LMFDB - Embedded newform 930.2.i.b.811.1

Error: no document with id 234107078 found in table mf_hecke_traces.

Error: table True does not exist

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(211,930)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("930.211"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [2,-2,1,2,1,-1,-3,-2,-1,-1,1] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

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

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000 q^{2} +(0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.50000 - 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 + 2.59808i) q^{21} +(-0.500000 - 0.866025i) q^{22} -4.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} -7.00000 q^{29} -1.00000 q^{30} +(3.50000 + 4.33013i) q^{31} -1.00000 q^{32} +1.00000 q^{33} +(1.00000 - 1.73205i) q^{34} -3.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-1.50000 - 2.59808i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{45} +4.00000 q^{46} -6.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.00000 + 1.73205i) q^{51} +(-2.50000 - 4.33013i) q^{53} +1.00000 q^{54} +(-0.500000 + 0.866025i) q^{55} +(1.50000 - 2.59808i) q^{56} +(1.00000 + 1.73205i) q^{57} +7.00000 q^{58} +(3.50000 - 6.06218i) q^{59} +1.00000 q^{60} +12.0000 q^{61} +(-3.50000 - 4.33013i) q^{62} +3.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} +(4.00000 + 6.92820i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-2.00000 + 3.46410i) q^{69} +3.00000 q^{70} +(0.500000 + 0.866025i) q^{72} +(3.00000 + 5.19615i) q^{73} +(2.00000 - 3.46410i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} -3.00000 q^{77} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{83} +(1.50000 + 2.59808i) q^{84} -2.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-3.50000 + 6.06218i) q^{87} +(-0.500000 - 0.866025i) q^{88} +6.00000 q^{89} +(-0.500000 + 0.866025i) q^{90} -4.00000 q^{92} +(5.50000 - 0.866025i) q^{93} +6.00000 q^{94} -2.00000 q^{95} +(-0.500000 + 0.866025i) q^{96} -5.00000 q^{97} +(1.00000 + 1.73205i) 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} - 3 q^{7} - 2 q^{8} - q^{9} - q^{10} + q^{11} + q^{12} + 3 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} + q^{18} - 2 q^{19} + q^{20} + 3 q^{21} - q^{22}+ \cdots + q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 + q^5 - q^6 - 3 * q^7 - 2 * q^8 - q^9 - q^10 + q^11 + q^12 + 3 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 + q^18 - 2 * q^19 + q^20 + 3 * q^21 - q^22 - 8 * q^23 - q^24 - q^25 - 2 * q^27 - 3 * q^28 - 14 * q^29 - 2 * q^30 + 7 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 - 6 * q^35 - q^36 - 4 * q^37 + 2 * q^38 - q^40 - 3 * q^42 - 8 * q^43 + q^44 + q^45 + 8 * q^46 - 12 * q^47 + q^48 - 2 * q^49 + q^50 + 2 * q^51 - 5 * q^53 + 2 * q^54 - q^55 + 3 * q^56 + 2 * q^57 + 14 * q^58 + 7 * q^59 + 2 * q^60 + 24 * q^61 - 7 * q^62 + 6 * q^63 + 2 * q^64 - 2 * q^66 + 8 * q^67 - 2 * q^68 - 4 * q^69 + 6 * q^70 + q^72 + 6 * q^73 + 4 * q^74 + q^75 - 2 * q^76 - 6 * q^77 - 8 * q^79 + q^80 - q^81 + 9 * q^83 + 3 * q^84 - 4 * q^85 + 8 * q^86 - 7 * q^87 - q^88 + 12 * q^89 - q^90 - 8 * q^92 + 11 * q^93 + 12 * q^94 - 4 * q^95 - q^96 - 10 * q^97 + 2 * q^98 + q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−1.00000			−0.707107
$2$	−1.00000			−0.707107
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	0.429919	+	0.902867i	$0.358542\pi$
$7$	−1.50000	+	2.59808i	−0.566947	+	0.981981i	−0.996866	+	0.0791130i	$0.974791\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	0.931505	−	0.363727i	$-0.118496\pi$
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i	−0.780750	+	0.624844i	$0.785163\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$13$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$14$	1.50000	−	2.59808i	0.400892	−	0.694365i
$15$	1.00000			0.258199
$16$	1.00000			0.250000
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	−0.957635	−	0.287984i	$-0.907015\pi$
$19$	−1.00000	+	1.73205i	−0.229416	+	0.397360i	0.728219	+	0.685344i	$0.240348\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$	1.50000	+	2.59808i	0.327327	+	0.566947i
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	−1.00000			−0.192450
$28$	−1.50000	+	2.59808i	−0.283473	+	0.490990i
$29$	−7.00000			−1.29987			−0.649934	−	0.759991i	$-0.725203\pi$
$29$	−7.00000			−1.29987			−0.649934	+	0.759991i	$0.725203\pi$
$30$	−1.00000			−0.182574
$31$	3.50000	+	4.33013i	0.628619	+	0.777714i
$31$	3.50000	+	4.33013i	0.628619	+	0.777714i
$32$	−1.00000			−0.176777
$33$	1.00000			0.174078
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$	−3.00000			−0.507093
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	−0.982274	−	0.187453i	$-0.939977\pi$
$37$	−2.00000	+	3.46410i	−0.328798	+	0.569495i	0.653476	+	0.756948i	$0.273310\pi$
$38$	1.00000	−	1.73205i	0.162221	−	0.280976i
$39$		0			0
$40$	−0.500000	−	0.866025i	−0.0790569	−	0.136931i
$41$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$41$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$42$	−1.50000	−	2.59808i	−0.231455	−	0.400892i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	0.500000	+	0.866025i	0.0753778	+	0.130558i
$45$	0.500000	−	0.866025i	0.0745356	−	0.129099i
$46$	4.00000			0.589768
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−1.00000	−	1.73205i	−0.142857	−	0.247436i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	1.00000	+	1.73205i	0.140028	+	0.242536i
$52$		0			0
$53$	−2.50000	−	4.33013i	−0.343401	−	0.594789i	0.641661	−	0.766989i	$-0.278246\pi$
$53$	−2.50000	−	4.33013i	−0.343401	−	0.594789i	−0.985062	+	0.172200i	$0.944912\pi$
$54$	1.00000			0.136083
$55$	−0.500000	+	0.866025i	−0.0674200	+	0.116775i
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	1.00000	+	1.73205i	0.132453	+	0.229416i
$58$	7.00000			0.919145
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	−0.543065	−	0.839691i	$-0.682736\pi$
$59$	3.50000	−	6.06218i	0.455661	−	0.789228i	0.998726	+	0.0504625i	$0.0160695\pi$
$60$	1.00000			0.129099
$61$	12.0000			1.53644			0.768221	−	0.640184i	$-0.221142\pi$
$61$	12.0000			1.53644			0.768221	+	0.640184i	$0.221142\pi$
$62$	−3.50000	−	4.33013i	−0.444500	−	0.549927i
$63$	3.00000			0.377964
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.00000			−0.123091
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	0.999915	−	0.0130248i	$-0.00414604\pi$
$67$	4.00000	+	6.92820i	0.488678	+	0.846415i	−0.511237	+	0.859440i	$0.670813\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	−2.00000	+	3.46410i	−0.240772	+	0.417029i
$70$	3.00000			0.358569
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	0.986447	−	0.164083i	$-0.0524664\pi$
$73$	3.00000	+	5.19615i	0.351123	+	0.608164i	−0.635323	+	0.772246i	$0.719133\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	−1.00000	+	1.73205i	−0.114708	+	0.198680i
$77$	−3.00000			−0.341882
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	0.999976	−	0.00698436i	$-0.00222321\pi$
$83$	4.50000	+	7.79423i	0.493939	+	0.855528i	−0.506036	+	0.862512i	$0.668890\pi$
$84$	1.50000	+	2.59808i	0.163663	+	0.283473i
$85$	−2.00000			−0.216930
$86$	4.00000	−	6.92820i	0.431331	−	0.747087i
$87$	−3.50000	+	6.06218i	−0.375239	+	0.649934i
$88$	−0.500000	−	0.866025i	−0.0533002	−	0.0923186i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$	−0.500000	+	0.866025i	−0.0527046	+	0.0912871i
$91$		0			0
$92$	−4.00000			−0.417029
$93$	5.50000	−	0.866025i	0.570323	−	0.0898027i
$94$	6.00000			0.618853
$95$	−2.00000			−0.205196
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−5.00000			−0.507673			−0.253837	−	0.967247i	$-0.581693\pi$
$97$	−5.00000			−0.507673			−0.253837	+	0.967247i	$0.581693\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$	0.500000	−	0.866025i	0.0502519	−	0.0870388i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−7.00000			−0.696526			−0.348263	−	0.937397i	$-0.613228\pi$
$101$	−7.00000			−0.696526			−0.348263	+	0.937397i	$0.613228\pi$
$102$	−1.00000	−	1.73205i	−0.0990148	−	0.171499i
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	0.889607	−	0.456727i	$-0.150978\pi$
$103$	0.500000	+	0.866025i	0.0492665	+	0.0853320i	−0.840341	+	0.542059i	$0.817645\pi$
$104$		0			0
$105$	−1.50000	+	2.59808i	−0.146385	+	0.253546i
$106$	2.50000	+	4.33013i	0.242821	+	0.420579i
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	−0.984124	−	0.177482i	$-0.943205\pi$
$107$	−3.50000	+	6.06218i	−0.338358	+	0.586053i	0.645766	+	0.763535i	$0.276538\pi$
$108$	−1.00000			−0.0962250
$109$	−6.00000			−0.574696			−0.287348	−	0.957826i	$-0.592774\pi$
$109$	−6.00000			−0.574696			−0.287348	+	0.957826i	$0.592774\pi$
$110$	0.500000	−	0.866025i	0.0476731	−	0.0825723i
$111$	2.00000	+	3.46410i	0.189832	+	0.328798i
$112$	−1.50000	+	2.59808i	−0.141737	+	0.245495i
$113$	2.00000	+	3.46410i	0.188144	+	0.325875i	0.944632	−	0.328133i	$-0.106419\pi$
$113$	2.00000	+	3.46410i	0.188144	+	0.325875i	−0.756487	+	0.654008i	$0.773086\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$	−2.00000	−	3.46410i	−0.186501	−	0.323029i
$116$	−7.00000			−0.649934
$117$		0			0
$118$	−3.50000	+	6.06218i	−0.322201	+	0.558069i
$119$	−3.00000	−	5.19615i	−0.275010	−	0.476331i
$120$	−1.00000			−0.0912871
$121$	5.00000	−	8.66025i	0.454545	−	0.787296i
$122$	−12.0000			−1.08643
$123$		0			0
$124$	3.50000	+	4.33013i	0.314309	+	0.388857i
$125$	−1.00000			−0.0894427
$126$	−3.00000			−0.267261
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	0.419064	+	0.907957i	$0.362358\pi$
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	−0.995846	+	0.0910585i	$0.970975\pi$
$128$	−1.00000			−0.0883883
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	−0.765331	−	0.643637i	$-0.777425\pi$
$131$	2.00000	−	3.46410i	0.174741	−	0.302660i	0.940072	+	0.340977i	$0.110758\pi$
$132$	1.00000			0.0870388
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$	−4.00000	−	6.92820i	−0.345547	−	0.598506i
$135$	−0.500000	−	0.866025i	−0.0430331	−	0.0745356i
$136$	1.00000	−	1.73205i	0.0857493	−	0.148522i
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	0.708942	−	0.705266i	$-0.249173\pi$
$137$	−3.00000	−	5.19615i	−0.256307	−	0.443937i	−0.965250	+	0.261329i	$0.915839\pi$
$138$	2.00000	−	3.46410i	0.170251	−	0.294884i
$139$	14.0000			1.18746			0.593732	−	0.804663i	$-0.297654\pi$
$139$	14.0000			1.18746			0.593732	+	0.804663i	$0.297654\pi$
$140$	−3.00000			−0.253546
$141$	−3.00000	+	5.19615i	−0.252646	+	0.437595i
$142$		0			0
$143$		0			0
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−3.50000	−	6.06218i	−0.290659	−	0.503436i
$146$	−3.00000	−	5.19615i	−0.248282	−	0.430037i
$147$	−2.00000			−0.164957
$148$	−2.00000	+	3.46410i	−0.164399	+	0.284747i
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	−0.973028	−	0.230689i	$-0.925902\pi$
$149$	−3.50000	+	6.06218i	−0.286731	+	0.496633i	0.686296	+	0.727322i	$0.259235\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	19.0000			1.54620			0.773099	−	0.634285i	$-0.218706\pi$
$151$	19.0000			1.54620			0.773099	+	0.634285i	$0.218706\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	2.00000			0.161690
$154$	3.00000			0.241747
$155$	−2.00000	+	5.19615i	−0.160644	+	0.417365i
$156$		0			0
$157$	−12.0000			−0.957704			−0.478852	−	0.877896i	$-0.658947\pi$
$157$	−12.0000			−0.957704			−0.478852	+	0.877896i	$0.658947\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$	−5.00000			−0.396526
$160$	−0.500000	−	0.866025i	−0.0395285	−	0.0684653i
$161$	6.00000	−	10.3923i	0.472866	−	0.819028i
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$		0			0			−	1.00000i	$-0.5\pi$
$163$		0			0				1.00000i	$0.5\pi$
$164$		0			0
$165$	0.500000	+	0.866025i	0.0389249	+	0.0674200i
$166$	−4.50000	−	7.79423i	−0.349268	−	0.604949i
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	−0.534875	−	0.844931i	$-0.679641\pi$
$167$	6.00000	−	10.3923i	0.464294	−	0.804181i	0.999169	+	0.0407502i	$0.0129748\pi$
$168$	−1.50000	−	2.59808i	−0.115728	−	0.200446i
$169$	6.50000	−	11.2583i	0.500000	−	0.866025i
$170$	2.00000			0.153393
$171$	2.00000			0.152944
$172$	−4.00000	+	6.92820i	−0.304997	+	0.528271i
$173$	2.50000	+	4.33013i	0.190071	+	0.329213i	0.945274	−	0.326278i	$-0.105795\pi$
$173$	2.50000	+	4.33013i	0.190071	+	0.329213i	−0.755202	+	0.655492i	$0.772461\pi$
$174$	3.50000	−	6.06218i	0.265334	−	0.459573i
$175$	−1.50000	−	2.59808i	−0.113389	−	0.196396i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	−3.50000	−	6.06218i	−0.263076	−	0.455661i
$178$	−6.00000			−0.449719
$179$	−2.50000	+	4.33013i	−0.186859	+	0.323649i	−0.944201	−	0.329369i	$-0.893164\pi$
$179$	−2.50000	+	4.33013i	−0.186859	+	0.323649i	0.757343	+	0.653018i	$0.226497\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	−9.00000	−	15.5885i	−0.668965	−	1.15868i	−0.978194	−	0.207693i	$-0.933404\pi$
$181$	−9.00000	−	15.5885i	−0.668965	−	1.15868i	0.309229	−	0.950988i	$-0.399929\pi$
$182$		0			0
$183$	6.00000	−	10.3923i	0.443533	−	0.768221i
$184$	4.00000			0.294884
$185$	−4.00000			−0.294086
$186$	−5.50000	+	0.866025i	−0.403280	+	0.0635001i
$187$	−2.00000			−0.146254
$188$	−6.00000			−0.437595
$189$	1.50000	−	2.59808i	0.109109	−	0.188982i
$190$	2.00000			0.145095
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	0.973674	−	0.227946i	$-0.0732010\pi$
$191$	4.00000	+	6.92820i	0.289430	+	0.501307i	−0.684244	+	0.729253i	$0.739868\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	−0.289980	−	0.957033i	$-0.593649\pi$
$193$	9.50000	−	16.4545i	0.683825	−	1.18442i	0.973805	−	0.227387i	$-0.0730182\pi$
$194$	5.00000			0.358979
$195$		0			0
$196$	−1.00000	−	1.73205i	−0.0714286	−	0.123718i
$197$	−7.00000	−	12.1244i	−0.498729	−	0.863825i	0.501270	−	0.865291i	$-0.332867\pi$
$197$	−7.00000	−	12.1244i	−0.498729	−	0.863825i	−0.999999	+	0.00146660i	$0.999533\pi$
$198$	−0.500000	+	0.866025i	−0.0355335	+	0.0615457i
$199$	2.50000	+	4.33013i	0.177220	+	0.306955i	0.940927	−	0.338608i	$-0.109956\pi$
$199$	2.50000	+	4.33013i	0.177220	+	0.306955i	−0.763707	+	0.645563i	$0.776623\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	8.00000			0.564276
$202$	7.00000			0.492518
$203$	10.5000	−	18.1865i	0.736956	−	1.27644i
$204$	1.00000	+	1.73205i	0.0700140	+	0.121268i
$205$		0			0
$206$	−0.500000	−	0.866025i	−0.0348367	−	0.0603388i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$		0			0
$209$	−2.00000			−0.138343
$210$	1.50000	−	2.59808i	0.103510	−	0.179284i
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	−0.999784	−	0.0207756i	$-0.993386\pi$
$211$	−7.00000	+	12.1244i	−0.481900	+	0.834675i	0.517884	+	0.855451i	$0.326720\pi$
$212$	−2.50000	−	4.33013i	−0.171701	−	0.297394i
$213$		0			0
$214$	3.50000	−	6.06218i	0.239255	−	0.414402i
$215$	−8.00000			−0.545595
$216$	1.00000			0.0680414
$217$	−16.5000	+	2.59808i	−1.12009	+	0.176369i
$218$	6.00000			0.406371
$219$	6.00000			0.405442
$220$	−0.500000	+	0.866025i	−0.0337100	+	0.0583874i
$221$		0			0
$222$	−2.00000	−	3.46410i	−0.134231	−	0.232495i
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	−0.427443	−	0.904042i	$-0.640586\pi$
$223$	8.50000	−	14.7224i	0.569202	−	0.985887i	0.996645	−	0.0818447i	$-0.0260811\pi$
$224$	1.50000	−	2.59808i	0.100223	−	0.173591i
$225$	1.00000			0.0666667
$226$	−2.00000	−	3.46410i	−0.133038	−	0.230429i
$227$	6.50000	+	11.2583i	0.431420	+	0.747242i	0.996996	−	0.0774548i	$-0.0246793\pi$
$227$	6.50000	+	11.2583i	0.431420	+	0.747242i	−0.565576	+	0.824696i	$0.691346\pi$
$228$	1.00000	+	1.73205i	0.0662266	+	0.114708i
$229$	10.0000	−	17.3205i	0.660819	−	1.14457i	−0.319582	−	0.947559i	$-0.603543\pi$
$229$	10.0000	−	17.3205i	0.660819	−	1.14457i	0.980401	−	0.197013i	$-0.0631241\pi$
$230$	2.00000	+	3.46410i	0.131876	+	0.228416i
$231$	−1.50000	+	2.59808i	−0.0986928	+	0.170941i
$232$	7.00000			0.459573
$233$	16.0000			1.04819			0.524097	−	0.851658i	$-0.324403\pi$
$233$	16.0000			1.04819			0.524097	+	0.851658i	$0.324403\pi$
$234$		0			0
$235$	−3.00000	−	5.19615i	−0.195698	−	0.338960i
$236$	3.50000	−	6.06218i	0.227831	−	0.394614i
$237$	4.00000	+	6.92820i	0.259828	+	0.450035i
$238$	3.00000	+	5.19615i	0.194461	+	0.336817i
$239$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$239$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$240$	1.00000			0.0645497
$241$	8.50000	−	14.7224i	0.547533	−	0.948355i	−0.450910	−	0.892570i	$-0.648900\pi$
$241$	8.50000	−	14.7224i	0.547533	−	0.948355i	0.998443	−	0.0557856i	$-0.0177663\pi$
$242$	−5.00000	+	8.66025i	−0.321412	+	0.556702i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	12.0000			0.768221
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$		0			0
$247$		0			0
$248$	−3.50000	−	4.33013i	−0.222250	−	0.274963i
$249$	9.00000			0.570352
$250$	1.00000			0.0632456
$251$	2.00000	−	3.46410i	0.126239	−	0.218652i	−0.795978	−	0.605326i	$-0.793043\pi$
$251$	2.00000	−	3.46410i	0.126239	−	0.218652i	0.922217	+	0.386674i	$0.126376\pi$
$252$	3.00000			0.188982
$253$	−2.00000	−	3.46410i	−0.125739	−	0.217786i
$254$	6.50000	−	11.2583i	0.407846	−	0.706410i
$255$	−1.00000	+	1.73205i	−0.0626224	+	0.108465i
$256$	1.00000			0.0625000
$257$	−14.0000	−	24.2487i	−0.873296	−	1.51259i	−0.858567	−	0.512702i	$-0.828645\pi$
$257$	−14.0000	−	24.2487i	−0.873296	−	1.51259i	−0.0147291	−	0.999892i	$-0.504689\pi$
$258$	−4.00000	−	6.92820i	−0.249029	−	0.431331i
$259$	−6.00000	−	10.3923i	−0.372822	−	0.645746i
$260$		0			0
$261$	3.50000	+	6.06218i	0.216645	+	0.375239i
$262$	−2.00000	+	3.46410i	−0.123560	+	0.214013i
$263$	6.00000			0.369976			0.184988	−	0.982741i	$-0.440775\pi$
$263$	6.00000			0.369976			0.184988	+	0.982741i	$0.440775\pi$
$264$	−1.00000			−0.0615457
$265$	2.50000	−	4.33013i	0.153574	−	0.265998i
$266$	3.00000	+	5.19615i	0.183942	+	0.318597i
$267$	3.00000	−	5.19615i	0.183597	−	0.317999i
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$	0.500000	+	0.866025i	0.0304290	+	0.0527046i
$271$	−17.0000			−1.03268			−0.516338	−	0.856385i	$-0.672705\pi$
$271$	−17.0000			−1.03268			−0.516338	+	0.856385i	$0.672705\pi$
$272$	−1.00000	+	1.73205i	−0.0606339	+	0.105021i
$273$		0			0
$274$	3.00000	+	5.19615i	0.181237	+	0.313911i
$275$	−1.00000			−0.0603023
$276$	−2.00000	+	3.46410i	−0.120386	+	0.208514i
$277$	−18.0000			−1.08152			−0.540758	−	0.841178i	$-0.681862\pi$
$277$	−18.0000			−1.08152			−0.540758	+	0.841178i	$0.681862\pi$
$278$	−14.0000			−0.839664
$279$	2.00000	−	5.19615i	0.119737	−	0.311086i
$280$	3.00000			0.179284
$281$	−2.00000			−0.119310			−0.0596550	−	0.998219i	$-0.519000\pi$
$281$	−2.00000			−0.119310			−0.0596550	+	0.998219i	$0.519000\pi$
$282$	3.00000	−	5.19615i	0.178647	−	0.309426i
$283$		0			0			−	1.00000i	$-0.5\pi$
$283$		0			0				1.00000i	$0.5\pi$
$284$		0			0
$285$	−1.00000	+	1.73205i	−0.0592349	+	0.102598i
$286$		0			0
$287$		0			0
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	6.50000	+	11.2583i	0.382353	+	0.662255i
$290$	3.50000	+	6.06218i	0.205527	+	0.355983i
$291$	−2.50000	+	4.33013i	−0.146553	+	0.253837i
$292$	3.00000	+	5.19615i	0.175562	+	0.304082i
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	−0.818878	−	0.573967i	$-0.805404\pi$
$293$	1.50000	−	2.59808i	0.0876309	−	0.151781i	0.906509	+	0.422186i	$0.138737\pi$
$294$	2.00000			0.116642
$295$	7.00000			0.407556
$296$	2.00000	−	3.46410i	0.116248	−	0.201347i
$297$	−0.500000	−	0.866025i	−0.0290129	−	0.0502519i
$298$	3.50000	−	6.06218i	0.202750	−	0.351173i
$299$		0			0
$300$	0.500000	+	0.866025i	0.0288675	+	0.0500000i
$301$	−12.0000	−	20.7846i	−0.691669	−	1.19800i
$302$	−19.0000			−1.09333
$303$	−3.50000	+	6.06218i	−0.201070	+	0.348263i
$304$	−1.00000	+	1.73205i	−0.0573539	+	0.0993399i
$305$	6.00000	+	10.3923i	0.343559	+	0.595062i
$306$	−2.00000			−0.114332
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	−0.893150	−	0.449758i	$-0.851510\pi$
$307$	−1.00000	+	1.73205i	−0.0570730	+	0.0988534i	0.836077	+	0.548612i	$0.184843\pi$
$308$	−3.00000			−0.170941
$309$	1.00000			0.0568880
$310$	2.00000	−	5.19615i	0.113592	−	0.295122i
$311$	−16.0000			−0.907277			−0.453638	−	0.891186i	$-0.649874\pi$
$311$	−16.0000			−0.907277			−0.453638	+	0.891186i	$0.649874\pi$
$312$		0			0
$313$	3.50000	−	6.06218i	0.197832	−	0.342655i	−0.749993	−	0.661445i	$-0.769943\pi$
$313$	3.50000	−	6.06218i	0.197832	−	0.342655i	0.947825	+	0.318791i	$0.103277\pi$
$314$	12.0000			0.677199
$315$	1.50000	+	2.59808i	0.0845154	+	0.146385i
$316$	−4.00000	+	6.92820i	−0.225018	+	0.389742i
$317$	3.50000	−	6.06218i	0.196580	−	0.340486i	−0.750838	−	0.660487i	$-0.770350\pi$
$317$	3.50000	−	6.06218i	0.196580	−	0.340486i	0.947417	+	0.320001i	$0.103683\pi$
$318$	5.00000			0.280386
$319$	−3.50000	−	6.06218i	−0.195962	−	0.339417i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	3.50000	+	6.06218i	0.195351	+	0.338358i
$322$	−6.00000	+	10.3923i	−0.334367	+	0.579141i
$323$	−2.00000	−	3.46410i	−0.111283	−	0.192748i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$		0			0
$326$		0			0
$327$	−3.00000	+	5.19615i	−0.165900	+	0.287348i
$328$		0			0
$329$	9.00000	−	15.5885i	0.496186	−	0.859419i
$330$	−0.500000	−	0.866025i	−0.0275241	−	0.0476731i
$331$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$331$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$332$	4.50000	+	7.79423i	0.246970	+	0.427764i
$333$	4.00000			0.219199
$334$	−6.00000	+	10.3923i	−0.328305	+	0.568642i
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$	1.50000	+	2.59808i	0.0818317	+	0.141737i
$337$	−7.00000			−0.381314			−0.190657	−	0.981657i	$-0.561062\pi$
$337$	−7.00000			−0.381314			−0.190657	+	0.981657i	$0.561062\pi$
$338$	−6.50000	+	11.2583i	−0.353553	+	0.612372i
$339$	4.00000			0.217250
$340$	−2.00000			−0.108465
$341$	−2.00000	+	5.19615i	−0.108306	+	0.281387i
$342$	−2.00000			−0.108148
$343$	−15.0000			−0.809924
$344$	4.00000	−	6.92820i	0.215666	−	0.373544i
$345$	−4.00000			−0.215353
$346$	−2.50000	−	4.33013i	−0.134401	−	0.232789i
$347$	15.5000	−	26.8468i	0.832084	−	1.44121i	−0.0642994	−	0.997931i	$-0.520481\pi$
$347$	15.5000	−	26.8468i	0.832084	−	1.44121i	0.896383	−	0.443280i	$-0.146185\pi$
$348$	−3.50000	+	6.06218i	−0.187620	+	0.324967i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$	1.50000	+	2.59808i	0.0801784	+	0.138873i
$351$		0			0
$352$	−0.500000	−	0.866025i	−0.0266501	−	0.0461593i
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	−0.999711	−	0.0240566i	$-0.992342\pi$
$353$	−9.00000	+	15.5885i	−0.479022	+	0.829690i	0.520689	+	0.853746i	$0.325675\pi$
$354$	3.50000	+	6.06218i	0.186023	+	0.322201i
$355$		0			0
$356$	6.00000			0.317999
$357$	−6.00000			−0.317554
$358$	2.50000	−	4.33013i	0.132129	−	0.228854i
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$	−0.500000	+	0.866025i	−0.0263523	+	0.0456435i
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	9.00000	+	15.5885i	0.473029	+	0.819311i
$363$	−5.00000	−	8.66025i	−0.262432	−	0.454545i
$364$		0			0
$365$	−3.00000	+	5.19615i	−0.157027	+	0.271979i
$366$	−6.00000	+	10.3923i	−0.313625	+	0.543214i
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	0.578101	−	0.815966i	$-0.303794\pi$
$367$	−8.00000	−	13.8564i	−0.417597	−	0.723299i	−0.995697	+	0.0926670i	$0.970461\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	4.00000			0.207950
$371$	15.0000			0.778761
$372$	5.50000	−	0.866025i	0.285162	−	0.0449013i
$373$	22.0000			1.13912			0.569558	−	0.821951i	$-0.307114\pi$
$373$	22.0000			1.13912			0.569558	+	0.821951i	$0.307114\pi$
$374$	2.00000			0.103418
$375$	−0.500000	+	0.866025i	−0.0258199	+	0.0447214i
$376$	6.00000			0.309426
$377$		0			0
$378$	−1.50000	+	2.59808i	−0.0771517	+	0.133631i
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	−0.965392	−	0.260804i	$-0.916012\pi$
$379$	−5.00000	+	8.66025i	−0.256833	+	0.444847i	0.708559	+	0.705652i	$0.249346\pi$
$380$	−2.00000			−0.102598
$381$	6.50000	+	11.2583i	0.333005	+	0.576782i
$382$	−4.00000	−	6.92820i	−0.204658	−	0.354478i
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	0.949938	−	0.312437i	$-0.101145\pi$
$383$	4.00000	+	6.92820i	0.204390	+	0.354015i	−0.745548	+	0.666452i	$0.767812\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−1.50000	−	2.59808i	−0.0764471	−	0.132410i
$386$	−9.50000	+	16.4545i	−0.483537	+	0.837511i
$387$	8.00000			0.406663
$388$	−5.00000			−0.253837
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	−0.182047	−	0.983290i	$-0.558272\pi$
$389$	15.0000	−	25.9808i	0.760530	−	1.31728i	0.942578	−	0.333987i	$-0.108394\pi$
$390$		0			0
$391$	4.00000	−	6.92820i	0.202289	−	0.350374i
$392$	1.00000	+	1.73205i	0.0505076	+	0.0874818i
$393$	−2.00000	−	3.46410i	−0.100887	−	0.174741i
$394$	7.00000	+	12.1244i	0.352655	+	0.610816i
$395$	−8.00000			−0.402524
$396$	0.500000	−	0.866025i	0.0251259	−	0.0435194i
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	0.446051	+	0.895008i	$0.352830\pi$
$397$	−11.0000	+	19.0526i	−0.552074	+	0.956221i	−0.998125	+	0.0612128i	$0.980503\pi$
$398$	−2.50000	−	4.33013i	−0.125314	−	0.217050i
$399$	−6.00000			−0.300376
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	32.0000			1.59800			0.799002	−	0.601329i	$-0.205362\pi$
$401$	32.0000			1.59800			0.799002	+	0.601329i	$0.205362\pi$
$402$	−8.00000			−0.399004
$403$		0			0
$404$	−7.00000			−0.348263
$405$	−1.00000			−0.0496904
$406$	−10.5000	+	18.1865i	−0.521106	+	0.902583i
$407$	−4.00000			−0.198273
$408$	−1.00000	−	1.73205i	−0.0495074	−	0.0857493i
$409$	−7.50000	+	12.9904i	−0.370851	+	0.642333i	−0.989697	−	0.143180i	$-0.954267\pi$
$409$	−7.50000	+	12.9904i	−0.370851	+	0.642333i	0.618846	+	0.785513i	$0.287601\pi$
$410$		0			0
$411$	−6.00000			−0.295958
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$	10.5000	+	18.1865i	0.516671	+	0.894901i
$414$	−2.00000	−	3.46410i	−0.0982946	−	0.170251i
$415$	−4.50000	+	7.79423i	−0.220896	+	0.382604i
$416$		0			0
$417$	7.00000	−	12.1244i	0.342791	−	0.593732i
$418$	2.00000			0.0978232
$419$	−21.0000			−1.02592			−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000			−1.02592			−0.512959	+	0.858413i	$0.671451\pi$
$420$	−1.50000	+	2.59808i	−0.0731925	+	0.126773i
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	0.512524	−	0.858673i	$-0.328710\pi$
$421$	−10.0000	−	17.3205i	−0.487370	−	0.844150i	−0.999895	+	0.0145228i	$0.995377\pi$
$422$	7.00000	−	12.1244i	0.340755	−	0.590204i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	2.50000	+	4.33013i	0.121411	+	0.210290i
$425$	−1.00000	−	1.73205i	−0.0485071	−	0.0840168i
$426$		0			0
$427$	−18.0000	+	31.1769i	−0.871081	+	1.50876i
$428$	−3.50000	+	6.06218i	−0.169179	+	0.293026i
$429$		0			0
$430$	8.00000			0.385794
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	0.237460	+	0.971397i	$0.423685\pi$
$431$	−15.0000	+	25.9808i	−0.722525	+	1.25145i	−0.959985	+	0.280052i	$0.909648\pi$
$432$	−1.00000			−0.0481125
$433$	26.0000			1.24948			0.624740	−	0.780833i	$-0.285205\pi$
$433$	26.0000			1.24948			0.624740	+	0.780833i	$0.285205\pi$
$434$	16.5000	−	2.59808i	0.792025	−	0.124712i
$435$	−7.00000			−0.335624
$436$	−6.00000			−0.287348
$437$	4.00000	−	6.92820i	0.191346	−	0.331421i
$438$	−6.00000			−0.286691
$439$	8.50000	+	14.7224i	0.405683	+	0.702663i	0.994401	−	0.105675i	$-0.0337004\pi$
$439$	8.50000	+	14.7224i	0.405683	+	0.702663i	−0.588718	+	0.808339i	$0.700367\pi$
$440$	0.500000	−	0.866025i	0.0238366	−	0.0412861i
$441$	−1.00000	+	1.73205i	−0.0476190	+	0.0824786i
$442$		0			0
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	0.524479	−	0.851423i	$-0.324260\pi$
$443$	−10.0000	−	17.3205i	−0.475114	−	0.822922i	−0.999594	+	0.0285009i	$0.990927\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$	3.00000	+	5.19615i	0.142214	+	0.246321i
$446$	−8.50000	+	14.7224i	−0.402487	+	0.697127i
$447$	3.50000	+	6.06218i	0.165544	+	0.286731i
$448$	−1.50000	+	2.59808i	−0.0708683	+	0.122748i
$449$	6.00000			0.283158			0.141579	−	0.989927i	$-0.454782\pi$
$449$	6.00000			0.283158			0.141579	+	0.989927i	$0.454782\pi$
$450$	−1.00000			−0.0471405
$451$		0			0
$452$	2.00000	+	3.46410i	0.0940721	+	0.162938i
$453$	9.50000	−	16.4545i	0.446349	−	0.773099i
$454$	−6.50000	−	11.2583i	−0.305060	−	0.528380i
$455$		0			0
$456$	−1.00000	−	1.73205i	−0.0468293	−	0.0811107i
$457$	14.0000			0.654892			0.327446	−	0.944870i	$-0.393812\pi$
$457$	14.0000			0.654892			0.327446	+	0.944870i	$0.393812\pi$
$458$	−10.0000	+	17.3205i	−0.467269	+	0.809334i
$459$	1.00000	−	1.73205i	0.0466760	−	0.0808452i
$460$	−2.00000	−	3.46410i	−0.0932505	−	0.161515i
$461$	7.00000			0.326023			0.163011	−	0.986624i	$-0.447879\pi$
$461$	7.00000			0.326023			0.163011	+	0.986624i	$0.447879\pi$
$462$	1.50000	−	2.59808i	0.0697863	−	0.120873i
$463$	−15.0000			−0.697109			−0.348555	−	0.937288i	$-0.613327\pi$
$463$	−15.0000			−0.697109			−0.348555	+	0.937288i	$0.613327\pi$
$464$	−7.00000			−0.324967
$465$	3.50000	+	4.33013i	0.162309	+	0.200805i
$466$	−16.0000			−0.741186
$467$	23.0000			1.06431			0.532157	−	0.846646i	$-0.321382\pi$
$467$	23.0000			1.06431			0.532157	+	0.846646i	$0.321382\pi$
$468$		0			0
$469$	−24.0000			−1.10822
$470$	3.00000	+	5.19615i	0.138380	+	0.239681i
$471$	−6.00000	+	10.3923i	−0.276465	+	0.478852i
$472$	−3.50000	+	6.06218i	−0.161101	+	0.279034i
$473$	−8.00000			−0.367840
$474$	−4.00000	−	6.92820i	−0.183726	−	0.318223i
$475$	−1.00000	−	1.73205i	−0.0458831	−	0.0794719i
$476$	−3.00000	−	5.19615i	−0.137505	−	0.238165i
$477$	−2.50000	+	4.33013i	−0.114467	+	0.198263i
$478$		0			0
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$	−1.00000			−0.0456435
$481$		0			0
$482$	−8.50000	+	14.7224i	−0.387164	+	0.670588i
$483$	−6.00000	−	10.3923i	−0.273009	−	0.472866i
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$	−2.50000	−	4.33013i	−0.113519	−	0.196621i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	12.5000	+	21.6506i	0.566429	+	0.981084i	0.996915	+	0.0784867i	$0.0250088\pi$
$487$	12.5000	+	21.6506i	0.566429	+	0.981084i	−0.430486	+	0.902597i	$0.641658\pi$
$488$	−12.0000			−0.543214
$489$		0			0
$490$	−1.00000	+	1.73205i	−0.0451754	+	0.0782461i
$491$	−5.50000	−	9.52628i	−0.248212	−	0.429915i	0.714818	−	0.699310i	$-0.246509\pi$
$491$	−5.50000	−	9.52628i	−0.248212	−	0.429915i	−0.963030	+	0.269395i	$0.913176\pi$
$492$		0			0
$493$	7.00000	−	12.1244i	0.315264	−	0.546054i
$494$		0			0
$495$	1.00000			0.0449467
$496$	3.50000	+	4.33013i	0.157155	+	0.194428i
$497$		0			0
$498$	−9.00000			−0.403300
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	−0.907314	−	0.420455i	$-0.861871\pi$
$499$	−2.00000	+	3.46410i	−0.0895323	+	0.155074i	0.817781	+	0.575529i	$0.195204\pi$
$500$	−1.00000			−0.0447214
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	−2.00000	+	3.46410i	−0.0892644	+	0.154610i
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.322151	+	0.946688i	$0.604406\pi$
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.658781	+	0.752335i	$0.728928\pi$
$504$	−3.00000			−0.133631
$505$	−3.50000	−	6.06218i	−0.155748	−	0.269763i
$506$	2.00000	+	3.46410i	0.0889108	+	0.153998i
$507$	−6.50000	−	11.2583i	−0.288675	−	0.500000i
$508$	−6.50000	+	11.2583i	−0.288391	+	0.499508i
$509$	13.5000	+	23.3827i	0.598377	+	1.03642i	0.993061	+	0.117602i	$0.0375208\pi$
$509$	13.5000	+	23.3827i	0.598377	+	1.03642i	−0.394684	+	0.918817i	$0.629146\pi$
$510$	1.00000	−	1.73205i	0.0442807	−	0.0766965i
$511$	−18.0000			−0.796273
$512$	−1.00000			−0.0441942
$513$	1.00000	−	1.73205i	0.0441511	−	0.0764719i
$514$	14.0000	+	24.2487i	0.617514	+	1.06956i
$515$	−0.500000	+	0.866025i	−0.0220326	+	0.0381616i
$516$	4.00000	+	6.92820i	0.176090	+	0.304997i
$517$	−3.00000	−	5.19615i	−0.131940	−	0.228527i
$518$	6.00000	+	10.3923i	0.263625	+	0.456612i
$519$	5.00000			0.219476
$520$		0			0
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	0.377320	+	0.926083i	$0.376846\pi$
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	−0.990671	+	0.136272i	$0.956488\pi$
$522$	−3.50000	−	6.06218i	−0.153191	−	0.265334i
$523$	20.0000			0.874539			0.437269	−	0.899331i	$-0.355946\pi$
$523$	20.0000			0.874539			0.437269	+	0.899331i	$0.355946\pi$
$524$	2.00000	−	3.46410i	0.0873704	−	0.151330i
$525$	−3.00000			−0.130931
$526$	−6.00000			−0.261612
$527$	−11.0000	+	1.73205i	−0.479168	+	0.0754493i
$528$	1.00000			0.0435194
$529$	−7.00000			−0.304348
$530$	−2.50000	+	4.33013i	−0.108593	+	0.188089i
$531$	−7.00000			−0.303774
$532$	−3.00000	−	5.19615i	−0.130066	−	0.225282i
$533$		0			0
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$	−7.00000			−0.302636
$536$	−4.00000	−	6.92820i	−0.172774	−	0.299253i
$537$	2.50000	+	4.33013i	0.107883	+	0.186859i
$538$	−9.00000	−	15.5885i	−0.388018	−	0.672066i
$539$	1.00000	−	1.73205i	0.0430730	−	0.0746047i
$540$	−0.500000	−	0.866025i	−0.0215166	−	0.0372678i
$541$	20.0000	−	34.6410i	0.859867	−	1.48933i	−0.0121878	−	0.999926i	$-0.503880\pi$
$541$	20.0000	−	34.6410i	0.859867	−	1.48933i	0.872055	−	0.489408i	$-0.162787\pi$
$542$	17.0000			0.730213
$543$	−18.0000			−0.772454
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	−3.00000	−	5.19615i	−0.128506	−	0.222579i
$546$		0			0
$547$	7.00000	+	12.1244i	0.299298	+	0.518400i	0.975976	−	0.217880i	$-0.0699141\pi$
$547$	7.00000	+	12.1244i	0.299298	+	0.518400i	−0.676677	+	0.736280i	$0.736581\pi$
$548$	−3.00000	−	5.19615i	−0.128154	−	0.221969i
$549$	−6.00000	−	10.3923i	−0.256074	−	0.443533i
$550$	1.00000			0.0426401
$551$	7.00000	−	12.1244i	0.298210	−	0.516515i
$552$	2.00000	−	3.46410i	0.0851257	−	0.147442i
$553$	−12.0000	−	20.7846i	−0.510292	−	0.883852i
$554$	18.0000			0.764747
$555$	−2.00000	+	3.46410i	−0.0848953	+	0.147043i
$556$	14.0000			0.593732
$557$	27.0000			1.14403			0.572013	−	0.820244i	$-0.306163\pi$
$557$	27.0000			1.14403			0.572013	+	0.820244i	$0.306163\pi$
$558$	−2.00000	+	5.19615i	−0.0846668	+	0.219971i
$559$		0			0
$560$	−3.00000			−0.126773
$561$	−1.00000	+	1.73205i	−0.0422200	+	0.0731272i
$562$	2.00000			0.0843649
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	0.904320	+	0.426855i	$0.140378\pi$
$563$	19.5000	+	33.7750i	0.821827	+	1.42345i	−0.0824933	+	0.996592i	$0.526288\pi$
$564$	−3.00000	+	5.19615i	−0.126323	+	0.218797i
$565$	−2.00000	+	3.46410i	−0.0841406	+	0.145736i
$566$		0			0
$567$	−1.50000	−	2.59808i	−0.0629941	−	0.109109i
$568$		0			0
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	0.999994	+	0.00354413i	$0.00112814\pi$
$569$	12.0000	+	20.7846i	0.503066	+	0.871336i	−0.496928	+	0.867792i	$0.665539\pi$
$570$	1.00000	−	1.73205i	0.0418854	−	0.0725476i
$571$	1.00000	+	1.73205i	0.0418487	+	0.0724841i	0.886191	−	0.463320i	$-0.153342\pi$
$571$	1.00000	+	1.73205i	0.0418487	+	0.0724841i	−0.844342	+	0.535804i	$0.820009\pi$
$572$		0			0
$573$	8.00000			0.334205
$574$		0			0
$575$	2.00000	−	3.46410i	0.0834058	−	0.144463i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−9.50000	−	16.4545i	−0.394807	−	0.683825i
$580$	−3.50000	−	6.06218i	−0.145330	−	0.251718i
$581$	−27.0000			−1.12015
$582$	2.50000	−	4.33013i	0.103628	−	0.179490i
$583$	2.50000	−	4.33013i	0.103539	−	0.179336i
$584$	−3.00000	−	5.19615i	−0.124141	−	0.215018i
$585$		0			0
$586$	−1.50000	+	2.59808i	−0.0619644	+	0.107326i
$587$	13.0000			0.536567			0.268284	−	0.963340i	$-0.413544\pi$
$587$	13.0000			0.536567			0.268284	+	0.963340i	$0.413544\pi$
$588$	−2.00000			−0.0824786
$589$	−11.0000	+	1.73205i	−0.453247	+	0.0713679i
$590$	−7.00000			−0.288185
$591$	−14.0000			−0.575883
$592$	−2.00000	+	3.46410i	−0.0821995	+	0.142374i
$593$	2.00000			0.0821302			0.0410651	−	0.999156i	$-0.486925\pi$
$593$	2.00000			0.0821302			0.0410651	+	0.999156i	$0.486925\pi$
$594$	0.500000	+	0.866025i	0.0205152	+	0.0355335i
$595$	3.00000	−	5.19615i	0.122988	−	0.213021i
$596$	−3.50000	+	6.06218i	−0.143366	+	0.248316i
$597$	5.00000			0.204636
$598$		0			0
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	0.981889	−	0.189456i	$-0.0606724\pi$
$599$	8.00000	+	13.8564i	0.326871	+	0.566157i	−0.655018	+	0.755613i	$0.727339\pi$
$600$	−0.500000	−	0.866025i	−0.0204124	−	0.0353553i
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	−0.469095	−	0.883148i	$-0.655420\pi$
$601$	13.0000	−	22.5167i	0.530281	−	0.918474i	0.999376	−	0.0353259i	$-0.0112469\pi$
$602$	12.0000	+	20.7846i	0.489083	+	0.847117i
$603$	4.00000	−	6.92820i	0.162893	−	0.282138i
$604$	19.0000			0.773099
$605$	10.0000			0.406558
$606$	3.50000	−	6.06218i	0.142178	−	0.246259i
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.682777	+	0.730627i	$0.260772\pi$
$607$	24.0000	+	41.5692i	0.974130	+	1.68724i	0.291353	+	0.956616i	$0.405895\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	−10.5000	−	18.1865i	−0.425481	−	0.736956i
$610$	−6.00000	−	10.3923i	−0.242933	−	0.420772i
$611$		0			0
$612$	2.00000			0.0808452
$613$	−14.0000	+	24.2487i	−0.565455	+	0.979396i	0.431553	+	0.902088i	$0.357966\pi$
$613$	−14.0000	+	24.2487i	−0.565455	+	0.979396i	−0.997007	+	0.0773084i	$0.975367\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$	3.00000			0.120873
$617$	16.0000	−	27.7128i	0.644136	−	1.11568i	−0.340365	−	0.940294i	$-0.610551\pi$
$617$	16.0000	−	27.7128i	0.644136	−	1.11568i	0.984500	−	0.175382i	$-0.0561162\pi$
$618$	−1.00000			−0.0402259
$619$	2.00000			0.0803868			0.0401934	−	0.999192i	$-0.487203\pi$
$619$	2.00000			0.0803868			0.0401934	+	0.999192i	$0.487203\pi$
$620$	−2.00000	+	5.19615i	−0.0803219	+	0.208683i
$621$	4.00000			0.160514
$622$	16.0000			0.641542
$623$	−9.00000	+	15.5885i	−0.360577	+	0.624538i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−3.50000	+	6.06218i	−0.139888	+	0.242293i
$627$	−1.00000	+	1.73205i	−0.0399362	+	0.0691714i
$628$	−12.0000			−0.478852
$629$	−4.00000	−	6.92820i	−0.159490	−	0.276246i
$630$	−1.50000	−	2.59808i	−0.0597614	−	0.103510i
$631$	−5.50000	−	9.52628i	−0.218952	−	0.379235i	0.735536	−	0.677485i	$-0.236930\pi$
$631$	−5.50000	−	9.52628i	−0.218952	−	0.379235i	−0.954488	+	0.298250i	$0.903597\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$	7.00000	+	12.1244i	0.278225	+	0.481900i
$634$	−3.50000	+	6.06218i	−0.139003	+	0.240760i
$635$	−13.0000			−0.515889
$636$	−5.00000			−0.198263
$637$		0			0
$638$	3.50000	+	6.06218i	0.138566	+	0.240004i
$639$		0			0
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	0.999556	−	0.0297987i	$-0.00948663\pi$
$641$	12.0000	+	20.7846i	0.473972	+	0.820943i	−0.525584	+	0.850741i	$0.676153\pi$
$642$	−3.50000	−	6.06218i	−0.138134	−	0.239255i
$643$	28.0000			1.10421			0.552106	−	0.833774i	$-0.313824\pi$
$643$	28.0000			1.10421			0.552106	+	0.833774i	$0.313824\pi$
$644$	6.00000	−	10.3923i	0.236433	−	0.409514i
$645$	−4.00000	+	6.92820i	−0.157500	+	0.272798i
$646$	2.00000	+	3.46410i	0.0786889	+	0.136293i
$647$	6.00000			0.235884			0.117942	−	0.993020i	$-0.462370\pi$
$647$	6.00000			0.235884			0.117942	+	0.993020i	$0.462370\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	7.00000			0.274774
$650$		0			0
$651$	−6.00000	+	15.5885i	−0.235159	+	0.610960i
$652$		0			0
$653$	3.00000			0.117399			0.0586995	−	0.998276i	$-0.481305\pi$
$653$	3.00000			0.117399			0.0586995	+	0.998276i	$0.481305\pi$
$654$	3.00000	−	5.19615i	0.117309	−	0.203186i
$655$	4.00000			0.156293
$656$		0			0
$657$	3.00000	−	5.19615i	0.117041	−	0.202721i
$658$	−9.00000	+	15.5885i	−0.350857	+	0.607701i
$659$	−51.0000			−1.98668			−0.993339	−	0.115229i	$-0.963240\pi$
$659$	−51.0000			−1.98668			−0.993339	+	0.115229i	$0.963240\pi$
$660$	0.500000	+	0.866025i	0.0194625	+	0.0337100i
$661$	−10.0000	−	17.3205i	−0.388955	−	0.673690i	0.603354	−	0.797473i	$-0.293830\pi$
$661$	−10.0000	−	17.3205i	−0.388955	−	0.673690i	−0.992309	+	0.123784i	$0.960497\pi$
$662$		0			0
$663$		0			0
$664$	−4.50000	−	7.79423i	−0.174634	−	0.302475i
$665$	3.00000	−	5.19615i	0.116335	−	0.201498i
$666$	−4.00000			−0.154997
$667$	28.0000			1.08416
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$	−8.50000	−	14.7224i	−0.328629	−	0.569202i
$670$	4.00000	−	6.92820i	0.154533	−	0.267660i
$671$	6.00000	+	10.3923i	0.231627	+	0.401190i
$672$	−1.50000	−	2.59808i	−0.0578638	−	0.100223i
$673$	5.50000	+	9.52628i	0.212009	+	0.367211i	0.952343	−	0.305028i	$-0.0986659\pi$
$673$	5.50000	+	9.52628i	0.212009	+	0.367211i	−0.740334	+	0.672239i	$0.765333\pi$
$674$	7.00000			0.269630
$675$	0.500000	−	0.866025i	0.0192450	−	0.0333333i
$676$	6.50000	−	11.2583i	0.250000	−	0.433013i
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	0.986695	+	0.162581i	$0.0519817\pi$
$677$	16.5000	+	28.5788i	0.634147	+	1.09837i	−0.352549	+	0.935793i	$0.614685\pi$
$678$	−4.00000			−0.153619
$679$	7.50000	−	12.9904i	0.287824	−	0.498525i
$680$	2.00000			0.0766965
$681$	13.0000			0.498161
$682$	2.00000	−	5.19615i	0.0765840	−	0.198971i
$683$	9.00000			0.344375			0.172188	−	0.985064i	$-0.444916\pi$
$683$	9.00000			0.344375			0.172188	+	0.985064i	$0.444916\pi$
$684$	2.00000			0.0764719
$685$	3.00000	−	5.19615i	0.114624	−	0.198535i
$686$	15.0000			0.572703
$687$	−10.0000	−	17.3205i	−0.381524	−	0.660819i
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$		0			0
$690$	4.00000			0.152277
$691$	−23.0000	−	39.8372i	−0.874961	−	1.51548i	−0.856804	−	0.515642i	$-0.827553\pi$
$691$	−23.0000	−	39.8372i	−0.874961	−	1.51548i	−0.0181572	−	0.999835i	$-0.505780\pi$
$692$	2.50000	+	4.33013i	0.0950357	+	0.164607i
$693$	1.50000	+	2.59808i	0.0569803	+	0.0986928i
$694$	−15.5000	+	26.8468i	−0.588372	+	1.01909i
$695$	7.00000	+	12.1244i	0.265525	+	0.459903i
$696$	3.50000	−	6.06218i	0.132667	−	0.229786i
$697$		0			0
$698$	26.0000			0.984115
$699$	8.00000	−	13.8564i	0.302588	−	0.524097i
$700$	−1.50000	−	2.59808i	−0.0566947	−	0.0981981i
$701$	−6.50000	+	11.2583i	−0.245502	+	0.425221i	−0.962273	−	0.272087i	$-0.912286\pi$
$701$	−6.50000	+	11.2583i	−0.245502	+	0.425221i	0.716771	+	0.697309i	$0.245619\pi$
$702$		0			0
$703$	−4.00000	−	6.92820i	−0.150863	−	0.261302i
$704$	0.500000	+	0.866025i	0.0188445	+	0.0326396i
$705$	−6.00000			−0.225973
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$	10.5000	−	18.1865i	0.394893	−	0.683975i
$708$	−3.50000	−	6.06218i	−0.131538	−	0.227831i
$709$	8.00000			0.300446			0.150223	−	0.988652i	$-0.452001\pi$
$709$	8.00000			0.300446			0.150223	+	0.988652i	$0.452001\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	−6.00000			−0.224860
$713$	−14.0000	−	17.3205i	−0.524304	−	0.648658i
$714$	6.00000			0.224544
$715$		0			0
$716$	−2.50000	+	4.33013i	−0.0934294	+	0.161824i
$717$		0			0
$718$	−10.0000	−	17.3205i	−0.373197	−	0.646396i
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	−0.438141	−	0.898906i	$-0.644363\pi$
$719$	15.0000	−	25.9808i	0.559406	−	0.968919i	0.997546	−	0.0700124i	$-0.0223039\pi$
$720$	0.500000	−	0.866025i	0.0186339	−	0.0322749i
$721$	−3.00000			−0.111726
$722$	−7.50000	−	12.9904i	−0.279121	−	0.483452i
$723$	−8.50000	−	14.7224i	−0.316118	−	0.547533i
$724$	−9.00000	−	15.5885i	−0.334482	−	0.579340i
$725$	3.50000	−	6.06218i	0.129987	−	0.225144i
$726$	5.00000	+	8.66025i	0.185567	+	0.321412i
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	−0.570049	−	0.821611i	$-0.693076\pi$
$727$	11.5000	−	19.9186i	0.426511	−	0.738739i	0.996560	+	0.0828714i	$0.0264091\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$	−8.00000	−	13.8564i	−0.295891	−	0.512498i
$732$	6.00000	−	10.3923i	0.221766	−	0.384111i
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	0.846967	−	0.531646i	$-0.178426\pi$
$733$	−1.00000	−	1.73205i	−0.0369358	−	0.0639748i	−0.883902	+	0.467671i	$0.845093\pi$
$734$	8.00000	+	13.8564i	0.295285	+	0.511449i
$735$	−1.00000	−	1.73205i	−0.0368856	−	0.0638877i
$736$	4.00000			0.147442
$737$	−4.00000	+	6.92820i	−0.147342	+	0.255204i
$738$		0			0
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	0.521475	−	0.853266i	$-0.325382\pi$
$739$	−13.0000	−	22.5167i	−0.478213	−	0.828289i	−0.999688	+	0.0249776i	$0.992049\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	−15.0000			−0.550667
$743$	42.0000			1.54083			0.770415	−	0.637542i	$-0.220049\pi$
$743$	42.0000			1.54083			0.770415	+	0.637542i	$0.220049\pi$
$744$	−5.50000	+	0.866025i	−0.201640	+	0.0317500i
$745$	−7.00000			−0.256460
$746$	−22.0000			−0.805477
$747$	4.50000	−	7.79423i	0.164646	−	0.285176i
$748$	−2.00000			−0.0731272
$749$	−10.5000	−	18.1865i	−0.383662	−	0.664521i
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	−0.969801	−	0.243898i	$-0.921574\pi$
$751$	−7.50000	+	12.9904i	−0.273679	+	0.474026i	0.696122	+	0.717923i	$0.254907\pi$
$752$	−6.00000			−0.218797
$753$	−2.00000	−	3.46410i	−0.0728841	−	0.126239i
$754$		0			0
$755$	9.50000	+	16.4545i	0.345740	+	0.598840i
$756$	1.50000	−	2.59808i	0.0545545	−	0.0944911i
$757$	12.0000	+	20.7846i	0.436147	+	0.755429i	0.997389	−	0.0722229i	$-0.0230093\pi$
$757$	12.0000	+	20.7846i	0.436147	+	0.755429i	−0.561241	+	0.827652i	$0.689676\pi$
$758$	5.00000	−	8.66025i	0.181608	−	0.314555i
$759$	−4.00000			−0.145191
$760$	2.00000			0.0725476
$761$	19.0000	−	32.9090i	0.688749	−	1.19295i	−0.283493	−	0.958974i	$-0.591493\pi$
$761$	19.0000	−	32.9090i	0.688749	−	1.19295i	0.972243	−	0.233975i	$-0.0751733\pi$
$762$	−6.50000	−	11.2583i	−0.235470	−	0.407846i
$763$	9.00000	−	15.5885i	0.325822	−	0.564340i
$764$	4.00000	+	6.92820i	0.144715	+	0.250654i
$765$	1.00000	+	1.73205i	0.0361551	+	0.0626224i
$766$	−4.00000	−	6.92820i	−0.144526	−	0.250326i
$767$		0			0
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−24.5000	+	42.4352i	−0.883493	+	1.53025i	−0.0360609	+	0.999350i	$0.511481\pi$
$769$	−24.5000	+	42.4352i	−0.883493	+	1.53025i	−0.847432	+	0.530904i	$0.821852\pi$
$770$	1.50000	+	2.59808i	0.0540562	+	0.0936282i
$771$	−28.0000			−1.00840
$772$	9.50000	−	16.4545i	0.341912	−	0.592210i
$773$	14.0000			0.503545			0.251773	−	0.967786i	$-0.418987\pi$
$773$	14.0000			0.503545			0.251773	+	0.967786i	$0.418987\pi$
$774$	−8.00000			−0.287554
$775$	−5.50000	+	0.866025i	−0.197566	+	0.0311086i
$776$	5.00000			0.179490
$777$	−12.0000			−0.430498
$778$	−15.0000	+	25.9808i	−0.537776	+	0.931455i
$779$		0			0
$780$		0			0
$781$		0			0
$782$	−4.00000	+	6.92820i	−0.143040	+	0.247752i
$783$	7.00000			0.250160
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	−6.00000	−	10.3923i	−0.214149	−	0.370917i
$786$	2.00000	+	3.46410i	0.0713376	+	0.123560i
$787$	−8.00000	+	13.8564i	−0.285169	+	0.493928i	−0.972650	−	0.232275i	$-0.925383\pi$
$787$	−8.00000	+	13.8564i	−0.285169	+	0.493928i	0.687481	+	0.726202i	$0.258716\pi$
$788$	−7.00000	−	12.1244i	−0.249365	−	0.431912i
$789$	3.00000	−	5.19615i	0.106803	−	0.184988i
$790$	8.00000			0.284627
$791$	−12.0000			−0.426671
$792$	−0.500000	+	0.866025i	−0.0177667	+	0.0307729i
$793$		0			0
$794$	11.0000	−	19.0526i	0.390375	−	0.676150i
$795$	−2.50000	−	4.33013i	−0.0886659	−	0.153574i
$796$	2.50000	+	4.33013i	0.0886102	+	0.153477i
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	0.838236	−	0.545308i	$-0.183587\pi$
$797$	−1.50000	−	2.59808i	−0.0531327	−	0.0920286i	−0.891368	+	0.453279i	$0.850254\pi$
$798$	6.00000			0.212398
$799$	6.00000	−	10.3923i	0.212265	−	0.367653i
$800$	0.500000	−	0.866025i	0.0176777	−	0.0306186i
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−32.0000			−1.12996
$803$	−3.00000	+	5.19615i	−0.105868	+	0.183368i
$804$	8.00000			0.282138
$805$	12.0000			0.422944
$806$		0			0
$807$	18.0000			0.633630
$808$	7.00000			0.246259
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	0.310457	+	0.950587i	$0.399518\pi$
$809$	−19.0000	+	32.9090i	−0.668004	+	1.15702i	−0.978461	+	0.206430i	$0.933815\pi$
$810$	1.00000			0.0351364
$811$	15.0000	+	25.9808i	0.526721	+	0.912308i	0.999515	+	0.0311349i	$0.00991216\pi$
$811$	15.0000	+	25.9808i	0.526721	+	0.912308i	−0.472794	+	0.881173i	$0.656755\pi$
$812$	10.5000	−	18.1865i	0.368478	−	0.638222i
$813$	−8.50000	+	14.7224i	−0.298108	+	0.516338i
$814$	4.00000			0.140200
$815$		0			0
$816$	1.00000	+	1.73205i	0.0350070	+	0.0606339i
$817$	−8.00000	−	13.8564i	−0.279885	−	0.484774i
$818$	7.50000	−	12.9904i	0.262231	−	0.454198i
$819$		0			0
$820$		0			0
$821$	41.0000			1.43091			0.715455	−	0.698659i	$-0.246219\pi$
$821$	41.0000			1.43091			0.715455	+	0.698659i	$0.246219\pi$
$822$	6.00000			0.209274
$823$	−0.500000	+	0.866025i	−0.0174289	+	0.0301877i	−0.874608	−	0.484830i	$-0.838881\pi$
$823$	−0.500000	+	0.866025i	−0.0174289	+	0.0301877i	0.857179	+	0.515018i	$0.172215\pi$
$824$	−0.500000	−	0.866025i	−0.0174183	−	0.0301694i
$825$	−0.500000	+	0.866025i	−0.0174078	+	0.0301511i
$826$	−10.5000	−	18.1865i	−0.365342	−	0.632790i
$827$	−8.00000	−	13.8564i	−0.278187	−	0.481834i	0.692747	−	0.721181i	$-0.256400\pi$
$827$	−8.00000	−	13.8564i	−0.278187	−	0.481834i	−0.970934	+	0.239346i	$0.923067\pi$
$828$	2.00000	+	3.46410i	0.0695048	+	0.120386i
$829$	−34.0000			−1.18087			−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000			−1.18087			−0.590434	+	0.807086i	$0.701044\pi$
$830$	4.50000	−	7.79423i	0.156197	−	0.270542i
$831$	−9.00000	+	15.5885i	−0.312207	+	0.540758i
$832$		0			0
$833$	4.00000			0.138592
$834$	−7.00000	+	12.1244i	−0.242390	+	0.419832i
$835$	12.0000			0.415277
$836$	−2.00000			−0.0691714
$837$	−3.50000	−	4.33013i	−0.120978	−	0.149671i
$838$	21.0000			0.725433
$839$	−26.0000			−0.897620			−0.448810	−	0.893627i	$-0.648152\pi$
$839$	−26.0000			−0.897620			−0.448810	+	0.893627i	$0.648152\pi$
$840$	1.50000	−	2.59808i	0.0517549	−	0.0896421i
$841$	20.0000			0.689655
$842$	10.0000	+	17.3205i	0.344623	+	0.596904i
$843$	−1.00000	+	1.73205i	−0.0344418	+	0.0596550i
$844$	−7.00000	+	12.1244i	−0.240950	+	0.417338i
$845$	13.0000			0.447214
$846$	−3.00000	−	5.19615i	−0.103142	−	0.178647i
$847$	15.0000	+	25.9808i	0.515406	+	0.892710i
$848$	−2.50000	−	4.33013i	−0.0858504	−	0.148697i
$849$		0			0
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$	8.00000	−	13.8564i	0.274236	−	0.474991i
$852$		0			0
$853$	−8.00000			−0.273915			−0.136957	−	0.990577i	$-0.543732\pi$
$853$	−8.00000			−0.273915			−0.136957	+	0.990577i	$0.543732\pi$
$854$	18.0000	−	31.1769i	0.615947	−	1.06685i
$855$	1.00000	+	1.73205i	0.0341993	+	0.0592349i
$856$	3.50000	−	6.06218i	0.119628	−	0.207201i
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	0.584967	−	0.811057i	$-0.301107\pi$
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	−0.994880	+	0.101068i	$0.967774\pi$
$858$		0			0
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	0.990533	+	0.137277i	$0.0438352\pi$
$859$	18.0000	+	31.1769i	0.614152	+	1.06374i	−0.376381	+	0.926465i	$0.622831\pi$
$860$	−8.00000			−0.272798
$861$		0			0
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$	1.00000			0.0340207
$865$	−2.50000	+	4.33013i	−0.0850026	+	0.147229i
$866$	−26.0000			−0.883516
$867$	13.0000			0.441503
$868$	−16.5000	+	2.59808i	−0.560046	+	0.0881845i
$869$	−8.00000			−0.271381
$870$	7.00000			0.237322
$871$		0			0
$872$	6.00000			0.203186
$873$	2.50000	+	4.33013i	0.0846122	+	0.146553i
$874$	−4.00000	+	6.92820i	−0.135302	+	0.234350i
$875$	1.50000	−	2.59808i	0.0507093	−	0.0878310i
$876$	6.00000			0.202721
$877$	−26.0000	−	45.0333i	−0.877958	−	1.52067i	−0.853578	−	0.520964i	$-0.825572\pi$
$877$	−26.0000	−	45.0333i	−0.877958	−	1.52067i	−0.0243792	−	0.999703i	$-0.507761\pi$
$878$	−8.50000	−	14.7224i	−0.286861	−	0.496858i
$879$	−1.50000	−	2.59808i	−0.0505937	−	0.0876309i
$880$	−0.500000	+	0.866025i	−0.0168550	+	0.0291937i
$881$	6.00000	+	10.3923i	0.202145	+	0.350126i	0.949219	−	0.314615i	$-0.101875\pi$
$881$	6.00000	+	10.3923i	0.202145	+	0.350126i	−0.747074	+	0.664741i	$0.768542\pi$
$882$	1.00000	−	1.73205i	0.0336718	−	0.0583212i
$883$	−32.0000			−1.07689			−0.538443	−	0.842662i	$-0.680987\pi$
$883$	−32.0000			−1.07689			−0.538443	+	0.842662i	$0.680987\pi$
$884$		0			0
$885$	3.50000	−	6.06218i	0.117651	−	0.203778i
$886$	10.0000	+	17.3205i	0.335957	+	0.581894i
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	−0.261540	−	0.965193i	$-0.584230\pi$
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	0.966651	−	0.256096i	$-0.0824362\pi$
$888$	−2.00000	−	3.46410i	−0.0671156	−	0.116248i
$889$	−19.5000	−	33.7750i	−0.654009	−	1.13278i
$890$	−3.00000	−	5.19615i	−0.100560	−	0.174175i
$891$	−1.00000			−0.0335013
$892$	8.50000	−	14.7224i	0.284601	−	0.492943i
$893$	6.00000	−	10.3923i	0.200782	−	0.347765i
$894$	−3.50000	−	6.06218i	−0.117058	−	0.202750i
$895$	−5.00000			−0.167132
$896$	1.50000	−	2.59808i	0.0501115	−	0.0867956i
$897$		0			0
$898$	−6.00000			−0.200223
$899$	−24.5000	−	30.3109i	−0.817121	−	1.01092i
$900$	1.00000			0.0333333
$901$	10.0000			0.333148
$902$		0			0
$903$	−24.0000			−0.798670
$904$	−2.00000	−	3.46410i	−0.0665190	−	0.115214i
$905$	9.00000	−	15.5885i	0.299170	−	0.518178i
$906$	−9.50000	+	16.4545i	−0.315616	+	0.546664i
$907$	40.0000			1.32818			0.664089	−	0.747653i	$-0.268820\pi$
$907$	40.0000			1.32818			0.664089	+	0.747653i	$0.268820\pi$
$908$	6.50000	+	11.2583i	0.215710	+	0.373621i
$909$	3.50000	+	6.06218i	0.116088	+	0.201070i
$910$		0			0
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	0.274162	+	0.961683i	$0.411599\pi$
$911$	−21.0000	+	36.3731i	−0.695761	+	1.20509i	−0.969923	+	0.243410i	$0.921734\pi$
$912$	1.00000	+	1.73205i	0.0331133	+	0.0573539i
$913$	−4.50000	+	7.79423i	−0.148928	+	0.257951i
$914$	−14.0000			−0.463079
$915$	12.0000			0.396708
$916$	10.0000	−	17.3205i	0.330409	−	0.572286i
$917$	6.00000	+	10.3923i	0.198137	+	0.343184i
$918$	−1.00000	+	1.73205i	−0.0330049	+	0.0571662i
$919$	17.5000	+	30.3109i	0.577272	+	0.999864i	0.995791	+	0.0916559i	$0.0292160\pi$
$919$	17.5000	+	30.3109i	0.577272	+	0.999864i	−0.418519	+	0.908208i	$0.637451\pi$
$920$	2.00000	+	3.46410i	0.0659380	+	0.114208i
$921$	1.00000	+	1.73205i	0.0329511	+	0.0570730i
$922$	−7.00000			−0.230533
$923$		0			0
$924$	−1.50000	+	2.59808i	−0.0493464	+	0.0854704i
$925$	−2.00000	−	3.46410i	−0.0657596	−	0.113899i
$926$	15.0000			0.492931
$927$	0.500000	−	0.866025i	0.0164222	−	0.0284440i
$928$	7.00000			0.229786
$929$	−42.0000			−1.37798			−0.688988	−	0.724773i	$-0.741945\pi$
$929$	−42.0000			−1.37798			−0.688988	+	0.724773i	$0.741945\pi$
$930$	−3.50000	−	4.33013i	−0.114770	−	0.141990i
$931$	4.00000			0.131095
$932$	16.0000			0.524097
$933$	−8.00000	+	13.8564i	−0.261908	+	0.453638i
$934$	−23.0000			−0.752583
$935$	−1.00000	−	1.73205i	−0.0327035	−	0.0566441i
$936$		0			0
$937$	−11.0000	+	19.0526i	−0.359354	+	0.622420i	−0.987853	−	0.155391i	$-0.950336\pi$
$937$	−11.0000	+	19.0526i	−0.359354	+	0.622420i	0.628499	+	0.777811i	$0.283670\pi$
$938$	24.0000			0.783628
$939$	−3.50000	−	6.06218i	−0.114218	−	0.197832i
$940$	−3.00000	−	5.19615i	−0.0978492	−	0.169480i
$941$	16.5000	+	28.5788i	0.537885	+	0.931644i	0.999018	+	0.0443125i	$0.0141097\pi$
$941$	16.5000	+	28.5788i	0.537885	+	0.931644i	−0.461133	+	0.887331i	$0.652557\pi$
$942$	6.00000	−	10.3923i	0.195491	−	0.338600i
$943$		0			0
$944$	3.50000	−	6.06218i	0.113915	−	0.197307i
$945$	3.00000			0.0975900
$946$	8.00000			0.260102
$947$	10.0000	−	17.3205i	0.324956	−	0.562841i	−0.656547	−	0.754285i	$-0.727984\pi$
$947$	10.0000	−	17.3205i	0.324956	−	0.562841i	0.981504	+	0.191444i	$0.0613171\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$		0			0
$950$	1.00000	+	1.73205i	0.0324443	+	0.0561951i
$951$	−3.50000	−	6.06218i	−0.113495	−	0.196580i
$952$	3.00000	+	5.19615i	0.0972306	+	0.168408i
$953$	−60.0000			−1.94359			−0.971795	−	0.235826i	$-0.924220\pi$
$953$	−60.0000			−1.94359			−0.971795	+	0.235826i	$0.924220\pi$
$954$	2.50000	−	4.33013i	0.0809405	−	0.140193i
$955$	−4.00000	+	6.92820i	−0.129437	+	0.224191i
$956$		0			0
$957$	−7.00000			−0.226278
$958$	15.0000	−	25.9808i	0.484628	−	0.839400i
$959$	18.0000			0.581250
$960$	1.00000			0.0322749
$961$	−6.50000	+	30.3109i	−0.209677	+	0.977771i
$962$		0			0
$963$	7.00000			0.225572
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	19.0000			0.611632
$966$	6.00000	+	10.3923i	0.193047	+	0.334367i
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	−0.794515	−	0.607244i	$-0.792275\pi$
$967$	4.00000	−	6.92820i	0.128631	−	0.222796i	0.923147	+	0.384448i	$0.125608\pi$
$968$	−5.00000	+	8.66025i	−0.160706	+	0.278351i
$969$	−4.00000			−0.128499
$970$	2.50000	+	4.33013i	0.0802702	+	0.139032i
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	0.960910	−	0.276861i	$-0.0892941\pi$
$971$	7.50000	+	12.9904i	0.240686	+	0.416881i	−0.720224	+	0.693742i	$0.755961\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−21.0000	+	36.3731i	−0.673229	+	1.16607i
$974$	−12.5000	−	21.6506i	−0.400526	−	0.693731i
$975$		0			0
$976$	12.0000			0.384111
$977$	−32.0000			−1.02377			−0.511885	−	0.859054i	$-0.671053\pi$
$977$	−32.0000			−1.02377			−0.511885	+	0.859054i	$0.671053\pi$
$978$		0			0
$979$	3.00000	+	5.19615i	0.0958804	+	0.166070i
$980$	1.00000	−	1.73205i	0.0319438	−	0.0553283i
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$	5.50000	+	9.52628i	0.175512	+	0.303996i
$983$	23.0000	+	39.8372i	0.733586	+	1.27061i	0.955341	+	0.295506i	$0.0954882\pi$
$983$	23.0000	+	39.8372i	0.733586	+	1.27061i	−0.221755	+	0.975102i	$0.571178\pi$
$984$		0			0
$985$	7.00000	−	12.1244i	0.223039	−	0.386314i
$986$	−7.00000	+	12.1244i	−0.222925	+	0.386118i
$987$	−9.00000	−	15.5885i	−0.286473	−	0.496186i
$988$		0			0
$989$	16.0000	−	27.7128i	0.508770	−	0.881216i
$990$	−1.00000			−0.0317821
$991$	20.0000			0.635321			0.317660	−	0.948205i	$-0.397103\pi$
$991$	20.0000			0.635321			0.317660	+	0.948205i	$0.397103\pi$
$992$	−3.50000	−	4.33013i	−0.111125	−	0.137482i
$993$		0			0
$994$		0			0
$995$	−2.50000	+	4.33013i	−0.0792553	+	0.137274i
$996$	9.00000			0.285176
$997$	−4.00000	−	6.92820i	−0.126681	−	0.219418i	0.795708	−	0.605681i	$-0.207099\pi$
$997$	−4.00000	−	6.92820i	−0.126681	−	0.219418i	−0.922389	+	0.386263i	$0.873766\pi$
$998$	2.00000	−	3.46410i	0.0633089	−	0.109654i
$999$	2.00000	−	3.46410i	0.0632772	−	0.109599i

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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} +(-1.50000 + 2.59808i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(0.500000 + 0.866025i) q^{11} +(0.500000 - 0.866025i) q^{12} +(1.50000 - 2.59808i) q^{14} +1.00000 q^{15} +1.00000 q^{16} +(-1.00000 + 1.73205i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{20} +(1.50000 + 2.59808i) q^{21} +(-0.500000 - 0.866025i) q^{22} -4.00000 q^{23} +(-0.500000 + 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{27} +(-1.50000 + 2.59808i) q^{28} -7.00000 q^{29} -1.00000 q^{30} +(3.50000 + 4.33013i) q^{31} -1.00000 q^{32} +1.00000 q^{33} +(1.00000 - 1.73205i) q^{34} -3.00000 q^{35} +(-0.500000 - 0.866025i) q^{36} +(-2.00000 + 3.46410i) q^{37} +(1.00000 - 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{40} +(-1.50000 - 2.59808i) q^{42} +(-4.00000 + 6.92820i) q^{43} +(0.500000 + 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{45} +4.00000 q^{46} -6.00000 q^{47} +(0.500000 - 0.866025i) q^{48} +(-1.00000 - 1.73205i) q^{49} +(0.500000 - 0.866025i) q^{50} +(1.00000 + 1.73205i) q^{51} +(-2.50000 - 4.33013i) q^{53} +1.00000 q^{54} +(-0.500000 + 0.866025i) q^{55} +(1.50000 - 2.59808i) q^{56} +(1.00000 + 1.73205i) q^{57} +7.00000 q^{58} +(3.50000 - 6.06218i) q^{59} +1.00000 q^{60} +12.0000 q^{61} +(-3.50000 - 4.33013i) q^{62} +3.00000 q^{63} +1.00000 q^{64} -1.00000 q^{66} +(4.00000 + 6.92820i) q^{67} +(-1.00000 + 1.73205i) q^{68} +(-2.00000 + 3.46410i) q^{69} +3.00000 q^{70} +(0.500000 + 0.866025i) q^{72} +(3.00000 + 5.19615i) q^{73} +(2.00000 - 3.46410i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-1.00000 + 1.73205i) q^{76} -3.00000 q^{77} +(-4.00000 + 6.92820i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(4.50000 + 7.79423i) q^{83} +(1.50000 + 2.59808i) q^{84} -2.00000 q^{85} +(4.00000 - 6.92820i) q^{86} +(-3.50000 + 6.06218i) q^{87} +(-0.500000 - 0.866025i) q^{88} +6.00000 q^{89} +(-0.500000 + 0.866025i) q^{90} -4.00000 q^{92} +(5.50000 - 0.866025i) q^{93} +6.00000 q^{94} -2.00000 q^{95} +(-0.500000 + 0.866025i) q^{96} -5.00000 q^{97} +(1.00000 + 1.73205i) q^{98} +(0.500000 - 0.866025i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} + q^{5} - q^{6} - 3 q^{7} - 2 q^{8} - q^{9} - q^{10} + q^{11} + q^{12} + 3 q^{14} + 2 q^{15} + 2 q^{16} - 2 q^{17} + q^{18} - 2 q^{19} + q^{20} + 3 q^{21} - q^{22}+ \cdots + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 + q^5 - q^6 - 3 * q^7 - 2 * q^8 - q^9 - q^10 + q^11 + q^12 + 3 * q^14 + 2 * q^15 + 2 * q^16 - 2 * q^17 + q^18 - 2 * q^19 + q^20 + 3 * q^21 - q^22 - 8 * q^23 - q^24 - q^25 - 2 * q^27 - 3 * q^28 - 14 * q^29 - 2 * q^30 + 7 * q^31 - 2 * q^32 + 2 * q^33 + 2 * q^34 - 6 * q^35 - q^36 - 4 * q^37 + 2 * q^38 - q^40 - 3 * q^42 - 8 * q^43 + q^44 + q^45 + 8 * q^46 - 12 * q^47 + q^48 - 2 * q^49 + q^50 + 2 * q^51 - 5 * q^53 + 2 * q^54 - q^55 + 3 * q^56 + 2 * q^57 + 14 * q^58 + 7 * q^59 + 2 * q^60 + 24 * q^61 - 7 * q^62 + 6 * q^63 + 2 * q^64 - 2 * q^66 + 8 * q^67 - 2 * q^68 - 4 * q^69 + 6 * q^70 + q^72 + 6 * q^73 + 4 * q^74 + q^75 - 2 * q^76 - 6 * q^77 - 8 * q^79 + q^80 - q^81 + 9 * q^83 + 3 * q^84 - 4 * q^85 + 8 * q^86 - 7 * q^87 - q^88 + 12 * q^89 - q^90 - 8 * q^92 + 11 * q^93 + 12 * q^94 - 4 * q^95 - q^96 - 10 * q^97 + 2 * q^98 + q^99

Introduction

L-functions

Modular forms

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Database

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