LMFDB - Embedded newform 87.2.f.b.17.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(17,87)] 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("87.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	87.17
Dual form			87.2.f.b.41.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36603 + 1.36603i) q^{2} +(1.50000 - 0.866025i) q^{3} +1.73205i q^{4} -3.73205 q^{5} +(3.23205 + 0.866025i) q^{6} -2.73205 q^{7} +(0.366025 - 0.366025i) q^{8} +(1.50000 - 2.59808i) q^{9} +(-5.09808 - 5.09808i) q^{10} +(0.366025 + 0.366025i) q^{11} +(1.50000 + 2.59808i) q^{12} +5.73205i q^{13} +(-3.73205 - 3.73205i) q^{14} +(-5.59808 + 3.23205i) q^{15} +4.46410 q^{16} +(0.732051 + 0.732051i) q^{17} +(5.59808 - 1.50000i) q^{18} +(1.73205 - 1.73205i) q^{19} -6.46410i q^{20} +(-4.09808 + 2.36603i) q^{21} +1.00000i q^{22} -1.46410i q^{23} +(0.232051 - 0.866025i) q^{24} +8.92820 q^{25} +(-7.83013 + 7.83013i) q^{26} -5.19615i q^{27} -4.73205i q^{28} +(-2.00000 - 5.00000i) q^{29} +(-12.0622 - 3.23205i) q^{30} +(0.633975 - 0.633975i) q^{31} +(5.36603 + 5.36603i) q^{32} +(0.866025 + 0.232051i) q^{33} +2.00000i q^{34} +10.1962 q^{35} +(4.50000 + 2.59808i) q^{36} +(-3.46410 - 3.46410i) q^{37} +4.73205 q^{38} +(4.96410 + 8.59808i) q^{39} +(-1.36603 + 1.36603i) q^{40} +(-5.19615 + 5.19615i) q^{41} +(-8.83013 - 2.36603i) q^{42} +(-3.56218 + 3.56218i) q^{43} +(-0.633975 + 0.633975i) q^{44} +(-5.59808 + 9.69615i) q^{45} +(2.00000 - 2.00000i) q^{46} +(-0.830127 + 0.830127i) q^{47} +(6.69615 - 3.86603i) q^{48} +0.464102 q^{49} +(12.1962 + 12.1962i) q^{50} +(1.73205 + 0.464102i) q^{51} -9.92820 q^{52} -3.92820i q^{53} +(7.09808 - 7.09808i) q^{54} +(-1.36603 - 1.36603i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(1.09808 - 4.09808i) q^{57} +(4.09808 - 9.56218i) q^{58} +0.535898i q^{59} +(-5.59808 - 9.69615i) q^{60} +(-2.00000 + 2.00000i) q^{61} +1.73205 q^{62} +(-4.09808 + 7.09808i) q^{63} +5.73205i q^{64} -21.3923i q^{65} +(0.866025 + 1.50000i) q^{66} +8.92820i q^{67} +(-1.26795 + 1.26795i) q^{68} +(-1.26795 - 2.19615i) q^{69} +(13.9282 + 13.9282i) q^{70} +16.7321 q^{71} +(-0.401924 - 1.50000i) q^{72} +(-4.00000 - 4.00000i) q^{73} -9.46410i q^{74} +(13.3923 - 7.73205i) q^{75} +(3.00000 + 3.00000i) q^{76} +(-1.00000 - 1.00000i) q^{77} +(-4.96410 + 18.5263i) q^{78} +(1.83013 - 1.83013i) q^{79} -16.6603 q^{80} +(-4.50000 - 7.79423i) q^{81} -14.1962 q^{82} +13.8564i q^{83} +(-4.09808 - 7.09808i) q^{84} +(-2.73205 - 2.73205i) q^{85} -9.73205 q^{86} +(-7.33013 - 5.76795i) q^{87} +0.267949 q^{88} +(-5.00000 - 5.00000i) q^{89} +(-20.8923 + 5.59808i) q^{90} -15.6603i q^{91} +2.53590 q^{92} +(0.401924 - 1.50000i) q^{93} -2.26795 q^{94} +(-6.46410 + 6.46410i) q^{95} +(12.6962 + 3.40192i) q^{96} +(-7.73205 - 7.73205i) q^{97} +(0.633975 + 0.633975i) q^{98} +(1.50000 - 0.401924i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{3} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9} - 10 q^{10} - 2 q^{11} + 6 q^{12} - 8 q^{14} - 12 q^{15} + 4 q^{16} - 4 q^{17} + 12 q^{18} - 6 q^{21} - 6 q^{24} + 8 q^{25} - 14 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^3 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9 - 10 * q^10 - 2 * q^11 + 6 * q^12 - 8 * q^14 - 12 * q^15 + 4 * q^16 - 4 * q^17 + 12 * q^18 - 6 * q^21 - 6 * q^24 + 8 * q^25 - 14 * q^26 - 8 * q^29 - 24 * q^30 + 6 * q^31 + 18 * q^32 + 20 * q^35 + 18 * q^36 + 12 * q^38 + 6 * q^39 - 2 * q^40 - 18 * q^42 + 10 * q^43 - 6 * q^44 - 12 * q^45 + 8 * q^46 + 14 * q^47 + 6 * q^48 - 12 * q^49 + 28 * q^50 - 12 * q^52 + 18 * q^54 - 2 * q^55 - 4 * q^56 - 6 * q^57 + 6 * q^58 - 12 * q^60 - 8 * q^61 - 6 * q^63 - 12 * q^68 - 12 * q^69 + 28 * q^70 + 60 * q^71 - 12 * q^72 - 16 * q^73 + 12 * q^75 + 12 * q^76 - 4 * q^77 - 6 * q^78 - 10 * q^79 - 32 * q^80 - 18 * q^81 - 36 * q^82 - 6 * q^84 - 4 * q^85 - 32 * q^86 - 12 * q^87 + 8 * q^88 - 20 * q^89 - 42 * q^90 + 24 * q^92 + 12 * q^93 - 16 * q^94 - 12 * q^95 + 30 * q^96 - 24 * q^97 + 6 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	1.36603	+	1.36603i	0.965926	+	0.965926i	0.999438	−	0.0335125i	$-0.0106693\pi$
$2$	1.36603	+	1.36603i	0.965926	+	0.965926i	−0.0335125	+	0.999438i	$0.510669\pi$
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$3$	1.50000	−	0.866025i	0.866025	−	0.500000i
$4$			1.73205i			0.866025i
$5$	−3.73205			−1.66902			−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−3.73205			−1.66902			−0.834512	+	0.550990i	$0.814250\pi$
$6$	3.23205	+	0.866025i	1.31948	+	0.353553i
$7$	−2.73205			−1.03262			−0.516309	−	0.856402i	$-0.672694\pi$
$7$	−2.73205			−1.03262			−0.516309	+	0.856402i	$0.672694\pi$
$8$	0.366025	−	0.366025i	0.129410	−	0.129410i
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−5.09808	−	5.09808i	−1.61215	−	1.61215i
$11$	0.366025	+	0.366025i	0.110361	+	0.110361i	0.760131	−	0.649770i	$-0.225135\pi$
$11$	0.366025	+	0.366025i	0.110361	+	0.110361i	−0.649770	+	0.760131i	$0.725135\pi$
$12$	1.50000	+	2.59808i	0.433013	+	0.750000i
$13$			5.73205i			1.58978i	0.606750	+	0.794892i	$0.292473\pi$
$13$			5.73205i			1.58978i	−0.606750	+	0.794892i	$0.707527\pi$
$14$	−3.73205	−	3.73205i	−0.997433	−	0.997433i
$15$	−5.59808	+	3.23205i	−1.44542	+	0.834512i
$16$	4.46410			1.11603
$17$	0.732051	+	0.732051i	0.177548	+	0.177548i	0.790286	−	0.612738i	$-0.209932\pi$
$17$	0.732051	+	0.732051i	0.177548	+	0.177548i	−0.612738	+	0.790286i	$0.709932\pi$
$18$	5.59808	−	1.50000i	1.31948	−	0.353553i
$19$	1.73205	−	1.73205i	0.397360	−	0.397360i	−0.479941	−	0.877301i	$-0.659342\pi$
$19$	1.73205	−	1.73205i	0.397360	−	0.397360i	0.877301	+	0.479941i	$0.159342\pi$
$20$		−	6.46410i		−	1.44542i
$21$	−4.09808	+	2.36603i	−0.894274	+	0.516309i
$22$			1.00000i			0.213201i
$23$		−	1.46410i		−	0.305286i	−0.988281	−	0.152643i	$-0.951221\pi$
$23$		−	1.46410i		−	0.305286i	0.988281	−	0.152643i	$-0.0487785\pi$
$24$	0.232051	−	0.866025i	0.0473672	−	0.176777i
$25$	8.92820			1.78564
$26$	−7.83013	+	7.83013i	−1.53561	+	1.53561i
$27$		−	5.19615i		−	1.00000i
$28$		−	4.73205i		−	0.894274i
$29$	−2.00000	−	5.00000i	−0.371391	−	0.928477i
$29$	−2.00000	−	5.00000i	−0.371391	−	0.928477i
$30$	−12.0622	−	3.23205i	−2.20224	−	0.590089i
$31$	0.633975	−	0.633975i	0.113865	−	0.113865i	−0.647878	−	0.761744i	$-0.724344\pi$
$31$	0.633975	−	0.633975i	0.113865	−	0.113865i	0.761744	+	0.647878i	$0.224344\pi$
$32$	5.36603	+	5.36603i	0.948588	+	0.948588i
$33$	0.866025	+	0.232051i	0.150756	+	0.0403949i
$34$			2.00000i			0.342997i
$35$	10.1962			1.72346
$36$	4.50000	+	2.59808i	0.750000	+	0.433013i
$37$	−3.46410	−	3.46410i	−0.569495	−	0.569495i	0.362492	−	0.931987i	$-0.381926\pi$
$37$	−3.46410	−	3.46410i	−0.569495	−	0.569495i	−0.931987	+	0.362492i	$0.881926\pi$
$38$	4.73205			0.767640
$39$	4.96410	+	8.59808i	0.794892	+	1.37679i
$40$	−1.36603	+	1.36603i	−0.215988	+	0.215988i
$41$	−5.19615	+	5.19615i	−0.811503	+	0.811503i	−0.984859	−	0.173356i	$-0.944539\pi$
$41$	−5.19615	+	5.19615i	−0.811503	+	0.811503i	0.173356	+	0.984859i	$0.444539\pi$
$42$	−8.83013	−	2.36603i	−1.36252	−	0.365086i
$43$	−3.56218	+	3.56218i	−0.543227	+	0.543227i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$	−3.56218	+	3.56218i	−0.543227	+	0.543227i	0.381246	+	0.924473i	$0.375495\pi$
$44$	−0.633975	+	0.633975i	−0.0955753	+	0.0955753i
$45$	−5.59808	+	9.69615i	−0.834512	+	1.44542i
$46$	2.00000	−	2.00000i	0.294884	−	0.294884i
$47$	−0.830127	+	0.830127i	−0.121086	+	0.121086i	−0.765053	−	0.643967i	$-0.777287\pi$
$47$	−0.830127	+	0.830127i	−0.121086	+	0.121086i	0.643967	+	0.765053i	$0.277287\pi$
$48$	6.69615	−	3.86603i	0.966506	−	0.558013i
$49$	0.464102			0.0663002
$50$	12.1962	+	12.1962i	1.72480	+	1.72480i
$51$	1.73205	+	0.464102i	0.242536	+	0.0649872i
$52$	−9.92820			−1.37679
$53$		−	3.92820i		−	0.539580i	−0.962919	−	0.269790i	$-0.913046\pi$
$53$		−	3.92820i		−	0.539580i	0.962919	−	0.269790i	$-0.0869543\pi$
$54$	7.09808	−	7.09808i	0.965926	−	0.965926i
$55$	−1.36603	−	1.36603i	−0.184195	−	0.184195i
$56$	−1.00000	+	1.00000i	−0.133631	+	0.133631i
$57$	1.09808	−	4.09808i	0.145444	−	0.542803i
$58$	4.09808	−	9.56218i	0.538104	−	1.25558i
$59$			0.535898i			0.0697680i	0.999391	+	0.0348840i	$0.0111062\pi$
$59$			0.535898i			0.0697680i	−0.999391	+	0.0348840i	$0.988894\pi$
$60$	−5.59808	−	9.69615i	−0.722709	−	1.25177i
$61$	−2.00000	+	2.00000i	−0.256074	+	0.256074i	−0.823455	−	0.567381i	$-0.807957\pi$
$61$	−2.00000	+	2.00000i	−0.256074	+	0.256074i	0.567381	+	0.823455i	$0.307957\pi$
$62$	1.73205			0.219971
$63$	−4.09808	+	7.09808i	−0.516309	+	0.894274i
$64$			5.73205i			0.716506i
$65$		−	21.3923i		−	2.65339i
$66$	0.866025	+	1.50000i	0.106600	+	0.184637i
$67$			8.92820i			1.09075i	0.838191	+	0.545377i	$0.183613\pi$
$67$			8.92820i			1.09075i	−0.838191	+	0.545377i	$0.816387\pi$
$68$	−1.26795	+	1.26795i	−0.153761	+	0.153761i
$69$	−1.26795	−	2.19615i	−0.152643	−	0.264386i
$70$	13.9282	+	13.9282i	1.66474	+	1.66474i
$71$	16.7321			1.98573			0.992865	−	0.119248i	$-0.0380482\pi$
$71$	16.7321			1.98573			0.992865	+	0.119248i	$0.0380482\pi$
$72$	−0.401924	−	1.50000i	−0.0473672	−	0.176777i
$73$	−4.00000	−	4.00000i	−0.468165	−	0.468165i	0.433155	−	0.901319i	$-0.357400\pi$
$73$	−4.00000	−	4.00000i	−0.468165	−	0.468165i	−0.901319	+	0.433155i	$0.857400\pi$
$74$		−	9.46410i		−	1.10018i
$75$	13.3923	−	7.73205i	1.54641	−	0.892820i
$76$	3.00000	+	3.00000i	0.344124	+	0.344124i
$77$	−1.00000	−	1.00000i	−0.113961	−	0.113961i
$78$	−4.96410	+	18.5263i	−0.562074	+	2.09769i
$79$	1.83013	−	1.83013i	0.205905	−	0.205905i	−0.596619	−	0.802525i	$-0.703490\pi$
$79$	1.83013	−	1.83013i	0.205905	−	0.205905i	0.802525	+	0.596619i	$0.203490\pi$
$80$	−16.6603			−1.86267
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−14.1962			−1.56770
$83$			13.8564i			1.52094i	0.649374	+	0.760469i	$0.275031\pi$
$83$			13.8564i			1.52094i	−0.649374	+	0.760469i	$0.724969\pi$
$84$	−4.09808	−	7.09808i	−0.447137	−	0.774464i
$85$	−2.73205	−	2.73205i	−0.296333	−	0.296333i
$86$	−9.73205			−1.04943
$87$	−7.33013	−	5.76795i	−0.785872	−	0.618389i
$88$	0.267949			0.0285635
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	0.390573	−	0.920572i	$-0.372277\pi$
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	−0.920572	+	0.390573i	$0.872277\pi$
$90$	−20.8923	+	5.59808i	−2.20224	+	0.590089i
$91$		−	15.6603i		−	1.64164i
$92$	2.53590			0.264386
$93$	0.401924	−	1.50000i	0.0416776	−	0.155543i
$94$	−2.26795			−0.233921
$95$	−6.46410	+	6.46410i	−0.663203	+	0.663203i
$96$	12.6962	+	3.40192i	1.29580	+	0.347207i
$97$	−7.73205	−	7.73205i	−0.785071	−	0.785071i	0.195611	−	0.980682i	$-0.437331\pi$
$97$	−7.73205	−	7.73205i	−0.785071	−	0.785071i	−0.980682	+	0.195611i	$0.937331\pi$
$98$	0.633975	+	0.633975i	0.0640411	+	0.0640411i
$99$	1.50000	−	0.401924i	0.150756	−	0.0403949i
$100$			15.4641i			1.54641i
$101$	4.19615	+	4.19615i	0.417533	+	0.417533i	0.884352	−	0.466820i	$-0.154600\pi$
$101$	4.19615	+	4.19615i	0.417533	+	0.417533i	−0.466820	+	0.884352i	$0.654600\pi$
$102$	1.73205	+	3.00000i	0.171499	+	0.297044i
$103$	10.7321			1.05746			0.528730	−	0.848790i	$-0.322668\pi$
$103$	10.7321			1.05746			0.528730	+	0.848790i	$0.322668\pi$
$104$	2.09808	+	2.09808i	0.205733	+	0.205733i
$105$	15.2942	−	8.83013i	1.49256	−	0.861732i
$106$	5.36603	−	5.36603i	0.521194	−	0.521194i
$107$			5.26795i			0.509272i	0.967037	+	0.254636i	$0.0819556\pi$
$107$			5.26795i			0.509272i	−0.967037	+	0.254636i	$0.918044\pi$
$108$	9.00000			0.866025
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		−	3.73205i		−	0.355837i
$111$	−8.19615	−	2.19615i	−0.777944	−	0.208450i
$112$	−12.1962			−1.15243
$113$	5.92820	−	5.92820i	0.557678	−	0.557678i	−0.370967	−	0.928646i	$-0.620974\pi$
$113$	5.92820	−	5.92820i	0.557678	−	0.557678i	0.928646	+	0.370967i	$0.120974\pi$
$114$	7.09808	−	4.09808i	0.664796	−	0.383820i
$115$			5.46410i			0.509530i
$116$	8.66025	−	3.46410i	0.804084	−	0.321634i
$117$	14.8923	+	8.59808i	1.37679	+	0.794892i
$118$	−0.732051	+	0.732051i	−0.0673907	+	0.0673907i
$119$	−2.00000	−	2.00000i	−0.183340	−	0.183340i
$120$	−0.866025	+	3.23205i	−0.0790569	+	0.295045i
$121$		−	10.7321i		−	0.975641i
$122$	−5.46410			−0.494697
$123$	−3.29423	+	12.2942i	−0.297031	+	1.10853i
$124$	1.09808	+	1.09808i	0.0986102	+	0.0986102i
$125$	−14.6603			−1.31125
$126$	−15.2942	+	4.09808i	−1.36252	+	0.365086i
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$	2.90192	−	2.90192i	0.256496	−	0.256496i
$129$	−2.25833	+	8.42820i	−0.198835	+	0.742062i
$130$	29.2224	−	29.2224i	2.56298	−	2.56298i
$131$	11.3923	−	11.3923i	0.995350	−	0.995350i	−0.00463894	−	0.999989i	$-0.501477\pi$
$131$	11.3923	−	11.3923i	0.995350	−	0.995350i	0.999989	+	0.00463894i	$0.00147663\pi$
$132$	−0.401924	+	1.50000i	−0.0349830	+	0.130558i
$133$	−4.73205	+	4.73205i	−0.410321	+	0.410321i
$134$	−12.1962	+	12.1962i	−1.05359	+	1.05359i
$135$			19.3923i			1.66902i
$136$	0.535898			0.0459529
$137$	4.73205	+	4.73205i	0.404286	+	0.404286i	0.879741	−	0.475454i	$-0.157716\pi$
$137$	4.73205	+	4.73205i	0.404286	+	0.404286i	−0.475454	+	0.879741i	$0.657716\pi$
$138$	1.26795	−	4.73205i	0.107935	−	0.402819i
$139$	−11.4641			−0.972372			−0.486186	−	0.873855i	$-0.661612\pi$
$139$	−11.4641			−0.972372			−0.486186	+	0.873855i	$0.661612\pi$
$140$			17.6603i			1.49256i
$141$	−0.526279	+	1.96410i	−0.0443207	+	0.165407i
$142$	22.8564	+	22.8564i	1.91807	+	1.91807i
$143$	−2.09808	+	2.09808i	−0.175450	+	0.175450i
$144$	6.69615	−	11.5981i	0.558013	−	0.966506i
$145$	7.46410	+	18.6603i	0.619860	+	1.54965i
$146$		−	10.9282i		−	0.904425i
$147$	0.696152	−	0.401924i	0.0574177	−	0.0331501i
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	−11.5359			−0.945058			−0.472529	−	0.881315i	$-0.656659\pi$
$149$	−11.5359			−0.945058			−0.472529	+	0.881315i	$0.656659\pi$
$150$	28.8564	+	7.73205i	2.35612	+	0.631319i
$151$		−	5.66025i		−	0.460625i	−0.973117	−	0.230312i	$-0.926025\pi$
$151$		−	5.66025i		−	0.460625i	0.973117	−	0.230312i	$-0.0739748\pi$
$152$		−	1.26795i		−	0.102844i
$153$	3.00000	−	0.803848i	0.242536	−	0.0649872i
$154$		−	2.73205i		−	0.220155i
$155$	−2.36603	+	2.36603i	−0.190044	+	0.190044i
$156$	−14.8923	+	8.59808i	−1.19234	+	0.688397i
$157$	5.53590	+	5.53590i	0.441813	+	0.441813i	0.892621	−	0.450808i	$-0.148864\pi$
$157$	5.53590	+	5.53590i	0.441813	+	0.441813i	−0.450808	+	0.892621i	$0.648864\pi$
$158$	5.00000			0.397779
$159$	−3.40192	−	5.89230i	−0.269790	−	0.467290i
$160$	−20.0263	−	20.0263i	−1.58322	−	1.58322i
$161$			4.00000i			0.315244i
$162$	4.50000	−	16.7942i	0.353553	−	1.31948i
$163$	9.09808	+	9.09808i	0.712616	+	0.712616i	0.967082	−	0.254466i	$-0.0818995\pi$
$163$	9.09808	+	9.09808i	0.712616	+	0.712616i	−0.254466	+	0.967082i	$0.581900\pi$
$164$	−9.00000	−	9.00000i	−0.702782	−	0.702782i
$165$	−3.23205	−	0.866025i	−0.251615	−	0.0674200i
$166$	−18.9282	+	18.9282i	−1.46911	+	1.46911i
$167$	3.26795			0.252882			0.126441	−	0.991974i	$-0.459645\pi$
$167$	3.26795			0.252882			0.126441	+	0.991974i	$0.459645\pi$
$168$	−0.633975	+	2.36603i	−0.0489122	+	0.182543i
$169$	−19.8564			−1.52742
$170$		−	7.46410i		−	0.572470i
$171$	−1.90192	−	7.09808i	−0.145444	−	0.542803i
$172$	−6.16987	−	6.16987i	−0.470448	−	0.470448i
$173$	−13.4641			−1.02366			−0.511828	−	0.859088i	$-0.671032\pi$
$173$	−13.4641			−1.02366			−0.511828	+	0.859088i	$0.671032\pi$
$174$	−2.13397	−	17.8923i	−0.161776	−	1.35641i
$175$	−24.3923			−1.84388
$176$	1.63397	+	1.63397i	0.123165	+	0.123165i
$177$	0.464102	+	0.803848i	0.0348840	+	0.0604209i
$178$		−	13.6603i		−	1.02388i
$179$	−16.5885			−1.23988			−0.619940	−	0.784649i	$-0.712843\pi$
$179$	−16.5885			−1.23988			−0.619940	+	0.784649i	$0.712843\pi$
$180$	−16.7942	−	9.69615i	−1.25177	−	0.722709i
$181$	16.3205			1.21309			0.606547	−	0.795048i	$-0.292554\pi$
$181$	16.3205			1.21309			0.606547	+	0.795048i	$0.292554\pi$
$182$	21.3923	−	21.3923i	1.58570	−	1.58570i
$183$	−1.26795	+	4.73205i	−0.0937295	+	0.349803i
$184$	−0.535898	−	0.535898i	−0.0395070	−	0.0395070i
$185$	12.9282	+	12.9282i	0.950500	+	0.950500i
$186$	2.59808	−	1.50000i	0.190500	−	0.109985i
$187$			0.535898i			0.0391888i
$188$	−1.43782	−	1.43782i	−0.104864	−	0.104864i
$189$			14.1962i			1.03262i
$190$	−17.6603			−1.28121
$191$	−15.9282	−	15.9282i	−1.15252	−	1.15252i	−0.986045	−	0.166479i	$-0.946760\pi$
$191$	−15.9282	−	15.9282i	−1.15252	−	1.15252i	−0.166479	−	0.986045i	$-0.553240\pi$
$192$	4.96410	+	8.59808i	0.358253	+	0.620513i
$193$	−9.92820	+	9.92820i	−0.714648	+	0.714648i	−0.967504	−	0.252856i	$-0.918630\pi$
$193$	−9.92820	+	9.92820i	−0.714648	+	0.714648i	0.252856	+	0.967504i	$0.418630\pi$
$194$		−	21.1244i		−	1.51664i
$195$	−18.5263	−	32.0885i	−1.32669	−	2.29790i
$196$			0.803848i			0.0574177i
$197$			24.9282i			1.77606i	0.459785	+	0.888030i	$0.347927\pi$
$197$			24.9282i			1.77606i	−0.459785	+	0.888030i	$0.652073\pi$
$198$	2.59808	+	1.50000i	0.184637	+	0.106600i
$199$	2.73205			0.193670			0.0968350	−	0.995300i	$-0.469128\pi$
$199$	2.73205			0.193670			0.0968350	+	0.995300i	$0.469128\pi$
$200$	3.26795	−	3.26795i	0.231079	−	0.231079i
$201$	7.73205	+	13.3923i	0.545377	+	0.944620i
$202$			11.4641i			0.806611i
$203$	5.46410	+	13.6603i	0.383505	+	0.958762i
$204$	−0.803848	+	3.00000i	−0.0562806	+	0.210042i
$205$	19.3923	−	19.3923i	1.35442	−	1.35442i
$206$	14.6603	+	14.6603i	1.02143	+	1.02143i
$207$	−3.80385	−	2.19615i	−0.264386	−	0.152643i
$208$			25.5885i			1.77424i
$209$	1.26795			0.0877059
$210$	32.9545	+	8.83013i	2.27408	+	0.609337i
$211$	14.0263	+	14.0263i	0.965609	+	0.965609i	0.999428	−	0.0338191i	$-0.0107670\pi$
$211$	14.0263	+	14.0263i	0.965609	+	0.965609i	−0.0338191	+	0.999428i	$0.510767\pi$
$212$	6.80385			0.467290
$213$	25.0981	−	14.4904i	1.71969	−	0.992865i
$214$	−7.19615	+	7.19615i	−0.491919	+	0.491919i
$215$	13.2942	−	13.2942i	0.906659	−	0.906659i
$216$	−1.90192	−	1.90192i	−0.129410	−	0.129410i
$217$	−1.73205	+	1.73205i	−0.117579	+	0.117579i
$218$	−9.56218	+	9.56218i	−0.647632	+	0.647632i
$219$	−9.46410	−	2.53590i	−0.639525	−	0.171360i
$220$	2.36603	−	2.36603i	0.159517	−	0.159517i
$221$	−4.19615	+	4.19615i	−0.282264	+	0.282264i
$222$	−8.19615	−	14.1962i	−0.550090	−	0.952783i
$223$	0.732051			0.0490217			0.0245109	−	0.999700i	$-0.492197\pi$
$223$	0.732051			0.0490217			0.0245109	+	0.999700i	$0.492197\pi$
$224$	−14.6603	−	14.6603i	−0.979529	−	0.979529i
$225$	13.3923	−	23.1962i	0.892820	−	1.54641i
$226$	16.1962			1.07735
$227$		−	9.12436i		−	0.605605i	−0.953053	−	0.302802i	$-0.902078\pi$
$227$		−	9.12436i		−	0.605605i	0.953053	−	0.302802i	$-0.0979222\pi$
$228$	7.09808	+	1.90192i	0.470082	+	0.125958i
$229$	−20.3205	−	20.3205i	−1.34282	−	1.34282i	−0.893243	−	0.449574i	$-0.851576\pi$
$229$	−20.3205	−	20.3205i	−1.34282	−	1.34282i	−0.449574	−	0.893243i	$-0.648424\pi$
$230$	−7.46410	+	7.46410i	−0.492168	+	0.492168i
$231$	−2.36603	−	0.633975i	−0.155673	−	0.0417125i
$232$	−2.56218	−	1.09808i	−0.168215	−	0.0720922i
$233$			20.1244i			1.31839i	0.751972	+	0.659195i	$0.229103\pi$
$233$			20.1244i			1.31839i	−0.751972	+	0.659195i	$0.770897\pi$
$234$	8.59808	+	32.0885i	0.562074	+	2.09769i
$235$	3.09808	−	3.09808i	0.202096	−	0.202096i
$236$	−0.928203			−0.0604209
$237$	1.16025	−	4.33013i	0.0753666	−	0.281272i
$238$		−	5.46410i		−	0.354185i
$239$			6.00000i			0.388108i	0.980991	+	0.194054i	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$	−24.9904	+	14.4282i	−1.61312	+	0.931337i
$241$		−	13.5359i		−	0.871924i	−0.899965	−	0.435962i	$-0.856408\pi$
$241$		−	13.5359i		−	0.871924i	0.899965	−	0.435962i	$-0.143592\pi$
$242$	14.6603	−	14.6603i	0.942397	−	0.942397i
$243$	−13.5000	−	7.79423i	−0.866025	−	0.500000i
$244$	−3.46410	−	3.46410i	−0.221766	−	0.221766i
$245$	−1.73205			−0.110657
$246$	−21.2942	+	12.2942i	−1.35767	+	0.783851i
$247$	9.92820	+	9.92820i	0.631716	+	0.631716i
$248$		−	0.464102i		−	0.0294705i
$249$	12.0000	+	20.7846i	0.760469	+	1.31717i
$250$	−20.0263	−	20.0263i	−1.26657	−	1.26657i
$251$	10.6340	+	10.6340i	0.671211	+	0.671211i	0.957995	−	0.286785i	$-0.0925864\pi$
$251$	10.6340	+	10.6340i	0.671211	+	0.671211i	−0.286785	+	0.957995i	$0.592586\pi$
$252$	−12.2942	−	7.09808i	−0.774464	−	0.447137i
$253$	0.535898	−	0.535898i	0.0336916	−	0.0336916i
$254$	24.5885			1.54282
$255$	−6.46410	−	1.73205i	−0.404798	−	0.108465i
$256$	19.3923			1.21202
$257$		−	9.92820i		−	0.619304i	−0.950850	−	0.309652i	$-0.899787\pi$
$257$		−	9.92820i		−	0.619304i	0.950850	−	0.309652i	$-0.100213\pi$
$258$	−14.5981	+	8.42820i	−0.908837	+	0.524717i
$259$	9.46410	+	9.46410i	0.588071	+	0.588071i
$260$	37.0526			2.29790
$261$	−15.9904	−	2.30385i	−0.989780	−	0.142605i
$262$	31.1244			1.92287
$263$	15.2942	+	15.2942i	0.943083	+	0.943083i	0.998465	−	0.0553827i	$-0.0176379\pi$
$263$	15.2942	+	15.2942i	0.943083	+	0.943083i	−0.0553827	+	0.998465i	$0.517638\pi$
$264$	0.401924	−	0.232051i	0.0247367	−	0.0142817i
$265$			14.6603i			0.900572i
$266$	−12.9282			−0.792679
$267$	−11.8301	−	3.16987i	−0.723992	−	0.193993i
$268$	−15.4641			−0.944620
$269$	2.00000	−	2.00000i	0.121942	−	0.121942i	−0.643502	−	0.765444i	$-0.722519\pi$
$269$	2.00000	−	2.00000i	0.121942	−	0.121942i	0.765444	+	0.643502i	$0.222519\pi$
$270$	−26.4904	+	26.4904i	−1.61215	+	1.61215i
$271$	−7.16987	−	7.16987i	−0.435539	−	0.435539i	0.454969	−	0.890507i	$-0.349650\pi$
$271$	−7.16987	−	7.16987i	−0.435539	−	0.435539i	−0.890507	+	0.454969i	$0.849650\pi$
$272$	3.26795	+	3.26795i	0.198149	+	0.198149i
$273$	−13.5622	−	23.4904i	−0.820820	−	1.42170i
$274$			12.9282i			0.781021i
$275$	3.26795	+	3.26795i	0.197065	+	0.197065i
$276$	3.80385	−	2.19615i	0.228965	−	0.132193i
$277$	5.60770			0.336934			0.168467	−	0.985707i	$-0.446118\pi$
$277$	5.60770			0.336934			0.168467	+	0.985707i	$0.446118\pi$
$278$	−15.6603	−	15.6603i	−0.939240	−	0.939240i
$279$	−0.696152	−	2.59808i	−0.0416776	−	0.155543i
$280$	3.73205	−	3.73205i	0.223033	−	0.223033i
$281$			1.73205i			0.103325i	0.998665	+	0.0516627i	$0.0164521\pi$
$281$			1.73205i			0.103325i	−0.998665	+	0.0516627i	$0.983548\pi$
$282$	−3.40192	+	1.96410i	−0.202582	+	0.116961i
$283$			6.00000i			0.356663i	0.983970	+	0.178331i	$0.0570699\pi$
$283$			6.00000i			0.356663i	−0.983970	+	0.178331i	$0.942930\pi$
$284$			28.9808i			1.71969i
$285$	−4.09808	+	15.2942i	−0.242749	+	0.905952i
$286$	−5.73205			−0.338943
$287$	14.1962	−	14.1962i	0.837972	−	0.837972i
$288$	21.9904	−	5.89230i	1.29580	−	0.347207i
$289$		−	15.9282i		−	0.936953i
$290$	−15.2942	+	35.6865i	−0.898108	+	2.09559i
$291$	−18.2942	−	4.90192i	−1.07243	−	0.287356i
$292$	6.92820	−	6.92820i	0.405442	−	0.405442i
$293$	−16.1244	−	16.1244i	−0.941995	−	0.941995i	0.0564126	−	0.998408i	$-0.482034\pi$
$293$	−16.1244	−	16.1244i	−0.941995	−	0.941995i	−0.998408	+	0.0564126i	$0.982034\pi$
$294$	1.50000	+	0.401924i	0.0874818	+	0.0234407i
$295$		−	2.00000i		−	0.116445i
$296$	−2.53590			−0.147396
$297$	1.90192	−	1.90192i	0.110361	−	0.110361i
$298$	−15.7583	−	15.7583i	−0.912856	−	0.912856i
$299$	8.39230			0.485340
$300$	13.3923	+	23.1962i	0.773205	+	1.33923i
$301$	9.73205	−	9.73205i	0.560946	−	0.560946i
$302$	7.73205	−	7.73205i	0.444930	−	0.444930i
$303$	9.92820	+	2.66025i	0.570360	+	0.152828i
$304$	7.73205	−	7.73205i	0.443464	−	0.443464i
$305$	7.46410	−	7.46410i	0.427393	−	0.427393i
$306$	5.19615	+	3.00000i	0.297044	+	0.171499i
$307$	2.49038	−	2.49038i	0.142134	−	0.142134i	−0.632460	−	0.774593i	$-0.717955\pi$
$307$	2.49038	−	2.49038i	0.142134	−	0.142134i	0.774593	+	0.632460i	$0.217955\pi$
$308$	1.73205	−	1.73205i	0.0986928	−	0.0986928i
$309$	16.0981	−	9.29423i	0.915788	−	0.528730i
$310$	−6.46410			−0.367136
$311$	−16.4641	−	16.4641i	−0.933594	−	0.933594i	0.0643348	−	0.997928i	$-0.479507\pi$
$311$	−16.4641	−	16.4641i	−0.933594	−	0.933594i	−0.997928	+	0.0643348i	$0.979507\pi$
$312$	4.96410	+	1.33013i	0.281037	+	0.0753036i
$313$	7.58846			0.428925			0.214462	−	0.976732i	$-0.431200\pi$
$313$	7.58846			0.428925			0.214462	+	0.976732i	$0.431200\pi$
$314$			15.1244i			0.853517i
$315$	15.2942	−	26.4904i	0.861732	−	1.49256i
$316$	3.16987	+	3.16987i	0.178319	+	0.178319i
$317$	−18.3923	+	18.3923i	−1.03301	+	1.03301i	−0.0335787	+	0.999436i	$0.510690\pi$
$317$	−18.3923	+	18.3923i	−1.03301	+	1.03301i	−0.999436	+	0.0335787i	$0.989310\pi$
$318$	3.40192	−	12.6962i	0.190770	−	0.711965i
$319$	1.09808	−	2.56218i	0.0614805	−	0.143454i
$320$		−	21.3923i		−	1.19587i
$321$	4.56218	+	7.90192i	0.254636	+	0.441042i
$322$	−5.46410	+	5.46410i	−0.304502	+	0.304502i
$323$	2.53590			0.141101
$324$	13.5000	−	7.79423i	0.750000	−	0.433013i
$325$			51.1769i			2.83878i
$326$			24.8564i			1.37667i
$327$	6.06218	+	10.5000i	0.335239	+	0.580651i
$328$			3.80385i			0.210032i
$329$	2.26795	−	2.26795i	0.125036	−	0.125036i
$330$	−3.23205	−	5.59808i	−0.177919	−	0.308164i
$331$	−2.36603	−	2.36603i	−0.130049	−	0.130049i	0.639086	−	0.769135i	$-0.279313\pi$
$331$	−2.36603	−	2.36603i	−0.130049	−	0.130049i	−0.769135	+	0.639086i	$0.779313\pi$
$332$	−24.0000			−1.31717
$333$	−14.1962	+	3.80385i	−0.777944	+	0.208450i
$334$	4.46410	+	4.46410i	0.244265	+	0.244265i
$335$		−	33.3205i		−	1.82049i
$336$	−18.2942	+	10.5622i	−0.998032	+	0.576214i
$337$	−1.07180	−	1.07180i	−0.0583845	−	0.0583845i	0.677312	−	0.735696i	$-0.263145\pi$
$337$	−1.07180	−	1.07180i	−0.0583845	−	0.0583845i	−0.735696	+	0.677312i	$0.763145\pi$
$338$	−27.1244	−	27.1244i	−1.47537	−	1.47537i
$339$	3.75833	−	14.0263i	0.204124	−	0.761803i
$340$	4.73205	−	4.73205i	0.256631	−	0.256631i
$341$	0.464102			0.0251325
$342$	7.09808	−	12.2942i	0.383820	−	0.664796i
$343$	17.8564			0.964155
$344$			2.60770i			0.140598i
$345$	4.73205	+	8.19615i	0.254765	+	0.441266i
$346$	−18.3923	−	18.3923i	−0.988776	−	0.988776i
$347$	−19.5167			−1.04771			−0.523855	−	0.851808i	$-0.675506\pi$
$347$	−19.5167			−1.04771			−0.523855	+	0.851808i	$0.675506\pi$
$348$	9.99038	−	12.6962i	0.535541	−	0.680585i
$349$	26.6603			1.42709			0.713545	−	0.700609i	$-0.247088\pi$
$349$	26.6603			1.42709			0.713545	+	0.700609i	$0.247088\pi$
$350$	−33.3205	−	33.3205i	−1.78106	−	1.78106i
$351$	29.7846			1.58978
$352$			3.92820i			0.209374i
$353$	8.78461			0.467558			0.233779	−	0.972290i	$-0.424891\pi$
$353$	8.78461			0.467558			0.233779	+	0.972290i	$0.424891\pi$
$354$	−0.464102	+	1.73205i	−0.0246667	+	0.0920575i
$355$	−62.4449			−3.31423
$356$	8.66025	−	8.66025i	0.458993	−	0.458993i
$357$	−4.73205	−	1.26795i	−0.250447	−	0.0671070i
$358$	−22.6603	−	22.6603i	−1.19763	−	1.19763i
$359$	6.49038	+	6.49038i	0.342549	+	0.342549i	0.857325	−	0.514776i	$-0.172125\pi$
$359$	6.49038	+	6.49038i	0.342549	+	0.342549i	−0.514776	+	0.857325i	$0.672125\pi$
$360$	1.50000	+	5.59808i	0.0790569	+	0.295045i
$361$			13.0000i			0.684211i
$362$	22.2942	+	22.2942i	1.17176	+	1.17176i
$363$	−9.29423	−	16.0981i	−0.487820	−	0.844930i
$364$	27.1244			1.42170
$365$	14.9282	+	14.9282i	0.781378	+	0.781378i
$366$	−8.19615	+	4.73205i	−0.428420	+	0.247348i
$367$	−7.53590	+	7.53590i	−0.393371	+	0.393371i	−0.875887	−	0.482516i	$-0.839723\pi$
$367$	−7.53590	+	7.53590i	−0.393371	+	0.393371i	0.482516	+	0.875887i	$0.339723\pi$
$368$		−	6.53590i		−	0.340707i
$369$	5.70577	+	21.2942i	0.297031	+	1.10853i
$370$			35.3205i			1.83623i
$371$			10.7321i			0.557180i
$372$	2.59808	+	0.696152i	0.134704	+	0.0360938i
$373$	−24.4641			−1.26670			−0.633352	−	0.773864i	$-0.718321\pi$
$373$	−24.4641			−1.26670			−0.633352	+	0.773864i	$0.718321\pi$
$374$	−0.732051	+	0.732051i	−0.0378534	+	0.0378534i
$375$	−21.9904	+	12.6962i	−1.13558	+	0.655626i
$376$			0.607695i			0.0313395i
$377$	28.6603	−	11.4641i	1.47608	−	0.590431i
$378$	−19.3923	+	19.3923i	−0.997433	+	0.997433i
$379$	−8.85641	+	8.85641i	−0.454923	+	0.454923i	−0.896985	−	0.442062i	$-0.854247\pi$
$379$	−8.85641	+	8.85641i	−0.454923	+	0.454923i	0.442062	+	0.896985i	$0.354247\pi$
$380$	−11.1962	−	11.1962i	−0.574351	−	0.574351i
$381$	5.70577	−	21.2942i	0.292316	−	1.09094i
$382$		−	43.5167i		−	2.22651i
$383$	−9.26795			−0.473570			−0.236785	−	0.971562i	$-0.576094\pi$
$383$	−9.26795			−0.473570			−0.236785	+	0.971562i	$0.576094\pi$
$384$	1.83975	−	6.86603i	0.0938841	−	0.350380i
$385$	3.73205	+	3.73205i	0.190203	+	0.190203i
$386$	−27.1244			−1.38059
$387$	3.91154	+	14.5981i	0.198835	+	0.742062i
$388$	13.3923	−	13.3923i	0.679891	−	0.679891i
$389$	−11.8038	+	11.8038i	−0.598479	+	0.598479i	−0.939908	−	0.341429i	$-0.889089\pi$
$389$	−11.8038	+	11.8038i	−0.598479	+	0.598479i	0.341429	+	0.939908i	$0.389089\pi$
$390$	18.5263	−	69.1410i	0.938115	−	3.50109i
$391$	1.07180	−	1.07180i	0.0542031	−	0.0542031i
$392$	0.169873	−	0.169873i	0.00857988	−	0.00857988i
$393$	7.22243	−	26.9545i	0.364323	−	1.35967i
$394$	−34.0526	+	34.0526i	−1.71554	+	1.71554i
$395$	−6.83013	+	6.83013i	−0.343661	+	0.343661i
$396$	0.696152	+	2.59808i	0.0349830	+	0.130558i
$397$	−8.32051			−0.417594			−0.208797	−	0.977959i	$-0.566955\pi$
$397$	−8.32051			−0.417594			−0.208797	+	0.977959i	$0.566955\pi$
$398$	3.73205	+	3.73205i	0.187071	+	0.187071i
$399$	−3.00000	+	11.1962i	−0.150188	+	0.560509i
$400$	39.8564			1.99282
$401$		−	26.2679i		−	1.31176i	−0.754866	−	0.655879i	$-0.772298\pi$
$401$		−	26.2679i		−	1.31176i	0.754866	−	0.655879i	$-0.227702\pi$
$402$	−7.73205	+	28.8564i	−0.385640	+	1.43923i
$403$	3.63397	+	3.63397i	0.181021	+	0.181021i
$404$	−7.26795	+	7.26795i	−0.361594	+	0.361594i
$405$	16.7942	+	29.0885i	0.834512	+	1.44542i
$406$	−11.1962	+	26.1244i	−0.555656	+	1.29653i
$407$		−	2.53590i		−	0.125700i
$408$	0.803848	−	0.464102i	0.0397964	−	0.0229765i
$409$	4.60770	−	4.60770i	0.227836	−	0.227836i	−0.583952	−	0.811788i	$-0.698494\pi$
$409$	4.60770	−	4.60770i	0.227836	−	0.227836i	0.811788	+	0.583952i	$0.198494\pi$
$410$	52.9808			2.61653
$411$	11.1962	+	3.00000i	0.552265	+	0.147979i
$412$			18.5885i			0.915788i
$413$		−	1.46410i		−	0.0720437i
$414$	−2.19615	−	8.19615i	−0.107935	−	0.402819i
$415$		−	51.7128i		−	2.53848i
$416$	−30.7583	+	30.7583i	−1.50805	+	1.50805i
$417$	−17.1962	+	9.92820i	−0.842099	+	0.486186i
$418$	1.73205	+	1.73205i	0.0847174	+	0.0847174i
$419$	−2.33975			−0.114304			−0.0571520	−	0.998365i	$-0.518202\pi$
$419$	−2.33975			−0.114304			−0.0571520	+	0.998365i	$0.518202\pi$
$420$	15.2942	+	26.4904i	0.746282	+	1.29260i
$421$	−6.19615	−	6.19615i	−0.301982	−	0.301982i	0.539807	−	0.841789i	$-0.318497\pi$
$421$	−6.19615	−	6.19615i	−0.301982	−	0.301982i	−0.841789	+	0.539807i	$0.818497\pi$
$422$			38.3205i			1.86541i
$423$	0.911543	+	3.40192i	0.0443207	+	0.165407i
$424$	−1.43782	−	1.43782i	−0.0698268	−	0.0698268i
$425$	6.53590	+	6.53590i	0.317038	+	0.317038i
$426$	54.0788	+	14.4904i	2.62013	+	0.702061i
$427$	5.46410	−	5.46410i	0.264426	−	0.264426i
$428$	−9.12436			−0.441042
$429$	−1.33013	+	4.96410i	−0.0642191	+	0.239669i
$430$	36.3205			1.75153
$431$		−	30.3923i		−	1.46395i	−0.681334	−	0.731973i	$-0.738600\pi$
$431$		−	30.3923i		−	1.46395i	0.681334	−	0.731973i	$-0.261400\pi$
$432$		−	23.1962i		−	1.11603i
$433$	5.46410	+	5.46410i	0.262588	+	0.262588i	0.826105	−	0.563517i	$-0.190552\pi$
$433$	5.46410	+	5.46410i	0.262588	+	0.262588i	−0.563517	+	0.826105i	$0.690552\pi$
$434$	−4.73205			−0.227146
$435$	27.3564	+	21.5263i	1.31164	+	1.03211i
$436$	−12.1244			−0.580651
$437$	−2.53590	−	2.53590i	−0.121308	−	0.121308i
$438$	−9.46410	−	16.3923i	−0.452212	−	0.783255i
$439$			26.2487i			1.25278i	0.779509	+	0.626391i	$0.215469\pi$
$439$			26.2487i			1.25278i	−0.779509	+	0.626391i	$0.784531\pi$
$440$	−1.00000			−0.0476731
$441$	0.696152	−	1.20577i	0.0331501	−	0.0574177i
$442$	−11.4641			−0.545292
$443$	−17.9282	+	17.9282i	−0.851795	+	0.851795i	−0.990354	−	0.138559i	$-0.955753\pi$
$443$	−17.9282	+	17.9282i	−0.851795	+	0.851795i	0.138559	+	0.990354i	$0.455753\pi$
$444$	3.80385	−	14.1962i	0.180523	−	0.673720i
$445$	18.6603	+	18.6603i	0.884581	+	0.884581i
$446$	1.00000	+	1.00000i	0.0473514	+	0.0473514i
$447$	−17.3038	+	9.99038i	−0.818444	+	0.472529i
$448$		−	15.6603i		−	0.739877i
$449$	−0.856406	−	0.856406i	−0.0404163	−	0.0404163i	0.686610	−	0.727026i	$-0.259098\pi$
$449$	−0.856406	−	0.856406i	−0.0404163	−	0.0404163i	−0.727026	+	0.686610i	$0.759098\pi$
$450$	49.9808	−	13.3923i	2.35612	−	0.631319i
$451$	−3.80385			−0.179116
$452$	10.2679	+	10.2679i	0.482964	+	0.482964i
$453$	−4.90192	−	8.49038i	−0.230312	−	0.398913i
$454$	12.4641	−	12.4641i	0.584969	−	0.584969i
$455$			58.4449i			2.73994i
$456$	−1.09808	−	1.90192i	−0.0514221	−	0.0890657i
$457$		−	28.2487i		−	1.32142i	−0.750642	−	0.660709i	$-0.770256\pi$
$457$		−	28.2487i		−	1.32142i	0.750642	−	0.660709i	$-0.229744\pi$
$458$		−	55.5167i		−	2.59412i
$459$	3.80385	−	3.80385i	0.177548	−	0.177548i
$460$	−9.46410			−0.441266
$461$	16.8564	−	16.8564i	0.785081	−	0.785081i	−0.195602	−	0.980683i	$-0.562666\pi$
$461$	16.8564	−	16.8564i	0.785081	−	0.785081i	0.980683	+	0.195602i	$0.0626661\pi$
$462$	−2.36603	−	4.09808i	−0.110077	−	0.190660i
$463$			22.0000i			1.02243i	0.859454	+	0.511213i	$0.170804\pi$
$463$			22.0000i			1.02243i	−0.859454	+	0.511213i	$0.829196\pi$
$464$	−8.92820	−	22.3205i	−0.414481	−	1.03620i
$465$	−1.50000	+	5.59808i	−0.0695608	+	0.259605i
$466$	−27.4904	+	27.4904i	−1.27347	+	1.27347i
$467$	−4.90192	−	4.90192i	−0.226834	−	0.226834i	0.584535	−	0.811369i	$-0.301277\pi$
$467$	−4.90192	−	4.90192i	−0.226834	−	0.226834i	−0.811369	+	0.584535i	$0.801277\pi$
$468$	−14.8923	+	25.7942i	−0.688397	+	1.19234i
$469$		−	24.3923i		−	1.12633i
$470$	8.46410			0.390420
$471$	13.0981	+	3.50962i	0.603527	+	0.161715i
$472$	0.196152	+	0.196152i	0.00902865	+	0.00902865i
$473$	−2.60770			−0.119902
$474$	7.50000	−	4.33013i	0.344486	−	0.198889i
$475$	15.4641	−	15.4641i	0.709542	−	0.709542i
$476$	3.46410	−	3.46410i	0.158777	−	0.158777i
$477$	−10.2058	−	5.89230i	−0.467290	−	0.269790i
$478$	−8.19615	+	8.19615i	−0.374883	+	0.374883i
$479$	2.90192	−	2.90192i	0.132592	−	0.132592i	−0.637696	−	0.770288i	$-0.720112\pi$
$479$	2.90192	−	2.90192i	0.132592	−	0.132592i	0.770288	+	0.637696i	$0.220112\pi$
$480$	−47.3827	−	12.6962i	−2.16271	−	0.579497i
$481$	19.8564	−	19.8564i	0.905374	−	0.905374i
$482$	18.4904	−	18.4904i	0.842214	−	0.842214i
$483$	3.46410	+	6.00000i	0.157622	+	0.273009i
$484$	18.5885			0.844930
$485$	28.8564	+	28.8564i	1.31030	+	1.31030i
$486$	−7.79423	−	29.0885i	−0.353553	−	1.31948i
$487$	−32.4449			−1.47022			−0.735109	−	0.677949i	$-0.762869\pi$
$487$	−32.4449			−1.47022			−0.735109	+	0.677949i	$0.762869\pi$
$488$			1.46410i			0.0662768i
$489$	21.5263	+	5.76795i	0.973452	+	0.260836i
$490$	−2.36603	−	2.36603i	−0.106886	−	0.106886i
$491$	28.5622	−	28.5622i	1.28899	−	1.28899i	0.353594	−	0.935399i	$-0.384959\pi$
$491$	28.5622	−	28.5622i	1.28899	−	1.28899i	0.935399	−	0.353594i	$-0.115041\pi$
$492$	−21.2942	−	5.70577i	−0.960018	−	0.257236i
$493$	2.19615	−	5.12436i	0.0989097	−	0.230789i
$494$			27.1244i			1.22038i
$495$	−5.59808	+	1.50000i	−0.251615	+	0.0674200i
$496$	2.83013	−	2.83013i	0.127076	−	0.127076i
$497$	−45.7128			−2.05050
$498$	−12.0000	+	44.7846i	−0.537733	+	2.00685i
$499$		−	38.6410i		−	1.72981i	−0.501936	−	0.864905i	$-0.667379\pi$
$499$		−	38.6410i		−	1.72981i	0.501936	−	0.864905i	$-0.332621\pi$
$500$		−	25.3923i		−	1.13558i
$501$	4.90192	−	2.83013i	0.219002	−	0.126441i
$502$			29.0526i			1.29668i
$503$	14.1699	−	14.1699i	0.631803	−	0.631803i	−0.316717	−	0.948520i	$-0.602580\pi$
$503$	14.1699	−	14.1699i	0.631803	−	0.631803i	0.948520	+	0.316717i	$0.102580\pi$
$504$	1.09808	+	4.09808i	0.0489122	+	0.182543i
$505$	−15.6603	−	15.6603i	−0.696872	−	0.696872i
$506$	1.46410			0.0650873
$507$	−29.7846	+	17.1962i	−1.32278	+	0.763708i
$508$	15.5885	+	15.5885i	0.691626	+	0.691626i
$509$			27.6410i			1.22517i	0.790406	+	0.612583i	$0.209870\pi$
$509$			27.6410i			1.22517i	−0.790406	+	0.612583i	$0.790130\pi$
$510$	−6.46410	−	11.1962i	−0.286235	−	0.495774i
$511$	10.9282	+	10.9282i	0.483435	+	0.483435i
$512$	20.6865	+	20.6865i	0.914224	+	0.914224i
$513$	−9.00000	−	9.00000i	−0.397360	−	0.397360i
$514$	13.5622	−	13.5622i	0.598202	−	0.598202i
$515$	−40.0526			−1.76493
$516$	−14.5981	−	3.91154i	−0.642644	−	0.172196i
$517$	−0.607695			−0.0267264
$518$			25.8564i			1.13607i
$519$	−20.1962	+	11.6603i	−0.886513	+	0.511828i
$520$	−7.83013	−	7.83013i	−0.343374	−	0.343374i
$521$	−18.3205			−0.802636			−0.401318	−	0.915939i	$-0.631448\pi$
$521$	−18.3205			−0.802636			−0.401318	+	0.915939i	$0.631448\pi$
$522$	−18.6962	−	24.9904i	−0.818308	−	1.09380i
$523$	20.9282			0.915126			0.457563	−	0.889177i	$-0.348722\pi$
$523$	20.9282			0.915126			0.457563	+	0.889177i	$0.348722\pi$
$524$	19.7321	+	19.7321i	0.861999	+	0.861999i
$525$	−36.5885	+	21.1244i	−1.59685	+	0.921942i
$526$			41.7846i			1.82190i
$527$	0.928203			0.0404332
$528$	3.86603	+	1.03590i	0.168247	+	0.0450817i
$529$	20.8564			0.906800
$530$	−20.0263	+	20.0263i	−0.869886	+	0.869886i
$531$	1.39230	+	0.803848i	0.0604209	+	0.0348840i
$532$	−8.19615	−	8.19615i	−0.355348	−	0.355348i
$533$	−29.7846	−	29.7846i	−1.29011	−	1.29011i
$534$	−11.8301	−	20.4904i	−0.511940	−	0.886706i
$535$		−	19.6603i		−	0.849987i
$536$	3.26795	+	3.26795i	0.141154	+	0.141154i
$537$	−24.8827	+	14.3660i	−1.07377	+	0.619940i
$538$	5.46410			0.235574
$539$	0.169873	+	0.169873i	0.00731695	+	0.00731695i
$540$	−33.5885			−1.44542
$541$	−15.2679	+	15.2679i	−0.656420	+	0.656420i	−0.954531	−	0.298111i	$-0.903643\pi$
$541$	−15.2679	+	15.2679i	−0.656420	+	0.656420i	0.298111	+	0.954531i	$0.403643\pi$
$542$		−	19.5885i		−	0.841396i
$543$	24.4808	−	14.1340i	1.05057	−	0.606547i
$544$			7.85641i			0.336841i
$545$		−	26.1244i		−	1.11904i
$546$	13.5622	−	50.6147i	0.580408	−	2.16611i
$547$	3.66025			0.156501			0.0782506	−	0.996934i	$-0.475067\pi$
$547$	3.66025			0.156501			0.0782506	+	0.996934i	$0.475067\pi$
$548$	−8.19615	+	8.19615i	−0.350122	+	0.350122i
$549$	2.19615	+	8.19615i	0.0937295	+	0.349803i
$550$			8.92820i			0.380700i
$551$	−12.1244	−	5.19615i	−0.516515	−	0.221364i
$552$	−1.26795	−	0.339746i	−0.0539675	−	0.0144605i
$553$	−5.00000	+	5.00000i	−0.212622	+	0.212622i
$554$	7.66025	+	7.66025i	0.325453	+	0.325453i
$555$	30.5885	+	8.19615i	1.29841	+	0.347907i
$556$		−	19.8564i		−	0.842099i
$557$	23.0718			0.977583			0.488792	−	0.872401i	$-0.337438\pi$
$557$	23.0718			0.977583			0.488792	+	0.872401i	$0.337438\pi$
$558$	2.59808	−	4.50000i	0.109985	−	0.190500i
$559$	−20.4186	−	20.4186i	−0.863614	−	0.863614i
$560$	45.5167			1.92343
$561$	0.464102	+	0.803848i	0.0195944	+	0.0339385i
$562$	−2.36603	+	2.36603i	−0.0998048	+	0.0998048i
$563$	15.9545	−	15.9545i	0.672401	−	0.672401i	−0.285868	−	0.958269i	$-0.592282\pi$
$563$	15.9545	−	15.9545i	0.672401	−	0.672401i	0.958269	+	0.285868i	$0.0922818\pi$
$564$	−3.40192	−	0.911543i	−0.143247	−	0.0383829i
$565$	−22.1244	+	22.1244i	−0.930779	+	0.930779i
$566$	−8.19615	+	8.19615i	−0.344510	+	0.344510i
$567$	12.2942	+	21.2942i	0.516309	+	0.894274i
$568$	6.12436	−	6.12436i	0.256972	−	0.256972i
$569$	15.7846	−	15.7846i	0.661725	−	0.661725i	−0.294061	−	0.955787i	$-0.595007\pi$
$569$	15.7846	−	15.7846i	0.661725	−	0.661725i	0.955787	+	0.294061i	$0.0950070\pi$
$570$	−26.4904	+	15.2942i	−1.10956	+	0.640605i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	−3.63397	−	3.63397i	−0.151944	−	0.151944i
$573$	−37.6865	−	10.0981i	−1.57438	−	0.421853i
$574$	38.7846			1.61884
$575$		−	13.0718i		−	0.545132i
$576$	14.8923	+	8.59808i	0.620513	+	0.358253i
$577$	12.3923	+	12.3923i	0.515898	+	0.515898i	0.916328	−	0.400429i	$-0.131139\pi$
$577$	12.3923	+	12.3923i	0.515898	+	0.515898i	−0.400429	+	0.916328i	$0.631139\pi$
$578$	21.7583	−	21.7583i	0.905027	−	0.905027i
$579$	−6.29423	+	23.4904i	−0.261579	+	0.976227i
$580$	−32.3205	+	12.9282i	−1.34204	+	0.536814i
$581$		−	37.8564i		−	1.57055i
$582$	−18.2942	−	31.6865i	−0.758320	−	1.31345i
$583$	1.43782	−	1.43782i	0.0595485	−	0.0595485i
$584$	−2.92820			−0.121170
$585$	−55.5788	−	32.0885i	−2.29790	−	1.32669i
$586$		−	44.0526i		−	1.81979i
$587$			21.6077i			0.891845i	0.895072	+	0.445923i	$0.147124\pi$
$587$			21.6077i			0.891845i	−0.895072	+	0.445923i	$0.852876\pi$
$588$	0.696152	+	1.20577i	0.0287088	+	0.0497252i
$589$		−	2.19615i		−	0.0904909i
$590$	2.73205	−	2.73205i	0.112477	−	0.112477i
$591$	21.5885	+	37.3923i	0.888030	+	1.53811i
$592$	−15.4641	−	15.4641i	−0.635571	−	0.635571i
$593$	−21.3923			−0.878477			−0.439238	−	0.898371i	$-0.644752\pi$
$593$	−21.3923			−0.878477			−0.439238	+	0.898371i	$0.644752\pi$
$594$	5.19615			0.213201
$595$	7.46410	+	7.46410i	0.305998	+	0.305998i
$596$		−	19.9808i		−	0.818444i
$597$	4.09808	−	2.36603i	0.167723	−	0.0968350i
$598$	11.4641	+	11.4641i	0.468802	+	0.468802i
$599$	0.437822	+	0.437822i	0.0178889	+	0.0178889i	0.715995	−	0.698106i	$-0.245973\pi$
$599$	0.437822	+	0.437822i	0.0178889	+	0.0178889i	−0.698106	+	0.715995i	$0.745973\pi$
$600$	2.07180	−	7.73205i	0.0845807	−	0.315660i
$601$	−21.5885	+	21.5885i	−0.880612	+	0.880612i	−0.993597	−	0.112985i	$-0.963959\pi$
$601$	−21.5885	+	21.5885i	−0.880612	+	0.880612i	0.112985	+	0.993597i	$0.463959\pi$
$602$	26.5885			1.08366
$603$	23.1962	+	13.3923i	0.944620	+	0.545377i
$604$	9.80385			0.398913
$605$			40.0526i			1.62837i
$606$	9.92820	+	17.1962i	0.403306	+	0.698546i
$607$	17.3660	+	17.3660i	0.704865	+	0.704865i	0.965451	−	0.260586i	$-0.0839156\pi$
$607$	17.3660	+	17.3660i	0.704865	+	0.704865i	−0.260586	+	0.965451i	$0.583916\pi$
$608$	18.5885			0.753861
$609$	20.0263	+	15.7583i	0.811506	+	0.638560i
$610$	20.3923			0.825660
$611$	−4.75833	−	4.75833i	−0.192501	−	0.192501i
$612$	1.39230	+	5.19615i	0.0562806	+	0.210042i
$613$		−	19.7846i		−	0.799093i	−0.916713	−	0.399546i	$-0.869168\pi$
$613$		−	19.7846i		−	0.799093i	0.916713	−	0.399546i	$-0.130832\pi$
$614$	6.80385			0.274581
$615$	12.2942	−	45.8827i	0.495751	−	1.85017i
$616$	−0.732051			−0.0294952
$617$	15.8038	−	15.8038i	0.636239	−	0.636239i	−0.313387	−	0.949626i	$-0.601464\pi$
$617$	15.8038	−	15.8038i	0.636239	−	0.636239i	0.949626	+	0.313387i	$0.101464\pi$
$618$	34.6865	+	9.29423i	1.39530	+	0.373869i
$619$	17.6865	+	17.6865i	0.710882	+	0.710882i	0.966720	−	0.255838i	$-0.0823513\pi$
$619$	17.6865	+	17.6865i	0.710882	+	0.710882i	−0.255838	+	0.966720i	$0.582351\pi$
$620$	−4.09808	−	4.09808i	−0.164583	−	0.164583i
$621$	−7.60770			−0.305286
$622$		−	44.9808i		−	1.80356i
$623$	13.6603	+	13.6603i	0.547287	+	0.547287i
$624$	22.1603	+	38.3827i	0.887120	+	1.53654i
$625$	10.0718			0.402872
$626$	10.3660	+	10.3660i	0.414310	+	0.414310i
$627$	1.90192	−	1.09808i	0.0759555	−	0.0438529i
$628$	−9.58846	+	9.58846i	−0.382621	+	0.382621i
$629$		−	5.07180i		−	0.202226i
$630$	57.0788	−	15.2942i	2.27408	−	0.609337i
$631$			22.5885i			0.899232i	0.893222	+	0.449616i	$0.148439\pi$
$631$			22.5885i			0.899232i	−0.893222	+	0.449616i	$0.851561\pi$
$632$		−	1.33975i		−	0.0532922i
$633$	33.1865	+	8.89230i	1.31905	+	0.353437i
$634$	−50.2487			−1.99563
$635$	−33.5885	+	33.5885i	−1.33292	+	1.33292i
$636$	10.2058	−	5.89230i	0.404685	−	0.233645i
$637$			2.66025i			0.105403i
$638$	5.00000	−	2.00000i	0.197952	−	0.0791808i
$639$	25.0981	−	43.4711i	0.992865	−	1.71969i
$640$	−10.8301	+	10.8301i	−0.428098	+	0.428098i
$641$	30.0526	+	30.0526i	1.18700	+	1.18700i	0.977891	+	0.209113i	$0.0670577\pi$
$641$	30.0526	+	30.0526i	1.18700	+	1.18700i	0.209113	+	0.977891i	$0.432942\pi$
$642$	−4.56218	+	17.0263i	−0.180055	+	0.671974i
$643$			12.4449i			0.490778i	0.969425	+	0.245389i	$0.0789156\pi$
$643$			12.4449i			0.490778i	−0.969425	+	0.245389i	$0.921084\pi$
$644$	−6.92820			−0.273009
$645$	8.42820	−	31.4545i	0.331860	−	1.23852i
$646$	3.46410	+	3.46410i	0.136293	+	0.136293i
$647$	9.85641			0.387495			0.193748	−	0.981051i	$-0.437936\pi$
$647$	9.85641			0.387495			0.193748	+	0.981051i	$0.437936\pi$
$648$	−4.50000	−	1.20577i	−0.176777	−	0.0473672i
$649$	−0.196152	+	0.196152i	−0.00769966	+	0.00769966i
$650$	−69.9090	+	69.9090i	−2.74206	+	2.74206i
$651$	−1.09808	+	4.09808i	−0.0430370	+	0.160616i
$652$	−15.7583	+	15.7583i	−0.617144	+	0.617144i
$653$	−9.39230	+	9.39230i	−0.367549	+	0.367549i	−0.866583	−	0.499033i	$-0.833688\pi$
$653$	−9.39230	+	9.39230i	−0.367549	+	0.367549i	0.499033	+	0.866583i	$0.333688\pi$
$654$	−6.06218	+	22.6244i	−0.237050	+	0.884682i
$655$	−42.5167	+	42.5167i	−1.66126	+	1.66126i
$656$	−23.1962	+	23.1962i	−0.905658	+	0.905658i
$657$	−16.3923	+	4.39230i	−0.639525	+	0.171360i
$658$	6.19615			0.241551
$659$	5.75833	+	5.75833i	0.224313	+	0.224313i	0.810312	−	0.585999i	$-0.199298\pi$
$659$	5.75833	+	5.75833i	0.224313	+	0.224313i	−0.585999	+	0.810312i	$0.699298\pi$
$660$	1.50000	−	5.59808i	0.0583874	−	0.217905i
$661$	−26.3923			−1.02654			−0.513271	−	0.858227i	$-0.671566\pi$
$661$	−26.3923			−1.02654			−0.513271	+	0.858227i	$0.671566\pi$
$662$		−	6.46410i		−	0.251234i
$663$	−2.66025	+	9.92820i	−0.103316	+	0.385579i
$664$	5.07180	+	5.07180i	0.196824	+	0.196824i
$665$	17.6603	−	17.6603i	0.684835	−	0.684835i
$666$	−24.5885	−	14.1962i	−0.952783	−	0.550090i
$667$	−7.32051	+	2.92820i	−0.283451	+	0.113380i
$668$			5.66025i			0.219002i
$669$	1.09808	−	0.633975i	0.0424541	−	0.0245109i
$670$	45.5167	−	45.5167i	1.75846	−	1.75846i
$671$	−1.46410			−0.0565210
$672$	−34.6865	−	9.29423i	−1.33806	−	0.358533i
$673$		−	10.3205i		−	0.397826i	−0.980017	−	0.198913i	$-0.936259\pi$
$673$		−	10.3205i		−	0.397826i	0.980017	−	0.198913i	$-0.0637412\pi$
$674$		−	2.92820i		−	0.112790i
$675$		−	46.3923i		−	1.78564i
$676$		−	34.3923i		−	1.32278i
$677$	−15.0526	+	15.0526i	−0.578517	+	0.578517i	−0.934494	−	0.355978i	$-0.884148\pi$
$677$	−15.0526	+	15.0526i	−0.578517	+	0.578517i	0.355978	+	0.934494i	$0.384148\pi$
$678$	24.2942	−	14.0263i	0.933014	−	0.538676i
$679$	21.1244	+	21.1244i	0.810678	+	0.810678i
$680$	−2.00000			−0.0766965
$681$	−7.90192	−	13.6865i	−0.302802	−	0.524469i
$682$	0.633975	+	0.633975i	0.0242761	+	0.0242761i
$683$			12.9282i			0.494684i	0.968928	+	0.247342i	$0.0795571\pi$
$683$			12.9282i			0.494684i	−0.968928	+	0.247342i	$0.920443\pi$
$684$	12.2942	−	3.29423i	0.470082	−	0.125958i
$685$	−17.6603	−	17.6603i	−0.674764	−	0.674764i
$686$	24.3923	+	24.3923i	0.931303	+	0.931303i
$687$	−48.0788	−	12.8827i	−1.83432	−	0.491505i
$688$	−15.9019	+	15.9019i	−0.606255	+	0.606255i
$689$	22.5167			0.857816
$690$	−4.73205	+	17.6603i	−0.180146	+	0.672314i
$691$	−25.7128			−0.978162			−0.489081	−	0.872239i	$-0.662668\pi$
$691$	−25.7128			−0.978162			−0.489081	+	0.872239i	$0.662668\pi$
$692$		−	23.3205i		−	0.886513i
$693$	−4.09808	+	1.09808i	−0.155673	+	0.0417125i
$694$	−26.6603	−	26.6603i	−1.01201	−	1.01201i
$695$	42.7846			1.62291
$696$	−4.79423	+	0.571797i	−0.181725	+	0.0216739i
$697$	−7.60770			−0.288162
$698$	36.4186	+	36.4186i	1.37846	+	1.37846i
$699$	17.4282	+	30.1865i	0.659195	+	1.14176i
$700$		−	42.2487i		−	1.59685i
$701$	41.1051			1.55252			0.776259	−	0.630414i	$-0.217115\pi$
$701$	41.1051			1.55252			0.776259	+	0.630414i	$0.217115\pi$
$702$	40.6865	+	40.6865i	1.53561	+	1.53561i
$703$	−12.0000			−0.452589
$704$	−2.09808	+	2.09808i	−0.0790742	+	0.0790742i
$705$	1.96410	−	7.33013i	0.0739723	−	0.276069i
$706$	12.0000	+	12.0000i	0.451626	+	0.451626i
$707$	−11.4641	−	11.4641i	−0.431152	−	0.431152i
$708$	−1.39230	+	0.803848i	−0.0523260	+	0.0302104i
$709$			9.58846i			0.360102i	0.983657	+	0.180051i	$0.0576263\pi$
$709$			9.58846i			0.360102i	−0.983657	+	0.180051i	$0.942374\pi$
$710$	−85.3013	−	85.3013i	−3.20130	−	3.20130i
$711$	−2.00962	−	7.50000i	−0.0753666	−	0.281272i
$712$	−3.66025			−0.137174
$713$	−0.928203	−	0.928203i	−0.0347615	−	0.0347615i
$714$	−4.73205	−	8.19615i	−0.177093	−	0.306733i
$715$	7.83013	−	7.83013i	0.292830	−	0.292830i
$716$		−	28.7321i		−	1.07377i
$717$	5.19615	+	9.00000i	0.194054	+	0.336111i
$718$			17.7321i			0.661754i
$719$		−	42.0526i		−	1.56830i	−0.620574	−	0.784148i	$-0.713100\pi$
$719$		−	42.0526i		−	1.56830i	0.620574	−	0.784148i	$-0.286900\pi$
$720$	−24.9904	+	43.2846i	−0.931337	+	1.61312i
$721$	−29.3205			−1.09195
$722$	−17.7583	+	17.7583i	−0.660897	+	0.660897i
$723$	−11.7224	−	20.3038i	−0.435962	−	0.755108i
$724$			28.2679i			1.05057i
$725$	−17.8564	−	44.6410i	−0.663170	−	1.65793i
$726$	9.29423	−	34.6865i	0.344941	−	1.28734i
$727$	34.3205	−	34.3205i	1.27288	−	1.27288i	0.328306	−	0.944572i	$-0.393522\pi$
$727$	34.3205	−	34.3205i	1.27288	−	1.27288i	0.944572	−	0.328306i	$-0.106478\pi$
$728$	−5.73205	−	5.73205i	−0.212444	−	0.212444i
$729$	−27.0000			−1.00000
$730$			40.7846i			1.50951i
$731$	−5.21539			−0.192898
$732$	−8.19615	−	2.19615i	−0.302939	−	0.0811721i
$733$	30.9808	+	30.9808i	1.14430	+	1.14430i	0.987655	+	0.156646i	$0.0500681\pi$
$733$	30.9808	+	30.9808i	1.14430	+	1.14430i	0.156646	+	0.987655i	$0.449932\pi$
$734$	−20.5885			−0.759934
$735$	−2.59808	+	1.50000i	−0.0958315	+	0.0553283i
$736$	7.85641	−	7.85641i	0.289591	−	0.289591i
$737$	−3.26795	+	3.26795i	−0.120376	+	0.120376i
$738$	−21.2942	+	36.8827i	−0.783851	+	1.35767i
$739$	32.6147	−	32.6147i	1.19975	−	1.19975i	0.225512	−	0.974240i	$-0.427594\pi$
$739$	32.6147	−	32.6147i	1.19975	−	1.19975i	0.974240	−	0.225512i	$-0.0724055\pi$
$740$	−22.3923	+	22.3923i	−0.823157	+	0.823157i
$741$	23.4904	+	6.29423i	0.862941	+	0.231224i
$742$	−14.6603	+	14.6603i	−0.538195	+	0.538195i
$743$	7.19615	−	7.19615i	0.264001	−	0.264001i	−0.562676	−	0.826677i	$-0.690228\pi$
$743$	7.19615	−	7.19615i	0.264001	−	0.264001i	0.826677	+	0.562676i	$0.190228\pi$
$744$	−0.401924	−	0.696152i	−0.0147352	−	0.0255222i
$745$	43.0526			1.57732
$746$	−33.4186	−	33.4186i	−1.22354	−	1.22354i
$747$	36.0000	+	20.7846i	1.31717	+	0.760469i
$748$	−0.928203			−0.0339385
$749$		−	14.3923i		−	0.525883i
$750$	−47.3827	−	12.6962i	−1.73017	−	0.463598i
$751$	30.7128	+	30.7128i	1.12073	+	1.12073i	0.991632	+	0.129094i	$0.0412069\pi$
$751$	30.7128	+	30.7128i	1.12073	+	1.12073i	0.129094	+	0.991632i	$0.458793\pi$
$752$	−3.70577	+	3.70577i	−0.135136	+	0.135136i
$753$	25.1603	+	6.74167i	0.916891	+	0.245680i
$754$	54.8109	+	23.4904i	1.99609	+	0.855469i
$755$			21.1244i			0.768794i
$756$	−24.5885			−0.894274
$757$	2.58846	−	2.58846i	0.0940791	−	0.0940791i	−0.658501	−	0.752580i	$-0.728809\pi$
$757$	2.58846	−	2.58846i	0.0940791	−	0.0940791i	0.752580	+	0.658501i	$0.228809\pi$
$758$	−24.1962			−0.878844
$759$	0.339746	−	1.26795i	0.0123320	−	0.0460236i
$760$			4.73205i			0.171650i
$761$			11.7128i			0.424589i	0.977206	+	0.212295i	$0.0680936\pi$
$761$			11.7128i			0.424589i	−0.977206	+	0.212295i	$0.931906\pi$
$762$	36.8827	−	21.2942i	1.33612	−	0.771409i
$763$		−	19.1244i		−	0.692348i
$764$	27.5885	−	27.5885i	0.998115	−	0.998115i
$765$	−11.1962	+	3.00000i	−0.404798	+	0.108465i
$766$	−12.6603	−	12.6603i	−0.457434	−	0.457434i
$767$	−3.07180			−0.110916
$768$	29.0885	−	16.7942i	1.04964	−	0.606010i
$769$	−2.19615	−	2.19615i	−0.0791953	−	0.0791953i	0.666400	−	0.745595i	$-0.267835\pi$
$769$	−2.19615	−	2.19615i	−0.0791953	−	0.0791953i	−0.745595	+	0.666400i	$0.767835\pi$
$770$			10.1962i			0.367444i
$771$	−8.59808	−	14.8923i	−0.309652	−	0.536333i
$772$	−17.1962	−	17.1962i	−0.618903	−	0.618903i
$773$	−3.00000	−	3.00000i	−0.107903	−	0.107903i	0.651094	−	0.758997i	$-0.274310\pi$
$773$	−3.00000	−	3.00000i	−0.107903	−	0.107903i	−0.758997	+	0.651094i	$0.774310\pi$
$774$	−14.5981	+	25.2846i	−0.524717	+	0.908837i
$775$	5.66025	−	5.66025i	0.203322	−	0.203322i
$776$	−5.66025			−0.203191
$777$	22.3923	+	6.00000i	0.803319	+	0.215249i
$778$	−32.2487			−1.15617
$779$			18.0000i			0.644917i
$780$	55.5788	−	32.0885i	1.99004	−	1.14895i
$781$	6.12436	+	6.12436i	0.219147	+	0.219147i
$782$	2.92820			0.104712
$783$	−25.9808	+	10.3923i	−0.928477	+	0.371391i
$784$	2.07180			0.0739927
$785$	−20.6603	−	20.6603i	−0.737396	−	0.737396i
$786$	46.6865	−	26.9545i	1.66525	−	0.961435i
$787$		−	31.5167i		−	1.12345i	−0.827325	−	0.561724i	$-0.810138\pi$
$787$		−	31.5167i		−	1.12345i	0.827325	−	0.561724i	$-0.189862\pi$
$788$	−43.1769			−1.53811
$789$	36.1865	+	9.69615i	1.28827	+	0.345192i
$790$	−18.6603			−0.663902
$791$	−16.1962	+	16.1962i	−0.575869	+	0.575869i
$792$	0.401924	−	0.696152i	0.0142817	−	0.0247367i
$793$	−11.4641	−	11.4641i	−0.407102	−	0.407102i
$794$	−11.3660	−	11.3660i	−0.403365	−	0.403365i
$795$	12.6962	+	21.9904i	0.450286	+	0.779918i
$796$			4.73205i			0.167723i
$797$	−22.3923	−	22.3923i	−0.793176	−	0.793176i	0.188833	−	0.982009i	$-0.439529\pi$
$797$	−22.3923	−	22.3923i	−0.793176	−	0.793176i	−0.982009	+	0.188833i	$0.939529\pi$
$798$	−19.3923	+	11.1962i	−0.686480	+	0.396339i
$799$	−1.21539			−0.0429974
$800$	47.9090	+	47.9090i	1.69384	+	1.69384i
$801$	−20.4904	+	5.49038i	−0.723992	+	0.193993i
$802$	35.8827	−	35.8827i	1.26706	−	1.26706i
$803$		−	2.92820i		−	0.103334i
$804$	−23.1962	+	13.3923i	−0.818065	+	0.472310i
$805$		−	14.9282i		−	0.526150i
$806$			9.92820i			0.349706i
$807$	1.26795	−	4.73205i	0.0446339	−	0.166576i
$808$	3.07180			0.108065
$809$	−34.7846	+	34.7846i	−1.22296	+	1.22296i	−0.256388	+	0.966574i	$0.582532\pi$
$809$	−34.7846	+	34.7846i	−1.22296	+	1.22296i	−0.966574	+	0.256388i	$0.917468\pi$
$810$	−16.7942	+	62.6769i	−0.590089	+	2.20224i
$811$			3.51666i			0.123487i	0.998092	+	0.0617433i	$0.0196660\pi$
$811$			3.51666i			0.123487i	−0.998092	+	0.0617433i	$0.980334\pi$
$812$	−23.6603	+	9.46410i	−0.830312	+	0.332125i
$813$	−16.9641	−	4.54552i	−0.594957	−	0.159418i
$814$	3.46410	−	3.46410i	0.121417	−	0.121417i
$815$	−33.9545	−	33.9545i	−1.18937	−	1.18937i
$816$	7.73205	+	2.07180i	0.270676	+	0.0725274i
$817$			12.3397i			0.431713i
$818$	12.5885			0.440145
$819$	−40.6865	−	23.4904i	−1.42170	−	0.820820i
$820$	33.5885	+	33.5885i	1.17296	+	1.17296i
$821$	−3.00000			−0.104701			−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000			−0.104701			−0.0523504	+	0.998629i	$0.516671\pi$
$822$	11.1962	+	19.3923i	0.390511	+	0.676384i
$823$	25.5359	−	25.5359i	0.890125	−	0.890125i	−0.104409	−	0.994534i	$-0.533295\pi$
$823$	25.5359	−	25.5359i	0.890125	−	0.890125i	0.994534	+	0.104409i	$0.0332951\pi$
$824$	3.92820	−	3.92820i	0.136845	−	0.136845i
$825$	7.73205	+	2.07180i	0.269195	+	0.0721307i
$826$	2.00000	−	2.00000i	0.0695889	−	0.0695889i
$827$	−5.36603	+	5.36603i	−0.186595	+	0.186595i	−0.794222	−	0.607627i	$-0.792121\pi$
$827$	−5.36603	+	5.36603i	−0.186595	+	0.186595i	0.607627	+	0.794222i	$0.292121\pi$
$828$	3.80385	−	6.58846i	0.132193	−	0.228965i
$829$	−10.1962	+	10.1962i	−0.354127	+	0.354127i	−0.861643	−	0.507516i	$-0.830564\pi$
$829$	−10.1962	+	10.1962i	−0.354127	+	0.354127i	0.507516	+	0.861643i	$0.330564\pi$
$830$	70.6410	−	70.6410i	2.45199	−	2.45199i
$831$	8.41154	−	4.85641i	0.291793	−	0.168467i
$832$	−32.8564			−1.13909
$833$	0.339746	+	0.339746i	0.0117715	+	0.0117715i
$834$	−37.0526	−	9.92820i	−1.28303	−	0.343786i
$835$	−12.1962			−0.422065
$836$			2.19615i			0.0759555i
$837$	−3.29423	−	3.29423i	−0.113865	−	0.113865i
$838$	−3.19615	−	3.19615i	−0.110409	−	0.110409i
$839$	14.0981	−	14.0981i	0.486720	−	0.486720i	−0.420550	−	0.907269i	$-0.638163\pi$
$839$	14.0981	−	14.0981i	0.486720	−	0.486720i	0.907269	+	0.420550i	$0.138163\pi$
$840$	2.36603	−	8.83013i	0.0816356	−	0.304668i
$841$	−21.0000	+	20.0000i	−0.724138	+	0.689655i
$842$		−	16.9282i		−	0.583384i
$843$	1.50000	+	2.59808i	0.0516627	+	0.0894825i
$844$	−24.2942	+	24.2942i	−0.836242	+	0.836242i
$845$	74.1051			2.54929
$846$	−3.40192	+	5.89230i	−0.116961	+	0.202582i
$847$			29.3205i			1.00746i
$848$		−	17.5359i		−	0.602185i
$849$	5.19615	+	9.00000i	0.178331	+	0.308879i
$850$			17.8564i			0.612470i
$851$	−5.07180	+	5.07180i	−0.173859	+	0.173859i
$852$	25.0981	+	43.4711i	0.859846	+	1.48930i
$853$	−24.8564	−	24.8564i	−0.851067	−	0.851067i	0.139197	−	0.990265i	$-0.455548\pi$
$853$	−24.8564	−	24.8564i	−0.851067	−	0.851067i	−0.990265	+	0.139197i	$0.955548\pi$
$854$	14.9282			0.510833
$855$	7.09808	+	26.4904i	0.242749	+	0.905952i
$856$	1.92820	+	1.92820i	0.0659046	+	0.0659046i
$857$		−	32.3205i		−	1.10405i	−0.833828	−	0.552024i	$-0.813856\pi$
$857$		−	32.3205i		−	1.10405i	0.833828	−	0.552024i	$-0.186144\pi$
$858$	−8.59808	+	4.96410i	−0.293533	+	0.169472i
$859$	−28.5429	−	28.5429i	−0.973873	−	0.973873i	0.0257947	−	0.999667i	$-0.491788\pi$
$859$	−28.5429	−	28.5429i	−0.973873	−	0.973873i	−0.999667	+	0.0257947i	$0.991788\pi$
$860$	23.0263	+	23.0263i	0.785190	+	0.785190i
$861$	9.00000	−	33.5885i	0.306719	−	1.14469i
$862$	41.5167	−	41.5167i	1.41406	−	1.41406i
$863$	−24.5885			−0.837001			−0.418500	−	0.908217i	$-0.637444\pi$
$863$	−24.5885			−0.837001			−0.418500	+	0.908217i	$0.637444\pi$
$864$	27.8827	−	27.8827i	0.948588	−	0.948588i
$865$	50.2487			1.70851
$866$			14.9282i			0.507281i
$867$	−13.7942	−	23.8923i	−0.468477	−	0.811425i
$868$	−3.00000	−	3.00000i	−0.101827	−	0.101827i
$869$	1.33975			0.0454478
$870$	7.96410	+	66.7750i	0.270008	+	2.26388i
$871$	−51.1769			−1.73406
$872$	2.56218	+	2.56218i	0.0867663	+	0.0867663i
$873$	−31.6865	+	8.49038i	−1.07243	+	0.287356i
$874$		−	6.92820i		−	0.234350i
$875$	40.0526			1.35402
$876$	4.39230	−	16.3923i	0.148402	−	0.553845i
$877$	22.2679			0.751935			0.375968	−	0.926633i	$-0.377310\pi$
$877$	22.2679			0.751935			0.375968	+	0.926633i	$0.377310\pi$
$878$	−35.8564	+	35.8564i	−1.21010	+	1.21010i
$879$	−38.1506	−	10.2224i	−1.28679	−	0.344794i
$880$	−6.09808	−	6.09808i	−0.205566	−	0.205566i
$881$	21.7321	+	21.7321i	0.732171	+	0.732171i	0.971050	−	0.238878i	$-0.0767797\pi$
$881$	21.7321	+	21.7321i	0.732171	+	0.732171i	−0.238878	+	0.971050i	$0.576780\pi$
$882$	2.59808	−	0.696152i	0.0874818	−	0.0234407i
$883$		−	33.1244i		−	1.11472i	−0.830270	−	0.557362i	$-0.811814\pi$
$883$		−	33.1244i		−	1.11472i	0.830270	−	0.557362i	$-0.188186\pi$
$884$	−7.26795	−	7.26795i	−0.244448	−	0.244448i
$885$	−1.73205	−	3.00000i	−0.0582223	−	0.100844i
$886$	−48.9808			−1.64554
$887$	21.4904	+	21.4904i	0.721576	+	0.721576i	0.968926	−	0.247350i	$-0.0795597\pi$
$887$	21.4904	+	21.4904i	0.721576	+	0.721576i	−0.247350	+	0.968926i	$0.579560\pi$
$888$	−3.80385	+	2.19615i	−0.127649	+	0.0736980i
$889$	−24.5885	+	24.5885i	−0.824670	+	0.824670i
$890$			50.9808i			1.70888i
$891$	1.20577	−	4.50000i	0.0403949	−	0.150756i
$892$			1.26795i			0.0424541i
$893$			2.87564i			0.0962298i
$894$	−37.2846	−	9.99038i	−1.24698	−	0.334128i
$895$	61.9090			2.06939
$896$	−7.92820	+	7.92820i	−0.264863	+	0.264863i
$897$	12.5885	−	7.26795i	0.420316	−	0.242670i
$898$		−	2.33975i		−	0.0780783i
$899$	−4.43782	−	1.90192i	−0.148010	−	0.0634327i
$900$	40.1769	+	23.1962i	1.33923	+	0.773205i
$901$	2.87564	−	2.87564i	0.0958016	−	0.0958016i
$902$	−5.19615	−	5.19615i	−0.173013	−	0.173013i
$903$	6.16987	−	23.0263i	0.205321	−	0.766267i
$904$		−	4.33975i		−	0.144338i
$905$	−60.9090			−2.02468
$906$	4.90192	−	18.2942i	0.162856	−	0.607785i
$907$	5.92820	+	5.92820i	0.196843	+	0.196843i	0.798645	−	0.601802i	$-0.205550\pi$
$907$	5.92820	+	5.92820i	0.196843	+	0.196843i	−0.601802	+	0.798645i	$0.705550\pi$
$908$	15.8038			0.524469
$909$	17.1962	−	4.60770i	0.570360	−	0.152828i
$910$	−79.8372	+	79.8372i	−2.64658	+	2.64658i
$911$	−22.0788	+	22.0788i	−0.731505	+	0.731505i	−0.970918	−	0.239413i	$-0.923045\pi$
$911$	−22.0788	+	22.0788i	−0.731505	+	0.731505i	0.239413	+	0.970918i	$0.423045\pi$
$912$	4.90192	−	18.2942i	0.162319	−	0.605782i
$913$	−5.07180	+	5.07180i	−0.167852	+	0.167852i
$914$	38.5885	−	38.5885i	1.27639	−	1.27639i
$915$	4.73205	−	17.6603i	0.156437	−	0.583830i
$916$	35.1962	−	35.1962i	1.16291	−	1.16291i
$917$	−31.1244	+	31.1244i	−1.02782	+	1.02782i
$918$	10.3923			0.342997
$919$	−42.4449			−1.40013			−0.700063	−	0.714081i	$-0.746845\pi$
$919$	−42.4449			−1.40013			−0.700063	+	0.714081i	$0.746845\pi$
$920$	2.00000	+	2.00000i	0.0659380	+	0.0659380i
$921$	1.57884	−	5.89230i	0.0520245	−	0.194158i
$922$	46.0526			1.51666
$923$			95.9090i			3.15688i
$924$	1.09808	−	4.09808i	0.0361241	−	0.134817i
$925$	−30.9282	−	30.9282i	−1.01691	−	1.01691i
$926$	−30.0526	+	30.0526i	−0.987588	+	0.987588i
$927$	16.0981	−	27.8827i	0.528730	−	0.915788i
$928$	16.0981	−	37.5622i	0.528445	−	1.23304i
$929$			34.2487i			1.12366i	0.827251	+	0.561832i	$0.189903\pi$
$929$			34.2487i			1.12366i	−0.827251	+	0.561832i	$0.810097\pi$
$930$	−9.69615	+	5.59808i	−0.317949	+	0.183568i
$931$	0.803848	−	0.803848i	0.0263450	−	0.0263450i
$932$	−34.8564			−1.14176
$933$	−38.9545	−	10.4378i	−1.27531	−	0.341719i
$934$		−	13.3923i		−	0.438210i
$935$		−	2.00000i		−	0.0654070i
$936$	8.59808	−	2.30385i	0.281037	−	0.0753036i
$937$			54.1051i			1.76754i	0.467924	+	0.883769i	$0.345002\pi$
$937$			54.1051i			1.76754i	−0.467924	+	0.883769i	$0.654998\pi$
$938$	33.3205	−	33.3205i	1.08795	−	1.08795i
$939$	11.3827	−	6.57180i	0.371460	−	0.214462i
$940$	5.36603	+	5.36603i	0.175020	+	0.175020i
$941$	26.8038			0.873780			0.436890	−	0.899515i	$-0.356080\pi$
$941$	26.8038			0.873780			0.436890	+	0.899515i	$0.356080\pi$
$942$	13.0981	+	22.6865i	0.426758	+	0.739167i
$943$	7.60770	+	7.60770i	0.247741	+	0.247741i
$944$			2.39230i			0.0778629i
$945$		−	52.9808i		−	1.72346i
$946$	−3.56218	−	3.56218i	−0.115816	−	0.115816i
$947$	−21.0981	−	21.0981i	−0.685595	−	0.685595i	0.275660	−	0.961255i	$-0.411104\pi$
$947$	−21.0981	−	21.0981i	−0.685595	−	0.685595i	−0.961255	+	0.275660i	$0.911104\pi$
$948$	7.50000	+	2.00962i	0.243589	+	0.0652694i
$949$	22.9282	−	22.9282i	0.744281	−	0.744281i
$950$	42.2487			1.37073
$951$	−11.6603	+	43.5167i	−0.378110	+	1.41112i
$952$	−1.46410			−0.0474518
$953$		−	7.58846i		−	0.245814i	−0.992418	−	0.122907i	$-0.960778\pi$
$953$		−	7.58846i		−	0.245814i	0.992418	−	0.122907i	$-0.0392217\pi$
$954$	−5.89230	−	21.9904i	−0.190770	−	0.711965i
$955$	59.4449	+	59.4449i	1.92359	+	1.92359i
$956$	−10.3923			−0.336111
$957$	−0.571797	−	4.79423i	−0.0184836	−	0.154975i
$958$	7.92820			0.256149
$959$	−12.9282	−	12.9282i	−0.417473	−	0.417473i
$960$	−18.5263	−	32.0885i	−0.597933	−	1.03565i
$961$			30.1962i			0.974069i
$962$	54.2487			1.74905
$963$	13.6865	+	7.90192i	0.441042	+	0.254636i
$964$	23.4449			0.755108
$965$	37.0526	−	37.0526i	1.19276	−	1.19276i
$966$	−3.46410	+	12.9282i	−0.111456	+	0.415958i
$967$	12.1699	+	12.1699i	0.391357	+	0.391357i	0.875171	−	0.483814i	$-0.160749\pi$
$967$	12.1699	+	12.1699i	0.391357	+	0.391357i	−0.483814	+	0.875171i	$0.660749\pi$
$968$	−3.92820	−	3.92820i	−0.126257	−	0.126257i
$969$	3.80385	−	2.19615i	0.122197	−	0.0705506i
$970$			78.8372i			2.53131i
$971$	25.7846	+	25.7846i	0.827468	+	0.827468i	0.987166	−	0.159698i	$-0.0510522\pi$
$971$	25.7846	+	25.7846i	0.827468	+	0.827468i	−0.159698	+	0.987166i	$0.551052\pi$
$972$	13.5000	−	23.3827i	0.433013	−	0.750000i
$973$	31.3205			1.00409
$974$	−44.3205	−	44.3205i	−1.42012	−	1.42012i
$975$	44.3205	+	76.7654i	1.41939	+	2.45846i
$976$	−8.92820	+	8.92820i	−0.285785	+	0.285785i
$977$			21.0000i			0.671850i	0.941889	+	0.335925i	$0.109049\pi$
$977$			21.0000i			0.671850i	−0.941889	+	0.335925i	$0.890951\pi$
$978$	21.5263	+	37.2846i	0.688335	+	1.19223i
$979$		−	3.66025i		−	0.116982i
$980$		−	3.00000i		−	0.0958315i
$981$	18.1865	+	10.5000i	0.580651	+	0.335239i
$982$	78.0333			2.49014
$983$	34.6865	−	34.6865i	1.10633	−	1.10633i	0.112699	−	0.993629i	$-0.464050\pi$
$983$	34.6865	−	34.6865i	1.10633	−	1.10633i	0.993629	−	0.112699i	$-0.0359497\pi$
$984$	3.29423	+	5.70577i	0.105016	+	0.181893i
$985$		−	93.0333i		−	2.96429i
$986$	10.0000	−	4.00000i	0.318465	−	0.127386i
$987$	1.43782	−	5.36603i	0.0457664	−	0.170802i
$988$	−17.1962	+	17.1962i	−0.547082	+	0.547082i
$989$	5.21539	+	5.21539i	0.165840	+	0.165840i
$990$	−9.69615	−	5.59808i	−0.308164	−	0.177919i
$991$			29.8038i			0.946750i	0.880861	+	0.473375i	$0.156965\pi$
$991$			29.8038i			0.946750i	−0.880861	+	0.473375i	$0.843035\pi$
$992$	6.80385			0.216022
$993$	−5.59808	−	1.50000i	−0.177650	−	0.0476011i
$994$	−62.4449	−	62.4449i	−1.98063	−	1.98063i
$995$	−10.1962			−0.323240
$996$	−36.0000	+	20.7846i	−1.14070	+	0.658586i
$997$	−18.9282	+	18.9282i	−0.599462	+	0.599462i	−0.940169	−	0.340707i	$-0.889334\pi$
$997$	−18.9282	+	18.9282i	−0.599462	+	0.599462i	0.340707	+	0.940169i	$0.389334\pi$
$998$	52.7846	−	52.7846i	1.67087	−	1.67087i
$999$	−18.0000	+	18.0000i	−0.569495	+	0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.f.b.17.2	yes	4
3.2	odd	2		87.2.f.a.17.1	✓	4
29.12	odd	4		87.2.f.a.41.1	yes	4
87.41	even	4	inner	87.2.f.b.41.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.f.a.17.1	✓	4	3.2	odd	2
87.2.f.a.41.1	yes	4	29.12	odd	4
87.2.f.b.17.2	yes	4	1.1	even	1	trivial
87.2.f.b.41.2	yes	4	87.41	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 + 1.36603i) q^{2} +(1.50000 - 0.866025i) q^{3} +1.73205i q^{4} -3.73205 q^{5} +(3.23205 + 0.866025i) q^{6} -2.73205 q^{7} +(0.366025 - 0.366025i) q^{8} +(1.50000 - 2.59808i) q^{9} +(-5.09808 - 5.09808i) q^{10} +(0.366025 + 0.366025i) q^{11} +(1.50000 + 2.59808i) q^{12} +5.73205i q^{13} +(-3.73205 - 3.73205i) q^{14} +(-5.59808 + 3.23205i) q^{15} +4.46410 q^{16} +(0.732051 + 0.732051i) q^{17} +(5.59808 - 1.50000i) q^{18} +(1.73205 - 1.73205i) q^{19} -6.46410i q^{20} +(-4.09808 + 2.36603i) q^{21} +1.00000i q^{22} -1.46410i q^{23} +(0.232051 - 0.866025i) q^{24} +8.92820 q^{25} +(-7.83013 + 7.83013i) q^{26} -5.19615i q^{27} -4.73205i q^{28} +(-2.00000 - 5.00000i) q^{29} +(-12.0622 - 3.23205i) q^{30} +(0.633975 - 0.633975i) q^{31} +(5.36603 + 5.36603i) q^{32} +(0.866025 + 0.232051i) q^{33} +2.00000i q^{34} +10.1962 q^{35} +(4.50000 + 2.59808i) q^{36} +(-3.46410 - 3.46410i) q^{37} +4.73205 q^{38} +(4.96410 + 8.59808i) q^{39} +(-1.36603 + 1.36603i) q^{40} +(-5.19615 + 5.19615i) q^{41} +(-8.83013 - 2.36603i) q^{42} +(-3.56218 + 3.56218i) q^{43} +(-0.633975 + 0.633975i) q^{44} +(-5.59808 + 9.69615i) q^{45} +(2.00000 - 2.00000i) q^{46} +(-0.830127 + 0.830127i) q^{47} +(6.69615 - 3.86603i) q^{48} +0.464102 q^{49} +(12.1962 + 12.1962i) q^{50} +(1.73205 + 0.464102i) q^{51} -9.92820 q^{52} -3.92820i q^{53} +(7.09808 - 7.09808i) q^{54} +(-1.36603 - 1.36603i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(1.09808 - 4.09808i) q^{57} +(4.09808 - 9.56218i) q^{58} +0.535898i q^{59} +(-5.59808 - 9.69615i) q^{60} +(-2.00000 + 2.00000i) q^{61} +1.73205 q^{62} +(-4.09808 + 7.09808i) q^{63} +5.73205i q^{64} -21.3923i q^{65} +(0.866025 + 1.50000i) q^{66} +8.92820i q^{67} +(-1.26795 + 1.26795i) q^{68} +(-1.26795 - 2.19615i) q^{69} +(13.9282 + 13.9282i) q^{70} +16.7321 q^{71} +(-0.401924 - 1.50000i) q^{72} +(-4.00000 - 4.00000i) q^{73} -9.46410i q^{74} +(13.3923 - 7.73205i) q^{75} +(3.00000 + 3.00000i) q^{76} +(-1.00000 - 1.00000i) q^{77} +(-4.96410 + 18.5263i) q^{78} +(1.83013 - 1.83013i) q^{79} -16.6603 q^{80} +(-4.50000 - 7.79423i) q^{81} -14.1962 q^{82} +13.8564i q^{83} +(-4.09808 - 7.09808i) q^{84} +(-2.73205 - 2.73205i) q^{85} -9.73205 q^{86} +(-7.33013 - 5.76795i) q^{87} +0.267949 q^{88} +(-5.00000 - 5.00000i) q^{89} +(-20.8923 + 5.59808i) q^{90} -15.6603i q^{91} +2.53590 q^{92} +(0.401924 - 1.50000i) q^{93} -2.26795 q^{94} +(-6.46410 + 6.46410i) q^{95} +(12.6962 + 3.40192i) q^{96} +(-7.73205 - 7.73205i) q^{97} +(0.633975 + 0.633975i) q^{98} +(1.50000 - 0.401924i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{3} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9} - 10 q^{10} - 2 q^{11} + 6 q^{12} - 8 q^{14} - 12 q^{15} + 4 q^{16} - 4 q^{17} + 12 q^{18} - 6 q^{21} - 6 q^{24} + 8 q^{25} - 14 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^3 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9 - 10 * q^10 - 2 * q^11 + 6 * q^12 - 8 * q^14 - 12 * q^15 + 4 * q^16 - 4 * q^17 + 12 * q^18 - 6 * q^21 - 6 * q^24 + 8 * q^25 - 14 * q^26 - 8 * q^29 - 24 * q^30 + 6 * q^31 + 18 * q^32 + 20 * q^35 + 18 * q^36 + 12 * q^38 + 6 * q^39 - 2 * q^40 - 18 * q^42 + 10 * q^43 - 6 * q^44 - 12 * q^45 + 8 * q^46 + 14 * q^47 + 6 * q^48 - 12 * q^49 + 28 * q^50 - 12 * q^52 + 18 * q^54 - 2 * q^55 - 4 * q^56 - 6 * q^57 + 6 * q^58 - 12 * q^60 - 8 * q^61 - 6 * q^63 - 12 * q^68 - 12 * q^69 + 28 * q^70 + 60 * q^71 - 12 * q^72 - 16 * q^73 + 12 * q^75 + 12 * q^76 - 4 * q^77 - 6 * q^78 - 10 * q^79 - 32 * q^80 - 18 * q^81 - 36 * q^82 - 6 * q^84 - 4 * q^85 - 32 * q^86 - 12 * q^87 + 8 * q^88 - 20 * q^89 - 42 * q^90 + 24 * q^92 + 12 * q^93 - 16 * q^94 - 12 * q^95 + 30 * q^96 - 24 * q^97 + 6 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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