LMFDB - Embedded newform 80.6.l.a.21.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,6,Mod(21,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(80, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("80.21");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	80.l (of order $4$, degree $2$, 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:	$12.8307055850$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$40$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			21.12
Character	$\chi$	$=$	80.21
Dual form			80.6.l.a.61.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.40887 - 4.51438i) q^{2} +(-13.5228 + 13.5228i) q^{3} +(-8.75923 + 30.7778i) q^{4} +(17.6777 + 17.6777i) q^{5} +(107.145 + 14.9496i) q^{6} +90.4254i q^{7} +(168.802 - 65.3752i) q^{8} -122.733i q^{9} +O(q^{10})$	\(q+(-3.40887 - 4.51438i) q^{2} +(-13.5228 + 13.5228i) q^{3} +(-8.75923 + 30.7778i) q^{4} +(17.6777 + 17.6777i) q^{5} +(107.145 + 14.9496i) q^{6} +90.4254i q^{7} +(168.802 - 65.3752i) q^{8} -122.733i q^{9} +(19.5428 - 140.065i) q^{10} +(234.581 + 234.581i) q^{11} +(-297.754 - 534.653i) q^{12} +(79.2296 - 79.2296i) q^{13} +(408.214 - 308.248i) q^{14} -478.104 q^{15} +(-870.552 - 539.180i) q^{16} -1830.78 q^{17} +(-554.065 + 418.382i) q^{18} +(18.5194 - 18.5194i) q^{19} +(-698.923 + 389.238i) q^{20} +(-1222.81 - 1222.81i) q^{21} +(259.332 - 1858.65i) q^{22} +2182.36i q^{23} +(-1398.62 + 3166.73i) q^{24} +625.000i q^{25} +(-627.755 - 87.5890i) q^{26} +(-1626.34 - 1626.34i) q^{27} +(-2783.10 - 792.056i) q^{28} +(-2900.05 + 2900.05i) q^{29} +(1629.79 + 2158.34i) q^{30} +4150.49 q^{31} +(533.534 + 5768.00i) q^{32} -6344.40 q^{33} +(6240.90 + 8264.84i) q^{34} +(-1598.51 + 1598.51i) q^{35} +(3777.47 + 1075.05i) q^{36} +(-8994.45 - 8994.45i) q^{37} +(-146.734 - 20.4734i) q^{38} +2142.81i q^{39} +(4139.71 + 1828.34i) q^{40} -19670.9i q^{41} +(-1351.82 + 9688.59i) q^{42} +(-6175.34 - 6175.34i) q^{43} +(-9274.66 + 5165.16i) q^{44} +(2169.64 - 2169.64i) q^{45} +(9852.01 - 7439.38i) q^{46} -7890.57 q^{47} +(19063.6 - 4481.08i) q^{48} +8630.25 q^{49} +(2821.49 - 2130.54i) q^{50} +(24757.3 - 24757.3i) q^{51} +(1744.53 + 3132.51i) q^{52} +(-16351.4 - 16351.4i) q^{53} +(-1797.94 + 12885.9i) q^{54} +8293.71i q^{55} +(5911.58 + 15264.0i) q^{56} +500.870i q^{57} +(22977.8 + 3206.04i) q^{58} +(5644.32 + 5644.32i) q^{59} +(4187.82 - 14715.0i) q^{60} +(-10538.4 + 10538.4i) q^{61} +(-14148.5 - 18736.9i) q^{62} +11098.2 q^{63} +(24220.2 - 22070.9i) q^{64} +2801.19 q^{65} +(21627.2 + 28641.0i) q^{66} +(9300.98 - 9300.98i) q^{67} +(16036.2 - 56347.5i) q^{68} +(-29511.7 - 29511.7i) q^{69} +(12665.4 + 1767.17i) q^{70} +30077.2i q^{71} +(-8023.72 - 20717.6i) q^{72} +89964.1i q^{73} +(-9943.45 + 71265.3i) q^{74} +(-8451.76 - 8451.76i) q^{75} +(407.773 + 732.205i) q^{76} +(-21212.1 + 21212.1i) q^{77} +(9673.48 - 7304.57i) q^{78} +29546.6 q^{79} +(-5857.88 - 24920.8i) q^{80} +73809.7 q^{81} +(-88801.9 + 67055.6i) q^{82} +(4504.74 - 4504.74i) q^{83} +(48346.2 - 26924.5i) q^{84} +(-32364.0 - 32364.0i) q^{85} +(-6826.90 + 48928.8i) q^{86} -78433.8i q^{87} +(54933.6 + 24262.0i) q^{88} +46696.7i q^{89} +(-17190.6 - 2398.56i) q^{90} +(7164.36 + 7164.36i) q^{91} +(-67168.4 - 19115.8i) q^{92} +(-56126.3 + 56126.3i) q^{93} +(26897.9 + 35621.0i) q^{94} +654.761 q^{95} +(-85214.4 - 70784.7i) q^{96} -94069.4 q^{97} +(-29419.4 - 38960.2i) q^{98} +(28791.0 - 28791.0i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) $ 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/80\mathbb{Z}\right)^\times$.

$n$	$17$	$21$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{4}\right)$	$1$

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 $

$2$	−3.40887	−	4.51438i	−0.602609	−	0.798037i
$2$	−3.40887	−	4.51438i	−0.602609	−	0.798037i
$3$	−13.5228	+	13.5228i	−0.867489	+	0.867489i	−0.992194	−	0.124705i	$-0.960202\pi$
$3$	−13.5228	+	13.5228i	−0.867489	+	0.867489i	0.124705	+	0.992194i	$0.460202\pi$
$4$	−8.75923	+	30.7778i	−0.273726	+	0.961808i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$5$	17.6777	+	17.6777i	0.316228	+	0.316228i
$6$	107.145	+	14.9496i	1.21505	+	0.169532i
$7$			90.4254i			0.697502i	0.937216	+	0.348751i	$0.113394\pi$
$7$			90.4254i			0.697502i	−0.937216	+	0.348751i	$0.886606\pi$
$8$	168.802	−	65.3752i	0.932508	−	0.361150i
$9$		−	122.733i		−	0.505076i
$10$	19.5428	−	140.065i	0.0617999	−	0.442923i
$11$	234.581	+	234.581i	0.584537	+	0.584537i	0.936147	−	0.351610i	$-0.114366\pi$
$11$	234.581	+	234.581i	0.584537	+	0.584537i	−0.351610	+	0.936147i	$0.614366\pi$
$12$	−297.754	−	534.653i	−0.596904	−	1.07181i
$13$	79.2296	−	79.2296i	0.130026	−	0.130026i	−0.639099	−	0.769125i	$-0.720693\pi$
$13$	79.2296	−	79.2296i	0.130026	−	0.130026i	0.769125	+	0.639099i	$0.220693\pi$
$14$	408.214	−	308.248i	0.556632	−	0.420320i
$15$	−478.104			−0.548648
$16$	−870.552	−	539.180i	−0.850148	−	0.526543i
$17$	−1830.78			−1.53644			−0.768218	−	0.640189i	$-0.778856\pi$
$17$	−1830.78			−1.53644			−0.768218	+	0.640189i	$0.778856\pi$
$18$	−554.065	+	418.382i	−0.403069	+	0.304363i
$19$	18.5194	−	18.5194i	0.0117691	−	0.0117691i	−0.701198	−	0.712967i	$-0.747351\pi$
$19$	18.5194	−	18.5194i	0.0117691	−	0.0117691i	0.712967	+	0.701198i	$0.247351\pi$
$20$	−698.923	+	389.238i	−0.390710	+	0.217591i
$21$	−1222.81	−	1222.81i	−0.605075	−	0.605075i
$22$	259.332	−	1858.65i	0.114235	−	0.818729i
$23$			2182.36i			0.860215i	0.902778	+	0.430108i	$0.141524\pi$
$23$			2182.36i			0.860215i	−0.902778	+	0.430108i	$0.858476\pi$
$24$	−1398.62	+	3166.73i	−0.495646	+	1.12223i
$25$			625.000i			0.200000i
$26$	−627.755	−	87.5890i	−0.182120	−	0.0254107i
$27$	−1626.34	−	1626.34i	−0.429342	−	0.429342i
$28$	−2783.10	−	792.056i	−0.670862	−	0.190924i
$29$	−2900.05	+	2900.05i	−0.640341	+	0.640341i	−0.950639	−	0.310298i	$-0.899571\pi$
$29$	−2900.05	+	2900.05i	−0.640341	+	0.640341i	0.310298	+	0.950639i	$0.399571\pi$
$30$	1629.79	+	2158.34i	0.330620	+	0.437842i
$31$	4150.49			0.775702			0.387851	−	0.921722i	$-0.373217\pi$
$31$	4150.49			0.775702			0.387851	+	0.921722i	$0.373217\pi$
$32$	533.534	+	5768.00i	0.0921058	+	0.995749i
$33$	−6344.40			−1.01416
$34$	6240.90	+	8264.84i	0.925869	+	1.22613i
$35$	−1598.51	+	1598.51i	−0.220569	+	0.220569i
$36$	3777.47	+	1075.05i	0.485786	+	0.138252i
$37$	−8994.45	−	8994.45i	−1.08012	−	1.08012i	−0.996498	−	0.0836183i	$-0.973352\pi$
$37$	−8994.45	−	8994.45i	−1.08012	−	1.08012i	−0.0836183	−	0.996498i	$-0.526648\pi$
$38$	−146.734	−	20.4734i	−0.0164844	−	0.00230002i
$39$			2142.81i			0.225592i
$40$	4139.71	+	1828.34i	0.409091	+	0.180679i
$41$		−	19670.9i		−	1.82753i	−0.406241	−	0.913766i	$-0.633161\pi$
$41$		−	19670.9i		−	1.82753i	0.406241	−	0.913766i	$-0.366839\pi$
$42$	−1351.82	+	9688.59i	−0.118249	+	0.847496i
$43$	−6175.34	−	6175.34i	−0.509319	−	0.509319i	0.404998	−	0.914317i	$-0.367272\pi$
$43$	−6175.34	−	6175.34i	−0.509319	−	0.509319i	−0.914317	+	0.404998i	$0.867272\pi$
$44$	−9274.66	+	5165.16i	−0.722215	+	0.402209i
$45$	2169.64	−	2169.64i	0.159719	−	0.159719i
$46$	9852.01	−	7439.38i	0.686483	−	0.518373i
$47$	−7890.57			−0.521031			−0.260516	−	0.965470i	$-0.583893\pi$
$47$	−7890.57			−0.521031			−0.260516	+	0.965470i	$0.583893\pi$
$48$	19063.6	−	4481.08i	1.19427	−	0.280724i
$49$	8630.25			0.513492
$50$	2821.49	−	2130.54i	0.159607	−	0.120522i
$51$	24757.3	−	24757.3i	1.33284	−	1.33284i
$52$	1744.53	+	3132.51i	0.0894683	+	0.160651i
$53$	−16351.4	−	16351.4i	−0.799588	−	0.799588i	0.183443	−	0.983030i	$-0.441276\pi$
$53$	−16351.4	−	16351.4i	−0.799588	−	0.799588i	−0.983030	+	0.183443i	$0.941276\pi$
$54$	−1797.94	+	12885.9i	−0.0839055	+	0.601356i
$55$			8293.71i			0.369694i
$56$	5911.58	+	15264.0i	0.251903	+	0.650425i
$57$			500.870i			0.0204192i
$58$	22977.8	+	3206.04i	0.896890	+	0.125141i
$59$	5644.32	+	5644.32i	0.211097	+	0.211097i	0.804733	−	0.593637i	$-0.202308\pi$
$59$	5644.32	+	5644.32i	0.211097	+	0.211097i	−0.593637	+	0.804733i	$0.702308\pi$
$60$	4187.82	−	14715.0i	0.150179	−	0.527694i
$61$	−10538.4	+	10538.4i	−0.362618	+	0.362618i	−0.864776	−	0.502158i	$-0.832540\pi$
$61$	−10538.4	+	10538.4i	−0.362618	+	0.362618i	0.502158	+	0.864776i	$0.332540\pi$
$62$	−14148.5	−	18736.9i	−0.467445	−	0.619039i
$63$	11098.2			0.352291
$64$	24220.2	−	22070.9i	0.739141	−	0.673551i
$65$	2801.19			0.0822354
$66$	21627.2	+	28641.0i	0.611141	+	0.809336i
$67$	9300.98	−	9300.98i	0.253129	−	0.253129i	−0.569123	−	0.822252i	$-0.692717\pi$
$67$	9300.98	−	9300.98i	0.253129	−	0.253129i	0.822252	+	0.569123i	$0.192717\pi$
$68$	16036.2	−	56347.5i	0.420562	−	1.47776i
$69$	−29511.7	−	29511.7i	−0.746227	−	0.746227i
$70$	12665.4	+	1767.17i	0.308939	+	0.0431055i
$71$			30077.2i			0.708096i	0.935227	+	0.354048i	$0.115195\pi$
$71$			30077.2i			0.708096i	−0.935227	+	0.354048i	$0.884805\pi$
$72$	−8023.72	−	20717.6i	−0.182408	−	0.470987i
$73$			89964.1i			1.97589i	0.154818	+	0.987943i	$0.450521\pi$
$73$			89964.1i			1.97589i	−0.154818	+	0.987943i	$0.549479\pi$
$74$	−9943.45	+	71265.3i	−0.211085	+	1.51286i
$75$	−8451.76	−	8451.76i	−0.173498	−	0.173498i
$76$	407.773	+	732.205i	0.00809812	+	0.0145411i
$77$	−21212.1	+	21212.1i	−0.407715	+	0.407715i
$78$	9673.48	−	7304.57i	0.180030	−	0.135943i
$79$	29546.6			0.532647			0.266323	−	0.963884i	$-0.414191\pi$
$79$	29546.6			0.532647			0.266323	+	0.963884i	$0.414191\pi$
$80$	−5857.88	−	24920.8i	−0.102333	−	0.435348i
$81$	73809.7			1.24997
$82$	−88801.9	+	67055.6i	−1.45844	+	1.10129i
$83$	4504.74	−	4504.74i	0.0717753	−	0.0717753i	−0.670308	−	0.742083i	$-0.733838\pi$
$83$	4504.74	−	4504.74i	0.0717753	−	0.0717753i	0.742083	+	0.670308i	$0.233838\pi$
$84$	48346.2	−	26924.5i	0.747591	−	0.416341i
$85$	−32364.0	−	32364.0i	−0.485864	−	0.485864i
$86$	−6826.90	+	48928.8i	−0.0995353	+	0.713375i
$87$		−	78433.8i		−	1.11098i
$88$	54933.6	+	24262.0i	0.756191	+	0.333979i
$89$			46696.7i			0.624901i	0.949934	+	0.312451i	$0.101150\pi$
$89$			46696.7i			0.624901i	−0.949934	+	0.312451i	$0.898850\pi$
$90$	−17190.6	−	2398.56i	−0.223710	−	0.0312136i
$91$	7164.36	+	7164.36i	0.0906931	+	0.0906931i
$92$	−67168.4	−	19115.8i	−0.827362	−	0.235463i
$93$	−56126.3	+	56126.3i	−0.672914	+	0.672914i
$94$	26897.9	+	35621.0i	0.313978	+	0.415802i
$95$	654.761			0.00744345
$96$	−85214.4	−	70784.7i	−0.943703	−	0.783901i
$97$	−94069.4			−1.01512			−0.507562	−	0.861615i	$-0.669453\pi$
$97$	−94069.4			−1.01512			−0.507562	+	0.861615i	$0.669453\pi$
$98$	−29419.4	−	38960.2i	−0.309434	−	0.409785i
$99$	28791.0	−	28791.0i	0.295235	−	0.295235i
$100$	−19236.2	−	5474.52i	−0.192362	−	0.0547452i
$101$	−63248.9	−	63248.9i	−0.616949	−	0.616949i	0.327798	−	0.944748i	$-0.393693\pi$
$101$	−63248.9	−	63248.9i	−0.616949	−	0.616949i	−0.944748	+	0.327798i	$0.893693\pi$
$102$	−196158.	−	27369.5i	−1.86684	−	0.260475i
$103$			122001.i			1.13311i	0.824024	+	0.566554i	$0.191724\pi$
$103$			122001.i			1.13311i	−0.824024	+	0.566554i	$0.808276\pi$
$104$	8194.45	−	18553.8i	0.0742911	−	0.168209i
$105$		−	43232.7i		−	0.382683i
$106$	−18076.7	+	129556.i	−0.156262	+	1.11994i
$107$	−68328.2	−	68328.2i	−0.576953	−	0.576953i	0.357110	−	0.934062i	$-0.383762\pi$
$107$	−68328.2	−	68328.2i	−0.576953	−	0.576953i	−0.934062	+	0.357110i	$0.883762\pi$
$108$	64300.9	−	35809.9i	0.530466	−	0.295422i
$109$	25897.5	−	25897.5i	0.208782	−	0.208782i	−0.594968	−	0.803749i	$-0.702835\pi$
$109$	25897.5	−	25897.5i	0.208782	−	0.208782i	0.803749	+	0.594968i	$0.202835\pi$
$110$	37440.9	−	28272.2i	0.295029	−	0.222781i
$111$	243261.			1.87398
$112$	48755.6	−	78720.0i	0.367265	−	0.592980i
$113$	−101724.			−0.749426			−0.374713	−	0.927141i	$-0.622259\pi$
$113$	−101724.			−0.749426			−0.374713	+	0.927141i	$0.622259\pi$
$114$	2261.12	−	1707.40i	0.0162953	−	0.0123048i
$115$	−38579.1	+	38579.1i	−0.272024	+	0.272024i
$116$	−63855.2	−	114660.i	−0.440607	−	0.791162i
$117$	−9724.11	−	9724.11i	−0.0656728	−	0.0656728i
$118$	6239.85	−	44721.3i	0.0412543	−	0.295672i
$119$		−	165549.i		−	1.07167i
$120$	−80704.9	+	31256.1i	−0.511619	+	0.198145i
$121$		−	50994.1i		−	0.316633i
$122$	83498.2	+	11650.3i	0.507899	+	0.0708658i
$123$	266006.	+	266006.i	1.58536	+	1.58536i
$124$	−36355.1	+	127743.i	−0.212330	+	0.746077i
$125$	−11048.5	+	11048.5i	−0.0632456	+	0.0632456i
$126$	−37832.3	−	50101.5i	−0.212294	−	0.281141i
$127$	278343.			1.53134			0.765669	−	0.643235i	$-0.222408\pi$
$127$	278343.			1.53134			0.765669	+	0.643235i	$0.222408\pi$
$128$	−182200.	−	34102.2i	−0.982931	−	0.183974i
$129$	167016.			0.883657
$130$	−9548.88	−	12645.6i	−0.0495558	−	0.0656269i
$131$	−270701.	+	270701.i	−1.37820	+	1.37820i	−0.530534	+	0.847663i	$0.678009\pi$
$131$	−270701.	+	270701.i	−1.37820	+	1.37820i	−0.847663	+	0.530534i	$0.821991\pi$
$132$	55572.1	−	195267.i	0.277601	−	0.975426i
$133$	1674.63	+	1674.63i	0.00820898	+	0.00820898i
$134$	−73694.0	−	10282.3i	−0.354544	−	0.0494686i
$135$		−	57500.0i		−	0.271540i
$136$	−309039.	+	119688.i	−1.43274	+	0.554884i
$137$			107009.i			0.487102i	0.969888	+	0.243551i	$0.0783123\pi$
$137$			107009.i			0.487102i	−0.969888	+	0.243551i	$0.921688\pi$
$138$	−32625.4	+	233828.i	−0.145834	+	1.04520i
$139$	113252.	+	113252.i	0.497174	+	0.497174i	0.910557	−	0.413383i	$-0.135653\pi$
$139$	113252.	+	113252.i	0.497174	+	0.497174i	−0.413383	+	0.910557i	$0.635653\pi$
$140$	−35197.0	−	63200.4i	−0.151770	−	0.272521i
$141$	106703.	−	106703.i	0.451989	−	0.451989i
$142$	135780.	−	102529.i	0.565087	−	0.426705i
$143$	37171.6			0.152010
$144$	−66175.4	+	106846.i	−0.265944	+	0.429389i
$145$	−102532.			−0.404987
$146$	406132.	−	306676.i	1.57683	−	1.19069i
$147$	−116705.	+	116705.i	−0.445449	+	0.445449i
$148$	355614.	−	198045.i	1.33452	−	0.743208i
$149$	−83119.9	−	83119.9i	−0.306718	−	0.306718i	0.536917	−	0.843635i	$-0.319589\pi$
$149$	−83119.9	−	83119.9i	−0.306718	−	0.306718i	−0.843635	+	0.536917i	$0.819589\pi$
$150$	−9343.50	+	66965.4i	−0.0339064	+	0.243009i
$151$			337720.i			1.20535i	0.797985	+	0.602677i	$0.205899\pi$
$151$			337720.i			1.20535i	−0.797985	+	0.602677i	$0.794101\pi$
$152$	1915.41	−	4336.83i	0.00672437	−	0.0152252i
$153$			224698.i			0.776016i
$154$	168069.	+	23450.2i	0.571065	+	0.0796791i
$155$	73371.0	+	73371.0i	0.245299	+	0.245299i
$156$	−65951.2	−	18769.4i	−0.216976	−	0.0617503i
$157$	−117288.	+	117288.i	−0.379755	+	0.379755i	−0.871014	−	0.491258i	$-0.836537\pi$
$157$	−117288.	+	117288.i	−0.379755	+	0.379755i	0.491258	+	0.871014i	$0.336537\pi$
$158$	−100720.	−	133384.i	−0.320977	−	0.425072i
$159$	442235.			1.38727
$160$	−92533.1	+	111396.i	−0.285757	+	0.344010i
$161$	−197341.			−0.600001
$162$	−251608.	−	333205.i	−0.753245	−	0.997526i
$163$	−73700.8	+	73700.8i	−0.217272	+	0.217272i	−0.807348	−	0.590076i	$-0.799098\pi$
$163$	−73700.8	+	73700.8i	−0.217272	+	0.217272i	0.590076	+	0.807348i	$0.299098\pi$
$164$	605428.	+	172302.i	1.75773	+	0.500243i
$165$	−112154.	−	112154.i	−0.320705	−	0.320705i
$166$	−35692.2	−	4980.04i	−0.100532	−	0.0140269i
$167$		−	670797.i		−	1.86123i	−0.366002	−	0.930614i	$-0.619274\pi$
$167$		−	670797.i		−	1.86123i	0.366002	−	0.930614i	$-0.380726\pi$
$168$	−286353.	−	126471.i	−0.782760	−	0.345714i
$169$			358738.i			0.966187i
$170$	−35778.7	+	256428.i	−0.0949515	+	0.680523i
$171$	−2272.95	−	2272.95i	−0.00594429	−	0.00594429i
$172$	244155.	−	135973.i	0.629281	−	0.350453i
$173$	395626.	−	395626.i	1.00501	−	1.00501i	0.00502102	−	0.999987i	$-0.498402\pi$
$173$	395626.	−	395626.i	1.00501	−	1.00501i	0.999987	−	0.00502102i	$-0.00159825\pi$
$174$	−354080.	+	267371.i	−0.886601	+	0.669485i
$175$	−56515.9			−0.139500
$176$	−77733.6	−	330697.i	−0.189159	−	0.804727i
$177$	−152654.			−0.366248
$178$	210807.	−	159183.i	0.498694	−	0.376571i
$179$	130068.	−	130068.i	0.303416	−	0.303416i	−0.538933	−	0.842349i	$-0.681172\pi$
$179$	130068.	−	130068.i	0.303416	−	0.303416i	0.842349	+	0.538933i	$0.181172\pi$
$180$	47772.5	+	85781.2i	0.109900	+	0.197338i
$181$	−65586.3	−	65586.3i	−0.148805	−	0.148805i	0.628779	−	0.777584i	$-0.283555\pi$
$181$	−65586.3	−	65586.3i	−0.148805	−	0.148805i	−0.777584	+	0.628779i	$0.783555\pi$
$182$	7920.27	−	56765.0i	0.0177240	−	0.127029i
$183$		−	285017.i		−	0.629134i
$184$	142672.	+	368387.i	0.310667	+	0.802157i
$185$		−	318002.i		−	0.683125i
$186$	444703.	+	62048.2i	0.942513	+	0.131506i
$187$	−429467.	−	429467.i	−0.898103	−	0.898103i
$188$	69115.3	−	242855.i	0.142620	−	0.501132i
$189$	147063.	−	147063.i	0.299467	−	0.299467i
$190$	−2232.00	−	2955.84i	−0.00448548	−	0.00594014i
$191$	−526152.			−1.04358			−0.521792	−	0.853073i	$-0.674736\pi$
$191$	−526152.			−1.04358			−0.521792	+	0.853073i	$0.674736\pi$
$192$	−29064.0	+	625986.i	−0.0568987	+	1.22550i
$193$	643627.			1.24377			0.621886	−	0.783108i	$-0.286367\pi$
$193$	643627.			1.24377			0.621886	+	0.783108i	$0.286367\pi$
$194$	320670.	+	424665.i	0.611722	+	0.810106i
$195$	−37880.0	+	37880.0i	−0.0713383	+	0.0713383i
$196$	−75594.3	+	265621.i	−0.140556	+	0.493880i
$197$	313928.	+	313928.i	0.576322	+	0.576322i	0.933888	−	0.357566i	$-0.116393\pi$
$197$	313928.	+	313928.i	0.576322	+	0.576322i	−0.357566	+	0.933888i	$0.616393\pi$
$198$	−228118.	−	31828.7i	−0.413520	−	0.0576973i
$199$		−	482626.i		−	0.863929i	−0.901891	−	0.431964i	$-0.857821\pi$
$199$		−	482626.i		−	0.863929i	0.901891	−	0.431964i	$-0.142179\pi$
$200$	40859.5	+	105501.i	0.0722301	+	0.186502i
$201$			251551.i			0.439173i
$202$	−69922.3	+	501137.i	−0.120569	+	0.864127i
$203$	−262238.	−	262238.i	−0.446639	−	0.446639i
$204$	545122.	+	978833.i	0.917104	+	1.64677i
$205$	347736.	−	347736.i	0.577916	−	0.577916i
$206$	550760.	−	415887.i	0.904263	−	0.682821i
$207$	267849.			0.434474
$208$	−111692.	+	26254.4i	−0.179005	+	0.0420770i
$209$	8688.64			0.0137590
$210$	−195169.	+	147375.i	−0.305395	+	0.230608i
$211$	−748930.	+	748930.i	−1.15807	+	1.15807i	−0.173182	+	0.984890i	$0.555405\pi$
$211$	−748930.	+	748930.i	−1.15807	+	1.15807i	−0.984890	+	0.173182i	$0.944595\pi$
$212$	646488.	−	360036.i	0.987918	−	0.550182i
$213$	−406729.	−	406729.i	−0.614266	−	0.614266i
$214$	−75537.4	+	541381.i	−0.112753	+	0.808106i
$215$		−	218331.i		−	0.322122i
$216$	−380853.	−	168207.i	−0.555421	−	0.245308i
$217$			375310.i			0.541054i
$218$	−205193.	−	28630.0i	−0.292429	−	0.0408018i
$219$	−1.21657e6	−	1.21657e6i	−1.71406	−	1.71406i
$220$	−255262.	−	72646.4i	−0.355574	−	0.101195i
$221$	−145052.	+	145052.i	−0.199776	+	0.199776i
$222$	−829244.	−	1.09817e6i	−1.12928	−	1.49550i
$223$	168670.			0.227131			0.113565	−	0.993531i	$-0.463773\pi$
$223$	168670.			0.227131			0.113565	+	0.993531i	$0.463773\pi$
$224$	−521573.	+	48245.0i	−0.694537	+	0.0642439i
$225$	76708.3			0.101015
$226$	346765.	+	459222.i	0.451610	+	0.598069i
$227$	−1.06102e6	+	1.06102e6i	−1.36665	+	1.36665i	−0.501491	+	0.865163i	$0.667215\pi$
$227$	−1.06102e6	+	1.06102e6i	−1.36665	+	1.36665i	−0.865163	+	0.501491i	$0.832785\pi$
$228$	−15415.7	−	4387.24i	−0.0196393	−	0.00558926i
$229$	−1.04178e6	−	1.04178e6i	−1.31277	−	1.31277i	−0.919367	−	0.393400i	$-0.871299\pi$
$229$	−1.04178e6	−	1.04178e6i	−1.31277	−	1.31277i	−0.393400	−	0.919367i	$-0.628701\pi$
$230$	305671.	+	42649.5i	0.381009	+	0.0531612i
$231$		−	573695.i		−	0.707377i
$232$	−299943.	+	679126.i	−0.365863	+	0.828382i
$233$			866526.i			1.04566i	0.852436	+	0.522832i	$0.175124\pi$
$233$			866526.i			1.04566i	−0.852436	+	0.522832i	$0.824876\pi$
$234$	−10750.1	+	77046.5i	−0.0128343	+	0.0919842i
$235$	−139487.	−	139487.i	−0.164765	−	0.164765i
$236$	−223160.	+	124280.i	−0.260817	+	0.145252i
$237$	−399553.	+	399553.i	−0.462065	+	0.462065i
$238$	−747351.	+	564335.i	−0.855229	+	0.645795i
$239$	−1.56014e6			−1.76673			−0.883363	−	0.468690i	$-0.844726\pi$
$239$	−1.56014e6			−1.76673			−0.883363	+	0.468690i	$0.844726\pi$
$240$	416214.	+	257784.i	0.466433	+	0.288887i
$241$	1.26261e6			1.40032			0.700159	−	0.713987i	$-0.253113\pi$
$241$	1.26261e6			1.40032			0.700159	+	0.713987i	$0.253113\pi$
$242$	−230207.	+	173832.i	−0.252685	+	0.190806i
$243$	−602914.	+	602914.i	−0.654998	+	0.654998i
$244$	−232041.	−	416657.i	−0.249511	−	0.448027i
$245$	152563.	+	152563.i	0.162380	+	0.162380i
$246$	294072.	−	2.10763e6i	0.309825	−	2.22053i
$247$		−	2934.58i		−	0.00306057i
$248$	700611.	−	271339.i	0.723348	−	0.280145i
$249$			121834.i			0.124529i
$250$	87540.3	+	12214.3i	0.0885846	+	0.0123600i
$251$	428714.	+	428714.i	0.429520	+	0.429520i	0.888465	−	0.458945i	$-0.151772\pi$
$251$	428714.	+	428714.i	0.429520	+	0.429520i	−0.458945	+	0.888465i	$0.651772\pi$
$252$	−97211.7	+	341579.i	−0.0964311	+	0.338836i
$253$	−511941.	+	511941.i	−0.502827	+	0.502827i
$254$	−948835.	−	1.25655e6i	−0.922797	−	1.22206i
$255$	875304.			0.842963
$256$	467145.	+	938769.i	0.445504	+	0.895280i
$257$	1.40119e6			1.32331			0.661657	−	0.749806i	$-0.269853\pi$
$257$	1.40119e6			1.32331			0.661657	+	0.749806i	$0.269853\pi$
$258$	−569336.	−	753974.i	−0.532500	−	0.705191i
$259$	813327.	−	813327.i	0.753383	−	0.753383i
$260$	−24536.2	+	86214.5i	−0.0225100	+	0.0790947i
$261$	355933.	+	355933.i	0.323420	+	0.323420i
$262$	2.14483e6	+	299263.i	1.93037	+	0.269339i
$263$			1.95803e6i			1.74554i	0.488131	+	0.872771i	$0.337679\pi$
$263$			1.95803e6i			1.74554i	−0.488131	+	0.872771i	$0.662321\pi$
$264$	−1.07095e6	+	414767.i	−0.945711	+	0.366264i
$265$		−	578111.i		−	0.505704i
$266$	1851.32	−	13268.5i	0.00160427	−	0.0114979i
$267$	−631472.	−	631472.i	−0.542095	−	0.542095i
$268$	204795.	+	367734.i	0.174173	+	0.312749i
$269$	827605.	−	827605.i	0.697337	−	0.697337i	−0.266499	−	0.963835i	$-0.585867\pi$
$269$	827605.	−	827605.i	0.697337	−	0.697337i	0.963835	+	0.266499i	$0.0858667\pi$
$270$	−259577.	+	196010.i	−0.216699	+	0.163632i
$271$	−683579.			−0.565412			−0.282706	−	0.959207i	$-0.591232\pi$
$271$	−683579.			−0.565412			−0.282706	+	0.959207i	$0.591232\pi$
$272$	1.59379e6	+	987121.i	1.30620	+	0.809000i
$273$	−193765.			−0.157351
$274$	483080.	−	364781.i	0.388725	−	0.293532i
$275$	−146613.	+	146613.i	−0.116907	+	0.116907i
$276$	1.16681e6	−	649807.i	0.921989	−	0.513466i
$277$	1.00981e6	+	1.00981e6i	0.790755	+	0.790755i	0.981617	−	0.190862i	$-0.0611283\pi$
$277$	1.00981e6	+	1.00981e6i	0.790755	+	0.790755i	−0.190862	+	0.981617i	$0.561128\pi$
$278$	125201.	−	897323.i	0.0971619	−	0.696364i
$279$		−	509404.i		−	0.391788i
$280$	−165329.	+	374334.i	−0.126024	+	0.285341i
$281$			1.34508e6i			1.01620i	0.861297	+	0.508102i	$0.169653\pi$
$281$			1.34508e6i			1.01620i	−0.861297	+	0.508102i	$0.830347\pi$
$282$	−845433.	−	117961.i	−0.633077	−	0.0883315i
$283$	1.29402e6	+	1.29402e6i	0.960448	+	0.960448i	0.999247	−	0.0387990i	$-0.0123532\pi$
$283$	1.29402e6	+	1.29402e6i	0.960448	+	0.960448i	−0.0387990	+	0.999247i	$0.512353\pi$
$284$	−925713.	−	263453.i	−0.681052	−	0.193824i
$285$	−8854.22	+	8854.22i	−0.00645711	+	0.00645711i
$286$	−126713.	−	167807.i	−0.0916022	−	0.121309i
$287$	1.77875e6			1.27471
$288$	707925.	−	65482.4i	0.502929	−	0.0465204i
$289$	1.93191e6			1.36063
$290$	349520.	+	462870.i	0.244049	+	0.323195i
$291$	1.27208e6	−	1.27208e6i	0.880609	−	0.880609i
$292$	−2.76890e6	−	788015.i	−1.90042	−	0.540851i
$293$	−1.64136e6	−	1.64136e6i	−1.11695	−	1.11695i	−0.992186	−	0.124765i	$-0.960182\pi$
$293$	−1.64136e6	−	1.64136e6i	−1.11695	−	1.11695i	−0.124765	−	0.992186i	$-0.539818\pi$
$294$	924686.	+	129019.i	0.623915	+	0.0870533i
$295$			199557.i			0.133509i
$296$	−2.10630e6	−	930267.i	−1.39730	−	0.617132i
$297$		−	763020.i		−	0.501932i
$298$	−91889.9	+	658580.i	−0.0599414	+	0.429603i
$299$	172908.	+	172908.i	0.111850	+	0.111850i
$300$	334158.	−	186096.i	0.214362	−	0.119381i
$301$	558407.	−	558407.i	0.355251	−	0.355251i
$302$	1.52460e6	−	1.15124e6i	0.961917	−	0.726357i
$303$	1.71061e6			1.07039
$304$	−26107.5	+	6136.82i	−0.0162025	+	0.00380855i
$305$	−372588.			−0.229340
$306$	1.01437e6	−	765966.i	0.619289	−	0.467634i
$307$	−584640.	+	584640.i	−0.354032	+	0.354032i	−0.861607	−	0.507575i	$-0.830542\pi$
$307$	−584640.	+	584640.i	−0.354032	+	0.354032i	0.507575	+	0.861607i	$0.330542\pi$
$308$	−467061.	−	838665.i	−0.280542	−	0.503746i
$309$	−1.64980e6	−	1.64980e6i	−0.982960	−	0.982960i
$310$	81112.3	−	581337.i	0.0479383	−	0.343576i
$311$		−	319493.i		−	0.187310i	−0.995605	−	0.0936549i	$-0.970145\pi$
$311$		−	319493.i		−	0.187310i	0.995605	−	0.0936549i	$-0.0298550\pi$
$312$	140087.	+	361711.i	0.0814725	+	0.210366i
$313$			1.22193e6i			0.704992i	0.935813	+	0.352496i	$0.114667\pi$
$313$			1.22193e6i			0.704992i	−0.935813	+	0.352496i	$0.885333\pi$
$314$	929301.	+	129663.i	0.531903	+	0.0742150i
$315$	196190.	+	196190.i	0.111404	+	0.111404i
$316$	−258805.	+	909379.i	−0.145799	+	0.512304i
$317$	428268.	−	428268.i	0.239368	−	0.239368i	−0.577220	−	0.816589i	$-0.695863\pi$
$317$	428268.	−	428268.i	0.239368	−	0.239368i	0.816589	+	0.577220i	$0.195863\pi$
$318$	−1.50752e6	−	1.99642e6i	−0.835980	−	1.10709i
$319$	−1.36060e6			−0.748605
$320$	818318.	+	37993.8i	0.446732	+	0.0207414i
$321$	1.84798e6			1.00100
$322$	672709.	+	890871.i	0.361566	+	0.478823i
$323$	−33905.1	+	33905.1i	−0.0180825	+	0.0180825i
$324$	−646516.	+	2.27170e6i	−0.342150	+	1.20223i
$325$	49518.5	+	49518.5i	0.0260051	+	0.0260051i
$326$	583949.	+	81476.9i	0.304320	+	0.0424610i
$327$			700415.i			0.362231i
$328$	−1.28599e6	−	3.32049e6i	−0.660014	−	1.70419i
$329$		−	713508.i		−	0.363420i
$330$	−123988.	+	888626.i	−0.0626749	+	0.449194i
$331$	−1.41060e6	−	1.41060e6i	−0.707676	−	0.707676i	0.258370	−	0.966046i	$-0.416815\pi$
$331$	−1.41060e6	−	1.41060e6i	−0.707676	−	0.707676i	−0.966046	+	0.258370i	$0.916815\pi$
$332$	99188.3	+	178104.i	0.0493873	+	0.0886808i
$333$	−1.10392e6	+	1.10392e6i	−0.545540	+	0.545540i
$334$	−3.02823e6	+	2.28666e6i	−1.48533	+	1.12159i
$335$	328839.			0.160093
$336$	405203.	+	1.72383e6i	0.195805	+	0.833002i
$337$	−1.91082e6			−0.916528			−0.458264	−	0.888816i	$-0.651529\pi$
$337$	−1.91082e6			−0.916528			−0.458264	+	0.888816i	$0.651529\pi$
$338$	1.61948e6	−	1.22289e6i	0.771053	−	0.582232i
$339$	1.37560e6	−	1.37560e6i	0.650119	−	0.650119i
$340$	1.27958e6	−	712610.i	0.600301	−	0.334314i
$341$	973628.	+	973628.i	0.453427	+	0.453427i
$342$	−2512.77	+	18009.2i	−0.00116168	+	0.00832585i
$343$			2.30017e6i			1.05566i
$344$	−1.44612e6	−	638695.i	−0.658884	−	0.291003i
$345$		−	1.04340e6i		−	0.471956i
$346$	−3.13464e6	−	437368.i	−1.40766	−	0.196407i
$347$	1.47780e6	+	1.47780e6i	0.658859	+	0.658859i	0.955110	−	0.296251i	$-0.0957365\pi$
$347$	1.47780e6	+	1.47780e6i	0.658859	+	0.658859i	−0.296251	+	0.955110i	$0.595736\pi$
$348$	2.41402e6	+	687020.i	1.06855	+	0.304103i
$349$	1.33928e6	−	1.33928e6i	0.588584	−	0.588584i	−0.348663	−	0.937248i	$-0.613364\pi$
$349$	1.33928e6	−	1.33928e6i	0.588584	−	0.588584i	0.937248	+	0.348663i	$0.113364\pi$
$350$	192655.	+	255134.i	0.0840641	+	0.111326i
$351$	−257709.			−0.111651
$352$	−1.22791e6	+	1.47822e6i	−0.528213	+	0.635891i
$353$	−1.14152e6			−0.487582			−0.243791	−	0.969828i	$-0.578391\pi$
$353$	−1.14152e6			−0.487582			−0.243791	+	0.969828i	$0.578391\pi$
$354$	520378.	+	689139.i	0.220704	+	0.292280i
$355$	−531696.	+	531696.i	−0.223920	+	0.223920i
$356$	−1.43723e6	−	409027.i	−0.601035	−	0.171052i
$357$	2.23869e6	+	2.23869e6i	0.929659	+	0.929659i
$358$	−1.03056e6	−	143792.i	−0.424978	−	0.0592961i
$359$			3.13917e6i			1.28552i	0.766067	+	0.642760i	$0.222211\pi$
$359$			3.13917e6i			1.28552i	−0.766067	+	0.642760i	$0.777789\pi$
$360$	224399.	−	508080.i	0.0912566	−	0.206622i
$361$			2.47541e6i			0.999723i
$362$	−72506.3	+	519656.i	−0.0290806	+	0.208423i
$363$	689584.	+	689584.i	0.274676	+	0.274676i
$364$	−283258.	+	157749.i	−0.112054	+	0.0624043i
$365$	−1.59035e6	+	1.59035e6i	−0.624830	+	0.624830i
$366$	−1.28668e6	+	971586.i	−0.502072	+	0.379122i
$367$	2.04587e6			0.792891			0.396446	−	0.918058i	$-0.370244\pi$
$367$	2.04587e6			0.792891			0.396446	+	0.918058i	$0.370244\pi$
$368$	1.17669e6	−	1.89986e6i	0.452940	−	0.731310i
$369$	−2.41428e6			−0.923041
$370$	−1.43558e6	+	1.08403e6i	−0.545159	+	0.411657i
$371$	1.47858e6	−	1.47858e6i	0.557714	−	0.557714i
$372$	−1.23582e6	−	2.21907e6i	−0.463020	−	0.831407i
$373$	1.01425e6	+	1.01425e6i	0.377462	+	0.377462i	0.870186	−	0.492723i	$-0.163999\pi$
$373$	1.01425e6	+	1.01425e6i	0.377462	+	0.377462i	−0.492723	+	0.870186i	$0.663999\pi$
$374$	−474780.	+	3.40278e6i	−0.175515	+	1.25792i
$375$		−	298815.i		−	0.109730i
$376$	−1.33194e6	+	515848.i	−0.485866	+	0.188171i
$377$			459540.i			0.166521i
$378$	−1.16521e6	−	162579.i	−0.419446	−	0.0585242i
$379$	68954.0	+	68954.0i	0.0246582	+	0.0246582i	0.719328	−	0.694670i	$-0.244450\pi$
$379$	68954.0	+	68954.0i	0.0246582	+	0.0246582i	−0.694670	+	0.719328i	$0.744450\pi$
$380$	−5735.20	+	20152.1i	−0.00203746	+	0.00715916i
$381$	−3.76398e6	+	3.76398e6i	−1.32842	+	1.32842i
$382$	1.79358e6	+	2.37525e6i	0.628873	+	0.832819i
$383$	−4.26580e6			−1.48595			−0.742974	−	0.669320i	$-0.766586\pi$
$383$	−4.26580e6			−1.48595			−0.742974	+	0.669320i	$0.766586\pi$
$384$	2.92501e6	−	2.00270e6i	1.01228	−	0.693087i
$385$	−749961.			−0.257862
$386$	−2.19404e6	−	2.90558e6i	−0.749508	−	0.992576i
$387$	−757920.	+	757920.i	−0.257245	+	0.257245i
$388$	823975.	−	2.89525e6i	0.277866	−	0.976354i
$389$	−384558.	−	384558.i	−0.128851	−	0.128851i	0.639740	−	0.768591i	$-0.279042\pi$
$389$	−384558.	−	384558.i	−0.128851	−	0.128851i	−0.768591	+	0.639740i	$0.779042\pi$
$390$	300132.	+	41876.7i	0.0999197	+	0.0139415i
$391$		−	3.99543e6i		−	1.32166i
$392$	1.45680e6	−	564204.i	0.478835	−	0.185448i
$393$		−	7.32128e6i		−	2.39114i
$394$	347051.	−	2.48733e6i	0.112630	−	0.807222i
$395$	522314.	+	522314.i	0.168438	+	0.168438i
$396$	633937.	+	1.13831e6i	0.203146	+	0.364773i
$397$	3.49619e6	−	3.49619e6i	1.11332	−	1.11332i	0.120619	−	0.992699i	$-0.461512\pi$
$397$	3.49619e6	−	3.49619e6i	1.11332	−	1.11332i	0.992699	−	0.120619i	$-0.0384880\pi$
$398$	−2.17876e6	+	1.64521e6i	−0.689447	+	0.520611i
$399$	−45291.4			−0.0142424
$400$	336988.	−	544095.i	0.105309	−	0.170030i
$401$	−2.86231e6			−0.888905			−0.444452	−	0.895802i	$-0.646602\pi$
$401$	−2.86231e6			−0.888905			−0.444452	+	0.895802i	$0.646602\pi$
$402$	1.13560e6	−	857505.i	0.350477	−	0.264650i
$403$	328842.	−	328842.i	0.100861	−	0.100861i
$404$	2.50068e6	−	1.39265e6i	0.762262	−	0.424512i
$405$	1.30478e6	+	1.30478e6i	0.395277	+	0.395277i
$406$	−289907.	+	2.07778e6i	−0.0872858	+	0.625582i
$407$		−	4.21986e6i		−	1.26274i
$408$	2.56057e6	−	5.79760e6i	0.761529	−	1.72424i
$409$			3.47468e6i			1.02709i	0.858064	+	0.513543i	$0.171667\pi$
$409$			3.47468e6i			1.02709i	−0.858064	+	0.513543i	$0.828333\pi$
$410$	−2.75520e6	−	384425.i	−0.809456	−	0.112941i
$411$	−1.44707e6	−	1.44707e6i	−0.422556	−	0.422556i
$412$	−3.75494e6	−	1.06864e6i	−1.08983	−	0.310161i
$413$	−510390.	+	510390.i	−0.147240	+	0.147240i
$414$	−913060.	−	1.20917e6i	−0.261818	−	0.346726i
$415$	159267.			0.0453947
$416$	499267.	+	414724.i	0.141449	+	0.117497i
$417$	−3.06297e6			−0.862586
$418$	−29618.4	−	39223.8i	−0.00829127	−	0.0109802i
$419$	−739845.	+	739845.i	−0.205876	+	0.205876i	−0.802512	−	0.596636i	$-0.796504\pi$
$419$	−739845.	+	739845.i	−0.205876	+	0.205876i	0.596636	+	0.802512i	$0.296504\pi$
$420$	1.33061e6	+	378685.i	0.368068	+	0.104750i
$421$	2.48700e6	+	2.48700e6i	0.683866	+	0.683866i	0.960869	−	0.277003i	$-0.0893412\pi$
$421$	2.48700e6	+	2.48700e6i	0.683866	+	0.683866i	−0.277003	+	0.960869i	$0.589341\pi$
$422$	5.93396e6	+	827950.i	1.62205	+	0.226320i
$423$			968437.i			0.263160i
$424$	−3.82913e6	−	1.69118e6i	−1.03439	−	0.456850i
$425$		−	1.14424e6i		−	0.307287i
$426$	−449643.	+	3.22262e6i	−0.120045	+	0.860369i
$427$	−952937.	−	952937.i	−0.252927	−	0.252927i
$428$	2.70150e6	−	1.50449e6i	0.712844	−	0.396991i
$429$	−502664.	+	502664.i	−0.131867	+	0.131867i
$430$	−985630.	+	744263.i	−0.257065	+	0.194113i
$431$	−5.37041e6			−1.39256			−0.696280	−	0.717770i	$-0.745163\pi$
$431$	−5.37041e6			−1.39256			−0.696280	+	0.717770i	$0.745163\pi$
$432$	538924.	+	2.29271e6i	0.138937	+	0.591071i
$433$	−5.77589e6			−1.48047			−0.740235	−	0.672348i	$-0.765286\pi$
$433$	−5.77589e6			−1.48047			−0.740235	+	0.672348i	$0.765286\pi$
$434$	1.69429e6	−	1.27938e6i	0.431781	−	0.326044i
$435$	1.38653e6	−	1.38653e6i	0.351322	−	0.351322i
$436$	570228.	+	1.02391e6i	0.143659	+	0.257957i
$437$	40416.1	+	40416.1i	0.0101240	+	0.0101240i
$438$	−1.34493e6	+	9.63917e6i	−0.334976	+	2.40079i
$439$		−	4.92868e6i		−	1.22059i	−0.792175	−	0.610294i	$-0.791051\pi$
$439$		−	4.92868e6i		−	1.22059i	0.792175	−	0.610294i	$-0.208949\pi$
$440$	542203.	+	1.39999e6i	0.133515	+	0.344742i
$441$		−	1.05922e6i		−	0.259352i
$442$	1.14928e6	+	160356.i	0.279815	+	0.0390419i
$443$	4.21588e6	+	4.21588e6i	1.02065	+	1.02065i	0.999782	+	0.0208723i	$0.00664433\pi$
$443$	4.21588e6	+	4.21588e6i	1.02065	+	1.02065i	0.0208723	+	0.999782i	$0.493356\pi$
$444$	−2.13078e6	+	7.48704e6i	−0.512956	+	1.80241i
$445$	−825490.	+	825490.i	−0.197611	+	0.197611i
$446$	−574974.	−	761441.i	−0.136871	−	0.181259i
$447$	2.24803e6			0.532150
$448$	1.99577e6	+	2.19012e6i	0.469803	+	0.515552i
$449$	−157968.			−0.0369789			−0.0184894	−	0.999829i	$-0.505886\pi$
$449$	−157968.			−0.0369789			−0.0184894	+	0.999829i	$0.505886\pi$
$450$	−261489.	−	346290.i	−0.0608726	−	0.0806138i
$451$	4.61443e6	−	4.61443e6i	1.06826	−	1.06826i
$452$	891026.	−	3.13086e6i	0.205137	−	0.720804i
$453$	−4.56693e6	−	4.56693e6i	−1.04563	−	1.04563i
$454$	8.40672e6	+	1.17297e6i	1.91420	+	0.267083i
$455$			253298.i			0.0573593i
$456$	32744.5	+	84547.9i	0.00737439	+	0.0190410i
$457$		−	7.57340e6i		−	1.69629i	−0.529763	−	0.848146i	$-0.677719\pi$
$457$		−	7.57340e6i		−	1.69629i	0.529763	−	0.848146i	$-0.322281\pi$
$458$	−1.15170e6	+	8.25429e6i	−0.256552	+	1.83872i
$459$	2.97748e6	+	2.97748e6i	0.659656	+	0.659656i
$460$	−849458.	−	1.52530e6i	−0.187175	−	0.336095i
$461$	−247109.	+	247109.i	−0.0541547	+	0.0541547i	−0.733666	−	0.679511i	$-0.762192\pi$
$461$	−247109.	+	247109.i	−0.0541547	+	0.0541547i	0.679511	+	0.733666i	$0.262192\pi$
$462$	−2.58988e6	+	1.95565e6i	−0.564513	+	0.426272i
$463$	7.86676e6			1.70547			0.852734	−	0.522346i	$-0.174943\pi$
$463$	7.86676e6			1.70547			0.852734	+	0.522346i	$0.174943\pi$
$464$	4.08830e6	−	960996.i	0.881552	−	0.207218i
$465$	−1.98437e6			−0.425588
$466$	3.91183e6	−	2.95387e6i	0.834478	−	0.630126i
$467$	−4.69311e6	+	4.69311e6i	−0.995793	+	0.995793i	−0.999991	−	0.00419863i	$-0.998664\pi$
$467$	−4.69311e6	+	4.69311e6i	−0.995793	+	0.995793i	0.00419863	+	0.999991i	$0.498664\pi$
$468$	384463.	−	214112.i	0.0811409	−	0.0451882i
$469$	841045.	+	841045.i	0.176558	+	0.176558i
$470$	−154204.	+	1.10519e6i	−0.0321997	+	0.230777i
$471$		−	3.17213e6i		−	0.658867i
$472$	1.32177e6	+	583773.i	0.273087	+	0.120612i
$473$		−	2.89724e6i		−	0.595431i
$474$	3.16576e6	+	441709.i	0.647190	+	0.0903006i
$475$	11574.7	+	11574.7i	0.00235382	+	0.00235382i
$476$	5.09525e6	+	1.45008e6i	1.03074	+	0.293343i
$477$	−2.00687e6	+	2.00687e6i	−0.403852	+	0.403852i
$478$	5.31832e6	+	7.04307e6i	1.06464	+	1.40991i
$479$	394910.			0.0786429			0.0393215	−	0.999227i	$-0.487480\pi$
$479$	394910.			0.0786429			0.0393215	+	0.999227i	$0.487480\pi$
$480$	−255085.	−	2.75770e6i	−0.0505337	−	0.546316i
$481$	−1.42525e6			−0.280886
$482$	−4.30407e6	−	5.69990e6i	−0.843843	−	1.11750i
$483$	2.66860e6	−	2.66860e6i	0.520495	−	0.520495i
$484$	1.56949e6	+	446669.i	0.304540	+	0.0866707i
$485$	−1.66293e6	−	1.66293e6i	−0.321010	−	0.321010i
$486$	4.77704e6	+	666527.i	0.917419	+	0.128005i
$487$			2.60339e6i			0.497412i	0.968579	+	0.248706i	$0.0800053\pi$
$487$			2.60339e6i			0.497412i	−0.968579	+	0.248706i	$0.919995\pi$
$488$	−1.08995e6	+	2.46785e6i	−0.207184	+	0.469104i
$489$		−	1.99328e6i		−	0.376962i
$490$	168660.	−	1.20879e6i	0.0317337	−	0.227437i
$491$	1.65420e6	+	1.65420e6i	0.309659	+	0.309659i	0.844777	−	0.535118i	$-0.179733\pi$
$491$	1.65420e6	+	1.65420e6i	0.309659	+	0.309659i	−0.535118	+	0.844777i	$0.679733\pi$
$492$	−1.05171e7	+	5.85709e6i	−1.95877	+	1.09086i
$493$	5.30937e6	−	5.30937e6i	0.983842	−	0.983842i
$494$	−13247.8	+	10003.6i	−0.00244245	+	0.00184433i
$495$	1.01791e6			0.186723
$496$	−3.61322e6	−	2.23786e6i	−0.659462	−	0.408441i
$497$	−2.71975e6			−0.493898
$498$	550003.	−	415315.i	0.0993784	−	0.0750420i
$499$	5.46828e6	−	5.46828e6i	0.983104	−	0.983104i	−0.0167555	−	0.999860i	$-0.505334\pi$
$499$	5.46828e6	−	5.46828e6i	0.983104	−	0.983104i	0.999860	+	0.0167555i	$0.00533370\pi$
$500$	−243274.	−	436827.i	−0.0435181	−	0.0781420i
$501$	9.07106e6	+	9.07106e6i	1.61460	+	1.61460i
$502$	473948.	−	3.39681e6i	0.0839405	−	0.601606i
$503$			9.27467e6i			1.63448i	0.576300	+	0.817238i	$0.304496\pi$
$503$			9.27467e6i			1.63448i	−0.576300	+	0.817238i	$0.695504\pi$
$504$	1.87340e6	−	725547.i	0.328514	−	0.127230i
$505$		−	2.23619e6i		−	0.390193i
$506$	4.05624e6	+	565956.i	0.704283	+	0.0982667i
$507$	−4.85115e6	−	4.85115e6i	−0.838157	−	0.838157i
$508$	−2.43807e6	+	8.56680e6i	−0.419167	+	1.47285i
$509$	−2.66021e6	+	2.66021e6i	−0.455115	+	0.455115i	−0.897048	−	0.441933i	$-0.854293\pi$
$509$	−2.66021e6	+	2.66021e6i	−0.455115	+	0.455115i	0.441933	+	0.897048i	$0.354293\pi$
$510$	−2.98380e6	−	3.95145e6i	−0.507977	−	0.672715i
$511$	−8.13503e6			−1.37818
$512$	2.64552e6	−	5.30901e6i	0.446001	−	0.895032i
$513$	−60238.0			−0.0101059
$514$	−4.77646e6	−	6.32549e6i	−0.797441	−	1.05605i
$515$	−2.15670e6	+	2.15670e6i	−0.358321	+	0.358321i
$516$	−1.46293e6	+	5.14040e6i	−0.241880	+	0.849909i
$517$	−1.85098e6	−	1.85098e6i	−0.304562	−	0.304562i
$518$	−6.44419e6	−	899140.i	−1.05522	−	0.147232i
$519$			1.07000e7i			1.74367i
$520$	472846.	−	183128.i	0.0766852	−	0.0296993i
$521$		−	7.63674e6i		−	1.23258i	−0.787521	−	0.616288i	$-0.788636\pi$
$521$		−	7.63674e6i		−	1.23258i	0.787521	−	0.616288i	$-0.211364\pi$
$522$	393488.	−	2.82015e6i	0.0632055	−	0.452997i
$523$	1.26901e6	+	1.26901e6i	0.202866	+	0.202866i	0.801227	−	0.598361i	$-0.204181\pi$
$523$	1.26901e6	+	1.26901e6i	0.202866	+	0.202866i	−0.598361	+	0.801227i	$0.704181\pi$
$524$	−5.96046e6	−	1.07027e7i	−0.948313	−	1.70281i
$525$	764254.	−	764254.i	0.121015	−	0.121015i
$526$	8.83929e6	−	6.67467e6i	1.39301	−	1.05188i
$527$	−7.59864e6			−1.19182
$528$	5.52313e6	+	3.42078e6i	0.862186	+	0.533999i
$529$	1.67364e6			0.260030
$530$	−2.60981e6	+	1.97070e6i	−0.403570	+	0.304741i
$531$	692746.	−	692746.i	0.106620	−	0.106620i
$532$	−66209.9	+	36873.0i	−0.0101425	+	0.00564845i
$533$	−1.55852e6	−	1.55852e6i	−0.237626	−	0.237626i
$534$	−698098.	+	5.00331e6i	−0.105941	+	0.759283i
$535$		−	2.41577e6i		−	0.364897i
$536$	961970.	−	2.17808e6i	0.144627	−	0.327462i
$537$			3.51778e6i			0.526421i
$538$	−6.55732e6	−	914926.i	−0.976722	−	0.136279i
$539$	2.02450e6	+	2.02450e6i	0.300155	+	0.300155i
$540$	1.76972e6	+	503655.i	0.261169	+	0.0743274i
$541$	−6.84477e6	+	6.84477e6i	−1.00546	+	1.00546i	−0.00547699	+	0.999985i	$0.501743\pi$
$541$	−6.84477e6	+	6.84477e6i	−1.00546	+	1.00546i	−0.999985	+	0.00547699i	$0.998257\pi$
$542$	2.33023e6	+	3.08593e6i	0.340722	+	0.451220i
$543$	1.77382e6			0.258173
$544$	−976784.	−	1.05599e7i	−0.141515	−	1.52990i
$545$	915616.			0.132045
$546$	660519.	+	874728.i	0.0948208	+	0.125572i
$547$	5.62052e6	−	5.62052e6i	0.803171	−	0.803171i	−0.180419	−	0.983590i	$-0.557745\pi$
$547$	5.62052e6	−	5.62052e6i	0.803171	−	0.803171i	0.983590	+	0.180419i	$0.0577454\pi$
$548$	−3.29352e6	−	937318.i	−0.468499	−	0.133332i
$549$	1.29341e6	+	1.29341e6i	0.183149	+	0.183149i
$550$	1.16165e6	+	162082.i	0.163746	+	0.0228470i
$551$			107415.i			0.0150725i
$552$	−6.91096e6	−	3.05230e6i	−0.965363	−	0.426363i
$553$			2.67176e6i			0.371522i
$554$	1.11636e6	−	8.00100e6i	0.154536	−	1.10757i
$555$	4.30028e6	+	4.30028e6i	0.592604	+	0.592604i
$556$	−4.47765e6	+	2.49365e6i	−0.614275	+	0.342096i
$557$	−3.01132e6	+	3.01132e6i	−0.411262	+	0.411262i	−0.882178	−	0.470916i	$-0.843924\pi$
$557$	−3.01132e6	+	3.01132e6i	−0.411262	+	0.411262i	0.470916	+	0.882178i	$0.343924\pi$
$558$	−2.29964e6	+	1.73649e6i	−0.312662	+	0.236095i
$559$	−978539.			−0.132449
$560$	2.25347e6	−	529701.i	0.303656	−	0.0713774i
$561$	1.16152e7			1.55819
$562$	6.07218e6	−	4.58519e6i	0.810968	−	0.612373i
$563$	6.57595e6	−	6.57595e6i	0.874354	−	0.874354i	−0.118589	−	0.992943i	$-0.537837\pi$
$563$	6.57595e6	−	6.57595e6i	0.874354	−	0.874354i	0.992943	+	0.118589i	$0.0378372\pi$
$564$	2.34945e6	+	4.21872e6i	0.311006	+	0.558448i
$565$	−1.79825e6	−	1.79825e6i	−0.236989	−	0.236989i
$566$	1.43055e6	−	1.02528e7i	0.187699	−	1.34525i
$567$			6.67427e6i			0.871859i
$568$	1.96631e6	+	5.07710e6i	0.255729	+	0.660305i
$569$			1.23305e7i			1.59661i	0.602251	+	0.798307i	$0.294271\pi$
$569$			1.23305e7i			1.59661i	−0.602251	+	0.798307i	$0.705729\pi$
$570$	70154.2	+	9788.43i	0.00904412	+	0.00126190i
$571$	886054.	+	886054.i	0.113729	+	0.113729i	0.761681	−	0.647952i	$-0.224374\pi$
$571$	886054.	+	886054.i	0.113729	+	0.113729i	−0.647952	+	0.761681i	$0.724374\pi$
$572$	−325594.	+	1.14406e6i	−0.0416089	+	0.146204i
$573$	7.11506e6	−	7.11506e6i	0.905298	−	0.905298i
$574$	−6.06352e6	−	8.02995e6i	−0.768149	−	1.01726i
$575$	−1.36398e6			−0.172043
$576$	−2.70884e6	−	2.97262e6i	−0.340194	−	0.373322i
$577$	2.29833e6			0.287390			0.143695	−	0.989622i	$-0.454102\pi$
$577$	2.29833e6			0.287390			0.143695	+	0.989622i	$0.454102\pi$
$578$	−6.58561e6	−	8.72135e6i	−0.819929	−	1.08584i
$579$	−8.70365e6	+	8.70365e6i	−1.07896	+	1.07896i
$580$	898104.	−	3.15573e6i	0.110855	−	0.389520i
$581$	407343.	+	407343.i	0.0500634	+	0.0500634i
$582$	−1.00790e7	−	1.40630e6i	−1.23342	−	0.172096i
$583$		−	7.67149e6i		−	0.934777i
$584$	5.88142e6	+	1.51861e7i	0.713592	+	1.84253i
$585$		−	343799.i		−	0.0415351i
$586$	−1.81454e6	+	1.30049e7i	−0.218284	+	1.56445i
$587$	−1.02684e7	−	1.02684e7i	−1.23000	−	1.23000i	−0.963962	−	0.266039i	$-0.914285\pi$
$587$	−1.02684e7	−	1.02684e7i	−1.23000	−	1.23000i	−0.266039	−	0.963962i	$-0.585715\pi$
$588$	−2.56969e6	−	4.61419e6i	−0.306505	−	0.550367i
$589$	76864.8	−	76864.8i	0.00912934	−	0.00912934i
$590$	900875.	−	680263.i	0.106545	−	0.0804539i
$591$	−8.49039e6			−0.999906
$592$	2.98051e6	+	1.26798e7i	0.349531	+	1.48699i
$593$	−1.65412e6			−0.193166			−0.0965829	−	0.995325i	$-0.530791\pi$
$593$	−1.65412e6			−0.193166			−0.0965829	+	0.995325i	$0.530791\pi$
$594$	−3.44456e6	+	2.60104e6i	−0.400560	+	0.302469i
$595$	2.92652e6	−	2.92652e6i	0.338891	−	0.338891i
$596$	3.28632e6	−	1.83019e6i	0.378961	−	0.211047i
$597$	6.52647e6	+	6.52647e6i	0.749449	+	0.749449i
$598$	191151.	−	1.36999e6i	0.0218587	−	0.156662i
$599$			1.20496e7i			1.37216i	0.727526	+	0.686081i	$0.240670\pi$
$599$			1.20496e7i			1.37216i	−0.727526	+	0.686081i	$0.759330\pi$
$600$	−1.97921e6	−	874138.i	−0.224447	−	0.0991293i
$601$			5.43468e6i			0.613745i	0.951751	+	0.306872i	$0.0992825\pi$
$601$			5.43468e6i			0.613745i	−0.951751	+	0.306872i	$0.900718\pi$
$602$	−4.42440e6	−	617325.i	−0.497580	−	0.0694261i
$603$	−1.14154e6	−	1.14154e6i	−0.127849	−	0.127849i
$604$	−1.03943e7	−	2.95817e6i	−1.15932	−	0.329937i
$605$	901457.	−	901457.i	0.100128	−	0.100128i
$606$	−5.83123e6	−	7.72233e6i	−0.645029	−	0.854214i
$607$	−7.41405e6			−0.816740			−0.408370	−	0.912817i	$-0.633903\pi$
$607$	−7.41405e6			−0.816740			−0.408370	+	0.912817i	$0.633903\pi$
$608$	116701.	+	96939.3i	0.0128031	+	0.0106351i
$609$	7.09241e6			0.774909
$610$	1.27010e6	+	1.68200e6i	0.138202	+	0.183022i
$611$	−625167.	+	625167.i	−0.0677474	+	0.0677474i
$612$	−6.91572e6	−	1.96818e6i	−0.746378	−	0.212416i
$613$	−6.24642e6	−	6.24642e6i	−0.671398	−	0.671398i	0.286640	−	0.958038i	$-0.407462\pi$
$613$	−6.24642e6	−	6.24642e6i	−0.671398	−	0.671398i	−0.958038	+	0.286640i	$0.907462\pi$
$614$	4.63225e6	+	646325.i	0.495873	+	0.0691879i
$615$			9.40474e6i			1.00267i
$616$	−2.19390e6	+	4.96739e6i	−0.232951	+	0.527444i
$617$			1.07410e7i			1.13588i	0.823071	+	0.567938i	$0.192259\pi$
$617$			1.07410e7i			1.13588i	−0.823071	+	0.567938i	$0.807741\pi$
$618$	−1.82387e6	+	1.30718e7i	−0.192098	+	1.37678i
$619$	−4.73215e6	−	4.73215e6i	−0.496400	−	0.496400i	0.413916	−	0.910315i	$-0.364161\pi$
$619$	−4.73215e6	−	4.73215e6i	−0.496400	−	0.496400i	−0.910315	+	0.413916i	$0.864161\pi$
$620$	−2.90087e6	+	1.61553e6i	−0.303075	+	0.168786i
$621$	3.54927e6	−	3.54927e6i	0.369326	−	0.369326i
$622$	−1.44231e6	+	1.08911e6i	−0.149480	+	0.112874i
$623$	−4.22257e6			−0.435870
$624$	1.15536e6	−	1.86543e6i	0.118784	−	0.191786i
$625$	−390625.			−0.0400000
$626$	5.51624e6	−	4.16539e6i	0.562610	−	0.424834i
$627$	−117495.	+	117495.i	−0.0119358	+	0.0119358i
$628$	−2.58252e6	−	4.63722e6i	−0.261303	−	0.469201i
$629$	1.64669e7	+	1.64669e7i	1.65953	+	1.65953i
$630$	216890.	−	1.55447e6i	0.0217715	−	0.156038i
$631$		−	3.91185e6i		−	0.391119i	−0.980692	−	0.195559i	$-0.937348\pi$
$631$		−	3.91185e6i		−	0.391119i	0.980692	−	0.195559i	$-0.0626523\pi$
$632$	4.98751e6	−	1.93161e6i	0.496697	−	0.192365i
$633$		−	2.02553e7i		−	2.00923i
$634$	−3.39327e6	−	473454.i	−0.335270	−	0.0467794i
$635$	4.92045e6	+	4.92045e6i	0.484251	+	0.484251i
$636$	−3.87364e6	+	1.36110e7i	−0.379731	+	1.33429i
$637$	683771.	−	683771.i	0.0667671	−	0.0667671i
$638$	4.63810e6	+	6.14225e6i	0.451116	+	0.597415i
$639$	3.69148e6			0.357642
$640$	−2.61802e6	−	3.82372e6i	−0.252652	−	0.369008i
$641$	1.06765e7			1.02632			0.513161	−	0.858292i	$-0.328474\pi$
$641$	1.06765e7			1.02632			0.513161	+	0.858292i	$0.328474\pi$
$642$	−6.29952e6	−	8.34248e6i	−0.603212	−	0.798836i
$643$	1.40900e6	−	1.40900e6i	0.134395	−	0.134395i	−0.636709	−	0.771104i	$-0.719705\pi$
$643$	1.40900e6	−	1.40900e6i	0.134395	−	0.134395i	0.771104	+	0.636709i	$0.219705\pi$
$644$	1.72855e6	−	6.07373e6i	0.164236	−	0.577086i
$645$	2.95245e6	+	2.95245e6i	0.279437	+	0.279437i
$646$	268638.	+	37482.4i	0.0253272	+	0.00353383i
$647$		−	7.88668e6i		−	0.740685i	−0.928895	−	0.370342i	$-0.879240\pi$
$647$		−	7.88668e6i		−	0.740685i	0.928895	−	0.370342i	$-0.120760\pi$
$648$	1.24592e7	−	4.82533e6i	1.16561	−	0.451429i
$649$			2.64811e6i			0.246788i
$650$	54743.2	−	392347.i	0.00508214	−	0.0364240i
$651$	−5.07524e6	−	5.07524e6i	−0.469358	−	0.469358i
$652$	−1.62279e6	−	2.91391e6i	−0.149501	−	0.268446i
$653$	−5.53904e6	+	5.53904e6i	−0.508337	+	0.508337i	−0.914016	−	0.405679i	$-0.867035\pi$
$653$	−5.53904e6	+	5.53904e6i	−0.508337	+	0.508337i	0.405679	+	0.914016i	$0.367035\pi$
$654$	3.16194e6	−	2.38762e6i	0.289074	−	0.218284i
$655$	−9.57072e6			−0.871649
$656$	−1.06062e7	+	1.71246e7i	−0.962274	+	1.55367i
$657$	1.10416e7			0.997972
$658$	−3.22105e6	+	2.43226e6i	−0.290023	+	0.219000i
$659$	−5.19721e6	+	5.19721e6i	−0.466183	+	0.466183i	−0.900676	−	0.434492i	$-0.856928\pi$
$659$	−5.19721e6	+	5.19721e6i	−0.466183	+	0.466183i	0.434492	+	0.900676i	$0.356928\pi$
$660$	4.43425e6	−	2.46948e6i	0.396242	−	0.220671i
$661$	4.10977e6	+	4.10977e6i	0.365859	+	0.365859i	0.865964	−	0.500106i	$-0.166705\pi$
$661$	4.10977e6	+	4.10977e6i	0.365859	+	0.365859i	−0.500106	+	0.865964i	$0.666705\pi$
$662$	−1.55943e6	+	1.11765e7i	−0.138300	+	0.991203i
$663$		−	3.92303e6i		−	0.346607i
$664$	465911.	−	1.05491e6i	0.0410093	−	0.0928527i
$665$			59207.0i			0.00519181i
$666$	8.74663e6	+	1.22039e6i	0.764108	+	0.106614i
$667$	−6.32897e6	−	6.32897e6i	−0.550831	−	0.550831i
$668$	2.06457e7	+	5.87566e6i	1.79014	+	0.509466i
$669$	−2.28090e6	+	2.28090e6i	−0.197033	+	0.197033i
$670$	−1.12097e6	−	1.48451e6i	−0.0964733	−	0.127760i
$671$	−4.94422e6			−0.423927
$672$	6.40073e6	−	7.70555e6i	0.546772	−	0.658234i
$673$	5.47059e6			0.465582			0.232791	−	0.972527i	$-0.425214\pi$
$673$	5.47059e6			0.465582			0.232791	+	0.972527i	$0.425214\pi$
$674$	6.51375e6	+	8.62618e6i	0.552308	+	0.731423i
$675$	1.01647e6	−	1.01647e6i	0.0858683	−	0.0858683i
$676$	−1.10412e7	−	3.14227e6i	−0.929286	−	0.264470i
$677$	−1.34149e7	−	1.34149e7i	−1.12490	−	1.12490i	−0.990994	−	0.133907i	$-0.957248\pi$
$677$	−1.34149e7	−	1.34149e7i	−1.12490	−	1.12490i	−0.133907	−	0.990994i	$-0.542752\pi$
$678$	−1.08992e7	−	1.52074e6i	−0.910586	−	0.127052i
$679$		−	8.50626e6i		−	0.708051i
$680$	−7.57890e6	−	3.34730e6i	−0.628541	−	0.277602i
$681$		−	2.86959e7i		−	2.37112i
$682$	1.07635e6	−	7.71429e6i	0.0886124	−	0.635090i
$683$	1.99794e6	+	1.99794e6i	0.163882	+	0.163882i	0.784284	−	0.620402i	$-0.213031\pi$
$683$	1.99794e6	+	1.99794e6i	0.163882	+	0.163882i	−0.620402	+	0.784284i	$0.713031\pi$
$684$	89865.9	−	50047.3i	0.00734438	−	0.00409016i
$685$	−1.89167e6	+	1.89167e6i	−0.154035	+	0.154035i
$686$	1.03839e7	−	7.84099e6i	0.842458	−	0.636151i
$687$	2.81756e7			2.27762
$688$	2.04633e6	+	8.70558e6i	0.164818	+	0.701175i
$689$	−2.59103e6			−0.207934
$690$	−4.71028e6	+	3.55680e6i	−0.376638	+	0.284405i
$691$	4.48729e6	−	4.48729e6i	0.357511	−	0.357511i	−0.505384	−	0.862895i	$-0.668649\pi$
$691$	4.48729e6	−	4.48729e6i	0.357511	−	0.357511i	0.862895	+	0.505384i	$0.168649\pi$
$692$	8.71114e6	+	1.56419e7i	0.691528	+	1.24172i
$693$	2.60343e6	+	2.60343e6i	0.205927	+	0.205927i
$694$	1.63372e6	−	1.17090e7i	0.128760	−	0.922828i
$695$			4.00406e6i			0.314440i
$696$	−5.12763e6	−	1.32398e7i	−0.401230	−	1.03599i
$697$			3.60132e7i			2.80788i
$698$	−1.06115e7	−	1.48059e6i	−0.824398	−	0.115026i
$699$	−1.17179e7	−	1.17179e7i	−0.907102	−	0.907102i
$700$	495035.	−	1.73944e6i	0.0381848	−	0.134172i
$701$	2.19585e6	−	2.19585e6i	0.168775	−	0.168775i	−0.617666	−	0.786441i	$-0.711922\pi$
$701$	2.19585e6	−	2.19585e6i	0.168775	−	0.168775i	0.786441	+	0.617666i	$0.211922\pi$
$702$	878497.	+	1.16340e6i	0.0672818	+	0.0891015i
$703$	−333145.			−0.0254240
$704$	1.08590e7	+	504175.i	0.825770	+	0.0383398i
$705$	3.77251e6			0.285863
$706$	3.89130e6	+	5.15327e6i	0.293821	+	0.389109i
$707$	5.71930e6	−	5.71930e6i	0.430323	−	0.430323i
$708$	1.33713e6	−	4.69837e6i	0.100252	−	0.352261i
$709$	3.64004e6	+	3.64004e6i	0.271951	+	0.271951i	0.829885	−	0.557934i	$-0.188406\pi$
$709$	3.64004e6	+	3.64004e6i	0.271951	+	0.271951i	−0.557934	+	0.829885i	$0.688406\pi$
$710$	4.21276e6	+	587795.i	0.313632	+	0.0437602i
$711$		−	3.62635e6i		−	0.269027i
$712$	3.05281e6	+	7.88250e6i	0.225683	+	0.582725i
$713$			9.05787e6i			0.667271i
$714$	2.47489e6	−	1.77377e7i	0.181682	−	1.30212i
$715$	657107.	+	657107.i	0.0480696	+	0.0480696i
$716$	2.86392e6	+	5.14252e6i	0.208775	+	0.374881i
$717$	2.10975e7	−	2.10975e7i	1.53262	−	1.53262i
$718$	1.41714e7	−	1.07010e7i	1.02589	−	0.774666i
$719$	1.01674e7			0.733480			0.366740	−	0.930324i	$-0.380474\pi$
$719$	1.01674e7			0.733480			0.366740	+	0.930324i	$0.380474\pi$
$720$	−3.05861e6	+	718957.i	−0.219884	+	0.0516859i
$721$	−1.10320e7			−0.790345
$722$	1.11750e7	−	8.43836e6i	0.797816	−	0.602442i
$723$	−1.70740e7	+	1.70740e7i	−1.21476	+	1.21476i
$724$	2.59309e6	−	1.44412e6i	0.183853	−	0.102390i
$725$	−1.81253e6	−	1.81253e6i	−0.128068	−	0.128068i
$726$	762342.	−	5.46375e6i	0.0536795	−	0.384724i
$727$		−	1.21518e7i		−	0.852719i	−0.904554	−	0.426359i	$-0.859796\pi$
$727$		−	1.21518e7i		−	0.852719i	0.904554	−	0.426359i	$-0.140204\pi$
$728$	1.67773e6	+	740987.i	0.117326	+	0.0518181i
$729$			1.62957e6i			0.113567i
$730$	1.26008e7	+	1.75815e6i	0.875165	+	0.122109i
$731$	1.13057e7	+	1.13057e7i	0.782536	+	0.782536i
$732$	8.77222e6	+	2.49653e6i	0.605106	+	0.172210i
$733$	−6.98495e6	+	6.98495e6i	−0.480179	+	0.480179i	−0.905189	−	0.425010i	$-0.860271\pi$
$733$	−6.98495e6	+	6.98495e6i	−0.480179	+	0.480179i	0.425010	+	0.905189i	$0.360271\pi$
$734$	−6.97412e6	−	9.23585e6i	−0.477803	−	0.632757i
$735$	−4.12616e6			−0.281726
$736$	−1.25879e7	+	1.16436e6i	−0.856559	+	0.0792308i
$737$	4.36368e6			0.295926
$738$	8.22995e6	+	1.08990e7i	0.556233	+	0.736621i
$739$	−1.29130e7	+	1.29130e7i	−0.869795	+	0.869795i	−0.992449	−	0.122654i	$-0.960859\pi$
$739$	−1.29130e7	+	1.29130e7i	−0.869795	+	0.869795i	0.122654	+	0.992449i	$0.460859\pi$
$740$	9.78742e6	+	2.78545e6i	0.657035	+	0.186989i
$741$	39683.7	+	39683.7i	0.00265502	+	0.00265502i
$742$	−1.17152e7	−	1.63459e6i	−0.781159	−	0.108993i
$743$			1.75591e6i			0.116689i	0.998297	+	0.0583445i	$0.0185822\pi$
$743$			1.75591e6i			0.116689i	−0.998297	+	0.0583445i	$0.981418\pi$
$744$	−5.80496e6	+	1.31435e7i	−0.384474	+	0.870520i
$745$		−	2.93873e6i		−	0.193986i
$746$	1.12127e6	−	8.03617e6i	0.0737669	−	0.528691i
$747$	−552882.	−	552882.i	−0.0362519	−	0.0362519i
$748$	1.69799e7	−	9.45628e6i	1.10964	−	0.617969i
$749$	6.17860e6	−	6.17860e6i	0.402425	−	0.402425i
$750$	−1.34896e6	+	1.01862e6i	−0.0875683	+	0.0661240i
$751$	−349847.			−0.0226349			−0.0113174	−	0.999936i	$-0.503603\pi$
$751$	−349847.			−0.0226349			−0.0113174	+	0.999936i	$0.503603\pi$
$752$	6.86915e6	+	4.25444e6i	0.442954	+	0.274346i
$753$	−1.15949e7			−0.745209
$754$	2.07454e6	−	1.56651e6i	0.132890	−	0.100347i
$755$	−5.97011e6	+	5.97011e6i	−0.381166	+	0.381166i
$756$	3.23812e6	+	5.81443e6i	0.206058	+	0.370001i
$757$	−5.70333e6	−	5.70333e6i	−0.361733	−	0.361733i	0.502718	−	0.864451i	$-0.332334\pi$
$757$	−5.70333e6	−	5.70333e6i	−0.361733	−	0.361733i	−0.864451	+	0.502718i	$0.832334\pi$
$758$	76229.3	−	546339.i	0.00481891	−	0.0345374i
$759$		−	1.38458e7i		−	0.872395i
$760$	110525.	−	42805.1i	0.00694107	−	0.00268820i
$761$		−	1.70225e7i		−	1.06552i	−0.846267	−	0.532759i	$-0.821155\pi$
$761$		−	1.70225e7i		−	1.06552i	0.846267	−	0.532759i	$-0.178845\pi$
$762$	2.98230e7	+	4.16112e6i	1.86064	+	0.259611i
$763$	2.34179e6	+	2.34179e6i	0.145625	+	0.145625i
$764$	4.60868e6	−	1.61938e7i	0.285656	−	1.00373i
$765$	−3.97214e6	+	3.97214e6i	−0.245398	+	0.245398i
$766$	1.45416e7	+	1.92574e7i	0.895445	+	1.18584i
$767$	894394.			0.0548960
$768$	−1.90119e7	−	6.37768e6i	−1.16312	−	0.390175i
$769$	−1.83892e7			−1.12136			−0.560682	−	0.828031i	$-0.689461\pi$
$769$	−1.83892e7			−1.12136			−0.560682	+	0.828031i	$0.689461\pi$
$770$	2.55652e6	+	3.38561e6i	0.155390	+	0.205783i
$771$	−1.89480e7	+	1.89480e7i	−1.14796	+	1.14796i
$772$	−5.63767e6	+	1.98094e7i	−0.340453	+	1.19627i
$773$	−1.38798e7	−	1.38798e7i	−0.835478	−	0.835478i	0.152782	−	0.988260i	$-0.451177\pi$
$773$	−1.38798e7	−	1.38798e7i	−0.835478	−	0.835478i	−0.988260	+	0.152782i	$0.951177\pi$
$774$	6.00519e6	+	837888.i	0.360308	+	0.0502729i
$775$			2.59406e6i			0.155140i
$776$	−1.58791e7	+	6.14981e6i	−0.946611	+	0.366612i
$777$			2.19969e7i			1.30710i
$778$	−425133.	+	3.04695e6i	−0.0251812	+	0.180475i
$779$	−364294.	−	364294.i	−0.0215084	−	0.0215084i
$780$	−834065.	−	1.49766e6i	−0.0490866	−	0.0881409i
$781$	−7.05556e6	+	7.05556e6i	−0.413908	+	0.413908i
$782$	−1.80369e7	+	1.36199e7i	−1.05474	+	0.796447i
$783$	9.43297e6			0.549850
$784$	−7.51308e6	−	4.65326e6i	−0.436544	−	0.270376i
$785$	−4.14675e6			−0.240178
$786$	−3.30510e7	+	2.49573e7i	−1.90822	+	1.44092i
$787$	8.59038e6	−	8.59038e6i	0.494397	−	0.494397i	−0.415292	−	0.909688i	$-0.636320\pi$
$787$	8.59038e6	−	8.59038e6i	0.494397	−	0.494397i	0.909688	+	0.415292i	$0.136320\pi$
$788$	−1.24118e7	+	6.91227e6i	−0.712065	+	0.396556i
$789$	−2.64781e7	−	2.64781e7i	−1.51424	−	1.51424i
$790$	577423.	−	4.13842e6i	0.0329175	−	0.235921i
$791$		−	9.19846e6i		−	0.522726i
$792$	2.97775e6	−	6.74218e6i	0.168685	−	0.381933i
$793$			1.66990e6i			0.0942992i
$794$	−2.77012e7	−	3.86508e6i	−1.55936	−	0.217574i
$795$	7.81768e6	+	7.81768e6i	0.438693	+	0.438693i
$796$	1.48542e7	+	4.22743e6i	0.830934	+	0.236480i
$797$	9.71311e6	−	9.71311e6i	0.541642	−	0.541642i	−0.382368	−	0.924010i	$-0.624891\pi$
$797$	9.71311e6	−	9.71311e6i	0.541642	−	0.541642i	0.924010	+	0.382368i	$0.124891\pi$
$798$	154392.	+	204462.i	0.00858260	+	0.0113660i
$799$	1.44459e7			0.800531
$800$	−3.60500e6	+	333459.i	−0.199150	+	0.0184212i
$801$	5.73125e6			0.315622
$802$	9.75723e6	+	1.29215e7i	0.535662	+	0.709379i
$803$	−2.11039e7	+	2.11039e7i	−1.15498	+	1.15498i
$804$	−7.74220e6	−	2.20339e6i	−0.422400	−	0.120213i
$805$	−3.48853e6	−	3.48853e6i	−0.189737	−	0.189737i
$806$	−2.60549e6	−	363538.i	−0.141271	−	0.0197111i
$807$			2.23831e7i			1.20986i
$808$	−1.48114e7	−	6.54163e6i	−0.798121	−	0.352499i
$809$		−	1.61356e7i		−	0.866788i	−0.901205	−	0.433394i	$-0.857316\pi$
$809$		−	1.61356e7i		−	0.866788i	0.901205	−	0.433394i	$-0.142684\pi$
$810$	1.44245e6	−	1.03381e7i	0.0772482	−	0.553642i
$811$	6.47833e6	+	6.47833e6i	0.345868	+	0.345868i	0.858568	−	0.512700i	$-0.171355\pi$
$811$	6.47833e6	+	6.47833e6i	0.345868	+	0.345868i	−0.512700	+	0.858568i	$0.671355\pi$
$812$	1.03681e7	−	5.77413e6i	0.551837	−	0.307324i
$813$	9.24391e6	−	9.24391e6i	0.490489	−	0.490489i
$814$	−1.90501e7	+	1.43850e7i	−1.00771	+	0.760935i
$815$	−2.60572e6			−0.137415
$816$	−3.49012e7	+	8.20388e6i	−1.83491	+	0.431314i
$817$	−228728.			−0.0119885
$818$	1.56860e7	−	1.18447e7i	0.819652	−	0.618931i
$819$	879306.	−	879306.i	0.0458068	−	0.0458068i
$820$	7.65667e6	+	1.37485e7i	0.397654	+	0.714035i
$821$	−2.01435e7	−	2.01435e7i	−1.04298	−	1.04298i	−0.999034	−	0.0439500i	$-0.986006\pi$
$821$	−2.01435e7	−	2.01435e7i	−1.04298	−	1.04298i	−0.0439500	−	0.999034i	$-0.513994\pi$
$822$	−1.59975e6	+	1.14655e7i	−0.0825794	+	0.591851i
$823$		−	2.00006e7i		−	1.02930i	−0.857400	−	0.514651i	$-0.827922\pi$
$823$		−	2.00006e7i		−	1.02930i	0.857400	−	0.514651i	$-0.172078\pi$
$824$	7.97586e6	+	2.05941e7i	0.409223	+	1.05663i
$825$		−	3.96525e6i		−	0.202832i
$826$	4.04394e6	+	564241.i	0.206231	+	0.0287749i
$827$	1.08404e7	+	1.08404e7i	0.551163	+	0.551163i	0.926777	−	0.375613i	$-0.122568\pi$
$827$	1.08404e7	+	1.08404e7i	0.551163	+	0.551163i	−0.375613	+	0.926777i	$0.622568\pi$
$828$	−2.34615e6	+	8.24380e6i	−0.118927	+	0.417880i
$829$	6.10861e6	−	6.10861e6i	0.308714	−	0.308714i	−0.535697	−	0.844410i	$-0.679951\pi$
$829$	6.10861e6	−	6.10861e6i	0.308714	−	0.308714i	0.844410	+	0.535697i	$0.179951\pi$
$830$	−542920.	−	718990.i	−0.0273552	−	0.0362266i
$831$	−2.73111e7			−1.37194
$832$	170285.	−	3.66762e6i	0.00852839	−	0.183686i
$833$	−1.58001e7			−0.788947
$834$	1.04413e7	+	1.38274e7i	0.519802	+	0.688376i
$835$	1.18581e7	−	1.18581e7i	0.588572	−	0.588572i
$836$	−76105.7	+	267418.i	−0.00376619	+	0.0132335i
$837$	−6.75013e6	−	6.75013e6i	−0.333041	−	0.333041i
$838$	5.86197e6	+	817906.i	0.288359	+	0.0402340i
$839$		−	3.37991e7i		−	1.65768i	−0.559487	−	0.828839i	$-0.689002\pi$
$839$		−	3.37991e7i		−	1.65768i	0.559487	−	0.828839i	$-0.310998\pi$
$840$	−2.82635e6	−	7.29777e6i	−0.138206	−	0.356855i
$841$			3.69052e6i			0.179927i
$842$	2.74941e6	−	1.97051e7i	0.133647	−	0.957854i
$843$	−1.81892e7	−	1.81892e7i	−0.881546	−	0.881546i
$844$	−1.64904e7	−	2.96105e7i	−0.796848	−	1.43084i
$845$	−6.34166e6	+	6.34166e6i	−0.305535	+	0.305535i
$846$	4.37189e6	−	3.30127e6i	0.210012	−	0.158583i
$847$	4.61116e6			0.220852
$848$	5.41840e6	+	2.30511e7i	0.258751	+	1.10079i
$849$	−3.49975e7			−1.66636
$850$	−5.16553e6	+	3.90056e6i	−0.245226	+	0.185174i
$851$	1.96291e7	−	1.96291e7i	0.929132	−	0.929132i
$852$	1.60809e7	−	8.95562e6i	0.758946	−	0.422665i
$853$	1.17987e7	+	1.17987e7i	0.555218	+	0.555218i	0.927942	−	0.372724i	$-0.121576\pi$
$853$	1.17987e7	+	1.17987e7i	0.555218	+	0.555218i	−0.372724	+	0.927942i	$0.621576\pi$
$854$	−1.05348e6	+	7.55035e6i	−0.0494290	+	0.354260i
$855$		−	80361.1i		−	0.00375950i
$856$	−1.60009e7	−	7.06696e6i	−0.746379	−	0.329646i
$857$			8.28922e6i			0.385533i	0.981245	+	0.192766i	$0.0617460\pi$
$857$			8.28922e6i			0.385533i	−0.981245	+	0.192766i	$0.938254\pi$
$858$	3.98273e6	+	555700.i	0.184698	+	0.0257705i
$859$	−146779.	−	146779.i	−0.00678706	−	0.00678706i	0.703705	−	0.710492i	$-0.251528\pi$
$859$	−146779.	−	146779.i	−0.00678706	−	0.00678706i	−0.710492	+	0.703705i	$0.751528\pi$
$860$	6.71977e6	+	1.91241e6i	0.309819	+	0.0881730i
$861$	−2.40537e7	+	2.40537e7i	−1.10579	+	1.10579i
$862$	1.83070e7	+	2.42440e7i	0.839169	+	1.11131i
$863$	2.71686e7			1.24177			0.620884	−	0.783902i	$-0.286774\pi$
$863$	2.71686e7			1.24177			0.620884	+	0.783902i	$0.286774\pi$
$864$	8.51304e6	−	1.02485e7i	0.387972	−	0.467062i
$865$	1.39875e7			0.635623
$866$	1.96893e7	+	2.60746e7i	0.892144	+	1.18147i
$867$	−2.61248e7	+	2.61248e7i	−1.18034	+	1.18034i
$868$	−1.15512e7	−	3.28742e6i	−0.520390	−	0.148100i
$869$	6.93107e6	+	6.93107e6i	0.311352	+	0.311352i
$870$	−1.09858e7	−	1.53282e6i	−0.492077	−	0.0686583i
$871$		−	1.47383e6i		−	0.0658265i
$872$	2.67850e6	−	6.06461e6i	0.119289	−	0.270092i
$873$			1.15455e7i			0.512714i
$874$	44680.4	−	320227.i	0.00197851	−	0.0141801i
$875$	−999069.	−	999069.i	−0.0441139	−	0.0441139i
$876$	4.80995e7	−	2.67871e7i	2.11778	−	1.17941i
$877$	−3.89603e6	+	3.89603e6i	−0.171050	+	0.171050i	−0.787441	−	0.616391i	$-0.788594\pi$
$877$	−3.89603e6	+	3.89603e6i	−0.171050	+	0.171050i	0.616391	+	0.787441i	$0.288594\pi$
$878$	−2.22499e7	+	1.68012e7i	−0.974074	+	0.735537i
$879$	4.43916e7			1.93789
$880$	4.47180e6	−	7.22010e6i	0.194660	−	0.314294i
$881$	2.60538e7			1.13092			0.565459	−	0.824777i	$-0.308699\pi$
$881$	2.60538e7			1.13092			0.565459	+	0.824777i	$0.308699\pi$
$882$	−4.78172e6	+	3.61074e6i	−0.206972	+	0.156288i
$883$	1.17398e7	−	1.17398e7i	0.506711	−	0.506711i	−0.406804	−	0.913515i	$-0.633357\pi$
$883$	1.17398e7	−	1.17398e7i	0.506711	−	0.506711i	0.913515	+	0.406804i	$0.133357\pi$
$884$	−3.19385e6	−	5.73493e6i	−0.137462	−	0.246830i
$885$	−2.69857e6	−	2.69857e6i	−0.115818	−	0.115818i
$886$	4.66069e6	−	3.34034e7i	0.199465	−	1.42957i
$887$		−	1.31295e7i		−	0.560324i	−0.959953	−	0.280162i	$-0.909612\pi$
$887$		−	1.31295e7i		−	0.560324i	0.959953	−	0.280162i	$-0.0903882\pi$
$888$	4.10629e7	−	1.59032e7i	1.74750	−	0.676788i
$889$			2.51693e7i			1.06811i
$890$	6.54056e6	+	912587.i	0.276783	+	0.0386188i
$891$	1.73144e7	+	1.73144e7i	0.730656	+	0.730656i
$892$	−1.47742e6	+	5.19130e6i	−0.0621715	+	0.218456i
$893$	−146129.	+	146129.i	−0.00613208	+	0.00613208i
$894$	−7.66325e6	−	1.01485e7i	−0.320678	−	0.424675i
$895$	4.59861e6			0.191897
$896$	3.08370e6	−	1.64755e7i	0.128322	−	0.685596i
$897$	−4.67640e6			−0.194057
$898$	538492.	+	713128.i	0.0222838	+	0.0295105i
$899$	−1.20366e7	+	1.20366e7i	−0.496714	+	0.496714i
$900$	−671906.	+	2.36092e6i	−0.0276504	+	0.0971571i
$901$	2.99359e7	+	2.99359e7i	1.22852	+	1.22852i
$902$	−3.65613e7	−	5.10130e6i	−1.49625	−	0.208768i
$903$			1.51025e7i			0.616352i
$904$	−1.71713e7	+	6.65025e6i	−0.698845	+	0.270655i
$905$		−	2.31882e6i		−	0.0941123i
$906$	−5.04878e6	+	3.61849e7i	−0.204346	+	1.46456i
$907$	−1.05664e7	−	1.05664e7i	−0.426491	−	0.426491i	0.460940	−	0.887431i	$-0.347512\pi$
$907$	−1.05664e7	−	1.05664e7i	−0.426491	−	0.426491i	−0.887431	+	0.460940i	$0.847512\pi$
$908$	−2.33622e7	−	4.19496e7i	−0.940370	−	1.68855i
$909$	−7.76275e6	+	7.76275e6i	−0.311606	+	0.311606i
$910$	1.14349e6	−	863461.i	0.0457749	−	0.0345652i
$911$	2.16312e7			0.863546			0.431773	−	0.901982i	$-0.357888\pi$
$911$	2.16312e7			0.863546			0.431773	+	0.901982i	$0.357888\pi$
$912$	270059.	−	436034.i	0.0107516	−	0.0173593i
$913$	2.11346e6			0.0839106
$914$	−3.41892e7	+	2.58167e7i	−1.35370	+	1.02220i
$915$	5.03844e6	−	5.03844e6i	0.198950	−	0.198950i
$916$	4.11890e7	−	2.29386e7i	1.62197	−	0.903292i
$917$	−2.44782e7	−	2.44782e7i	−0.961295	−	0.961295i
$918$	3.29163e6	−	2.35913e7i	0.128915	−	0.923944i
$919$			4.07817e6i			0.159286i	0.996823	+	0.0796428i	$0.0253780\pi$
$919$			4.07817e6i			0.159286i	−0.996823	+	0.0796428i	$0.974622\pi$
$920$	−3.99011e6	+	9.03433e6i	−0.155423	+	0.351906i
$921$		−	1.58120e7i		−	0.614238i
$922$	1.95791e6	+	273181.i	0.0758516	+	0.0105834i
$923$	2.38301e6	+	2.38301e6i	0.0920706	+	0.0920706i
$924$	1.76571e7	+	5.02512e6i	0.680361	+	0.193627i
$925$	5.62153e6	−	5.62153e6i	0.216023	−	0.216023i
$926$	−2.68168e7	−	3.55135e7i	−1.02773	−	1.36103i
$927$	1.49736e7			0.572306
$928$	−1.82748e7	−	1.51802e7i	−0.696598	−	0.578640i
$929$	2.13675e7			0.812296			0.406148	−	0.913807i	$-0.366872\pi$
$929$	2.13675e7			0.812296			0.406148	+	0.913807i	$0.366872\pi$
$930$	6.76444e6	+	8.95818e6i	0.256463	+	0.339635i
$931$	159828.	−	159828.i	0.00604335	−	0.00604335i
$932$	−2.66698e7	−	7.59010e6i	−1.00573	−	0.286225i
$933$	4.32045e6	+	4.32045e6i	0.162489	+	0.162489i
$934$	3.71847e7	+	5.18828e6i	1.39475	+	0.194606i
$935$		−	1.51840e7i		−	0.568010i
$936$	−2.27716e6	−	1.00573e6i	−0.0849581	−	0.0375226i
$937$			4.82622e7i			1.79580i	0.440199	+	0.897900i	$0.354908\pi$
$937$			4.82622e7i			1.79580i	−0.440199	+	0.897900i	$0.645092\pi$
$938$	929783.	−	6.66381e6i	0.0345044	−	0.247295i
$939$	−1.65239e7	−	1.65239e7i	−0.611573	−	0.611573i
$940$	5.51491e6	−	3.07131e6i	0.203572	−	0.113372i
$941$	675342.	−	675342.i	0.0248628	−	0.0248628i	−0.694566	−	0.719429i	$-0.744404\pi$
$941$	675342.	−	675342.i	0.0248628	−	0.0248628i	0.719429	+	0.694566i	$0.244404\pi$
$942$	−1.43202e7	+	1.08134e7i	−0.525801	+	0.397039i
$943$	4.29290e7			1.57207
$944$	−1.87037e6	−	7.95698e6i	−0.0683120	−	0.290615i
$945$	5.19945e6			0.189399
$946$	−1.30792e7	+	9.87631e6i	−0.475176	+	0.358812i
$947$	1.13522e7	−	1.13522e7i	0.411343	−	0.411343i	−0.470863	−	0.882206i	$-0.656057\pi$
$947$	1.13522e7	−	1.13522e7i	0.411343	−	0.411343i	0.882206	+	0.470863i	$0.156057\pi$
$948$	−8.79760e6	−	1.57971e7i	−0.317939	−	0.570897i
$949$	7.12781e6	+	7.12781e6i	0.256916	+	0.256916i
$950$	12795.9	−	91708.9i	0.000460004	−	0.00329687i
$951$			1.15828e7i			0.415299i
$952$	−1.08228e7	−	2.79450e7i	−0.387033	−	0.999337i
$953$			4.14033e6i			0.147674i	0.997270	+	0.0738368i	$0.0235244\pi$
$953$			4.14033e6i			0.147674i	−0.997270	+	0.0738368i	$0.976476\pi$
$954$	1.59009e7	+	2.21861e6i	0.565654	+	0.0789242i
$955$	−9.30114e6	−	9.30114e6i	−0.330010	−	0.330010i
$956$	1.36656e7	−	4.80178e7i	0.483598	−	1.69925i
$957$	1.83991e7	−	1.83991e7i	0.649407	−	0.649407i
$958$	−1.34620e6	−	1.78277e6i	−0.0473909	−	0.0627600i
$959$	−9.67635e6			−0.339754
$960$	−1.15798e7	+	1.05522e7i	−0.405528	+	0.369543i
$961$	−1.14026e7			−0.398286
$962$	4.85850e6	+	6.43413e6i	0.169264	+	0.224157i
$963$	−8.38614e6	+	8.38614e6i	−0.291405	+	0.291405i
$964$	−1.10595e7	+	3.88604e7i	−0.383303	+	1.34684i
$965$	1.13778e7	+	1.13778e7i	0.393315	+	0.393315i
$966$	−2.11440e7	−	2.95017e6i	−0.729029	−	0.101719i
$967$			5.25628e7i			1.80764i	0.427912	+	0.903821i	$0.359249\pi$
$967$			5.25628e7i			1.80764i	−0.427912	+	0.903821i	$0.640751\pi$
$968$	−3.33375e6	−	8.60791e6i	−0.114352	−	0.295263i
$969$		−	916984.i		−	0.0313727i
$970$	−1.83838e6	+	1.31758e7i	−0.0627345	+	0.449622i
$971$	3.45079e7	+	3.45079e7i	1.17455	+	1.17455i	0.981114	+	0.193432i	$0.0619620\pi$
$971$	3.45079e7	+	3.45079e7i	1.17455	+	1.17455i	0.193432	+	0.981114i	$0.438038\pi$
$972$	−1.32753e7	−	2.38375e7i	−0.450692	−	0.809272i
$973$	−1.02408e7	+	1.02408e7i	−0.346780	+	0.346780i
$974$	1.17527e7	−	8.87460e6i	0.396953	−	0.299745i
$975$	−1.33926e6			−0.0451183
$976$	1.48563e7	−	3.49212e6i	0.499213	−	0.117345i
$977$	6.56209e6			0.219941			0.109970	−	0.993935i	$-0.464924\pi$
$977$	6.56209e6			0.219941			0.109970	+	0.993935i	$0.464924\pi$
$978$	−8.99844e6	+	6.79484e6i	−0.300829	+	0.227160i
$979$	−1.09542e7	+	1.09542e7i	−0.365278	+	0.365278i
$980$	−6.03189e6	+	3.35922e6i	−0.200626	+	0.111731i
$981$	−3.17849e6	−	3.17849e6i	−0.105450	−	0.105450i
$982$	1.82873e6	−	1.31066e7i	0.0605162	−	0.433723i
$983$			1.97937e6i			0.0653345i	0.999466	+	0.0326672i	$0.0104002\pi$
$983$			1.97937e6i			0.0653345i	−0.999466	+	0.0326672i	$0.989600\pi$
$984$	6.22926e7	+	2.75122e7i	2.05092	+	0.905809i
$985$			1.10990e7i			0.364498i
$986$	−4.20674e7	−	5.86956e6i	−1.37801	−	0.192271i
$987$	9.64864e6	+	9.64864e6i	0.315263	+	0.315263i
$988$	90319.9	+	25704.6i	0.00294368	+	0.000837758i
$989$	1.34768e7	−	1.34768e7i	0.438124	−	0.438124i
$990$	−3.46994e6	−	4.59525e6i	−0.112521	−	0.149012i
$991$	−3.65298e7			−1.18158			−0.590790	−	0.806826i	$-0.701184\pi$
$991$	−3.65298e7			−1.18158			−0.590790	+	0.806826i	$0.701184\pi$
$992$	2.21443e6	+	2.39400e7i	0.0714467	+	0.772405i
$993$	3.81506e7			1.22780
$994$	9.27126e6	+	1.22780e7i	0.297627	+	0.394149i
$995$	8.53170e6	−	8.53170e6i	0.273198	−	0.273198i
$996$	−3.74978e6	−	1.06717e6i	−0.119773	−	0.0340867i
$997$	−2.67019e7	−	2.67019e7i	−0.850753	−	0.850753i	0.139472	−	0.990226i	$-0.455459\pi$
$997$	−2.67019e7	−	2.67019e7i	−0.850753	−	0.850753i	−0.990226	+	0.139472i	$0.955459\pi$
$998$	−4.33265e7	−	6.04524e6i	−1.37698	−	0.192126i
$999$			2.92562e7i			0.927478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.6.l.a.21.12	✓	80
4.3	odd	2		320.6.l.a.241.34		80
16.3	odd	4		320.6.l.a.81.34		80
16.13	even	4	inner	80.6.l.a.61.12	yes	80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.6.l.a.21.12	✓	80	1.1	even	1	trivial
80.6.l.a.61.12	yes	80	16.13	even	4	inner
320.6.l.a.81.34		80	16.3	odd	4
320.6.l.a.241.34		80	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	80.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.40887 - 4.51438i) q^{2} +(-13.5228 + 13.5228i) q^{3} +(-8.75923 + 30.7778i) q^{4} +(17.6777 + 17.6777i) q^{5} +(107.145 + 14.9496i) q^{6} +90.4254i q^{7} +(168.802 - 65.3752i) q^{8} -122.733i q^{9} +O(q^{10})\)	\(q+(-3.40887 - 4.51438i) q^{2} +(-13.5228 + 13.5228i) q^{3} +(-8.75923 + 30.7778i) q^{4} +(17.6777 + 17.6777i) q^{5} +(107.145 + 14.9496i) q^{6} +90.4254i q^{7} +(168.802 - 65.3752i) q^{8} -122.733i q^{9} +(19.5428 - 140.065i) q^{10} +(234.581 + 234.581i) q^{11} +(-297.754 - 534.653i) q^{12} +(79.2296 - 79.2296i) q^{13} +(408.214 - 308.248i) q^{14} -478.104 q^{15} +(-870.552 - 539.180i) q^{16} -1830.78 q^{17} +(-554.065 + 418.382i) q^{18} +(18.5194 - 18.5194i) q^{19} +(-698.923 + 389.238i) q^{20} +(-1222.81 - 1222.81i) q^{21} +(259.332 - 1858.65i) q^{22} +2182.36i q^{23} +(-1398.62 + 3166.73i) q^{24} +625.000i q^{25} +(-627.755 - 87.5890i) q^{26} +(-1626.34 - 1626.34i) q^{27} +(-2783.10 - 792.056i) q^{28} +(-2900.05 + 2900.05i) q^{29} +(1629.79 + 2158.34i) q^{30} +4150.49 q^{31} +(533.534 + 5768.00i) q^{32} -6344.40 q^{33} +(6240.90 + 8264.84i) q^{34} +(-1598.51 + 1598.51i) q^{35} +(3777.47 + 1075.05i) q^{36} +(-8994.45 - 8994.45i) q^{37} +(-146.734 - 20.4734i) q^{38} +2142.81i q^{39} +(4139.71 + 1828.34i) q^{40} -19670.9i q^{41} +(-1351.82 + 9688.59i) q^{42} +(-6175.34 - 6175.34i) q^{43} +(-9274.66 + 5165.16i) q^{44} +(2169.64 - 2169.64i) q^{45} +(9852.01 - 7439.38i) q^{46} -7890.57 q^{47} +(19063.6 - 4481.08i) q^{48} +8630.25 q^{49} +(2821.49 - 2130.54i) q^{50} +(24757.3 - 24757.3i) q^{51} +(1744.53 + 3132.51i) q^{52} +(-16351.4 - 16351.4i) q^{53} +(-1797.94 + 12885.9i) q^{54} +8293.71i q^{55} +(5911.58 + 15264.0i) q^{56} +500.870i q^{57} +(22977.8 + 3206.04i) q^{58} +(5644.32 + 5644.32i) q^{59} +(4187.82 - 14715.0i) q^{60} +(-10538.4 + 10538.4i) q^{61} +(-14148.5 - 18736.9i) q^{62} +11098.2 q^{63} +(24220.2 - 22070.9i) q^{64} +2801.19 q^{65} +(21627.2 + 28641.0i) q^{66} +(9300.98 - 9300.98i) q^{67} +(16036.2 - 56347.5i) q^{68} +(-29511.7 - 29511.7i) q^{69} +(12665.4 + 1767.17i) q^{70} +30077.2i q^{71} +(-8023.72 - 20717.6i) q^{72} +89964.1i q^{73} +(-9943.45 + 71265.3i) q^{74} +(-8451.76 - 8451.76i) q^{75} +(407.773 + 732.205i) q^{76} +(-21212.1 + 21212.1i) q^{77} +(9673.48 - 7304.57i) q^{78} +29546.6 q^{79} +(-5857.88 - 24920.8i) q^{80} +73809.7 q^{81} +(-88801.9 + 67055.6i) q^{82} +(4504.74 - 4504.74i) q^{83} +(48346.2 - 26924.5i) q^{84} +(-32364.0 - 32364.0i) q^{85} +(-6826.90 + 48928.8i) q^{86} -78433.8i q^{87} +(54933.6 + 24262.0i) q^{88} +46696.7i q^{89} +(-17190.6 - 2398.56i) q^{90} +(7164.36 + 7164.36i) q^{91} +(-67168.4 - 19115.8i) q^{92} +(-56126.3 + 56126.3i) q^{93} +(26897.9 + 35621.0i) q^{94} +654.761 q^{95} +(-85214.4 - 70784.7i) q^{96} -94069.4 q^{97} +(-29419.4 - 38960.2i) q^{98} +(28791.0 - 28791.0i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 44 q^{4} - 228 q^{6}+O(q^{10}) \) 80 * q + 44 * q^4 - 228 * q^6	\( 80 q + 44 q^{4} - 228 q^{6} - 100 q^{10} + 1208 q^{11} + 1572 q^{12} - 916 q^{14} - 1800 q^{15} + 2960 q^{16} + 6400 q^{18} + 2360 q^{19} - 3800 q^{20} - 3260 q^{22} - 13880 q^{24} - 880 q^{26} - 7464 q^{27} + 18764 q^{28} - 8144 q^{29} + 22400 q^{32} - 7440 q^{34} + 27948 q^{36} + 21296 q^{37} - 34820 q^{38} - 7260 q^{42} + 32072 q^{43} + 64392 q^{44} + 149268 q^{46} - 88360 q^{47} + 94040 q^{48} - 192080 q^{49} + 2500 q^{50} - 5920 q^{51} - 55016 q^{52} - 49456 q^{53} - 250784 q^{54} - 250352 q^{56} - 115988 q^{58} + 44984 q^{59} + 7700 q^{60} + 48080 q^{61} + 444328 q^{62} + 158760 q^{63} + 218096 q^{64} + 253440 q^{66} + 61160 q^{67} - 119792 q^{68} - 22320 q^{69} - 66200 q^{70} - 629480 q^{72} - 156664 q^{74} + 223232 q^{76} - 14896 q^{77} + 516176 q^{78} + 177680 q^{79} + 48400 q^{80} - 524880 q^{81} + 254476 q^{82} - 329240 q^{83} - 173248 q^{84} + 132400 q^{85} - 765740 q^{86} - 390400 q^{88} + 71100 q^{90} + 364832 q^{91} + 333532 q^{92} - 362352 q^{93} + 537844 q^{94} + 288800 q^{95} + 1151112 q^{96} + 52420 q^{98} + 659000 q^{99}+O(q^{100}) \) 80 * q + 44 * q^4 - 228 * q^6 - 100 * q^10 + 1208 * q^11 + 1572 * q^12 - 916 * q^14 - 1800 * q^15 + 2960 * q^16 + 6400 * q^18 + 2360 * q^19 - 3800 * q^20 - 3260 * q^22 - 13880 * q^24 - 880 * q^26 - 7464 * q^27 + 18764 * q^28 - 8144 * q^29 + 22400 * q^32 - 7440 * q^34 + 27948 * q^36 + 21296 * q^37 - 34820 * q^38 - 7260 * q^42 + 32072 * q^43 + 64392 * q^44 + 149268 * q^46 - 88360 * q^47 + 94040 * q^48 - 192080 * q^49 + 2500 * q^50 - 5920 * q^51 - 55016 * q^52 - 49456 * q^53 - 250784 * q^54 - 250352 * q^56 - 115988 * q^58 + 44984 * q^59 + 7700 * q^60 + 48080 * q^61 + 444328 * q^62 + 158760 * q^63 + 218096 * q^64 + 253440 * q^66 + 61160 * q^67 - 119792 * q^68 - 22320 * q^69 - 66200 * q^70 - 629480 * q^72 - 156664 * q^74 + 223232 * q^76 - 14896 * q^77 + 516176 * q^78 + 177680 * q^79 + 48400 * q^80 - 524880 * q^81 + 254476 * q^82 - 329240 * q^83 - 173248 * q^84 + 132400 * q^85 - 765740 * q^86 - 390400 * q^88 + 71100 * q^90 + 364832 * q^91 + 333532 * q^92 - 362352 * q^93 + 537844 * q^94 + 288800 * q^95 + 1151112 * q^96 + 52420 * q^98 + 659000 * q^99

Introduction

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