LMFDB - Embedded newform 630.2.j.d.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [630,2,Mod(211,630)]

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

lf = mfeigenbasis(mf)

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")

//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);

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

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.d.421.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} -1.73205i 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} -3.00000 q^{9} -1.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(1.50000 + 0.866025i) q^{12} +(3.50000 - 6.06218i) q^{13} +(0.500000 - 0.866025i) q^{14} +(1.50000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +2.00000 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} +1.73205i q^{24} +(-0.500000 - 0.866025i) q^{25} +7.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +1.73205i q^{30} +(-1.00000 + 1.73205i) 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} +2.00000 q^{37} +(1.00000 + 1.73205i) q^{38} +(-10.5000 - 6.06218i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.50000 - 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +3.00000 q^{44} +(1.50000 - 2.59808i) q^{45} +6.00000 q^{46} +(4.50000 + 7.79423i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +5.19615i q^{51} +(3.50000 + 6.06218i) q^{52} -12.0000 q^{53} +(-4.50000 + 2.59808i) q^{54} +3.00000 q^{55} +(0.500000 + 0.866025i) q^{56} -3.46410i q^{57} +(3.00000 - 5.19615i) q^{58} +(-1.50000 + 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} -2.00000 q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(3.50000 + 6.06218i) q^{65} +(-4.50000 - 2.59808i) q^{66} +(5.00000 - 8.66025i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-9.00000 - 5.19615i) q^{69} +(0.500000 + 0.866025i) q^{70} +3.00000 q^{71} +3.00000 q^{72} +11.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +(-1.50000 + 2.59808i) q^{77} -12.1244i q^{78} +(6.50000 + 11.2583i) q^{79} +1.00000 q^{80} +9.00000 q^{81} +(7.50000 + 12.9904i) q^{83} -1.73205i q^{84} +(1.50000 - 2.59808i) q^{85} +(1.00000 - 1.73205i) q^{86} +(-9.00000 + 5.19615i) q^{87} +(1.50000 + 2.59808i) q^{88} -18.0000 q^{89} +3.00000 q^{90} -7.00000 q^{91} +(3.00000 + 5.19615i) q^{92} +(3.00000 + 1.73205i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-1.00000 + 1.73205i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(3.50000 + 6.06218i) q^{97} -1.00000 q^{98} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) $ 2 * q + q^2 - q^4 - q^5 + 3 * q^6 - q^7 - 2 * q^8 - 6 * q^9	$ 2 q + q^{2} - q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9} - 2 q^{10} - 3 q^{11} + 3 q^{12} + 7 q^{13} + q^{14} + 3 q^{15} - q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} - q^{20} - 3 q^{21} + 3 q^{22} + 6 q^{23} - q^{25} + 14 q^{26} + 2 q^{28} - 6 q^{29} - 2 q^{31} + q^{32} - 9 q^{33} - 3 q^{34} + 2 q^{35} + 3 q^{36} + 4 q^{37} + 2 q^{38} - 21 q^{39} + q^{40} - 3 q^{42} - 2 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} + 9 q^{47} - 3 q^{48} - q^{49} + q^{50} + 7 q^{52} - 24 q^{53} - 9 q^{54} + 6 q^{55} + q^{56} + 6 q^{58} - 3 q^{60} - 14 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} + 7 q^{65} - 9 q^{66} + 10 q^{67} + 3 q^{68} - 18 q^{69} + q^{70} + 6 q^{71} + 6 q^{72} + 22 q^{73} + 2 q^{74} - 3 q^{75} - 2 q^{76} - 3 q^{77} + 13 q^{79} + 2 q^{80} + 18 q^{81} + 15 q^{83} + 3 q^{85} + 2 q^{86} - 18 q^{87} + 3 q^{88} - 36 q^{89} + 6 q^{90} - 14 q^{91} + 6 q^{92} + 6 q^{93} - 9 q^{94} - 2 q^{95} - 3 q^{96} + 7 q^{97} - 2 q^{98} + 9 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^4 - q^5 + 3 * q^6 - q^7 - 2 * q^8 - 6 * q^9 - 2 * q^10 - 3 * q^11 + 3 * q^12 + 7 * q^13 + q^14 + 3 * q^15 - q^16 - 6 * q^17 - 3 * q^18 + 4 * q^19 - q^20 - 3 * q^21 + 3 * q^22 + 6 * q^23 - q^25 + 14 * q^26 + 2 * q^28 - 6 * q^29 - 2 * q^31 + q^32 - 9 * q^33 - 3 * q^34 + 2 * q^35 + 3 * q^36 + 4 * q^37 + 2 * q^38 - 21 * q^39 + q^40 - 3 * q^42 - 2 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 + 9 * q^47 - 3 * q^48 - q^49 + q^50 + 7 * q^52 - 24 * q^53 - 9 * q^54 + 6 * q^55 + q^56 + 6 * q^58 - 3 * q^60 - 14 * q^61 - 4 * q^62 + 3 * q^63 + 2 * q^64 + 7 * q^65 - 9 * q^66 + 10 * q^67 + 3 * q^68 - 18 * q^69 + q^70 + 6 * q^71 + 6 * q^72 + 22 * q^73 + 2 * q^74 - 3 * q^75 - 2 * q^76 - 3 * q^77 + 13 * q^79 + 2 * q^80 + 18 * q^81 + 15 * q^83 + 3 * q^85 + 2 * q^86 - 18 * q^87 + 3 * q^88 - 36 * q^89 + 6 * q^90 - 14 * q^91 + 6 * q^92 + 6 * q^93 - 9 * q^94 - 2 * q^95 - 3 * q^96 + 7 * q^97 - 2 * q^98 + 9 * q^99

Display 100 coefficients 10 coefficients

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
$3$		−	1.73205i		−	1.00000i
$3$		−	1.73205i		−	1.00000i
$4$	−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
$9$	−3.00000			−1.00000
$10$	−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	$0.982718\pi$
$12$	1.50000	+	0.866025i	0.433013	+	0.250000i
$13$	3.50000	−	6.06218i	0.970725	−	1.68135i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	3.50000	−	6.06218i	0.970725	−	1.68135i	0.693375	−	0.720577i	$-0.256123\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	1.50000	+	0.866025i	0.387298	+	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.00000			−0.727607			−0.363803	−	0.931476i	$-0.618522\pi$
$17$	−3.00000			−0.727607			−0.363803	+	0.931476i	$0.618522\pi$
$18$	−1.50000	−	2.59808i	−0.353553	−	0.612372i
$19$	2.00000			0.458831			0.229416	−	0.973329i	$-0.426318\pi$
$19$	2.00000			0.458831			0.229416	+	0.973329i	$0.426318\pi$
$20$	−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	$-0.0484560\pi$
$24$			1.73205i			0.353553i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	7.00000			1.37281
$27$			5.19615i			1.00000i
$28$	1.00000			0.188982
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$			1.73205i			0.316228i
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	−0.941745	−	0.336327i	$-0.890815\pi$
$31$	−1.00000	+	1.73205i	−0.179605	+	0.311086i	0.762140	+	0.647412i	$0.224149\pi$
$32$	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
$37$	2.00000			0.328798			0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000			0.328798			0.164399	+	0.986394i	$0.447432\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	−10.5000	−	6.06218i	−1.68135	−	0.970725i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$	−1.50000	−	0.866025i	−0.231455	−	0.133631i
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	3.00000			0.452267
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$	6.00000			0.884652
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$	−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
$51$			5.19615i			0.727607i
$52$	3.50000	+	6.06218i	0.485363	+	0.840673i
$53$	−12.0000			−1.64833			−0.824163	−	0.566352i	$-0.808354\pi$
$53$	−12.0000			−1.64833			−0.824163	+	0.566352i	$0.808354\pi$
$54$	−4.50000	+	2.59808i	−0.612372	+	0.353553i
$55$	3.00000			0.404520
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		−	3.46410i		−	0.458831i
$58$	3.00000	−	5.19615i	0.393919	−	0.682288i
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	−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	$-0.520392\pi$
$62$	−2.00000			−0.254000
$63$	1.50000	+	2.59808i	0.188982	+	0.327327i
$64$	1.00000			0.125000
$65$	3.50000	+	6.06218i	0.434122	+	0.751921i
$66$	−4.50000	−	2.59808i	−0.553912	−	0.319801i
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	−0.380251	−	0.924883i	$-0.624162\pi$
$67$	5.00000	−	8.66025i	0.610847	−	1.05802i	0.991098	−	0.133135i	$-0.0425044\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$	−9.00000	−	5.19615i	−1.08347	−	0.625543i
$70$	0.500000	+	0.866025i	0.0597614	+	0.103510i
$71$	3.00000			0.356034			0.178017	−	0.984027i	$-0.443032\pi$
$71$	3.00000			0.356034			0.178017	+	0.984027i	$0.443032\pi$
$72$	3.00000			0.353553
$73$	11.0000			1.28745			0.643726	−	0.765256i	$-0.277388\pi$
$73$	11.0000			1.28745			0.643726	+	0.765256i	$0.277388\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$	−1.50000	+	0.866025i	−0.173205	+	0.100000i
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−1.50000	+	2.59808i	−0.170941	+	0.296078i
$78$		−	12.1244i		−	1.37281i
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$	1.00000			0.111803
$81$	9.00000			1.00000
$82$		0			0
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	0.903263	+	0.429087i	$0.141165\pi$
$83$	7.50000	+	12.9904i	0.823232	+	1.42588i	−0.0800311	+	0.996792i	$0.525502\pi$
$84$		−	1.73205i		−	0.188982i
$85$	1.50000	−	2.59808i	0.162698	−	0.281801i
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	−9.00000	+	5.19615i	−0.964901	+	0.557086i
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−18.0000			−1.90800			−0.953998	−	0.299813i	$-0.903076\pi$
$89$	−18.0000			−1.90800			−0.953998	+	0.299813i	$0.903076\pi$
$90$	3.00000			0.316228
$91$	−7.00000			−0.733799
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$	3.00000	+	1.73205i	0.311086	+	0.179605i
$94$	−4.50000	+	7.79423i	−0.464140	+	0.803913i
$95$	−1.00000	+	1.73205i	−0.102598	+	0.177705i
$96$	−1.50000	−	0.866025i	−0.153093	−	0.0883883i
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	0.987181	−	0.159602i	$-0.0510211\pi$
$97$	3.50000	+	6.06218i	0.355371	+	0.615521i	−0.631810	+	0.775123i	$0.717688\pi$
$98$	−1.00000			−0.101015
$99$	4.50000	+	7.79423i	0.452267	+	0.783349i
$100$	1.00000			0.100000
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$	−4.50000	+	2.59808i	−0.445566	+	0.257248i
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	−0.992990	−	0.118199i	$-0.962288\pi$
$103$	−4.00000	+	6.92820i	−0.394132	+	0.682656i	0.598858	+	0.800855i	$0.295621\pi$
$104$	−3.50000	+	6.06218i	−0.343203	+	0.594445i
$105$		−	1.73205i		−	0.169031i
$106$	−6.00000	−	10.3923i	−0.582772	−	1.00939i
$107$	6.00000			0.580042			0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000			0.580042			0.290021	+	0.957020i	$0.406338\pi$
$108$	−4.50000	−	2.59808i	−0.433013	−	0.250000i
$109$	−1.00000			−0.0957826			−0.0478913	−	0.998853i	$-0.515250\pi$
$109$	−1.00000			−0.0957826			−0.0478913	+	0.998853i	$0.515250\pi$
$110$	1.50000	+	2.59808i	0.143019	+	0.247717i
$111$		−	3.46410i		−	0.328798i
$112$	−0.500000	+	0.866025i	−0.0472456	+	0.0818317i
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	−0.971930	−	0.235269i	$-0.924403\pi$
$113$	−3.00000	+	5.19615i	−0.282216	+	0.488813i	0.689714	+	0.724082i	$0.257736\pi$
$114$	3.00000	−	1.73205i	0.280976	−	0.162221i
$115$	3.00000	+	5.19615i	0.279751	+	0.484544i
$116$	6.00000			0.557086
$117$	−10.5000	+	18.1865i	−0.970725	+	1.68135i
$118$		0			0
$119$	1.50000	+	2.59808i	0.137505	+	0.238165i
$120$	−1.50000	−	0.866025i	−0.136931	−	0.0790569i
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	7.00000	−	12.1244i	0.633750	−	1.09769i
$123$		0			0
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	1.00000			0.0894427
$126$	−1.50000	+	2.59808i	−0.133631	+	0.231455i
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	−3.00000	+	1.73205i	−0.264135	+	0.152499i
$130$	−3.50000	+	6.06218i	−0.306970	+	0.531688i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$		−	5.19615i		−	0.452267i
$133$	−1.00000	−	1.73205i	−0.0867110	−	0.150188i
$134$	10.0000			0.863868
$135$	−4.50000	−	2.59808i	−0.387298	−	0.223607i
$136$	3.00000			0.257248
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$		−	10.3923i		−	0.884652i
$139$	11.0000	−	19.0526i	0.933008	−	1.61602i	0.154859	−	0.987937i	$-0.450508\pi$
$139$	11.0000	−	19.0526i	0.933008	−	1.61602i	0.778148	−	0.628080i	$-0.216159\pi$
$140$	−0.500000	+	0.866025i	−0.0422577	+	0.0731925i
$141$	13.5000	−	7.79423i	1.13691	−	0.656392i
$142$	1.50000	+	2.59808i	0.125877	+	0.218026i
$143$	−21.0000			−1.75611
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	6.00000			0.498273
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$	1.50000	+	0.866025i	0.123718	+	0.0714286i
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$	−1.50000	−	0.866025i	−0.122474	−	0.0707107i
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$	−2.00000			−0.162221
$153$	9.00000			0.727607
$154$	−3.00000			−0.241747
$155$	−1.00000	−	1.73205i	−0.0803219	−	0.139122i
$156$	10.5000	−	6.06218i	0.840673	−	0.485363i
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	−0.948373	−	0.317156i	$-0.897272\pi$
$157$	−2.50000	+	4.33013i	−0.199522	+	0.345582i	0.748852	+	0.662738i	$0.230606\pi$
$158$	−6.50000	+	11.2583i	−0.517112	+	0.895665i
$159$			20.7846i			1.64833i
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−6.00000			−0.472866
$162$	4.50000	+	7.79423i	0.353553	+	0.612372i
$163$	2.00000			0.156652			0.0783260	−	0.996928i	$-0.475042\pi$
$163$	2.00000			0.156652			0.0783260	+	0.996928i	$0.475042\pi$
$164$		0			0
$165$		−	5.19615i		−	0.404520i
$166$	−7.50000	+	12.9904i	−0.582113	+	1.00825i
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	−0.985933	−	0.167139i	$-0.946547\pi$
$167$	−4.50000	+	7.79423i	−0.348220	+	0.603136i	0.637713	+	0.770274i	$0.279881\pi$
$168$	1.50000	−	0.866025i	0.115728	−	0.0668153i
$169$	−18.0000	−	31.1769i	−1.38462	−	2.39822i
$170$	3.00000			0.230089
$171$	−6.00000			−0.458831
$172$	2.00000			0.152499
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$	−9.00000	−	5.19615i	−0.682288	−	0.393919i
$175$	−0.500000	+	0.866025i	−0.0377964	+	0.0654654i
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$		0			0
$178$	−9.00000	−	15.5885i	−0.674579	−	1.16840i
$179$	−9.00000			−0.672692			−0.336346	−	0.941739i	$-0.609191\pi$
$179$	−9.00000			−0.672692			−0.336346	+	0.941739i	$0.609191\pi$
$180$	1.50000	+	2.59808i	0.111803	+	0.193649i
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	−3.50000	−	6.06218i	−0.259437	−	0.449359i
$183$	−21.0000	+	12.1244i	−1.55236	+	0.896258i
$184$	−3.00000	+	5.19615i	−0.221163	+	0.383065i
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$			3.46410i			0.254000i
$187$	4.50000	+	7.79423i	0.329073	+	0.569970i
$188$	−9.00000			−0.656392
$189$	4.50000	−	2.59808i	0.327327	−	0.188982i
$190$	−2.00000			−0.145095
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		−	1.73205i		−	0.125000i
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	−3.50000	+	6.06218i	−0.251285	+	0.435239i
$195$	10.5000	−	6.06218i	0.751921	−	0.434122i
$196$	−0.500000	−	0.866025i	−0.0357143	−	0.0618590i
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$	−4.50000	+	7.79423i	−0.319801	+	0.553912i
$199$	−4.00000			−0.283552			−0.141776	−	0.989899i	$-0.545281\pi$
$199$	−4.00000			−0.283552			−0.141776	+	0.989899i	$0.545281\pi$
$200$	0.500000	+	0.866025i	0.0353553	+	0.0612372i
$201$	−15.0000	−	8.66025i	−1.05802	−	0.610847i
$202$	−9.00000	+	15.5885i	−0.633238	+	1.09680i
$203$	−3.00000	+	5.19615i	−0.210559	+	0.364698i
$204$	−4.50000	−	2.59808i	−0.315063	−	0.181902i
$205$		0			0
$206$	−8.00000			−0.557386
$207$	−9.00000	+	15.5885i	−0.625543	+	1.08347i
$208$	−7.00000			−0.485363
$209$	−3.00000	−	5.19615i	−0.207514	−	0.359425i
$210$	1.50000	−	0.866025i	0.103510	−	0.0597614i
$211$	−8.50000	+	14.7224i	−0.585164	+	1.01353i	0.409691	+	0.912224i	$0.365637\pi$
$211$	−8.50000	+	14.7224i	−0.585164	+	1.01353i	−0.994855	+	0.101310i	$0.967697\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$		−	5.19615i		−	0.356034i
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$	2.00000			0.136399
$216$		−	5.19615i		−	0.353553i
$217$	2.00000			0.135769
$218$	−0.500000	−	0.866025i	−0.0338643	−	0.0586546i
$219$		−	19.0526i		−	1.28745i
$220$	−1.50000	+	2.59808i	−0.101130	+	0.175162i
$221$	−10.5000	+	18.1865i	−0.706306	+	1.22336i
$222$	3.00000	−	1.73205i	0.201347	−	0.116248i
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	0.986267	+	0.165161i	$0.0528144\pi$
$223$	9.50000	+	16.4545i	0.636167	+	1.10187i	−0.350100	+	0.936713i	$0.613852\pi$
$224$	−1.00000			−0.0668153
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$	−6.00000			−0.399114
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	0.811943	−	0.583736i	$-0.198410\pi$
$227$	−1.50000	−	2.59808i	−0.0995585	−	0.172440i	−0.911502	+	0.411296i	$0.865076\pi$
$228$	3.00000	+	1.73205i	0.198680	+	0.114708i
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	−0.652183	−	0.758062i	$-0.726147\pi$
$229$	5.00000	−	8.66025i	0.330409	−	0.572286i	0.982592	+	0.185776i	$0.0594799\pi$
$230$	−3.00000	+	5.19615i	−0.197814	+	0.342624i
$231$	4.50000	+	2.59808i	0.296078	+	0.170941i
$232$	3.00000	+	5.19615i	0.196960	+	0.341144i
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$	−21.0000			−1.37281
$235$	−9.00000			−0.587095
$236$		0			0
$237$	19.5000	−	11.2583i	1.26666	−	0.731307i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	−0.157893	−	0.987456i	$-0.550470\pi$
$239$	12.0000	−	20.7846i	0.776215	−	1.34444i	0.934109	−	0.356988i	$-0.116196\pi$
$240$		−	1.73205i		−	0.111803i
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	0.707953	−	0.706260i	$-0.249619\pi$
$241$	−4.00000	−	6.92820i	−0.257663	−	0.446285i	−0.965615	+	0.259975i	$0.916286\pi$
$242$	2.00000			0.128565
$243$		−	15.5885i		−	1.00000i
$244$	14.0000			0.896258
$245$	−0.500000	−	0.866025i	−0.0319438	−	0.0553283i
$246$		0			0
$247$	7.00000	−	12.1244i	0.445399	−	0.771454i
$248$	1.00000	−	1.73205i	0.0635001	−	0.109985i
$249$	22.5000	−	12.9904i	1.42588	−	0.823232i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	−6.00000			−0.378717			−0.189358	−	0.981908i	$-0.560641\pi$
$251$	−6.00000			−0.378717			−0.189358	+	0.981908i	$0.560641\pi$
$252$	−3.00000			−0.188982
$253$	−18.0000			−1.13165
$254$	4.00000	+	6.92820i	0.250982	+	0.434714i
$255$	−4.50000	−	2.59808i	−0.281801	−	0.162698i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	−0.0460033	−	0.998941i	$-0.514648\pi$
$257$	13.5000	−	23.3827i	0.842107	−	1.45857i	0.888110	−	0.459631i	$-0.152018\pi$
$258$	−3.00000	−	1.73205i	−0.186772	−	0.107833i
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$	−7.00000			−0.434122
$261$	9.00000	+	15.5885i	0.557086	+	0.964901i
$262$		0			0
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$	4.50000	−	2.59808i	0.276956	−	0.159901i
$265$	6.00000	−	10.3923i	0.368577	−	0.638394i
$266$	1.00000	−	1.73205i	0.0613139	−	0.106199i
$267$			31.1769i			1.90800i
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	18.0000			1.09748			0.548740	−	0.835993i	$-0.315108\pi$
$269$	18.0000			1.09748			0.548740	+	0.835993i	$0.315108\pi$
$270$		−	5.19615i		−	0.316228i
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	1.50000	+	2.59808i	0.0909509	+	0.157532i
$273$			12.1244i			0.733799i
$274$	3.00000	−	5.19615i	0.181237	−	0.313911i
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$	9.00000	−	5.19615i	0.541736	−	0.312772i
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	0.834419	−	0.551131i	$-0.185804\pi$
$277$	−1.00000	−	1.73205i	−0.0600842	−	0.104069i	−0.894503	+	0.447062i	$0.852470\pi$
$278$	22.0000			1.31947
$279$	3.00000	−	5.19615i	0.179605	−	0.311086i
$280$	−1.00000			−0.0597614
$281$	4.50000	+	7.79423i	0.268447	+	0.464965i	0.968461	−	0.249165i	$-0.0801561\pi$
$281$	4.50000	+	7.79423i	0.268447	+	0.464965i	−0.700014	+	0.714130i	$0.746823\pi$
$282$	13.5000	+	7.79423i	0.803913	+	0.464140i
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	−0.850782	−	0.525519i	$-0.823871\pi$
$283$	0.500000	−	0.866025i	0.0297219	−	0.0514799i	0.880504	+	0.474039i	$0.157204\pi$
$284$	−1.50000	+	2.59808i	−0.0890086	+	0.154167i
$285$	3.00000	+	1.73205i	0.177705	+	0.102598i
$286$	−10.5000	−	18.1865i	−0.620878	−	1.07539i
$287$		0			0
$288$	−1.50000	+	2.59808i	−0.0883883	+	0.153093i
$289$	−8.00000			−0.470588
$290$	3.00000	+	5.19615i	0.176166	+	0.305129i
$291$	10.5000	−	6.06218i	0.615521	−	0.355371i
$292$	−5.50000	+	9.52628i	−0.321863	+	0.557483i
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	−0.940252	−	0.340480i	$-0.889411\pi$
$293$	−3.00000	+	5.19615i	−0.175262	+	0.303562i	0.764990	+	0.644042i	$0.222744\pi$
$294$			1.73205i			0.101015i
$295$		0			0
$296$	−2.00000			−0.116248
$297$	13.5000	−	7.79423i	0.783349	−	0.452267i
$298$	15.0000			0.868927
$299$	−21.0000	−	36.3731i	−1.21446	−	2.10351i
$300$		−	1.73205i		−	0.100000i
$301$	−1.00000	+	1.73205i	−0.0576390	+	0.0998337i
$302$	2.50000	−	4.33013i	0.143859	−	0.249171i
$303$	27.0000	−	15.5885i	1.55111	−	0.895533i
$304$	−1.00000	−	1.73205i	−0.0573539	−	0.0993399i
$305$	14.0000			0.801638
$306$	4.50000	+	7.79423i	0.257248	+	0.445566i
$307$	29.0000			1.65512			0.827559	−	0.561379i	$-0.189729\pi$
$307$	29.0000			1.65512			0.827559	+	0.561379i	$0.189729\pi$
$308$	−1.50000	−	2.59808i	−0.0854704	−	0.148039i
$309$	12.0000	+	6.92820i	0.682656	+	0.394132i
$310$	1.00000	−	1.73205i	0.0567962	−	0.0983739i
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	−0.294384	−	0.955687i	$-0.595114\pi$
$311$	12.0000	−	20.7846i	0.680458	−	1.17859i	0.974841	−	0.222900i	$-0.0715523\pi$
$312$	10.5000	+	6.06218i	0.594445	+	0.343203i
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	0.972028	−	0.234863i	$-0.0754642\pi$
$313$	5.00000	+	8.66025i	0.282617	+	0.489506i	−0.689412	+	0.724370i	$0.742131\pi$
$314$	−5.00000			−0.282166
$315$	−3.00000			−0.169031
$316$	−13.0000			−0.731307
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	−0.999980	−	0.00635137i	$-0.997978\pi$
$317$	−9.00000	−	15.5885i	−0.505490	−	0.875535i	0.494489	−	0.869184i	$-0.335355\pi$
$318$	−18.0000	+	10.3923i	−1.00939	+	0.582772i
$319$	−9.00000	+	15.5885i	−0.503903	+	0.872786i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		−	10.3923i		−	0.580042i
$322$	−3.00000	−	5.19615i	−0.167183	−	0.289570i
$323$	−6.00000			−0.333849
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−7.00000			−0.388290
$326$	1.00000	+	1.73205i	0.0553849	+	0.0959294i
$327$			1.73205i			0.0957826i
$328$		0			0
$329$	4.50000	−	7.79423i	0.248093	−	0.429710i
$330$	4.50000	−	2.59808i	0.247717	−	0.143019i
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	0.532096	−	0.846684i	$-0.321405\pi$
$331$	−8.50000	−	14.7224i	−0.467202	−	0.809218i	−0.999298	+	0.0374662i	$0.988071\pi$
$332$	−15.0000			−0.823232
$333$	−6.00000			−0.328798
$334$	−9.00000			−0.492458
$335$	5.00000	+	8.66025i	0.273179	+	0.473160i
$336$	1.50000	+	0.866025i	0.0818317	+	0.0472456i
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	−0.393730	−	0.919226i	$-0.628816\pi$
$337$	11.0000	−	19.0526i	0.599208	−	1.03786i	0.992938	−	0.118633i	$-0.0378512\pi$
$338$	18.0000	−	31.1769i	0.979071	−	1.69580i
$339$	9.00000	+	5.19615i	0.488813	+	0.282216i
$340$	1.50000	+	2.59808i	0.0813489	+	0.140900i
$341$	6.00000			0.324918
$342$	−3.00000	−	5.19615i	−0.162221	−	0.280976i
$343$	1.00000			0.0539949
$344$	1.00000	+	1.73205i	0.0539164	+	0.0933859i
$345$	9.00000	−	5.19615i	0.484544	−	0.279751i
$346$	−3.00000	+	5.19615i	−0.161281	+	0.279347i
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	−0.980921	−	0.194409i	$-0.937721\pi$
$347$	−6.00000	+	10.3923i	−0.322097	+	0.557888i	0.658824	+	0.752297i	$0.271054\pi$
$348$		−	10.3923i		−	0.557086i
$349$	14.0000	+	24.2487i	0.749403	+	1.29800i	0.948109	+	0.317945i	$0.102993\pi$
$349$	14.0000	+	24.2487i	0.749403	+	1.29800i	−0.198706	+	0.980059i	$0.563674\pi$
$350$	−1.00000			−0.0534522
$351$	31.5000	+	18.1865i	1.68135	+	0.970725i
$352$	−3.00000			−0.159901
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	0.520689	−	0.853746i	$-0.325675\pi$
$353$	−9.00000	−	15.5885i	−0.479022	−	0.829690i	−0.999711	+	0.0240566i	$0.992342\pi$
$354$		0			0
$355$	−1.50000	+	2.59808i	−0.0796117	+	0.137892i
$356$	9.00000	−	15.5885i	0.476999	−	0.826187i
$357$	4.50000	−	2.59808i	0.238165	−	0.137505i
$358$	−4.50000	−	7.79423i	−0.237832	−	0.411938i
$359$	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
$361$	−15.0000			−0.789474
$362$	1.00000	+	1.73205i	0.0525588	+	0.0910346i
$363$	−3.00000	−	1.73205i	−0.157459	−	0.0909091i
$364$	3.50000	−	6.06218i	0.183450	−	0.317744i
$365$	−5.50000	+	9.52628i	−0.287883	+	0.498628i
$366$	−21.0000	−	12.1244i	−1.09769	−	0.633750i
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	0.999989	−	0.00473247i	$-0.00150640\pi$
$367$	9.50000	+	16.4545i	0.495896	+	0.858917i	−0.504093	+	0.863649i	$0.668173\pi$
$368$	−6.00000			−0.312772
$369$		0			0
$370$	−2.00000			−0.103975
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$	−3.00000	+	1.73205i	−0.155543	+	0.0898027i
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	−4.50000	+	7.79423i	−0.232689	+	0.403030i
$375$		−	1.73205i		−	0.0894427i
$376$	−4.50000	−	7.79423i	−0.232070	−	0.401957i
$377$	−42.0000			−2.16311
$378$	4.50000	+	2.59808i	0.231455	+	0.133631i
$379$	29.0000			1.48963			0.744815	−	0.667271i	$-0.232538\pi$
$379$	29.0000			1.48963			0.744815	+	0.667271i	$0.232538\pi$
$380$	−1.00000	−	1.73205i	−0.0512989	−	0.0888523i
$381$		−	13.8564i		−	0.709885i
$382$		0			0
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	−0.282079	−	0.959391i	$-0.591024\pi$
$383$	13.5000	−	23.3827i	0.689818	−	1.19480i	0.971897	−	0.235408i	$-0.0756427\pi$
$384$	1.50000	−	0.866025i	0.0765466	−	0.0441942i
$385$	−1.50000	−	2.59808i	−0.0764471	−	0.132410i
$386$	10.0000			0.508987
$387$	3.00000	+	5.19615i	0.152499	+	0.264135i
$388$	−7.00000			−0.355371
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	0.610835	−	0.791758i	$-0.290834\pi$
$389$	−7.50000	−	12.9904i	−0.380265	−	0.658638i	−0.991100	+	0.133120i	$0.957501\pi$
$390$	10.5000	+	6.06218i	0.531688	+	0.306970i
$391$	−9.00000	+	15.5885i	−0.455150	+	0.788342i
$392$	0.500000	−	0.866025i	0.0252538	−	0.0437409i
$393$		0			0
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−13.0000			−0.654101
$396$	−9.00000			−0.452267
$397$	26.0000			1.30490			0.652451	−	0.757831i	$-0.273741\pi$
$397$	26.0000			1.30490			0.652451	+	0.757831i	$0.273741\pi$
$398$	−2.00000	−	3.46410i	−0.100251	−	0.173640i
$399$	−3.00000	+	1.73205i	−0.150188	+	0.0867110i
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		−	17.3205i		−	0.863868i
$403$	7.00000	+	12.1244i	0.348695	+	0.603957i
$404$	−18.0000			−0.895533
$405$	−4.50000	+	7.79423i	−0.223607	+	0.387298i
$406$	−6.00000			−0.297775
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		−	5.19615i		−	0.257248i
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	0.134107	+	0.990967i	$0.457183\pi$
$409$	−16.0000	+	27.7128i	−0.791149	+	1.37031i	−0.925256	+	0.379344i	$0.876150\pi$
$410$		0			0
$411$	−9.00000	+	5.19615i	−0.443937	+	0.256307i
$412$	−4.00000	−	6.92820i	−0.197066	−	0.341328i
$413$		0			0
$414$	−18.0000			−0.884652
$415$	−15.0000			−0.736321
$416$	−3.50000	−	6.06218i	−0.171602	−	0.297223i
$417$	−33.0000	−	19.0526i	−1.61602	−	0.933008i
$418$	3.00000	−	5.19615i	0.146735	−	0.254152i
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	−0.681426	−	0.731887i	$-0.738640\pi$
$419$	6.00000	−	10.3923i	0.293119	−	0.507697i	0.974546	+	0.224189i	$0.0719734\pi$
$420$	1.50000	+	0.866025i	0.0731925	+	0.0422577i
$421$	18.5000	+	32.0429i	0.901635	+	1.56168i	0.825372	+	0.564590i	$0.190966\pi$
$421$	18.5000	+	32.0429i	0.901635	+	1.56168i	0.0762630	+	0.997088i	$0.475701\pi$
$422$	−17.0000			−0.827547
$423$	−13.5000	−	23.3827i	−0.656392	−	1.13691i
$424$	12.0000			0.582772
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$	4.50000	−	2.59808i	0.218026	−	0.125877i
$427$	−7.00000	+	12.1244i	−0.338754	+	0.586739i
$428$	−3.00000	+	5.19615i	−0.145010	+	0.251166i
$429$			36.3731i			1.75611i
$430$	1.00000	+	1.73205i	0.0482243	+	0.0835269i
$431$	−33.0000			−1.58955			−0.794777	−	0.606902i	$-0.792412\pi$
$431$	−33.0000			−1.58955			−0.794777	+	0.606902i	$0.792412\pi$
$432$	4.50000	−	2.59808i	0.216506	−	0.125000i
$433$	14.0000			0.672797			0.336399	−	0.941720i	$-0.390791\pi$
$433$	14.0000			0.672797			0.336399	+	0.941720i	$0.390791\pi$
$434$	1.00000	+	1.73205i	0.0480015	+	0.0831411i
$435$		−	10.3923i		−	0.498273i
$436$	0.500000	−	0.866025i	0.0239457	−	0.0414751i
$437$	6.00000	−	10.3923i	0.287019	−	0.497131i
$438$	16.5000	−	9.52628i	0.788400	−	0.455183i
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	0.754642	−	0.656136i	$-0.227810\pi$
$439$	−4.00000	−	6.92820i	−0.190910	−	0.330665i	−0.945552	+	0.325471i	$0.894477\pi$
$440$	−3.00000			−0.143019
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$	−21.0000			−0.998868
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	0.569057	−	0.822298i	$-0.307309\pi$
$443$	−9.00000	−	15.5885i	−0.427603	−	0.740630i	−0.996660	+	0.0816684i	$0.973975\pi$
$444$	3.00000	+	1.73205i	0.142374	+	0.0821995i
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	−9.50000	+	16.4545i	−0.449838	+	0.779142i
$447$	−22.5000	−	12.9904i	−1.06421	−	0.614424i
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	−1.50000	+	2.59808i	−0.0707107	+	0.122474i
$451$		0			0
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	−7.50000	+	4.33013i	−0.352381	+	0.203447i
$454$	1.50000	−	2.59808i	0.0703985	−	0.121934i
$455$	3.50000	−	6.06218i	0.164083	−	0.284199i
$456$			3.46410i			0.162221i
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.841316	−	0.540544i	$-0.818219\pi$
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.0474665	−	0.998873i	$-0.515115\pi$
$458$	10.0000			0.467269
$459$		−	15.5885i		−	0.727607i
$460$	−6.00000			−0.279751
$461$	21.0000	+	36.3731i	0.978068	+	1.69406i	0.669417	+	0.742887i	$0.266544\pi$
$461$	21.0000	+	36.3731i	0.978068	+	1.69406i	0.308651	+	0.951175i	$0.400123\pi$
$462$			5.19615i			0.241747i
$463$	−16.0000	+	27.7128i	−0.743583	+	1.28792i	0.207271	+	0.978284i	$0.433542\pi$
$463$	−16.0000	+	27.7128i	−0.743583	+	1.28792i	−0.950854	+	0.309640i	$0.899791\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	−3.00000	+	1.73205i	−0.139122	+	0.0803219i
$466$		0			0
$467$	3.00000			0.138823			0.0694117	−	0.997588i	$-0.477888\pi$
$467$	3.00000			0.138823			0.0694117	+	0.997588i	$0.477888\pi$
$468$	−10.5000	−	18.1865i	−0.485363	−	0.840673i
$469$	−10.0000			−0.461757
$470$	−4.50000	−	7.79423i	−0.207570	−	0.359521i
$471$	7.50000	+	4.33013i	0.345582	+	0.199522i
$472$		0			0
$473$	−3.00000	+	5.19615i	−0.137940	+	0.238919i
$474$	19.5000	+	11.2583i	0.895665	+	0.517112i
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$	−3.00000			−0.137505
$477$	36.0000			1.64833
$478$	24.0000			1.09773
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	0.926388	−	0.376571i	$-0.122897\pi$
$479$	3.00000	+	5.19615i	0.137073	+	0.237418i	−0.789314	+	0.613990i	$0.789564\pi$
$480$	1.50000	−	0.866025i	0.0684653	−	0.0395285i
$481$	7.00000	−	12.1244i	0.319173	−	0.552823i
$482$	4.00000	−	6.92820i	0.182195	−	0.315571i
$483$			10.3923i			0.472866i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$	−7.00000			−0.317854
$486$	13.5000	−	7.79423i	0.612372	−	0.353553i
$487$	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
$489$		−	3.46410i		−	0.156652i
$490$	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	$0.101571\pi$
$492$		0			0
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$	14.0000			0.629890
$495$	−9.00000			−0.404520
$496$	2.00000			0.0898027
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$	22.5000	+	12.9904i	1.00825	+	0.582113i
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	−0.916542	−	0.399937i	$-0.869032\pi$
$499$	−2.50000	+	4.33013i	−0.111915	+	0.193843i	0.804627	+	0.593780i	$0.202365\pi$
$500$	−0.500000	+	0.866025i	−0.0223607	+	0.0387298i
$501$	13.5000	+	7.79423i	0.603136	+	0.348220i
$502$	−3.00000	−	5.19615i	−0.133897	−	0.231916i
$503$	−24.0000			−1.07011			−0.535054	−	0.844818i	$-0.679709\pi$
$503$	−24.0000			−1.07011			−0.535054	+	0.844818i	$0.679709\pi$
$504$	−1.50000	−	2.59808i	−0.0668153	−	0.115728i
$505$	−18.0000			−0.800989
$506$	−9.00000	−	15.5885i	−0.400099	−	0.692991i
$507$	−54.0000	+	31.1769i	−2.39822	+	1.38462i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		−	5.19615i		−	0.230089i
$511$	−5.50000	−	9.52628i	−0.243306	−	0.421418i
$512$	−1.00000			−0.0441942
$513$			10.3923i			0.458831i
$514$	27.0000			1.19092
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$		−	3.46410i		−	0.152499i
$517$	13.5000	−	23.3827i	0.593729	−	1.02837i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$	9.00000	−	5.19615i	0.395056	−	0.228086i
$520$	−3.50000	−	6.06218i	−0.153485	−	0.265844i
$521$	6.00000			0.262865			0.131432	−	0.991325i	$-0.458042\pi$
$521$	6.00000			0.262865			0.131432	+	0.991325i	$0.458042\pi$
$522$	−9.00000	+	15.5885i	−0.393919	+	0.682288i
$523$	−13.0000			−0.568450			−0.284225	−	0.958758i	$-0.591736\pi$
$523$	−13.0000			−0.568450			−0.284225	+	0.958758i	$0.591736\pi$
$524$		0			0
$525$	1.50000	+	0.866025i	0.0654654	+	0.0377964i
$526$	−6.00000	+	10.3923i	−0.261612	+	0.453126i
$527$	3.00000	−	5.19615i	0.130682	−	0.226348i
$528$	4.50000	+	2.59808i	0.195837	+	0.113067i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	12.0000			0.521247
$531$		0			0
$532$	2.00000			0.0867110
$533$		0			0
$534$	−27.0000	+	15.5885i	−1.16840	+	0.674579i
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$	−5.00000	+	8.66025i	−0.215967	+	0.374066i
$537$			15.5885i			0.672692i
$538$	9.00000	+	15.5885i	0.388018	+	0.672066i
$539$	3.00000			0.129219
$540$	4.50000	−	2.59808i	0.193649	−	0.111803i
$541$	−43.0000			−1.84871			−0.924357	−	0.381528i	$-0.875398\pi$
$541$	−43.0000			−1.84871			−0.924357	+	0.381528i	$0.875398\pi$
$542$	−14.0000	−	24.2487i	−0.601351	−	1.04157i
$543$		−	3.46410i		−	0.148659i
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	0.500000	−	0.866025i	0.0214176	−	0.0370965i
$546$	−10.5000	+	6.06218i	−0.449359	+	0.259437i
$547$	11.0000	+	19.0526i	0.470326	+	0.814629i	0.999424	−	0.0339321i	$-0.0108030\pi$
$547$	11.0000	+	19.0526i	0.470326	+	0.814629i	−0.529098	+	0.848561i	$0.677470\pi$
$548$	6.00000			0.256307
$549$	21.0000	+	36.3731i	0.896258	+	1.55236i
$550$	−3.00000			−0.127920
$551$	−6.00000	−	10.3923i	−0.255609	−	0.442727i
$552$	9.00000	+	5.19615i	0.383065	+	0.221163i
$553$	6.50000	−	11.2583i	0.276408	−	0.478753i
$554$	1.00000	−	1.73205i	0.0424859	−	0.0735878i
$555$	3.00000	+	1.73205i	0.127343	+	0.0735215i
$556$	11.0000	+	19.0526i	0.466504	+	0.808008i
$557$	−6.00000			−0.254228			−0.127114	−	0.991888i	$-0.540571\pi$
$557$	−6.00000			−0.254228			−0.127114	+	0.991888i	$0.540571\pi$
$558$	6.00000			0.254000
$559$	−14.0000			−0.592137
$560$	−0.500000	−	0.866025i	−0.0211289	−	0.0365963i
$561$	13.5000	−	7.79423i	0.569970	−	0.329073i
$562$	−4.50000	+	7.79423i	−0.189821	+	0.328780i
$563$	7.50000	−	12.9904i	0.316087	−	0.547479i	−0.663581	−	0.748105i	$-0.730964\pi$
$563$	7.50000	−	12.9904i	0.316087	−	0.547479i	0.979668	+	0.200625i	$0.0642974\pi$
$564$			15.5885i			0.656392i
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	1.00000			0.0420331
$567$	−4.50000	−	7.79423i	−0.188982	−	0.327327i
$568$	−3.00000			−0.125877
$569$	−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	$0.893744\pi$
$570$			3.46410i			0.145095i
$571$	−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	$0.200030\pi$
$572$	10.5000	−	18.1865i	0.439027	−	0.760417i
$573$		0			0
$574$		0			0
$575$	−6.00000			−0.250217
$576$	−3.00000			−0.125000
$577$	23.0000			0.957503			0.478751	−	0.877951i	$-0.341090\pi$
$577$	23.0000			0.957503			0.478751	+	0.877951i	$0.341090\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−15.0000	−	8.66025i	−0.623379	−	0.359908i
$580$	−3.00000	+	5.19615i	−0.124568	+	0.215758i
$581$	7.50000	−	12.9904i	0.311152	−	0.538932i
$582$	10.5000	+	6.06218i	0.435239	+	0.251285i
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$	−11.0000			−0.455183
$585$	−10.5000	−	18.1865i	−0.434122	−	0.751921i
$586$	−6.00000			−0.247858
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	0.962872	−	0.269957i	$-0.0870095\pi$
$587$	6.00000	+	10.3923i	0.247647	+	0.428936i	−0.715226	+	0.698893i	$0.753676\pi$
$588$	−1.50000	+	0.866025i	−0.0618590	+	0.0357143i
$589$	−2.00000	+	3.46410i	−0.0824086	+	0.142736i
$590$		0			0
$591$		−	31.1769i		−	1.28245i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−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
$596$	7.50000	+	12.9904i	0.307212	+	0.532107i
$597$			6.92820i			0.283552i
$598$	21.0000	−	36.3731i	0.858754	−	1.48741i
$599$	−19.5000	+	33.7750i	−0.796748	+	1.38001i	0.124975	+	0.992160i	$0.460115\pi$
$599$	−19.5000	+	33.7750i	−0.796748	+	1.38001i	−0.921723	+	0.387849i	$0.873218\pi$
$600$	1.50000	−	0.866025i	0.0612372	−	0.0353553i
$601$	2.00000	+	3.46410i	0.0815817	+	0.141304i	0.903929	−	0.427682i	$-0.140670\pi$
$601$	2.00000	+	3.46410i	0.0815817	+	0.141304i	−0.822348	+	0.568985i	$0.807336\pi$
$602$	−2.00000			−0.0815139
$603$	−15.0000	+	25.9808i	−0.610847	+	1.05802i
$604$	5.00000			0.203447
$605$	1.00000	+	1.73205i	0.0406558	+	0.0704179i
$606$	27.0000	+	15.5885i	1.09680	+	0.633238i
$607$	−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	$0.941678\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	9.00000	+	5.19615i	0.364698	+	0.210559i
$610$	7.00000	+	12.1244i	0.283422	+	0.490901i
$611$	63.0000			2.54871
$612$	−4.50000	+	7.79423i	−0.181902	+	0.315063i
$613$	−46.0000			−1.85792			−0.928961	−	0.370177i	$-0.879297\pi$
$613$	−46.0000			−1.85792			−0.928961	+	0.370177i	$0.879297\pi$
$614$	14.5000	+	25.1147i	0.585172	+	1.01355i
$615$		0			0
$616$	1.50000	−	2.59808i	0.0604367	−	0.104679i
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	−0.719605	−	0.694383i	$-0.755677\pi$
$617$	6.00000	−	10.3923i	0.241551	−	0.418378i	0.961156	+	0.276005i	$0.0890106\pi$
$618$			13.8564i			0.557386i
$619$	17.0000	+	29.4449i	0.683288	+	1.18349i	0.973972	+	0.226670i	$0.0727838\pi$
$619$	17.0000	+	29.4449i	0.683288	+	1.18349i	−0.290684	+	0.956819i	$0.593883\pi$
$620$	2.00000			0.0803219
$621$	27.0000	+	15.5885i	1.08347	+	0.625543i
$622$	24.0000			0.962312
$623$	9.00000	+	15.5885i	0.360577	+	0.624538i
$624$			12.1244i			0.485363i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−5.00000	+	8.66025i	−0.199840	+	0.346133i
$627$	−9.00000	+	5.19615i	−0.359425	+	0.207514i
$628$	−2.50000	−	4.33013i	−0.0997609	−	0.172791i
$629$	−6.00000			−0.239236
$630$	−1.50000	−	2.59808i	−0.0597614	−	0.103510i
$631$	−7.00000			−0.278666			−0.139333	−	0.990246i	$-0.544496\pi$
$631$	−7.00000			−0.278666			−0.139333	+	0.990246i	$0.544496\pi$
$632$	−6.50000	−	11.2583i	−0.258556	−	0.447832i
$633$	25.5000	+	14.7224i	1.01353	+	0.585164i
$634$	9.00000	−	15.5885i	0.357436	−	0.619097i
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$	−18.0000	−	10.3923i	−0.713746	−	0.412082i
$637$	3.50000	+	6.06218i	0.138675	+	0.240192i
$638$	−18.0000			−0.712627
$639$	−9.00000			−0.356034
$640$	−1.00000			−0.0395285
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	9.00000	−	5.19615i	0.355202	−	0.205076i
$643$	15.5000	−	26.8468i	0.611260	−	1.05873i	−0.379768	−	0.925082i	$-0.623996\pi$
$643$	15.5000	−	26.8468i	0.611260	−	1.05873i	0.991028	−	0.133652i	$-0.0426705\pi$
$644$	3.00000	−	5.19615i	0.118217	−	0.204757i
$645$		−	3.46410i		−	0.136399i
$646$	−3.00000	−	5.19615i	−0.118033	−	0.204440i
$647$	36.0000			1.41531			0.707653	−	0.706560i	$-0.249754\pi$
$647$	36.0000			1.41531			0.707653	+	0.706560i	$0.249754\pi$
$648$	−9.00000			−0.353553
$649$		0			0
$650$	−3.50000	−	6.06218i	−0.137281	−	0.237778i
$651$		−	3.46410i		−	0.135769i
$652$	−1.00000	+	1.73205i	−0.0391630	+	0.0678323i
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$	−1.50000	+	0.866025i	−0.0586546	+	0.0338643i
$655$		0			0
$656$		0			0
$657$	−33.0000			−1.28745
$658$	9.00000			0.350857
$659$	1.50000	+	2.59808i	0.0584317	+	0.101207i	0.893762	−	0.448542i	$-0.148057\pi$
$659$	1.50000	+	2.59808i	0.0584317	+	0.101207i	−0.835330	+	0.549749i	$0.814723\pi$
$660$	4.50000	+	2.59808i	0.175162	+	0.101130i
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	−0.969442	−	0.245319i	$-0.921107\pi$
$661$	−7.00000	+	12.1244i	−0.272268	+	0.471583i	0.697174	+	0.716902i	$0.254441\pi$
$662$	8.50000	−	14.7224i	0.330362	−	0.572204i
$663$	31.5000	+	18.1865i	1.22336	+	0.706306i
$664$	−7.50000	−	12.9904i	−0.291056	−	0.504125i
$665$	2.00000			0.0775567
$666$	−3.00000	−	5.19615i	−0.116248	−	0.201347i
$667$	−36.0000			−1.39393
$668$	−4.50000	−	7.79423i	−0.174110	−	0.301568i
$669$	28.5000	−	16.4545i	1.10187	−	0.636167i
$670$	−5.00000	+	8.66025i	−0.193167	+	0.334575i
$671$	−21.0000	+	36.3731i	−0.810696	+	1.40417i
$672$			1.73205i			0.0668153i
$673$	−4.00000	−	6.92820i	−0.154189	−	0.267063i	0.778575	−	0.627552i	$-0.215943\pi$
$673$	−4.00000	−	6.92820i	−0.154189	−	0.267063i	−0.932763	+	0.360489i	$0.882610\pi$
$674$	22.0000			0.847408
$675$	4.50000	−	2.59808i	0.173205	−	0.100000i
$676$	36.0000			1.38462
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$			10.3923i			0.399114i
$679$	3.50000	−	6.06218i	0.134318	−	0.232645i
$680$	−1.50000	+	2.59808i	−0.0575224	+	0.0996317i
$681$	−4.50000	+	2.59808i	−0.172440	+	0.0995585i
$682$	3.00000	+	5.19615i	0.114876	+	0.198971i
$683$	48.0000			1.83667			0.918334	−	0.395805i	$-0.129534\pi$
$683$	48.0000			1.83667			0.918334	+	0.395805i	$0.129534\pi$
$684$	3.00000	−	5.19615i	0.114708	−	0.198680i
$685$	6.00000			0.229248
$686$	0.500000	+	0.866025i	0.0190901	+	0.0330650i
$687$	−15.0000	−	8.66025i	−0.572286	−	0.330409i
$688$	−1.00000	+	1.73205i	−0.0381246	+	0.0660338i
$689$	−42.0000	+	72.7461i	−1.60007	+	2.77141i
$690$	9.00000	+	5.19615i	0.342624	+	0.197814i
$691$	−1.00000	−	1.73205i	−0.0380418	−	0.0658903i	0.846378	−	0.532583i	$-0.178779\pi$
$691$	−1.00000	−	1.73205i	−0.0380418	−	0.0658903i	−0.884419	+	0.466693i	$0.845445\pi$
$692$	−6.00000			−0.228086
$693$	4.50000	−	7.79423i	0.170941	−	0.296078i
$694$	−12.0000			−0.455514
$695$	11.0000	+	19.0526i	0.417254	+	0.722705i
$696$	9.00000	−	5.19615i	0.341144	−	0.196960i
$697$		0			0
$698$	−14.0000	+	24.2487i	−0.529908	+	0.917827i
$699$		0			0
$700$	−0.500000	−	0.866025i	−0.0188982	−	0.0327327i
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$			36.3731i			1.37281i
$703$	4.00000			0.150863
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$			15.5885i			0.587095i
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$	9.00000	−	15.5885i	0.338480	−	0.586264i
$708$		0			0
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	0.985773	+	0.168080i	$0.0537568\pi$
$709$	17.0000	+	29.4449i	0.638448	+	1.10583i	−0.347325	+	0.937745i	$0.612910\pi$
$710$	−3.00000			−0.112588
$711$	−19.5000	−	33.7750i	−0.731307	−	1.26666i
$712$	18.0000			0.674579
$713$	6.00000	+	10.3923i	0.224702	+	0.389195i
$714$	4.50000	+	2.59808i	0.168408	+	0.0972306i
$715$	10.5000	−	18.1865i	0.392678	−	0.680138i
$716$	4.50000	−	7.79423i	0.168173	−	0.291284i
$717$	−36.0000	−	20.7846i	−1.34444	−	0.776215i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	18.0000			0.671287			0.335643	−	0.941989i	$-0.391046\pi$
$719$	18.0000			0.671287			0.335643	+	0.941989i	$0.391046\pi$
$720$	−3.00000			−0.111803
$721$	8.00000			0.297936
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	−12.0000	+	6.92820i	−0.446285	+	0.257663i
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−3.00000	+	5.19615i	−0.111417	+	0.192980i
$726$		−	3.46410i		−	0.128565i
$727$	9.50000	+	16.4545i	0.352335	+	0.610263i	0.986658	−	0.162805i	$-0.0520543\pi$
$727$	9.50000	+	16.4545i	0.352335	+	0.610263i	−0.634323	+	0.773068i	$0.718721\pi$
$728$	7.00000			0.259437
$729$	−27.0000			−1.00000
$730$	−11.0000			−0.407128
$731$	3.00000	+	5.19615i	0.110959	+	0.192187i
$732$		−	24.2487i		−	0.896258i
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	−0.360061	−	0.932929i	$-0.617244\pi$
$733$	17.0000	−	29.4449i	0.627909	−	1.08757i	0.987971	−	0.154642i	$-0.0494225\pi$
$734$	−9.50000	+	16.4545i	−0.350651	+	0.607346i
$735$	−1.50000	+	0.866025i	−0.0553283	+	0.0319438i
$736$	−3.00000	−	5.19615i	−0.110581	−	0.191533i
$737$	−30.0000			−1.10506
$738$		0			0
$739$	44.0000			1.61857			0.809283	−	0.587419i	$-0.199856\pi$
$739$	44.0000			1.61857			0.809283	+	0.587419i	$0.199856\pi$
$740$	−1.00000	−	1.73205i	−0.0367607	−	0.0636715i
$741$	−21.0000	−	12.1244i	−0.771454	−	0.445399i
$742$	−6.00000	+	10.3923i	−0.220267	+	0.381514i
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	−0.320166	−	0.947361i	$-0.603739\pi$
$743$	18.0000	−	31.1769i	0.660356	−	1.14377i	0.980522	−	0.196409i	$-0.0629279\pi$
$744$	−3.00000	−	1.73205i	−0.109985	−	0.0635001i
$745$	7.50000	+	12.9904i	0.274779	+	0.475931i
$746$	4.00000			0.146450
$747$	−22.5000	−	38.9711i	−0.823232	−	1.42588i
$748$	−9.00000			−0.329073
$749$	−3.00000	−	5.19615i	−0.109618	−	0.189863i
$750$	1.50000	−	0.866025i	0.0547723	−	0.0316228i
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	−0.827225	−	0.561870i	$-0.810082\pi$
$751$	2.00000	−	3.46410i	0.0729810	−	0.126407i	0.900207	+	0.435463i	$0.143415\pi$
$752$	4.50000	−	7.79423i	0.164098	−	0.284226i
$753$			10.3923i			0.378717i
$754$	−21.0000	−	36.3731i	−0.764775	−	1.32463i
$755$	5.00000			0.181969
$756$			5.19615i			0.188982i
$757$	−46.0000			−1.67190			−0.835949	−	0.548807i	$-0.815082\pi$
$757$	−46.0000			−1.67190			−0.835949	+	0.548807i	$0.815082\pi$
$758$	14.5000	+	25.1147i	0.526664	+	0.912208i
$759$			31.1769i			1.13165i
$760$	1.00000	−	1.73205i	0.0362738	−	0.0628281i
$761$	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	$0.131982\pi$
$762$	12.0000	−	6.92820i	0.434714	−	0.250982i
$763$	0.500000	+	0.866025i	0.0181012	+	0.0313522i
$764$		0			0
$765$	−4.50000	+	7.79423i	−0.162698	+	0.281801i
$766$	27.0000			0.975550
$767$		0			0
$768$	1.50000	+	0.866025i	0.0541266	+	0.0312500i
$769$	−7.00000	+	12.1244i	−0.252426	+	0.437215i	−0.964193	−	0.265200i	$-0.914562\pi$
$769$	−7.00000	+	12.1244i	−0.252426	+	0.437215i	0.711767	+	0.702416i	$0.247895\pi$
$770$	1.50000	−	2.59808i	0.0540562	−	0.0936282i
$771$	−40.5000	−	23.3827i	−1.45857	−	0.842107i
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	21.0000			0.755318			0.377659	−	0.925945i	$-0.376729\pi$
$773$	21.0000			0.755318			0.377659	+	0.925945i	$0.376729\pi$
$774$	−3.00000	+	5.19615i	−0.107833	+	0.186772i
$775$	2.00000			0.0718421
$776$	−3.50000	−	6.06218i	−0.125643	−	0.217620i
$777$	−3.00000	+	1.73205i	−0.107624	+	0.0621370i
$778$	7.50000	−	12.9904i	0.268888	−	0.465728i
$779$		0			0
$780$			12.1244i			0.434122i
$781$	−4.50000	−	7.79423i	−0.161023	−	0.278899i
$782$	−18.0000			−0.643679
$783$	27.0000	−	15.5885i	0.964901	−	0.557086i
$784$	1.00000			0.0357143
$785$	−2.50000	−	4.33013i	−0.0892288	−	0.154549i
$786$		0			0
$787$	12.5000	−	21.6506i	0.445577	−	0.771762i	−0.552515	−	0.833503i	$-0.686332\pi$
$787$	12.5000	−	21.6506i	0.445577	−	0.771762i	0.998092	+	0.0617409i	$0.0196653\pi$
$788$	−9.00000	+	15.5885i	−0.320612	+	0.555316i
$789$	18.0000	−	10.3923i	0.640817	−	0.369976i
$790$	−6.50000	−	11.2583i	−0.231260	−	0.400553i
$791$	6.00000			0.213335
$792$	−4.50000	−	7.79423i	−0.159901	−	0.276956i
$793$	−98.0000			−3.48008
$794$	13.0000	+	22.5167i	0.461353	+	0.799086i
$795$	−18.0000	−	10.3923i	−0.638394	−	0.368577i
$796$	2.00000	−	3.46410i	0.0708881	−	0.122782i
$797$	−19.5000	+	33.7750i	−0.690725	+	1.19637i	0.280875	+	0.959744i	$0.409375\pi$
$797$	−19.5000	+	33.7750i	−0.690725	+	1.19637i	−0.971601	+	0.236627i	$0.923958\pi$
$798$	−3.00000	−	1.73205i	−0.106199	−	0.0613139i
$799$	−13.5000	−	23.3827i	−0.477596	−	0.827220i
$800$	−1.00000			−0.0353553
$801$	54.0000			1.90800
$802$	6.00000			0.211867
$803$	−16.5000	−	28.5788i	−0.582272	−	1.00853i
$804$	15.0000	−	8.66025i	0.529009	−	0.305424i
$805$	3.00000	−	5.19615i	0.105736	−	0.183140i
$806$	−7.00000	+	12.1244i	−0.246564	+	0.427062i
$807$		−	31.1769i		−	1.09748i
$808$	−9.00000	−	15.5885i	−0.316619	−	0.548400i
$809$	33.0000			1.16022			0.580109	−	0.814539i	$-0.303010\pi$
$809$	33.0000			1.16022			0.580109	+	0.814539i	$0.303010\pi$
$810$	−9.00000			−0.316228
$811$	20.0000			0.702295			0.351147	−	0.936320i	$-0.385792\pi$
$811$	20.0000			0.702295			0.351147	+	0.936320i	$0.385792\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$			48.4974i			1.70088i
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	−1.00000	+	1.73205i	−0.0350285	+	0.0606711i
$816$	4.50000	−	2.59808i	0.157532	−	0.0909509i
$817$	−2.00000	−	3.46410i	−0.0699711	−	0.121194i
$818$	−32.0000			−1.11885
$819$	21.0000			0.733799
$820$		0			0
$821$	16.5000	+	28.5788i	0.575854	+	0.997408i	0.995948	+	0.0899279i	$0.0286637\pi$
$821$	16.5000	+	28.5788i	0.575854	+	0.997408i	−0.420094	+	0.907480i	$0.638003\pi$
$822$	−9.00000	−	5.19615i	−0.313911	−	0.181237i
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	4.00000	−	6.92820i	0.139347	−	0.241355i
$825$	4.50000	+	2.59808i	0.156670	+	0.0904534i
$826$		0			0
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	−9.00000	−	15.5885i	−0.312772	−	0.541736i
$829$	−16.0000			−0.555703			−0.277851	−	0.960624i	$-0.589622\pi$
$829$	−16.0000			−0.555703			−0.277851	+	0.960624i	$0.589622\pi$
$830$	−7.50000	−	12.9904i	−0.260329	−	0.450903i
$831$	−3.00000	+	1.73205i	−0.104069	+	0.0600842i
$832$	3.50000	−	6.06218i	0.121341	−	0.210168i
$833$	1.50000	−	2.59808i	0.0519719	−	0.0900180i
$834$		−	38.1051i		−	1.31947i
$835$	−4.50000	−	7.79423i	−0.155729	−	0.269730i
$836$	6.00000			0.207514
$837$	−9.00000	−	5.19615i	−0.311086	−	0.179605i
$838$	12.0000			0.414533
$839$	−18.0000	−	31.1769i	−0.621429	−	1.07635i	−0.989220	−	0.146438i	$-0.953219\pi$
$839$	−18.0000	−	31.1769i	−0.621429	−	1.07635i	0.367791	−	0.929909i	$-0.380114\pi$
$840$			1.73205i			0.0597614i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−18.5000	+	32.0429i	−0.637552	+	1.10427i
$843$	13.5000	−	7.79423i	0.464965	−	0.268447i
$844$	−8.50000	−	14.7224i	−0.292582	−	0.506767i
$845$	36.0000			1.23844
$846$	13.5000	−	23.3827i	0.464140	−	0.803913i
$847$	−2.00000			−0.0687208
$848$	6.00000	+	10.3923i	0.206041	+	0.356873i
$849$	−1.50000	−	0.866025i	−0.0514799	−	0.0297219i
$850$	−1.50000	+	2.59808i	−0.0514496	+	0.0891133i
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$	4.50000	+	2.59808i	0.154167	+	0.0890086i
$853$	23.0000	+	39.8372i	0.787505	+	1.36400i	0.927491	+	0.373845i	$0.121961\pi$
$853$	23.0000	+	39.8372i	0.787505	+	1.36400i	−0.139986	+	0.990153i	$0.544706\pi$
$854$	−14.0000			−0.479070
$855$	3.00000	−	5.19615i	0.102598	−	0.177705i
$856$	−6.00000			−0.205076
$857$	22.5000	+	38.9711i	0.768585	+	1.33123i	0.938330	+	0.345741i	$0.112372\pi$
$857$	22.5000	+	38.9711i	0.768585	+	1.33123i	−0.169745	+	0.985488i	$0.554294\pi$
$858$	−31.5000	+	18.1865i	−1.07539	+	0.620878i
$859$	−25.0000	+	43.3013i	−0.852989	+	1.47742i	0.0255092	+	0.999675i	$0.491879\pi$
$859$	−25.0000	+	43.3013i	−0.852989	+	1.47742i	−0.878498	+	0.477746i	$0.841454\pi$
$860$	−1.00000	+	1.73205i	−0.0340997	+	0.0590624i
$861$		0			0
$862$	−16.5000	−	28.5788i	−0.561992	−	0.973399i
$863$	18.0000			0.612727			0.306364	−	0.951915i	$-0.400888\pi$
$863$	18.0000			0.612727			0.306364	+	0.951915i	$0.400888\pi$
$864$	4.50000	+	2.59808i	0.153093	+	0.0883883i
$865$	−6.00000			−0.204006
$866$	7.00000	+	12.1244i	0.237870	+	0.412002i
$867$			13.8564i			0.470588i
$868$	−1.00000	+	1.73205i	−0.0339422	+	0.0587896i
$869$	19.5000	−	33.7750i	0.661492	−	1.14574i
$870$	9.00000	−	5.19615i	0.305129	−	0.176166i
$871$	−35.0000	−	60.6218i	−1.18593	−	2.05409i
$872$	1.00000			0.0338643
$873$	−10.5000	−	18.1865i	−0.355371	−	0.615521i
$874$	12.0000			0.405906
$875$	−0.500000	−	0.866025i	−0.0169031	−	0.0292770i
$876$	16.5000	+	9.52628i	0.557483	+	0.321863i
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	4.00000	−	6.92820i	0.134993	−	0.233816i
$879$	9.00000	+	5.19615i	0.303562	+	0.175262i
$880$	−1.50000	−	2.59808i	−0.0505650	−	0.0875811i
$881$	−36.0000			−1.21287			−0.606435	−	0.795133i	$-0.707401\pi$
$881$	−36.0000			−1.21287			−0.606435	+	0.795133i	$0.707401\pi$
$882$	3.00000			0.101015
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$	−10.5000	−	18.1865i	−0.353153	−	0.611679i
$885$		0			0
$886$	9.00000	−	15.5885i	0.302361	−	0.523704i
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	−0.994077	−	0.108678i	$-0.965338\pi$
$887$	−12.0000	+	20.7846i	−0.402921	+	0.697879i	0.591156	+	0.806557i	$0.298672\pi$
$888$			3.46410i			0.116248i
$889$	−4.00000	−	6.92820i	−0.134156	−	0.232364i
$890$	18.0000			0.603361
$891$	−13.5000	−	23.3827i	−0.452267	−	0.783349i
$892$	−19.0000			−0.636167
$893$	9.00000	+	15.5885i	0.301174	+	0.521648i
$894$		−	25.9808i		−	0.868927i
$895$	4.50000	−	7.79423i	0.150418	−	0.260532i
$896$	0.500000	−	0.866025i	0.0167038	−	0.0289319i
$897$	−63.0000	+	36.3731i	−2.10351	+	1.21446i
$898$	−15.0000	−	25.9808i	−0.500556	−	0.866989i
$899$	12.0000			0.400222
$900$	−3.00000			−0.100000
$901$	36.0000			1.19933
$902$		0			0
$903$	3.00000	+	1.73205i	0.0998337	+	0.0576390i
$904$	3.00000	−	5.19615i	0.0997785	−	0.172821i
$905$	−1.00000	+	1.73205i	−0.0332411	+	0.0575753i
$906$	−7.50000	−	4.33013i	−0.249171	−	0.143859i
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	0.726092	−	0.687598i	$-0.241335\pi$
$907$	−7.00000	−	12.1244i	−0.232431	−	0.402583i	−0.958523	+	0.285015i	$0.908001\pi$
$908$	3.00000			0.0995585
$909$	−27.0000	−	46.7654i	−0.895533	−	1.55111i
$910$	7.00000			0.232048
$911$	1.50000	+	2.59808i	0.0496972	+	0.0860781i	0.889804	−	0.456343i	$-0.150841\pi$
$911$	1.50000	+	2.59808i	0.0496972	+	0.0860781i	−0.840107	+	0.542421i	$0.817508\pi$
$912$	−3.00000	+	1.73205i	−0.0993399	+	0.0573539i
$913$	22.5000	−	38.9711i	0.744641	−	1.28976i
$914$	19.0000	−	32.9090i	0.628464	−	1.08853i
$915$		−	24.2487i		−	0.801638i
$916$	5.00000	+	8.66025i	0.165205	+	0.286143i
$917$		0			0
$918$	13.5000	−	7.79423i	0.445566	−	0.257248i
$919$	−16.0000			−0.527791			−0.263896	−	0.964551i	$-0.585007\pi$
$919$	−16.0000			−0.527791			−0.263896	+	0.964551i	$0.585007\pi$
$920$	−3.00000	−	5.19615i	−0.0989071	−	0.171312i
$921$		−	50.2295i		−	1.65512i
$922$	−21.0000	+	36.3731i	−0.691598	+	1.19788i
$923$	10.5000	−	18.1865i	0.345612	−	0.598617i
$924$	−4.50000	+	2.59808i	−0.148039	+	0.0854704i
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$	−32.0000			−1.05159
$927$	12.0000	−	20.7846i	0.394132	−	0.682656i
$928$	−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	$0.737920\pi$
$930$	−3.00000	−	1.73205i	−0.0983739	−	0.0567962i
$931$	−1.00000	+	1.73205i	−0.0327737	+	0.0567657i
$932$		0			0
$933$	−36.0000	−	20.7846i	−1.17859	−	0.680458i
$934$	1.50000	+	2.59808i	0.0490815	+	0.0850117i
$935$	−9.00000			−0.294331
$936$	10.5000	−	18.1865i	0.343203	−	0.594445i
$937$	−43.0000			−1.40475			−0.702374	−	0.711808i	$-0.747877\pi$
$937$	−43.0000			−1.40475			−0.702374	+	0.711808i	$0.747877\pi$
$938$	−5.00000	−	8.66025i	−0.163256	−	0.282767i
$939$	15.0000	−	8.66025i	0.489506	−	0.282617i
$940$	4.50000	−	7.79423i	0.146774	−	0.254220i
$941$	−6.00000	+	10.3923i	−0.195594	+	0.338779i	−0.947095	−	0.320953i	$-0.895997\pi$
$941$	−6.00000	+	10.3923i	−0.195594	+	0.338779i	0.751501	+	0.659732i	$0.229330\pi$
$942$			8.66025i			0.282166i
$943$		0			0
$944$		0			0
$945$			5.19615i			0.169031i
$946$	−6.00000			−0.195077
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	0.751918	−	0.659256i	$-0.229129\pi$
$947$	−6.00000	−	10.3923i	−0.194974	−	0.337705i	−0.946892	+	0.321552i	$0.895796\pi$
$948$			22.5167i			0.731307i
$949$	38.5000	−	66.6840i	1.24976	−	2.16465i
$950$	1.00000	−	1.73205i	0.0324443	−	0.0561951i
$951$	−27.0000	+	15.5885i	−0.875535	+	0.505490i
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	6.00000			0.194359			0.0971795	−	0.995267i	$-0.469018\pi$
$953$	6.00000			0.194359			0.0971795	+	0.995267i	$0.469018\pi$
$954$	18.0000	+	31.1769i	0.582772	+	1.00939i
$955$		0			0
$956$	12.0000	+	20.7846i	0.388108	+	0.672222i
$957$	27.0000	+	15.5885i	0.872786	+	0.503903i
$958$	−3.00000	+	5.19615i	−0.0969256	+	0.167880i
$959$	−3.00000	+	5.19615i	−0.0968751	+	0.167793i
$960$	1.50000	+	0.866025i	0.0484123	+	0.0279508i
$961$	13.5000	+	23.3827i	0.435484	+	0.754280i
$962$	14.0000			0.451378
$963$	−18.0000			−0.580042
$964$	8.00000			0.257663
$965$	5.00000	+	8.66025i	0.160956	+	0.278783i
$966$	−9.00000	+	5.19615i	−0.289570	+	0.167183i
$967$	23.0000	−	39.8372i	0.739630	−	1.28108i	−0.213032	−	0.977045i	$-0.568334\pi$
$967$	23.0000	−	39.8372i	0.739630	−	1.28108i	0.952662	−	0.304032i	$-0.0983329\pi$
$968$	−1.00000	+	1.73205i	−0.0321412	+	0.0556702i
$969$			10.3923i			0.333849i
$970$	−3.50000	−	6.06218i	−0.112378	−	0.194645i
$971$	30.0000			0.962746			0.481373	−	0.876516i	$-0.340138\pi$
$971$	30.0000			0.962746			0.481373	+	0.876516i	$0.340138\pi$
$972$	13.5000	+	7.79423i	0.433013	+	0.250000i
$973$	−22.0000			−0.705288
$974$	1.00000	+	1.73205i	0.0320421	+	0.0554985i
$975$			12.1244i			0.388290i
$976$	−7.00000	+	12.1244i	−0.224065	+	0.388091i
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	−0.991618	−	0.129205i	$-0.958757\pi$
$977$	−12.0000	+	20.7846i	−0.383914	+	0.664959i	0.607704	+	0.794164i	$0.292091\pi$
$978$	3.00000	−	1.73205i	0.0959294	−	0.0553849i
$979$	27.0000	+	46.7654i	0.862924	+	1.49463i
$980$	1.00000			0.0319438
$981$	3.00000			0.0957826
$982$	9.00000			0.287202
$983$	13.5000	+	23.3827i	0.430583	+	0.745792i	0.996924	−	0.0783795i	$-0.0249746\pi$
$983$	13.5000	+	23.3827i	0.430583	+	0.745792i	−0.566340	+	0.824171i	$0.691641\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	−9.00000	+	15.5885i	−0.286618	+	0.496438i
$987$	−13.5000	−	7.79423i	−0.429710	−	0.248093i
$988$	7.00000	+	12.1244i	0.222700	+	0.385727i
$989$	−12.0000			−0.381578
$990$	−4.50000	−	7.79423i	−0.143019	−	0.247717i
$991$	41.0000			1.30241			0.651204	−	0.758903i	$-0.274264\pi$
$991$	41.0000			1.30241			0.651204	+	0.758903i	$0.274264\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$	−25.5000	+	14.7224i	−0.809218	+	0.467202i
$994$	1.50000	−	2.59808i	0.0475771	−	0.0824060i
$995$	2.00000	−	3.46410i	0.0634043	−	0.109819i
$996$			25.9808i			0.823232i
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	0.583363	−	0.812211i	$-0.301736\pi$
$997$	−13.0000	−	22.5167i	−0.411714	−	0.713110i	−0.995077	+	0.0991016i	$0.968403\pi$
$998$	−5.00000			−0.158272
$999$			10.3923i			0.328798i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
630.2.j.d.211.1	✓	2	1.1	even	1	trivial
630.2.j.d.421.1	yes	2	9.7	even	3	inner
1890.2.j.d.631.1		2	3.2	odd	2
1890.2.j.d.1261.1		2	9.2	odd	6
5670.2.a.i.1.1		1	9.4	even	3
5670.2.a.j.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 $\F_{q}$

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)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} -1.73205i q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(1.50000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} -1.00000 q^{8} -3.00000 q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} -1.73205i 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} -3.00000 q^{9} -1.00000 q^{10} +(-1.50000 - 2.59808i) q^{11} +(1.50000 + 0.866025i) q^{12} +(3.50000 - 6.06218i) q^{13} +(0.500000 - 0.866025i) q^{14} +(1.50000 + 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} -3.00000 q^{17} +(-1.50000 - 2.59808i) q^{18} +2.00000 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} +1.73205i q^{24} +(-0.500000 - 0.866025i) q^{25} +7.00000 q^{26} +5.19615i q^{27} +1.00000 q^{28} +(-3.00000 - 5.19615i) q^{29} +1.73205i q^{30} +(-1.00000 + 1.73205i) 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} +2.00000 q^{37} +(1.00000 + 1.73205i) q^{38} +(-10.5000 - 6.06218i) q^{39} +(0.500000 - 0.866025i) q^{40} +(-1.50000 - 0.866025i) q^{42} +(-1.00000 - 1.73205i) q^{43} +3.00000 q^{44} +(1.50000 - 2.59808i) q^{45} +6.00000 q^{46} +(4.50000 + 7.79423i) q^{47} +(-1.50000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +5.19615i q^{51} +(3.50000 + 6.06218i) q^{52} -12.0000 q^{53} +(-4.50000 + 2.59808i) q^{54} +3.00000 q^{55} +(0.500000 + 0.866025i) q^{56} -3.46410i q^{57} +(3.00000 - 5.19615i) q^{58} +(-1.50000 + 0.866025i) q^{60} +(-7.00000 - 12.1244i) q^{61} -2.00000 q^{62} +(1.50000 + 2.59808i) q^{63} +1.00000 q^{64} +(3.50000 + 6.06218i) q^{65} +(-4.50000 - 2.59808i) q^{66} +(5.00000 - 8.66025i) q^{67} +(1.50000 - 2.59808i) q^{68} +(-9.00000 - 5.19615i) q^{69} +(0.500000 + 0.866025i) q^{70} +3.00000 q^{71} +3.00000 q^{72} +11.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(-1.50000 + 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} +(-1.50000 + 2.59808i) q^{77} -12.1244i q^{78} +(6.50000 + 11.2583i) q^{79} +1.00000 q^{80} +9.00000 q^{81} +(7.50000 + 12.9904i) q^{83} -1.73205i q^{84} +(1.50000 - 2.59808i) q^{85} +(1.00000 - 1.73205i) q^{86} +(-9.00000 + 5.19615i) q^{87} +(1.50000 + 2.59808i) q^{88} -18.0000 q^{89} +3.00000 q^{90} -7.00000 q^{91} +(3.00000 + 5.19615i) q^{92} +(3.00000 + 1.73205i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(-1.00000 + 1.73205i) q^{95} +(-1.50000 - 0.866025i) q^{96} +(3.50000 + 6.06218i) q^{97} -1.00000 q^{98} +(4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9}+O(q^{10}) \) 2 * q + q^2 - q^4 - q^5 + 3 * q^6 - q^7 - 2 * q^8 - 6 * q^9	\( 2 q + q^{2} - q^{4} - q^{5} + 3 q^{6} - q^{7} - 2 q^{8} - 6 q^{9} - 2 q^{10} - 3 q^{11} + 3 q^{12} + 7 q^{13} + q^{14} + 3 q^{15} - q^{16} - 6 q^{17} - 3 q^{18} + 4 q^{19} - q^{20} - 3 q^{21} + 3 q^{22} + 6 q^{23} - q^{25} + 14 q^{26} + 2 q^{28} - 6 q^{29} - 2 q^{31} + q^{32} - 9 q^{33} - 3 q^{34} + 2 q^{35} + 3 q^{36} + 4 q^{37} + 2 q^{38} - 21 q^{39} + q^{40} - 3 q^{42} - 2 q^{43} + 6 q^{44} + 3 q^{45} + 12 q^{46} + 9 q^{47} - 3 q^{48} - q^{49} + q^{50} + 7 q^{52} - 24 q^{53} - 9 q^{54} + 6 q^{55} + q^{56} + 6 q^{58} - 3 q^{60} - 14 q^{61} - 4 q^{62} + 3 q^{63} + 2 q^{64} + 7 q^{65} - 9 q^{66} + 10 q^{67} + 3 q^{68} - 18 q^{69} + q^{70} + 6 q^{71} + 6 q^{72} + 22 q^{73} + 2 q^{74} - 3 q^{75} - 2 q^{76} - 3 q^{77} + 13 q^{79} + 2 q^{80} + 18 q^{81} + 15 q^{83} + 3 q^{85} + 2 q^{86} - 18 q^{87} + 3 q^{88} - 36 q^{89} + 6 q^{90} - 14 q^{91} + 6 q^{92} + 6 q^{93} - 9 q^{94} - 2 q^{95} - 3 q^{96} + 7 q^{97} - 2 q^{98} + 9 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^4 - q^5 + 3 * q^6 - q^7 - 2 * q^8 - 6 * q^9 - 2 * q^10 - 3 * q^11 + 3 * q^12 + 7 * q^13 + q^14 + 3 * q^15 - q^16 - 6 * q^17 - 3 * q^18 + 4 * q^19 - q^20 - 3 * q^21 + 3 * q^22 + 6 * q^23 - q^25 + 14 * q^26 + 2 * q^28 - 6 * q^29 - 2 * q^31 + q^32 - 9 * q^33 - 3 * q^34 + 2 * q^35 + 3 * q^36 + 4 * q^37 + 2 * q^38 - 21 * q^39 + q^40 - 3 * q^42 - 2 * q^43 + 6 * q^44 + 3 * q^45 + 12 * q^46 + 9 * q^47 - 3 * q^48 - q^49 + q^50 + 7 * q^52 - 24 * q^53 - 9 * q^54 + 6 * q^55 + q^56 + 6 * q^58 - 3 * q^60 - 14 * q^61 - 4 * q^62 + 3 * q^63 + 2 * q^64 + 7 * q^65 - 9 * q^66 + 10 * q^67 + 3 * q^68 - 18 * q^69 + q^70 + 6 * q^71 + 6 * q^72 + 22 * q^73 + 2 * q^74 - 3 * q^75 - 2 * q^76 - 3 * q^77 + 13 * q^79 + 2 * q^80 + 18 * q^81 + 15 * q^83 + 3 * q^85 + 2 * q^86 - 18 * q^87 + 3 * q^88 - 36 * q^89 + 6 * q^90 - 14 * q^91 + 6 * q^92 + 6 * q^93 - 9 * q^94 - 2 * q^95 - 3 * q^96 + 7 * q^97 - 2 * q^98 + 9 * q^99

Introduction

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