LMFDB - Embedded newform 285.2.i.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [285,2,Mod(106,285)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(285, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4]))

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

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

chi := DirichletCharacter("285.106");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 285 = 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	285.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:	$2.27573645761$
Analytic rank:	$1$
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			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	285.121
Dual form			285.2.i.a.106.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} -2.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} -2.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} -3.00000 q^{11} +2.00000 q^{12} +(-3.00000 + 5.19615i) q^{13} +(2.00000 + 3.46410i) q^{14} +(0.500000 - 0.866025i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} -2.00000 q^{20} +(1.00000 + 1.73205i) q^{21} +(3.00000 + 5.19615i) q^{22} +(4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{25} +12.0000 q^{26} +1.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(-3.50000 + 6.06218i) q^{29} -2.00000 q^{30} +9.00000 q^{31} +(4.00000 - 6.92820i) q^{32} +(1.50000 + 2.59808i) q^{33} +(-6.00000 + 10.3923i) q^{34} +(-1.00000 - 1.73205i) q^{35} +(-1.00000 - 1.73205i) q^{36} -2.00000 q^{37} +(8.00000 + 3.46410i) q^{38} +6.00000 q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{42} +(-5.00000 - 8.66025i) q^{43} +(3.00000 - 5.19615i) q^{44} -1.00000 q^{45} -16.0000 q^{46} +(-2.00000 + 3.46410i) q^{47} +(2.00000 - 3.46410i) q^{48} -3.00000 q^{49} +2.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-6.00000 - 10.3923i) q^{52} +(-7.00000 + 12.1244i) q^{53} +(-1.00000 - 1.73205i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(4.00000 + 1.73205i) q^{57} +14.0000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(1.00000 + 1.73205i) q^{60} +(3.50000 - 6.06218i) q^{61} +(-9.00000 - 15.5885i) q^{62} +(1.00000 - 1.73205i) q^{63} -8.00000 q^{64} -6.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(-2.00000 + 3.46410i) q^{67} +12.0000 q^{68} -8.00000 q^{69} +(-2.00000 + 3.46410i) q^{70} +(-3.50000 - 6.06218i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(2.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(-1.00000 - 8.66025i) q^{76} +6.00000 q^{77} +(-6.00000 - 10.3923i) q^{78} +(-2.50000 - 4.33013i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -6.00000 q^{83} -4.00000 q^{84} +(3.00000 - 5.19615i) q^{85} +(-10.0000 + 17.3205i) q^{86} +7.00000 q^{87} +(-1.50000 + 2.59808i) q^{89} +(1.00000 + 1.73205i) q^{90} +(6.00000 - 10.3923i) q^{91} +(8.00000 + 13.8564i) q^{92} +(-4.50000 - 7.79423i) q^{93} +8.00000 q^{94} +(-4.00000 - 1.73205i) q^{95} -8.00000 q^{96} +(6.00000 + 10.3923i) q^{97} +(3.00000 + 5.19615i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 4 * q^7 - q^9	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 6 q^{13} + 4 q^{14} + q^{15} + 4 q^{16} - 6 q^{17} + 4 q^{18} - 7 q^{19} - 4 q^{20} + 2 q^{21} + 6 q^{22} + 8 q^{23} - q^{25} + 24 q^{26} + 2 q^{27} + 4 q^{28} - 7 q^{29} - 4 q^{30} + 18 q^{31} + 8 q^{32} + 3 q^{33} - 12 q^{34} - 2 q^{35} - 2 q^{36} - 4 q^{37} + 16 q^{38} + 12 q^{39} - 6 q^{41} + 4 q^{42} - 10 q^{43} + 6 q^{44} - 2 q^{45} - 32 q^{46} - 4 q^{47} + 4 q^{48} - 6 q^{49} + 4 q^{50} - 6 q^{51} - 12 q^{52} - 14 q^{53} - 2 q^{54} - 3 q^{55} + 8 q^{57} + 28 q^{58} - 3 q^{59} + 2 q^{60} + 7 q^{61} - 18 q^{62} + 2 q^{63} - 16 q^{64} - 12 q^{65} + 6 q^{66} - 4 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} - 7 q^{71} - 2 q^{73} + 4 q^{74} + 2 q^{75} - 2 q^{76} + 12 q^{77} - 12 q^{78} - 5 q^{79} - 4 q^{80} - q^{81} - 12 q^{82} - 12 q^{83} - 8 q^{84} + 6 q^{85} - 20 q^{86} + 14 q^{87} - 3 q^{89} + 2 q^{90} + 12 q^{91} + 16 q^{92} - 9 q^{93} + 16 q^{94} - 8 q^{95} - 16 q^{96} + 12 q^{97} + 6 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 4 * q^7 - q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 6 * q^13 + 4 * q^14 + q^15 + 4 * q^16 - 6 * q^17 + 4 * q^18 - 7 * q^19 - 4 * q^20 + 2 * q^21 + 6 * q^22 + 8 * q^23 - q^25 + 24 * q^26 + 2 * q^27 + 4 * q^28 - 7 * q^29 - 4 * q^30 + 18 * q^31 + 8 * q^32 + 3 * q^33 - 12 * q^34 - 2 * q^35 - 2 * q^36 - 4 * q^37 + 16 * q^38 + 12 * q^39 - 6 * q^41 + 4 * q^42 - 10 * q^43 + 6 * q^44 - 2 * q^45 - 32 * q^46 - 4 * q^47 + 4 * q^48 - 6 * q^49 + 4 * q^50 - 6 * q^51 - 12 * q^52 - 14 * q^53 - 2 * q^54 - 3 * q^55 + 8 * q^57 + 28 * q^58 - 3 * q^59 + 2 * q^60 + 7 * q^61 - 18 * q^62 + 2 * q^63 - 16 * q^64 - 12 * q^65 + 6 * q^66 - 4 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 - 7 * q^71 - 2 * q^73 + 4 * q^74 + 2 * q^75 - 2 * q^76 + 12 * q^77 - 12 * q^78 - 5 * q^79 - 4 * q^80 - q^81 - 12 * q^82 - 12 * q^83 - 8 * q^84 + 6 * q^85 - 20 * q^86 + 14 * q^87 - 3 * q^89 + 2 * q^90 + 12 * q^91 + 16 * q^92 - 9 * q^93 + 16 * q^94 - 8 * q^95 - 16 * q^96 + 12 * q^97 + 6 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/285\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$211$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−1.00000	+	1.73205i	−0.408248	+	0.707107i
$7$	−2.00000			−0.755929			−0.377964	−	0.925820i	$-0.623376\pi$
$7$	−2.00000			−0.755929			−0.377964	+	0.925820i	$0.623376\pi$
$8$		0			0
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$	2.00000			0.577350
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	0.0643593	+	0.997927i	$0.479500\pi$
$13$	−3.00000	+	5.19615i	−0.832050	+	1.44115i	−0.896410	+	0.443227i	$0.853834\pi$
$14$	2.00000	+	3.46410i	0.534522	+	0.925820i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$	2.00000			0.471405
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$19$	−3.50000	+	2.59808i	−0.802955	+	0.596040i
$20$	−2.00000			−0.447214
$21$	1.00000	+	1.73205i	0.218218	+	0.377964i
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	−0.0607377	−	0.998154i	$-0.519345\pi$
$23$	4.00000	−	6.92820i	0.834058	−	1.44463i	0.894795	−	0.446476i	$-0.147321\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	12.0000			2.35339
$27$	1.00000			0.192450
$28$	2.00000	−	3.46410i	0.377964	−	0.654654i
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	0.333205	+	0.942855i	$0.391870\pi$
$29$	−3.50000	+	6.06218i	−0.649934	+	1.12572i	−0.983138	+	0.182864i	$0.941463\pi$
$30$	−2.00000			−0.365148
$31$	9.00000			1.61645			0.808224	−	0.588875i	$-0.200429\pi$
$31$	9.00000			1.61645			0.808224	+	0.588875i	$0.200429\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$	1.50000	+	2.59808i	0.261116	+	0.452267i
$34$	−6.00000	+	10.3923i	−1.02899	+	1.78227i
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$	8.00000	+	3.46410i	1.29777	+	0.561951i
$39$	6.00000			0.960769
$40$		0			0
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	0.530831	−	0.847477i	$-0.321880\pi$
$41$	−3.00000	−	5.19615i	−0.468521	−	0.811503i	−0.999353	+	0.0359748i	$0.988546\pi$
$42$	2.00000	−	3.46410i	0.308607	−	0.534522i
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	−0.941562	−	0.336840i	$-0.890642\pi$
$43$	−5.00000	−	8.66025i	−0.762493	−	1.32068i	0.179069	−	0.983836i	$-0.442691\pi$
$44$	3.00000	−	5.19615i	0.452267	−	0.783349i
$45$	−1.00000			−0.149071
$46$	−16.0000			−2.35907
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	−0.974219	−	0.225605i	$-0.927564\pi$
$47$	−2.00000	+	3.46410i	−0.291730	+	0.505291i	0.682489	+	0.730896i	$0.260898\pi$
$48$	2.00000	−	3.46410i	0.288675	−	0.500000i
$49$	−3.00000			−0.428571
$50$	2.00000			0.282843
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	−6.00000	−	10.3923i	−0.832050	−	1.44115i
$53$	−7.00000	+	12.1244i	−0.961524	+	1.66541i	−0.242846	+	0.970065i	$0.578081\pi$
$53$	−7.00000	+	12.1244i	−0.961524	+	1.66541i	−0.718677	+	0.695344i	$0.755252\pi$
$54$	−1.00000	−	1.73205i	−0.136083	−	0.235702i
$55$	−1.50000	−	2.59808i	−0.202260	−	0.350325i
$56$		0			0
$57$	4.00000	+	1.73205i	0.529813	+	0.229416i
$58$	14.0000			1.83829
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	0.751710	−	0.659494i	$-0.229229\pi$
$59$	−1.50000	−	2.59808i	−0.195283	−	0.338241i	−0.946993	+	0.321253i	$0.895896\pi$
$60$	1.00000	+	1.73205i	0.129099	+	0.223607i
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	−0.550135	−	0.835076i	$-0.685424\pi$
$61$	3.50000	−	6.06218i	0.448129	−	0.776182i	0.998264	+	0.0588933i	$0.0187572\pi$
$62$	−9.00000	−	15.5885i	−1.14300	−	1.97974i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	−8.00000			−1.00000
$65$	−6.00000			−0.744208
$66$	3.00000	−	5.19615i	0.369274	−	0.639602i
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	12.0000			1.45521
$69$	−8.00000			−0.963087
$70$	−2.00000	+	3.46410i	−0.239046	+	0.414039i
$71$	−3.50000	−	6.06218i	−0.415374	−	0.719448i	0.580094	−	0.814550i	$-0.303016\pi$
$71$	−3.50000	−	6.06218i	−0.415374	−	0.719448i	−0.995468	+	0.0951014i	$0.969682\pi$
$72$		0			0
$73$	−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	$0.870674\pi$
$74$	2.00000	+	3.46410i	0.232495	+	0.402694i
$75$	1.00000			0.115470
$76$	−1.00000	−	8.66025i	−0.114708	−	0.993399i
$77$	6.00000			0.683763
$78$	−6.00000	−	10.3923i	−0.679366	−	1.17670i
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−6.00000	+	10.3923i	−0.662589	+	1.14764i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−4.00000			−0.436436
$85$	3.00000	−	5.19615i	0.325396	−	0.563602i
$86$	−10.0000	+	17.3205i	−1.07833	+	1.86772i
$87$	7.00000			0.750479
$88$		0			0
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$	1.00000	+	1.73205i	0.105409	+	0.182574i
$91$	6.00000	−	10.3923i	0.628971	−	1.08941i
$92$	8.00000	+	13.8564i	0.834058	+	1.44463i
$93$	−4.50000	−	7.79423i	−0.466628	−	0.808224i
$94$	8.00000			0.825137
$95$	−4.00000	−	1.73205i	−0.410391	−	0.177705i
$96$	−8.00000			−0.816497
$97$	6.00000	+	10.3923i	0.609208	+	1.05518i	0.991371	+	0.131084i	$0.0418458\pi$
$97$	6.00000	+	10.3923i	0.609208	+	1.05518i	−0.382164	+	0.924095i	$0.624821\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	1.50000	−	2.59808i	0.150756	−	0.261116i
$100$	−1.00000	−	1.73205i	−0.100000	−	0.173205i
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	−0.781697	−	0.623658i	$-0.785646\pi$
$101$	1.50000	−	2.59808i	0.149256	−	0.258518i	0.930953	+	0.365140i	$0.118979\pi$
$102$	12.0000			1.18818
$103$	−8.00000			−0.788263			−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000			−0.788263			−0.394132	+	0.919054i	$0.628955\pi$
$104$		0			0
$105$	−1.00000	+	1.73205i	−0.0975900	+	0.169031i
$106$	28.0000			2.71960
$107$	12.0000			1.16008			0.580042	−	0.814587i	$-0.303036\pi$
$107$	12.0000			1.16008			0.580042	+	0.814587i	$0.303036\pi$
$108$	−1.00000	+	1.73205i	−0.0962250	+	0.166667i
$109$	−1.50000	−	2.59808i	−0.143674	−	0.248851i	0.785203	−	0.619238i	$-0.212558\pi$
$109$	−1.50000	−	2.59808i	−0.143674	−	0.248851i	−0.928877	+	0.370387i	$0.879225\pi$
$110$	−3.00000	+	5.19615i	−0.286039	+	0.495434i
$111$	1.00000	+	1.73205i	0.0949158	+	0.164399i
$112$	−4.00000	−	6.92820i	−0.377964	−	0.654654i
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$	−1.00000	−	8.66025i	−0.0936586	−	0.811107i
$115$	8.00000			0.746004
$116$	−7.00000	−	12.1244i	−0.649934	−	1.12572i
$117$	−3.00000	−	5.19615i	−0.277350	−	0.480384i
$118$	−3.00000	+	5.19615i	−0.276172	+	0.478345i
$119$	6.00000	+	10.3923i	0.550019	+	0.952661i
$120$		0			0
$121$	−2.00000			−0.181818
$122$	−14.0000			−1.26750
$123$	−3.00000	+	5.19615i	−0.270501	+	0.468521i
$124$	−9.00000	+	15.5885i	−0.808224	+	1.39988i
$125$	−1.00000			−0.0894427
$126$	−4.00000			−0.356348
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$		0			0
$129$	−5.00000	+	8.66025i	−0.440225	+	0.762493i
$130$	6.00000	+	10.3923i	0.526235	+	0.911465i
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	0.986157	−	0.165812i	$-0.0530244\pi$
$131$	4.00000	+	6.92820i	0.349482	+	0.605320i	−0.636676	+	0.771132i	$0.719691\pi$
$132$	−6.00000			−0.522233
$133$	7.00000	−	5.19615i	0.606977	−	0.450564i
$134$	8.00000			0.691095
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$		0			0
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$	8.00000	+	13.8564i	0.681005	+	1.17954i
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	4.00000			0.338062
$141$	4.00000			0.336861
$142$	−7.00000	+	12.1244i	−0.587427	+	1.01745i
$143$	9.00000	−	15.5885i	0.752618	−	1.30357i
$144$	−4.00000			−0.333333
$145$	−7.00000			−0.581318
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$	2.00000	−	3.46410i	0.164399	−	0.284747i
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$	−1.00000	−	1.73205i	−0.0816497	−	0.141421i
$151$	5.00000			0.406894			0.203447	−	0.979086i	$-0.434786\pi$
$151$	5.00000			0.406894			0.203447	+	0.979086i	$0.434786\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$	−6.00000	−	10.3923i	−0.483494	−	0.837436i
$155$	4.50000	+	7.79423i	0.361449	+	0.626048i
$156$	−6.00000	+	10.3923i	−0.480384	+	0.832050i
$157$	10.0000	+	17.3205i	0.798087	+	1.38233i	0.920860	+	0.389892i	$0.127488\pi$
$157$	10.0000	+	17.3205i	0.798087	+	1.38233i	−0.122774	+	0.992435i	$0.539179\pi$
$158$	−5.00000	+	8.66025i	−0.397779	+	0.688973i
$159$	14.0000			1.11027
$160$	8.00000			0.632456
$161$	−8.00000	+	13.8564i	−0.630488	+	1.09204i
$162$	−1.00000	+	1.73205i	−0.0785674	+	0.136083i
$163$	−10.0000			−0.783260			−0.391630	−	0.920123i	$-0.628089\pi$
$163$	−10.0000			−0.783260			−0.391630	+	0.920123i	$0.628089\pi$
$164$	12.0000			0.937043
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	−11.0000	+	19.0526i	−0.851206	+	1.47433i	0.0289155	+	0.999582i	$0.490795\pi$
$167$	−11.0000	+	19.0526i	−0.851206	+	1.47433i	−0.880121	+	0.474749i	$0.842539\pi$
$168$		0			0
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$	−12.0000			−0.920358
$171$	−0.500000	−	4.33013i	−0.0382360	−	0.331133i
$172$	20.0000			1.52499
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	0.729155	−	0.684349i	$-0.239913\pi$
$173$	−3.00000	−	5.19615i	−0.228086	−	0.395056i	−0.957241	+	0.289292i	$0.906580\pi$
$174$	−7.00000	−	12.1244i	−0.530669	−	0.919145i
$175$	1.00000	−	1.73205i	0.0755929	−	0.130931i
$176$	−6.00000	−	10.3923i	−0.452267	−	0.783349i
$177$	−1.50000	+	2.59808i	−0.112747	+	0.195283i
$178$	6.00000			0.449719
$179$	1.00000			0.0747435			0.0373718	−	0.999301i	$-0.488101\pi$
$179$	1.00000			0.0747435			0.0373718	+	0.999301i	$0.488101\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	7.00000	−	12.1244i	0.520306	−	0.901196i	−0.479415	−	0.877588i	$-0.659151\pi$
$181$	7.00000	−	12.1244i	0.520306	−	0.901196i	0.999721	−	0.0236082i	$-0.00751541\pi$
$182$	−24.0000			−1.77900
$183$	−7.00000			−0.517455
$184$		0			0
$185$	−1.00000	−	1.73205i	−0.0735215	−	0.127343i
$186$	−9.00000	+	15.5885i	−0.659912	+	1.14300i
$187$	9.00000	+	15.5885i	0.658145	+	1.13994i
$188$	−4.00000	−	6.92820i	−0.291730	−	0.505291i
$189$	−2.00000			−0.145479
$190$	1.00000	+	8.66025i	0.0725476	+	0.628281i
$191$	−5.00000			−0.361787			−0.180894	−	0.983503i	$-0.557899\pi$
$191$	−5.00000			−0.361787			−0.180894	+	0.983503i	$0.557899\pi$
$192$	4.00000	+	6.92820i	0.288675	+	0.500000i
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$	12.0000	−	20.7846i	0.861550	−	1.49225i
$195$	3.00000	+	5.19615i	0.214834	+	0.372104i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	−6.00000			−0.426401
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	−0.602549	−	0.798082i	$-0.705848\pi$
$199$	5.50000	−	9.52628i	0.389885	−	0.675300i	0.992434	+	0.122782i	$0.0391815\pi$
$200$		0			0
$201$	4.00000			0.282138
$202$	−6.00000			−0.422159
$203$	7.00000	−	12.1244i	0.491304	−	0.850963i
$204$	−6.00000	−	10.3923i	−0.420084	−	0.727607i
$205$	3.00000	−	5.19615i	0.209529	−	0.362915i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$	4.00000	+	6.92820i	0.278019	+	0.481543i
$208$	−24.0000			−1.66410
$209$	10.5000	−	7.79423i	0.726300	−	0.539138i
$210$	4.00000			0.276026
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	0.550743	−	0.834675i	$-0.314345\pi$
$211$	−6.50000	−	11.2583i	−0.447478	−	0.775055i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−14.0000	−	24.2487i	−0.961524	−	1.66541i
$213$	−3.50000	+	6.06218i	−0.239816	+	0.415374i
$214$	−12.0000	−	20.7846i	−0.820303	−	1.42081i
$215$	5.00000	−	8.66025i	0.340997	−	0.590624i
$216$		0			0
$217$	−18.0000			−1.22192
$218$	−3.00000	+	5.19615i	−0.203186	+	0.351928i
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$	6.00000			0.404520
$221$	36.0000			2.42162
$222$	2.00000	−	3.46410i	0.134231	−	0.232495i
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	−8.00000	+	13.8564i	−0.534522	+	0.925820i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−6.00000	−	10.3923i	−0.399114	−	0.691286i
$227$	14.0000			0.929213			0.464606	−	0.885517i	$-0.346196\pi$
$227$	14.0000			0.929213			0.464606	+	0.885517i	$0.346196\pi$
$228$	−7.00000	+	5.19615i	−0.463586	+	0.344124i
$229$	29.0000			1.91637			0.958187	−	0.286143i	$-0.0923732\pi$
$229$	29.0000			1.91637			0.958187	+	0.286143i	$0.0923732\pi$
$230$	−8.00000	−	13.8564i	−0.527504	−	0.913664i
$231$	−3.00000	−	5.19615i	−0.197386	−	0.341882i
$232$		0			0
$233$	−8.00000	−	13.8564i	−0.524097	−	0.907763i	−0.999606	−	0.0280525i	$-0.991069\pi$
$233$	−8.00000	−	13.8564i	−0.524097	−	0.907763i	0.475509	−	0.879711i	$-0.342264\pi$
$234$	−6.00000	+	10.3923i	−0.392232	+	0.679366i
$235$	−4.00000			−0.260931
$236$	6.00000			0.390567
$237$	−2.50000	+	4.33013i	−0.162392	+	0.281272i
$238$	12.0000	−	20.7846i	0.777844	−	1.34727i
$239$	−9.00000			−0.582162			−0.291081	−	0.956698i	$-0.594015\pi$
$239$	−9.00000			−0.582162			−0.291081	+	0.956698i	$0.594015\pi$
$240$	4.00000			0.258199
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	0.299704	+	0.954032i	$0.403112\pi$
$241$	−10.5000	+	18.1865i	−0.676364	+	1.17150i	−0.976068	+	0.217465i	$0.930221\pi$
$242$	2.00000	+	3.46410i	0.128565	+	0.222681i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	7.00000	+	12.1244i	0.448129	+	0.776182i
$245$	−1.50000	−	2.59808i	−0.0958315	−	0.165985i
$246$	12.0000			0.765092
$247$	−3.00000	−	25.9808i	−0.190885	−	1.65312i
$248$		0			0
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$	1.00000	+	1.73205i	0.0632456	+	0.109545i
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	−0.909475	−	0.415759i	$-0.863516\pi$
$251$	−1.50000	+	2.59808i	−0.0946792	+	0.163989i	0.814795	+	0.579748i	$0.196849\pi$
$252$	2.00000	+	3.46410i	0.125988	+	0.218218i
$253$	−12.0000	+	20.7846i	−0.754434	+	1.30672i
$254$	−16.0000			−1.00393
$255$	−6.00000			−0.375735
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	−0.895528	−	0.445005i	$-0.853202\pi$
$257$	−1.00000	+	1.73205i	−0.0623783	+	0.108042i	0.833150	+	0.553047i	$0.186535\pi$
$258$	20.0000			1.24515
$259$	4.00000			0.248548
$260$	6.00000	−	10.3923i	0.372104	−	0.644503i
$261$	−3.50000	−	6.06218i	−0.216645	−	0.375239i
$262$	8.00000	−	13.8564i	0.494242	−	0.856052i
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	0.619586	−	0.784929i	$-0.287301\pi$
$263$	−6.00000	−	10.3923i	−0.369976	−	0.640817i	−0.989561	+	0.144112i	$0.953967\pi$
$264$		0			0
$265$	−14.0000			−0.860013
$266$	−16.0000	−	6.92820i	−0.981023	−	0.424795i
$267$	3.00000			0.183597
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	−0.985389	−	0.170321i	$-0.945520\pi$
$269$	−10.5000	−	18.1865i	−0.640196	−	1.10885i	0.345192	−	0.938532i	$-0.387814\pi$
$270$	1.00000	−	1.73205i	0.0608581	−	0.105409i
$271$	2.50000	+	4.33013i	0.151864	+	0.263036i	0.931913	−	0.362682i	$-0.118139\pi$
$271$	2.50000	+	4.33013i	0.151864	+	0.263036i	−0.780049	+	0.625719i	$0.784806\pi$
$272$	12.0000	−	20.7846i	0.727607	−	1.26025i
$273$	−12.0000			−0.726273
$274$	4.00000			0.241649
$275$	1.50000	−	2.59808i	0.0904534	−	0.156670i
$276$	8.00000	−	13.8564i	0.481543	−	0.834058i
$277$	16.0000			0.961347			0.480673	−	0.876900i	$-0.340392\pi$
$277$	16.0000			0.961347			0.480673	+	0.876900i	$0.340392\pi$
$278$	−8.00000			−0.479808
$279$	−4.50000	+	7.79423i	−0.269408	+	0.466628i
$280$		0			0
$281$	−7.00000	+	12.1244i	−0.417585	+	0.723278i	−0.995696	−	0.0926797i	$-0.970457\pi$
$281$	−7.00000	+	12.1244i	−0.417585	+	0.723278i	0.578111	+	0.815958i	$0.303790\pi$
$282$	−4.00000	−	6.92820i	−0.238197	−	0.412568i
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	0.936039	+	0.351895i	$0.114463\pi$
$283$	13.0000	+	22.5167i	0.772770	+	1.33848i	−0.163270	+	0.986581i	$0.552204\pi$
$284$	14.0000			0.830747
$285$	0.500000	+	4.33013i	0.0296174	+	0.256495i
$286$	−36.0000			−2.12872
$287$	6.00000	+	10.3923i	0.354169	+	0.613438i
$288$	4.00000	+	6.92820i	0.235702	+	0.408248i
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$	7.00000	+	12.1244i	0.411054	+	0.711967i
$291$	6.00000	−	10.3923i	0.351726	−	0.609208i
$292$	4.00000			0.234082
$293$	−12.0000			−0.701047			−0.350524	−	0.936554i	$-0.613996\pi$
$293$	−12.0000			−0.701047			−0.350524	+	0.936554i	$0.613996\pi$
$294$	3.00000	−	5.19615i	0.174964	−	0.303046i
$295$	1.50000	−	2.59808i	0.0873334	−	0.151266i
$296$		0			0
$297$	−3.00000			−0.174078
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	24.0000	+	41.5692i	1.38796	+	2.40401i
$300$	−1.00000	+	1.73205i	−0.0577350	+	0.100000i
$301$	10.0000	+	17.3205i	0.576390	+	0.998337i
$302$	−5.00000	−	8.66025i	−0.287718	−	0.498342i
$303$	−3.00000			−0.172345
$304$	−16.0000	−	6.92820i	−0.917663	−	0.397360i
$305$	7.00000			0.400819
$306$	−6.00000	−	10.3923i	−0.342997	−	0.594089i
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	0.542194	−	0.840254i	$-0.317594\pi$
$307$	−8.00000	−	13.8564i	−0.456584	−	0.790827i	−0.998778	+	0.0494267i	$0.984261\pi$
$308$	−6.00000	+	10.3923i	−0.341882	+	0.592157i
$309$	4.00000	+	6.92820i	0.227552	+	0.394132i
$310$	9.00000	−	15.5885i	0.511166	−	0.885365i
$311$	−8.00000			−0.453638			−0.226819	−	0.973937i	$-0.572833\pi$
$311$	−8.00000			−0.453638			−0.226819	+	0.973937i	$0.572833\pi$
$312$		0			0
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	−0.730554	−	0.682855i	$-0.760738\pi$
$313$	4.00000	−	6.92820i	0.226093	−	0.391605i	0.956647	+	0.291250i	$0.0940712\pi$
$314$	20.0000	−	34.6410i	1.12867	−	1.95491i
$315$	2.00000			0.112687
$316$	10.0000			0.562544
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	−0.983866	−	0.178908i	$-0.942743\pi$
$317$	−6.00000	+	10.3923i	−0.336994	+	0.583690i	0.646872	+	0.762598i	$0.276077\pi$
$318$	−14.0000	−	24.2487i	−0.785081	−	1.35980i
$319$	10.5000	−	18.1865i	0.587887	−	1.01825i
$320$	−4.00000	−	6.92820i	−0.223607	−	0.387298i
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$	32.0000			1.78329
$323$	24.0000	+	10.3923i	1.33540	+	0.578243i
$324$	2.00000			0.111111
$325$	−3.00000	−	5.19615i	−0.166410	−	0.288231i
$326$	10.0000	+	17.3205i	0.553849	+	0.959294i
$327$	−1.50000	+	2.59808i	−0.0829502	+	0.143674i
$328$		0			0
$329$	4.00000	−	6.92820i	0.220527	−	0.381964i
$330$	6.00000			0.330289
$331$	−8.00000			−0.439720			−0.219860	−	0.975531i	$-0.570560\pi$
$331$	−8.00000			−0.439720			−0.219860	+	0.975531i	$0.570560\pi$
$332$	6.00000	−	10.3923i	0.329293	−	0.570352i
$333$	1.00000	−	1.73205i	0.0547997	−	0.0949158i
$334$	44.0000			2.40757
$335$	−4.00000			−0.218543
$336$	−4.00000	+	6.92820i	−0.218218	+	0.377964i
$337$	6.00000	+	10.3923i	0.326841	+	0.566105i	0.981883	−	0.189487i	$-0.0606826\pi$
$337$	6.00000	+	10.3923i	0.326841	+	0.566105i	−0.655042	+	0.755592i	$0.727349\pi$
$338$	−23.0000	+	39.8372i	−1.25104	+	2.16686i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$	6.00000	+	10.3923i	0.325396	+	0.563602i
$341$	−27.0000			−1.46213
$342$	−7.00000	+	5.19615i	−0.378517	+	0.280976i
$343$	20.0000			1.07990
$344$		0			0
$345$	−4.00000	−	6.92820i	−0.215353	−	0.373002i
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	0.837935	−	0.545770i	$-0.183763\pi$
$347$	−1.00000	−	1.73205i	−0.0536828	−	0.0929814i	−0.891618	+	0.452788i	$0.850429\pi$
$348$	−7.00000	+	12.1244i	−0.375239	+	0.649934i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$	−4.00000			−0.213809
$351$	−3.00000	+	5.19615i	−0.160128	+	0.277350i
$352$	−12.0000	+	20.7846i	−0.639602	+	1.10782i
$353$	2.00000			0.106449			0.0532246	−	0.998583i	$-0.483050\pi$
$353$	2.00000			0.106449			0.0532246	+	0.998583i	$0.483050\pi$
$354$	6.00000			0.318896
$355$	3.50000	−	6.06218i	0.185761	−	0.321747i
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	6.00000	−	10.3923i	0.317554	−	0.550019i
$358$	−1.00000	−	1.73205i	−0.0528516	−	0.0915417i
$359$	16.0000	+	27.7128i	0.844448	+	1.46263i	0.886100	+	0.463494i	$0.153404\pi$
$359$	16.0000	+	27.7128i	0.844448	+	1.46263i	−0.0416523	+	0.999132i	$0.513262\pi$
$360$		0			0
$361$	5.50000	−	18.1865i	0.289474	−	0.957186i
$362$	−28.0000			−1.47165
$363$	1.00000	+	1.73205i	0.0524864	+	0.0909091i
$364$	12.0000	+	20.7846i	0.628971	+	1.08941i
$365$	1.00000	−	1.73205i	0.0523424	−	0.0906597i
$366$	7.00000	+	12.1244i	0.365896	+	0.633750i
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	−0.477677	−	0.878536i	$-0.658521\pi$
$367$	10.0000	−	17.3205i	0.521996	−	0.904123i	0.999673	−	0.0255875i	$-0.00814566\pi$
$368$	32.0000			1.66812
$369$	6.00000			0.312348
$370$	−2.00000	+	3.46410i	−0.103975	+	0.180090i
$371$	14.0000	−	24.2487i	0.726844	−	1.25893i
$372$	18.0000			0.933257
$373$	−24.0000			−1.24267			−0.621336	−	0.783544i	$-0.713410\pi$
$373$	−24.0000			−1.24267			−0.621336	+	0.783544i	$0.713410\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−21.0000	−	36.3731i	−1.08156	−	1.87331i
$378$	2.00000	+	3.46410i	0.102869	+	0.178174i
$379$	−25.0000			−1.28416			−0.642082	−	0.766636i	$-0.721929\pi$
$379$	−25.0000			−1.28416			−0.642082	+	0.766636i	$0.721929\pi$
$380$	7.00000	−	5.19615i	0.359092	−	0.266557i
$381$	−8.00000			−0.409852
$382$	5.00000	+	8.66025i	0.255822	+	0.443097i
$383$	17.0000	+	29.4449i	0.868659	+	1.50456i	0.863367	+	0.504576i	$0.168351\pi$
$383$	17.0000	+	29.4449i	0.868659	+	1.50456i	0.00529229	+	0.999986i	$0.498315\pi$
$384$		0			0
$385$	3.00000	+	5.19615i	0.152894	+	0.264820i
$386$	18.0000	−	31.1769i	0.916176	−	1.58686i
$387$	10.0000			0.508329
$388$	−24.0000			−1.21842
$389$	−18.5000	+	32.0429i	−0.937987	+	1.62464i	−0.168769	+	0.985656i	$0.553979\pi$
$389$	−18.5000	+	32.0429i	−0.937987	+	1.62464i	−0.769218	+	0.638986i	$0.779354\pi$
$390$	6.00000	−	10.3923i	0.303822	−	0.526235i
$391$	−48.0000			−2.42746
$392$		0			0
$393$	4.00000	−	6.92820i	0.201773	−	0.349482i
$394$	18.0000	+	31.1769i	0.906827	+	1.57067i
$395$	2.50000	−	4.33013i	0.125789	−	0.217872i
$396$	3.00000	+	5.19615i	0.150756	+	0.261116i
$397$	−6.00000	−	10.3923i	−0.301131	−	0.521575i	0.675261	−	0.737579i	$-0.264031\pi$
$397$	−6.00000	−	10.3923i	−0.301131	−	0.521575i	−0.976392	+	0.216004i	$0.930698\pi$
$398$	−22.0000			−1.10276
$399$	−8.00000	−	3.46410i	−0.400501	−	0.173422i
$400$	−4.00000			−0.200000
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	0.996119	+	0.0880147i	$0.0280523\pi$
$401$	11.5000	+	19.9186i	0.574283	+	0.994687i	−0.421837	+	0.906672i	$0.638614\pi$
$402$	−4.00000	−	6.92820i	−0.199502	−	0.345547i
$403$	−27.0000	+	46.7654i	−1.34497	+	2.32955i
$404$	3.00000	+	5.19615i	0.149256	+	0.258518i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	−28.0000			−1.38962
$407$	6.00000			0.297409
$408$		0			0
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	−0.969363	−	0.245633i	$-0.921004\pi$
$409$	−5.50000	+	9.52628i	−0.271957	+	0.471044i	0.697406	+	0.716677i	$0.254338\pi$
$410$	−12.0000			−0.592638
$411$	2.00000			0.0986527
$412$	8.00000	−	13.8564i	0.394132	−	0.682656i
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$	8.00000	−	13.8564i	0.393179	−	0.681005i
$415$	−3.00000	−	5.19615i	−0.147264	−	0.255069i
$416$	24.0000	+	41.5692i	1.17670	+	2.03810i
$417$	−4.00000			−0.195881
$418$	−24.0000	−	10.3923i	−1.17388	−	0.508304i
$419$	−9.00000			−0.439679			−0.219839	−	0.975536i	$-0.570553\pi$
$419$	−9.00000			−0.439679			−0.219839	+	0.975536i	$0.570553\pi$
$420$	−2.00000	−	3.46410i	−0.0975900	−	0.169031i
$421$	−4.50000	−	7.79423i	−0.219317	−	0.379867i	0.735283	−	0.677761i	$-0.237049\pi$
$421$	−4.50000	−	7.79423i	−0.219317	−	0.379867i	−0.954599	+	0.297893i	$0.903716\pi$
$422$	−13.0000	+	22.5167i	−0.632830	+	1.09609i
$423$	−2.00000	−	3.46410i	−0.0972433	−	0.168430i
$424$		0			0
$425$	6.00000			0.291043
$426$	14.0000			0.678302
$427$	−7.00000	+	12.1244i	−0.338754	+	0.586739i
$428$	−12.0000	+	20.7846i	−0.580042	+	1.00466i
$429$	−18.0000			−0.869048
$430$	−20.0000			−0.964486
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	−0.494211	−	0.869342i	$-0.664543\pi$
$431$	10.5000	−	18.1865i	0.505767	−	0.876014i	0.999978	−	0.00667224i	$-0.00212386\pi$
$432$	2.00000	+	3.46410i	0.0962250	+	0.166667i
$433$	5.00000	−	8.66025i	0.240285	−	0.416185i	−0.720511	−	0.693444i	$-0.756093\pi$
$433$	5.00000	−	8.66025i	0.240285	−	0.416185i	0.960795	+	0.277259i	$0.0894259\pi$
$434$	18.0000	+	31.1769i	0.864028	+	1.49654i
$435$	3.50000	+	6.06218i	0.167812	+	0.290659i
$436$	6.00000			0.287348
$437$	4.00000	+	34.6410i	0.191346	+	1.65710i
$438$	4.00000			0.191127
$439$	4.50000	+	7.79423i	0.214773	+	0.371998i	0.953202	−	0.302333i	$-0.0977654\pi$
$439$	4.50000	+	7.79423i	0.214773	+	0.371998i	−0.738429	+	0.674331i	$0.764432\pi$
$440$		0			0
$441$	1.50000	−	2.59808i	0.0714286	−	0.123718i
$442$	−36.0000	−	62.3538i	−1.71235	−	2.96587i
$443$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$443$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$444$	−4.00000			−0.189832
$445$	−3.00000			−0.142214
$446$	−8.00000	+	13.8564i	−0.378811	+	0.656120i
$447$	1.50000	−	2.59808i	0.0709476	−	0.122885i
$448$	16.0000			0.755929
$449$	13.0000			0.613508			0.306754	−	0.951789i	$-0.400757\pi$
$449$	13.0000			0.613508			0.306754	+	0.951789i	$0.400757\pi$
$450$	−1.00000	+	1.73205i	−0.0471405	+	0.0816497i
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	−2.50000	−	4.33013i	−0.117460	−	0.203447i
$454$	−14.0000	−	24.2487i	−0.657053	−	1.13805i
$455$	12.0000			0.562569
$456$		0			0
$457$	12.0000			0.561336			0.280668	−	0.959805i	$-0.409444\pi$
$457$	12.0000			0.561336			0.280668	+	0.959805i	$0.409444\pi$
$458$	−29.0000	−	50.2295i	−1.35508	−	2.34707i
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$	−8.00000	+	13.8564i	−0.373002	+	0.646058i
$461$	−16.5000	−	28.5788i	−0.768482	−	1.33105i	−0.938386	−	0.345589i	$-0.887679\pi$
$461$	−16.5000	−	28.5788i	−0.768482	−	1.33105i	0.169904	−	0.985461i	$-0.445654\pi$
$462$	−6.00000	+	10.3923i	−0.279145	+	0.483494i
$463$	−26.0000			−1.20832			−0.604161	−	0.796862i	$-0.706492\pi$
$463$	−26.0000			−1.20832			−0.604161	+	0.796862i	$0.706492\pi$
$464$	−28.0000			−1.29987
$465$	4.50000	−	7.79423i	0.208683	−	0.361449i
$466$	−16.0000	+	27.7128i	−0.741186	+	1.28377i
$467$	−18.0000			−0.832941			−0.416470	−	0.909149i	$-0.636733\pi$
$467$	−18.0000			−0.832941			−0.416470	+	0.909149i	$0.636733\pi$
$468$	12.0000			0.554700
$469$	4.00000	−	6.92820i	0.184703	−	0.319915i
$470$	4.00000	+	6.92820i	0.184506	+	0.319574i
$471$	10.0000	−	17.3205i	0.460776	−	0.798087i
$472$		0			0
$473$	15.0000	+	25.9808i	0.689701	+	1.19460i
$474$	10.0000			0.459315
$475$	−0.500000	−	4.33013i	−0.0229416	−	0.198680i
$476$	−24.0000			−1.10004
$477$	−7.00000	−	12.1244i	−0.320508	−	0.555136i
$478$	9.00000	+	15.5885i	0.411650	+	0.712999i
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	−0.642246	−	0.766498i	$-0.721997\pi$
$479$	7.50000	−	12.9904i	0.342684	−	0.593546i	0.984930	+	0.172953i	$0.0553307\pi$
$480$	−4.00000	−	6.92820i	−0.182574	−	0.316228i
$481$	6.00000	−	10.3923i	0.273576	−	0.473848i
$482$	42.0000			1.91305
$483$	16.0000			0.728025
$484$	2.00000	−	3.46410i	0.0909091	−	0.157459i
$485$	−6.00000	+	10.3923i	−0.272446	+	0.471890i
$486$	2.00000			0.0907218
$487$	−22.0000			−0.996915			−0.498458	−	0.866914i	$-0.666100\pi$
$487$	−22.0000			−0.996915			−0.498458	+	0.866914i	$0.666100\pi$
$488$		0			0
$489$	5.00000	+	8.66025i	0.226108	+	0.391630i
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	2.50000	+	4.33013i	0.112823	+	0.195416i	0.916908	−	0.399100i	$-0.130677\pi$
$491$	2.50000	+	4.33013i	0.112823	+	0.195416i	−0.804084	+	0.594515i	$0.797344\pi$
$492$	−6.00000	−	10.3923i	−0.270501	−	0.468521i
$493$	42.0000			1.89158
$494$	−42.0000	+	31.1769i	−1.88967	+	1.40272i
$495$	3.00000			0.134840
$496$	18.0000	+	31.1769i	0.808224	+	1.39988i
$497$	7.00000	+	12.1244i	0.313993	+	0.543852i
$498$	6.00000	−	10.3923i	0.268866	−	0.465690i
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	0.699903	−	0.714238i	$-0.253227\pi$
$499$	−6.00000	−	10.3923i	−0.268597	−	0.465223i	−0.968500	+	0.249015i	$0.919893\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$	22.0000			0.982888
$502$	6.00000			0.267793
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	−0.464107	−	0.885779i	$-0.653625\pi$
$503$	12.0000	−	20.7846i	0.535054	−	0.926740i	0.999161	−	0.0409609i	$-0.0130419\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$	48.0000			2.13386
$507$	−11.5000	+	19.9186i	−0.510733	+	0.884615i
$508$	8.00000	+	13.8564i	0.354943	+	0.614779i
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	−0.314459	−	0.949271i	$-0.601823\pi$
$509$	15.0000	−	25.9808i	0.664863	−	1.15158i	0.979322	−	0.202306i	$-0.0648436\pi$
$510$	6.00000	+	10.3923i	0.265684	+	0.460179i
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	32.0000			1.41421
$513$	−3.50000	+	2.59808i	−0.154529	+	0.114708i
$514$	4.00000			0.176432
$515$	−4.00000	−	6.92820i	−0.176261	−	0.305293i
$516$	−10.0000	−	17.3205i	−0.440225	−	0.762493i
$517$	6.00000	−	10.3923i	0.263880	−	0.457053i
$518$	−4.00000	−	6.92820i	−0.175750	−	0.304408i
$519$	−3.00000	+	5.19615i	−0.131685	+	0.228086i
$520$		0			0
$521$	−7.00000			−0.306676			−0.153338	−	0.988174i	$-0.549002\pi$
$521$	−7.00000			−0.306676			−0.153338	+	0.988174i	$0.549002\pi$
$522$	−7.00000	+	12.1244i	−0.306382	+	0.530669i
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	−0.518766	−	0.854916i	$-0.673608\pi$
$523$	11.0000	−	19.0526i	0.480996	−	0.833110i	0.999762	+	0.0218062i	$0.00694167\pi$
$524$	−16.0000			−0.698963
$525$	−2.00000			−0.0872872
$526$	−12.0000	+	20.7846i	−0.523225	+	0.906252i
$527$	−27.0000	−	46.7654i	−1.17614	−	2.03713i
$528$	−6.00000	+	10.3923i	−0.261116	+	0.452267i
$529$	−20.5000	−	35.5070i	−0.891304	−	1.54378i
$530$	14.0000	+	24.2487i	0.608121	+	1.05330i
$531$	3.00000			0.130189
$532$	2.00000	+	17.3205i	0.0867110	+	0.750939i
$533$	36.0000			1.55933
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$	6.00000	+	10.3923i	0.259403	+	0.449299i
$536$		0			0
$537$	−0.500000	−	0.866025i	−0.0215766	−	0.0373718i
$538$	−21.0000	+	36.3731i	−0.905374	+	1.56815i
$539$	9.00000			0.387657
$540$	−2.00000			−0.0860663
$541$	4.50000	−	7.79423i	0.193470	−	0.335100i	−0.752928	−	0.658103i	$-0.771359\pi$
$541$	4.50000	−	7.79423i	0.193470	−	0.335100i	0.946398	+	0.323003i	$0.104692\pi$
$542$	5.00000	−	8.66025i	0.214768	−	0.371990i
$543$	−14.0000			−0.600798
$544$	−48.0000			−2.05798
$545$	1.50000	−	2.59808i	0.0642529	−	0.111289i
$546$	12.0000	+	20.7846i	0.513553	+	0.889499i
$547$	−14.0000	+	24.2487i	−0.598597	+	1.03680i	0.394432	+	0.918925i	$0.370941\pi$
$547$	−14.0000	+	24.2487i	−0.598597	+	1.03680i	−0.993028	+	0.117875i	$0.962392\pi$
$548$	−2.00000	−	3.46410i	−0.0854358	−	0.147979i
$549$	3.50000	+	6.06218i	0.149376	+	0.258727i
$550$	−6.00000			−0.255841
$551$	−3.50000	−	30.3109i	−0.149105	−	1.29129i
$552$		0			0
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	−16.0000	−	27.7128i	−0.679775	−	1.17740i
$555$	−1.00000	+	1.73205i	−0.0424476	+	0.0735215i
$556$	4.00000	+	6.92820i	0.169638	+	0.293821i
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	−0.964686	−	0.263404i	$-0.915155\pi$
$557$	−6.00000	+	10.3923i	−0.254228	+	0.440336i	0.710457	+	0.703740i	$0.248488\pi$
$558$	18.0000			0.762001
$559$	60.0000			2.53773
$560$	4.00000	−	6.92820i	0.169031	−	0.292770i
$561$	9.00000	−	15.5885i	0.379980	−	0.658145i
$562$	28.0000			1.18111
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$	−4.00000	+	6.92820i	−0.168430	+	0.291730i
$565$	3.00000	+	5.19615i	0.126211	+	0.218604i
$566$	26.0000	−	45.0333i	1.09286	−	1.89289i
$567$	1.00000	+	1.73205i	0.0419961	+	0.0727393i
$568$		0			0
$569$	−11.0000			−0.461144			−0.230572	−	0.973055i	$-0.574060\pi$
$569$	−11.0000			−0.461144			−0.230572	+	0.973055i	$0.574060\pi$
$570$	7.00000	−	5.19615i	0.293198	−	0.217643i
$571$	−15.0000			−0.627730			−0.313865	−	0.949468i	$-0.601624\pi$
$571$	−15.0000			−0.627730			−0.313865	+	0.949468i	$0.601624\pi$
$572$	18.0000	+	31.1769i	0.752618	+	1.30357i
$573$	2.50000	+	4.33013i	0.104439	+	0.180894i
$574$	12.0000	−	20.7846i	0.500870	−	0.867533i
$575$	4.00000	+	6.92820i	0.166812	+	0.288926i
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	32.0000			1.33218			0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$	38.0000			1.58059
$579$	9.00000	−	15.5885i	0.374027	−	0.647834i
$580$	7.00000	−	12.1244i	0.290659	−	0.503436i
$581$	12.0000			0.497844
$582$	−24.0000			−0.994832
$583$	21.0000	−	36.3731i	0.869731	−	1.50642i
$584$		0			0
$585$	3.00000	−	5.19615i	0.124035	−	0.214834i
$586$	12.0000	+	20.7846i	0.495715	+	0.858604i
$587$	−11.0000	−	19.0526i	−0.454019	−	0.786383i	0.544613	−	0.838688i	$-0.316677\pi$
$587$	−11.0000	−	19.0526i	−0.454019	−	0.786383i	−0.998631	+	0.0523045i	$0.983343\pi$
$588$	−6.00000			−0.247436
$589$	−31.5000	+	23.3827i	−1.29793	+	0.963467i
$590$	−6.00000			−0.247016
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	−4.00000	−	6.92820i	−0.164399	−	0.284747i
$593$	5.00000	−	8.66025i	0.205325	−	0.355634i	−0.744911	−	0.667164i	$-0.767508\pi$
$593$	5.00000	−	8.66025i	0.205325	−	0.355634i	0.950236	+	0.311530i	$0.100841\pi$
$594$	3.00000	+	5.19615i	0.123091	+	0.213201i
$595$	−6.00000	+	10.3923i	−0.245976	+	0.426043i
$596$	−6.00000			−0.245770
$597$	−11.0000			−0.450200
$598$	48.0000	−	83.1384i	1.96287	−	3.39978i
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	−0.903988	−	0.427558i	$-0.859374\pi$
$599$	−2.00000	+	3.46410i	−0.0817178	+	0.141539i	0.822270	+	0.569097i	$0.192707\pi$
$600$		0			0
$601$	1.00000			0.0407909			0.0203954	−	0.999792i	$-0.493507\pi$
$601$	1.00000			0.0407909			0.0203954	+	0.999792i	$0.493507\pi$
$602$	20.0000	−	34.6410i	0.815139	−	1.41186i
$603$	−2.00000	−	3.46410i	−0.0814463	−	0.141069i
$604$	−5.00000	+	8.66025i	−0.203447	+	0.352381i
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$	3.00000	+	5.19615i	0.121867	+	0.211079i
$607$	−14.0000			−0.568242			−0.284121	−	0.958788i	$-0.591702\pi$
$607$	−14.0000			−0.568242			−0.284121	+	0.958788i	$0.591702\pi$
$608$	4.00000	+	34.6410i	0.162221	+	1.40488i
$609$	−14.0000			−0.567309
$610$	−7.00000	−	12.1244i	−0.283422	−	0.490901i
$611$	−12.0000	−	20.7846i	−0.485468	−	0.840855i
$612$	−6.00000	+	10.3923i	−0.242536	+	0.420084i
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	−16.0000	+	27.7128i	−0.645707	+	1.11840i
$615$	−6.00000			−0.241943
$616$		0			0
$617$	−14.0000	+	24.2487i	−0.563619	+	0.976216i	0.433558	+	0.901126i	$0.357258\pi$
$617$	−14.0000	+	24.2487i	−0.563619	+	0.976216i	−0.997177	+	0.0750907i	$0.976075\pi$
$618$	8.00000	−	13.8564i	0.321807	−	0.557386i
$619$	−16.0000			−0.643094			−0.321547	−	0.946894i	$-0.604203\pi$
$619$	−16.0000			−0.643094			−0.321547	+	0.946894i	$0.604203\pi$
$620$	−18.0000			−0.722897
$621$	4.00000	−	6.92820i	0.160514	−	0.278019i
$622$	8.00000	+	13.8564i	0.320771	+	0.555591i
$623$	3.00000	−	5.19615i	0.120192	−	0.208179i
$624$	12.0000	+	20.7846i	0.480384	+	0.832050i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−16.0000			−0.639489
$627$	−12.0000	−	5.19615i	−0.479234	−	0.207514i
$628$	−40.0000			−1.59617
$629$	6.00000	+	10.3923i	0.239236	+	0.414368i
$630$	−2.00000	−	3.46410i	−0.0796819	−	0.138013i
$631$	−14.5000	+	25.1147i	−0.577236	+	0.999802i	0.418559	+	0.908190i	$0.362535\pi$
$631$	−14.5000	+	25.1147i	−0.577236	+	0.999802i	−0.995795	+	0.0916122i	$0.970798\pi$
$632$		0			0
$633$	−6.50000	+	11.2583i	−0.258352	+	0.447478i
$634$	24.0000			0.953162
$635$	8.00000			0.317470
$636$	−14.0000	+	24.2487i	−0.555136	+	0.961524i
$637$	9.00000	−	15.5885i	0.356593	−	0.617637i
$638$	−42.0000			−1.66280
$639$	7.00000			0.276916
$640$		0			0
$641$	−9.50000	−	16.4545i	−0.375227	−	0.649913i	0.615134	−	0.788423i	$-0.289102\pi$
$641$	−9.50000	−	16.4545i	−0.375227	−	0.649913i	−0.990361	+	0.138510i	$0.955769\pi$
$642$	−12.0000	+	20.7846i	−0.473602	+	0.820303i
$643$	−16.0000	−	27.7128i	−0.630978	−	1.09289i	−0.987352	−	0.158543i	$-0.949320\pi$
$643$	−16.0000	−	27.7128i	−0.630978	−	1.09289i	0.356374	−	0.934344i	$-0.384013\pi$
$644$	−16.0000	−	27.7128i	−0.630488	−	1.09204i
$645$	−10.0000			−0.393750
$646$	−6.00000	−	51.9615i	−0.236067	−	2.04440i
$647$	2.00000			0.0786281			0.0393141	−	0.999227i	$-0.487483\pi$
$647$	2.00000			0.0786281			0.0393141	+	0.999227i	$0.487483\pi$
$648$		0			0
$649$	4.50000	+	7.79423i	0.176640	+	0.305950i
$650$	−6.00000	+	10.3923i	−0.235339	+	0.407620i
$651$	9.00000	+	15.5885i	0.352738	+	0.610960i
$652$	10.0000	−	17.3205i	0.391630	−	0.678323i
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$	6.00000			0.234619
$655$	−4.00000	+	6.92820i	−0.156293	+	0.270707i
$656$	12.0000	−	20.7846i	0.468521	−	0.811503i
$657$	2.00000			0.0780274
$658$	−16.0000			−0.623745
$659$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$659$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$660$	−3.00000	−	5.19615i	−0.116775	−	0.202260i
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	−0.982632	−	0.185565i	$-0.940588\pi$
$661$	−8.50000	+	14.7224i	−0.330612	+	0.572636i	0.652020	+	0.758202i	$0.273922\pi$
$662$	8.00000	+	13.8564i	0.310929	+	0.538545i
$663$	−18.0000	−	31.1769i	−0.699062	−	1.21081i
$664$		0			0
$665$	8.00000	+	3.46410i	0.310227	+	0.134332i
$666$	−4.00000			−0.154997
$667$	28.0000	+	48.4974i	1.08416	+	1.87783i
$668$	−22.0000	−	38.1051i	−0.851206	−	1.47433i
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$	4.00000	+	6.92820i	0.154533	+	0.267660i
$671$	−10.5000	+	18.1865i	−0.405348	+	0.702083i
$672$	16.0000			0.617213
$673$	−36.0000			−1.38770			−0.693849	−	0.720121i	$-0.744086\pi$
$673$	−36.0000			−1.38770			−0.693849	+	0.720121i	$0.744086\pi$
$674$	12.0000	−	20.7846i	0.462223	−	0.800593i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	46.0000			1.76923
$677$	30.0000			1.15299			0.576497	−	0.817099i	$-0.304419\pi$
$677$	30.0000			1.15299			0.576497	+	0.817099i	$0.304419\pi$
$678$	−6.00000	+	10.3923i	−0.230429	+	0.399114i
$679$	−12.0000	−	20.7846i	−0.460518	−	0.797640i
$680$		0			0
$681$	−7.00000	−	12.1244i	−0.268241	−	0.464606i
$682$	27.0000	+	46.7654i	1.03388	+	1.79074i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$	8.00000	+	3.46410i	0.305888	+	0.132453i
$685$	−2.00000			−0.0764161
$686$	−20.0000	−	34.6410i	−0.763604	−	1.32260i
$687$	−14.5000	−	25.1147i	−0.553210	−	0.958187i
$688$	20.0000	−	34.6410i	0.762493	−	1.32068i
$689$	−42.0000	−	72.7461i	−1.60007	−	2.77141i
$690$	−8.00000	+	13.8564i	−0.304555	+	0.527504i
$691$	−1.00000			−0.0380418			−0.0190209	−	0.999819i	$-0.506055\pi$
$691$	−1.00000			−0.0380418			−0.0190209	+	0.999819i	$0.506055\pi$
$692$	12.0000			0.456172
$693$	−3.00000	+	5.19615i	−0.113961	+	0.197386i
$694$	−2.00000	+	3.46410i	−0.0759190	+	0.131495i
$695$	4.00000			0.151729
$696$		0			0
$697$	−18.0000	+	31.1769i	−0.681799	+	1.18091i
$698$	2.00000	+	3.46410i	0.0757011	+	0.131118i
$699$	−8.00000	+	13.8564i	−0.302588	+	0.524097i
$700$	2.00000	+	3.46410i	0.0755929	+	0.130931i
$701$	−9.00000	−	15.5885i	−0.339925	−	0.588768i	0.644493	−	0.764610i	$-0.277068\pi$
$701$	−9.00000	−	15.5885i	−0.339925	−	0.588768i	−0.984418	+	0.175842i	$0.943735\pi$
$702$	12.0000			0.452911
$703$	7.00000	−	5.19615i	0.264010	−	0.195977i
$704$	24.0000			0.904534
$705$	2.00000	+	3.46410i	0.0753244	+	0.130466i
$706$	−2.00000	−	3.46410i	−0.0752710	−	0.130373i
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	−0.324104	−	0.946021i	$-0.605063\pi$
$709$	17.5000	−	30.3109i	0.657226	−	1.13835i	0.981331	−	0.192328i	$-0.0616038\pi$
$710$	−14.0000			−0.525411
$711$	5.00000			0.187515
$712$		0			0
$713$	36.0000	−	62.3538i	1.34821	−	2.33517i
$714$	−24.0000			−0.898177
$715$	18.0000			0.673162
$716$	−1.00000	+	1.73205i	−0.0373718	+	0.0647298i
$717$	4.50000	+	7.79423i	0.168056	+	0.291081i
$718$	32.0000	−	55.4256i	1.19423	−	2.06847i
$719$	−16.5000	−	28.5788i	−0.615346	−	1.06581i	−0.990324	−	0.138777i	$-0.955683\pi$
$719$	−16.5000	−	28.5788i	−0.615346	−	1.06581i	0.374978	−	0.927034i	$-0.377650\pi$
$720$	−2.00000	−	3.46410i	−0.0745356	−	0.129099i
$721$	16.0000			0.595871
$722$	−37.0000	+	8.66025i	−1.37700	+	0.322301i
$723$	21.0000			0.780998
$724$	14.0000	+	24.2487i	0.520306	+	0.901196i
$725$	−3.50000	−	6.06218i	−0.129987	−	0.225144i
$726$	2.00000	−	3.46410i	0.0742270	−	0.128565i
$727$	−7.00000	−	12.1244i	−0.259616	−	0.449667i	0.706523	−	0.707690i	$-0.250263\pi$
$727$	−7.00000	−	12.1244i	−0.259616	−	0.449667i	−0.966139	+	0.258022i	$0.916929\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−4.00000			−0.148047
$731$	−30.0000	+	51.9615i	−1.10959	+	1.92187i
$732$	7.00000	−	12.1244i	0.258727	−	0.448129i
$733$	14.0000			0.517102			0.258551	−	0.965998i	$-0.416755\pi$
$733$	14.0000			0.517102			0.258551	+	0.965998i	$0.416755\pi$
$734$	−40.0000			−1.47643
$735$	−1.50000	+	2.59808i	−0.0553283	+	0.0958315i
$736$	−32.0000	−	55.4256i	−1.17954	−	2.04302i
$737$	6.00000	−	10.3923i	0.221013	−	0.382805i
$738$	−6.00000	−	10.3923i	−0.220863	−	0.382546i
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	0.999239	+	0.0389959i	$0.0124159\pi$
$739$	14.5000	+	25.1147i	0.533391	+	0.923861i	−0.465848	+	0.884865i	$0.654251\pi$
$740$	4.00000			0.147043
$741$	−21.0000	+	15.5885i	−0.771454	+	0.572656i
$742$	−56.0000			−2.05582
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	0.915794	−	0.401648i	$-0.131563\pi$
$743$	3.00000	+	5.19615i	0.110059	+	0.190628i	−0.805735	+	0.592277i	$0.798229\pi$
$744$		0			0
$745$	−1.50000	+	2.59808i	−0.0549557	+	0.0951861i
$746$	24.0000	+	41.5692i	0.878702	+	1.52196i
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	−36.0000			−1.31629
$749$	−24.0000			−0.876941
$750$	1.00000	−	1.73205i	0.0365148	−	0.0632456i
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$	−16.0000			−0.583460
$753$	3.00000			0.109326
$754$	−42.0000	+	72.7461i	−1.52955	+	2.64926i
$755$	2.50000	+	4.33013i	0.0909843	+	0.157589i
$756$	2.00000	−	3.46410i	0.0727393	−	0.125988i
$757$	−23.0000	−	39.8372i	−0.835949	−	1.44791i	−0.893255	−	0.449550i	$-0.851584\pi$
$757$	−23.0000	−	39.8372i	−0.835949	−	1.44791i	0.0573060	−	0.998357i	$-0.481749\pi$
$758$	25.0000	+	43.3013i	0.908041	+	1.57277i
$759$	24.0000			0.871145
$760$		0			0
$761$	−30.0000			−1.08750			−0.543750	−	0.839248i	$-0.682996\pi$
$761$	−30.0000			−1.08750			−0.543750	+	0.839248i	$0.682996\pi$
$762$	8.00000	+	13.8564i	0.289809	+	0.501965i
$763$	3.00000	+	5.19615i	0.108607	+	0.188113i
$764$	5.00000	−	8.66025i	0.180894	−	0.313317i
$765$	3.00000	+	5.19615i	0.108465	+	0.187867i
$766$	34.0000	−	58.8897i	1.22847	−	2.12777i
$767$	18.0000			0.649942
$768$	16.0000			0.577350
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	−0.959097	−	0.283078i	$-0.908645\pi$
$769$	−6.50000	+	11.2583i	−0.234396	+	0.405986i	0.724701	+	0.689063i	$0.241978\pi$
$770$	6.00000	−	10.3923i	0.216225	−	0.374513i
$771$	2.00000			0.0720282
$772$	−36.0000			−1.29567

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:	\( N \)	\(=\)	\( 285 = 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	285.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} -2.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-1.00000 + 1.73205i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-1.00000 + 1.73205i) q^{6} -2.00000 q^{7} +(-0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} -3.00000 q^{11} +2.00000 q^{12} +(-3.00000 + 5.19615i) q^{13} +(2.00000 + 3.46410i) q^{14} +(0.500000 - 0.866025i) q^{15} +(2.00000 + 3.46410i) q^{16} +(-3.00000 - 5.19615i) q^{17} +2.00000 q^{18} +(-3.50000 + 2.59808i) q^{19} -2.00000 q^{20} +(1.00000 + 1.73205i) q^{21} +(3.00000 + 5.19615i) q^{22} +(4.00000 - 6.92820i) q^{23} +(-0.500000 + 0.866025i) q^{25} +12.0000 q^{26} +1.00000 q^{27} +(2.00000 - 3.46410i) q^{28} +(-3.50000 + 6.06218i) q^{29} -2.00000 q^{30} +9.00000 q^{31} +(4.00000 - 6.92820i) q^{32} +(1.50000 + 2.59808i) q^{33} +(-6.00000 + 10.3923i) q^{34} +(-1.00000 - 1.73205i) q^{35} +(-1.00000 - 1.73205i) q^{36} -2.00000 q^{37} +(8.00000 + 3.46410i) q^{38} +6.00000 q^{39} +(-3.00000 - 5.19615i) q^{41} +(2.00000 - 3.46410i) q^{42} +(-5.00000 - 8.66025i) q^{43} +(3.00000 - 5.19615i) q^{44} -1.00000 q^{45} -16.0000 q^{46} +(-2.00000 + 3.46410i) q^{47} +(2.00000 - 3.46410i) q^{48} -3.00000 q^{49} +2.00000 q^{50} +(-3.00000 + 5.19615i) q^{51} +(-6.00000 - 10.3923i) q^{52} +(-7.00000 + 12.1244i) q^{53} +(-1.00000 - 1.73205i) q^{54} +(-1.50000 - 2.59808i) q^{55} +(4.00000 + 1.73205i) q^{57} +14.0000 q^{58} +(-1.50000 - 2.59808i) q^{59} +(1.00000 + 1.73205i) q^{60} +(3.50000 - 6.06218i) q^{61} +(-9.00000 - 15.5885i) q^{62} +(1.00000 - 1.73205i) q^{63} -8.00000 q^{64} -6.00000 q^{65} +(3.00000 - 5.19615i) q^{66} +(-2.00000 + 3.46410i) q^{67} +12.0000 q^{68} -8.00000 q^{69} +(-2.00000 + 3.46410i) q^{70} +(-3.50000 - 6.06218i) q^{71} +(-1.00000 - 1.73205i) q^{73} +(2.00000 + 3.46410i) q^{74} +1.00000 q^{75} +(-1.00000 - 8.66025i) q^{76} +6.00000 q^{77} +(-6.00000 - 10.3923i) q^{78} +(-2.50000 - 4.33013i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-6.00000 + 10.3923i) q^{82} -6.00000 q^{83} -4.00000 q^{84} +(3.00000 - 5.19615i) q^{85} +(-10.0000 + 17.3205i) q^{86} +7.00000 q^{87} +(-1.50000 + 2.59808i) q^{89} +(1.00000 + 1.73205i) q^{90} +(6.00000 - 10.3923i) q^{91} +(8.00000 + 13.8564i) q^{92} +(-4.50000 - 7.79423i) q^{93} +8.00000 q^{94} +(-4.00000 - 1.73205i) q^{95} -8.00000 q^{96} +(6.00000 + 10.3923i) q^{97} +(3.00000 + 5.19615i) q^{98} +(1.50000 - 2.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 4 * q^7 - q^9	\( 2 q - 2 q^{2} - q^{3} - 2 q^{4} + q^{5} - 2 q^{6} - 4 q^{7} - q^{9} + 2 q^{10} - 6 q^{11} + 4 q^{12} - 6 q^{13} + 4 q^{14} + q^{15} + 4 q^{16} - 6 q^{17} + 4 q^{18} - 7 q^{19} - 4 q^{20} + 2 q^{21} + 6 q^{22} + 8 q^{23} - q^{25} + 24 q^{26} + 2 q^{27} + 4 q^{28} - 7 q^{29} - 4 q^{30} + 18 q^{31} + 8 q^{32} + 3 q^{33} - 12 q^{34} - 2 q^{35} - 2 q^{36} - 4 q^{37} + 16 q^{38} + 12 q^{39} - 6 q^{41} + 4 q^{42} - 10 q^{43} + 6 q^{44} - 2 q^{45} - 32 q^{46} - 4 q^{47} + 4 q^{48} - 6 q^{49} + 4 q^{50} - 6 q^{51} - 12 q^{52} - 14 q^{53} - 2 q^{54} - 3 q^{55} + 8 q^{57} + 28 q^{58} - 3 q^{59} + 2 q^{60} + 7 q^{61} - 18 q^{62} + 2 q^{63} - 16 q^{64} - 12 q^{65} + 6 q^{66} - 4 q^{67} + 24 q^{68} - 16 q^{69} - 4 q^{70} - 7 q^{71} - 2 q^{73} + 4 q^{74} + 2 q^{75} - 2 q^{76} + 12 q^{77} - 12 q^{78} - 5 q^{79} - 4 q^{80} - q^{81} - 12 q^{82} - 12 q^{83} - 8 q^{84} + 6 q^{85} - 20 q^{86} + 14 q^{87} - 3 q^{89} + 2 q^{90} + 12 q^{91} + 16 q^{92} - 9 q^{93} + 16 q^{94} - 8 q^{95} - 16 q^{96} + 12 q^{97} + 6 q^{98} + 3 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - q^3 - 2 * q^4 + q^5 - 2 * q^6 - 4 * q^7 - q^9 + 2 * q^10 - 6 * q^11 + 4 * q^12 - 6 * q^13 + 4 * q^14 + q^15 + 4 * q^16 - 6 * q^17 + 4 * q^18 - 7 * q^19 - 4 * q^20 + 2 * q^21 + 6 * q^22 + 8 * q^23 - q^25 + 24 * q^26 + 2 * q^27 + 4 * q^28 - 7 * q^29 - 4 * q^30 + 18 * q^31 + 8 * q^32 + 3 * q^33 - 12 * q^34 - 2 * q^35 - 2 * q^36 - 4 * q^37 + 16 * q^38 + 12 * q^39 - 6 * q^41 + 4 * q^42 - 10 * q^43 + 6 * q^44 - 2 * q^45 - 32 * q^46 - 4 * q^47 + 4 * q^48 - 6 * q^49 + 4 * q^50 - 6 * q^51 - 12 * q^52 - 14 * q^53 - 2 * q^54 - 3 * q^55 + 8 * q^57 + 28 * q^58 - 3 * q^59 + 2 * q^60 + 7 * q^61 - 18 * q^62 + 2 * q^63 - 16 * q^64 - 12 * q^65 + 6 * q^66 - 4 * q^67 + 24 * q^68 - 16 * q^69 - 4 * q^70 - 7 * q^71 - 2 * q^73 + 4 * q^74 + 2 * q^75 - 2 * q^76 + 12 * q^77 - 12 * q^78 - 5 * q^79 - 4 * q^80 - q^81 - 12 * q^82 - 12 * q^83 - 8 * q^84 + 6 * q^85 - 20 * q^86 + 14 * q^87 - 3 * q^89 + 2 * q^90 + 12 * q^91 + 16 * q^92 - 9 * q^93 + 16 * q^94 - 8 * q^95 - 16 * q^96 + 12 * q^97 + 6 * q^98 + 3 * q^99

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