LMFDB - Embedded newform 462.2.k.g.89.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(89,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("462.89");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.k (of order $6$, degree $2$, 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:	$3.68908857338$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 19 x^{18} - 42 x^{17} + 62 x^{16} - 42 x^{15} - 25 x^{14} + 6 x^{13} + 445 x^{12} + \cdots + 59049 $ x^20 - 6x^19 + 19x^18 - 42x^17 + 62x^16 - 42x^15 - 25x^14 + 6x^13 + 445x^12 - 1764x^11 + 3864x^10 - 5292x^9 + 4005x^8 + 162x^7 - 2025x^6 - 10206x^5 + 45198x^4 - 91854x^3 + 124659x^2 - 118098*x + 59049
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			89.8
Root			$1.44390 - 0.956629i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.106512 + 1.72877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0938814 + 0.162607i) q^{5} +(-0.772144 + 1.55042i) q^{6} +(-2.64498 - 0.0638828i) q^{7} +1.00000i q^{8} +(-2.97731 + 0.368271i) q^{9} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.106512 + 1.72877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0938814 + 0.162607i) q^{5} +(-0.772144 + 1.55042i) q^{6} +(-2.64498 - 0.0638828i) q^{7} +1.00000i q^{8} +(-2.97731 + 0.368271i) q^{9} +(-0.162607 + 0.0938814i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.44390 + 0.956629i) q^{12} +4.70512i q^{13} +(-2.25868 - 1.37781i) q^{14} +(-0.291111 - 0.144980i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.48653 + 2.57475i) q^{17} +(-2.76256 - 1.16972i) q^{18} +(1.61065 + 0.929908i) q^{19} -0.187763 q^{20} +(-0.171284 - 4.57937i) q^{21} -1.00000 q^{22} +(-2.05318 - 1.18540i) q^{23} +(-1.72877 + 0.106512i) q^{24} +(2.48237 + 4.29960i) q^{25} +(-2.35256 + 4.07475i) q^{26} +(-0.953778 - 5.10787i) q^{27} +(-1.26717 - 2.32256i) q^{28} -6.25425i q^{29} +(-0.179619 - 0.271112i) q^{30} +(8.78290 - 5.07081i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.956629 - 1.44390i) q^{33} +2.97307i q^{34} +(0.258702 - 0.424096i) q^{35} +(-1.80759 - 2.39429i) q^{36} +(-2.73168 + 4.73141i) q^{37} +(0.929908 + 1.61065i) q^{38} +(-8.13408 + 0.501153i) q^{39} +(-0.162607 - 0.0938814i) q^{40} +0.187763 q^{41} +(2.14135 - 4.05150i) q^{42} +7.86942 q^{43} +(-0.866025 - 0.500000i) q^{44} +(0.219631 - 0.518707i) q^{45} +(-1.18540 - 2.05318i) q^{46} +(2.79290 - 4.83744i) q^{47} +(-1.55042 - 0.772144i) q^{48} +(6.99184 + 0.337937i) q^{49} +4.96475i q^{50} +(-4.29283 + 2.84412i) q^{51} +(-4.07475 + 2.35256i) q^{52} +(-9.50430 + 5.48731i) q^{53} +(1.72794 - 4.90043i) q^{54} -0.187763i q^{55} +(0.0638828 - 2.64498i) q^{56} +(-1.43605 + 2.88349i) q^{57} +(3.12712 - 5.41634i) q^{58} +(2.32869 + 4.03341i) q^{59} +(-0.0199991 - 0.324599i) q^{60} +(10.8936 + 6.28942i) q^{61} +10.1416 q^{62} +(7.89845 - 0.783871i) q^{63} -1.00000 q^{64} +(-0.765087 - 0.441723i) q^{65} +(-0.106512 - 1.72877i) q^{66} +(-1.28973 - 2.23388i) q^{67} +(-1.48653 + 2.57475i) q^{68} +(1.83060 - 3.67573i) q^{69} +(0.436091 - 0.237927i) q^{70} -13.5203i q^{71} +(-0.368271 - 2.97731i) q^{72} +(-13.8911 + 8.02001i) q^{73} +(-4.73141 + 2.73168i) q^{74} +(-7.16862 + 4.74942i) q^{75} +1.85982i q^{76} +(2.32256 - 1.26717i) q^{77} +(-7.29490 - 3.63303i) q^{78} +(-3.99299 + 6.91606i) q^{79} +(-0.0938814 - 0.162607i) q^{80} +(8.72875 - 2.19292i) q^{81} +(0.162607 + 0.0938814i) q^{82} +14.7454 q^{83} +(3.88021 - 2.43802i) q^{84} -0.558232 q^{85} +(6.81512 + 3.93471i) q^{86} +(10.8122 - 0.666155i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(4.29254 - 7.43490i) q^{89} +(0.449559 - 0.339398i) q^{90} +(0.300576 - 12.4449i) q^{91} -2.37080i q^{92} +(9.70177 + 14.6435i) q^{93} +(4.83744 - 2.79290i) q^{94} +(-0.302420 + 0.174602i) q^{95} +(-0.956629 - 1.44390i) q^{96} -1.00552i q^{97} +(5.88614 + 3.78858i) q^{98} +(2.39429 - 1.80759i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	$ 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) $ 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/462\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	0.106512	+	1.72877i	0.0614949	+	0.998107i
$3$	0.106512	+	1.72877i	0.0614949	+	0.998107i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−0.0938814	+	0.162607i	−0.0419851	+	0.0727202i	−0.886254	−	0.463199i	$-0.846702\pi$
$5$	−0.0938814	+	0.162607i	−0.0419851	+	0.0727202i	0.844269	+	0.535919i	$0.180035\pi$
$6$	−0.772144	+	1.55042i	−0.315226	+	0.632955i
$7$	−2.64498	−	0.0638828i	−0.999708	−	0.0241454i
$7$	−2.64498	−	0.0638828i	−0.999708	−	0.0241454i
$8$			1.00000i			0.353553i
$9$	−2.97731	+	0.368271i	−0.992437	+	0.122757i
$10$	−0.162607	+	0.0938814i	−0.0514210	+	0.0296879i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$11$	−0.866025	+	0.500000i	−0.261116	+	0.150756i
$12$	−1.44390	+	0.956629i	−0.416819	+	0.276155i
$13$			4.70512i			1.30497i	0.757804	+	0.652483i	$0.226273\pi$
$13$			4.70512i			1.30497i	−0.757804	+	0.652483i	$0.773727\pi$
$14$	−2.25868	−	1.37781i	−0.603657	−	0.368236i
$15$	−0.291111	−	0.144980i	−0.0751645	−	0.0374337i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.48653	+	2.57475i	0.360538	+	0.624469i	0.988049	−	0.154138i	$-0.0492599\pi$
$17$	1.48653	+	2.57475i	0.360538	+	0.624469i	−0.627512	+	0.778607i	$0.715927\pi$
$18$	−2.76256	−	1.16972i	−0.651142	−	0.275706i
$19$	1.61065	+	0.929908i	0.369508	+	0.213336i	0.673244	−	0.739421i	$-0.264901\pi$
$19$	1.61065	+	0.929908i	0.369508	+	0.213336i	−0.303735	+	0.952756i	$0.598234\pi$
$20$	−0.187763			−0.0419851
$21$	−0.171284	−	4.57937i	−0.0373773	−	0.999301i
$22$	−1.00000			−0.213201
$23$	−2.05318	−	1.18540i	−0.428117	−	0.247173i	0.270427	−	0.962740i	$-0.412835\pi$
$23$	−2.05318	−	1.18540i	−0.428117	−	0.247173i	−0.698544	+	0.715567i	$0.746168\pi$
$24$	−1.72877	+	0.106512i	−0.352884	+	0.0217417i
$25$	2.48237	+	4.29960i	0.496475	+	0.859919i
$26$	−2.35256	+	4.07475i	−0.461375	+	0.799125i
$27$	−0.953778	−	5.10787i	−0.183555	−	0.983010i
$28$	−1.26717	−	2.32256i	−0.239472	−	0.438923i
$29$		−	6.25425i		−	1.16139i	−0.814123	−	0.580693i	$-0.802782\pi$
$29$		−	6.25425i		−	1.16139i	0.814123	−	0.580693i	$-0.197218\pi$
$30$	−0.179619	−	0.271112i	−0.0327939	−	0.0494980i
$31$	8.78290	−	5.07081i	1.57746	−	0.910745i	0.582243	−	0.813015i	$-0.302175\pi$
$31$	8.78290	−	5.07081i	1.57746	−	0.910745i	0.995213	−	0.0977300i	$-0.0311582\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	−0.956629	−	1.44390i	−0.166528	−	0.251352i
$34$			2.97307i			0.509877i
$35$	0.258702	−	0.424096i	0.0437287	−	0.0716853i
$36$	−1.80759	−	2.39429i	−0.301265	−	0.399048i
$37$	−2.73168	+	4.73141i	−0.449086	+	0.777840i	−0.998327	−	0.0578244i	$-0.981584\pi$
$37$	−2.73168	+	4.73141i	−0.449086	+	0.777840i	0.549241	+	0.835664i	$0.314917\pi$
$38$	0.929908	+	1.61065i	0.150851	+	0.261282i
$39$	−8.13408	+	0.501153i	−1.30250	+	0.0802487i
$40$	−0.162607	−	0.0938814i	−0.0257105	−	0.0148440i
$41$	0.187763			0.0293236			0.0146618	−	0.999893i	$-0.495333\pi$
$41$	0.187763			0.0293236			0.0146618	+	0.999893i	$0.495333\pi$
$42$	2.14135	−	4.05150i	0.330418	−	0.625159i
$43$	7.86942			1.20008			0.600038	−	0.799972i	$-0.295152\pi$
$43$	7.86942			1.20008			0.600038	+	0.799972i	$0.295152\pi$
$44$	−0.866025	−	0.500000i	−0.130558	−	0.0753778i
$45$	0.219631	−	0.518707i	0.0327406	−	0.0773242i
$46$	−1.18540	−	2.05318i	−0.174778	−	0.302724i
$47$	2.79290	−	4.83744i	0.407386	−	0.705613i	−0.587210	−	0.809434i	$-0.699774\pi$
$47$	2.79290	−	4.83744i	0.407386	−	0.705613i	0.994596	+	0.103822i	$0.0331071\pi$
$48$	−1.55042	−	0.772144i	−0.223783	−	0.111449i
$49$	6.99184	+	0.337937i	0.998834	+	0.0482768i
$50$			4.96475i			0.702121i
$51$	−4.29283	+	2.84412i	−0.601116	+	0.398257i
$52$	−4.07475	+	2.35256i	−0.565067	+	0.326241i
$53$	−9.50430	+	5.48731i	−1.30552	+	0.753740i	−0.981344	−	0.192258i	$-0.938419\pi$
$53$	−9.50430	+	5.48731i	−1.30552	+	0.753740i	−0.324172	+	0.945998i	$0.605086\pi$
$54$	1.72794	−	4.90043i	0.235143	−	0.666864i
$55$		−	0.187763i		−	0.0253179i
$56$	0.0638828	−	2.64498i	0.00853670	−	0.353450i
$57$	−1.43605	+	2.88349i	−0.190209	+	0.381928i
$58$	3.12712	−	5.41634i	0.410612	−	0.711200i
$59$	2.32869	+	4.03341i	0.303170	+	0.525105i	0.976852	−	0.213916i	$-0.0686218\pi$
$59$	2.32869	+	4.03341i	0.303170	+	0.525105i	−0.673682	+	0.739021i	$0.735288\pi$
$60$	−0.0199991	−	0.324599i	−0.00258187	−	0.0419056i
$61$	10.8936	+	6.28942i	1.39478	+	0.805278i	0.993840	−	0.110825i	$-0.0353495\pi$
$61$	10.8936	+	6.28942i	1.39478	+	0.805278i	0.400942	+	0.916103i	$0.368683\pi$
$62$	10.1416			1.28799
$63$	7.89845	−	0.783871i	0.995111	−	0.0987585i
$64$	−1.00000			−0.125000
$65$	−0.765087	−	0.441723i	−0.0948974	−	0.0547890i
$66$	−0.106512	−	1.72877i	−0.0131108	−	0.212797i
$67$	−1.28973	−	2.23388i	−0.157566	−	0.272912i	0.776424	−	0.630210i	$-0.217031\pi$
$67$	−1.28973	−	2.23388i	−0.157566	−	0.272912i	−0.933990	+	0.357298i	$0.883698\pi$
$68$	−1.48653	+	2.57475i	−0.180269	+	0.312235i
$69$	1.83060	−	3.67573i	0.220378	−	0.442506i
$70$	0.436091	−	0.237927i	0.0521228	−	0.0284377i
$71$		−	13.5203i		−	1.60457i	−0.596944	−	0.802283i	$-0.703619\pi$
$71$		−	13.5203i		−	1.60457i	0.596944	−	0.802283i	$-0.296381\pi$
$72$	−0.368271	−	2.97731i	−0.0434012	−	0.350879i
$73$	−13.8911	+	8.02001i	−1.62583	+	0.938671i	−0.640507	+	0.767953i	$0.721276\pi$
$73$	−13.8911	+	8.02001i	−1.62583	+	0.938671i	−0.985320	+	0.170719i	$0.945391\pi$
$74$	−4.73141	+	2.73168i	−0.550016	+	0.317552i
$75$	−7.16862	+	4.74942i	−0.827761	+	0.548416i
$76$			1.85982i			0.213336i
$77$	2.32256	−	1.26717i	0.264680	−	0.144407i
$78$	−7.29490	−	3.63303i	−0.825985	−	0.411360i
$79$	−3.99299	+	6.91606i	−0.449246	+	0.778117i	−0.998337	−	0.0576452i	$-0.981641\pi$
$79$	−3.99299	+	6.91606i	−0.449246	+	0.778117i	0.549091	+	0.835763i	$0.314974\pi$
$80$	−0.0938814	−	0.162607i	−0.0104963	−	0.0181801i
$81$	8.72875	−	2.19292i	0.969861	−	0.243657i
$82$	0.162607	+	0.0938814i	0.0179570	+	0.0103675i
$83$	14.7454			1.61851			0.809256	−	0.587456i	$-0.199870\pi$
$83$	14.7454			1.61851			0.809256	+	0.587456i	$0.199870\pi$
$84$	3.88021	−	2.43802i	0.423366	−	0.266010i
$85$	−0.558232			−0.0605488
$86$	6.81512	+	3.93471i	0.734893	+	0.424291i
$87$	10.8122	−	0.666155i	1.15919	−	0.0714193i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	4.29254	−	7.43490i	0.455008	−	0.788097i	−0.543680	−	0.839292i	$-0.682970\pi$
$89$	4.29254	−	7.43490i	0.455008	−	0.788097i	0.998689	+	0.0511950i	$0.0163030\pi$
$90$	0.449559	−	0.339398i	0.0473877	−	0.0357757i
$91$	0.300576	−	12.4449i	0.0315089	−	1.30458i
$92$		−	2.37080i		−	0.247173i
$93$	9.70177	+	14.6435i	1.00603	+	1.51846i
$94$	4.83744	−	2.79290i	0.498944	−	0.288065i
$95$	−0.302420	+	0.174602i	−0.0310276	+	0.0179138i
$96$	−0.956629	−	1.44390i	−0.0976355	−	0.147368i
$97$		−	1.00552i		−	0.102095i	−0.998696	−	0.0510474i	$-0.983744\pi$
$97$		−	1.00552i		−	0.102095i	0.998696	−	0.0510474i	$-0.0162559\pi$
$98$	5.88614	+	3.78858i	0.594590	+	0.382705i
$99$	2.39429	−	1.80759i	0.240635	−	0.181669i
$100$	−2.48237	+	4.29960i	−0.248237	+	0.429960i
$101$	8.20165	+	14.2057i	0.816094	+	1.41352i	0.908540	+	0.417799i	$0.137198\pi$
$101$	8.20165	+	14.2057i	0.816094	+	1.41352i	−0.0924454	+	0.995718i	$0.529468\pi$
$102$	−5.13976	+	0.316669i	−0.508912	+	0.0313549i
$103$	−4.39355	−	2.53662i	−0.432910	−	0.249940i	0.267676	−	0.963509i	$-0.413744\pi$
$103$	−4.39355	−	2.53662i	−0.432910	−	0.249940i	−0.700585	+	0.713569i	$0.747078\pi$
$104$	−4.70512			−0.461375
$105$	0.760720	+	0.402066i	0.0742387	+	0.0392376i
$106$	−10.9746			−1.06595
$107$	−0.0207756	−	0.0119948i	−0.00200846	−	0.00115958i	0.498995	−	0.866605i	$-0.333702\pi$
$107$	−0.0207756	−	0.0119948i	−0.00200846	−	0.00115958i	−0.501004	+	0.865445i	$0.667036\pi$
$108$	3.94665	−	3.37993i	0.379767	−	0.325234i
$109$	0.621447	+	1.07638i	0.0595239	+	0.103098i	0.894252	−	0.447564i	$-0.147708\pi$
$109$	0.621447	+	1.07638i	0.0595239	+	0.103098i	−0.834728	+	0.550663i	$0.814375\pi$
$110$	0.0938814	−	0.162607i	0.00895124	−	0.0155040i
$111$	−8.47050	−	4.21851i	−0.803984	−	0.400403i
$112$	1.37781	−	2.25868i	0.130191	−	0.213425i
$113$		−	12.6838i		−	1.19320i	−0.802541	−	0.596598i	$-0.796519\pi$
$113$		−	12.6838i		−	1.19320i	0.802541	−	0.596598i	$-0.203481\pi$
$114$	−2.68540	+	1.77915i	−0.251511	+	0.166633i
$115$	0.385510	−	0.222574i	0.0359490	−	0.0207552i
$116$	5.41634	−	3.12712i	0.502894	−	0.290346i
$117$	−1.73276	−	14.0086i	−0.160194	−	1.29510i
$118$			4.65738i			0.428747i
$119$	−3.76737	−	6.90513i	−0.345354	−	0.632993i
$120$	0.144980	−	0.291111i	0.0132348	−	0.0265747i
$121$	0.500000	−	0.866025i	0.0454545	−	0.0787296i
$122$	6.28942	+	10.8936i	0.569417	+	0.986260i
$123$	0.0199991	+	0.324599i	0.00180325	+	0.0292681i
$124$	8.78290	+	5.07081i	0.788728	+	0.455372i
$125$	−1.87101			−0.167348
$126$	7.23220	+	3.27037i	0.644295	+	0.291348i
$127$	−5.24437			−0.465363			−0.232681	−	0.972553i	$-0.574750\pi$
$127$	−5.24437			−0.465363			−0.232681	+	0.972553i	$0.574750\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	0.838191	+	13.6044i	0.0737986	+	1.19780i
$130$	−0.441723	−	0.765087i	−0.0387417	−	0.0671026i
$131$	1.00216	−	1.73580i	0.0875595	−	0.151657i	−0.818920	−	0.573908i	$-0.805427\pi$
$131$	1.00216	−	1.73580i	0.0875595	−	0.151657i	0.906479	+	0.422251i	$0.138760\pi$
$132$	0.772144	−	1.55042i	0.0672065	−	0.134947i
$133$	−4.20073	−	2.56248i	−0.364249	−	0.222195i
$134$		−	2.57946i		−	0.222832i
$135$	0.920119	+	0.324443i	0.0791912	+	0.0279236i
$136$	−2.57475	+	1.48653i	−0.220783	+	0.127469i
$137$	−7.81301	+	4.51084i	−0.667511	+	0.385387i	−0.795133	−	0.606435i	$-0.792599\pi$
$137$	−7.81301	+	4.51084i	−0.667511	+	0.385387i	0.127622	+	0.991823i	$0.459266\pi$
$138$	3.42321	−	2.26798i	0.291403	−	0.193063i
$139$			4.19064i			0.355445i	0.984081	+	0.177723i	$0.0568730\pi$
$139$			4.19064i			0.355445i	−0.984081	+	0.177723i	$0.943127\pi$
$140$	0.496629	+	0.0119948i	0.0419728	+	0.00101375i
$141$	8.66031	+	4.31304i	0.729329	+	0.363223i
$142$	6.76015	−	11.7089i	0.567300	−	0.982592i
$143$	−2.35256	−	4.07475i	−0.196731	−	0.340748i
$144$	1.16972	−	2.76256i	0.0974769	−	0.230213i
$145$	1.01699	+	0.587158i	0.0844562	+	0.0487608i
$146$	−16.0400			−1.32748
$147$	0.160500	+	12.1233i	0.0132378	+	0.999912i
$148$	−5.46337			−0.449086
$149$	−12.9762	−	7.49184i	−1.06306	−	0.613755i	−0.136780	−	0.990602i	$-0.543675\pi$
$149$	−12.9762	−	7.49184i	−1.06306	−	0.613755i	−0.926276	+	0.376846i	$0.877009\pi$
$150$	−8.58292	+	0.528807i	−0.700792	+	0.0431769i
$151$	0.274177	+	0.474889i	0.0223122	+	0.0386459i	0.876966	−	0.480553i	$-0.159564\pi$
$151$	0.274177	+	0.474889i	0.0223122	+	0.0386459i	−0.854654	+	0.519198i	$0.826231\pi$
$152$	−0.929908	+	1.61065i	−0.0754255	+	0.130641i
$153$	−5.37408	−	7.11839i	−0.434469	−	0.575488i
$154$	2.64498	+	0.0638828i	0.213139	+	0.00514782i
$155$			1.90422i			0.152951i
$156$	−4.50105	−	6.79375i	−0.360373	−	0.543935i
$157$	16.6072	−	9.58817i	1.32540	−	0.765219i	0.340814	−	0.940131i	$-0.389297\pi$
$157$	16.6072	−	9.58817i	1.32540	−	0.765219i	0.984584	+	0.174911i	$0.0559639\pi$
$158$	−6.91606	+	3.99299i	−0.550212	+	0.317665i
$159$	−10.4986	−	15.8463i	−0.832596	−	1.25669i
$160$		−	0.187763i		−	0.0148440i
$161$	5.35488	+	3.26653i	0.422024	+	0.257438i
$162$	8.65578	+	2.46526i	0.680062	+	0.193689i
$163$	−0.406286	+	0.703707i	−0.0318227	+	0.0551186i	−0.881498	−	0.472187i	$-0.843465\pi$
$163$	−0.406286	+	0.703707i	−0.0318227	+	0.0551186i	0.849675	+	0.527306i	$0.176798\pi$
$164$	0.0938814	+	0.162607i	0.00733091	+	0.0126975i
$165$	0.324599	−	0.0199991i	0.0252700	−	0.00155692i
$166$	12.7698	+	7.37268i	0.991132	+	0.572231i
$167$	−14.3973			−1.11409			−0.557047	−	0.830481i	$-0.688066\pi$
$167$	−14.3973			−1.11409			−0.557047	+	0.830481i	$0.688066\pi$
$168$	4.57937	−	0.171284i	0.353306	−	0.0132149i
$169$	−9.13815			−0.702935
$170$	−0.483443	−	0.279116i	−0.0370784	−	0.0214072i
$171$	−5.13786	−	2.17547i	−0.392902	−	0.166362i
$172$	3.93471	+	6.81512i	0.300019	+	0.519648i
$173$	−0.936038	+	1.62126i	−0.0711656	+	0.123262i	−0.899412	−	0.437101i	$-0.856005\pi$
$173$	−0.936038	+	1.62126i	−0.0711656	+	0.123262i	0.828247	+	0.560363i	$0.189339\pi$
$174$	9.69670	+	4.82918i	0.735105	+	0.366099i
$175$	−6.29116	−	11.5309i	−0.475567	−	0.871656i
$176$		−	1.00000i		−	0.0753778i
$177$	−6.72482	+	4.45538i	−0.505468	+	0.334887i
$178$	7.43490	−	4.29254i	0.557269	−	0.321739i
$179$	−3.52389	+	2.03452i	−0.263388	+	0.152067i	−0.625879	−	0.779920i	$-0.715260\pi$
$179$	−3.52389	+	2.03452i	−0.263388	+	0.152067i	0.362491	+	0.931987i	$0.381926\pi$
$180$	0.559028	−	0.0691477i	0.0416675	−	0.00515396i
$181$		−	13.0237i		−	0.968044i	−0.875056	−	0.484022i	$-0.839175\pi$
$181$		−	13.0237i		−	0.968044i	0.875056	−	0.484022i	$-0.160825\pi$
$182$	6.48278	−	10.6274i	0.480536	−	0.787752i
$183$	−9.71268	+	19.5025i	−0.717982	+	1.44166i
$184$	1.18540	−	2.05318i	0.0873890	−	0.151362i
$185$	−0.512909	−	0.888384i	−0.0377098	−	0.0653153i
$186$	1.08021	+	17.5326i	0.0792047	+	1.28555i
$187$	−2.57475	−	1.48653i	−0.188285	−	0.108706i
$188$	5.58579			0.407386
$189$	2.19642	+	13.5711i	0.159766	+	0.987155i
$190$	−0.349204			−0.0253340
$191$	4.63286	+	2.67479i	0.335222	+	0.193541i	0.658157	−	0.752880i	$-0.271336\pi$
$191$	4.63286	+	2.67479i	0.335222	+	0.193541i	−0.322935	+	0.946421i	$0.604670\pi$
$192$	−0.106512	−	1.72877i	−0.00768687	−	0.124763i
$193$	6.59123	+	11.4163i	0.474447	+	0.821766i	0.999572	−	0.0292588i	$-0.00931468\pi$
$193$	6.59123	+	11.4163i	0.474447	+	0.821766i	−0.525125	+	0.851025i	$0.675981\pi$
$194$	0.502758	−	0.870803i	0.0360959	−	0.0625200i
$195$	0.682148	−	1.36971i	0.0488496	−	0.0980870i
$196$	3.20326	+	6.22408i	0.228804	+	0.444577i
$197$		−	14.6635i		−	1.04473i	−0.852721	−	0.522366i	$-0.825049\pi$
$197$		−	14.6635i		−	1.04473i	0.852721	−	0.522366i	$-0.174951\pi$
$198$	2.97731	−	0.368271i	0.211588	−	0.0261719i
$199$	−1.82774	+	1.05525i	−0.129565	+	0.0748046i	−0.563382	−	0.826197i	$-0.690500\pi$
$199$	−1.82774	+	1.05525i	−0.129565	+	0.0748046i	0.433816	+	0.901001i	$0.357167\pi$
$200$	−4.29960	+	2.48237i	−0.304027	+	0.175530i
$201$	3.72450	−	2.46759i	0.262706	−	0.174050i
$202$			16.4033i			1.15413i
$203$	−0.399539	+	16.5424i	−0.0280421	+	1.16105i
$204$	−4.60950	−	2.29564i	−0.322729	−	0.160727i
$205$	−0.0176274	+	0.0305316i	−0.00123115	+	0.00213242i
$206$	−2.53662	−	4.39355i	−0.176735	−	0.306113i
$207$	6.54949	+	2.77318i	0.455221	+	0.192750i
$208$	−4.07475	−	2.35256i	−0.282533	−	0.163121i
$209$	−1.85982			−0.128646
$210$	0.457770	+	0.728560i	0.0315891	+	0.0502754i
$211$	−5.07097			−0.349100			−0.174550	−	0.984648i	$-0.555847\pi$
$211$	−5.07097			−0.349100			−0.174550	+	0.984648i	$0.555847\pi$
$212$	−9.50430	−	5.48731i	−0.652758	−	0.376870i
$213$	23.3735	−	1.44008i	1.60153	−	0.0986726i
$214$	−0.0119948	−	0.0207756i	−0.000819949	−	0.00142019i
$215$	−0.738793	+	1.27963i	−0.0503853	+	0.0872698i
$216$	5.10787	−	0.953778i	0.347546	−	0.0648963i
$217$	−23.5545	+	12.8511i	−1.59899	+	0.872391i
$218$			1.24289i			0.0841795i
$219$	−15.3443	−	23.1603i	−1.03687	−	1.56503i
$220$	0.162607	−	0.0938814i	0.0109630	−	0.00632948i
$221$	−12.1145	+	6.99432i	−0.814911	+	0.470489i
$222$	−5.22641	−	7.88858i	−0.350774	−	0.529447i
$223$		−	12.6276i		−	0.845610i	−0.906221	−	0.422805i	$-0.861046\pi$
$223$		−	12.6276i		−	0.845610i	0.906221	−	0.422805i	$-0.138954\pi$
$224$	2.32256	−	1.26717i	0.155183	−	0.0846661i
$225$	−8.97421	−	11.8870i	−0.598281	−	0.792470i
$226$	6.34192	−	10.9845i	0.421858	−	0.730680i
$227$	−0.180173	−	0.312069i	−0.0119585	−	0.0207128i	0.859984	−	0.510321i	$-0.170473\pi$
$227$	−0.180173	−	0.312069i	−0.0119585	−	0.0207128i	−0.871943	+	0.489608i	$0.837140\pi$
$228$	−3.21520	+	0.198093i	−0.212932	+	0.0131191i
$229$	9.52022	+	5.49650i	0.629114	+	0.363219i	0.780409	−	0.625270i	$-0.215011\pi$
$229$	9.52022	+	5.49650i	0.629114	+	0.363219i	−0.151295	+	0.988489i	$0.548344\pi$
$230$	0.445149			0.0293522
$231$	2.43802	+	3.88021i	0.160410	+	0.255299i
$232$	6.25425			0.410612
$233$	22.0707	+	12.7425i	1.44590	+	0.834791i	0.998234	−	0.0594100i	$-0.0189219\pi$
$233$	22.0707	+	12.7425i	1.44590	+	0.834791i	0.447666	+	0.894201i	$0.352255\pi$
$234$	5.50369	−	12.9982i	0.359787	−	0.849718i
$235$	0.524402	+	0.908291i	0.0342082	+	0.0592504i
$236$	−2.32869	+	4.03341i	−0.151585	+	0.262553i
$237$	−12.3816	−	6.16632i	−0.804271	−	0.400546i
$238$	0.189928	−	7.86371i	0.0123112	−	0.509728i
$239$		−	7.73209i		−	0.500148i	−0.968227	−	0.250074i	$-0.919545\pi$
$239$		−	7.73209i		−	0.500148i	0.968227	−	0.250074i	$-0.0804549\pi$
$240$	0.271112	−	0.179619i	0.0175002	−	0.0115944i
$241$	−5.73736	+	3.31247i	−0.369576	+	0.213375i	−0.673273	−	0.739394i	$-0.735112\pi$
$241$	−5.73736	+	3.31247i	−0.369576	+	0.213375i	0.303697	+	0.952769i	$0.401779\pi$
$242$	0.866025	−	0.500000i	0.0556702	−	0.0321412i
$243$	4.72077	+	14.8565i	0.302838	+	0.953042i
$244$			12.5788i			0.805278i
$245$	−0.711355	+	1.10520i	−0.0454468	+	0.0706085i
$246$	−0.144980	+	0.291111i	−0.00924358	+	0.0185605i
$247$	−4.37533	+	7.57829i	−0.278396	+	0.482195i
$248$	5.07081	+	8.78290i	0.321997	+	0.557715i
$249$	1.57056	+	25.4914i	0.0995303	+	1.61545i
$250$	−1.62034	−	0.935505i	−0.102479	−	0.0591665i
$251$	−25.8784			−1.63343			−0.816714	−	0.577042i	$-0.804207\pi$
$251$	−25.8784			−1.63343			−0.816714	+	0.577042i	$0.804207\pi$
$252$	4.62808	+	6.44832i	0.291542	+	0.406206i
$253$	2.37080			0.149051
$254$	−4.54176	−	2.62219i	−0.284975	−	0.164531i
$255$	−0.0594586	−	0.965056i	−0.00372344	−	0.0604342i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.64666	+	6.31620i	−0.227473	+	0.393994i	−0.957058	−	0.289895i	$-0.906380\pi$
$257$	−3.64666	+	6.31620i	−0.227473	+	0.393994i	0.729586	+	0.683889i	$0.239713\pi$
$258$	−6.07633	+	12.2009i	−0.378296	+	0.759594i
$259$	7.52750	−	12.3400i	0.467736	−	0.766770i
$260$		−	0.883447i		−	0.0547890i
$261$	2.30326	+	18.6208i	0.142568	+	1.15260i
$262$	1.73580	−	1.00216i	0.107238	−	0.0619139i
$263$	12.9008	−	7.44827i	0.795496	−	0.459280i	−0.0463977	−	0.998923i	$-0.514774\pi$
$263$	12.9008	−	7.44827i	0.795496	−	0.459280i	0.841894	+	0.539643i	$0.181441\pi$
$264$	1.44390	−	0.956629i	0.0888662	−	0.0588764i
$265$		−	2.06063i		−	0.126583i
$266$	−2.35670	−	4.31954i	−0.144498	−	0.264848i
$267$	13.3105	+	6.62892i	0.814586	+	0.405683i
$268$	1.28973	−	2.23388i	0.0787829	−	0.136456i
$269$	−7.12064	−	12.3333i	−0.434153	−	0.751975i	0.563073	−	0.826407i	$-0.309619\pi$
$269$	−7.12064	−	12.3333i	−0.434153	−	0.751975i	−0.997226	+	0.0744323i	$0.976286\pi$
$270$	0.634625	+	0.741035i	0.0386221	+	0.0450980i
$271$	−12.3382	−	7.12345i	−0.749491	−	0.432719i	0.0760187	−	0.997106i	$-0.475779\pi$
$271$	−12.3382	−	7.12345i	−0.749491	−	0.432719i	−0.825510	+	0.564387i	$0.809112\pi$
$272$	−2.97307			−0.180269
$273$	21.5465	−	0.805912i	1.30405	−	0.0487760i
$274$	−9.02169			−0.545020
$275$	−4.29960	−	2.48237i	−0.259275	−	0.149693i
$276$	4.09858	−	0.252520i	0.246705	−	0.0151999i
$277$	−5.59049	−	9.68302i	−0.335900	−	0.581796i	0.647757	−	0.761847i	$-0.275707\pi$
$277$	−5.59049	−	9.68302i	−0.335900	−	0.581796i	−0.983657	+	0.180051i	$0.942374\pi$
$278$	−2.09532	+	3.62920i	−0.125669	+	0.217665i
$279$	−24.2820	+	18.3319i	−1.45373	+	1.09750i
$280$	0.424096	+	0.258702i	0.0253446	+	0.0154604i
$281$			17.4964i			1.04375i	0.853023	+	0.521874i	$0.174767\pi$
$281$			17.4964i			1.04375i	−0.853023	+	0.521874i	$0.825233\pi$
$282$	5.34353	+	8.06535i	0.318203	+	0.480285i
$283$	−5.56926	+	3.21541i	−0.331058	+	0.191137i	−0.656311	−	0.754491i	$-0.727884\pi$
$283$	−5.56926	+	3.21541i	−0.331058	+	0.191137i	0.325253	+	0.945627i	$0.394551\pi$
$284$	11.7089	−	6.76015i	0.694797	−	0.401141i
$285$	−0.334059	−	0.504218i	−0.0197879	−	0.0298673i
$286$		−	4.70512i		−	0.278220i
$287$	−0.496629	−	0.0119948i	−0.0293151	−	0.000708032i
$288$	2.39429	−	1.80759i	0.141085	−	0.106513i
$289$	4.08043	−	7.06751i	0.240025	−	0.415736i
$290$	0.587158	+	1.01699i	0.0344791	+	0.0597196i
$291$	1.73831	−	0.107100i	0.101902	−	0.00627831i
$292$	−13.8911	−	8.02001i	−0.812913	−	0.469336i
$293$	8.00890			0.467885			0.233942	−	0.972250i	$-0.424837\pi$
$293$	8.00890			0.467885			0.233942	+	0.972250i	$0.424837\pi$
$294$	−5.92265	+	10.5793i	−0.345416	+	0.616999i
$295$	−0.874483			−0.0509144
$296$	−4.73141	−	2.73168i	−0.275008	−	0.158776i
$297$	3.37993	+	3.94665i	0.196123	+	0.229008i
$298$	−7.49184	−	12.9762i	−0.433991	−	0.751694i
$299$	5.57746	−	9.66044i	0.322553	−	0.558677i
$300$	−7.69743	−	3.83350i	−0.444411	−	0.221327i
$301$	−20.8145	−	0.502721i	−1.19973	−	0.0289763i
$302$			0.548354i			0.0315542i
$303$	−23.6848	+	15.6919i	−1.36066	+	0.901474i
$304$	−1.61065	+	0.929908i	−0.0923770	+	0.0533339i
$305$	−2.04541	+	1.18092i	−0.117120	+	0.0676193i
$306$	−1.09490	−	8.85175i	−0.0625910	−	0.506021i
$307$			2.11535i			0.120729i	0.998176	+	0.0603646i	$0.0192263\pi$
$307$			2.11535i			0.120729i	−0.998176	+	0.0603646i	$0.980774\pi$
$308$	2.25868	+	1.37781i	0.128700	+	0.0785082i
$309$	3.91727	−	7.86563i	0.222846	−	0.447460i
$310$	−0.952110	+	1.64910i	−0.0540762	+	0.0936628i
$311$	−2.71729	−	4.70648i	−0.154083	−	0.266880i	0.778642	−	0.627469i	$-0.215909\pi$
$311$	−2.71729	−	4.70648i	−0.154083	−	0.266880i	−0.932725	+	0.360589i	$0.882576\pi$
$312$	−0.501153	−	8.13408i	−0.0283722	−	0.460502i
$313$	24.6820	+	14.2502i	1.39511	+	0.805468i	0.993875	−	0.110507i	$-0.0352474\pi$
$313$	24.6820	+	14.2502i	1.39511	+	0.805468i	0.401236	+	0.915975i	$0.368581\pi$
$314$	19.1763			1.08218
$315$	−0.614055	+	1.35794i	−0.0345981	+	0.0765111i
$316$	−7.98598			−0.449246
$317$	−23.5911	−	13.6203i	−1.32501	−	0.764995i	−0.340486	−	0.940249i	$-0.610592\pi$
$317$	−23.5911	−	13.6203i	−1.32501	−	0.764995i	−0.984523	+	0.175255i	$0.943925\pi$
$318$	−1.16893	−	18.9726i	−0.0655505	−	1.06393i
$319$	3.12712	+	5.41634i	0.175085	+	0.303257i
$320$	0.0938814	−	0.162607i	0.00524813	−	0.00909003i
$321$	0.0185235	−	0.0371939i	0.00103388	−	0.00207596i
$322$	3.00420	+	5.50633i	0.167418	+	0.306856i
$323$			5.52936i			0.307662i
$324$	6.26350	+	6.46286i	0.347972	+	0.359048i
$325$	−20.2301	+	11.6799i	−1.12216	+	0.647882i
$326$	−0.703707	+	0.406286i	−0.0389747	+	0.0225021i
$327$	−1.79462	+	1.18899i	−0.0992428	+	0.0657512i
$328$			0.187763i			0.0103675i
$329$	−7.69618	+	12.6165i	−0.424304	+	0.695571i
$330$	0.291111	+	0.144980i	0.0160251	+	0.00798088i
$331$	16.9054	−	29.2809i	0.929203	−	1.60943i	0.144544	−	0.989498i	$-0.453828\pi$
$331$	16.9054	−	29.2809i	0.929203	−	1.60943i	0.784659	−	0.619928i	$-0.212838\pi$
$332$	7.37268	+	12.7698i	0.404628	+	0.700836i
$333$	6.39062	−	15.0929i	0.350204	−	0.827085i
$334$	−12.4684	−	7.19863i	−0.682240	−	0.393892i
$335$	0.484328			0.0264616
$336$	4.05150	+	2.14135i	0.221027	+	0.116820i
$337$	−1.83289			−0.0998438			−0.0499219	−	0.998753i	$-0.515897\pi$
$337$	−1.83289			−0.0998438			−0.0499219	+	0.998753i	$0.515897\pi$
$338$	−7.91387	−	4.56908i	−0.430458	−	0.248525i
$339$	21.9275	−	1.35099i	1.19094	−	0.0733754i
$340$	−0.279116	−	0.483443i	−0.0151372	−	0.0262184i
$341$	−5.07081	+	8.78290i	−0.274600	+	0.475621i
$342$	−3.36178	−	4.45294i	−0.181784	−	0.240787i
$343$	−18.4717	−	1.34050i	−0.997377	−	0.0723800i
$344$			7.86942i			0.424291i
$345$	0.425842	+	0.642752i	0.0229266	+	0.0346046i
$346$	−1.62126	+	0.936038i	−0.0871597	+	0.0503217i
$347$	−21.4218	+	12.3679i	−1.14998	+	0.663942i	−0.948882	−	0.315630i	$-0.897784\pi$
$347$	−21.4218	+	12.3679i	−1.14998	+	0.663942i	−0.201098	+	0.979571i	$0.564451\pi$
$348$	5.98300	+	9.03054i	0.320722	+	0.484088i
$349$		−	5.86269i		−	0.313823i	−0.987613	−	0.156911i	$-0.949846\pi$
$349$		−	5.86269i		−	0.313823i	0.987613	−	0.156911i	$-0.0501537\pi$
$350$	0.317162	−	13.1317i	0.0169530	−	0.701916i
$351$	24.0331	−	4.48764i	1.28279	−	0.239532i
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	10.7068	+	18.5447i	0.569864	+	0.987033i	0.996579	+	0.0826469i	$0.0263374\pi$
$353$	10.7068	+	18.5447i	0.569864	+	0.987033i	−0.426715	+	0.904386i	$0.640329\pi$
$354$	−8.05155	+	0.496069i	−0.427935	+	0.0263657i
$355$	2.19850	+	1.26931i	0.116684	+	0.0673678i
$356$	8.58508			0.455008
$357$	11.5361	−	7.24841i	0.610557	−	0.383627i
$358$	−4.06903			−0.215055
$359$	6.11309	+	3.52939i	0.322636	+	0.186274i	0.652567	−	0.757731i	$-0.273692\pi$
$359$	6.11309	+	3.52939i	0.322636	+	0.186274i	−0.329931	+	0.944005i	$0.607025\pi$
$360$	0.518707	+	0.219631i	0.0273382	+	0.0115755i
$361$	−7.77054	−	13.4590i	−0.408976	−	0.708367i
$362$	6.51185	−	11.2789i	0.342255	−	0.592804i
$363$	1.55042	+	0.772144i	0.0813758	+	0.0405270i
$364$	10.9279	−	5.96217i	0.572779	−	0.312502i
$365$		−	3.01172i		−	0.157641i
$366$	−18.1627	+	12.0333i	−0.949377	+	0.628990i
$367$	−11.4611	+	6.61709i	−0.598267	+	0.345409i	−0.768359	−	0.640019i	$-0.778927\pi$
$367$	−11.4611	+	6.61709i	−0.598267	+	0.345409i	0.170093	+	0.985428i	$0.445593\pi$
$368$	2.05318	−	1.18540i	0.107029	−	0.0617933i
$369$	−0.559028	+	0.0691477i	−0.0291018	+	0.00359968i
$370$		−	1.02582i		−	0.0533297i
$371$	25.4892	−	13.9067i	1.32334	−	0.721998i
$372$	−7.83079	+	15.7237i	−0.406008	+	0.815238i
$373$	16.8385	−	29.1651i	0.871863	−	1.51011i	0.0117954	−	0.999930i	$-0.496245\pi$
$373$	16.8385	−	29.1651i	0.871863	−	1.51011i	0.860067	−	0.510180i	$-0.170421\pi$
$374$	−1.48653	−	2.57475i	−0.0768669	−	0.133137i
$375$	−0.199286	−	3.23455i	−0.0102911	−	0.167031i
$376$	4.83744	+	2.79290i	0.249472	+	0.144033i
$377$	29.4270			1.51557
$378$	−4.88341	+	12.8512i	−0.251176	+	0.660992i
$379$	−14.6738			−0.753741			−0.376870	−	0.926266i	$-0.623000\pi$
$379$	−14.6738			−0.753741			−0.376870	+	0.926266i	$0.623000\pi$
$380$	−0.302420	−	0.174602i	−0.0155138	−	0.00895690i
$381$	−0.558590	−	9.06633i	−0.0286174	−	0.464482i
$382$	2.67479	+	4.63286i	0.136854	+	0.237038i
$383$	−8.55052	+	14.8099i	−0.436911	+	0.756753i	−0.997449	−	0.0713759i	$-0.977261\pi$
$383$	−8.55052	+	14.8099i	−0.436911	+	0.756753i	0.560538	+	0.828129i	$0.310594\pi$
$384$	0.772144	−	1.55042i	0.0394033	−	0.0791194i
$385$	−0.0119948	+	0.496629i	−0.000611312	+	0.0253106i
$386$			13.1825i			0.670970i
$387$	−23.4297	+	2.89808i	−1.19100	+	0.147318i
$388$	0.870803	−	0.502758i	0.0442083	−	0.0255237i
$389$	31.2503	−	18.0424i	1.58445	−	0.914784i	0.590255	−	0.807217i	$-0.299027\pi$
$389$	31.2503	−	18.0424i	1.58445	−	0.914784i	0.994198	−	0.107567i	$-0.0343061\pi$
$390$	1.27561	−	0.845131i	0.0645932	−	0.0427948i
$391$		−	7.04856i		−	0.356461i
$392$	−0.337937	+	6.99184i	−0.0170684	+	0.353141i
$393$	3.10755	+	1.54763i	0.156755	+	0.0780676i
$394$	7.33176	−	12.6990i	0.369369	−	0.639765i
$395$	−0.749735	−	1.29858i	−0.0377233	−	0.0653386i
$396$	2.76256	+	1.16972i	0.138824	+	0.0587808i
$397$	11.0710	+	6.39186i	0.555639	+	0.320798i	0.751393	−	0.659855i	$-0.229382\pi$
$397$	11.0710	+	6.39186i	0.555639	+	0.320798i	−0.195754	+	0.980653i	$0.562716\pi$
$398$	−2.11050			−0.105790
$399$	3.98252	−	7.53504i	0.199375	−	0.377224i
$400$	−4.96475			−0.248237
$401$	19.4819	+	11.2479i	0.972880	+	0.561692i	0.900113	−	0.435657i	$-0.143484\pi$
$401$	19.4819	+	11.2479i	0.972880	+	0.561692i	0.0727666	+	0.997349i	$0.476817\pi$
$402$	4.45931	−	0.274745i	0.222410	−	0.0137030i
$403$	23.8588	+	41.3246i	1.18849	+	2.05853i
$404$	−8.20165	+	14.2057i	−0.408047	+	0.706758i
$405$	−0.462883	+	1.62523i	−0.0230009	+	0.0807585i
$406$	−8.61719	+	14.1263i	−0.427664	+	0.701078i
$407$		−	5.46337i		−	0.270809i
$408$	−2.84412	−	4.29283i	−0.140805	−	0.212527i
$409$	−11.0911	+	6.40347i	−0.548421	+	0.316631i	−0.748485	−	0.663152i	$-0.769218\pi$
$409$	−11.0911	+	6.40347i	−0.548421	+	0.316631i	0.200064	+	0.979783i	$0.435885\pi$
$410$	−0.0305316	+	0.0176274i	−0.00150785	+	0.000870557i
$411$	−8.63041	−	13.0265i	−0.425707	−	0.642548i
$412$		−	5.07324i		−	0.249940i
$413$	−5.90167	−	10.8171i	−0.290402	−	0.532272i
$414$	4.28543	+	5.67639i	0.210618	+	0.278979i
$415$	−1.38431	+	2.39770i	−0.0679533	+	0.117699i
$416$	−2.35256	−	4.07475i	−0.115344	−	0.199781i
$417$	−7.24466	+	0.446354i	−0.354772	+	0.0218581i
$418$	−1.61065	−	0.929908i	−0.0787794	−	0.0454833i
$419$	21.3181			1.04146			0.520728	−	0.853723i	$-0.325661\pi$
$419$	21.3181			1.04146			0.520728	+	0.853723i	$0.325661\pi$
$420$	0.0321608	+	0.859836i	0.00156929	+	0.0419557i
$421$	30.4927			1.48612			0.743062	−	0.669222i	$-0.233373\pi$
$421$	30.4927			1.48612			0.743062	+	0.669222i	$0.233373\pi$
$422$	−4.39158	−	2.53548i	−0.213779	−	0.123425i
$423$	−6.53383	+	15.4311i	−0.317686	+	0.750286i
$424$	−5.48731	−	9.50430i	−0.266487	−	0.461570i
$425$	−7.38026	+	12.7830i	−0.357995	+	0.620066i
$426$	20.9621	+	10.4396i	1.01562	+	0.505802i
$427$	−28.4116	−	17.3313i	−1.37493	−	0.838721i
$428$		−	0.0239896i		−	0.00115958i
$429$	6.79375	−	4.50105i	0.328005	−	0.217313i
$430$	−1.27963	+	0.738793i	−0.0617091	+	0.0356278i
$431$	24.2725	−	14.0137i	1.16916	−	0.675017i	0.215680	−	0.976464i	$-0.430803\pi$
$431$	24.2725	−	14.0137i	1.16916	−	0.675017i	0.953483	+	0.301447i	$0.0974697\pi$
$432$	4.90043	+	1.72794i	0.235772	+	0.0831355i
$433$		−	0.785465i		−	0.0377471i	−0.999822	−	0.0188735i	$-0.993992\pi$
$433$		−	0.785465i		−	0.0377471i	0.999822	−	0.0188735i	$-0.00600799\pi$
$434$	−26.8244	−	0.647875i	−1.28761	−	0.0310990i
$435$	−0.906741	+	1.82068i	−0.0434749	+	0.0872949i
$436$	−0.621447	+	1.07638i	−0.0297619	+	0.0515492i
$437$	−2.20463	−	3.81853i	−0.105462	−	0.182665i
$438$	−1.70846	−	27.7296i	−0.0816334	−	1.32497i
$439$	−13.5483	−	7.82210i	−0.646624	−	0.373328i	0.140538	−	0.990075i	$-0.455117\pi$
$439$	−13.5483	−	7.82210i	−0.646624	−	0.373328i	−0.787161	+	0.616747i	$0.788450\pi$
$440$	0.187763			0.00895124
$441$	−20.9413	+	1.56875i	−0.997206	+	0.0747023i
$442$	−13.9886			−0.665372
$443$	22.0499	+	12.7305i	1.04762	+	0.604846i	0.921983	−	0.387230i	$-0.126568\pi$
$443$	22.0499	+	12.7305i	1.04762	+	0.604846i	0.125641	+	0.992076i	$0.459901\pi$
$444$	−0.581916	−	9.44492i	−0.0276165	−	0.448236i
$445$	0.805979	+	1.39600i	0.0382071	+	0.0661766i
$446$	6.31382	−	10.9359i	0.298968	−	0.517828i
$447$	11.5696	−	23.2309i	0.547221	−	1.09879i
$448$	2.64498	+	0.0638828i	0.124964	+	0.00301818i
$449$		−	36.6323i		−	1.72878i	−0.502819	−	0.864392i	$-0.667704\pi$
$449$		−	36.6323i		−	1.72878i	0.502819	−	0.864392i	$-0.332296\pi$
$450$	−1.82837	−	14.7816i	−0.0861903	−	0.696811i
$451$	−0.162607	+	0.0938814i	−0.00765688	+	0.00442070i
$452$	10.9845	−	6.34192i	0.516669	−	0.298299i
$453$	−0.791771	+	0.524571i	−0.0372007	+	0.0246465i
$454$		−	0.360346i		−	0.0169119i
$455$	1.99542	+	1.21723i	0.0935468	+	0.0570644i
$456$	−2.88349	−	1.43605i	−0.135032	−	0.0672490i
$457$	−7.87556	+	13.6409i	−0.368403	+	0.638093i	−0.989316	−	0.145787i	$-0.953429\pi$
$457$	−7.87556	+	13.6409i	−0.368403	+	0.638093i	0.620913	+	0.783879i	$0.286762\pi$
$458$	5.49650	+	9.52022i	0.256835	+	0.444851i
$459$	11.7337	−	10.0488i	0.547681	−	0.469036i
$460$	0.385510	+	0.222574i	0.0179745	+	0.0103776i
$461$	26.7742			1.24700			0.623500	−	0.781823i	$-0.285710\pi$
$461$	26.7742			1.24700			0.623500	+	0.781823i	$0.285710\pi$
$462$	0.171284	+	4.57937i	0.00796886	+	0.213052i
$463$	24.2990			1.12927			0.564635	−	0.825340i	$-0.309017\pi$
$463$	24.2990			1.12927			0.564635	+	0.825340i	$0.309017\pi$
$464$	5.41634	+	3.12712i	0.251447	+	0.145173i
$465$	−3.29196	+	0.202823i	−0.152661	+	0.00940569i
$466$	12.7425	+	22.0707i	0.590286	+	1.02241i
$467$	14.1426	−	24.4957i	0.654441	−	1.13352i	−0.327593	−	0.944819i	$-0.606238\pi$
$467$	14.1426	−	24.4957i	0.654441	−	1.13352i	0.982034	−	0.188705i	$-0.0604292\pi$
$468$	11.2654	−	8.50491i	0.520744	−	0.393140i
$469$	3.26861	+	5.99096i	0.150930	+	0.276637i
$470$			1.04880i			0.0483777i
$471$	18.3446	+	27.6888i	0.845276	+	1.27583i
$472$	−4.03341	+	2.32869i	−0.185653	+	0.107187i
$473$	−6.81512	+	3.93471i	−0.313360	+	0.180918i
$474$	−7.63962	−	11.5310i	−0.350899	−	0.529636i
$475$			9.23351i			0.423663i
$476$	4.09634	−	6.71521i	0.187755	−	0.307791i
$477$	26.2764	−	19.8376i	1.20312	−	0.908301i
$478$	3.86605	−	6.69619i	0.176829	−	0.306277i
$479$	−17.9713	−	31.1272i	−0.821130	−	1.42224i	−0.904841	−	0.425749i	$-0.860011\pi$
$479$	−17.9713	−	31.1272i	−0.821130	−	1.42224i	0.0837110	−	0.996490i	$-0.473323\pi$
$480$	0.324599	−	0.0199991i	0.0148159	−	0.000912828i
$481$	−22.2619	−	12.8529i	−1.01505	−	0.586042i
$482$	−6.62493			−0.301757
$483$	−5.07672	+	9.60530i	−0.230999	+	0.437056i
$484$	1.00000			0.0454545
$485$	0.163504	+	0.0943993i	0.00742435	+	0.00428645i
$486$	−3.33992	+	15.2265i	−0.151502	+	0.690686i
$487$	−0.157485	−	0.272773i	−0.00713635	−	0.0123605i	0.862435	−	0.506168i	$-0.168938\pi$
$487$	−0.157485	−	0.272773i	−0.00713635	−	0.0123605i	−0.869572	+	0.493807i	$0.835605\pi$
$488$	−6.28942	+	10.8936i	−0.284709	+	0.493130i
$489$	−1.25982	−	0.627422i	−0.0569712	−	0.0283730i
$490$	−1.16865	+	0.601453i	−0.0527943	+	0.0271709i
$491$			23.2238i			1.04808i	0.851695	+	0.524038i	$0.175575\pi$
$491$			23.2238i			1.04808i	−0.851695	+	0.524038i	$0.824425\pi$
$492$	−0.271112	+	0.179619i	−0.0122227	+	0.00809787i
$493$	16.1031	−	9.29716i	0.725249	−	0.418723i
$494$	−7.57829	+	4.37533i	−0.340964	+	0.196855i
$495$	0.0691477	+	0.559028i	0.00310796	+	0.0251265i
$496$			10.1416i			0.455372i
$497$	−0.863715	+	35.7609i	−0.0387429	+	1.60410i
$498$	−11.3855	+	22.8614i	−0.510198	+	1.02445i
$499$	11.1621	−	19.3334i	0.499686	−	0.865482i	−0.500314	−	0.865844i	$-0.666782\pi$
$499$	11.1621	−	19.3334i	0.499686	−	0.865482i	1.00000		0.000362452i	$0.000115372\pi$
$500$	−0.935505	−	1.62034i	−0.0418370	−	0.0724639i
$501$	−1.53349	−	24.8896i	−0.0685111	−	1.11199i
$502$	−22.4113	−	12.9392i	−1.00027	−	0.577504i
$503$	−10.0786			−0.449384			−0.224692	−	0.974430i	$-0.572138\pi$
$503$	−10.0786			−0.449384			−0.224692	+	0.974430i	$0.572138\pi$
$504$	0.783871	+	7.89845i	0.0349164	+	0.351825i
$505$	−3.07993			−0.137055
$506$	2.05318	+	1.18540i	0.0912748	+	0.0526975i
$507$	−0.973326	−	15.7978i	−0.0432269	−	0.701604i
$508$	−2.62219	−	4.54176i	−0.116341	−	0.201508i
$509$	−4.15651	+	7.19930i	−0.184234	+	0.319103i	−0.943318	−	0.331890i	$-0.892314\pi$
$509$	−4.15651	+	7.19930i	−0.184234	+	0.319103i	0.759084	+	0.650993i	$0.225647\pi$
$510$	0.431035	−	0.865492i	0.0190866	−	0.0383246i
$511$	37.2539	−	20.3254i	1.64802	−	0.899141i
$512$		−	1.00000i		−	0.0441942i
$513$	3.21365	−	9.11390i	0.141886	−	0.402389i
$514$	−6.31620	+	3.64666i	−0.278596	+	0.160847i
$515$	0.824946	−	0.476283i	0.0363515	−	0.0209875i
$516$	−11.3627	+	7.52812i	−0.500215	+	0.331407i
$517$			5.58579i			0.245663i
$518$	12.6890	−	6.92299i	0.557523	−	0.304179i
$519$	−2.90250	−	1.44551i	−0.127405	−	0.0634509i
$520$	0.441723	−	0.765087i	0.0193709	−	0.0335513i
$521$	2.19722	+	3.80570i	0.0962620	+	0.166731i	0.910135	−	0.414313i	$-0.135978\pi$
$521$	2.19722	+	3.80570i	0.0962620	+	0.166731i	−0.813873	+	0.581043i	$0.802645\pi$
$522$	−7.31574	+	17.2778i	−0.320201	+	0.756227i
$523$	21.5218	+	12.4256i	0.941084	+	0.543335i	0.890300	−	0.455375i	$-0.150495\pi$
$523$	21.5218	+	12.4256i	0.941084	+	0.543335i	0.0507839	+	0.998710i	$0.483828\pi$
$524$	2.00433			0.0875595
$525$	19.2643	−	12.1042i	0.840761	−	0.528269i
$526$	14.8965			0.649520
$527$	26.1122	+	15.0759i	1.13746	+	0.656715i
$528$	1.72877	−	0.106512i	0.0752352	−	0.00463535i
$529$	−8.68965	−	15.0509i	−0.377811	−	0.654387i
$530$	1.03031	−	1.78455i	0.0447539	−	0.0775161i
$531$	−8.41862	−	11.1511i	−0.365337	−	0.483918i
$532$	0.118810	−	4.91918i	0.00515108	−	0.213273i
$533$			0.883447i			0.0382663i
$534$	8.21273	+	12.3960i	0.355400	+	0.536429i
$535$	0.00390089	−	0.00225218i	0.000168650	−	9.73703e-5i
$536$	2.23388	−	1.28973i	0.0964890	−	0.0557079i
$537$	−3.89255	−	5.87530i	−0.167976	−	0.253538i
$538$		−	14.2413i		−	0.613985i
$539$	−6.22408	+	3.20326i	−0.268090	+	0.137974i
$540$	0.179084	+	0.959068i	0.00770655	+	0.0412717i
$541$	20.4396	−	35.4025i	0.878769	−	1.52207i	0.0260765	−	0.999660i	$-0.491699\pi$
$541$	20.4396	−	35.4025i	0.878769	−	1.52207i	0.852693	−	0.522413i	$-0.174968\pi$
$542$	−7.12345	−	12.3382i	−0.305979	−	0.529970i
$543$	22.5150	−	1.38719i	0.966212	−	0.0595298i
$544$	−2.57475	−	1.48653i	−0.110392	−	0.0637346i
$545$	−0.233370			−0.00999645
$546$	19.0628	+	10.0753i	0.815811	+	0.431183i
$547$	22.5428			0.963861			0.481931	−	0.876209i	$-0.339936\pi$
$547$	22.5428			0.963861			0.481931	+	0.876209i	$0.339936\pi$
$548$	−7.81301	−	4.51084i	−0.333755	−	0.192694i
$549$	−34.7498	−	14.7138i	−1.48309	−	0.627968i
$550$	−2.48237	−	4.29960i	−0.105849	−	0.183335i
$551$	5.81588	−	10.0734i	0.247765	−	0.429141i
$552$	3.67573	+	1.83060i	0.156450	+	0.0779156i
$553$	11.0032	−	18.0378i	0.467903	−	0.767043i
$554$		−	11.1810i		−	0.475034i
$555$	1.48118	−	0.981326i	0.0628727	−	0.0416550i
$556$	−3.62920	+	2.09532i	−0.153912	+	0.0888613i
$557$	−38.3279	+	22.1286i	−1.62400	+	0.937619i	−0.638170	+	0.769895i	$0.720308\pi$
$557$	−38.3279	+	22.1286i	−1.62400	+	0.937619i	−0.985834	+	0.167724i	$0.946358\pi$
$558$	−30.1948	+	3.73487i	−1.27825	+	0.158110i
$559$			37.0266i			1.56606i
$560$	0.237927	+	0.436091i	0.0100542	+	0.0184282i
$561$	2.29564	−	4.60950i	0.0969219	−	0.194613i
$562$	−8.74820	+	15.1523i	−0.369021	+	0.639163i
$563$	−12.8836	−	22.3151i	−0.542979	−	0.940468i	−0.998731	−	0.0503610i	$-0.983963\pi$
$563$	−12.8836	−	22.3151i	−0.542979	−	0.940468i	0.455752	−	0.890107i	$-0.349371\pi$
$564$	0.594956	+	9.65656i	0.0250522	+	0.406615i
$565$	2.06249	+	1.19078i	0.0867694	+	0.0500964i
$566$	−6.43083			−0.270308
$567$	−23.2275	+	5.24260i	−0.975462	+	0.220169i
$568$	13.5203			0.567300
$569$	−28.2052	−	16.2843i	−1.18242	−	0.682673i	−0.225850	−	0.974162i	$-0.572516\pi$
$569$	−28.2052	−	16.2843i	−1.18242	−	0.682673i	−0.956574	+	0.291490i	$0.905849\pi$
$570$	−0.0371946	−	0.603695i	−0.00155791	−	0.0252860i
$571$	17.8782	+	30.9660i	0.748181	+	1.29589i	0.948694	+	0.316197i	$0.102406\pi$
$571$	17.8782	+	30.9660i	0.748181	+	1.29589i	−0.200513	+	0.979691i	$0.564261\pi$
$572$	2.35256	−	4.07475i	0.0983655	−	0.170374i
$573$	−4.13064	+	8.29407i	−0.172560	+	0.346490i
$574$	−0.424096	−	0.258702i	−0.0177014	−	0.0107980i
$575$		−	11.7704i		−	0.490861i
$576$	2.97731	−	0.368271i	0.124055	−	0.0153446i
$577$	−36.6472	+	21.1583i	−1.52564	+	0.880830i	−0.526104	+	0.850420i	$0.676348\pi$
$577$	−36.6472	+	21.1583i	−1.52564	+	0.880830i	−0.999538	+	0.0304098i	$0.990319\pi$
$578$	7.06751	−	4.08043i	0.293970	−	0.169724i
$579$	−19.0342	+	12.6107i	−0.791035	+	0.524084i
$580$			1.17432i			0.0487608i
$581$	−39.0012	−	0.941974i	−1.61804	−	0.0390797i
$582$	1.55897	+	0.776404i	0.0646214	+	0.0321830i
$583$	5.48731	−	9.50430i	0.227261	−	0.393628i
$584$	−8.02001	−	13.8911i	−0.331870	−	0.574816i
$585$	2.44058	+	1.03339i	0.100905	+	0.0427253i
$586$	6.93591	+	4.00445i	0.286520	+	0.165422i
$587$	35.2011			1.45291			0.726453	−	0.687217i	$-0.241168\pi$
$587$	35.2011			1.45291			0.726453	+	0.687217i	$0.241168\pi$
$588$	−10.4188	+	6.20064i	−0.429665	+	0.255710i
$589$	18.8616			0.777177
$590$	−0.757325	−	0.437242i	−0.0311786	−	0.0180010i
$591$	25.3499	−	1.56185i	1.04276	−	0.0642457i
$592$	−2.73168	−	4.73141i	−0.112271	−	0.194460i
$593$	−13.4629	+	23.3184i	−0.552853	+	0.957570i	0.445214	+	0.895424i	$0.353128\pi$
$593$	−13.4629	+	23.3184i	−0.552853	+	0.957570i	−0.998067	+	0.0621457i	$0.980206\pi$
$594$	0.953778	+	5.10787i	0.0391340	+	0.209578i
$595$	1.47651	+	0.0356614i	0.0605311	+	0.00146198i
$596$		−	14.9837i		−	0.613755i
$597$	−2.01896	−	3.04736i	−0.0826306	−	0.124720i
$598$	9.66044	−	5.57746i	0.395045	−	0.228079i
$599$	−15.8188	+	9.13299i	−0.646338	+	0.373164i	−0.787052	−	0.616887i	$-0.788394\pi$
$599$	−15.8188	+	9.13299i	−0.646338	+	0.373164i	0.140714	+	0.990050i	$0.455060\pi$
$600$	−4.74942	−	7.16862i	−0.193894	−	0.292658i
$601$		−	12.1244i		−	0.494566i	−0.968943	−	0.247283i	$-0.920462\pi$
$601$		−	12.1244i		−	0.494566i	0.968943	−	0.247283i	$-0.0795377\pi$
$602$	−17.7745	−	10.8426i	−0.724435	−	0.441912i
$603$	4.66261	+	6.17599i	0.189876	+	0.251506i
$604$	−0.274177	+	0.474889i	−0.0111561	+	0.0193229i
$605$	0.0938814	+	0.162607i	0.00381682	+	0.00661093i
$606$	−28.3576	+	1.74715i	−1.15195	+	0.0709732i
$607$	36.4928	+	21.0691i	1.48120	+	0.855169i	0.999773	−	0.0213195i	$-0.00678671\pi$
$607$	36.4928	+	21.0691i	1.48120	+	0.855169i	0.481423	+	0.876488i	$0.340120\pi$
$608$	−1.85982			−0.0754255
$609$	−28.6405	+	1.07125i	−1.16057	+	0.0434094i
$610$	−2.36184			−0.0956281
$611$	22.7607	+	13.1409i	0.920800	+	0.531624i
$612$	3.47767	−	8.21329i	0.140576	−	0.332002i
$613$	−4.31207	−	7.46872i	−0.174163	−	0.301659i	0.765708	−	0.643188i	$-0.222389\pi$
$613$	−4.31207	−	7.46872i	−0.174163	−	0.301659i	−0.939871	+	0.341529i	$0.889055\pi$
$614$	−1.05767	+	1.83194i	−0.0426842	+	0.0739313i
$615$	−0.0546598	−	0.0272219i	−0.00220410	−	0.00109769i
$616$	1.26717	+	2.32256i	0.0510556	+	0.0935787i
$617$			15.6062i			0.628282i	0.949376	+	0.314141i	$0.101717\pi$
$617$			15.6062i			0.628282i	−0.949376	+	0.314141i	$0.898283\pi$
$618$	7.32527	−	4.85320i	0.294666	−	0.195225i
$619$	−25.6111	+	14.7866i	−1.02940	+	0.594322i	−0.916812	−	0.399320i	$-0.869246\pi$
$619$	−25.6111	+	14.7866i	−1.02940	+	0.594322i	−0.112585	+	0.993642i	$0.535913\pi$
$620$	−1.64910	+	0.952110i	−0.0662296	+	0.0382377i
$621$	−4.09660	+	11.6180i	−0.164391	+	0.466213i
$622$		−	5.43457i		−	0.217907i
$623$	−11.8286	+	19.3909i	−0.473904	+	0.776881i
$624$	3.63303	−	7.29490i	0.145438	−	0.292030i
$625$	−12.2362	+	21.1937i	−0.489448	+	0.847749i
$626$	14.2502	+	24.6820i	0.569552	+	0.986493i
$627$	−0.198093	−	3.21520i	−0.00791109	−	0.128403i
$628$	16.6072	+	9.58817i	0.662699	+	0.382610i
$629$	−16.2430			−0.647649
$630$	−1.21076	+	0.868981i	−0.0482377	+	0.0346210i
$631$	−30.6142			−1.21873			−0.609367	−	0.792888i	$-0.708576\pi$
$631$	−30.6142			−1.21873			−0.609367	+	0.792888i	$0.708576\pi$
$632$	−6.91606	−	3.99299i	−0.275106	−	0.158833i
$633$	−0.540120	−	8.76655i	−0.0214679	−	0.348439i
$634$	−13.6203	−	23.5911i	−0.540933	−	0.936923i
$635$	0.492349	−	0.852774i	0.0195383	−	0.0338413i
$636$	8.47399	−	17.0152i	0.336016	−	0.674698i
$637$	−1.59004	+	32.8974i	−0.0629995	+	1.30344i
$638$			6.25425i			0.247608i
$639$	4.97914	+	40.2542i	0.196972	+	1.59243i
$640$	0.162607	−	0.0938814i	0.00642762	−	0.00371099i
$641$	−23.4593	+	13.5443i	−0.926588	+	0.534966i	−0.885731	−	0.464199i	$-0.846342\pi$
$641$	−23.4593	+	13.5443i	−0.926588	+	0.534966i	−0.0408571	+	0.999165i	$0.513009\pi$
$642$	0.0346387	−	0.0229492i	0.00136708	−	0.000905732i
$643$			14.1386i			0.557571i	0.960353	+	0.278786i	$0.0899319\pi$
$643$			14.1386i			0.557571i	−0.960353	+	0.278786i	$0.910068\pi$
$644$	−0.151454	+	6.27073i	−0.00596810	+	0.247101i
$645$	−2.29087	−	1.14091i	−0.0902031	−	0.0449232i
$646$	−2.76468	+	4.78857i	−0.108775	+	0.188404i
$647$	−0.106419	−	0.184324i	−0.00418378	−	0.00724652i	0.863926	−	0.503619i	$-0.167998\pi$
$647$	−0.106419	−	0.184324i	−0.00418378	−	0.00724652i	−0.868110	+	0.496372i	$0.834665\pi$
$648$	2.19292	+	8.72875i	0.0861459	+	0.342898i
$649$	−4.03341	−	2.32869i	−0.158325	−	0.0914091i
$650$	−23.3597			−0.916244
$651$	−24.7255	−	39.3516i	−0.969069	−	1.54231i
$652$	−0.812571			−0.0318227
$653$	−19.4953	−	11.2556i	−0.762911	−	0.440467i	0.0674291	−	0.997724i	$-0.478520\pi$
$653$	−19.4953	−	11.2556i	−0.762911	−	0.440467i	−0.830340	+	0.557257i	$0.811854\pi$
$654$	−2.14868	+	0.132384i	−0.0840202	+	0.00517661i
$655$	0.188169	+	0.325919i	0.00735238	+	0.0127347i
$656$	−0.0938814	+	0.162607i	−0.00366545	+	0.00634875i
$657$	38.4045	−	28.9937i	1.49830	−	1.13115i
$658$	−12.9733	+	7.07812i	−0.505754	+	0.275934i
$659$			23.6271i			0.920380i	0.887820	+	0.460190i	$0.152219\pi$
$659$			23.6271i			0.920380i	−0.887820	+	0.460190i	$0.847781\pi$
$660$	0.179619	+	0.271112i	0.00699167	+	0.0105530i
$661$	−20.7034	+	11.9531i	−0.805270	+	0.464923i	−0.845311	−	0.534275i	$-0.820585\pi$
$661$	−20.7034	+	11.9531i	−0.805270	+	0.464923i	0.0400405	+	0.999198i	$0.487251\pi$
$662$	29.2809	−	16.9054i	1.13804	−	0.657046i
$663$	−13.3819	−	20.1983i	−0.519711	−	0.784436i
$664$			14.7454i			0.572231i
$665$	0.811049	−	0.442500i	0.0314511	−	0.0171594i
$666$	13.0809	−	9.87551i	0.506874	−	0.382668i
$667$	−7.41380	+	12.8411i	−0.287063	+	0.497208i
$668$	−7.19863	−	12.4684i	−0.278523	−	0.482417i
$669$	21.8303	−	1.34500i	0.844009	−	0.0520007i
$670$	0.419440	+	0.242164i	0.0162044	+	0.00935560i
$671$	−12.5788			−0.485601
$672$	2.43802	+	3.88021i	0.0940488	+	0.149682i
$673$	4.93143			0.190093			0.0950463	−	0.995473i	$-0.469700\pi$
$673$	4.93143			0.190093			0.0950463	+	0.995473i	$0.469700\pi$
$674$	−1.58733	−	0.916445i	−0.0611416	−	0.0353001i
$675$	19.5941	−	16.7805i	0.754178	−	0.645881i
$676$	−4.56908	−	7.91387i	−0.175734	−	0.304380i
$677$	−7.35012	+	12.7308i	−0.282488	+	0.489284i	−0.971997	−	0.234993i	$-0.924493\pi$
$677$	−7.35012	+	12.7308i	−0.282488	+	0.489284i	0.689509	+	0.724277i	$0.257826\pi$
$678$	19.6652	+	9.79375i	0.755239	+	0.376127i
$679$	−0.0642352	+	2.65957i	−0.00246512	+	0.102065i
$680$		−	0.558232i		−	0.0214072i
$681$	0.520306	−	0.344718i	0.0199382	−	0.0132096i
$682$	−8.78290	+	5.07081i	−0.336315	+	0.194171i
$683$	42.1416	−	24.3305i	1.61251	−	0.930980i	0.623718	−	0.781649i	$-0.285621\pi$
$683$	42.1416	−	24.3305i	1.61251	−	0.930980i	0.988787	−	0.149331i	$-0.0477120\pi$
$684$	−0.684917	−	5.53725i	−0.0261885	−	0.211722i
$685$		−	1.69394i		−	0.0647220i
$686$	−15.3267	−	10.3967i	−0.585176	−	0.396950i
$687$	−8.48818	+	17.0437i	−0.323844	+	0.650259i
$688$	−3.93471	+	6.81512i	−0.150009	+	0.259824i
$689$	−25.8185	−	44.7189i	−0.983605	−	1.70365i
$690$	0.0474138	+	0.769561i	0.00180501	+	0.0292967i
$691$	−3.26776	−	1.88664i	−0.124312	−	0.0717713i	0.436555	−	0.899678i	$-0.356199\pi$
$691$	−3.26776	−	1.88664i	−0.124312	−	0.0717713i	−0.560866	+	0.827906i	$0.689532\pi$
$692$	−1.87208			−0.0711656
$693$	−6.44832	+	4.62808i	−0.244952	+	0.175806i
$694$	−24.7357			−0.938955
$695$	−0.681428	−	0.393423i	−0.0258481	−	0.0149234i
$696$	0.666155	+	10.8122i	0.0252505	+	0.409834i
$697$	0.279116	+	0.483443i	0.0105723	+	0.0183117i
$698$	2.93134	−	5.07724i	0.110953	−	0.192176i
$699$	−19.6781	+	39.5125i	−0.744295	+	1.49450i
$700$	6.84050	−	11.2138i	0.258546	−	0.423840i
$701$			52.6270i			1.98769i	0.110759	+	0.993847i	$0.464672\pi$
$701$			52.6270i			1.98769i	−0.110759	+	0.993847i	$0.535328\pi$
$702$	23.0571	+	8.13016i	0.870235	+	0.306853i
$703$	−8.79956	+	5.08043i	−0.331882	+	0.191612i
$704$	0.866025	−	0.500000i	0.0326396	−	0.0188445i
$705$	−1.51437	+	1.00332i	−0.0570346	+	0.0377871i
$706$			21.4135i			0.805909i
$707$	−20.7857	−	38.0976i	−0.781726	−	1.43281i
$708$	−7.22088	−	3.59617i	−0.271377	−	0.135152i
$709$	10.1165	−	17.5223i	0.379933	−	0.658064i	−0.611119	−	0.791539i	$-0.709280\pi$
$709$	10.1165	−	17.5223i	0.379933	−	0.658064i	0.991052	+	0.133475i	$0.0426136\pi$
$710$	1.26931	+	2.19850i	0.0476362	+	0.0825083i
$711$	9.34138	−	22.0618i	0.350329	−	0.827381i
$712$	7.43490	+	4.29254i	0.278634	+	0.160870i
$713$	−24.0438			−0.900447
$714$	13.6148	−	0.509240i	0.509521	−	0.0190578i
$715$	0.883447			0.0330390
$716$	−3.52389	−	2.03452i	−0.131694	−	0.0760335i
$717$	13.3670	−	0.823563i	0.499201	−	0.0307565i
$718$	3.52939	+	6.11309i	0.131716	+	0.228138i
$719$	−12.0066	+	20.7960i	−0.447771	+	0.775562i	−0.998241	−	0.0592933i	$-0.981115\pi$
$719$	−12.0066	+	20.7960i	−0.447771	+	0.775562i	0.550470	+	0.834855i	$0.314449\pi$
$720$	0.339398	+	0.449559i	0.0126486	+	0.0167541i
$721$	11.4588	+	6.98998i	0.426748	+	0.260320i
$722$		−	15.5411i		−	0.578379i
$723$	−6.33760	−	9.56577i	−0.235698	−	0.355755i
$724$	11.2789	−	6.51185i	0.419175	−	0.242011i
$725$	26.8907	−	15.5254i	0.998697	−	0.576598i
$726$	0.956629	+	1.44390i	0.0355038	+	0.0535883i
$727$			7.57680i			0.281008i	0.990080	+	0.140504i	$0.0448723\pi$
$727$			7.57680i			0.281008i	−0.990080	+	0.140504i	$0.955128\pi$
$728$	12.4449	+	0.300576i	0.461240	+	0.0111401i
$729$	−25.1806	+	9.74354i	−0.932615	+	0.360872i
$730$	1.50586	−	2.60823i	0.0557344	−	0.0965348i
$731$	11.6982	+	20.2618i	0.432672	+	0.749411i
$732$	−21.7460	+	1.33980i	−0.803754	+	0.0495205i
$733$	43.7430	+	25.2551i	1.61569	+	0.932817i	0.988019	+	0.154335i	$0.0493235\pi$
$733$	43.7430	+	25.2551i	1.61569	+	0.932817i	0.627667	+	0.778482i	$0.284010\pi$
$734$	−13.2342			−0.488483
$735$	−1.98641	−	1.11205i	−0.0732697	−	0.0410187i
$736$	2.37080			0.0873890
$737$	2.23388	+	1.28973i	0.0822861	+	0.0475079i
$738$	−0.518707	−	0.219631i	−0.0190939	−	0.00808471i
$739$	−17.9352	−	31.0646i	−0.659756	−	1.14273i	−0.980679	−	0.195625i	$-0.937326\pi$
$739$	−17.9352	−	31.0646i	−0.659756	−	1.14273i	0.320923	−	0.947105i	$-0.396007\pi$
$740$	0.512909	−	0.888384i	0.0188549	−	0.0326576i
$741$	−13.5672	−	6.75677i	−0.498403	−	0.248216i
$742$	29.0277	+	0.701090i	1.06564	+	0.0257378i
$743$			18.8577i			0.691822i	0.938267	+	0.345911i	$0.112430\pi$
$743$			18.8577i			0.691822i	−0.938267	+	0.345911i	$0.887570\pi$
$744$	−14.6435	+	9.70177i	−0.536858	+	0.355684i
$745$	2.43646	−	1.40669i	0.0892649	−	0.0515371i
$746$	29.1651	−	16.8385i	1.06781	−	0.616500i
$747$	−43.9015	+	5.43029i	−1.60627	+	0.198684i
$748$		−	2.97307i		−	0.108706i
$749$	0.0541849	+	0.0330533i	0.00197987	+	0.00120774i
$750$	1.44469	−	2.90084i	0.0527526	−	0.105924i
$751$	−22.1637	+	38.3886i	−0.808764	+	1.40082i	0.104956	+	0.994477i	$0.466530\pi$
$751$	−22.1637	+	38.3886i	−0.808764	+	1.40082i	−0.913720	+	0.406343i	$0.866804\pi$
$752$	2.79290	+	4.83744i	0.101846	+	0.176403i
$753$	−2.75637	−	44.7378i	−0.100448	−	1.63034i
$754$	25.4845	+	14.7135i	0.928092	+	0.535834i
$755$	−0.102961			−0.00374712
$756$	−10.6547	+	8.68772i	−0.387509	+	0.315969i
$757$	−25.8451			−0.939355			−0.469677	−	0.882838i	$-0.655630\pi$
$757$	−25.8451			−0.939355			−0.469677	+	0.882838i	$0.655630\pi$
$758$	−12.7079	−	7.33688i	−0.461570	−	0.266488i
$759$	0.252520	+	4.09858i	0.00916589	+	0.148769i
$760$	−0.174602	−	0.302420i	−0.00633349	−	0.0109699i
$761$	3.59703	−	6.23024i	0.130392	−	0.225846i	−0.793436	−	0.608654i	$-0.791710\pi$
$761$	3.59703	−	6.23024i	0.130392	−	0.225846i	0.923828	+	0.382808i	$0.125043\pi$
$762$	4.04941	−	8.13096i	0.146695	−	0.294554i
$763$	−1.57495	−	2.88670i	−0.0570172	−	0.104506i
$764$			5.34957i			0.193541i
$765$	1.66203	−	0.205581i	0.0600908	−	0.00743279i
$766$	−14.8099	+	8.55052i	−0.535105	+	0.308943i
$767$	−18.9777	+	10.9568i	−0.685244	+	0.395626i
$768$	1.44390	−	0.956629i	0.0521024	−	0.0345194i
$769$			25.8990i			0.933943i	0.884272	+	0.466972i	$0.154655\pi$
$769$			25.8990i			0.933943i	−0.884272	+	0.466972i	$0.845345\pi$
$770$	−0.258702	+	0.424096i	−0.00932298	+	0.0152834i
$771$	−11.3077	−	5.63150i	−0.407237	−	0.202813i
$772$	−6.59123	+	11.4163i	−0.237224	+	0.410883i
$773$	0.846710	+	1.46654i	0.0304540	+	0.0527480i	0.880851	−	0.473394i	$-0.156971\pi$
$773$	0.846710	+	1.46654i	0.0304540	+	0.0527480i	−0.850397	+	0.526142i	$0.823638\pi$
$774$	−21.7398	−	9.20505i	−0.781420	−	0.330869i
$775$	43.6049	+	25.1753i	1.56633	+	0.904323i
$776$	1.00552			0.0360959
$777$	22.1348	+	11.6990i	0.794082	+	0.419699i
$778$	36.0847			1.29370
$779$	0.302420	+	0.174602i	0.0108353	+	0.00625577i
$780$	1.52728	−	0.0940980i	0.0546853	−	0.00336925i
$781$	6.76015	+	11.7089i	0.241897	+	0.418979i
$782$	3.52428	−	6.10423i	0.126028	−	0.218287i
$783$	−31.9459	+	5.96516i	−1.14165	+	0.213178i
$784$	−3.78858	+	5.88614i	−0.135306	+	0.210219i
$785$			3.60060i			0.128511i
$786$	1.91740	+	2.89406i	0.0683913	+	0.103228i
$787$	16.1228	−	9.30849i	0.574715	−	0.331812i	−0.184315	−	0.982867i	$-0.559007\pi$
$787$	16.1228	−	9.30849i	0.574715	−	0.331812i	0.759030	+	0.651055i	$0.225673\pi$
$788$	12.6990	−	7.33176i	0.452382	−	0.261183i
$789$	14.2505	+	21.5092i	0.507330	+	0.765747i
$790$		−	1.49947i		−	0.0533487i
$791$	−0.810279	+	33.5485i	−0.0288102	+	1.19285i
$792$	1.80759	+	2.39429i	0.0642298	+	0.0850774i
$793$	−29.5925	+	51.2557i	−1.05086	+	1.82014i
$794$	6.39186	+	11.0710i	0.226839	+	0.392896i
$795$	3.56236	−	0.219482i	0.126344	−	0.00778423i
$796$	−1.82774	−	1.05525i	−0.0647827	−	0.0374023i
$797$	−43.0989			−1.52664			−0.763321	−	0.646019i	$-0.776433\pi$
$797$	−43.0989			−1.52664			−0.763321	+	0.646019i	$0.776433\pi$
$798$	7.21648	−	4.53428i	0.255461	−	0.160512i
$799$	16.6069			0.587511
$800$	−4.29960	−	2.48237i	−0.152014	−	0.0877651i
$801$	−10.0422	+	23.7168i	−0.354822	+	0.837992i
$802$	11.2479	+	19.4819i	0.397176	+	0.687930i
$803$	8.02001	−	13.8911i	0.283020	−	0.490205i
$804$	3.99925	+	1.99172i	0.141043	+	0.0702425i
$805$	−1.03389	+	0.564077i	−0.0364397	+	0.0198811i
$806$			47.7176i			1.68078i
$807$	20.5630	−	13.6236i	0.723853	−	0.479574i
$808$	−14.2057	+	8.20165i	−0.499754	+	0.288533i
$809$	2.59018	−	1.49544i	0.0910660	−	0.0525770i	−0.453775	−	0.891116i	$-0.649923\pi$
$809$	2.59018	−	1.49544i	0.0910660	−	0.0525770i	0.544841	+	0.838539i	$0.316590\pi$
$810$	−1.21349	+	1.17605i	−0.0426375	+	0.0413223i
$811$		−	13.8788i		−	0.487350i	−0.969857	−	0.243675i	$-0.921647\pi$
$811$		−	13.8788i		−	0.487350i	0.969857	−	0.243675i	$-0.0783531\pi$
$812$	−14.5259	+	7.92517i	−0.509758	+	0.278119i
$813$	11.0007	−	22.0887i	0.385810	−	0.774683i
$814$	2.73168	−	4.73141i	0.0957454	−	0.165836i
$815$	−0.0762853	−	0.132130i	−0.00267216	−	0.00462831i
$816$	−0.316669	−	5.13976i	−0.0110856	−	0.179928i
$817$	12.6749	+	7.31784i	0.443438	+	0.256019i
$818$	−12.8069			−0.447784
$819$	3.68821	+	37.1632i	0.128876	+	1.29859i
$820$	−0.0352549			−0.00123115
$821$	4.66052	+	2.69075i	0.162653	+	0.0939079i	0.579117	−	0.815244i	$-0.303397\pi$
$821$	4.66052	+	2.69075i	0.162653	+	0.0939079i	−0.416464	+	0.909152i	$0.636731\pi$
$822$	−0.960921	−	15.5964i	−0.0335160	−	0.543989i
$823$	−14.1424	−	24.4953i	−0.492971	−	0.853852i	0.506996	−	0.861949i	$-0.330756\pi$
$823$	−14.1424	−	24.4953i	−0.492971	−	0.853852i	−0.999967	+	0.00809699i	$0.997423\pi$
$824$	2.53662	−	4.39355i	0.0883673	−	0.153057i
$825$	3.83350	−	7.69743i	0.133465	−	0.267990i
$826$	0.297527	−	12.3187i	0.0103523	−	0.428622i
$827$		−	11.1368i		−	0.387263i	−0.981074	−	0.193632i	$-0.937973\pi$
$827$		−	11.1368i		−	0.387263i	0.981074	−	0.193632i	$-0.0620267\pi$
$828$	0.873099	+	7.05862i	0.0303423	+	0.245304i
$829$	7.98993	−	4.61299i	0.277502	−	0.160216i	−0.354790	−	0.934946i	$-0.615448\pi$
$829$	7.98993	−	4.61299i	0.277502	−	0.160216i	0.632292	+	0.774730i	$0.282114\pi$
$830$	−2.39770	+	1.38431i	−0.0832255	+	0.0480503i
$831$	16.1443	−	10.6960i	0.560039	−	0.371042i
$832$		−	4.70512i		−	0.163121i
$833$	9.52350	+	18.5046i	0.329970	+	0.641147i
$834$	−6.49723	−	3.23577i	−0.224981	−	0.112046i
$835$	1.35164	−	2.34110i	0.0467753	−	0.0810172i
$836$	−0.929908	−	1.61065i	−0.0321615	−	0.0557054i
$837$	−34.2780	−	40.0255i	−1.18482	−	1.38348i
$838$	18.4620	+	10.6590i	0.637758	+	0.368210i
$839$	24.7473			0.854372			0.427186	−	0.904164i	$-0.359505\pi$
$839$	24.7473			0.854372			0.427186	+	0.904164i	$0.359505\pi$
$840$	−0.402066	+	0.760720i	−0.0138726	+	0.0262473i
$841$	−10.1156			−0.348815
$842$	26.4075	+	15.2464i	0.910062	+	0.525424i
$843$	−30.2473	+	1.86358i	−1.04177	+	0.0641852i
$844$	−2.53548	−	4.39158i	−0.0872749	−	0.151165i
$845$	0.857903	−	1.48593i	0.0295128	−	0.0511176i
$846$	−13.3740	+	10.0968i	−0.459808	+	0.347135i
$847$	−1.37781	+	2.25868i	−0.0473423	+	0.0776091i
$848$		−	10.9746i		−	0.376870i
$849$	−6.15192	−	9.28550i	−0.211133	−	0.318678i
$850$	−12.7830	+	7.38026i	−0.438453	+	0.253141i
$851$	11.2173	−	6.47628i	0.384522	−	0.222004i
$852$	12.9339	+	19.5220i	0.443109	+	0.668814i
$853$		−	49.3949i		−	1.69125i	−0.533777	−	0.845625i	$-0.679228\pi$
$853$		−	49.3949i		−	1.69125i	0.533777	−	0.845625i	$-0.320772\pi$
$854$	−15.9395	−	29.2151i	−0.545438	−	0.999721i
$855$	0.836097	−	0.631218i	0.0285939	−	0.0215872i
$856$	0.0119948	−	0.0207756i	0.000409974	−	0.000710096i
$857$	2.81854	+	4.88186i	0.0962796	+	0.166761i	0.910142	−	0.414297i	$-0.135972\pi$
$857$	2.81854	+	4.88186i	0.0962796	+	0.166761i	−0.813862	+	0.581058i	$0.802639\pi$
$858$	8.13408	−	0.501153i	0.277693	−	0.0171091i
$859$	−15.7390	−	9.08691i	−0.537007	−	0.310041i	0.206858	−	0.978371i	$-0.433676\pi$
$859$	−15.7390	−	9.08691i	−0.537007	−	0.310041i	−0.743865	+	0.668330i	$0.767010\pi$
$860$	−1.47759			−0.0503853
$861$	−0.0321608	−	0.859836i	−0.00109604	−	0.0293031i
$862$	28.0274			0.954618
$863$	31.0340	+	17.9175i	1.05641	+	0.609919i	0.924437	−	0.381335i	$-0.124535\pi$
$863$	31.0340	+	17.9175i	1.05641	+	0.609919i	0.131973	+	0.991253i	$0.457869\pi$
$864$	3.37993	+	3.94665i	0.114988	+	0.134268i
$865$	−0.175753	−	0.304413i	−0.00597578	−	0.0103504i
$866$	0.392733	−	0.680233i	0.0133456	−	0.0231153i
$867$	12.6527	+	6.30136i	0.429710	+	0.214005i
$868$	−22.9067	−	13.9733i	−0.777503	−	0.474284i
$869$		−	7.98598i		−	0.270906i
$870$	−1.69560	+	1.12338i	−0.0574862	+	0.0380863i
$871$	10.5107	−	6.06834i	0.356141	−	0.205618i
$872$	−1.07638	+	0.621447i	−0.0364508	+	0.0210449i
$873$	0.370303	+	2.99373i	0.0125329	+	0.101323i
$874$		−	4.40926i		−	0.149145i
$875$	4.94878	+	0.119525i	0.167299	+	0.00404069i
$876$	12.3852	−	24.8687i	0.418457	−	0.840236i
$877$	20.7676	−	35.9705i	0.701272	−	1.21464i	−0.266748	−	0.963766i	$-0.585949\pi$
$877$	20.7676	−	35.9705i	0.701272	−	1.21464i	0.968020	−	0.250872i	$-0.0807174\pi$
$878$	−7.82210	−	13.5483i	−0.263983	−	0.457232i
$879$	0.853046	+	13.8456i	0.0287725	+	0.466999i
$880$	0.162607	+	0.0938814i	0.00548149	+	0.00316474i
$881$	−18.5071			−0.623519			−0.311760	−	0.950161i	$-0.600918\pi$
$881$	−18.5071			−0.623519			−0.311760	+	0.950161i	$0.600918\pi$
$882$	−18.9201	−	9.11209i	−0.637073	−	0.306820i
$883$	−36.8028			−1.23851			−0.619256	−	0.785189i	$-0.712566\pi$
$883$	−36.8028			−1.23851			−0.619256	+	0.785189i	$0.712566\pi$
$884$	−12.1145	−	6.99432i	−0.407455	−	0.235245i
$885$	−0.0931432	−	1.51178i	−0.00313098	−	0.0508180i
$886$	12.7305	+	22.0499i	0.427691	+	0.740782i
$887$	19.1040	−	33.0891i	0.641450	−	1.11102i	−0.343659	−	0.939094i	$-0.611666\pi$
$887$	19.1040	−	33.0891i	0.641450	−	1.11102i	0.985109	−	0.171930i	$-0.0550002\pi$
$888$	4.21851	−	8.47050i	0.141564	−	0.284251i
$889$	13.8713	+	0.335025i	0.465227	+	0.0112364i
$890$			1.61196i			0.0540330i
$891$	−6.46286	+	6.26350i	−0.216514	+	0.209835i
$892$	10.9359	−	6.31382i	0.366160	−	0.211402i
$893$	8.99675	−	5.19427i	0.301065	−	0.173820i
$894$	21.6350	−	14.3338i	0.723583	−	0.479394i
$895$		−	0.764013i		−	0.0255381i
$896$	2.25868	+	1.37781i	0.0754572	+	0.0460295i
$897$	17.2948	+	8.61320i	0.577455	+	0.287586i
$898$	18.3161	−	31.7245i	0.611217	−	1.05866i
$899$	−31.7141	−	54.9305i	−1.05773	−	1.83203i
$900$	5.80738	−	13.7154i	0.193579	−	0.457181i
$901$	−28.2569	−	16.3142i	−0.941375	−	0.543503i
$902$	−0.187763			−0.00625182
$903$	−1.34791	−	36.0370i	−0.0448556	−	1.19924i
$904$	12.6838			0.421858
$905$	2.11775	+	1.22268i	0.0703964	+	0.0406434i
$906$	−0.947980	+	0.0584065i	−0.0314945	+	0.00194042i
$907$	−1.24230	−	2.15173i	−0.0412499	−	0.0714469i	0.844663	−	0.535298i	$-0.179801\pi$
$907$	−1.24230	−	2.15173i	−0.0412499	−	0.0714469i	−0.885913	+	0.463851i	$0.846467\pi$
$908$	0.180173	−	0.312069i	0.00597926	−	0.0103564i
$909$	−29.6504	−	39.2742i	−0.983441	−	1.30264i
$910$	1.11947	+	2.05186i	0.0371102	+	0.0680185i
$911$		−	5.28683i		−	0.175161i	−0.996157	−	0.0875803i	$-0.972087\pi$
$911$		−	5.28683i		−	0.175161i	0.996157	−	0.0875803i	$-0.0279134\pi$
$912$	−1.77915	−	2.68540i	−0.0589137	−	0.0889224i
$913$	−12.7698	+	7.37268i	−0.422620	+	0.244000i
$914$	−13.6409	+	7.87556i	−0.451200	+	0.260500i
$915$	−2.25940	−	3.41027i	−0.0746936	−	0.112740i
$916$			10.9930i			0.363219i
$917$	−2.76159	+	4.52713i	−0.0911958	+	0.149499i
$918$	15.1860	−	2.83565i	0.501214	−	0.0935903i
$919$	−8.58985	+	14.8781i	−0.283353	+	0.490782i	−0.972208	−	0.234117i	$-0.924780\pi$
$919$	−8.58985	+	14.8781i	−0.283353	+	0.490782i	0.688855	+	0.724899i	$0.258114\pi$
$920$	0.222574	+	0.385510i	0.00733806	+	0.0127099i
$921$	−3.65696	+	0.225311i	−0.120501	+	0.00742424i
$922$	23.1872	+	13.3871i	0.763629	+	0.440881i
$923$	63.6147			2.09390
$924$	−2.14135	+	4.05150i	−0.0704453	+	0.133284i
$925$	−27.1242			−0.891839
$926$	21.0436	+	12.1495i	0.691534	+	0.399258i
$927$	14.0151	+	5.93428i	0.460317	+	0.194907i
$928$	3.12712	+	5.41634i	0.102653	+	0.177800i
$929$	23.1396	−	40.0790i	0.759185	−	1.31495i	−0.184081	−	0.982911i	$-0.558931\pi$
$929$	23.1396	−	40.0790i	0.759185	−	1.31495i	0.943266	−	0.332037i	$-0.107736\pi$
$930$	−2.95234	−	1.47033i	−0.0968109	−	0.0482141i
$931$	10.9471	+	7.04607i	0.358778	+	0.230925i
$932$			25.4851i			0.834791i
$933$	7.84701	−	5.19887i	0.256900	−	0.170203i
$934$	24.4957	−	14.1426i	0.801523	−	0.462759i
$935$	0.483443	−	0.279116i	0.0158103	−	0.00912807i
$936$	14.0086	−	1.73276i	0.457885	−	0.0566370i
$937$		−	7.72600i		−	0.252397i	−0.992005	−	0.126199i	$-0.959722\pi$
$937$		−	7.72600i		−	0.252397i	0.992005	−	0.126199i	$-0.0402777\pi$
$938$	−0.164783	+	6.82263i	−0.00538037	+	0.222767i
$939$	−22.0064	+	44.1875i	−0.718151	+	1.44200i
$940$	−0.524402	+	0.908291i	−0.0171041	+	0.0296252i
$941$	19.7262	+	34.1667i	0.643055	+	1.11380i	0.984747	+	0.173992i	$0.0556665\pi$
$941$	19.7262	+	34.1667i	0.643055	+	1.11380i	−0.341693	+	0.939812i	$0.611000\pi$
$942$	2.04252	+	33.1515i	0.0665488	+	1.08014i
$943$	−0.385510	−	0.222574i	−0.0125539	−	0.00724802i
$944$	−4.65738			−0.151585
$945$	−2.41297	−	0.916924i	−0.0784939	−	0.0298275i
$946$	−7.86942			−0.255857
$947$	29.0176	+	16.7533i	0.942946	+	0.544410i	0.890882	−	0.454234i	$-0.150087\pi$
$947$	29.0176	+	16.7533i	0.942946	+	0.544410i	0.0520632	+	0.998644i	$0.483420\pi$
$948$	−0.850605	−	13.8059i	−0.0276264	−	0.448396i
$949$	−37.7351	−	65.3591i	−1.22493	−	2.12165i
$950$	−4.61676	+	7.99646i	−0.149787	+	0.259439i
$951$	21.0337	−	42.2344i	0.682065	−	1.36955i
$952$	6.90513	−	3.76737i	0.223797	−	0.122101i
$953$		−	7.29135i		−	0.236190i	−0.993002	−	0.118095i	$-0.962321\pi$
$953$		−	7.29135i		−	0.236190i	0.993002	−	0.118095i	$-0.0376787\pi$
$954$	32.6749	−	4.04164i	1.05789	−	0.130853i
$955$	−0.869880	+	0.502225i	−0.0281486	+	0.0162516i
$956$	6.69619	−	3.86605i	0.216570	−	0.125037i
$957$	−9.03054	+	5.98300i	−0.291916	+	0.193403i
$958$		−	35.9426i		−	1.16125i
$959$	20.9534	−	11.4320i	0.676621	−	0.369158i
$960$	0.291111	+	0.144980i	0.00939556	+	0.00467921i
$961$	35.9263	−	62.2261i	1.15891	−	2.00729i
$962$	−12.8529	−	22.2619i	−0.414394	−	0.717752i
$963$	0.0662728	+	0.0280612i	0.00213561	+	0.000904260i
$964$	−5.73736	−	3.31247i	−0.184788	−	0.106687i
$965$	−2.47518			−0.0796787
$966$	−9.19922	+	5.78007i	−0.295980	+	0.185971i
$967$	13.0472			0.419568			0.209784	−	0.977748i	$-0.432724\pi$
$967$	13.0472			0.419568			0.209784	+	0.977748i	$0.432724\pi$
$968$	0.866025	+	0.500000i	0.0278351	+	0.0160706i
$969$	−9.55901	+	0.588945i	−0.307080	+	0.0189196i
$970$	0.0943993	+	0.163504i	0.00303098	+	0.00524981i
$971$	−17.9357	+	31.0656i	−0.575586	+	0.996943i	0.420392	+	0.907343i	$0.361893\pi$
$971$	−17.9357	+	31.0656i	−0.575586	+	0.996943i	−0.995978	+	0.0896009i	$0.971441\pi$
$972$	−10.5057	+	11.5165i	−0.336970	+	0.369393i
$973$	0.267710	−	11.0841i	0.00858237	−	0.355341i
$974$		−	0.314971i		−	0.0100923i
$975$	−22.3466	−	33.7292i	−0.715663	−	1.08020i
$976$	−10.8936	+	6.28942i	−0.348696	+	0.201319i
$977$	−10.8868	+	6.28548i	−0.348299	+	0.201090i	−0.663936	−	0.747790i	$-0.731115\pi$
$977$	−10.8868	+	6.28548i	−0.348299	+	0.201090i	0.315637	+	0.948880i	$0.397782\pi$
$978$	−0.777329	−	1.17328i	−0.0248562	−	0.0375172i
$979$			8.58508i			0.274380i
$980$	−1.31281	−	0.0634521i	−0.0419361	−	0.00202690i
$981$	−2.24664	−	2.97585i	−0.0717297	−	0.0950116i
$982$	−11.6119	+	20.1124i	−0.370551	+	0.641813i
$983$	−17.5055	−	30.3205i	−0.558340	−	0.967073i	−0.997635	−	0.0687302i	$-0.978105\pi$
$983$	−17.5055	−	30.3205i	−0.558340	−	0.967073i	0.439296	−	0.898343i	$-0.355228\pi$
$984$	−0.324599	+	0.0199991i	−0.0103478	+	0.000637547i
$985$	2.38440	+	1.37663i	0.0759732	+	0.0438631i
$986$	18.5943			0.592164
$987$	−22.6308	−	11.9611i	−0.720347	−	0.380727i
$988$	−8.75066			−0.278396
$989$	−16.1573	−	9.32843i	−0.513773	−	0.296627i
$990$	−0.219631	+	0.518707i	−0.00698032	+	0.0164856i
$991$	2.77151	+	4.80040i	0.0880399	+	0.152490i	0.906683	−	0.421814i	$-0.138606\pi$
$991$	2.77151	+	4.80040i	0.0880399	+	0.152490i	−0.818643	+	0.574303i	$0.805273\pi$
$992$	−5.07081	+	8.78290i	−0.160998	+	0.278857i
$993$	52.4207	+	26.1067i	1.66352	+	0.828473i
$994$	−18.6285	+	30.5380i	−0.590859	+	0.968608i
$995$		−	0.396273i		−	0.0125627i
$996$	−21.2909	+	14.1058i	−0.674627	+	0.446960i
$997$	11.9995	−	6.92792i	0.380028	−	0.219410i	−0.297802	−	0.954628i	$-0.596254\pi$
$997$	11.9995	−	6.92792i	0.380028	−	0.219410i	0.677831	+	0.735218i	$0.262920\pi$
$998$	19.3334	−	11.1621i	0.611988	−	0.353331i
$999$	26.7729	+	9.44036i	0.847056	+	0.298680i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.k.g.89.8	yes	20
3.2	odd	2	inner	462.2.k.g.89.1	✓	20
7.3	odd	6	inner	462.2.k.g.353.1	yes	20
21.17	even	6	inner	462.2.k.g.353.8	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.k.g.89.1	✓	20	3.2	odd	2	inner
462.2.k.g.89.8	yes	20	1.1	even	1	trivial
462.2.k.g.353.1	yes	20	7.3	odd	6	inner
462.2.k.g.353.8	yes	20	21.17	even	6	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:	\( N \)	\(=\)	\( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	462.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.106512 + 1.72877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0938814 + 0.162607i) q^{5} +(-0.772144 + 1.55042i) q^{6} +(-2.64498 - 0.0638828i) q^{7} +1.00000i q^{8} +(-2.97731 + 0.368271i) q^{9} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.106512 + 1.72877i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-0.0938814 + 0.162607i) q^{5} +(-0.772144 + 1.55042i) q^{6} +(-2.64498 - 0.0638828i) q^{7} +1.00000i q^{8} +(-2.97731 + 0.368271i) q^{9} +(-0.162607 + 0.0938814i) q^{10} +(-0.866025 + 0.500000i) q^{11} +(-1.44390 + 0.956629i) q^{12} +4.70512i q^{13} +(-2.25868 - 1.37781i) q^{14} +(-0.291111 - 0.144980i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.48653 + 2.57475i) q^{17} +(-2.76256 - 1.16972i) q^{18} +(1.61065 + 0.929908i) q^{19} -0.187763 q^{20} +(-0.171284 - 4.57937i) q^{21} -1.00000 q^{22} +(-2.05318 - 1.18540i) q^{23} +(-1.72877 + 0.106512i) q^{24} +(2.48237 + 4.29960i) q^{25} +(-2.35256 + 4.07475i) q^{26} +(-0.953778 - 5.10787i) q^{27} +(-1.26717 - 2.32256i) q^{28} -6.25425i q^{29} +(-0.179619 - 0.271112i) q^{30} +(8.78290 - 5.07081i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-0.956629 - 1.44390i) q^{33} +2.97307i q^{34} +(0.258702 - 0.424096i) q^{35} +(-1.80759 - 2.39429i) q^{36} +(-2.73168 + 4.73141i) q^{37} +(0.929908 + 1.61065i) q^{38} +(-8.13408 + 0.501153i) q^{39} +(-0.162607 - 0.0938814i) q^{40} +0.187763 q^{41} +(2.14135 - 4.05150i) q^{42} +7.86942 q^{43} +(-0.866025 - 0.500000i) q^{44} +(0.219631 - 0.518707i) q^{45} +(-1.18540 - 2.05318i) q^{46} +(2.79290 - 4.83744i) q^{47} +(-1.55042 - 0.772144i) q^{48} +(6.99184 + 0.337937i) q^{49} +4.96475i q^{50} +(-4.29283 + 2.84412i) q^{51} +(-4.07475 + 2.35256i) q^{52} +(-9.50430 + 5.48731i) q^{53} +(1.72794 - 4.90043i) q^{54} -0.187763i q^{55} +(0.0638828 - 2.64498i) q^{56} +(-1.43605 + 2.88349i) q^{57} +(3.12712 - 5.41634i) q^{58} +(2.32869 + 4.03341i) q^{59} +(-0.0199991 - 0.324599i) q^{60} +(10.8936 + 6.28942i) q^{61} +10.1416 q^{62} +(7.89845 - 0.783871i) q^{63} -1.00000 q^{64} +(-0.765087 - 0.441723i) q^{65} +(-0.106512 - 1.72877i) q^{66} +(-1.28973 - 2.23388i) q^{67} +(-1.48653 + 2.57475i) q^{68} +(1.83060 - 3.67573i) q^{69} +(0.436091 - 0.237927i) q^{70} -13.5203i q^{71} +(-0.368271 - 2.97731i) q^{72} +(-13.8911 + 8.02001i) q^{73} +(-4.73141 + 2.73168i) q^{74} +(-7.16862 + 4.74942i) q^{75} +1.85982i q^{76} +(2.32256 - 1.26717i) q^{77} +(-7.29490 - 3.63303i) q^{78} +(-3.99299 + 6.91606i) q^{79} +(-0.0938814 - 0.162607i) q^{80} +(8.72875 - 2.19292i) q^{81} +(0.162607 + 0.0938814i) q^{82} +14.7454 q^{83} +(3.88021 - 2.43802i) q^{84} -0.558232 q^{85} +(6.81512 + 3.93471i) q^{86} +(10.8122 - 0.666155i) q^{87} +(-0.500000 - 0.866025i) q^{88} +(4.29254 - 7.43490i) q^{89} +(0.449559 - 0.339398i) q^{90} +(0.300576 - 12.4449i) q^{91} -2.37080i q^{92} +(9.70177 + 14.6435i) q^{93} +(4.83744 - 2.79290i) q^{94} +(-0.302420 + 0.174602i) q^{95} +(-0.956629 - 1.44390i) q^{96} -1.00552i q^{97} +(5.88614 + 3.78858i) q^{98} +(2.39429 - 1.80759i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9}+O(q^{10}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9	\( 20 q - 6 q^{3} + 10 q^{4} - 6 q^{7} - 2 q^{9} - 18 q^{10} - 6 q^{12} - 8 q^{15} - 10 q^{16} + 4 q^{18} + 36 q^{19} + 24 q^{21} - 20 q^{22} - 12 q^{25} - 22 q^{30} + 36 q^{31} - 4 q^{36} + 16 q^{37} + 4 q^{39} - 18 q^{40} + 32 q^{42} + 32 q^{43} + 24 q^{45} + 30 q^{46} - 42 q^{49} - 24 q^{52} - 36 q^{54} - 24 q^{57} + 32 q^{58} - 4 q^{60} + 42 q^{61} - 10 q^{63} - 20 q^{64} + 6 q^{66} - 10 q^{67} - 36 q^{70} - 4 q^{72} + 12 q^{73} - 108 q^{75} + 6 q^{79} + 42 q^{81} + 18 q^{82} + 18 q^{84} - 28 q^{85} + 36 q^{87} - 10 q^{88} - 112 q^{91} - 36 q^{93} + 42 q^{94} - 8 q^{99}+O(q^{100}) \) 20 * q - 6 * q^3 + 10 * q^4 - 6 * q^7 - 2 * q^9 - 18 * q^10 - 6 * q^12 - 8 * q^15 - 10 * q^16 + 4 * q^18 + 36 * q^19 + 24 * q^21 - 20 * q^22 - 12 * q^25 - 22 * q^30 + 36 * q^31 - 4 * q^36 + 16 * q^37 + 4 * q^39 - 18 * q^40 + 32 * q^42 + 32 * q^43 + 24 * q^45 + 30 * q^46 - 42 * q^49 - 24 * q^52 - 36 * q^54 - 24 * q^57 + 32 * q^58 - 4 * q^60 + 42 * q^61 - 10 * q^63 - 20 * q^64 + 6 * q^66 - 10 * q^67 - 36 * q^70 - 4 * q^72 + 12 * q^73 - 108 * q^75 + 6 * q^79 + 42 * q^81 + 18 * q^82 + 18 * q^84 - 28 * q^85 + 36 * q^87 - 10 * q^88 - 112 * q^91 - 36 * q^93 + 42 * q^94 - 8 * q^99

Introduction

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