LMFDB - Embedded newform 630.2.j.b.211.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [630,2,Mod(211,630)] 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("630.211"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(630, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	630.j (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [2,1,-3,-1,1,-3,-1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$5.03057532734$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	630.211
Dual form			630.2.j.b.421.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} -1.73205i q^{12} +(2.00000 - 3.46410i) q^{13} +(0.500000 - 0.866025i) q^{14} +1.73205i q^{15} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{17} +3.00000 q^{18} -7.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(5.00000 - 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.50000 + 2.59808i) q^{33} +(1.50000 + 2.59808i) q^{34} -1.00000 q^{35} +(1.50000 + 2.59808i) q^{36} +8.00000 q^{37} +(-3.50000 - 6.06218i) q^{38} +6.92820i q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.50000 + 7.79423i) q^{41} +1.73205i q^{42} +(0.500000 + 0.866025i) q^{43} +3.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +6.00000 q^{46} +(-6.00000 - 10.3923i) q^{47} +(1.50000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-4.50000 + 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +6.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} -3.00000 q^{55} +(0.500000 + 0.866025i) q^{56} +(10.5000 - 6.06218i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(-1.50000 - 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +10.0000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +5.19615i q^{66} +(3.50000 - 6.06218i) q^{67} +(-1.50000 + 2.59808i) q^{68} +10.3923i q^{69} +(-0.500000 - 0.866025i) q^{70} +6.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} -7.00000 q^{73} +(4.00000 + 6.92820i) q^{74} +(1.50000 + 0.866025i) q^{75} +(3.50000 - 6.06218i) q^{76} +(-1.50000 + 2.59808i) q^{77} +(-6.00000 + 3.46410i) q^{78} +(-1.00000 - 1.73205i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-1.50000 + 0.866025i) q^{84} +(1.50000 - 2.59808i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-9.00000 - 5.19615i) q^{87} +(1.50000 + 2.59808i) q^{88} +6.00000 q^{89} +(1.50000 - 2.59808i) q^{90} -4.00000 q^{91} +(3.00000 + 5.19615i) q^{92} +17.3205i q^{93} +(6.00000 - 10.3923i) q^{94} +(-3.50000 + 6.06218i) q^{95} +1.73205i q^{96} +(-5.50000 - 9.52628i) q^{97} -1.00000 q^{98} -9.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{10} - 3 q^{11} + 4 q^{13} + q^{14} - q^{16} + 6 q^{17} + 6 q^{18} - 14 q^{19} + q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) $ 2 * q + q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 - 2 * q^8 + 3 * q^9 + 2 * q^10 - 3 * q^11 + 4 * q^13 + q^14 - q^16 + 6 * q^17 + 6 * q^18 - 14 * q^19 + q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^24 - q^25 + 8 * q^26 + 2 * q^28 + 6 * q^29 - 3 * q^30 + 10 * q^31 + q^32 + 9 * q^33 + 3 * q^34 - 2 * q^35 + 3 * q^36 + 16 * q^37 - 7 * q^38 - q^40 - 9 * q^41 + q^43 + 6 * q^44 - 3 * q^45 + 12 * q^46 - 12 * q^47 + 3 * q^48 - q^49 + q^50 - 9 * q^51 + 4 * q^52 + 12 * q^53 - 9 * q^54 - 6 * q^55 + q^56 + 21 * q^57 - 6 * q^58 - 9 * q^59 - 3 * q^60 - 14 * q^61 + 20 * q^62 - 6 * q^63 + 2 * q^64 - 4 * q^65 + 7 * q^67 - 3 * q^68 - q^70 + 12 * q^71 - 3 * q^72 - 14 * q^73 + 8 * q^74 + 3 * q^75 + 7 * q^76 - 3 * q^77 - 12 * q^78 - 2 * q^79 - 2 * q^80 - 9 * q^81 - 18 * q^82 + 12 * q^83 - 3 * q^84 + 3 * q^85 - q^86 - 18 * q^87 + 3 * q^88 + 12 * q^89 + 3 * q^90 - 8 * q^91 + 6 * q^92 + 12 * q^94 - 7 * q^95 - 11 * q^97 - 2 * q^98 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/630\mathbb{Z}\right)^\times$.

$n$	$127$	$281$	$451$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−1.50000	−	0.866025i	−0.612372	−	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i
$8$	−1.00000			−0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	1.00000			0.316228
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$		−	1.73205i		−	0.500000i
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	2.00000	−	3.46410i	0.554700	−	0.960769i	0.997927	−	0.0643593i	$-0.0205004\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$			1.73205i			0.447214i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.00000			0.727607			0.363803	−	0.931476i	$-0.381478\pi$
$17$	3.00000			0.727607			0.363803	+	0.931476i	$0.381478\pi$
$18$	3.00000			0.707107
$19$	−7.00000			−1.60591			−0.802955	−	0.596040i	$-0.796740\pi$
$19$	−7.00000			−1.60591			−0.802955	+	0.596040i	$0.796740\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.50000	+	0.866025i	0.327327	+	0.188982i
$22$	1.50000	−	2.59808i	0.319801	−	0.553912i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	1.50000	−	0.866025i	0.306186	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	4.00000			0.784465
$27$			5.19615i			1.00000i
$28$	1.00000			0.188982
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	0.997738	+	0.0672232i	$0.0214140\pi$
$29$	3.00000	+	5.19615i	0.557086	+	0.964901i	−0.440652	+	0.897678i	$0.645253\pi$
$30$	−1.50000	+	0.866025i	−0.273861	+	0.158114i
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.830014	−	0.557743i	$-0.188333\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	4.50000	+	2.59808i	0.783349	+	0.452267i
$34$	1.50000	+	2.59808i	0.257248	+	0.445566i
$35$	−1.00000			−0.169031
$36$	1.50000	+	2.59808i	0.250000	+	0.433013i
$37$	8.00000			1.31519			0.657596	−	0.753371i	$-0.271573\pi$
$37$	8.00000			1.31519			0.657596	+	0.753371i	$0.271573\pi$
$38$	−3.50000	−	6.06218i	−0.567775	−	0.983415i
$39$			6.92820i			1.10940i
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	0.264704	+	0.964330i	$0.414726\pi$
$41$	−4.50000	+	7.79423i	−0.702782	+	1.21725i	−0.967486	+	0.252924i	$0.918608\pi$
$42$			1.73205i			0.267261i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	3.00000			0.452267
$45$	−1.50000	−	2.59808i	−0.223607	−	0.387298i
$46$	6.00000			0.884652
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.856560	−	0.516047i	$-0.827403\pi$
$47$	−6.00000	−	10.3923i	−0.875190	−	1.51587i	−0.0186297	−	0.999826i	$-0.505930\pi$
$48$	1.50000	+	0.866025i	0.216506	+	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−4.50000	+	2.59808i	−0.630126	+	0.363803i
$52$	2.00000	+	3.46410i	0.277350	+	0.480384i
$53$	6.00000			0.824163			0.412082	−	0.911147i	$-0.364802\pi$
$53$	6.00000			0.824163			0.412082	+	0.911147i	$0.364802\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	−3.00000			−0.404520
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	10.5000	−	6.06218i	1.39076	−	0.802955i
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	0.408919	+	0.912571i	$0.365906\pi$
$59$	−4.50000	+	7.79423i	−0.585850	+	1.01472i	−0.994769	+	0.102151i	$0.967427\pi$
$60$	−1.50000	−	0.866025i	−0.193649	−	0.111803i
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	−7.00000	−	12.1244i	−0.896258	−	1.55236i	−0.0640184	−	0.997949i	$-0.520392\pi$
$62$	10.0000			1.27000
$63$	−3.00000			−0.377964
$64$	1.00000			0.125000
$65$	−2.00000	−	3.46410i	−0.248069	−	0.429669i
$66$			5.19615i			0.639602i
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	−0.569066	−	0.822292i	$-0.692695\pi$
$67$	3.50000	−	6.06218i	0.427593	−	0.740613i	0.996659	+	0.0816792i	$0.0260283\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$			10.3923i			1.25109i
$70$	−0.500000	−	0.866025i	−0.0597614	−	0.103510i
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$	−1.50000	+	2.59808i	−0.176777	+	0.306186i
$73$	−7.00000			−0.819288			−0.409644	−	0.912245i	$-0.634347\pi$
$73$	−7.00000			−0.819288			−0.409644	+	0.912245i	$0.634347\pi$
$74$	4.00000	+	6.92820i	0.464991	+	0.805387i
$75$	1.50000	+	0.866025i	0.173205	+	0.100000i
$76$	3.50000	−	6.06218i	0.401478	−	0.695379i
$77$	−1.50000	+	2.59808i	−0.170941	+	0.296078i
$78$	−6.00000	+	3.46410i	−0.679366	+	0.392232i
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	0.804272	−	0.594261i	$-0.202555\pi$
$79$	−1.00000	−	1.73205i	−0.112509	−	0.194871i	−0.916781	+	0.399390i	$0.869222\pi$
$80$	−1.00000			−0.111803
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−9.00000			−0.993884
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$	−1.50000	+	0.866025i	−0.163663	+	0.0944911i
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	−0.500000	+	0.866025i	−0.0539164	+	0.0933859i
$87$	−9.00000	−	5.19615i	−0.964901	−	0.557086i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	1.50000	−	2.59808i	0.158114	−	0.273861i
$91$	−4.00000			−0.419314
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$			17.3205i			1.79605i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$	−3.50000	+	6.06218i	−0.359092	+	0.621966i
$96$			1.73205i			0.176777i
$97$	−5.50000	−	9.52628i	−0.558440	−	0.967247i	−0.997627	−	0.0688512i	$-0.978067\pi$
$97$	−5.50000	−	9.52628i	−0.558440	−	0.967247i	0.439187	−	0.898396i	$-0.355267\pi$
$98$	−1.00000			−0.101015
$99$	−9.00000			−0.904534
$100$	1.00000			0.100000
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	−4.50000	−	2.59808i	−0.445566	−	0.257248i
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	−0.750510	−	0.660859i	$-0.770192\pi$
$103$	2.00000	−	3.46410i	0.197066	−	0.341328i	0.947576	+	0.319531i	$0.103525\pi$
$104$	−2.00000	+	3.46410i	−0.196116	+	0.339683i
$105$	1.50000	−	0.866025i	0.146385	−	0.0845154i
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$	−1.50000	−	2.59808i	−0.143019	−	0.247717i
$111$	−12.0000	+	6.92820i	−1.13899	+	0.657596i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	10.5000	+	6.06218i	0.983415	+	0.567775i
$115$	−3.00000	−	5.19615i	−0.279751	−	0.484544i
$116$	−6.00000			−0.557086
$117$	−6.00000	−	10.3923i	−0.554700	−	0.960769i
$118$	−9.00000			−0.828517
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$		−	1.73205i		−	0.158114i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	7.00000	−	12.1244i	0.633750	−	1.09769i
$123$		−	15.5885i		−	1.40556i
$124$	5.00000	+	8.66025i	0.449013	+	0.777714i
$125$	−1.00000			−0.0894427
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	−10.0000			−0.887357			−0.443678	−	0.896186i	$-0.646327\pi$
$127$	−10.0000			−0.887357			−0.443678	+	0.896186i	$0.646327\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−1.50000	−	0.866025i	−0.132068	−	0.0762493i
$130$	2.00000	−	3.46410i	0.175412	−	0.303822i
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	0.475380	+	0.879781i	$0.342311\pi$
$131$	−6.00000	+	10.3923i	−0.524222	+	0.907980i	−0.999602	+	0.0281993i	$0.991023\pi$
$132$	−4.50000	+	2.59808i	−0.391675	+	0.226134i
$133$	3.50000	+	6.06218i	0.303488	+	0.525657i
$134$	7.00000			0.604708
$135$	4.50000	+	2.59808i	0.387298	+	0.223607i
$136$	−3.00000			−0.257248
$137$	10.5000	+	18.1865i	0.897076	+	1.55378i	0.831215	+	0.555952i	$0.187646\pi$
$137$	10.5000	+	18.1865i	0.897076	+	1.55378i	0.0658609	+	0.997829i	$0.479021\pi$
$138$	−9.00000	+	5.19615i	−0.766131	+	0.442326i
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	−0.999268	−	0.0382553i	$-0.987820\pi$
$139$	−5.50000	+	9.52628i	−0.466504	+	0.808008i	0.532764	+	0.846264i	$0.321153\pi$
$140$	0.500000	−	0.866025i	0.0422577	−	0.0731925i
$141$	18.0000	+	10.3923i	1.51587	+	0.875190i
$142$	3.00000	+	5.19615i	0.251754	+	0.436051i
$143$	−12.0000			−1.00349
$144$	−3.00000			−0.250000
$145$	6.00000			0.498273
$146$	−3.50000	−	6.06218i	−0.289662	−	0.501709i
$147$		−	1.73205i		−	0.142857i
$148$	−4.00000	+	6.92820i	−0.328798	+	0.569495i
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	−0.999953	−	0.00974235i	$-0.996899\pi$
$149$	−6.00000	+	10.3923i	−0.491539	+	0.851371i	0.508413	+	0.861113i	$0.330232\pi$
$150$			1.73205i			0.141421i
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	−0.996600	−	0.0823900i	$-0.973745\pi$
$151$	−7.00000	−	12.1244i	−0.569652	−	0.986666i	0.426948	−	0.904276i	$-0.359589\pi$
$152$	7.00000			0.567775
$153$	4.50000	−	7.79423i	0.363803	−	0.630126i
$154$	−3.00000			−0.241747
$155$	−5.00000	−	8.66025i	−0.401610	−	0.695608i
$156$	−6.00000	−	3.46410i	−0.480384	−	0.277350i
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	1.00000	−	1.73205i	0.0795557	−	0.137795i
$159$	−9.00000	+	5.19615i	−0.713746	+	0.412082i
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−6.00000			−0.472866
$162$	4.50000	−	7.79423i	0.353553	−	0.612372i
$163$	8.00000			0.626608			0.313304	−	0.949653i	$-0.398564\pi$
$163$	8.00000			0.626608			0.313304	+	0.949653i	$0.398564\pi$
$164$	−4.50000	−	7.79423i	−0.351391	−	0.608627i
$165$	4.50000	−	2.59808i	0.350325	−	0.202260i
$166$	−6.00000	+	10.3923i	−0.465690	+	0.806599i
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	−0.958440	−	0.285295i	$-0.907908\pi$
$167$	−3.00000	+	5.19615i	−0.232147	+	0.402090i	0.726293	+	0.687386i	$0.241242\pi$
$168$	−1.50000	−	0.866025i	−0.115728	−	0.0668153i
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	3.00000			0.230089
$171$	−10.5000	+	18.1865i	−0.802955	+	1.39076i
$172$	−1.00000			−0.0762493
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$		−	10.3923i		−	0.787839i
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$		−	15.5885i		−	1.17170i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$		0			0			−	1.00000i	$-0.5\pi$
$179$		0			0				1.00000i	$0.5\pi$
$180$	3.00000			0.223607
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$	−2.00000	−	3.46410i	−0.148250	−	0.256776i
$183$	21.0000	+	12.1244i	1.55236	+	0.896258i
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	4.00000	−	6.92820i	0.294086	−	0.509372i
$186$	−15.0000	+	8.66025i	−1.09985	+	0.635001i
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$	12.0000			0.875190
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$	−7.00000			−0.507833
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$	−1.50000	+	0.866025i	−0.108253	+	0.0625000i
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	−0.847469	−	0.530845i	$-0.821875\pi$
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	0.883460	+	0.468507i	$0.155208\pi$
$194$	5.50000	−	9.52628i	0.394877	−	0.683947i
$195$	6.00000	+	3.46410i	0.429669	+	0.248069i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	12.0000			0.854965			0.427482	−	0.904024i	$-0.359401\pi$
$197$	12.0000			0.854965			0.427482	+	0.904024i	$0.359401\pi$
$198$	−4.50000	−	7.79423i	−0.319801	−	0.553912i
$199$	20.0000			1.41776			0.708881	−	0.705328i	$-0.249200\pi$
$199$	20.0000			1.41776			0.708881	+	0.705328i	$0.249200\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$			12.1244i			0.855186i
$202$	6.00000	−	10.3923i	0.422159	−	0.731200i
$203$	3.00000	−	5.19615i	0.210559	−	0.364698i
$204$		−	5.19615i		−	0.363803i
$205$	4.50000	+	7.79423i	0.314294	+	0.544373i
$206$	4.00000			0.278693
$207$	−9.00000	−	15.5885i	−0.625543	−	1.08347i
$208$	−4.00000			−0.277350
$209$	10.5000	+	18.1865i	0.726300	+	1.25799i
$210$	1.50000	+	0.866025i	0.103510	+	0.0597614i
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	−0.788935	−	0.614477i	$-0.789367\pi$
$211$	2.00000	−	3.46410i	0.137686	−	0.238479i	0.926620	+	0.375999i	$0.122700\pi$
$212$	−3.00000	+	5.19615i	−0.206041	+	0.356873i
$213$	−9.00000	+	5.19615i	−0.616670	+	0.356034i
$214$	1.50000	+	2.59808i	0.102538	+	0.177601i
$215$	1.00000			0.0681994
$216$		−	5.19615i		−	0.353553i
$217$	−10.0000			−0.678844
$218$	−8.00000	−	13.8564i	−0.541828	−	0.938474i
$219$	10.5000	−	6.06218i	0.709524	−	0.409644i
$220$	1.50000	−	2.59808i	0.101130	−	0.175162i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$	−12.0000	−	6.92820i	−0.805387	−	0.464991i
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	0.983451	−	0.181173i	$-0.0579895\pi$
$223$	5.00000	+	8.66025i	0.334825	+	0.579934i	−0.648626	+	0.761107i	$0.724656\pi$
$224$	−1.00000			−0.0668153
$225$	−3.00000			−0.200000
$226$	6.00000			0.399114
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	0.911502	−	0.411296i	$-0.134924\pi$
$227$	1.50000	+	2.59808i	0.0995585	+	0.172440i	−0.811943	+	0.583736i	$0.801590\pi$
$228$			12.1244i			0.802955i
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	0.319582	+	0.947559i	$0.396457\pi$
$229$	−10.0000	+	17.3205i	−0.660819	+	1.14457i	−0.980401	+	0.197013i	$0.936876\pi$
$230$	3.00000	−	5.19615i	0.197814	−	0.342624i
$231$		−	5.19615i		−	0.341882i
$232$	−3.00000	−	5.19615i	−0.196960	−	0.341144i
$233$	9.00000			0.589610			0.294805	−	0.955557i	$-0.404745\pi$
$233$	9.00000			0.589610			0.294805	+	0.955557i	$0.404745\pi$
$234$	6.00000	−	10.3923i	0.392232	−	0.679366i
$235$	−12.0000			−0.782794
$236$	−4.50000	−	7.79423i	−0.292925	−	0.507361i
$237$	3.00000	+	1.73205i	0.194871	+	0.112509i
$238$	1.50000	−	2.59808i	0.0972306	−	0.168408i
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	−0.946590	−	0.322440i	$-0.895497\pi$
$239$	−3.00000	+	5.19615i	−0.194054	+	0.336111i	0.752536	+	0.658551i	$0.228830\pi$
$240$	1.50000	−	0.866025i	0.0968246	−	0.0559017i
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	0.774202	−	0.632938i	$-0.218151\pi$
$241$	−2.50000	−	4.33013i	−0.161039	−	0.278928i	−0.935242	+	0.354010i	$0.884818\pi$
$242$	2.00000			0.128565
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$	14.0000			0.896258
$245$	0.500000	+	0.866025i	0.0319438	+	0.0553283i
$246$	13.5000	−	7.79423i	0.860729	−	0.496942i
$247$	−14.0000	+	24.2487i	−0.890799	+	1.54291i
$248$	−5.00000	+	8.66025i	−0.317500	+	0.549927i
$249$	−18.0000	−	10.3923i	−1.14070	−	0.658586i
$250$	−0.500000	−	0.866025i	−0.0316228	−	0.0547723i
$251$	−9.00000			−0.568075			−0.284037	−	0.958813i	$-0.591674\pi$
$251$	−9.00000			−0.568075			−0.284037	+	0.958813i	$0.591674\pi$
$252$	1.50000	−	2.59808i	0.0944911	−	0.163663i
$253$	−18.0000			−1.13165
$254$	−5.00000	−	8.66025i	−0.313728	−	0.543393i
$255$			5.19615i			0.325396i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	−0.531487	−	0.847066i	$-0.678367\pi$
$257$	7.50000	−	12.9904i	0.467837	−	0.810318i	0.999325	+	0.0367485i	$0.0117000\pi$
$258$		−	1.73205i		−	0.107833i
$259$	−4.00000	−	6.92820i	−0.248548	−	0.430498i
$260$	4.00000			0.248069
$261$	18.0000			1.11417
$262$	−12.0000			−0.741362
$263$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$263$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$264$	−4.50000	−	2.59808i	−0.276956	−	0.159901i
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$	−3.50000	+	6.06218i	−0.214599	+	0.371696i
$267$	−9.00000	+	5.19615i	−0.550791	+	0.317999i
$268$	3.50000	+	6.06218i	0.213797	+	0.370306i
$269$	30.0000			1.82913			0.914566	−	0.404436i	$-0.132532\pi$
$269$	30.0000			1.82913			0.914566	+	0.404436i	$0.132532\pi$
$270$			5.19615i			0.316228i
$271$	20.0000			1.21491			0.607457	−	0.794353i	$-0.292190\pi$
$271$	20.0000			1.21491			0.607457	+	0.794353i	$0.292190\pi$
$272$	−1.50000	−	2.59808i	−0.0909509	−	0.157532i
$273$	6.00000	−	3.46410i	0.363137	−	0.209657i
$274$	−10.5000	+	18.1865i	−0.634328	+	1.09869i
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$	−9.00000	−	5.19615i	−0.541736	−	0.312772i
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$	−11.0000			−0.659736
$279$	−15.0000	−	25.9808i	−0.898027	−	1.55543i
$280$	1.00000			0.0597614
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	0.941526	−	0.336939i	$-0.109392\pi$
$281$	3.00000	+	5.19615i	0.178965	+	0.309976i	−0.762561	+	0.646916i	$0.776058\pi$
$282$			20.7846i			1.23771i
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	0.399188	+	0.916869i	$0.369292\pi$
$283$	−10.0000	+	17.3205i	−0.594438	+	1.02960i	−0.993626	+	0.112728i	$0.964041\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		−	12.1244i		−	0.718185i
$286$	−6.00000	−	10.3923i	−0.354787	−	0.614510i
$287$	9.00000			0.531253
$288$	−1.50000	−	2.59808i	−0.0883883	−	0.153093i
$289$	−8.00000			−0.470588
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$	16.5000	+	9.52628i	0.967247	+	0.558440i
$292$	3.50000	−	6.06218i	0.204822	−	0.354762i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$	1.50000	−	0.866025i	0.0874818	−	0.0505076i
$295$	4.50000	+	7.79423i	0.262000	+	0.453798i
$296$	−8.00000			−0.464991
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	−12.0000			−0.695141
$299$	−12.0000	−	20.7846i	−0.693978	−	1.20201i
$300$	−1.50000	+	0.866025i	−0.0866025	+	0.0500000i
$301$	0.500000	−	0.866025i	0.0288195	−	0.0499169i
$302$	7.00000	−	12.1244i	0.402805	−	0.697678i
$303$	18.0000	+	10.3923i	1.03407	+	0.597022i
$304$	3.50000	+	6.06218i	0.200739	+	0.347690i
$305$	−14.0000			−0.801638
$306$	9.00000			0.514496
$307$	17.0000			0.970241			0.485121	−	0.874447i	$-0.338776\pi$
$307$	17.0000			0.970241			0.485121	+	0.874447i	$0.338776\pi$
$308$	−1.50000	−	2.59808i	−0.0854704	−	0.148039i
$309$			6.92820i			0.394132i
$310$	5.00000	−	8.66025i	0.283981	−	0.491869i
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	0.489585	+	0.871956i	$0.337148\pi$
$311$	−9.00000	+	15.5885i	−0.510343	+	0.883940i	−0.999928	+	0.0119847i	$0.996185\pi$
$312$		−	6.92820i		−	0.392232i
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	0.879810	−	0.475325i	$-0.157669\pi$
$313$	0.500000	+	0.866025i	0.0282617	+	0.0489506i	−0.851549	+	0.524276i	$0.824336\pi$
$314$	4.00000			0.225733
$315$	−1.50000	+	2.59808i	−0.0845154	+	0.146385i
$316$	2.00000			0.112509
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	−0.976764	−	0.214318i	$-0.931247\pi$
$317$	−12.0000	−	20.7846i	−0.673987	−	1.16738i	0.302777	−	0.953062i	$-0.402086\pi$
$318$	−9.00000	−	5.19615i	−0.504695	−	0.291386i
$319$	9.00000	−	15.5885i	0.503903	−	0.872786i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	−4.50000	+	2.59808i	−0.251166	+	0.145010i
$322$	−3.00000	−	5.19615i	−0.167183	−	0.289570i
$323$	−21.0000			−1.16847
$324$	9.00000			0.500000
$325$	−4.00000			−0.221880
$326$	4.00000	+	6.92820i	0.221540	+	0.383718i
$327$	24.0000	−	13.8564i	1.32720	−	0.766261i
$328$	4.50000	−	7.79423i	0.248471	−	0.430364i
$329$	−6.00000	+	10.3923i	−0.330791	+	0.572946i
$330$	4.50000	+	2.59808i	0.247717	+	0.143019i
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−12.0000			−0.658586
$333$	12.0000	−	20.7846i	0.657596	−	1.13899i
$334$	−6.00000			−0.328305
$335$	−3.50000	−	6.06218i	−0.191225	−	0.331212i
$336$		−	1.73205i		−	0.0944911i
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	−0.926049	−	0.377403i	$-0.876817\pi$
$337$	−2.50000	+	4.33013i	−0.136184	+	0.235877i	0.789865	+	0.613280i	$0.210150\pi$
$338$	1.50000	−	2.59808i	0.0815892	−	0.141317i
$339$			10.3923i			0.564433i
$340$	1.50000	+	2.59808i	0.0813489	+	0.140900i
$341$	−30.0000			−1.62459
$342$	−21.0000			−1.13555
$343$	1.00000			0.0539949
$344$	−0.500000	−	0.866025i	−0.0269582	−	0.0466930i
$345$	9.00000	+	5.19615i	0.484544	+	0.279751i
$346$	3.00000	−	5.19615i	0.161281	−	0.279347i
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	−0.961162	−	0.275983i	$-0.910997\pi$
$347$	−4.50000	+	7.79423i	−0.241573	+	0.418416i	0.719590	+	0.694399i	$0.244330\pi$
$348$	9.00000	−	5.19615i	0.482451	−	0.278543i
$349$	−10.0000	−	17.3205i	−0.535288	−	0.927146i	−0.999149	−	0.0412379i	$-0.986870\pi$
$349$	−10.0000	−	17.3205i	−0.535288	−	0.927146i	0.463862	−	0.885908i	$-0.346463\pi$
$350$	−1.00000			−0.0534522
$351$	18.0000	+	10.3923i	0.960769	+	0.554700i
$352$	−3.00000			−0.159901
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	0.721063	−	0.692869i	$-0.243654\pi$
$353$	−4.50000	−	7.79423i	−0.239511	−	0.414845i	−0.960574	+	0.278024i	$0.910320\pi$
$354$	13.5000	−	7.79423i	0.717517	−	0.414259i
$355$	3.00000	−	5.19615i	0.159223	−	0.275783i
$356$	−3.00000	+	5.19615i	−0.159000	+	0.275396i
$357$	4.50000	+	2.59808i	0.238165	+	0.137505i
$358$		0			0
$359$	24.0000			1.26667			0.633336	−	0.773877i	$-0.281685\pi$
$359$	24.0000			1.26667			0.633336	+	0.773877i	$0.281685\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	30.0000			1.57895
$362$	10.0000	+	17.3205i	0.525588	+	0.910346i
$363$			3.46410i			0.181818i
$364$	2.00000	−	3.46410i	0.104828	−	0.181568i
$365$	−3.50000	+	6.06218i	−0.183198	+	0.317309i
$366$			24.2487i			1.26750i
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	0.956544	+	0.291587i	$0.0941834\pi$
$367$	14.0000	+	24.2487i	0.730794	+	1.26577i	−0.225750	+	0.974185i	$0.572483\pi$
$368$	−6.00000			−0.312772
$369$	13.5000	+	23.3827i	0.702782	+	1.21725i
$370$	8.00000			0.415900
$371$	−3.00000	−	5.19615i	−0.155752	−	0.269771i
$372$	−15.0000	−	8.66025i	−0.777714	−	0.449013i
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	4.50000	−	7.79423i	0.232689	−	0.403030i
$375$	1.50000	−	0.866025i	0.0774597	−	0.0447214i
$376$	6.00000	+	10.3923i	0.309426	+	0.535942i
$377$	24.0000			1.23606
$378$	4.50000	+	2.59808i	0.231455	+	0.133631i
$379$	5.00000			0.256833			0.128416	−	0.991720i	$-0.459011\pi$
$379$	5.00000			0.256833			0.128416	+	0.991720i	$0.459011\pi$
$380$	−3.50000	−	6.06218i	−0.179546	−	0.310983i
$381$	15.0000	−	8.66025i	0.768473	−	0.443678i
$382$	−6.00000	+	10.3923i	−0.306987	+	0.531717i
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	−0.671027	−	0.741433i	$-0.734147\pi$
$383$	6.00000	−	10.3923i	0.306586	−	0.531022i	0.977613	+	0.210411i	$0.0674801\pi$
$384$	−1.50000	−	0.866025i	−0.0765466	−	0.0441942i
$385$	1.50000	+	2.59808i	0.0764471	+	0.132410i
$386$	1.00000			0.0508987
$387$	3.00000			0.152499
$388$	11.0000			0.558440
$389$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$389$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$390$			6.92820i			0.350823i
$391$	9.00000	−	15.5885i	0.455150	−	0.788342i
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		−	20.7846i		−	1.04844i
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$	−2.00000			−0.100631
$396$	4.50000	−	7.79423i	0.226134	−	0.391675i
$397$	−4.00000			−0.200754			−0.100377	−	0.994949i	$-0.532005\pi$
$397$	−4.00000			−0.200754			−0.100377	+	0.994949i	$0.532005\pi$
$398$	10.0000	+	17.3205i	0.501255	+	0.868199i
$399$	−10.5000	−	6.06218i	−0.525657	−	0.303488i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	−0.615725	−	0.787961i	$-0.711137\pi$
$401$	7.50000	−	12.9904i	0.374532	−	0.648709i	0.990257	+	0.139253i	$0.0444700\pi$
$402$	−10.5000	+	6.06218i	−0.523692	+	0.302354i
$403$	−20.0000	−	34.6410i	−0.996271	−	1.72559i
$404$	12.0000			0.597022
$405$	−9.00000			−0.447214
$406$	6.00000			0.297775
$407$	−12.0000	−	20.7846i	−0.594818	−	1.03025i
$408$	4.50000	−	2.59808i	0.222783	−	0.128624i
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	−0.529657	−	0.848212i	$-0.677679\pi$
$409$	9.50000	−	16.4545i	0.469745	−	0.813622i	0.999402	+	0.0345902i	$0.0110126\pi$
$410$	−4.50000	+	7.79423i	−0.222239	+	0.384930i
$411$	−31.5000	−	18.1865i	−1.55378	−	0.897076i
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	9.00000			0.442861
$414$	9.00000	−	15.5885i	0.442326	−	0.766131i
$415$	12.0000			0.589057
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$		−	19.0526i		−	0.933008i
$418$	−10.5000	+	18.1865i	−0.513572	+	0.889532i
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	0.408481	+	0.912767i	$0.366058\pi$
$419$	−12.0000	+	20.7846i	−0.586238	+	1.01539i	−0.994720	+	0.102628i	$0.967275\pi$
$420$			1.73205i			0.0845154i
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	−0.986814	−	0.161859i	$-0.948251\pi$
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	0.353233	−	0.935536i	$-0.385082\pi$
$422$	4.00000			0.194717
$423$	−36.0000			−1.75038
$424$	−6.00000			−0.291386
$425$	−1.50000	−	2.59808i	−0.0727607	−	0.126025i
$426$	−9.00000	−	5.19615i	−0.436051	−	0.251754i
$427$	−7.00000	+	12.1244i	−0.338754	+	0.586739i
$428$	−1.50000	+	2.59808i	−0.0725052	+	0.125583i
$429$	18.0000	−	10.3923i	0.869048	−	0.501745i
$430$	0.500000	+	0.866025i	0.0241121	+	0.0417635i
$431$	12.0000			0.578020			0.289010	−	0.957326i	$-0.406674\pi$
$431$	12.0000			0.578020			0.289010	+	0.957326i	$0.406674\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	11.0000			0.528626			0.264313	−	0.964437i	$-0.414855\pi$
$433$	11.0000			0.528626			0.264313	+	0.964437i	$0.414855\pi$
$434$	−5.00000	−	8.66025i	−0.240008	−	0.415705i
$435$	−9.00000	+	5.19615i	−0.431517	+	0.249136i
$436$	8.00000	−	13.8564i	0.383131	−	0.663602i
$437$	−21.0000	+	36.3731i	−1.00457	+	1.73996i
$438$	10.5000	+	6.06218i	0.501709	+	0.289662i
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	0.960323	−	0.278889i	$-0.0899661\pi$
$439$	5.00000	+	8.66025i	0.238637	+	0.413331i	−0.721686	+	0.692220i	$0.756633\pi$
$440$	3.00000			0.143019
$441$	1.50000	+	2.59808i	0.0714286	+	0.123718i
$442$	12.0000			0.570782
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	0.631010	−	0.775775i	$-0.282641\pi$
$443$	−7.50000	−	12.9904i	−0.356336	−	0.617192i	−0.987346	+	0.158583i	$0.949307\pi$
$444$		−	13.8564i		−	0.657596i
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	−5.00000	+	8.66025i	−0.236757	+	0.410075i
$447$		−	20.7846i		−	0.983078i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−39.0000			−1.84052			−0.920262	−	0.391303i	$-0.872024\pi$
$449$	−39.0000			−1.84052			−0.920262	+	0.391303i	$0.872024\pi$
$450$	−1.50000	−	2.59808i	−0.0707107	−	0.122474i
$451$	27.0000			1.27138
$452$	3.00000	+	5.19615i	0.141108	+	0.244406i
$453$	21.0000	+	12.1244i	0.986666	+	0.569652i
$454$	−1.50000	+	2.59808i	−0.0703985	+	0.121934i
$455$	−2.00000	+	3.46410i	−0.0937614	+	0.162400i
$456$	−10.5000	+	6.06218i	−0.491708	+	0.283887i
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	0.708233	−	0.705979i	$-0.249493\pi$
$457$	−5.50000	−	9.52628i	−0.257279	−	0.445621i	−0.965512	+	0.260358i	$0.916159\pi$
$458$	−20.0000			−0.934539
$459$			15.5885i			0.727607i
$460$	6.00000			0.279751
$461$	12.0000	+	20.7846i	0.558896	+	0.968036i	0.997589	+	0.0693989i	$0.0221081\pi$
$461$	12.0000	+	20.7846i	0.558896	+	0.968036i	−0.438693	+	0.898637i	$0.644559\pi$
$462$	4.50000	−	2.59808i	0.209359	−	0.120873i
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	−0.815802	−	0.578331i	$-0.803704\pi$
$463$	2.00000	−	3.46410i	0.0929479	−	0.160990i	0.908750	+	0.417340i	$0.137038\pi$
$464$	3.00000	−	5.19615i	0.139272	−	0.241225i
$465$	15.0000	+	8.66025i	0.695608	+	0.401610i
$466$	4.50000	+	7.79423i	0.208458	+	0.361061i
$467$	−27.0000			−1.24941			−0.624705	−	0.780860i	$-0.714781\pi$
$467$	−27.0000			−1.24941			−0.624705	+	0.780860i	$0.714781\pi$
$468$	12.0000			0.554700
$469$	−7.00000			−0.323230
$470$	−6.00000	−	10.3923i	−0.276759	−	0.479361i
$471$			6.92820i			0.319235i
$472$	4.50000	−	7.79423i	0.207129	−	0.358758i
$473$	1.50000	−	2.59808i	0.0689701	−	0.119460i
$474$			3.46410i			0.159111i
$475$	3.50000	+	6.06218i	0.160591	+	0.278152i
$476$	3.00000			0.137505
$477$	9.00000	−	15.5885i	0.412082	−	0.713746i
$478$	−6.00000			−0.274434
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	0.287954	−	0.957644i	$-0.407025\pi$
$480$	1.50000	+	0.866025i	0.0684653	+	0.0395285i
$481$	16.0000	−	27.7128i	0.729537	−	1.26360i
$482$	2.50000	−	4.33013i	0.113872	−	0.197232i
$483$	9.00000	−	5.19615i	0.409514	−	0.236433i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−11.0000			−0.499484
$486$			15.5885i			0.707107i
$487$	2.00000			0.0906287			0.0453143	−	0.998973i	$-0.485571\pi$
$487$	2.00000			0.0906287			0.0453143	+	0.998973i	$0.485571\pi$
$488$	7.00000	+	12.1244i	0.316875	+	0.548844i
$489$	−12.0000	+	6.92820i	−0.542659	+	0.313304i
$490$	−0.500000	+	0.866025i	−0.0225877	+	0.0391230i
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	−0.746438	−	0.665455i	$-0.768237\pi$
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	0.949520	+	0.313707i	$0.101571\pi$
$492$	13.5000	+	7.79423i	0.608627	+	0.351391i
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	−28.0000			−1.25978
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$	−10.0000			−0.449013
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		−	20.7846i		−	0.931381i
$499$	−8.50000	+	14.7224i	−0.380512	+	0.659067i	−0.991136	−	0.132855i	$-0.957586\pi$
$499$	−8.50000	+	14.7224i	−0.380512	+	0.659067i	0.610623	+	0.791921i	$0.290919\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$		−	10.3923i		−	0.464294i
$502$	−4.50000	−	7.79423i	−0.200845	−	0.347873i
$503$	42.0000			1.87269			0.936344	−	0.351085i	$-0.114187\pi$
$503$	42.0000			1.87269			0.936344	+	0.351085i	$0.114187\pi$
$504$	3.00000			0.133631
$505$	−12.0000			−0.533993
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	4.50000	+	2.59808i	0.199852	+	0.115385i
$508$	5.00000	−	8.66025i	0.221839	−	0.384237i
$509$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$	−4.50000	+	2.59808i	−0.199263	+	0.115045i
$511$	3.50000	+	6.06218i	0.154831	+	0.268175i
$512$	−1.00000			−0.0441942
$513$		−	36.3731i		−	1.60591i
$514$	15.0000			0.661622
$515$	−2.00000	−	3.46410i	−0.0881305	−	0.152647i
$516$	1.50000	−	0.866025i	0.0660338	−	0.0381246i
$517$	−18.0000	+	31.1769i	−0.791639	+	1.37116i
$518$	4.00000	−	6.92820i	0.175750	−	0.304408i
$519$	9.00000	+	5.19615i	0.395056	+	0.228086i
$520$	2.00000	+	3.46410i	0.0877058	+	0.151911i
$521$	−15.0000			−0.657162			−0.328581	−	0.944476i	$-0.606570\pi$
$521$	−15.0000			−0.657162			−0.328581	+	0.944476i	$0.606570\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	−4.00000			−0.174908			−0.0874539	−	0.996169i	$-0.527873\pi$
$523$	−4.00000			−0.174908			−0.0874539	+	0.996169i	$0.527873\pi$
$524$	−6.00000	−	10.3923i	−0.262111	−	0.453990i
$525$		−	1.73205i		−	0.0755929i
$526$		0			0
$527$	15.0000	−	25.9808i	0.653410	−	1.13174i
$528$		−	5.19615i		−	0.226134i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	6.00000			0.260623
$531$	13.5000	+	23.3827i	0.585850	+	1.01472i
$532$	−7.00000			−0.303488
$533$	18.0000	+	31.1769i	0.779667	+	1.35042i
$534$	−9.00000	−	5.19615i	−0.389468	−	0.224860i
$535$	1.50000	−	2.59808i	0.0648507	−	0.112325i
$536$	−3.50000	+	6.06218i	−0.151177	+	0.261846i
$537$		0			0
$538$	15.0000	+	25.9808i	0.646696	+	1.12011i
$539$	3.00000			0.129219
$540$	−4.50000	+	2.59808i	−0.193649	+	0.111803i
$541$	−16.0000			−0.687894			−0.343947	−	0.938989i	$-0.611764\pi$
$541$	−16.0000			−0.687894			−0.343947	+	0.938989i	$0.611764\pi$
$542$	10.0000	+	17.3205i	0.429537	+	0.743980i
$543$	−30.0000	+	17.3205i	−1.28742	+	0.743294i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	−8.00000	+	13.8564i	−0.342682	+	0.593543i
$546$	6.00000	+	3.46410i	0.256776	+	0.148250i
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	0.925347	+	0.379122i	$0.123774\pi$
$547$	18.5000	+	32.0429i	0.791003	+	1.37006i	−0.134344	+	0.990935i	$0.542893\pi$
$548$	−21.0000			−0.897076
$549$	−42.0000			−1.79252
$550$	−3.00000			−0.127920
$551$	−21.0000	−	36.3731i	−0.894630	−	1.54954i
$552$		−	10.3923i		−	0.442326i
$553$	−1.00000	+	1.73205i	−0.0425243	+	0.0736543i
$554$	−11.0000	+	19.0526i	−0.467345	+	0.809466i
$555$			13.8564i			0.588172i
$556$	−5.50000	−	9.52628i	−0.233252	−	0.404004i
$557$		0			0			−	1.00000i	$-0.5\pi$
$557$		0			0				1.00000i	$0.5\pi$
$558$	15.0000	−	25.9808i	0.635001	−	1.09985i
$559$	4.00000			0.169182
$560$	0.500000	+	0.866025i	0.0211289	+	0.0365963i
$561$	13.5000	+	7.79423i	0.569970	+	0.329073i
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	13.5000	−	23.3827i	0.568957	−	0.985463i	−0.427712	−	0.903915i	$-0.640680\pi$
$563$	13.5000	−	23.3827i	0.568957	−	0.985463i	0.996669	−	0.0815478i	$-0.0259863\pi$
$564$	−18.0000	+	10.3923i	−0.757937	+	0.437595i
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	−20.0000			−0.840663
$567$	−4.50000	+	7.79423i	−0.188982	+	0.327327i
$568$	−6.00000			−0.251754
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	0.756151	−	0.654398i	$-0.227078\pi$
$569$	−4.50000	−	7.79423i	−0.188650	−	0.326751i	−0.944800	+	0.327647i	$0.893744\pi$
$570$	10.5000	−	6.06218i	0.439797	−	0.253917i
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	−0.913584	−	0.406651i	$-0.866697\pi$
$571$	−2.50000	+	4.33013i	−0.104622	+	0.181210i	0.808962	+	0.587861i	$0.200030\pi$
$572$	6.00000	−	10.3923i	0.250873	−	0.434524i
$573$	−18.0000	−	10.3923i	−0.751961	−	0.434145i
$574$	4.50000	+	7.79423i	0.187826	+	0.325325i
$575$	−6.00000			−0.250217
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	−31.0000			−1.29055			−0.645273	−	0.763952i	$-0.723257\pi$
$577$	−31.0000			−1.29055			−0.645273	+	0.763952i	$0.723257\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$			1.73205i			0.0719816i
$580$	−3.00000	+	5.19615i	−0.124568	+	0.215758i
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$			19.0526i			0.789754i
$583$	−9.00000	−	15.5885i	−0.372742	−	0.645608i
$584$	7.00000			0.289662
$585$	−12.0000			−0.496139
$586$	−18.0000			−0.743573
$587$	4.50000	+	7.79423i	0.185735	+	0.321702i	0.943824	−	0.330449i	$-0.107200\pi$
$587$	4.50000	+	7.79423i	0.185735	+	0.321702i	−0.758089	+	0.652151i	$0.773867\pi$
$588$	1.50000	+	0.866025i	0.0618590	+	0.0357143i
$589$	−35.0000	+	60.6218i	−1.44215	+	2.49788i
$590$	−4.50000	+	7.79423i	−0.185262	+	0.320883i
$591$	−18.0000	+	10.3923i	−0.740421	+	0.427482i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$	13.5000	+	7.79423i	0.553912	+	0.319801i
$595$	−3.00000			−0.122988
$596$	−6.00000	−	10.3923i	−0.245770	−	0.425685i
$597$	−30.0000	+	17.3205i	−1.22782	+	0.708881i
$598$	12.0000	−	20.7846i	0.490716	−	0.849946i
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	−0.509631	−	0.860393i	$-0.670218\pi$
$599$	12.0000	−	20.7846i	0.490307	−	0.849236i	0.999938	+	0.0111569i	$0.00355143\pi$
$600$	−1.50000	−	0.866025i	−0.0612372	−	0.0353553i
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	−0.963405	−	0.268049i	$-0.913621\pi$
$601$	−17.5000	−	30.3109i	−0.713840	−	1.23641i	0.249565	−	0.968358i	$-0.419712\pi$
$602$	1.00000			0.0407570
$603$	−10.5000	−	18.1865i	−0.427593	−	0.740613i
$604$	14.0000			0.569652
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$			20.7846i			0.844317i
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$	−3.50000	+	6.06218i	−0.141944	+	0.245854i
$609$			10.3923i			0.421117i
$610$	−7.00000	−	12.1244i	−0.283422	−	0.490901i
$611$	−48.0000			−1.94187
$612$	4.50000	+	7.79423i	0.181902	+	0.315063i
$613$	38.0000			1.53481			0.767403	−	0.641165i	$-0.221549\pi$
$613$	38.0000			1.53481			0.767403	+	0.641165i	$0.221549\pi$
$614$	8.50000	+	14.7224i	0.343032	+	0.594149i
$615$	−13.5000	−	7.79423i	−0.544373	−	0.314294i
$616$	1.50000	−	2.59808i	0.0604367	−	0.104679i
$617$	−10.5000	+	18.1865i	−0.422714	+	0.732162i	−0.996204	−	0.0870504i	$-0.972256\pi$
$617$	−10.5000	+	18.1865i	−0.422714	+	0.732162i	0.573490	+	0.819213i	$0.305589\pi$
$618$	−6.00000	+	3.46410i	−0.241355	+	0.139347i
$619$	3.50000	+	6.06218i	0.140677	+	0.243659i	0.927752	−	0.373198i	$-0.121739\pi$
$619$	3.50000	+	6.06218i	0.140677	+	0.243659i	−0.787075	+	0.616858i	$0.788405\pi$
$620$	10.0000			0.401610
$621$	27.0000	+	15.5885i	1.08347	+	0.625543i
$622$	−18.0000			−0.721734
$623$	−3.00000	−	5.19615i	−0.120192	−	0.208179i
$624$	6.00000	−	3.46410i	0.240192	−	0.138675i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$	−31.5000	−	18.1865i	−1.25799	−	0.726300i
$628$	2.00000	+	3.46410i	0.0798087	+	0.138233i
$629$	24.0000			0.956943
$630$	−3.00000			−0.119523
$631$	−10.0000			−0.398094			−0.199047	−	0.979990i	$-0.563785\pi$
$631$	−10.0000			−0.398094			−0.199047	+	0.979990i	$0.563785\pi$
$632$	1.00000	+	1.73205i	0.0397779	+	0.0688973i
$633$			6.92820i			0.275371i
$634$	12.0000	−	20.7846i	0.476581	−	0.825462i
$635$	−5.00000	+	8.66025i	−0.198419	+	0.343672i
$636$		−	10.3923i		−	0.412082i
$637$	2.00000	+	3.46410i	0.0792429	+	0.137253i
$638$	18.0000			0.712627
$639$	9.00000	−	15.5885i	0.356034	−	0.616670i
$640$	1.00000			0.0395285
$641$	7.50000	+	12.9904i	0.296232	+	0.513089i	0.975271	−	0.221013i	$-0.0709364\pi$
$641$	7.50000	+	12.9904i	0.296232	+	0.513089i	−0.679039	+	0.734103i	$0.737603\pi$
$642$	−4.50000	−	2.59808i	−0.177601	−	0.102538i
$643$	24.5000	−	42.4352i	0.966186	−	1.67348i	0.259791	−	0.965665i	$-0.416346\pi$
$643$	24.5000	−	42.4352i	0.966186	−	1.67348i	0.706395	−	0.707818i	$-0.250320\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$	−1.50000	+	0.866025i	−0.0590624	+	0.0340997i
$646$	−10.5000	−	18.1865i	−0.413117	−	0.715540i
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	4.50000	+	7.79423i	0.176777	+	0.306186i
$649$	27.0000			1.05984
$650$	−2.00000	−	3.46410i	−0.0784465	−	0.135873i
$651$	15.0000	−	8.66025i	0.587896	−	0.339422i
$652$	−4.00000	+	6.92820i	−0.156652	+	0.271329i
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	24.0000	+	13.8564i	0.938474	+	0.541828i
$655$	6.00000	+	10.3923i	0.234439	+	0.406061i
$656$	9.00000			0.351391
$657$	−10.5000	+	18.1865i	−0.409644	+	0.709524i
$658$	−12.0000			−0.467809
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	0.725175	−	0.688565i	$-0.241759\pi$
$659$	−6.00000	−	10.3923i	−0.233727	−	0.404827i	−0.958902	+	0.283738i	$0.908425\pi$
$660$			5.19615i			0.202260i
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	0.366723	+	0.930330i	$0.380480\pi$
$661$	−16.0000	+	27.7128i	−0.622328	+	1.07790i	−0.989051	+	0.147573i	$0.952854\pi$
$662$	−14.0000	+	24.2487i	−0.544125	+	0.942453i
$663$			20.7846i			0.807207i
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	7.00000			0.271448
$666$	24.0000			0.929981
$667$	36.0000			1.39393
$668$	−3.00000	−	5.19615i	−0.116073	−	0.201045i
$669$	−15.0000	−	8.66025i	−0.579934	−	0.334825i
$670$	3.50000	−	6.06218i	0.135217	−	0.234202i
$671$	−21.0000	+	36.3731i	−0.810696	+	1.40417i
$672$	1.50000	−	0.866025i	0.0578638	−	0.0334077i
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	0.946156	−	0.323711i	$-0.104931\pi$
$673$	5.00000	+	8.66025i	0.192736	+	0.333828i	−0.753420	+	0.657539i	$0.771597\pi$
$674$	−5.00000			−0.192593
$675$	4.50000	−	2.59808i	0.173205	−	0.100000i
$676$	3.00000			0.115385
$677$	12.0000	+	20.7846i	0.461197	+	0.798817i	0.999021	−	0.0442400i	$-0.0140866\pi$
$677$	12.0000	+	20.7846i	0.461197	+	0.798817i	−0.537823	+	0.843057i	$0.680753\pi$
$678$	−9.00000	+	5.19615i	−0.345643	+	0.199557i
$679$	−5.50000	+	9.52628i	−0.211071	+	0.365585i
$680$	−1.50000	+	2.59808i	−0.0575224	+	0.0996317i
$681$	−4.50000	−	2.59808i	−0.172440	−	0.0995585i
$682$	−15.0000	−	25.9808i	−0.574380	−	0.994855i
$683$	−9.00000			−0.344375			−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000			−0.344375			−0.172188	+	0.985064i	$0.555084\pi$
$684$	−10.5000	−	18.1865i	−0.401478	−	0.695379i
$685$	21.0000			0.802369
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$		−	34.6410i		−	1.32164i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	12.0000	−	20.7846i	0.457164	−	0.791831i
$690$			10.3923i			0.395628i
$691$	8.00000	+	13.8564i	0.304334	+	0.527123i	0.977113	−	0.212721i	$-0.0682327\pi$
$691$	8.00000	+	13.8564i	0.304334	+	0.527123i	−0.672779	+	0.739844i	$0.734899\pi$
$692$	6.00000			0.228086
$693$	4.50000	+	7.79423i	0.170941	+	0.296078i
$694$	−9.00000			−0.341635
$695$	5.50000	+	9.52628i	0.208627	+	0.361352i
$696$	9.00000	+	5.19615i	0.341144	+	0.196960i
$697$	−13.5000	+	23.3827i	−0.511349	+	0.885682i
$698$	10.0000	−	17.3205i	0.378506	−	0.655591i
$699$	−13.5000	+	7.79423i	−0.510617	+	0.294805i
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	6.00000			0.226617			0.113308	−	0.993560i	$-0.463855\pi$
$701$	6.00000			0.226617			0.113308	+	0.993560i	$0.463855\pi$
$702$			20.7846i			0.784465i
$703$	−56.0000			−2.11208
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$	18.0000	−	10.3923i	0.677919	−	0.391397i
$706$	4.50000	−	7.79423i	0.169360	−	0.293340i
$707$	−6.00000	+	10.3923i	−0.225653	+	0.390843i
$708$	13.5000	+	7.79423i	0.507361	+	0.292925i
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	−0.963512	−	0.267664i	$-0.913748\pi$
$709$	−19.0000	−	32.9090i	−0.713560	−	1.23592i	0.249952	−	0.968258i	$-0.419585\pi$
$710$	6.00000			0.225176
$711$	−6.00000			−0.225018
$712$	−6.00000			−0.224860
$713$	−30.0000	−	51.9615i	−1.12351	−	1.94597i
$714$			5.19615i			0.194461i
$715$	−6.00000	+	10.3923i	−0.224387	+	0.388650i
$716$		0			0
$717$		−	10.3923i		−	0.388108i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	12.0000			0.447524			0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000			0.447524			0.223762	+	0.974644i	$0.428166\pi$
$720$	−1.50000	+	2.59808i	−0.0559017	+	0.0968246i
$721$	−4.00000			−0.148968
$722$	15.0000	+	25.9808i	0.558242	+	0.966904i
$723$	7.50000	+	4.33013i	0.278928	+	0.161039i
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	3.00000	−	5.19615i	0.111417	−	0.192980i
$726$	−3.00000	+	1.73205i	−0.111340	+	0.0642824i
$727$	−10.0000	−	17.3205i	−0.370879	−	0.642382i	0.618822	−	0.785532i	$-0.287610\pi$
$727$	−10.0000	−	17.3205i	−0.370879	−	0.642382i	−0.989701	+	0.143149i	$0.954277\pi$
$728$	4.00000			0.148250
$729$	−27.0000			−1.00000
$730$	−7.00000			−0.259082
$731$	1.50000	+	2.59808i	0.0554795	+	0.0960933i
$732$	−21.0000	+	12.1244i	−0.776182	+	0.448129i
$733$	8.00000	−	13.8564i	0.295487	−	0.511798i	−0.679611	−	0.733572i	$-0.737852\pi$
$733$	8.00000	−	13.8564i	0.295487	−	0.511798i	0.975098	+	0.221774i	$0.0711849\pi$
$734$	−14.0000	+	24.2487i	−0.516749	+	0.895036i
$735$	−1.50000	−	0.866025i	−0.0553283	−	0.0319438i
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	−21.0000			−0.773545
$738$	−13.5000	+	23.3827i	−0.496942	+	0.860729i
$739$	−19.0000			−0.698926			−0.349463	−	0.936950i	$-0.613636\pi$
$739$	−19.0000			−0.698926			−0.349463	+	0.936950i	$0.613636\pi$
$740$	4.00000	+	6.92820i	0.147043	+	0.254686i
$741$		−	48.4974i		−	1.78160i
$742$	3.00000	−	5.19615i	0.110133	−	0.190757i
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	−0.805735	−	0.592277i	$-0.798229\pi$
$743$	3.00000	−	5.19615i	0.110059	−	0.190628i	0.915794	+	0.401648i	$0.131563\pi$
$744$		−	17.3205i		−	0.635001i
$745$	6.00000	+	10.3923i	0.219823	+	0.380745i
$746$	−14.0000			−0.512576
$747$	36.0000			1.31717
$748$	9.00000			0.329073
$749$	−1.50000	−	2.59808i	−0.0548088	−	0.0949316i
$750$	1.50000	+	0.866025i	0.0547723	+	0.0316228i
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	−6.00000	+	10.3923i	−0.218797	+	0.378968i
$753$	13.5000	−	7.79423i	0.491967	−	0.284037i
$754$	12.0000	+	20.7846i	0.437014	+	0.756931i
$755$	−14.0000			−0.509512
$756$			5.19615i			0.188982i
$757$	26.0000			0.944986			0.472493	−	0.881334i	$-0.343354\pi$
$757$	26.0000			0.944986			0.472493	+	0.881334i	$0.343354\pi$
$758$	2.50000	+	4.33013i	0.0908041	+	0.157277i
$759$	27.0000	−	15.5885i	0.980038	−	0.565825i
$760$	3.50000	−	6.06218i	0.126958	−	0.219898i
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	−0.806514	−	0.591215i	$-0.798649\pi$
$761$	3.00000	−	5.19615i	0.108750	−	0.188360i	0.915264	+	0.402854i	$0.131982\pi$
$762$	15.0000	+	8.66025i	0.543393	+	0.313728i
$763$	8.00000	+	13.8564i	0.289619	+	0.501636i
$764$	−12.0000			−0.434145
$765$	−4.50000	−	7.79423i	−0.162698	−	0.281801i
$766$	12.0000			0.433578
$767$	18.0000	+	31.1769i	0.649942	+	1.12573i
$768$		−	1.73205i		−	0.0625000i
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	−0.596643	−	0.802507i	$-0.703499\pi$
$769$	11.0000	−	19.0526i	0.396670	−	0.687053i	0.993313	+	0.115454i	$0.0368323\pi$
$770$	−1.50000	+	2.59808i	−0.0540562	+	0.0936282i
$771$			25.9808i			0.935674i
$772$	0.500000	+	0.866025i	0.0179954	+	0.0311689i
$773$	6.00000			0.215805			0.107903	−	0.994161i	$-0.465587\pi$
$773$	6.00000			0.215805			0.107903	+	0.994161i	$0.465587\pi$
$774$	1.50000	+	2.59808i	0.0539164	+	0.0933859i
$775$	−10.0000			−0.359211
$776$	5.50000	+	9.52628i	0.197438	+	0.341974i
$777$	12.0000	+	6.92820i	0.430498	+	0.248548i
$778$		0			0
$779$	31.5000	−	54.5596i	1.12860	−	1.95480i
$780$	−6.00000	+	3.46410i	−0.214834	+	0.124035i
$781$	−9.00000	−	15.5885i	−0.322045	−	0.557799i
$782$	18.0000			0.643679
$783$	−27.0000	+	15.5885i	−0.964901	+	0.557086i
$784$	1.00000			0.0357143
$785$	−2.00000	−	3.46410i	−0.0713831	−	0.123639i
$786$	18.0000	−	10.3923i	0.642039	−	0.370681i
$787$	−10.0000	+	17.3205i	−0.356462	+	0.617409i	−0.987367	−	0.158450i	$-0.949350\pi$
$787$	−10.0000	+	17.3205i	−0.356462	+	0.617409i	0.630905	+	0.775860i	$0.282684\pi$
$788$	−6.00000	+	10.3923i	−0.213741	+	0.370211i
$789$		0			0
$790$	−1.00000	−	1.73205i	−0.0355784	−	0.0616236i
$791$	−6.00000			−0.213335
$792$	9.00000			0.319801
$793$	−56.0000			−1.98862
$794$	−2.00000	−	3.46410i	−0.0709773	−	0.122936i
$795$			10.3923i			0.368577i
$796$	−10.0000	+	17.3205i	−0.354441	+	0.613909i
$797$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$797$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$798$		−	12.1244i		−	0.429198i
$799$	−18.0000	−	31.1769i	−0.636794	−	1.10296i
$800$	−1.00000			−0.0353553
$801$	9.00000	−	15.5885i	0.317999	−	0.550791i
$802$	15.0000			0.529668
$803$	10.5000	+	18.1865i	0.370537	+	0.641789i
$804$	−10.5000	−	6.06218i	−0.370306	−	0.213797i
$805$	−3.00000	+	5.19615i	−0.105736	+	0.183140i
$806$	20.0000	−	34.6410i	0.704470	−	1.22018i
$807$	−45.0000	+	25.9808i	−1.58408	+	0.914566i
$808$	6.00000	+	10.3923i	0.211079	+	0.365600i
$809$	33.0000			1.16022			0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000			1.16022			0.580109	+	0.814539i	$0.303010\pi$
$810$	−4.50000	−	7.79423i	−0.158114	−	0.273861i
$811$	47.0000			1.65039			0.825197	−	0.564846i	$-0.191064\pi$
$811$	47.0000			1.65039			0.825197	+	0.564846i	$0.191064\pi$
$812$	3.00000	+	5.19615i	0.105279	+	0.182349i
$813$	−30.0000	+	17.3205i	−1.05215	+	0.607457i
$814$	12.0000	−	20.7846i	0.420600	−	0.728500i
$815$	4.00000	−	6.92820i	0.140114	−	0.242684i
$816$	4.50000	+	2.59808i	0.157532	+	0.0909509i
$817$	−3.50000	−	6.06218i	−0.122449	−	0.212089i
$818$	19.0000			0.664319
$819$	−6.00000	+	10.3923i	−0.209657	+	0.363137i
$820$	−9.00000			−0.314294
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	0.577016	−	0.816733i	$-0.304217\pi$
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	−0.995819	+	0.0913446i	$0.970884\pi$
$822$		−	36.3731i		−	1.26866i
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	−0.272292	−	0.962215i	$-0.587782\pi$
$823$	20.0000	−	34.6410i	0.697156	−	1.20751i	0.969448	−	0.245295i	$-0.0788849\pi$
$824$	−2.00000	+	3.46410i	−0.0696733	+	0.120678i
$825$		−	5.19615i		−	0.180907i
$826$	4.50000	+	7.79423i	0.156575	+	0.271196i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	18.0000			0.625543
$829$	56.0000			1.94496			0.972480	−	0.232986i	$-0.0748495\pi$
$829$	56.0000			1.94496			0.972480	+	0.232986i	$0.0748495\pi$
$830$	6.00000	+	10.3923i	0.208263	+	0.360722i
$831$	−33.0000	−	19.0526i	−1.14476	−	0.660926i
$832$	2.00000	−	3.46410i	0.0693375	−	0.120096i
$833$	−1.50000	+	2.59808i	−0.0519719	+	0.0900180i
$834$	16.5000	−	9.52628i	0.571348	−	0.329868i
$835$	3.00000	+	5.19615i	0.103819	+	0.179820i
$836$	−21.0000			−0.726300
$837$	45.0000	+	25.9808i	1.55543	+	0.898027i
$838$	−24.0000			−0.829066
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	0.999785	+	0.0207443i	$0.00660359\pi$
$839$	15.0000	+	25.9808i	0.517858	+	0.896956i	−0.481927	+	0.876211i	$0.660063\pi$
$840$	−1.50000	+	0.866025i	−0.0517549	+	0.0298807i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	13.0000	−	22.5167i	0.448010	−	0.775975i
$843$	−9.00000	−	5.19615i	−0.309976	−	0.178965i
$844$	2.00000	+	3.46410i	0.0688428	+	0.119239i
$845$	−3.00000			−0.103203
$846$	−18.0000	−	31.1769i	−0.618853	−	1.07188i
$847$	−2.00000			−0.0687208
$848$	−3.00000	−	5.19615i	−0.103020	−	0.178437i
$849$		−	34.6410i		−	1.18888i
$850$	1.50000	−	2.59808i	0.0514496	−	0.0891133i
$851$	24.0000	−	41.5692i	0.822709	−	1.42497i
$852$		−	10.3923i		−	0.356034i
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	0.789386	−	0.613897i	$-0.210399\pi$
$853$	−4.00000	−	6.92820i	−0.136957	−	0.237217i	−0.926343	+	0.376680i	$0.877066\pi$
$854$	−14.0000			−0.479070
$855$	10.5000	+	18.1865i	0.359092	+	0.621966i
$856$	−3.00000			−0.102538
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$	18.0000	+	10.3923i	0.614510	+	0.354787i
$859$	27.5000	−	47.6314i	0.938288	−	1.62516i	0.169625	−	0.985509i	$-0.445745\pi$
$859$	27.5000	−	47.6314i	0.938288	−	1.62516i	0.768663	−	0.639654i	$-0.220922\pi$
$860$	−0.500000	+	0.866025i	−0.0170499	+	0.0295312i
$861$	−13.5000	+	7.79423i	−0.460079	+	0.265627i
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$	30.0000			1.02121			0.510606	−	0.859815i	$-0.329421\pi$
$863$	30.0000			1.02121			0.510606	+	0.859815i	$0.329421\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$	−6.00000			−0.204006
$866$	5.50000	+	9.52628i	0.186898	+	0.323716i
$867$	12.0000	−	6.92820i	0.407541	−	0.235294i
$868$	5.00000	−	8.66025i	0.169711	−	0.293948i
$869$	−3.00000	+	5.19615i	−0.101768	+	0.176267i
$870$	−9.00000	−	5.19615i	−0.305129	−	0.176166i
$871$	−14.0000	−	24.2487i	−0.474372	−	0.821636i
$872$	16.0000			0.541828
$873$	−33.0000			−1.11688
$874$	−42.0000			−1.42067
$875$	0.500000	+	0.866025i	0.0169031	+	0.0292770i
$876$			12.1244i			0.409644i
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	0.0421327	+	0.999112i	$0.486585\pi$
$877$	−25.0000	+	43.3013i	−0.844190	+	1.46218i	−0.886323	+	0.463068i	$0.846749\pi$
$878$	−5.00000	+	8.66025i	−0.168742	+	0.292269i
$879$		−	31.1769i		−	1.05157i
$880$	1.50000	+	2.59808i	0.0505650	+	0.0875811i
$881$	30.0000			1.01073			0.505363	−	0.862907i	$-0.331359\pi$
$881$	30.0000			1.01073			0.505363	+	0.862907i	$0.331359\pi$
$882$	−1.50000	+	2.59808i	−0.0505076	+	0.0874818i
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$	−13.5000	−	7.79423i	−0.453798	−	0.262000i
$886$	7.50000	−	12.9904i	0.251967	−	0.436420i
$887$	15.0000	−	25.9808i	0.503651	−	0.872349i	−0.496340	−	0.868128i	$-0.665323\pi$
$887$	15.0000	−	25.9808i	0.503651	−	0.872349i	0.999991	−	0.00422062i	$-0.00134347\pi$
$888$	12.0000	−	6.92820i	0.402694	−	0.232495i
$889$	5.00000	+	8.66025i	0.167695	+	0.290456i
$890$	6.00000			0.201120
$891$	−13.5000	+	23.3827i	−0.452267	+	0.783349i
$892$	−10.0000			−0.334825
$893$	42.0000	+	72.7461i	1.40548	+	2.43436i
$894$	18.0000	−	10.3923i	0.602010	−	0.347571i
$895$		0			0
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	36.0000	+	20.7846i	1.20201	+	0.693978i
$898$	−19.5000	−	33.7750i	−0.650723	−	1.12709i
$899$	60.0000			2.00111
$900$	1.50000	−	2.59808i	0.0500000	−	0.0866025i
$901$	18.0000			0.599667
$902$	13.5000	+	23.3827i	0.449501	+	0.778558i
$903$			1.73205i			0.0576390i
$904$	−3.00000	+	5.19615i	−0.0997785	+	0.172821i
$905$	10.0000	−	17.3205i	0.332411	−	0.575753i
$906$			24.2487i			0.805609i
$907$	3.50000	+	6.06218i	0.116216	+	0.201291i	0.918265	−	0.395966i	$-0.129590\pi$
$907$	3.50000	+	6.06218i	0.116216	+	0.201291i	−0.802049	+	0.597258i	$0.796257\pi$
$908$	−3.00000			−0.0995585
$909$	−36.0000			−1.19404
$910$	−4.00000			−0.132599
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	−0.969923	−	0.243410i	$-0.921734\pi$
$911$	−21.0000	−	36.3731i	−0.695761	−	1.20509i	0.274162	−	0.961683i	$-0.411599\pi$
$912$	−10.5000	−	6.06218i	−0.347690	−	0.200739i
$913$	18.0000	−	31.1769i	0.595713	−	1.03181i
$914$	5.50000	−	9.52628i	0.181924	−	0.315101i
$915$	21.0000	−	12.1244i	0.694239	−	0.400819i
$916$	−10.0000	−	17.3205i	−0.330409	−	0.572286i
$917$	12.0000			0.396275
$918$	−13.5000	+	7.79423i	−0.445566	+	0.257248i
$919$	−46.0000			−1.51740			−0.758700	−	0.651440i	$-0.774165\pi$
$919$	−46.0000			−1.51740			−0.758700	+	0.651440i	$0.774165\pi$
$920$	3.00000	+	5.19615i	0.0989071	+	0.171312i
$921$	−25.5000	+	14.7224i	−0.840254	+	0.485121i
$922$	−12.0000	+	20.7846i	−0.395199	+	0.684505i
$923$	12.0000	−	20.7846i	0.394985	−	0.684134i
$924$	4.50000	+	2.59808i	0.148039	+	0.0854704i
$925$	−4.00000	−	6.92820i	−0.131519	−	0.227798i
$926$	4.00000			0.131448
$927$	−6.00000	−	10.3923i	−0.197066	−	0.341328i
$928$	6.00000			0.196960
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	0.975050	−	0.221985i	$-0.0712536\pi$
$929$	9.00000	+	15.5885i	0.295280	+	0.511441i	−0.679770	+	0.733426i	$0.737920\pi$
$930$			17.3205i			0.567962i
$931$	3.50000	−	6.06218i	0.114708	−	0.198680i
$932$	−4.50000	+	7.79423i	−0.147402	+	0.255308i
$933$		−	31.1769i		−	1.02069i
$934$	−13.5000	−	23.3827i	−0.441733	−	0.765105i
$935$	−9.00000			−0.294331
$936$	6.00000	+	10.3923i	0.196116	+	0.339683i
$937$	38.0000			1.24141			0.620703	−	0.784046i	$-0.286847\pi$
$937$	38.0000			1.24141			0.620703	+	0.784046i	$0.286847\pi$
$938$	−3.50000	−	6.06218i	−0.114279	−	0.197937i
$939$	−1.50000	−	0.866025i	−0.0489506	−	0.0282617i
$940$	6.00000	−	10.3923i	0.195698	−	0.338960i
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	−0.601418	−	0.798935i	$-0.705397\pi$
$941$	12.0000	−	20.7846i	0.391189	−	0.677559i	0.992607	+	0.121376i	$0.0387306\pi$
$942$	−6.00000	+	3.46410i	−0.195491	+	0.112867i
$943$	27.0000	+	46.7654i	0.879241	+	1.52289i
$944$	9.00000			0.292925
$945$		−	5.19615i		−	0.169031i
$946$	3.00000			0.0975384
$947$	−19.5000	−	33.7750i	−0.633665	−	1.09754i	−0.986796	−	0.161966i	$-0.948217\pi$
$947$	−19.5000	−	33.7750i	−0.633665	−	1.09754i	0.353131	−	0.935574i	$-0.385117\pi$
$948$	−3.00000	+	1.73205i	−0.0974355	+	0.0562544i
$949$	−14.0000	+	24.2487i	−0.454459	+	0.787146i
$950$	−3.50000	+	6.06218i	−0.113555	+	0.196683i
$951$	36.0000	+	20.7846i	1.16738	+	0.673987i
$952$	1.50000	+	2.59808i	0.0486153	+	0.0842041i
$953$	39.0000			1.26333			0.631667	−	0.775240i	$-0.282371\pi$
$953$	39.0000			1.26333			0.631667	+	0.775240i	$0.282371\pi$
$954$	18.0000			0.582772
$955$	12.0000			0.388311
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$			31.1769i			1.00781i
$958$	15.0000	−	25.9808i	0.484628	−	0.839400i
$959$	10.5000	−	18.1865i	0.339063	−	0.587274i
$960$			1.73205i			0.0559017i
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	32.0000			1.03172
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$	5.00000			0.161039
$965$	−0.500000	−	0.866025i	−0.0160956	−	0.0278783i
$966$	9.00000	+	5.19615i	0.289570	+	0.167183i
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	−0.633165	−	0.774017i	$-0.718244\pi$
$967$	11.0000	−	19.0526i	0.353736	−	0.612689i	0.986901	+	0.161328i	$0.0515777\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$	31.5000	−	18.1865i	1.01193	−	0.584236i
$970$	−5.50000	−	9.52628i	−0.176594	−	0.305870i
$971$	−12.0000			−0.385098			−0.192549	−	0.981287i	$-0.561675\pi$
$971$	−12.0000			−0.385098			−0.192549	+	0.981287i	$0.561675\pi$
$972$	−13.5000	+	7.79423i	−0.433013	+	0.250000i
$973$	11.0000			0.352644
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$	6.00000	−	3.46410i	0.192154	−	0.110940i
$976$	−7.00000	+	12.1244i	−0.224065	+	0.388091i
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	−0.647737	−	0.761864i	$-0.724285\pi$
$977$	10.5000	−	18.1865i	0.335925	−	0.581839i	0.983662	+	0.180025i	$0.0576179\pi$
$978$	−12.0000	−	6.92820i	−0.383718	−	0.221540i
$979$	−9.00000	−	15.5885i	−0.287641	−	0.498209i
$980$	−1.00000			−0.0319438
$981$	−24.0000	+	41.5692i	−0.766261	+	1.32720i
$982$	9.00000			0.287202
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	0.996138	+	0.0878058i	$0.0279855\pi$
$983$	18.0000	+	31.1769i	0.574111	+	0.994389i	−0.422027	+	0.906583i	$0.638681\pi$
$984$			15.5885i			0.496942i
$985$	6.00000	−	10.3923i	0.191176	−	0.331126i
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$		−	20.7846i		−	0.661581i
$988$	−14.0000	−	24.2487i	−0.445399	−	0.771454i
$989$	6.00000			0.190789
$990$	−9.00000			−0.286039
$991$	−4.00000			−0.127064			−0.0635321	−	0.997980i	$-0.520237\pi$
$991$	−4.00000			−0.127064			−0.0635321	+	0.997980i	$0.520237\pi$
$992$	−5.00000	−	8.66025i	−0.158750	−	0.274963i
$993$	−42.0000	−	24.2487i	−1.33283	−	0.769510i
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$	10.0000	−	17.3205i	0.317021	−	0.549097i
$996$	18.0000	−	10.3923i	0.570352	−	0.329293i
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	0.934274	−	0.356555i	$-0.116049\pi$
$997$	5.00000	+	8.66025i	0.158352	+	0.274273i	−0.775923	+	0.630828i	$0.782715\pi$
$998$	−17.0000			−0.538126
$999$			41.5692i			1.31519i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	630.2.j.b.211.1	✓	2
3.2	odd	2		1890.2.j.a.631.1		2
9.2	odd	6		1890.2.j.a.1261.1		2
9.4	even	3		5670.2.a.e.1.1		1
9.5	odd	6		5670.2.a.q.1.1		1
9.7	even	3	inner	630.2.j.b.421.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.b.211.1	✓	2	1.1	even	1	trivial
630.2.j.b.421.1	yes	2	9.7	even	3	inner
1890.2.j.a.631.1		2	3.2	odd	2
1890.2.j.a.1261.1		2	9.2	odd	6
5670.2.a.e.1.1		1	9.4	even	3
5670.2.a.q.1.1		1	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{5} +(-1.50000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +1.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} -1.73205i q^{12} +(2.00000 - 3.46410i) q^{13} +(0.500000 - 0.866025i) q^{14} +1.73205i q^{15} +(-0.500000 - 0.866025i) q^{16} +3.00000 q^{17} +3.00000 q^{18} -7.00000 q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 + 0.866025i) q^{21} +(1.50000 - 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} +(1.50000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +4.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(3.00000 + 5.19615i) q^{29} +(-1.50000 + 0.866025i) q^{30} +(5.00000 - 8.66025i) q^{31} +(0.500000 - 0.866025i) q^{32} +(4.50000 + 2.59808i) q^{33} +(1.50000 + 2.59808i) q^{34} -1.00000 q^{35} +(1.50000 + 2.59808i) q^{36} +8.00000 q^{37} +(-3.50000 - 6.06218i) q^{38} +6.92820i q^{39} +(-0.500000 + 0.866025i) q^{40} +(-4.50000 + 7.79423i) q^{41} +1.73205i q^{42} +(0.500000 + 0.866025i) q^{43} +3.00000 q^{44} +(-1.50000 - 2.59808i) q^{45} +6.00000 q^{46} +(-6.00000 - 10.3923i) q^{47} +(1.50000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-4.50000 + 2.59808i) q^{51} +(2.00000 + 3.46410i) q^{52} +6.00000 q^{53} +(-4.50000 + 2.59808i) q^{54} -3.00000 q^{55} +(0.500000 + 0.866025i) q^{56} +(10.5000 - 6.06218i) q^{57} +(-3.00000 + 5.19615i) q^{58} +(-4.50000 + 7.79423i) q^{59} +(-1.50000 - 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} +10.0000 q^{62} -3.00000 q^{63} +1.00000 q^{64} +(-2.00000 - 3.46410i) q^{65} +5.19615i q^{66} +(3.50000 - 6.06218i) q^{67} +(-1.50000 + 2.59808i) q^{68} +10.3923i q^{69} +(-0.500000 - 0.866025i) q^{70} +6.00000 q^{71} +(-1.50000 + 2.59808i) q^{72} -7.00000 q^{73} +(4.00000 + 6.92820i) q^{74} +(1.50000 + 0.866025i) q^{75} +(3.50000 - 6.06218i) q^{76} +(-1.50000 + 2.59808i) q^{77} +(-6.00000 + 3.46410i) q^{78} +(-1.00000 - 1.73205i) q^{79} -1.00000 q^{80} +(-4.50000 - 7.79423i) q^{81} -9.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(-1.50000 + 0.866025i) q^{84} +(1.50000 - 2.59808i) q^{85} +(-0.500000 + 0.866025i) q^{86} +(-9.00000 - 5.19615i) q^{87} +(1.50000 + 2.59808i) q^{88} +6.00000 q^{89} +(1.50000 - 2.59808i) q^{90} -4.00000 q^{91} +(3.00000 + 5.19615i) q^{92} +17.3205i q^{93} +(6.00000 - 10.3923i) q^{94} +(-3.50000 + 6.06218i) q^{95} +1.73205i q^{96} +(-5.50000 - 9.52628i) q^{97} -1.00000 q^{98} -9.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 3 q^{3} - q^{4} + q^{5} - 3 q^{6} - q^{7} - 2 q^{8} + 3 q^{9} + 2 q^{10} - 3 q^{11} + 4 q^{13} + q^{14} - q^{16} + 6 q^{17} + 6 q^{18} - 14 q^{19} + q^{20} + 3 q^{21} + 3 q^{22} + 6 q^{23}+ \cdots - 18 q^{99}+O(q^{100}) \) 2 * q + q^2 - 3 * q^3 - q^4 + q^5 - 3 * q^6 - q^7 - 2 * q^8 + 3 * q^9 + 2 * q^10 - 3 * q^11 + 4 * q^13 + q^14 - q^16 + 6 * q^17 + 6 * q^18 - 14 * q^19 + q^20 + 3 * q^21 + 3 * q^22 + 6 * q^23 + 3 * q^24 - q^25 + 8 * q^26 + 2 * q^28 + 6 * q^29 - 3 * q^30 + 10 * q^31 + q^32 + 9 * q^33 + 3 * q^34 - 2 * q^35 + 3 * q^36 + 16 * q^37 - 7 * q^38 - q^40 - 9 * q^41 + q^43 + 6 * q^44 - 3 * q^45 + 12 * q^46 - 12 * q^47 + 3 * q^48 - q^49 + q^50 - 9 * q^51 + 4 * q^52 + 12 * q^53 - 9 * q^54 - 6 * q^55 + q^56 + 21 * q^57 - 6 * q^58 - 9 * q^59 - 3 * q^60 - 14 * q^61 + 20 * q^62 - 6 * q^63 + 2 * q^64 - 4 * q^65 + 7 * q^67 - 3 * q^68 - q^70 + 12 * q^71 - 3 * q^72 - 14 * q^73 + 8 * q^74 + 3 * q^75 + 7 * q^76 - 3 * q^77 - 12 * q^78 - 2 * q^79 - 2 * q^80 - 9 * q^81 - 18 * q^82 + 12 * q^83 - 3 * q^84 + 3 * q^85 - q^86 - 18 * q^87 + 3 * q^88 + 12 * q^89 + 3 * q^90 - 8 * q^91 + 6 * q^92 + 12 * q^94 - 7 * q^95 - 11 * q^97 - 2 * q^98 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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