LMFDB - Embedded newform 930.2.i.d.811.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.i (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:	$7.42608738798$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			811.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	930.811
Dual form			930.2.i.d.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(-2.50000 + 4.33013i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 - 4.33013i) q^{21} +(0.500000 + 0.866025i) q^{22} +2.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(-2.50000 + 4.33013i) q^{28} -9.00000 q^{29} +1.00000 q^{30} +(-5.50000 - 0.866025i) q^{31} +1.00000 q^{32} -1.00000 q^{33} +(-2.00000 + 3.46410i) q^{34} +5.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{38} +4.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(-2.50000 - 4.33013i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} +2.00000 q^{46} +8.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.00000 - 3.46410i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} +1.00000 q^{54} +(0.500000 - 0.866025i) q^{55} +(-2.50000 + 4.33013i) q^{56} +(-2.00000 - 3.46410i) q^{57} -9.00000 q^{58} +(1.50000 - 2.59808i) q^{59} +1.00000 q^{60} +6.00000 q^{61} +(-5.50000 - 0.866025i) q^{62} +5.00000 q^{63} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} -1.00000 q^{66} +(5.00000 + 8.66025i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-1.00000 + 1.73205i) q^{69} +5.00000 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-2.00000 + 3.46410i) q^{76} -5.00000 q^{77} +4.00000 q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} +(4.50000 + 7.79423i) q^{83} +(-2.50000 - 4.33013i) q^{84} +4.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(4.50000 - 7.79423i) q^{87} +(0.500000 + 0.866025i) q^{88} -6.00000 q^{89} +(-0.500000 + 0.866025i) q^{90} +20.0000 q^{91} +2.00000 q^{92} +(3.50000 - 4.33013i) q^{93} +8.00000 q^{94} +4.00000 q^{95} +(-0.500000 + 0.866025i) q^{96} -1.00000 q^{97} +(-9.00000 - 15.5885i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - q^{9} - q^{10} + q^{11} - q^{12} - 4 q^{13} - 5 q^{14} + 2 q^{15} + 2 q^{16} - 4 q^{17} - q^{18} - 4 q^{19} - q^{20} - 5 q^{21} + q^{22} + 4 q^{23} - q^{24} - q^{25} - 4 q^{26} + 2 q^{27} - 5 q^{28} - 18 q^{29} + 2 q^{30} - 11 q^{31} + 2 q^{32} - 2 q^{33} - 4 q^{34} + 10 q^{35} - q^{36} - 2 q^{37} - 4 q^{38} + 8 q^{39} - q^{40} + 2 q^{41} - 5 q^{42} - 8 q^{43} + q^{44} - q^{45} + 4 q^{46} + 16 q^{47} - q^{48} - 18 q^{49} - q^{50} - 4 q^{51} - 4 q^{52} + 9 q^{53} + 2 q^{54} + q^{55} - 5 q^{56} - 4 q^{57} - 18 q^{58} + 3 q^{59} + 2 q^{60} + 12 q^{61} - 11 q^{62} + 10 q^{63} + 2 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} - 4 q^{68} - 2 q^{69} + 10 q^{70} + 4 q^{71} - q^{72} - 2 q^{73} - 2 q^{74} - q^{75} - 4 q^{76} - 10 q^{77} + 8 q^{78} + 12 q^{79} - q^{80} - q^{81} + 2 q^{82} + 9 q^{83} - 5 q^{84} + 8 q^{85} - 8 q^{86} + 9 q^{87} + q^{88} - 12 q^{89} - q^{90} + 40 q^{91} + 4 q^{92} + 7 q^{93} + 16 q^{94} + 8 q^{95} - q^{96} - 2 q^{97} - 18 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 + 2 * q^8 - q^9 - q^10 + q^11 - q^12 - 4 * q^13 - 5 * q^14 + 2 * q^15 + 2 * q^16 - 4 * q^17 - q^18 - 4 * q^19 - q^20 - 5 * q^21 + q^22 + 4 * q^23 - q^24 - q^25 - 4 * q^26 + 2 * q^27 - 5 * q^28 - 18 * q^29 + 2 * q^30 - 11 * q^31 + 2 * q^32 - 2 * q^33 - 4 * q^34 + 10 * q^35 - q^36 - 2 * q^37 - 4 * q^38 + 8 * q^39 - q^40 + 2 * q^41 - 5 * q^42 - 8 * q^43 + q^44 - q^45 + 4 * q^46 + 16 * q^47 - q^48 - 18 * q^49 - q^50 - 4 * q^51 - 4 * q^52 + 9 * q^53 + 2 * q^54 + q^55 - 5 * q^56 - 4 * q^57 - 18 * q^58 + 3 * q^59 + 2 * q^60 + 12 * q^61 - 11 * q^62 + 10 * q^63 + 2 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 - 4 * q^68 - 2 * q^69 + 10 * q^70 + 4 * q^71 - q^72 - 2 * q^73 - 2 * q^74 - q^75 - 4 * q^76 - 10 * q^77 + 8 * q^78 + 12 * q^79 - q^80 - q^81 + 2 * q^82 + 9 * q^83 - 5 * q^84 + 8 * q^85 - 8 * q^86 + 9 * q^87 + q^88 - 12 * q^89 - q^90 + 40 * q^91 + 4 * q^92 + 7 * q^93 + 16 * q^94 + 8 * q^95 - q^96 - 2 * q^97 - 18 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.188982	+	0.981981i	$0.560519\pi$
$7$	−2.50000	+	4.33013i	−0.944911	+	1.63663i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	−0.997927	−	0.0643593i	$-0.979500\pi$
$13$	−2.00000	−	3.46410i	−0.554700	−	0.960769i	0.443227	−	0.896410i	$-0.353834\pi$
$14$	−2.50000	+	4.33013i	−0.668153	+	1.15728i
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	−0.998899	−	0.0469020i	$-0.985065\pi$
$19$	−2.00000	+	3.46410i	−0.458831	+	0.794719i	0.540068	+	0.841621i	$0.318398\pi$
$20$	−0.500000	−	0.866025i	−0.111803	−	0.193649i
$21$	−2.50000	−	4.33013i	−0.545545	−	0.944911i
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	2.00000			0.417029			0.208514	−	0.978019i	$-0.433137\pi$
$23$	2.00000			0.417029			0.208514	+	0.978019i	$0.433137\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$	1.00000			0.192450
$28$	−2.50000	+	4.33013i	−0.472456	+	0.818317i
$29$	−9.00000			−1.67126			−0.835629	−	0.549294i	$-0.814897\pi$
$29$	−9.00000			−1.67126			−0.835629	+	0.549294i	$0.814897\pi$
$30$	1.00000			0.182574
$31$	−5.50000	−	0.866025i	−0.987829	−	0.155543i
$31$	−5.50000	−	0.866025i	−0.987829	−	0.155543i
$32$	1.00000			0.176777
$33$	−1.00000			−0.174078
$34$	−2.00000	+	3.46410i	−0.342997	+	0.594089i
$35$	5.00000			0.845154
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	−2.00000	+	3.46410i	−0.324443	+	0.561951i
$39$	4.00000			0.640513
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$	−2.50000	−	4.33013i	−0.385758	−	0.668153i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	2.00000			0.294884
$47$	8.00000			1.16692			0.583460	−	0.812142i	$-0.301699\pi$
$47$	8.00000			1.16692			0.583460	+	0.812142i	$0.301699\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−9.00000	−	15.5885i	−1.28571	−	2.22692i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$	−2.00000	−	3.46410i	−0.277350	−	0.480384i
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	0.989828	+	0.142269i	$0.0454398\pi$
$53$	4.50000	+	7.79423i	0.618123	+	1.07062i	−0.371706	+	0.928351i	$0.621227\pi$
$54$	1.00000			0.136083
$55$	0.500000	−	0.866025i	0.0674200	−	0.116775i
$56$	−2.50000	+	4.33013i	−0.334077	+	0.578638i
$57$	−2.00000	−	3.46410i	−0.264906	−	0.458831i
$58$	−9.00000			−1.18176
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	−0.751710	−	0.659494i	$-0.770771\pi$
$59$	1.50000	−	2.59808i	0.195283	−	0.338241i	0.946993	+	0.321253i	$0.104104\pi$
$60$	1.00000			0.129099
$61$	6.00000			0.768221			0.384111	−	0.923287i	$-0.374508\pi$
$61$	6.00000			0.768221			0.384111	+	0.923287i	$0.374508\pi$
$62$	−5.50000	−	0.866025i	−0.698501	−	0.109985i
$63$	5.00000			0.629941
$64$	1.00000			0.125000
$65$	−2.00000	+	3.46410i	−0.248069	+	0.429669i
$66$	−1.00000			−0.123091
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	0.991098	+	0.133135i	$0.0425044\pi$
$67$	5.00000	+	8.66025i	0.610847	+	1.05802i	−0.380251	+	0.924883i	$0.624162\pi$
$68$	−2.00000	+	3.46410i	−0.242536	+	0.420084i
$69$	−1.00000	+	1.73205i	−0.120386	+	0.208514i
$70$	5.00000			0.597614
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	0.959955	−	0.280155i	$-0.0903858\pi$
$71$	2.00000	+	3.46410i	0.237356	+	0.411113i	−0.722599	+	0.691268i	$0.757052\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	0.801553	−	0.597924i	$-0.204008\pi$
$73$	−1.00000	−	1.73205i	−0.117041	−	0.202721i	−0.918594	+	0.395203i	$0.870674\pi$
$74$	−1.00000	+	1.73205i	−0.116248	+	0.201347i
$75$	−0.500000	−	0.866025i	−0.0577350	−	0.100000i
$76$	−2.00000	+	3.46410i	−0.229416	+	0.397360i
$77$	−5.00000			−0.569803
$78$	4.00000			0.452911
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	−0.301401	−	0.953498i	$-0.597454\pi$
$79$	6.00000	−	10.3923i	0.675053	−	1.16923i	0.976453	−	0.215728i	$-0.0692125\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.00000	+	1.73205i	0.110432	+	0.191273i
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	−2.50000	−	4.33013i	−0.272772	−	0.472456i
$85$	4.00000			0.433861
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$	4.50000	−	7.79423i	0.482451	−	0.835629i
$88$	0.500000	+	0.866025i	0.0533002	+	0.0923186i
$89$	−6.00000			−0.635999			−0.317999	−	0.948091i	$-0.603011\pi$
$89$	−6.00000			−0.635999			−0.317999	+	0.948091i	$0.603011\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$	20.0000			2.09657
$92$	2.00000			0.208514
$93$	3.50000	−	4.33013i	0.362933	−	0.449013i
$94$	8.00000			0.825137
$95$	4.00000			0.410391
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	−9.00000	−	15.5885i	−0.909137	−	1.57467i
$99$	0.500000	−	0.866025i	0.0502519	−	0.0870388i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−5.00000			−0.497519			−0.248759	−	0.968565i	$-0.580023\pi$
$101$	−5.00000			−0.497519			−0.248759	+	0.968565i	$0.580023\pi$
$102$	−2.00000	−	3.46410i	−0.198030	−	0.342997i
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	−0.985329	−	0.170664i	$-0.945409\pi$
$103$	−6.50000	−	11.2583i	−0.640464	−	1.10932i	0.344865	−	0.938652i	$-0.387925\pi$
$104$	−2.00000	−	3.46410i	−0.196116	−	0.339683i
$105$	−2.50000	+	4.33013i	−0.243975	+	0.422577i
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	−5.50000	+	9.52628i	−0.531705	+	0.920940i	0.467610	+	0.883935i	$0.345115\pi$
$107$	−5.50000	+	9.52628i	−0.531705	+	0.920940i	−0.999315	+	0.0370053i	$0.988218\pi$
$108$	1.00000			0.0962250
$109$	8.00000			0.766261			0.383131	−	0.923694i	$-0.374846\pi$
$109$	8.00000			0.766261			0.383131	+	0.923694i	$0.374846\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	−1.00000	−	1.73205i	−0.0949158	−	0.164399i
$112$	−2.50000	+	4.33013i	−0.236228	+	0.409159i
$113$	8.00000	+	13.8564i	0.752577	+	1.30350i	0.946570	+	0.322498i	$0.104523\pi$
$113$	8.00000	+	13.8564i	0.752577	+	1.30350i	−0.193993	+	0.981003i	$0.562144\pi$
$114$	−2.00000	−	3.46410i	−0.187317	−	0.324443i
$115$	−1.00000	−	1.73205i	−0.0932505	−	0.161515i
$116$	−9.00000			−0.835629
$117$	−2.00000	+	3.46410i	−0.184900	+	0.320256i
$118$	1.50000	−	2.59808i	0.138086	−	0.239172i
$119$	−10.0000	−	17.3205i	−0.916698	−	1.58777i
$120$	1.00000			0.0912871
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	6.00000			0.543214
$123$	−2.00000			−0.180334
$124$	−5.50000	−	0.866025i	−0.493915	−	0.0777714i
$125$	1.00000			0.0894427
$126$	5.00000			0.445435
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	−0.419064	−	0.907957i	$-0.637642\pi$
$127$	6.50000	−	11.2583i	0.576782	−	0.999015i	0.995846	−	0.0910585i	$-0.0290250\pi$
$128$	1.00000			0.0883883
$129$	−4.00000	−	6.92820i	−0.352180	−	0.609994i
$130$	−2.00000	+	3.46410i	−0.175412	+	0.303822i
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	−0.940072	−	0.340977i	$-0.889242\pi$
$131$	−2.00000	+	3.46410i	−0.174741	+	0.302660i	0.765331	+	0.643637i	$0.222575\pi$
$132$	−1.00000			−0.0870388
$133$	−10.0000	−	17.3205i	−0.867110	−	1.50188i
$134$	5.00000	+	8.66025i	0.431934	+	0.748132i
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	0.643013	−	0.765855i	$-0.277684\pi$
$137$	−4.00000	−	6.92820i	−0.341743	−	0.591916i	−0.984757	+	0.173939i	$0.944351\pi$
$138$	−1.00000	+	1.73205i	−0.0851257	+	0.147442i
$139$	−20.0000			−1.69638			−0.848189	−	0.529694i	$-0.822307\pi$
$139$	−20.0000			−1.69638			−0.848189	+	0.529694i	$0.822307\pi$
$140$	5.00000			0.422577
$141$	−4.00000	+	6.92820i	−0.336861	+	0.583460i
$142$	2.00000	+	3.46410i	0.167836	+	0.290701i
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	4.50000	+	7.79423i	0.373705	+	0.647275i
$146$	−1.00000	−	1.73205i	−0.0827606	−	0.143346i
$147$	18.0000			1.48461
$148$	−1.00000	+	1.73205i	−0.0821995	+	0.142374i
$149$	5.50000	−	9.52628i	0.450578	−	0.780423i	−0.547844	−	0.836580i	$-0.684551\pi$
$149$	5.50000	−	9.52628i	0.450578	−	0.780423i	0.998422	+	0.0561570i	$0.0178847\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	13.0000			1.05792			0.528962	−	0.848645i	$-0.322581\pi$
$151$	13.0000			1.05792			0.528962	+	0.848645i	$0.322581\pi$
$152$	−2.00000	+	3.46410i	−0.162221	+	0.280976i
$153$	4.00000			0.323381
$154$	−5.00000			−0.402911
$155$	2.00000	+	5.19615i	0.160644	+	0.417365i
$156$	4.00000			0.320256
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	6.00000	−	10.3923i	0.477334	−	0.826767i
$159$	−9.00000			−0.713746
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	−5.00000	+	8.66025i	−0.394055	+	0.682524i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	10.0000			0.783260			0.391630	−	0.920123i	$-0.371911\pi$
$163$	10.0000			0.783260			0.391630	+	0.920123i	$0.371911\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	4.50000	+	7.79423i	0.349268	+	0.604949i
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	−0.457132	−	0.889399i	$-0.651123\pi$
$167$	7.00000	−	12.1244i	0.541676	−	0.938211i	0.998808	−	0.0488118i	$-0.0155435\pi$
$168$	−2.50000	−	4.33013i	−0.192879	−	0.334077i
$169$	−1.50000	+	2.59808i	−0.115385	+	0.199852i
$170$	4.00000			0.306786
$171$	4.00000			0.305888
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	0.917397	−	0.397974i	$-0.130287\pi$
$173$	1.50000	+	2.59808i	0.114043	+	0.197528i	−0.803354	+	0.595502i	$0.796953\pi$
$174$	4.50000	−	7.79423i	0.341144	−	0.590879i
$175$	−2.50000	−	4.33013i	−0.188982	−	0.327327i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	1.50000	+	2.59808i	0.112747	+	0.195283i
$178$	−6.00000			−0.449719
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	−0.983742	−	0.179585i	$-0.942524\pi$
$179$	−4.50000	+	7.79423i	−0.336346	+	0.582568i	0.647397	+	0.762153i	$0.275858\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	0.989819	−	0.142331i	$-0.0454598\pi$
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	−0.618172	+	0.786043i	$0.712126\pi$
$182$	20.0000			1.48250
$183$	−3.00000	+	5.19615i	−0.221766	+	0.384111i
$184$	2.00000			0.147442
$185$	2.00000			0.147043
$186$	3.50000	−	4.33013i	0.256632	−	0.317500i
$187$	−4.00000			−0.292509
$188$	8.00000			0.583460
$189$	−2.50000	+	4.33013i	−0.181848	+	0.314970i
$190$	4.00000			0.290191
$191$	13.0000	+	22.5167i	0.940647	+	1.62925i	0.764241	+	0.644931i	$0.223114\pi$
$191$	13.0000	+	22.5167i	0.940647	+	1.62925i	0.176406	+	0.984317i	$0.443553\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−12.5000	+	21.6506i	−0.899770	+	1.55845i	−0.0719816	+	0.997406i	$0.522932\pi$
$193$	−12.5000	+	21.6506i	−0.899770	+	1.55845i	−0.827788	+	0.561041i	$0.810401\pi$
$194$	−1.00000			−0.0717958
$195$	−2.00000	−	3.46410i	−0.143223	−	0.248069i
$196$	−9.00000	−	15.5885i	−0.642857	−	1.11346i
$197$	11.0000	+	19.0526i	0.783718	+	1.35744i	0.929762	+	0.368161i	$0.120012\pi$
$197$	11.0000	+	19.0526i	0.783718	+	1.35744i	−0.146045	+	0.989278i	$0.546654\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$	−0.500000	−	0.866025i	−0.0354441	−	0.0613909i	0.847759	−	0.530381i	$-0.177951\pi$
$199$	−0.500000	−	0.866025i	−0.0354441	−	0.0613909i	−0.883203	+	0.468990i	$0.844618\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−10.0000			−0.705346
$202$	−5.00000			−0.351799
$203$	22.5000	−	38.9711i	1.57919	−	2.73524i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	−1.00000	−	1.73205i	−0.0695048	−	0.120386i
$208$	−2.00000	−	3.46410i	−0.138675	−	0.240192i
$209$	−4.00000			−0.276686
$210$	−2.50000	+	4.33013i	−0.172516	+	0.298807i
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	4.50000	+	7.79423i	0.309061	+	0.535310i
$213$	−4.00000			−0.274075
$214$	−5.50000	+	9.52628i	−0.375972	+	0.651203i
$215$	8.00000			0.545595
$216$	1.00000			0.0680414
$217$	17.5000	−	21.6506i	1.18798	−	1.46974i
$218$	8.00000			0.541828
$219$	2.00000			0.135147
$220$	0.500000	−	0.866025i	0.0337100	−	0.0583874i
$221$	16.0000			1.07628
$222$	−1.00000	−	1.73205i	−0.0671156	−	0.116248i
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	−0.976440	−	0.215788i	$-0.930768\pi$
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	0.675098	+	0.737728i	$0.264101\pi$
$224$	−2.50000	+	4.33013i	−0.167038	+	0.289319i
$225$	1.00000			0.0666667
$226$	8.00000	+	13.8564i	0.532152	+	0.921714i
$227$	6.50000	+	11.2583i	0.431420	+	0.747242i	0.996996	−	0.0774548i	$-0.0246793\pi$
$227$	6.50000	+	11.2583i	0.431420	+	0.747242i	−0.565576	+	0.824696i	$0.691346\pi$
$228$	−2.00000	−	3.46410i	−0.132453	−	0.229416i
$229$	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	$0.0594799\pi$
$230$	−1.00000	−	1.73205i	−0.0659380	−	0.114208i
$231$	2.50000	−	4.33013i	0.164488	−	0.284901i
$232$	−9.00000			−0.590879
$233$	10.0000			0.655122			0.327561	−	0.944830i	$-0.393773\pi$
$233$	10.0000			0.655122			0.327561	+	0.944830i	$0.393773\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$	−4.00000	−	6.92820i	−0.260931	−	0.451946i
$236$	1.50000	−	2.59808i	0.0976417	−	0.169120i
$237$	6.00000	+	10.3923i	0.389742	+	0.675053i
$238$	−10.0000	−	17.3205i	−0.648204	−	1.12272i
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	0.992195	−	0.124696i	$-0.0397955\pi$
$239$	6.00000	+	10.3923i	0.388108	+	0.672222i	−0.604087	+	0.796918i	$0.706462\pi$
$240$	1.00000			0.0645497
$241$	8.50000	−	14.7224i	0.547533	−	0.948355i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	8.50000	−	14.7224i	0.547533	−	0.948355i	0.998443	−	0.0557856i	$-0.0177663\pi$
$242$	5.00000	−	8.66025i	0.321412	−	0.556702i
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	6.00000			0.384111
$245$	−9.00000	+	15.5885i	−0.574989	+	0.995910i
$246$	−2.00000			−0.127515
$247$	16.0000			1.01806
$248$	−5.50000	−	0.866025i	−0.349250	−	0.0549927i
$249$	−9.00000			−0.570352
$250$	1.00000			0.0632456
$251$	−4.00000	+	6.92820i	−0.252478	+	0.437304i	−0.964207	−	0.265149i	$-0.914579\pi$
$251$	−4.00000	+	6.92820i	−0.252478	+	0.437304i	0.711730	+	0.702454i	$0.247912\pi$
$252$	5.00000			0.314970
$253$	1.00000	+	1.73205i	0.0628695	+	0.108893i
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$	−2.00000	+	3.46410i	−0.125245	+	0.216930i
$256$	1.00000			0.0625000
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	−0.997374	−	0.0724199i	$-0.976928\pi$
$257$	−9.00000	−	15.5885i	−0.561405	−	0.972381i	0.435970	−	0.899961i	$-0.356405\pi$
$258$	−4.00000	−	6.92820i	−0.249029	−	0.431331i
$259$	−5.00000	−	8.66025i	−0.310685	−	0.538122i
$260$	−2.00000	+	3.46410i	−0.124035	+	0.214834i
$261$	4.50000	+	7.79423i	0.278543	+	0.482451i
$262$	−2.00000	+	3.46410i	−0.123560	+	0.214013i
$263$	−26.0000			−1.60323			−0.801614	−	0.597841i	$-0.796025\pi$
$263$	−26.0000			−1.60323			−0.801614	+	0.597841i	$0.796025\pi$
$264$	−1.00000			−0.0615457
$265$	4.50000	−	7.79423i	0.276433	−	0.478796i
$266$	−10.0000	−	17.3205i	−0.613139	−	1.06199i
$267$	3.00000	−	5.19615i	0.183597	−	0.317999i
$268$	5.00000	+	8.66025i	0.305424	+	0.529009i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−3.00000			−0.182237			−0.0911185	−	0.995840i	$-0.529044\pi$
$271$	−3.00000			−0.182237			−0.0911185	+	0.995840i	$0.529044\pi$
$272$	−2.00000	+	3.46410i	−0.121268	+	0.210042i
$273$	−10.0000	+	17.3205i	−0.605228	+	1.04828i
$274$	−4.00000	−	6.92820i	−0.241649	−	0.418548i
$275$	−1.00000			−0.0603023
$276$	−1.00000	+	1.73205i	−0.0601929	+	0.104257i
$277$	−12.0000			−0.721010			−0.360505	−	0.932757i	$-0.617396\pi$
$277$	−12.0000			−0.721010			−0.360505	+	0.932757i	$0.617396\pi$
$278$	−20.0000			−1.19952
$279$	2.00000	+	5.19615i	0.119737	+	0.311086i
$280$	5.00000			0.298807
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	−4.00000	+	6.92820i	−0.238197	+	0.412568i
$283$	−24.0000			−1.42665			−0.713326	−	0.700832i	$-0.752812\pi$
$283$	−24.0000			−1.42665			−0.713326	+	0.700832i	$0.752812\pi$
$284$	2.00000	+	3.46410i	0.118678	+	0.205557i
$285$	−2.00000	+	3.46410i	−0.118470	+	0.205196i
$286$	2.00000	−	3.46410i	0.118262	−	0.204837i
$287$	−10.0000			−0.590281
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	4.50000	+	7.79423i	0.264249	+	0.457693i
$291$	0.500000	−	0.866025i	0.0293105	−	0.0507673i
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−15.5000	+	26.8468i	−0.905520	+	1.56841i	−0.0853015	+	0.996355i	$0.527185\pi$
$293$	−15.5000	+	26.8468i	−0.905520	+	1.56841i	−0.820218	+	0.572051i	$0.806148\pi$
$294$	18.0000			1.04978
$295$	−3.00000			−0.174667
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	0.500000	+	0.866025i	0.0290129	+	0.0502519i
$298$	5.50000	−	9.52628i	0.318606	−	0.551843i
$299$	−4.00000	−	6.92820i	−0.231326	−	0.400668i
$300$	−0.500000	−	0.866025i	−0.0288675	−	0.0500000i
$301$	−20.0000	−	34.6410i	−1.15278	−	1.99667i
$302$	13.0000			0.748066
$303$	2.50000	−	4.33013i	0.143621	−	0.248759i
$304$	−2.00000	+	3.46410i	−0.114708	+	0.198680i
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$	4.00000			0.228665
$307$	2.00000	−	3.46410i	0.114146	−	0.197707i	−0.803292	−	0.595585i	$-0.796920\pi$
$307$	2.00000	−	3.46410i	0.114146	−	0.197707i	0.917438	+	0.397879i	$0.130253\pi$
$308$	−5.00000			−0.284901
$309$	13.0000			0.739544
$310$	2.00000	+	5.19615i	0.113592	+	0.295122i
$311$	−16.0000			−0.907277			−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000			−0.907277			−0.453638	+	0.891186i	$0.649874\pi$
$312$	4.00000			0.226455
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	−0.879810	−	0.475325i	$-0.842331\pi$
$313$	−0.500000	+	0.866025i	−0.0282617	+	0.0489506i	0.851549	+	0.524276i	$0.175664\pi$
$314$	14.0000			0.790066
$315$	−2.50000	−	4.33013i	−0.140859	−	0.243975i
$316$	6.00000	−	10.3923i	0.337526	−	0.584613i
$317$	−11.5000	+	19.9186i	−0.645904	+	1.11874i	0.338188	+	0.941079i	$0.390186\pi$
$317$	−11.5000	+	19.9186i	−0.645904	+	1.11874i	−0.984092	+	0.177660i	$0.943147\pi$
$318$	−9.00000			−0.504695
$319$	−4.50000	−	7.79423i	−0.251952	−	0.436393i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−5.50000	−	9.52628i	−0.306980	−	0.531705i
$322$	−5.00000	+	8.66025i	−0.278639	+	0.482617i
$323$	−8.00000	−	13.8564i	−0.445132	−	0.770991i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	4.00000			0.221880
$326$	10.0000			0.553849
$327$	−4.00000	+	6.92820i	−0.221201	+	0.383131i
$328$	1.00000	+	1.73205i	0.0552158	+	0.0956365i
$329$	−20.0000	+	34.6410i	−1.10264	+	1.90982i
$330$	0.500000	+	0.866025i	0.0275241	+	0.0476731i
$331$	−17.0000	−	29.4449i	−0.934405	−	1.61844i	−0.775692	−	0.631111i	$-0.782599\pi$
$331$	−17.0000	−	29.4449i	−0.934405	−	1.61844i	−0.158712	−	0.987325i	$-0.550734\pi$
$332$	4.50000	+	7.79423i	0.246970	+	0.427764i
$333$	2.00000			0.109599
$334$	7.00000	−	12.1244i	0.383023	−	0.663415i
$335$	5.00000	−	8.66025i	0.273179	−	0.473160i
$336$	−2.50000	−	4.33013i	−0.136386	−	0.236228i
$337$	−27.0000			−1.47078			−0.735392	−	0.677642i	$-0.763002\pi$
$337$	−27.0000			−1.47078			−0.735392	+	0.677642i	$0.763002\pi$
$338$	−1.50000	+	2.59808i	−0.0815892	+	0.141317i
$339$	−16.0000			−0.869001
$340$	4.00000			0.216930
$341$	−2.00000	−	5.19615i	−0.108306	−	0.281387i
$342$	4.00000			0.216295
$343$	55.0000			2.96972
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$	2.00000			0.107676
$346$	1.50000	+	2.59808i	0.0806405	+	0.139673i
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	−0.489946	−	0.871753i	$-0.662984\pi$
$347$	9.50000	−	16.4545i	0.509987	−	0.883323i	0.999933	−	0.0115703i	$-0.00368303\pi$
$348$	4.50000	−	7.79423i	0.241225	−	0.417815i
$349$	−32.0000			−1.71292			−0.856460	−	0.516213i	$-0.827341\pi$
$349$	−32.0000			−1.71292			−0.856460	+	0.516213i	$0.827341\pi$
$350$	−2.50000	−	4.33013i	−0.133631	−	0.231455i
$351$	−2.00000	−	3.46410i	−0.106752	−	0.184900i
$352$	0.500000	+	0.866025i	0.0266501	+	0.0461593i
$353$	13.0000	−	22.5167i	0.691920	−	1.19844i	−0.279288	−	0.960207i	$-0.590098\pi$
$353$	13.0000	−	22.5167i	0.691920	−	1.19844i	0.971208	−	0.238233i	$-0.0765683\pi$
$354$	1.50000	+	2.59808i	0.0797241	+	0.138086i
$355$	2.00000	−	3.46410i	0.106149	−	0.183855i
$356$	−6.00000			−0.317999
$357$	20.0000			1.05851
$358$	−4.50000	+	7.79423i	−0.237832	+	0.411938i
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	0.967272	−	0.253741i	$-0.0816611\pi$
$359$	5.00000	+	8.66025i	0.263890	+	0.457071i	−0.703382	+	0.710812i	$0.748328\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	1.50000	+	2.59808i	0.0789474	+	0.136741i
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$	5.00000	+	8.66025i	0.262432	+	0.454545i
$364$	20.0000			1.04828
$365$	−1.00000	+	1.73205i	−0.0523424	+	0.0906597i
$366$	−3.00000	+	5.19615i	−0.156813	+	0.271607i
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	0.988269	+	0.152721i	$0.0488036\pi$
$367$	12.0000	+	20.7846i	0.626395	+	1.08495i	−0.361874	+	0.932227i	$0.617863\pi$
$368$	2.00000			0.104257
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$	2.00000			0.103975
$371$	−45.0000			−2.33628
$372$	3.50000	−	4.33013i	0.181467	−	0.224507i
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$	−4.00000			−0.206835
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	8.00000			0.412568
$377$	18.0000	+	31.1769i	0.927047	+	1.60569i
$378$	−2.50000	+	4.33013i	−0.128586	+	0.222718i
$379$	−13.0000	+	22.5167i	−0.667765	+	1.15660i	0.310763	+	0.950488i	$0.399416\pi$
$379$	−13.0000	+	22.5167i	−0.667765	+	1.15660i	−0.978528	+	0.206116i	$0.933918\pi$
$380$	4.00000			0.205196
$381$	6.50000	+	11.2583i	0.333005	+	0.576782i
$382$	13.0000	+	22.5167i	0.665138	+	1.15205i
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	0.629890	−	0.776684i	$-0.283100\pi$
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	−0.987573	+	0.157159i	$0.949767\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	2.50000	+	4.33013i	0.127412	+	0.220684i
$386$	−12.5000	+	21.6506i	−0.636233	+	1.10199i
$387$	8.00000			0.406663
$388$	−1.00000			−0.0507673
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	−0.779895	−	0.625910i	$-0.784728\pi$
$389$	3.00000	−	5.19615i	0.152106	−	0.263455i	0.932002	+	0.362454i	$0.118061\pi$
$390$	−2.00000	−	3.46410i	−0.101274	−	0.175412i
$391$	−4.00000	+	6.92820i	−0.202289	+	0.350374i
$392$	−9.00000	−	15.5885i	−0.454569	−	0.787336i
$393$	−2.00000	−	3.46410i	−0.100887	−	0.174741i
$394$	11.0000	+	19.0526i	0.554172	+	0.959854i
$395$	−12.0000			−0.603786
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	−0.986481	−	0.163876i	$-0.947600\pi$
$397$	−7.00000	+	12.1244i	−0.351320	+	0.608504i	0.635161	+	0.772380i	$0.280934\pi$
$398$	−0.500000	−	0.866025i	−0.0250627	−	0.0434099i
$399$	20.0000			1.00125
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	12.0000			0.599251			0.299626	−	0.954057i	$-0.403138\pi$
$401$	12.0000			0.599251			0.299626	+	0.954057i	$0.403138\pi$
$402$	−10.0000			−0.498755
$403$	8.00000	+	20.7846i	0.398508	+	1.03536i
$404$	−5.00000			−0.248759
$405$	1.00000			0.0496904
$406$	22.5000	−	38.9711i	1.11666	−	1.93411i
$407$	−2.00000			−0.0991363
$408$	−2.00000	−	3.46410i	−0.0990148	−	0.171499i
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	−0.999402	−	0.0345902i	$-0.988987\pi$
$409$	−9.50000	+	16.4545i	−0.469745	+	0.813622i	0.529657	+	0.848212i	$0.322321\pi$
$410$	1.00000	−	1.73205i	0.0493865	−	0.0855399i
$411$	8.00000			0.394611
$412$	−6.50000	−	11.2583i	−0.320232	−	0.554658i
$413$	7.50000	+	12.9904i	0.369051	+	0.639215i
$414$	−1.00000	−	1.73205i	−0.0491473	−	0.0851257i
$415$	4.50000	−	7.79423i	0.220896	−	0.382604i
$416$	−2.00000	−	3.46410i	−0.0980581	−	0.169842i
$417$	10.0000	−	17.3205i	0.489702	−	0.848189i
$418$	−4.00000			−0.195646
$419$	27.0000			1.31904			0.659518	−	0.751689i	$-0.270760\pi$
$419$	27.0000			1.31904			0.659518	+	0.751689i	$0.270760\pi$
$420$	−2.50000	+	4.33013i	−0.121988	+	0.211289i
$421$	−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	−	6.92820i	0.194717	−	0.337260i
$423$	−4.00000	−	6.92820i	−0.194487	−	0.336861i
$424$	4.50000	+	7.79423i	0.218539	+	0.378521i
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$	−4.00000			−0.193801
$427$	−15.0000	+	25.9808i	−0.725901	+	1.25730i
$428$	−5.50000	+	9.52628i	−0.265853	+	0.460470i
$429$	2.00000	+	3.46410i	0.0965609	+	0.167248i
$430$	8.00000			0.385794
$431$	−10.0000	+	17.3205i	−0.481683	+	0.834300i	−0.999779	−	0.0210230i	$-0.993308\pi$
$431$	−10.0000	+	17.3205i	−0.481683	+	0.834300i	0.518096	+	0.855323i	$0.326641\pi$
$432$	1.00000			0.0481125
$433$	−22.0000			−1.05725			−0.528626	−	0.848855i	$-0.677293\pi$
$433$	−22.0000			−1.05725			−0.528626	+	0.848855i	$0.677293\pi$
$434$	17.5000	−	21.6506i	0.840027	−	1.03926i
$435$	−9.00000			−0.431517
$436$	8.00000			0.383131
$437$	−4.00000	+	6.92820i	−0.191346	+	0.331421i
$438$	2.00000			0.0955637
$439$	7.50000	+	12.9904i	0.357955	+	0.619997i	0.987619	−	0.156871i	$-0.0501406\pi$
$439$	7.50000	+	12.9904i	0.357955	+	0.619997i	−0.629664	+	0.776868i	$0.716807\pi$
$440$	0.500000	−	0.866025i	0.0238366	−	0.0412861i
$441$	−9.00000	+	15.5885i	−0.428571	+	0.742307i
$442$	16.0000			0.761042
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	0.814595	−	0.580030i	$-0.196959\pi$
$443$	−2.00000	−	3.46410i	−0.0950229	−	0.164584i	−0.909618	+	0.415445i	$0.863626\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−4.50000	+	7.79423i	−0.213081	+	0.369067i
$447$	5.50000	+	9.52628i	0.260141	+	0.450578i
$448$	−2.50000	+	4.33013i	−0.118114	+	0.204579i
$449$	−10.0000			−0.471929			−0.235965	−	0.971762i	$-0.575825\pi$
$449$	−10.0000			−0.471929			−0.235965	+	0.971762i	$0.575825\pi$
$450$	1.00000			0.0471405
$451$	−1.00000	+	1.73205i	−0.0470882	+	0.0815591i
$452$	8.00000	+	13.8564i	0.376288	+	0.651751i
$453$	−6.50000	+	11.2583i	−0.305397	+	0.528962i
$454$	6.50000	+	11.2583i	0.305060	+	0.528380i
$455$	−10.0000	−	17.3205i	−0.468807	−	0.811998i
$456$	−2.00000	−	3.46410i	−0.0936586	−	0.162221i
$457$	−18.0000			−0.842004			−0.421002	−	0.907060i	$-0.638322\pi$
$457$	−18.0000			−0.842004			−0.421002	+	0.907060i	$0.638322\pi$
$458$	5.00000	−	8.66025i	0.233635	−	0.404667i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$	−1.00000	−	1.73205i	−0.0466252	−	0.0807573i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$	2.50000	−	4.33013i	0.116311	−	0.201456i
$463$	35.0000			1.62659			0.813294	−	0.581853i	$-0.197672\pi$
$463$	35.0000			1.62659			0.813294	+	0.581853i	$0.197672\pi$
$464$	−9.00000			−0.417815
$465$	−5.50000	−	0.866025i	−0.255056	−	0.0401610i
$466$	10.0000			0.463241
$467$	27.0000			1.24941			0.624705	−	0.780860i	$-0.285219\pi$
$467$	27.0000			1.24941			0.624705	+	0.780860i	$0.285219\pi$
$468$	−2.00000	+	3.46410i	−0.0924500	+	0.160128i
$469$	−50.0000			−2.30879
$470$	−4.00000	−	6.92820i	−0.184506	−	0.319574i
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	1.50000	−	2.59808i	0.0690431	−	0.119586i
$473$	−8.00000			−0.367840
$474$	6.00000	+	10.3923i	0.275589	+	0.477334i
$475$	−2.00000	−	3.46410i	−0.0917663	−	0.158944i
$476$	−10.0000	−	17.3205i	−0.458349	−	0.793884i
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	−0.942821	−	0.333300i	$-0.891838\pi$
$479$	−4.00000	+	6.92820i	−0.182765	+	0.316558i	0.760056	+	0.649857i	$0.225171\pi$
$480$	1.00000			0.0456435
$481$	8.00000			0.364769
$482$	8.50000	−	14.7224i	0.387164	−	0.670588i
$483$	−5.00000	−	8.66025i	−0.227508	−	0.394055i
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	0.500000	+	0.866025i	0.0227038	+	0.0393242i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	−0.891303	−	0.453409i	$-0.850208\pi$
$487$	−18.5000	−	32.0429i	−0.838315	−	1.45200i	0.0529875	−	0.998595i	$-0.483126\pi$
$488$	6.00000			0.271607
$489$	−5.00000	+	8.66025i	−0.226108	+	0.391630i
$490$	−9.00000	+	15.5885i	−0.406579	+	0.704215i
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	0.949520	−	0.313707i	$-0.101571\pi$
$491$	4.50000	+	7.79423i	0.203082	+	0.351749i	−0.746438	+	0.665455i	$0.768237\pi$
$492$	−2.00000			−0.0901670
$493$	18.0000	−	31.1769i	0.810679	−	1.40414i
$494$	16.0000			0.719874
$495$	−1.00000			−0.0449467
$496$	−5.50000	−	0.866025i	−0.246957	−	0.0388857i
$497$	−20.0000			−0.897123
$498$	−9.00000			−0.403300
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	−0.955968	−	0.293471i	$-0.905190\pi$
$499$	−5.00000	+	8.66025i	−0.223831	+	0.387686i	0.732137	+	0.681157i	$0.238523\pi$
$500$	1.00000			0.0447214
$501$	7.00000	+	12.1244i	0.312737	+	0.541676i
$502$	−4.00000	+	6.92820i	−0.178529	+	0.309221i
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	−0.309418	−	0.950926i	$-0.600134\pi$
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	0.978235	−	0.207499i	$-0.0665323\pi$
$504$	5.00000			0.222718
$505$	2.50000	+	4.33013i	0.111249	+	0.192688i
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$	−1.50000	−	2.59808i	−0.0666173	−	0.115385i
$508$	6.50000	−	11.2583i	0.288391	−	0.499508i
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	−0.867719	−	0.497056i	$-0.834414\pi$
$509$	−19.5000	−	33.7750i	−0.864322	−	1.49705i	0.00339621	−	0.999994i	$-0.498919\pi$
$510$	−2.00000	+	3.46410i	−0.0885615	+	0.153393i
$511$	10.0000			0.442374
$512$	1.00000			0.0441942
$513$	−2.00000	+	3.46410i	−0.0883022	+	0.152944i
$514$	−9.00000	−	15.5885i	−0.396973	−	0.687577i
$515$	−6.50000	+	11.2583i	−0.286424	+	0.496101i
$516$	−4.00000	−	6.92820i	−0.176090	−	0.304997i
$517$	4.00000	+	6.92820i	0.175920	+	0.304702i
$518$	−5.00000	−	8.66025i	−0.219687	−	0.380510i
$519$	−3.00000			−0.131685
$520$	−2.00000	+	3.46410i	−0.0877058	+	0.151911i
$521$	−10.0000	+	17.3205i	−0.438108	+	0.758825i	−0.997544	−	0.0700486i	$-0.977685\pi$
$521$	−10.0000	+	17.3205i	−0.438108	+	0.758825i	0.559436	+	0.828874i	$0.311018\pi$
$522$	4.50000	+	7.79423i	0.196960	+	0.341144i
$523$	−36.0000			−1.57417			−0.787085	−	0.616844i	$-0.788411\pi$
$523$	−36.0000			−1.57417			−0.787085	+	0.616844i	$0.788411\pi$
$524$	−2.00000	+	3.46410i	−0.0873704	+	0.151330i
$525$	5.00000			0.218218
$526$	−26.0000			−1.13365
$527$	14.0000	−	17.3205i	0.609850	−	0.754493i
$528$	−1.00000			−0.0435194
$529$	−19.0000			−0.826087
$530$	4.50000	−	7.79423i	0.195468	−	0.338560i
$531$	−3.00000			−0.130189
$532$	−10.0000	−	17.3205i	−0.433555	−	0.750939i
$533$	4.00000	−	6.92820i	0.173259	−	0.300094i
$534$	3.00000	−	5.19615i	0.129823	−	0.224860i
$535$	11.0000			0.475571
$536$	5.00000	+	8.66025i	0.215967	+	0.374066i
$537$	−4.50000	−	7.79423i	−0.194189	−	0.336346i
$538$	−5.00000	−	8.66025i	−0.215565	−	0.373370i
$539$	9.00000	−	15.5885i	0.387657	−	0.671442i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$	−3.00000			−0.128861
$543$	−10.0000			−0.429141
$544$	−2.00000	+	3.46410i	−0.0857493	+	0.148522i
$545$	−4.00000	−	6.92820i	−0.171341	−	0.296772i
$546$	−10.0000	+	17.3205i	−0.427960	+	0.741249i
$547$	21.0000	+	36.3731i	0.897895	+	1.55520i	0.830180	+	0.557495i	$0.188238\pi$
$547$	21.0000	+	36.3731i	0.897895	+	1.55520i	0.0677151	+	0.997705i	$0.478429\pi$
$548$	−4.00000	−	6.92820i	−0.170872	−	0.295958i
$549$	−3.00000	−	5.19615i	−0.128037	−	0.221766i
$550$	−1.00000			−0.0426401
$551$	18.0000	−	31.1769i	0.766826	−	1.32818i
$552$	−1.00000	+	1.73205i	−0.0425628	+	0.0737210i
$553$	30.0000	+	51.9615i	1.27573	+	2.20963i
$554$	−12.0000			−0.509831
$555$	−1.00000	+	1.73205i	−0.0424476	+	0.0735215i
$556$	−20.0000			−0.848189
$557$	−23.0000			−0.974541			−0.487271	−	0.873251i	$-0.662007\pi$
$557$	−23.0000			−0.974541			−0.487271	+	0.873251i	$0.662007\pi$
$558$	2.00000	+	5.19615i	0.0846668	+	0.219971i
$559$	32.0000			1.35346
$560$	5.00000			0.211289
$561$	2.00000	−	3.46410i	0.0844401	−	0.146254i
$562$	2.00000			0.0843649
$563$	23.5000	+	40.7032i	0.990407	+	1.71544i	0.614872	+	0.788627i	$0.289208\pi$
$563$	23.5000	+	40.7032i	0.990407	+	1.71544i	0.375535	+	0.926808i	$0.377459\pi$
$564$	−4.00000	+	6.92820i	−0.168430	+	0.291730i
$565$	8.00000	−	13.8564i	0.336563	−	0.582943i
$566$	−24.0000			−1.00880
$567$	−2.50000	−	4.33013i	−0.104990	−	0.181848i
$568$	2.00000	+	3.46410i	0.0839181	+	0.145350i
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	−0.999994	−	0.00354413i	$-0.998872\pi$
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	0.496928	−	0.867792i	$-0.334461\pi$
$570$	−2.00000	+	3.46410i	−0.0837708	+	0.145095i
$571$	21.0000	+	36.3731i	0.878823	+	1.52217i	0.852634	+	0.522508i	$0.175004\pi$
$571$	21.0000	+	36.3731i	0.878823	+	1.52217i	0.0261885	+	0.999657i	$0.491663\pi$
$572$	2.00000	−	3.46410i	0.0836242	−	0.144841i
$573$	−26.0000			−1.08617
$574$	−10.0000			−0.417392
$575$	−1.00000	+	1.73205i	−0.0417029	+	0.0722315i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	0.500000	+	0.866025i	0.0207973	+	0.0360219i
$579$	−12.5000	−	21.6506i	−0.519482	−	0.899770i
$580$	4.50000	+	7.79423i	0.186852	+	0.323638i
$581$	−45.0000			−1.86691
$582$	0.500000	−	0.866025i	0.0207257	−	0.0358979i
$583$	−4.50000	+	7.79423i	−0.186371	+	0.322804i
$584$	−1.00000	−	1.73205i	−0.0413803	−	0.0716728i
$585$	4.00000			0.165380
$586$	−15.5000	+	26.8468i	−0.640299	+	1.10903i
$587$	−27.0000			−1.11441			−0.557205	−	0.830375i	$-0.688126\pi$
$587$	−27.0000			−1.11441			−0.557205	+	0.830375i	$0.688126\pi$
$588$	18.0000			0.742307
$589$	14.0000	−	17.3205i	0.576860	−	0.713679i
$590$	−3.00000			−0.123508
$591$	−22.0000			−0.904959
$592$	−1.00000	+	1.73205i	−0.0410997	+	0.0711868i
$593$	16.0000			0.657041			0.328521	−	0.944497i	$-0.393450\pi$
$593$	16.0000			0.657041			0.328521	+	0.944497i	$0.393450\pi$
$594$	0.500000	+	0.866025i	0.0205152	+	0.0355335i
$595$	−10.0000	+	17.3205i	−0.409960	+	0.710072i
$596$	5.50000	−	9.52628i	0.225289	−	0.390212i
$597$	1.00000			0.0409273
$598$	−4.00000	−	6.92820i	−0.163572	−	0.283315i
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	0.954521	+	0.298143i	$0.0963673\pi$
$599$	18.0000	+	31.1769i	0.735460	+	1.27385i	−0.219061	+	0.975711i	$0.570299\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	−21.0000	+	36.3731i	−0.856608	+	1.48369i	0.0185374	+	0.999828i	$0.494099\pi$
$601$	−21.0000	+	36.3731i	−0.856608	+	1.48369i	−0.875145	+	0.483860i	$0.839234\pi$
$602$	−20.0000	−	34.6410i	−0.815139	−	1.41186i
$603$	5.00000	−	8.66025i	0.203616	−	0.352673i
$604$	13.0000			0.528962
$605$	−10.0000			−0.406558
$606$	2.50000	−	4.33013i	0.101556	−	0.175899i
$607$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$607$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$608$	−2.00000	+	3.46410i	−0.0811107	+	0.140488i
$609$	22.5000	+	38.9711i	0.911746	+	1.57919i
$610$	−3.00000	−	5.19615i	−0.121466	−	0.210386i
$611$	−16.0000	−	27.7128i	−0.647291	−	1.12114i
$612$	4.00000			0.161690
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	−0.961380	−	0.275225i	$-0.911248\pi$
$613$	−6.00000	+	10.3923i	−0.242338	+	0.419741i	0.719042	+	0.694967i	$0.244581\pi$
$614$	2.00000	−	3.46410i	0.0807134	−	0.139800i
$615$	1.00000	+	1.73205i	0.0403239	+	0.0698430i
$616$	−5.00000			−0.201456
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	−0.0398207	−	0.999207i	$-0.512679\pi$
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	0.885249	−	0.465118i	$-0.153988\pi$
$618$	13.0000			0.522937
$619$	−34.0000			−1.36658			−0.683288	−	0.730149i	$-0.739451\pi$
$619$	−34.0000			−1.36658			−0.683288	+	0.730149i	$0.739451\pi$
$620$	2.00000	+	5.19615i	0.0803219	+	0.208683i
$621$	2.00000			0.0802572
$622$	−16.0000			−0.641542
$623$	15.0000	−	25.9808i	0.600962	−	1.04090i
$624$	4.00000			0.160128
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−0.500000	+	0.866025i	−0.0199840	+	0.0346133i
$627$	2.00000	−	3.46410i	0.0798723	−	0.138343i
$628$	14.0000			0.558661
$629$	−4.00000	−	6.92820i	−0.159490	−	0.276246i
$630$	−2.50000	−	4.33013i	−0.0996024	−	0.172516i
$631$	−14.5000	−	25.1147i	−0.577236	−	0.999802i	−0.995795	−	0.0916122i	$-0.970798\pi$
$631$	−14.5000	−	25.1147i	−0.577236	−	0.999802i	0.418559	−	0.908190i	$-0.362535\pi$
$632$	6.00000	−	10.3923i	0.238667	−	0.413384i
$633$	4.00000	+	6.92820i	0.158986	+	0.275371i
$634$	−11.5000	+	19.9186i	−0.456723	+	0.791068i
$635$	−13.0000			−0.515889
$636$	−9.00000			−0.356873
$637$	−36.0000	+	62.3538i	−1.42637	+	2.47055i
$638$	−4.50000	−	7.79423i	−0.178157	−	0.308576i
$639$	2.00000	−	3.46410i	0.0791188	−	0.137038i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	0.919171	−	0.393860i	$-0.128860\pi$
$641$	3.00000	+	5.19615i	0.118493	+	0.205236i	−0.800678	+	0.599095i	$0.795527\pi$
$642$	−5.50000	−	9.52628i	−0.217068	−	0.375972i
$643$	26.0000			1.02534			0.512670	−	0.858586i	$-0.328656\pi$
$643$	26.0000			1.02534			0.512670	+	0.858586i	$0.328656\pi$
$644$	−5.00000	+	8.66025i	−0.197028	+	0.341262i
$645$	−4.00000	+	6.92820i	−0.157500	+	0.272798i
$646$	−8.00000	−	13.8564i	−0.314756	−	0.545173i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	3.00000			0.117760
$650$	4.00000			0.156893
$651$	10.0000	+	25.9808i	0.391931	+	1.01827i
$652$	10.0000			0.391630
$653$	33.0000			1.29139			0.645695	−	0.763596i	$-0.276568\pi$
$653$	33.0000			1.29139			0.645695	+	0.763596i	$0.276568\pi$
$654$	−4.00000	+	6.92820i	−0.156412	+	0.270914i
$655$	4.00000			0.156293
$656$	1.00000	+	1.73205i	0.0390434	+	0.0676252i
$657$	−1.00000	+	1.73205i	−0.0390137	+	0.0675737i
$658$	−20.0000	+	34.6410i	−0.779681	+	1.35045i
$659$	33.0000			1.28550			0.642749	−	0.766077i	$-0.277794\pi$
$659$	33.0000			1.28550			0.642749	+	0.766077i	$0.277794\pi$
$660$	0.500000	+	0.866025i	0.0194625	+	0.0337100i
$661$	15.0000	+	25.9808i	0.583432	+	1.01053i	0.995069	+	0.0991864i	$0.0316240\pi$
$661$	15.0000	+	25.9808i	0.583432	+	1.01053i	−0.411636	+	0.911348i	$0.635043\pi$
$662$	−17.0000	−	29.4449i	−0.660724	−	1.14441i
$663$	−8.00000	+	13.8564i	−0.310694	+	0.538138i
$664$	4.50000	+	7.79423i	0.174634	+	0.302475i
$665$	−10.0000	+	17.3205i	−0.387783	+	0.671660i
$666$	2.00000			0.0774984
$667$	−18.0000			−0.696963
$668$	7.00000	−	12.1244i	0.270838	−	0.469105i
$669$	−4.50000	−	7.79423i	−0.173980	−	0.301342i
$670$	5.00000	−	8.66025i	0.193167	−	0.334575i
$671$	3.00000	+	5.19615i	0.115814	+	0.200595i
$672$	−2.50000	−	4.33013i	−0.0964396	−	0.167038i
$673$	7.50000	+	12.9904i	0.289104	+	0.500742i	0.973596	−	0.228278i	$-0.0733094\pi$
$673$	7.50000	+	12.9904i	0.289104	+	0.500742i	−0.684492	+	0.729020i	$0.739976\pi$
$674$	−27.0000			−1.04000
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−1.50000	+	2.59808i	−0.0576923	+	0.0999260i
$677$	17.5000	+	30.3109i	0.672580	+	1.16494i	0.977170	+	0.212459i	$0.0681471\pi$
$677$	17.5000	+	30.3109i	0.672580	+	1.16494i	−0.304590	+	0.952483i	$0.598520\pi$
$678$	−16.0000			−0.614476
$679$	2.50000	−	4.33013i	0.0959412	−	0.166175i
$680$	4.00000			0.153393
$681$	−13.0000			−0.498161
$682$	−2.00000	−	5.19615i	−0.0765840	−	0.198971i
$683$	−39.0000			−1.49229			−0.746147	−	0.665782i	$-0.768098\pi$
$683$	−39.0000			−1.49229			−0.746147	+	0.665782i	$0.768098\pi$
$684$	4.00000			0.152944
$685$	−4.00000	+	6.92820i	−0.152832	+	0.264713i
$686$	55.0000			2.09991
$687$	5.00000	+	8.66025i	0.190762	+	0.330409i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	18.0000	−	31.1769i	0.685745	−	1.18775i
$690$	2.00000			0.0761387
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	0.991460	+	0.130410i	$0.0416295\pi$
$691$	16.0000	+	27.7128i	0.608669	+	1.05425i	−0.382791	+	0.923835i	$0.625037\pi$
$692$	1.50000	+	2.59808i	0.0570214	+	0.0987640i
$693$	2.50000	+	4.33013i	0.0949671	+	0.164488i
$694$	9.50000	−	16.4545i	0.360615	−	0.624604i
$695$	10.0000	+	17.3205i	0.379322	+	0.657004i
$696$	4.50000	−	7.79423i	0.170572	−	0.295439i
$697$	−8.00000			−0.303022
$698$	−32.0000			−1.21122
$699$	−5.00000	+	8.66025i	−0.189117	+	0.327561i
$700$	−2.50000	−	4.33013i	−0.0944911	−	0.163663i
$701$	−7.50000	+	12.9904i	−0.283271	+	0.490640i	−0.972188	−	0.234200i	$-0.924753\pi$
$701$	−7.50000	+	12.9904i	−0.283271	+	0.490640i	0.688917	+	0.724840i	$0.258086\pi$
$702$	−2.00000	−	3.46410i	−0.0754851	−	0.130744i
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	8.00000			0.301297
$706$	13.0000	−	22.5167i	0.489261	−	0.847426i
$707$	12.5000	−	21.6506i	0.470111	−	0.814256i
$708$	1.50000	+	2.59808i	0.0563735	+	0.0976417i
$709$	30.0000			1.12667			0.563337	−	0.826227i	$-0.309517\pi$
$709$	30.0000			1.12667			0.563337	+	0.826227i	$0.309517\pi$
$710$	2.00000	−	3.46410i	0.0750587	−	0.130005i
$711$	−12.0000			−0.450035
$712$	−6.00000			−0.224860
$713$	−11.0000	−	1.73205i	−0.411953	−	0.0648658i
$714$	20.0000			0.748481
$715$	−4.00000			−0.149592
$716$	−4.50000	+	7.79423i	−0.168173	+	0.291284i
$717$	−12.0000			−0.448148
$718$	5.00000	+	8.66025i	0.186598	+	0.323198i
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	−0.306253	−	0.951950i	$-0.599075\pi$
$719$	18.0000	−	31.1769i	0.671287	−	1.16270i	0.977539	−	0.210752i	$-0.0675914\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$	65.0000			2.42073
$722$	1.50000	+	2.59808i	0.0558242	+	0.0966904i
$723$	8.50000	+	14.7224i	0.316118	+	0.547533i
$724$	5.00000	+	8.66025i	0.185824	+	0.321856i
$725$	4.50000	−	7.79423i	0.167126	−	0.289470i
$726$	5.00000	+	8.66025i	0.185567	+	0.321412i
$727$	10.5000	−	18.1865i	0.389423	−	0.674501i	−0.602949	−	0.797780i	$-0.706008\pi$
$727$	10.5000	−	18.1865i	0.389423	−	0.674501i	0.992372	+	0.123279i	$0.0393409\pi$
$728$	20.0000			0.741249
$729$	1.00000			0.0370370
$730$	−1.00000	+	1.73205i	−0.0370117	+	0.0641061i
$731$	−16.0000	−	27.7128i	−0.591781	−	1.02500i
$732$	−3.00000	+	5.19615i	−0.110883	+	0.192055i
$733$	−25.0000	−	43.3013i	−0.923396	−	1.59937i	−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−25.0000	−	43.3013i	−0.923396	−	1.59937i	−0.129275	−	0.991609i	$-0.541265\pi$
$734$	12.0000	+	20.7846i	0.442928	+	0.767174i
$735$	−9.00000	−	15.5885i	−0.331970	−	0.574989i
$736$	2.00000			0.0737210
$737$	−5.00000	+	8.66025i	−0.184177	+	0.319005i
$738$	1.00000	−	1.73205i	0.0368105	−	0.0637577i
$739$	−6.00000	−	10.3923i	−0.220714	−	0.382287i	0.734311	−	0.678813i	$-0.237505\pi$
$739$	−6.00000	−	10.3923i	−0.220714	−	0.382287i	−0.955025	+	0.296526i	$0.904172\pi$
$740$	2.00000			0.0735215
$741$	−8.00000	+	13.8564i	−0.293887	+	0.509028i
$742$	−45.0000			−1.65200
$743$	38.0000			1.39408			0.697042	−	0.717030i	$-0.254499\pi$
$743$	38.0000			1.39408			0.697042	+	0.717030i	$0.254499\pi$
$744$	3.50000	−	4.33013i	0.128316	−	0.158750i
$745$	−11.0000			−0.403009
$746$	−4.00000			−0.146450
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$	−4.00000			−0.146254
$749$	−27.5000	−	47.6314i	−1.00483	−	1.74041i
$750$	−0.500000	+	0.866025i	−0.0182574	+	0.0316228i
$751$	7.50000	−	12.9904i	0.273679	−	0.474026i	−0.696122	−	0.717923i	$-0.745093\pi$
$751$	7.50000	−	12.9904i	0.273679	−	0.474026i	0.969801	+	0.243898i	$0.0784261\pi$
$752$	8.00000			0.291730
$753$	−4.00000	−	6.92820i	−0.145768	−	0.252478i
$754$	18.0000	+	31.1769i	0.655521	+	1.13540i
$755$	−6.50000	−	11.2583i	−0.236559	−	0.409733i
$756$	−2.50000	+	4.33013i	−0.0909241	+	0.157485i
$757$	−8.00000	−	13.8564i	−0.290765	−	0.503620i	0.683226	−	0.730207i	$-0.260576\pi$
$757$	−8.00000	−	13.8564i	−0.290765	−	0.503620i	−0.973991	+	0.226587i	$0.927243\pi$
$758$	−13.0000	+	22.5167i	−0.472181	+	0.817842i
$759$	−2.00000			−0.0725954
$760$	4.00000			0.145095
$761$	8.00000	−	13.8564i	0.290000	−	0.502294i	−0.683810	−	0.729661i	$-0.739678\pi$
$761$	8.00000	−	13.8564i	0.290000	−	0.502294i	0.973809	+	0.227366i	$0.0730114\pi$
$762$	6.50000	+	11.2583i	0.235470	+	0.407846i
$763$	−20.0000	+	34.6410i	−0.724049	+	1.25409i
$764$	13.0000	+	22.5167i	0.470323	+	0.814624i
$765$	−2.00000	−	3.46410i	−0.0723102	−	0.125245i
$766$	−7.00000	−	12.1244i	−0.252920	−	0.438071i
$767$	−12.0000			−0.433295
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	−0.749654	−	0.661830i	$-0.769780\pi$
$769$	5.50000	−	9.52628i	0.198335	−	0.343526i	0.947989	+	0.318304i	$0.103113\pi$
$770$	2.50000	+	4.33013i	0.0900937	+	0.156047i
$771$	18.0000			0.648254
$772$	−12.5000	+	21.6506i	−0.449885	+	0.779223i
$773$	−30.0000			−1.07903			−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000			−1.07903			−0.539513	+	0.841978i	$0.681391\pi$
$774$	8.00000			0.287554
$775$	3.50000	−	4.33013i	0.125724	−	0.155543i
$776$	−1.00000			−0.0358979
$777$	10.0000			0.358748
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$	−8.00000			−0.286630
$780$	−2.00000	−	3.46410i	−0.0716115	−	0.124035i
$781$	−2.00000	+	3.46410i	−0.0715656	+	0.123955i
$782$	−4.00000	+	6.92820i	−0.143040	+	0.247752i
$783$	−9.00000			−0.321634
$784$	−9.00000	−	15.5885i	−0.321429	−	0.556731i
$785$	−7.00000	−	12.1244i	−0.249841	−	0.432737i
$786$	−2.00000	−	3.46410i	−0.0713376	−	0.123560i
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	−0.713871	−	0.700278i	$-0.753059\pi$
$787$	7.00000	−	12.1244i	0.249523	−	0.432187i	0.963394	+	0.268091i	$0.0863928\pi$
$788$	11.0000	+	19.0526i	0.391859	+	0.678719i
$789$	13.0000	−	22.5167i	0.462812	−	0.801614i
$790$	−12.0000			−0.426941
$791$	−80.0000			−2.84447
$792$	0.500000	−	0.866025i	0.0177667	−	0.0307729i
$793$	−12.0000	−	20.7846i	−0.426132	−	0.738083i
$794$	−7.00000	+	12.1244i	−0.248421	+	0.430277i
$795$	4.50000	+	7.79423i	0.159599	+	0.276433i
$796$	−0.500000	−	0.866025i	−0.0177220	−	0.0306955i
$797$	−18.5000	−	32.0429i	−0.655304	−	1.13502i	−0.981818	−	0.189827i	$-0.939207\pi$
$797$	−18.5000	−	32.0429i	−0.655304	−	1.13502i	0.326514	−	0.945192i	$-0.394126\pi$
$798$	20.0000			0.707992
$799$	−16.0000	+	27.7128i	−0.566039	+	0.980409i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	3.00000	+	5.19615i	0.106000	+	0.183597i
$802$	12.0000			0.423735
$803$	1.00000	−	1.73205i	0.0352892	−	0.0611227i
$804$	−10.0000			−0.352673
$805$	10.0000			0.352454
$806$	8.00000	+	20.7846i	0.281788	+	0.732107i
$807$	10.0000			0.352017
$808$	−5.00000			−0.175899
$809$	6.00000	−	10.3923i	0.210949	−	0.365374i	−0.741063	−	0.671436i	$-0.765678\pi$
$809$	6.00000	−	10.3923i	0.210949	−	0.365374i	0.952012	+	0.306062i	$0.0990113\pi$
$810$	1.00000			0.0351364
$811$	−15.0000	−	25.9808i	−0.526721	−	0.912308i	−0.999515	−	0.0311349i	$-0.990088\pi$
$811$	−15.0000	−	25.9808i	−0.526721	−	0.912308i	0.472794	−	0.881173i	$-0.343245\pi$
$812$	22.5000	−	38.9711i	0.789595	−	1.36762i
$813$	1.50000	−	2.59808i	0.0526073	−	0.0911185i
$814$	−2.00000			−0.0701000
$815$	−5.00000	−	8.66025i	−0.175142	−	0.303355i
$816$	−2.00000	−	3.46410i	−0.0700140	−	0.121268i
$817$	−16.0000	−	27.7128i	−0.559769	−	0.969549i
$818$	−9.50000	+	16.4545i	−0.332160	+	0.575317i
$819$	−10.0000	−	17.3205i	−0.349428	−	0.605228i
$820$	1.00000	−	1.73205i	0.0349215	−	0.0604858i
$821$	15.0000			0.523504			0.261752	−	0.965135i	$-0.415700\pi$
$821$	15.0000			0.523504			0.261752	+	0.965135i	$0.415700\pi$
$822$	8.00000			0.279032
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	−0.982737	−	0.185006i	$-0.940770\pi$
$823$	−9.50000	+	16.4545i	−0.331149	+	0.573567i	0.651588	+	0.758573i	$0.274103\pi$
$824$	−6.50000	−	11.2583i	−0.226438	−	0.392203i
$825$	0.500000	−	0.866025i	0.0174078	−	0.0301511i
$826$	7.50000	+	12.9904i	0.260958	+	0.451993i
$827$	12.0000	+	20.7846i	0.417281	+	0.722752i	0.995665	−	0.0930129i	$-0.0296498\pi$
$827$	12.0000	+	20.7846i	0.417281	+	0.722752i	−0.578384	+	0.815765i	$0.696316\pi$
$828$	−1.00000	−	1.73205i	−0.0347524	−	0.0601929i
$829$	32.0000			1.11141			0.555703	−	0.831381i	$-0.312449\pi$
$829$	32.0000			1.11141			0.555703	+	0.831381i	$0.312449\pi$
$830$	4.50000	−	7.79423i	0.156197	−	0.270542i
$831$	6.00000	−	10.3923i	0.208138	−	0.360505i
$832$	−2.00000	−	3.46410i	−0.0693375	−	0.120096i
$833$	72.0000			2.49465
$834$	10.0000	−	17.3205i	0.346272	−	0.599760i
$835$	−14.0000			−0.484490
$836$	−4.00000			−0.138343
$837$	−5.50000	−	0.866025i	−0.190108	−	0.0299342i
$838$	27.0000			0.932700
$839$	4.00000			0.138095			0.0690477	−	0.997613i	$-0.478004\pi$
$839$	4.00000			0.138095			0.0690477	+	0.997613i	$0.478004\pi$
$840$	−2.50000	+	4.33013i	−0.0862582	+	0.149404i
$841$	52.0000			1.79310
$842$	−13.0000	−	22.5167i	−0.448010	−	0.775975i
$843$	−1.00000	+	1.73205i	−0.0344418	+	0.0596550i
$844$	4.00000	−	6.92820i	0.137686	−	0.238479i
$845$	3.00000			0.103203
$846$	−4.00000	−	6.92820i	−0.137523	−	0.238197i
$847$	25.0000	+	43.3013i	0.859010	+	1.48785i
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$	12.0000	−	20.7846i	0.411839	−	0.713326i
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	−2.00000	+	3.46410i	−0.0685591	+	0.118748i
$852$	−4.00000			−0.137038
$853$	−24.0000			−0.821744			−0.410872	−	0.911693i	$-0.634776\pi$
$853$	−24.0000			−0.821744			−0.410872	+	0.911693i	$0.634776\pi$
$854$	−15.0000	+	25.9808i	−0.513289	+	0.889043i
$855$	−2.00000	−	3.46410i	−0.0683986	−	0.118470i
$856$	−5.50000	+	9.52628i	−0.187986	+	0.325602i
$857$	2.00000	+	3.46410i	0.0683187	+	0.118331i	0.898161	−	0.439666i	$-0.144903\pi$
$857$	2.00000	+	3.46410i	0.0683187	+	0.118331i	−0.829843	+	0.557998i	$0.811570\pi$
$858$	2.00000	+	3.46410i	0.0682789	+	0.118262i
$859$	−15.0000	−	25.9808i	−0.511793	−	0.886452i	−0.999907	−	0.0136718i	$-0.995648\pi$
$859$	−15.0000	−	25.9808i	−0.511793	−	0.886452i	0.488113	−	0.872780i	$-0.337685\pi$
$860$	8.00000			0.272798
$861$	5.00000	−	8.66025i	0.170400	−	0.295141i
$862$	−10.0000	+	17.3205i	−0.340601	+	0.589939i
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$	1.00000			0.0340207
$865$	1.50000	−	2.59808i	0.0510015	−	0.0883372i
$866$	−22.0000			−0.747590
$867$	−1.00000			−0.0339618
$868$	17.5000	−	21.6506i	0.593989	−	0.734870i
$869$	12.0000			0.407072
$870$	−9.00000			−0.305129
$871$	20.0000	−	34.6410i	0.677674	−	1.17377i
$872$	8.00000			0.270914
$873$	0.500000	+	0.866025i	0.0169224	+	0.0293105i
$874$	−4.00000	+	6.92820i	−0.135302	+	0.234350i
$875$	−2.50000	+	4.33013i	−0.0845154	+	0.146385i
$876$	2.00000			0.0675737
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	0.848648	−	0.528958i	$-0.177417\pi$
$877$	−1.00000	−	1.73205i	−0.0337676	−	0.0584872i	−0.882415	+	0.470471i	$0.844084\pi$
$878$	7.50000	+	12.9904i	0.253113	+	0.438404i
$879$	−15.5000	−	26.8468i	−0.522802	−	0.905520i
$880$	0.500000	−	0.866025i	0.0168550	−	0.0291937i
$881$	−5.00000	−	8.66025i	−0.168454	−	0.291771i	0.769422	−	0.638740i	$-0.220544\pi$
$881$	−5.00000	−	8.66025i	−0.168454	−	0.291771i	−0.937877	+	0.346969i	$0.887211\pi$
$882$	−9.00000	+	15.5885i	−0.303046	+	0.524891i
$883$	26.0000			0.874970			0.437485	−	0.899226i	$-0.355869\pi$
$883$	26.0000			0.874970			0.437485	+	0.899226i	$0.355869\pi$
$884$	16.0000			0.538138
$885$	1.50000	−	2.59808i	0.0504219	−	0.0873334i
$886$	−2.00000	−	3.46410i	−0.0671913	−	0.116379i
$887$	−13.0000	+	22.5167i	−0.436497	+	0.756035i	−0.997417	−	0.0718351i	$-0.977114\pi$
$887$	−13.0000	+	22.5167i	−0.436497	+	0.756035i	0.560919	+	0.827871i	$0.310448\pi$
$888$	−1.00000	−	1.73205i	−0.0335578	−	0.0581238i
$889$	32.5000	+	56.2917i	1.09002	+	1.88796i
$890$	3.00000	+	5.19615i	0.100560	+	0.174175i
$891$	−1.00000			−0.0335013
$892$	−4.50000	+	7.79423i	−0.150671	+	0.260970i
$893$	−16.0000	+	27.7128i	−0.535420	+	0.927374i
$894$	5.50000	+	9.52628i	0.183948	+	0.318606i
$895$	9.00000			0.300837
$896$	−2.50000	+	4.33013i	−0.0835191	+	0.144659i
$897$	8.00000			0.267112
$898$	−10.0000			−0.333704
$899$	49.5000	+	7.79423i	1.65092	+	0.259952i
$900$	1.00000			0.0333333
$901$	−36.0000			−1.19933
$902$	−1.00000	+	1.73205i	−0.0332964	+	0.0576710i
$903$	40.0000			1.33112
$904$	8.00000	+	13.8564i	0.266076	+	0.460857i
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$	−6.50000	+	11.2583i	−0.215948	+	0.374033i
$907$	−12.0000			−0.398453			−0.199227	−	0.979953i	$-0.563843\pi$
$907$	−12.0000			−0.398453			−0.199227	+	0.979953i	$0.563843\pi$
$908$	6.50000	+	11.2583i	0.215710	+	0.373621i
$909$	2.50000	+	4.33013i	0.0829198	+	0.143621i
$910$	−10.0000	−	17.3205i	−0.331497	−	0.574169i
$911$	4.00000	−	6.92820i	0.132526	−	0.229542i	−0.792124	−	0.610361i	$-0.791025\pi$
$911$	4.00000	−	6.92820i	0.132526	−	0.229542i	0.924650	+	0.380819i	$0.124358\pi$
$912$	−2.00000	−	3.46410i	−0.0662266	−	0.114708i
$913$	−4.50000	+	7.79423i	−0.148928	+	0.257951i
$914$	−18.0000			−0.595387
$915$	6.00000			0.198354
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$	−10.0000	−	17.3205i	−0.330229	−	0.571974i
$918$	−2.00000	+	3.46410i	−0.0660098	+	0.114332i
$919$	12.5000	+	21.6506i	0.412337	+	0.714189i	0.995145	−	0.0984214i	$-0.0313793\pi$
$919$	12.5000	+	21.6506i	0.412337	+	0.714189i	−0.582808	+	0.812610i	$0.698046\pi$
$920$	−1.00000	−	1.73205i	−0.0329690	−	0.0571040i
$921$	2.00000	+	3.46410i	0.0659022	+	0.114146i
$922$	33.0000			1.08680
$923$	8.00000	−	13.8564i	0.263323	−	0.456089i
$924$	2.50000	−	4.33013i	0.0822440	−	0.142451i
$925$	−1.00000	−	1.73205i	−0.0328798	−	0.0569495i
$926$	35.0000			1.15017
$927$	−6.50000	+	11.2583i	−0.213488	+	0.369772i
$928$	−9.00000			−0.295439
$929$	24.0000			0.787414			0.393707	−	0.919236i	$-0.371192\pi$
$929$	24.0000			0.787414			0.393707	+	0.919236i	$0.371192\pi$
$930$	−5.50000	−	0.866025i	−0.180352	−	0.0283981i
$931$	72.0000			2.35970
$932$	10.0000			0.327561
$933$	8.00000	−	13.8564i	0.261908	−	0.453638i
$934$	27.0000			0.883467
$935$	2.00000	+	3.46410i	0.0654070	+	0.113288i
$936$	−2.00000	+	3.46410i	−0.0653720	+	0.113228i
$937$	17.0000	−	29.4449i	0.555366	−	0.961922i	−0.442509	−	0.896764i	$-0.645912\pi$
$937$	17.0000	−	29.4449i	0.555366	−	0.961922i	0.997875	−	0.0651578i	$-0.0207551\pi$
$938$	−50.0000			−1.63256
$939$	−0.500000	−	0.866025i	−0.0163169	−	0.0282617i
$940$	−4.00000	−	6.92820i	−0.130466	−	0.225973i
$941$	19.5000	+	33.7750i	0.635682	+	1.10103i	0.986370	+	0.164541i	$0.0526143\pi$
$941$	19.5000	+	33.7750i	0.635682	+	1.10103i	−0.350688	+	0.936492i	$0.614052\pi$
$942$	−7.00000	+	12.1244i	−0.228072	+	0.395033i
$943$	2.00000	+	3.46410i	0.0651290	+	0.112807i
$944$	1.50000	−	2.59808i	0.0488208	−	0.0845602i
$945$	5.00000			0.162650
$946$	−8.00000			−0.260102
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	6.00000	+	10.3923i	0.194871	+	0.337526i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$	−2.00000	−	3.46410i	−0.0648886	−	0.112390i
$951$	−11.5000	−	19.9186i	−0.372913	−	0.645904i
$952$	−10.0000	−	17.3205i	−0.324102	−	0.561361i
$953$	−2.00000			−0.0647864			−0.0323932	−	0.999475i	$-0.510313\pi$
$953$	−2.00000			−0.0647864			−0.0323932	+	0.999475i	$0.510313\pi$
$954$	4.50000	−	7.79423i	0.145693	−	0.252347i
$955$	13.0000	−	22.5167i	0.420670	−	0.728622i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$	9.00000			0.290929
$958$	−4.00000	+	6.92820i	−0.129234	+	0.223840i
$959$	40.0000			1.29167
$960$	1.00000			0.0322749
$961$	29.5000	+	9.52628i	0.951613	+	0.307299i
$962$	8.00000			0.257930
$963$	11.0000			0.354470
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	25.0000			0.804778
$966$	−5.00000	−	8.66025i	−0.160872	−	0.278639i
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	−0.708245	−	0.705967i	$-0.750513\pi$
$967$	8.00000	−	13.8564i	0.257263	−	0.445592i	0.965508	+	0.260375i	$0.0838461\pi$
$968$	5.00000	−	8.66025i	0.160706	−	0.278351i
$969$	16.0000			0.513994
$970$	0.500000	+	0.866025i	0.0160540	+	0.0278064i
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.807473	−	0.589904i	$-0.799166\pi$
$971$	−28.5000	−	49.3634i	−0.914609	−	1.58415i	−0.107135	−	0.994244i	$-0.534168\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	50.0000	−	86.6025i	1.60293	−	2.77635i
$974$	−18.5000	−	32.0429i	−0.592778	−	1.02672i
$975$	−2.00000	+	3.46410i	−0.0640513	+	0.110940i
$976$	6.00000			0.192055
$977$	20.0000			0.639857			0.319928	−	0.947442i	$-0.396341\pi$
$977$	20.0000			0.639857			0.319928	+	0.947442i	$0.396341\pi$
$978$	−5.00000	+	8.66025i	−0.159882	+	0.276924i
$979$	−3.00000	−	5.19615i	−0.0958804	−	0.166070i
$980$	−9.00000	+	15.5885i	−0.287494	+	0.497955i
$981$	−4.00000	−	6.92820i	−0.127710	−	0.221201i
$982$	4.50000	+	7.79423i	0.143601	+	0.248724i
$983$	−13.0000	−	22.5167i	−0.414636	−	0.718170i	0.580755	−	0.814079i	$-0.302758\pi$
$983$	−13.0000	−	22.5167i	−0.414636	−	0.718170i	−0.995390	+	0.0959088i	$0.969424\pi$
$984$	−2.00000			−0.0637577
$985$	11.0000	−	19.0526i	0.350489	−	0.607065i
$986$	18.0000	−	31.1769i	0.573237	−	0.992875i
$987$	−20.0000	−	34.6410i	−0.636607	−	1.10264i
$988$	16.0000			0.509028
$989$	−8.00000	+	13.8564i	−0.254385	+	0.440608i
$990$	−1.00000			−0.0317821
$991$	40.0000			1.27064			0.635321	−	0.772248i	$-0.280868\pi$
$991$	40.0000			1.27064			0.635321	+	0.772248i	$0.280868\pi$
$992$	−5.50000	−	0.866025i	−0.174625	−	0.0274963i
$993$	34.0000			1.07896
$994$	−20.0000			−0.634361
$995$	−0.500000	+	0.866025i	−0.0158511	+	0.0274549i
$996$	−9.00000			−0.285176
$997$	−21.0000	−	36.3731i	−0.665077	−	1.15195i	−0.979265	−	0.202586i	$-0.935066\pi$
$997$	−21.0000	−	36.3731i	−0.665077	−	1.15195i	0.314188	−	0.949361i	$-0.398268\pi$
$998$	−5.00000	+	8.66025i	−0.158272	+	0.274136i
$999$	−1.00000	+	1.73205i	−0.0316386	+	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.d.811.1	yes	2
31.25	even	3	inner	930.2.i.d.211.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.d.211.1	✓	2	31.25	even	3	inner
930.2.i.d.811.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 - 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-2.50000 + 4.33013i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(-2.00000 - 3.46410i) q^{13} +(-2.50000 + 4.33013i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-2.00000 + 3.46410i) q^{19} +(-0.500000 - 0.866025i) q^{20} +(-2.50000 - 4.33013i) q^{21} +(0.500000 + 0.866025i) q^{22} +2.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(-2.00000 - 3.46410i) q^{26} +1.00000 q^{27} +(-2.50000 + 4.33013i) q^{28} -9.00000 q^{29} +1.00000 q^{30} +(-5.50000 - 0.866025i) q^{31} +1.00000 q^{32} -1.00000 q^{33} +(-2.00000 + 3.46410i) q^{34} +5.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} +(-2.00000 + 3.46410i) q^{38} +4.00000 q^{39} +(-0.500000 - 0.866025i) q^{40} +(1.00000 + 1.73205i) q^{41} +(-2.50000 - 4.33013i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(0.500000 + 0.866025i) q^{44} +(-0.500000 + 0.866025i) q^{45} +2.00000 q^{46} +8.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-9.00000 - 15.5885i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-2.00000 - 3.46410i) q^{51} +(-2.00000 - 3.46410i) q^{52} +(4.50000 + 7.79423i) q^{53} +1.00000 q^{54} +(0.500000 - 0.866025i) q^{55} +(-2.50000 + 4.33013i) q^{56} +(-2.00000 - 3.46410i) q^{57} -9.00000 q^{58} +(1.50000 - 2.59808i) q^{59} +1.00000 q^{60} +6.00000 q^{61} +(-5.50000 - 0.866025i) q^{62} +5.00000 q^{63} +1.00000 q^{64} +(-2.00000 + 3.46410i) q^{65} -1.00000 q^{66} +(5.00000 + 8.66025i) q^{67} +(-2.00000 + 3.46410i) q^{68} +(-1.00000 + 1.73205i) q^{69} +5.00000 q^{70} +(2.00000 + 3.46410i) q^{71} +(-0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(-2.00000 + 3.46410i) q^{76} -5.00000 q^{77} +4.00000 q^{78} +(6.00000 - 10.3923i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.00000 + 1.73205i) q^{82} +(4.50000 + 7.79423i) q^{83} +(-2.50000 - 4.33013i) q^{84} +4.00000 q^{85} +(-4.00000 + 6.92820i) q^{86} +(4.50000 - 7.79423i) q^{87} +(0.500000 + 0.866025i) q^{88} -6.00000 q^{89} +(-0.500000 + 0.866025i) q^{90} +20.0000 q^{91} +2.00000 q^{92} +(3.50000 - 4.33013i) q^{93} +8.00000 q^{94} +4.00000 q^{95} +(-0.500000 + 0.866025i) q^{96} -1.00000 q^{97} +(-9.00000 - 15.5885i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} - 5 q^{7} + 2 q^{8} - q^{9} - q^{10} + q^{11} - q^{12} - 4 q^{13} - 5 q^{14} + 2 q^{15} + 2 q^{16} - 4 q^{17} - q^{18} - 4 q^{19} - q^{20} - 5 q^{21} + q^{22} + 4 q^{23} - q^{24} - q^{25} - 4 q^{26} + 2 q^{27} - 5 q^{28} - 18 q^{29} + 2 q^{30} - 11 q^{31} + 2 q^{32} - 2 q^{33} - 4 q^{34} + 10 q^{35} - q^{36} - 2 q^{37} - 4 q^{38} + 8 q^{39} - q^{40} + 2 q^{41} - 5 q^{42} - 8 q^{43} + q^{44} - q^{45} + 4 q^{46} + 16 q^{47} - q^{48} - 18 q^{49} - q^{50} - 4 q^{51} - 4 q^{52} + 9 q^{53} + 2 q^{54} + q^{55} - 5 q^{56} - 4 q^{57} - 18 q^{58} + 3 q^{59} + 2 q^{60} + 12 q^{61} - 11 q^{62} + 10 q^{63} + 2 q^{64} - 4 q^{65} - 2 q^{66} + 10 q^{67} - 4 q^{68} - 2 q^{69} + 10 q^{70} + 4 q^{71} - q^{72} - 2 q^{73} - 2 q^{74} - q^{75} - 4 q^{76} - 10 q^{77} + 8 q^{78} + 12 q^{79} - q^{80} - q^{81} + 2 q^{82} + 9 q^{83} - 5 q^{84} + 8 q^{85} - 8 q^{86} + 9 q^{87} + q^{88} - 12 q^{89} - q^{90} + 40 q^{91} + 4 q^{92} + 7 q^{93} + 16 q^{94} + 8 q^{95} - q^{96} - 2 q^{97} - 18 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 - 5 * q^7 + 2 * q^8 - q^9 - q^10 + q^11 - q^12 - 4 * q^13 - 5 * q^14 + 2 * q^15 + 2 * q^16 - 4 * q^17 - q^18 - 4 * q^19 - q^20 - 5 * q^21 + q^22 + 4 * q^23 - q^24 - q^25 - 4 * q^26 + 2 * q^27 - 5 * q^28 - 18 * q^29 + 2 * q^30 - 11 * q^31 + 2 * q^32 - 2 * q^33 - 4 * q^34 + 10 * q^35 - q^36 - 2 * q^37 - 4 * q^38 + 8 * q^39 - q^40 + 2 * q^41 - 5 * q^42 - 8 * q^43 + q^44 - q^45 + 4 * q^46 + 16 * q^47 - q^48 - 18 * q^49 - q^50 - 4 * q^51 - 4 * q^52 + 9 * q^53 + 2 * q^54 + q^55 - 5 * q^56 - 4 * q^57 - 18 * q^58 + 3 * q^59 + 2 * q^60 + 12 * q^61 - 11 * q^62 + 10 * q^63 + 2 * q^64 - 4 * q^65 - 2 * q^66 + 10 * q^67 - 4 * q^68 - 2 * q^69 + 10 * q^70 + 4 * q^71 - q^72 - 2 * q^73 - 2 * q^74 - q^75 - 4 * q^76 - 10 * q^77 + 8 * q^78 + 12 * q^79 - q^80 - q^81 + 2 * q^82 + 9 * q^83 - 5 * q^84 + 8 * q^85 - 8 * q^86 + 9 * q^87 + q^88 - 12 * q^89 - q^90 + 40 * q^91 + 4 * q^92 + 7 * q^93 + 16 * q^94 + 8 * q^95 - q^96 - 2 * q^97 - 18 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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