LMFDB - Embedded newform 63.6.f.b.43.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [63,6,Mod(22,63)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("63.22"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(63, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 63 = 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	63.f (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$10.1041806482$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			43.1
Character	$\chi$	$=$	63.43
Dual form			63.6.f.b.22.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-5.32234 + 9.21856i) q^{2} +(-5.57188 + 14.5586i) q^{3} +(-40.6546 - 70.4158i) q^{4} +(9.68441 + 16.7739i) q^{5} +(-104.554 - 128.851i) q^{6} +(24.5000 - 42.4352i) q^{7} +524.880 q^{8} +(-180.908 - 162.238i) q^{9} -206.175 q^{10} +(342.619 - 593.434i) q^{11} +(1251.68 - 199.527i) q^{12} +(10.5096 + 18.2031i) q^{13} +(260.795 + 451.709i) q^{14} +(-298.166 + 47.5297i) q^{15} +(-1492.64 + 2585.33i) q^{16} -566.915 q^{17} +(2458.46 - 804.227i) q^{18} -2762.91 q^{19} +(787.431 - 1363.87i) q^{20} +(481.288 + 593.131i) q^{21} +(3647.07 + 6316.92i) q^{22} +(802.784 + 1390.46i) q^{23} +(-2924.57 + 7641.54i) q^{24} +(1374.92 - 2381.44i) q^{25} -223.742 q^{26} +(3369.97 - 1729.81i) q^{27} -3984.15 q^{28} +(1194.61 - 2069.13i) q^{29} +(1148.78 - 3001.63i) q^{30} +(-1882.47 - 3260.54i) q^{31} +(-7490.61 - 12974.1i) q^{32} +(6730.56 + 8294.62i) q^{33} +(3017.31 - 5226.14i) q^{34} +949.072 q^{35} +(-4069.38 + 19334.5i) q^{36} +11576.9 q^{37} +(14705.1 - 25470.0i) q^{38} +(-323.571 + 51.5795i) q^{39} +(5083.15 + 8804.28i) q^{40} +(-4787.76 - 8292.64i) q^{41} +(-8029.39 + 1279.94i) q^{42} +(-3283.41 + 5687.04i) q^{43} -55716.2 q^{44} +(969.376 - 4605.72i) q^{45} -17090.8 q^{46} +(8816.10 - 15269.9i) q^{47} +(-29322.1 - 36136.0i) q^{48} +(-1200.50 - 2079.33i) q^{49} +(14635.6 + 25349.6i) q^{50} +(3158.78 - 8253.51i) q^{51} +(854.526 - 1480.08i) q^{52} -1608.88 q^{53} +(-1989.79 + 40272.9i) q^{54} +13272.3 q^{55} +(12859.6 - 22273.4i) q^{56} +(15394.6 - 40224.2i) q^{57} +(12716.3 + 22025.2i) q^{58} +(15261.2 + 26433.2i) q^{59} +(15468.6 + 19063.3i) q^{60} +(3975.64 - 6886.01i) q^{61} +40076.6 q^{62} +(-11316.9 + 3702.05i) q^{63} +63941.1 q^{64} +(-203.558 + 352.573i) q^{65} +(-112287. + 17899.3i) q^{66} +(-26909.6 - 46608.8i) q^{67} +(23047.7 + 39919.7i) q^{68} +(-24716.3 + 3939.95i) q^{69} +(-5051.28 + 8749.08i) q^{70} +74215.5 q^{71} +(-94955.0 - 85155.5i) q^{72} -90409.2 q^{73} +(-61616.0 + 106722. i) q^{74} +(27009.6 + 33286.1i) q^{75} +(112325. + 194552. i) q^{76} +(-16788.4 - 29078.3i) q^{77} +(1246.67 - 3257.39i) q^{78} +(30653.3 - 53093.1i) q^{79} -57821.4 q^{80} +(6406.55 + 58700.4i) q^{81} +101928. q^{82} +(-2938.50 + 5089.62i) q^{83} +(22199.2 - 58003.8i) q^{84} +(-5490.24 - 9509.37i) q^{85} +(-34950.9 - 60536.7i) q^{86} +(23467.5 + 28920.9i) q^{87} +(179834. - 311482. i) q^{88} -94191.4 q^{89} +(37298.7 + 33449.4i) q^{90} +1029.94 q^{91} +(65273.7 - 113057. i) q^{92} +(57957.9 - 9238.90i) q^{93} +(93844.5 + 162543. i) q^{94} +(-26757.1 - 46344.7i) q^{95} +(230622. - 36762.8i) q^{96} +(-20602.7 + 35684.9i) q^{97} +25557.9 q^{98} +(-158260. + 51771.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 4 q^{2} + 20 q^{3} - 240 q^{4} + 71 q^{5} - 266 q^{6} + 735 q^{7} + 42 q^{8} - 442 q^{9} + 134 q^{11} - 1400 q^{12} + 165 q^{13} - 196 q^{14} + 647 q^{15} - 3840 q^{16} - 2184 q^{17} + 9235 q^{18}+ \cdots - 518014 q^{99}+O(q^{100}) $ 30 * q + 4 * q^2 + 20 * q^3 - 240 * q^4 + 71 * q^5 - 266 * q^6 + 735 * q^7 + 42 * q^8 - 442 * q^9 + 134 * q^11 - 1400 * q^12 + 165 * q^13 - 196 * q^14 + 647 * q^15 - 3840 * q^16 - 2184 * q^17 + 9235 * q^18 - 894 * q^19 - 1214 * q^20 - 392 * q^21 - 96 * q^22 - 3564 * q^23 - 1620 * q^24 - 3576 * q^25 - 1730 * q^26 + 23879 * q^27 - 23520 * q^28 + 4073 * q^29 - 19868 * q^30 - 2217 * q^31 + 12107 * q^32 - 5506 * q^33 - 15654 * q^34 + 6958 * q^35 + 45898 * q^36 + 10014 * q^37 + 48685 * q^38 - 7126 * q^39 - 7485 * q^40 + 22294 * q^41 - 17689 * q^42 - 3153 * q^43 - 164960 * q^44 - 361 * q^45 - 36492 * q^46 + 74313 * q^47 + 16051 * q^48 - 36015 * q^49 + 111323 * q^50 + 10149 * q^51 + 33501 * q^52 - 55548 * q^53 + 35398 * q^54 + 77376 * q^55 + 1029 * q^56 + 46199 * q^57 - 3249 * q^58 + 90567 * q^59 - 49136 * q^60 - 3714 * q^61 - 357408 * q^62 + 2548 * q^63 + 94434 * q^64 + 79607 * q^65 - 284270 * q^66 - 11016 * q^67 + 241743 * q^68 + 199305 * q^69 + 107586 * q^71 - 85305 * q^72 - 240162 * q^73 + 95016 * q^74 - 147461 * q^75 + 122748 * q^76 - 6566 * q^77 + 174484 * q^78 + 11013 * q^79 - 592898 * q^80 - 120058 * q^81 + 162036 * q^82 + 7014 * q^83 - 53116 * q^84 - 36387 * q^85 + 170519 * q^86 + 654053 * q^87 - 108012 * q^88 - 152320 * q^89 + 25909 * q^90 + 16170 * q^91 + 153651 * q^92 - 594909 * q^93 - 266412 * q^94 - 64264 * q^95 + 1058867 * q^96 - 81033 * q^97 - 19208 * q^98 - 518014 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/63\mathbb{Z}\right)^\times$.

$n$	$10$	$29$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−5.32234	+	9.21856i	−0.940865	+	1.62963i	−0.177040	+	0.984204i	$0.556652\pi$
$2$	−5.32234	+	9.21856i	−0.940865	+	1.62963i	−0.763825	+	0.645423i	$0.776681\pi$
$3$	−5.57188	+	14.5586i	−0.357437	+	0.933937i
$3$	−5.57188	+	14.5586i	−0.357437	+	0.933937i
$4$	−40.6546	−	70.4158i	−1.27046	−	2.20049i
$5$	9.68441	+	16.7739i	0.173240	+	0.300061i	0.939551	−	0.342410i	$-0.111243\pi$
$5$	9.68441	+	16.7739i	0.173240	+	0.300061i	−0.766311	+	0.642470i	$0.777910\pi$
$6$	−104.554	−	128.851i	−1.18567	−	1.46120i
$7$	24.5000	−	42.4352i	0.188982	−	0.327327i
$7$	24.5000	−	42.4352i	0.188982	−	0.327327i
$8$	524.880			2.89958
$9$	−180.908	−	162.238i	−0.744478	−	0.667647i
$10$	−206.175			−0.651982
$11$	342.619	−	593.434i	0.853749	−	1.47874i	−0.0240512	−	0.999711i	$-0.507656\pi$
$11$	342.619	−	593.434i	0.853749	−	1.47874i	0.877801	−	0.479026i	$-0.159010\pi$
$12$	1251.68	−	199.527i	2.50923	−	0.399989i
$13$	10.5096	+	18.2031i	0.0172475	+	0.0298736i	0.874520	−	0.484989i	$-0.161176\pi$
$13$	10.5096	+	18.2031i	0.0172475	+	0.0298736i	−0.857273	+	0.514862i	$0.827843\pi$
$14$	260.795	+	451.709i	0.355614	+	0.615941i
$15$	−298.166	+	47.5297i	−0.342160	+	0.0545427i
$16$	−1492.64	+	2585.33i	−1.45766	+	2.52474i
$17$	−566.915			−0.475768			−0.237884	−	0.971294i	$-0.576454\pi$
$17$	−566.915			−0.475768			−0.237884	+	0.971294i	$0.576454\pi$
$18$	2458.46	−	804.227i	1.78847	−	0.585056i
$19$	−2762.91			−1.75583			−0.877914	−	0.478818i	$-0.841065\pi$
$19$	−2762.91			−1.75583			−0.877914	+	0.478818i	$0.841065\pi$
$20$	787.431	−	1363.87i	0.440187	−	0.762427i
$21$	481.288	+	593.131i	0.238154	+	0.293496i
$22$	3647.07	+	6316.92i	1.60653	+	2.78258i
$23$	802.784	+	1390.46i	0.316431	+	0.548075i	0.979741	−	0.200270i	$-0.0641820\pi$
$23$	802.784	+	1390.46i	0.316431	+	0.548075i	−0.663310	+	0.748345i	$0.730849\pi$
$24$	−2924.57	+	7641.54i	−1.03642	+	2.70802i
$25$	1374.92	−	2381.44i	0.439976	−	0.762060i
$26$	−223.742			−0.0649105
$27$	3369.97	−	1729.81i	0.889644	−	0.456655i
$28$	−3984.15			−0.960374
$29$	1194.61	−	2069.13i	0.263774	−	0.456871i	−0.703467	−	0.710728i	$-0.748366\pi$
$29$	1194.61	−	2069.13i	0.263774	−	0.456871i	0.967242	+	0.253857i	$0.0816992\pi$
$30$	1148.78	−	3001.63i	0.233042	−	0.608911i
$31$	−1882.47	−	3260.54i	−0.351823	−	0.609375i	0.634746	−	0.772721i	$-0.281105\pi$
$31$	−1882.47	−	3260.54i	−0.351823	−	0.609375i	−0.986569	+	0.163346i	$0.947771\pi$
$32$	−7490.61	−	12974.1i	−1.29313	−	2.23977i
$33$	6730.56	+	8294.62i	1.07589	+	1.32590i
$34$	3017.31	−	5226.14i	0.447634	−	0.775325i
$35$	949.072			0.130957
$36$	−4069.38	+	19334.5i	−0.523326	+	2.48643i
$37$	11576.9			1.39023			0.695115	−	0.718898i	$-0.255353\pi$
$37$	11576.9			1.39023			0.695115	+	0.718898i	$0.255353\pi$
$38$	14705.1	−	25470.0i	1.65200	−	2.86134i
$39$	−323.571	+	51.5795i	−0.0340650	+	0.00543020i
$40$	5083.15	+	8804.28i	0.502323	+	0.870049i
$41$	−4787.76	−	8292.64i	−0.444808	−	0.770430i	0.553231	−	0.833028i	$-0.313395\pi$
$41$	−4787.76	−	8292.64i	−0.444808	−	0.770430i	−0.998039	+	0.0625979i	$0.980061\pi$
$42$	−8029.39	+	1279.94i	−0.702360	+	0.111961i
$43$	−3283.41	+	5687.04i	−0.270804	+	0.469046i	−0.969068	−	0.246794i	$-0.920623\pi$
$43$	−3283.41	+	5687.04i	−0.270804	+	0.469046i	0.698264	+	0.715840i	$0.253956\pi$
$44$	−55716.2			−4.33860
$45$	969.376	−	4605.72i	0.0713610	−	0.339052i
$46$	−17090.8			−1.19088
$47$	8816.10	−	15269.9i	0.582146	−	1.00831i	−0.413079	−	0.910695i	$-0.635547\pi$
$47$	8816.10	−	15269.9i	0.582146	−	1.00831i	0.995225	−	0.0976108i	$-0.0311200\pi$
$48$	−29322.1	−	36136.0i	−1.83693	−	2.26379i
$49$	−1200.50	−	2079.33i	−0.0714286	−	0.123718i
$50$	14635.6	+	25349.6i	0.827916	+	1.43399i
$51$	3158.78	−	8253.51i	0.170057	−	0.444338i
$52$	854.526	−	1480.08i	0.0438245	−	0.0759062i
$53$	−1608.88			−0.0786745			−0.0393373	−	0.999226i	$-0.512525\pi$
$53$	−1608.88			−0.0786745			−0.0393373	+	0.999226i	$0.512525\pi$
$54$	−1989.79	+	40272.9i	−0.0928588	+	1.87944i
$55$	13272.3			0.591614
$56$	12859.6	−	22273.4i	0.547969	−	0.949110i
$57$	15394.6	−	40224.2i	0.627597	−	1.63983i
$58$	12716.3	+	22025.2i	0.496352	+	0.859707i
$59$	15261.2	+	26433.2i	0.570767	+	0.988598i	0.996487	+	0.0837431i	$0.0266875\pi$
$59$	15261.2	+	26433.2i	0.570767	+	0.988598i	−0.425720	+	0.904855i	$0.639979\pi$
$60$	15468.6	+	19063.3i	0.554720	+	0.683627i
$61$	3975.64	−	6886.01i	0.136799	−	0.236943i	−0.789484	−	0.613771i	$-0.789652\pi$
$61$	3975.64	−	6886.01i	0.136799	−	0.236943i	0.926283	+	0.376828i	$0.122985\pi$
$62$	40076.6			1.32407
$63$	−11316.9	+	3702.05i	−0.359232	+	0.117514i
$64$	63941.1			1.95133
$65$	−203.558	+	352.573i	−0.00597593	+	0.0103506i
$66$	−112287.	+	17899.3i	−3.17299	+	0.505797i
$67$	−26909.6	−	46608.8i	−0.732352	−	1.26847i	−0.955875	−	0.293773i	$-0.905089\pi$
$67$	−26909.6	−	46608.8i	−0.732352	−	1.26847i	0.223523	−	0.974699i	$-0.428244\pi$
$68$	23047.7	+	39919.7i	0.604442	+	1.04692i
$69$	−24716.3	+	3939.95i	−0.624972	+	0.0996249i
$70$	−5051.28	+	8749.08i	−0.123213	+	0.213411i
$71$	74215.5			1.74722			0.873612	−	0.486623i	$-0.161771\pi$
$71$	74215.5			1.74722			0.873612	+	0.486623i	$0.161771\pi$
$72$	−94955.0	−	85155.5i	−2.15867	−	1.93589i
$73$	−90409.2			−1.98566			−0.992831	−	0.119526i	$-0.961862\pi$
$73$	−90409.2			−1.98566			−0.992831	+	0.119526i	$0.961862\pi$
$74$	−61616.0	+	106722.i	−1.30802	+	2.26556i
$75$	27009.6	+	33286.1i	0.554453	+	0.683298i
$76$	112325.	+	194552.i	2.23070	+	3.86369i
$77$	−16788.4	−	29078.3i	−0.322687	−	0.558910i
$78$	1246.67	−	3257.39i	0.0232014	−	0.0606223i
$79$	30653.3	−	53093.1i	0.552598	−	0.957128i	−0.445488	−	0.895288i	$-0.646970\pi$
$79$	30653.3	−	53093.1i	0.552598	−	0.957128i	0.998086	−	0.0618402i	$-0.0196969\pi$
$80$	−57821.4			−1.01010
$81$	6406.55	+	58700.4i	0.108495	+	0.994097i
$82$	101928.			1.67402
$83$	−2938.50	+	5089.62i	−0.0468198	+	0.0810943i	−0.888486	−	0.458905i	$-0.848242\pi$
$83$	−2938.50	+	5089.62i	−0.0468198	+	0.0810943i	0.841666	+	0.539999i	$0.181575\pi$
$84$	22199.2	−	58003.8i	0.343273	−	0.896929i
$85$	−5490.24	−	9509.37i	−0.0824221	−	0.142759i
$86$	−34950.9	−	60536.7i	−0.509580	−	0.882618i
$87$	23467.5	+	28920.9i	0.332406	+	0.409651i
$88$	179834.	−	311482.i	2.47551	−	4.28771i
$89$	−94191.4			−1.26048			−0.630240	−	0.776400i	$-0.717044\pi$
$89$	−94191.4			−1.26048			−0.630240	+	0.776400i	$0.717044\pi$
$90$	37298.7	+	33449.4i	0.485386	+	0.435294i
$91$	1029.94			0.0130379
$92$	65273.7	−	113057.i	0.804023	−	1.39261i
$93$	57957.9	−	9238.90i	0.694873	−	0.110768i
$94$	93844.5	+	162543.i	1.09544	+	1.89736i
$95$	−26757.1	−	46344.7i	−0.304180	−	0.526855i
$96$	230622.	−	36762.8i	2.55401	−	0.407128i
$97$	−20602.7	+	35684.9i	−0.222328	+	0.385084i	−0.955515	−	0.294944i	$-0.904699\pi$
$97$	−20602.7	+	35684.9i	−0.222328	+	0.385084i	0.733186	+	0.680028i	$0.238032\pi$
$98$	25557.9			0.268819
$99$	−158260.	+	51771.2i	−1.62287	+	0.530885i
$100$	−223588.			−2.23588
$101$	49746.1	−	86162.7i	0.485238	−	0.840458i	−0.514618	−	0.857420i	$-0.672066\pi$
$101$	49746.1	−	86162.7i	0.485238	−	0.840458i	0.999856	+	0.0169621i	$0.00539947\pi$
$102$	59273.4	+	73047.4i	0.564104	+	0.695191i
$103$	−52621.0	−	91142.2i	−0.488727	−	0.846499i	0.511189	−	0.859468i	$-0.329205\pi$
$103$	−52621.0	−	91142.2i	−0.488727	−	0.846499i	−0.999916	+	0.0129689i	$0.995872\pi$
$104$	5516.27	+	9554.46i	0.0500106	+	0.0866209i
$105$	−5288.12	+	13817.2i	−0.0468089	+	0.122306i
$106$	8563.01	−	14831.6i	0.0740221	−	0.128210i
$107$	99883.5			0.843401			0.421701	−	0.906735i	$-0.361433\pi$
$107$	99883.5			0.843401			0.421701	+	0.906735i	$0.361433\pi$
$108$	−258810.	−	166974.i	−2.13512	−	1.37750i
$109$	−130287.			−1.05035			−0.525177	−	0.850993i	$-0.676001\pi$
$109$	−130287.			−1.05035			−0.525177	+	0.850993i	$0.676001\pi$
$110$	−70639.5	+	122351.i	−0.556629	+	0.964110i
$111$	−64505.0	+	168544.i	−0.496919	+	1.29839i
$112$	73139.4	+	126681.i	0.550943	+	0.954261i
$113$	−11901.0	−	20613.2i	−0.0876776	−	0.151862i	0.818851	−	0.574005i	$-0.194611\pi$
$113$	−11901.0	−	20613.2i	−0.0876776	−	0.151862i	−0.906529	+	0.422143i	$0.861278\pi$
$114$	288874.	+	356003.i	2.08183	+	2.56561i
$115$	−15549.0	+	26931.6i	−0.109637	+	0.189897i
$116$	−194266.			−1.34045
$117$	1051.97	−	4998.15i	0.00710461	−	0.0337555i
$118$	−324901.			−2.14806
$119$	−13889.4	+	24057.2i	−0.0899118	+	0.155732i
$120$	−156501.	+	24947.4i	−0.992120	+	0.158151i
$121$	−154251.	−	267170.i	−0.957776	−	1.65892i
$122$	42319.4	+	73299.3i	0.257419	+	0.445862i
$123$	147406.	−	23497.6i	0.878524	−	0.140043i
$124$	−153062.	+	265111.i	−0.893951	+	1.54837i
$125$	113789.			0.651366
$126$	26104.6	−	124029.i	0.146484	−	0.695979i
$127$	4095.45			0.0225316			0.0112658	−	0.999937i	$-0.496414\pi$
$127$	4095.45			0.0225316			0.0112658	+	0.999937i	$0.496414\pi$
$128$	−100617.	+	174274.i	−0.542808	+	0.940171i
$129$	−64500.8	−	79489.6i	−0.341264	−	0.420568i
$130$	−2166.81	−	3753.03i	−0.0112451	−	0.0194771i
$131$	−19533.0	−	33832.2i	−0.0994468	−	0.172247i	0.812009	−	0.583645i	$-0.198374\pi$
$131$	−19533.0	−	33832.2i	−0.0994468	−	0.172247i	−0.911456	+	0.411398i	$0.865041\pi$
$132$	310444.	−	811152.i	1.55077	−	4.05198i
$133$	−67691.2	+	117245.i	−0.331820	+	0.574730i
$134$	572888.			2.75618
$135$	61651.7	+	39775.3i	0.291146	+	0.187836i
$136$	−297562.			−1.37953
$137$	−75368.6	+	130542.i	−0.343075	+	0.594223i	−0.985002	−	0.172542i	$-0.944802\pi$
$137$	−75368.6	+	130542.i	−0.343075	+	0.594223i	0.641927	+	0.766766i	$0.278135\pi$
$138$	95227.7	−	248818.i	0.425663	−	1.11220i
$139$	79014.9	+	136858.i	0.346874	+	0.600804i	0.985692	−	0.168554i	$-0.0539097\pi$
$139$	79014.9	+	136858.i	0.346874	+	0.600804i	−0.638818	+	0.769358i	$0.720576\pi$
$140$	−38584.1	−	66829.7i	−0.166375	−	0.288170i
$141$	173187.	+	213433.i	0.733615	+	0.904093i
$142$	−395000.	+	684160.i	−1.64390	+	2.84732i
$143$	14403.2			0.0589003
$144$	689470.	−	225544.i	2.77083	−	0.906411i
$145$	46276.5			0.182785
$146$	481188.	−	833442.i	1.86824	−	3.23589i
$147$	36961.2	−	5891.88i	0.141076	−	0.0224885i
$148$	−470653.	−	815194.i	−1.76623	−	3.05919i
$149$	−19875.7	−	34425.6i	−0.0733425	−	0.127033i	0.827022	−	0.562170i	$-0.190033\pi$
$149$	−19875.7	−	34425.6i	−0.0733425	−	0.127033i	−0.900364	+	0.435137i	$0.856700\pi$
$150$	−450604.	+	71829.5i	−1.63519	+	0.260660i
$151$	142382.	−	246613.i	0.508175	−	0.880184i	−0.491781	−	0.870719i	$-0.663654\pi$
$151$	142382.	−	246613.i	0.508175	−	0.880184i	0.999955	−	0.00946519i	$-0.00301291\pi$
$152$	−1.45019e6			−5.09116
$153$	102560.	+	91975.2i	0.354199	+	0.317645i
$154$	357413.			1.21442
$155$	36461.3	−	63152.8i	0.121900	−	0.211136i
$156$	16786.7	+	20687.6i	0.0552272	+	0.0680610i
$157$	−31413.8	−	54410.3i	−0.101712	−	0.176170i	0.810678	−	0.585492i	$-0.199099\pi$
$157$	−31413.8	−	54410.3i	−0.101712	−	0.176170i	−0.912390	+	0.409322i	$0.865765\pi$
$158$	326294.	+	565159.i	1.03984	+	1.80106i
$159$	8964.50	−	23423.1i	0.0281212	−	0.0734771i
$160$	145084.	−	251293.i	0.448044	−	0.776034i
$161$	78672.9			0.239199
$162$	−575231.	−	253364.i	−1.72209	−	0.758504i
$163$	357419.			1.05368			0.526839	−	0.849965i	$-0.323377\pi$
$163$	357419.			1.05368			0.526839	+	0.849965i	$0.323377\pi$
$164$	−389289.	+	674268.i	−1.13022	+	1.95759i
$165$	−73951.6	+	193226.i	−0.211465	+	0.552531i
$166$	−31279.3	−	54177.4i	−0.0881023	−	0.152598i
$167$	51566.0	+	89315.0i	0.143078	+	0.247818i	0.928654	−	0.370947i	$-0.120967\pi$
$167$	51566.0	+	89315.0i	0.143078	+	0.247818i	−0.785576	+	0.618765i	$0.787633\pi$
$168$	252619.	+	311322.i	0.690545	+	0.851015i
$169$	185426.	−	321167.i	0.499405	−	0.864995i
$170$	116884.			0.310192
$171$	499832.	+	448249.i	1.30718	+	1.17227i
$172$	533943.			1.37618
$173$	336302.	−	582492.i	0.854307	−	1.47970i	−0.0229788	−	0.999736i	$-0.507315\pi$
$173$	336302.	−	582492.i	0.854307	−	1.47970i	0.877286	−	0.479968i	$-0.159352\pi$
$174$	−391511.	+	62409.7i	−0.980327	+	0.156271i
$175$	−67371.3	−	116691.i	−0.166295	−	0.288032i
$176$	1.02282e6	+	1.77157e6i	2.48895	+	4.31098i
$177$	−469865.	+	74899.8i	−1.12730	+	0.179700i
$178$	501318.	−	868309.i	1.18594	−	2.05411i
$179$	165363.			0.385750			0.192875	−	0.981223i	$-0.438219\pi$
$179$	165363.			0.385750			0.192875	+	0.981223i	$0.438219\pi$
$180$	−363725.	+	118984.i	−0.836742	+	0.273720i
$181$	−184682.			−0.419013			−0.209506	−	0.977807i	$-0.567186\pi$
$181$	−184682.			−0.419013			−0.209506	+	0.977807i	$0.567186\pi$
$182$	−5481.69	+	9494.56i	−0.0122669	+	0.0212469i
$183$	78099.2	+	96248.0i	0.172393	+	0.212453i
$184$	421365.	+	729826.i	0.917517	+	1.58919i
$185$	112115.	+	194189.i	0.240844	+	0.417153i
$186$	−223302.	+	583461.i	−0.473272	+	1.23660i
$187$	−194236.	+	336427.i	−0.406187	+	0.703536i
$188$	−1.43366e6			−2.95836
$189$	9159.48	−	185386.i	0.0186516	−	0.377504i
$190$	569642.			1.14477
$191$	−210120.	+	363939.i	−0.416758	+	0.721847i	−0.995611	−	0.0935853i	$-0.970167\pi$
$191$	−210120.	+	363939.i	−0.416758	+	0.721847i	0.578853	+	0.815432i	$0.303501\pi$
$192$	−356273.	+	930896.i	−0.697476	+	1.82242i
$193$	25389.8	+	43976.5i	0.0490644	+	0.0849821i	0.889515	−	0.456907i	$-0.151043\pi$
$193$	25389.8	+	43976.5i	0.0490644	+	0.0849821i	−0.840450	+	0.541889i	$0.817709\pi$
$194$	−219309.	−	379855.i	−0.418362	−	0.724624i
$195$	−3998.79	−	4928.03i	−0.00753081	−	0.00928084i
$196$	−97611.6	+	169068.i	−0.181494	+	0.314356i
$197$	−516023.			−0.947334			−0.473667	−	0.880704i	$-0.657070\pi$
$197$	−516023.			−0.947334			−0.473667	+	0.880704i	$0.657070\pi$
$198$	365060.	−	1.73448e6i	0.661760	−	3.14417i
$199$	141678.			0.253612			0.126806	−	0.991928i	$-0.459527\pi$
$199$	141678.			0.253612			0.126806	+	0.991928i	$0.459527\pi$
$200$	721670.	−	1.24997e6i	1.27574	−	2.20965i
$201$	828498.	−	132068.i	1.44644	−	0.230573i
$202$	529531.	+	917174.i	0.913088	+	1.58151i
$203$	−58536.1	−	101387.i	−0.0996973	−	0.172681i
$204$	−709596.	+	113115.i	−1.19381	+	0.190302i
$205$	92733.3	−	160619.i	0.154117	−	0.266939i
$206$	1.12027e6			1.83930
$207$	80355.9	−	381788.i	0.130344	−	0.619294i
$208$	−62748.2			−0.100564
$209$	−946625.	+	1.63960e6i	−1.49904	+	2.59641i
$210$	−99229.6	−	122289.i	−0.155272	−	0.191354i
$211$	−442504.	−	766439.i	−0.684244	−	1.18514i	−0.973674	−	0.227946i	$-0.926799\pi$
$211$	−442504.	−	766439.i	−0.684244	−	1.18514i	0.289430	−	0.957199i	$-0.406534\pi$
$212$	65408.3	+	113291.i	0.0999525	+	0.173123i
$213$	−413520.	+	1.08048e6i	−0.624522	+	1.63180i
$214$	−531614.	+	920782.i	−0.793527	+	1.37443i
$215$	−127192.			−0.187656
$216$	1.76883e6	−	907940.i	2.57959	−	1.32411i
$217$	−184482.			−0.265953
$218$	693433.	−	1.20106e6i	0.988242	−	1.71169i
$219$	503750.	−	1.31623e6i	0.709748	−	1.85448i
$220$	−539578.	−	934577.i	−0.751619	−	1.30184i
$221$	−5958.04	−	10319.6i	−0.00820584	−	0.0142129i
$222$	−1.21041e6	−	1.49169e6i	−1.64835	−	2.03140i
$223$	−479689.	+	830846.i	−0.645949	+	1.11882i	0.338133	+	0.941098i	$0.390205\pi$
$223$	−479689.	+	830846.i	−0.645949	+	1.11882i	−0.984082	+	0.177717i	$0.943129\pi$
$224$	−734080.			−0.977514
$225$	−635095.	+	207757.i	−0.836340	+	0.273589i
$226$	253365.			0.329971
$227$	108721.	−	188309.i	0.140038	−	0.242554i	−0.787472	−	0.616350i	$-0.788611\pi$
$227$	108721.	−	188309.i	0.140038	−	0.242554i	0.927511	+	0.373796i	$0.121944\pi$
$228$	−3.45828e6	+	551274.i	−4.40578	+	0.702312i
$229$	−111471.	−	193073.i	−0.140467	−	0.243295i	0.787206	−	0.616690i	$-0.211527\pi$
$229$	−111471.	−	193073.i	−0.140467	−	0.243295i	−0.927672	+	0.373395i	$0.878194\pi$
$230$	−165514.	−	286679.i	−0.206307	−	0.357335i
$231$	516883.	−	82394.8i	0.637327	−	0.101594i
$232$	627029.	−	1.08605e6i	0.764834	−	1.32473i
$233$	−795096.			−0.959466			−0.479733	−	0.877415i	$-0.659266\pi$
$233$	−795096.			−0.959466			−0.479733	+	0.877415i	$0.659266\pi$
$234$	40476.8	+	36299.6i	0.0483244	+	0.0433373i
$235$	341515.			0.403404
$236$	1.24088e6	−	2.14926e6i	1.45027	−	2.51194i
$237$	602166.	+	742099.i	0.696379	+	0.858205i
$238$	−147848.	−	256081.i	−0.169190	−	0.293045i
$239$	132005.	+	228640.i	0.149484	+	0.258915i	0.931037	−	0.364925i	$-0.118905\pi$
$239$	132005.	+	228640.i	0.149484	+	0.258915i	−0.781553	+	0.623839i	$0.785572\pi$
$240$	322174.	−	841801.i	0.361046	−	0.943369i
$241$	−253551.	+	439163.i	−0.281204	+	0.487060i	−0.971682	−	0.236294i	$-0.924067\pi$
$241$	−253551.	+	439163.i	−0.281204	+	0.487060i	0.690477	+	0.723354i	$0.257401\pi$
$242$	3.28390e6			3.60455
$243$	−890295.	−	233801.i	−0.967205	−	0.253999i
$244$	−646512.			−0.695187
$245$	23252.3	−	40274.1i	0.0247486	−	0.0428658i
$246$	−567933.	+	1.48394e6i	−0.598355	+	1.56343i
$247$	−29037.0	−	50293.6i	−0.0302837	−	0.0524530i
$248$	−988071.	−	1.71139e6i	−1.02014	−	1.76693i
$249$	−57725.1	−	71139.3i	−0.0590019	−	0.0727129i
$250$	−605623.	+	1.04897e6i	−0.612847	+	1.06148i
$251$	−836948.			−0.838521			−0.419261	−	0.907866i	$-0.637711\pi$
$251$	−836948.			−0.838521			−0.419261	+	0.907866i	$0.637711\pi$
$252$	720765.	+	646381.i	0.714977	+	0.641191i
$253$	1.10020e6			1.08061
$254$	−21797.3	+	37754.1i	−0.0211992	+	0.0367181i
$255$	169034.	−	26945.3i	0.162789	−	0.0259497i
$256$	−47976.5	−	83097.8i	−0.0457540	−	0.0792482i
$257$	637857.	+	1.10480e6i	0.602408	+	1.04340i	0.992455	+	0.122607i	$0.0391253\pi$
$257$	637857.	+	1.10480e6i	0.602408	+	1.04340i	−0.390047	+	0.920795i	$0.627541\pi$
$258$	1.07607e6	−	171534.i	1.00645	−	0.160436i
$259$	283633.	−	491267.i	0.262729	−	0.455060i
$260$	33102.3			0.0303686
$261$	−551808.	+	180511.i	−0.501402	+	0.164022i
$262$	415845.			0.374264
$263$	−611605.	+	1.05933e6i	−0.545233	+	0.944371i	0.453359	+	0.891328i	$0.350225\pi$
$263$	−611605.	+	1.05933e6i	−0.545233	+	0.944371i	−0.998592	+	0.0530431i	$0.983108\pi$
$264$	3.53274e6	+	4.35368e6i	3.11962	+	3.84456i
$265$	−15581.1	−	26987.2i	−0.0136296	−	0.0236071i
$266$	−720551.	−	1.24803e6i	−0.624397	−	1.08149i
$267$	524823.	−	1.37130e6i	0.450542	−	1.17721i
$268$	−2.18800e6	+	3.78972e6i	−1.86084	+	3.22307i
$269$	−1.86618e6			−1.57244			−0.786220	−	0.617947i	$-0.787965\pi$
$269$	−1.86618e6			−1.57244			−0.786220	+	0.617947i	$0.787965\pi$
$270$	−694803.	+	356642.i	−0.580032	+	0.297731i
$271$	1.75496e6			1.45159			0.725796	−	0.687910i	$-0.241471\pi$
$271$	1.75496e6			1.45159			0.725796	+	0.687910i	$0.241471\pi$
$272$	846201.	−	1.46566e6i	0.693507	−	1.20119i
$273$	−5738.71	+	14994.5i	−0.00466023	+	0.0121766i
$274$	−802274.	−	1.38958e6i	−0.645575	−	1.11817i
$275$	−942152.	−	1.63185e6i	−0.751258	−	1.30122i
$276$	1.28226e6	+	1.58024e6i	1.01322	+	1.24868i
$277$	−725221.	+	1.25612e6i	−0.567899	+	0.983630i	0.428875	+	0.903364i	$0.358910\pi$
$277$	−725221.	+	1.25612e6i	−0.567899	+	0.983630i	−0.996774	+	0.0802656i	$0.974423\pi$
$278$	−1.68218e6			−1.30545
$279$	−188429.	+	895267.i	−0.144923	+	0.688560i
$280$	498149.			0.379721
$281$	−434325.	+	752273.i	−0.328132	+	0.568342i	−0.982141	−	0.188145i	$-0.939753\pi$
$281$	−434325.	+	752273.i	−0.328132	+	0.568342i	0.654009	+	0.756487i	$0.273086\pi$
$282$	−2.88930e6	+	460575.i	−2.16357	+	0.344888i
$283$	−688404.	−	1.19235e6i	−0.510949	−	0.884989i	−0.999919	−	0.0126888i	$-0.995961\pi$
$283$	−688404.	−	1.19235e6i	−0.510949	−	0.884989i	0.488971	−	0.872300i	$-0.337372\pi$
$284$	−3.01720e6	−	5.22594e6i	−2.21977	−	3.84476i
$285$	823803.	−	131320.i	0.600774	−	0.0957677i
$286$	−76658.5	+	132776.i	−0.0554173	+	0.0959855i
$287$	−469200.			−0.336243
$288$	−749784.	+	3.56239e6i	−0.532666	+	2.53081i
$289$	−1.09846e6			−0.773645
$290$	−246299.	+	426603.i	−0.171976	+	0.297871i
$291$	−404728.	−	498780.i	−0.280176	−	0.345284i
$292$	3.67555e6	+	6.36623e6i	2.52269	+	4.36944i
$293$	−206054.	−	356897.i	−0.140221	−	0.242870i	0.787359	−	0.616495i	$-0.211448\pi$
$293$	−206054.	−	356897.i	−0.140221	−	0.242870i	−0.927580	+	0.373625i	$0.878115\pi$
$294$	−142405.	+	372088.i	−0.0960856	+	0.251060i
$295$	−295592.	+	511980.i	−0.197760	+	0.342530i
$296$	6.07647e6			4.03108
$297$	128090.	−	2.59252e6i	0.0842608	−	1.70542i
$298$	423140.			0.276022
$299$	−16873.9	+	29226.4i	−0.0109153	+	0.0189059i
$300$	1.24581e6	−	3.25514e6i	0.799185	−	2.08817i
$301$	160887.	+	278665.i	0.102354	+	0.177283i
$302$	1.51561e6	+	2.62512e6i	0.956248	+	1.65627i
$303$	977233.	+	1.20432e6i	0.611493	+	0.753593i
$304$	4.12403e6	−	7.14302e6i	2.55940	−	4.43300i
$305$	154007.			0.0947961
$306$	−1.39374e6	+	455928.i	−0.850897	+	0.278351i
$307$	2.34033e6			1.41720			0.708600	−	0.705611i	$-0.249327\pi$
$307$	2.34033e6			1.41720			0.708600	+	0.705611i	$0.249327\pi$
$308$	−1.36505e6	+	2.36433e6i	−0.819918	+	1.42014i
$309$	1.62011e6	−	258256.i	0.965266	−	0.153870i
$310$	388118.	+	672241.i	0.229382	+	0.397302i
$311$	1.04088e6	+	1.80286e6i	0.610238	+	1.05696i	0.991200	+	0.132373i	$0.0422597\pi$
$311$	1.04088e6	+	1.80286e6i	0.610238	+	1.05696i	−0.380962	+	0.924591i	$0.624407\pi$
$312$	−169836.	+	27073.1i	−0.0987742	+	0.0157453i
$313$	1.28682e6	−	2.22883e6i	0.742430	−	1.28593i	−0.208956	−	0.977925i	$-0.567006\pi$
$313$	1.28682e6	−	2.22883e6i	0.742430	−	1.28593i	0.951386	−	0.308002i	$-0.0996603\pi$
$314$	668780.			0.382789
$315$	−171695.	−	153976.i	−0.0974947	−	0.0874331i
$316$	−4.98479e6			−2.80821
$317$	907185.	−	1.57129e6i	0.507046	−	0.878230i	−0.492920	−	0.870074i	$-0.664071\pi$
$317$	907185.	−	1.57129e6i	0.507046	−	0.878230i	0.999967	−	0.00815553i	$-0.00259601\pi$
$318$	168215.	+	207306.i	0.0932820	+	0.114959i
$319$	−818596.	−	1.41785e6i	−0.450394	−	0.780106i
$320$	619232.	+	1.07254e6i	0.338048	+	0.585517i
$321$	−556539.	+	1.45417e6i	−0.301462	+	0.787684i
$322$	−418724.	+	725250.i	−0.225054	+	0.389806i
$323$	1.56633e6			0.835367
$324$	3.87298e6	−	2.83756e6i	2.04966	−	1.50170i
$325$	57799.6			0.0303540
$326$	−1.90230e6	+	3.29488e6i	−0.991370	+	1.71710i
$327$	725946.	−	1.89681e6i	0.375435	−	0.980965i
$328$	−2.51300e6	−	4.35264e6i	−1.28976	−	2.23392i
$329$	−431989.	−	748227.i	−0.220030	−	0.381104i
$330$	−1.38767e6	−	1.71014e6i	−0.701459	−	0.864465i
$331$	1.74607e6	−	3.02427e6i	0.875972	−	1.51723i	0.0202492	−	0.999795i	$-0.493554\pi$
$331$	1.74607e6	−	3.02427e6i	0.875972	−	1.51723i	0.855723	−	0.517434i	$-0.173113\pi$
$332$	477853.			0.237930
$333$	−2.09435e6	−	1.87821e6i	−1.03500	−	0.928183i
$334$	−1.09781e6			−0.538468
$335$	521207.	−	902757.i	0.253745	−	0.439500i
$336$	−2.25183e6	+	358958.i	−1.08815	+	0.173458i
$337$	−69563.1	−	120487.i	−0.0333660	−	0.0577916i	0.848860	−	0.528617i	$-0.177289\pi$
$337$	−69563.1	−	120487.i	−0.0333660	−	0.0577916i	−0.882226	+	0.470826i	$0.843956\pi$
$338$	1.97380e6	+	3.41871e6i	0.939746	+	1.62769i
$339$	366411.	−	58408.5i	0.173169	−	0.0276043i
$340$	−446406.	+	773199.i	−0.209427	+	0.362739i
$341$	−2.57989e6			−1.20147
$342$	−6.79248e6	+	2.22200e6i	−3.14024	+	1.02726i
$343$	−117649.			−0.0539949
$344$	−1.72340e6	+	2.98501e6i	−0.785217	+	1.36003i
$345$	−305451.	−	376432.i	−0.138164	−	0.170270i
$346$	3.57983e6	+	6.20044e6i	1.60758	+	2.78440i
$347$	363464.	+	629538.i	0.162046	+	0.280671i	0.935602	−	0.353056i	$-0.114857\pi$
$347$	363464.	+	629538.i	0.162046	+	0.280671i	−0.773556	+	0.633727i	$0.781524\pi$
$348$	1.08243e6	−	2.82825e6i	0.479127	−	1.25190i
$349$	−1.36726e6	+	2.36817e6i	−0.600882	+	1.04076i	0.391806	+	0.920048i	$0.371850\pi$
$349$	−1.36726e6	+	2.36817e6i	−0.600882	+	1.04076i	−0.992688	+	0.120710i	$0.961483\pi$
$350$	1.43429e6			0.625846
$351$	66904.9	+	43164.5i	0.0289861	+	0.0187007i
$352$	−1.02657e7			−4.41603
$353$	30144.8	−	52212.3i	0.0128758	−	0.0223016i	−0.859516	−	0.511109i	$-0.829235\pi$
$353$	30144.8	−	52212.3i	0.0128758	−	0.0223016i	0.872392	+	0.488808i	$0.162568\pi$
$354$	1.81031e6	−	4.73012e6i	0.767796	−	2.00615i
$355$	718733.	+	1.24488e6i	0.302689	+	0.524273i
$356$	3.82931e6	+	6.63256e6i	1.60138	+	2.77368i
$357$	−272850.	−	336255.i	−0.113306	−	0.139636i
$358$	−880118.	+	1.52441e6i	−0.362939	+	0.628628i
$359$	638473.			0.261461			0.130730	−	0.991418i	$-0.458268\pi$
$359$	638473.			0.261461			0.130730	+	0.991418i	$0.458268\pi$
$360$	508806.	−	2.41745e6i	0.206917	−	0.983107i
$361$	5.15755e6			2.08293
$362$	982938.	−	1.70250e6i	0.394235	−	0.682834i
$363$	4.74910e6	−	757040.i	1.89167	−	0.301545i
$364$	−41871.8	−	72524.0i	−0.0165641	−	0.0286899i
$365$	−875560.	−	1.51651e6i	−0.343996	−	0.595819i
$366$	−1.30294e6	+	207697.i	−0.508418	+	0.0810454i
$367$	−764341.	+	1.32388e6i	−0.296225	+	0.513077i	−0.975269	−	0.221020i	$-0.929061\pi$
$367$	−764341.	+	1.32388e6i	−0.296225	+	0.513077i	0.679044	+	0.734098i	$0.262395\pi$
$368$	−4.79308e6			−1.84499
$369$	−479238.	+	2.27696e6i	−0.183225	+	0.870543i
$370$	−2.38686e6			−0.906406
$371$	−39417.6	+	68273.2i	−0.0148681	+	0.0257523i
$372$	−3.00682e6	−	3.70555e6i	−1.12655	−	1.38834i
$373$	−429027.	−	743097.i	−0.159666	−	0.276550i	0.775082	−	0.631860i	$-0.217708\pi$
$373$	−429027.	−	743097.i	−0.159666	−	0.276550i	−0.934748	+	0.355311i	$0.884375\pi$
$374$	−2.06758e6	−	3.58115e6i	−0.764334	−	1.32387i
$375$	−634019.	+	1.65661e6i	−0.232822	+	0.608335i
$376$	4.62739e6	−	8.01488e6i	1.68798	−	2.92366i
$377$	50219.6			0.0181978
$378$	1.66024e6	+	1.07112e6i	0.597642	+	0.385576i
$379$	477174.			0.170639			0.0853196	−	0.996354i	$-0.472809\pi$
$379$	477174.			0.170639			0.0853196	+	0.996354i	$0.472809\pi$
$380$	−2.17560e6	+	3.76825e6i	−0.772893	+	1.33869i
$381$	−22819.4	+	59624.1i	−0.00805362	+	0.0210431i
$382$	−2.23666e6	−	3.87401e6i	−0.784227	−	1.35832i
$383$	1.78231e6	+	3.08704e6i	0.620848	+	1.07534i	0.989328	+	0.145704i	$0.0465448\pi$
$383$	1.78231e6	+	3.08704e6i	0.620848	+	1.07534i	−0.368480	+	0.929636i	$0.620122\pi$
$384$	−1.97656e6	−	2.43588e6i	−0.684041	−	0.843000i
$385$	325171.	−	563212.i	0.111805	−	0.193651i
$386$	−540533.			−0.184652
$387$	1.51665e6	−	496137.i	0.514764	−	0.168393i
$388$	3.35038e6			1.12983
$389$	−1.71160e6	+	2.96457e6i	−0.573492	+	0.993318i	0.422711	+	0.906264i	$0.361078\pi$
$389$	−1.71160e6	+	2.96457e6i	−0.573492	+	0.993318i	−0.996204	+	0.0870536i	$0.972255\pi$
$390$	66712.3	−	10634.4i	0.0222098	−	0.00354039i
$391$	−455110.	−	788274.i	−0.150548	−	0.260757i
$392$	−630118.	−	1.09140e6i	−0.207113	−	0.358730i
$393$	601386.	−	95865.2i	0.196414	−	0.0313097i
$394$	2.74645e6	−	4.75699e6i	0.891314	−	1.54380i
$395$	1.18744e6			0.382929
$396$	1.00795e7	+	9.03929e6i	3.22999	+	2.89665i
$397$	−3.41868e6			−1.08863			−0.544317	−	0.838880i	$-0.683211\pi$
$397$	−3.41868e6			−1.08863			−0.544317	+	0.838880i	$0.683211\pi$
$398$	−754059.	+	1.30607e6i	−0.238615	+	0.413293i
$399$	−1.32975e6	−	1.63877e6i	−0.418157	−	0.515329i
$400$	4.10454e6	+	7.10927e6i	1.28267	+	2.22165i
$401$	−880152.	−	1.52447e6i	−0.273336	−	0.473432i	0.696378	−	0.717675i	$-0.254794\pi$
$401$	−880152.	−	1.52447e6i	−0.273336	−	0.473432i	−0.969714	+	0.244243i	$0.921460\pi$
$402$	−3.19206e6	+	8.34047e6i	−0.985159	+	2.57410i
$403$	39568.0	−	68533.8i	0.0121362	−	0.0210205i
$404$	−8.08962e6			−2.46589
$405$	−922591.	+	675942.i	−0.279493	+	0.204773i
$406$	1.24620e6			0.375207
$407$	3.96646e6	−	6.87011e6i	1.18691	−	2.05579i
$408$	1.65798e6	−	4.33210e6i	0.493094	−	1.28839i
$409$	180926.	+	313372.i	0.0534800	+	0.0926302i	0.891526	−	0.452969i	$-0.149635\pi$
$409$	180926.	+	313372.i	0.0534800	+	0.0926302i	−0.838046	+	0.545600i	$0.816302\pi$
$410$	987116.	+	1.70973e6i	0.290007	+	0.502307i
$411$	−1.48057e6	−	1.82463e6i	−0.432340	−	0.532808i
$412$	−4.27857e6	+	7.41070e6i	−1.24181	+	2.15088i
$413$	1.49560e6			0.431460
$414$	3.09186e6	+	2.77277e6i	0.886581	+	0.795085i
$415$	−113830.			−0.0324443
$416$	157446.	−	272705.i	0.0446066	−	0.0772610i
$417$	−2.43273e6	+	387794.i	−0.685099	+	0.109210i
$418$	−1.00765e7	−	1.74530e7i	−2.82078	−	4.88574i
$419$	897132.	+	1.55388e6i	0.249644	+	0.432396i	0.963427	−	0.267971i	$-0.0863530\pi$
$419$	897132.	+	1.55388e6i	0.249644	+	0.432396i	−0.713783	+	0.700367i	$0.753020\pi$
$420$	1.18794e6	−	189365.i	0.328602	−	0.0523814i
$421$	−412139.	+	713846.i	−0.113328	+	0.196291i	−0.917110	−	0.398633i	$-0.869485\pi$
$421$	−412139.	+	713846.i	−0.113328	+	0.196291i	0.803782	+	0.594924i	$0.202818\pi$
$422$	9.42062e6			2.57512
$423$	−4.07227e6	+	1.33215e6i	−1.10659	+	0.361994i
$424$	−844469.			−0.228123
$425$	−779465.	+	1.35007e6i	−0.209327	+	0.362564i
$426$	−7.75955e6	−	9.56272e6i	−2.07163	−	2.55304i
$427$	−194806.	−	337414.i	−0.0517051	−	0.0895559i
$428$	−4.06072e6	−	7.03337e6i	−1.07150	−	1.85590i
$429$	−80252.8	+	209690.i	−0.0210531	+	0.0550092i
$430$	676958.	−	1.17252e6i	0.176559	−	0.305809i
$431$	−3.61199e6			−0.936598			−0.468299	−	0.883570i	$-0.655133\pi$
$431$	−3.61199e6			−0.936598			−0.468299	+	0.883570i	$0.655133\pi$
$432$	−558034.	+	1.12945e7i	−0.143864	+	2.91176i
$433$	772471.			0.197999			0.0989994	−	0.995087i	$-0.468436\pi$
$433$	772471.			0.197999			0.0989994	+	0.995087i	$0.468436\pi$
$434$	981877.	−	1.70066e6i	0.250226	−	0.433404i
$435$	−257848.	+	673724.i	−0.0653341	+	0.170710i
$436$	5.29677e6	+	9.17428e6i	1.33443	+	2.31130i
$437$	−2.21802e6	−	3.84172e6i	−0.555599	−	0.962325i
$438$	9.45267e6	+	1.16493e7i	2.35434	+	2.90144i
$439$	−921975.	+	1.59691e6i	−0.228327	+	0.395475i	−0.957313	−	0.289055i	$-0.906659\pi$
$439$	−921975.	+	1.59691e6i	−0.228327	+	0.395475i	0.728985	+	0.684530i	$0.239992\pi$
$440$	6.96635e6			1.71543
$441$	−120166.	+	570934.i	−0.0294229	+	0.139794i
$442$	126843.			0.0308824
$443$	−1.58212e6	+	2.74031e6i	−0.383028	+	0.663423i	−0.991493	−	0.130157i	$-0.958452\pi$
$443$	−1.58212e6	+	2.74031e6i	−0.383028	+	0.663423i	0.608466	+	0.793580i	$0.291785\pi$
$444$	1.44905e7	−	2.30990e6i	3.48841	−	0.556077i
$445$	−912188.	−	1.57996e6i	−0.218366	−	0.378220i
$446$	−5.10614e6	−	8.84409e6i	−1.21550	−	2.10531i
$447$	611936.	−	97546.9i	0.144856	−	0.0230911i
$448$	1.56656e6	−	2.71336e6i	0.368767	−	0.638722i
$449$	−7.11111e6			−1.66465			−0.832323	−	0.554291i	$-0.812989\pi$
$449$	−7.11111e6			−1.66465			−0.832323	+	0.554291i	$0.812989\pi$
$450$	1.46498e6	−	6.96042e6i	0.341035	−	1.62033i
$451$	−6.56152e6			−1.51902
$452$	−967663.	+	1.67604e6i	−0.222781	+	0.385868i
$453$	2.79701e6	+	3.44699e6i	0.640397	+	0.789213i
$454$	1.15729e6	+	2.00449e6i	0.263514	+	0.456420i
$455$	9974.36	+	17276.1i	0.00225869	+	0.00391217i
$456$	8.08031e6	−	2.11128e7i	1.81977	−	4.75483i
$457$	−1.06928e6	+	1.85205e6i	−0.239497	+	0.414821i	−0.960570	−	0.278038i	$-0.910316\pi$
$457$	−1.06928e6	+	1.85205e6i	−0.239497	+	0.414821i	0.721073	+	0.692859i	$0.243649\pi$
$458$	2.37314e6			0.528641
$459$	−1.91048e6	+	980652.i	−0.423264	+	0.217262i
$460$	2.52855e6			0.557156
$461$	3.29503e6	−	5.70716e6i	0.722116	−	1.25074i	−0.238034	−	0.971257i	$-0.576503\pi$
$461$	3.29503e6	−	5.70716e6i	0.722116	−	1.25074i	0.960150	−	0.279485i	$-0.0901636\pi$
$462$	−1.99147e6	+	5.20345e6i	−0.434078	+	1.13419i
$463$	1.33931e6	+	2.31975e6i	0.290354	+	0.502908i	0.973893	−	0.227006i	$-0.0728936\pi$
$463$	1.33931e6	+	2.31975e6i	0.290354	+	0.502908i	−0.683539	+	0.729914i	$0.739560\pi$
$464$	3.56626e6	+	6.17694e6i	0.768985	+	1.33192i
$465$	716261.	+	882707.i	0.153617	+	0.189315i
$466$	4.23177e6	−	7.32964e6i	0.902728	−	1.56357i
$467$	8.29780e6			1.76064			0.880320	−	0.474380i	$-0.157328\pi$
$467$	8.29780e6			1.76064			0.880320	+	0.474380i	$0.157328\pi$
$468$	−394716.	+	129122.i	−0.0833049	+	0.0272513i
$469$	−2.63714e6			−0.553606
$470$	−1.81766e6	+	3.14828e6i	−0.379549	+	0.657398i
$471$	967175.	−	154174.i	0.200887	−	0.0320229i
$472$	8.01030e6	+	1.38743e7i	1.65498	+	2.86652i
$473$	2.24992e6	+	3.89698e6i	0.462397	+	0.800895i
$474$	−1.00460e7	+	1.60141e6i	−2.05375	+	0.327383i
$475$	−3.79879e6	+	6.57969e6i	−0.772522	+	1.33805i
$476$	2.25867e6			0.456915
$477$	291060.	+	261022.i	0.0585715	+	0.0525268i
$478$	−2.81030e6			−0.562579
$479$	2.87689e6	−	4.98291e6i	0.572907	−	0.992303i	−0.423359	−	0.905962i	$-0.639149\pi$
$479$	2.87689e6	−	4.98291e6i	0.572907	−	0.992303i	0.996266	−	0.0863412i	$-0.0275175\pi$
$480$	2.85010e6	+	3.51241e6i	0.564620	+	0.695828i
$481$	121668.	+	210735.i	0.0239781	+	0.0415312i
$482$	−2.69897e6	−	4.67475e6i	−0.529151	−	0.916517i
$483$	−438356.	+	1.14537e6i	−0.0854986	+	0.223397i
$484$	−1.25420e7	+	2.17234e7i	−2.43362	+	4.21516i
$485$	−798100.			−0.154065
$486$	6.89376e6	−	6.96287e6i	1.32393	−	1.33720i
$487$	−2.79860e6			−0.534711			−0.267356	−	0.963598i	$-0.586150\pi$
$487$	−2.79860e6			−0.534711			−0.267356	+	0.963598i	$0.586150\pi$
$488$	2.08673e6	−	3.61433e6i	0.396659	−	0.687033i
$489$	−1.99150e6	+	5.20353e6i	−0.376623	+	0.984070i
$490$	247513.	+	428705.i	0.0465702	+	0.0806619i
$491$	2.17697e6	+	3.77061e6i	0.407519	+	0.705844i	0.994611	−	0.103677i	$-0.0330607\pi$
$491$	2.17697e6	+	3.77061e6i	0.407519	+	0.705844i	−0.587092	+	0.809520i	$0.699727\pi$
$492$	−7.64735e6	−	9.42445e6i	−1.42429	−	1.75527i
$493$	−677244.	+	1.17302e6i	−0.125495	+	0.217365i
$494$	618179.			0.113972
$495$	−2.40106e6	−	2.15327e6i	−0.440444	−	0.394989i
$496$	1.12394e7			2.05135
$497$	1.81828e6	−	3.14935e6i	0.330194	−	0.571913i
$498$	963034.	−	153514.i	0.174008	−	0.0277381i
$499$	213783.	+	370283.i	0.0384345	+	0.0665706i	0.884603	−	0.466345i	$-0.154430\pi$
$499$	213783.	+	370283.i	0.0384345	+	0.0665706i	−0.846168	+	0.532916i	$0.821096\pi$
$500$	−4.62604e6	−	8.01253e6i	−0.827531	−	1.43333i
$501$	−1.58762e6	+	253079.i	−0.282588	+	0.0450465i
$502$	4.45452e6	−	7.71545e6i	0.788935	−	1.36648i
$503$	2.86088e6			0.504173			0.252087	−	0.967705i	$-0.418883\pi$
$503$	2.86088e6			0.504173			0.252087	+	0.967705i	$0.418883\pi$
$504$	−5.93999e6	+	1.94313e6i	−1.04162	+	0.340742i
$505$	1.92705e6			0.336251
$506$	−5.85563e6	+	1.01422e7i	−1.01671	+	1.76099i
$507$	3.64258e6	+	4.48905e6i	0.629345	+	0.775594i
$508$	−166499.	−	288384.i	−0.0286254	−	0.0495806i
$509$	4.54402e6	+	7.87047e6i	0.777402	+	1.34650i	0.933434	+	0.358748i	$0.116796\pi$
$509$	4.54402e6	+	7.87047e6i	0.777402	+	1.34650i	−0.156032	+	0.987752i	$0.549870\pi$
$510$	−651262.	+	1.70167e6i	−0.110874	+	0.289700i
$511$	−2.21502e6	+	3.83654e6i	−0.375255	+	0.649960i
$512$	−5.41810e6			−0.913423
$513$	−9.31090e6	+	4.77929e6i	−1.56206	+	0.801807i
$514$	−1.35796e7			−2.26714
$515$	1.01921e6	−	1.76532e6i	0.169334	−	0.293295i
$516$	−2.97507e6	+	7.77349e6i	−0.491896	+	1.28526i
$517$	−6.04113e6	−	1.04636e7i	−0.994013	−	1.72168i
$518$	3.01919e6	+	5.22938e6i	0.494385	+	0.856300i
$519$	6.60646e6	+	8.14168e6i	1.07659	+	1.32677i
$520$	−106844.	+	185059.i	−0.0173277	+	0.0300124i
$521$	7.13852e6			1.15216			0.576081	−	0.817392i	$-0.304581\pi$
$521$	7.13852e6			1.15216			0.576081	+	0.817392i	$0.304581\pi$
$522$	1.27286e6	−	6.04761e6i	0.204457	−	0.971422i
$523$	3.52396e6			0.563349			0.281674	−	0.959510i	$-0.409110\pi$
$523$	3.52396e6			0.563349			0.281674	+	0.959510i	$0.409110\pi$
$524$	−1.58821e6	+	2.75086e6i	−0.252685	+	0.437664i
$525$	2.07424e6	−	330649.i	0.328444	−	0.0523562i
$526$	−6.51034e6	−	1.12762e7i	−1.02598	−	1.77705i
$527$	1.06720e6	+	1.84845e6i	0.167386	+	0.289922i
$528$	−3.14907e7	+	5.01983e6i	−4.91583	+	0.783618i
$529$	1.92925e6	−	3.34155e6i	0.299743	−	0.519170i
$530$	331711.			0.0512944
$531$	1.52760e6	−	7.25793e6i	0.235110	−	1.11706i
$532$	1.10078e7			1.68625
$533$	100635.	−	174305.i	0.0153437	−	0.0265761i
$534$	9.84811e6	+	1.21366e7i	1.49451	+	1.84181i
$535$	967313.	+	1.67543e6i	0.146111	+	0.253071i
$536$	−1.41243e7	−	2.44640e7i	−2.12351	−	3.67803i
$537$	−921384.	+	2.40746e6i	−0.137881	+	0.360266i
$538$	9.93247e6	−	1.72035e7i	1.47945	−	2.56249i
$539$	−1.64526e6			−0.243928
$540$	294386.	−	5.95830e6i	0.0434443	−	0.879302i
$541$	−264828.			−0.0389018			−0.0194509	−	0.999811i	$-0.506192\pi$
$541$	−264828.			−0.0389018			−0.0194509	+	0.999811i	$0.506192\pi$
$542$	−9.34051e6	+	1.61782e7i	−1.36575	+	2.36555i
$543$	1.02902e6	−	2.68871e6i	0.149770	−	0.391332i
$544$	4.24654e6	+	7.35522e6i	0.615230	+	1.06561i
$545$	−1.26176e6	−	2.18542e6i	−0.181963	−	0.315170i
$546$	−107685.	−	132709.i	−0.0154587	−	0.0190510i
$547$	−1.37781e6	+	2.38644e6i	−0.196889	+	0.341021i	−0.947518	−	0.319702i	$-0.896417\pi$
$547$	−1.37781e6	+	2.38644e6i	−0.196889	+	0.341021i	0.750629	+	0.660724i	$0.229750\pi$
$548$	1.22563e7			1.74345
$549$	−1.83640e6	+	600735.i	−0.260038	+	0.0850652i
$550$	2.00578e7			2.82733
$551$	−3.30061e6	+	5.71682e6i	−0.463143	+	0.802186i
$552$	−1.29731e7	+	2.06800e6i	−1.81215	+	0.288870i
$553$	−1.50201e6	−	2.60156e6i	−0.208862	−	0.361760i
$554$	−7.71974e6	−	1.33710e7i	−1.06863	−	1.85093i
$555$	−3.45182e6	+	550245.i	−0.475682	+	0.0758270i
$556$	6.42463e6	−	1.11278e7i	0.881376	−	1.52659i
$557$	−1.82948e6			−0.249856			−0.124928	−	0.992166i	$-0.539870\pi$
$557$	−1.82948e6			−0.249856			−0.124928	+	0.992166i	$0.539870\pi$
$558$	−7.25019e6	−	6.50196e6i	−0.985743	−	0.884013i
$559$	−138029.			−0.0186828
$560$	−1.41662e6	+	2.45367e6i	−0.190891	+	0.330632i
$561$	−3.81566e6	−	4.70234e6i	−0.511873	−	0.630823i
$562$	−4.62325e6	−	8.00770e6i	−0.617457	−	1.06947i
$563$	−6.72357e6	−	1.16456e7i	−0.893982	−	1.54842i	−0.835060	−	0.550159i	$-0.814567\pi$
$563$	−6.72357e6	−	1.16456e7i	−0.893982	−	1.54842i	−0.0589223	−	0.998263i	$-0.518766\pi$
$564$	7.98818e6	−	2.08721e7i	1.05743	−	2.76292i
$565$	230509.	−	399253.i	0.0303785	−	0.0526172i
$566$	1.46557e7			1.92294
$567$	2.64793e6	+	1.16630e6i	0.345898	+	0.152353i
$568$	3.89542e7			5.06621
$569$	845623.	−	1.46466e6i	0.109495	−	0.189652i	−0.806071	−	0.591819i	$-0.798410\pi$
$569$	845623.	−	1.46466e6i	0.109495	−	0.189652i	0.915566	+	0.402168i	$0.131743\pi$
$570$	−3.17398e6	+	8.29321e6i	−0.409182	+	1.06914i
$571$	−1.89804e6	−	3.28749e6i	−0.243621	−	0.421963i	0.718122	−	0.695917i	$-0.245002\pi$
$571$	−1.89804e6	−	3.28749e6i	−0.243621	−	0.421963i	−0.961743	+	0.273954i	$0.911669\pi$
$572$	−585554.	−	1.01421e6i	−0.0748302	−	0.129610i
$573$	−4.12769e6	−	5.08689e6i	−0.525195	−	0.647241i
$574$	2.49724e6	−	4.32535e6i	0.316360	−	0.547951i
$575$	4.41507e6			0.556888
$576$	−1.15675e7	−	1.03737e7i	−1.45272	−	1.30280i
$577$	6.69060e6			0.836615			0.418308	−	0.908305i	$-0.362623\pi$
$577$	6.69060e6			0.836615			0.418308	+	0.908305i	$0.362623\pi$
$578$	5.84640e6	−	1.01263e7i	0.727895	−	1.26075i
$579$	−781707.	+	124610.i	−0.0969053	+	0.0154474i
$580$	−1.88135e6	−	3.25860e6i	−0.232220	−	0.402217i
$581$	143986.	+	249392.i	0.0176962	+	0.0306508i
$582$	6.75213e6	−	1.07634e6i	0.826292	−	0.131717i
$583$	−551234.	+	954765.i	−0.0671683	+	0.116339i
$584$	−4.74539e7			−5.75758
$585$	94026.3	−	30758.5i	0.0113595	−	0.00371600i
$586$	4.38676e6			0.527716
$587$	3.24794e6	−	5.62560e6i	0.389057	−	0.673866i	−0.603266	−	0.797540i	$-0.706134\pi$
$587$	3.24794e6	−	5.62560e6i	0.389057	−	0.673866i	0.992323	+	0.123674i	$0.0394677\pi$
$588$	−1.91752e6	−	2.36312e6i	−0.228717	−	0.281866i
$589$	5.20109e6	+	9.00856e6i	0.617741	+	1.06996i
$590$	−3.14648e6	−	5.44986e6i	−0.372130	−	0.644548i
$591$	2.87522e6	−	7.51259e6i	0.338612	−	0.884751i
$592$	−1.72801e7	+	2.99300e7i	−2.02648	+	3.50997i
$593$	7.76664e6			0.906977			0.453488	−	0.891262i	$-0.350179\pi$
$593$	7.76664e6			0.906977			0.453488	+	0.891262i	$0.350179\pi$
$594$	2.32176e7	+	1.49791e7i	2.69992	+	1.74188i
$595$	−538043.			−0.0623053
$596$	−1.61607e6	+	2.79912e6i	−0.186357	+	0.322779i
$597$	−789414.	+	2.06264e6i	−0.0906503	+	0.236858i
$598$	−179617.	−	311105.i	−0.0205397	−	0.0355758i
$599$	4.75946e6	+	8.24363e6i	0.541989	+	0.938753i	0.998790	+	0.0491840i	$0.0156621\pi$
$599$	4.75946e6	+	8.24363e6i	0.541989	+	0.938753i	−0.456800	+	0.889569i	$0.651005\pi$
$600$	1.41768e7	+	1.74712e7i	1.60768	+	1.98128i
$601$	−570837.	+	988718.i	−0.0644653	+	0.111657i	−0.896457	−	0.443131i	$-0.853868\pi$
$601$	−570837.	+	988718.i	−0.0644653	+	0.111657i	0.831991	+	0.554789i	$0.187201\pi$
$602$	−3.42519e6			−0.385206
$603$	−2.69356e6	+	1.27977e7i	−0.301671	+	1.43330i
$604$	−2.31539e7			−2.58245
$605$	2.98766e6	−	5.17477e6i	0.331850	−	0.574781i
$606$	−1.63033e7	+	2.59886e6i	−1.80341	+	0.287476i
$607$	2.92820e6	+	5.07178e6i	0.322573	+	0.558713i	0.981018	−	0.193916i	$-0.0621188\pi$
$607$	2.92820e6	+	5.07178e6i	0.322573	+	0.558713i	−0.658445	+	0.752629i	$0.728785\pi$
$608$	2.06958e7	+	3.58463e7i	2.27051	+	3.93265i
$609$	1.80222e6	−	287287.i	0.196909	−	0.0313886i
$610$	−819677.	+	1.41972e6i	−0.0891904	+	0.154482i
$611$	370614.			0.0401623
$612$	2.30699e6	−	1.09610e7i	0.248982	−	1.18297i
$613$	9.01709e6			0.969204			0.484602	−	0.874735i	$-0.338965\pi$
$613$	9.01709e6			0.969204			0.484602	+	0.874735i	$0.338965\pi$
$614$	−1.24560e7	+	2.15745e7i	−1.33339	+	2.30951i
$615$	1.82169e6	+	2.24502e6i	0.194217	+	0.239349i
$616$	−8.81187e6	−	1.52626e7i	−0.935656	−	1.62060i
$617$	501584.	+	868769.i	0.0530433	+	0.0918737i	0.891328	−	0.453359i	$-0.149775\pi$
$617$	501584.	+	868769.i	0.0530433	+	0.0918737i	−0.838285	+	0.545233i	$0.816441\pi$
$618$	−6.24200e6	+	1.63096e7i	−0.657434	+	1.71779i
$619$	−864105.	+	1.49667e6i	−0.0906442	+	0.157000i	−0.907782	−	0.419441i	$-0.862226\pi$
$619$	−864105.	+	1.49667e6i	−0.0906442	+	0.157000i	0.817138	+	0.576442i	$0.195559\pi$
$620$	−5.92927e6			−0.619472
$621$	5.11059e6	+	3.29715e6i	0.531792	+	0.343092i
$622$	−2.21597e7			−2.29661
$623$	−2.30769e6	+	3.99703e6i	−0.238208	+	0.412589i
$624$	349626.	−	913529.i	0.0359453	−	0.0939206i
$625$	−3.19466e6	−	5.53331e6i	−0.327133	−	0.566611i
$626$	1.36977e7	+	2.37252e7i	1.39705	+	2.41977i
$627$	−1.85959e7	−	2.29173e7i	−1.88907	−	2.32806i
$628$	−2.55423e6	+	4.42406e6i	−0.258441	+	0.447632i
$629$	−6.56310e6			−0.661428
$630$	2.33325e6	−	763269.i	0.234213	−	0.0766172i
$631$	−1.39498e7			−1.39475			−0.697374	−	0.716708i	$-0.745648\pi$
$631$	−1.39498e7			−1.39475			−0.697374	+	0.716708i	$0.745648\pi$
$632$	1.60893e7	−	2.78675e7i	1.60230	−	2.77527i
$633$	1.36239e7	−	2.17174e6i	1.35142	−	0.215427i
$634$	9.65669e6	+	1.67259e7i	0.954125	+	1.65259i
$635$	39662.0	+	68696.6i	0.00390337	+	0.00676084i
$636$	−2.01380e6	+	321015.i	−0.197412	+	0.0314689i
$637$	25233.5	−	43705.7i	0.00246394	−	0.00426766i
$638$	1.74274e7			1.69504
$639$	−1.34262e7	−	1.20406e7i	−1.30077	−	1.16653i
$640$	−3.89766e6			−0.376144
$641$	2.47083e6	−	4.27960e6i	0.237518	−	0.411394i	−0.722483	−	0.691388i	$-0.756999\pi$
$641$	2.47083e6	−	4.27960e6i	0.237518	−	0.411394i	0.960002	+	0.279995i	$0.0903327\pi$
$642$	−1.04432e7	−	1.28701e7i	−0.999995	−	1.23238i
$643$	1.55690e6	+	2.69664e6i	0.148503	+	0.257214i	0.930674	−	0.365849i	$-0.119221\pi$
$643$	1.55690e6	+	2.69664e6i	0.148503	+	0.257214i	−0.782172	+	0.623063i	$0.785888\pi$
$644$	−3.19841e6	−	5.53981e6i	−0.303892	−	0.526357i
$645$	708698.	−	1.85174e6i	0.0670752	−	0.175259i
$646$	−8.33655e6	+	1.44393e7i	−0.785968	+	1.36134i
$647$	−5.08098e6			−0.477185			−0.238593	−	0.971120i	$-0.576686\pi$
$647$	−5.08098e6			−0.477185			−0.238593	+	0.971120i	$0.576686\pi$
$648$	3.36267e6	+	3.08107e7i	0.314591	+	2.88246i
$649$	2.09152e7			1.94917
$650$	−307629.	+	532829.i	−0.0285590	+	0.0494657i
$651$	1.02791e6	−	2.68581e6i	0.0950614	−	0.248384i
$652$	−1.45307e7	−	2.51679e7i	−1.33865	−	2.31861i
$653$	6.62774e6	+	1.14796e7i	0.608251	+	1.05352i	0.991529	+	0.129888i	$0.0414619\pi$
$653$	6.62774e6	+	1.14796e7i	0.608251	+	1.05352i	−0.383278	+	0.923633i	$0.625205\pi$
$654$	1.36221e7	+	1.67876e7i	1.24537	+	1.53477i
$655$	378331.	−	655289.i	0.0344563	−	0.0596801i
$656$	2.85856e7			2.59351
$657$	1.63558e7	+	1.46678e7i	1.47828	+	1.32572i
$658$	9.19676e6			0.828076
$659$	4.41497e6	−	7.64695e6i	0.396017	−	0.685922i	−0.597213	−	0.802083i	$-0.703725\pi$
$659$	4.41497e6	−	7.64695e6i	0.396017	−	0.685922i	0.993230	+	0.116160i	$0.0370586\pi$
$660$	1.66126e7	−	2.64817e6i	1.48450	−	0.236639i
$661$	1.91588e6	+	3.31840e6i	0.170555	+	0.295410i	0.938614	−	0.344969i	$-0.112111\pi$
$661$	1.91588e6	+	3.31840e6i	0.170555	+	0.295410i	−0.768059	+	0.640379i	$0.778777\pi$
$662$	1.85863e7	+	3.21924e7i	1.64834	+	2.85502i
$663$	183437.	−	29241.2i	0.0162071	−	0.00258352i
$664$	−1.54236e6	+	2.67144e6i	−0.135758	+	0.235139i
$665$	−2.62220e6			−0.229938
$666$	2.84612e7	−	9.31043e6i	2.48638	−	0.813362i
$667$	3.83607e6			0.333866
$668$	4.19279e6	−	7.26212e6i	0.363548	−	0.629684i
$669$	−9.42322e6	−	1.16130e7i	−0.814018	−	1.00318i
$670$	5.54808e6	+	9.60956e6i	0.477481	+	0.827021i
$671$	−2.72426e6	−	4.71856e6i	−0.233584	−	0.404579i
$672$	4.09021e6	−	1.06872e7i	0.349399	−	0.912937i
$673$	−6.79748e6	+	1.17736e7i	−0.578510	+	1.00201i	0.417141	+	0.908842i	$0.363032\pi$
$673$	−6.79748e6	+	1.17736e7i	−0.578510	+	1.00201i	−0.995651	+	0.0931662i	$0.970301\pi$
$674$	1.48095e6			0.125572
$675$	514024.	−	1.04037e7i	0.0434234	−	0.878879i
$676$	−3.01536e7			−2.53789
$677$	6.82164e6	−	1.18154e7i	0.572028	−	0.990782i	−0.424330	−	0.905508i	$-0.639490\pi$
$677$	6.82164e6	−	1.18154e7i	0.572028	−	0.990782i	0.996358	−	0.0852738i	$-0.0271765\pi$
$678$	−1.41172e6	+	3.68865e6i	−0.117944	+	0.308172i
$679$	1.00953e6	+	1.74856e6i	0.0840322	+	0.145548i
$680$	−2.88171e6	−	4.99128e6i	−0.238989	−	0.413942i
$681$	2.13575e6	+	2.63206e6i	0.176475	+	0.217485i
$682$	1.37310e7	−	2.37828e7i	1.13043	−	1.95796i
$683$	2.54456e6			0.208718			0.104359	−	0.994540i	$-0.466721\pi$
$683$	2.54456e6			0.208718			0.104359	+	0.994540i	$0.466721\pi$
$684$	1.12433e7	−	5.34194e7i	0.918870	−	4.36575i
$685$	−2.91960e6			−0.237737
$686$	626168.	−	1.08455e6i	0.0508020	−	0.0879916i
$687$	3.43199e6	−	547083.i	0.277430	−	0.0442244i
$688$	−9.80192e6	−	1.69774e7i	−0.789478	−	1.36742i
$689$	−16908.7	−	29286.7i	−0.00135694	−	0.00235029i
$690$	5.09587e6	−	812318.i	0.407470	−	0.0649537i
$691$	−2.44722e6	+	4.23871e6i	−0.194974	+	0.337706i	−0.946892	−	0.321551i	$-0.895796\pi$
$691$	−2.44722e6	+	4.23871e6i	−0.194974	+	0.337706i	0.751918	+	0.659257i	$0.229129\pi$
$692$	−5.46888e7			−4.34144
$693$	−1.68046e6	+	7.98421e6i	−0.132921	+	0.631537i
$694$	−7.73791e6			−0.609853
$695$	−1.53043e6	+	2.65078e6i	−0.120185	+	0.208167i
$696$	1.23176e7	+	1.51800e7i	0.963837	+	1.18782i
$697$	2.71425e6	+	4.70122e6i	0.211626	+	0.366546i
$698$	−1.45541e7	−	2.52084e7i	−1.13070	−	1.95843i
$699$	4.43018e6	−	1.15755e7i	0.342948	−	0.896081i
$700$	−5.47790e6	+	9.48800e6i	−0.422541	+	0.731863i
$701$	−5.48199e6			−0.421350			−0.210675	−	0.977556i	$-0.567566\pi$
$701$	−5.48199e6			−0.421350			−0.210675	+	0.977556i	$0.567566\pi$
$702$	−754004.	+	387031.i	−0.0577472	+	0.0296417i
$703$	−3.19858e7			−2.44101
$704$	2.19075e7	−	3.79449e7i	1.66595	−	2.88550i
$705$	−1.90288e6	+	4.97199e6i	−0.144191	+	0.376754i
$706$	320882.	+	555784.i	0.0242289	+	0.0419656i
$707$	−2.43756e6	−	4.22197e6i	−0.183403	−	0.317663i
$708$	2.43763e7	+	3.00409e7i	1.82761	+	2.25232i
$709$	5.56013e6	−	9.63042e6i	0.415402	−	0.719498i	−0.580068	−	0.814568i	$-0.696974\pi$
$709$	5.56013e6	−	9.63042e6i	0.415402	−	0.719498i	0.995471	+	0.0950698i	$0.0303074\pi$
$710$	−1.53014e7			−1.13916
$711$	−1.41592e7	+	4.63184e6i	−1.05042	+	0.343621i
$712$	−4.94391e7			−3.65486
$713$	3.02244e6	−	5.23502e6i	0.222656	−	0.385651i
$714$	4.55198e6	−	725618.i	0.334160	−	0.0532675i
$715$	139486.	+	241597.i	0.0102039	+	0.0176737i
$716$	−6.72276e6	−	1.16442e7i	−0.490078	−	0.848840i
$717$	−4.06420e6	+	647862.i	−0.295241	+	0.0470635i
$718$	−3.39817e6	+	5.88580e6i	−0.245999	+	0.426084i
$719$	−5.36650e6			−0.387141			−0.193570	−	0.981086i	$-0.562007\pi$
$719$	−5.36650e6			−0.387141			−0.193570	+	0.981086i	$0.562007\pi$
$720$	1.04604e7	+	9.38084e6i	0.751996	+	0.674389i
$721$	−5.15686e6			−0.369443
$722$	−2.74502e7	+	4.75452e7i	−1.95976	+	3.39440i
$723$	−4.98086e6	−	6.13832e6i	−0.354371	−	0.436721i
$724$	7.50815e6	+	1.30045e7i	0.532337	+	0.922035i
$725$	−3.28501e6	−	5.68980e6i	−0.232109	−	0.402024i
$726$	−1.82975e7	+	4.78091e7i	−1.28840	+	3.36643i
$727$	1.32420e7	−	2.29358e7i	0.929215	−	1.60945i	0.144578	−	0.989493i	$-0.453818\pi$
$727$	1.32420e7	−	2.29358e7i	0.929215	−	1.60945i	0.784638	−	0.619955i	$-0.212849\pi$
$728$	540595.			0.0378045
$729$	8.36445e6	−	1.16588e7i	0.582933	−	0.812520i
$730$	1.86401e7			1.29462
$731$	1.86142e6	−	3.22407e6i	0.128840	−	0.223157i
$732$	3.60229e6	−	9.41233e6i	0.248485	−	0.649261i
$733$	4.89273e6	+	8.47446e6i	0.336350	+	0.582575i	0.983743	−	0.179581i	$-0.0574742\pi$
$733$	4.89273e6	+	8.47446e6i	0.336350	+	0.582575i	−0.647393	+	0.762156i	$0.724141\pi$
$734$	−8.13617e6	−	1.40923e7i	−0.557416	−	0.965473i
$735$	456778.	+	562924.i	0.0311879	+	0.0384354i
$736$	1.20267e7	−	2.08308e7i	0.818373	−	1.41746i
$737$	−3.68790e7			−2.50098
$738$	−1.84397e7	−	1.65367e7i	−1.24627	−	1.11765i
$739$	5.97965e6			0.402777			0.201388	−	0.979511i	$-0.435455\pi$
$739$	5.97965e6			0.402777			0.201388	+	0.979511i	$0.435455\pi$
$740$	9.11599e6	−	1.57894e7i	0.611962	−	1.05995i
$741$	893997.	−	142509.i	0.0598123	−	0.00953450i
$742$	−419587.	−	726747.i	−0.0279777	−	0.0484589i
$743$	4.84220e6	+	8.38694e6i	0.321789	+	0.557354i	0.980857	−	0.194729i	$-0.0623826\pi$
$743$	4.84220e6	+	8.38694e6i	0.321789	+	0.557354i	−0.659068	+	0.752083i	$0.729049\pi$
$744$	3.04209e7	−	4.84931e6i	2.01484	−	0.321179i
$745$	384968.	−	666784.i	0.0254117	−	0.0440144i
$746$	9.13371e6			0.600897
$747$	1.35733e6	−	444019.i	0.0889987	−	0.0291139i
$748$	3.15863e7			2.06417
$749$	2.44715e6	−	4.23858e6i	0.159388	−	0.276068i
$750$	−1.18971e7	−	1.46618e7i	−0.772304	−	0.951774i
$751$	1.23778e7	+	2.14391e7i	0.800839	+	1.38709i	0.919064	+	0.394107i	$0.128946\pi$
$751$	1.23778e7	+	2.14391e7i	0.800839	+	1.38709i	−0.118225	+	0.992987i	$0.537720\pi$
$752$	2.63185e7	+	4.55851e7i	1.69714	+	2.93953i
$753$	4.66338e6	−	1.21848e7i	0.299718	−	0.783126i
$754$	−267286.	+	462953.i	−0.0171217	+	0.0296557i
$755$	5.51555e6			0.352145
$756$	−1.34264e7	+	6.89180e6i	−0.854391	+	0.438559i
$757$	2.48859e7			1.57839			0.789193	−	0.614146i	$-0.210499\pi$
$757$	2.48859e7			1.57839			0.789193	+	0.614146i	$0.210499\pi$
$758$	−2.53968e6	+	4.39886e6i	−0.160548	+	0.278078i
$759$	−6.13018e6	+	1.60174e7i	−0.386250	+	1.00922i
$760$	−1.40443e7	−	2.43254e7i	−0.881993	−	1.52766i
$761$	−215795.	−	373768.i	−0.0135076	−	0.0233959i	0.859193	−	0.511652i	$-0.170966\pi$
$761$	−215795.	−	373768.i	−0.0135076	−	0.0233959i	−0.872700	+	0.488256i	$0.837633\pi$
$762$	−428196.	−	527701.i	−0.0267150	−	0.0329231i
$763$	−3.19204e6	+	5.52877e6i	−0.198498	+	0.343809i
$764$	3.41694e7			2.11789
$765$	−549554.	+	2.61105e6i	−0.0339513	+	0.161310i
$766$	−3.79441e7			−2.33654
$767$	−320778.	+	555604.i	−0.0196887	+	0.0341018i
$768$	1.47711e6	−	235462.i	0.0903670	−	0.0144051i
$769$	6.50371e6	+	1.12647e7i	0.396593	+	0.686919i	0.993303	−	0.115538i	$-0.0368591\pi$
$769$	6.50371e6	+	1.12647e7i	0.396593	+	0.686919i	−0.596710	+	0.802457i	$0.703526\pi$
$770$	3.46134e6	+	5.99521e6i	0.210386	+	0.364399i
$771$	−1.96385e7	+	3.13051e6i	−1.18979	+	0.189662i
$772$	2.06443e6	−	3.57569e6i	0.124668	−	0.215932i
$773$	−1.81937e7			−1.09515			−0.547574	−	0.836757i	$-0.684449\pi$
$773$	−1.81937e7			−1.09515			−0.547574	+	0.836757i	$0.684449\pi$
$774$	−3.49846e6	+	1.66220e7i	−0.209906	+	0.997309i
$775$	−1.03530e7			−0.619175
$776$	−1.08139e7	+	1.87303e7i	−0.644659	+	1.11658i
$777$	5.57181e6	+	6.86660e6i	0.331089	+	0.408027i
$778$	−1.82194e7	−	3.15569e7i	−1.07916	−	1.86916i
$779$	1.32281e7	+	2.29118e7i	0.781007	+	1.35274i
$780$	−184442.	+	481925.i	−0.0108549	+	0.0283624i
$781$	2.54277e7	−	4.40420e7i	1.49169	−	2.58369i
$782$	9.68900e6			0.566581
$783$	446614.	−	9.03936e6i	0.0260332	−	0.526906i
$784$	7.16766e6			0.416474
$785$	608449.	−	1.05386e6i	0.0352411	−	0.0610394i
$786$	−2.31704e6	+	6.05414e6i	−0.133776	+	0.349539i
$787$	6.35293e6	+	1.10036e7i	0.365626	+	0.633283i	0.988876	−	0.148739i	$-0.0475215\pi$
$787$	6.35293e6	+	1.10036e7i	0.365626	+	0.633283i	−0.623250	+	0.782022i	$0.714188\pi$
$788$	2.09787e7	+	3.63361e7i	1.20355	+	2.08460i
$789$	−1.20146e7	−	1.48066e7i	−0.687097	−	0.846766i
$790$	−6.31994e6	+	1.09465e7i	−0.360284	+	0.624030i
$791$	−1.16630e6			−0.0662780
$792$	−8.30677e7	+	2.71736e7i	−4.70564	+	1.53934i
$793$	167129.			0.00943778
$794$	1.81953e7	−	3.15153e7i	1.02426	−	1.77407i
$795$	479713.	−	76469.6i	0.0269193	−	0.00429112i
$796$	−5.75986e6	−	9.97637e6i	−0.322203	−	0.558072i
$797$	−1.44525e7	−	2.50325e7i	−0.805932	−	1.39592i	−0.915660	−	0.401953i	$-0.868331\pi$
$797$	−1.44525e7	−	2.50325e7i	−0.805932	−	1.39592i	0.109728	−	0.993962i	$-0.465002\pi$
$798$	2.21845e7	−	3.53636e6i	1.23322	−	0.196584i
$799$	−4.99798e6	+	8.65675e6i	−0.276967	+	0.479720i
$800$	−4.11961e7			−2.27578
$801$	1.70400e7	+	1.52814e7i	0.938400	+	0.841556i
$802$	1.87379e7			1.02869
$803$	−3.09759e7	+	5.36519e7i	−1.69526	+	2.93627i
$804$	−4.29819e7	−	5.29701e7i	−2.34501	−	2.88995i
$805$	761900.	+	1.31965e6i	0.0414389	+	0.0717743i
$806$	421189.	+	729520.i	0.0228370	+	0.0395549i
$807$	1.03982e7	−	2.71691e7i	0.562047	−	1.46856i
$808$	2.61107e7	−	4.52251e7i	1.40699	−	2.43697i
$809$	−5.93719e6			−0.318941			−0.159470	−	0.987203i	$-0.550979\pi$
$809$	−5.93719e6			−0.318941			−0.159470	+	0.987203i	$0.550979\pi$
$810$	−1.32087e6	−	1.21026e7i	−0.0707371	−	0.648133i
$811$	−2.80244e7			−1.49618			−0.748091	−	0.663596i	$-0.769029\pi$
$811$	−2.80244e7			−1.49618			−0.748091	+	0.663596i	$0.769029\pi$
$812$	−4.75952e6	+	8.24373e6i	−0.253322	+	0.438767i
$813$	−9.77845e6	+	2.55499e7i	−0.518852	+	1.35570i
$814$	4.22217e7	+	7.31301e7i	2.23344	+	3.86844i
$815$	3.46139e6	+	5.99530e6i	0.182539	+	0.316167i
$816$	1.66231e7	+	2.04860e7i	0.873951	+	1.07704i
$817$	9.07176e6	−	1.57128e7i	0.475485	−	0.823564i
$818$	−3.85179e6			−0.201270
$819$	−186325.	−	167096.i	−0.00970645	−	0.00870473i
$820$	−1.50801e7			−0.783196
$821$	−4.15897e6	+	7.20355e6i	−0.215342	+	0.372983i	−0.953378	−	0.301778i	$-0.902420\pi$
$821$	−4.15897e6	+	7.20355e6i	−0.215342	+	0.372983i	0.738037	+	0.674761i	$0.235753\pi$
$822$	2.47006e7	−	3.93745e6i	1.27505	−	0.203252i
$823$	−839859.	−	1.45468e6i	−0.0432222	−	0.0748630i	0.843605	−	0.536964i	$-0.180429\pi$
$823$	−839859.	−	1.45468e6i	−0.0432222	−	0.0748630i	−0.886827	+	0.462101i	$0.847096\pi$
$824$	−2.76197e7	−	4.78387e7i	−1.41710	−	2.45449i
$825$	2.90072e7	−	4.62394e6i	1.48378	−	0.236525i
$826$	−7.96008e6	+	1.37873e7i	−0.405945	+	0.703118i
$827$	−6.72497e6			−0.341921			−0.170961	−	0.985278i	$-0.554687\pi$
$827$	−6.72497e6			−0.341921			−0.170961	+	0.985278i	$0.554687\pi$
$828$	−3.01508e7	+	9.86312e6i	−1.52835	+	0.499964i
$829$	2.56662e6			0.129711			0.0648554	−	0.997895i	$-0.479341\pi$
$829$	2.56662e6			0.129711			0.0648554	+	0.997895i	$0.479341\pi$
$830$	605844.	−	1.04935e6i	0.0305257	−	0.0528721i
$831$	−1.42466e7	−	1.75572e7i	−0.715661	−	0.881967i
$832$	671995.	+	1.16393e6i	0.0336556	+	0.0582933i
$833$	680581.	+	1.17880e6i	0.0339835	+	0.0588611i
$834$	9.37289e6	−	2.44902e7i	0.466615	−	1.21921i
$835$	−998773.	+	1.72993e6i	−0.0495736	+	0.0858640i
$836$	1.53939e8			7.61784
$837$	−1.19840e7	−	7.73159e6i	−0.591271	−	0.381466i
$838$	−1.90994e7			−0.939526
$839$	−2.23370e6	+	3.86889e6i	−0.109552	+	0.189750i	−0.915589	−	0.402116i	$-0.868275\pi$
$839$	−2.23370e6	+	3.86889e6i	−0.109552	+	0.189750i	0.806037	+	0.591865i	$0.201608\pi$
$840$	−2.77563e6	+	7.25237e6i	−0.135726	+	0.354635i
$841$	7.40137e6	+	1.28195e7i	0.360846	+	0.625004i
$842$	−4.38709e6	−	7.59866e6i	−0.213254	−	0.369366i
$843$	−8.53207e6	−	1.05148e7i	−0.413509	−	0.509601i
$844$	−3.59796e7	+	6.23185e7i	−1.73860	+	3.01135i
$845$	7.18295e6			0.346068
$846$	9.39351e6	−	4.46306e7i	0.451234	−	2.14391i
$847$	−1.51166e7			−0.724010
$848$	2.40148e6	−	4.15949e6i	0.114681	−	0.198633i
$849$	2.11947e7	−	3.37859e6i	1.00916	−	0.160867i
$850$	−8.29715e6	−	1.43711e7i	−0.393896	−	0.682248i
$851$	9.29373e6	+	1.60972e7i	0.439912	+	0.761951i
$852$	9.28941e7	−	1.48080e7i	4.38419	−	0.698871i
$853$	−1.48193e7	+	2.56678e7i	−0.697358	+	1.20786i	0.272021	+	0.962291i	$0.412308\pi$
$853$	−1.48193e7	+	2.56678e7i	−0.697358	+	1.20786i	−0.969379	+	0.245568i	$0.921025\pi$
$854$	4.14730e6			0.194590
$855$	−2.67830e6	+	1.27252e7i	−0.125298	+	0.595317i
$856$	5.24268e7			2.44551
$857$	2.86882e6	−	4.96894e6i	0.133429	−	0.231106i	−0.791567	−	0.611082i	$-0.790734\pi$
$857$	2.86882e6	−	4.96894e6i	0.133429	−	0.231106i	0.924996	+	0.379976i	$0.124068\pi$
$858$	−1.50591e6	−	1.85586e6i	−0.0698363	−	0.0860650i
$859$	−5.25950e6	−	9.10972e6i	−0.243199	−	0.421233i	0.718425	−	0.695605i	$-0.244863\pi$
$859$	−5.25950e6	−	9.10972e6i	−0.243199	−	0.421233i	−0.961624	+	0.274372i	$0.911530\pi$
$860$	5.17093e6	+	8.95631e6i	0.238409	+	0.412936i
$861$	2.61433e6	−	6.83092e6i	0.120186	−	0.314030i
$862$	1.92242e7	−	3.32973e7i	0.881213	−	1.52631i
$863$	2.63871e7			1.20605			0.603024	−	0.797723i	$-0.293962\pi$
$863$	2.63871e7			1.20605			0.603024	+	0.797723i	$0.293962\pi$
$864$	−4.76858e7	−	3.07650e7i	−2.17323	−	1.40208i
$865$	1.30275e7			0.592001
$866$	−4.11135e6	+	7.12107e6i	−0.186290	+	0.322664i
$867$	6.12052e6	−	1.59922e7i	0.276529	−	0.722536i
$868$	7.50005e6	+	1.29905e7i	0.337882	+	0.585228i
$869$	−2.10048e7	−	3.63814e7i	−0.943561	−	1.63429i
$870$	−4.83841e6	−	5.96277e6i	−0.216723	−	0.267085i
$871$	565617.	−	979678.i	0.0252626	−	0.0437560i
$872$	−6.83852e7			−3.04558
$873$	9.51666e6	−	3.11315e6i	0.422619	−	0.138250i
$874$	4.72201e7			2.09097
$875$	2.78783e6	−	4.82866e6i	0.123097	−	0.213209i
$876$	−1.13163e8	+	1.80390e7i	−4.98248	+	0.794243i
$877$	−6.03286e6	−	1.04492e7i	−0.264865	−	0.458759i	0.702663	−	0.711522i	$-0.251994\pi$
$877$	−6.03286e6	−	1.04492e7i	−0.264865	−	0.458759i	−0.967528	+	0.252763i	$0.918661\pi$
$878$	−9.81413e6	−	1.69986e7i	−0.429651	−	0.744177i
$879$	6.34404e6	−	1.01129e6i	0.276945	−	0.0441470i
$880$	−1.98107e7	+	3.43132e7i	−0.862371	+	1.49367i
$881$	2.01221e7			0.873441			0.436720	−	0.899597i	$-0.356140\pi$
$881$	2.01221e7			0.873441			0.436720	+	0.899597i	$0.356140\pi$
$882$	−4.62363e6	−	4.14646e6i	−0.200130	−	0.179476i
$883$	1.08017e7			0.466219			0.233109	−	0.972451i	$-0.425110\pi$
$883$	1.08017e7			0.466219			0.233109	+	0.972451i	$0.425110\pi$
$884$	−484443.	+	839080.i	−0.0208503	+	0.0361138i
$885$	−5.80673e6	−	7.15611e6i	−0.249215	−	0.307128i
$886$	−1.68412e7	−	2.91697e7i	−0.720755	−	1.24838i
$887$	1.19837e7	+	2.07563e7i	0.511424	+	0.885812i	0.999912	+	0.0132420i	$0.00421518\pi$
$887$	1.19837e7	+	2.07563e7i	0.511424	+	0.885812i	−0.488488	+	0.872570i	$0.662451\pi$
$888$	−3.38574e7	+	8.84651e7i	−1.44086	+	3.76478i
$889$	100338.	−	173791.i	0.00425807	−	0.00737519i
$890$	1.94199e7			0.821811
$891$	3.70299e7	+	1.63100e7i	1.56264	+	0.688273i
$892$	7.80063e7			3.28259
$893$	−2.43580e7	+	4.21894e7i	−1.02215	+	1.77041i
$894$	−2.35769e6	+	6.16034e6i	−0.0986603	+	0.257787i
$895$	1.60144e6	+	2.77378e6i	0.0668273	+	0.115748i
$896$	4.93023e6	+	8.53941e6i	0.205162	+	0.355351i
$897$	−331477.	−	408507.i	−0.0137554	−	0.0169519i
$898$	3.78478e7	−	6.55542e7i	1.56621	−	2.71275i
$899$	−8.99531e6			−0.371208
$900$	4.04489e7	+	3.62745e7i	1.66456	+	1.49278i
$901$	912098.			0.0374309
$902$	3.49226e7	−	6.04877e7i	1.42919	−	2.47543i
$903$	−4.95343e6	+	789612.i	−0.202156	+	0.0322251i
$904$	−6.24661e6	−	1.08194e7i	−0.254228	−	0.440336i
$905$	−1.78853e6	−	3.09783e6i	−0.0725898	−	0.125729i
$906$	−4.66629e7	+	7.43840e6i	−1.88865	+	0.301064i
$907$	1.05103e7	−	1.82044e7i	0.424227	−	0.734783i	−0.572121	−	0.820170i	$-0.693879\pi$
$907$	1.05103e7	−	1.82044e7i	0.424227	−	0.734783i	0.996348	+	0.0853862i	$0.0272124\pi$
$908$	−1.76799e7			−0.711650
$909$	−2.29783e7	+	7.51683e6i	−0.922378	+	0.301734i
$910$	−212348.			−0.00850049
$911$	1.16626e7	−	2.02002e7i	0.465585	−	0.806417i	−0.533643	−	0.845710i	$-0.679177\pi$
$911$	1.16626e7	−	2.02002e7i	0.465585	−	0.806417i	0.999228	+	0.0392930i	$0.0125106\pi$
$912$	8.10141e7	+	9.98404e7i	3.22533	+	3.97483i
$913$	2.01357e6	+	3.48761e6i	0.0799448	+	0.138468i
$914$	−1.13821e7	−	1.97144e7i	−0.450669	−	0.780582i
$915$	−858109.	+	2.24213e6i	−0.0338836	+	0.0885337i
$916$	−9.06361e6	+	1.56986e7i	−0.356913	+	0.618191i
$917$	−1.91424e6			−0.0751747
$918$	1.12804e6	−	2.28313e7i	0.0441793	−	0.894177i
$919$	−2.47403e7			−0.966311			−0.483155	−	0.875535i	$-0.660509\pi$
$919$	−2.47403e7			−0.966311			−0.483155	+	0.875535i	$0.660509\pi$
$920$	−8.16135e6	+	1.41359e7i	−0.317901	+	0.550621i
$921$	−1.30400e7	+	3.40720e7i	−0.506559	+	1.32358i
$922$	3.50745e7	+	6.07508e7i	1.35883	+	2.35356i
$923$	779974.	+	1.35096e6i	0.0301353	+	0.0521959i
$924$	−2.68156e7	−	3.30470e7i	−1.03325	−	1.27336i
$925$	1.59173e7	−	2.75696e7i	0.611668	−	1.05944i
$926$	−2.85130e7			−1.09274
$927$	−5.26718e6	+	2.50255e7i	−0.201316	+	0.956497i
$928$	−3.57935e7			−1.36438
$929$	6.76649e6	−	1.17199e7i	0.257231	−	0.445538i	−0.708268	−	0.705944i	$-0.750523\pi$
$929$	6.76649e6	−	1.17199e7i	0.257231	−	0.445538i	0.965499	+	0.260406i	$0.0838564\pi$
$930$	−1.19495e7	+	1.90483e6i	−0.453045	+	0.0722185i
$931$	3.31687e6	+	5.74498e6i	0.125416	+	0.217227i
$932$	3.23243e7	+	5.59873e7i	1.21896	+	2.11130i
$933$	−3.20468e7	+	5.10849e6i	−1.20526	+	0.192127i
$934$	−4.41637e7	+	7.64938e7i	−1.65653	+	2.86919i
$935$	−7.52425e6			−0.281471
$936$	552160.	−	2.62343e6i	0.0206004	−	0.0978768i
$937$	−2.06413e7			−0.768048			−0.384024	−	0.923323i	$-0.625462\pi$
$937$	−2.06413e7			−0.768048			−0.384024	+	0.923323i	$0.625462\pi$
$938$	1.40357e7	−	2.43106e7i	0.520869	−	0.902172i
$939$	2.52788e7	+	3.11531e7i	0.935604	+	1.15302i
$940$	−1.38841e7	−	2.40480e7i	−0.512506	−	0.887687i
$941$	−1.00538e7	−	1.74138e7i	−0.370133	−	0.641089i	0.619453	−	0.785034i	$-0.287355\pi$
$941$	−1.00538e7	−	1.74138e7i	−0.370133	−	0.641089i	−0.989586	+	0.143945i	$0.954021\pi$
$942$	−3.72636e6	+	9.73653e6i	−0.136823	+	0.357501i
$943$	7.68707e6	−	1.33144e7i	0.281502	−	0.487576i
$944$	−9.11181e7			−3.32793
$945$	3.19834e6	−	1.64171e6i	0.116505	−	0.0598022i
$946$	−4.78994e7			−1.74021
$947$	1.15377e7	−	1.99839e7i	0.418065	−	0.724110i	−0.577679	−	0.816264i	$-0.696042\pi$
$947$	1.15377e7	−	1.99839e7i	0.418065	−	0.724110i	0.995745	+	0.0921533i	$0.0293750\pi$
$948$	2.77747e7	−	7.25717e7i	1.00376	−	2.62269i
$949$	−950163.	−	1.64573e6i	−0.0342478	−	0.0593189i
$950$	−4.04368e7	−	7.00387e7i	−1.45368	−	2.51784i
$951$	1.78211e7	+	2.19624e7i	0.638975	+	0.787461i
$952$	−7.29027e6	+	1.26271e7i	−0.260706	+	0.451556i
$953$	3.80597e7			1.35748			0.678739	−	0.734379i	$-0.262527\pi$
$953$	3.80597e7			1.35748			0.678739	+	0.734379i	$0.262527\pi$
$954$	−3.95536e6	+	1.29390e6i	−0.140707	+	0.0460290i
$955$	−8.13956e6			−0.288797
$956$	1.07332e7	−	1.85905e7i	0.379827	−	0.657879i
$957$	2.52031e7	−	4.01755e6i	0.889558	−	0.141802i
$958$	3.06235e7	+	5.30415e7i	1.07806	+	1.86725i
$959$	3.69306e6	+	6.39657e6i	0.129670	+	0.224595i
$960$	−1.90650e7	+	3.03910e6i	−0.667667	+	0.106431i
$961$	7.22717e6	−	1.25178e7i	0.252441	−	0.437241i
$962$	−2.59024e6			−0.0902406
$963$	−1.80697e7	−	1.62049e7i	−0.627894	−	0.563094i
$964$	4.12320e7			1.42903
$965$	−491771.	+	851773.i	−0.0169998	+	0.0294446i
$966$	−8.22558e6	−	1.01371e7i	−0.283612	−	0.349518i
$967$	−2.14106e7	−	3.70842e7i	−0.736313	−	1.27533i	−0.954145	−	0.299345i	$-0.903232\pi$
$967$	−2.14106e7	−	3.70842e7i	−0.736313	−	1.27533i	0.217832	−	0.975986i	$-0.430102\pi$
$968$	−8.09631e7	−	1.40232e8i	−2.77715	−	4.81016i
$969$	−8.72742e6	+	2.28037e7i	−0.298591	+	0.780181i
$970$	4.24776e6	−	7.35734e6i	0.144954	−	0.251068i
$971$	−3.09516e7			−1.05350			−0.526750	−	0.850020i	$-0.676590\pi$
$971$	−3.09516e7			−1.05350			−0.526750	+	0.850020i	$0.676590\pi$
$972$	1.97313e7	+	7.21959e7i	0.669868	+	2.45102i
$973$	7.74346e6			0.262212
$974$	1.48951e7	−	2.57991e7i	0.503091	−	0.871379i
$975$	−322053.	+	841483.i	−0.0108496	+	0.0283487i
$976$	1.18684e7	+	2.05567e7i	0.398812	+	0.690762i
$977$	2.05557e7	+	3.56035e7i	0.688963	+	1.19332i	0.972174	+	0.234261i	$0.0752670\pi$
$977$	2.05557e7	+	3.56035e7i	0.688963	+	1.19332i	−0.283211	+	0.959058i	$0.591400\pi$
$978$	−3.73696e7	−	4.60537e7i	−1.24931	−	1.53963i
$979$	−3.22718e7	+	5.58964e7i	−1.07613	+	1.86392i
$980$	−3.78124e6			−0.125768
$981$	2.35700e7	+	2.11376e7i	0.781966	+	0.701266i
$982$	−4.63462e7			−1.53368
$983$	1.73288e7	−	3.00144e7i	0.571986	−	0.990709i	−0.424376	−	0.905486i	$-0.639506\pi$
$983$	1.73288e7	−	3.00144e7i	0.571986	−	0.990709i	0.996362	−	0.0852229i	$-0.0271602\pi$
$984$	7.73707e7	−	1.23334e7i	2.54735	−	0.406066i
$985$	−4.99738e6	−	8.65571e6i	−0.164116	−	0.284258i
$986$	−7.20905e6	−	1.24864e7i	−0.236149	−	0.409022i
$987$	1.33002e7	−	2.12014e6i	0.434574	−	0.0692742i
$988$	−2.36097e6	+	4.08933e6i	−0.0769483	+	0.133278i
$989$	−1.05435e7			−0.342763
$990$	3.26293e7	−	1.06739e7i	1.05808	−	0.346127i
$991$	3.20084e7			1.03533			0.517666	−	0.855582i	$-0.326801\pi$
$991$	3.20084e7			1.03533			0.517666	+	0.855582i	$0.326801\pi$
$992$	−2.82017e7	+	4.88468e7i	−0.909906	+	1.57600i
$993$	3.43004e7	+	4.22712e7i	1.10389	+	1.36042i
$994$	1.93550e7	+	3.35238e7i	0.621337	+	1.07619i
$995$	1.37207e6	+	2.37649e6i	0.0439358	+	0.0760990i
$996$	−2.66254e6	+	6.95689e6i	−0.0850449	+	0.222212i
$997$	1.38822e7	−	2.40446e7i	0.442302	−	0.766090i	−0.555558	−	0.831478i	$-0.687495\pi$
$997$	1.38822e7	−	2.40446e7i	0.442302	−	0.766090i	0.997860	+	0.0653881i	$0.0208285\pi$
$998$	−4.55130e6			−0.144647
$999$	3.90137e7	−	2.00257e7i	1.23681	−	0.634855i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	63.6.f.b.43.1	yes	30
3.2	odd	2		189.6.f.a.127.15		30
9.2	odd	6		567.6.a.h.1.1		15
9.4	even	3	inner	63.6.f.b.22.1	✓	30
9.5	odd	6		189.6.f.a.64.15		30
9.7	even	3		567.6.a.g.1.15		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
63.6.f.b.22.1	✓	30	9.4	even	3	inner
63.6.f.b.43.1	yes	30	1.1	even	1	trivial
189.6.f.a.64.15		30	9.5	odd	6
189.6.f.a.127.15		30	3.2	odd	2
567.6.a.g.1.15		15	9.7	even	3
567.6.a.h.1.1		15	9.2	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-5.32234 + 9.21856i) q^{2} +(-5.57188 + 14.5586i) q^{3} +(-40.6546 - 70.4158i) q^{4} +(9.68441 + 16.7739i) q^{5} +(-104.554 - 128.851i) q^{6} +(24.5000 - 42.4352i) q^{7} +524.880 q^{8} +(-180.908 - 162.238i) q^{9} -206.175 q^{10} +(342.619 - 593.434i) q^{11} +(1251.68 - 199.527i) q^{12} +(10.5096 + 18.2031i) q^{13} +(260.795 + 451.709i) q^{14} +(-298.166 + 47.5297i) q^{15} +(-1492.64 + 2585.33i) q^{16} -566.915 q^{17} +(2458.46 - 804.227i) q^{18} -2762.91 q^{19} +(787.431 - 1363.87i) q^{20} +(481.288 + 593.131i) q^{21} +(3647.07 + 6316.92i) q^{22} +(802.784 + 1390.46i) q^{23} +(-2924.57 + 7641.54i) q^{24} +(1374.92 - 2381.44i) q^{25} -223.742 q^{26} +(3369.97 - 1729.81i) q^{27} -3984.15 q^{28} +(1194.61 - 2069.13i) q^{29} +(1148.78 - 3001.63i) q^{30} +(-1882.47 - 3260.54i) q^{31} +(-7490.61 - 12974.1i) q^{32} +(6730.56 + 8294.62i) q^{33} +(3017.31 - 5226.14i) q^{34} +949.072 q^{35} +(-4069.38 + 19334.5i) q^{36} +11576.9 q^{37} +(14705.1 - 25470.0i) q^{38} +(-323.571 + 51.5795i) q^{39} +(5083.15 + 8804.28i) q^{40} +(-4787.76 - 8292.64i) q^{41} +(-8029.39 + 1279.94i) q^{42} +(-3283.41 + 5687.04i) q^{43} -55716.2 q^{44} +(969.376 - 4605.72i) q^{45} -17090.8 q^{46} +(8816.10 - 15269.9i) q^{47} +(-29322.1 - 36136.0i) q^{48} +(-1200.50 - 2079.33i) q^{49} +(14635.6 + 25349.6i) q^{50} +(3158.78 - 8253.51i) q^{51} +(854.526 - 1480.08i) q^{52} -1608.88 q^{53} +(-1989.79 + 40272.9i) q^{54} +13272.3 q^{55} +(12859.6 - 22273.4i) q^{56} +(15394.6 - 40224.2i) q^{57} +(12716.3 + 22025.2i) q^{58} +(15261.2 + 26433.2i) q^{59} +(15468.6 + 19063.3i) q^{60} +(3975.64 - 6886.01i) q^{61} +40076.6 q^{62} +(-11316.9 + 3702.05i) q^{63} +63941.1 q^{64} +(-203.558 + 352.573i) q^{65} +(-112287. + 17899.3i) q^{66} +(-26909.6 - 46608.8i) q^{67} +(23047.7 + 39919.7i) q^{68} +(-24716.3 + 3939.95i) q^{69} +(-5051.28 + 8749.08i) q^{70} +74215.5 q^{71} +(-94955.0 - 85155.5i) q^{72} -90409.2 q^{73} +(-61616.0 + 106722. i) q^{74} +(27009.6 + 33286.1i) q^{75} +(112325. + 194552. i) q^{76} +(-16788.4 - 29078.3i) q^{77} +(1246.67 - 3257.39i) q^{78} +(30653.3 - 53093.1i) q^{79} -57821.4 q^{80} +(6406.55 + 58700.4i) q^{81} +101928. q^{82} +(-2938.50 + 5089.62i) q^{83} +(22199.2 - 58003.8i) q^{84} +(-5490.24 - 9509.37i) q^{85} +(-34950.9 - 60536.7i) q^{86} +(23467.5 + 28920.9i) q^{87} +(179834. - 311482. i) q^{88} -94191.4 q^{89} +(37298.7 + 33449.4i) q^{90} +1029.94 q^{91} +(65273.7 - 113057. i) q^{92} +(57957.9 - 9238.90i) q^{93} +(93844.5 + 162543. i) q^{94} +(-26757.1 - 46344.7i) q^{95} +(230622. - 36762.8i) q^{96} +(-20602.7 + 35684.9i) q^{97} +25557.9 q^{98} +(-158260. + 51771.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 4 q^{2} + 20 q^{3} - 240 q^{4} + 71 q^{5} - 266 q^{6} + 735 q^{7} + 42 q^{8} - 442 q^{9} + 134 q^{11} - 1400 q^{12} + 165 q^{13} - 196 q^{14} + 647 q^{15} - 3840 q^{16} - 2184 q^{17} + 9235 q^{18}+ \cdots - 518014 q^{99}+O(q^{100}) \) 30 * q + 4 * q^2 + 20 * q^3 - 240 * q^4 + 71 * q^5 - 266 * q^6 + 735 * q^7 + 42 * q^8 - 442 * q^9 + 134 * q^11 - 1400 * q^12 + 165 * q^13 - 196 * q^14 + 647 * q^15 - 3840 * q^16 - 2184 * q^17 + 9235 * q^18 - 894 * q^19 - 1214 * q^20 - 392 * q^21 - 96 * q^22 - 3564 * q^23 - 1620 * q^24 - 3576 * q^25 - 1730 * q^26 + 23879 * q^27 - 23520 * q^28 + 4073 * q^29 - 19868 * q^30 - 2217 * q^31 + 12107 * q^32 - 5506 * q^33 - 15654 * q^34 + 6958 * q^35 + 45898 * q^36 + 10014 * q^37 + 48685 * q^38 - 7126 * q^39 - 7485 * q^40 + 22294 * q^41 - 17689 * q^42 - 3153 * q^43 - 164960 * q^44 - 361 * q^45 - 36492 * q^46 + 74313 * q^47 + 16051 * q^48 - 36015 * q^49 + 111323 * q^50 + 10149 * q^51 + 33501 * q^52 - 55548 * q^53 + 35398 * q^54 + 77376 * q^55 + 1029 * q^56 + 46199 * q^57 - 3249 * q^58 + 90567 * q^59 - 49136 * q^60 - 3714 * q^61 - 357408 * q^62 + 2548 * q^63 + 94434 * q^64 + 79607 * q^65 - 284270 * q^66 - 11016 * q^67 + 241743 * q^68 + 199305 * q^69 + 107586 * q^71 - 85305 * q^72 - 240162 * q^73 + 95016 * q^74 - 147461 * q^75 + 122748 * q^76 - 6566 * q^77 + 174484 * q^78 + 11013 * q^79 - 592898 * q^80 - 120058 * q^81 + 162036 * q^82 + 7014 * q^83 - 53116 * q^84 - 36387 * q^85 + 170519 * q^86 + 654053 * q^87 - 108012 * q^88 - 152320 * q^89 + 25909 * q^90 + 16170 * q^91 + 153651 * q^92 - 594909 * q^93 - 266412 * q^94 - 64264 * q^95 + 1058867 * q^96 - 81033 * q^97 - 19208 * q^98 - 518014 * q^99

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