LMFDB - Embedded newform 80.2.s.b.27.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [80,2,Mod(3,80)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("80.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 80 = 2^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	80.s (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:	$0.638803216170$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} + 2 x^{16} - 4 x^{15} - 5 x^{14} - 14 x^{13} - 10 x^{12} + 6 x^{11} + 37 x^{10} + 70 x^{9} + \cdots + 512 $ x^18 + 2x^16 - 4x^15 - 5x^14 - 14x^13 - 10x^12 + 6x^11 + 37x^10 + 70x^9 + 74x^8 + 24x^7 - 80x^6 - 224x^5 - 160x^4 - 256x^3 + 256*x^2 + 512
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			27.1
Root			$-0.480367 - 1.33013i$ of defining polynomial
Character	$\chi$	$=$	80.27
Dual form			80.2.s.b.3.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38031 - 0.307817i) q^{2} +2.85601 q^{3} +(1.81050 + 0.849763i) q^{4} +(-1.71489 + 1.43498i) q^{5} +(-3.94217 - 0.879127i) q^{6} +(-0.458895 - 0.458895i) q^{7} +(-2.23747 - 1.73024i) q^{8} +5.15678 q^{9} +O(q^{10})$	\(q+(-1.38031 - 0.307817i) q^{2} +2.85601 q^{3} +(1.81050 + 0.849763i) q^{4} +(-1.71489 + 1.43498i) q^{5} +(-3.94217 - 0.879127i) q^{6} +(-0.458895 - 0.458895i) q^{7} +(-2.23747 - 1.73024i) q^{8} +5.15678 q^{9} +(2.80878 - 1.45284i) q^{10} +(-0.492763 + 0.492763i) q^{11} +(5.17080 + 2.42693i) q^{12} -4.52109i q^{13} +(0.492160 + 0.774671i) q^{14} +(-4.89773 + 4.09831i) q^{15} +(2.55581 + 3.07699i) q^{16} +(-3.12823 - 3.12823i) q^{17} +(-7.11794 - 1.58734i) q^{18} +(-4.04508 + 4.04508i) q^{19} +(-4.32419 + 1.14077i) q^{20} +(-1.31061 - 1.31061i) q^{21} +(0.831845 - 0.528484i) q^{22} +(-1.80660 + 1.80660i) q^{23} +(-6.39024 - 4.94157i) q^{24} +(0.881683 - 4.92165i) q^{25} +(-1.39167 + 6.24050i) q^{26} +6.15978 q^{27} +(-0.440876 - 1.22078i) q^{28} +(3.83926 + 3.83926i) q^{29} +(8.02191 - 4.14932i) q^{30} -0.139949i q^{31} +(-2.58065 - 5.03391i) q^{32} +(-1.40733 + 1.40733i) q^{33} +(3.35500 + 5.28085i) q^{34} +(1.44546 + 0.128450i) q^{35} +(9.33634 + 4.38204i) q^{36} +5.84330i q^{37} +(6.82860 - 4.33831i) q^{38} -12.9123i q^{39} +(6.31986 - 0.243561i) q^{40} -4.55648i q^{41} +(1.40561 + 2.21247i) q^{42} +7.49928i q^{43} +(-1.31088 + 0.473414i) q^{44} +(-8.84330 + 7.39986i) q^{45} +(3.04976 - 1.93756i) q^{46} +(4.14073 - 4.14073i) q^{47} +(7.29940 + 8.78790i) q^{48} -6.57883i q^{49} +(-2.73196 + 6.52199i) q^{50} +(-8.93426 - 8.93426i) q^{51} +(3.84186 - 8.18543i) q^{52} +2.75773 q^{53} +(-8.50239 - 1.89608i) q^{54} +(0.137930 - 1.55214i) q^{55} +(0.232768 + 1.82076i) q^{56} +(-11.5528 + 11.5528i) q^{57} +(-4.11757 - 6.48115i) q^{58} +(3.62521 + 3.62521i) q^{59} +(-12.3499 + 3.25806i) q^{60} +(3.72781 - 3.72781i) q^{61} +(-0.0430787 + 0.193173i) q^{62} +(-2.36642 - 2.36642i) q^{63} +(2.01257 + 7.74271i) q^{64} +(6.48766 + 7.75317i) q^{65} +(2.37576 - 1.50935i) q^{66} +3.32677i q^{67} +(-3.00540 - 8.32192i) q^{68} +(-5.15965 + 5.15965i) q^{69} +(-1.95563 - 0.622235i) q^{70} +1.37056 q^{71} +(-11.5382 - 8.92244i) q^{72} +(2.55028 + 2.55028i) q^{73} +(1.79867 - 8.06556i) q^{74} +(2.51809 - 14.0563i) q^{75} +(-10.7610 + 3.88625i) q^{76} +0.452252 q^{77} +(-3.97461 + 17.8229i) q^{78} +3.86426 q^{79} +(-8.79833 - 1.60917i) q^{80} +2.12204 q^{81} +(-1.40256 + 6.28934i) q^{82} +14.4698 q^{83} +(-1.25915 - 3.48655i) q^{84} +(9.85351 + 0.875628i) q^{85} +(2.30840 - 10.3513i) q^{86} +(10.9650 + 10.9650i) q^{87} +(1.95514 - 0.249948i) q^{88} +3.35011 q^{89} +(14.4843 - 7.49197i) q^{90} +(-2.07470 + 2.07470i) q^{91} +(-4.80602 + 1.73566i) q^{92} -0.399696i q^{93} +(-6.99006 + 4.44089i) q^{94} +(1.13226 - 12.7415i) q^{95} +(-7.37035 - 14.3769i) q^{96} +(-4.95582 - 4.95582i) q^{97} +(-2.02507 + 9.08081i) q^{98} +(-2.54107 + 2.54107i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	$ 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) $ 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	−1.38031	−	0.307817i	−0.976025	−	0.217659i
$2$	−1.38031	−	0.307817i	−0.976025	−	0.217659i
$3$	2.85601			1.64892			0.824458	−	0.565923i	$-0.191480\pi$
$3$	2.85601			1.64892			0.824458	+	0.565923i	$0.191480\pi$
$4$	1.81050	+	0.849763i	0.905249	+	0.424882i
$5$	−1.71489	+	1.43498i	−0.766921	+	0.641741i
$5$	−1.71489	+	1.43498i	−0.766921	+	0.641741i
$6$	−3.94217	−	0.879127i	−1.60938	−	0.358902i
$7$	−0.458895	−	0.458895i	−0.173446	−	0.173446i	0.615046	−	0.788491i	$-0.289138\pi$
$7$	−0.458895	−	0.458895i	−0.173446	−	0.173446i	−0.788491	+	0.615046i	$0.789138\pi$
$8$	−2.23747	−	1.73024i	−0.791066	−	0.611731i
$9$	5.15678			1.71893
$10$	2.80878	−	1.45284i	0.888215	−	0.459428i
$11$	−0.492763	+	0.492763i	−0.148574	+	0.148574i	−0.777481	−	0.628907i	$-0.783503\pi$
$11$	−0.492763	+	0.492763i	−0.148574	+	0.148574i	0.628907	+	0.777481i	$0.283503\pi$
$12$	5.17080	+	2.42693i	1.49268	+	0.700594i
$13$		−	4.52109i		−	1.25393i	−0.779049	−	0.626963i	$-0.784298\pi$
$13$		−	4.52109i		−	1.25393i	0.779049	−	0.626963i	$-0.215702\pi$
$14$	0.492160	+	0.774671i	0.131535	+	0.207040i
$15$	−4.89773	+	4.09831i	−1.26459	+	1.05818i
$16$	2.55581	+	3.07699i	0.638951	+	0.769247i
$17$	−3.12823	−	3.12823i	−0.758708	−	0.758708i	0.217379	−	0.976087i	$-0.430249\pi$
$17$	−3.12823	−	3.12823i	−0.758708	−	0.758708i	−0.976087	+	0.217379i	$0.930249\pi$
$18$	−7.11794	−	1.58734i	−1.67772	−	0.374140i
$19$	−4.04508	+	4.04508i	−0.928005	+	0.928005i	−0.997577	−	0.0695721i	$-0.977837\pi$
$19$	−4.04508	+	4.04508i	−0.928005	+	0.928005i	0.0695721	+	0.997577i	$0.477837\pi$
$20$	−4.32419	+	1.14077i	−0.966919	+	0.255085i
$21$	−1.31061	−	1.31061i	−0.285998	−	0.285998i
$22$	0.831845	−	0.528484i	0.177350	−	0.112673i
$23$	−1.80660	+	1.80660i	−0.376701	+	0.376701i	−0.869911	−	0.493209i	$-0.835824\pi$
$23$	−1.80660	+	1.80660i	−0.376701	+	0.376701i	0.493209	+	0.869911i	$0.335824\pi$
$24$	−6.39024	−	4.94157i	−1.30440	−	1.00869i
$25$	0.881683	−	4.92165i	0.176337	−	0.984330i
$26$	−1.39167	+	6.24050i	−0.272928	+	1.22386i
$27$	6.15978			1.18545
$28$	−0.440876	−	1.22078i	−0.0833177	−	0.230706i
$29$	3.83926	+	3.83926i	0.712932	+	0.712932i	0.967148	−	0.254215i	$-0.0818172\pi$
$29$	3.83926	+	3.83926i	0.712932	+	0.712932i	−0.254215	+	0.967148i	$0.581817\pi$
$30$	8.02191	−	4.14932i	1.46459	−	0.757558i
$31$		−	0.139949i		−	0.0251356i	−0.999921	−	0.0125678i	$-0.995999\pi$
$31$		−	0.139949i		−	0.0251356i	0.999921	−	0.0125678i	$-0.00400057\pi$
$32$	−2.58065	−	5.03391i	−0.456199	−	0.889878i
$33$	−1.40733	+	1.40733i	−0.244985	+	0.244985i
$34$	3.35500	+	5.28085i	0.575378	+	0.905658i
$35$	1.44546	+	0.128450i	0.244327	+	0.0217120i
$36$	9.33634	+	4.38204i	1.55606	+	0.730340i
$37$			5.84330i			0.960633i	0.877095	+	0.480317i	$0.159478\pi$
$37$			5.84330i			0.960633i	−0.877095	+	0.480317i	$0.840522\pi$
$38$	6.82860	−	4.33831i	1.10774	−	0.703767i
$39$		−	12.9123i		−	2.06762i
$40$	6.31986	−	0.243561i	0.999258	−	0.0385104i
$41$		−	4.55648i		−	0.711602i	−0.934562	−	0.355801i	$-0.884208\pi$
$41$		−	4.55648i		−	0.711602i	0.934562	−	0.355801i	$-0.115792\pi$
$42$	1.40561	+	2.21247i	0.216891	+	0.341391i
$43$			7.49928i			1.14363i	0.820383	+	0.571815i	$0.193760\pi$
$43$			7.49928i			1.14363i	−0.820383	+	0.571815i	$0.806240\pi$
$44$	−1.31088	+	0.473414i	−0.197622	+	0.0713699i
$45$	−8.84330	+	7.39986i	−1.31828	+	1.10311i
$46$	3.04976	−	1.93756i	0.449662	−	0.285677i
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	−0.337381	−	0.941368i	$-0.609541\pi$
$47$	4.14073	−	4.14073i	0.603987	−	0.603987i	0.941368	+	0.337381i	$0.109541\pi$
$48$	7.29940	+	8.78790i	1.05358	+	1.26842i
$49$		−	6.57883i		−	0.939833i
$50$	−2.73196	+	6.52199i	−0.386357	+	0.922349i
$51$	−8.93426	−	8.93426i	−1.25105	−	1.25105i
$52$	3.84186	−	8.18543i	0.532770	−	1.13511i
$53$	2.75773			0.378803			0.189402	−	0.981900i	$-0.439345\pi$
$53$	2.75773			0.378803			0.189402	+	0.981900i	$0.439345\pi$
$54$	−8.50239	−	1.89608i	−1.15703	−	0.258024i
$55$	0.137930	−	1.55214i	0.0185985	−	0.209290i
$56$	0.232768	+	1.82076i	0.0311050	+	0.243309i
$57$	−11.5528	+	11.5528i	−1.53020	+	1.53020i
$58$	−4.11757	−	6.48115i	−0.540663	−	0.851016i
$59$	3.62521	+	3.62521i	0.471962	+	0.471962i	0.902549	−	0.430587i	$-0.141694\pi$
$59$	3.62521	+	3.62521i	0.471962	+	0.471962i	−0.430587	+	0.902549i	$0.641694\pi$
$60$	−12.3499	+	3.25806i	−1.59437	+	0.420614i
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	−0.426969	−	0.904266i	$-0.640419\pi$
$61$	3.72781	−	3.72781i	0.477298	−	0.477298i	0.904266	+	0.426969i	$0.140419\pi$
$62$	−0.0430787	+	0.193173i	−0.00547100	+	0.0245330i
$63$	−2.36642	−	2.36642i	−0.298141	−	0.298141i
$64$	2.01257	+	7.74271i	0.251571	+	0.967839i
$65$	6.48766	+	7.75317i	0.804696	+	0.961662i
$66$	2.37576	−	1.50935i	0.292435	−	0.185789i
$67$			3.32677i			0.406430i	0.979134	+	0.203215i	$0.0651390\pi$
$67$			3.32677i			0.406430i	−0.979134	+	0.203215i	$0.934861\pi$
$68$	−3.00540	−	8.32192i	−0.364459	−	1.00918i
$69$	−5.15965	+	5.15965i	−0.621149	+	0.621149i
$70$	−1.95563	−	0.622235i	−0.233743	−	0.0743714i
$71$	1.37056			0.162655			0.0813275	−	0.996687i	$-0.474084\pi$
$71$	1.37056			0.162655			0.0813275	+	0.996687i	$0.474084\pi$
$72$	−11.5382	−	8.92244i	−1.35978	−	1.05152i
$73$	2.55028	+	2.55028i	0.298488	+	0.298488i	0.840422	−	0.541933i	$-0.182307\pi$
$73$	2.55028	+	2.55028i	0.298488	+	0.298488i	−0.541933	+	0.840422i	$0.682307\pi$
$74$	1.79867	−	8.06556i	0.209091	−	0.937602i
$75$	2.51809	−	14.0563i	0.290764	−	1.62308i
$76$	−10.7610	+	3.88625i	−1.23437	+	0.445783i
$77$	0.452252			0.0515389
$78$	−3.97461	+	17.8229i	−0.450036	+	2.01805i
$79$	3.86426			0.434763			0.217382	−	0.976087i	$-0.430248\pi$
$79$	3.86426			0.434763			0.217382	+	0.976087i	$0.430248\pi$
$80$	−8.79833	−	1.60917i	−0.983683	−	0.179911i
$81$	2.12204			0.235782
$82$	−1.40256	+	6.28934i	−0.154887	+	0.694541i
$83$	14.4698			1.58827			0.794133	−	0.607744i	$-0.207925\pi$
$83$	14.4698			1.58827			0.794133	+	0.607744i	$0.207925\pi$
$84$	−1.25915	−	3.48655i	−0.137384	−	0.380414i
$85$	9.85351	+	0.875628i	1.06876	+	0.0949752i
$86$	2.30840	−	10.3513i	0.248922	−	1.11621i
$87$	10.9650	+	10.9650i	1.17557	+	1.17557i
$88$	1.95514	−	0.249948i	0.208419	−	0.0266445i
$89$	3.35011			0.355111			0.177556	−	0.984111i	$-0.443181\pi$
$89$	3.35011			0.355111			0.177556	+	0.984111i	$0.443181\pi$
$90$	14.4843	−	7.49197i	1.52678	−	0.789723i
$91$	−2.07470	+	2.07470i	−0.217488	+	0.217488i
$92$	−4.80602	+	1.73566i	−0.501062	+	0.180955i
$93$		−	0.399696i		−	0.0414466i
$94$	−6.99006	+	4.44089i	−0.720970	+	0.458043i
$95$	1.13226	−	12.7415i	0.116168	−	1.30725i
$96$	−7.37035	−	14.3769i	−0.752234	−	1.46733i
$97$	−4.95582	−	4.95582i	−0.503187	−	0.503187i	0.409240	−	0.912427i	$-0.365794\pi$
$97$	−4.95582	−	4.95582i	−0.503187	−	0.503187i	−0.912427	+	0.409240i	$0.865794\pi$
$98$	−2.02507	+	9.08081i	−0.204563	+	0.917300i
$99$	−2.54107	+	2.54107i	−0.255387	+	0.255387i
$100$	5.77852	−	8.16142i	0.577852	−	0.816142i
$101$	−1.84536	−	1.84536i	−0.183621	−	0.183621i	0.609311	−	0.792931i	$-0.291446\pi$
$101$	−1.84536	−	1.84536i	−0.183621	−	0.183621i	−0.792931	+	0.609311i	$0.791446\pi$
$102$	9.58191	+	15.0821i	0.948751	+	1.49335i
$103$	−11.6655	+	11.6655i	−1.14944	+	1.14944i	−0.162773	+	0.986664i	$0.552044\pi$
$103$	−11.6655	+	11.6655i	−1.14944	+	1.14944i	−0.986664	+	0.162773i	$0.947956\pi$
$104$	−7.82256	+	10.1158i	−0.767065	+	0.991938i
$105$	4.12823	+	0.366853i	0.402874	+	0.0358012i
$106$	−3.80651	−	0.848874i	−0.369721	−	0.0824500i
$107$	−15.3106			−1.48013			−0.740067	−	0.672534i	$-0.765206\pi$
$107$	−15.3106			−1.48013			−0.740067	+	0.672534i	$0.765206\pi$
$108$	11.1523	+	5.23435i	1.07313	+	0.503676i
$109$	−12.4798	−	12.4798i	−1.19535	−	1.19535i	−0.975544	−	0.219803i	$-0.929458\pi$
$109$	−12.4798	−	12.4798i	−1.19535	−	1.19535i	−0.219803	−	0.975544i	$-0.570542\pi$
$110$	−0.668159	+	2.09997i	−0.0637065	+	0.200224i
$111$			16.6885i			1.58400i
$112$	0.239168	−	2.58486i	0.0225993	−	0.244246i
$113$	2.53557	−	2.53557i	0.238526	−	0.238526i	−0.577713	−	0.816240i	$-0.696055\pi$
$113$	2.53557	−	2.53557i	0.238526	−	0.238526i	0.816240	+	0.577713i	$0.196055\pi$
$114$	19.5025	−	12.3903i	1.82658	−	1.16045i
$115$	0.505686	−	5.69053i	0.0471555	−	0.530645i
$116$	3.68851	+	10.2134i	0.342470	+	0.948293i
$117$		−	23.3143i		−	2.15541i
$118$	−3.88800	−	6.11980i	−0.357919	−	0.563373i
$119$			2.87106i			0.263189i
$120$	18.0496	−	0.695612i	1.64769	−	0.0635004i
$121$			10.5144i			0.955852i
$122$	−6.29301	+	3.99805i	−0.569743	+	0.361966i
$123$		−	13.0133i		−	1.17337i
$124$	0.118924	−	0.253378i	0.0106797	−	0.0227540i
$125$	5.55047	+	9.70527i	0.496449	+	0.868066i
$126$	2.53796	+	3.99481i	0.226100	+	0.355886i
$127$	0.615790	−	0.615790i	0.0546426	−	0.0546426i	−0.679257	−	0.733900i	$-0.737698\pi$
$127$	0.615790	−	0.615790i	0.0546426	−	0.0546426i	0.733900	+	0.679257i	$0.237698\pi$
$128$	−0.394630	−	11.3068i	−0.0348807	−	0.999391i
$129$			21.4180i			1.88575i
$130$	−6.56842	−	12.6988i	−0.576088	−	1.11376i
$131$	9.55413	+	9.55413i	0.834748	+	0.834748i	0.988162	−	0.153414i	$-0.0490268\pi$
$131$	9.55413	+	9.55413i	0.834748	+	0.834748i	−0.153414	+	0.988162i	$0.549027\pi$
$132$	−3.74388	+	1.35208i	−0.325863	+	0.117683i
$133$	3.71253			0.321917
$134$	1.02404	−	4.59197i	0.0884632	−	0.396686i
$135$	−10.5633	+	8.83914i	−0.909147	+	0.760752i
$136$	1.58676	+	12.4119i	0.136063	+	1.06431i
$137$	3.70277	−	3.70277i	0.316349	−	0.316349i	−0.531014	−	0.847363i	$-0.678189\pi$
$137$	3.70277	−	3.70277i	0.316349	−	0.316349i	0.847363	+	0.531014i	$0.178189\pi$
$138$	8.71013	−	5.53368i	0.741456	−	0.471058i
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	0.436128	−	0.899885i	$-0.356349\pi$
$139$	−5.46761	−	5.46761i	−0.463756	−	0.463756i	−0.899885	+	0.436128i	$0.856349\pi$
$140$	2.50784	+	1.46085i	0.211951	+	0.123465i
$141$	11.8260	−	11.8260i	0.995925	−	0.995925i
$142$	−1.89179	−	0.421880i	−0.158755	−	0.0354034i
$143$	2.22783	+	2.22783i	0.186300	+	0.186300i
$144$	13.1797	+	15.8674i	1.09831	+	1.32228i
$145$	−12.0931	−	1.07465i	−1.00428	−	0.0892450i
$146$	−2.73516	−	4.30520i	−0.226363	−	0.356301i
$147$		−	18.7892i		−	1.54971i
$148$	−4.96542	+	10.5793i	−0.408155	+	0.869612i
$149$	−4.21561	+	4.21561i	−0.345356	+	0.345356i	−0.858376	−	0.513021i	$-0.828526\pi$
$149$	−4.21561	+	4.21561i	−0.345356	+	0.345356i	0.513021	+	0.858376i	$0.328526\pi$
$150$	−7.80250	+	18.6269i	−0.637071	+	1.52088i
$151$	12.4417			1.01249			0.506244	−	0.862390i	$-0.331034\pi$
$151$	12.4417			1.01249			0.506244	+	0.862390i	$0.331034\pi$
$152$	16.0497	−	2.05181i	1.30180	−	0.166424i
$153$	−16.1316	−	16.1316i	−1.30416	−	1.30416i
$154$	−0.624247	−	0.139211i	−0.0503033	−	0.0112179i
$155$	0.200824	+	0.239997i	0.0161306	+	0.0192771i
$156$	10.9724	−	23.3777i	0.878493	−	1.87171i
$157$	7.50500			0.598964			0.299482	−	0.954102i	$-0.403186\pi$
$157$	7.50500			0.598964			0.299482	+	0.954102i	$0.403186\pi$
$158$	−5.33387	−	1.18948i	−0.424340	−	0.0946302i
$159$	7.87609			0.624615
$160$	11.6491	+	4.92942i	0.920940	+	0.389705i
$161$	1.65807			0.130675
$162$	−2.92907	−	0.653199i	−0.230129	−	0.0513202i
$163$	−23.7284			−1.85855			−0.929277	−	0.369383i	$-0.879569\pi$
$163$	−23.7284			−1.85855			−0.929277	+	0.369383i	$0.879569\pi$
$164$	3.87193	−	8.24949i	0.302347	−	0.644177i
$165$	0.393929	−	4.43291i	0.0306673	−	0.345102i
$166$	−19.9728	−	4.45404i	−1.55019	−	0.345701i
$167$	−0.402976	−	0.402976i	−0.0311832	−	0.0311832i	0.691343	−	0.722526i	$-0.257019\pi$
$167$	−0.402976	−	0.402976i	−0.0311832	−	0.0311832i	−0.722526	+	0.691343i	$0.757019\pi$
$168$	0.664788	+	5.20010i	0.0512895	+	0.401197i
$169$	−7.44028			−0.572330
$170$	−13.3313	−	4.24171i	−1.02247	−	0.325324i
$171$	−20.8596	+	20.8596i	−1.59517	+	1.59517i
$172$	−6.37261	+	13.5774i	−0.485907	+	1.03527i
$173$			15.4500i			1.17464i	0.809355	+	0.587320i	$0.199817\pi$
$173$			15.4500i			1.17464i	−0.809355	+	0.587320i	$0.800183\pi$
$174$	−11.7598	−	18.5102i	−0.891509	−	1.40325i
$175$	−2.66312	+	1.85392i	−0.201313	+	0.140143i
$176$	−2.77563	−	0.256820i	−0.209221	−	0.0193585i
$177$	10.3536	+	10.3536i	0.778225	+	0.778225i
$178$	−4.62419	−	1.03122i	−0.346597	−	0.0772932i
$179$	−5.20444	+	5.20444i	−0.388998	+	0.388998i	−0.874330	−	0.485332i	$-0.838699\pi$
$179$	−5.20444	+	5.20444i	−0.388998	+	0.388998i	0.485332	+	0.874330i	$0.338699\pi$
$180$	−22.2989	+	5.88272i	−1.66206	+	0.438472i
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	0.283402	−	0.959001i	$-0.408537\pi$
$181$	−9.08925	−	9.08925i	−0.675599	−	0.675599i	−0.959001	+	0.283402i	$0.908537\pi$
$182$	3.50236	−	2.22510i	0.259612	−	0.164936i
$183$	10.6467	−	10.6467i	0.787024	−	0.787024i
$184$	7.16804	−	0.916372i	0.528435	−	0.0675559i
$185$	−8.38500	−	10.0206i	−0.616478	−	0.736730i
$186$	−0.123033	+	0.551704i	−0.00902123	+	0.0404529i
$187$	3.08295			0.225448
$188$	11.0154	−	3.97814i	0.803382	−	0.290136i
$189$	−2.82669	−	2.82669i	−0.205611	−	0.205611i
$190$	−5.48490	+	17.2386i	−0.397917	+	1.25062i
$191$		−	15.1075i		−	1.09314i	−0.837413	−	0.546571i	$-0.815933\pi$
$191$		−	15.1075i		−	1.09314i	0.837413	−	0.546571i	$-0.184067\pi$
$192$	5.74791	+	22.1132i	0.414820	+	1.59589i
$193$	4.19166	−	4.19166i	0.301722	−	0.301722i	−0.539965	−	0.841687i	$-0.681563\pi$
$193$	4.19166	−	4.19166i	0.301722	−	0.301722i	0.841687	+	0.539965i	$0.181563\pi$
$194$	5.31507	+	8.36604i	0.381600	+	0.600647i
$195$	18.5288	+	22.1431i	1.32688	+	1.58570i
$196$	5.59045	−	11.9110i	0.399318	−	0.850783i
$197$		−	4.03184i		−	0.287256i	−0.989632	−	0.143628i	$-0.954123\pi$
$197$		−	4.03184i		−	0.287256i	0.989632	−	0.143628i	$-0.0458769\pi$
$198$	4.28964	−	2.72527i	0.304852	−	0.193677i
$199$		−	5.43055i		−	0.384961i	−0.981301	−	0.192481i	$-0.938347\pi$
$199$		−	5.43055i		−	0.384961i	0.981301	−	0.192481i	$-0.0616533\pi$
$200$	−10.4884	+	9.48654i	−0.741639	+	0.670800i
$201$			9.50129i			0.670169i
$202$	1.97914	+	3.11520i	0.139252	+	0.219185i
$203$		−	3.52363i		−	0.247310i
$204$	−8.58345	−	23.7675i	−0.600962	−	1.66405i
$205$	6.53844	+	7.81385i	0.456664	+	0.545743i
$206$	19.6928	−	12.5111i	1.37206	−	0.871693i
$207$	−9.31622	+	9.31622i	−0.647522	+	0.647522i
$208$	13.9114	−	11.5550i	0.964579	−	0.801197i
$209$		−	3.98653i		−	0.275754i
$210$	−5.58531	−	1.77711i	−0.385423	−	0.122632i
$211$	3.23020	+	3.23020i	0.222376	+	0.222376i	0.809498	−	0.587122i	$-0.199739\pi$
$211$	3.23020	+	3.23020i	0.222376	+	0.222376i	−0.587122	+	0.809498i	$0.699739\pi$
$212$	4.99286	+	2.34342i	0.342911	+	0.160946i
$213$	3.91432			0.268205
$214$	21.1334	+	4.71286i	1.44465	+	0.322165i
$215$	−10.7613	−	12.8604i	−0.733914	−	0.877074i
$216$	−13.7823	−	10.6579i	−0.937770	−	0.725176i
$217$	−0.0642220	+	0.0642220i	−0.00435967	+	0.00435967i
$218$	13.3845	+	21.0674i	0.906511	+	1.42687i
$219$	7.28363	+	7.28363i	0.492182	+	0.492182i
$220$	1.56867	−	2.69293i	0.105760	−	0.181557i
$221$	−14.1430	+	14.1430i	−0.951363	+	0.951363i
$222$	5.13700	−	23.0353i	0.344773	−	1.54603i
$223$	8.17319	+	8.17319i	0.547317	+	0.547317i	0.925664	−	0.378347i	$-0.123507\pi$
$223$	8.17319	+	8.17319i	0.547317	+	0.547317i	−0.378347	+	0.925664i	$0.623507\pi$
$224$	−1.12579	+	3.49428i	−0.0752199	+	0.233471i
$225$	4.54664	−	25.3799i	0.303110	−	1.69199i
$226$	−4.28035	+	2.71937i	−0.284725	+	0.180890i
$227$		−	1.54068i		−	0.102258i	−0.998692	−	0.0511292i	$-0.983718\pi$
$227$		−	1.54068i		−	0.102258i	0.998692	−	0.0511292i	$-0.0162820\pi$
$228$	−30.7334	+	11.0992i	−2.03537	+	0.735060i
$229$	17.5646	−	17.5646i	1.16070	−	1.16070i	0.176378	−	0.984322i	$-0.443562\pi$
$229$	17.5646	−	17.5646i	1.16070	−	1.16070i	0.984322	−	0.176378i	$-0.0564382\pi$
$230$	−2.44964	+	7.69903i	−0.161525	+	0.507659i
$231$	1.29164			0.0849834
$232$	−1.94741	−	15.2331i	−0.127854	−	1.00010i
$233$	−9.99018	−	9.99018i	−0.654479	−	0.654479i	0.299590	−	0.954068i	$-0.403150\pi$
$233$	−9.99018	−	9.99018i	−0.654479	−	0.654479i	−0.954068	+	0.299590i	$0.903150\pi$
$234$	−7.17652	+	32.1809i	−0.469144	+	2.10373i
$235$	−1.15904	+	13.0427i	−0.0756072	+	0.850814i
$236$	3.48286	+	9.64399i	0.226715	+	0.627771i
$237$	11.0364			0.716889
$238$	0.883759	−	3.96294i	0.0572856	−	0.256879i
$239$	−26.2762			−1.69967			−0.849833	−	0.527052i	$-0.823297\pi$
$239$	−26.2762			−1.69967			−0.849833	+	0.527052i	$0.823297\pi$
$240$	−25.1281	−	4.59580i	−1.62201	−	0.296658i
$241$	−0.113242			−0.00729456			−0.00364728	−	0.999993i	$-0.501161\pi$
$241$	−0.113242			−0.00729456			−0.00364728	+	0.999993i	$0.501161\pi$
$242$	3.23650	−	14.5131i	0.208050	−	0.932935i
$243$	−12.4188			−0.796665
$244$	9.91696	−	3.58144i	0.634868	−	0.229278i
$245$	9.44047	+	11.2820i	0.603130	+	0.720778i
$246$	−4.00572	+	17.9624i	−0.255395	+	1.14524i
$247$	18.2882	+	18.2882i	1.16365	+	1.16365i
$248$	−0.242145	+	0.313133i	−0.0153762	+	0.0198840i
$249$	41.3258			2.61892
$250$	−4.67391	−	15.1048i	−0.295604	−	0.955311i
$251$	19.2220	−	19.2220i	1.21328	−	1.21328i	0.243339	−	0.969941i	$-0.421757\pi$
$251$	19.2220	−	19.2220i	1.21328	−	1.21328i	0.969941	−	0.243339i	$-0.0782427\pi$
$252$	−2.27350	−	6.29529i	−0.143217	−	0.396566i
$253$		−	1.78045i		−	0.111936i
$254$	−1.03953	+	0.660430i	−0.0652260	+	0.0414390i
$255$	28.1417	+	2.50080i	1.76230	+	0.156606i
$256$	−2.93572	+	15.7284i	−0.183482	+	0.983023i
$257$	−0.757800	−	0.757800i	−0.0472703	−	0.0472703i	0.683077	−	0.730347i	$-0.260642\pi$
$257$	−0.757800	−	0.757800i	−0.0472703	−	0.0472703i	−0.730347	+	0.683077i	$0.760642\pi$
$258$	6.59282	−	29.5634i	0.410451	−	1.84054i
$259$	2.68146	−	2.68146i	0.166618	−	0.166618i
$260$	5.15755	+	19.5501i	0.319857	+	1.21244i
$261$	19.7982	+	19.7982i	1.22548	+	1.22548i
$262$	−10.2467	−	16.1286i	−0.633044	−	0.996425i
$263$	5.73017	−	5.73017i	0.353338	−	0.353338i	−0.508012	−	0.861350i	$-0.669620\pi$
$263$	5.73017	−	5.73017i	0.353338	−	0.353338i	0.861350	+	0.508012i	$0.169620\pi$
$264$	5.58389	−	0.713852i	0.343665	−	0.0439346i
$265$	−4.72919	+	3.95728i	−0.290512	+	0.243094i
$266$	−5.12443	−	1.14278i	−0.314199	−	0.0700682i
$267$	9.56795			0.585549
$268$	−2.82697	+	6.02311i	−0.172685	+	0.367920i
$269$	−9.78879	−	9.78879i	−0.596833	−	0.596833i	0.342635	−	0.939468i	$-0.388680\pi$
$269$	−9.78879	−	9.78879i	−0.596833	−	0.596833i	−0.939468	+	0.342635i	$0.888680\pi$
$270$	17.3015	−	8.94917i	1.05293	−	0.544629i
$271$		−	4.10159i		−	0.249154i	−0.992210	−	0.124577i	$-0.960243\pi$
$271$		−	4.10159i		−	0.249154i	0.992210	−	0.124577i	$-0.0397574\pi$
$272$	1.63038	−	17.6207i	0.0988565	−	1.06841i
$273$	−5.92537	+	5.92537i	−0.358620	+	0.358620i
$274$	−6.25074	+	3.97119i	−0.377621	+	0.239908i
$275$	1.99075	+	2.85967i	0.120046	+	0.172444i
$276$	−13.7260	+	4.95706i	−0.826209	+	0.298380i
$277$			24.6755i			1.48261i	0.671169	+	0.741305i	$0.265793\pi$
$277$			24.6755i			1.48261i	−0.671169	+	0.741305i	$0.734207\pi$
$278$	5.86396	+	9.23000i	0.351697	+	0.553578i
$279$		−	0.721688i		−	0.0432063i
$280$	−3.01192	−	2.78838i	−0.179997	−	0.166638i
$281$			23.6688i			1.41196i	0.708230	+	0.705981i	$0.249494\pi$
$281$			23.6688i			1.41196i	−0.708230	+	0.705981i	$0.750506\pi$
$282$	−19.9637	+	12.6832i	−1.18882	+	0.755275i
$283$		−	13.0492i		−	0.775694i	−0.921724	−	0.387847i	$-0.873219\pi$
$283$		−	13.0492i		−	0.775694i	0.921724	−	0.387847i	$-0.126781\pi$
$284$	2.48139	+	1.16465i	0.147243	+	0.0691091i
$285$	3.23375	−	36.3897i	0.191551	−	2.15554i
$286$	−2.38932	−	3.76085i	−0.141284	−	0.222384i
$287$	−2.09094	+	2.09094i	−0.123424	+	0.123424i
$288$	−13.3078	−	25.9588i	−0.784172	−	1.52963i
$289$			2.57168i			0.151275i
$290$	16.3615	+	5.20582i	0.960778	+	0.305696i
$291$	−14.1539	−	14.1539i	−0.829714	−	0.829714i
$292$	2.45015	+	6.78442i	0.143384	+	0.397028i
$293$	−31.6731			−1.85036			−0.925181	−	0.379526i	$-0.876087\pi$
$293$	−31.6731			−1.85036			−0.925181	+	0.379526i	$0.876087\pi$
$294$	−5.78363	+	25.9349i	−0.337308	+	1.51255i
$295$	−11.4189	−	1.01474i	−0.664835	−	0.0590802i
$296$	10.1103	−	13.0742i	0.587649	−	0.759924i
$297$	−3.03531	+	3.03531i	−0.176127	+	0.176127i
$298$	7.11646	−	4.52120i	0.412246	−	0.261906i
$299$	8.16779	+	8.16779i	0.472355	+	0.472355i
$300$	16.5035	−	23.3091i	0.952830	−	1.34575i
$301$	3.44138	−	3.44138i	0.198358	−	0.198358i
$302$	−17.1733	−	3.82975i	−0.988213	−	0.220377i
$303$	−5.27037	−	5.27037i	−0.302775	−	0.302775i
$304$	−22.7851	−	2.10823i	−1.30682	−	0.120915i
$305$	−1.04346	+	11.7421i	−0.0597482	+	0.672351i
$306$	17.3010	+	27.2322i	0.989033	+	1.55676i
$307$		−	27.3597i		−	1.56150i	−0.624843	−	0.780751i	$-0.714837\pi$
$307$		−	27.3597i		−	1.56150i	0.624843	−	0.780751i	$-0.285163\pi$
$308$	0.818802	+	0.384307i	0.0466556	+	0.0218979i
$309$	−33.3168	+	33.3168i	−1.89532	+	1.89532i
$310$	−0.203324	−	0.393087i	−0.0115480	−	0.0223259i
$311$	−15.8076			−0.896368			−0.448184	−	0.893941i	$-0.647929\pi$
$311$	−15.8076			−0.896368			−0.448184	+	0.893941i	$0.647929\pi$
$312$	−22.3413	+	28.8909i	−1.26483	+	1.63562i
$313$	13.8388	+	13.8388i	0.782217	+	0.782217i	0.980205	−	0.197988i	$-0.0634406\pi$
$313$	13.8388	+	13.8388i	0.782217	+	0.782217i	−0.197988	+	0.980205i	$0.563441\pi$
$314$	−10.3592	−	2.31016i	−0.584604	−	0.130370i
$315$	7.45390	+	0.662387i	0.419980	+	0.0373213i
$316$	6.99624	+	3.28371i	0.393569	+	0.184723i
$317$	−35.0092			−1.96631			−0.983156	−	0.182766i	$-0.941495\pi$
$317$	−35.0092			−1.96631			−0.983156	+	0.182766i	$0.941495\pi$
$318$	−10.8714	−	2.42439i	−0.609639	−	0.135953i
$319$	−3.78369			−0.211846
$320$	−14.5619	−	10.3899i	−0.814037	−	0.580813i
$321$	−43.7272			−2.44062
$322$	−2.28865	−	0.510383i	−0.127542	−	0.0284425i
$323$	25.3079			1.40817
$324$	3.84195	+	1.80323i	0.213442	+	0.100180i
$325$	−22.2512	−	3.98617i	−1.23428	−	0.221113i
$326$	32.7525	+	7.30401i	1.81400	+	0.404532i
$327$	−35.6424	−	35.6424i	−1.97103	−	1.97103i
$328$	−7.88378	+	10.1950i	−0.435309	+	0.562924i
$329$	−3.80032			−0.209518
$330$	−1.90827	+	5.99753i	−0.105047	+	0.330153i
$331$	16.8212	−	16.8212i	0.924578	−	0.924578i	−0.0727709	−	0.997349i	$-0.523184\pi$
$331$	16.8212	−	16.8212i	0.924578	−	0.924578i	0.997349	+	0.0727709i	$0.0231842\pi$
$332$	26.1975	+	12.2959i	1.43778	+	0.674825i
$333$			30.1326i			1.65126i
$334$	0.432188	+	0.680273i	0.0236483	+	0.0372229i
$335$	−4.77384	−	5.70504i	−0.260823	−	0.311700i
$336$	0.683066	−	7.38238i	0.0372643	−	0.402742i
$337$	14.4984	+	14.4984i	0.789777	+	0.789777i	0.981457	−	0.191680i	$-0.0613937\pi$
$337$	14.4984	+	14.4984i	0.789777	+	0.789777i	−0.191680	+	0.981457i	$0.561394\pi$
$338$	10.2699	+	2.29024i	0.558608	+	0.124573i
$339$	7.24160	−	7.24160i	0.393310	−	0.393310i
$340$	17.0957	+	9.95847i	0.927144	+	0.540074i
$341$	0.0689618	+	0.0689618i	0.00373449	+	0.00373449i
$342$	35.2136	−	22.3717i	1.90413	−	1.20972i
$343$	−6.23125	+	6.23125i	−0.336456	+	0.336456i
$344$	12.9755	−	16.7794i	0.699593	−	0.904687i
$345$	1.44424	−	16.2522i	0.0777555	−	0.874989i
$346$	4.75576	−	21.3257i	0.255671	−	1.14648i
$347$	−16.7705			−0.900286			−0.450143	−	0.892956i	$-0.648627\pi$
$347$	−16.7705			−0.900286			−0.450143	+	0.892956i	$0.648627\pi$
$348$	10.5344	+	29.1696i	0.564704	+	1.56366i
$349$	−1.86337	−	1.86337i	−0.0997439	−	0.0997439i	0.655474	−	0.755218i	$-0.272469\pi$
$349$	−1.86337	−	1.86337i	−0.0997439	−	0.0997439i	−0.755218	+	0.655474i	$0.772469\pi$
$350$	4.24659	−	1.73923i	0.226990	−	0.0929656i
$351$		−	27.8489i		−	1.48647i
$352$	3.75217	+	1.20888i	0.199991	+	0.0644333i
$353$	24.1362	−	24.1362i	1.28464	−	1.28464i	0.346642	−	0.937998i	$-0.387322\pi$
$353$	24.1362	−	24.1362i	1.28464	−	1.28464i	0.937998	−	0.346642i	$-0.112678\pi$
$354$	−11.1042	−	17.4782i	−0.590179	−	0.928955i
$355$	−2.35035	+	1.96672i	−0.124744	+	0.104382i
$356$	6.06537	+	2.84680i	0.321464	+	0.150880i
$357$			8.19976i			0.433978i
$358$	8.78574	−	5.58171i	0.464341	−	0.295003i
$359$			12.2500i			0.646532i	0.946308	+	0.323266i	$0.104781\pi$
$359$			12.2500i			0.646532i	−0.946308	+	0.323266i	$0.895219\pi$
$360$	32.5901	−	1.25599i	1.71765	−	0.0661965i
$361$		−	13.7253i		−	0.722386i
$362$	9.74814	+	15.3438i	0.512351	+	0.806451i
$363$			30.0291i			1.57612i
$364$	−5.51926	+	1.99324i	−0.289288	+	0.104474i
$365$	−8.03305	−	0.713853i	−0.420469	−	0.0373648i
$366$	−17.9729	+	11.4185i	−0.939458	+	0.596852i
$367$	−2.71307	+	2.71307i	−0.141621	+	0.141621i	−0.774363	−	0.632742i	$-0.781929\pi$
$367$	−2.71307	+	2.71307i	−0.141621	+	0.141621i	0.632742	+	0.774363i	$0.281929\pi$
$368$	−10.1762	−	0.941567i	−0.530470	−	0.0490826i
$369$		−	23.4967i		−	1.22319i
$370$	8.48938	+	16.4126i	0.441342	+	0.853249i
$371$	−1.26551	−	1.26551i	−0.0657018	−	0.0657018i
$372$	0.339647	−	0.723649i	0.0176099	−	0.0375195i
$373$	16.4846			0.853541			0.426771	−	0.904360i	$-0.359651\pi$
$373$	16.4846			0.853541			0.426771	+	0.904360i	$0.359651\pi$
$374$	−4.25542	−	0.948984i	−0.220043	−	0.0490708i
$375$	15.8522	+	27.7183i	0.818603	+	1.43137i
$376$	−16.4292	+	2.10033i	−0.847272	+	0.108316i
$377$	17.3576	−	17.3576i	0.893964	−	0.893964i
$378$	3.03160	+	4.77180i	0.155929	+	0.245435i
$379$	13.7716	+	13.7716i	0.707401	+	0.707401i	0.965988	−	0.258587i	$-0.0832568\pi$
$379$	13.7716	+	13.7716i	0.707401	+	0.707401i	−0.258587	+	0.965988i	$0.583257\pi$
$380$	12.8772	−	22.1062i	0.660585	−	1.13403i
$381$	1.75870	−	1.75870i	0.0901011	−	0.0901011i
$382$	−4.65034	+	20.8530i	−0.237932	+	1.06693i
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	0.347389	−	0.937721i	$-0.387068\pi$
$383$	−11.5530	−	11.5530i	−0.590332	−	0.590332i	−0.937721	+	0.347389i	$0.887068\pi$
$384$	−1.12707	−	32.2924i	−0.0575153	−	1.64791i
$385$	−0.775562	+	0.648972i	−0.0395263	+	0.0330747i
$386$	−7.07604	+	4.49552i	−0.360161	+	0.228816i
$387$			38.6722i			1.96582i
$388$	−4.76123	−	13.1838i	−0.241715	−	0.669305i
$389$	15.7728	−	15.7728i	0.799712	−	0.799712i	−0.183338	−	0.983050i	$-0.558690\pi$
$389$	15.7728	−	15.7728i	0.799712	−	0.799712i	0.983050	+	0.183338i	$0.0586903\pi$
$390$	−18.7595	−	36.2678i	−0.949922	−	1.83649i
$391$	11.3029			0.571612
$392$	−11.3829	+	14.7200i	−0.574925	+	0.743470i
$393$	27.2867	+	27.2867i	1.37643	+	1.37643i
$394$	−1.24107	+	5.56517i	−0.0625240	+	0.280369i
$395$	−6.62677	+	5.54512i	−0.333429	+	0.279006i
$396$	−6.75991	+	2.44129i	−0.339698	+	0.122680i
$397$	29.9558			1.50344			0.751720	−	0.659483i	$-0.229225\pi$
$397$	29.9558			1.50344			0.751720	+	0.659483i	$0.229225\pi$
$398$	−1.67161	+	7.49583i	−0.0837904	+	0.375732i
$399$	10.6030			0.530815
$400$	17.3973	−	9.86585i	0.869863	−	0.493293i
$401$	19.9241			0.994963			0.497481	−	0.867475i	$-0.334258\pi$
$401$	19.9241			0.994963			0.497481	+	0.867475i	$0.334258\pi$
$402$	2.92465	−	13.1147i	0.145868	−	0.654102i
$403$	−0.632724			−0.0315182
$404$	−1.77291	−	4.90915i	−0.0882054	−	0.244239i
$405$	−3.63906	+	3.04508i	−0.180826	+	0.151311i
$406$	−1.08463	+	4.86369i	−0.0538294	+	0.241381i
$407$	−2.87936	−	2.87936i	−0.142725	−	0.142725i
$408$	4.53179	+	35.4485i	0.224357	+	1.75496i
$409$	−5.89856			−0.291665			−0.145832	−	0.989309i	$-0.546586\pi$
$409$	−5.89856			−0.291665			−0.145832	+	0.989309i	$0.546586\pi$
$410$	−6.61982	−	12.7982i	−0.326930	−	0.632056i
$411$	10.5751	−	10.5751i	0.521634	−	0.521634i
$412$	−31.0333	+	11.2075i	−1.52890	+	0.552152i
$413$		−	3.32717i		−	0.163720i
$414$	15.7269	−	9.99156i	0.772936	−	0.491058i
$415$	−24.8141	+	20.7638i	−1.21808	+	1.01926i
$416$	−22.7588	+	11.6674i	−1.11584	+	0.572039i
$417$	−15.6155	−	15.6155i	−0.764696	−	0.764696i
$418$	−1.22712	+	5.50264i	−0.0600204	+	0.269143i
$419$	−8.24430	+	8.24430i	−0.402760	+	0.402760i	−0.879205	−	0.476444i	$-0.841925\pi$
$419$	−8.24430	+	8.24430i	−0.402760	+	0.402760i	0.476444	+	0.879205i	$0.341925\pi$
$420$	7.16242	+	4.17221i	0.349490	+	0.203583i
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	0.151304	−	0.988487i	$-0.451653\pi$
$421$	−17.1776	−	17.1776i	−0.837184	−	0.837184i	−0.988487	+	0.151304i	$0.951653\pi$
$422$	−3.46436	−	5.45297i	−0.168642	−	0.265447i
$423$	21.3528	−	21.3528i	1.03821	−	1.03821i
$424$	−6.17034	−	4.77152i	−0.299658	−	0.231725i
$425$	−18.1542	+	12.6380i	−0.880607	+	0.613031i
$426$	−5.40296	−	1.20489i	−0.261774	−	0.0583772i
$427$	−3.42135			−0.165571
$428$	−27.7198	−	13.0104i	−1.33989	−	0.628881i
$429$	6.36269	+	6.36269i	0.307194	+	0.307194i
$430$	10.8952	+	21.0639i	0.525415	+	1.01579i
$431$			32.1769i			1.54990i	0.632020	+	0.774952i	$0.282226\pi$
$431$			32.1769i			1.54990i	−0.632020	+	0.774952i	$0.717774\pi$
$432$	15.7432	+	18.9536i	0.757445	+	0.911904i
$433$	−20.3383	+	20.3383i	−0.977396	+	0.977396i	−0.999750	−	0.0223540i	$-0.992884\pi$
$433$	−20.3383	+	20.3383i	−0.977396	+	0.977396i	0.0223540	+	0.999750i	$0.492884\pi$
$434$	0.108415	−	0.0688775i	0.00520407	−	0.00330623i
$435$	−34.5381	−	3.06921i	−1.65598	−	0.147158i
$436$	−11.9898	−	33.1995i	−0.574206	−	1.58997i
$437$		−	14.6156i		−	0.699161i
$438$	−7.81163	−	12.2957i	−0.373254	−	0.587510i
$439$		−	35.4180i		−	1.69041i	−0.534444	−	0.845204i	$-0.679479\pi$
$439$		−	35.4180i		−	1.69041i	0.534444	−	0.845204i	$-0.320521\pi$
$440$	−2.99418	+	3.23421i	−0.142742	+	0.154185i
$441$		−	33.9256i		−	1.61550i
$442$	23.8752	−	15.1683i	1.13563	−	0.721481i
$443$			3.03787i			0.144333i	0.997393	+	0.0721667i	$0.0229913\pi$
$443$			3.03787i			0.144333i	−0.997393	+	0.0721667i	$0.977009\pi$
$444$	−14.1813	+	30.2145i	−0.673014	+	1.43392i
$445$	−5.74507	+	4.80733i	−0.272342	+	0.227890i
$446$	−8.76567	−	13.7974i	−0.415067	−	0.653324i
$447$	−12.0398	+	12.0398i	−0.569463	+	0.569463i
$448$	2.62953	−	4.47664i	0.124234	−	0.211502i
$449$		−	8.65559i		−	0.408483i	−0.978921	−	0.204241i	$-0.934527\pi$
$449$		−	8.65559i		−	0.408483i	0.978921	−	0.204241i	$-0.0654727\pi$
$450$	−14.0881	+	33.6325i	−0.664120	+	1.58545i
$451$	2.24526	+	2.24526i	0.105725	+	0.105725i
$452$	6.74527	−	2.43601i	0.317271	−	0.114580i
$453$	35.5335			1.66951
$454$	−0.474247	+	2.12661i	−0.0222575	+	0.0998068i
$455$	0.580733	−	6.53504i	0.0272252	−	0.306367i
$456$	45.8381	−	5.86000i	2.14656	−	0.274420i
$457$	13.5575	−	13.5575i	0.634193	−	0.634193i	−0.314924	−	0.949117i	$-0.601979\pi$
$457$	13.5575	−	13.5575i	0.634193	−	0.634193i	0.949117	+	0.314924i	$0.101979\pi$
$458$	−29.6512	+	18.8379i	−1.38551	+	0.880236i
$459$	−19.2692	−	19.2692i	−0.899411	−	0.899411i
$460$	5.75115	−	9.87298i	0.268149	−	0.460330i
$461$	−1.19682	+	1.19682i	−0.0557416	+	0.0557416i	−0.734428	−	0.678687i	$-0.762550\pi$
$461$	−1.19682	+	1.19682i	−0.0557416	+	0.0557416i	0.678687	+	0.734428i	$0.262550\pi$
$462$	−1.78286	−	0.397587i	−0.0829459	−	0.0184974i
$463$	21.1815	+	21.1815i	0.984390	+	0.984390i	0.999880	−	0.0154904i	$-0.00493096\pi$
$463$	21.1815	+	21.1815i	0.984390	+	0.984390i	−0.0154904	+	0.999880i	$0.504931\pi$
$464$	−2.00096	+	21.6258i	−0.0928921	+	1.00395i
$465$	0.573555	+	0.685435i	0.0265980	+	0.0317863i
$466$	10.7144	+	16.8647i	0.496334	+	0.781241i
$467$			24.8448i			1.14968i	0.818266	+	0.574840i	$0.194936\pi$
$467$			24.8448i			1.14968i	−0.818266	+	0.574840i	$0.805064\pi$
$468$	19.8116	−	42.2105i	0.915792	−	1.95118i
$469$	1.52664	−	1.52664i	0.0704936	−	0.0704936i
$470$	5.61460	−	17.6462i	0.258982	−	0.813959i
$471$	21.4343			0.987642
$472$	−1.83884	−	14.3838i	−0.0846394	−	0.662066i
$473$	−3.69537	−	3.69537i	−0.169913	−	0.169913i
$474$	−15.2336	−	3.39717i	−0.699701	−	0.156037i
$475$	16.3420	+	23.4749i	0.749822	+	1.07710i
$476$	−2.43972	+	5.19804i	−0.111824	+	0.238252i
$477$	14.2210			0.651135
$478$	36.2692	+	8.08825i	1.65892	+	0.369948i
$479$	23.5766			1.07724			0.538621	−	0.842548i	$-0.318946\pi$
$479$	23.5766			1.07724			0.538621	+	0.842548i	$0.318946\pi$
$480$	33.2698	+	14.0785i	1.51855	+	0.642591i
$481$	26.4181			1.20456
$482$	0.156309	+	0.0348578i	0.00711967	+	0.00158773i
$483$	4.73547			0.215471
$484$	−8.93472	+	19.0362i	−0.406124	+	0.865284i
$485$	15.6102	+	1.38719i	0.708821	+	0.0629891i
$486$	17.1417	+	3.82271i	0.777565	+	0.173401i
$487$	−2.63011	−	2.63011i	−0.119182	−	0.119182i	0.645001	−	0.764182i	$-0.276857\pi$
$487$	−2.63011	−	2.63011i	−0.119182	−	0.119182i	−0.764182	+	0.645001i	$0.776857\pi$
$488$	−14.7909	+	1.89089i	−0.669552	+	0.0855964i
$489$	−67.7686			−3.06460
$490$	−9.55798	−	18.4785i	−0.431786	−	0.834774i
$491$	−18.6899	+	18.6899i	−0.843465	+	0.843465i	−0.989308	−	0.145843i	$-0.953411\pi$
$491$	−18.6899	+	18.6899i	−0.843465	+	0.843465i	0.145843	+	0.989308i	$0.453411\pi$
$492$	11.0582	−	23.5606i	0.498544	−	1.06219i
$493$		−	24.0202i		−	1.08182i
$494$	−19.6139	−	30.8727i	−0.882472	−	1.38903i
$495$	0.711274	−	8.00403i	0.0319694	−	0.359754i
$496$	0.430623	−	0.357683i	0.0193355	−	0.0160605i
$497$	−0.628940	−	0.628940i	−0.0282118	−	0.0282118i
$498$	−57.0424	−	12.7208i	−2.55613	−	0.570032i
$499$	9.69342	−	9.69342i	0.433937	−	0.433937i	−0.456028	−	0.889965i	$-0.650728\pi$
$499$	9.69342	−	9.69342i	0.433937	−	0.433937i	0.889965	+	0.456028i	$0.150728\pi$
$500$	1.80192	+	22.2880i	0.0805845	+	0.996748i
$501$	−1.15090	−	1.15090i	−0.0514185	−	0.0514185i
$502$	−32.4491	+	20.6154i	−1.44827	+	0.920110i
$503$	−13.0434	+	13.0434i	−0.581577	+	0.581577i	−0.935336	−	0.353759i	$-0.884903\pi$
$503$	−13.0434	+	13.0434i	−0.581577	+	0.581577i	0.353759	+	0.935336i	$0.384903\pi$
$504$	1.20034	+	9.38926i	0.0534672	+	0.418231i
$505$	5.81265	+	0.516538i	0.258659	+	0.0229856i
$506$	−0.548051	+	2.45756i	−0.0243638	+	0.109252i
$507$	−21.2495			−0.943724
$508$	1.63816	−	0.591611i	0.0726817	−	0.0262485i
$509$	25.8539	+	25.8539i	1.14595	+	1.14595i	0.987341	+	0.158611i	$0.0507016\pi$
$509$	25.8539	+	25.8539i	1.14595	+	1.14595i	0.158611	+	0.987341i	$0.449298\pi$
$510$	−38.0744	−	12.1144i	−1.68596	−	0.536433i
$511$		−	2.34062i		−	0.103543i
$512$	8.89365	−	20.8063i	0.393047	−	0.919518i
$513$	−24.9168	+	24.9168i	−1.10010	+	1.10010i
$514$	0.812734	+	1.27926i	0.0358481	+	0.0564258i
$515$	3.26531	−	36.7448i	0.143887	−	1.61917i
$516$	−18.2002	+	38.7773i	−0.801221	+	1.70707i
$517$			4.08080i			0.179473i
$518$	−4.52664	+	2.87584i	−0.198889	+	0.126357i
$519$			44.1252i			1.93688i
$520$	−1.10116	−	28.5727i	−0.0482892	−	1.25300i
$521$		−	25.0528i		−	1.09758i	−0.835959	−	0.548792i	$-0.815088\pi$
$521$		−	25.0528i		−	1.09758i	0.835959	−	0.548792i	$-0.184912\pi$
$522$	−21.2334	−	33.4218i	−0.929361	−	1.46283i
$523$		−	40.3434i		−	1.76410i	−0.471160	−	0.882048i	$-0.656165\pi$
$523$		−	40.3434i		−	1.76410i	0.471160	−	0.882048i	$-0.343835\pi$
$524$	9.17898	+	25.4165i	0.400986	+	1.11032i
$525$	−7.60588	+	5.29481i	−0.331948	+	0.231084i
$526$	−9.67325	+	6.14556i	−0.421774	+	0.267959i
$527$	−0.437794	+	0.437794i	−0.0190706	+	0.0190706i
$528$	−7.92723	−	0.733479i	−0.344988	−	0.0319206i
$529$			16.4724i			0.716192i
$530$	7.74586	−	4.00653i	0.336459	−	0.174033i
$531$	18.6944	+	18.6944i	0.811267	+	0.811267i
$532$	6.72153	+	3.15477i	0.291415	+	0.136777i
$533$	−20.6003			−0.892296
$534$	−13.2067	−	2.94517i	−0.571510	−	0.127450i
$535$	26.2560	−	21.9704i	1.13515	−	0.949862i
$536$	5.75610	−	7.44356i	0.248626	−	0.321513i
$537$	−14.8639	+	14.8639i	−0.641425	+	0.641425i
$538$	10.4984	+	16.5247i	0.452618	+	0.712430i
$539$	3.24180	+	3.24180i	0.139634	+	0.139634i
$540$	−26.6361	+	7.02692i	−1.14623	+	0.302390i
$541$	−24.7446	+	24.7446i	−1.06385	+	1.06385i	−0.0660360	+	0.997817i	$0.521035\pi$
$541$	−24.7446	+	24.7446i	−1.06385	+	1.06385i	−0.997817	+	0.0660360i	$0.978965\pi$
$542$	−1.26254	+	5.66146i	−0.0542307	+	0.243181i
$543$	−25.9590	−	25.9590i	−1.11401	−	1.11401i
$544$	−7.67437	+	23.8201i	−0.329036	+	1.02128i
$545$	39.3097	+	3.49324i	1.68384	+	0.149634i
$546$	10.0028	−	6.35491i	0.428079	−	0.271965i
$547$			19.0254i			0.813465i	0.913547	+	0.406733i	$0.133332\pi$
$547$			19.0254i			0.813465i	−0.913547	+	0.406733i	$0.866668\pi$
$548$	9.85034	−	3.55738i	0.420786	−	0.151964i
$549$	19.2235	−	19.2235i	0.820440	−	0.820440i
$550$	−1.86759	−	4.56000i	−0.0796342	−	0.194439i
$551$	−31.0602			−1.32321
$552$	20.4720	−	2.61717i	0.871346	−	0.111394i
$553$	−1.77329	−	1.77329i	−0.0754079	−	0.0754079i
$554$	7.59554	−	34.0598i	0.322704	−	1.44706i
$555$	−23.9476	−	28.6189i	−1.01652	−	1.21481i
$556$	−5.25292	−	14.5453i	−0.222773	−	0.616856i
$557$	30.9517			1.31146			0.655732	−	0.754993i	$-0.272360\pi$
$557$	30.9517			1.31146			0.655732	+	0.754993i	$0.272360\pi$
$558$	−0.222148	+	0.996151i	−0.00940425	+	0.0421704i
$559$	33.9050			1.43403
$560$	3.29907	+	4.77594i	0.139411	+	0.201820i
$561$	8.80494			0.371745
$562$	7.28565	−	32.6702i	0.307327	−	1.37811i
$563$	3.50238			0.147608			0.0738039	−	0.997273i	$-0.476486\pi$
$563$	3.50238			0.147608			0.0738039	+	0.997273i	$0.476486\pi$
$564$	31.4601	−	11.3616i	1.32471	−	0.478410i
$565$	−0.709734	+	7.98670i	−0.0298587	+	0.336003i
$566$	−4.01676	+	18.0119i	−0.168837	+	0.757097i
$567$	−0.973793	−	0.973793i	−0.0408955	−	0.0408955i
$568$	−3.06658	−	2.37138i	−0.128671	−	0.0995011i
$569$	0.525780			0.0220418			0.0110209	−	0.999939i	$-0.496492\pi$
$569$	0.525780			0.0220418			0.0110209	+	0.999939i	$0.496492\pi$
$570$	−15.6649	+	49.2336i	−0.656131	+	2.06217i
$571$	−11.2487	+	11.2487i	−0.470743	+	0.470743i	−0.902155	−	0.431412i	$-0.858016\pi$
$571$	−11.2487	+	11.2487i	−0.470743	+	0.470743i	0.431412	+	0.902155i	$0.358016\pi$
$572$	2.14035	+	5.92660i	0.0894926	+	0.247804i
$573$		−	43.1472i		−	1.80250i
$574$	3.52977	−	2.24252i	0.147330	−	0.0936008i
$575$	7.29859	+	10.4843i	0.304372	+	0.437224i
$576$	10.3784	+	39.9275i	0.432432	+	1.66364i
$577$	−2.92884	−	2.92884i	−0.121929	−	0.121929i	0.643509	−	0.765438i	$-0.277478\pi$
$577$	−2.92884	−	2.92884i	−0.121929	−	0.121929i	−0.765438	+	0.643509i	$0.777478\pi$
$578$	0.791607	−	3.54971i	0.0329265	−	0.147649i
$579$	11.9714	−	11.9714i	0.497515	−	0.497515i
$580$	−20.9814	−	12.2220i	−0.871206	−	0.507489i
$581$	−6.64011	−	6.64011i	−0.275478	−	0.275478i
$582$	15.1799	+	23.8935i	0.629227	+	0.990416i
$583$	−1.35891	+	1.35891i	−0.0562801	+	0.0562801i
$584$	−1.29360	−	10.1188i	−0.0535295	−	0.418718i
$585$	33.4555	+	39.9814i	1.38321	+	1.65303i
$586$	43.7186	+	9.74951i	1.80600	+	0.402748i
$587$	23.1574			0.955809			0.477905	−	0.878412i	$-0.341396\pi$
$587$	23.1574			0.955809			0.477905	+	0.878412i	$0.341396\pi$
$588$	15.9664	−	34.0178i	0.658442	−	1.40287i
$589$	0.566106	+	0.566106i	0.0233260	+	0.0233260i
$590$	15.4493	+	4.91558i	0.636036	+	0.202371i
$591$		−	11.5150i		−	0.473662i
$592$	−17.9798	+	14.9343i	−0.738964	+	0.613798i
$593$	−13.9325	+	13.9325i	−0.572141	+	0.572141i	−0.932726	−	0.360585i	$-0.882577\pi$
$593$	−13.9325	+	13.9325i	−0.572141	+	0.572141i	0.360585	+	0.932726i	$0.382577\pi$
$594$	5.12398	−	3.25534i	0.210240	−	0.133568i
$595$	−4.11990	−	4.92354i	−0.168900	−	0.201846i
$596$	−11.2146	+	4.05008i	−0.459368	+	0.165898i
$597$		−	15.5097i		−	0.634769i
$598$	−8.75988	−	13.7882i	−0.358218	−	0.563843i
$599$			33.5311i			1.37004i	0.728523	+	0.685021i	$0.240207\pi$
$599$			33.5311i			1.37004i	−0.728523	+	0.685021i	$0.759793\pi$
$600$	−29.9548	+	27.0936i	−1.22290	+	1.10609i
$601$			19.4164i			0.792011i	0.918248	+	0.396005i	$0.129604\pi$
$601$			19.4164i			0.792011i	−0.918248	+	0.396005i	$0.870396\pi$
$602$	−5.80948	+	3.69085i	−0.236777	+	0.150428i
$603$			17.1554i			0.698623i
$604$	22.5256	+	10.5725i	0.916554	+	0.430187i
$605$	−15.0879	−	18.0310i	−0.613409	−	0.733063i
$606$	5.65243	+	8.89705i	0.229614	+	0.361418i
$607$	9.51495	−	9.51495i	0.386200	−	0.386200i	−0.487130	−	0.873330i	$-0.661956\pi$
$607$	9.51495	−	9.51495i	0.386200	−	0.386200i	0.873330	+	0.487130i	$0.161956\pi$
$608$	30.8015	+	9.92363i	1.24917	+	0.402456i
$609$		−	10.0635i		−	0.407794i
$610$	5.05471	−	15.8865i	0.204659	−	0.643227i
$611$	−18.7206	−	18.7206i	−0.757355	−	0.757355i
$612$	−15.4982	−	42.9143i	−0.626478	−	1.73471i
$613$	−9.37947			−0.378833			−0.189417	−	0.981897i	$-0.560660\pi$
$613$	−9.37947			−0.378833			−0.189417	+	0.981897i	$0.560660\pi$
$614$	−8.42177	+	37.7648i	−0.339875	+	1.52406i
$615$	18.6738	+	22.3164i	0.753002	+	0.899884i
$616$	−1.01190	−	0.782503i	−0.0407707	−	0.0315280i
$617$	3.54768	−	3.54768i	0.142824	−	0.142824i	−0.632079	−	0.774904i	$-0.717798\pi$
$617$	3.54768	−	3.54768i	0.142824	−	0.142824i	0.774904	+	0.632079i	$0.217798\pi$
$618$	56.2428	−	35.7319i	2.26242	−	1.43735i
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	0.0105527	−	0.999944i	$-0.496641\pi$
$619$	−24.6158	−	24.6158i	−0.989392	−	0.989392i	−0.999944	+	0.0105527i	$0.996641\pi$
$620$	0.159651	+	0.605168i	0.00641172	+	0.0243041i
$621$	−11.1282	+	11.1282i	−0.446561	+	0.446561i
$622$	21.8194	+	4.86585i	0.874877	+	0.195103i
$623$	−1.53735	−	1.53735i	−0.0615926	−	0.0615926i
$624$	39.7309	−	33.0013i	1.59051	−	1.32111i
$625$	−23.4453	−	8.67867i	−0.937811	−	0.347147i
$626$	−14.8420	−	23.3617i	−0.593206	−	0.933720i
$627$		−	11.3856i		−	0.454695i
$628$	13.5878	+	6.37747i	0.542211	+	0.254489i
$629$	18.2792	−	18.2792i	0.728840	−	0.728840i
$630$	−10.0848	−	3.20873i	−0.401787	−	0.127839i
$631$	−28.8921			−1.15018			−0.575088	−	0.818092i	$-0.695032\pi$
$631$	−28.8921			−1.15018			−0.575088	+	0.818092i	$0.695032\pi$
$632$	−8.64618	−	6.68608i	−0.343927	−	0.265958i
$633$	9.22547	+	9.22547i	0.366679	+	0.366679i
$634$	48.3235	+	10.7764i	1.91917	+	0.427986i
$635$	−0.172367	+	1.93966i	−0.00684016	+	0.0769729i
$636$	14.2596	+	6.69281i	0.565432	+	0.265387i
$637$	−29.7435			−1.17848
$638$	5.22265	+	1.16468i	0.206767	+	0.0461102i
$639$	7.06765			0.279592
$640$	16.9018	+	18.8237i	0.668101	+	0.744070i
$641$	−16.6914			−0.659271			−0.329636	−	0.944108i	$-0.606926\pi$
$641$	−16.6914			−0.659271			−0.329636	+	0.944108i	$0.606926\pi$
$642$	60.3570	+	13.4600i	2.38210	+	0.531223i
$643$	−5.22468			−0.206041			−0.103021	−	0.994679i	$-0.532851\pi$
$643$	−5.22468			−0.206041			−0.103021	+	0.994679i	$0.532851\pi$
$644$	3.00194	+	1.40897i	0.118293	+	0.0555212i
$645$	−30.7343	−	36.7295i	−1.21016	−	1.44622i
$646$	−34.9327	−	7.79019i	−1.37441	−	0.306501i
$647$	21.6797	+	21.6797i	0.852318	+	0.852318i	0.990418	−	0.138100i	$-0.0440996\pi$
$647$	21.6797	+	21.6797i	0.852318	+	0.852318i	−0.138100	+	0.990418i	$0.544100\pi$
$648$	−4.74801	−	3.67163i	−0.186519	−	0.144235i
$649$	−3.57273			−0.140242
$650$	29.4865	+	12.3514i	1.15656	+	0.484463i
$651$	−0.183418	+	0.183418i	−0.00718874	+	0.00718874i
$652$	−42.9603	−	20.1636i	−1.68245	−	0.789666i
$653$		−	22.7642i		−	0.890833i	−0.895323	−	0.445417i	$-0.853056\pi$
$653$		−	22.7642i		−	0.890833i	0.895323	−	0.445417i	$-0.146944\pi$
$654$	38.2261	+	60.1688i	1.49476	+	2.35279i
$655$	−30.0942	−	2.67431i	−1.17588	−	0.104494i
$656$	14.0202	−	11.6455i	0.547398	−	0.454679i
$657$	13.1513	+	13.1513i	0.513079	+	0.513079i
$658$	5.24560	+	1.16980i	0.204495	+	0.0456036i
$659$	1.66201	−	1.66201i	0.0647427	−	0.0647427i	−0.673994	−	0.738737i	$-0.735423\pi$
$659$	1.66201	−	1.66201i	0.0647427	−	0.0647427i	0.738737	+	0.673994i	$0.235423\pi$
$660$	4.48013	−	7.69104i	0.174389	−	0.299373i
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	0.589129	−	0.808039i	$-0.299471\pi$
$661$	−5.62818	−	5.62818i	−0.218911	−	0.218911i	−0.808039	+	0.589129i	$0.799471\pi$
$662$	−28.3963	+	18.0406i	−1.10365	+	0.701168i
$663$	−40.3926	+	40.3926i	−1.56872	+	1.56872i
$664$	−32.3758	−	25.0362i	−1.25642	−	0.971591i
$665$	−6.36657	+	5.32739i	−0.246885	+	0.206587i
$666$	9.27532	−	41.5923i	0.359411	−	1.61167i
$667$	−13.8720			−0.537125
$668$	−0.387153	−	1.07202i	−0.0149794	−	0.0414777i
$669$	23.3427	+	23.3427i	0.902481	+	0.902481i
$670$	4.83326	+	9.34418i	0.186725	+	0.360997i
$671$			3.67386i			0.141828i
$672$	−3.21526	+	9.97969i	−0.124031	+	0.384975i
$673$	0.278251	−	0.278251i	0.0107258	−	0.0107258i	−0.701724	−	0.712449i	$-0.747586\pi$
$673$	0.278251	−	0.278251i	0.0107258	−	0.0107258i	0.712449	+	0.701724i	$0.247586\pi$
$674$	−15.5494	−	24.4751i	−0.598940	−	0.942744i
$675$	5.43097	−	30.3163i	0.209038	−	1.16687i
$676$	−13.4706	−	6.32248i	−0.518101	−	0.243172i
$677$			26.3591i			1.01306i	0.862222	+	0.506531i	$0.169072\pi$
$677$			26.3591i			1.01306i	−0.862222	+	0.506531i	$0.830928\pi$
$678$	−12.2247	+	7.76655i	−0.469488	+	0.298273i
$679$			4.54840i			0.174551i
$680$	−20.5319	−	19.0081i	−0.787363	−	0.728927i
$681$		−	4.40019i		−	0.168616i
$682$	−0.0739609	−	0.116416i	−0.00283211	−	0.00445780i
$683$			2.83023i			0.108296i	0.998533	+	0.0541479i	$0.0172442\pi$
$683$			2.83023i			0.108296i	−0.998533	+	0.0541479i	$0.982756\pi$
$684$	−55.4919	+	20.0405i	−2.12179	+	0.766269i
$685$	−1.03645	+	11.6632i	−0.0396006	+	0.445629i
$686$	10.5191	−	6.68296i	0.401622	−	0.255157i
$687$	50.1646	−	50.1646i	1.91390	−	1.91390i
$688$	−23.0752	+	19.1667i	−0.879734	+	0.730724i
$689$		−	12.4679i		−	0.474991i
$690$	−6.99620	+	21.9885i	−0.266341	+	0.837087i
$691$	22.1815	+	22.1815i	0.843825	+	0.843825i	0.989354	−	0.145529i	$-0.0464884\pi$
$691$	22.1815	+	22.1815i	0.843825	+	0.843825i	−0.145529	+	0.989354i	$0.546488\pi$
$692$	−13.1288	+	27.9721i	−0.499083	+	1.06334i
$693$	2.33217			0.0885917
$694$	23.1484	+	5.16223i	0.878702	+	0.195956i
$695$	17.2222	+	1.53044i	0.653276	+	0.0580531i
$696$	−5.56183	−	43.5057i	−0.210821	−	1.64908i
$697$	−14.2537	+	14.2537i	−0.539898	+	0.539898i
$698$	1.99845	+	3.14560i	0.0756423	+	0.119063i
$699$	−28.5320	−	28.5320i	−1.07918	−	1.07918i
$700$	−6.39696	+	1.09350i	−0.241782	+	0.0413303i
$701$	16.2264	−	16.2264i	0.612864	−	0.612864i	−0.330828	−	0.943691i	$-0.607328\pi$
$701$	16.2264	−	16.2264i	0.612864	−	0.612864i	0.943691	+	0.330828i	$0.107328\pi$
$702$	−8.57237	+	38.4401i	−0.323543	+	1.45083i
$703$	−23.6366	−	23.6366i	−0.891472	−	0.891472i
$704$	−4.80704	−	2.82360i	−0.181172	−	0.106418i
$705$	−3.31022	+	37.2502i	−0.124670	+	1.40292i
$706$	−40.7449	+	25.8858i	−1.53345	+	0.974226i
$707$			1.69365i			0.0636965i
$708$	9.94708	+	27.5433i	0.373834	+	1.03514i
$709$	−25.3577	+	25.3577i	−0.952329	+	0.952329i	−0.998914	−	0.0465856i	$-0.985166\pi$
$709$	−25.3577	+	25.3577i	−0.952329	+	0.952329i	0.0465856	+	0.998914i	$0.485166\pi$
$710$	3.84959	−	1.99120i	0.144473	−	0.0747282i
$711$	19.9271			0.747326
$712$	−7.49579	−	5.79648i	−0.280916	−	0.217232i
$713$	0.252832	+	0.252832i	0.00946863	+	0.00946863i
$714$	2.52402	−	11.3182i	0.0944592	−	0.423573i
$715$	−7.01735	−	0.623594i	−0.262434	−	0.0233211i
$716$	−13.8452	+	5.00009i	−0.517418	+	0.186862i
$717$	−75.0450			−2.80261
$718$	3.77076	−	16.9088i	0.140724	−	0.631031i
$719$	−41.3374			−1.54163			−0.770813	−	0.637061i	$-0.780150\pi$
$719$	−41.3374			−1.54163			−0.770813	+	0.637061i	$0.780150\pi$
$720$	−45.3710	−	8.29813i	−1.69088	−	0.309253i
$721$	10.7065			0.398730
$722$	−4.22489	+	18.9452i	−0.157234	+	0.705067i
$723$	−0.323420			−0.0120281
$724$	−8.73236	−	24.1798i	−0.324536	−	0.898635i
$725$	22.2805	−	15.5105i	0.827477	−	0.576045i
$726$	9.24346	−	41.4494i	0.343057	−	1.53833i
$727$	−23.4630	−	23.4630i	−0.870193	−	0.870193i	0.122300	−	0.992493i	$-0.460973\pi$
$727$	−23.4630	−	23.4630i	−0.870193	−	0.870193i	−0.992493	+	0.122300i	$0.960973\pi$
$728$	8.23182	−	1.05237i	0.305092	−	0.0390033i
$729$	−41.8342			−1.54942
$730$	10.8683	+	3.45804i	0.402256	+	0.127988i
$731$	23.4595	−	23.4595i	0.867681	−	0.867681i
$732$	28.3229	−	10.2286i	1.04684	−	0.378061i
$733$			15.1628i			0.560051i	0.959993	+	0.280025i	$0.0903429\pi$
$733$			15.1628i			0.560051i	−0.959993	+	0.280025i	$0.909657\pi$
$734$	4.58000	−	2.90975i	0.169051	−	0.107401i
$735$	26.9621	+	32.2214i	0.994511	+	1.18850i
$736$	13.7564	+	4.43205i	0.507069	+	0.163368i
$737$	−1.63931	−	1.63931i	−0.0603848	−	0.0603848i
$738$	−7.23269	+	32.4327i	−0.266239	+	1.19387i
$739$	0.974343	−	0.974343i	0.0358418	−	0.0358418i	−0.688959	−	0.724801i	$-0.741932\pi$
$739$	0.974343	−	0.974343i	0.0358418	−	0.0358418i	0.724801	+	0.688959i	$0.241932\pi$
$740$	−6.66589	−	25.2676i	−0.245043	−	0.928854i
$741$	52.2312	+	52.2312i	1.91876	+	1.91876i
$742$	1.35724	+	2.13633i	0.0498260	+	0.0784272i
$743$	29.0897	−	29.0897i	1.06720	−	1.06720i	0.0696259	−	0.997573i	$-0.477819\pi$
$743$	29.0897	−	29.0897i	1.06720	−	1.06720i	0.997573	−	0.0696259i	$-0.0221806\pi$
$744$	−0.691569	+	0.894310i	−0.0253541	+	0.0327870i
$745$	1.18000	−	13.2786i	0.0432317	−	0.486490i
$746$	−22.7538	−	5.07424i	−0.833078	−	0.185781i
$747$	74.6176			2.73011
$748$	5.58168	+	2.61978i	0.204087	+	0.0957887i
$749$	7.02596	+	7.02596i	0.256723	+	0.256723i
$750$	−13.3487	−	43.1394i	−0.487426	−	1.57523i
$751$			7.77705i			0.283789i	0.989882	+	0.141894i	$0.0453193\pi$
$751$			7.77705i			0.283789i	−0.989882	+	0.141894i	$0.954681\pi$
$752$	23.3239	+	2.15808i	0.850534	+	0.0786970i
$753$	54.8981	−	54.8981i	2.00060	−	2.00060i
$754$	−29.3019	+	18.6159i	−1.06711	+	0.677952i
$755$	−21.3361	+	17.8535i	−0.776498	+	0.649755i
$756$	−2.71570	−	7.51973i	−0.0987690	−	0.273490i
$757$			1.42073i			0.0516372i	0.999667	+	0.0258186i	$0.00821923\pi$
$757$			1.42073i			0.0516372i	−0.999667	+	0.0258186i	$0.991781\pi$
$758$	−14.7699	−	23.2482i	−0.536469	−	0.844413i
$759$		−	5.08497i		−	0.184573i
$760$	−24.5791	+	26.5496i	−0.891579	+	0.963054i
$761$			26.6737i			0.966921i	0.875366	+	0.483460i	$0.160620\pi$
$761$			26.6737i			0.966921i	−0.875366	+	0.483460i	$0.839380\pi$
$762$	−2.96891	+	1.88619i	−0.107552	+	0.0683295i
$763$			11.4538i			0.414656i
$764$	12.8378	−	27.3521i	0.464456	−	0.989565i
$765$	50.8124	+	4.51542i	1.83713	+	0.163255i
$766$	12.3905	+	19.5029i	0.447687	+	0.704669i
$767$	16.3899	−	16.3899i	0.591805	−	0.591805i
$768$	−8.38443	+	44.9203i	−0.302547	+	1.62092i
$769$			45.8210i			1.65235i	0.563415	+	0.826174i	$0.309487\pi$
$769$			45.8210i			1.65235i	−0.563415	+	0.826174i	$0.690513\pi$
$770$	1.27028	−	0.657050i	0.0457777	−	0.0236784i
$771$	−2.16428	−	2.16428i	−0.0779447	−	0.0779447i
$772$	11.1509	−	4.02707i	0.401330	−	0.144937i
$773$	−18.5473			−0.667101			−0.333550	−	0.942732i	$-0.608247\pi$
$773$	−18.5473			−0.667101			−0.333550	+	0.942732i	$0.608247\pi$
$774$	11.9039	−	53.3795i	0.427878	−	1.91869i
$775$	−0.688782	−	0.123391i	−0.0247418	−	0.00443233i
$776$	2.51378	+	19.6633i	0.0902393	+	0.705870i
$777$	7.65827	−	7.65827i	0.274739	−	0.274739i
$778$	−26.6264	+	16.9162i	−0.954603	+	0.606474i
$779$	18.4313	+	18.4313i	0.660370	+	0.660370i
$780$	14.7300	+	55.8352i	0.527418	+	1.99922i
$781$	−0.675359	+	0.675359i	−0.0241662	+	0.0241662i
$782$	−15.6015	−	3.47922i	−0.557908	−	0.124417i
$783$	23.6490	+	23.6490i	0.845146	+	0.845146i
$784$	20.2430	−	16.8142i	0.722964	−	0.600508i
$785$	−12.8702	+	10.7695i	−0.459358	+	0.384380i
$786$	−29.2647	−	46.0633i	−1.04384	−	1.64302i
$787$		−	21.3016i		−	0.759319i	−0.925126	−	0.379659i	$-0.876041\pi$
$787$		−	21.3016i		−	0.759319i	0.925126	−	0.379659i	$-0.123959\pi$
$788$	3.42610	−	7.29963i	0.122050	−	0.260039i
$789$	16.3654	−	16.3654i	0.582624	−	0.582624i
$790$	10.8539	−	5.61415i	0.386163	−	0.199742i
$791$	−2.32712			−0.0827427
$792$	10.0822	−	1.28892i	0.358256	−	0.0458000i
$793$	−16.8538	−	16.8538i	−0.598496	−	0.598496i
$794$	−41.3482	−	9.22090i	−1.46739	−	0.327237i
$795$	−13.5066	+	11.3020i	−0.479030	+	0.400841i
$796$	4.61468	−	9.83200i	0.163563	−	0.348486i
$797$	−2.35457			−0.0834033			−0.0417016	−	0.999130i	$-0.513278\pi$
$797$	−2.35457			−0.0834033			−0.0417016	+	0.999130i	$0.513278\pi$
$798$	−14.6354	−	3.26378i	−0.518088	−	0.115537i
$799$	−25.9063			−0.916500
$800$	−27.0505	+	8.26274i	−0.956378	+	0.292132i
$801$	17.2758			0.610410
$802$	−27.5014	−	6.13297i	−0.971108	−	0.216563i
$803$	−2.51337			−0.0886949
$804$	−8.07384	+	17.2021i	−0.284742	+	0.606670i
$805$	−2.84341	+	2.37930i	−0.100217	+	0.0838592i
$806$	0.873354	+	0.194763i	0.0307626	+	0.00686023i
$807$	−27.9569	−	27.9569i	−0.984128	−	0.984128i
$808$	0.936037	+	7.32187i	0.0329297	+	0.257582i
$809$	23.9476			0.841952			0.420976	−	0.907072i	$-0.361688\pi$
$809$	23.9476			0.841952			0.420976	+	0.907072i	$0.361688\pi$
$810$	5.96035	−	3.08298i	0.209425	−	0.108325i
$811$	−1.33006	+	1.33006i	−0.0467048	+	0.0467048i	−0.730073	−	0.683369i	$-0.760514\pi$
$811$	−1.33006	+	1.33006i	−0.0467048	+	0.0467048i	0.683369	+	0.730073i	$0.260514\pi$
$812$	2.99425	−	6.37952i	0.105078	−	0.223877i
$813$		−	11.7142i		−	0.410834i
$814$	3.08809	+	4.86072i	0.108238	+	0.170368i
$815$	40.6916	−	34.0498i	1.42537	−	1.19271i
$816$	4.65638	−	50.3248i	0.163006	−	1.76172i
$817$	−30.3352	−	30.3352i	−1.06129	−	1.06129i
$818$	8.14182	+	1.81567i	0.284672	+	0.0634836i
$819$	−10.6988	+	10.6988i	−0.373846	+	0.373846i
$820$	5.19791	+	19.7031i	0.181519	+	0.688061i
$821$	36.4676	+	36.4676i	1.27273	+	1.27273i	0.944651	+	0.328076i	$0.106400\pi$
$821$	36.4676	+	36.4676i	1.27273	+	1.27273i	0.328076	+	0.944651i	$0.393600\pi$
$822$	−17.8522	+	11.3417i	−0.622666	+	0.395589i
$823$	26.3978	−	26.3978i	0.920170	−	0.920170i	−0.0768712	−	0.997041i	$-0.524493\pi$
$823$	26.3978	−	26.3978i	0.920170	−	0.920170i	0.997041	+	0.0768712i	$0.0244930\pi$
$824$	46.2853	−	5.91718i	1.61243	−	0.206135i
$825$	5.68559	+	8.16723i	0.197947	+	0.284346i
$826$	−1.02416	+	4.59252i	−0.0356351	+	0.159794i
$827$	−1.99830			−0.0694878			−0.0347439	−	0.999396i	$-0.511062\pi$
$827$	−1.99830			−0.0694878			−0.0347439	+	0.999396i	$0.511062\pi$
$828$	−24.7836	+	8.95041i	−0.861288	+	0.311048i
$829$	13.0376	+	13.0376i	0.452813	+	0.452813i	0.896287	−	0.443474i	$-0.146254\pi$
$829$	13.0376	+	13.0376i	0.452813	+	0.452813i	−0.443474	+	0.896287i	$0.646254\pi$
$830$	40.6425	−	21.0223i	1.41072	−	0.729694i
$831$			70.4735i			2.44470i
$832$	35.0055	−	9.09901i	1.21360	−	0.315451i
$833$	−20.5801	+	20.5801i	−0.713059	+	0.713059i
$834$	16.7475	+	26.3609i	0.579919	+	0.912805i
$835$	1.26932	+	0.112797i	0.0439266	+	0.00390352i
$836$	3.38761	−	7.21760i	0.117163	−	0.249626i
$837$		−	0.862057i		−	0.0297971i
$838$	13.9174	−	8.84194i	0.480769	−	0.305440i
$839$		−	15.4102i		−	0.532018i	−0.963971	−	0.266009i	$-0.914295\pi$
$839$		−	15.4102i		−	0.532018i	0.963971	−	0.266009i	$-0.0857050\pi$
$840$	−8.60207	−	7.96364i	−0.296799	−	0.274772i
$841$			0.479815i			0.0165453i
$842$	18.4228	+	28.9979i	0.634891	+	0.999333i
$843$			67.5983i			2.32821i
$844$	3.10336	+	8.59317i	0.106822	+	0.295789i
$845$	12.7593	−	10.6766i	0.438932	−	0.367287i
$846$	−36.0462	+	22.9007i	−1.23929	+	0.787343i
$847$	4.82499	−	4.82499i	0.165789	−	0.165789i
$848$	7.04822	+	8.48550i	0.242037	+	0.291393i
$849$		−	37.2686i		−	1.27906i
$850$	28.9485	−	11.8561i	0.992926	−	0.406661i
$851$	−10.5565	−	10.5565i	−0.361872	−	0.361872i
$852$	7.08686	+	3.32624i	0.242792	+	0.113955i
$853$	7.96419			0.272689			0.136344	−	0.990662i	$-0.456465\pi$
$853$	7.96419			0.272689			0.136344	+	0.990662i	$0.456465\pi$
$854$	4.72251	+	1.05315i	0.161601	+	0.0360380i
$855$	5.83883	−	65.7049i	0.199684	−	2.24706i
$856$	34.2571	+	26.4910i	1.17088	+	0.905443i
$857$	−5.35407	+	5.35407i	−0.182891	+	0.182891i	−0.792615	−	0.609723i	$-0.791281\pi$
$857$	−5.35407	+	5.35407i	−0.182891	+	0.182891i	0.609723	+	0.792615i	$0.291281\pi$
$858$	−6.82393	−	10.7410i	−0.232965	−	0.366692i
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.975824	−	0.218559i	$-0.929864\pi$
$859$	−35.0058	−	35.0058i	−1.19438	−	1.19438i	−0.218559	−	0.975824i	$-0.570136\pi$
$860$	−8.55499	−	32.4283i	−0.291723	−	1.10580i
$861$	−5.97175	+	5.97175i	−0.203517	+	0.203517i
$862$	9.90457	−	44.4140i	0.337351	−	1.51275i
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.955829	+	0.293923i	$0.0949610\pi$
$863$	36.7138	+	36.7138i	1.24975	+	1.24975i	0.293923	+	0.955829i	$0.405039\pi$
$864$	−15.8962	−	31.0078i	−0.540801	−	1.05491i
$865$	−22.1703	−	26.4950i	−0.753814	−	0.900856i
$866$	34.3336	−	21.8126i	1.16670	−	0.741224i
$867$			7.34475i			0.249441i
$868$	−0.170847	+	0.0617003i	−0.00579893	+	0.00209424i
$869$	−1.90416	+	1.90416i	−0.0645943	+	0.0645943i
$870$	46.7285	+	14.8679i	1.58424	+	0.504068i
$871$	15.0406			0.509633
$872$	6.33022	+	49.5162i	0.214368	+	1.67683i
$873$	−25.5561	−	25.5561i	−0.864942	−	0.864942i
$874$	−4.49894	+	20.1741i	−0.152179	+	0.682399i
$875$	1.90662	−	7.00078i	0.0644555	−	0.236669i
$876$	6.99764	+	19.3764i	0.236428	+	0.654667i
$877$	−14.3410			−0.484262			−0.242131	−	0.970244i	$-0.577846\pi$
$877$	−14.3410			−0.484262			−0.242131	+	0.970244i	$0.577846\pi$
$878$	−10.9022	+	48.8877i	−0.367933	+	1.64988i
$879$	−90.4586			−3.05109
$880$	5.12843	−	3.54255i	0.172879	−	0.119419i
$881$	−13.6397			−0.459533			−0.229767	−	0.973246i	$-0.573796\pi$
$881$	−13.6397			−0.459533			−0.229767	+	0.973246i	$0.573796\pi$
$882$	−10.4429	+	46.8277i	−0.351629	+	1.57677i
$883$	6.12563			0.206144			0.103072	−	0.994674i	$-0.467133\pi$
$883$	6.12563			0.206144			0.103072	+	0.994674i	$0.467133\pi$
$884$	−37.6242	+	13.5877i	−1.26544	+	0.457004i
$885$	−32.6125	−	2.89809i	−1.09626	−	0.0974184i
$886$	0.935105	−	4.19319i	0.0314155	−	0.140873i
$887$	25.5187	+	25.5187i	0.856834	+	0.856834i	0.990964	−	0.134130i	$-0.0428239\pi$
$887$	25.5187	+	25.5187i	0.856834	+	0.856834i	−0.134130	+	0.990964i	$0.542824\pi$
$888$	28.8751	−	37.3401i	0.968984	−	1.25305i
$889$	−0.565166			−0.0189551
$890$	9.40974	−	4.86717i	0.315415	−	0.163148i
$891$	−1.04566	+	1.04566i	−0.0350310	+	0.0350310i
$892$	7.85227	+	21.7428i	0.262913	+	0.728003i
$893$			33.4992i			1.12101i
$894$	20.3247	−	12.9126i	0.679759	−	0.431861i
$895$	1.45678	−	16.3933i	0.0486948	−	0.547967i
$896$	−5.00755	+	5.36973i	−0.167290	+	0.179390i
$897$	23.3273	+	23.3273i	0.778875	+	0.778875i
$898$	−2.66433	+	11.9474i	−0.0889100	+	0.398689i
$899$	0.537302	−	0.537302i	0.0179200	−	0.0179200i
$900$	29.7986	−	42.0866i	0.993285	−	1.40289i
$901$	−8.62682	−	8.62682i	−0.287401	−	0.287401i
$902$	−2.40802	−	3.79028i	−0.0801784	−	0.126203i
$903$	9.82861	−	9.82861i	0.327076	−	0.327076i
$904$	−10.0604	+	1.28613i	−0.334604	+	0.0427762i
$905$	28.6299	+	2.54418i	0.951691	+	0.0845715i
$906$	−49.0471	−	10.9378i	−1.62948	−	0.363384i
$907$	32.1815			1.06857			0.534284	−	0.845305i	$-0.320581\pi$
$907$	32.1815			1.06857			0.534284	+	0.845305i	$0.320581\pi$
$908$	1.30921	−	2.78940i	0.0434477	−	0.0925694i
$909$	−9.51614	−	9.51614i	−0.315630	−	0.315630i
$910$	−2.81318	+	8.84161i	−0.0932562	+	0.293096i
$911$		−	38.6282i		−	1.27981i	−0.768455	−	0.639904i	$-0.778974\pi$
$911$		−	38.6282i		−	1.27981i	0.768455	−	0.639904i	$-0.221026\pi$
$912$	−65.0744	−	6.02111i	−2.15483	−	0.199379i
$913$	−7.13018	+	7.13018i	−0.235974	+	0.235974i
$914$	−22.8868	+	14.5403i	−0.757027	+	0.480950i
$915$	−2.98012	+	33.5356i	−0.0985198	+	1.10865i
$916$	46.7264	−	16.8749i	1.54388	−	0.557563i
$917$		−	8.76867i		−	0.289567i
$918$	20.6661	+	32.5289i	0.682082	+	1.07361i
$919$			19.1924i			0.633099i	0.948576	+	0.316550i	$0.102524\pi$
$919$			19.1924i			0.633099i	−0.948576	+	0.316550i	$0.897476\pi$
$920$	−10.9774	+	11.8575i	−0.361915	+	0.390929i
$921$		−	78.1395i		−	2.57479i
$922$	2.02038	−	1.28358i	0.0665378	−	0.0422725i
$923$		−	6.19641i		−	0.203957i
$924$	2.33850	+	1.09758i	0.0769312	+	0.0361079i
$925$	28.7587	+	5.15194i	0.945580	+	0.169395i
$926$	−22.7170	−	35.7571i	−0.746527	−	1.17505i
$927$	−60.1564	+	60.1564i	−1.97580	+	1.97580i
$928$	9.41870	−	29.2343i	0.309184	−	0.959662i
$929$		−	16.8576i		−	0.553081i	−0.961002	−	0.276541i	$-0.910812\pi$
$929$		−	16.8576i		−	0.553081i	0.961002	−	0.276541i	$-0.0891880\pi$
$930$	−0.580694	−	1.12266i	−0.0190417	−	0.0368135i
$931$	26.6119	+	26.6119i	0.872170	+	0.872170i
$932$	−9.59792	−	26.5765i	−0.314390	−	0.870542i
$933$	−45.1467			−1.47804
$934$	7.64764	−	34.2935i	0.250239	−	1.12212i
$935$	−5.28692	+	4.42397i	−0.172901	+	0.144679i
$936$	−40.3392	+	52.1651i	−1.31853	+	1.70507i
$937$	23.9511	−	23.9511i	0.782449	−	0.782449i	−0.197795	−	0.980243i	$-0.563378\pi$
$937$	23.9511	−	23.9511i	0.782449	−	0.782449i	0.980243	+	0.197795i	$0.0633779\pi$
$938$	−2.57715	+	1.63730i	−0.0841470	+	0.0534599i
$939$	39.5238	+	39.5238i	1.28981	+	1.28981i
$940$	−13.1817	+	22.6289i	−0.429939	+	0.738075i
$941$	14.2496	−	14.2496i	0.464525	−	0.464525i	−0.435610	−	0.900135i	$-0.643467\pi$
$941$	14.2496	−	14.2496i	0.464525	−	0.464525i	0.900135	+	0.435610i	$0.143467\pi$
$942$	−29.5860	−	6.59784i	−0.963963	−	0.214969i
$943$	8.23171	+	8.23171i	0.268061	+	0.268061i
$944$	−1.88940	+	20.4200i	−0.0614946	+	0.664616i
$945$	8.90369	+	0.791222i	0.289637	+	0.0257385i
$946$	3.96325	+	6.23824i	0.128856	+	0.202823i
$947$			20.2943i			0.659477i	0.944072	+	0.329738i	$0.106961\pi$
$947$			20.2943i			0.659477i	−0.944072	+	0.329738i	$0.893039\pi$
$948$	19.9813	+	9.37829i	0.648963	+	0.304593i
$949$	11.5301	−	11.5301i	0.374282	−	0.374282i
$950$	−15.3310	−	37.4330i	−0.497403	−	1.21449i
$951$	−99.9866			−3.24229
$952$	4.96761	−	6.42391i	0.161001	−	0.208200i
$953$	10.9257	+	10.9257i	0.353919	+	0.353919i	0.861565	−	0.507647i	$-0.169484\pi$
$953$	10.9257	+	10.9257i	0.353919	+	0.353919i	−0.507647	+	0.861565i	$0.669484\pi$
$954$	−19.6293	−	4.37746i	−0.635524	−	0.141725i
$955$	21.6789	+	25.9077i	0.701514	+	0.838353i
$956$	−47.5730	−	22.3285i	−1.53862	−	0.722157i
$957$	−10.8062			−0.349316
$958$	−32.5429	−	7.25726i	−1.05141	−	0.234471i
$959$	−3.39836			−0.109739
$960$	−41.5890	−	29.6736i	−1.34228	−	0.957712i
$961$	30.9804			0.999368
$962$	−36.4651	−	8.13193i	−1.17568	−	0.262184i
$963$	−78.9535			−2.54424
$964$	−0.205024	−	0.0962289i	−0.00660339	−	0.00309932i
$965$	−1.17329	+	13.2032i	−0.0377696	+	0.425025i
$966$	−6.53641	−	1.45766i	−0.210305	−	0.0468993i
$967$	10.7569	+	10.7569i	0.345918	+	0.345918i	0.858586	−	0.512669i	$-0.171343\pi$
$967$	10.7569	+	10.7569i	0.345918	+	0.345918i	−0.512669	+	0.858586i	$0.671343\pi$
$968$	18.1923	−	23.5256i	0.584724	−	0.756142i
$969$	72.2796			2.32195
$970$	−21.1198	−	6.71982i	−0.678117	−	0.215760i
$971$	−18.7456	+	18.7456i	−0.601574	+	0.601574i	−0.940730	−	0.339156i	$-0.889858\pi$
$971$	−18.7456	+	18.7456i	−0.601574	+	0.601574i	0.339156	+	0.940730i	$0.389858\pi$
$972$	−22.4842	−	10.5530i	−0.721180	−	0.338488i
$973$			5.01811i			0.160873i
$974$	2.82077	+	4.43995i	0.0903832	+	0.142265i
$975$	−63.5497	−	11.3845i	−2.03522	−	0.364597i
$976$	20.9980	+	1.94287i	0.672130	+	0.0621899i
$977$	−26.3906	−	26.3906i	−0.844309	−	0.844309i	0.145107	−	0.989416i	$-0.453647\pi$
$977$	−26.3906	−	26.3906i	−0.844309	−	0.844309i	−0.989416	+	0.145107i	$0.953647\pi$
$978$	93.5415	+	20.8603i	2.99113	+	0.667039i
$979$	−1.65081	+	1.65081i	−0.0527602	+	0.0527602i
$980$	7.50496	+	28.4481i	0.239737	+	0.908742i
$981$	−64.3556	−	64.3556i	−2.05472	−	2.05472i
$982$	31.5509	−	20.0448i	1.00683	−	0.639655i
$983$	−4.87875	+	4.87875i	−0.155608	+	0.155608i	−0.780617	−	0.625009i	$-0.785095\pi$
$983$	−4.87875	+	4.87875i	−0.155608	+	0.155608i	0.625009	+	0.780617i	$0.285095\pi$
$984$	−22.5161	+	29.1170i	−0.717788	+	0.928215i
$985$	5.78559	+	6.91415i	0.184344	+	0.220303i
$986$	−7.39381	+	33.1553i	−0.235467	+	1.05588i
$987$	−10.8537			−0.345478
$988$	17.5701	+	48.6513i	0.558979	+	1.54781i
$989$	−13.5482	−	13.5482i	−0.430807	−	0.430807i
$990$	−3.44555	+	10.8291i	−0.109507	+	0.344171i
$991$		−	61.2103i		−	1.94441i	−0.234130	−	0.972205i	$-0.575224\pi$
$991$		−	61.2103i		−	1.94441i	0.234130	−	0.972205i	$-0.424776\pi$
$992$	−0.704492	+	0.361160i	−0.0223677	+	0.0114668i
$993$	48.0415	−	48.0415i	1.52455	−	1.52455i
$994$	0.674533	+	1.06173i	0.0213949	+	0.0336760i
$995$	7.79271	+	9.31279i	0.247046	+	0.295235i
$996$	74.8204	+	35.1172i	2.37077	+	1.11273i
$997$			39.1082i			1.23857i	0.785167	+	0.619284i	$0.212577\pi$
$997$			39.1082i			1.23857i	−0.785167	+	0.619284i	$0.787423\pi$
$998$	−16.3637	+	10.3961i	−0.517984	+	0.329083i
$999$			35.9935i			1.13878i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	80.2.s.b.27.1	yes	18
3.2	odd	2		720.2.z.g.667.9		18
4.3	odd	2		320.2.s.b.207.1		18
5.2	odd	4		400.2.j.d.43.5		18
5.3	odd	4		80.2.j.b.43.5	✓	18
5.4	even	2		400.2.s.d.107.9		18
8.3	odd	2		640.2.s.c.287.9		18
8.5	even	2		640.2.s.d.287.1		18
15.8	even	4		720.2.bd.g.523.5		18
16.3	odd	4		80.2.j.b.67.5	yes	18
16.5	even	4		640.2.j.c.607.1		18
16.11	odd	4		640.2.j.d.607.9		18
16.13	even	4		320.2.j.b.47.9		18
20.3	even	4		320.2.j.b.143.1		18
20.7	even	4		1600.2.j.d.143.9		18
20.19	odd	2		1600.2.s.d.207.9		18
40.3	even	4		640.2.j.c.543.9		18
40.13	odd	4		640.2.j.d.543.1		18
48.35	even	4		720.2.bd.g.307.5		18
80.3	even	4	inner	80.2.s.b.3.1	yes	18
80.13	odd	4		320.2.s.b.303.1		18
80.19	odd	4		400.2.j.d.307.5		18
80.29	even	4		1600.2.j.d.1007.1		18
80.43	even	4		640.2.s.d.223.1		18
80.53	odd	4		640.2.s.c.223.9		18
80.67	even	4		400.2.s.d.243.9		18
80.77	odd	4		1600.2.s.d.943.9		18
240.83	odd	4		720.2.z.g.163.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.j.b.43.5	✓	18	5.3	odd	4
80.2.j.b.67.5	yes	18	16.3	odd	4
80.2.s.b.3.1	yes	18	80.3	even	4	inner
80.2.s.b.27.1	yes	18	1.1	even	1	trivial
320.2.j.b.47.9		18	16.13	even	4
320.2.j.b.143.1		18	20.3	even	4
320.2.s.b.207.1		18	4.3	odd	2
320.2.s.b.303.1		18	80.13	odd	4
400.2.j.d.43.5		18	5.2	odd	4
400.2.j.d.307.5		18	80.19	odd	4
400.2.s.d.107.9		18	5.4	even	2
400.2.s.d.243.9		18	80.67	even	4
640.2.j.c.543.9		18	40.3	even	4
640.2.j.c.607.1		18	16.5	even	4
640.2.j.d.543.1		18	40.13	odd	4
640.2.j.d.607.9		18	16.11	odd	4
640.2.s.c.223.9		18	80.53	odd	4
640.2.s.c.287.9		18	8.3	odd	2
640.2.s.d.223.1		18	80.43	even	4
640.2.s.d.287.1		18	8.5	even	2
720.2.z.g.163.9		18	240.83	odd	4
720.2.z.g.667.9		18	3.2	odd	2
720.2.bd.g.307.5		18	48.35	even	4
720.2.bd.g.523.5		18	15.8	even	4
1600.2.j.d.143.9		18	20.7	even	4
1600.2.j.d.1007.1		18	80.29	even	4
1600.2.s.d.207.9		18	20.19	odd	2
1600.2.s.d.943.9		18	80.77	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-1.38031 - 0.307817i) q^{2} +2.85601 q^{3} +(1.81050 + 0.849763i) q^{4} +(-1.71489 + 1.43498i) q^{5} +(-3.94217 - 0.879127i) q^{6} +(-0.458895 - 0.458895i) q^{7} +(-2.23747 - 1.73024i) q^{8} +5.15678 q^{9} +O(q^{10})\)	\(q+(-1.38031 - 0.307817i) q^{2} +2.85601 q^{3} +(1.81050 + 0.849763i) q^{4} +(-1.71489 + 1.43498i) q^{5} +(-3.94217 - 0.879127i) q^{6} +(-0.458895 - 0.458895i) q^{7} +(-2.23747 - 1.73024i) q^{8} +5.15678 q^{9} +(2.80878 - 1.45284i) q^{10} +(-0.492763 + 0.492763i) q^{11} +(5.17080 + 2.42693i) q^{12} -4.52109i q^{13} +(0.492160 + 0.774671i) q^{14} +(-4.89773 + 4.09831i) q^{15} +(2.55581 + 3.07699i) q^{16} +(-3.12823 - 3.12823i) q^{17} +(-7.11794 - 1.58734i) q^{18} +(-4.04508 + 4.04508i) q^{19} +(-4.32419 + 1.14077i) q^{20} +(-1.31061 - 1.31061i) q^{21} +(0.831845 - 0.528484i) q^{22} +(-1.80660 + 1.80660i) q^{23} +(-6.39024 - 4.94157i) q^{24} +(0.881683 - 4.92165i) q^{25} +(-1.39167 + 6.24050i) q^{26} +6.15978 q^{27} +(-0.440876 - 1.22078i) q^{28} +(3.83926 + 3.83926i) q^{29} +(8.02191 - 4.14932i) q^{30} -0.139949i q^{31} +(-2.58065 - 5.03391i) q^{32} +(-1.40733 + 1.40733i) q^{33} +(3.35500 + 5.28085i) q^{34} +(1.44546 + 0.128450i) q^{35} +(9.33634 + 4.38204i) q^{36} +5.84330i q^{37} +(6.82860 - 4.33831i) q^{38} -12.9123i q^{39} +(6.31986 - 0.243561i) q^{40} -4.55648i q^{41} +(1.40561 + 2.21247i) q^{42} +7.49928i q^{43} +(-1.31088 + 0.473414i) q^{44} +(-8.84330 + 7.39986i) q^{45} +(3.04976 - 1.93756i) q^{46} +(4.14073 - 4.14073i) q^{47} +(7.29940 + 8.78790i) q^{48} -6.57883i q^{49} +(-2.73196 + 6.52199i) q^{50} +(-8.93426 - 8.93426i) q^{51} +(3.84186 - 8.18543i) q^{52} +2.75773 q^{53} +(-8.50239 - 1.89608i) q^{54} +(0.137930 - 1.55214i) q^{55} +(0.232768 + 1.82076i) q^{56} +(-11.5528 + 11.5528i) q^{57} +(-4.11757 - 6.48115i) q^{58} +(3.62521 + 3.62521i) q^{59} +(-12.3499 + 3.25806i) q^{60} +(3.72781 - 3.72781i) q^{61} +(-0.0430787 + 0.193173i) q^{62} +(-2.36642 - 2.36642i) q^{63} +(2.01257 + 7.74271i) q^{64} +(6.48766 + 7.75317i) q^{65} +(2.37576 - 1.50935i) q^{66} +3.32677i q^{67} +(-3.00540 - 8.32192i) q^{68} +(-5.15965 + 5.15965i) q^{69} +(-1.95563 - 0.622235i) q^{70} +1.37056 q^{71} +(-11.5382 - 8.92244i) q^{72} +(2.55028 + 2.55028i) q^{73} +(1.79867 - 8.06556i) q^{74} +(2.51809 - 14.0563i) q^{75} +(-10.7610 + 3.88625i) q^{76} +0.452252 q^{77} +(-3.97461 + 17.8229i) q^{78} +3.86426 q^{79} +(-8.79833 - 1.60917i) q^{80} +2.12204 q^{81} +(-1.40256 + 6.28934i) q^{82} +14.4698 q^{83} +(-1.25915 - 3.48655i) q^{84} +(9.85351 + 0.875628i) q^{85} +(2.30840 - 10.3513i) q^{86} +(10.9650 + 10.9650i) q^{87} +(1.95514 - 0.249948i) q^{88} +3.35011 q^{89} +(14.4843 - 7.49197i) q^{90} +(-2.07470 + 2.07470i) q^{91} +(-4.80602 + 1.73566i) q^{92} -0.399696i q^{93} +(-6.99006 + 4.44089i) q^{94} +(1.13226 - 12.7415i) q^{95} +(-7.37035 - 14.3769i) q^{96} +(-4.95582 - 4.95582i) q^{97} +(-2.02507 + 9.08081i) q^{98} +(-2.54107 + 2.54107i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9}+O(q^{10}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9	\( 18 q + 4 q^{4} + 2 q^{5} - 8 q^{6} + 2 q^{7} - 12 q^{8} + 10 q^{9} - 2 q^{11} - 12 q^{14} - 20 q^{15} - 6 q^{17} - 24 q^{18} - 2 q^{19} - 12 q^{20} - 16 q^{21} + 12 q^{22} - 2 q^{23} - 4 q^{24} - 6 q^{25} - 16 q^{26} - 24 q^{27} + 40 q^{28} + 14 q^{29} + 40 q^{30} + 20 q^{32} - 8 q^{33} + 28 q^{34} + 2 q^{35} - 4 q^{36} + 24 q^{38} + 44 q^{40} + 8 q^{42} - 44 q^{44} - 14 q^{45} + 12 q^{46} + 38 q^{47} + 4 q^{48} - 8 q^{50} + 8 q^{51} + 8 q^{52} + 12 q^{53} + 4 q^{54} - 6 q^{55} + 20 q^{56} - 24 q^{57} + 20 q^{58} + 10 q^{59} + 8 q^{60} + 14 q^{61} - 40 q^{62} - 6 q^{63} + 16 q^{64} + 4 q^{66} - 60 q^{68} - 32 q^{69} - 28 q^{70} + 24 q^{71} - 68 q^{72} - 14 q^{73} - 48 q^{74} + 16 q^{75} - 16 q^{76} - 44 q^{77} - 36 q^{78} - 16 q^{79} - 92 q^{80} + 2 q^{81} + 48 q^{82} + 40 q^{83} + 24 q^{84} + 14 q^{85} - 36 q^{86} + 24 q^{87} - 8 q^{88} + 12 q^{89} - 8 q^{90} - 8 q^{92} - 28 q^{94} + 34 q^{95} - 40 q^{96} + 18 q^{97} - 56 q^{98} + 22 q^{99}+O(q^{100}) \) 18 * q + 4 * q^4 + 2 * q^5 - 8 * q^6 + 2 * q^7 - 12 * q^8 + 10 * q^9 - 2 * q^11 - 12 * q^14 - 20 * q^15 - 6 * q^17 - 24 * q^18 - 2 * q^19 - 12 * q^20 - 16 * q^21 + 12 * q^22 - 2 * q^23 - 4 * q^24 - 6 * q^25 - 16 * q^26 - 24 * q^27 + 40 * q^28 + 14 * q^29 + 40 * q^30 + 20 * q^32 - 8 * q^33 + 28 * q^34 + 2 * q^35 - 4 * q^36 + 24 * q^38 + 44 * q^40 + 8 * q^42 - 44 * q^44 - 14 * q^45 + 12 * q^46 + 38 * q^47 + 4 * q^48 - 8 * q^50 + 8 * q^51 + 8 * q^52 + 12 * q^53 + 4 * q^54 - 6 * q^55 + 20 * q^56 - 24 * q^57 + 20 * q^58 + 10 * q^59 + 8 * q^60 + 14 * q^61 - 40 * q^62 - 6 * q^63 + 16 * q^64 + 4 * q^66 - 60 * q^68 - 32 * q^69 - 28 * q^70 + 24 * q^71 - 68 * q^72 - 14 * q^73 - 48 * q^74 + 16 * q^75 - 16 * q^76 - 44 * q^77 - 36 * q^78 - 16 * q^79 - 92 * q^80 + 2 * q^81 + 48 * q^82 + 40 * q^83 + 24 * q^84 + 14 * q^85 - 36 * q^86 + 24 * q^87 - 8 * q^88 + 12 * q^89 - 8 * q^90 - 8 * q^92 - 28 * q^94 + 34 * q^95 - 40 * q^96 + 18 * q^97 - 56 * q^98 + 22 * q^99

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