LMFDB - Embedded newform 429.2.bn.b.49.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(4,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 6, 5]))

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

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

chi := DirichletCharacter("429.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bn (of order $30$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.5
Character	$\chi$	$=$	429.49
Dual form			429.2.bn.b.394.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.646484 - 0.582097i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.129952 - 1.23641i) q^{4} +(-2.84399 - 0.924069i) q^{5} +(0.646484 - 0.582097i) q^{6} +(0.352201 - 0.0370178i) q^{7} +(-1.65836 + 2.28254i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.646484 - 0.582097i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.129952 - 1.23641i) q^{4} +(-2.84399 - 0.924069i) q^{5} +(0.646484 - 0.582097i) q^{6} +(0.352201 - 0.0370178i) q^{7} +(-1.65836 + 2.28254i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.30070 + 2.25288i) q^{10} +(-1.35844 + 3.02567i) q^{11} +1.24322 q^{12} +(3.37610 + 1.26567i) q^{13} +(-0.249240 - 0.181084i) q^{14} +(1.21629 - 2.73182i) q^{15} +(-0.0313389 + 0.00666129i) q^{16} +(3.77358 + 4.19099i) q^{17} +(0.511332 + 0.703789i) q^{18} +(0.471300 + 1.05856i) q^{19} +(-0.772946 + 3.63643i) q^{20} +0.354141i q^{21} +(2.63944 - 1.16530i) q^{22} +(0.327098 + 0.566550i) q^{23} +(-2.09669 - 1.88787i) q^{24} +(3.18930 + 2.31717i) q^{25} +(-1.44585 - 2.78346i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.0915384 - 0.430654i) q^{28} +(2.62563 + 1.16901i) q^{29} +(-2.37650 + 1.05808i) q^{30} +(0.924785 - 0.300481i) q^{31} +(4.91091 + 2.83531i) q^{32} +(-2.86710 - 1.66726i) q^{33} -4.90600i q^{34} +(-1.03586 - 0.220180i) q^{35} +(-0.129952 + 1.23641i) q^{36} +(-4.30706 + 9.67382i) q^{37} +(0.311495 - 0.958683i) q^{38} +(-1.61164 + 3.22531i) q^{39} +(6.82560 - 4.95909i) q^{40} +(-11.1239 - 1.16917i) q^{41} +(0.206144 - 0.228947i) q^{42} +(-1.08828 + 1.88496i) q^{43} +(3.91750 + 1.28639i) q^{44} +(2.58972 + 1.49518i) q^{45} +(0.118324 - 0.556668i) q^{46} +(-4.05230 + 5.57751i) q^{47} +(-0.00334899 - 0.0318635i) q^{48} +(-6.72436 + 1.42931i) q^{49} +(-0.713020 - 3.35450i) q^{50} +(-4.56248 + 3.31483i) q^{51} +(1.12616 - 4.33873i) q^{52} +(-0.103123 - 0.317381i) q^{53} +(-0.753382 + 0.434965i) q^{54} +(6.65931 - 7.34968i) q^{55} +(-0.499582 + 0.865302i) q^{56} +(-1.10202 + 0.358069i) q^{57} +(-1.01695 - 2.28412i) q^{58} +(12.7530 - 1.34039i) q^{59} +(-3.53571 - 1.14882i) q^{60} +(3.39698 + 3.77273i) q^{61} +(-0.772768 - 0.344059i) q^{62} +(-0.352201 - 0.0370178i) q^{63} +(-1.50460 - 4.63067i) q^{64} +(-8.43205 - 6.71931i) q^{65} +(0.883024 + 2.74679i) q^{66} +(12.9875 - 7.49833i) q^{67} +(4.69140 - 5.21032i) q^{68} +(-0.597637 + 0.266085i) q^{69} +(0.541504 + 0.745316i) q^{70} +(-4.62918 + 4.16813i) q^{71} +(2.09669 - 1.88787i) q^{72} +(-3.74952 - 5.16078i) q^{73} +(8.41555 - 3.74684i) q^{74} +(-2.63784 + 2.92962i) q^{75} +(1.24756 - 0.720281i) q^{76} +(-0.366439 + 1.11593i) q^{77} +(2.91934 - 1.14698i) q^{78} +(2.48651 + 7.65270i) q^{79} +(0.0952831 + 0.0100147i) q^{80} +(0.913545 + 0.406737i) q^{81} +(6.51088 + 7.23107i) q^{82} +(-15.5438 - 5.05050i) q^{83} +(0.437863 - 0.0460213i) q^{84} +(-6.85928 - 15.4062i) q^{85} +(1.80078 - 0.585110i) q^{86} +(-1.43706 + 2.48905i) q^{87} +(-4.65343 - 8.11834i) q^{88} +(-9.91052 + 5.72184i) q^{89} +(-0.803876 - 2.47408i) q^{90} +(1.23592 + 0.320795i) q^{91} +(0.657981 - 0.478051i) q^{92} +(0.202168 + 0.951128i) q^{93} +(5.86640 - 1.24694i) q^{94} +(-0.362193 - 3.44604i) q^{95} +(-3.33311 + 4.58763i) q^{96} +(-1.49049 + 7.01218i) q^{97} +(5.17919 + 2.99021i) q^{98} +(1.95782 - 2.67711i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9}+O(q^{10}) $ 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9	$ 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9} - 40 q^{10} + 15 q^{11} - 104 q^{12} + q^{13} - 6 q^{14} - 6 q^{15} + 32 q^{16} + 8 q^{17} - 12 q^{19} + 42 q^{20} - 9 q^{22} + 8 q^{23} + 30 q^{25} - 57 q^{26} - 28 q^{27} + 18 q^{28} - 10 q^{29} + 10 q^{30} + 30 q^{32} + 30 q^{33} - 12 q^{35} - 8 q^{36} + 30 q^{38} + 4 q^{39} + 20 q^{40} + 72 q^{41} - 12 q^{42} - 108 q^{43} + 6 q^{45} - 18 q^{46} + 2 q^{48} - 40 q^{49} + 111 q^{50} - 26 q^{51} + 13 q^{52} - 46 q^{53} - 38 q^{55} - 100 q^{56} - 12 q^{58} - 18 q^{59} - 46 q^{61} - 9 q^{62} + 52 q^{64} + 24 q^{65} - 32 q^{66} + 48 q^{67} - 8 q^{68} - 7 q^{69} + 18 q^{71} + 32 q^{74} - 216 q^{76} + 4 q^{77} - 26 q^{78} + 108 q^{79} - 66 q^{80} + 14 q^{81} + 39 q^{82} + 27 q^{84} + 6 q^{85} + 60 q^{87} + 28 q^{88} - 120 q^{89} - 20 q^{90} + 47 q^{91} + 78 q^{92} - 6 q^{93} - 50 q^{94} + 60 q^{95} - 69 q^{97} + 72 q^{98}+O(q^{100}) $ 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9 - 40 * q^10 + 15 * q^11 - 104 * q^12 + q^13 - 6 * q^14 - 6 * q^15 + 32 * q^16 + 8 * q^17 - 12 * q^19 + 42 * q^20 - 9 * q^22 + 8 * q^23 + 30 * q^25 - 57 * q^26 - 28 * q^27 + 18 * q^28 - 10 * q^29 + 10 * q^30 + 30 * q^32 + 30 * q^33 - 12 * q^35 - 8 * q^36 + 30 * q^38 + 4 * q^39 + 20 * q^40 + 72 * q^41 - 12 * q^42 - 108 * q^43 + 6 * q^45 - 18 * q^46 + 2 * q^48 - 40 * q^49 + 111 * q^50 - 26 * q^51 + 13 * q^52 - 46 * q^53 - 38 * q^55 - 100 * q^56 - 12 * q^58 - 18 * q^59 - 46 * q^61 - 9 * q^62 + 52 * q^64 + 24 * q^65 - 32 * q^66 + 48 * q^67 - 8 * q^68 - 7 * q^69 + 18 * q^71 + 32 * q^74 - 216 * q^76 + 4 * q^77 - 26 * q^78 + 108 * q^79 - 66 * q^80 + 14 * q^81 + 39 * q^82 + 27 * q^84 + 6 * q^85 + 60 * q^87 + 28 * q^88 - 120 * q^89 - 20 * q^90 + 47 * q^91 + 78 * q^92 - 6 * q^93 - 50 * q^94 + 60 * q^95 - 69 * q^97 + 72 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.646484	−	0.582097i	−0.457134	−	0.411605i	0.408129	−	0.912924i	$-0.366181\pi$
$2$	−0.646484	−	0.582097i	−0.457134	−	0.411605i	−0.865262	+	0.501320i	$0.832848\pi$
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	−0.129952	−	1.23641i	−0.0649760	−	0.618205i
$5$	−2.84399	−	0.924069i	−1.27187	−	0.413256i	−0.406162	−	0.913801i	$-0.633133\pi$
$5$	−2.84399	−	0.924069i	−1.27187	−	0.413256i	−0.865711	+	0.500545i	$0.833133\pi$
$6$	0.646484	−	0.582097i	0.263926	−	0.237640i
$7$	0.352201	−	0.0370178i	0.133119	−	0.0139914i	−0.0377344	−	0.999288i	$-0.512014\pi$
$7$	0.352201	−	0.0370178i	0.133119	−	0.0139914i	0.170854	+	0.985296i	$0.445347\pi$
$8$	−1.65836	+	2.28254i	−0.586320	+	0.807000i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	1.30070	+	2.25288i	0.411317	+	0.712422i
$11$	−1.35844	+	3.02567i	−0.409584	+	0.912272i
$11$	−1.35844	+	3.02567i	−0.409584	+	0.912272i
$12$	1.24322			0.358887
$13$	3.37610	+	1.26567i	0.936363	+	0.351034i
$13$	3.37610	+	1.26567i	0.936363	+	0.351034i
$14$	−0.249240	−	0.181084i	−0.0666123	−	0.0483967i
$15$	1.21629	−	2.73182i	0.314043	−	0.705353i
$16$	−0.0313389	+	0.00666129i	−0.00783473	+	0.00166532i
$17$	3.77358	+	4.19099i	0.915228	+	1.01646i	0.999799	+	0.0200467i	$0.00638148\pi$
$17$	3.77358	+	4.19099i	0.915228	+	1.01646i	−0.0845706	+	0.996417i	$0.526952\pi$
$18$	0.511332	+	0.703789i	0.120522	+	0.165885i
$19$	0.471300	+	1.05856i	0.108124	+	0.242850i	0.959502	−	0.281703i	$-0.0908993\pi$
$19$	0.471300	+	1.05856i	0.108124	+	0.242850i	−0.851378	+	0.524553i	$0.824233\pi$
$20$	−0.772946	+	3.63643i	−0.172836	+	0.813130i
$21$			0.354141i			0.0772799i
$22$	2.63944	−	1.16530i	0.562730	−	0.248444i
$23$	0.327098	+	0.566550i	0.0682046	+	0.118134i	0.898111	−	0.439769i	$-0.144940\pi$
$23$	0.327098	+	0.566550i	0.0682046	+	0.118134i	−0.829906	+	0.557903i	$0.811606\pi$
$24$	−2.09669	−	1.88787i	−0.427985	−	0.385360i
$25$	3.18930	+	2.31717i	0.637861	+	0.463433i
$26$	−1.44585	−	2.78346i	−0.283555	−	0.545881i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.0915384	−	0.430654i	−0.0172991	−	0.0813860i
$29$	2.62563	+	1.16901i	0.487567	+	0.217079i	0.635771	−	0.771878i	$-0.280682\pi$
$29$	2.62563	+	1.16901i	0.487567	+	0.217079i	−0.148203	+	0.988957i	$0.547349\pi$
$30$	−2.37650	+	1.05808i	−0.433887	+	0.193179i
$31$	0.924785	−	0.300481i	0.166096	−	0.0539680i	−0.224788	−	0.974408i	$-0.572169\pi$
$31$	0.924785	−	0.300481i	0.166096	−	0.0539680i	0.390885	+	0.920440i	$0.372169\pi$
$32$	4.91091	+	2.83531i	0.868134	+	0.501217i
$33$	−2.86710	−	1.66726i	−0.499097	−	0.290233i
$34$		−	4.90600i		−	0.841372i
$35$	−1.03586	−	0.220180i	−0.175093	−	0.0372171i
$36$	−0.129952	+	1.23641i	−0.0216587	+	0.206068i
$37$	−4.30706	+	9.67382i	−0.708076	+	1.59037i	0.0956834	+	0.995412i	$0.469496\pi$
$37$	−4.30706	+	9.67382i	−0.708076	+	1.59037i	−0.803760	+	0.594954i	$0.797170\pi$
$38$	0.311495	−	0.958683i	0.0505311	−	0.155519i
$39$	−1.61164	+	3.22531i	−0.258068	+	0.516463i
$40$	6.82560	−	4.95909i	1.07922	−	0.784101i
$41$	−11.1239	−	1.16917i	−1.73727	−	0.182594i	−0.817732	−	0.575600i	$-0.804769\pi$
$41$	−11.1239	−	1.16917i	−1.73727	−	0.182594i	−0.919536	+	0.393006i	$0.871435\pi$
$42$	0.206144	−	0.228947i	0.0318088	−	0.0353272i
$43$	−1.08828	+	1.88496i	−0.165961	+	0.287453i	−0.936996	−	0.349340i	$-0.886406\pi$
$43$	−1.08828	+	1.88496i	−0.165961	+	0.287453i	0.771035	+	0.636793i	$0.219739\pi$
$44$	3.91750	+	1.28639i	0.590585	+	0.193931i
$45$	2.58972	+	1.49518i	0.386053	+	0.222888i
$46$	0.118324	−	0.556668i	0.0174458	−	0.0820763i
$47$	−4.05230	+	5.57751i	−0.591088	+	0.813563i	−0.994856	−	0.101298i	$-0.967700\pi$
$47$	−4.05230	+	5.57751i	−0.591088	+	0.813563i	0.403768	+	0.914862i	$0.367700\pi$
$48$	−0.00334899	−	0.0318635i	−0.000483385	−	0.00459910i
$49$	−6.72436	+	1.42931i	−0.960623	+	0.204187i
$50$	−0.713020	−	3.35450i	−0.100836	−	0.474397i
$51$	−4.56248	+	3.31483i	−0.638875	+	0.464170i
$52$	1.12616	−	4.33873i	0.156170	−	0.601673i
$53$	−0.103123	−	0.317381i	−0.0141651	−	0.0435956i	0.943724	−	0.330734i	$-0.107296\pi$
$53$	−0.103123	−	0.317381i	−0.0141651	−	0.0435956i	−0.957889	+	0.287138i	$0.907296\pi$
$54$	−0.753382	+	0.434965i	−0.102522	+	0.0591913i
$55$	6.65931	−	7.34968i	0.897941	−	0.991031i
$56$	−0.499582	+	0.865302i	−0.0667595	+	0.115631i
$57$	−1.10202	+	0.358069i	−0.145966	+	0.0474274i
$58$	−1.01695	−	2.28412i	−0.133533	−	0.299919i
$59$	12.7530	−	1.34039i	1.66030	−	0.174504i	0.772589	−	0.634907i	$-0.218961\pi$
$59$	12.7530	−	1.34039i	1.66030	−	0.174504i	0.887710	+	0.460402i	$0.152295\pi$
$60$	−3.53571	−	1.14882i	−0.456458	−	0.148312i
$61$	3.39698	+	3.77273i	0.434939	+	0.483048i	0.920271	−	0.391281i	$-0.127968\pi$
$61$	3.39698	+	3.77273i	0.434939	+	0.483048i	−0.485332	+	0.874330i	$0.661301\pi$
$62$	−0.772768	−	0.344059i	−0.0981417	−	0.0436955i
$63$	−0.352201	−	0.0370178i	−0.0443731	−	0.00466380i
$64$	−1.50460	−	4.63067i	−0.188074	−	0.578834i
$65$	−8.43205	−	6.71931i	−1.04587	−	0.833428i
$66$	0.883024	+	2.74679i	0.108693	+	0.338106i
$67$	12.9875	−	7.49833i	1.58667	−	0.916066i	0.592823	−	0.805332i	$-0.298013\pi$
$67$	12.9875	−	7.49833i	1.58667	−	0.916066i	0.993850	−	0.110734i	$-0.0353201\pi$
$68$	4.69140	−	5.21032i	0.568915	−	0.631845i
$69$	−0.597637	+	0.266085i	−0.0719471	+	0.0320329i
$70$	0.541504	+	0.745316i	0.0647221	+	0.0890823i
$71$	−4.62918	+	4.16813i	−0.549382	+	0.494666i	−0.896432	−	0.443181i	$-0.853850\pi$
$71$	−4.62918	+	4.16813i	−0.549382	+	0.494666i	0.347050	+	0.937847i	$0.387183\pi$
$72$	2.09669	−	1.88787i	0.247097	−	0.222488i
$73$	−3.74952	−	5.16078i	−0.438849	−	0.604023i	0.531107	−	0.847305i	$-0.321776\pi$
$73$	−3.74952	−	5.16078i	−0.438849	−	0.604023i	−0.969956	+	0.243281i	$0.921776\pi$
$74$	8.41555	−	3.74684i	0.978288	−	0.435562i
$75$	−2.63784	+	2.92962i	−0.304592	+	0.338284i
$76$	1.24756	−	0.720281i	0.143105	−	0.0826219i
$77$	−0.366439	+	1.11593i	−0.0417596	+	0.127172i
$78$	2.91934	−	1.14698i	0.330550	−	0.129870i
$79$	2.48651	+	7.65270i	0.279755	+	0.860996i	0.987922	+	0.154952i	$0.0495221\pi$
$79$	2.48651	+	7.65270i	0.279755	+	0.860996i	−0.708168	+	0.706044i	$0.750478\pi$
$80$	0.0952831	+	0.0100147i	0.0106530	+	0.00111967i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	6.51088	+	7.23107i	0.719007	+	0.798538i
$83$	−15.5438	−	5.05050i	−1.70616	−	0.554365i	−0.716472	−	0.697616i	$-0.754244\pi$
$83$	−15.5438	−	5.05050i	−1.70616	−	0.554365i	−0.989686	+	0.143251i	$0.954244\pi$
$84$	0.437863	−	0.0460213i	0.0477748	−	0.00502134i
$85$	−6.85928	−	15.4062i	−0.743993	−	1.67104i
$86$	1.80078	−	0.585110i	0.194184	−	0.0630941i
$87$	−1.43706	+	2.48905i	−0.154069	+	0.266855i
$88$	−4.65343	−	8.11834i	−0.496057	−	0.865418i
$89$	−9.91052	+	5.72184i	−1.05051	+	0.606514i	−0.922793	−	0.385296i	$-0.874099\pi$
$89$	−9.91052	+	5.72184i	−1.05051	+	0.606514i	−0.127720	+	0.991810i	$0.540766\pi$
$90$	−0.803876	−	2.47408i	−0.0847360	−	0.260791i
$91$	1.23592	+	0.320795i	0.129560	+	0.0336284i
$92$	0.657981	−	0.478051i	0.0685993	−	0.0498403i
$93$	0.202168	+	0.951128i	0.0209639	+	0.0986273i
$94$	5.86640	−	1.24694i	0.605073	−	0.128612i
$95$	−0.362193	−	3.44604i	−0.0371603	−	0.353556i
$96$	−3.33311	+	4.58763i	−0.340184	+	0.468223i
$97$	−1.49049	+	7.01218i	−0.151336	+	0.711979i	0.835400	+	0.549643i	$0.185236\pi$
$97$	−1.49049	+	7.01218i	−0.151336	+	0.711979i	−0.986736	+	0.162336i	$0.948097\pi$
$98$	5.17919	+	2.99021i	0.523177	+	0.302056i
$99$	1.95782	−	2.67711i	0.196769	−	0.269060i
$100$	2.45051	−	4.24441i	0.245051	−	0.424441i
$101$	3.26631	−	3.62760i	0.325010	−	0.360960i	−0.558391	−	0.829578i	$-0.688581\pi$
$101$	3.26631	−	3.62760i	0.325010	−	0.360960i	0.883401	+	0.468618i	$0.155248\pi$
$102$	4.87913	+	0.512817i	0.483105	+	0.0507764i
$103$	−4.05937	+	2.94930i	−0.399981	+	0.290603i	−0.769533	−	0.638607i	$-0.779511\pi$
$103$	−4.05937	+	2.94930i	−0.399981	+	0.290603i	0.369552	+	0.929210i	$0.379511\pi$
$104$	−8.48776	+	5.60716i	−0.832293	+	0.549827i
$105$	0.327251	−	1.00717i	0.0319364	−	0.0982901i
$106$	−0.118079	+	0.265209i	−0.0114688	+	0.0257594i
$107$	1.79791	−	17.1060i	0.173811	−	1.65370i	−0.465718	−	0.884933i	$-0.654204\pi$
$107$	1.79791	−	17.1060i	0.173811	−	1.65370i	0.639529	−	0.768767i	$-0.279129\pi$
$108$	−1.21605	−	0.258480i	−0.117015	−	0.0248723i
$109$			12.1114i			1.16006i	0.814593	+	0.580032i	$0.196960\pi$
$109$			12.1114i			1.16006i	−0.814593	+	0.580032i	$0.803040\pi$
$110$	−8.58337	+	0.875092i	−0.818392	+	0.0834367i
$111$	−9.17061	−	5.29466i	−0.870436	−	0.502546i
$112$	−0.0107910	+	0.00350621i	−0.00101965	+	0.000331306i
$113$	11.8729	−	5.28614i	1.11690	−	0.497278i	0.236562	−	0.971616i	$-0.423979\pi$
$113$	11.8729	−	5.28614i	1.11690	−	0.497278i	0.880343	+	0.474338i	$0.157313\pi$
$114$	0.920871	+	0.409998i	0.0862475	+	0.0383998i
$115$	−0.406732	−	1.91352i	−0.0379280	−	0.178437i
$116$	1.10417	−	3.39827i	0.102519	−	0.315522i
$117$	−3.03918	−	1.93994i	−0.280972	−	0.179348i
$118$	−9.02486	−	6.55694i	−0.830805	−	0.603615i
$119$	1.48420	+	1.33638i	0.136056	+	0.122506i
$120$	4.21845	+	7.30658i	0.385090	+	0.666996i
$121$	−7.30930	−	8.22034i	−0.664482	−	0.747304i
$122$		−	4.41638i		−	0.399840i
$123$	2.32554	−	10.9408i	0.209687	−	0.986498i
$124$	−0.491695	−	1.10437i	−0.0441555	−	0.0991749i
$125$	1.85928	+	2.55908i	0.166299	+	0.228891i
$126$	0.206144	+	0.228947i	0.0183648	+	0.0203962i
$127$	−0.693110	+	0.147325i	−0.0615035	+	0.0130730i	−0.238561	−	0.971128i	$-0.576676\pi$
$127$	−0.693110	+	0.147325i	−0.0615035	+	0.0130730i	0.177057	+	0.984201i	$0.443342\pi$
$128$	2.89010	−	6.49127i	0.255451	−	0.573753i
$129$	−1.76087	−	1.27935i	−0.155036	−	0.112641i
$130$	1.53989	+	9.25220i	0.135058	+	0.811472i
$131$	0.231929			0.0202637			0.0101319	−	0.999949i	$-0.496775\pi$
$131$	0.231929			0.0202637			0.0101319	+	0.999949i	$0.496775\pi$
$132$	−1.68884	+	3.76157i	−0.146994	+	0.327403i
$133$	0.205178	+	0.355378i	0.0177912	+	0.0308152i
$134$	−12.7610	−	2.71243i	−1.10238	−	0.234318i
$135$	−1.75768	+	2.41924i	−0.151277	+	0.208215i
$136$	−15.8241	+	1.66318i	−1.35690	+	0.142616i
$137$	−7.59922	+	6.84237i	−0.649245	+	0.584583i	−0.926537	−	0.376203i	$-0.877230\pi$
$137$	−7.59922	+	6.84237i	−0.649245	+	0.584583i	0.277292	+	0.960786i	$0.410563\pi$
$138$	0.541251	+	0.175863i	0.0460743	+	0.0149705i
$139$	−0.397878	−	3.78556i	−0.0337476	−	0.321087i	−0.998352	−	0.0573859i	$-0.981723\pi$
$139$	−0.397878	−	3.78556i	−0.0337476	−	0.321087i	0.964604	−	0.263701i	$-0.0849432\pi$
$140$	−0.137620	+	1.30937i	−0.0116310	+	0.110662i
$141$	−5.12338	−	4.61311i	−0.431466	−	0.388494i
$142$	5.41895			0.454748
$143$	−8.41572	+	8.49563i	−0.703758	+	0.710440i
$144$	0.0320390			0.00266992
$145$	−6.38703	−	5.75091i	−0.530414	−	0.477587i
$146$	−0.580065	+	5.51895i	−0.0480065	+	0.456751i
$147$	−0.718590	−	6.83692i	−0.0592683	−	0.563900i
$148$	12.5205	+	4.06816i	1.02918	+	0.334401i
$149$	0.734171	−	0.661051i	0.0601456	−	0.0541554i	−0.638510	−	0.769614i	$-0.720449\pi$
$149$	0.734171	−	0.661051i	0.0601456	−	0.0541554i	0.698655	+	0.715458i	$0.253782\pi$
$150$	3.41065	−	0.358474i	0.278479	−	0.0292693i
$151$	−2.91951	+	4.01836i	−0.237587	+	0.327010i	−0.911116	−	0.412151i	$-0.864778\pi$
$151$	−2.91951	+	4.01836i	−0.237587	+	0.327010i	0.673529	+	0.739161i	$0.264778\pi$
$152$	−3.19779	−	0.679710i	−0.259375	−	0.0551318i
$153$	−2.81977	−	4.88398i	−0.227965	−	0.394846i
$154$	0.886476	−	0.508127i	0.0714343	−	0.0409461i
$155$	−2.90775			−0.233556
$156$	4.19724	+	1.57351i	0.336048	+	0.125982i
$157$	5.94401	+	4.31858i	0.474384	+	0.344660i	0.799147	−	0.601135i	$-0.205285\pi$
$157$	5.94401	+	4.31858i	0.474384	+	0.344660i	−0.324764	+	0.945795i	$0.605285\pi$
$158$	2.84712	−	6.39474i	0.226505	−	0.508738i
$159$	0.326421	−	0.0693830i	0.0258869	−	0.00550243i
$160$	−11.3466	−	12.6016i	−0.897024	−	0.996246i
$161$	0.136177	+	0.187431i	0.0107322	+	0.0147716i
$162$	−0.353833	−	0.794721i	−0.0277997	−	0.0624392i
$163$	3.87995	−	18.2537i	0.303901	−	1.42974i	−0.515682	−	0.856780i	$-0.672461\pi$
$163$	3.87995	−	18.2537i	0.303901	−	1.42974i	0.819583	−	0.572961i	$-0.194205\pi$
$164$			13.9057i			1.08585i
$165$	6.61333	+	7.39108i	0.514847	+	0.575394i
$166$	7.10897	+	12.3131i	0.551763	+	0.955682i
$167$	2.98864	+	2.69098i	0.231268	+	0.208235i	0.776615	−	0.629976i	$-0.216935\pi$
$167$	2.98864	+	2.69098i	0.231268	+	0.208235i	−0.545347	+	0.838211i	$0.683602\pi$
$168$	−0.808341	−	0.587294i	−0.0623649	−	0.0453108i
$169$	9.79615	+	8.54607i	0.753550	+	0.657390i
$170$	−4.53348	+	13.9526i	−0.347702	+	1.07012i
$171$	−0.240914	−	1.13341i	−0.0184232	−	0.0866743i
$172$	2.47200	+	1.10061i	0.188489	+	0.0839205i
$173$	13.4678	−	5.99625i	1.02394	−	0.455886i	0.175106	−	0.984550i	$-0.443973\pi$
$173$	13.4678	−	5.99625i	1.02394	−	0.455886i	0.848832	+	0.528663i	$0.177307\pi$
$174$	2.37791	−	0.772628i	0.180269	−	0.0585728i
$175$	1.20905	+	0.698047i	0.0913958	+	0.0527674i
$176$	0.0224171	−	0.103870i	0.00168975	−	0.00782949i
$177$			12.8232i			0.963854i
$178$	9.73766	+	2.06980i	0.729869	+	0.155138i
$179$	−1.12455	+	10.6993i	−0.0840525	+	0.799706i	0.868573	+	0.495561i	$0.165038\pi$
$179$	−1.12455	+	10.6993i	−0.0840525	+	0.799706i	−0.952626	+	0.304145i	$0.901629\pi$
$180$	1.51211	−	3.39626i	0.112706	−	0.253142i
$181$	−6.34154	+	19.5173i	−0.471363	+	1.45071i	0.379438	+	0.925217i	$0.376117\pi$
$181$	−6.34154	+	19.5173i	−0.471363	+	1.45071i	−0.850801	+	0.525489i	$0.823883\pi$
$182$	−0.612269	−	0.926814i	−0.0453844	−	0.0687000i
$183$	−4.10714	+	2.98401i	−0.303609	+	0.220585i
$184$	−1.83562	−	0.192932i	−0.135324	−	0.0142231i
$185$	21.1885	−	23.5322i	1.55781	−	1.73012i
$186$	0.422950	−	0.732571i	0.0310122	−	0.0537147i
$187$	−17.8067	+	5.72441i	−1.30216	+	0.418610i
$188$	7.42269	+	4.28549i	0.541356	+	0.312552i
$189$	0.0736300	−	0.346402i	0.00535580	−	0.0251970i
$190$	−1.77178	+	2.43864i	−0.128538	+	0.176918i
$191$	0.476442	+	4.53305i	0.0344742	+	0.328000i	0.998144	+	0.0609025i	$0.0193979\pi$
$191$	0.476442	+	4.53305i	0.0344742	+	0.328000i	−0.963670	+	0.267097i	$0.913935\pi$
$192$	4.76257	−	1.01232i	0.343709	−	0.0730576i
$193$	3.55987	+	16.7479i	0.256245	+	1.20554i	0.898475	+	0.439025i	$0.144676\pi$
$193$	3.55987	+	16.7479i	0.256245	+	1.20554i	−0.642230	+	0.766512i	$0.721991\pi$
$194$	5.04535	−	3.66566i	0.362235	−	0.263179i
$195$	7.56389	−	7.68350i	0.541662	−	0.550227i
$196$	2.64105	+	8.12832i	0.188647	+	0.580595i
$197$	21.6245	−	12.4849i	1.54068	−	0.889512i	0.541885	−	0.840453i	$-0.317711\pi$
$197$	21.6245	−	12.4849i	1.54068	−	0.889512i	0.998796	−	0.0490598i	$-0.0156225\pi$
$198$	−2.82404	+	0.591069i	−0.200696	+	0.0420055i
$199$	0.413297	−	0.715852i	0.0292979	−	0.0507454i	−0.851005	−	0.525158i	$-0.824006\pi$
$199$	0.413297	−	0.715852i	0.0292979	−	0.0507454i	0.880303	+	0.474413i	$0.157340\pi$
$200$	−10.5781	+	3.43702i	−0.747981	+	0.243034i
$201$	6.09969	+	13.7001i	0.430239	+	0.966332i
$202$	−4.22324	+	0.443880i	−0.297146	+	0.0312313i
$203$	0.968024	+	0.314530i	0.0679419	+	0.0220757i
$204$	4.69140	+	5.21032i	0.328463	+	0.364796i
$205$	30.5560	+	13.6044i	2.13412	+	0.950173i
$206$	4.34110	+	0.456268i	0.302459	+	0.0317897i
$207$	−0.202157	−	0.622177i	−0.0140509	−	0.0432443i
$208$	−0.114234	−	0.0171755i	−0.00792073	−	0.00119091i
$209$	−3.84307	−	0.0119857i	−0.265831	−	0.000829067i
$210$	−0.797836	+	0.460631i	−0.0550559	+	0.0317865i
$211$	−2.21420	+	2.45912i	−0.152432	+	0.169293i	−0.814524	−	0.580129i	$-0.803002\pi$
$211$	−2.21420	+	2.45912i	−0.152432	+	0.169293i	0.662092	+	0.749422i	$0.269669\pi$
$212$	−0.379012	+	0.168747i	−0.0260306	+	0.0115896i
$213$	−3.66142	−	5.03951i	−0.250876	−	0.345301i
$214$	−11.1197	+	10.0122i	−0.760126	+	0.684420i
$215$	4.83689	−	4.35516i	0.329873	−	0.297019i
$216$	1.65836	+	2.28254i	0.112837	+	0.155307i
$217$	0.314587	−	0.140063i	0.0213556	−	0.00950810i
$218$	7.05003	−	7.82985i	0.477488	−	0.530305i
$219$	5.52444	−	3.18954i	0.373307	−	0.215529i
$220$	−9.95261	−	7.27853i	−0.671005	−	0.490718i
$221$	7.43560	+	18.9253i	0.500172	+	1.27306i
$222$	2.84665	+	8.76110i	0.191055	+	0.588007i
$223$	−12.7167	−	1.33658i	−0.851572	−	0.0895038i	−0.331322	−	0.943518i	$-0.607495\pi$
$223$	−12.7167	−	1.33658i	−0.851572	−	0.0895038i	−0.520250	+	0.854014i	$0.674161\pi$
$224$	1.83458	+	0.816809i	0.122578	+	0.0545753i
$225$	−2.63784	−	2.92962i	−0.175856	−	0.195308i
$226$	−10.7527	−	3.49375i	−0.715257	−	0.232401i
$227$	9.86240	−	1.03658i	0.654590	−	0.0688002i	0.228589	−	0.973523i	$-0.426589\pi$
$227$	9.86240	−	1.03658i	0.654590	−	0.0688002i	0.426001	+	0.904723i	$0.359922\pi$
$228$	0.585930	+	1.31602i	0.0388041	+	0.0871555i
$229$	−18.2245	+	5.92151i	−1.20431	+	0.391304i	−0.841345	−	0.540499i	$-0.818236\pi$
$229$	−18.2245	+	5.92151i	−1.20431	+	0.391304i	−0.362965	+	0.931803i	$0.618236\pi$
$230$	−0.850911	+	1.47382i	−0.0561074	+	0.0971809i
$231$	−1.07151	−	0.481078i	−0.0705003	−	0.0316526i
$232$	−7.02256	+	4.05448i	−0.461053	+	0.266189i
$233$	−0.907231	−	2.79217i	−0.0594347	−	0.182921i	0.916931	−	0.399045i	$-0.130658\pi$
$233$	−0.907231	−	2.79217i	−0.0594347	−	0.182921i	−0.976366	+	0.216124i	$0.930658\pi$
$234$	0.835546	+	3.02324i	0.0546214	+	0.197636i
$235$	16.6787	−	12.1178i	1.08800	−	0.790478i
$236$	−3.31455	−	15.5938i	−0.215759	−	1.01507i
$237$	−7.87069	+	1.67297i	−0.511256	+	0.108671i
$238$	−0.181609	−	1.72790i	−0.0117720	−	0.112003i
$239$	2.96323	−	4.07854i	0.191676	−	0.263819i	−0.702353	−	0.711829i	$-0.747867\pi$
$239$	2.96323	−	4.07854i	0.191676	−	0.263819i	0.894028	+	0.448010i	$0.147867\pi$
$240$	−0.0199196	+	0.0937143i	−0.00128580	+	0.00604923i
$241$	17.3765	+	10.0323i	1.11932	+	0.646240i	0.941227	−	0.337774i	$-0.109674\pi$
$241$	17.3765	+	10.0323i	1.11932	+	0.646240i	0.178093	+	0.984014i	$0.443007\pi$
$242$	−0.0596881	+	9.56905i	−0.00383690	+	0.615122i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	4.22319	−	4.69033i	0.270362	−	0.300268i
$245$	20.4448	+	2.14884i	1.30617	+	0.137284i
$246$	−7.87203	+	5.71936i	−0.501902	+	0.364653i
$247$	0.251372	+	4.17031i	0.0159944	+	0.265350i
$248$	−0.847770	+	2.60917i	−0.0538334	+	0.165682i
$249$	6.64761	−	14.9308i	0.421275	−	0.946199i
$250$	0.287638	−	2.73669i	0.0181918	−	0.173084i
$251$	−8.36030	−	1.77704i	−0.527697	−	0.112165i	−0.0636437	−	0.997973i	$-0.520272\pi$
$251$	−8.36030	−	1.77704i	−0.527697	−	0.112165i	−0.464053	+	0.885807i	$0.653605\pi$
$252$			0.440275i			0.0277347i
$253$	−2.15853	+	0.220067i	−0.135706	+	0.0138355i
$254$	0.533842	+	0.308214i	0.0334962	+	0.0193391i
$255$	16.0388	−	5.21132i	1.00439	−	0.326345i
$256$	−14.5430	+	6.47497i	−0.908938	+	0.404685i
$257$	17.1755	+	7.64702i	1.07138	+	0.477008i	0.865159	−	0.501498i	$-0.167217\pi$
$257$	17.1755	+	7.64702i	1.07138	+	0.477008i	0.206219	+	0.978506i	$0.433884\pi$
$258$	0.393672	+	1.85208i	0.0245089	+	0.115305i
$259$	−1.15885	+	3.56656i	−0.0720073	+	0.221616i
$260$	−7.21207	+	11.2987i	−0.447273	+	0.700713i
$261$	−2.32520	−	1.68936i	−0.143927	−	0.104569i
$262$	−0.149938	−	0.135005i	−0.00926323	−	0.00834065i
$263$	−13.0825	−	22.6595i	−0.806699	−	1.39724i	−0.915138	−	0.403140i	$-0.867919\pi$
$263$	−13.0825	−	22.6595i	−0.806699	−	1.39724i	0.108439	−	0.994103i	$-0.465415\pi$
$264$	8.56028	−	3.77934i	0.526849	−	0.232602i
$265$			0.997921i			0.0613018i
$266$	0.0742204	−	0.349180i	0.00455075	−	0.0214096i
$267$	−4.65456	−	10.4543i	−0.284855	−	0.639794i
$268$	−10.9588	−	15.0834i	−0.669413	−	0.921367i
$269$	15.3375	+	17.0340i	0.935145	+	1.03858i	0.999174	+	0.0406360i	$0.0129384\pi$
$269$	15.3375	+	17.0340i	0.935145	+	1.03858i	−0.0640288	+	0.997948i	$0.520395\pi$
$270$	2.54455	−	0.540861i	0.154856	−	0.0329158i
$271$	7.49639	−	16.8372i	0.455373	−	1.02279i	−0.529309	−	0.848429i	$-0.677549\pi$
$271$	7.49639	−	16.8372i	0.455373	−	1.02279i	0.984683	−	0.174356i	$-0.0557844\pi$
$272$	−0.146177	−	0.106204i	−0.00886330	−	0.00643957i
$273$	−0.448226	+	1.19562i	−0.0271279	+	0.0723620i
$274$	8.89570			0.537409
$275$	−11.3434	+	6.50205i	−0.684035	+	0.392088i
$276$	0.406655	+	0.704346i	0.0244777	+	0.0423967i
$277$	−29.4439	−	6.25849i	−1.76911	−	0.376036i	−0.795806	−	0.605552i	$-0.792952\pi$
$277$	−29.4439	−	6.25849i	−1.76911	−	0.376036i	−0.973305	+	0.229516i	$0.926286\pi$
$278$	−1.94634	+	2.67891i	−0.116734	+	0.160670i
$279$	−0.967050	+	0.101641i	−0.0578957	+	0.00608509i
$280$	2.22041	−	1.99926i	0.132695	−	0.119479i
$281$	−16.4775	−	5.35385i	−0.982963	−	0.319384i	−0.226925	−	0.973912i	$-0.572867\pi$
$281$	−16.4775	−	5.35385i	−0.982963	−	0.319384i	−0.756038	+	0.654528i	$0.772867\pi$
$282$	0.626905	+	5.96460i	0.0373317	+	0.355187i
$283$	0.224941	−	2.14017i	0.0133714	−	0.127220i	−0.985800	−	0.167924i	$-0.946294\pi$
$283$	0.224941	−	2.14017i	0.0133714	−	0.127220i	0.999171	+	0.0407044i	$0.0129602\pi$
$284$	5.75509	+	5.18191i	0.341502	+	0.307490i
$285$	3.46502			0.205250
$286$	10.3859	−	0.593526i	0.614132	−	0.0350959i
$287$	−3.96114			−0.233819
$288$	−4.21410	−	3.79439i	−0.248318	−	0.223587i
$289$	−1.54747	+	14.7232i	−0.0910278	+	0.866072i
$290$	0.781529	+	7.43575i	0.0458929	+	0.436642i
$291$	−6.81797	−	2.21529i	−0.399676	−	0.129863i
$292$	−5.89358	+	5.30660i	−0.344896	+	0.310545i
$293$	8.39541	−	0.882393i	0.490465	−	0.0515499i	0.143932	−	0.989588i	$-0.454025\pi$
$293$	8.39541	−	0.882393i	0.490465	−	0.0515499i	0.346533	+	0.938038i	$0.387359\pi$
$294$	−3.51520	+	4.83825i	−0.205010	+	0.282173i
$295$	−37.5081	−	7.97258i	−2.18380	−	0.464182i
$296$	−14.9382	−	25.8738i	−0.868266	−	1.50388i
$297$	2.45780	+	2.22693i	0.142616	+	0.129220i
$298$	−0.859426			−0.0497852
$299$	0.387250	+	2.32673i	0.0223952	+	0.134558i
$300$	3.96501	+	2.88075i	0.228920	+	0.166320i
$301$	−0.313516	+	0.704169i	−0.0180708	+	0.0405876i
$302$	4.22650	−	0.898370i	0.243208	−	0.0516954i
$303$	3.26631	+	3.62760i	0.187645	+	0.208400i
$304$	−0.0218214	−	0.0300345i	−0.00125154	−	0.00172260i
$305$	−6.17472	−	13.8687i	−0.353564	−	0.794117i
$306$	−1.02002	+	4.79879i	−0.0583104	+	0.274329i
$307$			3.48649i			0.198985i	0.995038	+	0.0994923i	$0.0317219\pi$
$307$			3.48649i			0.198985i	−0.995038	+	0.0994923i	$0.968278\pi$
$308$	1.42736	+	0.308052i	0.0813316	+	0.0175529i
$309$	−2.50883	−	4.34542i	−0.142722	−	0.247202i
$310$	1.87981	+	1.69259i	0.106766	+	0.0961327i
$311$	15.1326	+	10.9945i	0.858090	+	0.623439i	0.927365	−	0.374159i	$-0.122069\pi$
$311$	15.1326	+	10.9945i	0.858090	+	0.623439i	−0.0692749	+	0.997598i	$0.522069\pi$
$312$	−4.68923	−	9.02737i	−0.265475	−	0.511074i
$313$	−2.50305	+	7.70361i	−0.141481	+	0.435434i	−0.996542	−	0.0830942i	$-0.973520\pi$
$313$	−2.50305	+	7.70361i	−0.141481	+	0.435434i	0.855061	+	0.518528i	$0.173520\pi$
$314$	−1.32888	−	6.25188i	−0.0749930	−	0.352814i
$315$	0.967450	+	0.430736i	0.0545096	+	0.0242692i
$316$	9.13875	−	4.06883i	0.514095	−	0.228890i
$317$	8.49042	−	2.75870i	0.476869	−	0.154944i	−0.0607134	−	0.998155i	$-0.519338\pi$
$317$	8.49042	−	2.75870i	0.476869	−	0.154944i	0.537583	+	0.843211i	$0.319338\pi$
$318$	−0.251414	−	0.145154i	−0.0140986	−	0.00813983i
$319$	−7.10377	+	6.35626i	−0.397735	+	0.355882i
$320$			14.5599i			0.813925i
$321$	16.8244	+	3.57613i	0.939044	+	0.199600i
$322$	0.0210670	−	0.200439i	0.00117402	−	0.0111700i
$323$	−2.65791	+	5.96976i	−0.147890	+	0.332167i
$324$	0.384176	−	1.18237i	0.0213431	−	0.0656874i
$325$	7.83465	+	11.8596i	0.434588	+	0.657852i
$326$	−13.1338	+	9.54224i	−0.727412	+	0.528496i
$327$	−12.0451	−	1.26599i	−0.666095	−	0.0700094i
$328$	21.1162	−	23.4519i	1.16595	−	1.29492i
$329$	−1.22076	+	2.11441i	−0.0673024	+	0.116571i
$330$	0.0269083	−	8.62782i	0.00148125	−	0.474946i
$331$	3.96332	+	2.28822i	0.217844	+	0.125772i	0.604951	−	0.796262i	$-0.293193\pi$
$331$	3.96332	+	2.28822i	0.217844	+	0.125772i	−0.387108	+	0.922034i	$0.626526\pi$
$332$	−4.22454	+	19.8749i	−0.231852	+	1.09078i
$333$	6.22424	−	8.56693i	0.341086	−	0.469465i
$334$	−0.365695	−	3.47936i	−0.0200100	−	0.190382i
$335$	−43.8653	+	9.32385i	−2.39662	+	0.509416i
$336$	−0.00235903	−	0.0110984i	−0.000128696	−	0.000605467i
$337$	−2.49907	+	1.81568i	−0.136133	+	0.0989064i	−0.653768	−	0.756695i	$-0.726813\pi$
$337$	−2.49907	+	1.81568i	−0.136133	+	0.0989064i	0.517635	+	0.855602i	$0.326813\pi$
$338$	−1.35841	−	11.2272i	−0.0738880	−	0.610680i
$339$	4.01613	+	12.3604i	0.218126	+	0.671323i
$340$	−18.1570	+	10.4829i	−0.984701	+	0.568518i
$341$	−0.347106	+	3.20627i	−0.0187969	+	0.173629i
$342$	−0.504009	+	0.872970i	−0.0272537	+	0.0472048i
$343$	−4.67307	+	1.51837i	−0.252322	+	0.0819844i
$344$	−2.49773	−	5.60999i	−0.134669	−	0.302470i
$345$	1.94556	−	0.204486i	0.104745	−	0.0110092i
$346$	−12.1971	−	3.96308i	−0.655721	−	0.213057i
$347$	6.18264	+	6.86652i	0.331902	+	0.368614i	0.885878	−	0.463918i	$-0.153557\pi$
$347$	6.18264	+	6.86652i	0.331902	+	0.368614i	−0.553976	+	0.832532i	$0.686890\pi$
$348$	3.26424	+	1.45333i	0.174982	+	0.0779068i
$349$	−15.7733	−	1.65784i	−0.844328	−	0.0887424i	−0.327520	−	0.944844i	$-0.606213\pi$
$349$	−15.7733	−	1.65784i	−0.844328	−	0.0887424i	−0.516807	+	0.856102i	$0.672880\pi$
$350$	−0.375302	−	1.15506i	−0.0200608	−	0.0617407i
$351$	2.24700	−	2.81975i	0.119936	−	0.150507i
$352$	−15.2499	+	11.0072i	−0.812820	+	0.586684i
$353$	−18.0945	+	10.4469i	−0.963073	+	0.556031i	−0.897118	−	0.441792i	$-0.854343\pi$
$353$	−18.0945	+	10.4469i	−0.963073	+	0.556031i	−0.0659559	+	0.997823i	$0.521010\pi$
$354$	7.46438	−	8.29003i	0.396727	−	0.440610i
$355$	17.0170	−	7.57645i	0.903168	−	0.402116i
$356$	8.36243	+	11.5099i	0.443208	+	0.610024i
$357$	−1.48420	+	1.33638i	−0.0785522	+	0.0707287i
$358$	6.95506	−	6.26236i	0.367586	−	0.330976i
$359$	−3.93537	−	5.41658i	−0.207701	−	0.285876i	0.692439	−	0.721476i	$-0.256536\pi$
$359$	−3.93537	−	5.41658i	−0.207701	−	0.285876i	−0.900140	+	0.435600i	$0.856536\pi$
$360$	−7.70750	+	3.43160i	−0.406221	+	0.180861i
$361$	11.8151	−	13.1220i	0.621845	−	0.690629i
$362$	15.4606	−	8.92621i	0.812593	−	0.469151i
$363$	8.93934	−	6.41000i	0.469194	−	0.336438i
$364$	0.236024	−	1.56979i	0.0123710	−	0.0822794i
$365$	5.89470	+	18.1420i	0.308543	+	0.949597i
$366$	4.39219	+	0.461638i	0.229583	+	0.0241302i
$367$	−2.51509	−	1.11979i	−0.131287	−	0.0584525i	0.340042	−	0.940410i	$-0.389559\pi$
$367$	−2.51509	−	1.11979i	−0.131287	−	0.0584525i	−0.471329	+	0.881958i	$0.656225\pi$
$368$	−0.0140248	−	0.0155762i	−0.000731095	−	0.000811963i
$369$	10.6378	+	3.45642i	0.553780	+	0.179934i
$370$	−27.3961	+	2.87945i	−1.42426	+	0.149695i
$371$	−0.0480688	−	0.107964i	−0.00249561	−	0.00560523i
$372$	1.14971	−	0.373564i	0.0596098	−	0.0193684i
$373$	3.14921	−	5.45459i	0.163060	−	0.282428i	−0.772905	−	0.634522i	$-0.781197\pi$
$373$	3.14921	−	5.45459i	0.163060	−	0.282428i	0.935965	+	0.352094i	$0.114530\pi$
$374$	14.8439	+	6.66449i	0.767561	+	0.344612i
$375$	−2.73941	+	1.58160i	−0.141463	+	0.0816735i
$376$	−6.01072	−	18.4991i	−0.309979	−	0.954017i
$377$	7.38483	+	7.26987i	0.380338	+	0.374417i
$378$	−0.249240	+	0.181084i	−0.0128195	+	0.00931394i
$379$	−7.68890	−	36.1734i	−0.394952	−	1.85810i	−0.503474	−	0.864011i	$-0.667945\pi$
$379$	−7.68890	−	36.1734i	−0.394952	−	1.85810i	0.108521	−	0.994094i	$-0.465388\pi$
$380$	−4.21365	+	0.895639i	−0.216156	+	0.0459453i
$381$	−0.0740682	−	0.704712i	−0.00379463	−	0.0361035i
$382$	2.33066	−	3.20788i	0.119247	−	0.164129i
$383$	5.74091	−	27.0088i	0.293347	−	1.38009i	−0.546589	−	0.837401i	$-0.684074\pi$
$383$	5.74091	−	27.0088i	0.293347	−	1.38009i	0.839935	−	0.542686i	$-0.182593\pi$
$384$	6.15362	+	3.55279i	0.314025	+	0.181303i
$385$	2.07334	−	2.83508i	0.105667	−	0.144489i
$386$	7.44748	−	12.8994i	0.379067	−	0.656563i
$387$	1.45640	−	1.61750i	0.0740332	−	0.0822221i
$388$	8.86362	+	0.931604i	0.449982	+	0.0472950i
$389$	−13.8598	+	10.0697i	−0.702720	+	0.510556i	−0.880817	−	0.473457i	$-0.843006\pi$
$389$	−13.8598	+	10.0697i	−0.702720	+	0.510556i	0.178097	+	0.984013i	$0.443006\pi$
$390$	−9.36248	+	0.564339i	−0.474088	+	0.0285764i
$391$	−1.14007	+	3.50879i	−0.0576560	+	0.177447i
$392$	7.88898	−	17.7189i	0.398454	−	0.894942i
$393$	−0.0242432	+	0.230658i	−0.00122291	+	0.0116352i
$394$	−21.2473	−	4.51626i	−1.07042	−	0.227526i
$395$		−	24.0619i		−	1.21069i
$396$	−3.56443	−	2.07277i	−0.179119	−	0.104161i
$397$	−16.2056	−	9.35633i	−0.813338	−	0.469581i	0.0347760	−	0.999395i	$-0.488928\pi$
$397$	−16.2056	−	9.35633i	−0.813338	−	0.469581i	−0.848114	+	0.529814i	$0.822262\pi$
$398$	−0.683885	+	0.222208i	−0.0342801	+	0.0111383i
$399$	−0.374878	+	0.166907i	−0.0187674	+	0.00835578i
$400$	−0.115385	−	0.0513725i	−0.00576923	−	0.00256863i
$401$	−2.23380	−	10.5092i	−0.111551	−	0.524804i	−0.998069	−	0.0621115i	$-0.980217\pi$
$401$	−2.23380	−	10.5092i	−0.111551	−	0.524804i	0.886519	−	0.462693i	$-0.153117\pi$
$402$	4.03145	−	12.4075i	0.201070	−	0.618831i
$403$	3.50248	+	0.156019i	0.174471	+	0.00777186i
$404$	−4.90967	−	3.56708i	−0.244265	−	0.177469i
$405$	−2.22226	−	2.00094i	−0.110425	−	0.0994273i
$406$	−0.442725	−	0.766823i	−0.0219721	−	0.0380568i
$407$	−23.4189	−	26.1730i	−1.16083	−	1.29735i
$408$		−	15.9112i		−	0.787724i
$409$	2.76692	−	13.0173i	0.136815	−	0.643665i	−0.855279	−	0.518168i	$-0.826614\pi$
$409$	2.76692	−	13.0173i	0.136815	−	0.643665i	0.992094	−	0.125497i	$-0.0400526\pi$
$410$	−11.8349	−	26.5816i	−0.584484	−	1.31277i
$411$	−6.01055	−	8.27281i	−0.296479	−	0.408068i
$412$	4.17407	+	4.63578i	0.205642	+	0.228388i
$413$	4.44200	−	0.944176i	0.218577	−	0.0464599i
$414$	−0.231476	+	0.519903i	−0.0113764	+	0.0255518i
$415$	39.5396	+	28.7272i	1.94092	+	1.41016i
$416$	12.9912	+	15.7879i	0.636944	+	0.774066i
$417$	3.80641			0.186401
$418$	2.47751	+	2.24479i	0.121179	+	0.109796i
$419$	−0.682637	−	1.18236i	−0.0333490	−	0.0577622i	0.848869	−	0.528603i	$-0.177284\pi$
$419$	−0.682637	−	1.18236i	−0.0333490	−	0.0577622i	−0.882218	+	0.470841i	$0.843951\pi$
$420$	−1.28781	−	0.273732i	−0.0628386	−	0.0133567i
$421$	6.90014	−	9.49723i	0.336292	−	0.462867i	−0.607062	−	0.794655i	$-0.707652\pi$
$421$	6.90014	−	9.49723i	0.336292	−	0.462867i	0.943354	+	0.331788i	$0.107652\pi$
$422$	2.86290	−	0.300902i	0.139364	−	0.0146477i
$423$	5.12338	−	4.61311i	0.249107	−	0.224297i
$424$	0.895451	+	0.290950i	0.0434869	+	0.0141298i
$425$	2.32389	+	22.1104i	0.112725	+	1.07251i
$426$	−0.566434	+	5.38926i	−0.0274438	+	0.261111i
$427$	1.33608	+	1.20301i	0.0646573	+	0.0582177i
$428$	−21.3837			−1.03362
$429$	−7.56941	−	9.25765i	−0.365454	−	0.446964i
$430$	−5.66210			−0.273051
$431$	−2.40411	−	2.16467i	−0.115802	−	0.104269i	0.609196	−	0.793020i	$-0.291492\pi$
$431$	−2.40411	−	2.16467i	−0.115802	−	0.104269i	−0.724998	+	0.688751i	$0.758159\pi$
$432$	−0.00334899	+	0.0318635i	−0.000161128	+	0.00153303i
$433$	0.780726	+	7.42812i	0.0375193	+	0.356972i	0.997134	+	0.0756549i	$0.0241047\pi$
$433$	0.780726	+	7.42812i	0.0375193	+	0.356972i	−0.959615	+	0.281318i	$0.909229\pi$
$434$	−0.284906	−	0.0925715i	−0.0136759	−	0.00444358i
$435$	6.38703	−	5.75091i	0.306235	−	0.275735i
$436$	14.9747	−	1.57390i	0.717158	−	0.0753763i
$437$	−0.445564	+	0.613266i	−0.0213142	+	0.0293365i
$438$	−5.42808	−	1.15377i	−0.259364	−	0.0551295i
$439$	4.04700	+	7.00960i	0.193153	+	0.334550i	0.946293	−	0.323309i	$-0.104795\pi$
$439$	4.04700	+	7.00960i	0.193153	+	0.334550i	−0.753141	+	0.657859i	$0.771462\pi$
$440$	5.73241	+	27.3886i	0.273282	+	1.30570i
$441$	6.87458			0.327361
$442$	6.20938	−	16.5632i	0.295350	−	0.787830i
$443$	−0.514780	−	0.374009i	−0.0244579	−	0.0177697i	0.575489	−	0.817809i	$-0.304812\pi$
$443$	−0.514780	−	0.374009i	−0.0244579	−	0.0177697i	−0.599947	+	0.800040i	$0.704812\pi$
$444$	−5.35463	+	12.0267i	−0.254119	+	0.570761i
$445$	33.4728	−	7.11487i	1.58676	−	0.337277i
$446$	7.44312	+	8.26642i	0.352442	+	0.391426i
$447$	0.580687	+	0.799248i	0.0274656	+	0.0378031i
$448$	−0.701337	−	1.57523i	−0.0331351	−	0.0744226i
$449$	3.09082	−	14.5412i	0.145865	−	0.686240i	−0.843060	−	0.537820i	$-0.819248\pi$
$449$	3.09082	−	14.5412i	0.145865	−	0.686240i	0.988924	−	0.148420i	$-0.0474186\pi$
$450$			3.42944i			0.161665i
$451$	18.6487	−	32.0691i	0.878132	−	1.51007i
$452$	−8.07874	−	13.9928i	−0.379992	−	0.658165i
$453$	−3.69118	−	3.32355i	−0.173427	−	0.156154i
$454$	−6.97928	−	5.07074i	−0.327554	−	0.237982i
$455$	−3.21851	−	2.05441i	−0.150886	−	0.0963123i
$456$	1.01025	−	3.10922i	0.0473091	−	0.145603i
$457$	4.94856	+	23.2811i	0.231484	+	1.08905i	0.928310	+	0.371806i	$0.121261\pi$
$457$	4.94856	+	23.2811i	0.231484	+	1.08905i	−0.696827	+	0.717240i	$0.745405\pi$
$458$	15.2288	+	6.78028i	0.711593	+	0.316822i
$459$	5.15197	−	2.29380i	0.240473	−	0.107066i
$460$	−2.31305	+	0.751554i	−0.107846	+	0.0350414i
$461$	16.6002	+	9.58410i	0.773146	+	0.446376i	0.833996	−	0.551771i	$-0.186048\pi$
$461$	16.6002	+	9.58410i	0.773146	+	0.446376i	−0.0608496	+	0.998147i	$0.519381\pi$
$462$	0.412682	+	0.934733i	0.0191997	+	0.0434877i
$463$		−	34.1619i		−	1.58764i	−0.608155	−	0.793819i	$-0.708090\pi$
$463$		−	34.1619i		−	1.58764i	0.608155	−	0.793819i	$-0.291910\pi$
$464$	−0.0900715	−	0.0191453i	−0.00418146	−	0.000888798i
$465$	0.303942	−	2.89182i	0.0140950	−	0.134105i
$466$	−1.03880	+	2.33319i	−0.0481216	+	0.108083i
$467$	2.95298	−	9.08834i	0.136648	−	0.420558i	−0.859195	−	0.511648i	$-0.829035\pi$
$467$	2.95298	−	9.08834i	0.136648	−	0.420558i	0.995843	+	0.0910900i	$0.0290351\pi$
$468$	−2.00362	+	4.00977i	−0.0926174	+	0.185352i
$469$	4.29663	−	3.12169i	0.198400	−	0.144146i
$470$	−17.8363	−	1.87467i	−0.822725	−	0.0864719i
$471$	−4.91624	+	5.46003i	−0.226528	+	0.251585i
$472$	−18.0896	+	31.3321i	−0.832642	+	1.44218i
$473$	−4.22489	−	5.85337i	−0.194261	−	0.269138i
$474$	6.06211	+	3.49996i	0.278442	+	0.160758i
$475$	−0.949732	+	4.46814i	−0.0435767	+	0.205012i
$476$	1.45944	−	2.00875i	0.0668933	−	0.0920707i
$477$	0.0348826	+	0.331886i	0.00159716	+	0.0151960i
$478$	−4.28979	+	0.911823i	−0.196210	+	0.0417058i
$479$	7.39902	+	34.8096i	0.338070	+	1.59049i	0.738557	+	0.674191i	$0.235508\pi$
$479$	7.39902	+	34.8096i	0.338070	+	1.59049i	−0.400487	+	0.916302i	$0.631159\pi$
$480$	13.7186	−	9.96717i	0.626167	−	0.454937i
$481$	−26.7850	+	27.2085i	−1.22129	+	1.24060i
$482$	−5.39386	−	16.6006i	−0.245683	−	0.756136i
$483$	−0.200638	+	0.115839i	−0.00912937	+	0.00527084i
$484$	−9.21386	+	10.1055i	−0.418812	+	0.459343i
$485$	10.7187	−	18.5653i	0.486710	−	0.843006i
$486$	0.827353	−	0.268823i	0.0375295	−	0.0121941i
$487$	14.9780	+	33.6412i	0.678720	+	1.52443i	0.842941	+	0.538007i	$0.180823\pi$
$487$	14.9780	+	33.6412i	0.678720	+	1.52443i	−0.164220	+	0.986424i	$0.552511\pi$
$488$	−14.2448	+	1.49719i	−0.644833	+	0.0677747i
$489$	17.7482	+	5.76672i	0.802599	+	0.260780i
$490$	−11.9664	−	13.2901i	−0.540588	−	0.600383i
$491$	3.63293	+	1.61748i	0.163952	+	0.0729960i	0.487072	−	0.873362i	$-0.338065\pi$
$491$	3.63293	+	1.61748i	0.163952	+	0.0729960i	−0.323120	+	0.946358i	$0.604732\pi$
$492$	−13.8295	−	1.45354i	−0.623483	−	0.0655307i
$493$	5.00875	+	15.4153i	0.225583	+	0.694272i
$494$	2.26502	−	2.84236i	0.101908	−	0.127884i
$495$	−8.04187	+	5.80453i	−0.361455	+	0.260894i
$496$	−0.0269802	+	0.0155770i	−0.00121144	+	0.000699428i
$497$	−1.47611	+	1.63938i	−0.0662124	+	0.0735363i
$498$	−12.9887	+	5.78296i	−0.582039	+	0.259141i
$499$	−0.745090	−	1.02553i	−0.0333548	−	0.0459090i	0.792014	−	0.610503i	$-0.209033\pi$
$499$	−0.745090	−	1.02553i	−0.0333548	−	0.0459090i	−0.825369	+	0.564594i	$0.809033\pi$
$500$	2.92246	−	2.63139i	0.130696	−	0.117680i
$501$	−2.98864	+	2.69098i	−0.133523	+	0.120224i
$502$	4.37039	+	6.01533i	0.195060	+	0.268477i
$503$	−24.8584	+	11.0677i	−1.10838	+	0.493483i	−0.877538	−	0.479508i	$-0.840815\pi$
$503$	−24.8584	+	11.0677i	−1.10838	+	0.493483i	−0.230843	+	0.972991i	$0.574149\pi$
$504$	0.668572	−	0.742524i	0.0297806	−	0.0330747i
$505$	−12.6415	+	7.29858i	−0.562540	+	0.324783i
$506$	1.52356	+	1.11421i	0.0677304	+	0.0495325i
$507$	−9.52323	+	8.84918i	−0.422942	+	0.393006i
$508$	0.272225	+	0.837823i	0.0120780	+	0.0371724i
$509$	1.71503	+	0.180257i	0.0760174	+	0.00798975i	0.142461	−	0.989800i	$-0.454499\pi$
$509$	1.71503	+	0.180257i	0.0760174	+	0.00798975i	−0.0664434	+	0.997790i	$0.521165\pi$
$510$	−13.4023	−	5.96710i	−0.593465	−	0.264228i
$511$	−1.51163	−	1.67883i	−0.0668704	−	0.0742671i
$512$	−0.344729	−	0.112009i	−0.0152350	−	0.00495016i
$513$	1.15239	−	0.121121i	0.0508791	−	0.00534761i
$514$	−6.65238	−	14.9415i	−0.293424	−	0.659041i
$515$	14.2702	−	4.63666i	0.628819	−	0.204316i
$516$	−1.35297	+	2.34342i	−0.0595613	+	0.103163i
$517$	−11.3709	−	19.8376i	−0.500091	−	0.872456i
$518$	2.82526	−	1.63117i	0.124135	−	0.0716694i
$519$	4.55563	+	14.0208i	0.199970	+	0.615445i
$520$	29.3205	−	8.10343i	1.28579	−	0.355359i
$521$	−2.50073	+	1.81689i	−0.109559	+	0.0795994i	−0.641216	−	0.767361i	$-0.721570\pi$
$521$	−2.50073	+	1.81689i	−0.109559	+	0.0795994i	0.531657	+	0.846960i	$0.321570\pi$
$522$	0.519837	+	2.44564i	0.0227526	+	0.107043i
$523$	37.7397	−	8.02183i	1.65024	−	0.350770i	0.713464	−	0.700692i	$-0.247125\pi$
$523$	37.7397	−	8.02183i	1.65024	−	0.350770i	0.936779	+	0.349922i	$0.113792\pi$
$524$	−0.0301396	−	0.286759i	−0.00131666	−	0.0125271i
$525$	−0.820603	+	1.12946i	−0.0358141	+	0.0492938i
$526$	−4.73242	+	22.2643i	−0.206343	+	0.970768i
$527$	4.74907	+	2.74187i	0.206873	+	0.119438i
$528$	0.100958	+	0.0331516i	0.00439362	+	0.00144274i
$529$	11.2860	−	19.5480i	0.490696	−	0.849911i
$530$	0.580887	−	0.645141i	0.0252321	−	0.0280231i
$531$	−12.7530	−	1.34039i	−0.553433	−	0.0581682i
$532$	0.412730	−	0.299866i	0.0178941	−	0.0130008i
$533$	−36.0758	−	18.0265i	−1.56262	−	0.780814i
$534$	−3.07633	+	9.46797i	−0.133126	+	0.409719i
$535$	−20.9204	+	46.9880i	−0.904467	+	2.03147i
$536$	−4.42273	+	42.0794i	−0.191033	+	1.81755i
$537$	−10.5232	−	2.23677i	−0.454109	−	0.0965238i
$538$		−	19.9402i		−	0.859682i
$539$	4.81001	−	22.2873i	0.207182	−	0.959981i
$540$	3.21959	+	1.85883i	0.138549	+	0.0799914i
$541$	14.7679	−	4.79838i	0.634921	−	0.206298i	0.0261673	−	0.999658i	$-0.491670\pi$
$541$	14.7679	−	4.79838i	0.634921	−	0.206298i	0.608754	+	0.793359i	$0.291670\pi$
$542$	−14.6472	+	6.52134i	−0.629150	+	0.280115i
$543$	−18.7475	−	8.34691i	−0.804531	−	0.358200i
$544$	6.64895	+	31.2808i	0.285071	+	1.34116i
$545$	11.1918	−	34.4448i	0.479404	−	1.47545i
$546$	0.985736	−	0.512036i	0.0421856	−	0.0219131i
$547$	23.8848	+	17.3533i	1.02124	+	0.741974i	0.966536	−	0.256529i	$-0.0825790\pi$
$547$	23.8848	+	17.3533i	1.02124	+	0.741974i	0.0547025	+	0.998503i	$0.482579\pi$
$548$	9.44750	+	8.50657i	0.403577	+	0.363383i
$549$	−2.53835	−	4.39656i	−0.108334	−	0.187640i
$550$	11.1182	+	2.39951i	0.474081	+	0.102315i
$551$			3.33033i			0.141877i
$552$	0.383749	−	1.80540i	0.0163335	−	0.0768428i
$553$	1.15904	+	2.60324i	0.0492873	+	0.110701i
$554$	15.3920	+	21.1852i	0.653942	+	0.900073i
$555$	21.1885	+	23.5322i	0.899403	+	0.998888i
$556$	−4.62880	+	0.983882i	−0.196305	+	0.0417259i
$557$	17.0170	−	38.2209i	0.721034	−	1.61947i	−0.0624426	−	0.998049i	$-0.519889\pi$
$557$	17.0170	−	38.2209i	0.721034	−	1.61947i	0.783477	−	0.621421i	$-0.213444\pi$
$558$	0.684348	+	0.497208i	0.0289707	+	0.0210485i
$559$	−6.05988	+	4.98641i	−0.256306	+	0.210902i
$560$	0.0339295			0.00143378
$561$	−3.83175	−	18.3075i	−0.161776	−	0.772944i
$562$	7.53596	+	13.0527i	0.317885	+	0.550593i
$563$	−5.64823	−	1.20057i	−0.238045	−	0.0505979i	0.0873445	−	0.996178i	$-0.472162\pi$
$563$	−5.64823	−	1.20057i	−0.238045	−	0.0505979i	−0.325389	+	0.945580i	$0.605495\pi$
$564$	−5.03790	+	6.93408i	−0.212134	+	0.291977i
$565$	−38.6511	+	4.06239i	−1.62606	+	0.170906i
$566$	−1.39121	+	1.25265i	−0.0584769	+	0.0526528i
$567$	0.336808	+	0.109436i	0.0141446	+	0.00459586i
$568$	−1.83707	−	17.4786i	−0.0770818	−	0.733384i
$569$	1.25823	−	11.9713i	0.0527479	−	0.501863i	−0.935971	−	0.352078i	$-0.885475\pi$
$569$	1.25823	−	11.9713i	0.0527479	−	0.501863i	0.988719	−	0.149785i	$-0.0478581\pi$
$570$	−2.24008	−	2.01698i	−0.0938268	−	0.0844820i
$571$	−9.18937			−0.384563			−0.192282	−	0.981340i	$-0.561589\pi$
$571$	−9.18937			−0.384563			−0.192282	+	0.981340i	$0.561589\pi$
$572$	11.5977	+	9.30126i	0.484925	+	0.388905i
$573$	−4.55802			−0.190414
$574$	2.56082	+	2.30577i	0.106886	+	0.0962410i
$575$	−0.269575	+	2.56484i	−0.0112421	+	0.106961i
$576$	0.508946	+	4.84230i	0.0212061	+	0.201763i
$577$	43.7640	+	14.2198i	1.82192	+	0.591977i	0.999741	+	0.0227435i	$0.00724010\pi$
$577$	43.7640	+	14.2198i	1.82192	+	0.591977i	0.822176	+	0.569233i	$0.192760\pi$
$578$	9.57076	−	8.61755i	0.398091	−	0.358443i
$579$	−17.0282	+	1.78974i	−0.707668	+	0.0743789i
$580$	−6.28048	+	8.64433i	−0.260783	+	0.358936i
$581$	−5.66151	−	1.20339i	−0.234879	−	0.0499251i
$582$	3.11820	+	5.40087i	0.129253	+	0.223873i
$583$	1.10037	+	0.119125i	0.0455728	+	0.00493365i
$584$	17.9978			0.744753
$585$	6.85076	+	8.32560i	0.283244	+	0.344221i
$586$	−5.94114	−	4.31649i	−0.245426	−	0.178313i
$587$	1.29719	−	2.91354i	0.0535408	−	0.120255i	−0.884794	−	0.465982i	$-0.845701\pi$
$587$	1.29719	−	2.91354i	0.0535408	−	0.120255i	0.938335	+	0.345727i	$0.112368\pi$
$588$	−8.35986	+	1.77694i	−0.344755	+	0.0732799i
$589$	0.753927	+	0.837321i	0.0310650	+	0.0345012i
$590$	19.6076	+	26.9875i	0.807230	+	1.11106i
$591$	10.1561	+	22.8111i	0.417768	+	0.938321i
$592$	0.0705385	−	0.331857i	0.00289911	−	0.0136393i
$593$		−	34.0325i		−	1.39755i	−0.715343	−	0.698774i	$-0.753729\pi$
$593$		−	34.0325i		−	1.39755i	0.715343	−	0.698774i	$-0.246271\pi$
$594$	−0.292638	−	2.87035i	−0.0120071	−	0.117772i
$595$	−2.98615	−	5.17216i	−0.122420	−	0.212038i
$596$	−0.912737	−	0.821832i	−0.0373871	−	0.0336635i
$597$	0.668729	+	0.485860i	0.0273692	+	0.0198849i
$598$	1.10403	−	1.72961i	0.0451472	−	0.0707291i
$599$	13.1136	−	40.3595i	0.535807	−	1.64904i	−0.206093	−	0.978532i	$-0.566075\pi$
$599$	13.1136	−	40.3595i	0.535807	−	1.64904i	0.741900	−	0.670511i	$-0.233925\pi$
$600$	−2.31248	−	10.8794i	−0.0944067	−	0.444149i
$601$	5.95704	+	2.65225i	0.242993	+	0.108187i	0.524620	−	0.851337i	$-0.324207\pi$
$601$	5.95704	+	2.65225i	0.242993	+	0.108187i	−0.281627	+	0.959524i	$0.590874\pi$
$602$	0.612578	−	0.272737i	0.0249668	−	0.0111160i
$603$	−14.2627	+	4.63422i	−0.580821	+	0.188720i
$604$	5.34774	+	3.08752i	0.217597	+	0.125629i
$605$	13.1914	+	30.1329i	0.536308	+	1.22508i
$606$		−	4.24650i		−	0.172502i
$607$	−40.5331	−	8.61557i	−1.64519	−	0.349695i	−0.710096	−	0.704105i	$-0.751349\pi$
$607$	−40.5331	−	8.61557i	−1.64519	−	0.349695i	−0.935090	+	0.354409i	$0.884682\pi$
$608$	−0.686830	+	6.53475i	−0.0278546	+	0.265019i
$609$	−0.413993	+	0.929843i	−0.0167758	+	0.0376792i
$610$	−4.08104	+	12.5602i	−0.165237	+	0.508546i
$611$	−20.7403	+	13.7014i	−0.839062	+	0.554298i
$612$	−5.67217	+	4.12107i	−0.229284	+	0.166584i
$613$	22.5411	+	2.36916i	0.910426	+	0.0956896i	0.548149	−	0.836381i	$-0.315333\pi$
$613$	22.5411	+	2.36916i	0.910426	+	0.0956896i	0.362277	+	0.932070i	$0.381999\pi$
$614$	2.02948	−	2.25396i	0.0819030	−	0.0909625i
$615$	−16.7239	+	28.9666i	−0.674371	+	1.16804i
$616$	−1.93946	−	2.68703i	−0.0781433	−	0.108263i
$617$	20.8467	+	12.0359i	0.839257	+	0.484545i	0.857012	−	0.515297i	$-0.172318\pi$
$617$	20.8467	+	12.0359i	0.839257	+	0.484545i	−0.0177544	+	0.999842i	$0.505652\pi$
$618$	−0.907537	+	4.26963i	−0.0365065	+	0.171750i
$619$	4.53030	−	6.23542i	0.182088	−	0.250623i	−0.708209	−	0.706003i	$-0.750497\pi$
$619$	4.53030	−	6.23542i	0.182088	−	0.250623i	0.890297	+	0.455380i	$0.150497\pi$
$620$	0.377867	+	3.59517i	0.0151755	+	0.144385i
$621$	0.639900	−	0.136015i	0.0256783	−	0.00545809i
$622$	−3.38313	−	15.9164i	−0.135651	−	0.638189i
$623$	−3.27868	+	2.38210i	−0.131358	+	0.0954369i
$624$	0.0290222	−	0.111813i	0.00116182	−	0.00447611i
$625$	−9.01405	−	27.7424i	−0.360562	−	1.10970i
$626$	6.10243	−	3.52324i	0.243902	−	0.140817i
$627$	0.413630	−	3.82076i	0.0165188	−	0.152587i
$628$	4.56710	−	7.91044i	0.182247	−	0.315661i
$629$	−56.7959	+	18.4541i	−2.26460	+	0.735814i
$630$	−0.374711	−	0.841614i	−0.0149288	−	0.0335307i
$631$	31.7569	−	3.33779i	1.26422	−	0.132875i	0.551413	−	0.834233i	$-0.314089\pi$
$631$	31.7569	−	3.33779i	1.26422	−	0.132875i	0.712810	+	0.701357i	$0.247422\pi$
$632$	−21.5912	−	7.01539i	−0.858850	−	0.279057i
$633$	−2.21420	−	2.45912i	−0.0880067	−	0.0977413i
$634$	−7.09476	−	3.15879i	−0.281769	−	0.125452i
$635$	2.10734	+	0.221490i	0.0836271	+	0.00878956i
$636$	−0.128205	−	0.394574i	−0.00508366	−	0.0156459i
$637$	−24.5112	−	3.68534i	−0.971168	−	0.146018i
$638$	8.29244	+	0.0258623i	0.328301	+	0.00102390i
$639$	5.39462	−	3.11459i	0.213408	−	0.123211i
$640$	−14.2178	+	15.7905i	−0.562008	+	0.624173i
$641$	−23.1653	+	10.3138i	−0.914974	+	0.407372i	−0.809547	−	0.587055i	$-0.800287\pi$
$641$	−23.1653	+	10.3138i	−0.914974	+	0.407372i	−0.105426	+	0.994427i	$0.533621\pi$
$642$	−8.79503	−	12.1053i	−0.347112	−	0.477759i
$643$	7.22822	−	6.50832i	0.285053	−	0.256663i	−0.514183	−	0.857681i	$-0.671905\pi$
$643$	7.22822	−	6.50832i	0.285053	−	0.256663i	0.799236	+	0.601018i	$0.205238\pi$
$644$	0.214045	−	0.192727i	0.00843456	−	0.00759451i
$645$	3.82571	+	5.26563i	0.150637	+	0.207334i
$646$	5.19328	−	2.31220i	0.204327	−	0.0909722i
$647$	−25.1562	+	27.9388i	−0.988991	+	1.09839i	0.00615555	+	0.999981i	$0.498041\pi$
$647$	−25.1562	+	27.9388i	−0.988991	+	1.09839i	−0.995146	+	0.0984047i	$0.968626\pi$
$648$	−2.44338	+	1.41069i	−0.0959852	+	0.0554171i
$649$	−13.2685	+	40.4072i	−0.520836	+	1.58612i
$650$	1.83846	−	12.2276i	0.0721103	−	0.479605i
$651$	0.106413	+	0.327504i	0.00417064	+	0.0128359i
$652$	−23.0733	−	2.42510i	−0.903620	−	0.0949742i
$653$	31.9772	+	14.2372i	1.25136	+	0.557143i	0.922047	−	0.387077i	$-0.126515\pi$
$653$	31.9772	+	14.2372i	1.25136	+	0.557143i	0.329316	+	0.944220i	$0.393182\pi$
$654$	7.05003	+	7.82985i	0.275678	+	0.306171i
$655$	−0.659604	−	0.214318i	−0.0257729	−	0.00837411i
$656$	0.356400	−	0.0374592i	0.0139151	−	0.00146254i
$657$	2.59460	+	5.82757i	0.101225	+	0.227355i
$658$	2.01999	−	0.656335i	0.0787475	−	0.0255866i
$659$	4.55987	−	7.89793i	0.177627	−	0.307660i	−0.763440	−	0.645879i	$-0.776491\pi$
$659$	4.55987	−	7.89793i	0.177627	−	0.307660i	0.941067	+	0.338219i	$0.109825\pi$
$660$	8.27899	−	9.13728i	0.322259	−	0.355668i
$661$	−30.5527	+	17.6396i	−1.18836	+	0.686102i	−0.957934	−	0.286987i	$-0.907346\pi$
$661$	−30.5527	+	17.6396i	−1.18836	+	0.686102i	−0.230429	+	0.973089i	$0.574013\pi$
$662$	−1.23025	−	3.78633i	−0.0478152	−	0.147160i
$663$	−19.5989	+	5.41663i	−0.761158	+	0.210364i
$664$	37.3053	−	27.1039i	1.44773	−	1.05184i
$665$	−0.255130	−	1.20029i	−0.00989351	−	0.0465453i
$666$	−9.01066	+	1.91528i	−0.349156	+	0.0742154i
$667$	0.196538	+	1.86993i	0.00760997	+	0.0724040i
$668$	2.93878	−	4.04488i	0.113705	−	0.156501i
$669$	2.65851	−	12.5073i	0.102784	−	0.483561i
$670$	33.7856	+	19.5061i	1.30525	+	0.753588i
$671$	−16.0296	+	5.15311i	−0.618815	+	0.198934i
$672$	−1.00410	+	1.73915i	−0.0387340	+	0.0670893i
$673$	25.7999	−	28.6537i	0.994512	−	1.10452i	−1.09788e−5	−	1.00000i	$-0.500003\pi$
$673$	25.7999	−	28.6537i	0.994512	−	1.10452i	0.994523	−	0.104518i	$-0.0333298\pi$
$674$	2.67251	+	0.280892i	0.102941	+	0.0108196i
$675$	3.18930	−	2.31717i	0.122756	−	0.0891877i
$676$	9.29342	−	13.2226i	0.357439	−	0.508563i
$677$	−9.13549	+	28.1162i	−0.351106	+	1.08059i	0.607128	+	0.794604i	$0.292322\pi$
$677$	−9.13549	+	28.1162i	−0.351106	+	1.08059i	−0.958233	+	0.285988i	$0.907678\pi$
$678$	4.59857	−	10.3286i	0.176607	−	0.396666i
$679$	−0.265375	+	2.52487i	−0.0101841	+	0.0968956i
$680$	46.5405	+	9.89248i	1.78475	+	0.379359i
$681$			9.91672i			0.380010i
$682$	2.09076	−	1.87076i	0.0800594	−	0.0716350i
$683$	−34.8906	−	20.1441i	−1.33505	−	0.770793i	−0.348983	−	0.937129i	$-0.613473\pi$
$683$	−34.8906	−	20.1441i	−1.33505	−	0.770793i	−0.986069	+	0.166336i	$0.946806\pi$
$684$	−1.37006	+	0.445158i	−0.0523854	+	0.0170211i
$685$	27.9349	−	12.4374i	1.06734	−	0.475210i
$686$	3.90491	+	1.73858i	0.149090	+	0.0663792i
$687$	−3.98409	−	18.7436i	−0.152002	−	0.715115i
$688$	0.0215493	−	0.0663218i	0.000821558	−	0.00252850i
$689$	0.0535448	−	1.20203i	0.00203990	−	0.0457937i
$690$	−1.37680	−	1.00031i	−0.0524140	−	0.0380810i
$691$	16.0751	+	14.4741i	0.611527	+	0.550621i	0.915632	−	0.402017i	$-0.131691\pi$
$691$	16.0751	+	14.4741i	0.611527	+	0.550621i	−0.304105	+	0.952638i	$0.598358\pi$
$692$	−9.16399	−	15.8725i	−0.348363	−	0.603382i
$693$	0.590446	−	1.01536i	0.0224292	−	0.0385702i
$694$		−	8.03800i		−	0.305118i
$695$	−2.36656	+	11.1338i	−0.0897686	+	0.422328i
$696$	−3.29821	−	7.40790i	−0.125018	−	0.280796i
$697$	−37.0771	−	51.0323i	−1.40440	−	1.93299i
$698$	9.23219	+	10.2534i	0.349444	+	0.388096i
$699$	2.87171	−	0.610400i	0.108618	−	0.0230874i
$700$	0.705953	−	1.58560i	0.0266825	−	0.0599299i
$701$	13.4848	+	9.79727i	0.509313	+	0.370038i	0.812563	−	0.582873i	$-0.198072\pi$
$701$	13.4848	+	9.79727i	0.509313	+	0.370038i	−0.303250	+	0.952911i	$0.598072\pi$
$702$	−3.09402	+	0.514954i	−0.116776	+	0.0194357i
$703$	−12.2702			−0.462779
$704$	16.0548	+	1.73806i	0.605086	+	0.0655057i
$705$	10.3080	+	17.8540i	0.388222	+	0.672420i
$706$	17.7789	+	3.77902i	0.669118	+	0.142225i
$707$	1.01611	−	1.39856i	0.0382148	−	0.0525981i
$708$	15.8548	−	1.66641i	0.595860	−	0.0626274i
$709$	15.2974	−	13.7738i	0.574505	−	0.517287i	−0.329869	−	0.944027i	$-0.607005\pi$
$709$	15.2974	−	13.7738i	0.574505	−	0.517287i	0.904374	+	0.426740i	$0.140338\pi$
$710$	−15.4114	−	5.00748i	−0.578381	−	0.187927i
$711$	−0.841091	−	8.00244i	−0.0315434	−	0.300115i
$712$	3.37490	−	32.1101i	0.126480	−	1.20338i
$713$	0.472732	+	0.425650i	0.0177040	+	0.0159407i
$714$	1.73742			0.0650212
$715$	31.7848	−	16.3848i	1.18868	−	0.612757i
$716$	13.3749			0.499844
$717$	3.74645	+	3.37332i	0.139914	+	0.125979i
$718$	−0.608816	+	5.79250i	−0.0227208	+	0.216174i
$719$	2.44920	+	23.3025i	0.0913396	+	0.869038i	0.940246	+	0.340495i	$0.110595\pi$
$719$	2.44920	+	23.3025i	0.0913396	+	0.869038i	−0.848907	+	0.528543i	$0.822739\pi$
$720$	−0.0911188	−	0.0296063i	−0.00339580	−	0.00110336i
$721$	−1.32054	+	1.18902i	−0.0491793	+	0.0442813i
$722$	−15.2765	+	1.60563i	−0.568533	+	0.0597552i
$723$	−11.7937	+	16.2327i	−0.438613	+	0.603700i
$724$	24.9554	+	5.30444i	0.927461	+	0.197138i
$725$	5.66516	+	9.81234i	0.210399	+	0.364421i
$726$	−9.51039	−	1.05960i	−0.352964	−	0.0393254i
$727$	21.1459			0.784259			0.392130	−	0.919910i	$-0.371738\pi$
$727$	21.1459			0.784259			0.392130	+	0.919910i	$0.371738\pi$
$728$	−2.78183	+	2.28904i	−0.103101	+	0.0848376i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	6.74959	−	15.1598i	0.249814	−	0.561090i
$731$	−12.0066	+	2.55207i	−0.444078	+	0.0943918i
$732$	4.22319	+	4.69033i	0.156094	+	0.173360i
$733$	14.3520	+	19.7538i	0.530102	+	0.729622i	0.987146	−	0.159822i	$-0.0510919\pi$
$733$	14.3520	+	19.7538i	0.530102	+	0.729622i	−0.457044	+	0.889444i	$0.651092\pi$
$734$	0.974139	+	2.18795i	0.0359561	+	0.0807588i
$735$	−4.27413	+	20.1082i	−0.157654	+	0.741702i
$736$			3.70970i			0.136741i
$737$	5.04477	+	49.4818i	0.185826	+	1.82268i
$738$	−4.86518	−	8.42674i	−0.179090	−	0.310193i
$739$	6.13656	+	5.52539i	0.225737	+	0.203255i	0.774237	−	0.632896i	$-0.218134\pi$
$739$	6.13656	+	5.52539i	0.225737	+	0.203255i	−0.548499	+	0.836151i	$0.684801\pi$
$740$	−31.8490	−	23.1396i	−1.17079	−	0.850630i
$741$	−4.17374	−	0.185920i	−0.153326	−	0.00682996i
$742$	−0.0317700	+	0.0977780i	−0.00116631	+	0.00358954i
$743$	1.49736	+	7.04451i	0.0549327	+	0.258438i	0.997041	−	0.0768704i	$-0.0244928\pi$
$743$	1.49736	+	7.04451i	0.0549327	+	0.258438i	−0.942108	+	0.335309i	$0.891159\pi$
$744$	−2.50626	−	1.11586i	−0.0918839	−	0.0409093i
$745$	−2.69883	+	1.20160i	−0.0988776	+	0.0440231i
$746$	−5.21102	+	1.69316i	−0.190789	+	0.0619911i
$747$	14.1541	+	8.17188i	0.517872	+	0.298994i
$748$	9.39174	+	21.2725i	0.343396	+	0.777799i
$749$		−	6.09130i		−	0.222571i
$750$	2.69163	+	0.572124i	0.0982845	+	0.0208910i
$751$	−1.30338	+	12.4008i	−0.0475609	+	0.452512i	0.944663	+	0.328043i	$0.106389\pi$
$751$	−1.30338	+	12.4008i	−0.0475609	+	0.452512i	−0.992224	+	0.124469i	$0.960277\pi$
$752$	0.0898412	−	0.201787i	0.00327617	−	0.00735840i
$753$	2.64119	−	8.12875i	0.0962503	−	0.296228i
$754$	−0.542403	−	8.99855i	−0.0197531	−	0.327708i
$755$	12.0163	−	8.73037i	0.437319	−	0.317731i
$756$	−0.437863	−	0.0460213i	−0.0159249	−	0.00167378i
$757$	−28.3953	+	31.5362i	−1.03205	+	1.14620i	−0.0429284	+	0.999078i	$0.513669\pi$
$757$	−28.3953	+	31.5362i	−1.03205	+	1.14620i	−0.989118	+	0.147125i	$0.952998\pi$
$758$	−16.0857	+	27.8613i	−0.584259	+	1.01197i
$759$	0.00676685	−	2.16971i	0.000245621	−	0.0787555i
$760$	8.46638	+	4.88807i	0.307108	+	0.177309i
$761$	1.24803	−	5.87152i	0.0452410	−	0.212842i	−0.949721	−	0.313099i	$-0.898633\pi$
$761$	1.24803	−	5.87152i	0.0452410	−	0.212842i	0.994962	+	0.100256i	$0.0319663\pi$
$762$	−0.362327	+	0.498700i	−0.0131257	+	0.0180660i
$763$	0.448339	+	4.26566i	0.0162309	+	0.154427i
$764$	5.54279	−	1.17816i	0.200531	−	0.0426242i
$765$	3.50626	+	16.4957i	0.126769	+	0.596402i
$766$	−19.4332	+	14.1190i	−0.702149	+	0.510141i
$767$	44.7520	+	11.6158i	1.61590	+	0.419422i
$768$	−4.91934	−	15.1402i	−0.177511	−	0.546324i
$769$	9.53951	−	5.50764i	0.344004	−	0.198611i	−0.318037	−	0.948078i	$-0.603024\pi$
$769$	9.53951	−	5.50764i	0.344004	−	0.198611i	0.662041	+	0.749468i	$0.269690\pi$
$770$	−2.99068	+	0.625945i	−0.107776	+	0.0225575i
$771$	−9.40046	+	16.2821i	−0.338549	+	0.586385i
$772$	20.2446	−	6.57787i	0.728619	−	0.236743i
$773$	−7.71629	−	17.3311i	−0.277536	−	0.623355i	0.719965	−	0.694010i	$-0.244158\pi$
$773$	−7.71629	−	17.3311i	−0.277536	−	0.623355i	−0.997501	+	0.0706549i	$0.977491\pi$
$774$	−1.88308	+	0.197920i	−0.0676861	+	0.00711409i
$775$	3.64568	+	1.18455i	0.130957	+	0.0425505i
$776$	−13.5338	−	15.0308i	−0.485836	−	0.539576i
$777$	−3.42589	−	1.52531i	−0.122903	−	0.0547201i
$778$	14.8217	+	1.55782i	0.531384	+	0.0558507i
$779$	−4.00507	−	12.3264i	−0.143497	−	0.441637i
$780$	−10.4829	−	8.35359i	−0.375348	−	0.299106i
$781$	−6.32293	−	19.6685i	−0.226252	−	0.703794i
$782$	2.77949	−	1.60474i	0.0993945	−	0.0573855i
$783$	1.92316	−	2.13588i	0.0687280	−	0.0763302i
$784$	0.201213	−	0.0895858i	0.00718618	−	0.00319949i
$785$	−12.9141	−	17.7747i	−0.460923	−	0.634405i
$786$	0.149938	−	0.135005i	0.00534813	−	0.00481547i
$787$	28.9736	−	26.0879i	1.03280	−	0.929933i	0.0352099	−	0.999380i	$-0.488790\pi$
$787$	28.9736	−	26.0879i	1.03280	−	0.929933i	0.997586	+	0.0694466i	$0.0221233\pi$
$788$	−18.2466	−	25.1143i	−0.650008	−	0.894660i
$789$	23.9028	−	10.6422i	0.850964	−	0.378873i
$790$	−14.0064	+	15.5557i	−0.498325	+	0.553446i
$791$	3.98595	−	2.30129i	0.141724	−	0.0818244i
$792$	2.86384	+	8.90844i	0.101762	+	0.316548i
$793$	6.69352	+	17.0366i	0.237694	+	0.604987i
$794$	5.03040	+	15.4820i	0.178522	+	0.549435i
$795$	−0.992455	−	0.104311i	−0.0351987	−	0.00369954i
$796$	−0.938795	−	0.417978i	−0.0332747	−	0.0148149i
$797$	17.2212	+	19.1261i	0.610005	+	0.677480i	0.966455	−	0.256835i	$-0.0826796\pi$
$797$	17.2212	+	19.1261i	0.610005	+	0.677480i	−0.356450	+	0.934314i	$0.616013\pi$
$798$	0.339509	+	0.110313i	0.0120185	+	0.00390504i
$799$	−38.6670	+	4.06406i	−1.36794	+	0.143776i
$800$	9.09249	+	20.4221i	0.321468	+	0.722029i
$801$	10.8836	−	3.53629i	0.384553	−	0.124949i
$802$	−4.67326	+	8.09432i	−0.165019	+	0.285821i
$803$	20.7083	−	4.33422i	0.730779	−	0.152951i
$804$	16.1463	−	9.32207i	0.569436	−	0.328764i
$805$	−0.214086	−	0.658889i	−0.00754554	−	0.0232228i
$806$	−2.17348	−	2.13965i	−0.0765576	−	0.0753659i
$807$	−18.5439	+	13.4730i	−0.652778	+	0.474271i
$808$	2.86343	+	13.4714i	0.100735	+	0.473921i
$809$	−43.1552	+	9.17292i	−1.51726	+	0.322503i	−0.889873	−	0.456208i	$-0.849207\pi$
$809$	−43.1552	+	9.17292i	−1.51726	+	0.322503i	−0.627383	+	0.778711i	$0.715874\pi$
$810$	0.271920	+	2.58715i	0.00955430	+	0.0909031i
$811$	−18.3009	+	25.1890i	−0.642632	+	0.884507i	−0.998753	−	0.0499333i	$-0.984099\pi$
$811$	−18.3009	+	25.1890i	−0.642632	+	0.884507i	0.356121	+	0.934440i	$0.384099\pi$
$812$	0.263091	−	1.23775i	0.00923270	−	0.0434364i
$813$	15.9613	+	9.21529i	0.559789	+	0.323194i
$814$	−0.0952864	+	30.5525i	−0.00333979	+	1.07086i
$815$	−27.9022	+	48.3281i	−0.977373	+	1.69286i
$816$	0.120902	−	0.134275i	0.00423241	−	0.00470057i
$817$	−2.50824	−	0.263627i	−0.0877522	−	0.00922313i
$818$	−9.36612	+	6.80488i	−0.327479	+	0.237927i
$819$	−1.14221	−	0.570746i	−0.0399122	−	0.0199435i
$820$	12.8498	−	39.5477i	0.448735	−	1.38106i
$821$	−12.1638	+	27.3203i	−0.424518	+	0.953484i	0.567024	+	0.823701i	$0.308095\pi$
$821$	−12.1638	+	27.3203i	−0.424518	+	0.953484i	−0.991542	+	0.129783i	$0.958572\pi$
$822$	−0.929854	+	8.84697i	−0.0324324	+	0.308573i
$823$	29.2664	+	6.22077i	1.02016	+	0.216842i	0.687486	−	0.726198i	$-0.258714\pi$
$823$	29.2664	+	6.22077i	1.02016	+	0.216842i	0.332678	+	0.943040i	$0.392048\pi$
$824$		−	14.1567i		−	0.493172i
$825$	−5.28072	−	11.9609i	−0.183851	−	0.416427i
$826$	−3.42129	−	1.97528i	−0.119042	−	0.0687288i
$827$	45.1480	−	14.6695i	1.56995	−	0.510107i	0.610506	−	0.792011i	$-0.290966\pi$
$827$	45.1480	−	14.6695i	1.56995	−	0.510107i	0.959443	+	0.281904i	$0.0909660\pi$
$828$	−0.742995	+	0.330803i	−0.0258209	+	0.0114962i
$829$	−35.2739	−	15.7049i	−1.22511	−	0.545455i	−0.310804	−	0.950474i	$-0.600598\pi$
$829$	−35.2739	−	15.7049i	−1.22511	−	0.545455i	−0.914308	+	0.405019i	$0.867265\pi$
$830$	−8.83971	−	41.5875i	−0.306831	−	1.44352i
$831$	9.30193	−	28.6284i	0.322680	−	0.993108i
$832$	0.781233	−	17.5379i	0.0270844	−	0.608019i
$833$	−31.3651	−	22.7881i	−1.08674	−	0.789561i
$834$	−2.46079	−	2.21570i	−0.0852100	−	0.0767235i
$835$	−6.01301	−	10.4148i	−0.208089	−	0.360421i
$836$	0.484595	+	4.75317i	0.0167601	+	0.164392i
$837$		−	0.972376i		−	0.0336102i
$838$	−0.246935	+	1.16174i	−0.00853024	+	0.0401316i
$839$	−12.6666	−	28.4497i	−0.437300	−	0.982191i	−0.988968	−	0.148128i	$-0.952675\pi$
$839$	−12.6666	−	28.4497i	−0.437300	−	0.982191i	0.551669	−	0.834063i	$-0.313991\pi$
$840$	1.75622	+	2.41722i	0.0605952	+	0.0834022i
$841$	−13.8774	−	15.4124i	−0.478532	−	0.531463i
$842$	−9.98915	+	2.12326i	−0.344249	+	0.0731723i
$843$	7.04688	−	15.8276i	0.242708	−	0.545130i
$844$	3.32822	+	2.41810i	0.114562	+	0.0832343i
$845$	−19.9630	−	33.3573i	−0.686749	−	1.14753i
$846$	−5.99746			−0.206197
$847$	−2.87864	−	2.62464i	−0.0989113	−	0.0901836i
$848$	0.00534593	+	0.00925943i	0.000183580	+	0.000317970i
$849$	2.10494	+	0.447418i	0.0722412	+	0.0153553i
$850$	11.3680	−	15.6467i	0.389920	−	0.536679i
$851$	−6.88953	+	0.724119i	−0.236170	+	0.0248225i
$852$	−5.75509	+	5.18191i	−0.197166	+	0.177529i
$853$	45.2084	+	14.6891i	1.54791	+	0.502946i	0.953545	−	0.301251i	$-0.0974043\pi$
$853$	45.2084	+	14.6891i	1.54791	+	0.502946i	0.594363	+	0.804197i	$0.297404\pi$
$854$	−0.163485	−	1.55545i	−0.00559433	−	0.0532265i
$855$	−0.362193	+	3.44604i	−0.0123868	+	0.117852i
$856$	36.0636	+	32.4718i	1.23263	+	1.10986i
$857$	−17.1832			−0.586966			−0.293483	−	0.955964i	$-0.594814\pi$
$857$	−17.1832			−0.586966			−0.293483	+	0.955964i	$0.594814\pi$
$858$	−0.495349	+	10.3911i	−0.0169109	+	0.354745i
$859$	−52.8779			−1.80417			−0.902085	−	0.431558i	$-0.857964\pi$
$859$	−52.8779			−1.80417			−0.902085	+	0.431558i	$0.857964\pi$
$860$	−6.01332	−	5.41442i	−0.205053	−	0.184630i
$861$	0.414052	−	3.93944i	0.0141109	−	0.134256i
$862$	0.294171	+	2.79885i	0.0100195	+	0.0953293i
$863$	34.9247	+	11.3477i	1.18885	+	0.386281i	0.835648	−	0.549265i	$-0.185092\pi$
$863$	34.9247	+	11.3477i	1.18885	+	0.386281i	0.353203	+	0.935547i	$0.385092\pi$
$864$	4.21410	−	3.79439i	0.143366	−	0.129088i
$865$	−43.8433	+	4.60811i	−1.49072	+	0.156681i
$866$	3.81916	−	5.25662i	0.129780	−	0.178627i
$867$	−14.4808	−	3.07799i	−0.491794	−	0.104534i
$868$	−0.214057	−	0.370757i	−0.00726556	−	0.0125843i
$869$	−26.5323	−	2.87234i	−0.900046	−	0.0974376i
$870$	−7.47671			−0.253484
$871$	53.3375	−	8.87725i	1.80727	−	0.300794i
$872$	−27.6449	−	20.0852i	−0.936173	−	0.680169i
$873$	2.91583	−	6.54906i	0.0986859	−	0.221652i
$874$	0.645031	−	0.137106i	0.0218185	−	0.00463766i
$875$	0.749573	+	0.832485i	0.0253402	+	0.0281431i
$876$	−4.66149	−	6.41598i	−0.157497	−	0.216776i
$877$	−2.48347	−	5.57797i	−0.0838609	−	0.188355i	0.866748	−	0.498747i	$-0.166206\pi$
$877$	−2.48347	−	5.57797i	−0.0838609	−	0.188355i	−0.950609	+	0.310392i	$0.899540\pi$
$878$	1.46395	−	6.88734i	0.0494059	−	0.232437i
$879$			8.44165i			0.284730i
$880$	−0.159737	+	0.274690i	−0.00538473	+	0.00925981i
$881$	24.8664	+	43.0698i	0.837769	+	1.45106i	0.891756	+	0.452517i	$0.149474\pi$
$881$	24.8664	+	43.0698i	0.837769	+	1.45106i	−0.0539871	+	0.998542i	$0.517193\pi$
$882$	−4.44431	−	4.00168i	−0.149648	−	0.134743i
$883$	−33.9436	−	24.6615i	−1.14229	−	0.829925i	−0.154856	−	0.987937i	$-0.549491\pi$
$883$	−33.9436	−	24.6615i	−1.14229	−	0.829925i	−0.987437	+	0.158012i	$0.949491\pi$
$884$	22.4332	−	11.6528i	0.754510	−	0.391927i
$885$	11.8496	−	36.4692i	0.398319	−	1.22590i
$886$	0.115087	+	0.541443i	0.00386643	+	0.0181901i
$887$	−45.6732	−	20.3350i	−1.53356	−	0.682783i	−0.545675	−	0.837997i	$-0.683727\pi$
$887$	−45.6732	−	20.3350i	−1.53356	−	0.682783i	−0.987881	+	0.155213i	$0.950394\pi$
$888$	27.2935	−	12.1518i	0.915909	−	0.407789i
$889$	−0.238660	+	0.0775454i	−0.00800440	+	0.00260079i
$890$	−25.7812	−	14.8848i	−0.864188	−	0.498939i
$891$	−2.47164	+	2.21156i	−0.0828031	+	0.0740900i
$892$			15.8967i			0.532262i
$893$	−7.81396	−	1.66091i	−0.261484	−	0.0555802i
$894$	0.0898345	−	0.854718i	0.00300451	−	0.0285860i
$895$	13.0851	−	29.3897i	0.437388	−	0.982389i
$896$	0.777603	−	2.39322i	0.0259779	−	0.0799518i
$897$	−2.35446	+	0.141919i	−0.0786132	+	0.00473854i
$898$	−10.4625	+	7.60147i	−0.349139	+	0.253664i
$899$	2.77941	+	0.292128i	0.0926985	+	0.00974300i
$900$	−3.27942	+	3.64217i	−0.109314	+	0.121406i
$901$	0.940995	−	1.62985i	0.0313491	−	0.0542982i
$902$	−30.7234	+	9.87681i	−1.02298	+	0.328862i
$903$	−0.667540	−	0.385405i	−0.0222144	−	0.0128255i
$904$	−7.62369	+	35.8666i	−0.253560	+	1.19291i
$905$	36.0706	−	49.6469i	1.19903	−	1.65032i
$906$	0.451659	+	4.29725i	0.0150054	+	0.142767i
$907$	21.8190	−	4.63778i	0.724489	−	0.153995i	0.169116	−	0.985596i	$-0.445909\pi$
$907$	21.8190	−	4.63778i	0.724489	−	0.153995i	0.555373	+	0.831601i	$0.312575\pi$
$908$	−2.56328	−	12.0593i	−0.0850653	−	0.400201i
$909$	−3.94915	+	2.86923i	−0.130985	+	0.0951663i
$910$	0.884848	+	3.20163i	0.0293324	+	0.106133i
$911$	16.3397	+	50.2883i	0.541357	+	1.66613i	0.729498	+	0.683983i	$0.239754\pi$
$911$	16.3397	+	50.2883i	0.541357	+	1.66613i	−0.188141	+	0.982142i	$0.560246\pi$
$912$	0.0321510	−	0.0185624i	0.00106462	−	0.000614661i
$913$	36.3964	−	40.1697i	1.20455	−	1.32942i
$914$	10.3527	−	17.9314i	0.342438	−	0.593119i
$915$	14.4381	−	4.69123i	0.477309	−	0.155087i
$916$	9.68972	+	21.7635i	0.320157	+	0.719085i
$917$	0.0816856	−	0.00858550i	0.00269749	−	0.000283518i
$918$	−4.66588	−	1.51604i	−0.153997	−	0.0500367i
$919$	−37.7150	−	41.8867i	−1.24410	−	1.38172i	−0.895876	−	0.444305i	$-0.853451\pi$
$919$	−37.7150	−	41.8867i	−1.24410	−	1.38172i	−0.348227	−	0.937410i	$-0.613216\pi$
$920$	5.04221	+	2.24494i	0.166237	+	0.0740134i
$921$	−3.46739	−	0.364438i	−0.114254	−	0.0120086i
$922$	−5.15286	−	15.8589i	−0.169700	−	0.522284i
$923$	−20.9041	+	8.21302i	−0.688066	+	0.270335i
$924$	−0.455564	+	1.38735i	−0.0149870	+	0.0456403i
$925$	−36.1524	+	20.8726i	−1.18868	+	0.686286i
$926$	−19.8855	+	22.0851i	−0.653479	+	0.725762i
$927$	4.58386	−	2.04086i	0.150554	−	0.0670308i
$928$	9.57973	+	13.1854i	0.314470	+	0.432831i
$929$	−27.0852	+	24.3876i	−0.888637	+	0.800132i	−0.980679	−	0.195623i	$-0.937327\pi$
$929$	−27.0852	+	24.3876i	−0.888637	+	0.800132i	0.0920424	+	0.995755i	$0.470660\pi$
$930$	−1.87981	+	1.69259i	−0.0616415	+	0.0555023i
$931$	−4.68219	−	6.44448i	−0.153453	−	0.211209i
$932$	−3.33437	+	1.48456i	−0.109221	+	0.0486283i
$933$	−12.5160	+	13.9004i	−0.409756	+	0.455080i
$934$	−7.19935	+	4.15655i	−0.235570	+	0.136006i
$935$	55.9319	+	0.174439i	1.82917	+	0.00570477i
$936$	9.46807	−	3.71992i	0.309474	−	0.121589i
$937$	−0.240653	−	0.740653i	−0.00786178	−	0.0241961i	0.947049	−	0.321090i	$-0.104049\pi$
$937$	−0.240653	−	0.740653i	−0.00786178	−	0.0241961i	−0.954910	+	0.296894i	$0.904049\pi$
$938$	−4.59483	−	0.482936i	−0.150027	−	0.0157684i
$939$	−7.39977	−	3.29459i	−0.241482	−	0.107515i
$940$	−17.1500	−	19.0470i	−0.559371	−	0.621245i
$941$	34.9318	+	11.3500i	1.13874	+	0.370000i	0.816893	−	0.576790i	$-0.195695\pi$
$941$	34.9318	+	11.3500i	1.13874	+	0.370000i	0.321851	+	0.946790i	$0.395695\pi$
$942$	6.35654	−	0.668099i	0.207107	−	0.0217679i
$943$	−2.97622	−	6.68470i	−0.0969191	−	0.217684i
$944$	−0.390736	+	0.126958i	−0.0127174	+	0.00413213i
$945$	−0.529503	+	0.917126i	−0.0172247	+	0.0298341i
$946$	−0.675902	+	6.24341i	−0.0219755	+	0.202991i
$947$	5.70141	−	3.29171i	0.185271	−	0.106966i	−0.404496	−	0.914540i	$-0.632553\pi$
$947$	5.70141	−	3.29171i	0.185271	−	0.106966i	0.589767	+	0.807574i	$0.299220\pi$
$948$	3.09128	+	9.51399i	0.100400	+	0.309000i
$949$	−6.12693	−	22.1690i	−0.198889	−	0.719636i
$950$	3.21488	−	2.33575i	0.104304	−	0.0757816i
$951$	1.85610	+	8.73227i	0.0601882	+	0.283163i
$952$	−5.51169	+	1.17155i	−0.178635	+	0.0379700i
$953$	−1.05535	−	10.0410i	−0.0341863	−	0.325261i	−0.998228	−	0.0595089i	$-0.981047\pi$
$953$	−1.05535	−	10.0410i	−0.0341863	−	0.325261i	0.964042	−	0.265752i	$-0.0856201\pi$
$954$	0.170639	−	0.234864i	0.00552463	−	0.00760400i
$955$	2.83385	−	13.3322i	0.0917013	−	0.431420i
$956$	−5.42783	−	3.13376i	−0.175548	−	0.101353i
$957$	−5.57890	−	7.72927i	−0.180340	−	0.249852i
$958$	15.4792	−	26.8108i	0.500112	−	0.866219i
$959$	−2.42316	+	2.69119i	−0.0782480	+	0.0869032i
$960$	−14.4802	−	1.52193i	−0.467346	−	0.0491200i
$961$	−24.3146	+	17.6656i	−0.784342	+	0.569857i
$962$	33.1540	−	1.99842i	1.06893	−	0.0644315i
$963$	−5.31516	+	16.3584i	−0.171279	+	0.527142i
$964$	10.1460	−	22.7882i	0.326780	−	0.733960i
$965$	5.35194	−	50.9203i	0.172285	−	1.63918i
$966$	0.197139	+	0.0419032i	0.00634284	+	0.00134821i
$967$		−	49.0303i		−	1.57671i	−0.615222	−	0.788354i	$-0.710934\pi$
$967$		−	49.0303i		−	1.57671i	0.615222	−	0.788354i	$-0.289066\pi$
$968$	30.8848	−	3.05147i	0.992674	−	0.0980780i
$969$	−5.65923	−	3.26736i	−0.181801	−	0.104963i
$970$	−17.7362	+	5.76286i	−0.569477	+	0.185034i
$971$	−21.0847	+	9.38753i	−0.676642	+	0.301260i	−0.716137	−	0.697959i	$-0.754092\pi$
$971$	−21.0847	+	9.38753i	−0.676642	+	0.301260i	0.0394956	+	0.999220i	$0.487425\pi$
$972$	1.13574	+	0.505663i	0.0364288	+	0.0162192i
$973$	−0.280266	−	1.31855i	−0.00898492	−	0.0422707i
$974$	9.89940	−	30.4672i	0.317197	−	0.976233i
$975$	−12.6136	+	6.55207i	−0.403958	+	0.209834i
$976$	−0.131589	−	0.0956049i	−0.00421206	−	0.00306024i
$977$	31.6913	+	28.5349i	1.01389	+	0.912914i	0.996214	−	0.0869300i	$-0.0277057\pi$
$977$	31.6913	+	28.5349i	1.01389	+	0.912914i	0.0176789	+	0.999844i	$0.494372\pi$
$978$	−8.11711	−	14.0592i	−0.259557	−	0.449565i
$979$	−3.84957	−	37.7587i	−0.123033	−	1.20677i
$980$		−	25.5574i		−	0.816401i
$981$	2.51811	−	11.8468i	0.0803970	−	0.378238i
$982$	−1.40710	−	3.16040i	−0.0449023	−	0.100852i
$983$	29.7715	+	40.9769i	0.949562	+	1.30696i	0.951721	+	0.306963i	$0.0993128\pi$
$983$	29.7715	+	40.9769i	0.949562	+	1.30696i	−0.00215902	+	0.999998i	$0.500687\pi$
$984$	21.1162	+	23.4519i	0.673161	+	0.747621i
$985$	−73.0368	+	15.5244i	−2.32715	+	0.494650i
$986$	5.73515	−	12.8814i	0.182644	−	0.410226i
$987$	−1.97522	−	1.43508i	−0.0628721	−	0.0456792i
$988$	5.12354	−	0.852739i	0.163002	−	0.0271292i
$989$	−1.42390			−0.0452773
$990$	8.57774	+	0.928613i	0.272619	+	0.0295133i
$991$	−4.15783	−	7.20158i	−0.132078	−	0.228766i	0.792399	−	0.610003i	$-0.208832\pi$
$991$	−4.15783	−	7.20158i	−0.132078	−	0.228766i	−0.924477	+	0.381237i	$0.875498\pi$
$992$	5.39349	+	1.14642i	0.171243	+	0.0363989i
$993$	−2.68997	+	3.70242i	−0.0853635	+	0.117493i
$994$	1.90856	−	0.200598i	0.0605358	−	0.00636257i
$995$	−1.83691	+	1.65396i	−0.0582340	+	0.0524341i
$996$	−19.3244	−	6.27889i	−0.612318	−	0.198954i
$997$	1.01069	+	9.61604i	0.0320088	+	0.304543i	0.998800	+	0.0489756i	$0.0155956\pi$
$997$	1.01069	+	9.61604i	0.0320088	+	0.304543i	−0.966791	+	0.255568i	$0.917738\pi$
$998$	−0.115268	+	1.09670i	−0.00364875	+	0.0347155i
$999$	7.86939	+	7.08563i	0.248977	+	0.224179i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bn.b.49.5	✓	112
11.9	even	5	inner	429.2.bn.b.361.10	yes	112
13.4	even	6	inner	429.2.bn.b.82.10	yes	112
143.108	even	30	inner	429.2.bn.b.394.5	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bn.b.49.5	✓	112	1.1	even	1	trivial
429.2.bn.b.82.10	yes	112	13.4	even	6	inner
429.2.bn.b.361.10	yes	112	11.9	even	5	inner
429.2.bn.b.394.5	yes	112	143.108	even	30	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:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.646484 - 0.582097i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.129952 - 1.23641i) q^{4} +(-2.84399 - 0.924069i) q^{5} +(0.646484 - 0.582097i) q^{6} +(0.352201 - 0.0370178i) q^{7} +(-1.65836 + 2.28254i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.646484 - 0.582097i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(-0.129952 - 1.23641i) q^{4} +(-2.84399 - 0.924069i) q^{5} +(0.646484 - 0.582097i) q^{6} +(0.352201 - 0.0370178i) q^{7} +(-1.65836 + 2.28254i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(1.30070 + 2.25288i) q^{10} +(-1.35844 + 3.02567i) q^{11} +1.24322 q^{12} +(3.37610 + 1.26567i) q^{13} +(-0.249240 - 0.181084i) q^{14} +(1.21629 - 2.73182i) q^{15} +(-0.0313389 + 0.00666129i) q^{16} +(3.77358 + 4.19099i) q^{17} +(0.511332 + 0.703789i) q^{18} +(0.471300 + 1.05856i) q^{19} +(-0.772946 + 3.63643i) q^{20} +0.354141i q^{21} +(2.63944 - 1.16530i) q^{22} +(0.327098 + 0.566550i) q^{23} +(-2.09669 - 1.88787i) q^{24} +(3.18930 + 2.31717i) q^{25} +(-1.44585 - 2.78346i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.0915384 - 0.430654i) q^{28} +(2.62563 + 1.16901i) q^{29} +(-2.37650 + 1.05808i) q^{30} +(0.924785 - 0.300481i) q^{31} +(4.91091 + 2.83531i) q^{32} +(-2.86710 - 1.66726i) q^{33} -4.90600i q^{34} +(-1.03586 - 0.220180i) q^{35} +(-0.129952 + 1.23641i) q^{36} +(-4.30706 + 9.67382i) q^{37} +(0.311495 - 0.958683i) q^{38} +(-1.61164 + 3.22531i) q^{39} +(6.82560 - 4.95909i) q^{40} +(-11.1239 - 1.16917i) q^{41} +(0.206144 - 0.228947i) q^{42} +(-1.08828 + 1.88496i) q^{43} +(3.91750 + 1.28639i) q^{44} +(2.58972 + 1.49518i) q^{45} +(0.118324 - 0.556668i) q^{46} +(-4.05230 + 5.57751i) q^{47} +(-0.00334899 - 0.0318635i) q^{48} +(-6.72436 + 1.42931i) q^{49} +(-0.713020 - 3.35450i) q^{50} +(-4.56248 + 3.31483i) q^{51} +(1.12616 - 4.33873i) q^{52} +(-0.103123 - 0.317381i) q^{53} +(-0.753382 + 0.434965i) q^{54} +(6.65931 - 7.34968i) q^{55} +(-0.499582 + 0.865302i) q^{56} +(-1.10202 + 0.358069i) q^{57} +(-1.01695 - 2.28412i) q^{58} +(12.7530 - 1.34039i) q^{59} +(-3.53571 - 1.14882i) q^{60} +(3.39698 + 3.77273i) q^{61} +(-0.772768 - 0.344059i) q^{62} +(-0.352201 - 0.0370178i) q^{63} +(-1.50460 - 4.63067i) q^{64} +(-8.43205 - 6.71931i) q^{65} +(0.883024 + 2.74679i) q^{66} +(12.9875 - 7.49833i) q^{67} +(4.69140 - 5.21032i) q^{68} +(-0.597637 + 0.266085i) q^{69} +(0.541504 + 0.745316i) q^{70} +(-4.62918 + 4.16813i) q^{71} +(2.09669 - 1.88787i) q^{72} +(-3.74952 - 5.16078i) q^{73} +(8.41555 - 3.74684i) q^{74} +(-2.63784 + 2.92962i) q^{75} +(1.24756 - 0.720281i) q^{76} +(-0.366439 + 1.11593i) q^{77} +(2.91934 - 1.14698i) q^{78} +(2.48651 + 7.65270i) q^{79} +(0.0952831 + 0.0100147i) q^{80} +(0.913545 + 0.406737i) q^{81} +(6.51088 + 7.23107i) q^{82} +(-15.5438 - 5.05050i) q^{83} +(0.437863 - 0.0460213i) q^{84} +(-6.85928 - 15.4062i) q^{85} +(1.80078 - 0.585110i) q^{86} +(-1.43706 + 2.48905i) q^{87} +(-4.65343 - 8.11834i) q^{88} +(-9.91052 + 5.72184i) q^{89} +(-0.803876 - 2.47408i) q^{90} +(1.23592 + 0.320795i) q^{91} +(0.657981 - 0.478051i) q^{92} +(0.202168 + 0.951128i) q^{93} +(5.86640 - 1.24694i) q^{94} +(-0.362193 - 3.44604i) q^{95} +(-3.33311 + 4.58763i) q^{96} +(-1.49049 + 7.01218i) q^{97} +(5.17919 + 2.99021i) q^{98} +(1.95782 - 2.67711i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9}+O(q^{10}) \) 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9	\( 112 q + 14 q^{3} - 8 q^{4} + 14 q^{9} - 40 q^{10} + 15 q^{11} - 104 q^{12} + q^{13} - 6 q^{14} - 6 q^{15} + 32 q^{16} + 8 q^{17} - 12 q^{19} + 42 q^{20} - 9 q^{22} + 8 q^{23} + 30 q^{25} - 57 q^{26} - 28 q^{27} + 18 q^{28} - 10 q^{29} + 10 q^{30} + 30 q^{32} + 30 q^{33} - 12 q^{35} - 8 q^{36} + 30 q^{38} + 4 q^{39} + 20 q^{40} + 72 q^{41} - 12 q^{42} - 108 q^{43} + 6 q^{45} - 18 q^{46} + 2 q^{48} - 40 q^{49} + 111 q^{50} - 26 q^{51} + 13 q^{52} - 46 q^{53} - 38 q^{55} - 100 q^{56} - 12 q^{58} - 18 q^{59} - 46 q^{61} - 9 q^{62} + 52 q^{64} + 24 q^{65} - 32 q^{66} + 48 q^{67} - 8 q^{68} - 7 q^{69} + 18 q^{71} + 32 q^{74} - 216 q^{76} + 4 q^{77} - 26 q^{78} + 108 q^{79} - 66 q^{80} + 14 q^{81} + 39 q^{82} + 27 q^{84} + 6 q^{85} + 60 q^{87} + 28 q^{88} - 120 q^{89} - 20 q^{90} + 47 q^{91} + 78 q^{92} - 6 q^{93} - 50 q^{94} + 60 q^{95} - 69 q^{97} + 72 q^{98}+O(q^{100}) \) 112 * q + 14 * q^3 - 8 * q^4 + 14 * q^9 - 40 * q^10 + 15 * q^11 - 104 * q^12 + q^13 - 6 * q^14 - 6 * q^15 + 32 * q^16 + 8 * q^17 - 12 * q^19 + 42 * q^20 - 9 * q^22 + 8 * q^23 + 30 * q^25 - 57 * q^26 - 28 * q^27 + 18 * q^28 - 10 * q^29 + 10 * q^30 + 30 * q^32 + 30 * q^33 - 12 * q^35 - 8 * q^36 + 30 * q^38 + 4 * q^39 + 20 * q^40 + 72 * q^41 - 12 * q^42 - 108 * q^43 + 6 * q^45 - 18 * q^46 + 2 * q^48 - 40 * q^49 + 111 * q^50 - 26 * q^51 + 13 * q^52 - 46 * q^53 - 38 * q^55 - 100 * q^56 - 12 * q^58 - 18 * q^59 - 46 * q^61 - 9 * q^62 + 52 * q^64 + 24 * q^65 - 32 * q^66 + 48 * q^67 - 8 * q^68 - 7 * q^69 + 18 * q^71 + 32 * q^74 - 216 * q^76 + 4 * q^77 - 26 * q^78 + 108 * q^79 - 66 * q^80 + 14 * q^81 + 39 * q^82 + 27 * q^84 + 6 * q^85 + 60 * q^87 + 28 * q^88 - 120 * q^89 - 20 * q^90 + 47 * q^91 + 78 * q^92 - 6 * q^93 - 50 * q^94 + 60 * q^95 - 69 * q^97 + 72 * q^98

Introduction

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