LMFDB - Embedded newform 50.3.f.a.33.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [50,3,Mod(3,50)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(50, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([7]))

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

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

chi := DirichletCharacter("50.3");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 50 = 2 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	50.f (of order $20$, degree $8$, 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:	$1.36240132180$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$2$ over $\Q(\zeta_{20})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 30x^{14} + 351x^{12} + 2130x^{10} + 7341x^{8} + 14480x^{6} + 15196x^{4} + 6560x^{2} + 16 $ x^16 + 30x^14 + 351x^12 + 2130x^10 + 7341x^8 + 14480x^6 + 15196x^4 + 6560*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			33.2
Root			$-1.23012i$ of defining polynomial
Character	$\chi$	$=$	50.33
Dual form			50.3.f.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.26007 + 0.642040i) q^{2} +(2.50268 + 0.396386i) q^{3} +(1.17557 + 1.61803i) q^{4} +(-3.83232 - 3.21144i) q^{5} +(2.89907 + 2.10629i) q^{6} +(-1.84619 + 1.84619i) q^{7} +(0.442463 + 2.79360i) q^{8} +(-2.45322 - 0.797099i) q^{9} +O(q^{10})$	\(q+(1.26007 + 0.642040i) q^{2} +(2.50268 + 0.396386i) q^{3} +(1.17557 + 1.61803i) q^{4} +(-3.83232 - 3.21144i) q^{5} +(2.89907 + 2.10629i) q^{6} +(-1.84619 + 1.84619i) q^{7} +(0.442463 + 2.79360i) q^{8} +(-2.45322 - 0.797099i) q^{9} +(-2.76713 - 6.50715i) q^{10} +(0.224918 + 0.692225i) q^{11} +(2.30071 + 4.51540i) q^{12} +(10.9494 - 5.57900i) q^{13} +(-3.51167 + 1.14101i) q^{14} +(-8.31810 - 9.55628i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-20.9271 + 3.31453i) q^{17} +(-2.57947 - 2.57947i) q^{18} +(-4.52135 + 6.22310i) q^{19} +(0.691055 - 9.97609i) q^{20} +(-5.35223 + 3.88862i) q^{21} +(-0.161023 + 1.01666i) q^{22} +(18.0093 - 35.3452i) q^{23} +7.16689i q^{24} +(4.37333 + 24.6145i) q^{25} +17.3790 q^{26} +(-26.1430 - 13.3205i) q^{27} +(-5.15753 - 0.816872i) q^{28} +(28.3088 + 38.9637i) q^{29} +(-4.34591 - 17.3822i) q^{30} +(31.6215 + 22.9744i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(0.288509 + 1.82157i) q^{33} +(-28.4978 - 9.25950i) q^{34} +(13.0041 - 1.14626i) q^{35} +(-1.59420 - 4.90644i) q^{36} +(8.18285 + 16.0598i) q^{37} +(-9.69270 + 4.93868i) q^{38} +(29.6143 - 9.62228i) q^{39} +(7.27583 - 12.1269i) q^{40} +(-2.02980 + 6.24709i) q^{41} +(-9.24086 + 1.46361i) q^{42} +(15.0496 + 15.0496i) q^{43} +(-0.855637 + 1.17768i) q^{44} +(6.84168 + 10.9331i) q^{45} +(45.3860 - 32.9749i) q^{46} +(13.1485 - 83.0166i) q^{47} +(-4.60142 + 9.03080i) q^{48} +42.1832i q^{49} +(-10.2928 + 33.8239i) q^{50} -53.6878 q^{51} +(21.8988 + 11.1580i) q^{52} +(-64.5712 - 10.2271i) q^{53} +(-24.3898 - 33.5696i) q^{54} +(1.36108 - 3.37514i) q^{55} +(-5.97440 - 4.34066i) q^{56} +(-13.7822 + 13.7822i) q^{57} +(10.6549 + 67.2725i) q^{58} +(-74.4974 - 24.2057i) q^{59} +(5.68387 - 24.6931i) q^{60} +(-20.0819 - 61.8056i) q^{61} +(25.0950 + 49.2517i) q^{62} +(6.00071 - 3.05752i) q^{63} +(-7.60845 + 2.47214i) q^{64} +(-59.8783 - 13.7828i) q^{65} +(-0.805979 + 2.48055i) q^{66} +(61.2025 - 9.69353i) q^{67} +(-29.9644 - 29.9644i) q^{68} +(59.0818 - 81.3191i) q^{69} +(17.1221 + 6.90478i) q^{70} +(-43.2855 + 31.4488i) q^{71} +(1.14132 - 7.20601i) q^{72} +(-15.4463 + 30.3151i) q^{73} +25.4902i q^{74} +(1.18821 + 63.3358i) q^{75} -15.3843 q^{76} +(-1.69322 - 0.862739i) q^{77} +(43.4941 + 6.88879i) q^{78} +(-13.7883 - 18.9780i) q^{79} +(16.9540 - 10.6095i) q^{80} +(-41.3660 - 30.0541i) q^{81} +(-6.56858 + 6.56858i) q^{82} +(-8.10529 - 51.1748i) q^{83} +(-12.5839 - 4.08874i) q^{84} +(90.8439 + 54.5039i) q^{85} +(9.30114 + 28.6260i) q^{86} +(55.4032 + 108.735i) q^{87} +(-1.83428 + 0.934615i) q^{88} +(142.975 - 46.4555i) q^{89} +(1.60154 + 18.1691i) q^{90} +(-9.91480 + 30.5146i) q^{91} +(78.3609 - 12.4112i) q^{92} +(70.0319 + 70.0319i) q^{93} +(69.8680 - 96.1651i) q^{94} +(37.3123 - 9.32888i) q^{95} +(-11.5963 + 8.42518i) q^{96} +(9.98239 - 63.0263i) q^{97} +(-27.0833 + 53.1539i) q^{98} -1.87746i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/50\mathbb{Z}\right)^\times$.

$n$	$27$
$\chi(n)$	$e\left(\frac{3}{20}\right)$

Coefficient data

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

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

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

$2$	1.26007	+	0.642040i	0.630037	+	0.321020i
$2$	1.26007	+	0.642040i	0.630037	+	0.321020i
$3$	2.50268	+	0.396386i	0.834227	+	0.132129i	0.558913	−	0.829226i	$-0.311218\pi$
$3$	2.50268	+	0.396386i	0.834227	+	0.132129i	0.275313	+	0.961355i	$0.411218\pi$
$4$	1.17557	+	1.61803i	0.293893	+	0.404508i
$5$	−3.83232	−	3.21144i	−0.766464	−	0.642288i
$5$	−3.83232	−	3.21144i	−0.766464	−	0.642288i
$6$	2.89907	+	2.10629i	0.483178	+	0.351049i
$7$	−1.84619	+	1.84619i	−0.263742	+	0.263742i	−0.826572	−	0.562831i	$-0.809712\pi$
$7$	−1.84619	+	1.84619i	−0.263742	+	0.263742i	0.562831	+	0.826572i	$0.309712\pi$
$8$	0.442463	+	2.79360i	0.0553079	+	0.349201i
$9$	−2.45322	−	0.797099i	−0.272580	−	0.0885666i
$10$	−2.76713	−	6.50715i	−0.276713	−	0.650715i
$11$	0.224918	+	0.692225i	0.0204470	+	0.0629295i	0.960759	−	0.277383i	$-0.0894671\pi$
$11$	0.224918	+	0.692225i	0.0204470	+	0.0629295i	−0.940312	+	0.340313i	$0.889467\pi$
$12$	2.30071	+	4.51540i	0.191726	+	0.376283i
$13$	10.9494	−	5.57900i	0.842262	−	0.429154i	0.0210512	−	0.999778i	$-0.493299\pi$
$13$	10.9494	−	5.57900i	0.842262	−	0.429154i	0.821211	+	0.570624i	$0.193299\pi$
$14$	−3.51167	+	1.14101i	−0.250833	+	0.0815007i
$15$	−8.31810	−	9.55628i	−0.554540	−	0.637085i
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	−20.9271	+	3.31453i	−1.23101	+	0.194973i	−0.737849	−	0.674966i	$-0.764158\pi$
$17$	−20.9271	+	3.31453i	−1.23101	+	0.194973i	−0.493160	+	0.869939i	$0.664158\pi$
$18$	−2.57947	−	2.57947i	−0.143304	−	0.143304i
$19$	−4.52135	+	6.22310i	−0.237966	+	0.327532i	−0.911251	−	0.411851i	$-0.864882\pi$
$19$	−4.52135	+	6.22310i	−0.237966	+	0.327532i	0.673286	+	0.739382i	$0.264882\pi$
$20$	0.691055	−	9.97609i	0.0345528	−	0.498805i
$21$	−5.35223	+	3.88862i	−0.254868	+	0.185173i
$22$	−0.161023	+	1.01666i	−0.00731923	+	0.0462118i
$23$	18.0093	−	35.3452i	0.783012	−	1.53675i	−0.0595970	−	0.998223i	$-0.518982\pi$
$23$	18.0093	−	35.3452i	0.783012	−	1.53675i	0.842609	−	0.538525i	$-0.181018\pi$
$24$			7.16689i			0.298620i
$25$	4.37333	+	24.6145i	0.174933	+	0.984580i
$26$	17.3790			0.668423
$27$	−26.1430	−	13.3205i	−0.968258	−	0.493352i
$28$	−5.15753	−	0.816872i	−0.184197	−	0.0291740i
$29$	28.3088	+	38.9637i	0.976165	+	1.34358i	0.938870	+	0.344272i	$0.111874\pi$
$29$	28.3088	+	38.9637i	0.976165	+	1.34358i	0.0372955	+	0.999304i	$0.488126\pi$
$30$	−4.34591	−	17.3822i	−0.144864	−	0.579406i
$31$	31.6215	+	22.9744i	1.02005	+	0.741110i	0.966293	−	0.257445i	$-0.0828805\pi$
$31$	31.6215	+	22.9744i	1.02005	+	0.741110i	0.0537567	+	0.998554i	$0.482880\pi$
$32$	−4.00000	+	4.00000i	−0.125000	+	0.125000i
$33$	0.288509	+	1.82157i	0.00874269	+	0.0551992i
$34$	−28.4978	−	9.25950i	−0.838171	−	0.272338i
$35$	13.0041	−	1.14626i	0.371546	−	0.0327504i
$36$	−1.59420	−	4.90644i	−0.0442833	−	0.136290i
$37$	8.18285	+	16.0598i	0.221158	+	0.434047i	0.974751	−	0.223294i	$-0.0716810\pi$
$37$	8.18285	+	16.0598i	0.221158	+	0.434047i	−0.753593	+	0.657341i	$0.771681\pi$
$38$	−9.69270	+	4.93868i	−0.255071	+	0.129965i
$39$	29.6143	−	9.62228i	0.759342	−	0.246725i
$40$	7.27583	−	12.1269i	0.181896	−	0.303173i
$41$	−2.02980	+	6.24709i	−0.0495074	+	0.152368i	−0.972754	−	0.231840i	$-0.925525\pi$
$41$	−2.02980	+	6.24709i	−0.0495074	+	0.152368i	0.923247	+	0.384208i	$0.125525\pi$
$42$	−9.24086	+	1.46361i	−0.220020	+	0.0348478i
$43$	15.0496	+	15.0496i	0.349990	+	0.349990i	0.860106	−	0.510116i	$-0.170397\pi$
$43$	15.0496	+	15.0496i	0.349990	+	0.349990i	−0.510116	+	0.860106i	$0.670397\pi$
$44$	−0.855637	+	1.17768i	−0.0194463	+	0.0267655i
$45$	6.84168	+	10.9331i	0.152037	+	0.242958i
$46$	45.3860	−	32.9749i	0.986653	−	0.716845i
$47$	13.1485	−	83.0166i	0.279756	−	1.76631i	−0.302350	−	0.953197i	$-0.597771\pi$
$47$	13.1485	−	83.0166i	0.279756	−	1.76631i	0.582106	−	0.813113i	$-0.302229\pi$
$48$	−4.60142	+	9.03080i	−0.0958630	+	0.188142i
$49$			42.1832i			0.860881i
$50$	−10.2928	+	33.8239i	−0.205855	+	0.676479i
$51$	−53.6878			−1.05270
$52$	21.8988	+	11.1580i	0.421131	+	0.214577i
$53$	−64.5712	−	10.2271i	−1.21832	−	0.192964i	−0.486024	−	0.873945i	$-0.661553\pi$
$53$	−64.5712	−	10.2271i	−1.21832	−	0.192964i	−0.732300	+	0.680982i	$0.761553\pi$
$54$	−24.3898	−	33.5696i	−0.451663	−	0.621660i
$55$	1.36108	−	3.37514i	0.0247469	−	0.0613661i
$56$	−5.97440	−	4.34066i	−0.106686	−	0.0775117i
$57$	−13.7822	+	13.7822i	−0.241794	+	0.241794i
$58$	10.6549	+	67.2725i	0.183706	+	1.15987i
$59$	−74.4974	−	24.2057i	−1.26267	−	0.410266i	−0.400224	−	0.916417i	$-0.631068\pi$
$59$	−74.4974	−	24.2057i	−1.26267	−	0.410266i	−0.862445	+	0.506151i	$0.831068\pi$
$60$	5.68387	−	24.6931i	0.0947312	−	0.411551i
$61$	−20.0819	−	61.8056i	−0.329211	−	1.01321i	−0.969504	−	0.245076i	$-0.921187\pi$
$61$	−20.0819	−	61.8056i	−0.329211	−	1.01321i	0.640293	−	0.768131i	$-0.278813\pi$
$62$	25.0950	+	49.2517i	0.404758	+	0.794382i
$63$	6.00071	−	3.05752i	0.0952494	−	0.0485320i
$64$	−7.60845	+	2.47214i	−0.118882	+	0.0386271i
$65$	−59.8783	−	13.7828i	−0.921204	−	0.212044i
$66$	−0.805979	+	2.48055i	−0.0122118	+	0.0375841i
$67$	61.2025	−	9.69353i	0.913470	−	0.144679i	0.318032	−	0.948080i	$-0.396978\pi$
$67$	61.2025	−	9.69353i	0.913470	−	0.144679i	0.595439	+	0.803401i	$0.296978\pi$
$68$	−29.9644	−	29.9644i	−0.440652	−	0.440652i
$69$	59.0818	−	81.3191i	0.856258	−	1.17854i
$70$	17.1221	+	6.90478i	0.244601	+	0.0986398i
$71$	−43.2855	+	31.4488i	−0.609656	+	0.442941i	−0.849293	−	0.527922i	$-0.822971\pi$
$71$	−43.2855	+	31.4488i	−0.609656	+	0.442941i	0.239637	+	0.970862i	$0.422971\pi$
$72$	1.14132	−	7.20601i	0.0158517	−	0.100084i
$73$	−15.4463	+	30.3151i	−0.211594	+	0.415276i	−0.972272	−	0.233853i	$-0.924866\pi$
$73$	−15.4463	+	30.3151i	−0.211594	+	0.415276i	0.760678	+	0.649129i	$0.224866\pi$
$74$			25.4902i			0.344462i
$75$	1.18821	+	63.3358i	0.0158429	+	0.844477i
$76$	−15.3843			−0.202426
$77$	−1.69322	−	0.862739i	−0.0219899	−	0.0112044i
$78$	43.4941	+	6.88879i	0.557617	+	0.0883178i
$79$	−13.7883	−	18.9780i	−0.174536	−	0.240228i	0.712783	−	0.701385i	$-0.247435\pi$
$79$	−13.7883	−	18.9780i	−0.174536	−	0.240228i	−0.887319	+	0.461157i	$0.847435\pi$
$80$	16.9540	−	10.6095i	0.211926	−	0.132618i
$81$	−41.3660	−	30.0541i	−0.510691	−	0.371039i
$82$	−6.56858	+	6.56858i	−0.0801046	+	0.0801046i
$83$	−8.10529	−	51.1748i	−0.0976541	−	0.616564i	−0.987172	−	0.159663i	$-0.948959\pi$
$83$	−8.10529	−	51.1748i	−0.0976541	−	0.616564i	0.889517	−	0.456901i	$-0.151041\pi$
$84$	−12.5839	−	4.08874i	−0.149808	−	0.0486755i
$85$	90.8439	+	54.5039i	1.06875	+	0.641222i
$86$	9.30114	+	28.6260i	0.108153	+	0.332860i
$87$	55.4032	+	108.735i	0.636819	+	1.24983i
$88$	−1.83428	+	0.934615i	−0.0208441	+	0.0106206i
$89$	142.975	−	46.4555i	1.60646	−	0.521972i	0.637770	−	0.770227i	$-0.279857\pi$
$89$	142.975	−	46.4555i	1.60646	−	0.521972i	0.968695	+	0.248255i	$0.0798570\pi$
$90$	1.60154	+	18.1691i	0.0177949	+	0.201879i
$91$	−9.91480	+	30.5146i	−0.108954	+	0.335326i
$92$	78.3609	−	12.4112i	0.851749	−	0.134904i
$93$	70.0319	+	70.0319i	0.753031	+	0.753031i
$94$	69.8680	−	96.1651i	0.743277	−	1.02303i
$95$	37.3123	−	9.32888i	0.392761	−	0.0981987i
$96$	−11.5963	+	8.42518i	−0.120794	+	0.0877623i
$97$	9.98239	−	63.0263i	0.102911	−	0.649756i	−0.881273	−	0.472608i	$-0.843313\pi$
$97$	9.98239	−	63.0263i	0.102911	−	0.649756i	0.984184	−	0.177148i	$-0.0566873\pi$
$98$	−27.0833	+	53.1539i	−0.276360	+	0.542386i
$99$		−	1.87746i		−	0.0189643i
$100$	−34.6859	+	36.0123i	−0.346859	+	0.360123i
$101$	−60.0228			−0.594285			−0.297142	−	0.954833i	$-0.596034\pi$
$101$	−60.0228			−0.594285			−0.297142	+	0.954833i	$0.596034\pi$
$102$	−67.6506	−	34.4697i	−0.663241	−	0.337938i
$103$	36.9917	+	5.85890i	0.359142	+	0.0568825i	0.333398	−	0.942786i	$-0.391805\pi$
$103$	36.9917	+	5.85890i	0.359142	+	0.0568825i	0.0257438	+	0.999669i	$0.491805\pi$
$104$	20.4302	+	28.1198i	0.196445	+	0.270383i
$105$	32.9995	+	2.28591i	0.314281	+	0.0217706i
$106$	−74.7983	−	54.3441i	−0.705644	−	0.512681i
$107$	−9.46731	+	9.46731i	−0.0884795	+	0.0884795i	−0.749961	−	0.661482i	$-0.769928\pi$
$107$	−9.46731	+	9.46731i	−0.0884795	+	0.0884795i	0.661482	+	0.749961i	$0.269928\pi$
$108$	−9.17987	−	57.9594i	−0.0849988	−	0.536661i
$109$	−159.887	−	51.9505i	−1.46685	−	0.476610i	−0.536698	−	0.843774i	$-0.680329\pi$
$109$	−159.887	−	51.9505i	−1.46685	−	0.476610i	−0.930156	+	0.367164i	$0.880329\pi$
$110$	3.88203	−	3.37905i	0.0352912	−	0.0307186i
$111$	14.1132	+	43.4360i	0.127146	+	0.391315i
$112$	−4.74131	−	9.30535i	−0.0423331	−	0.0830835i
$113$	−107.749	+	54.9006i	−0.953527	+	0.485846i	−0.860294	−	0.509798i	$-0.829720\pi$
$113$	−107.749	+	54.9006i	−0.953527	+	0.485846i	−0.0932331	+	0.995644i	$0.529720\pi$
$114$	−26.2154	+	8.51789i	−0.229959	+	0.0747183i
$115$	−182.526	+	77.6184i	−1.58718	+	0.674943i
$116$	−29.7656	+	91.6092i	−0.256600	+	0.789734i
$117$	−31.3083	+	4.95875i	−0.267593	+	0.0423825i
$118$	−78.3313	−	78.3313i	−0.663824	−	0.663824i
$119$	32.5163	−	44.7548i	0.273246	−	0.376091i
$120$	23.0160	−	27.4658i	0.191800	−	0.228882i
$121$	97.4625	−	70.8106i	0.805475	−	0.585212i
$122$	14.3770	−	90.7730i	0.117844	−	0.744041i
$123$	−7.55620	+	14.8299i	−0.0614326	+	0.120568i
$124$			78.1728i			0.630425i
$125$	62.2880	−	108.375i	0.498304	−	0.867003i
$126$	9.52438			0.0755904
$127$	−20.8642	−	10.6308i	−0.164285	−	0.0837074i	0.369915	−	0.929066i	$-0.379387\pi$
$127$	−20.8642	−	10.6308i	−0.164285	−	0.0837074i	−0.534200	+	0.845358i	$0.679387\pi$
$128$	−11.1744	−	1.76985i	−0.0873001	−	0.0138270i
$129$	31.6988	+	43.6297i	0.245727	+	0.338215i
$130$	−66.6019	−	55.8116i	−0.512322	−	0.429320i
$131$	87.8890	+	63.8551i	0.670908	+	0.487443i	0.870329	−	0.492471i	$-0.163906\pi$
$131$	87.8890	+	63.8551i	0.670908	+	0.487443i	−0.199421	+	0.979914i	$0.563906\pi$
$132$	−2.60820	+	2.60820i	−0.0197591	+	0.0197591i
$133$	−3.14176	−	19.8363i	−0.0236223	−	0.149145i
$134$	83.3433	+	27.0799i	0.621965	+	0.202089i
$135$	57.4102	+	135.005i	0.425261	+	1.00004i
$136$	−18.5190	−	56.9956i	−0.136169	−	0.419085i
$137$	−7.27525	−	14.2785i	−0.0531040	−	0.104223i	0.862929	−	0.505325i	$-0.168627\pi$
$137$	−7.27525	−	14.2785i	−0.0531040	−	0.104223i	−0.916033	+	0.401102i	$0.868627\pi$
$138$	126.658	−	64.5352i	0.917808	−	0.467647i
$139$	−190.092	+	61.7647i	−1.36757	+	0.444350i	−0.898563	−	0.438844i	$-0.855388\pi$
$139$	−190.092	+	61.7647i	−1.36757	+	0.444350i	−0.469007	+	0.883195i	$0.655388\pi$
$140$	17.1420	+	19.6936i	0.122443	+	0.140669i
$141$	65.8132	−	202.552i	0.466760	−	1.43654i
$142$	−74.7343	+	11.8368i	−0.526298	+	0.0833574i
$143$	6.32464	+	6.32464i	0.0442283	+	0.0442283i
$144$	6.06469	−	8.34733i	0.0421159	−	0.0579676i
$145$	16.6412	−	240.233i	0.114767	−	1.65678i
$146$	−38.9270	+	28.2821i	−0.266623	+	0.193713i
$147$	−16.7208	+	105.571i	−0.113747	+	0.718170i
$148$	−16.3657	+	32.1195i	−0.110579	+	0.217024i
$149$			278.483i			1.86902i	0.355942	+	0.934508i	$0.384160\pi$
$149$			278.483i			1.86902i	−0.355942	+	0.934508i	$0.615840\pi$
$150$	−39.1668	+	80.5706i	−0.261112	+	0.537137i
$151$	216.796			1.43574			0.717869	−	0.696178i	$-0.245118\pi$
$151$	216.796			1.43574			0.717869	+	0.696178i	$0.245118\pi$
$152$	−19.3854	−	9.87736i	−0.127536	−	0.0649826i
$153$	53.9809	+	8.54973i	0.352816	+	0.0558806i
$154$	−1.57967	−	2.17423i	−0.0102576	−	0.0141184i
$155$	−47.4030	−	189.596i	−0.305826	−	1.22320i
$156$	50.3829	+	36.6053i	0.322967	+	0.234649i
$157$	−113.262	+	113.262i	−0.721414	+	0.721414i	−0.968893	−	0.247479i	$-0.920398\pi$
$157$	−113.262	+	113.262i	−0.721414	+	0.721414i	0.247479	+	0.968893i	$0.420398\pi$
$158$	−5.18968	−	32.7663i	−0.0328461	−	0.207382i
$159$	−157.547	−	51.1902i	−0.990863	−	0.321951i
$160$	28.1750	−	2.48352i	0.176094	−	0.0155220i
$161$	32.0054	+	98.5026i	0.198792	+	0.611817i
$162$	−32.8282	−	64.4290i	−0.202643	−	0.397710i
$163$	−47.7817	+	24.3460i	−0.293139	+	0.149362i	−0.594376	−	0.804188i	$-0.702601\pi$
$163$	−47.7817	+	24.3460i	−0.293139	+	0.149362i	0.301236	+	0.953550i	$0.402601\pi$
$164$	−12.4942	+	4.05960i	−0.0761840	+	0.0247537i
$165$	4.74421	−	7.90737i	0.0287528	−	0.0479235i
$166$	22.6430	−	69.6879i	0.136404	−	0.419807i
$167$	261.151	−	41.3623i	1.56378	−	0.247678i	0.686309	−	0.727310i	$-0.259230\pi$
$167$	261.151	−	41.3623i	1.56378	−	0.247678i	0.877470	+	0.479632i	$0.159230\pi$
$168$	−13.2314	−	13.2314i	−0.0787586	−	0.0787586i
$169$	−10.5714	+	14.5502i	−0.0625525	+	0.0860961i
$170$	79.4764	+	127.004i	0.467508	+	0.747084i
$171$	16.0523	−	11.6627i	0.0938730	−	0.0682027i
$172$	−6.65888	+	42.0425i	−0.0387144	+	0.244433i
$173$	18.7438	−	36.7868i	0.108346	−	0.212641i	−0.830467	−	0.557067i	$-0.811927\pi$
$173$	18.7438	−	36.7868i	0.108346	−	0.212641i	0.938813	+	0.344426i	$0.111927\pi$
$174$			172.585i			0.991868i
$175$	−53.5171	−	37.3691i	−0.305812	−	0.213538i
$176$	−2.91139			−0.0165420
$177$	−176.849	−	90.1088i	−0.999144	−	0.509089i
$178$	209.986	+	33.2585i	1.17970	+	0.186845i
$179$	84.9216	+	116.885i	0.474422	+	0.652986i	0.977421	−	0.211301i	$-0.0677700\pi$
$179$	84.9216	+	116.885i	0.474422	+	0.652986i	−0.502999	+	0.864287i	$0.667770\pi$
$180$	−9.64725	+	23.9227i	−0.0535958	+	0.132904i
$181$	−35.1000	−	25.5016i	−0.193923	−	0.140893i	0.486587	−	0.873632i	$-0.338242\pi$
$181$	−35.1000	−	25.5016i	−0.193923	−	0.140893i	−0.680510	+	0.732739i	$0.738242\pi$
$182$	−32.0850	+	32.0850i	−0.176291	+	0.176291i
$183$	−25.7596	−	162.640i	−0.140763	−	0.888742i
$184$	106.709	+	34.6718i	0.579940	+	0.188434i
$185$	20.2156	−	87.8248i	0.109274	−	0.474729i
$186$	43.2821	+	133.209i	0.232699	+	0.716175i
$187$	−7.00128	−	13.7408i	−0.0374400	−	0.0734802i
$188$	149.781	−	76.3171i	0.796706	−	0.405942i
$189$	72.8572	−	23.6727i	0.385488	−	0.125253i
$190$	53.0058	+	12.2009i	0.278978	+	0.0642154i
$191$	−48.7314	+	149.980i	−0.255138	+	0.785235i	0.738664	+	0.674074i	$0.235457\pi$
$191$	−48.7314	+	149.980i	−0.255138	+	0.785235i	−0.993802	+	0.111161i	$0.964543\pi$
$192$	−20.0214	+	3.17109i	−0.104278	+	0.0165161i
$193$	76.0787	+	76.0787i	0.394190	+	0.394190i	0.876178	−	0.481988i	$-0.160085\pi$
$193$	76.0787	+	76.0787i	0.394190	+	0.394190i	−0.481988	+	0.876178i	$0.660085\pi$
$194$	53.0440	−	73.0087i	0.273422	−	0.376334i
$195$	−144.393	−	58.2289i	−0.740476	−	0.298610i
$196$	−68.2538	+	49.5893i	−0.348234	+	0.253006i
$197$	−5.96711	+	37.6748i	−0.0302899	+	0.191243i	−0.998194	−	0.0600782i	$-0.980865\pi$
$197$	−5.96711	+	37.6748i	−0.0302899	+	0.191243i	0.967904	+	0.251321i	$0.0808650\pi$
$198$	1.20540	−	2.36574i	0.00608790	−	0.0119482i
$199$		−	201.504i		−	1.01259i	−0.862362	−	0.506293i	$-0.831016\pi$
$199$		−	201.504i		−	1.01259i	0.862362	−	0.506293i	$-0.168984\pi$
$200$	−66.8282	+	23.1084i	−0.334141	+	0.115542i
$201$	157.013			0.781158
$202$	−75.6331	−	38.5370i	−0.374421	−	0.190777i
$203$	−124.198	−	19.6710i	−0.611813	−	0.0969016i
$204$	−63.1138	−	86.8687i	−0.309381	−	0.425827i
$205$	27.8410	−	17.4223i	0.135810	−	0.0849866i
$206$	42.8506	+	31.1328i	0.208012	+	0.151130i
$207$	−72.3544	+	72.3544i	−0.349538	+	0.349538i
$208$	7.68958	+	48.5501i	0.0369691	+	0.233414i
$209$	−5.32471	−	1.73010i	−0.0254771	−	0.00827801i
$210$	40.1142	+	24.0674i	0.191020	+	0.114607i
$211$	6.78952	+	20.8960i	0.0321778	+	0.0990332i	0.965856	−	0.259081i	$-0.0834198\pi$
$211$	6.78952	+	20.8960i	0.0321778	+	0.0990332i	−0.933678	+	0.358114i	$0.883420\pi$
$212$	−59.3603	−	116.501i	−0.280001	−	0.549533i
$213$	−120.796	+	61.5485i	−0.567116	+	0.288960i
$214$	−18.0079	+	5.85112i	−0.0841490	+	0.0273417i
$215$	−9.34398	−	106.005i	−0.0434604	−	0.493049i
$216$	25.6449	−	78.9270i	0.118727	−	0.365403i
$217$	−100.795	+	15.9643i	−0.464491	+	0.0735682i
$218$	−168.115	−	168.115i	−0.771171	−	0.771171i
$219$	−50.6737	+	69.7464i	−0.231387	+	0.318477i
$220$	7.06113	−	1.76543i	0.0320961	−	0.00802469i
$221$	−210.648	+	153.045i	−0.953159	+	0.692510i
$222$	−10.1039	+	63.7938i	−0.0455133	+	0.287359i
$223$	190.231	−	373.349i	0.853053	−	1.67421i	0.121328	−	0.992613i	$-0.461285\pi$
$223$	190.231	−	373.349i	0.853053	−	1.67421i	0.731726	−	0.681599i	$-0.238715\pi$
$224$		−	14.7695i		−	0.0659354i
$225$	8.89147	−	63.8708i	0.0395176	−	0.283870i
$226$	−171.020			−0.756724
$227$	98.4029	+	50.1388i	0.433493	+	0.220876i	0.657100	−	0.753804i	$-0.271783\pi$
$227$	98.4029	+	50.1388i	0.433493	+	0.220876i	−0.223607	+	0.974679i	$0.571783\pi$
$228$	−38.5021	−	6.09813i	−0.168869	−	0.0267462i
$229$	−7.87652	−	10.8411i	−0.0343953	−	0.0473410i	0.791473	−	0.611204i	$-0.209315\pi$
$229$	−7.87652	−	10.8411i	−0.0343953	−	0.0473410i	−0.825868	+	0.563863i	$0.809315\pi$
$230$	−279.831	−	19.3842i	−1.21665	−	0.0842790i
$231$	−3.89561	−	2.83033i	−0.0168641	−	0.0122525i
$232$	−96.3236	+	96.3236i	−0.415188	+	0.415188i
$233$	47.5283	+	300.082i	0.203984	+	1.28790i	0.850894	+	0.525338i	$0.176061\pi$
$233$	47.5283	+	300.082i	0.203984	+	1.28790i	−0.646909	+	0.762567i	$0.723939\pi$
$234$	−42.6345	−	13.8528i	−0.182199	−	0.0592000i
$235$	−316.992	+	275.920i	−1.34890	+	1.17413i
$236$	−48.4114	−	148.995i	−0.205133	−	0.631334i
$237$	−26.9852	−	52.9614i	−0.113862	−	0.223466i
$238$	69.7072	−	35.5176i	0.292887	−	0.149234i
$239$	272.615	−	88.5779i	1.14065	−	0.370619i	0.323035	−	0.946387i	$-0.395297\pi$
$239$	272.615	−	88.5779i	1.14065	−	0.370619i	0.817613	+	0.575768i	$0.195297\pi$
$240$	46.6360	−	19.8317i	0.194317	−	0.0826322i
$241$	−18.3766	+	56.5573i	−0.0762514	+	0.234678i	−0.981916	−	0.189317i	$-0.939373\pi$
$241$	−18.3766	+	56.5573i	−0.0762514	+	0.234678i	0.905665	+	0.423995i	$0.139373\pi$
$242$	168.273	−	26.6518i	0.695343	−	0.110132i
$243$	95.1119	+	95.1119i	0.391407	+	0.391407i
$244$	76.3959	−	105.150i	0.313098	−	0.430943i
$245$	135.469	−	161.659i	0.552933	−	0.659834i
$246$	−19.0427	+	13.8354i	−0.0774095	+	0.0562413i
$247$	−14.7874	+	93.3639i	−0.0598680	+	0.377991i
$248$	−50.1900	+	98.5034i	−0.202379	+	0.397191i
$249$		−	131.287i		−	0.527257i
$250$	148.069	−	96.5695i	0.592275	−	0.386278i
$251$	−130.804			−0.521132			−0.260566	−	0.965456i	$-0.583909\pi$
$251$	−130.804			−0.521132			−0.260566	+	0.965456i	$0.583909\pi$
$252$	12.0014	+	6.11503i	0.0476247	+	0.0242660i
$253$	28.5174	+	4.51672i	0.112717	+	0.0178526i
$254$	−19.4650	−	26.7913i	−0.0766339	−	0.105477i
$255$	205.749	+	172.415i	0.806858	+	0.676137i
$256$	−12.9443	−	9.40456i	−0.0505636	−	0.0367366i
$257$	64.9358	−	64.9358i	0.252668	−	0.252668i	−0.569395	−	0.822064i	$-0.692823\pi$
$257$	64.9358	−	64.9358i	0.252668	−	0.252668i	0.822064	+	0.569395i	$0.192823\pi$
$258$	11.9309	+	75.3285i	0.0462437	+	0.291971i
$259$	−44.7565	−	14.5423i	−0.172805	−	0.0561477i
$260$	−48.0900	−	113.088i	−0.184962	−	0.434953i
$261$	−38.3897	−	118.151i	−0.147087	−	0.452688i
$262$	69.7491	+	136.890i	0.266218	+	0.522482i
$263$	−139.472	+	71.0644i	−0.530311	+	0.270207i	−0.698577	−	0.715535i	$-0.746183\pi$
$263$	−139.472	+	71.0644i	−0.530311	+	0.270207i	0.168266	+	0.985742i	$0.446183\pi$
$264$	−4.96110	+	1.61196i	−0.0187920	+	0.00610590i
$265$	214.614	+	246.560i	0.809864	+	0.930415i
$266$	8.77684	−	27.0123i	0.0329956	−	0.101550i
$267$	376.236	−	59.5899i	1.40912	−	0.223183i
$268$	87.6323	+	87.6323i	0.326986	+	0.326986i
$269$	−194.659	+	267.925i	−0.723640	+	0.996005i	0.275755	+	0.961228i	$0.411072\pi$
$269$	−194.659	+	267.925i	−0.723640	+	0.996005i	−0.999395	+	0.0347774i	$0.988928\pi$
$270$	−14.3374	+	206.976i	−0.0531017	+	0.766577i
$271$	151.790	−	110.282i	0.560111	−	0.406945i	−0.271388	−	0.962470i	$-0.587483\pi$
$271$	151.790	−	110.282i	0.560111	−	0.406945i	0.831500	+	0.555525i	$0.187483\pi$
$272$	13.2581	−	83.7086i	0.0487431	−	0.307752i
$273$	−36.9091	+	72.4383i	−0.135198	+	0.265342i
$274$		−	22.6629i		−	0.0827114i
$275$	−16.0551	+	8.56356i	−0.0583823	+	0.0311402i
$276$	201.032			0.728377
$277$	250.094	+	127.429i	0.902865	+	0.460033i	0.842840	−	0.538164i	$-0.180882\pi$
$277$	250.094	+	127.429i	0.902865	+	0.460033i	0.0600250	+	0.998197i	$0.480882\pi$
$278$	−279.186	−	44.2186i	−1.00426	−	0.159060i
$279$	−59.2617	−	81.5668i	−0.212408	−	0.292354i
$280$	8.95606	+	35.8212i	0.0319859	+	0.127933i
$281$	−253.823	−	184.413i	−0.903284	−	0.656274i	0.0360233	−	0.999351i	$-0.488531\pi$
$281$	−253.823	−	184.413i	−0.903284	−	0.656274i	−0.939307	+	0.343077i	$0.888531\pi$
$282$	212.976	−	212.976i	0.755234	−	0.755234i
$283$	14.7828	+	93.3349i	0.0522360	+	0.329805i	0.999943	+	0.0106639i	$0.00339450\pi$
$283$	14.7828	+	93.3349i	0.0522360	+	0.329805i	−0.947707	+	0.319141i	$0.896606\pi$
$284$	−101.770	−	33.0672i	−0.358347	−	0.116434i
$285$	97.0787	−	8.55712i	0.340627	−	0.0300250i
$286$	3.90884	+	12.0302i	0.0136673	+	0.0420636i
$287$	−7.78592	−	15.2807i	−0.0271286	−	0.0532430i
$288$	13.0013	−	6.62448i	0.0451433	−	0.0230017i
$289$	152.104	−	49.4215i	0.526311	−	0.171009i
$290$	175.208	−	292.027i	0.604167	−	1.00699i
$291$	49.9655	−	153.778i	0.171703	−	0.528447i
$292$	−67.2092	+	10.6449i	−0.230168	+	0.0364551i
$293$	100.122	+	100.122i	0.341714	+	0.341714i	0.857012	−	0.515297i	$-0.172318\pi$
$293$	100.122	+	100.122i	0.341714	+	0.341714i	−0.515297	+	0.857012i	$0.672318\pi$
$294$	−88.8502	+	122.292i	−0.302211	+	0.415958i
$295$	207.763	+	332.008i	0.704281	+	1.12545i
$296$	−41.2440	+	29.9655i	−0.139338	+	0.101235i
$297$	3.34078	−	21.0928i	0.0112484	−	0.0710196i
$298$	−178.797	+	350.910i	−0.599991	+	1.17755i
$299$		−	487.483i		−	1.63038i
$300$	−101.083	+	76.3782i	−0.336942	+	0.254594i
$301$	−55.5688			−0.184614
$302$	273.179	+	139.192i	0.904568	+	0.460900i
$303$	−150.218	−	23.7922i	−0.495768	−	0.0785220i
$304$	−18.0854	−	24.8924i	−0.0594914	−	0.0818829i
$305$	−121.525	+	301.350i	−0.398442	+	0.988034i
$306$	62.5306	+	45.4312i	0.204348	+	0.148468i
$307$	268.414	−	268.414i	0.874313	−	0.874313i	−0.118626	−	0.992939i	$-0.537849\pi$
$307$	268.414	−	268.414i	0.874313	−	0.874313i	0.992939	+	0.118626i	$0.0378490\pi$
$308$	−0.594559	−	3.75390i	−0.00193039	−	0.0121880i
$309$	90.2559	+	29.3259i	0.292090	+	0.0949059i
$310$	61.9968	−	269.339i	0.199990	−	0.868836i
$311$	−24.7131	−	76.0590i	−0.0794632	−	0.244563i	0.903431	−	0.428733i	$-0.141040\pi$
$311$	−24.7131	−	76.0590i	−0.0794632	−	0.244563i	−0.982894	+	0.184171i	$0.941040\pi$
$312$	39.9841	+	78.4732i	0.128154	+	0.251517i
$313$	−148.268	+	75.5464i	−0.473700	+	0.241362i	−0.674507	−	0.738269i	$-0.735644\pi$
$313$	−148.268	+	75.5464i	−0.473700	+	0.241362i	0.200807	+	0.979631i	$0.435644\pi$
$314$	−215.437	+	69.9998i	−0.686106	+	0.222929i
$315$	−32.8157	−	7.55354i	−0.104177	−	0.0239795i
$316$	14.4979	−	44.6200i	0.0458795	−	0.141202i
$317$	−476.155	+	75.4156i	−1.50207	+	0.237904i	−0.852632	−	0.522513i	$-0.824995\pi$
$317$	−476.155	+	75.4156i	−1.50207	+	0.237904i	−0.649436	+	0.760417i	$0.724995\pi$
$318$	−165.655	−	165.655i	−0.520928	−	0.520928i
$319$	−20.6045	+	28.3597i	−0.0645909	+	0.0889018i
$320$	37.0971	+	14.9601i	0.115929	+	0.0467502i
$321$	−27.4463	+	19.9409i	−0.0855026	+	0.0621213i
$322$	−22.9134	+	144.669i	−0.0711595	+	0.449284i
$323$	73.9922	−	145.218i	0.229078	−	0.449591i
$324$		−	102.262i		−	0.315624i
$325$	185.210	+	245.116i	0.569876	+	0.754202i
$326$	−75.8395			−0.232637
$327$	−379.554	−	193.392i	−1.16072	−	0.591414i
$328$	−18.3500	−	2.90636i	−0.0559452	−	0.00886084i
$329$	128.990	+	177.539i	0.392066	+	0.539633i
$330$	11.0549	−	6.91790i	0.0334997	−	0.0209633i
$331$	−219.259	−	159.301i	−0.662413	−	0.481271i	0.205064	−	0.978749i	$-0.434260\pi$
$331$	−219.259	−	159.301i	−0.662413	−	0.481271i	−0.867477	+	0.497477i	$0.834260\pi$
$332$	73.2742	−	73.2742i	0.220706	−	0.220706i
$333$	−7.27312	−	45.9206i	−0.0218412	−	0.137900i
$334$	355.626	+	115.550i	1.06475	+	0.345957i
$335$	−265.678	−	159.399i	−0.793068	−	0.475819i
$336$	−8.17748	−	25.1677i	−0.0243377	−	0.0749039i
$337$	−180.144	−	353.552i	−0.534551	−	1.04912i	−0.987506	−	0.157582i	$-0.949630\pi$
$337$	−180.144	−	353.552i	−0.534551	−	1.04912i	0.452955	−	0.891533i	$-0.350370\pi$
$338$	−22.6625	+	11.5471i	−0.0670489	+	0.0341631i
$339$	−291.422	+	94.6888i	−0.859652	+	0.279318i
$340$	18.6043	+	211.062i	0.0547185	+	0.620770i
$341$	−8.79121	+	27.0566i	−0.0257807	+	0.0793448i
$342$	27.7150	−	4.38962i	0.0810379	−	0.0128351i
$343$	−168.342	−	168.342i	−0.490792	−	0.490792i
$344$	−35.3837	+	48.7014i	−0.102859	+	0.141574i
$345$	−487.572	+	121.903i	−1.41325	+	0.353343i
$346$	47.2372	−	34.3198i	0.136524	−	0.0991903i
$347$	18.6937	−	118.028i	0.0538724	−	0.340137i	−0.946000	−	0.324167i	$-0.894916\pi$
$347$	18.6937	−	118.028i	0.0538724	−	0.340137i	0.999872	−	0.0159706i	$-0.00508382\pi$
$348$	−110.806	+	217.470i	−0.318409	+	0.624913i
$349$		−	282.531i		−	0.809544i	−0.914418	−	0.404772i	$-0.867351\pi$
$349$		−	282.531i		−	0.809544i	0.914418	−	0.404772i	$-0.132649\pi$
$350$	−43.4431	−	81.4479i	−0.124123	−	0.232708i
$351$	−360.565			−1.02725
$352$	−3.66857	−	1.86923i	−0.0104221	−	0.00531031i
$353$	−401.912	−	63.6566i	−1.13856	−	0.180330i	−0.441445	−	0.897288i	$-0.645534\pi$
$353$	−401.912	−	63.6566i	−1.13856	−	0.180330i	−0.697116	+	0.716958i	$0.745534\pi$
$354$	−164.989	−	227.087i	−0.466070	−	0.641490i
$355$	266.880	+	18.4871i	0.751774	+	0.0520762i
$356$	243.244	+	176.727i	0.683270	+	0.496425i
$357$	99.1180	−	99.1180i	0.277641	−	0.277641i
$358$	31.9630	+	201.806i	0.0892820	+	0.563704i
$359$	539.418	+	175.268i	1.50256	+	0.488210i	0.940763	−	0.339066i	$-0.110111\pi$
$359$	539.418	+	175.268i	1.50256	+	0.488210i	0.561795	+	0.827277i	$0.310111\pi$
$360$	−27.5156	+	23.9505i	−0.0764321	+	0.0665291i
$361$	93.2707	+	287.058i	0.258368	+	0.795174i
$362$	−27.8555	−	54.6695i	−0.0769489	−	0.151021i
$363$	271.986	−	138.584i	0.749272	−	0.381773i
$364$	−61.0293	+	19.8296i	−0.167663	+	0.0544769i
$365$	156.550	−	66.5723i	0.428905	−	0.182390i
$366$	71.9622	−	221.477i	0.196618	−	0.605128i
$367$	−396.398	+	62.7832i	−1.08010	+	0.171071i	−0.671030	−	0.741430i	$-0.734148\pi$
$367$	−396.398	+	62.7832i	−1.08010	+	0.171071i	−0.409073	+	0.912502i	$0.634148\pi$
$368$	112.200	+	112.200i	0.304893	+	0.304893i
$369$	9.95910	−	13.7075i	0.0269894	−	0.0371478i
$370$	81.8601	−	97.6865i	0.221244	−	0.264018i
$371$	138.092	−	100.330i	0.372216	−	0.270430i
$372$	−30.9866	+	195.641i	−0.0832972	+	0.525918i
$373$	187.274	−	367.546i	0.502075	−	0.985379i	−0.491357	−	0.870958i	$-0.663499\pi$
$373$	187.274	−	367.546i	0.502075	−	0.985379i	0.993432	−	0.114420i	$-0.0365011\pi$
$374$		−	21.8095i		−	0.0583142i
$375$	198.845	−	246.539i	0.530254	−	0.657437i
$376$	237.733			0.632269
$377$	527.343	+	268.695i	1.39879	+	0.712719i
$378$	107.004	+	16.9478i	0.283080	+	0.0448355i
$379$	68.8055	+	94.7026i	0.181545	+	0.249875i	0.890084	−	0.455796i	$-0.150645\pi$
$379$	68.8055	+	94.7026i	0.181545	+	0.249875i	−0.708539	+	0.705671i	$0.750645\pi$
$380$	58.9577	+	49.4059i	0.155152	+	0.130015i
$381$	−48.0025	−	34.8759i	−0.125991	−	0.0915377i
$382$	−157.698	+	157.698i	−0.412822	+	0.412822i
$383$	−14.3249	−	90.4436i	−0.0374017	−	0.236145i	0.961905	−	0.273385i	$-0.0881434\pi$
$383$	−14.3249	−	90.4436i	−0.0374017	−	0.236145i	−0.999306	+	0.0372401i	$0.988143\pi$
$384$	−27.2645	−	8.85876i	−0.0710012	−	0.0230697i
$385$	3.71833	+	8.74397i	0.00965800	+	0.0227116i
$386$	47.0192	+	144.710i	0.121811	+	0.374897i
$387$	−24.9239	−	48.9159i	−0.0644028	−	0.126398i
$388$	113.714	−	57.9401i	0.293077	−	0.149330i
$389$	206.217	−	67.0040i	0.530121	−	0.172247i	−0.0317127	−	0.999497i	$-0.510096\pi$
$389$	206.217	−	67.0040i	0.530121	−	0.172247i	0.561833	+	0.827250i	$0.310096\pi$
$390$	−144.560	−	166.079i	−0.370668	−	0.425843i
$391$	−259.730	+	799.367i	−0.664271	+	2.04442i
$392$	−117.843	+	18.6645i	−0.300620	+	0.0476135i
$393$	194.647	+	194.647i	0.495285	+	0.495285i
$394$	−31.7077	+	43.6420i	−0.0804765	+	0.110766i
$395$	−8.10542	+	117.010i	−0.0205201	+	0.296228i
$396$	3.03780	−	2.20709i	0.00767120	−	0.00557346i
$397$	21.2893	−	134.416i	0.0536255	−	0.338578i	−0.946259	−	0.323409i	$-0.895171\pi$
$397$	21.2893	−	134.416i	0.0536255	−	0.338578i	0.999885	−	0.0151696i	$-0.00482882\pi$
$398$	129.374	−	253.910i	0.325060	−	0.637966i
$399$		−	50.8893i		−	0.127542i
$400$	−99.0449	−	13.7881i	−0.247612	−	0.0344702i
$401$	−23.8319			−0.0594311			−0.0297156	−	0.999558i	$-0.509460\pi$
$401$	−23.8319			−0.0594311			−0.0297156	+	0.999558i	$0.509460\pi$
$402$	197.848	+	100.808i	0.492158	+	0.250767i
$403$	474.412	+	75.1394i	1.17720	+	0.186450i
$404$	−70.5610	−	97.1189i	−0.174656	−	0.240393i
$405$	62.0106	+	248.021i	0.153112	+	0.612398i
$406$	−143.869	−	104.527i	−0.354357	−	0.257456i
$407$	−9.27649	+	9.27649i	−0.0227924	+	0.0227924i
$408$	−23.7549	−	149.982i	−0.0582228	−	0.367604i
$409$	287.240	+	93.3299i	0.702298	+	0.228190i	0.638332	−	0.769762i	$-0.279625\pi$
$409$	287.240	+	93.3299i	0.702298	+	0.228190i	0.0639666	+	0.997952i	$0.479625\pi$
$410$	46.2675	−	4.07830i	0.112847	−	0.00994708i
$411$	−12.5478	−	38.6183i	−0.0305300	−	0.0939618i
$412$	34.0064	+	66.7413i	0.0825398	+	0.161993i
$413$	182.225	−	92.8482i	0.441223	−	0.224814i
$414$	−137.626	+	44.7175i	−0.332430	+	0.108013i
$415$	−133.283	+	222.148i	−0.321163	+	0.535296i
$416$	−21.4816	+	66.1137i	−0.0516385	+	0.158927i
$417$	−500.223	+	79.2275i	−1.19957	+	0.189994i
$418$	−5.59874	−	5.59874i	−0.0133941	−	0.0133941i
$419$	−400.071	+	550.650i	−0.954823	+	1.31420i	−0.00547150	+	0.999985i	$0.501742\pi$
$419$	−400.071	+	550.650i	−0.954823	+	1.31420i	−0.949351	+	0.314216i	$0.898258\pi$
$420$	35.0946	+	56.0816i	0.0835586	+	0.133528i
$421$	218.505	−	158.753i	0.519014	−	0.377086i	−0.297218	−	0.954810i	$-0.596059\pi$
$421$	218.505	−	158.753i	0.519014	−	0.377086i	0.816232	+	0.577724i	$0.196059\pi$
$422$	−4.86076	+	30.6896i	−0.0115184	+	0.0727243i
$423$	−98.4287	+	193.177i	−0.232692	+	0.456684i
$424$		−	184.912i		−	0.436112i
$425$	−173.107	−	500.616i	−0.407310	−	1.17792i
$426$	−191.728			−0.450066
$427$	151.180	+	77.0300i	0.354051	+	0.180398i
$428$	−26.4479	−	4.18894i	−0.0617942	−	0.00978724i
$429$	13.3216	+	18.3356i	0.0310526	+	0.0427402i
$430$	56.2856	−	139.574i	0.130897	−	0.324590i
$431$	668.833	+	485.936i	1.55182	+	1.12746i	0.942340	+	0.334656i	$0.108620\pi$
$431$	668.833	+	485.936i	1.55182	+	1.12746i	0.609476	+	0.792804i	$0.291380\pi$
$432$	82.9887	−	82.9887i	0.192104	−	0.192104i
$433$	−113.968	−	719.567i	−0.263206	−	1.66182i	−0.665568	−	0.746337i	$-0.731811\pi$
$433$	−113.968	−	719.567i	−0.263206	−	1.66182i	0.402362	−	0.915481i	$-0.368189\pi$
$434$	−137.258	−	44.5979i	−0.316263	−	0.102760i
$435$	136.873	−	594.631i	0.314650	−	1.36697i
$436$	−103.901	−	319.774i	−0.238305	−	0.733427i
$437$	138.531	+	271.881i	0.317003	+	0.622154i
$438$	−108.633	+	55.3510i	−0.248020	+	0.126372i
$439$	−472.354	+	153.477i	−1.07598	+	0.349606i	−0.792813	−	0.609465i	$-0.791384\pi$
$439$	−472.354	+	153.477i	−1.07598	+	0.349606i	−0.283164	+	0.959071i	$0.591384\pi$
$440$	10.0310	+	2.30895i	0.0227978	+	0.00524761i
$441$	33.6242	−	103.485i	0.0762453	−	0.234659i
$442$	−363.693	+	57.6033i	−0.822835	+	0.130324i
$443$	367.664	+	367.664i	0.829940	+	0.829940i	0.987508	−	0.157568i	$-0.0503653\pi$
$443$	367.664	+	367.664i	0.829940	+	0.829940i	−0.157568	+	0.987508i	$0.550365\pi$
$444$	−53.6898	+	73.8977i	−0.120923	+	0.166436i
$445$	−697.116	−	281.124i	−1.56655	−	0.631740i
$446$	479.410	−	348.312i	1.07491	−	0.780968i
$447$	−110.387	+	696.955i	−0.246950	+	1.55918i
$448$	9.48262	−	18.6107i	0.0211666	−	0.0415417i
$449$			43.4706i			0.0968165i	0.998828	+	0.0484082i	$0.0154148\pi$
$449$			43.4706i			0.0968165i	−0.998828	+	0.0484082i	$0.984585\pi$
$450$	52.2115	−	74.7732i	0.116025	−	0.166163i
$451$	−4.78093			−0.0106007
$452$	−215.497	−	109.801i	−0.476764	−	0.242923i
$453$	542.572	+	85.9350i	1.19773	+	0.189702i
$454$	91.8038	+	126.357i	0.202211	+	0.278320i
$455$	135.993	−	85.1010i	0.298885	−	0.187035i
$456$	−44.6002	−	32.4040i	−0.0978075	−	0.0710613i
$457$	181.132	−	181.132i	0.396349	−	0.396349i	−0.480594	−	0.876943i	$-0.659579\pi$
$457$	181.132	−	181.132i	0.396349	−	0.396349i	0.876943	+	0.480594i	$0.159579\pi$
$458$	−2.96458	−	18.7176i	−0.00647288	−	0.0408682i
$459$	591.249	+	192.108i	1.28812	+	0.418537i
$460$	−340.162	−	204.088i	−0.739482	−	0.443669i
$461$	−64.2056	−	197.605i	−0.139275	−	0.428643i	0.856956	−	0.515390i	$-0.172353\pi$
$461$	−64.2056	−	197.605i	−0.139275	−	0.428643i	−0.996230	+	0.0867467i	$0.972353\pi$
$462$	−3.09158	−	6.06756i	−0.00669172	−	0.0131332i
$463$	−265.262	+	135.158i	−0.572919	+	0.291917i	−0.716347	−	0.697744i	$-0.754187\pi$
$463$	−265.262	+	135.158i	−0.572919	+	0.291917i	0.143428	+	0.989661i	$0.454187\pi$
$464$	−183.218	+	59.5313i	−0.394867	+	0.128300i
$465$	−43.4814	−	493.288i	−0.0935085	−	1.06083i
$466$	−132.775	+	408.640i	−0.284925	+	0.876910i
$467$	−222.042	+	35.1679i	−0.475464	+	0.0753060i	−0.389567	−	0.920998i	$-0.627375\pi$
$467$	−222.042	+	35.1679i	−0.475464	+	0.0753060i	−0.0858964	+	0.996304i	$0.527375\pi$
$468$	−44.8286	−	44.8286i	−0.0957876	−	0.0957876i
$469$	−95.0955	+	130.888i	−0.202762	+	0.279078i
$470$	−576.585	+	144.158i	−1.22678	+	0.306720i
$471$	−328.354	+	238.563i	−0.697142	+	0.506504i
$472$	34.6587	−	218.827i	0.0734295	−	0.463616i
$473$	−7.03277	+	13.8026i	−0.0148684	+	0.0291810i
$474$		−	84.0608i		−	0.177343i
$475$	−172.952	−	84.0750i	−0.364109	−	0.177000i
$476$	110.640			0.232437
$477$	150.255	+	76.5589i	0.315001	+	0.160501i
$478$	400.385	+	63.4148i	0.837626	+	0.132667i
$479$	−135.106	−	185.957i	−0.282058	−	0.388219i	0.644356	−	0.764725i	$-0.277125\pi$
$479$	−135.106	−	185.957i	−0.282058	−	0.388219i	−0.926414	+	0.376506i	$0.877125\pi$
$480$	71.4975	+	4.95271i	0.148953	+	0.0103182i
$481$	179.195	+	130.193i	0.372546	+	0.270671i
$482$	−59.4679	+	59.4679i	−0.123377	+	0.123377i
$483$	41.0544	+	259.207i	0.0849987	+	0.536661i
$484$	229.148	+	74.4547i	0.473446	+	0.153832i
$485$	−240.661	+	209.479i	−0.496208	+	0.431916i
$486$	58.7824	+	180.914i	0.120951	+	0.372250i
$487$	−200.863	−	394.215i	−0.412449	−	0.809477i	−1.00000		0.000289730i	$-0.999908\pi$
$487$	−200.863	−	394.215i	−0.412449	−	0.809477i	0.587551	−	0.809187i	$-0.300092\pi$
$488$	163.775	−	83.4475i	0.335604	−	0.170999i
$489$	−129.233	+	41.9903i	−0.264280	+	0.0858696i
$490$	274.492	−	116.726i	0.560188	−	0.238217i
$491$	220.205	−	677.722i	0.448483	−	1.38029i	−0.430135	−	0.902764i	$-0.641534\pi$
$491$	220.205	−	677.722i	0.448483	−	1.38029i	0.878618	−	0.477524i	$-0.158466\pi$
$492$	−32.8781	+	5.20738i	−0.0668254	+	0.0105841i
$493$	−721.569	−	721.569i	−1.46363	−	1.46363i
$494$	−78.5765	+	108.151i	−0.159062	+	0.218930i
$495$	−6.02935	+	7.19503i	−0.0121805	+	0.0145354i
$496$	−126.486	+	91.8976i	−0.255012	+	0.185277i
$497$	21.8529	−	137.974i	0.0439697	−	0.277613i
$498$	84.2915	−	165.431i	0.169260	−	0.332191i
$499$			413.251i			0.828158i	0.910241	+	0.414079i	$0.135896\pi$
$499$			413.251i			0.828158i	−0.910241	+	0.414079i	$0.864104\pi$
$500$	248.579	−	26.6188i	0.497158	−	0.0532376i
$501$	669.973			1.33727
$502$	−164.823	−	83.9815i	−0.328333	−	0.167294i
$503$	−246.237	−	39.0001i	−0.489537	−	0.0775350i	−0.0932137	−	0.995646i	$-0.529714\pi$
$503$	−246.237	−	39.0001i	−0.489537	−	0.0775350i	−0.396323	+	0.918111i	$0.629714\pi$
$504$	11.1966	+	15.4108i	0.0222154	+	0.0305769i
$505$	230.026	+	192.759i	0.455498	+	0.381702i
$506$	33.0342	+	24.0007i	0.0652849	+	0.0474322i
$507$	−32.2243	+	32.2243i	−0.0635587	+	0.0635587i
$508$	−7.32627	−	46.2563i	−0.0144218	−	0.0910557i
$509$	−318.506	−	103.489i	−0.625749	−	0.203318i	−0.0210580	−	0.999778i	$-0.506703\pi$
$509$	−318.506	−	103.489i	−0.625749	−	0.203318i	−0.604691	+	0.796460i	$0.706703\pi$
$510$	148.561	+	349.354i	0.291297	+	0.685009i
$511$	−27.4507	−	84.4844i	−0.0537195	−	0.165332i
$512$	−10.2726	−	20.1612i	−0.0200637	−	0.0393773i
$513$	201.096	−	102.464i	0.392001	−	0.199734i
$514$	123.515	−	40.1325i	0.240302	−	0.0780789i
$515$	−122.948	−	141.250i	−0.238735	−	0.274271i
$516$	−33.3301	+	102.580i	−0.0645932	+	0.198798i
$517$	60.4235	−	9.57014i	0.116873	−	0.0185109i
$518$	−47.0598	−	47.0598i	−0.0908490	−	0.0908490i
$519$	61.4916	−	84.6359i	0.118481	−	0.163075i
$520$	12.0099	−	173.375i	0.0230959	−	0.333413i
$521$	−208.409	+	151.418i	−0.400018	+	0.290630i	−0.769548	−	0.638589i	$-0.779519\pi$
$521$	−208.409	+	151.418i	−0.400018	+	0.290630i	0.369530	+	0.929219i	$0.379519\pi$
$522$	27.4840	−	173.527i	0.0526514	−	0.332428i
$523$	−351.099	+	689.071i	−0.671317	+	1.31753i	0.264273	+	0.964448i	$0.414868\pi$
$523$	−351.099	+	689.071i	−0.671317	+	1.31753i	−0.935591	+	0.353087i	$0.885132\pi$
$524$			217.274i			0.414644i
$525$	−119.124	−	114.736i	−0.226902	−	0.218545i
$526$	−221.371			−0.420857
$527$	−737.898	−	375.978i	−1.40019	−	0.713430i
$528$	−7.28629	−	1.15403i	−0.0137998	−	0.00218567i
$529$	−614.011	−	845.113i	−1.16070	−	1.59757i
$530$	112.128	+	448.474i	0.211562	+	0.846178i
$531$	163.464	+	118.764i	0.307842	+	0.223661i
$532$	28.4025	−	28.4025i	0.0533881	−	0.0533881i
$533$	12.6274	+	79.7262i	0.0236912	+	0.149580i
$534$	512.344	+	166.471i	0.959446	+	0.311743i
$535$	66.6854	−	5.87807i	0.124646	−	0.0109870i
$536$	54.1598	+	166.687i	0.101044	+	0.310982i
$537$	166.200	+	326.186i	0.309498	+	0.607424i
$538$	−417.304	+	212.627i	−0.775657	+	0.395217i
$539$	−29.2002	+	9.48773i	−0.0541748	+	0.0176025i
$540$	−150.953	+	251.600i	−0.279542	+	0.465925i
$541$	19.0936	−	58.7641i	0.0352932	−	0.108621i	−0.931858	−	0.362823i	$-0.881813\pi$
$541$	19.0936	−	58.7641i	0.0352932	−	0.108621i	0.967151	+	0.254202i	$0.0818128\pi$
$542$	262.072	−	41.5082i	0.483528	−	0.0765833i
$543$	−77.7356	−	77.7356i	−0.143159	−	0.143159i
$544$	70.4504	−	96.9667i	0.129504	−	0.178248i
$545$	445.903	+	712.558i	0.818170	+	1.30745i
$546$	−93.0165	+	67.5804i	−0.170360	+	0.123774i
$547$	13.3557	−	84.3244i	0.0244162	−	0.154158i	−0.972468	−	0.233036i	$-0.925134\pi$
$547$	13.3557	−	84.3244i	0.0244162	−	0.154158i	0.996884	+	0.0788784i	$0.0251339\pi$
$548$	14.5505	−	28.5570i	0.0265520	−	0.0521113i
$549$			167.630i			0.305337i
$550$	−25.7288	+	0.482687i	−0.0467796	+	0.000877612i
$551$	−370.469			−0.672357
$552$	253.315	+	129.070i	0.458904	+	0.233823i
$553$	60.4930	+	9.58114i	0.109391	+	0.0173258i
$554$	233.322	+	321.140i	0.421159	+	0.579675i
$555$	85.4057	−	211.784i	0.153884	−	0.381593i
$556$	−323.404	−	234.967i	−0.581662	−	0.422602i
$557$	59.2331	−	59.2331i	0.106343	−	0.106343i	−0.651933	−	0.758276i	$-0.726042\pi$
$557$	59.2331	−	59.2331i	0.106343	−	0.106343i	0.758276	+	0.651933i	$0.226042\pi$
$558$	−22.3050	−	140.828i	−0.0399732	−	0.252381i
$559$	248.745	+	80.8223i	0.444983	+	0.144584i
$560$	−11.7133	+	50.8875i	−0.0209167	+	0.0908705i
$561$	−12.0753	−	37.1640i	−0.0215246	−	0.0662460i
$562$	−201.435	−	395.338i	−0.358425	−	0.703449i
$563$	254.074	−	129.457i	0.451286	−	0.229942i	−0.213548	−	0.976933i	$-0.568502\pi$
$563$	254.074	−	129.457i	0.451286	−	0.229942i	0.664834	+	0.746991i	$0.268502\pi$
$564$	405.104	−	131.626i	0.718270	−	0.233380i
$565$	589.237	+	135.631i	1.04290	+	0.240055i
$566$	−41.2973	+	127.100i	−0.0729634	+	0.224558i
$567$	131.855	−	20.8838i	0.232549	−	0.0368321i
$568$	−107.008	−	107.008i	−0.188394	−	0.188394i
$569$	139.865	−	192.508i	0.245809	−	0.338327i	−0.668229	−	0.743955i	$-0.732947\pi$
$569$	139.865	−	192.508i	0.245809	−	0.338327i	0.914038	+	0.405629i	$0.132947\pi$
$570$	127.820	+	51.5458i	0.224246	+	0.0904311i
$571$	774.265	−	562.537i	1.35598	−	0.985178i	0.357292	−	0.933993i	$-0.383700\pi$
$571$	774.265	−	562.537i	1.35598	−	0.985178i	0.998689	−	0.0511852i	$-0.0162999\pi$
$572$	−2.79842	+	17.6685i	−0.00489235	+	0.0308891i
$573$	−181.409	+	356.035i	−0.316595	+	0.621353i
$574$		−	24.2537i		−	0.0422539i
$575$	948.765	+	288.713i	1.65003	+	0.502110i
$576$	20.6357			0.0358259
$577$	898.960	+	458.043i	1.55799	+	0.793836i	0.999367	−	0.0355856i	$-0.0113296\pi$
$577$	898.960	+	458.043i	1.55799	+	0.793836i	0.558624	+	0.829421i	$0.311330\pi$
$578$	223.393	+	35.3819i	0.386492	+	0.0612144i
$579$	160.244	+	220.557i	0.276760	+	0.380928i
$580$	408.269	−	255.485i	0.703911	−	0.440492i
$581$	109.442	+	79.5146i	0.188369	+	0.136858i
$582$	161.692	−	161.692i	0.277821	−	0.277821i
$583$	−7.44376	−	46.9981i	−0.0127680	−	0.0806142i
$584$	−91.5229	−	29.7376i	−0.156717	−	0.0509205i
$585$	135.908	+	81.5413i	0.232322	+	0.139387i
$586$	61.8790	+	190.444i	0.105596	+	0.324990i
$587$	3.26148	+	6.40101i	0.00555618	+	0.0109046i	0.893768	−	0.448530i	$-0.148052\pi$
$587$	3.26148	+	6.40101i	0.00555618	+	0.0109046i	−0.888212	+	0.459434i	$0.848052\pi$
$588$	−190.474	+	97.0513i	−0.323935	+	0.165053i
$589$	−285.944	+	92.9088i	−0.485473	+	0.157740i
$590$	48.6344	+	551.746i	0.0824311	+	0.935163i
$591$	−29.8675	+	91.9228i	−0.0505373	+	0.155538i
$592$	−71.2095	+	11.2785i	−0.120286	+	0.0190515i
$593$	161.092	+	161.092i	0.271655	+	0.271655i	0.829766	−	0.558111i	$-0.188474\pi$
$593$	161.092	+	161.092i	0.271655	+	0.271655i	−0.558111	+	0.829766i	$0.688474\pi$
$594$	17.7521	−	24.4336i	0.0298856	−	0.0411340i
$595$	−268.340	+	67.0907i	−0.450991	+	0.112757i
$596$	−450.596	+	327.377i	−0.756033	+	0.549290i
$597$	79.8735	−	504.301i	0.133791	−	0.844726i
$598$	312.983	−	614.264i	0.523384	−	1.02720i
$599$		−	1018.75i		−	1.70076i	−0.526173	−	0.850378i	$-0.676373\pi$
$599$		−	1018.75i		−	1.70076i	0.526173	−	0.850378i	$-0.323627\pi$
$600$	−176.409	+	31.3432i	−0.294016	+	0.0522386i
$601$	56.8591			0.0946075			0.0473038	−	0.998881i	$-0.484937\pi$
$601$	56.8591			0.0946075			0.0473038	+	0.998881i	$0.484937\pi$
$602$	−70.0207	−	35.6773i	−0.116314	−	0.0592647i
$603$	−157.870	−	25.0041i	−0.261807	−	0.0414662i
$604$	254.859	+	350.784i	0.421953	+	0.580768i
$605$	−600.911	−	41.6258i	−0.993242	−	0.0688030i
$606$	−174.010	−	126.426i	−0.287145	−	0.208623i
$607$	−171.454	+	171.454i	−0.282462	+	0.282462i	−0.834090	−	0.551628i	$-0.814007\pi$
$607$	−171.454	+	171.454i	−0.282462	+	0.282462i	0.551628	+	0.834090i	$0.314007\pi$
$608$	−6.80701	−	42.9778i	−0.0111957	−	0.0706871i
$609$	−303.031	−	98.4606i	−0.497587	−	0.161676i
$610$	−346.609	+	301.700i	−0.568212	+	0.494590i
$611$	−319.181	−	982.338i	−0.522391	−	1.60776i
$612$	49.6246	+	97.3937i	0.0810859	+	0.159140i
$613$	−537.789	+	274.017i	−0.877307	+	0.447010i	−0.833815	−	0.552043i	$-0.813848\pi$
$613$	−537.789	+	274.017i	−0.877307	+	0.447010i	−0.0434918	+	0.999054i	$0.513848\pi$
$614$	510.554	−	165.889i	0.831521	−	0.270177i
$615$	76.5830	−	32.5666i	0.124525	−	0.0529538i
$616$	1.66096	−	5.11192i	0.00269637	−	0.00829857i
$617$	−138.102	+	21.8733i	−0.223829	+	0.0354510i	−0.267341	−	0.963602i	$-0.586145\pi$
$617$	−138.102	+	21.8733i	−0.223829	+	0.0354510i	0.0435126	+	0.999053i	$0.486145\pi$
$618$	94.9007	+	94.9007i	0.153561	+	0.153561i
$619$	−97.5904	+	134.322i	−0.157658	+	0.216998i	−0.880538	−	0.473976i	$-0.842818\pi$
$619$	−97.5904	+	134.322i	−0.157658	+	0.216998i	0.722879	+	0.690974i	$0.242818\pi$
$620$	251.047	−	299.583i	0.404914	−	0.483198i
$621$	−941.632	+	684.136i	−1.51632	+	1.10167i
$622$	17.6926	−	111.707i	0.0284447	−	0.179593i
$623$	−178.194	+	349.726i	−0.286026	+	0.561358i
$624$			124.553i			0.199605i
$625$	−586.748	+	215.295i	−0.938797	+	0.344472i
$626$	−235.332			−0.375930
$627$	−12.6403	−	6.44054i	−0.0201599	−	0.0102720i
$628$	−316.409	−	50.1143i	−0.503836	−	0.0797998i
$629$	−224.474	−	308.962i	−0.356875	−	0.491196i
$630$	−36.5005	−	30.5870i	−0.0579373	−	0.0485507i
$631$	−583.662	−	424.055i	−0.924979	−	0.672037i	0.0197794	−	0.999804i	$-0.493704\pi$
$631$	−583.662	−	424.055i	−0.924979	−	0.672037i	−0.944758	+	0.327768i	$0.893704\pi$
$632$	46.9162	−	46.9162i	0.0742345	−	0.0742345i
$633$	8.70913	+	54.9873i	0.0137585	+	0.0868677i
$634$	−648.410	−	210.681i	−1.02273	−	0.332305i
$635$	45.8180	+	107.745i	0.0721543	+	0.169677i
$636$	−102.380	−	315.095i	−0.160975	−	0.495432i
$637$	235.340	+	461.881i	0.369451	+	0.725087i
$638$	−44.1712	+	22.5064i	−0.0692339	+	0.0352764i
$639$	131.257	−	42.6479i	0.205410	−	0.0667416i
$640$	37.1402	+	42.6686i	0.0580315	+	0.0666697i
$641$	295.691	−	910.042i	0.461296	−	1.41972i	−0.402286	−	0.915514i	$-0.631784\pi$
$641$	295.691	−	910.042i	0.461296	−	1.41972i	0.863582	−	0.504209i	$-0.168216\pi$
$642$	−47.3873	+	7.50541i	−0.0738120	+	0.0116907i
$643$	47.9432	+	47.9432i	0.0745618	+	0.0745618i	0.743404	−	0.668842i	$-0.233210\pi$
$643$	47.9432	+	47.9432i	0.0745618	+	0.0745618i	−0.668842	+	0.743404i	$0.733210\pi$
$644$	−121.756	+	167.583i	−0.189062	+	0.260222i
$645$	18.6340	−	269.002i	0.0288900	−	0.417057i
$646$	186.471	−	135.479i	0.288655	−	0.209720i
$647$	−155.194	+	979.858i	−0.239867	+	1.51446i	0.514203	+	0.857669i	$0.328088\pi$
$647$	−155.194	+	979.858i	−0.239867	+	1.51446i	−0.754070	+	0.656794i	$0.771912\pi$
$648$	65.6564	−	128.858i	0.101322	−	0.198855i
$649$		−	57.0133i		−	0.0878479i
$650$	76.0042	+	427.776i	0.116929	+	0.658116i
$651$	−258.585			−0.397211
$652$	−95.5634	−	48.6920i	−0.146570	−	0.0746810i
$653$	−302.339	−	47.8858i	−0.463000	−	0.0733320i	−0.0794232	−	0.996841i	$-0.525308\pi$
$653$	−302.339	−	47.8858i	−0.463000	−	0.0733320i	−0.383577	+	0.923509i	$0.625308\pi$
$654$	−354.100	−	487.377i	−0.541438	−	0.745225i
$655$	−131.752	−	526.963i	−0.201148	−	0.804524i
$656$	−21.2564	−	15.4437i	−0.0324030	−	0.0235422i
$657$	62.0574	−	62.0574i	0.0944557	−	0.0944557i
$658$	48.5494	+	306.529i	0.0737833	+	0.465850i
$659$	−535.335	−	173.941i	−0.812345	−	0.263947i	−0.126754	−	0.991934i	$-0.540456\pi$
$659$	−535.335	−	173.941i	−0.812345	−	0.263947i	−0.685591	+	0.727987i	$0.740456\pi$
$660$	18.3715	−	1.61938i	0.0278357	−	0.00245361i
$661$	357.954	+	1101.67i	0.541534	+	1.66667i	0.729092	+	0.684415i	$0.239943\pi$
$661$	357.954	+	1101.67i	0.541534	+	1.66667i	−0.187559	+	0.982253i	$0.560057\pi$
$662$	−174.005	−	341.504i	−0.262847	−	0.515866i
$663$	−587.850	+	299.524i	−0.886651	+	0.451771i
$664$	139.376	−	45.2860i	0.209903	−	0.0682018i
$665$	−51.6628	+	86.1086i	−0.0776885	+	0.129487i
$666$	20.3182	−	62.5330i	0.0305078	−	0.0938934i
$667$	1887.00	−	298.872i	2.82909	−	0.448083i
$668$	373.927	+	373.927i	0.559771	+	0.559771i
$669$	624.077	−	858.969i	0.932851	−	1.28396i
$670$	−232.433	−	371.431i	−0.346914	−	0.554374i
$671$	38.2666	−	27.8023i	0.0570292	−	0.0414342i
$672$	5.85443	−	36.9634i	0.00871195	−	0.0550051i
$673$	−18.8241	+	36.9443i	−0.0279704	+	0.0548950i	−0.904569	−	0.426328i	$-0.859807\pi$
$673$	−18.8241	+	36.9443i	−0.0279704	+	0.0548950i	0.876598	+	0.481223i	$0.159807\pi$
$674$		−	561.161i		−	0.832583i
$675$	213.546	−	701.751i	0.316364	−	1.03963i
$676$	−35.9702			−0.0532103
$677$	215.524	+	109.815i	0.318352	+	0.162209i	0.605863	−	0.795569i	$-0.292828\pi$
$677$	215.524	+	109.815i	0.318352	+	0.162209i	−0.287511	+	0.957777i	$0.592828\pi$
$678$	−428.007	−	67.7897i	−0.631279	−	0.0999848i
$679$	97.9293	+	134.788i	0.144226	+	0.198510i
$680$	−112.067	+	277.898i	−0.164805	+	0.408673i
$681$	226.397	+	164.487i	0.332447	+	0.241537i
$682$	−28.4490	+	28.4490i	−0.0417140	+	0.0417140i
$683$	169.356	+	1069.27i	0.247959	+	1.56555i	0.726300	+	0.687377i	$0.241238\pi$
$683$	169.356	+	1069.27i	0.247959	+	1.56555i	−0.478341	+	0.878174i	$0.658762\pi$
$684$	37.7412	+	12.2629i	0.0551772	+	0.0179281i
$685$	−17.9734	+	78.0837i	−0.0262385	+	0.113991i
$686$	−104.041	−	320.205i	−0.151663	−	0.466771i
$687$	−15.4152	−	30.2539i	−0.0224384	−	0.0440378i
$688$	−75.8542	+	38.6497i	−0.110253	+	0.0561768i
$689$	−764.074	+	248.263i	−1.10896	+	0.360323i
$690$	−692.643	−	159.433i	−1.00383	−	0.231063i
$691$	−60.8202	+	187.185i	−0.0880177	+	0.270891i	−0.985371	−	0.170422i	$-0.945487\pi$
$691$	−60.8202	+	187.185i	−0.0880177	+	0.270891i	0.897353	+	0.441313i	$0.145487\pi$
$692$	81.5570	−	12.9174i	0.117857	−	0.0186667i
$693$	3.46615	+	3.46615i	0.00500167	+	0.00500167i
$694$	99.3339	−	136.721i	0.143132	−	0.197005i
$695$	926.847	+	373.767i	1.33359	+	0.537795i
$696$	−279.249	+	202.886i	−0.401219	+	0.291503i
$697$	21.7718	−	137.462i	0.0312364	−	0.197219i
$698$	181.396	−	356.010i	0.259880	−	0.510043i
$699$			769.849i			1.10136i
$700$	−2.44868	−	130.523i	−0.00349811	−	0.186461i
$701$	179.635			0.256255			0.128127	−	0.991758i	$-0.459103\pi$
$701$	179.635			0.256255			0.128127	+	0.991758i	$0.459103\pi$
$702$	−454.339	−	231.497i	−0.647206	−	0.329768i
$703$	−136.939	−	21.6890i	−0.194792	−	0.0308521i
$704$	−3.42255	−	4.71073i	−0.00486157	−	0.00669138i
$705$	−902.701	+	564.889i	−1.28043	+	0.801261i
$706$	−465.569	−	338.255i	−0.659446	−	0.479115i
$707$	110.814	−	110.814i	0.156738	−	0.156738i
$708$	−62.0988	−	392.076i	−0.0877101	−	0.553780i
$709$	−65.4964	−	21.2811i	−0.0923785	−	0.0300156i	0.262463	−	0.964942i	$-0.415465\pi$
$709$	−65.4964	−	21.2811i	−0.0923785	−	0.0300156i	−0.354842	+	0.934926i	$0.615465\pi$
$710$	324.419	+	194.642i	0.456928	+	0.274144i
$711$	18.6984	+	57.5479i	0.0262988	+	0.0809394i
$712$	193.040	+	378.862i	0.271123	+	0.532109i
$713$	1381.52	−	703.918i	1.93761	−	0.987262i
$714$	188.534	−	61.2583i	0.264053	−	0.0857959i
$715$	−3.92685	−	44.5492i	−0.00549209	−	0.0623066i
$716$	−89.2919	+	274.812i	−0.124709	+	0.383816i
$717$	717.379	−	113.622i	1.00053	−	0.158468i
$718$	567.178	+	567.178i	0.789941	+	0.789941i
$719$	666.444	−	917.282i	0.926904	−	1.27577i	−0.0341503	−	0.999417i	$-0.510872\pi$
$719$	666.444	−	917.282i	0.926904	−	1.27577i	0.961055	−	0.276358i	$-0.0891275\pi$
$720$	−50.0488	+	12.5133i	−0.0695122	+	0.0173795i
$721$	−79.1103	+	57.4770i	−0.109723	+	0.0797185i
$722$	−66.7745	+	421.597i	−0.0924854	+	0.583930i
$723$	−68.4092	+	134.261i	−0.0946186	+	0.185699i
$724$		−	86.7719i		−	0.119851i
$725$	−835.269	+	867.208i	−1.15210	+	1.19615i
$726$	431.698			0.594626
$727$	−632.182	−	322.113i	−0.869577	−	0.443071i	−0.0385192	−	0.999258i	$-0.512264\pi$
$727$	−632.182	−	322.113i	−0.869577	−	0.443071i	−0.831058	+	0.556186i	$0.812264\pi$
$728$	−89.6327	−	14.1964i	−0.123122	−	0.0195006i
$729$	470.821	+	648.029i	0.645845	+	0.888929i
$730$	240.007	+	16.6256i	0.328777	+	0.0227747i
$731$	−364.827	−	265.062i	−0.499079	−	0.362602i
$732$	232.875	−	232.875i	0.318135	−	0.318135i
$733$	153.930	+	971.877i	0.210000	+	1.32589i	0.837142	+	0.546985i	$0.184225\pi$
$733$	153.930	+	971.877i	0.210000	+	1.32589i	−0.627142	+	0.778905i	$0.715775\pi$
$734$	−539.799	−	175.391i	−0.735422	−	0.238953i
$735$	403.114	−	350.884i	0.548454	−	0.477393i
$736$	69.3437	+	213.418i	0.0942170	+	0.289970i
$737$	20.4756	+	40.1857i	0.0277824	+	0.0545260i
$738$	21.3500	−	10.8784i	0.0289295	−	0.0147403i
$739$	1239.16	−	402.628i	1.67681	−	0.544828i	0.692520	−	0.721399i	$-0.256500\pi$
$739$	1239.16	−	402.628i	1.67681	−	0.544828i	0.984288	+	0.176571i	$0.0565005\pi$
$740$	165.868	−	70.5347i	0.224146	−	0.0953172i
$741$	−74.0162	+	227.798i	−0.0998869	+	0.307420i
$742$	238.422	−	37.7623i	0.321323	−	0.0508926i
$743$	−314.184	−	314.184i	−0.422859	−	0.422859i	0.463328	−	0.886187i	$-0.346655\pi$
$743$	−314.184	−	314.184i	−0.422859	−	0.422859i	−0.886187	+	0.463328i	$0.846655\pi$
$744$	−164.655	+	226.628i	−0.221310	+	0.304608i
$745$	894.332	−	1067.24i	1.20045	−	1.43253i
$746$	471.958	−	342.898i	0.632652	−	0.459649i
$747$	−20.9073	+	132.004i	−0.0279884	+	0.176712i
$748$	14.0026	−	27.4816i	0.0187200	−	0.0367401i
$749$		−	34.9569i		−	0.0466715i
$750$	408.847	−	182.990i	0.545130	−	0.243987i
$751$	87.3707			0.116339			0.0581696	−	0.998307i	$-0.481474\pi$
$751$	87.3707			0.116339			0.0581696	+	0.998307i	$0.481474\pi$
$752$	299.561	+	152.634i	0.398353	+	0.202971i
$753$	−327.361	−	51.8489i	−0.434743	−	0.0688565i
$754$	491.979	+	677.151i	0.652492	+	0.898078i
$755$	−830.833	−	696.228i	−1.10044	−	0.922157i
$756$	123.952	+	90.0564i	0.163958	+	0.119122i
$757$	−436.322	+	436.322i	−0.576382	+	0.576382i	−0.933905	−	0.357522i	$-0.883622\pi$
$757$	−436.322	+	436.322i	−0.576382	+	0.576382i	0.357522	+	0.933905i	$0.383622\pi$
$758$	25.8971	+	163.508i	0.0341651	+	0.215710i
$759$	69.5797	+	22.6078i	0.0916728	+	0.0297863i
$760$	42.5705	+	100.108i	0.0560139	+	0.131721i
$761$	328.146	+	1009.93i	0.431203	+	1.32711i	0.896928	+	0.442177i	$0.145794\pi$
$761$	328.146	+	1009.93i	0.431203	+	1.32711i	−0.465724	+	0.884930i	$0.654206\pi$
$762$	−38.0950	−	74.7656i	−0.0499934	−	0.0981176i
$763$	391.093	−	199.272i	0.512573	−	0.261169i
$764$	−299.960	+	97.4628i	−0.392617	+	0.127569i
$765$	−179.415	−	206.122i	−0.234529	−	0.269440i
$766$	40.0180	−	123.163i	0.0522428	−	0.160787i
$767$	−950.747	+	150.584i	−1.23957	+	0.196328i
$768$	−28.6675	−	28.6675i	−0.0373275	−	0.0373275i
$769$	−495.875	+	682.513i	−0.644831	+	0.887534i	−0.998862	−	0.0477002i	$-0.984811\pi$
$769$	−495.875	+	682.513i	−0.644831	+	0.887534i	0.354031	+	0.935234i	$0.384811\pi$
$770$	−0.928604	+	13.4054i	−0.00120598	+	0.0174095i
$771$	188.253	−	136.774i	0.244168	−	0.177398i
$772$	−33.6620	+	212.534i	−0.0436037	+	0.275303i
$773$	253.631	−	497.779i	0.328113	−	0.643958i	−0.666740	−	0.745291i	$-0.732311\pi$
$773$	253.631	−	497.779i	0.328113	−	0.643958i	0.994853	+	0.101333i	$0.0323108\pi$
$774$		−	77.6397i		−	0.100310i
$775$	−427.212	+	878.823i	−0.551241	+	1.13397i
$776$	180.488			0.232587
$777$	−106.247	−	54.1355i	−0.136740	−	0.0696724i
$778$	302.868	+	47.9695i	0.389290	+	0.0616575i
$779$	−29.6988	−	40.8769i	−0.0381243	−	0.0524736i
$780$	−75.5276	−	302.085i	−0.0968302	−	0.387288i
$781$	−31.5053	−	22.8899i	−0.0403397	−	0.0293085i
$782$	−840.504	+	840.504i	−1.07481	+	1.07481i
$783$	−221.060	−	1395.72i	−0.282324	−	1.78252i
$784$	−160.474	−	52.1412i	−0.204687	−	0.0665067i
$785$	797.790	−	70.3222i	1.01629	−	0.0895824i
$786$	120.298	+	370.240i	0.153051	+	0.471044i
$787$	−244.196	−	479.262i	−0.310287	−	0.608973i	0.682221	−	0.731146i	$-0.261014\pi$
$787$	−244.196	−	479.262i	−0.310287	−	0.608973i	−0.992509	+	0.122172i	$0.961014\pi$
$788$	−67.9739	+	34.6344i	−0.0862613	+	0.0439523i
$789$	−377.222	+	122.567i	−0.478102	+	0.155345i
$790$	−85.3386	+	142.237i	−0.108024	+	0.180047i
$791$	97.5674	−	300.282i	0.123347	−	0.379623i
$792$	5.24489	−	0.830708i	0.00662233	−	0.00104887i
$793$	−564.698	−	564.698i	−0.712104	−	0.712104i
$794$	113.126	−	155.705i	0.142476	−	0.196102i
$795$	439.377	+	702.130i	0.552676	+	0.883183i
$796$	326.041	−	236.883i	0.409599	−	0.297591i
$797$	159.378	−	1006.27i	0.199972	−	1.26258i	−0.659622	−	0.751598i	$-0.729283\pi$
$797$	159.378	−	1006.27i	0.199972	−	1.26258i	0.859594	−	0.510978i	$-0.170717\pi$
$798$	32.6729	−	64.1242i	0.0409435	−	0.0803562i
$799$			1780.88i			2.22889i
$800$	−115.951	−	80.9647i	−0.144939	−	0.101206i
$801$	−387.780			−0.484119
$802$	−30.0299	−	15.3010i	−0.0374438	−	0.0190786i
$803$	−24.4590	−	3.87393i	−0.0304596	−	0.00482432i
$804$	184.580	+	254.052i	0.229577	+	0.315985i
$805$	193.680	−	480.277i	0.240596	−	0.596617i
$806$	549.551	+	399.272i	0.681825	+	0.495375i
$807$	−593.372	+	593.372i	−0.735281	+	0.735281i
$808$	−26.5579	−	167.680i	−0.0328687	−	0.207525i
$809$	−509.810	−	165.647i	−0.630173	−	0.204756i	−0.0235211	−	0.999723i	$-0.507488\pi$
$809$	−509.810	−	165.647i	−0.630173	−	0.204756i	−0.606652	+	0.794968i	$0.707488\pi$
$810$	−81.1015	+	352.338i	−0.100125	+	0.434985i
$811$	−337.483	−	1038.67i	−0.416132	−	1.28072i	−0.911234	−	0.411889i	$-0.864869\pi$
$811$	−337.483	−	1038.67i	−0.416132	−	1.28072i	0.495102	−	0.868835i	$-0.335131\pi$
$812$	−114.175	−	224.081i	−0.140610	−	0.275962i
$813$	423.596	−	215.833i	0.521029	−	0.265477i
$814$	−17.6449	+	5.73319i	−0.0216768	+	0.00704323i
$815$	261.300	+	60.1464i	0.320614	+	0.0737992i
$816$	66.3618	−	204.240i	0.0813257	−	0.250295i
$817$	−161.699	+	25.6106i	−0.197918	+	0.0313472i
$818$	302.022	+	302.022i	0.369220	+	0.369220i
$819$	48.6464	−	66.9560i	0.0593973	−	0.0817534i
$820$	60.9188	+	24.5666i	0.0742913	+	0.0299592i
$821$	−353.280	+	256.673i	−0.430304	+	0.312634i	−0.781770	−	0.623566i	$-0.785683\pi$
$821$	−353.280	+	256.673i	−0.430304	+	0.312634i	0.351466	+	0.936200i	$0.385683\pi$
$822$	8.98326	−	56.7181i	0.0109285	−	0.0690001i
$823$	154.326	−	302.881i	0.187516	−	0.368021i	−0.778041	−	0.628214i	$-0.783786\pi$
$823$	154.326	−	302.881i	0.187516	−	0.368021i	0.965557	+	0.260193i	$0.0837862\pi$
$824$			105.932i			0.128559i
$825$	−43.5754	+	15.0678i	−0.0528186	+	0.0182640i
$826$	289.229			0.350156
$827$	−1176.24	−	599.324i	−1.42230	−	0.724696i	−0.437632	−	0.899154i	$-0.644183\pi$
$827$	−1176.24	−	599.324i	−1.42230	−	0.724696i	−0.984665	+	0.174458i	$0.944183\pi$
$828$	−202.129	−	32.0142i	−0.244118	−	0.0386645i
$829$	94.2063	+	129.664i	0.113638	+	0.156410i	0.862047	−	0.506828i	$-0.169182\pi$
$829$	94.2063	+	129.664i	0.113638	+	0.156410i	−0.748409	+	0.663238i	$0.769182\pi$
$830$	−310.574	+	194.350i	−0.374185	+	0.234156i
$831$	575.393	+	418.048i	0.692411	+	0.503066i
$832$	−69.5160	+	69.5160i	−0.0835529	+	0.0835529i
$833$	−139.817	−	882.773i	−0.167848	−	1.05975i
$834$	−681.185	−	221.330i	−0.816768	−	0.265384i
$835$	−1133.65	−	680.157i	−1.35766	−	0.814559i
$836$	−3.46021	−	10.6494i	−0.00413901	−	0.0127386i
$837$	−520.650	−	1021.83i	−0.622044	−	1.22083i
$838$	−857.658	+	436.999i	−1.02346	+	0.521478i
$839$	556.528	−	180.827i	0.663323	−	0.215527i	0.0420436	−	0.999116i	$-0.486613\pi$
$839$	556.528	−	180.827i	0.663323	−	0.215527i	0.621279	+	0.783589i	$0.286613\pi$
$840$	8.21515	+	93.1991i	0.00977994	+	0.110951i
$841$	−456.900	+	1406.19i	−0.543282	+	1.67205i
$842$	377.258	−	59.7518i	0.448050	−	0.0709642i
$843$	−562.139	−	562.139i	−0.666831	−	0.666831i
$844$	−25.8289	+	35.5504i	−0.0306029	+	0.0421213i
$845$	87.2401	−	21.8119i	0.103243	−	0.0258129i
$846$	−248.055	+	180.222i	−0.293209	+	0.213029i
$847$	−49.2044	+	310.664i	−0.0580926	+	0.366782i
$848$	118.721	−	233.002i	0.140001	−	0.274767i
$849$			239.447i			0.282034i
$850$	103.288	−	741.954i	0.121515	−	0.872887i
$851$	715.002			0.840191
$852$	−241.591	−	123.097i	−0.283558	−	0.144480i
$853$	734.339	+	116.308i	0.860890	+	0.136352i	0.571242	−	0.820782i	$-0.306462\pi$
$853$	734.339	+	116.308i	0.860890	+	0.136352i	0.289648	+	0.957133i	$0.406462\pi$
$854$	141.042	+	194.127i	0.165154	+	0.227315i
$855$	−98.9714	−	6.85586i	−0.115756	−	0.00801855i
$856$	−30.6368	−	22.2590i	−0.0357907	−	0.0260035i
$857$	−818.405	+	818.405i	−0.954964	+	0.954964i	−0.999029	−	0.0440643i	$-0.985969\pi$
$857$	−818.405	+	818.405i	−0.954964	+	0.954964i	0.0440643	+	0.999029i	$0.485969\pi$
$858$	5.01399	+	31.6571i	0.00584382	+	0.0368964i
$859$	−749.275	−	243.454i	−0.872264	−	0.283416i	−0.161523	−	0.986869i	$-0.551641\pi$
$859$	−749.275	−	243.454i	−0.872264	−	0.283416i	−0.710742	+	0.703453i	$0.751641\pi$
$860$	160.536	−	139.736i	0.186670	−	0.162483i
$861$	−13.4286	−	41.3290i	−0.0155965	−	0.0480012i
$862$	530.789	+	1041.73i	0.615764	+	1.20851i
$863$	940.039	−	478.974i	1.08927	−	0.555010i	0.185332	−	0.982676i	$-0.440664\pi$
$863$	940.039	−	478.974i	1.08927	−	0.555010i	0.903937	+	0.427666i	$0.140664\pi$
$864$	157.854	−	51.2899i	0.182701	−	0.0593633i
$865$	−189.971	+	80.7842i	−0.219620	+	0.0933921i
$866$	318.382	−	979.880i	0.367647	−	1.13150i
$867$	400.257	−	63.3945i	0.461658	−	0.0731194i
$868$	−144.322	−	144.322i	−0.166269	−	0.166269i
$869$	10.0358	−	13.8131i	0.0115487	−	0.0158954i
$870$	554.246	−	661.401i	0.637065	−	0.760231i
$871$	616.051	−	447.587i	0.707292	−	0.513878i
$872$	74.3849	−	469.648i	0.0853038	−	0.538587i
$873$	−74.7273	+	146.661i	−0.0855982	+	0.167996i
$874$			431.533i			0.493744i
$875$	85.0861	+	315.077i	0.0972413	+	0.360088i
$876$	−172.423			−0.196829
$877$	−607.027	−	309.296i	−0.692163	−	0.352674i	0.0722637	−	0.997386i	$-0.476978\pi$
$877$	−607.027	−	309.296i	−0.692163	−	0.352674i	−0.764426	+	0.644711i	$0.776978\pi$
$878$	−693.739	−	109.877i	−0.790135	−	0.125145i
$879$	210.887	+	290.261i	0.239917	+	0.330217i
$880$	11.1574	+	9.34976i	0.0126788	+	0.0106247i
$881$	−1031.43	−	749.378i	−1.17075	−	0.850599i	−0.179651	−	0.983730i	$-0.557497\pi$
$881$	−1031.43	−	749.378i	−1.17075	−	0.850599i	−0.991098	+	0.133131i	$0.957497\pi$
$882$	108.810	−	108.810i	0.123367	−	0.123367i
$883$	159.690	+	1008.24i	0.180849	+	1.14184i	0.896390	+	0.443266i	$0.146180\pi$
$883$	159.690	+	1008.24i	0.180849	+	1.14184i	−0.715541	+	0.698571i	$0.753820\pi$
$884$	−495.263	−	160.921i	−0.560253	−	0.182037i
$885$	388.361	+	913.264i	0.438826	+	1.03194i
$886$	227.229	+	699.338i	0.256466	+	0.789320i
$887$	24.1860	+	47.4677i	0.0272672	+	0.0535149i	0.904238	−	0.427028i	$-0.140440\pi$
$887$	24.1860	+	47.4677i	0.0272672	+	0.0535149i	−0.876971	+	0.480543i	$0.840440\pi$
$888$	−115.098	+	58.6456i	−0.129615	+	0.0660423i
$889$	58.1459	−	18.8927i	0.0654059	−	0.0212517i
$890$	−697.925	−	801.813i	−0.784185	−	0.900914i
$891$	11.5003	−	35.3942i	0.0129072	−	0.0397242i
$892$	827.722	−	131.098i	0.927939	−	0.146971i
$893$	457.171	+	457.171i	0.511950	+	0.511950i
$894$	−586.568	+	807.342i	−0.656116	+	0.903067i
$895$	49.9209	−	720.659i	0.0557775	−	0.805206i
$896$	23.8976	−	17.3626i	0.0266714	−	0.0193779i
$897$	193.231	−	1220.01i	0.215420	−	1.36011i
$898$	−27.9098	+	54.7762i	−0.0310800	+	0.0609980i
$899$			1882.47i			2.09396i
$900$	113.798	−	60.6979i	0.126442	−	0.0674421i
$901$	1385.19			1.53739
$902$	−6.02432	−	3.06955i	−0.00667885	−	0.00340304i
$903$	−139.071	−	22.0267i	−0.154010	−	0.0243928i
$904$	−201.046	−	276.715i	−0.222395	−	0.306101i
$905$	52.6174	+	210.452i	0.0581408	+	0.232543i
$906$	628.507	+	456.637i	0.693717	+	0.504015i
$907$	545.754	−	545.754i	0.601714	−	0.601714i	−0.339053	−	0.940767i	$-0.610107\pi$
$907$	545.754	−	545.754i	0.601714	−	0.601714i	0.940767	+	0.339053i	$0.110107\pi$
$908$	34.5533	+	218.161i	0.0380543	+	0.240265i
$909$	147.249	+	47.8441i	0.161990	+	0.0526338i
$910$	225.999	−	19.9209i	0.248350	−	0.0218911i
$911$	286.195	+	880.816i	0.314154	+	0.966868i	0.976101	+	0.217317i	$0.0697305\pi$
$911$	286.195	+	880.816i	0.314154	+	0.966868i	−0.661947	+	0.749551i	$0.730270\pi$
$912$	−35.3950	−	69.4665i	−0.0388103	−	0.0761694i
$913$	33.6015	−	17.1208i	0.0368033	−	0.0187522i
$914$	344.533	−	111.945i	0.376951	−	0.122479i
$915$	−423.589	+	706.013i	−0.462939	+	0.771599i
$916$	8.28186	−	25.4889i	0.00904133	−	0.0278264i
$917$	−280.149	+	44.3712i	−0.305506	+	0.0483873i
$918$	621.676	+	621.676i	0.677207	+	0.677207i
$919$	921.461	−	1268.28i	1.00268	−	1.38007i	0.0790096	−	0.996874i	$-0.474824\pi$
$919$	921.461	−	1268.28i	1.00268	−	1.38007i	0.923668	−	0.383194i	$-0.125176\pi$
$920$	−297.596	−	475.563i	−0.323474	−	0.516916i
$921$	778.150	−	565.359i	0.844897	−	0.613854i
$922$	45.9661	−	290.219i	0.0498548	−	0.314771i
$923$	−298.498	+	585.836i	−0.323400	+	0.634708i
$924$		−	9.63049i		−	0.0104226i
$925$	−359.517	+	271.651i	−0.388667	+	0.293677i
$926$	−421.025			−0.454671
$927$	−86.0785	−	43.8592i	−0.0928571	−	0.0473131i
$928$	−269.090	−	42.6197i	−0.289968	−	0.0459264i
$929$	−166.174	−	228.719i	−0.178874	−	0.246199i	0.710160	−	0.704041i	$-0.248623\pi$
$929$	−166.174	−	228.719i	−0.178874	−	0.246199i	−0.889034	+	0.457842i	$0.848623\pi$
$930$	261.920	−	649.496i	0.281635	−	0.698382i
$931$	−262.510	−	190.725i	−0.281966	−	0.204860i
$932$	−429.670	+	429.670i	−0.461019	+	0.461019i
$933$	−31.7002	−	200.147i	−0.0339766	−	0.214520i
$934$	−302.368	−	98.2453i	−0.323734	−	0.105188i
$935$	−17.2966	+	75.1433i	−0.0184990	+	0.0803672i
$936$	−27.7056	−	85.2690i	−0.0296000	−	0.0910994i
$937$	821.106	+	1611.51i	0.876314	+	1.71986i	0.671418	+	0.741079i	$0.265685\pi$
$937$	821.106	+	1611.51i	0.876314	+	1.71986i	0.204895	+	0.978784i	$0.434315\pi$
$938$	−203.862	+	103.873i	−0.217337	+	0.110739i
$939$	−401.013	+	130.297i	−0.427064	+	0.138762i
$940$	−819.095	−	188.540i	−0.871377	−	0.200575i
$941$	364.832	−	1122.84i	0.387707	−	1.19324i	−0.546790	−	0.837270i	$-0.684150\pi$
$941$	364.832	−	1122.84i	0.387707	−	1.19324i	0.934497	−	0.355970i	$-0.115850\pi$
$942$	−566.917	+	89.7909i	−0.601823	+	0.0953194i
$943$	184.249	+	184.249i	0.195386	+	0.195386i
$944$	184.168	−	253.485i	0.195093	−	0.268523i
$945$	−355.235	−	143.255i	−0.375910	−	0.151592i
$946$	−17.7236	+	12.8770i	−0.0187353	+	0.0136120i
$947$	−204.601	+	1291.80i	−0.216052	+	1.36410i	0.606354	+	0.795195i	$0.292632\pi$
$947$	−204.601	+	1291.80i	−0.216052	+	1.36410i	−0.822405	+	0.568902i	$0.807368\pi$
$948$	53.9704	−	105.923i	0.0569308	−	0.111733i
$949$			418.108i			0.440577i
$950$	−163.953	−	216.983i	−0.172582	−	0.228403i
$951$	−1221.56			−1.28450
$952$	139.414	+	71.0352i	0.146444	+	0.0746168i
$953$	1175.37	+	186.161i	1.23334	+	0.195342i	0.738868	−	0.673850i	$-0.235361\pi$
$953$	1175.37	+	186.161i	1.23334	+	0.195342i	0.494474	+	0.869192i	$0.335361\pi$
$954$	140.179	+	192.940i	0.146938	+	0.202243i
$955$	668.405	−	418.273i	0.699901	−	0.437982i
$956$	463.800	+	336.971i	0.485147	+	0.352480i
$957$	−62.8079	+	62.8079i	−0.0656300	+	0.0656300i
$958$	−50.8513	−	321.063i	−0.0530807	−	0.335138i
$959$	39.7923	+	12.9293i	0.0414936	+	0.0134821i
$960$	86.9123	+	52.1450i	0.0905336	+	0.0543177i
$961$	175.134	+	539.006i	0.182241	+	0.560881i
$962$	142.210	+	279.102i	0.147827	+	0.290127i
$963$	30.7718	−	15.6790i	0.0319541	−	0.0162814i
$964$	−113.115	+	36.7532i	−0.117339	+	0.0381257i
$965$	−47.2358	−	535.880i	−0.0489490	−	0.555316i
$966$	−114.690	+	352.978i	−0.118726	+	0.365402i
$967$	414.000	−	65.5712i	0.428129	−	0.0678089i	0.0613481	−	0.998116i	$-0.480460\pi$
$967$	414.000	−	65.5712i	0.428129	−	0.0678089i	0.366780	+	0.930308i	$0.380460\pi$
$968$	240.940	+	240.940i	0.248905	+	0.248905i
$969$	242.741	−	334.104i	0.250507	−	0.344793i
$970$	−437.744	+	109.445i	−0.451283	+	0.112830i
$971$	−878.393	+	638.190i	−0.904627	+	0.657250i	−0.939650	−	0.342136i	$-0.888850\pi$
$971$	−878.393	+	638.190i	−0.904627	+	0.657250i	0.0350230	+	0.999387i	$0.488850\pi$
$972$	−42.0835	+	265.705i	−0.0432958	+	0.273359i
$973$	236.917	−	464.976i	0.243491	−	0.477879i
$974$		−	625.702i		−	0.642405i
$975$	366.361	+	686.860i	0.375755	+	0.704472i
$976$	259.945			0.266337
$977$	−425.470	−	216.788i	−0.435486	−	0.221891i	0.222483	−	0.974937i	$-0.428584\pi$
$977$	−425.470	−	216.788i	−0.435486	−	0.221891i	−0.657968	+	0.753046i	$0.728584\pi$
$978$	−189.802	−	30.0617i	−0.194072	−	0.0307379i
$979$	64.3153	+	88.5225i	0.0656949	+	0.0904213i
$980$	420.823	+	29.1509i	0.429411	+	0.0297458i
$981$	350.829	+	254.892i	0.357623	+	0.259829i
$982$	712.599	−	712.599i	0.725661	−	0.725661i
$983$	−55.8936	−	352.898i	−0.0568602	−	0.359001i	−0.999670	−	0.0256713i	$-0.991828\pi$
$983$	−55.8936	−	352.898i	−0.0568602	−	0.359001i	0.942810	−	0.333330i	$-0.108172\pi$
$984$	−44.7722	−	14.5474i	−0.0455002	−	0.0147839i
$985$	143.858	−	125.219i	0.146049	−	0.127126i
$986$	−445.954	−	1372.51i	−0.452286	−	1.39199i
$987$	252.446	+	495.454i	0.255771	+	0.501979i
$988$	−168.450	+	85.8293i	−0.170495	+	0.0868718i
$989$	802.962	−	260.898i	0.811893	−	0.263800i
$990$	−12.2169	+	5.19519i	−0.0123403	+	0.00524766i
$991$	−326.239	+	1004.06i	−0.329202	+	1.01318i	0.640307	+	0.768119i	$0.278807\pi$
$991$	−326.239	+	1004.06i	−0.329202	+	1.01318i	−0.969508	+	0.245059i	$0.921193\pi$
$992$	−218.384	+	34.5886i	−0.220145	+	0.0348675i
$993$	−485.590	−	485.590i	−0.489013	−	0.489013i
$994$	116.121	−	159.827i	0.116822	−	0.160792i
$995$	−647.119	+	772.229i	−0.650371	+	0.776110i
$996$	212.427	−	154.337i	0.213280	−	0.154957i
$997$	157.009	−	991.318i	0.157482	−	0.994301i	−0.774705	−	0.632323i	$-0.782102\pi$
$997$	157.009	−	991.318i	0.157482	−	0.994301i	0.932187	−	0.361978i	$-0.117898\pi$
$998$	−265.323	+	520.726i	−0.265855	+	0.521770i
$999$		−	528.849i		−	0.529379i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	50.3.f.a.33.2	✓	16
4.3	odd	2		400.3.bg.a.33.1		16
5.2	odd	4		250.3.f.a.107.2		16
5.3	odd	4		250.3.f.c.107.1		16
5.4	even	2		250.3.f.b.143.1		16
25.3	odd	20		250.3.f.b.7.1		16
25.4	even	10		250.3.f.c.243.1		16
25.21	even	5		250.3.f.a.243.2		16
25.22	odd	20	inner	50.3.f.a.47.2	yes	16
100.47	even	20		400.3.bg.a.97.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
50.3.f.a.33.2	✓	16	1.1	even	1	trivial
50.3.f.a.47.2	yes	16	25.22	odd	20	inner
250.3.f.a.107.2		16	5.2	odd	4
250.3.f.a.243.2		16	25.21	even	5
250.3.f.b.7.1		16	25.3	odd	20
250.3.f.b.143.1		16	5.4	even	2
250.3.f.c.107.1		16	5.3	odd	4
250.3.f.c.243.1		16	25.4	even	10
400.3.bg.a.33.1		16	4.3	odd	2
400.3.bg.a.97.1		16	100.47	even	20

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:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	50.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.26007 + 0.642040i) q^{2} +(2.50268 + 0.396386i) q^{3} +(1.17557 + 1.61803i) q^{4} +(-3.83232 - 3.21144i) q^{5} +(2.89907 + 2.10629i) q^{6} +(-1.84619 + 1.84619i) q^{7} +(0.442463 + 2.79360i) q^{8} +(-2.45322 - 0.797099i) q^{9} +O(q^{10})\)	\(q+(1.26007 + 0.642040i) q^{2} +(2.50268 + 0.396386i) q^{3} +(1.17557 + 1.61803i) q^{4} +(-3.83232 - 3.21144i) q^{5} +(2.89907 + 2.10629i) q^{6} +(-1.84619 + 1.84619i) q^{7} +(0.442463 + 2.79360i) q^{8} +(-2.45322 - 0.797099i) q^{9} +(-2.76713 - 6.50715i) q^{10} +(0.224918 + 0.692225i) q^{11} +(2.30071 + 4.51540i) q^{12} +(10.9494 - 5.57900i) q^{13} +(-3.51167 + 1.14101i) q^{14} +(-8.31810 - 9.55628i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-20.9271 + 3.31453i) q^{17} +(-2.57947 - 2.57947i) q^{18} +(-4.52135 + 6.22310i) q^{19} +(0.691055 - 9.97609i) q^{20} +(-5.35223 + 3.88862i) q^{21} +(-0.161023 + 1.01666i) q^{22} +(18.0093 - 35.3452i) q^{23} +7.16689i q^{24} +(4.37333 + 24.6145i) q^{25} +17.3790 q^{26} +(-26.1430 - 13.3205i) q^{27} +(-5.15753 - 0.816872i) q^{28} +(28.3088 + 38.9637i) q^{29} +(-4.34591 - 17.3822i) q^{30} +(31.6215 + 22.9744i) q^{31} +(-4.00000 + 4.00000i) q^{32} +(0.288509 + 1.82157i) q^{33} +(-28.4978 - 9.25950i) q^{34} +(13.0041 - 1.14626i) q^{35} +(-1.59420 - 4.90644i) q^{36} +(8.18285 + 16.0598i) q^{37} +(-9.69270 + 4.93868i) q^{38} +(29.6143 - 9.62228i) q^{39} +(7.27583 - 12.1269i) q^{40} +(-2.02980 + 6.24709i) q^{41} +(-9.24086 + 1.46361i) q^{42} +(15.0496 + 15.0496i) q^{43} +(-0.855637 + 1.17768i) q^{44} +(6.84168 + 10.9331i) q^{45} +(45.3860 - 32.9749i) q^{46} +(13.1485 - 83.0166i) q^{47} +(-4.60142 + 9.03080i) q^{48} +42.1832i q^{49} +(-10.2928 + 33.8239i) q^{50} -53.6878 q^{51} +(21.8988 + 11.1580i) q^{52} +(-64.5712 - 10.2271i) q^{53} +(-24.3898 - 33.5696i) q^{54} +(1.36108 - 3.37514i) q^{55} +(-5.97440 - 4.34066i) q^{56} +(-13.7822 + 13.7822i) q^{57} +(10.6549 + 67.2725i) q^{58} +(-74.4974 - 24.2057i) q^{59} +(5.68387 - 24.6931i) q^{60} +(-20.0819 - 61.8056i) q^{61} +(25.0950 + 49.2517i) q^{62} +(6.00071 - 3.05752i) q^{63} +(-7.60845 + 2.47214i) q^{64} +(-59.8783 - 13.7828i) q^{65} +(-0.805979 + 2.48055i) q^{66} +(61.2025 - 9.69353i) q^{67} +(-29.9644 - 29.9644i) q^{68} +(59.0818 - 81.3191i) q^{69} +(17.1221 + 6.90478i) q^{70} +(-43.2855 + 31.4488i) q^{71} +(1.14132 - 7.20601i) q^{72} +(-15.4463 + 30.3151i) q^{73} +25.4902i q^{74} +(1.18821 + 63.3358i) q^{75} -15.3843 q^{76} +(-1.69322 - 0.862739i) q^{77} +(43.4941 + 6.88879i) q^{78} +(-13.7883 - 18.9780i) q^{79} +(16.9540 - 10.6095i) q^{80} +(-41.3660 - 30.0541i) q^{81} +(-6.56858 + 6.56858i) q^{82} +(-8.10529 - 51.1748i) q^{83} +(-12.5839 - 4.08874i) q^{84} +(90.8439 + 54.5039i) q^{85} +(9.30114 + 28.6260i) q^{86} +(55.4032 + 108.735i) q^{87} +(-1.83428 + 0.934615i) q^{88} +(142.975 - 46.4555i) q^{89} +(1.60154 + 18.1691i) q^{90} +(-9.91480 + 30.5146i) q^{91} +(78.3609 - 12.4112i) q^{92} +(70.0319 + 70.0319i) q^{93} +(69.8680 - 96.1651i) q^{94} +(37.3123 - 9.32888i) q^{95} +(-11.5963 + 8.42518i) q^{96} +(9.98239 - 63.0263i) q^{97} +(-27.0833 + 53.1539i) q^{98} -1.87746i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9	\( 16 q - 4 q^{2} + 2 q^{3} + 4 q^{6} - 2 q^{7} + 8 q^{8} - 40 q^{9} + 10 q^{10} + 32 q^{11} + 4 q^{12} - 8 q^{13} - 30 q^{14} + 16 q^{16} - 62 q^{17} - 16 q^{18} + 30 q^{19} - 20 q^{20} - 68 q^{21} - 48 q^{22} - 18 q^{23} + 70 q^{25} - 56 q^{26} - 40 q^{27} + 44 q^{28} + 100 q^{29} + 120 q^{30} + 132 q^{31} - 64 q^{32} - 36 q^{33} + 100 q^{34} + 150 q^{35} + 48 q^{36} + 138 q^{37} + 20 q^{38} - 320 q^{39} - 88 q^{41} - 8 q^{42} - 78 q^{43} + 40 q^{44} - 20 q^{45} - 26 q^{46} - 22 q^{47} - 8 q^{48} - 20 q^{50} - 168 q^{51} - 16 q^{52} + 182 q^{53} + 80 q^{54} + 280 q^{55} + 48 q^{56} + 280 q^{57} - 120 q^{58} - 350 q^{59} - 140 q^{60} + 372 q^{61} - 158 q^{62} + 22 q^{63} - 910 q^{65} - 202 q^{66} - 112 q^{67} - 196 q^{68} - 30 q^{69} - 20 q^{70} + 122 q^{71} - 132 q^{72} - 248 q^{73} - 80 q^{75} + 40 q^{76} + 16 q^{77} + 438 q^{78} + 760 q^{79} + 80 q^{80} - 144 q^{81} + 352 q^{82} + 132 q^{83} - 20 q^{84} - 30 q^{85} + 264 q^{86} + 770 q^{87} + 116 q^{88} + 550 q^{89} - 140 q^{90} - 798 q^{91} + 384 q^{92} + 54 q^{93} + 190 q^{94} + 40 q^{95} - 16 q^{96} - 292 q^{97} - 24 q^{98}+O(q^{100}) \) 16 * q - 4 * q^2 + 2 * q^3 + 4 * q^6 - 2 * q^7 + 8 * q^8 - 40 * q^9 + 10 * q^10 + 32 * q^11 + 4 * q^12 - 8 * q^13 - 30 * q^14 + 16 * q^16 - 62 * q^17 - 16 * q^18 + 30 * q^19 - 20 * q^20 - 68 * q^21 - 48 * q^22 - 18 * q^23 + 70 * q^25 - 56 * q^26 - 40 * q^27 + 44 * q^28 + 100 * q^29 + 120 * q^30 + 132 * q^31 - 64 * q^32 - 36 * q^33 + 100 * q^34 + 150 * q^35 + 48 * q^36 + 138 * q^37 + 20 * q^38 - 320 * q^39 - 88 * q^41 - 8 * q^42 - 78 * q^43 + 40 * q^44 - 20 * q^45 - 26 * q^46 - 22 * q^47 - 8 * q^48 - 20 * q^50 - 168 * q^51 - 16 * q^52 + 182 * q^53 + 80 * q^54 + 280 * q^55 + 48 * q^56 + 280 * q^57 - 120 * q^58 - 350 * q^59 - 140 * q^60 + 372 * q^61 - 158 * q^62 + 22 * q^63 - 910 * q^65 - 202 * q^66 - 112 * q^67 - 196 * q^68 - 30 * q^69 - 20 * q^70 + 122 * q^71 - 132 * q^72 - 248 * q^73 - 80 * q^75 + 40 * q^76 + 16 * q^77 + 438 * q^78 + 760 * q^79 + 80 * q^80 - 144 * q^81 + 352 * q^82 + 132 * q^83 - 20 * q^84 - 30 * q^85 + 264 * q^86 + 770 * q^87 + 116 * q^88 + 550 * q^89 - 140 * q^90 - 798 * q^91 + 384 * q^92 + 54 * q^93 + 190 * q^94 + 40 * q^95 - 16 * q^96 - 292 * q^97 - 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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