LMFDB - Embedded newform 430.2.q.a.81.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(31,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([0, 34]))

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

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

chi := DirichletCharacter("430.31");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.q (of order $21$, 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:	$3.43356728692$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$3$ over $\Q(\zeta_{21})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{21}]$

Embedding invariants

Embedding label			81.3
Character	$\chi$	$=$	430.81
Dual form			430.2.q.a.361.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.222521 + 0.974928i) q^{2} +(2.38912 + 0.736945i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-1.25010 + 2.16523i) q^{6} +(0.287026 + 0.497143i) q^{7} +(0.623490 - 0.781831i) q^{8} +(2.68608 + 1.83134i) q^{9} +O(q^{10})$	\(q+(-0.222521 + 0.974928i) q^{2} +(2.38912 + 0.736945i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-1.25010 + 2.16523i) q^{6} +(0.287026 + 0.497143i) q^{7} +(0.623490 - 0.781831i) q^{8} +(2.68608 + 1.83134i) q^{9} +(-0.988831 + 0.149042i) q^{10} +(4.11874 - 1.98348i) q^{11} +(-1.83277 - 1.70056i) q^{12} +(0.587602 + 0.0885668i) q^{13} +(-0.548548 + 0.169205i) q^{14} +(0.186840 + 2.49320i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-1.07509 + 2.73928i) q^{17} +(-2.38313 + 2.21122i) q^{18} +(-5.59903 + 3.81735i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(0.319371 + 1.39926i) q^{21} +(1.01724 + 4.45684i) q^{22} +(0.344899 - 4.60236i) q^{23} +(2.06576 - 1.40841i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-0.217100 + 0.553162i) q^{26} +(0.391232 + 0.490589i) q^{27} +(-0.0428989 - 0.572446i) q^{28} +(-4.24638 + 1.30983i) q^{29} +(-2.47227 - 0.372635i) q^{30} +(1.54792 + 1.43626i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(11.3019 - 1.70348i) q^{33} +(-2.43137 - 1.65768i) q^{34} +(-0.357915 + 0.448811i) q^{35} +(-1.62549 - 2.81543i) q^{36} +(4.26272 - 7.38325i) q^{37} +(-2.47574 - 6.30809i) q^{38} +(1.33858 + 0.644627i) q^{39} +(0.955573 + 0.294755i) q^{40} +(-1.10854 + 4.85685i) q^{41} -1.43524 q^{42} +(4.21095 - 5.02672i) q^{43} -4.57145 q^{44} +(-0.723410 + 3.16947i) q^{45} +(4.41022 + 1.36037i) q^{46} +(-8.34992 - 4.02111i) q^{47} +(0.913424 + 2.32737i) q^{48} +(3.33523 - 5.77679i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-4.58722 + 5.75219i) q^{51} +(-0.490984 - 0.334747i) q^{52} +(-8.68531 + 1.30910i) q^{53} +(-0.565347 + 0.272257i) q^{54} +(3.35111 + 3.10938i) q^{55} +(0.567639 + 0.0855579i) q^{56} +(-16.1899 + 4.99393i) q^{57} +(-0.332086 - 4.43138i) q^{58} +(5.49714 + 6.89320i) q^{59} +(0.913424 - 2.32737i) q^{60} +(2.24005 - 2.07847i) q^{61} +(-1.74469 + 1.18951i) q^{62} +(-0.139463 + 1.86101i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.132231 + 0.579341i) q^{65} +(-0.854130 + 11.3976i) q^{66} +(-4.68241 + 3.19241i) q^{67} +(2.15715 - 2.00155i) q^{68} +(4.21569 - 10.7414i) q^{69} +(-0.357915 - 0.448811i) q^{70} +(-1.03717 - 13.8401i) q^{71} +(3.10654 - 0.958242i) q^{72} +(7.03925 + 1.06100i) q^{73} +(6.24959 + 5.79877i) q^{74} +(-2.25260 + 1.08479i) q^{75} +(6.70084 - 1.00999i) q^{76} +(2.16826 + 1.47829i) q^{77} +(-0.926328 + 1.16158i) q^{78} +(3.09222 + 5.35589i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.98998 - 7.61835i) q^{81} +(-4.48840 - 2.16150i) q^{82} +(3.07159 + 0.947461i) q^{83} +(0.319371 - 1.39926i) q^{84} -2.94270 q^{85} +(3.96366 + 5.22392i) q^{86} -11.1104 q^{87} +(1.01724 - 4.45684i) q^{88} +(2.42242 + 0.747217i) q^{89} +(-2.92903 - 1.41055i) q^{90} +(0.124627 + 0.317543i) q^{91} +(-2.30763 + 3.99694i) q^{92} +(2.63971 + 4.57211i) q^{93} +(5.77833 - 7.24579i) q^{94} +(-5.59903 - 3.81735i) q^{95} +(-2.47227 + 0.372635i) q^{96} +(2.00914 - 0.967549i) q^{97} +(4.88980 + 4.53707i) q^{98} +(14.6957 + 2.21502i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) $ 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{2}{21}\right)$

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 $

$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$2$	−0.222521	+	0.974928i	−0.157346	+	0.689378i
$3$	2.38912	+	0.736945i	1.37936	+	0.425476i	0.893697	−	0.448671i	$-0.148103\pi$
$3$	2.38912	+	0.736945i	1.37936	+	0.425476i	0.485661	+	0.874147i	$0.338579\pi$
$4$	−0.900969	−	0.433884i	−0.450484	−	0.216942i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$5$	0.365341	+	0.930874i	0.163385	+	0.416299i
$6$	−1.25010	+	2.16523i	−0.510350	+	0.883952i
$7$	0.287026	+	0.497143i	0.108485	+	0.187902i	0.915157	−	0.403098i	$-0.132067\pi$
$7$	0.287026	+	0.497143i	0.108485	+	0.187902i	−0.806671	+	0.591000i	$0.798733\pi$
$8$	0.623490	−	0.781831i	0.220437	−	0.276419i
$9$	2.68608	+	1.83134i	0.895361	+	0.610447i
$10$	−0.988831	+	0.149042i	−0.312696	+	0.0471313i
$11$	4.11874	−	1.98348i	1.24185	−	0.598042i	0.306532	−	0.951860i	$-0.400831\pi$
$11$	4.11874	−	1.98348i	1.24185	−	0.598042i	0.935314	+	0.353819i	$0.115117\pi$
$12$	−1.83277	−	1.70056i	−0.529076	−	0.490911i
$13$	0.587602	+	0.0885668i	0.162972	+	0.0245640i	0.230021	−	0.973186i	$-0.426120\pi$
$13$	0.587602	+	0.0885668i	0.162972	+	0.0245640i	−0.0670496	+	0.997750i	$0.521359\pi$
$14$	−0.548548	+	0.169205i	−0.146606	+	0.0452218i
$15$	0.186840	+	2.49320i	0.0482418	+	0.643743i
$16$	0.623490	+	0.781831i	0.155872	+	0.195458i
$17$	−1.07509	+	2.73928i	−0.260748	+	0.664374i	−0.999959	−	0.00909995i	$-0.997103\pi$
$17$	−1.07509	+	2.73928i	−0.260748	+	0.664374i	0.739211	+	0.673474i	$0.235199\pi$
$18$	−2.38313	+	2.21122i	−0.561710	+	0.521191i
$19$	−5.59903	+	3.81735i	−1.28451	+	0.875761i	−0.996640	−	0.0819098i	$-0.973898\pi$
$19$	−5.59903	+	3.81735i	−1.28451	+	0.875761i	−0.287866	+	0.957671i	$0.592946\pi$
$20$	0.0747301	−	0.997204i	0.0167102	−	0.222982i
$21$	0.319371	+	1.39926i	0.0696924	+	0.305343i
$22$	1.01724	+	4.45684i	0.216877	+	0.950201i
$23$	0.344899	−	4.60236i	0.0719164	−	0.959658i	−0.838215	−	0.545339i	$-0.816401\pi$
$23$	0.344899	−	4.60236i	0.0719164	−	0.959658i	0.910132	−	0.414319i	$-0.135980\pi$
$24$	2.06576	−	1.40841i	0.421671	−	0.287490i
$25$	−0.733052	+	0.680173i	−0.146610	+	0.136035i
$26$	−0.217100	+	0.553162i	−0.0425768	+	0.108484i
$27$	0.391232	+	0.490589i	0.0752926	+	0.0944140i
$28$	−0.0428989	−	0.572446i	−0.00810713	−	0.108182i
$29$	−4.24638	+	1.30983i	−0.788533	+	0.243230i	−0.662763	−	0.748829i	$-0.730616\pi$
$29$	−4.24638	+	1.30983i	−0.788533	+	0.243230i	−0.125770	+	0.992059i	$0.540140\pi$
$30$	−2.47227	−	0.372635i	−0.451373	−	0.0680335i
$31$	1.54792	+	1.43626i	0.278014	+	0.257959i	0.806839	−	0.590772i	$-0.201177\pi$
$31$	1.54792	+	1.43626i	0.278014	+	0.257959i	−0.528825	+	0.848731i	$0.677367\pi$
$32$	−0.900969	+	0.433884i	−0.159270	+	0.0767005i
$33$	11.3019	−	1.70348i	1.96740	−	0.296538i
$34$	−2.43137	−	1.65768i	−0.416977	−	0.284290i
$35$	−0.357915	+	0.448811i	−0.0604987	+	0.0758629i
$36$	−1.62549	−	2.81543i	−0.270915	−	0.469238i
$37$	4.26272	−	7.38325i	0.700787	−	1.21380i	−0.267403	−	0.963585i	$-0.586166\pi$
$37$	4.26272	−	7.38325i	0.700787	−	1.21380i	0.968190	−	0.250214i	$-0.0805011\pi$
$38$	−2.47574	−	6.30809i	−0.401619	−	1.02331i
$39$	1.33858	+	0.644627i	0.214345	+	0.103223i
$40$	0.955573	+	0.294755i	0.151089	+	0.0466049i
$41$	−1.10854	+	4.85685i	−0.173125	+	0.758512i	0.811574	+	0.584250i	$0.198611\pi$
$41$	−1.10854	+	4.85685i	−0.173125	+	0.758512i	−0.984699	+	0.174262i	$0.944246\pi$
$42$	−1.43524			−0.221462
$43$	4.21095	−	5.02672i	0.642164	−	0.766567i
$43$	4.21095	−	5.02672i	0.642164	−	0.766567i
$44$	−4.57145			−0.689173
$45$	−0.723410	+	3.16947i	−0.107840	+	0.472476i
$46$	4.41022	+	1.36037i	0.650251	+	0.200576i
$47$	−8.34992	−	4.02111i	−1.21796	−	0.586539i	−0.289218	−	0.957263i	$-0.593395\pi$
$47$	−8.34992	−	4.02111i	−1.21796	−	0.586539i	−0.928743	+	0.370724i	$0.879110\pi$
$48$	0.913424	+	2.32737i	0.131841	+	0.335926i
$49$	3.33523	−	5.77679i	0.476462	−	0.825256i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−4.58722	+	5.75219i	−0.642339	+	0.805468i
$52$	−0.490984	−	0.334747i	−0.0680872	−	0.0464211i
$53$	−8.68531	+	1.30910i	−1.19302	+	0.179819i	−0.715379	−	0.698737i	$-0.753746\pi$
$53$	−8.68531	+	1.30910i	−1.19302	+	0.179819i	−0.477640	+	0.878555i	$0.658508\pi$
$54$	−0.565347	+	0.272257i	−0.0769339	+	0.0370494i
$55$	3.35111	+	3.10938i	0.451864	+	0.419268i
$56$	0.567639	+	0.0855579i	0.0758540	+	0.0114332i
$57$	−16.1899	+	4.99393i	−2.14441	+	0.661462i
$58$	−0.332086	−	4.43138i	−0.0436050	−	0.581869i
$59$	5.49714	+	6.89320i	0.715667	+	0.897418i	0.998084	−	0.0618739i	$-0.0197077\pi$
$59$	5.49714	+	6.89320i	0.715667	+	0.897418i	−0.282417	+	0.959292i	$0.591136\pi$
$60$	0.913424	−	2.32737i	0.117923	−	0.300462i
$61$	2.24005	−	2.07847i	0.286810	−	0.266120i	−0.523626	−	0.851948i	$-0.675421\pi$
$61$	2.24005	−	2.07847i	0.286810	−	0.266120i	0.810435	+	0.585828i	$0.199231\pi$
$62$	−1.74469	+	1.18951i	−0.221576	+	0.151068i
$63$	−0.139463	+	1.86101i	−0.0175707	+	0.234465i
$64$	−0.222521	−	0.974928i	−0.0278151	−	0.121866i
$65$	0.132231	+	0.579341i	0.0164012	+	0.0718584i
$66$	−0.854130	+	11.3976i	−0.105136	+	1.40294i
$67$	−4.68241	+	3.19241i	−0.572048	+	0.390016i	−0.814514	−	0.580144i	$-0.802996\pi$
$67$	−4.68241	+	3.19241i	−0.572048	+	0.390016i	0.242466	+	0.970160i	$0.422044\pi$
$68$	2.15715	−	2.00155i	0.261593	−	0.242723i
$69$	4.21569	−	10.7414i	0.507510	−	1.29311i
$70$	−0.357915	−	0.448811i	−0.0427790	−	0.0536432i
$71$	−1.03717	−	13.8401i	−0.123089	−	1.64251i	−0.627188	−	0.778868i	$-0.715794\pi$
$71$	−1.03717	−	13.8401i	−0.123089	−	1.64251i	0.504099	−	0.863646i	$-0.331825\pi$
$72$	3.10654	−	0.958242i	0.366110	−	0.112930i
$73$	7.03925	+	1.06100i	0.823882	+	0.124180i	0.547434	−	0.836849i	$-0.315605\pi$
$73$	7.03925	+	1.06100i	0.823882	+	0.124180i	0.276448	+	0.961029i	$0.410843\pi$
$74$	6.24959	+	5.79877i	0.726500	+	0.674094i
$75$	−2.25260	+	1.08479i	−0.260108	+	0.125261i
$76$	6.70084	−	1.00999i	0.768639	−	0.115854i
$77$	2.16826	+	1.47829i	0.247096	+	0.168467i
$78$	−0.926328	+	1.16158i	−0.104886	+	0.131523i
$79$	3.09222	+	5.35589i	0.347902	+	0.602584i	0.985877	−	0.167473i	$-0.0535608\pi$
$79$	3.09222	+	5.35589i	0.347902	+	0.602584i	−0.637974	+	0.770058i	$0.720227\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−2.98998	−	7.61835i	−0.332220	−	0.846483i
$82$	−4.48840	−	2.16150i	−0.495661	−	0.238698i
$83$	3.07159	+	0.947461i	0.337151	+	0.103997i	0.458708	−	0.888587i	$-0.348312\pi$
$83$	3.07159	+	0.947461i	0.337151	+	0.103997i	−0.121557	+	0.992584i	$0.538789\pi$
$84$	0.319371	−	1.39926i	0.0348462	−	0.152671i
$85$	−2.94270			−0.319181
$86$	3.96366	+	5.22392i	0.427413	+	0.563310i
$87$	−11.1104			−1.19116
$88$	1.01724	−	4.45684i	0.108439	−	0.475101i
$89$	2.42242	+	0.747217i	0.256776	+	0.0792048i	0.420470	−	0.907306i	$-0.361865\pi$
$89$	2.42242	+	0.747217i	0.256776	+	0.0792048i	−0.163695	+	0.986511i	$0.552341\pi$
$90$	−2.92903	−	1.41055i	−0.308747	−	0.148685i
$91$	0.124627	+	0.317543i	0.0130644	+	0.0332876i
$92$	−2.30763	+	3.99694i	−0.240587	+	0.416709i
$93$	2.63971	+	4.57211i	0.273725	+	0.474106i
$94$	5.77833	−	7.24579i	0.595989	−	0.747346i
$95$	−5.59903	−	3.81735i	−0.574448	−	0.391652i
$96$	−2.47227	+	0.372635i	−0.252325	+	0.0380319i
$97$	2.00914	−	0.967549i	0.203997	−	0.0982397i	−0.329096	−	0.944296i	$-0.606744\pi$
$97$	2.00914	−	0.967549i	0.203997	−	0.0982397i	0.533093	+	0.846057i	$0.321030\pi$
$98$	4.88980	+	4.53707i	0.493944	+	0.458313i
$99$	14.6957	+	2.21502i	1.47697	+	0.222618i
$100$	0.955573	−	0.294755i	0.0955573	−	0.0294755i
$101$	−0.224835	−	3.00021i	−0.0223719	−	0.298532i	−0.997155	−	0.0753779i	$-0.975984\pi$
$101$	−0.224835	−	3.00021i	−0.0223719	−	0.298532i	0.974783	−	0.223154i	$-0.0716354\pi$
$102$	−4.58722	−	5.75219i	−0.454202	−	0.569552i
$103$	0.190493	−	0.485368i	0.0187698	−	0.0478247i	−0.921182	−	0.389133i	$-0.872775\pi$
$103$	0.190493	−	0.485368i	0.0187698	−	0.0478247i	0.939951	+	0.341308i	$0.110870\pi$
$104$	0.435608	−	0.404186i	0.0427149	−	0.0396336i
$105$	−1.18585	+	0.808499i	−0.115727	+	0.0789015i
$106$	0.656385	−	8.75885i	0.0637538	−	0.850735i
$107$	−1.47958	−	6.48245i	−0.143036	−	0.626682i	−0.994720	−	0.102626i	$-0.967275\pi$
$107$	−1.47958	−	6.48245i	−0.143036	−	0.626682i	0.851684	−	0.524056i	$-0.175582\pi$
$108$	−0.139629	−	0.611755i	−0.0134358	−	0.0588662i
$109$	0.394997	−	5.27087i	0.0378339	−	0.504858i	−0.945808	−	0.324725i	$-0.894728\pi$
$109$	0.394997	−	5.27087i	0.0378339	−	0.504858i	0.983642	−	0.180133i	$-0.0576528\pi$
$110$	−3.77711	+	2.57519i	−0.360134	+	0.245535i
$111$	15.6252	−	14.4981i	1.48308	−	1.37610i
$112$	−0.209724	+	0.534369i	−0.0198171	+	0.0504931i
$113$	−7.81839	−	9.80395i	−0.735492	−	0.922278i	0.263611	−	0.964629i	$-0.415087\pi$
$113$	−7.81839	−	9.80395i	−0.735492	−	0.922278i	−0.999103	+	0.0423513i	$0.986515\pi$
$114$	−1.26613	−	16.8953i	−0.118583	−	1.58239i
$115$	4.41022	−	1.36037i	0.411255	−	0.126855i
$116$	4.39417	+	0.662315i	0.407989	+	0.0614944i
$117$	1.41615	+	1.31400i	0.130923	+	0.121479i
$118$	−7.94360	+	3.82544i	−0.731268	+	0.352160i
$119$	−1.67039	+	0.251771i	−0.153125	+	0.0230798i
$120$	2.06576	+	1.40841i	0.188577	+	0.128570i
$121$	6.17142	−	7.73872i	0.561038	−	0.703520i
$122$	1.52790	+	2.64639i	0.138329	+	0.239593i
$123$	−6.22767	+	10.7866i	−0.561530	+	0.972599i
$124$	−0.771456	−	1.96564i	−0.0692788	−	0.176519i
$125$	−0.900969	−	0.433884i	−0.0805851	−	0.0388077i
$126$	−1.78331	−	0.550080i	−0.158870	−	0.0490050i
$127$	1.15957	−	5.08042i	0.102895	−	0.450814i	−0.897065	−	0.441899i	$-0.854305\pi$
$127$	1.15957	−	5.08042i	0.102895	−	0.450814i	0.999960	−	0.00891518i	$-0.00283783\pi$
$128$	1.00000			0.0883883
$129$	13.7649	−	8.90618i	1.21193	−	0.784146i
$130$	−0.594239			−0.0521183
$131$	−4.43020	+	19.4100i	−0.387069	+	1.69586i	0.287611	+	0.957747i	$0.407139\pi$
$131$	−4.43020	+	19.4100i	−0.387069	+	1.69586i	−0.674680	+	0.738111i	$0.735718\pi$
$132$	−10.9217	−	3.36891i	−0.950616	−	0.293226i
$133$	−3.50483	−	1.68784i	−0.303908	−	0.146354i
$134$	−2.07044	−	5.27539i	−0.178859	−	0.455725i
$135$	−0.313744	+	0.543420i	−0.0270028	+	0.0467702i
$136$	1.47135	+	2.54845i	0.126167	+	0.218528i
$137$	−11.5058	+	14.4278i	−0.983006	+	1.23265i	−0.0104589	+	0.999945i	$0.503329\pi$
$137$	−11.5058	+	14.4278i	−0.983006	+	1.23265i	−0.972547	+	0.232705i	$0.925242\pi$
$138$	9.53402	+	6.50018i	0.811589	+	0.553332i
$139$	20.1496	−	3.03706i	1.70907	−	0.257600i	0.779539	−	0.626353i	$-0.215453\pi$
$139$	20.1496	−	3.03706i	1.70907	−	0.257600i	0.929527	+	0.368753i	$0.120215\pi$
$140$	0.517202	−	0.249071i	0.0437116	−	0.0210504i
$141$	−16.9856	−	15.7603i	−1.43045	−	1.32726i
$142$	13.7239	+	2.06854i	1.15168	+	0.173588i
$143$	2.59585	−	0.800714i	0.217076	−	0.0669591i
$144$	0.242946	+	3.24189i	0.0202455	+	0.270157i
$145$	−2.77067	−	3.47431i	−0.230091	−	0.288525i
$146$	−2.60078	+	6.62667i	−0.215242	+	0.548427i
$147$	12.2254	−	11.3436i	1.00834	−	0.935601i
$148$	−7.04405	+	4.80255i	−0.579018	+	0.394767i
$149$	1.08344	−	14.4575i	0.0887586	−	1.18440i	−0.757939	−	0.652326i	$-0.773793\pi$
$149$	1.08344	−	14.4575i	0.0887586	−	1.18440i	0.846697	−	0.532075i	$-0.178588\pi$
$150$	−0.556346	−	2.43751i	−0.0454254	−	0.199022i
$151$	1.29007	+	5.65218i	0.104985	+	0.459968i	0.999906	+	0.0137430i	$0.00437466\pi$
$151$	1.29007	+	5.65218i	0.104985	+	0.459968i	−0.894921	+	0.446225i	$0.852768\pi$
$152$	−0.506410	+	6.75758i	−0.0410753	+	0.548112i
$153$	−7.90434	+	5.38909i	−0.639028	+	0.435682i
$154$	−1.92371	+	1.78494i	−0.155017	+	0.143835i
$155$	−0.771456	+	1.96564i	−0.0619648	+	0.157884i
$156$	−0.926328	−	1.16158i	−0.0741656	−	0.0930007i
$157$	−0.290434	−	3.87558i	−0.0231792	−	0.309305i	−0.996728	−	0.0808264i	$-0.974244\pi$
$157$	−0.290434	−	3.87558i	−0.0231792	−	0.309305i	0.973549	−	0.228478i	$-0.0733750\pi$
$158$	−5.90969	+	1.82290i	−0.470150	+	0.145022i
$159$	−21.7150	−	3.27301i	−1.72211	−	0.259566i
$160$	−0.733052	−	0.680173i	−0.0579528	−	0.0537724i
$161$	2.38702	−	1.14953i	0.188124	−	0.0905957i
$162$	8.09268	−	1.21977i	0.635821	−	0.0958345i
$163$	−2.39440	−	1.63248i	−0.187544	−	0.127865i	0.465908	−	0.884833i	$-0.345728\pi$
$163$	−2.39440	−	1.63248i	−0.187544	−	0.127865i	−0.653452	+	0.756968i	$0.726680\pi$
$164$	3.10607	−	3.89489i	0.242543	−	0.304140i
$165$	5.71476	+	9.89826i	0.444894	+	0.770579i
$166$	−1.60720	+	2.78375i	−0.124743	+	0.216061i
$167$	−3.19295	−	8.13550i	−0.247078	−	0.629544i	0.752500	−	0.658592i	$-0.228848\pi$
$167$	−3.19295	−	8.13550i	−0.247078	−	0.629544i	−0.999578	+	0.0290480i	$0.990752\pi$
$168$	1.29311	+	0.622727i	0.0997653	+	0.0480444i
$169$	−12.0850	−	3.72773i	−0.929616	−	0.286749i
$170$	0.654813	−	2.86892i	0.0502218	−	0.220036i
$171$	−22.0303			−1.68470
$172$	−5.97495	+	2.70185i	−0.455585	+	0.206014i
$173$	−10.3693			−0.788364			−0.394182	−	0.919032i	$-0.628972\pi$
$173$	−10.3693			−0.788364			−0.394182	+	0.919032i	$0.628972\pi$
$174$	2.47229	−	10.8318i	0.187424	−	0.821158i
$175$	−0.548548	−	0.169205i	−0.0414663	−	0.0127907i
$176$	4.11874	+	1.98348i	0.310462	+	0.149510i
$177$	8.05341	+	20.5198i	0.605331	+	1.54236i
$178$	−1.26752	+	2.19541i	−0.0950047	+	0.164553i
$179$	8.04177	+	13.9288i	0.601070	+	1.04108i	0.992659	+	0.120944i	$0.0385921\pi$
$179$	8.04177	+	13.9288i	0.601070	+	1.04108i	−0.391589	+	0.920140i	$0.628075\pi$
$180$	2.02695	−	2.54171i	0.151080	−	0.189448i
$181$	0.928246	+	0.632868i	0.0689960	+	0.0470407i	0.597327	−	0.801998i	$-0.296230\pi$
$181$	0.928246	+	0.632868i	0.0689960	+	0.0470407i	−0.528331	+	0.849039i	$0.677182\pi$
$182$	−0.337314	+	0.0508419i	−0.0250034	+	0.00376865i
$183$	6.88347	−	3.31490i	0.508841	−	0.245045i
$184$	−3.38323	−	3.13918i	−0.249415	−	0.231423i
$185$	8.43022	+	1.27065i	0.619802	+	0.0934202i
$186$	−5.04487	+	1.55614i	−0.369908	+	0.114101i
$187$	1.00530	+	13.4148i	0.0735149	+	0.980988i
$188$	5.77833	+	7.24579i	0.421428	+	0.528454i
$189$	−0.131599	+	0.335310i	−0.00957245	+	0.0243902i
$190$	4.96755	−	4.60921i	0.360384	−	0.334387i
$191$	−8.98776	+	6.12775i	−0.650332	+	0.443389i	−0.843028	−	0.537870i	$-0.819229\pi$
$191$	−8.98776	+	6.12775i	−0.650332	+	0.443389i	0.192696	+	0.981258i	$0.438277\pi$
$192$	0.186840	−	2.49320i	0.0134840	−	0.179932i
$193$	0.700207	+	3.06781i	0.0504020	+	0.220826i	0.993856	−	0.110676i	$-0.0353017\pi$
$193$	0.700207	+	3.06781i	0.0504020	+	0.220826i	−0.943454	+	0.331502i	$0.892445\pi$
$194$	0.496216	+	2.17406i	0.0356262	+	0.156089i
$195$	−0.111028	+	1.48156i	−0.00795085	+	0.106097i
$196$	−5.51140	+	3.75761i	−0.393671	+	0.268400i
$197$	−16.3493	+	15.1700i	−1.16484	+	1.08082i	−0.169391	+	0.985549i	$0.554180\pi$
$197$	−16.3493	+	15.1700i	−1.16484	+	1.08082i	−0.995452	+	0.0952670i	$0.969630\pi$
$198$	−5.42958	+	13.8344i	−0.385864	+	0.983165i
$199$	9.64862	+	12.0990i	0.683973	+	0.857675i	0.995713	−	0.0924926i	$-0.0294834\pi$
$199$	9.64862	+	12.0990i	0.683973	+	0.857675i	−0.311741	+	0.950167i	$0.600912\pi$
$200$	0.0747301	+	0.997204i	0.00528422	+	0.0705130i
$201$	−13.5395	+	4.17637i	−0.955001	+	0.294579i
$202$	2.97502	+	0.448412i	0.209322	+	0.0315502i
$203$	−1.86999	−	1.73510i	−0.131248	−	0.121780i
$204$	6.62872	−	3.19223i	0.464103	−	0.223500i
$205$	−4.92611	+	0.742491i	−0.344054	+	0.0518578i
$206$	0.430810	+	0.293721i	0.0300159	+	0.0204645i
$207$	9.35491	−	11.7307i	0.650211	−	0.815339i
$208$	0.297120	+	0.514627i	0.0206015	+	0.0356829i
$209$	−15.4893	+	26.8282i	−1.07142	+	1.85575i
$210$	−0.524352	−	1.33603i	−0.0361837	−	0.0921946i
$211$	14.3410	+	6.90625i	0.987273	+	0.475446i	0.856601	−	0.515980i	$-0.172572\pi$
$211$	14.3410	+	6.90625i	0.987273	+	0.475446i	0.130672	+	0.991426i	$0.458286\pi$
$212$	8.39319	+	2.58896i	0.576447	+	0.177810i
$213$	7.72145	−	33.8299i	0.529065	−	2.31799i
$214$	6.64916			0.454527
$215$	6.21767	+	2.08340i	0.424042	+	0.142086i
$216$	0.627487			0.0426951
$217$	−0.269733	+	1.18178i	−0.0183107	+	0.0802242i
$218$	5.05082	+	1.55797i	0.342085	+	0.105519i
$219$	16.0357	+	7.72239i	1.08359	+	0.521831i
$220$	−1.67014	−	4.25545i	−0.112601	−	0.286902i
$221$	−0.874335	+	1.51439i	−0.0588141	+	0.101869i
$222$	10.6576	+	18.4596i	0.715294	+	1.23893i
$223$	−12.0501	+	15.1104i	−0.806938	+	1.01187i	0.192594	+	0.981278i	$0.438310\pi$
$223$	−12.0501	+	15.1104i	−0.806938	+	1.01187i	−0.999532	+	0.0305894i	$0.990262\pi$
$224$	−0.474303	−	0.323374i	−0.0316907	−	0.0216064i
$225$	−3.21466	+	0.484533i	−0.214311	+	0.0323022i
$226$	11.2979	−	5.44078i	0.751525	−	0.361915i
$227$	11.0046	+	10.2107i	0.730399	+	0.677711i	0.954955	−	0.296750i	$-0.0959028\pi$
$227$	11.0046	+	10.2107i	0.730399	+	0.677711i	−0.224556	+	0.974461i	$0.572093\pi$
$228$	16.7534	+	2.52517i	1.10952	+	0.167233i
$229$	−19.9349	+	6.14911i	−1.31734	+	0.406345i	−0.872214	−	0.489124i	$-0.837316\pi$
$229$	−19.9349	+	6.14911i	−1.31734	+	0.406345i	−0.445123	+	0.895469i	$0.646840\pi$
$230$	0.344899	+	4.60236i	0.0227420	+	0.303471i
$231$	4.09080	+	5.12970i	0.269155	+	0.337509i
$232$	−1.62350	+	4.13662i	−0.106588	+	0.271582i
$233$	−7.43825	+	6.90169i	−0.487296	+	0.452145i	−0.885151	−	0.465303i	$-0.845945\pi$
$233$	−7.43825	+	6.90169i	−0.487296	+	0.452145i	0.397855	+	0.917448i	$0.369755\pi$
$234$	−1.59618	+	1.08825i	−0.104345	+	0.0711414i
$235$	0.692577	−	9.24180i	0.0451788	−	0.602869i
$236$	−1.96191	−	8.59568i	−0.127709	−	0.559531i
$237$	3.44069	+	15.0747i	0.223497	+	0.979204i
$238$	0.126239	−	1.68454i	0.00818284	−	0.109192i
$239$	8.00500	−	5.45772i	0.517800	−	0.353030i	−0.276050	−	0.961143i	$-0.589026\pi$
$239$	8.00500	−	5.45772i	0.517800	−	0.353030i	0.793851	+	0.608113i	$0.208073\pi$
$240$	−1.83277	+	1.70056i	−0.118305	+	0.109771i
$241$	−4.12523	+	10.5109i	−0.265730	+	0.677068i	−0.999998	−	0.00179066i	$-0.999430\pi$
$241$	−4.12523	+	10.5109i	−0.265730	+	0.677068i	0.734269	+	0.678859i	$0.237525\pi$
$242$	6.17142	+	7.73872i	0.396714	+	0.497464i
$243$	−1.66979	−	22.2818i	−0.107117	−	1.42938i
$244$	−2.92003	+	0.900710i	−0.186936	+	0.0576621i
$245$	6.59596	+	0.994181i	0.421401	+	0.0635159i
$246$	−9.13041	−	8.47178i	−0.582134	−	0.540141i
$247$	−3.62809	+	1.74720i	−0.230850	+	0.111172i
$248$	2.08802	−	0.314718i	0.132589	−	0.0199846i
$249$	6.64017	+	4.52719i	0.420804	+	0.286899i
$250$	0.623490	−	0.781831i	0.0394330	−	0.0494474i
$251$	11.1996	+	19.3983i	0.706913	+	1.22441i	0.965997	+	0.258554i	$0.0832461\pi$
$251$	11.1996	+	19.3983i	0.706913	+	1.22441i	−0.259084	+	0.965855i	$0.583421\pi$
$252$	0.933113	−	1.61620i	0.0587806	−	0.101811i
$253$	−7.70813	−	19.6400i	−0.484606	−	1.23476i
$254$	4.69501	+	2.26100i	0.294591	+	0.141868i
$255$	−7.03046	−	2.16861i	−0.440265	−	0.135804i
$256$	−0.222521	+	0.974928i	−0.0139076	+	0.0609330i
$257$	−9.74573			−0.607922			−0.303961	−	0.952684i	$-0.598309\pi$
$257$	−9.74573			−0.607922			−0.303961	+	0.952684i	$0.598309\pi$
$258$	5.61991	+	15.4016i	0.349881	+	0.958860i
$259$	4.89404			0.304101
$260$	0.132231	−	0.579341i	0.00820060	−	0.0359292i
$261$	−13.8049	−	4.25824i	−0.854500	−	0.263578i
$262$	−17.9375	−	8.63825i	−1.10818	−	0.533673i
$263$	8.50345	+	21.6664i	0.524345	+	1.33601i	0.910475	+	0.413565i	$0.135716\pi$
$263$	8.50345	+	21.6664i	0.524345	+	1.33601i	−0.386130	+	0.922445i	$0.626188\pi$
$264$	5.71476	−	9.89826i	0.351719	−	0.609196i
$265$	−4.39171	−	7.60666i	−0.269780	−	0.467273i
$266$	2.42542	−	3.04138i	0.148712	−	0.186479i
$267$	5.23678	+	3.57038i	0.320486	+	0.218504i
$268$	5.60385	−	0.844644i	0.342309	−	0.0515948i
$269$	−18.2966	+	8.81117i	−1.11556	+	0.537226i	−0.898519	−	0.438936i	$-0.855356\pi$
$269$	−18.2966	+	8.81117i	−1.11556	+	0.537226i	−0.217043	+	0.976162i	$0.569641\pi$
$270$	−0.459981	−	0.426800i	−0.0279935	−	0.0259742i
$271$	8.09413	+	1.21999i	0.491684	+	0.0741094i	0.390204	−	0.920728i	$-0.372404\pi$
$271$	8.09413	+	1.21999i	0.491684	+	0.0741094i	0.101479	+	0.994838i	$0.467642\pi$
$272$	−2.81197	+	0.867377i	−0.170500	+	0.0525924i
$273$	0.0637355	+	0.850491i	0.00385745	+	0.0514741i
$274$	−11.5058	−	14.4278i	−0.695090	−	0.871616i
$275$	−1.67014	+	4.25545i	−0.100713	+	0.256613i
$276$	−8.45873	+	7.84855i	−0.509156	+	0.472427i
$277$	−3.35433	+	2.28694i	−0.201542	+	0.137409i	−0.659886	−	0.751366i	$-0.729395\pi$
$277$	−3.35433	+	2.28694i	−0.201542	+	0.137409i	0.458344	+	0.888775i	$0.348443\pi$
$278$	−1.52279	+	20.3202i	−0.0913309	+	1.21873i
$279$	1.52756	+	6.69266i	0.0914524	+	0.400679i
$280$	0.127738	+	0.559658i	0.00763383	+	0.0334460i
$281$	2.33496	−	31.1578i	0.139292	−	1.85872i	−0.291887	−	0.956453i	$-0.594283\pi$
$281$	2.33496	−	31.1578i	0.139292	−	1.85872i	0.431178	−	0.902267i	$-0.358098\pi$
$282$	19.1449	−	13.0527i	1.14006	−	0.777279i
$283$	−16.0940	+	14.9331i	−0.956690	+	0.887679i	−0.993749	−	0.111634i	$-0.964392\pi$
$283$	−16.0940	+	14.9331i	−0.956690	+	0.887679i	0.0370589	+	0.999313i	$0.488201\pi$
$284$	−5.07052	+	12.9195i	−0.300880	+	0.766630i
$285$	−10.5636	−	13.2463i	−0.625731	−	0.784642i
$286$	0.203007	+	2.70894i	0.0120041	+	0.160183i
$287$	−2.73273	+	0.842934i	−0.161308	+	0.0497568i
$288$	−3.21466	−	0.484533i	−0.189426	−	0.0285514i
$289$	6.11402	+	5.67299i	0.359648	+	0.333705i
$290$	4.00373	−	1.92809i	0.235107	−	0.113222i
$291$	5.51309	−	0.830965i	0.323183	−	0.0487120i
$292$	−5.88180	−	4.01014i	−0.344206	−	0.234676i
$293$	14.7943	−	18.5514i	0.864290	−	1.08379i	−0.131426	−	0.991326i	$-0.541956\pi$
$293$	14.7943	−	18.5514i	0.864290	−	1.08379i	0.995716	−	0.0924599i	$-0.0294730\pi$
$294$	8.33873	+	14.4431i	0.486325	+	0.842339i
$295$	−4.40836	+	7.63551i	−0.256665	+	0.444557i
$296$	−3.11469	−	7.93611i	−0.181038	−	0.461277i
$297$	2.58446	+	1.24461i	0.149965	+	0.0722195i
$298$	13.8539	+	4.27336i	0.802534	+	0.247549i
$299$	0.610280	−	2.67381i	0.0352934	−	0.154630i
$300$	2.50020			0.144349
$301$	3.70765	+	0.650647i	0.213705	+	0.0375027i
$302$	−5.79753			−0.333611
$303$	1.67384	−	7.33355i	0.0961593	−	0.421301i
$304$	−6.47546	−	1.99742i	−0.371393	−	0.114560i
$305$	2.75317	+	1.32586i	0.157646	+	0.0759184i
$306$	−3.49509	−	8.90534i	−0.199801	−	0.509085i
$307$	14.9681	−	25.9255i	0.854275	−	1.47965i	−0.0230401	−	0.999735i	$-0.507335\pi$
$307$	14.9681	−	25.9255i	0.854275	−	1.47965i	0.877316	−	0.479914i	$-0.159332\pi$
$308$	−1.31212	−	2.27267i	−0.0747652	−	0.129497i
$309$	0.812799	−	1.01922i	0.0462385	−	0.0579813i
$310$	−1.74469	−	1.18951i	−0.0990917	−	0.0675596i
$311$	−24.4385	+	3.68352i	−1.38578	+	0.208873i	−0.799224	−	0.601034i	$-0.794756\pi$
$311$	−24.4385	+	3.68352i	−1.38578	+	0.208873i	−0.586559	+	0.809907i	$0.699518\pi$
$312$	1.33858	−	0.644627i	0.0757823	−	0.0364948i
$313$	−19.8697	−	18.4364i	−1.12310	−	1.04209i	−0.998757	−	0.0498462i	$-0.984127\pi$
$313$	−19.8697	−	18.4364i	−1.12310	−	1.04209i	−0.124344	−	0.992239i	$-0.539683\pi$
$314$	3.84303	+	0.579244i	0.216875	+	0.0326886i
$315$	−1.78331	+	0.550080i	−0.100478	+	0.0309935i
$316$	−0.462164	−	6.16715i	−0.0259988	−	0.346930i
$317$	−13.4589	−	16.8769i	−0.755927	−	0.947903i	0.243833	−	0.969817i	$-0.421595\pi$
$317$	−13.4589	−	16.8769i	−0.755927	−	0.947903i	−0.999760	+	0.0219145i	$0.993024\pi$
$318$	8.02298	−	20.4422i	0.449906	−	1.14634i
$319$	−14.8917	+	13.8175i	−0.833775	+	0.773630i
$320$	0.826239	−	0.563320i	0.0461882	−	0.0314905i
$321$	1.24233	−	16.5777i	0.0693400	−	0.925278i
$322$	0.589546	+	2.58297i	0.0328541	+	0.143943i
$323$	−4.43736	−	19.4413i	−0.246901	−	1.08174i
$324$	−0.611597	+	8.16120i	−0.0339776	+	0.453400i
$325$	−0.490984	+	0.334747i	−0.0272349	+	0.0185684i
$326$	2.12435	−	1.97111i	0.117657	−	0.109170i
$327$	4.82804	−	12.3016i	0.266991	−	0.680283i
$328$	3.10607	+	3.89489i	0.171504	+	0.215059i
$329$	−0.397575	−	5.30527i	−0.0219190	−	0.292489i
$330$	−10.9217	+	3.36891i	−0.601222	+	0.185453i
$331$	18.1764	+	2.73965i	0.999066	+	0.150585i	0.628159	−	0.778085i	$-0.283809\pi$
$331$	18.1764	+	2.73965i	0.999066	+	0.150585i	0.370907	+	0.928670i	$0.379047\pi$
$332$	−2.35632	−	2.18635i	−0.129320	−	0.119991i
$333$	24.9713	−	12.0255i	1.36842	−	0.658995i
$334$	8.64203	−	1.30258i	0.472871	−	0.0712738i
$335$	−4.68241	−	3.19241i	−0.255828	−	0.174420i
$336$	−0.894857	+	1.12212i	−0.0488185	+	0.0612164i
$337$	4.33662	+	7.51125i	0.236231	+	0.409164i	0.959630	−	0.281266i	$-0.0907545\pi$
$337$	4.33662	+	7.51125i	0.236231	+	0.409164i	−0.723399	+	0.690431i	$0.757421\pi$
$338$	6.32344	−	10.9525i	0.343950	−	0.595738i
$339$	−11.4541	−	29.1845i	−0.622100	−	1.58509i
$340$	2.65128	+	1.27679i	0.143786	+	0.0692437i
$341$	9.22424	+	2.84530i	0.499521	+	0.154082i
$342$	4.90221	−	21.4780i	0.265081	−	1.16140i
$343$	7.84755			0.423728
$344$	−1.30456	−	6.42636i	−0.0703373	−	0.346486i
$345$	11.5391			0.621242
$346$	2.30739	−	10.1093i	0.124046	−	0.543481i
$347$	−3.91512	−	1.20765i	−0.210175	−	0.0648303i	0.187880	−	0.982192i	$-0.439838\pi$
$347$	−3.91512	−	1.20765i	−0.210175	−	0.0648303i	−0.398055	+	0.917362i	$0.630315\pi$
$348$	10.0101	+	4.82061i	0.536598	+	0.258412i
$349$	4.51695	+	11.5090i	0.241787	+	0.616063i	0.999325	−	0.0367274i	$-0.0116933\pi$
$349$	4.51695	+	11.5090i	0.241787	+	0.616063i	−0.757538	+	0.652791i	$0.773598\pi$
$350$	0.287026	−	0.497143i	0.0153422	−	0.0265734i
$351$	0.186439	+	0.322922i	0.00995137	+	0.0172363i
$352$	−2.85025	+	3.57411i	−0.151919	+	0.190501i
$353$	7.55313	+	5.14963i	0.402012	+	0.274087i	0.747402	−	0.664372i	$-0.231301\pi$
$353$	7.55313	+	5.14963i	0.402012	+	0.274087i	−0.345390	+	0.938459i	$0.612253\pi$
$354$	−21.7973	+	3.28542i	−1.15852	+	0.174618i
$355$	12.5044	−	6.02182i	0.663666	−	0.319605i
$356$	−1.85832	−	1.72427i	−0.0984906	−	0.0913859i
$357$	−4.17631	−	0.629477i	−0.221034	−	0.0333155i
$358$	−15.3690	+	4.74071i	−0.812276	+	0.250554i
$359$	2.76287	+	36.8679i	0.145818	+	1.94581i	0.291699	+	0.956510i	$0.405779\pi$
$359$	2.76287	+	36.8679i	0.145818	+	1.94581i	−0.145881	+	0.989302i	$0.546602\pi$
$360$	2.02695	+	2.54171i	0.106830	+	0.133960i
$361$	9.83546	−	25.0603i	0.517656	−	1.31897i
$362$	−0.823555	+	0.764147i	−0.0432851	+	0.0401627i
$363$	20.4473	−	13.9407i	1.07320	−	0.731698i
$364$	0.0254922	−	0.340170i	0.00133616	−	0.0178298i
$365$	1.58407	+	6.94028i	0.0829142	+	0.363271i
$366$	1.70008	+	7.44852i	0.0888644	+	0.389341i
$367$	−0.169093	+	2.25638i	−0.00882656	+	0.117782i	−0.999877	−	0.0157085i	$-0.995000\pi$
$367$	−0.169093	+	2.25638i	−0.00882656	+	0.117782i	0.991050	+	0.133491i	$0.0426187\pi$
$368$	3.81331	−	2.59987i	0.198783	−	0.135528i
$369$	−11.8722	+	11.0158i	−0.618041	+	0.573458i
$370$	−3.11469	+	7.93611i	−0.161925	+	0.412579i
$371$	−3.14372	−	3.94209i	−0.163214	−	0.204663i
$372$	−0.394532	−	5.26466i	−0.0204555	−	0.272960i
$373$	−10.9015	+	3.36265i	−0.564456	+	0.174112i	−0.563834	−	0.825888i	$-0.690674\pi$
$373$	−10.9015	+	3.36265i	−0.564456	+	0.174112i	−0.000621998		1.00000i	$0.500198\pi$
$374$	−13.3022	−	2.00498i	−0.687839	−	0.103675i
$375$	−1.83277	−	1.70056i	−0.0946440	−	0.0878168i
$376$	−8.34992	+	4.02111i	−0.430614	+	0.207373i
$377$	−2.61119	+	0.393574i	−0.134483	+	0.0202701i
$378$	−0.297619	−	0.202913i	−0.0153079	−	0.0104367i
$379$	11.5033	−	14.4246i	0.590883	−	0.740944i	−0.393043	−	0.919520i	$-0.628578\pi$
$379$	11.5033	−	14.4246i	0.590883	−	0.740944i	0.983926	+	0.178576i	$0.0571492\pi$
$380$	3.38826	+	5.86864i	0.173814	+	0.301055i
$381$	6.51434	−	11.2832i	0.333740	−	0.578054i
$382$	−3.97415	−	10.1260i	−0.203335	−	0.518090i
$383$	13.7973	+	6.64444i	0.705010	+	0.339515i	0.751801	−	0.659390i	$-0.229185\pi$
$383$	13.7973	+	6.64444i	0.705010	+	0.339515i	−0.0467912	+	0.998905i	$0.514900\pi$
$384$	2.38912	+	0.736945i	0.121919	+	0.0376071i
$385$	−0.583950	+	2.55845i	−0.0297609	+	0.130391i
$386$	−3.14670			−0.160163
$387$	20.5166	−	5.79050i	1.04292	−	0.294347i
$388$	−2.22997			−0.113210
$389$	−1.61931	+	7.09465i	−0.0821021	+	0.359713i	−0.999245	−	0.0388451i	$-0.987632\pi$
$389$	−1.61931	+	7.09465i	−0.0821021	+	0.359713i	0.917143	+	0.398558i	$0.130489\pi$
$390$	−1.41971	−	0.437922i	−0.0718897	−	0.0221750i
$391$	12.2364	+	5.89272i	0.618820	+	0.298008i
$392$	−2.43699	−	6.20936i	−0.123087	−	0.313620i
$393$	−24.8884	+	43.1079i	−1.25545	+	2.17451i
$394$	−11.1516	−	19.3151i	−0.561807	−	0.973079i
$395$	−3.85594	+	4.83520i	−0.194013	+	0.243285i
$396$	−12.2793	−	8.37189i	−0.617058	−	0.420703i
$397$	22.7555	−	3.42983i	1.14206	−	0.172138i	0.449353	−	0.893354i	$-0.351654\pi$
$397$	22.7555	−	3.42983i	1.14206	−	0.172138i	0.692711	+	0.721216i	$0.256416\pi$
$398$	−13.9427	+	6.71443i	−0.698883	+	0.336564i
$399$	−7.12962	−	6.61532i	−0.356927	−	0.331180i
$400$	−0.988831	−	0.149042i	−0.0494415	−	0.00745211i
$401$	−3.43874	+	1.06071i	−0.171722	+	0.0529693i	−0.379424	−	0.925223i	$-0.623878\pi$
$401$	−3.43874	+	1.06071i	−0.171722	+	0.0529693i	0.207702	+	0.978192i	$0.433402\pi$
$402$	−1.05885	−	14.1293i	−0.0528105	−	0.704708i
$403$	0.782354	+	0.981041i	0.0389718	+	0.0488691i
$404$	−1.09917	+	2.80065i	−0.0546859	+	0.139337i
$405$	5.99936	−	5.56659i	0.298111	−	0.276606i
$406$	2.10771	−	1.43701i	0.104604	−	0.0713178i
$407$	2.91251	−	38.8647i	0.144368	−	1.92645i
$408$	1.63716	+	7.17286i	0.0810515	+	0.355110i
$409$	2.59419	+	11.3659i	0.128275	+	0.562008i	0.997690	+	0.0679264i	$0.0216383\pi$
$409$	2.59419	+	11.3659i	0.128275	+	0.562008i	−0.869416	+	0.494081i	$0.835505\pi$
$410$	0.372287	−	4.96782i	0.0183859	−	0.245343i
$411$	−38.1212	+	25.9906i	−1.88038	+	1.28202i
$412$	−0.382221	+	0.354649i	−0.0188307	+	0.0174723i
$413$	−1.84908	+	4.71139i	−0.0909874	+	0.231832i
$414$	9.35491	+	11.7307i	0.459769	+	0.576532i
$415$	0.240212	+	3.20541i	0.0117916	+	0.157347i
$416$	−0.567839	+	0.175155i	−0.0278406	+	0.00858769i
$417$	50.3779	+	7.59325i	2.46702	+	0.371843i
$418$	−22.7089	−	21.0708i	−1.11073	−	1.03061i
$419$	−32.4090	+	15.6073i	−1.58328	+	0.762468i	−0.998802	−	0.0489405i	$-0.984416\pi$
$419$	−32.4090	+	15.6073i	−1.58328	+	0.762468i	−0.584479	+	0.811409i	$0.698701\pi$
$420$	1.41921	−	0.213911i	0.0692503	−	0.0104378i
$421$	31.6977	+	21.6111i	1.54485	+	1.05326i	0.972399	+	0.233325i	$0.0749605\pi$
$421$	31.6977	+	21.6111i	1.54485	+	1.05326i	0.572453	+	0.819937i	$0.305992\pi$
$422$	−9.92426	+	12.4446i	−0.483105	+	0.605795i
$423$	−15.0646	−	26.0926i	−0.732464	−	1.26866i
$424$	−4.39171	+	7.60666i	−0.213280	+	0.369412i
$425$	−1.07509	−	2.73928i	−0.0521495	−	0.132875i
$426$	31.2635	+	15.0557i	1.51472	+	0.729452i
$427$	1.67625	+	0.517054i	0.0811193	+	0.0250220i
$428$	−1.47958	+	6.48245i	−0.0715181	+	0.313341i
$429$	6.79188			0.327915
$430$	−3.41472	+	5.59818i	−0.164673	+	0.269968i
$431$	5.80701			0.279714			0.139857	−	0.990172i	$-0.455336\pi$
$431$	5.80701			0.279714			0.139857	+	0.990172i	$0.455336\pi$
$432$	−0.139629	+	0.611755i	−0.00671791	+	0.0294331i
$433$	−10.4321	−	3.21788i	−0.501335	−	0.154641i	0.0337655	−	0.999430i	$-0.489250\pi$
$433$	−10.4321	−	3.21788i	−0.501335	−	0.154641i	−0.535101	+	0.844788i	$0.679726\pi$
$434$	−1.09213	−	0.525940i	−0.0524237	−	0.0252459i
$435$	−4.05908	−	10.3424i	−0.194618	−	0.495878i
$436$	−2.64283	+	4.57751i	−0.126568	+	0.219223i
$437$	15.6377	+	27.0853i	0.748054	+	1.29567i
$438$	−11.0971	+	13.9153i	−0.530238	+	0.664897i
$439$	−31.7127	−	21.6213i	−1.51356	−	1.03193i	−0.982856	−	0.184376i	$-0.940974\pi$
$439$	−31.7127	−	21.6213i	−1.51356	−	1.03193i	−0.530708	−	0.847555i	$-0.678074\pi$
$440$	4.52039	−	0.681340i	0.215501	−	0.0324816i
$441$	19.5380	−	9.40899i	0.930380	−	0.448047i
$442$	−1.28187	−	1.18940i	−0.0609721	−	0.0565739i
$443$	26.4909	+	3.99286i	1.25862	+	0.189706i	0.744273	−	0.667876i	$-0.232796\pi$
$443$	26.4909	+	3.99286i	1.25862	+	0.189706i	0.514347	+	0.857582i	$0.328034\pi$
$444$	−20.3683	+	6.28279i	−0.966636	+	0.298168i
$445$	0.189444	+	2.52795i	0.00898050	+	0.119836i
$446$	−12.0501	−	15.1104i	−0.570591	−	0.715499i
$447$	13.2428	−	33.7421i	0.626364	−	1.59595i
$448$	0.420809	−	0.390454i	0.0198814	−	0.0184472i
$449$	9.20992	−	6.27922i	0.434643	−	0.296335i	−0.326164	−	0.945313i	$-0.605756\pi$
$449$	9.20992	−	6.27922i	0.434643	−	0.296335i	0.760806	+	0.648979i	$0.224804\pi$
$450$	0.242946	−	3.24189i	0.0114526	−	0.152824i
$451$	5.06765	+	22.2028i	0.238627	+	1.04549i
$452$	2.79035	+	12.2253i	0.131247	+	0.575031i
$453$	−1.08321	+	14.4544i	−0.0508937	+	0.679129i
$454$	−12.4035	+	8.45656i	−0.582125	+	0.396886i
$455$	−0.250061	+	0.232023i	−0.0117231	+	0.0108774i
$456$	−6.18984	+	15.7715i	−0.289866	+	0.738566i
$457$	24.5401	+	30.7723i	1.14794	+	1.43947i	0.879329	+	0.476216i	$0.157992\pi$
$457$	24.5401	+	30.7723i	1.14794	+	1.43947i	0.268607	+	0.963250i	$0.413437\pi$
$458$	−1.55900	−	20.8034i	−0.0728474	−	0.972080i
$459$	−1.76447	+	0.544268i	−0.0823586	+	0.0254043i
$460$	−4.56371	−	0.687869i	−0.212784	−	0.0320721i
$461$	−10.5023	−	9.74467i	−0.489139	−	0.453855i	0.396632	−	0.917978i	$-0.370179\pi$
$461$	−10.5023	−	9.74467i	−0.489139	−	0.453855i	−0.885771	+	0.464123i	$0.846369\pi$
$462$	−5.91138	+	2.84677i	−0.275022	+	0.132444i
$463$	−23.7078	+	3.57337i	−1.10179	+	0.166069i	−0.674666	−	0.738123i	$-0.735712\pi$
$463$	−23.7078	+	3.57337i	−1.10179	+	0.166069i	−0.427127	+	0.904192i	$0.640474\pi$
$464$	−3.67164	−	2.50328i	−0.170452	−	0.116212i
$465$	−3.29167	+	4.12762i	−0.152647	+	0.191414i
$466$	−5.07348	−	8.78753i	−0.235025	−	0.407075i
$467$	7.07129	−	12.2478i	0.327220	−	0.566762i	−0.654739	−	0.755855i	$-0.727221\pi$
$467$	7.07129	−	12.2478i	0.327220	−	0.566762i	0.981959	+	0.189093i	$0.0605547\pi$
$468$	−0.705787	−	1.79832i	−0.0326250	−	0.0831272i
$469$	−2.93106	−	1.41152i	−0.135344	−	0.0651781i
$470$	8.85598	+	2.73171i	0.408496	+	0.126004i
$471$	2.16221	−	9.47324i	0.0996292	−	0.436504i
$472$	8.81673			0.405823
$473$	7.37341	−	29.0561i	0.339030	−	1.33600i
$474$	−15.4623			−0.710208
$475$	1.50792	−	6.60663i	0.0691881	−	0.303133i
$476$	1.61421	+	0.497918i	0.0739873	+	0.0228221i
$477$	−25.7269	−	12.3894i	−1.17795	−	0.567272i
$478$	3.53960	+	9.01875i	0.161898	+	0.412508i
$479$	−5.08691	+	8.81079i	−0.232427	+	0.402575i	−0.958522	−	0.285019i	$-0.908000\pi$
$479$	−5.08691	+	8.81079i	−0.232427	+	0.402575i	0.726095	+	0.687595i	$0.241333\pi$
$480$	−1.25010	−	2.16523i	−0.0570589	−	0.0988289i
$481$	3.15870	−	3.96088i	0.144024	−	0.180601i
$482$	−9.32945	−	6.36071i	−0.424945	−	0.289722i
$483$	6.55002	−	0.987257i	0.298036	−	0.0449218i
$484$	−8.91796	+	4.29466i	−0.405362	+	0.195212i
$485$	1.63469	+	1.51677i	0.0742272	+	0.0688728i
$486$	22.0947	+	3.33024i	1.00224	+	0.151063i
$487$	38.7882	−	11.9646i	1.75766	−	0.542167i	0.763098	−	0.646283i	$-0.223677\pi$
$487$	38.7882	−	11.9646i	1.75766	−	0.542167i	0.994565	+	0.104115i	$0.0332011\pi$
$488$	−0.228360	−	3.04725i	−0.0103374	−	0.137942i
$489$	−4.51747	−	5.66473i	−0.204287	−	0.256168i
$490$	−2.43699	+	6.20936i	−0.110092	+	0.280510i
$491$	−11.2099	+	10.4013i	−0.505897	+	0.469404i	−0.891345	−	0.453326i	$-0.850237\pi$
$491$	−11.2099	+	10.4013i	−0.505897	+	0.469404i	0.385448	+	0.922730i	$0.374047\pi$
$492$	10.2911	−	7.01634i	0.463958	−	0.316321i
$493$	0.977230	−	13.0402i	0.0440122	−	0.587302i
$494$	−0.896065	−	3.92592i	−0.0403159	−	0.176635i
$495$	3.30704	+	14.4891i	0.148640	+	0.651235i
$496$	−0.157800	+	2.10570i	−0.00708545	+	0.0945487i
$497$	6.58279	−	4.48807i	0.295279	−	0.201318i
$498$	−5.89126	+	5.46629i	−0.263994	+	0.244951i
$499$	−12.8473	+	32.7344i	−0.575124	+	1.46539i	0.286618	+	0.958045i	$0.407469\pi$
$499$	−12.8473	+	32.7344i	−0.575124	+	1.46539i	−0.861742	+	0.507346i	$0.830626\pi$
$500$	0.623490	+	0.781831i	0.0278833	+	0.0349646i
$501$	−1.63291	−	21.7897i	−0.0729532	−	0.973492i
$502$	−21.4041	+	6.60228i	−0.955311	+	0.294674i
$503$	24.8114	+	3.73972i	1.10629	+	0.166746i	0.676685	−	0.736273i	$-0.263416\pi$
$503$	24.8114	+	3.73972i	1.10629	+	0.166746i	0.429602	+	0.903018i	$0.358654\pi$
$504$	1.36804	+	1.26936i	0.0609374	+	0.0565416i
$505$	2.71068	−	1.30539i	0.120624	−	0.0580892i
$506$	20.8628	−	3.14456i	0.927465	−	0.139793i
$507$	−26.1254	−	17.8120i	−1.16027	−	0.791058i
$508$	−3.24905	+	4.07418i	−0.144153	+	0.180762i
$509$	−9.48355	−	16.4260i	−0.420351	−	0.728069i	0.575623	−	0.817715i	$-0.304760\pi$
$509$	−9.48355	−	16.4260i	−0.420351	−	0.728069i	−0.995974	+	0.0896463i	$0.971426\pi$
$510$	3.67866	−	6.37163i	0.162894	−	0.282141i
$511$	1.49298	+	3.80405i	0.0660455	+	0.168281i
$512$	−0.900969	−	0.433884i	−0.0398176	−	0.0191751i
$513$	−4.06327	−	1.25335i	−0.179398	−	0.0553369i
$514$	2.16863	−	9.50139i	0.0956541	−	0.419088i
$515$	0.521411			0.0229761
$516$	−16.2660	+	2.05184i	−0.716070	+	0.0903272i
$517$	−42.3669			−1.86330
$518$	−1.08903	+	4.77134i	−0.0478491	+	0.209640i
$519$	−24.7735	−	7.64161i	−1.08744	−	0.335429i
$520$	0.535391	+	0.257831i	0.0234785	+	0.0113066i
$521$	3.20279	+	8.16058i	0.140317	+	0.357521i	0.983707	−	0.179781i	$-0.0575388\pi$
$521$	3.20279	+	8.16058i	0.140317	+	0.357521i	−0.843390	+	0.537302i	$0.819444\pi$
$522$	7.22335	−	12.5112i	0.316157	−	0.547601i
$523$	2.58320	+	4.47423i	0.112955	+	0.195644i	0.916961	−	0.398978i	$-0.130635\pi$
$523$	2.58320	+	4.47423i	0.112955	+	0.195644i	−0.804005	+	0.594622i	$0.797302\pi$
$524$	12.4131	−	15.5656i	0.542271	−	0.679986i
$525$	−1.18585	−	0.808499i	−0.0517548	−	0.0352858i
$526$	−23.0154	+	3.46901i	−1.00352	+	0.151256i
$527$	−5.59846	+	2.69608i	−0.243873	+	0.117443i
$528$	8.37844	+	7.77405i	0.364625	+	0.338322i
$529$	1.68036	+	0.253274i	0.0730593	+	0.0110119i
$530$	8.39319	−	2.58896i	0.364577	−	0.112457i
$531$	2.14199	+	28.5828i	0.0929543	+	1.24039i
$532$	2.42542	+	3.04138i	0.105155	+	0.131861i
$533$	−1.08154	+	2.75571i	−0.0468466	+	0.119363i
$534$	−4.64615	+	4.31100i	−0.201059	+	0.186555i
$535$	5.49380	−	3.74561i	0.237517	−	0.161937i
$536$	−0.423506	+	5.65130i	−0.0182927	+	0.244099i
$537$	8.94801	+	39.2038i	0.386135	+	1.69177i
$538$	−4.51888	−	19.7985i	−0.194823	−	0.853574i
$539$	2.27880	−	30.4085i	0.0981548	−	1.30979i
$540$	0.518455	−	0.353476i	0.0223107	−	0.0152112i
$541$	9.55551	−	8.86621i	0.410823	−	0.381188i	−0.447512	−	0.894278i	$-0.647690\pi$
$541$	9.55551	−	8.86621i	0.410823	−	0.381188i	0.858335	+	0.513090i	$0.171499\pi$
$542$	−2.99052	+	7.61972i	−0.128454	+	0.327295i
$543$	1.75130	+	2.19606i	0.0751555	+	0.0942421i
$544$	−0.219908	−	2.93447i	−0.00942849	−	0.125815i
$545$	5.05082	−	1.55797i	0.216354	−	0.0667362i
$546$	−0.843350	−	0.127115i	−0.0360921	−	0.00544000i
$547$	−5.69393	−	5.28319i	−0.243455	−	0.225893i	0.549002	−	0.835821i	$-0.315008\pi$
$547$	−5.69393	−	5.28319i	−0.243455	−	0.225893i	−0.792457	+	0.609928i	$0.791198\pi$
$548$	16.6264	−	8.00683i	0.710243	−	0.342035i
$549$	9.82335	−	1.48063i	0.419250	−	0.0631918i
$550$	−3.77711	−	2.57519i	−0.161057	−	0.109807i
$551$	18.7755	−	23.5437i	0.799863	−	1.00300i
$552$	−5.76953	−	9.99312i	−0.245567	−	0.425335i
$553$	−1.77509	+	3.07455i	−0.0754847	+	0.130743i
$554$	−1.48320	−	3.77912i	−0.0630150	−	0.160560i
$555$	19.2044	+	9.24835i	0.815181	+	0.392571i
$556$	−19.4719	−	6.00628i	−0.825792	−	0.254723i
$557$	5.18309	−	22.7086i	0.219615	−	0.962194i	−0.738149	−	0.674638i	$-0.764300\pi$
$557$	5.18309	−	22.7086i	0.219615	−	0.962194i	0.957764	−	0.287557i	$-0.0928429\pi$
$558$	−6.86477			−0.290609
$559$	2.91956	−	2.58076i	0.123484	−	0.109155i
$560$	−0.574051			−0.0242581
$561$	−7.48420	+	32.7904i	−0.315983	+	1.38441i
$562$	29.8571	+	9.20968i	1.25944	+	0.388487i
$563$	−17.2424	−	8.30352i	−0.726682	−	0.349952i	0.0336960	−	0.999432i	$-0.489272\pi$
$563$	−17.2424	−	8.30352i	−0.726682	−	0.349952i	−0.760378	+	0.649480i	$0.774986\pi$
$564$	8.46535	+	21.5694i	0.356456	+	0.908234i
$565$	6.26986	−	10.8597i	0.263775	−	0.456872i
$566$	−10.9774	−	19.0134i	−0.461415	−	0.799194i
$567$	2.92921	−	3.67311i	0.123015	−	0.154256i
$568$	−11.4673	−	7.81825i	−0.481156	−	0.328046i
$569$	43.1538	−	6.50439i	1.80910	−	0.272678i	0.844342	−	0.535805i	$-0.179992\pi$
$569$	43.1538	−	6.50439i	1.80910	−	0.272678i	0.964761	+	0.263127i	$0.0847537\pi$
$570$	15.2648	−	7.35114i	0.639372	−	0.307905i
$571$	−33.9485	−	31.4996i	−1.42070	−	1.31822i	−0.878311	−	0.478091i	$-0.841329\pi$
$571$	−33.9485	−	31.4996i	−1.42070	−	1.31822i	−0.542390	−	0.840127i	$-0.682480\pi$
$572$	−2.68620	−	0.404879i	−0.112316	−	0.0169288i
$573$	−25.9887	+	8.01644i	−1.08569	+	0.334892i
$574$	−0.213711	−	2.85178i	−0.00892014	−	0.119031i
$575$	2.87757	+	3.60836i	0.120003	+	0.150479i
$576$	1.18771	−	3.02625i	0.0494881	−	0.126094i
$577$	−7.92283	+	7.35131i	−0.329832	+	0.306039i	−0.827653	−	0.561241i	$-0.810324\pi$
$577$	−7.92283	+	7.35131i	−0.329832	+	0.306039i	0.497821	+	0.867280i	$0.334134\pi$
$578$	−6.89125	+	4.69837i	−0.286638	+	0.195427i
$579$	−0.587929	+	7.84537i	−0.0244335	+	0.326042i
$580$	0.988839	+	4.33239i	0.0410593	+	0.179893i
$581$	0.410602	+	1.79897i	0.0170347	+	0.0746337i
$582$	−0.416648	+	5.55978i	−0.0172706	+	0.230460i
$583$	−33.1759	+	22.6190i	−1.37401	+	0.936782i
$584$	5.21842	−	4.84199i	0.215940	−	0.200363i
$585$	−0.705787	+	1.79832i	−0.0291807	+	0.0743512i
$586$	14.7943	+	18.5514i	0.611146	+	0.766352i
$587$	−2.25744	−	30.1234i	−0.0931743	−	1.24333i	−0.826299	−	0.563231i	$-0.809558\pi$
$587$	−2.25744	−	30.1234i	−0.0931743	−	1.24333i	0.733125	−	0.680094i	$-0.238061\pi$
$588$	−15.9365	+	4.91577i	−0.657211	+	0.202723i
$589$	−14.1495	−	2.13270i	−0.583021	−	0.0878762i
$590$	−6.46312	−	5.99690i	−0.266082	−	0.246888i
$591$	−50.2400	+	24.1943i	−2.06660	+	0.995220i
$592$	8.43022	−	1.27065i	0.346480	−	0.0522235i
$593$	17.7027	+	12.0695i	0.726963	+	0.495635i	0.869363	−	0.494174i	$-0.164529\pi$
$593$	17.7027	+	12.0695i	0.726963	+	0.495635i	−0.142400	+	0.989809i	$0.545482\pi$
$594$	−1.78850	+	2.24271i	−0.0733830	+	0.0920194i
$595$	−0.844630	−	1.46294i	−0.0346265	−	0.0599748i
$596$	−7.24900	+	12.5556i	−0.296931	+	0.514299i
$597$	14.1354	+	36.0164i	0.578524	+	1.47405i
$598$	2.47097	+	1.18996i	0.101046	+	0.0486610i
$599$	13.8621	+	4.27589i	0.566390	+	0.174708i	0.564708	−	0.825291i	$-0.308989\pi$
$599$	13.8621	+	4.27589i	0.566390	+	0.174708i	0.00168119	+	0.999999i	$0.499465\pi$
$600$	−0.556346	+	2.43751i	−0.0227127	+	0.0995109i
$601$	10.2522			0.418195			0.209098	−	0.977895i	$-0.432947\pi$
$601$	10.2522			0.418195			0.209098	+	0.977895i	$0.432947\pi$
$602$	−1.45936	+	3.46991i	−0.0594792	+	0.141423i
$603$	−18.4237			−0.750273
$604$	1.29007	−	5.65218i	0.0524923	−	0.229984i
$605$	9.45844	+	2.91754i	0.384540	+	0.118615i
$606$	6.77722	+	3.26374i	0.275306	+	0.132580i
$607$	4.35832	+	11.1048i	0.176899	+	0.450731i	0.991631	−	0.129107i	$-0.0412111\pi$
$607$	4.35832	+	11.1048i	0.176899	+	0.450731i	−0.814732	+	0.579838i	$0.803116\pi$
$608$	3.38826	−	5.86864i	0.137412	−	0.238005i
$609$	−3.18896	−	5.52344i	−0.129223	−	0.223821i
$610$	−1.90525	+	2.38911i	−0.0771415	+	0.0967324i
$611$	−4.55030	−	3.10234i	−0.184085	−	0.125507i
$612$	9.45980	−	1.42584i	0.382390	−	0.0576360i
$613$	0.704332	−	0.339188i	0.0284477	−	0.0136997i	−0.419606	−	0.907706i	$-0.637832\pi$
$613$	0.704332	−	0.339188i	0.0284477	−	0.0136997i	0.448054	+	0.894007i	$0.352117\pi$
$614$	21.9448	+	20.3618i	0.885620	+	0.821736i
$615$	−12.3162	−	1.85637i	−0.496638	−	0.0748562i
$616$	2.50766	−	0.773511i	0.101037	−	0.0311656i
$617$	−3.23038	−	43.1064i	−0.130050	−	1.73540i	−0.556467	−	0.830870i	$-0.687843\pi$
$617$	−3.23038	−	43.1064i	−0.130050	−	1.73540i	0.426417	−	0.904527i	$-0.359776\pi$
$618$	0.812799	+	1.01922i	0.0326956	+	0.0409990i
$619$	7.16803	−	18.2639i	0.288108	−	0.734086i	−0.711402	−	0.702785i	$-0.751940\pi$
$619$	7.16803	−	18.2639i	0.288108	−	0.734086i	0.999510	−	0.0313013i	$-0.00996513\pi$
$620$	1.54792	−	1.43626i	0.0621658	−	0.0576814i
$621$	2.39280	−	1.63139i	0.0960199	−	0.0654653i
$622$	1.84692	−	24.6455i	0.0740549	−	0.988193i
$623$	0.323822	+	1.41876i	0.0129737	+	0.0568413i
$624$	0.330603	+	1.44846i	0.0132347	+	0.0579850i
$625$	0.0747301	−	0.997204i	0.00298920	−	0.0398882i
$626$	22.3956	−	15.2690i	0.895106	−	0.610273i
$627$	−56.7767	+	52.6811i	−2.26744	+	2.10388i
$628$	−1.41988	+	3.61779i	−0.0566593	+	0.144365i
$629$	15.6420	+	19.6145i	0.623688	+	0.782080i
$630$	−0.139463	−	1.86101i	−0.00555635	−	0.0741443i
$631$	18.4048	−	5.67714i	0.732685	−	0.226003i	0.0941085	−	0.995562i	$-0.470000\pi$
$631$	18.4048	−	5.67714i	0.732685	−	0.226003i	0.638576	+	0.769559i	$0.279524\pi$
$632$	6.11537	+	0.921744i	0.243256	+	0.0366650i
$633$	29.1727	+	27.0684i	1.15951	+	1.07587i
$634$	19.4487	−	9.36599i	0.772406	−	0.371971i
$635$	5.15286	−	0.776669i	0.204485	−	0.0308212i
$636$	18.1444	+	12.3706i	0.719473	+	0.490528i
$637$	2.47142	−	3.09907i	0.0979213	−	0.122789i
$638$	−10.1573	−	17.5930i	−0.402132	−	0.696514i
$639$	22.5599	−	39.0750i	0.892457	−	1.54578i
$640$	0.365341	+	0.930874i	0.0144414	+	0.0367960i
$641$	13.3568	+	6.43230i	0.527562	+	0.254060i	0.678653	−	0.734459i	$-0.262564\pi$
$641$	13.3568	+	6.43230i	0.527562	+	0.254060i	−0.151091	+	0.988520i	$0.548279\pi$
$642$	15.8856	+	4.90007i	0.626956	+	0.193390i
$643$	−4.66837	+	20.4535i	−0.184103	+	0.806606i	0.795547	+	0.605892i	$0.207184\pi$
$643$	−4.66837	+	20.4535i	−0.184103	+	0.806606i	−0.979650	+	0.200715i	$0.935674\pi$
$644$	−2.64940			−0.104401
$645$	13.3194	+	9.55957i	0.524451	+	0.376408i
$646$	19.9413			0.784580
$647$	9.98673	−	43.7547i	0.392619	−	1.72018i	−0.262748	−	0.964865i	$-0.584629\pi$
$647$	9.98673	−	43.7547i	0.392619	−	1.72018i	0.655366	−	0.755311i	$-0.272514\pi$
$648$	−7.82049	−	2.41230i	−0.307218	−	0.0947641i
$649$	36.3138	+	17.4878i	1.42544	+	0.686456i
$650$	−0.217100	−	0.553162i	−0.00851537	−	0.0216968i
$651$	−1.51533	+	2.62463i	−0.0593904	+	0.102867i
$652$	1.44898	+	2.50970i	0.0567464	+	0.0982876i
$653$	−10.7847	+	13.5236i	−0.422040	+	0.529221i	−0.946711	−	0.322084i	$-0.895617\pi$
$653$	−10.7847	+	13.5236i	−0.422040	+	0.529221i	0.524671	+	0.851305i	$0.324188\pi$
$654$	10.9189	+	7.44436i	0.426962	+	0.291098i
$655$	−19.6868	+	2.96730i	−0.769226	+	0.115942i
$656$	−4.48840	+	2.16150i	−0.175243	+	0.0843924i
$657$	16.9650	+	15.7412i	0.661866	+	0.614122i
$658$	5.26072	+	0.792926i	0.205084	+	0.0309115i
$659$	−38.3041	+	11.8153i	−1.49212	+	0.460257i	−0.930236	−	0.366961i	$-0.880398\pi$
$659$	−38.3041	+	11.8153i	−1.49212	+	0.460257i	−0.561881	+	0.827218i	$0.689922\pi$
$660$	−0.854130	−	11.3976i	−0.0332469	−	0.443650i
$661$	7.65726	+	9.60190i	0.297833	+	0.373471i	0.908120	−	0.418710i	$-0.137517\pi$
$661$	7.65726	+	9.60190i	0.297833	+	0.373471i	−0.610287	+	0.792180i	$0.708946\pi$
$662$	−6.71560	+	17.1111i	−0.261009	+	0.665041i
$663$	−3.20491	+	2.97373i	−0.124469	+	0.115490i
$664$	2.65586	−	1.81074i	0.103067	−	0.0702702i
$665$	0.290705	−	3.87920i	0.0112731	−	0.150429i
$666$	6.16739	+	27.0211i	0.238982	+	1.04705i
$667$	4.56375	+	19.9951i	0.176709	+	0.774214i
$668$	−0.653114	+	8.71520i	−0.0252697	+	0.337201i
$669$	−39.9248	+	27.2203i	−1.54358	+	1.05240i
$670$	4.15431	−	3.85464i	0.160495	−	0.148918i
$671$	5.10360	−	13.0038i	0.197022	−	0.502005i
$672$	−0.894857	−	1.12212i	−0.0345199	−	0.0432865i
$673$	3.35433	+	44.7604i	0.129300	+	1.72539i	0.564825	+	0.825210i	$0.308944\pi$
$673$	3.35433	+	44.7604i	0.129300	+	1.72539i	−0.435526	+	0.900176i	$0.643437\pi$
$674$	−8.28792	+	2.55649i	−0.319239	+	0.0984721i
$675$	−0.620479	−	0.0935222i	−0.0238822	−	0.00359967i
$676$	9.27082	+	8.60206i	0.356570	+	0.330849i
$677$	17.4769	−	8.41641i	0.671690	−	0.323469i	−0.0667678	−	0.997769i	$-0.521269\pi$
$677$	17.4769	−	8.41641i	0.671690	−	0.323469i	0.738458	+	0.674300i	$0.235554\pi$
$678$	31.0016	−	4.67274i	1.19061	−	0.179455i
$679$	1.05768	+	0.721116i	0.0405902	+	0.0276739i
$680$	−1.83474	+	2.30070i	−0.0703592	+	0.0882277i
$681$	18.7665	+	32.5045i	0.719132	+	1.24557i
$682$	−4.82655	+	8.35983i	−0.184818	+	0.320114i
$683$	3.40166	+	8.66728i	0.130161	+	0.331644i	0.981066	−	0.193676i	$-0.0620409\pi$
$683$	3.40166	+	8.66728i	0.130161	+	0.331644i	−0.850905	+	0.525320i	$0.823946\pi$
$684$	19.8486	+	9.55860i	0.758932	+	0.365482i
$685$	−17.6340	−	5.43937i	−0.673761	−	0.207828i
$686$	−1.74624	+	7.65079i	−0.0666719	+	0.292109i
$687$	−52.1585			−1.98997
$688$	6.55553	+	0.158146i	0.249927	+	0.00602927i
$689$	−5.21945			−0.198845
$690$	−2.56768	+	11.2498i	−0.0977500	+	0.428271i
$691$	40.0907	+	12.3663i	1.52512	+	0.470438i	0.940192	−	0.340645i	$-0.110645\pi$
$691$	40.0907	+	12.3663i	1.52512	+	0.470438i	0.584931	+	0.811083i	$0.301122\pi$
$692$	9.34242	+	4.49907i	0.355145	+	0.171029i
$693$	3.11686	+	7.94162i	0.118400	+	0.301677i
$694$	2.04857	−	3.54823i	0.0777627	−	0.134689i
$695$	10.1886	+	17.6472i	0.386476	+	0.669395i
$696$	−6.92721	+	8.68644i	−0.262575	+	0.329259i
$697$	−12.1125	−	8.25816i	−0.458793	−	0.312800i
$698$	−12.2256	+	1.84271i	−0.462745	+	0.0697476i
$699$	−22.8570	+	11.0074i	−0.864533	+	0.416337i
$700$	0.420809	+	0.390454i	0.0159051	+	0.0147578i
$701$	−27.0980	−	4.08436i	−1.02348	−	0.154264i	−0.384207	−	0.923247i	$-0.625525\pi$
$701$	−27.0980	−	4.08436i	−1.02348	−	0.154264i	−0.639269	+	0.768983i	$0.720763\pi$
$702$	−0.356312	+	0.109908i	−0.0134481	+	0.00414820i
$703$	4.31737	+	57.6114i	0.162833	+	2.17285i
$704$	−2.85025	−	3.57411i	−0.107423	−	0.134704i
$705$	8.46535	−	21.5694i	0.318824	−	0.812349i
$706$	−6.70125	+	6.21785i	−0.252205	+	0.234012i
$707$	1.42700	−	0.972912i	0.0536679	−	0.0365901i
$708$	1.64732	−	21.9819i	0.0619099	−	0.826131i
$709$	−7.84136	−	34.3552i	−0.294488	−	1.29024i	−0.878207	−	0.478281i	$-0.841260\pi$
$709$	−7.84136	−	34.3552i	−0.294488	−	1.29024i	0.583718	−	0.811956i	$-0.301597\pi$
$710$	3.08834	+	13.5309i	0.115903	+	0.507806i
$711$	−1.50248	+	20.0493i	−0.0563476	+	0.751906i
$712$	2.09455	−	1.42804i	0.0784966	−	0.0535180i
$713$	7.14404	−	6.62870i	0.267546	−	0.248247i
$714$	1.54301	−	3.93153i	0.0577457	−	0.147134i
$715$	1.69373	+	2.12388i	0.0633421	+	0.0794284i
$716$	−1.20192	−	16.0386i	−0.0449180	−	0.599389i
$717$	23.1469	−	7.13988i	0.864438	−	0.266644i
$718$	−36.5583	−	5.51028i	−1.36434	−	0.205642i
$719$	14.8870	+	13.8131i	0.555192	+	0.515143i	0.907113	−	0.420887i	$-0.138281\pi$
$719$	14.8870	+	13.8131i	0.555192	+	0.515143i	−0.351921	+	0.936030i	$0.614471\pi$
$720$	−2.92903	+	1.41055i	−0.109158	+	0.0525679i
$721$	0.295973	−	0.0446108i	0.0110226	−	0.00166139i
$722$	22.2434	+	15.1653i	0.827815	+	0.564395i
$723$	−17.6017	+	22.0718i	−0.654613	+	0.820858i
$724$	−0.561730	−	0.972945i	−0.0208765	−	0.0361592i
$725$	2.22190	−	3.84845i	0.0825194	−	0.142928i
$726$	9.04124	+	23.0367i	0.335552	+	0.854973i
$727$	18.2350	+	8.78152i	0.676299	+	0.325689i	0.740315	−	0.672260i	$-0.234676\pi$
$727$	18.2350	+	8.78152i	0.676299	+	0.325689i	−0.0640156	+	0.997949i	$0.520391\pi$
$728$	0.325969	+	0.100548i	0.0120812	+	0.00372656i
$729$	6.96775	−	30.5277i	0.258065	−	1.13066i
$730$	−7.11876			−0.263477
$731$	9.24246	+	16.9392i	0.341845	+	0.626517i
$732$	−7.64008			−0.282385
$733$	7.30132	−	31.9892i	0.269680	−	1.18155i	−0.640706	−	0.767787i	$-0.721358\pi$
$733$	7.30132	−	31.9892i	0.269680	−	1.18155i	0.910386	−	0.413760i	$-0.135785\pi$
$734$	−2.16218	−	0.666946i	−0.0798077	−	0.0246174i
$735$	15.0259	+	7.23608i	0.554238	+	0.266907i
$736$	1.68615	+	4.29623i	0.0621521	+	0.158361i
$737$	−12.9535	+	22.4362i	−0.477150	+	0.826448i
$738$	−8.09777	−	14.0257i	−0.298083	−	0.516295i
$739$	14.6287	−	18.3437i	0.538124	−	0.674786i	−0.436223	−	0.899839i	$-0.643684\pi$
$739$	14.6287	−	18.3437i	0.538124	−	0.674786i	0.974347	+	0.225053i	$0.0722555\pi$
$740$	−7.04405	−	4.80255i	−0.258945	−	0.176545i
$741$	−9.95553	+	1.50056i	−0.365726	+	0.0551243i
$742$	4.54280	−	2.18770i	0.166771	−	0.0803129i
$743$	−37.3980	−	34.7003i	−1.37200	−	1.27303i	−0.925757	−	0.378118i	$-0.876571\pi$
$743$	−37.3980	−	34.7003i	−1.37200	−	1.27303i	−0.446243	−	0.894912i	$-0.647238\pi$
$744$	5.22045	+	0.786857i	0.191391	+	0.0288476i
$745$	13.8539	−	4.27336i	0.507567	−	0.156564i
$746$	−0.852543	−	11.3764i	−0.0312138	−	0.416519i
$747$	6.51543	+	8.17009i	0.238387	+	0.298928i
$748$	4.91472	−	12.5225i	0.179700	−	0.457868i
$749$	2.79803	−	2.59619i	0.102238	−	0.0948628i
$750$	2.06576	−	1.40841i	0.0754308	−	0.0514279i
$751$	−0.101537	+	1.35491i	−0.00370513	+	0.0494415i	−0.998750	−	0.0499864i	$-0.984082\pi$
$751$	−0.101537	+	1.35491i	−0.00370513	+	0.0494415i	0.995045	+	0.0994279i	$0.0317013\pi$
$752$	−2.06226	−	9.03535i	−0.0752029	−	0.329485i
$753$	12.4617	+	54.5983i	0.454130	+	1.98967i
$754$	0.197339	−	2.63330i	0.00718665	−	0.0958991i
$755$	−4.79015	+	3.26587i	−0.174331	+	0.118857i
$756$	0.264053	−	0.245005i	0.00960350	−	0.00891074i
$757$	15.4347	−	39.3269i	0.560982	−	1.42936i	−0.315964	−	0.948771i	$-0.602328\pi$
$757$	15.4347	−	39.3269i	0.560982	−	1.42936i	0.876946	−	0.480588i	$-0.159577\pi$
$758$	11.5033	+	14.4246i	0.417817	+	0.523926i
$759$	−3.94203	−	52.6028i	−0.143087	−	1.90936i
$760$	−6.47546	+	1.99742i	−0.234890	+	0.0724539i
$761$	−31.9435	−	4.81471i	−1.15795	−	0.174533i	−0.458153	−	0.888873i	$-0.651489\pi$
$761$	−31.9435	−	4.81471i	−1.15795	−	0.174533i	−0.699799	+	0.714340i	$0.746727\pi$
$762$	9.55070	+	8.86176i	0.345985	+	0.321028i
$763$	2.73375	−	1.31650i	0.0989684	−	0.0476607i
$764$	10.7564	−	1.62127i	0.389154	−	0.0586555i
$765$	−7.90434	−	5.38909i	−0.285782	−	0.194843i
$766$	−9.54804	+	11.9729i	−0.344985	+	0.432597i
$767$	2.61962	+	4.53732i	0.0945892	+	0.163833i
$768$	−1.25010	+	2.16523i	−0.0451090	+	0.0781311i
$769$	0.542192	+	1.38148i	0.0195519	+	0.0498175i	0.940316	−	0.340301i	$-0.110529\pi$
$769$	0.542192	+	1.38148i	0.0195519	+	0.0498175i	−0.920764	+	0.390119i	$0.872434\pi$
$770$	−2.36437	−	1.13862i	−0.0852058	−	0.0410330i
$771$	−23.2837	−	7.18207i	−0.838542	−	0.258656i
$772$	0.700207	−	3.06781i	0.0252010	−	0.110413i
$773$	−0.212521			−0.00764385			−0.00382192	−	0.999993i	$-0.501217\pi$
$773$	−0.212521			−0.00764385			−0.00382192	+	0.999993i	$0.501217\pi$
$774$	1.07995	+	21.2907i	0.0388179	+	0.765278i
$775$	−2.11160			−0.0758511
$776$	0.496216	−	2.17406i	0.0178131	−	0.0780443i
$777$	11.6924	+	3.60664i	0.419464	+	0.129388i
$778$	−6.55644	−	3.15742i	−0.235060	−	0.113199i
$779$	−12.3335	−	31.4253i	−0.441895	−	1.12593i
$780$	0.742857	−	1.28667i	0.0265986	−	0.0460701i
$781$	−31.7233	−	54.9464i	−1.13515	−	1.96614i
$782$	−8.46783	+	10.6183i	−0.302809	+	0.379710i
$783$	−2.30391	−	1.57078i	−0.0823350	−	0.0561351i
$784$	6.59596	−	0.994181i	0.235570	−	0.0355065i
$785$	3.50156	−	1.68626i	0.124976	−	0.0601854i
$786$	−36.4889	−	33.8568i	−1.30152	−	1.20763i
$787$	−39.5507	−	5.96131i	−1.40983	−	0.212498i	−0.600393	−	0.799705i	$-0.704989\pi$
$787$	−39.5507	−	5.96131i	−1.40983	−	0.212498i	−0.809436	+	0.587207i	$0.800227\pi$
$788$	21.3123	−	6.57396i	0.759218	−	0.234188i
$789$	4.34877	+	58.0302i	0.154820	+	2.06593i
$790$	−3.85594	−	4.83520i	−0.137188	−	0.172029i
$791$	2.62989	−	6.70084i	0.0935080	−	0.238254i
$792$	10.8944	−	10.1085i	0.387115	−	0.359190i
$793$	1.50034	−	1.02292i	0.0532788	−	0.0363249i
$794$	−1.71973	+	22.9481i	−0.0610308	+	0.814399i
$795$	−4.88662	−	21.4097i	−0.173310	−	0.759322i
$796$	−3.44355	−	15.0872i	−0.122054	−	0.534751i
$797$	3.95481	−	52.7733i	0.140087	−	1.86933i	−0.277548	−	0.960712i	$-0.589522\pi$
$797$	3.95481	−	52.7733i	0.140087	−	1.86933i	0.417635	−	0.908615i	$-0.362859\pi$
$798$	8.03595	−	5.47882i	0.284470	−	0.193948i
$799$	19.9919	−	18.5498i	0.707262	−	0.656243i
$800$	0.365341	−	0.930874i	0.0129168	−	0.0329114i
$801$	5.13840	+	6.44335i	0.181557	+	0.227665i
$802$	−0.268925	−	3.58855i	−0.00949606	−	0.126716i
$803$	31.0973	−	9.59225i	1.09740	−	0.338503i
$804$	14.0107	+	2.11177i	0.494120	+	0.0744765i
$805$	1.94215	+	1.80205i	0.0684516	+	0.0635138i
$806$	−1.13053	+	0.544437i	−0.0398214	+	0.0191770i
$807$	−50.2060	+	7.56734i	−1.76734	+	0.266383i
$808$	−2.48584	−	1.69482i	−0.0874516	−	0.0596235i
$809$	4.20419	−	5.27189i	0.147812	−	0.185350i	−0.702414	−	0.711769i	$-0.747894\pi$
$809$	4.20419	−	5.27189i	0.147812	−	0.185350i	0.850225	+	0.526419i	$0.176466\pi$
$810$	4.09204	+	7.08763i	0.143780	+	0.249034i
$811$	−3.31704	+	5.74528i	−0.116477	+	0.201744i	−0.918369	−	0.395725i	$-0.870493\pi$
$811$	−3.31704	+	5.74528i	−0.116477	+	0.201744i	0.801892	+	0.597469i	$0.203827\pi$
$812$	0.931974	+	2.37463i	0.0327059	+	0.0833332i
$813$	18.4388	+	8.87965i	0.646676	+	0.311423i
$814$	37.2422	+	11.4877i	1.30534	+	0.402643i
$815$	0.644856	−	2.82530i	0.0225883	−	0.0989659i
$816$	−7.35733			−0.257558
$817$	−4.38847	+	44.2194i	−0.153533	+	1.54704i
$818$	−11.6582			−0.407619
$819$	−0.246772	+	1.08118i	−0.00862293	+	0.0377795i
$820$	4.76042	+	1.46840i	0.166241	+	0.0512786i
$821$	11.3795	+	5.48007i	0.397147	+	0.191256i	0.621788	−	0.783186i	$-0.286407\pi$
$821$	11.3795	+	5.48007i	0.397147	+	0.191256i	−0.224641	+	0.974442i	$0.572121\pi$
$822$	−16.8562	−	42.9489i	−0.587927	−	1.49801i
$823$	−23.8750	+	41.3528i	−0.832232	+	1.44147i	0.0640329	+	0.997948i	$0.479604\pi$
$823$	−23.8750	+	41.3528i	−0.832232	+	1.44147i	−0.896265	+	0.443520i	$0.853730\pi$
$824$	−0.260705	−	0.451555i	−0.00908210	−	0.0157307i
$825$	−7.12619	+	8.93596i	−0.248102	+	0.311110i
$826$	−4.18180	−	2.85111i	−0.145504	−	0.0992026i
$827$	−19.5402	+	2.94522i	−0.679481	+	0.102415i	−0.479710	−	0.877427i	$-0.659258\pi$
$827$	−19.5402	+	2.94522i	−0.679481	+	0.102415i	−0.199771	+	0.979843i	$0.564020\pi$
$828$	−13.5182	+	6.51004i	−0.469791	+	0.226239i
$829$	−19.9645	−	18.5244i	−0.693397	−	0.643379i	0.252593	−	0.967573i	$-0.418717\pi$
$829$	−19.9645	−	18.5244i	−0.693397	−	0.643379i	−0.945991	+	0.324194i	$0.894907\pi$
$830$	−3.17850	−	0.479081i	−0.110327	−	0.0166292i
$831$	−9.69925	+	2.99182i	−0.336463	+	0.103785i
$832$	−0.0444076	−	0.592578i	−0.00153956	−	0.0205439i
$833$	12.2386	+	15.3467i	0.424042	+	0.531732i
$834$	−18.6130	+	47.4252i	−0.644516	+	1.64220i
$835$	6.40661	−	5.94447i	0.221710	−	0.205717i
$836$	25.5957	−	17.4509i	0.885246	−	0.603550i
$837$	−0.0990178	+	1.32130i	−0.00342255	+	0.0456708i
$838$	−8.00435	−	35.0694i	−0.276506	−	1.21145i
$839$	−5.64415	−	24.7287i	−0.194858	−	0.853728i	−0.973940	−	0.226806i	$-0.927172\pi$
$839$	−5.64415	−	24.7287i	−0.194858	−	0.853728i	0.779082	−	0.626922i	$-0.215686\pi$
$840$	−0.107256	+	1.43123i	−0.00370067	+	0.0493820i
$841$	−7.64486	+	5.21218i	−0.263616	+	0.179730i
$842$	−28.1227	+	26.0941i	−0.969172	+	0.899261i
$843$	28.5401	−	72.7190i	0.982973	−	2.50457i
$844$	−9.92426	−	12.4446i	−0.341607	−	0.428362i
$845$	−0.945102	−	12.6115i	−0.0325125	−	0.433849i
$846$	28.7906	−	8.88071i	0.989840	−	0.305325i
$847$	5.61860	+	0.846868i	0.193057	+	0.0290987i
$848$	−6.43870	−	5.97424i	−0.221106	−	0.205156i
$849$	−49.4554	+	23.8165i	−1.69730	+	0.817379i
$850$	2.90983	−	0.438587i	0.0998065	−	0.0150434i
$851$	−32.5102	−	22.1650i	−1.11443	−	0.759808i
$852$	−21.6350	+	27.1295i	−0.741204	+	0.929440i
$853$	5.26761	+	9.12377i	0.180360	+	0.312392i	0.942003	−	0.335604i	$-0.108941\pi$
$853$	5.26761	+	9.12377i	0.180360	+	0.312392i	−0.761643	+	0.647996i	$0.775607\pi$
$854$	−0.877090	+	1.51916i	−0.0300134	+	0.0519848i
$855$	−8.04858	−	20.5074i	−0.275256	−	0.701340i
$856$	−5.99069	−	2.88496i	−0.204757	−	0.0986060i
$857$	−31.7069	−	9.78029i	−1.08309	−	0.334088i	−0.298692	−	0.954350i	$-0.596550\pi$
$857$	−31.7069	−	9.78029i	−1.08309	−	0.334088i	−0.784395	+	0.620261i	$0.787027\pi$
$858$	−1.51133	+	6.62159i	−0.0515961	+	0.226057i
$859$	7.17357			0.244759			0.122380	−	0.992483i	$-0.460947\pi$
$859$	7.17357			0.244759			0.122380	+	0.992483i	$0.460947\pi$
$860$	−4.69798	−	4.57482i	−0.160200	−	0.156000i
$861$	−7.15000			−0.243671
$862$	−1.29218	+	5.66142i	−0.0440119	+	0.192829i
$863$	−28.1008	−	8.66795i	−0.956562	−	0.295060i	−0.223104	−	0.974795i	$-0.571619\pi$
$863$	−28.1008	−	8.66795i	−0.956562	−	0.295060i	−0.733459	+	0.679734i	$0.762095\pi$
$864$	−0.565347	−	0.272257i	−0.0192335	−	0.00926236i
$865$	−3.78833	−	9.65251i	−0.128807	−	0.328195i
$866$	5.45856	−	9.45451i	0.185489	−	0.321277i
$867$	10.4264	+	18.0591i	0.354101	+	0.613320i
$868$	0.755775	−	0.947711i	0.0256527	−	0.0321674i
$869$	23.3594	+	15.9261i	0.792412	+	0.540257i
$870$	10.9863	−	1.65592i	0.372470	−	0.0561408i
$871$	−3.03414	+	1.46116i	−0.102808	+	0.0495097i
$872$	−3.87466	−	3.59516i	−0.131212	−	0.121747i
$873$	7.16861	+	1.08049i	0.242621	+	0.0365692i
$874$	−29.8860	+	9.21860i	−1.01091	+	0.311824i
$875$	−0.0428989	−	0.572446i	−0.00145025	−	0.0193522i
$876$	−11.0971	−	13.9153i	−0.374935	−	0.470153i
$877$	9.69123	−	24.6928i	0.327249	−	0.833818i	−0.668669	−	0.743560i	$-0.733136\pi$
$877$	9.69123	−	24.6928i	0.327249	−	0.833818i	0.995918	−	0.0902578i	$-0.0287691\pi$
$878$	28.1360	−	26.1064i	0.949544	−	0.881048i
$879$	49.0166	−	33.4190i	1.65329	−	1.12719i
$880$	−0.341625	+	4.55867i	−0.0115162	+	0.153673i
$881$	11.6989	+	51.2562i	0.394146	+	1.72686i	0.649808	+	0.760099i	$0.274849\pi$
$881$	11.6989	+	51.2562i	0.394146	+	1.72686i	−0.255662	+	0.966766i	$0.582293\pi$
$882$	4.82548	+	21.1418i	0.162482	+	0.711882i
$883$	2.15455	−	28.7505i	0.0725064	−	0.967531i	−0.835748	−	0.549113i	$-0.814966\pi$
$883$	2.15455	−	28.7505i	0.0725064	−	0.967531i	0.908255	−	0.418418i	$-0.137415\pi$
$884$	1.44482	−	0.985061i	0.0485945	−	0.0331312i
$885$	−16.1591	+	14.9934i	−0.543181	+	0.503998i
$886$	−9.78753	+	24.9382i	−0.328818	+	0.837816i
$887$	34.3379	+	43.0584i	1.15295	+	1.44576i	0.874312	+	0.485364i	$0.161313\pi$
$887$	34.3379	+	43.0584i	1.15295	+	1.44576i	0.278642	+	0.960395i	$0.410116\pi$
$888$	−1.59289	−	21.2557i	−0.0534540	−	0.713294i
$889$	2.85852	−	0.881736i	0.0958716	−	0.0295725i
$890$	−2.50673	−	0.377828i	−0.0840257	−	0.0126648i
$891$	−27.4258	−	25.4474i	−0.918799	−	0.852521i
$892$	17.4130	−	8.38564i	0.583029	−	0.280772i
$893$	62.1015	−	9.36029i	2.07815	−	0.313230i
$894$	29.9494	+	20.4191i	1.00166	+	0.682918i
$895$	−10.0279	+	12.5746i	−0.335196	+	0.420323i
$896$	0.287026	+	0.497143i	0.00958885	+	0.0166084i
$897$	3.42848	−	5.93831i	0.114474	−	0.198274i
$898$	4.07238	+	10.3763i	0.135897	+	0.346260i
$899$	−8.45429	−	4.07137i	−0.281966	−	0.135788i
$900$	3.10654	+	0.958242i	0.103551	+	0.0319414i
$901$	5.75149	−	25.1989i	0.191610	−	0.839498i
$902$	−22.7738			−0.758286
$903$	8.37852	+	4.28681i	0.278820	+	0.142656i
$904$	−12.5397			−0.417065
$905$	−0.249993	+	1.09529i	−0.00831006	+	0.0364088i
$906$	−13.8510	−	4.27247i	−0.460169	−	0.141943i
$907$	−46.8146	−	22.5447i	−1.55445	−	0.748586i	−0.557774	−	0.829993i	$-0.688344\pi$
$907$	−46.8146	−	22.5447i	−1.55445	−	0.748586i	−0.996681	+	0.0814069i	$0.974059\pi$
$908$	−5.48450	−	13.9743i	−0.182009	−	0.463752i
$909$	4.89048	−	8.47056i	0.162207	−	0.280951i
$910$	−0.170562	−	0.295422i	−0.00565407	−	0.00979314i
$911$	−28.7780	+	36.0865i	−0.953459	+	1.19560i	0.0271512	+	0.999631i	$0.491356\pi$
$911$	−28.7780	+	36.0865i	−0.953459	+	1.19560i	−0.980610	+	0.195968i	$0.937215\pi$
$912$	−13.9987	−	9.54413i	−0.463542	−	0.316038i
$913$	14.5304	−	2.19010i	0.480885	−	0.0724817i
$914$	−35.4614	+	17.0773i	−1.17296	+	0.564867i
$915$	5.60057	+	5.19657i	0.185149	+	0.171793i
$916$	20.6288	+	3.10928i	0.681593	+	0.102734i
$917$	−10.9211	+	3.36872i	−0.360647	+	0.111245i
$918$	−0.137990	−	1.84135i	−0.00455434	−	0.0607734i
$919$	19.4386	+	24.3753i	0.641221	+	0.804066i	0.991155	−	0.132708i	$-0.0423674\pi$
$919$	19.4386	+	24.3753i	0.641221	+	0.804066i	−0.349934	+	0.936774i	$0.613796\pi$
$920$	1.68615	−	4.29623i	0.0555906	−	0.141642i
$921$	54.8663	−	50.9085i	1.80791	−	1.67749i
$922$	11.8373	−	8.07055i	0.389842	−	0.265789i
$923$	0.616327	−	8.22431i	0.0202867	−	0.270707i
$924$	−1.45999	−	6.39663i	−0.0480301	−	0.210434i
$925$	1.89709	+	8.31169i	0.0623759	+	0.273287i
$926$	1.79170	−	23.9085i	0.0588788	−	0.785683i
$927$	1.40055	−	0.954880i	0.0460002	−	0.0313624i
$928$	3.25754	−	3.02255i	0.106934	−	0.0992202i
$929$	12.5317	−	31.9302i	0.411151	−	1.04760i	−0.563944	−	0.825813i	$-0.690717\pi$
$929$	12.5317	−	31.9302i	0.411151	−	1.04760i	0.975096	−	0.221784i	$-0.0711880\pi$
$930$	−3.29167	−	4.12762i	−0.107938	−	0.135350i
$931$	3.37799	+	45.0762i	0.110709	+	1.47731i
$932$	9.69617	−	2.99087i	0.317609	−	0.0979693i
$933$	−61.1011	−	9.20951i	−2.00036	−	0.301506i
$934$	10.3672	+	9.61940i	0.339227	+	0.314756i
$935$	−12.1202	+	5.83679i	−0.396373	+	0.190883i
$936$	1.91028	−	0.287928i	0.0624395	−	0.00941124i
$937$	−32.3488	−	22.0550i	−1.05679	−	0.720507i	−0.0953279	−	0.995446i	$-0.530390\pi$
$937$	−32.3488	−	22.0550i	−1.05679	−	0.720507i	−0.961462	+	0.274939i	$0.911342\pi$
$938$	2.02836	−	2.54348i	0.0662281	−	0.0830475i
$939$	−33.8844	−	58.6896i	−1.10578	−	1.91526i
$940$	−4.63386	+	8.02608i	−0.151140	+	0.261782i
$941$	−0.112222	−	0.285936i	−0.00365832	−	0.00932126i	0.929033	−	0.369997i	$-0.120641\pi$
$941$	−0.112222	−	0.285936i	−0.00365832	−	0.00932126i	−0.932691	+	0.360676i	$0.882546\pi$
$942$	8.75459	+	4.21599i	0.285240	+	0.137364i
$943$	21.9706	+	6.77703i	0.715461	+	0.220691i
$944$	−1.96191	+	8.59568i	−0.0638546	+	0.279765i
$945$	−0.360210			−0.0117176
$946$	26.6868	+	13.6541i	0.867664	+	0.443934i
$947$	34.1370			1.10930			0.554652	−	0.832083i	$-0.312852\pi$
$947$	34.1370			1.10930			0.554652	+	0.832083i	$0.312852\pi$
$948$	3.44069	−	15.0747i	0.111748	−	0.489602i
$949$	4.04231	+	1.24689i	0.131219	+	0.0404757i
$950$	6.10544	+	2.94022i	0.198087	+	0.0953935i
$951$	−19.7175	−	50.2395i	−0.639385	−	1.62913i
$952$	−0.844630	+	1.46294i	−0.0273746	+	0.0474143i
$953$	−17.4875	−	30.2892i	−0.566475	−	0.981164i	−0.996911	−	0.0785427i	$-0.974973\pi$
$953$	−17.4875	−	30.2892i	−0.566475	−	0.981164i	0.430435	−	0.902621i	$-0.358360\pi$
$954$	17.8035	−	22.3249i	0.576411	−	0.722796i
$955$	−8.98776	−	6.12775i	−0.290837	−	0.198289i
$956$	−9.58027	+	1.44399i	−0.309848	+	0.0467021i
$957$	−45.7607	+	22.0372i	−1.47923	+	0.712362i
$958$	−7.45794	−	6.91996i	−0.240955	−	0.223574i
$959$	−10.4751	−	1.57887i	−0.338260	−	0.0509845i
$960$	2.38912	−	0.736945i	0.0771085	−	0.0237848i
$961$	−1.98342	−	26.4669i	−0.0639813	−	0.853771i
$962$	3.15870	+	3.96088i	0.101840	+	0.127704i
$963$	7.89731	−	20.1220i	0.254487	−	0.648423i
$964$	8.27723	−	7.68015i	0.266592	−	0.247361i
$965$	−2.59993	+	1.77260i	−0.0836946	+	0.0570620i
$966$	−0.495013	+	6.60549i	−0.0159268	+	0.212528i
$967$	3.07969	+	13.4930i	0.0990361	+	0.433905i	1.00000		1.14120e-5i	$3.63255e-6\pi$
$967$	3.07969	+	13.4930i	0.0990361	+	0.433905i	−0.900964	+	0.433894i	$0.857139\pi$
$968$	−2.20255	−	9.65002i	−0.0707928	−	0.310163i
$969$	3.72583	−	49.7177i	0.119691	−	1.59716i
$970$	−1.84249	+	1.25619i	−0.0591588	+	0.0403338i
$971$	13.8805	−	12.8792i	0.445447	−	0.413314i	−0.425295	−	0.905055i	$-0.639830\pi$
$971$	13.8805	−	12.8792i	0.445447	−	0.413314i	0.870742	+	0.491741i	$0.163639\pi$
$972$	−8.16328	+	20.7997i	−0.261837	+	0.667151i
$973$	7.29330	+	9.14551i	0.233813	+	0.293192i
$974$	3.03342	+	40.4781i	0.0971969	+	1.29700i
$975$	−1.41971	+	0.437922i	−0.0454671	+	0.0140247i
$976$	3.02166	+	0.455442i	0.0967210	+	0.0145783i
$977$	21.7901	+	20.2183i	0.697128	+	0.646840i	0.946924	−	0.321458i	$-0.104173\pi$
$977$	21.7901	+	20.2183i	0.697128	+	0.646840i	−0.249796	+	0.968299i	$0.580364\pi$
$978$	6.52793	−	3.14369i	0.208740	−	0.100524i
$979$	11.4594	−	1.72722i	0.366244	−	0.0552023i
$980$	−5.51140	−	3.75761i	−0.176055	−	0.120032i
$981$	10.7138	−	13.4346i	0.342064	−	0.428934i
$982$	−7.64607	−	13.2434i	−0.243996	−	0.422613i
$983$	3.62127	−	6.27223i	0.115501	−	0.200053i	−0.802479	−	0.596680i	$-0.796486\pi$
$983$	3.62127	−	6.27223i	0.115501	−	0.200053i	0.917980	+	0.396627i	$0.129819\pi$
$984$	4.55045	+	11.5944i	0.145063	+	0.369614i
$985$	−20.0944	−	9.67696i	−0.640261	−	0.308334i
$986$	12.4958	+	3.85445i	0.397948	+	0.122751i
$987$	2.95984	−	12.9679i	0.0942127	−	0.412773i
$988$	4.02688			0.128112
$989$	−21.6824	−	21.1140i	−0.689460	−	0.671387i
$990$	−14.8617			−0.472335
$991$	2.53986	−	11.1279i	0.0806814	−	0.353488i	−0.918432	−	0.395578i	$-0.870544\pi$
$991$	2.53986	−	11.1279i	0.0806814	−	0.353488i	0.999114	+	0.0420895i	$0.0134015\pi$
$992$	−2.01779	−	0.622406i	−0.0640649	−	0.0197614i
$993$	41.4066	+	19.9404i	1.31400	+	0.632789i
$994$	2.91074	+	7.41644i	0.0923230	+	0.235235i
$995$	−7.73759	+	13.4019i	−0.245298	+	0.424869i
$996$	−4.01831	−	6.95992i	−0.127325	−	0.220534i
$997$	−39.0431	+	48.9585i	−1.23651	+	1.55053i	−0.517147	+	0.855897i	$0.673006\pi$
$997$	−39.0431	+	48.9585i	−1.23651	+	1.55053i	−0.719361	+	0.694636i	$0.755565\pi$
$998$	−29.0549	−	19.8093i	−0.919715	−	0.627051i
$999$	5.28986	−	0.797318i	0.167364	−	0.0252260i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.q.a.81.3	✓	36
43.17	even	21	inner	430.2.q.a.361.3	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.q.a.81.3	✓	36	1.1	even	1	trivial
430.2.q.a.361.3	yes	36	43.17	even	21	inner

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.q (of order \(21\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.222521 + 0.974928i) q^{2} +(2.38912 + 0.736945i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-1.25010 + 2.16523i) q^{6} +(0.287026 + 0.497143i) q^{7} +(0.623490 - 0.781831i) q^{8} +(2.68608 + 1.83134i) q^{9} +O(q^{10})\)	\(q+(-0.222521 + 0.974928i) q^{2} +(2.38912 + 0.736945i) q^{3} +(-0.900969 - 0.433884i) q^{4} +(0.365341 + 0.930874i) q^{5} +(-1.25010 + 2.16523i) q^{6} +(0.287026 + 0.497143i) q^{7} +(0.623490 - 0.781831i) q^{8} +(2.68608 + 1.83134i) q^{9} +(-0.988831 + 0.149042i) q^{10} +(4.11874 - 1.98348i) q^{11} +(-1.83277 - 1.70056i) q^{12} +(0.587602 + 0.0885668i) q^{13} +(-0.548548 + 0.169205i) q^{14} +(0.186840 + 2.49320i) q^{15} +(0.623490 + 0.781831i) q^{16} +(-1.07509 + 2.73928i) q^{17} +(-2.38313 + 2.21122i) q^{18} +(-5.59903 + 3.81735i) q^{19} +(0.0747301 - 0.997204i) q^{20} +(0.319371 + 1.39926i) q^{21} +(1.01724 + 4.45684i) q^{22} +(0.344899 - 4.60236i) q^{23} +(2.06576 - 1.40841i) q^{24} +(-0.733052 + 0.680173i) q^{25} +(-0.217100 + 0.553162i) q^{26} +(0.391232 + 0.490589i) q^{27} +(-0.0428989 - 0.572446i) q^{28} +(-4.24638 + 1.30983i) q^{29} +(-2.47227 - 0.372635i) q^{30} +(1.54792 + 1.43626i) q^{31} +(-0.900969 + 0.433884i) q^{32} +(11.3019 - 1.70348i) q^{33} +(-2.43137 - 1.65768i) q^{34} +(-0.357915 + 0.448811i) q^{35} +(-1.62549 - 2.81543i) q^{36} +(4.26272 - 7.38325i) q^{37} +(-2.47574 - 6.30809i) q^{38} +(1.33858 + 0.644627i) q^{39} +(0.955573 + 0.294755i) q^{40} +(-1.10854 + 4.85685i) q^{41} -1.43524 q^{42} +(4.21095 - 5.02672i) q^{43} -4.57145 q^{44} +(-0.723410 + 3.16947i) q^{45} +(4.41022 + 1.36037i) q^{46} +(-8.34992 - 4.02111i) q^{47} +(0.913424 + 2.32737i) q^{48} +(3.33523 - 5.77679i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-4.58722 + 5.75219i) q^{51} +(-0.490984 - 0.334747i) q^{52} +(-8.68531 + 1.30910i) q^{53} +(-0.565347 + 0.272257i) q^{54} +(3.35111 + 3.10938i) q^{55} +(0.567639 + 0.0855579i) q^{56} +(-16.1899 + 4.99393i) q^{57} +(-0.332086 - 4.43138i) q^{58} +(5.49714 + 6.89320i) q^{59} +(0.913424 - 2.32737i) q^{60} +(2.24005 - 2.07847i) q^{61} +(-1.74469 + 1.18951i) q^{62} +(-0.139463 + 1.86101i) q^{63} +(-0.222521 - 0.974928i) q^{64} +(0.132231 + 0.579341i) q^{65} +(-0.854130 + 11.3976i) q^{66} +(-4.68241 + 3.19241i) q^{67} +(2.15715 - 2.00155i) q^{68} +(4.21569 - 10.7414i) q^{69} +(-0.357915 - 0.448811i) q^{70} +(-1.03717 - 13.8401i) q^{71} +(3.10654 - 0.958242i) q^{72} +(7.03925 + 1.06100i) q^{73} +(6.24959 + 5.79877i) q^{74} +(-2.25260 + 1.08479i) q^{75} +(6.70084 - 1.00999i) q^{76} +(2.16826 + 1.47829i) q^{77} +(-0.926328 + 1.16158i) q^{78} +(3.09222 + 5.35589i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-2.98998 - 7.61835i) q^{81} +(-4.48840 - 2.16150i) q^{82} +(3.07159 + 0.947461i) q^{83} +(0.319371 - 1.39926i) q^{84} -2.94270 q^{85} +(3.96366 + 5.22392i) q^{86} -11.1104 q^{87} +(1.01724 - 4.45684i) q^{88} +(2.42242 + 0.747217i) q^{89} +(-2.92903 - 1.41055i) q^{90} +(0.124627 + 0.317543i) q^{91} +(-2.30763 + 3.99694i) q^{92} +(2.63971 + 4.57211i) q^{93} +(5.77833 - 7.24579i) q^{94} +(-5.59903 - 3.81735i) q^{95} +(-2.47227 + 0.372635i) q^{96} +(2.00914 - 0.967549i) q^{97} +(4.88980 + 4.53707i) q^{98} +(14.6957 + 2.21502i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9}+O(q^{10}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9	\( 36 q - 6 q^{2} + 5 q^{3} - 6 q^{4} + 3 q^{5} + 5 q^{6} + q^{7} - 6 q^{8} + 12 q^{9} + 3 q^{10} + 9 q^{11} - 16 q^{12} + 21 q^{13} - 6 q^{14} + 5 q^{15} - 6 q^{16} - 37 q^{17} + 19 q^{18} + 7 q^{19} + 3 q^{20} - 8 q^{21} + 16 q^{22} + 13 q^{23} + 5 q^{24} + 3 q^{25} - 21 q^{26} - 28 q^{27} - 6 q^{28} + 4 q^{29} - 2 q^{30} + 13 q^{31} - 6 q^{32} - 54 q^{33} - 23 q^{34} - 2 q^{35} - 9 q^{36} + 17 q^{37} + 28 q^{38} + 8 q^{39} + 3 q^{40} + 10 q^{41} - 50 q^{42} + 14 q^{43} - 26 q^{44} + 4 q^{45} - 8 q^{46} + 13 q^{47} - 2 q^{48} + 5 q^{49} - 18 q^{50} + 17 q^{51} - 7 q^{52} - 71 q^{53} + 7 q^{54} - 29 q^{55} + q^{56} - 70 q^{57} + 25 q^{58} + 8 q^{59} - 2 q^{60} + 25 q^{61} - 15 q^{62} + 88 q^{63} - 6 q^{64} + 7 q^{65} + 44 q^{66} + 26 q^{67} - 9 q^{68} + 78 q^{69} - 2 q^{70} - 60 q^{71} - 23 q^{72} + 7 q^{73} + 17 q^{74} - 10 q^{75} - 35 q^{76} - 5 q^{77} + 57 q^{78} + 52 q^{79} - 18 q^{80} + q^{81} - 4 q^{82} - 101 q^{83} - 8 q^{84} - 24 q^{85} + 49 q^{86} - 18 q^{87} + 16 q^{88} + 14 q^{89} - 3 q^{90} + 35 q^{91} + 6 q^{92} + 28 q^{93} - 15 q^{94} + 7 q^{95} - 2 q^{96} + 11 q^{97} + 12 q^{98} + 78 q^{99}+O(q^{100}) \) 36 * q - 6 * q^2 + 5 * q^3 - 6 * q^4 + 3 * q^5 + 5 * q^6 + q^7 - 6 * q^8 + 12 * q^9 + 3 * q^10 + 9 * q^11 - 16 * q^12 + 21 * q^13 - 6 * q^14 + 5 * q^15 - 6 * q^16 - 37 * q^17 + 19 * q^18 + 7 * q^19 + 3 * q^20 - 8 * q^21 + 16 * q^22 + 13 * q^23 + 5 * q^24 + 3 * q^25 - 21 * q^26 - 28 * q^27 - 6 * q^28 + 4 * q^29 - 2 * q^30 + 13 * q^31 - 6 * q^32 - 54 * q^33 - 23 * q^34 - 2 * q^35 - 9 * q^36 + 17 * q^37 + 28 * q^38 + 8 * q^39 + 3 * q^40 + 10 * q^41 - 50 * q^42 + 14 * q^43 - 26 * q^44 + 4 * q^45 - 8 * q^46 + 13 * q^47 - 2 * q^48 + 5 * q^49 - 18 * q^50 + 17 * q^51 - 7 * q^52 - 71 * q^53 + 7 * q^54 - 29 * q^55 + q^56 - 70 * q^57 + 25 * q^58 + 8 * q^59 - 2 * q^60 + 25 * q^61 - 15 * q^62 + 88 * q^63 - 6 * q^64 + 7 * q^65 + 44 * q^66 + 26 * q^67 - 9 * q^68 + 78 * q^69 - 2 * q^70 - 60 * q^71 - 23 * q^72 + 7 * q^73 + 17 * q^74 - 10 * q^75 - 35 * q^76 - 5 * q^77 + 57 * q^78 + 52 * q^79 - 18 * q^80 + q^81 - 4 * q^82 - 101 * q^83 - 8 * q^84 - 24 * q^85 + 49 * q^86 - 18 * q^87 + 16 * q^88 + 14 * q^89 - 3 * q^90 + 35 * q^91 + 6 * q^92 + 28 * q^93 - 15 * q^94 + 7 * q^95 - 2 * q^96 + 11 * q^97 + 12 * q^98 + 78 * q^99

Introduction

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