LMFDB - Embedded newform 930.2.i.e.211.1

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			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.e.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +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} +(3.00000 - 5.19615i) q^{13} +1.00000 q^{15} +1.00000 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.500000 - 0.866025i) q^{22} +7.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.00000 - 5.19615i) q^{26} +1.00000 q^{27} +6.00000 q^{29} +1.00000 q^{30} +(2.00000 + 5.19615i) q^{31} +1.00000 q^{32} -1.00000 q^{33} +(0.500000 + 0.866025i) q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +(-2.00000 - 3.46410i) q^{38} -6.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.00000 - 1.73205i) q^{41} +(3.50000 + 6.06218i) q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +7.00000 q^{46} +3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{51} +(3.00000 - 5.19615i) q^{52} +(2.00000 - 3.46410i) q^{53} +1.00000 q^{54} +(0.500000 + 0.866025i) q^{55} +(-2.00000 + 3.46410i) q^{57} +6.00000 q^{58} +(-6.00000 - 10.3923i) q^{59} +1.00000 q^{60} -14.0000 q^{61} +(2.00000 + 5.19615i) q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} -1.00000 q^{66} +(-2.50000 + 4.33013i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-3.50000 - 6.06218i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-2.00000 - 3.46410i) q^{76} -6.00000 q^{78} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-8.00000 + 13.8564i) q^{83} -1.00000 q^{85} +(3.50000 + 6.06218i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(0.500000 - 0.866025i) q^{88} +4.00000 q^{89} +(-0.500000 - 0.866025i) q^{90} +7.00000 q^{92} +(3.50000 - 4.33013i) q^{93} +3.00000 q^{94} +4.00000 q^{95} +(-0.500000 - 0.866025i) q^{96} -6.00000 q^{97} +(3.50000 - 6.06218i) 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} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^8 - q^9	$ 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{8} - q^{9} - q^{10} + q^{11} - q^{12} + 6 q^{13} + 2 q^{15} + 2 q^{16} + q^{17} - q^{18} - 4 q^{19} - q^{20} + q^{22} + 14 q^{23} - q^{24} - q^{25} + 6 q^{26} + 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} - 2 q^{33} + q^{34} - q^{36} - 7 q^{37} - 4 q^{38} - 12 q^{39} - q^{40} + 2 q^{41} + 7 q^{43} + q^{44} - q^{45} + 14 q^{46} + 6 q^{47} - q^{48} + 7 q^{49} - q^{50} + q^{51} + 6 q^{52} + 4 q^{53} + 2 q^{54} + q^{55} - 4 q^{57} + 12 q^{58} - 12 q^{59} + 2 q^{60} - 28 q^{61} + 4 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{66} - 5 q^{67} + q^{68} - 7 q^{69} - 6 q^{71} - q^{72} - 2 q^{73} - 7 q^{74} - q^{75} - 4 q^{76} - 12 q^{78} - 3 q^{79} - q^{80} - q^{81} + 2 q^{82} - 16 q^{83} - 2 q^{85} + 7 q^{86} - 6 q^{87} + q^{88} + 8 q^{89} - q^{90} + 14 q^{92} + 7 q^{93} + 6 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 7 q^{98} + q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^8 - q^9 - q^10 + q^11 - q^12 + 6 * q^13 + 2 * q^15 + 2 * q^16 + q^17 - q^18 - 4 * q^19 - q^20 + q^22 + 14 * q^23 - q^24 - q^25 + 6 * q^26 + 2 * q^27 + 12 * q^29 + 2 * q^30 + 4 * q^31 + 2 * q^32 - 2 * q^33 + q^34 - q^36 - 7 * q^37 - 4 * q^38 - 12 * q^39 - q^40 + 2 * q^41 + 7 * q^43 + q^44 - q^45 + 14 * q^46 + 6 * q^47 - q^48 + 7 * q^49 - q^50 + q^51 + 6 * q^52 + 4 * q^53 + 2 * q^54 + q^55 - 4 * q^57 + 12 * q^58 - 12 * q^59 + 2 * q^60 - 28 * q^61 + 4 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^66 - 5 * q^67 + q^68 - 7 * q^69 - 6 * q^71 - q^72 - 2 * q^73 - 7 * q^74 - q^75 - 4 * q^76 - 12 * q^78 - 3 * q^79 - q^80 - q^81 + 2 * q^82 - 16 * q^83 - 2 * q^85 + 7 * q^86 - 6 * q^87 + q^88 + 8 * q^89 - q^90 + 14 * q^92 + 7 * q^93 + 6 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 7 * q^98 + q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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			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
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	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	−0.780750	−	0.624844i	$-0.785163\pi$
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i	0.931505	+	0.363727i	$0.118496\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	3.00000	−	5.19615i	0.832050	−	1.44115i	−0.0643593	−	0.997927i	$-0.520500\pi$
$13$	3.00000	−	5.19615i	0.832050	−	1.44115i	0.896410	−	0.443227i	$-0.146166\pi$
$14$		0			0
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	0.920268	−	0.391289i	$-0.127971\pi$
$17$	0.500000	+	0.866025i	0.121268	+	0.210042i	−0.799000	+	0.601331i	$0.794637\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	0.540068	−	0.841621i	$-0.318398\pi$
$19$	−2.00000	−	3.46410i	−0.458831	−	0.794719i	−0.998899	+	0.0469020i	$0.985065\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	0.500000	−	0.866025i	0.106600	−	0.184637i
$23$	7.00000			1.45960			0.729800	−	0.683660i	$-0.239613\pi$
$23$	7.00000			1.45960			0.729800	+	0.683660i	$0.239613\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	3.00000	−	5.19615i	0.588348	−	1.01905i
$27$	1.00000			0.192450
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$	1.00000			0.182574
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$31$	2.00000	+	5.19615i	0.359211	+	0.933257i
$32$	1.00000			0.176777
$33$	−1.00000			−0.174078
$34$	0.500000	+	0.866025i	0.0857493	+	0.148522i
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	−0.995998	−	0.0893706i	$-0.971514\pi$
$37$	−3.50000	−	6.06218i	−0.575396	−	0.996616i	0.420602	−	0.907245i	$-0.361819\pi$
$38$	−2.00000	−	3.46410i	−0.324443	−	0.561951i
$39$	−6.00000			−0.960769
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$		0			0
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	0.999223	+	0.0394140i	$0.0125491\pi$
$43$	3.50000	+	6.06218i	0.533745	+	0.924473i	−0.465478	+	0.885059i	$0.654118\pi$
$44$	0.500000	−	0.866025i	0.0753778	−	0.130558i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	7.00000			1.03209
$47$	3.00000			0.437595			0.218797	−	0.975770i	$-0.429787\pi$
$47$	3.00000			0.437595			0.218797	+	0.975770i	$0.429787\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	0.500000	−	0.866025i	0.0700140	−	0.121268i
$52$	3.00000	−	5.19615i	0.416025	−	0.720577i
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	−0.695344	−	0.718677i	$-0.744748\pi$
$53$	2.00000	−	3.46410i	0.274721	−	0.475831i	0.970065	+	0.242846i	$0.0780811\pi$
$54$	1.00000			0.136083
$55$	0.500000	+	0.866025i	0.0674200	+	0.116775i
$56$		0			0
$57$	−2.00000	+	3.46410i	−0.264906	+	0.458831i
$58$	6.00000			0.787839
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	−0.931282	−	0.364299i	$-0.881308\pi$
$59$	−6.00000	−	10.3923i	−0.781133	−	1.35296i	0.150148	−	0.988663i	$-0.452025\pi$
$60$	1.00000			0.129099
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	2.00000	+	5.19615i	0.254000	+	0.659912i
$63$		0			0
$64$	1.00000			0.125000
$65$	3.00000	+	5.19615i	0.372104	+	0.644503i
$66$	−1.00000			−0.123091
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−2.50000	+	4.33013i	−0.305424	+	0.529009i	0.671932	+	0.740613i	$0.265465\pi$
$68$	0.500000	+	0.866025i	0.0606339	+	0.105021i
$69$	−3.50000	−	6.06218i	−0.421350	−	0.729800i
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	−0.918594	−	0.395203i	$-0.870674\pi$
$73$	−1.00000	+	1.73205i	−0.117041	+	0.202721i	0.801553	+	0.597924i	$0.204008\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−2.00000	−	3.46410i	−0.229416	−	0.397360i
$77$		0			0
$78$	−6.00000			−0.679366
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	0.769222	−	0.638982i	$-0.220644\pi$
$79$	−1.50000	−	2.59808i	−0.168763	−	0.292306i	−0.937985	+	0.346675i	$0.887311\pi$
$80$	−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
$83$	−8.00000	+	13.8564i	−0.878114	+	1.52094i	−0.0247060	+	0.999695i	$0.507865\pi$
$83$	−8.00000	+	13.8564i	−0.878114	+	1.52094i	−0.853408	+	0.521243i	$0.825468\pi$
$84$		0			0
$85$	−1.00000			−0.108465
$86$	3.50000	+	6.06218i	0.377415	+	0.653701i
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	4.00000			0.423999			0.212000	−	0.977270i	$-0.432002\pi$
$89$	4.00000			0.423999			0.212000	+	0.977270i	$0.432002\pi$
$90$	−0.500000	−	0.866025i	−0.0527046	−	0.0912871i
$91$		0			0
$92$	7.00000			0.729800
$93$	3.50000	−	4.33013i	0.362933	−	0.449013i
$94$	3.00000			0.309426
$95$	4.00000			0.410391
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	−6.00000			−0.609208			−0.304604	−	0.952479i	$-0.598524\pi$
$97$	−6.00000			−0.609208			−0.304604	+	0.952479i	$0.598524\pi$
$98$	3.50000	−	6.06218i	0.353553	−	0.612372i
$99$	0.500000	+	0.866025i	0.0502519	+	0.0870388i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	15.0000			1.49256			0.746278	−	0.665635i	$-0.231839\pi$
$101$	15.0000			1.49256			0.746278	+	0.665635i	$0.231839\pi$
$102$	0.500000	−	0.866025i	0.0495074	−	0.0857493i
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	−0.812545	−	0.582899i	$-0.801918\pi$
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	0.911078	+	0.412235i	$0.135252\pi$
$104$	3.00000	−	5.19615i	0.294174	−	0.509525i
$105$		0			0
$106$	2.00000	−	3.46410i	0.194257	−	0.336463i
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	0.946357	−	0.323122i	$-0.104732\pi$
$107$	2.00000	+	3.46410i	0.193347	+	0.334887i	−0.753010	+	0.658009i	$0.771399\pi$
$108$	1.00000			0.0962250
$109$	−12.0000			−1.14939			−0.574696	−	0.818367i	$-0.694880\pi$
$109$	−12.0000			−1.14939			−0.574696	+	0.818367i	$0.694880\pi$
$110$	0.500000	+	0.866025i	0.0476731	+	0.0825723i
$111$	−3.50000	+	6.06218i	−0.332205	+	0.575396i
$112$		0			0
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.0582609	+	0.998301i	$0.518556\pi$
$113$	−9.50000	+	16.4545i	−0.893685	+	1.54791i	−0.835424	+	0.549606i	$0.814778\pi$
$114$	−2.00000	+	3.46410i	−0.187317	+	0.324443i
$115$	−3.50000	+	6.06218i	−0.326377	+	0.565301i
$116$	6.00000			0.557086
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	−6.00000	−	10.3923i	−0.552345	−	0.956689i
$119$		0			0
$120$	1.00000			0.0912871
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	−14.0000			−1.26750
$123$	−2.00000			−0.180334
$124$	2.00000	+	5.19615i	0.179605	+	0.466628i
$125$	1.00000			0.0894427
$126$		0			0
$127$	9.00000	+	15.5885i	0.798621	+	1.38325i	0.920514	+	0.390709i	$0.127770\pi$
$127$	9.00000	+	15.5885i	0.798621	+	1.38325i	−0.121894	+	0.992543i	$0.538897\pi$
$128$	1.00000			0.0883883
$129$	3.50000	−	6.06218i	0.308158	−	0.533745i
$130$	3.00000	+	5.19615i	0.263117	+	0.455733i
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	0.887041	−	0.461690i	$-0.152757\pi$
$131$	0.500000	+	0.866025i	0.0436852	+	0.0756650i	−0.843356	+	0.537355i	$0.819423\pi$
$132$	−1.00000			−0.0870388
$133$		0			0
$134$	−2.50000	+	4.33013i	−0.215967	+	0.374066i
$135$	−0.500000	+	0.866025i	−0.0430331	+	0.0745356i
$136$	0.500000	+	0.866025i	0.0428746	+	0.0742611i
$137$	3.50000	−	6.06218i	0.299025	−	0.517927i	−0.676888	−	0.736086i	$-0.736672\pi$
$137$	3.50000	−	6.06218i	0.299025	−	0.517927i	0.975913	+	0.218159i	$0.0700052\pi$
$138$	−3.50000	−	6.06218i	−0.297940	−	0.516047i
$139$	−10.0000			−0.848189			−0.424094	−	0.905618i	$-0.639408\pi$
$139$	−10.0000			−0.848189			−0.424094	+	0.905618i	$0.639408\pi$
$140$		0			0
$141$	−1.50000	−	2.59808i	−0.126323	−	0.218797i
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−3.00000	−	5.19615i	−0.250873	−	0.434524i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	−1.00000	+	1.73205i	−0.0827606	+	0.143346i
$147$	−7.00000			−0.577350
$148$	−3.50000	−	6.06218i	−0.287698	−	0.498308i
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	−0.996207	−	0.0870170i	$-0.972267\pi$
$149$	−7.00000	−	12.1244i	−0.573462	−	0.993266i	0.422744	−	0.906249i	$-0.361067\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	−7.00000			−0.569652			−0.284826	−	0.958579i	$-0.591936\pi$
$151$	−7.00000			−0.569652			−0.284826	+	0.958579i	$0.591936\pi$
$152$	−2.00000	−	3.46410i	−0.162221	−	0.280976i
$153$	−1.00000			−0.0808452
$154$		0			0
$155$	−5.50000	−	0.866025i	−0.441771	−	0.0695608i
$156$	−6.00000			−0.480384
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−1.50000	−	2.59808i	−0.119334	−	0.206692i
$159$	−4.00000			−0.317221
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$		0			0
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	5.00000			0.391630			0.195815	−	0.980641i	$-0.437265\pi$
$163$	5.00000			0.391630			0.195815	+	0.980641i	$0.437265\pi$
$164$	1.00000	−	1.73205i	0.0780869	−	0.135250i
$165$	0.500000	−	0.866025i	0.0389249	−	0.0674200i
$166$	−8.00000	+	13.8564i	−0.620920	+	1.07547i
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.785687	+	0.618624i	$0.212310\pi$
$167$	12.0000	+	20.7846i	0.928588	+	1.60836i	0.142901	+	0.989737i	$0.454357\pi$
$168$		0			0
$169$	−11.5000	−	19.9186i	−0.884615	−	1.53220i
$170$	−1.00000			−0.0766965
$171$	4.00000			0.305888
$172$	3.50000	+	6.06218i	0.266872	+	0.462237i
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	−0.901533	−	0.432710i	$-0.857557\pi$
$173$	−1.00000	+	1.73205i	−0.0760286	+	0.131685i	0.825505	+	0.564396i	$0.190891\pi$
$174$	−3.00000	−	5.19615i	−0.227429	−	0.393919i
$175$		0			0
$176$	0.500000	−	0.866025i	0.0376889	−	0.0652791i
$177$	−6.00000	+	10.3923i	−0.450988	+	0.781133i
$178$	4.00000			0.299813
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	0.995009	−	0.0997838i	$-0.0318151\pi$
$179$	5.50000	+	9.52628i	0.411089	+	0.712028i	−0.583920	+	0.811811i	$0.698482\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−10.0000	+	17.3205i	−0.743294	+	1.28742i	0.207693	+	0.978194i	$0.433404\pi$
$181$	−10.0000	+	17.3205i	−0.743294	+	1.28742i	−0.950988	+	0.309229i	$0.899929\pi$
$182$		0			0
$183$	7.00000	+	12.1244i	0.517455	+	0.896258i
$184$	7.00000			0.516047
$185$	7.00000			0.514650
$186$	3.50000	−	4.33013i	0.256632	−	0.317500i
$187$	1.00000			0.0731272
$188$	3.00000			0.218797
$189$		0			0
$190$	4.00000			0.290191
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	−0.736839	−	0.676068i	$-0.763683\pi$
$191$	3.00000	−	5.19615i	0.217072	−	0.375980i	0.953912	+	0.300088i	$0.0970159\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	0.628037	−	0.778183i	$-0.283859\pi$
$193$	−5.00000	−	8.66025i	−0.359908	−	0.623379i	−0.987945	+	0.154805i	$0.950525\pi$
$194$	−6.00000			−0.430775
$195$	3.00000	−	5.19615i	0.214834	−	0.372104i
$196$	3.50000	−	6.06218i	0.250000	−	0.433013i
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	−0.972606	−	0.232458i	$-0.925323\pi$
$197$	−4.00000	+	6.92820i	−0.284988	+	0.493614i	0.687618	+	0.726073i	$0.258656\pi$
$198$	0.500000	+	0.866025i	0.0355335	+	0.0615457i
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	5.00000			0.352673
$202$	15.0000			1.05540
$203$		0			0
$204$	0.500000	−	0.866025i	0.0350070	−	0.0606339i
$205$	1.00000	+	1.73205i	0.0698430	+	0.120972i
$206$	1.00000	−	1.73205i	0.0696733	−	0.120678i
$207$	−3.50000	+	6.06218i	−0.243267	+	0.421350i
$208$	3.00000	−	5.19615i	0.208013	−	0.360288i
$209$	−4.00000			−0.276686
$210$		0			0
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	0.970229	−	0.242190i	$-0.0778659\pi$
$211$	4.00000	+	6.92820i	0.275371	+	0.476957i	−0.694857	+	0.719148i	$0.744533\pi$
$212$	2.00000	−	3.46410i	0.137361	−	0.237915i
$213$	6.00000			0.411113
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	−7.00000			−0.477396
$216$	1.00000			0.0680414
$217$		0			0
$218$	−12.0000			−0.812743
$219$	2.00000			0.135147
$220$	0.500000	+	0.866025i	0.0337100	+	0.0583874i
$221$	6.00000			0.403604
$222$	−3.50000	+	6.06218i	−0.234905	+	0.406867i
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	0.530607	−	0.847618i	$-0.321964\pi$
$223$	−7.00000	−	12.1244i	−0.468755	−	0.811907i	−0.999362	+	0.0357107i	$0.988630\pi$
$224$		0			0
$225$	1.00000			0.0666667
$226$	−9.50000	+	16.4545i	−0.631931	+	1.09454i
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	−0.702202	−	0.711977i	$-0.747800\pi$
$227$	4.00000	−	6.92820i	0.265489	−	0.459841i	0.967692	+	0.252136i	$0.0811332\pi$
$228$	−2.00000	+	3.46410i	−0.132453	+	0.229416i
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	−0.980401	−	0.197013i	$-0.936876\pi$
$229$	−10.0000	−	17.3205i	−0.660819	−	1.14457i	0.319582	−	0.947559i	$-0.396457\pi$
$230$	−3.50000	+	6.06218i	−0.230783	+	0.399728i
$231$		0			0
$232$	6.00000			0.393919
$233$	25.0000			1.63780			0.818902	−	0.573933i	$-0.194583\pi$
$233$	25.0000			1.63780			0.818902	+	0.573933i	$0.194583\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	−1.50000	+	2.59808i	−0.0978492	+	0.169480i
$236$	−6.00000	−	10.3923i	−0.390567	−	0.676481i
$237$	−1.50000	+	2.59808i	−0.0974355	+	0.168763i
$238$		0			0
$239$	−9.00000	+	15.5885i	−0.582162	+	1.00833i	0.413061	+	0.910703i	$0.364460\pi$
$239$	−9.00000	+	15.5885i	−0.582162	+	1.00833i	−0.995223	+	0.0976302i	$0.968874\pi$
$240$	1.00000			0.0645497
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	−0.995509	−	0.0946700i	$-0.969820\pi$
$241$	−9.00000	−	15.5885i	−0.579741	−	1.00414i	0.415768	−	0.909471i	$-0.363513\pi$
$242$	5.00000	+	8.66025i	0.321412	+	0.556702i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−14.0000			−0.896258
$245$	3.50000	+	6.06218i	0.223607	+	0.387298i
$246$	−2.00000			−0.127515
$247$	−24.0000			−1.52708
$248$	2.00000	+	5.19615i	0.127000	+	0.329956i
$249$	16.0000			1.01396
$250$	1.00000			0.0632456
$251$	−1.50000	−	2.59808i	−0.0946792	−	0.163989i	0.814795	−	0.579748i	$-0.196849\pi$
$251$	−1.50000	−	2.59808i	−0.0946792	−	0.163989i	−0.909475	+	0.415759i	$0.863516\pi$
$252$		0			0
$253$	3.50000	−	6.06218i	0.220043	−	0.381126i
$254$	9.00000	+	15.5885i	0.564710	+	0.978107i
$255$	0.500000	+	0.866025i	0.0313112	+	0.0542326i
$256$	1.00000			0.0625000
$257$	−11.5000	+	19.9186i	−0.717350	+	1.24249i	0.244696	+	0.969600i	$0.421312\pi$
$257$	−11.5000	+	19.9186i	−0.717350	+	1.24249i	−0.962046	+	0.272887i	$0.912021\pi$
$258$	3.50000	−	6.06218i	0.217900	−	0.377415i
$259$		0			0
$260$	3.00000	+	5.19615i	0.186052	+	0.322252i
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$	0.500000	+	0.866025i	0.0308901	+	0.0535032i
$263$	−11.0000			−0.678289			−0.339145	−	0.940734i	$-0.610138\pi$
$263$	−11.0000			−0.678289			−0.339145	+	0.940734i	$0.610138\pi$
$264$	−1.00000			−0.0615457
$265$	2.00000	+	3.46410i	0.122859	+	0.212798i
$266$		0			0
$267$	−2.00000	−	3.46410i	−0.122398	−	0.212000i
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	12.5000	−	21.6506i	0.762138	−	1.32006i	−0.179608	−	0.983738i	$-0.557483\pi$
$269$	12.5000	−	21.6506i	0.762138	−	1.32006i	0.941746	−	0.336324i	$-0.109184\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	−28.0000			−1.70088			−0.850439	−	0.526073i	$-0.823664\pi$
$271$	−28.0000			−1.70088			−0.850439	+	0.526073i	$0.823664\pi$
$272$	0.500000	+	0.866025i	0.0303170	+	0.0525105i
$273$		0			0
$274$	3.50000	−	6.06218i	0.211443	−	0.366230i
$275$	−1.00000			−0.0603023
$276$	−3.50000	−	6.06218i	−0.210675	−	0.364900i
$277$	13.0000			0.781094			0.390547	−	0.920583i	$-0.372286\pi$
$277$	13.0000			0.781094			0.390547	+	0.920583i	$0.372286\pi$
$278$	−10.0000			−0.599760
$279$	−5.50000	−	0.866025i	−0.329276	−	0.0518476i
$280$		0			0
$281$	22.0000			1.31241			0.656205	−	0.754583i	$-0.272161\pi$
$281$	22.0000			1.31241			0.656205	+	0.754583i	$0.272161\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−19.0000			−1.12943			−0.564716	−	0.825285i	$-0.691014\pi$
$283$	−19.0000			−1.12943			−0.564716	+	0.825285i	$0.691014\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$	−2.00000	−	3.46410i	−0.118470	−	0.205196i
$286$	−3.00000	−	5.19615i	−0.177394	−	0.307255i
$287$		0			0
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	8.00000	−	13.8564i	0.470588	−	0.815083i
$290$	−3.00000	+	5.19615i	−0.176166	+	0.305129i
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	−1.00000	+	1.73205i	−0.0585206	+	0.101361i
$293$	−8.00000	−	13.8564i	−0.467365	−	0.809500i	0.531940	−	0.846782i	$-0.321463\pi$
$293$	−8.00000	−	13.8564i	−0.467365	−	0.809500i	−0.999305	+	0.0372823i	$0.988130\pi$
$294$	−7.00000			−0.408248
$295$	12.0000			0.698667
$296$	−3.50000	−	6.06218i	−0.203433	−	0.352357i
$297$	0.500000	−	0.866025i	0.0290129	−	0.0502519i
$298$	−7.00000	−	12.1244i	−0.405499	−	0.702345i
$299$	21.0000	−	36.3731i	1.21446	−	2.10351i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$		0			0
$302$	−7.00000			−0.402805
$303$	−7.50000	−	12.9904i	−0.430864	−	0.746278i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$	7.00000	−	12.1244i	0.400819	−	0.694239i
$306$	−1.00000			−0.0571662
$307$	−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	$0.984261\pi$
$308$		0			0
$309$	−2.00000			−0.113776
$310$	−5.50000	−	0.866025i	−0.312379	−	0.0491869i
$311$	−6.00000			−0.340229			−0.170114	−	0.985424i	$-0.554414\pi$
$311$	−6.00000			−0.340229			−0.170114	+	0.985424i	$0.554414\pi$
$312$	−6.00000			−0.339683
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	0.768699	−	0.639611i	$-0.220905\pi$
$313$	−3.00000	−	5.19615i	−0.169570	−	0.293704i	−0.938269	+	0.345907i	$0.887571\pi$
$314$	14.0000			0.790066
$315$		0			0
$316$	−1.50000	−	2.59808i	−0.0843816	−	0.146153i
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	0.983866	−	0.178908i	$-0.0572566\pi$
$317$	6.00000	+	10.3923i	0.336994	+	0.583690i	−0.646872	+	0.762598i	$0.723923\pi$
$318$	−4.00000			−0.224309
$319$	3.00000	−	5.19615i	0.167968	−	0.290929i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	2.00000	−	3.46410i	0.111629	−	0.193347i
$322$		0			0
$323$	2.00000	−	3.46410i	0.111283	−	0.192748i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−6.00000			−0.332820
$326$	5.00000			0.276924
$327$	6.00000	+	10.3923i	0.331801	+	0.574696i
$328$	1.00000	−	1.73205i	0.0552158	−	0.0956365i
$329$		0			0
$330$	0.500000	−	0.866025i	0.0275241	−	0.0476731i
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	−8.00000	+	13.8564i	−0.439057	+	0.760469i
$333$	7.00000			0.383598
$334$	12.0000	+	20.7846i	0.656611	+	1.13728i
$335$	−2.50000	−	4.33013i	−0.136590	−	0.236580i
$336$		0			0
$337$	8.00000			0.435788			0.217894	−	0.975972i	$-0.430081\pi$
$337$	8.00000			0.435788			0.217894	+	0.975972i	$0.430081\pi$
$338$	−11.5000	−	19.9186i	−0.625518	−	1.08343i
$339$	19.0000			1.03194
$340$	−1.00000			−0.0542326
$341$	5.50000	+	0.866025i	0.297842	+	0.0468979i
$342$	4.00000			0.216295
$343$		0			0
$344$	3.50000	+	6.06218i	0.188707	+	0.326851i
$345$	7.00000			0.376867
$346$	−1.00000	+	1.73205i	−0.0537603	+	0.0931156i
$347$	7.00000	+	12.1244i	0.375780	+	0.650870i	0.990443	−	0.137920i	$-0.0440416\pi$
$347$	7.00000	+	12.1244i	0.375780	+	0.650870i	−0.614664	+	0.788789i	$0.710708\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	18.0000			0.963518			0.481759	−	0.876304i	$-0.339998\pi$
$349$	18.0000			0.963518			0.481759	+	0.876304i	$0.339998\pi$
$350$		0			0
$351$	3.00000	−	5.19615i	0.160128	−	0.277350i
$352$	0.500000	−	0.866025i	0.0266501	−	0.0461593i
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	0.974456	−	0.224580i	$-0.0721011\pi$
$353$	5.50000	+	9.52628i	0.292735	+	0.507033i	−0.681720	+	0.731613i	$0.738768\pi$
$354$	−6.00000	+	10.3923i	−0.318896	+	0.552345i
$355$	−3.00000	−	5.19615i	−0.159223	−	0.275783i
$356$	4.00000			0.212000
$357$		0			0
$358$	5.50000	+	9.52628i	0.290684	+	0.503480i
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	0.471696	+	0.881761i	$0.343642\pi$
$359$	−10.0000	+	17.3205i	−0.527780	+	0.914141i	−0.999476	+	0.0323801i	$0.989691\pi$
$360$	−0.500000	−	0.866025i	−0.0263523	−	0.0456435i
$361$	1.50000	−	2.59808i	0.0789474	−	0.136741i
$362$	−10.0000	+	17.3205i	−0.525588	+	0.910346i
$363$	5.00000	−	8.66025i	0.262432	−	0.454545i
$364$		0			0
$365$	−1.00000	−	1.73205i	−0.0523424	−	0.0906597i
$366$	7.00000	+	12.1244i	0.365896	+	0.633750i
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	−0.809093	−	0.587680i	$-0.800041\pi$
$367$	2.00000	−	3.46410i	0.104399	−	0.180825i	0.913493	+	0.406855i	$0.133375\pi$
$368$	7.00000			0.364900
$369$	1.00000	+	1.73205i	0.0520579	+	0.0901670i
$370$	7.00000			0.363913
$371$		0			0
$372$	3.50000	−	4.33013i	0.181467	−	0.224507i
$373$	−19.0000			−0.983783			−0.491891	−	0.870657i	$-0.663694\pi$
$373$	−19.0000			−0.983783			−0.491891	+	0.870657i	$0.663694\pi$
$374$	1.00000			0.0517088
$375$	−0.500000	−	0.866025i	−0.0258199	−	0.0447214i
$376$	3.00000			0.154713
$377$	18.0000	−	31.1769i	0.927047	−	1.60569i
$378$		0			0
$379$	−3.00000	−	5.19615i	−0.154100	−	0.266908i	0.778631	−	0.627482i	$-0.215914\pi$
$379$	−3.00000	−	5.19615i	−0.154100	−	0.266908i	−0.932731	+	0.360573i	$0.882581\pi$
$380$	4.00000			0.205196
$381$	9.00000	−	15.5885i	0.461084	−	0.798621i
$382$	3.00000	−	5.19615i	0.153493	−	0.265858i
$383$	−9.50000	+	16.4545i	−0.485427	+	0.840785i	−0.999860	−	0.0167461i	$-0.994669\pi$
$383$	−9.50000	+	16.4545i	−0.485427	+	0.840785i	0.514432	+	0.857531i	$0.328003\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$		0			0
$386$	−5.00000	−	8.66025i	−0.254493	−	0.440795i
$387$	−7.00000			−0.355830
$388$	−6.00000			−0.304604
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	0.729103	−	0.684403i	$-0.239937\pi$
$389$	−4.50000	−	7.79423i	−0.228159	−	0.395183i	−0.957263	+	0.289220i	$0.906604\pi$
$390$	3.00000	−	5.19615i	0.151911	−	0.263117i
$391$	3.50000	+	6.06218i	0.177003	+	0.306578i
$392$	3.50000	−	6.06218i	0.176777	−	0.306186i
$393$	0.500000	−	0.866025i	0.0252217	−	0.0436852i
$394$	−4.00000	+	6.92820i	−0.201517	+	0.349038i
$395$	3.00000			0.150946
$396$	0.500000	+	0.866025i	0.0251259	+	0.0435194i
$397$	10.5000	+	18.1865i	0.526980	+	0.912756i	0.999506	+	0.0314391i	$0.0100090\pi$
$397$	10.5000	+	18.1865i	0.526980	+	0.912756i	−0.472526	+	0.881317i	$0.656658\pi$
$398$	−8.00000	+	13.8564i	−0.401004	+	0.694559i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	2.00000			0.0998752			0.0499376	−	0.998752i	$-0.484098\pi$
$401$	2.00000			0.0998752			0.0499376	+	0.998752i	$0.484098\pi$
$402$	5.00000			0.249377
$403$	33.0000	+	5.19615i	1.64385	+	0.258839i
$404$	15.0000			0.746278
$405$	1.00000			0.0496904
$406$		0			0
$407$	−7.00000			−0.346977
$408$	0.500000	−	0.866025i	0.0247537	−	0.0428746i
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	0.529657	−	0.848212i	$-0.322321\pi$
$409$	−9.50000	−	16.4545i	−0.469745	−	0.813622i	−0.999402	+	0.0345902i	$0.988987\pi$
$410$	1.00000	+	1.73205i	0.0493865	+	0.0855399i
$411$	−7.00000			−0.345285
$412$	1.00000	−	1.73205i	0.0492665	−	0.0853320i
$413$		0			0
$414$	−3.50000	+	6.06218i	−0.172016	+	0.297940i
$415$	−8.00000	−	13.8564i	−0.392705	−	0.680184i
$416$	3.00000	−	5.19615i	0.147087	−	0.254762i
$417$	5.00000	+	8.66025i	0.244851	+	0.424094i
$418$	−4.00000			−0.195646
$419$	7.00000			0.341972			0.170986	−	0.985273i	$-0.445305\pi$
$419$	7.00000			0.341972			0.170986	+	0.985273i	$0.445305\pi$
$420$		0			0
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	0.353233	+	0.935536i	$0.385082\pi$
$421$	−13.0000	+	22.5167i	−0.633581	+	1.09739i	−0.986814	+	0.161859i	$0.948251\pi$
$422$	4.00000	+	6.92820i	0.194717	+	0.337260i
$423$	−1.50000	+	2.59808i	−0.0729325	+	0.126323i
$424$	2.00000	−	3.46410i	0.0971286	−	0.168232i
$425$	0.500000	−	0.866025i	0.0242536	−	0.0420084i
$426$	6.00000			0.290701
$427$		0			0
$428$	2.00000	+	3.46410i	0.0966736	+	0.167444i
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$	−7.00000			−0.337570
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	−0.959985	−	0.280052i	$-0.909648\pi$
$431$	−15.0000	−	25.9808i	−0.722525	−	1.25145i	0.237460	−	0.971397i	$-0.423685\pi$
$432$	1.00000			0.0481125
$433$	8.00000			0.384455			0.192228	−	0.981350i	$-0.438429\pi$
$433$	8.00000			0.384455			0.192228	+	0.981350i	$0.438429\pi$
$434$		0			0
$435$	6.00000			0.287678
$436$	−12.0000			−0.574696
$437$	−14.0000	−	24.2487i	−0.669711	−	1.15997i
$438$	2.00000			0.0955637
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	−0.0586141	−	0.998281i	$-0.518668\pi$
$439$	17.5000	−	30.3109i	0.835229	−	1.44666i	0.893843	−	0.448379i	$-0.147999\pi$
$440$	0.500000	+	0.866025i	0.0238366	+	0.0412861i
$441$	3.50000	+	6.06218i	0.166667	+	0.288675i
$442$	6.00000			0.285391
$443$	−17.0000	+	29.4449i	−0.807694	+	1.39897i	0.106763	+	0.994285i	$0.465952\pi$
$443$	−17.0000	+	29.4449i	−0.807694	+	1.39897i	−0.914457	+	0.404683i	$0.867382\pi$
$444$	−3.50000	+	6.06218i	−0.166103	+	0.287698i
$445$	−2.00000	+	3.46410i	−0.0948091	+	0.164214i
$446$	−7.00000	−	12.1244i	−0.331460	−	0.574105i
$447$	−7.00000	+	12.1244i	−0.331089	+	0.573462i
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	1.00000			0.0471405
$451$	−1.00000	−	1.73205i	−0.0470882	−	0.0815591i
$452$	−9.50000	+	16.4545i	−0.446842	+	0.773954i
$453$	3.50000	+	6.06218i	0.164444	+	0.284826i
$454$	4.00000	−	6.92820i	0.187729	−	0.325157i
$455$		0			0
$456$	−2.00000	+	3.46410i	−0.0936586	+	0.162221i
$457$	32.0000			1.49690			0.748448	−	0.663193i	$-0.230799\pi$
$457$	32.0000			1.49690			0.748448	+	0.663193i	$0.230799\pi$
$458$	−10.0000	−	17.3205i	−0.467269	−	0.809334i
$459$	0.500000	+	0.866025i	0.0233380	+	0.0404226i
$460$	−3.50000	+	6.06218i	−0.163188	+	0.282650i
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$		0			0
$463$	20.0000			0.929479			0.464739	−	0.885448i	$-0.346148\pi$
$463$	20.0000			0.929479			0.464739	+	0.885448i	$0.346148\pi$
$464$	6.00000			0.278543
$465$	2.00000	+	5.19615i	0.0927478	+	0.240966i
$466$	25.0000			1.15810
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$	3.00000	+	5.19615i	0.138675	+	0.240192i
$469$		0			0
$470$	−1.50000	+	2.59808i	−0.0691898	+	0.119840i
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$	−6.00000	−	10.3923i	−0.276172	−	0.478345i
$473$	7.00000			0.321860
$474$	−1.50000	+	2.59808i	−0.0688973	+	0.119334i
$475$	−2.00000	+	3.46410i	−0.0917663	+	0.158944i
$476$		0			0
$477$	2.00000	+	3.46410i	0.0915737	+	0.158610i
$478$	−9.00000	+	15.5885i	−0.411650	+	0.712999i
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	0.583803	−	0.811895i	$-0.301564\pi$
$479$	−9.00000	−	15.5885i	−0.411220	−	0.712255i	−0.995023	+	0.0996406i	$0.968231\pi$
$480$	1.00000			0.0456435
$481$	−42.0000			−1.91504
$482$	−9.00000	−	15.5885i	−0.409939	−	0.710035i
$483$		0			0
$484$	5.00000	+	8.66025i	0.227273	+	0.393648i
$485$	3.00000	−	5.19615i	0.136223	−	0.235945i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	0.233933	+	0.972253i	$0.424840\pi$
$487$	−16.0000	+	27.7128i	−0.725029	+	1.25579i	−0.958962	+	0.283535i	$0.908493\pi$
$488$	−14.0000			−0.633750
$489$	−2.50000	−	4.33013i	−0.113054	−	0.195815i
$490$	3.50000	+	6.06218i	0.158114	+	0.273861i
$491$	14.5000	−	25.1147i	0.654376	−	1.13341i	−0.327674	−	0.944791i	$-0.606265\pi$
$491$	14.5000	−	25.1147i	0.654376	−	1.13341i	0.982050	−	0.188621i	$-0.0604019\pi$
$492$	−2.00000			−0.0901670
$493$	3.00000	+	5.19615i	0.135113	+	0.234023i
$494$	−24.0000			−1.07981
$495$	−1.00000			−0.0449467
$496$	2.00000	+	5.19615i	0.0898027	+	0.233314i
$497$		0			0
$498$	16.0000			0.716977
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	0.998233	−	0.0594153i	$-0.0189236\pi$
$499$	10.0000	+	17.3205i	0.447661	+	0.775372i	−0.550572	+	0.834788i	$0.685590\pi$
$500$	1.00000			0.0447214
$501$	12.0000	−	20.7846i	0.536120	−	0.928588i
$502$	−1.50000	−	2.59808i	−0.0669483	−	0.115958i
$503$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$503$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$504$		0			0
$505$	−7.50000	+	12.9904i	−0.333746	+	0.578064i
$506$	3.50000	−	6.06218i	0.155594	−	0.269497i
$507$	−11.5000	+	19.9186i	−0.510733	+	0.884615i
$508$	9.00000	+	15.5885i	0.399310	+	0.691626i
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	0.342126	+	0.939654i	$0.388853\pi$
$509$	−14.5000	+	25.1147i	−0.642701	+	1.11319i	−0.984827	+	0.173537i	$0.944480\pi$
$510$	0.500000	+	0.866025i	0.0221404	+	0.0383482i
$511$		0			0
$512$	1.00000			0.0441942
$513$	−2.00000	−	3.46410i	−0.0883022	−	0.152944i
$514$	−11.5000	+	19.9186i	−0.507243	+	0.878571i
$515$	1.00000	+	1.73205i	0.0440653	+	0.0763233i
$516$	3.50000	−	6.06218i	0.154079	−	0.266872i
$517$	1.50000	−	2.59808i	0.0659699	−	0.114263i
$518$		0			0
$519$	2.00000			0.0877903
$520$	3.00000	+	5.19615i	0.131559	+	0.227866i
$521$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$521$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$522$	−3.00000	+	5.19615i	−0.131306	+	0.227429i
$523$	29.0000			1.26808			0.634041	−	0.773300i	$-0.281395\pi$
$523$	29.0000			1.26808			0.634041	+	0.773300i	$0.281395\pi$
$524$	0.500000	+	0.866025i	0.0218426	+	0.0378325i
$525$		0			0
$526$	−11.0000			−0.479623
$527$	−3.50000	+	4.33013i	−0.152462	+	0.188623i
$528$	−1.00000			−0.0435194
$529$	26.0000			1.13043
$530$	2.00000	+	3.46410i	0.0868744	+	0.150471i
$531$	12.0000			0.520756
$532$		0			0
$533$	−6.00000	−	10.3923i	−0.259889	−	0.450141i
$534$	−2.00000	−	3.46410i	−0.0865485	−	0.149906i
$535$	−4.00000			−0.172935
$536$	−2.50000	+	4.33013i	−0.107984	+	0.187033i
$537$	5.50000	−	9.52628i	0.237343	−	0.411089i
$538$	12.5000	−	21.6506i	0.538913	−	0.933425i
$539$	−3.50000	−	6.06218i	−0.150756	−	0.261116i
$540$	−0.500000	+	0.866025i	−0.0215166	+	0.0372678i
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	0.953262	−	0.302144i	$-0.0977023\pi$
$541$	5.00000	+	8.66025i	0.214967	+	0.372333i	−0.738296	+	0.674477i	$0.764369\pi$
$542$	−28.0000			−1.20270
$543$	20.0000			0.858282
$544$	0.500000	+	0.866025i	0.0214373	+	0.0371305i
$545$	6.00000	−	10.3923i	0.257012	−	0.445157i
$546$		0			0
$547$	8.50000	−	14.7224i	0.363434	−	0.629486i	−0.625090	−	0.780553i	$-0.714938\pi$
$547$	8.50000	−	14.7224i	0.363434	−	0.629486i	0.988524	+	0.151067i	$0.0482710\pi$
$548$	3.50000	−	6.06218i	0.149513	−	0.258963i
$549$	7.00000	−	12.1244i	0.298753	−	0.517455i
$550$	−1.00000			−0.0426401
$551$	−12.0000	−	20.7846i	−0.511217	−	0.885454i
$552$	−3.50000	−	6.06218i	−0.148970	−	0.258023i
$553$		0			0
$554$	13.0000			0.552317
$555$	−3.50000	−	6.06218i	−0.148567	−	0.257325i
$556$	−10.0000			−0.424094
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$	−5.50000	−	0.866025i	−0.232834	−	0.0366618i
$559$	42.0000			1.77641
$560$		0			0
$561$	−0.500000	−	0.866025i	−0.0211100	−	0.0365636i
$562$	22.0000			0.928014
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	−0.990961	−	0.134148i	$-0.957170\pi$
$563$	−9.00000	+	15.5885i	−0.379305	+	0.656975i	0.611656	+	0.791123i	$0.290503\pi$
$564$	−1.50000	−	2.59808i	−0.0631614	−	0.109399i
$565$	−9.50000	−	16.4545i	−0.399668	−	0.692245i
$566$	−19.0000			−0.798630
$567$		0			0
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−17.0000	+	29.4449i	−0.712677	+	1.23439i	0.251172	+	0.967943i	$0.419184\pi$
$569$	−17.0000	+	29.4449i	−0.712677	+	1.23439i	−0.963849	+	0.266450i	$0.914149\pi$
$570$	−2.00000	−	3.46410i	−0.0837708	−	0.145095i
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	−0.308443	−	0.951243i	$-0.599808\pi$
$571$	16.0000	−	27.7128i	0.669579	−	1.15975i	0.978022	−	0.208502i	$-0.0668588\pi$
$572$	−3.00000	−	5.19615i	−0.125436	−	0.217262i
$573$	−6.00000			−0.250654
$574$		0			0
$575$	−3.50000	−	6.06218i	−0.145960	−	0.252810i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−16.0000	−	27.7128i	−0.666089	−	1.15370i	−0.978989	−	0.203913i	$-0.934634\pi$
$577$	−16.0000	−	27.7128i	−0.666089	−	1.15370i	0.312900	−	0.949786i	$-0.398699\pi$
$578$	8.00000	−	13.8564i	0.332756	−	0.576351i
$579$	−5.00000	+	8.66025i	−0.207793	+	0.359908i
$580$	−3.00000	+	5.19615i	−0.124568	+	0.215758i
$581$		0			0
$582$	3.00000	+	5.19615i	0.124354	+	0.215387i
$583$	−2.00000	−	3.46410i	−0.0828315	−	0.143468i
$584$	−1.00000	+	1.73205i	−0.0413803	+	0.0716728i
$585$	−6.00000			−0.248069
$586$	−8.00000	−	13.8564i	−0.330477	−	0.572403i
$587$	18.0000			0.742940			0.371470	−	0.928445i	$-0.378854\pi$
$587$	18.0000			0.742940			0.371470	+	0.928445i	$0.378854\pi$
$588$	−7.00000			−0.288675
$589$	14.0000	−	17.3205i	0.576860	−	0.713679i
$590$	12.0000			0.494032
$591$	8.00000			0.329076
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	6.00000			0.246390			0.123195	−	0.992382i	$-0.460686\pi$
$593$	6.00000			0.246390			0.123195	+	0.992382i	$0.460686\pi$
$594$	0.500000	−	0.866025i	0.0205152	−	0.0355335i
$595$		0			0
$596$	−7.00000	−	12.1244i	−0.286731	−	0.496633i
$597$	16.0000			0.654836
$598$	21.0000	−	36.3731i	0.858754	−	1.48741i
$599$	−17.0000	+	29.4449i	−0.694601	+	1.20308i	0.275714	+	0.961240i	$0.411086\pi$
$599$	−17.0000	+	29.4449i	−0.694601	+	1.20308i	−0.970315	+	0.241845i	$0.922248\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	21.5000	+	37.2391i	0.877003	+	1.51901i	0.854613	+	0.519265i	$0.173794\pi$
$601$	21.5000	+	37.2391i	0.877003	+	1.51901i	0.0223900	+	0.999749i	$0.492872\pi$
$602$		0			0
$603$	−2.50000	−	4.33013i	−0.101808	−	0.176336i
$604$	−7.00000			−0.284826
$605$	−10.0000			−0.406558
$606$	−7.50000	−	12.9904i	−0.304667	−	0.527698i
$607$	−10.0000	+	17.3205i	−0.405887	+	0.703018i	−0.994424	−	0.105453i	$-0.966371\pi$
$607$	−10.0000	+	17.3205i	−0.405887	+	0.703018i	0.588537	+	0.808470i	$0.299704\pi$
$608$	−2.00000	−	3.46410i	−0.0811107	−	0.140488i
$609$		0			0
$610$	7.00000	−	12.1244i	0.283422	−	0.490901i
$611$	9.00000	−	15.5885i	0.364101	−	0.630641i
$612$	−1.00000			−0.0404226
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$	−8.00000	−	13.8564i	−0.322854	−	0.559199i
$615$	1.00000	−	1.73205i	0.0403239	−	0.0698430i
$616$		0			0
$617$	3.50000	+	6.06218i	0.140905	+	0.244054i	0.927838	−	0.372985i	$-0.121666\pi$
$617$	3.50000	+	6.06218i	0.140905	+	0.244054i	−0.786933	+	0.617039i	$0.788332\pi$
$618$	−2.00000			−0.0804518
$619$	36.0000			1.44696			0.723481	−	0.690344i	$-0.242541\pi$
$619$	36.0000			1.44696			0.723481	+	0.690344i	$0.242541\pi$
$620$	−5.50000	−	0.866025i	−0.220885	−	0.0347804i
$621$	7.00000			0.280900
$622$	−6.00000			−0.240578
$623$		0			0
$624$	−6.00000			−0.240192
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.00000	−	5.19615i	−0.119904	−	0.207680i
$627$	2.00000	+	3.46410i	0.0798723	+	0.138343i
$628$	14.0000			0.558661
$629$	3.50000	−	6.06218i	0.139554	−	0.241715i
$630$		0			0
$631$	−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	$0.970798\pi$
$632$	−1.50000	−	2.59808i	−0.0596668	−	0.103346i
$633$	4.00000	−	6.92820i	0.158986	−	0.275371i
$634$	6.00000	+	10.3923i	0.238290	+	0.412731i
$635$	−18.0000			−0.714308
$636$	−4.00000			−0.158610
$637$	−21.0000	−	36.3731i	−0.832050	−	1.44115i
$638$	3.00000	−	5.19615i	0.118771	−	0.205718i
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$	−0.500000	+	0.866025i	−0.0197642	+	0.0342327i
$641$	−2.00000	+	3.46410i	−0.0789953	+	0.136824i	−0.902817	−	0.430026i	$-0.858505\pi$
$641$	−2.00000	+	3.46410i	−0.0789953	+	0.136824i	0.823821	+	0.566849i	$0.191838\pi$
$642$	2.00000	−	3.46410i	0.0789337	−	0.136717i
$643$	−4.00000			−0.157745			−0.0788723	−	0.996885i	$-0.525132\pi$
$643$	−4.00000			−0.157745			−0.0788723	+	0.996885i	$0.525132\pi$
$644$		0			0
$645$	3.50000	+	6.06218i	0.137812	+	0.238698i
$646$	2.00000	−	3.46410i	0.0786889	−	0.136293i
$647$		0			0			−	1.00000i	$-0.5\pi$
$647$		0			0				1.00000i	$0.5\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−12.0000			−0.471041
$650$	−6.00000			−0.235339
$651$		0			0
$652$	5.00000			0.195815
$653$	−12.0000			−0.469596			−0.234798	−	0.972044i	$-0.575443\pi$
$653$	−12.0000			−0.469596			−0.234798	+	0.972044i	$0.575443\pi$
$654$	6.00000	+	10.3923i	0.234619	+	0.406371i
$655$	−1.00000			−0.0390732
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	−1.00000	−	1.73205i	−0.0390137	−	0.0675737i
$658$		0			0
$659$	−37.0000			−1.44132			−0.720658	−	0.693291i	$-0.756160\pi$
$659$	−37.0000			−1.44132			−0.720658	+	0.693291i	$0.756160\pi$
$660$	0.500000	−	0.866025i	0.0194625	−	0.0337100i
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	−0.752252	−	0.658876i	$-0.771032\pi$
$661$	5.00000	−	8.66025i	0.194477	−	0.336845i	0.946729	+	0.322031i	$0.104366\pi$
$662$	−2.00000	+	3.46410i	−0.0777322	+	0.134636i
$663$	−3.00000	−	5.19615i	−0.116510	−	0.201802i
$664$	−8.00000	+	13.8564i	−0.310460	+	0.537733i
$665$		0			0
$666$	7.00000			0.271244
$667$	42.0000			1.62625
$668$	12.0000	+	20.7846i	0.464294	+	0.804181i
$669$	−7.00000	+	12.1244i	−0.270636	+	0.468755i
$670$	−2.50000	−	4.33013i	−0.0965834	−	0.167287i
$671$	−7.00000	+	12.1244i	−0.270232	+	0.468056i
$672$		0			0
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	−0.946156	−	0.323711i	$-0.895069\pi$
$673$	−5.00000	+	8.66025i	−0.192736	+	0.333828i	0.753420	+	0.657539i	$0.228403\pi$
$674$	8.00000			0.308148
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	25.0000	−	43.3013i	0.960828	−	1.66420i	0.240399	−	0.970674i	$-0.422722\pi$
$677$	25.0000	−	43.3013i	0.960828	−	1.66420i	0.720429	−	0.693529i	$-0.243945\pi$
$678$	19.0000			0.729691
$679$		0			0
$680$	−1.00000			−0.0383482
$681$	−8.00000			−0.306561
$682$	5.50000	+	0.866025i	0.210606	+	0.0331618i
$683$	−4.00000			−0.153056			−0.0765279	−	0.997067i	$-0.524383\pi$
$683$	−4.00000			−0.153056			−0.0765279	+	0.997067i	$0.524383\pi$
$684$	4.00000			0.152944
$685$	3.50000	+	6.06218i	0.133728	+	0.231624i
$686$		0			0
$687$	−10.0000	+	17.3205i	−0.381524	+	0.660819i
$688$	3.50000	+	6.06218i	0.133436	+	0.231118i
$689$	−12.0000	−	20.7846i	−0.457164	−	0.791831i
$690$	7.00000			0.266485
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	−0.577325	−	0.816514i	$-0.695903\pi$
$691$	11.0000	−	19.0526i	0.418460	−	0.724793i	0.995785	+	0.0917209i	$0.0292368\pi$
$692$	−1.00000	+	1.73205i	−0.0380143	+	0.0658427i
$693$		0			0
$694$	7.00000	+	12.1244i	0.265716	+	0.460234i
$695$	5.00000	−	8.66025i	0.189661	−	0.328502i
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$	2.00000			0.0757554
$698$	18.0000			0.681310
$699$	−12.5000	−	21.6506i	−0.472793	−	0.818902i
$700$		0			0
$701$	−12.5000	−	21.6506i	−0.472118	−	0.817733i	0.527373	−	0.849634i	$-0.323177\pi$
$701$	−12.5000	−	21.6506i	−0.472118	−	0.817733i	−0.999491	+	0.0319010i	$0.989844\pi$
$702$	3.00000	−	5.19615i	0.113228	−	0.196116i
$703$	−14.0000	+	24.2487i	−0.528020	+	0.914557i
$704$	0.500000	−	0.866025i	0.0188445	−	0.0326396i
$705$	3.00000			0.112987
$706$	5.50000	+	9.52628i	0.206995	+	0.358526i
$707$		0			0
$708$	−6.00000	+	10.3923i	−0.225494	+	0.390567i
$709$	−10.0000			−0.375558			−0.187779	−	0.982211i	$-0.560129\pi$
$709$	−10.0000			−0.375558			−0.187779	+	0.982211i	$0.560129\pi$
$710$	−3.00000	−	5.19615i	−0.112588	−	0.195008i
$711$	3.00000			0.112509
$712$	4.00000			0.149906
$713$	14.0000	+	36.3731i	0.524304	+	1.36218i
$714$		0			0
$715$	6.00000			0.224387
$716$	5.50000	+	9.52628i	0.205545	+	0.356014i
$717$	18.0000			0.672222
$718$	−10.0000	+	17.3205i	−0.373197	+	0.646396i
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	0.826319	−	0.563202i	$-0.190431\pi$
$719$	−2.00000	−	3.46410i	−0.0745874	−	0.129189i	−0.900907	+	0.434013i	$0.857097\pi$
$720$	−0.500000	−	0.866025i	−0.0186339	−	0.0322749i
$721$		0			0
$722$	1.50000	−	2.59808i	0.0558242	−	0.0966904i
$723$	−9.00000	+	15.5885i	−0.334714	+	0.579741i
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$	5.00000	−	8.66025i	0.185567	−	0.321412i
$727$	−12.0000	−	20.7846i	−0.445055	−	0.770859i	0.553001	−	0.833181i	$-0.313483\pi$
$727$	−12.0000	−	20.7846i	−0.445055	−	0.770859i	−0.998056	+	0.0623223i	$0.980149\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	−1.00000	−	1.73205i	−0.0370117	−	0.0641061i
$731$	−3.50000	+	6.06218i	−0.129452	+	0.224218i
$732$	7.00000	+	12.1244i	0.258727	+	0.448129i
$733$	17.5000	−	30.3109i	0.646377	−	1.11956i	−0.337604	−	0.941288i	$-0.609617\pi$
$733$	17.5000	−	30.3109i	0.646377	−	1.11956i	0.983982	−	0.178270i	$-0.0570501\pi$
$734$	2.00000	−	3.46410i	0.0738213	−	0.127862i
$735$	3.50000	−	6.06218i	0.129099	−	0.223607i
$736$	7.00000			0.258023
$737$	2.50000	+	4.33013i	0.0920887	+	0.159502i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	19.0000	−	32.9090i	0.698926	−	1.21058i	−0.269913	−	0.962885i	$-0.586995\pi$
$739$	19.0000	−	32.9090i	0.698926	−	1.21058i	0.968839	−	0.247691i	$-0.0796718\pi$
$740$	7.00000			0.257325
$741$	12.0000	+	20.7846i	0.440831	+	0.763542i
$742$		0			0
$743$	−27.0000			−0.990534			−0.495267	−	0.868741i	$-0.664930\pi$
$743$	−27.0000			−0.990534			−0.495267	+	0.868741i	$0.664930\pi$
$744$	3.50000	−	4.33013i	0.128316	−	0.158750i
$745$	14.0000			0.512920
$746$	−19.0000			−0.695639
$747$	−8.00000	−	13.8564i	−0.292705	−	0.506979i
$748$	1.00000			0.0365636
$749$		0			0
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	0.998752	−	0.0499348i	$-0.0159013\pi$
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	−0.542621	+	0.839978i	$0.682568\pi$
$752$	3.00000			0.109399
$753$	−1.50000	+	2.59808i	−0.0546630	+	0.0946792i
$754$	18.0000	−	31.1769i	0.655521	−	1.13540i
$755$	3.50000	−	6.06218i	0.127378	−	0.220625i
$756$		0			0
$757$	9.50000	−	16.4545i	0.345283	−	0.598048i	−0.640122	−	0.768273i	$-0.721116\pi$
$757$	9.50000	−	16.4545i	0.345283	−	0.598048i	0.985405	+	0.170225i	$0.0544495\pi$
$758$	−3.00000	−	5.19615i	−0.108965	−	0.188733i
$759$	−7.00000			−0.254084
$760$	4.00000			0.145095
$761$	8.00000	+	13.8564i	0.290000	+	0.502294i	0.973809	−	0.227366i	$-0.0730114\pi$
$761$	8.00000	+	13.8564i	0.290000	+	0.502294i	−0.683810	+	0.729661i	$0.739678\pi$
$762$	9.00000	−	15.5885i	0.326036	−	0.564710i
$763$		0			0
$764$	3.00000	−	5.19615i	0.108536	−	0.187990i
$765$	0.500000	−	0.866025i	0.0180775	−	0.0313112i
$766$	−9.50000	+	16.4545i	−0.343249	+	0.594525i
$767$	−72.0000			−2.59977
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	0.999364	−	0.0356685i	$-0.0113561\pi$
$769$	13.0000	+	22.5167i	0.468792	+	0.811972i	−0.530572	+	0.847640i	$0.678023\pi$
$770$		0			0
$771$	23.0000			0.828325
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	−30.0000			−1.07903			−0.539513	−	0.841978i	$-0.681391\pi$
$773$	−30.0000			−1.07903			−0.539513	+	0.841978i	$0.681391\pi$
$774$	−7.00000			−0.251610
$775$	3.50000	−	4.33013i	0.125724	−	0.155543i
$776$	−6.00000			−0.215387
$777$		0			0
$778$	−4.50000	−	7.79423i	−0.161333	−	0.279437i
$779$	−8.00000			−0.286630
$780$	3.00000	−	5.19615i	0.107417	−	0.186052i
$781$	3.00000	+	5.19615i	0.107348	+	0.185933i
$782$	3.50000	+	6.06218i	0.125160	+	0.216783i
$783$	6.00000			0.214423
$784$	3.50000	−	6.06218i	0.125000	−	0.216506i
$785$	−7.00000	+	12.1244i	−0.249841	+	0.432737i
$786$	0.500000	−	0.866025i	0.0178344	−	0.0308901i
$787$	4.50000	+	7.79423i	0.160408	+	0.277834i	0.935015	−	0.354608i	$-0.115386\pi$
$787$	4.50000	+	7.79423i	0.160408	+	0.277834i	−0.774607	+	0.632443i	$0.782052\pi$
$788$	−4.00000	+	6.92820i	−0.142494	+	0.246807i
$789$	5.50000	+	9.52628i	0.195805	+	0.339145i
$790$	3.00000			0.106735
$791$		0			0
$792$	0.500000	+	0.866025i	0.0177667	+	0.0307729i
$793$	−42.0000	+	72.7461i	−1.49146	+	2.58329i
$794$	10.5000	+	18.1865i	0.372631	+	0.645416i
$795$	2.00000	−	3.46410i	0.0709327	−	0.122859i
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	−0.952506	−	0.304520i	$-0.901504\pi$
$797$	−6.00000	+	10.3923i	−0.212531	+	0.368114i	0.739975	+	0.672634i	$0.234837\pi$
$798$		0			0
$799$	1.50000	+	2.59808i	0.0530662	+	0.0919133i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−2.00000	+	3.46410i	−0.0706665	+	0.122398i
$802$	2.00000			0.0706225
$803$	1.00000	+	1.73205i	0.0352892	+	0.0611227i
$804$	5.00000			0.176336
$805$		0			0
$806$	33.0000	+	5.19615i	1.16238	+	0.183027i
$807$	−25.0000			−0.880042
$808$	15.0000			0.527698
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	0.952012	−	0.306062i	$-0.0990113\pi$
$809$	6.00000	+	10.3923i	0.210949	+	0.365374i	−0.741063	+	0.671436i	$0.765678\pi$
$810$	1.00000			0.0351364
$811$	−10.0000	+	17.3205i	−0.351147	+	0.608205i	−0.986451	−	0.164057i	$-0.947542\pi$
$811$	−10.0000	+	17.3205i	−0.351147	+	0.608205i	0.635303	+	0.772263i	$0.280875\pi$
$812$		0			0
$813$	14.0000	+	24.2487i	0.491001	+	0.850439i
$814$	−7.00000			−0.245350
$815$	−2.50000	+	4.33013i	−0.0875712	+	0.151678i
$816$	0.500000	−	0.866025i	0.0175035	−	0.0303170i
$817$	14.0000	−	24.2487i	0.489798	−	0.848355i
$818$	−9.50000	−	16.4545i	−0.332160	−	0.575317i
$819$		0			0
$820$	1.00000	+	1.73205i	0.0349215	+	0.0604858i
$821$	−15.0000			−0.523504			−0.261752	−	0.965135i	$-0.584300\pi$
$821$	−15.0000			−0.523504			−0.261752	+	0.965135i	$0.584300\pi$
$822$	−7.00000			−0.244153
$823$	23.0000	+	39.8372i	0.801730	+	1.38864i	0.918477	+	0.395475i	$0.129420\pi$
$823$	23.0000	+	39.8372i	0.801730	+	1.38864i	−0.116747	+	0.993162i	$0.537247\pi$
$824$	1.00000	−	1.73205i	0.0348367	−	0.0603388i
$825$	0.500000	+	0.866025i	0.0174078	+	0.0301511i
$826$		0			0
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	0.362441	+	0.932007i	$0.381944\pi$
$827$	−18.0000	+	31.1769i	−0.625921	+	1.08413i	−0.988362	+	0.152121i	$0.951390\pi$
$828$	−3.50000	+	6.06218i	−0.121633	+	0.210675i
$829$	−38.0000			−1.31979			−0.659897	−	0.751356i	$-0.729400\pi$
$829$	−38.0000			−1.31979			−0.659897	+	0.751356i	$0.729400\pi$
$830$	−8.00000	−	13.8564i	−0.277684	−	0.480963i
$831$	−6.50000	−	11.2583i	−0.225483	−	0.390547i
$832$	3.00000	−	5.19615i	0.104006	−	0.180144i
$833$	7.00000			0.242536
$834$	5.00000	+	8.66025i	0.173136	+	0.299880i
$835$	−24.0000			−0.830554
$836$	−4.00000			−0.138343
$837$	2.00000	+	5.19615i	0.0691301	+	0.179605i
$838$	7.00000			0.241811
$839$	−6.00000			−0.207143			−0.103572	−	0.994622i	$-0.533027\pi$
$839$	−6.00000			−0.207143			−0.103572	+	0.994622i	$0.533027\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	−13.0000	+	22.5167i	−0.448010	+	0.775975i
$843$	−11.0000	−	19.0526i	−0.378860	−	0.656205i
$844$	4.00000	+	6.92820i	0.137686	+	0.238479i
$845$	23.0000			0.791224
$846$	−1.50000	+	2.59808i	−0.0515711	+	0.0893237i
$847$		0			0
$848$	2.00000	−	3.46410i	0.0686803	−	0.118958i
$849$	9.50000	+	16.4545i	0.326039	+	0.564716i
$850$	0.500000	−	0.866025i	0.0171499	−	0.0297044i
$851$	−24.5000	−	42.4352i	−0.839849	−	1.45466i
$852$	6.00000			0.205557
$853$	−14.0000			−0.479351			−0.239675	−	0.970853i	$-0.577041\pi$
$853$	−14.0000			−0.479351			−0.239675	+	0.970853i	$0.577041\pi$
$854$		0			0
$855$	−2.00000	+	3.46410i	−0.0683986	+	0.118470i
$856$	2.00000	+	3.46410i	0.0683586	+	0.118401i
$857$	4.50000	−	7.79423i	0.153717	−	0.266246i	−0.778874	−	0.627180i	$-0.784209\pi$
$857$	4.50000	−	7.79423i	0.153717	−	0.266246i	0.932591	+	0.360935i	$0.117542\pi$
$858$	−3.00000	+	5.19615i	−0.102418	+	0.177394i
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	−0.984655	−	0.174512i	$-0.944165\pi$
$859$	−10.0000	+	17.3205i	−0.341196	+	0.590968i	0.643459	+	0.765480i	$0.277499\pi$
$860$	−7.00000			−0.238698
$861$		0			0
$862$	−15.0000	−	25.9808i	−0.510902	−	0.884908i
$863$	15.5000	−	26.8468i	0.527626	−	0.913875i	−0.471855	−	0.881676i	$-0.656416\pi$
$863$	15.5000	−	26.8468i	0.527626	−	0.913875i	0.999481	−	0.0321993i	$-0.0102511\pi$
$864$	1.00000			0.0340207
$865$	−1.00000	−	1.73205i	−0.0340010	−	0.0588915i
$866$	8.00000			0.271851
$867$	−16.0000			−0.543388
$868$		0			0
$869$	−3.00000			−0.101768
$870$	6.00000			0.203419
$871$	15.0000	+	25.9808i	0.508256	+	0.880325i
$872$	−12.0000			−0.406371
$873$	3.00000	−	5.19615i	0.101535	−	0.175863i
$874$	−14.0000	−	24.2487i	−0.473557	−	0.820225i
$875$		0			0
$876$	2.00000			0.0675737
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	0.363898	+	0.931439i	$0.381446\pi$
$877$	−18.5000	+	32.0429i	−0.624701	+	1.08201i	−0.988599	+	0.150574i	$0.951888\pi$
$878$	17.5000	−	30.3109i	0.590596	−	1.02294i
$879$	−8.00000	+	13.8564i	−0.269833	+	0.467365i
$880$	0.500000	+	0.866025i	0.0168550	+	0.0291937i
$881$	−10.0000	+	17.3205i	−0.336909	+	0.583543i	−0.983850	−	0.178997i	$-0.942715\pi$
$881$	−10.0000	+	17.3205i	−0.336909	+	0.583543i	0.646941	+	0.762540i	$0.276048\pi$
$882$	3.50000	+	6.06218i	0.117851	+	0.204124i
$883$	1.00000			0.0336527			0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000			0.0336527			0.0168263	+	0.999858i	$0.494644\pi$
$884$	6.00000			0.201802
$885$	−6.00000	−	10.3923i	−0.201688	−	0.349334i
$886$	−17.0000	+	29.4449i	−0.571126	+	0.989220i
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	0.634141	−	0.773217i	$-0.281354\pi$
$887$	−10.5000	−	18.1865i	−0.352555	−	0.610644i	−0.986696	+	0.162573i	$0.948021\pi$
$888$	−3.50000	+	6.06218i	−0.117452	+	0.203433i
$889$		0			0
$890$	−2.00000	+	3.46410i	−0.0670402	+	0.116117i
$891$	−1.00000			−0.0335013
$892$	−7.00000	−	12.1244i	−0.234377	−	0.405953i
$893$	−6.00000	−	10.3923i	−0.200782	−	0.347765i
$894$	−7.00000	+	12.1244i	−0.234115	+	0.405499i
$895$	−11.0000			−0.367689
$896$		0			0
$897$	−42.0000			−1.40234
$898$	−30.0000			−1.00111
$899$	12.0000	+	31.1769i	0.400222	+	1.03981i
$900$	1.00000			0.0333333
$901$	4.00000			0.133259
$902$	−1.00000	−	1.73205i	−0.0332964	−	0.0576710i
$903$		0			0
$904$	−9.50000	+	16.4545i	−0.315965	+	0.547268i
$905$	−10.0000	−	17.3205i	−0.332411	−	0.575753i
$906$	3.50000	+	6.06218i	0.116280	+	0.201402i
$907$	48.0000			1.59381			0.796907	−	0.604102i	$-0.206468\pi$
$907$	48.0000			1.59381			0.796907	+	0.604102i	$0.206468\pi$
$908$	4.00000	−	6.92820i	0.132745	−	0.229920i
$909$	−7.50000	+	12.9904i	−0.248759	+	0.430864i
$910$		0			0
$911$	14.0000	+	24.2487i	0.463841	+	0.803396i	0.999148	−	0.0412615i	$-0.0131377\pi$
$911$	14.0000	+	24.2487i	0.463841	+	0.803396i	−0.535308	+	0.844657i	$0.679804\pi$
$912$	−2.00000	+	3.46410i	−0.0662266	+	0.114708i
$913$	8.00000	+	13.8564i	0.264761	+	0.458580i
$914$	32.0000			1.05847
$915$	−14.0000			−0.462826
$916$	−10.0000	−	17.3205i	−0.330409	−	0.572286i
$917$		0			0
$918$	0.500000	+	0.866025i	0.0165025	+	0.0285831i
$919$	−12.5000	+	21.6506i	−0.412337	+	0.714189i	−0.995145	−	0.0984214i	$-0.968621\pi$
$919$	−12.5000	+	21.6506i	−0.412337	+	0.714189i	0.582808	+	0.812610i	$0.301954\pi$
$920$	−3.50000	+	6.06218i	−0.115392	+	0.199864i
$921$	−8.00000	+	13.8564i	−0.263609	+	0.456584i
$922$	33.0000			1.08680
$923$	18.0000	+	31.1769i	0.592477	+	1.02620i
$924$		0			0
$925$	−3.50000	+	6.06218i	−0.115079	+	0.199323i
$926$	20.0000			0.657241
$927$	1.00000	+	1.73205i	0.0328443	+	0.0568880i
$928$	6.00000			0.196960
$929$	−56.0000			−1.83730			−0.918650	−	0.395072i	$-0.870720\pi$
$929$	−56.0000			−1.83730			−0.918650	+	0.395072i	$0.870720\pi$
$930$	2.00000	+	5.19615i	0.0655826	+	0.170389i
$931$	−28.0000			−0.917663
$932$	25.0000			0.818902
$933$	3.00000	+	5.19615i	0.0982156	+	0.170114i
$934$	12.0000			0.392652
$935$	−0.500000	+	0.866025i	−0.0163517	+	0.0283221i
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	−23.0000	−	39.8372i	−0.751377	−	1.30142i	−0.947155	−	0.320775i	$-0.896057\pi$
$937$	−23.0000	−	39.8372i	−0.751377	−	1.30142i	0.195778	−	0.980648i	$-0.437277\pi$
$938$		0			0
$939$	−3.00000	+	5.19615i	−0.0979013	+	0.169570i
$940$	−1.50000	+	2.59808i	−0.0489246	+	0.0847399i
$941$	−30.5000	+	52.8275i	−0.994272	+	1.72213i	−0.404572	+	0.914506i	$0.632580\pi$
$941$	−30.5000	+	52.8275i	−0.994272	+	1.72213i	−0.589699	+	0.807623i	$0.700754\pi$
$942$	−7.00000	−	12.1244i	−0.228072	−	0.395033i
$943$	7.00000	−	12.1244i	0.227951	−	0.394823i
$944$	−6.00000	−	10.3923i	−0.195283	−	0.338241i
$945$		0			0
$946$	7.00000			0.227590
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	0.681930	−	0.731417i	$-0.261141\pi$
$947$	−9.00000	−	15.5885i	−0.292461	−	0.506557i	−0.974391	+	0.224860i	$0.927807\pi$
$948$	−1.50000	+	2.59808i	−0.0487177	+	0.0843816i
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$	−2.00000	+	3.46410i	−0.0648886	+	0.112390i
$951$	6.00000	−	10.3923i	0.194563	−	0.336994i
$952$		0			0
$953$	18.0000			0.583077			0.291539	−	0.956559i	$-0.405833\pi$
$953$	18.0000			0.583077			0.291539	+	0.956559i	$0.405833\pi$
$954$	2.00000	+	3.46410i	0.0647524	+	0.112154i
$955$	3.00000	+	5.19615i	0.0970777	+	0.168144i
$956$	−9.00000	+	15.5885i	−0.291081	+	0.504167i
$957$	−6.00000			−0.193952
$958$	−9.00000	−	15.5885i	−0.290777	−	0.503640i
$959$		0			0
$960$	1.00000			0.0322749
$961$	−23.0000	+	20.7846i	−0.741935	+	0.670471i
$962$	−42.0000			−1.35413
$963$	−4.00000			−0.128898
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$	10.0000			0.321911
$966$		0			0
$967$	28.0000	+	48.4974i	0.900419	+	1.55957i	0.826951	+	0.562274i	$0.190074\pi$
$967$	28.0000	+	48.4974i	0.900419	+	1.55957i	0.0734686	+	0.997298i	$0.476593\pi$
$968$	5.00000	+	8.66025i	0.160706	+	0.278351i
$969$	−4.00000			−0.128499
$970$	3.00000	−	5.19615i	0.0963242	−	0.166838i
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	−0.469897	−	0.882721i	$-0.655709\pi$
$971$	16.5000	−	28.5788i	0.529510	−	0.917139i	0.999408	−	0.0344175i	$-0.0109576\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$		0			0
$974$	−16.0000	+	27.7128i	−0.512673	+	0.887976i
$975$	3.00000	+	5.19615i	0.0960769	+	0.166410i
$976$	−14.0000			−0.448129
$977$	−30.0000			−0.959785			−0.479893	−	0.877327i	$-0.659324\pi$
$977$	−30.0000			−0.959785			−0.479893	+	0.877327i	$0.659324\pi$
$978$	−2.50000	−	4.33013i	−0.0799412	−	0.138462i
$979$	2.00000	−	3.46410i	0.0639203	−	0.110713i
$980$	3.50000	+	6.06218i	0.111803	+	0.193649i
$981$	6.00000	−	10.3923i	0.191565	−	0.331801i
$982$	14.5000	−	25.1147i	0.462714	−	0.801443i
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	−0.608712	−	0.793391i	$-0.708314\pi$
$983$	12.0000	−	20.7846i	0.382741	−	0.662926i	0.991453	+	0.130465i	$0.0416470\pi$
$984$	−2.00000			−0.0637577
$985$	−4.00000	−	6.92820i	−0.127451	−	0.220751i
$986$	3.00000	+	5.19615i	0.0955395	+	0.165479i
$987$		0			0
$988$	−24.0000			−0.763542
$989$	24.5000	+	42.4352i	0.779055	+	1.34936i
$990$	−1.00000			−0.0317821
$991$	−40.0000			−1.27064			−0.635321	−	0.772248i	$-0.719132\pi$
$991$	−40.0000			−1.27064			−0.635321	+	0.772248i	$0.719132\pi$
$992$	2.00000	+	5.19615i	0.0635001	+	0.164978i
$993$	4.00000			0.126936
$994$		0			0
$995$	−8.00000	−	13.8564i	−0.253617	−	0.439278i
$996$	16.0000			0.506979
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	−0.687584	−	0.726105i	$-0.741329\pi$
$997$	9.00000	−	15.5885i	0.285033	−	0.493691i	0.972617	+	0.232413i	$0.0746622\pi$
$998$	10.0000	+	17.3205i	0.316544	+	0.548271i
$999$	−3.50000	−	6.06218i	−0.110735	−	0.191799i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.e.211.1	✓	2	1.1	even	1	trivial
930.2.i.e.811.1	yes	2	31.5	even	3	inner

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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +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} +(3.00000 - 5.19615i) q^{13} +1.00000 q^{15} +1.00000 q^{16} +(0.500000 + 0.866025i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-2.00000 - 3.46410i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(0.500000 - 0.866025i) q^{22} +7.00000 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(3.00000 - 5.19615i) q^{26} +1.00000 q^{27} +6.00000 q^{29} +1.00000 q^{30} +(2.00000 + 5.19615i) q^{31} +1.00000 q^{32} -1.00000 q^{33} +(0.500000 + 0.866025i) q^{34} +(-0.500000 + 0.866025i) q^{36} +(-3.50000 - 6.06218i) q^{37} +(-2.00000 - 3.46410i) q^{38} -6.00000 q^{39} +(-0.500000 + 0.866025i) q^{40} +(1.00000 - 1.73205i) q^{41} +(3.50000 + 6.06218i) q^{43} +(0.500000 - 0.866025i) q^{44} +(-0.500000 - 0.866025i) q^{45} +7.00000 q^{46} +3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.50000 - 6.06218i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(0.500000 - 0.866025i) q^{51} +(3.00000 - 5.19615i) q^{52} +(2.00000 - 3.46410i) q^{53} +1.00000 q^{54} +(0.500000 + 0.866025i) q^{55} +(-2.00000 + 3.46410i) q^{57} +6.00000 q^{58} +(-6.00000 - 10.3923i) q^{59} +1.00000 q^{60} -14.0000 q^{61} +(2.00000 + 5.19615i) q^{62} +1.00000 q^{64} +(3.00000 + 5.19615i) q^{65} -1.00000 q^{66} +(-2.50000 + 4.33013i) q^{67} +(0.500000 + 0.866025i) q^{68} +(-3.50000 - 6.06218i) q^{69} +(-3.00000 + 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.00000 + 1.73205i) q^{73} +(-3.50000 - 6.06218i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-2.00000 - 3.46410i) q^{76} -6.00000 q^{78} +(-1.50000 - 2.59808i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} +(-8.00000 + 13.8564i) q^{83} -1.00000 q^{85} +(3.50000 + 6.06218i) q^{86} +(-3.00000 - 5.19615i) q^{87} +(0.500000 - 0.866025i) q^{88} +4.00000 q^{89} +(-0.500000 - 0.866025i) q^{90} +7.00000 q^{92} +(3.50000 - 4.33013i) q^{93} +3.00000 q^{94} +4.00000 q^{95} +(-0.500000 - 0.866025i) q^{96} -6.00000 q^{97} +(3.50000 - 6.06218i) q^{98} +(0.500000 + 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} - q^{3} + 2 q^{4} - q^{5} - q^{6} + 2 q^{8} - q^{9} - q^{10} + q^{11} - q^{12} + 6 q^{13} + 2 q^{15} + 2 q^{16} + q^{17} - q^{18} - 4 q^{19} - q^{20} + q^{22} + 14 q^{23} - q^{24} - q^{25} + 6 q^{26} + 2 q^{27} + 12 q^{29} + 2 q^{30} + 4 q^{31} + 2 q^{32} - 2 q^{33} + q^{34} - q^{36} - 7 q^{37} - 4 q^{38} - 12 q^{39} - q^{40} + 2 q^{41} + 7 q^{43} + q^{44} - q^{45} + 14 q^{46} + 6 q^{47} - q^{48} + 7 q^{49} - q^{50} + q^{51} + 6 q^{52} + 4 q^{53} + 2 q^{54} + q^{55} - 4 q^{57} + 12 q^{58} - 12 q^{59} + 2 q^{60} - 28 q^{61} + 4 q^{62} + 2 q^{64} + 6 q^{65} - 2 q^{66} - 5 q^{67} + q^{68} - 7 q^{69} - 6 q^{71} - q^{72} - 2 q^{73} - 7 q^{74} - q^{75} - 4 q^{76} - 12 q^{78} - 3 q^{79} - q^{80} - q^{81} + 2 q^{82} - 16 q^{83} - 2 q^{85} + 7 q^{86} - 6 q^{87} + q^{88} + 8 q^{89} - q^{90} + 14 q^{92} + 7 q^{93} + 6 q^{94} + 8 q^{95} - q^{96} - 12 q^{97} + 7 q^{98} + q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 - q^3 + 2 * q^4 - q^5 - q^6 + 2 * q^8 - q^9 - q^10 + q^11 - q^12 + 6 * q^13 + 2 * q^15 + 2 * q^16 + q^17 - q^18 - 4 * q^19 - q^20 + q^22 + 14 * q^23 - q^24 - q^25 + 6 * q^26 + 2 * q^27 + 12 * q^29 + 2 * q^30 + 4 * q^31 + 2 * q^32 - 2 * q^33 + q^34 - q^36 - 7 * q^37 - 4 * q^38 - 12 * q^39 - q^40 + 2 * q^41 + 7 * q^43 + q^44 - q^45 + 14 * q^46 + 6 * q^47 - q^48 + 7 * q^49 - q^50 + q^51 + 6 * q^52 + 4 * q^53 + 2 * q^54 + q^55 - 4 * q^57 + 12 * q^58 - 12 * q^59 + 2 * q^60 - 28 * q^61 + 4 * q^62 + 2 * q^64 + 6 * q^65 - 2 * q^66 - 5 * q^67 + q^68 - 7 * q^69 - 6 * q^71 - q^72 - 2 * q^73 - 7 * q^74 - q^75 - 4 * q^76 - 12 * q^78 - 3 * q^79 - q^80 - q^81 + 2 * q^82 - 16 * q^83 - 2 * q^85 + 7 * q^86 - 6 * q^87 + q^88 + 8 * q^89 - q^90 + 14 * q^92 + 7 * q^93 + 6 * q^94 + 8 * q^95 - q^96 - 12 * q^97 + 7 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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