LMFDB - Embedded newform 462.2.g.e.419.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [462,2,Mod(419,462)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(462, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1, 0]))

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

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

chi := DirichletCharacter("462.419");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 462 = 2 \cdot 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	462.g (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.342102016.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} + 4x^{4} + 4x^{2} + 16 $ x^8 + x^6 + 4x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			419.3
Root			$0.599676 + 1.28078i$ of defining polynomial
Character	$\chi$	$=$	462.419
Dual form			462.2.g.e.419.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(0.468213 + 1.66757i) q^{3} -1.00000 q^{4} +3.33513 q^{5} +(1.66757 - 0.468213i) q^{6} +(1.56155 - 2.13578i) q^{7} +1.00000i q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(0.468213 + 1.66757i) q^{3} -1.00000 q^{4} +3.33513 q^{5} +(1.66757 - 0.468213i) q^{6} +(1.56155 - 2.13578i) q^{7} +1.00000i q^{8} +(-2.56155 + 1.56155i) q^{9} -3.33513i q^{10} -1.00000i q^{11} +(-0.468213 - 1.66757i) q^{12} -5.20798i q^{13} +(-2.13578 - 1.56155i) q^{14} +(1.56155 + 5.56155i) q^{15} +1.00000 q^{16} +2.39871 q^{17} +(1.56155 + 2.56155i) q^{18} +5.73384i q^{19} -3.33513 q^{20} +(4.29269 + 1.60399i) q^{21} -1.00000 q^{22} +6.00000i q^{23} +(-1.66757 + 0.468213i) q^{24} +6.12311 q^{25} -5.20798 q^{26} +(-3.80335 - 3.54042i) q^{27} +(-1.56155 + 2.13578i) q^{28} +2.00000i q^{29} +(5.56155 - 1.56155i) q^{30} -4.27156i q^{31} -1.00000i q^{32} +(1.66757 - 0.468213i) q^{33} -2.39871i q^{34} +(5.20798 - 7.12311i) q^{35} +(2.56155 - 1.56155i) q^{36} -8.24621 q^{37} +5.73384 q^{38} +(8.68466 - 2.43845i) q^{39} +3.33513i q^{40} +6.14441 q^{41} +(1.60399 - 4.29269i) q^{42} +2.87689 q^{43} +1.00000i q^{44} +(-8.54312 + 5.20798i) q^{45} +6.00000 q^{46} -6.14441 q^{47} +(0.468213 + 1.66757i) q^{48} +(-2.12311 - 6.67026i) q^{49} -6.12311i q^{50} +(1.12311 + 4.00000i) q^{51} +5.20798i q^{52} +2.00000i q^{53} +(-3.54042 + 3.80335i) q^{54} -3.33513i q^{55} +(2.13578 + 1.56155i) q^{56} +(-9.56155 + 2.68466i) q^{57} +2.00000 q^{58} +11.3524 q^{59} +(-1.56155 - 5.56155i) q^{60} +3.33513i q^{61} -4.27156 q^{62} +(-0.664868 + 7.90936i) q^{63} -1.00000 q^{64} -17.3693i q^{65} +(-0.468213 - 1.66757i) q^{66} -12.0000 q^{67} -2.39871 q^{68} +(-10.0054 + 2.80928i) q^{69} +(-7.12311 - 5.20798i) q^{70} +15.3693i q^{71} +(-1.56155 - 2.56155i) q^{72} -10.4160i q^{73} +8.24621i q^{74} +(2.86692 + 10.2107i) q^{75} -5.73384i q^{76} +(-2.13578 - 1.56155i) q^{77} +(-2.43845 - 8.68466i) q^{78} -15.1231 q^{79} +3.33513 q^{80} +(4.12311 - 8.00000i) q^{81} -6.14441i q^{82} -5.73384 q^{83} +(-4.29269 - 1.60399i) q^{84} +8.00000 q^{85} -2.87689i q^{86} +(-3.33513 + 0.936426i) q^{87} +1.00000 q^{88} -13.3405 q^{89} +(5.20798 + 8.54312i) q^{90} +(-11.1231 - 8.13254i) q^{91} -6.00000i q^{92} +(7.12311 - 2.00000i) q^{93} +6.14441i q^{94} +19.1231i q^{95} +(1.66757 - 0.468213i) q^{96} +1.87285i q^{97} +(-6.67026 + 2.12311i) q^{98} +(1.56155 + 2.56155i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9	$ 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9} - 4 q^{15} + 8 q^{16} - 4 q^{18} + 12 q^{21} - 8 q^{22} + 16 q^{25} + 4 q^{28} + 28 q^{30} + 4 q^{36} + 20 q^{39} - 8 q^{42} + 56 q^{43} + 48 q^{46} + 16 q^{49} - 24 q^{51} - 60 q^{57} + 16 q^{58} + 4 q^{60} - 32 q^{63} - 8 q^{64} - 96 q^{67} - 24 q^{70} + 4 q^{72} - 36 q^{78} - 88 q^{79} - 12 q^{84} + 64 q^{85} + 8 q^{88} - 56 q^{91} + 24 q^{93} - 4 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9 - 4 * q^15 + 8 * q^16 - 4 * q^18 + 12 * q^21 - 8 * q^22 + 16 * q^25 + 4 * q^28 + 28 * q^30 + 4 * q^36 + 20 * q^39 - 8 * q^42 + 56 * q^43 + 48 * q^46 + 16 * q^49 - 24 * q^51 - 60 * q^57 + 16 * q^58 + 4 * q^60 - 32 * q^63 - 8 * q^64 - 96 * q^67 - 24 * q^70 + 4 * q^72 - 36 * q^78 - 88 * q^79 - 12 * q^84 + 64 * q^85 + 8 * q^88 - 56 * q^91 + 24 * q^93 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$155$	$199$	$211$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	0.468213	+	1.66757i	0.270323	+	0.962770i
$3$	0.468213	+	1.66757i	0.270323	+	0.962770i
$4$	−1.00000			−0.500000
$5$	3.33513			1.49152			0.745758	−	0.666217i	$-0.232087\pi$
$5$	3.33513			1.49152			0.745758	+	0.666217i	$0.232087\pi$
$6$	1.66757	−	0.468213i	0.680781	−	0.191147i
$7$	1.56155	−	2.13578i	0.590211	−	0.807249i
$7$	1.56155	−	2.13578i	0.590211	−	0.807249i
$8$			1.00000i			0.353553i
$9$	−2.56155	+	1.56155i	−0.853851	+	0.520518i
$10$		−	3.33513i		−	1.05466i
$11$		−	1.00000i		−	0.301511i
$11$		−	1.00000i		−	0.301511i
$12$	−0.468213	−	1.66757i	−0.135162	−	0.481385i
$13$		−	5.20798i		−	1.44444i	−0.691666	−	0.722218i	$-0.743123\pi$
$13$		−	5.20798i		−	1.44444i	0.691666	−	0.722218i	$-0.256877\pi$
$14$	−2.13578	−	1.56155i	−0.570811	−	0.417343i
$15$	1.56155	+	5.56155i	0.403191	+	1.43599i
$16$	1.00000			0.250000
$17$	2.39871			0.581772			0.290886	−	0.956758i	$-0.406050\pi$
$17$	2.39871			0.581772			0.290886	+	0.956758i	$0.406050\pi$
$18$	1.56155	+	2.56155i	0.368062	+	0.603764i
$19$			5.73384i			1.31543i	0.753266	+	0.657716i	$0.228477\pi$
$19$			5.73384i			1.31543i	−0.753266	+	0.657716i	$0.771523\pi$
$20$	−3.33513			−0.745758
$21$	4.29269	+	1.60399i	0.936742	+	0.350020i
$22$	−1.00000			−0.213201
$23$			6.00000i			1.25109i	0.780189	+	0.625543i	$0.215123\pi$
$23$			6.00000i			1.25109i	−0.780189	+	0.625543i	$0.784877\pi$
$24$	−1.66757	+	0.468213i	−0.340390	+	0.0955736i
$25$	6.12311			1.22462
$26$	−5.20798			−1.02137
$27$	−3.80335	−	3.54042i	−0.731954	−	0.681354i
$28$	−1.56155	+	2.13578i	−0.295106	+	0.403624i
$29$			2.00000i			0.371391i	0.982607	+	0.185695i	$0.0594537\pi$
$29$			2.00000i			0.371391i	−0.982607	+	0.185695i	$0.940546\pi$
$30$	5.56155	−	1.56155i	1.01540	−	0.285099i
$31$		−	4.27156i		−	0.767195i	−0.923500	−	0.383597i	$-0.874685\pi$
$31$		−	4.27156i		−	0.767195i	0.923500	−	0.383597i	$-0.125315\pi$
$32$		−	1.00000i		−	0.176777i
$33$	1.66757	−	0.468213i	0.290286	−	0.0815055i
$34$		−	2.39871i		−	0.411375i
$35$	5.20798	−	7.12311i	0.880310	−	1.20402i
$36$	2.56155	−	1.56155i	0.426925	−	0.260259i
$37$	−8.24621			−1.35567			−0.677834	−	0.735215i	$-0.737081\pi$
$37$	−8.24621			−1.35567			−0.677834	+	0.735215i	$0.737081\pi$
$38$	5.73384			0.930151
$39$	8.68466	−	2.43845i	1.39066	−	0.390464i
$40$			3.33513i			0.527331i
$41$	6.14441			0.959596			0.479798	−	0.877379i	$-0.340710\pi$
$41$	6.14441			0.959596			0.479798	+	0.877379i	$0.340710\pi$
$42$	1.60399	−	4.29269i	0.247501	−	0.662377i
$43$	2.87689			0.438722			0.219361	−	0.975644i	$-0.429603\pi$
$43$	2.87689			0.438722			0.219361	+	0.975644i	$0.429603\pi$
$44$			1.00000i			0.150756i
$45$	−8.54312	+	5.20798i	−1.27353	+	0.776361i
$46$	6.00000			0.884652
$47$	−6.14441			−0.896254			−0.448127	−	0.893970i	$-0.647909\pi$
$47$	−6.14441			−0.896254			−0.448127	+	0.893970i	$0.647909\pi$
$48$	0.468213	+	1.66757i	0.0675808	+	0.240692i
$49$	−2.12311	−	6.67026i	−0.303301	−	0.952895i
$50$		−	6.12311i		−	0.865938i
$51$	1.12311	+	4.00000i	0.157266	+	0.560112i
$52$			5.20798i			0.722218i
$53$			2.00000i			0.274721i	0.990521	+	0.137361i	$0.0438619\pi$
$53$			2.00000i			0.274721i	−0.990521	+	0.137361i	$0.956138\pi$
$54$	−3.54042	+	3.80335i	−0.481790	+	0.517570i
$55$		−	3.33513i		−	0.449709i
$56$	2.13578	+	1.56155i	0.285406	+	0.208671i
$57$	−9.56155	+	2.68466i	−1.26646	+	0.355592i
$58$	2.00000			0.262613
$59$	11.3524			1.47796			0.738978	−	0.673730i	$-0.235309\pi$
$59$	11.3524			1.47796			0.738978	+	0.673730i	$0.235309\pi$
$60$	−1.56155	−	5.56155i	−0.201596	−	0.717993i
$61$			3.33513i			0.427020i	0.976941	+	0.213510i	$0.0684896\pi$
$61$			3.33513i			0.427020i	−0.976941	+	0.213510i	$0.931510\pi$
$62$	−4.27156			−0.542488
$63$	−0.664868	+	7.90936i	−0.0837655	+	0.996485i
$64$	−1.00000			−0.125000
$65$		−	17.3693i		−	2.15440i
$66$	−0.468213	−	1.66757i	−0.0576331	−	0.205263i
$67$	−12.0000			−1.46603			−0.733017	−	0.680211i	$-0.761888\pi$
$67$	−12.0000			−1.46603			−0.733017	+	0.680211i	$0.761888\pi$
$68$	−2.39871			−0.290886
$69$	−10.0054	+	2.80928i	−1.20451	+	0.338197i
$70$	−7.12311	−	5.20798i	−0.851374	−	0.622473i
$71$			15.3693i			1.82400i	0.410188	+	0.912001i	$0.365463\pi$
$71$			15.3693i			1.82400i	−0.410188	+	0.912001i	$0.634537\pi$
$72$	−1.56155	−	2.56155i	−0.184031	−	0.301882i
$73$		−	10.4160i		−	1.21910i	−0.792749	−	0.609549i	$-0.791351\pi$
$73$		−	10.4160i		−	1.21910i	0.792749	−	0.609549i	$-0.208649\pi$
$74$			8.24621i			0.958603i
$75$	2.86692	+	10.2107i	0.331043	+	1.17903i
$76$		−	5.73384i		−	0.657716i
$77$	−2.13578	−	1.56155i	−0.243395	−	0.177955i
$78$	−2.43845	−	8.68466i	−0.276100	−	0.983344i
$79$	−15.1231			−1.70148			−0.850741	−	0.525585i	$-0.823847\pi$
$79$	−15.1231			−1.70148			−0.850741	+	0.525585i	$0.823847\pi$
$80$	3.33513			0.372879
$81$	4.12311	−	8.00000i	0.458123	−	0.888889i
$82$		−	6.14441i		−	0.678537i
$83$	−5.73384			−0.629370			−0.314685	−	0.949196i	$-0.601899\pi$
$83$	−5.73384			−0.629370			−0.314685	+	0.949196i	$0.601899\pi$
$84$	−4.29269	−	1.60399i	−0.468371	−	0.175010i
$85$	8.00000			0.867722
$86$		−	2.87689i		−	0.310223i
$87$	−3.33513	+	0.936426i	−0.357564	+	0.100395i
$88$	1.00000			0.106600
$89$	−13.3405			−1.41409			−0.707047	−	0.707167i	$-0.749973\pi$
$89$	−13.3405			−1.41409			−0.707047	+	0.707167i	$0.749973\pi$
$90$	5.20798	+	8.54312i	0.548970	+	0.900524i
$91$	−11.1231	−	8.13254i	−1.16602	−	0.852522i
$92$		−	6.00000i		−	0.625543i
$93$	7.12311	−	2.00000i	0.738632	−	0.207390i
$94$			6.14441i			0.633748i
$95$			19.1231i			1.96199i
$96$	1.66757	−	0.468213i	0.170195	−	0.0477868i
$97$			1.87285i			0.190159i	0.995470	+	0.0950797i	$0.0303106\pi$
$97$			1.87285i			0.190159i	−0.995470	+	0.0950797i	$0.969689\pi$
$98$	−6.67026	+	2.12311i	−0.673798	+	0.214466i
$99$	1.56155	+	2.56155i	0.156942	+	0.257446i
$100$	−6.12311			−0.612311
$101$	1.46228			0.145502			0.0727511	−	0.997350i	$-0.476822\pi$
$101$	1.46228			0.145502			0.0727511	+	0.997350i	$0.476822\pi$
$102$	4.00000	−	1.12311i	0.396059	−	0.111204i
$103$			12.8147i			1.26267i	0.775511	+	0.631334i	$0.217492\pi$
$103$			12.8147i			1.26267i	−0.775511	+	0.631334i	$0.782508\pi$
$104$	5.20798			0.510685
$105$	14.3167	+	5.34953i	1.39717	+	0.522060i
$106$	2.00000			0.194257
$107$			2.24621i			0.217149i	0.994088	+	0.108575i	$0.0346287\pi$
$107$			2.24621i			0.217149i	−0.994088	+	0.108575i	$0.965371\pi$
$108$	3.80335	+	3.54042i	0.365977	+	0.340677i
$109$	−3.12311			−0.299139			−0.149570	−	0.988751i	$-0.547789\pi$
$109$	−3.12311			−0.299139			−0.149570	+	0.988751i	$0.547789\pi$
$110$	−3.33513			−0.317992
$111$	−3.86098	−	13.7511i	−0.366468	−	1.30520i
$112$	1.56155	−	2.13578i	0.147553	−	0.201812i
$113$		−	11.1231i		−	1.04637i	−0.852218	−	0.523187i	$-0.824743\pi$
$113$		−	11.1231i		−	1.04637i	0.852218	−	0.523187i	$-0.175257\pi$
$114$	2.68466	+	9.56155i	0.251441	+	0.895521i
$115$			20.0108i			1.86602i
$116$		−	2.00000i		−	0.185695i
$117$	8.13254	+	13.3405i	0.751854	+	1.23333i
$118$		−	11.3524i		−	1.04507i
$119$	3.74571	−	5.12311i	0.343368	−	0.469634i
$120$	−5.56155	+	1.56155i	−0.507698	+	0.142550i
$121$	−1.00000			−0.0909091
$122$	3.33513			0.301949
$123$	2.87689	+	10.2462i	0.259401	+	0.923870i
$124$			4.27156i			0.383597i
$125$	3.74571			0.335026
$126$	7.90936	+	0.664868i	0.704622	+	0.0592311i
$127$	−2.24621			−0.199319			−0.0996595	−	0.995022i	$-0.531775\pi$
$127$	−2.24621			−0.199319			−0.0996595	+	0.995022i	$0.531775\pi$
$128$			1.00000i			0.0883883i
$129$	1.34700	+	4.79741i	0.118597	+	0.422389i
$130$	−17.3693			−1.52339
$131$	10.5312			0.920119			0.460060	−	0.887888i	$-0.347828\pi$
$131$	10.5312			0.920119			0.460060	+	0.887888i	$0.347828\pi$
$132$	−1.66757	+	0.468213i	−0.145143	+	0.0407527i
$133$	12.2462	+	8.95369i	1.06188	+	0.776383i
$134$			12.0000i			1.03664i
$135$	−12.6847	−	11.8078i	−1.09172	−	1.01625i
$136$			2.39871i			0.205687i
$137$		−	16.4924i		−	1.40904i	−0.709683	−	0.704521i	$-0.751162\pi$
$137$		−	16.4924i		−	1.40904i	0.709683	−	0.704521i	$-0.248838\pi$
$138$	2.80928	+	10.0054i	0.239142	+	0.851716i
$139$		−	6.55498i		−	0.555987i	−0.960583	−	0.277993i	$-0.910331\pi$
$139$		−	6.55498i		−	0.555987i	0.960583	−	0.277993i	$-0.0896693\pi$
$140$	−5.20798	+	7.12311i	−0.440155	+	0.602012i
$141$	−2.87689	−	10.2462i	−0.242278	−	0.862887i
$142$	15.3693			1.28976
$143$	−5.20798			−0.435514
$144$	−2.56155	+	1.56155i	−0.213463	+	0.130129i
$145$			6.67026i			0.553935i
$146$	−10.4160			−0.862032
$147$	10.1290	−	6.66352i	0.835429	−	0.549598i
$148$	8.24621			0.677834
$149$		−	12.2462i		−	1.00325i	−0.865086	−	0.501624i	$-0.832736\pi$
$149$		−	12.2462i		−	1.00325i	0.865086	−	0.501624i	$-0.167264\pi$
$150$	10.2107	−	2.86692i	0.833699	−	0.234083i
$151$	−18.2462			−1.48486			−0.742428	−	0.669926i	$-0.766326\pi$
$151$	−18.2462			−1.48486			−0.742428	+	0.669926i	$0.766326\pi$
$152$	−5.73384			−0.465076
$153$	−6.14441	+	3.74571i	−0.496746	+	0.302822i
$154$	−1.56155	+	2.13578i	−0.125834	+	0.172106i
$155$		−	14.2462i		−	1.14428i
$156$	−8.68466	+	2.43845i	−0.695329	+	0.195232i
$157$		−	0.115279i		−	0.00920029i	−0.999989	−	0.00460015i	$-0.998536\pi$
$157$		−	0.115279i		−	0.00920029i	0.999989	−	0.00460015i	$-0.00146428\pi$
$158$			15.1231i			1.20313i
$159$	−3.33513	+	0.936426i	−0.264493	+	0.0742634i
$160$		−	3.33513i		−	0.263665i
$161$	12.8147	+	9.36932i	1.00994	+	0.738406i
$162$	−8.00000	−	4.12311i	−0.628539	−	0.323942i
$163$	16.0000			1.25322			0.626608	−	0.779334i	$-0.284443\pi$
$163$	16.0000			1.25322			0.626608	+	0.779334i	$0.284443\pi$
$164$	−6.14441			−0.479798
$165$	5.56155	−	1.56155i	0.432966	−	0.121567i
$166$			5.73384i			0.445032i
$167$	1.87285			0.144926			0.0724628	−	0.997371i	$-0.476914\pi$
$167$	1.87285			0.144926			0.0724628	+	0.997371i	$0.476914\pi$
$168$	−1.60399	+	4.29269i	−0.123751	+	0.331188i
$169$	−14.1231			−1.08639
$170$		−	8.00000i		−	0.613572i
$171$	−8.95369	−	14.6875i	−0.684706	−	1.12318i
$172$	−2.87689			−0.219361
$173$	−15.6240			−1.18787			−0.593934	−	0.804514i	$-0.702426\pi$
$173$	−15.6240			−1.18787			−0.593934	+	0.804514i	$0.702426\pi$
$174$	0.936426	+	3.33513i	0.0709903	+	0.252836i
$175$	9.56155	−	13.0776i	0.722785	−	0.988574i
$176$		−	1.00000i		−	0.0753778i
$177$	5.31534	+	18.9309i	0.399526	+	1.42293i
$178$			13.3405i			0.999915i
$179$			2.24621i			0.167890i	0.996470	+	0.0839449i	$0.0267520\pi$
$179$			2.24621i			0.167890i	−0.996470	+	0.0839449i	$0.973248\pi$
$180$	8.54312	−	5.20798i	0.636766	−	0.388180i
$181$			0.936426i			0.0696040i	0.999394	+	0.0348020i	$0.0110801\pi$
$181$			0.936426i			0.0696040i	−0.999394	+	0.0348020i	$0.988920\pi$
$182$	−8.13254	+	11.1231i	−0.602824	+	0.824499i
$183$	−5.56155	+	1.56155i	−0.411122	+	0.115433i
$184$	−6.00000			−0.442326
$185$	−27.5022			−2.02200
$186$	−2.00000	−	7.12311i	−0.146647	−	0.522291i
$187$		−	2.39871i		−	0.175411i
$188$	6.14441			0.448127
$189$	−13.5007	+	2.59455i	−0.982030	+	0.188726i
$190$	19.1231			1.38734
$191$			15.3693i			1.11208i	0.831154	+	0.556042i	$0.187681\pi$
$191$			15.3693i			1.11208i	−0.831154	+	0.556042i	$0.812319\pi$
$192$	−0.468213	−	1.66757i	−0.0337904	−	0.120346i
$193$	15.3693			1.10631			0.553154	−	0.833079i	$-0.313424\pi$
$193$	15.3693			1.10631			0.553154	+	0.833079i	$0.313424\pi$
$194$	1.87285			0.134463
$195$	28.9645	−	8.13254i	2.07419	−	0.582384i
$196$	2.12311	+	6.67026i	0.151650	+	0.476447i
$197$		−	18.4924i		−	1.31753i	−0.752349	−	0.658765i	$-0.771079\pi$
$197$		−	18.4924i		−	1.31753i	0.752349	−	0.658765i	$-0.228921\pi$
$198$	2.56155	−	1.56155i	0.182042	−	0.110975i
$199$			4.27156i			0.302803i	0.988472	+	0.151401i	$0.0483786\pi$
$199$			4.27156i			0.302803i	−0.988472	+	0.151401i	$0.951621\pi$
$200$			6.12311i			0.432969i
$201$	−5.61856	−	20.0108i	−0.396303	−	1.41145i
$202$		−	1.46228i		−	0.102886i
$203$	4.27156	+	3.12311i	0.299805	+	0.219199i
$204$	−1.12311	−	4.00000i	−0.0786331	−	0.280056i
$205$	20.4924			1.43125
$206$	12.8147			0.892841
$207$	−9.36932	−	15.3693i	−0.651213	−	1.06824i
$208$		−	5.20798i		−	0.361109i
$209$	5.73384			0.396618
$210$	5.34953	−	14.3167i	0.369152	−	0.987946i
$211$	23.3693			1.60881			0.804405	−	0.594081i	$-0.202484\pi$
$211$	23.3693			1.60881			0.804405	+	0.594081i	$0.202484\pi$
$212$		−	2.00000i		−	0.137361i
$213$	−25.6294	+	7.19612i	−1.75609	+	0.493070i
$214$	2.24621			0.153548
$215$	9.59482			0.654361
$216$	3.54042	−	3.80335i	0.240895	−	0.258785i
$217$	−9.12311	−	6.67026i	−0.619317	−	0.452807i
$218$			3.12311i			0.211523i
$219$	17.3693	−	4.87689i	1.17371	−	0.329550i
$220$			3.33513i			0.224855i
$221$		−	12.4924i		−	0.840331i
$222$	−13.7511	+	3.86098i	−0.922914	+	0.259132i
$223$		−	10.9418i		−	0.732719i	−0.930473	−	0.366359i	$-0.880604\pi$
$223$		−	10.9418i		−	0.732719i	0.930473	−	0.366359i	$-0.119396\pi$
$224$	−2.13578	−	1.56155i	−0.142703	−	0.104336i
$225$	−15.6847	+	9.56155i	−1.04564	+	0.637437i
$226$	−11.1231			−0.739898
$227$	−0.936426			−0.0621528			−0.0310764	−	0.999517i	$-0.509894\pi$
$227$	−0.936426			−0.0621528			−0.0310764	+	0.999517i	$0.509894\pi$
$228$	9.56155	−	2.68466i	0.633229	−	0.177796i
$229$			2.80928i			0.185642i	0.995683	+	0.0928212i	$0.0295885\pi$
$229$			2.80928i			0.185642i	−0.995683	+	0.0928212i	$0.970412\pi$
$230$	20.0108			1.31947
$231$	1.60399	−	4.29269i	0.105535	−	0.282438i
$232$	−2.00000			−0.131306
$233$			17.1231i			1.12177i	0.827893	+	0.560886i	$0.189539\pi$
$233$			17.1231i			1.12177i	−0.827893	+	0.560886i	$0.810461\pi$
$234$	13.3405	−	8.13254i	0.872098	−	0.531641i
$235$	−20.4924			−1.33678
$236$	−11.3524			−0.738978
$237$	−7.08084	−	25.2188i	−0.459950	−	1.63814i
$238$	−5.12311	−	3.74571i	−0.332082	−	0.242798i
$239$			5.36932i			0.347312i	0.984806	+	0.173656i	$0.0555581\pi$
$239$			5.36932i			0.347312i	−0.984806	+	0.173656i	$0.944442\pi$
$240$	1.56155	+	5.56155i	0.100798	+	0.358997i
$241$		−	3.74571i		−	0.241282i	−0.992696	−	0.120641i	$-0.961505\pi$
$241$		−	3.74571i		−	0.241282i	0.992696	−	0.120641i	$-0.0384950\pi$
$242$			1.00000i			0.0642824i
$243$	15.2710	+	3.12985i	0.979636	+	0.200780i
$244$		−	3.33513i		−	0.213510i
$245$	−7.08084	−	22.2462i	−0.452378	−	1.42126i
$246$	10.2462	−	2.87689i	0.653275	−	0.183424i
$247$	29.8617			1.90006
$248$	4.27156			0.271244
$249$	−2.68466	−	9.56155i	−0.170133	−	0.605939i
$250$		−	3.74571i		−	0.236899i
$251$	−19.8955			−1.25579			−0.627897	−	0.778297i	$-0.716084\pi$
$251$	−19.8955			−1.25579			−0.627897	+	0.778297i	$0.716084\pi$
$252$	0.664868	−	7.90936i	0.0418827	−	0.498243i
$253$	6.00000			0.377217
$254$			2.24621i			0.140940i
$255$	3.74571	+	13.3405i	0.234565	+	0.835416i
$256$	1.00000			0.0625000
$257$	21.8836			1.36506			0.682532	−	0.730856i	$-0.260879\pi$
$257$	21.8836			1.36506			0.682532	+	0.730856i	$0.260879\pi$
$258$	4.79741	−	1.34700i	0.298674	−	0.0838606i
$259$	−12.8769	+	17.6121i	−0.800131	+	1.09436i
$260$			17.3693i			1.07720i
$261$	−3.12311	−	5.12311i	−0.193315	−	0.317112i
$262$		−	10.5312i		−	0.650623i
$263$		−	2.24621i		−	0.138507i	−0.997599	−	0.0692537i	$-0.977938\pi$
$263$		−	2.24621i		−	0.138507i	0.997599	−	0.0692537i	$-0.0220618\pi$
$264$	0.468213	+	1.66757i	0.0288165	+	0.102632i
$265$			6.67026i			0.409751i
$266$	8.95369	−	12.2462i	0.548986	−	0.750863i
$267$	−6.24621	−	22.2462i	−0.382262	−	1.36145i
$268$	12.0000			0.733017
$269$	3.33513			0.203347			0.101673	−	0.994818i	$-0.467580\pi$
$269$	3.33513			0.203347			0.101673	+	0.994818i	$0.467580\pi$
$270$	−11.8078	+	12.6847i	−0.718598	+	0.771964i
$271$		−	8.01726i		−	0.487014i	−0.969899	−	0.243507i	$-0.921702\pi$
$271$		−	8.01726i		−	0.487014i	0.969899	−	0.243507i	$-0.0782979\pi$
$272$	2.39871			0.145443
$273$	8.35357	−	22.3563i	0.505581	−	1.35306i
$274$	−16.4924			−0.996344
$275$		−	6.12311i		−	0.369237i
$276$	10.0054	−	2.80928i	0.602254	−	0.169099i
$277$	27.6155			1.65926			0.829628	−	0.558316i	$-0.188552\pi$
$277$	27.6155			1.65926			0.829628	+	0.558316i	$0.188552\pi$
$278$	−6.55498			−0.393142
$279$	6.67026	+	10.9418i	0.399338	+	0.655070i
$280$	7.12311	+	5.20798i	0.425687	+	0.311237i
$281$			25.1231i			1.49872i	0.662163	+	0.749359i	$0.269638\pi$
$281$			25.1231i			1.49872i	−0.662163	+	0.749359i	$0.730362\pi$
$282$	−10.2462	+	2.87689i	−0.610153	+	0.171317i
$283$		−	19.8955i		−	1.18267i	−0.806428	−	0.591333i	$-0.798602\pi$
$283$		−	19.8955i		−	1.18267i	0.806428	−	0.591333i	$-0.201398\pi$
$284$		−	15.3693i		−	0.912001i
$285$	−31.8890	+	8.95369i	−1.88894	+	0.530371i
$286$			5.20798i			0.307955i
$287$	9.59482	−	13.1231i	0.566364	−	0.774632i
$288$	1.56155	+	2.56155i	0.0920154	+	0.150941i
$289$	−11.2462			−0.661542
$290$	6.67026			0.391691
$291$	−3.12311	+	0.876894i	−0.183080	+	0.0514045i
$292$			10.4160i			0.609549i
$293$	20.4214			1.19303			0.596514	−	0.802602i	$-0.296552\pi$
$293$	20.4214			1.19303			0.596514	+	0.802602i	$0.296552\pi$
$294$	−6.66352	−	10.1290i	−0.388625	−	0.590738i
$295$	37.8617			2.20440
$296$		−	8.24621i		−	0.479301i
$297$	−3.54042	+	3.80335i	−0.205436	+	0.220692i
$298$	−12.2462			−0.709404
$299$	31.2479			1.80711
$300$	−2.86692	−	10.2107i	−0.165522	−	0.589514i
$301$	4.49242	−	6.14441i	0.258939	−	0.354158i
$302$			18.2462i			1.04995i
$303$	0.684658	+	2.43845i	0.0393326	+	0.140085i
$304$			5.73384i			0.328858i
$305$			11.1231i			0.636907i
$306$	3.74571	+	6.14441i	0.214128	+	0.351253i
$307$			8.42784i			0.481002i	0.970649	+	0.240501i	$0.0773117\pi$
$307$			8.42784i			0.481002i	−0.970649	+	0.240501i	$0.922688\pi$
$308$	2.13578	+	1.56155i	0.121697	+	0.0889777i
$309$	−21.3693	+	6.00000i	−1.21566	+	0.341328i
$310$	−14.2462			−0.809130
$311$	−18.6638			−1.05833			−0.529163	−	0.848520i	$-0.677494\pi$
$311$	−18.6638			−1.05833			−0.529163	+	0.848520i	$0.677494\pi$
$312$	2.43845	+	8.68466i	0.138050	+	0.491672i
$313$			10.4160i			0.588745i	0.955691	+	0.294373i	$0.0951107\pi$
$313$			10.4160i			0.588745i	−0.955691	+	0.294373i	$0.904889\pi$
$314$	−0.115279			−0.00650559
$315$	−2.21742	+	26.3788i	−0.124938	+	1.48627i
$316$	15.1231			0.850741
$317$			24.7386i			1.38946i	0.719271	+	0.694730i	$0.244476\pi$
$317$			24.7386i			1.38946i	−0.719271	+	0.694730i	$0.755524\pi$
$318$	0.936426	+	3.33513i	0.0525122	+	0.187025i
$319$	2.00000			0.111979
$320$	−3.33513			−0.186440
$321$	−3.74571	+	1.05171i	−0.209065	+	0.0587005i
$322$	9.36932	−	12.8147i	0.522132	−	0.714134i
$323$			13.7538i			0.765281i
$324$	−4.12311	+	8.00000i	−0.229061	+	0.444444i
$325$		−	31.8890i		−	1.76889i
$326$		−	16.0000i		−	0.886158i
$327$	−1.46228	−	5.20798i	−0.0808642	−	0.288002i
$328$			6.14441i			0.339268i
$329$	−9.59482	+	13.1231i	−0.528980	+	0.723500i
$330$	−1.56155	−	5.56155i	−0.0859607	−	0.306153i
$331$	20.0000			1.09930			0.549650	−	0.835395i	$-0.314761\pi$
$331$	20.0000			1.09930			0.549650	+	0.835395i	$0.314761\pi$
$332$	5.73384			0.314685
$333$	21.1231	−	12.8769i	1.15754	−	0.705649i
$334$		−	1.87285i		−	0.102478i
$335$	−40.0216			−2.18661
$336$	4.29269	+	1.60399i	0.234186	+	0.0875050i
$337$	−3.36932			−0.183538			−0.0917692	−	0.995780i	$-0.529252\pi$
$337$	−3.36932			−0.183538			−0.0917692	+	0.995780i	$0.529252\pi$
$338$			14.1231i			0.768196i
$339$	18.5485	−	5.20798i	1.00742	−	0.282859i
$340$	−8.00000			−0.433861
$341$	−4.27156			−0.231318
$342$	−14.6875	+	8.95369i	−0.794211	+	0.484160i
$343$	−17.5616	−	5.88148i	−0.948235	−	0.317570i
$344$			2.87689i			0.155112i
$345$	−33.3693	+	9.36932i	−1.79654	+	0.504427i
$346$			15.6240i			0.839949i
$347$			4.00000i			0.214731i	0.994220	+	0.107366i	$0.0342415\pi$
$347$			4.00000i			0.214731i	−0.994220	+	0.107366i	$0.965758\pi$
$348$	3.33513	−	0.936426i	0.178782	−	0.0501977i
$349$			21.2425i			1.13709i	0.822654	+	0.568543i	$0.192493\pi$
$349$			21.2425i			1.13709i	−0.822654	+	0.568543i	$0.807507\pi$
$350$	−13.0776	−	9.56155i	−0.699027	−	0.511086i
$351$	−18.4384	+	19.8078i	−0.984172	+	1.05726i
$352$	−1.00000			−0.0533002
$353$	12.2888			0.654068			0.327034	−	0.945013i	$-0.393951\pi$
$353$	12.2888			0.654068			0.327034	+	0.945013i	$0.393951\pi$
$354$	18.9309	−	5.31534i	1.00616	−	0.282507i
$355$			51.2587i			2.72053i
$356$	13.3405			0.707047
$357$	10.2969	+	3.84751i	0.544970	+	0.203632i
$358$	2.24621			0.118716
$359$		−	7.12311i		−	0.375943i	−0.982174	−	0.187972i	$-0.939809\pi$
$359$		−	7.12311i		−	0.375943i	0.982174	−	0.187972i	$-0.0601913\pi$
$360$	−5.20798	−	8.54312i	−0.274485	−	0.450262i
$361$	−13.8769			−0.730363
$362$	0.936426			0.0492175
$363$	−0.468213	−	1.66757i	−0.0245748	−	0.0875245i
$364$	11.1231	+	8.13254i	0.583009	+	0.426261i
$365$		−	34.7386i		−	1.81830i
$366$	1.56155	+	5.56155i	0.0816237	+	0.290707i
$367$			25.3341i			1.32243i	0.750198	+	0.661213i	$0.229958\pi$
$367$			25.3341i			1.32243i	−0.750198	+	0.661213i	$0.770042\pi$
$368$			6.00000i			0.312772i
$369$	−15.7392	+	9.59482i	−0.819352	+	0.499487i
$370$			27.5022i			1.42977i
$371$	4.27156	+	3.12311i	0.221768	+	0.162144i
$372$	−7.12311	+	2.00000i	−0.369316	+	0.103695i
$373$	−23.6155			−1.22277			−0.611383	−	0.791335i	$-0.709386\pi$
$373$	−23.6155			−1.22277			−0.611383	+	0.791335i	$0.709386\pi$
$374$	−2.39871			−0.124034
$375$	1.75379	+	6.24621i	0.0905653	+	0.322553i
$376$		−	6.14441i		−	0.316874i
$377$	10.4160			0.536450
$378$	2.59455	+	13.5007i	0.133449	+	0.694400i
$379$	−18.7386			−0.962539			−0.481269	−	0.876573i	$-0.659824\pi$
$379$	−18.7386			−0.962539			−0.481269	+	0.876573i	$0.659824\pi$
$380$		−	19.1231i		−	0.980995i
$381$	−1.05171	−	3.74571i	−0.0538805	−	0.191898i
$382$	15.3693			0.786363
$383$	16.7909			0.857977			0.428988	−	0.903310i	$-0.358870\pi$
$383$	16.7909			0.857977			0.428988	+	0.903310i	$0.358870\pi$
$384$	−1.66757	+	0.468213i	−0.0850976	+	0.0238934i
$385$	−7.12311	−	5.20798i	−0.363027	−	0.265423i
$386$		−	15.3693i		−	0.782278i
$387$	−7.36932	+	4.49242i	−0.374603	+	0.228363i
$388$		−	1.87285i		−	0.0950797i
$389$			12.2462i			0.620908i	0.950588	+	0.310454i	$0.100481\pi$
$389$			12.2462i			0.620908i	−0.950588	+	0.310454i	$0.899519\pi$
$390$	−8.13254	−	28.9645i	−0.411807	−	1.46667i
$391$			14.3922i			0.727847i
$392$	6.67026	−	2.12311i	0.336899	−	0.107233i
$393$	4.93087	+	17.5616i	0.248729	+	0.885863i
$394$	−18.4924			−0.931635
$395$	−50.4376			−2.53779
$396$	−1.56155	−	2.56155i	−0.0784710	−	0.128723i
$397$		−	2.80928i		−	0.140994i	−0.997512	−	0.0704968i	$-0.977542\pi$
$397$		−	2.80928i		−	0.140994i	0.997512	−	0.0704968i	$-0.0224585\pi$
$398$	4.27156			0.214114
$399$	−9.19703	+	24.6136i	−0.460427	+	1.23222i
$400$	6.12311			0.306155
$401$		−	5.36932i		−	0.268131i	−0.990972	−	0.134065i	$-0.957197\pi$
$401$		−	5.36932i		−	0.268131i	0.990972	−	0.134065i	$-0.0428032\pi$
$402$	−20.0108	+	5.61856i	−0.998048	+	0.280228i
$403$	−22.2462			−1.10816
$404$	−1.46228			−0.0727511
$405$	13.7511	−	26.6811i	0.683298	−	1.32579i
$406$	3.12311	−	4.27156i	0.154997	−	0.211994i
$407$			8.24621i			0.408750i
$408$	−4.00000	+	1.12311i	−0.198030	+	0.0556020i
$409$		−	7.49141i		−	0.370426i	−0.982698	−	0.185213i	$-0.940702\pi$
$409$		−	7.49141i		−	0.370426i	0.982698	−	0.185213i	$-0.0592976\pi$
$410$		−	20.4924i		−	1.01205i
$411$	27.5022	−	7.72197i	1.35658	−	0.380897i
$412$		−	12.8147i		−	0.631334i
$413$	17.7274	−	24.2462i	0.872307	−	1.19308i
$414$	−15.3693	+	9.36932i	−0.755361	+	0.460477i
$415$	−19.1231			−0.938716
$416$	−5.20798			−0.255342
$417$	10.9309	−	3.06913i	0.535287	−	0.150296i
$418$		−	5.73384i		−	0.280451i
$419$	23.8718			1.16621			0.583106	−	0.812396i	$-0.301837\pi$
$419$	23.8718			1.16621			0.583106	+	0.812396i	$0.301837\pi$
$420$	−14.3167	−	5.34953i	−0.698583	−	0.261030i
$421$	8.24621			0.401896			0.200948	−	0.979602i	$-0.435598\pi$
$421$	8.24621			0.401896			0.200948	+	0.979602i	$0.435598\pi$
$422$		−	23.3693i		−	1.13760i
$423$	15.7392	−	9.59482i	0.765268	−	0.466516i
$424$	−2.00000			−0.0971286
$425$	14.6875			0.712450
$426$	7.19612	+	25.6294i	0.348653	+	1.24175i
$427$	7.12311	+	5.20798i	0.344711	+	0.252032i
$428$		−	2.24621i		−	0.108575i
$429$	−2.43845	−	8.68466i	−0.117729	−	0.419299i
$430$		−	9.59482i		−	0.462703i
$431$			11.6155i			0.559500i	0.960073	+	0.279750i	$0.0902516\pi$
$431$			11.6155i			0.559500i	−0.960073	+	0.279750i	$0.909748\pi$
$432$	−3.80335	−	3.54042i	−0.182989	−	0.170338i
$433$		−	20.0108i		−	0.961657i	−0.876815	−	0.480829i	$-0.840336\pi$
$433$		−	20.0108i		−	0.961657i	0.876815	−	0.480829i	$-0.159664\pi$
$434$	−6.67026	+	9.12311i	−0.320183	+	0.437923i
$435$	−11.1231	+	3.12311i	−0.533312	+	0.149741i
$436$	3.12311			0.149570
$437$	−34.4030			−1.64572
$438$	−4.87689	−	17.3693i	−0.233027	−	0.829938i
$439$		−	23.4612i		−	1.11974i	−0.828580	−	0.559871i	$-0.810851\pi$
$439$		−	23.4612i		−	1.11974i	0.828580	−	0.559871i	$-0.189149\pi$
$440$	3.33513			0.158996
$441$	15.8544	+	13.7709i	0.754972	+	0.655757i
$442$	−12.4924			−0.594204
$443$		−	26.7386i		−	1.27039i	−0.772351	−	0.635195i	$-0.780920\pi$
$443$		−	26.7386i		−	1.27039i	0.772351	−	0.635195i	$-0.219080\pi$
$444$	3.86098	+	13.7511i	0.183234	+	0.652598i
$445$	−44.4924			−2.10914
$446$	−10.9418			−0.518110
$447$	20.4214	−	5.73384i	0.965897	−	0.271201i
$448$	−1.56155	+	2.13578i	−0.0737764	+	0.100906i
$449$		−	17.7538i		−	0.837853i	−0.908020	−	0.418927i	$-0.862406\pi$
$449$		−	17.7538i		−	0.837853i	0.908020	−	0.418927i	$-0.137594\pi$
$450$	9.56155	+	15.6847i	0.450736	+	0.739382i
$451$		−	6.14441i		−	0.289329i
$452$			11.1231i			0.523187i
$453$	−8.54312	−	30.4268i	−0.401391	−	1.42957i
$454$			0.936426i			0.0439487i
$455$	−37.0970	−	27.1231i	−1.73914	−	1.27155i
$456$	−2.68466	−	9.56155i	−0.125721	−	0.447761i
$457$	25.6155			1.19824			0.599122	−	0.800658i	$-0.295516\pi$
$457$	25.6155			1.19824			0.599122	+	0.800658i	$0.295516\pi$
$458$	2.80928			0.131269
$459$	−9.12311	−	8.49242i	−0.425830	−	0.396392i
$460$		−	20.0108i		−	0.933008i
$461$	34.8136			1.62143			0.810715	−	0.585440i	$-0.199078\pi$
$461$	34.8136			1.62143			0.810715	+	0.585440i	$0.199078\pi$
$462$	−4.29269	−	1.60399i	−0.199714	−	0.0746245i
$463$	17.3693			0.807221			0.403610	−	0.914931i	$-0.367755\pi$
$463$	17.3693			0.807221			0.403610	+	0.914931i	$0.367755\pi$
$464$			2.00000i			0.0928477i
$465$	23.7565	−	6.67026i	1.10168	−	0.309326i
$466$	17.1231			0.793213
$467$	−0.115279			−0.00533449			−0.00266725	−	0.999996i	$-0.500849\pi$
$467$	−0.115279			−0.00533449			−0.00266725	+	0.999996i	$0.500849\pi$
$468$	−8.13254	−	13.3405i	−0.375927	−	0.616666i
$469$	−18.7386	+	25.6294i	−0.865270	+	1.18345i
$470$			20.4924i			0.945245i
$471$	0.192236	−	0.0539753i	0.00885776	−	0.00248705i
$472$			11.3524i			0.522536i
$473$		−	2.87689i		−	0.132280i
$474$	−25.2188	+	7.08084i	−1.15834	+	0.325234i
$475$			35.1089i			1.61091i
$476$	−3.74571	+	5.12311i	−0.171684	+	0.234817i
$477$	−3.12311	−	5.12311i	−0.142997	−	0.234571i
$478$	5.36932			0.245587
$479$	31.2479			1.42775			0.713877	−	0.700271i	$-0.246938\pi$
$479$	31.2479			1.42775			0.713877	+	0.700271i	$0.246938\pi$
$480$	5.56155	−	1.56155i	0.253849	−	0.0712748i
$481$			42.9461i			1.95818i
$482$	−3.74571			−0.170612
$483$	−9.62395	+	25.7562i	−0.437905	+	1.17195i
$484$	1.00000			0.0454545
$485$			6.24621i			0.283626i
$486$	3.12985	−	15.2710i	0.141973	−	0.692708i
$487$	36.4924			1.65363			0.826815	−	0.562474i	$-0.190150\pi$
$487$	36.4924			1.65363			0.826815	+	0.562474i	$0.190150\pi$
$488$	−3.33513			−0.150974
$489$	7.49141	+	26.6811i	0.338773	+	1.20656i
$490$	−22.2462	+	7.08084i	−1.00498	+	0.319880i
$491$			14.7386i			0.665145i	0.943078	+	0.332573i	$0.107917\pi$
$491$			14.7386i			0.665145i	−0.943078	+	0.332573i	$0.892083\pi$
$492$	−2.87689	−	10.2462i	−0.129700	−	0.461935i
$493$			4.79741i			0.216065i
$494$		−	29.8617i		−	1.34354i
$495$	5.20798	+	8.54312i	0.234082	+	0.383985i
$496$		−	4.27156i		−	0.191799i
$497$	32.8255	+	24.0000i	1.47242	+	1.07655i
$498$	−9.56155	+	2.68466i	−0.428463	+	0.120302i
$499$	24.0000			1.07439			0.537194	−	0.843459i	$-0.319484\pi$
$499$	24.0000			1.07439			0.537194	+	0.843459i	$0.319484\pi$
$500$	−3.74571			−0.167513
$501$	0.876894	+	3.12311i	0.0391768	+	0.139530i
$502$			19.8955i			0.887980i
$503$	−38.9699			−1.73758			−0.868791	−	0.495180i	$-0.835102\pi$
$503$	−38.9699			−1.73758			−0.868791	+	0.495180i	$0.835102\pi$
$504$	−7.90936	−	0.664868i	−0.352311	−	0.0296156i
$505$	4.87689			0.217019
$506$		−	6.00000i		−	0.266733i
$507$	−6.61262	−	23.5512i	−0.293677	−	1.04595i
$508$	2.24621			0.0996595
$509$	−6.25969			−0.277456			−0.138728	−	0.990331i	$-0.544301\pi$
$509$	−6.25969			−0.277456			−0.138728	+	0.990331i	$0.544301\pi$
$510$	13.3405	−	3.74571i	0.590729	−	0.165863i
$511$	−22.2462	−	16.2651i	−0.984114	−	0.719525i
$512$		−	1.00000i		−	0.0441942i
$513$	20.3002	−	21.8078i	0.896275	−	0.962836i
$514$		−	21.8836i		−	0.965246i
$515$			42.7386i			1.88329i
$516$	−1.34700	−	4.79741i	−0.0592984	−	0.211194i
$517$			6.14441i			0.270231i
$518$	17.6121	+	12.8769i	0.773831	+	0.565778i
$519$	−7.31534	−	26.0540i	−0.321108	−	1.14364i
$520$	17.3693			0.761695
$521$	−11.4677			−0.502408			−0.251204	−	0.967934i	$-0.580826\pi$
$521$	−11.4677			−0.502408			−0.251204	+	0.967934i	$0.580826\pi$
$522$	−5.12311	+	3.12311i	−0.224232	+	0.136695i
$523$		−	40.9580i		−	1.79097i	−0.445093	−	0.895484i	$-0.646829\pi$
$523$		−	40.9580i		−	1.79097i	0.445093	−	0.895484i	$-0.353171\pi$
$524$	−10.5312			−0.460060
$525$	26.2846	+	9.82141i	1.14715	+	0.428642i
$526$	−2.24621			−0.0979395
$527$		−	10.2462i		−	0.446332i
$528$	1.66757	−	0.468213i	0.0725715	−	0.0203764i
$529$	−13.0000			−0.565217
$530$	6.67026			0.289738
$531$	−29.0798	+	17.7274i	−1.26195	+	0.769302i
$532$	−12.2462	−	8.95369i	−0.530941	−	0.388192i
$533$		−	32.0000i		−	1.38607i
$534$	−22.2462	+	6.24621i	−0.962688	+	0.270300i
$535$			7.49141i			0.323882i
$536$		−	12.0000i		−	0.518321i
$537$	−3.74571	+	1.05171i	−0.161639	+	0.0453845i
$538$		−	3.33513i		−	0.143788i
$539$	−6.67026	+	2.12311i	−0.287309	+	0.0914486i
$540$	12.6847	+	11.8078i	0.545861	+	0.508125i
$541$	−19.6155			−0.843337			−0.421669	−	0.906750i	$-0.638555\pi$
$541$	−19.6155			−0.843337			−0.421669	+	0.906750i	$0.638555\pi$
$542$	−8.01726			−0.344371
$543$	−1.56155	+	0.438447i	−0.0670126	+	0.0188156i
$544$		−	2.39871i		−	0.102844i
$545$	−10.4160			−0.446171
$546$	−22.3563	−	8.35357i	−0.956760	−	0.357500i
$547$	−10.8769			−0.465062			−0.232531	−	0.972589i	$-0.574701\pi$
$547$	−10.8769			−0.465062			−0.232531	+	0.972589i	$0.574701\pi$
$548$			16.4924i			0.704521i
$549$	−5.20798	−	8.54312i	−0.222271	−	0.364611i
$550$	−6.12311			−0.261090
$551$	−11.4677			−0.488539
$552$	−2.80928	−	10.0054i	−0.119571	−	0.425858i
$553$	−23.6155	+	32.2996i	−1.00423	+	1.37352i
$554$		−	27.6155i		−	1.17327i
$555$	−12.8769	−	45.8617i	−0.546594	−	1.94672i
$556$			6.55498i			0.277993i
$557$		−	10.4924i		−	0.444578i	−0.974981	−	0.222289i	$-0.928647\pi$
$557$		−	10.4924i		−	0.444578i	0.974981	−	0.222289i	$-0.0713529\pi$
$558$	10.9418	−	6.67026i	0.463204	−	0.282375i
$559$		−	14.9828i		−	0.633706i
$560$	5.20798	−	7.12311i	0.220078	−	0.301006i
$561$	4.00000	−	1.12311i	0.168880	−	0.0474176i
$562$	25.1231			1.05975
$563$	−23.6412			−0.996359			−0.498179	−	0.867074i	$-0.665998\pi$
$563$	−23.6412			−0.996359			−0.498179	+	0.867074i	$0.665998\pi$
$564$	2.87689	+	10.2462i	0.121139	+	0.431443i
$565$		−	37.0970i		−	1.56068i
$566$	−19.8955			−0.836271
$567$	−10.6478	−	21.2985i	−0.447165	−	0.894451i
$568$	−15.3693			−0.644882
$569$			32.2462i			1.35183i	0.736979	+	0.675916i	$0.236252\pi$
$569$			32.2462i			1.35183i	−0.736979	+	0.675916i	$0.763748\pi$
$570$	8.95369	+	31.8890i	0.375029	+	1.33568i
$571$	−18.8769			−0.789973			−0.394987	−	0.918687i	$-0.629251\pi$
$571$	−18.8769			−0.789973			−0.394987	+	0.918687i	$0.629251\pi$
$572$	5.20798			0.217757
$573$	−25.6294	+	7.19612i	−1.07068	+	0.300622i
$574$	−13.1231	−	9.59482i	−0.547748	−	0.400480i
$575$			36.7386i			1.53211i
$576$	2.56155	−	1.56155i	0.106731	−	0.0650647i
$577$			35.2242i			1.46640i	0.680012	+	0.733201i	$0.261974\pi$
$577$			35.2242i			1.46640i	−0.680012	+	0.733201i	$0.738026\pi$
$578$			11.2462i			0.467781i
$579$	7.19612	+	25.6294i	0.299060	+	1.06512i
$580$		−	6.67026i		−	0.276968i
$581$	−8.95369	+	12.2462i	−0.371462	+	0.508058i
$582$	0.876894	+	3.12311i	0.0363484	+	0.129457i
$583$	2.00000			0.0828315
$584$	10.4160			0.431016
$585$	27.1231	+	44.4924i	1.12140	+	1.83954i
$586$		−	20.4214i		−	0.843599i
$587$	22.8201			0.941885			0.470943	−	0.882164i	$-0.343914\pi$
$587$	22.8201			0.941885			0.470943	+	0.882164i	$0.343914\pi$
$588$	−10.1290	+	6.66352i	−0.417715	+	0.274799i
$589$	24.4924			1.00919
$590$		−	37.8617i		−	1.55874i
$591$	30.8373	−	8.65840i	1.26848	−	0.356159i
$592$	−8.24621			−0.338917
$593$	37.3923			1.53552			0.767759	−	0.640738i	$-0.221372\pi$
$593$	37.3923			1.53552			0.767759	+	0.640738i	$0.221372\pi$
$594$	3.80335	+	3.54042i	0.156053	+	0.145265i
$595$	12.4924	−	17.0862i	0.512139	−	0.700467i
$596$			12.2462i			0.501624i
$597$	−7.12311	+	2.00000i	−0.291529	+	0.0818546i
$598$		−	31.2479i		−	1.27782i
$599$			38.1080i			1.55705i	0.627614	+	0.778524i	$0.284031\pi$
$599$			38.1080i			1.55705i	−0.627614	+	0.778524i	$0.715969\pi$
$600$	−10.2107	+	2.86692i	−0.416849	+	0.117041i
$601$			2.92456i			0.119295i	0.998219	+	0.0596476i	$0.0189977\pi$
$601$			2.92456i			0.119295i	−0.998219	+	0.0596476i	$0.981002\pi$
$602$	−6.14441	−	4.49242i	−0.250428	−	0.183097i
$603$	30.7386	−	18.7386i	1.25177	−	0.763096i
$604$	18.2462			0.742428
$605$	−3.33513			−0.135592
$606$	2.43845	−	0.684658i	0.0990551	−	0.0278123i
$607$		−	35.7500i		−	1.45105i	−0.688196	−	0.725524i	$-0.741597\pi$
$607$		−	35.7500i		−	1.45105i	0.688196	−	0.725524i	$-0.258403\pi$
$608$	5.73384			0.232538
$609$	−3.20798	+	8.58538i	−0.129994	+	0.347897i
$610$	11.1231			0.450361
$611$			32.0000i			1.29458i
$612$	6.14441	−	3.74571i	0.248373	−	0.151411i
$613$	10.6307			0.429369			0.214685	−	0.976683i	$-0.431128\pi$
$613$	10.6307			0.429369			0.214685	+	0.976683i	$0.431128\pi$
$614$	8.42784			0.340120
$615$	9.59482	+	34.1725i	0.386901	+	1.37797i
$616$	1.56155	−	2.13578i	0.0629168	−	0.0860530i
$617$		−	19.6155i		−	0.789691i	−0.918747	−	0.394846i	$-0.870798\pi$
$617$		−	19.6155i		−	0.789691i	0.918747	−	0.394846i	$-0.129202\pi$
$618$	6.00000	+	21.3693i	0.241355	+	0.859600i
$619$			14.5722i			0.585708i	0.956157	+	0.292854i	$0.0946050\pi$
$619$			14.5722i			0.585708i	−0.956157	+	0.292854i	$0.905395\pi$
$620$			14.2462i			0.572142i
$621$	21.2425	−	22.8201i	0.852433	−	0.915738i
$622$			18.6638i			0.748350i
$623$	−20.8319	+	28.4924i	−0.834614	+	1.14152i
$624$	8.68466	−	2.43845i	0.347665	−	0.0976160i
$625$	−18.1231			−0.724924
$626$	10.4160			0.416306
$627$	2.68466	+	9.56155i	0.107215	+	0.381852i
$628$			0.115279i			0.00460015i
$629$	−19.7802			−0.788690
$630$	26.3788	+	2.21742i	1.05095	+	0.0883442i
$631$	27.1231			1.07975			0.539877	−	0.841744i	$-0.318471\pi$
$631$	27.1231			1.07975			0.539877	+	0.841744i	$0.318471\pi$
$632$		−	15.1231i		−	0.601565i
$633$	10.9418	+	38.9699i	0.434898	+	1.54891i
$634$	24.7386			0.982497
$635$	−7.49141			−0.297288
$636$	3.33513	−	0.936426i	0.132247	−	0.0371317i
$637$	−34.7386	+	11.0571i	−1.37639	+	0.438098i
$638$		−	2.00000i		−	0.0791808i
$639$	−24.0000	−	39.3693i	−0.949425	−	1.55743i
$640$			3.33513i			0.131833i
$641$			37.3693i			1.47600i	0.674801	+	0.738000i	$0.264229\pi$
$641$			37.3693i			1.47600i	−0.674801	+	0.738000i	$0.735771\pi$
$642$	1.05171	+	3.74571i	0.0415075	+	0.147831i
$643$		−	19.3697i		−	0.763865i	−0.924190	−	0.381932i	$-0.875259\pi$
$643$		−	19.3697i		−	0.763865i	0.924190	−	0.381932i	$-0.124741\pi$
$644$	−12.8147	−	9.36932i	−0.504969	−	0.369203i
$645$	4.49242	+	16.0000i	0.176889	+	0.629999i
$646$	13.7538			0.541136
$647$	−5.09271			−0.200215			−0.100107	−	0.994977i	$-0.531919\pi$
$647$	−5.09271			−0.200215			−0.100107	+	0.994977i	$0.531919\pi$
$648$	8.00000	+	4.12311i	0.314270	+	0.161971i
$649$		−	11.3524i		−	0.445621i
$650$	−31.8890			−1.25079
$651$	6.85155	−	18.3365i	0.268533	−	0.718664i
$652$	−16.0000			−0.626608
$653$			26.4924i			1.03673i	0.855160	+	0.518364i	$0.173459\pi$
$653$			26.4924i			1.03673i	−0.855160	+	0.518364i	$0.826541\pi$
$654$	−5.20798	+	1.46228i	−0.203648	+	0.0571796i
$655$	35.1231			1.37237
$656$	6.14441			0.239899
$657$	16.2651	+	26.6811i	0.634561	+	1.04093i
$658$	13.1231	+	9.59482i	0.511592	+	0.374045i
$659$		−	40.4924i		−	1.57736i	−0.614803	−	0.788680i	$-0.710765\pi$
$659$		−	40.4924i		−	1.57736i	0.614803	−	0.788680i	$-0.289235\pi$
$660$	−5.56155	+	1.56155i	−0.216483	+	0.0607834i
$661$			4.68213i			0.182114i	0.995846	+	0.0910569i	$0.0290245\pi$
$661$			4.68213i			0.182114i	−0.995846	+	0.0910569i	$0.970975\pi$
$662$		−	20.0000i		−	0.777322i
$663$	20.8319	−	5.84912i	0.809045	−	0.227161i
$664$		−	5.73384i		−	0.222516i
$665$	40.8427	+	29.8617i	1.58381	+	1.15799i
$666$	−12.8769	−	21.1231i	−0.498970	−	0.818504i
$667$	−12.0000			−0.464642
$668$	−1.87285			−0.0724628
$669$	18.2462	−	5.12311i	0.705439	−	0.198071i
$670$			40.0216i			1.54617i
$671$	3.33513			0.128751
$672$	1.60399	−	4.29269i	0.0618754	−	0.165594i
$673$	30.4924			1.17540			0.587698	−	0.809080i	$-0.300034\pi$
$673$	30.4924			1.17540			0.587698	+	0.809080i	$0.300034\pi$
$674$			3.36932i			0.129781i
$675$	−23.2883	−	21.6784i	−0.896366	−	0.834400i
$676$	14.1231			0.543196
$677$	−0.410574			−0.0157796			−0.00788981	−	0.999969i	$-0.502511\pi$
$677$	−0.410574			−0.0157796			−0.00788981	+	0.999969i	$0.502511\pi$
$678$	−5.20798	−	18.5485i	−0.200011	−	0.712351i
$679$	4.00000	+	2.92456i	0.153506	+	0.112234i
$680$			8.00000i			0.306786i
$681$	−0.438447	−	1.56155i	−0.0168013	−	0.0598388i
$682$			4.27156i			0.163566i
$683$		−	13.7538i		−	0.526274i	−0.964758	−	0.263137i	$-0.915243\pi$
$683$		−	13.7538i		−	0.526274i	0.964758	−	0.263137i	$-0.0847571\pi$
$684$	8.95369	+	14.6875i	0.342353	+	0.561592i
$685$		−	55.0044i		−	2.10161i
$686$	−5.88148	+	17.5616i	−0.224556	+	0.670503i
$687$	−4.68466	+	1.31534i	−0.178731	+	0.0501834i
$688$	2.87689			0.109681
$689$	10.4160			0.396817
$690$	9.36932	+	33.3693i	0.356684	+	1.27035i
$691$		−	38.5593i		−	1.46687i	−0.679762	−	0.733433i	$-0.737917\pi$
$691$		−	38.5593i		−	1.46687i	0.679762	−	0.733433i	$-0.262083\pi$
$692$	15.6240			0.593934
$693$	7.90936	+	0.664868i	0.300452	+	0.0252562i
$694$	4.00000			0.151838
$695$		−	21.8617i		−	0.829263i
$696$	−0.936426	−	3.33513i	−0.0354952	−	0.126418i
$697$	14.7386			0.558266
$698$	21.2425			0.804041
$699$	−28.5539	+	8.01726i	−1.08001	+	0.303241i
$700$	−9.56155	+	13.0776i	−0.361393	+	0.494287i
$701$			4.24621i			0.160377i	0.996780	+	0.0801886i	$0.0255523\pi$
$701$			4.24621i			0.160377i	−0.996780	+	0.0801886i	$0.974448\pi$
$702$	19.8078	+	18.4384i	0.747596	+	0.695914i
$703$		−	47.2824i		−	1.78329i
$704$			1.00000i			0.0376889i
$705$	−9.59482	−	34.1725i	−0.361362	−	1.28701i
$706$		−	12.2888i		−	0.462496i
$707$	2.28343	−	3.12311i	0.0858771	−	0.117456i
$708$	−5.31534	−	18.9309i	−0.199763	−	0.711466i
$709$	−12.7386			−0.478409			−0.239205	−	0.970969i	$-0.576887\pi$
$709$	−12.7386			−0.478409			−0.239205	+	0.970969i	$0.576887\pi$
$710$	51.2587			1.92370
$711$	38.7386	−	23.6155i	1.45281	−	0.885651i
$712$		−	13.3405i		−	0.499957i
$713$	25.6294			0.959827
$714$	3.84751	−	10.2969i	0.143989	−	0.385352i
$715$	−17.3693			−0.649576
$716$		−	2.24621i		−	0.0839449i
$717$	−8.95369	+	2.51398i	−0.334382	+	0.0938865i
$718$	−7.12311			−0.265832
$719$	−19.4849			−0.726666			−0.363333	−	0.931659i	$-0.618361\pi$
$719$	−19.4849			−0.726666			−0.363333	+	0.931659i	$0.618361\pi$
$720$	−8.54312	+	5.20798i	−0.318383	+	0.194090i
$721$	27.3693	+	20.0108i	1.01929	+	0.745241i
$722$			13.8769i			0.516445i
$723$	6.24621	−	1.75379i	0.232299	−	0.0652241i
$724$		−	0.936426i		−	0.0348020i
$725$			12.2462i			0.454813i
$726$	−1.66757	+	0.468213i	−0.0618892	+	0.0173770i
$727$			14.9181i			0.553281i	0.960973	+	0.276641i	$0.0892212\pi$
$727$			14.9181i			0.553281i	−0.960973	+	0.276641i	$0.910779\pi$
$728$	8.13254	−	11.1231i	0.301412	−	0.412250i
$729$	1.93087	+	26.9309i	0.0715137	+	0.997440i
$730$	−34.7386			−1.28573
$731$	6.90082			0.255236
$732$	5.56155	−	1.56155i	0.205561	−	0.0577167i
$733$		−	43.3567i		−	1.60142i	−0.599054	−	0.800708i	$-0.704457\pi$
$733$		−	43.3567i		−	1.60142i	0.599054	−	0.800708i	$-0.295543\pi$
$734$	25.3341			0.935097
$735$	33.7817	−	22.2237i	1.24606	−	0.819735i
$736$	6.00000			0.221163
$737$			12.0000i			0.442026i
$738$	9.59482	+	15.7392i	0.353190	+	0.579369i
$739$	−52.3542			−1.92588			−0.962939	−	0.269718i	$-0.913070\pi$
$739$	−52.3542			−1.92588			−0.962939	+	0.269718i	$0.913070\pi$
$740$	27.5022			1.01100
$741$	13.9817	+	49.7964i	0.513629	+	1.82932i
$742$	3.12311	−	4.27156i	0.114653	−	0.156814i
$743$		−	11.1231i		−	0.408067i	−0.978964	−	0.204034i	$-0.934595\pi$
$743$		−	11.1231i		−	0.408067i	0.978964	−	0.204034i	$-0.0654052\pi$
$744$	2.00000	+	7.12311i	0.0733236	+	0.261146i
$745$		−	40.8427i		−	1.49636i
$746$			23.6155i			0.864626i
$747$	14.6875	−	8.95369i	0.537389	−	0.327598i
$748$			2.39871i			0.0877054i
$749$	4.79741	+	3.50758i	0.175294	+	0.128164i
$750$	6.24621	−	1.75379i	0.228079	−	0.0640393i
$751$	−44.4924			−1.62355			−0.811776	−	0.583969i	$-0.801499\pi$
$751$	−44.4924			−1.62355			−0.811776	+	0.583969i	$0.801499\pi$
$752$	−6.14441			−0.224064
$753$	−9.31534	−	33.1771i	−0.339470	−	1.20904i
$754$		−	10.4160i		−	0.379327i
$755$	−60.8535			−2.21469
$756$	13.5007	−	2.59455i	0.491015	−	0.0943630i
$757$	16.2462			0.590479			0.295239	−	0.955423i	$-0.404601\pi$
$757$	16.2462			0.590479			0.295239	+	0.955423i	$0.404601\pi$
$758$			18.7386i			0.680618i
$759$	2.80928	+	10.0054i	0.101970	+	0.363173i
$760$	−19.1231			−0.693668
$761$	−29.0798			−1.05414			−0.527070	−	0.849822i	$-0.676710\pi$
$761$	−29.0798			−1.05414			−0.527070	+	0.849822i	$0.676710\pi$
$762$	−3.74571	+	1.05171i	−0.135693	+	0.0380993i
$763$	−4.87689	+	6.67026i	−0.176555	+	0.241480i
$764$		−	15.3693i		−	0.556042i
$765$	−20.4924	+	12.4924i	−0.740905	+	0.451664i
$766$		−	16.7909i		−	0.606681i
$767$		−	59.1231i		−	2.13481i
$768$	0.468213	+	1.66757i	0.0168952	+	0.0601731i
$769$			14.9828i			0.540294i	0.962819	+	0.270147i	$0.0870724\pi$
$769$			14.9828i			0.540294i	−0.962819	+	0.270147i	$0.912928\pi$
$770$	−5.20798	+	7.12311i	−0.187683	+	0.256699i
$771$	10.2462	+	36.4924i	0.369008	+	1.31424i
$772$	−15.3693			−0.553154
$773$	22.5248			0.810160			0.405080	−	0.914281i	$-0.367244\pi$
$773$	22.5248			0.810160			0.405080	+	0.914281i	$0.367244\pi$
$774$	4.49242	+	7.36932i	0.161477	+	0.264885i
$775$		−	26.1552i		−	0.939523i
$776$	−1.87285			−0.0672315
$777$	−35.3984	−	13.2269i	−1.26991	−	0.474511i
$778$	12.2462			0.439048
$779$			35.2311i			1.26228i
$780$	−28.9645	+	8.13254i	−1.03709	+	0.291192i
$781$	15.3693			0.549957
$782$	14.3922			0.514665
$783$	7.08084	−	7.60669i	0.253048	−	0.271841i
$784$	−2.12311	−	6.67026i	−0.0758252	−	0.238224i
$785$		−	0.384472i		−	0.0137224i
$786$	17.5616	−	4.93087i	0.626400	−	0.175878i
$787$		−	19.0744i		−	0.679928i	−0.940439	−	0.339964i	$-0.889585\pi$
$787$		−	19.0744i		−	0.679928i	0.940439	−	0.339964i	$-0.110415\pi$
$788$			18.4924i			0.658765i
$789$	3.74571	−	1.05171i	0.133351	−	0.0374417i
$790$			50.4376i			1.79449i
$791$	−23.7565	−	17.3693i	−0.844684	−	0.617582i
$792$	−2.56155	+	1.56155i	−0.0910208	+	0.0554874i
$793$	17.3693			0.616803
$794$	−2.80928			−0.0996976
$795$	−11.1231	+	3.12311i	−0.394496	+	0.110765i
$796$		−	4.27156i		−	0.151401i
$797$	−50.8481			−1.80113			−0.900567	−	0.434718i	$-0.856848\pi$
$797$	−50.8481			−1.80113			−0.900567	+	0.434718i	$0.856848\pi$
$798$	24.6136	+	9.19703i	0.871312	+	0.325571i
$799$	−14.7386			−0.521415
$800$		−	6.12311i		−	0.216484i
$801$	34.1725	−	20.8319i	1.20742	−	0.736060i
$802$	−5.36932			−0.189597
$803$	−10.4160			−0.367572
$804$	5.61856	+	20.0108i	0.198151	+	0.705726i
$805$	42.7386	+	31.2479i	1.50634	+	1.10134i
$806$			22.2462i			0.783589i
$807$	1.56155	+	5.56155i	0.0549693	+	0.195776i
$808$			1.46228i			0.0514428i
$809$		−	32.7386i		−	1.15103i	−0.817792	−	0.575515i	$-0.804802\pi$
$809$		−	32.7386i		−	1.15103i	0.817792	−	0.575515i	$-0.195198\pi$
$810$	−26.6811	−	13.7511i	−0.937477	−	0.483164i
$811$		−	26.7963i		−	0.940947i	−0.882414	−	0.470473i	$-0.844083\pi$
$811$		−	26.7963i		−	0.940947i	0.882414	−	0.470473i	$-0.155917\pi$
$812$	−4.27156	−	3.12311i	−0.149902	−	0.109600i
$813$	13.3693	−	3.75379i	0.468882	−	0.131651i
$814$	8.24621			0.289030
$815$	53.3621			1.86919
$816$	1.12311	+	4.00000i	0.0393166	+	0.140028i
$817$			16.4956i			0.577110i
$818$	−7.49141			−0.261931
$819$	41.1918	+	3.46262i	1.43936	+	0.120994i
$820$	−20.4924			−0.715626
$821$		−	46.4924i		−	1.62260i	−0.584632	−	0.811298i	$-0.698761\pi$
$821$		−	46.4924i		−	1.62260i	0.584632	−	0.811298i	$-0.301239\pi$
$822$	−7.72197	−	27.5022i	−0.269335	−	0.959249i
$823$	4.87689			0.169998			0.0849989	−	0.996381i	$-0.472911\pi$
$823$	4.87689			0.169998			0.0849989	+	0.996381i	$0.472911\pi$
$824$	−12.8147			−0.446420
$825$	10.2107	−	2.86692i	0.355490	−	0.0998133i
$826$	−24.2462	−	17.7274i	−0.843634	−	0.616814i
$827$		−	8.49242i		−	0.295310i	−0.989039	−	0.147655i	$-0.952827\pi$
$827$		−	8.49242i		−	0.295310i	0.989039	−	0.147655i	$-0.0471726\pi$
$828$	9.36932	+	15.3693i	0.325606	+	0.534121i
$829$		−	6.78554i		−	0.235672i	−0.993033	−	0.117836i	$-0.962404\pi$
$829$		−	6.78554i		−	0.235672i	0.993033	−	0.117836i	$-0.0375957\pi$
$830$			19.1231i			0.663773i
$831$	12.9300	+	46.0507i	0.448535	+	1.59748i
$832$			5.20798i			0.180554i
$833$	−5.09271	−	16.0000i	−0.176452	−	0.554367i
$834$	−3.06913	−	10.9309i	−0.106275	−	0.378505i
$835$	6.24621			0.216159
$836$	−5.73384			−0.198309
$837$	−15.1231	+	16.2462i	−0.522731	+	0.561551i
$838$		−	23.8718i		−	0.824637i
$839$	−50.9634			−1.75945			−0.879726	−	0.475481i	$-0.842274\pi$
$839$	−50.9634			−1.75945			−0.879726	+	0.475481i	$0.842274\pi$
$840$	−5.34953	+	14.3167i	−0.184576	+	0.493973i
$841$	25.0000			0.862069
$842$		−	8.24621i		−	0.284183i
$843$	−41.8944	+	11.7630i	−1.44292	+	0.405138i
$844$	−23.3693			−0.804405
$845$	−47.1024			−1.62037
$846$	−9.59482	−	15.7392i	−0.329877	−	0.541126i
$847$	−1.56155	+	2.13578i	−0.0536556	+	0.0733862i
$848$			2.00000i			0.0686803i
$849$	33.1771	−	9.31534i	1.13863	−	0.319702i
$850$		−	14.6875i		−	0.503778i
$851$		−	49.4773i		−	1.69606i
$852$	25.6294	−	7.19612i	0.878047	−	0.246535i
$853$			13.9817i			0.478723i	0.970931	+	0.239361i	$0.0769381\pi$
$853$			13.9817i			0.478723i	−0.970931	+	0.239361i	$0.923062\pi$
$854$	5.20798	−	7.12311i	0.178214	−	0.243748i
$855$	−29.8617	−	48.9848i	−1.02125	−	1.67525i
$856$	−2.24621			−0.0767739
$857$	21.1272			0.721693			0.360846	−	0.932625i	$-0.382488\pi$
$857$	21.1272			0.721693			0.360846	+	0.932625i	$0.382488\pi$
$858$	−8.68466	+	2.43845i	−0.296489	+	0.0832472i
$859$		−	37.7382i		−	1.28761i	−0.765190	−	0.643805i	$-0.777355\pi$
$859$		−	37.7382i		−	1.28761i	0.765190	−	0.643805i	$-0.222645\pi$
$860$	−9.59482			−0.327181
$861$	26.3761	+	9.85559i	0.898894	+	0.335878i
$862$	11.6155			0.395626
$863$			7.36932i			0.250854i	0.992103	+	0.125427i	$0.0400302\pi$
$863$			7.36932i			0.250854i	−0.992103	+	0.125427i	$0.959970\pi$
$864$	−3.54042	+	3.80335i	−0.120447	+	0.129392i
$865$	−52.1080			−1.77172
$866$	−20.0108			−0.679994
$867$	−5.26562	−	18.7538i	−0.178830	−	0.636912i
$868$	9.12311	+	6.67026i	0.309658	+	0.226404i
$869$			15.1231i			0.513016i
$870$	3.12311	+	11.1231i	0.105883	+	0.377109i
$871$			62.4958i			2.11759i
$872$		−	3.12311i		−	0.105762i
$873$	−2.92456	−	4.79741i	−0.0989813	−	0.162368i
$874$			34.4030i			1.16370i
$875$	5.84912	−	8.00000i	0.197736	−	0.270449i
$876$	−17.3693	+	4.87689i	−0.586855	+	0.164775i
$877$	23.1231			0.780812			0.390406	−	0.920643i	$-0.372335\pi$
$877$	23.1231			0.780812			0.390406	+	0.920643i	$0.372335\pi$
$878$	−23.4612			−0.791777
$879$	9.56155	+	34.0540i	0.322503	+	1.14861i
$880$		−	3.33513i		−	0.112427i
$881$	−36.2759			−1.22217			−0.611083	−	0.791567i	$-0.709266\pi$
$881$	−36.2759			−1.22217			−0.611083	+	0.791567i	$0.709266\pi$
$882$	13.7709	−	15.8544i	0.463690	−	0.533846i
$883$	−4.49242			−0.151182			−0.0755910	−	0.997139i	$-0.524084\pi$
$883$	−4.49242			−0.151182			−0.0755910	+	0.997139i	$0.524084\pi$
$884$			12.4924i			0.420166i
$885$	17.7274	+	63.1369i	0.595899	+	2.12233i
$886$	−26.7386			−0.898302
$887$	−14.1617			−0.475503			−0.237751	−	0.971326i	$-0.576410\pi$
$887$	−14.1617			−0.475503			−0.237751	+	0.971326i	$0.576410\pi$
$888$	13.7511	−	3.86098i	0.461457	−	0.129566i
$889$	−3.50758	+	4.79741i	−0.117640	+	0.160900i
$890$			44.4924i			1.49139i
$891$	−8.00000	−	4.12311i	−0.268010	−	0.138129i
$892$			10.9418i			0.366359i
$893$		−	35.2311i		−	1.17896i
$894$	−5.73384	−	20.4214i	−0.191768	−	0.682993i
$895$			7.49141i			0.250410i
$896$	2.13578	+	1.56155i	0.0713514	+	0.0521678i
$897$	14.6307	+	52.1080i	0.488504	+	1.73983i
$898$	−17.7538			−0.592452
$899$	8.54312			0.284929
$900$	15.6847	−	9.56155i	0.522822	−	0.318718i
$901$			4.79741i			0.159825i
$902$	−6.14441			−0.204587
$903$	12.3496	+	4.61452i	0.410970	+	0.153562i
$904$	11.1231			0.369949
$905$			3.12311i			0.103816i
$906$	−30.4268	+	8.54312i	−1.01086	+	0.283826i
$907$	28.4924			0.946075			0.473038	−	0.881042i	$-0.343157\pi$
$907$	28.4924			0.946075			0.473038	+	0.881042i	$0.343157\pi$
$908$	0.936426			0.0310764
$909$	−3.74571	+	2.28343i	−0.124237	+	0.0757365i
$910$	−27.1231	+	37.0970i	−0.899122	+	1.22975i
$911$		−	14.4924i		−	0.480155i	−0.970754	−	0.240078i	$-0.922827\pi$
$911$		−	14.4924i		−	0.480155i	0.970754	−	0.240078i	$-0.0771729\pi$
$912$	−9.56155	+	2.68466i	−0.316615	+	0.0888979i
$913$			5.73384i			0.189762i
$914$		−	25.6155i		−	0.847286i
$915$	−18.5485	+	5.20798i	−0.613195	+	0.172171i
$916$		−	2.80928i		−	0.0928212i
$917$	16.4451	−	22.4924i	0.543065	−	0.742765i
$918$	−8.49242	+	9.12311i	−0.280292	+	0.301107i
$919$	−1.86174			−0.0614131			−0.0307066	−	0.999528i	$-0.509776\pi$
$919$	−1.86174			−0.0614131			−0.0307066	+	0.999528i	$0.509776\pi$
$920$	−20.0108			−0.659736
$921$	−14.0540	+	3.94602i	−0.463094	+	0.130026i
$922$		−	34.8136i		−	1.14652i
$923$	80.0432			2.63465
$924$	−1.60399	+	4.29269i	−0.0527675	+	0.141219i
$925$	−50.4924			−1.66018
$926$		−	17.3693i		−	0.570791i
$927$	−20.0108	−	32.8255i	−0.657241	−	1.07813i
$928$	2.00000			0.0656532
$929$	−56.2867			−1.84671			−0.923353	−	0.383952i	$-0.874563\pi$
$929$	−56.2867			−1.84671			−0.923353	+	0.383952i	$0.874563\pi$
$930$	−6.67026	−	23.7565i	−0.218727	−	0.779006i
$931$	38.2462	−	12.1735i	1.25347	−	0.398972i
$932$		−	17.1231i		−	0.560886i
$933$	−8.73863	−	31.1231i	−0.286090	−	1.01892i
$934$			0.115279i			0.00377206i
$935$		−	8.00000i		−	0.261628i
$936$	−13.3405	+	8.13254i	−0.436049	+	0.265820i
$937$			20.0108i			0.653724i	0.945072	+	0.326862i	$0.105991\pi$
$937$			20.0108i			0.653724i	−0.945072	+	0.326862i	$0.894009\pi$
$938$	25.6294	+	18.7386i	0.836828	+	0.611838i
$939$	−17.3693	+	4.87689i	−0.566826	+	0.159151i
$940$	20.4924			0.668389
$941$	24.1671			0.787824			0.393912	−	0.919148i	$-0.371121\pi$
$941$	24.1671			0.787824			0.393912	+	0.919148i	$0.371121\pi$
$942$	−0.0539753	−	0.192236i	−0.00175861	−	0.00626339i
$943$			36.8665i			1.20054i
$944$	11.3524			0.369489
$945$	−45.0265	+	8.65318i	−1.46471	+	0.281488i
$946$	−2.87689			−0.0935359
$947$			40.0000i			1.29983i	0.760009	+	0.649913i	$0.225195\pi$
$947$			40.0000i			1.29983i	−0.760009	+	0.649913i	$0.774805\pi$
$948$	7.08084	+	25.2188i	0.229975	+	0.819068i
$949$	−54.2462			−1.76091
$950$	35.1089			1.13908
$951$	−41.2533	+	11.5830i	−1.33773	+	0.375603i
$952$	5.12311	+	3.74571i	0.166041	+	0.121399i
$953$		−	7.36932i		−	0.238716i	−0.992851	−	0.119358i	$-0.961916\pi$
$953$		−	7.36932i		−	0.238716i	0.992851	−	0.119358i	$-0.0380836\pi$
$954$	−5.12311	+	3.12311i	−0.165867	+	0.101114i
$955$			51.2587i			1.65869i
$956$		−	5.36932i		−	0.173656i
$957$	0.936426	+	3.33513i	0.0302704	+	0.107810i
$958$		−	31.2479i		−	1.00957i
$959$	−35.2242	−	25.7538i	−1.13745	−	0.831633i
$960$	−1.56155	−	5.56155i	−0.0503989	−	0.179498i
$961$	12.7538			0.411413
$962$	42.9461			1.38464
$963$	−3.50758	−	5.75379i	−0.113030	−	0.185413i
$964$			3.74571i			0.120641i
$965$	51.2587			1.65008
$966$	25.7562	+	9.62395i	0.828691	+	0.309646i
$967$	−10.2462			−0.329496			−0.164748	−	0.986336i	$-0.552681\pi$
$967$	−10.2462			−0.329496			−0.164748	+	0.986336i	$0.552681\pi$
$968$		−	1.00000i		−	0.0321412i
$969$	−22.9354	+	6.43971i	−0.736790	+	0.206873i
$970$	6.24621			0.200554
$971$	23.6412			0.758683			0.379341	−	0.925257i	$-0.376151\pi$
$971$	23.6412			0.758683			0.379341	+	0.925257i	$0.376151\pi$
$972$	−15.2710	−	3.12985i	−0.489818	−	0.100390i
$973$	−14.0000	−	10.2360i	−0.448819	−	0.328150i
$974$		−	36.4924i		−	1.16929i
$975$	53.1771	−	14.9309i	1.70303	−	0.478171i
$976$			3.33513i			0.106755i
$977$			42.7386i			1.36733i	0.729796	+	0.683665i	$0.239615\pi$
$977$			42.7386i			1.36733i	−0.729796	+	0.683665i	$0.760385\pi$
$978$	26.6811	−	7.49141i	0.853166	−	0.239549i
$979$			13.3405i			0.426365i
$980$	7.08084	+	22.2462i	0.226189	+	0.710629i
$981$	8.00000	−	4.87689i	0.255420	−	0.155707i
$982$	14.7386			0.470329
$983$	−39.2652			−1.25236			−0.626182	−	0.779677i	$-0.715383\pi$
$983$	−39.2652			−1.25236			−0.626182	+	0.779677i	$0.715383\pi$
$984$	−10.2462	+	2.87689i	−0.326637	+	0.0917120i
$985$		−	61.6747i		−	1.96512i
$986$	4.79741			0.152781
$987$	−26.3761	−	9.85559i	−0.839559	−	0.313707i
$988$	−29.8617			−0.950028
$989$			17.2614i			0.548880i
$990$	8.54312	−	5.20798i	0.271518	−	0.165521i
$991$	31.6155			1.00430			0.502150	−	0.864780i	$-0.332542\pi$
$991$	31.6155			1.00430			0.502150	+	0.864780i	$0.332542\pi$
$992$	−4.27156			−0.135622
$993$	9.36426	+	33.3513i	0.297166	+	1.05837i
$994$	24.0000	−	32.8255i	0.761234	−	1.04116i
$995$			14.2462i			0.451635i
$996$	2.68466	+	9.56155i	0.0850667	+	0.302969i
$997$		−	38.5593i		−	1.22119i	−0.791945	−	0.610593i	$-0.790931\pi$
$997$		−	38.5593i		−	1.22119i	0.791945	−	0.610593i	$-0.209069\pi$
$998$		−	24.0000i		−	0.759707i
$999$	31.3632	+	29.1950i	0.992287	+	0.923690i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	462.2.g.e.419.3	yes	8
3.2	odd	2	inner	462.2.g.e.419.6	yes	8
7.6	odd	2	inner	462.2.g.e.419.2	✓	8
21.20	even	2	inner	462.2.g.e.419.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
462.2.g.e.419.2	✓	8	7.6	odd	2	inner
462.2.g.e.419.3	yes	8	1.1	even	1	trivial
462.2.g.e.419.6	yes	8	3.2	odd	2	inner
462.2.g.e.419.7	yes	8	21.20	even	2	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.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(0.468213 + 1.66757i) q^{3} -1.00000 q^{4} +3.33513 q^{5} +(1.66757 - 0.468213i) q^{6} +(1.56155 - 2.13578i) q^{7} +1.00000i q^{8} +(-2.56155 + 1.56155i) q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(0.468213 + 1.66757i) q^{3} -1.00000 q^{4} +3.33513 q^{5} +(1.66757 - 0.468213i) q^{6} +(1.56155 - 2.13578i) q^{7} +1.00000i q^{8} +(-2.56155 + 1.56155i) q^{9} -3.33513i q^{10} -1.00000i q^{11} +(-0.468213 - 1.66757i) q^{12} -5.20798i q^{13} +(-2.13578 - 1.56155i) q^{14} +(1.56155 + 5.56155i) q^{15} +1.00000 q^{16} +2.39871 q^{17} +(1.56155 + 2.56155i) q^{18} +5.73384i q^{19} -3.33513 q^{20} +(4.29269 + 1.60399i) q^{21} -1.00000 q^{22} +6.00000i q^{23} +(-1.66757 + 0.468213i) q^{24} +6.12311 q^{25} -5.20798 q^{26} +(-3.80335 - 3.54042i) q^{27} +(-1.56155 + 2.13578i) q^{28} +2.00000i q^{29} +(5.56155 - 1.56155i) q^{30} -4.27156i q^{31} -1.00000i q^{32} +(1.66757 - 0.468213i) q^{33} -2.39871i q^{34} +(5.20798 - 7.12311i) q^{35} +(2.56155 - 1.56155i) q^{36} -8.24621 q^{37} +5.73384 q^{38} +(8.68466 - 2.43845i) q^{39} +3.33513i q^{40} +6.14441 q^{41} +(1.60399 - 4.29269i) q^{42} +2.87689 q^{43} +1.00000i q^{44} +(-8.54312 + 5.20798i) q^{45} +6.00000 q^{46} -6.14441 q^{47} +(0.468213 + 1.66757i) q^{48} +(-2.12311 - 6.67026i) q^{49} -6.12311i q^{50} +(1.12311 + 4.00000i) q^{51} +5.20798i q^{52} +2.00000i q^{53} +(-3.54042 + 3.80335i) q^{54} -3.33513i q^{55} +(2.13578 + 1.56155i) q^{56} +(-9.56155 + 2.68466i) q^{57} +2.00000 q^{58} +11.3524 q^{59} +(-1.56155 - 5.56155i) q^{60} +3.33513i q^{61} -4.27156 q^{62} +(-0.664868 + 7.90936i) q^{63} -1.00000 q^{64} -17.3693i q^{65} +(-0.468213 - 1.66757i) q^{66} -12.0000 q^{67} -2.39871 q^{68} +(-10.0054 + 2.80928i) q^{69} +(-7.12311 - 5.20798i) q^{70} +15.3693i q^{71} +(-1.56155 - 2.56155i) q^{72} -10.4160i q^{73} +8.24621i q^{74} +(2.86692 + 10.2107i) q^{75} -5.73384i q^{76} +(-2.13578 - 1.56155i) q^{77} +(-2.43845 - 8.68466i) q^{78} -15.1231 q^{79} +3.33513 q^{80} +(4.12311 - 8.00000i) q^{81} -6.14441i q^{82} -5.73384 q^{83} +(-4.29269 - 1.60399i) q^{84} +8.00000 q^{85} -2.87689i q^{86} +(-3.33513 + 0.936426i) q^{87} +1.00000 q^{88} -13.3405 q^{89} +(5.20798 + 8.54312i) q^{90} +(-11.1231 - 8.13254i) q^{91} -6.00000i q^{92} +(7.12311 - 2.00000i) q^{93} +6.14441i q^{94} +19.1231i q^{95} +(1.66757 - 0.468213i) q^{96} +1.87285i q^{97} +(-6.67026 + 2.12311i) q^{98} +(1.56155 + 2.56155i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9	\( 8 q - 8 q^{4} - 4 q^{7} - 4 q^{9} - 4 q^{15} + 8 q^{16} - 4 q^{18} + 12 q^{21} - 8 q^{22} + 16 q^{25} + 4 q^{28} + 28 q^{30} + 4 q^{36} + 20 q^{39} - 8 q^{42} + 56 q^{43} + 48 q^{46} + 16 q^{49} - 24 q^{51} - 60 q^{57} + 16 q^{58} + 4 q^{60} - 32 q^{63} - 8 q^{64} - 96 q^{67} - 24 q^{70} + 4 q^{72} - 36 q^{78} - 88 q^{79} - 12 q^{84} + 64 q^{85} + 8 q^{88} - 56 q^{91} + 24 q^{93} - 4 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 4 * q^7 - 4 * q^9 - 4 * q^15 + 8 * q^16 - 4 * q^18 + 12 * q^21 - 8 * q^22 + 16 * q^25 + 4 * q^28 + 28 * q^30 + 4 * q^36 + 20 * q^39 - 8 * q^42 + 56 * q^43 + 48 * q^46 + 16 * q^49 - 24 * q^51 - 60 * q^57 + 16 * q^58 + 4 * q^60 - 32 * q^63 - 8 * q^64 - 96 * q^67 - 24 * q^70 + 4 * q^72 - 36 * q^78 - 88 * q^79 - 12 * q^84 + 64 * q^85 + 8 * q^88 - 56 * q^91 + 24 * q^93 - 4 * q^99

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