LMFDB - Embedded newform 73.2.k.a.19.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [73,2,Mod(6,73)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(73, base_ring=CyclotomicField(36))

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

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

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

chi := DirichletCharacter("73.6");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	73.k (of order $36$, degree $12$, 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:	$0.582907934755$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$6$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			19.2
Character	$\chi$	$=$	73.19
Dual form			73.2.k.a.50.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.53348 + 0.558142i) q^{2} +(-1.59146 - 0.918831i) q^{3} +(0.507960 - 0.426229i) q^{4} +(2.94657 - 1.37401i) q^{5} +(2.95332 + 0.520750i) q^{6} +(-1.04180 - 3.88804i) q^{7} +(1.09085 - 1.88940i) q^{8} +(0.188501 + 0.326493i) q^{9} +O(q^{10})$	\(q+(-1.53348 + 0.558142i) q^{2} +(-1.59146 - 0.918831i) q^{3} +(0.507960 - 0.426229i) q^{4} +(2.94657 - 1.37401i) q^{5} +(2.95332 + 0.520750i) q^{6} +(-1.04180 - 3.88804i) q^{7} +(1.09085 - 1.88940i) q^{8} +(0.188501 + 0.326493i) q^{9} +(-3.75163 + 3.75163i) q^{10} +(1.13422 + 2.43235i) q^{11} +(-1.20003 + 0.211598i) q^{12} +(-1.95431 + 1.36842i) q^{13} +(3.76766 + 5.38077i) q^{14} +(-5.95184 - 0.520718i) q^{15} +(-0.848531 + 4.81226i) q^{16} +(2.29570 + 0.615132i) q^{17} +(-0.471293 - 0.395462i) q^{18} +(-2.35136 - 6.46031i) q^{19} +(0.911098 - 1.95386i) q^{20} +(-1.91447 + 7.14490i) q^{21} +(-3.09691 - 3.09691i) q^{22} +(1.12864 - 3.10092i) q^{23} +(-3.47208 + 2.00461i) q^{24} +(3.58044 - 4.26701i) q^{25} +(2.23312 - 3.18923i) q^{26} +4.82018i q^{27} +(-2.18639 - 1.53092i) q^{28} +(5.84480 + 2.72548i) q^{29} +(9.41768 - 2.52346i) q^{30} +(0.748599 + 8.55652i) q^{31} +(-0.627022 - 3.55602i) q^{32} +(0.429845 - 4.91315i) q^{33} +(-3.86375 + 0.338035i) q^{34} +(-8.41193 - 10.0249i) q^{35} +(0.234912 + 0.0855009i) q^{36} +(-0.702095 - 0.255542i) q^{37} +(7.21155 + 8.59439i) q^{38} +(4.36755 - 0.382111i) q^{39} +(0.618203 - 7.06609i) q^{40} +(0.255980 + 1.45174i) q^{41} +(-1.05206 - 12.0251i) q^{42} +(6.15292 - 1.64867i) q^{43} +(1.61288 + 0.752097i) q^{44} +(1.00404 + 0.703033i) q^{45} +5.38515i q^{46} +(-3.45756 + 4.93791i) q^{47} +(5.77206 - 6.87887i) q^{48} +(-7.96933 + 4.60110i) q^{49} +(-3.10895 + 8.54178i) q^{50} +(-3.08832 - 3.08832i) q^{51} +(-0.409449 + 1.52809i) q^{52} +(0.985852 - 2.11417i) q^{53} +(-2.69035 - 7.39167i) q^{54} +(6.68414 + 5.60866i) q^{55} +(-8.48252 - 2.27288i) q^{56} +(-2.19383 + 12.4418i) q^{57} +(-10.4841 - 0.917241i) q^{58} +(2.20711 + 3.15207i) q^{59} +(-3.24524 + 2.27234i) q^{60} +(5.67708 - 1.00102i) q^{61} +(-5.92372 - 12.7035i) q^{62} +(1.07304 - 1.07304i) q^{63} +(-1.94020 - 3.36053i) q^{64} +(-3.87828 + 6.71738i) q^{65} +(2.08308 + 7.77415i) q^{66} +(7.52003 + 1.32598i) q^{67} +(1.42831 - 0.666033i) q^{68} +(-4.64541 + 3.89797i) q^{69} +(18.4949 + 10.6780i) q^{70} +(-1.82847 + 0.665509i) q^{71} +0.822503 q^{72} +(-7.44139 - 4.19830i) q^{73} +1.21928 q^{74} +(-9.61880 + 3.50096i) q^{75} +(-3.94797 - 2.27936i) q^{76} +(8.27544 - 6.94392i) q^{77} +(-6.48430 + 3.02368i) q^{78} +(7.04357 + 1.24197i) q^{79} +(4.11183 + 15.3455i) q^{80} +(4.99444 - 8.65062i) q^{81} +(-1.20282 - 2.08334i) q^{82} +(-3.15944 + 3.15944i) q^{83} +(2.07289 + 4.44533i) q^{84} +(7.60965 - 1.34179i) q^{85} +(-8.51521 + 5.96242i) q^{86} +(-6.79753 - 9.70787i) q^{87} +(5.83295 + 0.510317i) q^{88} +(2.97856 - 16.8923i) q^{89} +(-1.93207 - 0.517695i) q^{90} +(7.35646 + 6.17281i) q^{91} +(-0.748397 - 2.05620i) q^{92} +(6.67063 - 14.3052i) q^{93} +(2.54606 - 9.50201i) q^{94} +(-15.8050 - 15.8050i) q^{95} +(-2.26950 + 6.23540i) q^{96} +(-12.2197 + 7.05505i) q^{97} +(9.65278 - 11.5037i) q^{98} +(-0.580343 + 0.828816i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) $ 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/73\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{31}{36}\right)$

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 $

$2$	−1.53348	+	0.558142i	−1.08434	+	0.394666i	−0.821520	−	0.570180i	$-0.806874\pi$
$2$	−1.53348	+	0.558142i	−1.08434	+	0.394666i	−0.262817	+	0.964846i	$0.584651\pi$
$3$	−1.59146	−	0.918831i	−0.918831	−	0.530487i	−0.0355691	−	0.999367i	$-0.511324\pi$
$3$	−1.59146	−	0.918831i	−0.918831	−	0.530487i	−0.883262	+	0.468880i	$0.844658\pi$
$4$	0.507960	−	0.426229i	0.253980	−	0.213115i
$5$	2.94657	−	1.37401i	1.31775	−	0.614475i	0.368682	−	0.929556i	$-0.379809\pi$
$5$	2.94657	−	1.37401i	1.31775	−	0.614475i	0.949065	+	0.315080i	$0.102031\pi$
$6$	2.95332	+	0.520750i	1.20569	+	0.212595i
$7$	−1.04180	−	3.88804i	−0.393762	−	1.46954i	−0.823878	−	0.566767i	$-0.808194\pi$
$7$	−1.04180	−	3.88804i	−0.393762	−	1.46954i	0.430116	−	0.902774i	$-0.358473\pi$
$8$	1.09085	−	1.88940i	0.385673	−	0.668005i
$9$	0.188501	+	0.326493i	0.0628336	+	0.108831i
$10$	−3.75163	+	3.75163i	−1.18637	+	1.18637i
$11$	1.13422	+	2.43235i	0.341981	+	0.733381i	0.999804	−	0.0197917i	$-0.00630029\pi$
$11$	1.13422	+	2.43235i	0.341981	+	0.733381i	−0.657823	+	0.753173i	$0.728523\pi$
$12$	−1.20003	+	0.211598i	−0.346419	+	0.0610831i
$13$	−1.95431	+	1.36842i	−0.542027	+	0.379532i	−0.812289	−	0.583255i	$-0.801779\pi$
$13$	−1.95431	+	1.36842i	−0.542027	+	0.379532i	0.270262	+	0.962787i	$0.412890\pi$
$14$	3.76766	+	5.38077i	1.00695	+	1.43807i
$15$	−5.95184	−	0.520718i	−1.53676	−	0.134449i
$16$	−0.848531	+	4.81226i	−0.212133	+	1.20306i
$17$	2.29570	+	0.615132i	0.556790	+	0.149191i	0.526231	−	0.850342i	$-0.323605\pi$
$17$	2.29570	+	0.615132i	0.556790	+	0.149191i	0.0305586	+	0.999533i	$0.490271\pi$
$18$	−0.471293	−	0.395462i	−0.111085	−	0.0932112i
$19$	−2.35136	−	6.46031i	−0.539439	−	1.48210i	−0.847534	−	0.530741i	$-0.821914\pi$
$19$	−2.35136	−	6.46031i	−0.539439	−	1.48210i	0.308095	−	0.951356i	$-0.400309\pi$
$20$	0.911098	−	1.95386i	0.203728	−	0.436895i
$21$	−1.91447	+	7.14490i	−0.417772	+	1.55915i
$22$	−3.09691	−	3.09691i	−0.660263	−	0.660263i
$23$	1.12864	−	3.10092i	0.235338	−	0.646587i	−0.764659	−	0.644435i	$-0.777093\pi$
$23$	1.12864	−	3.10092i	0.235338	−	0.646587i	0.999998	−	0.00215199i	$-0.000685002\pi$
$24$	−3.47208	+	2.00461i	−0.708736	+	0.409189i
$25$	3.58044	−	4.26701i	0.716089	−	0.853401i
$26$	2.23312	−	3.18923i	0.437952	−	0.625460i
$27$			4.82018i			0.927645i
$28$	−2.18639	−	1.53092i	−0.413188	−	0.289318i
$29$	5.84480	+	2.72548i	1.08535	+	0.506108i	0.881158	−	0.472822i	$-0.156765\pi$
$29$	5.84480	+	2.72548i	1.08535	+	0.506108i	0.204194	+	0.978930i	$0.434543\pi$
$30$	9.41768	−	2.52346i	1.71943	−	0.460719i
$31$	0.748599	+	8.55652i	0.134452	+	1.53680i	0.701236	+	0.712930i	$0.252632\pi$
$31$	0.748599	+	8.55652i	0.134452	+	1.53680i	−0.566783	+	0.823867i	$0.691812\pi$
$32$	−0.627022	−	3.55602i	−0.110843	−	0.628622i
$33$	0.429845	−	4.91315i	0.0748264	−	0.855270i
$34$	−3.86375	+	0.338035i	−0.662628	+	0.0579724i
$35$	−8.41193	−	10.0249i	−1.42188	−	1.69453i
$36$	0.234912	+	0.0855009i	0.0391520	+	0.0142502i
$37$	−0.702095	−	0.255542i	−0.115424	−	0.0420108i	0.283663	−	0.958924i	$-0.408450\pi$
$37$	−0.702095	−	0.255542i	−0.115424	−	0.0420108i	−0.399086	+	0.916913i	$0.630673\pi$
$38$	7.21155	+	8.59439i	1.16987	+	1.39419i
$39$	4.36755	−	0.382111i	0.699368	−	0.0611868i
$40$	0.618203	−	7.06609i	0.0977465	−	1.11725i
$41$	0.255980	+	1.45174i	0.0399774	+	0.226723i	0.998250	−	0.0591323i	$-0.0188334\pi$
$41$	0.255980	+	1.45174i	0.0399774	+	0.226723i	−0.958273	+	0.285855i	$0.907722\pi$
$42$	−1.05206	−	12.0251i	−0.162337	−	1.85552i
$43$	6.15292	−	1.64867i	0.938312	−	0.251420i	0.242917	−	0.970047i	$-0.421896\pi$
$43$	6.15292	−	1.64867i	0.938312	−	0.251420i	0.695395	+	0.718627i	$0.255229\pi$
$44$	1.61288	+	0.752097i	0.243151	+	0.113383i
$45$	1.00404	+	0.703033i	0.149673	+	0.104802i
$46$			5.38515i			0.793998i
$47$	−3.45756	+	4.93791i	−0.504337	+	0.720268i	−0.987909	−	0.155037i	$-0.950450\pi$
$47$	−3.45756	+	4.93791i	−0.504337	+	0.720268i	0.483572	+	0.875305i	$0.339339\pi$
$48$	5.77206	−	6.87887i	0.833125	−	0.992879i
$49$	−7.96933	+	4.60110i	−1.13848	+	0.657300i
$50$	−3.10895	+	8.54178i	−0.439672	+	1.20799i
$51$	−3.08832	−	3.08832i	−0.432451	−	0.432451i
$52$	−0.409449	+	1.52809i	−0.0567804	+	0.211907i
$53$	0.985852	−	2.11417i	0.135417	−	0.290403i	−0.826892	−	0.562361i	$-0.809893\pi$
$53$	0.985852	−	2.11417i	0.135417	−	0.290403i	0.962309	+	0.271958i	$0.0876711\pi$
$54$	−2.69035	−	7.39167i	−0.366110	−	1.00588i
$55$	6.68414	+	5.60866i	0.901289	+	0.756271i
$56$	−8.48252	−	2.27288i	−1.13352	−	0.303727i
$57$	−2.19383	+	12.4418i	−0.290580	+	1.64796i
$58$	−10.4841	−	0.917241i	−1.37663	−	0.120440i
$59$	2.20711	+	3.15207i	0.287341	+	0.410365i	0.936709	−	0.350109i	$-0.113856\pi$
$59$	2.20711	+	3.15207i	0.287341	+	0.410365i	−0.649368	+	0.760474i	$0.724967\pi$
$60$	−3.24524	+	2.27234i	−0.418959	+	0.293358i
$61$	5.67708	−	1.00102i	0.726875	−	0.128168i	0.202047	−	0.979376i	$-0.435241\pi$
$61$	5.67708	−	1.00102i	0.726875	−	0.128168i	0.524828	+	0.851208i	$0.324130\pi$
$62$	−5.92372	−	12.7035i	−0.752313	−	1.61334i
$63$	1.07304	−	1.07304i	0.135190	−	0.135190i
$64$	−1.94020	−	3.36053i	−0.242525	−	0.420066i
$65$	−3.87828	+	6.71738i	−0.481042	+	0.833189i
$66$	2.08308	+	7.77415i	0.256409	+	0.956932i
$67$	7.52003	+	1.32598i	0.918718	+	0.161995i	0.612959	−	0.790114i	$-0.289979\pi$
$67$	7.52003	+	1.32598i	0.918718	+	0.161995i	0.305758	+	0.952109i	$0.401090\pi$
$68$	1.42831	−	0.666033i	0.173208	−	0.0807683i
$69$	−4.64541	+	3.89797i	−0.559242	+	0.469260i
$70$	18.4949	+	10.6780i	2.21056	+	1.27627i
$71$	−1.82847	+	0.665509i	−0.217000	+	0.0789814i	−0.448232	−	0.893917i	$-0.647946\pi$
$71$	−1.82847	+	0.665509i	−0.217000	+	0.0789814i	0.231233	+	0.972898i	$0.425724\pi$
$72$	0.822503			0.0969329
$73$	−7.44139	−	4.19830i	−0.870949	−	0.491374i
$73$	−7.44139	−	4.19830i	−0.870949	−	0.491374i
$74$	1.21928			0.141738
$75$	−9.61880	+	3.50096i	−1.11068	+	0.404256i
$76$	−3.94797	−	2.27936i	−0.452863	−	0.261461i
$77$	8.27544	−	6.94392i	0.943074	−	0.791333i
$78$	−6.48430	+	3.02368i	−0.734202	+	0.342364i
$79$	7.04357	+	1.24197i	0.792464	+	0.139733i	0.555205	−	0.831714i	$-0.312640\pi$
$79$	7.04357	+	1.24197i	0.792464	+	0.139733i	0.237259	+	0.971446i	$0.423751\pi$
$80$	4.11183	+	15.3455i	0.459716	+	1.71568i
$81$	4.99444	−	8.65062i	0.554938	−	0.961180i
$82$	−1.20282	−	2.08334i	−0.132829	−	0.230066i
$83$	−3.15944	+	3.15944i	−0.346794	+	0.346794i	−0.858914	−	0.512120i	$-0.828860\pi$
$83$	−3.15944	+	3.15944i	−0.346794	+	0.346794i	0.512120	+	0.858914i	$0.328860\pi$
$84$	2.07289	+	4.44533i	0.226171	+	0.485025i
$85$	7.60965	−	1.34179i	0.825382	−	0.145537i
$86$	−8.51521	+	5.96242i	−0.918219	+	0.642944i
$87$	−6.79753	−	9.70787i	−0.728771	−	1.04079i
$88$	5.83295	+	0.510317i	0.621795	+	0.0544000i
$89$	2.97856	−	16.8923i	0.315727	−	1.79058i	−0.252388	−	0.967626i	$-0.581216\pi$
$89$	2.97856	−	16.8923i	0.315727	−	1.79058i	0.568115	−	0.822949i	$-0.307673\pi$
$90$	−1.93207	−	0.517695i	−0.203658	−	0.0545699i
$91$	7.35646	+	6.17281i	0.771167	+	0.647086i
$92$	−0.748397	−	2.05620i	−0.0780258	−	0.214374i
$93$	6.67063	−	14.3052i	0.691712	−	1.48338i
$94$	2.54606	−	9.50201i	0.262606	−	0.980058i
$95$	−15.8050	−	15.8050i	−1.62156	−	1.62156i
$96$	−2.26950	+	6.23540i	−0.231630	+	0.636398i
$97$	−12.2197	+	7.05505i	−1.24072	+	0.716332i	−0.969241	−	0.246112i	$-0.920847\pi$
$97$	−12.2197	+	7.05505i	−1.24072	+	0.716332i	−0.271481	+	0.962444i	$0.587513\pi$
$98$	9.65278	−	11.5037i	0.975078	−	1.16205i
$99$	−0.580343	+	0.828816i	−0.0583267	+	0.0832992i
$100$		−	3.69356i		−	0.369356i
$101$	3.49469	+	2.44701i	0.347735	+	0.243487i	0.734375	−	0.678744i	$-0.237475\pi$
$101$	3.49469	+	2.44701i	0.347735	+	0.243487i	−0.386640	+	0.922231i	$0.626364\pi$
$102$	6.45961	+	3.01217i	0.639597	+	0.298249i
$103$	−12.1452	+	3.25430i	−1.19670	+	0.320655i	−0.801532	−	0.597952i	$-0.795981\pi$
$103$	−12.1452	+	3.25430i	−1.19670	+	0.320655i	−0.395171	+	0.918608i	$0.629315\pi$
$104$	0.453647	+	5.18521i	0.0444838	+	0.508452i
$105$	4.17603	+	23.6835i	0.407539	+	2.31127i
$106$	−0.331782	+	3.79228i	−0.0322255	+	0.368339i
$107$	5.29841	−	0.463551i	0.512216	−	0.0448131i	0.171882	−	0.985118i	$-0.445015\pi$
$107$	5.29841	−	0.463551i	0.512216	−	0.0448131i	0.340335	+	0.940304i	$0.389460\pi$
$108$	2.05450	+	2.44846i	0.197695	+	0.235603i
$109$	3.20934	+	1.16811i	0.307399	+	0.111884i	0.491114	−	0.871095i	$-0.336590\pi$
$109$	3.20934	+	1.16811i	0.307399	+	0.111884i	−0.183714	+	0.982980i	$0.558812\pi$
$110$	−13.3804	−	4.87008i	−1.27578	−	0.464344i
$111$	0.882558	+	1.05179i	0.0837687	+	0.0998317i
$112$	19.5942	−	1.71427i	1.85148	−	0.161984i
$113$	−1.18746	+	13.5728i	−0.111707	+	1.27682i	0.708893	+	0.705316i	$0.249195\pi$
$113$	−1.18746	+	13.5728i	−0.111707	+	1.27682i	−0.820600	+	0.571503i	$0.806361\pi$
$114$	−3.58011	−	20.3038i	−0.335308	−	1.90163i
$115$	−0.935066	−	10.6878i	−0.0871953	−	0.996647i
$116$	4.13060	−	1.10679i	0.383517	−	0.102763i
$117$	−0.815169	−	0.380119i	−0.0753624	−	0.0351420i
$118$	−5.14386	−	3.60177i	−0.473531	−	0.331570i
$119$		−	9.56662i		−	0.876971i
$120$	−7.47639	+	10.6774i	−0.682498	+	0.974708i
$121$	2.44080	−	2.90884i	0.221891	−	0.264440i
$122$	−8.14699	+	4.70367i	−0.737594	+	0.425850i
$123$	0.926517	−	2.54559i	0.0835413	−	0.229528i
$124$	4.02730	+	4.02730i	0.361662	+	0.361662i
$125$	0.479789	−	1.79060i	0.0429136	−	0.160156i
$126$	−1.04658	+	2.24440i	−0.0932367	+	0.199947i
$127$	0.509050	+	1.39860i	0.0451709	+	0.124106i	0.960227	−	0.279221i	$-0.0900761\pi$
$127$	0.509050	+	1.39860i	0.0451709	+	0.124106i	−0.915056	+	0.403327i	$0.867854\pi$
$128$	10.3831	+	8.71246i	0.917745	+	0.770080i
$129$	−11.3070	−	3.02970i	−0.995525	−	0.266750i
$130$	2.19803	−	12.4656i	0.192780	−	1.09331i
$131$	19.8807	+	1.73933i	1.73698	+	0.151966i	0.911185	−	0.411998i	$-0.135169\pi$
$131$	19.8807	+	1.73933i	1.73698	+	0.151966i	0.825799	+	0.563965i	$0.190725\pi$
$132$	−1.87578	−	2.67890i	−0.163266	−	0.233168i
$133$	−22.6683	+	15.8725i	−1.96559	+	1.37632i
$134$	−12.2719	+	2.16387i	−1.06013	+	0.186930i
$135$	6.62297	+	14.2030i	0.570015	+	1.22240i
$136$	3.66649	−	3.66649i	0.314399	−	0.314399i
$137$	3.79049	+	6.56532i	0.323843	+	0.560913i	0.981278	−	0.192599i	$-0.0616915\pi$
$137$	3.79049	+	6.56532i	0.323843	+	0.560913i	−0.657434	+	0.753512i	$0.728358\pi$
$138$	4.94805	−	8.57027i	0.421206	−	0.729550i
$139$	−4.81737	−	17.9787i	−0.408604	−	1.52493i	−0.797311	−	0.603569i	$-0.793745\pi$
$139$	−4.81737	−	17.9787i	−0.408604	−	1.52493i	0.388707	−	0.921362i	$-0.372922\pi$
$140$	−8.54585	−	1.50686i	−0.722256	−	0.127353i
$141$	10.0397	−	4.68158i	0.845494	−	0.394260i
$142$	2.43248	−	2.04110i	0.204129	−	0.171285i
$143$	−5.54510	−	3.20146i	−0.463704	−	0.267720i
$144$	−1.73112	+	0.630075i	−0.144260	+	0.0525063i
$145$	20.9669			1.74121
$146$	13.7545	+	2.28466i	1.13833	+	0.189080i
$147$	16.9105			1.39476
$148$	−0.465556	+	0.169448i	−0.0382684	+	0.0139286i
$149$	−9.30837	−	5.37419i	−0.762572	−	0.440271i	0.0676467	−	0.997709i	$-0.478451\pi$
$149$	−9.30837	−	5.37419i	−0.762572	−	0.440271i	−0.830218	+	0.557438i	$0.811784\pi$
$150$	12.7962	−	10.7373i	1.04481	−	0.876698i
$151$	−12.9717	+	6.04880i	−1.05562	+	0.492244i	−0.871366	−	0.490634i	$-0.836765\pi$
$151$	−12.9717	+	6.04880i	−1.05562	+	0.492244i	−0.184256	+	0.982878i	$0.558987\pi$
$152$	−14.7711	−	2.60454i	−1.19809	−	0.211256i
$153$	0.231906	+	0.865484i	0.0187485	+	0.0699702i
$154$	−8.81456	+	15.2673i	−0.710297	+	1.23027i
$155$	13.9625	+	24.1838i	1.12150	+	1.94249i
$156$	2.05568	−	2.05568i	0.164586	−	0.164586i
$157$	−3.37420	−	7.23600i	−0.269291	−	0.577495i	0.724435	−	0.689343i	$-0.242101\pi$
$157$	−3.37420	−	7.23600i	−0.269291	−	0.577495i	−0.993725	+	0.111848i	$0.964323\pi$
$158$	−11.4944	+	2.02677i	−0.914445	+	0.161241i
$159$	−3.51151	+	2.45878i	−0.278481	+	0.194994i
$160$	−6.73357	−	9.61653i	−0.532335	−	0.760254i
$161$	−13.2323	−	1.15768i	−1.04285	−	0.0912378i
$162$	−2.83061	+	16.0532i	−0.222394	+	1.26126i
$163$	1.20651	+	0.323284i	0.0945014	+	0.0253216i	0.305760	−	0.952109i	$-0.401090\pi$
$163$	1.20651	+	0.323284i	0.0945014	+	0.0253216i	−0.211258	+	0.977430i	$0.567756\pi$
$164$	0.748800	+	0.628318i	0.0584715	+	0.0490634i
$165$	−5.48414	−	15.0676i	−0.426940	−	1.17301i
$166$	3.08153	−	6.60837i	0.239173	−	0.512909i
$167$	2.55446	−	9.53339i	0.197670	−	0.737716i	−0.793889	−	0.608063i	$-0.791947\pi$
$167$	2.55446	−	9.53339i	0.197670	−	0.737716i	0.991559	−	0.129653i	$-0.0413864\pi$
$168$	11.4112	+	11.4112i	0.880394	+	0.880394i
$169$	−2.49952	+	6.86738i	−0.192271	+	0.528260i
$170$	−10.9204	+	6.30487i	−0.837553	+	0.483562i
$171$	1.66601	−	1.98548i	0.127403	−	0.151833i
$172$	2.42273	−	3.46001i	0.184731	−	0.263824i
$173$			9.75110i			0.741363i	0.928760	+	0.370681i	$0.120876\pi$
$173$			9.75110i			0.741363i	−0.928760	+	0.370681i	$0.879124\pi$
$174$	15.8423	+	11.0929i	1.20100	+	0.840949i
$175$	−20.3204	−	9.47555i	−1.53608	−	0.716284i
$176$	−12.6675	+	3.39425i	−0.954850	+	0.255851i
$177$	−0.616302	−	7.04436i	−0.0463241	−	0.529487i
$178$	4.86071	+	27.5664i	0.364326	+	2.06619i
$179$	−1.64024	+	18.7481i	−0.122598	+	1.40130i	0.646864	+	0.762605i	$0.276080\pi$
$179$	−1.64024	+	18.7481i	−0.122598	+	1.40130i	−0.769462	+	0.638692i	$0.779476\pi$
$180$	0.809663	−	0.0708364i	0.0603487	−	0.00527983i
$181$	−10.9480	−	13.0473i	−0.813755	−	0.969796i	0.186164	−	0.982519i	$-0.440395\pi$
$181$	−10.9480	−	13.0473i	−0.813755	−	0.969796i	−0.999919	+	0.0127229i	$0.995950\pi$
$182$	−14.7263	−	5.35994i	−1.09159	−	0.397305i
$183$	−9.95462	−	3.62319i	−0.735867	−	0.267834i
$184$	−4.62771	−	5.51509i	−0.341159	−	0.406578i
$185$	−2.41989	+	0.211713i	−0.177914	+	0.0155654i
$186$	−2.24496	+	25.6600i	−0.164608	+	1.88148i
$187$	1.10762	+	6.28165i	0.0809975	+	0.459359i
$188$	0.348378	+	3.98197i	0.0254080	+	0.290415i
$189$	18.7411	−	5.02165i	1.36321	−	0.365272i
$190$	33.0581	+	15.4152i	2.39829	+	1.11834i
$191$	−0.354086	−	0.247934i	−0.0256207	−	0.0179398i	0.560696	−	0.828022i	$-0.310534\pi$
$191$	−0.354086	−	0.247934i	−0.0256207	−	0.0179398i	−0.586317	+	0.810082i	$0.699423\pi$
$192$			7.13087i			0.514626i
$193$	−4.37022	+	6.24132i	−0.314575	+	0.449260i	−0.945038	−	0.326959i	$-0.893976\pi$
$193$	−4.37022	+	6.24132i	−0.314575	+	0.449260i	0.630463	+	0.776219i	$0.282865\pi$
$194$	14.8010	−	17.6391i	1.06265	−	1.26642i
$195$	12.3443	−	7.12697i	0.883992	−	0.510373i
$196$	−2.08698	+	5.73394i	−0.149070	+	0.409567i
$197$	−5.18078	−	5.18078i	−0.369115	−	0.369115i	0.498039	−	0.867155i	$-0.334054\pi$
$197$	−5.18078	−	5.18078i	−0.369115	−	0.369115i	−0.867155	+	0.498039i	$0.834054\pi$
$198$	0.427350	−	1.59489i	0.0303704	−	0.113344i
$199$	−5.36988	+	11.5157i	−0.380660	+	0.816329i	0.618864	+	0.785498i	$0.287593\pi$
$199$	−5.36988	+	11.5157i	−0.380660	+	0.816329i	−0.999525	+	0.0308309i	$0.990185\pi$
$200$	−4.15638	−	11.4196i	−0.293900	−	0.807484i
$201$	−10.7495	−	9.01989i	−0.758210	−	0.636214i
$202$	−6.72483	−	1.80191i	−0.473158	−	0.126782i
$203$	4.50766	−	25.5642i	0.316376	−	1.79426i
$204$	−2.88508	−	0.252411i	−0.201996	−	0.0176723i
$205$	2.74896	+	3.92592i	0.191996	+	0.274198i
$206$	16.8081	−	11.7692i	1.17108	−	0.819996i
$207$	1.22518	−	0.216032i	0.0851559	−	0.0150153i
$208$	−4.92690	−	10.5658i	−0.341619	−	0.732605i
$209$	13.0468	−	13.0468i	0.902463	−	0.902463i
$210$	−19.6226	−	33.9874i	−1.35409	−	2.34535i
$211$	4.84920	−	8.39905i	0.333832	−	0.578215i	−0.649427	−	0.760424i	$-0.724991\pi$
$211$	4.84920	−	8.39905i	0.333832	−	0.578215i	0.983260	+	0.182209i	$0.0583247\pi$
$212$	−0.400346	−	1.49411i	−0.0274959	−	0.102616i
$213$	3.52143	+	0.620924i	0.241285	+	0.0425450i
$214$	−7.86629	+	3.66811i	−0.537729	+	0.250747i
$215$	15.8647	−	13.3121i	1.08197	−	0.907877i
$216$	9.10727	+	5.25808i	0.619671	+	0.357767i
$217$	32.4882	−	11.8247i	2.20544	−	0.802716i
$218$	−5.57344			−0.377481
$219$	7.98516	+	13.5188i	0.539587	+	0.913517i
$220$	5.78585			0.390082
$221$	−5.32827	+	1.93933i	−0.358418	+	0.130453i
$222$	−1.94044	−	1.12031i	−0.130234	−	0.0751904i
$223$	−5.21089	+	4.37245i	−0.348947	+	0.292801i	−0.800367	−	0.599510i	$-0.795362\pi$
$223$	−5.21089	+	4.37245i	−0.348947	+	0.292801i	0.451420	+	0.892312i	$0.350918\pi$
$224$	−13.1727	+	6.14254i	−0.880139	+	0.410416i
$225$	2.06807	+	0.364656i	0.137871	+	0.0243104i
$226$	−5.75458	−	21.4764i	−0.382789	−	1.42859i
$227$	6.94784	−	12.0340i	0.461144	−	0.798725i	−0.537874	−	0.843025i	$-0.680772\pi$
$227$	6.94784	−	12.0340i	0.461144	−	0.798725i	0.999018	+	0.0442999i	$0.0141057\pi$
$228$	4.18870	+	7.25503i	0.277403	+	0.480476i
$229$	5.23853	−	5.23853i	0.346172	−	0.346172i	−0.512509	−	0.858682i	$-0.671284\pi$
$229$	5.23853	−	5.23853i	0.346172	−	0.346172i	0.858682	+	0.512509i	$0.171284\pi$
$230$	7.39925	+	15.8677i	0.487892	+	1.04629i
$231$	−19.5503	+	3.44725i	−1.28632	+	0.226813i
$232$	11.5253	−	8.07011i	0.756673	−	0.529828i
$233$	−3.77013	−	5.38430i	−0.246989	−	0.352737i	0.676445	−	0.736493i	$-0.263519\pi$
$233$	−3.77013	−	5.38430i	−0.246989	−	0.352737i	−0.923435	+	0.383755i	$0.874631\pi$
$234$	1.46221	+	0.127927i	0.0955875	+	0.00836283i
$235$	−3.40322	+	19.3006i	−0.222002	+	1.25903i
$236$	2.46463	+	0.660395i	0.160434	+	0.0429880i
$237$	−10.0684	−	8.44840i	−0.654014	−	0.548783i
$238$	5.33954	+	14.6703i	0.346111	+	0.950932i
$239$	−9.69171	+	20.7839i	−0.626904	+	1.34440i	0.294446	+	0.955668i	$0.404865\pi$
$239$	−9.69171	+	20.7839i	−0.626904	+	1.34440i	−0.921351	+	0.388733i	$0.872913\pi$
$240$	7.55615	−	28.1999i	0.487747	−	1.82030i
$241$	−13.2947	−	13.2947i	−0.856388	−	0.856388i	0.134522	−	0.990911i	$-0.457050\pi$
$241$	−13.2947	−	13.2947i	−0.856388	−	0.856388i	−0.990911	+	0.134522i	$0.957050\pi$
$242$	−2.11939	+	5.82297i	−0.136239	+	0.374314i
$243$	−3.37371	+	1.94781i	−0.216424	+	0.124952i
$244$	2.45706	−	2.92821i	0.157297	−	0.187460i
$245$	−17.1603	+	24.5074i	−1.09633	+	1.56572i
$246$			4.42074i			0.281856i
$247$	13.4357	+	9.40778i	0.854893	+	0.598603i
$248$	16.9833	+	7.91945i	1.07844	+	0.502886i
$249$	7.93112	−	2.12514i	0.502614	−	0.134675i
$250$	0.263659	+	3.01364i	0.0166753	+	0.190599i
$251$	2.13291	+	12.0963i	0.134628	+	0.763513i	0.975118	+	0.221686i	$0.0711560\pi$
$251$	2.13291	+	12.0963i	0.134628	+	0.763513i	−0.840490	+	0.541827i	$0.817733\pi$
$252$	0.0877005	−	1.00242i	0.00552461	−	0.0631466i
$253$	8.82265	−	0.771882i	0.554676	−	0.0485278i
$254$	−1.56124	−	1.86061i	−0.0979609	−	0.116745i
$255$	−13.3433	−	4.85658i	−0.835592	−	0.304131i
$256$	−13.4923	−	4.91081i	−0.843271	−	0.306926i
$257$	9.09487	+	10.8388i	0.567322	+	0.676109i	0.971079	−	0.238758i	$-0.0767402\pi$
$257$	9.09487	+	10.8388i	0.567322	+	0.676109i	−0.403757	+	0.914866i	$0.632296\pi$
$258$	19.0301	−	1.66492i	1.18476	−	0.103653i
$259$	−0.262116	+	2.99600i	−0.0162871	+	0.186162i
$260$	0.893131	+	5.06520i	0.0553896	+	0.314130i
$261$	0.211901	+	2.42204i	0.0131164	+	0.149921i
$262$	−31.4575	+	8.42901i	−1.94345	+	0.520746i
$263$	5.27249	+	2.45860i	0.325116	+	0.151604i	0.578322	−	0.815808i	$-0.303708\pi$
$263$	5.27249	+	2.45860i	0.325116	+	0.151604i	−0.253207	+	0.967412i	$0.581485\pi$
$264$	−8.81403	−	6.17165i	−0.542466	−	0.379839i
$265$		−	7.58411i		−	0.465888i
$266$	25.9023	−	36.9924i	1.58817	−	2.26815i
$267$	−20.2614	+	24.1466i	−1.23998	+	1.47775i
$268$	4.38505	−	2.53171i	0.267859	−	0.154649i
$269$	−3.48151	+	9.56536i	−0.212271	+	0.583211i	−0.999438	−	0.0335301i	$-0.989325\pi$
$269$	−3.48151	+	9.56536i	−0.212271	+	0.583211i	0.787166	+	0.616741i	$0.211547\pi$
$270$	−18.0835	−	18.0835i	−1.10053	−	1.10053i
$271$	−1.40171	+	5.23124i	−0.0851476	+	0.317775i	−0.995342	−	0.0964059i	$-0.969265\pi$
$271$	−1.40171	+	5.23124i	−0.0851476	+	0.317775i	0.910195	+	0.414181i	$0.135932\pi$
$272$	−4.90815	+	10.5256i	−0.297600	+	0.638205i
$273$	−6.03577	−	16.5831i	−0.365301	−	1.00366i
$274$	−9.47704	−	7.95218i	−0.572529	−	0.480409i
$275$	14.4399	+	3.86915i	0.870757	+	0.233319i
$276$	−0.698259	+	3.96002i	−0.0420302	+	0.238365i
$277$	−2.94934	−	0.258034i	−0.177209	−	0.0155037i	−0.00179397	−	0.999998i	$-0.500571\pi$
$277$	−2.94934	−	0.258034i	−0.177209	−	0.0155037i	−0.175415	+	0.984495i	$0.556127\pi$
$278$	17.4220	+	24.8812i	1.04490	+	1.49228i
$279$	−2.65253	+	1.85732i	−0.158803	+	0.111195i
$280$	−28.1173	+	4.95784i	−1.68033	+	0.296287i
$281$	−8.70947	−	18.6775i	−0.519564	−	1.11421i	−0.974645	−	0.223758i	$-0.928168\pi$
$281$	−8.70947	−	18.6775i	−0.519564	−	1.11421i	0.455081	−	0.890450i	$-0.349610\pi$
$282$	−12.7827	+	12.7827i	−0.761199	+	0.761199i
$283$	9.03931	+	15.6565i	0.537331	+	0.930685i	0.999047	+	0.0436569i	$0.0139008\pi$
$283$	9.03931	+	15.6565i	0.537331	+	0.930685i	−0.461715	+	0.887028i	$0.652766\pi$
$284$	−0.645131	+	1.11740i	−0.0382815	+	0.0663055i
$285$	10.6309	+	39.6751i	0.629721	+	2.35015i
$286$	10.2902	+	1.81444i	0.608471	+	0.107290i
$287$	5.37773	−	2.50768i	0.317437	−	0.148023i
$288$	1.04282	−	0.875032i	0.0614489	−	0.0515617i
$289$	−9.83057	−	5.67568i	−0.578269	−	0.333864i
$290$	−32.1525	+	11.7025i	−1.88806	+	0.687197i
$291$	25.9296			1.52002
$292$	−5.56937	+	1.03917i	−0.325922	+	0.0608128i
$293$	−23.8196			−1.39156			−0.695779	−	0.718256i	$-0.744941\pi$
$293$	−23.8196			−1.39156			−0.695779	+	0.718256i	$0.744941\pi$
$294$	−25.9320	+	9.43848i	−1.51239	+	0.550463i
$295$	10.8344	+	6.25522i	0.630801	+	0.364193i
$296$	−1.24870	+	1.04778i	−0.0725792	+	0.0609012i
$297$	−11.7244	+	5.46716i	−0.680317	+	0.317237i
$298$	17.2738	+	3.04584i	1.00064	+	0.176441i
$299$	2.03765	+	7.60461i	0.117840	+	0.439786i
$300$	−3.39376	+	5.87816i	−0.195939	+	0.339376i
$301$	−12.8202	−	22.2052i	−0.738944	−	1.27989i
$302$	16.5158	−	16.5158i	0.950377	−	0.950377i
$303$	−3.31328	−	7.10535i	−0.190343	−	0.408192i
$304$	33.0839	−	5.83358i	1.89749	−	0.334579i
$305$	15.3525	−	10.7499i	0.879081	−	0.615539i
$306$	−0.838687	−	1.19777i	−0.0479445	−	0.0684719i
$307$	−2.15968	−	0.188948i	−0.123260	−	0.0107838i	0.0253590	−	0.999678i	$-0.491927\pi$
$307$	−2.15968	−	0.188948i	−0.123260	−	0.0107838i	−0.148619	+	0.988895i	$0.547483\pi$
$308$	1.24389	−	7.05447i	0.0708774	−	0.401966i
$309$	22.3188	+	5.98030i	1.26967	+	0.340207i
$310$	−34.9093	−	29.2924i	−1.98272	−	1.66370i
$311$	−4.33175	−	11.9014i	−0.245631	−	0.674866i	−0.999834	−	0.0182245i	$-0.994199\pi$
$311$	−4.33175	−	11.9014i	−0.245631	−	0.674866i	0.754203	−	0.656642i	$-0.228024\pi$
$312$	4.04237	−	8.66889i	0.228854	−	0.490779i
$313$	−2.27221	+	8.47998i	−0.128433	+	0.479317i	−0.999939	−	0.0110675i	$-0.996477\pi$
$313$	−2.27221	+	8.47998i	−0.128433	+	0.479317i	0.871506	+	0.490385i	$0.163144\pi$
$314$	9.21300	+	9.21300i	0.519920	+	0.519920i
$315$	1.68742	−	4.63615i	0.0950754	−	0.261217i
$316$	4.10722	−	2.37130i	0.231049	−	0.133396i
$317$	−2.04053	+	2.43181i	−0.114608	+	0.136584i	−0.820298	−	0.571936i	$-0.806192\pi$
$317$	−2.04053	+	2.43181i	−0.114608	+	0.136584i	0.705691	+	0.708520i	$0.250637\pi$
$318$	4.01249	−	5.73042i	0.225009	−	0.321346i
$319$			17.3079i			0.969056i
$320$	−10.3343	−	7.23618i	−0.577707	−	0.404515i
$321$	−8.85814	−	4.13062i	−0.494413	−	0.230549i
$322$	20.9377	−	5.61024i	1.16681	−	0.312646i
$323$	−1.42408	−	16.2773i	−0.0792381	−	0.905696i
$324$	−1.15017	−	6.52294i	−0.0638984	−	0.362386i
$325$	−1.15823	+	13.2386i	−0.0642468	+	0.734345i
$326$	−2.03061	+	0.177655i	−0.112465	+	0.00983941i
$327$	−4.03426	−	4.80784i	−0.223095	−	0.265874i
$328$	3.02215	+	1.09997i	0.166870	+	0.0607358i
$329$	22.8009	+	8.29884i	1.25705	+	0.457530i
$330$	16.8197	+	20.0449i	0.925893	+	1.10344i
$331$	25.2811	−	2.21181i	1.38957	−	0.121572i	0.632328	−	0.774701i	$-0.282100\pi$
$331$	25.2811	−	2.21181i	1.38957	−	0.121572i	0.757247	+	0.653129i	$0.226544\pi$
$332$	−0.258224	+	2.95151i	−0.0141719	+	0.161985i
$333$	−0.0489129	−	0.277399i	−0.00268041	−	0.0152014i
$334$	1.40376	+	16.0450i	0.0768103	+	0.877946i
$335$	23.9802	−	6.42548i	1.31018	−	0.351061i
$336$	−32.7586	−	15.2756i	−1.78713	−	0.833352i
$337$	8.49938	+	5.95133i	0.462991	+	0.324190i	0.781691	−	0.623666i	$-0.214357\pi$
$337$	8.49938	+	5.95133i	0.462991	+	0.324190i	−0.318700	+	0.947856i	$0.603246\pi$
$338$		−	11.9261i		−	0.648694i
$339$	14.3609	−	20.5095i	0.779976	−	1.11392i
$340$	3.29349	−	3.92503i	0.178614	−	0.212864i
$341$	−19.9634	+	11.5259i	−1.08108	+	0.624160i
$342$	−1.44663	+	3.97457i	−0.0782245	+	0.214920i
$343$	6.26798	+	6.26798i	0.338439	+	0.338439i
$344$	3.59690	−	13.4238i	0.193932	−	0.723763i
$345$	−8.33220	+	17.8685i	−0.448591	+	0.962006i
$346$	−5.44250	−	14.9532i	−0.292591	−	0.803887i
$347$	−6.71760	−	5.63674i	−0.360620	−	0.302596i	0.444418	−	0.895820i	$-0.353411\pi$
$347$	−6.71760	−	5.63674i	−0.360620	−	0.302596i	−0.805038	+	0.593224i	$0.797855\pi$
$348$	−7.59065	−	2.03391i	−0.406902	−	0.109029i
$349$	−0.560282	+	3.17752i	−0.0299912	+	0.170089i	−0.996124	−	0.0879551i	$-0.971967\pi$
$349$	−0.560282	+	3.17752i	−0.0299912	+	0.170089i	0.966133	+	0.258044i	$0.0830779\pi$
$350$	36.4497	+	3.18893i	1.94832	+	0.170456i
$351$	−6.59604	−	9.42012i	−0.352070	−	0.502809i
$352$	7.93830	−	5.55846i	0.423113	−	0.296267i
$353$	14.3743	−	2.53458i	0.765069	−	0.134902i	0.222522	−	0.974928i	$-0.428571\pi$
$353$	14.3743	−	2.53458i	0.765069	−	0.134902i	0.542547	+	0.840025i	$0.317460\pi$
$354$	4.87684	+	10.4584i	0.259201	+	0.555859i
$355$	−4.47331	+	4.47331i	−0.237418	+	0.237418i
$356$	−5.68698	−	9.85014i	−0.301409	−	0.522056i
$357$	−8.79011	+	15.2249i	−0.465222	+	0.805788i
$358$	−7.94881	−	29.6654i	−0.420108	−	1.56786i
$359$	−21.3097	−	3.75748i	−1.12468	−	0.198312i	−0.419787	−	0.907623i	$-0.637895\pi$
$359$	−21.3097	−	3.75748i	−1.12468	−	0.198312i	−0.704896	+	0.709310i	$0.749006\pi$
$360$	2.42356	−	1.13013i	0.127733	−	0.0595629i
$361$	−21.6519	+	18.1681i	−1.13957	+	0.956214i
$362$	24.0707	+	13.8973i	1.26513	+	0.730423i
$363$	−6.55717	+	2.38662i	−0.344162	+	0.125265i
$364$	6.36782			0.333764
$365$	−27.6951	−	2.14605i	−1.44963	−	0.112329i
$366$	17.2875			0.903632
$367$	1.67816	−	0.610800i	0.0875992	−	0.0318835i	−0.297849	−	0.954613i	$-0.596269\pi$
$367$	1.67816	−	0.610800i	0.0875992	−	0.0318835i	0.385448	+	0.922730i	$0.374047\pi$
$368$	13.9647	+	8.06255i	0.727962	+	0.420289i
$369$	−0.425729	+	0.357229i	−0.0221626	+	0.0185966i
$370$	3.59270	−	1.67530i	0.186775	−	0.0870948i
$371$	−9.24702	−	1.63050i	−0.480081	−	0.0846513i
$372$	−2.70888	−	10.1097i	−0.140449	−	0.524163i
$373$	−14.1538	+	24.5150i	−0.732854	+	1.26934i	0.222804	+	0.974863i	$0.428479\pi$
$373$	−14.1538	+	24.5150i	−0.732854	+	1.26934i	−0.955658	+	0.294478i	$0.904854\pi$
$374$	−5.20458	−	9.01459i	−0.269122	−	0.466133i
$375$	−2.40882	+	2.40882i	−0.124391	+	0.124391i
$376$	5.55803	+	11.9192i	0.286633	+	0.614687i
$377$	−15.1521	+	2.67173i	−0.780374	+	0.137601i
$378$	−25.9363	+	18.1608i	−1.33402	+	0.934091i
$379$	−5.75960	−	8.22556i	−0.295851	−	0.422519i	0.643516	−	0.765433i	$-0.277475\pi$
$379$	−5.75960	−	8.22556i	−0.295851	−	0.422519i	−0.939367	+	0.342914i	$0.888586\pi$
$380$	−14.7648	−	1.29176i	−0.757420	−	0.0662657i
$381$	0.474946	−	2.69356i	0.0243322	−	0.137995i
$382$	0.681367	+	0.182572i	0.0348618	+	0.00934118i
$383$	−17.0348	−	14.2939i	−0.870439	−	0.730385i	0.0937517	−	0.995596i	$-0.470114\pi$
$383$	−17.0348	−	14.2939i	−0.870439	−	0.730385i	−0.964190	+	0.265211i	$0.914558\pi$
$384$	−8.51904	−	23.4059i	−0.434735	−	1.19443i
$385$	14.8432	−	31.8313i	0.756478	−	1.62227i
$386$	3.21811	−	12.0102i	0.163798	−	0.611301i
$387$	1.69811	+	1.69811i	0.0863199	+	0.0863199i
$388$	−3.20005	+	8.79207i	−0.162458	+	0.446350i
$389$	25.5186	−	14.7332i	1.29384	−	0.747001i	0.314510	−	0.949254i	$-0.398160\pi$
$389$	25.5186	−	14.7332i	1.29384	−	0.747001i	0.979333	+	0.202253i	$0.0648263\pi$
$390$	−14.9519	+	17.8190i	−0.757118	+	0.902298i
$391$	4.49850	−	6.42453i	0.227499	−	0.324902i
$392$			20.0764i			1.01401i
$393$	−30.0412	−	21.0351i	−1.51538	−	1.06108i
$394$	10.8363	+	5.05303i	0.545923	+	0.254568i
$395$	22.4609	−	6.01837i	1.13013	−	0.302817i
$396$	0.0584743	+	0.668365i	0.00293845	+	0.0335866i
$397$	−4.56252	−	25.8753i	−0.228986	−	1.29865i	−0.854916	−	0.518767i	$-0.826391\pi$
$397$	−4.56252	−	25.8753i	−0.228986	−	1.29865i	0.625930	−	0.779880i	$-0.284720\pi$
$398$	1.80720	−	20.6563i	0.0905866	−	1.03541i
$399$	50.6599	−	4.43217i	2.53617	−	0.221886i
$400$	17.4958	+	20.8507i	0.874791	+	1.04254i
$401$	18.5836	+	6.76388i	0.928020	+	0.337772i	0.761425	−	0.648253i	$-0.224500\pi$
$401$	18.5836	+	6.76388i	0.928020	+	0.337772i	0.166596	+	0.986025i	$0.446722\pi$
$402$	21.5185	+	7.83211i	1.07325	+	0.390630i
$403$	−13.1719	−	15.6977i	−0.656140	−	0.781957i
$404$	2.81815	−	0.246556i	0.140208	−	0.0122666i
$405$	2.83044	−	32.3521i	0.140646	−	1.60759i
$406$	7.35605	+	41.7182i	0.365074	+	2.07044i
$407$	−0.174766	−	1.99758i	−0.00866282	−	0.0990165i
$408$	−9.20397	+	2.46620i	−0.455664	+	0.122095i
$409$	−7.53787	−	3.51497i	−0.372724	−	0.173804i	0.227225	−	0.973842i	$-0.427035\pi$
$409$	−7.53787	−	3.51497i	−0.372724	−	0.173804i	−0.599949	+	0.800038i	$0.704812\pi$
$410$	−6.40671	−	4.48603i	−0.316405	−	0.221549i
$411$		−	13.9313i		−	0.687179i
$412$	−4.78220	+	6.82969i	−0.235602	+	0.336475i
$413$	9.95603	−	11.8651i	0.489904	−	0.583845i
$414$	−1.75822	+	1.01511i	−0.0864116	+	0.0498898i
$415$	−4.96842	+	13.6506i	−0.243890	+	0.670082i
$416$	6.09152	+	6.09152i	0.298662	+	0.298662i
$417$	−8.85270	+	33.0387i	−0.433519	+	1.61791i
$418$	−12.7250	+	27.2889i	−0.622402	+	1.33475i
$419$	9.17991	+	25.2216i	0.448468	+	1.23216i	0.933791	+	0.357820i	$0.116480\pi$
$419$	9.17991	+	25.2216i	0.448468	+	1.23216i	−0.485323	+	0.874335i	$0.661298\pi$
$420$	12.2158	+	10.2503i	0.596072	+	0.500164i
$421$	28.2316	+	7.56463i	1.37592	+	0.368677i	0.869639	−	0.493689i	$-0.164352\pi$
$421$	28.2316	+	7.56463i	1.37592	+	0.368677i	0.506285	+	0.862366i	$0.331019\pi$
$422$	−2.74829	+	15.5864i	−0.133785	+	0.758732i
$423$	−2.26395	−	0.198070i	−0.110077	−	0.00963048i
$424$	−2.91910	−	4.16890i	−0.141764	−	0.202460i
$425$	10.8444	−	7.59333i	0.526031	−	0.368331i
$426$	−5.74663	+	1.01329i	−0.278425	+	0.0490938i
$427$	−9.80637	−	21.0298i	−0.474564	−	1.01771i
$428$	2.49380	−	2.49380i	0.120542	−	0.120542i
$429$	5.88321	+	10.1900i	0.284044	+	0.491978i
$430$	−16.8983	+	29.2687i	−0.814907	+	1.41146i
$431$	2.50316	+	9.34193i	0.120573	+	0.449985i	0.999643	−	0.0267073i	$-0.00850222\pi$
$431$	2.50316	+	9.34193i	0.120573	+	0.449985i	−0.879070	+	0.476692i	$0.841836\pi$
$432$	−23.1960	−	4.09008i	−1.11602	−	0.196784i
$433$	20.3874	−	9.50679i	0.979755	−	0.456867i	0.134315	−	0.990939i	$-0.457116\pi$
$433$	20.3874	−	9.50679i	0.979755	−	0.456867i	0.845439	+	0.534071i	$0.179339\pi$
$434$	−43.2202	+	36.2661i	−2.07464	+	1.74083i
$435$	−33.3681	−	19.2651i	−1.59988	−	0.923690i
$436$	2.12810	−	0.774565i	0.101917	−	0.0370949i
$437$	−22.6868			−1.08525
$438$	−19.7905	−	16.2740i	−0.945629	−	0.777603i
$439$	−29.6202			−1.41370			−0.706849	−	0.707365i	$-0.749884\pi$
$439$	−29.6202			−1.41370			−0.706849	+	0.707365i	$0.749884\pi$
$440$	17.8884	−	6.51084i	0.852795	−	0.310392i
$441$	−3.00445	−	1.73462i	−0.143069	−	0.0826011i
$442$	7.08838	−	5.94786i	0.337160	−	0.282911i
$443$	−6.35307	+	2.96248i	−0.301843	+	0.140752i	−0.567639	−	0.823277i	$-0.692143\pi$
$443$	−6.35307	+	2.96248i	−0.301843	+	0.140752i	0.265796	+	0.964029i	$0.414365\pi$
$444$	0.896608	+	0.158096i	0.0425512	+	0.00750292i
$445$	−14.4336	−	53.8668i	−0.684216	−	2.55353i
$446$	5.55036	−	9.61351i	0.262817	−	0.455213i
$447$	9.87595	+	17.1056i	0.467116	+	0.809069i
$448$	−11.0446	+	11.0446i	−0.521807	+	0.521807i
$449$	5.68131	+	12.1836i	0.268118	+	0.574980i	0.993561	−	0.113302i	$-0.0361428\pi$
$449$	5.68131	+	12.1836i	0.268118	+	0.574980i	−0.725443	+	0.688282i	$0.758365\pi$
$450$	−3.37487	+	0.595081i	−0.159093	+	0.0280524i
$451$	−3.24079	+	2.26923i	−0.152603	+	0.106854i
$452$	5.18193	+	7.40056i	0.243737	+	0.348093i
$453$	26.2018	+	2.29236i	1.23107	+	0.107704i
$454$	−3.93771	+	22.3318i	−0.184806	+	1.04809i
$455$	30.1578	+	8.08077i	1.41382	+	0.378832i
$456$	21.1145	+	17.7172i	0.988778	+	0.829683i
$457$	8.56881	+	23.5426i	0.400832	+	1.10128i	0.961875	+	0.273490i	$0.0881781\pi$
$457$	8.56881	+	23.5426i	0.400832	+	1.10128i	−0.561043	+	0.827787i	$0.689600\pi$
$458$	−5.10936	+	10.9571i	−0.238745	+	0.511989i
$459$	−2.96505	+	11.0657i	−0.138397	+	0.516503i
$460$	−5.03045	−	5.03045i	−0.234546	−	0.234546i
$461$	−1.98481	+	5.45322i	−0.0924418	+	0.253982i	−0.977293	−	0.211892i	$-0.932038\pi$
$461$	−1.98481	+	5.45322i	−0.0924418	+	0.253982i	0.884851	+	0.465873i	$0.154260\pi$
$462$	28.0561	−	16.1982i	1.30529	−	0.753607i
$463$	3.23874	−	3.85978i	0.150517	−	0.179379i	−0.685517	−	0.728056i	$-0.740424\pi$
$463$	3.23874	−	3.85978i	0.150517	−	0.179379i	0.836034	+	0.548677i	$0.184868\pi$
$464$	−18.0752	+	25.8140i	−0.839119	+	1.19839i
$465$		−	51.3168i		−	2.37976i
$466$	8.78664	+	6.15247i	0.407033	+	0.285008i
$467$	10.0999	+	4.70965i	0.467367	+	0.217937i	0.642012	−	0.766695i	$-0.278100\pi$
$467$	10.0999	+	4.70965i	0.467367	+	0.217937i	−0.174645	+	0.984631i	$0.555878\pi$
$468$	−0.576091	+	0.154363i	−0.0266298	+	0.00713544i
$469$	−2.67887	−	30.6196i	−0.123699	−	1.41388i
$470$	−5.55371	−	31.4967i	−0.256174	−	1.45283i
$471$	−1.27875	+	14.6161i	−0.0589215	+	0.673476i
$472$	8.36315	−	0.731681i	0.384945	−	0.0336783i
$473$	10.9889	+	13.0961i	0.505272	+	0.602159i
$474$	20.1552	+	7.33588i	0.925757	+	0.336948i
$475$	−35.9851	−	13.0975i	−1.65111	−	0.600955i
$476$	−4.07757	−	4.85946i	−0.186895	−	0.222733i
$477$	0.876095	−	0.0766484i	0.0401136	−	0.00350949i
$478$	3.26168	−	37.2812i	0.149186	−	1.70520i
$479$	−2.50098	−	14.1838i	−0.114273	−	0.648074i	−0.987108	−	0.160058i	$-0.948832\pi$
$479$	−2.50098	−	14.1838i	−0.114273	−	0.648074i	0.872835	−	0.488016i	$-0.162279\pi$
$480$	1.88025	+	21.4914i	0.0858213	+	0.980942i
$481$	1.72180	−	0.461354i	0.0785072	−	0.0210359i
$482$	27.8076	+	12.9669i	1.26660	+	0.590626i
$483$	19.9950	+	14.0007i	0.909805	+	0.637052i
$484$		−	2.51791i		−	0.114451i
$485$	−26.3125	+	37.5782i	−1.19479	+	1.70634i
$486$	4.08637	−	4.86995i	0.185362	−	0.220905i
$487$	−4.57604	+	2.64198i	−0.207360	+	0.119719i	−0.600084	−	0.799937i	$-0.704866\pi$
$487$	−4.57604	+	2.64198i	−0.207360	+	0.119719i	0.392724	+	0.919656i	$0.371533\pi$
$488$	4.30149	−	11.8182i	0.194719	−	0.534987i
$489$	−1.62308	−	1.62308i	−0.0733981	−	0.0733981i
$490$	12.6364	−	47.1596i	0.570853	−	2.13045i
$491$	5.96665	−	12.7955i	0.269271	−	0.577454i	−0.724452	−	0.689326i	$-0.757907\pi$
$491$	5.96665	−	12.7955i	0.269271	−	0.577454i	0.993723	+	0.111872i	$0.0356847\pi$
$492$	−0.614369	−	1.68796i	−0.0276979	−	0.0760993i
$493$	11.7414	+	9.85220i	0.528806	+	0.443721i
$494$	−25.8543	−	6.92764i	−1.16324	−	0.311689i
$495$	−0.571222	+	3.23956i	−0.0256745	+	0.145608i
$496$	−41.8114	−	3.65802i	−1.87739	−	0.164250i
$497$	4.49242	+	6.41585i	0.201513	+	0.287790i
$498$	−10.9761	+	7.68556i	−0.491851	+	0.344398i
$499$	−22.9785	+	4.05172i	−1.02866	+	0.181380i	−0.662413	−	0.749139i	$-0.730468\pi$
$499$	−22.9785	+	4.05172i	−1.02866	+	0.181380i	−0.366244	+	0.930519i	$0.619357\pi$
$500$	−0.519490	−	1.11405i	−0.0232323	−	0.0498219i
$501$	−12.8249	+	12.8249i	−0.572974	+	0.572974i
$502$	−10.0222	−	17.3590i	−0.447315	−	0.774772i
$503$	16.7336	−	28.9835i	0.746115	−	1.29231i	−0.203557	−	0.979063i	$-0.565250\pi$
$503$	16.7336	−	28.9835i	0.746115	−	1.29231i	0.949672	−	0.313246i	$-0.101416\pi$
$504$	−0.856881	−	3.19792i	−0.0381685	−	0.142447i
$505$	13.6596	+	2.40855i	0.607843	+	0.107179i
$506$	−13.0986	+	6.10797i	−0.582303	+	0.271532i
$507$	10.2879	−	8.63253i	0.456900	−	0.383384i
$508$	0.854702	+	0.493463i	0.0379213	+	0.0218939i
$509$	−37.3154	+	13.5817i	−1.65398	+	0.601999i	−0.989399	−	0.145220i	$-0.953611\pi$
$509$	−37.3154	+	13.5817i	−1.65398	+	0.601999i	−0.664579	+	0.747218i	$0.731389\pi$
$510$	23.1725			1.02609
$511$	−8.57073	+	33.3062i	−0.379147	+	1.47338i
$512$	−3.67714			−0.162508
$513$	31.1399	−	11.3340i	1.37486	−	0.500408i
$514$	−19.9965	−	11.5450i	−0.882006	−	0.509226i
$515$	−31.3153	+	26.2766i	−1.37992	+	1.15789i
$516$	−7.03485	+	3.28040i	−0.309692	+	0.144412i
$517$	−15.9324	−	2.80931i	−0.700705	−	0.123553i
$518$	−1.27024	−	4.74061i	−0.0558112	−	0.208290i
$519$	8.95962	−	15.5185i	0.393283	−	0.681187i
$520$	8.46123	+	14.6553i	0.371049	+	0.642676i
$521$	−15.3169	+	15.3169i	−0.671047	+	0.671047i	−0.957957	−	0.286911i	$-0.907372\pi$
$521$	−15.3169	+	15.3169i	−0.671047	+	0.671047i	0.286911	+	0.957957i	$0.407372\pi$
$522$	−1.67679	−	3.59589i	−0.0733912	−	0.157388i
$523$	−17.0216	+	3.00137i	−0.744303	+	0.131241i	−0.532924	−	0.846163i	$-0.678907\pi$
$523$	−17.0216	+	3.00137i	−0.744303	+	0.131241i	−0.211380	+	0.977404i	$0.567796\pi$
$524$	10.8399	−	7.59021i	0.473545	−	0.331580i
$525$	23.6327	+	33.7510i	1.03142	+	1.47301i
$526$	−9.45752	−	0.827426i	−0.412368	−	0.0360775i
$527$	−3.54483	+	20.1037i	−0.154415	+	0.875731i
$528$	23.2786	+	6.23749i	1.01307	+	0.271452i
$529$	9.27715	+	7.78445i	0.403354	+	0.338454i
$530$	4.23301	+	11.6301i	0.183870	+	0.505180i
$531$	−0.613089	+	1.31477i	−0.0266058	+	0.0570563i
$532$	−4.74926	+	17.7245i	−0.205907	+	0.768454i
$533$	−2.48685	−	2.48685i	−0.107717	−	0.107717i
$534$	17.5933	−	48.3371i	0.761336	−	2.09175i
$535$	14.9752	−	8.64594i	0.647435	−	0.373797i
$536$	10.7085	−	12.7619i	0.462538	−	0.551231i
$537$	19.8367	−	28.3298i	0.856017	−	1.22252i
$538$		−	16.6115i		−	0.716173i
$539$	−20.2305	−	14.1655i	−0.871388	−	0.610153i
$540$	9.41794	+	4.39166i	0.405284	+	0.188987i
$541$	−6.62260	+	1.77452i	−0.284728	+	0.0762926i	−0.398356	−	0.917231i	$-0.630419\pi$
$541$	−6.62260	+	1.77452i	−0.284728	+	0.0762926i	0.113629	+	0.993523i	$0.463753\pi$
$542$	−0.770283	−	8.80437i	−0.0330865	−	0.378180i
$543$	5.43502	+	30.8236i	0.233239	+	1.32277i
$544$	0.747964	−	8.54927i	0.0320687	−	0.366547i
$545$	11.0615	−	0.967760i	0.473825	−	0.0414543i
$546$	18.5115	+	22.0611i	0.792219	+	0.944130i
$547$	17.1607	+	6.24598i	0.733739	+	0.267059i	0.681746	−	0.731589i	$-0.261221\pi$
$547$	17.1607	+	6.24598i	0.733739	+	0.267059i	0.0519921	+	0.998647i	$0.483443\pi$
$548$	4.72375	+	1.71930i	0.201789	+	0.0734450i
$549$	1.39696	+	1.66483i	0.0596208	+	0.0710533i
$550$	−24.3028	+	2.12622i	−1.03628	+	0.0906625i
$551$	3.86418	−	44.1678i	0.164620	−	1.88161i
$552$	2.29739	+	13.0291i	0.0977834	+	0.554557i
$553$	−2.50914	−	28.6796i	−0.106699	−	1.21958i
$554$	4.66678	−	1.25046i	0.198273	−	0.0531270i
$555$	4.04569	+	1.88654i	0.171730	+	0.0800790i
$556$	−10.1101	−	7.07914i	−0.428762	−	0.300223i
$557$		−	4.73943i		−	0.200816i	−0.994946	−	0.100408i	$-0.967985\pi$
$557$		−	4.73943i		−	0.200816i	0.994946	−	0.100408i	$-0.0320148\pi$
$558$	3.03097	−	4.32867i	0.128311	−	0.183247i
$559$	−9.76863	+	11.6418i	−0.413169	+	0.492395i
$560$	55.3804	−	31.9739i	2.34025	−	1.35114i
$561$	4.00903	−	11.0147i	0.169261	−	0.465042i
$562$	23.7806	+	23.7806i	1.00312	+	1.00312i
$563$	−0.391987	+	1.46291i	−0.0165203	+	0.0616545i	−0.973694	−	0.227860i	$-0.926827\pi$
$563$	−0.391987	+	1.46291i	−0.0165203	+	0.0616545i	0.957174	+	0.289514i	$0.0934938\pi$
$564$	3.10433	−	6.65726i	0.130716	−	0.280321i
$565$	15.1502	+	41.6247i	0.637372	+	1.75117i
$566$	−22.6002	−	18.9638i	−0.949958	−	0.797109i
$567$	−38.8371	−	10.4064i	−1.63101	−	0.437027i
$568$	−0.737168	+	4.18069i	−0.0309309	+	0.175418i
$569$	32.8892	+	2.87743i	1.37879	+	0.120628i	0.752309	−	0.658810i	$-0.228940\pi$
$569$	32.8892	+	2.87743i	1.37879	+	0.120628i	0.626479	+	0.779438i	$0.284495\pi$
$570$	−38.4467	−	54.9076i	−1.61035	−	2.29983i
$571$	−0.987227	+	0.691264i	−0.0413142	+	0.0289285i	−0.594051	−	0.804427i	$-0.702472\pi$
$571$	−0.987227	+	0.691264i	−0.0413142	+	0.0289285i	0.552737	+	0.833356i	$0.313583\pi$
$572$	−4.18124	+	0.737266i	−0.174827	+	0.0308266i
$573$	0.335705	+	0.719922i	0.0140243	+	0.0300752i
$574$	−6.84702	+	6.84702i	−0.285789	+	0.285789i
$575$	−9.19061	−	15.9186i	−0.383275	−	0.663851i
$576$	0.731459	−	1.26692i	0.0304775	−	0.0527885i
$577$	7.22707	+	26.9718i	0.300867	+	1.12285i	0.936445	+	0.350814i	$0.114095\pi$
$577$	7.22707	+	26.9718i	0.300867	+	1.12285i	−0.635578	+	0.772037i	$0.719238\pi$
$578$	18.2429	+	3.21671i	0.758803	+	0.133797i
$579$	12.6897	−	5.91733i	0.527368	−	0.245916i
$580$	10.6504	−	8.93672i	0.442233	−	0.371077i
$581$	15.5755	+	8.99253i	0.646182	+	0.373073i
$582$	−39.7626	+	14.4724i	−1.64821	+	0.599900i
$583$	6.26057			0.259286
$584$	−16.0497	+	9.48008i	−0.664141	+	0.392289i
$585$	−2.92424			−0.120902
$586$	36.5270	−	13.2948i	1.50892	−	0.549201i
$587$	−9.27623	−	5.35563i	−0.382871	−	0.221051i	0.296196	−	0.955127i	$-0.404282\pi$
$587$	−9.27623	−	5.35563i	−0.382871	−	0.221051i	−0.679067	+	0.734077i	$0.737615\pi$
$588$	8.58987	−	7.20776i	0.354240	−	0.297243i
$589$	53.5176	−	24.9556i	2.20515	−	1.02828i
$590$	−20.1056	−	3.54516i	−0.827736	−	0.145952i
$591$	3.48475	+	13.0053i	0.143344	+	0.534966i
$592$	1.82548	−	3.16183i	0.0750269	−	0.129950i
$593$	−14.8375	−	25.6993i	−0.609304	−	1.05535i	−0.991355	−	0.131205i	$-0.958116\pi$
$593$	−14.8375	−	25.6993i	−0.609304	−	1.05535i	0.382051	−	0.924141i	$-0.375218\pi$
$594$	14.9277	−	14.9277i	0.612490	−	0.612490i
$595$	−13.1446	−	28.1887i	−0.538877	−	1.15563i
$596$	−7.01892	+	1.23762i	−0.287506	+	0.0506951i
$597$	19.1270	−	13.3928i	0.782815	−	0.548133i
$598$	−7.36915	−	10.5242i	−0.301347	−	0.430368i
$599$	−5.22719	−	0.457320i	−0.213577	−	0.0186856i	−0.0201351	−	0.999797i	$-0.506410\pi$
$599$	−5.22719	−	0.457320i	−0.213577	−	0.0186856i	−0.193442	+	0.981112i	$0.561965\pi$
$600$	−3.87792	+	21.9928i	−0.158316	+	0.897852i
$601$	−43.8300	−	11.7442i	−1.78786	−	0.479056i	−0.795882	−	0.605451i	$-0.792993\pi$
$601$	−43.8300	−	11.7442i	−1.78786	−	0.479056i	−0.991980	+	0.126395i	$0.959659\pi$
$602$	32.0532	+	26.8959i	1.30639	+	1.09619i
$603$	0.984608	+	2.70519i	0.0400963	+	0.110164i
$604$	−4.01093	+	8.60146i	−0.163202	+	0.349988i
$605$	3.19523	−	11.9248i	0.129905	−	0.484811i
$606$	9.04666	+	9.04666i	0.367495	+	0.367495i
$607$	−2.03436	+	5.58937i	−0.0825723	+	0.226866i	−0.974107	−	0.226086i	$-0.927407\pi$
$607$	−2.03436	+	5.58937i	−0.0825723	+	0.226866i	0.891535	+	0.452952i	$0.149629\pi$
$608$	−21.4986	+	12.4122i	−0.871885	+	0.503383i
$609$	−30.6630	+	36.5427i	−1.24253	+	1.48078i
$610$	−17.5428	+	25.0537i	−0.710288	+	1.01440i
$611$		−	14.3816i		−	0.581817i
$612$	0.486693	+	0.340786i	0.0196734	+	0.0137755i
$613$	38.6381	+	18.0172i	1.56058	+	0.727710i	0.995268	−	0.0971683i	$-0.0309785\pi$
$613$	38.6381	+	18.0172i	1.56058	+	0.727710i	0.565311	+	0.824878i	$0.308756\pi$
$614$	3.41730	−	0.915663i	0.137911	−	0.0369531i
$615$	−0.767607	−	8.77379i	−0.0309529	−	0.353793i
$616$	−4.09262	−	23.2104i	−0.164896	−	0.935173i
$617$	−3.77368	+	43.1334i	−0.151923	+	1.73649i	0.412463	+	0.910974i	$0.364669\pi$
$617$	−3.77368	+	43.1334i	−0.151923	+	1.73649i	−0.564386	+	0.825511i	$0.690887\pi$
$618$	−37.5633	+	3.28637i	−1.51102	+	0.132197i
$619$	0.898084	+	1.07030i	0.0360971	+	0.0430188i	0.783791	−	0.621025i	$-0.213283\pi$
$619$	0.898084	+	1.07030i	0.0360971	+	0.0430188i	−0.747694	+	0.664044i	$0.768839\pi$
$620$	17.4003	+	6.33317i	0.698811	+	0.254346i
$621$	14.9470	+	5.44027i	0.599803	+	0.218310i
$622$	13.2853	+	15.8329i	0.532694	+	0.634840i
$623$	−68.7808	+	6.01754i	−2.75564	+	0.241088i
$624$	−1.86718	+	21.3420i	−0.0747472	+	0.854365i
$625$	3.78970	+	21.4924i	0.151588	+	0.859697i
$626$	−1.24865	−	14.2721i	−0.0499061	−	0.570429i
$627$	−32.7512	+	8.77566i	−1.30796	+	0.350466i
$628$	−4.79815	−	2.23741i	−0.191467	−	0.0892826i
$629$	−1.45461	−	1.01853i	−0.0579991	−	0.0406114i
$630$			8.05128i			0.320771i
$631$	22.3661	−	31.9421i	0.890380	−	1.27159i	−0.0713092	−	0.997454i	$-0.522718\pi$
$631$	22.3661	−	31.9421i	0.890380	−	1.27159i	0.961690	−	0.274141i	$-0.0883934\pi$
$632$	10.0300	−	11.9533i	0.398974	−	0.475478i
$633$	−15.4346	+	8.91118i	−0.613471	+	0.354188i
$634$	1.77182	−	4.86804i	0.0703681	−	0.193335i
$635$	3.42165	+	3.42165i	0.135784	+	0.135784i
$636$	−0.735700	+	2.74567i	−0.0291724	+	0.108873i
$637$	9.27829	−	19.8974i	0.367619	−	0.788362i
$638$	−9.66027	−	26.5414i	−0.382454	−	1.05078i
$639$	−0.561953	−	0.471534i	−0.0222305	−	0.0186536i
$640$	42.5655	+	11.4054i	1.68255	+	0.450838i
$641$	−5.33003	+	30.2281i	−0.210524	+	1.19394i	0.677984	+	0.735077i	$0.262854\pi$
$641$	−5.33003	+	30.2281i	−0.210524	+	1.19394i	−0.888508	+	0.458862i	$0.848257\pi$
$642$	15.8893	+	1.39013i	0.627100	+	0.0548641i
$643$	26.3277	+	37.5999i	1.03826	+	1.48279i	0.867471	+	0.497488i	$0.165744\pi$
$643$	26.3277	+	37.5999i	1.03826	+	1.48279i	0.170793	+	0.985307i	$0.445367\pi$
$644$	−7.21493	+	5.05195i	−0.284308	+	0.199075i
$645$	−37.4797	+	6.60868i	−1.47576	+	0.260217i
$646$	11.2689	+	24.1662i	0.443368	+	0.950806i
$647$	−7.78770	+	7.78770i	−0.306166	+	0.306166i	−0.843420	−	0.537254i	$-0.819462\pi$
$647$	−7.78770	+	7.78770i	−0.306166	+	0.306166i	0.537254	+	0.843420i	$0.319462\pi$
$648$	−10.8963	−	18.8730i	−0.428049	−	0.741402i
$649$	−5.16359	+	8.94360i	−0.202689	+	0.351067i
$650$	−5.61290	−	20.9476i	−0.220156	−	0.821633i
$651$	−62.5687	−	11.0325i	−2.45226	−	0.432400i
$652$	0.750654	−	0.350036i	0.0293979	−	0.0137085i
$653$	9.87705	−	8.28783i	0.386519	−	0.324328i	−0.428736	−	0.903430i	$-0.641041\pi$
$653$	9.87705	−	8.28783i	0.386519	−	0.324328i	0.815255	+	0.579102i	$0.196597\pi$
$654$	8.86993	+	5.12105i	0.346842	+	0.200249i
$655$	60.9697	−	22.1912i	2.38228	−	0.867080i
$656$	−7.20334			−0.281243
$657$	−0.0319935	−	3.22095i	−0.00124819	−	0.125661i
$658$	−39.5967			−1.54364
$659$	−31.6753	+	11.5289i	−1.23389	+	0.449101i	−0.874929	−	0.484251i	$-0.839092\pi$
$659$	−31.6753	+	11.5289i	−1.23389	+	0.449101i	−0.358965	+	0.933351i	$0.616870\pi$
$660$	−9.20796	−	5.31622i	−0.358419	−	0.206933i
$661$	20.6473	−	17.3252i	0.803088	−	0.673871i	−0.145859	−	0.989305i	$-0.546595\pi$
$661$	20.6473	−	17.3252i	0.803088	−	0.673871i	0.948947	+	0.315434i	$0.102150\pi$
$662$	−37.5336	+	17.5022i	−1.45879	+	0.680243i
$663$	10.2616	+	1.80941i	0.398529	+	0.0702715i
$664$	2.52299	+	9.41592i	0.0979109	+	0.365409i
$665$	−44.9848	+	77.9159i	−1.74444	+	3.02145i
$666$	0.229835	+	0.398087i	0.00890594	+	0.0154255i
$667$	15.0482	−	15.0482i	0.582668	−	0.582668i
$668$	−2.76584	−	5.93137i	−0.107014	−	0.229491i
$669$	12.3105	−	2.17067i	0.475951	−	0.0839229i
$670$	−33.1869	+	23.2377i	−1.28212	+	0.897752i
$671$	8.87391	+	12.6733i	0.342573	+	0.489245i
$672$	26.6078	+	2.32788i	1.02642	+	0.0898001i
$673$	6.72821	−	38.1576i	0.259354	−	1.47087i	−0.525292	−	0.850922i	$-0.676044\pi$
$673$	6.72821	−	38.1576i	0.259354	−	1.47087i	0.784645	−	0.619945i	$-0.212845\pi$
$674$	−16.3554	−	4.38240i	−0.629985	−	0.168804i
$675$	20.5678	+	17.2584i	0.791653	+	0.664276i
$676$	1.65742	+	4.55372i	0.0637469	+	0.175143i
$677$	−15.1843	+	32.5628i	−0.583579	+	1.25149i	0.363830	+	0.931465i	$0.381469\pi$
$677$	−15.1843	+	32.5628i	−0.583579	+	1.25149i	−0.947409	+	0.320024i	$0.896309\pi$
$678$	−10.5750	+	39.4664i	−0.406130	+	1.51570i
$679$	40.1608	+	40.1608i	1.54123	+	1.54123i
$680$	5.76579	−	15.8414i	0.221108	−	0.607489i
$681$	−22.1144	+	12.7678i	−0.847427	+	0.489262i
$682$	24.1804	−	28.8171i	0.925917	−	1.10346i
$683$	25.6697	−	36.6601i	0.982222	−	1.40276i	0.0679361	−	0.997690i	$-0.478359\pi$
$683$	25.6697	−	36.6601i	0.982222	−	1.40276i	0.914286	−	0.405069i	$-0.132753\pi$
$684$		−	1.71865i		−	0.0657141i
$685$	20.1898	+	14.1370i	0.771411	+	0.540148i
$686$	−13.1103	−	6.11342i	−0.500552	−	0.233411i
$687$	−13.1503	+	3.52360i	−0.501714	+	0.134434i
$688$	2.71288	+	31.0084i	0.103428	+	1.18218i
$689$	0.966411	+	5.48079i	0.0368173	+	0.208801i
$690$	2.80415	−	32.0516i	0.106752	−	1.22018i
$691$	−6.88195	+	0.602092i	−0.261802	+	0.0229047i	−0.217301	−	0.976105i	$-0.569725\pi$
$691$	−6.88195	+	0.602092i	−0.261802	+	0.0229047i	−0.0445008	+	0.999009i	$0.514170\pi$
$692$	4.15620	+	4.95317i	0.157995	+	0.188291i
$693$	3.82707	+	1.39294i	0.145378	+	0.0529134i
$694$	13.4474	+	4.89447i	0.510458	+	0.185791i
$695$	−38.8976	−	46.3563i	−1.47547	−	1.75840i
$696$	−25.7571	+	2.25346i	−0.976322	+	0.0854171i
$697$	−0.305354	+	3.49022i	−0.0115661	+	0.132201i
$698$	−0.914324	−	5.18539i	−0.0346077	−	0.196270i
$699$	1.05275	+	12.0330i	0.0398188	+	0.455131i
$700$	−14.3607	+	3.84794i	−0.542783	+	0.145438i
$701$	−14.2100	−	6.62623i	−0.536704	−	0.250269i	0.135316	−	0.990803i	$-0.456795\pi$
$701$	−14.2100	−	6.62623i	−0.536704	−	0.250269i	−0.672020	+	0.740533i	$0.734573\pi$
$702$	15.3727	+	10.7641i	0.580205	+	0.406264i
$703$			5.13662i			0.193731i
$704$	5.97335	−	8.53083i	0.225129	−	0.321518i
$705$	23.1501	−	27.5892i	0.871883	−	1.03907i
$706$	−20.6282	+	11.9097i	−0.776351	+	0.448226i
$707$	5.87331	−	16.1368i	0.220889	−	0.606886i
$708$	−3.31557	−	3.31557i	−0.124607	−	0.124607i
$709$	−0.884537	+	3.30114i	−0.0332195	+	0.123977i	−0.980544	−	0.196297i	$-0.937108\pi$
$709$	−0.884537	+	3.30114i	−0.0332195	+	0.123977i	0.947325	+	0.320274i	$0.103775\pi$
$710$	4.36300	−	9.35649i	0.163740	−	0.351143i
$711$	0.922224	+	2.53379i	0.0345861	+	0.0950246i
$712$	−28.6671	−	24.0546i	−1.07435	−	0.901483i
$713$	27.3780	+	7.33591i	1.02531	+	0.274732i
$714$	4.98182	−	28.2533i	0.186440	−	1.05735i
$715$	−20.7379	−	1.81433i	−0.775552	−	0.0678520i
$716$	7.15780	+	10.2224i	0.267500	+	0.382029i
$717$	34.5209	−	24.1718i	1.28921	−	0.902712i
$718$	34.7753	−	6.13182i	1.29780	−	0.228838i
$719$	−8.35796	−	17.9237i	−0.311699	−	0.668441i	0.686582	−	0.727053i	$-0.259110\pi$
$719$	−8.35796	−	17.9237i	−0.311699	−	0.668441i	−0.998281	+	0.0586115i	$0.981333\pi$
$720$	−4.23513	+	4.23513i	−0.157834	+	0.157834i
$721$	25.3057	+	43.8307i	0.942432	+	1.63234i
$722$	23.0624	−	39.9453i	0.858294	−	1.48661i
$723$	8.94244	+	33.3737i	0.332573	+	1.24118i
$724$	−11.1223	−	1.96115i	−0.413355	−	0.0728857i
$725$	32.5566	−	15.1814i	1.20912	−	0.563823i
$726$	8.72325	−	7.31967i	0.323750	−	0.271659i
$727$	−19.8028	−	11.4331i	−0.734445	−	0.424032i	0.0856011	−	0.996329i	$-0.472719\pi$
$727$	−19.8028	−	11.4331i	−0.734445	−	0.424032i	−0.820046	+	0.572297i	$0.806052\pi$
$728$	19.6877	−	7.16574i	0.729675	−	0.265580i
$729$	−22.8078			−0.844733
$730$	43.6678	−	12.1669i	1.61622	−	0.450316i
$731$	15.1394			0.559952
$732$	−6.60086	+	2.40252i	−0.243975	+	0.0887995i
$733$	−10.0068	−	5.77744i	−0.369610	−	0.213394i	0.303678	−	0.952775i	$-0.401785\pi$
$733$	−10.0068	−	5.77744i	−0.369610	−	0.213394i	−0.673288	+	0.739380i	$0.735119\pi$
$734$	−2.23252	+	1.87330i	−0.0824037	+	0.0691449i
$735$	49.8281	−	23.2352i	1.83794	−	0.857043i
$736$	−11.7346	−	2.06913i	−0.432544	−	0.0762692i
$737$	5.30414	+	19.7953i	0.195380	+	0.729169i
$738$	0.453464	−	0.785423i	0.0166922	−	0.0289118i
$739$	−6.44142	−	11.1569i	−0.236951	−	0.410412i	0.722887	−	0.690967i	$-0.242815\pi$
$739$	−6.44142	−	11.1569i	−0.236951	−	0.410412i	−0.959838	+	0.280555i	$0.909482\pi$
$740$	−1.13897	+	1.13897i	−0.0418693	+	0.0418693i
$741$	−12.7382	−	27.3173i	−0.467951	−	1.00352i
$742$	15.0902	−	2.66081i	0.553979	−	0.0976814i
$743$	−8.04550	+	5.63352i	−0.295161	+	0.206674i	−0.711771	−	0.702411i	$-0.752107\pi$
$743$	−8.04550	+	5.63352i	−0.295161	+	0.206674i	0.416611	+	0.909085i	$0.363218\pi$
$744$	−19.7517	−	28.2083i	−0.724131	−	1.03417i
$745$	−34.8120	−	3.04565i	−1.27541	−	0.111584i
$746$	8.02168	−	45.4932i	0.293695	−	1.66563i
$747$	−1.62709	−	0.435978i	−0.0595322	−	0.0159516i
$748$	3.24005	+	2.71872i	0.118468	+	0.0994064i
$749$	−7.32217	−	20.1175i	−0.267546	−	0.735077i
$750$	2.34942	−	5.03835i	0.0857887	−	0.183975i
$751$	9.48746	−	35.4077i	0.346202	−	1.29205i	−0.544999	−	0.838437i	$-0.683470\pi$
$751$	9.48746	−	35.4077i	0.346202	−	1.29205i	0.891201	−	0.453608i	$-0.149863\pi$
$752$	−20.8286	−	20.8286i	−0.759543	−	0.759543i
$753$	7.72003	−	21.2106i	0.281334	−	0.772958i
$754$	21.7443	−	12.5541i	0.791882	−	0.457193i
$755$	−29.9109	+	35.6464i	−1.08857	+	1.29731i
$756$	7.37934	−	10.5388i	0.268384	−	0.383292i
$757$		−	46.8615i		−	1.70321i	−0.524184	−	0.851605i	$-0.675630\pi$
$757$		−	46.8615i		−	1.70321i	0.524184	−	0.851605i	$-0.324370\pi$
$758$	13.4233	+	9.39909i	0.487556	+	0.341390i
$759$	−14.7501	−	6.87811i	−0.535396	−	0.249659i
$760$	−47.1028	+	12.6211i	−1.70860	+	0.457817i
$761$	3.26816	+	37.3552i	0.118471	+	1.35412i	0.789982	+	0.613130i	$0.210090\pi$
$761$	3.26816	+	37.3552i	0.118471	+	1.35412i	−0.671511	+	0.740994i	$0.734354\pi$
$762$	0.775065	+	4.39561i	0.0280776	+	0.159236i
$763$	1.19816	−	13.6950i	0.0433762	−	0.495792i
$764$	−0.285538	+	0.0249813i	−0.0103304	+	0.000903793i
$765$	1.87251	+	2.23157i	0.0677007	+	0.0806826i
$766$	34.1007	+	12.4116i	1.23211	+	0.448450i
$767$	−8.62672	−	3.13987i	−0.311493	−	0.113374i
$768$	16.9603	+	20.2126i	0.612004	+	0.729358i
$769$	35.0404	−	3.06564i	1.26359	−	0.110550i	0.564410	−	0.825495i	$-0.309104\pi$
$769$	35.0404	−	3.06564i	1.26359	−	0.110550i	0.699181	+	0.714945i	$0.253548\pi$
$770$	−4.99537	+	57.0973i	−0.180021	+	2.05765i
$771$	−4.51507	−	25.6063i	−0.162606	−	0.922187i
$772$	0.440335	+	5.03305i	0.0158480	+	0.181143i
$773$	12.7551	−	3.41771i	0.458768	−	0.122926i	−0.0220314	−	0.999757i	$-0.507013\pi$
$773$	12.7551	−	3.41771i	0.458768	−	0.122926i	0.480799	+	0.876831i	$0.340347\pi$
$774$	−3.55181	−	1.65624i	−0.127667	−	0.0595322i
$775$	39.1910	+	27.4419i	1.40778	+	0.985741i
$776$			30.7839i			1.10508i
$777$	3.16996	−	4.52717i	0.113722	−	0.162411i
$778$	−30.9091	+	36.8361i	−1.10815	+	1.32064i
$779$	8.77676	−	5.06727i	0.314460	−	0.181554i
$780$	3.23268	−	8.88171i	0.115748	−	0.318016i
$781$	−3.69265	−	3.69265i	−0.132133	−	0.132133i
$782$	−3.31258	+	12.3627i	−0.118458	+	0.442090i
$783$	−13.1373	+	28.1730i	−0.469489	+	1.00682i
$784$	−15.3794	−	42.2547i	−0.549266	−	1.50910i
$785$	−19.8846	−	16.6852i	−0.709713	−	0.595520i
$786$	57.8083	+	15.4897i	2.06195	+	0.552498i
$787$	6.90958	−	39.1862i	0.246300	−	1.39684i	−0.571155	−	0.820843i	$-0.693504\pi$
$787$	6.90958	−	39.1862i	0.246300	−	1.39684i	0.817454	−	0.575993i	$-0.195385\pi$
$788$	−4.83983	−	0.423430i	−0.172412	−	0.0150841i
$789$	−6.13192	−	8.75730i	−0.218302	−	0.311768i
$790$	−31.0843	+	21.7654i	−1.10593	+	0.774379i
$791$	54.0086	−	9.52317i	1.92032	−	0.338605i
$792$	0.932902	+	2.00061i	0.0331492	+	0.0710887i
$793$	−9.72493	+	9.72493i	−0.345342	+	0.345342i
$794$	21.4387	+	37.1329i	0.760830	+	1.31780i
$795$	−6.96851	+	12.0698i	−0.247148	+	0.428072i
$796$	2.18066	+	8.13833i	0.0772914	+	0.288456i
$797$	21.6159	+	3.81147i	0.765675	+	0.135009i	0.542827	−	0.839844i	$-0.317354\pi$
$797$	21.6159	+	3.81147i	0.765675	+	0.135009i	0.222847	+	0.974853i	$0.428465\pi$
$798$	−75.2123	+	35.0721i	−2.66249	+	1.24154i
$799$	−10.9750	+	9.20911i	−0.388267	+	0.325795i
$800$	−17.4186	−	10.0566i	−0.615840	−	0.355555i
$801$	6.07667	−	2.21173i	0.214708	−	0.0781475i
$802$	−32.2728			−1.13959
$803$	1.77153	−	22.8619i	0.0625159	−	0.806778i
$804$	−9.30485			−0.328157
$805$	−40.5806	+	14.7701i	−1.43028	+	0.520579i
$806$	28.9604	+	16.7203i	1.02009	+	0.588948i
$807$	14.3296	−	12.0240i	0.504427	−	0.423265i
$808$	8.43556	−	3.93357i	0.296762	−	0.138382i
$809$	13.9883	+	2.46651i	0.491802	+	0.0867179i	0.414049	−	0.910255i	$-0.364114\pi$
$809$	13.9883	+	2.46651i	0.491802	+	0.0867179i	0.0777531	+	0.996973i	$0.475225\pi$
$810$	13.7166	+	51.1911i	0.481953	+	1.79867i
$811$	1.70364	−	2.95080i	0.0598230	−	0.103617i	−0.834563	−	0.550913i	$-0.814280\pi$
$811$	1.70364	−	2.95080i	0.0598230	−	0.103617i	0.894386	+	0.447296i	$0.147613\pi$
$812$	−8.60650	−	14.9069i	−0.302029	−	0.523129i
$813$	7.03739	−	7.03739i	0.246812	−	0.246812i
$814$	1.38294	+	2.96571i	0.0484719	+	0.103948i
$815$	3.99927	−	0.705180i	0.140088	−	0.0247014i
$816$	17.4823	−	12.2413i	0.612004	−	0.428530i
$817$	−25.1187	−	35.8732i	−0.878791	−	1.25504i
$818$	13.5211	+	1.18294i	0.472753	+	0.0413605i
$819$	−0.628679	+	3.56541i	−0.0219678	+	0.124586i
$820$	3.06971	+	0.822525i	0.107199	+	0.0287238i
$821$	4.75780	+	3.99227i	0.166048	+	0.139331i	0.722025	−	0.691867i	$-0.243211\pi$
$821$	4.75780	+	3.99227i	0.166048	+	0.139331i	−0.555977	+	0.831198i	$0.687656\pi$
$822$	7.77564	+	21.3634i	0.271207	+	0.745134i
$823$	−17.9666	+	38.5295i	−0.626276	+	1.34305i	0.295504	+	0.955341i	$0.404512\pi$
$823$	−17.9666	+	38.5295i	−0.626276	+	1.34305i	−0.921781	+	0.387712i	$0.873265\pi$
$824$	−7.09988	+	26.4971i	−0.247336	+	0.923071i
$825$	−19.4254	−	19.4254i	−0.676306	−	0.676306i
$826$	−8.64497	+	23.7519i	−0.300797	+	0.826433i
$827$	−1.78461	+	1.03035i	−0.0620571	+	0.0358287i	−0.530708	−	0.847555i	$-0.678074\pi$
$827$	−1.78461	+	1.03035i	−0.0620571	+	0.0358287i	0.468650	+	0.883384i	$0.344740\pi$
$828$	0.530263	−	0.631943i	0.0184279	−	0.0219615i
$829$	−17.1050	+	24.4284i	−0.594080	+	0.848434i	−0.997790	−	0.0664535i	$-0.978832\pi$
$829$	−17.1050	+	24.4284i	−0.594080	+	0.848434i	0.403710	+	0.914887i	$0.367720\pi$
$830$		−	23.7061i		−	0.822850i
$831$	4.45667	+	3.12059i	0.154600	+	0.108252i
$832$	8.39036	+	3.91249i	0.290883	+	0.135641i
$833$	−21.1255	+	5.66056i	−0.731955	+	0.196127i
$834$	−4.86484	−	55.6054i	−0.168456	−	1.92546i
$835$	−5.57205	−	31.6007i	−0.192829	−	1.09359i
$836$	1.06632	−	12.1881i	0.0368796	−	0.421536i
$837$	−41.2440	+	3.60838i	−1.42560	+	0.124724i
$838$	−28.1545	−	33.5532i	−0.972580	−	1.15908i
$839$	−32.2500	−	11.7380i	−1.11339	−	0.405242i	−0.281156	−	0.959662i	$-0.590718\pi$
$839$	−32.2500	−	11.7380i	−1.11339	−	0.405242i	−0.832237	+	0.554420i	$0.812940\pi$
$840$	49.3030	+	17.9448i	1.70112	+	0.619156i
$841$	8.09263	+	9.64442i	0.279056	+	0.332566i
$842$	−47.5148	+	4.15701i	−1.63747	+	0.143260i
$843$	−3.30069	+	37.7271i	−0.113682	+	1.29939i
$844$	−1.11672	−	6.33325i	−0.0384392	−	0.218000i
$845$	2.07082	+	23.6696i	0.0712384	+	0.814258i
$846$	3.58228	−	0.959868i	0.123161	−	0.0330009i
$847$	−13.8525	−	6.45952i	−0.475977	−	0.221952i
$848$	9.33739	+	6.53811i	0.320647	+	0.224520i
$849$		−	33.2224i		−	1.14019i
$850$	−12.3916	+	17.6970i	−0.425027	+	0.607001i
$851$	−1.58483	+	1.88873i	−0.0543272	+	0.0647447i
$852$	2.05340	−	1.18553i	0.0703485	−	0.0406157i
$853$	−3.97475	+	10.9205i	−0.136093	+	0.373912i	−0.988953	−	0.148227i	$-0.952643\pi$
$853$	−3.97475	+	10.9205i	−0.136093	+	0.373912i	0.852861	+	0.522139i	$0.174866\pi$
$854$	26.7756	+	26.7756i	0.916241	+	0.916241i
$855$	2.18096	−	8.13947i	0.0745874	−	0.278364i
$856$	4.90392	−	10.5165i	0.167613	−	0.359446i
$857$	−17.6409	−	48.4680i	−0.602602	−	1.65564i	−0.745981	−	0.665968i	$-0.768019\pi$
$857$	−17.6409	−	48.4680i	−0.602602	−	1.65564i	0.143379	−	0.989668i	$-0.454203\pi$
$858$	−14.7093	−	12.3426i	−0.502166	−	0.421368i
$859$	−6.21900	−	1.66638i	−0.212190	−	0.0568561i	0.151158	−	0.988510i	$-0.451700\pi$
$859$	−6.21900	−	1.66638i	−0.212190	−	0.0568561i	−0.363348	+	0.931654i	$0.618366\pi$
$860$	2.38465	−	13.5240i	0.0813159	−	0.461165i
$861$	−10.8626	−	0.950353i	−0.370196	−	0.0323879i
$862$	−9.05269	−	12.9286i	−0.308336	−	0.440349i
$863$	5.70054	−	3.99156i	0.194049	−	0.135874i	−0.472514	−	0.881323i	$-0.656654\pi$
$863$	5.70054	−	3.99156i	0.194049	−	0.135874i	0.666563	+	0.745449i	$0.267765\pi$
$864$	17.1407	−	3.02236i	0.583138	−	0.102823i
$865$	13.3981	+	28.7323i	0.455549	+	0.976928i
$866$	−25.9576	+	25.9576i	−0.882074	+	0.882074i
$867$	10.4300	+	18.0653i	0.354221	+	0.613529i
$868$	11.4627	−	19.8539i	0.389068	−	0.673886i
$869$	4.96807	+	18.5411i	0.168530	+	0.628964i
$870$	61.9221	+	10.9185i	2.09936	+	0.370173i
$871$	−16.5110	+	7.69918i	−0.559452	+	0.260877i
$872$	5.70793	−	4.78952i	0.193295	−	0.162194i
$873$	−4.60685	−	2.65977i	−0.155918	−	0.0900194i
$874$	34.7898	−	12.6624i	1.17678	−	0.428313i
$875$	−7.46175			−0.252253
$876$	9.81826	+	3.46351i	0.331728	+	0.117021i
$877$	6.58402			0.222327			0.111163	−	0.993802i	$-0.464542\pi$
$877$	6.58402			0.222327			0.111163	+	0.993802i	$0.464542\pi$
$878$	45.4222	−	16.5323i	1.53292	−	0.557939i
$879$	37.9081	+	21.8862i	1.27861	+	0.738204i
$880$	−32.6620	+	27.4067i	−1.10104	+	0.923879i
$881$	5.93993	−	2.76984i	0.200121	−	0.0933182i	−0.319974	−	0.947426i	$-0.603674\pi$
$881$	5.93993	−	2.76984i	0.200121	−	0.0933182i	0.520095	+	0.854108i	$0.325896\pi$
$882$	5.57545	+	0.983102i	0.187735	+	0.0331028i
$883$	−4.78364	−	17.8528i	−0.160982	−	0.600794i	−0.998519	−	0.0544123i	$-0.982671\pi$
$883$	−4.78364	−	17.8528i	−0.160982	−	0.600794i	0.837536	−	0.546382i	$-0.183995\pi$
$884$	−1.87995	+	3.25616i	−0.0632295	+	0.109517i
$885$	−11.4950	−	19.9099i	−0.386400	−	0.669264i
$886$	8.08884	−	8.08884i	0.271750	−	0.271750i
$887$	−11.7161	−	25.1253i	−0.393389	−	0.843625i	−0.998859	−	0.0477573i	$-0.984793\pi$
$887$	−11.7161	−	25.1253i	−0.393389	−	0.843625i	0.605470	−	0.795868i	$-0.292985\pi$
$888$	2.94999	−	0.520164i	0.0989953	−	0.0174555i
$889$	4.90750	−	3.43627i	0.164592	−	0.115249i
$890$	52.1990	+	74.5478i	1.74971	+	2.49885i
$891$	26.7061	+	2.33648i	0.894689	+	0.0782752i
$892$	−0.783256	+	4.44206i	−0.0262253	+	0.148731i
$893$	40.0304	+	10.7261i	1.33957	+	0.358936i
$894$	−24.6920	−	20.7190i	−0.825824	−	0.692948i
$895$	20.9269	+	57.4963i	0.699510	+	1.92189i
$896$	23.0573	−	49.4465i	0.770290	−	1.65189i
$897$	3.74451	−	13.9747i	0.125026	−	0.466602i
$898$	−15.5124	−	15.5124i	−0.517655	−	0.517655i
$899$	−18.9452	+	52.0514i	−0.631857	+	1.73601i
$900$	1.20592	−	0.696239i	0.0401974	−	0.0232080i
$901$	3.56371	−	4.24707i	0.118724	−	0.141490i
$902$	3.70315	−	5.28864i	0.123301	−	0.176093i
$903$			47.1184i			1.56800i
$904$	24.3491	+	17.0494i	0.809839	+	0.567055i
$905$	−50.1860	−	23.4021i	−1.66824	−	0.777913i
$906$	−41.4595	+	11.1090i	−1.37740	+	0.369073i
$907$	1.21609	+	13.9000i	0.0403798	+	0.461543i	0.989287	+	0.145986i	$0.0466356\pi$
$907$	1.21609	+	13.9000i	0.0403798	+	0.461543i	−0.948907	+	0.315556i	$0.897809\pi$
$908$	−1.60002	−	9.07417i	−0.0530985	−	0.301137i
$909$	−0.140179	+	1.60226i	−0.00464945	+	0.0531435i
$910$	−50.7568	+	4.44064i	−1.68257	+	0.147206i
$911$	−6.35987	−	7.57940i	−0.210712	−	0.251117i	0.650329	−	0.759653i	$-0.274631\pi$
$911$	−6.35987	−	7.57940i	−0.210712	−	0.251117i	−0.861041	+	0.508536i	$0.830187\pi$
$912$	−58.0118	−	21.1146i	−1.92096	−	0.699173i
$913$	−11.2684	−	4.10135i	−0.372929	−	0.135735i
$914$	−26.2803	−	31.3196i	−0.869274	−	1.03596i
$915$	−34.3103	+	3.00176i	−1.13426	+	0.0992352i
$916$	0.428150	−	4.89378i	0.0141465	−	0.161695i
$917$	−13.9490	−	79.1089i	−0.460638	−	2.61241i
$918$	−1.62939	−	18.6240i	−0.0537778	−	0.614684i
$919$	−23.7238	+	6.35677i	−0.782576	+	0.209691i	−0.627920	−	0.778278i	$-0.716093\pi$
$919$	−23.7238	+	6.35677i	−0.782576	+	0.209691i	−0.154656	+	0.987968i	$0.549427\pi$
$920$	−21.2137	−	9.89209i	−0.699394	−	0.326133i
$921$	3.26344	+	2.28509i	0.107534	+	0.0752962i
$922$		−	9.47022i		−	0.311885i
$923$	2.66270	−	3.80273i	0.0876438	−	0.125168i
$924$	−8.46147	+	10.0840i	−0.278362	+	0.331739i
$925$	−3.60421	+	2.08089i	−0.118506	+	0.0684193i
$926$	−2.81225	+	7.72660i	−0.0924163	+	0.253912i
$927$	−3.35189	−	3.35189i	−0.110090	−	0.110090i
$928$	6.02702	−	22.4932i	0.197847	−	0.738374i
$929$	13.7665	−	29.5223i	0.451663	−	0.968594i	−0.540230	−	0.841517i	$-0.681663\pi$
$929$	13.7665	−	29.5223i	0.451663	−	0.968594i	0.991893	−	0.127077i	$-0.0405595\pi$
$930$	28.6421	+	78.6935i	0.939211	+	2.58046i
$931$	48.4633	+	40.6655i	1.58832	+	1.33276i
$932$	−4.21002	−	1.12807i	−0.137904	−	0.0369512i
$933$	−4.04155	+	22.9208i	−0.132314	+	0.750392i
$934$	−18.1167	−	1.58500i	−0.592795	−	0.0518629i
$935$	11.8947	+	16.9874i	0.388999	+	0.555548i
$936$	−1.60742	+	1.12553i	−0.0525403	+	0.0367891i
$937$	15.5518	−	2.74221i	0.508056	−	0.0895841i	0.0862565	−	0.996273i	$-0.472510\pi$
$937$	15.5518	−	2.74221i	0.508056	−	0.0895841i	0.421800	+	0.906689i	$0.361398\pi$
$938$	21.1981	+	45.4594i	0.692142	+	1.48430i
$939$	11.4078	−	11.4078i	0.372280	−	0.372280i
$940$	6.49779	+	11.2545i	0.211934	+	0.367081i
$941$	−9.04851	+	15.6725i	−0.294973	+	0.510908i	−0.974979	−	0.222299i	$-0.928644\pi$
$941$	−9.04851	+	15.6725i	−0.294973	+	0.510908i	0.680006	+	0.733207i	$0.261977\pi$
$942$	−6.19695	−	23.1273i	−0.201907	−	0.753529i
$943$	4.79063	+	0.844717i	0.156004	+	0.0275078i
$944$	−17.0414	+	7.94653i	−0.554650	+	0.258637i
$945$	48.3221	−	40.5470i	1.57192	−	1.31900i
$946$	−24.1608	−	13.9493i	−0.785536	−	0.453530i
$947$	23.8526	−	8.68164i	0.775106	−	0.282115i	0.0759755	−	0.997110i	$-0.475793\pi$
$947$	23.8526	−	8.68164i	0.775106	−	0.282115i	0.699130	+	0.714994i	$0.253571\pi$
$948$	−8.71531			−0.283060
$949$	20.2878	−	1.97819i	0.658570	−	0.0642147i
$950$	62.4928			2.02753
$951$	5.48184	−	1.99523i	0.177761	−	0.0646997i
$952$	−18.0752	−	10.4357i	−0.585821	−	0.338224i
$953$	0.474855	−	0.398451i	0.0153821	−	0.0129071i	−0.635064	−	0.772459i	$-0.719026\pi$
$953$	0.474855	−	0.398451i	0.0153821	−	0.0129071i	0.650446	+	0.759552i	$0.274582\pi$
$954$	−1.30070	+	0.606525i	−0.0421116	+	0.0196370i
$955$	−1.38400	−	0.244037i	−0.0447852	−	0.00789685i
$956$	3.93572	+	14.6883i	0.127290	+	0.475053i
$957$	15.9030	−	27.5449i	0.514072	−	0.890399i
$958$	11.7518	+	20.3547i	0.379683	+	0.657631i
$959$	21.5773	−	21.5773i	0.696768	−	0.696768i
$960$	9.79787	+	21.0116i	0.316225	+	0.678147i
$961$	−42.1246	+	7.42771i	−1.35886	+	0.239603i
$962$	−2.38285	+	1.66849i	−0.0768261	+	0.0537942i
$963$	1.15010	+	1.64251i	0.0370615	+	0.0529293i
$964$	−12.4198	−	1.08659i	−0.400014	−	0.0349967i
$965$	−4.30153	+	24.3952i	−0.138471	+	0.785309i
$966$	−38.4764	−	10.3097i	−1.23796	−	0.331710i
$967$	20.8838	+	17.5236i	0.671578	+	0.563521i	0.913532	−	0.406767i	$-0.133344\pi$
$967$	20.8838	+	17.5236i	0.671578	+	0.563521i	−0.241954	+	0.970288i	$0.577788\pi$
$968$	−2.83342	−	7.78475i	−0.0910695	−	0.250211i
$969$	−12.6898	+	27.2133i	−0.407654	+	0.874216i
$970$	19.3758	−	72.3116i	0.622121	−	2.32179i
$971$	38.5055	+	38.5055i	1.23570	+	1.23570i	0.961742	+	0.273958i	$0.0883329\pi$
$971$	38.5055	+	38.5055i	1.23570	+	1.23570i	0.273958	+	0.961742i	$0.411667\pi$
$972$	−0.883495	+	2.42738i	−0.0283381	+	0.0778584i
$973$	−64.8831	+	37.4603i	−2.08006	+	1.20092i
$974$	5.54268	−	6.60551i	0.177599	−	0.211654i
$975$	14.0073	−	20.0045i	0.448593	−	0.640657i
$976$			28.1690i			0.901666i
$977$	−2.62629	−	1.83895i	−0.0840224	−	0.0588331i	0.530810	−	0.847491i	$-0.321888\pi$
$977$	−2.62629	−	1.83895i	−0.0840224	−	0.0588331i	−0.614833	+	0.788657i	$0.710777\pi$
$978$	3.39487	+	1.58305i	0.108556	+	0.0506205i
$979$	44.4662	−	11.9147i	1.42115	−	0.380795i
$980$	1.72904	+	19.7630i	0.0552321	+	0.631305i
$981$	0.223586	+	1.26802i	0.00713854	+	0.0404847i
$982$	−2.00804	+	22.9520i	−0.0640790	+	0.732426i
$983$	9.76965	−	0.854733i	0.311603	−	0.0272618i	0.0697184	−	0.997567i	$-0.477790\pi$
$983$	9.76965	−	0.854733i	0.311603	−	0.0272618i	0.241885	+	0.970305i	$0.422234\pi$
$984$	−3.79895	−	4.52741i	−0.121106	−	0.144329i
$985$	−22.3840	−	8.14710i	−0.713213	−	0.259588i
$986$	−23.5042	−	8.55482i	−0.748525	−	0.272441i
$987$	−28.6615	−	34.1574i	−0.912305	−	1.08724i
$988$	10.8347	−	0.947911i	0.344697	−	0.0301571i
$989$	1.83206	−	20.9405i	0.0582560	−	0.665869i
$990$	−0.932177	−	5.28664i	−0.0296265	−	0.168020i
$991$	−4.20990	−	48.1193i	−0.133732	−	1.52856i	−0.705833	−	0.708378i	$-0.749427\pi$
$991$	−4.20990	−	48.1193i	−0.133732	−	1.52856i	0.572101	−	0.820183i	$-0.306128\pi$
$992$	29.9578	−	8.02716i	0.951160	−	0.254863i
$993$	−42.2662	−	19.7090i	−1.34128	−	0.625448i
$994$	−10.4700	−	7.33118i	−0.332089	−	0.232531i
$995$			41.3102i			1.30962i
$996$	3.12290	−	4.45996i	0.0989528	−	0.141319i
$997$	−19.4812	+	23.2168i	−0.616975	+	0.735282i	−0.980547	−	0.196284i	$-0.937113\pi$
$997$	−19.4812	+	23.2168i	−0.616975	+	0.735282i	0.363572	+	0.931566i	$0.381557\pi$
$998$	32.9757	−	19.0385i	1.04383	−	0.602653i
$999$	1.23176	−	3.38423i	0.0389711	−	0.107072i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	73.2.k.a.19.2	✓	72
3.2	odd	2		657.2.cc.d.19.5		72
73.14	odd	72		5329.2.a.o.1.51		72
73.50	even	36	inner	73.2.k.a.50.2	yes	72
73.59	odd	72		5329.2.a.o.1.52		72
219.50	odd	36		657.2.cc.d.415.5		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
73.2.k.a.19.2	✓	72	1.1	even	1	trivial
73.2.k.a.50.2	yes	72	73.50	even	36	inner
657.2.cc.d.19.5		72	3.2	odd	2
657.2.cc.d.415.5		72	219.50	odd	36
5329.2.a.o.1.51		72	73.14	odd	72
5329.2.a.o.1.52		72	73.59	odd	72

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:	\( N \)	\(=\)	\( 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	73.k (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.53348 + 0.558142i) q^{2} +(-1.59146 - 0.918831i) q^{3} +(0.507960 - 0.426229i) q^{4} +(2.94657 - 1.37401i) q^{5} +(2.95332 + 0.520750i) q^{6} +(-1.04180 - 3.88804i) q^{7} +(1.09085 - 1.88940i) q^{8} +(0.188501 + 0.326493i) q^{9} +O(q^{10})\)	\(q+(-1.53348 + 0.558142i) q^{2} +(-1.59146 - 0.918831i) q^{3} +(0.507960 - 0.426229i) q^{4} +(2.94657 - 1.37401i) q^{5} +(2.95332 + 0.520750i) q^{6} +(-1.04180 - 3.88804i) q^{7} +(1.09085 - 1.88940i) q^{8} +(0.188501 + 0.326493i) q^{9} +(-3.75163 + 3.75163i) q^{10} +(1.13422 + 2.43235i) q^{11} +(-1.20003 + 0.211598i) q^{12} +(-1.95431 + 1.36842i) q^{13} +(3.76766 + 5.38077i) q^{14} +(-5.95184 - 0.520718i) q^{15} +(-0.848531 + 4.81226i) q^{16} +(2.29570 + 0.615132i) q^{17} +(-0.471293 - 0.395462i) q^{18} +(-2.35136 - 6.46031i) q^{19} +(0.911098 - 1.95386i) q^{20} +(-1.91447 + 7.14490i) q^{21} +(-3.09691 - 3.09691i) q^{22} +(1.12864 - 3.10092i) q^{23} +(-3.47208 + 2.00461i) q^{24} +(3.58044 - 4.26701i) q^{25} +(2.23312 - 3.18923i) q^{26} +4.82018i q^{27} +(-2.18639 - 1.53092i) q^{28} +(5.84480 + 2.72548i) q^{29} +(9.41768 - 2.52346i) q^{30} +(0.748599 + 8.55652i) q^{31} +(-0.627022 - 3.55602i) q^{32} +(0.429845 - 4.91315i) q^{33} +(-3.86375 + 0.338035i) q^{34} +(-8.41193 - 10.0249i) q^{35} +(0.234912 + 0.0855009i) q^{36} +(-0.702095 - 0.255542i) q^{37} +(7.21155 + 8.59439i) q^{38} +(4.36755 - 0.382111i) q^{39} +(0.618203 - 7.06609i) q^{40} +(0.255980 + 1.45174i) q^{41} +(-1.05206 - 12.0251i) q^{42} +(6.15292 - 1.64867i) q^{43} +(1.61288 + 0.752097i) q^{44} +(1.00404 + 0.703033i) q^{45} +5.38515i q^{46} +(-3.45756 + 4.93791i) q^{47} +(5.77206 - 6.87887i) q^{48} +(-7.96933 + 4.60110i) q^{49} +(-3.10895 + 8.54178i) q^{50} +(-3.08832 - 3.08832i) q^{51} +(-0.409449 + 1.52809i) q^{52} +(0.985852 - 2.11417i) q^{53} +(-2.69035 - 7.39167i) q^{54} +(6.68414 + 5.60866i) q^{55} +(-8.48252 - 2.27288i) q^{56} +(-2.19383 + 12.4418i) q^{57} +(-10.4841 - 0.917241i) q^{58} +(2.20711 + 3.15207i) q^{59} +(-3.24524 + 2.27234i) q^{60} +(5.67708 - 1.00102i) q^{61} +(-5.92372 - 12.7035i) q^{62} +(1.07304 - 1.07304i) q^{63} +(-1.94020 - 3.36053i) q^{64} +(-3.87828 + 6.71738i) q^{65} +(2.08308 + 7.77415i) q^{66} +(7.52003 + 1.32598i) q^{67} +(1.42831 - 0.666033i) q^{68} +(-4.64541 + 3.89797i) q^{69} +(18.4949 + 10.6780i) q^{70} +(-1.82847 + 0.665509i) q^{71} +0.822503 q^{72} +(-7.44139 - 4.19830i) q^{73} +1.21928 q^{74} +(-9.61880 + 3.50096i) q^{75} +(-3.94797 - 2.27936i) q^{76} +(8.27544 - 6.94392i) q^{77} +(-6.48430 + 3.02368i) q^{78} +(7.04357 + 1.24197i) q^{79} +(4.11183 + 15.3455i) q^{80} +(4.99444 - 8.65062i) q^{81} +(-1.20282 - 2.08334i) q^{82} +(-3.15944 + 3.15944i) q^{83} +(2.07289 + 4.44533i) q^{84} +(7.60965 - 1.34179i) q^{85} +(-8.51521 + 5.96242i) q^{86} +(-6.79753 - 9.70787i) q^{87} +(5.83295 + 0.510317i) q^{88} +(2.97856 - 16.8923i) q^{89} +(-1.93207 - 0.517695i) q^{90} +(7.35646 + 6.17281i) q^{91} +(-0.748397 - 2.05620i) q^{92} +(6.67063 - 14.3052i) q^{93} +(2.54606 - 9.50201i) q^{94} +(-15.8050 - 15.8050i) q^{95} +(-2.26950 + 6.23540i) q^{96} +(-12.2197 + 7.05505i) q^{97} +(9.65278 - 11.5037i) q^{98} +(-0.580343 + 0.828816i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9}+O(q^{10}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9	\( 72 q - 12 q^{2} - 18 q^{3} - 12 q^{4} - 12 q^{5} - 24 q^{6} - 18 q^{7} - 24 q^{8} + 36 q^{9} - 6 q^{11} + 6 q^{12} - 12 q^{13} - 12 q^{14} - 30 q^{15} + 30 q^{17} - 12 q^{18} - 6 q^{19} + 60 q^{20} - 30 q^{21} - 12 q^{22} - 12 q^{23} - 18 q^{24} + 36 q^{25} + 12 q^{26} + 120 q^{28} - 6 q^{29} - 72 q^{30} - 18 q^{31} - 18 q^{32} - 60 q^{33} - 60 q^{34} - 36 q^{35} + 60 q^{36} - 6 q^{37} + 48 q^{38} + 78 q^{39} - 18 q^{40} + 54 q^{42} - 24 q^{43} + 48 q^{44} + 36 q^{47} + 30 q^{48} - 18 q^{49} + 132 q^{50} - 18 q^{51} - 24 q^{53} - 6 q^{54} + 72 q^{55} + 24 q^{56} - 6 q^{57} - 18 q^{58} - 66 q^{60} - 36 q^{61} - 36 q^{62} + 12 q^{63} - 84 q^{64} + 24 q^{65} + 156 q^{66} - 54 q^{67} - 84 q^{68} - 6 q^{69} - 162 q^{70} + 48 q^{71} - 72 q^{72} - 36 q^{73} + 144 q^{74} + 6 q^{75} - 180 q^{76} - 24 q^{77} - 198 q^{78} - 36 q^{79} - 126 q^{80} - 48 q^{81} + 30 q^{82} - 48 q^{83} - 126 q^{84} - 6 q^{85} - 120 q^{86} + 6 q^{87} + 6 q^{88} + 6 q^{89} + 210 q^{90} + 48 q^{91} + 96 q^{92} + 144 q^{93} - 6 q^{94} - 12 q^{95} + 162 q^{96} - 18 q^{97} + 186 q^{98} + 78 q^{99}+O(q^{100}) \) 72 * q - 12 * q^2 - 18 * q^3 - 12 * q^4 - 12 * q^5 - 24 * q^6 - 18 * q^7 - 24 * q^8 + 36 * q^9 - 6 * q^11 + 6 * q^12 - 12 * q^13 - 12 * q^14 - 30 * q^15 + 30 * q^17 - 12 * q^18 - 6 * q^19 + 60 * q^20 - 30 * q^21 - 12 * q^22 - 12 * q^23 - 18 * q^24 + 36 * q^25 + 12 * q^26 + 120 * q^28 - 6 * q^29 - 72 * q^30 - 18 * q^31 - 18 * q^32 - 60 * q^33 - 60 * q^34 - 36 * q^35 + 60 * q^36 - 6 * q^37 + 48 * q^38 + 78 * q^39 - 18 * q^40 + 54 * q^42 - 24 * q^43 + 48 * q^44 + 36 * q^47 + 30 * q^48 - 18 * q^49 + 132 * q^50 - 18 * q^51 - 24 * q^53 - 6 * q^54 + 72 * q^55 + 24 * q^56 - 6 * q^57 - 18 * q^58 - 66 * q^60 - 36 * q^61 - 36 * q^62 + 12 * q^63 - 84 * q^64 + 24 * q^65 + 156 * q^66 - 54 * q^67 - 84 * q^68 - 6 * q^69 - 162 * q^70 + 48 * q^71 - 72 * q^72 - 36 * q^73 + 144 * q^74 + 6 * q^75 - 180 * q^76 - 24 * q^77 - 198 * q^78 - 36 * q^79 - 126 * q^80 - 48 * q^81 + 30 * q^82 - 48 * q^83 - 126 * q^84 - 6 * q^85 - 120 * q^86 + 6 * q^87 + 6 * q^88 + 6 * q^89 + 210 * q^90 + 48 * q^91 + 96 * q^92 + 144 * q^93 - 6 * q^94 - 12 * q^95 + 162 * q^96 - 18 * q^97 + 186 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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