813e10	−	1.70464e10i	0.615895	−	0.730027i
$918$	2.74640e9			0.117170
$919$	−1.67412e10	+	2.89966e10i	−0.711511	+	1.23237i	0.252778	+	0.967524i	$0.418656\pi$
$919$	−1.67412e10	+	2.89966e10i	−0.711511	+	1.23237i	−0.964290	+	0.264850i	$0.914678\pi$
$920$	8.27527e9	+	1.43332e10i	0.350368	+	0.606856i
$921$	6.00918e8	+	1.04082e9i	0.0253458	+	0.0439002i
$922$	−8.05748e9	+	1.39560e10i	−0.338564	+	0.586411i
$923$	−1.74002e10			−0.728365
$924$	−8.79187e8	−	1.57447e8i	−0.0366631	−	0.00656570i
$925$	−1.14037e10			−0.473751
$926$	1.01507e9	−	1.75816e9i	0.0420107	−	0.0727646i
$927$	−1.13565e10	−	1.96701e10i	−0.468239	−	0.811013i
$928$	−1.61745e9	−	2.80150e9i	−0.0664374	−	0.115073i
$929$	−1.07021e10	+	1.85365e10i	−0.437938	+	0.758532i	−0.997530	−	0.0702367i	$-0.977625\pi$
$929$	−1.07021e10	+	1.85365e10i	−0.437938	+	0.758532i	0.559592	+	0.828768i	$0.310958\pi$
$930$	4.67176e8			0.0190454
$931$	−1.51079e10	+	1.25401e10i	−0.613592	+	0.509305i
$932$	1.94512e10			0.787031
$933$	−5.89408e8	+	1.02088e9i	−0.0237591	+	0.0411520i
$934$	−5.81604e9	−	1.00737e10i	−0.233568	−	0.404552i
$935$	3.36579e10	+	5.82972e10i	1.34662	+	2.33242i
$936$	−2.23508e9	+	3.87127e9i	−0.0890896	+	0.154308i
$937$	1.23173e10			0.489132			0.244566	−	0.969633i	$-0.421355\pi$
$937$	1.23173e10			0.489132			0.244566	+	0.969633i	$0.421355\pi$
$938$	−2.12171e10	−	3.79959e9i	−0.839413	−	0.150324i
$939$	−2.85554e9			−0.112553
$940$	1.35024e10	−	2.33869e10i	0.530230	−	0.918386i
$941$	1.57825e10	+	2.73361e10i	0.617465	+	1.06948i	0.989947	+	0.141441i	$0.0451735\pi$
$941$	1.57825e10	+	2.73361e10i	0.617465	+	1.06948i	−0.372482	+	0.928039i	$0.621493\pi$
$942$	−2.73346e8	−	4.73448e8i	−0.0106545	−	0.0184542i
$943$	1.80375e10	−	3.12419e10i	0.700464	−	1.21324i
$944$	−5.94354e7			−0.00229955
$945$	−3.14197e9	+	3.72421e9i	−0.121113	+	0.143557i
$946$	1.31366e10			0.504502
$947$	−5.91852e9	+	1.02512e10i	−0.226458	+	0.392237i	−0.956756	−	0.290892i	$-0.906048\pi$
$947$	−5.91852e9	+	1.02512e10i	−0.226458	+	0.392237i	0.730298	+	0.683129i	$0.239381\pi$
$948$	−1.59135e8	−	2.75630e8i	−0.00606649	−	0.0105075i
$949$	−3.00703e9	−	5.20832e9i	−0.114210	−	0.197818i
$950$	1.08683e10	−	1.88245e10i	0.411273	−	0.712345i
$951$	5.66522e8			0.0213592
$952$	4.42058e9	+	1.22471e10i	0.166054	+	0.460049i
$953$	−4.24105e10			−1.58726			−0.793630	−	0.608400i	$-0.791812\pi$
$953$	−4.24105e10			−1.58726			−0.793630	+	0.608400i	$0.791812\pi$
$954$	−1.60198e10	+	2.77471e10i	−0.597361	+	1.03466i
$955$	4.02151e10	+	6.96546e10i	1.49409	+	2.58784i
$956$	2.16298e9	+	3.74639e9i	0.0800662	+	0.138679i
$957$	7.59090e8	−	1.31478e9i	0.0279964	−	0.0484911i
$958$	−3.52008e10			−1.29352
$959$	−6.60034e9	−	1.82861e10i	−0.241658	−	0.669507i
$960$	3.22372e8			0.0117600
$961$	1.26288e10	−	2.18737e10i	0.459019	−	0.795044i
$962$	−1.60362e9	−	2.77755e9i	−0.0580749	−	0.100589i
$963$	4.25977e9	+	7.37814e9i	0.153707	+	0.266229i
$964$	7.81400e9	−	1.35343e10i	0.280934	−	0.486592i
$965$	−2.17840e10			−0.780354
$966$	−9.68794e8	+	1.14832e9i	−0.0345789	+	0.0409868i
$967$	−5.25820e9			−0.187001			−0.0935006	−	0.995619i	$-0.529806\pi$
$967$	−5.25820e9			−0.187001			−0.0935006	+	0.995619i	$0.529806\pi$
$968$	2.70150e9	−	4.67914e9i	0.0957286	−	0.165807i
$969$	−9.37292e8	−	1.62344e9i	−0.0330934	−	0.0573195i
$970$	1.81436e10	+	3.14256e10i	0.638295	+	1.10556i
$971$	1.73147e10	−	2.99900e10i	0.606944	−	1.05126i	−0.384797	−	0.923001i	$-0.625729\pi$
$971$	1.73147e10	−	2.99900e10i	0.606944	−	1.05126i	0.991741	−	0.128256i	$-0.0409380\pi$
$972$	−2.56433e9			−0.0895659
$973$	−2.41289e9	−	4.32106e8i	−0.0839737	−	0.0150382i
$974$	−5.45145e9			−0.189041
$975$	6.40587e8	−	1.10953e9i	0.0221341	−	0.0383374i
$976$	−4.15615e9	−	7.19867e9i	−0.143093	−	0.247844i
$977$	−2.24932e9	−	3.89594e9i	−0.0771650	−	0.133654i	0.824861	−	0.565336i	$-0.191253\pi$
$977$	−2.24932e9	−	3.89594e9i	−0.0771650	−	0.133654i	−0.902026	+	0.431682i	$0.857920\pi$
$978$	1.03738e9	−	1.79680e9i	0.0354612	−	0.0614206i
$979$	−4.82017e10			−1.64181
$980$	−2.16648e10	−	8.01664e9i	−0.735297	−	0.272083i
$981$	4.02735e10			1.36200
$982$	−1.79718e10	+	3.11281e10i	−0.605621	+	1.04897i
$983$	1.06779e10	+	1.84947e10i	0.358551	+	0.621028i	0.987719	−	0.156241i	$-0.0499377\pi$
$983$	1.06779e10	+	1.84947e10i	0.358551	+	0.621028i	−0.629168	+	0.777269i	$0.716604\pi$
$984$	−3.51335e8	−	6.08530e8i	−0.0117554	−	0.0203610i
$985$	5.80873e9	−	1.00610e10i	0.193666	−	0.335440i
$986$	−2.21317e10			−0.735268
$987$	2.41302e9	+	4.32128e8i	0.0798823	+	0.0143055i
$988$	6.11332e9			0.201664
$989$	1.10484e10	−	1.91365e10i	0.363173	−	0.629035i
$990$	−2.09385e10	−	3.62665e10i	−0.685839	−	1.18791i
$991$	−1.86484e10	−	3.23000e10i	−0.608674	−	1.05425i	−0.991459	−	0.130417i	$-0.958368\pi$
$991$	−1.86484e10	−	3.23000e10i	−0.608674	−	1.05425i	0.382785	−	0.923837i	$-0.374965\pi$
$992$	−7.78025e8	+	1.34758e9i	−0.0253048	+	0.0438292i
$993$	1.91285e9			0.0619953
$994$	2.03313e10	−	2.40989e10i	0.656617	−	0.778295i
$995$	2.32004e10			0.746646
$996$	−1.41423e8	+	2.44952e8i	−0.00453537	+	0.00785549i
$997$	−5.94162e9	−	1.02912e10i	−0.189877	−	0.328876i	0.755332	−	0.655342i	$-0.227475\pi$
$997$	−5.94162e9	−	1.02912e10i	−0.189877	−	0.328876i	−0.945209	+	0.326466i	$0.894142\pi$
$998$	−1.24994e10	−	2.16496e10i	−0.398045	−	0.689435i
$999$	6.12916e8	−	1.06160e9i	0.0194501	−	0.0336886i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.8.c.b.9.2	✓	4
3.2	odd	2		126.8.g.d.37.1		4
4.3	odd	2		112.8.i.b.65.1		4
7.2	even	3		98.8.a.f.1.1		2
7.3	odd	6		98.8.c.m.67.1		4
7.4	even	3	inner	14.8.c.b.11.2	yes	4
7.5	odd	6		98.8.a.d.1.2		2
7.6	odd	2		98.8.c.m.79.1		4
21.11	odd	6		126.8.g.d.109.1		4
28.11	odd	6		112.8.i.b.81.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.c.b.9.2	✓	4	1.1	even	1	trivial
14.8.c.b.11.2	yes	4	7.4	even	3	inner
98.8.a.d.1.2		2	7.5	odd	6
98.8.a.f.1.1		2	7.2	even	3
98.8.c.m.67.1		4	7.3	odd	6
98.8.c.m.79.1		4	7.6	odd	2
112.8.i.b.65.1		4	4.3	odd	2
112.8.i.b.81.1		4	28.11	odd	6
126.8.g.d.37.1		4	3.2	odd	2
126.8.g.d.109.1		4	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 14 = 2 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	14.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.00000 - 6.92820i) q^{2} +(1.40292 + 2.42993i) q^{3} +(-32.0000 - 55.4256i) q^{4} +(219.141 - 379.563i) q^{5} +22.4467 q^{6} +(-893.282 - 159.971i) q^{7} -512.000 q^{8} +(1089.56 - 1887.18i) q^{9} +(-1753.13 - 3036.51i) q^{10} +(2740.43 + 4746.57i) q^{11} +(89.7870 - 155.516i) q^{12} +4006.54 q^{13} +(-4681.44 + 5548.96i) q^{14} +1229.75 q^{15} +(-2048.00 + 3547.24i) q^{16} +(14011.5 + 24268.6i) q^{17} +(-8716.51 - 15097.4i) q^{18} +(-11920.6 + 20647.0i) q^{19} -28050.0 q^{20} +(-864.487 - 2395.04i) q^{21} +43846.9 q^{22} +(36877.3 - 63873.3i) q^{23} +(-718.296 - 1244.13i) q^{24} +(-56983.0 - 98697.4i) q^{25} +(16026.2 - 27758.1i) q^{26} +12250.7 q^{27} +(19718.5 + 54629.8i) q^{28} -98721.3 q^{29} +(4919.00 - 8519.96i) q^{30} +(23743.4 + 41124.8i) q^{31} +(16384.0 + 28377.9i) q^{32} +(-7689.23 + 13318.1i) q^{33} +224184. q^{34} +(-256474. + 304001. i) q^{35} -139464. q^{36} +(50031.2 - 86656.7i) q^{37} +(95364.6 + 165176. i) q^{38} +(5620.87 + 9735.63i) q^{39} +(-112200. + 194336. i) q^{40} +489123. q^{41} +(-20051.3 - 3590.82i) q^{42} +299600. q^{43} +(175388. - 303781. i) q^{44} +(-477536. - 827116. i) q^{45} +(-295018. - 510986. i) q^{46} +(-481369. + 833756. i) q^{47} -11492.7 q^{48} +(772362. + 285798. i) q^{49} -911728. q^{50} +(-39314.1 + 68093.9i) q^{51} +(-128209. - 222065. i) q^{52} +(-918933. - 1.59164e6i) q^{53} +(49002.7 - 84875.1i) q^{54} +2.40216e6 q^{55} +(457360. + 81905.0i) q^{56} -66894.5 q^{57} +(-394885. + 683961. i) q^{58} +(7255.29 + 12566.5i) q^{59} +(-39352.0 - 68159.7i) q^{60} +(-1.01469e6 + 1.75749e6i) q^{61} +379895. q^{62} +(-1.27518e6 + 1.51148e6i) q^{63} +262144. q^{64} +(877997. - 1.52074e6i) q^{65} +(61513.8 + 106545. i) q^{66} +(1.48449e6 + 2.57121e6i) q^{67} +(896736. - 1.55319e6i) q^{68} +206944. q^{69} +(1.08028e6 + 2.99290e6i) q^{70} -4.34296e6 q^{71} +(-557857. + 966236. i) q^{72} +(-750529. - 1.29995e6i) q^{73} +(-400250. - 693253. i) q^{74} +(159885. - 276929. i) q^{75} +1.52583e6 q^{76} +(-1.68867e6 - 4.67841e6i) q^{77} +89933.9 q^{78} +(886182. - 1.53491e6i) q^{79} +(897601. + 1.55469e6i) q^{80} +(-2.36569e6 - 4.09749e6i) q^{81} +(1.95649e6 - 3.38874e6i) q^{82} -1.57509e6 q^{83} +(-105083. + 124556. i) q^{84} +1.22820e7 q^{85} +(1.19840e6 - 2.07569e6i) q^{86} +(-138498. - 239886. i) q^{87} +(-1.40310e6 - 2.43024e6i) q^{88} +(-4.39727e6 + 7.61629e6i) q^{89} -7.64057e6 q^{90} +(-3.57897e6 - 640929. i) q^{91} -4.72029e6 q^{92} +(-66620.4 + 115390. i) q^{93} +(3.85096e6 + 6.67005e6i) q^{94} +(5.22457e6 + 9.04922e6i) q^{95} +(-45970.9 + 79624.0i) q^{96} -1.03493e7 q^{97} +(5.06951e6 - 4.20789e6i) q^{98} +1.19435e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 16 q^{2} - 56 q^{3} - 128 q^{4} + 14 q^{5} - 896 q^{6} - 1848 q^{7} - 2048 q^{8} + 908 q^{9} - 112 q^{10} - 2408 q^{11} - 3584 q^{12} + 21448 q^{13} - 22176 q^{14} + 52360 q^{15} - 8192 q^{16} + 35098 q^{17}+ \cdots + 43942528 q^{99}+O(q^{100}) \) 4 * q + 16 * q^2 - 56 * q^3 - 128 * q^4 + 14 * q^5 - 896 * q^6 - 1848 * q^7 - 2048 * q^8 + 908 * q^9 - 112 * q^10 - 2408 * q^11 - 3584 * q^12 + 21448 * q^13 - 22176 * q^14 + 52360 * q^15 - 8192 * q^16 + 35098 * q^17 - 7264 * q^18 + 2408 * q^19 - 1792 * q^20 - 92302 * q^21 - 38528 * q^22 + 61684 * q^23 + 28672 * q^24 - 215856 * q^25 + 85792 * q^26 - 83216 * q^27 - 59136 * q^28 - 191320 * q^29 + 209440 * q^30 + 166012 * q^31 + 65536 * q^32 - 479290 * q^33 + 561568 * q^34 + 166600 * q^35 - 116224 * q^36 + 559814 * q^37 - 19264 * q^38 - 383784 * q^39 - 7168 * q^40 + 1611960 * q^41 - 11200 * q^42 + 535952 * q^43 - 154112 * q^44 - 1494388 * q^45 - 493472 * q^46 - 1769292 * q^47 + 458752 * q^48 - 98588 * q^49 - 3453696 * q^50 + 337424 * q^51 - 686336 * q^52 - 2317194 * q^53 - 332864 * q^54 + 11498536 * q^55 + 946176 * q^56 - 3220996 * q^57 - 765280 * q^58 - 660352 * q^59 - 1675520 * q^60 - 1463042 * q^61 + 2656192 * q^62 - 514472 * q^63 + 1048576 * q^64 - 1094100 * q^65 + 3834320 * q^66 + 1784280 * q^67 + 2246272 * q^68 + 1833524 * q^69 + 7388416 * q^70 + 548800 * q^71 - 464896 * q^72 - 4549062 * q^73 - 4478512 * q^74 - 5671960 * q^75 - 308224 * q^76 - 15527806 * q^77 - 6140544 * q^78 + 8673964 * q^79 + 57344 * q^80 + 1215782 * q^81 + 6447840 * q^82 - 21188720 * q^83 + 5817728 * q^84 + 18560332 * q^85 + 2143808 * q^86 - 457016 * q^87 + 1232896 * q^88 - 1779750 * q^89 - 23910208 * q^90 - 7570640 * q^91 - 7895552 * q^92 + 6836730 * q^93 + 14154336 * q^94 + 21586180 * q^95 + 1835008 * q^96 - 3497928 * q^97 + 4337872 * q^98 + 43942528 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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