LMFDB - Embedded newform 60.7.f.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [60,7,Mod(19,60)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(60, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

N = Newforms(chi, 7, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("60.19");

S:= CuspForms(chi, 7);

N := Newforms(S);

Level:	$ N $	$=$	$ 60 = 2^{2} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 7 $
Character orbit:	$[\chi]$	$=$	60.f (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$13.8032450172$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	60.19
Dual form			60.7.f.a.19.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-7.93273 + 1.03526i) q^{2} +15.5885 q^{3} +(61.8565 - 16.4248i) q^{4} +(-80.2400 - 95.8465i) q^{5} +(-123.659 + 16.1381i) q^{6} -143.606 q^{7} +(-473.687 + 194.331i) q^{8} +243.000 q^{9} +O(q^{10})$	\(q+(-7.93273 + 1.03526i) q^{2} +15.5885 q^{3} +(61.8565 - 16.4248i) q^{4} +(-80.2400 - 95.8465i) q^{5} +(-123.659 + 16.1381i) q^{6} -143.606 q^{7} +(-473.687 + 194.331i) q^{8} +243.000 q^{9} +(735.748 + 677.255i) q^{10} +1568.78i q^{11} +(964.247 - 256.038i) q^{12} -3878.76i q^{13} +(1139.19 - 148.669i) q^{14} +(-1250.82 - 1494.10i) q^{15} +(3556.45 - 2031.96i) q^{16} +5035.60i q^{17} +(-1927.65 + 251.567i) q^{18} +11740.4i q^{19} +(-6537.63 - 4610.80i) q^{20} -2238.59 q^{21} +(-1624.09 - 12444.7i) q^{22} -21747.5 q^{23} +(-7384.05 + 3029.32i) q^{24} +(-2748.09 + 15381.4i) q^{25} +(4015.52 + 30769.2i) q^{26} +3788.00 q^{27} +(-8882.95 + 2358.70i) q^{28} -40105.7 q^{29} +(11469.2 + 10557.4i) q^{30} -223.114i q^{31} +(-26108.8 + 19800.9i) q^{32} +24454.9i q^{33} +(-5213.14 - 39946.1i) q^{34} +(11522.9 + 13764.1i) q^{35} +(15031.1 - 3991.23i) q^{36} +17396.7i q^{37} +(-12154.3 - 93133.1i) q^{38} -60464.0i q^{39} +(56634.6 + 29808.1i) q^{40} +2197.54 q^{41} +(17758.2 - 2317.52i) q^{42} -3196.47 q^{43} +(25766.9 + 97039.2i) q^{44} +(-19498.3 - 23290.7i) q^{45} +(172517. - 22514.2i) q^{46} +10495.8 q^{47} +(55439.6 - 31675.2i) q^{48} -97026.4 q^{49} +(5876.12 - 124862. i) q^{50} +78497.3i q^{51} +(-63708.0 - 239927. i) q^{52} +199848. i q^{53} +(-30049.2 + 3921.55i) q^{54} +(150362. - 125879. i) q^{55} +(68024.2 - 27907.1i) q^{56} +183014. i q^{57} +(318148. - 41519.7i) q^{58} -149784. i q^{59} +(-101911. - 71875.2i) q^{60} +226558. q^{61} +(230.980 + 1769.90i) q^{62} -34896.2 q^{63} +(186615. - 184104. i) q^{64} +(-371766. + 311232. i) q^{65} +(-25317.0 - 193994. i) q^{66} -235597. q^{67} +(82708.9 + 311485. i) q^{68} -339009. q^{69} +(-105658. - 97257.8i) q^{70} -170700. i q^{71} +(-115106. + 47222.5i) q^{72} -245829. i q^{73} +(-18010.0 - 138003. i) q^{74} +(-42838.5 + 239773. i) q^{75} +(192833. + 726217. i) q^{76} -225286. i q^{77} +(62595.7 + 479644. i) q^{78} +373075. i q^{79} +(-480126. - 177828. i) q^{80} +59049.0 q^{81} +(-17432.5 + 2275.02i) q^{82} +380458. q^{83} +(-138471. + 36768.5i) q^{84} +(482645. - 404057. i) q^{85} +(25356.8 - 3309.17i) q^{86} -625186. q^{87} +(-304863. - 743111. i) q^{88} +421299. q^{89} +(178787. + 164573. i) q^{90} +557013. i q^{91} +(-1.34522e6 + 357198. i) q^{92} -3478.00i q^{93} +(-83260.6 + 10865.9i) q^{94} +(1.12527e6 - 942046. i) q^{95} +(-406995. + 308665. i) q^{96} -855309. i q^{97} +(769684. - 100447. i) q^{98} +381213. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	$ 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) $ 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

$n$	$31$	$37$	$41$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	−7.93273	+	1.03526i	−0.991592	+	0.129407i
$2$	−7.93273	+	1.03526i	−0.991592	+	0.129407i
$3$	15.5885			0.577350
$3$	15.5885			0.577350
$4$	61.8565	−	16.4248i	0.966508	−	0.256638i
$5$	−80.2400	−	95.8465i	−0.641920	−	0.766772i
$5$	−80.2400	−	95.8465i	−0.641920	−	0.766772i
$6$	−123.659	+	16.1381i	−0.572496	+	0.0747132i
$7$	−143.606			−0.418676			−0.209338	−	0.977843i	$-0.567131\pi$
$7$	−143.606			−0.418676			−0.209338	+	0.977843i	$0.567131\pi$
$8$	−473.687	+	194.331i	−0.925170	+	0.379553i
$9$	243.000			0.333333
$10$	735.748	+	677.255i	0.735748	+	0.677255i
$11$			1568.78i			1.17865i	0.807897	+	0.589324i	$0.200606\pi$
$11$			1568.78i			1.17865i	−0.807897	+	0.589324i	$0.799394\pi$
$12$	964.247	−	256.038i	0.558013	−	0.148170i
$13$		−	3878.76i		−	1.76548i	−0.469860	−	0.882741i	$-0.655695\pi$
$13$		−	3878.76i		−	1.76548i	0.469860	−	0.882741i	$-0.344305\pi$
$14$	1139.19	−	148.669i	0.415155	−	0.0541796i
$15$	−1250.82	−	1494.10i	−0.370613	−	0.442696i
$16$	3556.45	−	2031.96i	0.868274	−	0.496085i
$17$			5035.60i			1.02495i	0.858701	+	0.512477i	$0.171272\pi$
$17$			5035.60i			1.02495i	−0.858701	+	0.512477i	$0.828728\pi$
$18$	−1927.65	+	251.567i	−0.330531	+	0.0431357i
$19$			11740.4i			1.71167i	0.517247	+	0.855836i	$0.326957\pi$
$19$			11740.4i			1.71167i	−0.517247	+	0.855836i	$0.673043\pi$
$20$	−6537.63	−	4610.80i	−0.817203	−	0.576350i
$21$	−2238.59			−0.241723
$22$	−1624.09	−	12444.7i	−0.152525	−	1.16874i
$23$	−21747.5			−1.78741			−0.893706	−	0.448652i	$-0.851904\pi$
$23$	−21747.5			−1.78741			−0.893706	+	0.448652i	$0.851904\pi$
$24$	−7384.05	+	3029.32i	−0.534147	+	0.219135i
$25$	−2748.09	+	15381.4i	−0.175878	+	0.984412i
$26$	4015.52	+	30769.2i	0.228466	+	1.75064i
$27$	3788.00			0.192450
$28$	−8882.95	+	2358.70i	−0.404653	+	0.107448i
$29$	−40105.7			−1.64442			−0.822208	−	0.569187i	$-0.807258\pi$
$29$	−40105.7			−1.64442			−0.822208	+	0.569187i	$0.807258\pi$
$30$	11469.2	+	10557.4i	0.424784	+	0.391014i
$31$		−	223.114i		−	0.00748930i	−0.999993	−	0.00374465i	$-0.998808\pi$
$31$		−	223.114i		−	0.00748930i	0.999993	−	0.00374465i	$-0.00119196\pi$
$32$	−26108.8	+	19800.9i	−0.796776	+	0.604275i
$33$			24454.9i			0.680492i
$34$	−5213.14	−	39946.1i	−0.132636	−	1.01634i
$35$	11522.9	+	13764.1i	0.268756	+	0.321029i
$36$	15031.1	−	3991.23i	0.322169	−	0.0855460i
$37$			17396.7i			0.343448i	0.985145	+	0.171724i	$0.0549337\pi$
$37$			17396.7i			0.343448i	−0.985145	+	0.171724i	$0.945066\pi$
$38$	−12154.3	−	93133.1i	−0.221503	−	1.69728i
$39$		−	60464.0i		−	1.01930i
$40$	56634.6	+	29808.1i	0.884915	+	0.465752i
$41$	2197.54			0.0318849			0.0159425	−	0.999873i	$-0.494925\pi$
$41$	2197.54			0.0318849			0.0159425	+	0.999873i	$0.494925\pi$
$42$	17758.2	−	2317.52i	0.239690	−	0.0312806i
$43$	−3196.47			−0.0402036			−0.0201018	−	0.999798i	$-0.506399\pi$
$43$	−3196.47			−0.0402036			−0.0201018	+	0.999798i	$0.506399\pi$
$44$	25766.9	+	97039.2i	0.302486	+	1.13917i
$45$	−19498.3	−	23290.7i	−0.213973	−	0.255591i
$46$	172517.	−	22514.2i	1.77238	−	0.231304i
$47$	10495.8			0.101093			0.0505467	−	0.998722i	$-0.483904\pi$
$47$	10495.8			0.101093			0.0505467	+	0.998722i	$0.483904\pi$
$48$	55439.6	−	31675.2i	0.501298	−	0.286415i
$49$	−97026.4			−0.824711
$50$	5876.12	−	124862.i	0.0470090	−	0.998894i
$51$			78497.3i			0.591758i
$52$	−63708.0	−	239927.i	−0.453090	−	1.70635i
$53$			199848.i			1.34237i	0.741289	+	0.671186i	$0.234215\pi$
$53$			199848.i			1.34237i	−0.741289	+	0.671186i	$0.765785\pi$
$54$	−30049.2	+	3921.55i	−0.190832	+	0.0249044i
$55$	150362.	−	125879.i	0.903753	−	0.756597i
$56$	68024.2	−	27907.1i	0.387346	−	0.158910i
$57$			183014.i			0.988235i
$58$	318148.	−	41519.7i	1.63059	−	0.212799i
$59$		−	149784.i		−	0.729304i	−0.931144	−	0.364652i	$-0.881188\pi$
$59$		−	149784.i		−	0.729304i	0.931144	−	0.364652i	$-0.118812\pi$
$60$	−101911.	−	71875.2i	−0.471812	−	0.332756i
$61$	226558.			0.998137			0.499068	−	0.866563i	$-0.333676\pi$
$61$	226558.			0.998137			0.499068	+	0.866563i	$0.333676\pi$
$62$	230.980	+	1769.90i	0.000969168	+	0.00742632i
$63$	−34896.2			−0.139559
$64$	186615.	−	184104.i	0.711879	−	0.702302i
$65$	−371766.	+	311232.i	−1.35372	+	1.13330i
$66$	−25317.0	−	193994.i	−0.0880605	−	0.674770i
$67$	−235597.			−0.783330			−0.391665	−	0.920108i	$-0.628101\pi$
$67$	−235597.			−0.783330			−0.391665	+	0.920108i	$0.628101\pi$
$68$	82708.9	+	311485.i	0.263042	+	0.990626i
$69$	−339009.			−1.03196
$70$	−105658.	−	97257.8i	−0.308040	−	0.283550i
$71$		−	170700.i		−	0.476934i	−0.971151	−	0.238467i	$-0.923355\pi$
$71$		−	170700.i		−	0.476934i	0.971151	−	0.238467i	$-0.0766448\pi$
$72$	−115106.	+	47222.5i	−0.308390	+	0.126518i
$73$		−	245829.i		−	0.631923i	−0.948772	−	0.315962i	$-0.897673\pi$
$73$		−	245829.i		−	0.631923i	0.948772	−	0.315962i	$-0.102327\pi$
$74$	−18010.0	−	138003.i	−0.0444446	−	0.340560i
$75$	−42838.5	+	239773.i	−0.101543	+	0.568351i
$76$	192833.	+	726217.i	0.439280	+	1.65434i
$77$		−	225286.i		−	0.493471i
$78$	62595.7	+	479644.i	0.131905	+	1.01073i
$79$			373075.i			0.756684i	0.925666	+	0.378342i	$0.123506\pi$
$79$			373075.i			0.756684i	−0.925666	+	0.378342i	$0.876494\pi$
$80$	−480126.	−	177828.i	−0.937746	−	0.347321i
$81$	59049.0			0.111111
$82$	−17432.5	+	2275.02i	−0.0316168	+	0.00412614i
$83$	380458.			0.665384			0.332692	−	0.943036i	$-0.392043\pi$
$83$	380458.			0.665384			0.332692	+	0.943036i	$0.392043\pi$
$84$	−138471.	+	36768.5i	−0.233627	+	0.0620352i
$85$	482645.	−	404057.i	0.785906	−	0.657939i
$86$	25356.8	−	3309.17i	0.0398656	−	0.00520264i
$87$	−625186.			−0.949404
$88$	−304863.	−	743111.i	−0.447359	−	1.09045i
$89$	421299.			0.597614			0.298807	−	0.954314i	$-0.403411\pi$
$89$	421299.			0.597614			0.298807	+	0.954314i	$0.403411\pi$
$90$	178787.	+	164573.i	0.245249	+	0.225752i
$91$			557013.i			0.739165i
$92$	−1.34522e6	+	357198.i	−1.72755	+	0.458718i
$93$		−	3478.00i		−	0.00432395i
$94$	−83260.6	+	10865.9i	−0.100243	+	0.0130822i
$95$	1.12527e6	−	942046.i	1.31246	−	1.09876i
$96$	−406995.	+	308665.i	−0.460019	+	0.348878i
$97$		−	855309.i		−	0.937147i	−0.883425	−	0.468573i	$-0.844768\pi$
$97$		−	855309.i		−	0.937147i	0.883425	−	0.468573i	$-0.155232\pi$
$98$	769684.	−	100447.i	0.817776	−	0.106723i
$99$			381213.i			0.392882i
$100$	82650.3	+	996579.i	0.0826503	+	0.996579i
$101$	514825.			0.499684			0.249842	−	0.968287i	$-0.419621\pi$
$101$	514825.			0.499684			0.249842	+	0.968287i	$0.419621\pi$
$102$	−81264.8	−	622698.i	−0.0765776	−	0.586782i
$103$	−1.35064e6			−1.23603			−0.618015	−	0.786166i	$-0.712063\pi$
$103$	−1.35064e6			−1.23603			−0.618015	+	0.786166i	$0.712063\pi$
$104$	753765.	+	1.83732e6i	0.670094	+	1.63337i
$105$	179625.	+	214561.i	0.155166	+	0.185346i
$106$	−206894.	−	1.58534e6i	−0.173712	−	1.33108i
$107$	−717435.			−0.585641			−0.292820	−	0.956167i	$-0.594594\pi$
$107$	−717435.			−0.585641			−0.292820	+	0.956167i	$0.594594\pi$
$108$	234312.	−	62217.2i	0.186004	−	0.0493900i
$109$	339995.			0.262538			0.131269	−	0.991347i	$-0.458095\pi$
$109$	339995.			0.262538			0.131269	+	0.991347i	$0.458095\pi$
$110$	−1.06246e6	+	1.15423e6i	−0.798245	+	0.867187i
$111$			271187.i			0.198290i
$112$	−510727.	+	291802.i	−0.363525	+	0.207699i
$113$		−	465203.i		−	0.322409i	−0.986921	−	0.161205i	$-0.948462\pi$
$113$		−	465203.i		−	0.322409i	0.986921	−	0.161205i	$-0.0515379\pi$
$114$	−189467.	−	1.45180e6i	−0.127885	−	0.979925i
$115$	1.74502e6	+	2.08442e6i	1.14738	+	1.37054i
$116$	−2.48080e6	+	658729.i	−1.58934	+	0.422020i
$117$		−	942540.i		−	0.588494i
$118$	155065.	+	1.18819e6i	0.0943771	+	0.723171i
$119$		−	723141.i		−	0.429124i
$120$	882846.	+	464662.i	0.510906	+	0.268902i
$121$	−689508.			−0.389209
$122$	−1.79722e6	+	234546.i	−0.989744	+	0.129166i
$123$	34256.3			0.0184088
$124$	−3664.60	−	13801.0i	−0.00192204	−	0.00723846i
$125$	1.69476e6	−	970812.i	0.867719	−	0.497056i
$126$	276822.	−	36126.5i	0.138385	−	0.0180599i
$127$	−1.03009e6			−0.502878			−0.251439	−	0.967873i	$-0.580904\pi$
$127$	−1.03009e6			−0.502878			−0.251439	+	0.967873i	$0.580904\pi$
$128$	−1.28977e6	+	1.65364e6i	−0.615010	+	0.788519i
$129$	−49828.1			−0.0232116
$130$	2.62691e6	−	2.85379e6i	1.19568	−	1.29895i
$131$		−	2.41236e6i		−	1.07307i	−0.843878	−	0.536536i	$-0.819733\pi$
$131$		−	2.41236e6i		−	1.07307i	0.843878	−	0.536536i	$-0.180267\pi$
$132$	401667.	+	1.51269e6i	0.174640	+	0.657701i
$133$		−	1.68598e6i		−	0.716636i
$134$	1.86892e6	−	243903.i	0.776743	−	0.101368i
$135$	−303949.	−	363066.i	−0.123538	−	0.147565i
$136$	−978574.	−	2.38530e6i	−0.389024	−	0.948257i
$137$		−	527604.i		−	0.205185i	−0.994723	−	0.102593i	$-0.967286\pi$
$137$		−	527604.i		−	0.205185i	0.994723	−	0.102593i	$-0.0327138\pi$
$138$	2.68927e6	−	350962.i	1.02329	−	0.133543i
$139$		−	2.19739e6i		−	0.818204i	−0.912489	−	0.409102i	$-0.865842\pi$
$139$		−	2.19739e6i		−	0.818204i	0.912489	−	0.409102i	$-0.134158\pi$
$140$	938841.	+	662137.i	0.342143	+	0.241304i
$141$	163614.			0.0583663
$142$	176718.	+	1.35412e6i	0.0617186	+	0.472924i
$143$	6.08493e6			2.08088
$144$	864217.	−	493767.i	0.289425	−	0.165362i
$145$	3.21808e6	+	3.84399e6i	1.05558	+	1.26089i
$146$	254496.	+	1.95009e6i	0.0817753	+	0.626610i
$147$	−1.51249e6			−0.476147
$148$	285737.	+	1.07610e6i	0.0881417	+	0.331945i
$149$	−3.55467e6			−1.07458			−0.537292	−	0.843396i	$-0.680553\pi$
$149$	−3.55467e6			−1.07458			−0.537292	+	0.843396i	$0.680553\pi$
$150$	91599.7	−	1.94640e6i	0.0271406	−	0.576712i
$151$		−	28179.2i		−	0.00818459i	−0.999992	−	0.00409230i	$-0.998697\pi$
$151$		−	28179.2i		−	0.00818459i	0.999992	−	0.00409230i	$-0.00130262\pi$
$152$	−2.28152e6	−	5.56126e6i	−0.649670	−	1.58359i
$153$			1.22365e6i			0.341652i
$154$	233229.	+	1.78713e6i	0.0638586	+	0.489322i
$155$	−21384.7	+	17902.6i	−0.00574258	+	0.00480753i
$156$	−993110.	−	3.74009e6i	−0.261591	−	0.985163i
$157$			2.51703e6i			0.650413i	0.945643	+	0.325207i	$0.105434\pi$
$157$			2.51703e6i			0.650413i	−0.945643	+	0.325207i	$0.894566\pi$
$158$	−386228.	−	2.95950e6i	−0.0979203	−	0.750322i
$159$			3.11533e6i			0.775019i
$160$	3.99281e6	+	913611.i	0.974807	+	0.223050i
$161$	3.12306e6			0.748346
$162$	−468420.	+	61130.9i	−0.110177	+	0.0143786i
$163$	−2.44319e6			−0.564150			−0.282075	−	0.959392i	$-0.591023\pi$
$163$	−2.44319e6			−0.564150			−0.282075	+	0.959392i	$0.591023\pi$
$164$	135932.	−	36094.2i	0.0308170	−	0.00818288i
$165$	2.34391e6	−	1.96226e6i	0.521782	−	0.436822i
$166$	−3.01807e6	+	393871.i	−0.659789	+	0.0861054i
$167$	−595753.			−0.127914			−0.0639569	−	0.997953i	$-0.520372\pi$
$167$	−595753.			−0.127914			−0.0639569	+	0.997953i	$0.520372\pi$
$168$	1.06039e6	−	435028.i	0.223634	−	0.0917465i
$169$	−1.02180e7			−2.11693
$170$	−3.41039e6	+	3.70493e6i	−0.694156	+	0.754108i
$171$			2.85291e6i			0.570557i
$172$	−197722.	+	52501.5i	−0.0388571	+	0.0103178i
$173$			3.88556e6i			0.750440i	0.926936	+	0.375220i	$0.122433\pi$
$173$			3.88556e6i			0.750440i	−0.926936	+	0.375220i	$0.877567\pi$
$174$	4.95943e6	−	647228.i	0.941421	−	0.122860i
$175$	394641.	−	2.20886e6i	0.0736357	−	0.412149i
$176$	3.18770e6	+	5.57929e6i	0.584709	+	1.02339i
$177$		−	2.33490e6i		−	0.421064i
$178$	−3.34205e6	+	436153.i	−0.592589	+	0.0773354i
$179$		−	4.77301e6i		−	0.832211i	−0.909316	−	0.416106i	$-0.863395\pi$
$179$		−	4.77301e6i		−	0.832211i	0.909316	−	0.416106i	$-0.136605\pi$
$180$	−1.58864e6	−	1.12042e6i	−0.272401	−	0.192117i
$181$	−5.55733e6			−0.937196			−0.468598	−	0.883412i	$-0.655241\pi$
$181$	−5.55733e6			−0.937196			−0.468598	+	0.883412i	$0.655241\pi$
$182$	−576651.	−	4.41863e6i	−0.0956531	−	0.732949i
$183$	3.53169e6			0.576275
$184$	1.03015e7	−	4.22621e6i	1.65366	−	0.678418i
$185$	1.66741e6	−	1.39591e6i	0.263346	−	0.220466i
$186$	3600.62	+	27590.0i	0.000559549	+	0.00428759i
$187$	−7.89975e6			−1.20806
$188$	649235.	−	172392.i	0.0977076	−	0.0259444i
$189$	−543978.			−0.0805742
$190$	−7.95122e6	+	8.63795e6i	−1.15924	+	1.25936i
$191$		−	2.75996e6i		−	0.396098i	−0.980192	−	0.198049i	$-0.936540\pi$
$191$		−	2.75996e6i		−	0.396098i	0.980192	−	0.198049i	$-0.0634605\pi$
$192$	2.90904e6	−	2.86990e6i	0.411004	−	0.405474i
$193$			1.01132e7i			1.40675i	0.710820	+	0.703374i	$0.248324\pi$
$193$			1.01132e7i			1.40675i	−0.710820	+	0.703374i	$0.751676\pi$
$194$	885464.	+	6.78493e6i	0.121273	+	0.929267i
$195$	−5.79526e6	+	4.85163e6i	−0.781572	+	0.654310i
$196$	−6.00171e6	+	1.59364e6i	−0.797089	+	0.211652i
$197$			5.31570e6i			0.695284i	0.937627	+	0.347642i	$0.113017\pi$
$197$			5.31570e6i			0.695284i	−0.937627	+	0.347642i	$0.886983\pi$
$198$	−394654.	−	3.02406e6i	−0.0508418	−	0.389579i
$199$			1.03986e7i			1.31952i	0.751477	+	0.659759i	$0.229342\pi$
$199$			1.03986e7i			1.31952i	−0.751477	+	0.659759i	$0.770658\pi$
$200$	−1.68736e6	−	7.82003e6i	−0.210920	−	0.977503i
$201$	−3.67259e6			−0.452256
$202$	−4.08397e6	+	532976.i	−0.495483	+	0.0646627i
$203$	5.75941e6			0.688477
$204$	1.28930e6	+	4.85556e6i	0.151867	+	0.571938i
$205$	−176331.	−	210627.i	−0.0204676	−	0.0244485i
$206$	1.07143e7	−	1.39826e6i	1.22564	−	0.159951i
$207$	−5.28463e6			−0.595804
$208$	−7.88151e6	−	1.37946e7i	−0.875829	−	1.53292i
$209$	−1.84180e7			−2.01746
$210$	−1.64704e6	−	1.51610e6i	−0.177847	−	0.163708i
$211$			5.65069e6i			0.601525i	0.953699	+	0.300763i	$0.0972412\pi$
$211$			5.65069e6i			0.601525i	−0.953699	+	0.300763i	$0.902759\pi$
$212$	3.28247e6	+	1.23619e7i	0.344504	+	1.29741i
$213$		−	2.66095e6i		−	0.275358i
$214$	5.69122e6	−	742729.i	0.580716	−	0.0757860i
$215$	256485.	+	306370.i	0.0258075	+	0.0308270i
$216$	−1.79432e6	+	736125.i	−0.178049	+	0.0730450i
$217$			32040.4i			0.00313559i
$218$	−2.69709e6	+	351982.i	−0.260331	+	0.0339743i
$219$		−	3.83209e6i		−	0.364841i
$220$	7.23332e6	−	1.02561e7i	0.679313	−	0.963194i
$221$	1.95319e7			1.80954
$222$	−280748.	−	2.15125e6i	−0.0256601	−	0.196622i
$223$	−1.20891e7			−1.09013			−0.545065	−	0.838394i	$-0.683495\pi$
$223$	−1.20891e7			−1.09013			−0.545065	+	0.838394i	$0.683495\pi$
$224$	3.74937e6	−	2.84352e6i	0.333591	−	0.252995i
$225$	−667786.	+	3.73769e6i	−0.0586259	+	0.328137i
$226$	481604.	+	3.69033e6i	0.0417220	+	0.319698i
$227$	5.54653e6			0.474181			0.237090	−	0.971488i	$-0.423806\pi$
$227$	5.54653e6			0.474181			0.237090	+	0.971488i	$0.423806\pi$
$228$	3.00598e6	+	1.13206e7i	0.253618	+	0.955136i
$229$	−5.82739e6			−0.485252			−0.242626	−	0.970120i	$-0.578009\pi$
$229$	−5.82739e6			−0.485252			−0.242626	+	0.970120i	$0.578009\pi$
$230$	−1.60006e7	−	1.47286e7i	−1.31509	−	1.21053i
$231$		−	3.51186e6i		−	0.284906i
$232$	1.89975e7	−	7.79378e6i	1.52136	−	0.624143i
$233$		−	6.44278e6i		−	0.509338i	−0.967028	−	0.254669i	$-0.918034\pi$
$233$		−	6.44278e6i		−	0.509338i	0.967028	−	0.254669i	$-0.0819664\pi$
$234$	975771.	+	7.47692e6i	0.0761553	+	0.583546i
$235$	−842185.	−	1.00599e6i	−0.0648939	−	0.0775156i
$236$	−2.46017e6	−	9.26509e6i	−0.187167	−	0.704878i
$237$			5.81566e6i			0.436872i
$238$	748637.	+	5.73649e6i	0.0555316	+	0.425515i
$239$		−	2.58807e7i		−	1.89576i	−0.318632	−	0.947878i	$-0.603223\pi$
$239$		−	2.58807e7i		−	1.89576i	0.318632	−	0.947878i	$-0.396777\pi$
$240$	−7.48443e6	−	2.77207e6i	−0.541408	−	0.200526i
$241$	2.39919e7			1.71401			0.857005	−	0.515308i	$-0.172323\pi$
$241$	2.39919e7			1.71401			0.857005	+	0.515308i	$0.172323\pi$
$242$	5.46968e6	−	713818.i	0.385937	−	0.0503664i
$243$	920483.			0.0641500
$244$	1.40141e7	−	3.72118e6i	0.964707	−	0.256160i
$245$	7.78540e6	+	9.29964e6i	0.529398	+	0.632365i
$246$	−271746.	+	35464.0i	−0.0182540	+	0.00238223i
$247$	4.55381e7			3.02193
$248$	43357.9	+	105686.i	0.00284258	+	0.00692887i
$249$	5.93075e6			0.384159
$250$	−1.24391e7	+	9.45570e6i	−0.796100	+	0.605165i
$251$			2.34272e7i			1.48149i	0.671787	+	0.740744i	$0.265527\pi$
$251$			2.34272e7i			1.48149i	−0.671787	+	0.740744i	$0.734473\pi$
$252$	−2.15856e6	+	573164.i	−0.134884	+	0.0358160i
$253$		−	3.41170e7i		−	2.10673i
$254$	8.17141e6	−	1.06640e6i	0.498650	−	0.0650760i
$255$	7.52368e6	−	6.29862e6i	0.453743	−	0.379861i
$256$	8.51946e6	−	1.44532e7i	0.507799	−	0.861475i
$257$		−	1.57956e7i		−	0.930544i	−0.885168	−	0.465272i	$-0.845957\pi$
$257$		−	1.57956e7i		−	0.930544i	0.885168	−	0.465272i	$-0.154043\pi$
$258$	395273.	−	51584.8i	0.0230164	−	0.00300374i
$259$		−	2.49826e6i		−	0.143793i
$260$	−1.78842e7	+	2.53579e7i	−1.01754	+	1.44276i
$261$	−9.74568e6			−0.548139
$262$	2.49741e6	+	1.91366e7i	0.138863	+	1.06405i
$263$	−8.68016e6			−0.477156			−0.238578	−	0.971123i	$-0.576681\pi$
$263$	−8.68016e6			−0.477156			−0.238578	+	0.971123i	$0.576681\pi$
$264$	−4.75234e6	−	1.15839e7i	−0.258283	−	0.629571i
$265$	1.91548e7	−	1.60358e7i	1.02929	−	0.861695i
$266$	1.74543e6	+	1.33745e7i	0.0927377	+	0.710610i
$267$	6.56740e6			0.345032
$268$	−1.45732e7	+	3.86963e6i	−0.757094	+	0.201032i
$269$	−3.33952e7			−1.71564			−0.857822	−	0.513946i	$-0.828183\pi$
$269$	−3.33952e7			−1.71564			−0.857822	+	0.513946i	$0.828183\pi$
$270$	2.78701e6	+	2.56544e6i	0.141595	+	0.130338i
$271$		−	2.69520e7i		−	1.35420i	−0.735889	−	0.677102i	$-0.763236\pi$
$271$		−	2.69520e7i		−	1.35420i	0.735889	−	0.677102i	$-0.236764\pi$
$272$	1.02322e7	+	1.79089e7i	0.508465	+	0.889941i
$273$			8.68297e6i			0.426757i
$274$	546205.	+	4.18534e6i	0.0265524	+	0.203460i
$275$	−2.41301e7	−	4.31115e6i	−1.16027	−	0.207298i
$276$	−2.09699e7	+	5.56817e6i	−0.997400	+	0.264841i
$277$			9.32384e6i			0.438688i	0.975648	+	0.219344i	$0.0703917\pi$
$277$			9.32384e6i			0.438688i	−0.975648	+	0.219344i	$0.929608\pi$
$278$	2.27486e6	+	1.74313e7i	0.105881	+	0.811324i
$279$		−	54216.6i		−	0.00249643i
$280$	−8.13305e6	−	4.28062e6i	−0.370493	−	0.194999i
$281$	2.95827e7			1.33327			0.666636	−	0.745384i	$-0.267734\pi$
$281$	2.95827e7			1.33327			0.666636	+	0.745384i	$0.267734\pi$
$282$	−1.29790e6	+	169382.i	−0.0578756	+	0.00755302i
$283$	−8.93801e6			−0.394350			−0.197175	−	0.980368i	$-0.563177\pi$
$283$	−8.93801e6			−0.394350			−0.197175	+	0.980368i	$0.563177\pi$
$284$	−2.80372e6	−	1.05589e7i	−0.122399	−	0.460960i
$285$	1.75413e7	−	1.46851e7i	0.757750	−	0.634367i
$286$	−4.82701e7	+	6.29946e6i	−2.06338	+	0.269281i
$287$	−315580.			−0.0133494
$288$	−6.34443e6	+	4.81161e6i	−0.265592	+	0.201425i
$289$	−1.21971e6			−0.0505318
$290$	−2.95077e7	−	2.71618e7i	−1.20988	−	1.11369i
$291$		−	1.33329e7i		−	0.541062i
$292$	−4.03770e6	−	1.52061e7i	−0.162175	−	0.610759i
$293$			2.26330e7i			0.899787i	0.893082	+	0.449894i	$0.148538\pi$
$293$			2.26330e7i			0.899787i	−0.893082	+	0.449894i	$0.851462\pi$
$294$	1.19982e7	−	1.56582e6i	0.472143	−	0.0616168i
$295$	−1.43562e7	+	1.20186e7i	−0.559209	+	0.468155i
$296$	−3.38071e6	−	8.24057e6i	−0.130357	−	0.317748i
$297$			5.94253e6i			0.226831i
$298$	2.81982e7	−	3.68000e6i	1.06555	−	0.139059i
$299$			8.43532e7i			3.15565i
$300$	1.28839e6	+	1.55351e7i	0.0477182	+	0.575375i
$301$	459032.			0.0168323
$302$	29172.7	+	223538.i	0.00105914	+	0.00811577i
$303$	8.02533e6			0.288493
$304$	2.38560e7	+	4.17540e7i	0.849135	+	1.48620i
$305$	−1.81790e7	−	2.17148e7i	−0.640724	−	0.765343i
$306$	−1.26679e6	−	9.70690e6i	−0.0442121	−	0.338779i
$307$	9.53548e6			0.329555			0.164777	−	0.986331i	$-0.447309\pi$
$307$	9.53548e6			0.329555			0.164777	+	0.986331i	$0.447309\pi$
$308$	−3.70028e6	−	1.39354e7i	−0.126643	−	0.476943i
$309$	−2.10544e7			−0.713622
$310$	151105.	−	164155.i	0.00507217	−	0.00551024i
$311$			1.49513e7i			0.497047i	0.968626	+	0.248523i	$0.0799453\pi$
$311$			1.49513e7i			0.497047i	−0.968626	+	0.248523i	$0.920055\pi$
$312$	1.17500e7	+	2.86410e7i	0.386879	+	0.943027i
$313$		−	5.65882e6i		−	0.184541i	−0.995734	−	0.0922706i	$-0.970588\pi$
$313$		−	5.65882e6i		−	0.184541i	0.995734	−	0.0922706i	$-0.0294125\pi$
$314$	−2.60577e6	−	1.99669e7i	−0.0841681	−	0.644944i
$315$	2.80007e6	+	3.34468e6i	0.0895854	+	0.107010i
$316$	6.12769e6	+	2.30771e7i	0.194194	+	0.731341i
$317$		−	1.34418e7i		−	0.421969i	−0.977489	−	0.210984i	$-0.932333\pi$
$317$		−	1.34418e7i		−	0.421969i	0.977489	−	0.210984i	$-0.0676669\pi$
$318$	−3.22516e6	−	2.47131e7i	−0.100293	−	0.768502i
$319$		−	6.29170e7i		−	1.93819i
$320$	−3.26197e7	−	3.11385e6i	−0.995475	−	0.0950272i
$321$	−1.11837e7			−0.338120
$322$	−2.47744e7	+	3.23317e6i	−0.742054	+	0.0968413i
$323$	−5.91198e7			−1.75439
$324$	3.65256e6	−	969870.i	0.107390	−	0.0285153i
$325$	5.96610e7	+	1.06592e7i	1.73796	+	0.310509i
$326$	1.93812e7	−	2.52933e6i	0.559407	−	0.0730050i
$327$	5.29999e6			0.151577
$328$	−1.04095e6	+	427051.i	−0.0294990	+	0.0121020i
$329$	−1.50726e6			−0.0423254
$330$	−1.65622e7	+	1.79926e7i	−0.460867	+	0.500671i
$331$			4.96648e7i			1.36951i	0.728774	+	0.684755i	$0.240091\pi$
$331$			4.96648e7i			1.36951i	−0.728774	+	0.684755i	$0.759909\pi$
$332$	2.35338e7	−	6.24895e6i	0.643098	−	0.170763i
$333$			4.22739e6i			0.114483i
$334$	4.72595e6	−	616758.i	0.126838	−	0.0165529i
$335$	1.89043e7	+	2.25811e7i	0.502835	+	0.600635i
$336$	−7.96144e6	+	4.54874e6i	−0.209881	+	0.119915i
$337$		−	2.90061e7i		−	0.757878i	−0.925422	−	0.378939i	$-0.876289\pi$
$337$		−	2.90061e7i		−	0.757878i	0.925422	−	0.378939i	$-0.123711\pi$
$338$	8.10567e7	−	1.05783e7i	2.09913	−	0.273945i
$339$		−	7.25180e6i		−	0.186143i
$340$	2.32181e7	−	3.29209e7i	0.590732	−	0.837596i
$341$	350016.			0.00882724
$342$	−2.95349e6	−	2.26314e7i	−0.0738342	−	0.565760i
$343$	3.08286e7			0.763962
$344$	1.51413e6	−	621174.i	0.0371952	−	0.0152594i
$345$	2.72021e7	+	3.24928e7i	0.662438	+	0.791280i
$346$	−4.02256e6	−	3.08231e7i	−0.0971122	−	0.744130i
$347$	−2.93928e7			−0.703481			−0.351740	−	0.936098i	$-0.614410\pi$
$347$	−2.93928e7			−0.703481			−0.351740	+	0.936098i	$0.614410\pi$
$348$	−3.86718e7	+	1.02686e7i	−0.917607	+	0.243653i
$349$	−4.15224e7			−0.976801			−0.488401	−	0.872620i	$-0.662419\pi$
$349$	−4.15224e7			−0.976801			−0.488401	+	0.872620i	$0.662419\pi$
$350$	−843845.	+	1.79309e7i	−0.0196815	+	0.418213i
$351$		−	1.46927e7i		−	0.339767i
$352$	−3.10632e7	−	4.09589e7i	−0.712226	−	0.939118i
$353$		−	5.41710e7i		−	1.23152i	−0.787933	−	0.615761i	$-0.788848\pi$
$353$		−	5.41710e7i		−	1.23152i	0.787933	−	0.615761i	$-0.211152\pi$
$354$	2.41722e6	+	1.85221e7i	0.0544886	+	0.417523i
$355$	−1.63610e7	+	1.36970e7i	−0.365699	+	0.306153i
$356$	2.60601e7	−	6.91976e6i	0.577598	−	0.153370i
$357$		−	1.12727e7i		−	0.247755i
$358$	4.94130e6	+	3.78630e7i	0.107694	+	0.825214i
$359$		−	5.22320e7i		−	1.12890i	−0.825469	−	0.564448i	$-0.809089\pi$
$359$		−	5.22320e7i		−	1.12890i	0.825469	−	0.564448i	$-0.190911\pi$
$360$	1.37622e7	+	7.24337e6i	0.294972	+	0.155251i
$361$	−9.07902e7			−1.92982
$362$	4.40848e7	−	5.75326e6i	0.929315	−	0.121280i
$363$	−1.07484e7			−0.224710
$364$	9.14884e6	+	3.44549e7i	0.189698	+	0.714408i
$365$	−2.35618e7	+	1.97253e7i	−0.484541	+	0.405644i
$366$	−2.80160e7	+	3.65621e6i	−0.571429	+	0.0745740i
$367$	3.08439e7			0.623980			0.311990	−	0.950085i	$-0.399004\pi$
$367$	3.08439e7			0.623980			0.311990	+	0.950085i	$0.399004\pi$
$368$	−7.73437e7	+	4.41900e7i	−1.55196	+	0.886709i
$369$	534003.			0.0106283
$370$	−1.17820e7	+	1.27996e7i	−0.232602	+	0.252691i
$371$		−	2.86994e7i		−	0.562019i
$372$	−57125.5	−	215137.i	−0.00110969	−	0.00417913i
$373$			9.32456e7i			1.79681i	0.439170	+	0.898404i	$0.355273\pi$
$373$			9.32456e7i			1.79681i	−0.439170	+	0.898404i	$0.644727\pi$
$374$	6.26666e7	−	8.17827e6i	1.19790	−	0.156331i
$375$	2.64187e7	−	1.51335e7i	0.500978	−	0.286975i
$376$	−4.97174e6	+	2.03967e6i	−0.0935287	+	0.0383703i
$377$			1.55560e8i			2.90319i
$378$	4.31523e6	−	563157.i	0.0798967	−	0.0104269i
$379$			3.66043e7i			0.672379i	0.941794	+	0.336189i	$0.109138\pi$
$379$			3.66043e7i			0.672379i	−0.941794	+	0.336189i	$0.890862\pi$
$380$	5.41324e7	−	7.67541e7i	0.986522	−	1.39878i
$381$	−1.60575e7			−0.290337
$382$	2.85726e6	+	2.18940e7i	0.0512578	+	0.392767i
$383$	3.75898e7			0.669073			0.334537	−	0.942383i	$-0.391420\pi$
$383$	3.75898e7			0.669073			0.334537	+	0.942383i	$0.391420\pi$
$384$	−2.01055e7	+	2.57778e7i	−0.355076	+	0.455252i
$385$	−2.15928e7	+	1.80769e7i	−0.378380	+	0.316769i
$386$	−1.04698e7	−	8.02253e7i	−0.182043	−	1.39492i
$387$	−776743.			−0.0134012
$388$	−1.40483e7	−	5.29064e7i	−0.240507	−	0.905760i
$389$	−1.40687e7			−0.239005			−0.119502	−	0.992834i	$-0.538130\pi$
$389$	−1.40687e7			−0.239005			−0.119502	+	0.992834i	$0.538130\pi$
$390$	4.09495e7	−	4.44862e7i	0.690328	−	0.749949i
$391$		−	1.09511e8i		−	1.83202i
$392$	4.59601e7	−	1.88552e7i	0.762998	−	0.313021i
$393$		−	3.76050e7i		−	0.619538i
$394$	−5.50312e6	−	4.21680e7i	−0.0899746	−	0.689437i
$395$	3.57579e7	−	2.99355e7i	0.580204	−	0.485731i
$396$	6.26136e6	+	2.35805e7i	0.100829	+	0.379724i
$397$			5.35899e7i			0.856469i	0.903668	+	0.428234i	$0.140864\pi$
$397$			5.35899e7i			0.856469i	−0.903668	+	0.428234i	$0.859136\pi$
$398$	−1.07652e7	−	8.24893e7i	−0.170755	−	1.30842i
$399$		−	2.62819e7i		−	0.413750i
$400$	2.14811e7	+	6.02873e7i	0.335642	+	0.941990i
$401$	6.63361e7			1.02877			0.514384	−	0.857560i	$-0.328021\pi$
$401$	6.63361e7			1.02877			0.514384	+	0.857560i	$0.328021\pi$
$402$	2.91337e7	−	3.80207e6i	0.448453	−	0.0585251i
$403$	−865405.			−0.0132222
$404$	3.18453e7	−	8.45591e6i	0.482949	−	0.128238i
$405$	−4.73809e6	−	5.65964e6i	−0.0713244	−	0.0851969i
$406$	−4.56878e7	+	5.96246e6i	−0.682688	+	0.0890938i
$407$	−2.72915e7			−0.404804
$408$	−1.52545e7	−	3.71831e7i	−0.224603	−	0.547477i
$409$	4.77129e7			0.697374			0.348687	−	0.937239i	$-0.386628\pi$
$409$	4.77129e7			0.697374			0.348687	+	0.937239i	$0.386628\pi$
$410$	1.61684e6	+	1.48830e6i	0.0234593	+	0.0215942i
$411$		−	8.22453e6i		−	0.118464i
$412$	−8.35460e7	+	2.21841e7i	−1.19463	+	0.317212i
$413$			2.15098e7i			0.305342i
$414$	4.19216e7	−	5.47095e6i	0.590794	−	0.0771013i
$415$	−3.05279e7	−	3.64655e7i	−0.427123	−	0.510197i
$416$	7.68029e7	+	1.01270e8i	1.06684	+	1.40669i
$417$		−	3.42538e7i		−	0.472390i
$418$	1.46105e8	−	1.90674e7i	2.00049	−	0.261073i
$419$			4.33308e7i			0.589053i	0.955643	+	0.294526i	$0.0951619\pi$
$419$			4.33308e7i			0.589053i	−0.955643	+	0.294526i	$0.904838\pi$
$420$	1.46351e7	+	1.03217e7i	0.197536	+	0.139317i
$421$	−5.83065e7			−0.781395			−0.390697	−	0.920519i	$-0.627766\pi$
$421$	−5.83065e7			−0.781395			−0.390697	+	0.920519i	$0.627766\pi$
$422$	−5.84991e6	−	4.48254e7i	−0.0778416	−	0.596467i
$423$	2.55049e6			0.0336978
$424$	−3.88367e7	−	9.46656e7i	−0.509501	−	1.24192i
$425$	−7.74548e7	−	1.38383e7i	−1.00898	−	0.180267i
$426$	2.75476e6	+	2.11086e7i	0.0356333	+	0.273043i
$427$	−3.25350e7			−0.417896
$428$	−4.43780e7	+	1.17837e7i	−0.566026	+	0.150298i
$429$	9.48546e7			1.20140
$430$	−2.35180e6	−	2.16483e6i	−0.0295798	−	0.0272281i
$431$			1.41316e8i			1.76506i	0.470255	+	0.882531i	$0.344162\pi$
$431$			1.41316e8i			1.76506i	−0.470255	+	0.882531i	$0.655838\pi$
$432$	1.34718e7	−	7.69707e6i	0.167099	−	0.0954716i
$433$			6.37747e7i			0.785569i	0.919631	+	0.392785i	$0.128488\pi$
$433$			6.37747e7i			0.785569i	−0.919631	+	0.392785i	$0.871512\pi$
$434$	−33170.0	−	254168.i	−0.000405767	−	0.00310922i
$435$	5.01649e7	+	5.99218e7i	0.609442	+	0.727976i
$436$	2.10309e7	−	5.58435e6i	0.253745	−	0.0673773i
$437$		−	2.55323e8i		−	3.05947i
$438$	3.96720e6	+	3.03990e7i	0.0472130	+	0.361773i
$439$			8.13434e7i			0.961455i	0.876870	+	0.480728i	$0.159627\pi$
$439$			8.13434e7i			0.961455i	−0.876870	+	0.480728i	$0.840373\pi$
$440$	−4.67623e7	+	8.88472e7i	−0.548957	+	1.04300i
$441$	−2.35774e7			−0.274904
$442$	−1.54941e8	+	2.02205e7i	−1.79432	+	0.234167i
$443$	−2.93915e7			−0.338073			−0.169036	−	0.985610i	$-0.554066\pi$
$443$	−2.93915e7			−0.338073			−0.169036	+	0.985610i	$0.554066\pi$
$444$	4.45420e6	+	1.67747e7i	0.0508887	+	0.191648i
$445$	−3.38050e7	−	4.03800e7i	−0.383620	−	0.458233i
$446$	9.58993e7	−	1.25153e7i	1.08096	−	0.141070i
$447$	−5.54118e7			−0.620412
$448$	−2.67990e7	+	2.64384e7i	−0.298046	+	0.294037i
$449$	−6.13990e6			−0.0678300			−0.0339150	−	0.999425i	$-0.510798\pi$
$449$	−6.13990e6			−0.0678300			−0.0339150	+	0.999425i	$0.510798\pi$
$450$	1.42790e6	−	3.03414e7i	0.0156697	−	0.332965i
$451$			3.44746e6i			0.0375811i
$452$	−7.64088e6	−	2.87758e7i	−0.0827424	−	0.311611i
$453$		−	439270.i		−	0.00472538i
$454$	−4.39991e7	+	5.74208e6i	−0.470193	+	0.0613623i
$455$	5.33877e7	−	4.46947e7i	0.566770	−	0.474484i
$456$	−3.55653e7	−	8.66914e7i	−0.375087	−	0.914285i
$457$		−	1.81452e7i		−	0.190113i	−0.995472	−	0.0950567i	$-0.969697\pi$
$457$		−	1.81452e7i		−	0.190113i	0.995472	−	0.0950567i	$-0.0303032\pi$
$458$	4.62271e7	−	6.03284e6i	0.481172	−	0.0627951i
$459$			1.90748e7i			0.197253i
$460$	1.42177e8	+	1.00273e8i	1.46068	+	1.03017i
$461$	1.58024e8			1.61294			0.806472	−	0.591272i	$-0.201374\pi$
$461$	1.58024e8			1.61294			0.806472	+	0.591272i	$0.201374\pi$
$462$	3.63567e6	+	2.78586e7i	0.0368688	+	0.282510i
$463$	1.30644e8			1.31627			0.658137	−	0.752898i	$-0.271345\pi$
$463$	1.30644e8			1.31627			0.658137	+	0.752898i	$0.271345\pi$
$464$	−1.42634e8	+	8.14933e7i	−1.42780	+	0.815770i
$465$	−333354.	+	279074.i	−0.00331548	+	0.00277563i
$466$	6.66993e6	+	5.11089e7i	0.0659119	+	0.505055i
$467$	−1.60687e8			−1.57772			−0.788859	−	0.614574i	$-0.789328\pi$
$467$	−1.60687e8			−1.57772			−0.788859	+	0.614574i	$0.789328\pi$
$468$	−1.54811e7	−	5.83022e7i	−0.151030	−	0.568784i
$469$	3.38330e7			0.327961
$470$	7.72229e6	+	7.10836e6i	0.0743793	+	0.0684661i
$471$			3.92366e7i			0.375516i
$472$	2.91076e7	+	7.09506e7i	0.276809	+	0.674730i
$473$		−	5.01456e6i		−	0.0473859i
$474$	−6.02070e6	−	4.61341e7i	−0.0565343	−	0.433199i
$475$	−1.80584e8	−	3.22636e7i	−1.68499	−	0.301045i
$476$	−1.18775e7	−	4.47310e7i	−0.110129	−	0.414751i
$477$			4.85631e7i			0.447457i
$478$	2.67932e7	+	2.05305e8i	0.245324	+	1.87982i
$479$		−	8.69380e7i		−	0.791048i	−0.918456	−	0.395524i	$-0.870563\pi$
$479$		−	8.69380e7i		−	0.791048i	0.918456	−	0.395524i	$-0.129437\pi$
$480$	6.22417e7	+	1.42418e7i	0.562805	+	0.128778i
$481$	6.74776e7			0.606351
$482$	−1.90321e8	+	2.48378e7i	−1.69960	+	0.221805i
$483$	4.86837e7			0.432058
$484$	−4.26505e7	+	1.13250e7i	−0.376174	+	0.0998859i
$485$	−8.19783e7	+	6.86300e7i	−0.718578	+	0.601573i
$486$	−7.30194e6	+	952936.i	−0.0636106	+	0.00830147i
$487$	9.33645e6			0.0808342			0.0404171	−	0.999183i	$-0.487131\pi$
$487$	9.33645e6			0.0808342			0.0404171	+	0.999183i	$0.487131\pi$
$488$	−1.07318e8	+	4.40273e7i	−0.923446	+	0.378846i
$489$	−3.80856e7			−0.325712
$490$	−7.13870e7	−	6.57116e7i	−0.606779	−	0.558540i
$491$			4.23949e7i			0.358154i	0.983835	+	0.179077i	$0.0573111\pi$
$491$			4.23949e7i			0.358154i	−0.983835	+	0.179077i	$0.942689\pi$
$492$	2.11897e6	−	562653.i	0.0177922	−	0.00472439i
$493$		−	2.01956e8i		−	1.68545i
$494$	−3.61242e8	+	4.71436e7i	−2.99652	+	0.391059i
$495$	3.65380e7	−	3.05886e7i	0.301251	−	0.252199i
$496$	−453359.	−	793493.i	−0.00371533	−	0.00650276i
$497$			2.45135e7i			0.199681i
$498$	−4.70470e7	+	6.13985e6i	−0.380929	+	0.0497130i
$499$		−	2.31844e7i		−	0.186592i	−0.995638	−	0.0932962i	$-0.970260\pi$
$499$		−	2.31844e7i		−	0.186592i	0.995638	−	0.0932962i	$-0.0297404\pi$
$500$	8.88867e7	−	8.78872e7i	0.711093	−	0.703098i
$501$	−9.28688e6			−0.0738510
$502$	−2.42531e7	−	1.85841e8i	−0.191715	−	1.46903i
$503$	1.79093e8			1.40726			0.703632	−	0.710565i	$-0.251561\pi$
$503$	1.79093e8			1.40726			0.703632	+	0.710565i	$0.251561\pi$
$504$	1.65299e7	−	6.78142e6i	0.129115	−	0.0529699i
$505$	−4.13096e7	−	4.93442e7i	−0.320757	−	0.383144i
$506$	3.53198e7	+	2.70641e8i	0.272626	+	2.08901i
$507$	−1.59283e8			−1.22221
$508$	−6.37176e7	+	1.69190e7i	−0.486036	+	0.129058i
$509$	1.21665e8			0.922595			0.461298	−	0.887245i	$-0.347384\pi$
$509$	1.21665e8			0.922595			0.461298	+	0.887245i	$0.347384\pi$
$510$	−5.31627e7	+	5.77542e7i	−0.400771	+	0.435385i
$511$			3.53024e7i			0.264571i
$512$	−5.26199e7	+	1.23473e8i	−0.392048	+	0.919945i
$513$			4.44724e7i			0.329412i
$514$	1.63525e7	+	1.25302e8i	0.120419	+	0.922719i
$515$	1.08376e8	+	1.29454e8i	0.793432	+	0.947753i
$516$	−3.08219e6	+	818417.i	−0.0224342	+	0.00595697i
$517$			1.64656e7i			0.119154i
$518$	2.58634e6	+	1.98180e7i	0.0186079	+	0.142584i
$519$			6.05700e7i			0.433267i
$520$	1.15619e8	−	2.19672e8i	0.822276	−	1.56230i
$521$	−6.60811e7			−0.467266			−0.233633	−	0.972325i	$-0.575061\pi$
$521$	−6.60811e7			−0.467266			−0.233633	+	0.972325i	$0.575061\pi$
$522$	7.73099e7	−	1.00893e7i	0.543530	−	0.0709330i
$523$	−7.09676e7			−0.496083			−0.248042	−	0.968749i	$-0.579787\pi$
$523$	−7.09676e7			−0.496083			−0.248042	+	0.968749i	$0.579787\pi$
$524$	−3.96226e7	−	1.49220e8i	−0.275391	−	1.03713i
$525$	6.15185e6	−	3.44328e7i	0.0425136	−	0.237955i
$526$	6.88574e7	−	8.98619e6i	0.473144	−	0.0617474i
$527$	1.12351e6			0.00767619
$528$	4.96914e7	+	8.69725e7i	0.337582	+	0.590854i
$529$	3.24916e8			2.19484
$530$	−1.35348e8	+	1.47038e8i	−0.909129	+	0.987648i
$531$		−	3.63974e7i		−	0.243101i
$532$	−2.76920e7	−	1.04289e8i	−0.183916	−	0.692634i
$533$		−	8.52375e6i		−	0.0562923i
$534$	−5.20974e7	+	6.79895e6i	−0.342131	+	0.0446496i
$535$	5.75670e7	+	6.87636e7i	0.375934	+	0.449053i
$536$	1.11599e8	−	4.57837e7i	0.724713	−	0.297315i
$537$		−	7.44039e7i		−	0.480478i
$538$	2.64915e8	−	3.45726e7i	1.70122	−	0.222017i
$539$		−	1.52213e8i		−	0.972043i
$540$	−2.47645e7	−	1.74657e7i	−0.157271	−	0.110919i
$541$	−1.30210e7			−0.0822345			−0.0411172	−	0.999154i	$-0.513092\pi$
$541$	−1.30210e7			−0.0822345			−0.0411172	+	0.999154i	$0.513092\pi$
$542$	2.79023e7	+	2.13803e8i	0.175243	+	1.34282i
$543$	−8.66302e7			−0.541090
$544$	−9.97093e7	−	1.31473e8i	−0.619354	−	0.816659i
$545$	−2.72812e7	−	3.25873e7i	−0.168529	−	0.201307i
$546$	−8.98910e6	−	6.88797e7i	−0.0552254	−	0.423168i
$547$	2.06228e8			1.26004			0.630021	−	0.776578i	$-0.283046\pi$
$547$	2.06228e8			1.26004			0.630021	+	0.776578i	$0.283046\pi$
$548$	−8.66580e6	−	3.26357e7i	−0.0526583	−	0.198313i
$549$	5.50536e7			0.332712
$550$	1.95881e8	+	9.21834e6i	1.17734	+	0.0554070i
$551$		−	4.70855e8i		−	2.81470i
$552$	1.60584e8	−	6.58800e7i	0.954741	−	0.391685i
$553$		−	5.35757e7i		−	0.316805i
$554$	−9.65257e6	−	7.39635e7i	−0.0567693	−	0.434999i
$555$	2.59923e7	−	2.17601e7i	0.152043	−	0.127286i
$556$	−3.60917e7	−	1.35923e8i	−0.209982	−	0.790801i
$557$		−	2.48107e6i		−	0.0143573i	−0.999974	−	0.00717865i	$-0.997715\pi$
$557$		−	2.48107e6i		−	0.0143573i	0.999974	−	0.00717865i	$-0.00228505\pi$
$558$	56128.1	+	430086.i	0.000323056	+	0.00247544i
$559$			1.23984e7i			0.0709788i
$560$	6.89489e7	+	2.55372e7i	0.392612	+	0.145415i
$561$	−1.23145e8			−0.697474
$562$	−2.34671e8	+	3.06257e7i	−1.32206	+	0.172535i
$563$	1.47289e8			0.825361			0.412680	−	0.910876i	$-0.364593\pi$
$563$	1.47289e8			0.825361			0.412680	+	0.910876i	$0.364593\pi$
$564$	1.01206e7	−	2.68733e6i	0.0564115	−	0.0149790i
$565$	−4.45881e7	+	3.73279e7i	−0.247214	+	0.206961i
$566$	7.09028e7	−	9.25313e6i	0.391034	−	0.0510316i
$567$	−8.47978e6			−0.0465195
$568$	3.31723e7	+	8.08583e7i	0.181022	+	0.441245i
$569$	9.59654e7			0.520928			0.260464	−	0.965484i	$-0.416124\pi$
$569$	9.59654e7			0.520928			0.260464	+	0.965484i	$0.416124\pi$
$570$	−1.23947e8	+	1.34652e8i	−0.669287	+	0.727092i
$571$			3.67358e8i			1.97325i	0.163011	+	0.986624i	$0.447879\pi$
$571$			3.67358e8i			1.97325i	−0.163011	+	0.986624i	$0.552121\pi$
$572$	3.76392e8	−	9.99439e7i	2.01119	−	0.534033i
$573$		−	4.30235e7i		−	0.228687i
$574$	2.50341e6	−	326706.i	0.0132372	−	0.00172751i
$575$	5.97639e7	−	3.34507e8i	0.314366	−	1.75955i
$576$	4.53474e7	−	4.47373e7i	0.237293	−	0.234101i
$577$		−	2.14798e8i		−	1.11816i	−0.829115	−	0.559078i	$-0.811155\pi$
$577$		−	2.14798e8i		−	1.11816i	0.829115	−	0.559078i	$-0.188845\pi$
$578$	9.67567e6	−	1.26272e6i	0.0501069	−	0.00653917i
$579$			1.57649e8i			0.812187i
$580$	2.62196e8	+	1.84919e8i	1.34382	+	0.947759i
$581$	−5.46359e7			−0.278580
$582$	1.38030e7	+	1.05767e8i	0.0700173	+	0.536513i
$583$	−3.13518e8			−1.58218
$584$	4.77722e7	+	1.16446e8i	0.239848	+	0.584636i
$585$	−9.03391e7	+	7.56294e7i	−0.451241	+	0.377766i
$586$	−2.34310e7	−	1.79542e8i	−0.116439	−	0.892222i
$587$	1.34919e8			0.667050			0.333525	−	0.942741i	$-0.391762\pi$
$587$	1.34919e8			0.667050			0.333525	+	0.942741i	$0.391762\pi$
$588$	−9.35574e7	+	2.48424e7i	−0.460200	+	0.122197i
$589$	2.61943e6			0.0128192
$590$	1.01442e8	−	1.10203e8i	0.493925	−	0.536584i
$591$			8.28636e7i			0.401422i
$592$	3.53494e7	+	6.18704e7i	0.170379	+	0.298207i
$593$			2.80226e8i			1.34383i	0.740628	+	0.671915i	$0.234528\pi$
$593$			2.80226e8i			1.34383i	−0.740628	+	0.671915i	$0.765472\pi$
$594$	−6.15204e6	−	4.71405e7i	−0.0293535	−	0.224923i
$595$	−6.93105e7	+	5.80249e7i	−0.329040	+	0.275463i
$596$	−2.19879e8	+	5.83848e7i	−1.03859	+	0.275779i
$597$			1.62098e8i			0.761824i
$598$	−8.73273e7	−	6.69152e8i	−0.408363	−	3.12911i
$599$			1.49142e8i			0.693937i	0.937877	+	0.346969i	$0.112789\pi$
$599$			1.49142e8i			0.693937i	−0.937877	+	0.346969i	$0.887211\pi$
$600$	−2.63033e7	−	1.21902e8i	−0.121775	−	0.564362i
$601$	−2.09302e8			−0.964161			−0.482080	−	0.876127i	$-0.660119\pi$
$601$	−2.09302e8			−0.964161			−0.482080	+	0.876127i	$0.660119\pi$
$602$	−3.64138e6	+	475216.i	−0.0166908	+	0.00217822i
$603$	−5.72500e7			−0.261110
$604$	−462838.	−	1.74306e6i	−0.00210048	−	0.00791047i
$605$	5.53261e7	+	6.60869e7i	0.249841	+	0.298435i
$606$	−6.36628e7	+	8.30828e6i	−0.286067	+	0.0373330i
$607$	1.45876e8			0.652258			0.326129	−	0.945325i	$-0.394256\pi$
$607$	1.45876e8			0.652258			0.326129	+	0.945325i	$0.394256\pi$
$608$	−2.32469e8	−	3.06526e8i	−1.03432	−	1.36382i
$609$	8.97803e7			0.397493
$610$	1.66690e8	+	1.53438e8i	0.734377	+	0.675993i
$611$		−	4.07108e7i		−	0.178479i
$612$	2.00983e7	+	7.56908e7i	0.0876807	+	0.330209i
$613$			2.18756e8i			0.949684i	0.880071	+	0.474842i	$0.157495\pi$
$613$			2.18756e8i			0.949684i	−0.880071	+	0.474842i	$0.842505\pi$
$614$	−7.56424e7	+	9.87167e6i	−0.326784	+	0.0426467i
$615$	−2.74872e6	−	3.28334e6i	−0.0118170	−	0.0141153i
$616$	4.37800e7	+	1.06715e8i	0.187298	+	0.456545i
$617$			2.56428e8i			1.09172i	0.837877	+	0.545859i	$0.183797\pi$
$617$			2.56428e8i			1.09172i	−0.837877	+	0.545859i	$0.816203\pi$
$618$	1.67019e8	−	2.17968e7i	0.707622	−	0.0923478i
$619$			5.25164e7i			0.221423i	0.993853	+	0.110712i	$0.0353130\pi$
$619$			5.25164e7i			0.221423i	−0.993853	+	0.110712i	$0.964687\pi$
$620$	−1.02873e6	+	1.45863e6i	−0.00431645	+	0.00612028i
$621$	−8.23792e7			−0.343988
$622$	−1.54784e7	−	1.18605e8i	−0.0643214	−	0.492867i
$623$	−6.05010e7			−0.250206
$624$	−1.22861e8	−	2.15037e8i	−0.505660	−	0.885033i
$625$	−2.29037e8	−	8.45391e7i	−0.938134	−	0.346272i
$626$	5.85834e6	+	4.48899e7i	0.0238809	+	0.182989i
$627$	−2.87109e8			−1.16478
$628$	4.13418e7	+	1.55695e8i	0.166921	+	0.628629i
$629$	−8.76027e7			−0.352018
$630$	−2.56748e7	−	2.36336e7i	−0.102680	−	0.0945168i
$631$		−	3.92931e8i		−	1.56397i	−0.623297	−	0.781985i	$-0.714207\pi$
$631$		−	3.92931e8i		−	1.56397i	0.623297	−	0.781985i	$-0.285793\pi$
$632$	−7.25001e7	−	1.76721e8i	−0.287202	−	0.700062i
$633$			8.80855e7i			0.347291i
$634$	1.39157e7	+	1.06630e8i	0.0546058	+	0.418421i
$635$	8.26542e7	+	9.87302e7i	0.322807	+	0.385593i
$636$	5.11687e7	+	1.92703e8i	0.198899	+	0.749062i
$637$			3.76343e8i			1.45601i
$638$	6.51352e7	+	4.99103e8i	0.250815	+	1.92189i
$639$		−	4.14801e7i		−	0.158978i
$640$	2.61987e8	−	9.06843e6i	0.999401	−	0.0345933i
$641$	−4.43610e8			−1.68433			−0.842165	−	0.539219i	$-0.818719\pi$
$641$	−4.43610e8			−1.68433			−0.842165	+	0.539219i	$0.818719\pi$
$642$	8.87173e7	−	1.15780e7i	0.335277	−	0.0437551i
$643$	−4.69895e8			−1.76753			−0.883767	−	0.467927i	$-0.845001\pi$
$643$	−4.69895e8			−1.76753			−0.883767	+	0.467927i	$0.845001\pi$
$644$	1.93181e8	−	5.12957e7i	0.723282	−	0.192054i
$645$	3.99820e6	+	4.77584e6i	0.0149000	+	0.0177980i
$646$	4.68981e8	−	6.12041e7i	1.73963	−	0.227030i
$647$	−7.12899e7			−0.263218			−0.131609	−	0.991302i	$-0.542014\pi$
$647$	−7.12899e7			−0.263218			−0.131609	+	0.991302i	$0.542014\pi$
$648$	−2.79707e7	+	1.14751e7i	−0.102797	+	0.0421725i
$649$	2.34978e8			0.859592
$650$	−4.84310e8	−	2.27921e7i	−1.76353	−	0.0829935i
$651$			499460.i			0.00181033i
$652$	−1.51127e8	+	4.01290e7i	−0.545255	+	0.144782i
$653$		−	3.07313e8i		−	1.10367i	−0.833952	−	0.551837i	$-0.813927\pi$
$653$		−	3.07313e8i		−	1.10367i	0.833952	−	0.551837i	$-0.186073\pi$
$654$	−4.20434e7	+	5.48685e6i	−0.150302	+	0.0196151i
$655$	−2.31216e8	+	1.93568e8i	−0.822801	+	0.688826i
$656$	7.81545e6	−	4.46533e6i	0.0276849	−	0.0158176i
$657$		−	5.97364e7i		−	0.210641i
$658$	1.19567e7	−	1.56040e6i	0.0419695	−	0.00547720i
$659$		−	1.56295e8i		−	0.546122i	−0.961997	−	0.273061i	$-0.911964\pi$
$659$		−	1.56295e8i		−	0.546122i	0.961997	−	0.273061i	$-0.0880360\pi$
$660$	1.12756e8	−	1.59877e8i	0.392202	−	0.556100i
$661$	2.76572e7			0.0957644			0.0478822	−	0.998853i	$-0.484753\pi$
$661$	2.76572e7			0.0957644			0.0478822	+	0.998853i	$0.484753\pi$
$662$	−5.14158e7	−	3.93978e8i	−0.177224	−	1.35799i
$663$	3.04472e8			1.04474
$664$	−1.80218e8	+	7.39348e7i	−0.615593	+	0.252548i
$665$	−1.61596e8	+	1.35283e8i	−0.549496	+	0.460023i
$666$	−4.37643e6	−	3.35347e7i	−0.0148149	−	0.113520i
$667$	8.72196e8			2.93925
$668$	−3.68512e7	+	9.78515e6i	−0.123630	+	0.0328275i
$669$	−1.88450e8			−0.629386
$670$	−1.73340e8	−	1.59559e8i	−0.576333	−	0.530514i
$671$			3.55420e8i			1.17645i
$672$	5.84469e7	−	4.43261e7i	0.192599	−	0.146067i
$673$		−	2.88925e8i		−	0.947851i	−0.880565	−	0.473926i	$-0.842837\pi$
$673$		−	2.88925e8i		−	0.947851i	0.880565	−	0.473926i	$-0.157163\pi$
$674$	3.00288e7	+	2.30098e8i	0.0980748	+	0.751506i
$675$	−1.04097e7	+	5.82648e7i	−0.0338477	+	0.189450i
$676$	−6.32050e8	+	1.67829e8i	−2.04603	+	0.543284i
$677$			1.02252e8i			0.329540i	0.986332	+	0.164770i	$0.0526881\pi$
$677$			1.02252e8i			0.329540i	−0.986332	+	0.164770i	$0.947312\pi$
$678$	7.50747e6	+	5.75266e7i	0.0240882	+	0.184578i
$679$			1.22827e8i			0.392361i
$680$	−1.50102e8	+	2.85189e8i	−0.477374	+	0.906998i
$681$	8.64618e7			0.273768
$682$	−2.77658e6	+	362356.i	−0.00875302	+	0.00114231i
$683$	−1.71355e8			−0.537818			−0.268909	−	0.963166i	$-0.586663\pi$
$683$	−1.71355e8			−0.537818			−0.268909	+	0.963166i	$0.586663\pi$
$684$	4.68585e7	+	1.76471e8i	0.146427	+	0.551448i
$685$	−5.05690e7	+	4.23349e7i	−0.157330	+	0.131712i
$686$	−2.44555e8	+	3.19155e7i	−0.757538	+	0.0988621i
$687$	−9.08400e7			−0.280161
$688$	−1.13681e7	+	6.49512e6i	−0.0349078	+	0.0199444i
$689$	7.75165e8			2.36993
$690$	−2.49425e8	−	2.29596e8i	−0.759265	−	0.698903i
$691$		−	1.78401e8i		−	0.540708i	−0.962761	−	0.270354i	$-0.912859\pi$
$691$		−	1.78401e8i		−	0.540708i	0.962761	−	0.270354i	$-0.0871408\pi$
$692$	6.38197e7	+	2.40347e8i	0.192591	+	0.725306i
$693$		−	5.47444e7i		−	0.164490i
$694$	2.33165e8	−	3.04291e7i	0.697566	−	0.0910354i
$695$	−2.10612e8	+	1.76318e8i	−0.627376	+	0.525222i
$696$	2.96142e8	−	1.21493e8i	0.878360	−	0.360349i
$697$			1.10659e7i			0.0326806i
$698$	3.29386e8	−	4.29863e7i	0.968588	−	0.126405i
$699$		−	1.00433e8i		−	0.294066i
$700$	−1.18691e7	−	1.43114e8i	−0.0346037	−	0.417243i
$701$	−3.64044e8			−1.05682			−0.528408	−	0.848991i	$-0.677211\pi$
$701$	−3.64044e8			−1.05682			−0.528408	+	0.848991i	$0.677211\pi$
$702$	1.52108e7	+	1.16554e8i	0.0439683	+	0.336910i
$703$	−2.04243e8			−0.587870
$704$	2.88819e8	+	2.92758e8i	0.827766	+	0.839054i
$705$	−1.31284e7	−	1.56818e7i	−0.0374665	−	0.0447537i
$706$	5.60809e7	+	4.29724e8i	0.159368	+	1.22117i
$707$	−7.39319e7			−0.209206
$708$	−3.83503e7	−	1.44428e8i	−0.108061	−	0.406961i
$709$	−4.12018e8			−1.15605			−0.578026	−	0.816018i	$-0.696177\pi$
$709$	−4.12018e8			−1.15605			−0.578026	+	0.816018i	$0.696177\pi$
$710$	1.15607e8	−	1.25592e8i	0.323006	−	0.350903i
$711$			9.06572e7i			0.252228i
$712$	−1.99564e8	+	8.18715e7i	−0.552894	+	0.226826i
$713$			4.85215e6i			0.0133865i
$714$	1.16701e7	+	8.94230e7i	0.0320612	+	0.245671i
$715$	−4.88254e8	−	5.83219e8i	−1.33576	−	1.59556i
$716$	−7.83959e7	−	2.95242e8i	−0.213577	−	0.804339i
$717$		−	4.03440e8i		−	1.09452i
$718$	5.40736e7	+	4.14343e8i	0.146087	+	1.11940i
$719$			3.87039e8i			1.04128i	0.853776	+	0.520641i	$0.174307\pi$
$719$			3.87039e8i			1.04128i	−0.853776	+	0.520641i	$0.825693\pi$
$720$	−1.16671e8	−	4.32123e7i	−0.312582	−	0.115774i
$721$	1.93960e8			0.517496
$722$	7.20214e8	−	9.39912e7i	1.91360	−	0.249733i
$723$	3.73997e8			0.989584
$724$	−3.43757e8	+	9.12781e7i	−0.905807	+	0.240520i
$725$	1.10214e8	−	6.16883e8i	0.289216	−	1.61878i
$726$	8.52639e7	−	1.11273e7i	0.222821	−	0.0290791i
$727$	4.91602e8			1.27941			0.639706	−	0.768619i	$-0.279056\pi$
$727$	4.91602e8			1.27941			0.639706	+	0.768619i	$0.279056\pi$
$728$	−1.08245e8	−	2.63850e8i	−0.280552	−	0.683853i
$729$	1.43489e7			0.0370370
$730$	1.66489e8	−	1.80868e8i	0.427973	−	0.464936i
$731$		−	1.60962e7i		−	0.0412069i
$732$	2.18458e8	−	5.80074e7i	0.556974	−	0.147894i
$733$			2.92669e8i			0.743130i	0.928407	+	0.371565i	$0.121179\pi$
$733$			2.92669e8i			0.743130i	−0.928407	+	0.371565i	$0.878821\pi$
$734$	−2.44676e8	+	3.19313e7i	−0.618733	+	0.0807474i
$735$	1.21362e8	+	1.44967e8i	0.305648	+	0.365096i
$736$	5.67799e8	−	4.30618e8i	1.42417	−	1.08009i
$737$		−	3.69599e8i		−	0.923269i
$738$	−4.23610e6	+	552830.i	−0.0105389	+	0.00137538i
$739$		−	2.64415e8i		−	0.655167i	−0.944822	−	0.327583i	$-0.893766\pi$
$739$		−	2.64415e8i		−	0.655167i	0.944822	−	0.327583i	$-0.106234\pi$
$740$	8.02125e7	−	1.13733e8i	0.197946	−	0.280667i
$741$	7.09869e8			1.74471
$742$	2.97112e7	+	2.27664e8i	0.0727292	+	0.557293i
$743$	2.47114e8			0.602464			0.301232	−	0.953551i	$-0.402602\pi$
$743$	2.47114e8			0.602464			0.301232	+	0.953551i	$0.402602\pi$
$744$	675883.	+	1.64748e6i	0.00164117	+	0.00400039i
$745$	2.85227e8	+	3.40703e8i	0.689797	+	0.823961i
$746$	−9.65331e7	−	7.39692e8i	−0.232520	−	1.78170i
$747$	9.24512e7			0.221795
$748$	−4.88651e8	+	1.29752e8i	−1.16760	+	0.310034i
$749$	1.03028e8			0.245193
$750$	−1.93906e8	+	1.47400e8i	−0.459629	+	0.349392i
$751$			3.88949e8i			0.918276i	0.888365	+	0.459138i	$0.151842\pi$
$751$			3.88949e8i			0.918276i	−0.888365	+	0.459138i	$0.848158\pi$
$752$	3.73279e7	−	2.13271e7i	0.0877768	−	0.0501510i
$753$			3.65193e8i			0.855338i
$754$	−1.61045e8	−	1.23402e9i	−0.375693	−	2.87878i
$755$	−2.70087e6	+	2.26110e6i	−0.00627572	+	0.00525385i
$756$	−3.36486e7	+	8.93474e6i	−0.0778756	+	0.0206784i
$757$			3.98638e8i			0.918948i	0.888191	+	0.459474i	$0.151962\pi$
$757$			3.98638e8i			0.918948i	−0.888191	+	0.459474i	$0.848038\pi$
$758$	−3.78948e7	−	2.90372e8i	−0.0870106	−	0.666725i
$759$		−	5.31831e8i		−	1.21632i
$760$	−3.49958e8	+	6.64911e8i	−0.797214	+	1.51469i
$761$	2.05271e8			0.465773			0.232887	−	0.972504i	$-0.425183\pi$
$761$	2.05271e8			0.465773			0.232887	+	0.972504i	$0.425183\pi$
$762$	1.27380e8	−	1.66236e7i	0.287896	−	0.0375716i
$763$	−4.88252e7			−0.109918
$764$	−4.53318e7	−	1.70721e8i	−0.101654	−	0.382831i
$765$	1.17283e8	−	9.81858e7i	0.261969	−	0.219313i
$766$	−2.98190e8	+	3.89151e7i	−0.663447	+	0.0865828i
$767$	−5.80976e8			−1.28757
$768$	1.32805e8	−	2.25302e8i	0.293178	−	0.497373i
$769$	−5.15212e8			−1.13294			−0.566470	−	0.824082i	$-0.691691\pi$
$769$	−5.15212e8			−1.13294			−0.566470	+	0.824082i	$0.691691\pi$
$770$	1.52576e8	−	1.65754e8i	0.334206	−	0.363070i
$771$		−	2.46229e8i		−	0.537250i
$772$	1.66107e8	+	6.25567e8i	0.361025	+	1.35963i
$773$			2.25469e8i			0.488145i	0.969757	+	0.244072i	$0.0784834\pi$
$773$			2.25469e8i			0.488145i	−0.969757	+	0.244072i	$0.921517\pi$
$774$	6.16169e6	−	804128.i	0.0132885	−	0.00173421i
$775$	3.43181e6	+	613136.i	0.00737255	+	0.00131720i
$776$	1.66213e8	+	4.05149e8i	0.355697	+	0.867020i
$777$		−	3.89440e7i		−	0.0830191i
$778$	1.11603e8	−	1.45647e7i	0.236995	−	0.0309289i
$779$			2.57999e7i			0.0545766i
$780$	−2.78787e8	+	3.95291e8i	−0.587474	+	0.832977i
$781$	2.67790e8			0.562137
$782$	1.13373e8	+	8.68725e8i	0.237076	+	1.81661i
$783$	−1.51920e8			−0.316468
$784$	−3.45069e8	+	1.97154e8i	−0.716075	+	0.409127i
$785$	2.41248e8	−	2.01966e8i	0.498718	−	0.417513i
$786$	3.89308e7	+	2.98310e8i	0.0801726	+	0.614329i
$787$	8.23340e8			1.68910			0.844549	−	0.535478i	$-0.179869\pi$
$787$	8.23340e8			1.68910			0.844549	+	0.535478i	$0.179869\pi$
$788$	8.73095e7	+	3.28811e8i	0.178436	+	0.671997i
$789$	−1.35310e8			−0.275486
$790$	−2.52667e8	+	2.74489e8i	−0.512469	+	0.556729i
$791$			6.68058e7i			0.134985i
$792$	−7.40816e7	−	1.80576e8i	−0.149120	−	0.363483i
$793$		−	8.78765e8i		−	1.76219i
$794$	−5.54793e7	−	4.25114e8i	−0.110833	−	0.849267i
$795$	2.98593e8	−	2.49974e8i	0.594262	−	0.497500i
$796$	1.70795e8	+	6.43221e8i	0.338638	+	1.27532i
$797$		−	1.31438e8i		−	0.259624i	−0.991539	−	0.129812i	$-0.958563\pi$
$797$		−	1.31438e8i		−	0.259624i	0.991539	−	0.129812i	$-0.0414374\pi$
$798$	2.72085e7	+	2.08487e8i	0.0535421	+	0.410271i
$799$			5.28528e7i			0.103616i
$800$	−2.32817e8	−	4.56005e8i	−0.454720	−	0.890634i
$801$	1.02376e8			0.199205
$802$	−5.26227e8	+	6.86749e7i	−1.02012	+	0.133130i
$803$	3.85651e8			0.744814
$804$	−2.27173e8	+	6.03216e7i	−0.437108	+	0.116066i
$805$	−2.50594e8	−	2.99334e8i	−0.480378	−	0.573811i
$806$	6.86503e6	−	895917.i	0.0131110	−	0.00171105i
$807$	−5.20580e8			−0.990528
$808$	−2.43866e8	+	1.00047e8i	−0.462293	+	0.189657i
$809$	−6.41573e8			−1.21172			−0.605858	−	0.795573i	$-0.707170\pi$
$809$	−6.41573e8			−1.21172			−0.605858	+	0.795573i	$0.707170\pi$
$810$	4.34452e7	+	3.99913e7i	0.0817498	+	0.0752506i
$811$		−	3.32626e8i		−	0.623582i	−0.950151	−	0.311791i	$-0.899071\pi$
$811$		−	3.32626e8i		−	0.623582i	0.950151	−	0.311791i	$-0.100929\pi$
$812$	3.56257e8	−	9.45973e7i	0.665418	−	0.176689i
$813$		−	4.20141e8i		−	0.781850i
$814$	2.16496e8	−	2.82537e7i	0.401400	−	0.0523845i
$815$	1.96042e8	+	2.34171e8i	0.362139	+	0.432574i
$816$	1.59504e8	+	2.79172e8i	0.293562	+	0.513808i
$817$		−	3.75277e7i		−	0.0688155i
$818$	−3.78494e8	+	4.93951e7i	−0.691511	+	0.0902452i
$819$			1.35354e8i			0.246388i
$820$	−1.43667e7	−	1.01324e7i	−0.0260565	−	0.0183769i
$821$	6.97205e8			1.25988			0.629942	−	0.776642i	$-0.283078\pi$
$821$	6.97205e8			1.25988			0.629942	+	0.776642i	$0.283078\pi$
$822$	8.51450e6	+	6.52430e7i	0.0153300	+	0.117468i
$823$	−5.53566e8			−0.993047			−0.496523	−	0.868023i	$-0.665390\pi$
$823$	−5.53566e8			−0.993047			−0.496523	+	0.868023i	$0.665390\pi$
$824$	6.39782e8	−	2.62472e8i	1.14354	−	0.469139i
$825$	−3.76151e8	−	6.72041e7i	−0.669885	−	0.119683i
$826$	−2.22682e7	−	1.70631e8i	−0.0395134	−	0.302774i
$827$	−4.25348e8			−0.752018			−0.376009	−	0.926616i	$-0.622704\pi$
$827$	−4.25348e8			−0.752018			−0.376009	+	0.926616i	$0.622704\pi$
$828$	−3.26889e8	+	8.67991e7i	−0.575849	+	0.152906i
$829$	−1.52812e8			−0.268222			−0.134111	−	0.990966i	$-0.542818\pi$
$829$	−1.52812e8			−0.268222			−0.134111	+	0.990966i	$0.542818\pi$
$830$	2.79921e8	+	2.57667e8i	0.489555	+	0.450635i
$831$			1.45344e8i			0.253277i
$832$	−7.14097e8	−	7.23835e8i	−1.23990	−	1.25681i
$833$		−	4.88586e8i		−	0.845291i
$834$	3.54615e7	+	2.71727e8i	0.0611307	+	0.468418i
$835$	4.78032e7	+	5.71009e7i	0.0821104	+	0.0980806i
$836$	−1.13928e9	+	3.02513e8i	−1.94989	+	0.517756i
$837$		−	845153.i		−	0.00144132i
$838$	−4.48585e7	−	3.43731e8i	−0.0762276	−	0.584100i
$839$			3.56914e8i			0.604334i	0.953255	+	0.302167i	$0.0977101\pi$
$839$			3.56914e8i			0.604334i	−0.953255	+	0.302167i	$0.902290\pi$
$840$	−1.26782e8	−	6.67282e7i	−0.213904	−	0.112583i
$841$	1.01364e9			1.70411
$842$	4.62530e8	−	6.03622e7i	0.774824	−	0.101118i
$843$	4.61148e8			0.769765
$844$	9.28116e7	+	3.49532e8i	0.154374	+	0.581379i
$845$	8.19893e8	+	9.79360e8i	1.35890	+	1.62320i
$846$	−2.02323e7	+	2.64041e6i	−0.0334145	+	0.00436074i
$847$	9.90173e7			0.162952
$848$	4.06085e8	+	7.10751e8i	0.665931	+	1.16555i
$849$	−1.39330e8			−0.227678
$850$	6.28754e8	+	2.95898e7i	1.02382	+	0.0481821i
$851$		−	3.78333e8i		−	0.613883i
$852$	−4.37056e7	−	1.64597e8i	−0.0706673	−	0.266135i
$853$			5.26433e8i			0.848195i	0.905617	+	0.424098i	$0.139409\pi$
$853$			5.26433e8i			0.848195i	−0.905617	+	0.424098i	$0.860591\pi$
$854$	2.58092e8	−	3.36821e7i	0.414382	−	0.0540786i
$855$	2.73441e8	−	2.28917e8i	0.437487	−	0.366252i
$856$	3.39840e8	−	1.39420e8i	0.541817	−	0.222282i
$857$		−	6.08907e8i		−	0.967405i	−0.875233	−	0.483702i	$-0.839292\pi$
$857$		−	6.08907e8i		−	0.967405i	0.875233	−	0.483702i	$-0.160708\pi$
$858$	−7.52456e8	+	9.81989e7i	−1.19130	+	0.155469i
$859$		−	1.36881e8i		−	0.215956i	−0.994153	−	0.107978i	$-0.965562\pi$
$859$		−	1.36881e8i		−	0.215956i	0.994153	−	0.107978i	$-0.0344376\pi$
$860$	2.08973e7	+	1.47383e7i	0.0328545	+	0.0231714i
$861$	−4.91940e6			−0.00770731
$862$	−1.46298e8	−	1.12102e9i	−0.228411	−	1.75022i
$863$	−1.14016e8			−0.177391			−0.0886956	−	0.996059i	$-0.528270\pi$
$863$	−1.14016e8			−0.177391			−0.0886956	+	0.996059i	$0.528270\pi$
$864$	−9.88999e7	+	7.50056e7i	−0.153340	+	0.116293i
$865$	3.72418e8	−	3.11778e8i	0.575416	−	0.481722i
$866$	−6.60231e7	−	5.05907e8i	−0.101658	−	0.778964i
$867$	−1.90135e7			−0.0291745
$868$	526258.	+	1.98191e6i	0.000804710	+	0.00303057i
$869$	−5.85272e8			−0.891864
$870$	−4.59979e8	−	4.23410e8i	−0.698522	−	0.642989i
$871$			9.13824e8i			1.38295i
$872$	−1.61051e8	+	6.60715e7i	−0.242893	+	0.0996472i
$873$		−	2.07840e8i		−	0.312382i
$874$	2.64325e8	+	2.02541e9i	0.395916	+	3.03374i
$875$	−2.43378e8	+	1.39414e8i	−0.363293	+	0.208105i
$876$	−6.29415e7	−	2.37040e8i	−0.0936320	−	0.352622i
$877$		−	4.75175e8i		−	0.704457i	−0.935914	−	0.352229i	$-0.885424\pi$
$877$		−	4.75175e8i		−	0.704457i	0.935914	−	0.352229i	$-0.114576\pi$
$878$	−8.42113e7	−	6.45276e8i	−0.124419	−	0.953371i
$879$			3.52814e8i			0.519493i
$880$	2.78974e8	−	7.53212e8i	0.409369	−	1.10527i
$881$	−1.06776e9			−1.56151			−0.780755	−	0.624837i	$-0.785165\pi$
$881$	−1.06776e9			−1.56151			−0.780755	+	0.624837i	$0.785165\pi$
$882$	1.87033e8	−	2.44087e7i	0.272592	−	0.0355745i
$883$	1.10522e9			1.60534			0.802671	−	0.596422i	$-0.203411\pi$
$883$	1.10522e9			1.60534			0.802671	+	0.596422i	$0.203411\pi$
$884$	1.20818e9	−	3.20808e8i	1.74893	−	0.464396i
$885$	−2.23792e8	+	1.87352e8i	−0.322860	+	0.270289i
$886$	2.33155e8	−	3.04277e7i	0.335230	−	0.0437490i
$887$	−1.10318e9			−1.58079			−0.790395	−	0.612598i	$-0.790124\pi$
$887$	−1.10318e9			−1.58079			−0.790395	+	0.612598i	$0.790124\pi$
$888$	−5.27001e7	−	1.28458e8i	−0.0752614	−	0.183452i
$889$	1.47926e8			0.210543
$890$	3.09970e8	+	2.85327e8i	0.439693	+	0.404737i
$891$			9.26349e7i			0.130961i
$892$	−7.47787e8	+	1.98561e8i	−1.05362	+	0.279768i
$893$			1.23225e8i			0.173039i
$894$	4.39567e8	−	5.73655e7i	0.615195	−	0.0802856i
$895$	−4.57477e8	+	3.82987e8i	−0.638116	+	0.534213i
$896$	1.85218e8	−	2.37473e8i	0.257490	−	0.330134i
$897$			1.31494e9i			1.82191i
$898$	4.87062e7	−	6.35637e6i	0.0672597	−	0.00877769i
$899$			8.94812e6i			0.0123155i
$900$	2.00840e7	+	2.42169e8i	0.0275501	+	0.332193i
$901$	−1.00636e9			−1.37587
$902$	−3.56900e6	−	2.73478e7i	−0.00486326	−	0.0372651i
$903$	7.15560e6			0.00971813
$904$	9.04034e7	+	2.20361e8i	0.122371	+	0.298283i
$905$	4.45920e8	+	5.32650e8i	0.601605	+	0.718615i
$906$	454757.	+	3.48461e6i	0.000611497	+	0.00468564i
$907$	−9.34213e8			−1.25206			−0.626028	−	0.779800i	$-0.715321\pi$
$907$	−9.34213e8			−1.25206			−0.626028	+	0.779800i	$0.715321\pi$
$908$	3.43089e8	−	9.11008e7i	0.458299	−	0.121693i
$909$	1.25103e8			0.166561
$910$	−3.77240e8	+	4.09821e8i	−0.500603	+	0.543839i
$911$			1.26470e9i			1.67275i	0.548155	+	0.836377i	$0.315331\pi$
$911$			1.26470e9i			1.67275i	−0.548155	+	0.836377i	$0.684669\pi$
$912$	3.71878e8	+	6.50881e8i	0.490248	+	0.858058i
$913$			5.96854e8i			0.784253i
$914$	1.87849e7	+	1.43941e8i	0.0246020	+	0.188515i
$915$	−2.83383e8	−	3.38500e8i	−0.369922	−	0.441871i
$916$	−3.60462e8	+	9.57139e7i	−0.469000	+	0.124534i
$917$			3.46429e8i			0.449269i
$918$	−1.97473e7	−	1.51316e8i	−0.0255259	−	0.195594i
$919$		−	1.39700e9i		−	1.79990i	−0.435993	−	0.899950i	$-0.643603\pi$
$919$		−	1.39700e9i		−	1.79990i	0.435993	−	0.899950i	$-0.356397\pi$
$920$	−1.23166e9	−	6.48250e8i	−1.58171	−	0.832490i
$921$	1.48643e8			0.190269
$922$	−1.25356e9	+	1.63595e8i	−1.59938	+	0.208726i
$923$	−6.62105e8			−0.842018
$924$	−5.76817e7	−	2.17231e8i	−0.0731176	−	0.275363i
$925$	−2.67586e8	−	4.78076e7i	−0.338094	−	0.0604048i
$926$	−1.03636e9	+	1.35250e8i	−1.30521	+	0.170335i
$927$	−3.28206e8			−0.412010
$928$	1.04711e9	−	7.94127e8i	1.31023	−	0.993679i
$929$	−1.13181e9			−1.41165			−0.705825	−	0.708386i	$-0.749423\pi$
$929$	−1.13181e9			−1.41165			−0.705825	+	0.708386i	$0.749423\pi$
$930$	2.35549e6	−	2.55893e6i	0.00292842	−	0.00318134i
$931$		−	1.13912e9i		−	1.41163i
$932$	−1.05822e8	−	3.98528e8i	−0.130715	−	0.492279i
$933$			2.33067e8i			0.286970i
$934$	1.27468e9	−	1.66352e8i	1.56445	−	0.204168i
$935$	6.33876e8	+	7.57163e8i	0.775478	+	0.926306i
$936$	1.83165e8	+	4.46469e8i	0.223365	+	0.544457i
$937$			4.15887e8i			0.505541i	0.967526	+	0.252770i	$0.0813417\pi$
$937$			4.15887e8i			0.505541i	−0.967526	+	0.252770i	$0.918658\pi$
$938$	−2.68388e8	+	3.50259e7i	−0.325203	+	0.0424405i
$939$		−	8.82123e7i		−	0.106545i
$940$	−6.86178e7	−	4.83941e7i	−0.0826139	−	0.0582652i
$941$	−9.66470e8			−1.15990			−0.579949	−	0.814653i	$-0.696927\pi$
$941$	−9.66470e8			−1.15990			−0.579949	+	0.814653i	$0.696927\pi$
$942$	−4.06199e7	−	3.11253e8i	−0.0485944	−	0.372359i
$943$	−4.77909e7			−0.0569915
$944$	−3.04355e8	−	5.32698e8i	−0.361797	−	0.633235i
$945$	4.36488e7	+	5.21384e7i	0.0517222	+	0.0617820i
$946$	5.19136e6	+	3.97792e7i	0.00613207	+	0.0469875i
$947$	7.38750e8			0.869857			0.434928	−	0.900465i	$-0.356774\pi$
$947$	7.38750e8			0.869857			0.434928	+	0.900465i	$0.356774\pi$
$948$	9.55213e7	+	3.59736e8i	0.112118	+	0.422240i
$949$	−9.53512e8			−1.11565
$950$	1.46592e9	+	6.89878e7i	1.70978	+	0.0804640i
$951$		−	2.09537e8i		−	0.243624i
$952$	1.40529e8	+	3.42543e8i	0.162875	+	0.397012i
$953$			1.55167e9i			1.79275i	0.443293	+	0.896377i	$0.353810\pi$
$953$			1.55167e9i			1.79275i	−0.443293	+	0.896377i	$0.646190\pi$
$954$	−5.02753e7	−	3.85238e8i	−0.0579041	−	0.443695i
$955$	−2.64532e8	+	2.21459e8i	−0.303716	+	0.254263i
$956$	−4.25086e8	−	1.60089e9i	−0.486523	−	1.83226i
$957$		−	9.80778e8i		−	1.11901i
$958$	9.00031e7	+	6.89656e8i	0.102367	+	0.784397i
$959$			7.57669e7i			0.0859061i
$960$	−5.08491e8	−	4.85401e7i	−0.574738	−	0.0548640i
$961$	8.87454e8			0.999944
$962$	−5.35281e8	+	6.98566e7i	−0.601253	+	0.0784661i
$963$	−1.74337e8			−0.195214
$964$	1.48405e9	−	3.94063e8i	1.65660	−	0.439880i
$965$	9.69314e8	−	8.11483e8i	1.07865	−	0.903020i
$966$	−3.86195e8	+	5.04001e7i	−0.428425	+	0.0559114i
$967$	7.67779e8			0.849096			0.424548	−	0.905405i	$-0.360433\pi$
$967$	7.67779e8			0.849096			0.424548	+	0.905405i	$0.360433\pi$
$968$	3.26611e8	−	1.33993e8i	0.360085	−	0.147726i
$969$	−9.21586e8			−1.01290
$970$	5.79262e8	−	6.29292e8i	0.634688	−	0.689504i
$971$		−	8.79174e8i		−	0.960323i	−0.877180	−	0.480161i	$-0.840578\pi$
$971$		−	8.79174e8i		−	0.960323i	0.877180	−	0.480161i	$-0.159422\pi$
$972$	5.69378e7	−	1.51188e7i	0.0620015	−	0.0164633i
$973$			3.15557e8i			0.342562i
$974$	−7.40636e7	+	9.66562e6i	−0.0801545	+	0.0104605i
$975$	9.30023e8	+	1.66160e8i	1.00341	+	0.179272i
$976$	8.05742e8	−	4.60358e8i	0.866656	−	0.495161i
$977$			4.02377e8i			0.431469i	0.976452	+	0.215734i	$0.0692146\pi$
$977$			4.02377e8i			0.431469i	−0.976452	+	0.215734i	$0.930785\pi$
$978$	3.02123e8	−	3.94284e7i	0.322974	−	0.0421495i
$979$			6.60925e8i			0.704376i
$980$	6.34322e8	+	4.47369e8i	0.673956	+	0.475322i
$981$	8.26187e7			0.0875127
$982$	−4.38896e7	−	3.36308e8i	−0.0463476	−	0.355142i
$983$	2.86965e8			0.302112			0.151056	−	0.988525i	$-0.451733\pi$
$983$	2.86965e8			0.302112			0.151056	+	0.988525i	$0.451733\pi$
$984$	−1.62268e7	+	6.65706e6i	−0.0170312	+	0.00698710i
$985$	5.09491e8	−	4.26532e8i	0.533124	−	0.446316i
$986$	2.09076e8	+	1.60206e9i	0.218109	+	1.67128i
$987$	−2.34959e7			−0.0244366
$988$	2.81683e9	−	7.47955e8i	2.92072	−	0.775541i
$989$	6.95151e7			0.0718605
$990$	−2.58179e8	+	2.80477e8i	−0.266082	+	0.289062i
$991$		−	5.51206e8i		−	0.566360i	−0.959067	−	0.283180i	$-0.908611\pi$
$991$		−	5.51206e8i		−	0.566360i	0.959067	−	0.283180i	$-0.0913894\pi$
$992$	4.41784e6	+	5.82522e6i	0.00452559	+	0.00596729i
$993$			7.74198e8i			0.790686i
$994$	−2.53777e7	−	1.94459e8i	−0.0258401	−	0.198002i
$995$	9.96669e8	−	8.34383e8i	1.01177	−	0.847025i
$996$	3.66855e8	−	9.74115e7i	0.371293	−	0.0985899i
$997$		−	7.29498e8i		−	0.736103i	−0.929805	−	0.368052i	$-0.880025\pi$
$997$		−	7.29498e8i		−	0.736103i	0.929805	−	0.368052i	$-0.119975\pi$
$998$	2.40018e7	+	1.83916e8i	0.0241464	+	0.185023i
$999$			6.58985e7i			0.0660966i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	60.7.f.a.19.2	yes	36
3.2	odd	2		180.7.f.g.19.35		36
4.3	odd	2	inner	60.7.f.a.19.36	yes	36
5.4	even	2	inner	60.7.f.a.19.35	yes	36
12.11	even	2		180.7.f.g.19.1		36
15.14	odd	2		180.7.f.g.19.2		36
20.19	odd	2	inner	60.7.f.a.19.1	✓	36
60.59	even	2		180.7.f.g.19.36		36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.7.f.a.19.1	✓	36	20.19	odd	2	inner
60.7.f.a.19.2	yes	36	1.1	even	1	trivial
60.7.f.a.19.35	yes	36	5.4	even	2	inner
60.7.f.a.19.36	yes	36	4.3	odd	2	inner
180.7.f.g.19.1		36	12.11	even	2
180.7.f.g.19.2		36	15.14	odd	2
180.7.f.g.19.35		36	3.2	odd	2
180.7.f.g.19.36		36	60.59	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 60 = 2^{2} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	60.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-7.93273 + 1.03526i) q^{2} +15.5885 q^{3} +(61.8565 - 16.4248i) q^{4} +(-80.2400 - 95.8465i) q^{5} +(-123.659 + 16.1381i) q^{6} -143.606 q^{7} +(-473.687 + 194.331i) q^{8} +243.000 q^{9} +O(q^{10})\)	\(q+(-7.93273 + 1.03526i) q^{2} +15.5885 q^{3} +(61.8565 - 16.4248i) q^{4} +(-80.2400 - 95.8465i) q^{5} +(-123.659 + 16.1381i) q^{6} -143.606 q^{7} +(-473.687 + 194.331i) q^{8} +243.000 q^{9} +(735.748 + 677.255i) q^{10} +1568.78i q^{11} +(964.247 - 256.038i) q^{12} -3878.76i q^{13} +(1139.19 - 148.669i) q^{14} +(-1250.82 - 1494.10i) q^{15} +(3556.45 - 2031.96i) q^{16} +5035.60i q^{17} +(-1927.65 + 251.567i) q^{18} +11740.4i q^{19} +(-6537.63 - 4610.80i) q^{20} -2238.59 q^{21} +(-1624.09 - 12444.7i) q^{22} -21747.5 q^{23} +(-7384.05 + 3029.32i) q^{24} +(-2748.09 + 15381.4i) q^{25} +(4015.52 + 30769.2i) q^{26} +3788.00 q^{27} +(-8882.95 + 2358.70i) q^{28} -40105.7 q^{29} +(11469.2 + 10557.4i) q^{30} -223.114i q^{31} +(-26108.8 + 19800.9i) q^{32} +24454.9i q^{33} +(-5213.14 - 39946.1i) q^{34} +(11522.9 + 13764.1i) q^{35} +(15031.1 - 3991.23i) q^{36} +17396.7i q^{37} +(-12154.3 - 93133.1i) q^{38} -60464.0i q^{39} +(56634.6 + 29808.1i) q^{40} +2197.54 q^{41} +(17758.2 - 2317.52i) q^{42} -3196.47 q^{43} +(25766.9 + 97039.2i) q^{44} +(-19498.3 - 23290.7i) q^{45} +(172517. - 22514.2i) q^{46} +10495.8 q^{47} +(55439.6 - 31675.2i) q^{48} -97026.4 q^{49} +(5876.12 - 124862. i) q^{50} +78497.3i q^{51} +(-63708.0 - 239927. i) q^{52} +199848. i q^{53} +(-30049.2 + 3921.55i) q^{54} +(150362. - 125879. i) q^{55} +(68024.2 - 27907.1i) q^{56} +183014. i q^{57} +(318148. - 41519.7i) q^{58} -149784. i q^{59} +(-101911. - 71875.2i) q^{60} +226558. q^{61} +(230.980 + 1769.90i) q^{62} -34896.2 q^{63} +(186615. - 184104. i) q^{64} +(-371766. + 311232. i) q^{65} +(-25317.0 - 193994. i) q^{66} -235597. q^{67} +(82708.9 + 311485. i) q^{68} -339009. q^{69} +(-105658. - 97257.8i) q^{70} -170700. i q^{71} +(-115106. + 47222.5i) q^{72} -245829. i q^{73} +(-18010.0 - 138003. i) q^{74} +(-42838.5 + 239773. i) q^{75} +(192833. + 726217. i) q^{76} -225286. i q^{77} +(62595.7 + 479644. i) q^{78} +373075. i q^{79} +(-480126. - 177828. i) q^{80} +59049.0 q^{81} +(-17432.5 + 2275.02i) q^{82} +380458. q^{83} +(-138471. + 36768.5i) q^{84} +(482645. - 404057. i) q^{85} +(25356.8 - 3309.17i) q^{86} -625186. q^{87} +(-304863. - 743111. i) q^{88} +421299. q^{89} +(178787. + 164573. i) q^{90} +557013. i q^{91} +(-1.34522e6 + 357198. i) q^{92} -3478.00i q^{93} +(-83260.6 + 10865.9i) q^{94} +(1.12527e6 - 942046. i) q^{95} +(-406995. + 308665. i) q^{96} -855309. i q^{97} +(769684. - 100447. i) q^{98} +381213. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9}+O(q^{10}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9	\( 36 q - 66 q^{4} + 44 q^{5} - 162 q^{6} + 8748 q^{9} - 1422 q^{10} + 15484 q^{14} + 1266 q^{16} - 2188 q^{20} - 9234 q^{24} + 13812 q^{25} - 32052 q^{26} - 36920 q^{29} - 24300 q^{30} - 156204 q^{34} - 16038 q^{36} + 7674 q^{40} + 341848 q^{41} + 74892 q^{44} + 10692 q^{45} + 478080 q^{46} + 482556 q^{49} - 191448 q^{50} - 39366 q^{54} - 926132 q^{56} + 126846 q^{60} - 455976 q^{61} - 618 q^{64} - 624192 q^{65} - 127332 q^{66} - 541728 q^{69} - 1871304 q^{70} - 612324 q^{74} - 1566456 q^{76} + 2360972 q^{80} + 2125764 q^{81} + 858276 q^{84} + 2280864 q^{85} + 5157592 q^{86} - 1806104 q^{89} - 345546 q^{90} - 3121992 q^{94} - 4040118 q^{96}+O(q^{100}) \) 36 * q - 66 * q^4 + 44 * q^5 - 162 * q^6 + 8748 * q^9 - 1422 * q^10 + 15484 * q^14 + 1266 * q^16 - 2188 * q^20 - 9234 * q^24 + 13812 * q^25 - 32052 * q^26 - 36920 * q^29 - 24300 * q^30 - 156204 * q^34 - 16038 * q^36 + 7674 * q^40 + 341848 * q^41 + 74892 * q^44 + 10692 * q^45 + 478080 * q^46 + 482556 * q^49 - 191448 * q^50 - 39366 * q^54 - 926132 * q^56 + 126846 * q^60 - 455976 * q^61 - 618 * q^64 - 624192 * q^65 - 127332 * q^66 - 541728 * q^69 - 1871304 * q^70 - 612324 * q^74 - 1566456 * q^76 + 2360972 * q^80 + 2125764 * q^81 + 858276 * q^84 + 2280864 * q^85 + 5157592 * q^86 - 1806104 * q^89 - 345546 * q^90 - 3121992 * q^94 - 4040118 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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