LMFDB - Embedded newform 14.8.c.b.11.1

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			11.1
Root			$-7.45146 - 12.9063i$ of defining polynomial
Character	$\chi$	$=$	14.11
Dual form			14.8.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} +(-29.4029 + 50.9274i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-212.141 - 367.439i) q^{5} -470.447 q^{6} +(-30.7182 + 906.973i) q^{7} -512.000 q^{8} +(-635.564 - 1100.83i) q^{9} +(1697.13 - 2939.51i) q^{10} +(-3944.43 + 6831.96i) q^{11} +(-1881.79 - 3259.35i) q^{12} +6717.46 q^{13} +(-6406.56 + 3415.07i) q^{14} +24950.2 q^{15} +(-2048.00 - 3547.24i) q^{16} +(3537.51 - 6127.14i) q^{17} +(5084.51 - 8806.63i) q^{18} +(13124.6 + 22732.4i) q^{19} +27154.0 q^{20} +(-45286.5 - 28232.0i) q^{21} -63110.9 q^{22} +(-6035.27 - 10453.4i) q^{23} +(15054.3 - 26074.8i) q^{24} +(-50945.0 + 88239.4i) q^{25} +(26869.8 + 46539.9i) q^{26} -53858.7 q^{27} +(-49286.5 - 30725.7i) q^{28} +3061.25 q^{29} +(99801.0 + 172860. i) q^{30} +(59262.6 - 102646. i) q^{31} +(16384.0 - 28377.9i) q^{32} +(-231956. - 401759. i) q^{33} +56600.1 q^{34} +(339774. - 181119. i) q^{35} +81352.1 q^{36} +(229876. + 398156. i) q^{37} +(-104997. + 181859. i) q^{38} +(-197513. + 342102. i) q^{39} +(108616. + 188129. i) q^{40} +316857. q^{41} +(14451.3 - 426682. i) q^{42} -31624.2 q^{43} +(-252444. - 437245. i) q^{44} +(-269658. + 467062. i) q^{45} +(48282.2 - 83627.2i) q^{46} +(-403277. - 698496. i) q^{47} +240869. q^{48} +(-821656. - 55721.1i) q^{49} -815120. q^{50} +(208026. + 360312. i) q^{51} +(-214959. + 372319. i) q^{52} +(-239664. + 415110. i) q^{53} +(-215435. - 373144. i) q^{54} +3.34710e6 q^{55} +(15727.7 - 464370. i) q^{56} -1.54360e6 q^{57} +(12245.0 + 21209.0i) q^{58} +(-337431. + 584448. i) q^{59} +(-798408. + 1.38288e6i) q^{60} +(283165. + 490455. i) q^{61} +948201. q^{62} +(1.01794e6 - 542623. i) q^{63} +262144. q^{64} +(-1.42505e6 - 2.46825e6i) q^{65} +(1.85565e6 - 3.21407e6i) q^{66} +(-592349. + 1.02598e6i) q^{67} +(226400. + 392137. i) q^{68} +709818. q^{69} +(2.61392e6 + 1.62954e6i) q^{70} +4.61736e6 q^{71} +(325409. + 563624. i) q^{72} +(-1.52400e6 + 2.63965e6i) q^{73} +(-1.83901e6 + 3.18525e6i) q^{74} +(-2.99587e6 - 5.18899e6i) q^{75} -1.67995e6 q^{76} +(-6.07524e6 - 3.78736e6i) q^{77} -3.16021e6 q^{78} +(3.45080e6 + 5.97696e6i) q^{79} +(-868929. + 1.50503e6i) q^{80} +(2.97358e6 - 5.15039e6i) q^{81} +(1.26743e6 + 2.19525e6i) q^{82} -9.01927e6 q^{83} +(3.01395e6 - 1.60661e6i) q^{84} -3.00180e6 q^{85} +(-126497. - 219099. i) q^{86} +(-90009.8 + 155902. i) q^{87} +(2.01955e6 - 3.49796e6i) q^{88} +(3.50739e6 + 6.07498e6i) q^{89} -4.31453e6 q^{90} +(-206348. + 6.09255e6i) q^{91} +772515. q^{92} +(3.48499e6 + 6.03617e6i) q^{93} +(3.22621e6 - 5.58796e6i) q^{94} +(5.56852e6 - 9.64496e6i) q^{95} +(963475. + 1.66879e6i) q^{96} +8.60029e6 q^{97} +(-2.90058e6 - 5.91548e6i) q^{98} +1.00278e7 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 $\left(\mathbb{Z}/14\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$2$	4.00000	+	6.92820i	0.353553	+	0.612372i
$3$	−29.4029	+	50.9274i	−0.628733	+	1.08900i	0.359074	+	0.933309i	$0.383093\pi$
$3$	−29.4029	+	50.9274i	−0.628733	+	1.08900i	−0.987806	+	0.155688i	$0.950241\pi$
$4$	−32.0000	+	55.4256i	−0.250000	+	0.433013i
$5$	−212.141	−	367.439i	−0.758978	−	1.31459i	−0.943372	−	0.331737i	$-0.892365\pi$
$5$	−212.141	−	367.439i	−0.758978	−	1.31459i	0.184394	−	0.982852i	$-0.440968\pi$
$6$	−470.447			−0.889162
$7$	−30.7182	+	906.973i	−0.0338495	+	0.999427i
$7$	−30.7182	+	906.973i	−0.0338495	+	0.999427i
$8$	−512.000			−0.353553
$9$	−635.564	−	1100.83i	−0.290610	−	0.503351i
$10$	1697.13	−	2939.51i	0.536679	−	0.929555i
$11$	−3944.43	+	6831.96i	−0.893532	+	1.54764i	−0.0579219	+	0.998321i	$0.518447\pi$
$11$	−3944.43	+	6831.96i	−0.893532	+	1.54764i	−0.835611	+	0.549322i	$0.814886\pi$
$12$	−1881.79	−	3259.35i	−0.314366	−	0.544499i
$13$	6717.46			0.848014			0.424007	−	0.905659i	$-0.360623\pi$
$13$	6717.46			0.848014			0.424007	+	0.905659i	$0.360623\pi$
$14$	−6406.56	+	3415.07i	−0.623989	+	0.332622i
$15$	24950.2			1.90878
$16$	−2048.00	−	3547.24i	−0.125000	−	0.216506i
$17$	3537.51	−	6127.14i	0.174633	−	0.302473i	−0.765401	−	0.643553i	$-0.777459\pi$
$17$	3537.51	−	6127.14i	0.174633	−	0.302473i	0.940034	+	0.341080i	$0.110793\pi$
$18$	5084.51	−	8806.63i	0.205492	−	0.355923i
$19$	13124.6	+	22732.4i	0.438983	+	0.760341i	0.997611	−	0.0690773i	$-0.0220055\pi$
$19$	13124.6	+	22732.4i	0.438983	+	0.760341i	−0.558628	+	0.829418i	$0.688672\pi$
$20$	27154.0			0.758978
$21$	−45286.5	−	28232.0i	−1.06709	−	0.665234i
$22$	−63110.9			−1.26365
$23$	−6035.27	−	10453.4i	−0.103431	−	0.179147i	0.809665	−	0.586892i	$-0.199649\pi$
$23$	−6035.27	−	10453.4i	−0.103431	−	0.179147i	−0.913096	+	0.407745i	$0.866315\pi$
$24$	15054.3	−	26074.8i	0.222291	−	0.385019i
$25$	−50945.0	+	88239.4i	−0.652096	+	1.12946i
$26$	26869.8	+	46539.9i	0.299818	+	0.519301i
$27$	−53858.7			−0.526602
$28$	−49286.5	−	30725.7i	−0.424302	−	0.264514i
$29$	3061.25			0.0233081			0.0116540	−	0.999932i	$-0.496290\pi$
$29$	3061.25			0.0233081			0.0116540	+	0.999932i	$0.496290\pi$
$30$	99801.0	+	172860.i	0.674855	+	1.16888i
$31$	59262.6	−	102646.i	0.357285	−	0.618835i	−0.630221	−	0.776415i	$-0.717036\pi$
$31$	59262.6	−	102646.i	0.357285	−	0.618835i	0.987506	+	0.157580i	$0.0503692\pi$
$32$	16384.0	−	28377.9i	0.0883883	−	0.153093i
$33$	−231956.	−	401759.i	−1.12359	−	1.94611i
$34$	56600.1			0.246968
$35$	339774.	−	181119.i	1.33953	−	0.714045i
$36$	81352.1			0.290610
$37$	229876.	+	398156.i	0.746083	+	1.29225i	0.949687	+	0.313200i	$0.101401\pi$
$37$	229876.	+	398156.i	0.746083	+	1.29225i	−0.203604	+	0.979053i	$0.565266\pi$
$38$	−104997.	+	181859.i	−0.310408	+	0.537642i
$39$	−197513.	+	342102.i	−0.533174	+	0.923485i
$40$	108616.	+	188129.i	0.268339	+	0.464777i
$41$	316857.			0.717992			0.358996	−	0.933339i	$-0.383119\pi$
$41$	316857.			0.717992			0.358996	+	0.933339i	$0.383119\pi$
$42$	14451.3	−	426682.i	0.0300977	−	0.888653i
$43$	−31624.2			−0.0606569			−0.0303284	−	0.999540i	$-0.509655\pi$
$43$	−31624.2			−0.0606569			−0.0303284	+	0.999540i	$0.509655\pi$
$44$	−252444.	−	437245.i	−0.446766	−	0.773822i
$45$	−269658.	+	467062.i	−0.441133	+	0.764065i
$46$	48282.2	−	83627.2i	0.0731365	−	0.126676i
$47$	−403277.	−	698496.i	−0.566579	−	0.981344i	−0.996901	−	0.0786682i	$-0.974933\pi$
$47$	−403277.	−	698496.i	−0.566579	−	0.981344i	0.430322	−	0.902676i	$-0.358400\pi$
$48$	240869.			0.314366
$49$	−821656.	−	55721.1i	−0.997708	−	0.0676602i
$50$	−815120.			−0.922204
$51$	208026.	+	360312.i	0.219595	+	0.380349i
$52$	−214959.	+	372319.i	−0.212004	+	0.367201i
$53$	−239664.	+	415110.i	−0.221125	+	0.382999i	−0.955150	−	0.296123i	$-0.904306\pi$
$53$	−239664.	+	415110.i	−0.221125	+	0.382999i	0.734025	+	0.679122i	$0.237639\pi$
$54$	−215435.	−	373144.i	−0.186182	−	0.322477i
$55$	3.34710e6			2.71269
$56$	15727.7	−	464370.i	0.0119676	−	0.353351i
$57$	−1.54360e6			−1.10401
$58$	12245.0	+	21209.0i	0.00824065	+	0.0142732i
$59$	−337431.	+	584448.i	−0.213896	+	0.370479i	−0.952931	−	0.303189i	$-0.901949\pi$
$59$	−337431.	+	584448.i	−0.213896	+	0.370479i	0.739034	+	0.673668i	$0.235282\pi$
$60$	−798408.	+	1.38288e6i	−0.477195	+	0.826525i
$61$	283165.	+	490455.i	0.159729	+	0.276659i	0.934771	−	0.355251i	$-0.115605\pi$
$61$	283165.	+	490455.i	0.159729	+	0.276659i	−0.775042	+	0.631910i	$0.782271\pi$
$62$	948201.			0.505277
$63$	1.01794e6	−	542623.i	0.512899	−	0.273405i
$64$	262144.			0.125000
$65$	−1.42505e6	−	2.46825e6i	−0.643625	−	1.11479i
$66$	1.85565e6	−	3.21407e6i	0.794495	−	1.37611i
$67$	−592349.	+	1.02598e6i	−0.240611	+	0.416751i	−0.960889	−	0.276935i	$-0.910681\pi$
$67$	−592349.	+	1.02598e6i	−0.240611	+	0.416751i	0.720277	+	0.693686i	$0.244015\pi$
$68$	226400.	+	392137.i	0.0873164	+	0.151237i
$69$	709818.			0.260121
$70$	2.61392e6	+	1.62954e6i	0.910856	+	0.567836i
$71$	4.61736e6			1.53105			0.765524	−	0.643407i	$-0.222480\pi$
$71$	4.61736e6			1.53105			0.765524	+	0.643407i	$0.222480\pi$
$72$	325409.	+	563624.i	0.102746	+	0.177961i
$73$	−1.52400e6	+	2.63965e6i	−0.458517	+	0.794175i	−0.998883	−	0.0472553i	$-0.984953\pi$
$73$	−1.52400e6	+	2.63965e6i	−0.458517	+	0.794175i	0.540366	+	0.841430i	$0.318286\pi$
$74$	−1.83901e6	+	3.18525e6i	−0.527560	+	0.913761i
$75$	−2.99587e6	−	5.18899e6i	−0.819989	−	1.42026i
$76$	−1.67995e6			−0.438983
$77$	−6.07524e6	−	3.78736e6i	−1.51651	−	0.945407i
$78$	−3.16021e6			−0.754022
$79$	3.45080e6	+	5.97696e6i	0.787454	+	1.36391i	0.927522	+	0.373768i	$0.121934\pi$
$79$	3.45080e6	+	5.97696e6i	0.787454	+	1.36391i	−0.140069	+	0.990142i	$0.544732\pi$
$80$	−868929.	+	1.50503e6i	−0.189745	+	0.328647i
$81$	2.97358e6	−	5.15039e6i	0.621702	−	1.07682i
$82$	1.26743e6	+	2.19525e6i	0.253849	+	0.439679i
$83$	−9.01927e6			−1.73140			−0.865701	−	0.500562i	$-0.833127\pi$
$83$	−9.01927e6			−1.73140			−0.865701	+	0.500562i	$0.833127\pi$
$84$	3.01395e6	−	1.60661e6i	0.554828	−	0.295755i
$85$	−3.00180e6			−0.530170
$86$	−126497.	−	219099.i	−0.0214455	−	0.0371446i
$87$	−90009.8	+	155902.i	−0.0146545	+	0.0253824i
$88$	2.01955e6	−	3.49796e6i	0.315911	−	0.547175i
$89$	3.50739e6	+	6.07498e6i	0.527374	+	0.913439i	0.999491	+	0.0319032i	$0.0101568\pi$
$89$	3.50739e6	+	6.07498e6i	0.527374	+	0.913439i	−0.472116	+	0.881536i	$0.656510\pi$
$90$	−4.31453e6			−0.623856
$91$	−206348.	+	6.09255e6i	−0.0287049	+	0.847528i
$92$	772515.			0.103431
$93$	3.48499e6	+	6.03617e6i	0.449273	+	0.778164i
$94$	3.22621e6	−	5.58796e6i	0.400632	−	0.693915i
$95$	5.56852e6	−	9.64496e6i	0.666357	−	1.15416i
$96$	963475.	+	1.66879e6i	0.111145	+	0.192509i
$97$	8.60029e6			0.956779			0.478390	−	0.878148i	$-0.341221\pi$
$97$	8.60029e6			0.956779			0.478390	+	0.878148i	$0.341221\pi$
$98$	−2.90058e6	−	5.91548e6i	−0.311310	−	0.634891i
$99$	1.00278e7			1.03868
$100$	−3.26048e6	−	5.64732e6i	−0.326048	−	0.564732i
$101$	2.95178e6	−	5.11262e6i	0.285075	−	0.493764i	−0.687553	−	0.726134i	$-0.741315\pi$
$101$	2.95178e6	−	5.11262e6i	0.285075	−	0.493764i	0.972627	+	0.232371i	$0.0746483\pi$
$102$	−1.66421e6	+	2.88249e6i	−0.155277	+	0.268948i
$103$	−3.68525e6	−	6.38303e6i	−0.332305	−	0.575568i	0.650659	−	0.759370i	$-0.274493\pi$
$103$	−3.68525e6	−	6.38303e6i	−0.332305	−	0.575568i	−0.982963	+	0.183802i	$0.941159\pi$
$104$	−3.43934e6			−0.299818
$105$	−766427.	+	2.26292e7i	−0.0646112	+	1.90768i
$106$	−3.83463e6			−0.312718
$107$	−3.30235e6	−	5.71983e6i	−0.260603	−	0.451378i	0.705799	−	0.708412i	$-0.250588\pi$
$107$	−3.30235e6	−	5.71983e6i	−0.260603	−	0.451378i	−0.966402	+	0.257034i	$0.917255\pi$
$108$	1.72348e6	−	2.98515e6i	0.131650	−	0.228025i
$109$	−1.57280e6	+	2.72417e6i	−0.116327	+	0.201484i	−0.918309	−	0.395863i	$-0.870445\pi$
$109$	−1.57280e6	+	2.72417e6i	−0.116327	+	0.201484i	0.801982	+	0.597348i	$0.203779\pi$
$110$	1.33884e7	+	2.31894e7i	0.959080	+	1.66117i
$111$	−2.70361e7			−1.87635
$112$	3.28016e6	−	1.74852e6i	0.220613	−	0.117600i
$113$	2.26100e7			1.47409			0.737047	−	0.675841i	$-0.236220\pi$
$113$	2.26100e7			1.47409			0.737047	+	0.675841i	$0.236220\pi$
$114$	−6.17441e6	−	1.06944e7i	−0.390327	−	0.676066i
$115$	−2.56066e6	+	4.43519e6i	−0.157003	+	0.271938i
$116$	−97960.1	+	169672.i	−0.00582702	+	0.0100927i
$117$	−4.26937e6	−	7.39477e6i	−0.246441	−	0.426849i
$118$	−5.39890e6			−0.302495
$119$	5.44848e6	+	3.39664e6i	0.296388	+	0.184771i
$120$	−1.27745e7			−0.674855
$121$	−2.13735e7	−	3.70200e7i	−1.09680	−	1.89971i
$122$	−2.26532e6	+	3.92364e6i	−0.112946	+	0.195628i
$123$	−9.31652e6	+	1.61367e7i	−0.451425	+	0.781891i
$124$	3.79280e6	+	6.56933e6i	0.178642	+	0.309418i
$125$	1.00831e7			0.461751
$126$	7.83118e6	+	4.88203e6i	0.348763	+	0.217422i
$127$	−1.76143e7			−0.763047			−0.381524	−	0.924359i	$-0.624601\pi$
$127$	−1.76143e7			−0.763047			−0.381524	+	0.924359i	$0.624601\pi$
$128$	1.04858e6	+	1.81619e6i	0.0441942	+	0.0765466i
$129$	929844.	−	1.61054e6i	0.0381370	−	0.0660552i
$130$	1.14004e7	−	1.97460e7i	0.455111	−	0.788276i
$131$	−2.41997e6	−	4.19152e6i	−0.0940505	−	0.162900i	0.815161	−	0.579234i	$-0.196648\pi$
$131$	−2.41997e6	−	4.19152e6i	−0.0940505	−	0.162900i	−0.909212	+	0.416334i	$0.863315\pi$
$132$	2.96903e7			1.12359
$133$	−2.10209e7	+	1.12053e7i	−0.774764	+	0.412994i
$134$	−9.47758e6			−0.340276
$135$	1.14256e7	+	1.97898e7i	0.399679	+	0.692265i
$136$	−1.81120e6	+	3.13710e6i	−0.0617420	+	0.106940i
$137$	2.73018e7	−	4.72881e7i	0.907130	−	1.57120i	0.0890984	−	0.996023i	$-0.471601\pi$
$137$	2.73018e7	−	4.72881e7i	0.907130	−	1.57120i	0.818032	−	0.575173i	$-0.195065\pi$
$138$	2.83927e6	+	4.91777e6i	0.0919667	+	0.159291i
$139$	5.28540e6			0.166927			0.0834633	−	0.996511i	$-0.473402\pi$
$139$	5.28540e6			0.166927			0.0834633	+	0.996511i	$0.473402\pi$
$140$	−834123.	+	2.46280e7i	−0.0256911	+	0.758543i
$141$	4.74300e7			1.42491
$142$	1.84694e7	+	3.19900e7i	0.541308	+	0.937572i
$143$	−2.64966e7	+	4.58934e7i	−0.757728	+	1.31242i
$144$	−2.60327e6	+	4.50899e6i	−0.0726524	+	0.125838i
$145$	−649417.	−	1.12482e6i	−0.0176903	−	0.0306405i
$146$	−2.43840e7			−0.648441
$147$	2.69968e7	−	4.02064e7i	0.700974	−	1.04396i
$148$	−2.94241e7			−0.746083
$149$	1.29671e7	+	2.24596e7i	0.321136	+	0.556225i	0.980723	−	0.195404i	$-0.0626019\pi$
$149$	1.29671e7	+	2.24596e7i	0.321136	+	0.556225i	−0.659586	+	0.751629i	$0.729269\pi$
$150$	2.39669e7	−	4.15119e7i	0.579820	−	1.00428i
$151$	2.29593e7	−	3.97666e7i	0.542673	−	0.939938i	−0.456076	−	0.889941i	$-0.650745\pi$
$151$	2.29593e7	−	3.97666e7i	0.542673	−	0.939938i	0.998749	−	0.0499970i	$-0.0159212\pi$
$152$	−6.71978e6	−	1.16390e7i	−0.155204	−	0.268821i
$153$	−8.99324e6			−0.203000
$154$	1.93865e6	−	5.72399e7i	0.0427738	−	1.26292i
$155$	−5.02881e7			−1.08469
$156$	−1.26408e7	−	2.18945e7i	−0.266587	−	0.461743i
$157$	−3.90042e6	+	6.75572e6i	−0.0804381	+	0.139323i	−0.903438	−	0.428718i	$-0.858965\pi$
$157$	−3.90042e6	+	6.75572e6i	−0.0804381	+	0.139323i	0.823000	+	0.568041i	$0.192299\pi$
$158$	−2.76064e7	+	4.78157e7i	−0.556814	+	0.964430i
$159$	−1.40936e7	−	2.44109e7i	−0.278057	−	0.481608i
$160$	−1.39029e7			−0.268339
$161$	9.66634e6	−	5.15272e6i	0.182546	−	0.0973073i
$162$	4.75773e7			0.879219
$163$	3.28712e7	+	5.69346e7i	0.594510	+	1.02972i	0.993616	+	0.112817i	$0.0359873\pi$
$163$	3.28712e7	+	5.69346e7i	0.594510	+	1.02972i	−0.399106	+	0.916905i	$0.630679\pi$
$164$	−1.01394e7	+	1.75620e7i	−0.179498	+	0.310900i
$165$	−9.84146e7	+	1.70459e8i	−1.70556	+	2.95411i
$166$	−3.60771e7	−	6.24873e7i	−0.612143	−	1.06026i
$167$	2.42648e7			0.403152			0.201576	−	0.979473i	$-0.435394\pi$
$167$	2.42648e7			0.403152			0.201576	+	0.979473i	$0.435394\pi$
$168$	2.31867e7	+	1.44548e7i	0.377274	+	0.235196i
$169$	−1.76243e7			−0.280872
$170$	−1.20072e7	−	2.07971e7i	−0.187444	−	0.324662i
$171$	1.66830e7	−	2.88958e7i	0.255145	−	0.441925i
$172$	1.01197e6	−	1.75279e6i	0.0151642	−	0.0262652i
$173$	1.73925e7	+	3.01246e7i	0.255388	+	0.442344i	0.965001	−	0.262247i	$-0.0844636\pi$
$173$	1.73925e7	+	3.01246e7i	0.255388	+	0.442344i	−0.709613	+	0.704592i	$0.751130\pi$
$174$	−1.44016e6			−0.0207247
$175$	−7.84658e7	−	4.89163e7i	−1.10674	−	0.689954i
$176$	3.23128e7			0.446766
$177$	−1.98429e7	−	3.43690e7i	−0.268967	−	0.465865i
$178$	−2.80591e7	+	4.85998e7i	−0.372910	+	0.645899i
$179$	3.19751e7	−	5.53825e7i	0.416703	−	0.721751i	−0.578903	−	0.815397i	$-0.696519\pi$
$179$	3.19751e7	−	5.53825e7i	0.416703	−	0.721751i	0.995606	+	0.0936461i	$0.0298522\pi$
$180$	−1.72581e7	−	2.98919e7i	−0.220567	−	0.382032i
$181$	1.03303e8			1.29491			0.647454	−	0.762104i	$-0.275834\pi$
$181$	1.03303e8			1.29491			0.647454	+	0.762104i	$0.275834\pi$
$182$	−4.30358e7	+	2.29406e7i	−0.529152	+	0.282068i
$183$	−3.33035e7			−0.401708
$184$	3.09006e6	+	5.35214e6i	0.0365683	+	0.0633381i
$185$	9.75321e7	−	1.68931e8i	1.13252	−	1.96159i
$186$	−2.78799e7	+	4.82894e7i	−0.317684	+	0.550245i
$187$	2.79069e7	+	4.83362e7i	0.312080	+	0.540539i
$188$	5.16194e7			0.566579
$189$	1.65444e6	−	4.88483e7i	0.0178252	−	0.526300i
$190$	8.90963e7			0.942371
$191$	4.27228e7	+	7.39981e7i	0.443652	+	0.768429i	0.997957	−	0.0638852i	$-0.0203491\pi$
$191$	4.27228e7	+	7.39981e7i	0.443652	+	0.768429i	−0.554305	+	0.832314i	$0.687016\pi$
$192$	−7.70780e6	+	1.33503e7i	−0.0785916	+	0.136125i
$193$	−2.24321e7	+	3.88535e7i	−0.224605	+	0.389027i	−0.956201	−	0.292712i	$-0.905442\pi$
$193$	−2.24321e7	+	3.88535e7i	−0.224605	+	0.389027i	0.731596	+	0.681738i	$0.238776\pi$
$194$	3.44011e7	+	5.95845e7i	0.338273	+	0.585905i
$195$	1.67602e8			1.61867
$196$	2.93814e7	−	4.37577e7i	0.278725	−	0.415105i
$197$	−1.97306e8			−1.83869			−0.919345	−	0.393452i	$-0.871281\pi$
$197$	−1.97306e8			−1.83869			−0.919345	+	0.393452i	$0.871281\pi$
$198$	4.01110e7	+	6.94743e7i	0.367228	+	0.636057i
$199$	−2.70550e7	+	4.68606e7i	−0.243367	+	0.421523i	−0.961671	−	0.274205i	$-0.911585\pi$
$199$	−2.70550e7	+	4.68606e7i	−0.243367	+	0.421523i	0.718304	+	0.695729i	$0.244919\pi$
$200$	2.60839e7	−	4.51786e7i	0.230551	−	0.399326i
$201$	−3.48336e7	−	6.03335e7i	−0.302560	−	0.524050i
$202$	4.72284e7			0.403156
$203$	−94036.2	+	2.77647e6i	−0.000788967	+	0.0232947i
$204$	−2.66273e7			−0.219595
$205$	−6.72183e7	−	1.16426e8i	−0.544940	−	0.943864i
$206$	2.94820e7	−	5.10643e7i	0.234975	−	0.406988i
$207$	−7.67160e6	+	1.32876e7i	−0.0601159	+	0.104124i
$208$	−1.37574e7	−	2.38284e7i	−0.106002	−	0.183600i
$209$	−2.07076e8			−1.56898
$210$	−1.59845e8	+	8.52068e7i	−1.19106	+	0.634902i
$211$	9.24251e7			0.677331			0.338666	−	0.940907i	$-0.390024\pi$
$211$	9.24251e7			0.677331			0.338666	+	0.940907i	$0.390024\pi$
$212$	−1.53385e7	−	2.65671e7i	−0.110562	−	0.191500i
$213$	−1.35764e8	+	2.35150e8i	−0.962621	+	1.66731i
$214$	2.64188e7	−	4.57586e7i	0.184274	−	0.319172i
$215$	6.70879e6	+	1.16200e7i	0.0460373	+	0.0797389i
$216$	2.75756e7			0.186182
$217$	9.12765e7	+	5.69026e7i	0.606387	+	0.378027i
$218$	−2.51648e7			−0.164511
$219$	−8.96202e7	−	1.55227e8i	−0.576569	−	0.998648i
$220$	−1.07107e8	+	1.85515e8i	−0.678172	+	1.17463i
$221$	2.37630e7	−	4.11588e7i	0.148091	−	0.256501i
$222$	−1.08144e8	−	1.87311e8i	−0.663389	−	1.14902i
$223$	−3.72959e7			−0.225213			−0.112607	−	0.993640i	$-0.535920\pi$
$223$	−3.72959e7			−0.225213			−0.112607	+	0.993640i	$0.535920\pi$
$224$	2.52347e7	+	1.57316e7i	0.150013	+	0.0935198i
$225$	1.29515e8			0.758022
$226$	9.04398e7	+	1.56646e8i	0.521171	+	0.902695i
$227$	5.71956e7	−	9.90658e7i	0.324543	−	0.562125i	−0.656877	−	0.753998i	$-0.728123\pi$
$227$	5.71956e7	−	9.90658e7i	0.324543	−	0.562125i	0.981420	+	0.191873i	$0.0614561\pi$
$228$	4.93953e7	−	8.55552e7i	0.276003	−	0.478051i
$229$	4.17127e7	+	7.22486e7i	0.229533	+	0.397562i	0.957670	−	0.287869i	$-0.0929469\pi$
$229$	4.17127e7	+	7.22486e7i	0.229533	+	0.397562i	−0.728137	+	0.685432i	$0.759614\pi$
$230$	−4.09705e7			−0.222036
$231$	3.71510e8	−	1.98036e8i	1.98303	−	1.05707i
$232$	−1.56736e6			−0.00824065
$233$	1.52762e7	+	2.64592e7i	0.0791170	+	0.137035i	0.902869	−	0.429915i	$-0.141457\pi$
$233$	1.52762e7	+	2.64592e7i	0.0791170	+	0.137035i	−0.823752	+	0.566950i	$0.808123\pi$
$234$	3.41550e7	−	5.91581e7i	0.174260	−	0.301828i
$235$	−1.71103e8	+	2.96359e8i	−0.860042	+	1.48964i
$236$	−2.15956e7	−	3.74047e7i	−0.106948	−	0.185240i
$237$	−4.05854e8			−1.98039
$238$	−1.73865e6	+	5.13347e7i	−0.00835975	+	0.246827i
$239$	5.35396e6			0.0253678			0.0126839	−	0.999920i	$-0.495962\pi$
$239$	5.35396e6			0.0253678			0.0126839	+	0.999920i	$0.495962\pi$
$240$	−5.10981e7	−	8.85045e7i	−0.238597	−	0.413263i
$241$	9.27620e7	−	1.60668e8i	0.426884	−	0.739385i	−0.569710	−	0.821846i	$-0.692944\pi$
$241$	9.27620e7	−	1.60668e8i	0.426884	−	0.739385i	0.996594	+	0.0824604i	$0.0262778\pi$
$242$	1.70988e8	−	2.96160e8i	0.775555	−	1.34330i
$243$	1.15969e8	+	2.00865e8i	0.518467	+	0.898012i
$244$	−3.62451e7			−0.159729
$245$	1.53833e8	+	3.13729e8i	0.668294	+	1.36293i
$246$	−1.49064e8			−0.638412
$247$	8.81638e7	+	1.52704e8i	0.372264	+	0.644780i
$248$	−3.03424e7	+	5.25546e7i	−0.126319	+	0.218791i
$249$	2.65193e8	−	4.59327e8i	1.08859	−	1.88549i
$250$	4.03323e7	+	6.98576e7i	0.163254	+	0.282764i
$251$	1.50737e6			0.00601673			0.00300837	−	0.999995i	$-0.499042\pi$
$251$	1.50737e6			0.00601673			0.00300837	+	0.999995i	$0.499042\pi$
$252$	−2.49899e6	+	7.37842e7i	−0.00983700	+	0.290443i
$253$	9.52229e7			0.369675
$254$	−7.04571e7	−	1.22035e8i	−0.269778	−	0.467269i
$255$	8.82617e7	−	1.52874e8i	0.333335	−	0.577354i
$256$	−8.38861e6	+	1.45295e7i	−0.0312500	+	0.0541266i
$257$	1.58688e8	+	2.74855e8i	0.583145	+	1.01004i	0.995104	+	0.0988349i	$0.0315116\pi$
$257$	1.58688e8	+	2.74855e8i	0.583145	+	1.01004i	−0.411958	+	0.911203i	$0.635155\pi$
$258$	1.48775e7			0.0539338
$259$	−3.68178e8	+	1.96260e8i	−1.31677	+	0.701913i
$260$	1.82406e8			0.643625
$261$	−1.94562e6	−	3.36992e6i	−0.00677355	−	0.0117321i
$262$	1.93598e7	−	3.35321e7i	0.0665037	−	0.115188i
$263$	−6.83571e7	+	1.18398e8i	−0.231707	+	0.401328i	−0.958310	−	0.285729i	$-0.907764\pi$
$263$	−6.83571e7	+	1.18398e8i	−0.231707	+	0.401328i	0.726604	+	0.687057i	$0.241098\pi$
$264$	1.18761e8	+	2.05701e8i	0.397248	+	0.688053i
$265$	2.03370e8			0.671316
$266$	−1.61716e8	−	1.00815e8i	−0.526827	−	0.328429i
$267$	−4.12510e8			−1.32631
$268$	−3.79103e7	−	6.56626e7i	−0.120306	−	0.208375i
$269$	−9.36123e7	+	1.62141e8i	−0.293224	+	0.507879i	−0.974570	−	0.224082i	$-0.928062\pi$
$269$	−9.36123e7	+	1.62141e8i	−0.293224	+	0.507879i	0.681346	+	0.731961i	$0.261395\pi$
$270$	−9.14050e7	+	1.58318e8i	−0.282616	+	0.489505i
$271$	−2.27535e8	−	3.94103e8i	−0.694475	−	1.20287i	−0.970357	−	0.241674i	$-0.922303\pi$
$271$	−2.27535e8	−	3.94103e8i	−0.694475	−	1.20287i	0.275882	−	0.961191i	$-0.411030\pi$
$272$	−2.89793e7			−0.0873164
$273$	−3.04210e8	−	1.89648e8i	−0.904908	−	0.564128i
$274$	4.36829e8			1.28288
$275$	−4.01899e8	−	6.96109e8i	−1.16534	−	2.01843i
$276$	−2.27142e7	+	3.93421e7i	−0.0650302	+	0.112636i
$277$	2.48231e8	−	4.29950e8i	0.701742	−	1.21545i	−0.266112	−	0.963942i	$-0.585739\pi$
$277$	2.48231e8	−	4.29950e8i	0.701742	−	1.21545i	0.967854	−	0.251511i	$-0.0809275\pi$
$278$	2.11416e7	+	3.66183e7i	0.0590175	+	0.102221i
$279$	−1.50661e8			−0.415322
$280$	−1.73964e8	+	9.27329e7i	−0.473594	+	0.252453i
$281$	−2.68528e7			−0.0721968			−0.0360984	−	0.999348i	$-0.511493\pi$
$281$	−2.68528e7			−0.0721968			−0.0360984	+	0.999348i	$0.511493\pi$
$282$	1.89720e8	+	3.28605e8i	0.503781	+	0.872574i
$283$	1.68539e8	−	2.91918e8i	0.442026	−	0.765612i	−0.555813	−	0.831307i	$-0.687593\pi$
$283$	1.68539e8	−	2.91918e8i	0.442026	−	0.765612i	0.997840	+	0.0656950i	$0.0209264\pi$
$284$	−1.47755e8	+	2.55920e8i	−0.382762	+	0.662964i
$285$	3.27461e8	+	5.67180e8i	0.837921	+	1.45132i
$286$	−4.23945e8			−1.07159
$287$	−9.73327e6	+	2.87381e8i	−0.0243037	+	0.717581i
$288$	−4.16523e7			−0.102746
$289$	1.80141e8	+	3.12014e8i	0.439007	+	0.760382i
$290$	5.19534e6	−	8.99859e6i	0.0125089	−	0.0216661i
$291$	−2.52874e8	+	4.37990e8i	−0.601559	+	1.04193i
$292$	−9.75361e7	−	1.68938e8i	−0.229259	−	0.397087i
$293$	−5.65397e8			−1.31316			−0.656579	−	0.754258i	$-0.727997\pi$
$293$	−5.65397e8			−1.31316			−0.656579	+	0.754258i	$0.727997\pi$
$294$	3.86545e8	+	2.62138e7i	0.887125	+	0.0601609i
$295$	2.86332e8			0.649371
$296$	−1.17696e8	−	2.03856e8i	−0.263780	−	0.456881i
$297$	2.12442e8	−	3.67960e8i	0.470536	−	0.814992i
$298$	−1.03736e8	+	1.79677e8i	−0.227078	+	0.393310i
$299$	−4.05417e7	−	7.02202e7i	−0.0877107	−	0.151919i
$300$	3.83471e8			0.819989
$301$	971439.	−	2.86823e7i	0.00205321	−	0.0606221i
$302$	3.67348e8			0.767456
$303$	1.73582e8	+	3.00652e8i	0.358471	+	0.620891i
$304$	5.37583e7	−	9.31120e7i	0.109746	−	0.190085i
$305$	1.20142e8	−	2.08091e8i	0.242462	−	0.419957i
$306$	−3.59730e7	−	6.23070e7i	−0.0717714	−	0.124312i
$307$	7.13941e8			1.40824			0.704122	−	0.710079i	$-0.251341\pi$
$307$	7.13941e8			1.40824			0.704122	+	0.710079i	$0.251341\pi$
$308$	4.04324e8	−	2.15528e8i	0.788501	−	0.420317i
$309$	4.33428e8			0.835723
$310$	−2.01152e8	−	3.48406e8i	−0.383494	−	0.664232i
$311$	−2.28426e8	+	3.95646e8i	−0.430611	+	0.745840i	−0.996926	−	0.0783491i	$-0.975035\pi$
$311$	−2.28426e8	+	3.95646e8i	−0.430611	+	0.745840i	0.566315	+	0.824189i	$0.308368\pi$
$312$	1.01127e8	−	1.75156e8i	0.188506	−	0.326501i
$313$	−4.80069e8	−	8.31504e8i	−0.884909	−	1.53271i	−0.845818	−	0.533472i	$-0.820887\pi$
$313$	−4.80069e8	−	8.31504e8i	−0.884909	−	1.53271i	−0.0390914	−	0.999236i	$-0.512446\pi$
$314$	−6.24066e7			−0.113757
$315$	−4.15329e8	−	2.58920e8i	−0.748695	−	0.466744i
$316$	−4.41702e8			−0.787454
$317$	2.87942e8	+	4.98730e8i	0.507688	+	0.879342i	0.999960	+	0.00890063i	$0.00283320\pi$
$317$	2.87942e8	+	4.98730e8i	0.507688	+	0.879342i	−0.492272	+	0.870441i	$0.663833\pi$
$318$	1.12749e8	−	1.95287e8i	0.196616	−	0.340549i
$319$	−1.20749e7	+	2.09144e7i	−0.0208265	+	0.0360726i
$320$	−5.56115e7	−	9.63219e7i	−0.0948723	−	0.164324i
$321$	3.88394e8			0.655398
$322$	7.43644e7	+	4.63595e7i	0.124128	+	0.0773825i
$323$	1.85713e8			0.306643
$324$	1.90309e8	+	3.29625e8i	0.310851	+	0.538409i
$325$	−3.42221e8	+	5.92744e8i	−0.552987	+	0.957802i
$326$	−2.62970e8	+	4.55477e8i	−0.420382	+	0.728123i
$327$	−9.24898e7	−	1.60197e8i	−0.146277	−	0.253359i
$328$	−1.62231e8			−0.253849
$329$	6.45904e8	−	3.44304e8i	0.999960	−	0.533036i
$330$	−1.57463e9			−2.41202
$331$	2.23337e8	+	3.86831e8i	0.338503	+	0.586304i	0.984151	−	0.177330i	$-0.0567461\pi$
$331$	2.23337e8	+	3.86831e8i	0.338503	+	0.586304i	−0.645648	+	0.763635i	$0.723413\pi$
$332$	2.88616e8	−	4.99898e8i	0.432850	−	0.749719i
$333$	2.92201e8	−	5.06108e8i	0.433638	−	0.751083i
$334$	9.70591e7	+	1.68111e8i	0.142536	+	0.246879i
$335$	5.02646e8			0.730475
$336$	−7.39905e6	+	2.18461e8i	−0.0106412	+	0.314186i
$337$	−1.08980e9			−1.55111			−0.775555	−	0.631280i	$-0.782530\pi$
$337$	−1.08980e9			−1.55111			−0.775555	+	0.631280i	$0.782530\pi$
$338$	−7.04971e7	−	1.22105e8i	−0.0993032	−	0.171998i
$339$	−6.64799e8	+	1.15147e9i	−0.926811	+	1.60528i
$340$	9.60576e7	−	1.66377e8i	0.132543	−	0.229570i
$341$	4.67515e8	+	8.09759e8i	0.638491	+	1.10590i
$342$	2.66928e8			0.360830
$343$	7.57773e7	−	7.43508e8i	0.101393	−	0.994846i
$344$	1.61916e7			0.0214455
$345$	−1.50581e8	−	2.60815e8i	−0.197426	−	0.341952i
$346$	−1.39140e8	+	2.40997e8i	−0.180586	+	0.312785i
$347$	−5.50402e8	+	9.53325e8i	−0.707175	+	1.22486i	0.258725	+	0.965951i	$0.416698\pi$
$347$	−5.50402e8	+	9.53325e8i	−0.707175	+	1.22486i	−0.965901	+	0.258913i	$0.916636\pi$
$348$	−5.76063e6	−	9.97770e6i	−0.00732727	−	0.0126912i
$349$	−9.17714e8			−1.15563			−0.577814	−	0.816168i	$-0.696094\pi$
$349$	−9.17714e8			−1.15563			−0.577814	+	0.816168i	$0.696094\pi$
$350$	2.50390e7	−	7.39292e8i	0.0312161	−	0.921675i
$351$	−3.61793e8			−0.446566
$352$	1.29251e8	+	2.23870e8i	0.157956	+	0.273587i
$353$	−1.06680e8	+	1.84776e8i	−0.129084	+	0.223581i	−0.923322	−	0.384027i	$-0.874537\pi$
$353$	−1.06680e8	+	1.84776e8i	−0.129084	+	0.223581i	0.794238	+	0.607607i	$0.207870\pi$
$354$	1.58743e8	−	2.74952e8i	0.190189	−	0.329416i
$355$	−9.79530e8	−	1.69660e9i	−1.16203	−	2.01270i
$356$	−4.48946e8			−0.527374
$357$	−3.33183e8	+	1.77606e8i	−0.387565	+	0.206594i
$358$	5.11602e8			0.589307
$359$	−5.94524e7	−	1.02975e8i	−0.0678171	−	0.117463i	0.830123	−	0.557580i	$-0.188270\pi$
$359$	−5.94524e7	−	1.02975e8i	−0.0678171	−	0.117463i	−0.897940	+	0.440118i	$0.854937\pi$
$360$	1.38065e8	−	2.39135e8i	0.155964	−	0.270138i
$361$	1.02427e8	−	1.77409e8i	0.114588	−	0.198472i
$362$	4.13213e8	+	7.15706e8i	0.457819	+	0.792966i
$363$	2.51378e9			2.75838
$364$	−3.31080e8	−	2.06399e8i	−0.359814	−	0.224312i
$365$	1.29321e9			1.39202
$366$	−1.33214e8	−	2.30733e8i	−0.142025	−	0.245995i
$367$	−1.37498e8	+	2.38153e8i	−0.145199	+	0.251492i	−0.929447	−	0.368955i	$-0.879716\pi$
$367$	−1.37498e8	+	2.38153e8i	−0.145199	+	0.251492i	0.784248	+	0.620447i	$0.213049\pi$
$368$	−2.47205e7	+	4.28171e7i	−0.0258577	+	0.0447868i
$369$	−2.01383e8	−	3.48805e8i	−0.208656	−	0.361402i
$370$	1.56051e9			1.60163
$371$	−3.69132e8	−	2.30120e8i	−0.375295	−	0.233962i
$372$	−4.46078e8			−0.449273
$373$	−4.47876e8	−	7.75745e8i	−0.446866	−	0.773995i	0.551314	−	0.834298i	$-0.314127\pi$
$373$	−4.47876e8	−	7.75745e8i	−0.446866	−	0.773995i	−0.998180	+	0.0603032i	$0.980793\pi$
$374$	−2.23255e8	+	3.86690e8i	−0.220674	+	0.382219i
$375$	−2.96472e8	+	5.13505e8i	−0.290318	+	0.502846i
$376$	2.06478e8	+	3.57630e8i	0.200316	+	0.346957i
$377$	2.05638e7			0.0197656
$378$	3.45049e8	−	1.83931e8i	0.328594	−	0.175160i
$379$	1.69750e9			1.60167			0.800833	−	0.598887i	$-0.204390\pi$
$379$	1.69750e9			1.60167			0.800833	+	0.598887i	$0.204390\pi$
$380$	3.56385e8	+	6.17277e8i	0.333179	+	0.577082i
$381$	5.17911e8	−	8.97048e8i	0.479753	−	0.830956i
$382$	−3.41782e8	+	5.91984e8i	−0.313710	+	0.543361i
$383$	−6.24533e8	−	1.08172e9i	−0.568014	−	0.983830i	−0.996762	−	0.0804057i	$-0.974378\pi$
$383$	−6.24533e8	−	1.08172e9i	−0.568014	−	0.983830i	0.428748	−	0.903424i	$-0.358955\pi$
$384$	−1.23325e8			−0.111145
$385$	−1.02817e8	+	3.03573e9i	−0.0918231	+	2.71113i
$386$	−3.58913e8			−0.317639
$387$	2.00992e7	+	3.48128e7i	0.0176275	+	0.0305317i
$388$	−2.75209e8	+	4.76676e8i	−0.239195	+	0.414298i
$389$	−6.80349e8	+	1.17840e9i	−0.586014	+	1.01501i	0.408734	+	0.912653i	$0.365970\pi$
$389$	−6.80349e8	+	1.17840e9i	−0.586014	+	1.01501i	−0.994748	+	0.102352i	$0.967363\pi$
$390$	6.70409e8	+	1.16118e9i	0.572287	+	0.991230i
$391$	−8.53992e7			−0.0722496
$392$	4.20688e8	+	2.85292e7i	0.352743	+	0.0239215i
$393$	2.84617e8			0.236531
$394$	−7.89224e8	−	1.36698e9i	−0.650075	−	1.12596i
$395$	1.46411e9	−	2.53592e9i	1.19532	−	2.07036i
$396$	−3.20888e8	+	5.55795e8i	−0.259669	+	0.449760i
$397$	−1.03304e9	−	1.78928e9i	−0.828610	−	1.43519i	−0.899129	−	0.437684i	$-0.855799\pi$
$397$	−1.03304e9	−	1.78928e9i	−0.828610	−	1.43519i	0.0705188	−	0.997510i	$-0.477535\pi$
$398$	−4.32879e8			−0.344172
$399$	4.74167e7	−	1.40001e9i	0.0373703	−	1.10338i
$400$	4.17342e8			0.326048
$401$	7.29599e7	+	1.26370e8i	0.0565040	+	0.0978677i	0.892894	−	0.450267i	$-0.148671\pi$
$401$	7.29599e7	+	1.26370e8i	0.0565040	+	0.0978677i	−0.836390	+	0.548135i	$0.815338\pi$
$402$	2.78669e8	−	4.82668e8i	0.213942	−	0.370559i
$403$	3.98094e8	−	6.89519e8i	0.302983	−	0.524781i
$404$	1.88914e8	+	3.27208e8i	0.142537	+	0.246882i
$405$	−2.52327e9			−1.88743
$406$	−1.96121e7	+	1.04544e7i	−0.0145440	+	0.00775278i
$407$	−3.62692e9			−2.66660
$408$	−1.06509e8	−	1.84480e8i	−0.0776385	−	0.134474i
$409$	−5.95951e8	+	1.03222e9i	−0.430704	+	0.746001i	−0.996934	−	0.0782460i	$-0.975068\pi$
$409$	−5.95951e8	+	1.03222e9i	−0.430704	+	0.746001i	0.566230	+	0.824247i	$0.308401\pi$
$410$	5.37746e8	−	9.31404e8i	0.385331	−	0.667413i
$411$	1.60551e9	+	2.78082e9i	1.14069	+	1.97572i
$412$	4.71712e8			0.332305
$413$	−5.19713e8	−	3.23994e8i	−0.363027	−	0.226314i
$414$	−1.22746e8			−0.0850168
$415$	1.91336e9	+	3.31403e9i	1.31410	+	2.27608i
$416$	1.10059e8	−	1.90627e8i	0.0749546	−	0.129825i
$417$	−1.55406e8	+	2.69171e8i	−0.104952	+	0.181783i
$418$	−8.28304e8	−	1.43467e9i	−0.554719	−	0.960801i
$419$	5.89725e8			0.391652			0.195826	−	0.980639i	$-0.437261\pi$
$419$	5.89725e8			0.391652			0.195826	+	0.980639i	$0.437261\pi$
$420$	−1.22971e9	−	7.66614e8i	−0.809899	−	0.504899i
$421$	2.35971e9			1.54124			0.770622	−	0.637292i	$-0.219946\pi$
$421$	2.35971e9			1.54124			0.770622	+	0.637292i	$0.219946\pi$
$422$	3.69700e8	+	6.40340e8i	0.239473	+	0.414779i
$423$	−5.12616e8	+	8.87877e8i	−0.329307	+	0.570376i
$424$	1.22708e8	−	2.12537e8i	0.0781794	−	0.135411i
$425$	3.60437e8	+	6.24295e8i	0.227755	+	0.394483i
$426$	−2.17222e9			−1.36135
$427$	−4.53528e8	+	2.41757e8i	−0.281907	+	0.150273i
$428$	4.22700e8			0.260603
$429$	−1.55815e9	−	2.69880e9i	−0.952817	−	1.65033i
$430$	−5.36703e7	+	9.29597e7i	−0.0325533	+	0.0563839i
$431$	1.29323e9	−	2.23994e9i	0.778045	−	1.34761i	−0.155022	−	0.987911i	$-0.549545\pi$
$431$	1.29323e9	−	2.23994e9i	0.778045	−	1.34761i	0.933067	−	0.359703i	$-0.117122\pi$
$432$	1.10303e8	+	1.91050e8i	0.0658252	+	0.114013i
$433$	−1.48937e9			−0.881649			−0.440825	−	0.897593i	$-0.645314\pi$
$433$	−1.48937e9			−0.881649			−0.440825	+	0.897593i	$0.645314\pi$
$434$	−2.91270e7	+	8.59992e8i	−0.0171034	+	0.504987i
$435$	7.63790e7			0.0444899
$436$	−1.00659e8	−	1.74347e8i	−0.0581635	−	0.100742i
$437$	1.58421e8	−	2.74393e8i	0.0908086	−	0.157285i
$438$	7.16962e8	−	1.24181e9i	0.407696	−	0.706150i
$439$	1.33593e9	+	2.31390e9i	0.753629	+	1.30532i	0.946053	+	0.324012i	$0.105032\pi$
$439$	1.33593e9	+	2.31390e9i	0.753629	+	1.30532i	−0.192424	+	0.981312i	$0.561635\pi$
$440$	−1.71372e9			−0.959080
$441$	4.60875e8	+	9.39916e8i	0.255887	+	0.521860i
$442$	3.80209e8			0.209433
$443$	−6.94903e7	−	1.20361e8i	−0.0379762	−	0.0657767i	0.846413	−	0.532528i	$-0.178758\pi$
$443$	−6.94903e7	−	1.20361e8i	−0.0379762	−	0.0657767i	−0.884389	+	0.466751i	$0.845424\pi$
$444$	8.65154e8	−	1.49849e9i	0.469087	−	0.812482i
$445$	1.48812e9	−	2.57750e9i	0.800532	−	1.38656i
$446$	−1.49184e8	−	2.58393e8i	−0.0796249	−	0.137914i
$447$	−1.52508e9			−0.807636
$448$	−8.05259e6	+	2.37757e8i	−0.00423119	+	0.124928i
$449$	−9.13167e8			−0.476089			−0.238044	−	0.971254i	$-0.576506\pi$
$449$	−9.13167e8			−0.476089			−0.238044	+	0.971254i	$0.576506\pi$
$450$	5.18061e8	+	8.97308e8i	0.268001	+	0.464192i
$451$	−1.24982e9	+	2.16475e9i	−0.641549	+	1.11120i
$452$	−7.23519e8	+	1.25317e9i	−0.368524	+	0.638301i
$453$	1.35014e9	+	2.33851e9i	0.682393	+	1.18194i
$454$	9.15130e8			0.458973
$455$	2.28241e9	−	1.21666e9i	1.13594	−	0.605521i
$456$	7.90325e8			0.390327
$457$	4.12098e8	+	7.13774e8i	0.201973	+	0.349828i	0.949164	−	0.314782i	$-0.101931\pi$
$457$	4.12098e8	+	7.13774e8i	0.201973	+	0.349828i	−0.747191	+	0.664609i	$0.768598\pi$
$458$	−3.33702e8	+	5.77988e8i	−0.162304	+	0.281119i
$459$	−1.90525e8	+	3.30000e8i	−0.0919620	+	0.159283i
$460$	−1.63882e8	−	2.83852e8i	−0.0785016	−	0.135969i
$461$	1.64108e9			0.780147			0.390073	−	0.920784i	$-0.372450\pi$
$461$	1.64108e9			0.780147			0.390073	+	0.920784i	$0.372450\pi$
$462$	2.85807e9	+	1.78175e9i	1.34842	+	0.840621i
$463$	2.87188e9			1.34472			0.672361	−	0.740224i	$-0.265280\pi$
$463$	2.87188e9			1.34472			0.672361	+	0.740224i	$0.265280\pi$
$464$	−6.26945e6	−	1.08590e7i	−0.00291351	−	0.00504635i
$465$	1.47862e9	−	2.56104e9i	0.681977	−	1.18122i
$466$	−1.22210e8	+	2.11673e8i	−0.0559441	+	0.0968981i
$467$	−1.47195e9	−	2.54949e9i	−0.668782	−	1.15836i	−0.978245	−	0.207453i	$-0.933483\pi$
$467$	−1.47195e9	−	2.54949e9i	−0.668782	−	1.15836i	0.309463	−	0.950911i	$-0.399851\pi$
$468$	5.46480e8			0.246441
$469$	−9.12338e8	−	5.68760e8i	−0.408367	−	0.254580i
$470$	−2.73765e9			−1.21628
$471$	−2.29367e8	−	3.97276e8i	−0.101148	−	0.175194i
$472$	1.72765e8	−	2.99237e8i	0.0756238	−	0.130984i
$473$	1.24740e8	−	2.16055e8i	0.0541989	−	0.0938752i
$474$	−1.62342e9	−	2.81184e9i	−0.700174	−	1.21274i
$475$	−2.67453e9			−1.14504
$476$	−3.62612e8	+	1.93293e8i	−0.154105	+	0.0821471i
$477$	6.09287e8			0.257044
$478$	2.14159e7	+	3.70933e7i	0.00896887	+	0.0155345i
$479$	−4.19445e8	+	7.26500e8i	−0.174382	+	0.302038i	−0.939947	−	0.341320i	$-0.889126\pi$
$479$	−4.19445e8	+	7.26500e8i	−0.174382	+	0.302038i	0.765566	+	0.643358i	$0.222459\pi$
$480$	4.08785e8	−	7.08036e8i	0.168714	−	0.292221i
$481$	1.54418e9	+	2.67460e9i	0.632689	+	1.09585i
$482$	1.48419e9			0.603706
$483$	−2.18043e7	+	6.43786e8i	−0.00880497	+	0.259972i
$484$	2.73581e9			1.09680
$485$	−1.82447e9	−	3.16008e9i	−0.726175	−	1.25777i
$486$	−9.27755e8	+	1.60692e9i	−0.366612	+	0.634990i
$487$	−1.22668e8	+	2.12468e8i	−0.0481261	+	0.0833569i	−0.889085	−	0.457742i	$-0.848658\pi$
$487$	−1.22668e8	+	2.12468e8i	−0.0481261	+	0.0833569i	0.840959	+	0.541099i	$0.181992\pi$
$488$	−1.44980e8	−	2.51113e8i	−0.0564728	−	0.0978138i
$489$	−3.86604e9			−1.49515
$490$	−1.55825e9	+	2.32070e9i	−0.598343	+	0.891113i
$491$	−4.86528e9			−1.85491			−0.927455	−	0.373936i	$-0.878008\pi$
$491$	−4.86528e9			−1.85491			−0.927455	+	0.373936i	$0.878008\pi$
$492$	−5.96257e8	−	1.03275e9i	−0.225713	−	0.390946i
$493$	1.08292e7	−	1.87567e7i	0.00407036	−	0.00705006i
$494$	−7.05310e8	+	1.22163e9i	−0.263230	+	0.455928i
$495$	−2.12730e9	−	3.68459e9i	−0.788333	−	1.36543i
$496$	−4.85479e8			−0.178642
$497$	−1.41837e8	+	4.18782e9i	−0.0518253	+	1.53017i
$498$	4.24308e9			1.53950
$499$	−9.41538e8	−	1.63079e9i	−0.339223	−	0.587552i	0.645063	−	0.764129i	$-0.276831\pi$
$499$	−9.41538e8	−	1.63079e9i	−0.339223	−	0.587552i	−0.984287	+	0.176577i	$0.943498\pi$
$500$	−3.22659e8	+	5.58861e8i	−0.115438	+	0.199944i
$501$	−7.13456e8	+	1.23574e9i	−0.253475	+	0.439031i
$502$	6.02946e6	+	1.04433e7i	0.00212724	+	0.00368448i
$503$	4.05510e9			1.42074			0.710369	−	0.703830i	$-0.248528\pi$
$503$	4.05510e9			1.42074			0.710369	+	0.703830i	$0.248528\pi$
$504$	−5.21188e8	+	2.77823e8i	−0.181337	+	0.0966633i
$505$	−2.50477e9			−0.865462
$506$	3.80892e8	+	6.59724e8i	0.130700	+	0.226379i
$507$	5.18206e8	−	8.97558e8i	0.176593	−	0.305869i
$508$	5.63656e8	−	9.76282e8i	0.190762	−	0.330409i
$509$	2.94236e9	+	5.09632e9i	0.988972	+	1.71295i	0.622745	+	0.782425i	$0.286017\pi$
$509$	2.94236e9	+	5.09632e9i	0.988972	+	1.71295i	0.366227	+	0.930526i	$0.380649\pi$
$510$	1.41219e9			0.471408
$511$	−2.34727e9	−	1.46331e9i	−0.778199	−	0.485137i
$512$	−1.34218e8			−0.0441942
$513$	−7.06872e8	−	1.22434e9i	−0.231169	−	0.400397i
$514$	−1.26950e9	+	2.19884e9i	−0.412346	+	0.714204i
$515$	−1.56358e9	+	2.70821e9i	−0.504424	+	0.873688i
$516$	5.95100e7	+	1.03074e8i	0.0190685	+	0.0330276i
$517$	6.36279e9			2.02503
$518$	−2.83245e9	−	1.76577e9i	−0.895380	−	0.558188i
$519$	−2.04556e9			−0.642282
$520$	7.29624e8	+	1.26375e9i	0.227556	+	0.394138i
$521$	1.82384e9	−	3.15899e9i	0.565009	−	0.978625i	−0.432039	−	0.901855i	$-0.642206\pi$
$521$	1.82384e9	−	3.15899e9i	0.565009	−	0.978625i	0.997049	−	0.0767702i	$-0.0244608\pi$
$522$	1.55650e7	−	2.69593e7i	0.00478963	−	0.00829587i
$523$	−1.17775e9	−	2.03993e9i	−0.359996	−	0.623532i	0.627964	−	0.778243i	$-0.283889\pi$
$523$	−1.17775e9	−	2.03993e9i	−0.359996	−	0.623532i	−0.987960	+	0.154711i	$0.950555\pi$
$524$	3.09757e8			0.0940505
$525$	4.79830e9	−	2.55777e9i	1.44720	−	0.771444i
$526$	−1.09371e9			−0.327683
$527$	−4.19283e8	−	7.26220e8i	−0.124787	−	0.216138i
$528$	−9.50091e8	+	1.64561e9i	−0.280897	+	0.486527i
$529$	1.62956e9	−	2.82249e9i	0.478604	−	0.828967i
$530$	8.13481e8	+	1.40899e9i	0.237346	+	0.411095i
$531$	8.57836e8			0.248641
$532$	5.16049e7	−	1.52366e9i	0.0148594	−	0.438731i
$533$	2.12847e9			0.608867
$534$	−1.65004e9	−	2.85795e9i	−0.468922	−	0.812196i
$535$	−1.40113e9	+	2.42682e9i	−0.395584	+	0.685172i
$536$	3.03283e8	−	5.25301e8i	0.0850689	−	0.147344i
$537$	1.88032e9	+	3.25682e9i	0.523990	+	0.907576i
$538$	−1.49780e9			−0.414682
$539$	3.62165e9	−	5.39373e9i	0.996199	−	1.48364i
$540$	−1.46248e9			−0.399679
$541$	2.74393e8	+	4.75263e8i	0.0745045	+	0.129046i	0.900871	−	0.434088i	$-0.142929\pi$
$541$	2.74393e8	+	4.75263e8i	0.0745045	+	0.129046i	−0.826366	+	0.563133i	$0.809596\pi$
$542$	1.82028e9	−	3.15282e9i	0.491068	−	0.850555i
$543$	−3.03742e9	+	5.26096e9i	−0.814151	+	1.41015i
$544$	−1.15917e8	−	2.00774e8i	−0.0308710	−	0.0534702i
$545$	1.33462e9			0.353159
$546$	9.70758e7	−	2.86622e9i	0.0255233	−	0.753590i
$547$	1.19987e8			0.0313457			0.0156729	−	0.999877i	$-0.495011\pi$
$547$	1.19987e8			0.0313457			0.0156729	+	0.999877i	$0.495011\pi$
$548$	1.74732e9	+	3.02644e9i	0.453565	+	0.785598i
$549$	3.59938e8	−	6.23431e8i	0.0928378	−	0.160800i
$550$	3.21519e9	−	5.56887e9i	0.824019	−	1.42724i
$551$	4.01777e7	+	6.95897e7i	0.0102318	+	0.0177221i
$552$	−3.63427e8			−0.0919667
$553$	−5.52694e9	+	2.94618e9i	−1.38978	+	0.740835i
$554$	3.97170e9			0.992413
$555$	5.73546e9	+	9.93410e9i	1.42411	+	2.46663i
$556$	−1.69133e8	+	2.92946e8i	−0.0417317	+	0.0722814i
$557$	1.53796e8	−	2.66382e8i	0.0377096	−	0.0653149i	−0.846555	−	0.532302i	$-0.821327\pi$
$557$	1.53796e8	−	2.66382e8i	0.0377096	−	0.0653149i	0.884264	+	0.466987i	$0.154660\pi$
$558$	−6.02642e8	−	1.04381e9i	−0.146838	−	0.254332i
$559$	−2.12434e8			−0.0514379
$560$	−1.33833e9	−	8.34327e8i	−0.322036	−	0.200760i
$561$	−3.28218e9			−0.784860
$562$	−1.07411e8	−	1.86042e8i	−0.0255254	−	0.0442113i
$563$	−6.69100e8	+	1.15892e9i	−0.158020	+	0.273699i	−0.934155	−	0.356869i	$-0.883844\pi$
$563$	−6.69100e8	+	1.15892e9i	−0.158020	+	0.273699i	0.776135	+	0.630567i	$0.217178\pi$
$564$	−1.51776e9	+	2.62884e9i	−0.356227	+	0.617003i
$565$	−4.79650e9	−	8.30778e9i	−1.11881	−	1.93783i
$566$	2.69663e9			0.625120
$567$	4.57992e9	+	2.85517e9i	1.05516	+	0.657795i
$568$	−2.36409e9			−0.541308
$569$	3.24443e9	+	5.61952e9i	0.738322	+	1.27881i	0.953250	+	0.302182i	$0.0977149\pi$
$569$	3.24443e9	+	5.61952e9i	0.738322	+	1.27881i	−0.214928	+	0.976630i	$0.568952\pi$
$570$	−2.61969e9	+	4.53744e9i	−0.592500	+	1.02624i
$571$	−3.48596e9	+	6.03786e9i	−0.783603	+	1.35724i	0.146227	+	0.989251i	$0.453287\pi$
$571$	−3.48596e9	+	6.03786e9i	−0.783603	+	1.35724i	−0.929830	+	0.367989i	$0.880046\pi$
$572$	−1.69578e9	−	2.93718e9i	−0.378864	−	0.656212i
$573$	−5.02470e9			−1.11576
$574$	−2.02996e9	+	1.08209e9i	−0.448019	+	0.238820i
$575$	1.22987e9			0.269787
$576$	−1.66609e8	−	2.88576e8i	−0.0363262	−	0.0629189i
$577$	2.26789e9	−	3.92810e9i	0.491481	−	0.851270i	−0.508471	−	0.861079i	$-0.669789\pi$
$577$	2.26789e9	−	3.92810e9i	0.491481	−	0.851270i	0.999952	+	0.00980933i	$0.00312246\pi$
$578$	−1.44113e9	+	2.49611e9i	−0.310425	+	0.537671i
$579$	−1.31914e9	−	2.28481e9i	−0.282433	−	0.489188i
$580$	8.31254e7			0.0176903
$581$	2.77055e8	−	8.18023e9i	0.0586071	−	1.73041i
$582$	−4.04598e9			−0.850732
$583$	−1.89068e9	−	3.27475e9i	−0.395164	−	0.684445i
$584$	7.80289e8	−	1.35150e9i	0.162110	−	0.280783i
$585$	−1.81142e9	+	3.13747e9i	−0.374087	+	0.647938i
$586$	−2.26159e9	−	3.91718e9i	−0.464271	−	0.804141i
$587$	−5.05375e9			−1.03129			−0.515644	−	0.856803i	$-0.672447\pi$
$587$	−5.05375e9			−1.03129			−0.515644	+	0.856803i	$0.672447\pi$
$588$	1.36457e9	+	2.78292e9i	0.276805	+	0.564521i
$589$	3.11118e9			0.627368
$590$	1.14533e9	+	1.98377e9i	0.229587	+	0.397657i
$591$	5.80137e9	−	1.00483e10i	1.15604	−	2.00233i
$592$	9.41571e8	−	1.63085e9i	0.186521	−	0.323063i
$593$	−1.90968e8	−	3.30766e8i	−0.0376070	−	0.0651373i	0.846609	−	0.532215i	$-0.178640\pi$
$593$	−1.90968e8	−	3.30766e8i	−0.0376070	−	0.0651373i	−0.884216	+	0.467078i	$0.845307\pi$
$594$	3.39907e9			0.665438
$595$	9.22098e7	−	2.72255e9i	0.0179460	−	0.529867i
$596$	−1.65978e9			−0.321136
$597$	−1.59099e9	−	2.75568e9i	−0.306025	−	0.530051i
$598$	3.24333e8	−	5.61762e8i	0.0620208	−	0.107423i
$599$	−8.94729e8	+	1.54972e9i	−0.170097	+	0.294617i	−0.938454	−	0.345405i	$-0.887742\pi$
$599$	−8.94729e8	+	1.54972e9i	−0.170097	+	0.294617i	0.768356	+	0.640022i	$0.221075\pi$
$600$	1.53388e9	+	2.65676e9i	0.289910	+	0.502138i
$601$	−3.92179e8			−0.0736925			−0.0368463	−	0.999321i	$-0.511731\pi$
$601$	−3.92179e8			−0.0736925			−0.0368463	+	0.999321i	$0.511731\pi$
$602$	2.02603e8	−	1.07999e8i	0.0378492	−	0.0201758i
$603$	1.50590e9			0.279696
$604$	1.46939e9	+	2.54506e9i	0.271337	+	0.469969i
$605$	−9.06840e9	+	1.57069e10i	−1.66490	+	2.88368i
$606$	−1.38865e9	+	2.40522e9i	−0.253478	+	0.439036i
$607$	5.59514e8	+	9.69107e8i	0.101543	+	0.175878i	0.912321	−	0.409477i	$-0.134289\pi$
$607$	5.59514e8	+	9.69107e8i	0.101543	+	0.175878i	−0.810777	+	0.585354i	$0.800955\pi$
$608$	8.60132e8			0.155204
$609$	−1.38634e8	−	8.64254e7i	−0.0248718	−	0.0155053i
$610$	1.92227e9			0.342893
$611$	−2.70899e9	−	4.69211e9i	−0.480467	−	0.832193i
$612$	2.87784e8	−	4.98456e8i	0.0507500	−	0.0879016i
$613$	2.22809e9	−	3.85916e9i	0.390680	−	0.676677i	−0.601860	−	0.798602i	$-0.705573\pi$
$613$	2.22809e9	−	3.85916e9i	0.390680	−	0.676677i	0.992539	+	0.121925i	$0.0389066\pi$
$614$	2.85576e9	+	4.94633e9i	0.497890	+	0.862370i
$615$	7.90566e9			1.37049
$616$	3.11052e9	+	1.93913e9i	0.536168	+	0.334252i
$617$	−2.50707e9			−0.429704			−0.214852	−	0.976647i	$-0.568927\pi$
$617$	−2.50707e9			−0.429704			−0.214852	+	0.976647i	$0.568927\pi$
$618$	1.73371e9	+	3.00288e9i	0.295473	+	0.511774i
$619$	7.42231e7	−	1.28558e8i	0.0125783	−	0.0217862i	−0.859668	−	0.510854i	$-0.829329\pi$
$619$	7.42231e7	−	1.28558e8i	0.0125783	−	0.0217862i	0.872246	+	0.489067i	$0.162663\pi$
$620$	1.60922e9	−	2.78725e9i	0.271171	−	0.469683i
$621$	3.25052e8	+	5.63006e8i	0.0544668	+	0.0943392i
$622$	−3.65482e9			−0.608975
$623$	−5.61758e9	+	2.99450e9i	−0.930767	+	0.496153i
$624$	1.61803e9			0.266587
$625$	1.84105e9	+	3.18879e9i	0.301637	+	0.522451i
$626$	3.84055e9	−	6.65203e9i	0.625725	−	1.08379i
$627$	6.08864e9	−	1.05458e10i	0.986470	−	1.70862i
$628$	−2.49627e8	−	4.32366e8i	−0.0402191	−	0.0696615i
$629$	3.25275e9			0.521163
$630$	1.32535e8	−	3.91316e9i	0.0211172	−	0.623499i
$631$	6.90977e9			1.09487			0.547433	−	0.836850i	$-0.315605\pi$
$631$	6.90977e9			1.09487			0.547433	+	0.836850i	$0.315605\pi$
$632$	−1.76681e9	−	3.06020e9i	−0.278407	−	0.482215i
$633$	−2.71757e9	+	4.70696e9i	−0.425860	+	0.737612i
$634$	−2.30353e9	+	3.98984e9i	−0.358990	+	0.621789i
$635$	3.73671e9	+	6.47217e9i	0.579136	+	1.00309i
$636$	1.80399e9			0.278057
$637$	−5.51944e9	−	3.74304e8i	−0.846071	−	0.0573768i
$638$	−1.93199e8			−0.0294531
$639$	−2.93462e9	−	5.08292e9i	−0.444938	−	0.770655i
$640$	4.44892e8	−	7.70575e8i	0.0670848	−	0.116194i
$641$	7.83493e8	−	1.35705e9i	0.117498	−	0.203513i	−0.801277	−	0.598293i	$-0.795846\pi$
$641$	7.83493e8	−	1.35705e9i	0.117498	−	0.203513i	0.918776	+	0.394780i	$0.129179\pi$
$642$	1.55358e9	+	2.69088e9i	0.231718	+	0.401348i
$643$	7.91354e9			1.17390			0.586952	−	0.809622i	$-0.300328\pi$
$643$	7.91354e9			1.17390			0.586952	+	0.809622i	$0.300328\pi$
$644$	−2.37302e7	+	7.00650e8i	−0.00350108	+	0.103371i
$645$	−7.89032e8			−0.115781
$646$	7.42852e8	+	1.28666e9i	0.108415	+	0.187780i
$647$	−1.93426e9	+	3.35023e9i	−0.280769	+	0.486307i	−0.971574	−	0.236734i	$-0.923923\pi$
$647$	−1.93426e9	+	3.35023e9i	−0.280769	+	0.486307i	0.690805	+	0.723041i	$0.257256\pi$
$648$	−1.52247e9	+	2.63700e9i	−0.219805	+	0.380713i
$649$	−2.66195e9	−	4.61063e9i	−0.382247	−	0.662070i
$650$	−5.47554e9			−0.782042
$651$	−5.58170e9	+	2.97537e9i	−0.792926	+	0.422675i
$652$	−4.20752e9			−0.594510
$653$	−3.34714e9	−	5.79742e9i	−0.470412	−	0.814777i	0.529016	−	0.848612i	$-0.322561\pi$
$653$	−3.34714e9	−	5.79742e9i	−0.470412	−	0.814777i	−0.999427	+	0.0338348i	$0.989228\pi$
$654$	7.39918e8	−	1.28158e9i	0.103434	−	0.179152i
$655$	−1.02675e9	+	1.77838e9i	−0.142765	+	0.247276i
$656$	−6.48923e8	−	1.12397e9i	−0.0897490	−	0.155450i
$657$	3.87440e9			0.532998
$658$	4.96903e9	+	3.09774e9i	0.679956	+	0.423891i
$659$	−4.20015e9			−0.571696			−0.285848	−	0.958275i	$-0.592275\pi$
$659$	−4.20015e9			−0.571696			−0.285848	+	0.958275i	$0.592275\pi$
$660$	−6.29854e9	−	1.09094e10i	−0.852778	−	1.47705i
$661$	4.50337e9	−	7.80006e9i	0.606502	−	1.05049i	−0.385310	−	0.922787i	$-0.625906\pi$
$661$	4.50337e9	−	7.80006e9i	0.606502	−	1.05049i	0.991812	−	0.127705i	$-0.0407611\pi$
$662$	−1.78670e9	+	3.09465e9i	−0.239358	+	0.414580i
$663$	1.39741e9	+	2.42038e9i	0.186220	+	0.322542i
$664$	4.61786e9			0.612143
$665$	8.57666e9	+	5.34677e9i	1.13095	+	0.705043i
$666$	4.67522e9			0.613257
$667$	−1.84755e7	−	3.20005e7i	−0.00241077	−	0.00417557i
$668$	−7.76473e8	+	1.34489e9i	−0.100788	+	0.174570i
$669$	1.09661e9	−	1.89938e9i	0.141599	−	0.245257i
$670$	2.01058e9	+	3.48243e9i	0.258262	+	0.447322i
$671$	−4.46770e9			−0.570893
$672$	−1.54314e9	+	8.22583e8i	−0.196161	+	0.104565i
$673$	−6.02502e9			−0.761913			−0.380957	−	0.924593i	$-0.624405\pi$
$673$	−6.02502e9			−0.761913			−0.380957	+	0.924593i	$0.624405\pi$
$674$	−4.35920e9	−	7.55036e9i	−0.548400	−	0.949857i
$675$	2.74383e9	−	4.75246e9i	0.343395	−	0.594778i
$676$	5.63977e8	−	9.76837e8i	0.0702179	−	0.121621i
$677$	3.88772e9	+	6.73374e9i	0.481543	+	0.834057i	0.999776	−	0.0211827i	$-0.00674317\pi$
$677$	3.88772e9	+	6.73374e9i	0.481543	+	0.834057i	−0.518233	+	0.855240i	$0.673410\pi$
$678$	−1.06368e10			−1.31071
$679$	−2.64185e8	+	7.80022e9i	−0.0323865	+	0.956231i
$680$	1.53692e9			0.187444
$681$	3.36344e9	+	5.82565e9i	0.408102	+	0.706853i
$682$	−3.74012e9	+	6.47807e9i	−0.451481	+	0.781989i
$683$	3.80036e9	−	6.58242e9i	0.456407	−	0.790520i	−0.542361	−	0.840146i	$-0.682469\pi$
$683$	3.80036e9	−	6.58242e9i	0.456407	−	0.790520i	0.998768	+	0.0496253i	$0.0158027\pi$
$684$	1.06771e9	+	1.84933e9i	0.127573	+	0.220962i
$685$	−2.31673e10			−2.75397
$686$	5.45428e9	−	2.44903e9i	0.645065	−	0.289641i
$687$	−4.90590e9			−0.577259
$688$	6.47664e7	+	1.12179e8i	0.00758211	+	0.0131326i
$689$	−1.60993e9	+	2.78849e9i	−0.187517	+	0.324789i
$690$	1.20465e9	−	2.08652e9i	0.139601	−	0.241797i
$691$	2.51431e9	+	4.35491e9i	0.289898	+	0.502118i	0.973785	−	0.227470i	$-0.0730453\pi$
$691$	2.51431e9	+	4.35491e9i	0.289898	+	0.502118i	−0.683887	+	0.729588i	$0.739712\pi$
$692$	−2.22624e9			−0.255388
$693$	−3.08034e8	+	9.09490e9i	−0.0351587	+	1.03808i
$694$	−8.80644e9			−1.00010
$695$	−1.12125e9	−	1.94206e9i	−0.126694	−	0.219440i
$696$	4.60850e7	−	7.98216e7i	0.00518117	−	0.00897404i
$697$	1.12088e9	−	1.94143e9i	0.125385	−	0.217173i
$698$	−3.67086e9	−	6.35811e9i	−0.408576	−	0.707675i
$699$	−1.79666e9			−0.198974
$700$	5.22212e9	−	2.78369e9i	0.575445	−	0.306745i
$701$	1.07254e10			1.17598			0.587989	−	0.808869i	$-0.299920\pi$
$701$	1.07254e10			1.17598			0.587989	+	0.808869i	$0.299920\pi$
$702$	−1.44717e9	−	2.50658e9i	−0.157885	−	0.273465i
$703$	−6.03404e9	+	1.04513e10i	−0.655035	+	1.13455i
$704$	−1.03401e9	+	1.79096e9i	−0.111692	+	0.193455i
$705$	−1.00619e10	−	1.74276e10i	−1.08147	−	1.87317i
$706$	−1.70689e9			−0.182553
$707$	4.54634e9	+	2.83423e9i	0.483831	+	0.301625i
$708$	2.53990e9			0.268967
$709$	7.38414e9	+	1.27897e10i	0.778105	+	1.34772i	0.933033	+	0.359792i	$0.117152\pi$
$709$	7.38414e9	+	1.27897e10i	0.778105	+	1.34772i	−0.154927	+	0.987926i	$0.549514\pi$
$710$	7.83624e9	−	1.35728e10i	0.821681	−	1.42319i
$711$	4.38641e9	−	7.59748e9i	0.457683	−	0.792731i
$712$	−1.79578e9	−	3.11039e9i	−0.186455	−	0.322950i
$713$	−1.43066e9			−0.147817
$714$	−2.56322e9	−	1.59794e9i	−0.263537	−	0.164292i
$715$	2.24840e10			2.30040
$716$	2.04641e9	+	3.54448e9i	0.208351	+	0.360875i
$717$	−1.57422e8	+	2.72663e8i	−0.0159496	+	0.0276255i
$718$	4.75620e8	−	8.23797e8i	0.0479539	−	0.0830586i
$719$	−6.19788e9	−	1.07350e10i	−0.621859	−	1.07709i	−0.989139	−	0.146981i	$-0.953044\pi$
$719$	−6.19788e9	−	1.07350e10i	−0.621859	−	1.07709i	0.367280	−	0.930110i	$-0.380289\pi$
$720$	2.20904e9			0.220567
$721$	5.90244e9	−	3.14634e9i	0.586487	−	0.312631i
$722$	1.63883e9			0.162052
$723$	5.45494e9	+	9.44824e9i	0.536792	+	0.929752i
$724$	−3.30570e9	+	5.72565e9i	−0.323727	+	0.560712i
$725$	−1.55956e8	+	2.70123e8i	−0.0151991	+	0.0263256i
$726$	1.00551e10	+	1.74160e10i	0.975234	+	1.68915i
$727$	1.18455e10			1.14336			0.571681	−	0.820476i	$-0.306291\pi$
$727$	1.18455e10			1.14336			0.571681	+	0.820476i	$0.306291\pi$
$728$	1.05650e8	−	3.11939e9i	0.0101487	−	0.299647i
$729$	−6.32921e8			−0.0605066
$730$	5.17285e9	+	8.95964e9i	0.492153	+	0.852434i
$731$	−1.11871e8	+	1.93766e8i	−0.0105927	+	0.0183471i
$732$	1.06571e9	−	1.84587e9i	0.100427	−	0.173945i
$733$	3.69991e9	+	6.40844e9i	0.346998	+	0.601019i	0.985715	−	0.168423i	$-0.0538676\pi$
$733$	3.69991e9	+	6.40844e9i	0.346998	+	0.601019i	−0.638716	+	0.769442i	$0.720534\pi$
$734$	−2.19996e9			−0.205343
$735$	−2.05005e10	−	1.39026e9i	−1.90440	−	0.129148i
$736$	−3.95527e8			−0.0365683
$737$	−4.67296e9	−	8.09381e9i	−0.429988	−	0.744760i
$738$	1.61106e9	−	2.79044e9i	0.147542	−	0.255550i
$739$	5.92456e9	−	1.02616e10i	0.540009	−	0.935323i	−0.458894	−	0.888491i	$-0.651754\pi$
$739$	5.92456e9	−	1.02616e10i	0.540009	−	0.935323i	0.998903	−	0.0468318i	$-0.0149125\pi$
$740$	6.24205e9	+	1.08116e10i	0.566261	+	0.980793i
$741$	−1.03691e10			−0.936218
$742$	1.17793e8	−	3.47790e9i	0.0105853	−	0.312538i
$743$	4.53308e9			0.405446			0.202723	−	0.979236i	$-0.435021\pi$
$743$	4.53308e9			0.405446			0.202723	+	0.979236i	$0.435021\pi$
$744$	−1.78431e9	−	3.09052e9i	−0.158842	−	0.275123i
$745$	5.50169e9	−	9.52920e9i	0.487471	−	0.844325i
$746$	3.58301e9	−	6.20596e9i	0.315982	−	0.547297i
$747$	5.73232e9	+	9.92866e9i	0.503162	+	0.871503i
$748$	−3.57209e9			−0.312080
$749$	5.28917e9	−	2.81943e9i	0.459940	−	0.245175i
$750$	−4.74355e9			−0.410572
$751$	−1.08837e10	−	1.88510e10i	−0.937638	−	1.62404i	−0.769862	−	0.638211i	$-0.779675\pi$
$751$	−1.08837e10	−	1.88510e10i	−0.937638	−	1.62404i	−0.167776	−	0.985825i	$-0.553658\pi$
$752$	−1.65182e9	+	2.86104e9i	−0.141645	+	0.245336i
$753$	−4.43210e7	+	7.67661e7i	−0.00378292	+	0.00655220i
$754$	8.22554e7	+	1.42470e8i	0.00698819	+	0.0121039i
$755$	−1.94824e10			−1.64751
$756$	2.65451e9	+	1.65485e9i	0.223438	+	0.139294i
$757$	2.03442e9			0.170453			0.0852266	−	0.996362i	$-0.472839\pi$
$757$	2.03442e9			0.170453			0.0852266	+	0.996362i	$0.472839\pi$
$758$	6.78999e9	+	1.17606e10i	0.566275	+	0.980817i
$759$	−2.79983e9	+	4.84945e9i	−0.232427	+	0.402575i
$760$	−2.85108e9	+	4.93822e9i	−0.235593	+	0.408059i
$761$	−6.30476e9	−	1.09202e10i	−0.518587	−	0.898220i	−0.999767	−	0.0215975i	$-0.993125\pi$
$761$	−6.30476e9	−	1.09202e10i	−0.518587	−	0.898220i	0.481179	−	0.876622i	$-0.340209\pi$
$762$	8.28657e9			0.678473
$763$	−2.42243e9	−	1.51017e9i	−0.197431	−	0.123080i
$764$	−5.46852e9			−0.443652
$765$	1.90783e9	+	3.30447e9i	0.154073	+	0.266862i
$766$	4.99626e9	−	8.65378e9i	0.401647	−	0.695673i
$767$	−2.26668e9	+	3.92601e9i	−0.181387	+	0.314172i
$768$	−4.93299e8	−	8.54419e8i	−0.0392958	−	0.0680623i
$769$	1.47113e10			1.16657			0.583284	−	0.812268i	$-0.301768\pi$
$769$	1.47113e10			1.16657			0.583284	+	0.812268i	$0.301768\pi$
$770$	−2.14434e10	+	1.14306e10i	−1.69269	+	0.902300i
$771$	−1.86635e10			−1.46657
$772$	−1.43565e9	−	2.48662e9i	−0.112302	−	0.194513i
$773$	−2.89303e8	+	5.01088e8i	−0.0225281	+	0.0390198i	−0.877070	−	0.480363i	$-0.840505\pi$
$773$	−2.89303e8	+	5.01088e8i	−0.0225281	+	0.0390198i	0.854542	+	0.519383i	$0.173838\pi$
$774$	−1.60794e8	+	2.78503e8i	−0.0124645	+	0.0215892i
$775$	6.03827e9	+	1.04586e10i	0.465968	+	0.807081i
$776$	−4.40335e9			−0.338273
$777$	8.30499e8	−	2.45210e10i	0.0635135	−	1.87527i
$778$	−1.08856e10			−0.828749
$779$	4.15861e9	+	7.20293e9i	0.315186	+	0.545919i
$780$	−5.36327e9	+	9.28946e9i	−0.404668	+	0.700905i
$781$	−1.82129e10	+	3.15456e10i	−1.36804	+	2.36952i
$782$	−3.41597e8	−	5.91663e8i	−0.0255441	−	0.0442436i
$783$	−1.64875e8			−0.0122741
$784$	1.48509e9	+	3.02873e9i	0.110065	+	0.224468i
$785$	3.30975e9			0.244203
$786$	1.13847e9	+	1.97189e9i	0.0836262	+	0.144845i
$787$	−1.66639e9	+	2.88627e9i	−0.121861	+	0.211069i	−0.920502	−	0.390739i	$-0.872220\pi$
$787$	−1.66639e9	+	2.88627e9i	−0.121861	+	0.211069i	0.798641	+	0.601808i	$0.205553\pi$
$788$	6.31379e9	−	1.09358e10i	0.459673	−	0.796176i
$789$	−4.01980e9	−	6.96249e9i	−0.291363	−	0.504656i
$790$	2.34258e10			1.69044
$791$	−6.94537e8	+	2.05066e10i	−0.0498974	+	1.47325i
$792$	−5.13421e9			−0.367228
$793$	1.90215e9	+	3.29461e9i	0.135453	+	0.234611i
$794$	8.26432e9	−	1.43142e10i	0.585916	−	1.01484i
$795$	−5.97968e9	+	1.03571e10i	−0.422078	+	0.731061i
$796$	−1.73152e9	−	2.99908e9i	−0.121683	−	0.210762i
$797$	1.88465e10			1.31864			0.659322	−	0.751861i	$-0.270843\pi$
$797$	1.88465e10			1.31864			0.659322	+	0.751861i	$0.270843\pi$
$798$	9.88919e9	−	5.27151e9i	0.688891	−	0.367219i
$799$	−5.70637e9			−0.395773
$800$	1.66937e9	+	2.89143e9i	0.115275	+	0.199663i
$801$	4.45834e9	−	7.72207e9i	0.306520	−	0.530909i
$802$	−5.83679e8	+	1.01096e9i	−0.0399543	+	0.0692029i
$803$	−1.20227e10	−	2.08238e10i	−0.819400	−	1.41924i
$804$	4.45870e9			0.302560
$805$	−3.94393e9	−	2.45869e9i	−0.266467	−	0.166118i
$806$	6.36950e9			0.428482
$807$	−5.50495e9	−	9.53485e9i	−0.368719	−	0.638641i
$808$	−1.51131e9	+	2.61766e9i	−0.100789	+	0.174572i
$809$	−4.69404e8	+	8.13032e8i	−0.0311693	+	0.0539868i	−0.881189	−	0.472764i	$-0.843256\pi$
$809$	−4.69404e8	+	8.13032e8i	−0.0311693	+	0.0539868i	0.850020	+	0.526750i	$0.176590\pi$
$810$	−1.00931e10	−	1.74817e10i	−0.667308	−	1.15581i
$811$	−2.78193e10			−1.83136			−0.915679	−	0.401910i	$-0.868346\pi$
$811$	−2.78193e10			−1.83136			−0.915679	+	0.401910i	$0.868346\pi$
$812$	−1.50879e8	−	9.40592e7i	−0.00988967	−	0.00616531i
$813$	2.67608e10			1.74656
$814$	−1.45077e10	−	2.51280e10i	−0.942785	−	1.63295i
$815$	1.39467e10	−	2.41563e10i	0.902441	−	1.56307i
$816$	8.52075e8	−	1.47584e9i	0.0548987	−	0.0950874i
$817$	−4.15054e8	−	7.18895e8i	−0.0266273	−	0.0461199i
$818$	−9.53521e9			−0.609107
$819$	6.83800e9	−	3.64505e9i	0.434946	−	0.231851i
$820$	8.60394e9			0.544940
$821$	4.27495e9	+	7.40443e9i	0.269606	+	0.466972i	0.968760	−	0.248000i	$-0.0797732\pi$
$821$	4.27495e9	+	7.40443e9i	0.269606	+	0.466972i	−0.699154	+	0.714971i	$0.746440\pi$
$822$	−1.28441e10	+	2.22466e10i	−0.806586	+	1.39705i
$823$	−6.44756e9	+	1.11675e10i	−0.403177	+	0.698324i	−0.994107	−	0.108399i	$-0.965428\pi$
$823$	−6.44756e9	+	1.11675e10i	−0.403177	+	0.698324i	0.590930	+	0.806723i	$0.298761\pi$
$824$	1.88685e9	+	3.26811e9i	0.117487	+	0.203494i
$825$	4.72680e10			2.93075
$826$	1.65844e8	−	4.89666e9i	0.0102393	−	0.302322i
$827$	4.73751e9			0.291260			0.145630	−	0.989339i	$-0.453479\pi$
$827$	4.73751e9			0.291260			0.145630	+	0.989339i	$0.453479\pi$
$828$	−4.90982e8	−	8.50406e8i	−0.0300580	−	0.0520619i
$829$	−7.03830e9	+	1.21907e10i	−0.429069	+	0.743169i	−0.996791	−	0.0800516i	$-0.974491\pi$
$829$	−7.03830e9	+	1.21907e10i	−0.429069	+	0.743169i	0.567722	+	0.823220i	$0.307825\pi$
$830$	−1.53068e10	+	2.65122e10i	−0.929207	+	1.60943i
$831$	1.45975e10	+	2.52835e10i	0.882417	+	1.52839i
$832$	1.76094e9			0.106002
$833$	−3.24802e9	+	4.83729e9i	−0.194698	+	0.289964i
$834$	−2.48650e9			−0.148425
$835$	−5.14755e9	−	8.91582e9i	−0.305984	−	0.529979i
$836$	6.62643e9	−	1.14773e10i	0.392245	−	0.679389i
$837$	−3.19180e9	+	5.52837e9i	−0.188147	+	0.325880i
$838$	2.35890e9	+	4.08574e9i	0.138470	+	0.239837i
$839$	1.66762e10			0.974833			0.487416	−	0.873170i	$-0.337939\pi$
$839$	1.66762e10			0.974833			0.487416	+	0.873170i	$0.337939\pi$
$840$	3.92410e8	−	1.15861e10i	0.0228435	−	0.674468i
$841$	−1.72405e10			−0.999457
$842$	9.43884e9	+	1.63486e10i	0.544912	+	0.943815i
$843$	7.89551e8	−	1.36754e9i	0.0453925	−	0.0786221i
$844$	−2.95760e9	+	5.12272e9i	−0.169333	+	0.293293i
$845$	3.73883e9	+	6.47585e9i	0.213176	+	0.369231i
$846$	−8.20185e9			−0.465710
$847$	3.42327e10	−	1.82480e10i	1.93575	−	1.03187i
$848$	1.96333e9			0.110562
$849$	9.91108e9	+	1.71665e10i	0.555833	+	0.962731i
$850$	−2.88349e9	+	4.99436e9i	−0.161047	+	0.278942i
$851$	2.77472e9	−	4.80596e9i	0.154336	−	0.267317i
$852$	−8.68888e9	−	1.50496e10i	−0.481310	−	0.833654i
$853$	2.75175e10			1.51805			0.759027	−	0.651060i	$-0.225675\pi$
$853$	2.75175e10			1.51805			0.759027	+	0.651060i	$0.225675\pi$
$854$	−3.48905e9	−	2.17511e9i	−0.191692	−	0.119503i
$855$	−1.41566e10			−0.774600
$856$	1.69080e9	+	2.92855e9i	0.0921371	+	0.159586i
$857$	−1.78022e10	+	3.08344e10i	−0.966144	+	1.67341i	−0.259634	+	0.965707i	$0.583602\pi$
$857$	−1.78022e10	+	3.08344e10i	−0.966144	+	1.67341i	−0.706510	+	0.707704i	$0.749731\pi$
$858$	1.24652e10	−	2.15904e10i	0.673743	−	1.16696i
$859$	−7.28789e9	−	1.26230e10i	−0.392307	−	0.679495i	0.600447	−	0.799665i	$-0.294990\pi$
$859$	−7.28789e9	−	1.26230e10i	−0.392307	−	0.679495i	−0.992753	+	0.120169i	$0.961656\pi$
$860$	−8.58725e8			−0.0460373
$861$	−1.43493e10	−	8.94552e9i	−0.766163	−	0.477633i
$862$	2.06917e10			1.10032
$863$	−3.26274e9	−	5.65123e9i	−0.172800	−	0.299299i	0.766598	−	0.642128i	$-0.221948\pi$
$863$	−3.26274e9	−	5.65123e9i	−0.172800	−	0.299299i	−0.939398	+	0.342829i	$0.888615\pi$
$864$	−8.82420e8	+	1.52840e9i	−0.0465455	+	0.0806191i
$865$	7.37931e9	−	1.27813e10i	0.387667	−	0.671459i
$866$	−5.95749e9	−	1.03187e10i	−0.311710	−	0.539898i
$867$	−2.11867e10			−1.10407
$868$	−6.07471e9	+	3.23817e9i	−0.315287	+	0.168066i
$869$	−5.44458e10			−2.81446
$870$	3.05516e8	+	5.29170e8i	0.0157296	+	0.0272444i
$871$	−3.97908e9	+	6.89196e9i	−0.204042	+	0.353411i
$872$	8.05273e8	−	1.39477e9i	0.0411278	−	0.0712354i
$873$	−5.46603e9	−	9.46744e9i	−0.278049	−	0.481596i
$874$	2.53473e9			0.128423
$875$	−3.09734e8	+	9.14508e9i	−0.0156301	+	0.461487i
$876$	1.14714e10			0.576569
$877$	−1.88472e9	−	3.26443e9i	−0.0943514	−	0.163421i	0.814986	−	0.579480i	$-0.196744\pi$
$877$	−1.88472e9	−	3.26443e9i	−0.0943514	−	0.163421i	−0.909338	+	0.416059i	$0.863411\pi$
$878$	−1.06874e10	+	1.85112e10i	−0.532896	+	0.923003i
$879$	1.66243e10	−	2.87942e10i	0.825625	−	1.43002i
$880$	−6.85487e9	−	1.18730e10i	−0.339086	−	0.587314i
$881$	−6.65654e9			−0.327969			−0.163985	−	0.986463i	$-0.552435\pi$
$881$	−6.65654e9			−0.327969			−0.163985	+	0.986463i	$0.552435\pi$
$882$	−4.66843e9	+	6.95270e9i	−0.229103	+	0.341204i
$883$	−2.18423e10			−1.06767			−0.533834	−	0.845590i	$-0.679249\pi$
$883$	−2.18423e10			−1.06767			−0.533834	+	0.845590i	$0.679249\pi$
$884$	1.52084e9	+	2.63416e9i	0.0740456	+	0.128251i
$885$	−8.41900e9	+	1.45821e10i	−0.408281	+	0.707163i
$886$	5.55923e8	−	9.62886e8i	0.0268532	−	0.0465111i
$887$	4.55208e9	+	7.88443e9i	0.219017	+	0.379348i	0.954508	−	0.298187i	$-0.0963818\pi$
$887$	4.55208e9	+	7.88443e9i	0.219017	+	0.379348i	−0.735491	+	0.677534i	$0.763048\pi$
$888$	1.38425e10			0.663389
$889$	5.41078e8	−	1.59757e10i	0.0258288	−	0.762610i
$890$	2.38100e10			1.13212
$891$	2.34582e10	+	4.06308e10i	1.11102	+	1.92435i
$892$	1.19347e9	−	2.06715e9i	0.0563033	−	0.0975202i
$893$	1.05857e10	−	1.83349e10i	0.497437	−	0.861586i
$894$	−6.10031e9	−	1.05660e10i	−0.285542	−	0.494574i
$895$	−2.71329e10			−1.26507
$896$	−1.67944e9	+	8.95240e8i	−0.0779986	+	0.0415778i
$897$	4.76817e9			0.220586
$898$	−3.65267e9	−	6.32660e9i	−0.168323	−	0.291544i
$899$	1.81418e8	−	3.14225e8i	0.00832762	−	0.0144239i
$900$	−4.14449e9	+	7.17846e9i	−0.189506	+	0.328233i
$901$	1.69563e9	+	2.93691e9i	0.0772313	+	0.133769i
$902$	−1.99971e10			−0.907287
$903$	1.43215e9	+	8.92816e8i	0.0647264	+	0.0403511i
$904$	−1.15763e10			−0.521171
$905$	−2.19148e10	−	3.79576e10i	−0.982807	−	1.70227i
$906$	−1.08011e10	+	1.87081e10i	−0.482525	+	0.835757i
$907$	−7.58589e9	+	1.31391e10i	−0.337583	+	0.584712i	−0.983978	−	0.178292i	$-0.942943\pi$
$907$	−7.58589e9	+	1.31391e10i	−0.337583	+	0.584712i	0.646394	+	0.763004i	$0.276276\pi$
$908$	3.66052e9	+	6.34021e9i	0.162272	+	0.281063i
$909$	−7.50416e9			−0.331382
$910$	1.75589e10	+	1.09464e10i	0.772419	+	0.481533i
$911$	1.48713e10			0.651679			0.325839	−	0.945425i	$-0.394353\pi$
$911$	1.48713e10			0.651679			0.325839	+	0.945425i	$0.394353\pi$
$912$	3.16130e9	+	5.47553e9i	0.138001	+	0.239026i
$913$	3.55759e10	−	6.16193e10i	1.54706	−	2.67959i
$914$	−3.29678e9	+	5.71019e9i	−0.142817	+	0.247365i
$915$	7.06503e9	+	1.22370e10i	0.304888	+	0.528081i
$916$	−5.33923e9			−0.229533
$917$	3.87593e9	−	2.06609e9i	0.165990	−	0.0884825i
$918$	−3.04841e9			−0.130054
$919$	1.55406e10	+	2.69171e10i	0.660486	+	1.14400i	0.980488	+	0.196579i	$0.0629831\pi$
$919$	1.55406e10	+	2.69171e10i	0.660486	+	1.14400i	−0.320002	+	0.947417i	$0.603684\pi$
$920$	1.31106e9	−	2.27081e9i	0.0555090	−	0.0961445i
$921$	−2.09920e10	+	3.63591e10i	−0.885410	+	1.53357i
$922$	6.56432e9	+	1.13697e10i	0.275824	+	0.477740i
$923$	3.10169e10			1.29835
$924$	−9.12033e8	+	2.69283e10i	−0.0380328	+	1.12294i
$925$	−4.68441e10			−1.94607
$926$	1.14875e10	+	1.98969e10i	0.475431	+	0.823470i
$927$	−4.68442e9	+	8.11365e9i	−0.193142	+	0.334532i
$928$	5.01556e7	−	8.68720e7i	0.00206016	−	0.00356830i
$929$	1.49789e10	+	2.59442e10i	0.612950	+	1.06166i	0.990740	+	0.135770i	$0.0433508\pi$
$929$	1.49789e10	+	2.59442e10i	0.612950	+	1.06166i	−0.377790	+	0.925891i	$0.623316\pi$
$930$	2.36579e10			0.964462
$931$	−9.51721e9	−	1.94095e10i	−0.386532	−	0.788300i
$932$	−1.95535e9			−0.0791170
$933$	−1.34328e10	−	2.32663e10i	−0.541478	−	0.937868i
$934$	1.17756e10	−	2.03960e10i	0.472900	−	0.819087i
$935$	1.18404e10	−	2.05082e10i	0.473724	−	0.820515i
$936$	2.18592e9	+	3.78612e9i	0.0871301	+	0.150914i
$937$	−1.75637e10			−0.697473			−0.348736	−	0.937221i	$-0.613389\pi$
$937$	−1.75637e10			−0.697473			−0.348736	+	0.937221i	$0.613389\pi$
$938$	2.91134e8	−	8.59591e9i	0.0115182	−	0.340081i
$939$	5.64618e10			2.22549
$940$	−1.09506e10	−	1.89670e10i	−0.430021	−	0.744819i
$941$	8.69121e9	−	1.50536e10i	0.340029	−	0.588948i	−0.644408	−	0.764681i	$-0.722896\pi$
$941$	8.69121e9	−	1.50536e10i	0.340029	−	0.588948i	0.984438	+	0.175733i	$0.0562296\pi$
$942$	1.83494e9	−	3.17821e9i	0.0715226	−	0.123881i
$943$	−1.91232e9	−	3.31223e9i	−0.0742624	−	0.128626i
$944$	2.76424e9			0.106948
$945$	−1.82998e10	+	9.75483e9i	−0.705397	+	0.376018i
$946$	1.99583e9			0.0766488
$947$	−2.00818e10	−	3.47828e10i	−0.768385	−	1.33088i	−0.938438	−	0.345447i	$-0.887727\pi$
$947$	−2.00818e10	−	3.47828e10i	−0.768385	−	1.33088i	0.170054	−	0.985435i	$-0.445606\pi$
$948$	1.29873e10	−	2.24947e10i	0.495098	−	0.857535i
$949$	−1.02374e10	+	1.77317e10i	−0.388829	+	0.673472i
$950$	−1.06981e10	−	1.85297e10i	−0.404832	−	0.701189i
$951$	−3.38653e10			−1.27680
$952$	−2.78962e9	−	1.73908e9i	−0.104789	−	0.0653265i
$953$	3.96693e10			1.48467			0.742335	−	0.670029i	$-0.233718\pi$
$953$	3.96693e10			1.48467			0.742335	+	0.670029i	$0.233718\pi$
$954$	2.43715e9	+	4.22126e9i	0.0908788	+	0.157407i
$955$	1.81265e10	−	3.13960e10i	0.673445	−	1.16644i
$956$	−1.71327e8	+	2.96747e8i	−0.00634195	+	0.0109846i
$957$	−7.10075e8	−	1.22989e9i	−0.0261886	−	0.0453600i
$958$	−6.71112e9			−0.246613
$959$	4.20504e10	+	2.62146e10i	1.53959	+	0.959795i
$960$	6.54056e9			0.238597
$961$	6.73220e9	+	1.16605e10i	0.244695	+	0.423824i
$962$	−1.23534e10	+	2.13968e10i	−0.447379	+	0.774883i
$963$	−4.19770e9	+	7.27063e9i	−0.151468	+	0.262349i
$964$	5.93677e9	+	1.02828e10i	0.213442	+	0.369693i
$965$	1.90350e10			0.681880
$966$	−4.54750e9	+	2.42408e9i	−0.162313	+	0.0865220i
$967$	3.37872e10			1.20160			0.600800	−	0.799400i	$-0.294849\pi$
$967$	3.37872e10			1.20160			0.600800	+	0.799400i	$0.294849\pi$
$968$	1.09432e10	+	1.89543e10i	0.387777	+	0.671650i
$969$	−5.46051e9	+	9.45788e9i	−0.192797	+	0.333934i
$970$	1.45958e10	−	2.52806e10i	0.513483	−	0.889379i
$971$	7.77704e9	+	1.34702e10i	0.272613	+	0.472180i	0.969530	−	0.244972i	$-0.0787787\pi$
$971$	7.77704e9	+	1.34702e10i	0.272613	+	0.472180i	−0.696917	+	0.717152i	$0.745445\pi$
$972$	−1.48441e10			−0.518467
$973$	−1.62358e8	+	4.79371e9i	−0.00565039	+	0.166831i
$974$	−1.96269e9			−0.0680606
$975$	−2.01246e10	−	3.48568e10i	−0.695362	−	1.20440i
$976$	1.15984e9	−	2.00891e9i	0.0399323	−	0.0691648i
$977$	1.01465e8	−	1.75742e8i	0.00348083	−	0.00602898i	−0.864280	−	0.503011i	$-0.832225\pi$
$977$	1.01465e8	−	1.75742e8i	0.00348083	−	0.00602898i	0.867761	+	0.496982i	$0.165559\pi$
$978$	−1.54642e10	−	2.67847e10i	−0.528616	−	0.915590i
$979$	−5.53387e10			−1.88490
$980$	−2.23113e10	−	1.51305e9i	−0.757239	−	0.0513527i
$981$	3.99846e9			0.135223
$982$	−1.94611e10	−	3.37076e10i	−0.655809	−	1.13590i
$983$	−2.28447e10	+	3.95681e10i	−0.767092	+	1.32864i	0.172041	+	0.985090i	$0.444964\pi$
$983$	−2.28447e10	+	3.95681e10i	−0.767092	+	1.32864i	−0.939133	+	0.343553i	$0.888369\pi$
$984$	4.77006e9	−	8.26198e9i	0.159603	−	0.276440i
$985$	4.18567e10	+	7.24979e10i	1.39553	+	2.41712i
$986$	1.73267e8			0.00575635
$987$	−1.45696e9	+	4.30177e10i	−0.0482324	+	1.42409i
$988$	−1.12850e10			−0.372264
$989$	1.90861e8	+	3.30580e8i	0.00627378	+	0.0108665i
$990$	1.70184e10	−	2.94767e10i	0.557436	−	0.965507i
$991$	5.59741e9	−	9.69501e9i	0.182696	−	0.316439i	−0.760102	−	0.649804i	$-0.774851\pi$
$991$	5.59741e9	−	9.69501e9i	0.182696	−	0.316439i	0.942798	+	0.333365i	$0.108184\pi$
$992$	−1.94192e9	−	3.36350e9i	−0.0631596	−	0.109396i
$993$	−2.62670e10			−0.851312
$994$	−2.95814e10	+	1.57686e10i	−0.955358	+	0.509261i
$995$	2.29579e10			0.738840
$996$	1.69723e10	+	2.93969e10i	0.544294	+	0.942746i
$997$	−9.08278e9	+	1.57318e10i	−0.290259	+	0.502744i	−0.973871	−	0.227102i	$-0.927075\pi$
$997$	−9.08278e9	+	1.57318e10i	−0.290259	+	0.502744i	0.683612	+	0.729846i	$0.260408\pi$
$998$	7.53230e9	−	1.30463e10i	0.239867	−	0.415462i
$999$	−1.23808e10	−	2.14442e10i	−0.392889	−	0.680503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	14.8.c.b.11.1	yes	4
3.2	odd	2		126.8.g.d.109.2		4
4.3	odd	2		112.8.i.b.81.2		4
7.2	even	3	inner	14.8.c.b.9.1	✓	4
7.3	odd	6		98.8.a.d.1.1		2
7.4	even	3		98.8.a.f.1.2		2
7.5	odd	6		98.8.c.m.79.2		4
7.6	odd	2		98.8.c.m.67.2		4
21.2	odd	6		126.8.g.d.37.2		4
28.23	odd	6		112.8.i.b.65.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
14.8.c.b.9.1	✓	4	7.2	even	3	inner
14.8.c.b.11.1	yes	4	1.1	even	1	trivial
98.8.a.d.1.1		2	7.3	odd	6
98.8.a.f.1.2		2	7.4	even	3
98.8.c.m.67.2		4	7.6	odd	2
98.8.c.m.79.2		4	7.5	odd	6
112.8.i.b.65.2		4	28.23	odd	6
112.8.i.b.81.2		4	4.3	odd	2
126.8.g.d.37.2		4	21.2	odd	6
126.8.g.d.109.2		4	3.2	odd	2

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} +(-29.4029 + 50.9274i) q^{3} +(-32.0000 + 55.4256i) q^{4} +(-212.141 - 367.439i) q^{5} -470.447 q^{6} +(-30.7182 + 906.973i) q^{7} -512.000 q^{8} +(-635.564 - 1100.83i) q^{9} +(1697.13 - 2939.51i) q^{10} +(-3944.43 + 6831.96i) q^{11} +(-1881.79 - 3259.35i) q^{12} +6717.46 q^{13} +(-6406.56 + 3415.07i) q^{14} +24950.2 q^{15} +(-2048.00 - 3547.24i) q^{16} +(3537.51 - 6127.14i) q^{17} +(5084.51 - 8806.63i) q^{18} +(13124.6 + 22732.4i) q^{19} +27154.0 q^{20} +(-45286.5 - 28232.0i) q^{21} -63110.9 q^{22} +(-6035.27 - 10453.4i) q^{23} +(15054.3 - 26074.8i) q^{24} +(-50945.0 + 88239.4i) q^{25} +(26869.8 + 46539.9i) q^{26} -53858.7 q^{27} +(-49286.5 - 30725.7i) q^{28} +3061.25 q^{29} +(99801.0 + 172860. i) q^{30} +(59262.6 - 102646. i) q^{31} +(16384.0 - 28377.9i) q^{32} +(-231956. - 401759. i) q^{33} +56600.1 q^{34} +(339774. - 181119. i) q^{35} +81352.1 q^{36} +(229876. + 398156. i) q^{37} +(-104997. + 181859. i) q^{38} +(-197513. + 342102. i) q^{39} +(108616. + 188129. i) q^{40} +316857. q^{41} +(14451.3 - 426682. i) q^{42} -31624.2 q^{43} +(-252444. - 437245. i) q^{44} +(-269658. + 467062. i) q^{45} +(48282.2 - 83627.2i) q^{46} +(-403277. - 698496. i) q^{47} +240869. q^{48} +(-821656. - 55721.1i) q^{49} -815120. q^{50} +(208026. + 360312. i) q^{51} +(-214959. + 372319. i) q^{52} +(-239664. + 415110. i) q^{53} +(-215435. - 373144. i) q^{54} +3.34710e6 q^{55} +(15727.7 - 464370. i) q^{56} -1.54360e6 q^{57} +(12245.0 + 21209.0i) q^{58} +(-337431. + 584448. i) q^{59} +(-798408. + 1.38288e6i) q^{60} +(283165. + 490455. i) q^{61} +948201. q^{62} +(1.01794e6 - 542623. i) q^{63} +262144. q^{64} +(-1.42505e6 - 2.46825e6i) q^{65} +(1.85565e6 - 3.21407e6i) q^{66} +(-592349. + 1.02598e6i) q^{67} +(226400. + 392137. i) q^{68} +709818. q^{69} +(2.61392e6 + 1.62954e6i) q^{70} +4.61736e6 q^{71} +(325409. + 563624. i) q^{72} +(-1.52400e6 + 2.63965e6i) q^{73} +(-1.83901e6 + 3.18525e6i) q^{74} +(-2.99587e6 - 5.18899e6i) q^{75} -1.67995e6 q^{76} +(-6.07524e6 - 3.78736e6i) q^{77} -3.16021e6 q^{78} +(3.45080e6 + 5.97696e6i) q^{79} +(-868929. + 1.50503e6i) q^{80} +(2.97358e6 - 5.15039e6i) q^{81} +(1.26743e6 + 2.19525e6i) q^{82} -9.01927e6 q^{83} +(3.01395e6 - 1.60661e6i) q^{84} -3.00180e6 q^{85} +(-126497. - 219099. i) q^{86} +(-90009.8 + 155902. i) q^{87} +(2.01955e6 - 3.49796e6i) q^{88} +(3.50739e6 + 6.07498e6i) q^{89} -4.31453e6 q^{90} +(-206348. + 6.09255e6i) q^{91} +772515. q^{92} +(3.48499e6 + 6.03617e6i) q^{93} +(3.22621e6 - 5.58796e6i) q^{94} +(5.56852e6 - 9.64496e6i) q^{95} +(963475. + 1.66879e6i) q^{96} +8.60029e6 q^{97} +(-2.90058e6 - 5.91548e6i) q^{98} +1.00278e7 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

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Database

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