LMFDB - Embedded newform 40.6.f.a.29.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,6,Mod(29,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("40.29");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	40.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:	$6.41535279252$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			29.15
Character	$\chi$	$=$	40.29
Dual form			40.6.f.a.29.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.685452 - 5.61517i) q^{2} -28.9041 q^{3} +(-31.0603 - 7.69787i) q^{4} +(40.5064 + 38.5257i) q^{5} +(-19.8124 + 162.302i) q^{6} -128.100i q^{7} +(-64.5152 + 169.132i) q^{8} +592.448 q^{9} +O(q^{10})$	\(q+(0.685452 - 5.61517i) q^{2} -28.9041 q^{3} +(-31.0603 - 7.69787i) q^{4} +(40.5064 + 38.5257i) q^{5} +(-19.8124 + 162.302i) q^{6} -128.100i q^{7} +(-64.5152 + 169.132i) q^{8} +592.448 q^{9} +(244.094 - 201.043i) q^{10} +433.553i q^{11} +(897.771 + 222.500i) q^{12} -78.5787 q^{13} +(-719.302 - 87.8063i) q^{14} +(-1170.80 - 1113.55i) q^{15} +(905.486 + 478.196i) q^{16} +1487.27i q^{17} +(406.095 - 3326.70i) q^{18} -98.3252i q^{19} +(-961.577 - 1508.43i) q^{20} +3702.61i q^{21} +(2434.47 + 297.180i) q^{22} +2363.01i q^{23} +(1864.76 - 4888.63i) q^{24} +(156.542 + 3121.08i) q^{25} +(-53.8620 + 441.233i) q^{26} -10100.5 q^{27} +(-986.095 + 3978.82i) q^{28} -1024.44i q^{29} +(-7055.31 + 5810.97i) q^{30} +4308.96 q^{31} +(3305.82 - 4756.68i) q^{32} -12531.5i q^{33} +(8351.29 + 1019.45i) q^{34} +(4935.13 - 5188.86i) q^{35} +(-18401.6 - 4560.59i) q^{36} -6647.54 q^{37} +(-552.113 - 67.3973i) q^{38} +2271.25 q^{39} +(-9129.23 + 4365.46i) q^{40} -4441.16 q^{41} +(20790.8 + 2537.96i) q^{42} -7066.93 q^{43} +(3337.43 - 13466.3i) q^{44} +(23998.0 + 22824.5i) q^{45} +(13268.7 + 1619.73i) q^{46} +15560.5i q^{47} +(-26172.3 - 13821.8i) q^{48} +397.456 q^{49} +(17632.7 + 1260.34i) q^{50} -42988.3i q^{51} +(2440.68 + 604.888i) q^{52} +26793.6 q^{53} +(-6923.41 + 56716.0i) q^{54} +(-16702.9 + 17561.7i) q^{55} +(21665.8 + 8264.38i) q^{56} +2842.00i q^{57} +(-5752.40 - 702.205i) q^{58} +32902.0i q^{59} +(27793.5 + 43599.9i) q^{60} +19242.7i q^{61} +(2953.59 - 24195.6i) q^{62} -75892.5i q^{63} +(-24443.6 - 21823.2i) q^{64} +(-3182.94 - 3027.30i) q^{65} +(-70366.4 - 8589.73i) q^{66} +1066.77 q^{67} +(11448.8 - 46195.1i) q^{68} -68300.6i q^{69} +(-25753.6 - 31268.3i) q^{70} +12397.2 q^{71} +(-38221.9 + 100202. i) q^{72} +37248.9i q^{73} +(-4556.57 + 37327.1i) q^{74} +(-4524.72 - 90212.0i) q^{75} +(-756.894 + 3054.01i) q^{76} +55538.0 q^{77} +(1556.83 - 12753.5i) q^{78} -50784.5 q^{79} +(18255.2 + 54254.5i) q^{80} +147981. q^{81} +(-3044.21 + 24937.9i) q^{82} -38676.4 q^{83} +(28502.2 - 115004. i) q^{84} +(-57298.2 + 60244.1i) q^{85} +(-4844.04 + 39682.0i) q^{86} +29610.5i q^{87} +(-73327.9 - 27970.8i) q^{88} -132425. q^{89} +(144613. - 119108. i) q^{90} +10065.9i q^{91} +(18190.1 - 73395.7i) q^{92} -124547. q^{93} +(87375.1 + 10666.0i) q^{94} +(3788.05 - 3982.80i) q^{95} +(-95551.9 + 137488. i) q^{96} -95071.6i q^{97} +(272.437 - 2231.78i) q^{98} +256858. i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9}+O(q^{10}) $ 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9	$ 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36} + 23360 q^{39} - 22496 q^{40} - 2480 q^{41} + 10712 q^{44} + 58372 q^{46} - 38420 q^{49} + 45624 q^{50} - 3568 q^{54} - 48776 q^{55} + 110944 q^{56} + 111688 q^{60} - 46944 q^{64} + 37200 q^{65} - 136120 q^{66} - 112852 q^{70} - 69232 q^{71} + 34176 q^{74} - 13944 q^{76} - 35984 q^{79} - 47064 q^{80} + 122596 q^{81} - 165688 q^{84} - 73676 q^{86} - 178744 q^{89} + 51496 q^{90} + 314740 q^{94} + 89416 q^{95} - 236176 q^{96}+O(q^{100}) $ 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/40\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	0.685452	−	5.61517i	0.121172	−	0.992632i
$2$	0.685452	−	5.61517i	0.121172	−	0.992632i
$3$	−28.9041			−1.85420			−0.927100	−	0.374814i	$-0.877707\pi$
$3$	−28.9041			−1.85420			−0.927100	+	0.374814i	$0.877707\pi$
$4$	−31.0603	−	7.69787i	−0.970635	−	0.240558i
$5$	40.5064	+	38.5257i	0.724601	+	0.689169i
$5$	40.5064	+	38.5257i	0.724601	+	0.689169i
$6$	−19.8124	+	162.302i	−0.224677	+	1.84054i
$7$		−	128.100i		−	0.988105i	−0.869432	−	0.494053i	$-0.835515\pi$
$7$		−	128.100i		−	0.988105i	0.869432	−	0.494053i	$-0.164485\pi$
$8$	−64.5152	+	169.132i	−0.356400	+	0.934334i
$9$	592.448			2.43806
$10$	244.094	−	201.043i	0.771892	−	0.635754i
$11$			433.553i			1.08034i	0.841556	+	0.540170i	$0.181640\pi$
$11$			433.553i			1.08034i	−0.841556	+	0.540170i	$0.818360\pi$
$12$	897.771	+	222.500i	1.79975	+	0.446043i
$13$	−78.5787			−0.128957			−0.0644787	−	0.997919i	$-0.520538\pi$
$13$	−78.5787			−0.128957			−0.0644787	+	0.997919i	$0.520538\pi$
$14$	−719.302	−	87.8063i	−0.980824	−	0.119731i
$15$	−1170.80	−	1113.55i	−1.34356	−	1.27786i
$16$	905.486	+	478.196i	0.884263	+	0.466988i
$17$			1487.27i			1.24815i	0.781363	+	0.624077i	$0.214525\pi$
$17$			1487.27i			1.24815i	−0.781363	+	0.624077i	$0.785475\pi$
$18$	406.095	−	3326.70i	0.295425	−	2.42009i
$19$		−	98.3252i		−	0.0624857i	−0.999512	−	0.0312429i	$-0.990053\pi$
$19$		−	98.3252i		−	0.0624857i	0.999512	−	0.0312429i	$-0.00994653\pi$
$20$	−961.577	−	1508.43i	−0.537538	−	0.843240i
$21$			3702.61i			1.83214i
$22$	2434.47	+	297.180i	1.07238	+	0.130907i
$23$			2363.01i			0.931419i	0.884938	+	0.465710i	$0.154201\pi$
$23$			2363.01i			0.931419i	−0.884938	+	0.465710i	$0.845799\pi$
$24$	1864.76	−	4888.63i	0.660836	−	1.73244i
$25$	156.542	+	3121.08i	0.0500935	+	0.998745i
$26$	−53.8620	+	441.233i	−0.0156260	+	0.128007i
$27$	−10100.5			−2.66645
$28$	−986.095	+	3978.82i	−0.237697	+	0.959089i
$29$		−	1024.44i		−	0.226199i	−0.993584	−	0.113100i	$-0.963922\pi$
$29$		−	1024.44i		−	0.226199i	0.993584	−	0.113100i	$-0.0360779\pi$
$30$	−7055.31	+	5810.97i	−1.43124	+	1.17882i
$31$	4308.96			0.805320			0.402660	−	0.915350i	$-0.368086\pi$
$31$	4308.96			0.805320			0.402660	+	0.915350i	$0.368086\pi$
$32$	3305.82	−	4756.68i	0.570695	−	0.821162i
$33$		−	12531.5i		−	2.00317i
$34$	8351.29	+	1019.45i	1.23896	+	0.151241i
$35$	4935.13	−	5188.86i	0.680971	−	0.715982i
$36$	−18401.6	−	4560.59i	−2.36646	−	0.586495i
$37$	−6647.54			−0.798283			−0.399141	−	0.916889i	$-0.630692\pi$
$37$	−6647.54			−0.798283			−0.399141	+	0.916889i	$0.630692\pi$
$38$	−552.113	−	67.3973i	−0.0620253	−	0.00757152i
$39$	2271.25			0.239113
$40$	−9129.23	+	4365.46i	−0.902161	+	0.431400i
$41$	−4441.16			−0.412608			−0.206304	−	0.978488i	$-0.566144\pi$
$41$	−4441.16			−0.412608			−0.206304	+	0.978488i	$0.566144\pi$
$42$	20790.8	+	2537.96i	1.81864	+	0.222005i
$43$	−7066.93			−0.582854			−0.291427	−	0.956593i	$-0.594130\pi$
$43$	−7066.93			−0.582854			−0.291427	+	0.956593i	$0.594130\pi$
$44$	3337.43	−	13466.3i	0.259885	−	1.04862i
$45$	23998.0	+	22824.5i	1.76662	+	1.68023i
$46$	13268.7	+	1619.73i	0.924556	+	0.112862i
$47$			15560.5i			1.02750i	0.857941	+	0.513748i	$0.171743\pi$
$47$			15560.5i			1.02750i	−0.857941	+	0.513748i	$0.828257\pi$
$48$	−26172.3	−	13821.8i	−1.63960	−	0.865890i
$49$	397.456			0.0236482
$50$	17632.7	+	1260.34i	0.997455	+	0.0712955i
$51$		−	42988.3i		−	2.31433i
$52$	2440.68	+	604.888i	0.125171	+	0.0310218i
$53$	26793.6			1.31021			0.655105	−	0.755538i	$-0.272624\pi$
$53$	26793.6			1.31021			0.655105	+	0.755538i	$0.272624\pi$
$54$	−6923.41	+	56716.0i	−0.323099	+	2.64680i
$55$	−16702.9	+	17561.7i	−0.744536	+	0.782816i
$56$	21665.8	+	8264.38i	0.923220	+	0.352160i
$57$			2842.00i			0.115861i
$58$	−5752.40	−	702.205i	−0.224533	−	0.0274090i
$59$			32902.0i			1.23053i	0.788320	+	0.615266i	$0.210951\pi$
$59$			32902.0i			1.23053i	−0.788320	+	0.615266i	$0.789049\pi$
$60$	27793.5	+	43599.9i	0.996703	+	1.56354i
$61$			19242.7i			0.662126i	0.943609	+	0.331063i	$0.107407\pi$
$61$			19242.7i			0.662126i	−0.943609	+	0.331063i	$0.892593\pi$
$62$	2953.59	−	24195.6i	0.0975822	−	0.799386i
$63$		−	75892.5i		−	2.40906i
$64$	−24443.6	−	21823.2i	−0.745959	−	0.665992i
$65$	−3182.94	−	3027.30i	−0.0934427	−	0.0888734i
$66$	−70366.4	−	8589.73i	−1.98841	−	0.242728i
$67$	1066.77			0.0290326			0.0145163	−	0.999895i	$-0.495379\pi$
$67$	1066.77			0.0290326			0.0145163	+	0.999895i	$0.495379\pi$
$68$	11448.8	−	46195.1i	0.300254	−	1.21150i
$69$		−	68300.6i		−	1.72704i
$70$	−25753.6	−	31268.3i	−0.628192	−	0.762710i
$71$	12397.2			0.291862			0.145931	−	0.989295i	$-0.453382\pi$
$71$	12397.2			0.291862			0.145931	+	0.989295i	$0.453382\pi$
$72$	−38221.9	+	100202.i	−0.868923	+	2.27796i
$73$			37248.9i			0.818100i	0.912512	+	0.409050i	$0.134140\pi$
$73$			37248.9i			0.818100i	−0.912512	+	0.409050i	$0.865860\pi$
$74$	−4556.57	+	37327.1i	−0.0967295	+	0.792401i
$75$	−4524.72	−	90212.0i	−0.0928834	−	1.85187i
$76$	−756.894	+	3054.01i	−0.0150315	+	0.0606508i
$77$	55538.0			1.06749
$78$	1556.83	−	12753.5i	0.0289738	−	0.237351i
$79$	−50784.5			−0.915510			−0.457755	−	0.889078i	$-0.651346\pi$
$79$	−50784.5			−0.915510			−0.457755	+	0.889078i	$0.651346\pi$
$80$	18255.2	+	54254.5i	0.318904	+	0.947787i
$81$	147981.			2.50607
$82$	−3044.21	+	24937.9i	−0.0499965	+	0.409567i
$83$	−38676.4			−0.616242			−0.308121	−	0.951347i	$-0.599700\pi$
$83$	−38676.4			−0.616242			−0.308121	+	0.951347i	$0.599700\pi$
$84$	28502.2	−	115004.i	0.440738	−	1.77834i
$85$	−57298.2	+	60244.1i	−0.860188	+	0.904413i
$86$	−4844.04	+	39682.0i	−0.0706256	+	0.578559i
$87$			29610.5i			0.419419i
$88$	−73327.9	−	27970.8i	−1.00940	−	0.385033i
$89$	−132425.			−1.77213			−0.886067	−	0.463558i	$-0.846573\pi$
$89$	−132425.			−1.77213			−0.886067	+	0.463558i	$0.846573\pi$
$90$	144613.	−	119108.i	1.88192	−	1.55001i
$91$			10065.9i			0.127424i
$92$	18190.1	−	73395.7i	0.224061	−	0.904068i
$93$	−124547.			−1.49322
$94$	87375.1	+	10666.0i	1.01992	+	0.124504i
$95$	3788.05	−	3982.80i	0.0430632	−	0.0452772i
$96$	−95551.9	+	137488.i	−1.05818	+	1.52260i
$97$		−	95071.6i		−	1.02594i	−0.858407	−	0.512969i	$-0.828545\pi$
$97$		−	95071.6i		−	1.02594i	0.858407	−	0.512969i	$-0.171455\pi$
$98$	272.437	−	2231.78i	0.00286551	−	0.0234740i
$99$			256858.i			2.63393i
$100$	19163.4	−	98146.6i	0.191634	−	0.981466i
$101$			49284.2i			0.480734i	0.970682	+	0.240367i	$0.0772677\pi$
$101$			49284.2i			0.480734i	−0.970682	+	0.240367i	$0.922732\pi$
$102$	−241387.	−	29466.4i	−2.29727	−	0.280432i
$103$			143185.i			1.32986i	0.746906	+	0.664930i	$0.231539\pi$
$103$			143185.i			1.32986i	−0.746906	+	0.664930i	$0.768461\pi$
$104$	5069.52	−	13290.2i	0.0459604	−	0.120489i
$105$	−142646.	+	149980.i	−1.26266	+	1.32757i
$106$	18365.7	−	150450.i	0.158761	−	1.30056i
$107$	168772.			1.42508			0.712541	−	0.701630i	$-0.247544\pi$
$107$	168772.			1.42508			0.712541	+	0.701630i	$0.247544\pi$
$108$	313725.	+	77752.3i	2.58815	+	0.641437i
$109$		−	169878.i		−	1.36953i	−0.728763	−	0.684766i	$-0.759905\pi$
$109$		−	169878.i		−	1.36953i	0.728763	−	0.684766i	$-0.240095\pi$
$110$	87162.8	+	105828.i	0.686831	+	0.833906i
$111$	192141.			1.48018
$112$	61256.8	−	115992.i	0.461434	−	0.873745i
$113$		−	176203.i		−	1.29813i	−0.760733	−	0.649064i	$-0.775161\pi$
$113$		−	176203.i		−	1.29813i	0.760733	−	0.649064i	$-0.224839\pi$
$114$	15958.3	+	1948.06i	0.115007	+	0.0140391i
$115$	−91036.5	+	95717.0i	−0.641905	+	0.674908i
$116$	−7886.00	+	31819.4i	−0.0544141	+	0.219557i
$117$	−46553.8			−0.314406
$118$	184751.	+	22552.8i	1.22146	+	0.149106i
$119$	190519.			1.23331
$120$	263872.	−	126180.i	1.67279	−	0.799902i
$121$	−26917.2			−0.167135
$122$	108051.	+	13189.9i	0.657247	+	0.0802311i
$123$	128368.			0.765057
$124$	−133838.	−	33169.8i	−0.781672	−	0.193726i
$125$	−113901.	+	132455.i	−0.652005	+	0.758214i
$126$	−426149.	−	52020.7i	−2.39131	−	0.291910i
$127$			28671.3i			0.157739i	0.996885	+	0.0788694i	$0.0251310\pi$
$127$			28671.3i			0.157739i	−0.996885	+	0.0788694i	$0.974869\pi$
$128$	−139296.	+	122296.i	−0.751474	+	0.659763i
$129$	204263.			1.08073
$130$	−19180.6	+	15797.7i	−0.0995412	+	0.0819852i
$131$		−	42028.2i		−	0.213975i	−0.994260	−	0.106987i	$-0.965880\pi$
$131$		−	42028.2i		−	0.213975i	0.994260	−	0.106987i	$-0.0341204\pi$
$132$	−96465.6	+	389231.i	−0.481878	+	1.94434i
$133$	−12595.4			−0.0617425
$134$	731.223	−	5990.12i	0.00351793	−	0.0288186i
$135$	−409135.	−	389129.i	−1.93211	−	1.83763i
$136$	−251546.	−	95951.6i	−1.16619	−	0.444841i
$137$		−	49062.2i		−	0.223329i	−0.993746	−	0.111665i	$-0.964382\pi$
$137$		−	49062.2i		−	0.223329i	0.993746	−	0.111665i	$-0.0356182\pi$
$138$	−383520.	−	46816.8i	−1.71431	−	0.209269i
$139$		−	85502.0i		−	0.375352i	−0.982231	−	0.187676i	$-0.939904\pi$
$139$		−	85502.0i		−	0.375352i	0.982231	−	0.187676i	$-0.0600956\pi$
$140$	−193230.	+	123178.i	−0.833209	+	0.531144i
$141$		−	449764.i		−	1.90518i
$142$	8497.69	−	69612.4i	0.0353655	−	0.289712i
$143$		−	34068.0i		−	0.139318i
$144$	536454.	+	283307.i	2.15589	+	1.13855i
$145$	39467.2	−	41496.4i	0.155889	−	0.163904i
$146$	209159.	+	25532.4i	0.812072	+	0.0991308i
$147$	−11488.1			−0.0438486
$148$	206475.	+	51171.9i	0.774841	+	0.192034i
$149$			29442.1i			0.108643i	0.998523	+	0.0543216i	$0.0172996\pi$
$149$			29442.1i			0.108643i	−0.998523	+	0.0543216i	$0.982700\pi$
$150$	−509657.	−	36429.0i	−1.84948	−	0.132196i
$151$	131978.			0.471041			0.235520	−	0.971869i	$-0.424321\pi$
$151$	131978.			0.471041			0.235520	+	0.971869i	$0.424321\pi$
$152$	16630.0	+	6343.47i	0.0583825	+	0.0222699i
$153$			881132.i			3.04307i
$154$	38068.7	−	311856.i	0.129350	−	1.05962i
$155$	174541.	+	166006.i	0.583536	+	0.555001i
$156$	−70545.7	−	17483.8i	−0.232091	−	0.0575206i
$157$	−360997.			−1.16884			−0.584419	−	0.811452i	$-0.698678\pi$
$157$	−360997.			−1.16884			−0.584419	+	0.811452i	$0.698678\pi$
$158$	−34810.3	+	285164.i	−0.110934	+	0.908764i
$159$	−774444.			−2.42939
$160$	317161.	−	65317.0i	0.979445	−	0.201709i
$161$	302701.			0.920340
$162$	101434.	−	830939.i	0.303666	−	2.48761i
$163$	139344.			0.410788			0.205394	−	0.978679i	$-0.434152\pi$
$163$	139344.			0.410788			0.205394	+	0.978679i	$0.434152\pi$
$164$	137944.	+	34187.5i	0.400491	+	0.0992562i
$165$	482784.	−	507605.i	1.38052	−	1.45150i
$166$	−26510.9	+	217175.i	−0.0746713	+	0.611701i
$167$			440004.i			1.22086i	0.792071	+	0.610429i	$0.209003\pi$
$167$			440004.i			1.22086i	−0.792071	+	0.610429i	$0.790997\pi$
$168$	−626232.	−	238875.i	−1.71183	−	0.652976i
$169$	−365118.			−0.983370
$170$	299006.	+	363033.i	0.793519	+	0.963439i
$171$		−	58252.6i		−	0.152344i
$172$	219501.	+	54400.3i	0.565738	+	0.140210i
$173$	711657.			1.80782			0.903910	−	0.427722i	$-0.140684\pi$
$173$	711657.			1.80782			0.903910	+	0.427722i	$0.140684\pi$
$174$	166268.	+	20296.6i	0.416328	+	0.0508218i
$175$	399809.	−	20053.0i	0.986865	−	0.0494977i
$176$	−207323.	+	392576.i	−0.504506	+	0.955305i
$177$		−	951005.i		−	2.28165i
$178$	−90771.3	+	743592.i	−0.214733	+	1.75908i
$179$		−	813579.i		−	1.89787i	−0.315468	−	0.948936i	$-0.602161\pi$
$179$		−	813579.i		−	1.89787i	0.315468	−	0.948936i	$-0.397839\pi$
$180$	−569685.	−	893669.i	−1.31055	−	2.05587i
$181$			415019.i			0.941612i	0.882237	+	0.470806i	$0.156037\pi$
$181$			415019.i			0.941612i	−0.882237	+	0.470806i	$0.843963\pi$
$182$	56521.8	+	6899.70i	0.126485	+	0.0154402i
$183$		−	556192.i		−	1.22771i
$184$	−399661.	−	152450.i	−0.870257	−	0.331957i
$185$	−269268.	−	256101.i	−0.578437	−	0.550151i
$186$	−85370.9	+	699352.i	−0.180937	+	1.48222i
$187$	−644811.			−1.34843
$188$	119783.	−	483315.i	0.247173	−	0.997323i
$189$			1.29387e6i			2.63473i
$190$	−19767.6	−	24000.6i	−0.0397256	−	0.0482322i
$191$	598242.			1.18657			0.593285	−	0.804992i	$-0.297831\pi$
$191$	598242.			1.18657			0.593285	+	0.804992i	$0.297831\pi$
$192$	706520.	+	630781.i	1.38316	+	1.23488i
$193$		−	150045.i		−	0.289954i	−0.989435	−	0.144977i	$-0.953689\pi$
$193$		−	150045.i		−	0.289954i	0.989435	−	0.144977i	$-0.0463107\pi$
$194$	−533843.	−	65167.0i	−1.01838	−	0.124315i
$195$	92000.2	+	87501.4i	0.173262	+	0.164789i
$196$	−12345.1	−	3059.56i	−0.0229538	−	0.00568878i
$197$	−120180.			−0.220630			−0.110315	−	0.993897i	$-0.535186\pi$
$197$	−120180.			−0.220630			−0.110315	+	0.993897i	$0.535186\pi$
$198$	1.44230e6	+	176064.i	2.61452	+	0.319159i
$199$	994244.			1.77976			0.889878	−	0.456199i	$-0.150789\pi$
$199$	994244.			1.77976			0.889878	+	0.456199i	$0.150789\pi$
$200$	−537975.	−	174881.i	−0.951014	−	0.309148i
$201$	−30834.2			−0.0538322
$202$	276739.	+	33782.0i	0.477191	+	0.0582515i
$203$	−131230.			−0.223509
$204$	−330918.	+	1.33523e6i	−0.556730	+	2.24637i
$205$	−179896.	−	171099.i	−0.298976	−	0.284356i
$206$	804011.	+	98146.8i	1.32006	+	0.161142i
$207$			1.39996e6i			2.27086i
$208$	−71151.9	−	37576.0i	−0.114032	−	0.0602217i
$209$	42629.2			0.0675059
$210$	744384.	+	903784.i	1.16479	+	1.41422i
$211$			854741.i			1.32169i	0.750524	+	0.660843i	$0.229801\pi$
$211$			854741.i			1.32169i	−0.750524	+	0.660843i	$0.770199\pi$
$212$	−832216.	−	206253.i	−1.27173	−	0.315182i
$213$	−358330.			−0.541171
$214$	115685.	−	947682.i	0.172680	−	1.41458i
$215$	−286256.	−	272258.i	−0.422336	−	0.401684i
$216$	651636.	−	1.70832e6i	0.950321	−	2.49135i
$217$		−	551977.i		−	0.795741i
$218$	−953897.	−	116444.i	−1.35944	−	0.165949i
$219$		−	1.07665e6i		−	1.51692i
$220$	653986.	−	416895.i	0.910986	−	0.580724i
$221$		−	116868.i		−	0.160959i
$222$	131704.	−	1.07891e6i	0.179356	−	1.46927i
$223$			135422.i			0.182359i	0.995834	+	0.0911797i	$0.0290638\pi$
$223$			135422.i			0.182359i	−0.995834	+	0.0911797i	$0.970936\pi$
$224$	−609329.	−	423475.i	−0.811394	−	0.563907i
$225$	92743.2	+	1.84908e6i	0.122131	+	2.43500i
$226$	−989412.	−	120779.i	−1.28856	−	0.157297i
$227$	−538983.			−0.694241			−0.347120	−	0.937821i	$-0.612840\pi$
$227$	−538983.			−0.694241			−0.347120	+	0.937821i	$0.612840\pi$
$228$	21877.4	−	88273.5i	0.0278713	−	0.112459i
$229$			1.04360e6i			1.31507i	0.753426	+	0.657533i	$0.228400\pi$
$229$			1.04360e6i			1.31507i	−0.753426	+	0.657533i	$0.771600\pi$
$230$	475066.	+	576795.i	0.592154	+	0.718955i
$231$	−1.60528e6			−1.97934
$232$	173266.	+	66091.9i	0.211346	+	0.0806173i
$233$		−	466145.i		−	0.562512i	−0.959633	−	0.281256i	$-0.909249\pi$
$233$		−	466145.i		−	0.562512i	0.959633	−	0.281256i	$-0.0907510\pi$
$234$	−31910.4	+	261408.i	−0.0380972	+	0.312089i
$235$	−599481.	+	630302.i	−0.708118	+	0.744525i
$236$	253276.	−	1.02195e6i	0.296015	−	1.19440i
$237$	1.46788e6			1.69754
$238$	130592.	−	1.06980e6i	0.149442	−	1.22422i
$239$	−1.49073e6			−1.68812			−0.844061	−	0.536248i	$-0.819841\pi$
$239$	−1.49073e6			−1.68812			−0.844061	+	0.536248i	$0.819841\pi$
$240$	−527649.	−	1.56818e6i	−0.591313	−	1.75739i
$241$	−248170.			−0.275237			−0.137619	−	0.990485i	$-0.543945\pi$
$241$	−248170.			−0.275237			−0.137619	+	0.990485i	$0.543945\pi$
$242$	−18450.5	+	151145.i	−0.0202521	+	0.165903i
$243$	−1.82284e6			−1.98031
$244$	148127.	−	597683.i	0.159280	−	0.642682i
$245$	16099.5	+	15312.3i	0.0171355	+	0.0162976i
$246$	87990.1	−	720808.i	0.0927035	−	0.759420i
$247$			7726.27i			0.00805800i
$248$	−277994.	+	728785.i	−0.287016	+	0.752438i
$249$	1.11791e6			1.14264
$250$	665682.	+	730363.i	0.673623	+	0.739076i
$251$		−	1.70931e6i		−	1.71252i	−0.516545	−	0.856260i	$-0.672782\pi$
$251$		−	1.70931e6i		−	1.71252i	0.516545	−	0.856260i	$-0.327218\pi$
$252$	−584210.	+	2.35724e6i	−0.579519	+	2.33832i
$253$	−1.02449e6			−1.00625
$254$	160994.	+	19652.8i	0.156576	+	0.0191135i
$255$	1.65615e6	−	1.74130e6i	1.59496	−	1.67696i
$256$	591233.	+	866000.i	0.563844	+	0.825882i
$257$			445935.i			0.421152i	0.977578	+	0.210576i	$0.0675339\pi$
$257$			445935.i			0.421152i	−0.977578	+	0.210576i	$0.932466\pi$
$258$	140013.	−	1.14697e6i	0.130954	−	1.07276i
$259$			851549.i			0.788787i
$260$	75559.5	+	118531.i	0.0693195	+	0.108742i
$261$		−	606928.i		−	0.551487i
$262$	−235996.	−	28808.3i	−0.212398	−	0.0259277i
$263$		−	616116.i		−	0.549254i	−0.961551	−	0.274627i	$-0.911446\pi$
$263$		−	616116.i		−	0.549254i	0.961551	−	0.274627i	$-0.0885544\pi$
$264$	2.11948e6	+	808470.i	1.87163	+	0.713928i
$265$	1.08531e6	+	1.03224e6i	0.949379	+	0.902955i
$266$	−8633.57	+	70725.5i	−0.00748146	+	0.0612875i
$267$	3.82764e6			3.28589
$268$	−33134.3	−	8211.88i	−0.0281800	−	0.00698402i
$269$		−	945945.i		−	0.797049i	−0.917158	−	0.398524i	$-0.869522\pi$
$269$		−	945945.i		−	0.797049i	0.917158	−	0.398524i	$-0.130478\pi$
$270$	−2.46547e6	+	2.03063e6i	−2.05821	+	1.69521i
$271$	−859288.			−0.710748			−0.355374	−	0.934724i	$-0.615646\pi$
$271$	−859288.			−0.710748			−0.355374	+	0.934724i	$0.615646\pi$
$272$	−711208.	+	1.34670e6i	−0.582873	+	1.10370i
$273$		−	290946.i		−	0.236269i
$274$	−275492.	−	33629.8i	−0.221683	−	0.0270612i
$275$	−1.35315e6	+	67869.4i	−1.07898	+	0.0541180i
$276$	−525769.	+	2.12144e6i	−0.415453	+	1.67632i
$277$	−1.32686e6			−1.03903			−0.519514	−	0.854462i	$-0.673887\pi$
$277$	−1.32686e6			−1.03903			−0.519514	+	0.854462i	$0.673887\pi$
$278$	−480108.	−	58607.5i	−0.372587	−	0.0454822i
$279$	2.55284e6			1.96342
$280$	559214.	+	1.16945e6i	0.426268	+	0.891430i
$281$	−651484.			−0.492196			−0.246098	−	0.969245i	$-0.579148\pi$
$281$	−651484.			−0.492196			−0.246098	+	0.969245i	$0.579148\pi$
$282$	−2.52550e6	−	308292.i	−1.89115	−	0.230855i
$283$	1.94978e6			1.44717			0.723585	−	0.690235i	$-0.242493\pi$
$283$	1.94978e6			1.44717			0.723585	+	0.690235i	$0.242493\pi$
$284$	−385061.	−	95432.0i	−0.283291	−	0.0702099i
$285$	−109490.	+	115119.i	−0.0798478	+	0.0839531i
$286$	−191298.	−	23352.0i	−0.138291	−	0.0168814i
$287$			568912.i			0.407700i
$288$	1.95853e6	−	2.81809e6i	1.39139	−	2.00204i
$289$	−792120.			−0.557887
$290$	−205956.	−	250059.i	−0.143807	−	0.174601i
$291$			2.74796e6i			1.90230i
$292$	286737.	−	1.15696e6i	0.196801	−	0.794076i
$293$	1.80561e6			1.22872			0.614362	−	0.789024i	$-0.289413\pi$
$293$	1.80561e6			1.22872			0.614362	+	0.789024i	$0.289413\pi$
$294$	−7874.56	+	64507.8i	−0.00531322	+	0.0435255i
$295$	−1.26757e6	+	1.33274e6i	−0.848044	+	0.891645i
$296$	428868.	−	1.12432e6i	0.284508	−	0.745863i
$297$		−	4.37910e6i		−	2.88067i
$298$	165322.	+	20181.1i	0.107843	+	0.0131645i
$299$		−	185682.i		−	0.120113i
$300$	−553901.	+	2.83684e6i	−0.355327	+	1.81984i
$301$			905272.i			0.575921i
$302$	90464.5	−	741078.i	0.0570770	−	0.467570i
$303$		−	1.42452e6i		−	0.891377i
$304$	47018.8	−	89032.1i	0.0291801	−	0.0552539i
$305$	−741337.	+	779451.i	−0.456316	+	0.479777i
$306$	4.94771e6	+	603974.i	3.02065	+	0.368735i
$307$	−333416.			−0.201902			−0.100951	−	0.994891i	$-0.532188\pi$
$307$	−333416.			−0.201902			−0.100951	+	0.994891i	$0.532188\pi$
$308$	−1.72503e6	−	427524.i	−1.03614	−	0.256793i
$309$		−	4.13865e6i		−	2.46583i
$310$	1.05179e6	−	866287.i	0.621620	−	0.511985i
$311$	126148.			0.0739573			0.0369787	−	0.999316i	$-0.488227\pi$
$311$	126148.			0.0739573			0.0369787	+	0.999316i	$0.488227\pi$
$312$	−146530.	+	384142.i	−0.0852198	+	0.223411i
$313$			1.61358e6i			0.930955i	0.885060	+	0.465477i	$0.154117\pi$
$313$			1.61358e6i			0.930955i	−0.885060	+	0.465477i	$0.845883\pi$
$314$	−247446.	+	2.02706e6i	−0.141631	+	1.16023i
$315$	2.92381e6	−	3.07413e6i	1.66025	−	1.74561i
$316$	1.57738e6	+	390932.i	0.888626	+	0.220234i
$317$	1.62558e6			0.908571			0.454286	−	0.890856i	$-0.349895\pi$
$317$	1.62558e6			0.908571			0.454286	+	0.890856i	$0.349895\pi$
$318$	−530845.	+	4.34864e6i	−0.294374	+	2.41149i
$319$	444149.			0.244372
$320$	−149367.	−	1.82569e6i	−0.0815417	−	0.996670i
$321$	−4.87820e6			−2.64239
$322$	207487.	−	1.69972e6i	0.111519	−	0.913559i
$323$	146236.			0.0779918
$324$	−4.59634e6	−	1.13914e6i	−2.43248	−	0.602857i
$325$	−12300.9	−	245250.i	−0.00645993	−	0.128796i
$326$	95513.4	−	782438.i	0.0497760	−	0.407761i
$327$			4.91019e6i			2.53939i
$328$	286523.	−	751145.i	0.147053	−	0.385513i
$329$	1.99330e6			1.01527
$330$	−2.51937e6	−	3.05885e6i	−1.27352	−	1.54623i
$331$		−	325105.i		−	0.163100i	−0.996669	−	0.0815499i	$-0.974013\pi$
$331$		−	325105.i		−	0.163100i	0.996669	−	0.0815499i	$-0.0259870\pi$
$332$	1.20130e6	+	297726.i	0.598146	+	0.148242i
$333$	−3.93833e6			−1.94626
$334$	2.47070e6	+	301602.i	1.21186	+	0.147934i
$335$	43211.2	+	41098.2i	0.0210370	+	0.0200083i
$336$	−1.77057e6	+	3.35266e6i	−0.855591	+	1.62010i
$337$			805090.i			0.386162i	0.981183	+	0.193081i	$0.0618480\pi$
$337$			805090.i			0.386162i	−0.981183	+	0.193081i	$0.938152\pi$
$338$	−250271.	+	2.05020e6i	−0.119157	+	0.976124i
$339$			5.09300e6i			2.40699i
$340$	2.24345e6	−	1.43013e6i	1.05249	−	0.670930i
$341$			1.86816e6i			0.870020i
$342$	−327098.	−	39929.4i	−0.151221	−	0.0184598i
$343$		−	2.20389e6i		−	1.01147i
$344$	455924.	−	1.19525e6i	0.207729	−	0.544580i
$345$	2.63133e6	−	2.76661e6i	1.19022	−	1.25141i
$346$	487807.	−	3.99608e6i	0.219057	−	1.79450i
$347$	−2.17010e6			−0.967512			−0.483756	−	0.875203i	$-0.660728\pi$
$347$	−2.17010e6			−0.967512			−0.483756	+	0.875203i	$0.660728\pi$
$348$	227938.	−	919712.i	0.100895	−	0.407103i
$349$		−	3.51347e6i		−	1.54409i	−0.635569	−	0.772044i	$-0.719234\pi$
$349$		−	3.51347e6i		−	1.54409i	0.635569	−	0.772044i	$-0.280766\pi$
$350$	161449.	−	2.25874e6i	0.0704474	−	0.985591i
$351$	793684.			0.343859
$352$	2.06227e6	+	1.43325e6i	0.887134	+	0.616545i
$353$			2.21866e6i			0.947665i	0.880615	+	0.473833i	$0.157130\pi$
$353$			2.21866e6i			0.947665i	−0.880615	+	0.473833i	$0.842870\pi$
$354$	−5.34005e6	−	651868.i	−2.26484	−	0.276472i
$355$	502166.	+	477611.i	0.211484	+	0.201142i
$356$	4.11318e6	+	1.01939e6i	1.72009	+	0.426301i
$357$	−5.50679e6			−2.28680
$358$	−4.56839e6	−	557670.i	−1.88389	−	0.229969i
$359$	−1.82259e6			−0.746366			−0.373183	−	0.927758i	$-0.621734\pi$
$359$	−1.82259e6			−0.746366			−0.373183	+	0.927758i	$0.621734\pi$
$360$	−5.40859e6	+	2.58631e6i	−2.19952	+	1.05178i
$361$	2.46643e6			0.996096
$362$	2.33041e6	+	284476.i	0.934674	+	0.114097i
$363$	778019.			0.309901
$364$	77486.0	−	312650.i	0.0306528	−	0.123682i
$365$	−1.43504e6	+	1.50882e6i	−0.563809	+	0.592796i
$366$	−3.12311e6	−	381243.i	−1.21867	−	0.148765i
$367$		−	2.02561e6i		−	0.785036i	−0.919744	−	0.392518i	$-0.871604\pi$
$367$		−	2.02561e6i		−	0.785036i	0.919744	−	0.392518i	$-0.128396\pi$
$368$	−1.12998e6	+	2.13967e6i	−0.434962	+	0.823620i
$369$	−2.63116e6			−1.00596
$370$	−1.62262e6	+	1.33644e6i	−0.616188	+	0.507512i
$371$		−	3.43225e6i		−	1.29462i
$372$	3.86846e6	+	958744.i	1.44938	+	0.359208i
$373$	3.39891e6			1.26493			0.632466	−	0.774588i	$-0.282043\pi$
$373$	3.39891e6			1.26493			0.632466	+	0.774588i	$0.282043\pi$
$374$	−441987.	+	3.62073e6i	−0.163392	+	1.33849i
$375$	3.29220e6	−	3.82848e6i	1.20895	−	1.40588i
$376$	−2.63179e6	−	1.00389e6i	−0.960024	−	0.366199i
$377$			80499.2i			0.0291701i
$378$	7.26531e6	+	886887.i	2.61532	+	0.319256i
$379$			3.13155e6i			1.11986i	0.828542	+	0.559928i	$0.189171\pi$
$379$			3.13155e6i			1.11986i	−0.828542	+	0.559928i	$0.810829\pi$
$380$	−148317.	+	94547.3i	−0.0526905	+	0.0335884i
$381$		−	828719.i		−	0.292479i
$382$	410067.	−	3.35923e6i	0.143779	−	1.17783i
$383$			1.68971e6i			0.588592i	0.955714	+	0.294296i	$0.0950852\pi$
$383$			1.68971e6i			0.588592i	−0.955714	+	0.294296i	$0.904915\pi$
$384$	4.02623e6	−	3.53486e6i	1.39338	−	1.22333i
$385$	2.24965e6	+	2.13964e6i	0.773504	+	0.735680i
$386$	−842529.	−	102849.i	−0.287817	−	0.0351343i
$387$	−4.18679e6			−1.42103
$388$	−731848.	+	2.95295e6i	−0.246798	+	0.995812i
$389$			3.88788e6i			1.30268i	0.758784	+	0.651342i	$0.225794\pi$
$389$			3.88788e6i			1.30268i	−0.758784	+	0.651342i	$0.774206\pi$
$390$	554397.	−	456619.i	0.184569	−	0.152017i
$391$	−3.51443e6			−1.16255
$392$	−25642.0	+	67222.7i	−0.00842822	+	0.0220953i
$393$			1.21479e6i			0.396752i
$394$	−82377.4	+	674829.i	−0.0267342	+	0.219005i
$395$	−2.05710e6	−	1.95651e6i	−0.663380	−	0.630941i
$396$	1.97726e6	−	7.97808e6i	0.633614	−	2.55659i
$397$	−213582.			−0.0680123			−0.0340061	−	0.999422i	$-0.510827\pi$
$397$	−213582.			−0.0680123			−0.0340061	+	0.999422i	$0.510827\pi$
$398$	681507.	−	5.58285e6i	0.215657	−	1.76664i
$399$	364060.			0.114483
$400$	−1.35074e6	+	2.90095e6i	−0.422106	+	0.906546i
$401$	3.71761e6			1.15452			0.577261	−	0.816560i	$-0.304121\pi$
$401$	3.71761e6			1.15452			0.577261	+	0.816560i	$0.304121\pi$
$402$	−21135.3	+	173139.i	−0.00652295	+	0.0534355i
$403$	−338593.			−0.103852
$404$	379383.	−	1.53078e6i	0.115644	−	0.466617i
$405$	5.99419e6	+	5.70107e6i	1.81590	+	1.72711i
$406$	−89952.2	+	736882.i	−0.0270830	+	0.221862i
$407$		−	2.88206e6i		−	0.862417i
$408$	7.27071e6	+	2.77340e6i	2.16235	+	0.824825i
$409$	−1.38621e6			−0.409752			−0.204876	−	0.978788i	$-0.565679\pi$
$409$	−1.38621e6			−0.409752			−0.204876	+	0.978788i	$0.565679\pi$
$410$	−1.08406e6	+	892865.i	−0.318488	+	0.262317i
$411$			1.41810e6i			0.414097i
$412$	1.10222e6	−	4.44739e6i	0.319909	−	1.29081i
$413$	4.21474e6			1.21589
$414$	7.86101e6	+	959605.i	2.25412	+	0.275164i
$415$	−1.56664e6	−	1.49004e6i	−0.446530	−	0.424695i
$416$	−259767.	+	373774.i	−0.0735954	+	0.105895i
$417$			2.47136e6i			0.695979i
$418$	29220.3	−	239370.i	0.00817982	−	0.0670084i
$419$			721117.i			0.200665i	0.994954	+	0.100332i	$0.0319906\pi$
$419$			721117.i			0.200665i	−0.994954	+	0.100332i	$0.968009\pi$
$420$	5.58514e6	−	3.56034e6i	1.54494	−	0.984847i
$421$		−	1.36768e6i		−	0.376079i	−0.982161	−	0.188040i	$-0.939787\pi$
$421$		−	1.36768e6i		−	0.376079i	0.982161	−	0.188040i	$-0.0602133\pi$
$422$	4.79952e6	+	585884.i	1.31195	+	0.160151i
$423$			9.21882e6i			2.50510i
$424$	−1.72859e6	+	4.53166e6i	−0.466958	+	1.22417i
$425$	−4.64189e6	+	232821.i	−1.24659	+	0.0625244i
$426$	−245618.	+	2.01209e6i	−0.0655748	+	0.537183i
$427$	2.46498e6			0.654250
$428$	−5.24210e6	−	1.29918e6i	−1.38323	−	0.342815i
$429$			984707.i			0.258323i
$430$	−1.72499e6	+	1.42076e6i	−0.449900	+	0.370552i
$431$	−2.51906e6			−0.653198			−0.326599	−	0.945163i	$-0.605903\pi$
$431$	−2.51906e6			−0.653198			−0.326599	+	0.945163i	$0.605903\pi$
$432$	−9.14586e6	−	4.83002e6i	−2.35784	−	1.24520i
$433$		−	4.29790e6i		−	1.10163i	−0.834626	−	0.550817i	$-0.814316\pi$
$433$		−	4.29790e6i		−	1.10163i	0.834626	−	0.550817i	$-0.185684\pi$
$434$	−3.09945e6	−	378354.i	−0.789877	−	0.0964215i
$435$	−1.14077e6	+	1.19942e6i	−0.289050	+	0.303911i
$436$	−1.30770e6	+	5.27648e6i	−0.329452	+	1.32931i
$437$	232343.			0.0582004
$438$	−6.04556e6	−	737990.i	−1.50574	−	0.183808i
$439$	−386299.			−0.0956670			−0.0478335	−	0.998855i	$-0.515232\pi$
$439$	−386299.			−0.0956670			−0.0478335	+	0.998855i	$0.515232\pi$
$440$	−1.89266e6	−	3.95800e6i	−0.466059	−	0.974641i
$441$	235472.			0.0576558
$442$	−656233.	−	80107.4i	−0.159773	−	0.0195037i
$443$	1.13129e6			0.273884			0.136942	−	0.990579i	$-0.456273\pi$
$443$	1.13129e6			0.273884			0.136942	+	0.990579i	$0.456273\pi$
$444$	−5.96797e6	−	1.47908e6i	−1.43671	−	0.356069i
$445$	−5.36408e6	−	5.10178e6i	−1.28409	−	1.22130i
$446$	760420.	+	92825.6i	0.181016	+	0.0220969i
$447$		−	850998.i		−	0.201446i
$448$	−2.79555e6	+	3.13122e6i	−0.658070	+	0.737086i
$449$	4.41752e6			1.03410			0.517051	−	0.855955i	$-0.327030\pi$
$449$	4.41752e6			1.03410			0.517051	+	0.855955i	$0.327030\pi$
$450$	1.04465e7	+	746685.i	2.43185	+	0.173823i
$451$		−	1.92548e6i		−	0.445757i
$452$	−1.35639e6	+	5.47293e6i	−0.312276	+	1.26001i
$453$	−3.81470e6			−0.873404
$454$	−369447.	+	3.02648e6i	−0.0841225	+	0.689125i
$455$	−387796.	+	407734.i	−0.0878163	+	0.0923312i
$456$	−480675.	−	183353.i	−0.108253	−	0.0412928i
$457$		−	2.26658e6i		−	0.507668i	−0.967248	−	0.253834i	$-0.918308\pi$
$457$		−	2.26658e6i		−	0.507668i	0.967248	−	0.253834i	$-0.0816917\pi$
$458$	5.86002e6	+	715341.i	1.30538	+	0.159349i
$459$		−	1.50222e7i		−	3.32814i
$460$	3.56444e6	−	2.27221e6i	0.785410	−	0.500673i
$461$			8.97491e6i			1.96688i	0.181233	+	0.983440i	$0.441991\pi$
$461$			8.97491e6i			1.96688i	−0.181233	+	0.983440i	$0.558009\pi$
$462$	−1.10034e6	+	9.01391e6i	−0.239841	+	1.96475i
$463$			2.13135e6i			0.462063i	0.972946	+	0.231032i	$0.0742101\pi$
$463$			2.13135e6i			0.462063i	−0.972946	+	0.231032i	$0.925790\pi$
$464$	489883.	−	927616.i	0.105633	−	0.200020i
$465$	−5.04495e6	−	4.79825e6i	−1.08199	−	1.02908i
$466$	−2.61749e6	−	319520.i	−0.558367	−	0.0681607i
$467$	−1.21641e6			−0.258099			−0.129050	−	0.991638i	$-0.541193\pi$
$467$	−1.21641e6			−0.258099			−0.129050	+	0.991638i	$0.541193\pi$
$468$	1.44598e6	+	358365.i	0.305173	+	0.0756330i
$469$		−	136653.i		−	0.0286872i
$470$	3.12834e6	+	3.79823e6i	0.653235	+	0.793116i
$471$	1.04343e7			2.16726
$472$	−5.56480e6	−	2.12268e6i	−1.14973	−	0.438561i
$473$		−	3.06389e6i		−	0.629680i
$474$	1.00616e6	−	8.24240e6i	0.205694	−	1.68503i
$475$	306881.	−	15392.1i	0.0624073	−	0.00313013i
$476$	−5.91758e6	−	1.46659e6i	−1.19709	−	0.296682i
$477$	1.58738e7			3.19437
$478$	−1.02182e6	+	8.37069e6i	−0.204553	+	1.67568i
$479$	9.14993e6			1.82213			0.911065	−	0.412264i	$-0.135262\pi$
$479$	9.14993e6			1.82213			0.911065	+	0.412264i	$0.135262\pi$
$480$	−9.16727e6	+	1.88793e6i	−1.81609	+	0.374010i
$481$	522355.			0.102945
$482$	−170109.	+	1.39352e6i	−0.0333511	+	0.273209i
$483$	−8.74929e6			−1.70650
$484$	836057.	+	207205.i	0.162227	+	0.0402057i
$485$	3.66270e6	−	3.85101e6i	0.707045	−	0.743396i
$486$	−1.24947e6	+	1.02356e7i	−0.239958	+	1.96572i
$487$		−	5.29419e6i		−	1.01153i	−0.862672	−	0.505763i	$-0.831211\pi$
$487$		−	5.29419e6i		−	1.01153i	0.862672	−	0.505763i	$-0.168789\pi$
$488$	−3.25456e6	−	1.24144e6i	−0.618646	−	0.235981i
$489$	−4.02760e6			−0.761684
$490$	97016.5	−	79905.8i	0.0182539	−	0.0150345i
$491$		−	5.58951e6i		−	1.04633i	−0.852231	−	0.523166i	$-0.824751\pi$
$491$		−	5.58951e6i		−	1.04633i	0.852231	−	0.523166i	$-0.175249\pi$
$492$	−3.98715e6	−	988159.i	−0.742591	−	0.184041i
$493$	1.52362e6			0.282332
$494$	43384.3	+	5295.99i	0.00799863	+	0.000976405i
$495$	−9.89562e6	+	1.04044e7i	−1.81522	+	1.90855i
$496$	3.90170e6	+	2.06053e6i	0.712115	+	0.376075i
$497$		−	1.58808e6i		−	0.288390i
$498$	766273.	−	6.27725e6i	0.138455	−	1.13422i
$499$		−	3.40479e6i		−	0.612123i	−0.952012	−	0.306062i	$-0.900989\pi$
$499$		−	3.40479e6i		−	0.612123i	0.952012	−	0.306062i	$-0.0990114\pi$
$500$	4.55741e6	−	3.23729e6i	0.815254	−	0.579104i
$501$		−	1.27179e7i		−	2.26372i
$502$	−9.59805e6	−	1.17165e6i	−1.69990	−	0.207510i
$503$		−	1.05370e7i		−	1.85693i	−0.371421	−	0.928465i	$-0.621129\pi$
$503$		−	1.05370e7i		−	1.85693i	0.371421	−	0.928465i	$-0.378871\pi$
$504$	1.28359e7	+	4.89622e6i	2.25086	+	0.858587i
$505$	−1.89871e6	+	1.99633e6i	−0.331307	+	0.348340i
$506$	−702238.	+	5.75268e6i	−0.121929	+	0.998835i
$507$	1.05534e7			1.82336
$508$	220708.	−	890540.i	0.0379454	−	0.153107i
$509$			7.81588e6i			1.33716i	0.743640	+	0.668580i	$0.233098\pi$
$509$			7.81588e6i			1.33716i	−0.743640	+	0.668580i	$0.766902\pi$
$510$	−8.64250e6	−	1.04932e7i	−1.47134	−	1.78641i
$511$	4.77158e6			0.808369
$512$	5.26800e6	−	2.72627e6i	0.888118	−	0.459615i
$513$			993134.i			0.166615i
$514$	2.50400e6	+	305667.i	0.418049	+	0.0510318i
$515$	−5.51632e6	+	5.79993e6i	−0.916498	+	0.963618i
$516$	−6.34448e6	−	1.57239e6i	−1.04899	−	0.259978i
$517$	−6.74632e6			−1.11005
$518$	4.78159e6	+	583696.i	0.782975	+	0.0955790i
$519$	−2.05698e7			−3.35206
$520$	717363.	−	343032.i	0.116340	−	0.0556322i
$521$	−977378.			−0.157750			−0.0788748	−	0.996885i	$-0.525133\pi$
$521$	−977378.			−0.157750			−0.0788748	+	0.996885i	$0.525133\pi$
$522$	−3.40800e6	−	416020.i	−0.547424	−	0.0668248i
$523$	6.82809e6			1.09155			0.545777	−	0.837931i	$-0.316235\pi$
$523$	6.82809e6			1.09155			0.545777	+	0.837931i	$0.316235\pi$
$524$	−323527.	+	1.30541e6i	−0.0514734	+	0.207691i
$525$	−1.15561e7	+	579615.i	−1.82984	+	0.0917786i
$526$	−3.45960e6	−	422318.i	−0.545207	−	0.0665542i
$527$			6.40860e6i			1.00516i
$528$	5.99250e6	−	1.13471e7i	0.935456	−	1.77133i
$529$	852544.			0.132458
$530$	6.54014e6	−	5.38666e6i	1.01134	−	0.832971i
$531$			1.94928e7i			3.00011i
$532$	391218.	+	96958.0i	0.0599294	+	0.0148527i
$533$	348981.			0.0532088
$534$	2.62367e6	−	2.14929e7i	0.398158	−	3.26168i
$535$	6.83634e6	+	6.50204e6i	1.03262	+	0.982122i
$536$	−68823.1	+	180426.i	−0.0103472	+	0.0271261i
$537$			2.35158e7i			3.51904i
$538$	−5.31164e6	−	648400.i	−0.791176	−	0.0965800i
$539$			172318.i			0.0255481i
$540$	9.71240e6	+	1.52359e7i	1.43332	+	2.24846i
$541$		−	4.14464e6i		−	0.608827i	−0.952540	−	0.304414i	$-0.901540\pi$
$541$		−	4.14464e6i		−	0.608827i	0.952540	−	0.304414i	$-0.0984605\pi$
$542$	−589001.	+	4.82505e6i	−0.0861227	+	0.705511i
$543$		−	1.19958e7i		−	1.74594i
$544$	7.07447e6	+	4.91665e6i	1.02494	+	0.712316i
$545$	6.54468e6	−	6.88117e6i	0.943838	−	0.992364i
$546$	−1.63371e6	−	199430.i	−0.234528	−	0.0286292i
$547$	−2.25850e6			−0.322739			−0.161369	−	0.986894i	$-0.551591\pi$
$547$	−2.25850e6			−0.322739			−0.161369	+	0.986894i	$0.551591\pi$
$548$	−377674.	+	1.52389e6i	−0.0537237	+	0.216771i
$549$			1.14003e7i			1.61430i
$550$	−546423.	+	7.64470e6i	−0.0770234	+	1.07759i
$551$	−100728.			−0.0141342
$552$	1.15519e7	+	4.40643e6i	1.61363	+	0.615516i
$553$			6.50548e6i			0.904620i
$554$	−909502.	+	7.45057e6i	−0.125901	+	1.03137i
$555$	7.78296e6	+	7.40238e6i	1.07254	+	1.02009i
$556$	−658183.	+	2.65572e6i	−0.0902941	+	0.364330i
$557$	1.08783e7			1.48567			0.742835	−	0.669474i	$-0.233481\pi$
$557$	1.08783e7			1.48567			0.742835	+	0.669474i	$0.233481\pi$
$558$	1.74985e6	−	1.43346e7i	0.237911	−	1.94895i
$559$	555310.			0.0751633
$560$	6.94999e6	−	2.33848e6i	0.936513	−	0.315111i
$561$	1.86377e7			2.50026
$562$	−446561.	+	3.65820e6i	−0.0596404	+	0.488569i
$563$	−3.08080e6			−0.409630			−0.204815	−	0.978801i	$-0.565659\pi$
$563$	−3.08080e6			−0.409630			−0.204815	+	0.978801i	$0.565659\pi$
$564$	−3.46222e6	+	1.39698e7i	−0.458308	+	1.84924i
$565$	6.78835e6	−	7.13737e6i	0.894630	−	0.940626i
$566$	1.33648e6	−	1.09483e7i	0.175356	−	1.43651i
$567$		−	1.89563e7i		−	2.47626i
$568$	−799808.	+	2.09677e6i	−0.104020	+	0.272697i
$569$	−828106.			−0.107227			−0.0536136	−	0.998562i	$-0.517074\pi$
$569$	−828106.			−0.107227			−0.0536136	+	0.998562i	$0.517074\pi$
$570$	571365.	+	693715.i	0.0736592	+	0.0894322i
$571$		−	1.09946e7i		−	1.41120i	−0.708609	−	0.705601i	$-0.750677\pi$
$571$		−	1.09946e7i		−	1.41120i	0.708609	−	0.705601i	$-0.249323\pi$
$572$	−262251.	+	1.05816e6i	−0.0335141	+	0.135227i
$573$	−1.72917e7			−2.20014
$574$	3.19454e6	+	389962.i	0.404696	+	0.0494018i
$575$	−7.37512e6	+	369910.i	−0.930250	+	0.0466581i
$576$	−1.44816e7	−	1.29291e7i	−1.81869	−	1.62373i
$577$		−	1.05176e7i		−	1.31516i	−0.753384	−	0.657580i	$-0.771580\pi$
$577$		−	1.05176e7i		−	1.31516i	0.753384	−	0.657580i	$-0.228420\pi$
$578$	−542960.	+	4.44789e6i	−0.0676003	+	0.553776i
$579$			4.33692e6i			0.537632i
$580$	−1.54530e6	+	985077.i	−0.190740	+	0.121591i
$581$			4.95444e6i			0.608912i
$582$	1.54303e7	+	1.88360e6i	1.88828	+	0.230505i
$583$			1.16164e7i			1.41547i
$584$	−6.30000e6	−	2.40312e6i	−0.764379	−	0.291571i
$585$	−1.88573e6	−	1.79352e6i	−0.227819	−	0.216679i
$586$	1.23766e6	−	1.01388e7i	0.148887	−	1.21967i
$587$	−1.07272e7			−1.28497			−0.642484	−	0.766299i	$-0.722096\pi$
$587$	−1.07272e7			−1.28497			−0.642484	+	0.766299i	$0.722096\pi$
$588$	356825.	+	88434.0i	0.0425610	+	0.0105481i
$589$		−	423680.i		−	0.0503210i
$590$	6.61473e6	+	8.03118e6i	0.782315	+	0.949837i
$591$	3.47368e6			0.409093
$592$	−6.01926e6	−	3.17883e6i	−0.705892	−	0.372789i
$593$		−	8.76839e6i		−	1.02396i	−0.858997	−	0.511980i	$-0.828912\pi$
$593$		−	8.76839e6i		−	1.02396i	0.858997	−	0.511980i	$-0.171088\pi$
$594$	−2.45894e7	−	3.00167e6i	−2.85945	−	0.349057i
$595$	7.71725e6	+	7.33988e6i	0.893655	+	0.849956i
$596$	226641.	−	914480.i	0.0261350	−	0.105453i
$597$	−2.87378e7			−3.30002
$598$	−1.04264e6	−	127276.i	−0.119228	−	0.0145544i
$599$	6.28188e6			0.715356			0.357678	−	0.933845i	$-0.383568\pi$
$599$	6.28188e6			0.715356			0.357678	+	0.933845i	$0.383568\pi$
$600$	1.55497e7	+	5.05477e6i	1.76337	+	0.573222i
$601$	−1.18519e7			−1.33844			−0.669222	−	0.743063i	$-0.733372\pi$
$601$	−1.18519e7			−1.33844			−0.669222	+	0.743063i	$0.733372\pi$
$602$	5.08326e6	+	620521.i	0.571677	+	0.0697855i
$603$	632008.			0.0707831
$604$	−4.09927e6	−	1.01595e6i	−0.457209	−	0.113313i
$605$	−1.09032e6	−	1.03700e6i	−0.121106	−	0.115184i
$606$	−7.99891e6	−	976439.i	−0.884809	−	0.108010i
$607$		−	7.80939e6i		−	0.860291i	−0.902760	−	0.430145i	$-0.858462\pi$
$607$		−	7.80939e6i		−	0.860291i	0.902760	−	0.430145i	$-0.141538\pi$
$608$	−467701.	−	325046.i	−0.0513109	−	0.0356603i
$609$	3.79310e6			0.414430
$610$	3.86860e6	+	4.69701e6i	0.420949	+	0.511089i
$611$		−	1.22273e6i		−	0.132503i
$612$	6.78283e6	−	2.73682e7i	0.732036	−	2.95371i
$613$	9.77560e6			1.05073			0.525366	−	0.850876i	$-0.323928\pi$
$613$	9.77560e6			1.05073			0.525366	+	0.850876i	$0.323928\pi$
$614$	−228541.	+	1.87219e6i	−0.0244648	+	0.200414i
$615$	5.19973e6	+	4.94547e6i	0.554361	+	0.527253i
$616$	−3.58305e6	+	9.39328e6i	−0.380453	+	0.997391i
$617$			1.46302e7i			1.54717i	0.633691	+	0.773586i	$0.281539\pi$
$617$			1.46302e7i			1.54717i	−0.633691	+	0.773586i	$0.718461\pi$
$618$	−2.32392e7	−	2.83685e6i	−2.44766	−	0.298789i
$619$			7.48407e6i			0.785076i	0.919736	+	0.392538i	$0.128403\pi$
$619$			7.48407e6i			0.785076i	−0.919736	+	0.392538i	$0.871597\pi$
$620$	−4.14340e6	−	6.49978e6i	−0.432890	−	0.679078i
$621$		−	2.38675e7i		−	2.48358i
$622$	86468.8	−	708345.i	0.00896155	−	0.0734123i
$623$			1.69637e7i			1.75105i
$624$	2.05658e6	+	1.08610e6i	0.211439	+	0.111663i
$625$	−9.71661e6	+	977161.i	−0.994981	+	0.100061i
$626$	9.06050e6	+	1.10603e6i	0.924095	+	0.112806i
$627$	−1.23216e6			−0.125169
$628$	1.12127e7	+	2.77891e6i	1.13452	+	0.281174i
$629$		−	9.88670e6i		−	0.996380i
$630$	−1.52577e7	−	1.85249e7i	−1.53157	−	1.85953i
$631$	9.89503e6			0.989335			0.494668	−	0.869082i	$-0.335290\pi$
$631$	9.89503e6			0.989335			0.494668	+	0.869082i	$0.335290\pi$
$632$	3.27637e6	−	8.58930e6i	0.326287	−	0.855392i
$633$		−	2.47055e7i		−	2.45067i
$634$	1.11425e6	−	9.12789e6i	0.110093	−	0.901877i
$635$	−1.10458e6	+	1.16137e6i	−0.108709	+	0.114298i
$636$	2.40545e7	+	5.96157e6i	2.35805	+	0.584410i
$637$	−31231.6			−0.00304962
$638$	304443.	−	2.49397e6i	0.0296111	−	0.242572i
$639$	7.34470e6			0.711577
$640$	−1.03539e7	−	412700.i	−0.999207	−	0.0398276i
$641$	−1.34899e7			−1.29677			−0.648386	−	0.761312i	$-0.724556\pi$
$641$	−1.34899e7			−1.29677			−0.648386	+	0.761312i	$0.724556\pi$
$642$	−3.34377e6	+	2.73919e7i	−0.320183	+	2.62292i
$643$	1.56805e7			1.49566			0.747828	−	0.663893i	$-0.231097\pi$
$643$	1.56805e7			1.49566			0.747828	+	0.663893i	$0.231097\pi$
$644$	−9.40197e6	−	2.33015e6i	−0.893314	−	0.221396i
$645$	8.27398e6	+	7.86939e6i	0.783096	+	0.744803i
$646$	100238.	−	821142.i	0.00945042	−	0.0774171i
$647$			1.70592e7i			1.60213i	0.598579	+	0.801064i	$0.295732\pi$
$647$			1.70592e7i			1.60213i	−0.598579	+	0.801064i	$0.704268\pi$
$648$	−9.54703e6	+	2.50284e7i	−0.893163	+	2.34151i
$649$	−1.42648e7			−1.32939
$650$	−1.38555e6	−	99035.7i	−0.128629	−	0.00919408i
$651$			1.59544e7i			1.47546i
$652$	−4.32806e6	−	1.07265e6i	−0.398725	−	0.0988185i
$653$	−8.71978e6			−0.800245			−0.400122	−	0.916462i	$-0.631032\pi$
$653$	−8.71978e6			−0.800245			−0.400122	+	0.916462i	$0.631032\pi$
$654$	2.75715e7	+	3.36570e6i	2.52067	+	0.307702i
$655$	1.61917e6	−	1.70241e6i	0.147465	−	0.155046i
$656$	−4.02141e6	−	2.12375e6i	−0.364854	−	0.192683i
$657$			2.20681e7i			1.99458i
$658$	1.36631e6	−	1.11927e7i	0.123023	−	1.00779i
$659$		−	9.58270e6i		−	0.859556i	−0.902935	−	0.429778i	$-0.858592\pi$
$659$		−	9.58270e6i		−	0.859556i	0.902935	−	0.429778i	$-0.141408\pi$
$660$	−1.89029e7	+	1.20500e7i	−1.68915	+	1.07678i
$661$			1.66657e7i			1.48361i	0.670616	+	0.741804i	$0.266030\pi$
$661$			1.66657e7i			1.48361i	−0.670616	+	0.741804i	$0.733970\pi$
$662$	−1.82552e6	−	222844.i	−0.161898	−	0.0197631i
$663$			3.37796e6i			0.298450i
$664$	2.49522e6	−	6.54144e6i	0.219628	−	0.575776i
$665$	−510196.	−	485248.i	−0.0447387	−	0.0425510i
$666$	−2.69953e6	+	2.21144e7i	−0.235832	+	1.93192i
$667$	2.42076e6			0.210686
$668$	3.38709e6	−	1.36666e7i	0.293688	−	1.18501i
$669$		−	3.91427e6i		−	0.338131i
$670$	260393.	−	214467.i	0.0224100	−	0.0184576i
$671$	−8.34271e6			−0.715321
$672$	1.76121e7	+	1.22402e7i	1.50449	+	1.04560i
$673$		−	4.89257e6i		−	0.416389i	−0.978087	−	0.208194i	$-0.933241\pi$
$673$		−	4.89257e6i		−	0.416389i	0.978087	−	0.208194i	$-0.0667587\pi$
$674$	4.52072e6	+	551851.i	0.383317	+	0.0467920i
$675$	−1.58115e6	−	3.15244e7i	−0.133572	−	2.66310i
$676$	1.13407e7	+	2.81063e6i	0.954493	+	0.236558i
$677$	−1.32965e7			−1.11498			−0.557490	−	0.830184i	$-0.688235\pi$
$677$	−1.32965e7			−1.11498			−0.557490	+	0.830184i	$0.688235\pi$
$678$	2.85981e7	+	3.49101e6i	2.38926	+	0.291660i
$679$	−1.21786e7			−1.01374
$680$	−6.49262e6	−	1.35776e7i	−0.538453	−	1.12604i
$681$	1.55788e7			1.28726
$682$	1.04901e7	+	1.28054e6i	0.863609	+	0.105422i
$683$	−4.92824e6			−0.404241			−0.202120	−	0.979361i	$-0.564783\pi$
$683$	−4.92824e6			−0.404241			−0.202120	+	0.979361i	$0.564783\pi$
$684$	−448421.	+	1.80934e6i	−0.0366476	+	0.147870i
$685$	1.89015e6	−	1.98733e6i	0.153911	−	0.161824i
$686$	−1.23752e7	−	1.51066e6i	−1.00402	−	0.122562i
$687$		−	3.01645e7i		−	2.43839i
$688$	−6.39900e6	−	3.37938e6i	−0.515396	−	0.272186i
$689$	−2.10540e6			−0.168961
$690$	−1.37314e7	−	1.66717e7i	−1.09797	−	1.33309i
$691$		−	1.24185e7i		−	0.989403i	−0.869063	−	0.494702i	$-0.835277\pi$
$691$		−	1.24185e7i		−	0.989403i	0.869063	−	0.494702i	$-0.164723\pi$
$692$	−2.21043e7	−	5.47824e6i	−1.75473	−	0.434886i
$693$	3.29034e7			2.60260
$694$	−1.48750e6	+	1.21855e7i	−0.117235	+	0.960383i
$695$	3.29402e6	−	3.46338e6i	0.258681	−	0.271981i
$696$	−5.00810e6	−	1.91033e6i	−0.391877	−	0.149481i
$697$		−	6.60522e6i		−	0.514998i
$698$	−1.97287e7	−	2.40831e6i	−1.53271	−	0.187100i
$699$			1.34735e7i			1.04301i
$700$	−1.25726e7	−	2.45482e6i	−0.969792	−	0.189354i
$701$			2.45892e7i			1.88994i	0.327153	+	0.944971i	$0.393911\pi$
$701$			2.45892e7i			1.88994i	−0.327153	+	0.944971i	$0.606089\pi$
$702$	544033.	−	4.45667e6i	0.0416660	−	0.341325i
$703$			653621.i			0.0498813i
$704$	9.46153e6	−	1.05976e7i	0.719498	−	0.805889i
$705$	1.73275e7	−	1.82183e7i	1.31299	−	1.38050i
$706$	1.24582e7	+	1.52079e6i	0.940682	+	0.114831i
$707$	6.31330e6			0.475015
$708$	−7.32071e6	+	2.95385e7i	−0.548870	+	2.21465i
$709$		−	2.05841e7i		−	1.53786i	−0.639334	−	0.768930i	$-0.720790\pi$
$709$		−	2.05841e7i		−	1.53786i	0.639334	−	0.768930i	$-0.279210\pi$
$710$	3.02608e6	−	2.49237e6i	0.225286	−	0.185552i
$711$	−3.00872e7			−2.23207
$712$	8.54345e6	−	2.23974e7i	0.631588	−	1.65576i
$713$			1.01821e7i			0.750091i
$714$	−3.77464e6	+	3.09216e7i	−0.277096	+	2.26995i
$715$	1.31249e6	−	1.37997e6i	0.0960135	−	0.100950i
$716$	−6.26282e6	+	2.52700e7i	−0.456549	+	1.84214i
$717$	4.30882e7			3.13011
$718$	−1.24930e6	+	1.02341e7i	−0.0904387	+	0.740867i
$719$	5.88556e6			0.424586			0.212293	−	0.977206i	$-0.431907\pi$
$719$	5.88556e6			0.424586			0.212293	+	0.977206i	$0.431907\pi$
$720$	1.08152e7	+	3.21430e7i	0.777508	+	2.31076i
$721$	1.83420e7			1.31404
$722$	1.69062e6	−	1.38494e7i	0.120699	−	0.988756i
$723$	7.17315e6			0.510345
$724$	3.19476e6	−	1.28906e7i	0.226513	−	0.913961i
$725$	3.19735e6	−	160368.i	0.225915	−	0.0113311i
$726$	533295.	−	4.36871e6i	0.0375514	−	0.307618i
$727$		−	7.65798e6i		−	0.537376i	−0.963227	−	0.268688i	$-0.913410\pi$
$727$		−	7.65798e6i		−	0.537376i	0.963227	−	0.268688i	$-0.0865900\pi$
$728$	−1.70247e6	−	649404.i	−0.119056	−	0.0454137i
$729$	1.67283e7			1.16582
$730$	7.48864e6	+	9.09222e6i	0.520110	+	0.631485i
$731$		−	1.05104e7i		−	0.727491i
$732$	−4.28149e6	+	1.72755e7i	−0.295337	+	1.19166i
$733$	−1.64697e7			−1.13220			−0.566102	−	0.824335i	$-0.691549\pi$
$733$	−1.64697e7			−1.13220			−0.566102	+	0.824335i	$0.691549\pi$
$734$	−1.13741e7	−	1.38846e6i	−0.779252	−	0.0951244i
$735$	−465343.	−	442588.i	−0.0317727	−	0.0302191i
$736$	1.12401e7	+	7.81168e6i	0.764846	+	0.531557i
$737$			462503.i			0.0313650i
$738$	−1.80354e6	+	1.47744e7i	−0.121894	+	0.998549i
$739$			1.03197e7i			0.695116i	0.937658	+	0.347558i	$0.112989\pi$
$739$			1.03197e7i			0.695116i	−0.937658	+	0.347558i	$0.887011\pi$
$740$	6.39212e6	+	1.00274e7i	0.429107	+	0.673144i
$741$		−	223321.i		−	0.0149412i
$742$	−1.92727e7	−	2.35264e6i	−1.28509	−	0.156872i
$743$		−	1.43842e7i		−	0.955903i	−0.878386	−	0.477952i	$-0.841379\pi$
$743$		−	1.43842e7i		−	0.955903i	0.878386	−	0.477952i	$-0.158621\pi$
$744$	8.03516e6	−	2.10649e7i	0.532185	−	1.39517i
$745$	−1.13428e6	+	1.19259e6i	−0.0748735	+	0.0787230i
$746$	2.32979e6	−	1.90854e7i	0.153274	−	1.25561i
$747$	−2.29138e7			−1.50243
$748$	2.00280e7	+	4.96367e6i	1.30883	+	0.324376i
$749$		−	2.16196e7i		−	1.40813i
$750$	−1.92409e7	−	2.11105e7i	−1.24903	−	1.37039i
$751$	−3.39860e6			−0.219887			−0.109944	−	0.993938i	$-0.535067\pi$
$751$	−3.39860e6			−0.219887			−0.109944	+	0.993938i	$0.535067\pi$
$752$	−7.44099e6	+	1.40898e7i	−0.479829	+	0.908577i
$753$			4.94060e7i			3.17536i
$754$	452017.	+	55178.3i	0.0289552	+	0.00353460i
$755$	5.34595e6	+	5.08454e6i	0.341317	+	0.324627i
$756$	9.96005e6	−	4.01880e7i	0.633807	−	2.55736i
$757$	8.89557e6			0.564201			0.282101	−	0.959385i	$-0.408969\pi$
$757$	8.89557e6			0.564201			0.282101	+	0.959385i	$0.408969\pi$
$758$	1.75842e7	+	2.14653e6i	1.11160	+	0.135695i
$759$	2.96119e7			1.86579
$760$	429235.	+	897633.i	0.0269563	+	0.0563722i
$761$	−1.68168e7			−1.05264			−0.526321	−	0.850286i	$-0.676429\pi$
$761$	−1.68168e7			−1.05264			−0.526321	+	0.850286i	$0.676429\pi$
$762$	−4.65340e6	−	568048.i	−0.290324	−	0.0354403i
$763$	−2.17614e7			−1.35324
$764$	−1.85816e7	−	4.60519e6i	−1.15173	−	0.285439i
$765$	−3.39462e7	+	3.56915e7i	−2.09719	+	2.20501i
$766$	9.48800e6	+	1.15821e6i	0.584255	+	0.0713209i
$767$		−	2.58540e6i		−	0.158686i
$768$	−1.70891e7	−	2.50310e7i	−1.04548	−	1.53135i
$769$	1.14740e7			0.699681			0.349840	−	0.936809i	$-0.386236\pi$
$769$	1.14740e7			0.699681			0.349840	+	0.936809i	$0.386236\pi$
$770$	1.35565e7	−	1.11655e7i	0.823986	−	0.678661i
$771$		−	1.28894e7i		−	0.780900i
$772$	−1.15503e6	+	4.66045e6i	−0.0697507	+	0.281439i
$773$	−5.97879e6			−0.359886			−0.179943	−	0.983677i	$-0.557591\pi$
$773$	−5.97879e6			−0.359886			−0.179943	+	0.983677i	$0.557591\pi$
$774$	−2.86985e6	+	2.35095e7i	−0.172189	+	1.41056i
$775$	674535.	+	1.34486e7i	0.0403413	+	0.804309i
$776$	1.60797e7	+	6.13356e6i	0.958569	+	0.365644i
$777$		−	2.46133e7i		−	1.46257i
$778$	2.18311e7	+	2.66496e6i	1.29309	+	0.157849i
$779$			436679.i			0.0257821i
$780$	−2.18398e6	−	3.42603e6i	−0.128532	−	0.201630i
$781$			5.37484e6i			0.315310i
$782$	−2.40898e6	+	1.97341e7i	−0.140869	+	1.15399i
$783$			1.03474e7i			0.603149i
$784$	359891.	+	190062.i	0.0209113	+	0.0110435i
$785$	−1.46227e7	−	1.39077e7i	−0.846942	−	0.805527i
$786$	6.82124e6	+	832679.i	0.393829	+	0.0480752i
$787$	−1.28293e6			−0.0738356			−0.0369178	−	0.999318i	$-0.511754\pi$
$787$	−1.28293e6			−0.0738356			−0.0369178	+	0.999318i	$0.511754\pi$
$788$	3.73281e6	+	925126.i	0.214151	+	0.0530744i
$789$			1.78083e7i			1.01843i
$790$	−1.23962e7	+	1.02099e7i	−0.706675	+	0.582039i
$791$	−2.25716e7			−1.28269
$792$	−4.34430e7	−	1.65712e7i	−2.46097	−	0.938732i
$793$		−	1.51206e6i		−	0.0853860i
$794$	−146400.	+	1.19930e6i	−0.00824119	+	0.0675112i
$795$	−3.13700e7	−	2.98360e7i	−1.76034	−	1.67426i
$796$	−3.08815e7	−	7.65356e6i	−1.72749	−	0.428135i
$797$	1.38090e7			0.770047			0.385024	−	0.922907i	$-0.374193\pi$
$797$	1.38090e7			0.770047			0.385024	+	0.922907i	$0.374193\pi$
$798$	249546.	−	2.04426e6i	0.0138721	−	0.113639i
$799$	−2.31428e7			−1.28247
$800$	1.53635e7	+	9.57310e6i	0.848719	+	0.528844i
$801$	−7.84552e7			−4.32057
$802$	2.54824e6	−	2.08750e7i	0.139896	−	1.14602i
$803$	−1.61494e7			−0.883826
$804$	957719.	+	237357.i	0.0522514	+	0.0129498i
$805$	1.22613e7	+	1.16617e7i	0.666880	+	0.634270i
$806$	−232089.	+	1.90126e6i	−0.0125840	+	0.103087i
$807$			2.73417e7i			1.47789i
$808$	−8.33556e6	−	3.17958e6i	−0.449166	−	0.171333i
$809$	2.36073e7			1.26816			0.634082	−	0.773266i	$-0.281378\pi$
$809$	2.36073e7			1.26816			0.634082	+	0.773266i	$0.281378\pi$
$810$	3.61212e7	−	2.97506e7i	1.93442	−	1.59325i
$811$		−	1.59317e6i		−	0.0850569i	−0.999095	−	0.0425284i	$-0.986459\pi$
$811$		−	1.59317e6i		−	0.0850569i	0.999095	−	0.0425284i	$-0.0135413\pi$
$812$	4.07606e6	+	1.01019e6i	0.216945	+	0.0537669i
$813$	2.48370e7			1.31787
$814$	−1.61833e7	−	1.97552e6i	−0.856062	−	0.104501i
$815$	5.64431e6	+	5.36831e6i	0.297658	+	0.283102i
$816$	2.05568e7	−	3.89253e7i	1.08076	−	2.04647i
$817$			694857.i			0.0364200i
$818$	−950181.	+	7.78381e6i	−0.0496504	+	0.406732i
$819$			5.96353e6i			0.310666i
$820$	4.27052e6	+	6.69920e6i	0.221792	+	0.347927i
$821$			9.05321e6i			0.468754i	0.972146	+	0.234377i	$0.0753050\pi$
$821$			9.05321e6i			0.468754i	−0.972146	+	0.234377i	$0.924695\pi$
$822$	7.96287e6	+	972039.i	0.411046	+	0.0501769i
$823$			1.59075e7i			0.818657i	0.912387	+	0.409329i	$0.134237\pi$
$823$			1.59075e7i			0.818657i	−0.912387	+	0.409329i	$0.865763\pi$
$824$	−2.42173e7	−	9.23764e6i	−1.24253	−	0.473961i
$825$	3.91117e7	−	1.96170e6i	2.00065	−	0.100346i
$826$	2.88901e6	−	2.36665e7i	0.147332	−	1.20694i
$827$	2.64781e7			1.34624			0.673122	−	0.739532i	$-0.264953\pi$
$827$	2.64781e7			1.34624			0.673122	+	0.739532i	$0.264953\pi$
$828$	1.07767e7	−	4.34832e7i	0.546273	−	2.20417i
$829$			1.54704e7i			0.781835i	0.920426	+	0.390918i	$0.127842\pi$
$829$			1.54704e7i			0.781835i	−0.920426	+	0.390918i	$0.872158\pi$
$830$	−9.44067e6	+	7.77563e6i	−0.475672	+	0.391778i
$831$	3.83518e7			1.92657
$832$	1.92074e6	+	1.71484e6i	0.0961970	+	0.0858847i
$833$			591125.i			0.0295166i
$834$	1.38771e7	+	1.69400e6i	0.690850	+	0.0843331i
$835$	−1.69514e7	+	1.78230e7i	−0.841377	+	0.884635i
$836$	−1.32408e6	−	328154.i	−0.0655235	−	0.0162391i
$837$	−4.35227e7			−2.14735
$838$	4.04920e6	+	494292.i	0.199186	+	0.0243149i
$839$	3.82791e7			1.87740			0.938701	−	0.344733i	$-0.112030\pi$
$839$	3.82791e7			1.87740			0.938701	+	0.344733i	$0.112030\pi$
$840$	−1.61636e7	−	3.38020e7i	−0.790387	−	1.65289i
$841$	1.94617e7			0.948834
$842$	−7.67976e6	−	937480.i	−0.373308	−	0.0455703i
$843$	1.88306e7			0.912630
$844$	6.57968e6	−	2.65485e7i	0.317943	−	1.28288i
$845$	−1.47896e7	−	1.40664e7i	−0.712551	−	0.677708i
$846$	5.17652e7	+	6.31906e6i	2.48664	+	0.303547i
$847$			3.44809e6i			0.165147i
$848$	2.42612e7	+	1.28126e7i	1.15857	+	0.611853i
$849$	−5.63567e7			−2.68334
$850$	−1.87446e6	+	2.62246e7i	−0.0889877	+	1.24498i
$851$		−	1.57082e7i		−	0.743536i
$852$	1.11298e7	+	2.75838e6i	0.525279	+	0.130183i
$853$	−2.94396e7			−1.38535			−0.692676	−	0.721249i	$-0.743568\pi$
$853$	−2.94396e7			−1.38535			−0.692676	+	0.721249i	$0.743568\pi$
$854$	1.68963e6	−	1.38413e7i	0.0792767	−	0.649429i
$855$	2.24422e6	−	2.35961e6i	0.104991	−	0.110389i
$856$	−1.08883e7	+	2.85448e7i	−0.507899	+	1.33150i
$857$		−	1.36598e7i		−	0.635320i	−0.948205	−	0.317660i	$-0.897103\pi$
$857$		−	1.36598e7i		−	0.635320i	0.948205	−	0.317660i	$-0.102897\pi$
$858$	5.52930e6	+	674970.i	0.256420	+	0.0313016i
$859$			1.49700e7i			0.692212i	0.938195	+	0.346106i	$0.112496\pi$
$859$			1.49700e7i			0.692212i	−0.938195	+	0.346106i	$0.887504\pi$
$860$	6.79539e6	+	1.06600e7i	0.313306	+	0.491485i
$861$		−	1.64439e7i		−	0.755957i
$862$	−1.72669e6	+	1.41449e7i	−0.0791493	+	0.648385i
$863$		−	2.36162e6i		−	0.107940i	−0.998543	−	0.0539701i	$-0.982812\pi$
$863$		−	2.36162e6i		−	0.107940i	0.998543	−	0.0539701i	$-0.0171876\pi$
$864$	−3.33904e7	+	4.80448e7i	−1.52173	+	2.18959i
$865$	2.88267e7	+	2.74171e7i	1.30995	+	1.24589i
$866$	−2.41335e7	−	2.94601e6i	−1.09352	−	0.133487i
$867$	2.28955e7			1.03443
$868$	−4.24904e6	+	1.71446e7i	−0.191422	+	0.772374i
$869$		−	2.20178e7i		−	0.989063i
$870$	5.95299e6	+	7.22774e6i	0.266647	+	0.323746i
$871$	−83825.7			−0.00374397
$872$	2.87320e7	+	1.09597e7i	1.27960	+	0.488100i
$873$		−	5.63250e7i		−	2.50130i
$874$	159260.	−	1.30465e6i	0.00705226	−	0.0577716i
$875$	1.69674e7	+	1.45906e7i	0.749195	+	0.644250i
$876$	−8.28789e6	+	3.34410e7i	−0.364908	+	1.47238i
$877$	1.52212e7			0.668268			0.334134	−	0.942526i	$-0.391556\pi$
$877$	1.52212e7			0.668268			0.334134	+	0.942526i	$0.391556\pi$
$878$	−264789.	+	2.16913e6i	−0.0115922	+	0.0949620i
$879$	−5.21895e7			−2.27830
$880$	−2.35222e7	+	7.91458e6i	−1.02393	+	0.344525i
$881$	2.72576e7			1.18317			0.591586	−	0.806242i	$-0.298502\pi$
$881$	2.72576e7			1.18317			0.591586	+	0.806242i	$0.298502\pi$
$882$	161405.	−	1.32222e6i	0.00698627	−	0.0572310i
$883$	−1.90157e7			−0.820748			−0.410374	−	0.911917i	$-0.634602\pi$
$883$	−1.90157e7			−0.820748			−0.410374	+	0.911917i	$0.634602\pi$
$884$	−899633.	+	3.62995e6i	−0.0387200	+	0.156232i
$885$	3.66381e7	−	3.85218e7i	1.57244	−	1.65329i
$886$	775449.	−	6.35241e6i	0.0331871	−	0.271866i
$887$		−	2.99966e7i		−	1.28016i	−0.768310	−	0.640078i	$-0.778902\pi$
$887$		−	2.99966e7i		−	1.28016i	0.768310	−	0.640078i	$-0.221098\pi$
$888$	−1.23960e7	+	3.24973e7i	−0.527534	+	1.38298i
$889$	3.67279e6			0.155862
$890$	−3.23242e7	+	2.66232e7i	−1.36790	+	1.12664i
$891$			6.41576e7i			2.70741i
$892$	1.04246e6	−	4.20626e6i	0.0438681	−	0.177004i
$893$	1.52999e6			0.0642038
$894$	−4.77850e6	−	583318.i	−0.199962	−	0.0244097i
$895$	3.13437e7	−	3.29552e7i	1.30795	−	1.37520i
$896$	1.56661e7	+	1.78438e7i	0.651915	+	0.742535i
$897$			5.36698e6i			0.222714i
$898$	3.02800e6	−	2.48052e7i	0.125304	−	1.02648i
$899$		−	4.41427e6i		−	0.182163i
$900$	1.13533e7	−	5.81468e7i	0.467214	−	2.39287i
$901$			3.98493e7i			1.63534i
$902$	−1.08119e7	−	1.31983e6i	−0.442472	−	0.0540132i
$903$		−	2.61661e7i		−	1.06787i
$904$	2.98017e7	+	1.13678e7i	1.21289	+	0.462653i
$905$	−1.59889e7	+	1.68110e7i	−0.648929	+	0.682293i
$906$	−2.61480e6	+	2.14202e7i	−0.105832	+	0.866968i
$907$	−1.81689e7			−0.733348			−0.366674	−	0.930349i	$-0.619504\pi$
$907$	−1.81689e7			−0.733348			−0.366674	+	0.930349i	$0.619504\pi$
$908$	1.67410e7	+	4.14902e6i	0.673854	+	0.167005i
$909$			2.91984e7i			1.17206i
$910$	2.02368e6	+	2.45702e6i	0.0810100	+	0.0983572i
$911$	−2.14560e6			−0.0856550			−0.0428275	−	0.999082i	$-0.513637\pi$
$911$	−2.14560e6			−0.0856550			−0.0428275	+	0.999082i	$0.513637\pi$
$912$	−1.35904e6	+	2.57339e6i	−0.0541058	+	0.102452i
$913$		−	1.67683e7i		−	0.665751i
$914$	−1.27272e7	−	1.55363e6i	−0.503927	−	0.0615151i
$915$	2.14277e7	−	2.25294e7i	0.846101	−	0.889603i
$916$	8.03353e6	−	3.24147e7i	0.316350	−	1.27645i
$917$	−5.38380e6			−0.211430
$918$	−8.43521e7	−	1.02970e7i	−3.30361	−	0.403277i
$919$	−4.88257e6			−0.190704			−0.0953519	−	0.995444i	$-0.530398\pi$
$919$	−4.88257e6			−0.190704			−0.0953519	+	0.995444i	$0.530398\pi$
$920$	−1.03156e7	−	2.15724e7i	−0.401814	−	0.840290i
$921$	9.63709e6			0.374366
$922$	5.03957e7	+	6.15188e6i	1.95239	+	0.238331i
$923$	−974156.			−0.0376378
$924$	4.98604e7	+	1.23572e7i	1.92122	+	0.476147i
$925$	−1.04062e6	−	2.07475e7i	−0.0399888	−	0.797281i
$926$	1.19679e7	+	1.46094e6i	0.458658	+	0.0559891i
$927$			8.48300e7i			3.24228i
$928$	−4.87293e6	−	3.38661e6i	−0.185746	−	0.129091i
$929$	3.34515e7			1.27168			0.635838	−	0.771823i	$-0.280655\pi$
$929$	3.34515e7			1.27168			0.635838	+	0.771823i	$0.280655\pi$
$930$	−3.04011e7	+	2.50393e7i	−1.15261	+	0.949324i
$931$		−	39080.0i		−	0.00147768i
$932$	−3.58832e6	+	1.44786e7i	−0.135317	+	0.545993i
$933$	−3.64621e6			−0.137132
$934$	−833790.	+	6.83034e6i	−0.0312744	+	0.256198i
$935$	−2.61190e7	−	2.48418e7i	−0.977074	−	0.929296i
$936$	3.00343e6	−	7.87376e6i	0.112054	−	0.293760i
$937$			3.63111e7i			1.35111i	0.737310	+	0.675554i	$0.236096\pi$
$937$			3.63111e7i			1.35111i	−0.737310	+	0.675554i	$0.763904\pi$
$938$	−767333.	−	93669.4i	−0.0284758	−	0.00347609i
$939$		−	4.66390e7i		−	1.72618i
$940$	2.34720e7	−	1.49627e7i	0.866425	−	0.552318i
$941$		−	3.70043e7i		−	1.36232i	−0.732136	−	0.681158i	$-0.761477\pi$
$941$		−	3.70043e7i		−	1.36232i	0.732136	−	0.681158i	$-0.238523\pi$
$942$	7.15222e6	−	5.85904e7i	0.262611	−	2.15129i
$943$		−	1.04945e7i		−	0.384311i
$944$	−1.57336e7	+	2.97923e7i	−0.574644	+	1.08811i
$945$	−4.98473e7	+	5.24101e7i	−1.81577	+	1.90913i
$946$	−1.72043e7	−	2.10015e6i	−0.625040	−	0.0762996i
$947$	1.25663e7			0.455335			0.227668	−	0.973739i	$-0.426890\pi$
$947$	1.25663e7			0.455335			0.227668	+	0.973739i	$0.426890\pi$
$948$	−4.55928e7	−	1.12995e7i	−1.64769	−	0.408357i
$949$		−	2.92697e6i		−	0.105500i
$950$	123923.	−	1.73374e6i	0.00445495	−	0.0623267i
$951$	−4.69858e7			−1.68467
$952$	−1.22914e7	+	3.22230e7i	−0.439550	+	1.15232i
$953$			3.08701e7i			1.10105i	0.834819	+	0.550524i	$0.185572\pi$
$953$			3.08701e7i			1.10105i	−0.834819	+	0.550524i	$0.814428\pi$
$954$	1.08807e7	−	8.91341e7i	0.387068	−	3.17083i
$955$	2.42327e7	+	2.30477e7i	0.859791	+	0.817747i
$956$	4.63025e7	+	1.14754e7i	1.63855	+	0.406092i
$957$	−1.28377e7			−0.453115
$958$	6.27184e6	−	5.13785e7i	0.220791	−	1.80870i
$959$	−6.28485e6			−0.220673
$960$	4.31732e6	+	5.27699e7i	0.151195	+	1.84803i
$961$	−1.00620e7			−0.351460
$962$	358050.	−	2.93312e6i	0.0124740	−	0.102186i
$963$	9.99885e7			3.47443
$964$	7.70825e6	+	1.91038e6i	0.267155	+	0.0662107i
$965$	5.78059e6	−	6.07779e6i	0.199827	−	0.210101i
$966$	−5.99722e6	+	4.91288e7i	−0.206779	+	1.69392i
$967$		−	2.55508e7i		−	0.878696i	−0.898317	−	0.439348i	$-0.855209\pi$
$967$		−	2.55508e7i		−	0.878696i	0.898317	−	0.439348i	$-0.144791\pi$
$968$	1.73657e6	−	4.55258e6i	0.0595667	−	0.156160i
$969$	−4.22683e6			−0.144612
$970$	−1.91135e7	−	2.32064e7i	−0.652244	−	0.791913i
$971$			2.78585e7i			0.948221i	0.880465	+	0.474110i	$0.157230\pi$
$971$			2.78585e7i			0.948221i	−0.880465	+	0.474110i	$0.842770\pi$
$972$	5.66181e7	+	1.40320e7i	1.92216	+	0.476380i
$973$	−1.09528e7			−0.370888
$974$	−2.97278e7	−	3.62892e6i	−1.00407	−	0.122569i
$975$	355546.	+	7.08874e6i	0.0119780	+	0.238813i
$976$	−9.20176e6	+	1.74239e7i	−0.309205	+	0.585493i
$977$		−	1.73322e7i		−	0.580920i	−0.956887	−	0.290460i	$-0.906192\pi$
$977$		−	1.73322e7i		−	0.580920i	0.956887	−	0.290460i	$-0.0938084\pi$
$978$	−2.76073e6	+	2.26157e7i	−0.0922947	+	0.756071i
$979$		−	5.74135e7i		−	1.91451i
$980$	−382184.	−	599536.i	−0.0127118	−	0.0199411i
$981$		−	1.00644e8i		−	3.33900i
$982$	−3.13860e7	−	3.83134e6i	−1.03862	−	0.126786i
$983$		−	1.02000e7i		−	0.336681i	−0.985729	−	0.168340i	$-0.946159\pi$
$983$		−	1.02000e7i		−	0.336681i	0.985729	−	0.168340i	$-0.0538408\pi$
$984$	−8.28169e6	+	2.17112e7i	−0.272666	+	0.714819i
$985$	−4.86805e6	−	4.63000e6i	−0.159869	−	0.152051i
$986$	1.04437e6	−	8.55539e6i	0.0342107	−	0.280251i
$987$	−5.76146e7			−1.88252
$988$	59475.8	−	239980.i	0.00193842	−	0.00782138i
$989$		−	1.66992e7i		−	0.542881i
$990$	5.16395e7	+	6.26973e7i	1.67453	+	2.03311i
$991$	1.05292e7			0.340573			0.170286	−	0.985395i	$-0.445531\pi$
$991$	1.05292e7			0.340573			0.170286	+	0.985395i	$0.445531\pi$
$992$	1.42447e7	−	2.04963e7i	0.459592	−	0.661298i
$993$			9.39687e6i			0.302420i
$994$	−8.91733e6	−	1.08855e6i	−0.286265	−	0.0349448i
$995$	4.02733e7	+	3.83040e7i	1.28961	+	1.22655i
$996$	−3.47226e7	−	8.60551e6i	−1.10908	−	0.274871i
$997$	−4.69241e7			−1.49506			−0.747529	−	0.664229i	$-0.768760\pi$
$997$	−4.69241e7			−1.49506			−0.747529	+	0.664229i	$0.768760\pi$
$998$	−1.91185e7	−	2.33382e6i	−0.607613	−	0.0741722i
$999$	6.71435e7			2.12858

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.f.a.29.15	yes	28
4.3	odd	2		160.6.f.a.49.27		28
5.2	odd	4		200.6.d.e.101.28		28
5.3	odd	4		200.6.d.e.101.1		28
5.4	even	2	inner	40.6.f.a.29.14	yes	28
8.3	odd	2		160.6.f.a.49.1		28
8.5	even	2	inner	40.6.f.a.29.13	✓	28
20.3	even	4		800.6.d.e.401.6		28
20.7	even	4		800.6.d.e.401.23		28
20.19	odd	2		160.6.f.a.49.2		28
40.3	even	4		800.6.d.e.401.5		28
40.13	odd	4		200.6.d.e.101.2		28
40.19	odd	2		160.6.f.a.49.28		28
40.27	even	4		800.6.d.e.401.24		28
40.29	even	2	inner	40.6.f.a.29.16	yes	28
40.37	odd	4		200.6.d.e.101.27		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.13	✓	28	8.5	even	2	inner
40.6.f.a.29.14	yes	28	5.4	even	2	inner
40.6.f.a.29.15	yes	28	1.1	even	1	trivial
40.6.f.a.29.16	yes	28	40.29	even	2	inner
160.6.f.a.49.1		28	8.3	odd	2
160.6.f.a.49.2		28	20.19	odd	2
160.6.f.a.49.27		28	4.3	odd	2
160.6.f.a.49.28		28	40.19	odd	2
200.6.d.e.101.1		28	5.3	odd	4
200.6.d.e.101.2		28	40.13	odd	4
200.6.d.e.101.27		28	40.37	odd	4
200.6.d.e.101.28		28	5.2	odd	4
800.6.d.e.401.5		28	40.3	even	4
800.6.d.e.401.6		28	20.3	even	4
800.6.d.e.401.23		28	20.7	even	4
800.6.d.e.401.24		28	40.27	even	4

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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	40.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(0.685452 - 5.61517i) q^{2} -28.9041 q^{3} +(-31.0603 - 7.69787i) q^{4} +(40.5064 + 38.5257i) q^{5} +(-19.8124 + 162.302i) q^{6} -128.100i q^{7} +(-64.5152 + 169.132i) q^{8} +592.448 q^{9} +O(q^{10})\)	\(q+(0.685452 - 5.61517i) q^{2} -28.9041 q^{3} +(-31.0603 - 7.69787i) q^{4} +(40.5064 + 38.5257i) q^{5} +(-19.8124 + 162.302i) q^{6} -128.100i q^{7} +(-64.5152 + 169.132i) q^{8} +592.448 q^{9} +(244.094 - 201.043i) q^{10} +433.553i q^{11} +(897.771 + 222.500i) q^{12} -78.5787 q^{13} +(-719.302 - 87.8063i) q^{14} +(-1170.80 - 1113.55i) q^{15} +(905.486 + 478.196i) q^{16} +1487.27i q^{17} +(406.095 - 3326.70i) q^{18} -98.3252i q^{19} +(-961.577 - 1508.43i) q^{20} +3702.61i q^{21} +(2434.47 + 297.180i) q^{22} +2363.01i q^{23} +(1864.76 - 4888.63i) q^{24} +(156.542 + 3121.08i) q^{25} +(-53.8620 + 441.233i) q^{26} -10100.5 q^{27} +(-986.095 + 3978.82i) q^{28} -1024.44i q^{29} +(-7055.31 + 5810.97i) q^{30} +4308.96 q^{31} +(3305.82 - 4756.68i) q^{32} -12531.5i q^{33} +(8351.29 + 1019.45i) q^{34} +(4935.13 - 5188.86i) q^{35} +(-18401.6 - 4560.59i) q^{36} -6647.54 q^{37} +(-552.113 - 67.3973i) q^{38} +2271.25 q^{39} +(-9129.23 + 4365.46i) q^{40} -4441.16 q^{41} +(20790.8 + 2537.96i) q^{42} -7066.93 q^{43} +(3337.43 - 13466.3i) q^{44} +(23998.0 + 22824.5i) q^{45} +(13268.7 + 1619.73i) q^{46} +15560.5i q^{47} +(-26172.3 - 13821.8i) q^{48} +397.456 q^{49} +(17632.7 + 1260.34i) q^{50} -42988.3i q^{51} +(2440.68 + 604.888i) q^{52} +26793.6 q^{53} +(-6923.41 + 56716.0i) q^{54} +(-16702.9 + 17561.7i) q^{55} +(21665.8 + 8264.38i) q^{56} +2842.00i q^{57} +(-5752.40 - 702.205i) q^{58} +32902.0i q^{59} +(27793.5 + 43599.9i) q^{60} +19242.7i q^{61} +(2953.59 - 24195.6i) q^{62} -75892.5i q^{63} +(-24443.6 - 21823.2i) q^{64} +(-3182.94 - 3027.30i) q^{65} +(-70366.4 - 8589.73i) q^{66} +1066.77 q^{67} +(11448.8 - 46195.1i) q^{68} -68300.6i q^{69} +(-25753.6 - 31268.3i) q^{70} +12397.2 q^{71} +(-38221.9 + 100202. i) q^{72} +37248.9i q^{73} +(-4556.57 + 37327.1i) q^{74} +(-4524.72 - 90212.0i) q^{75} +(-756.894 + 3054.01i) q^{76} +55538.0 q^{77} +(1556.83 - 12753.5i) q^{78} -50784.5 q^{79} +(18255.2 + 54254.5i) q^{80} +147981. q^{81} +(-3044.21 + 24937.9i) q^{82} -38676.4 q^{83} +(28502.2 - 115004. i) q^{84} +(-57298.2 + 60244.1i) q^{85} +(-4844.04 + 39682.0i) q^{86} +29610.5i q^{87} +(-73327.9 - 27970.8i) q^{88} -132425. q^{89} +(144613. - 119108. i) q^{90} +10065.9i q^{91} +(18190.1 - 73395.7i) q^{92} -124547. q^{93} +(87375.1 + 10666.0i) q^{94} +(3788.05 - 3982.80i) q^{95} +(-95551.9 + 137488. i) q^{96} -95071.6i q^{97} +(272.437 - 2231.78i) q^{98} +256858. i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9}+O(q^{10}) \) 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9	\( 28 q - 12 q^{4} - 156 q^{6} + 1940 q^{9} - 16 q^{10} - 692 q^{14} - 488 q^{15} + 1560 q^{16} + 2732 q^{20} - 2224 q^{24} + 1556 q^{25} - 9976 q^{26} - 15012 q^{30} + 4368 q^{31} + 13016 q^{34} - 34116 q^{36} + 23360 q^{39} - 22496 q^{40} - 2480 q^{41} + 10712 q^{44} + 58372 q^{46} - 38420 q^{49} + 45624 q^{50} - 3568 q^{54} - 48776 q^{55} + 110944 q^{56} + 111688 q^{60} - 46944 q^{64} + 37200 q^{65} - 136120 q^{66} - 112852 q^{70} - 69232 q^{71} + 34176 q^{74} - 13944 q^{76} - 35984 q^{79} - 47064 q^{80} + 122596 q^{81} - 165688 q^{84} - 73676 q^{86} - 178744 q^{89} + 51496 q^{90} + 314740 q^{94} + 89416 q^{95} - 236176 q^{96}+O(q^{100}) \) 28 * q - 12 * q^4 - 156 * q^6 + 1940 * q^9 - 16 * q^10 - 692 * q^14 - 488 * q^15 + 1560 * q^16 + 2732 * q^20 - 2224 * q^24 + 1556 * q^25 - 9976 * q^26 - 15012 * q^30 + 4368 * q^31 + 13016 * q^34 - 34116 * q^36 + 23360 * q^39 - 22496 * q^40 - 2480 * q^41 + 10712 * q^44 + 58372 * q^46 - 38420 * q^49 + 45624 * q^50 - 3568 * q^54 - 48776 * q^55 + 110944 * q^56 + 111688 * q^60 - 46944 * q^64 + 37200 * q^65 - 136120 * q^66 - 112852 * q^70 - 69232 * q^71 + 34176 * q^74 - 13944 * q^76 - 35984 * q^79 - 47064 * q^80 + 122596 * q^81 - 165688 * q^84 - 73676 * q^86 - 178744 * q^89 + 51496 * q^90 + 314740 * q^94 + 89416 * q^95 - 236176 * q^96

Introduction

L-functions

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