LMFDB - Embedded newform 287.2.r.a.9.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(9,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 9]))

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

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

chi := DirichletCharacter("287.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.r (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$4$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			9.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	287.9
Dual form			287.2.r.a.32.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.36603 - 1.36603i) q^{6} +(2.50000 - 0.866025i) q^{7} +3.00000i q^{8} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.36603 - 1.36603i) q^{6} +(2.50000 - 0.866025i) q^{7} +3.00000i q^{8} +(-0.633975 - 0.366025i) q^{9} +(0.866025 + 1.50000i) q^{10} +(-1.13397 + 4.23205i) q^{11} +(1.86603 - 0.500000i) q^{12} +(-1.73205 - 1.73205i) q^{13} +(-2.59808 - 0.500000i) q^{14} +(2.36603 - 2.36603i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.46410 + 1.73205i) q^{17} +(0.366025 + 0.633975i) q^{18} +(1.40192 + 5.23205i) q^{19} +1.73205i q^{20} +(0.366025 + 5.09808i) q^{21} +(3.09808 - 3.09808i) q^{22} +(-3.73205 + 6.46410i) q^{23} +(-5.59808 - 1.50000i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(0.633975 + 2.36603i) q^{26} +(-3.09808 + 3.09808i) q^{27} +(-2.00000 - 1.73205i) q^{28} +(6.73205 + 6.73205i) q^{29} +(-3.23205 + 0.866025i) q^{30} +(-0.366025 - 0.633975i) q^{31} +(4.33013 - 2.50000i) q^{32} +(-7.33013 - 4.23205i) q^{33} +(-4.73205 - 4.73205i) q^{34} +(-4.50000 - 0.866025i) q^{35} +0.732051i q^{36} +(-0.267949 + 0.464102i) q^{37} +(1.40192 - 5.23205i) q^{38} +(4.09808 - 2.36603i) q^{39} +(2.59808 - 4.50000i) q^{40} +(4.00000 - 5.00000i) q^{41} +(2.23205 - 4.59808i) q^{42} +5.46410i q^{43} +(4.23205 - 1.13397i) q^{44} +(0.633975 + 1.09808i) q^{45} +(6.46410 - 3.73205i) q^{46} +(-1.63397 - 6.09808i) q^{47} +(1.36603 + 1.36603i) q^{48} +(5.50000 - 4.33013i) q^{49} +2.00000i q^{50} +(-6.46410 + 11.1962i) q^{51} +(-0.633975 + 2.36603i) q^{52} +(0.366025 - 1.36603i) q^{53} +(4.23205 - 1.13397i) q^{54} +(5.36603 - 5.36603i) q^{55} +(2.59808 + 7.50000i) q^{56} -10.4641 q^{57} +(-2.46410 - 9.19615i) q^{58} +(-5.36603 - 9.29423i) q^{59} +(-3.23205 - 0.866025i) q^{60} +(-6.06218 - 3.50000i) q^{61} +0.732051i q^{62} +(-1.90192 - 0.366025i) q^{63} -7.00000 q^{64} +(1.09808 + 4.09808i) q^{65} +(4.23205 + 7.33013i) q^{66} +(2.36603 + 0.633975i) q^{67} +(-1.73205 - 6.46410i) q^{68} +(-10.1962 - 10.1962i) q^{69} +(3.46410 + 3.00000i) q^{70} +(6.63397 + 6.63397i) q^{71} +(1.09808 - 1.90192i) q^{72} +(-3.92820 + 2.26795i) q^{73} +(0.464102 - 0.267949i) q^{74} +(3.73205 - 1.00000i) q^{75} +(3.83013 - 3.83013i) q^{76} +(0.830127 + 11.5622i) q^{77} -4.73205 q^{78} +(10.3301 - 2.76795i) q^{79} +(-1.50000 + 0.866025i) q^{80} +(-5.33013 - 9.23205i) q^{81} +(-5.96410 + 2.33013i) q^{82} +0.732051 q^{83} +(4.23205 - 2.86603i) q^{84} +(-8.19615 - 8.19615i) q^{85} +(2.73205 - 4.73205i) q^{86} +(-15.9282 + 9.19615i) q^{87} +(-12.6962 - 3.40192i) q^{88} +(-6.83013 + 1.83013i) q^{89} -1.26795i q^{90} +(-5.83013 - 2.83013i) q^{91} +7.46410 q^{92} +(1.36603 - 0.366025i) q^{93} +(-1.63397 + 6.09808i) q^{94} +(2.42820 - 9.06218i) q^{95} +(2.50000 + 9.33013i) q^{96} +(-5.46410 + 5.46410i) q^{97} +(-6.92820 + 1.00000i) q^{98} +(2.26795 - 2.26795i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9}+O(q^{10}) $ 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9	$ 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9} - 8 q^{11} + 4 q^{12} + 6 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + 16 q^{19} - 2 q^{21} + 2 q^{22} - 8 q^{23} - 12 q^{24} - 4 q^{25} + 6 q^{26} - 2 q^{27} - 8 q^{28} + 20 q^{29} - 6 q^{30} + 2 q^{31} - 12 q^{33} - 12 q^{34} - 18 q^{35} - 8 q^{37} + 16 q^{38} + 6 q^{39} + 16 q^{41} + 2 q^{42} + 10 q^{44} + 6 q^{45} + 12 q^{46} - 10 q^{47} + 2 q^{48} + 22 q^{49} - 12 q^{51} - 6 q^{52} - 2 q^{53} + 10 q^{54} + 18 q^{55} - 28 q^{57} + 4 q^{58} - 18 q^{59} - 6 q^{60} - 18 q^{63} - 28 q^{64} - 6 q^{65} + 10 q^{66} + 6 q^{67} - 20 q^{69} + 30 q^{71} - 6 q^{72} + 12 q^{73} - 12 q^{74} + 8 q^{75} - 2 q^{76} - 14 q^{77} - 12 q^{78} + 24 q^{79} - 6 q^{80} - 4 q^{81} - 10 q^{82} - 4 q^{83} + 10 q^{84} - 12 q^{85} + 4 q^{86} - 36 q^{87} - 30 q^{88} - 10 q^{89} - 6 q^{91} + 16 q^{92} + 2 q^{93} - 10 q^{94} - 18 q^{95} + 10 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) $ 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9 - 8 * q^11 + 4 * q^12 + 6 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + 16 * q^19 - 2 * q^21 + 2 * q^22 - 8 * q^23 - 12 * q^24 - 4 * q^25 + 6 * q^26 - 2 * q^27 - 8 * q^28 + 20 * q^29 - 6 * q^30 + 2 * q^31 - 12 * q^33 - 12 * q^34 - 18 * q^35 - 8 * q^37 + 16 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 10 * q^44 + 6 * q^45 + 12 * q^46 - 10 * q^47 + 2 * q^48 + 22 * q^49 - 12 * q^51 - 6 * q^52 - 2 * q^53 + 10 * q^54 + 18 * q^55 - 28 * q^57 + 4 * q^58 - 18 * q^59 - 6 * q^60 - 18 * q^63 - 28 * q^64 - 6 * q^65 + 10 * q^66 + 6 * q^67 - 20 * q^69 + 30 * q^71 - 6 * q^72 + 12 * q^73 - 12 * q^74 + 8 * q^75 - 2 * q^76 - 14 * q^77 - 12 * q^78 + 24 * q^79 - 6 * q^80 - 4 * q^81 - 10 * q^82 - 4 * q^83 + 10 * q^84 - 12 * q^85 + 4 * q^86 - 36 * q^87 - 30 * q^88 - 10 * q^89 - 6 * q^91 + 16 * q^92 + 2 * q^93 - 10 * q^94 - 18 * q^95 + 10 * q^96 - 8 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	0.161521	−	0.986869i	$-0.448360\pi$
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i	−0.773893	+	0.633316i	$0.781693\pi$
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	0.657437	+	0.753510i	$0.271641\pi$
$3$	−0.500000	+	1.86603i	−0.288675	+	1.07735i	−0.946112	+	0.323840i	$0.895026\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	0.125567	−	0.992085i	$-0.459925\pi$
$5$	−1.50000	−	0.866025i	−0.670820	−	0.387298i	−0.796387	+	0.604787i	$0.793258\pi$
$6$	1.36603	−	1.36603i	0.557678	−	0.557678i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$7$	2.50000	−	0.866025i	0.944911	−	0.327327i
$8$			3.00000i			1.06066i
$9$	−0.633975	−	0.366025i	−0.211325	−	0.122008i
$10$	0.866025	+	1.50000i	0.273861	+	0.474342i
$11$	−1.13397	+	4.23205i	−0.341906	+	1.27601i	0.554279	+	0.832331i	$0.312994\pi$
$11$	−1.13397	+	4.23205i	−0.341906	+	1.27601i	−0.896185	+	0.443680i	$0.853673\pi$
$12$	1.86603	−	0.500000i	0.538675	−	0.144338i
$13$	−1.73205	−	1.73205i	−0.480384	−	0.480384i	0.424870	−	0.905254i	$-0.360320\pi$
$13$	−1.73205	−	1.73205i	−0.480384	−	0.480384i	−0.905254	+	0.424870i	$0.860320\pi$
$14$	−2.59808	−	0.500000i	−0.694365	−	0.133631i
$15$	2.36603	−	2.36603i	0.610905	−	0.610905i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	6.46410	+	1.73205i	1.56777	+	0.420084i	0.935115	−	0.354345i	$-0.115296\pi$
$17$	6.46410	+	1.73205i	1.56777	+	0.420084i	0.632660	+	0.774429i	$0.281963\pi$
$18$	0.366025	+	0.633975i	0.0862730	+	0.149429i
$19$	1.40192	+	5.23205i	0.321623	+	1.20031i	0.917663	+	0.397360i	$0.130073\pi$
$19$	1.40192	+	5.23205i	0.321623	+	1.20031i	−0.596040	+	0.802955i	$0.703260\pi$
$20$			1.73205i			0.387298i
$21$	0.366025	+	5.09808i	0.0798733	+	1.11249i
$22$	3.09808	−	3.09808i	0.660512	−	0.660512i
$23$	−3.73205	+	6.46410i	−0.778186	+	1.34786i	0.154800	+	0.987946i	$0.450527\pi$
$23$	−3.73205	+	6.46410i	−0.778186	+	1.34786i	−0.932986	+	0.359912i	$0.882807\pi$
$24$	−5.59808	−	1.50000i	−1.14270	−	0.306186i
$25$	−1.00000	−	1.73205i	−0.200000	−	0.346410i
$26$	0.633975	+	2.36603i	0.124333	+	0.464016i
$27$	−3.09808	+	3.09808i	−0.596225	+	0.596225i
$28$	−2.00000	−	1.73205i	−0.377964	−	0.327327i
$29$	6.73205	+	6.73205i	1.25011	+	1.25011i	0.955670	+	0.294441i	$0.0951333\pi$
$29$	6.73205	+	6.73205i	1.25011	+	1.25011i	0.294441	+	0.955670i	$0.404867\pi$
$30$	−3.23205	+	0.866025i	−0.590089	+	0.158114i
$31$	−0.366025	−	0.633975i	−0.0657401	−	0.113865i	0.831282	−	0.555851i	$-0.187607\pi$
$31$	−0.366025	−	0.633975i	−0.0657401	−	0.113865i	−0.897022	+	0.441986i	$0.854274\pi$
$32$	4.33013	−	2.50000i	0.765466	−	0.441942i
$33$	−7.33013	−	4.23205i	−1.27601	−	0.736705i
$34$	−4.73205	−	4.73205i	−0.811540	−	0.811540i
$35$	−4.50000	−	0.866025i	−0.760639	−	0.146385i
$36$			0.732051i			0.122008i
$37$	−0.267949	+	0.464102i	−0.0440506	+	0.0762978i	−0.887210	−	0.461366i	$-0.847360\pi$
$37$	−0.267949	+	0.464102i	−0.0440506	+	0.0762978i	0.843159	+	0.537664i	$0.180693\pi$
$38$	1.40192	−	5.23205i	0.227422	−	0.848751i
$39$	4.09808	−	2.36603i	0.656217	−	0.378867i
$40$	2.59808	−	4.50000i	0.410792	−	0.711512i
$41$	4.00000	−	5.00000i	0.624695	−	0.780869i
$41$	4.00000	−	5.00000i	0.624695	−	0.780869i
$42$	2.23205	−	4.59808i	0.344413	−	0.709499i
$43$			5.46410i			0.833268i	0.909074	+	0.416634i	$0.136790\pi$
$43$			5.46410i			0.833268i	−0.909074	+	0.416634i	$0.863210\pi$
$44$	4.23205	−	1.13397i	0.638006	−	0.170953i
$45$	0.633975	+	1.09808i	0.0945074	+	0.163692i
$46$	6.46410	−	3.73205i	0.953080	−	0.550261i
$47$	−1.63397	−	6.09808i	−0.238340	−	0.889496i	−0.976615	−	0.214996i	$-0.931026\pi$
$47$	−1.63397	−	6.09808i	−0.238340	−	0.889496i	0.738275	−	0.674500i	$-0.235641\pi$
$48$	1.36603	+	1.36603i	0.197169	+	0.197169i
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$			2.00000i			0.282843i
$51$	−6.46410	+	11.1962i	−0.905155	+	1.56777i
$52$	−0.633975	+	2.36603i	−0.0879165	+	0.328109i
$53$	0.366025	−	1.36603i	0.0502775	−	0.187638i	−0.936220	−	0.351414i	$-0.885701\pi$
$53$	0.366025	−	1.36603i	0.0502775	−	0.187638i	0.986498	+	0.163776i	$0.0523675\pi$
$54$	4.23205	−	1.13397i	0.575909	−	0.154314i
$55$	5.36603	−	5.36603i	0.723555	−	0.723555i
$56$	2.59808	+	7.50000i	0.347183	+	1.00223i
$57$	−10.4641			−1.38600
$58$	−2.46410	−	9.19615i	−0.323552	−	1.20751i
$59$	−5.36603	−	9.29423i	−0.698597	−	1.21001i	−0.968953	−	0.247245i	$-0.920475\pi$
$59$	−5.36603	−	9.29423i	−0.698597	−	1.21001i	0.270356	−	0.962760i	$-0.412859\pi$
$60$	−3.23205	−	0.866025i	−0.417256	−	0.111803i
$61$	−6.06218	−	3.50000i	−0.776182	−	0.448129i	0.0588933	−	0.998264i	$-0.481243\pi$
$61$	−6.06218	−	3.50000i	−0.776182	−	0.448129i	−0.835076	+	0.550135i	$0.814576\pi$
$62$			0.732051i			0.0929705i
$63$	−1.90192	−	0.366025i	−0.239620	−	0.0461149i
$64$	−7.00000			−0.875000
$65$	1.09808	+	4.09808i	0.136200	+	0.508304i
$66$	4.23205	+	7.33013i	0.520929	+	0.902276i
$67$	2.36603	+	0.633975i	0.289056	+	0.0774523i	0.400433	−	0.916326i	$-0.368860\pi$
$67$	2.36603	+	0.633975i	0.289056	+	0.0774523i	−0.111377	+	0.993778i	$0.535526\pi$
$68$	−1.73205	−	6.46410i	−0.210042	−	0.783887i
$69$	−10.1962	−	10.1962i	−1.22747	−	1.22747i
$70$	3.46410	+	3.00000i	0.414039	+	0.358569i
$71$	6.63397	+	6.63397i	0.787308	+	0.787308i	0.981052	−	0.193744i	$-0.0620632\pi$
$71$	6.63397	+	6.63397i	0.787308	+	0.787308i	−0.193744	+	0.981052i	$0.562063\pi$
$72$	1.09808	−	1.90192i	0.129410	−	0.224144i
$73$	−3.92820	+	2.26795i	−0.459761	+	0.265443i	−0.711944	−	0.702236i	$-0.752185\pi$
$73$	−3.92820	+	2.26795i	−0.459761	+	0.265443i	0.252183	+	0.967680i	$0.418852\pi$
$74$	0.464102	−	0.267949i	0.0539507	−	0.0311485i
$75$	3.73205	−	1.00000i	0.430940	−	0.115470i
$76$	3.83013	−	3.83013i	0.439346	−	0.439346i
$77$	0.830127	+	11.5622i	0.0946018	+	1.31763i
$78$	−4.73205			−0.535799
$79$	10.3301	−	2.76795i	1.16223	−	0.311419i	0.374374	−	0.927278i	$-0.377858\pi$
$79$	10.3301	−	2.76795i	1.16223	−	0.311419i	0.787856	+	0.615859i	$0.211191\pi$
$80$	−1.50000	+	0.866025i	−0.167705	+	0.0968246i
$81$	−5.33013	−	9.23205i	−0.592236	−	1.02578i
$82$	−5.96410	+	2.33013i	−0.658625	+	0.257319i
$83$	0.732051			0.0803530			0.0401765	−	0.999193i	$-0.487208\pi$
$83$	0.732051			0.0803530			0.0401765	+	0.999193i	$0.487208\pi$
$84$	4.23205	−	2.86603i	0.461755	−	0.312709i
$85$	−8.19615	−	8.19615i	−0.888998	−	0.888998i
$86$	2.73205	−	4.73205i	0.294605	−	0.510270i
$87$	−15.9282	+	9.19615i	−1.70768	+	0.985931i
$88$	−12.6962	−	3.40192i	−1.35341	−	0.362646i
$89$	−6.83013	+	1.83013i	−0.723992	+	0.193993i	−0.601952	−	0.798532i	$-0.705610\pi$
$89$	−6.83013	+	1.83013i	−0.723992	+	0.193993i	−0.122040	+	0.992525i	$0.538944\pi$
$90$		−	1.26795i		−	0.133654i
$91$	−5.83013	−	2.83013i	−0.611163	−	0.296678i
$92$	7.46410			0.778186
$93$	1.36603	−	0.366025i	0.141650	−	0.0379551i
$94$	−1.63397	+	6.09808i	−0.168532	+	0.628969i
$95$	2.42820	−	9.06218i	0.249128	−	0.929760i
$96$	2.50000	+	9.33013i	0.255155	+	0.952252i
$97$	−5.46410	+	5.46410i	−0.554795	+	0.554795i	−0.927821	−	0.373026i	$-0.878320\pi$
$97$	−5.46410	+	5.46410i	−0.554795	+	0.554795i	0.373026	+	0.927821i	$0.378320\pi$
$98$	−6.92820	+	1.00000i	−0.699854	+	0.101015i
$99$	2.26795	−	2.26795i	0.227937	−	0.227937i
$100$	−1.00000	+	1.73205i	−0.100000	+	0.173205i
$101$	8.46410	+	2.26795i	0.842210	+	0.225669i	0.654033	−	0.756466i	$-0.273076\pi$
$101$	8.46410	+	2.26795i	0.842210	+	0.225669i	0.188176	+	0.982135i	$0.439742\pi$
$102$	11.1962	−	6.46410i	1.10858	−	0.640041i
$103$	−7.56218	−	4.36603i	−0.745124	−	0.430197i	0.0788057	−	0.996890i	$-0.474889\pi$
$103$	−7.56218	−	4.36603i	−0.745124	−	0.430197i	−0.823929	+	0.566693i	$0.808223\pi$
$104$	5.19615	−	5.19615i	0.509525	−	0.509525i
$105$	3.86603	−	7.96410i	0.377285	−	0.777217i
$106$	−1.00000	+	1.00000i	−0.0971286	+	0.0971286i
$107$	−10.0263	+	17.3660i	−0.969277	+	1.67884i	−0.271621	+	0.962404i	$0.587560\pi$
$107$	−10.0263	+	17.3660i	−0.969277	+	1.67884i	−0.697656	+	0.716433i	$0.745774\pi$
$108$	4.23205	+	1.13397i	0.407229	+	0.109117i
$109$	9.46410	+	2.53590i	0.906497	+	0.242895i	0.681804	−	0.731535i	$-0.261196\pi$
$109$	9.46410	+	2.53590i	0.906497	+	0.242895i	0.224692	+	0.974430i	$0.427862\pi$
$110$	−7.33013	+	1.96410i	−0.698900	+	0.187270i
$111$	−0.732051	−	0.732051i	−0.0694832	−	0.0694832i
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	−19.5885			−1.84273			−0.921364	−	0.388702i	$-0.872924\pi$
$113$	−19.5885			−1.84273			−0.921364	+	0.388702i	$0.872924\pi$
$114$	9.06218	+	5.23205i	0.848751	+	0.490026i
$115$	11.1962	−	6.46410i	1.04405	−	0.602781i
$116$	2.46410	−	9.19615i	0.228786	−	0.853841i
$117$	0.464102	+	1.73205i	0.0429062	+	0.160128i
$118$			10.7321i			0.987965i
$119$	17.6603	−	1.26795i	1.61891	−	0.116233i
$120$	7.09808	+	7.09808i	0.647963	+	0.647963i
$121$	−7.09808	−	4.09808i	−0.645280	−	0.372552i
$122$	3.50000	+	6.06218i	0.316875	+	0.548844i
$123$	7.33013	+	9.96410i	0.660935	+	0.898433i
$124$	−0.366025	+	0.633975i	−0.0328701	+	0.0569326i
$125$			12.1244i			1.08444i
$126$	1.46410	+	1.26795i	0.130433	+	0.112958i
$127$	17.1244			1.51954			0.759770	−	0.650191i	$-0.225311\pi$
$127$	17.1244			1.51954			0.759770	+	0.650191i	$0.225311\pi$
$128$	−2.59808	−	1.50000i	−0.229640	−	0.132583i
$129$	−10.1962	−	2.73205i	−0.897721	−	0.240544i
$130$	1.09808	−	4.09808i	0.0963077	−	0.359425i
$131$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$131$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$132$			8.46410i			0.736705i
$133$	8.03590	+	11.8660i	0.696801	+	1.02891i
$134$	−1.73205	−	1.73205i	−0.149626	−	0.149626i
$135$	7.33013	−	1.96410i	0.630877	−	0.169043i
$136$	−5.19615	+	19.3923i	−0.445566	+	1.66288i
$137$	−8.09808	−	2.16987i	−0.691865	−	0.185385i	−0.104281	−	0.994548i	$-0.533254\pi$
$137$	−8.09808	−	2.16987i	−0.691865	−	0.185385i	−0.587584	+	0.809163i	$0.699921\pi$
$138$	3.73205	+	13.9282i	0.317693	+	1.18565i
$139$	21.5167			1.82502			0.912510	−	0.409055i	$-0.134142\pi$
$139$	21.5167			1.82502			0.912510	+	0.409055i	$0.134142\pi$
$140$	1.50000	+	4.33013i	0.126773	+	0.365963i
$141$	12.1962			1.02710
$142$	−2.42820	−	9.06218i	−0.203770	−	0.760481i
$143$	9.29423	−	5.36603i	0.777222	−	0.448730i
$144$	−0.633975	+	0.366025i	−0.0528312	+	0.0305021i
$145$	−4.26795	−	15.9282i	−0.354434	−	1.32277i
$146$	4.53590			0.375394
$147$	5.33013	+	12.4282i	0.439621	+	1.02506i
$148$	0.535898			0.0440506
$149$	−1.90192	−	7.09808i	−0.155812	−	0.581497i	−0.999034	−	0.0439329i	$-0.986011\pi$
$149$	−1.90192	−	7.09808i	−0.155812	−	0.581497i	0.843223	−	0.537564i	$-0.180655\pi$
$150$	−3.73205	−	1.00000i	−0.304721	−	0.0816497i
$151$	−0.366025	+	1.36603i	−0.0297867	+	0.111166i	−0.979219	−	0.202807i	$-0.934993\pi$
$151$	−0.366025	+	1.36603i	−0.0297867	+	0.111166i	0.949432	+	0.313973i	$0.101660\pi$
$152$	−15.6962	+	4.20577i	−1.27313	+	0.341133i
$153$	−3.46410	−	3.46410i	−0.280056	−	0.280056i
$154$	5.06218	−	10.4282i	0.407922	−	0.840329i
$155$			1.26795i			0.101844i
$156$	−4.09808	−	2.36603i	−0.328109	−	0.189434i
$157$	4.80385	−	17.9282i	0.383389	−	1.43083i	−0.457302	−	0.889311i	$-0.651184\pi$
$157$	4.80385	−	17.9282i	0.383389	−	1.43083i	0.840691	−	0.541515i	$-0.182149\pi$
$158$	−10.3301	−	2.76795i	−0.821821	−	0.220206i
$159$	2.36603	+	1.36603i	0.187638	+	0.108333i
$160$	−8.66025			−0.684653
$161$	−3.73205	+	19.3923i	−0.294127	+	1.52833i
$162$			10.6603i			0.837549i
$163$	6.90192	−	11.9545i	0.540600	−	0.936347i	−0.458269	−	0.888813i	$-0.651530\pi$
$163$	6.90192	−	11.9545i	0.540600	−	0.936347i	0.998870	−	0.0475339i	$-0.0151362\pi$
$164$	−6.33013	−	0.964102i	−0.494300	−	0.0752837i
$165$	7.33013	+	12.6962i	0.570650	+	0.988394i
$166$	−0.633975	−	0.366025i	−0.0492060	−	0.0284091i
$167$	1.92820	+	1.92820i	0.149209	+	0.149209i	0.777765	−	0.628556i	$-0.216354\pi$
$167$	1.92820	+	1.92820i	0.149209	+	0.149209i	−0.628556	+	0.777765i	$0.716354\pi$
$168$	−15.2942	+	1.09808i	−1.17998	+	0.0847184i
$169$		−	7.00000i		−	0.538462i
$170$	3.00000	+	11.1962i	0.230089	+	0.858706i
$171$	1.02628	−	3.83013i	0.0784816	−	0.292897i
$172$	4.73205	−	2.73205i	0.360815	−	0.208317i
$173$	−0.0621778	−	0.0358984i	−0.00472729	−	0.00272930i	0.497634	−	0.867387i	$-0.334202\pi$
$173$	−0.0621778	−	0.0358984i	−0.00472729	−	0.00272930i	−0.502362	+	0.864658i	$0.667535\pi$
$174$	18.3923			1.39432
$175$	−4.00000	−	3.46410i	−0.302372	−	0.261861i
$176$	3.09808	+	3.09808i	0.233526	+	0.233526i
$177$	20.0263	−	5.36603i	1.50527	−	0.403335i
$178$	6.83013	+	1.83013i	0.511940	+	0.137174i
$179$	−8.33013	−	2.23205i	−0.622623	−	0.166831i	−0.0663030	−	0.997800i	$-0.521120\pi$
$179$	−8.33013	−	2.23205i	−0.622623	−	0.166831i	−0.556320	+	0.830968i	$0.687787\pi$
$180$	0.633975	−	1.09808i	0.0472537	−	0.0818458i
$181$	7.73205	−	7.73205i	0.574719	−	0.574719i	−0.358725	−	0.933443i	$-0.616788\pi$
$181$	7.73205	−	7.73205i	0.574719	−	0.574719i	0.933443	+	0.358725i	$0.116788\pi$
$182$	3.63397	+	5.36603i	0.269368	+	0.397756i
$183$	9.56218	−	9.56218i	0.706857	−	0.706857i
$184$	−19.3923	−	11.1962i	−1.42962	−	0.825391i
$185$	0.803848	−	0.464102i	0.0591000	−	0.0341214i
$186$	−1.36603	−	0.366025i	−0.100162	−	0.0268383i
$187$	−14.6603	+	25.3923i	−1.07206	+	1.85687i
$188$	−4.46410	+	4.46410i	−0.325578	+	0.325578i
$189$	−5.06218	+	10.4282i	−0.368219	+	0.758540i
$190$	−6.63397	+	6.63397i	−0.481279	+	0.481279i
$191$	−1.97372	−	7.36603i	−0.142813	−	0.532987i	−0.999843	−	0.0177197i	$-0.994359\pi$
$191$	−1.97372	−	7.36603i	−0.142813	−	0.532987i	0.857030	−	0.515267i	$-0.172307\pi$
$192$	3.50000	−	13.0622i	0.252591	−	0.942681i
$193$	−2.36603	+	8.83013i	−0.170310	+	0.635606i	0.826993	+	0.562213i	$0.190050\pi$
$193$	−2.36603	+	8.83013i	−0.170310	+	0.635606i	−0.997303	+	0.0733939i	$0.976617\pi$
$194$	7.46410	−	2.00000i	0.535891	−	0.143592i
$195$	−8.19615			−0.586939
$196$	−6.50000	−	2.59808i	−0.464286	−	0.185577i
$197$			0.0717968i			0.00511531i	0.999997	+	0.00255765i	$0.000814127\pi$
$197$			0.0717968i			0.00511531i	−0.999997	+	0.00255765i	$0.999186\pi$
$198$	−3.09808	+	0.830127i	−0.220171	+	0.0589946i
$199$	−12.2942	−	3.29423i	−0.871515	−	0.233522i	−0.204772	−	0.978810i	$-0.565645\pi$
$199$	−12.2942	−	3.29423i	−0.871515	−	0.233522i	−0.666743	+	0.745288i	$0.732312\pi$
$200$	5.19615	−	3.00000i	0.367423	−	0.212132i
$201$	−2.36603	+	4.09808i	−0.166887	+	0.289056i
$202$	−6.19615	−	6.19615i	−0.435960	−	0.435960i
$203$	22.6603	+	11.0000i	1.59044	+	0.772049i
$204$	12.9282			0.905155
$205$	−10.3301	+	4.03590i	−0.721487	+	0.281879i
$206$	4.36603	+	7.56218i	0.304195	+	0.526882i
$207$	4.73205	−	2.73205i	0.328900	−	0.189891i
$208$	−2.36603	+	0.633975i	−0.164054	+	0.0439582i
$209$	−23.7321			−1.64158
$210$	−7.33013	+	4.96410i	−0.505827	+	0.342556i
$211$	−5.16987	+	5.16987i	−0.355909	+	0.355909i	−0.862302	−	0.506394i	$-0.830978\pi$
$211$	−5.16987	+	5.16987i	−0.355909	+	0.355909i	0.506394	+	0.862302i	$0.330978\pi$
$212$	−1.36603	+	0.366025i	−0.0938190	+	0.0251387i
$213$	−15.6962	+	9.06218i	−1.07548	+	0.620930i
$214$	17.3660	−	10.0263i	1.18712	−	0.685382i
$215$	4.73205	−	8.19615i	0.322723	−	0.558973i
$216$	−9.29423	−	9.29423i	−0.632392	−	0.632392i
$217$	−1.46410	−	1.26795i	−0.0993897	−	0.0860740i
$218$	−6.92820	−	6.92820i	−0.469237	−	0.469237i
$219$	−2.26795	−	8.46410i	−0.153254	−	0.571951i
$220$	−7.33013	−	1.96410i	−0.494197	−	0.132420i
$221$	−8.19615	−	14.1962i	−0.551333	−	0.954937i
$222$	0.267949	+	1.00000i	0.0179836	+	0.0671156i
$223$	8.92820			0.597877			0.298938	−	0.954272i	$-0.403368\pi$
$223$	8.92820			0.597877			0.298938	+	0.954272i	$0.403368\pi$
$224$	8.66025	−	10.0000i	0.578638	−	0.668153i
$225$			1.46410i			0.0976068i
$226$	16.9641	+	9.79423i	1.12844	+	0.651502i
$227$	−15.4282	−	4.13397i	−1.02401	−	0.274382i	−0.292535	−	0.956255i	$-0.594499\pi$
$227$	−15.4282	−	4.13397i	−1.02401	−	0.274382i	−0.731470	+	0.681873i	$0.761166\pi$
$228$	5.23205	+	9.06218i	0.346501	+	0.600157i
$229$	0.803848	+	3.00000i	0.0531197	+	0.198246i	0.987386	−	0.158330i	$-0.0506109\pi$
$229$	0.803848	+	3.00000i	0.0531197	+	0.198246i	−0.934267	+	0.356575i	$0.883944\pi$
$230$	−12.9282			−0.852460
$231$	−21.9904	−	4.23205i	−1.44686	−	0.278449i
$232$	−20.1962	+	20.1962i	−1.32594	+	1.32594i
$233$	5.63397	−	1.50962i	0.369094	−	0.0988984i	−0.0695043	−	0.997582i	$-0.522142\pi$
$233$	5.63397	−	1.50962i	0.369094	−	0.0988984i	0.438598	+	0.898683i	$0.355475\pi$
$234$	0.464102	−	1.73205i	0.0303393	−	0.113228i
$235$	−2.83013	+	10.5622i	−0.184617	+	0.689001i
$236$	−5.36603	+	9.29423i	−0.349299	+	0.605003i
$237$			20.6603i			1.34203i
$238$	−15.9282	−	7.73205i	−1.03247	−	0.501194i
$239$	2.75833	+	2.75833i	0.178422	+	0.178422i	0.790667	−	0.612246i	$-0.209734\pi$
$239$	2.75833	+	2.75833i	0.178422	+	0.178422i	−0.612246	+	0.790667i	$0.709734\pi$
$240$	−0.866025	−	3.23205i	−0.0559017	−	0.208628i
$241$	16.0526	−	9.26795i	1.03404	−	0.597001i	0.115898	−	0.993261i	$-0.463025\pi$
$241$	16.0526	−	9.26795i	1.03404	−	0.597001i	0.918138	+	0.396260i	$0.129692\pi$
$242$	4.09808	+	7.09808i	0.263434	+	0.456282i
$243$	7.19615	−	1.92820i	0.461633	−	0.123694i
$244$			7.00000i			0.448129i
$245$	−12.0000	+	1.73205i	−0.766652	+	0.110657i
$246$	−1.36603	−	12.2942i	−0.0870946	−	0.783851i
$247$	6.63397	−	11.4904i	0.422110	−	0.731115i
$248$	1.90192	−	1.09808i	0.120772	−	0.0697279i
$249$	−0.366025	+	1.36603i	−0.0231959	+	0.0865683i
$250$	6.06218	−	10.5000i	0.383406	−	0.664078i
$251$		−	4.73205i		−	0.298684i	−0.988786	−	0.149342i	$-0.952284\pi$
$251$		−	4.73205i		−	0.298684i	0.988786	−	0.149342i	$-0.0477156\pi$
$252$	0.633975	+	1.83013i	0.0399366	+	0.115287i
$253$	−23.1244	−	23.1244i	−1.45382	−	1.45382i
$254$	−14.8301	−	8.56218i	−0.930525	−	0.537239i
$255$	19.3923	−	11.1962i	1.21439	−	0.701130i
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	13.4641	−	3.60770i	0.839868	−	0.225042i	0.186854	−	0.982388i	$-0.440171\pi$
$257$	13.4641	−	3.60770i	0.839868	−	0.225042i	0.653014	+	0.757346i	$0.273504\pi$
$258$	7.46410	+	7.46410i	0.464695	+	0.464695i
$259$	−0.267949	+	1.39230i	−0.0166496	+	0.0865136i
$260$	3.00000	−	3.00000i	0.186052	−	0.186052i
$261$	−1.80385	−	6.73205i	−0.111655	−	0.416703i
$262$		0			0
$263$	21.7583	+	5.83013i	1.34168	+	0.359501i	0.857056	−	0.515224i	$-0.172291\pi$
$263$	21.7583	+	5.83013i	1.34168	+	0.359501i	0.484620	+	0.874725i	$0.338958\pi$
$264$	12.6962	−	21.9904i	0.781394	−	1.35341i
$265$	−1.73205	+	1.73205i	−0.106399	+	0.106399i
$266$	−1.02628	−	14.2942i	−0.0629252	−	0.876435i
$267$		−	13.6603i		−	0.835994i
$268$	−0.633975	−	2.36603i	−0.0387262	−	0.144528i
$269$	−5.50000	−	9.52628i	−0.335341	−	0.580828i	0.648209	−	0.761462i	$-0.275518\pi$
$269$	−5.50000	−	9.52628i	−0.335341	−	0.580828i	−0.983550	+	0.180635i	$0.942185\pi$
$270$	−7.33013	−	1.96410i	−0.446097	−	0.119531i
$271$	3.26795	−	5.66025i	0.198514	−	0.343836i	−0.749533	−	0.661967i	$-0.769722\pi$
$271$	3.26795	−	5.66025i	0.198514	−	0.343836i	0.948047	+	0.318131i	$0.103055\pi$
$272$	4.73205	−	4.73205i	0.286923	−	0.286923i
$273$	8.19615	−	9.46410i	0.496054	−	0.572793i
$274$	5.92820	+	5.92820i	0.358136	+	0.358136i
$275$	8.46410	−	2.26795i	0.510405	−	0.136762i
$276$	−3.73205	+	13.9282i	−0.224643	+	0.838379i
$277$	−2.79423	−	4.83975i	−0.167889	−	0.290792i	0.769789	−	0.638299i	$-0.220362\pi$
$277$	−2.79423	−	4.83975i	−0.167889	−	0.290792i	−0.937677	+	0.347507i	$0.887028\pi$
$278$	−18.6340	−	10.7583i	−1.11759	−	0.645242i
$279$			0.535898i			0.0320834i
$280$	2.59808	−	13.5000i	0.155265	−	0.806779i
$281$	−0.196152	+	0.196152i	−0.0117015	+	0.0117015i	−0.712933	−	0.701232i	$-0.752634\pi$
$281$	−0.196152	+	0.196152i	−0.0117015	+	0.0117015i	0.701232	+	0.712933i	$0.252634\pi$
$282$	−10.5622	−	6.09808i	−0.628969	−	0.363135i
$283$	1.90192	+	3.29423i	0.113058	+	0.195822i	0.917002	−	0.398883i	$-0.130602\pi$
$283$	1.90192	+	3.29423i	0.113058	+	0.195822i	−0.803944	+	0.594705i	$0.797269\pi$
$284$	2.42820	−	9.06218i	0.144087	−	0.537741i
$285$	15.6962	+	9.06218i	0.929760	+	0.536797i
$286$	−10.7321			−0.634599
$287$	5.66987	−	15.9641i	0.334682	−	0.942331i
$288$	−3.66025			−0.215683
$289$	24.0622	+	13.8923i	1.41542	+	0.817194i
$290$	−4.26795	+	15.9282i	−0.250623	+	0.935336i
$291$	−7.46410	−	12.9282i	−0.437553	−	0.757865i
$292$	3.92820	+	2.26795i	0.229881	+	0.132722i
$293$	7.12436	−	7.12436i	0.416209	−	0.416209i	−0.467686	−	0.883895i	$-0.654912\pi$
$293$	7.12436	−	7.12436i	0.416209	−	0.416209i	0.883895	+	0.467686i	$0.154912\pi$
$294$	1.59808	−	13.4282i	0.0932017	−	0.783149i
$295$			18.5885i			1.08226i
$296$	−1.39230	−	0.803848i	−0.0809261	−	0.0467227i
$297$	−9.59808	−	16.6244i	−0.556937	−	0.964643i
$298$	−1.90192	+	7.09808i	−0.110175	+	0.411181i
$299$	17.6603	−	4.73205i	1.02132	−	0.273662i
$300$	−2.73205	−	2.73205i	−0.157735	−	0.157735i
$301$	4.73205	+	13.6603i	0.272751	+	0.787364i
$302$	1.00000	−	1.00000i	0.0575435	−	0.0575435i
$303$	−8.46410	+	14.6603i	−0.486250	+	0.842210i
$304$	5.23205	+	1.40192i	0.300079	+	0.0804058i
$305$	6.06218	+	10.5000i	0.347119	+	0.601228i
$306$	1.26795	+	4.73205i	0.0724838	+	0.270513i
$307$		−	22.0000i		−	1.25561i	−0.778372	−	0.627803i	$-0.783954\pi$
$307$		−	22.0000i		−	1.25561i	0.778372	−	0.627803i	$-0.216046\pi$
$308$	9.59808	−	6.50000i	0.546901	−	0.370372i
$309$	11.9282	−	11.9282i	0.678572	−	0.678572i
$310$	0.633975	−	1.09808i	0.0360073	−	0.0623665i
$311$	−1.36603	−	0.366025i	−0.0774602	−	0.0207554i	0.219881	−	0.975527i	$-0.429433\pi$
$311$	−1.36603	−	0.366025i	−0.0774602	−	0.0207554i	−0.297341	+	0.954771i	$0.596100\pi$
$312$	7.09808	+	12.2942i	0.401849	+	0.696024i
$313$	6.05256	+	22.5885i	0.342111	+	1.27678i	0.895951	+	0.444152i	$0.146495\pi$
$313$	6.05256	+	22.5885i	0.342111	+	1.27678i	−0.553840	+	0.832623i	$0.686838\pi$
$314$	−13.1244	+	13.1244i	−0.740650	+	0.740650i
$315$	2.53590	+	2.19615i	0.142882	+	0.123739i
$316$	−7.56218	−	7.56218i	−0.425406	−	0.425406i
$317$	−15.4641	+	4.14359i	−0.868550	+	0.232727i	−0.665461	−	0.746433i	$-0.731765\pi$
$317$	−15.4641	+	4.14359i	−0.868550	+	0.232727i	−0.203090	+	0.979160i	$0.565098\pi$
$318$	−1.36603	−	2.36603i	−0.0766029	−	0.132680i
$319$	−36.1244	+	20.8564i	−2.02258	+	1.16773i
$320$	10.5000	+	6.06218i	0.586968	+	0.338886i
$321$	−27.3923	−	27.3923i	−1.52889	−	1.52889i
$322$	12.9282	−	14.9282i	0.720461	−	0.831916i
$323$			36.2487i			2.01693i
$324$	−5.33013	+	9.23205i	−0.296118	+	0.512892i
$325$	−1.26795	+	4.73205i	−0.0703332	+	0.262487i
$326$	−11.9545	+	6.90192i	−0.662098	+	0.382262i
$327$	−9.46410	+	16.3923i	−0.523366	+	0.906497i
$328$	15.0000	+	12.0000i	0.828236	+	0.662589i
$329$	−9.36603	−	13.8301i	−0.516366	−	0.762480i
$330$		−	14.6603i		−	0.807020i
$331$	22.4904	−	6.02628i	1.23618	−	0.331234i	0.419199	−	0.907894i	$-0.362311\pi$
$331$	22.4904	−	6.02628i	1.23618	−	0.331234i	0.816984	+	0.576660i	$0.195644\pi$
$332$	−0.366025	−	0.633975i	−0.0200883	−	0.0347939i
$333$	0.339746	−	0.196152i	0.0186180	−	0.0107491i
$334$	−0.705771	−	2.63397i	−0.0386181	−	0.144125i
$335$	−3.00000	−	3.00000i	−0.163908	−	0.163908i
$336$	4.59808	+	2.23205i	0.250846	+	0.121768i
$337$		−	10.8038i		−	0.588523i	−0.955725	−	0.294262i	$-0.904926\pi$
$337$		−	10.8038i		−	0.588523i	0.955725	−	0.294262i	$-0.0950737\pi$
$338$	−3.50000	+	6.06218i	−0.190375	+	0.329739i
$339$	9.79423	−	36.5526i	0.531949	−	1.98526i
$340$	−3.00000	+	11.1962i	−0.162698	+	0.607197i
$341$	3.09808	−	0.830127i	0.167770	−	0.0449539i
$342$	−2.80385	+	2.80385i	−0.151615	+	0.151615i
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	−16.3923			−0.883814
$345$	6.46410	+	24.1244i	0.348016	+	1.29881i
$346$	0.0358984	+	0.0621778i	0.00192991	+	0.00334270i
$347$	−14.6962	−	3.93782i	−0.788931	−	0.211393i	−0.158212	−	0.987405i	$-0.550573\pi$
$347$	−14.6962	−	3.93782i	−0.788931	−	0.211393i	−0.630718	+	0.776012i	$0.717240\pi$
$348$	15.9282	+	9.19615i	0.853841	+	0.492966i
$349$		−	3.46410i		−	0.185429i	−0.995693	−	0.0927146i	$-0.970446\pi$
$349$		−	3.46410i		−	0.185429i	0.995693	−	0.0927146i	$-0.0295544\pi$
$350$	1.73205	+	5.00000i	0.0925820	+	0.267261i
$351$	10.7321			0.572834
$352$	5.66987	+	21.1603i	0.302205	+	1.12785i
$353$	10.3301	+	17.8923i	0.549817	+	0.952311i	0.998287	+	0.0585131i	$0.0186360\pi$
$353$	10.3301	+	17.8923i	0.549817	+	0.952311i	−0.448469	+	0.893798i	$0.648031\pi$
$354$	−20.0263	−	5.36603i	−1.06438	−	0.285201i
$355$	−4.20577	−	15.6962i	−0.223219	−	0.833065i
$356$	5.00000	+	5.00000i	0.264999	+	0.264999i
$357$	−6.46410	+	33.5885i	−0.342117	+	1.77769i
$358$	6.09808	+	6.09808i	0.322293	+	0.322293i
$359$	6.29423	−	10.9019i	0.332197	−	0.575382i	−0.650746	−	0.759296i	$-0.725544\pi$
$359$	6.29423	−	10.9019i	0.332197	−	0.575382i	0.982942	+	0.183914i	$0.0588769\pi$
$360$	−3.29423	+	1.90192i	−0.173621	+	0.100240i
$361$	−8.95448	+	5.16987i	−0.471289	+	0.272099i
$362$	−10.5622	+	2.83013i	−0.555136	+	0.148748i
$363$	11.1962	−	11.1962i	0.587646	−	0.587646i
$364$	0.464102	+	6.46410i	0.0243255	+	0.338811i
$365$	7.85641			0.411223
$366$	−13.0622	+	3.50000i	−0.682771	+	0.182948i
$367$	7.68653	−	4.43782i	0.401234	−	0.231652i	−0.285782	−	0.958295i	$-0.592253\pi$
$367$	7.68653	−	4.43782i	0.401234	−	0.231652i	0.687016	+	0.726642i	$0.258920\pi$
$368$	3.73205	+	6.46410i	0.194547	+	0.336965i
$369$	−4.36603	+	1.70577i	−0.227286	+	0.0887989i
$370$	−0.928203			−0.0482550
$371$	−0.267949	−	3.73205i	−0.0139112	−	0.193758i
$372$	−1.00000	−	1.00000i	−0.0518476	−	0.0518476i
$373$	−7.42820	+	12.8660i	−0.384618	+	0.666178i	−0.991716	−	0.128449i	$-0.959000\pi$
$373$	−7.42820	+	12.8660i	−0.384618	+	0.666178i	0.607098	+	0.794627i	$0.292333\pi$
$374$	25.3923	−	14.6603i	1.31300	−	0.758064i
$375$	−22.6244	−	6.06218i	−1.16832	−	0.313050i
$376$	18.2942	−	4.90192i	0.943453	−	0.252797i
$377$		−	23.3205i		−	1.20107i
$378$	9.59808	−	6.50000i	0.493672	−	0.334324i
$379$	−14.5885			−0.749359			−0.374679	−	0.927154i	$-0.622247\pi$
$379$	−14.5885			−0.749359			−0.374679	+	0.927154i	$0.622247\pi$
$380$	−9.06218	+	2.42820i	−0.464880	+	0.124564i
$381$	−8.56218	+	31.9545i	−0.438654	+	1.63708i
$382$	−1.97372	+	7.36603i	−0.100984	+	0.376879i
$383$	−3.16025	−	11.7942i	−0.161481	−	0.602657i	−0.998463	−	0.0554256i	$-0.982348\pi$
$383$	−3.16025	−	11.7942i	−0.161481	−	0.602657i	0.836981	−	0.547231i	$-0.184318\pi$
$384$	4.09808	−	4.09808i	0.209129	−	0.209129i
$385$	8.76795	−	18.0622i	0.446856	−	0.920534i
$386$	6.46410	−	6.46410i	0.329014	−	0.329014i
$387$	2.00000	−	3.46410i	0.101666	−	0.176090i
$388$	7.46410	+	2.00000i	0.378932	+	0.101535i
$389$	17.5981	−	10.1603i	0.892258	−	0.515145i	0.0175775	−	0.999846i	$-0.494405\pi$
$389$	17.5981	−	10.1603i	0.892258	−	0.515145i	0.874680	+	0.484700i	$0.161071\pi$
$390$	7.09808	+	4.09808i	0.359425	+	0.207514i
$391$	−35.3205	+	35.3205i	−1.78623	+	1.78623i
$392$	12.9904	+	16.5000i	0.656113	+	0.833376i
$393$		0			0
$394$	0.0358984	−	0.0621778i	0.00180853	−	0.00313247i
$395$	−17.8923	−	4.79423i	−0.900260	−	0.241224i
$396$	−3.09808	−	0.830127i	−0.155684	−	0.0417155i
$397$	12.2942	−	3.29423i	0.617030	−	0.165333i	0.0632526	−	0.997998i	$-0.479853\pi$
$397$	12.2942	−	3.29423i	0.617030	−	0.165333i	0.553777	+	0.832665i	$0.313186\pi$
$398$	9.00000	+	9.00000i	0.451129	+	0.451129i
$399$	−26.1603	+	9.06218i	−1.30965	+	0.453676i
$400$	−2.00000			−0.100000
$401$	11.5526	+	6.66987i	0.576907	+	0.333078i	0.759903	−	0.650036i	$-0.225246\pi$
$401$	11.5526	+	6.66987i	0.576907	+	0.333078i	−0.182996	+	0.983114i	$0.558580\pi$
$402$	4.09808	−	2.36603i	0.204393	−	0.118007i
$403$	−0.464102	+	1.73205i	−0.0231185	+	0.0862796i
$404$	−2.26795	−	8.46410i	−0.112835	−	0.421105i
$405$			18.4641i			0.917489i
$406$	−14.1244	−	20.8564i	−0.700980	−	1.03509i
$407$	−1.66025	−	1.66025i	−0.0822957	−	0.0822957i
$408$	−33.5885	−	19.3923i	−1.66288	−	0.960062i
$409$	16.9904	+	29.4282i	0.840120	+	1.45513i	0.889792	+	0.456365i	$0.150849\pi$
$409$	16.9904	+	29.4282i	0.840120	+	1.45513i	−0.0496722	+	0.998766i	$0.515818\pi$
$410$	10.9641	+	1.66987i	0.541478	+	0.0824691i
$411$	8.09808	−	14.0263i	0.399449	−	0.691865i
$412$			8.73205i			0.430197i
$413$	−21.4641	−	18.5885i	−1.05618	−	0.914678i
$414$	−5.46410			−0.268546
$415$	−1.09808	−	0.633975i	−0.0539024	−	0.0311206i
$416$	−11.8301	−	3.16987i	−0.580020	−	0.155416i
$417$	−10.7583	+	40.1506i	−0.526838	+	1.96619i
$418$	20.5526	+	11.8660i	1.00526	+	0.580386i
$419$			0.928203i			0.0453457i	0.999743	+	0.0226728i	$0.00721761\pi$
$419$			0.928203i			0.0453457i	−0.999743	+	0.0226728i	$0.992782\pi$
$420$	−8.83013	+	0.633975i	−0.430866	+	0.0309348i
$421$	8.32051	+	8.32051i	0.405517	+	0.405517i	0.880172	−	0.474655i	$-0.157427\pi$
$421$	8.32051	+	8.32051i	0.405517	+	0.405517i	−0.474655	+	0.880172i	$0.657427\pi$
$422$	7.06218	−	1.89230i	0.343781	−	0.0921160i
$423$	−1.19615	+	4.46410i	−0.0581589	+	0.217052i
$424$	4.09808	+	1.09808i	0.199020	+	0.0533273i
$425$	−3.46410	−	12.9282i	−0.168034	−	0.627110i
$426$	18.1244			0.878128
$427$	−18.1865	−	3.50000i	−0.880108	−	0.169377i
$428$	20.0526			0.969277
$429$	5.36603	+	20.0263i	0.259074	+	0.966878i
$430$	−8.19615	+	4.73205i	−0.395254	+	0.228200i
$431$	20.5359	−	11.8564i	0.989179	−	0.571103i	0.0841505	−	0.996453i	$-0.473182\pi$
$431$	20.5359	−	11.8564i	0.989179	−	0.571103i	0.905029	+	0.425350i	$0.139849\pi$
$432$	1.13397	+	4.23205i	0.0545584	+	0.203615i
$433$	−15.2487			−0.732806			−0.366403	−	0.930456i	$-0.619411\pi$
$433$	−15.2487			−0.732806			−0.366403	+	0.930456i	$0.619411\pi$
$434$	0.633975	+	1.83013i	0.0304318	+	0.0878489i
$435$	31.8564			1.52740
$436$	−2.53590	−	9.46410i	−0.121448	−	0.453248i
$437$	−39.0526	−	10.4641i	−1.86814	−	0.500566i
$438$	−2.26795	+	8.46410i	−0.108367	+	0.404430i
$439$	−4.40192	+	1.17949i	−0.210092	+	0.0562941i	−0.362330	−	0.932050i	$-0.618019\pi$
$439$	−4.40192	+	1.17949i	−0.210092	+	0.0562941i	0.152238	+	0.988344i	$0.451352\pi$
$440$	16.0981	+	16.0981i	0.767446	+	0.767446i
$441$	−5.07180	+	0.732051i	−0.241514	+	0.0348596i
$442$			16.3923i			0.779702i
$443$	−18.9282	−	10.9282i	−0.899306	−	0.519215i	−0.0223311	−	0.999751i	$-0.507109\pi$
$443$	−18.9282	−	10.9282i	−0.899306	−	0.519215i	−0.876975	+	0.480536i	$0.840442\pi$
$444$	−0.267949	+	1.00000i	−0.0127163	+	0.0474579i
$445$	11.8301	+	3.16987i	0.560802	+	0.150266i
$446$	−7.73205	−	4.46410i	−0.366123	−	0.211381i
$447$	14.1962			0.671455
$448$	−17.5000	+	6.06218i	−0.826797	+	0.286411i
$449$		−	40.8564i		−	1.92813i	−0.265661	−	0.964067i	$-0.585590\pi$
$449$		−	40.8564i		−	1.92813i	0.265661	−	0.964067i	$-0.414410\pi$
$450$	0.732051	−	1.26795i	0.0345092	−	0.0597717i
$451$	16.6244	+	22.5981i	0.782810	+	1.06410i
$452$	9.79423	+	16.9641i	0.460682	+	0.797924i
$453$	−2.36603	−	1.36603i	−0.111166	−	0.0641815i
$454$	11.2942	+	11.2942i	0.530064	+	0.530064i
$455$	6.29423	+	9.29423i	0.295078	+	0.435720i
$456$		−	31.3923i		−	1.47008i
$457$	−2.87564	−	10.7321i	−0.134517	−	0.502024i	−0.999999	−	0.00108490i	$-0.999655\pi$
$457$	−2.87564	−	10.7321i	−0.134517	−	0.502024i	0.865482	−	0.500939i	$-0.167012\pi$
$458$	0.803848	−	3.00000i	0.0375613	−	0.140181i
$459$	−25.3923	+	14.6603i	−1.18521	+	0.684282i
$460$	−11.1962	−	6.46410i	−0.522023	−	0.301390i
$461$	10.4115			0.484914			0.242457	−	0.970162i	$-0.422047\pi$
$461$	10.4115			0.484914			0.242457	+	0.970162i	$0.422047\pi$
$462$	16.9282	+	14.6603i	0.787571	+	0.682057i
$463$	−4.29423	−	4.29423i	−0.199570	−	0.199570i	0.600246	−	0.799816i	$-0.295069\pi$
$463$	−4.29423	−	4.29423i	−0.199570	−	0.199570i	−0.799816	+	0.600246i	$0.795069\pi$
$464$	9.19615	−	2.46410i	0.426921	−	0.114393i
$465$	−2.36603	−	0.633975i	−0.109722	−	0.0293999i
$466$	−5.63397	−	1.50962i	−0.260989	−	0.0699317i
$467$	3.00000	−	5.19615i	0.138823	−	0.240449i	−0.788228	−	0.615383i	$-0.789001\pi$
$467$	3.00000	−	5.19615i	0.138823	−	0.240449i	0.927052	+	0.374934i	$0.122335\pi$
$468$	1.26795	−	1.26795i	0.0586110	−	0.0586110i
$469$	6.46410	−	0.464102i	0.298484	−	0.0214302i
$470$	7.73205	−	7.73205i	0.356653	−	0.356653i
$471$	31.0526	+	17.9282i	1.43083	+	0.826088i
$472$	27.8827	−	16.0981i	1.28340	−	0.740974i
$473$	−23.1244	−	6.19615i	−1.06326	−	0.284899i
$474$	10.3301	−	17.8923i	0.474478	−	0.821821i
$475$	7.66025	−	7.66025i	0.351477	−	0.351477i
$476$	−9.92820	−	14.6603i	−0.455058	−	0.671952i
$477$	−0.732051	+	0.732051i	−0.0335183	+	0.0335183i
$478$	−1.00962	−	3.76795i	−0.0461789	−	0.172342i
$479$	7.59808	−	28.3564i	0.347165	−	1.29564i	−0.542898	−	0.839799i	$-0.682673\pi$
$479$	7.59808	−	28.3564i	0.347165	−	1.29564i	0.890063	−	0.455838i	$-0.150661\pi$
$480$	4.33013	−	16.1603i	0.197642	−	0.737611i
$481$	1.26795	−	0.339746i	0.0578135	−	0.0154911i
$482$	−18.5359			−0.844287
$483$	−34.3205	−	16.6603i	−1.56164	−	0.758068i
$484$			8.19615i			0.372552i
$485$	12.9282	−	3.46410i	0.587039	−	0.157297i
$486$	−7.19615	−	1.92820i	−0.326424	−	0.0874651i
$487$	3.50962	−	2.02628i	0.159036	−	0.0918195i	−0.418370	−	0.908277i	$-0.637398\pi$
$487$	3.50962	−	2.02628i	0.159036	−	0.0918195i	0.577406	+	0.816457i	$0.304065\pi$
$488$	10.5000	−	18.1865i	0.475313	−	0.823266i
$489$	18.8564	+	18.8564i	0.852716	+	0.852716i
$490$	11.2583	+	4.50000i	0.508600	+	0.203289i
$491$	−5.12436			−0.231259			−0.115629	−	0.993292i	$-0.536889\pi$
$491$	−5.12436			−0.231259			−0.115629	+	0.993292i	$0.536889\pi$
$492$	4.96410	−	11.3301i	0.223799	−	0.510802i
$493$	31.8564	+	55.1769i	1.43474	+	2.48504i
$494$	−11.4904	+	6.63397i	−0.516977	+	0.298477i
$495$	−5.36603	+	1.43782i	−0.241185	+	0.0646253i
$496$	−0.732051			−0.0328701
$497$	22.3301	+	10.8397i	1.00164	+	0.486229i
$498$	1.00000	−	1.00000i	0.0448111	−	0.0448111i
$499$	13.0981	−	3.50962i	0.586350	−	0.157112i	0.0465657	−	0.998915i	$-0.485172\pi$
$499$	13.0981	−	3.50962i	0.586350	−	0.157112i	0.539785	+	0.841803i	$0.318506\pi$
$500$	10.5000	−	6.06218i	0.469574	−	0.271109i
$501$	−4.56218	+	2.63397i	−0.203823	+	0.117677i
$502$	−2.36603	+	4.09808i	−0.105601	+	0.182906i
$503$	9.43782	+	9.43782i	0.420812	+	0.420812i	0.885483	−	0.464671i	$-0.153828\pi$
$503$	9.43782	+	9.43782i	0.420812	+	0.420812i	−0.464671	+	0.885483i	$0.653828\pi$
$504$	1.09808	−	5.70577i	0.0489122	−	0.254155i
$505$	−10.7321	−	10.7321i	−0.477570	−	0.477570i
$506$	8.46410	+	31.5885i	0.376275	+	1.40428i
$507$	13.0622	+	3.50000i	0.580112	+	0.155440i
$508$	−8.56218	−	14.8301i	−0.379885	−	0.657980i
$509$	0.803848	+	3.00000i	0.0356299	+	0.132973i	0.981450	−	0.191719i	$-0.0614062\pi$
$509$	0.803848	+	3.00000i	0.0356299	+	0.132973i	−0.945820	+	0.324692i	$0.894740\pi$
$510$	−22.3923			−0.991548
$511$	−7.85641	+	9.07180i	−0.347547	+	0.401313i
$512$		−	11.0000i		−	0.486136i
$513$	−20.5526	−	11.8660i	−0.907418	−	0.523898i
$514$	−13.4641	−	3.60770i	−0.593876	−	0.159129i
$515$	7.56218	+	13.0981i	0.333229	+	0.577170i
$516$	2.73205	+	10.1962i	0.120272	+	0.448861i
$517$	27.6603			1.21650
$518$	0.928203	−	1.07180i	0.0407829	−	0.0470920i
$519$	0.0980762	−	0.0980762i	0.00430507	−	0.00430507i
$520$	−12.2942	+	3.29423i	−0.539138	+	0.144461i
$521$	−9.02628	+	33.6865i	−0.395448	+	1.47583i	0.425566	+	0.904927i	$0.360075\pi$
$521$	−9.02628	+	33.6865i	−0.395448	+	1.47583i	−0.821015	+	0.570907i	$0.806592\pi$
$522$	−1.80385	+	6.73205i	−0.0789523	+	0.294654i
$523$	−17.7321	+	30.7128i	−0.775368	+	1.34298i	0.159219	+	0.987243i	$0.449102\pi$
$523$	−17.7321	+	30.7128i	−0.775368	+	1.34298i	−0.934587	+	0.355734i	$0.884231\pi$
$524$		0			0
$525$	8.46410	−	5.73205i	0.369404	−	0.250167i
$526$	−15.9282	−	15.9282i	−0.694503	−	0.694503i
$527$	−1.26795	−	4.73205i	−0.0552327	−	0.206131i
$528$	−7.33013	+	4.23205i	−0.319003	+	0.184176i
$529$	−16.3564	−	28.3301i	−0.711148	−	1.23174i
$530$	2.36603	−	0.633975i	0.102774	−	0.0275381i
$531$			7.85641i			0.340939i
$532$	6.25833	−	12.8923i	0.271333	−	0.558952i
$533$	−15.5885	+	1.73205i	−0.675211	+	0.0750234i
$534$	−6.83013	+	11.8301i	−0.295569	+	0.511940i
$535$	30.0788	−	17.3660i	1.30042	−	0.750799i
$536$	−1.90192	+	7.09808i	−0.0821506	+	0.306590i
$537$	8.33013	−	14.4282i	0.359472	−	0.622623i
$538$			11.0000i			0.474244i
$539$	12.0885	+	28.1865i	0.520687	+	1.21408i
$540$	−5.36603	−	5.36603i	−0.230917	−	0.230917i
$541$	12.1244	+	7.00000i	0.521267	+	0.300954i	0.737453	−	0.675399i	$-0.236028\pi$
$541$	12.1244	+	7.00000i	0.521267	+	0.300954i	−0.216186	+	0.976352i	$0.569362\pi$
$542$	−5.66025	+	3.26795i	−0.243129	+	0.140370i
$543$	10.5622	+	18.2942i	0.453266	+	0.785080i
$544$	32.3205	−	8.66025i	1.38573	−	0.371305i
$545$	−12.0000	−	12.0000i	−0.514024	−	0.514024i
$546$	−11.8301	+	4.09808i	−0.506283	+	0.175381i
$547$	−24.4641	+	24.4641i	−1.04601	+	1.04601i	−0.0471202	+	0.998889i	$0.515004\pi$
$547$	−24.4641	+	24.4641i	−1.04601	+	1.04601i	−0.998889	+	0.0471202i	$0.984996\pi$
$548$	2.16987	+	8.09808i	0.0926924	+	0.345933i
$549$	2.56218	+	4.43782i	0.109351	+	0.189402i
$550$	−8.46410	−	2.26795i	−0.360911	−	0.0967057i
$551$	−25.7846	+	44.6603i	−1.09846	+	1.90259i
$552$	30.5885	−	30.5885i	1.30193	−	1.30193i
$553$	23.4282	−	15.8660i	0.996269	−	0.674692i
$554$			5.58846i			0.237431i
$555$	0.464102	+	1.73205i	0.0197000	+	0.0735215i
$556$	−10.7583	−	18.6340i	−0.456255	−	0.790257i
$557$	−16.5622	−	4.43782i	−0.701762	−	0.188037i	−0.109742	−	0.993960i	$-0.535003\pi$
$557$	−16.5622	−	4.43782i	−0.701762	−	0.188037i	−0.592020	+	0.805924i	$0.701669\pi$
$558$	0.267949	−	0.464102i	0.0113432	−	0.0196470i
$559$	9.46410	−	9.46410i	0.400289	−	0.400289i
$560$	−3.00000	+	3.46410i	−0.126773	+	0.146385i
$561$	−40.0526	−	40.0526i	−1.69102	−	1.69102i
$562$	0.267949	−	0.0717968i	0.0113028	−	0.00302856i
$563$	5.16025	−	19.2583i	0.217479	−	0.811642i	−0.767800	−	0.640689i	$-0.778649\pi$
$563$	5.16025	−	19.2583i	0.217479	−	0.811642i	0.985279	−	0.170953i	$-0.0546846\pi$
$564$	−6.09808	−	10.5622i	−0.256775	−	0.444748i
$565$	29.3827	+	16.9641i	1.23614	+	0.713685i
$566$		−	3.80385i		−	0.159888i
$567$	−21.3205	−	18.4641i	−0.895377	−	0.775419i
$568$	−19.9019	+	19.9019i	−0.835066	+	0.835066i
$569$	7.39230	+	4.26795i	0.309902	+	0.178922i	0.646882	−	0.762590i	$-0.276072\pi$
$569$	7.39230	+	4.26795i	0.309902	+	0.178922i	−0.336981	+	0.941511i	$0.609406\pi$
$570$	−9.06218	−	15.6962i	−0.379573	−	0.657439i
$571$	−4.50000	+	16.7942i	−0.188319	+	0.702817i	0.805576	+	0.592492i	$0.201856\pi$
$571$	−4.50000	+	16.7942i	−0.188319	+	0.702817i	−0.993896	+	0.110325i	$0.964811\pi$
$572$	−9.29423	−	5.36603i	−0.388611	−	0.224365i
$573$	14.7321			0.615440
$574$	−12.8923	+	10.9904i	−0.538114	+	0.458730i
$575$	14.9282			0.622549
$576$	4.43782	+	2.56218i	0.184909	+	0.106757i
$577$	6.70577	−	25.0263i	0.279165	−	1.04186i	−0.673834	−	0.738883i	$-0.735354\pi$
$577$	6.70577	−	25.0263i	0.279165	−	1.04186i	0.952999	−	0.302975i	$-0.0979797\pi$
$578$	−13.8923	−	24.0622i	−0.577844	−	1.00085i
$579$	−15.2942	−	8.83013i	−0.635606	−	0.366968i
$580$	−11.6603	+	11.6603i	−0.484166	+	0.484166i
$581$	1.83013	−	0.633975i	0.0759265	−	0.0263017i
$582$			14.9282i			0.618794i
$583$	5.36603	+	3.09808i	0.222238	+	0.128309i
$584$	−6.80385	−	11.7846i	−0.281545	−	0.487651i
$585$	0.803848	−	3.00000i	0.0332350	−	0.124035i
$586$	−9.73205	+	2.60770i	−0.402027	+	0.107723i
$587$	−10.5622	−	10.5622i	−0.435948	−	0.435948i	0.454698	−	0.890646i	$-0.349747\pi$
$587$	−10.5622	−	10.5622i	−0.435948	−	0.435948i	−0.890646	+	0.454698i	$0.849747\pi$
$588$	8.09808	−	10.8301i	0.333959	−	0.446627i
$589$	2.80385	−	2.80385i	0.115531	−	0.115531i
$590$	9.29423	−	16.0981i	0.382637	−	0.662747i
$591$	−0.133975	−	0.0358984i	−0.00551098	−	0.00147666i
$592$	0.267949	+	0.464102i	0.0110126	+	0.0190745i
$593$	3.07180	+	11.4641i	0.126144	+	0.470774i	0.999878	−	0.0156293i	$-0.00497517\pi$
$593$	3.07180	+	11.4641i	0.126144	+	0.470774i	−0.873734	+	0.486404i	$0.838309\pi$
$594$			19.1962i			0.787628i
$595$	−27.5885	−	13.3923i	−1.13102	−	0.549031i
$596$	−5.19615	+	5.19615i	−0.212843	+	0.212843i
$597$	12.2942	−	21.2942i	0.503169	−	0.871515i
$598$	−17.6603	−	4.73205i	−0.722181	−	0.193508i
$599$	21.8564	+	37.8564i	0.893029	+	1.54677i	0.836226	+	0.548385i	$0.184757\pi$
$599$	21.8564	+	37.8564i	0.893029	+	1.54677i	0.0568029	+	0.998385i	$0.481909\pi$
$600$	3.00000	+	11.1962i	0.122474	+	0.457081i
$601$	7.73205	−	7.73205i	0.315397	−	0.315397i	−0.531599	−	0.846996i	$-0.678409\pi$
$601$	7.73205	−	7.73205i	0.315397	−	0.315397i	0.846996	+	0.531599i	$0.178409\pi$
$602$	2.73205	−	14.1962i	0.111350	−	0.578592i
$603$	−1.26795	−	1.26795i	−0.0516349	−	0.0516349i
$604$	1.36603	−	0.366025i	0.0555828	−	0.0148934i
$605$	7.09808	+	12.2942i	0.288578	+	0.499831i
$606$	14.6603	−	8.46410i	0.595532	−	0.343831i
$607$	15.9737	+	9.22243i	0.648353	+	0.374327i	0.787825	−	0.615899i	$-0.211207\pi$
$607$	15.9737	+	9.22243i	0.648353	+	0.374327i	−0.139472	+	0.990226i	$0.544540\pi$
$608$	19.1506	+	19.1506i	0.776661	+	0.776661i
$609$	−31.8564	+	36.7846i	−1.29089	+	1.49059i
$610$		−	12.1244i		−	0.490901i
$611$	−7.73205	+	13.3923i	−0.312805	+	0.541795i
$612$	−1.26795	+	4.73205i	−0.0512538	+	0.191282i
$613$	−5.76795	+	3.33013i	−0.232965	+	0.134503i	−0.611939	−	0.790905i	$-0.709610\pi$
$613$	−5.76795	+	3.33013i	−0.232965	+	0.134503i	0.378974	+	0.925407i	$0.376277\pi$
$614$	−11.0000	+	19.0526i	−0.443924	+	0.768899i
$615$	−2.36603	−	21.2942i	−0.0954074	−	0.858666i
$616$	−34.6865	+	2.49038i	−1.39756	+	0.100340i
$617$		−	44.3205i		−	1.78428i	−0.451763	−	0.892138i	$-0.649205\pi$
$617$		−	44.3205i		−	1.78428i	0.451763	−	0.892138i	$-0.350795\pi$
$618$	−16.2942	+	4.36603i	−0.655450	+	0.175627i
$619$	−7.22243	−	12.5096i	−0.290294	−	0.502804i	0.683585	−	0.729871i	$-0.260420\pi$
$619$	−7.22243	−	12.5096i	−0.290294	−	0.502804i	−0.973879	+	0.227067i	$0.927086\pi$
$620$	1.09808	−	0.633975i	0.0440998	−	0.0254610i
$621$	−8.46410	−	31.5885i	−0.339653	−	1.26760i
$622$	1.00000	+	1.00000i	0.0400963	+	0.0400963i
$623$	−15.4904	+	10.4904i	−0.620609	+	0.420288i
$624$		−	4.73205i		−	0.189434i
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	6.05256	−	22.5885i	0.241909	−	0.902816i
$627$	11.8660	−	44.2846i	0.473883	−	1.76856i
$628$	−17.9282	+	4.80385i	−0.715413	+	0.191694i
$629$	−2.53590	+	2.53590i	−0.101113	+	0.101113i
$630$	−1.09808	−	3.16987i	−0.0437484	−	0.126291i
$631$	0.0525589			0.00209234			0.00104617	−	0.999999i	$-0.499667\pi$
$631$	0.0525589			0.00209234			0.00104617	+	0.999999i	$0.499667\pi$
$632$	8.30385	+	30.9904i	0.330309	+	1.23273i
$633$	−7.06218	−	12.2321i	−0.280696	−	0.486180i
$634$	15.4641	+	4.14359i	0.614158	+	0.164563i
$635$	−25.6865	−	14.8301i	−1.01934	−	0.588516i
$636$		−	2.73205i		−	0.108333i
$637$	−17.0263	−	2.02628i	−0.674606	−	0.0802841i
$638$	41.7128			1.65143
$639$	−1.77757	−	6.63397i	−0.0703195	−	0.262436i
$640$	2.59808	+	4.50000i	0.102698	+	0.177878i
$641$	−34.9545	−	9.36603i	−1.38062	−	0.369936i	−0.509273	−	0.860605i	$-0.670086\pi$
$641$	−34.9545	−	9.36603i	−1.38062	−	0.369936i	−0.871346	+	0.490669i	$0.836752\pi$
$642$	10.0263	+	37.4186i	0.395706	+	1.47679i
$643$	−5.36603	−	5.36603i	−0.211615	−	0.211615i	0.593338	−	0.804953i	$-0.297810\pi$
$643$	−5.36603	−	5.36603i	−0.211615	−	0.211615i	−0.804953	+	0.593338i	$0.797810\pi$
$644$	18.6603	−	6.46410i	0.735317	−	0.254721i
$645$	12.9282	+	12.9282i	0.509048	+	0.509048i
$646$	18.1244	−	31.3923i	0.713093	−	1.23511i
$647$	−26.6147	+	15.3660i	−1.04633	+	0.604101i	−0.921621	−	0.388092i	$-0.873134\pi$
$647$	−26.6147	+	15.3660i	−1.04633	+	0.604101i	−0.124713	+	0.992193i	$0.539801\pi$
$648$	27.6962	−	15.9904i	1.08801	−	0.628161i
$649$	45.4186	−	12.1699i	1.78284	−	0.477709i
$650$	3.46410	−	3.46410i	0.135873	−	0.135873i
$651$	3.09808	−	2.09808i	0.121423	−	0.0822301i
$652$	−13.8038			−0.540600
$653$	15.3923	−	4.12436i	0.602347	−	0.161399i	0.0552572	−	0.998472i	$-0.482402\pi$
$653$	15.3923	−	4.12436i	0.602347	−	0.161399i	0.547090	+	0.837074i	$0.315735\pi$
$654$	16.3923	−	9.46410i	0.640990	−	0.370076i
$655$		0			0
$656$	−2.33013	−	5.96410i	−0.0909762	−	0.232859i
$657$	3.32051			0.129545
$658$	1.19615	+	16.6603i	0.0466309	+	0.649484i
$659$	34.4641	+	34.4641i	1.34253	+	1.34253i	0.893533	+	0.448998i	$0.148219\pi$
$659$	34.4641	+	34.4641i	1.34253	+	1.34253i	0.448998	+	0.893533i	$0.351781\pi$
$660$	7.33013	−	12.6962i	0.285325	−	0.494197i
$661$	0.232051	−	0.133975i	0.00902573	−	0.00521101i	−0.495480	−	0.868619i	$-0.665008\pi$
$661$	0.232051	−	0.133975i	0.00902573	−	0.00521101i	0.504506	+	0.863408i	$0.331675\pi$
$662$	−22.4904	−	6.02628i	−0.874113	−	0.234218i
$663$	30.5885	−	8.19615i	1.18796	−	0.318312i
$664$			2.19615i			0.0852272i
$665$	−1.77757	−	24.7583i	−0.0689311	−	0.960087i
$666$	−0.392305			−0.0152015
$667$	−68.6410	+	18.3923i	−2.65779	+	0.712153i
$668$	0.705771	−	2.63397i	0.0273071	−	0.101912i
$669$	−4.46410	+	16.6603i	−0.172592	+	0.644123i
$670$	1.09808	+	4.09808i	0.0424224	+	0.158322i
$671$	21.6865	−	21.6865i	0.837199	−	0.837199i
$672$	14.3301	+	21.1603i	0.552797	+	0.816275i
$673$	−26.6603	+	26.6603i	−1.02768	+	1.02768i	−0.0280713	+	0.999606i	$0.508937\pi$
$673$	−26.6603	+	26.6603i	−1.02768	+	1.02768i	−0.999606	+	0.0280713i	$0.991063\pi$
$674$	−5.40192	+	9.35641i	−0.208074	+	0.360395i
$675$	8.46410	+	2.26795i	0.325783	+	0.0872934i
$676$	−6.06218	+	3.50000i	−0.233161	+	0.134615i
$677$	−31.2846	−	18.0622i	−1.20237	−	0.694186i	−0.241285	−	0.970454i	$-0.577569\pi$
$677$	−31.2846	−	18.0622i	−1.20237	−	0.694186i	−0.961080	+	0.276268i	$0.910902\pi$
$678$	−26.7583	+	26.7583i	−1.02765	+	1.02765i
$679$	−8.92820	+	18.3923i	−0.342633	+	0.705832i
$680$	24.5885	−	24.5885i	0.942924	−	0.942924i
$681$	15.4282	−	26.7224i	0.591210	−	1.02401i
$682$	−3.09808	−	0.830127i	−0.118631	−	0.0317872i
$683$	28.2224	+	7.56218i	1.07990	+	0.289359i	0.754555	−	0.656236i	$-0.227853\pi$
$683$	28.2224	+	7.56218i	1.07990	+	0.289359i	0.325346	+	0.945595i	$0.394519\pi$
$684$	−3.83013	+	1.02628i	−0.146449	+	0.0392408i
$685$	10.2679	+	10.2679i	0.392318	+	0.392318i
$686$	−16.4545	+	8.50000i	−0.628235	+	0.324532i
$687$	−6.00000			−0.228914
$688$	4.73205	+	2.73205i	0.180408	+	0.104158i
$689$	−3.00000	+	1.73205i	−0.114291	+	0.0659859i
$690$	6.46410	−	24.1244i	0.246084	−	0.918399i
$691$	7.28461	+	27.1865i	0.277120	+	1.03422i	0.954408	+	0.298506i	$0.0964884\pi$
$691$	7.28461	+	27.1865i	0.277120	+	1.03422i	−0.677288	+	0.735718i	$0.736845\pi$
$692$			0.0717968i			0.00272930i
$693$	3.70577	−	7.63397i	0.140771	−	0.289991i
$694$	10.7583	+	10.7583i	0.408381	+	0.408381i
$695$	−32.2750	−	18.6340i	−1.22426	−	0.706827i
$696$	−27.5885	−	47.7846i	−1.04574	−	1.81127i
$697$	34.5167	−	25.3923i	1.30741	−	0.961802i
$698$	−1.73205	+	3.00000i	−0.0655591	+	0.113552i
$699$			11.2679i			0.426193i
$700$	−1.00000	+	5.19615i	−0.0377964	+	0.196396i
$701$	25.0526			0.946222			0.473111	−	0.881003i	$-0.343131\pi$
$701$	25.0526			0.946222			0.473111	+	0.881003i	$0.343131\pi$
$702$	−9.29423	−	5.36603i	−0.350788	−	0.202528i
$703$	−2.80385	−	0.751289i	−0.105749	−	0.0283354i
$704$	7.93782	−	29.6244i	0.299168	−	1.11651i
$705$	−18.2942	−	10.5622i	−0.689001	−	0.397795i
$706$		−	20.6603i		−	0.777559i
$707$	23.1244	−	1.66025i	0.869681	−	0.0624403i
$708$	−14.6603	−	14.6603i	−0.550966	−	0.550966i
$709$	−20.1962	+	5.41154i	−0.758482	+	0.203235i	−0.617277	−	0.786746i	$-0.711764\pi$
$709$	−20.1962	+	5.41154i	−0.758482	+	0.203235i	−0.141205	+	0.989980i	$0.545098\pi$
$710$	−4.20577	+	15.6962i	−0.157840	+	0.589066i
$711$	−7.56218	−	2.02628i	−0.283604	−	0.0759914i
$712$	−5.49038	−	20.4904i	−0.205761	−	0.767909i
$713$	5.46410			0.204632
$714$	22.3923	−	25.8564i	0.838011	−	0.967652i
$715$	−18.5885			−0.695169
$716$	2.23205	+	8.33013i	0.0834157	+	0.311311i
$717$	−6.52628	+	3.76795i	−0.243728	+	0.140717i
$718$	−10.9019	+	6.29423i	−0.406856	+	0.234899i
$719$	0.918584	+	3.42820i	0.0342574	+	0.127850i	0.980937	−	0.194326i	$-0.0622521\pi$
$719$	0.918584	+	3.42820i	0.0342574	+	0.127850i	−0.946680	+	0.322177i	$0.895585\pi$
$720$	1.26795			0.0472537
$721$	−22.6865	−	4.36603i	−0.844891	−	0.162599i
$722$	10.3397			0.384805
$723$	9.26795	+	34.5885i	0.344679	+	1.28636i
$724$	−10.5622	−	2.83013i	−0.392540	−	0.105181i
$725$	4.92820	−	18.3923i	0.183029	−	0.683073i
$726$	−15.2942	+	4.09808i	−0.567622	+	0.152094i
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	0.649283	−	0.760547i	$-0.275069\pi$
$727$	−3.00000	−	3.00000i	−0.111264	−	0.111264i	−0.760547	+	0.649283i	$0.775069\pi$
$728$	8.49038	−	17.4904i	0.314674	−	0.648237i
$729$		−	17.5885i		−	0.651424i
$730$	−6.80385	−	3.92820i	−0.251822	−	0.145389i
$731$	−9.46410	+	35.3205i	−0.350042	+	1.30638i
$732$	−13.0622	−	3.50000i	−0.482792	−	0.129364i
$733$	−28.0526	−	16.1962i	−1.03614	−	0.598219i	−0.117406	−	0.993084i	$-0.537458\pi$
$733$	−28.0526	−	16.1962i	−1.03614	−	0.598219i	−0.918739	+	0.394865i	$0.870791\pi$
$734$	−8.87564			−0.327606
$735$	2.76795	−	23.2583i	0.102097	−	0.857896i
$736$			37.3205i			1.37565i
$737$	−5.36603	+	9.29423i	−0.197660	+	0.342357i
$738$	4.63397	+	0.705771i	0.170579	+	0.0259798i
$739$	−23.0263	−	39.8827i	−0.847035	−	1.46711i	−0.883842	−	0.467786i	$-0.845052\pi$
$739$	−23.0263	−	39.8827i	−0.847035	−	1.46711i	0.0368064	−	0.999322i	$-0.488282\pi$
$740$	−0.803848	−	0.464102i	−0.0295500	−	0.0170607i
$741$	18.1244	+	18.1244i	0.665815	+	0.665815i
$742$	−1.63397	+	3.36603i	−0.0599851	+	0.123571i
$743$			15.8564i			0.581715i	0.956766	+	0.290858i	$0.0939406\pi$
$743$			15.8564i			0.581715i	−0.956766	+	0.290858i	$0.906059\pi$
$744$	1.09808	+	4.09808i	0.0402574	+	0.150243i
$745$	−3.29423	+	12.2942i	−0.120691	+	0.450426i
$746$	12.8660	−	7.42820i	0.471059	−	0.271966i
$747$	−0.464102	−	0.267949i	−0.0169806	−	0.00980375i
$748$	29.3205			1.07206
$749$	−10.0263	+	52.0981i	−0.366352	+	1.90362i
$750$	16.5622	+	16.5622i	0.604765	+	0.604765i
$751$	29.0885	−	7.79423i	1.06145	−	0.284415i	0.314476	−	0.949265i	$-0.398171\pi$
$751$	29.0885	−	7.79423i	1.06145	−	0.284415i	0.746977	+	0.664850i	$0.231505\pi$
$752$	−6.09808	−	1.63397i	−0.222374	−	0.0595849i
$753$	8.83013	+	2.36603i	0.321788	+	0.0862228i
$754$	−11.6603	+	20.1962i	−0.424641	+	0.735500i
$755$	1.73205	−	1.73205i	0.0630358	−	0.0630358i
$756$	11.5622	−	0.830127i	0.420512	−	0.0301914i
$757$	20.1962	−	20.1962i	0.734042	−	0.734042i	−0.237376	−	0.971418i	$-0.576287\pi$
$757$	20.1962	−	20.1962i	0.734042	−	0.734042i	0.971418	+	0.237376i	$0.0762874\pi$
$758$	12.6340	+	7.29423i	0.458887	+	0.264938i
$759$	54.7128	−	31.5885i	1.98595	−	1.14659i
$760$	27.1865	+	7.28461i	0.986159	+	0.264241i
$761$	12.1244	−	21.0000i	0.439508	−	0.761249i	−0.558144	−	0.829744i	$-0.688486\pi$
$761$	12.1244	−	21.0000i	0.439508	−	0.761249i	0.997651	+	0.0684947i	$0.0218196\pi$
$762$	23.3923	−	23.3923i	0.847414	−	0.847414i
$763$	25.8564	−	1.85641i	0.936065	−	0.0672064i
$764$	−5.39230	+	5.39230i	−0.195087	+	0.195087i
$765$	2.19615	+	8.19615i	0.0794021	+	0.296333i
$766$	−3.16025	+	11.7942i	−0.114185	+	0.426143i
$767$	−6.80385	+	25.3923i	−0.245673	+	0.916863i
$768$	−31.7224	+	8.50000i	−1.14468	+	0.306717i
$769$	−49.2487			−1.77595			−0.887977	−	0.459888i	$-0.847890\pi$
$769$	−49.2487			−1.77595			−0.887977	+	0.459888i	$0.847890\pi$
$770$	−16.6244	+	11.2583i	−0.599100	+	0.405722i
$771$			26.9282i			0.969796i
$772$	8.83013	−	2.36603i	0.317803	−	0.0851551i
$773$	2.63397	+	0.705771i	0.0947375	+	0.0253848i	0.305876	−	0.952071i	$-0.401051\pi$
$773$	2.63397	+	0.705771i	0.0947375	+	0.0253848i	−0.211139	+	0.977456i	$0.567717\pi$
$774$	−3.46410	+	2.00000i	−0.124515	+	0.0718885i
$775$	−0.732051	+	1.26795i	−0.0262960	+	0.0455461i
$776$	−16.3923	−	16.3923i	−0.588449	−	0.588449i
$777$	−2.46410	−	1.19615i	−0.0883992	−	0.0429117i
$778$	−20.3205			−0.728526
$779$	31.7679	+	13.9186i	1.13820	+	0.498685i
$780$	4.09808	+	7.09808i	0.146735	+	0.254152i
$781$	−35.5981	+	20.5526i	−1.27380	+	0.735428i
$782$	48.2487	−	12.9282i	1.72537	−	0.462312i
$783$	−41.7128			−1.49069
$784$	−1.00000	−	6.92820i	−0.0357143	−	0.247436i
$785$	−22.7321	+	22.7321i	−0.811342	+	0.811342i
$786$		0			0
$787$	16.7321	−	9.66025i	0.596433	−	0.344351i	−0.171204	−	0.985236i	$-0.554766\pi$
$787$	16.7321	−	9.66025i	0.596433	−	0.344351i	0.767637	+	0.640885i	$0.221432\pi$
$788$	0.0621778	−	0.0358984i	0.00221499	−	0.00127883i
$789$	−21.7583	+	37.6865i	−0.774617	+	1.34168i
$790$	13.0981	+	13.0981i	0.466009	+	0.466009i
$791$	−48.9711	+	16.9641i	−1.74121	+	0.603174i
$792$	6.80385	+	6.80385i	0.241764	+	0.241764i
$793$	4.43782	+	16.5622i	0.157592	+	0.588140i
$794$	−12.2942	−	3.29423i	−0.436306	−	0.116908i
$795$	−2.36603	−	4.09808i	−0.0839143	−	0.145344i
$796$	3.29423	+	12.2942i	0.116761	+	0.435757i
$797$	−20.7846			−0.736229			−0.368114	−	0.929781i	$-0.619996\pi$
$797$	−20.7846			−0.736229			−0.368114	+	0.929781i	$0.619996\pi$
$798$	27.1865	+	5.23205i	0.962393	+	0.185213i
$799$		−	42.2487i		−	1.49465i
$800$	−8.66025	−	5.00000i	−0.306186	−	0.176777i
$801$	5.00000	+	1.33975i	0.176666	+	0.0473376i
$802$	−6.66987	−	11.5526i	−0.235521	−	0.407935i
$803$	−5.14359	−	19.1962i	−0.181513	−	0.677418i
$804$	4.73205			0.166887
$805$	22.3923	−	25.8564i	0.789225	−	0.911319i
$806$	1.26795	−	1.26795i	0.0446616	−	0.0446616i
$807$	20.5263	−	5.50000i	0.722559	−	0.193609i
$808$	−6.80385	+	25.3923i	−0.239359	+	0.893298i
$809$	−1.07180	+	4.00000i	−0.0376824	+	0.140633i	−0.982204	−	0.187816i	$-0.939859\pi$
$809$	−1.07180	+	4.00000i	−0.0376824	+	0.140633i	0.944522	+	0.328449i	$0.106526\pi$
$810$	9.23205	−	15.9904i	0.324381	−	0.561845i
$811$		−	42.1962i		−	1.48171i	−0.671666	−	0.740854i	$-0.734421\pi$
$811$		−	42.1962i		−	1.48171i	0.671666	−	0.740854i	$-0.265579\pi$
$812$	−1.80385	−	25.1244i	−0.0633026	−	0.881692i
$813$	8.92820	+	8.92820i	0.313126	+	0.313126i
$814$	0.607695	+	2.26795i	0.0212997	+	0.0794916i
$815$	−20.7058	+	11.9545i	−0.725292	+	0.418747i
$816$	6.46410	+	11.1962i	0.226289	+	0.391944i
$817$	−28.5885	+	7.66025i	−1.00018	+	0.267998i
$818$		−	33.9808i		−	1.18811i
$819$	2.66025	+	3.92820i	0.0929568	+	0.137263i
$820$	8.66025	+	6.92820i	0.302429	+	0.241943i
$821$	18.1340	−	31.4090i	0.632880	−	1.09618i	−0.354080	−	0.935215i	$-0.615206\pi$
$821$	18.1340	−	31.4090i	0.632880	−	1.09618i	0.986960	−	0.160965i	$-0.0514607\pi$
$822$	−14.0263	+	8.09808i	−0.489223	+	0.282453i
$823$	−10.3827	+	38.7487i	−0.361918	+	1.35070i	0.509634	+	0.860391i	$0.329781\pi$
$823$	−10.3827	+	38.7487i	−0.361918	+	1.35070i	−0.871552	+	0.490304i	$0.836886\pi$
$824$	13.0981	−	22.6865i	0.456293	−	0.790323i
$825$			16.9282i			0.589364i
$826$	9.29423	+	26.8301i	0.323388	+	0.933540i
$827$	−13.0526	−	13.0526i	−0.453882	−	0.453882i	0.442759	−	0.896641i	$-0.354000\pi$
$827$	−13.0526	−	13.0526i	−0.453882	−	0.453882i	−0.896641	+	0.442759i	$0.854000\pi$
$828$	−4.73205	−	2.73205i	−0.164450	−	0.0949453i
$829$	28.1769	−	16.2679i	0.978625	−	0.565009i	0.0767701	−	0.997049i	$-0.475539\pi$
$829$	28.1769	−	16.2679i	0.978625	−	0.565009i	0.901855	+	0.432040i	$0.142206\pi$
$830$	0.633975	+	1.09808i	0.0220056	+	0.0381148i
$831$	10.4282	−	2.79423i	0.361750	−	0.0969307i
$832$	12.1244	+	12.1244i	0.420336	+	0.420336i
$833$	43.0526	−	18.4641i	1.49168	−	0.639743i
$834$	29.3923	−	29.3923i	1.01777	−	1.01777i
$835$	−1.22243	−	4.56218i	−0.0423040	−	0.157881i
$836$	11.8660	+	20.5526i	0.410395	+	0.710825i
$837$	3.09808	+	0.830127i	0.107085	+	0.0286934i
$838$	0.464102	−	0.803848i	0.0160321	−	0.0277685i
$839$	−34.0070	+	34.0070i	−1.17405	+	1.17405i	−0.192819	+	0.981234i	$0.561763\pi$
$839$	−34.0070	+	34.0070i	−1.17405	+	1.17405i	−0.981234	+	0.192819i	$0.938237\pi$
$840$	23.8923	+	11.5981i	0.824363	+	0.400172i
$841$			61.6410i			2.12555i
$842$	−3.04552	−	11.3660i	−0.104955	−	0.391699i
$843$	−0.267949	−	0.464102i	−0.00922866	−	0.0159845i
$844$	7.06218	+	1.89230i	0.243090	+	0.0651358i
$845$	−6.06218	+	10.5000i	−0.208545	+	0.361211i
$846$	3.26795	−	3.26795i	0.112354	−	0.112354i
$847$	−21.2942	−	4.09808i	−0.731678	−	0.140812i
$848$	−1.00000	−	1.00000i	−0.0343401	−	0.0343401i
$849$	−7.09808	+	1.90192i	−0.243605	+	0.0652739i
$850$	−3.46410	+	12.9282i	−0.118818	+	0.443434i
$851$	−2.00000	−	3.46410i	−0.0685591	−	0.118748i
$852$	15.6962	+	9.06218i	0.537741	+	0.310465i
$853$		−	4.75129i		−	0.162681i	−0.996686	−	0.0813405i	$-0.974080\pi$
$853$		−	4.75129i		−	0.162681i	0.996686	−	0.0813405i	$-0.0259201\pi$
$854$	14.0000	+	12.1244i	0.479070	+	0.414887i
$855$	−4.85641	+	4.85641i	−0.166086	+	0.166086i
$856$	−52.0981	−	30.0788i	−1.78068	−	1.02807i
$857$	24.1147	+	41.7679i	0.823744	+	1.42677i	0.902876	+	0.429902i	$0.141452\pi$
$857$	24.1147	+	41.7679i	0.823744	+	1.42677i	−0.0791319	+	0.996864i	$0.525215\pi$
$858$	5.36603	−	20.0263i	0.183193	−	0.683686i
$859$	11.9545	+	6.90192i	0.407882	+	0.235491i	0.689879	−	0.723925i	$-0.257664\pi$
$859$	11.9545	+	6.90192i	0.407882	+	0.235491i	−0.281997	+	0.959415i	$0.590997\pi$
$860$	−9.46410			−0.322723
$861$	26.9545	+	18.5622i	0.918606	+	0.632597i
$862$	−23.7128			−0.807662
$863$	−7.68653	−	4.43782i	−0.261653	−	0.151065i	0.363436	−	0.931619i	$-0.381604\pi$
$863$	−7.68653	−	4.43782i	−0.261653	−	0.151065i	−0.625088	+	0.780554i	$0.714937\pi$
$864$	−5.66987	+	21.1603i	−0.192893	+	0.719886i
$865$	0.0621778	+	0.107695i	0.00211411	+	0.00366175i
$866$	13.2058	+	7.62436i	0.448750	+	0.259086i
$867$	−37.9545	+	37.9545i	−1.28900	+	1.28900i
$868$	−0.366025	+	1.90192i	−0.0124237	+	0.0645555i
$869$			46.8564i			1.58949i
$870$	−27.5885	−	15.9282i	−0.935336	−	0.540017i
$871$	−3.00000	−	5.19615i	−0.101651	−	0.176065i
$872$	−7.60770	+	28.3923i	−0.257629	+	0.961485i
$873$	5.46410	−	1.46410i	0.184932	−	0.0495523i
$874$	28.5885	+	28.5885i	0.967019	+	0.967019i
$875$	10.5000	+	30.3109i	0.354965	+	1.02470i
$876$	−6.19615	+	6.19615i	−0.209349	+	0.209349i
$877$	−2.42820	+	4.20577i	−0.0819946	+	0.142019i	−0.904107	−	0.427307i	$-0.859462\pi$
$877$	−2.42820	+	4.20577i	−0.0819946	+	0.142019i	0.822112	+	0.569326i	$0.192796\pi$
$878$	4.40192	+	1.17949i	0.148558	+	0.0398059i
$879$	9.73205	+	16.8564i	0.328254	+	0.568552i
$880$	−1.96410	−	7.33013i	−0.0662099	−	0.247099i
$881$			35.9282i			1.21045i	0.796054	+	0.605226i	$0.206917\pi$
$881$			35.9282i			1.21045i	−0.796054	+	0.605226i	$0.793083\pi$
$882$	4.75833	+	1.90192i	0.160221	+	0.0640411i
$883$	−3.53590	+	3.53590i	−0.118992	+	0.118992i	−0.764096	−	0.645103i	$-0.776814\pi$
$883$	−3.53590	+	3.53590i	−0.118992	+	0.118992i	0.645103	+	0.764096i	$0.276814\pi$
$884$	−8.19615	+	14.1962i	−0.275666	+	0.477468i
$885$	−34.6865	−	9.29423i	−1.16598	−	0.312422i
$886$	10.9282	+	18.9282i	0.367140	+	0.635905i
$887$	2.79423	+	10.4282i	0.0938210	+	0.350145i	0.996838	−	0.0794599i	$-0.0253196\pi$
$887$	2.79423	+	10.4282i	0.0938210	+	0.350145i	−0.903017	+	0.429605i	$0.858653\pi$
$888$	2.19615	−	2.19615i	0.0736980	−	0.0736980i
$889$	42.8109	−	14.8301i	1.43583	−	0.497386i
$890$	−8.66025	−	8.66025i	−0.290292	−	0.290292i
$891$	45.1147	−	12.0885i	1.51140	−	0.404979i
$892$	−4.46410	−	7.73205i	−0.149469	−	0.258888i
$893$	29.6147	−	17.0981i	0.991019	−	0.572165i
$894$	−12.2942	−	7.09808i	−0.411181	−	0.237395i
$895$	10.5622	+	10.5622i	0.353055	+	0.353055i
$896$	−7.79423	−	1.50000i	−0.260387	−	0.0501115i
$897$			35.3205i			1.17932i
$898$	−20.4282	+	35.3827i	−0.681698	+	1.18074i
$899$	1.80385	−	6.73205i	0.0601617	−	0.224526i
$900$	1.26795	−	0.732051i	0.0422650	−	0.0244017i
$901$	4.73205	−	8.19615i	0.157647	−	0.273053i
$902$	−3.09808	−	27.8827i	−0.103155	−	0.928392i
$903$	−27.8564	+	2.00000i	−0.927003	+	0.0665558i
$904$		−	58.7654i		−	1.95451i
$905$	−18.2942	+	4.90192i	−0.608121	+	0.162945i
$906$	1.36603	+	2.36603i	0.0453832	+	0.0786059i
$907$	13.2224	−	7.63397i	0.439044	−	0.253482i	−0.264148	−	0.964482i	$-0.585091\pi$
$907$	13.2224	−	7.63397i	0.439044	−	0.253482i	0.703192	+	0.711000i	$0.251757\pi$
$908$	4.13397	+	15.4282i	0.137191	+	0.512003i
$909$	−4.53590	−	4.53590i	−0.150446	−	0.150446i
$910$	−0.803848	−	11.1962i	−0.0266473	−	0.371149i
$911$		−	7.85641i		−	0.260294i	−0.991495	−	0.130147i	$-0.958455\pi$
$911$		−	7.85641i		−	0.260294i	0.991495	−	0.130147i	$-0.0415450\pi$
$912$	−5.23205	+	9.06218i	−0.173251	+	0.300079i
$913$	−0.830127	+	3.09808i	−0.0274732	+	0.102531i
$914$	−2.87564	+	10.7321i	−0.0951179	+	0.354985i
$915$	−22.6244	+	6.06218i	−0.747938	+	0.200409i
$916$	2.19615	−	2.19615i	0.0725629	−	0.0725629i
$917$		0			0
$918$	29.3205			0.967721
$919$	−5.47372	−	20.4282i	−0.180561	−	0.673864i	−0.995537	−	0.0943694i	$-0.969917\pi$
$919$	−5.47372	−	20.4282i	−0.180561	−	0.673864i	0.814976	−	0.579495i	$-0.196750\pi$
$920$	19.3923	+	33.5885i	0.639345	+	1.10738i
$921$	41.0526	+	11.0000i	1.35273	+	0.362462i
$922$	−9.01666	−	5.20577i	−0.296948	−	0.171443i
$923$		−	22.9808i		−	0.756421i
$924$	7.33013	+	21.1603i	0.241143	+	0.696121i
$925$	1.07180			0.0352405
$926$	1.57180	+	5.86603i	0.0516524	+	0.192770i
$927$	3.19615	+	5.53590i	0.104975	+	0.181823i
$928$	45.9808	+	12.3205i	1.50939	+	0.404440i
$929$	−0.150635	−	0.562178i	−0.00494218	−	0.0184445i	0.963411	−	0.268029i	$-0.0863725\pi$
$929$	−0.150635	−	0.562178i	−0.00494218	−	0.0184445i	−0.968353	+	0.249585i	$0.919706\pi$
$930$	1.73205	+	1.73205i	0.0567962	+	0.0567962i
$931$	30.3660	+	22.7058i	0.995206	+	0.744152i
$932$	−4.12436	−	4.12436i	−0.135098	−	0.135098i
$933$	1.36603	−	2.36603i	0.0447217	−	0.0774602i
$934$	−5.19615	+	3.00000i	−0.170023	+	0.0981630i
$935$	43.9808	−	25.3923i	1.43832	−	0.830417i
$936$	−5.19615	+	1.39230i	−0.169842	+	0.0455089i
$937$	23.4641	−	23.4641i	0.766539	−	0.766539i	−0.210957	−	0.977495i	$-0.567658\pi$
$937$	23.4641	−	23.4641i	0.766539	−	0.766539i	0.977495	+	0.210957i	$0.0676579\pi$
$938$	−5.83013	−	2.83013i	−0.190360	−	0.0924069i
$939$	−45.1769			−1.47429
$940$	10.5622	−	2.83013i	0.344500	−	0.0923086i
$941$	15.9904	−	9.23205i	0.521272	−	0.300956i	−0.216183	−	0.976353i	$-0.569361\pi$
$941$	15.9904	−	9.23205i	0.521272	−	0.300956i	0.737455	+	0.675397i	$0.236028\pi$
$942$	−17.9282	−	31.0526i	−0.584132	−	1.01175i
$943$	17.3923	+	44.5167i	0.566371	+	1.44966i
$944$	−10.7321			−0.349299
$945$	16.6244	−	11.2583i	0.540790	−	0.366234i
$946$	16.9282	+	16.9282i	0.550383	+	0.550383i
$947$	−18.6603	+	32.3205i	−0.606377	+	1.05028i	0.385455	+	0.922726i	$0.374044\pi$
$947$	−18.6603	+	32.3205i	−0.606377	+	1.05028i	−0.991832	+	0.127549i	$0.959289\pi$
$948$	17.8923	−	10.3301i	0.581115	−	0.335507i
$949$	10.7321	+	2.87564i	0.348377	+	0.0933474i
$950$	−10.4641	+	2.80385i	−0.339500	+	0.0909688i
$951$		−	30.9282i		−	1.00292i
$952$	3.80385	+	52.9808i	0.123283	+	1.71712i
$953$	−2.28719			−0.0740893			−0.0370446	−	0.999314i	$-0.511794\pi$
$953$	−2.28719			−0.0740893			−0.0370446	+	0.999314i	$0.511794\pi$
$954$	1.00000	−	0.267949i	0.0323762	−	0.00867518i
$955$	−3.41858	+	12.7583i	−0.110623	+	0.412850i
$956$	1.00962	−	3.76795i	0.0326534	−	0.121864i
$957$	−20.8564	−	77.8372i	−0.674192	−	2.51612i
$958$	−20.7583	+	20.7583i	−0.670671	+	0.670671i
$959$	−22.1244	+	1.58846i	−0.714433	+	0.0512940i
$960$	−16.5622	+	16.5622i	−0.534542	+	0.534542i
$961$	15.2321	−	26.3827i	0.491356	−	0.851054i
$962$	−1.26795	−	0.339746i	−0.0408803	−	0.0109538i
$963$	12.7128	−	7.33975i	0.409665	−	0.236520i
$964$	−16.0526	−	9.26795i	−0.517018	−	0.298501i
$965$	11.1962	−	11.1962i	0.360417	−	0.360417i
$966$	21.3923	+	31.5885i	0.688286	+	1.01634i
$967$	23.1506	−	23.1506i	0.744474	−	0.744474i	−0.228961	−	0.973436i	$-0.573533\pi$
$967$	23.1506	−	23.1506i	0.744474	−	0.744474i	0.973436	+	0.228961i	$0.0735329\pi$
$968$	12.2942	−	21.2942i	0.395151	−	0.684422i
$969$	−67.6410	−	18.1244i	−2.17294	−	0.582238i
$970$	−12.9282	−	3.46410i	−0.415100	−	0.111226i
$971$	−8.29423	+	2.22243i	−0.266174	+	0.0713212i	−0.389438	−	0.921053i	$-0.627331\pi$
$971$	−8.29423	+	2.22243i	−0.266174	+	0.0713212i	0.123263	+	0.992374i	$0.460664\pi$
$972$	−5.26795	−	5.26795i	−0.168970	−	0.168970i
$973$	53.7917	−	18.6340i	1.72448	−	0.597378i
$974$	−4.05256			−0.129852
$975$	−8.19615	−	4.73205i	−0.262487	−	0.151547i
$976$	−6.06218	+	3.50000i	−0.194046	+	0.112032i
$977$	4.58142	−	17.0981i	0.146572	−	0.547016i	−0.853108	−	0.521735i	$-0.825285\pi$
$977$	4.58142	−	17.0981i	0.146572	−	0.547016i	0.999680	−	0.0252814i	$-0.00804818\pi$
$978$	−6.90192	−	25.7583i	−0.220699	−	0.823661i
$979$		−	30.9808i		−	0.990149i
$980$	7.50000	+	9.52628i	0.239579	+	0.304306i
$981$	−5.07180	−	5.07180i	−0.161930	−	0.161930i
$982$	4.43782	+	2.56218i	0.141617	+	0.0817624i
$983$	−1.19615	−	2.07180i	−0.0381513	−	0.0660801i	0.846319	−	0.532676i	$-0.178814\pi$
$983$	−1.19615	−	2.07180i	−0.0381513	−	0.0660801i	−0.884471	+	0.466596i	$0.845480\pi$
$984$	−29.8923	+	21.9904i	−0.952932	+	0.701028i
$985$	0.0621778	−	0.107695i	0.00198115	−	0.00343145i
$986$		−	63.7128i		−	2.02903i
$987$	30.4904	−	10.5622i	0.970520	−	0.336198i
$988$	−13.2679			−0.422110
$989$	−35.3205	−	20.3923i	−1.12313	−	0.648438i
$990$	5.36603	+	1.43782i	0.170543	+	0.0456970i
$991$	−10.2058	+	38.0885i	−0.324197	+	1.20992i	0.590920	+	0.806730i	$0.298765\pi$
$991$	−10.2058	+	38.0885i	−0.324197	+	1.20992i	−0.915117	+	0.403189i	$0.867902\pi$
$992$	−3.16987	−	1.83013i	−0.100644	−	0.0581066i
$993$			44.9808i			1.42742i
$994$	−13.9186	−	20.5526i	−0.441471	−	0.651888i
$995$	15.5885	+	15.5885i	0.494187	+	0.494187i
$996$	1.36603	−	0.366025i	0.0432842	−	0.0115980i
$997$	−0.882686	+	3.29423i	−0.0279549	+	0.104329i	−0.978494	−	0.206277i	$-0.933865\pi$
$997$	−0.882686	+	3.29423i	−0.0279549	+	0.104329i	0.950539	+	0.310606i	$0.100532\pi$
$998$	−13.0981	−	3.50962i	−0.414612	−	0.111095i
$999$	−0.607695	−	2.26795i	−0.0192266	−	0.0717547i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.r.a.9.1	✓	4
7.4	even	3		287.2.r.b.214.1	yes	4
41.32	even	4		287.2.r.b.114.1	yes	4
287.32	even	12	inner	287.2.r.a.32.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.r.a.9.1	✓	4	1.1	even	1	trivial
287.2.r.a.32.1	yes	4	287.32	even	12	inner
287.2.r.b.114.1	yes	4	41.32	even	4
287.2.r.b.214.1	yes	4	7.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.36603 - 1.36603i) q^{6} +(2.50000 - 0.866025i) q^{7} +3.00000i q^{8} +(-0.633975 - 0.366025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.500000 + 1.86603i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 - 0.866025i) q^{5} +(1.36603 - 1.36603i) q^{6} +(2.50000 - 0.866025i) q^{7} +3.00000i q^{8} +(-0.633975 - 0.366025i) q^{9} +(0.866025 + 1.50000i) q^{10} +(-1.13397 + 4.23205i) q^{11} +(1.86603 - 0.500000i) q^{12} +(-1.73205 - 1.73205i) q^{13} +(-2.59808 - 0.500000i) q^{14} +(2.36603 - 2.36603i) q^{15} +(0.500000 - 0.866025i) q^{16} +(6.46410 + 1.73205i) q^{17} +(0.366025 + 0.633975i) q^{18} +(1.40192 + 5.23205i) q^{19} +1.73205i q^{20} +(0.366025 + 5.09808i) q^{21} +(3.09808 - 3.09808i) q^{22} +(-3.73205 + 6.46410i) q^{23} +(-5.59808 - 1.50000i) q^{24} +(-1.00000 - 1.73205i) q^{25} +(0.633975 + 2.36603i) q^{26} +(-3.09808 + 3.09808i) q^{27} +(-2.00000 - 1.73205i) q^{28} +(6.73205 + 6.73205i) q^{29} +(-3.23205 + 0.866025i) q^{30} +(-0.366025 - 0.633975i) q^{31} +(4.33013 - 2.50000i) q^{32} +(-7.33013 - 4.23205i) q^{33} +(-4.73205 - 4.73205i) q^{34} +(-4.50000 - 0.866025i) q^{35} +0.732051i q^{36} +(-0.267949 + 0.464102i) q^{37} +(1.40192 - 5.23205i) q^{38} +(4.09808 - 2.36603i) q^{39} +(2.59808 - 4.50000i) q^{40} +(4.00000 - 5.00000i) q^{41} +(2.23205 - 4.59808i) q^{42} +5.46410i q^{43} +(4.23205 - 1.13397i) q^{44} +(0.633975 + 1.09808i) q^{45} +(6.46410 - 3.73205i) q^{46} +(-1.63397 - 6.09808i) q^{47} +(1.36603 + 1.36603i) q^{48} +(5.50000 - 4.33013i) q^{49} +2.00000i q^{50} +(-6.46410 + 11.1962i) q^{51} +(-0.633975 + 2.36603i) q^{52} +(0.366025 - 1.36603i) q^{53} +(4.23205 - 1.13397i) q^{54} +(5.36603 - 5.36603i) q^{55} +(2.59808 + 7.50000i) q^{56} -10.4641 q^{57} +(-2.46410 - 9.19615i) q^{58} +(-5.36603 - 9.29423i) q^{59} +(-3.23205 - 0.866025i) q^{60} +(-6.06218 - 3.50000i) q^{61} +0.732051i q^{62} +(-1.90192 - 0.366025i) q^{63} -7.00000 q^{64} +(1.09808 + 4.09808i) q^{65} +(4.23205 + 7.33013i) q^{66} +(2.36603 + 0.633975i) q^{67} +(-1.73205 - 6.46410i) q^{68} +(-10.1962 - 10.1962i) q^{69} +(3.46410 + 3.00000i) q^{70} +(6.63397 + 6.63397i) q^{71} +(1.09808 - 1.90192i) q^{72} +(-3.92820 + 2.26795i) q^{73} +(0.464102 - 0.267949i) q^{74} +(3.73205 - 1.00000i) q^{75} +(3.83013 - 3.83013i) q^{76} +(0.830127 + 11.5622i) q^{77} -4.73205 q^{78} +(10.3301 - 2.76795i) q^{79} +(-1.50000 + 0.866025i) q^{80} +(-5.33013 - 9.23205i) q^{81} +(-5.96410 + 2.33013i) q^{82} +0.732051 q^{83} +(4.23205 - 2.86603i) q^{84} +(-8.19615 - 8.19615i) q^{85} +(2.73205 - 4.73205i) q^{86} +(-15.9282 + 9.19615i) q^{87} +(-12.6962 - 3.40192i) q^{88} +(-6.83013 + 1.83013i) q^{89} -1.26795i q^{90} +(-5.83013 - 2.83013i) q^{91} +7.46410 q^{92} +(1.36603 - 0.366025i) q^{93} +(-1.63397 + 6.09808i) q^{94} +(2.42820 - 9.06218i) q^{95} +(2.50000 + 9.33013i) q^{96} +(-5.46410 + 5.46410i) q^{97} +(-6.92820 + 1.00000i) q^{98} +(2.26795 - 2.26795i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9}+O(q^{10}) \) 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9	\( 4 q - 2 q^{3} - 2 q^{4} - 6 q^{5} + 2 q^{6} + 10 q^{7} - 6 q^{9} - 8 q^{11} + 4 q^{12} + 6 q^{15} + 2 q^{16} + 12 q^{17} - 2 q^{18} + 16 q^{19} - 2 q^{21} + 2 q^{22} - 8 q^{23} - 12 q^{24} - 4 q^{25} + 6 q^{26} - 2 q^{27} - 8 q^{28} + 20 q^{29} - 6 q^{30} + 2 q^{31} - 12 q^{33} - 12 q^{34} - 18 q^{35} - 8 q^{37} + 16 q^{38} + 6 q^{39} + 16 q^{41} + 2 q^{42} + 10 q^{44} + 6 q^{45} + 12 q^{46} - 10 q^{47} + 2 q^{48} + 22 q^{49} - 12 q^{51} - 6 q^{52} - 2 q^{53} + 10 q^{54} + 18 q^{55} - 28 q^{57} + 4 q^{58} - 18 q^{59} - 6 q^{60} - 18 q^{63} - 28 q^{64} - 6 q^{65} + 10 q^{66} + 6 q^{67} - 20 q^{69} + 30 q^{71} - 6 q^{72} + 12 q^{73} - 12 q^{74} + 8 q^{75} - 2 q^{76} - 14 q^{77} - 12 q^{78} + 24 q^{79} - 6 q^{80} - 4 q^{81} - 10 q^{82} - 4 q^{83} + 10 q^{84} - 12 q^{85} + 4 q^{86} - 36 q^{87} - 30 q^{88} - 10 q^{89} - 6 q^{91} + 16 q^{92} + 2 q^{93} - 10 q^{94} - 18 q^{95} + 10 q^{96} - 8 q^{97} + 16 q^{99}+O(q^{100}) \) 4 * q - 2 * q^3 - 2 * q^4 - 6 * q^5 + 2 * q^6 + 10 * q^7 - 6 * q^9 - 8 * q^11 + 4 * q^12 + 6 * q^15 + 2 * q^16 + 12 * q^17 - 2 * q^18 + 16 * q^19 - 2 * q^21 + 2 * q^22 - 8 * q^23 - 12 * q^24 - 4 * q^25 + 6 * q^26 - 2 * q^27 - 8 * q^28 + 20 * q^29 - 6 * q^30 + 2 * q^31 - 12 * q^33 - 12 * q^34 - 18 * q^35 - 8 * q^37 + 16 * q^38 + 6 * q^39 + 16 * q^41 + 2 * q^42 + 10 * q^44 + 6 * q^45 + 12 * q^46 - 10 * q^47 + 2 * q^48 + 22 * q^49 - 12 * q^51 - 6 * q^52 - 2 * q^53 + 10 * q^54 + 18 * q^55 - 28 * q^57 + 4 * q^58 - 18 * q^59 - 6 * q^60 - 18 * q^63 - 28 * q^64 - 6 * q^65 + 10 * q^66 + 6 * q^67 - 20 * q^69 + 30 * q^71 - 6 * q^72 + 12 * q^73 - 12 * q^74 + 8 * q^75 - 2 * q^76 - 14 * q^77 - 12 * q^78 + 24 * q^79 - 6 * q^80 - 4 * q^81 - 10 * q^82 - 4 * q^83 + 10 * q^84 - 12 * q^85 + 4 * q^86 - 36 * q^87 - 30 * q^88 - 10 * q^89 - 6 * q^91 + 16 * q^92 + 2 * q^93 - 10 * q^94 - 18 * q^95 + 10 * q^96 - 8 * q^97 + 16 * q^99

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