LMFDB - Embedded newform 31.7.h.a.11.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,7,Mod(3,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([1])) N = Newforms(chi, 7, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.3"); S:= CuspForms(chi, 7); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	31.h (of order $30$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$7.13167659222$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$15$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			11.5
Character	$\chi$	$=$	31.11
Dual form			31.7.h.a.17.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.31599 - 7.12789i) q^{2} +(-16.2945 + 14.6716i) q^{3} +(6.33409 - 4.60199i) q^{4} +(-92.6733 - 160.515i) q^{5} +(142.315 + 82.1659i) q^{6} +(60.8261 + 578.722i) q^{7} +(-435.526 - 316.428i) q^{8} +(-25.9475 + 246.874i) q^{9} +(-929.502 + 1032.32i) q^{10} +(65.5293 - 147.181i) q^{11} +(-35.6921 + 167.918i) q^{12} +(774.922 + 3645.72i) q^{13} +(3984.19 - 1773.88i) q^{14} +(3865.07 + 1255.84i) q^{15} +(-1091.95 + 3360.67i) q^{16} +(-21.4797 - 48.2441i) q^{17} +(1819.79 - 386.808i) q^{18} +(-7816.18 - 1661.38i) q^{19} +(-1325.69 - 590.235i) q^{20} +(-9481.91 - 8537.55i) q^{21} +(-1200.86 - 126.215i) q^{22} +(-2117.21 + 2914.10i) q^{23} +(11739.2 - 1233.84i) q^{24} +(-9364.18 + 16219.2i) q^{25} +(24191.6 - 13967.0i) q^{26} +(-12594.6 - 17335.0i) q^{27} +(3048.55 + 3385.76i) q^{28} +(-31846.9 + 10347.7i) q^{29} -30458.3i q^{30} +(4204.27 - 29492.8i) q^{31} -7970.31 q^{32} +(1091.62 + 3359.66i) q^{33} +(-294.132 + 264.838i) q^{34} +(87256.5 - 63395.5i) q^{35} +(971.758 + 1683.13i) q^{36} +(58877.9 + 33993.2i) q^{37} +(6260.07 + 59560.6i) q^{38} +(-66115.5 - 48035.7i) q^{39} +(-10429.8 + 99232.9i) q^{40} +(-46507.4 + 51651.7i) q^{41} +(-38894.7 + 87358.9i) q^{42} +(24528.1 - 115396. i) q^{43} +(-262.257 - 1233.82i) q^{44} +(42031.6 - 18713.7i) q^{45} +(25674.8 + 8342.25i) q^{46} +(-35671.1 + 109784. i) q^{47} +(-31513.8 - 70781.0i) q^{48} +(-216141. + 45942.2i) q^{49} +(137296. + 29183.2i) q^{50} +(1057.82 + 470.971i) q^{51} +(21686.0 + 19526.1i) q^{52} +(-66897.2 - 7031.18i) q^{53} +(-94392.8 + 129921. i) q^{54} +(-29697.6 + 3121.34i) q^{55} +(156633. - 271296. i) q^{56} +(151736. - 87604.6i) q^{57} +(147514. + 203036. i) q^{58} +(-2215.41 - 2460.46i) q^{59} +(30261.1 - 9832.42i) q^{60} +93762.2i q^{61} +(-219959. + 38337.6i) q^{62} -144450. q^{63} +(88343.9 + 271895. i) q^{64} +(513378. - 462247. i) q^{65} +(21419.1 - 15561.9i) q^{66} +(-67908.2 - 117621. i) q^{67} +(-358.073 - 206.733i) q^{68} +(-8255.58 - 78546.6i) q^{69} +(-653962. - 475131. i) q^{70} +(-46361.9 + 441104. i) q^{71} +(89418.9 - 99309.7i) q^{72} +(-68772.1 + 154465. i) q^{73} +(105939. - 498403. i) q^{74} +(-85377.9 - 401672. i) q^{75} +(-57154.1 + 25446.6i) q^{76} +(89162.8 + 28970.7i) q^{77} +(-189270. + 582514. i) q^{78} +(-97297.2 - 218533. i) q^{79} +(640633. - 136171. i) q^{80} +(282546. + 60057.0i) q^{81} +(475878. + 211875. i) q^{82} +(-188983. - 170161. i) q^{83} +(-99349.0 - 10442.0i) q^{84} +(-5753.30 + 7918.74i) q^{85} +(-879334. + 92421.7i) q^{86} +(367111. - 635856. i) q^{87} +(-75112.0 + 43365.9i) q^{88} +(-180728. - 248751. i) q^{89} +(-230734. - 256256. i) q^{90} +(-2.06272e6 + 670219. i) q^{91} +28201.5i q^{92} +(364201. + 542254. i) q^{93} +865145. q^{94} +(457675. + 1.40858e6i) q^{95} +(129872. - 116937. i) q^{96} +(-11338.7 + 8238.02i) q^{97} +(828051. + 1.43423e6i) q^{98} +(34634.9 + 19996.5i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) $ 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{23}{30}\right)$

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 $

$2$	−2.31599	−	7.12789i	−0.289499	−	0.890986i	−0.985014	−	0.172475i	$-0.944824\pi$
$2$	−2.31599	−	7.12789i	−0.289499	−	0.890986i	0.695515	−	0.718512i	$-0.255176\pi$
$3$	−16.2945	+	14.6716i	−0.603499	+	0.543393i	−0.913237	−	0.407429i	$-0.866425\pi$
$3$	−16.2945	+	14.6716i	−0.603499	+	0.543393i	0.309738	+	0.950822i	$0.399759\pi$
$4$	6.33409	−	4.60199i	0.0989702	−	0.0719061i
$5$	−92.6733	−	160.515i	−0.741386	−	1.28412i	−0.951864	−	0.306520i	$-0.900835\pi$
$5$	−92.6733	−	160.515i	−0.741386	−	1.28412i	0.210478	−	0.977599i	$-0.432498\pi$
$6$	142.315	+	82.1659i	0.658868	+	0.380398i
$7$	60.8261	+	578.722i	0.177336	+	1.68724i	0.615340	+	0.788262i	$0.289019\pi$
$7$	60.8261	+	578.722i	0.177336	+	1.68724i	−0.438004	+	0.898973i	$0.644314\pi$
$8$	−435.526	−	316.428i	−0.850637	−	0.618024i
$9$	−25.9475	+	246.874i	−0.0355933	+	0.338648i
$10$	−929.502	+	1032.32i	−0.929502	+	1.03232i
$11$	65.5293	−	147.181i	0.0492331	−	0.110579i	−0.887254	−	0.461281i	$-0.847390\pi$
$11$	65.5293	−	147.181i	0.0492331	−	0.110579i	0.936487	+	0.350701i	$0.114057\pi$
$12$	−35.6921	+	167.918i	−0.0206552	+	0.0971749i
$13$	774.922	+	3645.72i	0.352718	+	1.65941i	0.694398	+	0.719591i	$0.255671\pi$
$13$	774.922	+	3645.72i	0.352718	+	1.65941i	−0.341680	+	0.939817i	$0.610996\pi$
$14$	3984.19	−	1773.88i	1.45196	−	0.646456i
$15$	3865.07	+	1255.84i	1.14521	+	0.372100i
$16$	−1091.95	+	3360.67i	−0.266589	+	0.820477i
$17$	−21.4797	−	48.2441i	−0.00437200	−	0.00981968i	0.911346	−	0.411641i	$-0.135044\pi$
$17$	−21.4797	−	48.2441i	−0.00437200	−	0.00981968i	−0.915718	+	0.401821i	$0.868377\pi$
$18$	1819.79	−	386.808i	0.312035	−	0.0663250i
$19$	−7816.18	−	1661.38i	−1.13955	−	0.242219i	−0.400779	−	0.916175i	$-0.631261\pi$
$19$	−7816.18	−	1661.38i	−1.13955	−	0.242219i	−0.738772	+	0.673956i	$0.764594\pi$
$20$	−1325.69	−	590.235i	−0.165711	−	0.0737793i
$21$	−9481.91	−	8537.55i	−1.02385	−	0.921882i
$22$	−1200.86	−	126.215i	−0.112778	−	0.0118534i
$23$	−2117.21	+	2914.10i	−0.174013	+	0.239508i	−0.887111	−	0.461556i	$-0.847291\pi$
$23$	−2117.21	+	2914.10i	−0.174013	+	0.239508i	0.713098	+	0.701064i	$0.247291\pi$
$24$	11739.2	−	1233.84i	0.849189	−	0.0892533i
$25$	−9364.18	+	16219.2i	−0.599308	+	1.03803i
$26$	24191.6	−	13967.0i	1.37640	−	0.794664i
$27$	−12594.6	−	17335.0i	−0.639872	−	0.880708i
$28$	3048.55	+	3385.76i	0.138873	+	0.154235i
$29$	−31846.9	+	10347.7i	−1.30579	+	0.424277i	−0.877592	−	0.479408i	$-0.840851\pi$
$29$	−31846.9	+	10347.7i	−1.30579	+	0.424277i	−0.428198	+	0.903685i	$0.640851\pi$
$30$		−	30458.3i		−	1.12809i
$31$	4204.27	−	29492.8i	0.141125	−	0.989992i
$31$	4204.27	−	29492.8i	0.141125	−	0.989992i
$32$	−7970.31			−0.243235
$33$	1091.62	+	3359.66i	0.0303759	+	0.0934874i
$34$	−294.132	+	264.838i	−0.00748351	+	0.00673818i
$35$	87256.5	−	63395.5i	2.03514	−	1.47861i
$36$	971.758	+	1683.13i	0.0208282	+	0.0360754i
$37$	58877.9	+	33993.2i	1.16238	+	0.671099i	0.951873	−	0.306493i	$-0.0991557\pi$
$37$	58877.9	+	33993.2i	1.16238	+	0.671099i	0.210505	+	0.977593i	$0.432489\pi$
$38$	6260.07	+	59560.6i	0.114085	+	1.08545i
$39$	−66115.5	−	48035.7i	−1.11458	−	0.809786i
$40$	−10429.8	+	99232.9i	−0.162966	+	1.55051i
$41$	−46507.4	+	51651.7i	−0.674793	+	0.749433i	−0.979153	−	0.203124i	$-0.934891\pi$
$41$	−46507.4	+	51651.7i	−0.674793	+	0.749433i	0.304360	+	0.952557i	$0.401557\pi$
$42$	−38894.7	+	87358.9i	−0.524979	+	1.17912i
$43$	24528.1	−	115396.i	0.308502	−	1.45139i	−0.501600	−	0.865100i	$-0.667255\pi$
$43$	24528.1	−	115396.i	0.308502	−	1.45139i	0.810102	−	0.586289i	$-0.199412\pi$
$44$	−262.257	−	1233.82i	−0.00307872	−	0.0144842i
$45$	42031.6	−	18713.7i	0.461253	−	0.205363i
$46$	25674.8	+	8342.25i	0.263775	+	0.0857057i
$47$	−35671.1	+	109784.i	−0.343576	+	1.05742i	0.618766	+	0.785576i	$0.287633\pi$
$47$	−35671.1	+	109784.i	−0.343576	+	1.05742i	−0.962342	+	0.271843i	$0.912367\pi$
$48$	−31513.8	−	70781.0i	−0.284955	−	0.640020i
$49$	−216141.	+	45942.2i	−1.83717	+	0.390502i
$50$	137296.	+	29183.2i	1.09837	+	0.233466i
$51$	1057.82	+	470.971i	0.00797444	+	0.00355045i
$52$	21686.0	+	19526.1i	0.154230	+	0.138869i
$53$	−66897.2	−	7031.18i	−0.449345	−	0.0472281i	−0.122846	−	0.992426i	$-0.539202\pi$
$53$	−66897.2	−	7031.18i	−0.449345	−	0.0472281i	−0.326499	+	0.945198i	$0.605869\pi$
$54$	−94392.8	+	129921.i	−0.599456	+	0.825081i
$55$	−29697.6	+	3121.34i	−0.178498	+	0.0187609i
$56$	156633.	−	271296.i	0.891904	−	1.54482i
$57$	151736.	−	87604.6i	0.819338	−	0.473045i
$58$	147514.	+	203036.i	0.756050	+	1.04061i
$59$	−2215.41	−	2460.46i	−0.0107869	−	0.0119801i	0.737727	−	0.675099i	$-0.235899\pi$
$59$	−2215.41	−	2460.46i	−0.0107869	−	0.0119801i	−0.748514	+	0.663119i	$0.769232\pi$
$60$	30261.1	−	9832.42i	0.140098	−	0.0455205i
$61$			93762.2i			0.413084i	0.978438	+	0.206542i	$0.0662210\pi$
$61$			93762.2i			0.413084i	−0.978438	+	0.206542i	$0.933779\pi$
$62$	−219959.	+	38337.6i	−0.922925	+	0.160861i
$63$	−144450.			−0.577691
$64$	88343.9	+	271895.i	0.337005	+	1.03720i
$65$	513378.	−	462247.i	1.86938	−	1.68319i
$66$	21419.1	−	15561.9i	0.0745022	−	0.0541290i
$67$	−67908.2	−	117621.i	−0.225787	−	0.391074i	0.730769	−	0.682625i	$-0.239162\pi$
$67$	−67908.2	−	117621.i	−0.225787	−	0.391074i	−0.956555	+	0.291552i	$0.905829\pi$
$68$	−358.073	−	206.733i	−0.00113879	−	0.000657482i
$69$	−8255.58	−	78546.6i	−0.0251305	−	0.239100i
$70$	−653962.	−	475131.i	−1.90659	−	1.38522i
$71$	−46361.9	+	441104.i	−0.129535	+	1.23244i	0.715839	+	0.698265i	$0.246044\pi$
$71$	−46361.9	+	441104.i	−0.129535	+	1.23244i	−0.845374	+	0.534175i	$0.820622\pi$
$72$	89418.9	−	99309.7i	0.239570	−	0.266069i
$73$	−68772.1	+	154465.i	−0.176784	+	0.397064i	−0.980104	−	0.198484i	$-0.936398\pi$
$73$	−68772.1	+	154465.i	−0.176784	+	0.397064i	0.803320	+	0.595548i	$0.203065\pi$
$74$	105939.	−	498403.i	0.261433	−	1.22995i
$75$	−85377.9	−	401672.i	−0.202377	−	0.952110i
$76$	−57154.1	+	25446.6i	−0.130199	+	0.0579682i
$77$	89162.8	+	28970.7i	0.195304	+	0.0634582i
$78$	−189270.	+	582514.i	−0.398840	+	1.22750i
$79$	−97297.2	−	218533.i	−0.197342	−	0.443237i	0.787586	−	0.616205i	$-0.211331\pi$
$79$	−97297.2	−	218533.i	−0.197342	−	0.443237i	−0.984927	+	0.172968i	$0.944664\pi$
$80$	640633.	−	136171.i	1.25124	−	0.265958i
$81$	282546.	+	60057.0i	0.531660	+	0.113008i
$82$	475878.	+	211875.i	0.863086	+	0.384271i
$83$	−188983.	−	170161.i	−0.330513	−	0.297596i	0.487120	−	0.873335i	$-0.338048\pi$
$83$	−188983.	−	170161.i	−0.330513	−	0.297596i	−0.817633	+	0.575740i	$0.804714\pi$
$84$	−99349.0	−	10442.0i	−0.167620	−	0.0176176i
$85$	−5753.30	+	7918.74i	−0.00936829	+	0.0128944i
$86$	−879334.	+	92421.7i	−1.38248	+	0.145304i
$87$	367111.	−	635856.i	0.557494	−	0.965608i
$88$	−75112.0	+	43365.9i	−0.110220	+	0.0636357i
$89$	−180728.	−	248751.i	−0.256364	−	0.352854i	0.661364	−	0.750066i	$-0.269978\pi$
$89$	−180728.	−	248751.i	−0.256364	−	0.352854i	−0.917727	+	0.397211i	$0.869978\pi$
$90$	−230734.	−	256256.i	−0.316508	−	0.351517i
$91$	−2.06272e6	+	670219.i	−2.73726	+	0.889390i
$92$			28201.5i			0.0362168i
$93$	364201.	+	542254.i	0.452785	+	0.674145i
$94$	865145.			1.04161
$95$	457675.	+	1.40858e6i	0.533810	+	1.64290i
$96$	129872.	−	116937.i	0.146792	−	0.132172i
$97$	−11338.7	+	8238.02i	−0.0124236	+	0.00902625i	−0.593980	−	0.804480i	$-0.702444\pi$
$97$	−11338.7	+	8238.02i	−0.0124236	+	0.00902625i	0.581556	+	0.813506i	$0.302444\pi$
$98$	828051.	+	1.43423e6i	0.879790	+	1.52384i
$99$	34634.9	+	19996.5i	0.0356951	+	0.0206086i
$100$	15327.1	+	145828.i	0.0153271	+	0.145828i
$101$	928766.	+	674788.i	0.901451	+	0.654943i	0.938838	−	0.344358i	$-0.111904\pi$
$101$	928766.	+	674788.i	0.901451	+	0.654943i	−0.0373872	+	0.999301i	$0.511904\pi$
$102$	907.131	−	8630.77i	0.000854810	−	0.00813297i
$103$	30884.1	−	34300.2i	0.0282633	−	0.0313896i	−0.728847	−	0.684676i	$-0.759944\pi$
$103$	30884.1	−	34300.2i	0.0282633	−	0.0313896i	0.757111	+	0.653287i	$0.226610\pi$
$104$	816110.	−	1.83301e6i	0.725519	−	1.62954i
$105$	−491684.	+	2.31319e6i	−0.424735	+	1.99822i
$106$	104816.	+	493120.i	0.0880054	+	0.414033i
$107$	1.49476e6	−	665509.i	1.22017	−	0.543254i	0.307341	−	0.951600i	$-0.400561\pi$
$107$	1.49476e6	−	665509.i	1.22017	−	0.543254i	0.912827	+	0.408346i	$0.133894\pi$
$108$	−159551.	−	51841.1i	−0.126656	−	0.0411532i
$109$	684739.	−	2.10741e6i	0.528744	−	1.62731i	−0.228047	−	0.973650i	$-0.573234\pi$
$109$	684739.	−	2.10741e6i	0.528744	−	1.62731i	0.756791	−	0.653657i	$-0.226766\pi$
$110$	91027.9	+	204452.i	0.0683906	+	0.153608i
$111$	−1.45812e6	+	309933.i	−1.06616	+	0.226620i
$112$	−2.01131e6	−	427518.i	−1.43161	−	0.304299i
$113$	−685961.	−	305410.i	−0.475406	−	0.211664i	0.155024	−	0.987911i	$-0.450455\pi$
$113$	−685961.	−	305410.i	−0.475406	−	0.211664i	−0.630429	+	0.776247i	$0.717121\pi$
$114$	−975854.	−	878663.i	−0.658674	−	0.593073i
$115$	663965.	+	69785.5i	0.436568	+	0.0458851i
$116$	−154101.	+	212102.i	−0.0987263	+	0.135885i
$117$	−920142.	+	96710.8i	−0.574509	+	0.0603834i
$118$	−12407.0	+	21489.6i	−0.00755130	+	0.0130792i
$119$	26613.4	−	15365.2i	0.0157928	−	0.00911798i
$120$	−1.28596e6	−	1.76997e6i	−0.744189	−	1.02429i
$121$	1.16804e6	+	1.29724e6i	0.659327	+	0.732256i
$122$	668327.	−	217153.i	0.368052	−	0.119587i
$123$		−	1.52397e6i		−	0.818960i
$124$	−109095.	−	206158.i	−0.0572192	−	0.108127i
$125$	575198.			0.294501
$126$	334545.	+	1.02962e6i	0.167241	+	0.514714i
$127$	1.35965e6	−	1.22423e6i	0.663767	−	0.597659i	−0.266812	−	0.963748i	$-0.585970\pi$
$127$	1.35965e6	−	1.22423e6i	0.663767	−	0.597659i	0.930579	+	0.366090i	$0.119304\pi$
$128$	1.32075e6	−	959582.i	0.629783	−	0.457564i
$129$	1.29337e6	+	2.24018e6i	0.602494	+	1.04355i
$130$	−4.48383e6	−	2.58874e6i	−2.04089	−	1.17831i
$131$	35984.4	+	342368.i	0.0160066	+	0.152293i	0.999606	−	0.0280752i	$-0.00893778\pi$
$131$	35984.4	+	342368.i	0.0160066	+	0.152293i	−0.983599	+	0.180368i	$0.942271\pi$
$132$	22375.5	+	16256.8i	0.00972862	+	0.00706826i
$133$	486049.	−	4.62445e6i	0.206598	−	1.96564i
$134$	−681111.	+	756451.i	−0.283076	+	0.314388i
$135$	−1.61534e6	+	3.62811e6i	−0.656541	+	1.47462i
$136$	−5910.85	+	27808.3i	−0.00234981	+	0.0110550i
$137$	421138.	+	1.98130e6i	0.163781	+	0.770527i	0.980970	+	0.194158i	$0.0621974\pi$
$137$	421138.	+	1.98130e6i	0.163781	+	0.770527i	−0.817190	+	0.576369i	$0.804469\pi$
$138$	−540752.	+	240758.i	−0.205760	+	0.0916102i
$139$	−2.97758e6	−	967475.i	−1.10871	−	0.360243i	−0.303264	−	0.952907i	$-0.598076\pi$
$139$	−2.97758e6	−	967475.i	−1.10871	−	0.360243i	−0.805450	+	0.592664i	$0.798076\pi$
$140$	260945.	−	803107.i	0.0950966	−	0.292677i
$141$	−1.02947e6	−	2.31223e6i	−0.367246	−	0.824848i
$142$	3.25151e6	−	691130.i	1.13559	−	0.241376i
$143$	587361.	+	124847.i	0.200862	+	0.0426945i
$144$	−801330.	−	356775.i	−0.268364	−	0.119483i
$145$	4.61232e6	+	4.15295e6i	1.51292	+	1.36224i
$146$	1.26028e6	+	132461.i	0.404957	+	0.0425627i
$147$	2.84786e6	−	3.91974e6i	0.896532	−	1.23397i
$148$	529375.	−	55639.5i	0.163297	−	0.0171632i
$149$	594740.	−	1.03012e6i	0.179791	−	0.311407i	−0.762018	−	0.647556i	$-0.775791\pi$
$149$	594740.	−	1.03012e6i	0.179791	−	0.311407i	0.941809	+	0.336149i	$0.109125\pi$
$150$	−2.66534e6	+	1.53883e6i	−0.789729	+	0.455950i
$151$	1.73912e6	+	2.39369e6i	0.505124	+	0.695243i	0.983087	−	0.183136i	$-0.0586250\pi$
$151$	1.73912e6	+	2.39369e6i	0.505124	+	0.695243i	−0.477964	+	0.878379i	$0.658625\pi$
$152$	2.87844e6	+	3.19684e6i	0.819647	+	0.910310i
$153$	12467.6	−	4050.96i	0.00348103	−	0.00113105i
$154$		−	702639.i		−	0.192384i
$155$	−5.12366e6	+	2.05835e6i	−1.37590	+	0.552745i
$156$	−639842.			−0.168538
$157$	−360524.	−	1.10958e6i	−0.0931612	−	0.286721i	0.893609	−	0.448847i	$-0.148165\pi$
$157$	−360524.	−	1.10958e6i	−0.0931612	−	0.286721i	−0.986770	+	0.162126i	$0.948165\pi$
$158$	−1.33234e6	+	1.19964e6i	−0.337788	+	0.304146i
$159$	1.19321e6	−	866920.i	0.296843	−	0.215669i
$160$	738635.	+	1.27935e6i	0.180331	+	0.312342i
$161$	−1.81523e6	−	1.04802e6i	−0.434965	−	0.251127i
$162$	−226294.	−	2.15305e6i	−0.0532266	−	0.506417i
$163$	3.69351e6	+	2.68349e6i	0.852857	+	0.619637i	0.925932	−	0.377690i	$-0.123281\pi$
$163$	3.69351e6	+	2.68349e6i	0.852857	+	0.619637i	−0.0730756	+	0.997326i	$0.523281\pi$
$164$	−56881.7	+	541193.i	−0.0128956	+	0.122693i
$165$	438111.	−	486572.i	0.0975287	−	0.108317i
$166$	−775207.	+	1.74114e6i	−0.169470	+	0.380636i
$167$	−335690.	+	1.57930e6i	−0.0720758	+	0.339090i	−0.999380	−	0.0352196i	$-0.988787\pi$
$167$	−335690.	+	1.57930e6i	−0.0720758	+	0.339090i	0.927304	+	0.374310i	$0.122120\pi$
$168$	1.42810e6	+	6.71867e6i	0.301183	+	1.41695i
$169$	−8.28126e6	+	3.68705e6i	−1.71568	+	0.763870i
$170$	69768.5	+	22669.2i	0.0142008	+	0.00461412i
$171$	612963.	−	1.88650e6i	0.122587	−	0.377285i
$172$	−375686.	−	843804.i	−0.0738311	−	0.165827i
$173$	4.42854e6	−	941314.i	0.855307	−	0.181801i	0.240666	−	0.970608i	$-0.422634\pi$
$173$	4.42854e6	−	941314.i	0.855307	−	0.181801i	0.614641	+	0.788807i	$0.289301\pi$
$174$	−5.38254e6	−	1.14409e6i	−1.02174	−	0.217177i
$175$	−9.95601e6	−	4.43270e6i	−1.85768	−	0.827093i
$176$	423073.	+	380937.i	0.0776028	+	0.0698739i
$177$	72197.9	+	7588.30i	0.0130198	+	0.00136844i
$178$	−1.35451e6	+	1.86432e6i	−0.240171	+	0.330568i
$179$	3.45425e6	−	363056.i	0.602274	−	0.0633015i	0.201516	−	0.979485i	$-0.435413\pi$
$179$	3.45425e6	−	363056.i	0.602274	−	0.0633015i	0.400758	+	0.916184i	$0.368747\pi$
$180$	180112.	−	311963.i	0.0308834	−	0.0534917i
$181$	−5.89715e6	+	3.40472e6i	−0.994503	+	0.574177i	−0.906617	−	0.421954i	$-0.861344\pi$
$181$	−5.89715e6	+	3.40472e6i	−0.994503	+	0.574177i	−0.0878860	+	0.996131i	$0.528011\pi$
$182$	9.55449e6	+	1.31506e7i	1.58487	+	2.18139i
$183$	−1.37564e6	−	1.52781e6i	−0.224467	−	0.249296i
$184$	1.84421e6	−	599219.i	0.296044	−	0.0961904i
$185$		−	1.26010e7i		−	1.99018i
$186$	3.02164e6	−	3.85184e6i	0.469573	−	0.598590i
$187$	−8508.17			−0.00130110
$188$	279282.	+	859542.i	0.0420310	+	0.129358i
$189$	9.26604e6	−	8.34318e6i	1.37249	−	1.23579i
$190$	8.98022e6	−	6.52451e6i	1.30926	−	0.951234i
$191$	−5.85688e6	−	1.01444e7i	−0.840556	−	1.45589i	−0.889426	−	0.457080i	$-0.848895\pi$
$191$	−5.85688e6	−	1.01444e7i	−0.840556	−	1.45589i	0.0488697	−	0.998805i	$-0.484438\pi$
$192$	−5.42865e6	−	3.13423e6i	−0.766987	−	0.442820i
$193$	814403.	+	7.74853e6i	0.113284	+	1.07782i	0.892494	+	0.451060i	$0.148954\pi$
$193$	814403.	+	7.74853e6i	0.113284	+	1.07782i	−0.779210	+	0.626763i	$0.784380\pi$
$194$	84979.9	+	61741.5i	0.0116389	+	0.00845614i
$195$	−1.58331e6	+	1.50642e7i	−0.213531	+	2.03161i
$196$	−1.15763e6	+	1.28568e6i	−0.153745	+	0.170752i
$197$	−605102.	+	1.35908e6i	−0.0791461	+	0.177765i	−0.948784	−	0.315924i	$-0.897685\pi$
$197$	−605102.	+	1.35908e6i	−0.0791461	+	0.177765i	0.869638	+	0.493689i	$0.164352\pi$
$198$	62318.5	−	293185.i	0.00802826	−	0.0377700i
$199$	995047.	+	4.68133e6i	0.126265	+	0.594032i	0.995095	+	0.0989211i	$0.0315391\pi$
$199$	995047.	+	4.68133e6i	0.126265	+	0.594032i	−0.868830	+	0.495111i	$0.835128\pi$
$200$	9.21057e6	−	4.10081e6i	1.15132	−	0.512601i
$201$	2.83221e6	+	920241.i	0.348769	+	0.113322i
$202$	2.65880e6	−	8.18294e6i	0.322576	−	0.992786i
$203$	−7.92556e6	−	1.78011e7i	−0.947418	−	2.12794i
$204$	8867.72	−	1884.89i	0.00104453	−	0.000222022i
$205$	1.26009e7	+	2.67839e6i	1.46264	+	0.310894i
$206$	−316015.	−	140699.i	−0.0361499	−	0.0160950i
$207$	−664479.	−	598299.i	−0.0749152	−	0.0674540i
$208$	−1.30982e7	−	1.37668e6i	−1.45554	−	0.152983i
$209$	−756712.	+	1.04153e6i	−0.0828880	+	0.114086i
$210$	1.76269e7	−	1.85266e6i	1.90335	−	0.200050i
$211$	−3.16824e6	+	5.48755e6i	−0.337264	+	0.584159i	−0.983917	−	0.178625i	$-0.942835\pi$
$211$	−3.16824e6	+	5.48755e6i	−0.337264	+	0.584159i	0.646653	+	0.762785i	$0.276168\pi$
$212$	−456090.	+	263324.i	−0.0478678	+	0.0276365i
$213$	−5.71626e6	−	7.86775e6i	−0.591525	−	0.814164i
$214$	−8.20553e6	−	9.11316e6i	−0.837269	−	0.929882i
$215$	−2.07958e7	+	6.75697e6i	−2.09248	+	0.679887i
$216$			1.15351e7i			1.14462i
$217$	1.73239e7	+	639165.i	1.69538	+	0.0625510i
$218$	−1.66072e7			−1.60298
$219$	−1.14564e6	−	3.52591e6i	−0.109073	−	0.335691i
$220$	−173743.	+	156439.i	−0.0163169	+	0.0146918i
$221$	159239.	−	115694.i	0.0147528	−	0.0107185i
$222$	5.58616e6	+	9.67551e6i	0.510569	+	0.884332i
$223$	−9.34654e6	−	5.39623e6i	−0.842823	−	0.486604i	0.0154000	−	0.999881i	$-0.495098\pi$
$223$	−9.34654e6	−	5.39623e6i	−0.842823	−	0.486604i	−0.858223	+	0.513278i	$0.828431\pi$
$224$	−484803.	−	4.61259e6i	−0.0431341	−	0.410394i
$225$	−3.76114e6	−	2.73262e6i	−0.330196	−	0.239901i
$226$	−588246.	+	5.59678e6i	−0.0509605	+	0.484856i
$227$	−1.63032e6	+	1.81066e6i	−0.139379	+	0.154796i	−0.808793	−	0.588094i	$-0.799879\pi$
$227$	−1.63032e6	+	1.81066e6i	−0.139379	+	0.154796i	0.669414	+	0.742890i	$0.266545\pi$
$228$	557952.	−	1.25318e6i	0.0470752	−	0.105733i
$229$	−3.27394e6	+	1.54027e7i	−0.272624	+	1.28259i	0.602275	+	0.798289i	$0.294261\pi$
$229$	−3.27394e6	+	1.54027e7i	−0.272624	+	1.28259i	−0.874899	+	0.484306i	$0.839072\pi$
$230$	−1.04031e6	−	4.89429e6i	−0.0855029	−	0.402260i
$231$	−1.87791e6	+	836099.i	−0.152349	+	0.0678300i
$232$	1.71445e7	+	5.57058e6i	1.37297	+	0.446104i
$233$	1.51075e6	−	4.64961e6i	0.119433	−	0.367577i	−0.873413	−	0.486981i	$-0.838098\pi$
$233$	1.51075e6	−	4.64961e6i	0.119433	−	0.367577i	0.992846	+	0.119404i	$0.0380982\pi$
$234$	2.82038e6	+	6.33469e6i	0.220121	+	0.494399i
$235$	2.09278e7	−	4.44834e6i	1.61257	−	0.342763i
$236$	−25355.6	−	5389.50i	−0.00192903	−	0.000410027i
$237$	4.79164e6	+	2.13338e6i	0.359947	+	0.160259i
$238$	−171158.	−	154111.i	−0.0126960	−	0.0114315i
$239$	−1.23948e7	−	1.30274e6i	−0.907915	−	0.0954257i	−0.360954	−	0.932584i	$-0.617549\pi$
$239$	−1.23948e7	−	1.30274e6i	−0.907915	−	0.0954257i	−0.546961	+	0.837158i	$0.684215\pi$
$240$	−8.44093e6	+	1.16179e7i	−0.610599	+	0.840418i
$241$	−1.10787e7	+	1.16442e6i	−0.791479	+	0.0831878i	−0.491636	−	0.870801i	$-0.663601\pi$
$241$	−1.10787e7	+	1.16442e6i	−0.791479	+	0.0831878i	−0.299843	+	0.953989i	$0.596934\pi$
$242$	6.54140e6	−	1.13300e7i	0.461556	−	0.799439i
$243$	8.04262e6	−	4.64341e6i	0.560504	−	0.323607i
$244$	431493.	+	593899.i	0.0297032	+	0.0408830i
$245$	2.74049e7	+	3.04362e7i	1.86350	+	2.06963i
$246$	−1.08627e7	+	3.52951e6i	−0.729682	+	0.237088i
$247$		−	2.97830e7i		−	1.97641i
$248$	−1.11634e7	+	1.15146e7i	−0.731885	+	0.754905i
$249$	5.57592e6			0.361176
$250$	−1.33215e6	−	4.09995e6i	−0.0852579	−	0.262397i
$251$	−2.00653e6	+	1.80669e6i	−0.126889	+	0.114252i	−0.730132	−	0.683306i	$-0.760542\pi$
$251$	−2.00653e6	+	1.80669e6i	−0.126889	+	0.114252i	0.603243	+	0.797557i	$0.293875\pi$
$252$	−914958.	+	664756.i	−0.0571741	+	0.0415394i
$253$	290160.	+	502573.i	0.0179175	+	0.0310340i
$254$	−1.18751e7	−	6.85611e6i	−0.724665	−	0.418386i
$255$	−22433.7	−	213442.i	−0.00135294	−	0.0128724i
$256$	4.90374e6	+	3.56278e6i	0.292286	+	0.212358i
$257$	−3.01604e6	+	2.86957e7i	−0.177680	+	1.69051i	0.435199	+	0.900334i	$0.356678\pi$
$257$	−3.01604e6	+	2.86957e7i	−0.177680	+	1.69051i	−0.612879	+	0.790177i	$0.709989\pi$
$258$	1.29723e7	−	1.44072e7i	0.755367	−	0.838920i
$259$	−1.60913e7	+	3.61416e7i	−0.926171	+	2.08022i
$260$	1.12453e6	−	5.29047e6i	0.0639807	−	0.301006i
$261$	−1.72823e6	−	8.13068e6i	−0.0972031	−	0.457305i
$262$	2.35702e6	−	1.04941e6i	0.131057	−	0.0583503i
$263$	1.71558e7	+	5.57425e6i	0.943068	+	0.306421i	0.739896	−	0.672722i	$-0.234875\pi$
$263$	1.71558e7	+	5.57425e6i	0.943068	+	0.306421i	0.203172	+	0.979143i	$0.434875\pi$
$264$	587662.	−	1.80864e6i	0.0319386	−	0.0982969i
$265$	5.07097e6	+	1.13896e7i	0.272492	+	0.612027i
$266$	−3.40882e7	+	7.24568e6i	−1.81117	+	0.384976i
$267$	6.59446e6	+	1.40170e6i	0.346454	+	0.0736410i
$268$	−971425.	−	432506.i	−0.0504667	−	0.0224692i
$269$	−1.24004e7	−	1.11654e7i	−0.637057	−	0.573609i	0.286020	−	0.958224i	$-0.407668\pi$
$269$	−1.24004e7	−	1.11654e7i	−0.637057	−	0.573609i	−0.923077	+	0.384615i	$0.874334\pi$
$270$	2.96019e7	+	3.11128e6i	1.50393	+	0.158069i
$271$	1.62892e7	−	2.24201e7i	0.818449	−	1.12650i	−0.171516	−	0.985181i	$-0.554866\pi$
$271$	1.62892e7	−	2.24201e7i	0.818449	−	1.12650i	0.989964	−	0.141317i	$-0.0451336\pi$
$272$	185587.	−	19506.0i	0.00922235	−	0.000969308i
$273$	2.37778e7	−	4.11843e7i	1.16865	−	2.02415i
$274$	1.31471e7	−	7.59049e6i	0.639114	−	0.368993i
$275$	1.77354e6	+	2.44107e6i	0.0852791	+	0.117377i
$276$	−413762.	−	459529.i	−0.0196799	−	0.0218568i
$277$	1.65349e7	−	5.37252e6i	0.777970	−	0.252778i	0.106997	−	0.994259i	$-0.465877\pi$
$277$	1.65349e7	−	5.37252e6i	0.777970	−	0.252778i	0.670973	+	0.741482i	$0.265877\pi$
$278$			2.34645e7i			1.09214i
$279$	7.17193e6	+	1.80319e6i	0.330235	+	0.0830289i
$280$	−5.80626e7			−2.64498
$281$	4.08007e6	+	1.25572e7i	0.183886	+	0.565942i	0.999927	−	0.0120509i	$-0.00383600\pi$
$281$	4.08007e6	+	1.25572e7i	0.183886	+	0.565942i	−0.816042	+	0.577993i	$0.803836\pi$
$282$	−1.40971e7	+	1.26931e7i	−0.628611	+	0.566003i
$283$	−1.77504e7	+	1.28964e7i	−0.783159	+	0.568998i	−0.905925	−	0.423437i	$-0.860823\pi$
$283$	−1.77504e7	+	1.28964e7i	−0.783159	+	0.568998i	0.122767	+	0.992436i	$0.460823\pi$
$284$	1.73629e6	+	3.00735e6i	0.0757998	+	0.131289i
$285$	−2.81237e7	−	1.62372e7i	−1.21489	−	0.701418i
$286$	−470425.	−	4.47579e6i	−0.0201091	−	0.191325i
$287$	−3.27208e7	−	2.37731e7i	−1.38413	−	1.00563i
$288$	206810.	−	1.96766e6i	0.00865752	−	0.0823708i
$289$	1.61493e7	−	1.79356e7i	0.669053	−	0.743059i
$290$	1.89197e7	−	4.24943e7i	0.775746	−	1.74235i
$291$	63892.5	−	300590.i	0.00259281	−	0.0121982i
$292$	275235.	+	1.29488e6i	0.0110549	+	0.0520093i
$293$	−39508.0	+	17590.1i	−0.00157066	+	0.000699304i	−0.407522	−	0.913195i	$-0.633607\pi$
$293$	−39508.0	+	17590.1i	−0.00157066	+	0.000699304i	0.405951	+	0.913895i	$0.366940\pi$
$294$	−3.45351e7	−	1.12211e7i	−1.35900	−	0.441565i
$295$	−189631.	+	583625.i	−0.00738659	+	0.0227336i
$296$	−1.48865e7	−	3.34356e7i	−0.574007	−	1.28924i
$297$	−3.37669e6	+	717739.i	−0.128891	+	0.0273966i
$298$	−8.71999e6	−	1.85349e6i	−0.329509	−	0.0700393i
$299$	−1.22647e7	−	5.46057e6i	−0.458819	−	0.204279i
$300$	−2.38928e6	−	2.15132e6i	−0.0884918	−	0.0796784i
$301$	6.82739e7	+	7.17587e6i	2.50354	+	0.263133i
$302$	1.30342e7	−	1.79400e7i	0.473219	−	0.651330i
$303$	−2.50340e7	+	2.63118e6i	−0.899916	+	0.0945850i
$304$	1.41182e7	−	2.44535e7i	0.502527	−	0.870402i
$305$	1.50502e7	−	8.68926e6i	0.530449	−	0.306255i
$306$	−57749.6	−	79485.5i	−0.00201551	−	0.00277411i
$307$	1.70679e7	+	1.89558e7i	0.589881	+	0.655130i	0.961998	−	0.273056i	$-0.0880346\pi$
$307$	1.70679e7	+	1.89558e7i	0.589881	+	0.655130i	−0.372117	+	0.928186i	$0.621368\pi$
$308$	698088.	−	226823.i	0.0238923	−	0.00776309i
$309$			1.01202e6i			0.0343016i
$310$	2.65381e7	+	3.17538e7i	0.890808	+	1.06589i
$311$	357166.			0.0118738			0.00593689	−	0.999982i	$-0.498110\pi$
$311$	357166.			0.0118738			0.00593689	+	0.999982i	$0.498110\pi$
$312$	1.35952e7	+	4.18416e7i	0.447632	+	1.37767i
$313$	−1.68147e7	+	1.51400e7i	−0.548347	+	0.493734i	−0.896100	−	0.443853i	$-0.853611\pi$
$313$	−1.68147e7	+	1.51400e7i	−0.548347	+	0.493734i	0.347753	+	0.937586i	$0.386945\pi$
$314$	−7.07399e6	+	5.13955e6i	−0.228494	+	0.166011i
$315$	1.33866e7	+	2.31863e7i	0.428292	+	0.741823i
$316$	−1.62198e6	−	936449.i	−0.0514024	−	0.0296772i
$317$	5.01419e6	+	4.77068e7i	0.157407	+	1.49762i	0.733191	+	0.680022i	$0.238030\pi$
$317$	5.01419e6	+	4.77068e7i	0.157407	+	1.49762i	−0.575785	+	0.817601i	$0.695303\pi$
$318$	−8.94278e6	−	6.49731e6i	−0.278094	−	0.202047i
$319$	−563920.	+	5.36534e6i	−0.0173718	+	0.165282i
$320$	3.54560e7	−	3.93779e7i	1.08203	−	1.20172i
$321$	−1.45922e7	+	3.27746e7i	−0.441170	+	0.990884i
$322$	−3.26614e6	+	1.53660e7i	−0.0978290	+	0.460249i
$323$	87737.0	+	412770.i	0.00260361	+	0.0122490i
$324$	2.06605e6	−	919866.i	0.0607444	−	0.0270452i
$325$	−6.63873e7	−	2.15705e7i	−1.93390	−	0.628364i
$326$	1.05735e7	−	3.25418e7i	0.305187	−	0.939268i
$327$	1.97616e7	+	4.43853e7i	0.565171	+	1.26939i
$328$	3.65992e7	−	7.77941e6i	1.03717	−	0.220458i
$329$	−6.57043e7	−	1.39659e7i	−1.84504	−	0.392176i
$330$	−4.48289e6	−	1.99591e6i	−0.124743	−	0.0555392i
$331$	−1.77414e6	−	1.59744e6i	−0.0489219	−	0.0440494i	0.644307	−	0.764767i	$-0.277146\pi$
$331$	−1.77414e6	−	1.59744e6i	−0.0489219	−	0.0440494i	−0.693229	+	0.720717i	$0.743813\pi$
$332$	−1.98012e6	−	208119.i	−0.0541099	−	0.00568718i
$333$	−9.91978e6	+	1.36534e7i	−0.268639	+	0.369750i
$334$	1.20345e7	−	1.26488e6i	0.322990	−	0.0339477i
$335$	−1.25866e7	+	2.18006e7i	−0.334790	+	0.579873i
$336$	3.90457e7	−	2.25430e7i	1.02933	−	0.594284i
$337$	−1.34666e6	−	1.85352e6i	−0.0351860	−	0.0484293i	0.791062	−	0.611737i	$-0.209529\pi$
$337$	−1.34666e6	−	1.85352e6i	−0.0351860	−	0.0484293i	−0.826248	+	0.563307i	$0.809529\pi$
$338$	4.54602e7	+	5.04887e7i	1.17728	+	1.30751i
$339$	1.56582e7	−	5.08767e6i	0.401924	−	0.130593i
$340$			76634.7i			0.00194979i
$341$	−4.06529e6	−	2.55143e6i	−0.102525	−	0.0643459i
$342$	−1.48664e7			−0.371645
$343$	−1.85791e7	−	5.71806e7i	−0.460407	−	1.41699i
$344$	−4.71971e7	+	4.24964e7i	−1.15942	+	1.04394i
$345$	−1.18428e7	+	8.60432e6i	−0.288402	+	0.209536i
$346$	−1.69660e7	−	2.93860e7i	−0.409593	−	0.709435i
$347$	4.72535e7	+	2.72818e7i	1.13096	+	0.652958i	0.944175	−	0.329443i	$-0.106861\pi$
$347$	4.72535e7	+	2.72818e7i	1.13096	+	0.652958i	0.186781	+	0.982402i	$0.440194\pi$
$348$	−600882.	−	5.71701e6i	−0.0142578	−	0.135654i
$349$	−4.19723e6	−	3.04947e6i	−0.0987385	−	0.0717377i	0.537321	−	0.843378i	$-0.319437\pi$
$349$	−4.19723e6	−	3.04947e6i	−0.0987385	−	0.0717377i	−0.636059	+	0.771640i	$0.719437\pi$
$350$	−8.53777e6	+	8.12315e7i	−0.199132	+	1.89461i
$351$	5.34386e7	−	5.93496e7i	1.23576	−	1.37245i
$352$	−522288.	+	1.17308e6i	−0.0119752	+	0.0268967i
$353$	−1.17945e7	+	5.54888e7i	−0.268137	+	1.26148i	0.613553	+	0.789653i	$0.289740\pi$
$353$	−1.17945e7	+	5.54888e7i	−0.268137	+	1.26148i	−0.881690	+	0.471830i	$0.843594\pi$
$354$	−113121.	−	532193.i	−0.00254996	−	0.0119966i
$355$	7.51002e7	−	3.34368e7i	1.67863	−	0.747376i
$356$	−2.28950e6	−	743904.i	−0.0507447	−	0.0164880i
$357$	−208218.	+	640830.i	−0.00457629	+	0.0140844i
$358$	−1.05878e7	−	2.37806e7i	−0.230759	−	0.518292i
$359$	−4.13877e7	+	8.79723e6i	−0.894516	+	0.190135i	−0.632162	−	0.774836i	$-0.717832\pi$
$359$	−4.13877e7	+	8.79723e6i	−0.894516	+	0.190135i	−0.262354	+	0.964972i	$0.584499\pi$
$360$	−2.42274e7	−	5.14970e6i	−0.519278	−	0.110376i
$361$	1.53539e7	+	6.83601e6i	0.326361	+	0.145305i
$362$	3.79262e7	+	3.41489e7i	0.799491	+	0.719865i
$363$	−3.80651e7	−	4.00080e6i	−0.795806	−	0.0836426i
$364$	−9.98113e6	+	1.37378e7i	−0.206955	+	0.284849i
$365$	3.11672e7	−	3.27580e6i	0.640943	−	0.0673658i
$366$	−7.70406e6	+	1.33438e7i	−0.157136	+	0.272168i
$367$	−2.71613e6	+	1.56816e6i	−0.0549481	+	0.0317243i	−0.527222	−	0.849727i	$-0.676767\pi$
$367$	−2.71613e6	+	1.56816e6i	−0.0549481	+	0.0317243i	0.472274	+	0.881452i	$0.343433\pi$
$368$	−7.48143e6	−	1.02973e7i	−0.150121	−	0.206624i
$369$	−1.15447e7	−	1.28217e7i	−0.229776	−	0.255192i
$370$	−8.98189e7	+	2.91839e7i	−1.77322	+	0.576154i
$371$		−	3.91425e7i		−	0.766526i
$372$	4.80233e6	+	1.75864e6i	0.0932874	+	0.0341623i
$373$	2.76613e7			0.533023			0.266512	−	0.963832i	$-0.414129\pi$
$373$	2.76613e7			0.533023			0.266512	+	0.963832i	$0.414129\pi$
$374$	19704.8	+	60645.3i	0.000376667	+	0.00115926i
$375$	−9.37255e6	+	8.43908e6i	−0.177731	+	0.160030i
$376$	5.02746e7	−	3.65266e7i	0.945769	−	0.687141i
$377$	−6.24037e7	−	1.08086e8i	−1.16462	−	2.01719i
$378$	−8.09294e7	−	4.67246e7i	−1.49841	−	0.865108i
$379$	−8.59493e6	−	8.17753e7i	−0.157879	−	1.50212i	−0.730847	−	0.682542i	$-0.760875\pi$
$379$	−8.59493e6	−	8.17753e7i	−0.157879	−	1.50212i	0.572968	−	0.819578i	$-0.305792\pi$
$380$	9.38122e6	+	6.81585e6i	0.170965	+	0.124214i
$381$	−4.19329e6	+	3.98965e7i	−0.0758193	+	0.721373i
$382$	−5.87438e7	+	6.52416e7i	−1.05383	+	1.17040i
$383$	−2.02260e7	+	4.54284e7i	−0.360010	+	0.808595i	0.639207	+	0.769034i	$0.279263\pi$
$383$	−2.02260e7	+	4.54284e7i	−0.360010	+	0.808595i	−0.999217	+	0.0395607i	$0.987404\pi$
$384$	−7.44233e6	+	3.50134e7i	−0.131436	+	0.618359i
$385$	−3.61277e6	−	1.69968e7i	−0.0633080	−	0.297841i
$386$	5.33445e7	−	2.37505e7i	0.927529	−	0.412963i
$387$	2.78518e7	+	9.04958e6i	0.480529	+	0.156133i
$388$	−33908.9	+	104361.i	−0.000580521	+	0.00178666i
$389$	−4.48972e7	−	1.00841e8i	−0.762730	−	1.71312i	−0.698966	−	0.715155i	$-0.746356\pi$
$389$	−4.48972e7	−	1.00841e8i	−0.762730	−	1.71312i	−0.0637642	−	0.997965i	$-0.520311\pi$
$390$	1.11043e8	−	2.36028e7i	1.87196	−	0.397896i
$391$	186065.	+	39549.3i	0.00311268	+	0.000661620i
$392$	1.08672e8	+	4.83841e7i	1.80410	+	0.803238i
$393$	−5.60944e6	−	5.05076e6i	−0.0924148	−	0.0832107i
$394$	1.10888e7	+	1.16548e6i	0.181299	+	0.0190553i
$395$	−2.60610e7	+	3.58698e7i	−0.422862	+	0.582020i
$396$	311404.	−	32729.9i	0.00501463	−	0.000527059i
$397$	−1.85632e7	+	3.21523e7i	−0.296675	+	0.513855i	−0.975373	−	0.220562i	$-0.929211\pi$
$397$	−1.85632e7	+	3.21523e7i	−0.296675	+	0.513855i	0.678698	+	0.734417i	$0.262544\pi$
$398$	3.10635e7	−	1.79345e7i	0.492720	−	0.284472i
$399$	5.99282e7	+	8.24841e7i	0.943436	+	1.29853i
$400$	−4.42824e7	−	4.91805e7i	−0.691912	−	0.768446i
$401$	1.20085e8	−	3.90178e7i	1.86232	−	0.605104i	0.868280	−	0.496075i	$-0.165226\pi$
$401$	1.20085e8	−	3.90178e7i	1.86232	−	0.605104i	0.994039	−	0.109029i	$-0.0347743\pi$
$402$		−	2.23190e7i		−	0.343555i
$403$	1.10781e8	−	7.52707e6i	1.69258	−	0.115003i
$404$	8.98826e6			0.136311
$405$	−1.65444e7	−	5.09185e7i	−0.249050	−	0.766497i
$406$	−1.08529e8	+	9.77197e7i	−1.62169	+	1.46017i
$407$	8.86138e6	−	6.43817e6i	0.131437	−	0.0954947i
$408$	−311679.	−	539844.i	−0.00458909	−	0.00794854i
$409$	−9.22329e7	−	5.32507e7i	−1.34808	−	0.778315i	−0.360103	−	0.932913i	$-0.617258\pi$
$409$	−9.22329e7	−	5.32507e7i	−1.34808	−	0.778315i	−0.987977	+	0.154598i	$0.950592\pi$
$410$	−1.00922e7	−	9.60206e7i	−0.146431	−	1.39320i
$411$	−3.59310e7	−	2.61054e7i	−0.517540	−	0.376015i
$412$	37773.3	−	359389.i	0.000540124	−	0.00513893i
$413$	1.28917e6	−	1.43177e6i	0.0183003	−	0.0203246i
$414$	−2.72568e6	+	6.12199e6i	−0.0384127	+	0.0862763i
$415$	−9.79971e6	+	4.61040e7i	−0.137110	+	0.645052i
$416$	−6.17636e6	−	2.90575e7i	−0.0857932	−	0.403625i
$417$	6.27126e7	−	2.79214e7i	0.864861	−	0.385061i
$418$	9.17642e6	+	2.98160e6i	0.125645	+	0.0408244i
$419$	−379376.	+	1.16760e6i	−0.00515737	+	0.0158728i	−0.953602	−	0.301070i	$-0.902656\pi$
$419$	−379376.	+	1.16760e6i	−0.00515737	+	0.0158728i	0.948445	+	0.316943i	$0.102656\pi$
$420$	7.53090e6	+	1.69147e7i	0.101648	+	0.228305i
$421$	−2.79156e7	+	5.93364e6i	−0.374111	+	0.0795197i	−0.391130	−	0.920335i	$-0.627916\pi$
$421$	−2.79156e7	+	5.93364e6i	−0.374111	+	0.0795197i	0.0170191	+	0.999855i	$0.494582\pi$
$422$	4.64523e7	+	9.87374e6i	0.618115	+	0.131384i
$423$	−2.61774e7	−	1.16549e7i	−0.345863	−	0.153988i
$424$	2.69106e7	+	2.42304e7i	0.353042	+	0.317880i
$425$	983622.	+	103383.i	0.0128133	+	0.00134673i
$426$	−4.28417e7	+	5.89665e7i	−0.554163	+	0.762740i
$427$	−5.42622e7	+	5.70319e6i	−0.696970	+	0.0732545i
$428$	6.40527e6	−	1.10943e7i	0.0816970	−	0.141503i
$429$	−1.14025e7	+	6.58321e6i	−0.144420	+	0.0833807i
$430$	9.63258e7	+	1.32581e8i	1.21154	+	1.66754i
$431$	−4.37008e7	−	4.85347e7i	−0.545830	−	0.606206i	0.405607	−	0.914047i	$-0.367060\pi$
$431$	−4.37008e7	−	4.85347e7i	−0.545830	−	0.606206i	−0.951438	+	0.307841i	$0.900393\pi$
$432$	7.20098e7	−	2.33974e7i	0.893183	−	0.290213i
$433$			1.37703e7i			0.169621i	0.996397	+	0.0848106i	$0.0270285\pi$
$433$			1.37703e7i			0.169621i	−0.996397	+	0.0848106i	$0.972971\pi$
$434$	−3.55661e7	−	1.24963e8i	−0.435077	−	1.52866i
$435$	−1.36086e8			−1.65327
$436$	−5.36107e6	−	1.64997e7i	−0.0646833	−	0.199075i
$437$	2.13900e7	−	1.92596e7i	0.256310	−	0.230783i
$438$	−2.24790e7	+	1.63320e7i	−0.267520	+	0.194364i
$439$	1.41511e7	+	2.45105e7i	0.167262	+	0.289706i	0.937456	−	0.348103i	$-0.113174\pi$
$439$	1.41511e7	+	2.45105e7i	0.167262	+	0.289706i	−0.770194	+	0.637809i	$0.779841\pi$
$440$	1.39218e7	+	8.03773e6i	0.163432	+	0.0943572i
$441$	−5.73362e6	−	5.45517e7i	−0.0668518	−	0.636052i
$442$	−1.19345e6	−	867094.i	−0.0138210	−	0.0100415i
$443$	−6.73387e6	+	6.40685e7i	−0.0774557	+	0.736942i	0.885016	+	0.465560i	$0.154147\pi$
$443$	−6.73387e6	+	6.40685e7i	−0.0774557	+	0.736942i	−0.962472	+	0.271381i	$0.912520\pi$
$444$	−7.80956e6	+	8.67339e6i	−0.0892232	+	0.0990923i
$445$	−2.31796e7	+	5.20622e7i	−0.263042	+	0.590803i
$446$	−1.68172e7	+	7.91187e7i	−0.189561	+	0.891815i
$447$	5.42254e6	+	2.55110e7i	0.0607128	+	0.285631i
$448$	−1.51978e8	+	6.76648e7i	−1.69023	+	0.752539i
$449$	−1.05936e8	−	3.44207e7i	−1.17032	−	0.380260i	−0.341557	−	0.939861i	$-0.610954\pi$
$449$	−1.05936e8	−	3.44207e7i	−1.17032	−	0.380260i	−0.828762	+	0.559602i	$0.810954\pi$
$450$	−1.07671e7	+	3.31377e7i	−0.118157	+	0.363651i
$451$	4.55456e6	+	1.02297e7i	0.0496497	+	0.111515i
$452$	−5.75043e6	+	1.22229e6i	−0.0622709	+	0.0132361i
$453$	−6.34572e7	−	1.34882e7i	−0.682632	−	0.145098i
$454$	1.66820e7	+	7.42730e6i	0.178271	+	0.0793713i
$455$	2.98739e8	+	2.68986e8i	3.17145	+	2.85559i
$456$	−9.38054e7	−	9.85935e6i	−0.989312	−	0.103981i
$457$	−9.12831e6	+	1.25640e7i	−0.0956405	+	0.131638i	−0.854155	−	0.520018i	$-0.825925\pi$
$457$	−9.12831e6	+	1.25640e7i	−0.0956405	+	0.131638i	0.758515	+	0.651656i	$0.225925\pi$
$458$	1.17371e8	−	1.23362e7i	1.22170	−	0.128406i
$459$	−565782.	+	979964.i	−0.00585075	+	0.0101338i
$460$	4.52677e6	−	2.61353e6i	0.0465066	−	0.0268506i
$461$	1.03263e8	+	1.42129e8i	1.05400	+	1.45071i	0.885290	+	0.465039i	$0.153960\pi$
$461$	1.03263e8	+	1.42129e8i	1.05400	+	1.45071i	0.168709	+	0.985666i	$0.446040\pi$
$462$	1.03088e7	+	1.14491e7i	0.104540	+	0.116104i
$463$	−8.56139e7	+	2.78176e7i	−0.862584	+	0.280270i	−0.706707	−	0.707506i	$-0.749820\pi$
$463$	−8.56139e7	+	2.78176e7i	−0.862584	+	0.280270i	−0.155876	+	0.987777i	$0.549820\pi$
$464$		−	1.18326e8i		−	1.18448i
$465$	5.32880e7	−	1.08712e8i	0.529994	−	1.08123i
$466$	−3.66408e7			−0.362082
$467$	1.31620e7	+	4.05084e7i	0.129232	+	0.397736i	0.994648	−	0.103318i	$-0.0329459\pi$
$467$	1.31620e7	+	4.05084e7i	0.129232	+	0.397736i	−0.865416	+	0.501054i	$0.832946\pi$
$468$	−5.38320e6	+	4.84706e6i	−0.0525174	+	0.0472869i
$469$	6.39389e7	−	4.64544e7i	0.619793	−	0.450306i
$470$	−8.01758e7	−	1.38869e8i	−0.772235	−	1.33755i
$471$	2.21539e7	+	1.27905e7i	0.212025	+	0.122413i
$472$	186309.	+	1.77261e6i	0.00177177	+	0.0168573i
$473$	−1.53767e7	−	1.11719e7i	−0.145305	−	0.105570i
$474$	4.10907e6	−	3.90952e7i	0.0385841	−	0.367103i
$475$	1.00138e8	−	1.11215e8i	0.934373	−	1.03773i
$476$	97861.0	−	219799.i	0.000907379	−	0.00203801i
$477$	3.47163e6	−	1.63328e7i	0.0319874	−	0.150489i
$478$	1.94204e7	+	9.13658e7i	0.177817	+	0.836565i
$479$	1.61607e8	−	7.19519e7i	1.47046	−	0.654690i	0.493817	−	0.869566i	$-0.335601\pi$
$479$	1.61607e8	−	7.19519e7i	1.47046	−	0.654690i	0.976641	+	0.214876i	$0.0689346\pi$
$480$	−3.08058e7	−	1.00094e7i	−0.278554	−	0.0905076i
$481$	−7.83039e7	+	2.40995e8i	−0.703636	+	2.16557i
$482$	3.39581e7	+	7.62712e7i	0.303251	+	0.681114i
$483$	4.49545e7	−	9.55537e6i	0.398962	−	0.0848020i
$484$	1.33683e7	+	2.84153e6i	0.117907	+	0.0250620i
$485$	2.37312e6	+	1.05658e6i	0.0208015	+	0.00926140i
$486$	−5.17243e7	−	4.65728e7i	−0.450595	−	0.405717i
$487$	1.73609e7	+	1.82470e6i	0.150309	+	0.0157981i	0.179384	−	0.983779i	$-0.442590\pi$
$487$	1.73609e7	+	1.82470e6i	0.150309	+	0.0157981i	−0.0290751	+	0.999577i	$0.509256\pi$
$488$	2.96690e7	−	4.08359e7i	0.255296	−	0.351385i
$489$	−9.95548e7	+	1.04636e7i	−0.851404	+	0.0894862i
$490$	1.53476e8	−	2.65829e8i	1.30453	−	2.25951i
$491$	6.66638e7	−	3.84884e7i	0.563178	−	0.325151i	−0.191242	−	0.981543i	$-0.561252\pi$
$491$	6.66638e7	−	3.84884e7i	0.563178	−	0.325151i	0.754420	+	0.656392i	$0.227918\pi$
$492$	−7.01331e6	−	9.65300e6i	−0.0588882	−	0.0810526i
$493$	1.18328e6	+	1.31416e6i	0.00987519	+	0.0109675i
$494$	−2.12290e8	+	6.89773e7i	−1.76096	+	0.572170i
$495$		−	7.41256e6i		−	0.0611157i
$496$	9.45250e7	+	4.63338e7i	0.774643	+	0.379711i
$497$	−2.58096e8			−2.10239
$498$	−1.29138e7	−	3.97445e7i	−0.104560	−	0.321803i
$499$	−1.21384e8	+	1.09294e8i	−0.976919	+	0.879622i	−0.992743	−	0.120253i	$-0.961629\pi$
$499$	−1.21384e8	+	1.09294e8i	−0.976919	+	0.879622i	0.0158242	+	0.999875i	$0.494963\pi$
$500$	3.64336e6	−	2.64705e6i	0.0291469	−	0.0211764i
$501$	−1.77010e7	−	3.06590e7i	−0.140761	−	0.243806i
$502$	1.75250e7	+	1.01181e7i	0.138531	+	0.0799808i
$503$	−1.13967e7	−	1.08432e8i	−0.0895519	−	0.852029i	−0.943433	−	0.331562i	$-0.892424\pi$
$503$	−1.13967e7	−	1.08432e8i	−0.0895519	−	0.852029i	0.853882	−	0.520467i	$-0.174242\pi$
$504$	6.29117e7	+	4.57080e7i	0.491405	+	0.357027i
$505$	2.22417e7	−	2.11616e8i	0.172701	−	1.64314i
$506$	2.91027e6	−	3.23219e6i	0.0224637	−	0.0249485i
$507$	8.08437e7	−	1.81578e8i	0.620329	−	1.39328i
$508$	2.97824e6	−	1.40115e7i	0.0227179	−	0.106879i
$509$	3.95738e7	+	1.86180e8i	0.300092	+	1.41182i	0.827145	+	0.561989i	$0.189964\pi$
$509$	3.95738e7	+	1.86180e8i	0.300092	+	1.41182i	−0.527053	+	0.849833i	$0.676703\pi$
$510$	−1.46943e6	+	654234.i	−0.0110774	+	0.00493200i
$511$	−9.35751e7	−	3.04044e7i	−0.701290	−	0.227863i
$512$	4.63249e7	−	1.42573e8i	0.345148	−	1.06226i
$513$	6.96416e7	+	1.56418e8i	0.515842	+	1.15860i
$514$	2.11525e8	−	4.49611e7i	1.55766	−	0.331091i
$515$	−8.36782e6	−	1.77864e6i	−0.0612620	−	0.0130216i
$516$	1.85016e7	+	8.23743e6i	0.134666	+	0.0599574i
$517$	1.38207e7	+	1.24442e7i	0.100013	+	0.0900524i
$518$	2.94881e8	+	3.09932e7i	2.12157	+	0.222986i
$519$	−5.83500e7	+	8.03119e7i	−0.417387	+	0.574484i
$520$	−3.69858e8	+	3.88736e7i	−2.63042	+	0.276468i
$521$	−1.18217e8	+	2.04757e8i	−0.835921	+	1.44786i	0.0573566	+	0.998354i	$0.481733\pi$
$521$	−1.18217e8	+	2.04757e8i	−0.835921	+	1.44786i	−0.893278	+	0.449505i	$0.851601\pi$
$522$	−5.39520e7	+	3.11492e7i	−0.379312	+	0.218996i
$523$	−1.45406e8	−	2.00134e8i	−1.01643	−	1.39900i	−0.914676	−	0.404188i	$-0.867554\pi$
$523$	−1.45406e8	−	2.00134e8i	−1.01643	−	1.39900i	−0.101755	−	0.994809i	$-0.532446\pi$
$524$	1.80350e6	+	2.00299e6i	0.0125350	+	0.0139215i
$525$	2.27263e8	−	7.38422e7i	1.57055	−	0.510301i
$526$		−	1.35194e8i		−	0.928969i
$527$	−1.51316e6	+	430665.i	−0.0103384	+	0.00294244i
$528$	−1.24827e7			−0.0848022
$529$	4.17362e7	+	1.28451e8i	0.281933	+	0.867702i
$530$	6.94394e7	−	6.25236e7i	0.466422	−	0.419968i
$531$	664909.	−	483085.i	0.00444098	−	0.00322656i
$532$	−1.82030e7	−	3.15285e7i	−0.120895	−	0.209396i
$533$	−2.24347e8	−	1.29527e8i	−1.48163	−	0.855418i
$534$	−5.28158e6	−	5.02509e7i	−0.0346849	−	0.330005i
$535$	−2.45348e8	−	1.78256e8i	−1.60222	−	1.16408i
$536$	−7.64264e6	+	7.27149e7i	−0.0496306	+	0.472203i
$537$	−5.09585e7	+	5.65951e7i	−0.329074	+	0.365474i
$538$	−5.08663e7	+	1.14247e8i	−0.326650	+	0.733668i
$539$	−7.40173e6	+	3.48224e7i	−0.0472680	+	0.222378i
$540$	6.46481e6	+	3.04145e7i	0.0410558	+	0.193152i
$541$	2.49094e8	−	1.10904e8i	1.57316	−	0.700415i	0.579723	−	0.814814i	$-0.303161\pi$
$541$	2.49094e8	−	1.10904e8i	1.57316	−	0.700415i	0.993435	+	0.114399i	$0.0364942\pi$
$542$	−1.97534e8	−	6.41827e7i	−1.24063	−	0.403107i
$543$	4.61382e7	−	1.41999e8i	0.288178	−	0.886921i
$544$	171199.	+	384520.i	0.00106342	+	0.00238849i
$545$	−4.01728e8	+	8.53898e7i	−2.48166	+	0.527493i
$546$	−3.48626e8	−	7.41028e7i	−2.14182	−	0.455257i
$547$	2.00313e8	+	8.91849e7i	1.22390	+	0.544916i	0.913946	−	0.405835i	$-0.133019\pi$
$547$	2.00313e8	+	8.91849e7i	1.22390	+	0.544916i	0.309955	+	0.950751i	$0.399686\pi$
$548$	1.17854e7	+	1.06116e7i	0.0716149	+	0.0644824i
$549$	−2.31475e7	−	2.43290e6i	−0.139890	−	0.0147030i
$550$	1.32921e7	−	1.82951e7i	0.0798927	−	0.109963i
$551$	2.66113e8	−	2.79696e7i	1.59078	−	0.167198i
$552$	−2.12588e7	+	3.68214e7i	−0.126393	+	0.218919i
$553$	1.20552e8	−	6.96005e7i	0.712849	−	0.411564i
$554$	−7.65895e7	−	1.05416e8i	−0.450443	−	0.619982i
$555$	1.84878e8	+	2.05327e8i	1.08145	+	1.20107i
$556$	−2.33126e7	+	7.57472e6i	−0.135633	+	0.0440699i
$557$		−	6.02727e7i		−	0.348783i	−0.984676	−	0.174391i	$-0.944204\pi$
$557$		−	6.02727e7i		−	0.348783i	0.984676	−	0.174391i	$-0.0557958\pi$
$558$	−3.75719e6	−	5.52969e7i	−0.0216252	−	0.318272i
$559$	4.39707e8			2.51726
$560$	1.17772e8	+	3.62465e8i	0.670623	+	2.06396i
$561$	138636.	−	124828.i	0.000785213	−	0.000707009i
$562$	8.00566e7	−	5.81645e7i	0.451012	−	0.327679i
$563$	1.40884e8	+	2.44019e8i	0.789473	+	1.36741i	0.926290	+	0.376812i	$0.122980\pi$
$563$	1.40884e8	+	2.44019e8i	0.789473	+	1.36741i	−0.136817	+	0.990596i	$0.543687\pi$
$564$	−1.71616e7	−	9.90827e6i	−0.0956579	−	0.0552281i
$565$	1.45475e7	+	1.38410e8i	0.0806572	+	0.767402i
$566$	1.33034e8	+	9.66551e7i	0.733693	+	0.533059i
$567$	−1.75701e7	+	1.67168e8i	−0.0963885	+	0.917076i
$568$	1.59770e8	−	1.77442e8i	0.871864	−	0.968304i
$569$	3.42411e7	−	7.69067e7i	0.185871	−	0.417472i	−0.796443	−	0.604713i	$-0.793288\pi$
$569$	3.42411e7	−	7.69067e7i	0.185871	−	0.417472i	0.982314	+	0.187241i	$0.0599545\pi$
$570$	−5.06029e7	+	2.38068e8i	−0.273244	+	1.28551i
$571$	−5.19970e7	−	2.44627e8i	−0.279299	−	1.31400i	−0.864304	−	0.502970i	$-0.832241\pi$
$571$	−5.19970e7	−	2.44627e8i	−0.279299	−	1.31400i	0.585004	−	0.811030i	$-0.301093\pi$
$572$	4.29495e6	−	1.91223e6i	0.0229493	−	0.0102177i
$573$	2.44270e8	+	7.93681e7i	1.29839	+	0.421873i
$574$	−9.36706e7	+	2.88289e8i	−0.495299	+	1.52437i
$575$	−2.74384e7	−	6.16277e7i	−0.144330	−	0.324170i
$576$	−6.94161e7	+	1.47548e7i	−0.363239	+	0.0772089i
$577$	2.13289e7	+	4.53359e6i	0.111030	+	0.0236001i	0.263092	−	0.964771i	$-0.415258\pi$
$577$	2.13289e7	+	4.53359e6i	0.111030	+	0.0236001i	−0.152062	+	0.988371i	$0.548591\pi$
$578$	−1.65245e8	−	7.35718e7i	−0.855746	−	0.381002i
$579$	−1.26954e8	−	1.14310e8i	−0.654048	−	0.588907i
$580$	4.83267e7	+	5.07934e6i	0.247687	+	0.0260329i
$581$	8.69809e7	−	1.19719e8i	0.443502	−	0.610428i
$582$	−2.29055e6	+	240747.i	−0.0116191	+	0.00122121i
$583$	−5.41858e6	+	9.38525e6i	−0.0273451	+	0.0473631i
$584$	7.88290e7	−	4.55119e7i	0.395774	−	0.228500i
$585$	1.00796e8	+	1.38734e8i	0.503473	+	0.692971i
$586$	216881.	+	240870.i	0.00107777	+	0.00119699i
$587$	−1.54149e8	+	5.00859e7i	−0.762123	+	0.247629i	−0.664190	−	0.747564i	$-0.731223\pi$
$587$	−1.54149e8	+	5.00859e7i	−0.762123	+	0.247629i	−0.0979336	+	0.995193i	$0.531223\pi$
$588$		−	3.79338e7i		−	0.186592i
$589$	−8.18601e7	+	2.23536e8i	−0.400614	+	1.09396i
$590$	4.59920e6			0.0223937
$591$	−1.00801e7	−	3.10233e7i	−0.0488317	−	0.150288i
$592$	−1.78532e8	+	1.60751e8i	−0.860499	+	0.774797i
$593$	−3.00676e8	+	2.18454e8i	−1.44190	+	1.04760i	−0.454257	+	0.890870i	$0.650095\pi$
$593$	−3.00676e8	+	2.18454e8i	−1.44190	+	1.04760i	−0.987641	+	0.156730i	$0.949905\pi$
$594$	1.29364e7	+	2.24064e7i	0.0617238	+	0.106909i
$595$	−4.93270e6	−	2.84790e6i	−0.0234171	−	0.0135199i
$596$	−973460.	−	9.26186e6i	−0.00459811	−	0.0437481i
$597$	−8.48963e7	−	6.16808e7i	−0.398994	−	0.289886i
$598$	−1.05175e7	+	1.00068e8i	−0.0491825	+	0.467940i
$599$	−8.96887e7	+	9.96094e7i	−0.417309	+	0.463468i	−0.914745	−	0.404032i	$-0.867608\pi$
$599$	−8.96887e7	+	9.96094e7i	−0.417309	+	0.463468i	0.497436	+	0.867501i	$0.334275\pi$
$600$	−8.99159e7	+	2.01954e8i	−0.416277	+	0.934975i
$601$	3.10794e7	−	1.46217e8i	0.143169	−	0.673557i	−0.846758	−	0.531978i	$-0.821449\pi$
$601$	3.10794e7	−	1.46217e8i	0.143169	−	0.673557i	0.989927	−	0.141579i	$-0.0452178\pi$
$602$	−1.06973e8	−	5.03268e8i	−0.490325	−	2.30680i
$603$	3.07995e7	−	1.37128e7i	0.140473	−	0.0625425i
$604$	2.20314e7	+	7.15845e6i	0.0999844	+	0.0324869i
$605$	9.99799e7	−	3.07707e8i	0.451489	−	1.38954i
$606$	7.67332e7	+	1.72346e8i	0.344799	+	0.774430i
$607$	7.97174e7	−	1.69445e7i	0.356440	−	0.0757638i	−0.0262112	−	0.999656i	$-0.508344\pi$
$607$	7.97174e7	−	1.69445e7i	0.356440	−	0.0757638i	0.382652	+	0.923893i	$0.375011\pi$
$608$	6.22974e7	+	1.32417e7i	0.277178	+	0.0589160i
$609$	3.90313e8	+	1.73779e8i	1.72807	+	0.769387i
$610$	−9.67923e7	−	8.71522e7i	−0.426433	−	0.383962i
$611$	−4.27885e8	−	4.49725e7i	−1.87587	−	0.197162i
$612$	60328.3	−	83034.8i	0.000263188	−	0.000362248i
$613$	−2.20568e8	+	2.31827e7i	−0.957550	+	0.100643i	−0.570394	−	0.821371i	$-0.693209\pi$
$613$	−2.20568e8	+	2.31827e7i	−0.957550	+	0.100643i	−0.387157	+	0.922014i	$0.626543\pi$
$614$	9.55858e7	−	1.65560e8i	0.412941	−	0.715235i
$615$	−2.44621e8	+	1.41232e8i	−1.05164	+	0.607166i
$616$	−2.96656e7	−	4.08312e7i	−0.126914	−	0.174683i
$617$	8.85951e7	+	9.83949e7i	0.377185	+	0.418906i	0.901610	−	0.432550i	$-0.142386\pi$
$617$	8.85951e7	+	9.83949e7i	0.377185	+	0.418906i	−0.524425	+	0.851457i	$0.675720\pi$
$618$	7.21359e6	−	2.34384e6i	0.0305623	−	0.00993029i
$619$			2.03663e8i			0.858698i	0.903139	+	0.429349i	$0.141257\pi$
$619$			2.03663e8i			0.858698i	−0.903139	+	0.429349i	$0.858743\pi$
$620$	−2.29812e7	+	3.66168e7i	−0.0964270	+	0.153640i
$621$	7.71812e7			0.322283
$622$	−827193.	−	2.54584e6i	−0.00343744	−	0.0105794i
$623$	1.32965e8	−	1.19722e8i	0.549886	−	0.495120i
$624$	2.33627e8	−	1.69740e8i	0.961545	−	0.698603i
$625$	9.30098e7	+	1.61098e8i	0.380968	+	0.659856i
$626$	1.46859e8	+	8.47890e7i	0.598656	+	0.345634i
$627$	−2.95062e6	−	2.80733e7i	−0.0119705	−	0.113891i
$628$	−7.38986e6	−	5.36905e6i	−0.0298372	−	0.0216780i
$629$	375293.	−	3.57067e6i	0.00150806	−	0.0143482i
$630$	1.34266e8	−	1.49118e8i	0.536964	−	0.596359i
$631$	1.04626e7	−	2.34995e7i	0.0416441	−	0.0935341i	−0.891526	−	0.452970i	$-0.850364\pi$
$631$	1.04626e7	−	2.34995e7i	0.0416441	−	0.0935341i	0.933170	+	0.359436i	$0.117031\pi$
$632$	−2.67746e7	+	1.25965e8i	−0.106065	+	0.498996i
$633$	−2.88864e7	−	1.35900e8i	−0.113889	−	0.535807i
$634$	3.28436e8	−	1.46229e8i	1.28879	−	0.573808i
$635$	−3.22511e8	−	1.04790e8i	−1.25957	−	0.409260i
$636$	3.56837e6	−	1.09823e7i	0.0138707	−	0.0426896i
$637$	−3.34984e8	−	7.52387e8i	−1.29600	−	2.91087i
$638$	3.95496e7	−	8.40653e6i	0.152293	−	0.0323709i
$639$	−1.07694e8	−	2.28911e7i	−0.412752	−	0.0877332i
$640$	−2.76426e8	−	1.23073e8i	−1.05448	−	0.469485i
$641$	−1.03892e8	−	9.35448e7i	−0.394465	−	0.355178i	0.447902	−	0.894083i	$-0.352171\pi$
$641$	−1.03892e8	−	9.35448e7i	−0.394465	−	0.355178i	−0.842366	+	0.538905i	$0.818838\pi$
$642$	2.67409e8	+	2.81059e7i	1.01058	+	0.106216i
$643$	7.21062e7	−	9.92457e7i	0.271231	−	0.373318i	−0.651574	−	0.758585i	$-0.725891\pi$
$643$	7.21062e7	−	9.92457e7i	0.271231	−	0.373318i	0.922805	+	0.385268i	$0.125891\pi$
$644$	−1.63208e7	+	1.71539e6i	−0.0611062	+	0.00642252i
$645$	2.39721e8	−	4.15209e8i	0.893361	−	1.54735i
$646$	2.73898e6	−	1.58135e6i	0.0101600	−	0.00586585i
$647$	1.90674e7	+	2.62441e7i	0.0704011	+	0.0968988i	0.842766	−	0.538281i	$-0.180926\pi$
$647$	1.90674e7	+	2.62441e7i	0.0704011	+	0.0968988i	−0.772364	+	0.635180i	$0.780926\pi$
$648$	−1.04052e8	−	1.15562e8i	−0.382408	−	0.424707i
$649$	−507308.	+	164834.i	−0.00185583	+	0.000602994i
$650$			5.23159e8i			1.90499i
$651$	−2.91661e8	+	2.43754e8i	−1.05715	+	0.883506i
$652$	3.57444e7			0.128963
$653$	−8.90602e7	−	2.74099e8i	−0.319848	−	0.984392i	−0.973713	−	0.227780i	$-0.926853\pi$
$653$	−8.90602e7	−	2.74099e8i	−0.319848	−	0.984392i	0.653864	−	0.756612i	$-0.273147\pi$
$654$	2.70606e8	−	2.43655e8i	0.967396	−	0.871047i
$655$	5.16204e7	−	3.75044e7i	0.183695	−	0.133462i
$656$	−1.22801e8	−	2.12697e8i	−0.435000	−	0.753442i
$657$	−3.63489e7	−	2.09860e7i	−0.128172	−	0.0740004i
$658$	5.26234e7	+	5.00678e8i	0.184714	+	1.75744i
$659$	8.95842e7	+	6.50868e7i	0.313022	+	0.227424i	0.733192	−	0.680021i	$-0.238030\pi$
$659$	8.95842e7	+	6.50868e7i	0.313022	+	0.227424i	−0.420170	+	0.907445i	$0.638030\pi$
$660$	535840.	−	5.09817e6i	0.00186382	−	0.0177330i
$661$	−1.00625e8	+	1.11756e8i	−0.348419	+	0.386959i	−0.891726	−	0.452575i	$-0.850505\pi$
$661$	−1.00625e8	+	1.11756e8i	−0.348419	+	0.386959i	0.543307	+	0.839534i	$0.317172\pi$
$662$	−7.27749e6	+	1.63455e7i	−0.0250846	+	0.0563410i
$663$	−897302.	+	4.22147e6i	−0.00307892	+	0.0144852i
$664$	2.84633e7	+	1.33909e8i	0.0972257	+	0.457411i
$665$	−7.87336e8	+	3.50545e8i	−2.67729	+	1.19201i
$666$	1.20294e8	+	3.90859e7i	0.407213	+	0.132312i
$667$	3.72726e7	−	1.14713e8i	0.125607	−	0.386577i
$668$	5.14162e6	+	1.15483e7i	0.0172493	+	0.0387425i
$669$	2.31468e8	−	4.92001e7i	0.773060	−	0.164319i
$670$	1.84542e8	+	3.92257e7i	0.613581	+	0.130421i
$671$	1.38000e7	+	6.14417e6i	0.0456786	+	0.0203374i
$672$	7.55737e7	+	6.80469e7i	0.249036	+	0.224233i
$673$	2.14844e8	+	2.25810e7i	0.704820	+	0.0740796i	0.450156	−	0.892950i	$-0.351368\pi$
$673$	2.14844e8	+	2.25810e7i	0.704820	+	0.0740796i	0.254664	+	0.967029i	$0.418035\pi$
$674$	−1.00928e7	+	1.38916e7i	−0.0329636	+	0.0453704i
$675$	3.99098e8	−	4.19469e7i	1.29768	−	0.136392i
$676$	−3.54865e7	+	6.14644e7i	−0.114874	+	0.198968i
$677$	4.99601e8	−	2.88445e8i	1.61012	−	0.929601i	0.620775	−	0.783989i	$-0.286818\pi$
$677$	4.99601e8	−	2.88445e8i	1.61012	−	0.929601i	0.989342	−	0.145612i	$-0.0465151\pi$
$678$	−7.25286e7	−	9.98271e7i	−0.232713	−	0.320302i
$679$	−5.45721e6	−	6.06084e6i	−0.0174326	−	0.0193608i
$680$	5.01143e6	−	1.62831e6i	0.0159380	−	0.00517858i
$681$		−	5.34232e7i		−	0.169156i
$682$	−8.77116e6	+	3.48860e7i	−0.0276506	+	0.109976i
$683$	−2.27797e8			−0.714965			−0.357483	−	0.933920i	$-0.616365\pi$
$683$	−2.27797e8			−0.714965			−0.357483	+	0.933920i	$0.616365\pi$
$684$	−4.79911e6	−	1.47701e7i	−0.0149966	−	0.0461548i
$685$	2.78999e8	−	2.51212e8i	0.868023	−	0.781572i
$686$	−3.64548e8	+	2.64860e8i	−1.12923	+	0.820433i
$687$	−1.72635e8	−	2.99012e8i	−0.532425	−	0.922187i
$688$	3.61023e8	+	2.08437e8i	1.10859	+	0.640044i
$689$	−2.62064e7	−	2.49337e8i	−0.0801215	−	0.762305i
$690$	8.87585e7	+	6.44868e7i	0.270186	+	0.196302i
$691$	−5.21684e7	+	4.96349e8i	−0.158115	+	1.50436i	0.571554	+	0.820564i	$0.306341\pi$
$691$	−5.21684e7	+	4.96349e8i	−0.158115	+	1.50436i	−0.729669	+	0.683800i	$0.760326\pi$
$692$	2.37188e7	−	2.63424e7i	0.0715773	−	0.0794946i
$693$	−9.46569e6	+	2.12603e7i	−0.0284415	+	0.0638806i
$694$	8.50232e7	−	4.00003e8i	0.254366	−	1.19670i
$695$	1.20648e8	+	5.67606e8i	0.359391	+	1.69080i
$696$	−3.61089e8	+	1.60767e8i	−1.07099	+	0.476837i
$697$	3.49085e6	+	1.13425e6i	0.0103094	+	0.00334972i
$698$	−1.20155e7	+	3.69799e7i	−0.0353326	+	0.108743i
$699$	4.36004e7	+	9.79280e7i	0.127661	+	0.286731i
$700$	−8.34615e7	+	1.77403e7i	−0.243328	+	0.0517210i
$701$	2.84302e8	+	6.04303e7i	0.825327	+	0.175429i	0.601167	−	0.799124i	$-0.294703\pi$
$701$	2.84302e8	+	6.04303e7i	0.825327	+	0.175429i	0.224160	+	0.974552i	$0.428036\pi$
$702$	−5.46801e8	−	2.43451e8i	−1.58058	−	0.703722i
$703$	−4.03725e8	−	3.63516e8i	−1.16204	−	1.04630i
$704$	4.58069e7	+	4.81450e6i	0.131284	+	0.0137985i
$705$	−2.75743e8	+	3.79527e8i	−0.786931	+	1.08312i
$706$	4.22834e8	−	4.44417e7i	1.20159	−	0.126292i
$707$	−3.34021e8	+	5.78542e8i	−0.945183	+	1.63710i
$708$	492229.	−	284189.i	0.00138697	−	0.000800768i
$709$	2.41065e8	+	3.31797e8i	0.676387	+	0.930967i	0.999884	−	0.0152626i	$-0.00485843\pi$
$709$	2.41065e8	+	3.31797e8i	0.676387	+	0.930967i	−0.323497	+	0.946229i	$0.604858\pi$
$710$	−4.12265e8	−	4.57867e8i	−1.15186	−	1.27928i
$711$	5.64748e7	−	1.83498e7i	0.157125	−	0.0510531i
$712$			1.65525e8i			0.458590i
$713$	7.70436e7	+	7.46943e7i	0.212553	+	0.206072i
$714$	5.04999e6			0.0138738
$715$	−3.43928e7	−	1.05850e8i	−0.0940913	−	0.289583i
$716$	2.02087e7	−	1.81960e7i	0.0550554	−	0.0495721i
$717$	2.21080e8	−	1.60624e8i	0.599779	−	0.435765i
$718$	1.58559e8	+	2.74633e8i	0.428369	+	0.741958i
$719$	−9.40444e7	−	5.42966e7i	−0.253015	−	0.146078i	0.368129	−	0.929775i	$-0.379998\pi$
$719$	−9.40444e7	−	5.42966e7i	−0.253015	−	0.146078i	−0.621144	+	0.783696i	$0.713332\pi$
$720$	1.69942e7	+	1.61689e8i	0.0455306	+	0.433195i
$721$	2.17288e7	+	1.57869e7i	0.0579737	+	0.0421203i
$722$	1.31668e7	−	1.25273e8i	0.0349838	−	0.332849i
$723$	1.63438e8	−	1.81517e8i	0.432453	−	0.480288i
$724$	−2.16846e7	+	4.87044e7i	−0.0571394	+	0.128337i
$725$	1.30389e8	−	6.13431e8i	0.342157	−	1.60972i
$726$	5.96412e7	+	2.80590e8i	0.155861	+	0.733267i
$727$	1.57151e8	−	6.99682e7i	0.408991	−	0.182095i	−0.191920	−	0.981411i	$-0.561471\pi$
$727$	1.57151e8	−	6.99682e7i	0.408991	−	0.182095i	0.600911	+	0.799316i	$0.294805\pi$
$728$	1.11045e9	+	3.60806e8i	2.87808	+	0.935145i
$729$	−1.27996e8	+	3.93931e8i	−0.330380	+	1.01681i
$730$	−9.55325e7	−	2.14570e8i	−0.245574	−	0.551569i
$731$	−6.09401e6	+	1.29532e6i	−0.0156009	+	0.00331608i
$732$	−1.57444e7	−	3.34657e6i	−0.0401414	−	0.00853232i
$733$	−5.88433e8	−	2.61987e8i	−1.49412	−	0.665224i	−0.512957	−	0.858414i	$-0.671450\pi$
$733$	−5.88433e8	−	2.61987e8i	−1.49412	−	0.665224i	−0.981161	+	0.193190i	$0.938117\pi$
$734$	1.74682e7	+	1.57284e7i	0.0441733	+	0.0397739i
$735$	−8.93096e8	−	9.38682e7i	−2.24924	−	0.236405i
$736$	1.68749e7	−	2.32262e7i	0.0423259	−	0.0582566i
$737$	−2.17615e7	+	2.28723e6i	−0.0543608	+	0.00571356i
$738$	−6.46543e7	+	1.11984e8i	−0.160853	+	0.278605i
$739$	−6.22545e8	+	3.59427e8i	−1.54254	+	0.890588i	−0.543867	+	0.839172i	$0.683040\pi$
$739$	−6.22545e8	+	3.59427e8i	−1.54254	+	0.890588i	−0.998677	+	0.0514164i	$0.983626\pi$
$740$	−5.79899e7	−	7.98162e7i	−0.143106	−	0.196968i
$741$	4.36965e8	+	4.85299e8i	1.07397	+	1.19276i
$742$	−2.79004e8	+	9.06538e7i	−0.682964	+	0.221909i
$743$		−	5.98193e8i		−	1.45839i	−0.684303	−	0.729197i	$-0.739894\pi$
$743$		−	5.98193e8i		−	1.45839i	0.684303	−	0.729197i	$-0.260106\pi$
$744$	1.29653e7	−	3.51409e8i	0.0314820	−	0.853286i
$745$	−2.20466e8			−0.533179
$746$	−6.40633e7	−	1.97167e8i	−0.154310	−	0.474916i
$747$	4.69121e7	−	4.22398e7i	0.112544	−	0.101335i
$748$	−53891.5	+	39154.5i	−0.000128770	+	9.35571e-5i
$749$	4.76065e8	+	8.24569e8i	1.13298	+	1.96237i
$750$	8.18596e7	+	4.72616e7i	0.194038	+	0.112028i
$751$	1.06246e7	+	1.01087e8i	0.0250838	+	0.238657i	0.999879	+	0.0155551i	$0.00495154\pi$
$751$	1.06246e7	+	1.01087e8i	0.0250838	+	0.238657i	−0.974795	+	0.223102i	$0.928382\pi$
$752$	−3.29998e8	−	2.39758e8i	−0.775994	−	0.563792i
$753$	6.18833e6	−	5.88780e7i	0.0144940	−	0.137901i
$754$	−6.25901e8	+	6.95133e8i	−1.46013	+	1.62164i
$755$	2.23053e8	−	5.00985e8i	0.518283	−	1.16408i
$756$	2.02968e7	−	9.54887e7i	0.0469744	−	0.220997i
$757$	1.12172e8	+	5.27728e8i	0.258581	+	1.21653i	0.895311	+	0.445442i	$0.146954\pi$
$757$	1.12172e8	+	5.27728e8i	0.258581	+	1.21653i	−0.636729	+	0.771087i	$0.719713\pi$
$758$	−5.62980e8	+	2.50655e8i	−1.29266	+	0.575530i
$759$	−1.21016e7	−	3.93203e6i	−0.0276768	−	0.00899274i
$760$	2.46385e8	−	7.58294e8i	0.561272	−	1.72742i
$761$	1.93082e8	+	4.33670e8i	0.438115	+	0.984023i	0.988791	+	0.149304i	$0.0477034\pi$
$761$	1.93082e8	+	4.33670e8i	0.438115	+	0.984023i	−0.550676	+	0.834719i	$0.685630\pi$
$762$	2.94089e8	−	6.25106e7i	0.664683	−	0.141283i
$763$	1.26125e9	+	2.68088e8i	2.83941	+	0.603536i
$764$	−8.37826e7	−	3.73024e7i	−0.187877	−	0.0836482i
$765$	−1.80565e6	−	1.62581e6i	−0.00403320	−	0.00363151i
$766$	3.70652e8	+	3.89571e7i	0.824670	+	0.0866763i
$767$	7.25338e6	−	9.98343e6i	0.0160751	−	0.0221255i
$768$	−1.32176e8	+	1.38922e7i	−0.291788	+	0.0306682i
$769$	−2.32298e7	+	4.02351e7i	−0.0510817	+	0.0884762i	−0.890436	−	0.455109i	$-0.849600\pi$
$769$	−2.32298e7	+	4.02351e7i	−0.0510817	+	0.0884762i	0.839354	+	0.543585i	$0.182934\pi$
$770$	−1.12784e8	+	6.51158e7i	−0.247044	+	0.142631i
$771$	−3.71868e8	−	5.11832e8i	−0.811382	−	1.11677i
$772$	4.08171e7	+	4.53320e7i	0.0887137	+	0.0985265i
$773$	2.30743e8	−	7.49731e7i	0.499563	−	0.162318i	−0.0483872	−	0.998829i	$-0.515408\pi$
$773$	2.30743e8	−	7.49731e7i	0.499563	−	0.162318i	0.547951	+	0.836511i	$0.315408\pi$
$774$		−	2.19483e8i		−	0.473345i
$775$	4.38982e8	+	3.44366e8i	0.943065	+	0.739802i
$776$	7.54503e6			0.0161464
$777$	−2.68057e8	−	8.24993e8i	−0.571431	−	1.75868i
$778$	−6.14801e8	+	5.53569e8i	−1.30556	+	1.17553i
$779$	4.49323e8	−	3.26452e8i	0.950487	−	0.690570i
$780$	5.92962e7	+	1.02704e8i	0.124952	+	0.216423i
$781$	6.18841e7	+	3.57288e7i	0.129905	+	0.0750007i
$782$	−149022.	−	1.41785e6i	−0.000311623	−	0.00296489i
$783$	5.80476e8	+	4.21740e8i	1.20920	+	0.878537i
$784$	8.16182e7	−	7.76545e8i	0.169371	−	1.61146i
$785$	−1.44693e8	+	1.60698e8i	−0.299115	+	0.332201i
$786$	−2.30099e7	+	5.16810e7i	−0.0473856	+	0.106430i
$787$	1.88498e7	−	8.86815e7i	0.0386708	−	0.181932i	−0.954573	−	0.297977i	$-0.903688\pi$
$787$	1.88498e7	−	8.86815e7i	0.0386708	−	0.181932i	0.993244	+	0.116045i	$0.0370216\pi$
$788$	2.42170e6	+	1.13932e7i	0.00494928	+	0.0232845i
$789$	−3.61327e8	+	1.60873e8i	−0.735647	+	0.327531i
$790$	3.16033e8	+	1.02685e8i	0.640990	+	0.208270i
$791$	1.35023e8	−	4.15558e8i	0.272821	−	0.839657i
$792$	−8.75696e6	−	1.96685e7i	−0.0176270	−	0.0395908i
$793$	−3.41831e8	+	7.26584e7i	−0.685475	+	0.145702i
$794$	2.72170e8	+	5.78516e7i	0.543725	+	0.115572i
$795$	−2.49733e8	−	1.11188e8i	−0.497020	−	0.221287i
$796$	2.78461e7	+	2.50728e7i	0.0552110	+	0.0497122i
$797$	−1.05627e8	−	1.11018e7i	−0.208641	−	0.0219290i	−0.000368492	−	1.00000i	$-0.500117\pi$
$797$	−1.05627e8	−	1.11018e7i	−0.208641	−	0.0219290i	−0.208272	+	0.978071i	$0.566784\pi$
$798$	4.49144e8	−	6.18194e8i	0.883847	−	1.21651i
$799$	6.06265e6	−	637210.i	0.0118856	−	0.00124923i
$800$	7.46354e7	−	1.29272e8i	0.145772	−	0.252485i
$801$	6.60998e7	−	3.81627e7i	0.128618	−	0.0742578i
$802$	−5.56230e8	−	7.65584e8i	−1.07828	−	1.48412i
$803$	1.82277e7	+	2.02439e7i	0.0352034	+	0.0390974i
$804$	2.21744e7	−	7.20491e6i	0.0426662	−	0.0138631i
$805$			3.88496e8i			0.744730i
$806$	−3.10219e8	−	7.72199e8i	−0.592466	−	1.47477i
$807$	3.65872e8			0.696158
$808$	−1.90980e8	−	5.87776e8i	−0.362038	−	1.11424i
$809$	2.07057e8	−	1.86435e8i	0.391061	−	0.352113i	−0.450023	−	0.893017i	$-0.648584\pi$
$809$	2.07057e8	−	1.86435e8i	0.391061	−	0.352113i	0.841084	+	0.540904i	$0.181918\pi$
$810$	−3.24625e8	+	2.35854e8i	−0.610839	+	0.443800i
$811$	−4.11018e8	−	7.11904e8i	−0.770545	−	1.33462i	−0.937264	−	0.348619i	$-0.886651\pi$
$811$	−4.11018e8	−	7.11904e8i	−0.770545	−	1.33462i	0.166719	−	0.986004i	$-0.446683\pi$
$812$	−1.32122e8	−	7.62805e7i	−0.246778	−	0.142477i
$813$	6.35158e7	+	6.04313e8i	0.118198	+	1.12458i
$814$	−6.64135e7	−	4.82522e7i	−0.123135	−	0.0894631i
$815$	8.84505e7	−	8.41550e8i	0.163391	−	1.55456i
$816$	−2.73786e6	+	3.04070e6i	−0.00503896	+	0.00559634i
$817$	−3.83432e8	+	8.61202e8i	−0.703108	+	1.57921i
$818$	−1.65954e8	+	7.80754e8i	−0.303200	+	1.42644i
$819$	−1.11937e8	−	5.26623e8i	−0.203762	−	0.958624i
$820$	9.21409e7	−	4.10238e7i	0.167113	−	0.0744036i
$821$	5.76028e8	+	1.87163e8i	1.04091	+	0.338213i	0.779096	−	0.626905i	$-0.215679\pi$
$821$	5.76028e8	+	1.87163e8i	1.04091	+	0.338213i	0.261816	+	0.965118i	$0.415679\pi$
$822$	−1.02861e8	+	3.16572e8i	−0.185197	+	0.569977i
$823$	1.66328e8	+	3.73578e8i	0.298377	+	0.670165i	0.999062	−	0.0433054i	$-0.0137888\pi$
$823$	1.66328e8	+	3.73578e8i	0.298377	+	0.670165i	−0.700685	+	0.713471i	$0.747122\pi$
$824$	−2.43044e7	+	5.16606e6i	−0.0434413	+	0.00923374i
$825$	−6.47132e7	−	1.37552e7i	−0.115247	−	0.0244966i
$826$	−1.31912e7	−	5.87309e6i	−0.0234069	−	0.0104214i
$827$	−5.88128e8	−	5.29553e8i	−1.03981	−	0.936252i	−0.0417921	−	0.999126i	$-0.513307\pi$
$827$	−5.88128e8	−	5.29553e8i	−1.03981	−	0.936252i	−0.998021	+	0.0628740i	$0.979973\pi$
$828$	−6.96224e6	−	731761.i	−0.0122647	−	0.00128907i
$829$	3.71545e8	−	5.11388e8i	0.652151	−	0.897609i	−0.347039	−	0.937851i	$-0.612813\pi$
$829$	3.71545e8	−	5.11388e8i	0.652151	−	0.897609i	0.999190	+	0.0402417i	$0.0128128\pi$
$830$	3.51320e8	−	3.69253e7i	0.614425	−	0.0645787i
$831$	−1.90604e8	+	3.30136e8i	−0.332146	+	0.575294i
$832$	−9.22792e8	+	5.32774e8i	−1.60226	+	0.925067i
$833$	6.85907e6	+	9.44070e6i	0.0118667	+	0.0163331i
$834$	−3.44263e8	−	3.82342e8i	−0.593460	−	0.659105i
$835$	2.84611e8	−	9.24756e7i	0.488868	−	0.158843i
$836$			1.00795e7i			0.0172512i
$837$	−5.64209e8	+	2.98570e8i	−0.962195	+	0.509177i
$838$	9.20116e6			0.0156355
$839$	2.40540e8	+	7.40307e8i	0.407289	+	1.25351i	0.918969	+	0.394330i	$0.129023\pi$
$839$	2.40540e8	+	7.40307e8i	0.407289	+	1.25351i	−0.511680	+	0.859176i	$0.670977\pi$
$840$	9.46100e8	−	8.51872e8i	1.59624	−	1.43726i
$841$	4.25930e8	−	3.09456e8i	0.716061	−	0.520249i
$842$	1.06947e8	+	1.85237e8i	0.179156	+	0.310307i
$843$	−2.50716e8	−	1.44751e8i	−0.418504	−	0.241623i
$844$	5.18572e6	+	4.93389e7i	0.00862545	+	0.0820657i
$845$	1.35928e9	+	9.87573e8i	2.25288	+	1.63681i
$846$	−2.24484e7	+	2.13582e8i	−0.0370744	+	0.352739i
$847$	−6.79692e8	+	7.54874e8i	−1.11857	+	1.24229i
$848$	9.66778e7	−	2.17142e8i	0.158540	−	0.356087i
$849$	1.00022e8	−	4.70568e8i	0.163446	−	0.768953i
$850$	−1.54116e6	−	7.25058e6i	−0.00250952	−	0.0118064i
$851$	−2.23717e8	+	9.96051e7i	−0.363003	+	0.161619i
$852$	−7.24146e7	−	2.35289e7i	−0.117087	−	0.0380438i
$853$	−4.90192e6	+	1.50865e7i	−0.00789803	+	0.0243076i	−0.954928	−	0.296838i	$-0.904068\pi$
$853$	−4.90192e6	+	1.50865e7i	−0.00789803	+	0.0243076i	0.947030	+	0.321146i	$0.104068\pi$
$854$	1.66323e8	+	3.73567e8i	0.267041	+	0.599784i
$855$	−3.59617e8	+	7.64390e7i	−0.575364	+	0.122297i
$856$	−8.61593e8	−	1.83137e8i	−1.37366	−	0.291981i
$857$	3.18316e8	+	1.41724e8i	0.505727	+	0.225164i	0.643709	−	0.765270i	$-0.277395\pi$
$857$	3.18316e8	+	1.41724e8i	0.505727	+	0.225164i	−0.137982	+	0.990435i	$0.544061\pi$
$858$	7.33324e7	+	6.60288e7i	0.116100	+	0.104537i
$859$	−5.37008e8	−	5.64418e7i	−0.847230	−	0.0890474i	−0.329043	−	0.944315i	$-0.606726\pi$
$859$	−5.37008e8	−	5.64418e7i	−0.847230	−	0.0890474i	−0.518187	+	0.855268i	$0.673393\pi$
$860$	−1.00627e8	+	1.38501e8i	−0.158205	+	0.217750i
$861$	8.81957e8	−	9.26974e7i	1.38178	−	0.145231i
$862$	−2.44739e8	+	4.23900e8i	−0.382104	+	0.661823i
$863$	−7.50890e8	+	4.33527e8i	−1.16827	+	0.674502i	−0.953272	−	0.302112i	$-0.902308\pi$
$863$	−7.50890e8	+	4.33527e8i	−1.16827	+	0.674502i	−0.215000	+	0.976614i	$0.568975\pi$
$864$	1.00383e8	+	1.38165e8i	0.155639	+	0.214219i
$865$	−5.61502e8	−	6.23611e8i	−0.867567	−	0.963531i
$866$	9.81532e7	−	3.18919e7i	0.151130	−	0.0491052i
$867$			5.29188e8i			0.811994i
$868$	1.12672e8	−	7.56757e7i	0.172289	−	0.115717i
$869$	−3.85398e7			−0.0587286
$870$	3.15173e8	+	9.70004e8i	0.478621	+	1.47304i
$871$	3.76188e8	−	3.38721e8i	0.569312	−	0.512611i
$872$	−9.65066e8	+	7.01161e8i	−1.45548	+	1.05747i
$873$	−1.73954e6	−	3.01298e6i	−0.00261452	−	0.00452849i
$874$	−1.86819e8	−	1.07860e8i	−0.279826	−	0.161557i
$875$	3.49871e7	+	3.32880e8i	0.0522256	+	0.496893i
$876$	−2.34828e7	−	1.70613e7i	−0.0349331	−	0.0253804i
$877$	8.01131e7	−	7.62226e8i	0.118769	−	1.13002i	−0.759053	−	0.651029i	$-0.774337\pi$
$877$	8.01131e7	−	7.62226e8i	0.118769	−	1.13002i	0.877822	−	0.478987i	$-0.158996\pi$
$878$	1.41934e8	−	1.57634e8i	0.209702	−	0.232898i
$879$	385687.	−	866268.i	0.000567896	−	0.00127552i
$880$	2.19384e7	−	1.03212e8i	0.0321927	−	0.151455i
$881$	−2.25266e8	−	1.05979e9i	−0.329433	−	1.54986i	−0.761588	−	0.648061i	$-0.775580\pi$
$881$	−2.25266e8	−	1.05979e9i	−0.329433	−	1.54986i	0.432155	−	0.901799i	$-0.357753\pi$
$882$	−3.75560e8	+	1.67210e8i	−0.547360	+	0.243700i
$883$	1.03456e8	+	3.36148e7i	0.150270	+	0.0488256i	0.383186	−	0.923671i	$-0.374827\pi$
$883$	1.03456e8	+	3.36148e7i	0.150270	+	0.0488256i	−0.232916	+	0.972497i	$0.574827\pi$
$884$	476214.	−	1.46564e6i	0.000689359	−	0.00212163i
$885$	−5.47278e6	−	1.22921e7i	−0.00789547	−	0.0177335i
$886$	4.72269e8	−	1.00384e8i	0.679028	−	0.144332i
$887$	5.14779e7	+	1.09420e7i	0.0737649	+	0.0156792i	0.244646	−	0.969612i	$-0.421328\pi$
$887$	5.14779e7	+	1.09420e7i	0.0737649	+	0.0156792i	−0.170881	+	0.985292i	$0.554661\pi$
$888$	7.33121e8	+	3.26406e8i	1.04698	+	0.466144i
$889$	7.91193e8	+	7.12393e8i	1.12610	+	1.01394i
$890$	4.24778e8	+	4.46459e7i	0.602548	+	0.0633303i
$891$	2.73543e7	−	3.76499e7i	0.0386716	−	0.0532269i
$892$	−8.40352e7	+	8.83246e6i	−0.118404	+	0.0124448i
$893$	4.61205e8	−	7.98831e8i	0.647649	−	1.12176i
$894$	1.69281e8	−	9.77346e7i	0.236917	−	0.136784i
$895$	−3.78392e8	−	5.20812e8i	−0.527804	−	0.726461i
$896$	6.35667e8	+	7.05980e8i	0.883702	+	0.981450i
$897$	2.79961e8	−	9.09650e7i	0.387901	−	0.126037i
$898$			8.34817e8i			1.15282i
$899$	1.71290e8	+	9.82761e8i	0.235751	+	1.35260i
$900$	−3.63989e7			−0.0499299
$901$	1.09772e6	+	3.37842e6i	0.00150077	+	0.00461891i
$902$	6.23679e7	−	5.61563e7i	0.0849848	−	0.0765207i
$903$	−1.21777e9	+	8.84760e8i	−1.65387	+	1.20161i
$904$	2.02114e8	+	3.50071e8i	0.273584	+	0.473862i
$905$	1.09302e9	+	6.31053e8i	1.47462	+	0.851374i
$906$	5.08237e7	+	4.83555e8i	0.0683410	+	0.650221i
$907$	−2.12124e8	−	1.54117e8i	−0.284294	−	0.206552i	0.436494	−	0.899707i	$-0.356220\pi$
$907$	−2.12124e8	−	1.54117e8i	−0.284294	−	0.206552i	−0.720788	+	0.693155i	$0.756220\pi$
$908$	−1.99400e6	+	1.89716e7i	−0.00266359	+	0.0253423i
$909$	−1.90687e8	+	2.11779e8i	−0.253881	+	0.281963i
$910$	1.22543e9	−	2.75235e9i	1.62616	−	3.65241i
$911$	1.53647e8	−	7.22853e8i	0.203221	−	0.956081i	−0.751765	−	0.659431i	$-0.770797\pi$
$911$	1.53647e8	−	7.22853e8i	0.203221	−	0.956081i	0.954986	−	0.296650i	$-0.0958694\pi$
$912$	1.28723e8	+	6.05594e8i	0.169696	+	0.798356i
$913$	−3.74285e7	+	1.66642e7i	−0.0491801	+	0.0218964i
$914$	1.10696e8	+	3.59674e7i	0.144975	+	0.0471053i
$915$	−1.17750e8	+	3.62398e8i	−0.153709	+	0.473067i
$916$	5.01455e7	+	1.12629e8i	0.0652447	+	0.146542i
$917$	−1.95947e8	+	4.16498e7i	−0.254115	+	0.0540139i
$918$	8.29542e6	+	1.76325e6i	0.0107229	+	0.00227921i
$919$	4.26594e8	+	1.89932e8i	0.549627	+	0.244710i	0.662710	−	0.748876i	$-0.269406\pi$
$919$	4.26594e8	+	1.89932e8i	0.549627	+	0.244710i	−0.113084	+	0.993585i	$0.536073\pi$
$920$	−2.67092e8	−	2.40491e8i	−0.343003	−	0.308841i
$921$	−5.56224e8	−	5.84615e7i	−0.711985	−	0.0748327i
$922$	7.73923e8	−	1.06521e9i	0.987427	−	1.35908i
$923$	−1.64407e9	+	1.72798e8i	−2.09081	+	0.219753i
$924$	−8.04713e6	+	1.39380e7i	−0.0102006	+	0.0176679i
$925$	−1.10269e9	+	6.36637e8i	−1.39324	+	0.804390i
$926$	3.96562e8	+	5.45821e8i	0.499434	+	0.687412i
$927$	7.66648e6	+	8.51449e6i	0.00962402	+	0.0106886i
$928$	2.53830e8	−	8.24743e7i	0.317613	−	0.103199i
$929$		−	1.08402e9i		−	1.35204i	−0.736882	−	0.676021i	$-0.763703\pi$
$929$		−	1.08402e9i		−	1.35204i	0.736882	−	0.676021i	$-0.236297\pi$
$930$	−8.98303e8	−	1.28055e8i	−1.11680	−	0.159202i
$931$	1.76572e9			2.18813
$932$	−1.18282e7	−	3.64035e7i	−0.0146107	−	0.0449671i
$933$	−5.81983e6	+	5.24020e6i	−0.00716581	+	0.00645212i
$934$	2.58256e8	−	1.87634e8i	0.316964	−	0.230288i
$935$	788480.	+	1.36569e6i	0.000964619	+	0.00167077i
$936$	4.31348e8	+	2.49039e8i	0.526017	+	0.303696i
$937$	3.79625e7	+	3.61189e8i	0.0461462	+	0.439052i	0.993064	+	0.117576i	$0.0375123\pi$
$937$	3.79625e7	+	3.61189e8i	0.0461462	+	0.439052i	−0.946918	+	0.321476i	$0.895821\pi$
$938$	−4.79204e8	−	3.48162e8i	−0.580646	−	0.421864i
$939$	5.18580e7	−	4.93396e8i	0.0626353	−	0.595935i
$940$	1.12087e8	−	1.24486e8i	0.134950	−	0.149877i
$941$	−3.94204e8	+	8.85396e8i	−0.473099	+	1.06260i	0.506611	+	0.862175i	$0.330898\pi$
$941$	−3.94204e8	+	8.85396e8i	−0.473099	+	1.06260i	−0.979710	+	0.200423i	$0.935769\pi$
$942$	3.98614e7	−	1.87533e8i	0.0476870	−	0.224349i
$943$	−5.20518e7	−	2.44885e8i	−0.0620728	−	0.292029i
$944$	1.06879e7	−	4.75857e6i	0.0127051	−	0.00565666i
$945$	−2.19792e9	−	7.14147e8i	−2.60445	−	0.846238i
$946$	−4.40194e7	+	1.35478e8i	−0.0519960	+	0.160027i
$947$	−4.40562e8	−	9.89518e8i	−0.518749	−	1.16513i	−0.963068	−	0.269260i	$-0.913221\pi$
$947$	−4.40562e8	−	9.89518e8i	−0.518749	−	1.16513i	0.444319	−	0.895869i	$-0.353446\pi$
$948$	4.01685e7	−	8.53807e6i	0.0471477	−	0.0100215i
$949$	−6.16427e8	−	1.31026e8i	−0.721246	−	0.153306i
$950$	−1.02465e9	−	4.56203e8i	−1.19510	−	0.532092i
$951$	−7.81639e8	−	7.03791e8i	−0.908793	−	0.818281i
$952$	−1.64528e7	−	1.72926e6i	−0.0190691	−	0.00200424i
$953$	2.88183e8	−	3.96649e8i	0.332958	−	0.458277i	−0.609410	−	0.792855i	$-0.708594\pi$
$953$	2.88183e8	−	3.96649e8i	0.332958	−	0.458277i	0.942368	+	0.334578i	$0.108594\pi$
$954$	−1.24458e8	+	1.30811e7i	−0.143344	+	0.0150660i
$955$	−1.08555e9	+	1.88023e9i	−1.24635	+	2.15875i
$956$	−8.45049e7	+	4.87889e7i	−0.0967182	+	0.0558403i
$957$	−6.95294e7	−	9.56990e7i	−0.0793291	−	0.109187i
$958$	−8.87145e8	−	9.85275e8i	−1.00902	−	1.12063i
$959$	−1.12100e9	+	3.64236e8i	−1.27102	+	0.412978i
$960$			1.16184e9i			1.31320i
$961$	−8.52152e8	−	2.47992e8i	−0.960167	−	0.279426i
$962$	1.89913e9			2.13319
$963$	1.25512e8	+	3.86286e8i	0.140542	+	0.432544i
$964$	−6.48151e7	+	5.83598e7i	−0.0723511	+	0.0651452i
$965$	1.16828e9	−	8.48805e8i	1.30006	−	0.944552i
$966$	−1.72224e8	−	2.98300e8i	−0.191056	−	0.330919i
$967$	6.34636e8	+	3.66407e8i	0.701852	+	0.405214i	0.808037	−	0.589132i	$-0.200530\pi$
$967$	6.34636e8	+	3.66407e8i	0.701852	+	0.405214i	−0.106185	+	0.994346i	$0.533864\pi$
$968$	−9.82284e7	−	9.34581e8i	−0.108296	−	1.03036i
$969$	−7.48563e6	−	5.43863e6i	−0.00822730	−	0.00597748i
$970$	2.03506e6	−	1.93623e7i	0.00222978	−	0.0212150i
$971$	9.38608e8	−	1.04243e9i	1.02524	−	1.13865i	0.0349865	−	0.999388i	$-0.488861\pi$
$971$	9.38608e8	−	1.04243e9i	1.02524	−	1.13865i	0.990256	−	0.139259i	$-0.0444721\pi$
$972$	2.95738e7	−	6.64238e7i	0.0322039	−	0.0723311i
$973$	3.78784e8	−	1.78204e9i	0.411200	−	1.93455i
$974$	−2.72014e7	−	1.27972e8i	−0.0294384	−	0.138497i
$975$	1.39822e9	−	6.22528e8i	1.50856	−	0.671653i
$976$	−3.15104e8	−	1.02384e8i	−0.338926	−	0.110124i
$977$	−5.20909e8	+	1.60319e9i	−0.558571	+	1.71911i	0.127750	+	0.991806i	$0.459225\pi$
$977$	−5.20909e8	+	1.60319e9i	−0.558571	+	1.71911i	−0.686321	+	0.727299i	$0.740775\pi$
$978$	3.05152e8	+	6.85382e8i	0.326212	+	0.732683i
$979$	−4.84545e7	+	1.02993e7i	−0.0516400	+	0.0109764i
$980$	3.13652e8	+	6.66688e7i	0.333250	+	0.0708345i
$981$	5.02498e8	+	2.23726e8i	0.532264	+	0.236979i
$982$	−4.28734e8	−	3.86034e8i	−0.452745	−	0.407653i
$983$	1.02363e9	+	1.07587e8i	1.07766	+	0.113266i	0.626685	−	0.779272i	$-0.284411\pi$
$983$	1.02363e9	+	1.07587e8i	1.07766	+	0.113266i	0.450971	+	0.892539i	$0.351078\pi$
$984$	−4.82229e8	+	6.63731e8i	−0.506137	+	0.696638i
$985$	2.74229e8	−	2.88227e7i	0.286949	−	0.0301596i
$986$	6.62674e6	−	1.14778e7i	0.00691304	−	0.0119737i
$987$	1.27552e9	−	7.36421e8i	1.32659	−	0.765905i
$988$	−1.37061e8	−	1.88649e8i	−0.142116	−	0.195606i
$989$	2.84343e8	+	3.15794e8i	0.293936	+	0.326449i
$990$	−5.28359e7	+	1.71674e7i	−0.0544532	+	0.0176929i
$991$		−	1.06584e9i		−	1.09514i	−0.836759	−	0.547572i	$-0.815552\pi$
$991$		−	1.06584e9i		−	1.09514i	0.836759	−	0.547572i	$-0.184448\pi$
$992$	−3.35093e7	+	2.35067e8i	−0.0343266	+	0.240800i
$993$	5.23456e7			0.0534604
$994$	5.97749e8	+	1.83968e9i	0.608639	+	1.87320i
$995$	6.59208e8	−	5.93554e8i	0.669196	−	0.602547i
$996$	3.53184e7	−	2.56603e7i	0.0357456	−	0.0259707i
$997$	3.38564e8	+	5.86410e8i	0.341630	+	0.591720i	0.984736	−	0.174057i	$-0.0556878\pi$
$997$	3.38564e8	+	5.86410e8i	0.341630	+	0.591720i	−0.643106	+	0.765777i	$0.722354\pi$
$998$	1.06016e9	+	6.12085e8i	1.06655	+	0.615772i
$999$	−1.52273e8	−	1.44878e9i	−0.152730	−	1.45313i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.7.h.a.11.5	✓	120
31.17	odd	30	inner	31.7.h.a.17.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.7.h.a.11.5	✓	120	1.1	even	1	trivial
31.7.h.a.17.5	yes	120	31.17	odd	30	inner

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:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	31.h (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.31599 - 7.12789i) q^{2} +(-16.2945 + 14.6716i) q^{3} +(6.33409 - 4.60199i) q^{4} +(-92.6733 - 160.515i) q^{5} +(142.315 + 82.1659i) q^{6} +(60.8261 + 578.722i) q^{7} +(-435.526 - 316.428i) q^{8} +(-25.9475 + 246.874i) q^{9} +(-929.502 + 1032.32i) q^{10} +(65.5293 - 147.181i) q^{11} +(-35.6921 + 167.918i) q^{12} +(774.922 + 3645.72i) q^{13} +(3984.19 - 1773.88i) q^{14} +(3865.07 + 1255.84i) q^{15} +(-1091.95 + 3360.67i) q^{16} +(-21.4797 - 48.2441i) q^{17} +(1819.79 - 386.808i) q^{18} +(-7816.18 - 1661.38i) q^{19} +(-1325.69 - 590.235i) q^{20} +(-9481.91 - 8537.55i) q^{21} +(-1200.86 - 126.215i) q^{22} +(-2117.21 + 2914.10i) q^{23} +(11739.2 - 1233.84i) q^{24} +(-9364.18 + 16219.2i) q^{25} +(24191.6 - 13967.0i) q^{26} +(-12594.6 - 17335.0i) q^{27} +(3048.55 + 3385.76i) q^{28} +(-31846.9 + 10347.7i) q^{29} -30458.3i q^{30} +(4204.27 - 29492.8i) q^{31} -7970.31 q^{32} +(1091.62 + 3359.66i) q^{33} +(-294.132 + 264.838i) q^{34} +(87256.5 - 63395.5i) q^{35} +(971.758 + 1683.13i) q^{36} +(58877.9 + 33993.2i) q^{37} +(6260.07 + 59560.6i) q^{38} +(-66115.5 - 48035.7i) q^{39} +(-10429.8 + 99232.9i) q^{40} +(-46507.4 + 51651.7i) q^{41} +(-38894.7 + 87358.9i) q^{42} +(24528.1 - 115396. i) q^{43} +(-262.257 - 1233.82i) q^{44} +(42031.6 - 18713.7i) q^{45} +(25674.8 + 8342.25i) q^{46} +(-35671.1 + 109784. i) q^{47} +(-31513.8 - 70781.0i) q^{48} +(-216141. + 45942.2i) q^{49} +(137296. + 29183.2i) q^{50} +(1057.82 + 470.971i) q^{51} +(21686.0 + 19526.1i) q^{52} +(-66897.2 - 7031.18i) q^{53} +(-94392.8 + 129921. i) q^{54} +(-29697.6 + 3121.34i) q^{55} +(156633. - 271296. i) q^{56} +(151736. - 87604.6i) q^{57} +(147514. + 203036. i) q^{58} +(-2215.41 - 2460.46i) q^{59} +(30261.1 - 9832.42i) q^{60} +93762.2i q^{61} +(-219959. + 38337.6i) q^{62} -144450. q^{63} +(88343.9 + 271895. i) q^{64} +(513378. - 462247. i) q^{65} +(21419.1 - 15561.9i) q^{66} +(-67908.2 - 117621. i) q^{67} +(-358.073 - 206.733i) q^{68} +(-8255.58 - 78546.6i) q^{69} +(-653962. - 475131. i) q^{70} +(-46361.9 + 441104. i) q^{71} +(89418.9 - 99309.7i) q^{72} +(-68772.1 + 154465. i) q^{73} +(105939. - 498403. i) q^{74} +(-85377.9 - 401672. i) q^{75} +(-57154.1 + 25446.6i) q^{76} +(89162.8 + 28970.7i) q^{77} +(-189270. + 582514. i) q^{78} +(-97297.2 - 218533. i) q^{79} +(640633. - 136171. i) q^{80} +(282546. + 60057.0i) q^{81} +(475878. + 211875. i) q^{82} +(-188983. - 170161. i) q^{83} +(-99349.0 - 10442.0i) q^{84} +(-5753.30 + 7918.74i) q^{85} +(-879334. + 92421.7i) q^{86} +(367111. - 635856. i) q^{87} +(-75112.0 + 43365.9i) q^{88} +(-180728. - 248751. i) q^{89} +(-230734. - 256256. i) q^{90} +(-2.06272e6 + 670219. i) q^{91} +28201.5i q^{92} +(364201. + 542254. i) q^{93} +865145. q^{94} +(457675. + 1.40858e6i) q^{95} +(129872. - 116937. i) q^{96} +(-11338.7 + 8238.02i) q^{97} +(828051. + 1.43423e6i) q^{98} +(34634.9 + 19996.5i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 6 q^{2} - 7 q^{3} - 1034 q^{4} + 68 q^{5} + 1431 q^{6} - 1753 q^{7} + 811 q^{8} - 3488 q^{9} + 1158 q^{10} + 633 q^{11} + 12777 q^{12} - 10627 q^{13} + 16244 q^{14} + 8395 q^{15} - 4178 q^{16} + 1713 q^{17}+ \cdots - 3201573 q^{99}+O(q^{100}) \) 120 * q - 6 * q^2 - 7 * q^3 - 1034 * q^4 + 68 * q^5 + 1431 * q^6 - 1753 * q^7 + 811 * q^8 - 3488 * q^9 + 1158 * q^10 + 633 * q^11 + 12777 * q^12 - 10627 * q^13 + 16244 * q^14 + 8395 * q^15 - 4178 * q^16 + 1713 * q^17 - 10077 * q^18 - 8345 * q^19 + 60861 * q^20 - 31195 * q^21 - 43117 * q^22 - 67730 * q^23 - 29436 * q^24 - 85880 * q^25 + 25485 * q^26 + 18770 * q^27 + 322940 * q^28 + 48150 * q^29 + 49476 * q^31 - 395322 * q^32 - 92548 * q^33 - 457978 * q^34 + 157789 * q^35 + 129427 * q^36 + 238344 * q^37 + 185830 * q^38 + 309716 * q^39 + 606677 * q^40 + 35959 * q^41 - 164607 * q^42 - 311135 * q^43 - 702621 * q^44 + 772689 * q^45 - 287890 * q^46 + 150530 * q^47 - 523632 * q^48 + 784094 * q^49 - 1034303 * q^50 - 1566491 * q^51 - 1080753 * q^52 - 1164247 * q^53 + 989080 * q^54 + 1197682 * q^55 + 1178042 * q^56 + 2398464 * q^57 + 2436965 * q^58 - 1106237 * q^59 + 1934095 * q^60 - 520303 * q^62 - 3411888 * q^63 + 235127 * q^64 - 583738 * q^65 - 4572168 * q^66 + 111900 * q^67 - 1524354 * q^68 - 2029246 * q^69 + 3662018 * q^70 + 1528315 * q^71 + 6241105 * q^72 + 2588381 * q^73 - 1260273 * q^74 + 707440 * q^75 + 1167086 * q^76 - 597130 * q^77 - 3405041 * q^78 - 1879167 * q^79 - 4997402 * q^80 - 6030051 * q^81 - 1060742 * q^82 + 2947757 * q^83 - 10179536 * q^84 + 2714035 * q^85 + 4916650 * q^86 + 3744039 * q^87 + 11144193 * q^88 + 2916290 * q^89 - 993633 * q^90 + 3702510 * q^91 - 975871 * q^93 - 7349352 * q^94 + 574613 * q^95 + 9276322 * q^96 - 9366930 * q^97 - 3320822 * q^98 - 3201573 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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