LMFDB - Embedded newform 111.2.e.b.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [111,2,Mod(10,111)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(111, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("111.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 111 = 3 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	111.e (of order $3$, 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:	$0.886339462436$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 9x^{8} - 2x^{7} + 67x^{6} - 12x^{5} + 127x^{4} - 40x^{3} + 199x^{2} - 42x + 9 $ x^10 + 9x^8 - 2x^7 + 67x^6 - 12x^5 + 127x^4 - 40x^3 + 199x^2 - 42x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$-1.35095 + 2.33992i$ of defining polynomial
Character	$\chi$	$=$	111.100
Dual form			111.2.e.b.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.35095 - 2.33992i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.65014 + 4.59018i) q^{4} +(-0.580820 + 1.00601i) q^{5} +2.70190 q^{6} +(-2.02675 + 3.51043i) q^{7} +8.91704 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.35095 - 2.33992i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.65014 + 4.59018i) q^{4} +(-0.580820 + 1.00601i) q^{5} +2.70190 q^{6} +(-2.02675 + 3.51043i) q^{7} +8.91704 q^{8} +(-0.500000 - 0.866025i) q^{9} +3.13864 q^{10} -4.30028 q^{11} +(-2.65014 - 4.59018i) q^{12} +(1.08082 - 1.87204i) q^{13} +10.9522 q^{14} +(-0.580820 - 1.00601i) q^{15} +(-6.74621 - 11.6848i) q^{16} +(1.56932 + 2.71814i) q^{17} +(-1.35095 + 2.33992i) q^{18} +(-1.55176 + 2.68773i) q^{19} +(-3.07851 - 5.33214i) q^{20} +(-2.02675 - 3.51043i) q^{21} +(5.80947 + 10.0623i) q^{22} +1.51195 q^{23} +(-4.45852 + 7.72238i) q^{24} +(1.82530 + 3.16150i) q^{25} -5.84054 q^{26} +1.00000 q^{27} +(-10.7423 - 18.6063i) q^{28} -8.54245 q^{29} +(-1.56932 + 2.71814i) q^{30} -1.05812 q^{31} +(-9.31056 + 16.1264i) q^{32} +(2.15014 - 3.72415i) q^{33} +(4.24015 - 7.34416i) q^{34} +(-2.35435 - 4.07786i) q^{35} +5.30028 q^{36} +(6.08255 - 0.0503293i) q^{37} +8.38543 q^{38} +(1.08082 + 1.87204i) q^{39} +(-5.17920 + 8.97063i) q^{40} +(0.515248 - 0.892436i) q^{41} +(-5.47608 + 9.48485i) q^{42} +6.43892 q^{43} +(11.3963 - 19.7391i) q^{44} +1.16164 q^{45} +(-2.04257 - 3.53784i) q^{46} +0.292195 q^{47} +13.4924 q^{48} +(-4.71542 - 8.16734i) q^{49} +(4.93177 - 8.54208i) q^{50} -3.13864 q^{51} +(5.72865 + 9.92232i) q^{52} +(1.09607 + 1.89845i) q^{53} +(-1.35095 - 2.33992i) q^{54} +(2.49769 - 4.32613i) q^{55} +(-18.0726 + 31.3027i) q^{56} +(-1.55176 - 2.68773i) q^{57} +(11.5404 + 19.9886i) q^{58} +(0.988500 + 1.71213i) q^{59} +6.15702 q^{60} +(6.98867 - 12.1047i) q^{61} +(1.42946 + 2.47590i) q^{62} +4.05350 q^{63} +23.3277 q^{64} +(1.25552 + 2.17463i) q^{65} -11.6189 q^{66} +(-3.79827 + 6.57879i) q^{67} -16.6357 q^{68} +(-0.755975 + 1.30939i) q^{69} +(-6.36123 + 11.0180i) q^{70} +(-3.51323 + 6.08510i) q^{71} +(-4.45852 - 7.72238i) q^{72} -3.54245 q^{73} +(-8.33500 - 14.1647i) q^{74} -3.65059 q^{75} +(-8.22478 - 14.2457i) q^{76} +(8.71559 - 15.0958i) q^{77} +(2.92027 - 5.05806i) q^{78} +(-4.96394 + 8.59779i) q^{79} +15.6733 q^{80} +(-0.500000 + 0.866025i) q^{81} -2.78430 q^{82} +(1.94869 + 3.37523i) q^{83} +21.4847 q^{84} -3.64597 q^{85} +(-8.69867 - 15.0665i) q^{86} +(4.27122 - 7.39798i) q^{87} -38.3458 q^{88} +(7.47544 + 12.9478i) q^{89} +(-1.56932 - 2.71814i) q^{90} +(4.38110 + 7.58829i) q^{91} +(-4.00688 + 6.94012i) q^{92} +(0.529058 - 0.916355i) q^{93} +(-0.394741 - 0.683711i) q^{94} +(-1.80259 - 3.12218i) q^{95} +(-9.31056 - 16.1264i) q^{96} -10.7041 q^{97} +(-12.7406 + 22.0674i) q^{98} +(2.15014 + 3.72415i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{3} - 8 q^{4} + 2 q^{5} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 5 * q^3 - 8 * q^4 + 2 * q^5 + 6 * q^8 - 5 * q^9	\( 10 q - 5 q^{3} - 8 q^{4} + 2 q^{5} + 6 q^{8} - 5 q^{9} + 10 q^{10} - 6 q^{11} - 8 q^{12} + 3 q^{13} + 22 q^{14} + 2 q^{15} - 18 q^{16} + 5 q^{17} - 7 q^{19} - 2 q^{20} + 3 q^{22} - 14 q^{23} - 3 q^{24} - 7 q^{25} - 10 q^{26} + 10 q^{27} + q^{28} - 10 q^{29} - 5 q^{30} - 12 q^{31} - 6 q^{32} + 3 q^{33} - 2 q^{34} + q^{35} + 16 q^{36} + 21 q^{37} + 66 q^{38} + 3 q^{39} - 34 q^{40} - 18 q^{41} - 11 q^{42} + 6 q^{43} + 46 q^{44} - 4 q^{45} - 30 q^{46} - 12 q^{47} + 36 q^{48} - 29 q^{49} + 28 q^{50} - 10 q^{51} + 10 q^{52} - 20 q^{53} + 4 q^{55} - 74 q^{56} - 7 q^{57} + 34 q^{58} + 7 q^{59} + 4 q^{60} - 3 q^{61} - 28 q^{62} + 74 q^{64} + 30 q^{65} - 6 q^{66} + 5 q^{67} - 88 q^{68} + 7 q^{69} - 6 q^{71} - 3 q^{72} + 40 q^{73} + 45 q^{74} + 14 q^{75} + 24 q^{76} - q^{77} + 5 q^{78} - 3 q^{79} - 58 q^{80} - 5 q^{81} - 8 q^{82} - 4 q^{83} - 2 q^{84} + 56 q^{85} - q^{86} + 5 q^{87} - 18 q^{88} + 31 q^{89} - 5 q^{90} - q^{91} - q^{92} + 6 q^{93} - 53 q^{94} - 2 q^{95} - 6 q^{96} - 16 q^{97} - 51 q^{98} + 3 q^{99}+O(q^{100}) \) 10 * q - 5 * q^3 - 8 * q^4 + 2 * q^5 + 6 * q^8 - 5 * q^9 + 10 * q^10 - 6 * q^11 - 8 * q^12 + 3 * q^13 + 22 * q^14 + 2 * q^15 - 18 * q^16 + 5 * q^17 - 7 * q^19 - 2 * q^20 + 3 * q^22 - 14 * q^23 - 3 * q^24 - 7 * q^25 - 10 * q^26 + 10 * q^27 + q^28 - 10 * q^29 - 5 * q^30 - 12 * q^31 - 6 * q^32 + 3 * q^33 - 2 * q^34 + q^35 + 16 * q^36 + 21 * q^37 + 66 * q^38 + 3 * q^39 - 34 * q^40 - 18 * q^41 - 11 * q^42 + 6 * q^43 + 46 * q^44 - 4 * q^45 - 30 * q^46 - 12 * q^47 + 36 * q^48 - 29 * q^49 + 28 * q^50 - 10 * q^51 + 10 * q^52 - 20 * q^53 + 4 * q^55 - 74 * q^56 - 7 * q^57 + 34 * q^58 + 7 * q^59 + 4 * q^60 - 3 * q^61 - 28 * q^62 + 74 * q^64 + 30 * q^65 - 6 * q^66 + 5 * q^67 - 88 * q^68 + 7 * q^69 - 6 * q^71 - 3 * q^72 + 40 * q^73 + 45 * q^74 + 14 * q^75 + 24 * q^76 - q^77 + 5 * q^78 - 3 * q^79 - 58 * q^80 - 5 * q^81 - 8 * q^82 - 4 * q^83 - 2 * q^84 + 56 * q^85 - q^86 + 5 * q^87 - 18 * q^88 + 31 * q^89 - 5 * q^90 - q^91 - q^92 + 6 * q^93 - 53 * q^94 - 2 * q^95 - 6 * q^96 - 16 * q^97 - 51 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/111\mathbb{Z}\right)^\times$.

$n$	$38$	$76$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.35095	−	2.33992i	−0.955267	−	1.65457i	−0.733756	−	0.679413i	$-0.762234\pi$
$2$	−1.35095	−	2.33992i	−0.955267	−	1.65457i	−0.221511	−	0.975158i	$-0.571099\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−2.65014	+	4.59018i	−1.32507	+	2.29509i
$5$	−0.580820	+	1.00601i	−0.259751	+	0.449901i	−0.966175	−	0.257887i	$-0.916974\pi$
$5$	−0.580820	+	1.00601i	−0.259751	+	0.449901i	0.706424	+	0.707789i	$0.250307\pi$
$6$	2.70190			1.10305
$7$	−2.02675	+	3.51043i	−0.766039	+	1.32682i	0.173657	+	0.984806i	$0.444442\pi$
$7$	−2.02675	+	3.51043i	−0.766039	+	1.32682i	−0.939696	+	0.342012i	$0.888892\pi$
$8$	8.91704			3.15265
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	3.13864			0.992525
$11$	−4.30028			−1.29658			−0.648292	−	0.761392i	$-0.724516\pi$
$11$	−4.30028			−1.29658			−0.648292	+	0.761392i	$0.724516\pi$
$12$	−2.65014	−	4.59018i	−0.765030	−	1.32507i
$13$	1.08082	−	1.87204i	0.299766	−	0.519209i	−0.676317	−	0.736611i	$-0.736425\pi$
$13$	1.08082	−	1.87204i	0.299766	−	0.519209i	0.976082	+	0.217402i	$0.0697582\pi$
$14$	10.9522			2.92709
$15$	−0.580820	−	1.00601i	−0.149967	−	0.259751i
$16$	−6.74621	−	11.6848i	−1.68655	−	2.92119i
$17$	1.56932	+	2.71814i	0.380616	+	0.659246i	0.991150	−	0.132743i	$-0.0423786\pi$
$17$	1.56932	+	2.71814i	0.380616	+	0.659246i	−0.610534	+	0.791990i	$0.709045\pi$
$18$	−1.35095	+	2.33992i	−0.318422	+	0.551524i
$19$	−1.55176	+	2.68773i	−0.355999	+	0.616608i	−0.987288	−	0.158939i	$-0.949193\pi$
$19$	−1.55176	+	2.68773i	−0.355999	+	0.616608i	0.631290	+	0.775547i	$0.282526\pi$
$20$	−3.07851	−	5.33214i	−0.688376	−	1.19230i
$21$	−2.02675	−	3.51043i	−0.442273	−	0.766039i
$22$	5.80947	+	10.0623i	1.23858	+	2.14529i
$23$	1.51195			0.315263			0.157632	−	0.987498i	$-0.449614\pi$
$23$	1.51195			0.315263			0.157632	+	0.987498i	$0.449614\pi$
$24$	−4.45852	+	7.72238i	−0.910092	+	1.57632i
$25$	1.82530	+	3.16150i	0.365059	+	0.632301i
$26$	−5.84054			−1.14542
$27$	1.00000			0.192450
$28$	−10.7423	−	18.6063i	−2.03011	−	3.51625i
$29$	−8.54245			−1.58629			−0.793146	−	0.609031i	$-0.791558\pi$
$29$	−8.54245			−1.58629			−0.793146	+	0.609031i	$0.791558\pi$
$30$	−1.56932	+	2.71814i	−0.286517	+	0.496263i
$31$	−1.05812			−0.190043			−0.0950216	−	0.995475i	$-0.530292\pi$
$31$	−1.05812			−0.190043			−0.0950216	+	0.995475i	$0.530292\pi$
$32$	−9.31056	+	16.1264i	−1.64589	+	2.85077i
$33$	2.15014	−	3.72415i	0.374291	−	0.648292i
$34$	4.24015	−	7.34416i	0.727180	−	1.25951i
$35$	−2.35435	−	4.07786i	−0.397958	−	0.689284i
$36$	5.30028			0.883380
$37$	6.08255	−	0.0503293i	0.999966	−	0.00827409i
$37$	6.08255	−	0.0503293i	0.999966	−	0.00827409i
$38$	8.38543			1.36030
$39$	1.08082	+	1.87204i	0.173070	+	0.299766i
$40$	−5.17920	+	8.97063i	−0.818903	+	1.41838i
$41$	0.515248	−	0.892436i	0.0804683	−	0.139375i	−0.822983	−	0.568066i	$-0.807692\pi$
$41$	0.515248	−	0.892436i	0.0804683	−	0.139375i	0.903451	+	0.428691i	$0.141025\pi$
$42$	−5.47608	+	9.48485i	−0.844977	+	1.46354i
$43$	6.43892			0.981926			0.490963	−	0.871180i	$-0.336645\pi$
$43$	6.43892			0.981926			0.490963	+	0.871180i	$0.336645\pi$
$44$	11.3963	−	19.7391i	1.71806	−	2.97577i
$45$	1.16164			0.173167
$46$	−2.04257	−	3.53784i	−0.301161	−	0.521626i
$47$	0.292195			0.0426210			0.0213105	−	0.999773i	$-0.493216\pi$
$47$	0.292195			0.0426210			0.0213105	+	0.999773i	$0.493216\pi$
$48$	13.4924			1.94746
$49$	−4.71542	−	8.16734i	−0.673631	−	1.16676i
$50$	4.93177	−	8.54208i	0.697458	−	1.20803i
$51$	−3.13864			−0.439498
$52$	5.72865	+	9.92232i	0.794421	+	1.37598i
$53$	1.09607	+	1.89845i	0.150557	+	0.260772i	0.931432	−	0.363915i	$-0.118560\pi$
$53$	1.09607	+	1.89845i	0.150557	+	0.260772i	−0.780876	+	0.624687i	$0.785227\pi$
$54$	−1.35095	−	2.33992i	−0.183841	−	0.318422i
$55$	2.49769	−	4.32613i	0.336789	−	0.583335i
$56$	−18.0726	+	31.3027i	−2.41505	+	4.18299i
$57$	−1.55176	−	2.68773i	−0.205536	−	0.355999i
$58$	11.5404	+	19.9886i	1.51533	+	2.62463i
$59$	0.988500	+	1.71213i	0.128692	+	0.222901i	0.923170	−	0.384392i	$-0.125589\pi$
$59$	0.988500	+	1.71213i	0.128692	+	0.222901i	−0.794478	+	0.607293i	$0.792256\pi$
$60$	6.15702			0.794868
$61$	6.98867	−	12.1047i	0.894808	−	1.54985i	0.0607649	−	0.998152i	$-0.480646\pi$
$61$	6.98867	−	12.1047i	0.894808	−	1.54985i	0.834043	−	0.551700i	$-0.186021\pi$
$62$	1.42946	+	2.47590i	0.181542	+	0.314440i
$63$	4.05350			0.510693
$64$	23.3277			2.91596
$65$	1.25552	+	2.17463i	0.155729	+	0.269730i
$66$	−11.6189			−1.43019
$67$	−3.79827	+	6.57879i	−0.464032	+	0.803727i	−0.999157	−	0.0410455i	$-0.986931\pi$
$67$	−3.79827	+	6.57879i	−0.464032	+	0.803727i	0.535125	+	0.844773i	$0.320264\pi$
$68$	−16.6357			−2.01737
$69$	−0.755975	+	1.30939i	−0.0910087	+	0.157632i
$70$	−6.36123	+	11.0180i	−0.760313	+	1.31690i
$71$	−3.51323	+	6.08510i	−0.416944	+	0.722168i	−0.995630	−	0.0933818i	$-0.970232\pi$
$71$	−3.51323	+	6.08510i	−0.416944	+	0.722168i	0.578686	+	0.815550i	$0.303566\pi$
$72$	−4.45852	−	7.72238i	−0.525442	−	0.910092i
$73$	−3.54245			−0.414612			−0.207306	−	0.978276i	$-0.566470\pi$
$73$	−3.54245			−0.414612			−0.207306	+	0.978276i	$0.566470\pi$
$74$	−8.33500	−	14.1647i	−0.968924	−	1.64661i
$75$	−3.65059			−0.421534
$76$	−8.22478	−	14.2457i	−0.943447	−	1.63410i
$77$	8.71559	−	15.0958i	0.993233	−	1.72033i
$78$	2.92027	−	5.05806i	0.330656	−	0.572712i
$79$	−4.96394	+	8.59779i	−0.558486	+	0.967327i	0.439137	+	0.898420i	$0.355284\pi$
$79$	−4.96394	+	8.59779i	−0.558486	+	0.967327i	−0.997623	+	0.0689066i	$0.978049\pi$
$80$	15.6733			1.75233
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−2.78430			−0.307475
$83$	1.94869	+	3.37523i	0.213896	+	0.370479i	0.952931	−	0.303189i	$-0.0980512\pi$
$83$	1.94869	+	3.37523i	0.213896	+	0.370479i	−0.739034	+	0.673668i	$0.764718\pi$
$84$	21.4847			2.34417
$85$	−3.64597			−0.395461
$86$	−8.69867	−	15.0665i	−0.938002	−	1.62467i
$87$	4.27122	−	7.39798i	0.457923	−	0.793146i
$88$	−38.3458			−4.08767
$89$	7.47544	+	12.9478i	0.792395	+	1.37247i	0.924480	+	0.381229i	$0.124499\pi$
$89$	7.47544	+	12.9478i	0.792395	+	1.37247i	−0.132086	+	0.991238i	$0.542167\pi$
$90$	−1.56932	−	2.71814i	−0.165421	−	0.286517i
$91$	4.38110	+	7.58829i	0.459264	+	0.795469i
$92$	−4.00688	+	6.94012i	−0.417746	+	0.723558i
$93$	0.529058	−	0.916355i	0.0548607	−	0.0950216i
$94$	−0.394741	−	0.683711i	−0.0407144	−	0.0705194i
$95$	−1.80259	−	3.12218i	−0.184942	−	0.320329i
$96$	−9.31056	−	16.1264i	−0.950255	−	1.64589i
$97$	−10.7041			−1.08684			−0.543418	−	0.839462i	$-0.682870\pi$
$97$	−10.7041			−1.08684			−0.543418	+	0.839462i	$0.682870\pi$
$98$	−12.7406	+	22.0674i	−1.28700	+	2.22914i
$99$	2.15014	+	3.72415i	0.216097	+	0.374291i
$100$	−19.3492			−1.93492
$101$	12.1570			1.20967			0.604834	−	0.796351i	$-0.293239\pi$
$101$	12.1570			1.20967			0.604834	+	0.796351i	$0.293239\pi$
$102$	4.24015	+	7.34416i	0.419838	+	0.727180i
$103$	8.21514			0.809462			0.404731	−	0.914436i	$-0.367365\pi$
$103$	8.21514			0.809462			0.404731	+	0.914436i	$0.367365\pi$
$104$	9.63772	−	16.6930i	0.945056	−	1.63689i
$105$	4.70871			0.459523
$106$	2.96147	−	5.12942i	0.287644	−	0.498213i
$107$	−0.350310	+	0.606754i	−0.0338657	+	0.0586572i	−0.882462	−	0.470385i	$-0.844115\pi$
$107$	−0.350310	+	0.606754i	−0.0338657	+	0.0586572i	0.848596	+	0.529042i	$0.177449\pi$
$108$	−2.65014	+	4.59018i	−0.255010	+	0.441690i
$109$	0.298547	+	0.517099i	0.0285956	+	0.0495291i	0.879969	−	0.475031i	$-0.157563\pi$
$109$	0.298547	+	0.517099i	0.0285956	+	0.0495291i	−0.851373	+	0.524560i	$0.824230\pi$
$110$	−13.4970			−1.28689
$111$	−2.99769	+	5.29281i	−0.284528	+	0.502371i
$112$	54.6915			5.16786
$113$	7.21732	+	12.5008i	0.678949	+	1.17597i	0.975298	+	0.220894i	$0.0708974\pi$
$113$	7.21732	+	12.5008i	0.678949	+	1.17597i	−0.296349	+	0.955080i	$0.595769\pi$
$114$	−4.19271	+	7.26199i	−0.392684	+	0.680148i
$115$	−0.878172	+	1.52104i	−0.0818899	+	0.141838i
$116$	22.6387	−	39.2114i	2.10195	−	3.64068i
$117$	−2.16164			−0.199844
$118$	2.67083	−	4.62602i	0.245870	−	0.425859i
$119$	−12.7225			−1.16627
$120$	−5.17920	−	8.97063i	−0.472794	−	0.818903i
$121$	7.49242			0.681129
$122$	−37.7654			−3.41912
$123$	0.515248	+	0.892436i	0.0464584	+	0.0804683i
$124$	2.80415	−	4.85694i	0.251820	−	0.436166i
$125$	−10.0489			−0.898799
$126$	−5.47608	−	9.48485i	−0.487848	−	0.844977i
$127$	1.42091	+	2.46109i	0.126086	+	0.218387i	0.922157	−	0.386816i	$-0.126425\pi$
$127$	1.42091	+	2.46109i	0.126086	+	0.218387i	−0.796071	+	0.605203i	$0.793092\pi$
$128$	−12.8934	−	22.3320i	−1.13963	−	1.97389i
$129$	−3.21946	+	5.57627i	−0.283458	+	0.490963i
$130$	3.39231	−	5.87565i	0.297525	−	0.515328i
$131$	0.811331	+	1.40527i	0.0708863	+	0.122779i	0.899290	−	0.437353i	$-0.144084\pi$
$131$	0.811331	+	1.40527i	0.0708863	+	0.122779i	−0.828404	+	0.560132i	$0.810751\pi$
$132$	11.3963	+	19.7391i	0.991925	+	1.71806i
$133$	−6.29006	−	10.8947i	−0.545418	−	0.944691i
$134$	20.5251			1.77310
$135$	−0.580820	+	1.00601i	−0.0499891	+	0.0865836i
$136$	13.9937	+	24.2378i	1.19995	+	2.07837i
$137$	18.4343			1.57495			0.787474	−	0.616347i	$-0.211388\pi$
$137$	18.4343			1.57495			0.787474	+	0.616347i	$0.211388\pi$
$138$	4.08514			0.347751
$139$	−6.17503	−	10.6955i	−0.523759	−	0.907178i	−0.999618	−	0.0276556i	$-0.991196\pi$
$139$	−6.17503	−	10.6955i	−0.523759	−	0.907178i	0.475858	−	0.879522i	$-0.342138\pi$
$140$	24.9575			2.10929
$141$	−0.146097	+	0.253048i	−0.0123036	+	0.0213105i
$142$	18.9848			1.59317
$143$	−4.64783	+	8.05028i	−0.388671	+	0.673198i
$144$	−6.74621	+	11.6848i	−0.562184	+	0.973731i
$145$	4.96163	−	8.59379i	0.412041	−	0.713675i
$146$	4.78567	+	8.28903i	0.396065	+	0.686005i
$147$	9.43084			0.777842
$148$	−15.8886	+	28.0534i	−1.30604	+	2.30597i
$149$	−17.8381			−1.46135			−0.730677	−	0.682723i	$-0.760796\pi$
$149$	−17.8381			−1.46135			−0.730677	+	0.682723i	$0.760796\pi$
$150$	4.93177	+	8.54208i	0.402677	+	0.697458i
$151$	4.67734	−	8.10139i	0.380636	−	0.659282i	−0.610517	−	0.792003i	$-0.709038\pi$
$151$	4.67734	−	8.10139i	0.380636	−	0.659282i	0.991153	+	0.132722i	$0.0423716\pi$
$152$	−13.8371	+	23.9666i	−1.12234	+	1.94395i
$153$	1.56932	−	2.71814i	0.126872	−	0.219749i
$154$	−47.0973			−3.79521
$155$	0.614575	−	1.06447i	0.0493638	−	0.0855007i
$156$	−11.4573			−0.917318
$157$	−7.11952	−	12.3314i	−0.568199	−	0.984150i	−0.996744	−	0.0806298i	$-0.974307\pi$
$157$	−7.11952	−	12.3314i	−0.568199	−	0.984150i	0.428545	−	0.903521i	$-0.359026\pi$
$158$	26.8242			2.13401
$159$	−2.19214			−0.173848
$160$	−10.8155	−	18.7330i	−0.855043	−	1.48098i
$161$	−3.06434	+	5.30760i	−0.241504	+	0.418297i
$162$	2.70190			0.212282
$163$	−1.37117	−	2.37493i	−0.107398	−	0.186019i	0.807317	−	0.590117i	$-0.200919\pi$
$163$	−1.37117	−	2.37493i	−0.107398	−	0.186019i	−0.914715	+	0.404099i	$0.867585\pi$
$164$	2.73096	+	4.73016i	0.213252	+	0.369364i
$165$	2.49769	+	4.32613i	0.194445	+	0.336789i
$166$	5.26517	−	9.11953i	0.408656	−	0.707813i
$167$	−3.00746	+	5.20907i	−0.232724	+	0.403090i	−0.958609	−	0.284727i	$-0.908097\pi$
$167$	−3.00746	+	5.20907i	−0.232724	+	0.403090i	0.725885	+	0.687816i	$0.241431\pi$
$168$	−18.0726	−	31.3027i	−1.39433	−	2.41505i
$169$	4.16365	+	7.21166i	0.320281	+	0.554743i
$170$	4.92553	+	8.53127i	0.377771	+	0.654319i
$171$	3.10353			0.237333
$172$	−17.0640	+	29.5558i	−1.30112	+	2.25361i
$173$	−10.5830	−	18.3303i	−0.804611	−	1.39363i	−0.916553	−	0.399912i	$-0.869041\pi$
$173$	−10.5830	−	18.3303i	−0.804611	−	1.39363i	0.111942	−	0.993715i	$-0.464293\pi$
$174$	−23.0809			−1.74976
$175$	−14.7977			−1.11860
$176$	29.0106	+	50.2478i	2.18676	+	3.78757i
$177$	−1.97700			−0.148600
$178$	20.1979	−	34.9838i	1.51390	−	2.62215i
$179$	3.82032			0.285544			0.142772	−	0.989756i	$-0.454398\pi$
$179$	3.82032			0.285544			0.142772	+	0.989756i	$0.454398\pi$
$180$	−3.07851	+	5.33214i	−0.229459	+	0.397434i
$181$	−9.64828	+	16.7113i	−0.717151	+	1.24214i	0.244973	+	0.969530i	$0.421221\pi$
$181$	−9.64828	+	16.7113i	−0.717151	+	1.24214i	−0.962124	+	0.272612i	$0.912112\pi$
$182$	11.8373	−	20.5028i	0.877440	−	1.51977i
$183$	6.98867	+	12.1047i	0.516617	+	0.894808i
$184$	13.4821			0.993915
$185$	−3.48224	+	6.14834i	−0.256019	+	0.452035i
$186$	−2.85893			−0.209627
$187$	−6.74852	−	11.6888i	−0.493501	−	0.854768i
$188$	−0.774357	+	1.34123i	−0.0564758	+	0.0978189i
$189$	−2.02675	+	3.51043i	−0.147424	+	0.255346i
$190$	−4.87043	+	8.43582i	−0.353338	+	0.611999i
$191$	−3.21167			−0.232388			−0.116194	−	0.993227i	$-0.537069\pi$
$191$	−3.21167			−0.232388			−0.116194	+	0.993227i	$0.537069\pi$
$192$	−11.6638	+	20.2023i	−0.841764	+	1.45798i
$193$	−3.10814			−0.223729			−0.111865	−	0.993723i	$-0.535682\pi$
$193$	−3.10814			−0.223729			−0.111865	+	0.993723i	$0.535682\pi$
$194$	14.4607	+	25.0467i	1.03822	+	1.79825i
$195$	−2.51105			−0.179820
$196$	49.9861			3.57043
$197$	1.19070	+	2.06235i	0.0848337	+	0.146936i	0.905320	−	0.424729i	$-0.139631\pi$
$197$	1.19070	+	2.06235i	0.0848337	+	0.146936i	−0.820487	+	0.571666i	$0.806297\pi$
$198$	5.80947	−	10.0623i	0.412861	−	0.715097i
$199$	21.5413			1.52702			0.763511	−	0.645795i	$-0.223474\pi$
$199$	21.5413			1.52702			0.763511	+	0.645795i	$0.223474\pi$
$200$	16.2762	+	28.1913i	1.15090	+	1.99342i
$201$	−3.79827	−	6.57879i	−0.267909	−	0.464032i
$202$	−16.4235	−	28.4464i	−1.15556	−	2.00148i
$203$	17.3134	−	29.9877i	1.21516	−	2.10472i
$204$	8.31784	−	14.4069i	0.582365	−	1.00869i
$205$	0.598533	+	1.03669i	0.0418034	+	0.0724056i
$206$	−11.0983	−	19.2227i	−0.773252	−	1.33931i
$207$	−0.755975	−	1.30939i	−0.0525439	−	0.0910087i
$208$	−29.1658			−2.02228
$209$	6.67302	−	11.5580i	0.461582	−	0.799484i
$210$	−6.36123	−	11.0180i	−0.438967	−	0.760313i
$211$	25.6687			1.76711			0.883554	−	0.468330i	$-0.155144\pi$
$211$	25.6687			1.76711			0.883554	+	0.468330i	$0.155144\pi$
$212$	−11.6189			−0.797992
$213$	−3.51323	−	6.08510i	−0.240723	−	0.416944i
$214$	1.89301			0.129403
$215$	−3.73986	+	6.47762i	−0.255056	+	0.441770i
$216$	8.91704			0.606728
$217$	2.14453	−	3.71444i	0.145580	−	0.252153i
$218$	0.806646	−	1.39715i	0.0546329	−	0.0946270i
$219$	1.77122	−	3.06785i	0.119688	−	0.207306i
$220$	13.2385	+	22.9297i	0.892537	+	1.54592i
$221$	6.78461			0.456382
$222$	16.4345	−	0.135985i	1.10301	−	0.00912672i
$223$	−24.3581			−1.63114			−0.815571	−	0.578657i	$-0.803577\pi$
$223$	−24.3581			−1.63114			−0.815571	+	0.578657i	$0.803577\pi$
$224$	−37.7403	−	65.3682i	−2.52163	−	4.36760i
$225$	1.82530	−	3.16150i	0.121686	−	0.210767i
$226$	19.5005	−	33.7759i	1.29715	−	2.24674i
$227$	−0.250906	+	0.434582i	−0.0166532	+	0.0288442i	−0.874232	−	0.485509i	$-0.838634\pi$
$227$	−0.250906	+	0.434582i	−0.0166532	+	0.0288442i	0.857579	+	0.514353i	$0.171968\pi$
$228$	16.4496			1.08940
$229$	−1.16865	+	2.02416i	−0.0772264	+	0.133760i	−0.902052	−	0.431627i	$-0.857940\pi$
$229$	−1.16865	+	2.02416i	−0.0772264	+	0.133760i	0.824826	+	0.565387i	$0.191273\pi$
$230$	4.74547			0.312907
$231$	8.71559	+	15.0958i	0.573444	+	0.993233i
$232$	−76.1733			−5.00103
$233$	10.2217			0.669648			0.334824	−	0.942281i	$-0.391323\pi$
$233$	10.2217			0.669648			0.334824	+	0.942281i	$0.391323\pi$
$234$	2.92027	+	5.05806i	0.190904	+	0.330656i
$235$	−0.169713	+	0.293951i	−0.0110708	+	0.0191752i
$236$	−10.4787			−0.682102
$237$	−4.96394	−	8.59779i	−0.322442	−	0.558486i
$238$	17.1874	+	29.7695i	1.11410	+	1.92967i
$239$	−7.35564	−	12.7403i	−0.475797	−	0.824104i	0.523819	−	0.851830i	$-0.324507\pi$
$239$	−7.35564	−	12.7403i	−0.475797	−	0.824104i	−0.999616	+	0.0277257i	$0.991173\pi$
$240$	−7.83667	+	13.5735i	−0.505855	+	0.876166i
$241$	−8.38053	+	14.5155i	−0.539837	+	0.935025i	0.459075	+	0.888397i	$0.348181\pi$
$241$	−8.38053	+	14.5155i	−0.539837	+	0.935025i	−0.998912	+	0.0466279i	$0.985152\pi$
$242$	−10.1219	−	17.5316i	−0.650660	−	1.12698i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	37.0419	+	64.1585i	2.37137	+	4.10733i
$245$	10.9552			0.699905
$246$	1.39215	−	2.41128i	0.0887603	−	0.153737i
$247$	3.35435	+	5.80991i	0.213432	+	0.369676i
$248$	−9.43526			−0.599139
$249$	−3.89738			−0.246986
$250$	13.5755	+	23.5135i	0.858593	+	1.48713i
$251$	−8.27613			−0.522385			−0.261192	−	0.965287i	$-0.584116\pi$
$251$	−8.27613			−0.522385			−0.261192	+	0.965287i	$0.584116\pi$
$252$	−10.7423	+	18.6063i	−0.676704	+	1.17208i
$253$	−6.50181			−0.408765
$254$	3.83917	−	6.64964i	0.240891	−	0.417236i
$255$	1.82299	−	3.15750i	0.114160	−	0.197731i
$256$	−11.5091	+	19.9343i	−0.719317	+	1.24589i
$257$	2.82760	+	4.89756i	0.176381	+	0.305501i	0.940638	−	0.339410i	$-0.110228\pi$
$257$	2.82760	+	4.89756i	0.176381	+	0.305501i	−0.764257	+	0.644912i	$0.776894\pi$
$258$	17.3973			1.08311
$259$	−12.1511	+	21.4544i	−0.755034	+	1.33311i
$260$	−13.3093			−0.825406
$261$	4.27122	+	7.39798i	0.264382	+	0.457923i
$262$	2.19214	−	3.79689i	0.135431	−	0.234573i
$263$	3.96366	−	6.86525i	0.244409	−	0.423330i	−0.717556	−	0.696501i	$-0.754739\pi$
$263$	3.96366	−	6.86525i	0.244409	−	0.423330i	0.961965	+	0.273171i	$0.0880726\pi$
$264$	19.1729	−	33.2084i	1.18001	−	2.04384i
$265$	−2.54648			−0.156429
$266$	−16.9951	+	29.4365i	−1.04204	+	1.80486i
$267$	−14.9509			−0.914979
$268$	−20.1319	−	34.8694i	−1.22975	−	2.12999i
$269$	−25.6084			−1.56137			−0.780686	−	0.624924i	$-0.785130\pi$
$269$	−25.6084			−1.56137			−0.780686	+	0.624924i	$0.785130\pi$
$270$	3.13864			0.191012
$271$	−4.04571	−	7.00737i	−0.245759	−	0.425667i	0.716586	−	0.697499i	$-0.245704\pi$
$271$	−4.04571	−	7.00737i	−0.245759	−	0.425667i	−0.962345	+	0.271832i	$0.912371\pi$
$272$	21.1739	−	36.6743i	1.28386	−	2.22371i
$273$	−8.76220			−0.530313
$274$	−24.9039	−	43.1347i	−1.50450	−	2.60586i
$275$	−7.84928	−	13.5954i	−0.473330	−	0.819831i
$276$	−4.00688	−	6.94012i	−0.241186	−	0.417746i
$277$	−1.30701	+	2.26380i	−0.0785304	+	0.136019i	−0.902616	−	0.430446i	$-0.858356\pi$
$277$	−1.30701	+	2.26380i	−0.0785304	+	0.136019i	0.824086	+	0.566465i	$0.191689\pi$
$278$	−16.6843	+	28.8981i	−1.00066	+	1.73319i
$279$	0.529058	+	0.916355i	0.0316739	+	0.0548607i
$280$	−20.9939	−	36.3624i	−1.25462	−	2.17307i
$281$	5.39903	+	9.35140i	0.322079	+	0.557858i	0.980917	−	0.194428i	$-0.0622849\pi$
$281$	5.39903	+	9.35140i	0.322079	+	0.557858i	−0.658838	+	0.752285i	$0.728952\pi$
$282$	0.789481			0.0470129
$283$	2.74880	−	4.76106i	0.163399	−	0.283016i	−0.772686	−	0.634788i	$-0.781088\pi$
$283$	2.74880	−	4.76106i	0.163399	−	0.283016i	0.936086	+	0.351772i	$0.114421\pi$
$284$	−18.6211	−	32.2527i	−1.10496	−	1.91385i
$285$	3.60518			0.213552
$286$	25.1160			1.48514
$287$	2.08856	+	3.61749i	0.123284	+	0.213534i
$288$	18.6211			1.09726
$289$	3.57447	−	6.19116i	0.210263	−	0.364186i
$290$	−26.8117			−1.57444
$291$	5.35204	−	9.27001i	0.313742	−	0.543418i
$292$	9.38798	−	16.2605i	0.549390	−	0.951572i
$293$	3.82300	−	6.62163i	0.223342	−	0.386840i	−0.732479	−	0.680790i	$-0.761637\pi$
$293$	3.82300	−	6.62163i	0.223342	−	0.386840i	0.955821	+	0.293950i	$0.0949700\pi$
$294$	−12.7406	−	22.0674i	−0.743047	−	1.28700i
$295$	−2.29656			−0.133711
$296$	54.2384	−	0.448789i	3.15254	−	0.0260853i
$297$	−4.30028			−0.249528
$298$	24.0984	+	41.7397i	1.39598	+	2.41792i
$299$	1.63415	−	2.83043i	0.0945051	−	0.163688i
$300$	9.67458	−	16.7569i	0.558562	−	0.967458i
$301$	−13.0501	+	22.6034i	−0.752194	+	1.30284i
$302$	−25.2754			−1.45444
$303$	−6.07851	+	10.5283i	−0.349201	+	0.604834i
$304$	41.8741			2.40164
$305$	8.11832	+	14.0613i	0.464854	+	0.805150i
$306$	−8.48030			−0.484787
$307$	−7.18439			−0.410035			−0.205017	−	0.978758i	$-0.565725\pi$
$307$	−7.18439			−0.410035			−0.205017	+	0.978758i	$0.565725\pi$
$308$	46.1951	+	80.0122i	2.63221	+	4.55912i
$309$	−4.10757	+	7.11452i	−0.233671	+	0.404731i
$310$	−3.32104			−0.188623
$311$	−7.66897	−	13.2830i	−0.434868	−	0.753213i	0.562417	−	0.826854i	$-0.309871\pi$
$311$	−7.66897	−	13.2830i	−0.434868	−	0.753213i	−0.997285	+	0.0736409i	$0.976538\pi$
$312$	9.63772	+	16.6930i	0.545628	+	0.945056i
$313$	10.8992	+	18.8779i	0.616059	+	1.06704i	0.990198	+	0.139672i	$0.0446049\pi$
$313$	10.8992	+	18.8779i	0.616059	+	1.06704i	−0.374139	+	0.927373i	$0.622062\pi$
$314$	−19.2363	+	33.3182i	−1.08556	+	1.88025i
$315$	−2.35435	+	4.07786i	−0.132653	+	0.229761i
$316$	−26.3103	−	45.5707i	−1.48007	−	2.56355i
$317$	7.58300	+	13.1341i	0.425904	+	0.737687i	0.996504	−	0.0835405i	$-0.0266228\pi$
$317$	7.58300	+	13.1341i	0.425904	+	0.737687i	−0.570600	+	0.821228i	$0.693289\pi$
$318$	2.96147	+	5.12942i	0.166071	+	0.287644i
$319$	36.7349			2.05676
$320$	−13.5492	+	23.4679i	−0.757422	+	1.31189i
$321$	−0.350310	−	0.606754i	−0.0195524	−	0.0338657i
$322$	16.5591			0.922804
$323$	−9.74085			−0.541995
$324$	−2.65014	−	4.59018i	−0.147230	−	0.255010i
$325$	7.89127			0.437729
$326$	−3.70476	+	6.41683i	−0.205187	+	0.355395i
$327$	−0.597094			−0.0330194
$328$	4.59449	−	7.95789i	0.253688	−	0.439401i
$329$	−0.592205	+	1.02573i	−0.0326493	+	0.0565503i
$330$	6.74852	−	11.6888i	0.371494	−	0.643446i
$331$	4.25870	+	7.37628i	0.234079	+	0.405437i	0.959005	−	0.283390i	$-0.0914592\pi$
$331$	4.25870	+	7.37628i	0.234079	+	0.405437i	−0.724925	+	0.688827i	$0.758126\pi$
$332$	−20.6572			−1.13371
$333$	−3.08486	−	5.24248i	−0.169049	−	0.287286i
$334$	16.2517			0.889254
$335$	−4.41222	−	7.64219i	−0.241065	−	0.417538i
$336$	−27.3457	+	47.3642i	−1.49183	+	2.58393i
$337$	−2.96654	+	5.13820i	−0.161598	+	0.279896i	−0.935442	−	0.353481i	$-0.884998\pi$
$337$	−2.96654	+	5.13820i	−0.161598	+	0.279896i	0.773844	+	0.633376i	$0.218331\pi$
$338$	11.2498	−	19.4852i	0.611908	−	1.05986i
$339$	−14.4346			−0.783982
$340$	9.66234	−	16.7357i	0.524014	−	0.907619i
$341$	4.55019			0.246407
$342$	−4.19271	−	7.26199i	−0.226716	−	0.392684i
$343$	9.85338			0.532033
$344$	57.4161			3.09567
$345$	−0.878172	−	1.52104i	−0.0472792	−	0.0818899i
$346$	−28.5943	+	49.5267i	−1.53724	+	2.66257i
$347$	32.1157			1.72406			0.862031	−	0.506855i	$-0.169192\pi$
$347$	32.1157			1.72406			0.862031	+	0.506855i	$0.169192\pi$
$348$	22.6387	+	39.2114i	1.21356	+	2.10195i
$349$	−11.9514	−	20.7004i	−0.639744	−	1.10807i	−0.985489	−	0.169741i	$-0.945707\pi$
$349$	−11.9514	−	20.7004i	−0.639744	−	1.10807i	0.345744	−	0.938329i	$-0.387626\pi$
$350$	19.9909	+	34.6253i	1.06856	+	1.85080i
$351$	1.08082	−	1.87204i	0.0576899	−	0.0999219i
$352$	40.0380	−	69.3479i	2.13403	−	3.69626i
$353$	−4.17734	−	7.23536i	−0.222337	−	0.385100i	0.733180	−	0.680035i	$-0.238035\pi$
$353$	−4.17734	−	7.23536i	−0.222337	−	0.385100i	−0.955517	+	0.294935i	$0.904702\pi$
$354$	2.67083	+	4.62602i	0.141953	+	0.245870i
$355$	−4.08112	−	7.06870i	−0.216603	−	0.375168i
$356$	−79.2438			−4.19991
$357$	6.36123	−	11.0180i	0.336672	−	0.583133i
$358$	−5.16107	−	8.93923i	−0.272771	−	0.472453i
$359$	−9.62957			−0.508229			−0.254115	−	0.967174i	$-0.581784\pi$
$359$	−9.62957			−0.508229			−0.254115	+	0.967174i	$0.581784\pi$
$360$	10.3584			0.545935
$361$	4.68407	+	8.11304i	0.246530	+	0.427002i
$362$	52.1374			2.74028
$363$	−3.74621	+	6.48862i	−0.196625	+	0.340564i
$364$	−46.4421			−2.43423
$365$	2.05753	−	3.56374i	0.107696	−	0.186535i
$366$	18.8827	−	32.7058i	0.987015	−	1.70956i
$367$	−15.7849	+	27.3403i	−0.823965	+	1.42715i	0.0787419	+	0.996895i	$0.474910\pi$
$367$	−15.7849	+	27.3403i	−0.823965	+	1.42715i	−0.902707	+	0.430255i	$0.858424\pi$
$368$	−10.1999	−	17.6668i	−0.531708	−	0.920946i
$369$	−1.03050			−0.0536455
$370$	19.0910	−	0.157966i	0.992491	−	0.00821225i
$371$	−8.88582			−0.461329
$372$	2.80415	+	4.85694i	0.145389	+	0.251820i
$373$	−2.05983	+	3.56774i	−0.106654	+	0.184730i	−0.914413	−	0.404783i	$-0.867347\pi$
$373$	−2.05983	+	3.56774i	−0.106654	+	0.184730i	0.807759	+	0.589513i	$0.200680\pi$
$374$	−18.2338	+	31.5819i	−0.942850	+	1.63306i
$375$	5.02444	−	8.70258i	0.259461	−	0.449399i
$376$	2.60551			0.134369
$377$	−9.23285	+	15.9918i	−0.475516	+	0.823618i
$378$	10.9522			0.563318
$379$	−13.0498	−	22.6029i	−0.670322	−	1.16103i	−0.977813	−	0.209481i	$-0.932823\pi$
$379$	−13.0498	−	22.6029i	−0.670322	−	1.16103i	0.307491	−	0.951551i	$-0.400511\pi$
$380$	19.1085			0.980244
$381$	−2.84183			−0.145591
$382$	4.33881	+	7.51504i	0.221993	+	0.384503i
$383$	10.7059	−	18.5432i	0.547048	−	0.947515i	−0.451427	−	0.892308i	$-0.649085\pi$
$383$	10.7059	−	18.5432i	0.547048	−	0.947515i	0.998475	−	0.0552072i	$-0.0175819\pi$
$384$	25.7868			1.31593
$385$	10.1244	+	17.5359i	0.515986	+	0.893714i
$386$	4.19895	+	7.27280i	0.213721	+	0.370176i
$387$	−3.21946	−	5.57627i	−0.163654	−	0.283458i
$388$	28.3673	−	49.1337i	1.44013	−	2.49438i
$389$	−0.426061	+	0.737959i	−0.0216022	+	0.0374160i	−0.876624	−	0.481175i	$-0.840210\pi$
$389$	−0.426061	+	0.737959i	−0.0216022	+	0.0374160i	0.855022	+	0.518591i	$0.173543\pi$
$390$	3.39231	+	5.87565i	0.171776	+	0.297525i
$391$	2.37273	+	4.10970i	0.119994	+	0.207836i
$392$	−42.0476	−	72.8285i	−2.12372	−	3.67840i
$393$	−1.62266			−0.0818524
$394$	3.21715	−	5.57227i	0.162078	−	0.280727i
$395$	−5.76631	−	9.98754i	−0.290135	−	0.502528i
$396$	−22.7927			−1.14538
$397$	20.9733			1.05262			0.526310	−	0.850293i	$-0.323575\pi$
$397$	20.9733			1.05262			0.526310	+	0.850293i	$0.323575\pi$
$398$	−29.1012	−	50.4048i	−1.45871	−	2.52657i
$399$	12.5801			0.629794
$400$	24.6277	−	42.6563i	1.23138	−	2.13282i
$401$	32.4291			1.61943			0.809717	−	0.586821i	$-0.199621\pi$
$401$	32.4291			1.61943			0.809717	+	0.586821i	$0.199621\pi$
$402$	−10.2625	+	17.7753i	−0.511849	+	0.886549i
$403$	−1.14363	+	1.98083i	−0.0569684	+	0.0986722i
$404$	−32.2178	+	55.8029i	−1.60290	+	2.77630i
$405$	−0.580820	−	1.00601i	−0.0288612	−	0.0499891i
$406$	−93.5582			−4.64322
$407$	−26.1567	+	0.216430i	−1.29654	+	0.0107281i
$408$	−27.9874			−1.38558
$409$	2.55350	+	4.42279i	0.126262	+	0.218693i	0.922226	−	0.386652i	$-0.126369\pi$
$409$	2.55350	+	4.42279i	0.126262	+	0.218693i	−0.795963	+	0.605345i	$0.793035\pi$
$410$	1.61718	−	2.80104i	0.0798668	−	0.138333i
$411$	−9.21715	+	15.9646i	−0.454649	+	0.787474i
$412$	−21.7713	+	37.7089i	−1.07259	+	1.85779i
$413$	−8.01376			−0.394331
$414$	−2.04257	+	3.53784i	−0.100387	+	0.173875i
$415$	−4.52735			−0.222239
$416$	20.1261	+	34.8594i	0.986763	+	1.70912i
$417$	12.3501			0.604785
$418$	−36.0597			−1.76374
$419$	−17.7983	−	30.8276i	−0.869504	−	1.50603i	−0.862504	−	0.506050i	$-0.831105\pi$
$419$	−17.7983	−	30.8276i	−0.869504	−	1.50603i	−0.00700054	−	0.999975i	$-0.502228\pi$
$420$	−12.4787	+	21.6138i	−0.608900	+	1.05465i
$421$	14.3926			0.701452			0.350726	−	0.936478i	$-0.385935\pi$
$421$	14.3926			0.701452			0.350726	+	0.936478i	$0.385935\pi$
$422$	−34.6772	−	60.0627i	−1.68806	−	2.92381i
$423$	−0.146097	−	0.253048i	−0.00710349	−	0.0123036i
$424$	9.77369	+	16.9285i	0.474652	+	0.822122i
$425$	−5.72895	+	9.92283i	−0.277895	+	0.481328i
$426$	−9.49242	+	16.4414i	−0.459909	+	0.796586i
$427$	28.3286	+	49.0665i	1.37091	+	2.37449i
$428$	−1.85674	−	3.21597i	−0.0897490	−	0.155450i
$429$	−4.64783	−	8.05028i	−0.224399	−	0.388671i
$430$	20.2095			0.974587
$431$	16.9043	−	29.2790i	0.814249	−	1.41032i	−0.0956162	−	0.995418i	$-0.530482\pi$
$431$	16.9043	−	29.2790i	0.814249	−	1.41032i	0.909866	−	0.414903i	$-0.136185\pi$
$432$	−6.74621	−	11.6848i	−0.324577	−	0.562184i
$433$	34.9664			1.68038			0.840190	−	0.542292i	$-0.182443\pi$
$433$	34.9664			1.68038			0.840190	+	0.542292i	$0.182443\pi$
$434$	−11.5886			−0.556273
$435$	4.96163	+	8.59379i	0.237892	+	0.412041i
$436$	−3.16477			−0.151565
$437$	−2.34619	+	4.06372i	−0.112233	+	0.194394i
$438$	−9.57135			−0.457337
$439$	17.0088	−	29.4601i	0.811784	−	1.40605i	−0.0998297	−	0.995005i	$-0.531830\pi$
$439$	17.0088	−	29.4601i	0.811784	−	1.40605i	0.911614	−	0.411047i	$-0.134837\pi$
$440$	22.2720	−	38.5763i	1.06178	−	1.83905i
$441$	−4.71542	+	8.16734i	−0.224544	+	0.388921i
$442$	−9.16568	−	15.8754i	−0.435967	−	0.755117i
$443$	38.5186			1.83008			0.915038	−	0.403368i	$-0.132161\pi$
$443$	38.5186			1.83008			0.915038	+	0.403368i	$0.132161\pi$
$444$	−16.3506	−	27.7866i	−0.775967	−	1.31870i
$445$	−17.3675			−0.823300
$446$	32.9067	+	56.9960i	1.55818	+	2.69884i
$447$	8.91905	−	15.4483i	0.421857	−	0.730677i
$448$	−47.2793	+	81.8901i	−2.23374	+	3.86894i
$449$	−15.0718	+	26.1051i	−0.711282	+	1.23198i	0.253094	+	0.967442i	$0.418552\pi$
$449$	−15.0718	+	26.1051i	−0.711282	+	1.23198i	−0.964376	+	0.264535i	$0.914781\pi$
$450$	−9.86354			−0.464972
$451$	−2.21571	+	3.83773i	−0.104334	+	0.180711i
$452$	−76.5077			−3.59862
$453$	4.67734	+	8.10139i	0.219761	+	0.380636i
$454$	1.35585			0.0636331
$455$	−10.1785			−0.477177
$456$	−13.8371	−	23.9666i	−0.647983	−	1.12234i
$457$	10.7683	−	18.6512i	0.503718	−	0.872465i	−0.496273	−	0.868167i	$-0.665298\pi$
$457$	10.7683	−	18.6512i	0.503718	−	0.872465i	0.999991	−	0.00429850i	$-0.00136826\pi$
$458$	6.31514			0.295087
$459$	1.56932	+	2.71814i	0.0732496	+	0.126872i
$460$	−4.65456	−	8.06193i	−0.217020	−	0.375889i
$461$	13.6926	+	23.7163i	0.637727	+	1.10458i	0.985930	+	0.167157i	$0.0534587\pi$
$461$	13.6926	+	23.7163i	0.637727	+	1.10458i	−0.348203	+	0.937419i	$0.613208\pi$
$462$	23.5487	−	40.7875i	1.09558	−	1.89761i
$463$	7.51109	−	13.0096i	0.349070	−	0.604607i	−0.637014	−	0.770852i	$-0.719831\pi$
$463$	7.51109	−	13.0096i	0.349070	−	0.604607i	0.986085	+	0.166245i	$0.0531641\pi$
$464$	57.6291	+	99.8166i	2.67537	+	4.63387i
$465$	0.614575	+	1.06447i	0.0285002	+	0.0493638i
$466$	−13.8091	−	23.9180i	−0.639693	−	1.10798i
$467$	0.540986			0.0250338			0.0125169	−	0.999922i	$-0.496016\pi$
$467$	0.540986			0.0250338			0.0125169	+	0.999922i	$0.496016\pi$
$468$	5.72865	−	9.92232i	0.264807	−	0.458659i
$469$	−15.3963	−	26.6671i	−0.710933	−	1.23137i
$470$	0.917094			0.0423024
$471$	14.2390			0.656100
$472$	8.81449	+	15.2672i	0.405720	+	0.702728i
$473$	−27.6892			−1.27315
$474$	−13.4121	+	23.2304i	−0.616037	+	1.06701i
$475$	−11.3297			−0.519842
$476$	33.7163	−	58.3984i	1.54539	−	2.67669i
$477$	1.09607	−	1.89845i	0.0501855	−	0.0869239i
$478$	−19.8742	+	34.4232i	−0.909026	+	1.57448i
$479$	−1.18250	−	2.04814i	−0.0540296	−	0.0935821i	0.837746	−	0.546061i	$-0.183873\pi$
$479$	−1.18250	−	2.04814i	−0.0540296	−	0.0935821i	−0.891775	+	0.452479i	$0.850540\pi$
$480$	21.6311			0.987318
$481$	6.47993	−	11.4412i	0.295459	−	0.521672i
$482$	45.2867			2.06275
$483$	−3.06434	−	5.30760i	−0.139432	−	0.241504i
$484$	−19.8560	+	34.3915i	−0.902544	+	1.56325i
$485$	6.21715	−	10.7684i	0.282306	−	0.488969i
$486$	−1.35095	+	2.33992i	−0.0612804	+	0.106141i
$487$	14.3040			0.648176			0.324088	−	0.946027i	$-0.394943\pi$
$487$	14.3040			0.648176			0.324088	+	0.946027i	$0.394943\pi$
$488$	62.3183	−	107.938i	2.82101	−	4.88614i
$489$	2.74233			0.124012
$490$	−14.8000	−	25.6344i	−0.668596	−	1.15804i
$491$	10.2948			0.464596			0.232298	−	0.972645i	$-0.425376\pi$
$491$	10.2948			0.464596			0.232298	+	0.972645i	$0.425376\pi$
$492$	−5.46192			−0.246242
$493$	−13.4058	−	23.2196i	−0.603768	−	1.04576i
$494$	9.06314	−	15.6978i	0.407770	−	0.706278i
$495$	−4.99538			−0.224526
$496$	7.13827	+	12.3638i	0.320518	+	0.555153i
$497$	−14.2409	−	24.6659i	−0.638791	−	1.10642i
$498$	5.26517	+	9.11953i	0.235938	+	0.408656i
$499$	−15.4250	+	26.7169i	−0.690517	+	1.19601i	0.281151	+	0.959663i	$0.409284\pi$
$499$	−15.4250	+	26.7169i	−0.690517	+	1.19601i	−0.971669	+	0.236348i	$0.924050\pi$
$500$	26.6309	−	46.1261i	1.19097	−	2.06282i
$501$	−3.00746	−	5.20907i	−0.134363	−	0.232724i
$502$	11.1807	+	19.3655i	0.499017	+	0.864323i
$503$	10.1654	+	17.6070i	0.453254	+	0.785059i	0.998586	−	0.0531609i	$-0.0169296\pi$
$503$	10.1654	+	17.6070i	0.453254	+	0.785059i	−0.545332	+	0.838220i	$0.683596\pi$
$504$	36.1452			1.61003
$505$	−7.06105	+	12.2301i	−0.314212	+	0.544232i
$506$	8.78363	+	15.2137i	0.390480	+	0.676331i
$507$	−8.32731			−0.369829
$508$	−15.0625			−0.668290
$509$	15.2120	+	26.3479i	0.674258	+	1.16785i	0.976685	+	0.214677i	$0.0688698\pi$
$509$	15.2120	+	26.3479i	0.674258	+	1.16785i	−0.302427	+	0.953173i	$0.597797\pi$
$510$	−9.85106			−0.436212
$511$	7.17965	−	12.4355i	0.317609	−	0.550115i
$512$	10.6192			0.469305
$513$	−1.55176	+	2.68773i	−0.0685120	+	0.118666i
$514$	7.63991	−	13.2327i	0.336982	−	0.583670i
$515$	−4.77152	+	8.26451i	−0.210258	+	0.364178i
$516$	−17.0640	−	29.5558i	−0.751203	−	1.30112i
$517$	−1.25652			−0.0552616
$518$	66.6171	−	0.551215i	2.92699	−	0.0242190i
$519$	21.1660			0.929085
$520$	11.1956	+	19.3913i	0.490958	+	0.850364i
$521$	7.49307	−	12.9784i	0.328277	−	0.568593i	−0.653893	−	0.756587i	$-0.726865\pi$
$521$	7.49307	−	12.9784i	0.328277	−	0.568593i	0.982170	+	0.187994i	$0.0601986\pi$
$522$	11.5404	−	19.9886i	0.505111	−	0.874878i
$523$	17.9189	−	31.0365i	0.783541	−	1.35713i	−0.146326	−	0.989236i	$-0.546745\pi$
$523$	17.9189	−	31.0365i	0.783541	−	1.35713i	0.929867	−	0.367896i	$-0.119922\pi$
$524$	−8.60056			−0.375717
$525$	7.39883	−	12.8151i	0.322911	−	0.559299i
$526$	−21.4188			−0.933905
$527$	−1.66052	−	2.87611i	−0.0723335	−	0.125285i
$528$	−58.0212			−2.52505
$529$	−20.7140			−0.900609
$530$	3.44017	+	5.95854i	0.149431	+	0.258822i
$531$	0.988500	−	1.71213i	0.0428972	−	0.0743002i
$532$	66.6782			2.89087
$533$	−1.11378	−	1.92913i	−0.0482432	−	0.0835597i
$534$	20.1979	+	34.9838i	0.874049	+	1.51390i
$535$	−0.406934	−	0.704831i	−0.0175933	−	0.0304725i
$536$	−33.8693	+	58.6633i	−1.46293	+	2.53387i
$537$	−1.91016	+	3.30849i	−0.0824295	+	0.142772i
$538$	34.5957	+	59.9215i	1.49153	+	2.58340i
$539$	20.2776	+	35.1219i	0.873419	+	1.51281i
$540$	−3.07851	−	5.33214i	−0.132478	−	0.229459i
$541$	−43.0453			−1.85066			−0.925332	−	0.379158i	$-0.876214\pi$
$541$	−43.0453			−1.85066			−0.925332	+	0.379158i	$0.876214\pi$
$542$	−10.9311	+	18.9332i	−0.469531	+	0.813252i
$543$	−9.64828	−	16.7113i	−0.414047	−	0.717151i
$544$	−58.4450			−2.50581
$545$	−0.693609			−0.0297110
$546$	11.8373	+	20.5028i	0.506590	+	0.877440i
$547$	−9.54873			−0.408274			−0.204137	−	0.978942i	$-0.565439\pi$
$547$	−9.54873			−0.408274			−0.204137	+	0.978942i	$0.565439\pi$
$548$	−48.8535	+	84.6167i	−2.08692	+	3.61465i
$549$	−13.9773			−0.596538
$550$	−21.2080	+	36.7333i	−0.904312	+	1.56632i
$551$	13.2559	−	22.9598i	0.564718	−	0.978121i
$552$	−6.74106	+	11.6759i	−0.286919	+	0.496958i
$553$	−20.1213	−	34.8511i	−0.855645	−	1.48202i
$554$	7.06281			0.300070
$555$	−3.58350	−	6.08988i	−0.152111	−	0.258501i
$556$	65.4588			2.77607
$557$	−2.28644	−	3.96023i	−0.0968796	−	0.167800i	0.813512	−	0.581548i	$-0.197553\pi$
$557$	−2.28644	−	3.96023i	−0.0968796	−	0.167800i	−0.910392	+	0.413748i	$0.864220\pi$
$558$	1.42946	−	2.47590i	0.0605140	−	0.104813i
$559$	6.95932	−	12.0539i	0.294348	−	0.509825i
$560$	−31.7659	+	55.0202i	−1.34236	+	2.32503i
$561$	13.4970			0.569845
$562$	14.5877	−	25.2666i	0.615343	−	1.06581i
$563$	29.1633			1.22909			0.614543	−	0.788883i	$-0.289340\pi$
$563$	29.1633			1.22909			0.614543	+	0.788883i	$0.289340\pi$
$564$	−0.774357	−	1.34123i	−0.0326063	−	0.0564758i
$565$	−16.7679			−0.705430
$566$	−14.8540			−0.624359
$567$	−2.02675	−	3.51043i	−0.0851154	−	0.147424i
$568$	−31.3277	+	54.2611i	−1.31448	+	2.27674i
$569$	−21.8948			−0.917876			−0.458938	−	0.888468i	$-0.651770\pi$
$569$	−21.8948			−0.917876			−0.458938	+	0.888468i	$0.651770\pi$
$570$	−4.87043	−	8.43582i	−0.204000	−	0.353338i
$571$	5.44391	+	9.42914i	0.227821	+	0.394597i	0.957162	−	0.289553i	$-0.0935067\pi$
$571$	5.44391	+	9.42914i	0.227821	+	0.394597i	−0.729341	+	0.684150i	$0.760173\pi$
$572$	−24.6348	−	42.6687i	−1.03003	−	1.78407i
$573$	1.60583	−	2.78139i	0.0670847	−	0.116194i
$574$	5.64308	−	9.77410i	0.235538	−	0.407963i
$575$	2.75976	+	4.78004i	0.115090	+	0.199341i
$576$	−11.6638	−	20.2023i	−0.485993	−	0.841764i
$577$	19.5683	+	33.8932i	0.814637	+	1.41099i	0.909588	+	0.415511i	$0.136397\pi$
$577$	19.5683	+	33.8932i	0.814637	+	1.41099i	−0.0949506	+	0.995482i	$0.530269\pi$
$578$	−19.3157			−0.803429
$579$	1.55407	−	2.69173i	0.0645850	−	0.111865i
$580$	26.2980	+	45.5495i	1.09197	+	1.89134i
$581$	−15.7980			−0.655411
$582$	−28.9214			−1.19883
$583$	−4.71340	−	8.16385i	−0.195209	−	0.338112i
$584$	−31.5881			−1.30713
$585$	1.25552	−	2.17463i	0.0519096	−	0.0899100i
$586$	−20.6588			−0.853405
$587$	0.876903	−	1.51884i	0.0361937	−	0.0626892i	−0.847361	−	0.531017i	$-0.821810\pi$
$587$	0.876903	−	1.51884i	0.0361937	−	0.0626892i	0.883555	+	0.468328i	$0.155143\pi$
$588$	−24.9930	+	43.2892i	−1.03070	+	1.78522i
$589$	1.64194	−	2.84393i	0.0676551	−	0.117182i
$590$	3.10255	+	5.37377i	0.127730	+	0.221235i
$591$	−2.38140			−0.0979576
$592$	−41.6223	−	70.7338i	−1.71066	−	2.90714i
$593$	−25.9327			−1.06493			−0.532464	−	0.846453i	$-0.678734\pi$
$593$	−25.9327			−1.06493			−0.532464	+	0.846453i	$0.678734\pi$
$594$	5.80947	+	10.0623i	0.238366	+	0.412861i
$595$	7.38947	−	12.7989i	0.302939	−	0.524705i
$596$	47.2735	−	81.8801i	1.93640	−	3.35394i
$597$	−10.7706	+	18.6553i	−0.440813	+	0.763511i
$598$	−8.83061			−0.361111
$599$	−2.37549	+	4.11448i	−0.0970601	+	0.168113i	−0.910467	−	0.413583i	$-0.864277\pi$
$599$	−2.37549	+	4.11448i	−0.0970601	+	0.168113i	0.813406	+	0.581696i	$0.197611\pi$
$600$	−32.5525			−1.32895
$601$	1.50462	+	2.60608i	0.0613747	+	0.106304i	0.895080	−	0.445905i	$-0.147118\pi$
$601$	1.50462	+	2.60608i	0.0613747	+	0.106304i	−0.833705	+	0.552209i	$0.813785\pi$
$602$	70.5201			2.87418
$603$	7.59653			0.309355
$604$	24.7912	+	42.9396i	1.00874	+	1.74719i
$605$	−4.35175	+	7.53745i	−0.176924	+	0.306441i
$606$	32.8471			1.33432
$607$	2.79797	+	4.84623i	0.113566	+	0.196702i	0.917206	−	0.398414i	$-0.130439\pi$
$607$	2.79797	+	4.84623i	0.113566	+	0.196702i	−0.803640	+	0.595116i	$0.797106\pi$
$608$	−28.8956	−	50.0486i	−1.17187	−	2.02974i
$609$	17.3134	+	29.9877i	0.701574	+	1.21516i
$610$	21.9349	−	37.9924i	0.888119	−	1.53827i
$611$	0.315810	−	0.546999i	0.0127763	−	0.0221292i
$612$	8.31784	+	14.4069i	0.336229	+	0.582365i
$613$	6.63991	+	11.5007i	0.268184	+	0.464508i	0.968393	−	0.249430i	$-0.0802433\pi$
$613$	6.63991	+	11.5007i	0.268184	+	0.464508i	−0.700209	+	0.713938i	$0.746910\pi$
$614$	9.70576	+	16.8109i	0.391693	+	0.678432i
$615$	−1.19707			−0.0482704
$616$	77.7172	−	134.610i	3.13132	−	5.42360i
$617$	2.45573	+	4.25346i	0.0988641	+	0.171238i	0.911215	−	0.411932i	$-0.135146\pi$
$617$	2.45573	+	4.25346i	0.0988641	+	0.171238i	−0.812351	+	0.583169i	$0.801812\pi$
$618$	22.1965			0.892874
$619$	−31.0601			−1.24841			−0.624205	−	0.781260i	$-0.714577\pi$
$619$	−31.0601			−1.24841			−0.624205	+	0.781260i	$0.714577\pi$
$620$	3.25742	+	5.64202i	0.130821	+	0.226589i
$621$	1.51195			0.0606725
$622$	−20.7208	+	35.8895i	−0.830829	+	1.43904i
$623$	−60.6033			−2.42802
$624$	14.5829	−	25.2583i	0.583782	−	1.01114i
$625$	−3.28989	+	5.69825i	−0.131595	+	0.227930i
$626$	29.4486	−	51.0064i	1.17700	−	2.03863i
$627$	6.67302	+	11.5580i	0.266495	+	0.461582i
$628$	75.4709			3.01162
$629$	9.68228	+	16.4543i	0.386058	+	0.656075i
$630$	12.7225			0.506875
$631$	−3.27708	−	5.67607i	−0.130458	−	0.225961i	0.793395	−	0.608707i	$-0.208312\pi$
$631$	−3.27708	−	5.67607i	−0.130458	−	0.225961i	−0.923853	+	0.382747i	$0.874978\pi$
$632$	−44.2636	+	76.6668i	−1.76071	+	3.04964i
$633$	−12.8344	+	22.2298i	−0.510120	+	0.883554i
$634$	20.4885	−	35.4872i	0.813704	−	1.40938i
$635$	−3.30118			−0.131003
$636$	5.80947	−	10.0623i	0.230361	−	0.398996i
$637$	−20.3861			−0.807726
$638$	−49.6271	−	85.9567i	−1.96476	−	3.40306i
$639$	7.02647			0.277963
$640$	29.9550			1.18408
$641$	8.51682	+	14.7516i	0.336394	+	0.582652i	0.983752	−	0.179535i	$-0.0574593\pi$
$641$	8.51682	+	14.7516i	0.336394	+	0.582652i	−0.647358	+	0.762186i	$0.724126\pi$
$642$	−0.946503	+	1.63939i	−0.0373555	+	0.0647016i
$643$	−30.3227			−1.19581			−0.597906	−	0.801566i	$-0.704000\pi$
$643$	−30.3227			−1.19581			−0.597906	+	0.801566i	$0.704000\pi$
$644$	−16.2419	−	28.1318i	−0.640020	−	1.10855i
$645$	−3.73986	−	6.47762i	−0.147257	−	0.255056i
$646$	13.1594	+	22.7928i	0.517750	+	0.896770i
$647$	12.4047	−	21.4856i	0.487680	−	0.844686i	−0.512220	−	0.858854i	$-0.671177\pi$
$647$	12.4047	−	21.4856i	0.487680	−	0.844686i	0.999900	+	0.0141680i	$0.00450997\pi$
$648$	−4.45852	+	7.72238i	−0.175147	+	0.303364i
$649$	−4.25083	−	7.36265i	−0.166860	−	0.289009i
$650$	−10.6607	−	18.4649i	−0.418148	−	0.724253i
$651$	2.14453	+	3.71444i	0.0840509	+	0.145580i
$652$	14.5351			0.569239
$653$	−6.12796	+	10.6139i	−0.239806	+	0.415356i	−0.960658	−	0.277733i	$-0.910417\pi$
$653$	−6.12796	+	10.6139i	−0.239806	+	0.415356i	0.720853	+	0.693088i	$0.243750\pi$
$654$	0.806646	+	1.39715i	0.0315423	+	0.0546329i
$655$	−1.88495			−0.0736511
$656$	−13.9039			−0.542856
$657$	1.77122	+	3.06785i	0.0691020	+	0.119688i
$658$	3.20016			0.124755
$659$	−14.7993	+	25.6331i	−0.576497	+	0.998522i	0.419380	+	0.907811i	$0.362247\pi$
$659$	−14.7993	+	25.6331i	−0.576497	+	0.998522i	−0.995877	+	0.0907116i	$0.971086\pi$
$660$	−26.4769			−1.03061
$661$	13.0331	−	22.5741i	0.506931	−	0.878030i	−0.493037	−	0.870008i	$-0.664113\pi$
$661$	13.0331	−	22.5741i	0.506931	−	0.878030i	0.999968	−	0.00802139i	$-0.00255331\pi$
$662$	11.5066	−	19.9300i	0.447216	−	0.774601i
$663$	−3.39231	+	5.87565i	−0.131746	+	0.228191i
$664$	17.3765	+	30.0970i	0.674340	+	1.16799i
$665$	14.6136			0.566691
$666$	−8.09947	+	14.3007i	−0.313848	+	0.554139i
$667$	−12.9158			−0.500100
$668$	−15.9404	−	27.6095i	−0.616751	−	1.06824i
$669$	12.1791	−	21.0948i	0.470870	−	0.815571i
$670$	−11.9214	+	20.6485i	−0.460564	+	0.797720i
$671$	−30.0532	+	52.0538i	−1.16019	+	2.00951i
$672$	75.4807			2.91173
$673$	−12.1666	+	21.0731i	−0.468987	+	0.812310i	−0.999372	−	0.0354474i	$-0.988714\pi$
$673$	−12.1666	+	21.0731i	−0.468987	+	0.812310i	0.530384	+	0.847757i	$0.322048\pi$
$674$	16.0306			0.617476
$675$	1.82530	+	3.16150i	0.0702557	+	0.121686i
$676$	−44.1371			−1.69758
$677$	36.2092			1.39163			0.695817	−	0.718219i	$-0.255043\pi$
$677$	36.2092			1.39163			0.695817	+	0.718219i	$0.255043\pi$
$678$	19.5005	+	33.7759i	0.748912	+	1.29715i
$679$	21.6945	−	37.5760i	0.832558	−	1.44203i
$680$	−32.5113			−1.24675
$681$	−0.250906	−	0.434582i	−0.00961474	−	0.0166532i
$682$	−6.14709	−	10.6471i	−0.235384	−	0.407698i
$683$	19.4874	+	33.7532i	0.745666	+	1.29153i	0.949883	+	0.312606i	$0.101202\pi$
$683$	19.4874	+	33.7532i	0.745666	+	1.29153i	−0.204217	+	0.978926i	$0.565465\pi$
$684$	−8.22478	+	14.2457i	−0.314482	+	0.544699i
$685$	−10.7070	+	18.5451i	−0.409094	+	0.708572i
$686$	−13.3114	−	23.0561i	−0.508233	−	0.880286i
$687$	−1.16865	−	2.02416i	−0.0445867	−	0.0772264i
$688$	−43.4383	−	75.2374i	−1.65607	−	2.86840i
$689$	4.73861			0.180527
$690$	−2.37273	+	4.10970i	−0.0903285	+	0.156453i
$691$	−4.80239	−	8.31798i	−0.182691	−	0.316431i	0.760105	−	0.649801i	$-0.225148\pi$
$691$	−4.80239	−	8.31798i	−0.182691	−	0.316431i	−0.942796	+	0.333370i	$0.891814\pi$
$692$	112.186			4.26466
$693$	−17.4312			−0.662156
$694$	−43.3868	−	75.1481i	−1.64694	−	2.85258i
$695$	14.3463			0.544187
$696$	38.0867	−	65.9681i	1.44367	−	2.50051i
$697$	3.23436			0.122510
$698$	−32.2916	+	55.9306i	−1.22225	+	2.11700i
$699$	−5.11087	+	8.85228i	−0.193311	+	0.334824i
$700$	39.2159	−	67.9239i	1.48222	−	2.56728i
$701$	−1.63221	−	2.82707i	−0.0616477	−	0.106777i	0.833554	−	0.552437i	$-0.186302\pi$
$701$	−1.63221	−	2.82707i	−0.0616477	−	0.106777i	−0.895202	+	0.445661i	$0.852969\pi$
$702$	−5.84054			−0.220437
$703$	−9.30341	+	16.4264i	−0.350885	+	0.619532i
$704$	−100.315			−3.78078
$705$	−0.169713	−	0.293951i	−0.00639174	−	0.0110708i
$706$	−11.2868	+	19.5493i	−0.424783	+	0.735746i
$707$	−24.6392	+	42.6764i	−0.926653	+	1.60501i
$708$	5.23933	−	9.07478i	0.196906	−	0.341051i
$709$	40.4153			1.51783			0.758915	−	0.651190i	$-0.225730\pi$
$709$	40.4153			1.51783			0.758915	+	0.651190i	$0.225730\pi$
$710$	−11.0268	+	19.0989i	−0.413828	+	0.716770i
$711$	9.92787			0.372324
$712$	66.6588	+	115.456i	2.49814	+	4.32691i
$713$	−1.59982			−0.0599137
$714$	−34.3749			−1.28645
$715$	−5.39911	−	9.35153i	−0.201915	−	0.349727i
$716$	−10.1244	+	17.5359i	−0.378366	+	0.655349i
$717$	14.7113			0.549403
$718$	13.0091	+	22.5324i	0.485495	+	0.840901i
$719$	−0.258299	−	0.447388i	−0.00963294	−	0.0166847i	0.861169	−	0.508319i	$-0.169733\pi$
$719$	−0.258299	−	0.447388i	−0.00963294	−	0.0166847i	−0.870802	+	0.491634i	$0.836400\pi$
$720$	−7.83667	−	13.5735i	−0.292055	−	0.505855i
$721$	−16.6500	+	28.8387i	−0.620079	+	1.07401i
$722$	12.6559	−	21.9206i	0.471004	−	0.815802i
$723$	−8.38053	−	14.5155i	−0.311675	−	0.539837i
$724$	−51.1386	−	88.5747i	−1.90055	−	3.29185i
$725$	−15.5925	−	27.0070i	−0.579091	−	1.00301i
$726$	20.2438			0.751318
$727$	−6.85052	+	11.8654i	−0.254072	+	0.440065i	−0.964643	−	0.263560i	$-0.915103\pi$
$727$	−6.85052	+	11.8654i	−0.254072	+	0.440065i	0.710571	+	0.703625i	$0.248437\pi$
$728$	39.0665	+	67.6651i	1.44790	+	2.50784i
$729$	1.00000			0.0370370
$730$	−11.1185			−0.411513
$731$	10.1047	+	17.5019i	0.373737	+	0.647331i
$732$	−74.0838			−2.73822
$733$	14.6226	−	25.3271i	0.540099	−	0.935478i	−0.458799	−	0.888540i	$-0.651720\pi$
$733$	14.6226	−	25.3271i	0.540099	−	0.935478i	0.998898	−	0.0469382i	$-0.0149464\pi$
$734$	85.2986			3.14843
$735$	−5.47762	+	9.48752i	−0.202045	+	0.349952i
$736$	−14.0771	+	24.3823i	−0.518889	+	0.898743i
$737$	16.3336	−	28.2907i	0.601656	−	1.04210i
$738$	1.39215	+	2.41128i	0.0512458	+	0.0887603i
$739$	16.8170			0.618625			0.309312	−	0.950961i	$-0.399901\pi$
$739$	16.8170			0.618625			0.309312	+	0.950961i	$0.399901\pi$
$740$	−18.9936	−	32.2781i	−0.698218	−	1.18657i
$741$	−6.70871			−0.246450
$742$	12.0043	+	20.7921i	0.440692	+	0.763301i
$743$	−19.1246	+	33.1249i	−0.701615	+	1.21523i	0.266284	+	0.963895i	$0.414204\pi$
$743$	−19.1246	+	33.1249i	−0.701615	+	1.21523i	−0.967899	+	0.251338i	$0.919129\pi$
$744$	4.71763	−	8.17117i	0.172957	−	0.299570i
$745$	10.3607	−	17.9453i	0.379588	−	0.657466i
$746$	11.1309			0.407533
$747$	1.94869	−	3.37523i	0.0712988	−	0.123493i
$748$	71.5381			2.61569
$749$	−1.41998	−	2.45948i	−0.0518849	−	0.0898673i
$750$	−27.1511			−0.991418
$751$	−32.3774			−1.18147			−0.590735	−	0.806866i	$-0.701162\pi$
$751$	−32.3774			−1.18147			−0.590735	+	0.806866i	$0.701162\pi$
$752$	−1.97121	−	3.41423i	−0.0718825	−	0.124504i
$753$	4.13807	−	7.16734i	0.150799	−	0.261192i
$754$	49.8925			1.81698
$755$	5.43339	+	9.41090i	0.197741	+	0.342498i
$756$	−10.7423	−	18.6063i	−0.390695	−	0.676704i
$757$	−1.26838	−	2.19689i	−0.0460999	−	0.0798474i	0.842055	−	0.539392i	$-0.181346\pi$
$757$	−1.26838	−	2.19689i	−0.0460999	−	0.0798474i	−0.888155	+	0.459545i	$0.848013\pi$
$758$	−35.2592	+	61.0708i	−1.28067	+	2.21819i
$759$	3.25091	−	5.63073i	0.118000	−	0.204383i
$760$	−16.0738	−	27.8406i	−0.583057	−	1.00988i
$761$	−18.3073	−	31.7092i	−0.663640	−	1.14946i	−0.979652	−	0.200703i	$-0.935677\pi$
$761$	−18.3073	−	31.7092i	−0.663640	−	1.14946i	0.316012	−	0.948755i	$-0.397656\pi$
$762$	3.83917	+	6.64964i	0.139079	+	0.240891i
$763$	−2.42032			−0.0876215
$764$	8.51138	−	14.7421i	0.307931	−	0.533352i
$765$	1.82299	+	3.15750i	0.0659102	+	0.114160i
$766$	−57.8529			−2.09031
$767$	4.27356			0.154309
$768$	−11.5091	−	19.9343i	−0.415298	−	0.719317i
$769$	42.2855			1.52485			0.762426	−	0.647075i	$-0.224008\pi$
$769$	42.2855			1.52485			0.762426	+	0.647075i	$0.224008\pi$
$770$	27.3551	−	47.3804i	0.985809	−	1.70747i
$771$	−5.65521			−0.203667
$772$	8.23702	−	14.2669i	0.296457	−	0.513478i
$773$	10.2712	−	17.7903i	0.369430	−	0.639872i	−0.620046	−	0.784565i	$-0.712886\pi$
$773$	10.2712	−	17.7903i	0.369430	−	0.639872i	0.989477	+	0.144693i	$0.0462195\pi$
$774$	−8.69867	+	15.0665i	−0.312667	+	0.541556i
$775$	−1.93137	−	3.34524i	−0.0693770	−	0.120164i
$776$	−95.4488			−3.42641
$777$	−12.5045	−	21.2504i	−0.448596	−	0.762353i
$778$	2.30235			0.0825433
$779$	1.59909	+	2.76970i	0.0572932	+	0.0992347i
$780$	6.65463	−	11.5262i	0.238274	−	0.412703i
$781$	15.1079	−	26.1676i	0.540603	−	0.936352i
$782$	6.41090	−	11.1040i	0.229253	−	0.397078i
$783$	−8.54245			−0.305282
$784$	−63.6224	+	110.197i	−2.27223	+	3.93561i
$785$	16.5406			0.590361
$786$	2.19214	+	3.79689i	0.0781909	+	0.135431i
$787$	−40.9843			−1.46093			−0.730466	−	0.682949i	$-0.760697\pi$
$787$	−40.9843			−1.46093			−0.730466	+	0.682949i	$0.760697\pi$
$788$	−12.6221			−0.449643
$789$	3.96366	+	6.86525i	0.141110	+	0.244409i
$790$	−15.5800	+	26.9854i	−0.554312	+	0.960096i
$791$	−58.5108			−2.08040
$792$	19.1729	+	33.2084i	0.681279	+	1.18001i
$793$	−15.1070	−	26.1661i	−0.536465	−	0.929185i
$794$	−28.3339	−	49.0758i	−1.00553	−	1.74164i
$795$	1.27324	−	2.20531i	0.0451571	−	0.0782144i
$796$	−57.0875	+	98.8784i	−2.02341	+	3.50465i
$797$	−18.4033	−	31.8754i	−0.651877	−	1.12908i	−0.982667	−	0.185380i	$-0.940648\pi$
$797$	−18.4033	−	31.8754i	−0.651877	−	1.12908i	0.330790	−	0.943705i	$-0.392685\pi$
$798$	−16.9951	−	29.4365i	−0.601622	−	1.04204i
$799$	0.458547	+	0.794226i	0.0162222	+	0.0280977i
$800$	−67.9781			−2.40339
$801$	7.47544	−	12.9478i	0.264132	−	0.457489i
$802$	−43.8102	−	75.8815i	−1.54699	−	2.67947i
$803$	15.2335			0.537579
$804$	40.2638			1.41999
$805$	−3.55967	−	6.16552i	−0.125462	−	0.217306i
$806$	6.17997			0.217680
$807$	12.8042	−	22.1775i	0.450729	−	0.780686i
$808$	108.405			3.81366
$809$	−8.50519	+	14.7314i	−0.299026	+	0.517929i	−0.975913	−	0.218158i	$-0.929995\pi$
$809$	−8.50519	+	14.7314i	−0.299026	+	0.517929i	0.676887	+	0.736087i	$0.263329\pi$
$810$	−1.56932	+	2.71814i	−0.0551403	+	0.0955058i
$811$	15.1309	−	26.2075i	0.531318	−	0.920269i	−0.468014	−	0.883721i	$-0.655030\pi$
$811$	15.1309	−	26.2075i	0.531318	−	0.920269i	0.999332	−	0.0365481i	$-0.0116362\pi$
$812$	91.7658	+	158.943i	3.22035	+	5.57781i
$813$	8.09141			0.283778
$814$	35.8429	+	60.9121i	1.25629	+	2.13497i
$815$	3.18560			0.111587
$816$	21.1739	+	36.6743i	0.741236	+	1.28386i
$817$	−9.99168	+	17.3061i	−0.349565	+	0.605464i
$818$	6.89930	−	11.9499i	0.241228	−	0.417820i
$819$	4.38110	−	7.58829i	0.153088	−	0.265156i
$820$	−6.34479			−0.221570
$821$	−16.4200	+	28.4402i	−0.573061	+	0.992571i	0.423188	+	0.906042i	$0.360911\pi$
$821$	−16.4200	+	28.4402i	−0.573061	+	0.992571i	−0.996249	+	0.0865293i	$0.972422\pi$
$822$	49.8077			1.73724
$823$	16.1055	+	27.8955i	0.561401	+	0.972376i	0.997375	+	0.0724160i	$0.0230709\pi$
$823$	16.1055	+	27.8955i	0.561401	+	0.972376i	−0.435973	+	0.899960i	$0.643596\pi$
$824$	73.2547			2.55195
$825$	15.6986			0.546554
$826$	10.8262	+	18.7515i	0.376692	+	0.652449i
$827$	6.75134	−	11.6937i	0.234767	−	0.406629i	−0.724438	−	0.689340i	$-0.757901\pi$
$827$	6.75134	−	11.6937i	0.234767	−	0.406629i	0.959205	+	0.282711i	$0.0912339\pi$
$828$	8.01376			0.278498
$829$	25.1703	+	43.5963i	0.874202	+	1.51416i	0.857611	+	0.514300i	$0.171948\pi$
$829$	25.1703	+	43.5963i	0.874202	+	1.51416i	0.0165912	+	0.999862i	$0.494719\pi$
$830$	6.11623	+	10.5936i	0.212297	+	0.367710i
$831$	−1.30701	−	2.26380i	−0.0453396	−	0.0785304i
$832$	25.2130	−	43.6702i	0.874103	−	1.51399i
$833$	14.8000	−	25.6344i	0.512790	−	0.888178i
$834$	−16.6843	−	28.8981i	−0.577731	−	1.00066i
$835$	−3.49358	−	6.05106i	−0.120900	−	0.209406i
$836$	35.3689	+	61.2607i	1.22326	+	2.11874i
$837$	−1.05812			−0.0365738
$838$	−48.0893	+	83.2931i	−1.66122	+	2.87731i
$839$	12.5391	+	21.7183i	0.432897	+	0.749799i	0.997121	−	0.0758221i	$-0.0241581\pi$
$839$	12.5391	+	21.7183i	0.432897	+	0.749799i	−0.564225	+	0.825621i	$0.690825\pi$
$840$	41.9877			1.44871
$841$	43.9734			1.51632
$842$	−19.4437	−	33.6775i	−0.670074	−	1.16060i
$843$	−10.7981			−0.371905
$844$	−68.0257	+	117.824i	−2.34154	+	4.05567i
$845$	−9.67334			−0.332773
$846$	−0.394741	+	0.683711i	−0.0135715	+	0.0235065i
$847$	−15.1852	+	26.3016i	−0.521771	+	0.903734i
$848$	14.7886	−	25.6146i	0.507843	−	0.879610i
$849$	2.74880	+	4.76106i	0.0943385	+	0.163399i
$850$	30.9581			1.06185
$851$	9.19652	−	0.0760955i	0.315253	−	0.00260852i
$852$	37.2423			1.27590
$853$	−13.4170	−	23.2388i	−0.459388	−	0.795683i	0.539541	−	0.841959i	$-0.318598\pi$
$853$	−13.4170	−	23.2388i	−0.459388	−	0.795683i	−0.998929	+	0.0462765i	$0.985264\pi$
$854$	76.5410	−	132.573i	2.61918	−	4.53655i
$855$	−1.80259	+	3.12218i	−0.0616473	+	0.106776i
$856$	−3.12373	+	5.41045i	−0.106767	+	0.184926i
$857$	−26.4536			−0.903637			−0.451819	−	0.892110i	$-0.649225\pi$
$857$	−26.4536			−0.903637			−0.451819	+	0.892110i	$0.649225\pi$
$858$	−12.5580	+	21.7511i	−0.428723	+	0.742570i
$859$	−9.76797			−0.333279			−0.166639	−	0.986018i	$-0.553292\pi$
$859$	−9.76797			−0.333279			−0.166639	+	0.986018i	$0.553292\pi$
$860$	−19.8223	−	34.3332i	−0.675935	−	1.17075i
$861$	−4.17711			−0.142356
$862$	−91.3473			−3.11130
$863$	−4.83123	−	8.36793i	−0.164457	−	0.284848i	0.772005	−	0.635616i	$-0.219254\pi$
$863$	−4.83123	−	8.36793i	−0.164457	−	0.284848i	−0.936462	+	0.350768i	$0.885920\pi$
$864$	−9.31056	+	16.1264i	−0.316752	+	0.548630i
$865$	24.5873			0.835993
$866$	−47.2380	−	81.8186i	−1.60521	−	2.78031i
$867$	3.57447	+	6.19116i	0.121395	+	0.210263i
$868$	11.3666	+	19.6876i	0.385809	+	0.668240i
$869$	21.3463	−	36.9729i	0.724124	−	1.25422i
$870$	13.4058	−	23.2196i	0.454500	−	0.787218i
$871$	8.21049	+	14.2210i	0.278202	+	0.481860i
$872$	2.66216	+	4.61099i	0.0901520	+	0.156148i
$873$	5.35204	+	9.27001i	0.181139	+	0.313742i
$874$	12.6783			0.428852
$875$	20.3665	−	35.2759i	0.688515	−	1.19254i
$876$	9.38798	+	16.2605i	0.317191	+	0.549390i
$877$	16.8564			0.569200			0.284600	−	0.958646i	$-0.408139\pi$
$877$	16.8564			0.569200			0.284600	+	0.958646i	$0.408139\pi$
$878$	−91.9121			−3.10188
$879$	3.82300	+	6.62163i	0.128947	+	0.223342i
$880$	−67.3998			−2.27205
$881$	20.7076	−	35.8667i	0.697658	−	1.20838i	−0.271618	−	0.962405i	$-0.587559\pi$
$881$	20.7076	−	35.8667i	0.697658	−	1.20838i	0.969276	−	0.245975i	$-0.0791080\pi$
$882$	25.4812			0.857997
$883$	7.95524	−	13.7789i	0.267715	−	0.463696i	−0.700556	−	0.713597i	$-0.747065\pi$
$883$	7.95524	−	13.7789i	0.267715	−	0.463696i	0.968271	+	0.249901i	$0.0803980\pi$
$884$	−17.9802	+	31.1426i	−0.604739	+	1.04744i
$885$	1.14828	−	1.98888i	0.0385991	−	0.0668555i
$886$	−52.0368	−	90.1304i	−1.74821	−	3.02799i
$887$	−12.4844			−0.419184			−0.209592	−	0.977789i	$-0.567214\pi$
$887$	−12.4844			−0.419184			−0.209592	+	0.977789i	$0.567214\pi$
$888$	−26.7305	+	47.1962i	−0.897018	+	1.58380i
$889$	−11.5193			−0.386346
$890$	23.4627	+	40.6386i	0.786472	+	1.36221i
$891$	2.15014	−	3.72415i	0.0720324	−	0.124764i
$892$	64.5525	−	111.808i	2.16138	−	3.74362i
$893$	−0.453417	+	0.785341i	−0.0151730	+	0.0262804i
$894$	−48.1968			−1.61194
$895$	−2.21892	+	3.84328i	−0.0741703	+	0.128467i
$896$	104.527			3.49199
$897$	1.63415	+	2.83043i	0.0545626	+	0.0945051i
$898$	81.4451			2.71786
$899$	9.03889			0.301464
$900$	9.67458	+	16.7569i	0.322486	+	0.558562i
$901$	−3.44017	+	5.95854i	−0.114609	+	0.198508i
$902$	11.9733			0.398667
$903$	−13.0501	−	22.6034i	−0.434279	−	0.752194i
$904$	64.3572	+	111.470i	2.14049	+	3.70743i
$905$	−11.2078	−	19.4125i	−0.372561	−	0.645295i
$906$	12.6377	−	21.8892i	0.419860	−	0.727219i
$907$	−10.9587	+	18.9811i	−0.363879	+	0.630257i	−0.988596	−	0.150595i	$-0.951881\pi$
$907$	−10.9587	+	18.9811i	−0.363879	+	0.630257i	0.624717	+	0.780852i	$0.285215\pi$
$908$	−1.32987	−	2.30341i	−0.0441334	−	0.0764413i
$909$	−6.07851	−	10.5283i	−0.201611	−	0.349201i
$910$	13.7507	+	23.8169i	0.455831	+	0.789523i
$911$	45.4951			1.50732			0.753660	−	0.657264i	$-0.228286\pi$
$911$	45.4951			1.50732			0.753660	+	0.657264i	$0.228286\pi$
$912$	−20.9370	+	36.2640i	−0.693294	+	1.20082i
$913$	−8.37991	−	14.5144i	−0.277334	−	0.480357i
$914$	−58.1896			−1.92474
$915$	−16.2366			−0.536767
$916$	−6.19416	−	10.7286i	−0.204661	−	0.354483i
$917$	−6.57745			−0.217207
$918$	4.24015	−	7.34416i	0.139946	−	0.242393i
$919$	54.8685			1.80995			0.904973	−	0.425470i	$-0.139891\pi$
$919$	54.8685			1.80995			0.904973	+	0.425470i	$0.139891\pi$
$920$	−7.83069	+	13.5632i	−0.258170	+	0.447164i
$921$	3.59220	−	6.22187i	0.118367	−	0.205017i
$922$	36.9960	−	64.0790i	1.21840	−	2.11033i
$923$	7.59435	+	13.1538i	0.249971	+	0.432963i
$924$	−92.3901			−3.03941
$925$	11.2616	+	19.1382i	0.370278	+	0.629259i
$926$	−40.5885			−1.33382
$927$	−4.10757	−	7.11452i	−0.134910	−	0.233671i
$928$	79.5350	−	137.759i	2.61086	−	4.52215i
$929$	9.63342	−	16.6856i	0.316062	−	0.547436i	−0.663601	−	0.748087i	$-0.730973\pi$
$929$	9.63342	−	16.6856i	0.316062	−	0.547436i	0.979663	+	0.200651i	$0.0643059\pi$
$930$	1.66052	−	2.87611i	0.0544507	−	0.0943113i
$931$	29.2688			0.959247
$932$	−27.0890	+	46.9196i	−0.887331	+	1.53690i
$933$	15.3379			0.502142
$934$	−0.730845	−	1.26586i	−0.0239140	−	0.0414202i
$935$	15.6787			0.512749
$936$	−19.2754			−0.630037
$937$	−15.4861	−	26.8227i	−0.505908	−	0.876258i	−0.999977	−	0.00683513i	$-0.997824\pi$
$937$	−15.4861	−	26.8227i	−0.505908	−	0.876258i	0.494069	−	0.869423i	$-0.335509\pi$
$938$	−41.5992	+	72.0519i	−1.35826	+	2.35258i
$939$	−21.7984			−0.711363
$940$	−0.899524	−	1.55802i	−0.0293392	−	0.0508171i
$941$	24.0763	+	41.7014i	0.784866	+	1.35943i	0.929079	+	0.369881i	$0.120602\pi$
$941$	24.0763	+	41.7014i	0.784866	+	1.35943i	−0.144213	+	0.989547i	$0.546065\pi$
$942$	−19.2363	−	33.3182i	−0.626751	−	1.08556i
$943$	0.779030	−	1.34932i	0.0253687	−	0.0439399i
$944$	13.3373	−	23.1008i	0.434091	−	0.751867i
$945$	−2.35435	−	4.07786i	−0.0765871	−	0.132653i
$946$	37.4067	+	64.7904i	1.21620	+	2.10652i
$947$	−29.5326	−	51.1519i	−0.959679	−	1.66221i	−0.723277	−	0.690558i	$-0.757365\pi$
$947$	−29.5326	−	51.1519i	−0.959679	−	1.66221i	−0.236402	−	0.971655i	$-0.575968\pi$
$948$	52.6205			1.70903
$949$	−3.82875	+	6.63159i	−0.124286	+	0.215270i
$950$	15.3059	+	26.5106i	0.496588	+	0.860116i
$951$	−15.1660			−0.491792
$952$	−113.447			−3.67683
$953$	−5.61548	−	9.72629i	−0.181903	−	0.315065i	0.760625	−	0.649191i	$-0.224892\pi$
$953$	−5.61548	−	9.72629i	−0.181903	−	0.315065i	−0.942529	+	0.334126i	$0.891559\pi$
$954$	−5.92294			−0.191762
$955$	1.86540	−	3.23097i	0.0603630	−	0.104552i
$956$	77.9739			2.52186
$957$	−18.3675	+	31.8134i	−0.593736	+	1.02838i
$958$	−3.19499	+	5.53389i	−0.103225	+	0.178792i
$959$	−37.3617	+	64.7124i	−1.20647	+	2.08967i
$960$	−13.5492	−	23.4679i	−0.437298	−	0.757422i
$961$	−29.8804			−0.963884
$962$	−35.5254	+	0.293951i	−1.14539	+	0.00947735i
$963$	0.700620			0.0225772
$964$	−44.4191	−	76.9362i	−1.43064	−	2.47795i
$965$	1.80527	−	3.12682i	0.0581138	−	0.100656i
$966$	−8.27956	+	14.3406i	−0.266390	+	0.461402i
$967$	4.71460	−	8.16593i	0.151611	−	0.262598i	−0.780209	−	0.625519i	$-0.784887\pi$
$967$	4.71460	−	8.16593i	0.151611	−	0.262598i	0.931820	+	0.362921i	$0.118220\pi$
$968$	66.8102			2.14736
$969$	4.87043	−	8.43582i	0.156461	−	0.270998i
$970$	−33.5963			−1.07871
$971$	−3.71005	−	6.42600i	−0.119061	−	0.206220i	0.800335	−	0.599554i	$-0.204655\pi$
$971$	−3.71005	−	6.42600i	−0.119061	−	0.206220i	−0.919396	+	0.393333i	$0.871322\pi$
$972$	5.30028			0.170007
$973$	50.0609			1.60488
$974$	−19.3240	−	33.4702i	−0.619181	−	1.07245i
$975$	−3.94563	+	6.83404i	−0.126361	+	0.218864i
$976$	−188.588			−6.03656
$977$	8.13922	+	14.0975i	0.260397	+	0.451020i	0.966347	−	0.257241i	$-0.0828134\pi$
$977$	8.13922	+	14.0975i	0.260397	+	0.451020i	−0.705951	+	0.708261i	$0.749480\pi$
$978$	−3.70476	−	6.41683i	−0.118465	−	0.205187i
$979$	−32.1465	−	55.6793i	−1.02741	−	1.77952i
$980$	−29.0329	+	50.2865i	−0.927423	+	1.60634i
$981$	0.298547	−	0.517099i	0.00953188	−	0.0165097i
$982$	−13.9077	−	24.0889i	−0.443813	−	0.768707i
$983$	28.4588	+	49.2921i	0.907696	+	1.57218i	0.817257	+	0.576273i	$0.195494\pi$
$983$	28.4588	+	49.2921i	0.907696	+	1.57218i	0.0904388	+	0.995902i	$0.471173\pi$
$984$	4.59449	+	7.95789i	0.146467	+	0.253688i
$985$	−2.76633			−0.0881425
$986$	−36.2213	+	62.7371i	−1.15352	+	1.99796i
$987$	−0.592205	−	1.02573i	−0.0188501	−	0.0326493i
$988$	−35.5580			−1.13125
$989$	9.73533			0.309566
$990$	6.74852	+	11.6888i	0.214482	+	0.371494i
$991$	7.64014			0.242697			0.121349	−	0.992610i	$-0.461278\pi$
$991$	7.64014			0.242697			0.121349	+	0.992610i	$0.461278\pi$
$992$	9.85165	−	17.0636i	0.312790	−	0.541769i
$993$	−8.51740			−0.270291
$994$	−38.4775	+	66.6450i	−1.22043	+	2.11385i
$995$	−12.5116	+	21.6708i	−0.396645	+	0.687009i
$996$	10.3286	−	17.8896i	0.327274	−	0.566855i
$997$	15.0528	+	26.0723i	0.476728	+	0.825718i	0.999644	−	0.0266665i	$-0.00848922\pi$
$997$	15.0528	+	26.0723i	0.476728	+	0.825718i	−0.522916	+	0.852384i	$0.675156\pi$
$998$	83.3536			2.63851
$999$	6.08255	−	0.0503293i	0.192444	−	0.00159235i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	111.2.e.b.100.1	yes	10
3.2	odd	2		333.2.f.c.100.5		10
4.3	odd	2		1776.2.q.q.433.2		10
37.10	even	3	inner	111.2.e.b.10.1	✓	10
37.11	even	6		4107.2.a.k.1.1		5
37.26	even	3		4107.2.a.j.1.5		5
111.47	odd	6		333.2.f.c.10.5		10
148.47	odd	6		1776.2.q.q.1009.2		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
111.2.e.b.10.1	✓	10	37.10	even	3	inner
111.2.e.b.100.1	yes	10	1.1	even	1	trivial
333.2.f.c.10.5		10	111.47	odd	6
333.2.f.c.100.5		10	3.2	odd	2
1776.2.q.q.433.2		10	4.3	odd	2
1776.2.q.q.1009.2		10	148.47	odd	6
4107.2.a.j.1.5		5	37.26	even	3
4107.2.a.k.1.1		5	37.11	even	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 111 = 3 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	111.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.35095 - 2.33992i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.65014 + 4.59018i) q^{4} +(-0.580820 + 1.00601i) q^{5} +2.70190 q^{6} +(-2.02675 + 3.51043i) q^{7} +8.91704 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.35095 - 2.33992i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-2.65014 + 4.59018i) q^{4} +(-0.580820 + 1.00601i) q^{5} +2.70190 q^{6} +(-2.02675 + 3.51043i) q^{7} +8.91704 q^{8} +(-0.500000 - 0.866025i) q^{9} +3.13864 q^{10} -4.30028 q^{11} +(-2.65014 - 4.59018i) q^{12} +(1.08082 - 1.87204i) q^{13} +10.9522 q^{14} +(-0.580820 - 1.00601i) q^{15} +(-6.74621 - 11.6848i) q^{16} +(1.56932 + 2.71814i) q^{17} +(-1.35095 + 2.33992i) q^{18} +(-1.55176 + 2.68773i) q^{19} +(-3.07851 - 5.33214i) q^{20} +(-2.02675 - 3.51043i) q^{21} +(5.80947 + 10.0623i) q^{22} +1.51195 q^{23} +(-4.45852 + 7.72238i) q^{24} +(1.82530 + 3.16150i) q^{25} -5.84054 q^{26} +1.00000 q^{27} +(-10.7423 - 18.6063i) q^{28} -8.54245 q^{29} +(-1.56932 + 2.71814i) q^{30} -1.05812 q^{31} +(-9.31056 + 16.1264i) q^{32} +(2.15014 - 3.72415i) q^{33} +(4.24015 - 7.34416i) q^{34} +(-2.35435 - 4.07786i) q^{35} +5.30028 q^{36} +(6.08255 - 0.0503293i) q^{37} +8.38543 q^{38} +(1.08082 + 1.87204i) q^{39} +(-5.17920 + 8.97063i) q^{40} +(0.515248 - 0.892436i) q^{41} +(-5.47608 + 9.48485i) q^{42} +6.43892 q^{43} +(11.3963 - 19.7391i) q^{44} +1.16164 q^{45} +(-2.04257 - 3.53784i) q^{46} +0.292195 q^{47} +13.4924 q^{48} +(-4.71542 - 8.16734i) q^{49} +(4.93177 - 8.54208i) q^{50} -3.13864 q^{51} +(5.72865 + 9.92232i) q^{52} +(1.09607 + 1.89845i) q^{53} +(-1.35095 - 2.33992i) q^{54} +(2.49769 - 4.32613i) q^{55} +(-18.0726 + 31.3027i) q^{56} +(-1.55176 - 2.68773i) q^{57} +(11.5404 + 19.9886i) q^{58} +(0.988500 + 1.71213i) q^{59} +6.15702 q^{60} +(6.98867 - 12.1047i) q^{61} +(1.42946 + 2.47590i) q^{62} +4.05350 q^{63} +23.3277 q^{64} +(1.25552 + 2.17463i) q^{65} -11.6189 q^{66} +(-3.79827 + 6.57879i) q^{67} -16.6357 q^{68} +(-0.755975 + 1.30939i) q^{69} +(-6.36123 + 11.0180i) q^{70} +(-3.51323 + 6.08510i) q^{71} +(-4.45852 - 7.72238i) q^{72} -3.54245 q^{73} +(-8.33500 - 14.1647i) q^{74} -3.65059 q^{75} +(-8.22478 - 14.2457i) q^{76} +(8.71559 - 15.0958i) q^{77} +(2.92027 - 5.05806i) q^{78} +(-4.96394 + 8.59779i) q^{79} +15.6733 q^{80} +(-0.500000 + 0.866025i) q^{81} -2.78430 q^{82} +(1.94869 + 3.37523i) q^{83} +21.4847 q^{84} -3.64597 q^{85} +(-8.69867 - 15.0665i) q^{86} +(4.27122 - 7.39798i) q^{87} -38.3458 q^{88} +(7.47544 + 12.9478i) q^{89} +(-1.56932 - 2.71814i) q^{90} +(4.38110 + 7.58829i) q^{91} +(-4.00688 + 6.94012i) q^{92} +(0.529058 - 0.916355i) q^{93} +(-0.394741 - 0.683711i) q^{94} +(-1.80259 - 3.12218i) q^{95} +(-9.31056 - 16.1264i) q^{96} -10.7041 q^{97} +(-12.7406 + 22.0674i) q^{98} +(2.15014 + 3.72415i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{3} - 8 q^{4} + 2 q^{5} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 5 * q^3 - 8 * q^4 + 2 * q^5 + 6 * q^8 - 5 * q^9	\( 10 q - 5 q^{3} - 8 q^{4} + 2 q^{5} + 6 q^{8} - 5 q^{9} + 10 q^{10} - 6 q^{11} - 8 q^{12} + 3 q^{13} + 22 q^{14} + 2 q^{15} - 18 q^{16} + 5 q^{17} - 7 q^{19} - 2 q^{20} + 3 q^{22} - 14 q^{23} - 3 q^{24} - 7 q^{25} - 10 q^{26} + 10 q^{27} + q^{28} - 10 q^{29} - 5 q^{30} - 12 q^{31} - 6 q^{32} + 3 q^{33} - 2 q^{34} + q^{35} + 16 q^{36} + 21 q^{37} + 66 q^{38} + 3 q^{39} - 34 q^{40} - 18 q^{41} - 11 q^{42} + 6 q^{43} + 46 q^{44} - 4 q^{45} - 30 q^{46} - 12 q^{47} + 36 q^{48} - 29 q^{49} + 28 q^{50} - 10 q^{51} + 10 q^{52} - 20 q^{53} + 4 q^{55} - 74 q^{56} - 7 q^{57} + 34 q^{58} + 7 q^{59} + 4 q^{60} - 3 q^{61} - 28 q^{62} + 74 q^{64} + 30 q^{65} - 6 q^{66} + 5 q^{67} - 88 q^{68} + 7 q^{69} - 6 q^{71} - 3 q^{72} + 40 q^{73} + 45 q^{74} + 14 q^{75} + 24 q^{76} - q^{77} + 5 q^{78} - 3 q^{79} - 58 q^{80} - 5 q^{81} - 8 q^{82} - 4 q^{83} - 2 q^{84} + 56 q^{85} - q^{86} + 5 q^{87} - 18 q^{88} + 31 q^{89} - 5 q^{90} - q^{91} - q^{92} + 6 q^{93} - 53 q^{94} - 2 q^{95} - 6 q^{96} - 16 q^{97} - 51 q^{98} + 3 q^{99}+O(q^{100}) \) 10 * q - 5 * q^3 - 8 * q^4 + 2 * q^5 + 6 * q^8 - 5 * q^9 + 10 * q^10 - 6 * q^11 - 8 * q^12 + 3 * q^13 + 22 * q^14 + 2 * q^15 - 18 * q^16 + 5 * q^17 - 7 * q^19 - 2 * q^20 + 3 * q^22 - 14 * q^23 - 3 * q^24 - 7 * q^25 - 10 * q^26 + 10 * q^27 + q^28 - 10 * q^29 - 5 * q^30 - 12 * q^31 - 6 * q^32 + 3 * q^33 - 2 * q^34 + q^35 + 16 * q^36 + 21 * q^37 + 66 * q^38 + 3 * q^39 - 34 * q^40 - 18 * q^41 - 11 * q^42 + 6 * q^43 + 46 * q^44 - 4 * q^45 - 30 * q^46 - 12 * q^47 + 36 * q^48 - 29 * q^49 + 28 * q^50 - 10 * q^51 + 10 * q^52 - 20 * q^53 + 4 * q^55 - 74 * q^56 - 7 * q^57 + 34 * q^58 + 7 * q^59 + 4 * q^60 - 3 * q^61 - 28 * q^62 + 74 * q^64 + 30 * q^65 - 6 * q^66 + 5 * q^67 - 88 * q^68 + 7 * q^69 - 6 * q^71 - 3 * q^72 + 40 * q^73 + 45 * q^74 + 14 * q^75 + 24 * q^76 - q^77 + 5 * q^78 - 3 * q^79 - 58 * q^80 - 5 * q^81 - 8 * q^82 - 4 * q^83 - 2 * q^84 + 56 * q^85 - q^86 + 5 * q^87 - 18 * q^88 + 31 * q^89 - 5 * q^90 - q^91 - q^92 + 6 * q^93 - 53 * q^94 - 2 * q^95 - 6 * q^96 - 16 * q^97 - 51 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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