LMFDB - Embedded newform 798.2.bc.b.103.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(31,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.31"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 1, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [28,0,28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			103.7
Character	$\chi$	$=$	798.103
Dual form			798.2.bc.b.31.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(3.52979 - 2.03792i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-1.41205 + 2.23744i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +(-2.03792 + 3.52979i) q^{10} +(-0.485128 - 0.840267i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.85511 + 3.21315i) q^{13} +(0.104149 - 2.64370i) q^{14} +(3.52979 - 2.03792i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.48798i q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.296922 + 4.34877i) q^{19} -4.07585i q^{20} +(-1.41205 + 2.23744i) q^{21} +(0.840267 + 0.485128i) q^{22} +2.51497 q^{23} +1.00000i q^{24} +(5.80626 - 10.0567i) q^{25} +(-3.21315 - 1.85511i) q^{26} +1.00000 q^{27} +(1.23165 + 2.34159i) q^{28} +(2.39269 - 1.38142i) q^{29} +(-2.03792 + 3.52979i) q^{30} +(0.648141 + 1.12261i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.485128 - 0.840267i) q^{33} +(-3.74399 - 6.48478i) q^{34} +(-0.424495 + 10.7753i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-8.55440 - 4.93889i) q^{37} +(-2.43153 - 3.61769i) q^{38} +(1.85511 + 3.21315i) q^{39} +(2.03792 + 3.52979i) q^{40} +(5.12688 - 8.88001i) q^{41} +(0.104149 - 2.64370i) q^{42} +(4.80115 - 8.31583i) q^{43} -0.970257 q^{44} +(3.52979 - 2.03792i) q^{45} +(-2.17802 + 1.25748i) q^{46} -2.66241i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-3.01225 - 6.31873i) q^{49} +11.6125i q^{50} +7.48798i q^{51} +3.71023 q^{52} +(9.32846 + 5.38579i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-3.42480 - 1.97731i) q^{55} +(-2.23744 - 1.41205i) q^{56} +(0.296922 + 4.34877i) q^{57} +(-1.38142 + 2.39269i) q^{58} -9.51740 q^{59} -4.07585i q^{60} -13.7763i q^{61} +(-1.12261 - 0.648141i) q^{62} +(-1.41205 + 2.23744i) q^{63} -1.00000 q^{64} +(13.0963 + 7.56116i) q^{65} +(0.840267 + 0.485128i) q^{66} +(-6.16944 - 3.56193i) q^{67} +(6.48478 + 3.74399i) q^{68} +2.51497 q^{69} +(-5.02004 - 9.54395i) q^{70} +(-0.430764 - 0.248702i) q^{71} +1.00000i q^{72} -2.13903i q^{73} +9.87777 q^{74} +(5.80626 - 10.0567i) q^{75} +(3.91461 + 1.91725i) q^{76} +(2.56507 + 0.101051i) q^{77} +(-3.21315 - 1.85511i) q^{78} +(-9.93203 + 5.73426i) q^{79} +(-3.52979 - 2.03792i) q^{80} +1.00000 q^{81} +10.2538i q^{82} +17.0639i q^{83} +(1.23165 + 2.34159i) q^{84} +(15.2599 + 26.4310i) q^{85} +9.60229i q^{86} +(2.39269 - 1.38142i) q^{87} +(0.840267 - 0.485128i) q^{88} -0.721440 q^{89} +(-2.03792 + 3.52979i) q^{90} +(-9.80874 - 0.386417i) q^{91} +(1.25748 - 2.17802i) q^{92} +(0.648141 + 1.12261i) q^{93} +(1.33120 + 2.30571i) q^{94} +(9.91054 + 14.7451i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-7.84588 + 13.5895i) q^{97} +(5.76805 + 3.96605i) q^{98} +(-0.485128 - 0.840267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} + 14 q^{4} + 6 q^{5} - 8 q^{7} + 28 q^{9} + 2 q^{10} + 14 q^{12} + 2 q^{13} - 8 q^{14} + 6 q^{15} - 14 q^{16} + 12 q^{19} - 8 q^{21} - 12 q^{22} + 24 q^{23} + 14 q^{25} + 24 q^{26} + 28 q^{27}+ \cdots + 28 q^{98}+O(q^{100}) $ 28 * q + 28 * q^3 + 14 * q^4 + 6 * q^5 - 8 * q^7 + 28 * q^9 + 2 * q^10 + 14 * q^12 + 2 * q^13 - 8 * q^14 + 6 * q^15 - 14 * q^16 + 12 * q^19 - 8 * q^21 - 12 * q^22 + 24 * q^23 + 14 * q^25 + 24 * q^26 + 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 4 * q^34 - 10 * q^35 + 14 * q^36 - 24 * q^37 - 6 * q^38 + 2 * q^39 - 2 * q^40 + 4 * q^41 - 8 * q^42 - 14 * q^43 + 6 * q^45 - 12 * q^46 - 14 * q^48 - 24 * q^49 + 4 * q^52 + 24 * q^53 + 18 * q^55 - 4 * q^56 + 12 * q^57 - 2 * q^58 + 44 * q^59 - 12 * q^62 - 8 * q^63 - 28 * q^64 - 24 * q^65 - 12 * q^66 - 18 * q^67 + 6 * q^68 + 24 * q^69 + 6 * q^70 - 6 * q^71 + 12 * q^74 + 14 * q^75 + 40 * q^77 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 28 * q^81 + 2 * q^84 + 28 * q^85 + 18 * q^87 - 12 * q^88 + 16 * q^89 + 2 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 - 18 * q^94 + 26 * q^95 - 40 * q^97 + 28 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{1}{6}\right)$	$1$

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
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	3.52979	−	2.03792i	1.57857	−	0.911387i	0.583509	−	0.812107i	$-0.301679\pi$
$5$	3.52979	−	2.03792i	1.57857	−	0.911387i	0.995060	−	0.0992804i	$-0.0316541\pi$
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	−1.41205	+	2.23744i	−0.533703	+	0.845672i
$7$	−1.41205	+	2.23744i	−0.533703	+	0.845672i
$8$			1.00000i			0.353553i
$9$	1.00000			0.333333
$10$	−2.03792	+	3.52979i	−0.644448	+	1.11622i
$11$	−0.485128	−	0.840267i	−0.146272	−	0.253350i	0.783575	−	0.621297i	$-0.213394\pi$
$11$	−0.485128	−	0.840267i	−0.146272	−	0.253350i	−0.929847	+	0.367947i	$0.880061\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	1.85511	+	3.21315i	0.514516	+	0.891168i	0.999858	+	0.0168439i	$0.00536184\pi$
$13$	1.85511	+	3.21315i	0.514516	+	0.891168i	−0.485342	+	0.874324i	$0.661305\pi$
$14$	0.104149	−	2.64370i	0.0278350	−	0.706559i
$15$	3.52979	−	2.03792i	0.911387	−	0.526190i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$			7.48798i			1.81610i	0.418859	+	0.908051i	$0.362430\pi$
$17$			7.48798i			1.81610i	−0.418859	+	0.908051i	$0.637570\pi$
$18$	−0.866025	+	0.500000i	−0.204124	+	0.117851i
$19$	0.296922	+	4.34877i	0.0681185	+	0.997677i
$19$	0.296922	+	4.34877i	0.0681185	+	0.997677i
$20$		−	4.07585i		−	0.911387i
$21$	−1.41205	+	2.23744i	−0.308134	+	0.488249i
$22$	0.840267	+	0.485128i	0.179146	+	0.103430i
$23$	2.51497			0.524407			0.262203	−	0.965013i	$-0.415551\pi$
$23$	2.51497			0.524407			0.262203	+	0.965013i	$0.415551\pi$
$24$			1.00000i			0.204124i
$25$	5.80626	−	10.0567i	1.16125	−	2.01135i
$26$	−3.21315	−	1.85511i	−0.630151	−	0.363818i
$27$	1.00000			0.192450
$28$	1.23165	+	2.34159i	0.232761	+	0.442518i
$29$	2.39269	−	1.38142i	0.444312	−	0.256524i	−0.261113	−	0.965308i	$-0.584089\pi$
$29$	2.39269	−	1.38142i	0.444312	−	0.256524i	0.705425	+	0.708785i	$0.250756\pi$
$30$	−2.03792	+	3.52979i	−0.372072	+	0.644448i
$31$	0.648141	+	1.12261i	0.116410	+	0.201627i	0.918342	−	0.395787i	$-0.129528\pi$
$31$	0.648141	+	1.12261i	0.116410	+	0.201627i	−0.801933	+	0.597414i	$0.796195\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−0.485128	−	0.840267i	−0.0844500	−	0.146272i
$34$	−3.74399	−	6.48478i	−0.642089	−	1.11213i
$35$	−0.424495	+	10.7753i	−0.0717528	+	1.82136i
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−8.55440	−	4.93889i	−1.40633	−	0.811948i	−0.411302	−	0.911499i	$-0.634926\pi$
$37$	−8.55440	−	4.93889i	−1.40633	−	0.811948i	−0.995032	+	0.0995513i	$0.968259\pi$
$38$	−2.43153	−	3.61769i	−0.394446	−	0.586867i
$39$	1.85511	+	3.21315i	0.297056	+	0.514516i
$40$	2.03792	+	3.52979i	0.322224	+	0.558108i
$41$	5.12688	−	8.88001i	0.800683	−	1.38682i	−0.118484	−	0.992956i	$-0.537803\pi$
$41$	5.12688	−	8.88001i	0.800683	−	1.38682i	0.919167	−	0.393868i	$-0.128863\pi$
$42$	0.104149	−	2.64370i	0.0160705	−	0.407932i
$43$	4.80115	−	8.31583i	0.732168	−	1.26815i	−0.223787	−	0.974638i	$-0.571842\pi$
$43$	4.80115	−	8.31583i	0.732168	−	1.26815i	0.955955	−	0.293514i	$-0.0948247\pi$
$44$	−0.970257			−0.146272
$45$	3.52979	−	2.03792i	0.526190	−	0.303796i
$46$	−2.17802	+	1.25748i	−0.321132	+	0.185406i
$47$		−	2.66241i		−	0.388352i	−0.980967	−	0.194176i	$-0.937797\pi$
$47$		−	2.66241i		−	0.388352i	0.980967	−	0.194176i	$-0.0622033\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−3.01225	−	6.31873i	−0.430322	−	0.902676i
$50$			11.6125i			1.64226i
$51$			7.48798i			1.04853i
$52$	3.71023			0.514516
$53$	9.32846	+	5.38579i	1.28136	+	0.739795i	0.977098	−	0.212792i	$-0.0682556\pi$
$53$	9.32846	+	5.38579i	1.28136	+	0.739795i	0.304266	+	0.952587i	$0.401589\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$	−3.42480	−	1.97731i	−0.461800	−	0.266620i
$56$	−2.23744	−	1.41205i	−0.298990	−	0.188693i
$57$	0.296922	+	4.34877i	0.0393282	+	0.576009i
$58$	−1.38142	+	2.39269i	−0.181390	+	0.314176i
$59$	−9.51740			−1.23906			−0.619530	−	0.784973i	$-0.712677\pi$
$59$	−9.51740			−1.23906			−0.619530	+	0.784973i	$0.712677\pi$
$60$		−	4.07585i		−	0.526190i
$61$		−	13.7763i		−	1.76387i	−0.471368	−	0.881937i	$-0.656240\pi$
$61$		−	13.7763i		−	1.76387i	0.471368	−	0.881937i	$-0.343760\pi$
$62$	−1.12261	−	0.648141i	−0.142572	−	0.0823140i
$63$	−1.41205	+	2.23744i	−0.177901	+	0.281891i
$64$	−1.00000			−0.125000
$65$	13.0963	+	7.56116i	1.62440	+	0.937847i
$66$	0.840267	+	0.485128i	0.103430	+	0.0597152i
$67$	−6.16944	−	3.56193i	−0.753717	−	0.435159i	0.0733182	−	0.997309i	$-0.476641\pi$
$67$	−6.16944	−	3.56193i	−0.753717	−	0.435159i	−0.827035	+	0.562150i	$0.809974\pi$
$68$	6.48478	+	3.74399i	0.786396	+	0.454026i
$69$	2.51497			0.302766
$70$	−5.02004	−	9.54395i	−0.600009	−	1.14072i
$71$	−0.430764	−	0.248702i	−0.0511223	−	0.0295155i	0.474221	−	0.880406i	$-0.342730\pi$
$71$	−0.430764	−	0.248702i	−0.0511223	−	0.0295155i	−0.525343	+	0.850890i	$0.676063\pi$
$72$			1.00000i			0.117851i
$73$		−	2.13903i		−	0.250354i	−0.992134	−	0.125177i	$-0.960050\pi$
$73$		−	2.13903i		−	0.250354i	0.992134	−	0.125177i	$-0.0399499\pi$
$74$	9.87777			1.14827
$75$	5.80626	−	10.0567i	0.670449	−	1.16125i
$76$	3.91461	+	1.91725i	0.449037	+	0.219923i
$77$	2.56507	+	0.101051i	0.292317	+	0.0115159i
$78$	−3.21315	−	1.85511i	−0.363818	−	0.210050i
$79$	−9.93203	+	5.73426i	−1.11744	+	0.645155i	−0.940746	−	0.339111i	$-0.889874\pi$
$79$	−9.93203	+	5.73426i	−1.11744	+	0.645155i	−0.176694	+	0.984266i	$0.556540\pi$
$80$	−3.52979	−	2.03792i	−0.394642	−	0.227847i
$81$	1.00000			0.111111
$82$			10.2538i			1.13234i
$83$			17.0639i			1.87301i	0.350655	+	0.936505i	$0.385959\pi$
$83$			17.0639i			1.87301i	−0.350655	+	0.936505i	$0.614041\pi$
$84$	1.23165	+	2.34159i	0.134385	+	0.255488i
$85$	15.2599	+	26.4310i	1.65517	+	2.86684i
$86$			9.60229i			1.03544i
$87$	2.39269	−	1.38142i	0.256524	−	0.148104i
$88$	0.840267	−	0.485128i	0.0895728	−	0.0517149i
$89$	−0.721440			−0.0764725			−0.0382363	−	0.999269i	$-0.512174\pi$
$89$	−0.721440			−0.0764725			−0.0382363	+	0.999269i	$0.512174\pi$
$90$	−2.03792	+	3.52979i	−0.214816	+	0.372072i
$91$	−9.80874	−	0.386417i	−1.02824	−	0.0405075i
$92$	1.25748	−	2.17802i	0.131102	−	0.227075i
$93$	0.648141	+	1.12261i	0.0672091	+	0.116410i
$94$	1.33120	+	2.30571i	0.137303	+	0.237816i
$95$	9.91054	+	14.7451i	1.01680	+	1.51282i
$96$	0.866025	+	0.500000i	0.0883883	+	0.0510310i
$97$	−7.84588	+	13.5895i	−0.796629	+	1.37980i	0.125171	+	0.992135i	$0.460052\pi$
$97$	−7.84588	+	13.5895i	−0.796629	+	1.37980i	−0.921800	+	0.387666i	$0.873281\pi$
$98$	5.76805	+	3.96605i	0.582661	+	0.400632i
$99$	−0.485128	−	0.840267i	−0.0487572	−	0.0844500i
$100$	−5.80626	−	10.0567i	−0.580626	−	1.00567i
$101$	3.22004	+	1.85909i	0.320406	+	0.184987i	0.651574	−	0.758585i	$-0.274109\pi$
$101$	3.22004	+	1.85909i	0.320406	+	0.184987i	−0.331167	+	0.943572i	$0.607442\pi$
$102$	−3.74399	−	6.48478i	−0.370710	−	0.642089i
$103$	1.12602	−	1.95033i	0.110950	−	0.192172i	−0.805203	−	0.592999i	$-0.797944\pi$
$103$	1.12602	−	1.95033i	0.110950	−	0.192172i	0.916154	+	0.400827i	$0.131277\pi$
$104$	−3.21315	+	1.85511i	−0.315076	+	0.181909i
$105$	−0.424495	+	10.7753i	−0.0414265	+	1.05156i
$106$	−10.7716			−1.04623
$107$	−5.70984	−	3.29658i	−0.551991	−	0.318692i	0.197934	−	0.980215i	$-0.436577\pi$
$107$	−5.70984	−	3.29658i	−0.551991	−	0.318692i	−0.749925	+	0.661523i	$0.769910\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$		−	7.79600i		−	0.746721i	−0.927686	−	0.373361i	$-0.878205\pi$
$109$		−	7.79600i		−	0.746721i	0.927686	−	0.373361i	$-0.121795\pi$
$110$	3.95462			0.377058
$111$	−8.55440	−	4.93889i	−0.811948	−	0.468778i
$112$	2.64370	+	0.104149i	0.249806	+	0.00984116i
$113$			10.2155i			0.960994i	0.876996	+	0.480497i	$0.159544\pi$
$113$			10.2155i			0.960994i	−0.876996	+	0.480497i	$0.840456\pi$
$114$	−2.43153	−	3.61769i	−0.227734	−	0.338828i
$115$	8.87729	−	5.12531i	0.827812	−	0.477937i
$116$		−	2.76284i		−	0.256524i
$117$	1.85511	+	3.21315i	0.171505	+	0.297056i
$118$	8.24231	−	4.75870i	0.758766	−	0.438074i
$119$	−16.7539	−	10.5734i	−1.53583	−	0.969260i
$120$	2.03792	+	3.52979i	0.186036	+	0.322224i
$121$	5.02930	−	8.71100i	0.457209	−	0.791910i
$122$	6.88815	+	11.9306i	0.623623	+	1.08015i
$123$	5.12688	−	8.88001i	0.462275	−	0.800683i
$124$	1.29628			0.116410
$125$		−	26.9516i		−	2.41063i
$126$	0.104149	−	2.64370i	0.00927833	−	0.235520i
$127$	−4.63310	+	2.67492i	−0.411122	+	0.237361i	−0.691272	−	0.722595i	$-0.742949\pi$
$127$	−4.63310	+	2.67492i	−0.411122	+	0.237361i	0.280150	+	0.959956i	$0.409616\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.80115	−	8.31583i	0.422717	−	0.732168i
$130$	−15.1223			−1.32632
$131$	1.47219	−	0.849970i	0.128626	−	0.0742622i	−0.434306	−	0.900765i	$-0.643006\pi$
$131$	1.47219	−	0.849970i	0.128626	−	0.0742622i	0.562932	+	0.826503i	$0.309673\pi$
$132$	−0.970257			−0.0844500
$133$	−10.1494	−	5.47633i	−0.880063	−	0.474858i
$134$	7.12386			0.615408
$135$	3.52979	−	2.03792i	0.303796	−	0.175397i
$136$	−7.48798			−0.642089
$137$	1.10858	−	1.92011i	0.0947120	−	0.164046i	−0.814776	−	0.579775i	$-0.803140\pi$
$137$	1.10858	−	1.92011i	0.0947120	−	0.164046i	0.909488	+	0.415729i	$0.136474\pi$
$138$	−2.17802	+	1.25748i	−0.185406	+	0.107044i
$139$	−13.6907	+	7.90435i	−1.16123	+	0.670438i	−0.951599	−	0.307341i	$-0.900561\pi$
$139$	−13.6907	+	7.90435i	−1.16123	+	0.670438i	−0.209634	+	0.977780i	$0.567227\pi$
$140$	9.11945	+	5.75528i	0.770734	+	0.486410i
$141$		−	2.66241i		−	0.224215i
$142$	0.497403			0.0417412
$143$	1.79994	−	3.11758i	0.150518	−	0.260705i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	5.63047	−	9.75225i	0.467585	−	0.809880i
$146$	1.06951	+	1.85245i	0.0885135	+	0.153310i
$147$	−3.01225	−	6.31873i	−0.248446	−	0.521160i
$148$	−8.55440	+	4.93889i	−0.703167	+	0.405974i
$149$	−6.51615	−	11.2863i	−0.533824	−	0.924610i	−0.999219	−	0.0395074i	$-0.987421\pi$
$149$	−6.51615	−	11.2863i	−0.533824	−	0.924610i	0.465395	−	0.885103i	$-0.345912\pi$
$150$			11.6125i			0.948159i
$151$	−12.1248	+	7.00028i	−0.986706	+	0.569675i	−0.904288	−	0.426923i	$-0.859598\pi$
$151$	−12.1248	+	7.00028i	−0.986706	+	0.569675i	−0.0824181	+	0.996598i	$0.526264\pi$
$152$	−4.34877	+	0.296922i	−0.352732	+	0.0240835i
$153$			7.48798i			0.605368i
$154$	−2.27194	+	1.19502i	−0.183078	+	0.0962976i
$155$	4.57560	+	2.64172i	0.367521	+	0.212188i
$156$	3.71023			0.297056
$157$		−	7.95372i		−	0.634776i	−0.948296	−	0.317388i	$-0.897194\pi$
$157$		−	7.95372i		−	0.634776i	0.948296	−	0.317388i	$-0.102806\pi$
$158$	5.73426	−	9.93203i	0.456193	−	0.790150i
$159$	9.32846	+	5.38579i	0.739795	+	0.427121i
$160$	4.07585			0.322224
$161$	−3.55125	+	5.62708i	−0.279877	+	0.443476i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	10.8199	−	18.7407i	0.847484	−	1.46789i	−0.0359628	−	0.999353i	$-0.511450\pi$
$163$	10.8199	−	18.7407i	0.847484	−	1.46789i	0.883447	−	0.468532i	$-0.155217\pi$
$164$	−5.12688	−	8.88001i	−0.400342	−	0.693412i
$165$	−3.42480	−	1.97731i	−0.266620	−	0.153933i
$166$	−8.53197	−	14.7778i	−0.662209	−	1.14698i
$167$	0.0757722	+	0.131241i	0.00586343	+	0.0101558i	0.868942	−	0.494914i	$-0.164800\pi$
$167$	0.0757722	+	0.131241i	0.00586343	+	0.0101558i	−0.863079	+	0.505069i	$0.831467\pi$
$168$	−2.23744	−	1.41205i	−0.172622	−	0.108942i
$169$	−0.382903	+	0.663208i	−0.0294541	+	0.0510160i
$170$	−26.4310	−	15.2599i	−2.02716	−	1.17038i
$171$	0.296922	+	4.34877i	0.0227062	+	0.332559i
$172$	−4.80115	−	8.31583i	−0.366084	−	0.634076i
$173$	−4.57227	−	7.91941i	−0.347624	−	0.602102i	0.638203	−	0.769868i	$-0.279678\pi$
$173$	−4.57227	−	7.91941i	−0.347624	−	0.602102i	−0.985827	+	0.167766i	$0.946345\pi$
$174$	−1.38142	+	2.39269i	−0.104725	+	0.181390i
$175$	14.3026	+	27.1917i	1.08118	+	2.05550i
$176$	−0.485128	+	0.840267i	−0.0365679	+	0.0633375i
$177$	−9.51740			−0.715372
$178$	0.624786	−	0.360720i	0.0468297	−	0.0270371i
$179$	5.49625	−	3.17326i	0.410809	−	0.237181i	−0.280328	−	0.959904i	$-0.590443\pi$
$179$	5.49625	−	3.17326i	0.410809	−	0.237181i	0.691137	+	0.722723i	$0.257110\pi$
$180$		−	4.07585i		−	0.303796i
$181$	7.25677	+	12.5691i	0.539392	+	0.934254i	0.998937	+	0.0460992i	$0.0146790\pi$
$181$	7.25677	+	12.5691i	0.539392	+	0.934254i	−0.459545	+	0.888154i	$0.651988\pi$
$182$	8.68782	−	4.56972i	0.643984	−	0.338730i
$183$		−	13.7763i		−	1.01837i
$184$			2.51497i			0.185406i
$185$	−40.2603			−2.95999
$186$	−1.12261	−	0.648141i	−0.0823140	−	0.0475240i
$187$	6.29191	−	3.63263i	0.460110	−	0.265644i
$188$	−2.30571	−	1.33120i	−0.168161	−	0.0970880i
$189$	−1.41205	+	2.23744i	−0.102711	+	0.162750i
$190$	−15.9553	−	7.81440i	−1.15752	−	0.566916i
$191$	−3.41302	+	5.91152i	−0.246957	+	0.427743i	−0.962680	−	0.270642i	$-0.912764\pi$
$191$	−3.41302	+	5.91152i	−0.246957	+	0.427743i	0.715723	+	0.698384i	$0.246097\pi$
$192$	−1.00000			−0.0721688
$193$			13.2487i			0.953660i	0.878996	+	0.476830i	$0.158214\pi$
$193$			13.2487i			0.953660i	−0.878996	+	0.476830i	$0.841786\pi$
$194$		−	15.6918i		−	1.12660i
$195$	13.0963	+	7.56116i	0.937847	+	0.541466i
$196$	−6.97831	−	0.550678i	−0.498450	−	0.0393341i
$197$	−6.85013			−0.488052			−0.244026	−	0.969769i	$-0.578468\pi$
$197$	−6.85013			−0.488052			−0.244026	+	0.969769i	$0.578468\pi$
$198$	0.840267	+	0.485128i	0.0597152	+	0.0344766i
$199$	7.33932	+	4.23736i	0.520271	+	0.300378i	0.737045	−	0.675843i	$-0.236220\pi$
$199$	7.33932	+	4.23736i	0.520271	+	0.300378i	−0.216775	+	0.976222i	$0.569554\pi$
$200$	10.0567	+	5.80626i	0.711119	+	0.410565i
$201$	−6.16944	−	3.56193i	−0.435159	−	0.251239i
$202$	−3.71819			−0.261611
$203$	−0.287748	+	7.30413i	−0.0201959	+	0.512650i
$204$	6.48478	+	3.74399i	0.454026	+	0.262132i
$205$		−	41.7927i		−	2.91893i
$206$			2.25205i			0.156908i
$207$	2.51497			0.174802
$208$	1.85511	−	3.21315i	0.128629	−	0.222792i
$209$	3.51009	−	2.35921i	0.242798	−	0.163190i
$210$	−5.02004	−	9.54395i	−0.346415	−	0.658595i
$211$	−1.35940	−	0.784849i	−0.0935848	−	0.0540312i	0.452477	−	0.891776i	$-0.350540\pi$
$211$	−1.35940	−	0.784849i	−0.0935848	−	0.0540312i	−0.546062	+	0.837745i	$0.683874\pi$
$212$	9.32846	−	5.38579i	0.640682	−	0.369898i
$213$	−0.430764	−	0.248702i	−0.0295155	−	0.0170408i
$214$	6.59315			0.450699
$215$		−	39.1375i		−	2.66915i
$216$			1.00000i			0.0680414i
$217$	−3.42698	−	0.135006i	−0.232639	−	0.00916484i
$218$	3.89800	+	6.75153i	0.264006	+	0.457271i
$219$		−	2.13903i		−	0.144542i
$220$	−3.42480	+	1.97731i	−0.230900	+	0.133310i
$221$	−24.0600	+	13.8911i	−1.61845	+	0.934415i
$222$	9.87777			0.662953
$223$	−9.83556	+	17.0357i	−0.658638	+	1.14079i	0.322331	+	0.946627i	$0.395534\pi$
$223$	−9.83556	+	17.0357i	−0.658638	+	1.14079i	−0.980968	+	0.194167i	$0.937800\pi$
$224$	−2.34159	+	1.23165i	−0.156454	+	0.0822934i
$225$	5.80626	−	10.0567i	0.387084	−	0.670449i
$226$	−5.10775	−	8.84689i	−0.339763	−	0.588486i
$227$	−4.47042	−	7.74299i	−0.296712	−	0.513921i	0.678670	−	0.734444i	$-0.262557\pi$
$227$	−4.47042	−	7.74299i	−0.296712	−	0.513921i	−0.975382	+	0.220523i	$0.929224\pi$
$228$	3.91461	+	1.91725i	0.259251	+	0.126973i
$229$	7.36441	+	4.25184i	0.486654	+	0.280970i	0.723185	−	0.690654i	$-0.242677\pi$
$229$	7.36441	+	4.25184i	0.486654	+	0.280970i	−0.236531	+	0.971624i	$0.576011\pi$
$230$	−5.12531	+	8.87729i	−0.337953	+	0.585351i
$231$	2.56507	+	0.101051i	0.168769	+	0.00664869i
$232$	1.38142	+	2.39269i	0.0906948	+	0.157088i
$233$	0.235089	+	0.407186i	0.0154012	+	0.0266756i	0.873623	−	0.486603i	$-0.161764\pi$
$233$	0.235089	+	0.407186i	0.0154012	+	0.0266756i	−0.858222	+	0.513279i	$0.828431\pi$
$234$	−3.21315	−	1.85511i	−0.210050	−	0.121273i
$235$	−5.42578	−	9.39773i	−0.353939	−	0.613040i
$236$	−4.75870	+	8.24231i	−0.309765	+	0.536529i
$237$	−9.93203	+	5.73426i	−0.645155	+	0.372480i
$238$	19.7960	+	0.779866i	1.28318	+	0.0505512i
$239$	−12.3419			−0.798329			−0.399164	−	0.916879i	$-0.630700\pi$
$239$	−12.3419			−0.798329			−0.399164	+	0.916879i	$0.630700\pi$
$240$	−3.52979	−	2.03792i	−0.227847	−	0.131547i
$241$	−8.42418	+	14.5911i	−0.542649	+	0.939896i	0.456101	+	0.889928i	$0.349245\pi$
$241$	−8.42418	+	14.5911i	−0.542649	+	0.939896i	−0.998751	+	0.0499684i	$0.984088\pi$
$242$			10.0586i			0.646591i
$243$	1.00000			0.0641500
$244$	−11.9306	−	6.88815i	−0.763780	−	0.440968i
$245$	−23.5097	−	16.1650i	−1.50198	−	1.03275i
$246$			10.2538i			0.653755i
$247$	−13.4225	+	9.02153i	−0.854050	+	0.574026i
$248$	−1.12261	+	0.648141i	−0.0712860	+	0.0411570i
$249$			17.0639i			1.08138i
$250$	13.4758	+	23.3408i	0.852286	+	1.47620i
$251$	1.39946	−	0.807976i	0.0883329	−	0.0509990i	−0.455183	−	0.890398i	$-0.650426\pi$
$251$	1.39946	−	0.807976i	0.0883329	−	0.0509990i	0.543516	+	0.839399i	$0.317093\pi$
$252$	1.23165	+	2.34159i	0.0775869	+	0.147506i
$253$	−1.22008	−	2.11324i	−0.0767058	−	0.132858i
$254$	2.67492	−	4.63310i	0.167840	−	0.290707i
$255$	15.2599	+	26.4310i	0.955614	+	1.65517i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−18.0462			−1.12569			−0.562846	−	0.826562i	$-0.690294\pi$
$257$	−18.0462			−1.12569			−0.562846	+	0.826562i	$0.690294\pi$
$258$			9.60229i			0.597813i
$259$	23.1297	−	12.1660i	1.43721	−	0.755959i
$260$	13.0963	−	7.56116i	0.812199	−	0.468923i
$261$	2.39269	−	1.38142i	0.148104	−	0.0855079i
$262$	−0.849970	+	1.47219i	−0.0525113	+	0.0909523i
$263$	21.6076			1.33238			0.666191	−	0.745781i	$-0.267924\pi$
$263$	21.6076			1.33238			0.666191	+	0.745781i	$0.267924\pi$
$264$	0.840267	−	0.485128i	0.0517149	−	0.0298576i
$265$	43.9033			2.69696
$266$	11.5278	−	0.332051i	0.706814	−	0.0203594i
$267$	−0.721440			−0.0441514
$268$	−6.16944	+	3.56193i	−0.376859	+	0.217579i
$269$	10.7019			0.652509			0.326254	−	0.945282i	$-0.394213\pi$
$269$	10.7019			0.652509			0.326254	+	0.945282i	$0.394213\pi$
$270$	−2.03792	+	3.52979i	−0.124024	+	0.214816i
$271$	−5.62728	+	3.24891i	−0.341833	+	0.197357i	−0.661082	−	0.750314i	$-0.729903\pi$
$271$	−5.62728	+	3.24891i	−0.341833	+	0.197357i	0.319249	+	0.947671i	$0.396569\pi$
$272$	6.48478	−	3.74399i	0.393198	−	0.227013i
$273$	−9.80874	−	0.386417i	−0.593652	−	0.0233870i
$274$			2.21715i			0.133943i
$275$	−11.2671			−0.679434
$276$	1.25748	−	2.17802i	0.0756916	−	0.131102i
$277$	−5.34502	−	9.25785i	−0.321151	−	0.556250i	0.659575	−	0.751639i	$-0.270736\pi$
$277$	−5.34502	−	9.25785i	−0.321151	−	0.556250i	−0.980726	+	0.195389i	$0.937403\pi$
$278$	7.90435	−	13.6907i	0.474072	−	0.821116i
$279$	0.648141	+	1.12261i	0.0388032	+	0.0672091i
$280$	−10.7753	−	0.424495i	−0.643948	−	0.0253684i
$281$	−4.64102	+	2.67950i	−0.276860	+	0.159845i	−0.632001	−	0.774967i	$-0.717766\pi$
$281$	−4.64102	+	2.67950i	−0.276860	+	0.159845i	0.355141	+	0.934813i	$0.384433\pi$
$282$	1.33120	+	2.30571i	0.0792720	+	0.137303i
$283$		−	13.5724i		−	0.806793i	−0.915025	−	0.403397i	$-0.867830\pi$
$283$		−	13.5724i		−	0.806793i	0.915025	−	0.403397i	$-0.132170\pi$
$284$	−0.430764	+	0.248702i	−0.0255611	+	0.0147577i
$285$	9.91054	+	14.7451i	0.587050	+	0.873427i
$286$			3.59988i			0.212865i
$287$	12.6291	+	24.0100i	0.745471	+	1.41727i
$288$	0.866025	+	0.500000i	0.0510310	+	0.0294628i
$289$	−39.0699			−2.29823
$290$			11.2609i			0.661265i
$291$	−7.84588	+	13.5895i	−0.459934	+	0.796629i
$292$	−1.85245	−	1.06951i	−0.108406	−	0.0625885i
$293$	17.3263			1.01221			0.506106	−	0.862471i	$-0.331084\pi$
$293$	17.3263			1.01221			0.506106	+	0.862471i	$0.331084\pi$
$294$	5.76805	+	3.96605i	0.336400	+	0.231305i
$295$	−33.5944	+	19.3957i	−1.95594	+	1.12926i
$296$	4.93889	−	8.55440i	0.287067	−	0.497214i
$297$	−0.485128	−	0.840267i	−0.0281500	−	0.0487572i
$298$	11.2863	+	6.51615i	0.653798	+	0.377471i
$299$	4.66555	+	8.08097i	0.269816	+	0.467335i
$300$	−5.80626	−	10.0567i	−0.335225	−	0.580626i
$301$	11.8267	+	22.4846i	0.681680	+	1.29599i
$302$	7.00028	−	12.1248i	0.402821	−	0.697707i
$303$	3.22004	+	1.85909i	0.184987	+	0.106802i
$304$	3.61769	−	2.43153i	0.207489	−	0.139458i
$305$	−28.0750	−	48.6274i	−1.60757	−	2.78440i
$306$	−3.74399	−	6.48478i	−0.214030	−	0.370710i
$307$	10.4330	−	18.0706i	0.595446	−	1.03134i	−0.398038	−	0.917369i	$-0.630309\pi$
$307$	10.4330	−	18.0706i	0.595446	−	1.03134i	0.993484	−	0.113973i	$-0.0363578\pi$
$308$	1.37005	−	2.17089i	0.0780657	−	0.123698i
$309$	1.12602	−	1.95033i	0.0640572	−	0.110950i
$310$	−5.28345			−0.300080
$311$	18.1423	−	10.4745i	1.02875	−	0.593952i	0.112127	−	0.993694i	$-0.464234\pi$
$311$	18.1423	−	10.4745i	1.02875	−	0.593952i	0.916628	+	0.399742i	$0.130900\pi$
$312$	−3.21315	+	1.85511i	−0.181909	+	0.105025i
$313$		−	6.93607i		−	0.392050i	−0.980599	−	0.196025i	$-0.937197\pi$
$313$		−	6.93607i		−	0.392050i	0.980599	−	0.196025i	$-0.0628034\pi$
$314$	3.97686	+	6.88812i	0.224427	+	0.388719i
$315$	−0.424495	+	10.7753i	−0.0239176	+	0.607120i
$316$			11.4685i			0.645155i
$317$		−	9.39350i		−	0.527592i	−0.964579	−	0.263796i	$-0.915025\pi$
$317$		−	9.39350i		−	0.527592i	0.964579	−	0.263796i	$-0.0849745\pi$
$318$	−10.7716			−0.604040
$319$	−2.32153	−	1.34033i	−0.129981	−	0.0750443i
$320$	−3.52979	+	2.03792i	−0.197321	+	0.113923i
$321$	−5.70984	−	3.29658i	−0.318692	−	0.183997i
$322$	0.261931	−	6.64882i	0.0145969	−	0.370524i
$323$	−32.5636	+	2.22334i	−1.81188	+	0.123710i
$324$	0.500000	−	0.866025i	0.0277778	−	0.0481125i
$325$	43.0851			2.38993
$326$			21.6399i			1.19852i
$327$		−	7.79600i		−	0.431120i
$328$	8.88001	+	5.12688i	0.490316	+	0.283084i
$329$	5.95697	+	3.75944i	0.328418	+	0.207265i
$330$	3.95462			0.217695
$331$	−16.7710	−	9.68272i	−0.921816	−	0.532211i	−0.0376019	−	0.999293i	$-0.511972\pi$
$331$	−16.7710	−	9.68272i	−0.921816	−	0.532211i	−0.884214	+	0.467082i	$0.845305\pi$
$332$	14.7778	+	8.53197i	0.811037	+	0.468252i
$333$	−8.55440	−	4.93889i	−0.468778	−	0.270649i
$334$	−0.131241	−	0.0757722i	−0.00718120	−	0.00414607i
$335$	−29.0357			−1.58639
$336$	2.64370	+	0.104149i	0.144226	+	0.00568179i
$337$	19.3232	+	11.1562i	1.05260	+	0.607719i	0.923376	−	0.383897i	$-0.125418\pi$
$337$	19.3232	+	11.1562i	1.05260	+	0.607719i	0.129224	+	0.991615i	$0.458751\pi$
$338$		−	0.765806i		−	0.0416544i
$339$			10.2155i			0.554830i
$340$	30.5199			1.65517
$341$	0.628863	−	1.08922i	0.0340549	−	0.0589847i
$342$	−2.43153	−	3.61769i	−0.131482	−	0.195622i
$343$	18.3912	+	2.18261i	0.993031	+	0.117850i
$344$	8.31583	+	4.80115i	0.448359	+	0.258860i
$345$	8.87729	−	5.12531i	0.477937	−	0.275937i
$346$	7.91941	+	4.57227i	0.425750	+	0.245807i
$347$	2.46989			0.132591			0.0662953	−	0.997800i	$-0.478882\pi$
$347$	2.46989			0.132591			0.0662953	+	0.997800i	$0.478882\pi$
$348$		−	2.76284i		−	0.148104i
$349$			4.96655i			0.265853i	0.991126	+	0.132927i	$0.0424375\pi$
$349$			4.96655i			0.265853i	−0.991126	+	0.132927i	$0.957563\pi$
$350$	−25.9823	−	16.3974i	−1.38881	−	0.876479i
$351$	1.85511	+	3.21315i	0.0990187	+	0.171505i
$352$		−	0.970257i		−	0.0517149i
$353$	29.6058	−	17.0929i	1.57576	−	0.909764i	0.580316	−	0.814391i	$-0.302929\pi$
$353$	29.6058	−	17.0929i	1.57576	−	0.909764i	0.995442	−	0.0953725i	$-0.0304042\pi$
$354$	8.24231	−	4.75870i	0.438074	−	0.252922i
$355$	−2.02734			−0.107600
$356$	−0.360720	+	0.624786i	−0.0191181	+	0.0331136i
$357$	−16.7539	−	10.5734i	−0.886710	−	0.559602i
$358$	−3.17326	+	5.49625i	−0.167712	+	0.290486i
$359$	12.0107	+	20.8032i	0.633902	+	1.09795i	0.986747	+	0.162268i	$0.0518810\pi$
$359$	12.0107	+	20.8032i	0.633902	+	1.09795i	−0.352845	+	0.935682i	$0.614786\pi$
$360$	2.03792	+	3.52979i	0.107408	+	0.186036i
$361$	−18.8237	+	2.58249i	−0.990720	+	0.135921i
$362$	−12.5691	−	7.25677i	−0.660617	−	0.381407i
$363$	5.02930	−	8.71100i	0.263970	−	0.457209i
$364$	−5.23902	+	8.30141i	−0.274599	+	0.435112i
$365$	−4.35917	−	7.55030i	−0.228169	−	0.395201i
$366$	6.88815	+	11.9306i	0.360049	+	0.623623i
$367$	−18.4748	−	10.6664i	−0.964376	−	0.556783i	−0.0668590	−	0.997762i	$-0.521298\pi$
$367$	−18.4748	−	10.6664i	−0.964376	−	0.556783i	−0.897517	+	0.440980i	$0.854631\pi$
$368$	−1.25748	−	2.17802i	−0.0655508	−	0.113537i
$369$	5.12688	−	8.88001i	0.266894	−	0.462275i
$370$	34.8664	−	20.1301i	1.81262	−	1.04652i
$371$	−25.2226	+	13.2669i	−1.30949	+	0.688782i
$372$	1.29628			0.0672091
$373$	8.29433	+	4.78873i	0.429464	+	0.247951i	0.699118	−	0.715006i	$-0.253576\pi$
$373$	8.29433	+	4.78873i	0.429464	+	0.247951i	−0.269654	+	0.962957i	$0.586909\pi$
$374$	−3.63263	+	6.29191i	−0.187839	+	0.325347i
$375$		−	26.9516i		−	1.39178i
$376$	2.66241			0.137303
$377$	8.87744	+	5.12539i	0.457212	+	0.263971i
$378$	0.104149	−	2.64370i	0.00535685	−	0.135977i
$379$		−	24.4666i		−	1.25676i	−0.777905	−	0.628382i	$-0.783718\pi$
$379$		−	24.4666i		−	1.25676i	0.777905	−	0.628382i	$-0.216282\pi$
$380$	17.7249	−	1.21021i	0.909270	−	0.0620823i
$381$	−4.63310	+	2.67492i	−0.237361	+	0.137041i
$382$		−	6.82603i		−	0.349250i
$383$	3.56288	+	6.17110i	0.182055	+	0.315328i	0.942580	−	0.333980i	$-0.108392\pi$
$383$	3.56288	+	6.17110i	0.182055	+	0.315328i	−0.760525	+	0.649308i	$0.775058\pi$
$384$	0.866025	−	0.500000i	0.0441942	−	0.0255155i
$385$	9.26008	−	4.87072i	0.471937	−	0.248235i
$386$	−6.62433	−	11.4737i	−0.337170	−	0.583995i
$387$	4.80115	−	8.31583i	0.244056	−	0.422717i
$388$	7.84588	+	13.5895i	0.398314	+	0.689901i
$389$	−4.61460	+	7.99272i	−0.233969	+	0.405247i	−0.958973	−	0.283499i	$-0.908505\pi$
$389$	−4.61460	+	7.99272i	−0.233969	+	0.405247i	0.725003	+	0.688745i	$0.241838\pi$
$390$	−15.1223			−0.765749
$391$			18.8320i			0.952376i
$392$	6.31873	−	3.01225i	0.319144	−	0.152142i
$393$	1.47219	−	0.849970i	0.0742622	−	0.0428753i
$394$	5.93239	−	3.42507i	0.298869	−	0.172552i
$395$	−23.3720	+	40.4814i	−1.17597	+	2.03684i
$396$	−0.970257			−0.0487572
$397$	−11.5716	+	6.68086i	−0.580762	+	0.335303i	−0.761436	−	0.648240i	$-0.775505\pi$
$397$	−11.5716	+	6.68086i	−0.580762	+	0.335303i	0.180674	+	0.983543i	$0.442172\pi$
$398$	−8.47472			−0.424799
$399$	−10.1494	−	5.47633i	−0.508104	−	0.274159i
$400$	−11.6125			−0.580626
$401$	22.4815	−	12.9797i	1.12267	−	0.648176i	0.180592	−	0.983558i	$-0.442199\pi$
$401$	22.4815	−	12.9797i	1.12267	−	0.648176i	0.942082	+	0.335382i	$0.108865\pi$
$402$	7.12386			0.355306
$403$	−2.40475	+	4.16515i	−0.119789	+	0.207481i
$404$	3.22004	−	1.85909i	0.160203	−	0.0924933i
$405$	3.52979	−	2.03792i	0.175397	−	0.101265i
$406$	−3.40287	−	6.46944i	−0.168882	−	0.321073i
$407$			9.58397i			0.475060i
$408$	−7.48798			−0.370710
$409$	−3.10176	+	5.37241i	−0.153372	+	0.265648i	−0.932465	−	0.361260i	$-0.882347\pi$
$409$	−3.10176	+	5.37241i	−0.153372	+	0.265648i	0.779093	+	0.626908i	$0.215680\pi$
$410$	20.8964	+	36.1936i	1.03200	+	1.78747i
$411$	1.10858	−	1.92011i	0.0546820	−	0.0947120i
$412$	−1.12602	−	1.95033i	−0.0554752	−	0.0960859i
$413$	13.4390	−	21.2946i	0.661290	−	1.04784i
$414$	−2.17802	+	1.25748i	−0.107044	+	0.0618019i
$415$	34.7750	+	60.2320i	1.70704	+	2.95667i
$416$			3.71023i			0.181909i
$417$	−13.6907	+	7.90435i	−0.670438	+	0.387078i
$418$	−1.86022	+	3.79818i	−0.0909864	+	0.185775i
$419$		−	7.95386i		−	0.388571i	−0.980945	−	0.194286i	$-0.937761\pi$
$419$		−	7.95386i		−	0.388571i	0.980945	−	0.194286i	$-0.0622389\pi$
$420$	9.11945	+	5.75528i	0.444984	+	0.280829i
$421$	−12.8689	−	7.42985i	−0.627191	−	0.362109i	0.152472	−	0.988308i	$-0.451276\pi$
$421$	−12.8689	−	7.42985i	−0.627191	−	0.362109i	−0.779663	+	0.626199i	$0.784610\pi$
$422$	1.56970			0.0764117
$423$		−	2.66241i		−	0.129451i
$424$	−5.38579	+	9.32846i	−0.261557	+	0.453030i
$425$	75.3047	+	43.4772i	3.65282	+	2.10895i
$426$	0.497403			0.0240993
$427$	30.8236	+	19.4528i	1.49166	+	0.941385i
$428$	−5.70984	+	3.29658i	−0.275995	+	0.159346i
$429$	1.79994	−	3.11758i	0.0869018	−	0.150518i
$430$	19.5687	+	33.8940i	0.943688	+	1.63452i
$431$	−6.45734	−	3.72815i	−0.311039	−	0.179579i	0.336352	−	0.941736i	$-0.390807\pi$
$431$	−6.45734	−	3.72815i	−0.311039	−	0.179579i	−0.647391	+	0.762158i	$0.724140\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−5.01071	−	8.67881i	−0.240799	−	0.417077i	0.720143	−	0.693826i	$-0.244076\pi$
$433$	−5.01071	−	8.67881i	−0.240799	−	0.417077i	−0.960942	+	0.276749i	$0.910743\pi$
$434$	3.03536	−	1.59657i	0.145702	−	0.0766379i
$435$	5.63047	−	9.75225i	0.269960	−	0.467585i
$436$	−6.75153	−	3.89800i	−0.323340	−	0.186680i
$437$	0.746747	+	10.9370i	0.0357218	+	0.523188i
$438$	1.06951	+	1.85245i	0.0511033	+	0.0885135i
$439$	−10.4471	−	18.0950i	−0.498615	−	0.863627i	0.501384	−	0.865225i	$-0.332825\pi$
$439$	−10.4471	−	18.0950i	−0.498615	−	0.863627i	−0.999999	+	0.00159840i	$0.999491\pi$
$440$	1.97731	−	3.42480i	0.0942645	−	0.163271i
$441$	−3.01225	−	6.31873i	−0.143441	−	0.300892i
$442$	13.8911	−	24.0600i	0.660731	−	1.14442i
$443$	−10.4343			−0.495747			−0.247874	−	0.968792i	$-0.579732\pi$
$443$	−10.4343			−0.495747			−0.247874	+	0.968792i	$0.579732\pi$
$444$	−8.55440	+	4.93889i	−0.405974	+	0.234389i
$445$	−2.54653	+	1.47024i	−0.120717	+	0.0696960i
$446$		−	19.6711i		−	0.931455i
$447$	−6.51615	−	11.2863i	−0.308203	−	0.533824i
$448$	1.41205	−	2.23744i	0.0667129	−	0.105709i
$449$			19.7533i			0.932214i	0.884728	+	0.466107i	$0.154344\pi$
$449$			19.7533i			0.932214i	−0.884728	+	0.466107i	$0.845656\pi$
$450$			11.6125i			0.547420i
$451$	−9.94877			−0.468469
$452$	8.84689	+	5.10775i	0.416123	+	0.240248i
$453$	−12.1248	+	7.00028i	−0.569675	+	0.328902i
$454$	7.74299	+	4.47042i	0.363397	+	0.209807i
$455$	−35.4102	+	18.6255i	−1.66006	+	0.873176i
$456$	−4.34877	+	0.296922i	−0.203650	+	0.0139046i
$457$	−4.05777	+	7.02827i	−0.189815	+	0.328769i	−0.945188	−	0.326526i	$-0.894122\pi$
$457$	−4.05777	+	7.02827i	−0.189815	+	0.328769i	0.755374	+	0.655294i	$0.227455\pi$
$458$	−8.50369			−0.397351
$459$			7.48798i			0.349509i
$460$		−	10.2506i		−	0.477937i
$461$	29.0623	+	16.7791i	1.35357	+	0.781483i	0.988747	−	0.149596i	$-0.0477971\pi$
$461$	29.0623	+	16.7791i	1.35357	+	0.781483i	0.364820	+	0.931078i	$0.381130\pi$
$462$	−2.27194	+	1.19502i	−0.105700	+	0.0555974i
$463$	14.8883			0.691917			0.345959	−	0.938250i	$-0.387554\pi$
$463$	14.8883			0.691917			0.345959	+	0.938250i	$0.387554\pi$
$464$	−2.39269	−	1.38142i	−0.111078	−	0.0641309i
$465$	4.57560	+	2.64172i	0.212188	+	0.122507i
$466$	−0.407186	−	0.235089i	−0.0188625	−	0.0108903i
$467$	7.71786	+	4.45591i	0.357140	+	0.206195i	0.667825	−	0.744318i	$-0.267225\pi$
$467$	7.71786	+	4.45591i	0.357140	+	0.206195i	−0.310686	+	0.950513i	$0.600559\pi$
$468$	3.71023			0.171505
$469$	16.6811	−	8.77413i	0.770263	−	0.405152i
$470$	9.39773	+	5.42578i	0.433485	+	0.250273i
$471$		−	7.95372i		−	0.366488i
$472$		−	9.51740i		−	0.438074i
$473$	−9.31669			−0.428382
$474$	5.73426	−	9.93203i	0.263383	−	0.456193i
$475$	45.4585	+	22.2641i	2.08578	+	1.02155i
$476$	−17.5338	+	9.22261i	−0.803659	+	0.422718i
$477$	9.32846	+	5.38579i	0.427121	+	0.246598i
$478$	10.6884	−	6.17093i	0.488875	−	0.282252i
$479$	15.3581	+	8.86702i	0.701730	+	0.405144i	0.807992	−	0.589194i	$-0.200555\pi$
$479$	15.3581	+	8.86702i	0.701730	+	0.405144i	−0.106261	+	0.994338i	$0.533888\pi$
$480$	4.07585			0.186036
$481$		−	36.6488i		−	1.67104i
$482$		−	16.8484i		−	0.767422i
$483$	−3.55125	+	5.62708i	−0.161587	+	0.256041i
$484$	−5.02930	−	8.71100i	−0.228605	−	0.395955i
$485$			63.9572i			2.90415i
$486$	−0.866025	+	0.500000i	−0.0392837	+	0.0226805i
$487$	12.2636	−	7.08040i	0.555717	−	0.320844i	−0.195707	−	0.980662i	$-0.562700\pi$
$487$	12.2636	−	7.08040i	0.555717	−	0.320844i	0.751425	+	0.659819i	$0.229367\pi$
$488$	13.7763			0.623623
$489$	10.8199	−	18.7407i	0.489295	−	0.847484i
$490$	28.4425	+	2.24448i	1.28490	+	0.101395i
$491$	5.82747	−	10.0935i	0.262990	−	0.455512i	−0.704045	−	0.710155i	$-0.748625\pi$
$491$	5.82747	−	10.0935i	0.262990	−	0.455512i	0.967035	+	0.254643i	$0.0819580\pi$
$492$	−5.12688	−	8.88001i	−0.231137	−	0.400342i
$493$	10.3441	+	17.9165i	0.465873	+	0.806916i
$494$	7.11342	−	14.5241i	0.320048	−	0.653470i
$495$	−3.42480	−	1.97731i	−0.153933	−	0.0888734i
$496$	0.648141	−	1.12261i	0.0291024	−	0.0504068i
$497$	1.16471	−	0.612629i	0.0522445	−	0.0274802i
$498$	−8.53197	−	14.7778i	−0.382327	−	0.662209i
$499$	−3.61136	−	6.25506i	−0.161667	−	0.280015i	0.773800	−	0.633430i	$-0.218354\pi$
$499$	−3.61136	−	6.25506i	−0.161667	−	0.280015i	−0.935467	+	0.353415i	$0.885020\pi$
$500$	−23.3408	−	13.4758i	−1.04383	−	0.602657i
$501$	0.0757722	+	0.131241i	0.00338525	+	0.00586343i
$502$	−0.807976	+	1.39946i	−0.0360617	+	0.0624608i
$503$	−25.1228	+	14.5047i	−1.12017	+	0.646731i	−0.941444	−	0.337168i	$-0.890531\pi$
$503$	−25.1228	+	14.5047i	−1.12017	+	0.646731i	−0.178726	+	0.983899i	$0.557197\pi$
$504$	−2.23744	−	1.41205i	−0.0996634	−	0.0628975i
$505$	15.1548			0.674378
$506$	2.11324	+	1.22008i	0.0939451	+	0.0542392i
$507$	−0.382903	+	0.663208i	−0.0170053	+	0.0294541i
$508$			5.34985i			0.237361i
$509$	27.3749			1.21337			0.606686	−	0.794942i	$-0.292499\pi$
$509$	27.3749			1.21337			0.606686	+	0.794942i	$0.292499\pi$
$510$	−26.4310	−	15.2599i	−1.17038	−	0.675721i
$511$	4.78594	+	3.02040i	0.211717	+	0.133615i
$512$		−	1.00000i		−	0.0441942i
$513$	0.296922	+	4.34877i	0.0131094	+	0.192003i
$514$	15.6285	−	9.02311i	0.689343	−	0.397992i
$515$		−	9.17900i		−	0.404475i
$516$	−4.80115	−	8.31583i	−0.211359	−	0.366084i
$517$	−2.23713	+	1.29161i	−0.0983890	+	0.0568049i
$518$	−13.9479	+	22.1009i	−0.612834	+	0.971057i
$519$	−4.57227	−	7.91941i	−0.200701	−	0.347624i
$520$	−7.56116	+	13.0963i	−0.331579	+	0.574312i
$521$	−12.8508	−	22.2583i	−0.563005	−	0.975154i	−0.997232	−	0.0743503i	$-0.976312\pi$
$521$	−12.8508	−	22.2583i	−0.563005	−	0.975154i	0.434227	−	0.900804i	$-0.357022\pi$
$522$	−1.38142	+	2.39269i	−0.0604632	+	0.104725i
$523$	−7.63131			−0.333694			−0.166847	−	0.985983i	$-0.553359\pi$
$523$	−7.63131			−0.333694			−0.166847	+	0.985983i	$0.553359\pi$
$524$		−	1.69994i		−	0.0742622i
$525$	14.3026	+	27.1917i	0.624218	+	1.18674i
$526$	−18.7127	+	10.8038i	−0.815914	+	0.471068i
$527$	−8.40611	+	4.85327i	−0.366176	+	0.211412i
$528$	−0.485128	+	0.840267i	−0.0211125	+	0.0365679i
$529$	−16.6749			−0.724998
$530$	−38.0214	+	21.9517i	−1.65154	+	0.953519i
$531$	−9.51740			−0.413020
$532$	−9.81733	+	6.05146i	−0.425635	+	0.262364i
$533$	38.0438			1.64786
$534$	0.624786	−	0.360720i	0.0270371	−	0.0156099i
$535$	−26.8727			−1.16181
$536$	3.56193	−	6.16944i	0.153852	−	0.266479i
$537$	5.49625	−	3.17326i	0.237181	−	0.136936i
$538$	−9.26815	+	5.35097i	−0.399578	+	0.230697i
$539$	−3.84809	+	5.59649i	−0.165749	+	0.241058i
$540$		−	4.07585i		−	0.175397i
$541$	−27.2962			−1.17355			−0.586777	−	0.809748i	$-0.699604\pi$
$541$	−27.2962			−1.17355			−0.586777	+	0.809748i	$0.699604\pi$
$542$	3.24891	−	5.62728i	0.139553	−	0.241712i
$543$	7.25677	+	12.5691i	0.311418	+	0.539392i
$544$	−3.74399	+	6.48478i	−0.160522	+	0.278033i
$545$	−15.8876	−	27.5182i	−0.680552	−	1.17875i
$546$	8.68782	−	4.56972i	0.371805	−	0.195566i
$547$	−16.3761	+	9.45474i	−0.700191	+	0.404256i	−0.807419	−	0.589979i	$-0.799136\pi$
$547$	−16.3761	+	9.45474i	−0.700191	+	0.404256i	0.107227	+	0.994235i	$0.465803\pi$
$548$	−1.10858	−	1.92011i	−0.0473560	−	0.0820230i
$549$		−	13.7763i		−	0.587958i
$550$	9.75762	−	5.63357i	0.416066	−	0.240216i
$551$	6.71794	+	9.99511i	0.286194	+	0.425806i
$552$			2.51497i			0.107044i
$553$	1.19443	−	30.3193i	0.0507925	−	1.28931i
$554$	9.25785	+	5.34502i	0.393328	+	0.227088i
$555$	−40.2603			−1.70895
$556$			15.8087i			0.670438i
$557$	2.07110	−	3.58724i	0.0877552	−	0.151996i	−0.818807	−	0.574069i	$-0.805364\pi$
$557$	2.07110	−	3.58724i	0.0877552	−	0.151996i	0.906562	+	0.422073i	$0.138697\pi$
$558$	−1.12261	−	0.648141i	−0.0475240	−	0.0274380i
$559$	35.6267			1.50685
$560$	9.54395	−	5.02004i	0.403305	−	0.212135i
$561$	6.29191	−	3.63263i	0.265644	−	0.153370i
$562$	2.67950	−	4.64102i	0.113028	−	0.195770i
$563$	−3.24552	−	5.62141i	−0.136782	−	0.236914i	0.789494	−	0.613758i	$-0.210343\pi$
$563$	−3.24552	−	5.62141i	−0.136782	−	0.236914i	−0.926277	+	0.376843i	$0.877009\pi$
$564$	−2.30571	−	1.33120i	−0.0970880	−	0.0560538i
$565$	20.8184	+	36.0586i	0.875837	+	1.51699i
$566$	6.78618	+	11.7540i	0.285244	+	0.494058i
$567$	−1.41205	+	2.23744i	−0.0593004	+	0.0939635i
$568$	0.248702	−	0.430764i	0.0104353	−	0.0180745i
$569$	−22.6885	−	13.0992i	−0.951152	−	0.549148i	−0.0577133	−	0.998333i	$-0.518381\pi$
$569$	−22.6885	−	13.0992i	−0.951152	−	0.549148i	−0.893439	+	0.449185i	$0.851714\pi$
$570$	−15.9553	−	7.81440i	−0.668296	−	0.327309i
$571$	10.2510	+	17.7552i	0.428991	+	0.743034i	0.996784	−	0.0801376i	$-0.0255360\pi$
$571$	10.2510	+	17.7552i	0.428991	+	0.743034i	−0.567793	+	0.823171i	$0.692203\pi$
$572$	−1.79994	−	3.11758i	−0.0752592	−	0.130353i
$573$	−3.41302	+	5.91152i	−0.142581	+	0.246957i
$574$	−22.9421	−	14.4788i	−0.957586	−	0.604332i
$575$	14.6025	−	25.2924i	0.608968	−	1.05476i
$576$	−1.00000			−0.0416667
$577$	−34.4102	+	19.8667i	−1.43251	+	0.827062i	−0.997312	−	0.0732710i	$-0.976656\pi$
$577$	−34.4102	+	19.8667i	−1.43251	+	0.827062i	−0.435201	+	0.900333i	$0.643323\pi$
$578$	33.8355	−	19.5349i	1.40737	−	0.812547i
$579$			13.2487i			0.550596i
$580$	−5.63047	−	9.75225i	−0.233792	−	0.404940i
$581$	−38.1795	−	24.0951i	−1.58395	−	0.999631i
$582$		−	15.6918i		−	0.650445i
$583$		−	10.4512i		−	0.432845i
$584$	2.13903			0.0885135
$585$	13.0963	+	7.56116i	0.541466	+	0.312616i
$586$	−15.0050	+	8.66314i	−0.619851	+	0.357871i
$587$	−15.2614	−	8.81115i	−0.629904	−	0.363675i	0.150811	−	0.988563i	$-0.451812\pi$
$587$	−15.2614	−	8.81115i	−0.629904	−	0.363675i	−0.780715	+	0.624887i	$0.785145\pi$
$588$	−6.97831	−	0.550678i	−0.287780	−	0.0227096i
$589$	−4.68954	+	3.15195i	−0.193229	+	0.129874i
$590$	19.3957	−	33.5944i	0.798510	−	1.38306i
$591$	−6.85013			−0.281777
$592$			9.87777i			0.405974i
$593$		−	15.9546i		−	0.655176i	−0.944821	−	0.327588i	$-0.893764\pi$
$593$		−	15.9546i		−	0.655176i	0.944821	−	0.327588i	$-0.106236\pi$
$594$	0.840267	+	0.485128i	0.0344766	+	0.0199051i
$595$	−80.6854	−	3.17861i	−3.30778	−	0.130310i
$596$	−13.0323			−0.533824
$597$	7.33932	+	4.23736i	0.300378	+	0.173424i
$598$	−8.08097	−	4.66555i	−0.330455	−	0.190789i
$599$	−7.60634	−	4.39152i	−0.310787	−	0.179433i	0.336492	−	0.941686i	$-0.390760\pi$
$599$	−7.60634	−	4.39152i	−0.310787	−	0.179433i	−0.647278	+	0.762254i	$0.724093\pi$
$600$	10.0567	+	5.80626i	0.410565	+	0.237040i
$601$	−8.16815			−0.333186			−0.166593	−	0.986026i	$-0.553277\pi$
$601$	−8.16815			−0.333186			−0.166593	+	0.986026i	$0.553277\pi$
$602$	−21.4845	−	13.5589i	−0.875644	−	0.552619i
$603$	−6.16944	−	3.56193i	−0.251239	−	0.145053i
$604$			14.0006i			0.569675i
$605$		−	40.9973i		−	1.66678i
$606$	−3.71819			−0.151041
$607$	7.02409	−	12.1661i	0.285099	−	0.493806i	−0.687534	−	0.726152i	$-0.741307\pi$
$607$	7.02409	−	12.1661i	0.285099	−	0.493806i	0.972633	+	0.232346i	$0.0746402\pi$
$608$	−1.91725	+	3.91461i	−0.0777546	+	0.158758i
$609$	−0.287748	+	7.30413i	−0.0116601	+	0.295978i
$610$	48.6274	+	28.0750i	1.96886	+	1.13672i
$611$	8.55472	−	4.93907i	0.346087	−	0.199813i
$612$	6.48478	+	3.74399i	0.262132	+	0.151342i
$613$	−15.8363			−0.639621			−0.319811	−	0.947481i	$-0.603619\pi$
$613$	−15.8363			−0.639621			−0.319811	+	0.947481i	$0.603619\pi$
$614$			20.8661i			0.842087i
$615$		−	41.7927i		−	1.68524i
$616$	−0.101051	+	2.56507i	−0.00407147	+	0.103350i
$617$	−21.5429	−	37.3134i	−0.867285	−	1.50218i	−0.864761	−	0.502184i	$-0.832530\pi$
$617$	−21.5429	−	37.3134i	−0.867285	−	1.50218i	−0.00252400	−	0.999997i	$-0.500803\pi$
$618$			2.25205i			0.0905906i
$619$	35.7535	−	20.6423i	1.43705	−	0.829684i	0.439410	−	0.898287i	$-0.355187\pi$
$619$	35.7535	−	20.6423i	1.43705	−	0.829684i	0.997644	+	0.0686028i	$0.0218541\pi$
$620$	4.57560	−	2.64172i	0.183760	−	0.106094i
$621$	2.51497			0.100922
$622$	−10.4745	+	18.1423i	−0.419987	+	0.727440i
$623$	1.01871	−	1.61418i	0.0408136	−	0.0646706i
$624$	1.85511	−	3.21315i	0.0742640	−	0.128629i
$625$	−25.8941	−	44.8498i	−1.03576	−	1.79399i
$626$	3.46804	+	6.00681i	0.138611	+	0.240081i
$627$	3.51009	−	2.35921i	0.140179	−	0.0942177i
$628$	−6.88812	−	3.97686i	−0.274866	−	0.158694i
$629$	36.9823	−	64.0552i	1.47458	−	2.55405i
$630$	−5.02004	−	9.54395i	−0.200003	−	0.380240i
$631$	5.05007	+	8.74698i	0.201040	+	0.348212i	0.948864	−	0.315686i	$-0.102235\pi$
$631$	5.05007	+	8.74698i	0.201040	+	0.348212i	−0.747824	+	0.663897i	$0.768901\pi$
$632$	−5.73426	−	9.93203i	−0.228097	−	0.395075i
$633$	−1.35940	−	0.784849i	−0.0540312	−	0.0311949i
$634$	4.69675	+	8.13501i	0.186532	+	0.323083i
$635$	−10.9026	+	18.8838i	−0.432656	+	0.749382i
$636$	9.32846	−	5.38579i	0.369898	−	0.213561i
$637$	14.7150	−	21.4008i	0.583028	−	0.847930i
$638$	2.68067			0.106129
$639$	−0.430764	−	0.248702i	−0.0170408	−	0.00983849i
$640$	2.03792	−	3.52979i	0.0805560	−	0.139527i
$641$		−	22.7786i		−	0.899701i	−0.893104	−	0.449851i	$-0.851477\pi$
$641$		−	22.7786i		−	0.899701i	0.893104	−	0.449851i	$-0.148523\pi$
$642$	6.59315			0.260211
$643$	6.73718	+	3.88971i	0.265688	+	0.153395i	0.626927	−	0.779078i	$-0.284313\pi$
$643$	6.73718	+	3.88971i	0.265688	+	0.153395i	−0.361238	+	0.932474i	$0.617646\pi$
$644$	3.09757	+	5.88901i	0.122061	+	0.232059i
$645$		−	39.1375i		−	1.54104i
$646$	27.0892	−	18.2072i	1.06581	−	0.716355i
$647$	36.1528	−	20.8728i	1.42131	−	0.820596i	0.424903	−	0.905239i	$-0.360308\pi$
$647$	36.1528	−	20.8728i	1.42131	−	0.820596i	0.996411	+	0.0846425i	$0.0269748\pi$
$648$			1.00000i			0.0392837i
$649$	4.61716	+	7.99716i	0.181239	+	0.313916i
$650$	−37.3128	+	21.5426i	−1.46353	+	0.844969i
$651$	−3.42698	−	0.135006i	−0.134314	−	0.00529132i
$652$	−10.8199	−	18.7407i	−0.423742	−	0.733943i
$653$	−0.316827	+	0.548760i	−0.0123984	+	0.0214746i	−0.872158	−	0.489224i	$-0.837280\pi$
$653$	−0.316827	+	0.548760i	−0.0123984	+	0.0214746i	0.859760	+	0.510699i	$0.170613\pi$
$654$	3.89800	+	6.75153i	0.152424	+	0.264006i
$655$	3.46435	−	6.00043i	0.135363	−	0.234456i
$656$	−10.2538			−0.400342
$657$		−	2.13903i		−	0.0834513i
$658$	−7.03861	−	0.277287i	−0.274393	−	0.0108098i
$659$	2.65971	−	1.53559i	0.103608	−	0.0598179i	−0.447301	−	0.894384i	$-0.647615\pi$
$659$	2.65971	−	1.53559i	0.103608	−	0.0598179i	0.550909	+	0.834566i	$0.314281\pi$
$660$	−3.42480	+	1.97731i	−0.133310	+	0.0769666i
$661$	−16.4857	+	28.5541i	−0.641221	+	1.11063i	0.343940	+	0.938992i	$0.388238\pi$
$661$	−16.4857	+	28.5541i	−0.641221	+	1.11063i	−0.985161	+	0.171635i	$0.945095\pi$
$662$	19.3654			0.752659
$663$	−24.0600	+	13.8911i	−0.934415	+	0.539484i
$664$	−17.0639			−0.662209
$665$	−46.9855	+	1.35339i	−1.82202	+	0.0524822i
$666$	9.87777			0.382756
$667$	6.01754	−	3.47423i	0.233000	−	0.134523i
$668$	0.151544			0.00586343
$669$	−9.83556	+	17.0357i	−0.380265	+	0.658638i
$670$	25.1457	−	14.5179i	0.971463	−	0.560874i
$671$	−11.5758	+	6.68327i	−0.446877	+	0.258005i
$672$	−2.34159	+	1.23165i	−0.0903287	+	0.0475121i
$673$			14.2527i			0.549400i	0.961530	+	0.274700i	$0.0885786\pi$
$673$			14.2527i			0.549400i	−0.961530	+	0.274700i	$0.911421\pi$
$674$	−22.3125			−0.859444
$675$	5.80626	−	10.0567i	0.223483	−	0.387084i
$676$	0.382903	+	0.663208i	0.0147270	+	0.0255080i
$677$	−14.3151	+	24.7946i	−0.550176	+	0.952933i	0.448086	+	0.893991i	$0.352106\pi$
$677$	−14.3151	+	24.7946i	−0.550176	+	0.952933i	−0.998261	+	0.0589419i	$0.981227\pi$
$678$	−5.10775	−	8.84689i	−0.196162	−	0.339763i
$679$	−19.3268	−	36.7436i	−0.741696	−	1.41009i
$680$	−26.4310	+	15.2599i	−1.01358	+	0.585192i
$681$	−4.47042	−	7.74299i	−0.171307	−	0.296712i
$682$			1.25773i			0.0481608i
$683$	2.69797	−	1.55767i	0.103235	−	0.0596027i	−0.447494	−	0.894287i	$-0.647683\pi$
$683$	2.69797	−	1.55767i	0.103235	−	0.0596027i	0.550729	+	0.834684i	$0.314350\pi$
$684$	3.91461	+	1.91725i	0.149679	+	0.0733077i
$685$		−	9.03677i		−	0.345277i
$686$	−17.0186	+	7.30540i	−0.649771	+	0.278922i
$687$	7.36441	+	4.25184i	0.280970	+	0.162218i
$688$	−9.60229			−0.366084
$689$			39.9650i			1.52255i
$690$	−5.12531	+	8.87729i	−0.195117	+	0.337953i
$691$	−27.5558	−	15.9093i	−1.04827	−	0.605219i	−0.126106	−	0.992017i	$-0.540248\pi$
$691$	−27.5558	−	15.9093i	−1.04827	−	0.605219i	−0.922165	+	0.386797i	$0.873581\pi$
$692$	−9.14455			−0.347624
$693$	2.56507	+	0.101051i	0.0974389	+	0.00383862i
$694$	−2.13899	+	1.23494i	−0.0811948	+	0.0468778i
$695$	−32.2169	+	55.8014i	−1.22206	+	2.11667i
$696$	1.38142	+	2.39269i	0.0523627	+	0.0906948i
$697$	66.4934	+	38.3900i	2.51862	+	1.45412i
$698$	−2.48327	−	4.30116i	−0.0939933	−	0.162801i
$699$	0.235089	+	0.407186i	0.00889188	+	0.0154012i
$700$	30.7000	+	1.20943i	1.16035	+	0.0457123i
$701$	−4.37494	+	7.57761i	−0.165239	+	0.286203i	−0.936740	−	0.350025i	$-0.886173\pi$
$701$	−4.37494	+	7.57761i	−0.165239	+	0.286203i	0.771501	+	0.636228i	$0.219506\pi$
$702$	−3.21315	−	1.85511i	−0.121273	−	0.0700168i
$703$	18.9381	−	38.6676i	0.714264	−	1.45838i
$704$	0.485128	+	0.840267i	0.0182840	+	0.0316688i
$705$	−5.42578	−	9.39773i	−0.204347	−	0.353939i
$706$	−17.0929	+	29.6058i	−0.643300	+	1.11423i
$707$	−8.70645	+	4.57952i	−0.327440	+	0.172231i
$708$	−4.75870	+	8.24231i	−0.178843	+	0.309765i
$709$	11.7630			0.441770			0.220885	−	0.975300i	$-0.429106\pi$
$709$	11.7630			0.441770			0.220885	+	0.975300i	$0.429106\pi$
$710$	1.75573	−	1.01367i	0.0658913	−	0.0380424i
$711$	−9.93203	+	5.73426i	−0.372480	+	0.215052i
$712$		−	0.721440i		−	0.0270371i
$713$	1.63005	+	2.82333i	0.0610459	+	0.105735i
$714$	19.7960	+	0.779866i	0.740846	+	0.0291858i
$715$		−	14.6725i		−	0.548722i
$716$		−	6.34652i		−	0.237181i
$717$	−12.3419			−0.460915
$718$	−20.8032	−	12.0107i	−0.776368	−	0.448236i
$719$	−21.5446	+	12.4388i	−0.803476	+	0.463887i	−0.844685	−	0.535263i	$-0.820212\pi$
$719$	−21.5446	+	12.4388i	−0.803476	+	0.463887i	0.0412089	+	0.999151i	$0.486879\pi$
$720$	−3.52979	−	2.03792i	−0.131547	−	0.0759489i
$721$	2.77374	+	5.27336i	0.103300	+	0.196390i
$722$	15.0105	−	11.6483i	0.558634	−	0.433506i
$723$	−8.42418	+	14.5911i	−0.313299	+	0.542649i
$724$	14.5135			0.539392
$725$		−	32.0836i		−	1.19156i
$726$			10.0586i			0.373310i
$727$	43.3648	+	25.0367i	1.60831	+	0.928559i	0.989748	+	0.142825i	$0.0456187\pi$
$727$	43.3648	+	25.0367i	1.60831	+	0.928559i	0.618564	+	0.785734i	$0.287715\pi$
$728$	0.386417	−	9.80874i	0.0143216	−	0.363536i
$729$	1.00000			0.0370370
$730$	7.55030	+	4.35917i	0.279449	+	0.161340i
$731$	62.2688	+	35.9509i	2.30309	+	1.32969i
$732$	−11.9306	−	6.88815i	−0.440968	−	0.254593i
$733$	19.1045	+	11.0300i	0.705640	+	0.407402i	0.809445	−	0.587196i	$-0.199768\pi$
$733$	19.1045	+	11.0300i	0.705640	+	0.407402i	−0.103804	+	0.994598i	$0.533102\pi$
$734$	21.3328			0.787410
$735$	−23.5097	−	16.1650i	−0.867168	−	0.596256i
$736$	2.17802	+	1.25748i	0.0802830	+	0.0463514i
$737$			6.91197i			0.254606i
$738$			10.2538i			0.377446i
$739$	−50.3486			−1.85210			−0.926052	−	0.377395i	$-0.876820\pi$
$739$	−50.3486			−1.85210			−0.926052	+	0.377395i	$0.876820\pi$
$740$	−20.1301	+	34.8664i	−0.739999	+	1.28172i
$741$	−13.4225	+	9.02153i	−0.493086	+	0.331414i
$742$	15.2100	−	24.1007i	0.558376	−	0.884766i
$743$	18.1811	+	10.4968i	0.666998	+	0.385092i	0.794938	−	0.606690i	$-0.207503\pi$
$743$	18.1811	+	10.4968i	0.666998	+	0.385092i	−0.127940	+	0.991782i	$0.540837\pi$
$744$	−1.12261	+	0.648141i	−0.0411570	+	0.0237620i
$745$	−46.0013	−	26.5588i	−1.68536	−	0.973041i
$746$	−9.57747			−0.350656
$747$			17.0639i			0.624337i
$748$		−	7.26527i		−	0.265644i
$749$	15.4384	−	8.12049i	0.564108	−	0.296716i
$750$	13.4758	+	23.3408i	0.492067	+	0.852286i
$751$			35.0358i			1.27847i	0.769010	+	0.639237i	$0.220750\pi$
$751$			35.0358i			1.27847i	−0.769010	+	0.639237i	$0.779250\pi$
$752$	−2.30571	+	1.33120i	−0.0840807	+	0.0485440i
$753$	1.39946	−	0.807976i	0.0509990	−	0.0294443i
$754$	−10.2508			−0.373312
$755$	−28.5321	+	49.4190i	−1.03839	+	1.79854i
$756$	1.23165	+	2.34159i	0.0447948	+	0.0851627i
$757$	9.36580	−	16.2220i	0.340406	−	0.589600i	−0.644102	−	0.764939i	$-0.722769\pi$
$757$	9.36580	−	16.2220i	0.340406	−	0.589600i	0.984508	+	0.175339i	$0.0561023\pi$
$758$	12.2333	+	21.1887i	0.444333	+	0.769608i
$759$	−1.22008	−	2.11324i	−0.0442861	−	0.0767058i
$760$	−14.7451	+	9.91054i	−0.534863	+	0.359493i
$761$	−31.0528	−	17.9284i	−1.12566	−	0.649903i	−0.182824	−	0.983146i	$-0.558524\pi$
$761$	−31.0528	−	17.9284i	−1.12566	−	0.649903i	−0.942841	+	0.333243i	$0.891857\pi$
$762$	2.67492	−	4.63310i	0.0969023	−	0.167840i
$763$	17.4431	+	11.0083i	0.631481	+	0.398527i
$764$	3.41302	+	5.91152i	0.123479	+	0.213871i
$765$	15.2599	+	26.4310i	0.551724	+	0.955614i
$766$	−6.17110	−	3.56288i	−0.222971	−	0.128732i
$767$	−17.6559	−	30.5809i	−0.637517	−	1.10421i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	−14.7852	+	8.53622i	−0.533167	+	0.307824i	−0.742305	−	0.670062i	$-0.766267\pi$
$769$	−14.7852	+	8.53622i	−0.533167	+	0.307824i	0.209138	+	0.977886i	$0.432934\pi$
$770$	−5.58410	+	8.84821i	−0.201237	+	0.318867i
$771$	−18.0462			−0.649919
$772$	11.4737	+	6.62433i	0.412947	+	0.238415i
$773$	−3.14071	+	5.43987i	−0.112963	+	0.195658i	−0.916964	−	0.398970i	$-0.869368\pi$
$773$	−3.14071	+	5.43987i	−0.112963	+	0.195658i	0.804000	+	0.594629i	$0.202701\pi$
$774$			9.60229i			0.345147i
$775$	15.0531			0.540724
$776$	−13.5895	−	7.84588i	−0.487833	−	0.281651i
$777$	23.1297	−	12.1660i	0.829772	−	0.436453i
$778$		−	9.22919i		−	0.330883i
$779$	40.1394	+	19.6590i	1.43814	+	0.704355i
$780$	13.0963	−	7.56116i	0.468923	−	0.270733i
$781$			0.482609i			0.0172691i
$782$	−9.41601	−	16.3090i	−0.336716	−	0.583209i
$783$	2.39269	−	1.38142i	0.0855079	−	0.0493680i
$784$	−3.96605	+	5.76805i	−0.141645	+	0.206002i
$785$	−16.2091	−	28.0749i	−0.578527	−	1.00204i
$786$	−0.849970	+	1.47219i	−0.0303174	+	0.0525113i
$787$	−12.3838	−	21.4493i	−0.441434	−	0.764586i	0.556362	−	0.830940i	$-0.312197\pi$
$787$	−12.3838	−	21.4493i	−0.441434	−	0.764586i	−0.997796	+	0.0663537i	$0.978863\pi$
$788$	−3.42507	+	5.93239i	−0.122013	+	0.211333i
$789$	21.6076			0.769251
$790$		−	46.7439i		−	1.66307i
$791$	−22.8566	−	14.4248i	−0.812685	−	0.512886i
$792$	0.840267	−	0.485128i	0.0298576	−	0.0172383i
$793$	44.2653	−	25.5566i	1.57191	−	0.907542i
$794$	6.68086	−	11.5716i	0.237095	−	0.410660i
$795$	43.9033			1.55709
$796$	7.33932	−	4.23736i	0.260135	−	0.150189i
$797$	15.8875			0.562764			0.281382	−	0.959596i	$-0.409207\pi$
$797$	15.8875			0.562764			0.281382	+	0.959596i	$0.409207\pi$
$798$	11.5278	−	0.332051i	0.408079	−	0.0117545i
$799$	19.9361			0.705287
$800$	10.0567	−	5.80626i	0.355559	−	0.205282i
$801$	−0.721440			−0.0254908
$802$	−12.9797	+	22.4815i	−0.458330	+	0.793850i
$803$	−1.79735	+	1.03770i	−0.0634272	+	0.0366197i
$804$	−6.16944	+	3.56193i	−0.217579	+	0.125620i
$805$	−1.06759	+	27.0996i	−0.0376276	+	0.955134i
$806$		−	4.80950i		−	0.169408i
$807$	10.7019			0.376726
$808$	−1.85909	+	3.22004i	−0.0654027	+	0.113281i
$809$	15.2941	+	26.4902i	0.537713	+	0.931347i	0.999027	+	0.0441095i	$0.0140450\pi$
$809$	15.2941	+	26.4902i	0.537713	+	0.931347i	−0.461313	+	0.887237i	$0.652622\pi$
$810$	−2.03792	+	3.52979i	−0.0716053	+	0.124024i
$811$	0.304033	+	0.526601i	0.0106760	+	0.0184915i	0.871314	−	0.490726i	$-0.163268\pi$
$811$	0.304033	+	0.526601i	0.0106760	+	0.0184915i	−0.860638	+	0.509217i	$0.829935\pi$
$812$	6.18169	+	3.90126i	0.216935	+	0.136908i
$813$	−5.62728	+	3.24891i	−0.197357	+	0.113944i
$814$	−4.79199	−	8.29997i	−0.167959	−	0.290914i
$815$		−	88.2009i		−	3.08954i
$816$	6.48478	−	3.74399i	0.227013	−	0.131066i
$817$	37.5892	+	18.4100i	1.31508	+	0.644083i
$818$		−	6.20352i		−	0.216901i
$819$	−9.80874	−	0.386417i	−0.342745	−	0.0135025i
$820$	−36.1936	−	20.8964i	−1.26393	−	0.729732i
$821$	−21.5668			−0.752686			−0.376343	−	0.926480i	$-0.622819\pi$
$821$	−21.5668			−0.752686			−0.376343	+	0.926480i	$0.622819\pi$
$822$			2.21715i			0.0773321i
$823$	−11.9772	+	20.7451i	−0.417499	+	0.723130i	−0.995687	−	0.0927737i	$-0.970427\pi$
$823$	−11.9772	+	20.7451i	−0.417499	+	0.723130i	0.578188	+	0.815904i	$0.303760\pi$
$824$	1.95033	+	1.12602i	0.0679430	+	0.0392269i
$825$	−11.2671			−0.392271
$826$	−0.991228	+	25.1612i	−0.0344892	+	0.875469i
$827$	31.9154	−	18.4264i	1.10981	−	0.640748i	0.171029	−	0.985266i	$-0.445291\pi$
$827$	31.9154	−	18.4264i	1.10981	−	0.640748i	0.938780	+	0.344518i	$0.111958\pi$
$828$	1.25748	−	2.17802i	0.0437005	−	0.0756916i
$829$	11.6590	+	20.1940i	0.404934	+	0.701366i	0.994314	−	0.106490i	$-0.0339613\pi$
$829$	11.6590	+	20.1940i	0.404934	+	0.701366i	−0.589380	+	0.807856i	$0.700628\pi$
$830$	−60.2320	−	34.7750i	−2.09068	−	1.20706i
$831$	−5.34502	−	9.25785i	−0.185417	−	0.321151i
$832$	−1.85511	−	3.21315i	−0.0643145	−	0.111396i
$833$	47.3145	−	22.5557i	1.63935	−	0.781509i
$834$	7.90435	−	13.6907i	0.273705	−	0.474072i
$835$	0.534919	+	0.308836i	0.0185116	+	0.0106877i
$836$	−0.288090	−	4.21943i	−0.00996381	−	0.145932i
$837$	0.648141	+	1.12261i	0.0224030	+	0.0388032i
$838$	3.97693	+	6.88824i	0.137381	+	0.237950i
$839$	7.89487	−	13.6743i	0.272561	−	0.472090i	−0.696956	−	0.717114i	$-0.745463\pi$
$839$	7.89487	−	13.6743i	0.272561	−	0.472090i	0.969517	+	0.245024i	$0.0787959\pi$
$840$	−10.7753	−	0.424495i	−0.371784	−	0.0146465i
$841$	−10.6833	+	18.5041i	−0.368391	+	0.638072i
$842$	14.8597			0.512099
$843$	−4.64102	+	2.67950i	−0.159845	+	0.0922867i
$844$	−1.35940	+	0.784849i	−0.0467924	+	0.0270156i
$845$			3.12131i			0.107376i
$846$	1.33120	+	2.30571i	0.0457677	+	0.0792720i
$847$	12.3887	+	23.5531i	0.425682	+	0.809294i
$848$		−	10.7716i		−	0.369898i
$849$		−	13.5724i		−	0.465802i
$850$	−86.9544			−2.98251
$851$	−21.5140	−	12.4211i	−0.737491	−	0.425791i
$852$	−0.430764	+	0.248702i	−0.0147577	+	0.00852038i
$853$	15.3678	+	8.87262i	0.526185	+	0.303793i	0.739461	−	0.673199i	$-0.235080\pi$
$853$	15.3678	+	8.87262i	0.526185	+	0.303793i	−0.213277	+	0.976992i	$0.568414\pi$
$854$	−36.4204	−	1.43479i	−1.24628	−	0.0490974i
$855$	9.91054	+	14.7451i	0.338933	+	0.504273i
$856$	3.29658	−	5.70984i	0.112675	−	0.195158i
$857$	23.6632			0.808319			0.404160	−	0.914688i	$-0.367564\pi$
$857$	23.6632			0.808319			0.404160	+	0.914688i	$0.367564\pi$
$858$			3.59988i			0.122898i
$859$		−	27.0225i		−	0.921997i	−0.887401	−	0.460999i	$-0.847491\pi$
$859$		−	27.0225i		−	0.921997i	0.887401	−	0.460999i	$-0.152509\pi$
$860$	−33.8940	−	19.5687i	−1.15578	−	0.667288i
$861$	12.6291	+	24.0100i	0.430398	+	0.818260i
$862$	7.45630			0.253963
$863$	−24.9978	−	14.4325i	−0.850933	−	0.491287i	0.0100322	−	0.999950i	$-0.496807\pi$
$863$	−24.9978	−	14.4325i	−0.850933	−	0.491287i	−0.860966	+	0.508663i	$0.830140\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$	−32.2783	−	18.6359i	−1.09750	−	0.633639i
$866$	8.67881	+	5.01071i	0.294918	+	0.170271i
$867$	−39.0699			−1.32688
$868$	−1.83041	+	2.90035i	−0.0621282	+	0.0984443i
$869$	9.63662	+	5.56371i	0.326900	+	0.188736i
$870$			11.2609i			0.381781i
$871$		−	26.4311i		−	0.895585i
$872$	7.79600			0.264006
$873$	−7.84588	+	13.5895i	−0.265543	+	0.459934i
$874$	−6.11521	−	9.09836i	−0.206850	−	0.307757i
$875$	60.3026	+	38.0569i	2.03860	+	1.28656i
$876$	−1.85245	−	1.06951i	−0.0625885	−	0.0361355i
$877$	13.6341	−	7.87163i	0.460390	−	0.265806i	−0.251818	−	0.967774i	$-0.581029\pi$
$877$	13.6341	−	7.87163i	0.460390	−	0.265806i	0.712208	+	0.701968i	$0.247695\pi$
$878$	18.0950	+	10.4471i	0.610676	+	0.352574i
$879$	17.3263			0.584401
$880$			3.95462i			0.133310i
$881$			17.0246i			0.573575i	0.957994	+	0.286787i	$0.0925873\pi$
$881$			17.0246i			0.573575i	−0.957994	+	0.286787i	$0.907413\pi$
$882$	5.76805	+	3.96605i	0.194220	+	0.133544i
$883$	1.18000	+	2.04382i	0.0397102	+	0.0687801i	0.885197	−	0.465216i	$-0.154023\pi$
$883$	1.18000	+	2.04382i	0.0397102	+	0.0687801i	−0.845487	+	0.533996i	$0.820690\pi$
$884$			27.7821i			0.934415i
$885$	−33.5944	+	19.3957i	−1.12926	+	0.651980i
$886$	9.03634	−	5.21714i	0.303582	−	0.175273i
$887$	43.1515			1.44889			0.724443	−	0.689335i	$-0.242097\pi$
$887$	43.1515			1.44889			0.724443	+	0.689335i	$0.242097\pi$
$888$	4.93889	−	8.55440i	0.165738	−	0.287067i
$889$	0.557181	−	14.1434i	0.0186873	−	0.474354i
$890$	1.47024	−	2.54653i	0.0492825	−	0.0853599i
$891$	−0.485128	−	0.840267i	−0.0162524	−	0.0281500i
$892$	9.83556	+	17.0357i	0.329319	+	0.570397i
$893$	11.5782	−	0.790526i	0.387450	−	0.0264539i
$894$	11.2863	+	6.51615i	0.377471	+	0.217933i
$895$	12.9337	−	22.4019i	0.432327	−	0.748812i
$896$	−0.104149	+	2.64370i	−0.00347937	+	0.0883198i
$897$	4.66555	+	8.08097i	0.155778	+	0.269816i
$898$	−9.87663	−	17.1068i	−0.329587	−	0.570862i
$899$	3.10161	+	1.79071i	0.103444	+	0.0597236i
$900$	−5.80626	−	10.0567i	−0.193542	−	0.335225i
$901$	−40.3287	+	69.8514i	−1.34354	+	2.32709i
$902$	8.61589	−	4.97439i	0.286878	−	0.165629i
$903$	11.8267	+	22.4846i	0.393568	+	0.748240i
$904$	−10.2155			−0.339763
$905$	51.2297	+	29.5775i	1.70293	+	0.983189i
$906$	7.00028	−	12.1248i	0.232569	−	0.402821i
$907$			53.7052i			1.78325i	0.452774	+	0.891625i	$0.350434\pi$
$907$			53.7052i			1.78325i	−0.452774	+	0.891625i	$0.649566\pi$
$908$	−8.94084			−0.296712
$909$	3.22004	+	1.85909i	0.106802	+	0.0616622i
$910$	21.3534	−	33.8353i	0.707859	−	1.12163i
$911$			20.9585i			0.694385i	0.937794	+	0.347193i	$0.112865\pi$
$911$			20.9585i			0.694385i	−0.937794	+	0.347193i	$0.887135\pi$
$912$	3.61769	−	2.43153i	0.119794	−	0.0805160i
$913$	14.3383	−	8.27820i	0.474527	−	0.273968i
$914$		−	8.11555i		−	0.268438i
$915$	−28.0750	−	48.6274i	−0.928132	−	1.60757i
$916$	7.36441	−	4.25184i	0.243327	−	0.140485i
$917$	−0.177047	+	4.49413i	−0.00584661	+	0.148409i
$918$	−3.74399	−	6.48478i	−0.123570	−	0.214030i
$919$	19.3534	−	33.5211i	0.638411	−	1.10576i	−0.347370	−	0.937728i	$-0.612925\pi$
$919$	19.3534	−	33.5211i	0.638411	−	1.10576i	0.985781	−	0.168033i	$-0.0537414\pi$
$920$	5.12531	+	8.87729i	0.168976	+	0.292676i
$921$	10.4330	−	18.0706i	0.343781	−	0.595446i
$922$	−33.5583			−1.10518
$923$		−	1.84548i		−	0.0607448i
$924$	1.37005	−	2.17089i	0.0450712	−	0.0714170i
$925$	−99.3382	+	57.3529i	−3.26622	+	1.88575i
$926$	−12.8936	+	7.44414i	−0.423711	+	0.244630i
$927$	1.12602	−	1.95033i	0.0369835	−	0.0640572i
$928$	2.76284			0.0906948
$929$	30.5654	−	17.6469i	1.00282	−	0.578977i	0.0937365	−	0.995597i	$-0.470119\pi$
$929$	30.5654	−	17.6469i	1.00282	−	0.578977i	0.909081	+	0.416620i	$0.136786\pi$
$930$	−5.28345			−0.173251
$931$	26.5843	−	14.9758i	0.871266	−	0.490811i
$932$	0.470178			0.0154012
$933$	18.1423	−	10.4745i	0.593952	−	0.342918i
$934$	−8.91181			−0.291603
$935$	14.8061	−	25.6448i	0.484210	−	0.838676i
$936$	−3.21315	+	1.85511i	−0.105025	+	0.0606363i
$937$	−0.638730	+	0.368771i	−0.0208664	+	0.0120472i	−0.510397	−	0.859939i	$-0.670502\pi$
$937$	−0.638730	+	0.368771i	−0.0208664	+	0.0120472i	0.489531	+	0.871986i	$0.337168\pi$
$938$	−10.0592	+	15.9392i	−0.328445	+	0.520433i
$939$		−	6.93607i		−	0.226350i
$940$	−10.8516			−0.353939
$941$	−11.9616	+	20.7180i	−0.389936	+	0.675389i	−0.992441	−	0.122727i	$-0.960836\pi$
$941$	−11.9616	+	20.7180i	−0.389936	+	0.675389i	0.602505	+	0.798115i	$0.294169\pi$
$942$	3.97686	+	6.88812i	0.129573	+	0.224427i
$943$	12.8939	−	22.3329i	0.419884	−	0.727260i
$944$	4.75870	+	8.24231i	0.154882	+	0.268264i
$945$	−0.424495	+	10.7753i	−0.0138088	+	0.350521i
$946$	8.06849	−	4.65834i	0.262329	−	0.151456i
$947$	−6.89884	−	11.9491i	−0.224182	−	0.388295i	0.731892	−	0.681421i	$-0.238638\pi$
$947$	−6.89884	−	11.9491i	−0.224182	−	0.388295i	−0.956074	+	0.293126i	$0.905304\pi$
$948$			11.4685i			0.372480i
$949$	6.87302	−	3.96814i	0.223108	−	0.128811i
$950$	−50.5002	+	3.44801i	−1.63844	+	0.111868i
$951$		−	9.39350i		−	0.304605i
$952$	10.5734	−	16.7539i	0.342685	−	0.542997i
$953$	−20.2313	−	11.6806i	−0.655357	−	0.378370i	0.135149	−	0.990825i	$-0.456849\pi$
$953$	−20.2313	−	11.6806i	−0.655357	−	0.378370i	−0.790506	+	0.612455i	$0.790182\pi$
$954$	−10.7716			−0.348743
$955$			27.8219i			0.900295i
$956$	−6.17093	+	10.6884i	−0.199582	+	0.345687i
$957$	−2.32153	−	1.34033i	−0.0750443	−	0.0433269i
$958$	−17.7340			−0.572961
$959$	2.73077	+	5.19165i	0.0881810	+	0.167647i
$960$	−3.52979	+	2.03792i	−0.113923	+	0.0657737i
$961$	14.6598	−	25.3916i	0.472898	−	0.819083i
$962$	18.3244	+	31.7388i	0.590802	+	1.02330i
$963$	−5.70984	−	3.29658i	−0.183997	−	0.106231i
$964$	8.42418	+	14.5911i	0.271325	+	0.469948i
$965$	26.9998	+	46.7650i	0.869153	+	1.50542i
$966$	0.261931	−	6.64882i	0.00842750	−	0.213922i
$967$	−8.02350	+	13.8971i	−0.258018	+	0.446901i	−0.965711	−	0.259620i	$-0.916403\pi$
$967$	−8.02350	+	13.8971i	−0.258018	+	0.446901i	0.707693	+	0.706520i	$0.249736\pi$
$968$	8.71100	+	5.02930i	0.279982	+	0.161648i
$969$	−32.5636	+	2.22334i	−1.04609	+	0.0714241i
$970$	−31.9786	−	55.3886i	−1.02677	−	1.77842i
$971$	8.79358	+	15.2309i	0.282199	+	0.488784i	0.971926	−	0.235286i	$-0.0756027\pi$
$971$	8.79358	+	15.2309i	0.282199	+	0.488784i	−0.689727	+	0.724070i	$0.742269\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	1.64646	−	41.7935i	0.0527831	−	1.33984i
$974$	−7.08040	+	12.2636i	−0.226871	+	0.392952i
$975$	43.0851			1.37983
$976$	−11.9306	+	6.88815i	−0.381890	+	0.220484i
$977$	−40.7937	+	23.5523i	−1.30511	+	0.753503i	−0.981275	−	0.192611i	$-0.938304\pi$
$977$	−40.7937	+	23.5523i	−1.30511	+	0.753503i	−0.323831	+	0.946115i	$0.604971\pi$
$978$			21.6399i			0.691968i
$979$	0.349991	+	0.606202i	0.0111858	+	0.0193743i
$980$	−25.7542	+	12.2775i	−0.822687	+	0.392190i
$981$		−	7.79600i		−	0.248907i
$982$			11.6549i			0.371924i
$983$	−32.0560			−1.02243			−0.511214	−	0.859454i	$-0.670804\pi$
$983$	−32.0560			−1.02243			−0.511214	+	0.859454i	$0.670804\pi$
$984$	8.88001	+	5.12688i	0.283084	+	0.163439i
$985$	−24.1795	+	13.9600i	−0.770423	+	0.444804i
$986$	−17.9165	−	10.3441i	−0.570576	−	0.329422i
$987$	5.95697	+	3.75944i	0.189612	+	0.119664i
$988$	1.10165	+	16.1350i	0.0350481	+	0.513321i
$989$	12.0747	−	20.9140i	0.383954	−	0.665027i
$990$	3.95462			0.125686
$991$			4.40607i			0.139963i	0.997548	+	0.0699817i	$0.0222941\pi$
$991$			4.40607i			0.139963i	−0.997548	+	0.0699817i	$0.977706\pi$
$992$			1.29628i			0.0411570i
$993$	−16.7710	−	9.68272i	−0.532211	−	0.307272i
$994$	−0.702357	+	1.11291i	−0.0222774	+	0.0352993i
$995$	34.5416			1.09504
$996$	14.7778	+	8.53197i	0.468252	+	0.270346i
$997$	8.62982	+	4.98243i	0.273309	+	0.157795i	0.630391	−	0.776278i	$-0.282895\pi$
$997$	8.62982	+	4.98243i	0.273309	+	0.157795i	−0.357081	+	0.934073i	$0.616228\pi$
$998$	6.25506	+	3.61136i	0.198000	+	0.114316i
$999$	−8.55440	−	4.93889i	−0.270649	−	0.156259i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.bc.b.103.7	yes	28
7.3	odd	6		798.2.m.b.787.1	yes	28
19.12	odd	6		798.2.m.b.145.14	✓	28
133.31	even	6	inner	798.2.bc.b.31.7	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.m.b.145.14	✓	28	19.12	odd	6
798.2.m.b.787.1	yes	28	7.3	odd	6
798.2.bc.b.31.7	yes	28	133.31	even	6	inner
798.2.bc.b.103.7	yes	28	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +1.00000 q^{3} +(0.500000 - 0.866025i) q^{4} +(3.52979 - 2.03792i) q^{5} +(-0.866025 + 0.500000i) q^{6} +(-1.41205 + 2.23744i) q^{7} +1.00000i q^{8} +1.00000 q^{9} +(-2.03792 + 3.52979i) q^{10} +(-0.485128 - 0.840267i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.85511 + 3.21315i) q^{13} +(0.104149 - 2.64370i) q^{14} +(3.52979 - 2.03792i) q^{15} +(-0.500000 - 0.866025i) q^{16} +7.48798i q^{17} +(-0.866025 + 0.500000i) q^{18} +(0.296922 + 4.34877i) q^{19} -4.07585i q^{20} +(-1.41205 + 2.23744i) q^{21} +(0.840267 + 0.485128i) q^{22} +2.51497 q^{23} +1.00000i q^{24} +(5.80626 - 10.0567i) q^{25} +(-3.21315 - 1.85511i) q^{26} +1.00000 q^{27} +(1.23165 + 2.34159i) q^{28} +(2.39269 - 1.38142i) q^{29} +(-2.03792 + 3.52979i) q^{30} +(0.648141 + 1.12261i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-0.485128 - 0.840267i) q^{33} +(-3.74399 - 6.48478i) q^{34} +(-0.424495 + 10.7753i) q^{35} +(0.500000 - 0.866025i) q^{36} +(-8.55440 - 4.93889i) q^{37} +(-2.43153 - 3.61769i) q^{38} +(1.85511 + 3.21315i) q^{39} +(2.03792 + 3.52979i) q^{40} +(5.12688 - 8.88001i) q^{41} +(0.104149 - 2.64370i) q^{42} +(4.80115 - 8.31583i) q^{43} -0.970257 q^{44} +(3.52979 - 2.03792i) q^{45} +(-2.17802 + 1.25748i) q^{46} -2.66241i q^{47} +(-0.500000 - 0.866025i) q^{48} +(-3.01225 - 6.31873i) q^{49} +11.6125i q^{50} +7.48798i q^{51} +3.71023 q^{52} +(9.32846 + 5.38579i) q^{53} +(-0.866025 + 0.500000i) q^{54} +(-3.42480 - 1.97731i) q^{55} +(-2.23744 - 1.41205i) q^{56} +(0.296922 + 4.34877i) q^{57} +(-1.38142 + 2.39269i) q^{58} -9.51740 q^{59} -4.07585i q^{60} -13.7763i q^{61} +(-1.12261 - 0.648141i) q^{62} +(-1.41205 + 2.23744i) q^{63} -1.00000 q^{64} +(13.0963 + 7.56116i) q^{65} +(0.840267 + 0.485128i) q^{66} +(-6.16944 - 3.56193i) q^{67} +(6.48478 + 3.74399i) q^{68} +2.51497 q^{69} +(-5.02004 - 9.54395i) q^{70} +(-0.430764 - 0.248702i) q^{71} +1.00000i q^{72} -2.13903i q^{73} +9.87777 q^{74} +(5.80626 - 10.0567i) q^{75} +(3.91461 + 1.91725i) q^{76} +(2.56507 + 0.101051i) q^{77} +(-3.21315 - 1.85511i) q^{78} +(-9.93203 + 5.73426i) q^{79} +(-3.52979 - 2.03792i) q^{80} +1.00000 q^{81} +10.2538i q^{82} +17.0639i q^{83} +(1.23165 + 2.34159i) q^{84} +(15.2599 + 26.4310i) q^{85} +9.60229i q^{86} +(2.39269 - 1.38142i) q^{87} +(0.840267 - 0.485128i) q^{88} -0.721440 q^{89} +(-2.03792 + 3.52979i) q^{90} +(-9.80874 - 0.386417i) q^{91} +(1.25748 - 2.17802i) q^{92} +(0.648141 + 1.12261i) q^{93} +(1.33120 + 2.30571i) q^{94} +(9.91054 + 14.7451i) q^{95} +(0.866025 + 0.500000i) q^{96} +(-7.84588 + 13.5895i) q^{97} +(5.76805 + 3.96605i) q^{98} +(-0.485128 - 0.840267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} + 14 q^{4} + 6 q^{5} - 8 q^{7} + 28 q^{9} + 2 q^{10} + 14 q^{12} + 2 q^{13} - 8 q^{14} + 6 q^{15} - 14 q^{16} + 12 q^{19} - 8 q^{21} - 12 q^{22} + 24 q^{23} + 14 q^{25} + 24 q^{26} + 28 q^{27}+ \cdots + 28 q^{98}+O(q^{100}) \) 28 * q + 28 * q^3 + 14 * q^4 + 6 * q^5 - 8 * q^7 + 28 * q^9 + 2 * q^10 + 14 * q^12 + 2 * q^13 - 8 * q^14 + 6 * q^15 - 14 * q^16 + 12 * q^19 - 8 * q^21 - 12 * q^22 + 24 * q^23 + 14 * q^25 + 24 * q^26 + 28 * q^27 + 2 * q^28 + 18 * q^29 + 2 * q^30 + 4 * q^31 - 4 * q^34 - 10 * q^35 + 14 * q^36 - 24 * q^37 - 6 * q^38 + 2 * q^39 - 2 * q^40 + 4 * q^41 - 8 * q^42 - 14 * q^43 + 6 * q^45 - 12 * q^46 - 14 * q^48 - 24 * q^49 + 4 * q^52 + 24 * q^53 + 18 * q^55 - 4 * q^56 + 12 * q^57 - 2 * q^58 + 44 * q^59 - 12 * q^62 - 8 * q^63 - 28 * q^64 - 24 * q^65 - 12 * q^66 - 18 * q^67 + 6 * q^68 + 24 * q^69 + 6 * q^70 - 6 * q^71 + 12 * q^74 + 14 * q^75 + 40 * q^77 + 24 * q^78 - 24 * q^79 - 6 * q^80 + 28 * q^81 + 2 * q^84 + 28 * q^85 + 18 * q^87 - 12 * q^88 + 16 * q^89 + 2 * q^90 - 20 * q^91 + 12 * q^92 + 4 * q^93 - 18 * q^94 + 26 * q^95 - 40 * q^97 + 28 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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