LMFDB - Embedded newform 1950.2.i.s.451.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(451,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1950.451");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			451.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1950.451
Dual form			1950.2.i.s.601.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} -2.00000 q^{21} +(0.500000 + 0.866025i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} -3.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +2.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-2.50000 + 4.33013i) q^{37} -6.00000 q^{38} +(-3.50000 - 0.866025i) q^{39} +(-5.00000 + 8.66025i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(2.50000 + 4.33013i) q^{43} +1.00000 q^{44} +(1.50000 + 2.59808i) q^{46} -3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} -2.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -14.0000 q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{56} +6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(2.50000 + 4.33013i) q^{59} +(5.00000 + 8.66025i) q^{61} +(-1.50000 + 2.59808i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -1.00000 q^{66} +(1.00000 - 1.73205i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(0.500000 + 0.866025i) q^{72} +2.00000 q^{73} +(2.50000 + 4.33013i) q^{74} +(-3.00000 + 5.19615i) q^{76} -2.00000 q^{77} +(-2.50000 + 2.59808i) q^{78} +5.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.00000 + 8.66025i) q^{82} +6.00000 q^{83} +(1.00000 + 1.73205i) q^{84} +5.00000 q^{86} +(0.500000 + 0.866025i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(-5.00000 + 5.19615i) q^{91} +3.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(-1.50000 - 2.59808i) q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - q^3 - q^4 + q^6 + 2 * q^7 - 2 * q^8 - q^9	$ 2 q + q^{2} - q^{3} - q^{4} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{11} + 2 q^{12} + 2 q^{13} + 4 q^{14} - q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{21} + q^{22} - 3 q^{23} + q^{24} + 7 q^{26} + 2 q^{27} + 2 q^{28} + q^{29} - 6 q^{31} + q^{32} - q^{33} + 4 q^{34} - q^{36} - 5 q^{37} - 12 q^{38} - 7 q^{39} - 10 q^{41} - 2 q^{42} + 5 q^{43} + 2 q^{44} + 3 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} - 4 q^{51} + 5 q^{52} - 28 q^{53} + q^{54} - 2 q^{56} + 12 q^{57} - q^{58} + 5 q^{59} + 10 q^{61} - 3 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{66} + 2 q^{68} - 3 q^{69} - 4 q^{71} + q^{72} + 4 q^{73} + 5 q^{74} - 6 q^{76} - 4 q^{77} - 5 q^{78} + 10 q^{79} - q^{81} + 10 q^{82} + 12 q^{83} + 2 q^{84} + 10 q^{86} + q^{87} + q^{88} - 10 q^{89} - 10 q^{91} + 6 q^{92} + 3 q^{93} - 3 q^{94} - 2 q^{96} - 10 q^{97} - 3 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q + q^2 - q^3 - q^4 + q^6 + 2 * q^7 - 2 * q^8 - q^9 - q^11 + 2 * q^12 + 2 * q^13 + 4 * q^14 - q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^21 + q^22 - 3 * q^23 + q^24 + 7 * q^26 + 2 * q^27 + 2 * q^28 + q^29 - 6 * q^31 + q^32 - q^33 + 4 * q^34 - q^36 - 5 * q^37 - 12 * q^38 - 7 * q^39 - 10 * q^41 - 2 * q^42 + 5 * q^43 + 2 * q^44 + 3 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 4 * q^51 + 5 * q^52 - 28 * q^53 + q^54 - 2 * q^56 + 12 * q^57 - q^58 + 5 * q^59 + 10 * q^61 - 3 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^66 + 2 * q^68 - 3 * q^69 - 4 * q^71 + q^72 + 4 * q^73 + 5 * q^74 - 6 * q^76 - 4 * q^77 - 5 * q^78 + 10 * q^79 - q^81 + 10 * q^82 + 12 * q^83 + 2 * q^84 + 10 * q^86 + q^87 + q^88 - 10 * q^89 - 10 * q^91 + 6 * q^92 + 3 * q^93 - 3 * q^94 - 2 * q^96 - 10 * q^97 - 3 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	0.990766	−	0.135583i	$-0.0432908\pi$
$7$	1.00000	+	1.73205i	0.377964	+	0.654654i	−0.612801	+	0.790237i	$0.709957\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	−0.931505	−	0.363727i	$-0.881504\pi$
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i	0.780750	+	0.624844i	$0.214837\pi$
$12$	1.00000			0.288675
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$13$	1.00000	+	3.46410i	0.277350	+	0.960769i
$14$	2.00000			0.534522
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	−1.00000			−0.235702
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	−0.972404	−	0.233301i	$-0.925047\pi$
$19$	−3.00000	−	5.19615i	−0.688247	−	1.19208i	0.284157	−	0.958778i	$-0.408286\pi$
$20$		0			0
$21$	−2.00000			−0.436436
$22$	0.500000	+	0.866025i	0.106600	+	0.184637i
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	−0.978961	−	0.204046i	$-0.934591\pi$
$23$	−1.50000	+	2.59808i	−0.312772	+	0.541736i	0.666190	+	0.745782i	$0.267924\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$		0			0
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$	1.00000			0.192450
$28$	1.00000	−	1.73205i	0.188982	−	0.327327i
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	−0.815861	−	0.578249i	$-0.803736\pi$
$29$	0.500000	−	0.866025i	0.0928477	−	0.160817i	0.908708	+	0.417432i	$0.137070\pi$
$30$		0			0
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	2.00000			0.342997
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	−0.994999	−	0.0998840i	$-0.968153\pi$
$37$	−2.50000	+	4.33013i	−0.410997	+	0.711868i	0.584002	+	0.811752i	$0.301486\pi$
$38$	−6.00000			−0.973329
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$		0			0
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	0.150567	+	0.988600i	$0.451890\pi$
$41$	−5.00000	+	8.66025i	−0.780869	+	1.35250i	−0.931436	+	0.363905i	$0.881443\pi$
$42$	−1.00000	+	1.73205i	−0.154303	+	0.267261i
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	−0.609994	+	0.792406i	$0.708828\pi$
$44$	1.00000			0.150756
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	1.50000	−	2.59808i	0.214286	−	0.371154i
$50$		0			0
$51$	−2.00000			−0.280056
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$	−14.0000			−1.92305			−0.961524	−	0.274721i	$-0.911414\pi$
$53$	−14.0000			−1.92305			−0.961524	+	0.274721i	$0.911414\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$		0			0
$56$	−1.00000	−	1.73205i	−0.133631	−	0.231455i
$57$	6.00000			0.794719
$58$	−0.500000	−	0.866025i	−0.0656532	−	0.113715i
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	0.981608	−	0.190909i	$-0.0611434\pi$
$59$	2.50000	+	4.33013i	0.325472	+	0.563735i	−0.656136	+	0.754643i	$0.727810\pi$
$60$		0			0
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	0.985391	+	0.170305i	$0.0544754\pi$
$61$	5.00000	+	8.66025i	0.640184	+	1.10883i	−0.345207	+	0.938527i	$0.612191\pi$
$62$	−1.50000	+	2.59808i	−0.190500	+	0.329956i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.00000			−0.123091
$67$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$67$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$	−1.50000	−	2.59808i	−0.180579	−	0.312772i
$70$		0			0
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	0.722599	−	0.691268i	$-0.242948\pi$
$71$	−2.00000	−	3.46410i	−0.237356	−	0.411113i	−0.959955	+	0.280155i	$0.909614\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	2.00000			0.234082			0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000			0.234082			0.117041	+	0.993127i	$0.462659\pi$
$74$	2.50000	+	4.33013i	0.290619	+	0.503367i
$75$		0			0
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	−2.00000			−0.227921
$78$	−2.50000	+	2.59808i	−0.283069	+	0.294174i
$79$	5.00000			0.562544			0.281272	−	0.959628i	$-0.409244\pi$
$79$	5.00000			0.562544			0.281272	+	0.959628i	$0.409244\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	5.00000	+	8.66025i	0.552158	+	0.956365i
$83$	6.00000			0.658586			0.329293	−	0.944228i	$-0.393190\pi$
$83$	6.00000			0.658586			0.329293	+	0.944228i	$0.393190\pi$
$84$	1.00000	+	1.73205i	0.109109	+	0.188982i
$85$		0			0
$86$	5.00000			0.539164
$87$	0.500000	+	0.866025i	0.0536056	+	0.0928477i
$88$	0.500000	−	0.866025i	0.0533002	−	0.0923186i
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	0.469389	+	0.882992i	$0.344474\pi$
$89$	−5.00000	+	8.66025i	−0.529999	+	0.917985i	−0.999388	+	0.0349934i	$0.988859\pi$
$90$		0			0
$91$	−5.00000	+	5.19615i	−0.524142	+	0.544705i
$92$	3.00000			0.312772
$93$	1.50000	−	2.59808i	0.155543	−	0.269408i
$94$	−1.50000	+	2.59808i	−0.154713	+	0.267971i
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	−1.50000	−	2.59808i	−0.151523	−	0.262445i
$99$	1.00000			0.100504
$100$		0			0
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$	−1.00000	+	1.73205i	−0.0990148	+	0.171499i
$103$	6.00000			0.591198			0.295599	−	0.955312i	$-0.404481\pi$
$103$	6.00000			0.591198			0.295599	+	0.955312i	$0.404481\pi$
$104$	−1.00000	−	3.46410i	−0.0980581	−	0.339683i
$105$		0			0
$106$	−7.00000	+	12.1244i	−0.679900	+	1.17762i
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	−0.973814	−	0.227345i	$-0.926996\pi$
$107$	−3.00000	+	5.19615i	−0.290021	+	0.502331i	0.683793	+	0.729676i	$0.260329\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−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			0
$111$	−2.50000	−	4.33013i	−0.237289	−	0.410997i
$112$	−2.00000			−0.188982
$113$	8.50000	+	14.7224i	0.799613	+	1.38497i	0.919868	+	0.392227i	$0.128295\pi$
$113$	8.50000	+	14.7224i	0.799613	+	1.38497i	−0.120256	+	0.992743i	$0.538371\pi$
$114$	3.00000	−	5.19615i	0.280976	−	0.486664i
$115$		0			0
$116$	−1.00000			−0.0928477
$117$	2.50000	−	2.59808i	0.231125	−	0.240192i
$118$	5.00000			0.460287
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$		0			0
$121$	5.00000	+	8.66025i	0.454545	+	0.787296i
$122$	10.0000			0.905357
$123$	−5.00000	−	8.66025i	−0.450835	−	0.780869i
$124$	1.50000	+	2.59808i	0.134704	+	0.233314i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	−7.00000	+	12.1244i	−0.621150	+	1.07586i	0.368122	+	0.929777i	$0.380001\pi$
$127$	−7.00000	+	12.1244i	−0.621150	+	1.07586i	−0.989272	+	0.146085i	$0.953333\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−5.00000			−0.440225
$130$		0			0
$131$	13.0000			1.13582			0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000			1.13582			0.567908	+	0.823092i	$0.307753\pi$
$132$	−0.500000	+	0.866025i	−0.0435194	+	0.0753778i
$133$	6.00000	−	10.3923i	0.520266	−	0.901127i
$134$		0			0
$135$		0			0
$136$	−1.00000	−	1.73205i	−0.0857493	−	0.148522i
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	0.607233	−	0.794524i	$-0.292279\pi$
$137$	−4.50000	−	7.79423i	−0.384461	−	0.665906i	−0.991694	+	0.128618i	$0.958946\pi$
$138$	−3.00000			−0.255377
$139$	−5.00000	−	8.66025i	−0.424094	−	0.734553i	0.572241	−	0.820086i	$-0.306074\pi$
$139$	−5.00000	−	8.66025i	−0.424094	−	0.734553i	−0.996335	+	0.0855324i	$0.972741\pi$
$140$		0			0
$141$	1.50000	−	2.59808i	0.126323	−	0.218797i
$142$	−4.00000			−0.335673
$143$	−3.50000	−	0.866025i	−0.292685	−	0.0724207i
$144$	1.00000			0.0833333
$145$		0			0
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	1.50000	+	2.59808i	0.123718	+	0.214286i
$148$	5.00000			0.410997
$149$	−5.50000	−	9.52628i	−0.450578	−	0.780423i	0.547844	−	0.836580i	$-0.315449\pi$
$149$	−5.50000	−	9.52628i	−0.450578	−	0.780423i	−0.998422	+	0.0561570i	$0.982115\pi$
$150$		0			0
$151$	24.0000			1.95309			0.976546	−	0.215308i	$-0.0690756\pi$
$151$	24.0000			1.95309			0.976546	+	0.215308i	$0.0690756\pi$
$152$	3.00000	+	5.19615i	0.243332	+	0.421464i
$153$	1.00000	−	1.73205i	0.0808452	−	0.140028i
$154$	−1.00000	+	1.73205i	−0.0805823	+	0.139573i
$155$		0			0
$156$	1.00000	+	3.46410i	0.0800641	+	0.277350i
$157$	−25.0000			−1.99522			−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−25.0000			−1.99522			−0.997609	+	0.0691164i	$0.977982\pi$
$158$	2.50000	−	4.33013i	0.198889	−	0.344486i
$159$	7.00000	−	12.1244i	0.555136	−	0.961524i
$160$		0			0
$161$	−6.00000			−0.472866
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	8.50000	+	14.7224i	0.665771	+	1.15315i	0.979076	+	0.203497i	$0.0652307\pi$
$163$	8.50000	+	14.7224i	0.665771	+	1.15315i	−0.313304	+	0.949653i	$0.601436\pi$
$164$	10.0000			0.780869
$165$		0			0
$166$	3.00000	−	5.19615i	0.232845	−	0.403300i
$167$	−3.50000	+	6.06218i	−0.270838	+	0.469105i	−0.969077	−	0.246760i	$-0.920634\pi$
$167$	−3.50000	+	6.06218i	−0.270838	+	0.469105i	0.698239	+	0.715865i	$0.253967\pi$
$168$	2.00000			0.154303
$169$	−11.0000	+	6.92820i	−0.846154	+	0.532939i
$170$		0			0
$171$	−3.00000	+	5.19615i	−0.229416	+	0.397360i
$172$	2.50000	−	4.33013i	0.190623	−	0.330169i
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	0.931984	−	0.362500i	$-0.118077\pi$
$173$	2.00000	+	3.46410i	0.152057	+	0.263371i	−0.779926	+	0.625871i	$0.784744\pi$
$174$	1.00000			0.0758098
$175$		0			0
$176$	−0.500000	−	0.866025i	−0.0376889	−	0.0652791i
$177$	−5.00000			−0.375823
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	3.50000	−	6.06218i	0.261602	−	0.453108i	−0.705066	−	0.709142i	$-0.749082\pi$
$179$	3.50000	−	6.06218i	0.261602	−	0.453108i	0.966668	+	0.256034i	$0.0824158\pi$
$180$		0			0
$181$	16.0000			1.18927			0.594635	−	0.803996i	$-0.297296\pi$
$181$	16.0000			1.18927			0.594635	+	0.803996i	$0.297296\pi$
$182$	2.00000	+	6.92820i	0.148250	+	0.513553i
$183$	−10.0000			−0.739221
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	−1.50000	−	2.59808i	−0.109985	−	0.190500i
$187$	−2.00000			−0.146254
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	1.00000	+	1.73205i	0.0727393	+	0.125988i
$190$		0			0
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.863743	−	0.503932i	$-0.831886\pi$
$191$	−12.0000	−	20.7846i	−0.868290	−	1.50392i	−0.00454614	−	0.999990i	$-0.501447\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	−3.00000			−0.214286
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	−0.996649	−	0.0818013i	$-0.973933\pi$
$197$	−6.00000	+	10.3923i	−0.427482	+	0.740421i	0.569166	+	0.822222i	$0.307266\pi$
$198$	0.500000	−	0.866025i	0.0355335	−	0.0615457i
$199$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$199$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$200$		0			0
$201$		0			0
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	2.00000			0.140372
$204$	1.00000	+	1.73205i	0.0700140	+	0.121268i
$205$		0			0
$206$	3.00000	−	5.19615i	0.209020	−	0.362033i
$207$	3.00000			0.208514
$208$	−3.50000	−	0.866025i	−0.242681	−	0.0600481i
$209$	6.00000			0.415029
$210$		0			0
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	−0.694857	−	0.719148i	$-0.744533\pi$
$211$	4.00000	−	6.92820i	0.275371	−	0.476957i	0.970229	+	0.242190i	$0.0778659\pi$
$212$	7.00000	+	12.1244i	0.480762	+	0.832704i
$213$	4.00000			0.274075
$214$	3.00000	+	5.19615i	0.205076	+	0.355202i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$	−3.00000	−	5.19615i	−0.203653	−	0.352738i
$218$	−3.00000	+	5.19615i	−0.203186	+	0.351928i
$219$	−1.00000	+	1.73205i	−0.0675737	+	0.117041i
$220$		0			0
$221$	−5.00000	+	5.19615i	−0.336336	+	0.349531i
$222$	−5.00000			−0.335578
$223$	5.00000	−	8.66025i	0.334825	−	0.579934i	−0.648626	−	0.761107i	$-0.724656\pi$
$223$	5.00000	−	8.66025i	0.334825	−	0.579934i	0.983451	+	0.181173i	$0.0579895\pi$
$224$	−1.00000	+	1.73205i	−0.0668153	+	0.115728i
$225$		0			0
$226$	17.0000			1.13082
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	0.979630	+	0.200812i	$0.0643581\pi$
$227$	10.0000	+	17.3205i	0.663723	+	1.14960i	−0.315906	+	0.948790i	$0.602309\pi$
$228$	−3.00000	−	5.19615i	−0.198680	−	0.344124i
$229$	22.0000			1.45380			0.726900	−	0.686743i	$-0.240960\pi$
$229$	22.0000			1.45380			0.726900	+	0.686743i	$0.240960\pi$
$230$		0			0
$231$	1.00000	−	1.73205i	0.0657952	−	0.113961i
$232$	−0.500000	+	0.866025i	−0.0328266	+	0.0568574i
$233$	−3.00000			−0.196537			−0.0982683	−	0.995160i	$-0.531330\pi$
$233$	−3.00000			−0.196537			−0.0982683	+	0.995160i	$0.531330\pi$
$234$	−1.00000	−	3.46410i	−0.0653720	−	0.226455i
$235$		0			0
$236$	2.50000	−	4.33013i	0.162736	−	0.281867i
$237$	−2.50000	+	4.33013i	−0.162392	+	0.281272i
$238$	2.00000	+	3.46410i	0.129641	+	0.224544i
$239$	−8.00000			−0.517477			−0.258738	−	0.965947i	$-0.583307\pi$
$239$	−8.00000			−0.517477			−0.258738	+	0.965947i	$0.583307\pi$
$240$		0			0
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	10.0000			0.642824
$243$	−0.500000	−	0.866025i	−0.0320750	−	0.0555556i
$244$	5.00000	−	8.66025i	0.320092	−	0.554416i
$245$		0			0
$246$	−10.0000			−0.637577
$247$	15.0000	−	15.5885i	0.954427	−	0.991870i
$248$	3.00000			0.190500
$249$	−3.00000	+	5.19615i	−0.190117	+	0.329293i
$250$		0			0
$251$	−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	$0.863516\pi$
$252$	−2.00000			−0.125988
$253$	−1.50000	−	2.59808i	−0.0943042	−	0.163340i
$254$	7.00000	+	12.1244i	0.439219	+	0.760750i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	−0.326929	−	0.945049i	$-0.606014\pi$
$257$	10.5000	−	18.1865i	0.654972	−	1.13444i	0.981901	−	0.189396i	$-0.0606529\pi$
$258$	−2.50000	+	4.33013i	−0.155643	+	0.269582i
$259$	−10.0000			−0.621370
$260$		0			0
$261$	−1.00000			−0.0618984
$262$	6.50000	−	11.2583i	0.401571	−	0.695542i
$263$	11.5000	−	19.9186i	0.709120	−	1.22823i	−0.256063	−	0.966660i	$-0.582426\pi$
$263$	11.5000	−	19.9186i	0.709120	−	1.22823i	0.965184	−	0.261573i	$-0.0842411\pi$
$264$	0.500000	+	0.866025i	0.0307729	+	0.0533002i
$265$		0			0
$266$	−6.00000	−	10.3923i	−0.367884	−	0.637193i
$267$	−5.00000	−	8.66025i	−0.305995	−	0.529999i
$268$		0			0
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	−0.998361	−	0.0572259i	$-0.981774\pi$
$269$	−9.00000	−	15.5885i	−0.548740	−	0.950445i	0.449622	−	0.893219i	$-0.351559\pi$
$270$		0			0
$271$	14.5000	−	25.1147i	0.880812	−	1.52561i	0.0303728	−	0.999539i	$-0.490331\pi$
$271$	14.5000	−	25.1147i	0.880812	−	1.52561i	0.850439	−	0.526073i	$-0.176336\pi$
$272$	−2.00000			−0.121268
$273$	−2.00000	−	6.92820i	−0.121046	−	0.419314i
$274$	−9.00000			−0.543710
$275$		0			0
$276$	−1.50000	+	2.59808i	−0.0902894	+	0.156386i
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	−0.996484	−	0.0837823i	$-0.973300\pi$
$277$	−9.50000	−	16.4545i	−0.570800	−	0.988654i	0.425684	−	0.904872i	$-0.360033\pi$
$278$	−10.0000			−0.599760
$279$	1.50000	+	2.59808i	0.0898027	+	0.155543i
$280$		0			0
$281$	−30.0000			−1.78965			−0.894825	−	0.446417i	$-0.852700\pi$
$281$	−30.0000			−1.78965			−0.894825	+	0.446417i	$0.852700\pi$
$282$	−1.50000	−	2.59808i	−0.0893237	−	0.154713i
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	−0.991960	−	0.126550i	$-0.959610\pi$
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	0.605575	+	0.795788i	$0.292943\pi$
$284$	−2.00000	+	3.46410i	−0.118678	+	0.205557i
$285$		0			0
$286$	−2.50000	+	2.59808i	−0.147828	+	0.153627i
$287$	−20.0000			−1.18056
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$		0			0
$291$	10.0000			0.586210
$292$	−1.00000	−	1.73205i	−0.0585206	−	0.101361i
$293$	−7.00000	−	12.1244i	−0.408944	−	0.708312i	0.585827	−	0.810436i	$-0.300770\pi$
$293$	−7.00000	−	12.1244i	−0.408944	−	0.708312i	−0.994772	+	0.102123i	$0.967436\pi$
$294$	3.00000			0.174964
$295$		0			0
$296$	2.50000	−	4.33013i	0.145310	−	0.251684i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	−11.0000			−0.637213
$299$	−10.5000	−	2.59808i	−0.607231	−	0.150251i
$300$		0			0
$301$	−5.00000	+	8.66025i	−0.288195	+	0.499169i
$302$	12.0000	−	20.7846i	0.690522	−	1.19602i
$303$	−7.00000	−	12.1244i	−0.402139	−	0.696526i
$304$	6.00000			0.344124
$305$		0			0
$306$	−1.00000	−	1.73205i	−0.0571662	−	0.0990148i
$307$		0			0			−	1.00000i	$-0.5\pi$
$307$		0			0				1.00000i	$0.5\pi$
$308$	1.00000	+	1.73205i	0.0569803	+	0.0986928i
$309$	−3.00000	+	5.19615i	−0.170664	+	0.295599i
$310$		0			0
$311$		0			0			−	1.00000i	$-0.5\pi$
$311$		0			0				1.00000i	$0.5\pi$
$312$	3.50000	+	0.866025i	0.198148	+	0.0490290i
$313$	12.0000			0.678280			0.339140	−	0.940736i	$-0.389864\pi$
$313$	12.0000			0.678280			0.339140	+	0.940736i	$0.389864\pi$
$314$	−12.5000	+	21.6506i	−0.705416	+	1.22182i
$315$		0			0
$316$	−2.50000	−	4.33013i	−0.140636	−	0.243589i
$317$	−12.0000			−0.673987			−0.336994	−	0.941507i	$-0.609410\pi$
$317$	−12.0000			−0.673987			−0.336994	+	0.941507i	$0.609410\pi$
$318$	−7.00000	−	12.1244i	−0.392541	−	0.679900i
$319$	0.500000	+	0.866025i	0.0279946	+	0.0484881i
$320$		0			0
$321$	−3.00000	−	5.19615i	−0.167444	−	0.290021i
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	6.00000	−	10.3923i	0.333849	−	0.578243i
$324$	1.00000			0.0555556
$325$		0			0
$326$	17.0000			0.941543
$327$	3.00000	−	5.19615i	0.165900	−	0.287348i
$328$	5.00000	−	8.66025i	0.276079	−	0.478183i
$329$	−3.00000	−	5.19615i	−0.165395	−	0.286473i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	−3.00000	−	5.19615i	−0.164646	−	0.285176i
$333$	5.00000			0.273998
$334$	3.50000	+	6.06218i	0.191511	+	0.331708i
$335$		0			0
$336$	1.00000	−	1.73205i	0.0545545	−	0.0944911i
$337$	22.0000			1.19842			0.599208	−	0.800593i	$-0.295482\pi$
$337$	22.0000			1.19842			0.599208	+	0.800593i	$0.295482\pi$
$338$	0.500000	+	12.9904i	0.0271964	+	0.706584i
$339$	−17.0000			−0.923313
$340$		0			0
$341$	1.50000	−	2.59808i	0.0812296	−	0.140694i
$342$	3.00000	+	5.19615i	0.162221	+	0.280976i
$343$	20.0000			1.07990
$344$	−2.50000	−	4.33013i	−0.134791	−	0.233465i
$345$		0			0
$346$	4.00000			0.215041
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	0.516667	−	0.856186i	$-0.327172\pi$
$347$	−9.00000	−	15.5885i	−0.483145	−	0.836832i	−0.999813	+	0.0193540i	$0.993839\pi$
$348$	0.500000	−	0.866025i	0.0268028	−	0.0464238i
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	−0.952998	−	0.302975i	$-0.902020\pi$
$349$	−4.00000	+	6.92820i	−0.214115	+	0.370858i	0.738883	+	0.673833i	$0.235353\pi$
$350$		0			0
$351$	1.00000	+	3.46410i	0.0533761	+	0.184900i
$352$	−1.00000			−0.0533002
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	−0.989960	−	0.141344i	$-0.954858\pi$
$353$	−7.00000	+	12.1244i	−0.372572	+	0.645314i	0.617388	+	0.786659i	$0.288191\pi$
$354$	−2.50000	+	4.33013i	−0.132874	+	0.230144i
$355$		0			0
$356$	10.0000			0.529999
$357$	−2.00000	−	3.46410i	−0.105851	−	0.183340i
$358$	−3.50000	−	6.06218i	−0.184981	−	0.320396i
$359$	12.0000			0.633336			0.316668	−	0.948536i	$-0.397436\pi$
$359$	12.0000			0.633336			0.316668	+	0.948536i	$0.397436\pi$
$360$		0			0
$361$	−8.50000	+	14.7224i	−0.447368	+	0.774865i
$362$	8.00000	−	13.8564i	0.420471	−	0.728277i
$363$	−10.0000			−0.524864
$364$	7.00000	+	1.73205i	0.366900	+	0.0907841i
$365$		0			0
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	18.0000	−	31.1769i	0.939592	−	1.62742i	0.173360	−	0.984859i	$-0.444538\pi$
$367$	18.0000	−	31.1769i	0.939592	−	1.62742i	0.766233	−	0.642563i	$-0.222129\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$	10.0000			0.520579
$370$		0			0
$371$	−14.0000	−	24.2487i	−0.726844	−	1.25893i
$372$	−3.00000			−0.155543
$373$	18.5000	+	32.0429i	0.957894	+	1.65912i	0.727603	+	0.685999i	$0.240634\pi$
$373$	18.5000	+	32.0429i	0.957894	+	1.65912i	0.230291	+	0.973122i	$0.426032\pi$
$374$	−1.00000	+	1.73205i	−0.0517088	+	0.0895622i
$375$		0			0
$376$	3.00000			0.154713
$377$	3.50000	+	0.866025i	0.180259	+	0.0446026i
$378$	2.00000			0.102869
$379$	15.0000	−	25.9808i	0.770498	−	1.33454i	−0.166792	−	0.985992i	$-0.553341\pi$
$379$	15.0000	−	25.9808i	0.770498	−	1.33454i	0.937290	−	0.348550i	$-0.113326\pi$
$380$		0			0
$381$	−7.00000	−	12.1244i	−0.358621	−	0.621150i
$382$	−24.0000			−1.22795
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	−0.971897	−	0.235408i	$-0.924357\pi$
$383$	−13.5000	−	23.3827i	−0.689818	−	1.19480i	0.282079	−	0.959391i	$-0.408976\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	2.00000	+	3.46410i	0.101797	+	0.176318i
$387$	2.50000	−	4.33013i	0.127082	−	0.220113i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	−1.00000			−0.0507020			−0.0253510	−	0.999679i	$-0.508070\pi$
$389$	−1.00000			−0.0507020			−0.0253510	+	0.999679i	$0.508070\pi$
$390$		0			0
$391$	−6.00000			−0.303433
$392$	−1.50000	+	2.59808i	−0.0757614	+	0.131223i
$393$	−6.50000	+	11.2583i	−0.327882	+	0.567908i
$394$	6.00000	+	10.3923i	0.302276	+	0.523557i
$395$		0			0
$396$	−0.500000	−	0.866025i	−0.0251259	−	0.0435194i
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	0.655534	−	0.755166i	$-0.272444\pi$
$397$	−6.50000	−	11.2583i	−0.326226	−	0.565039i	−0.981760	+	0.190126i	$0.939110\pi$
$398$		0			0
$399$	6.00000	+	10.3923i	0.300376	+	0.520266i
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$		0			0
$403$	−3.00000	−	10.3923i	−0.149441	−	0.517678i
$404$	14.0000			0.696526
$405$		0			0
$406$	1.00000	−	1.73205i	0.0496292	−	0.0859602i
$407$	−2.50000	−	4.33013i	−0.123920	−	0.214636i
$408$	2.00000			0.0990148
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	0.984803	+	0.173675i	$0.0555643\pi$
$409$	13.0000	+	22.5167i	0.642809	+	1.11338i	−0.341994	+	0.939702i	$0.611102\pi$
$410$		0			0
$411$	9.00000			0.443937
$412$	−3.00000	−	5.19615i	−0.147799	−	0.255996i
$413$	−5.00000	+	8.66025i	−0.246034	+	0.426143i
$414$	1.50000	−	2.59808i	0.0737210	−	0.127688i
$415$		0			0
$416$	−2.50000	+	2.59808i	−0.122573	+	0.127381i
$417$	10.0000			0.489702
$418$	3.00000	−	5.19615i	0.146735	−	0.254152i
$419$	−2.00000	+	3.46410i	−0.0977064	+	0.169232i	−0.910735	−	0.412991i	$-0.864484\pi$
$419$	−2.00000	+	3.46410i	−0.0977064	+	0.169232i	0.813029	+	0.582224i	$0.197817\pi$
$420$		0			0
$421$	28.0000			1.36464			0.682318	−	0.731055i	$-0.260972\pi$
$421$	28.0000			1.36464			0.682318	+	0.731055i	$0.260972\pi$
$422$	−4.00000	−	6.92820i	−0.194717	−	0.337260i
$423$	1.50000	+	2.59808i	0.0729325	+	0.126323i
$424$	14.0000			0.679900
$425$		0			0
$426$	2.00000	−	3.46410i	0.0969003	−	0.167836i
$427$	−10.0000	+	17.3205i	−0.483934	+	0.838198i
$428$	6.00000			0.290021
$429$	2.50000	−	2.59808i	0.120701	−	0.125436i
$430$		0			0
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	−0.973574	−	0.228373i	$-0.926659\pi$
$431$	−6.00000	+	10.3923i	−0.289010	+	0.500580i	0.684564	+	0.728953i	$0.259993\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	0.991693	−	0.128624i	$-0.0410559\pi$
$433$	8.00000	+	13.8564i	0.384455	+	0.665896i	−0.607238	+	0.794520i	$0.707723\pi$
$434$	−6.00000			−0.288009
$435$		0			0
$436$	3.00000	+	5.19615i	0.143674	+	0.248851i
$437$	18.0000			0.861057
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	0.310228	+	0.950662i	$0.399595\pi$
$439$	−14.0000	+	24.2487i	−0.668184	+	1.15733i	−0.978412	+	0.206666i	$0.933739\pi$
$440$		0			0
$441$	−3.00000			−0.142857
$442$	2.00000	+	6.92820i	0.0951303	+	0.329541i
$443$	−16.0000			−0.760183			−0.380091	−	0.924949i	$-0.624107\pi$
$443$	−16.0000			−0.760183			−0.380091	+	0.924949i	$0.624107\pi$
$444$	−2.50000	+	4.33013i	−0.118645	+	0.205499i
$445$		0			0
$446$	−5.00000	−	8.66025i	−0.236757	−	0.410075i
$447$	11.0000			0.520282
$448$	1.00000	+	1.73205i	0.0472456	+	0.0818317i
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	0.881680	+	0.471848i	$0.156413\pi$
$449$	18.0000	+	31.1769i	0.849473	+	1.47133i	−0.0322072	+	0.999481i	$0.510254\pi$
$450$		0			0
$451$	−5.00000	−	8.66025i	−0.235441	−	0.407795i
$452$	8.50000	−	14.7224i	0.399806	−	0.692485i
$453$	−12.0000	+	20.7846i	−0.563809	+	0.976546i
$454$	20.0000			0.938647
$455$		0			0
$456$	−6.00000			−0.280976
$457$	7.00000	−	12.1244i	0.327446	−	0.567153i	−0.654558	−	0.756012i	$-0.727145\pi$
$457$	7.00000	−	12.1244i	0.327446	−	0.567153i	0.982004	+	0.188858i	$0.0604787\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	1.00000	+	1.73205i	0.0466760	+	0.0808452i
$460$		0			0
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	−0.987801	−	0.155719i	$-0.950230\pi$
$461$	−13.5000	−	23.3827i	−0.628758	−	1.08904i	0.359044	−	0.933321i	$-0.383103\pi$
$462$	−1.00000	−	1.73205i	−0.0465242	−	0.0805823i
$463$	−10.0000			−0.464739			−0.232370	−	0.972628i	$-0.574648\pi$
$463$	−10.0000			−0.464739			−0.232370	+	0.972628i	$0.574648\pi$
$464$	0.500000	+	0.866025i	0.0232119	+	0.0402042i
$465$		0			0
$466$	−1.50000	+	2.59808i	−0.0694862	+	0.120354i
$467$	2.00000			0.0925490			0.0462745	−	0.998929i	$-0.485265\pi$
$467$	2.00000			0.0925490			0.0462745	+	0.998929i	$0.485265\pi$
$468$	−3.50000	−	0.866025i	−0.161788	−	0.0400320i
$469$		0			0
$470$		0			0
$471$	12.5000	−	21.6506i	0.575970	−	0.997609i
$472$	−2.50000	−	4.33013i	−0.115072	−	0.199310i
$473$	−5.00000			−0.229900
$474$	2.50000	+	4.33013i	0.114829	+	0.198889i
$475$		0			0
$476$	4.00000			0.183340
$477$	7.00000	+	12.1244i	0.320508	+	0.555136i
$478$	−4.00000	+	6.92820i	−0.182956	+	0.316889i
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	−0.816711	−	0.577047i	$-0.804205\pi$
$479$	2.00000	−	3.46410i	0.0913823	−	0.158279i	0.908093	+	0.418769i	$0.137538\pi$
$480$		0			0
$481$	−17.5000	−	4.33013i	−0.797931	−	0.197437i
$482$	7.00000			0.318841
$483$	3.00000	−	5.19615i	0.136505	−	0.236433i
$484$	5.00000	−	8.66025i	0.227273	−	0.393648i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	0.887793	−	0.460243i	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$	−5.00000	−	8.66025i	−0.226339	−	0.392031i
$489$	−17.0000			−0.768767
$490$		0			0
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	0.457263	+	0.889332i	$0.348830\pi$
$491$	−12.0000	+	20.7846i	−0.541552	+	0.937996i	−0.998815	+	0.0486647i	$0.984503\pi$
$492$	−5.00000	+	8.66025i	−0.225417	+	0.390434i
$493$	2.00000			0.0900755
$494$	−6.00000	−	20.7846i	−0.269953	−	0.935144i
$495$		0			0
$496$	1.50000	−	2.59808i	0.0673520	−	0.116657i
$497$	4.00000	−	6.92820i	0.179425	−	0.310772i
$498$	3.00000	+	5.19615i	0.134433	+	0.232845i
$499$	−40.0000			−1.79065			−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000			−1.79065			−0.895323	+	0.445418i	$0.853055\pi$
$500$		0			0
$501$	−3.50000	−	6.06218i	−0.156368	−	0.270838i
$502$	−3.00000			−0.133897
$503$	20.0000	+	34.6410i	0.891756	+	1.54457i	0.837769	+	0.546025i	$0.183860\pi$
$503$	20.0000	+	34.6410i	0.891756	+	1.54457i	0.0539870	+	0.998542i	$0.482807\pi$
$504$	−1.00000	+	1.73205i	−0.0445435	+	0.0771517i
$505$		0			0
$506$	−3.00000			−0.133366
$507$	−0.500000	−	12.9904i	−0.0222058	−	0.576923i
$508$	14.0000			0.621150
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	−0.748894	−	0.662690i	$-0.769415\pi$
$509$	4.50000	−	7.79423i	0.199459	−	0.345473i	0.948353	+	0.317217i	$0.102748\pi$
$510$		0			0
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	−1.00000			−0.0441942
$513$	−3.00000	−	5.19615i	−0.132453	−	0.229416i
$514$	−10.5000	−	18.1865i	−0.463135	−	0.802174i
$515$		0			0
$516$	2.50000	+	4.33013i	0.110056	+	0.190623i
$517$	1.50000	−	2.59808i	0.0659699	−	0.114263i
$518$	−5.00000	+	8.66025i	−0.219687	+	0.380510i
$519$	−4.00000			−0.175581
$520$		0			0
$521$	22.0000			0.963837			0.481919	−	0.876216i	$-0.339940\pi$
$521$	22.0000			0.963837			0.481919	+	0.876216i	$0.339940\pi$
$522$	−0.500000	+	0.866025i	−0.0218844	+	0.0379049i
$523$	16.5000	−	28.5788i	0.721495	−	1.24967i	−0.238906	−	0.971043i	$-0.576789\pi$
$523$	16.5000	−	28.5788i	0.721495	−	1.24967i	0.960401	−	0.278623i	$-0.0898779\pi$
$524$	−6.50000	−	11.2583i	−0.283954	−	0.491822i
$525$		0			0
$526$	−11.5000	−	19.9186i	−0.501424	−	0.868492i
$527$	−3.00000	−	5.19615i	−0.130682	−	0.226348i
$528$	1.00000			0.0435194
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	2.50000	−	4.33013i	0.108491	−	0.187912i
$532$	−12.0000			−0.520266
$533$	−35.0000	−	8.66025i	−1.51602	−	0.375117i
$534$	−10.0000			−0.432742
$535$		0			0
$536$		0			0
$537$	3.50000	+	6.06218i	0.151036	+	0.261602i
$538$	−18.0000			−0.776035
$539$	1.50000	+	2.59808i	0.0646096	+	0.111907i
$540$		0			0
$541$	−8.00000			−0.343947			−0.171973	−	0.985102i	$-0.555014\pi$
$541$	−8.00000			−0.343947			−0.171973	+	0.985102i	$0.555014\pi$
$542$	−14.5000	−	25.1147i	−0.622828	−	1.07877i
$543$	−8.00000	+	13.8564i	−0.343313	+	0.594635i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$		0			0
$546$	−7.00000	−	1.73205i	−0.299572	−	0.0741249i
$547$	20.0000			0.855138			0.427569	−	0.903983i	$-0.359370\pi$
$547$	20.0000			0.855138			0.427569	+	0.903983i	$0.359370\pi$
$548$	−4.50000	+	7.79423i	−0.192230	+	0.332953i
$549$	5.00000	−	8.66025i	0.213395	−	0.369611i
$550$		0			0
$551$	−6.00000			−0.255609
$552$	1.50000	+	2.59808i	0.0638442	+	0.110581i
$553$	5.00000	+	8.66025i	0.212622	+	0.368271i
$554$	−19.0000			−0.807233
$555$		0			0
$556$	−5.00000	+	8.66025i	−0.212047	+	0.367277i
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	0.240561	+	0.970634i	$0.422669\pi$
$557$	−17.0000	+	29.4449i	−0.720313	+	1.24762i	−0.960874	+	0.276985i	$0.910665\pi$
$558$	3.00000			0.127000
$559$	−12.5000	+	12.9904i	−0.528694	+	0.549435i
$560$		0			0
$561$	1.00000	−	1.73205i	0.0422200	−	0.0731272i
$562$	−15.0000	+	25.9808i	−0.632737	+	1.09593i
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	−0.999978	−	0.00664037i	$-0.997886\pi$
$563$	−12.0000	−	20.7846i	−0.505740	−	0.875967i	0.494238	−	0.869326i	$-0.335447\pi$
$564$	−3.00000			−0.126323
$565$		0			0
$566$	6.50000	+	11.2583i	0.273215	+	0.473223i
$567$	−2.00000			−0.0839921
$568$	2.00000	+	3.46410i	0.0839181	+	0.145350i
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$		0			0
$571$	4.00000			0.167395			0.0836974	−	0.996491i	$-0.473327\pi$
$571$	4.00000			0.167395			0.0836974	+	0.996491i	$0.473327\pi$
$572$	1.00000	+	3.46410i	0.0418121	+	0.144841i
$573$	24.0000			1.00261
$574$	−10.0000	+	17.3205i	−0.417392	+	0.722944i
$575$		0			0
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	−6.50000	−	11.2583i	−0.270364	−	0.468285i
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$		0			0
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	5.00000	−	8.66025i	0.207257	−	0.358979i
$583$	7.00000	−	12.1244i	0.289910	−	0.502140i
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−14.0000			−0.578335
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	−0.989792	−	0.142520i	$-0.954479\pi$
$587$	−9.00000	+	15.5885i	−0.371470	+	0.643404i	0.618322	+	0.785925i	$0.287813\pi$
$588$	1.50000	−	2.59808i	0.0618590	−	0.107143i
$589$	9.00000	+	15.5885i	0.370839	+	0.642311i
$590$		0			0
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	−2.50000	−	4.33013i	−0.102749	−	0.177967i
$593$	35.0000			1.43728			0.718639	−	0.695383i	$-0.244765\pi$
$593$	35.0000			1.43728			0.718639	+	0.695383i	$0.244765\pi$
$594$	0.500000	+	0.866025i	0.0205152	+	0.0355335i
$595$		0			0
$596$	−5.50000	+	9.52628i	−0.225289	+	0.390212i
$597$		0			0
$598$	−7.50000	+	7.79423i	−0.306698	+	0.318730i
$599$	30.0000			1.22577			0.612883	−	0.790173i	$-0.290010\pi$
$599$	30.0000			1.22577			0.612883	+	0.790173i	$0.290010\pi$
$600$		0			0
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	−0.731774	−	0.681547i	$-0.761308\pi$
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	0.956124	+	0.292962i	$0.0946409\pi$
$602$	5.00000	+	8.66025i	0.203785	+	0.352966i
$603$		0			0
$604$	−12.0000	−	20.7846i	−0.488273	−	0.845714i
$605$		0			0
$606$	−14.0000			−0.568711
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	0.746532	−	0.665350i	$-0.231718\pi$
$607$	−5.00000	−	8.66025i	−0.202944	−	0.351509i	−0.949476	+	0.313841i	$0.898384\pi$
$608$	3.00000	−	5.19615i	0.121666	−	0.210732i
$609$	−1.00000	+	1.73205i	−0.0405220	+	0.0701862i
$610$		0			0
$611$	−3.00000	−	10.3923i	−0.121367	−	0.420428i
$612$	−2.00000			−0.0808452
$613$	−18.5000	+	32.0429i	−0.747208	+	1.29420i	0.201948	+	0.979396i	$0.435273\pi$
$613$	−18.5000	+	32.0429i	−0.747208	+	1.29420i	−0.949156	+	0.314806i	$0.898061\pi$
$614$		0			0
$615$		0			0
$616$	2.00000			0.0805823
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	0.894639	−	0.446790i	$-0.147433\pi$
$617$	1.50000	+	2.59808i	0.0603877	+	0.104595i	−0.834251	+	0.551385i	$0.814100\pi$
$618$	3.00000	+	5.19615i	0.120678	+	0.209020i
$619$	−10.0000			−0.401934			−0.200967	−	0.979598i	$-0.564408\pi$
$619$	−10.0000			−0.401934			−0.200967	+	0.979598i	$0.564408\pi$
$620$		0			0
$621$	−1.50000	+	2.59808i	−0.0601929	+	0.104257i
$622$		0			0
$623$	−20.0000			−0.801283
$624$	2.50000	−	2.59808i	0.100080	−	0.104006i
$625$		0			0
$626$	6.00000	−	10.3923i	0.239808	−	0.415360i
$627$	−3.00000	+	5.19615i	−0.119808	+	0.207514i
$628$	12.5000	+	21.6506i	0.498804	+	0.863954i
$629$	−10.0000			−0.398726
$630$		0			0
$631$	−24.0000	−	41.5692i	−0.955425	−	1.65484i	−0.733393	−	0.679805i	$-0.762064\pi$
$631$	−24.0000	−	41.5692i	−0.955425	−	1.65484i	−0.222032	−	0.975039i	$-0.571269\pi$
$632$	−5.00000			−0.198889
$633$	4.00000	+	6.92820i	0.158986	+	0.275371i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	−14.0000			−0.555136
$637$	10.5000	+	2.59808i	0.416025	+	0.102940i
$638$	1.00000			0.0395904
$639$	−2.00000	+	3.46410i	−0.0791188	+	0.137038i
$640$		0			0
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$	−6.00000			−0.236801
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	−0.926750	−	0.375680i	$-0.877409\pi$
$643$	−20.0000	−	34.6410i	−0.788723	−	1.36611i	0.138027	−	0.990429i	$-0.455924\pi$
$644$	3.00000	+	5.19615i	0.118217	+	0.204757i
$645$		0			0
$646$	−6.00000	−	10.3923i	−0.236067	−	0.408880i
$647$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$647$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	−5.00000			−0.196267
$650$		0			0
$651$	6.00000			0.235159
$652$	8.50000	−	14.7224i	0.332886	−	0.576575i
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	−0.986634	−	0.162951i	$-0.947899\pi$
$653$	−9.00000	+	15.5885i	−0.352197	+	0.610023i	0.634437	+	0.772975i	$0.281232\pi$
$654$	−3.00000	−	5.19615i	−0.117309	−	0.203186i
$655$		0			0
$656$	−5.00000	−	8.66025i	−0.195217	−	0.338126i
$657$	−1.00000	−	1.73205i	−0.0390137	−	0.0675737i
$658$	−6.00000			−0.233904
$659$	6.50000	+	11.2583i	0.253204	+	0.438562i	0.964406	−	0.264425i	$-0.0851823\pi$
$659$	6.50000	+	11.2583i	0.253204	+	0.438562i	−0.711202	+	0.702988i	$0.751849\pi$
$660$		0			0
$661$	6.00000	−	10.3923i	0.233373	−	0.404214i	−0.725426	−	0.688301i	$-0.758357\pi$
$661$	6.00000	−	10.3923i	0.233373	−	0.404214i	0.958799	+	0.284087i	$0.0916904\pi$
$662$	−4.00000			−0.155464
$663$	−2.00000	−	6.92820i	−0.0776736	−	0.269069i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	2.50000	−	4.33013i	0.0968730	−	0.167789i
$667$	1.50000	+	2.59808i	0.0580802	+	0.100598i
$668$	7.00000			0.270838
$669$	5.00000	+	8.66025i	0.193311	+	0.334825i
$670$		0			0
$671$	−10.0000			−0.386046
$672$	−1.00000	−	1.73205i	−0.0385758	−	0.0668153i
$673$	−8.00000	+	13.8564i	−0.308377	+	0.534125i	−0.978008	−	0.208569i	$-0.933119\pi$
$673$	−8.00000	+	13.8564i	−0.308377	+	0.534125i	0.669630	+	0.742695i	$0.266453\pi$
$674$	11.0000	−	19.0526i	0.423704	−	0.733877i
$675$		0			0
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$	−8.50000	+	14.7224i	−0.326441	+	0.565412i
$679$	10.0000	−	17.3205i	0.383765	−	0.664700i
$680$		0			0
$681$	−20.0000			−0.766402
$682$	−1.50000	−	2.59808i	−0.0574380	−	0.0994855i
$683$	−22.0000	−	38.1051i	−0.841807	−	1.45805i	−0.888366	−	0.459136i	$-0.848159\pi$
$683$	−22.0000	−	38.1051i	−0.841807	−	1.45805i	0.0465592	−	0.998916i	$-0.485174\pi$
$684$	6.00000			0.229416
$685$		0			0
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$	−11.0000	+	19.0526i	−0.419676	+	0.726900i
$688$	−5.00000			−0.190623
$689$	−14.0000	−	48.4974i	−0.533358	−	1.84760i
$690$		0			0
$691$	7.00000	−	12.1244i	0.266293	−	0.461232i	−0.701609	−	0.712562i	$-0.747535\pi$
$691$	7.00000	−	12.1244i	0.266293	−	0.461232i	0.967901	+	0.251330i	$0.0808679\pi$
$692$	2.00000	−	3.46410i	0.0760286	−	0.131685i
$693$	1.00000	+	1.73205i	0.0379869	+	0.0657952i
$694$	−18.0000			−0.683271
$695$		0			0
$696$	−0.500000	−	0.866025i	−0.0189525	−	0.0328266i
$697$	−20.0000			−0.757554
$698$	4.00000	+	6.92820i	0.151402	+	0.262236i
$699$	1.50000	−	2.59808i	0.0567352	−	0.0982683i
$700$		0			0
$701$	23.0000			0.868698			0.434349	−	0.900745i	$-0.356978\pi$
$701$	23.0000			0.868698			0.434349	+	0.900745i	$0.356978\pi$
$702$	3.50000	+	0.866025i	0.132099	+	0.0326860i
$703$	30.0000			1.13147
$704$	−0.500000	+	0.866025i	−0.0188445	+	0.0326396i
$705$		0			0
$706$	7.00000	+	12.1244i	0.263448	+	0.456306i
$707$	−28.0000			−1.05305
$708$	2.50000	+	4.33013i	0.0939558	+	0.162736i
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$		0			0
$711$	−2.50000	−	4.33013i	−0.0937573	−	0.162392i
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$	4.50000	−	7.79423i	0.168526	−	0.291896i
$714$	−4.00000			−0.149696
$715$		0			0
$716$	−7.00000			−0.261602
$717$	4.00000	−	6.92820i	0.149383	−	0.258738i
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.833744	+	0.552151i	$0.186193\pi$
$719$	24.0000	+	41.5692i	0.895049	+	1.55027i	0.0613050	+	0.998119i	$0.480474\pi$
$720$		0			0
$721$	6.00000	+	10.3923i	0.223452	+	0.387030i
$722$	8.50000	+	14.7224i	0.316337	+	0.547912i
$723$	−7.00000			−0.260333
$724$	−8.00000	−	13.8564i	−0.297318	−	0.514969i
$725$		0			0
$726$	−5.00000	+	8.66025i	−0.185567	+	0.321412i
$727$	32.0000			1.18681			0.593407	−	0.804902i	$-0.297782\pi$
$727$	32.0000			1.18681			0.593407	+	0.804902i	$0.297782\pi$
$728$	5.00000	−	5.19615i	0.185312	−	0.192582i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−5.00000	+	8.66025i	−0.184932	+	0.320311i
$732$	5.00000	+	8.66025i	0.184805	+	0.320092i
$733$	−14.0000			−0.517102			−0.258551	−	0.965998i	$-0.583245\pi$
$733$	−14.0000			−0.517102			−0.258551	+	0.965998i	$0.583245\pi$
$734$	−18.0000	−	31.1769i	−0.664392	−	1.15076i
$735$		0			0
$736$	−3.00000			−0.110581
$737$		0			0
$738$	5.00000	−	8.66025i	0.184053	−	0.318788i
$739$	−12.0000	+	20.7846i	−0.441427	+	0.764574i	−0.997796	−	0.0663614i	$-0.978861\pi$
$739$	−12.0000	+	20.7846i	−0.441427	+	0.764574i	0.556369	+	0.830936i	$0.312194\pi$
$740$		0			0
$741$	6.00000	+	20.7846i	0.220416	+	0.763542i
$742$	−28.0000			−1.02791
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	−0.970173	−	0.242415i	$-0.922060\pi$
$743$	−7.50000	+	12.9904i	−0.275148	+	0.476571i	0.695024	+	0.718986i	$0.255394\pi$
$744$	−1.50000	+	2.59808i	−0.0549927	+	0.0952501i
$745$		0			0
$746$	37.0000			1.35467
$747$	−3.00000	−	5.19615i	−0.109764	−	0.190117i
$748$	1.00000	+	1.73205i	0.0365636	+	0.0633300i
$749$	−12.0000			−0.438470
$750$		0			0
$751$	−20.5000	+	35.5070i	−0.748056	+	1.29567i	0.200698	+	0.979653i	$0.435679\pi$
$751$	−20.5000	+	35.5070i	−0.748056	+	1.29567i	−0.948753	+	0.316017i	$0.897654\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	3.00000			0.109326
$754$	2.50000	−	2.59808i	0.0910446	−	0.0946164i
$755$		0			0
$756$	1.00000	−	1.73205i	0.0363696	−	0.0629941i
$757$	−27.0000	+	46.7654i	−0.981332	+	1.69972i	−0.324109	+	0.946020i	$0.605065\pi$
$757$	−27.0000	+	46.7654i	−0.981332	+	1.69972i	−0.657222	+	0.753697i	$0.728269\pi$
$758$	−15.0000	−	25.9808i	−0.544825	−	0.943664i
$759$	3.00000			0.108893
$760$		0			0
$761$	10.0000	+	17.3205i	0.362500	+	0.627868i	0.988372	−	0.152058i	$-0.0485900\pi$
$761$	10.0000	+	17.3205i	0.362500	+	0.627868i	−0.625872	+	0.779926i	$0.715257\pi$
$762$	−14.0000			−0.507166
$763$	−6.00000	−	10.3923i	−0.217215	−	0.376227i
$764$	−12.0000	+	20.7846i	−0.434145	+	0.751961i
$765$		0			0
$766$	−27.0000			−0.975550
$767$	−12.5000	+	12.9904i	−0.451349	+	0.469055i
$768$	1.00000			0.0360844
$769$	14.5000	−	25.1147i	0.522883	−	0.905661i	−0.476762	−	0.879032i	$-0.658190\pi$
$769$	14.5000	−	25.1147i	0.522883	−	0.905661i	0.999645	−	0.0266282i	$-0.00847701\pi$
$770$		0			0
$771$	10.5000	+	18.1865i	0.378148	+	0.654972i
$772$	4.00000			0.143963
$773$	−8.00000	−	13.8564i	−0.287740	−	0.498380i	0.685530	−	0.728044i	$-0.259571\pi$
$773$	−8.00000	−	13.8564i	−0.287740	−	0.498380i	−0.973270	+	0.229664i	$0.926237\pi$
$774$	−2.50000	−	4.33013i	−0.0898606	−	0.155643i
$775$		0			0
$776$	5.00000	+	8.66025i	0.179490	+	0.310885i
$777$	5.00000	−	8.66025i	0.179374	−	0.310685i
$778$	−0.500000	+	0.866025i	−0.0179259	+	0.0310485i
$779$	60.0000			2.14972
$780$		0			0
$781$	4.00000			0.143131
$782$	−3.00000	+	5.19615i	−0.107280	+	0.185814i
$783$	0.500000	−	0.866025i	0.0178685	−	0.0309492i
$784$	1.50000	+	2.59808i	0.0535714	+	0.0927884i
$785$		0			0
$786$	6.50000	+	11.2583i	0.231847	+	0.401571i
$787$	12.5000	+	21.6506i	0.445577	+	0.771762i	0.998092	−	0.0617409i	$-0.0196653\pi$
$787$	12.5000	+	21.6506i	0.445577	+	0.771762i	−0.552515	+	0.833503i	$0.686332\pi$
$788$	12.0000			0.427482
$789$	11.5000	+	19.9186i	0.409411	+	0.709120i
$790$		0			0
$791$	−17.0000	+	29.4449i	−0.604450	+	1.04694i
$792$	−1.00000			−0.0355335
$793$	−25.0000	+	25.9808i	−0.887776	+	0.922604i
$794$	−13.0000			−0.461353
$795$		0			0
$796$		0			0
$797$	−26.0000	−	45.0333i	−0.920967	−	1.59516i	−0.797922	−	0.602761i	$-0.794067\pi$
$797$	−26.0000	−	45.0333i	−0.920967	−	1.59516i	−0.123045	−	0.992401i	$-0.539266\pi$
$798$	12.0000			0.424795
$799$	−3.00000	−	5.19615i	−0.106132	−	0.183827i
$800$		0			0
$801$	10.0000			0.353333
$802$	−6.00000	−	10.3923i	−0.211867	−	0.366965i
$803$	−1.00000	+	1.73205i	−0.0352892	+	0.0611227i
$804$		0			0
$805$		0			0
$806$	−10.5000	−	2.59808i	−0.369847	−	0.0915133i
$807$	18.0000			0.633630
$808$	7.00000	−	12.1244i	0.246259	−	0.426533i
$809$	−1.00000	+	1.73205i	−0.0351581	+	0.0608957i	−0.883069	−	0.469243i	$-0.844527\pi$
$809$	−1.00000	+	1.73205i	−0.0351581	+	0.0608957i	0.847911	+	0.530139i	$0.177860\pi$
$810$		0			0
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$	−1.00000	−	1.73205i	−0.0350931	−	0.0607831i
$813$	14.5000	+	25.1147i	0.508537	+	0.880812i
$814$	−5.00000			−0.175250
$815$		0			0
$816$	1.00000	−	1.73205i	0.0350070	−	0.0606339i
$817$	15.0000	−	25.9808i	0.524784	−	0.908952i
$818$	26.0000			0.909069
$819$	7.00000	+	1.73205i	0.244600	+	0.0605228i
$820$		0			0
$821$	−11.5000	+	19.9186i	−0.401353	+	0.695163i	−0.993889	−	0.110380i	$-0.964793\pi$
$821$	−11.5000	+	19.9186i	−0.401353	+	0.695163i	0.592537	+	0.805543i	$0.298127\pi$
$822$	4.50000	−	7.79423i	0.156956	−	0.271855i
$823$	−11.0000	−	19.0526i	−0.383436	−	0.664130i	0.608115	−	0.793849i	$-0.291926\pi$
$823$	−11.0000	−	19.0526i	−0.383436	−	0.664130i	−0.991551	+	0.129719i	$0.958593\pi$
$824$	−6.00000			−0.209020
$825$		0			0
$826$	5.00000	+	8.66025i	0.173972	+	0.301329i
$827$	18.0000			0.625921			0.312961	−	0.949766i	$-0.398679\pi$
$827$	18.0000			0.625921			0.312961	+	0.949766i	$0.398679\pi$
$828$	−1.50000	−	2.59808i	−0.0521286	−	0.0902894i
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	−0.998480	−	0.0551154i	$-0.982447\pi$
$829$	−13.0000	+	22.5167i	−0.451509	+	0.782036i	0.546971	+	0.837151i	$0.315781\pi$
$830$		0			0
$831$	19.0000			0.659103
$832$	1.00000	+	3.46410i	0.0346688	+	0.120096i
$833$	6.00000			0.207888
$834$	5.00000	−	8.66025i	0.173136	−	0.299880i
$835$		0			0
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$	−3.00000			−0.103695
$838$	2.00000	+	3.46410i	0.0690889	+	0.119665i
$839$	−19.0000	−	32.9090i	−0.655953	−	1.13614i	−0.981654	−	0.190671i	$-0.938934\pi$
$839$	−19.0000	−	32.9090i	−0.655953	−	1.13614i	0.325701	−	0.945473i	$-0.394400\pi$
$840$		0			0
$841$	14.0000	+	24.2487i	0.482759	+	0.836162i
$842$	14.0000	−	24.2487i	0.482472	−	0.835666i
$843$	15.0000	−	25.9808i	0.516627	−	0.894825i
$844$	−8.00000			−0.275371
$845$		0			0
$846$	3.00000			0.103142
$847$	−10.0000	+	17.3205i	−0.343604	+	0.595140i
$848$	7.00000	−	12.1244i	0.240381	−	0.416352i
$849$	−6.50000	−	11.2583i	−0.223079	−	0.386385i
$850$		0			0
$851$	−7.50000	−	12.9904i	−0.257097	−	0.445305i
$852$	−2.00000	−	3.46410i	−0.0685189	−	0.118678i
$853$	−7.00000			−0.239675			−0.119838	−	0.992793i	$-0.538237\pi$
$853$	−7.00000			−0.239675			−0.119838	+	0.992793i	$0.538237\pi$
$854$	10.0000	+	17.3205i	0.342193	+	0.592696i
$855$		0			0
$856$	3.00000	−	5.19615i	0.102538	−	0.177601i
$857$	35.0000			1.19558			0.597789	−	0.801654i	$-0.296046\pi$
$857$	35.0000			1.19558			0.597789	+	0.801654i	$0.296046\pi$
$858$	−1.00000	−	3.46410i	−0.0341394	−	0.118262i
$859$	18.0000			0.614152			0.307076	−	0.951685i	$-0.400649\pi$
$859$	18.0000			0.614152			0.307076	+	0.951685i	$0.400649\pi$
$860$		0			0
$861$	10.0000	−	17.3205i	0.340799	−	0.590281i
$862$	6.00000	+	10.3923i	0.204361	+	0.353963i
$863$	51.0000			1.73606			0.868030	−	0.496512i	$-0.165386\pi$
$863$	51.0000			1.73606			0.868030	+	0.496512i	$0.165386\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$		0			0
$866$	16.0000			0.543702
$867$	6.50000	+	11.2583i	0.220752	+	0.382353i
$868$	−3.00000	+	5.19615i	−0.101827	+	0.176369i
$869$	−2.50000	+	4.33013i	−0.0848067	+	0.146889i
$870$		0			0
$871$		0			0
$872$	6.00000			0.203186
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$	9.00000	−	15.5885i	0.304430	−	0.527287i
$875$		0			0
$876$	2.00000			0.0675737
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	0.954652	−	0.297724i	$-0.0962275\pi$
$877$	6.50000	+	11.2583i	0.219489	+	0.380167i	−0.735163	+	0.677891i	$0.762894\pi$
$878$	14.0000	+	24.2487i	0.472477	+	0.818354i
$879$	14.0000			0.472208
$880$		0			0
$881$	−27.0000	+	46.7654i	−0.909653	+	1.57557i	−0.0951067	+	0.995467i	$0.530319\pi$
$881$	−27.0000	+	46.7654i	−0.909653	+	1.57557i	−0.814546	+	0.580098i	$0.803014\pi$
$882$	−1.50000	+	2.59808i	−0.0505076	+	0.0874818i
$883$	1.00000			0.0336527			0.0168263	−	0.999858i	$-0.494644\pi$
$883$	1.00000			0.0336527			0.0168263	+	0.999858i	$0.494644\pi$
$884$	7.00000	+	1.73205i	0.235435	+	0.0582552i
$885$		0			0
$886$	−8.00000	+	13.8564i	−0.268765	+	0.465515i
$887$	0.500000	−	0.866025i	0.0167884	−	0.0290783i	−0.857509	−	0.514469i	$-0.827989\pi$
$887$	0.500000	−	0.866025i	0.0167884	−	0.0290783i	0.874298	+	0.485390i	$0.161323\pi$
$888$	2.50000	+	4.33013i	0.0838945	+	0.145310i
$889$	−28.0000			−0.939090
$890$		0			0
$891$	−0.500000	−	0.866025i	−0.0167506	−	0.0290129i
$892$	−10.0000			−0.334825
$893$	9.00000	+	15.5885i	0.301174	+	0.521648i
$894$	5.50000	−	9.52628i	0.183948	−	0.318606i
$895$		0			0
$896$	2.00000			0.0668153
$897$	7.50000	−	7.79423i	0.250418	−	0.260242i
$898$	36.0000			1.20134
$899$	−1.50000	+	2.59808i	−0.0500278	+	0.0866507i
$900$		0			0
$901$	−14.0000	−	24.2487i	−0.466408	−	0.807842i
$902$	−10.0000			−0.332964
$903$	−5.00000	−	8.66025i	−0.166390	−	0.288195i
$904$	−8.50000	−	14.7224i	−0.282706	−	0.489661i
$905$		0			0
$906$	12.0000	+	20.7846i	0.398673	+	0.690522i
$907$	−26.5000	+	45.8993i	−0.879918	+	1.52406i	−0.0284883	+	0.999594i	$0.509069\pi$
$907$	−26.5000	+	45.8993i	−0.879918	+	1.52406i	−0.851430	+	0.524469i	$0.824264\pi$
$908$	10.0000	−	17.3205i	0.331862	−	0.574801i
$909$	14.0000			0.464351
$910$		0			0
$911$	34.0000			1.12647			0.563235	−	0.826297i	$-0.309557\pi$
$911$	34.0000			1.12647			0.563235	+	0.826297i	$0.309557\pi$
$912$	−3.00000	+	5.19615i	−0.0993399	+	0.172062i
$913$	−3.00000	+	5.19615i	−0.0992855	+	0.171968i
$914$	−7.00000	−	12.1244i	−0.231539	−	0.401038i
$915$		0			0
$916$	−11.0000	−	19.0526i	−0.363450	−	0.629514i
$917$	13.0000	+	22.5167i	0.429298	+	0.743566i
$918$	2.00000			0.0660098
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.793742	+	0.608254i	$0.208130\pi$
$919$	28.0000	+	48.4974i	0.923635	+	1.59978i	0.129893	+	0.991528i	$0.458537\pi$
$920$		0			0
$921$		0			0
$922$	−27.0000			−0.889198
$923$	10.0000	−	10.3923i	0.329154	−	0.342067i
$924$	−2.00000			−0.0657952
$925$		0			0
$926$	−5.00000	+	8.66025i	−0.164310	+	0.284594i
$927$	−3.00000	−	5.19615i	−0.0985329	−	0.170664i
$928$	1.00000			0.0328266
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	0.599228	−	0.800578i	$-0.295474\pi$
$929$	−12.0000	−	20.7846i	−0.393707	−	0.681921i	−0.992935	+	0.118657i	$0.962141\pi$
$930$		0			0
$931$	−18.0000			−0.589926
$932$	1.50000	+	2.59808i	0.0491341	+	0.0851028i
$933$		0			0
$934$	1.00000	−	1.73205i	0.0327210	−	0.0566744i
$935$		0			0
$936$	−2.50000	+	2.59808i	−0.0817151	+	0.0849208i
$937$	18.0000			0.588034			0.294017	−	0.955800i	$-0.405008\pi$
$937$	18.0000			0.588034			0.294017	+	0.955800i	$0.405008\pi$
$938$		0			0
$939$	−6.00000	+	10.3923i	−0.195803	+	0.339140i
$940$		0			0
$941$	26.0000			0.847576			0.423788	−	0.905761i	$-0.360700\pi$
$941$	26.0000			0.847576			0.423788	+	0.905761i	$0.360700\pi$
$942$	−12.5000	−	21.6506i	−0.407272	−	0.705416i
$943$	−15.0000	−	25.9808i	−0.488467	−	0.846050i
$944$	−5.00000			−0.162736
$945$		0			0
$946$	−2.50000	+	4.33013i	−0.0812820	+	0.140785i
$947$	26.0000	−	45.0333i	0.844886	−	1.46339i	−0.0408333	−	0.999166i	$-0.513001\pi$
$947$	26.0000	−	45.0333i	0.844886	−	1.46339i	0.885720	−	0.464220i	$-0.153665\pi$
$948$	5.00000			0.162392
$949$	2.00000	+	6.92820i	0.0649227	+	0.224899i
$950$		0			0
$951$	6.00000	−	10.3923i	0.194563	−	0.336994i
$952$	2.00000	−	3.46410i	0.0648204	−	0.112272i
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	0.961553	−	0.274620i	$-0.0885520\pi$
$953$	7.50000	+	12.9904i	0.242949	+	0.420800i	−0.718604	+	0.695419i	$0.755219\pi$
$954$	14.0000			0.453267
$955$		0			0
$956$	4.00000	+	6.92820i	0.129369	+	0.224074i
$957$	−1.00000			−0.0323254
$958$	−2.00000	−	3.46410i	−0.0646171	−	0.111920i
$959$	9.00000	−	15.5885i	0.290625	−	0.503378i
$960$		0			0
$961$	−22.0000			−0.709677
$962$	−12.5000	+	12.9904i	−0.403016	+	0.418827i
$963$	6.00000			0.193347
$964$	3.50000	−	6.06218i	0.112727	−	0.195250i
$965$		0			0
$966$	−3.00000	−	5.19615i	−0.0965234	−	0.167183i
$967$	−16.0000			−0.514525			−0.257263	−	0.966342i	$-0.582821\pi$
$967$	−16.0000			−0.514525			−0.257263	+	0.966342i	$0.582821\pi$
$968$	−5.00000	−	8.66025i	−0.160706	−	0.278351i
$969$	6.00000	+	10.3923i	0.192748	+	0.333849i
$970$		0			0
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	0.985024	+	0.172418i	$0.0551581\pi$
$971$	20.0000	+	34.6410i	0.641831	+	1.11168i	−0.343193	+	0.939265i	$0.611509\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	10.0000	−	17.3205i	0.320585	−	0.555270i
$974$	2.00000			0.0640841
$975$		0			0
$976$	−10.0000			−0.320092
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	0.364900	+	0.931047i	$0.381103\pi$
$977$	−19.5000	+	33.7750i	−0.623860	+	1.08056i	−0.988760	+	0.149511i	$0.952230\pi$
$978$	−8.50000	+	14.7224i	−0.271800	+	0.470771i
$979$	−5.00000	−	8.66025i	−0.159801	−	0.276783i
$980$		0			0
$981$	3.00000	+	5.19615i	0.0957826	+	0.165900i
$982$	12.0000	+	20.7846i	0.382935	+	0.663264i
$983$	25.0000			0.797376			0.398688	−	0.917087i	$-0.369466\pi$
$983$	25.0000			0.797376			0.398688	+	0.917087i	$0.369466\pi$
$984$	5.00000	+	8.66025i	0.159394	+	0.276079i
$985$		0			0
$986$	1.00000	−	1.73205i	0.0318465	−	0.0551597i
$987$	6.00000			0.190982
$988$	−21.0000	−	5.19615i	−0.668099	−	0.165312i
$989$	−15.0000			−0.476972
$990$		0			0
$991$	−19.5000	+	33.7750i	−0.619438	+	1.07290i	0.370151	+	0.928972i	$0.379306\pi$
$991$	−19.5000	+	33.7750i	−0.619438	+	1.07290i	−0.989588	+	0.143926i	$0.954027\pi$
$992$	−1.50000	−	2.59808i	−0.0476250	−	0.0824890i
$993$	4.00000			0.126936
$994$	−4.00000	−	6.92820i	−0.126872	−	0.219749i
$995$		0			0
$996$	6.00000			0.190117
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	0.849756	−	0.527176i	$-0.176749\pi$
$997$	−1.00000	−	1.73205i	−0.0316703	−	0.0548546i	−0.881426	+	0.472322i	$0.843416\pi$
$998$	−20.0000	+	34.6410i	−0.633089	+	1.09654i
$999$	−2.50000	+	4.33013i	−0.0790965	+	0.136999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.i.s.451.1		2
5.2	odd	4		1950.2.z.h.1699.2		4
5.3	odd	4		1950.2.z.h.1699.1		4
5.4	even	2		390.2.i.a.61.1	✓	2
13.3	even	3	inner	1950.2.i.s.601.1		2
15.14	odd	2		1170.2.i.k.451.1		2
65.3	odd	12		1950.2.z.h.1849.2		4
65.4	even	6		5070.2.a.f.1.1		1
65.9	even	6		5070.2.a.o.1.1		1
65.19	odd	12		5070.2.b.g.1351.1		2
65.29	even	6		390.2.i.a.211.1	yes	2
65.42	odd	12		1950.2.z.h.1849.1		4
65.59	odd	12		5070.2.b.g.1351.2		2
195.29	odd	6		1170.2.i.k.991.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.i.a.61.1	✓	2	5.4	even	2
390.2.i.a.211.1	yes	2	65.29	even	6
1170.2.i.k.451.1		2	15.14	odd	2
1170.2.i.k.991.1		2	195.29	odd	6
1950.2.i.s.451.1		2	1.1	even	1	trivial
1950.2.i.s.601.1		2	13.3	even	3	inner
1950.2.z.h.1699.1		4	5.3	odd	4
1950.2.z.h.1699.2		4	5.2	odd	4
1950.2.z.h.1849.1		4	65.42	odd	12
1950.2.z.h.1849.2		4	65.3	odd	12
5070.2.a.f.1.1		1	65.4	even	6
5070.2.a.o.1.1		1	65.9	even	6
5070.2.b.g.1351.1		2	65.19	odd	12
5070.2.b.g.1351.2		2	65.59	odd	12

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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(1.00000 + 1.73205i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{11} +1.00000 q^{12} +(1.00000 + 3.46410i) q^{13} +2.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} -1.00000 q^{18} +(-3.00000 - 5.19615i) q^{19} -2.00000 q^{21} +(0.500000 + 0.866025i) q^{22} +(-1.50000 + 2.59808i) q^{23} +(0.500000 - 0.866025i) q^{24} +(3.50000 + 0.866025i) q^{26} +1.00000 q^{27} +(1.00000 - 1.73205i) q^{28} +(0.500000 - 0.866025i) q^{29} -3.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.500000 - 0.866025i) q^{33} +2.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(-2.50000 + 4.33013i) q^{37} -6.00000 q^{38} +(-3.50000 - 0.866025i) q^{39} +(-5.00000 + 8.66025i) q^{41} +(-1.00000 + 1.73205i) q^{42} +(2.50000 + 4.33013i) q^{43} +1.00000 q^{44} +(1.50000 + 2.59808i) q^{46} -3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(1.50000 - 2.59808i) q^{49} -2.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -14.0000 q^{53} +(0.500000 - 0.866025i) q^{54} +(-1.00000 - 1.73205i) q^{56} +6.00000 q^{57} +(-0.500000 - 0.866025i) q^{58} +(2.50000 + 4.33013i) q^{59} +(5.00000 + 8.66025i) q^{61} +(-1.50000 + 2.59808i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -1.00000 q^{66} +(1.00000 - 1.73205i) q^{68} +(-1.50000 - 2.59808i) q^{69} +(-2.00000 - 3.46410i) q^{71} +(0.500000 + 0.866025i) q^{72} +2.00000 q^{73} +(2.50000 + 4.33013i) q^{74} +(-3.00000 + 5.19615i) q^{76} -2.00000 q^{77} +(-2.50000 + 2.59808i) q^{78} +5.00000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(5.00000 + 8.66025i) q^{82} +6.00000 q^{83} +(1.00000 + 1.73205i) q^{84} +5.00000 q^{86} +(0.500000 + 0.866025i) q^{87} +(0.500000 - 0.866025i) q^{88} +(-5.00000 + 8.66025i) q^{89} +(-5.00000 + 5.19615i) q^{91} +3.00000 q^{92} +(1.50000 - 2.59808i) q^{93} +(-1.50000 + 2.59808i) q^{94} -1.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(-1.50000 - 2.59808i) q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - q^3 - q^4 + q^6 + 2 * q^7 - 2 * q^8 - q^9	\( 2 q + q^{2} - q^{3} - q^{4} + q^{6} + 2 q^{7} - 2 q^{8} - q^{9} - q^{11} + 2 q^{12} + 2 q^{13} + 4 q^{14} - q^{16} + 2 q^{17} - 2 q^{18} - 6 q^{19} - 4 q^{21} + q^{22} - 3 q^{23} + q^{24} + 7 q^{26} + 2 q^{27} + 2 q^{28} + q^{29} - 6 q^{31} + q^{32} - q^{33} + 4 q^{34} - q^{36} - 5 q^{37} - 12 q^{38} - 7 q^{39} - 10 q^{41} - 2 q^{42} + 5 q^{43} + 2 q^{44} + 3 q^{46} - 6 q^{47} - q^{48} + 3 q^{49} - 4 q^{51} + 5 q^{52} - 28 q^{53} + q^{54} - 2 q^{56} + 12 q^{57} - q^{58} + 5 q^{59} + 10 q^{61} - 3 q^{62} + 2 q^{63} + 2 q^{64} - 2 q^{66} + 2 q^{68} - 3 q^{69} - 4 q^{71} + q^{72} + 4 q^{73} + 5 q^{74} - 6 q^{76} - 4 q^{77} - 5 q^{78} + 10 q^{79} - q^{81} + 10 q^{82} + 12 q^{83} + 2 q^{84} + 10 q^{86} + q^{87} + q^{88} - 10 q^{89} - 10 q^{91} + 6 q^{92} + 3 q^{93} - 3 q^{94} - 2 q^{96} - 10 q^{97} - 3 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q + q^2 - q^3 - q^4 + q^6 + 2 * q^7 - 2 * q^8 - q^9 - q^11 + 2 * q^12 + 2 * q^13 + 4 * q^14 - q^16 + 2 * q^17 - 2 * q^18 - 6 * q^19 - 4 * q^21 + q^22 - 3 * q^23 + q^24 + 7 * q^26 + 2 * q^27 + 2 * q^28 + q^29 - 6 * q^31 + q^32 - q^33 + 4 * q^34 - q^36 - 5 * q^37 - 12 * q^38 - 7 * q^39 - 10 * q^41 - 2 * q^42 + 5 * q^43 + 2 * q^44 + 3 * q^46 - 6 * q^47 - q^48 + 3 * q^49 - 4 * q^51 + 5 * q^52 - 28 * q^53 + q^54 - 2 * q^56 + 12 * q^57 - q^58 + 5 * q^59 + 10 * q^61 - 3 * q^62 + 2 * q^63 + 2 * q^64 - 2 * q^66 + 2 * q^68 - 3 * q^69 - 4 * q^71 + q^72 + 4 * q^73 + 5 * q^74 - 6 * q^76 - 4 * q^77 - 5 * q^78 + 10 * q^79 - q^81 + 10 * q^82 + 12 * q^83 + 2 * q^84 + 10 * q^86 + q^87 + q^88 - 10 * q^89 - 10 * q^91 + 6 * q^92 + 3 * q^93 - 3 * q^94 - 2 * q^96 - 10 * q^97 - 3 * q^98 + 2 * q^99

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