LMFDB - Embedded newform 798.2.k.l.505.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(463,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

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

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.463"); S:= CuspForms(chi, 2); N := Newforms(S);

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

Newform invariants

comment:select newform

sage:traces = [4,2,2,-2,-6,-2,-4,-4,-2,6,6,-4,1,-2,6,-2,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			505.1
Root			$2.38600 - 4.13267i$ of defining polynomial
Character	$\chi$	$=$	798.505
Dual form			798.2.k.l.463.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{10} -2.77200 q^{11} -1.00000 q^{12} +(-1.88600 - 3.26665i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.38600 + 4.13267i) q^{17} -1.00000 q^{18} +(-4.27200 - 0.866025i) q^{19} +3.00000 q^{20} +(-0.500000 + 0.866025i) q^{21} +(-1.38600 + 2.40062i) q^{22} +(2.88600 + 4.99870i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} -3.77200 q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +3.00000 q^{30} -7.54400 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.38600 + 2.40062i) q^{33} +(2.38600 + 4.13267i) q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.22800 q^{37} +(-2.88600 + 3.26665i) q^{38} -3.77200 q^{39} +(1.50000 - 2.59808i) q^{40} +(0.613999 - 1.06348i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-3.00000 + 5.19615i) q^{43} +(1.38600 + 2.40062i) q^{44} +3.00000 q^{45} +5.77200 q^{46} +(-5.77200 - 9.99740i) q^{47} +(0.500000 + 0.866025i) q^{48} +1.00000 q^{49} -4.00000 q^{50} +(2.38600 + 4.13267i) q^{51} +(-1.88600 + 3.26665i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.15800 - 7.20187i) q^{55} +1.00000 q^{56} +(-2.88600 + 3.26665i) q^{57} +(-0.113999 + 0.197452i) q^{59} +(1.50000 - 2.59808i) q^{60} +(3.11400 + 5.39360i) q^{61} +(-3.77200 + 6.53330i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +11.3160 q^{65} +(1.38600 + 2.40062i) q^{66} +4.77200 q^{68} +5.77200 q^{69} +(-1.50000 - 2.59808i) q^{70} +(6.88600 - 11.9269i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-0.613999 + 1.06348i) q^{74} -4.00000 q^{75} +(1.38600 + 4.13267i) q^{76} +2.77200 q^{77} +(-1.88600 + 3.26665i) q^{78} +(4.00000 - 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.613999 - 1.06348i) q^{82} -6.22800 q^{83} +1.00000 q^{84} +(-7.15800 - 12.3980i) q^{85} +(3.00000 + 5.19615i) q^{86} +2.77200 q^{88} +(8.15800 + 14.1301i) q^{89} +(1.50000 - 2.59808i) q^{90} +(1.88600 + 3.26665i) q^{91} +(2.88600 - 4.99870i) q^{92} +(-3.77200 + 6.53330i) q^{93} -11.5440 q^{94} +(8.65800 - 9.79995i) q^{95} +1.00000 q^{96} +(5.77200 - 9.99740i) q^{97} +(0.500000 - 0.866025i) q^{98} +(1.38600 + 2.40062i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9} + 6 q^{10} + 6 q^{11} - 4 q^{12} + q^{13} - 2 q^{14} + 6 q^{15} - 2 q^{16} - q^{17} - 4 q^{18} + 12 q^{20} - 2 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9 + 6 * q^10 + 6 * q^11 - 4 * q^12 + q^13 - 2 * q^14 + 6 * q^15 - 2 * q^16 - q^17 - 4 * q^18 + 12 * q^20 - 2 * q^21 + 3 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 2 * q^26 - 4 * q^27 + 2 * q^28 + 12 * q^30 + 4 * q^31 + 2 * q^32 + 3 * q^33 + q^34 + 6 * q^35 - 2 * q^36 - 22 * q^37 - 3 * q^38 + 2 * q^39 + 6 * q^40 + 11 * q^41 + 2 * q^42 - 12 * q^43 - 3 * q^44 + 12 * q^45 + 6 * q^46 - 6 * q^47 + 2 * q^48 + 4 * q^49 - 16 * q^50 + q^51 + q^52 + 8 * q^53 - 2 * q^54 - 9 * q^55 + 4 * q^56 - 3 * q^57 - 9 * q^59 + 6 * q^60 + 21 * q^61 + 2 * q^62 + 2 * q^63 + 4 * q^64 - 6 * q^65 - 3 * q^66 + 2 * q^68 + 6 * q^69 - 6 * q^70 + 19 * q^71 + 2 * q^72 + 4 * q^73 - 11 * q^74 - 16 * q^75 - 3 * q^76 - 6 * q^77 + q^78 + 16 * q^79 - 6 * q^80 - 2 * q^81 - 11 * q^82 - 42 * q^83 + 4 * q^84 - 3 * q^85 + 12 * q^86 - 6 * q^88 + 7 * q^89 + 6 * q^90 - q^91 + 3 * q^92 + 2 * q^93 - 12 * q^94 + 9 * q^95 + 4 * q^96 + 6 * q^97 + 2 * q^98 - 3 * q^99

Character values

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

$n$	$115$	$211$	$533$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	0.306851	+	0.951757i	$0.400725\pi$
$5$	−1.50000	+	2.59808i	−0.670820	+	1.16190i	−0.977672	+	0.210138i	$0.932609\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−1.00000			−0.377964
$7$	−1.00000			−0.377964
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	−2.77200			−0.835790			−0.417895	−	0.908495i	$-0.637232\pi$
$11$	−2.77200			−0.835790			−0.417895	+	0.908495i	$0.637232\pi$
$12$	−1.00000			−0.288675
$13$	−1.88600	−	3.26665i	−0.523083	−	0.906006i	−0.999639	−	0.0268618i	$-0.991449\pi$
$13$	−1.88600	−	3.26665i	−0.523083	−	0.906006i	0.476557	−	0.879144i	$-0.341885\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$	1.50000	+	2.59808i	0.387298	+	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.38600	+	4.13267i	−0.578690	+	1.00232i	0.416940	+	0.908934i	$0.363103\pi$
$17$	−2.38600	+	4.13267i	−0.578690	+	1.00232i	−0.995630	+	0.0933867i	$0.970231\pi$
$18$	−1.00000			−0.235702
$19$	−4.27200	−	0.866025i	−0.980064	−	0.198680i
$19$	−4.27200	−	0.866025i	−0.980064	−	0.198680i
$20$	3.00000			0.670820
$21$	−0.500000	+	0.866025i	−0.109109	+	0.188982i
$22$	−1.38600	+	2.40062i	−0.295496	+	0.511815i
$23$	2.88600	+	4.99870i	0.601773	+	1.04230i	0.992553	+	0.121817i	$0.0388721\pi$
$23$	2.88600	+	4.99870i	0.601773	+	1.04230i	−0.390780	+	0.920484i	$0.627795\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−2.00000	−	3.46410i	−0.400000	−	0.692820i
$26$	−3.77200			−0.739750
$27$	−1.00000			−0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$	3.00000			0.547723
$31$	−7.54400			−1.35494			−0.677472	−	0.735549i	$-0.736924\pi$
$31$	−7.54400			−1.35494			−0.677472	+	0.735549i	$0.736924\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−1.38600	+	2.40062i	−0.241272	+	0.417895i
$34$	2.38600	+	4.13267i	0.409196	+	0.708748i
$35$	1.50000	−	2.59808i	0.253546	−	0.439155i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.22800			−0.201882			−0.100941	−	0.994892i	$-0.532185\pi$
$37$	−1.22800			−0.201882			−0.100941	+	0.994892i	$0.532185\pi$
$38$	−2.88600	+	3.26665i	−0.468171	+	0.529921i
$39$	−3.77200			−0.604004
$40$	1.50000	−	2.59808i	0.237171	−	0.410792i
$41$	0.613999	−	1.06348i	0.0958905	−	0.166087i	−0.814089	−	0.580740i	$-0.802763\pi$
$41$	0.613999	−	1.06348i	0.0958905	−	0.166087i	0.909980	+	0.414652i	$0.136097\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	−0.998828	−	0.0484030i	$-0.984587\pi$
$43$	−3.00000	+	5.19615i	−0.457496	+	0.792406i	0.541332	+	0.840809i	$0.317920\pi$
$44$	1.38600	+	2.40062i	0.208948	+	0.361908i
$45$	3.00000			0.447214
$46$	5.77200			0.851035
$47$	−5.77200	−	9.99740i	−0.841933	−	1.45827i	−0.888258	−	0.459344i	$-0.848084\pi$
$47$	−5.77200	−	9.99740i	−0.841933	−	1.45827i	0.0463253	−	0.998926i	$-0.485249\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	1.00000			0.142857
$50$	−4.00000			−0.565685
$51$	2.38600	+	4.13267i	0.334107	+	0.578690i
$52$	−1.88600	+	3.26665i	−0.261541	+	0.453003i
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	0.970065	−	0.242846i	$-0.0780811\pi$
$53$	2.00000	+	3.46410i	0.274721	+	0.475831i	−0.695344	+	0.718677i	$0.744748\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	4.15800	−	7.20187i	0.560665	−	0.971100i
$56$	1.00000			0.133631
$57$	−2.88600	+	3.26665i	−0.382260	+	0.432678i
$58$		0			0
$59$	−0.113999	+	0.197452i	−0.0148414	+	0.0257061i	−0.873351	−	0.487092i	$-0.838058\pi$
$59$	−0.113999	+	0.197452i	−0.0148414	+	0.0257061i	0.858509	+	0.512798i	$0.171391\pi$
$60$	1.50000	−	2.59808i	0.193649	−	0.335410i
$61$	3.11400	+	5.39360i	0.398707	+	0.690580i	0.993567	−	0.113249i	$-0.0361258\pi$
$61$	3.11400	+	5.39360i	0.398707	+	0.690580i	−0.594860	+	0.803829i	$0.702792\pi$
$62$	−3.77200	+	6.53330i	−0.479045	+	0.829730i
$63$	0.500000	+	0.866025i	0.0629941	+	0.109109i
$64$	1.00000			0.125000
$65$	11.3160			1.40358
$66$	1.38600	+	2.40062i	0.170605	+	0.295496i
$67$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$67$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$68$	4.77200			0.578690
$69$	5.77200			0.694867
$70$	−1.50000	−	2.59808i	−0.179284	−	0.310530i
$71$	6.88600	−	11.9269i	0.817218	−	1.41546i	−0.0905063	−	0.995896i	$-0.528849\pi$
$71$	6.88600	−	11.9269i	0.817218	−	1.41546i	0.907724	−	0.419567i	$-0.137818\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$	−0.613999	+	1.06348i	−0.0713759	+	0.123627i
$75$	−4.00000			−0.461880
$76$	1.38600	+	4.13267i	0.158985	+	0.474050i
$77$	2.77200			0.315899
$78$	−1.88600	+	3.26665i	−0.213548	+	0.369875i
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−1.50000	−	2.59808i	−0.167705	−	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−0.613999	−	1.06348i	−0.0678049	−	0.117441i
$83$	−6.22800			−0.683612			−0.341806	−	0.939771i	$-0.611039\pi$
$83$	−6.22800			−0.683612			−0.341806	+	0.939771i	$0.611039\pi$
$84$	1.00000			0.109109
$85$	−7.15800	−	12.3980i	−0.776394	−	1.34475i
$86$	3.00000	+	5.19615i	0.323498	+	0.560316i
$87$		0			0
$88$	2.77200			0.295496
$89$	8.15800	+	14.1301i	0.864747	+	1.49778i	0.867299	+	0.497788i	$0.165854\pi$
$89$	8.15800	+	14.1301i	0.864747	+	1.49778i	−0.00255203	+	0.999997i	$0.500812\pi$
$90$	1.50000	−	2.59808i	0.158114	−	0.273861i
$91$	1.88600	+	3.26665i	0.197707	+	0.342438i
$92$	2.88600	−	4.99870i	0.300886	−	0.521151i
$93$	−3.77200	+	6.53330i	−0.391138	+	0.677472i
$94$	−11.5440			−1.19067
$95$	8.65800	−	9.79995i	0.888292	−	1.00545i
$96$	1.00000			0.102062
$97$	5.77200	−	9.99740i	0.586058	−	1.01508i	−0.408685	−	0.912676i	$-0.634012\pi$
$97$	5.77200	−	9.99740i	0.586058	−	1.01508i	0.994743	−	0.102407i	$-0.0326543\pi$
$98$	0.500000	−	0.866025i	0.0505076	−	0.0874818i
$99$	1.38600	+	2.40062i	0.139298	+	0.241272i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−3.61400	−	6.25963i	−0.359606	−	0.622856i	0.628289	−	0.777980i	$-0.283756\pi$
$101$	−3.61400	−	6.25963i	−0.359606	−	0.622856i	−0.987895	+	0.155124i	$0.950422\pi$
$102$	4.77200			0.472499
$103$	−8.31601			−0.819400			−0.409700	−	0.912220i	$-0.634367\pi$
$103$	−8.31601			−0.819400			−0.409700	+	0.912220i	$0.634367\pi$
$104$	1.88600	+	3.26665i	0.184938	+	0.320321i
$105$	−1.50000	−	2.59808i	−0.146385	−	0.253546i
$106$	4.00000			0.388514
$107$	15.5440			1.50270			0.751348	−	0.659906i	$-0.229404\pi$
$107$	15.5440			1.50270			0.751348	+	0.659906i	$0.229404\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	−0.613999	+	1.06348i	−0.0588104	+	0.101863i	−0.893932	−	0.448203i	$-0.852064\pi$
$109$	−0.613999	+	1.06348i	−0.0588104	+	0.101863i	0.835121	+	0.550066i	$0.185397\pi$
$110$	−4.15800	−	7.20187i	−0.396450	−	0.686672i
$111$	−0.613999	+	1.06348i	−0.0582782	+	0.100941i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	1.77200			0.166696			0.0833480	−	0.996521i	$-0.473439\pi$
$113$	1.77200			0.166696			0.0833480	+	0.996521i	$0.473439\pi$
$114$	1.38600	+	4.13267i	0.129811	+	0.387060i
$115$	−17.3160			−1.61473
$116$		0			0
$117$	−1.88600	+	3.26665i	−0.174361	+	0.302002i
$118$	0.113999	+	0.197452i	0.0104945	+	0.0181769i
$119$	2.38600	−	4.13267i	0.218724	−	0.378842i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	−3.31601			−0.301455
$122$	6.22800			0.563856
$123$	−0.613999	−	1.06348i	−0.0553624	−	0.0958905i
$124$	3.77200	+	6.53330i	0.338736	+	0.586708i
$125$	−3.00000			−0.268328
$126$	1.00000			0.0890871
$127$	−3.88600	−	6.73075i	−0.344827	−	0.597258i	0.640495	−	0.767962i	$-0.278729\pi$
$127$	−3.88600	−	6.73075i	−0.344827	−	0.597258i	−0.985322	+	0.170704i	$0.945396\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	3.00000	+	5.19615i	0.264135	+	0.457496i
$130$	5.65800	−	9.79995i	0.496240	−	0.859512i
$131$	−8.65800	+	14.9961i	−0.756453	+	1.31022i	0.188195	+	0.982132i	$0.439736\pi$
$131$	−8.65800	+	14.9961i	−0.756453	+	1.31022i	−0.944649	+	0.328084i	$0.893597\pi$
$132$	2.77200			0.241272
$133$	4.27200	+	0.866025i	0.370430	+	0.0750939i
$134$		0			0
$135$	1.50000	−	2.59808i	0.129099	−	0.223607i
$136$	2.38600	−	4.13267i	0.204598	−	0.354374i
$137$	1.88600	+	3.26665i	0.161132	+	0.279089i	0.935275	−	0.353922i	$-0.115152\pi$
$137$	1.88600	+	3.26665i	0.161132	+	0.279089i	−0.774143	+	0.633011i	$0.781819\pi$
$138$	2.88600	−	4.99870i	0.245673	−	0.425518i
$139$	−8.15800	−	14.1301i	−0.691953	−	1.19850i	−0.971197	−	0.238277i	$-0.923417\pi$
$139$	−8.15800	−	14.1301i	−0.691953	−	1.19850i	0.279244	−	0.960220i	$-0.409916\pi$
$140$	−3.00000			−0.253546
$141$	−11.5440			−0.972180
$142$	−6.88600	−	11.9269i	−0.577860	−	1.00088i
$143$	5.22800	+	9.05516i	0.437187	+	0.757230i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$	0.500000	−	0.866025i	0.0412393	−	0.0714286i
$148$	0.613999	+	1.06348i	0.0504704	+	0.0874173i
$149$	1.22800	−	2.12696i	0.100602	−	0.174247i	−0.811331	−	0.584587i	$-0.801257\pi$
$149$	1.22800	−	2.12696i	0.100602	−	0.174247i	0.911933	+	0.410340i	$0.134590\pi$
$150$	−2.00000	+	3.46410i	−0.163299	+	0.282843i
$151$	−10.2280			−0.832343			−0.416171	−	0.909286i	$-0.636628\pi$
$151$	−10.2280			−0.832343			−0.416171	+	0.909286i	$0.636628\pi$
$152$	4.27200	+	0.866025i	0.346505	+	0.0702439i
$153$	4.77200			0.385793
$154$	1.38600	−	2.40062i	0.111687	−	0.193448i
$155$	11.3160	−	19.5999i	0.908923	−	1.57430i
$156$	1.88600	+	3.26665i	0.151001	+	0.261541i
$157$	−7.88600	+	13.6590i	−0.629371	+	1.09010i	0.358307	+	0.933604i	$0.383354\pi$
$157$	−7.88600	+	13.6590i	−0.629371	+	1.09010i	−0.987678	+	0.156499i	$0.949979\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	4.00000			0.317221
$160$	−3.00000			−0.237171
$161$	−2.88600	−	4.99870i	−0.227449	−	0.393953i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	−1.22800			−0.0958905
$165$	−4.15800	−	7.20187i	−0.323700	−	0.560665i
$166$	−3.11400	+	5.39360i	−0.241693	+	0.418625i
$167$	3.00000	+	5.19615i	0.232147	+	0.402090i	0.958440	−	0.285295i	$-0.0920916\pi$
$167$	3.00000	+	5.19615i	0.232147	+	0.402090i	−0.726293	+	0.687386i	$0.758758\pi$
$168$	0.500000	−	0.866025i	0.0385758	−	0.0668153i
$169$	−0.613999	+	1.06348i	−0.0472307	+	0.0818060i
$170$	−14.3160			−1.09799
$171$	1.38600	+	4.13267i	0.105990	+	0.316034i
$172$	6.00000			0.457496
$173$	−1.88600	+	3.26665i	−0.143390	+	0.248359i	−0.928771	−	0.370654i	$-0.879134\pi$
$173$	−1.88600	+	3.26665i	−0.143390	+	0.248359i	0.785381	+	0.619013i	$0.212467\pi$
$174$		0			0
$175$	2.00000	+	3.46410i	0.151186	+	0.261861i
$176$	1.38600	−	2.40062i	0.104474	−	0.180954i
$177$	0.113999	+	0.197452i	0.00856869	+	0.0148414i
$178$	16.3160			1.22294
$179$	−7.22800			−0.540246			−0.270123	−	0.962826i	$-0.587064\pi$
$179$	−7.22800			−0.540246			−0.270123	+	0.962826i	$0.587064\pi$
$180$	−1.50000	−	2.59808i	−0.111803	−	0.193649i
$181$	−8.65800	−	14.9961i	−0.643544	−	1.11465i	−0.984636	−	0.174621i	$-0.944130\pi$
$181$	−8.65800	−	14.9961i	−0.643544	−	1.11465i	0.341091	−	0.940030i	$-0.389203\pi$
$182$	3.77200			0.279599
$183$	6.22800			0.460387
$184$	−2.88600	−	4.99870i	−0.212759	−	0.368509i
$185$	1.84200	−	3.19043i	0.135426	−	0.234565i
$186$	3.77200	+	6.53330i	0.276577	+	0.479045i
$187$	6.61400	−	11.4558i	0.483664	−	0.837730i
$188$	−5.77200	+	9.99740i	−0.420967	+	0.729135i
$189$	1.00000			0.0727393
$190$	−4.15800	−	12.3980i	−0.301653	−	0.899447i
$191$	−17.7720			−1.28594			−0.642968	−	0.765893i	$-0.722297\pi$
$191$	−17.7720			−1.28594			−0.642968	+	0.765893i	$0.722297\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	2.72800	−	4.72503i	0.196366	−	0.340115i	−0.750982	−	0.660323i	$-0.770419\pi$
$193$	2.72800	−	4.72503i	0.196366	−	0.340115i	0.947347	+	0.320208i	$0.103753\pi$
$194$	−5.77200	−	9.99740i	−0.414406	−	0.717772i
$195$	5.65800	−	9.79995i	0.405178	−	0.701789i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	−8.00000			−0.569976			−0.284988	−	0.958531i	$-0.591990\pi$
$197$	−8.00000			−0.569976			−0.284988	+	0.958531i	$0.591990\pi$
$198$	2.77200			0.196998
$199$	13.3160	+	23.0640i	0.943947	+	1.63496i	0.757847	+	0.652433i	$0.226251\pi$
$199$	13.3160	+	23.0640i	0.943947	+	1.63496i	0.186100	+	0.982531i	$0.440415\pi$
$200$	2.00000	+	3.46410i	0.141421	+	0.244949i
$201$		0			0
$202$	−7.22800			−0.508560
$203$		0			0
$204$	2.38600	−	4.13267i	0.167053	−	0.289345i
$205$	1.84200	+	3.19043i	0.128651	+	0.222829i
$206$	−4.15800	+	7.20187i	−0.289702	+	0.501778i
$207$	2.88600	−	4.99870i	0.200591	−	0.347434i
$208$	3.77200			0.261541
$209$	11.8420	+	2.40062i	0.819128	+	0.166055i
$210$	−3.00000			−0.207020
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	−0.926620	−	0.375999i	$-0.877300\pi$
$211$	−2.00000	+	3.46410i	−0.137686	+	0.238479i	0.788935	+	0.614477i	$0.210633\pi$
$212$	2.00000	−	3.46410i	0.137361	−	0.237915i
$213$	−6.88600	−	11.9269i	−0.471821	−	0.817218i
$214$	7.77200	−	13.4615i	0.531283	−	0.920209i
$215$	−9.00000	−	15.5885i	−0.613795	−	1.06312i
$216$	1.00000			0.0680414
$217$	7.54400			0.512120
$218$	0.613999	+	1.06348i	0.0415853	+	0.0720278i
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$	−8.31601			−0.560665
$221$	18.0000			1.21081
$222$	0.613999	+	1.06348i	0.0412089	+	0.0713759i
$223$	13.9300	−	24.1275i	0.932822	−	1.61570i	0.154350	−	0.988016i	$-0.450672\pi$
$223$	13.9300	−	24.1275i	0.932822	−	1.61570i	0.778472	−	0.627679i	$-0.215995\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−2.00000	+	3.46410i	−0.133333	+	0.230940i
$226$	0.886001	−	1.53460i	0.0589359	−	0.102080i
$227$	5.77200			0.383101			0.191551	−	0.981483i	$-0.438648\pi$
$227$	5.77200			0.383101			0.191551	+	0.981483i	$0.438648\pi$
$228$	4.27200	+	0.866025i	0.282920	+	0.0573539i
$229$	−2.68399			−0.177363			−0.0886817	−	0.996060i	$-0.528265\pi$
$229$	−2.68399			−0.177363			−0.0886817	+	0.996060i	$0.528265\pi$
$230$	−8.65800	+	14.9961i	−0.570892	+	0.988814i
$231$	1.38600	−	2.40062i	0.0911922	−	0.157949i
$232$		0			0
$233$	−14.6580	+	25.3884i	−0.960278	+	1.66325i	−0.238478	+	0.971148i	$0.576648\pi$
$233$	−14.6580	+	25.3884i	−0.960278	+	1.66325i	−0.721800	+	0.692102i	$0.756685\pi$
$234$	1.88600	+	3.26665i	0.123292	+	0.213548i
$235$	34.6320			2.25914
$236$	0.227998			0.0148414
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	−2.38600	−	4.13267i	−0.154661	−	0.267882i
$239$	18.0880			1.17002			0.585008	−	0.811028i	$-0.301091\pi$
$239$	18.0880			1.17002			0.585008	+	0.811028i	$0.301091\pi$
$240$	−3.00000			−0.193649
$241$	7.77200	+	13.4615i	0.500639	+	0.867132i	1.00000		0.000737607i	$0.000234788\pi$
$241$	7.77200	+	13.4615i	0.500639	+	0.867132i	−0.499361	+	0.866394i	$0.666432\pi$
$242$	−1.65800	+	2.87175i	−0.106580	+	0.184603i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	3.11400	−	5.39360i	0.199353	−	0.345290i
$245$	−1.50000	+	2.59808i	−0.0958315	+	0.165985i
$246$	−1.22800			−0.0782943
$247$	5.22800	+	15.5885i	0.332650	+	0.991870i
$248$	7.54400			0.479045
$249$	−3.11400	+	5.39360i	−0.197342	+	0.341806i
$250$	−1.50000	+	2.59808i	−0.0948683	+	0.164317i
$251$	7.88600	+	13.6590i	0.497760	+	0.862146i	0.999997	−	0.00258464i	$-0.000822718\pi$
$251$	7.88600	+	13.6590i	0.497760	+	0.862146i	−0.502237	+	0.864730i	$0.667489\pi$
$252$	0.500000	−	0.866025i	0.0314970	−	0.0545545i
$253$	−8.00000	−	13.8564i	−0.502956	−	0.871145i
$254$	−7.77200			−0.487659
$255$	−14.3160			−0.896503
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.1580	+	17.5942i	0.633639	+	1.09749i	0.986802	+	0.161933i	$0.0517728\pi$
$257$	10.1580	+	17.5942i	0.633639	+	1.09749i	−0.353163	+	0.935562i	$0.614894\pi$
$258$	6.00000			0.373544
$259$	1.22800			0.0763041
$260$	−5.65800	−	9.79995i	−0.350894	−	0.607767i
$261$		0			0
$262$	8.65800	+	14.9961i	0.534893	+	0.926462i
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	−0.536614	−	0.843828i	$-0.680297\pi$
$263$	7.50000	−	12.9904i	0.462470	−	0.801021i	0.999083	+	0.0428069i	$0.0136300\pi$
$264$	1.38600	−	2.40062i	0.0853025	−	0.147748i
$265$	−12.0000			−0.737154
$266$	2.88600	−	3.26665i	0.176952	−	0.200291i
$267$	16.3160			0.998523
$268$		0			0
$269$	−10.3860	+	17.9891i	−0.633246	+	1.09681i	0.353638	+	0.935382i	$0.384944\pi$
$269$	−10.3860	+	17.9891i	−0.633246	+	1.09681i	−0.986884	+	0.161431i	$0.948389\pi$
$270$	−1.50000	−	2.59808i	−0.0912871	−	0.158114i
$271$	−9.61400	+	16.6519i	−0.584009	+	1.01153i	0.410989	+	0.911640i	$0.365183\pi$
$271$	−9.61400	+	16.6519i	−0.584009	+	1.01153i	−0.994998	+	0.0998929i	$0.968150\pi$
$272$	−2.38600	−	4.13267i	−0.144673	−	0.250580i
$273$	3.77200			0.228292
$274$	3.77200			0.227875
$275$	5.54400	+	9.60250i	0.334316	+	0.579052i
$276$	−2.88600	−	4.99870i	−0.173717	−	0.300886i
$277$	18.3160			1.10050			0.550251	−	0.834999i	$-0.314532\pi$
$277$	18.3160			1.10050			0.550251	+	0.834999i	$0.314532\pi$
$278$	−16.3160			−0.978569
$279$	3.77200	+	6.53330i	0.225824	+	0.391138i
$280$	−1.50000	+	2.59808i	−0.0896421	+	0.155265i
$281$	7.77200	+	13.4615i	0.463639	+	0.803046i	0.999139	−	0.0414892i	$-0.0132102\pi$
$281$	7.77200	+	13.4615i	0.463639	+	0.803046i	−0.535500	+	0.844535i	$0.679877\pi$
$282$	−5.77200	+	9.99740i	−0.343718	+	0.595337i
$283$	14.5000	−	25.1147i	0.861936	−	1.49292i	−0.00812260	−	0.999967i	$-0.502586\pi$
$283$	14.5000	−	25.1147i	0.861936	−	1.49292i	0.870058	−	0.492949i	$-0.164081\pi$
$284$	−13.7720			−0.817218
$285$	−4.15800	−	12.3980i	−0.246299	−	0.734396i
$286$	10.4560			0.618276
$287$	−0.613999	+	1.06348i	−0.0362432	+	0.0627751i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−2.88600	−	4.99870i	−0.169765	−	0.294041i
$290$		0			0
$291$	−5.77200	−	9.99740i	−0.338361	−	0.586058i
$292$	−2.00000			−0.117041
$293$	−29.6320			−1.73112			−0.865560	−	0.500805i	$-0.833037\pi$
$293$	−29.6320			−1.73112			−0.865560	+	0.500805i	$0.833037\pi$
$294$	−0.500000	−	0.866025i	−0.0291606	−	0.0505076i
$295$	−0.341997	−	0.592357i	−0.0199118	−	0.0344883i
$296$	1.22800			0.0713759
$297$	2.77200			0.160848
$298$	−1.22800	−	2.12696i	−0.0711360	−	0.123211i
$299$	10.8860	−	18.8551i	0.629554	−	1.09042i
$300$	2.00000	+	3.46410i	0.115470	+	0.200000i
$301$	3.00000	−	5.19615i	0.172917	−	0.299501i
$302$	−5.11400	+	8.85771i	−0.294278	+	0.509704i
$303$	−7.22800			−0.415238
$304$	2.88600	−	3.26665i	0.165524	−	0.187355i
$305$	−18.6840			−1.06984
$306$	2.38600	−	4.13267i	0.136399	−	0.236249i
$307$	−1.11400	+	1.92950i	−0.0635793	+	0.110123i	−0.896063	−	0.443927i	$-0.853585\pi$
$307$	−1.11400	+	1.92950i	−0.0635793	+	0.110123i	0.832484	+	0.554050i	$0.186918\pi$
$308$	−1.38600	−	2.40062i	−0.0789747	−	0.136788i
$309$	−4.15800	+	7.20187i	−0.236541	+	0.409700i
$310$	−11.3160	−	19.5999i	−0.642706	−	1.11320i
$311$	−29.0880			−1.64943			−0.824715	−	0.565549i	$-0.808664\pi$
$311$	−29.0880			−1.64943			−0.824715	+	0.565549i	$0.808664\pi$
$312$	3.77200			0.213548
$313$	−12.0000	−	20.7846i	−0.678280	−	1.17482i	−0.975499	−	0.220006i	$-0.929392\pi$
$313$	−12.0000	−	20.7846i	−0.678280	−	1.17482i	0.297218	−	0.954810i	$-0.403941\pi$
$314$	7.88600	+	13.6590i	0.445033	+	0.770819i
$315$	−3.00000			−0.169031
$316$	−8.00000			−0.450035
$317$	−11.3160	−	19.5999i	−0.635570	−	1.10084i	−0.986394	−	0.164398i	$-0.947432\pi$
$317$	−11.3160	−	19.5999i	−0.635570	−	1.10084i	0.350824	−	0.936441i	$-0.385902\pi$
$318$	2.00000	−	3.46410i	0.112154	−	0.194257i
$319$		0			0
$320$	−1.50000	+	2.59808i	−0.0838525	+	0.145237i
$321$	7.77200	−	13.4615i	0.433791	−	0.751348i
$322$	−5.77200			−0.321661
$323$	13.7720	−	15.5885i	0.766295	−	0.867365i
$324$	1.00000			0.0555556
$325$	−7.54400	+	13.0666i	−0.418466	+	0.724804i
$326$	−5.00000	+	8.66025i	−0.276924	+	0.479647i
$327$	0.613999	+	1.06348i	0.0339542	+	0.0588104i
$328$	−0.613999	+	1.06348i	−0.0339024	+	0.0587207i
$329$	5.77200	+	9.99740i	0.318221	+	0.551175i
$330$	−8.31601			−0.457781
$331$	15.0880			0.829312			0.414656	−	0.909978i	$-0.363902\pi$
$331$	15.0880			0.829312			0.414656	+	0.909978i	$0.363902\pi$
$332$	3.11400	+	5.39360i	0.170903	+	0.296013i
$333$	0.613999	+	1.06348i	0.0336469	+	0.0582782i
$334$	6.00000			0.328305
$335$		0			0
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	−5.88600	+	10.1949i	−0.320631	+	0.555349i	−0.980618	−	0.195928i	$-0.937228\pi$
$337$	−5.88600	+	10.1949i	−0.320631	+	0.555349i	0.659987	+	0.751277i	$0.270562\pi$
$338$	0.613999	+	1.06348i	0.0333971	+	0.0578456i
$339$	0.886001	−	1.53460i	0.0481210	−	0.0833480i
$340$	−7.15800	+	12.3980i	−0.388197	+	0.672377i
$341$	20.9120			1.13245
$342$	4.27200	+	0.866025i	0.231003	+	0.0468293i
$343$	−1.00000			−0.0539949
$344$	3.00000	−	5.19615i	0.161749	−	0.280158i
$345$	−8.65800	+	14.9961i	−0.466131	+	0.807363i
$346$	1.88600	+	3.26665i	0.101392	+	0.175616i
$347$	7.77200	−	13.4615i	0.417223	−	0.722651i	−0.578436	−	0.815728i	$-0.696337\pi$
$347$	7.77200	−	13.4615i	0.417223	−	0.722651i	0.995659	+	0.0930764i	$0.0296701\pi$
$348$		0			0
$349$	−18.6320			−0.997349			−0.498674	−	0.866789i	$-0.666180\pi$
$349$	−18.6320			−0.997349			−0.498674	+	0.866789i	$0.666180\pi$
$350$	4.00000			0.213809
$351$	1.88600	+	3.26665i	0.100667	+	0.174361i
$352$	−1.38600	−	2.40062i	−0.0738741	−	0.127954i
$353$	5.22800			0.278258			0.139129	−	0.990274i	$-0.455570\pi$
$353$	5.22800			0.278258			0.139129	+	0.990274i	$0.455570\pi$
$354$	0.227998			0.0121180
$355$	20.6580	+	35.7807i	1.09641	+	1.89904i
$356$	8.15800	−	14.1301i	0.432373	−	0.748892i
$357$	−2.38600	−	4.13267i	−0.126281	−	0.218724i
$358$	−3.61400	+	6.25963i	−0.191006	+	0.330832i
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$	−3.00000			−0.158114
$361$	17.5000	+	7.39932i	0.921053	+	0.389438i
$362$	−17.3160			−0.910109
$363$	−1.65800	+	2.87175i	−0.0870226	+	0.150728i
$364$	1.88600	−	3.26665i	0.0988533	−	0.171219i
$365$	3.00000	+	5.19615i	0.157027	+	0.271979i
$366$	3.11400	−	5.39360i	0.162771	−	0.281928i
$367$	12.1580	+	21.0583i	0.634643	+	1.09923i	0.986591	+	0.163214i	$0.0521860\pi$
$367$	12.1580	+	21.0583i	0.634643	+	1.09923i	−0.351948	+	0.936019i	$0.614481\pi$
$368$	−5.77200			−0.300886
$369$	−1.22800			−0.0639270
$370$	−1.84200	−	3.19043i	−0.0957609	−	0.165863i
$371$	−2.00000	−	3.46410i	−0.103835	−	0.179847i
$372$	7.54400			0.391138
$373$	−30.3160			−1.56970			−0.784852	−	0.619684i	$-0.787261\pi$
$373$	−30.3160			−1.56970			−0.784852	+	0.619684i	$0.787261\pi$
$374$	−6.61400	−	11.4558i	−0.342002	−	0.592364i
$375$	−1.50000	+	2.59808i	−0.0774597	+	0.134164i
$376$	5.77200	+	9.99740i	0.297668	+	0.515577i
$377$		0			0
$378$	0.500000	−	0.866025i	0.0257172	−	0.0445435i
$379$	0.455996			0.0234230			0.0117115	−	0.999931i	$-0.496272\pi$
$379$	0.455996			0.0234230			0.0117115	+	0.999931i	$0.496272\pi$
$380$	−12.8160	−	2.59808i	−0.657447	−	0.133278i
$381$	−7.77200			−0.398172
$382$	−8.88600	+	15.3910i	−0.454647	+	0.787472i
$383$	−16.0000	+	27.7128i	−0.817562	+	1.41606i	0.0899119	+	0.995950i	$0.471341\pi$
$383$	−16.0000	+	27.7128i	−0.817562	+	1.41606i	−0.907474	+	0.420109i	$0.861992\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−4.15800	+	7.20187i	−0.211911	+	0.367041i
$386$	−2.72800	−	4.72503i	−0.138851	−	0.240498i
$387$	6.00000			0.304997
$388$	−11.5440			−0.586058
$389$	9.54400	+	16.5307i	0.483900	+	0.838140i	0.999829	−	0.0184917i	$-0.00588644\pi$
$389$	9.54400	+	16.5307i	0.483900	+	0.838140i	−0.515929	+	0.856631i	$0.672553\pi$
$390$	−5.65800	−	9.79995i	−0.286504	−	0.496240i
$391$	−27.5440			−1.39296
$392$	−1.00000			−0.0505076
$393$	8.65800	+	14.9961i	0.436738	+	0.756453i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	12.0000	+	20.7846i	0.603786	+	1.04579i
$396$	1.38600	−	2.40062i	0.0696492	−	0.120636i
$397$	−4.54400	+	7.87045i	−0.228057	+	0.395006i	−0.957232	−	0.289321i	$-0.906571\pi$
$397$	−4.54400	+	7.87045i	−0.228057	+	0.395006i	0.729175	+	0.684327i	$0.239904\pi$
$398$	26.6320			1.33494
$399$	2.88600	−	3.26665i	0.144481	−	0.163537i
$400$	4.00000			0.200000
$401$	−19.9740	+	34.5960i	−0.997454	+	1.72764i	−0.436973	+	0.899475i	$0.643950\pi$
$401$	−19.9740	+	34.5960i	−0.997454	+	1.72764i	−0.560481	+	0.828167i	$0.689384\pi$
$402$		0			0
$403$	14.2280	+	24.6436i	0.708747	+	1.22759i
$404$	−3.61400	+	6.25963i	−0.179803	+	0.311428i
$405$	−1.50000	−	2.59808i	−0.0745356	−	0.129099i
$406$		0			0
$407$	3.40401			0.168731
$408$	−2.38600	−	4.13267i	−0.118125	−	0.204598i
$409$	13.5440	+	23.4589i	0.669708	+	1.15997i	0.977986	+	0.208672i	$0.0669140\pi$
$409$	13.5440	+	23.4589i	0.669708	+	1.15997i	−0.308278	+	0.951296i	$0.599753\pi$
$410$	3.68399			0.181940
$411$	3.77200			0.186059
$412$	4.15800	+	7.20187i	0.204850	+	0.354811i
$413$	0.113999	−	0.197452i	0.00560953	−	0.00971599i
$414$	−2.88600	−	4.99870i	−0.141839	−	0.245673i
$415$	9.34200	−	16.1808i	0.458581	−	0.794285i
$416$	1.88600	−	3.26665i	0.0924688	−	0.160161i
$417$	−16.3160			−0.798998
$418$	8.00000	−	9.05516i	0.391293	−	0.442902i
$419$	1.54400			0.0754295			0.0377148	−	0.999289i	$-0.487992\pi$
$419$	1.54400			0.0754295			0.0377148	+	0.999289i	$0.487992\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	−11.3860	+	19.7211i	−0.554920	+	0.961149i	0.442990	+	0.896527i	$0.353918\pi$
$421$	−11.3860	+	19.7211i	−0.554920	+	0.961149i	−0.997910	+	0.0646226i	$0.979416\pi$
$422$	2.00000	+	3.46410i	0.0973585	+	0.168630i
$423$	−5.77200	+	9.99740i	−0.280644	+	0.486090i
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$	19.0880			0.925904
$426$	−13.7720			−0.667256
$427$	−3.11400	−	5.39360i	−0.150697	−	0.261015i
$428$	−7.77200	−	13.4615i	−0.375674	−	0.650686i
$429$	10.4560			0.504820
$430$	−18.0000			−0.868037
$431$	−13.3860	−	23.1852i	−0.644781	−	1.11679i	−0.984352	−	0.176213i	$-0.943615\pi$
$431$	−13.3860	−	23.1852i	−0.644781	−	1.11679i	0.339571	−	0.940580i	$-0.389718\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	6.00000	+	10.3923i	0.288342	+	0.499422i	0.973414	−	0.229053i	$-0.0735628\pi$
$433$	6.00000	+	10.3923i	0.288342	+	0.499422i	−0.685072	+	0.728475i	$0.740229\pi$
$434$	3.77200	−	6.53330i	0.181062	−	0.313608i
$435$		0			0
$436$	1.22800			0.0588104
$437$	−8.00000	−	23.8538i	−0.382692	−	1.14108i
$438$	−2.00000			−0.0955637
$439$	10.3860	−	17.9891i	0.495697	−	0.858572i	−0.504291	−	0.863534i	$-0.668246\pi$
$439$	10.3860	−	17.9891i	0.495697	−	0.858572i	0.999988	+	0.00496182i	$0.00157940\pi$
$440$	−4.15800	+	7.20187i	−0.198225	+	0.343336i
$441$	−0.500000	−	0.866025i	−0.0238095	−	0.0412393i
$442$	9.00000	−	15.5885i	0.428086	−	0.741467i
$443$	15.7720	+	27.3179i	0.749350	+	1.29791i	0.948134	+	0.317870i	$0.102967\pi$
$443$	15.7720	+	27.3179i	0.749350	+	1.29791i	−0.198784	+	0.980043i	$0.563699\pi$
$444$	1.22800			0.0582782
$445$	−48.9480			−2.32036
$446$	−13.9300	−	24.1275i	−0.659605	−	1.14247i
$447$	−1.22800	−	2.12696i	−0.0580823	−	0.100602i
$448$	−1.00000			−0.0472456
$449$	15.7720			0.744327			0.372163	−	0.928167i	$-0.378616\pi$
$449$	15.7720			0.744327			0.372163	+	0.928167i	$0.378616\pi$
$450$	2.00000	+	3.46410i	0.0942809	+	0.163299i
$451$	−1.70201	+	2.94796i	−0.0801444	+	0.138814i
$452$	−0.886001	−	1.53460i	−0.0416740	−	0.0721814i
$453$	−5.11400	+	8.85771i	−0.240277	+	0.416171i
$454$	2.88600	−	4.99870i	0.135447	−	0.234601i
$455$	−11.3160			−0.530503
$456$	2.88600	−	3.26665i	0.135149	−	0.152975i
$457$	−3.91199			−0.182995			−0.0914976	−	0.995805i	$-0.529165\pi$
$457$	−3.91199			−0.182995			−0.0914976	+	0.995805i	$0.529165\pi$
$458$	−1.34200	+	2.32441i	−0.0627074	+	0.108612i
$459$	2.38600	−	4.13267i	0.111369	−	0.192897i
$460$	8.65800	+	14.9961i	0.403681	+	0.699197i
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	−0.951584	−	0.307388i	$-0.900545\pi$
$461$	−4.50000	+	7.79423i	−0.209586	+	0.363013i	0.741998	+	0.670402i	$0.233878\pi$
$462$	−1.38600	−	2.40062i	−0.0644826	−	0.111687i
$463$	36.8600			1.71303			0.856515	−	0.516122i	$-0.172625\pi$
$463$	36.8600			1.71303			0.856515	+	0.516122i	$0.172625\pi$
$464$		0			0
$465$	−11.3160	−	19.5999i	−0.524767	−	0.908923i
$466$	14.6580	+	25.3884i	0.679019	+	1.17610i
$467$	−31.0880			−1.43858			−0.719291	−	0.694709i	$-0.755533\pi$
$467$	−31.0880			−1.43858			−0.719291	+	0.694709i	$0.755533\pi$
$468$	3.77200			0.174361
$469$		0			0
$470$	17.3160	−	29.9922i	0.798728	−	1.38344i
$471$	7.88600	+	13.6590i	0.363368	+	0.629371i
$472$	0.113999	−	0.197452i	0.00524723	−	0.00908847i
$473$	8.31601	−	14.4037i	0.382370	−	0.662285i
$474$	−8.00000			−0.367452
$475$	5.54400	+	16.5307i	0.254376	+	0.758481i
$476$	−4.77200			−0.218724
$477$	2.00000	−	3.46410i	0.0915737	−	0.158610i
$478$	9.04400	−	15.6647i	0.413663	−	0.716486i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$	−1.50000	+	2.59808i	−0.0684653	+	0.118585i
$481$	2.31601	+	4.01144i	0.105601	+	0.182906i
$482$	15.5440			0.708010
$483$	−5.77200			−0.262635
$484$	1.65800	+	2.87175i	0.0753638	+	0.130534i
$485$	17.3160	+	29.9922i	0.786279	+	1.36188i
$486$	1.00000			0.0453609
$487$	−0.911993			−0.0413263			−0.0206632	−	0.999786i	$-0.506578\pi$
$487$	−0.911993			−0.0413263			−0.0206632	+	0.999786i	$0.506578\pi$
$488$	−3.11400	−	5.39360i	−0.140964	−	0.244157i
$489$	−5.00000	+	8.66025i	−0.226108	+	0.391630i
$490$	1.50000	+	2.59808i	0.0677631	+	0.117369i
$491$	−3.38600	+	5.86473i	−0.152808	+	0.264671i	−0.932259	−	0.361792i	$-0.882165\pi$
$491$	−3.38600	+	5.86473i	−0.152808	+	0.264671i	0.779451	+	0.626464i	$0.215498\pi$
$492$	−0.613999	+	1.06348i	−0.0276812	+	0.0479453i
$493$		0			0
$494$	16.1140	+	3.26665i	0.725003	+	0.146974i
$495$	−8.31601			−0.373777
$496$	3.77200	−	6.53330i	0.169368	−	0.293354i
$497$	−6.88600	+	11.9269i	−0.308879	+	0.534995i
$498$	3.11400	+	5.39360i	0.139542	+	0.241693i
$499$	−13.7720	+	23.8538i	−0.616519	+	1.06784i	0.373596	+	0.927591i	$0.378125\pi$
$499$	−13.7720	+	23.8538i	−0.616519	+	1.06784i	−0.990116	+	0.140252i	$0.955209\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$	6.00000			0.268060
$502$	15.7720			0.703939
$503$	−12.5440	−	21.7269i	−0.559309	−	0.968752i	−0.997554	−	0.0698968i	$-0.977733\pi$
$503$	−12.5440	−	21.7269i	−0.559309	−	0.968752i	0.438245	−	0.898856i	$-0.355600\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$	21.6840			0.964925
$506$	−16.0000			−0.711287
$507$	0.613999	+	1.06348i	0.0272687	+	0.0472307i
$508$	−3.88600	+	6.73075i	−0.172413	+	0.298629i
$509$	5.81601	+	10.0736i	0.257790	+	0.446505i	0.965650	−	0.259848i	$-0.0836724\pi$
$509$	5.81601	+	10.0736i	0.257790	+	0.446505i	−0.707860	+	0.706353i	$0.750339\pi$
$510$	−7.15800	+	12.3980i	−0.316962	+	0.548994i
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$	−1.00000			−0.0441942
$513$	4.27200	+	0.866025i	0.188613	+	0.0382360i
$514$	20.3160			0.896101
$515$	12.4740	−	21.6056i	0.549670	−	0.952057i
$516$	3.00000	−	5.19615i	0.132068	−	0.228748i
$517$	16.0000	+	27.7128i	0.703679	+	1.21881i
$518$	0.613999	−	1.06348i	0.0269776	−	0.0467265i
$519$	1.88600	+	3.26665i	0.0827863	+	0.143390i
$520$	−11.3160			−0.496240
$521$	10.0000			0.438108			0.219054	−	0.975713i	$-0.429703\pi$
$521$	10.0000			0.438108			0.219054	+	0.975713i	$0.429703\pi$
$522$		0			0
$523$	−0.158003	−	0.273669i	−0.00690898	−	0.0119667i	0.862550	−	0.505971i	$-0.168866\pi$
$523$	−0.158003	−	0.273669i	−0.00690898	−	0.0119667i	−0.869459	+	0.494005i	$0.835533\pi$
$524$	17.3160			0.756453
$525$	4.00000			0.174574
$526$	−7.50000	−	12.9904i	−0.327016	−	0.566408i
$527$	18.0000	−	31.1769i	0.784092	−	1.35809i
$528$	−1.38600	−	2.40062i	−0.0603179	−	0.104474i
$529$	−5.15800	+	8.93392i	−0.224261	+	0.388431i
$530$	−6.00000	+	10.3923i	−0.260623	+	0.451413i
$531$	0.227998			0.00989428
$532$	−1.38600	−	4.13267i	−0.0600908	−	0.179174i
$533$	−4.63201			−0.200635
$534$	8.15800	−	14.1301i	0.353031	−	0.611468i
$535$	−23.3160	+	40.3845i	−1.00804	+	1.74597i
$536$		0			0
$537$	−3.61400	+	6.25963i	−0.155956	+	0.270123i
$538$	10.3860	+	17.9891i	0.447772	+	0.775564i
$539$	−2.77200			−0.119399
$540$	−3.00000			−0.129099
$541$	−13.3860	−	23.1852i	−0.575509	−	0.996811i	−0.995986	−	0.0895079i	$-0.971471\pi$
$541$	−13.3860	−	23.1852i	−0.575509	−	0.996811i	0.420477	−	0.907303i	$-0.361863\pi$
$542$	9.61400	+	16.6519i	0.412957	+	0.715262i
$543$	−17.3160			−0.743101
$544$	−4.77200			−0.204598
$545$	−1.84200	−	3.19043i	−0.0789025	−	0.136663i
$546$	1.88600	−	3.26665i	0.0807134	−	0.139800i
$547$	−14.5440	−	25.1910i	−0.621857	−	1.07709i	−0.989140	−	0.146978i	$-0.953045\pi$
$547$	−14.5440	−	25.1910i	−0.621857	−	1.07709i	0.367283	−	0.930109i	$-0.380288\pi$
$548$	1.88600	−	3.26665i	0.0805660	−	0.139544i
$549$	3.11400	−	5.39360i	0.132902	−	0.230193i
$550$	11.0880			0.472794
$551$		0			0
$552$	−5.77200			−0.245673
$553$	−4.00000	+	6.92820i	−0.170097	+	0.294617i
$554$	9.15800	−	15.8621i	0.389086	−	0.673917i
$555$	−1.84200	−	3.19043i	−0.0781884	−	0.135426i
$556$	−8.15800	+	14.1301i	−0.345976	+	0.599249i
$557$	−17.7720	−	30.7820i	−0.753024	−	1.30428i	−0.946351	−	0.323141i	$-0.895261\pi$
$557$	−17.7720	−	30.7820i	−0.753024	−	1.30428i	0.193327	−	0.981134i	$-0.438072\pi$
$558$	7.54400			0.319363
$559$	22.6320			0.957232
$560$	1.50000	+	2.59808i	0.0633866	+	0.109789i
$561$	−6.61400	−	11.4558i	−0.279243	−	0.483664i
$562$	15.5440			0.655684
$563$	−44.4040			−1.87141			−0.935703	−	0.352789i	$-0.885233\pi$
$563$	−44.4040			−1.87141			−0.935703	+	0.352789i	$0.885233\pi$
$564$	5.77200	+	9.99740i	0.243045	+	0.420967i
$565$	−2.65800	+	4.60380i	−0.111823	+	0.193683i
$566$	−14.5000	−	25.1147i	−0.609480	−	1.05565i
$567$	0.500000	−	0.866025i	0.0209980	−	0.0363696i
$568$	−6.88600	+	11.9269i	−0.288930	+	0.500442i
$569$	8.22800			0.344936			0.172468	−	0.985015i	$-0.444826\pi$
$569$	8.22800			0.344936			0.172468	+	0.985015i	$0.444826\pi$
$570$	−12.8160	−	2.59808i	−0.536803	−	0.108821i
$571$	−38.6320			−1.61670			−0.808350	−	0.588703i	$-0.799639\pi$
$571$	−38.6320			−1.61670			−0.808350	+	0.588703i	$0.799639\pi$
$572$	5.22800	−	9.05516i	0.218594	−	0.378615i
$573$	−8.88600	+	15.3910i	−0.371218	+	0.642968i
$574$	0.613999	+	1.06348i	0.0256278	+	0.0443887i
$575$	11.5440	−	19.9948i	0.481418	−	0.833841i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	41.5440			1.72950			0.864750	−	0.502203i	$-0.167477\pi$
$577$	41.5440			1.72950			0.864750	+	0.502203i	$0.167477\pi$
$578$	−5.77200			−0.240084
$579$	−2.72800	−	4.72503i	−0.113372	−	0.196366i
$580$		0			0
$581$	6.22800			0.258381
$582$	−11.5440			−0.478514
$583$	−5.54400	−	9.60250i	−0.229609	−	0.397695i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	−5.65800	−	9.79995i	−0.233930	−	0.405178i
$586$	−14.8160	+	25.6621i	−0.612044	+	1.06009i
$587$	4.77200	−	8.26535i	0.196962	−	0.341147i	−0.750580	−	0.660779i	$-0.770226\pi$
$587$	4.77200	−	8.26535i	0.196962	−	0.341147i	0.947542	+	0.319632i	$0.103559\pi$
$588$	−1.00000			−0.0412393
$589$	32.2280	+	6.53330i	1.32793	+	0.269200i
$590$	−0.683994			−0.0281596
$591$	−4.00000	+	6.92820i	−0.164538	+	0.284988i
$592$	0.613999	−	1.06348i	0.0252352	−	0.0437087i
$593$	−6.15800	−	10.6660i	−0.252879	−	0.437999i	0.711438	−	0.702748i	$-0.248044\pi$
$593$	−6.15800	−	10.6660i	−0.252879	−	0.437999i	−0.964317	+	0.264749i	$0.914711\pi$
$594$	1.38600	−	2.40062i	0.0568683	−	0.0984988i
$595$	7.15800	+	12.3980i	0.293450	+	0.508269i
$596$	−2.45600			−0.100602
$597$	26.6320			1.08998
$598$	−10.8860	−	18.8551i	−0.445162	−	0.771043i
$599$	−4.81601	−	8.34157i	−0.196777	−	0.340827i	0.750705	−	0.660638i	$-0.229714\pi$
$599$	−4.81601	−	8.34157i	−0.196777	−	0.340827i	−0.947481	+	0.319811i	$0.896381\pi$
$600$	4.00000			0.163299
$601$	−19.5440			−0.797217			−0.398608	−	0.917121i	$-0.630507\pi$
$601$	−19.5440			−0.797217			−0.398608	+	0.917121i	$0.630507\pi$
$602$	−3.00000	−	5.19615i	−0.122271	−	0.211779i
$603$		0			0
$604$	5.11400	+	8.85771i	0.208086	+	0.360415i
$605$	4.97401	−	8.61524i	0.202222	−	0.350259i
$606$	−3.61400	+	6.25963i	−0.146809	+	0.254280i
$607$	23.0880			0.937113			0.468557	−	0.883433i	$-0.344774\pi$
$607$	23.0880			0.937113			0.468557	+	0.883433i	$0.344774\pi$
$608$	−1.38600	−	4.13267i	−0.0562098	−	0.167602i
$609$		0			0
$610$	−9.34200	+	16.1808i	−0.378246	+	0.655142i
$611$	−21.7720	+	37.7102i	−0.880801	+	1.52559i
$612$	−2.38600	−	4.13267i	−0.0964484	−	0.167053i
$613$	8.38600	−	14.5250i	0.338707	−	0.586658i	−0.645482	−	0.763775i	$-0.723344\pi$
$613$	8.38600	−	14.5250i	0.338707	−	0.586658i	0.984190	+	0.177117i	$0.0566770\pi$
$614$	1.11400	+	1.92950i	0.0449573	+	0.0778684i
$615$	3.68399			0.148553
$616$	−2.77200			−0.111687
$617$	11.6580	+	20.1923i	0.469334	+	0.812910i	0.999385	−	0.0350557i	$-0.0111609\pi$
$617$	11.6580	+	20.1923i	0.469334	+	0.812910i	−0.530052	+	0.847965i	$0.677828\pi$
$618$	4.15800	+	7.20187i	0.167259	+	0.289702i
$619$	−41.7720			−1.67896			−0.839479	−	0.543392i	$-0.817140\pi$
$619$	−41.7720			−1.67896			−0.839479	+	0.543392i	$0.817140\pi$
$620$	−22.6320			−0.908923
$621$	−2.88600	−	4.99870i	−0.115811	−	0.200591i
$622$	−14.5440	+	25.1910i	−0.583161	+	1.01007i
$623$	−8.15800	−	14.1301i	−0.326843	−	0.566110i
$624$	1.88600	−	3.26665i	0.0755005	−	0.130771i
$625$	14.5000	−	25.1147i	0.580000	−	1.00459i
$626$	−24.0000			−0.959233
$627$	8.00000	−	9.05516i	0.319489	−	0.361628i
$628$	15.7720			0.629371
$629$	2.93000	−	5.07492i	0.116827	−	0.202350i
$630$	−1.50000	+	2.59808i	−0.0597614	+	0.103510i
$631$	16.3160	+	28.2602i	0.649530	+	1.12502i	0.983235	+	0.182341i	$0.0583676\pi$
$631$	16.3160	+	28.2602i	0.649530	+	1.12502i	−0.333705	+	0.942677i	$0.608299\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	2.00000	+	3.46410i	0.0794929	+	0.137686i
$634$	−22.6320			−0.898832
$635$	23.3160			0.925267
$636$	−2.00000	−	3.46410i	−0.0793052	−	0.137361i
$637$	−1.88600	−	3.26665i	−0.0747261	−	0.129429i
$638$		0			0
$639$	−13.7720			−0.544812
$640$	1.50000	+	2.59808i	0.0592927	+	0.102698i
$641$	6.65800	−	11.5320i	0.262975	−	0.455487i	−0.704056	−	0.710145i	$-0.748630\pi$
$641$	6.65800	−	11.5320i	0.262975	−	0.455487i	0.967031	+	0.254658i	$0.0819629\pi$
$642$	−7.77200	−	13.4615i	−0.306736	−	0.531283i
$643$	20.5880	−	35.6595i	0.811912	−	1.40627i	−0.0996126	−	0.995026i	$-0.531760\pi$
$643$	20.5880	−	35.6595i	0.811912	−	1.40627i	0.911524	−	0.411246i	$-0.134906\pi$
$644$	−2.88600	+	4.99870i	−0.113724	+	0.196976i
$645$	−18.0000			−0.708749
$646$	−6.61400	−	19.7211i	−0.260224	−	0.775918i
$647$	−10.6320			−0.417987			−0.208994	−	0.977917i	$-0.567019\pi$
$647$	−10.6320			−0.417987			−0.208994	+	0.977917i	$0.567019\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	0.316006	−	0.547338i	0.0124043	−	0.0214849i
$650$	7.54400	+	13.0666i	0.295900	+	0.512514i
$651$	3.77200	−	6.53330i	0.147836	−	0.256060i
$652$	5.00000	+	8.66025i	0.195815	+	0.339162i
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$	1.22800			0.0480185
$655$	−25.9740	−	44.9883i	−1.01489	−	1.75784i
$656$	0.613999	+	1.06348i	0.0239726	+	0.0415218i
$657$	−2.00000			−0.0780274
$658$	11.5440			0.450032
$659$	−1.61400	−	2.79553i	−0.0628725	−	0.108898i	0.832876	−	0.553460i	$-0.186693\pi$
$659$	−1.61400	−	2.79553i	−0.0628725	−	0.108898i	−0.895748	+	0.444562i	$0.853359\pi$
$660$	−4.15800	+	7.20187i	−0.161850	+	0.280332i
$661$	−7.65800	−	13.2640i	−0.297862	−	0.515912i	0.677785	−	0.735260i	$-0.262940\pi$
$661$	−7.65800	−	13.2640i	−0.297862	−	0.515912i	−0.975647	+	0.219349i	$0.929607\pi$
$662$	7.54400	−	13.0666i	0.293206	−	0.507848i
$663$	9.00000	−	15.5885i	0.349531	−	0.605406i
$664$	6.22800			0.241693
$665$	−8.65800	+	9.79995i	−0.335743	+	0.380026i
$666$	1.22800			0.0475840
$667$		0			0
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$	−13.9300	−	24.1275i	−0.538565	−	0.932822i
$670$		0			0
$671$	−8.63201	−	14.9511i	−0.333235	−	0.577180i
$672$	−1.00000			−0.0385758
$673$	−23.4560			−0.904162			−0.452081	−	0.891977i	$-0.649318\pi$
$673$	−23.4560			−0.904162			−0.452081	+	0.891977i	$0.649318\pi$
$674$	5.88600	+	10.1949i	0.226720	+	0.392691i
$675$	2.00000	+	3.46410i	0.0769800	+	0.133333i
$676$	1.22800			0.0472307
$677$	14.3160			0.550209			0.275104	−	0.961414i	$-0.411288\pi$
$677$	14.3160			0.550209			0.275104	+	0.961414i	$0.411288\pi$
$678$	−0.886001	−	1.53460i	−0.0340267	−	0.0589359i
$679$	−5.77200	+	9.99740i	−0.221509	+	0.383665i
$680$	7.15800	+	12.3980i	0.274497	+	0.475443i
$681$	2.88600	−	4.99870i	0.110592	−	0.191551i
$682$	10.4560	−	18.1103i	0.400381	−	0.693480i
$683$	17.2280			0.659211			0.329606	−	0.944119i	$-0.393084\pi$
$683$	17.2280			0.659211			0.329606	+	0.944119i	$0.393084\pi$
$684$	2.88600	−	3.26665i	0.110349	−	0.124903i
$685$	−11.3160			−0.432362
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	−1.34200	+	2.32441i	−0.0512004	+	0.0886817i
$688$	−3.00000	−	5.19615i	−0.114374	−	0.198101i
$689$	7.54400	−	13.0666i	0.287404	−	0.497798i
$690$	8.65800	+	14.9961i	0.329605	+	0.570892i
$691$	−27.6320			−1.05117			−0.525586	−	0.850741i	$-0.676154\pi$
$691$	−27.6320			−1.05117			−0.525586	+	0.850741i	$0.676154\pi$
$692$	3.77200			0.143390
$693$	−1.38600	−	2.40062i	−0.0526498	−	0.0911922i
$694$	−7.77200	−	13.4615i	−0.295021	−	0.510992i
$695$	48.9480			1.85670
$696$		0			0
$697$	2.93000	+	5.07492i	0.110982	+	0.192226i
$698$	−9.31601	+	16.1358i	−0.352616	+	0.610749i
$699$	14.6580	+	25.3884i	0.554417	+	0.960278i
$700$	2.00000	−	3.46410i	0.0755929	−	0.130931i
$701$	−18.5440	+	32.1192i	−0.700397	+	1.21312i	0.267930	+	0.963438i	$0.413661\pi$
$701$	−18.5440	+	32.1192i	−0.700397	+	1.21312i	−0.968327	+	0.249685i	$0.919673\pi$
$702$	3.77200			0.142365
$703$	5.24601	+	1.06348i	0.197857	+	0.0401098i
$704$	−2.77200			−0.104474
$705$	17.3160	−	29.9922i	0.652159	−	1.12957i
$706$	2.61400	−	4.52758i	0.0983792	−	0.170398i
$707$	3.61400	+	6.25963i	0.135918	+	0.235418i
$708$	0.113999	−	0.197452i	0.00428435	−	0.00742071i
$709$	−8.15800	−	14.1301i	−0.306380	−	0.530666i	0.671187	−	0.741288i	$-0.265785\pi$
$709$	−8.15800	−	14.1301i	−0.306380	−	0.530666i	−0.977568	+	0.210622i	$0.932451\pi$
$710$	41.3160			1.55056
$711$	−8.00000			−0.300023
$712$	−8.15800	−	14.1301i	−0.305734	−	0.529547i
$713$	−21.7720	−	37.7102i	−0.815368	−	1.41226i
$714$	−4.77200			−0.178588
$715$	−31.3680			−1.17310
$716$	3.61400	+	6.25963i	0.135061	+	0.233933i
$717$	9.04400	−	15.6647i	0.337755	−	0.585008i
$718$	−12.0000	−	20.7846i	−0.447836	−	0.775675i
$719$	−3.45600	+	5.98596i	−0.128887	+	0.223239i	−0.923246	−	0.384210i	$-0.874474\pi$
$719$	−3.45600	+	5.98596i	−0.128887	+	0.223239i	0.794359	+	0.607449i	$0.207807\pi$
$720$	−1.50000	+	2.59808i	−0.0559017	+	0.0968246i
$721$	8.31601			0.309704
$722$	15.1580	−	11.4558i	0.564122	−	0.426340i
$723$	15.5440			0.578088
$724$	−8.65800	+	14.9961i	−0.321772	+	0.557326i
$725$		0			0
$726$	1.65800	+	2.87175i	0.0615343	+	0.106580i
$727$	24.1580	−	41.8429i	0.895971	−	1.55187i	0.0633721	−	0.997990i	$-0.479814\pi$
$727$	24.1580	−	41.8429i	0.895971	−	1.55187i	0.832599	−	0.553877i	$-0.186852\pi$
$728$	−1.88600	−	3.26665i	−0.0698998	−	0.121070i
$729$	1.00000			0.0370370
$730$	6.00000			0.222070
$731$	−14.3160	−	24.7960i	−0.529497	−	0.917115i
$732$	−3.11400	−	5.39360i	−0.115097	−	0.199353i
$733$	42.4040			1.56623			0.783114	−	0.621878i	$-0.213630\pi$
$733$	42.4040			1.56623			0.783114	+	0.621878i	$0.213630\pi$
$734$	24.3160			0.897520
$735$	1.50000	+	2.59808i	0.0553283	+	0.0958315i
$736$	−2.88600	+	4.99870i	−0.106379	+	0.184255i
$737$		0			0
$738$	−0.613999	+	1.06348i	−0.0226016	+	0.0391472i
$739$	−2.77200	+	4.80125i	−0.101970	+	0.176617i	−0.912496	−	0.409085i	$-0.865848\pi$
$739$	−2.77200	+	4.80125i	−0.101970	+	0.176617i	0.810526	+	0.585702i	$0.199181\pi$
$740$	−3.68399			−0.135426
$741$	16.1140	+	3.26665i	0.591963	+	0.120003i
$742$	−4.00000			−0.146845
$743$	−23.2720	+	40.3083i	−0.853767	+	1.47877i	0.0240173	+	0.999712i	$0.492354\pi$
$743$	−23.2720	+	40.3083i	−0.853767	+	1.47877i	−0.877784	+	0.479056i	$0.840979\pi$
$744$	3.77200	−	6.53330i	0.138288	−	0.239522i
$745$	3.68399	+	6.38087i	0.134971	+	0.233777i
$746$	−15.1580	+	26.2544i	−0.554974	+	0.961243i
$747$	3.11400	+	5.39360i	0.113935	+	0.197342i
$748$	−13.2280			−0.483664
$749$	−15.5440			−0.567966
$750$	1.50000	+	2.59808i	0.0547723	+	0.0948683i
$751$	−4.31601	−	7.47554i	−0.157493	−	0.272786i	0.776471	−	0.630153i	$-0.217008\pi$
$751$	−4.31601	−	7.47554i	−0.157493	−	0.272786i	−0.933964	+	0.357367i	$0.883675\pi$
$752$	11.5440			0.420967
$753$	15.7720			0.574764
$754$		0			0
$755$	15.3420	−	26.5731i	0.558352	−	0.967095i
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	1.61400	−	2.79553i	0.0586618	−	0.101605i	−0.835203	−	0.549942i	$-0.814650\pi$
$757$	1.61400	−	2.79553i	0.0586618	−	0.101605i	0.893865	+	0.448336i	$0.147983\pi$
$758$	0.227998	−	0.394904i	0.00828126	−	0.0143436i
$759$	−16.0000			−0.580763
$760$	−8.65800	+	9.79995i	−0.314059	+	0.355481i
$761$	21.5440			0.780970			0.390485	−	0.920609i	$-0.372307\pi$
$761$	21.5440			0.780970			0.390485	+	0.920609i	$0.372307\pi$
$762$	−3.88600	+	6.73075i	−0.140775	+	0.243829i
$763$	0.613999	−	1.06348i	0.0222283	−	0.0385005i
$764$	8.88600	+	15.3910i	0.321484	+	0.556827i
$765$	−7.15800	+	12.3980i	−0.258798	+	0.448252i
$766$	16.0000	+	27.7128i	0.578103	+	1.00130i
$767$	0.860009			0.0310531
$768$	−1.00000			−0.0360844
$769$	−2.22800	−	3.85901i	−0.0803437	−	0.139159i	0.823054	−	0.567963i	$-0.192268\pi$
$769$	−2.22800	−	3.85901i	−0.0803437	−	0.139159i	−0.903398	+	0.428804i	$0.858935\pi$
$770$	4.15800	+	7.20187i	0.149844	+	0.259537i
$771$	20.3160			0.731663
$772$	−5.45600			−0.196366
$773$	−26.2720	−	45.5044i	−0.944938	−	1.63668i	−0.755875	−	0.654716i	$-0.772788\pi$
$773$	−26.2720	−	45.5044i	−0.944938	−	1.63668i	−0.189063	−	0.981965i	$-0.560545\pi$
$774$	3.00000	−	5.19615i	0.107833	−	0.186772i
$775$	15.0880	+	26.1332i	0.541977	+	0.938732i
$776$	−5.77200	+	9.99740i	−0.207203	+	0.358886i
$777$	0.613999	−	1.06348i	0.0220271	−	0.0381520i
$778$	19.0880			0.684338
$779$	−3.54400	+	4.01144i	−0.126977	+	0.143725i
$780$	−11.3160			−0.405178
$781$	−19.0880	+	33.0614i	−0.683023	+	1.18303i
$782$	−13.7720	+	23.8538i	−0.492486	+	0.853010i
$783$		0			0
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$	−23.6580	−	40.9769i	−0.844390	−	1.46253i
$786$	17.3160			0.617641
$787$	32.5440			1.16007			0.580034	−	0.814592i	$-0.303039\pi$
$787$	32.5440			1.16007			0.580034	+	0.814592i	$0.303039\pi$
$788$	4.00000	+	6.92820i	0.142494	+	0.246807i
$789$	−7.50000	−	12.9904i	−0.267007	−	0.462470i
$790$	24.0000			0.853882
$791$	−1.77200			−0.0630051
$792$	−1.38600	−	2.40062i	−0.0492494	−	0.0853025i
$793$	11.7460	−	20.3447i	0.417113	−	0.722461i
$794$	4.54400	+	7.87045i	0.161261	+	0.279312i
$795$	−6.00000	+	10.3923i	−0.212798	+	0.368577i
$796$	13.3160	−	23.0640i	0.471973	−	0.817482i
$797$	23.1760			0.820937			0.410468	−	0.911875i	$-0.365365\pi$
$797$	23.1760			0.820937			0.410468	+	0.911875i	$0.365365\pi$
$798$	−1.38600	−	4.13267i	−0.0490639	−	0.146295i
$799$	55.0880			1.94887
$800$	2.00000	−	3.46410i	0.0707107	−	0.122474i
$801$	8.15800	−	14.1301i	0.288249	−	0.499262i
$802$	19.9740	+	34.5960i	0.705307	+	1.22163i
$803$	−2.77200	+	4.80125i	−0.0978218	+	0.169432i
$804$		0			0
$805$	17.3160			0.610309
$806$	28.4560			1.00232
$807$	10.3860	+	17.9891i	0.365605	+	0.633246i
$808$	3.61400	+	6.25963i	0.127140	+	0.220213i
$809$	29.3160			1.03070			0.515348	−	0.856981i	$-0.327663\pi$
$809$	29.3160			1.03070			0.515348	+	0.856981i	$0.327663\pi$
$810$	−3.00000			−0.105409
$811$	−21.2460	−	36.7992i	−0.746048	−	1.29219i	−0.949703	−	0.313151i	$-0.898615\pi$
$811$	−21.2460	−	36.7992i	−0.746048	−	1.29219i	0.203655	−	0.979043i	$-0.434718\pi$
$812$		0			0
$813$	9.61400	+	16.6519i	0.337178	+	0.584009i
$814$	1.70201	−	2.94796i	0.0596553	−	0.103326i
$815$	15.0000	−	25.9808i	0.525427	−	0.910066i
$816$	−4.77200			−0.167053
$817$	17.3160	−	19.5999i	0.605810	−	0.685714i
$818$	27.0880			0.947110
$819$	1.88600	−	3.26665i	0.0659022	−	0.114146i
$820$	1.84200	−	3.19043i	0.0643253	−	0.111415i
$821$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$821$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$822$	1.88600	−	3.26665i	0.0657818	−	0.113937i
$823$	23.2020	+	40.1871i	0.808771	+	1.40083i	0.913715	+	0.406355i	$0.133200\pi$
$823$	23.2020	+	40.1871i	0.808771	+	1.40083i	−0.104944	+	0.994478i	$0.533466\pi$
$824$	8.31601			0.289702
$825$	11.0880			0.386035
$826$	−0.113999	−	0.197452i	−0.00396653	−	0.00687024i
$827$	−2.61400	−	4.52758i	−0.0908977	−	0.157439i	0.816991	−	0.576650i	$-0.195640\pi$
$827$	−2.61400	−	4.52758i	−0.0908977	−	0.157439i	−0.907889	+	0.419210i	$0.862307\pi$
$828$	−5.77200			−0.200591
$829$	−28.6840			−0.996236			−0.498118	−	0.867109i	$-0.665975\pi$
$829$	−28.6840			−0.996236			−0.498118	+	0.867109i	$0.665975\pi$
$830$	−9.34200	−	16.1808i	−0.324265	−	0.561644i
$831$	9.15800	−	15.8621i	0.317688	−	0.550251i
$832$	−1.88600	−	3.26665i	−0.0653853	−	0.113251i
$833$	−2.38600	+	4.13267i	−0.0826700	+	0.143189i
$834$	−8.15800	+	14.1301i	−0.282489	+	0.489284i
$835$	−18.0000			−0.622916
$836$	−3.84200	−	11.4558i	−0.132878	−	0.396207i
$837$	7.54400			0.260759
$838$	0.772002	−	1.33715i	0.0266684	−	0.0461910i
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	−0.978517	−	0.206165i	$-0.933902\pi$
$839$	−9.00000	+	15.5885i	−0.310715	+	0.538173i	0.667803	+	0.744338i	$0.267235\pi$
$840$	1.50000	+	2.59808i	0.0517549	+	0.0896421i
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	11.3860	+	19.7211i	0.392388	+	0.679635i
$843$	15.5440			0.535364
$844$	4.00000			0.137686
$845$	−1.84200	−	3.19043i	−0.0633666	−	0.109754i
$846$	5.77200	+	9.99740i	0.198446	+	0.343718i
$847$	3.31601			0.113939
$848$	−4.00000			−0.137361
$849$	−14.5000	−	25.1147i	−0.497639	−	0.861936i
$850$	9.54400	−	16.5307i	0.327357	−	0.566998i
$851$	−3.54400	−	6.13839i	−0.121487	−	0.210421i
$852$	−6.88600	+	11.9269i	−0.235911	+	0.408609i
$853$	3.77200	−	6.53330i	0.129151	−	0.223696i	−0.794197	−	0.607660i	$-0.792108\pi$
$853$	3.77200	−	6.53330i	0.129151	−	0.223696i	0.923348	+	0.383965i	$0.125442\pi$
$854$	−6.22800			−0.213118
$855$	−12.8160	−	2.59808i	−0.438298	−	0.0888523i
$856$	−15.5440			−0.531283
$857$	27.4740	−	47.5864i	0.938494	−	1.62552i	0.170213	−	0.985407i	$-0.445554\pi$
$857$	27.4740	−	47.5864i	0.938494	−	1.62552i	0.768281	−	0.640112i	$-0.221112\pi$
$858$	5.22800	−	9.05516i	0.178481	−	0.309138i
$859$	22.4740	+	38.9261i	0.766803	+	1.32814i	0.939288	+	0.343130i	$0.111487\pi$
$859$	22.4740	+	38.9261i	0.766803	+	1.32814i	−0.172485	+	0.985012i	$0.555180\pi$
$860$	−9.00000	+	15.5885i	−0.306897	+	0.531562i
$861$	0.613999	+	1.06348i	0.0209250	+	0.0362432i
$862$	−26.7720			−0.911858
$863$	−42.4920			−1.44645			−0.723223	−	0.690615i	$-0.757340\pi$
$863$	−42.4920			−1.44645			−0.723223	+	0.690615i	$0.757340\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−5.65800	−	9.79995i	−0.192378	−	0.333208i
$866$	12.0000			0.407777
$867$	−5.77200			−0.196027
$868$	−3.77200	−	6.53330i	−0.128030	−	0.221755i
$869$	−11.0880	+	19.2050i	−0.376135	+	0.651485i
$870$		0			0
$871$		0			0
$872$	0.613999	−	1.06348i	0.0207926	−	0.0360139i
$873$	−11.5440			−0.390705
$874$	−24.6580	−	4.99870i	−0.834069	−	0.169084i
$875$	3.00000			0.101419
$876$	−1.00000	+	1.73205i	−0.0337869	+	0.0585206i
$877$	10.3160	−	17.8678i	0.348347	−	0.603354i	−0.637609	−	0.770360i	$-0.720077\pi$
$877$	10.3160	−	17.8678i	0.348347	−	0.603354i	0.985956	+	0.167006i	$0.0534098\pi$
$878$	−10.3860	−	17.9891i	−0.350511	−	0.607102i
$879$	−14.8160	+	25.6621i	−0.499731	+	0.865560i
$880$	4.15800	+	7.20187i	0.140166	+	0.242775i
$881$	−23.2280			−0.782571			−0.391286	−	0.920269i	$-0.627970\pi$
$881$	−23.2280			−0.782571			−0.391286	+	0.920269i	$0.627970\pi$
$882$	−1.00000			−0.0336718
$883$	−4.54400	−	7.87045i	−0.152918	−	0.264862i	0.779381	−	0.626550i	$-0.215534\pi$
$883$	−4.54400	−	7.87045i	−0.152918	−	0.264862i	−0.932299	+	0.361689i	$0.882200\pi$
$884$	−9.00000	−	15.5885i	−0.302703	−	0.524297i
$885$	−0.683994			−0.0229922
$886$	31.5440			1.05974
$887$	−18.0880	−	31.3293i	−0.607336	−	1.05194i	−0.991678	−	0.128746i	$-0.958905\pi$
$887$	−18.0880	−	31.3293i	−0.607336	−	1.05194i	0.384342	−	0.923191i	$-0.374428\pi$
$888$	0.613999	−	1.06348i	0.0206045	−	0.0356880i
$889$	3.88600	+	6.73075i	0.130332	+	0.225742i
$890$	−24.4740	+	42.3902i	−0.820371	+	1.42092i
$891$	1.38600	−	2.40062i	0.0464328	−	0.0804239i
$892$	−27.8600			−0.932822
$893$	16.0000	+	47.7076i	0.535420	+	1.59647i
$894$	−2.45600			−0.0821408
$895$	10.8420	−	18.7789i	0.362408	−	0.627709i
$896$	−0.500000	+	0.866025i	−0.0167038	+	0.0289319i
$897$	−10.8860	−	18.8551i	−0.363473	−	0.629554i
$898$	7.88600	−	13.6590i	0.263159	−	0.455805i
$899$		0			0
$900$	4.00000			0.133333
$901$	−19.0880			−0.635914
$902$	1.70201	+	2.94796i	0.0566706	+	0.0981564i
$903$	−3.00000	−	5.19615i	−0.0998337	−	0.172917i
$904$	−1.77200			−0.0589359
$905$	51.9480			1.72681
$906$	5.11400	+	8.85771i	0.169901	+	0.294278i
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	−0.937018	−	0.349281i	$-0.886426\pi$
$907$	−5.00000	+	8.66025i	−0.166022	+	0.287559i	0.770996	+	0.636841i	$0.219759\pi$
$908$	−2.88600	−	4.99870i	−0.0957753	−	0.165888i
$909$	−3.61400	+	6.25963i	−0.119869	+	0.207619i
$910$	−5.65800	+	9.79995i	−0.187561	+	0.324865i
$911$	−16.5440			−0.548127			−0.274064	−	0.961712i	$-0.588368\pi$
$911$	−16.5440			−0.548127			−0.274064	+	0.961712i	$0.588368\pi$
$912$	−1.38600	−	4.13267i	−0.0458951	−	0.136847i
$913$	17.2640			0.571356
$914$	−1.95600	+	3.38788i	−0.0646986	+	0.112061i
$915$	−9.34200	+	16.1808i	−0.308837	+	0.534921i
$916$	1.34200	+	2.32441i	0.0443408	+	0.0768006i
$917$	8.65800	−	14.9961i	0.285912	−	0.495215i
$918$	−2.38600	−	4.13267i	−0.0787498	−	0.136399i
$919$	−11.7720			−0.388323			−0.194161	−	0.980970i	$-0.562199\pi$
$919$	−11.7720			−0.388323			−0.194161	+	0.980970i	$0.562199\pi$
$920$	17.3160			0.570892
$921$	1.11400	+	1.92950i	0.0367075	+	0.0635793i
$922$	4.50000	+	7.79423i	0.148200	+	0.256689i
$923$	−51.9480			−1.70989
$924$	−2.77200			−0.0911922
$925$	2.45600	+	4.25391i	0.0807527	+	0.139868i
$926$	18.4300	−	31.9217i	0.605648	−	1.04901i
$927$	4.15800	+	7.20187i	0.136567	+	0.236541i
$928$		0			0
$929$	11.7020	−	20.2685i	0.383930	−	0.664987i	−0.607690	−	0.794174i	$-0.707904\pi$
$929$	11.7020	−	20.2685i	0.383930	−	0.664987i	0.991620	+	0.129188i	$0.0412369\pi$
$930$	−22.6320			−0.742133
$931$	−4.27200	−	0.866025i	−0.140009	−	0.0283828i
$932$	29.3160			0.960278
$933$	−14.5440	+	25.1910i	−0.476149	+	0.824715i
$934$	−15.5440	+	26.9230i	−0.508615	+	0.880948i
$935$	19.8420	+	34.3673i	0.648903	+	1.12393i
$936$	1.88600	−	3.26665i	0.0616459	−	0.106774i
$937$	18.5440	+	32.1192i	0.605806	+	1.04929i	0.991924	+	0.126837i	$0.0404827\pi$
$937$	18.5440	+	32.1192i	0.605806	+	1.04929i	−0.386117	+	0.922450i	$0.626184\pi$
$938$		0			0
$939$	−24.0000			−0.783210
$940$	−17.3160	−	29.9922i	−0.564786	−	0.978238i
$941$	12.9560	+	22.4404i	0.422353	+	0.731538i	0.996169	−	0.0874468i	$-0.0278708\pi$
$941$	12.9560	+	22.4404i	0.422353	+	0.731538i	−0.573816	+	0.818984i	$0.694537\pi$
$942$	15.7720			0.513880
$943$	7.08801			0.230817
$944$	−0.113999	−	0.197452i	−0.00371035	−	0.00642652i
$945$	−1.50000	+	2.59808i	−0.0487950	+	0.0845154i
$946$	−8.31601	−	14.4037i	−0.270377	−	0.468306i
$947$	−3.93000	+	6.80697i	−0.127708	+	0.221197i	−0.922788	−	0.385308i	$-0.874095\pi$
$947$	−3.93000	+	6.80697i	−0.127708	+	0.221197i	0.795080	+	0.606504i	$0.207429\pi$
$948$	−4.00000	+	6.92820i	−0.129914	+	0.225018i
$949$	−7.54400			−0.244889
$950$	17.0880	+	3.46410i	0.554408	+	0.112390i
$951$	−22.6320			−0.733893
$952$	−2.38600	+	4.13267i	−0.0773307	+	0.133941i
$953$	−18.8600	+	32.6665i	−0.610936	+	1.05817i	0.380147	+	0.924926i	$0.375873\pi$
$953$	−18.8600	+	32.6665i	−0.610936	+	1.05817i	−0.991083	+	0.133246i	$0.957460\pi$
$954$	−2.00000	−	3.46410i	−0.0647524	−	0.112154i
$955$	26.6580	−	46.1730i	0.862633	−	1.49412i
$956$	−9.04400	−	15.6647i	−0.292504	−	0.506632i
$957$		0			0
$958$	−18.0000			−0.581554
$959$	−1.88600	−	3.26665i	−0.0609021	−	0.105486i
$960$	1.50000	+	2.59808i	0.0484123	+	0.0838525i
$961$	25.9120			0.835871
$962$	4.63201			0.149342
$963$	−7.77200	−	13.4615i	−0.250449	−	0.433791i
$964$	7.77200	−	13.4615i	0.250319	−	0.433566i
$965$	8.18399	+	14.1751i	0.263452	+	0.456312i
$966$	−2.88600	+	4.99870i	−0.0928556	+	0.160831i
$967$	6.34200	−	10.9847i	0.203945	−	0.353243i	−0.745851	−	0.666113i	$-0.767957\pi$
$967$	6.34200	−	10.9847i	0.203945	−	0.353243i	0.949796	+	0.312870i	$0.101290\pi$
$968$	3.31601			0.106580
$969$	−6.61400	−	19.7211i	−0.212472	−	0.633534i
$970$	34.6320			1.11197
$971$	3.34200	−	5.78851i	0.107250	−	0.185762i	−0.807405	−	0.589997i	$-0.799129\pi$
$971$	3.34200	−	5.78851i	0.107250	−	0.185762i	0.914655	+	0.404235i	$0.132462\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	8.15800	+	14.1301i	0.261534	+	0.452989i
$974$	−0.455996	+	0.789809i	−0.0146111	+	0.0253071i
$975$	7.54400	+	13.0666i	0.241601	+	0.418466i
$976$	−6.22800			−0.199353
$977$	−26.2280			−0.839108			−0.419554	−	0.907730i	$-0.637814\pi$
$977$	−26.2280			−0.839108			−0.419554	+	0.907730i	$0.637814\pi$
$978$	5.00000	+	8.66025i	0.159882	+	0.276924i
$979$	−22.6140	−	39.1686i	−0.722747	−	1.25183i
$980$	3.00000			0.0958315
$981$	1.22800			0.0392070
$982$	3.38600	+	5.86473i	0.108052	+	0.187151i
$983$	30.8600	−	53.4511i	0.984281	−	1.70483i	0.339195	−	0.940716i	$-0.389846\pi$
$983$	30.8600	−	53.4511i	0.984281	−	1.70483i	0.645087	−	0.764109i	$-0.276821\pi$
$984$	0.613999	+	1.06348i	0.0195736	+	0.0339024i
$985$	12.0000	−	20.7846i	0.382352	−	0.662253i
$986$		0			0
$987$	11.5440			0.367450
$988$	10.8860	−	12.3218i	0.346330	−	0.392009i
$989$	−34.6320			−1.10123
$990$	−4.15800	+	7.20187i	−0.132150	+	0.228891i
$991$	14.8860	−	25.7833i	0.472869	−	0.819034i	−0.526648	−	0.850083i	$-0.676552\pi$
$991$	14.8860	−	25.7833i	0.472869	−	0.819034i	0.999518	+	0.0310493i	$0.00988490\pi$
$992$	−3.77200	−	6.53330i	−0.119761	−	0.207432i
$993$	7.54400	−	13.0666i	0.239402	−	0.414656i
$994$	6.88600	+	11.9269i	0.218411	+	0.378298i
$995$	−79.8960			−2.53287
$996$	6.22800			0.197342
$997$	3.11400	+	5.39360i	0.0986213	+	0.170817i	0.911114	−	0.412154i	$-0.135223\pi$
$997$	3.11400	+	5.39360i	0.0986213	+	0.170817i	−0.812493	+	0.582971i	$0.801890\pi$
$998$	13.7720	+	23.8538i	0.435945	+	0.755079i
$999$	1.22800			0.0388521

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.k.l.505.1	yes	4
3.2	odd	2		2394.2.o.m.505.2		4
19.7	even	3	inner	798.2.k.l.463.1	✓	4
57.26	odd	6		2394.2.o.m.1261.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.k.l.463.1	✓	4	19.7	even	3	inner
798.2.k.l.505.1	yes	4	1.1	even	1	trivial
2394.2.o.m.505.2		4	3.2	odd	2
2394.2.o.m.1261.2		4	57.26	odd	6

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.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 2.59808i) q^{5} +(-0.500000 - 0.866025i) q^{6} -1.00000 q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.50000 + 2.59808i) q^{10} -2.77200 q^{11} -1.00000 q^{12} +(-1.88600 - 3.26665i) q^{13} +(-0.500000 + 0.866025i) q^{14} +(1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.38600 + 4.13267i) q^{17} -1.00000 q^{18} +(-4.27200 - 0.866025i) q^{19} +3.00000 q^{20} +(-0.500000 + 0.866025i) q^{21} +(-1.38600 + 2.40062i) q^{22} +(2.88600 + 4.99870i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(-2.00000 - 3.46410i) q^{25} -3.77200 q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +3.00000 q^{30} -7.54400 q^{31} +(0.500000 + 0.866025i) q^{32} +(-1.38600 + 2.40062i) q^{33} +(2.38600 + 4.13267i) q^{34} +(1.50000 - 2.59808i) q^{35} +(-0.500000 + 0.866025i) q^{36} -1.22800 q^{37} +(-2.88600 + 3.26665i) q^{38} -3.77200 q^{39} +(1.50000 - 2.59808i) q^{40} +(0.613999 - 1.06348i) q^{41} +(0.500000 + 0.866025i) q^{42} +(-3.00000 + 5.19615i) q^{43} +(1.38600 + 2.40062i) q^{44} +3.00000 q^{45} +5.77200 q^{46} +(-5.77200 - 9.99740i) q^{47} +(0.500000 + 0.866025i) q^{48} +1.00000 q^{49} -4.00000 q^{50} +(2.38600 + 4.13267i) q^{51} +(-1.88600 + 3.26665i) q^{52} +(2.00000 + 3.46410i) q^{53} +(-0.500000 + 0.866025i) q^{54} +(4.15800 - 7.20187i) q^{55} +1.00000 q^{56} +(-2.88600 + 3.26665i) q^{57} +(-0.113999 + 0.197452i) q^{59} +(1.50000 - 2.59808i) q^{60} +(3.11400 + 5.39360i) q^{61} +(-3.77200 + 6.53330i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +11.3160 q^{65} +(1.38600 + 2.40062i) q^{66} +4.77200 q^{68} +5.77200 q^{69} +(-1.50000 - 2.59808i) q^{70} +(6.88600 - 11.9269i) q^{71} +(0.500000 + 0.866025i) q^{72} +(1.00000 - 1.73205i) q^{73} +(-0.613999 + 1.06348i) q^{74} -4.00000 q^{75} +(1.38600 + 4.13267i) q^{76} +2.77200 q^{77} +(-1.88600 + 3.26665i) q^{78} +(4.00000 - 6.92820i) q^{79} +(-1.50000 - 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-0.613999 - 1.06348i) q^{82} -6.22800 q^{83} +1.00000 q^{84} +(-7.15800 - 12.3980i) q^{85} +(3.00000 + 5.19615i) q^{86} +2.77200 q^{88} +(8.15800 + 14.1301i) q^{89} +(1.50000 - 2.59808i) q^{90} +(1.88600 + 3.26665i) q^{91} +(2.88600 - 4.99870i) q^{92} +(-3.77200 + 6.53330i) q^{93} -11.5440 q^{94} +(8.65800 - 9.79995i) q^{95} +1.00000 q^{96} +(5.77200 - 9.99740i) q^{97} +(0.500000 - 0.866025i) q^{98} +(1.38600 + 2.40062i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 6 q^{5} - 2 q^{6} - 4 q^{7} - 4 q^{8} - 2 q^{9} + 6 q^{10} + 6 q^{11} - 4 q^{12} + q^{13} - 2 q^{14} + 6 q^{15} - 2 q^{16} - q^{17} - 4 q^{18} + 12 q^{20} - 2 q^{21}+ \cdots - 3 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 6 * q^5 - 2 * q^6 - 4 * q^7 - 4 * q^8 - 2 * q^9 + 6 * q^10 + 6 * q^11 - 4 * q^12 + q^13 - 2 * q^14 + 6 * q^15 - 2 * q^16 - q^17 - 4 * q^18 + 12 * q^20 - 2 * q^21 + 3 * q^22 + 3 * q^23 - 2 * q^24 - 8 * q^25 + 2 * q^26 - 4 * q^27 + 2 * q^28 + 12 * q^30 + 4 * q^31 + 2 * q^32 + 3 * q^33 + q^34 + 6 * q^35 - 2 * q^36 - 22 * q^37 - 3 * q^38 + 2 * q^39 + 6 * q^40 + 11 * q^41 + 2 * q^42 - 12 * q^43 - 3 * q^44 + 12 * q^45 + 6 * q^46 - 6 * q^47 + 2 * q^48 + 4 * q^49 - 16 * q^50 + q^51 + q^52 + 8 * q^53 - 2 * q^54 - 9 * q^55 + 4 * q^56 - 3 * q^57 - 9 * q^59 + 6 * q^60 + 21 * q^61 + 2 * q^62 + 2 * q^63 + 4 * q^64 - 6 * q^65 - 3 * q^66 + 2 * q^68 + 6 * q^69 - 6 * q^70 + 19 * q^71 + 2 * q^72 + 4 * q^73 - 11 * q^74 - 16 * q^75 - 3 * q^76 - 6 * q^77 + q^78 + 16 * q^79 - 6 * q^80 - 2 * q^81 - 11 * q^82 - 42 * q^83 + 4 * q^84 - 3 * q^85 + 12 * q^86 - 6 * q^88 + 7 * q^89 + 6 * q^90 - q^91 + 3 * q^92 + 2 * q^93 - 12 * q^94 + 9 * q^95 + 4 * q^96 + 6 * q^97 + 2 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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