LMFDB - Embedded newform 40.6.f.a.29.4

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			29.4
Character	$\chi$	$=$	40.29
Dual form			40.6.f.a.29.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-5.32791 + 1.90088i) q^{2} +21.6833 q^{3} +(24.7733 - 20.2555i) q^{4} +(36.8367 + 42.0483i) q^{5} +(-115.527 + 41.2175i) q^{6} -236.448i q^{7} +(-93.4865 + 155.011i) q^{8} +227.167 q^{9} +O(q^{10})$	\(q+(-5.32791 + 1.90088i) q^{2} +21.6833 q^{3} +(24.7733 - 20.2555i) q^{4} +(36.8367 + 42.0483i) q^{5} +(-115.527 + 41.2175i) q^{6} -236.448i q^{7} +(-93.4865 + 155.011i) q^{8} +227.167 q^{9} +(-276.192 - 154.007i) q^{10} +192.686i q^{11} +(537.167 - 439.206i) q^{12} +975.206 q^{13} +(449.461 + 1259.78i) q^{14} +(798.742 + 911.747i) q^{15} +(203.430 - 1003.59i) q^{16} +670.908i q^{17} +(-1210.32 + 431.818i) q^{18} +456.924i q^{19} +(1764.27 + 295.529i) q^{20} -5126.98i q^{21} +(-366.273 - 1026.61i) q^{22} -2029.03i q^{23} +(-2027.10 + 3361.15i) q^{24} +(-411.118 + 3097.84i) q^{25} +(-5195.81 + 1853.75i) q^{26} -343.317 q^{27} +(-4789.37 - 5857.60i) q^{28} +2782.43i q^{29} +(-5988.75 - 3339.39i) q^{30} -963.333 q^{31} +(823.849 + 5733.73i) q^{32} +4178.07i q^{33} +(-1275.32 - 3574.54i) q^{34} +(9942.24 - 8709.97i) q^{35} +(5627.67 - 4601.37i) q^{36} -8727.50 q^{37} +(-868.560 - 2434.45i) q^{38} +21145.7 q^{39} +(-9961.66 + 1779.13i) q^{40} -1812.39 q^{41} +(9745.80 + 27316.1i) q^{42} +254.225 q^{43} +(3902.94 + 4773.46i) q^{44} +(8368.07 + 9551.98i) q^{45} +(3856.96 + 10810.5i) q^{46} -19737.7i q^{47} +(4411.05 - 21761.2i) q^{48} -39100.7 q^{49} +(-3698.23 - 17286.5i) q^{50} +14547.5i q^{51} +(24159.0 - 19753.3i) q^{52} -23002.2 q^{53} +(1829.16 - 652.606i) q^{54} +(-8102.10 + 7097.90i) q^{55} +(36652.0 + 22104.7i) q^{56} +9907.64i q^{57} +(-5289.09 - 14824.6i) q^{58} +24661.0i q^{59} +(38255.3 + 6408.05i) q^{60} +189.904i q^{61} +(5132.55 - 1831.18i) q^{62} -53713.2i q^{63} +(-15288.6 - 28982.8i) q^{64} +(35923.3 + 41005.7i) q^{65} +(-7942.02 - 22260.4i) q^{66} -24912.8 q^{67} +(13589.6 + 16620.6i) q^{68} -43996.2i q^{69} +(-36414.7 + 65305.0i) q^{70} -38239.7 q^{71} +(-21237.0 + 35213.3i) q^{72} -44775.5i q^{73} +(46499.4 - 16590.0i) q^{74} +(-8914.41 + 67171.5i) q^{75} +(9255.22 + 11319.5i) q^{76} +45560.2 q^{77} +(-112662. + 40195.5i) q^{78} +69761.6 q^{79} +(49692.9 - 28415.0i) q^{80} -62645.8 q^{81} +(9656.28 - 3445.15i) q^{82} -4339.15 q^{83} +(-103850. - 127012. i) q^{84} +(-28210.5 + 24714.0i) q^{85} +(-1354.49 + 483.253i) q^{86} +60332.4i q^{87} +(-29868.3 - 18013.5i) q^{88} -5562.17 q^{89} +(-62741.5 - 34985.3i) q^{90} -230586. i q^{91} +(-41099.1 - 50265.8i) q^{92} -20888.3 q^{93} +(37519.0 + 105161. i) q^{94} +(-19212.9 + 16831.6i) q^{95} +(17863.8 + 124326. i) q^{96} +98102.9i q^{97} +(208325. - 74326.0i) q^{98} +43771.8i 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 $

$2$	−5.32791	+	1.90088i	−0.941851	+	0.336032i
$2$	−5.32791	+	1.90088i	−0.941851	+	0.336032i
$3$	21.6833			1.39099			0.695493	−	0.718533i	$-0.255186\pi$
$3$	21.6833			1.39099			0.695493	+	0.718533i	$0.255186\pi$
$4$	24.7733	−	20.2555i	0.774165	−	0.632984i
$5$	36.8367	+	42.0483i	0.658955	+	0.752183i
$5$	36.8367	+	42.0483i	0.658955	+	0.752183i
$6$	−115.527	+	41.2175i	−1.31010	+	0.467416i
$7$		−	236.448i		−	1.82386i	−0.410349	−	0.911929i	$-0.634593\pi$
$7$		−	236.448i		−	1.82386i	0.410349	−	0.911929i	$-0.365407\pi$
$8$	−93.4865	+	155.011i	−0.516445	+	0.856321i
$9$	227.167			0.934843
$10$	−276.192	−	154.007i	−0.873394	−	0.487014i
$11$			192.686i			0.480140i	0.970756	+	0.240070i	$0.0771704\pi$
$11$			192.686i			0.480140i	−0.970756	+	0.240070i	$0.922830\pi$
$12$	537.167	−	439.206i	1.07685	−	0.880472i
$13$	975.206			1.60043			0.800217	−	0.599710i	$-0.204718\pi$
$13$	975.206			1.60043			0.800217	+	0.599710i	$0.204718\pi$
$14$	449.461	+	1259.78i	0.612875	+	1.71780i
$15$	798.742	+	911.747i	0.916597	+	1.04628i
$16$	203.430	−	1003.59i	0.198663	−	0.980068i
$17$			670.908i			0.563042i	0.959555	+	0.281521i	$0.0908388\pi$
$17$			670.908i			0.563042i	−0.959555	+	0.281521i	$0.909161\pi$
$18$	−1210.32	+	431.818i	−0.880482	+	0.314137i
$19$			456.924i			0.290376i	0.989404	+	0.145188i	$0.0463786\pi$
$19$			456.924i			0.290376i	−0.989404	+	0.145188i	$0.953621\pi$
$20$	1764.27	+	295.529i	0.986259	+	0.165206i
$21$		−	5126.98i		−	2.53696i
$22$	−366.273	−	1026.61i	−0.161342	−	0.452220i
$23$		−	2029.03i		−	0.799778i	−0.916564	−	0.399889i	$-0.869049\pi$
$23$		−	2029.03i		−	0.799778i	0.916564	−	0.399889i	$-0.130951\pi$
$24$	−2027.10	+	3361.15i	−0.718367	+	1.19113i
$25$	−411.118	+	3097.84i	−0.131558	+	0.991309i
$26$	−5195.81	+	1853.75i	−1.50737	+	0.537797i
$27$	−343.317			−0.0906329
$28$	−4789.37	−	5857.60i	−1.15447	−	1.41197i
$29$			2782.43i			0.614370i	0.951650	+	0.307185i	$0.0993870\pi$
$29$			2782.43i			0.614370i	−0.951650	+	0.307185i	$0.900613\pi$
$30$	−5988.75	−	3339.39i	−1.21488	−	0.677430i
$31$	−963.333			−0.180041			−0.0900207	−	0.995940i	$-0.528693\pi$
$31$	−963.333			−0.180041			−0.0900207	+	0.995940i	$0.528693\pi$
$32$	823.849	+	5733.73i	0.142224	+	0.989835i
$33$			4178.07i			0.667868i
$34$	−1275.32	−	3574.54i	−0.189200	−	0.530301i
$35$	9942.24	−	8709.97i	1.37187	−	1.20184i
$36$	5627.67	−	4601.37i	0.723722	−	0.591740i
$37$	−8727.50			−1.04806			−0.524030	−	0.851700i	$-0.675572\pi$
$37$	−8727.50			−1.04806			−0.524030	+	0.851700i	$0.675572\pi$
$38$	−868.560	−	2434.45i	−0.0975755	−	0.273490i
$39$	21145.7			2.22618
$40$	−9961.66	+	1779.13i	−0.984423	+	0.175816i
$41$	−1812.39			−0.168381			−0.0841905	−	0.996450i	$-0.526830\pi$
$41$	−1812.39			−0.168381			−0.0841905	+	0.996450i	$0.526830\pi$
$42$	9745.80	+	27316.1i	0.852500	+	2.38944i
$43$	254.225			0.0209675			0.0104838	−	0.999945i	$-0.496663\pi$
$43$	254.225			0.0209675			0.0104838	+	0.999945i	$0.496663\pi$
$44$	3902.94	+	4773.46i	0.303921	+	0.371707i
$45$	8368.07	+	9551.98i	0.616019	+	0.703173i
$46$	3856.96	+	10810.5i	0.268751	+	0.753272i
$47$		−	19737.7i		−	1.30332i	−0.758511	−	0.651660i	$-0.774073\pi$
$47$		−	19737.7i		−	1.30332i	0.758511	−	0.651660i	$-0.225927\pi$
$48$	4411.05	−	21761.2i	0.276337	−	1.36326i
$49$	−39100.7			−2.32646
$50$	−3698.23	−	17286.5i	−0.209204	−	0.977872i
$51$			14547.5i			0.783183i
$52$	24159.0	−	19753.3i	1.23900	−	1.01305i
$53$	−23002.2			−1.12481			−0.562405	−	0.826862i	$-0.690124\pi$
$53$	−23002.2			−1.12481			−0.562405	+	0.826862i	$0.690124\pi$
$54$	1829.16	−	652.606i	0.0853626	−	0.0304556i
$55$	−8102.10	+	7097.90i	−0.361153	+	0.316390i
$56$	36652.0	+	22104.7i	1.56181	+	0.941922i
$57$			9907.64i			0.403908i
$58$	−5289.09	−	14824.6i	−0.206448	−	0.578645i
$59$			24661.0i			0.922319i	0.887317	+	0.461159i	$0.152566\pi$
$59$			24661.0i			0.922319i	−0.887317	+	0.461159i	$0.847434\pi$
$60$	38255.3	+	6408.05i	1.37187	+	0.229799i
$61$			189.904i			0.00653447i	0.999995	+	0.00326723i	$0.00103999\pi$
$61$			189.904i			0.00653447i	−0.999995	+	0.00326723i	$0.998960\pi$
$62$	5132.55	−	1831.18i	0.169572	−	0.0604997i
$63$		−	53713.2i		−	1.70502i
$64$	−15288.6	−	28982.8i	−0.466570	−	0.884484i
$65$	35923.3	+	41005.7i	1.05461	+	1.20382i
$66$	−7942.02	−	22260.4i	−0.224425	−	0.629032i
$67$	−24912.8			−0.678010			−0.339005	−	0.940785i	$-0.610090\pi$
$67$	−24912.8			−0.678010			−0.339005	+	0.940785i	$0.610090\pi$
$68$	13589.6	+	16620.6i	0.356396	+	0.435887i
$69$		−	43996.2i		−	1.11248i
$70$	−36414.7	+	65305.0i	−0.888244	+	1.59295i
$71$	−38239.7			−0.900262			−0.450131	−	0.892963i	$-0.648623\pi$
$71$	−38239.7			−0.900262			−0.450131	+	0.892963i	$0.648623\pi$
$72$	−21237.0	+	35213.3i	−0.482795	+	0.800525i
$73$		−	44775.5i		−	0.983407i	−0.870763	−	0.491704i	$-0.836374\pi$
$73$		−	44775.5i		−	0.983407i	0.870763	−	0.491704i	$-0.163626\pi$
$74$	46499.4	−	16590.0i	0.987115	−	0.352181i
$75$	−8914.41	+	67171.5i	−0.182995	+	1.37890i
$76$	9255.22	+	11319.5i	0.183803	+	0.224799i
$77$	45560.2			0.875707
$78$	−112662.	+	40195.5i	−2.09673	+	0.748069i
$79$	69761.6			1.25762			0.628809	−	0.777560i	$-0.283543\pi$
$79$	69761.6			1.25762			0.628809	+	0.777560i	$0.283543\pi$
$80$	49692.9	−	28415.0i	0.868100	−	0.496390i
$81$	−62645.8			−1.06091
$82$	9656.28	−	3445.15i	0.158590	−	0.0565814i
$83$	−4339.15			−0.0691368			−0.0345684	−	0.999402i	$-0.511006\pi$
$83$	−4339.15			−0.0691368			−0.0345684	+	0.999402i	$0.511006\pi$
$84$	−103850.	−	127012.i	−1.60586	−	1.96403i
$85$	−28210.5	+	24714.0i	−0.423510	+	0.371019i
$86$	−1354.49	+	483.253i	−0.0197483	+	0.00704577i
$87$			60332.4i			0.854580i
$88$	−29868.3	−	18013.5i	−0.411154	−	0.247966i
$89$	−5562.17			−0.0744336			−0.0372168	−	0.999307i	$-0.511849\pi$
$89$	−5562.17			−0.0744336			−0.0372168	+	0.999307i	$0.511849\pi$
$90$	−62741.5	−	34985.3i	−0.816486	−	0.455281i
$91$		−	230586.i		−	2.91896i
$92$	−41099.1	−	50265.8i	−0.506247	−	0.619160i
$93$	−20888.3			−0.250435
$94$	37519.0	+	105161.i	0.437958	+	1.22753i
$95$	−19212.9	+	16831.6i	−0.218415	+	0.191344i
$96$	17863.8	+	124326.i	0.197831	+	1.37685i
$97$			98102.9i			1.05865i	0.848419	+	0.529325i	$0.177555\pi$
$97$			98102.9i			1.05865i	−0.848419	+	0.529325i	$0.822445\pi$
$98$	208325.	−	74326.0i	2.19117	−	0.781764i
$99$			43771.8i			0.448855i
$100$	52563.5	+	85071.0i	0.525635	+	0.850710i
$101$			19871.5i			0.193833i	0.995293	+	0.0969163i	$0.0308979\pi$
$101$			19871.5i			0.193833i	−0.995293	+	0.0969163i	$0.969102\pi$
$102$	−27653.1	−	77507.9i	−0.263175	−	0.737641i
$103$			120201.i			1.11639i	0.829711	+	0.558194i	$0.188505\pi$
$103$			120201.i			1.11639i	−0.829711	+	0.558194i	$0.811495\pi$
$104$	−91168.5	+	151167.i	−0.826536	+	1.37048i
$105$	215581.	−	188861.i	1.90826	−	1.67174i
$106$	122554.	−	43724.5i	1.05940	−	0.377972i
$107$	125007.			1.05554			0.527769	−	0.849388i	$-0.323029\pi$
$107$	125007.			1.05554			0.527769	+	0.849388i	$0.323029\pi$
$108$	−8505.09	+	6954.05i	−0.0701648	+	0.0573692i
$109$			31222.3i			0.251709i	0.992049	+	0.125854i	$0.0401672\pi$
$109$			31222.3i			0.251709i	−0.992049	+	0.125854i	$0.959833\pi$
$110$	29675.0	−	53218.1i	0.233835	−	0.419351i
$111$	−189241.			−1.45784
$112$	−237297.	−	48100.8i	−1.78750	−	0.362332i
$113$		−	18028.4i		−	0.132819i	−0.997792	−	0.0664097i	$-0.978846\pi$
$113$		−	18028.4i		−	0.132819i	0.997792	−	0.0664097i	$-0.0211544\pi$
$114$	−18833.3	−	52787.0i	−0.135726	−	0.380421i
$115$	85317.4	−	74742.9i	0.601579	−	0.527018i
$116$	56359.6	+	68930.0i	0.388886	+	0.475624i
$117$	221534.			1.49615
$118$	−46877.8	−	131392.i	−0.309929	−	0.868686i
$119$	158635.			1.02691
$120$	−216002.	+	38577.4i	−1.36932	+	0.244557i
$121$	123923.			0.769466
$122$	−360.986	−	1011.79i	−0.00219579	−	0.00615449i
$123$	−39298.7			−0.234216
$124$	−23864.9	+	19512.8i	−0.139382	+	0.113963i
$125$	−145403.	+	96827.3i	−0.832336	+	0.554272i
$126$	102103.	+	286179.i	0.572941	+	1.60587i
$127$			66022.6i			0.363231i	0.983370	+	0.181616i	$0.0581326\pi$
$127$			66022.6i			0.363231i	−0.983370	+	0.181616i	$0.941867\pi$
$128$	136549.	+	125356.i	0.736654	+	0.676270i
$129$	5512.45			0.0291656
$130$	−269344.	−	150189.i	−1.39781	−	0.779434i
$131$			147752.i			0.752238i	0.926571	+	0.376119i	$0.122742\pi$
$131$			147752.i			0.752238i	−0.926571	+	0.376119i	$0.877258\pi$
$132$	84628.8	+	103504.i	0.422750	+	0.517040i
$133$	108039.			0.529604
$134$	132733.	−	47356.4i	0.638584	−	0.227833i
$135$	−12646.7	−	14435.9i	−0.0597230	−	0.0681725i
$136$	−103998.	−	62720.8i	−0.482144	−	0.290780i
$137$		−	357827.i		−	1.62881i	−0.580295	−	0.814406i	$-0.697063\pi$
$137$		−	357827.i		−	1.62881i	0.580295	−	0.814406i	$-0.302937\pi$
$138$	83631.7	+	234408.i	0.373829	+	1.04779i
$139$			49329.3i			0.216555i	0.994121	+	0.108277i	$0.0345335\pi$
$139$			49329.3i			0.216555i	−0.994121	+	0.108277i	$0.965467\pi$
$140$	69877.3	−	417159.i	0.301312	−	1.79880i
$141$		−	427979.i		−	1.81290i
$142$	203738.	−	72689.3i	0.847912	−	0.302517i
$143$			187908.i			0.768432i
$144$	46212.6	−	227982.i	0.185718	−	0.916209i
$145$	−116997.	+	102496.i	−0.462118	+	0.404842i
$146$	85113.1	+	238560.i	0.330456	+	0.926223i
$147$	−847834.			−3.23607
$148$	−216209.	+	176780.i	−0.811370	+	0.663405i
$149$			310847.i			1.14705i	0.819189	+	0.573524i	$0.194424\pi$
$149$			310847.i			1.14705i	−0.819189	+	0.573524i	$0.805576\pi$
$150$	−80190.0	−	374829.i	−0.291000	−	1.36021i
$151$	−367611.			−1.31204			−0.656019	−	0.754744i	$-0.727761\pi$
$151$	−367611.			−1.31204			−0.656019	+	0.754744i	$0.727761\pi$
$152$	−70828.1	−	42716.2i	−0.248655	−	0.149963i
$153$			152408.i			0.526355i
$154$	−242741.	+	86604.6i	−0.824785	+	0.294266i
$155$	−35486.0	−	40506.5i	−0.118639	−	0.135424i
$156$	523848.	−	428317.i	1.72343	−	1.40914i
$157$	−51468.7			−0.166646			−0.0833228	−	0.996523i	$-0.526553\pi$
$157$	−51468.7			−0.166646			−0.0833228	+	0.996523i	$0.526553\pi$
$158$	−371684.	+	132609.i	−1.18449	+	0.422600i
$159$	−498764.			−1.56459
$160$	−210746.	+	245853.i	−0.650817	+	0.759234i
$161$	−479761.			−1.45868
$162$	333771.	−	119082.i	0.999220	−	0.356500i
$163$	471607.			1.39031			0.695155	−	0.718860i	$-0.255336\pi$
$163$	471607.			1.39031			0.695155	+	0.718860i	$0.255336\pi$
$164$	−44898.9	+	36710.9i	−0.130355	+	0.106582i
$165$	−175681.	+	153906.i	−0.502359	+	0.440095i
$166$	23118.6	−	8248.21i	0.0651165	−	0.0232322i
$167$		−	644743.i		−	1.78894i	−0.447130	−	0.894469i	$-0.647554\pi$
$167$		−	644743.i		−	1.78894i	0.447130	−	0.894469i	$-0.352446\pi$
$168$	794737.	+	479304.i	2.17245	+	1.31020i
$169$	579733.			1.56139
$170$	103325.	−	185299.i	0.274209	−	0.491757i
$171$			103798.i			0.271455i
$172$	6297.99	−	5149.46i	0.0162323	−	0.0132721i
$173$	−162302.			−0.412295			−0.206147	−	0.978521i	$-0.566093\pi$
$173$	−162302.			−0.412295			−0.206147	+	0.978521i	$0.566093\pi$
$174$	−114685.	−	321446.i	−0.287166	−	0.804887i
$175$	732478.	+	97208.1i	1.80801	+	0.239943i
$176$	193377.	+	39198.1i	0.470570	+	0.0953858i
$177$			534733.i			1.28293i
$178$	29634.8	−	10573.0i	0.0701054	−	0.0250121i
$179$		−	74777.3i		−	0.174436i	−0.996189	−	0.0872182i	$-0.972202\pi$
$179$		−	74777.3i		−	0.174436i	0.996189	−	0.0872182i	$-0.0277977\pi$
$180$	400784.	+	67134.4i	0.921997	+	0.154441i
$181$		−	69208.2i		−	0.157022i	−0.996913	−	0.0785111i	$-0.974983\pi$
$181$		−	69208.2i		−	0.157022i	0.996913	−	0.0785111i	$-0.0250166\pi$
$182$	438317.	+	1.22854e6i	0.980866	+	2.74923i
$183$			4117.76i			0.00908935i
$184$	314522.	+	189687.i	0.684867	+	0.413041i
$185$	−321492.	−	366977.i	−0.690623	−	0.788332i
$186$	111291.	−	39706.2i	0.235872	−	0.0841542i
$187$	−129274.			−0.270339
$188$	−399796.	−	488967.i	−0.824981	−	1.00899i
$189$			81176.7i			0.165301i
$190$	70369.6	−	126199.i	0.141417	−	0.253612i
$191$	712525.			1.41324			0.706621	−	0.707592i	$-0.250218\pi$
$191$	712525.			1.41324			0.706621	+	0.707592i	$0.250218\pi$
$192$	−331507.	−	628443.i	−0.648992	−	1.23031i
$193$		−	191610.i		−	0.370276i	−0.982713	−	0.185138i	$-0.940727\pi$
$193$		−	191610.i		−	0.370276i	0.982713	−	0.185138i	$-0.0592732\pi$
$194$	−186482.	−	522684.i	−0.355741	−	0.997091i
$195$	778938.	+	889141.i	1.46695	+	1.67450i
$196$	−968654.	+	792005.i	−1.80106	+	1.47261i
$197$	447522.			0.821578			0.410789	−	0.911730i	$-0.365253\pi$
$197$	447522.			0.821578			0.410789	+	0.911730i	$0.365253\pi$
$198$	−83205.1	−	233212.i	−0.150830	−	0.422755i
$199$	116939.			0.209328			0.104664	−	0.994508i	$-0.466623\pi$
$199$	116939.			0.209328			0.104664	+	0.994508i	$0.466623\pi$
$200$	−441764.	−	353334.i	−0.780936	−	0.624612i
$201$	−540193.			−0.943103
$202$	−37773.4	−	105874.i	−0.0651340	−	0.182561i
$203$	657902.			1.12052
$204$	294667.	+	360390.i	0.495742	+	0.606313i
$205$	−66762.6	−	76208.1i	−0.110955	−	0.126653i
$206$	−228488.	−	640420.i	−0.375142	−	1.05147i
$207$		−	460929.i		−	0.747667i
$208$	198387.	−	978706.i	0.317946	−	1.56853i
$209$	−88042.7			−0.139421
$210$	−789593.	+	1.41603e6i	−1.23553	+	2.21577i
$211$		−	669883.i		−	1.03584i	−0.855429	−	0.517920i	$-0.826706\pi$
$211$		−	669883.i		−	1.03584i	0.855429	−	0.517920i	$-0.173294\pi$
$212$	−569839.	+	465920.i	−0.870788	+	0.711987i
$213$	−829164.			−1.25225
$214$	−666024.	+	237623.i	−0.994159	+	0.354694i
$215$	9364.81	+	10689.7i	0.0138167	+	0.0157714i
$216$	32095.5	−	53217.8i	0.0468069	−	0.0776108i
$217$			227778.i			0.328370i
$218$	−59350.0	−	166350.i	−0.0845822	−	0.237072i
$219$		−	970882.i		−	1.36791i
$220$	−56944.2	+	339950.i	−0.0793219	+	0.473542i
$221$			654273.i			0.901111i
$222$	1.00826e6	−	359726.i	1.37306	−	0.489880i
$223$			1718.93i			0.00231470i	0.999999	+	0.00115735i	$0.000368396\pi$
$223$			1718.93i			0.00231470i	−0.999999	+	0.00115735i	$0.999632\pi$
$224$	1.35573e6	−	194798.i	1.80532	−	0.259396i
$225$	−93392.3	+	703726.i	−0.122986	+	0.926718i
$226$	34269.9	+	96053.8i	0.0446316	+	0.125096i
$227$	−713312.			−0.918787			−0.459393	−	0.888233i	$-0.651933\pi$
$227$	−713312.			−0.918787			−0.459393	+	0.888233i	$0.651933\pi$
$228$	200684.	+	245445.i	0.255668	+	0.312692i
$229$		−	1.17021e6i		−	1.47461i	−0.675561	−	0.737304i	$-0.736098\pi$
$229$		−	1.17021e6i		−	1.47461i	0.675561	−	0.737304i	$-0.263902\pi$
$230$	−312486.	+	560402.i	−0.389503	+	0.698522i
$231$	987896.			1.21810
$232$	−431307.	−	260120.i	−0.526098	−	0.317288i
$233$			1.52755e6i			1.84334i	0.387976	+	0.921669i	$0.373174\pi$
$233$			1.52755e6i			1.84334i	−0.387976	+	0.921669i	$0.626826\pi$
$234$	−1.18032e6	+	421111.i	−1.40915	+	0.502756i
$235$	829936.	−	727070.i	0.980335	−	0.858829i
$236$	499521.	+	610934.i	0.583813	+	0.714027i
$237$	1.51266e6			1.74933
$238$	−845193.	+	301547.i	−0.967193	+	0.345074i
$239$	−567244.			−0.642355			−0.321178	−	0.947019i	$-0.604079\pi$
$239$	−567244.			−0.642355			−0.321178	+	0.947019i	$0.604079\pi$
$240$	1.07751e6	−	616132.i	1.20751	−	0.690471i
$241$	688312.			0.763383			0.381692	−	0.924290i	$-0.375342\pi$
$241$	688312.			0.763383			0.381692	+	0.924290i	$0.375342\pi$
$242$	−660252.	+	235564.i	−0.724722	+	0.258565i
$243$	−1.27494e6			−1.38508
$244$	3846.60	+	4704.55i	0.00413621	+	0.00505875i
$245$	−1.44034e6	−	1.64412e6i	−1.53303	−	1.74992i
$246$	209380.	−	74702.4i	0.220596	−	0.0787040i
$247$			445595.i			0.464727i
$248$	90058.6	−	149327.i	0.0929814	−	0.154173i
$249$	−94087.1			−0.0961683
$250$	590637.	−	792282.i	0.597683	−	0.801733i
$251$			663210.i			0.664457i	0.943199	+	0.332229i	$0.107801\pi$
$251$			663210.i			0.664457i	−0.943199	+	0.332229i	$0.892199\pi$
$252$	−1.08799e6	−	1.33065e6i	−1.07925	−	1.31997i
$253$	390966.			0.384005
$254$	−125501.	−	351762.i	−0.122057	−	0.342109i
$255$	−611698.	+	535882.i	−0.589097	+	0.516082i
$256$	−965808.	−	408321.i	−0.921066	−	0.389406i
$257$			1.68030e6i			1.58691i	0.608628	+	0.793456i	$0.291720\pi$
$257$			1.68030e6i			1.58691i	−0.608628	+	0.793456i	$0.708280\pi$
$258$	−29369.8	+	10478.5i	−0.0274696	+	0.00980056i
$259$			2.06360e6i			1.91151i
$260$	1.72053e6	+	288202.i	1.57844	+	0.264401i
$261$			632077.i			0.574339i
$262$	−280859.	−	787210.i	−0.252776	−	0.708496i
$263$		−	1.66101e6i		−	1.48075i	−0.672194	−	0.740375i	$-0.734648\pi$
$263$		−	1.66101e6i		−	1.48075i	0.672194	−	0.740375i	$-0.265352\pi$
$264$	−647645.	−	390593.i	−0.571909	−	0.344917i
$265$	−847323.	−	967202.i	−0.741199	−	0.846063i
$266$	−575622.	+	205369.i	−0.498807	+	0.177964i
$267$	−120606.			−0.103536
$268$	−617173.	+	504622.i	−0.524892	+	0.429170i
$269$			686913.i			0.578790i	0.957210	+	0.289395i	$0.0934541\pi$
$269$			686913.i			0.578790i	−0.957210	+	0.289395i	$0.906546\pi$
$270$	94821.2	+	52873.3i	0.0791583	+	0.0441395i
$271$	237762.			0.196662			0.0983309	−	0.995154i	$-0.468650\pi$
$271$	237762.			0.196662			0.0983309	+	0.995154i	$0.468650\pi$
$272$	673316.	+	136483.i	0.551819	+	0.111855i
$273$		−	4.99986e6i		−	4.06024i
$274$	680187.	+	1.90647e6i	0.547333	+	1.53410i
$275$	−596909.	−	79216.5i	−0.475967	−	0.0631661i
$276$	−891164.	−	1.08993e6i	−0.704182	−	0.861243i
$277$	2.37393e6			1.85895			0.929475	−	0.368886i	$-0.120261\pi$
$277$	2.37393e6			1.85895			0.929475	+	0.368886i	$0.120261\pi$
$278$	−93769.3	−	262822.i	−0.0727693	−	0.203962i
$279$	−218837.			−0.168310
$280$	420672.	+	2.35542e6i	0.320663	+	1.79545i
$281$	726368.			0.548771			0.274386	−	0.961620i	$-0.411526\pi$
$281$	726368.			0.548771			0.274386	+	0.961620i	$0.411526\pi$
$282$	813538.	+	2.28023e6i	0.609193	+	1.70748i
$283$	1.05205e6			0.780853			0.390427	−	0.920634i	$-0.372328\pi$
$283$	1.05205e6			0.780853			0.390427	+	0.920634i	$0.372328\pi$
$284$	−947323.	+	774564.i	−0.696951	+	0.569851i
$285$	−416599.	+	364964.i	−0.303813	+	0.266157i
$286$	−357192.	−	1.00116e6i	−0.258218	−	0.723748i
$287$			428537.i			0.307103i
$288$	187151.	+	1.30251e6i	0.132957	+	0.925340i
$289$	969740.			0.682984
$290$	428515.	−	768485.i	0.299207	−	0.536587i
$291$			2.12720e6i			1.47257i
$292$	−906950.	−	1.10924e6i	−0.622481	−	0.761319i
$293$	−1.54163e6			−1.04909			−0.524544	−	0.851383i	$-0.675764\pi$
$293$	−1.54163e6			−1.04909			−0.524544	+	0.851383i	$0.675764\pi$
$294$	4.51719e6	−	1.61164e6i	3.04789	−	1.08742i
$295$	−1.03695e6	+	908430.i	−0.693752	+	0.607766i
$296$	815904.	−	1.35286e6i	0.541265	−	0.897474i
$297$		−	66152.3i		−	0.0435165i
$298$	−590885.	−	1.65617e6i	−0.385445	−	1.08035i
$299$		−	1.97872e6i		−	1.27999i
$300$	1.13975e6	+	1.84462e6i	0.731151	+	1.18333i
$301$		−	60111.1i		−	0.0382418i
$302$	1.95860e6	−	698786.i	1.23574	−	0.440887i
$303$			430880.i			0.269619i
$304$	458564.	+	92952.3i	0.284588	+	0.0576867i
$305$	−7985.15	+	6995.44i	−0.00491511	+	0.00430592i
$306$	−289710.	−	812016.i	−0.176872	−	0.495748i
$307$	−2.21416e6			−1.34080			−0.670398	−	0.742002i	$-0.733877\pi$
$307$	−2.21416e6			−1.34080			−0.670398	+	0.742002i	$0.733877\pi$
$308$	1.12867e6	−	922844.i	0.677941	−	0.554308i
$309$			2.60636e6i			1.55288i
$310$	266064.	+	148360.i	0.157247	+	0.0876826i
$311$	−1.53824e6			−0.901827			−0.450913	−	0.892568i	$-0.648902\pi$
$311$	−1.53824e6			−0.901827			−0.450913	+	0.892568i	$0.648902\pi$
$312$	−1.97684e6	+	3.27781e6i	−1.14970	+	1.90633i
$313$			2.33683e6i			1.34824i	0.738622	+	0.674120i	$0.235477\pi$
$313$			2.33683e6i			1.34824i	−0.738622	+	0.674120i	$0.764523\pi$
$314$	274221.	−	97836.0i	0.156955	−	0.0559983i
$315$	2.25855e6	−	1.97862e6i	1.28249	−	1.12353i
$316$	1.72822e6	−	1.41306e6i	0.973604	−	0.796052i
$317$	−1.15261e6			−0.644220			−0.322110	−	0.946702i	$-0.604392\pi$
$317$	−1.15261e6			−0.644220			−0.322110	+	0.946702i	$0.604392\pi$
$318$	2.65737e6	−	948092.i	1.47361	−	0.525754i
$319$	−536135.			−0.294983
$320$	655497.	−	1.71049e6i	0.357846	−	0.933781i
$321$	2.71056e6			1.46824
$322$	2.55613e6	−	911971.i	1.37386	−	0.490164i
$323$	−306554.			−0.163494
$324$	−1.55194e6	+	1.26892e6i	−0.821321	+	0.671540i
$325$	−400925.	+	3.02103e6i	−0.210550	+	1.58652i
$326$	−2.51268e6	+	896471.i	−1.30946	+	0.467189i
$327$			677003.i			0.350123i
$328$	169434.	−	280940.i	0.0869595	−	0.144188i
$329$	−4.66694e6			−2.37707
$330$	643453.	−	1.15395e6i	0.325261	−	0.583312i
$331$		−	2.04520e6i		−	1.02604i	−0.858376	−	0.513022i	$-0.828526\pi$
$331$		−	2.04520e6i		−	1.02604i	0.858376	−	0.513022i	$-0.171474\pi$
$332$	−107495.	+	87891.5i	−0.0535232	+	0.0437625i
$333$	−1.98260e6			−0.979770
$334$	1.22558e6	+	3.43513e6i	0.601141	+	1.68491i
$335$	−917706.	−	1.04754e6i	−0.446778	−	0.509988i
$336$	−5.14539e6	−	1.04298e6i	−2.48639	−	0.503999i
$337$		−	3.68207e6i		−	1.76611i	−0.469273	−	0.883053i	$-0.655484\pi$
$337$		−	3.68207e6i		−	1.76611i	0.469273	−	0.883053i	$-0.344516\pi$
$338$	−3.08877e6	+	1.10201e6i	−1.47060	+	0.524677i
$339$		−	390916.i		−	0.184750i
$340$	−198273.	+	1.18366e6i	−0.0930177	+	0.555305i
$341$		−	185620.i		−	0.0864450i
$342$	−197308.	−	553026.i	−0.0912177	−	0.255670i
$343$			5.27132e6i			2.41927i
$344$	−23766.6	+	39407.6i	−0.0108286	+	0.0179549i
$345$	1.84996e6	−	1.62067e6i	0.836789	−	0.733074i
$346$	864729.	−	308517.i	0.388320	−	0.138544i
$347$	−2.20981e6			−0.985215			−0.492607	−	0.870252i	$-0.663956\pi$
$347$	−2.20981e6			−0.985215			−0.492607	+	0.870252i	$0.663956\pi$
$348$	1.22206e6	+	1.49463e6i	0.540935	+	0.661586i
$349$		−	4.13502e6i		−	1.81725i	−0.417618	−	0.908623i	$-0.637135\pi$
$349$		−	4.13502e6i		−	1.81725i	0.417618	−	0.908623i	$-0.362865\pi$
$350$	−4.08736e6	+	874441.i	−1.78350	+	0.381558i
$351$	−334805.			−0.145052
$352$	−1.10481e6	+	158744.i	−0.475259	+	0.0682873i
$353$		−	376581.i		−	0.160850i	−0.996761	−	0.0804251i	$-0.974372\pi$
$353$		−	376581.i		−	0.160850i	0.996761	−	0.0804251i	$-0.0256278\pi$
$354$	−1.01647e6	−	2.84901e6i	−0.431107	−	1.20833i
$355$	−1.40862e6	−	1.60791e6i	−0.593232	−	0.677161i
$356$	−137793.	+	112664.i	−0.0576239	+	0.0471153i
$357$	3.43973e6			1.42841
$358$	142143.	+	398407.i	0.0586162	+	0.164293i
$359$	4.04157e6			1.65506			0.827530	−	0.561422i	$-0.189746\pi$
$359$	4.04157e6			1.65506			0.827530	+	0.561422i	$0.189746\pi$
$360$	−2.26296e6	+	404159.i	−0.920281	+	0.164360i
$361$	2.26732e6			0.915682
$362$	131557.	+	368735.i	0.0527645	+	0.147891i
$363$	2.68707e6			1.07032
$364$	−4.67062e6	−	5.71236e6i	−1.84766	−	2.25976i
$365$	1.88273e6	−	1.64938e6i	0.739702	−	0.648021i
$366$	−7827.38	−	21939.0i	−0.00305431	−	0.00856081i
$367$		−	4.17682e6i		−	1.61875i	−0.587289	−	0.809377i	$-0.699805\pi$
$367$		−	4.17682e6i		−	1.61875i	0.587289	−	0.809377i	$-0.300195\pi$
$368$	−2.03632e6	−	412767.i	−0.783837	−	0.158886i
$369$	−411716.			−0.157410
$370$	2.41046e6	+	1.34410e6i	0.915369	+	0.510419i
$371$			5.43882e6i			2.05149i
$372$	−517471.	+	423102.i	−0.193878	+	0.158521i
$373$	3.84926e6			1.43254			0.716268	−	0.697826i	$-0.245849\pi$
$373$	3.84926e6			1.43254			0.716268	+	0.697826i	$0.245849\pi$
$374$	688762.	−	245736.i	0.254619	−	0.0908425i
$375$	−3.15282e6	+	2.09954e6i	−1.15777	+	0.770984i
$376$	3.05955e6	+	1.84521e6i	1.11606	+	0.673093i
$377$			2.71345e6i			0.983259i
$378$	−154307.	−	432502.i	−0.0555466	−	0.155689i
$379$			771105.i			0.275750i	0.990450	+	0.137875i	$0.0440272\pi$
$379$			771105.i			0.275750i	−0.990450	+	0.137875i	$0.955973\pi$
$380$	−135034.	+	806139.i	−0.0479717	+	0.286386i
$381$			1.43159e6i			0.505250i
$382$	−3.79627e6	+	1.35443e6i	−1.33106	+	0.474895i
$383$		−	571373.i		−	0.199032i	−0.995036	−	0.0995160i	$-0.968271\pi$
$383$		−	571373.i		−	0.199032i	0.995036	−	0.0995160i	$-0.0317294\pi$
$384$	2.96084e6	+	2.71813e6i	1.02468	+	0.940682i
$385$	1.67829e6	+	1.91573e6i	0.577051	+	0.658691i
$386$	364229.	+	1.02088e6i	0.124425	+	0.348745i
$387$	57751.5			0.0196014
$388$	1.98712e6	+	2.43033e6i	0.670109	+	0.819570i
$389$		−	5.01422e6i		−	1.68008i	−0.542525	−	0.840040i	$-0.682532\pi$
$389$		−	5.01422e6i		−	1.68008i	0.542525	−	0.840040i	$-0.317468\pi$
$390$	−5.84026e6	−	3.25659e6i	−1.94433	−	1.08418i
$391$	1.36129e6			0.450308
$392$	3.65539e6	−	6.06103e6i	1.20149	−	1.99219i
$393$			3.20376e6i			1.04635i
$394$	−2.38436e6	+	850688.i	−0.773804	+	0.276077i
$395$	2.56979e6	+	2.93336e6i	0.828713	+	0.945959i
$396$	886619.	+	1.08437e6i	0.284118	+	0.347488i
$397$	−5.51448e6			−1.75602			−0.878008	−	0.478647i	$-0.841127\pi$
$397$	−5.51448e6			−1.75602			−0.878008	+	0.478647i	$0.841127\pi$
$398$	−623042.	+	222288.i	−0.197156	+	0.0703409i
$399$	2.34264e6			0.736671
$400$	3.02533e6	+	1.04279e6i	0.945414	+	0.325871i
$401$	646084.			0.200645			0.100322	−	0.994955i	$-0.468013\pi$
$401$	646084.			0.200645			0.100322	+	0.994955i	$0.468013\pi$
$402$	2.87810e6	−	1.02685e6i	0.888262	−	0.316913i
$403$	−939448.			−0.288144
$404$	402507.	+	492282.i	0.122693	+	0.150058i
$405$	−2.30766e6	−	2.63415e6i	−0.699093	−	0.798000i
$406$	−3.50524e6	+	1.25059e6i	−1.05537	+	0.376532i
$407$		−	1.68167e6i		−	0.503215i
$408$	−2.25502e6	−	1.36000e6i	−0.670656	−	0.404471i
$409$	1.02076e6			0.301726			0.150863	−	0.988555i	$-0.451795\pi$
$409$	1.02076e6			0.301726			0.150863	+	0.988555i	$0.451795\pi$
$410$	500568.	+	279122.i	0.147063	+	0.0820039i
$411$		−	7.75887e6i		−	2.26566i
$412$	2.43473e6	+	2.97777e6i	0.706655	+	0.864268i
$413$	5.83105e6			1.68218
$414$	876173.	+	2.45579e6i	0.251240	+	0.704190i
$415$	−159840.	−	182454.i	−0.0455580	−	0.0520035i
$416$	803422.	+	5.59157e6i	0.227620	+	1.58417i
$417$			1.06962e6i			0.301225i
$418$	469084.	−	167359.i	0.131314	−	0.0468499i
$419$			1.63720e6i			0.455581i	0.973710	+	0.227790i	$0.0731501\pi$
$419$			1.63720e6i			0.455581i	−0.973710	+	0.227790i	$0.926850\pi$
$420$	1.51517e6	−	9.04540e6i	0.419121	−	2.50210i
$421$			3.24490e6i			0.892270i	0.894966	+	0.446135i	$0.147200\pi$
$421$			3.24490e6i			0.892270i	−0.894966	+	0.446135i	$0.852800\pi$
$422$	1.27337e6	+	3.56908e6i	0.348076	+	0.975607i
$423$		−	4.48374e6i		−	1.21840i
$424$	2.15039e6	−	3.56558e6i	0.580902	−	0.963198i
$425$	−2.07836e6	−	275822.i	−0.558148	−	0.0740725i
$426$	4.41771e6	−	1.57615e6i	1.17943	−	0.420797i
$427$	44902.5			0.0119179
$428$	3.09682e6	−	2.53207e6i	0.817160	−	0.668138i
$429$			4.07447e6i			1.06888i
$430$	−70214.9	−	39152.5i	−0.0183129	−	0.0102115i
$431$	3.39290e6			0.879789			0.439894	−	0.898049i	$-0.355016\pi$
$431$	3.39290e6			0.879789			0.439894	+	0.898049i	$0.355016\pi$
$432$	−69841.1	+	344549.i	−0.0180054	+	0.0888264i
$433$			2.40449e6i			0.616315i	0.951335	+	0.308158i	$0.0997124\pi$
$433$			2.40449e6i			0.616315i	−0.951335	+	0.308158i	$0.900288\pi$
$434$	−432980.	−	1.21358e6i	−0.110343	−	0.309275i
$435$	−2.53688e6	+	2.22245e6i	−0.642800	+	0.563129i
$436$	632423.	+	773478.i	0.159328	+	0.194864i
$437$	927114.			0.232236
$438$	1.84553e6	+	5.17277e6i	0.459660	+	1.28836i
$439$	−5.28610e6			−1.30910			−0.654552	−	0.756017i	$-0.727143\pi$
$439$	−5.28610e6			−1.30910			−0.654552	+	0.756017i	$0.727143\pi$
$440$	−342813.	−	1.91947e6i	−0.0844161	−	0.472661i
$441$	−8.88239e6			−2.17487
$442$	−1.24370e6	−	3.48591e6i	−0.302802	−	0.848712i
$443$	4.55556e6			1.10289			0.551445	−	0.834211i	$-0.314077\pi$
$443$	4.55556e6			1.10289			0.551445	+	0.834211i	$0.314077\pi$
$444$	−4.68813e6	+	3.83318e6i	−1.12861	+	0.922787i
$445$	−204892.	−	233880.i	−0.0490484	−	0.0559877i
$446$	−3267.48	−	9158.29i	−0.000777814	−	0.00218010i
$447$			6.74020e6i			1.59553i
$448$	−6.85293e6	+	3.61495e6i	−1.61317	+	0.850957i
$449$	−3.24132e6			−0.758762			−0.379381	−	0.925241i	$-0.623863\pi$
$449$	−3.24132e6			−0.758762			−0.379381	+	0.925241i	$0.623863\pi$
$450$	−840116.	−	3.92692e6i	−0.195573	−	0.914157i
$451$		−	349222.i		−	0.0808464i
$452$	−365174.	−	446623.i	−0.0840725	−	0.102824i
$453$	−7.97104e6			−1.82503
$454$	3.80046e6	−	1.35592e6i	0.865360	−	0.308742i
$455$	9.69573e6	−	8.49401e6i	2.19559	−	1.92346i
$456$	−1.53579e6	−	926230.i	−0.345875	−	0.208596i
$457$		−	5.12416e6i		−	1.14771i	−0.818957	−	0.573855i	$-0.805447\pi$
$457$		−	5.12416e6i		−	1.14771i	0.818957	−	0.573855i	$-0.194553\pi$
$458$	2.22444e6	+	6.23480e6i	0.495516	+	1.38886i
$459$		−	230334.i		−	0.0510301i
$460$	599638.	−	3.57977e6i	0.132128	−	0.788789i
$461$		−	789831.i		−	0.173094i	−0.996248	−	0.0865470i	$-0.972417\pi$
$461$		−	789831.i		−	0.173094i	0.996248	−	0.0865470i	$-0.0275833\pi$
$462$	−5.26342e6	+	1.87788e6i	−1.14726	+	0.409319i
$463$		−	73457.7i		−	0.0159252i	−0.999968	−	0.00796260i	$-0.997465\pi$
$463$		−	73457.7i		−	0.0159252i	0.999968	−	0.00796260i	$-0.00253460\pi$
$464$	2.79242e6	+	566032.i	0.602124	+	0.122052i
$465$	−769454.	−	878316.i	−0.165025	−	0.188373i
$466$	−2.90369e6	−	8.13864e6i	−0.619421	−	1.73615i
$467$	5.37276e6			1.14000			0.570001	−	0.821644i	$-0.306943\pi$
$467$	5.37276e6			1.14000			0.570001	+	0.821644i	$0.306943\pi$
$468$	5.48813e6	−	4.48729e6i	1.15827	−	0.947042i
$469$			5.89060e6i			1.23659i
$470$	−3.03975e6	+	5.45138e6i	−0.634735	+	1.13831i
$471$	−1.11601e6			−0.231802
$472$	−3.82272e6	−	2.30547e6i	−0.789800	−	0.476327i
$473$			48985.6i			0.0100674i
$474$	−8.05934e6	+	2.87540e6i	−1.64761	+	0.587831i
$475$	−1.41548e6	−	187850.i	−0.287852	−	0.0382011i
$476$	3.92991e6	−	3.21323e6i	0.794996	−	0.650016i
$477$	−5.22533e6			−1.05152
$478$	3.02223e6	−	1.07827e6i	0.605003	−	0.215852i
$479$	2.42372e6			0.482663			0.241331	−	0.970443i	$-0.422416\pi$
$479$	2.42372e6			0.482663			0.241331	+	0.970443i	$0.422416\pi$
$480$	−4.56967e6	+	5.33091e6i	−0.905278	+	1.05608i
$481$	−8.51111e6			−1.67735
$482$	−3.66726e6	+	1.30840e6i	−0.718993	+	0.256521i
$483$	−1.04028e7			−2.02901
$484$	3.06998e6	−	2.51013e6i	0.595693	−	0.487060i
$485$	−4.12506e6	+	3.61379e6i	−0.796299	+	0.697603i
$486$	6.79278e6	−	2.42352e6i	1.30454	−	0.465432i
$487$		−	4.49413e6i		−	0.858663i	−0.903147	−	0.429332i	$-0.858749\pi$
$487$		−	4.49413e6i		−	0.858663i	0.903147	−	0.429332i	$-0.141251\pi$
$488$	−29437.2	−	17753.5i	−0.00559560	−	0.00337469i
$489$	1.02260e7			1.93390
$490$	1.07993e7	+	6.02180e6i	2.03191	+	1.13302i
$491$		−	3.33347e6i		−	0.624011i	−0.950080	−	0.312006i	$-0.898999\pi$
$491$		−	3.33347e6i		−	0.624011i	0.950080	−	0.312006i	$-0.101001\pi$
$492$	−973559.	+	796015.i	−0.181322	+	0.148255i
$493$	−1.86676e6			−0.345916
$494$	−847025.	−	2.37409e6i	−0.156163	−	0.437703i
$495$	−1.84053e6	+	1.61241e6i	−0.337621	+	0.295775i
$496$	−195971.	+	966791.i	−0.0357675	+	0.176453i
$497$			9.04171e6i			1.64195i
$498$	501288.	−	178849.i	0.0905761	−	0.0323156i
$499$			6.47383e6i			1.16388i	0.813230	+	0.581942i	$0.197707\pi$
$499$			6.47383e6i			1.16388i	−0.813230	+	0.581942i	$0.802293\pi$
$500$	−1.64083e6	+	5.34394e6i	−0.293520	+	0.955953i
$501$		−	1.39802e7i		−	2.48839i
$502$	−1.26069e6	−	3.53353e6i	−0.223279	−	0.625819i
$503$		−	754370.i		−	0.132943i	−0.997788	−	0.0664713i	$-0.978826\pi$
$503$		−	754370.i		−	0.132943i	0.997788	−	0.0664713i	$-0.0211741\pi$
$504$	8.32611e6	+	5.02146e6i	1.46004	+	0.880548i
$505$	−835562.	+	732000.i	−0.145798	+	0.127727i
$506$	−2.08303e6	+	743181.i	−0.361676	+	0.129038i
$507$	1.25705e7			2.17187
$508$	1.33732e6	+	1.63560e6i	0.229920	+	0.281201i
$509$			2.62746e6i			0.449513i	0.974415	+	0.224757i	$0.0721587\pi$
$509$			2.62746e6i			0.449513i	−0.974415	+	0.224757i	$0.927841\pi$
$510$	2.24042e6	−	4.01790e6i	0.381421	−	0.684028i
$511$	−1.05871e7			−1.79359
$512$	5.92191e6	+	339610.i	0.998360	+	0.0572540i
$513$		−	156870.i		−	0.0263176i
$514$	−3.19405e6	−	8.95246e6i	−0.533253	−	1.49463i
$515$	−5.05424e6	+	4.42780e6i	−0.839727	+	0.735648i
$516$	136561.	−	111657.i	0.0225790	−	0.0184613i
$517$	3.80317e6			0.625776
$518$	−3.92267e6	−	1.09947e7i	−0.642329	−	1.80036i
$519$	−3.51924e6			−0.573497
$520$	−9.71467e6	+	1.73502e6i	−1.57550	+	0.281381i
$521$	5.10889e6			0.824580			0.412290	−	0.911053i	$-0.364729\pi$
$521$	5.10889e6			0.824580			0.412290	+	0.911053i	$0.364729\pi$
$522$	−1.20150e6	−	3.36765e6i	−0.192996	−	0.540942i
$523$	−2.60300e6			−0.416121			−0.208060	−	0.978116i	$-0.566715\pi$
$523$	−2.60300e6			−0.416121			−0.208060	+	0.978116i	$0.566715\pi$
$524$	2.99279e6	+	3.66030e6i	0.476154	+	0.582356i
$525$	1.58826e7	+	2.10780e6i	2.51491	+	0.333757i
$526$	3.15738e6	+	8.84969e6i	0.497579	+	1.39465i
$527$		−	646308.i		−	0.101371i
$528$	4.19306e6	+	849946.i	0.654556	+	0.132680i
$529$	2.31937e6			0.360355
$530$	6.35300e6	+	3.54250e6i	0.982402	+	0.547798i
$531$			5.60216e6i			0.862223i
$532$	2.67648e6	−	2.18838e6i	0.410001	−	0.335231i
$533$	−1.76746e6			−0.269483
$534$	642580.	−	229259.i	0.0975156	−	0.0347915i
$535$	4.60483e6	+	5.25632e6i	0.695551	+	0.793957i
$536$	2.32901e6	−	3.86175e6i	0.350155	−	0.580594i
$537$		−	1.62142e6i		−	0.242639i
$538$	−1.30574e6	−	3.65981e6i	−0.194492	−	0.545134i
$539$		−	7.53415e6i		−	1.11702i
$540$	−605705.	−	101460.i	−0.0893875	−	0.0149731i
$541$		−	2.80703e6i		−	0.412339i	−0.978516	−	0.206169i	$-0.933900\pi$
$541$		−	2.80703e6i		−	0.412339i	0.978516	−	0.206169i	$-0.0660998\pi$
$542$	−1.26678e6	+	451959.i	−0.185226	+	0.0660847i
$543$		−	1.50066e6i		−	0.218416i
$544$	−3.84681e6	+	552726.i	−0.557318	+	0.0800779i
$545$	−1.31284e6	+	1.15013e6i	−0.189331	+	0.165865i
$546$	9.50416e6	+	2.66388e7i	1.36437	+	3.82414i
$547$	−6.42557e6			−0.918213			−0.459106	−	0.888381i	$-0.651830\pi$
$547$	−6.42557e6			−0.918213			−0.459106	+	0.888381i	$0.651830\pi$
$548$	−7.24795e6	−	8.86454e6i	−1.03101	−	1.26097i
$549$			43139.9i			0.00610870i
$550$	3.33086e6	−	712597.i	0.469515	−	0.100447i
$551$	−1.27136e6			−0.178398
$552$	6.81988e6	+	4.11305e6i	0.952640	+	0.574535i
$553$		−	1.64950e7i		−	2.29372i
$554$	−1.26481e7	+	4.51256e6i	−1.75085	+	0.624667i
$555$	−6.97102e6	−	7.95728e6i	−0.960647	−	1.09656i
$556$	999189.	+	1.22205e6i	0.137076	+	0.167649i
$557$	−6.14000e6			−0.838553			−0.419276	−	0.907859i	$-0.637716\pi$
$557$	−6.14000e6			−0.838553			−0.419276	+	0.907859i	$0.637716\pi$
$558$	1.16595e6	−	415984.i	0.158523	−	0.0565577i
$559$	247922.			0.0335572
$560$	−6.71868e6	−	1.17498e7i	−0.905344	−	1.58329i
$561$	−2.80310e6			−0.376037
$562$	−3.87003e6	+	1.38074e6i	−0.516860	+	0.184405i
$563$	4.04571e6			0.537927			0.268964	−	0.963150i	$-0.413319\pi$
$563$	4.04571e6			0.537927			0.268964	+	0.963150i	$0.413319\pi$
$564$	−8.66891e6	−	1.06024e7i	−1.14754	−	1.40348i
$565$	758064.	−	664107.i	0.0999045	−	0.0875219i
$566$	−5.60522e6	+	1.99982e6i	−0.735447	+	0.262392i
$567$			1.48125e7i			1.93495i
$568$	3.57490e6	−	5.92756e6i	0.464935	−	0.770913i
$569$	3.29664e6			0.426865			0.213433	−	0.976958i	$-0.431536\pi$
$569$	3.29664e6			0.426865			0.213433	+	0.976958i	$0.431536\pi$
$570$	1.52585e6	−	2.73640e6i	0.196709	−	0.352771i
$571$			8.76573e6i			1.12512i	0.826758	+	0.562558i	$0.190183\pi$
$571$			8.76573e6i			1.12512i	−0.826758	+	0.562558i	$0.809817\pi$
$572$	3.80617e6	+	4.65510e6i	0.486405	+	0.594893i
$573$	1.54499e7			1.96580
$574$	−814600.	−	2.28321e6i	−0.103196	−	0.289245i
$575$	6.28562e6	+	834172.i	0.792827	+	0.105217i
$576$	−3.47305e6	−	6.58393e6i	−0.436169	−	0.826854i
$577$		−	8.81970e6i		−	1.10284i	−0.834226	−	0.551422i	$-0.814085\pi$
$577$		−	8.81970e6i		−	1.10284i	0.834226	−	0.551422i	$-0.185915\pi$
$578$	−5.16669e6	+	1.84336e6i	−0.643269	+	0.229505i
$579$		−	4.15475e6i		−	0.515049i
$580$	−822290.	+	4.90898e6i	−0.101497	+	0.605928i
$581$			1.02598e6i			0.126096i
$582$	−4.04356e6	−	1.13335e7i	−0.494830	−	1.38694i
$583$		−	4.43219e6i		−	0.540066i
$584$	6.94068e6	+	4.18590e6i	0.842112	+	0.507875i
$585$	8.16059e6	+	9.31514e6i	0.985898	+	1.12538i
$586$	8.21369e6	−	2.93047e6i	0.988085	−	0.352527i
$587$	1.29013e7			1.54539			0.772693	−	0.634780i	$-0.218909\pi$
$587$	1.29013e7			1.54539			0.772693	+	0.634780i	$0.218909\pi$
$588$	−2.10036e7	+	1.71733e7i	−2.50525	+	2.04838i
$589$		−	440170.i		−	0.0522796i
$590$	3.79798e6	−	6.81116e6i	0.449182	−	0.805548i
$591$	9.70377e6			1.14280
$592$	−1.77544e6	+	8.75883e6i	−0.208210	+	1.02717i
$593$			1.26142e7i			1.47307i	0.676398	+	0.736536i	$0.263540\pi$
$593$			1.26142e7i			1.47307i	−0.676398	+	0.736536i	$0.736460\pi$
$594$	125748.	+	352453.i	0.0146229	+	0.0409860i
$595$	5.84358e6	+	6.67033e6i	0.676685	+	0.772422i
$596$	6.29636e6	+	7.70070e6i	0.726063	+	0.888004i
$597$	2.53563e6			0.291172
$598$	3.76133e6	+	1.05425e7i	0.430119	+	1.20556i
$599$	−1.12524e7			−1.28138			−0.640688	−	0.767802i	$-0.721351\pi$
$599$	−1.12524e7			−1.28138			−0.640688	+	0.767802i	$0.721351\pi$
$600$	−9.57891e6	−	7.66145e6i	−1.08627	−	0.868826i
$601$	1.11847e7			1.26310			0.631549	−	0.775336i	$-0.282420\pi$
$601$	1.11847e7			1.26310			0.631549	+	0.775336i	$0.282420\pi$
$602$	114264.	+	320267.i	0.0128505	+	0.0360181i
$603$	−5.65937e6			−0.633833
$604$	−9.10693e6	+	7.44614e6i	−1.01573	+	0.830499i
$605$	4.56492e6	+	5.21076e6i	0.507043	+	0.578779i
$606$	−819053.	−	2.29569e6i	−0.0906005	−	0.253940i
$607$			1.18645e7i			1.30701i	0.756922	+	0.653505i	$0.226702\pi$
$607$			1.18645e7i			1.30701i	−0.756922	+	0.653505i	$0.773298\pi$
$608$	−2.61988e6	+	376436.i	−0.287424	+	0.0412983i
$609$	1.42655e7			1.55863
$610$	29246.6	−	52449.9i	0.00318238	−	0.00570717i
$611$		−	1.92483e7i		−	2.08588i
$612$	3.08710e6	+	3.77564e6i	0.333174	+	0.407486i
$613$	1.85839e6			0.199750			0.0998748	−	0.995000i	$-0.468156\pi$
$613$	1.85839e6			0.199750			0.0998748	+	0.995000i	$0.468156\pi$
$614$	1.17968e7	−	4.20886e6i	1.26283	−	0.450550i
$615$	−1.44764e6	−	1.65245e6i	−0.154337	−	0.176173i
$616$	−4.25926e6	+	7.06231e6i	−0.452254	+	0.749886i
$617$		−	6.78893e6i		−	0.717940i	−0.933349	−	0.358970i	$-0.883128\pi$
$617$		−	6.78893e6i		−	0.717940i	0.933349	−	0.358970i	$-0.116872\pi$
$618$	−4.95438e6	−	1.38864e7i	−0.521817	−	1.46258i
$619$		−	1.53528e7i		−	1.61050i	−0.592933	−	0.805252i	$-0.702030\pi$
$619$		−	1.53528e7i		−	1.61050i	0.592933	−	0.805252i	$-0.297970\pi$
$620$	−1.69958e6	−	284693.i	−0.177567	−	0.0297439i
$621$			696602.i			0.0724862i
$622$	8.19561e6	−	2.92402e6i	0.849386	−	0.303043i
$623$			1.31517e6i			0.135756i
$624$	4.30168e6	−	2.12216e7i	0.442259	−	2.18181i
$625$	−9.42759e6	−	2.54715e6i	−0.965385	−	0.260829i
$626$	−4.44205e6	−	1.24504e7i	−0.453052	−	1.26984i
$627$	−1.90906e6			−0.193933
$628$	−1.27505e6	+	1.04252e6i	−0.129011	+	0.105484i
$629$		−	5.85535e6i		−	0.590101i
$630$	−8.27222e6	+	1.48351e7i	−0.830368	+	1.48915i
$631$	−1.36354e7			−1.36331			−0.681657	−	0.731672i	$-0.738740\pi$
$631$	−1.36354e7			−1.36331			−0.681657	+	0.731672i	$0.738740\pi$
$632$	−6.52177e6	+	1.08138e7i	−0.649490	+	1.07692i
$633$		−	1.45253e7i		−	1.44084i
$634$	6.14100e6	−	2.19098e6i	0.606759	−	0.216479i
$635$	−2.77614e6	+	2.43205e6i	−0.273216	+	0.239353i
$636$	−1.23560e7	+	1.01027e7i	−1.21125	+	0.990364i
$637$	−3.81313e7			−3.72334
$638$	2.85648e6	−	1.01913e6i	0.277830	−	0.0991239i
$639$	−8.68679e6			−0.841603
$640$	−240990.	+	1.03593e7i	−0.0232568	+	0.999730i
$641$	−9.20659e6			−0.885022			−0.442511	−	0.896763i	$-0.645912\pi$
$641$	−9.20659e6			−0.885022			−0.442511	+	0.896763i	$0.645912\pi$
$642$	−1.44416e7	+	5.15246e6i	−1.38286	+	0.493375i
$643$	−2.77419e6			−0.264611			−0.132306	−	0.991209i	$-0.542238\pi$
$643$	−2.77419e6			−0.264611			−0.132306	+	0.991209i	$0.542238\pi$
$644$	−1.18853e7	+	9.71780e6i	−1.12926	+	0.923322i
$645$	203060.	+	231789.i	0.0192188	+	0.0219378i
$646$	1.63329e6	−	582724.i	0.153986	−	0.0549391i
$647$		−	4.39670e6i		−	0.412921i	−0.978455	−	0.206460i	$-0.933806\pi$
$647$		−	4.39670e6i		−	0.412921i	0.978455	−	0.206460i	$-0.0661944\pi$
$648$	5.85653e6	−	9.71076e6i	0.547902	−	0.908481i
$649$	−4.75183e6			−0.442842
$650$	−3.60654e6	−	1.68579e7i	−0.334817	−	1.56502i
$651$			4.93899e6i			0.456758i
$652$	1.16833e7	−	9.55264e6i	1.07633	−	0.880044i
$653$	−6.49195e6			−0.595788			−0.297894	−	0.954599i	$-0.596284\pi$
$653$	−6.49195e6			−0.595788			−0.297894	+	0.954599i	$0.596284\pi$
$654$	−1.28690e6	−	3.60701e6i	−0.117653	−	0.329764i
$655$	−6.21272e6	+	5.44269e6i	−0.565820	+	0.495691i
$656$	−368696.	+	1.81890e6i	−0.0334510	+	0.165025i
$657$		−	1.01715e7i		−	0.919331i
$658$	2.48650e7	−	8.87131e6i	2.23885	−	0.798772i
$659$			1.08903e7i			0.976850i	0.872606	+	0.488425i	$0.162428\pi$
$659$			1.08903e7i			0.976850i	−0.872606	+	0.488425i	$0.837572\pi$
$660$	−1.23474e6	+	7.37125e6i	−0.110336	+	0.658691i
$661$			1.61309e7i			1.43600i	0.696042	+	0.718001i	$0.254943\pi$
$661$			1.61309e7i			1.43600i	−0.696042	+	0.718001i	$0.745057\pi$
$662$	3.88769e6	+	1.08966e7i	0.344784	+	0.966380i
$663$			1.41868e7i			1.25343i
$664$	405651.	−	672613.i	0.0357053	−	0.0592032i
$665$	3.97979e6	+	4.54285e6i	0.348985	+	0.398359i
$666$	1.05631e7	−	3.76869e6i	0.922797	−	0.329234i
$667$	5.64565e6			0.491360
$668$	−1.30596e7	−	1.59724e7i	−1.13237	−	1.38493i
$669$			37272.0i			0.00321972i
$670$	6.88071e6	+	3.83676e6i	0.592170	+	0.330200i
$671$	−36591.8			−0.00313746
$672$	2.93968e7	−	4.22386e6i	2.51117	−	0.360816i
$673$			2.20227e7i			1.87428i	0.348957	+	0.937139i	$0.386536\pi$
$673$			2.20227e7i			1.87428i	−0.348957	+	0.937139i	$0.613464\pi$
$674$	6.99918e6	+	1.96177e7i	0.593469	+	1.66341i
$675$	141144.	−	1.06354e6i	0.0119235	−	0.0898452i
$676$	1.43619e7	−	1.17428e7i	1.20877	−	0.988335i
$677$	8.56722e6			0.718403			0.359202	−	0.933260i	$-0.383049\pi$
$677$	8.56722e6			0.718403			0.359202	+	0.933260i	$0.383049\pi$
$678$	743086.	+	2.08277e6i	0.0620819	+	0.174007i
$679$	2.31963e7			1.93083
$680$	−1.19363e6	−	6.68336e6i	−0.0989915	−	0.554271i
$681$	−1.54670e7			−1.27802
$682$	352843.	+	988969.i	0.0290483	+	0.0814183i
$683$	−1.45813e7			−1.19603			−0.598017	−	0.801483i	$-0.704045\pi$
$683$	−1.45813e7			−1.19603			−0.598017	+	0.801483i	$0.704045\pi$
$684$	2.10248e6	+	2.57142e6i	0.171827	+	0.210151i
$685$	1.50460e7	−	1.31811e7i	1.22516	−	1.07331i
$686$	−1.00202e7	−	2.80851e7i	−0.812951	−	2.27859i
$687$		−	2.53741e7i		−	2.05116i
$688$	51717.1	−	255138.i	0.00416546	−	0.0205496i
$689$	−2.24318e7			−1.80018
$690$	−6.77574e6	+	1.21514e7i	−0.541793	+	0.971634i
$691$		−	1.29644e7i		−	1.03290i	−0.856318	−	0.516449i	$-0.827254\pi$
$691$		−	1.29644e7i		−	1.03290i	0.856318	−	0.516449i	$-0.172746\pi$
$692$	−4.02075e6	+	3.28750e6i	−0.319184	+	0.260976i
$693$	1.03498e7			0.818648
$694$	1.17737e7	−	4.20059e6i	0.927925	−	0.331064i
$695$	−2.07421e6	+	1.81713e6i	−0.162889	+	0.142700i
$696$	−9.35217e6	−	5.64027e6i	−0.731794	−	0.441343i
$697$		−	1.21595e6i		−	0.0948055i
$698$	7.86019e6	+	2.20310e7i	0.610653	+	1.71157i
$699$			3.31223e7i			2.56406i
$700$	2.01149e7	−	1.24285e7i	1.55157	−	0.958683i
$701$			846059.i			0.0650288i	0.999471	+	0.0325144i	$0.0103515\pi$
$701$			846059.i			0.0650288i	−0.999471	+	0.0325144i	$0.989649\pi$
$702$	1.78381e6	−	636425.i	0.136617	−	0.0487421i
$703$		−	3.98781e6i		−	0.304331i
$704$	5.58457e6	−	2.94589e6i	0.424676	−	0.224019i
$705$	1.79958e7	−	1.57653e7i	1.36363	−	1.19462i
$706$	715837.	+	2.00639e6i	0.0540508	+	0.151497i
$707$	4.69858e6			0.353523
$708$	1.08313e7	+	1.32471e7i	0.812076	+	0.993201i
$709$			1.99203e7i			1.48827i	0.668031	+	0.744133i	$0.267137\pi$
$709$			1.99203e7i			1.48827i	−0.668031	+	0.744133i	$0.732863\pi$
$710$	1.05615e7	+	5.88920e6i	0.786284	+	0.438440i
$711$	1.58475e7			1.17568
$712$	519988.	−	862195.i	0.0384409	−	0.0637391i
$713$			1.95463e6i			0.143993i
$714$	−1.83266e7	+	6.53854e6i	−1.34535	+	0.479993i
$715$	−7.90122e6	+	6.92191e6i	−0.578001	+	0.506362i
$716$	−1.51465e6	−	1.85248e6i	−0.110415	−	0.135043i
$717$	−1.22997e7			−0.893508
$718$	−2.15331e7	+	7.68255e6i	−1.55882	+	0.556153i
$719$	1.24447e7			0.897767			0.448883	−	0.893590i	$-0.351822\pi$
$719$	1.24447e7			0.897767			0.448883	+	0.893590i	$0.351822\pi$
$720$	1.12886e7	−	6.45495e6i	0.811537	−	0.464046i
$721$	2.84213e7			2.03613
$722$	−1.20801e7	+	4.30991e6i	−0.862436	+	0.307699i
$723$	1.49249e7			1.06186
$724$	−1.40185e6	−	1.71451e6i	−0.0993925	−	0.121561i
$725$	−8.61953e6	−	1.14391e6i	−0.609030	−	0.0808251i
$726$	−1.43165e7	+	5.10781e6i	−1.00808	+	0.359661i
$727$		−	4.45620e6i		−	0.312700i	−0.987702	−	0.156350i	$-0.950027\pi$
$727$		−	4.45620e6i		−	0.312700i	0.987702	−	0.156350i	$-0.0499728\pi$
$728$	3.57432e7	+	2.15566e7i	2.49957	+	1.50748i
$729$	−1.24221e7			−0.865717
$730$	−6.89576e6	+	1.23666e7i	−0.478933	+	0.858902i
$731$			170562.i			0.0118056i
$732$	83407.2	+	102010.i	0.00575341	+	0.00703666i
$733$	1.16096e7			0.798101			0.399051	−	0.916929i	$-0.369340\pi$
$733$	1.16096e7			0.798101			0.399051	+	0.916929i	$0.369340\pi$
$734$	7.93966e6	+	2.22537e7i	0.543953	+	1.52462i
$735$	−3.12314e7	−	3.56500e7i	−2.13242	−	2.43411i
$736$	1.16339e7	−	1.67162e6i	0.791648	−	0.113748i
$737$		−	4.80035e6i		−	0.325540i
$738$	2.19359e6	−	782624.i	0.148256	−	0.0528947i
$739$			2.17540e6i			0.146531i	0.997312	+	0.0732653i	$0.0233420\pi$
$739$			2.17540e6i			0.146531i	−0.997312	+	0.0732653i	$0.976658\pi$
$740$	−1.53977e7	−	2.57923e6i	−1.03366	−	0.173145i
$741$			9.66198e6i			0.646429i
$742$	−1.03386e7	−	2.89776e7i	−0.689367	−	1.93220i
$743$		−	1.20942e7i		−	0.803720i	−0.915701	−	0.401860i	$-0.868364\pi$
$743$		−	1.20942e7i		−	0.803720i	0.915701	−	0.401860i	$-0.131636\pi$
$744$	1.95277e6	−	3.23790e6i	0.129336	−	0.214453i
$745$	−1.30706e7	+	1.14506e7i	−0.862789	+	0.755852i
$746$	−2.05085e7	+	7.31700e6i	−1.34923	+	0.481378i
$747$	−985710.			−0.0646320
$748$	−3.20255e6	+	2.61851e6i	−0.209287	+	0.171120i
$749$		−	2.95576e7i		−	1.92515i
$750$	1.28070e7	−	1.71793e7i	0.831368	−	1.11520i
$751$	−410935.			−0.0265873			−0.0132936	−	0.999912i	$-0.504232\pi$
$751$	−410935.			−0.0265873			−0.0132936	+	0.999912i	$0.504232\pi$
$752$	−1.98085e7	−	4.01524e6i	−1.27734	−	0.258921i
$753$			1.43806e7i			0.924251i
$754$	−5.15795e6	−	1.44570e7i	−0.330406	−	0.926083i
$755$	−1.35416e7	−	1.54574e7i	−0.864573	−	0.986892i
$756$	1.64427e6	+	2.01101e6i	0.104633	+	0.127971i
$757$	2.24651e7			1.42485			0.712424	−	0.701750i	$-0.247597\pi$
$757$	2.24651e7			1.42485			0.712424	+	0.701750i	$0.247597\pi$
$758$	−1.46578e6	−	4.10838e6i	−0.0926608	−	0.259715i
$759$	8.47744e6			0.534146
$760$	−812927.	−	4.55172e6i	−0.0510525	−	0.285852i
$761$	1.00934e7			0.631793			0.315897	−	0.948794i	$-0.397695\pi$
$761$	1.00934e7			0.631793			0.315897	+	0.948794i	$0.397695\pi$
$762$	−2.72129e6	−	7.62738e6i	−0.169780	−	0.475870i
$763$	7.38245e6			0.459081
$764$	1.76516e7	−	1.44325e7i	1.09408	−	0.894560i
$765$	−6.40849e6	+	5.61420e6i	−0.395915	+	0.346844i
$766$	1.08611e6	+	3.04422e6i	0.0668811	+	0.187458i
$767$			2.40496e7i			1.47611i
$768$	−2.09419e7	−	8.85377e6i	−1.28119	−	0.541658i
$769$	−2.06066e7			−1.25658			−0.628290	−	0.777980i	$-0.716245\pi$
$769$	−2.06066e7			−1.25658			−0.628290	+	0.777980i	$0.716245\pi$
$770$	−1.25833e7	−	7.01660e6i	−0.764837	−	0.426481i
$771$			3.64344e7i			2.20737i
$772$	−3.88116e6	−	4.74681e6i	−0.234379	−	0.286655i
$773$	−2.40425e7			−1.44721			−0.723605	−	0.690215i	$-0.757516\pi$
$773$	−2.40425e7			−1.44721			−0.723605	+	0.690215i	$0.757516\pi$
$774$	−307695.	+	109779.i	−0.0184615	+	0.00658668i
$775$	396043.	−	2.98425e6i	0.0236858	−	0.178476i
$776$	−1.52070e7	−	9.17130e6i	−0.906544	−	0.546734i
$777$			4.47458e7i			2.65888i
$778$	9.53146e6	+	2.67153e7i	0.564561	+	1.58238i
$779$		−	828127.i		−	0.0488937i
$780$	3.73068e7	+	6.24917e6i	2.19559	+	0.367778i
$781$		−	7.36825e6i		−	0.432252i
$782$	−7.25285e6	+	2.58766e6i	−0.424123	+	0.151318i
$783$		−	955257.i		−	0.0556821i
$784$	−7.95428e6	+	3.92411e7i	−0.462180	+	2.28009i
$785$	−1.89594e6	−	2.16417e6i	−0.109812	−	0.125348i
$786$	−6.08997e6	−	1.70693e7i	−0.351608	−	0.985508i
$787$	1.44261e7			0.830256			0.415128	−	0.909763i	$-0.363737\pi$
$787$	1.44261e7			0.830256			0.415128	+	0.909763i	$0.363737\pi$
$788$	1.10866e7	−	9.06478e6i	0.636037	−	0.520046i
$789$		−	3.60161e7i		−	2.05970i
$790$	−1.92676e7	−	1.07438e7i	−1.09840	−	0.612478i
$791$	−4.26279e6			−0.242244
$792$	−6.78509e6	−	4.09207e6i	−0.384364	−	0.231809i
$793$			185196.i			0.0104580i
$794$	2.93807e7	−	1.04824e7i	1.65390	−	0.590077i
$795$	−1.83728e7	−	2.09722e7i	−1.03100	−	1.17686i
$796$	2.89697e6	−	2.36866e6i	0.162054	−	0.132501i
$797$	−7.27613e6			−0.405746			−0.202873	−	0.979205i	$-0.565028\pi$
$797$	−7.27613e6			−0.405746			−0.202873	+	0.979205i	$0.565028\pi$
$798$	−1.24814e7	+	4.45309e6i	−0.693834	+	0.247545i
$799$	1.32422e7			0.733824
$800$	−1.81009e7	+	194910.i	−0.999942	+	0.0107673i
$801$	−1.26354e6			−0.0695838
$802$	−3.44228e6	+	1.22813e6i	−0.188977	+	0.0674231i
$803$	8.62760e6			0.472173
$804$	−1.33824e7	+	1.09419e7i	−0.730117	+	0.596969i
$805$	−1.76728e7	−	2.01731e7i	−0.961205	−	1.09720i
$806$	5.00529e6	−	1.78578e6i	0.271389	−	0.0968257i
$807$			1.48946e7i			0.805089i
$808$	−3.08029e6	−	1.85772e6i	−0.165983	−	0.100104i
$809$	−1.86768e7			−1.00330			−0.501650	−	0.865070i	$-0.667274\pi$
$809$	−1.86768e7			−1.00330			−0.501650	+	0.865070i	$0.667274\pi$
$810$	1.73022e7	+	9.64791e6i	0.926594	+	0.516679i
$811$			7.20855e6i			0.384854i	0.981311	+	0.192427i	$0.0616358\pi$
$811$			7.20855e6i			0.384854i	−0.981311	+	0.192427i	$0.938364\pi$
$812$	1.62984e7	−	1.33261e7i	0.867470	−	0.709273i
$813$	5.15548e6			0.273554
$814$	3.19665e6	+	8.95976e6i	0.169096	+	0.473953i
$815$	1.73724e7	+	1.98303e7i	0.916151	+	1.04577i
$816$	1.45997e7	+	2.95941e6i	0.767573	+	0.155589i
$817$			116162.i			0.00608846i
$818$	−5.43849e6	+	1.94034e6i	−0.284181	+	0.101390i
$819$		−	5.23814e7i		−	2.72877i
$820$	−3.19756e6	−	535615.i	−0.166067	−	0.0278175i
$821$		−	6.00999e6i		−	0.311183i	−0.987821	−	0.155592i	$-0.950272\pi$
$821$		−	6.00999e6i		−	0.311183i	0.987821	−	0.155592i	$-0.0497284\pi$
$822$	1.47487e7	+	4.13386e7i	0.761333	+	2.13391i
$823$			2.98829e6i			0.153788i	0.997039	+	0.0768940i	$0.0245003\pi$
$823$			2.98829e6i			0.153788i	−0.997039	+	0.0768940i	$0.975500\pi$
$824$	−1.86324e7	−	1.12372e7i	−0.955985	−	0.576552i
$825$	−1.29430e7	−	1.71768e6i	−0.662063	−	0.0878632i
$826$	−3.10673e7	+	1.10842e7i	−1.58436	+	0.565266i
$827$	−6.14178e6			−0.312270			−0.156135	−	0.987736i	$-0.549904\pi$
$827$	−6.14178e6			−0.312270			−0.156135	+	0.987736i	$0.549904\pi$
$828$	−9.33634e6	−	1.14187e7i	−0.473261	−	0.578817i
$829$			3.62053e7i			1.82972i	0.403768	+	0.914862i	$0.367700\pi$
$829$			3.62053e7i			1.82972i	−0.403768	+	0.914862i	$0.632300\pi$
$830$	1.19844e6	+	668260.i	0.0603836	+	0.0336706i
$831$	5.14746e7			2.58577
$832$	−1.49095e7	−	2.82642e7i	−0.746714	−	1.41556i
$833$		−	2.62330e7i		−	1.30989i
$834$	−2.03323e6	−	5.69886e6i	−0.101221	−	0.283709i
$835$	2.71103e7	−	2.37502e7i	1.34561	−	1.17883i
$836$	−2.18111e6	+	1.78335e6i	−0.107935	+	0.0882512i
$837$	330729.			0.0163177
$838$	−3.11212e6	−	8.72283e6i	−0.153090	−	0.429089i
$839$	−1.12551e7			−0.552005			−0.276002	−	0.961157i	$-0.589010\pi$
$839$	−1.12551e7			−0.552005			−0.276002	+	0.961157i	$0.589010\pi$
$840$	9.12156e6	+	5.10733e7i	0.446037	+	2.49744i
$841$	1.27692e7			0.622550
$842$	−6.16818e6	−	1.72885e7i	−0.299831	−	0.840385i
$843$	1.57501e7			0.763333
$844$	−1.35688e7	−	1.65952e7i	−0.655671	−	0.801912i
$845$	2.13554e7	+	2.43768e7i	1.02889	+	1.17445i
$846$	8.52308e6	+	2.38890e7i	0.409421	+	1.14755i
$847$		−	2.93014e7i		−	1.40340i
$848$	−4.67934e6	+	2.30847e7i	−0.223458	+	1.10239i
$849$	2.28119e7			1.08616
$850$	1.15976e7	−	2.48117e6i	0.550583	−	0.117790i
$851$			1.77084e7i			0.838215i
$852$	−2.05411e7	+	1.67951e7i	−0.969449	+	0.792655i
$853$	−1.79575e6			−0.0845032			−0.0422516	−	0.999107i	$-0.513453\pi$
$853$	−1.79575e6			−0.0845032			−0.0422516	+	0.999107i	$0.513453\pi$
$854$	−239237.	+	85354.5i	−0.0112249	+	0.00400481i
$855$	−4.36453e6	+	3.82357e6i	−0.204184	+	0.178877i
$856$	−1.16864e7	+	1.93774e7i	−0.545127	+	0.903878i
$857$			2.19588e6i			0.102131i	0.998695	+	0.0510653i	$0.0162617\pi$
$857$			2.19588e6i			0.102131i	−0.998695	+	0.0510653i	$0.983738\pi$
$858$	−7.74511e6	−	2.17084e7i	−0.359178	−	1.00672i
$859$		−	3.86186e6i		−	0.178572i	−0.996006	−	0.0892860i	$-0.971541\pi$
$859$		−	3.86186e6i		−	0.178572i	0.996006	−	0.0892860i	$-0.0284585\pi$
$860$	448523.	+	75130.9i	0.0206794	+	0.00346396i
$861$			9.29212e6i			0.427176i
$862$	−1.80771e7	+	6.44952e6i	−0.828630	+	0.295637i
$863$			1.07467e7i			0.491188i	0.969373	+	0.245594i	$0.0789830\pi$
$863$			1.07467e7i			0.491188i	−0.969373	+	0.245594i	$0.921017\pi$
$864$	−282841.	−	1.96849e6i	−0.0128902	−	0.0897116i
$865$	−5.97866e6	−	6.82451e6i	−0.271684	−	0.310121i
$866$	−4.57065e6	−	1.28109e7i	−0.207102	−	0.580477i
$867$	2.10272e7			0.950022
$868$	4.61376e6	+	5.64282e6i	0.207853	+	0.254212i
$869$			1.34421e7i			0.603833i
$870$	9.29164e6	−	1.66633e7i	0.416192	−	0.746385i
$871$	−2.42951e7			−1.08511
$872$	−4.83978e6	−	2.91886e6i	−0.215543	−	0.129994i
$873$			2.22857e7i			0.989672i
$874$	−4.93958e6	+	1.76234e6i	−0.218732	+	0.0780388i
$875$	2.28946e7	+	3.43803e7i	1.01091	+	1.51806i
$876$	−1.96657e7	−	2.40519e7i	−0.865863	−	1.05898i
$877$	2.12160e7			0.931460			0.465730	−	0.884927i	$-0.345792\pi$
$877$	2.12160e7			0.931460			0.465730	+	0.884927i	$0.345792\pi$
$878$	2.81639e7	−	1.00483e7i	1.23298	−	0.439901i
$879$	−3.34278e7			−1.45927
$880$	5.47516e6	+	9.57512e6i	0.238336	+	0.416809i
$881$	3.72206e7			1.61564			0.807818	−	0.589432i	$-0.200649\pi$
$881$	3.72206e7			1.61564			0.807818	+	0.589432i	$0.200649\pi$
$882$	4.73246e7	−	1.68844e7i	2.04840	−	0.730826i
$883$	−2.67206e7			−1.15331			−0.576654	−	0.816989i	$-0.695642\pi$
$883$	−2.67206e7			−1.15331			−0.576654	+	0.816989i	$0.695642\pi$
$884$	1.32526e7	+	1.62085e7i	0.570389	+	0.697609i
$885$	−2.24846e7	+	1.96978e7i	−0.965000	+	0.845394i
$886$	−2.42716e7	+	8.65959e6i	−1.03876	+	0.370606i
$887$		−	1.29413e7i		−	0.552290i	−0.961116	−	0.276145i	$-0.910943\pi$
$887$		−	1.29413e7i		−	0.552290i	0.961116	−	0.276145i	$-0.0890570\pi$
$888$	1.76915e7	−	2.93344e7i	0.752891	−	1.24837i
$889$	1.56109e7			0.662482
$890$	1.53622e6	+	856615.i	0.0650099	+	0.0362502i
$891$		−	1.20709e7i		−	0.509386i
$892$	34817.7	+	42583.4i	0.00146517	+	0.00179196i
$893$	9.01862e6			0.378453
$894$	−1.28123e7	−	3.59112e7i	−0.536148	−	1.50275i
$895$	3.14426e6	−	2.75455e6i	0.131208	−	0.114946i
$896$	2.96402e7	−	3.22868e7i	1.23342	−	1.34355i
$897$		−	4.29053e7i		−	1.78045i
$898$	1.72694e7	−	6.16137e6i	0.714640	−	0.254968i
$899$		−	2.68041e6i		−	0.110612i
$900$	1.19407e7	+	1.93253e7i	0.491386	+	0.795280i
$901$		−	1.54323e7i		−	0.633315i
$902$	663831.	+	1.86063e6i	0.0271670	+	0.0761452i
$903$		−	1.30341e6i		−	0.0531938i
$904$	2.79460e6	+	1.68541e6i	0.113736	+	0.0685939i
$905$	2.91009e6	−	2.54940e6i	0.118109	−	0.103470i
$906$	4.24690e7	−	1.51520e7i	1.71890	−	0.613268i
$907$	−3.82873e7			−1.54538			−0.772692	−	0.634781i	$-0.781090\pi$
$907$	−3.82873e7			−1.54538			−0.772692	+	0.634781i	$0.781090\pi$
$908$	−1.76711e7	+	1.44485e7i	−0.711293	+	0.581577i
$909$			4.51414e6i			0.181203i
$910$	−3.55119e7	+	6.36858e7i	−1.42158	+	2.54941i
$911$	−1.48261e7			−0.591876			−0.295938	−	0.955207i	$-0.595632\pi$
$911$	−1.48261e7			−0.591876			−0.295938	+	0.955207i	$0.595632\pi$
$912$	9.94320e6	+	2.01551e6i	0.395858	+	0.0802415i
$913$		−	836091.i		−	0.0331953i
$914$	9.74044e6	+	2.73011e7i	0.385668	+	1.08097i
$915$	−173145.	+	151684.i	−0.00683685	+	0.00598947i
$916$	−2.37033e7	−	2.89901e7i	−0.933404	−	1.14159i
$917$	3.49357e7			1.37197
$918$	437838.	+	1.22720e6i	0.0171477	+	0.0480627i
$919$	2.75810e7			1.07726			0.538631	−	0.842542i	$-0.318942\pi$
$919$	2.75810e7			1.07726			0.538631	+	0.842542i	$0.318942\pi$
$920$	3.60991e6	+	2.02125e7i	0.140613	+	0.787320i
$921$	−4.80103e7			−1.86503
$922$	1.50138e6	+	4.20815e6i	0.0581651	+	0.163029i
$923$	−3.72916e7			−1.44081
$924$	2.44734e7	−	2.00103e7i	0.943007	−	0.771035i
$925$	3.58803e6	−	2.70364e7i	0.137880	−	1.03895i
$926$	139635.	+	391376.i	0.00535138	+	0.0149992i
$927$			2.73057e7i			1.04365i
$928$	−1.59537e7	+	2.29230e6i	−0.608124	+	0.0873781i
$929$	3.07295e7			1.16820			0.584099	−	0.811682i	$-0.301448\pi$
$929$	3.07295e7			1.16820			0.584099	+	0.811682i	$0.301448\pi$
$930$	5.76916e6	+	3.21695e6i	0.218728	+	0.121965i
$931$		−	1.78661e7i		−	0.675546i
$932$	3.09412e7	+	3.78424e7i	1.16680	+	1.42705i
$933$	−3.33542e7			−1.25443
$934$	−2.86256e7	+	1.02130e7i	−1.07371	+	0.383077i
$935$	−4.76204e6	−	5.43576e6i	−0.178141	−	0.203344i
$936$	−2.07105e7	+	3.43402e7i	−0.772681	+	1.28119i
$937$		−	9.51349e6i		−	0.353990i	−0.984212	−	0.176995i	$-0.943362\pi$
$937$		−	9.51349e6i		−	0.353990i	0.984212	−	0.176995i	$-0.0566377\pi$
$938$	−1.11973e7	−	3.13846e7i	−0.415535	−	1.16469i
$939$			5.06703e7i			1.87538i
$940$	5.83306e6	−	3.48227e7i	0.215316	−	1.28541i
$941$			2.64149e7i			0.972466i	0.873829	+	0.486233i	$0.161629\pi$
$941$			2.64149e7i			0.972466i	−0.873829	+	0.486233i	$0.838371\pi$
$942$	5.94601e6	−	2.12141e6i	0.218323	−	0.0778928i
$943$			3.67741e6i			0.134667i
$944$	2.47495e7	+	5.01680e6i	0.903935	+	0.183230i
$945$	−3.41334e6	+	2.99028e6i	−0.124337	+	0.108926i
$946$	−93115.9	−	260991.i	−0.00338295	−	0.00948194i
$947$	−4.05240e7			−1.46837			−0.734187	−	0.678947i	$-0.762437\pi$
$947$	−4.05240e7			−1.46837			−0.734187	+	0.678947i	$0.762437\pi$
$948$	3.74737e7	−	3.06398e7i	1.35427	−	1.10730i
$949$		−	4.36653e7i		−	1.57388i
$950$	7.89862e6	−	1.68981e6i	0.283950	−	0.0607477i
$951$	−2.49924e7			−0.896101
$952$	−1.48302e7	+	2.45901e7i	−0.530341	+	0.879362i
$953$		−	3.84770e7i		−	1.37236i	−0.727431	−	0.686181i	$-0.759286\pi$
$953$		−	3.84770e7i		−	1.37236i	0.727431	−	0.686181i	$-0.240714\pi$
$954$	2.78401e7	−	9.93275e6i	0.990375	−	0.353345i
$955$	2.62471e7	+	2.99605e7i	0.931263	+	1.06302i
$956$	−1.40525e7	+	1.14898e7i	−0.497289	+	0.406601i
$957$	−1.16252e7			−0.410318
$958$	−1.29134e7	+	4.60721e6i	−0.454596	+	0.162190i
$959$	−8.46074e7			−2.97072
$960$	1.42134e7	−	3.70891e7i	0.497758	−	1.29888i
$961$	−2.77011e7			−0.967585
$962$	4.53464e7	−	1.61786e7i	1.57981	−	0.563643i
$963$	2.83974e7			0.986762
$964$	1.70517e7	−	1.39421e7i	0.590985	−	0.483209i
$965$	8.05688e6	−	7.05828e6i	0.278515	−	0.243995i
$966$	5.54253e7	−	1.97746e7i	1.91102	−	0.681811i
$967$			9.84732e6i			0.338651i	0.985560	+	0.169325i	$0.0541588\pi$
$967$			9.84732e6i			0.338651i	−0.985560	+	0.169325i	$0.945841\pi$
$968$	−1.15851e7	+	1.92094e7i	−0.397387	+	0.658909i
$969$	−6.64711e6			−0.227417
$970$	1.51086e7	−	2.70952e7i	0.515578	−	0.924619i
$971$			1.96906e7i			0.670211i	0.942181	+	0.335105i	$0.108772\pi$
$971$			1.96906e7i			0.670211i	−0.942181	+	0.335105i	$0.891228\pi$
$972$	−3.15845e7	+	2.58246e7i	−1.07228	+	0.876734i
$973$	1.16638e7			0.394965
$974$	8.54281e6	+	2.39443e7i	0.288538	+	0.808732i
$975$	−8.69338e6	+	6.55060e7i	−0.292871	+	2.20683i
$976$	190586.	+	38632.3i	0.00640422	+	0.00129815i
$977$			2.36761e7i			0.793549i	0.917916	+	0.396775i	$0.129871\pi$
$977$			2.36761e7i			0.793549i	−0.917916	+	0.396775i	$0.870129\pi$
$978$	−5.44833e7	+	1.94385e7i	−1.82145	+	0.649853i
$979$		−	1.07175e6i		−	0.0357386i
$980$	−6.89844e7	−	1.15554e7i	−2.29449	−	0.384344i
$981$			7.09267e6i			0.235308i
$982$	6.33653e6	+	1.77604e7i	0.209688	+	0.587725i
$983$		−	2.18805e7i		−	0.722225i	−0.932522	−	0.361112i	$-0.882397\pi$
$983$		−	2.18805e7i		−	0.722225i	0.932522	−	0.361112i	$-0.117603\pi$
$984$	3.67390e6	−	6.09172e6i	0.120959	−	0.200564i
$985$	1.64852e7	+	1.88175e7i	0.541383	+	0.617977i
$986$	9.94591e6	−	3.54849e6i	0.325801	−	0.116239i
$987$	−1.01195e8			−3.30647
$988$	9.02574e6	+	1.10388e7i	0.294165	+	0.359775i
$989$		−	515831.i		−	0.0167694i
$990$	6.74117e6	−	1.20894e7i	0.218599	−	0.392028i
$991$	3.03505e7			0.981706			0.490853	−	0.871242i	$-0.336685\pi$
$991$	3.03505e7			0.981706			0.490853	+	0.871242i	$0.336685\pi$
$992$	−793641.	−	5.52350e6i	−0.0256062	−	0.178211i
$993$		−	4.43467e7i		−	1.42721i
$994$	−1.71873e7	−	4.81734e7i	−0.551748	−	1.54647i
$995$	4.30765e6	+	4.91709e6i	0.137938	+	0.157453i
$996$	−2.33085e6	+	1.90578e6i	−0.0744501	+	0.0608730i
$997$	−4.83451e6			−0.154033			−0.0770167	−	0.997030i	$-0.524539\pi$
$997$	−4.83451e6			−0.154033			−0.0770167	+	0.997030i	$0.524539\pi$
$998$	−1.23060e7	−	3.44920e7i	−0.391102	−	1.09620i
$999$	2.99630e6			0.0949886

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.6.f.a.29.4	yes	28
4.3	odd	2		160.6.f.a.49.4		28
5.2	odd	4		200.6.d.e.101.11		28
5.3	odd	4		200.6.d.e.101.18		28
5.4	even	2	inner	40.6.f.a.29.25	yes	28
8.3	odd	2		160.6.f.a.49.26		28
8.5	even	2	inner	40.6.f.a.29.26	yes	28
20.3	even	4		800.6.d.e.401.27		28
20.7	even	4		800.6.d.e.401.2		28
20.19	odd	2		160.6.f.a.49.25		28
40.3	even	4		800.6.d.e.401.28		28
40.13	odd	4		200.6.d.e.101.17		28
40.19	odd	2		160.6.f.a.49.3		28
40.27	even	4		800.6.d.e.401.1		28
40.29	even	2	inner	40.6.f.a.29.3	✓	28
40.37	odd	4		200.6.d.e.101.12		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.6.f.a.29.3	✓	28	40.29	even	2	inner
40.6.f.a.29.4	yes	28	1.1	even	1	trivial
40.6.f.a.29.25	yes	28	5.4	even	2	inner
40.6.f.a.29.26	yes	28	8.5	even	2	inner
160.6.f.a.49.3		28	40.19	odd	2
160.6.f.a.49.4		28	4.3	odd	2
160.6.f.a.49.25		28	20.19	odd	2
160.6.f.a.49.26		28	8.3	odd	2
200.6.d.e.101.11		28	5.2	odd	4
200.6.d.e.101.12		28	40.37	odd	4
200.6.d.e.101.17		28	40.13	odd	4
200.6.d.e.101.18		28	5.3	odd	4
800.6.d.e.401.1		28	40.27	even	4
800.6.d.e.401.2		28	20.7	even	4
800.6.d.e.401.27		28	20.3	even	4
800.6.d.e.401.28		28	40.3	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)

\(f(q)\)	\(=\)	\(q+(-5.32791 + 1.90088i) q^{2} +21.6833 q^{3} +(24.7733 - 20.2555i) q^{4} +(36.8367 + 42.0483i) q^{5} +(-115.527 + 41.2175i) q^{6} -236.448i q^{7} +(-93.4865 + 155.011i) q^{8} +227.167 q^{9} +O(q^{10})\)	\(q+(-5.32791 + 1.90088i) q^{2} +21.6833 q^{3} +(24.7733 - 20.2555i) q^{4} +(36.8367 + 42.0483i) q^{5} +(-115.527 + 41.2175i) q^{6} -236.448i q^{7} +(-93.4865 + 155.011i) q^{8} +227.167 q^{9} +(-276.192 - 154.007i) q^{10} +192.686i q^{11} +(537.167 - 439.206i) q^{12} +975.206 q^{13} +(449.461 + 1259.78i) q^{14} +(798.742 + 911.747i) q^{15} +(203.430 - 1003.59i) q^{16} +670.908i q^{17} +(-1210.32 + 431.818i) q^{18} +456.924i q^{19} +(1764.27 + 295.529i) q^{20} -5126.98i q^{21} +(-366.273 - 1026.61i) q^{22} -2029.03i q^{23} +(-2027.10 + 3361.15i) q^{24} +(-411.118 + 3097.84i) q^{25} +(-5195.81 + 1853.75i) q^{26} -343.317 q^{27} +(-4789.37 - 5857.60i) q^{28} +2782.43i q^{29} +(-5988.75 - 3339.39i) q^{30} -963.333 q^{31} +(823.849 + 5733.73i) q^{32} +4178.07i q^{33} +(-1275.32 - 3574.54i) q^{34} +(9942.24 - 8709.97i) q^{35} +(5627.67 - 4601.37i) q^{36} -8727.50 q^{37} +(-868.560 - 2434.45i) q^{38} +21145.7 q^{39} +(-9961.66 + 1779.13i) q^{40} -1812.39 q^{41} +(9745.80 + 27316.1i) q^{42} +254.225 q^{43} +(3902.94 + 4773.46i) q^{44} +(8368.07 + 9551.98i) q^{45} +(3856.96 + 10810.5i) q^{46} -19737.7i q^{47} +(4411.05 - 21761.2i) q^{48} -39100.7 q^{49} +(-3698.23 - 17286.5i) q^{50} +14547.5i q^{51} +(24159.0 - 19753.3i) q^{52} -23002.2 q^{53} +(1829.16 - 652.606i) q^{54} +(-8102.10 + 7097.90i) q^{55} +(36652.0 + 22104.7i) q^{56} +9907.64i q^{57} +(-5289.09 - 14824.6i) q^{58} +24661.0i q^{59} +(38255.3 + 6408.05i) q^{60} +189.904i q^{61} +(5132.55 - 1831.18i) q^{62} -53713.2i q^{63} +(-15288.6 - 28982.8i) q^{64} +(35923.3 + 41005.7i) q^{65} +(-7942.02 - 22260.4i) q^{66} -24912.8 q^{67} +(13589.6 + 16620.6i) q^{68} -43996.2i q^{69} +(-36414.7 + 65305.0i) q^{70} -38239.7 q^{71} +(-21237.0 + 35213.3i) q^{72} -44775.5i q^{73} +(46499.4 - 16590.0i) q^{74} +(-8914.41 + 67171.5i) q^{75} +(9255.22 + 11319.5i) q^{76} +45560.2 q^{77} +(-112662. + 40195.5i) q^{78} +69761.6 q^{79} +(49692.9 - 28415.0i) q^{80} -62645.8 q^{81} +(9656.28 - 3445.15i) q^{82} -4339.15 q^{83} +(-103850. - 127012. i) q^{84} +(-28210.5 + 24714.0i) q^{85} +(-1354.49 + 483.253i) q^{86} +60332.4i q^{87} +(-29868.3 - 18013.5i) q^{88} -5562.17 q^{89} +(-62741.5 - 34985.3i) q^{90} -230586. i q^{91} +(-41099.1 - 50265.8i) q^{92} -20888.3 q^{93} +(37519.0 + 105161. i) q^{94} +(-19212.9 + 16831.6i) q^{95} +(17863.8 + 124326. i) q^{96} +98102.9i q^{97} +(208325. - 74326.0i) q^{98} +43771.8i 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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