LMFDB - Embedded newform 429.2.n.d.157.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(157,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 8, 0]))

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

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

chi := DirichletCharacter("429.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.n (of order $5$, degree $4$, 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:	$36$
Relative dimension:	$9$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			157.4
Character	$\chi$	$=$	429.157
Dual form			429.2.n.d.235.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.214873 + 0.156114i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.596235 + 1.83502i) q^{4} +(-3.10912 - 2.25891i) q^{5} +(-0.214873 - 0.156114i) q^{6} +(-0.868527 + 2.67305i) q^{7} +(-0.322507 - 0.992575i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.214873 + 0.156114i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.596235 + 1.83502i) q^{4} +(-3.10912 - 2.25891i) q^{5} +(-0.214873 - 0.156114i) q^{6} +(-0.868527 + 2.67305i) q^{7} +(-0.322507 - 0.992575i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.02072 q^{10} +(1.88601 - 2.72818i) q^{11} -1.92946 q^{12} +(0.809017 - 0.587785i) q^{13} +(-0.230679 - 0.709957i) q^{14} +(1.18758 - 3.65499i) q^{15} +(-2.89767 - 2.10528i) q^{16} +(-2.81985 - 2.04874i) q^{17} +(0.0820742 - 0.252599i) q^{18} +(-1.45151 - 4.46729i) q^{19} +(5.99892 - 4.35847i) q^{20} -2.81061 q^{21} +(0.0206550 + 0.880646i) q^{22} -8.27252 q^{23} +(0.844335 - 0.613445i) q^{24} +(3.01888 + 9.29116i) q^{25} +(-0.0820742 + 0.252599i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-4.38727 - 3.18754i) q^{28} +(0.784449 - 2.41429i) q^{29} +(0.315418 + 0.970758i) q^{30} +(-3.85987 + 2.80436i) q^{31} +3.03861 q^{32} +(3.17746 + 0.950650i) q^{33} +0.925747 q^{34} +(8.73854 - 6.34892i) q^{35} +(-0.596235 - 1.83502i) q^{36} +(2.99563 - 9.21961i) q^{37} +(1.00930 + 0.733299i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-1.23942 + 3.81455i) q^{40} +(3.26387 + 10.0452i) q^{41} +(0.603925 - 0.438777i) q^{42} -7.76099 q^{43} +(3.88177 + 5.08751i) q^{44} +3.84309 q^{45} +(1.77754 - 1.29146i) q^{46} +(1.73153 + 5.32909i) q^{47} +(1.10681 - 3.40642i) q^{48} +(-0.727751 - 0.528742i) q^{49} +(-2.09916 - 1.52513i) q^{50} +(1.07709 - 3.31493i) q^{51} +(0.596235 + 1.83502i) q^{52} +(-8.20627 + 5.96221i) q^{53} +0.265598 q^{54} +(-12.0265 + 4.22191i) q^{55} +2.93331 q^{56} +(3.80011 - 2.76094i) q^{57} +(0.208348 + 0.641229i) q^{58} +(0.599939 - 1.84642i) q^{59} +(5.99892 + 4.35847i) q^{60} +(-0.435811 - 0.316635i) q^{61} +(0.391582 - 1.20516i) q^{62} +(-0.868527 - 2.67305i) q^{63} +(5.14243 - 3.73620i) q^{64} -3.84309 q^{65} +(-0.831161 + 0.291779i) q^{66} +0.204566 q^{67} +(5.44078 - 3.95296i) q^{68} +(-2.55635 - 7.86763i) q^{69} +(-0.886519 + 2.72842i) q^{70} +(-7.34476 - 5.33628i) q^{71} +(0.844335 + 0.613445i) q^{72} +(-4.24948 + 13.0786i) q^{73} +(0.795634 + 2.44871i) q^{74} +(-7.90354 + 5.74225i) q^{75} +9.06303 q^{76} +(5.65451 + 7.41091i) q^{77} -0.265598 q^{78} +(-10.2631 + 7.45655i) q^{79} +(4.25358 + 13.0912i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.26952 - 1.64890i) q^{82} +(-14.3350 - 10.4150i) q^{83} +(1.67579 - 5.15754i) q^{84} +(4.13933 + 12.7396i) q^{85} +(1.66763 - 1.21160i) q^{86} +2.53853 q^{87} +(-3.31618 - 0.992151i) q^{88} +11.4126 q^{89} +(-0.825776 + 0.599961i) q^{90} +(0.868527 + 2.67305i) q^{91} +(4.93237 - 15.1803i) q^{92} +(-3.85987 - 2.80436i) q^{93} +(-1.20401 - 0.874762i) q^{94} +(-5.57828 + 17.1682i) q^{95} +(0.938982 + 2.88989i) q^{96} +(11.3500 - 8.24625i) q^{97} +0.238918 q^{98} +(0.0777681 + 3.31571i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) $ 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$	$1$

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 $

$2$	−0.214873	+	0.156114i	−0.151938	+	0.110390i	−0.661157	−	0.750247i	$-0.729934\pi$
$2$	−0.214873	+	0.156114i	−0.151938	+	0.110390i	0.509219	+	0.860637i	$0.329934\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.596235	+	1.83502i	−0.298118	+	0.917512i
$5$	−3.10912	−	2.25891i	−1.39044	−	1.01021i	−0.995817	−	0.0913724i	$-0.970875\pi$
$5$	−3.10912	−	2.25891i	−1.39044	−	1.01021i	−0.394625	−	0.918842i	$-0.629125\pi$
$6$	−0.214873	−	0.156114i	−0.0877216	−	0.0637335i
$7$	−0.868527	+	2.67305i	−0.328273	+	1.01032i	0.641669	+	0.766982i	$0.278242\pi$
$7$	−0.868527	+	2.67305i	−0.328273	+	1.01032i	−0.969942	+	0.243337i	$0.921758\pi$
$8$	−0.322507	−	0.992575i	−0.114024	−	0.350928i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$	1.02072			0.322778
$11$	1.88601	−	2.72818i	0.568654	−	0.822577i
$11$	1.88601	−	2.72818i	0.568654	−	0.822577i
$12$	−1.92946			−0.556986
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$13$	0.809017	−	0.587785i	0.224381	−	0.163022i
$14$	−0.230679	−	0.709957i	−0.0616515	−	0.189744i
$15$	1.18758	−	3.65499i	0.306632	−	0.943715i
$16$	−2.89767	−	2.10528i	−0.724419	−	0.526321i
$17$	−2.81985	−	2.04874i	−0.683914	−	0.496892i	0.190740	−	0.981641i	$-0.438911\pi$
$17$	−2.81985	−	2.04874i	−0.683914	−	0.496892i	−0.874654	+	0.484748i	$0.838911\pi$
$18$	0.0820742	−	0.252599i	0.0193451	−	0.0595380i
$19$	−1.45151	−	4.46729i	−0.333000	−	1.02487i	−0.967699	−	0.252108i	$-0.918876\pi$
$19$	−1.45151	−	4.46729i	−0.333000	−	1.02487i	0.634699	−	0.772759i	$-0.281124\pi$
$20$	5.99892	−	4.35847i	1.34140	−	0.974583i
$21$	−2.81061			−0.613326
$22$	0.0206550	+	0.880646i	0.00440367	+	0.187754i
$23$	−8.27252			−1.72494			−0.862469	−	0.506109i	$-0.831083\pi$
$23$	−8.27252			−1.72494			−0.862469	+	0.506109i	$0.831083\pi$
$24$	0.844335	−	0.613445i	0.172349	−	0.125219i
$25$	3.01888	+	9.29116i	0.603776	+	1.85823i
$26$	−0.0820742	+	0.252599i	−0.0160961	+	0.0495386i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−4.38727	−	3.18754i	−0.829116	−	0.602388i
$29$	0.784449	−	2.41429i	0.145669	−	0.448322i	−0.851428	−	0.524472i	$-0.824263\pi$
$29$	0.784449	−	2.41429i	0.145669	−	0.448322i	0.997096	+	0.0761500i	$0.0242628\pi$
$30$	0.315418	+	0.970758i	0.0575872	+	0.177235i
$31$	−3.85987	+	2.80436i	−0.693254	+	0.503678i	−0.877728	−	0.479159i	$-0.840942\pi$
$31$	−3.85987	+	2.80436i	−0.693254	+	0.503678i	0.184474	+	0.982837i	$0.440942\pi$
$32$	3.03861			0.537155
$33$	3.17746	+	0.950650i	0.553125	+	0.165487i
$34$	0.925747			0.158764
$35$	8.73854	−	6.34892i	1.47708	−	1.07316i
$36$	−0.596235	−	1.83502i	−0.0993725	−	0.305837i
$37$	2.99563	−	9.21961i	0.492479	−	1.51569i	−0.328370	−	0.944549i	$-0.606499\pi$
$37$	2.99563	−	9.21961i	0.492479	−	1.51569i	0.820849	−	0.571145i	$-0.193501\pi$
$38$	1.00930	+	0.733299i	0.163730	+	0.118957i
$39$	0.809017	+	0.587785i	0.129546	+	0.0941210i
$40$	−1.23942	+	3.81455i	−0.195970	+	0.603134i
$41$	3.26387	+	10.0452i	0.509732	+	1.56879i	0.792668	+	0.609654i	$0.208692\pi$
$41$	3.26387	+	10.0452i	0.509732	+	1.56879i	−0.282936	+	0.959139i	$0.591308\pi$
$42$	0.603925	−	0.438777i	0.0931877	−	0.0677048i
$43$	−7.76099			−1.18354			−0.591770	−	0.806107i	$-0.701571\pi$
$43$	−7.76099			−1.18354			−0.591770	+	0.806107i	$0.701571\pi$
$44$	3.88177	+	5.08751i	0.585198	+	0.766971i
$45$	3.84309			0.572893
$46$	1.77754	−	1.29146i	0.262084	−	0.190415i
$47$	1.73153	+	5.32909i	0.252569	+	0.777328i	0.994299	+	0.106629i	$0.0340057\pi$
$47$	1.73153	+	5.32909i	0.252569	+	0.777328i	−0.741730	+	0.670699i	$0.765994\pi$
$48$	1.10681	−	3.40642i	0.159755	−	0.491675i
$49$	−0.727751	−	0.528742i	−0.103964	−	0.0755346i
$50$	−2.09916	−	1.52513i	−0.296866	−	0.215686i
$51$	1.07709	−	3.31493i	0.150822	−	0.464183i
$52$	0.596235	+	1.83502i	0.0826830	+	0.254472i
$53$	−8.20627	+	5.96221i	−1.12722	+	0.818972i	−0.985288	−	0.170905i	$-0.945331\pi$
$53$	−8.20627	+	5.96221i	−1.12722	+	0.818972i	−0.141931	+	0.989877i	$0.545331\pi$
$54$	0.265598			0.0361433
$55$	−12.0265	+	4.22191i	−1.62166	+	0.569283i
$56$	2.93331			0.391980
$57$	3.80011	−	2.76094i	0.503336	−	0.365695i
$58$	0.208348	+	0.641229i	0.0273574	+	0.0841975i
$59$	0.599939	−	1.84642i	0.0781054	−	0.240384i	−0.904379	−	0.426731i	$-0.859665\pi$
$59$	0.599939	−	1.84642i	0.0781054	−	0.240384i	0.982484	+	0.186348i	$0.0596651\pi$
$60$	5.99892	+	4.35847i	0.774457	+	0.562676i
$61$	−0.435811	−	0.316635i	−0.0557998	−	0.0405410i	0.559536	−	0.828806i	$-0.310979\pi$
$61$	−0.435811	−	0.316635i	−0.0557998	−	0.0405410i	−0.615336	+	0.788265i	$0.710979\pi$
$62$	0.391582	−	1.20516i	0.0497309	−	0.153056i
$63$	−0.868527	−	2.67305i	−0.109424	−	0.336773i
$64$	5.14243	−	3.73620i	0.642804	−	0.467025i
$65$	−3.84309			−0.476676
$66$	−0.831161	+	0.291779i	−0.102309	+	0.0359155i
$67$	0.204566			0.0249917			0.0124959	−	0.999922i	$-0.496022\pi$
$67$	0.204566			0.0249917			0.0124959	+	0.999922i	$0.496022\pi$
$68$	5.44078	−	3.95296i	0.659791	−	0.479366i
$69$	−2.55635	−	7.86763i	−0.307748	−	0.947151i
$70$	−0.886519	+	2.72842i	−0.105959	+	0.326109i
$71$	−7.34476	−	5.33628i	−0.871663	−	0.633300i	0.0593700	−	0.998236i	$-0.481091\pi$
$71$	−7.34476	−	5.33628i	−0.871663	−	0.633300i	−0.931033	+	0.364936i	$0.881091\pi$
$72$	0.844335	+	0.613445i	0.0995058	+	0.0722952i
$73$	−4.24948	+	13.0786i	−0.497364	+	1.53073i	0.315875	+	0.948801i	$0.397702\pi$
$73$	−4.24948	+	13.0786i	−0.497364	+	1.53073i	−0.813239	+	0.581929i	$0.802298\pi$
$74$	0.795634	+	2.44871i	0.0924905	+	0.284657i
$75$	−7.90354	+	5.74225i	−0.912622	+	0.663058i
$76$	9.06303			1.03960
$77$	5.65451	+	7.41091i	0.644392	+	0.844551i
$78$	−0.265598			−0.0300730
$79$	−10.2631	+	7.45655i	−1.15468	+	0.838927i	−0.989097	−	0.147268i	$-0.952952\pi$
$79$	−10.2631	+	7.45655i	−1.15468	+	0.838927i	−0.165587	+	0.986195i	$0.552952\pi$
$80$	4.25358	+	13.0912i	0.475565	+	1.46364i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−2.26952	−	1.64890i	−0.250626	−	0.182091i
$83$	−14.3350	−	10.4150i	−1.57347	−	1.14319i	−0.923735	−	0.383032i	$-0.874880\pi$
$83$	−14.3350	−	10.4150i	−1.57347	−	1.14319i	−0.649735	−	0.760161i	$-0.725120\pi$
$84$	1.67579	−	5.15754i	0.182843	−	0.562734i
$85$	4.13933	+	12.7396i	0.448974	+	1.38180i
$86$	1.66763	−	1.21160i	0.179825	−	0.130650i
$87$	2.53853			0.272159
$88$	−3.31618	−	0.992151i	−0.353505	−	0.105764i
$89$	11.4126			1.20973			0.604865	−	0.796328i	$-0.293227\pi$
$89$	11.4126			1.20973			0.604865	+	0.796328i	$0.293227\pi$
$90$	−0.825776	+	0.599961i	−0.0870444	+	0.0632415i
$91$	0.868527	+	2.67305i	0.0910464	+	0.280212i
$92$	4.93237	−	15.1803i	0.514235	−	1.58265i
$93$	−3.85987	−	2.80436i	−0.400250	−	0.290799i
$94$	−1.20401	−	0.874762i	−0.124184	−	0.0902248i
$95$	−5.57828	+	17.1682i	−0.572320	+	1.76142i
$96$	0.938982	+	2.88989i	0.0958344	+	0.294948i
$97$	11.3500	−	8.24625i	1.15242	−	0.837280i	0.163617	−	0.986524i	$-0.447684\pi$
$97$	11.3500	−	8.24625i	1.15242	−	0.837280i	0.988800	+	0.149244i	$0.0476839\pi$
$98$	0.238918			0.0241344
$99$	0.0777681	+	3.31571i	0.00781599	+	0.333242i
$100$	−18.8495			−1.88495
$101$	−2.90157	+	2.10811i	−0.288717	+	0.209765i	−0.722711	−	0.691151i	$-0.757104\pi$
$101$	−2.90157	+	2.10811i	−0.288717	+	0.209765i	0.433994	+	0.900916i	$0.357104\pi$
$102$	0.286072	+	0.880438i	0.0283253	+	0.0871764i
$103$	−0.682645	+	2.10097i	−0.0672630	+	0.207014i	−0.979039	−	0.203674i	$-0.934712\pi$
$103$	−0.682645	+	2.10097i	−0.0672630	+	0.207014i	0.911776	+	0.410689i	$0.134712\pi$
$104$	−0.844335	−	0.613445i	−0.0827938	−	0.0601533i
$105$	8.73854	+	6.34892i	0.852794	+	0.619591i
$106$	0.832521	−	2.56224i	0.0808616	−	0.248866i
$107$	−0.105358	−	0.324257i	−0.0101853	−	0.0313472i	0.945835	−	0.324649i	$-0.105246\pi$
$107$	−0.105358	−	0.324257i	−0.0101853	−	0.0313472i	−0.956020	+	0.293301i	$0.905246\pi$
$108$	1.56096	−	1.13411i	0.150204	−	0.109129i
$109$	5.20110			0.498175			0.249088	−	0.968481i	$-0.419869\pi$
$109$	5.20110			0.498175			0.249088	+	0.968481i	$0.419869\pi$
$110$	1.92508	−	2.78469i	0.183549	−	0.265510i
$111$	9.69407			0.920121
$112$	8.14424	−	5.91714i	0.769559	−	0.559117i
$113$	−1.25172	−	3.85239i	−0.117752	−	0.362402i	0.874759	−	0.484557i	$-0.161019\pi$
$113$	−1.25172	−	3.85239i	−0.117752	−	0.362402i	−0.992511	+	0.122155i	$0.961019\pi$
$114$	−0.385518	+	1.18650i	−0.0361071	+	0.111126i
$115$	25.7203	+	18.6869i	2.39843	+	1.74256i
$116$	3.96256	+	2.87897i	0.367914	+	0.267305i
$117$	−0.309017	+	0.951057i	−0.0285686	+	0.0879252i
$118$	0.159342	+	0.490405i	0.0146687	+	0.0451455i
$119$	7.92550	−	5.75821i	0.726530	−	0.527855i
$120$	−4.01086			−0.366139
$121$	−3.88592	−	10.2908i	−0.353266	−	0.935523i
$122$	0.143075			0.0129534
$123$	−8.54493	+	6.20826i	−0.770471	+	0.559780i
$124$	−2.84468	−	8.75502i	−0.255460	−	0.786224i
$125$	5.66393	−	17.4318i	0.506597	−	1.55915i
$126$	0.603925	+	0.438777i	0.0538019	+	0.0390894i
$127$	2.54058	+	1.84584i	0.225440	+	0.163792i	0.694772	−	0.719230i	$-0.255505\pi$
$127$	2.54058	+	1.84584i	0.225440	+	0.163792i	−0.469332	+	0.883022i	$0.655505\pi$
$128$	−2.39966	+	7.38539i	−0.212102	+	0.652783i
$129$	−2.39828	−	7.38114i	−0.211156	−	0.649873i
$130$	0.825776	−	0.599961i	0.0724253	−	0.0526201i
$131$	7.87005			0.687609			0.343805	−	0.939041i	$-0.388284\pi$
$131$	7.87005			0.687609			0.343805	+	0.939041i	$0.388284\pi$
$132$	−3.63898	+	5.26391i	−0.316733	+	0.458164i
$133$	13.2020			1.14476
$134$	−0.0439558	+	0.0319357i	−0.00379720	+	0.00275883i
$135$	1.18758	+	3.65499i	0.102211	+	0.314572i
$136$	−1.12411	+	3.45964i	−0.0963913	+	0.296662i
$137$	−1.03272	−	0.750316i	−0.0882314	−	0.0641039i	0.542795	−	0.839865i	$-0.317366\pi$
$137$	−1.03272	−	0.750316i	−0.0882314	−	0.0641039i	−0.631026	+	0.775761i	$0.717366\pi$
$138$	1.77754	+	1.29146i	0.151314	+	0.109936i
$139$	−5.28458	+	16.2642i	−0.448232	+	1.37952i	0.430669	+	0.902510i	$0.358278\pi$
$139$	−5.28458	+	16.2642i	−0.448232	+	1.37952i	−0.878900	+	0.477005i	$0.841722\pi$
$140$	6.44019	+	19.8209i	0.544296	+	1.67517i
$141$	−4.53320	+	3.29356i	−0.381764	+	0.277368i
$142$	2.41126			0.202349
$143$	−0.0777681	−	3.31571i	−0.00650330	−	0.277274i
$144$	3.58172			0.298477
$145$	−7.89260	+	5.73431i	−0.655445	+	0.476209i
$146$	−1.12865	−	3.47364i	−0.0934080	−	0.287480i
$147$	0.277976	−	0.855522i	0.0229271	−	0.0705623i
$148$	15.1321	+	10.9941i	1.24385	+	0.903711i
$149$	−14.2510	−	10.3539i	−1.16748	−	0.848227i	−0.176779	−	0.984251i	$-0.556568\pi$
$149$	−14.2510	−	10.3539i	−1.16748	−	0.848227i	−0.990706	+	0.136023i	$0.956568\pi$
$150$	0.801808	−	2.46771i	0.0654674	−	0.201488i
$151$	−5.55441	−	17.0947i	−0.452011	−	1.39115i	−0.874608	−	0.484830i	$-0.838882\pi$
$151$	−5.55441	−	17.0947i	−0.452011	−	1.39115i	0.422597	−	0.906318i	$-0.361118\pi$
$152$	−3.96600	+	2.88147i	−0.321685	+	0.233718i
$153$	3.48552			0.281788
$154$	−2.37195	−	0.709653i	−0.191137	−	0.0571855i
$155$	18.3356			1.47275
$156$	−1.56096	+	1.13411i	−0.124977	+	0.0908012i
$157$	5.13065	+	15.7905i	0.409470	+	1.26022i	0.917104	+	0.398647i	$0.130520\pi$
$157$	5.13065	+	15.7905i	0.409470	+	1.26022i	−0.507634	+	0.861573i	$0.669480\pi$
$158$	1.04118	−	3.20442i	0.0828318	−	0.254930i
$159$	−8.20627	−	5.96221i	−0.650800	−	0.472834i
$160$	−9.44740	−	6.86394i	−0.746883	−	0.542642i
$161$	7.18491	−	22.1129i	0.566250	−	1.74274i
$162$	0.0820742	+	0.252599i	0.00644836	+	0.0198460i
$163$	2.54292	−	1.84754i	0.199177	−	0.144710i	−0.483726	−	0.875219i	$-0.660717\pi$
$163$	2.54292	−	1.84754i	0.199177	−	0.144710i	0.682903	+	0.730509i	$0.260717\pi$
$164$	−20.3792			−1.59135
$165$	−7.73168	−	10.1333i	−0.601911	−	0.788875i
$166$	4.70613			0.365267
$167$	−5.81403	+	4.22414i	−0.449903	+	0.326874i	−0.789557	−	0.613677i	$-0.789690\pi$
$167$	−5.81403	+	4.22414i	−0.449903	+	0.326874i	0.339655	+	0.940550i	$0.389690\pi$
$168$	0.906443	+	2.78975i	0.0699336	+	0.215234i
$169$	0.309017	−	0.951057i	0.0237705	−	0.0731582i
$170$	−2.87826	−	2.09118i	−0.220753	−	0.160386i
$171$	3.80011	+	2.76094i	0.290601	+	0.211134i
$172$	4.62737	−	14.2416i	0.352834	−	1.08591i
$173$	2.32188	+	7.14601i	0.176529	+	0.543301i	0.999700	−	0.0244929i	$-0.00779710\pi$
$173$	2.32188	+	7.14601i	0.176529	+	0.543301i	−0.823171	+	0.567794i	$0.807797\pi$
$174$	−0.545462	+	0.396302i	−0.0413514	+	0.0300435i
$175$	−27.4577			−2.07561
$176$	−11.2086	+	3.93479i	−0.844883	+	0.296596i
$177$	1.94144			0.145928
$178$	−2.45225	+	1.78167i	−0.183804	+	0.133542i
$179$	−1.68480	−	5.18529i	−0.125928	−	0.387567i	0.868141	−	0.496318i	$-0.165315\pi$
$179$	−1.68480	−	5.18529i	−0.125928	−	0.387567i	−0.994069	+	0.108751i	$0.965315\pi$
$180$	−2.29138	+	7.05215i	−0.170790	+	0.525636i
$181$	−0.662557	−	0.481376i	−0.0492474	−	0.0357804i	0.562889	−	0.826532i	$-0.309690\pi$
$181$	−0.662557	−	0.481376i	−0.0492474	−	0.0357804i	−0.612137	+	0.790752i	$0.709690\pi$
$182$	−0.603925	−	0.438777i	−0.0447659	−	0.0325243i
$183$	0.166465	−	0.512326i	0.0123054	−	0.0378722i
$184$	2.66795	+	8.21109i	0.196684	+	0.605330i
$185$	−30.1400	+	21.8980i	−2.21594	+	1.60997i
$186$	1.26718			0.0929145
$187$	−10.9076	+	3.82910i	−0.797642	+	0.280012i
$188$	−10.8114			−0.788503
$189$	2.27383	−	1.65204i	0.165397	−	0.120168i
$190$	−1.48158	−	4.55983i	−0.107485	−	0.330805i
$191$	1.45406	−	4.47514i	0.105212	−	0.323810i	−0.884568	−	0.466411i	$-0.845547\pi$
$191$	1.45406	−	4.47514i	0.105212	−	0.323810i	0.989780	+	0.142601i	$0.0455467\pi$
$192$	5.14243	+	3.73620i	0.371123	+	0.269637i
$193$	−7.36741	−	5.35274i	−0.530318	−	0.385299i	0.290159	−	0.956979i	$-0.406292\pi$
$193$	−7.36741	−	5.35274i	−0.530318	−	0.385299i	−0.820477	+	0.571680i	$0.806292\pi$
$194$	−1.15145	+	3.54380i	−0.0826693	+	0.254430i
$195$	−1.18758	−	3.65499i	−0.0850443	−	0.261739i
$196$	1.40416	−	1.02019i	0.100297	−	0.0728704i
$197$	−11.0104			−0.784457			−0.392228	−	0.919868i	$-0.628296\pi$
$197$	−11.0104			−0.784457			−0.392228	+	0.919868i	$0.628296\pi$
$198$	−0.534341	−	0.700317i	−0.0379740	−	0.0497694i
$199$	13.6457			0.967321			0.483660	−	0.875256i	$-0.339307\pi$
$199$	13.6457			0.967321			0.483660	+	0.875256i	$0.339307\pi$
$200$	8.24857	−	5.99293i	0.583262	−	0.423764i
$201$	0.0632144	+	0.194554i	0.00445880	+	0.0137228i
$202$	0.294362	−	0.905954i	0.0207113	−	0.0637427i
$203$	5.77220	+	4.19375i	0.405129	+	0.294343i
$204$	5.44078	+	3.95296i	0.380931	+	0.276762i
$205$	12.5433	−	38.6045i	0.876066	−	2.69625i
$206$	−0.181309	−	0.558012i	−0.0126324	−	0.0388785i
$207$	6.69261	−	4.86246i	0.465168	−	0.337965i
$208$	−3.58172			−0.248348
$209$	−14.9251	−	4.46538i	−1.03239	−	0.308877i
$210$	−2.86884			−0.197968
$211$	0.341530	−	0.248136i	0.0235119	−	0.0170824i	−0.575967	−	0.817473i	$-0.695374\pi$
$211$	0.341530	−	0.248136i	0.0235119	−	0.0170824i	0.599479	+	0.800390i	$0.295374\pi$
$212$	−6.04792	−	18.6136i	−0.415373	−	1.27839i
$213$	2.80545	−	8.63428i	0.192226	−	0.591611i
$214$	0.0732598	+	0.0532264i	0.00500794	+	0.00363848i
$215$	24.1299	+	17.5314i	1.64564	+	1.19563i
$216$	−0.322507	+	0.992575i	−0.0219438	+	0.0675362i
$217$	−4.14380	−	12.7533i	−0.281300	−	0.865751i
$218$	−1.11758	+	0.811967i	−0.0756919	+	0.0549933i
$219$	−13.7516			−0.929248
$220$	−0.576656	−	24.5862i	−0.0388782	−	1.65760i
$221$	−3.48552			−0.234462
$222$	−2.08300	+	1.51338i	−0.139802	+	0.101572i
$223$	−5.62272	−	17.3050i	−0.376525	−	1.15883i	−0.942444	−	0.334365i	$-0.891478\pi$
$223$	−5.62272	−	17.3050i	−0.376525	−	1.15883i	0.565918	−	0.824461i	$-0.308522\pi$
$224$	−2.63911	+	8.12236i	−0.176333	+	0.542698i
$225$	−7.90354	−	5.74225i	−0.526902	−	0.382817i
$226$	0.870373	+	0.632363i	0.0578964	+	0.0420642i
$227$	−0.0987250	+	0.303844i	−0.00655261	+	0.0201669i	−0.954279	−	0.298916i	$-0.903375\pi$
$227$	−0.0987250	+	0.303844i	−0.00655261	+	0.0201669i	0.947727	+	0.319083i	$0.103375\pi$
$228$	2.80063	+	8.61945i	0.185476	+	0.570837i
$229$	10.2210	−	7.42602i	0.675426	−	0.490725i	−0.196411	−	0.980522i	$-0.562929\pi$
$229$	10.2210	−	7.42602i	0.675426	−	0.490725i	0.871837	+	0.489796i	$0.162929\pi$
$230$	−8.44388			−0.556773
$231$	−5.30085	+	7.66786i	−0.348770	+	0.504508i
$232$	−2.64935			−0.173938
$233$	3.30804	−	2.40343i	0.216717	−	0.157454i	−0.474131	−	0.880454i	$-0.657238\pi$
$233$	3.30804	−	2.40343i	0.216717	−	0.157454i	0.690847	+	0.723001i	$0.257238\pi$
$234$	−0.0820742	−	0.252599i	−0.00536536	−	0.0165129i
$235$	6.65440	−	20.4802i	0.434085	−	1.33598i
$236$	3.03052	+	2.20180i	0.197270	+	0.143325i
$237$	−10.2631	−	7.45655i	−0.666657	−	0.484355i
$238$	−0.804037	+	2.47457i	−0.0521180	+	0.160403i
$239$	3.44172	+	10.5925i	0.222627	+	0.685174i	0.998524	+	0.0543148i	$0.0172975\pi$
$239$	3.44172	+	10.5925i	0.222627	+	0.685174i	−0.775897	+	0.630859i	$0.782703\pi$
$240$	−11.1360	+	8.09079i	−0.718827	+	0.522258i
$241$	5.25579			0.338555			0.169277	−	0.985568i	$-0.445857\pi$
$241$	5.25579			0.338555			0.169277	+	0.985568i	$0.445857\pi$
$242$	2.44152	+	1.60456i	0.156947	+	0.103145i
$243$	1.00000			0.0641500
$244$	0.840878	−	0.610934i	0.0538317	−	0.0391110i
$245$	1.06829	+	3.28785i	0.0682503	+	0.210053i
$246$	0.866878	−	2.66798i	0.0552701	−	0.170104i
$247$	−3.80011	−	2.76094i	−0.241795	−	0.175674i
$248$	4.02838	+	2.92679i	0.255802	+	0.185851i
$249$	5.47548	−	16.8518i	0.346994	−	1.06794i
$250$	1.50433	+	4.62984i	0.0951420	+	0.292817i
$251$	11.2852	−	8.19916i	0.712314	−	0.517526i	−0.171606	−	0.985166i	$-0.554895\pi$
$251$	11.2852	−	8.19916i	0.712314	−	0.517526i	0.883919	+	0.467640i	$0.154895\pi$
$252$	5.42296			0.341614
$253$	−15.6021	+	22.5689i	−0.980893	+	1.41889i
$254$	−0.834066			−0.0523339
$255$	−10.8369	+	7.87348i	−0.678634	+	0.493056i
$256$	3.29113	+	10.1290i	0.205695	+	0.633065i
$257$	2.30795	−	7.10315i	0.143966	−	0.443082i	−0.852910	−	0.522057i	$-0.825165\pi$
$257$	2.30795	−	7.10315i	0.143966	−	0.443082i	0.996877	+	0.0789749i	$0.0251647\pi$
$258$	1.66763	+	1.21160i	0.103822	+	0.0754311i
$259$	22.0427	+	16.0150i	1.36967	+	0.995122i
$260$	2.29138	−	7.05215i	0.142106	−	0.437356i
$261$	0.784449	+	2.41429i	0.0485562	+	0.149441i
$262$	−1.69106	+	1.22863i	−0.104474	+	0.0759049i
$263$	13.2782			0.818771			0.409386	−	0.912361i	$-0.365743\pi$
$263$	13.2782			0.818771			0.409386	+	0.912361i	$0.365743\pi$
$264$	−0.0811631	−	3.46046i	−0.00499525	−	0.212977i
$265$	38.9824			2.39467
$266$	−2.83675	+	2.06102i	−0.173932	+	0.126369i
$267$	3.52668	+	10.8540i	0.215829	+	0.664254i
$268$	−0.121970	+	0.375384i	−0.00745048	+	0.0229302i
$269$	−7.06500	−	5.13303i	−0.430761	−	0.312966i	0.351192	−	0.936303i	$-0.385776\pi$
$269$	−7.06500	−	5.13303i	−0.430761	−	0.312966i	−0.781953	+	0.623337i	$0.785776\pi$
$270$	−0.825776	−	0.599961i	−0.0502551	−	0.0365125i
$271$	3.14789	−	9.68819i	0.191220	−	0.588516i	−0.808780	−	0.588112i	$-0.799871\pi$
$271$	3.14789	−	9.68819i	0.191220	−	0.588516i	1.00000		0.000403919i	$-0.000128571\pi$
$272$	3.85782	+	11.8732i	0.233915	+	0.719916i
$273$	−2.27383	+	1.65204i	−0.137619	+	0.0999858i
$274$	0.339039			0.0204821
$275$	31.0416	+	9.28719i	1.87188	+	0.560039i
$276$	15.9615			0.960768
$277$	−6.10474	+	4.43535i	−0.366798	+	0.266494i	−0.755882	−	0.654708i	$-0.772792\pi$
$277$	−6.10474	+	4.43535i	−0.366798	+	0.266494i	0.389084	+	0.921202i	$0.372792\pi$
$278$	−1.40357	−	4.31975i	−0.0841806	−	0.259081i
$279$	1.47434	−	4.53755i	0.0882665	−	0.271656i
$280$	−9.12002	−	6.62608i	−0.545026	−	0.395984i
$281$	−3.08707	−	2.24289i	−0.184159	−	0.133799i	0.491886	−	0.870660i	$-0.336308\pi$
$281$	−3.08707	−	2.24289i	−0.184159	−	0.133799i	−0.676045	+	0.736860i	$0.736308\pi$
$282$	0.459890	−	1.41539i	0.0273860	−	0.0842855i
$283$	−4.31466	−	13.2792i	−0.256480	−	0.789364i	−0.993534	−	0.113531i	$-0.963784\pi$
$283$	−4.31466	−	13.2792i	−0.256480	−	0.789364i	0.737054	−	0.675833i	$-0.236216\pi$
$284$	14.1714	−	10.2961i	0.840918	−	0.610963i
$285$	−18.0517			−1.06929
$286$	0.534341	+	0.700317i	0.0315962	+	0.0414106i
$287$	−29.6860			−1.75231
$288$	−2.45829	+	1.78605i	−0.144856	+	0.105244i
$289$	−1.49908	−	4.61370i	−0.0881812	−	0.271394i
$290$	0.800699	−	2.46430i	0.0470187	−	0.144709i
$291$	11.3500	+	8.24625i	0.665349	+	0.483404i
$292$	−21.4658	−	15.5958i	−1.25619	−	0.912675i
$293$	−6.18038	+	19.0213i	−0.361062	+	1.11123i	0.591349	+	0.806416i	$0.298596\pi$
$293$	−6.18038	+	19.0213i	−0.361062	+	1.11123i	−0.952411	+	0.304818i	$0.901404\pi$
$294$	0.0738298	+	0.227225i	0.00430584	+	0.0132520i
$295$	−6.03618	+	4.38554i	−0.351440	+	0.255336i
$296$	−10.1173			−0.588054
$297$	−3.12940	+	1.09857i	−0.181586	+	0.0637457i
$298$	4.67855			0.271021
$299$	−6.69261	+	4.86246i	−0.387043	+	0.281203i
$300$	−5.82480	−	17.9269i	−0.336295	−	1.03501i
$301$	6.74063	−	20.7455i	0.388523	−	1.19575i
$302$	3.86222	+	2.80607i	0.222246	+	0.161471i
$303$	−2.90157	−	2.10811i	−0.166691	−	0.121108i
$304$	−5.19891	+	16.0006i	−0.298178	+	0.917698i
$305$	0.639739	+	1.96891i	0.0366313	+	0.112740i
$306$	−0.748945	+	0.544141i	−0.0428144	+	0.0311064i
$307$	8.22729			0.469556			0.234778	−	0.972049i	$-0.424564\pi$
$307$	8.22729			0.469556			0.234778	+	0.972049i	$0.424564\pi$
$308$	−16.9706	+	5.95752i	−0.966990	+	0.339461i
$309$	−2.20909			−0.125671
$310$	−3.93983	+	2.86245i	−0.223767	+	0.162577i
$311$	5.08114	+	15.6381i	0.288125	+	0.886758i	0.985445	+	0.169997i	$0.0543759\pi$
$311$	5.08114	+	15.6381i	0.288125	+	0.886758i	−0.697319	+	0.716761i	$0.745624\pi$
$312$	0.322507	−	0.992575i	0.0182584	−	0.0561935i
$313$	7.06017	+	5.12951i	0.399064	+	0.289937i	0.769160	−	0.639057i	$-0.220675\pi$
$313$	7.06017	+	5.12951i	0.399064	+	0.289937i	−0.370096	+	0.928994i	$0.620675\pi$
$314$	−3.56756	−	2.59199i	−0.201329	−	0.146274i
$315$	−3.33783	+	10.2728i	−0.188065	+	0.578805i
$316$	−7.56374	−	23.2788i	−0.425494	−	1.30953i
$317$	−1.24086	+	0.901535i	−0.0696935	+	0.0506353i	−0.622086	−	0.782949i	$-0.713715\pi$
$317$	−1.24086	+	0.901535i	−0.0696935	+	0.0506353i	0.552393	+	0.833584i	$0.313715\pi$
$318$	2.69409			0.151077
$319$	−5.10713	−	6.69349i	−0.285944	−	0.374764i
$320$	−24.4282			−1.36558
$321$	0.275830	−	0.200402i	0.0153953	−	0.0111854i
$322$	1.90830	+	5.87313i	0.106345	+	0.327297i
$323$	−5.05928	+	15.5709i	−0.281506	+	0.866386i
$324$	1.56096	+	1.13411i	0.0867202	+	0.0630059i
$325$	7.90354	+	5.74225i	0.438409	+	0.318523i
$326$	−0.257978	+	0.793973i	−0.0142881	+	0.0439741i
$327$	1.60723	+	4.94654i	0.0888799	+	0.273544i
$328$	8.91797	−	6.47928i	0.492412	−	0.357759i
$329$	−15.7488			−0.868260
$330$	3.24328	+	0.970342i	0.178537	+	0.0534156i
$331$	10.8784			0.597929			0.298965	−	0.954264i	$-0.403359\pi$
$331$	10.8784			0.597929			0.298965	+	0.954264i	$0.403359\pi$
$332$	27.6588	−	20.0953i	1.51797	−	1.10287i
$333$	2.99563	+	9.21961i	0.164160	+	0.505232i
$334$	0.589829	−	1.81531i	0.0322740	−	0.0993292i
$335$	−0.636021	−	0.462096i	−0.0347496	−	0.0252470i
$336$	8.14424	+	5.91714i	0.444305	+	0.322806i
$337$	−0.834084	+	2.56705i	−0.0454354	+	0.139836i	−0.971201	−	0.238263i	$-0.923422\pi$
$337$	−0.834084	+	2.56705i	−0.0454354	+	0.139836i	0.925765	+	0.378099i	$0.123422\pi$
$338$	0.0820742	+	0.252599i	0.00446425	+	0.0137395i
$339$	3.27704	−	2.38091i	0.177984	−	0.129313i
$340$	−25.8454			−1.40166
$341$	0.371037	+	15.8195i	0.0200928	+	0.856673i
$342$	−1.24756			−0.0674605
$343$	−13.8714	+	10.0782i	−0.748986	+	0.544170i
$344$	2.50297	+	7.70336i	0.134951	+	0.415337i
$345$	−9.82426	+	30.2360i	−0.528921	+	1.62785i
$346$	−1.61450	−	1.17301i	−0.0867963	−	0.0630612i
$347$	−1.82509	−	1.32601i	−0.0979760	−	0.0711837i	0.537719	−	0.843124i	$-0.319286\pi$
$347$	−1.82509	−	1.32601i	−0.0979760	−	0.0711837i	−0.635695	+	0.771941i	$0.719286\pi$
$348$	−1.51356	+	4.65827i	−0.0811354	+	0.249709i
$349$	−1.75140	−	5.39027i	−0.0937506	−	0.288535i	0.893175	−	0.449708i	$-0.148472\pi$
$349$	−1.75140	−	5.39027i	−0.0937506	−	0.288535i	−0.986926	+	0.161174i	$0.948472\pi$
$350$	5.89993	−	4.28655i	0.315365	−	0.229126i
$351$	−1.00000			−0.0533761
$352$	5.73085	−	8.28987i	0.305455	−	0.441851i
$353$	−3.40470			−0.181214			−0.0906070	−	0.995887i	$-0.528881\pi$
$353$	−3.40470			−0.181214			−0.0906070	+	0.995887i	$0.528881\pi$
$354$	−0.417164	+	0.303087i	−0.0221720	+	0.0161089i
$355$	10.7816	+	33.1823i	0.572227	+	1.76113i
$356$	−6.80458	+	20.9423i	−0.360642	+	1.10994i
$357$	7.92550	+	5.75821i	0.419462	+	0.304757i
$358$	1.17152	+	0.851157i	0.0619166	+	0.0449851i
$359$	−4.76842	+	14.6757i	−0.251668	+	0.774554i	0.742800	+	0.669513i	$0.233497\pi$
$359$	−4.76842	+	14.6757i	−0.251668	+	0.774554i	−0.994468	+	0.105041i	$0.966503\pi$
$360$	−1.23942	−	3.81455i	−0.0653233	−	0.201045i
$361$	−2.47850	+	1.80073i	−0.130447	+	0.0947755i
$362$	0.217515			0.0114324
$363$	8.58627	−	6.87575i	0.450662	−	0.360883i
$364$	−5.42296			−0.284240
$365$	42.7554	−	31.0636i	2.23792	−	1.62595i
$366$	0.0442127	+	0.136073i	0.00231104	+	0.00711264i
$367$	−10.7816	+	33.1824i	−0.562796	+	1.73211i	0.111616	+	0.993751i	$0.464397\pi$
$367$	−10.7816	+	33.1824i	−0.562796	+	1.73211i	−0.674411	+	0.738356i	$0.735603\pi$
$368$	23.9711	+	17.4160i	1.24958	+	0.907872i
$369$	−8.54493	−	6.20826i	−0.444832	−	0.323189i
$370$	3.05769	−	9.41060i	0.158962	−	0.489234i
$371$	−8.80992	−	27.1141i	−0.457388	−	1.40770i
$372$	7.44746	−	5.41090i	0.386133	−	0.280542i
$373$	−36.4447			−1.88703			−0.943517	−	0.331325i	$-0.892504\pi$
$373$	−36.4447			−1.88703			−0.943517	+	0.331325i	$0.892504\pi$
$374$	1.74597	−	2.52560i	0.0902820	−	0.130596i
$375$	18.3289			0.946498
$376$	4.73109	−	3.43734i	0.243987	−	0.177267i
$377$	−0.784449	−	2.41429i	−0.0404012	−	0.124342i
$378$	−0.230679	+	0.709957i	−0.0118648	+	0.0365162i
$379$	7.43935	+	5.40500i	0.382134	+	0.277636i	0.762224	−	0.647313i	$-0.224107\pi$
$379$	7.43935	+	5.40500i	0.382134	+	0.277636i	−0.380091	+	0.924949i	$0.624107\pi$
$380$	−28.1781	−	20.4726i	−1.44550	−	1.05022i
$381$	−0.970416	+	2.98663i	−0.0497159	+	0.153010i
$382$	0.386196	+	1.18859i	0.0197595	+	0.0608135i
$383$	−9.60925	+	6.98153i	−0.491010	+	0.356739i	−0.805572	−	0.592497i	$-0.798142\pi$
$383$	−9.60925	+	6.98153i	−0.491010	+	0.356739i	0.314563	+	0.949237i	$0.398142\pi$
$384$	−7.76546			−0.396280
$385$	−0.840007	−	35.8144i	−0.0428107	−	1.82527i
$386$	2.41870			0.123109
$387$	6.27877	−	4.56179i	0.319168	−	0.231889i
$388$	8.36480	+	25.7442i	0.424659	+	1.30696i
$389$	9.86654	−	30.3661i	0.500254	−	1.53962i	−0.308353	−	0.951272i	$-0.599778\pi$
$389$	9.86654	−	30.3661i	0.500254	−	1.53962i	0.808606	−	0.588350i	$-0.200222\pi$
$390$	0.825776	+	0.599961i	0.0418148	+	0.0303802i
$391$	23.3272	+	16.9482i	1.17971	+	0.857109i
$392$	−0.290111	+	0.892871i	−0.0146528	+	0.0450968i
$393$	2.43198	+	7.48486i	0.122677	+	0.377561i
$394$	2.36583	−	1.71888i	0.119189	−	0.0865959i
$395$	48.7527			2.45302
$396$	−6.13078	−	1.83424i	−0.308083	−	0.0921740i
$397$	35.3779			1.77557			0.887784	−	0.460261i	$-0.152244\pi$
$397$	35.3779			1.77557			0.887784	+	0.460261i	$0.152244\pi$
$398$	−2.93210	+	2.13030i	−0.146973	+	0.106782i
$399$	4.07964	+	12.5558i	0.204237	+	0.628578i
$400$	10.8128	−	33.2784i	0.540640	−	1.66392i
$401$	10.9570	+	7.96071i	0.547166	+	0.397539i	0.826739	−	0.562585i	$-0.190193\pi$
$401$	10.9570	+	7.96071i	0.547166	+	0.397539i	−0.279574	+	0.960124i	$0.590193\pi$
$402$	−0.0439558	−	0.0319357i	−0.00219232	−	0.00159281i
$403$	−1.47434	+	4.53755i	−0.0734421	+	0.226032i
$404$	−2.13842	−	6.58138i	−0.106390	−	0.327436i
$405$	−3.10912	+	2.25891i	−0.154493	+	0.112246i
$406$	−1.89500			−0.0940471
$407$	−19.5030	−	25.5609i	−0.966725	−	1.26701i
$408$	−3.63769			−0.180092
$409$	13.5346	−	9.83344i	0.669242	−	0.486233i	−0.200530	−	0.979688i	$-0.564266\pi$
$409$	13.5346	−	9.83344i	0.669242	−	0.486233i	0.869771	+	0.493455i	$0.164266\pi$
$410$	3.33149	+	10.2533i	0.164530	+	0.506372i
$411$	0.394465	−	1.21404i	0.0194575	−	0.0598841i
$412$	−3.44830	−	2.50534i	−0.169886	−	0.123429i
$413$	4.41452	+	3.20733i	0.217224	+	0.157823i
$414$	−0.678960	+	2.08963i	−0.0333691	+	0.102699i
$415$	21.0427	+	64.7629i	1.03295	+	3.17909i
$416$	2.45829	−	1.78605i	0.120527	−	0.0875683i
$417$	−17.1012			−0.837452
$418$	3.90412	−	1.37054i	0.190957	−	0.0670353i
$419$	8.99455			0.439412			0.219706	−	0.975566i	$-0.429490\pi$
$419$	8.99455			0.439412			0.219706	+	0.975566i	$0.429490\pi$
$420$	−16.8606	+	12.2500i	−0.822715	+	0.597738i
$421$	−5.57189	−	17.1485i	−0.271557	−	0.835768i	−0.990110	−	0.140295i	$-0.955195\pi$
$421$	−5.57189	−	17.1485i	−0.271557	−	0.835768i	0.718552	−	0.695473i	$-0.244805\pi$
$422$	−0.0346480	+	0.106636i	−0.00168664	+	0.00519094i
$423$	−4.53320	−	3.29356i	−0.220411	−	0.160138i
$424$	8.56452	+	6.22249i	0.415930	+	0.302191i
$425$	10.5224	−	32.3846i	0.510411	−	1.57088i
$426$	0.745121	+	2.29325i	0.0361012	+	0.111108i
$427$	1.22490	−	0.889939i	0.0592769	−	0.0430672i
$428$	0.657838			0.0317978
$429$	3.12940	−	1.09857i	0.151089	−	0.0530396i
$430$	−7.92176			−0.382021
$431$	−3.98384	+	2.89443i	−0.191895	+	0.139420i	−0.679584	−	0.733597i	$-0.737840\pi$
$431$	−3.98384	+	2.89443i	−0.191895	+	0.139420i	0.487690	+	0.873017i	$0.337840\pi$
$432$	1.10681	+	3.40642i	0.0532516	+	0.163892i
$433$	0.660909	−	2.03407i	0.0317612	−	0.0977511i	−0.933919	−	0.357484i	$-0.883635\pi$
$433$	0.660909	−	2.03407i	0.0317612	−	0.0977511i	0.965680	+	0.259733i	$0.0836346\pi$
$434$	2.88137	+	2.09344i	0.138310	+	0.100488i
$435$	−7.89260	−	5.73431i	−0.378421	−	0.274939i
$436$	−3.10108	+	9.54414i	−0.148515	+	0.457081i
$437$	12.0077	+	36.9558i	0.574404	+	1.76783i
$438$	2.95485	−	2.14683i	0.141188	−	0.102579i
$439$	2.88763			0.137819			0.0689095	−	0.997623i	$-0.478048\pi$
$439$	2.88763			0.137819			0.0689095	+	0.997623i	$0.478048\pi$
$440$	8.06921	+	10.5757i	0.384685	+	0.504175i
$441$	0.899550			0.0428357
$442$	0.748945	−	0.544141i	0.0356237	−	0.0258821i
$443$	5.37352	+	16.5380i	0.255304	+	0.785744i	0.993770	+	0.111453i	$0.0355505\pi$
$443$	5.37352	+	16.5380i	0.255304	+	0.785744i	−0.738466	+	0.674291i	$0.764450\pi$
$444$	−5.77995	+	17.7888i	−0.274304	+	0.844221i
$445$	−35.4831	−	25.7800i	−1.68206	−	1.22209i
$446$	3.90973	+	2.84058i	0.185131	+	0.134506i
$447$	5.44338	−	16.7530i	0.257463	−	0.792390i
$448$	5.52071	+	16.9910i	0.260829	+	0.802749i
$449$	2.90891	−	2.11345i	0.137280	−	0.0997398i	−0.517026	−	0.855970i	$-0.672961\pi$
$449$	2.90891	−	2.11345i	0.137280	−	0.0997398i	0.654306	+	0.756230i	$0.272961\pi$
$450$	2.59471			0.122316
$451$	33.5607	+	10.0409i	1.58031	+	0.472806i
$452$	7.81554			0.367612
$453$	14.5416	−	10.5651i	0.683225	−	0.496392i
$454$	−0.0262211	−	0.0807004i	−0.00123062	−	0.00378746i
$455$	3.33783	−	10.2728i	0.156480	−	0.481595i
$456$	−3.96600	−	2.88147i	−0.185725	−	0.134937i
$457$	1.38475	+	1.00608i	0.0647757	+	0.0470623i	0.619702	−	0.784837i	$-0.287254\pi$
$457$	1.38475	+	1.00608i	0.0647757	+	0.0470623i	−0.554926	+	0.831900i	$0.687254\pi$
$458$	−1.03692	+	3.19131i	−0.0484520	+	0.149120i
$459$	1.07709	+	3.31493i	0.0502741	+	0.154728i
$460$	−49.6262	+	36.0555i	−2.31383	+	1.68110i
$461$	−4.83005			−0.224958			−0.112479	−	0.993654i	$-0.535879\pi$
$461$	−4.83005			−0.224958			−0.112479	+	0.993654i	$0.535879\pi$
$462$	−0.0580534	−	2.47516i	−0.00270089	−	0.115155i
$463$	−37.5619			−1.74565			−0.872825	−	0.488033i	$-0.837715\pi$
$463$	−37.5619			−1.74565			−0.872825	+	0.488033i	$0.837715\pi$
$464$	−7.35584	+	5.34433i	−0.341486	+	0.248104i
$465$	5.66602	+	17.4382i	0.262755	+	0.808677i
$466$	−0.335598	+	1.03287i	−0.0155463	+	0.0478466i
$467$	−21.4771	−	15.6040i	−0.993839	−	0.722067i	−0.0330809	−	0.999453i	$-0.510532\pi$
$467$	−21.4771	−	15.6040i	−0.993839	−	0.722067i	−0.960759	+	0.277386i	$0.910532\pi$
$468$	−1.56096	−	1.13411i	−0.0721556	−	0.0524241i
$469$	−0.177671	+	0.546816i	−0.00820410	+	0.0252496i
$470$	1.76740	+	5.43948i	0.0815239	+	0.250905i
$471$	−13.4322	+	9.75907i	−0.618923	+	0.449674i
$472$	−2.02620			−0.0932632
$473$	−14.6373	+	21.1734i	−0.673024	+	0.973552i
$474$	3.36933			0.154758
$475$	37.1244	−	26.9725i	1.70338	−	1.23758i
$476$	5.84099	+	17.9767i	0.267722	+	0.823962i
$477$	3.13452	−	9.64705i	0.143520	−	0.441708i
$478$	−2.39318	−	1.73875i	−0.109462	−	0.0795285i
$479$	−31.5421	−	22.9167i	−1.44120	−	1.04709i	−0.987791	−	0.155785i	$-0.950209\pi$
$479$	−31.5421	−	22.9167i	−1.44120	−	1.04709i	−0.453404	−	0.891305i	$-0.649791\pi$
$480$	3.60859	−	11.1061i	0.164709	−	0.506921i
$481$	−2.99563	−	9.21961i	−0.136589	−	0.420378i
$482$	−1.12933	+	0.820504i	−0.0514394	+	0.0373729i
$483$	23.2508			1.05795
$484$	21.2007	−	0.995048i	0.963668	−	0.0452294i
$485$	−53.9161			−2.44820
$486$	−0.214873	+	0.156114i	−0.00974684	+	0.00708150i
$487$	0.231035	+	0.711053i	0.0104692	+	0.0322209i	0.956155	−	0.292862i	$-0.0946077\pi$
$487$	0.231035	+	0.711053i	0.0104692	+	0.0322209i	−0.945685	+	0.325083i	$0.894608\pi$
$488$	−0.173732	+	0.534692i	−0.00786448	+	0.0242044i
$489$	2.54292	+	1.84754i	0.114995	+	0.0835486i
$490$	−0.742826	−	0.539695i	−0.0335575	−	0.0243809i
$491$	−11.3587	+	34.9586i	−0.512612	+	1.57766i	0.274973	+	0.961452i	$0.411331\pi$
$491$	−11.3587	+	34.9586i	−0.512612	+	1.57766i	−0.787585	+	0.616206i	$0.788669\pi$
$492$	−6.29751	−	19.3817i	−0.283914	−	0.873796i
$493$	−7.15827	+	5.20079i	−0.322392	+	0.234232i
$494$	1.24756			0.0561305
$495$	7.24810	−	10.4846i	0.325778	−	0.471249i
$496$	17.0886			0.767302
$497$	20.6433	−	14.9982i	0.925978	−	0.672762i
$498$	1.45428	+	4.47580i	0.0651676	+	0.200565i
$499$	−2.87484	+	8.84785i	−0.128696	+	0.396084i	−0.994556	−	0.104201i	$-0.966771\pi$
$499$	−2.87484	+	8.84785i	−0.128696	+	0.396084i	0.865861	+	0.500285i	$0.166771\pi$
$500$	28.6107	+	20.7869i	1.27951	+	0.929617i
$501$	−5.81403	−	4.22414i	−0.259752	−	0.188721i
$502$	−1.14487	+	3.52356i	−0.0510982	+	0.157264i
$503$	−0.215229	−	0.662405i	−0.00959657	−	0.0295352i	0.946144	−	0.323747i	$-0.104943\pi$
$503$	−0.215229	−	0.662405i	−0.00959657	−	0.0295352i	−0.955740	+	0.294212i	$0.904943\pi$
$504$	−2.37310	+	1.72416i	−0.105706	+	0.0768001i
$505$	13.7834			0.613352
$506$	−0.170869	−	7.28516i	−0.00759606	−	0.323865i
$507$	1.00000			0.0444116
$508$	−4.90195	+	3.56147i	−0.217489	+	0.158015i
$509$	−3.11918	−	9.59986i	−0.138255	−	0.425506i	0.857827	−	0.513939i	$-0.171814\pi$
$509$	−3.11918	−	9.59986i	−0.138255	−	0.425506i	−0.996082	+	0.0884326i	$0.971814\pi$
$510$	1.09940	−	3.38360i	0.0486822	−	0.149828i
$511$	−31.2689	−	22.7182i	−1.38325	−	1.00499i
$512$	−14.8532	−	10.7915i	−0.656427	−	0.476922i
$513$	−1.45151	+	4.46729i	−0.0640858	+	0.197236i
$514$	0.612987	+	1.88658i	0.0270377	+	0.0832135i
$515$	6.86832	−	4.99013i	0.302654	−	0.219891i
$516$	14.9745			0.659215
$517$	17.8044	+	5.32681i	0.783036	+	0.234273i
$518$	−7.23656			−0.317956
$519$	−6.07876	+	4.41648i	−0.266828	+	0.193862i
$520$	1.23942	+	3.81455i	0.0543523	+	0.167279i
$521$	3.02348	−	9.30532i	0.132461	−	0.407673i	−0.862725	−	0.505673i	$-0.831244\pi$
$521$	3.02348	−	9.30532i	0.132461	−	0.407673i	0.995186	+	0.0979993i	$0.0312443\pi$
$522$	−0.545462	−	0.396302i	−0.0238742	−	0.0173456i
$523$	2.04805	+	1.48800i	0.0895550	+	0.0650655i	0.631662	−	0.775244i	$-0.282373\pi$
$523$	2.04805	+	1.48800i	0.0895550	+	0.0650655i	−0.542107	+	0.840310i	$0.682373\pi$
$524$	−4.69240	+	14.4417i	−0.204988	+	0.630889i
$525$	−8.48491	−	26.1139i	−0.370312	−	1.13970i
$526$	−2.85314	+	2.07293i	−0.124403	+	0.0903838i
$527$	16.6297			0.724400
$528$	−7.20586	−	9.44413i	−0.313595	−	0.411003i
$529$	45.4345			1.97541
$530$	−8.37627	+	6.08571i	−0.363842	+	0.264346i
$531$	0.599939	+	1.84642i	0.0260351	+	0.0801279i
$532$	−7.87149	+	24.2260i	−0.341272	+	1.05033i
$533$	8.54493	+	6.20826i	0.370122	+	0.268910i
$534$	−2.45225	−	1.78167i	−0.106119	−	0.0771003i
$535$	−0.404898	+	1.24615i	−0.0175053	+	0.0538757i
$536$	−0.0659741	−	0.203047i	−0.00284965	−	0.00877031i
$537$	4.41087	−	3.20468i	0.190343	−	0.138292i
$538$	2.31942			0.0999972
$539$	−2.81505	+	0.988221i	−0.121253	+	0.0425657i
$540$	−7.41507			−0.319094
$541$	−3.34344	+	2.42915i	−0.143746	+	0.104437i	−0.657334	−	0.753599i	$-0.728316\pi$
$541$	−3.34344	+	2.42915i	−0.143746	+	0.104437i	0.513588	+	0.858037i	$0.328316\pi$
$542$	0.836071	+	2.57316i	0.0359123	+	0.110527i
$543$	0.253074	−	0.778882i	0.0108604	−	0.0334250i
$544$	−8.56841	−	6.22532i	−0.367368	−	0.266908i
$545$	−16.1709	−	11.7488i	−0.692683	−	0.503264i
$546$	0.230679	−	0.709957i	0.00987215	−	0.0303833i
$547$	−2.76578	−	8.51219i	−0.118256	−	0.363955i	0.874356	−	0.485285i	$-0.161284\pi$
$547$	−2.76578	−	8.51219i	−0.118256	−	0.363955i	−0.992612	+	0.121330i	$0.961284\pi$
$548$	1.99259	−	1.44770i	0.0851194	−	0.0618428i
$549$	0.538692			0.0229908
$550$	−8.11987	+	2.85048i	−0.346232	+	0.121545i
$551$	−11.9240			−0.507978
$552$	−6.98477	+	5.07474i	−0.297292	+	0.215995i
$553$	−11.0180	−	33.9099i	−0.468533	−	1.44200i
$554$	0.619321	−	1.90608i	0.0263124	−	0.0809814i
$555$	−30.1400	−	21.8980i	−1.27937	−	0.929519i
$556$	−26.6944	−	19.3946i	−1.13210	−	0.822516i
$557$	−2.19754	+	6.76333i	−0.0931128	+	0.286572i	−0.986757	−	0.162204i	$-0.948140\pi$
$557$	−2.19754	+	6.76333i	−0.0931128	+	0.286572i	0.893644	+	0.448776i	$0.148140\pi$
$558$	0.391582	+	1.20516i	0.0165770	+	0.0510187i
$559$	−6.27877	+	4.56179i	−0.265564	+	0.192943i
$560$	−38.6877			−1.63485
$561$	−7.01233	−	9.19048i	−0.296061	−	0.388022i
$562$	1.01348			0.0427509
$563$	−9.15754	+	6.65334i	−0.385944	+	0.280405i	−0.763791	−	0.645463i	$-0.776664\pi$
$563$	−9.15754	+	6.65334i	−0.385944	+	0.280405i	0.377847	+	0.925868i	$0.376664\pi$
$564$	−3.34091	−	10.2823i	−0.140678	−	0.432961i
$565$	−4.81045	+	14.8050i	−0.202377	+	0.622853i
$566$	3.00017	+	2.17975i	0.126107	+	0.0916219i
$567$	2.27383	+	1.65204i	0.0954921	+	0.0693790i
$568$	−2.92792	+	9.01121i	−0.122853	+	0.378102i
$569$	4.95800	+	15.2592i	0.207850	+	0.639697i	0.999584	+	0.0288312i	$0.00917853\pi$
$569$	4.95800	+	15.2592i	0.207850	+	0.639697i	−0.791734	+	0.610866i	$0.790821\pi$
$570$	3.87883	−	2.81813i	0.162466	−	0.118039i
$571$	28.5925			1.19656			0.598280	−	0.801287i	$-0.295851\pi$
$571$	28.5925			1.19656			0.598280	+	0.801287i	$0.295851\pi$
$572$	6.13078	+	1.83424i	0.256341	+	0.0766934i
$573$	4.70545			0.196573
$574$	6.37873	−	4.63442i	0.266243	−	0.193437i
$575$	−24.9737	−	76.8613i	−1.04148	−	3.20534i
$576$	−1.96424	+	6.04529i	−0.0818431	+	0.251887i
$577$	21.0744	+	15.3114i	0.877339	+	0.637424i	0.932546	−	0.361051i	$-0.117582\pi$
$577$	21.0744	+	15.3114i	0.877339	+	0.637424i	−0.0552072	+	0.998475i	$0.517582\pi$
$578$	1.04238	+	0.757331i	0.0433572	+	0.0315008i
$579$	2.81410	−	8.66091i	0.116950	−	0.359935i
$580$	−5.81675	−	17.9021i	−0.241527	−	0.743345i
$581$	40.2901	−	29.2725i	1.67152	−	1.21443i
$582$	−3.72617			−0.154455
$583$	0.788842	+	33.6330i	0.0326705	+	1.39294i
$584$	14.3519			0.593888
$585$	3.10912	−	2.25891i	0.128546	−	0.0933944i
$586$	−1.64150	−	5.05200i	−0.0678096	−	0.208696i
$587$	7.70230	−	23.7052i	0.317908	−	0.978420i	−0.656633	−	0.754210i	$-0.728020\pi$
$587$	7.70230	−	23.7052i	0.317908	−	0.978420i	0.974541	−	0.224210i	$-0.0719800\pi$
$588$	1.40416	+	1.02019i	0.0579068	+	0.0420717i
$589$	18.1306	+	13.1726i	0.747057	+	0.542768i
$590$	0.612366	−	1.88467i	0.0252107	−	0.0775906i
$591$	−3.40239	−	10.4715i	−0.139956	−	0.430740i
$592$	−28.0903	+	20.4088i	−1.15450	+	0.838796i
$593$	38.8183			1.59408			0.797038	−	0.603930i	$-0.206399\pi$
$593$	38.8183			1.59408			0.797038	+	0.603930i	$0.206399\pi$
$594$	0.500920	−	0.724598i	0.0205530	−	0.0297306i
$595$	−37.6486			−1.54344
$596$	27.4966	−	19.9775i	1.12631	−	0.818309i
$597$	4.21677	+	12.9779i	0.172581	+	0.531149i
$598$	0.678960	−	2.08963i	0.0277648	−	0.0854511i
$599$	−2.63401	−	1.91372i	−0.107623	−	0.0781926i	0.532672	−	0.846322i	$-0.321188\pi$
$599$	−2.63401	−	1.91372i	−0.107623	−	0.0781926i	−0.640295	+	0.768129i	$0.721188\pi$
$600$	8.24857	+	5.99293i	0.336746	+	0.244661i
$601$	8.34131	−	25.6719i	0.340249	−	1.04718i	−0.623829	−	0.781561i	$-0.714424\pi$
$601$	8.34131	−	25.6719i	0.340249	−	1.04718i	0.964078	−	0.265618i	$-0.0855761\pi$
$602$	1.79030	+	5.50997i	0.0729670	+	0.224569i
$603$	−0.165498	+	0.120241i	−0.00673958	+	0.00489659i
$604$	34.6809			1.41115
$605$	−11.1641	+	40.7731i	−0.453884	+	1.65766i
$606$	0.952576			0.0386958
$607$	−14.1119	+	10.2529i	−0.572783	+	0.416152i	−0.836115	−	0.548554i	$-0.815179\pi$
$607$	−14.1119	+	10.2529i	−0.572783	+	0.416152i	0.263332	+	0.964705i	$0.415179\pi$
$608$	−4.41057	−	13.5744i	−0.178872	−	0.550513i
$609$	−2.20478	+	6.78563i	−0.0893424	+	0.274968i
$610$	−0.444839	−	0.323194i	−0.0180110	−	0.0130857i
$611$	4.53320	+	3.29356i	0.183393	+	0.133243i
$612$	−2.07819	+	6.39602i	−0.0840059	+	0.258544i
$613$	−4.00537	−	12.3273i	−0.161775	−	0.497893i	0.837009	−	0.547189i	$-0.184302\pi$
$613$	−4.00537	−	12.3273i	−0.161775	−	0.497893i	−0.998784	+	0.0492960i	$0.984302\pi$
$614$	−1.76782	+	1.28440i	−0.0713435	+	0.0518341i
$615$	40.5911			1.63679
$616$	5.53226	−	8.00260i	0.222901	−	0.322434i
$617$	−2.03817			−0.0820535			−0.0410267	−	0.999158i	$-0.513063\pi$
$617$	−2.03817			−0.0820535			−0.0410267	+	0.999158i	$0.513063\pi$
$618$	0.474673	−	0.344870i	0.0190942	−	0.0138727i
$619$	−0.175696	−	0.540736i	−0.00706181	−	0.0217340i	0.947464	−	0.319864i	$-0.103637\pi$
$619$	−0.175696	−	0.540736i	−0.00706181	−	0.0217340i	−0.954525	+	0.298130i	$0.903637\pi$
$620$	−10.9323	+	33.6463i	−0.439053	+	1.35127i
$621$	6.69261	+	4.86246i	0.268565	+	0.195124i
$622$	−3.53314	−	2.56698i	−0.141666	−	0.102926i
$623$	−9.91213	+	30.5064i	−0.397121	+	1.22221i
$624$	−1.10681	−	3.40642i	−0.0443080	−	0.136366i
$625$	−17.4690	+	12.6919i	−0.698758	+	0.507678i
$626$	−2.31783			−0.0926391
$627$	−0.365292	−	15.5745i	−0.0145883	−	0.621987i
$628$	−32.0350			−1.27834
$629$	−27.3358	+	19.8606i	−1.08995	+	0.791895i
$630$	−0.886519	−	2.72842i	−0.0353198	−	0.108703i
$631$	8.40406	−	25.8650i	0.334560	−	1.02967i	−0.632378	−	0.774660i	$-0.717921\pi$
$631$	8.40406	−	25.8650i	0.334560	−	1.02967i	0.966938	−	0.255011i	$-0.0820790\pi$
$632$	10.7111	+	7.78206i	0.426064	+	0.309554i
$633$	0.341530	+	0.248136i	0.0135746	+	0.00986253i
$634$	0.125884	−	0.387431i	0.00499950	−	0.0153869i
$635$	−3.72939	−	11.4779i	−0.147996	−	0.455486i
$636$	15.8337	−	11.5038i	0.627845	−	0.456156i
$637$	−0.899550			−0.0356414
$638$	2.14234	+	0.640955i	0.0848159	+	0.0253757i
$639$	9.07862			0.359145
$640$	24.1438	−	17.5415i	0.954366	−	0.693388i
$641$	−5.23943	−	16.1253i	−0.206945	−	0.636911i	−0.999628	−	0.0272772i	$-0.991316\pi$
$641$	−5.23943	−	16.1253i	−0.206945	−	0.636911i	0.792683	−	0.609634i	$-0.208684\pi$
$642$	−0.0279828	+	0.0861221i	−0.00110439	+	0.00339897i
$643$	−20.6553	−	15.0070i	−0.814567	−	0.591818i	0.100584	−	0.994929i	$-0.467929\pi$
$643$	−20.6553	−	15.0070i	−0.814567	−	0.591818i	−0.915151	+	0.403111i	$0.867929\pi$
$644$	36.2937	+	26.3689i	1.43017	+	1.03908i
$645$	−9.21678	+	28.3663i	−0.362910	+	1.11692i
$646$	−1.34373	−	4.13558i	−0.0528685	−	0.162712i
$647$	−9.10743	+	6.61693i	−0.358050	+	0.260139i	−0.752238	−	0.658891i	$-0.771026\pi$
$647$	−9.10743	+	6.61693i	−0.358050	+	0.260139i	0.394188	+	0.919030i	$0.371026\pi$
$648$	−1.04366			−0.0409987
$649$	−3.90588	−	5.11911i	−0.153319	−	0.200943i
$650$	−2.59471			−0.101773
$651$	10.8486	−	7.88198i	0.425191	−	0.308919i
$652$	1.87410	+	5.76789i	0.0733954	+	0.225888i
$653$	−10.7355	+	33.0404i	−0.420112	+	1.29297i	0.487486	+	0.873131i	$0.337914\pi$
$653$	−10.7355	+	33.0404i	−0.420112	+	1.29297i	−0.907598	+	0.419841i	$0.862086\pi$
$654$	−1.11758	−	0.811967i	−0.0437007	−	0.0317504i
$655$	−24.4689	−	17.7777i	−0.956080	−	0.694633i
$656$	11.6903	−	35.9790i	0.456429	−	1.40475i
$657$	−4.24948	−	13.0786i	−0.165788	−	0.510243i
$658$	3.38400	−	2.45862i	0.131922	−	0.0958469i
$659$	11.8754			0.462601			0.231300	−	0.972882i	$-0.425702\pi$
$659$	11.8754			0.462601			0.231300	+	0.972882i	$0.425702\pi$
$660$	23.2047	−	8.14600i	0.903242	−	0.317083i
$661$	−42.8311			−1.66594			−0.832969	−	0.553320i	$-0.813361\pi$
$661$	−42.8311			−1.66594			−0.832969	+	0.553320i	$0.813361\pi$
$662$	−2.33747	+	1.69827i	−0.0908484	+	0.0660052i
$663$	−1.07709	−	3.31493i	−0.0418306	−	0.128741i
$664$	−5.71451	+	17.5875i	−0.221766	+	0.682526i
$665$	−41.0466	−	29.8221i	−1.59172	−	1.15645i
$666$	−2.08300	−	1.51338i	−0.0807144	−	0.0586425i
$667$	−6.48937	+	19.9722i	−0.251269	+	0.773328i
$668$	−4.28486	−	13.1875i	−0.165786	−	0.510238i
$669$	14.7205	−	10.6951i	0.569127	−	0.413495i
$670$	0.208804			0.00806680
$671$	−1.68578	+	0.591792i	−0.0650789	+	0.0228459i
$672$	−8.54035			−0.329451
$673$	−27.7053	+	20.1291i	−1.06796	+	0.775918i	−0.975544	−	0.219803i	$-0.929459\pi$
$673$	−27.7053	+	20.1291i	−1.06796	+	0.775918i	−0.0924150	+	0.995721i	$0.529459\pi$
$674$	−0.221531	−	0.681802i	−0.00853305	−	0.0262620i
$675$	3.01888	−	9.29116i	0.116197	−	0.357617i
$676$	1.56096	+	1.13411i	0.0600371	+	0.0436195i
$677$	38.2046	+	27.7572i	1.46832	+	1.06680i	0.981096	+	0.193521i	$0.0619909\pi$
$677$	38.2046	+	27.7572i	1.46832	+	1.06680i	0.487225	+	0.873276i	$0.338009\pi$
$678$	−0.332453	+	1.02319i	−0.0127678	+	0.0392952i
$679$	12.1849	+	37.5012i	0.467613	+	1.43917i
$680$	11.3100	−	8.21720i	0.433719	−	0.315115i
$681$	−0.319481			−0.0122425
$682$	−2.54938	−	3.34126i	−0.0976207	−	0.127943i
$683$	−48.5588			−1.85805			−0.929025	−	0.370016i	$-0.879352\pi$
$683$	−48.5588			−1.85805			−0.929025	+	0.370016i	$0.879352\pi$
$684$	−7.33214	+	5.32712i	−0.280352	+	0.203687i
$685$	1.51596	+	4.66565i	0.0579219	+	0.178265i
$686$	1.40725	−	4.33106i	0.0537289	−	0.165361i
$687$	10.2210	+	7.42602i	0.389957	+	0.283320i
$688$	22.4888	+	16.3391i	0.857378	+	0.622922i
$689$	−3.13452	+	9.64705i	−0.119416	+	0.367523i
$690$	−2.60930	−	8.03061i	−0.0993345	−	0.305720i
$691$	−10.7956	+	7.84345i	−0.410683	+	0.298379i	−0.773878	−	0.633334i	$-0.781686\pi$
$691$	−10.7956	+	7.84345i	−0.410683	+	0.298379i	0.363195	+	0.931713i	$0.381686\pi$
$692$	−14.4975			−0.551111
$693$	−8.93062	−	2.67191i	−0.339246	−	0.101497i
$694$	0.599171			0.0227442
$695$	53.1698	−	38.6302i	2.01685	−	1.46533i
$696$	−0.818695	−	2.51968i	−0.0310325	−	0.0955084i
$697$	11.3763	−	35.0127i	0.430909	−	1.32620i
$698$	1.21783	+	0.884805i	0.0460955	+	0.0334903i
$699$	3.30804	+	2.40343i	0.125121	+	0.0909061i
$700$	16.3713	−	50.3856i	0.618776	−	1.90440i
$701$	−9.20656	−	28.3349i	−0.347727	−	1.07019i	−0.960108	−	0.279631i	$-0.909788\pi$
$701$	−9.20656	−	28.3349i	−0.347727	−	1.07019i	0.612381	−	0.790563i	$-0.290212\pi$
$702$	0.214873	−	0.156114i	0.00810986	−	0.00589216i
$703$	−45.5349			−1.71738
$704$	−0.494325	−	21.0760i	−0.0186306	−	0.794331i
$705$	21.5341			0.811021
$706$	0.731579	−	0.531523i	0.0275333	−	0.0200041i
$707$	−3.11501	−	9.58700i	−0.117152	−	0.360556i
$708$	−1.15756	+	3.56259i	−0.0435036	+	0.133890i
$709$	22.9967	+	16.7081i	0.863658	+	0.627484i	0.928878	−	0.370387i	$-0.120775\pi$
$709$	22.9967	+	16.7081i	0.863658	+	0.627484i	−0.0652195	+	0.997871i	$0.520775\pi$
$710$	−7.49691	−	5.44682i	−0.281354	−	0.204416i
$711$	3.92014	−	12.0649i	0.147017	−	0.452471i
$712$	−3.68064	−	11.3278i	−0.137938	−	0.424528i
$713$	31.9309	−	23.1991i	1.19582	−	0.868814i
$714$	−2.60192			−0.0973743
$715$	−7.24810	+	10.4846i	−0.271064	+	0.392103i
$716$	10.5197			0.393138
$717$	−9.01055	+	6.54655i	−0.336505	+	0.244485i
$718$	−1.26648	−	3.89783i	−0.0472647	−	0.145466i
$719$	−2.29132	+	7.05195i	−0.0854517	+	0.262993i	−0.984648	−	0.174552i	$-0.944152\pi$
$719$	−2.29132	+	7.05195i	−0.0854517	+	0.262993i	0.899196	+	0.437546i	$0.144152\pi$
$720$	−11.1360	−	8.09079i	−0.415015	−	0.301526i
$721$	−5.02310	−	3.64949i	−0.187070	−	0.135914i
$722$	0.251442	−	0.773859i	0.00935770	−	0.0288000i
$723$	1.62413	+	4.99855i	0.0604019	+	0.185898i
$724$	1.27838	−	0.928794i	0.0475104	−	0.0345184i
$725$	24.7997			0.921038
$726$	−0.771555	+	2.81786i	−0.0286351	+	0.104580i
$727$	−51.8111			−1.92157			−0.960783	−	0.277300i	$-0.910560\pi$
$727$	−51.8111			−1.92157			−0.960783	+	0.277300i	$0.910560\pi$
$728$	2.37310	−	1.72416i	0.0879529	−	0.0639015i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	−4.33751	+	13.3495i	−0.160538	+	0.494087i
$731$	21.8848	+	15.9002i	0.809439	+	0.588092i
$732$	0.840878	+	0.610934i	0.0310798	+	0.0225808i
$733$	−4.36895	+	13.4463i	−0.161371	+	0.496649i	−0.998751	−	0.0499731i	$-0.984086\pi$
$733$	−4.36895	+	13.4463i	−0.161371	+	0.496649i	0.837380	+	0.546622i	$0.184086\pi$
$734$	−2.86357	−	8.81317i	−0.105696	−	0.325300i
$735$	−2.79681	+	2.03200i	−0.103162	+	0.0749515i
$736$	−25.1369			−0.926560
$737$	0.385814	−	0.558093i	0.0142116	−	0.0205576i
$738$	2.80528			0.103264
$739$	−29.5646	+	21.4799i	−1.08755	+	0.790152i	−0.978984	−	0.203937i	$-0.934626\pi$
$739$	−29.5646	+	21.4799i	−1.08755	+	0.790152i	−0.108567	+	0.994089i	$0.534626\pi$
$740$	−22.2128	−	68.3641i	−0.816560	−	2.51311i
$741$	1.45151	−	4.46729i	0.0533226	−	0.164110i
$742$	6.12592	+	4.45074i	0.224890	+	0.163392i
$743$	−15.4186	−	11.2023i	−0.565654	−	0.410972i	0.267870	−	0.963455i	$-0.413680\pi$
$743$	−15.4186	−	11.2023i	−0.565654	−	0.410972i	−0.833524	+	0.552483i	$0.813680\pi$
$744$	−1.53870	+	4.73564i	−0.0564116	+	0.173617i
$745$	20.9194	+	64.3833i	0.766427	+	2.35882i
$746$	7.83098	−	5.68954i	0.286713	−	0.208309i
$747$	17.7190			0.648305
$748$	−0.523004	−	22.2987i	−0.0191229	−	0.815322i
$749$	0.958263			0.0350142
$750$	−3.93838	+	2.86140i	−0.143809	+	0.104484i
$751$	−7.10573	−	21.8692i	−0.259292	−	0.798018i	−0.992954	−	0.118503i	$-0.962190\pi$
$751$	−7.10573	−	21.8692i	−0.259292	−	0.798018i	0.733662	−	0.679515i	$-0.237810\pi$
$752$	6.20185	−	19.0873i	0.226158	−	0.696043i
$753$	11.2852	+	8.19916i	0.411254	+	0.298794i
$754$	0.545462	+	0.396302i	0.0198646	+	0.0144325i
$755$	−21.3461	+	65.6964i	−0.776863	+	2.39094i
$756$	1.67579	+	5.15754i	0.0609478	+	0.187578i
$757$	−10.4439	+	7.58795i	−0.379591	+	0.275789i	−0.761177	−	0.648545i	$-0.775378\pi$
$757$	−10.4439	+	7.58795i	−0.379591	+	0.275789i	0.381586	+	0.924333i	$0.375378\pi$
$758$	−2.44232			−0.0887089
$759$	−26.2856	−	7.86427i	−0.954107	−	0.285455i
$760$	18.8398			0.683390
$761$	−19.7639	+	14.3593i	−0.716441	+	0.520525i	−0.885245	−	0.465125i	$-0.846009\pi$
$761$	−19.7639	+	14.3593i	−0.716441	+	0.520525i	0.168804	+	0.985650i	$0.446009\pi$
$762$	−0.257740	−	0.793243i	−0.00933695	−	0.0287362i
$763$	−4.51730	+	13.9028i	−0.163537	+	0.503316i
$764$	7.34503	+	5.33648i	0.265734	+	0.193067i
$765$	−10.8369	−	7.87348i	−0.391810	−	0.284666i
$766$	0.974852	−	3.00028i	0.0352228	−	0.108405i
$767$	−0.599939	−	1.84642i	−0.0216625	−	0.0666704i
$768$	−8.61628	+	6.26009i	−0.310913	+	0.225892i
$769$	−16.5359			−0.596300			−0.298150	−	0.954519i	$-0.596370\pi$
$769$	−16.5359			−0.596300			−0.298150	+	0.954519i	$0.596370\pi$
$770$	5.77165	+	7.56442i	0.207996	+	0.272603i
$771$	7.46869			0.268978
$772$	14.2151	−	10.3279i	0.511613	−	0.371709i
$773$	−9.40850	−	28.9564i	−0.338400	−	1.04149i	−0.965023	−	0.262166i	$-0.915563\pi$
$773$	−9.40850	−	28.9564i	−0.338400	−	1.04149i	0.626622	−	0.779323i	$-0.284437\pi$
$774$	−0.636977	+	1.96041i	−0.0228957	+	0.0704656i
$775$	−37.7083	−	27.3967i	−1.35452	−	0.984118i
$776$	−11.8455	−	8.60625i	−0.425228	−	0.308946i
$777$	−8.41957	+	25.9128i	−0.302050	+	0.929615i
$778$	2.62053	+	8.06517i	0.0939506	+	0.289150i
$779$	40.1372	−	29.1614i	1.43806	−	1.04481i
$780$	7.41507			0.265502
$781$	−28.4106	+	9.97353i	−1.01661	+	0.356881i
$782$	−7.65826			−0.273859
$783$	−2.05372	+	1.49211i	−0.0733938	+	0.0533237i
$784$	0.995633	+	3.06424i	0.0355583	+	0.109437i
$785$	19.7175	−	60.6843i	0.703748	−	2.16591i
$786$	−1.69106	−	1.22863i	−0.0603182	−	0.0438237i
$787$	−14.7524	−	10.7182i	−0.525865	−	0.382064i	0.292944	−	0.956130i	$-0.405365\pi$
$787$	−14.7524	−	10.7182i	−0.525865	−	0.382064i	−0.818809	+	0.574066i	$0.805365\pi$
$788$	6.56478	−	20.2043i	0.233860	−	0.719748i
$789$	4.10320	+	12.6284i	0.146078	+	0.449581i
$790$	−10.4757	+	7.61101i	−0.372707	+	0.270788i
$791$	11.3848			0.404796
$792$	3.26601	−	1.14653i	0.116053	−	0.0407402i
$793$	−0.538692			−0.0191295
$794$	−7.60177	+	5.52301i	−0.269777	+	0.196004i
$795$	12.0462	+	37.0744i	0.427235	+	1.31490i
$796$	−8.13607	+	25.0403i	−0.288375	+	0.887528i
$797$	−8.64821	−	6.28329i	−0.306335	−	0.222566i	0.423987	−	0.905668i	$-0.360630\pi$
$797$	−8.64821	−	6.28329i	−0.306335	−	0.222566i	−0.730322	+	0.683103i	$0.760630\pi$
$798$	−2.83675	−	2.06102i	−0.100420	−	0.0729594i
$799$	6.03528	−	18.5747i	0.213513	−	0.657125i
$800$	9.17320	+	28.2322i	0.324322	+	0.998159i
$801$	−9.23296	+	6.70814i	−0.326231	+	0.237020i
$802$	−3.59714			−0.127020
$803$	27.6661	+	36.2597i	0.976315	+	1.27958i
$804$	−0.394702			−0.0139201
$805$	−72.2897	+	52.5215i	−2.54788	+	1.85114i
$806$	−0.391582	−	1.20516i	−0.0137929	−	0.0424501i
$807$	2.69859	−	8.30541i	0.0949949	−	0.292364i
$808$	3.02824	+	2.20014i	0.106533	+	0.0774008i
$809$	−26.6561	−	19.3668i	−0.937178	−	0.680900i	0.0105614	−	0.999944i	$-0.496638\pi$
$809$	−26.6561	−	19.3668i	−0.937178	−	0.680900i	−0.947740	+	0.319044i	$0.896638\pi$
$810$	0.315418	−	0.970758i	0.0110827	−	0.0341089i
$811$	−7.77933	−	23.9423i	−0.273169	−	0.840728i	−0.989698	−	0.143171i	$-0.954270\pi$
$811$	−7.77933	−	23.9423i	−0.273169	−	0.840728i	0.716529	−	0.697557i	$-0.245730\pi$
$812$	−11.1372	+	8.09166i	−0.390840	+	0.283962i
$813$	10.1868			0.357266
$814$	8.18109	+	2.44766i	0.286747	+	0.0857905i
$815$	−12.0797			−0.423132
$816$	−10.0999	+	7.33802i	−0.353568	+	0.256882i
$817$	11.2652	+	34.6706i	0.394118	+	1.21297i
$818$	−1.37307	+	4.22589i	−0.0480084	+	0.147755i
$819$	−2.27383	−	1.65204i	−0.0794542	−	0.0577269i
$820$	63.3613	+	46.0347i	2.21267	+	1.60760i
$821$	−4.30588	+	13.2521i	−0.150276	+	0.462503i	−0.997652	−	0.0684915i	$-0.978181\pi$
$821$	−4.30588	+	13.2521i	−0.150276	+	0.462503i	0.847375	+	0.530994i	$0.178181\pi$
$822$	0.104769	+	0.322446i	0.00365424	+	0.0112466i
$823$	39.6696	−	28.8216i	1.38280	−	1.00466i	0.386182	−	0.922422i	$-0.373794\pi$
$823$	39.6696	−	28.8216i	1.38280	−	1.00466i	0.996613	−	0.0822371i	$-0.0262065\pi$
$824$	2.30552			0.0803168
$825$	0.759741	+	32.3922i	0.0264508	+	1.12775i
$826$	−1.44927			−0.0504266
$827$	0.169702	−	0.123295i	0.00590111	−	0.00428740i	−0.584831	−	0.811155i	$-0.698839\pi$
$827$	0.169702	−	0.123295i	0.00590111	−	0.00428740i	0.590732	+	0.806868i	$0.298839\pi$
$828$	4.93237	+	15.1803i	0.171412	+	0.527551i
$829$	9.91313	−	30.5095i	0.344297	−	1.05964i	−0.617662	−	0.786444i	$-0.711920\pi$
$829$	9.91313	−	30.5095i	0.344297	−	1.05964i	0.961959	−	0.273194i	$-0.0880802\pi$
$830$	−14.6319	−	10.6307i	−0.507882	−	0.368998i
$831$	−6.10474	−	4.43535i	−0.211771	−	0.153861i
$832$	1.96424	−	6.04529i	0.0680976	−	0.209583i
$833$	0.968892	+	2.98194i	0.0335701	+	0.103318i
$834$	3.67460	−	2.66975i	0.127241	−	0.0924459i
$835$	27.6185			0.955776
$836$	17.0930	−	24.7256i	0.591173	−	0.855152i
$837$	4.77107			0.164912
$838$	−1.93269	+	1.40418i	−0.0667635	+	0.0485065i
$839$	−2.11475	−	6.50853i	−0.0730093	−	0.224700i	0.907893	−	0.419203i	$-0.137690\pi$
$839$	−2.11475	−	6.50853i	−0.0730093	−	0.224700i	−0.980902	+	0.194503i	$0.937690\pi$
$840$	3.48354	−	10.7212i	0.120194	−	0.369918i
$841$	18.2481	+	13.2580i	0.629244	+	0.457172i
$842$	3.87438	+	2.81490i	0.133520	+	0.0970080i
$843$	1.17916	−	3.62907i	0.0406123	−	0.124992i
$844$	0.251704	+	0.774664i	0.00866399	+	0.0266650i
$845$	−3.10912	+	2.25891i	−0.106957	+	0.0777088i
$846$	1.48823			0.0511665
$847$	30.8828	−	1.44947i	1.06114	−	0.0498044i
$848$	36.3312			1.24762
$849$	11.2959	−	8.20697i	0.387675	−	0.281663i
$850$	2.79472	+	8.60127i	0.0958582	+	0.295021i
$851$	−24.7814	+	76.2694i	−0.849496	+	2.61448i
$852$	14.1714	+	10.2961i	0.485504	+	0.352740i
$853$	39.8031	+	28.9186i	1.36283	+	0.990156i	0.998259	+	0.0589808i	$0.0187851\pi$
$853$	39.8031	+	28.9186i	1.36283	+	0.990156i	0.364573	+	0.931175i	$0.381215\pi$
$854$	−0.124265	+	0.382448i	−0.00425226	+	0.0130871i
$855$	−5.57828	−	17.1682i	−0.190773	−	0.587140i
$856$	−0.287871	+	0.209151i	−0.00983924	+	0.00714863i
$857$	−48.3190			−1.65054			−0.825272	−	0.564735i	$-0.808978\pi$
$857$	−48.3190			−1.65054			−0.825272	+	0.564735i	$0.808978\pi$
$858$	−0.500920	+	0.724598i	−0.0171011	+	0.0247374i
$859$	4.55314			0.155351			0.0776755	−	0.996979i	$-0.475250\pi$
$859$	4.55314			0.155351			0.0776755	+	0.996979i	$0.475250\pi$
$860$	−46.5575	+	33.8260i	−1.58760	+	1.15346i
$861$	−9.17349	−	28.2331i	−0.312632	−	0.962182i
$862$	0.404158	−	1.24387i	0.0137657	−	0.0423664i
$863$	20.6221	+	14.9828i	0.701983	+	0.510020i	0.880577	−	0.473902i	$-0.157155\pi$
$863$	20.6221	+	14.9828i	0.701983	+	0.510020i	−0.178595	+	0.983923i	$0.557155\pi$
$864$	−2.45829	−	1.78605i	−0.0836326	−	0.0607626i
$865$	8.92318	−	27.4627i	0.303397	−	0.933760i
$866$	0.175536	+	0.540244i	0.00596495	+	0.0183582i
$867$	3.92464	−	2.85142i	0.133288	−	0.0968393i
$868$	25.8733			0.878197
$869$	0.986554	+	42.0626i	0.0334665	+	1.42688i
$870$	2.59112			0.0878471
$871$	0.165498	−	0.120241i	0.00560767	−	0.00407421i
$872$	−1.67739	−	5.16248i	−0.0568037	−	0.174824i
$873$	−4.33531	+	13.3427i	−0.146728	+	0.451583i
$874$	−8.34945	−	6.06623i	−0.282424	−	0.205193i
$875$	41.6768	+	30.2799i	1.40893	+	1.02365i
$876$	8.19920	−	25.2345i	0.277025	−	0.852596i
$877$	−14.9257	−	45.9366i	−0.504005	−	1.55117i	−0.802437	−	0.596737i	$-0.796464\pi$
$877$	−14.9257	−	45.9366i	−0.504005	−	1.55117i	0.298432	−	0.954431i	$-0.403536\pi$
$878$	−0.620474	+	0.450801i	−0.0209400	+	0.0152138i
$879$	−20.0001			−0.674588
$880$	43.7373	+	13.0856i	1.47439	+	0.441114i
$881$	−16.5910			−0.558964			−0.279482	−	0.960151i	$-0.590163\pi$
$881$	−16.5910			−0.558964			−0.279482	+	0.960151i	$0.590163\pi$
$882$	−0.193289	+	0.140433i	−0.00650838	+	0.00472861i
$883$	5.39102	+	16.5918i	0.181422	+	0.558360i	0.999868	−	0.0162232i	$-0.00516422\pi$
$883$	5.39102	+	16.5918i	0.181422	+	0.558360i	−0.818446	+	0.574583i	$0.805164\pi$
$884$	2.07819	−	6.39602i	0.0698972	−	0.215121i
$885$	−6.03618	−	4.38554i	−0.202904	−	0.147418i
$886$	−3.73644	−	2.71469i	−0.125528	−	0.0912017i
$887$	5.47856	−	16.8613i	0.183952	−	0.566146i	−0.815977	−	0.578085i	$-0.803800\pi$
$887$	5.47856	−	16.8613i	0.183952	−	0.566146i	0.999929	+	0.0119385i	$0.00380022\pi$
$888$	−3.12641	−	9.62210i	−0.104915	−	0.322896i
$889$	−7.14060	+	5.18795i	−0.239488	+	0.173998i
$890$	11.6490			0.390475
$891$	−2.01184	−	2.63676i	−0.0673993	−	0.0883347i
$892$	35.1075			1.17549
$893$	21.2933	−	15.4705i	0.712552	−	0.517700i
$894$	1.44575	+	4.44956i	0.0483531	+	0.148816i
$895$	−6.47484	+	19.9275i	−0.216430	+	0.666103i
$896$	−17.6574	−	12.8288i	−0.589891	−	0.428581i
$897$	−6.69261	−	4.86246i	−0.223460	−	0.162353i
$898$	−0.295107	+	0.908246i	−0.00984785	+	0.0303086i
$899$	3.74266	+	11.5187i	0.124825	+	0.384171i
$900$	15.2495	−	11.0794i	0.508318	−	0.369315i
$901$	35.3554			1.17786
$902$	−8.77883	+	3.08180i	−0.292303	+	0.102613i
$903$	21.8131			0.725896
$904$	−3.42010	+	2.48484i	−0.113751	+	0.0826447i
$905$	0.972585	+	2.99331i	0.0323298	+	0.0995010i
$906$	−1.47524	+	4.54032i	−0.0490115	+	0.150842i
$907$	−11.7049	−	8.50407i	−0.388653	−	0.282373i	0.376250	−	0.926518i	$-0.377213\pi$
$907$	−11.7049	−	8.50407i	−0.388653	−	0.282373i	−0.764903	+	0.644145i	$0.777213\pi$
$908$	−0.498698	−	0.362325i	−0.0165499	−	0.0120242i
$909$	1.10830	−	3.41100i	0.0367600	−	0.113136i
$910$	0.886519	+	2.72842i	0.0293878	+	0.0904464i
$911$	9.87832	−	7.17702i	0.327283	−	0.237785i	−0.411994	−	0.911187i	$-0.635167\pi$
$911$	9.87832	−	7.17702i	0.327283	−	0.237785i	0.739277	+	0.673401i	$0.235167\pi$
$912$	−16.8240			−0.557099
$913$	−55.4499	+	19.4657i	−1.83512	+	0.644219i
$914$	−0.454608			−0.0150371
$915$	−1.67486	+	1.21686i	−0.0553691	+	0.0402280i
$916$	7.53278	+	23.1835i	0.248890	+	0.766005i
$917$	−6.83535	+	21.0370i	−0.225723	+	0.694704i
$918$	−0.748945	−	0.544141i	−0.0247189	−	0.0179593i
$919$	29.7089	+	21.5848i	0.980007	+	0.712017i	0.957710	−	0.287734i	$-0.0929020\pi$
$919$	29.7089	+	21.5848i	0.980007	+	0.712017i	0.0222971	+	0.999751i	$0.492902\pi$
$920$	10.2531	−	31.5559i	0.338036	−	1.04037i
$921$	2.54237	+	7.82462i	0.0837740	+	0.257830i
$922$	1.03785	−	0.754040i	0.0341797	−	0.0248330i
$923$	−9.07862			−0.298826
$924$	−10.9101	−	14.2990i	−0.358917	−	0.470404i
$925$	94.7044			3.11386
$926$	8.07105	−	5.86396i	0.265231	−	0.192702i
$927$	−0.682645	−	2.10097i	−0.0224210	−	0.0690048i
$928$	2.38363	−	7.33607i	0.0782466	−	0.240818i
$929$	−20.3948	−	14.8177i	−0.669130	−	0.486151i	0.200604	−	0.979672i	$-0.435710\pi$
$929$	−20.3948	−	14.8177i	−0.669130	−	0.486151i	−0.869734	+	0.493521i	$0.835710\pi$
$930$	−3.93983	−	2.86245i	−0.129192	−	0.0938636i
$931$	−1.30571	+	4.01855i	−0.0427928	+	0.131703i
$932$	2.43798	+	7.50334i	0.0798588	+	0.245780i
$933$	−13.3026	+	9.66491i	−0.435508	+	0.316415i
$934$	7.05085			0.230711
$935$	42.5626	+	12.7341i	1.39195	+	0.416450i
$936$	1.04366			0.0341129
$937$	11.2858	−	8.19960i	0.368690	−	0.267869i	−0.387977	−	0.921669i	$-0.626826\pi$
$937$	11.2858	−	8.19960i	0.368690	−	0.267869i	0.756668	+	0.653800i	$0.226826\pi$
$938$	−0.0471891	−	0.145233i	−0.00154078	−	0.00474203i
$939$	−2.69674	+	8.29972i	−0.0880049	+	0.270851i
$940$	33.6140	+	24.4220i	1.09637	+	0.796557i
$941$	40.6372	+	29.5246i	1.32473	+	0.962476i	0.999860	+	0.0167182i	$0.00532182\pi$
$941$	40.6372	+	29.5246i	1.32473	+	0.962476i	0.324874	+	0.945757i	$0.394678\pi$
$942$	1.36269	−	4.19392i	0.0443988	−	0.136645i
$943$	−27.0005	−	83.0989i	−0.879256	−	2.70607i
$944$	−5.62567	+	4.08729i	−0.183100	+	0.133030i
$945$	−10.8014			−0.351371
$946$	−0.160304	−	6.83468i	−0.00521192	−	0.222215i
$947$	12.5499			0.407817			0.203909	−	0.978990i	$-0.434635\pi$
$947$	12.5499			0.407817			0.203909	+	0.978990i	$0.434635\pi$
$948$	19.8021	−	14.3871i	0.643143	−	0.467271i
$949$	4.24948	+	13.0786i	0.137944	+	0.424548i
$950$	−3.76625	+	11.5913i	−0.122193	+	0.376072i
$951$	−1.24086	−	0.901535i	−0.0402375	−	0.0292343i
$952$	−8.27149	−	6.00959i	−0.268081	−	0.194772i
$953$	7.64557	−	23.5306i	0.247664	−	0.762232i	−0.747523	−	0.664236i	$-0.768757\pi$
$953$	7.64557	−	23.5306i	0.247664	−	0.762232i	0.995187	−	0.0979958i	$-0.0312432\pi$
$954$	0.832521	+	2.56224i	0.0269539	+	0.0829554i
$955$	−14.6298	+	10.6292i	−0.473409	+	0.343952i
$956$	−21.4896			−0.695024
$957$	4.78770	−	6.92557i	0.154764	−	0.223872i
$958$	10.3552			0.334560
$959$	2.90258	−	2.10885i	0.0937293	−	0.0680983i
$960$	−7.54872	−	23.2326i	−0.243634	−	0.749828i
$961$	−2.54535	+	7.83378i	−0.0821081	+	0.252703i
$962$	2.08300	+	1.51338i	0.0671585	+	0.0487935i
$963$	0.275830	+	0.200402i	0.00888849	+	0.00645787i
$964$	−3.13368	+	9.64449i	−0.100929	+	0.310628i
$965$	10.8148	+	33.2846i	0.348142	+	1.07147i
$966$	−4.99598	+	3.62979i	−0.160743	+	0.116787i
$967$	40.6134			1.30604			0.653019	−	0.757341i	$-0.273502\pi$
$967$	40.6134			1.30604			0.653019	+	0.757341i	$0.273502\pi$
$968$	−8.96111	+	7.17591i	−0.288021	+	0.230643i
$969$	−16.3722			−0.525950
$970$	11.5851	−	8.41708i	0.371975	−	0.270256i
$971$	−8.07953	−	24.8662i	−0.259284	−	0.797995i	−0.992955	−	0.118490i	$-0.962195\pi$
$971$	−8.07953	−	24.8662i	−0.259284	−	0.797995i	0.733671	−	0.679505i	$-0.237805\pi$
$972$	−0.596235	+	1.83502i	−0.0191243	+	0.0588584i
$973$	−38.8854	−	28.2519i	−1.24661	−	0.905714i
$974$	−0.160649	−	0.116718i	−0.00514752	−	0.00373989i
$975$	−3.01888	+	9.29116i	−0.0966816	+	0.297555i
$976$	0.596231	+	1.83501i	0.0190849	+	0.0587373i
$977$	11.5981	−	8.42654i	0.371057	−	0.269589i	−0.386592	−	0.922251i	$-0.626348\pi$
$977$	11.5981	−	8.42654i	0.371057	−	0.269589i	0.757649	+	0.652662i	$0.226348\pi$
$978$	−0.834833			−0.0266950
$979$	21.5242	−	31.1355i	0.687917	−	0.995096i
$980$	−6.67022			−0.213072
$981$	−4.20778	+	3.05713i	−0.134344	+	0.0976067i
$982$	−3.01685	−	9.28492i	−0.0962716	−	0.296294i
$983$	−11.1691	+	34.3748i	−0.356238	+	1.09639i	0.599051	+	0.800711i	$0.295545\pi$
$983$	−11.1691	+	34.3748i	−0.356238	+	1.09639i	−0.955288	+	0.295676i	$0.904455\pi$
$984$	8.91797	+	6.47928i	0.284294	+	0.206552i
$985$	34.2326	+	24.8714i	1.09074	+	0.792470i
$986$	0.726202	−	2.23502i	0.0231270	−	0.0711775i
$987$	−4.86665	−	14.9780i	−0.154907	−	0.476755i
$988$	7.33214	−	5.32712i	0.233267	−	0.169478i
$989$	64.2029			2.04153
$990$	0.0793791	+	3.38440i	0.00252283	+	0.107563i
$991$	−19.4343			−0.617351			−0.308675	−	0.951167i	$-0.599886\pi$
$991$	−19.4343			−0.617351			−0.308675	+	0.951167i	$0.599886\pi$
$992$	−11.7286	+	8.52136i	−0.372385	+	0.270553i
$993$	3.36160	+	10.3459i	0.106677	+	0.328319i
$994$	−2.09425	+	6.44543i	−0.0664255	+	0.204437i
$995$	−42.4263	−	30.8245i	−1.34500	−	0.977202i
$996$	27.6588	+	20.0953i	0.876401	+	0.636743i
$997$	−14.0226	+	43.1570i	−0.444099	+	1.36680i	0.439371	+	0.898306i	$0.355201\pi$
$997$	−14.0226	+	43.1570i	−0.444099	+	1.36680i	−0.883469	+	0.468489i	$0.844799\pi$
$998$	−0.763551	−	2.34997i	−0.0241698	−	0.0743870i
$999$	−7.84267	+	5.69803i	−0.248131	+	0.180278i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.n.d.157.4	✓	36
11.2	odd	10		4719.2.a.br.1.8		18
11.4	even	5	inner	429.2.n.d.235.4	yes	36
11.9	even	5		4719.2.a.bq.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.n.d.157.4	✓	36	1.1	even	1	trivial
429.2.n.d.235.4	yes	36	11.4	even	5	inner
4719.2.a.bq.1.11		18	11.9	even	5
4719.2.a.br.1.8		18	11.2	odd	10

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.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.214873 + 0.156114i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.596235 + 1.83502i) q^{4} +(-3.10912 - 2.25891i) q^{5} +(-0.214873 - 0.156114i) q^{6} +(-0.868527 + 2.67305i) q^{7} +(-0.322507 - 0.992575i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.214873 + 0.156114i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.596235 + 1.83502i) q^{4} +(-3.10912 - 2.25891i) q^{5} +(-0.214873 - 0.156114i) q^{6} +(-0.868527 + 2.67305i) q^{7} +(-0.322507 - 0.992575i) q^{8} +(-0.809017 + 0.587785i) q^{9} +1.02072 q^{10} +(1.88601 - 2.72818i) q^{11} -1.92946 q^{12} +(0.809017 - 0.587785i) q^{13} +(-0.230679 - 0.709957i) q^{14} +(1.18758 - 3.65499i) q^{15} +(-2.89767 - 2.10528i) q^{16} +(-2.81985 - 2.04874i) q^{17} +(0.0820742 - 0.252599i) q^{18} +(-1.45151 - 4.46729i) q^{19} +(5.99892 - 4.35847i) q^{20} -2.81061 q^{21} +(0.0206550 + 0.880646i) q^{22} -8.27252 q^{23} +(0.844335 - 0.613445i) q^{24} +(3.01888 + 9.29116i) q^{25} +(-0.0820742 + 0.252599i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-4.38727 - 3.18754i) q^{28} +(0.784449 - 2.41429i) q^{29} +(0.315418 + 0.970758i) q^{30} +(-3.85987 + 2.80436i) q^{31} +3.03861 q^{32} +(3.17746 + 0.950650i) q^{33} +0.925747 q^{34} +(8.73854 - 6.34892i) q^{35} +(-0.596235 - 1.83502i) q^{36} +(2.99563 - 9.21961i) q^{37} +(1.00930 + 0.733299i) q^{38} +(0.809017 + 0.587785i) q^{39} +(-1.23942 + 3.81455i) q^{40} +(3.26387 + 10.0452i) q^{41} +(0.603925 - 0.438777i) q^{42} -7.76099 q^{43} +(3.88177 + 5.08751i) q^{44} +3.84309 q^{45} +(1.77754 - 1.29146i) q^{46} +(1.73153 + 5.32909i) q^{47} +(1.10681 - 3.40642i) q^{48} +(-0.727751 - 0.528742i) q^{49} +(-2.09916 - 1.52513i) q^{50} +(1.07709 - 3.31493i) q^{51} +(0.596235 + 1.83502i) q^{52} +(-8.20627 + 5.96221i) q^{53} +0.265598 q^{54} +(-12.0265 + 4.22191i) q^{55} +2.93331 q^{56} +(3.80011 - 2.76094i) q^{57} +(0.208348 + 0.641229i) q^{58} +(0.599939 - 1.84642i) q^{59} +(5.99892 + 4.35847i) q^{60} +(-0.435811 - 0.316635i) q^{61} +(0.391582 - 1.20516i) q^{62} +(-0.868527 - 2.67305i) q^{63} +(5.14243 - 3.73620i) q^{64} -3.84309 q^{65} +(-0.831161 + 0.291779i) q^{66} +0.204566 q^{67} +(5.44078 - 3.95296i) q^{68} +(-2.55635 - 7.86763i) q^{69} +(-0.886519 + 2.72842i) q^{70} +(-7.34476 - 5.33628i) q^{71} +(0.844335 + 0.613445i) q^{72} +(-4.24948 + 13.0786i) q^{73} +(0.795634 + 2.44871i) q^{74} +(-7.90354 + 5.74225i) q^{75} +9.06303 q^{76} +(5.65451 + 7.41091i) q^{77} -0.265598 q^{78} +(-10.2631 + 7.45655i) q^{79} +(4.25358 + 13.0912i) q^{80} +(0.309017 - 0.951057i) q^{81} +(-2.26952 - 1.64890i) q^{82} +(-14.3350 - 10.4150i) q^{83} +(1.67579 - 5.15754i) q^{84} +(4.13933 + 12.7396i) q^{85} +(1.66763 - 1.21160i) q^{86} +2.53853 q^{87} +(-3.31618 - 0.992151i) q^{88} +11.4126 q^{89} +(-0.825776 + 0.599961i) q^{90} +(0.868527 + 2.67305i) q^{91} +(4.93237 - 15.1803i) q^{92} +(-3.85987 - 2.80436i) q^{93} +(-1.20401 - 0.874762i) q^{94} +(-5.57828 + 17.1682i) q^{95} +(0.938982 + 2.88989i) q^{96} +(11.3500 - 8.24625i) q^{97} +0.238918 q^{98} +(0.0777681 + 3.31571i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9}+O(q^{10}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9	\( 36 q + 3 q^{2} - 9 q^{3} - 11 q^{4} + 3 q^{6} + q^{7} - q^{8} - 9 q^{9} + 6 q^{10} - 10 q^{11} + 54 q^{12} + 9 q^{13} - 5 q^{14} - 10 q^{15} - 13 q^{16} - 2 q^{18} + 10 q^{19} + 37 q^{20} - 14 q^{21} - 9 q^{22} + 18 q^{23} + 4 q^{24} - 31 q^{25} + 2 q^{26} - 9 q^{27} + 12 q^{28} + 10 q^{29} + q^{30} - 28 q^{31} - 74 q^{32} + 5 q^{33} + 40 q^{34} - 14 q^{35} - 11 q^{36} - 26 q^{37} + 7 q^{38} + 9 q^{39} - 72 q^{40} + 26 q^{41} - 5 q^{42} + 4 q^{43} - 68 q^{44} + 20 q^{45} - 57 q^{46} - 28 q^{48} - 18 q^{49} + 11 q^{50} - 5 q^{51} + 11 q^{52} + 11 q^{53} - 2 q^{54} - 32 q^{55} + 72 q^{56} + 50 q^{58} + 55 q^{59} + 37 q^{60} + 14 q^{61} - 50 q^{62} + q^{63} - q^{64} - 20 q^{65} - 14 q^{66} + 104 q^{67} - 9 q^{68} + 8 q^{69} + 44 q^{70} - 8 q^{71} + 4 q^{72} - 3 q^{73} + 69 q^{74} - 21 q^{75} - 52 q^{76} + 2 q^{77} + 2 q^{78} - 19 q^{79} - 159 q^{80} - 9 q^{81} + 58 q^{82} + 12 q^{83} - 8 q^{84} + 63 q^{86} - 97 q^{88} + 118 q^{89} - 4 q^{90} - q^{91} + 98 q^{92} - 28 q^{93} - 99 q^{94} - 45 q^{95} + q^{96} + 50 q^{97} - 186 q^{98}+O(q^{100}) \) 36 * q + 3 * q^2 - 9 * q^3 - 11 * q^4 + 3 * q^6 + q^7 - q^8 - 9 * q^9 + 6 * q^10 - 10 * q^11 + 54 * q^12 + 9 * q^13 - 5 * q^14 - 10 * q^15 - 13 * q^16 - 2 * q^18 + 10 * q^19 + 37 * q^20 - 14 * q^21 - 9 * q^22 + 18 * q^23 + 4 * q^24 - 31 * q^25 + 2 * q^26 - 9 * q^27 + 12 * q^28 + 10 * q^29 + q^30 - 28 * q^31 - 74 * q^32 + 5 * q^33 + 40 * q^34 - 14 * q^35 - 11 * q^36 - 26 * q^37 + 7 * q^38 + 9 * q^39 - 72 * q^40 + 26 * q^41 - 5 * q^42 + 4 * q^43 - 68 * q^44 + 20 * q^45 - 57 * q^46 - 28 * q^48 - 18 * q^49 + 11 * q^50 - 5 * q^51 + 11 * q^52 + 11 * q^53 - 2 * q^54 - 32 * q^55 + 72 * q^56 + 50 * q^58 + 55 * q^59 + 37 * q^60 + 14 * q^61 - 50 * q^62 + q^63 - q^64 - 20 * q^65 - 14 * q^66 + 104 * q^67 - 9 * q^68 + 8 * q^69 + 44 * q^70 - 8 * q^71 + 4 * q^72 - 3 * q^73 + 69 * q^74 - 21 * q^75 - 52 * q^76 + 2 * q^77 + 2 * q^78 - 19 * q^79 - 159 * q^80 - 9 * q^81 + 58 * q^82 + 12 * q^83 - 8 * q^84 + 63 * q^86 - 97 * q^88 + 118 * q^89 - 4 * q^90 - q^91 + 98 * q^92 - 28 * q^93 - 99 * q^94 - 45 * q^95 + q^96 + 50 * q^97 - 186 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more