LMFDB - Embedded newform 40.3.i.a.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [40,3,Mod(13,40)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(40, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("40.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 40 = 2^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	40.i (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:	$1.08992105744$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{18} - 3x^{16} + 11x^{14} + x^{12} - 40x^{10} + 4x^{8} + 176x^{6} - 192x^{4} - 256x^{2} + 1024 $ x^20 - x^18 - 3x^16 + 11x^14 + x^12 - 40x^10 + 4x^8 + 176x^6 - 192x^4 - 256*x^2 + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{20} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			37.3
Root			$0.0552378 - 1.41313i$ of defining polynomial
Character	$\chi$	$=$	40.37
Dual form			40.3.i.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.46837 - 1.35790i) q^{2} +(-2.57493 - 2.57493i) q^{3} +(0.312234 + 3.98780i) q^{4} +(-4.90427 + 0.973739i) q^{5} +(0.284467 + 7.27744i) q^{6} +(-4.07624 - 4.07624i) q^{7} +(4.95654 - 6.27955i) q^{8} +4.26050i q^{9} +O(q^{10})$	\(q+(-1.46837 - 1.35790i) q^{2} +(-2.57493 - 2.57493i) q^{3} +(0.312234 + 3.98780i) q^{4} +(-4.90427 + 0.973739i) q^{5} +(0.284467 + 7.27744i) q^{6} +(-4.07624 - 4.07624i) q^{7} +(4.95654 - 6.27955i) q^{8} +4.26050i q^{9} +(8.52353 + 5.22967i) q^{10} -16.0988i q^{11} +(9.46430 - 11.0723i) q^{12} +(9.77892 + 9.77892i) q^{13} +(0.450325 + 11.5206i) q^{14} +(15.1354 + 10.1208i) q^{15} +(-15.8050 + 2.49025i) q^{16} +(-12.0592 - 12.0592i) q^{17} +(5.78531 - 6.25599i) q^{18} +9.55189 q^{19} +(-5.41435 - 19.2532i) q^{20} +20.9920i q^{21} +(-21.8605 + 23.6391i) q^{22} +(-2.56986 + 2.56986i) q^{23} +(-28.9321 + 3.40666i) q^{24} +(23.1037 - 9.55096i) q^{25} +(-1.08033 - 27.6379i) q^{26} +(-12.2039 + 12.2039i) q^{27} +(14.9825 - 17.5280i) q^{28} -10.1419 q^{29} +(-8.48143 - 35.4135i) q^{30} -24.9787 q^{31} +(26.5892 + 17.8050i) q^{32} +(-41.4533 + 41.4533i) q^{33} +(1.33225 + 34.0825i) q^{34} +(23.9602 + 16.0218i) q^{35} +(-16.9900 + 1.33027i) q^{36} +(26.8701 - 26.8701i) q^{37} +(-14.0257 - 12.9705i) q^{38} -50.3600i q^{39} +(-18.1935 + 35.6230i) q^{40} +62.0782 q^{41} +(28.5050 - 30.8241i) q^{42} +(-13.5064 - 13.5064i) q^{43} +(64.1988 - 5.02660i) q^{44} +(-4.14861 - 20.8946i) q^{45} +(7.26313 - 0.283907i) q^{46} +(11.9511 + 11.9511i) q^{47} +(47.1090 + 34.2846i) q^{48} -15.7685i q^{49} +(-46.8940 - 17.3480i) q^{50} +62.1031i q^{51} +(-35.9430 + 42.0497i) q^{52} +(-45.8494 - 45.8494i) q^{53} +(34.4914 - 1.34823i) q^{54} +(15.6761 + 78.9530i) q^{55} +(-45.8010 + 5.39291i) q^{56} +(-24.5954 - 24.5954i) q^{57} +(14.8922 + 13.7717i) q^{58} -28.9288 q^{59} +(-35.6340 + 63.5171i) q^{60} -68.7976i q^{61} +(36.6780 + 33.9184i) q^{62} +(17.3668 - 17.3668i) q^{63} +(-14.8655 - 62.2496i) q^{64} +(-57.4806 - 38.4363i) q^{65} +(117.158 - 4.57958i) q^{66} +(14.7732 - 14.7732i) q^{67} +(44.3243 - 51.8549i) q^{68} +13.2344 q^{69} +(-13.4265 - 56.0614i) q^{70} -31.1277 q^{71} +(26.7540 + 21.1173i) q^{72} +(-25.6249 + 25.6249i) q^{73} +(-75.9420 + 2.96849i) q^{74} +(-84.0833 - 34.8972i) q^{75} +(2.98242 + 38.0910i) q^{76} +(-65.6227 + 65.6227i) q^{77} +(-68.3837 + 73.9473i) q^{78} -70.6564i q^{79} +(75.0872 - 27.6028i) q^{80} +101.193 q^{81} +(-91.1539 - 84.2958i) q^{82} +(96.2577 + 96.2577i) q^{83} +(-83.7120 + 6.55443i) q^{84} +(70.8840 + 47.3990i) q^{85} +(1.49212 + 38.1726i) q^{86} +(26.1148 + 26.1148i) q^{87} +(-101.093 - 79.7945i) q^{88} +103.919i q^{89} +(-22.2810 + 36.3145i) q^{90} -79.7225i q^{91} +(-11.0505 - 9.44569i) q^{92} +(64.3182 + 64.3182i) q^{93} +(-1.32031 - 33.7771i) q^{94} +(-46.8450 + 9.30105i) q^{95} +(-22.6186 - 114.312i) q^{96} +(30.8277 + 30.8277i) q^{97} +(-21.4120 + 23.1540i) q^{98} +68.5890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	$ 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31} + 128 q^{32} + 32 q^{33} + 220 q^{36} - 188 q^{38} + 156 q^{40} - 8 q^{41} - 284 q^{42} - 240 q^{46} + 188 q^{47} - 256 q^{48} - 274 q^{50} - 332 q^{52} + 96 q^{55} - 360 q^{56} - 40 q^{57} + 268 q^{58} - 340 q^{60} + 336 q^{62} + 228 q^{63} - 60 q^{65} + 616 q^{66} + 396 q^{68} + 300 q^{70} + 248 q^{71} + 668 q^{72} - 124 q^{73} + 424 q^{76} - 368 q^{78} + 496 q^{80} + 132 q^{81} - 676 q^{82} - 672 q^{86} - 488 q^{87} - 304 q^{88} - 474 q^{90} - 628 q^{92} - 488 q^{95} - 1024 q^{96} + 100 q^{97} + 546 q^{98}+O(q^{100}) $ 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.46837	−	1.35790i	−0.734186	−	0.678948i
$2$	−1.46837	−	1.35790i	−0.734186	−	0.678948i
$3$	−2.57493	−	2.57493i	−0.858309	−	0.858309i	0.132830	−	0.991139i	$-0.457594\pi$
$3$	−2.57493	−	2.57493i	−0.858309	−	0.858309i	−0.991139	+	0.132830i	$0.957594\pi$
$4$	0.312234	+	3.98780i	0.0780585	+	0.996949i
$5$	−4.90427	+	0.973739i	−0.980853	+	0.194748i
$5$	−4.90427	+	0.973739i	−0.980853	+	0.194748i
$6$	0.284467	+	7.27744i	0.0474111	+	1.21291i
$7$	−4.07624	−	4.07624i	−0.582320	−	0.582320i	0.353220	−	0.935540i	$-0.385087\pi$
$7$	−4.07624	−	4.07624i	−0.582320	−	0.582320i	−0.935540	+	0.353220i	$0.885087\pi$
$8$	4.95654	−	6.27955i	0.619567	−	0.784944i
$9$			4.26050i			0.473388i
$10$	8.52353	+	5.22967i	0.852353	+	0.522967i
$11$		−	16.0988i		−	1.46353i	−0.681557	−	0.731765i	$-0.738697\pi$
$11$		−	16.0988i		−	1.46353i	0.681557	−	0.731765i	$-0.261303\pi$
$12$	9.46430	−	11.0723i	0.788692	−	0.922688i
$13$	9.77892	+	9.77892i	0.752225	+	0.752225i	0.974894	−	0.222669i	$-0.0714770\pi$
$13$	9.77892	+	9.77892i	0.752225	+	0.752225i	−0.222669	+	0.974894i	$0.571477\pi$
$14$	0.450325	+	11.5206i	0.0321661	+	0.822897i
$15$	15.1354	+	10.1208i	1.00903	+	0.674721i
$16$	−15.8050	+	2.49025i	−0.987814	+	0.155641i
$17$	−12.0592	−	12.0592i	−0.709364	−	0.709364i	0.257037	−	0.966402i	$-0.417254\pi$
$17$	−12.0592	−	12.0592i	−0.709364	−	0.709364i	−0.966402	+	0.257037i	$0.917254\pi$
$18$	5.78531	−	6.25599i	0.321406	−	0.347555i
$19$	9.55189			0.502731			0.251366	−	0.967892i	$-0.419120\pi$
$19$	9.55189			0.502731			0.251366	+	0.967892i	$0.419120\pi$
$20$	−5.41435	−	19.2532i	−0.270718	−	0.962659i
$21$			20.9920i			0.999621i
$22$	−21.8605	+	23.6391i	−0.993661	+	1.07450i
$23$	−2.56986	+	2.56986i	−0.111733	+	0.111733i	−0.760763	−	0.649030i	$-0.775175\pi$
$23$	−2.56986	+	2.56986i	−0.111733	+	0.111733i	0.649030	+	0.760763i	$0.275175\pi$
$24$	−28.9321	+	3.40666i	−1.20550	+	0.141944i
$25$	23.1037	−	9.55096i	0.924147	−	0.382038i
$26$	−1.08033	−	27.6379i	−0.0415513	−	1.06299i
$27$	−12.2039	+	12.2039i	−0.451995	+	0.451995i
$28$	14.9825	−	17.5280i	0.535088	−	0.625998i
$29$	−10.1419			−0.349722			−0.174861	−	0.984593i	$-0.555948\pi$
$29$	−10.1419			−0.349722			−0.174861	+	0.984593i	$0.555948\pi$
$30$	−8.48143	−	35.4135i	−0.282714	−	1.18045i
$31$	−24.9787			−0.805763			−0.402882	−	0.915252i	$-0.631991\pi$
$31$	−24.9787			−0.805763			−0.402882	+	0.915252i	$0.631991\pi$
$32$	26.5892	+	17.8050i	0.830911	+	0.556405i
$33$	−41.4533	+	41.4533i	−1.25616	+	1.25616i
$34$	1.33225	+	34.0825i	0.0391837	+	1.00243i
$35$	23.9602	+	16.0218i	0.684576	+	0.457765i
$36$	−16.9900	+	1.33027i	−0.471944	+	0.0369520i
$37$	26.8701	−	26.8701i	0.726218	−	0.726218i	−0.243646	−	0.969864i	$-0.578344\pi$
$37$	26.8701	−	26.8701i	0.726218	−	0.726218i	0.969864	+	0.243646i	$0.0783437\pi$
$38$	−14.0257	−	12.9705i	−0.369098	−	0.341328i
$39$		−	50.3600i		−	1.29128i
$40$	−18.1935	+	35.6230i	−0.454838	+	0.890574i
$41$	62.0782			1.51410			0.757051	−	0.653356i	$-0.226639\pi$
$41$	62.0782			1.51410			0.757051	+	0.653356i	$0.226639\pi$
$42$	28.5050	−	30.8241i	0.678691	−	0.733908i
$43$	−13.5064	−	13.5064i	−0.314101	−	0.314101i	0.532395	−	0.846496i	$-0.321292\pi$
$43$	−13.5064	−	13.5064i	−0.314101	−	0.314101i	−0.846496	+	0.532395i	$0.821292\pi$
$44$	64.1988	−	5.02660i	1.45906	−	0.114241i
$45$	−4.14861	−	20.8946i	−0.0921914	−	0.464325i
$46$	7.26313	−	0.283907i	0.157894	−	0.00617190i
$47$	11.9511	+	11.9511i	0.254279	+	0.254279i	0.822723	−	0.568443i	$-0.192454\pi$
$47$	11.9511	+	11.9511i	0.254279	+	0.254279i	−0.568443	+	0.822723i	$0.692454\pi$
$48$	47.1090	+	34.2846i	0.981437	+	0.714262i
$49$		−	15.7685i		−	0.321806i
$50$	−46.8940	−	17.3480i	−0.937880	−	0.346961i
$51$			62.1031i			1.21771i
$52$	−35.9430	+	42.0497i	−0.691212	+	0.808647i
$53$	−45.8494	−	45.8494i	−0.865084	−	0.865084i	0.126839	−	0.991923i	$-0.459517\pi$
$53$	−45.8494	−	45.8494i	−0.865084	−	0.865084i	−0.991923	+	0.126839i	$0.959517\pi$
$54$	34.4914	−	1.34823i	0.638730	−	0.0249672i
$55$	15.6761	+	78.9530i	0.285019	+	1.43551i
$56$	−45.8010	+	5.39291i	−0.817875	+	0.0963020i
$57$	−24.5954	−	24.5954i	−0.431499	−	0.431499i
$58$	14.8922	+	13.7717i	0.256761	+	0.237443i
$59$	−28.9288			−0.490319			−0.245159	−	0.969483i	$-0.578840\pi$
$59$	−28.9288			−0.490319			−0.245159	+	0.969483i	$0.578840\pi$
$60$	−35.6340	+	63.5171i	−0.593899	+	1.05862i
$61$		−	68.7976i		−	1.12783i	−0.825833	−	0.563915i	$-0.809295\pi$
$61$		−	68.7976i		−	1.12783i	0.825833	−	0.563915i	$-0.190705\pi$
$62$	36.6780	+	33.9184i	0.591580	+	0.547072i
$63$	17.3668	−	17.3668i	0.275664	−	0.275664i
$64$	−14.8655	−	62.2496i	−0.232273	−	0.972651i
$65$	−57.4806	−	38.4363i	−0.884317	−	0.591328i
$66$	117.158	−	4.57958i	1.77512	−	0.0693876i
$67$	14.7732	−	14.7732i	0.220495	−	0.220495i	−0.588212	−	0.808707i	$-0.700168\pi$
$67$	14.7732	−	14.7732i	0.220495	−	0.220495i	0.808707	+	0.588212i	$0.200168\pi$
$68$	44.3243	−	51.8549i	0.651828	−	0.762572i
$69$	13.2344			0.191803
$70$	−13.4265	−	56.0614i	−0.191808	−	0.800877i
$71$	−31.1277			−0.438419			−0.219209	−	0.975678i	$-0.570348\pi$
$71$	−31.1277			−0.438419			−0.219209	+	0.975678i	$0.570348\pi$
$72$	26.7540	+	21.1173i	0.371583	+	0.293296i
$73$	−25.6249	+	25.6249i	−0.351026	+	0.351026i	−0.860491	−	0.509465i	$-0.829843\pi$
$73$	−25.6249	+	25.6249i	−0.351026	+	0.351026i	0.509465	+	0.860491i	$0.329843\pi$
$74$	−75.9420	+	2.96849i	−1.02624	+	0.0401147i
$75$	−84.0833	−	34.8972i	−1.12111	−	0.465296i
$76$	2.98242	+	38.0910i	0.0392424	+	0.501197i
$77$	−65.6227	+	65.6227i	−0.852243	+	0.852243i
$78$	−68.3837	+	73.9473i	−0.876714	+	0.948042i
$79$		−	70.6564i		−	0.894385i	−0.894438	−	0.447192i	$-0.852424\pi$
$79$		−	70.6564i		−	0.894385i	0.894438	−	0.447192i	$-0.147576\pi$
$80$	75.0872	−	27.6028i	0.938590	−	0.345035i
$81$	101.193			1.24929
$82$	−91.1539	−	84.2958i	−1.11163	−	1.02800i
$83$	96.2577	+	96.2577i	1.15973	+	1.15973i	0.984533	+	0.175197i	$0.0560564\pi$
$83$	96.2577	+	96.2577i	1.15973	+	1.15973i	0.175197	+	0.984533i	$0.443944\pi$
$84$	−83.7120	+	6.55443i	−0.996571	+	0.0780289i
$85$	70.8840	+	47.3990i	0.833930	+	0.557635i
$86$	1.49212	+	38.1726i	0.0173503	+	0.443867i
$87$	26.1148	+	26.1148i	0.300170	+	0.300170i
$88$	−101.093	−	79.7945i	−1.14879	−	0.906755i
$89$			103.919i			1.16763i	0.811886	+	0.583816i	$0.198441\pi$
$89$			103.919i			1.16763i	−0.811886	+	0.583816i	$0.801559\pi$
$90$	−22.2810	+	36.3145i	−0.247567	+	0.403494i
$91$		−	79.7225i		−	0.876072i
$92$	−11.0505	−	9.44569i	−0.120114	−	0.102671i
$93$	64.3182	+	64.3182i	0.691594	+	0.691594i
$94$	−1.32031	−	33.7771i	−0.0140458	−	0.359331i
$95$	−46.8450	+	9.30105i	−0.493106	+	0.0979058i
$96$	−22.6186	−	114.312i	−0.235611	−	1.19075i
$97$	30.8277	+	30.8277i	0.317811	+	0.317811i	0.847926	−	0.530115i	$-0.177851\pi$
$97$	30.8277	+	30.8277i	0.317811	+	0.317811i	−0.530115	+	0.847926i	$0.677851\pi$
$98$	−21.4120	+	23.1540i	−0.218490	+	0.236266i
$99$	68.5890			0.692818
$100$	45.3010	+	89.1505i	0.453010	+	0.891505i
$101$			71.7064i			0.709964i	0.934873	+	0.354982i	$0.115513\pi$
$101$			71.7064i			0.709964i	−0.934873	+	0.354982i	$0.884487\pi$
$102$	84.3296	−	91.1904i	0.826760	−	0.894024i
$103$	56.0903	−	56.0903i	0.544566	−	0.544566i	−0.380298	−	0.924864i	$-0.624179\pi$
$103$	56.0903	−	56.0903i	0.544566	−	0.544566i	0.924864	+	0.380298i	$0.124179\pi$
$104$	109.877	−	12.9376i	1.05651	−	0.124400i
$105$	−20.4408	−	102.951i	−0.194674	−	0.980482i
$106$	5.06525	+	129.583i	0.0477853	+	1.22248i
$107$	67.1991	−	67.1991i	0.628029	−	0.628029i	−0.319543	−	0.947572i	$-0.603529\pi$
$107$	67.1991	−	67.1991i	0.628029	−	0.628029i	0.947572	+	0.319543i	$0.103529\pi$
$108$	−52.4770	−	44.8561i	−0.485898	−	0.415334i
$109$	93.2447			0.855456			0.427728	−	0.903908i	$-0.359314\pi$
$109$	93.2447			0.855456			0.427728	+	0.903908i	$0.359314\pi$
$110$	84.1917	−	137.219i	0.765379	−	1.24744i
$111$	−138.377			−1.24664
$112$	74.5759	+	54.2742i	0.665857	+	0.484591i
$113$	40.5022	−	40.5022i	0.358427	−	0.358427i	−0.504806	−	0.863233i	$-0.668436\pi$
$113$	40.5022	−	40.5022i	0.358427	−	0.358427i	0.863233	+	0.504806i	$0.168436\pi$
$114$	2.71720	+	69.5133i	0.0238350	+	0.609766i
$115$	10.1009	−	15.1057i	0.0878341	−	0.131354i
$116$	−3.16666	−	40.4440i	−0.0272988	−	0.348655i
$117$	−41.6631	+	41.6631i	−0.356095	+	0.356095i
$118$	42.4782	+	39.2823i	0.359985	+	0.332901i
$119$			98.3124i			0.826154i
$120$	138.574	−	44.8795i	1.15478	−	0.373996i
$121$	−138.172			−1.14192
$122$	−93.4200	+	101.020i	−0.765738	+	0.828037i
$123$	−159.847	−	159.847i	−1.29957	−	1.29957i
$124$	−7.79918	−	99.6098i	−0.0628966	−	0.803305i
$125$	−104.006	+	69.3374i	−0.832051	+	0.554699i
$126$	−49.0833	+	1.91861i	−0.389550	+	0.0152271i
$127$	94.0337	+	94.0337i	0.740423	+	0.740423i	0.972659	−	0.232237i	$-0.0746044\pi$
$127$	94.0337	+	94.0337i	0.740423	+	0.740423i	−0.232237	+	0.972659i	$0.574604\pi$
$128$	−62.7005	+	111.591i	−0.489848	+	0.871808i
$129$			69.5557i			0.539192i
$130$	32.2103	+	134.492i	0.247772	+	1.03455i
$131$			10.9456i			0.0835542i	0.999127	+	0.0417771i	$0.0133019\pi$
$131$			10.9456i			0.0835542i	−0.999127	+	0.0417771i	$0.986698\pi$
$132$	−178.250	−	152.364i	−1.35038	−	1.15427i
$133$	−38.9358	−	38.9358i	−0.292751	−	0.292751i
$134$	−41.7529	+	1.63208i	−0.311589	+	0.0121797i
$135$	47.9677	−	71.7345i	0.355316	−	0.531366i
$136$	−135.498	+	15.9544i	−0.996310	+	0.117312i
$137$	−45.9736	−	45.9736i	−0.335574	−	0.335574i	0.519125	−	0.854698i	$-0.326258\pi$
$137$	−45.9736	−	45.9736i	−0.335574	−	0.335574i	−0.854698	+	0.519125i	$0.826258\pi$
$138$	−19.4331	−	17.9710i	−0.140819	−	0.130224i
$139$	−182.191			−1.31072			−0.655362	−	0.755315i	$-0.727484\pi$
$139$	−182.191			−1.31072			−0.655362	+	0.755315i	$0.727484\pi$
$140$	−56.4104	+	100.551i	−0.402931	+	0.718220i
$141$		−	61.5466i		−	0.436500i
$142$	45.7071	+	42.2683i	0.321881	+	0.297664i
$143$	157.429	−	157.429i	1.10090	−	1.10090i
$144$	−10.6097	−	67.3372i	−0.0736785	−	0.467620i
$145$	49.7388	−	9.87561i	0.343026	−	0.0681077i
$146$	72.4228	−	2.83092i	0.496046	−	0.0193899i
$147$	−40.6028	+	40.6028i	−0.276209	+	0.276209i
$148$	115.542	+	98.7625i	0.780689	+	0.667314i
$149$	−238.037			−1.59757			−0.798783	−	0.601620i	$-0.794522\pi$
$149$	−238.037			−1.59757			−0.798783	+	0.601620i	$0.794522\pi$
$150$	76.0787	+	165.418i	0.507191	+	1.10279i
$151$	−37.8666			−0.250772			−0.125386	−	0.992108i	$-0.540017\pi$
$151$	−37.8666			−0.250772			−0.125386	+	0.992108i	$0.540017\pi$
$152$	47.3443	−	59.9816i	0.311476	−	0.394616i
$153$	51.3782	−	51.3782i	0.335805	−	0.335805i
$154$	185.467	−	7.24971i	1.20433	−	0.0470761i
$155$	122.502	−	24.3227i	0.790336	−	0.156921i
$156$	200.825	−	15.7241i	1.28734	−	0.100796i
$157$	113.671	−	113.671i	0.724021	−	0.724021i	−0.245401	−	0.969422i	$-0.578919\pi$
$157$	113.671	−	113.671i	0.724021	−	0.724021i	0.969422	+	0.245401i	$0.0789195\pi$
$158$	−95.9441	+	103.750i	−0.607241	+	0.656645i
$159$			236.118i			1.48502i
$160$	−147.738	−	61.4294i	−0.923361	−	0.383934i
$161$	20.9508			0.130129
$162$	−148.588	−	137.409i	−0.917213	−	0.848205i
$163$	93.7110	+	93.7110i	0.574914	+	0.574914i	0.933498	−	0.358584i	$-0.116740\pi$
$163$	93.7110	+	93.7110i	0.574914	+	0.574914i	−0.358584	+	0.933498i	$0.616740\pi$
$164$	19.3829	+	247.555i	0.118189	+	1.50948i
$165$	162.933	−	243.663i	0.987475	−	1.47674i
$166$	−10.6341	−	272.050i	−0.0640610	−	1.63886i
$167$	−151.931	−	151.931i	−0.909764	−	0.909764i	0.0864890	−	0.996253i	$-0.472435\pi$
$167$	−151.931	−	151.931i	−0.909764	−	0.909764i	−0.996253	+	0.0864890i	$0.972435\pi$
$168$	131.821	+	104.048i	0.784646	+	0.619333i
$169$			22.2547i			0.131685i
$170$	−39.7212	−	165.853i	−0.233654	−	0.975603i
$171$			40.6958i			0.237987i
$172$	49.6434	−	58.0777i	0.288625	−	0.337661i
$173$	−13.7300	−	13.7300i	−0.0793643	−	0.0793643i	0.666310	−	0.745675i	$-0.267873\pi$
$173$	−13.7300	−	13.7300i	−0.0793643	−	0.0793643i	−0.745675	+	0.666310i	$0.767873\pi$
$174$	−2.88505	−	73.8074i	−0.0165807	−	0.424180i
$175$	−133.108	−	55.2441i	−0.760618	−	0.315681i
$176$	40.0901	+	254.442i	0.227785	+	1.44570i
$177$	74.4895	+	74.4895i	0.420845	+	0.420845i
$178$	141.111	−	152.592i	0.792761	−	0.857259i
$179$	191.697			1.07093			0.535467	−	0.844556i	$-0.320136\pi$
$179$	191.697			1.07093			0.535467	+	0.844556i	$0.320136\pi$
$180$	82.0281	−	23.0678i	0.455712	−	0.128155i
$181$			199.631i			1.10293i	0.834197	+	0.551467i	$0.185932\pi$
$181$			199.631i			1.10293i	−0.834197	+	0.551467i	$0.814068\pi$
$182$	−108.255	+	117.062i	−0.594807	+	0.643200i
$183$	−177.149	+	177.149i	−0.968026	+	0.968026i
$184$	3.39996	+	28.8752i	0.0184780	+	0.156931i
$185$	−105.613	+	157.942i	−0.570884	+	0.853742i
$186$	−7.10560	−	181.781i	−0.0382021	−	0.977315i
$187$	−194.139	+	194.139i	−1.03818	+	1.03818i
$188$	−43.9271	+	51.3902i	−0.233655	+	0.273352i
$189$	99.4919			0.526412
$190$	81.4158	+	49.9533i	0.428504	+	0.262912i
$191$	234.558			1.22805			0.614026	−	0.789286i	$-0.289549\pi$
$191$	234.558			1.22805			0.614026	+	0.789286i	$0.289549\pi$
$192$	−122.011	+	198.566i	−0.635473	+	1.03420i
$193$	110.986	−	110.986i	0.575059	−	0.575059i	−0.358479	−	0.933538i	$-0.616705\pi$
$193$	110.986	−	110.986i	0.575059	−	0.575059i	0.933538	+	0.358479i	$0.116705\pi$
$194$	−3.40571	−	87.1274i	−0.0175552	−	0.449110i
$195$	49.0375	+	246.979i	0.251475	+	1.26656i
$196$	62.8816	−	4.92346i	0.320825	−	0.0251197i
$197$	201.862	−	201.862i	1.02468	−	1.02468i	0.0249934	−	0.999688i	$-0.492044\pi$
$197$	201.862	−	201.862i	1.02468	−	1.02468i	0.999688	−	0.0249934i	$-0.00795649\pi$
$198$	−100.714	−	93.1368i	−0.508658	−	0.470388i
$199$		−	289.714i		−	1.45585i	−0.685656	−	0.727926i	$-0.740485\pi$
$199$		−	289.714i		−	1.45585i	0.685656	−	0.727926i	$-0.259515\pi$
$200$	54.5385	−	192.420i	0.272692	−	0.962101i
$201$	−76.0797			−0.378506
$202$	97.3699	−	105.292i	0.482029	−	0.521246i
$203$	41.3410	+	41.3410i	0.203650	+	0.203650i
$204$	−247.654	+	19.3907i	−1.21399	+	0.0950524i
$205$	−304.448	+	60.4480i	−1.48511	+	0.294868i
$206$	−158.526	+	6.19661i	−0.769545	+	0.0300806i
$207$	−10.9489	−	10.9489i	−0.0528932	−	0.0528932i
$208$	−178.908	−	130.204i	−0.860135	−	0.625981i
$209$		−	153.774i		−	0.735762i
$210$	−109.782	+	178.926i	−0.522769	+	0.852030i
$211$			29.4861i			0.139744i	0.997556	+	0.0698722i	$0.0222592\pi$
$211$			29.4861i			0.139744i	−0.997556	+	0.0698722i	$0.977741\pi$
$212$	168.522	−	197.154i	0.794917	−	0.929971i
$213$	80.1517	+	80.1517i	0.376299	+	0.376299i
$214$	−189.923	+	7.42386i	−0.887489	+	0.0346909i
$215$	79.3904	+	53.0871i	0.369258	+	0.246917i
$216$	16.1459	+	137.124i	0.0747494	+	0.634832i
$217$	101.819	+	101.819i	0.469212	+	0.469212i
$218$	−136.918	−	126.617i	−0.628064	−	0.580810i
$219$	131.964			0.602577
$220$	−309.954	+	87.1647i	−1.40888	+	0.396203i
$221$		−	235.852i		−	1.06720i
$222$	203.189	+	187.901i	0.915264	+	0.846403i
$223$	−139.228	+	139.228i	−0.624341	+	0.624341i	−0.946638	−	0.322298i	$-0.895545\pi$
$223$	−139.228	+	139.228i	−0.624341	+	0.624341i	0.322298	+	0.946638i	$0.395545\pi$
$224$	−35.8065	−	180.961i	−0.159850	−	0.807862i
$225$	40.6918	+	98.4331i	0.180852	+	0.437480i
$226$	−114.470	+	4.47451i	−0.506505	+	0.0197987i
$227$	−16.1777	+	16.1777i	−0.0712674	+	0.0712674i	−0.741842	−	0.670575i	$-0.766048\pi$
$227$	−16.1777	+	16.1777i	−0.0712674	+	0.0712674i	0.670575	+	0.741842i	$0.266048\pi$
$228$	90.4020	−	105.761i	0.396500	−	0.463864i
$229$	22.7832			0.0994899			0.0497449	−	0.998762i	$-0.484159\pi$
$229$	22.7832			0.0994899			0.0497449	+	0.998762i	$0.484159\pi$
$230$	−35.3439	+	8.46475i	−0.153669	+	0.0368033i
$231$	337.947			1.46298
$232$	−50.2689	+	63.6868i	−0.216676	+	0.274512i
$233$	−54.2441	+	54.2441i	−0.232807	+	0.232807i	−0.813863	−	0.581056i	$-0.802640\pi$
$233$	−54.2441	+	54.2441i	−0.232807	+	0.232807i	0.581056	+	0.813863i	$0.302640\pi$
$234$	117.751	−	4.60275i	0.503210	−	0.0196699i
$235$	−70.2488	−	46.9742i	−0.298931	−	0.199890i
$236$	−9.03255	−	115.362i	−0.0382735	−	0.488822i
$237$	−181.935	+	181.935i	−0.767659	+	0.767659i
$238$	133.498	−	144.359i	0.560916	−	0.606551i
$239$			136.882i			0.572727i	0.958121	+	0.286364i	$0.0924465\pi$
$239$			136.882i			0.572727i	−0.958121	+	0.286364i	$0.907553\pi$
$240$	−264.419	−	122.269i	−1.10175	−	0.509453i
$241$	−336.536			−1.39641			−0.698207	−	0.715896i	$-0.746019\pi$
$241$	−336.536			−1.39641			−0.698207	+	0.715896i	$0.746019\pi$
$242$	202.889	+	187.624i	0.838382	+	0.775305i
$243$	−150.729	−	150.729i	−0.620283	−	0.620283i
$244$	274.351	−	21.4809i	1.12439	−	0.0880366i
$245$	15.3544	+	77.3330i	0.0626711	+	0.315645i
$246$	17.6592	+	451.770i	0.0717853	+	1.83646i
$247$	93.4072	+	93.4072i	0.378167	+	0.378167i
$248$	−123.808	+	156.855i	−0.499224	+	0.632479i
$249$		−	495.713i		−	1.99081i
$250$	246.873	+	39.4168i	0.987492	+	0.157667i
$251$		−	136.655i		−	0.544444i	−0.962234	−	0.272222i	$-0.912241\pi$
$251$		−	136.655i		−	0.544444i	0.962234	−	0.272222i	$-0.0877585\pi$
$252$	74.6778	+	63.8328i	0.296340	+	0.253305i
$253$	41.3718	+	41.3718i	0.163525	+	0.163525i
$254$	−10.3884	−	265.764i	−0.0408993	−	1.04632i
$255$	−60.4722	−	304.570i	−0.237146	−	1.19439i
$256$	243.597	−	78.7169i	0.951552	−	0.307488i
$257$	−110.399	−	110.399i	−0.429570	−	0.429570i	0.458912	−	0.888482i	$-0.348239\pi$
$257$	−110.399	−	110.399i	−0.429570	−	0.429570i	−0.888482	+	0.458912i	$0.848239\pi$
$258$	94.4495	−	102.134i	0.366083	−	0.395867i
$259$	−219.058			−0.845782
$260$	135.329	−	241.222i	0.520495	−	0.927776i
$261$		−	43.2097i		−	0.165555i
$262$	14.8630	−	16.0722i	0.0567290	−	0.0613443i
$263$	−335.915	+	335.915i	−1.27724	+	1.27724i	−0.335039	+	0.942204i	$0.608750\pi$
$263$	−335.915	+	335.915i	−1.27724	+	1.27724i	−0.942204	+	0.335039i	$0.891250\pi$
$264$	54.8432	+	465.773i	0.207739	+	1.76429i
$265$	269.503	+	180.212i	1.01699	+	0.680047i
$266$	4.30146	+	110.043i	0.0161709	+	0.413696i
$267$	267.584	−	267.584i	1.00219	−	1.00219i
$268$	63.5251	+	54.2997i	0.237034	+	0.202611i
$269$	228.300			0.848699			0.424350	−	0.905498i	$-0.360503\pi$
$269$	228.300			0.848699			0.424350	+	0.905498i	$0.360503\pi$
$270$	−167.842	+	40.1978i	−0.621638	+	0.148881i
$271$	19.8387			0.0732057			0.0366029	−	0.999330i	$-0.488346\pi$
$271$	19.8387			0.0732057			0.0366029	+	0.999330i	$0.488346\pi$
$272$	220.626	+	160.565i	0.811126	+	0.590314i
$273$	−205.280	+	205.280i	−0.751940	+	0.751940i
$274$	5.07896	+	129.934i	0.0185364	+	0.474211i
$275$	−153.759	−	371.942i	−0.559125	−	1.35252i
$276$	4.13224	+	52.7762i	0.0149719	+	0.191218i
$277$	−247.644	+	247.644i	−0.894023	+	0.894023i	−0.994899	−	0.100876i	$-0.967836\pi$
$277$	−247.644	+	247.644i	−0.894023	+	0.894023i	0.100876	+	0.994899i	$0.467836\pi$
$278$	267.524	+	247.396i	0.962315	+	0.889914i
$279$		−	106.421i		−	0.381439i
$280$	219.369	−	71.0465i	0.783461	−	0.253738i
$281$	358.106			1.27440			0.637200	−	0.770699i	$-0.280093\pi$
$281$	358.106			1.27440			0.637200	+	0.770699i	$0.280093\pi$
$282$	−83.5739	+	90.3733i	−0.296361	+	0.320473i
$283$	88.1863	+	88.1863i	0.311612	+	0.311612i	0.845534	−	0.533922i	$-0.179282\pi$
$283$	88.1863	+	88.1863i	0.311612	+	0.311612i	−0.533922	+	0.845534i	$0.679282\pi$
$284$	−9.71914	−	124.131i	−0.0342223	−	0.437081i
$285$	144.572	+	96.6730i	0.507270	+	0.339203i
$286$	−444.937	+	17.3921i	−1.55573	+	0.0608115i
$287$	−253.046	−	253.046i	−0.881692	−	0.881692i
$288$	−75.8580	+	113.283i	−0.263396	+	0.393344i
$289$			1.84834i			0.00639563i
$290$	−86.4451	−	53.0391i	−0.298087	−	0.182893i
$291$		−	158.758i		−	0.545561i
$292$	−110.188	−	94.1858i	−0.377355	−	0.322554i
$293$	−167.672	−	167.672i	−0.572260	−	0.572260i	0.360500	−	0.932759i	$-0.382606\pi$
$293$	−167.672	−	167.672i	−0.572260	−	0.572260i	−0.932759	+	0.360500i	$0.882606\pi$
$294$	114.754	−	4.48562i	0.390321	−	0.0152572i
$295$	141.875	−	28.1691i	0.480931	−	0.0954885i
$296$	−35.5494	−	301.914i	−0.120099	−	1.01998i
$297$	196.468	+	196.468i	0.661509	+	0.661509i
$298$	349.527	+	323.230i	1.17291	+	1.08466i
$299$	−50.2610			−0.168097
$300$	112.909	−	346.203i	0.376365	−	1.15401i
$301$			110.110i			0.365815i
$302$	55.6022	+	51.4189i	0.184113	+	0.170261i
$303$	184.639	−	184.639i	0.609369	−	0.609369i
$304$	−150.968	+	23.7866i	−0.496605	+	0.0782454i
$305$	66.9909	+	337.402i	0.219642	+	1.10624i
$306$	−145.208	+	5.67603i	−0.474537	+	0.0185491i
$307$	150.578	−	150.578i	0.490481	−	0.490481i	−0.417977	−	0.908458i	$-0.637261\pi$
$307$	150.578	−	150.578i	0.490481	−	0.490481i	0.908458	+	0.417977i	$0.137261\pi$
$308$	−282.180	−	241.200i	−0.916168	−	0.783118i
$309$	−288.857			−0.934811
$310$	−212.906	−	130.630i	−0.686794	−	0.421388i
$311$	321.652			1.03425			0.517125	−	0.855910i	$-0.327002\pi$
$311$	321.652			1.03425			0.517125	+	0.855910i	$0.327002\pi$
$312$	−316.238	−	249.611i	−1.01358	−	0.800036i
$313$	148.596	−	148.596i	0.474748	−	0.474748i	−0.428699	−	0.903447i	$-0.641028\pi$
$313$	148.596	−	148.596i	0.474748	−	0.474748i	0.903447	+	0.428699i	$0.141028\pi$
$314$	−321.266	+	12.5579i	−1.02314	+	0.0399934i
$315$	−68.2607	+	102.082i	−0.216701	+	0.324071i
$316$	281.763	−	22.0613i	0.891656	−	0.0698143i
$317$	−59.1929	+	59.1929i	−0.186728	+	0.186728i	−0.794280	−	0.607552i	$-0.792152\pi$
$317$	−59.1929	+	59.1929i	−0.186728	+	0.186728i	0.607552	+	0.794280i	$0.292152\pi$
$318$	320.624	−	346.709i	1.00825	−	1.09028i
$319$			163.274i			0.511829i
$320$	133.519	+	290.814i	0.417247	+	0.908793i
$321$	−346.065			−1.07809
$322$	−30.7635	−	28.4490i	−0.0955389	−	0.0883509i
$323$	−115.188	−	115.188i	−0.356620	−	0.356620i
$324$	31.5958	+	403.536i	0.0975178	+	1.24548i
$325$	319.327	+	132.531i	0.982545	+	0.407787i
$326$	−10.3528	−	264.852i	−0.0317570	−	0.812431i
$327$	−240.098	−	240.098i	−0.734245	−	0.734245i
$328$	307.693	−	389.823i	0.938088	−	1.18848i
$329$		−	97.4314i		−	0.296144i
$330$	−570.116	+	136.541i	−1.72762	+	0.413761i
$331$			349.544i			1.05602i	0.849237	+	0.528012i	$0.177062\pi$
$331$			349.544i			1.05602i	−0.849237	+	0.528012i	$0.822938\pi$
$332$	−353.801	+	413.911i	−1.06567	+	1.24672i
$333$	114.480	+	114.480i	0.343783	+	0.343783i
$334$	16.7846	+	429.397i	0.0502534	+	1.28562i
$335$	−58.0663	+	86.8368i	−0.173332	+	0.259214i
$336$	−52.2754	−	331.780i	−0.155582	−	0.987440i
$337$	−340.837	−	340.837i	−1.01139	−	1.01139i	−0.999934	−	0.0114512i	$-0.996355\pi$
$337$	−340.837	−	340.837i	−1.01139	−	1.01139i	−0.0114512	−	0.999934i	$-0.503645\pi$
$338$	30.2196	−	32.6782i	0.0894071	−	0.0966811i
$339$	−208.581			−0.615282
$340$	−166.885	+	297.471i	−0.490838	+	0.874913i
$341$			402.127i			1.17926i
$342$	55.2607	−	59.7566i	0.161581	−	0.174727i
$343$	−264.012	+	264.012i	−0.769715	+	0.769715i
$344$	−151.759	+	17.8691i	−0.441159	+	0.0519449i
$345$	−64.9051	+	12.8869i	−0.188131	+	0.0373533i
$346$	1.51683	+	38.8047i	0.00438391	+	0.112152i
$347$	−37.6510	+	37.6510i	−0.108504	+	0.108504i	−0.759275	−	0.650770i	$-0.774446\pi$
$347$	−37.6510	+	37.6510i	−0.108504	+	0.108504i	0.650770	+	0.759275i	$0.274446\pi$
$348$	−95.9864	+	112.294i	−0.275823	+	0.322685i
$349$	−16.2380			−0.0465271			−0.0232635	−	0.999729i	$-0.507406\pi$
$349$	−16.2380			−0.0465271			−0.0232635	+	0.999729i	$0.507406\pi$
$350$	120.436	+	261.866i	0.344104	+	0.748188i
$351$	−238.682			−0.680004
$352$	286.639	−	428.054i	0.814316	−	1.21606i
$353$	186.688	−	186.688i	0.528860	−	0.528860i	−0.391372	−	0.920232i	$-0.628000\pi$
$353$	186.688	−	186.688i	0.528860	−	0.528860i	0.920232	+	0.391372i	$0.128000\pi$
$354$	−8.22928	−	210.527i	−0.0232465	−	0.594710i
$355$	152.659	−	30.3103i	0.430025	−	0.0853812i
$356$	−414.408	+	32.4471i	−1.16407	+	0.0911435i
$357$	253.147	−	253.147i	0.709096	−	0.709096i
$358$	−281.483	−	260.305i	−0.786265	−	0.727109i
$359$			253.509i			0.706152i	0.935595	+	0.353076i	$0.114864\pi$
$359$			253.509i			0.706152i	−0.935595	+	0.353076i	$0.885136\pi$
$360$	−151.771	−	77.5135i	−0.421587	−	0.215315i
$361$	−269.761			−0.747261
$362$	271.078	−	293.133i	0.748835	−	0.809758i
$363$	355.784	+	355.784i	0.980121	+	0.980121i
$364$	317.917	−	24.8921i	0.873398	−	0.0683848i
$365$	100.719	−	150.623i	0.275943	−	0.412666i
$366$	500.670	−	19.5706i	1.36795	−	0.0534717i
$367$	357.084	+	357.084i	0.972980	+	0.972980i	0.999644	−	0.0266642i	$-0.00848848\pi$
$367$	357.084	+	357.084i	0.972980	+	0.972980i	−0.0266642	+	0.999644i	$0.508488\pi$
$368$	34.2172	−	47.0164i	0.0929814	−	0.127762i
$369$			264.484i			0.716759i
$370$	369.549	−	88.5060i	0.998782	−	0.239205i
$371$			373.787i			1.00751i
$372$	−236.406	+	276.570i	−0.635499	+	0.743468i
$373$	−289.649	−	289.649i	−0.776539	−	0.776539i	0.202702	−	0.979241i	$-0.435028\pi$
$373$	−289.649	−	289.649i	−0.776539	−	0.776539i	−0.979241	+	0.202702i	$0.935028\pi$
$374$	548.689	−	21.4476i	1.46708	−	0.0573466i
$375$	446.348	+	89.2701i	1.19026	+	0.238054i
$376$	134.284	−	15.8115i	0.357138	−	0.0420518i
$377$	−99.1773	−	99.1773i	−0.263070	−	0.263070i
$378$	−146.091	−	135.100i	−0.386484	−	0.357407i
$379$	577.250			1.52309			0.761544	−	0.648114i	$-0.224442\pi$
$379$	577.250			1.52309			0.761544	+	0.648114i	$0.224442\pi$
$380$	−51.7173	−	183.904i	−0.136098	−	0.483959i
$381$		−	484.260i		−	1.27102i
$382$	−344.419	−	318.506i	−0.901619	−	0.833784i
$383$	368.331	−	368.331i	0.961700	−	0.961700i	−0.0375933	−	0.999293i	$-0.511969\pi$
$383$	368.331	−	368.331i	0.961700	−	0.961700i	0.999293	+	0.0375933i	$0.0119692\pi$
$384$	448.789	−	125.890i	1.16872	−	0.327840i
$385$	257.932	−	385.731i	0.669953	−	1.00190i
$386$	−313.677	+	12.2613i	−0.812636	+	0.0317650i
$387$	57.5438	−	57.5438i	0.148692	−	0.148692i
$388$	−113.309	+	132.560i	−0.292034	+	0.341650i
$389$	664.738			1.70884			0.854418	−	0.519586i	$-0.173914\pi$
$389$	664.738			1.70884			0.854418	+	0.519586i	$0.173914\pi$
$390$	263.367	−	429.245i	0.675299	−	1.10063i
$391$	61.9810			0.158519
$392$	−99.0192	−	78.1572i	−0.252600	−	0.199381i
$393$	28.1841	−	28.1841i	0.0717153	−	0.0717153i
$394$	−570.517	+	22.3009i	−1.44801	+	0.0566012i
$395$	68.8009	+	346.518i	0.174180	+	0.877260i
$396$	21.4158	+	273.519i	0.0540803	+	0.690704i
$397$	12.3083	−	12.3083i	0.0310032	−	0.0310032i	−0.691435	−	0.722438i	$-0.743021\pi$
$397$	12.3083	−	12.3083i	0.0310032	−	0.0310032i	0.722438	+	0.691435i	$0.243021\pi$
$398$	−393.402	+	425.409i	−0.988448	+	1.06887i
$399$			200.514i			0.502541i
$400$	−341.370	+	208.487i	−0.853424	+	0.521217i
$401$	204.388			0.509695			0.254847	−	0.966981i	$-0.417975\pi$
$401$	204.388			0.509695			0.254847	+	0.966981i	$0.417975\pi$
$402$	111.713	+	103.308i	0.277894	+	0.256986i
$403$	−244.264	−	244.264i	−0.606115	−	0.606115i
$404$	−285.950	+	22.3892i	−0.707798	+	0.0554187i
$405$	−496.276	+	98.5353i	−1.22537	+	0.243297i
$406$	−4.56718	−	116.841i	−0.0112492	−	0.287785i
$407$	−432.576	−	432.576i	−1.06284	−	1.06284i
$408$	389.979	+	307.816i	0.955832	+	0.754452i
$409$			679.776i			1.66204i	0.556239	+	0.831022i	$0.312244\pi$
$409$			679.776i			1.66204i	−0.556239	+	0.831022i	$0.687756\pi$
$410$	529.125	+	324.649i	1.29055	+	0.791826i
$411$			236.757i			0.576052i
$412$	241.190	+	206.163i	0.585412	+	0.500396i
$413$	117.921	+	117.921i	0.285522	+	0.285522i
$414$	1.20959	+	30.9445i	0.00292171	+	0.0747452i
$415$	−565.803	−	378.343i	−1.36338	−	0.911671i
$416$	85.8999	+	434.127i	0.206490	+	1.04357i
$417$	469.128	+	469.128i	1.12501	+	1.12501i
$418$	−208.810	+	225.798i	−0.499545	+	0.540186i
$419$	−738.655			−1.76290			−0.881450	−	0.472277i	$-0.843432\pi$
$419$	−738.655			−1.76290			−0.881450	+	0.472277i	$0.843432\pi$
$420$	404.164	−	113.658i	0.962294	−	0.270615i
$421$		−	743.556i		−	1.76617i	−0.469217	−	0.883083i	$-0.655464\pi$
$421$		−	743.556i		−	1.76617i	0.469217	−	0.883083i	$-0.344536\pi$
$422$	40.0390	−	43.2965i	0.0948792	−	0.102598i
$423$	−50.9177	+	50.9177i	−0.120373	+	0.120373i
$424$	−515.168	+	60.6593i	−1.21502	+	0.143064i
$425$	−393.788	−	163.435i	−0.926561	−	0.384552i
$426$	−8.85481	−	226.530i	−0.0207859	−	0.531761i
$427$	−280.436	+	280.436i	−0.656758	+	0.656758i
$428$	288.958	+	246.994i	0.675135	+	0.577089i
$429$	−810.738			−1.88983
$430$	−44.4879	−	185.756i	−0.103460	−	0.431990i
$431$	−425.523			−0.987293			−0.493646	−	0.869663i	$-0.664336\pi$
$431$	−425.523			−0.987293			−0.493646	+	0.869663i	$0.664336\pi$
$432$	162.492	−	223.273i	0.376138	−	0.516836i
$433$	71.2826	−	71.2826i	0.164625	−	0.164625i	−0.619987	−	0.784612i	$-0.712862\pi$
$433$	71.2826	−	71.2826i	0.164625	−	0.164625i	0.784612	+	0.619987i	$0.212862\pi$
$434$	−11.2485	−	287.768i	−0.0259183	−	0.663060i
$435$	−153.503	−	102.645i	−0.352880	−	0.235965i
$436$	29.1141	+	371.841i	0.0667756	+	0.852846i
$437$	−24.5471	+	24.5471i	−0.0561718	+	0.0561718i
$438$	−193.773	−	179.194i	−0.442404	−	0.409119i
$439$		−	822.022i		−	1.87249i	−0.351350	−	0.936244i	$-0.614277\pi$
$439$		−	822.022i		−	1.87249i	0.351350	−	0.936244i	$-0.385723\pi$
$440$	573.488	+	292.895i	1.30338	+	0.665670i
$441$	67.1817			0.152339
$442$	−320.262	+	346.318i	−0.724576	+	0.783526i
$443$	136.545	+	136.545i	0.308228	+	0.308228i	0.844222	−	0.535994i	$-0.180063\pi$
$443$	136.545	+	136.545i	0.308228	+	0.308228i	−0.535994	+	0.844222i	$0.680063\pi$
$444$	−43.2059	−	551.818i	−0.0973107	−	1.24283i
$445$	−101.190	−	509.647i	−0.227394	−	1.14527i
$446$	393.496	−	15.3813i	0.882277	−	0.0344872i
$447$	612.928	+	612.928i	1.37120	+	1.37120i
$448$	−193.149	+	314.340i	−0.431137	+	0.701651i
$449$		−	184.949i		−	0.411912i	−0.978561	−	0.205956i	$-0.933970\pi$
$449$		−	184.949i		−	0.411912i	0.978561	−	0.205956i	$-0.0660304\pi$
$450$	73.9112	−	199.792i	0.164247	−	0.443981i
$451$		−	999.386i		−	2.21593i
$452$	174.161	+	148.868i	0.385312	+	0.329355i
$453$	97.5037	+	97.5037i	0.215240	+	0.215240i
$454$	45.7225	−	1.78724i	0.100710	−	0.00393666i
$455$	77.6290	+	390.980i	0.170613	+	0.859298i
$456$	−276.356	+	32.5400i	−0.606045	+	0.0713597i
$457$	1.00862	+	1.00862i	0.00220704	+	0.00220704i	0.708209	−	0.706002i	$-0.249503\pi$
$457$	1.00862	+	1.00862i	0.00220704	+	0.00220704i	−0.706002	+	0.708209i	$0.749503\pi$
$458$	−33.4542	−	30.9372i	−0.0730441	−	0.0675485i
$459$	294.338			0.641259
$460$	63.3922	+	35.5639i	0.137809	+	0.0773128i
$461$			366.482i			0.794973i	0.917608	+	0.397486i	$0.130117\pi$
$461$			366.482i			0.794973i	−0.917608	+	0.397486i	$0.869883\pi$
$462$	−496.233	−	458.898i	−1.07410	−	0.993285i
$463$	189.208	−	189.208i	0.408656	−	0.408656i	−0.472614	−	0.881270i	$-0.656689\pi$
$463$	189.208	−	189.208i	0.408656	−	0.408656i	0.881270	+	0.472614i	$0.156689\pi$
$464$	160.294	−	25.2560i	0.345460	−	0.0544310i
$465$	−378.063	−	252.805i	−0.813039	−	0.543666i
$466$	153.308	−	5.99265i	0.328988	−	0.0128598i
$467$	−606.765	+	606.765i	−1.29928	+	1.29928i	−0.370417	+	0.928866i	$0.620785\pi$
$467$	−606.765	+	606.765i	−1.29928	+	1.29928i	−0.928866	+	0.370417i	$0.879215\pi$
$468$	−179.152	−	153.135i	−0.382804	−	0.327212i
$469$	−120.438			−0.256797
$470$	39.3652	+	164.366i	0.0837558	+	0.349715i
$471$	−585.391			−1.24287
$472$	−143.387	+	181.660i	−0.303785	+	0.384872i
$473$	−217.437	+	217.437i	−0.459697	+	0.459697i
$474$	514.197	−	20.0994i	1.08480	−	0.0424038i
$475$	220.684	−	91.2297i	0.464597	−	0.192063i
$476$	−392.050	+	30.6965i	−0.823634	+	0.0644883i
$477$	195.341	−	195.341i	0.409521	−	0.409521i
$478$	185.871	−	200.993i	0.388852	−	0.420488i
$479$			404.491i			0.844449i	0.906491	+	0.422225i	$0.138751\pi$
$479$			404.491i			0.844449i	−0.906491	+	0.422225i	$0.861249\pi$
$480$	222.238	+	538.590i	0.462995	+	1.12206i
$481$	525.520			1.09256
$482$	494.160	+	456.981i	1.02523	+	0.948093i
$483$	−53.9467	−	53.9467i	−0.111691	−	0.111691i
$484$	−43.1421	−	551.003i	−0.0891366	−	1.13844i
$485$	−181.205	−	121.169i	−0.373620	−	0.249833i
$486$	16.6519	+	426.000i	0.0342631	+	0.876543i
$487$	332.025	+	332.025i	0.681776	+	0.681776i	0.960400	−	0.278624i	$-0.0898783\pi$
$487$	332.025	+	332.025i	0.681776	+	0.681776i	−0.278624	+	0.960400i	$0.589878\pi$
$488$	−432.018	−	340.998i	−0.885283	−	0.698766i
$489$		−	482.598i		−	0.986908i
$490$	82.4642	−	134.403i	0.168294	−	0.274293i
$491$		−	453.520i		−	0.923665i	−0.886967	−	0.461833i	$-0.847192\pi$
$491$		−	453.520i		−	0.923665i	0.886967	−	0.461833i	$-0.152808\pi$
$492$	587.527	−	687.346i	1.19416	−	1.39704i
$493$	122.304	+	122.304i	0.248081	+	0.248081i
$494$	−10.3192	−	263.994i	−0.0208891	−	0.534401i
$495$	−336.379	+	66.7878i	−0.679553	+	0.134925i
$496$	394.788	−	62.2031i	0.795944	−	0.125409i
$497$	126.884	+	126.884i	0.255300	+	0.255300i
$498$	−673.127	+	727.891i	−1.35166	+	1.46163i
$499$	929.441			1.86261			0.931303	−	0.364245i	$-0.118673\pi$
$499$	929.441			1.86261			0.931303	+	0.364245i	$0.118673\pi$
$500$	−308.978	−	393.107i	−0.617955	−	0.786213i
$501$			782.420i			1.56172i
$502$	−185.564	+	200.661i	−0.369649	+	0.399723i
$503$	557.709	−	557.709i	1.10877	−	1.10877i	0.115452	−	0.993313i	$-0.463168\pi$
$503$	557.709	−	557.709i	1.10877	−	1.10877i	0.993313	−	0.115452i	$-0.0368317\pi$
$504$	−22.9765	−	195.135i	−0.0455883	−	0.387173i
$505$	−69.8233	−	351.667i	−0.138264	−	0.696371i
$506$	−4.57058	−	116.928i	−0.00903276	−	0.231083i
$507$	57.3043	−	57.3043i	0.113026	−	0.113026i
$508$	−345.626	+	404.347i	−0.680367	+	0.795960i
$509$	289.521			0.568803			0.284402	−	0.958705i	$-0.408205\pi$
$509$	289.521			0.568803			0.284402	+	0.958705i	$0.408205\pi$
$510$	−324.779	+	529.337i	−0.636821	+	1.03792i
$511$	208.906			0.408819
$512$	−464.581	−	215.194i	−0.907385	−	0.420301i
$513$	−116.570	+	116.570i	−0.227232	+	0.227232i
$514$	12.1964	+	312.018i	0.0237285	+	0.607040i
$515$	−220.464	+	329.699i	−0.428086	+	0.640192i
$516$	−277.374	+	21.7177i	−0.537547	+	0.0420885i
$517$	192.399	−	192.399i	0.372145	−	0.372145i
$518$	321.658	+	297.458i	0.620962	+	0.574242i
$519$			70.7076i			0.136238i
$520$	−526.267	+	170.441i	−1.01205	+	0.327771i
$521$	−92.4339			−0.177416			−0.0887081	−	0.996058i	$-0.528274\pi$
$521$	−92.4339			−0.177416			−0.0887081	+	0.996058i	$0.528274\pi$
$522$	−58.6743	+	63.4480i	−0.112403	+	0.121548i
$523$	−73.4105	−	73.4105i	−0.140364	−	0.140364i	0.633433	−	0.773797i	$-0.281645\pi$
$523$	−73.4105	−	73.4105i	−0.140364	−	0.140364i	−0.773797	+	0.633433i	$0.781645\pi$
$524$	−43.6488	+	3.41759i	−0.0832992	+	0.00652211i
$525$	200.494	+	484.993i	0.381894	+	0.923796i
$526$	949.386	−	37.1104i	1.80492	−	0.0705521i
$527$	301.223	+	301.223i	0.571580	+	0.571580i
$528$	551.941	−	758.400i	1.04534	−	1.43636i
$529$			515.792i			0.975031i
$530$	−151.021	−	630.577i	−0.284946	−	1.18977i
$531$		−	123.251i		−	0.232111i
$532$	143.111	−	167.425i	0.269006	−	0.314709i
$533$	607.058	+	607.058i	1.13895	+	1.13895i
$534$	−756.265	+	29.5615i	−1.41623	+	0.0553587i
$535$	−264.128	+	394.997i	−0.493697	+	0.738311i
$536$	−19.5451	−	165.993i	−0.0364647	−	0.309688i
$537$	−493.606	−	493.606i	−0.919192	−	0.919192i
$538$	−335.230	−	310.008i	−0.623103	−	0.576223i
$539$	−253.855			−0.470973
$540$	301.039	+	168.887i	0.557480	+	0.312754i
$541$			1018.70i			1.88300i	0.337015	+	0.941499i	$0.390583\pi$
$541$			1018.70i			1.88300i	−0.337015	+	0.941499i	$0.609417\pi$
$542$	−29.1307	−	26.9390i	−0.0537466	−	0.0497029i
$543$	514.035	−	514.035i	0.946658	−	0.946658i
$544$	−105.930	−	535.357i	−0.194725	−	0.984113i
$545$	−457.297	+	90.7960i	−0.839077	+	0.166598i
$546$	580.175	−	22.6784i	1.06259	−	0.0415355i
$547$	664.385	−	664.385i	1.21460	−	1.21460i	0.245101	−	0.969498i	$-0.421179\pi$
$547$	664.385	−	664.385i	1.21460	−	1.21460i	0.969498	−	0.245101i	$-0.0788211\pi$
$548$	168.979	−	197.688i	0.308355	−	0.360744i
$549$	293.112			0.533902
$550$	−279.283	+	754.938i	−0.507787	+	1.37262i
$551$	−96.8748			−0.175816
$552$	65.5969	−	83.1062i	0.118835	−	0.150555i
$553$	−288.013	+	288.013i	−0.520818	+	0.520818i
$554$	699.910	−	27.3587i	1.26338	−	0.0493839i
$555$	678.637	−	134.743i	1.22277	−	0.242780i
$556$	−56.8861	−	726.539i	−0.102313	−	1.30672i
$557$	−46.6729	+	46.6729i	−0.0837934	+	0.0837934i	−0.747761	−	0.663968i	$-0.768871\pi$
$557$	−46.6729	+	46.6729i	−0.0837934	+	0.0837934i	0.663968	+	0.747761i	$0.268871\pi$
$558$	−144.509	+	156.266i	−0.258977	+	0.280047i
$559$		−	264.155i		−	0.472550i
$560$	−418.589	−	193.558i	−0.747481	−	0.345639i
$561$	999.787			1.78215
$562$	−525.833	−	486.271i	−0.935647	−	0.865252i
$563$	−546.560	−	546.560i	−0.970798	−	0.970798i	0.0287871	−	0.999586i	$-0.490836\pi$
$563$	−546.560	−	546.560i	−0.970798	−	0.970798i	−0.999586	+	0.0287871i	$0.990836\pi$
$564$	245.435	−	19.2169i	0.435169	−	0.0340726i
$565$	−159.195	+	238.072i	−0.281761	+	0.421367i
$566$	−9.74244	−	249.238i	−0.0172128	−	0.440350i
$567$	−412.486	−	412.486i	−0.727488	−	0.727488i
$568$	−154.286	+	195.468i	−0.271630	+	0.344134i
$569$			728.906i			1.28103i	0.767946	+	0.640515i	$0.221279\pi$
$569$			728.906i			1.28103i	−0.767946	+	0.640515i	$0.778721\pi$
$570$	−81.0137	−	338.266i	−0.142129	−	0.593449i
$571$			958.495i			1.67863i	0.543649	+	0.839313i	$0.317042\pi$
$571$			958.495i			1.67863i	−0.543649	+	0.839313i	$0.682958\pi$
$572$	676.950	+	578.641i	1.18348	+	1.01161i
$573$	−603.970	−	603.970i	−1.05405	−	1.05405i
$574$	27.9554	+	715.175i	0.0487028	+	1.24595i
$575$	−34.8286	+	83.9179i	−0.0605715	+	0.145944i
$576$	265.214	−	63.3343i	0.460442	−	0.109955i
$577$	−129.063	−	129.063i	−0.223680	−	0.223680i	0.586366	−	0.810046i	$-0.300558\pi$
$577$	−129.063	−	129.063i	−0.223680	−	0.223680i	−0.810046	+	0.586366i	$0.800558\pi$
$578$	2.50985	−	2.71405i	0.00434230	−	0.00469558i
$579$	−571.564			−0.987156
$580$	54.9121	+	195.265i	0.0946760	+	0.336663i
$581$		−	784.739i		−	1.35067i
$582$	−215.577	+	233.116i	−0.370408	+	0.400543i
$583$	−738.122	+	738.122i	−1.26608	+	1.26608i
$584$	33.9020	+	287.923i	0.0580514	+	0.493019i
$585$	163.758	−	244.896i	0.279928	−	0.418625i
$586$	18.5237	+	473.886i	0.0316104	+	0.808680i
$587$	338.276	−	338.276i	0.576279	−	0.576279i	−0.357597	−	0.933876i	$-0.616404\pi$
$587$	338.276	−	338.276i	0.576279	−	0.576279i	0.933876	+	0.357597i	$0.116404\pi$
$588$	−174.593	−	149.238i	−0.296927	−	0.253806i
$589$	−238.593			−0.405082
$590$	−246.575	−	151.288i	−0.417924	−	0.256421i
$591$	−1039.56			−1.75899
$592$	−357.769	+	491.595i	−0.604339	+	0.830397i
$593$	233.374	−	233.374i	0.393549	−	0.393549i	−0.482402	−	0.875950i	$-0.660235\pi$
$593$	233.374	−	233.374i	0.393549	−	0.393549i	0.875950	+	0.482402i	$0.160235\pi$
$594$	−21.7049	−	555.272i	−0.0365403	−	0.934801i
$595$	−95.7306	−	482.150i	−0.160892	−	0.810336i
$596$	−74.3233	−	949.244i	−0.124703	−	1.59269i
$597$	−745.993	+	745.993i	−1.24957	+	1.24957i
$598$	73.8019	+	68.2493i	0.123415	+	0.114129i
$599$		−	758.974i		−	1.26707i	−0.773715	−	0.633534i	$-0.781604\pi$
$599$		−	758.974i		−	1.26707i	0.773715	−	0.633534i	$-0.218396\pi$
$600$	−635.901	+	355.035i	−1.05983	+	0.591726i
$601$	28.2787			0.0470527			0.0235263	−	0.999723i	$-0.492511\pi$
$601$	28.2787			0.0470527			0.0235263	+	0.999723i	$0.492511\pi$
$602$	149.518	−	161.683i	0.248369	−	0.268576i
$603$	62.9410	+	62.9410i	0.104380	+	0.104380i
$604$	−11.8232	−	151.004i	−0.0195749	−	0.250007i
$605$	677.634	−	134.544i	1.12006	−	0.222387i
$606$	−521.839	+	20.3981i	−0.861120	+	0.0336602i
$607$	−135.556	−	135.556i	−0.223321	−	0.223321i	0.586574	−	0.809895i	$-0.300476\pi$
$607$	−135.556	−	135.556i	−0.223321	−	0.223321i	−0.809895	+	0.586574i	$0.800476\pi$
$608$	253.977	+	170.071i	0.417725	+	0.279722i
$609$		−	212.900i		−	0.349590i
$610$	359.789	−	586.398i	0.589818	−	0.961308i
$611$			233.738i			0.382551i
$612$	220.928	+	188.844i	0.360993	+	0.308568i
$613$	174.164	+	174.164i	0.284118	+	0.284118i	0.834749	−	0.550631i	$-0.185613\pi$
$613$	174.164	+	174.164i	0.284118	+	0.284118i	−0.550631	+	0.834749i	$0.685613\pi$
$614$	−425.573	+	16.6352i	−0.693115	+	0.0270931i
$615$	939.580	+	628.282i	1.52777	+	1.02160i
$616$	86.8196	+	737.343i	0.140941	+	1.19698i
$617$	307.689	+	307.689i	0.498686	+	0.498686i	0.911029	−	0.412343i	$-0.135289\pi$
$617$	307.689	+	307.689i	0.498686	+	0.498686i	−0.412343	+	0.911029i	$0.635289\pi$
$618$	424.149	+	392.237i	0.686325	+	0.634688i
$619$	−787.518			−1.27224			−0.636121	−	0.771589i	$-0.719462\pi$
$619$	−787.518			−1.27224			−0.636121	+	0.771589i	$0.719462\pi$
$620$	135.243	+	480.919i	0.218134	+	0.775675i
$621$		−	62.7246i		−	0.101006i
$622$	−472.304	−	436.770i	−0.759332	−	0.702202i
$623$	423.600	−	423.600i	0.679935	−	0.679935i
$624$	125.409	+	795.941i	0.200976	+	1.27555i
$625$	442.558	−	441.324i	0.708094	−	0.706119i
$626$	−419.973	+	16.4163i	−0.670883	+	0.0262241i
$627$	−395.958	+	395.958i	−0.631511	+	0.631511i
$628$	488.790	+	417.806i	0.778328	+	0.665296i
$629$	−648.062			−1.03031
$630$	238.849	−	57.2037i	0.379126	−	0.0907995i
$631$	966.178			1.53118			0.765592	−	0.643326i	$-0.222446\pi$
$631$	966.178			1.53118			0.765592	+	0.643326i	$0.222446\pi$
$632$	−443.690	−	350.211i	−0.702042	−	0.554132i
$633$	75.9245	−	75.9245i	0.119944	−	0.119944i
$634$	167.295	−	6.53938i	0.263872	−	0.0103145i
$635$	−552.730	−	369.602i	−0.870442	−	0.582050i
$636$	−941.590	+	73.7240i	−1.48049	+	0.115918i
$637$	154.199	−	154.199i	0.242071	−	0.242071i
$638$	221.709	−	239.746i	0.347506	−	0.375778i
$639$		−	132.620i		−	0.207542i
$640$	198.839	−	608.328i	0.310686	−	0.950513i
$641$	−362.736			−0.565890			−0.282945	−	0.959136i	$-0.591311\pi$
$641$	−362.736			−0.565890			−0.282945	+	0.959136i	$0.591311\pi$
$642$	508.153	+	469.921i	0.791515	+	0.731964i
$643$	624.712	+	624.712i	0.971558	+	0.971558i	0.999607	−	0.0280482i	$-0.00892920\pi$
$643$	624.712	+	624.712i	0.971558	+	0.971558i	−0.0280482	+	0.999607i	$0.508929\pi$
$644$	6.54154	+	83.5474i	0.0101577	+	0.129732i
$645$	−67.7292	−	341.120i	−0.105006	−	0.528868i
$646$	12.7255	+	325.553i	0.0196989	+	0.503951i
$647$	206.963	+	206.963i	0.319880	+	0.319880i	0.848721	−	0.528841i	$-0.177373\pi$
$647$	206.963	+	206.963i	0.319880	+	0.319880i	−0.528841	+	0.848721i	$0.677373\pi$
$648$	501.565	−	635.444i	0.774020	−	0.980624i
$649$			465.720i			0.717596i
$650$	−288.928	−	628.218i	−0.444504	−	0.966489i
$651$		−	524.353i		−	0.805458i
$652$	−344.440	+	402.960i	−0.528283	+	0.618037i
$653$	−594.423	−	594.423i	−0.910295	−	0.910295i	0.0859998	−	0.996295i	$-0.472592\pi$
$653$	−594.423	−	594.423i	−0.910295	−	0.910295i	−0.996295	+	0.0859998i	$0.972592\pi$
$654$	26.5250	+	678.582i	0.0405581	+	1.03759i
$655$	−10.6582	−	53.6801i	−0.0162720	−	0.0819544i
$656$	−981.147	+	154.590i	−1.49565	+	0.235656i
$657$	−109.175	−	109.175i	−0.166172	−	0.166172i
$658$	−132.302	+	143.066i	−0.201066	+	0.217425i
$659$	677.106			1.02747			0.513737	−	0.857948i	$-0.328261\pi$
$659$	677.106			1.02747			0.513737	+	0.857948i	$0.328261\pi$
$660$	1022.55	+	573.665i	1.54932	+	0.869190i
$661$		−	1093.20i		−	1.65386i	−0.562306	−	0.826929i	$-0.690086\pi$
$661$		−	1093.20i		−	1.65386i	0.562306	−	0.826929i	$-0.309914\pi$
$662$	474.644	−	513.260i	0.716985	−	0.775317i
$663$	−607.301	+	607.301i	−0.915990	+	0.915990i
$664$	1081.56	−	127.350i	1.62885	−	0.191792i
$665$	228.865	+	153.038i	0.344158	+	0.230133i
$666$	−12.6472	−	323.551i	−0.0189898	−	0.485812i
$667$	26.0634	−	26.0634i	0.0390756	−	0.0390756i
$668$	558.430	−	653.306i	0.835973	−	0.978003i
$669$	717.004			1.07175
$670$	203.178	−	48.6606i	0.303251	−	0.0726278i
$671$	−1107.56			−1.65061
$672$	−373.763	+	558.161i	−0.556195	+	0.830596i
$673$	−842.562	+	842.562i	−1.25195	+	1.25195i	−0.297103	+	0.954845i	$0.596021\pi$
$673$	−842.562	+	842.562i	−1.25195	+	1.25195i	−0.954845	+	0.297103i	$0.903979\pi$
$674$	37.6542	+	963.297i	0.0558667	+	1.42922i
$675$	−165.396	+	398.513i	−0.245030	+	0.590389i
$676$	−88.7473	+	6.94868i	−0.131283	+	0.0102791i
$677$	190.367	−	190.367i	0.281193	−	0.281193i	−0.552392	−	0.833585i	$-0.686285\pi$
$677$	190.367	−	190.367i	0.281193	−	0.281193i	0.833585	+	0.552392i	$0.186285\pi$
$678$	306.274	+	283.231i	0.451732	+	0.417745i
$679$		−	251.322i		−	0.370136i
$680$	648.984	−	210.185i	0.954388	−	0.309095i
$681$	83.3128			0.122339
$682$	546.047	−	590.473i	0.800656	−	0.865795i
$683$	−83.1153	−	83.1153i	−0.121692	−	0.121692i	0.643638	−	0.765330i	$-0.277424\pi$
$683$	−83.1153	−	83.1153i	−0.121692	−	0.121692i	−0.765330	+	0.643638i	$0.777424\pi$
$684$	−162.287	+	12.7066i	−0.237261	+	0.0185769i
$685$	270.233	+	180.700i	0.394501	+	0.263796i
$686$	746.169	−	29.1669i	1.08771	−	0.0425174i
$687$	−58.6650	−	58.6650i	−0.0853931	−	0.0853931i
$688$	247.102	+	179.834i	0.359160	+	0.261387i
$689$		−	896.716i		−	1.30148i
$690$	112.804	+	69.2117i	0.163484	+	0.100307i
$691$			402.568i			0.582588i	0.956634	+	0.291294i	$0.0940858\pi$
$691$			402.568i			0.582588i	−0.956634	+	0.291294i	$0.905914\pi$
$692$	50.4656	−	59.0395i	0.0729271	−	0.0853172i
$693$	−279.585	−	279.585i	−0.403442	−	0.403442i
$694$	106.412	−	4.15951i	0.153331	−	0.00599354i
$695$	893.511	−	177.406i	1.28563	−	0.255261i
$696$	293.428	−	34.5501i	0.421592	−	0.0496410i
$697$	−748.613	−	748.613i	−1.07405	−	1.07405i
$698$	23.8434	+	22.0495i	0.0341595	+	0.0315895i
$699$	279.349			0.399641
$700$	178.741	−	548.057i	0.255345	−	0.782938i
$701$		−	98.8085i		−	0.140954i	−0.997513	−	0.0704768i	$-0.977548\pi$
$701$		−	98.8085i		−	0.140954i	0.997513	−	0.0704768i	$-0.0224521\pi$
$702$	350.473	+	324.105i	0.499250	+	0.461688i
$703$	256.660	−	256.660i	0.365092	−	0.365092i
$704$	−1002.15	+	239.317i	−1.42350	+	0.339938i
$705$	59.9303	+	301.841i	0.0850075	+	0.428143i
$706$	−527.629	+	20.6244i	−0.747350	+	0.0292131i
$707$	292.293	−	292.293i	0.413427	−	0.413427i
$708$	−273.791	+	320.307i	−0.386710	+	0.452411i
$709$	274.018			0.386486			0.193243	−	0.981151i	$-0.438099\pi$
$709$	274.018			0.386486			0.193243	+	0.981151i	$0.438099\pi$
$710$	−265.318	−	162.788i	−0.373688	−	0.229279i
$711$	301.031			0.423392
$712$	652.565	+	515.079i	0.916525	+	0.723426i
$713$	64.1918	−	64.1918i	0.0900305	−	0.0900305i
$714$	−715.462	+	27.9666i	−1.00205	+	0.0391689i
$715$	−618.780	+	925.370i	−0.865427	+	1.29422i
$716$	59.8543	+	764.449i	0.0835954	+	1.06767i
$717$	352.461	−	352.461i	0.491577	−	0.491577i
$718$	344.238	−	372.245i	0.479441	−	0.518447i
$719$			1235.00i			1.71766i	0.512257	+	0.858832i	$0.328809\pi$
$719$			1235.00i			1.71766i	−0.512257	+	0.858832i	$0.671191\pi$
$720$	117.602	+	319.909i	0.163336	+	0.444318i
$721$	−457.275			−0.634223
$722$	396.110	+	366.308i	0.548629	+	0.507352i
$723$	866.555	+	866.555i	1.19856	+	1.19856i
$724$	−796.087	+	62.3316i	−1.09957	+	0.0860933i
$725$	−234.316	+	96.8653i	−0.323195	+	0.133607i
$726$	−39.3055	−	1005.54i	−0.0541397	−	1.38504i
$727$	−357.322	−	357.322i	−0.491502	−	0.491502i	0.417278	−	0.908779i	$-0.362984\pi$
$727$	−357.322	−	357.322i	−0.491502	−	0.491502i	−0.908779	+	0.417278i	$0.862984\pi$
$728$	−500.621	−	395.148i	−0.687667	−	0.542785i
$729$		−	134.503i		−	0.184503i
$730$	−352.424	+	84.4045i	−0.482773	+	0.115623i
$731$			325.751i			0.445624i
$732$	−761.745	−	651.121i	−1.04064	−	0.889510i
$733$	−284.715	−	284.715i	−0.388425	−	0.388425i	0.485701	−	0.874125i	$-0.338565\pi$
$733$	−284.715	−	284.715i	−0.388425	−	0.388425i	−0.874125	+	0.485701i	$0.838565\pi$
$734$	−39.4491	−	1009.21i	−0.0537453	−	1.37495i
$735$	159.590	−	238.663i	0.217130	−	0.324712i
$736$	−114.087	+	22.5742i	−0.155009	+	0.0306714i
$737$	−237.831	−	237.831i	−0.322701	−	0.322701i
$738$	359.142	−	388.361i	0.486642	−	0.526234i
$739$	−394.960			−0.534452			−0.267226	−	0.963634i	$-0.586107\pi$
$739$	−394.960			−0.534452			−0.267226	+	0.963634i	$0.586107\pi$
$740$	−662.818	−	371.850i	−0.895700	−	0.502500i
$741$		−	481.034i		−	0.649168i
$742$	507.564	−	548.858i	0.684048	−	0.739701i
$743$	−498.663	+	498.663i	−0.671148	+	0.671148i	−0.957981	−	0.286833i	$-0.907398\pi$
$743$	−498.663	+	498.663i	−0.671148	+	0.671148i	0.286833	+	0.957981i	$0.407398\pi$
$744$	722.685	−	85.0937i	0.971351	−	0.114373i
$745$	1167.40	−	231.786i	1.56698	−	0.311122i
$746$	31.9992	+	818.626i	0.0428943	+	1.09735i
$747$	−410.105	+	410.105i	−0.549003	+	0.549003i
$748$	−834.803	−	713.570i	−1.11605	−	0.953970i
$749$	−547.839			−0.731428
$750$	−534.185	−	737.176i	−0.712246	−	0.982901i
$751$	803.935			1.07049			0.535243	−	0.844698i	$-0.320220\pi$
$751$	803.935			1.07049			0.535243	+	0.844698i	$0.320220\pi$
$752$	−218.649	−	159.127i	−0.290757	−	0.211604i
$753$	−351.878	+	351.878i	−0.467301	+	0.467301i
$754$	10.9567	+	280.302i	0.0145314	+	0.371753i
$755$	185.708	−	36.8722i	0.245971	−	0.0488373i
$756$	31.0647	+	396.753i	0.0410909	+	0.524806i
$757$	−705.439	+	705.439i	−0.931888	+	0.931888i	−0.997824	−	0.0659357i	$-0.978997\pi$
$757$	−705.439	+	705.439i	−0.931888	+	0.931888i	0.0659357	+	0.997824i	$0.478997\pi$
$758$	−847.618	−	783.846i	−1.11823	−	1.03410i
$759$		−	213.059i		−	0.280710i
$760$	−173.783	+	340.267i	−0.228661	+	0.447719i
$761$	1225.32			1.61015			0.805075	−	0.593173i	$-0.202125\pi$
$761$	1225.32			1.61015			0.805075	+	0.593173i	$0.202125\pi$
$762$	−657.574	+	711.073i	−0.862959	+	0.933167i
$763$	−380.088	−	380.088i	−0.498149	−	0.498149i
$764$	73.2370	+	935.370i	0.0958599	+	1.22431i
$765$	−201.943	+	302.001i	−0.263978	+	0.394773i
$766$	−1041.00	+	40.6916i	−1.35901	+	0.0531222i
$767$	−282.892	−	282.892i	−0.368830	−	0.368830i
$768$	−829.935	−	424.555i	−1.08065	−	0.552806i
$769$			440.431i			0.572732i	0.958120	+	0.286366i	$0.0924473\pi$
$769$			440.431i			0.572732i	−0.958120	+	0.286366i	$0.907553\pi$
$770$	−902.523	+	216.152i	−1.17211	+	0.280716i
$771$			568.541i			0.737407i
$772$	477.245	+	407.937i	0.618192	+	0.528416i
$773$	857.180	+	857.180i	1.10890	+	1.10890i	0.993295	+	0.115606i	$0.0368809\pi$
$773$	857.180	+	857.180i	1.10890	+	1.10890i	0.115606	+	0.993295i	$0.463119\pi$
$774$	−162.634	+	6.35718i	−0.210122	+	0.00821342i
$775$	−577.099	+	238.570i	−0.744643	+	0.307832i
$776$	346.383	−	40.7854i	0.446370	−	0.0525585i
$777$	564.057	+	564.057i	0.725943	+	0.725943i
$778$	−976.082	−	902.645i	−1.25460	−	1.16021i
$779$	592.964			0.761186
$780$	−969.591	+	272.667i	−1.24306	+	0.349573i
$781$			501.120i			0.641639i
$782$	−91.0112	−	84.1638i	−0.116383	−	0.107626i
$783$	123.771	−	123.771i	0.158073	−	0.158073i
$784$	39.2675	+	249.222i	0.0500861	+	0.317885i
$785$	−446.788	+	668.161i	−0.569157	+	0.851160i
$786$	−79.6559	+	3.11366i	−0.101343	+	0.00396140i
$787$	−74.0822	+	74.0822i	−0.0941324	+	0.0941324i	−0.752605	−	0.658472i	$-0.771203\pi$
$787$	−74.0822	+	74.0822i	−0.0941324	+	0.0941324i	0.658472	+	0.752605i	$0.271203\pi$
$788$	868.013	+	741.957i	1.10154	+	0.941570i
$789$	1729.91			2.19254
$790$	369.510	−	602.242i	0.467734	−	0.762331i
$791$	−330.194			−0.417438
$792$	339.964	−	430.708i	0.429248	−	0.543823i
$793$	672.767	−	672.767i	0.848381	−	0.848381i
$794$	−34.7865	+	1.35977i	−0.0438117	+	0.00171255i
$795$	−229.917	−	1157.99i	−0.289204	−	1.45659i
$796$	1155.32	−	90.4586i	1.45141	−	0.113642i
$797$	38.9824	−	38.9824i	0.0489114	−	0.0489114i	−0.682228	−	0.731139i	$-0.738989\pi$
$797$	38.9824	−	38.9824i	0.0489114	−	0.0489114i	0.731139	+	0.682228i	$0.238989\pi$
$798$	272.277	−	294.429i	0.341199	−	0.368958i
$799$		−	288.242i		−	0.360753i
$800$	784.361	+	157.408i	0.980452	+	0.196760i
$801$	−442.747			−0.552743
$802$	−300.117	−	277.537i	−0.374211	−	0.346056i
$803$	412.531	+	412.531i	0.513737	+	0.513737i
$804$	−23.7546	−	303.390i	−0.0295456	−	0.377351i
$805$	−102.748	+	20.4006i	−0.127637	+	0.0253424i
$806$	26.9853	+	690.357i	0.0334805	+	0.856522i
$807$	−587.856	−	587.856i	−0.728446	−	0.728446i
$808$	450.284	+	355.415i	0.557282	+	0.439871i
$809$		−	819.967i		−	1.01356i	−0.862076	−	0.506778i	$-0.830836\pi$
$809$		−	819.967i		−	1.01356i	0.862076	−	0.506778i	$-0.169164\pi$
$810$	862.518	+	529.205i	1.06484	+	0.653339i
$811$		−	758.180i		−	0.934870i	−0.884027	−	0.467435i	$-0.845178\pi$
$811$		−	758.180i		−	0.934870i	0.884027	−	0.467435i	$-0.154822\pi$
$812$	−151.951	+	177.768i	−0.187132	+	0.218926i
$813$	−51.0833	−	51.0833i	−0.0628331	−	0.0628331i
$814$	47.7892	+	1222.58i	0.0587091	+	1.50194i
$815$	−550.834	−	368.334i	−0.675870	−	0.451943i
$816$	−154.652	−	981.541i	−0.189525	−	1.20287i
$817$	−129.011	−	129.011i	−0.157908	−	0.157908i
$818$	923.066	−	998.164i	1.12844	−	1.22025i
$819$	339.657			0.414722
$820$	−336.113	−	1195.20i	−0.409894	−	1.45756i
$821$		−	271.357i		−	0.330520i	−0.986250	−	0.165260i	$-0.947154\pi$
$821$		−	271.357i		−	0.330520i	0.986250	−	0.165260i	$-0.0528464\pi$
$822$	321.492	−	347.648i	0.391109	−	0.422929i
$823$	−236.257	+	236.257i	−0.287068	+	0.287068i	−0.835920	−	0.548852i	$-0.815065\pi$
$823$	−236.257	+	236.257i	−0.287068	+	0.287068i	0.548852	+	0.835920i	$0.315065\pi$
$824$	−74.2080	−	630.235i	−0.0900583	−	0.764848i
$825$	−561.805	+	1353.64i	−0.680975	+	1.64078i
$826$	−13.0274	−	333.276i	−0.0157716	−	0.403481i
$827$	624.826	−	624.826i	0.755533	−	0.755533i	−0.219973	−	0.975506i	$-0.570597\pi$
$827$	624.826	−	624.826i	0.755533	−	0.755533i	0.975506	+	0.219973i	$0.0705969\pi$
$828$	40.2433	−	47.0806i	0.0486031	−	0.0568606i
$829$	−831.834			−1.00342			−0.501709	−	0.865036i	$-0.667295\pi$
$829$	−831.834			−1.00342			−0.501709	+	0.865036i	$0.667295\pi$
$830$	317.058	+	1323.85i	0.381998	+	1.59500i
$831$	1275.33			1.53470
$832$	463.366	−	754.103i	0.556931	−	0.906374i
$833$	−190.156	+	190.156i	−0.228278	+	0.228278i
$834$	−51.8272	−	1325.88i	−0.0621429	−	1.58978i
$835$	893.049	+	597.167i	1.06952	+	0.715170i
$836$	613.220	−	48.0136i	0.733517	−	0.0574325i
$837$	304.836	−	304.836i	0.364201	−	0.364201i
$838$	1084.62	+	1003.02i	1.29430	+	1.19692i
$839$		−	906.142i		−	1.08003i	−0.841657	−	0.540013i	$-0.818419\pi$
$839$		−	906.142i		−	1.08003i	0.841657	−	0.540013i	$-0.181581\pi$
$840$	−747.799	−	381.920i	−0.890237	−	0.454666i
$841$	−738.141			−0.877694
$842$	−1009.67	+	1091.82i	−1.19914	+	1.29669i
$843$	−922.098	−	922.098i	−1.09383	−	1.09383i
$844$	−117.584	+	9.20655i	−0.139318	+	0.0109082i
$845$	−21.6703	−	109.143i	−0.0256453	−	0.129163i
$846$	143.907	−	5.62517i	0.170103	−	0.00664914i
$847$	563.224	+	563.224i	0.664964	+	0.664964i
$848$	838.828	+	610.475i	0.989184	+	0.719900i
$849$		−	454.147i		−	0.534919i
$850$	356.300	+	774.707i	0.419177	+	0.911420i
$851$			138.105i			0.162285i
$852$	−294.602	+	344.654i	−0.345777	+	0.404524i
$853$	606.365	+	606.365i	0.710861	+	0.710861i	0.966715	−	0.255854i	$-0.0823567\pi$
$853$	606.365	+	606.365i	0.710861	+	0.710861i	−0.255854	+	0.966715i	$0.582357\pi$
$854$	792.586	−	30.9813i	0.928087	−	0.0362779i
$855$	−39.6271	−	199.583i	−0.0463475	−	0.233430i
$856$	−88.9051	−	755.055i	−0.103861	−	0.882073i
$857$	464.442	+	464.442i	0.541939	+	0.541939i	0.924097	−	0.382158i	$-0.124819\pi$
$857$	464.442	+	464.442i	0.541939	+	0.541939i	−0.382158	+	0.924097i	$0.624819\pi$
$858$	1190.46	+	1100.90i	1.38749	+	1.28310i
$859$	−1097.54			−1.27769			−0.638846	−	0.769335i	$-0.720588\pi$
$859$	−1097.54			−1.27769			−0.638846	+	0.769335i	$0.720588\pi$
$860$	−186.912	+	333.168i	−0.217340	+	0.387405i
$861$			1303.15i			1.51353i
$862$	624.826	+	577.816i	0.724857	+	0.670321i
$863$	−600.183	+	600.183i	−0.695461	+	0.695461i	−0.963428	−	0.267967i	$-0.913648\pi$
$863$	−600.183	+	600.183i	−0.695461	+	0.695461i	0.267967	+	0.963428i	$0.413648\pi$
$864$	−541.780	+	107.201i	−0.627061	+	0.124075i
$865$	80.7052	+	53.9662i	0.0933008	+	0.0623887i
$866$	−201.464	+	7.87499i	−0.232637	+	0.00909353i
$867$	4.75933	−	4.75933i	0.00548943	−	0.00548943i
$868$	−374.242	+	437.825i	−0.431155	+	0.504407i
$869$	−1137.49			−1.30896
$870$	86.0182	+	359.162i	0.0988715	+	0.412830i
$871$	288.931			0.331724
$872$	462.171	−	585.534i	0.530012	−	0.671485i
$873$	−131.341	+	131.341i	−0.150448	+	0.150448i
$874$	69.3766	−	2.71185i	0.0793783	−	0.00310281i
$875$	706.591	+	141.319i	0.807533	+	0.161508i
$876$	41.2037	+	526.247i	0.0470362	+	0.600738i
$877$	143.644	−	143.644i	0.163791	−	0.163791i	−0.620453	−	0.784244i	$-0.713051\pi$
$877$	143.644	−	143.644i	0.163791	−	0.163791i	0.784244	+	0.620453i	$0.213051\pi$
$878$	−1116.22	+	1207.03i	−1.27132	+	1.37476i
$879$			863.487i			0.982351i
$880$	−444.373	−	1208.82i	−0.504970	−	1.37365i
$881$	−539.456			−0.612322			−0.306161	−	0.951980i	$-0.599045\pi$
$881$	−539.456			−0.612322			−0.306161	+	0.951980i	$0.599045\pi$
$882$	−98.6477	−	91.2258i	−0.111846	−	0.103431i
$883$	−1104.94	−	1104.94i	−1.25135	−	1.25135i	−0.955114	−	0.296238i	$-0.904268\pi$
$883$	−1104.94	−	1104.94i	−1.25135	−	1.25135i	−0.296238	−	0.955114i	$-0.595732\pi$
$884$	940.529	−	73.6410i	1.06395	−	0.0833042i
$885$	−437.850	−	292.783i	−0.494746	−	0.330828i
$886$	−15.0849	−	385.913i	−0.0170258	−	0.435567i
$887$	585.130	+	585.130i	0.659673	+	0.659673i	0.955303	−	0.295630i	$-0.0955295\pi$
$887$	585.130	+	585.130i	0.659673	+	0.659673i	−0.295630	+	0.955303i	$0.595530\pi$
$888$	−685.870	+	868.944i	−0.772376	+	0.978541i
$889$		−	766.608i		−	0.862326i
$890$	−543.463	+	885.758i	−0.610633	+	0.995233i
$891$		−	1629.08i		−	1.82838i
$892$	−598.684	−	511.741i	−0.671171	−	0.573701i
$893$	114.156	+	114.156i	0.127834	+	0.127834i
$894$	−67.7137	−	1732.30i	−0.0757424	−	1.93770i
$895$	−940.134	+	186.663i	−1.05043	+	0.208562i
$896$	710.456	−	199.291i	0.792920	−	0.222423i
$897$	129.418	+	129.418i	0.144279	+	0.144279i
$898$	−251.141	+	271.573i	−0.279667	+	0.302420i
$899$	253.332			0.281793
$900$	−379.826	+	193.005i	−0.422028	+	0.214450i
$901$			1105.81i			1.22732i
$902$	−1357.06	+	1467.47i	−1.50450	+	1.62691i
$903$	283.526	−	283.526i	0.313982	−	0.313982i
$904$	−53.5849	−	455.087i	−0.0592753	−	0.503414i
$905$	−194.389	−	979.044i	−0.214794	−	1.08182i
$906$	−10.7718	−	275.572i	−0.0118894	−	0.304163i
$907$	−776.585	+	776.585i	−0.856213	+	0.856213i	−0.990890	−	0.134677i	$-0.957000\pi$
$907$	−776.585	+	776.585i	−0.856213	+	0.856213i	0.134677	+	0.990890i	$0.457000\pi$
$908$	−69.5646	−	59.4621i	−0.0766130	−	0.0654869i
$909$	−305.505			−0.336089
$910$	416.923	−	679.517i	0.458157	−	0.746722i
$911$	1188.92			1.30508			0.652538	−	0.757756i	$-0.273704\pi$
$911$	1188.92			1.30508			0.652538	+	0.757756i	$0.273704\pi$
$912$	449.980	+	327.482i	0.493399	+	0.359082i
$913$	1549.64	−	1549.64i	1.69730	−	1.69730i
$914$	−0.111428	−	2.85063i	−0.000121912	−	0.00311885i
$915$	696.288	−	1041.28i	0.760971	−	1.13801i
$916$	7.11368	+	90.8547i	0.00776603	+	0.0991863i
$917$	44.6169	−	44.6169i	0.0486553	−	0.0486553i
$918$	−432.197	−	399.680i	−0.470803	−	0.435382i
$919$			626.443i			0.681657i	0.940125	+	0.340829i	$0.110708\pi$
$919$			626.443i			0.681657i	−0.940125	+	0.340829i	$0.889292\pi$
$920$	−44.7912	−	138.301i	−0.0486861	−	0.150327i
$921$	−775.453			−0.841968
$922$	497.645	−	538.133i	0.539745	−	0.583658i
$923$	−304.396	−	304.396i	−0.329790	−	0.329790i
$924$	105.519	+	1347.67i	0.114198	+	1.45851i
$925$	364.162	−	877.431i	0.393689	−	0.948574i
$926$	−534.752	+	20.9029i	−0.577486	+	0.0225733i
$927$	238.972	+	238.972i	0.257791	+	0.257791i
$928$	−269.666	−	180.577i	−0.290588	−	0.194587i
$929$		−	288.725i		−	0.310791i	−0.987852	−	0.155396i	$-0.950335\pi$
$929$		−	288.725i		−	0.310791i	0.987852	−	0.155396i	$-0.0496653\pi$
$930$	211.855	+	884.581i	0.227801	+	0.951163i
$931$		−	150.619i		−	0.161782i
$932$	−233.251	−	199.377i	−0.250269	−	0.213924i
$933$	−828.230	−	828.230i	−0.887706	−	0.887706i
$934$	1714.88	−	67.0328i	1.83606	−	0.0717695i
$935$	763.068	−	1141.15i	0.816116	−	1.22048i
$936$	55.1207	+	468.130i	0.0588896	+	0.500139i
$937$	422.496	+	422.496i	0.450903	+	0.450903i	0.895654	−	0.444751i	$-0.146708\pi$
$937$	422.496	+	422.496i	0.450903	+	0.450903i	−0.444751	+	0.895654i	$0.646708\pi$
$938$	176.848	+	163.542i	0.188537	+	0.174352i
$939$	−765.249			−0.814961
$940$	165.390	−	294.805i	0.175946	−	0.313622i
$941$			512.796i			0.544947i	0.962163	+	0.272474i	$0.0878418\pi$
$941$			512.796i			0.544947i	−0.962163	+	0.272474i	$0.912158\pi$
$942$	859.571	+	794.900i	0.912496	+	0.843843i
$943$	−159.533	+	159.533i	−0.169176	+	0.169176i
$944$	457.220	−	72.0399i	0.484343	−	0.0763135i
$945$	−487.935	+	96.8792i	−0.516333	+	0.102518i
$946$	614.534	−	24.0214i	0.649613	−	0.0253926i
$947$	−320.049	+	320.049i	−0.337961	+	0.337961i	−0.855599	−	0.517638i	$-0.826811\pi$
$947$	−320.049	+	320.049i	−0.337961	+	0.337961i	0.517638	+	0.855599i	$0.326811\pi$
$948$	−782.326	−	668.714i	−0.825239	−	0.705394i
$949$	−501.167			−0.528101
$950$	−447.926	−	165.706i	−0.471501	−	0.174428i
$951$	304.835			0.320541
$952$	617.357	+	487.289i	0.648485	+	0.511858i
$953$	−305.376	+	305.376i	−0.320436	+	0.320436i	−0.848934	−	0.528498i	$-0.822755\pi$
$953$	−305.376	+	305.376i	−0.320436	+	0.320436i	0.528498	+	0.848934i	$0.322755\pi$
$954$	−552.087	+	21.5805i	−0.578708	+	0.0226210i
$955$	−1150.34	+	228.398i	−1.20454	+	0.239161i
$956$	−545.857	+	42.7391i	−0.570980	+	0.0447062i
$957$	420.417	−	420.417i	0.439308	−	0.439308i
$958$	549.257	−	593.944i	0.573338	−	0.619983i
$959$			374.799i			0.390823i
$960$	405.022	−	1092.63i	0.421898	−	1.13815i
$961$	−337.067			−0.350746
$962$	−771.660	−	713.602i	−0.802141	−	0.741790i
$963$	286.301	+	286.301i	0.297302	+	0.297302i
$964$	−105.078	−	1342.04i	−0.109002	−	1.39215i
$965$	−436.235	+	652.379i	−0.452057	+	0.676040i
$966$	5.95980	+	152.468i	0.00616956	+	0.157834i
$967$	−781.188	−	781.188i	−0.807847	−	0.807847i	0.176460	−	0.984308i	$-0.443535\pi$
$967$	−781.188	−	781.188i	−0.807847	−	0.807847i	−0.984308	+	0.176460i	$0.943535\pi$
$968$	−684.857	+	867.660i	−0.707497	+	0.896343i
$969$			593.202i			0.612180i
$970$	101.542	+	423.980i	0.104682	+	0.437092i
$971$		−	715.056i		−	0.736412i	−0.929744	−	0.368206i	$-0.879972\pi$
$971$		−	715.056i		−	0.736412i	0.929744	−	0.368206i	$-0.120028\pi$
$972$	554.013	−	648.138i	0.569972	−	0.666809i
$973$	742.653	+	742.653i	0.763261	+	0.763261i
$974$	−36.6807	−	938.392i	−0.0376598	−	0.963441i
$975$	−480.986	−	1163.50i	−0.493319	−	1.19333i
$976$	171.323	+	1087.35i	0.175536	+	1.11409i
$977$	1011.38	+	1011.38i	1.03519	+	1.03519i	0.999358	+	0.0358337i	$0.0114087\pi$
$977$	1011.38	+	1011.38i	1.03519	+	1.03519i	0.0358337	+	0.999358i	$0.488591\pi$
$978$	−655.318	+	708.633i	−0.670059	+	0.724574i
$979$	1672.98			1.70886
$980$	−303.594	+	85.3763i	−0.309790	+	0.0871187i
$981$			397.269i			0.404963i
$982$	−615.833	+	665.936i	−0.627121	+	0.678142i
$983$	−819.077	+	819.077i	−0.833242	+	0.833242i	−0.987959	−	0.154717i	$-0.950554\pi$
$983$	−819.077	+	819.077i	−0.833242	+	0.833242i	0.154717	+	0.987959i	$0.450554\pi$
$984$	−1796.05	+	211.479i	−1.82526	+	0.214918i
$985$	−793.425	+	1186.55i	−0.805507	+	1.20462i
$986$	−13.5116	−	345.663i	−0.0137034	−	0.350571i
$987$	−250.879	+	250.879i	−0.254183	+	0.254183i
$988$	−343.324	+	401.654i	−0.347494	+	0.406532i
$989$	69.4190			0.0701911
$990$	584.620	+	358.698i	0.590526	+	0.362321i
$991$	−1356.82			−1.36914			−0.684571	−	0.728946i	$-0.740010\pi$
$991$	−1356.82			−1.36914			−0.684571	+	0.728946i	$0.740010\pi$
$992$	−664.161	−	444.744i	−0.669518	−	0.448331i
$993$	900.049	−	900.049i	0.906394	−	0.906394i
$994$	−14.0176	−	358.609i	−0.0141022	−	0.360773i
$995$	282.106	+	1420.84i	0.283524	+	1.42798i
$996$	1976.80	−	154.778i	1.98474	−	0.155400i
$997$	389.935	−	389.935i	0.391109	−	0.391109i	−0.483974	−	0.875082i	$-0.660807\pi$
$997$	389.935	−	389.935i	0.391109	−	0.391109i	0.875082	+	0.483974i	$0.160807\pi$
$998$	−1364.76	−	1262.08i	−1.36750	−	1.26461i
$999$			655.838i			0.656494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	40.3.i.a.37.3	yes	20
3.2	odd	2		360.3.u.b.37.8		20
4.3	odd	2		160.3.m.a.17.9		20
5.2	odd	4		200.3.i.b.93.7		20
5.3	odd	4	inner	40.3.i.a.13.4	yes	20
5.4	even	2		200.3.i.b.157.8		20
8.3	odd	2		160.3.m.a.17.2		20
8.5	even	2	inner	40.3.i.a.37.4	yes	20
15.8	even	4		360.3.u.b.253.7		20
20.3	even	4		160.3.m.a.113.2		20
20.7	even	4		800.3.m.b.593.9		20
20.19	odd	2		800.3.m.b.657.2		20
24.5	odd	2		360.3.u.b.37.7		20
40.3	even	4		160.3.m.a.113.9		20
40.13	odd	4	inner	40.3.i.a.13.3	✓	20
40.19	odd	2		800.3.m.b.657.9		20
40.27	even	4		800.3.m.b.593.2		20
40.29	even	2		200.3.i.b.157.7		20
40.37	odd	4		200.3.i.b.93.8		20
120.53	even	4		360.3.u.b.253.8		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
40.3.i.a.13.3	✓	20	40.13	odd	4	inner
40.3.i.a.13.4	yes	20	5.3	odd	4	inner
40.3.i.a.37.3	yes	20	1.1	even	1	trivial
40.3.i.a.37.4	yes	20	8.5	even	2	inner
160.3.m.a.17.2		20	8.3	odd	2
160.3.m.a.17.9		20	4.3	odd	2
160.3.m.a.113.2		20	20.3	even	4
160.3.m.a.113.9		20	40.3	even	4
200.3.i.b.93.7		20	5.2	odd	4
200.3.i.b.93.8		20	40.37	odd	4
200.3.i.b.157.7		20	40.29	even	2
200.3.i.b.157.8		20	5.4	even	2
360.3.u.b.37.7		20	24.5	odd	2
360.3.u.b.37.8		20	3.2	odd	2
360.3.u.b.253.7		20	15.8	even	4
360.3.u.b.253.8		20	120.53	even	4
800.3.m.b.593.2		20	40.27	even	4
800.3.m.b.593.9		20	20.7	even	4
800.3.m.b.657.2		20	20.19	odd	2
800.3.m.b.657.9		20	40.19	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:	\( N \)	\(=\)	\( 40 = 2^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	40.i (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.46837 - 1.35790i) q^{2} +(-2.57493 - 2.57493i) q^{3} +(0.312234 + 3.98780i) q^{4} +(-4.90427 + 0.973739i) q^{5} +(0.284467 + 7.27744i) q^{6} +(-4.07624 - 4.07624i) q^{7} +(4.95654 - 6.27955i) q^{8} +4.26050i q^{9} +O(q^{10})\)	\(q+(-1.46837 - 1.35790i) q^{2} +(-2.57493 - 2.57493i) q^{3} +(0.312234 + 3.98780i) q^{4} +(-4.90427 + 0.973739i) q^{5} +(0.284467 + 7.27744i) q^{6} +(-4.07624 - 4.07624i) q^{7} +(4.95654 - 6.27955i) q^{8} +4.26050i q^{9} +(8.52353 + 5.22967i) q^{10} -16.0988i q^{11} +(9.46430 - 11.0723i) q^{12} +(9.77892 + 9.77892i) q^{13} +(0.450325 + 11.5206i) q^{14} +(15.1354 + 10.1208i) q^{15} +(-15.8050 + 2.49025i) q^{16} +(-12.0592 - 12.0592i) q^{17} +(5.78531 - 6.25599i) q^{18} +9.55189 q^{19} +(-5.41435 - 19.2532i) q^{20} +20.9920i q^{21} +(-21.8605 + 23.6391i) q^{22} +(-2.56986 + 2.56986i) q^{23} +(-28.9321 + 3.40666i) q^{24} +(23.1037 - 9.55096i) q^{25} +(-1.08033 - 27.6379i) q^{26} +(-12.2039 + 12.2039i) q^{27} +(14.9825 - 17.5280i) q^{28} -10.1419 q^{29} +(-8.48143 - 35.4135i) q^{30} -24.9787 q^{31} +(26.5892 + 17.8050i) q^{32} +(-41.4533 + 41.4533i) q^{33} +(1.33225 + 34.0825i) q^{34} +(23.9602 + 16.0218i) q^{35} +(-16.9900 + 1.33027i) q^{36} +(26.8701 - 26.8701i) q^{37} +(-14.0257 - 12.9705i) q^{38} -50.3600i q^{39} +(-18.1935 + 35.6230i) q^{40} +62.0782 q^{41} +(28.5050 - 30.8241i) q^{42} +(-13.5064 - 13.5064i) q^{43} +(64.1988 - 5.02660i) q^{44} +(-4.14861 - 20.8946i) q^{45} +(7.26313 - 0.283907i) q^{46} +(11.9511 + 11.9511i) q^{47} +(47.1090 + 34.2846i) q^{48} -15.7685i q^{49} +(-46.8940 - 17.3480i) q^{50} +62.1031i q^{51} +(-35.9430 + 42.0497i) q^{52} +(-45.8494 - 45.8494i) q^{53} +(34.4914 - 1.34823i) q^{54} +(15.6761 + 78.9530i) q^{55} +(-45.8010 + 5.39291i) q^{56} +(-24.5954 - 24.5954i) q^{57} +(14.8922 + 13.7717i) q^{58} -28.9288 q^{59} +(-35.6340 + 63.5171i) q^{60} -68.7976i q^{61} +(36.6780 + 33.9184i) q^{62} +(17.3668 - 17.3668i) q^{63} +(-14.8655 - 62.2496i) q^{64} +(-57.4806 - 38.4363i) q^{65} +(117.158 - 4.57958i) q^{66} +(14.7732 - 14.7732i) q^{67} +(44.3243 - 51.8549i) q^{68} +13.2344 q^{69} +(-13.4265 - 56.0614i) q^{70} -31.1277 q^{71} +(26.7540 + 21.1173i) q^{72} +(-25.6249 + 25.6249i) q^{73} +(-75.9420 + 2.96849i) q^{74} +(-84.0833 - 34.8972i) q^{75} +(2.98242 + 38.0910i) q^{76} +(-65.6227 + 65.6227i) q^{77} +(-68.3837 + 73.9473i) q^{78} -70.6564i q^{79} +(75.0872 - 27.6028i) q^{80} +101.193 q^{81} +(-91.1539 - 84.2958i) q^{82} +(96.2577 + 96.2577i) q^{83} +(-83.7120 + 6.55443i) q^{84} +(70.8840 + 47.3990i) q^{85} +(1.49212 + 38.1726i) q^{86} +(26.1148 + 26.1148i) q^{87} +(-101.093 - 79.7945i) q^{88} +103.919i q^{89} +(-22.2810 + 36.3145i) q^{90} -79.7225i q^{91} +(-11.0505 - 9.44569i) q^{92} +(64.3182 + 64.3182i) q^{93} +(-1.32031 - 33.7771i) q^{94} +(-46.8450 + 9.30105i) q^{95} +(-22.6186 - 114.312i) q^{96} +(30.8277 + 30.8277i) q^{97} +(-21.4120 + 23.1540i) q^{98} +68.5890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8}+O(q^{10}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8	\( 20 q - 2 q^{2} - 16 q^{6} - 4 q^{7} + 4 q^{8} + 6 q^{10} - 44 q^{12} - 4 q^{15} - 56 q^{16} - 12 q^{17} + 10 q^{18} - 24 q^{20} + 92 q^{22} - 4 q^{23} - 28 q^{25} + 100 q^{26} + 68 q^{28} + 100 q^{30} - 136 q^{31} + 128 q^{32} + 32 q^{33} + 220 q^{36} - 188 q^{38} + 156 q^{40} - 8 q^{41} - 284 q^{42} - 240 q^{46} + 188 q^{47} - 256 q^{48} - 274 q^{50} - 332 q^{52} + 96 q^{55} - 360 q^{56} - 40 q^{57} + 268 q^{58} - 340 q^{60} + 336 q^{62} + 228 q^{63} - 60 q^{65} + 616 q^{66} + 396 q^{68} + 300 q^{70} + 248 q^{71} + 668 q^{72} - 124 q^{73} + 424 q^{76} - 368 q^{78} + 496 q^{80} + 132 q^{81} - 676 q^{82} - 672 q^{86} - 488 q^{87} - 304 q^{88} - 474 q^{90} - 628 q^{92} - 488 q^{95} - 1024 q^{96} + 100 q^{97} + 546 q^{98}+O(q^{100}) \) 20 * q - 2 * q^2 - 16 * q^6 - 4 * q^7 + 4 * q^8 + 6 * q^10 - 44 * q^12 - 4 * q^15 - 56 * q^16 - 12 * q^17 + 10 * q^18 - 24 * q^20 + 92 * q^22 - 4 * q^23 - 28 * q^25 + 100 * q^26 + 68 * q^28 + 100 * q^30 - 136 * q^31 + 128 * q^32 + 32 * q^33 + 220 * q^36 - 188 * q^38 + 156 * q^40 - 8 * q^41 - 284 * q^42 - 240 * q^46 + 188 * q^47 - 256 * q^48 - 274 * q^50 - 332 * q^52 + 96 * q^55 - 360 * q^56 - 40 * q^57 + 268 * q^58 - 340 * q^60 + 336 * q^62 + 228 * q^63 - 60 * q^65 + 616 * q^66 + 396 * q^68 + 300 * q^70 + 248 * q^71 + 668 * q^72 - 124 * q^73 + 424 * q^76 - 368 * q^78 + 496 * q^80 + 132 * q^81 - 676 * q^82 - 672 * q^86 - 488 * q^87 - 304 * q^88 - 474 * q^90 - 628 * q^92 - 488 * q^95 - 1024 * q^96 + 100 * q^97 + 546 * q^98

Introduction

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