LMFDB - Embedded newform 462.2.k.g.89.1

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			89.1
Root			$-0.106512 + 1.72877i$ of defining polynomial
Character	$\chi$	$=$	462.89
Dual form			462.2.k.g.353.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-1.44390 - 0.956629i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.0938814 - 0.162607i) q^{5} +(0.772144 + 1.55042i) q^{6} +(-2.64498 - 0.0638828i) q^{7} -1.00000i q^{8} +(1.16972 + 2.76256i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.44390 - 0.956629i) 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} +(1.16972 + 2.76256i) q^{9} +(-0.162607 + 0.0938814i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.106512 - 1.72877i) 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} +(0.368271 - 2.97731i) q^{18} +(1.61065 + 0.929908i) q^{19} +0.187763 q^{20} +(3.75799 + 2.62250i) q^{21} -1.00000 q^{22} +(2.05318 + 1.18540i) q^{23} +(-0.956629 + 1.44390i) 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} +(0.324599 + 0.0199991i) q^{30} +(8.78290 - 5.07081i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.72877 - 0.106512i) 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} +(4.50105 - 6.79375i) q^{39} +(-0.162607 - 0.0938814i) q^{40} -0.187763 q^{41} +(-1.94326 - 4.15015i) q^{42} +7.86942 q^{43} +(0.866025 + 0.500000i) q^{44} +(0.559028 + 0.0691477i) 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} +(-0.316669 + 5.13976i) q^{51} +(-4.07475 + 2.35256i) q^{52} +(9.50430 - 5.48731i) q^{53} +(-3.37993 + 3.94665i) 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} +(-0.271112 - 0.179619i) q^{60} +(10.8936 + 6.28942i) q^{61} -10.1416 q^{62} +(-2.91741 - 7.38165i) q^{63} -1.00000 q^{64} +(0.765087 + 0.441723i) q^{65} +(1.44390 + 0.956629i) 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} +(2.76256 - 1.16972i) q^{72} +(-13.8911 + 8.02001i) q^{73} +(4.73141 - 2.73168i) q^{74} +(0.528807 - 8.58292i) 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} +(-6.26350 + 6.46286i) q^{81} +(0.162607 + 0.0938814i) q^{82} -14.7454 q^{83} +(-0.392162 + 4.56576i) q^{84} -0.558232 q^{85} +(-6.81512 - 3.93471i) q^{86} +(5.98300 - 9.03054i) 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} +(-17.5326 - 1.08021i) q^{93} +(4.83744 - 2.79290i) q^{94} +(0.302420 - 0.174602i) q^{95} +(-1.72877 - 0.106512i) 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
$3$	−1.44390	−	0.956629i	−0.833639	−	0.552310i
$3$	−1.44390	−	0.956629i	−0.833639	−	0.552310i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.0938814	−	0.162607i	0.0419851	−	0.0727202i	−0.844269	−	0.535919i	$-0.819965\pi$
$5$	0.0938814	−	0.162607i	0.0419851	−	0.0727202i	0.886254	+	0.463199i	$0.153298\pi$
$6$	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
$9$	1.16972	+	2.76256i	0.389908	+	0.920854i
$10$	−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
$12$	0.106512	−	1.72877i	0.0307475	−	0.499054i
$13$			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	0.627512	−	0.778607i	$-0.284073\pi$
$17$	−1.48653	−	2.57475i	−0.360538	−	0.624469i	−0.988049	+	0.154138i	$0.950740\pi$
$18$	0.368271	−	2.97731i	0.0868024	−	0.701759i
$19$	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
$21$	3.75799	+	2.62250i	0.820060	+	0.572277i
$22$	−1.00000			−0.213201
$23$	2.05318	+	1.18540i	0.428117	+	0.247173i	0.698544	−	0.715567i	$-0.253832\pi$
$23$	2.05318	+	1.18540i	0.428117	+	0.247173i	−0.270427	+	0.962740i	$0.587165\pi$
$24$	−0.956629	+	1.44390i	−0.195271	+	0.294736i
$25$	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	$0.197218\pi$
$29$			6.25425i			1.16139i	−0.814123	+	0.580693i	$0.802782\pi$
$30$	0.324599	+	0.0199991i	0.0592635	+	0.00365131i
$31$	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
$33$	−1.72877	−	0.106512i	−0.300941	−	0.0185414i
$34$			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
$39$	4.50105	−	6.79375i	0.720745	−	1.08787i
$40$	−0.162607	−	0.0938814i	−0.0257105	−	0.0148440i
$41$	−0.187763			−0.0293236			−0.0146618	−	0.999893i	$-0.504667\pi$
$41$	−0.187763			−0.0293236			−0.0146618	+	0.999893i	$0.504667\pi$
$42$	−1.94326	−	4.15015i	−0.299852	−	0.640382i
$43$	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
$45$	0.559028	+	0.0691477i	0.0833350	+	0.0103079i
$46$	−1.18540	−	2.05318i	−0.174778	−	0.302724i
$47$	−2.79290	+	4.83744i	−0.407386	+	0.705613i	−0.994596	−	0.103822i	$-0.966893\pi$
$47$	−2.79290	+	4.83744i	−0.407386	+	0.705613i	0.587210	+	0.809434i	$0.300226\pi$
$48$	1.55042	−	0.772144i	0.223783	−	0.111449i
$49$	6.99184	+	0.337937i	0.998834	+	0.0482768i
$50$		−	4.96475i		−	0.702121i
$51$	−0.316669	+	5.13976i	−0.0443425	+	0.719710i
$52$	−4.07475	+	2.35256i	−0.565067	+	0.326241i
$53$	9.50430	−	5.48731i	1.30552	−	0.753740i	0.324172	−	0.945998i	$-0.394914\pi$
$53$	9.50430	−	5.48731i	1.30552	−	0.753740i	0.981344	+	0.192258i	$0.0615810\pi$
$54$	−3.37993	+	3.94665i	−0.459950	+	0.537072i
$55$		−	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	0.673682	−	0.739021i	$-0.264712\pi$
$59$	−2.32869	−	4.03341i	−0.303170	−	0.525105i	−0.976852	+	0.213916i	$0.931378\pi$
$60$	−0.271112	−	0.179619i	−0.0350004	−	0.0231888i
$61$	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
$63$	−2.91741	−	7.38165i	−0.367560	−	0.930000i
$64$	−1.00000			−0.125000
$65$	0.765087	+	0.441723i	0.0948974	+	0.0547890i
$66$	1.44390	+	0.956629i	0.177732	+	0.117753i
$67$	−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	$0.296381\pi$
$71$			13.5203i			1.60457i	−0.596944	+	0.802283i	$0.703619\pi$
$72$	2.76256	−	1.16972i	0.325571	−	0.137853i
$73$	−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
$75$	0.528807	−	8.58292i	0.0610613	−	0.991070i
$76$			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
$81$	−6.26350	+	6.46286i	−0.695944	+	0.718096i
$82$	0.162607	+	0.0938814i	0.0179570	+	0.0103675i
$83$	−14.7454			−1.61851			−0.809256	−	0.587456i	$-0.800130\pi$
$83$	−14.7454			−1.61851			−0.809256	+	0.587456i	$0.800130\pi$
$84$	−0.392162	+	4.56576i	−0.0427884	+	0.498166i
$85$	−0.558232			−0.0605488
$86$	−6.81512	−	3.93471i	−0.734893	−	0.424291i
$87$	5.98300	−	9.03054i	0.641444	−	0.968176i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	−4.29254	+	7.43490i	−0.455008	+	0.788097i	−0.998689	−	0.0511950i	$-0.983697\pi$
$89$	−4.29254	+	7.43490i	−0.455008	+	0.788097i	0.543680	+	0.839292i	$0.317030\pi$
$90$	−0.449559	−	0.339398i	−0.0473877	−	0.0357757i
$91$	0.300576	−	12.4449i	0.0315089	−	1.30458i
$92$			2.37080i			0.247173i
$93$	−17.5326	−	1.08021i	−1.81804	−	0.112012i
$94$	4.83744	−	2.79290i	0.498944	−	0.288065i
$95$	0.302420	−	0.174602i	0.0310276	−	0.0179138i
$96$	−1.72877	−	0.106512i	−0.176442	−	0.0108709i
$97$		−	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	$-0.862802\pi$
$101$	−8.20165	−	14.2057i	−0.816094	−	1.41352i	0.0924454	−	0.995718i	$-0.470532\pi$
$102$	2.84412	−	4.29283i	0.281610	−	0.425053i
$103$	−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
$105$	0.779244	−	0.364872i	0.0760464	−	0.0356079i
$106$	−10.9746			−1.06595
$107$	0.0207756	+	0.0119948i	0.00200846	+	0.00115958i	0.501004	−	0.865445i	$-0.332964\pi$
$107$	0.0207756	+	0.0119948i	0.00200846	+	0.00115958i	−0.498995	+	0.866605i	$0.666298\pi$
$108$	4.90043	−	1.72794i	0.471544	−	0.166271i
$109$	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	$0.203481\pi$
$113$			12.6838i			1.19320i	−0.802541	+	0.596598i	$0.796519\pi$
$114$	−0.198093	+	3.21520i	−0.0185531	+	0.301131i
$115$	0.385510	−	0.222574i	0.0359490	−	0.0207552i
$116$	−5.41634	+	3.12712i	−0.502894	+	0.290346i
$117$	−12.9982	+	5.50369i	−1.20168	+	0.508816i
$118$			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
$123$	0.271112	+	0.179619i	0.0244453	+	0.0161957i
$124$	8.78290	+	5.07081i	0.788728	+	0.455372i
$125$	1.87101			0.167348
$126$	−1.16427	+	7.85140i	−0.103721	+	0.699458i
$127$	−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
$129$	−11.3627	−	7.52812i	−1.00043	−	0.662814i
$130$	−0.441723	−	0.765087i	−0.0387417	−	0.0671026i
$131$	−1.00216	+	1.73580i	−0.0875595	+	0.151657i	−0.906479	−	0.422251i	$-0.861240\pi$
$131$	−1.00216	+	1.73580i	−0.0875595	+	0.151657i	0.818920	+	0.573908i	$0.194573\pi$
$132$	−0.772144	−	1.55042i	−0.0672065	−	0.134947i
$133$	−4.20073	−	2.56248i	−0.364249	−	0.222195i
$134$			2.57946i			0.222832i
$135$	−0.741035	−	0.634625i	−0.0637781	−	0.0546198i
$136$	−2.57475	+	1.48653i	−0.220783	+	0.127469i
$137$	7.81301	−	4.51084i	0.667511	−	0.385387i	−0.127622	−	0.991823i	$-0.540734\pi$
$137$	7.81301	−	4.51084i	0.667511	−	0.385387i	0.795133	+	0.606435i	$0.207401\pi$
$138$	−0.252520	+	4.09858i	−0.0214959	+	0.348894i
$139$			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
$144$	−2.97731	−	0.368271i	−0.248109	−	0.0306893i
$145$	1.01699	+	0.587158i	0.0844562	+	0.0487608i
$146$	16.0400			1.32748
$147$	−9.77227	−	7.17654i	−0.806003	−	0.591911i
$148$	−5.46337			−0.449086
$149$	12.9762	+	7.49184i	1.06306	+	0.613755i	0.926276	−	0.376846i	$-0.122991\pi$
$149$	12.9762	+	7.49184i	1.06306	+	0.613755i	0.136780	+	0.990602i	$0.456325\pi$
$150$	−4.74942	+	7.16862i	−0.387788	+	0.585315i
$151$	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
$156$	8.13408	+	0.501153i	0.651248	+	0.0401244i
$157$	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
$159$	−18.9726	−	1.16893i	−1.50463	−	0.0927024i
$160$		−	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
$165$	−0.179619	+	0.271112i	−0.0139833	+	0.0211060i
$166$	12.7698	+	7.37268i	0.991132	+	0.572231i
$167$	14.3973			1.11409			0.557047	−	0.830481i	$-0.311934\pi$
$167$	14.3973			1.11409			0.557047	+	0.830481i	$0.311934\pi$
$168$	2.62250	−	3.75799i	0.202331	−	0.289935i
$169$	−9.13815			−0.702935
$170$	0.483443	+	0.279116i	0.0370784	+	0.0214072i
$171$	−0.684917	+	5.53725i	−0.0523769	+	0.423444i
$172$	3.93471	+	6.81512i	0.300019	+	0.519648i
$173$	0.936038	−	1.62126i	0.0711656	−	0.123262i	−0.828247	−	0.560363i	$-0.810661\pi$
$173$	0.936038	−	1.62126i	0.0711656	−	0.123262i	0.899412	+	0.437101i	$0.143995\pi$
$174$	−9.69670	+	4.82918i	−0.735105	+	0.366099i
$175$	−6.29116	−	11.5309i	−0.475567	−	0.871656i
$176$			1.00000i			0.0753778i
$177$	−0.496069	+	8.05155i	−0.0372868	+	0.605192i
$178$	7.43490	−	4.29254i	0.557269	−	0.321739i
$179$	3.52389	−	2.03452i	0.263388	−	0.152067i	−0.362491	−	0.931987i	$-0.618074\pi$
$179$	3.52389	−	2.03452i	0.263388	−	0.152067i	0.625879	+	0.779920i	$0.284740\pi$
$180$	0.219631	+	0.518707i	0.0163703	+	0.0386621i
$181$		−	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
$186$	14.6435	+	9.70177i	1.07372	+	0.711368i
$187$	−2.57475	−	1.48653i	−0.188285	−	0.108706i
$188$	−5.58579			−0.407386
$189$	−2.84903	+	13.4493i	−0.207236	+	0.978291i
$190$	−0.349204			−0.0253340
$191$	−4.63286	−	2.67479i	−0.335222	−	0.193541i	0.322935	−	0.946421i	$-0.395330\pi$
$191$	−4.63286	−	2.67479i	−0.335222	−	0.193541i	−0.658157	+	0.752880i	$0.728664\pi$
$192$	1.44390	+	0.956629i	0.104205	+	0.0690387i
$193$	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	$0.174951\pi$
$197$			14.6635i			1.04473i	−0.852721	+	0.522366i	$0.825049\pi$
$198$	−1.16972	−	2.76256i	−0.0831286	−	0.196327i
$199$	−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
$201$	−0.274745	+	4.45931i	−0.0193790	+	0.314535i
$202$			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
$207$	−0.873099	+	7.05862i	−0.0606845	+	0.490608i
$208$	−4.07475	−	2.35256i	−0.282533	−	0.163121i
$209$	1.85982			0.128646
$210$	−0.857281	−	0.0736334i	−0.0591580	−	0.00508119i
$211$	−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
$213$	12.9339	−	19.5220i	0.886217	−	1.33763i
$214$	−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
$219$	27.7296	+	1.70846i	1.87379	+	0.115447i
$220$	0.162607	−	0.0938814i	0.0109630	−	0.00632948i
$221$	12.1145	−	6.99432i	0.814911	−	0.470489i
$222$	−9.44492	−	0.581916i	−0.633901	−	0.0390556i
$223$		−	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	0.871943	−	0.489608i	$-0.162860\pi$
$227$	0.180173	+	0.312069i	0.0119585	+	0.0207128i	−0.859984	+	0.510321i	$0.829527\pi$
$228$	1.77915	−	2.68540i	0.117827	−	0.177845i
$229$	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
$231$	4.56576	+	0.392162i	0.300405	+	0.0258024i
$232$	6.25425			0.410612
$233$	−22.0707	−	12.7425i	−1.44590	−	0.834791i	−0.447666	−	0.894201i	$-0.647745\pi$
$233$	−22.0707	−	12.7425i	−1.44590	−	0.834791i	−0.998234	+	0.0594100i	$0.981078\pi$
$234$	14.0086	+	1.73276i	0.915771	+	0.113274i
$235$	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	$0.0804549\pi$
$239$			7.73209i			0.500148i	−0.968227	+	0.250074i	$0.919545\pi$
$240$	0.0199991	−	0.324599i	0.00129093	−	0.0209528i
$241$	−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
$243$	15.2265	−	3.33992i	0.976778	−	0.214256i
$244$			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
$249$	21.2909	+	14.1058i	1.34925	+	0.893920i
$250$	−1.62034	−	0.935505i	−0.102479	−	0.0591665i
$251$	25.8784			1.63343			0.816714	−	0.577042i	$-0.195793\pi$
$251$	25.8784			1.63343			0.816714	+	0.577042i	$0.195793\pi$
$252$	4.93399	−	6.21738i	0.310812	−	0.391658i
$253$	2.37080			0.149051
$254$	4.54176	+	2.62219i	0.284975	+	0.164531i
$255$	0.806034	+	0.534021i	0.0504758	+	0.0334417i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.64666	−	6.31620i	0.227473	−	0.393994i	−0.729586	−	0.683889i	$-0.760287\pi$
$257$	3.64666	−	6.31620i	0.227473	−	0.393994i	0.957058	+	0.289895i	$0.0936205\pi$
$258$	6.07633	+	12.2009i	0.378296	+	0.759594i
$259$	7.52750	−	12.3400i	0.467736	−	0.766770i
$260$			0.883447i			0.0547890i
$261$	−17.2778	+	7.31574i	−1.06947	+	0.452833i
$262$	1.73580	−	1.00216i	0.107238	−	0.0619139i
$263$	−12.9008	+	7.44827i	−0.795496	+	0.459280i	−0.841894	−	0.539643i	$-0.818559\pi$
$263$	−12.9008	+	7.44827i	−0.795496	+	0.459280i	0.0463977	+	0.998923i	$0.485226\pi$
$264$	−0.106512	+	1.72877i	−0.00655538	+	0.106399i
$265$		−	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	0.997226	−	0.0744323i	$-0.0237145\pi$
$269$	7.12064	+	12.3333i	0.434153	+	0.751975i	−0.563073	+	0.826407i	$0.690381\pi$
$270$	0.324443	+	0.920119i	0.0197449	+	0.0559967i
$271$	−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
$273$	−12.3392	+	17.6818i	−0.746802	+	1.07015i
$274$	−9.02169			−0.545020
$275$	4.29960	+	2.48237i	0.259275	+	0.149693i
$276$	2.26798	−	3.42321i	0.136516	−	0.206053i
$277$	−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	$-0.825233\pi$
$281$		−	17.4964i		−	1.04375i	0.853023	−	0.521874i	$-0.174767\pi$
$282$	−9.65656	−	0.594956i	−0.575040	−	0.0354291i
$283$	−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
$285$	−0.603695	−	0.0371946i	−0.0357598	−	0.00220322i
$286$		−	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
$291$	−0.961906	+	1.45187i	−0.0563879	+	0.0851102i
$292$	−13.8911	−	8.02001i	−0.812913	−	0.469336i
$293$	−8.00890			−0.467885			−0.233942	−	0.972250i	$-0.575163\pi$
$293$	−8.00890			−0.467885			−0.233942	+	0.972250i	$0.575163\pi$
$294$	4.87476	+	11.1012i	0.284302	+	0.647435i
$295$	−0.874483			−0.0509144
$296$	4.73141	+	2.73168i	0.275008	+	0.158776i
$297$	−1.72794	−	4.90043i	−0.100265	−	0.284352i
$298$	−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
$303$	−1.74715	+	28.3576i	−0.100371	+	1.62910i
$304$	−1.61065	+	0.929908i	−0.0923770	+	0.0533339i
$305$	2.04541	−	1.18092i	0.117120	−	0.0676193i
$306$	−8.21329	+	3.47767i	−0.469522	+	0.198805i
$307$			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	0.932725	−	0.360589i	$-0.117424\pi$
$311$	2.71729	+	4.70648i	0.154083	+	0.266880i	−0.778642	+	0.627469i	$0.784091\pi$
$312$	−6.79375	−	4.50105i	−0.384620	−	0.254822i
$313$	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
$315$	−1.47420	−	0.218606i	−0.0830618	−	0.0123171i
$316$	−7.98598			−0.449246
$317$	23.5911	+	13.6203i	1.32501	+	0.764995i	0.984523	−	0.175255i	$-0.0560749\pi$
$317$	23.5911	+	13.6203i	1.32501	+	0.764995i	0.340486	+	0.940249i	$0.389408\pi$
$318$	15.8463	+	10.4986i	0.888617	+	0.588734i
$319$	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
$324$	−8.72875	−	2.19292i	−0.484931	−	0.121829i
$325$	−20.2301	+	11.6799i	−1.12216	+	0.647882i
$326$	0.703707	−	0.406286i	0.0389747	−	0.0225021i
$327$	0.132384	−	2.14868i	0.00732083	−	0.118822i
$328$			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
$333$	−16.2661	−	2.01200i	−0.891379	−	0.110257i
$334$	−12.4684	−	7.19863i	−0.682240	−	0.393892i
$335$	−0.484328			−0.0264616
$336$	−4.15015	+	1.94326i	−0.226409	+	0.106014i
$337$	−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
$339$	12.1337	−	18.3143i	0.659013	−	0.994694i
$340$	−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
$345$	−0.769561	−	0.0474138i	−0.0414318	−	0.00255267i
$346$	−1.62126	+	0.936038i	−0.0871597	+	0.0503217i
$347$	21.4218	−	12.3679i	1.14998	−	0.663942i	0.201098	−	0.979571i	$-0.435549\pi$
$347$	21.4218	−	12.3679i	1.14998	−	0.663942i	0.948882	+	0.315630i	$0.102216\pi$
$348$	10.8122	+	0.666155i	0.579593	+	0.0357096i
$349$		−	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	$-0.973663\pi$
$353$	−10.7068	−	18.5447i	−0.569864	−	0.987033i	0.426715	−	0.904386i	$-0.359671\pi$
$354$	4.45538	−	6.72482i	0.236801	−	0.357420i
$355$	2.19850	+	1.26931i	0.116684	+	0.0673678i
$356$	−8.58508			−0.455008
$357$	1.16592	−	13.5743i	0.0617072	−	0.718430i
$358$	−4.06903			−0.215055
$359$	−6.11309	−	3.52939i	−0.322636	−	0.186274i	0.329931	−	0.944005i	$-0.392975\pi$
$359$	−6.11309	−	3.52939i	−0.322636	−	0.186274i	−0.652567	+	0.757731i	$0.726308\pi$
$360$	0.0691477	−	0.559028i	0.00364440	−	0.0294634i
$361$	−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
$366$	−1.33980	+	21.7460i	−0.0700326	+	1.13668i
$367$	−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
$369$	−0.219631	−	0.518707i	−0.0114335	−	0.0270028i
$370$		−	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
$375$	−2.70156	−	1.78986i	−0.139508	−	0.0924280i
$376$	4.83744	+	2.79290i	0.249472	+	0.144033i
$377$	−29.4270			−1.51557
$378$	9.19197	−	10.2229i	0.472784	−	0.525809i
$379$	−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
$381$	7.57237	+	5.01692i	0.387944	+	0.257024i
$382$	2.67479	+	4.63286i	0.136854	+	0.237038i
$383$	8.55052	−	14.8099i	0.436911	−	0.756753i	−0.560538	−	0.828129i	$-0.689406\pi$
$383$	8.55052	−	14.8099i	0.436911	−	0.756753i	0.997449	+	0.0713759i	$0.0227390\pi$
$384$	−0.772144	−	1.55042i	−0.0394033	−	0.0791194i
$385$	−0.0119948	+	0.496629i	−0.000611312	+	0.0253106i
$386$		−	13.1825i		−	0.670970i
$387$	9.20505	+	21.7398i	0.467919	+	1.10509i
$388$	0.870803	−	0.502758i	0.0442083	−	0.0255237i
$389$	−31.2503	+	18.0424i	−1.58445	+	0.914784i	−0.590255	+	0.807217i	$0.700973\pi$
$389$	−31.2503	+	18.0424i	−1.58445	+	0.914784i	−0.994198	+	0.107567i	$0.965694\pi$
$390$	−0.0940980	+	1.52728i	−0.00476484	+	0.0773368i
$391$		−	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
$396$	−0.368271	+	2.97731i	−0.0185063	+	0.149615i
$397$	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
$399$	3.61411	+	7.71852i	0.180932	+	0.386409i
$400$	−4.96475			−0.248237
$401$	−19.4819	−	11.2479i	−0.972880	−	0.561692i	−0.0727666	−	0.997349i	$-0.523183\pi$
$401$	−19.4819	−	11.2479i	−0.972880	−	0.561692i	−0.900113	+	0.435657i	$0.856516\pi$
$402$	2.46759	−	3.72450i	0.123072	−	0.185761i
$403$	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
$408$	5.13976	+	0.316669i	0.254456	+	0.0156774i
$409$	−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
$411$	−15.5964	−	0.960921i	−0.769316	−	0.0473987i
$412$		−	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
$417$	4.00888	−	6.05088i	0.196316	−	0.296313i
$418$	−1.61065	−	0.929908i	−0.0787794	−	0.0454833i
$419$	−21.3181			−1.04146			−0.520728	−	0.853723i	$-0.674339\pi$
$419$	−21.3181			−1.04146			−0.520728	+	0.853723i	$0.674339\pi$
$420$	0.705610	+	0.492409i	0.0344303	+	0.0240271i
$421$	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
$423$	−16.6306	−	2.05709i	−0.808609	−	0.100019i
$424$	−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
$429$	0.501153	−	8.13408i	0.0241959	−	0.392717i
$430$	−1.27963	+	0.738793i	−0.0617091	+	0.0356278i
$431$	−24.2725	+	14.0137i	−1.16916	+	0.675017i	−0.953483	−	0.301447i	$-0.902530\pi$
$431$	−24.2725	+	14.0137i	−1.16916	+	0.675017i	−0.215680	+	0.976464i	$0.569197\pi$
$432$	3.94665	+	3.37993i	0.189883	+	0.162617i
$433$		−	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
$438$	−23.1603	−	15.3443i	−1.10664	−	0.733181i
$439$	−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
$441$	7.24494	+	19.7107i	0.344997	+	0.938604i
$442$	−13.9886			−0.665372
$443$	−22.0499	−	12.7305i	−1.04762	−	0.604846i	−0.125641	−	0.992076i	$-0.540099\pi$
$443$	−22.0499	−	12.7305i	−1.04762	−	0.604846i	−0.921983	+	0.387230i	$0.873432\pi$
$444$	7.88858	+	5.22641i	0.374376	+	0.248035i
$445$	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	$0.332296\pi$
$449$			36.6323i			1.72878i	−0.502819	+	0.864392i	$0.667704\pi$
$450$	13.7154	−	5.80738i	0.646551	−	0.273762i
$451$	−0.162607	+	0.0938814i	−0.00765688	+	0.00442070i
$452$	−10.9845	+	6.34192i	−0.516669	+	0.298299i
$453$	0.0584065	−	0.947980i	0.00274418	−	0.0445400i
$454$		−	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
$459$	−14.5693	+	5.13728i	−0.680038	+	0.239788i
$460$	0.385510	+	0.222574i	0.0179745	+	0.0103776i
$461$	−26.7742			−1.24700			−0.623500	−	0.781823i	$-0.714290\pi$
$461$	−26.7742			−1.24700			−0.623500	+	0.781823i	$0.714290\pi$
$462$	−3.75799	−	2.62250i	−0.174837	−	0.122010i
$463$	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
$465$	−1.82163	+	2.74951i	−0.0844762	+	0.127506i
$466$	12.7425	+	22.0707i	0.590286	+	1.02241i
$467$	−14.1426	+	24.4957i	−0.654441	+	1.13352i	0.327593	+	0.944819i	$0.393762\pi$
$467$	−14.1426	+	24.4957i	−0.654441	+	1.13352i	−0.982034	+	0.188705i	$0.939571\pi$
$468$	−11.2654	−	8.50491i	−0.520744	−	0.393140i
$469$	3.26861	+	5.99096i	0.150930	+	0.276637i
$470$		−	1.04880i		−	0.0483777i
$471$	−33.1515	−	2.04252i	−1.52754	−	0.0941142i
$472$	−4.03341	+	2.32869i	−0.185653	+	0.107187i
$473$	6.81512	−	3.93471i	0.313360	−	0.180918i
$474$	−13.8059	−	0.850605i	−0.634128	−	0.0390696i
$475$			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	$0.139989\pi$
$479$	17.9713	+	31.1272i	0.821130	+	1.42224i	−0.0837110	+	0.996490i	$0.526677\pi$
$480$	−0.179619	+	0.271112i	−0.00819846	+	0.0123745i
$481$	−22.2619	−	12.8529i	−1.01505	−	0.586042i
$482$	6.62493			0.301757
$483$	4.60709	+	9.83919i	0.209630	+	0.447698i
$484$	1.00000			0.0454545
$485$	−0.163504	−	0.0943993i	−0.00742435	−	0.00428645i
$486$	−14.8565	−	4.72077i	−0.673903	−	0.214139i
$487$	−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	$-0.824425\pi$
$491$		−	23.2238i		−	1.04808i	0.851695	−	0.524038i	$-0.175575\pi$
$492$	−0.0199991	+	0.324599i	−0.000901627	+	0.0146341i
$493$	16.1031	−	9.29716i	0.725249	−	0.418723i
$494$	7.57829	−	4.37533i	0.340964	−	0.196855i
$495$	0.518707	−	0.219631i	0.0233141	−	0.00987166i
$496$			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
$501$	−20.7883	−	13.7728i	−0.928752	−	0.615325i
$502$	−22.4113	−	12.9392i	−1.00027	−	0.577504i
$503$	10.0786			0.449384			0.224692	−	0.974430i	$-0.427862\pi$
$503$	10.0786			0.449384			0.224692	+	0.974430i	$0.427862\pi$
$504$	−7.38165	+	2.91741i	−0.328805	+	0.129952i
$505$	−3.07993			−0.137055
$506$	−2.05318	−	1.18540i	−0.0912748	−	0.0526975i
$507$	13.1946	+	8.74182i	0.585994	+	0.388238i
$508$	−2.62219	−	4.54176i	−0.116341	−	0.201508i
$509$	4.15651	−	7.19930i	0.184234	−	0.319103i	−0.759084	−	0.650993i	$-0.774353\pi$
$509$	4.15651	−	7.19930i	0.184234	−	0.319103i	0.943318	+	0.331890i	$0.107686\pi$
$510$	−0.431035	−	0.865492i	−0.0190866	−	0.0383246i
$511$	37.2539	−	20.3254i	1.64802	−	0.899141i
$512$			1.00000i			0.0441942i
$513$	6.28605	−	7.34005i	0.277536	−	0.324071i
$514$	−6.31620	+	3.64666i	−0.278596	+	0.160847i
$515$	−0.824946	+	0.476283i	−0.0363515	+	0.0209875i
$516$	0.838191	−	13.6044i	0.0368993	−	0.598902i
$517$			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	0.813873	−	0.581043i	$-0.197355\pi$
$521$	−2.19722	−	3.80570i	−0.0962620	−	0.166731i	−0.910135	+	0.414313i	$0.864022\pi$
$522$	18.6208	+	2.30326i	0.815012	+	0.100811i
$523$	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
$525$	−1.94698	+	22.6679i	−0.0849733	+	0.989306i
$526$	14.8965			0.649520
$527$	−26.1122	−	15.0759i	−1.13746	−	0.656715i
$528$	0.956629	−	1.44390i	0.0416319	−	0.0628379i
$529$	−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
$534$	−14.8416	−	0.914417i	−0.642261	−	0.0395707i
$535$	0.00390089	−	0.00225218i	0.000168650	−	9.73703e-5i
$536$	−2.23388	+	1.28973i	−0.0964890	+	0.0557079i
$537$	−7.03443	−	0.433402i	−0.303558	−	0.0187027i
$538$		−	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
$543$	−12.4588	+	18.8050i	−0.534660	+	0.806999i
$544$	−2.57475	−	1.48653i	−0.110392	−	0.0637346i
$545$	0.233370			0.00999645
$546$	19.5269	−	9.14327i	0.835676	−	0.391296i
$547$	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
$549$	−4.63243	+	37.4511i	−0.197707	+	1.59837i
$550$	−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
$555$	0.109262	−	1.77341i	0.00463792	−	0.0752769i
$556$	−3.62920	+	2.09532i	−0.153912	+	0.0888613i
$557$	38.3279	−	22.1286i	1.62400	−	0.937619i	0.638170	−	0.769895i	$-0.279692\pi$
$557$	38.3279	−	22.1286i	1.62400	−	0.937619i	0.985834	−	0.167724i	$-0.0536418\pi$
$558$	−11.8629	−	28.0169i	−0.502196	−	1.18605i
$559$			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	$0.0160372\pi$
$563$	12.8836	+	22.3151i	0.542979	+	0.940468i	−0.455752	+	0.890107i	$0.650629\pi$
$564$	8.06535	+	5.34353i	0.339613	+	0.225003i
$565$	2.06249	+	1.19078i	0.0867694	+	0.0500964i
$566$	6.43083			0.270308
$567$	16.9797	−	16.6940i	0.713080	−	0.701083i
$568$	13.5203			0.567300
$569$	28.2052	+	16.2843i	1.18242	+	0.682673i	0.956574	−	0.291490i	$-0.0941508\pi$
$569$	28.2052	+	16.2843i	1.18242	+	0.682673i	0.225850	+	0.974162i	$0.427484\pi$
$570$	0.504218	+	0.334059i	0.0211194	+	0.0139922i
$571$	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
$576$	−1.16972	−	2.76256i	−0.0487385	−	0.115107i
$577$	−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
$579$	1.40409	−	22.7895i	0.0583522	−	0.947098i
$580$			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
$585$	−0.325348	+	2.63030i	−0.0134515	+	0.108749i
$586$	6.93591	+	4.00445i	0.286520	+	0.165422i
$587$	−35.2011			−1.45291			−0.726453	−	0.687217i	$-0.758832\pi$
$587$	−35.2011			−1.45291			−0.726453	+	0.687217i	$0.758832\pi$
$588$	1.32893	−	12.0513i	0.0548043	−	0.496987i
$589$	18.8616			0.777177
$590$	0.757325	+	0.437242i	0.0311786	+	0.0180010i
$591$	14.0275	−	21.1727i	0.577016	−	0.870930i
$592$	−2.73168	−	4.73141i	−0.112271	−	0.194460i
$593$	13.4629	−	23.3184i	0.552853	−	0.957570i	−0.445214	−	0.895424i	$-0.646872\pi$
$593$	13.4629	−	23.3184i	0.552853	−	0.957570i	0.998067	−	0.0621457i	$-0.0197944\pi$
$594$	−0.953778	+	5.10787i	−0.0391340	+	0.209578i
$595$	1.47651	+	0.0356614i	0.0605311	+	0.00146198i
$596$			14.9837i			0.613755i
$597$	3.64857	+	0.224794i	0.149326	+	0.00920021i
$598$	9.66044	−	5.57746i	0.395045	−	0.228079i
$599$	15.8188	−	9.13299i	0.646338	−	0.373164i	−0.140714	−	0.990050i	$-0.544940\pi$
$599$	15.8188	−	9.13299i	0.646338	−	0.373164i	0.787052	+	0.616887i	$0.211606\pi$
$600$	−8.58292	−	0.528807i	−0.350396	−	0.0215884i
$601$		−	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
$606$	15.6919	−	23.6848i	0.637438	−	0.962129i
$607$	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
$609$	−16.4018	+	23.5034i	−0.664634	+	0.952406i
$610$	−2.36184			−0.0956281
$611$	−22.7607	−	13.1409i	−0.920800	−	0.531624i
$612$	8.85175	+	1.09490i	0.357811	+	0.0442585i
$613$	−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	$-0.898283\pi$
$617$		−	15.6062i		−	0.628282i	0.949376	−	0.314141i	$-0.101717\pi$
$618$	0.540362	−	8.77047i	0.0217366	−	0.352800i
$619$	−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
$621$	8.01315	−	9.35674i	0.321556	−	0.375473i
$622$		−	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
$627$	−2.68540	−	1.77915i	−0.107244	−	0.0710526i
$628$	16.6072	+	9.58817i	0.662699	+	0.382610i
$629$	16.2430			0.647649
$630$	1.16739	+	0.926419i	0.0465100	+	0.0369094i
$631$	−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
$633$	7.32199	+	4.85103i	0.291023	+	0.192811i
$634$	−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
$639$	−37.3507	+	15.8150i	−1.47757	+	0.625632i
$640$	0.162607	−	0.0938814i	0.00642762	−	0.00371099i
$641$	23.4593	−	13.5443i	0.926588	−	0.534966i	0.0408571	−	0.999165i	$-0.486991\pi$
$641$	23.4593	−	13.5443i	0.926588	−	0.534966i	0.885731	+	0.464199i	$0.153658\pi$
$642$	−0.00255519	+	0.0414726i	−0.000100845	+	0.00163679i
$643$			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	0.868110	−	0.496372i	$-0.165335\pi$
$647$	0.106419	+	0.184324i	0.00418378	+	0.00724652i	−0.863926	+	0.503619i	$0.832002\pi$
$648$	6.46286	+	6.26350i	0.253885	+	0.246053i
$649$	−4.03341	−	2.32869i	−0.158325	−	0.0914091i
$650$	23.3597			0.916244
$651$	46.3043	+	3.97716i	1.81481	+	0.155877i
$652$	−0.812571			−0.0318227
$653$	19.4953	+	11.2556i	0.762911	+	0.440467i	0.830340	−	0.557257i	$-0.188146\pi$
$653$	19.4953	+	11.2556i	0.762911	+	0.440467i	−0.0674291	+	0.997724i	$0.521480\pi$
$654$	−1.18899	+	1.79462i	−0.0464932	+	0.0701753i
$655$	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	$-0.847781\pi$
$659$		−	23.6271i		−	0.920380i	0.887820	−	0.460190i	$-0.152219\pi$
$660$	−0.324599	−	0.0199991i	−0.0126350	−	0.000778462i
$661$	−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
$663$	−24.1832	−	1.48996i	−0.939197	−	0.0578654i
$664$			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
$669$	−12.0800	+	18.2331i	−0.467039	+	0.704933i
$670$	0.419440	+	0.242164i	0.0162044	+	0.00935560i
$671$	12.5788			0.485601
$672$	4.56576	+	0.392162i	0.176128	+	0.0151280i
$673$	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
$675$	24.3294	−	8.57877i	0.936439	−	0.330197i
$676$	−4.56908	−	7.91387i	−0.175734	−	0.304380i
$677$	7.35012	−	12.7308i	0.282488	−	0.489284i	−0.689509	−	0.724277i	$-0.742174\pi$
$677$	7.35012	−	12.7308i	0.282488	−	0.489284i	0.971997	+	0.234993i	$0.0755069\pi$
$678$	−19.6652	+	9.79375i	−0.755239	+	0.376127i
$679$	−0.0642352	+	2.65957i	−0.00246512	+	0.102065i
$680$			0.558232i			0.0214072i
$681$	0.0383813	−	0.622957i	0.00147078	−	0.0238718i
$682$	−8.78290	+	5.07081i	−0.336315	+	0.194171i
$683$	−42.1416	+	24.3305i	−1.61251	+	0.930980i	−0.623718	+	0.781649i	$0.714379\pi$
$683$	−42.1416	+	24.3305i	−1.61251	+	0.930980i	−0.988787	+	0.149331i	$0.952288\pi$
$684$	−5.13786	+	2.17547i	−0.196451	+	0.0831812i
$685$		−	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
$690$	0.642752	+	0.425842i	0.0244692	+	0.0162115i
$691$	−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
$693$	−6.21738	−	4.93399i	−0.236179	−	0.187427i
$694$	−24.7357			−0.938955
$695$	0.681428	+	0.393423i	0.0258481	+	0.0149234i
$696$	−9.03054	−	5.98300i	−0.342302	−	0.226785i
$697$	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	$-0.535328\pi$
$701$		−	52.6270i		−	1.98769i	0.110759	−	0.993847i	$-0.464672\pi$
$702$	−18.5695	−	15.9030i	−0.700860	−	0.600219i
$703$	−8.79956	+	5.08043i	−0.331882	+	0.191612i
$704$	−0.866025	+	0.500000i	−0.0326396	+	0.0188445i
$705$	0.111711	−	1.81314i	0.00420726	−	0.0682870i
$706$			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
$711$	−23.7767	−	2.94101i	−0.891697	−	0.110296i
$712$	7.43490	+	4.29254i	0.278634	+	0.160870i
$713$	24.0438			0.900447
$714$	−7.79689	+	11.1728i	−0.291791	+	0.418130i
$715$	0.883447			0.0330390
$716$	3.52389	+	2.03452i	0.131694	+	0.0760335i
$717$	7.39674	−	11.1644i	0.276236	−	0.416942i
$718$	3.52939	+	6.11309i	0.131716	+	0.228138i
$719$	12.0066	−	20.7960i	0.447771	−	0.775562i	−0.550470	−	0.834855i	$-0.685551\pi$
$719$	12.0066	−	20.7960i	0.447771	−	0.775562i	0.998241	+	0.0592933i	$0.0188847\pi$
$720$	−0.339398	+	0.449559i	−0.0126486	+	0.0167541i
$721$	11.4588	+	6.98998i	0.426748	+	0.260320i
$722$			15.5411i			0.578379i
$723$	11.4530	+	0.705637i	0.425942	+	0.0262429i
$724$	11.2789	−	6.51185i	0.419175	−	0.242011i
$725$	−26.8907	+	15.5254i	−0.998697	+	0.576598i
$726$	1.72877	+	0.106512i	0.0641608	+	0.00395304i
$727$			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
$732$	12.0333	−	18.1627i	0.444763	−	0.671311i
$733$	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
$735$	−2.08439	+	0.915299i	−0.0768840	+	0.0337613i
$736$	2.37080			0.0873890
$737$	−2.23388	−	1.28973i	−0.0822861	−	0.0475079i
$738$	−0.0691477	+	0.559028i	−0.00254536	+	0.0205781i
$739$	−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	$-0.887570\pi$
$743$		−	18.8577i		−	0.691822i	0.938267	−	0.345911i	$-0.112430\pi$
$744$	−1.08021	+	17.5326i	−0.0396023	+	0.642775i
$745$	2.43646	−	1.40669i	0.0892649	−	0.0515371i
$746$	−29.1651	+	16.8385i	−1.06781	+	0.616500i
$747$	−17.2480	−	40.7349i	−0.631070	−	1.49041i
$748$		−	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
$753$	−37.3659	−	24.7560i	−1.36169	−	0.902159i
$754$	25.4845	+	14.7135i	0.928092	+	0.535834i
$755$	0.102961			0.00374712
$756$	−13.0719	+	4.25731i	−0.475421	+	0.154837i
$757$	−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
$759$	−3.42321	−	2.26798i	−0.124255	−	0.0823224i
$760$	−0.174602	−	0.302420i	−0.00633349	−	0.0109699i
$761$	−3.59703	+	6.23024i	−0.130392	+	0.225846i	−0.923828	−	0.382808i	$-0.874957\pi$
$761$	−3.59703	+	6.23024i	−0.130392	+	0.225846i	0.793436	+	0.608654i	$0.208290\pi$
$762$	−4.04941	−	8.13096i	−0.146695	−	0.294554i
$763$	−1.57495	−	2.88670i	−0.0570172	−	0.104506i
$764$		−	5.34957i		−	0.193541i
$765$	−0.652977	−	1.54215i	−0.0236084	−	0.0557566i
$766$	−14.8099	+	8.55052i	−0.535105	+	0.308943i
$767$	18.9777	−	10.9568i	0.685244	−	0.395626i
$768$	−0.106512	+	1.72877i	−0.00384343	+	0.0623817i
$769$			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	0.850397	−	0.526142i	$-0.176362\pi$
$773$	−0.846710	−	1.46654i	−0.0304540	−	0.0527480i	−0.880851	+	0.473394i	$0.843029\pi$
$774$	2.89808	−	23.4297i	0.104169	−	0.842164i
$775$	43.6049	+	25.1753i	1.56633	+	0.904323i
$776$	−1.00552			−0.0360959
$777$	−22.6738	+	10.6167i	−0.813418	+	0.380874i
$778$	36.0847			1.29370
$779$	−0.302420	−	0.174602i	−0.0108353	−	0.00625577i
$780$	0.845131	−	1.27561i	0.0302605	−	0.0456743i
$781$	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
$786$	−3.46503	−	0.213486i	−0.123593	−	0.00761478i
$787$	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
$789$	25.7527	+	1.58666i	0.916821	+	0.0564868i
$790$		−	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
$795$	−1.97125	+	2.97535i	−0.0699132	+	0.105525i
$796$	−1.82774	−	1.05525i	−0.0647827	−	0.0374023i
$797$	43.0989			1.52664			0.763321	−	0.646019i	$-0.223567\pi$
$797$	43.0989			1.52664			0.763321	+	0.646019i	$0.223567\pi$
$798$	0.729349	−	8.49148i	0.0258187	−	0.300595i
$799$	16.6069			0.587511
$800$	4.29960	+	2.48237i	0.152014	+	0.0877651i
$801$	−25.5604	−	3.16164i	−0.903134	−	0.111711i
$802$	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
$807$	1.51687	−	24.6199i	0.0533964	−	0.866662i
$808$	−14.2057	+	8.20165i	−0.499754	+	0.288533i
$809$	−2.59018	+	1.49544i	−0.0910660	+	0.0525770i	−0.544841	−	0.838539i	$-0.683410\pi$
$809$	−2.59018	+	1.49544i	−0.0910660	+	0.0525770i	0.453775	+	0.891116i	$0.350077\pi$
$810$	0.411748	−	1.63894i	0.0144674	−	0.0575863i
$811$		−	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
$816$	−4.29283	−	2.84412i	−0.150279	−	0.0995642i
$817$	12.6749	+	7.31784i	0.443438	+	0.256019i
$818$	12.8069			0.447784
$819$	34.7315	−	13.7268i	1.21362	−	0.479652i
$820$	−0.0352549			−0.00123115
$821$	−4.66052	−	2.69075i	−0.162653	−	0.0939079i	0.416464	−	0.909152i	$-0.363269\pi$
$821$	−4.66052	−	2.69075i	−0.162653	−	0.0939079i	−0.579117	+	0.815244i	$0.696603\pi$
$822$	13.0265	+	8.63041i	0.454350	+	0.301020i
$823$	−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	$0.0620267\pi$
$827$			11.1368i			0.387263i	−0.981074	+	0.193632i	$0.937973\pi$
$828$	−6.54949	+	2.77318i	−0.227611	+	0.0963748i
$829$	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
$831$	−1.19091	+	19.3294i	−0.0413123	+	0.670529i
$832$		−	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
$837$	−17.5241	−	49.6983i	−0.605721	−	1.71783i
$838$	18.4620	+	10.6590i	0.637758	+	0.368210i
$839$	−24.7473			−0.854372			−0.427186	−	0.904164i	$-0.640495\pi$
$839$	−24.7473			−0.854372			−0.427186	+	0.904164i	$0.640495\pi$
$840$	−0.364872	−	0.779244i	−0.0125893	−	0.0268865i
$841$	−10.1156			−0.348815
$842$	−26.4075	−	15.2464i	−0.910062	−	0.525424i
$843$	−16.7376	+	25.2632i	−0.576472	+	0.870109i
$844$	−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
$849$	11.1174	+	0.684963i	0.381550	+	0.0235079i
$850$	−12.7830	+	7.38026i	−0.438453	+	0.253141i
$851$	−11.2173	+	6.47628i	−0.384522	+	0.222004i
$852$	23.3735	+	1.44008i	0.800764	+	0.0493363i
$853$		−	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	0.813862	−	0.581058i	$-0.197361\pi$
$857$	−2.81854	−	4.88186i	−0.0962796	−	0.166761i	−0.910142	+	0.414297i	$0.864028\pi$
$858$	−4.50105	+	6.79375i	−0.153663	+	0.231935i
$859$	−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
$861$	−0.705610	−	0.492409i	−0.0240471	−	0.0167813i
$862$	28.0274			0.954618
$863$	−31.0340	−	17.9175i	−1.05641	−	0.609919i	−0.131973	−	0.991253i	$-0.542131\pi$
$863$	−31.0340	−	17.9175i	−1.05641	−	0.609919i	−0.924437	+	0.381335i	$0.875465\pi$
$864$	−1.72794	−	4.90043i	−0.0587856	−	0.166716i
$865$	−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
$870$	−0.125079	+	2.03013i	−0.00424058	+	0.0688277i
$871$	10.5107	−	6.06834i	0.356141	−	0.205618i
$872$	1.07638	−	0.621447i	0.0364508	−	0.0210449i
$873$	2.77780	−	1.17618i	0.0940144	−	0.0398075i
$874$		−	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
$879$	11.5641	+	7.66154i	0.390047	+	0.258417i
$880$	0.162607	+	0.0938814i	0.00548149	+	0.00316474i
$881$	18.5071			0.623519			0.311760	−	0.950161i	$-0.399082\pi$
$881$	18.5071			0.623519			0.311760	+	0.950161i	$0.399082\pi$
$882$	3.58104	−	20.6924i	0.120580	−	0.696750i
$883$	−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
$885$	1.26267	+	0.836556i	0.0424442	+	0.0281205i
$886$	12.7305	+	22.0499i	0.427691	+	0.740782i
$887$	−19.1040	+	33.0891i	−0.641450	+	1.11102i	0.343659	+	0.939094i	$0.388334\pi$
$887$	−19.1040	+	33.0891i	−0.641450	+	1.11102i	−0.985109	+	0.171930i	$0.945000\pi$
$888$	−4.21851	−	8.47050i	−0.141564	−	0.284251i
$889$	13.8713	+	0.335025i	0.465227	+	0.0112364i
$890$		−	1.61196i		−	0.0540330i
$891$	−2.19292	+	8.72875i	−0.0734654	+	0.292424i
$892$	10.9359	−	6.31382i	0.366160	−	0.211402i
$893$	−8.99675	+	5.19427i	−0.301065	+	0.173820i
$894$	−1.59595	+	25.9034i	−0.0533764	+	0.866338i
$895$		−	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
$900$	−14.7816	−	1.82837i	−0.492720	−	0.0609458i
$901$	−28.2569	−	16.3142i	−0.941375	−	0.543503i
$902$	0.187763			0.00625182
$903$	29.5732	+	20.6376i	0.984134	+	0.686776i
$904$	12.6838			0.421858
$905$	−2.11775	−	1.22268i	−0.0703964	−	0.0406434i
$906$	−0.524571	+	0.791771i	−0.0174277	+	0.0263048i
$907$	−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	$0.0279134\pi$
$911$			5.28683i			0.175161i	−0.996157	+	0.0875803i	$0.972087\pi$
$912$	3.21520	+	0.198093i	0.106466	+	0.00655953i
$913$	−12.7698	+	7.37268i	−0.422620	+	0.244000i
$914$	13.6409	−	7.87556i	0.451200	−	0.260500i
$915$	−4.08308	−	0.251565i	−0.134983	−	0.00831648i
$916$			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
$921$	2.02360	−	3.05436i	0.0666800	−	0.100645i
$922$	23.1872	+	13.3871i	0.763629	+	0.440881i
$923$	−63.6147			−2.09390
$924$	1.94326	+	4.15015i	0.0639286	+	0.136530i
$925$	−27.1242			−0.891839
$926$	−21.0436	−	12.1495i	−0.691534	−	0.399258i
$927$	1.86833	−	15.1046i	0.0613639	−	0.496100i
$928$	3.12712	+	5.41634i	0.102653	+	0.177800i
$929$	−23.1396	+	40.0790i	−0.759185	+	1.31495i	0.184081	+	0.982911i	$0.441069\pi$
$929$	−23.1396	+	40.0790i	−0.759185	+	1.31495i	−0.943266	+	0.332037i	$0.892264\pi$
$930$	2.95234	−	1.47033i	0.0968109	−	0.0482141i
$931$	10.9471	+	7.04607i	0.358778	+	0.230925i
$932$		−	25.4851i		−	0.834791i
$933$	0.578849	−	9.39514i	0.0189507	−	0.307583i
$934$	24.4957	−	14.1426i	0.801523	−	0.462759i
$935$	−0.483443	+	0.279116i	−0.0158103	+	0.00912807i
$936$	5.50369	+	12.9982i	0.179894	+	0.424859i
$937$		−	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	$-0.944333\pi$
$941$	−19.7262	−	34.1667i	−0.643055	−	1.11380i	0.341693	−	0.939812i	$-0.389000\pi$
$942$	27.6888	+	18.3446i	0.902150	+	0.597701i
$943$	−0.385510	−	0.222574i	−0.0125539	−	0.00724802i
$944$	4.65738			0.151585
$945$	1.91948	+	1.72591i	0.0624407	+	0.0561439i
$946$	−7.86942			−0.255857
$947$	−29.0176	−	16.7533i	−0.942946	−	0.544410i	−0.0520632	−	0.998644i	$-0.516580\pi$
$947$	−29.0176	−	16.7533i	−0.942946	−	0.544410i	−0.890882	+	0.454234i	$0.849913\pi$
$948$	11.5310	+	7.63962i	0.374509	+	0.248123i
$949$	−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	$0.0376787\pi$
$953$			7.29135i			0.236190i	−0.993002	+	0.118095i	$0.962321\pi$
$954$	−12.8373	−	30.3181i	−0.415622	−	0.981584i
$955$	−0.869880	+	0.502225i	−0.0281486	+	0.0162516i
$956$	−6.69619	+	3.86605i	−0.216570	+	0.125037i
$957$	0.666155	−	10.8122i	0.0215337	−	0.349508i
$958$		−	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
$963$	−0.00883469	+	0.0714246i	−0.000284694	+	0.00230162i
$964$	−5.73736	−	3.31247i	−0.184788	−	0.106687i
$965$	2.47518			0.0796787
$966$	0.929738	−	10.8245i	0.0299138	−	0.348274i
$967$	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
$969$	−5.28955	+	7.98387i	−0.169925	+	0.256479i
$970$	0.0943993	+	0.163504i	0.00303098	+	0.00524981i
$971$	17.9357	−	31.0656i	0.575586	−	0.996943i	−0.420392	−	0.907343i	$-0.638107\pi$
$971$	17.9357	−	31.0656i	0.575586	−	0.996943i	0.995978	−	0.0896009i	$-0.0285592\pi$
$972$	10.5057	+	11.5165i	0.336970	+	0.369393i
$973$	0.267710	−	11.0841i	0.00858237	−	0.355341i
$974$			0.314971i			0.0100923i
$975$	40.3836	+	2.48810i	1.29331	+	0.0796829i
$976$	−10.8936	+	6.28942i	−0.348696	+	0.201319i
$977$	10.8868	−	6.28548i	0.348299	−	0.201090i	−0.315637	−	0.948880i	$-0.602218\pi$
$977$	10.8868	−	6.28548i	0.348299	−	0.201090i	0.663936	+	0.747790i	$0.268885\pi$
$978$	−1.40475	−	0.0865488i	−0.0449190	−	0.00276753i
$979$			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	$0.0218948\pi$
$983$	17.5055	+	30.3205i	0.558340	+	0.967073i	−0.439296	+	0.898343i	$0.644772\pi$
$984$	0.179619	−	0.271112i	0.00572606	−	0.00864273i
$985$	2.38440	+	1.37663i	0.0759732	+	0.0438631i
$986$	−18.5943			−0.592164
$987$	−23.1819	+	10.8546i	−0.737887	+	0.345507i
$988$	−8.75066			−0.278396
$989$	16.1573	+	9.32843i	0.513773	+	0.296627i
$990$	−0.559028	−	0.0691477i	−0.0177671	−	0.00219766i
$991$	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
$996$	−1.57056	+	25.4914i	−0.0497652	+	0.807725i
$997$	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
$999$	21.5620	+	18.4658i	0.682192	+	0.584232i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.44390 - 0.956629i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.0938814 - 0.162607i) q^{5} +(0.772144 + 1.55042i) q^{6} +(-2.64498 - 0.0638828i) q^{7} -1.00000i q^{8} +(1.16972 + 2.76256i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-1.44390 - 0.956629i) 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} +(1.16972 + 2.76256i) q^{9} +(-0.162607 + 0.0938814i) q^{10} +(0.866025 - 0.500000i) q^{11} +(0.106512 - 1.72877i) 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} +(0.368271 - 2.97731i) q^{18} +(1.61065 + 0.929908i) q^{19} +0.187763 q^{20} +(3.75799 + 2.62250i) q^{21} -1.00000 q^{22} +(2.05318 + 1.18540i) q^{23} +(-0.956629 + 1.44390i) 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} +(0.324599 + 0.0199991i) q^{30} +(8.78290 - 5.07081i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-1.72877 - 0.106512i) 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} +(4.50105 - 6.79375i) q^{39} +(-0.162607 - 0.0938814i) q^{40} -0.187763 q^{41} +(-1.94326 - 4.15015i) q^{42} +7.86942 q^{43} +(0.866025 + 0.500000i) q^{44} +(0.559028 + 0.0691477i) 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} +(-0.316669 + 5.13976i) q^{51} +(-4.07475 + 2.35256i) q^{52} +(9.50430 - 5.48731i) q^{53} +(-3.37993 + 3.94665i) 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} +(-0.271112 - 0.179619i) q^{60} +(10.8936 + 6.28942i) q^{61} -10.1416 q^{62} +(-2.91741 - 7.38165i) q^{63} -1.00000 q^{64} +(0.765087 + 0.441723i) q^{65} +(1.44390 + 0.956629i) 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} +(2.76256 - 1.16972i) q^{72} +(-13.8911 + 8.02001i) q^{73} +(4.73141 - 2.73168i) q^{74} +(0.528807 - 8.58292i) 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} +(-6.26350 + 6.46286i) q^{81} +(0.162607 + 0.0938814i) q^{82} -14.7454 q^{83} +(-0.392162 + 4.56576i) q^{84} -0.558232 q^{85} +(-6.81512 - 3.93471i) q^{86} +(5.98300 - 9.03054i) 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} +(-17.5326 - 1.08021i) q^{93} +(4.83744 - 2.79290i) q^{94} +(0.302420 - 0.174602i) q^{95} +(-1.72877 - 0.106512i) 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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