LMFDB - Embedded newform 231.2.i.a.67.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [231,2,Mod(67,231)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(231, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("231.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 231 = 3 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	231.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:	$1.84454428669$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			67.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	231.67
Dual form			231.2.i.a.100.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +4.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-2.50000 + 0.866025i) q^{21} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.50000 + 0.866025i) q^{28} -5.00000 q^{29} +(5.00000 - 8.66025i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(-0.500000 - 0.866025i) q^{33} +3.00000 q^{34} -1.00000 q^{36} +(5.50000 + 9.52628i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(2.00000 - 3.46410i) q^{39} +10.0000 q^{41} +(2.00000 + 1.73205i) q^{42} -3.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{46} +(4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(1.50000 + 2.59808i) q^{51} +(2.00000 - 3.46410i) q^{52} +(4.00000 - 6.92820i) q^{53} +(0.500000 + 0.866025i) q^{54} +(6.00000 + 5.19615i) q^{56} -1.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(4.50000 - 7.79423i) q^{59} +(1.00000 + 1.73205i) q^{61} -10.0000 q^{62} +(-0.500000 + 2.59808i) q^{63} +7.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} +1.00000 q^{69} -7.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(5.50000 - 9.52628i) q^{74} +(-2.50000 - 4.33013i) q^{75} -1.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} -4.00000 q^{78} +(4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.00000 - 8.66025i) q^{82} +8.00000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(1.50000 + 2.59808i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-8.00000 - 6.92820i) q^{91} +1.00000 q^{92} +(-5.00000 - 8.66025i) q^{93} +(4.50000 - 7.79423i) q^{94} +(2.50000 + 4.33013i) q^{96} -1.00000 q^{97} +(5.50000 - 4.33013i) q^{98} -1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 + q^4 - 2 * q^6 - 4 * q^7 - 6 * q^8 - q^9	$ 2 q - q^{2} + q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - 6 q^{8} - q^{9} + q^{11} - q^{12} + 8 q^{13} - q^{14} + q^{16} - 3 q^{17} - q^{18} - q^{19} - 5 q^{21} - 2 q^{22} + q^{23} - 3 q^{24} + 5 q^{25} - 4 q^{26} - 2 q^{27} - 5 q^{28} - 10 q^{29} + 10 q^{31} - 5 q^{32} - q^{33} + 6 q^{34} - 2 q^{36} + 11 q^{37} - q^{38} + 4 q^{39} + 20 q^{41} + 4 q^{42} - 6 q^{43} - q^{44} + q^{46} + 9 q^{47} + 2 q^{48} + 2 q^{49} - 10 q^{50} + 3 q^{51} + 4 q^{52} + 8 q^{53} + q^{54} + 12 q^{56} - 2 q^{57} + 5 q^{58} + 9 q^{59} + 2 q^{61} - 20 q^{62} - q^{63} + 14 q^{64} - q^{66} - 4 q^{67} + 3 q^{68} + 2 q^{69} - 14 q^{71} + 3 q^{72} - 4 q^{73} + 11 q^{74} - 5 q^{75} - 2 q^{76} - 5 q^{77} - 8 q^{78} + 8 q^{79} - q^{81} - 10 q^{82} + 16 q^{83} - q^{84} + 3 q^{86} - 5 q^{87} - 3 q^{88} - 16 q^{91} + 2 q^{92} - 10 q^{93} + 9 q^{94} + 5 q^{96} - 2 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 + q^4 - 2 * q^6 - 4 * q^7 - 6 * q^8 - q^9 + q^11 - q^12 + 8 * q^13 - q^14 + q^16 - 3 * q^17 - q^18 - q^19 - 5 * q^21 - 2 * q^22 + q^23 - 3 * q^24 + 5 * q^25 - 4 * q^26 - 2 * q^27 - 5 * q^28 - 10 * q^29 + 10 * q^31 - 5 * q^32 - q^33 + 6 * q^34 - 2 * q^36 + 11 * q^37 - q^38 + 4 * q^39 + 20 * q^41 + 4 * q^42 - 6 * q^43 - q^44 + q^46 + 9 * q^47 + 2 * q^48 + 2 * q^49 - 10 * q^50 + 3 * q^51 + 4 * q^52 + 8 * q^53 + q^54 + 12 * q^56 - 2 * q^57 + 5 * q^58 + 9 * q^59 + 2 * q^61 - 20 * q^62 - q^63 + 14 * q^64 - q^66 - 4 * q^67 + 3 * q^68 + 2 * q^69 - 14 * q^71 + 3 * q^72 - 4 * q^73 + 11 * q^74 - 5 * q^75 - 2 * q^76 - 5 * q^77 - 8 * q^78 + 8 * q^79 - q^81 - 10 * q^82 + 16 * q^83 - q^84 + 3 * q^86 - 5 * q^87 - 3 * q^88 - 16 * q^91 + 2 * q^92 - 10 * q^93 + 9 * q^94 + 5 * q^96 - 2 * q^97 + 11 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/231\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$211$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	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		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	−1.00000			−0.408248
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$7$	−2.00000	−	1.73205i	−0.755929	−	0.654654i
$8$	−3.00000			−1.06066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$	4.00000			1.10940			0.554700	−	0.832050i	$-0.312833\pi$
$13$	4.00000			1.10940			0.554700	+	0.832050i	$0.312833\pi$
$14$	−0.500000	+	2.59808i	−0.133631	+	0.694365i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$		0			0
$21$	−2.50000	+	0.866025i	−0.545545	+	0.188982i
$22$	−1.00000			−0.213201
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	0.913434	−	0.406986i	$-0.133420\pi$
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i	−0.809177	+	0.587565i	$0.800087\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	−2.00000	−	3.46410i	−0.392232	−	0.679366i
$27$	−1.00000			−0.192450
$28$	−2.50000	+	0.866025i	−0.472456	+	0.163663i
$29$	−5.00000			−0.928477			−0.464238	−	0.885710i	$-0.653672\pi$
$29$	−5.00000			−0.928477			−0.464238	+	0.885710i	$0.653672\pi$
$30$		0			0
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.0680129	−	0.997684i	$-0.478334\pi$
$31$	5.00000	−	8.66025i	0.898027	−	1.55543i	0.830014	−	0.557743i	$-0.188333\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$	−0.500000	−	0.866025i	−0.0870388	−	0.150756i
$34$	3.00000			0.514496
$35$		0			0
$36$	−1.00000			−0.166667
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	2.00000	−	3.46410i	0.320256	−	0.554700i
$40$		0			0
$41$	10.0000			1.56174			0.780869	−	0.624695i	$-0.214777\pi$
$41$	10.0000			1.56174			0.780869	+	0.624695i	$0.214777\pi$
$42$	2.00000	+	1.73205i	0.308607	+	0.267261i
$43$	−3.00000			−0.457496			−0.228748	−	0.973486i	$-0.573463\pi$
$43$	−3.00000			−0.457496			−0.228748	+	0.973486i	$0.573463\pi$
$44$	−0.500000	−	0.866025i	−0.0753778	−	0.130558i
$45$		0			0
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$	1.00000			0.144338
$49$	1.00000	+	6.92820i	0.142857	+	0.989743i
$50$	−5.00000			−0.707107
$51$	1.50000	+	2.59808i	0.210042	+	0.363803i
$52$	2.00000	−	3.46410i	0.277350	−	0.480384i
$53$	4.00000	−	6.92820i	0.549442	−	0.951662i	−0.448871	−	0.893597i	$-0.648174\pi$
$53$	4.00000	−	6.92820i	0.549442	−	0.951662i	0.998313	−	0.0580651i	$-0.0184931\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	6.00000	+	5.19615i	0.801784	+	0.694365i
$57$	−1.00000			−0.132453
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	−0.408919	−	0.912571i	$-0.634094\pi$
$59$	4.50000	−	7.79423i	0.585850	−	1.01472i	0.994769	−	0.102151i	$-0.0325726\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−10.0000			−1.27000
$63$	−0.500000	+	2.59808i	−0.0629941	+	0.327327i
$64$	7.00000			0.875000
$65$		0			0
$66$	−0.500000	+	0.866025i	−0.0615457	+	0.106600i
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	−0.961946	−	0.273241i	$-0.911904\pi$
$67$	−2.00000	+	3.46410i	−0.244339	+	0.423207i	0.717607	+	0.696449i	$0.245238\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$	1.00000			0.120386
$70$		0			0
$71$	−7.00000			−0.830747			−0.415374	−	0.909651i	$-0.636349\pi$
$71$	−7.00000			−0.830747			−0.415374	+	0.909651i	$0.636349\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	−0.959006	−	0.283387i	$-0.908542\pi$
$73$	−2.00000	+	3.46410i	−0.234082	+	0.405442i	0.724923	+	0.688830i	$0.241875\pi$
$74$	5.50000	−	9.52628i	0.639362	−	1.10741i
$75$	−2.50000	−	4.33013i	−0.288675	−	0.500000i
$76$	−1.00000			−0.114708
$77$	−2.50000	+	0.866025i	−0.284901	+	0.0986928i
$78$	−4.00000			−0.452911
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	0.998388	−	0.0567635i	$-0.0180781\pi$
$79$	4.00000	+	6.92820i	0.450035	+	0.779484i	−0.548352	+	0.836247i	$0.684745\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.00000	−	8.66025i	−0.552158	−	0.956365i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$	−0.500000	+	2.59808i	−0.0545545	+	0.283473i
$85$		0			0
$86$	1.50000	+	2.59808i	0.161749	+	0.280158i
$87$	−2.50000	+	4.33013i	−0.268028	+	0.464238i
$88$	−1.50000	+	2.59808i	−0.159901	+	0.276956i
$89$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$89$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$90$		0			0
$91$	−8.00000	−	6.92820i	−0.838628	−	0.726273i
$92$	1.00000			0.104257
$93$	−5.00000	−	8.66025i	−0.518476	−	0.898027i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$		0			0
$96$	2.50000	+	4.33013i	0.255155	+	0.441942i
$97$	−1.00000			−0.101535			−0.0507673	−	0.998711i	$-0.516167\pi$
$97$	−1.00000			−0.101535			−0.0507673	+	0.998711i	$0.516167\pi$
$98$	5.50000	−	4.33013i	0.555584	−	0.437409i
$99$	−1.00000			−0.100504
$100$	−2.50000	−	4.33013i	−0.250000	−	0.433013i
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	−0.714423	−	0.699715i	$-0.753311\pi$
$101$	2.50000	−	4.33013i	0.248759	−	0.430864i	0.963182	+	0.268851i	$0.0866439\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	0.947576	−	0.319531i	$-0.103525\pi$
$103$	2.00000	+	3.46410i	0.197066	+	0.341328i	−0.750510	+	0.660859i	$0.770192\pi$
$104$	−12.0000			−1.17670
$105$		0			0
$106$	−8.00000			−0.777029
$107$	−5.00000	−	8.66025i	−0.483368	−	0.837218i	0.516449	−	0.856318i	$-0.327253\pi$
$107$	−5.00000	−	8.66025i	−0.483368	−	0.837218i	−0.999818	+	0.0190994i	$0.993920\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	0.307290	+	0.951616i	$0.400578\pi$
$109$	−7.00000	+	12.1244i	−0.670478	+	1.16130i	−0.977769	+	0.209687i	$0.932756\pi$
$110$		0			0
$111$	11.0000			1.04407
$112$	0.500000	−	2.59808i	0.0472456	−	0.245495i
$113$	−12.0000			−1.12887			−0.564433	−	0.825479i	$-0.690905\pi$
$113$	−12.0000			−1.12887			−0.564433	+	0.825479i	$0.690905\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$		0			0
$116$	−2.50000	+	4.33013i	−0.232119	+	0.402042i
$117$	−2.00000	−	3.46410i	−0.184900	−	0.320256i
$118$	−9.00000			−0.828517
$119$	7.50000	−	2.59808i	0.687524	−	0.238165i
$120$		0			0
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	1.00000	−	1.73205i	0.0905357	−	0.156813i
$123$	5.00000	−	8.66025i	0.450835	−	0.780869i
$124$	−5.00000	−	8.66025i	−0.449013	−	0.777714i
$125$		0			0
$126$	2.50000	−	0.866025i	0.222718	−	0.0771517i
$127$	−19.0000			−1.68598			−0.842989	−	0.537931i	$-0.819206\pi$
$127$	−19.0000			−1.68598			−0.842989	+	0.537931i	$0.819206\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	−1.50000	+	2.59808i	−0.132068	+	0.228748i
$130$		0			0
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	−0.990972	−	0.134069i	$-0.957196\pi$
$131$	−7.00000	−	12.1244i	−0.611593	−	1.05931i	0.379379	−	0.925241i	$-0.376138\pi$
$132$	−1.00000			−0.0870388
$133$	−0.500000	+	2.59808i	−0.0433555	+	0.225282i
$134$	4.00000			0.345547
$135$		0			0
$136$	4.50000	−	7.79423i	0.385872	−	0.668350i
$137$	−10.0000	+	17.3205i	−0.854358	+	1.47979i	0.0228820	+	0.999738i	$0.492716\pi$
$137$	−10.0000	+	17.3205i	−0.854358	+	1.47979i	−0.877240	+	0.480053i	$0.840618\pi$
$138$	−0.500000	−	0.866025i	−0.0425628	−	0.0737210i
$139$	−13.0000			−1.10265			−0.551323	−	0.834292i	$-0.685877\pi$
$139$	−13.0000			−1.10265			−0.551323	+	0.834292i	$0.685877\pi$
$140$		0			0
$141$	9.00000			0.757937
$142$	3.50000	+	6.06218i	0.293713	+	0.508727i
$143$	2.00000	−	3.46410i	0.167248	−	0.289683i
$144$	0.500000	−	0.866025i	0.0416667	−	0.0721688i
$145$		0			0
$146$	4.00000			0.331042
$147$	6.50000	+	2.59808i	0.536111	+	0.214286i
$148$	11.0000			0.904194
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	0.920904	−	0.389789i	$-0.127452\pi$
$149$	1.50000	+	2.59808i	0.122885	+	0.212843i	−0.798019	+	0.602632i	$0.794119\pi$
$150$	−2.50000	+	4.33013i	−0.204124	+	0.353553i
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$	1.50000	+	2.59808i	0.121666	+	0.210732i
$153$	3.00000			0.242536
$154$	2.00000	+	1.73205i	0.161165	+	0.139573i
$155$		0			0
$156$	−2.00000	−	3.46410i	−0.160128	−	0.277350i
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	−0.971219	−	0.238190i	$-0.923446\pi$
$157$	−3.50000	+	6.06218i	−0.279330	+	0.483814i	0.691888	+	0.722005i	$0.256779\pi$
$158$	4.00000	−	6.92820i	0.318223	−	0.551178i
$159$	−4.00000	−	6.92820i	−0.317221	−	0.549442i
$160$		0			0
$161$	0.500000	−	2.59808i	0.0394055	−	0.204757i
$162$	1.00000			0.0785674
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	0.902528	−	0.430632i	$-0.141709\pi$
$163$	1.00000	+	1.73205i	0.0783260	+	0.135665i	−0.824202	+	0.566296i	$0.808376\pi$
$164$	5.00000	−	8.66025i	0.390434	−	0.676252i
$165$		0			0
$166$	−4.00000	−	6.92820i	−0.310460	−	0.537733i
$167$	12.0000			0.928588			0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000			0.928588			0.464294	+	0.885681i	$0.346308\pi$
$168$	7.50000	−	2.59808i	0.578638	−	0.200446i
$169$	3.00000			0.230769
$170$		0			0
$171$	−0.500000	+	0.866025i	−0.0382360	+	0.0662266i
$172$	−1.50000	+	2.59808i	−0.114374	+	0.198101i
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	0.892956	+	0.450145i	$0.148628\pi$
$173$	11.0000	+	19.0526i	0.836315	+	1.44854i	−0.0566411	+	0.998395i	$0.518039\pi$
$174$	5.00000			0.379049
$175$	−12.5000	+	4.33013i	−0.944911	+	0.327327i
$176$	1.00000			0.0753778
$177$	−4.50000	−	7.79423i	−0.338241	−	0.585850i
$178$		0			0
$179$	0.500000	−	0.866025i	0.0373718	−	0.0647298i	−0.846735	−	0.532016i	$-0.821435\pi$
$179$	0.500000	−	0.866025i	0.0373718	−	0.0647298i	0.884106	+	0.467286i	$0.154768\pi$
$180$		0			0
$181$	−10.0000			−0.743294			−0.371647	−	0.928374i	$-0.621207\pi$
$181$	−10.0000			−0.743294			−0.371647	+	0.928374i	$0.621207\pi$
$182$	−2.00000	+	10.3923i	−0.148250	+	0.770329i
$183$	2.00000			0.147844
$184$	−1.50000	−	2.59808i	−0.110581	−	0.191533i
$185$		0			0
$186$	−5.00000	+	8.66025i	−0.366618	+	0.635001i
$187$	1.50000	+	2.59808i	0.109691	+	0.189990i
$188$	9.00000			0.656392
$189$	2.00000	+	1.73205i	0.145479	+	0.125988i
$190$		0			0
$191$	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	$0.739868\pi$
$192$	3.50000	−	6.06218i	0.252591	−	0.437500i
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	−0.628037	−	0.778183i	$-0.716141\pi$
$193$	5.00000	−	8.66025i	0.359908	−	0.623379i	0.987945	+	0.154805i	$0.0494748\pi$
$194$	0.500000	+	0.866025i	0.0358979	+	0.0621770i
$195$		0			0
$196$	6.50000	+	2.59808i	0.464286	+	0.185577i
$197$	−1.00000			−0.0712470			−0.0356235	−	0.999365i	$-0.511342\pi$
$197$	−1.00000			−0.0712470			−0.0356235	+	0.999365i	$0.511342\pi$
$198$	0.500000	+	0.866025i	0.0355335	+	0.0615457i
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	−0.256391	−	0.966573i	$-0.582534\pi$
$199$	10.0000	−	17.3205i	0.708881	−	1.22782i	0.965272	−	0.261245i	$-0.0841331\pi$
$200$	−7.50000	+	12.9904i	−0.530330	+	0.918559i
$201$	2.00000	+	3.46410i	0.141069	+	0.244339i
$202$	−5.00000			−0.351799
$203$	10.0000	+	8.66025i	0.701862	+	0.607831i
$204$	3.00000			0.210042
$205$		0			0
$206$	2.00000	−	3.46410i	0.139347	−	0.241355i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	2.00000	+	3.46410i	0.138675	+	0.240192i
$209$	−1.00000			−0.0691714
$210$		0			0
$211$	20.0000			1.37686			0.688428	−	0.725304i	$-0.258301\pi$
$211$	20.0000			1.37686			0.688428	+	0.725304i	$0.258301\pi$
$212$	−4.00000	−	6.92820i	−0.274721	−	0.475831i
$213$	−3.50000	+	6.06218i	−0.239816	+	0.415374i
$214$	−5.00000	+	8.66025i	−0.341793	+	0.592003i
$215$		0			0
$216$	3.00000			0.204124
$217$	−25.0000	+	8.66025i	−1.69711	+	0.587896i
$218$	14.0000			0.948200
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$		0			0
$221$	−6.00000	+	10.3923i	−0.403604	+	0.699062i
$222$	−5.50000	−	9.52628i	−0.369136	−	0.639362i
$223$		0			0			−	1.00000i	$-0.5\pi$
$223$		0			0				1.00000i	$0.5\pi$
$224$	12.5000	−	4.33013i	0.835191	−	0.289319i
$225$	−5.00000			−0.333333
$226$	6.00000	+	10.3923i	0.399114	+	0.691286i
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	−0.999184	−	0.0403978i	$-0.987137\pi$
$227$	−7.00000	+	12.1244i	−0.464606	+	0.804722i	0.534577	+	0.845120i	$0.320471\pi$
$228$	−0.500000	+	0.866025i	−0.0331133	+	0.0573539i
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	0.958187	+	0.286143i	$0.0923732\pi$
$229$	11.0000	+	19.0526i	0.726900	+	1.25903i	−0.231287	+	0.972886i	$0.574293\pi$
$230$		0			0
$231$	−0.500000	+	2.59808i	−0.0328976	+	0.170941i
$232$	15.0000			0.984798
$233$	−12.5000	−	21.6506i	−0.818902	−	1.41838i	−0.906492	−	0.422224i	$-0.861250\pi$
$233$	−12.5000	−	21.6506i	−0.818902	−	1.41838i	0.0875895	−	0.996157i	$-0.472084\pi$
$234$	−2.00000	+	3.46410i	−0.130744	+	0.226455i
$235$		0			0
$236$	−4.50000	−	7.79423i	−0.292925	−	0.507361i
$237$	8.00000			0.519656
$238$	−6.00000	−	5.19615i	−0.388922	−	0.336817i
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	−0.794393	−	0.607404i	$-0.792211\pi$
$241$	2.00000	−	3.46410i	0.128831	−	0.223142i	0.923224	+	0.384262i	$0.125544\pi$
$242$	−0.500000	+	0.866025i	−0.0321412	+	0.0556702i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	2.00000			0.128037
$245$		0			0
$246$	−10.0000			−0.637577
$247$	−2.00000	−	3.46410i	−0.127257	−	0.220416i
$248$	−15.0000	+	25.9808i	−0.952501	+	1.64978i
$249$	4.00000	−	6.92820i	0.253490	−	0.439057i
$250$		0			0
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$	2.00000	+	1.73205i	0.125988	+	0.109109i
$253$	1.00000			0.0628695
$254$	9.50000	+	16.4545i	0.596083	+	1.03245i
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	−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	$-0.504689\pi$
$258$	3.00000			0.186772
$259$	5.50000	−	28.5788i	0.341753	−	1.77580i
$260$		0			0
$261$	2.50000	+	4.33013i	0.154746	+	0.268028i
$262$	−7.00000	+	12.1244i	−0.432461	+	0.749045i
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.133281	−	0.991078i	$-0.457449\pi$
$263$	15.0000	−	25.9808i	0.924940	−	1.60204i	0.791658	−	0.610964i	$-0.209218\pi$
$264$	1.50000	+	2.59808i	0.0923186	+	0.159901i
$265$		0			0
$266$	2.50000	−	0.866025i	0.153285	−	0.0530994i
$267$		0			0
$268$	2.00000	+	3.46410i	0.122169	+	0.211604i
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	0.307029	+	0.951700i	$0.400665\pi$
$269$	−11.0000	+	19.0526i	−0.670682	+	1.16166i	−0.977711	+	0.209955i	$0.932668\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$	−3.00000			−0.181902
$273$	−10.0000	+	3.46410i	−0.605228	+	0.209657i
$274$	20.0000			1.20824
$275$	−2.50000	−	4.33013i	−0.150756	−	0.261116i
$276$	0.500000	−	0.866025i	0.0300965	−	0.0521286i
$277$	−16.0000	+	27.7128i	−0.961347	+	1.66510i	−0.242222	+	0.970221i	$0.577876\pi$
$277$	−16.0000	+	27.7128i	−0.961347	+	1.66510i	−0.719125	+	0.694881i	$0.755457\pi$
$278$	6.50000	+	11.2583i	0.389844	+	0.675230i
$279$	−10.0000			−0.598684
$280$		0			0
$281$	9.00000			0.536895			0.268447	−	0.963294i	$-0.413489\pi$
$281$	9.00000			0.536895			0.268447	+	0.963294i	$0.413489\pi$
$282$	−4.50000	−	7.79423i	−0.267971	−	0.464140i
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−3.50000	+	6.06218i	−0.207687	+	0.359724i
$285$		0			0
$286$	−4.00000			−0.236525
$287$	−20.0000	−	17.3205i	−1.18056	−	1.02240i
$288$	5.00000			0.294628
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−0.500000	+	0.866025i	−0.0293105	+	0.0507673i
$292$	2.00000	+	3.46410i	0.117041	+	0.202721i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$	−1.00000	−	6.92820i	−0.0583212	−	0.404061i
$295$		0			0
$296$	−16.5000	−	28.5788i	−0.959043	−	1.66111i
$297$	−0.500000	+	0.866025i	−0.0290129	+	0.0502519i
$298$	1.50000	−	2.59808i	0.0868927	−	0.150503i
$299$	2.00000	+	3.46410i	0.115663	+	0.200334i
$300$	−5.00000			−0.288675
$301$	6.00000	+	5.19615i	0.345834	+	0.299501i
$302$	−1.00000			−0.0575435
$303$	−2.50000	−	4.33013i	−0.143621	−	0.248759i
$304$	0.500000	−	0.866025i	0.0286770	−	0.0496700i
$305$		0			0
$306$	−1.50000	−	2.59808i	−0.0857493	−	0.148522i
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$	−0.500000	+	2.59808i	−0.0284901	+	0.148039i
$309$	4.00000			0.227552
$310$		0			0
$311$	−8.50000	+	14.7224i	−0.481991	+	0.834833i	−0.999786	−	0.0206719i	$-0.993419\pi$
$311$	−8.50000	+	14.7224i	−0.481991	+	0.834833i	0.517796	+	0.855504i	$0.326753\pi$
$312$	−6.00000	+	10.3923i	−0.339683	+	0.588348i
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	0.964720	−	0.263278i	$-0.0848035\pi$
$313$	4.50000	+	7.79423i	0.254355	+	0.440556i	−0.710365	+	0.703833i	$0.751470\pi$
$314$	7.00000			0.395033
$315$		0			0
$316$	8.00000			0.450035
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	0.646872	−	0.762598i	$-0.276077\pi$
$317$	−6.00000	−	10.3923i	−0.336994	−	0.583690i	−0.983866	+	0.178908i	$0.942743\pi$
$318$	−4.00000	+	6.92820i	−0.224309	+	0.388514i
$319$	−2.50000	+	4.33013i	−0.139973	+	0.242441i
$320$		0			0
$321$	−10.0000			−0.558146
$322$	−2.50000	+	0.866025i	−0.139320	+	0.0482617i
$323$	3.00000			0.166924
$324$	0.500000	+	0.866025i	0.0277778	+	0.0481125i
$325$	10.0000	−	17.3205i	0.554700	−	0.960769i
$326$	1.00000	−	1.73205i	0.0553849	−	0.0959294i
$327$	7.00000	+	12.1244i	0.387101	+	0.670478i
$328$	−30.0000			−1.65647
$329$	4.50000	−	23.3827i	0.248093	−	1.28913i
$330$		0			0
$331$	−9.00000	−	15.5885i	−0.494685	−	0.856819i	0.505296	−	0.862946i	$-0.331383\pi$
$331$	−9.00000	−	15.5885i	−0.494685	−	0.856819i	−0.999981	+	0.00612670i	$0.998050\pi$
$332$	4.00000	−	6.92820i	0.219529	−	0.380235i
$333$	5.50000	−	9.52628i	0.301398	−	0.522037i
$334$	−6.00000	−	10.3923i	−0.328305	−	0.568642i
$335$		0			0
$336$	−2.00000	−	1.73205i	−0.109109	−	0.0944911i
$337$	−2.00000			−0.108947			−0.0544735	−	0.998515i	$-0.517348\pi$
$337$	−2.00000			−0.108947			−0.0544735	+	0.998515i	$0.517348\pi$
$338$	−1.50000	−	2.59808i	−0.0815892	−	0.141317i
$339$	−6.00000	+	10.3923i	−0.325875	+	0.564433i
$340$		0			0
$341$	−5.00000	−	8.66025i	−0.270765	−	0.468979i
$342$	1.00000			0.0540738
$343$	10.0000	−	15.5885i	0.539949	−	0.841698i
$344$	9.00000			0.485247
$345$		0			0
$346$	11.0000	−	19.0526i	0.591364	−	1.02427i
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	−0.195507	−	0.980702i	$-0.562635\pi$
$347$	14.0000	−	24.2487i	0.751559	−	1.30174i	0.947067	−	0.321037i	$-0.104031\pi$
$348$	2.50000	+	4.33013i	0.134014	+	0.232119i
$349$	24.0000			1.28469			0.642345	−	0.766415i	$-0.277962\pi$
$349$	24.0000			1.28469			0.642345	+	0.766415i	$0.277962\pi$
$350$	10.0000	+	8.66025i	0.534522	+	0.462910i
$351$	−4.00000			−0.213504
$352$	2.50000	+	4.33013i	0.133250	+	0.230797i
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	0.347024	+	0.937856i	$0.387192\pi$
$353$	−12.0000	+	20.7846i	−0.638696	+	1.10625i	−0.985719	+	0.168397i	$0.946141\pi$
$354$	−4.50000	+	7.79423i	−0.239172	+	0.414259i
$355$		0			0
$356$		0			0
$357$	1.50000	−	7.79423i	0.0793884	−	0.412514i
$358$	−1.00000			−0.0528516
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$		0			0
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	5.00000	+	8.66025i	0.262794	+	0.455173i
$363$	−1.00000			−0.0524864
$364$	−10.0000	+	3.46410i	−0.524142	+	0.181568i
$365$		0			0
$366$	−1.00000	−	1.73205i	−0.0522708	−	0.0905357i
$367$	−14.0000	+	24.2487i	−0.730794	+	1.26577i	0.225750	+	0.974185i	$0.427517\pi$
$367$	−14.0000	+	24.2487i	−0.730794	+	1.26577i	−0.956544	+	0.291587i	$0.905817\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	−5.00000	−	8.66025i	−0.260290	−	0.450835i
$370$		0			0
$371$	−20.0000	+	6.92820i	−1.03835	+	0.359694i
$372$	−10.0000			−0.518476
$373$	3.00000	+	5.19615i	0.155334	+	0.269047i	0.933181	−	0.359408i	$-0.117021\pi$
$373$	3.00000	+	5.19615i	0.155334	+	0.269047i	−0.777847	+	0.628454i	$0.783688\pi$
$374$	1.50000	−	2.59808i	0.0775632	−	0.134343i
$375$		0			0
$376$	−13.5000	−	23.3827i	−0.696209	−	1.20587i
$377$	−20.0000			−1.03005
$378$	0.500000	−	2.59808i	0.0257172	−	0.133631i
$379$	34.0000			1.74646			0.873231	−	0.487306i	$-0.162020\pi$
$379$	34.0000			1.74646			0.873231	+	0.487306i	$0.162020\pi$
$380$		0			0
$381$	−9.50000	+	16.4545i	−0.486700	+	0.842989i
$382$	4.00000	−	6.92820i	0.204658	−	0.354478i
$383$	−6.50000	−	11.2583i	−0.332134	−	0.575274i	0.650796	−	0.759253i	$-0.274435\pi$
$383$	−6.50000	−	11.2583i	−0.332134	−	0.575274i	−0.982930	+	0.183979i	$0.941102\pi$
$384$	3.00000			0.153093
$385$		0			0
$386$	−10.0000			−0.508987
$387$	1.50000	+	2.59808i	0.0762493	+	0.132068i
$388$	−0.500000	+	0.866025i	−0.0253837	+	0.0439658i
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	−0.492947	−	0.870059i	$-0.664080\pi$
$389$	10.0000	−	17.3205i	0.507020	−	0.878185i	0.999967	−	0.00812520i	$-0.00258636\pi$
$390$		0			0
$391$	−3.00000			−0.151717
$392$	−3.00000	−	20.7846i	−0.151523	−	1.04978i
$393$	−14.0000			−0.706207
$394$	0.500000	+	0.866025i	0.0251896	+	0.0436297i
$395$		0			0
$396$	−0.500000	+	0.866025i	−0.0251259	+	0.0435194i
$397$	16.5000	+	28.5788i	0.828111	+	1.43433i	0.899518	+	0.436884i	$0.143918\pi$
$397$	16.5000	+	28.5788i	0.828111	+	1.43433i	−0.0714068	+	0.997447i	$0.522749\pi$
$398$	−20.0000			−1.00251
$399$	2.00000	+	1.73205i	0.100125	+	0.0867110i
$400$	5.00000			0.250000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	2.00000	−	3.46410i	0.0997509	−	0.172774i
$403$	20.0000	−	34.6410i	0.996271	−	1.72559i
$404$	−2.50000	−	4.33013i	−0.124380	−	0.215432i
$405$		0			0
$406$	2.50000	−	12.9904i	0.124073	−	0.644702i
$407$	11.0000			0.545250
$408$	−4.50000	−	7.79423i	−0.222783	−	0.385872i
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	−0.715523	−	0.698589i	$-0.753812\pi$
$409$	5.00000	−	8.66025i	0.247234	−	0.428222i	0.962757	+	0.270367i	$0.0871450\pi$
$410$		0			0
$411$	10.0000	+	17.3205i	0.493264	+	0.854358i
$412$	4.00000			0.197066
$413$	−22.5000	+	7.79423i	−1.10715	+	0.383529i
$414$	−1.00000			−0.0491473
$415$		0			0
$416$	−10.0000	+	17.3205i	−0.490290	+	0.849208i
$417$	−6.50000	+	11.2583i	−0.318306	+	0.551323i
$418$	0.500000	+	0.866025i	0.0244558	+	0.0423587i
$419$	7.00000			0.341972			0.170986	−	0.985273i	$-0.445305\pi$
$419$	7.00000			0.341972			0.170986	+	0.985273i	$0.445305\pi$
$420$		0			0
$421$	−3.00000			−0.146211			−0.0731055	−	0.997324i	$-0.523291\pi$
$421$	−3.00000			−0.146211			−0.0731055	+	0.997324i	$0.523291\pi$
$422$	−10.0000	−	17.3205i	−0.486792	−	0.843149i
$423$	4.50000	−	7.79423i	0.218797	−	0.378968i
$424$	−12.0000	+	20.7846i	−0.582772	+	1.00939i
$425$	7.50000	+	12.9904i	0.363803	+	0.630126i
$426$	7.00000			0.339151
$427$	1.00000	−	5.19615i	0.0483934	−	0.251459i
$428$	−10.0000			−0.483368
$429$	−2.00000	−	3.46410i	−0.0965609	−	0.167248i
$430$		0			0
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	0.302300	+	0.953213i	$0.402245\pi$
$431$	−14.0000	+	24.2487i	−0.674356	+	1.16802i	−0.976657	+	0.214807i	$0.931088\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−11.0000			−0.528626			−0.264313	−	0.964437i	$-0.585145\pi$
$433$	−11.0000			−0.528626			−0.264313	+	0.964437i	$0.585145\pi$
$434$	20.0000	+	17.3205i	0.960031	+	0.831411i
$435$		0			0
$436$	7.00000	+	12.1244i	0.335239	+	0.580651i
$437$	0.500000	−	0.866025i	0.0239182	−	0.0414276i
$438$	2.00000	−	3.46410i	0.0955637	−	0.165521i
$439$	−0.500000	−	0.866025i	−0.0238637	−	0.0413331i	0.853847	−	0.520524i	$-0.174263\pi$
$439$	−0.500000	−	0.866025i	−0.0238637	−	0.0413331i	−0.877711	+	0.479191i	$0.840930\pi$
$440$		0			0
$441$	5.50000	−	4.33013i	0.261905	−	0.206197i
$442$	12.0000			0.570782
$443$	17.5000	+	30.3109i	0.831450	+	1.44011i	0.896888	+	0.442257i	$0.145822\pi$
$443$	17.5000	+	30.3109i	0.831450	+	1.44011i	−0.0654382	+	0.997857i	$0.520845\pi$
$444$	5.50000	−	9.52628i	0.261018	−	0.452097i
$445$		0			0
$446$		0			0
$447$	3.00000			0.141895
$448$	−14.0000	−	12.1244i	−0.661438	−	0.572822i
$449$	−24.0000			−1.13263			−0.566315	−	0.824189i	$-0.691631\pi$
$449$	−24.0000			−1.13263			−0.566315	+	0.824189i	$0.691631\pi$
$450$	2.50000	+	4.33013i	0.117851	+	0.204124i
$451$	5.00000	−	8.66025i	0.235441	−	0.407795i
$452$	−6.00000	+	10.3923i	−0.282216	+	0.488813i
$453$	−0.500000	−	0.866025i	−0.0234920	−	0.0406894i
$454$	14.0000			0.657053
$455$		0			0
$456$	3.00000			0.140488
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	0.575036	−	0.818128i	$-0.304988\pi$
$457$	−9.00000	−	15.5885i	−0.421002	−	0.729197i	−0.996038	+	0.0889312i	$0.971655\pi$
$458$	11.0000	−	19.0526i	0.513996	−	0.890268i
$459$	1.50000	−	2.59808i	0.0700140	−	0.121268i
$460$		0			0
$461$	33.0000			1.53696			0.768482	−	0.639872i	$-0.221013\pi$
$461$	33.0000			1.53696			0.768482	+	0.639872i	$0.221013\pi$
$462$	2.50000	−	0.866025i	0.116311	−	0.0402911i
$463$	−32.0000			−1.48717			−0.743583	−	0.668644i	$-0.766875\pi$
$463$	−32.0000			−1.48717			−0.743583	+	0.668644i	$0.766875\pi$
$464$	−2.50000	−	4.33013i	−0.116060	−	0.201021i
$465$		0			0
$466$	−12.5000	+	21.6506i	−0.579051	+	1.00295i
$467$	3.50000	+	6.06218i	0.161961	+	0.280524i	0.935572	−	0.353137i	$-0.114885\pi$
$467$	3.50000	+	6.06218i	0.161961	+	0.280524i	−0.773611	+	0.633661i	$0.781552\pi$
$468$	−4.00000			−0.184900
$469$	10.0000	−	3.46410i	0.461757	−	0.159957i
$470$		0			0
$471$	3.50000	+	6.06218i	0.161271	+	0.279330i
$472$	−13.5000	+	23.3827i	−0.621388	+	1.07628i
$473$	−1.50000	+	2.59808i	−0.0689701	+	0.119460i
$474$	−4.00000	−	6.92820i	−0.183726	−	0.318223i
$475$	−5.00000			−0.229416
$476$	1.50000	−	7.79423i	0.0687524	−	0.357248i
$477$	−8.00000			−0.366295
$478$		0			0
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	−0.957351	−	0.288929i	$-0.906701\pi$
$479$	−5.00000	+	8.66025i	−0.228456	+	0.395697i	0.728895	+	0.684626i	$0.240034\pi$
$480$		0			0
$481$	22.0000	+	38.1051i	1.00311	+	1.73744i
$482$	−4.00000			−0.182195
$483$	−2.00000	−	1.73205i	−0.0910032	−	0.0788110i
$484$	−1.00000			−0.0454545
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	−0.907776	−	0.419456i	$-0.862221\pi$
$487$	−2.00000	+	3.46410i	−0.0906287	+	0.156973i	0.817147	+	0.576429i	$0.195554\pi$
$488$	−3.00000	−	5.19615i	−0.135804	−	0.235219i
$489$	2.00000			0.0904431
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	−5.00000	−	8.66025i	−0.225417	−	0.390434i
$493$	7.50000	−	12.9904i	0.337783	−	0.585057i
$494$	−2.00000	+	3.46410i	−0.0899843	+	0.155857i
$495$		0			0
$496$	10.0000			0.449013
$497$	14.0000	+	12.1244i	0.627986	+	0.543852i
$498$	−8.00000			−0.358489
$499$	7.00000	+	12.1244i	0.313363	+	0.542761i	0.979088	−	0.203436i	$-0.0652110\pi$
$499$	7.00000	+	12.1244i	0.313363	+	0.542761i	−0.665725	+	0.746197i	$0.731878\pi$
$500$		0			0
$501$	6.00000	−	10.3923i	0.268060	−	0.464294i
$502$	7.50000	+	12.9904i	0.334741	+	0.579789i
$503$	10.0000			0.445878			0.222939	−	0.974832i	$-0.428435\pi$
$503$	10.0000			0.445878			0.222939	+	0.974832i	$0.428435\pi$
$504$	1.50000	−	7.79423i	0.0668153	−	0.347183i
$505$		0			0
$506$	−0.500000	−	0.866025i	−0.0222277	−	0.0384995i
$507$	1.50000	−	2.59808i	0.0666173	−	0.115385i
$508$	−9.50000	+	16.4545i	−0.421494	+	0.730050i
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	0.967811	−	0.251679i	$-0.0809826\pi$
$509$	6.00000	+	10.3923i	0.265945	+	0.460631i	−0.701866	+	0.712309i	$0.747649\pi$
$510$		0			0
$511$	10.0000	−	3.46410i	0.442374	−	0.153243i
$512$	−11.0000			−0.486136
$513$	0.500000	+	0.866025i	0.0220755	+	0.0382360i
$514$	−14.0000	+	24.2487i	−0.617514	+	1.06956i
$515$		0			0
$516$	1.50000	+	2.59808i	0.0660338	+	0.114374i
$517$	9.00000			0.395820
$518$	−27.5000	+	9.52628i	−1.20828	+	0.418561i
$519$	22.0000			0.965693
$520$		0			0
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	−0.954519	−	0.298150i	$-0.903630\pi$
$521$	−5.00000	+	8.66025i	−0.219054	+	0.379413i	0.735465	+	0.677563i	$0.236964\pi$
$522$	2.50000	−	4.33013i	0.109422	−	0.189525i
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	0.990873	+	0.134801i	$0.0430394\pi$
$523$	14.0000	+	24.2487i	0.612177	+	1.06032i	−0.378695	+	0.925521i	$0.623627\pi$
$524$	−14.0000			−0.611593
$525$	−2.50000	+	12.9904i	−0.109109	+	0.566947i
$526$	−30.0000			−1.30806
$527$	15.0000	+	25.9808i	0.653410	+	1.13174i
$528$	0.500000	−	0.866025i	0.0217597	−	0.0376889i
$529$	11.0000	−	19.0526i	0.478261	−	0.828372i
$530$		0			0
$531$	−9.00000			−0.390567
$532$	2.00000	+	1.73205i	0.0867110	+	0.0750939i
$533$	40.0000			1.73259
$534$		0			0
$535$		0			0
$536$	6.00000	−	10.3923i	0.259161	−	0.448879i
$537$	−0.500000	−	0.866025i	−0.0215766	−	0.0373718i
$538$	22.0000			0.948487
$539$	6.50000	+	2.59808i	0.279975	+	0.111907i
$540$		0			0
$541$	−6.00000	−	10.3923i	−0.257960	−	0.446800i	0.707735	−	0.706478i	$-0.249717\pi$
$541$	−6.00000	−	10.3923i	−0.257960	−	0.446800i	−0.965695	+	0.259678i	$0.916384\pi$
$542$	4.00000	−	6.92820i	0.171815	−	0.297592i
$543$	−5.00000	+	8.66025i	−0.214571	+	0.371647i
$544$	−7.50000	−	12.9904i	−0.321560	−	0.556958i
$545$		0			0
$546$	8.00000	+	6.92820i	0.342368	+	0.296500i
$547$	−13.0000			−0.555840			−0.277920	−	0.960604i	$-0.589645\pi$
$547$	−13.0000			−0.555840			−0.277920	+	0.960604i	$0.589645\pi$
$548$	10.0000	+	17.3205i	0.427179	+	0.739895i
$549$	1.00000	−	1.73205i	0.0426790	−	0.0739221i
$550$	−2.50000	+	4.33013i	−0.106600	+	0.184637i
$551$	2.50000	+	4.33013i	0.106504	+	0.184470i
$552$	−3.00000			−0.127688
$553$	4.00000	−	20.7846i	0.170097	−	0.883852i
$554$	32.0000			1.35955
$555$		0			0
$556$	−6.50000	+	11.2583i	−0.275661	+	0.477460i
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	−0.0747252	−	0.997204i	$-0.523808\pi$
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	0.900967	−	0.433888i	$-0.142859\pi$
$558$	5.00000	+	8.66025i	0.211667	+	0.366618i
$559$	−12.0000			−0.507546
$560$		0			0
$561$	3.00000			0.126660
$562$	−4.50000	−	7.79423i	−0.189821	−	0.328780i
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	−0.964315	−	0.264758i	$-0.914708\pi$
$563$	−6.00000	+	10.3923i	−0.252870	+	0.437983i	0.711445	+	0.702742i	$0.248041\pi$
$564$	4.50000	−	7.79423i	0.189484	−	0.328196i
$565$		0			0
$566$	−4.00000			−0.168133
$567$	2.50000	−	0.866025i	0.104990	−	0.0363696i
$568$	21.0000			0.881140
$569$	−21.5000	−	37.2391i	−0.901327	−	1.56114i	−0.825773	−	0.564002i	$-0.809261\pi$
$569$	−21.5000	−	37.2391i	−0.901327	−	1.56114i	−0.0755536	−	0.997142i	$-0.524072\pi$
$570$		0			0
$571$	6.50000	−	11.2583i	0.272017	−	0.471146i	−0.697362	−	0.716720i	$-0.745643\pi$
$571$	6.50000	−	11.2583i	0.272017	−	0.471146i	0.969378	+	0.245573i	$0.0789761\pi$
$572$	−2.00000	−	3.46410i	−0.0836242	−	0.144841i
$573$	8.00000			0.334205
$574$	−5.00000	+	25.9808i	−0.208696	+	1.08442i
$575$	5.00000			0.208514
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	19.0000	−	32.9090i	0.790980	−	1.37002i	−0.134380	−	0.990930i	$-0.542904\pi$
$577$	19.0000	−	32.9090i	0.790980	−	1.37002i	0.925361	−	0.379088i	$-0.123762\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	−5.00000	−	8.66025i	−0.207793	−	0.359908i
$580$		0			0
$581$	−16.0000	−	13.8564i	−0.663792	−	0.574861i
$582$	1.00000			0.0414513
$583$	−4.00000	−	6.92820i	−0.165663	−	0.286937i
$584$	6.00000	−	10.3923i	0.248282	−	0.430037i
$585$		0			0
$586$	−10.5000	−	18.1865i	−0.433751	−	0.751279i
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$	5.50000	−	4.33013i	0.226816	−	0.178571i
$589$	−10.0000			−0.412043
$590$		0			0
$591$	−0.500000	+	0.866025i	−0.0205673	+	0.0356235i
$592$	−5.50000	+	9.52628i	−0.226049	+	0.391528i
$593$	−0.500000	−	0.866025i	−0.0205325	−	0.0355634i	0.855577	−	0.517676i	$-0.173203\pi$
$593$	−0.500000	−	0.866025i	−0.0205325	−	0.0355634i	−0.876109	+	0.482113i	$0.839870\pi$
$594$	1.00000			0.0410305
$595$		0			0
$596$	3.00000			0.122885
$597$	−10.0000	−	17.3205i	−0.409273	−	0.708881i
$598$	2.00000	−	3.46410i	0.0817861	−	0.141658i
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	0.0905757	+	0.995890i	$0.471129\pi$
$599$	−20.0000	+	34.6410i	−0.817178	+	1.41539i	−0.907754	+	0.419504i	$0.862204\pi$
$600$	7.50000	+	12.9904i	0.306186	+	0.530330i
$601$	30.0000			1.22373			0.611863	−	0.790964i	$-0.290420\pi$
$601$	30.0000			1.22373			0.611863	+	0.790964i	$0.290420\pi$
$602$	1.50000	−	7.79423i	0.0611354	−	0.317669i
$603$	4.00000			0.162893
$604$	−0.500000	−	0.866025i	−0.0203447	−	0.0352381i
$605$		0			0
$606$	−2.50000	+	4.33013i	−0.101556	+	0.175899i
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	−0.911621	−	0.411033i	$-0.865168\pi$
$607$	−20.0000	−	34.6410i	−0.811775	−	1.40604i	0.0998457	−	0.995003i	$-0.468165\pi$
$608$	5.00000			0.202777
$609$	12.5000	−	4.33013i	0.506526	−	0.175466i
$610$		0			0
$611$	18.0000	+	31.1769i	0.728202	+	1.26128i
$612$	1.50000	−	2.59808i	0.0606339	−	0.105021i
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	−0.658012	−	0.753007i	$-0.728603\pi$
$613$	8.00000	−	13.8564i	0.323117	−	0.559655i	0.981129	+	0.193352i	$0.0619359\pi$
$614$	6.00000	+	10.3923i	0.242140	+	0.419399i
$615$		0			0
$616$	7.50000	−	2.59808i	0.302184	−	0.104679i
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−2.00000	−	3.46410i	−0.0804518	−	0.139347i
$619$	−9.00000	+	15.5885i	−0.361741	+	0.626553i	−0.988247	−	0.152863i	$-0.951151\pi$
$619$	−9.00000	+	15.5885i	−0.361741	+	0.626553i	0.626507	+	0.779416i	$0.284484\pi$
$620$		0			0
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	17.0000			0.681638
$623$		0			0
$624$	4.00000			0.160128
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	4.50000	−	7.79423i	0.179856	−	0.311520i
$627$	−0.500000	+	0.866025i	−0.0199681	+	0.0345857i
$628$	3.50000	+	6.06218i	0.139665	+	0.241907i
$629$	−33.0000			−1.31580
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$	−12.0000	−	20.7846i	−0.477334	−	0.826767i
$633$	10.0000	−	17.3205i	0.397464	−	0.688428i
$634$	−6.00000	+	10.3923i	−0.238290	+	0.412731i
$635$		0			0
$636$	−8.00000			−0.317221
$637$	4.00000	+	27.7128i	0.158486	+	1.09802i
$638$	5.00000			0.197952
$639$	3.50000	+	6.06218i	0.138458	+	0.239816i
$640$		0			0
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	−0.800678	−	0.599095i	$-0.795527\pi$
$641$	3.00000	−	5.19615i	0.118493	−	0.205236i	0.919171	+	0.393860i	$0.128860\pi$
$642$	5.00000	+	8.66025i	0.197334	+	0.341793i
$643$	−42.0000			−1.65632			−0.828159	−	0.560493i	$-0.810612\pi$
$643$	−42.0000			−1.65632			−0.828159	+	0.560493i	$0.810612\pi$
$644$	−2.00000	−	1.73205i	−0.0788110	−	0.0682524i
$645$		0			0
$646$	−1.50000	−	2.59808i	−0.0590167	−	0.102220i
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	−0.527710	−	0.849425i	$-0.676949\pi$
$647$	12.0000	−	20.7846i	0.471769	−	0.817127i	0.999478	+	0.0322975i	$0.0102824\pi$
$648$	1.50000	−	2.59808i	0.0589256	−	0.102062i
$649$	−4.50000	−	7.79423i	−0.176640	−	0.305950i
$650$	−20.0000			−0.784465
$651$	−5.00000	+	25.9808i	−0.195965	+	1.01827i
$652$	2.00000			0.0783260
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	0.999396	−	0.0347583i	$-0.0110661\pi$
$653$	12.0000	+	20.7846i	0.469596	+	0.813365i	−0.529799	+	0.848123i	$0.677733\pi$
$654$	7.00000	−	12.1244i	0.273722	−	0.474100i
$655$		0			0
$656$	5.00000	+	8.66025i	0.195217	+	0.338126i
$657$	4.00000			0.156055
$658$	−22.5000	+	7.79423i	−0.877141	+	0.303851i
$659$	−6.00000			−0.233727			−0.116863	−	0.993148i	$-0.537284\pi$
$659$	−6.00000			−0.233727			−0.116863	+	0.993148i	$0.537284\pi$
$660$		0			0
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	−0.998209	−	0.0598209i	$-0.980947\pi$
$661$	−11.5000	+	19.9186i	−0.447298	+	0.774743i	0.550911	+	0.834564i	$0.314280\pi$
$662$	−9.00000	+	15.5885i	−0.349795	+	0.605863i
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$	−24.0000			−0.931381
$665$		0			0
$666$	−11.0000			−0.426241
$667$	−2.50000	−	4.33013i	−0.0968004	−	0.167663i
$668$	6.00000	−	10.3923i	0.232147	−	0.402090i
$669$		0			0
$670$		0			0
$671$	2.00000			0.0772091
$672$	2.50000	−	12.9904i	0.0964396	−	0.501115i
$673$	−44.0000			−1.69608			−0.848038	−	0.529936i	$-0.822216\pi$
$673$	−44.0000			−1.69608			−0.848038	+	0.529936i	$0.822216\pi$
$674$	1.00000	+	1.73205i	0.0385186	+	0.0667161i
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	1.50000	−	2.59808i	0.0576923	−	0.0999260i
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	−0.999760	−	0.0219013i	$-0.993028\pi$
$677$	−13.5000	−	23.3827i	−0.518847	−	0.898670i	0.480913	−	0.876768i	$-0.340305\pi$
$678$	12.0000			0.460857
$679$	2.00000	+	1.73205i	0.0767530	+	0.0664700i
$680$		0			0
$681$	7.00000	+	12.1244i	0.268241	+	0.464606i
$682$	−5.00000	+	8.66025i	−0.191460	+	0.331618i
$683$	0.500000	−	0.866025i	0.0191320	−	0.0331375i	−0.856301	−	0.516477i	$-0.827243\pi$
$683$	0.500000	−	0.866025i	0.0191320	−	0.0331375i	0.875433	+	0.483340i	$0.160576\pi$
$684$	0.500000	+	0.866025i	0.0191180	+	0.0331133i
$685$		0			0
$686$	−18.5000	−	0.866025i	−0.706333	−	0.0330650i
$687$	22.0000			0.839352
$688$	−1.50000	−	2.59808i	−0.0571870	−	0.0990507i
$689$	16.0000	−	27.7128i	0.609551	−	1.05577i
$690$		0			0
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	0.577325	−	0.816514i	$-0.304097\pi$
$691$	−11.0000	−	19.0526i	−0.418460	−	0.724793i	−0.995785	+	0.0917209i	$0.970763\pi$
$692$	22.0000			0.836315
$693$	2.00000	+	1.73205i	0.0759737	+	0.0657952i
$694$	−28.0000			−1.06287
$695$		0			0
$696$	7.50000	−	12.9904i	0.284287	−	0.492399i
$697$	−15.0000	+	25.9808i	−0.568166	+	0.984092i
$698$	−12.0000	−	20.7846i	−0.454207	−	0.786709i
$699$	−25.0000			−0.945587
$700$	−2.50000	+	12.9904i	−0.0944911	+	0.490990i
$701$	−23.0000			−0.868698			−0.434349	−	0.900745i	$-0.643022\pi$
$701$	−23.0000			−0.868698			−0.434349	+	0.900745i	$0.643022\pi$
$702$	2.00000	+	3.46410i	0.0754851	+	0.130744i
$703$	5.50000	−	9.52628i	0.207436	−	0.359290i
$704$	3.50000	−	6.06218i	0.131911	−	0.228477i
$705$		0			0
$706$	24.0000			0.903252
$707$	−12.5000	+	4.33013i	−0.470111	+	0.162851i
$708$	−9.00000			−0.338241
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	0.690127	−	0.723688i	$-0.257554\pi$
$709$	−7.50000	−	12.9904i	−0.281668	−	0.487864i	−0.971796	+	0.235824i	$0.924221\pi$
$710$		0			0
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$		0			0
$713$	10.0000			0.374503
$714$	−7.50000	+	2.59808i	−0.280680	+	0.0972306i
$715$		0			0
$716$	−0.500000	−	0.866025i	−0.0186859	−	0.0323649i
$717$		0			0
$718$	3.00000	−	5.19615i	0.111959	−	0.193919i
$719$	−25.5000	−	44.1673i	−0.950990	−	1.64716i	−0.743290	−	0.668970i	$-0.766736\pi$
$719$	−25.5000	−	44.1673i	−0.950990	−	1.64716i	−0.207700	−	0.978193i	$-0.566598\pi$
$720$		0			0
$721$	2.00000	−	10.3923i	0.0744839	−	0.387030i
$722$	−18.0000			−0.669891
$723$	−2.00000	−	3.46410i	−0.0743808	−	0.128831i
$724$	−5.00000	+	8.66025i	−0.185824	+	0.321856i
$725$	−12.5000	+	21.6506i	−0.464238	+	0.804084i
$726$	0.500000	+	0.866025i	0.0185567	+	0.0321412i
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$	24.0000	+	20.7846i	0.889499	+	0.770329i
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.50000	−	7.79423i	0.166439	−	0.288280i
$732$	1.00000	−	1.73205i	0.0369611	−	0.0640184i
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$	−5.00000			−0.184302
$737$	2.00000	+	3.46410i	0.0736709	+	0.127602i
$738$	−5.00000	+	8.66025i	−0.184053	+	0.318788i
$739$	−18.0000	+	31.1769i	−0.662141	+	1.14686i	0.317911	+	0.948120i	$0.397019\pi$
$739$	−18.0000	+	31.1769i	−0.662141	+	1.14686i	−0.980052	+	0.198741i	$0.936315\pi$
$740$		0			0
$741$	−4.00000			−0.146944
$742$	16.0000	+	13.8564i	0.587378	+	0.508685i
$743$	18.0000			0.660356			0.330178	−	0.943919i	$-0.392891\pi$
$743$	18.0000			0.660356			0.330178	+	0.943919i	$0.392891\pi$
$744$	15.0000	+	25.9808i	0.549927	+	0.952501i
$745$		0			0
$746$	3.00000	−	5.19615i	0.109838	−	0.190245i
$747$	−4.00000	−	6.92820i	−0.146352	−	0.253490i
$748$	3.00000			0.109691
$749$	−5.00000	+	25.9808i	−0.182696	+	0.949316i
$750$		0			0
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	0.989423	+	0.145062i	$0.0463382\pi$
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	−0.369084	+	0.929396i	$0.620328\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	−7.50000	+	12.9904i	−0.273315	+	0.473396i
$754$	10.0000	+	17.3205i	0.364179	+	0.630776i
$755$		0			0
$756$	2.50000	−	0.866025i	0.0909241	−	0.0314970i
$757$	45.0000			1.63555			0.817776	−	0.575536i	$-0.195207\pi$
$757$	45.0000			1.63555			0.817776	+	0.575536i	$0.195207\pi$
$758$	−17.0000	−	29.4449i	−0.617468	−	1.06949i
$759$	0.500000	−	0.866025i	0.0181489	−	0.0314347i
$760$		0			0
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	−0.998684	−	0.0512772i	$-0.983671\pi$
$761$	−15.0000	−	25.9808i	−0.543750	−	0.941802i	0.454935	−	0.890525i	$-0.349663\pi$
$762$	19.0000			0.688297
$763$	35.0000	−	12.1244i	1.26709	−	0.438931i
$764$	8.00000			0.289430
$765$		0			0
$766$	−6.50000	+	11.2583i	−0.234855	+	0.406780i
$767$	18.0000	−	31.1769i	0.649942	−	1.12573i
$768$	−8.50000	−	14.7224i	−0.306717	−	0.531250i
$769$	−30.0000			−1.08183			−0.540914	−	0.841078i	$-0.681921\pi$
$769$	−30.0000			−1.08183			−0.540914	+	0.841078i	$0.681921\pi$
$770$		0			0
$771$	−28.0000			−1.00840
$772$	−5.00000	−	8.66025i	−0.179954	−	0.311689i
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	−0.657542	−	0.753418i	$-0.728404\pi$
$773$	9.00000	−	15.5885i	0.323708	−	0.560678i	0.981250	+	0.192740i	$0.0617373\pi$
$774$	1.50000	−	2.59808i	0.0539164	−	0.0933859i
$775$	−25.0000	−	43.3013i	−0.898027	−	1.55543i
$776$	3.00000			0.107694
$777$	−22.0000	−	19.0526i	−0.789246	−	0.683507i
$778$	−20.0000			−0.717035
$779$	−5.00000	−	8.66025i	−0.179144	−	0.310286i
$780$		0			0
$781$	−3.50000	+	6.06218i	−0.125240	+	0.216922i
$782$	1.50000	+	2.59808i	0.0536399	+	0.0929070i
$783$	5.00000			0.178685
$784$	−5.50000	+	4.33013i	−0.196429	+	0.154647i
$785$		0			0
$786$	7.00000	+	12.1244i	0.249682	+	0.432461i
$787$	−0.500000	+	0.866025i	−0.0178231	+	0.0308705i	−0.874799	−	0.484485i	$-0.839007\pi$
$787$	−0.500000	+	0.866025i	−0.0178231	+	0.0308705i	0.856976	+	0.515356i	$0.172340\pi$
$788$	−0.500000	+	0.866025i	−0.0178118	+	0.0308509i
$789$	−15.0000	−	25.9808i	−0.534014	−	0.924940i
$790$		0			0
$791$	24.0000	+	20.7846i	0.853342	+	0.739016i
$792$	3.00000			0.106600
$793$	4.00000	+	6.92820i	0.142044	+	0.246028i
$794$	16.5000	−	28.5788i	0.585563	−	1.01423i
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	50.0000			1.77109			0.885545	−	0.464553i	$-0.153785\pi$
$797$	50.0000			1.77109			0.885545	+	0.464553i	$0.153785\pi$
$798$	0.500000	−	2.59808i	0.0176998	−	0.0919709i
$799$	−27.0000			−0.955191
$800$	12.5000	+	21.6506i	0.441942	+	0.765466i
$801$		0			0
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	2.00000	+	3.46410i	0.0705785	+	0.122245i
$804$	4.00000			0.141069
$805$		0			0
$806$	−40.0000			−1.40894
$807$	11.0000	+	19.0526i	0.387218	+	0.670682i
$808$	−7.50000	+	12.9904i	−0.263849	+	0.457000i
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	−0.808458	−	0.588555i	$-0.799697\pi$
$809$	3.00000	−	5.19615i	0.105474	−	0.182687i	0.913932	+	0.405868i	$0.133031\pi$
$810$		0			0
$811$	44.0000			1.54505			0.772524	−	0.634985i	$-0.218994\pi$
$811$	44.0000			1.54505			0.772524	+	0.634985i	$0.218994\pi$
$812$	12.5000	−	4.33013i	0.438664	−	0.151958i
$813$	8.00000			0.280572
$814$	−5.50000	−	9.52628i	−0.192775	−	0.333896i
$815$		0			0
$816$	−1.50000	+	2.59808i	−0.0525105	+	0.0909509i
$817$	1.50000	+	2.59808i	0.0524784	+	0.0908952i
$818$	−10.0000			−0.349642
$819$	−2.00000	+	10.3923i	−0.0698857	+	0.363137i
$820$		0			0
$821$	19.0000	+	32.9090i	0.663105	+	1.14853i	0.979795	+	0.200002i	$0.0640949\pi$
$821$	19.0000	+	32.9090i	0.663105	+	1.14853i	−0.316691	+	0.948529i	$0.602572\pi$
$822$	10.0000	−	17.3205i	0.348790	−	0.604122i
$823$	−5.00000	+	8.66025i	−0.174289	+	0.301877i	−0.939915	−	0.341409i	$-0.889096\pi$
$823$	−5.00000	+	8.66025i	−0.174289	+	0.301877i	0.765626	+	0.643286i	$0.222429\pi$
$824$	−6.00000	−	10.3923i	−0.209020	−	0.362033i
$825$	−5.00000			−0.174078
$826$	18.0000	+	15.5885i	0.626300	+	0.542392i
$827$	−2.00000			−0.0695468			−0.0347734	−	0.999395i	$-0.511071\pi$
$827$	−2.00000			−0.0695468			−0.0347734	+	0.999395i	$0.511071\pi$
$828$	−0.500000	−	0.866025i	−0.0173762	−	0.0300965i
$829$	15.5000	−	26.8468i	0.538337	−	0.932427i	−0.460657	−	0.887578i	$-0.652386\pi$
$829$	15.5000	−	26.8468i	0.538337	−	0.932427i	0.998994	−	0.0448490i	$-0.0142807\pi$
$830$		0			0
$831$	16.0000	+	27.7128i	0.555034	+	0.961347i
$832$	28.0000			0.970725
$833$	−19.5000	−	7.79423i	−0.675635	−	0.270054i
$834$	13.0000			0.450153
$835$		0			0
$836$	−0.500000	+	0.866025i	−0.0172929	+	0.0299521i
$837$	−5.00000	+	8.66025i	−0.172825	+	0.299342i
$838$	−3.50000	−	6.06218i	−0.120905	−	0.209414i
$839$	−36.0000			−1.24286			−0.621429	−	0.783470i	$-0.713448\pi$
$839$	−36.0000			−1.24286			−0.621429	+	0.783470i	$0.713448\pi$
$840$		0			0
$841$	−4.00000			−0.137931
$842$	1.50000	+	2.59808i	0.0516934	+	0.0895356i
$843$	4.50000	−	7.79423i	0.154988	−	0.268447i
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$		0			0
$846$	−9.00000			−0.309426
$847$	−0.500000	+	2.59808i	−0.0171802	+	0.0892710i
$848$	8.00000			0.274721
$849$	−2.00000	−	3.46410i	−0.0686398	−	0.118888i
$850$	7.50000	−	12.9904i	0.257248	−	0.445566i
$851$	−5.50000	+	9.52628i	−0.188538	+	0.326557i
$852$	3.50000	+	6.06218i	0.119908	+	0.207687i
$853$	20.0000			0.684787			0.342393	−	0.939557i	$-0.388762\pi$
$853$	20.0000			0.684787			0.342393	+	0.939557i	$0.388762\pi$
$854$	−5.00000	+	1.73205i	−0.171096	+	0.0592696i
$855$		0			0
$856$	15.0000	+	25.9808i	0.512689	+	0.888004i
$857$	8.50000	−	14.7224i	0.290354	−	0.502909i	−0.683539	−	0.729914i	$-0.739560\pi$
$857$	8.50000	−	14.7224i	0.290354	−	0.502909i	0.973894	+	0.227005i	$0.0728935\pi$
$858$	−2.00000	+	3.46410i	−0.0682789	+	0.118262i
$859$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$859$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$860$		0			0
$861$	−25.0000	+	8.66025i	−0.851998	+	0.295141i
$862$	28.0000			0.953684
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	0.998629	+	0.0523446i	$0.0166694\pi$
$863$	16.0000	+	27.7128i	0.544646	+	0.943355i	−0.453983	+	0.891010i	$0.649997\pi$
$864$	2.50000	−	4.33013i	0.0850517	−	0.147314i
$865$		0			0
$866$	5.50000	+	9.52628i	0.186898	+	0.323716i
$867$	8.00000			0.271694
$868$	−5.00000	+	25.9808i	−0.169711	+	0.881845i
$869$	8.00000			0.271381
$870$		0			0
$871$	−8.00000	+	13.8564i	−0.271070	+	0.469506i
$872$	21.0000	−	36.3731i	0.711150	−	1.23175i
$873$	0.500000	+	0.866025i	0.0169224	+	0.0293105i
$874$	−1.00000			−0.0338255
$875$		0			0
$876$	4.00000			0.135147
$877$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$877$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$878$	−0.500000	+	0.866025i	−0.0168742	+	0.0292269i
$879$	10.5000	−	18.1865i	0.354156	−	0.613417i
$880$		0			0
$881$	20.0000			0.673817			0.336909	−	0.941537i	$-0.390619\pi$
$881$	20.0000			0.673817			0.336909	+	0.941537i	$0.390619\pi$
$882$	−6.50000	−	2.59808i	−0.218866	−	0.0874818i
$883$	−18.0000			−0.605748			−0.302874	−	0.953031i	$-0.597946\pi$
$883$	−18.0000			−0.605748			−0.302874	+	0.953031i	$0.597946\pi$
$884$	6.00000	+	10.3923i	0.201802	+	0.349531i
$885$		0			0
$886$	17.5000	−	30.3109i	0.587924	−	1.01831i
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	0.999052	+	0.0435339i	$0.0138616\pi$
$887$	16.0000	+	27.7128i	0.537227	+	0.930505i	−0.461825	+	0.886971i	$0.652805\pi$
$888$	−33.0000			−1.10741
$889$	38.0000	+	32.9090i	1.27448	+	1.10373i
$890$		0			0
$891$	0.500000	+	0.866025i	0.0167506	+	0.0290129i
$892$		0			0
$893$	4.50000	−	7.79423i	0.150587	−	0.260824i
$894$	−1.50000	−	2.59808i	−0.0501675	−	0.0868927i
$895$		0			0
$896$	1.50000	−	7.79423i	0.0501115	−	0.260387i
$897$	4.00000			0.133556
$898$	12.0000	+	20.7846i	0.400445	+	0.693591i
$899$	−25.0000	+	43.3013i	−0.833797	+	1.44418i
$900$	−2.50000	+	4.33013i	−0.0833333	+	0.144338i
$901$	12.0000	+	20.7846i	0.399778	+	0.692436i
$902$	−10.0000			−0.332964
$903$	7.50000	−	2.59808i	0.249584	−	0.0864586i
$904$	36.0000			1.19734
$905$		0			0
$906$	−0.500000	+	0.866025i	−0.0166114	+	0.0287718i
$907$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$907$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$908$	7.00000	+	12.1244i	0.232303	+	0.402361i
$909$	−5.00000			−0.165840
$910$		0			0
$911$	−45.0000			−1.49092			−0.745458	−	0.666552i	$-0.767769\pi$
$911$	−45.0000			−1.49092			−0.745458	+	0.666552i	$0.767769\pi$
$912$	−0.500000	−	0.866025i	−0.0165567	−	0.0286770i
$913$	4.00000	−	6.92820i	0.132381	−	0.229290i
$914$	−9.00000	+	15.5885i	−0.297694	+	0.515620i
$915$		0			0
$916$	22.0000			0.726900
$917$	−7.00000	+	36.3731i	−0.231160	+	1.20114i
$918$	−3.00000			−0.0990148
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	0.991197	+	0.132398i	$0.0422678\pi$
$919$	18.5000	+	32.0429i	0.610259	+	1.05700i	−0.380938	+	0.924601i	$0.624399\pi$
$920$		0			0
$921$	−6.00000	+	10.3923i	−0.197707	+	0.342438i
$922$	−16.5000	−	28.5788i	−0.543399	−	0.941194i
$923$	−28.0000			−0.921631
$924$	2.00000	+	1.73205i	0.0657952	+	0.0569803i
$925$	55.0000			1.80839
$926$	16.0000	+	27.7128i	0.525793	+	0.910700i
$927$	2.00000	−	3.46410i	0.0656886	−	0.113776i
$928$	12.5000	−	21.6506i	0.410333	−	0.710717i
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		0			0
$931$	5.50000	−	4.33013i	0.180255	−	0.141914i
$932$	−25.0000			−0.818902
$933$	8.50000	+	14.7224i	0.278278	+	0.481991i
$934$	3.50000	−	6.06218i	0.114523	−	0.198361i
$935$		0			0
$936$	6.00000	+	10.3923i	0.196116	+	0.339683i
$937$	16.0000			0.522697			0.261349	−	0.965244i	$-0.415833\pi$
$937$	16.0000			0.522697			0.261349	+	0.965244i	$0.415833\pi$
$938$	−8.00000	−	6.92820i	−0.261209	−	0.226214i
$939$	9.00000			0.293704
$940$		0			0
$941$	−23.5000	+	40.7032i	−0.766078	+	1.32689i	0.173597	+	0.984817i	$0.444461\pi$
$941$	−23.5000	+	40.7032i	−0.766078	+	1.32689i	−0.939675	+	0.342069i	$0.888872\pi$
$942$	3.50000	−	6.06218i	0.114036	−	0.197516i
$943$	5.00000	+	8.66025i	0.162822	+	0.282017i
$944$	9.00000			0.292925
$945$		0			0
$946$	3.00000			0.0975384
$947$	−10.5000	−	18.1865i	−0.341204	−	0.590983i	0.643452	−	0.765486i	$-0.277501\pi$
$947$	−10.5000	−	18.1865i	−0.341204	−	0.590983i	−0.984657	+	0.174503i	$0.944168\pi$
$948$	4.00000	−	6.92820i	0.129914	−	0.225018i
$949$	−8.00000	+	13.8564i	−0.259691	+	0.449798i
$950$	2.50000	+	4.33013i	0.0811107	+	0.140488i
$951$	−12.0000			−0.389127
$952$	−22.5000	+	7.79423i	−0.729229	+	0.252612i
$953$	−34.0000			−1.10137			−0.550684	−	0.834714i	$-0.685633\pi$
$953$	−34.0000			−1.10137			−0.550684	+	0.834714i	$0.685633\pi$
$954$	4.00000	+	6.92820i	0.129505	+	0.224309i
$955$		0			0
$956$		0			0
$957$	2.50000	+	4.33013i	0.0808135	+	0.139973i
$958$	10.0000			0.323085
$959$	50.0000	−	17.3205i	1.61458	−	0.559308i
$960$		0			0
$961$	−34.5000	−	59.7558i	−1.11290	−	1.92760i
$962$	22.0000	−	38.1051i	0.709308	−	1.22856i
$963$	−5.00000	+	8.66025i	−0.161123	+	0.279073i
$964$	−2.00000	−	3.46410i	−0.0644157	−	0.111571i
$965$		0			0
$966$	−0.500000	+	2.59808i	−0.0160872	+	0.0835917i
$967$	−31.0000			−0.996893			−0.498446	−	0.866921i	$-0.666096\pi$
$967$	−31.0000			−0.996893			−0.498446	+	0.866921i	$0.666096\pi$
$968$	1.50000	+	2.59808i	0.0482118	+	0.0835053i
$969$	1.50000	−	2.59808i	0.0481869	−	0.0834622i
$970$		0			0
$971$	16.0000	+	27.7128i	0.513464	+	0.889346i	0.999878	+	0.0156178i	$0.00497150\pi$
$971$	16.0000	+	27.7128i	0.513464	+	0.889346i	−0.486414	+	0.873729i	$0.661695\pi$
$972$	1.00000			0.0320750
$973$	26.0000	+	22.5167i	0.833522	+	0.721851i
$974$	4.00000			0.128168
$975$	−10.0000	−	17.3205i	−0.320256	−	0.554700i
$976$	−1.00000	+	1.73205i	−0.0320092	+	0.0554416i
$977$	−26.0000	+	45.0333i	−0.831814	+	1.44074i	0.0647848	+	0.997899i	$0.479364\pi$
$977$	−26.0000	+	45.0333i	−0.831814	+	1.44074i	−0.896599	+	0.442844i	$0.853969\pi$
$978$	−1.00000	−	1.73205i	−0.0319765	−	0.0553849i
$979$		0			0
$980$		0			0
$981$	14.0000			0.446986
$982$	−6.00000	−	10.3923i	−0.191468	−	0.331632i
$983$	−9.50000	+	16.4545i	−0.303003	+	0.524816i	−0.976815	−	0.214087i	$-0.931323\pi$
$983$	−9.50000	+	16.4545i	−0.303003	+	0.524816i	0.673812	+	0.738903i	$0.264656\pi$
$984$	−15.0000	+	25.9808i	−0.478183	+	0.828236i
$985$		0			0
$986$	−15.0000			−0.477697
$987$	−18.0000	−	15.5885i	−0.572946	−	0.496186i
$988$	−4.00000			−0.127257
$989$	−1.50000	−	2.59808i	−0.0476972	−	0.0826140i
$990$		0			0
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	−0.710530	−	0.703667i	$-0.751545\pi$
$991$	8.00000	−	13.8564i	0.254128	−	0.440163i	0.964658	+	0.263504i	$0.0848781\pi$
$992$	25.0000	+	43.3013i	0.793751	+	1.37482i
$993$	−18.0000			−0.571213
$994$	3.50000	−	18.1865i	0.111013	−	0.576842i
$995$		0			0
$996$	−4.00000	−	6.92820i	−0.126745	−	0.219529i
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	−0.997938	−	0.0641836i	$-0.979556\pi$
$997$	−14.0000	+	24.2487i	−0.443384	+	0.767964i	0.554554	+	0.832148i	$0.312889\pi$
$998$	7.00000	−	12.1244i	0.221581	−	0.383790i
$999$	−5.50000	−	9.52628i	−0.174012	−	0.301398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	231.2.i.a.67.1	✓	2
3.2	odd	2		693.2.i.e.298.1		2
7.2	even	3	inner	231.2.i.a.100.1	yes	2
7.3	odd	6		1617.2.a.h.1.1		1
7.4	even	3		1617.2.a.g.1.1		1
21.2	odd	6		693.2.i.e.100.1		2
21.11	odd	6		4851.2.a.e.1.1		1
21.17	even	6		4851.2.a.d.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
231.2.i.a.67.1	✓	2	1.1	even	1	trivial
231.2.i.a.100.1	yes	2	7.2	even	3	inner
693.2.i.e.100.1		2	21.2	odd	6
693.2.i.e.298.1		2	3.2	odd	2
1617.2.a.g.1.1		1	7.4	even	3
1617.2.a.h.1.1		1	7.3	odd	6
4851.2.a.d.1.1		1	21.17	even	6
4851.2.a.e.1.1		1	21.11	odd	6

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:	\( N \)	\(=\)	\( 231 = 3 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	231.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +(-2.00000 - 1.73205i) q^{7} -3.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{11} +(-0.500000 - 0.866025i) q^{12} +4.00000 q^{13} +(-0.500000 + 2.59808i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(-2.50000 + 0.866025i) q^{21} -1.00000 q^{22} +(0.500000 + 0.866025i) q^{23} +(-1.50000 + 2.59808i) q^{24} +(2.50000 - 4.33013i) q^{25} +(-2.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(-2.50000 + 0.866025i) q^{28} -5.00000 q^{29} +(5.00000 - 8.66025i) q^{31} +(-2.50000 + 4.33013i) q^{32} +(-0.500000 - 0.866025i) q^{33} +3.00000 q^{34} -1.00000 q^{36} +(5.50000 + 9.52628i) q^{37} +(-0.500000 + 0.866025i) q^{38} +(2.00000 - 3.46410i) q^{39} +10.0000 q^{41} +(2.00000 + 1.73205i) q^{42} -3.00000 q^{43} +(-0.500000 - 0.866025i) q^{44} +(0.500000 - 0.866025i) q^{46} +(4.50000 + 7.79423i) q^{47} +1.00000 q^{48} +(1.00000 + 6.92820i) q^{49} -5.00000 q^{50} +(1.50000 + 2.59808i) q^{51} +(2.00000 - 3.46410i) q^{52} +(4.00000 - 6.92820i) q^{53} +(0.500000 + 0.866025i) q^{54} +(6.00000 + 5.19615i) q^{56} -1.00000 q^{57} +(2.50000 + 4.33013i) q^{58} +(4.50000 - 7.79423i) q^{59} +(1.00000 + 1.73205i) q^{61} -10.0000 q^{62} +(-0.500000 + 2.59808i) q^{63} +7.00000 q^{64} +(-0.500000 + 0.866025i) q^{66} +(-2.00000 + 3.46410i) q^{67} +(1.50000 + 2.59808i) q^{68} +1.00000 q^{69} -7.00000 q^{71} +(1.50000 + 2.59808i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(5.50000 - 9.52628i) q^{74} +(-2.50000 - 4.33013i) q^{75} -1.00000 q^{76} +(-2.50000 + 0.866025i) q^{77} -4.00000 q^{78} +(4.00000 + 6.92820i) q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.00000 - 8.66025i) q^{82} +8.00000 q^{83} +(-0.500000 + 2.59808i) q^{84} +(1.50000 + 2.59808i) q^{86} +(-2.50000 + 4.33013i) q^{87} +(-1.50000 + 2.59808i) q^{88} +(-8.00000 - 6.92820i) q^{91} +1.00000 q^{92} +(-5.00000 - 8.66025i) q^{93} +(4.50000 - 7.79423i) q^{94} +(2.50000 + 4.33013i) q^{96} -1.00000 q^{97} +(5.50000 - 4.33013i) q^{98} -1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 + q^4 - 2 * q^6 - 4 * q^7 - 6 * q^8 - q^9	\( 2 q - q^{2} + q^{3} + q^{4} - 2 q^{6} - 4 q^{7} - 6 q^{8} - q^{9} + q^{11} - q^{12} + 8 q^{13} - q^{14} + q^{16} - 3 q^{17} - q^{18} - q^{19} - 5 q^{21} - 2 q^{22} + q^{23} - 3 q^{24} + 5 q^{25} - 4 q^{26} - 2 q^{27} - 5 q^{28} - 10 q^{29} + 10 q^{31} - 5 q^{32} - q^{33} + 6 q^{34} - 2 q^{36} + 11 q^{37} - q^{38} + 4 q^{39} + 20 q^{41} + 4 q^{42} - 6 q^{43} - q^{44} + q^{46} + 9 q^{47} + 2 q^{48} + 2 q^{49} - 10 q^{50} + 3 q^{51} + 4 q^{52} + 8 q^{53} + q^{54} + 12 q^{56} - 2 q^{57} + 5 q^{58} + 9 q^{59} + 2 q^{61} - 20 q^{62} - q^{63} + 14 q^{64} - q^{66} - 4 q^{67} + 3 q^{68} + 2 q^{69} - 14 q^{71} + 3 q^{72} - 4 q^{73} + 11 q^{74} - 5 q^{75} - 2 q^{76} - 5 q^{77} - 8 q^{78} + 8 q^{79} - q^{81} - 10 q^{82} + 16 q^{83} - q^{84} + 3 q^{86} - 5 q^{87} - 3 q^{88} - 16 q^{91} + 2 q^{92} - 10 q^{93} + 9 q^{94} + 5 q^{96} - 2 q^{97} + 11 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 + q^4 - 2 * q^6 - 4 * q^7 - 6 * q^8 - q^9 + q^11 - q^12 + 8 * q^13 - q^14 + q^16 - 3 * q^17 - q^18 - q^19 - 5 * q^21 - 2 * q^22 + q^23 - 3 * q^24 + 5 * q^25 - 4 * q^26 - 2 * q^27 - 5 * q^28 - 10 * q^29 + 10 * q^31 - 5 * q^32 - q^33 + 6 * q^34 - 2 * q^36 + 11 * q^37 - q^38 + 4 * q^39 + 20 * q^41 + 4 * q^42 - 6 * q^43 - q^44 + q^46 + 9 * q^47 + 2 * q^48 + 2 * q^49 - 10 * q^50 + 3 * q^51 + 4 * q^52 + 8 * q^53 + q^54 + 12 * q^56 - 2 * q^57 + 5 * q^58 + 9 * q^59 + 2 * q^61 - 20 * q^62 - q^63 + 14 * q^64 - q^66 - 4 * q^67 + 3 * q^68 + 2 * q^69 - 14 * q^71 + 3 * q^72 - 4 * q^73 + 11 * q^74 - 5 * q^75 - 2 * q^76 - 5 * q^77 - 8 * q^78 + 8 * q^79 - q^81 - 10 * q^82 + 16 * q^83 - q^84 + 3 * q^86 - 5 * q^87 - 3 * q^88 - 16 * q^91 + 2 * q^92 - 10 * q^93 + 9 * q^94 + 5 * q^96 - 2 * q^97 + 11 * q^98 - 2 * q^99

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