LMFDB - Embedded newform 370.2.e.a.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(121,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("370.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.95446487479$
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			121.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	370.121
Dual form			370.2.e.a.211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -5.00000 q^{11} +(-1.00000 + 1.73205i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +1.00000 q^{23} +(1.00000 + 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{26} -4.00000 q^{27} -2.00000 q^{29} +(1.00000 + 1.73205i) q^{30} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(5.00000 + 8.66025i) q^{33} +(-2.00000 - 3.46410i) q^{34} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} +5.00000 q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.00000 - 8.66025i) q^{41} +6.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +1.00000 q^{45} +(0.500000 - 0.866025i) q^{46} +9.00000 q^{47} +2.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} -8.00000 q^{51} +(-0.500000 + 0.866025i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(2.50000 + 4.33013i) q^{55} +(5.00000 - 8.66025i) q^{57} +(-1.00000 + 1.73205i) q^{58} +(-0.500000 + 0.866025i) q^{59} +2.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +10.0000 q^{66} +(-4.00000 - 6.92820i) q^{67} -4.00000 q^{68} +(-1.00000 - 1.73205i) q^{69} +(-7.00000 - 12.1244i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-5.50000 - 2.59808i) q^{74} +2.00000 q^{75} +(2.50000 - 4.33013i) q^{76} +(1.00000 + 1.73205i) q^{78} +(4.00000 + 6.92820i) q^{79} +1.00000 q^{80} +(5.50000 + 9.52628i) q^{81} -10.0000 q^{82} +(-1.00000 + 1.73205i) q^{83} -4.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(2.00000 + 3.46410i) q^{87} +5.00000 q^{88} +(-0.500000 + 0.866025i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-0.500000 - 0.866025i) q^{92} +(4.00000 + 6.92820i) q^{93} +(4.50000 - 7.79423i) q^{94} +(2.50000 - 4.33013i) q^{95} +(1.00000 - 1.73205i) q^{96} +10.0000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - 4 * q^6 - 2 * q^8 - q^9	$ 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - 4 q^{6} - 2 q^{8} - q^{9} - 2 q^{10} - 10 q^{11} - 2 q^{12} - q^{13} - 2 q^{15} - q^{16} + 4 q^{17} + q^{18} + 5 q^{19} - q^{20} - 5 q^{22} + 2 q^{23} + 2 q^{24} - q^{25} - 2 q^{26} - 8 q^{27} - 4 q^{29} + 2 q^{30} - 8 q^{31} + q^{32} + 10 q^{33} - 4 q^{34} + 2 q^{36} - q^{37} + 10 q^{38} - 2 q^{39} + q^{40} - 10 q^{41} + 12 q^{43} + 5 q^{44} + 2 q^{45} + q^{46} + 18 q^{47} + 4 q^{48} + 7 q^{49} + q^{50} - 16 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} + 5 q^{55} + 10 q^{57} - 2 q^{58} - q^{59} + 4 q^{60} - 2 q^{61} - 4 q^{62} + 2 q^{64} - q^{65} + 20 q^{66} - 8 q^{67} - 8 q^{68} - 2 q^{69} - 14 q^{71} + q^{72} + 24 q^{73} - 11 q^{74} + 4 q^{75} + 5 q^{76} + 2 q^{78} + 8 q^{79} + 2 q^{80} + 11 q^{81} - 20 q^{82} - 2 q^{83} - 8 q^{85} + 6 q^{86} + 4 q^{87} + 10 q^{88} - q^{89} + q^{90} - q^{92} + 8 q^{93} + 9 q^{94} + 5 q^{95} + 2 q^{96} + 20 q^{97} - 7 q^{98} + 5 q^{99}+O(q^{100}) $ 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - 4 * q^6 - 2 * q^8 - q^9 - 2 * q^10 - 10 * q^11 - 2 * q^12 - q^13 - 2 * q^15 - q^16 + 4 * q^17 + q^18 + 5 * q^19 - q^20 - 5 * q^22 + 2 * q^23 + 2 * q^24 - q^25 - 2 * q^26 - 8 * q^27 - 4 * q^29 + 2 * q^30 - 8 * q^31 + q^32 + 10 * q^33 - 4 * q^34 + 2 * q^36 - q^37 + 10 * q^38 - 2 * q^39 + q^40 - 10 * q^41 + 12 * q^43 + 5 * q^44 + 2 * q^45 + q^46 + 18 * q^47 + 4 * q^48 + 7 * q^49 + q^50 - 16 * q^51 - q^52 + 6 * q^53 - 4 * q^54 + 5 * q^55 + 10 * q^57 - 2 * q^58 - q^59 + 4 * q^60 - 2 * q^61 - 4 * q^62 + 2 * q^64 - q^65 + 20 * q^66 - 8 * q^67 - 8 * q^68 - 2 * q^69 - 14 * q^71 + q^72 + 24 * q^73 - 11 * q^74 + 4 * q^75 + 5 * q^76 + 2 * q^78 + 8 * q^79 + 2 * q^80 + 11 * q^81 - 20 * q^82 - 2 * q^83 - 8 * q^85 + 6 * q^86 + 4 * q^87 + 10 * q^88 - q^89 + q^90 - q^92 + 8 * q^93 + 9 * q^94 + 5 * q^95 + 2 * q^96 + 20 * q^97 - 7 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	−0.995782	−	0.0917517i	$-0.970753\pi$
$3$	−1.00000	−	1.73205i	−0.577350	−	1.00000i	0.418432	−	0.908248i	$-0.362580\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$	−2.00000			−0.816497
$7$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$7$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.00000			−0.316228
$11$	−5.00000			−1.50756			−0.753778	−	0.657129i	$-0.771771\pi$
$11$	−5.00000			−1.50756			−0.753778	+	0.657129i	$0.771771\pi$
$12$	−1.00000	+	1.73205i	−0.288675	+	0.500000i
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	0.788320	−	0.615265i	$-0.210951\pi$
$13$	−0.500000	−	0.866025i	−0.138675	−	0.240192i	−0.926995	+	0.375073i	$0.877618\pi$
$14$		0			0
$15$	−1.00000	+	1.73205i	−0.258199	+	0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	−0.500000	+	0.866025i	−0.111803	+	0.193649i
$21$		0			0
$22$	−2.50000	+	4.33013i	−0.533002	+	0.923186i
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$	1.00000	+	1.73205i	0.204124	+	0.353553i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.00000			−0.196116
$27$	−4.00000			−0.769800
$28$		0			0
$29$	−2.00000			−0.371391			−0.185695	−	0.982607i	$-0.559454\pi$
$29$	−2.00000			−0.371391			−0.185695	+	0.982607i	$0.559454\pi$
$30$	1.00000	+	1.73205i	0.182574	+	0.316228i
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	5.00000	+	8.66025i	0.870388	+	1.50756i
$34$	−2.00000	−	3.46410i	−0.342997	−	0.594089i
$35$		0			0
$36$	1.00000			0.166667
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$37$	−0.500000	−	6.06218i	−0.0821995	−	0.996616i
$38$	5.00000			0.811107
$39$	−1.00000	+	1.73205i	−0.160128	+	0.277350i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	−0.931436	−	0.363905i	$-0.881443\pi$
$41$	−5.00000	−	8.66025i	−0.780869	−	1.35250i	0.150567	−	0.988600i	$-0.451890\pi$
$42$		0			0
$43$	6.00000			0.914991			0.457496	−	0.889212i	$-0.348747\pi$
$43$	6.00000			0.914991			0.457496	+	0.889212i	$0.348747\pi$
$44$	2.50000	+	4.33013i	0.376889	+	0.652791i
$45$	1.00000			0.149071
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$	2.00000			0.288675
$49$	3.50000	−	6.06218i	0.500000	−	0.866025i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−8.00000			−1.12022
$52$	−0.500000	+	0.866025i	−0.0693375	+	0.120096i
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	−0.583036	−	0.812447i	$-0.698135\pi$
$53$	3.00000	−	5.19615i	0.412082	−	0.713746i	0.995117	+	0.0987002i	$0.0314685\pi$
$54$	−2.00000	+	3.46410i	−0.272166	+	0.471405i
$55$	2.50000	+	4.33013i	0.337100	+	0.583874i
$56$		0			0
$57$	5.00000	−	8.66025i	0.662266	−	1.14708i
$58$	−1.00000	+	1.73205i	−0.131306	+	0.227429i
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	−0.896736	−	0.442566i	$-0.854068\pi$
$59$	−0.500000	+	0.866025i	−0.0650945	+	0.112747i	0.831641	+	0.555313i	$0.187402\pi$
$60$	2.00000			0.258199
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$		0			0
$64$	1.00000			0.125000
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$	10.0000			1.23091
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	0.511237	−	0.859440i	$-0.329187\pi$
$67$	−4.00000	−	6.92820i	−0.488678	−	0.846415i	−0.999915	+	0.0130248i	$0.995854\pi$
$68$	−4.00000			−0.485071
$69$	−1.00000	−	1.73205i	−0.120386	−	0.208514i
$70$		0			0
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	−0.897447	−	0.441123i	$-0.854580\pi$
$71$	−7.00000	−	12.1244i	−0.830747	−	1.43890i	0.0666994	−	0.997773i	$-0.478753\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	−5.50000	−	2.59808i	−0.639362	−	0.302020i
$75$	2.00000			0.230940
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$		0			0
$78$	1.00000	+	1.73205i	0.113228	+	0.196116i
$79$	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	$0.684745\pi$
$80$	1.00000			0.111803
$81$	5.50000	+	9.52628i	0.611111	+	1.05848i
$82$	−10.0000			−1.10432
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	0.805910	+	0.592037i	$0.201676\pi$
$84$		0			0
$85$	−4.00000			−0.433861
$86$	3.00000	−	5.19615i	0.323498	−	0.560316i
$87$	2.00000	+	3.46410i	0.214423	+	0.371391i
$88$	5.00000			0.533002
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	−0.891308	−	0.453398i	$-0.850212\pi$
$89$	−0.500000	+	0.866025i	−0.0529999	+	0.0917985i	0.838308	+	0.545197i	$0.183545\pi$
$90$	0.500000	−	0.866025i	0.0527046	−	0.0912871i
$91$		0			0
$92$	−0.500000	−	0.866025i	−0.0521286	−	0.0902894i
$93$	4.00000	+	6.92820i	0.414781	+	0.718421i
$94$	4.50000	−	7.79423i	0.464140	−	0.803913i
$95$	2.50000	−	4.33013i	0.256495	−	0.444262i
$96$	1.00000	−	1.73205i	0.102062	−	0.176777i
$97$	10.0000			1.01535			0.507673	−	0.861550i	$-0.330506\pi$
$97$	10.0000			1.01535			0.507673	+	0.861550i	$0.330506\pi$
$98$	−3.50000	−	6.06218i	−0.353553	−	0.612372i
$99$	2.50000	−	4.33013i	0.251259	−	0.435194i
$100$	1.00000			0.100000
$101$		0			0			−	1.00000i	$-0.5\pi$
$101$		0			0				1.00000i	$0.5\pi$
$102$	−4.00000	+	6.92820i	−0.396059	+	0.685994i
$103$	−1.00000			−0.0985329			−0.0492665	−	0.998786i	$-0.515688\pi$
$103$	−1.00000			−0.0985329			−0.0492665	+	0.998786i	$0.515688\pi$
$104$	0.500000	+	0.866025i	0.0490290	+	0.0849208i
$105$		0			0
$106$	−3.00000	−	5.19615i	−0.291386	−	0.504695i
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	0.605308	−	0.795991i	$-0.293050\pi$
$107$	−4.00000	−	6.92820i	−0.386695	−	0.669775i	−0.992003	+	0.126217i	$0.959717\pi$
$108$	2.00000	+	3.46410i	0.192450	+	0.333333i
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	−0.991508	−	0.130046i	$-0.958487\pi$
$109$	−4.00000	+	6.92820i	−0.383131	+	0.663602i	0.608377	+	0.793648i	$0.291821\pi$
$110$	5.00000			0.476731
$111$	−10.0000	+	6.92820i	−0.949158	+	0.657596i
$112$		0			0
$113$	−2.00000	+	3.46410i	−0.188144	+	0.325875i	−0.944632	−	0.328133i	$-0.893581\pi$
$113$	−2.00000	+	3.46410i	−0.188144	+	0.325875i	0.756487	+	0.654008i	$0.226914\pi$
$114$	−5.00000	−	8.66025i	−0.468293	−	0.811107i
$115$	−0.500000	−	0.866025i	−0.0466252	−	0.0807573i
$116$	1.00000	+	1.73205i	0.0928477	+	0.160817i
$117$	1.00000			0.0924500
$118$	0.500000	+	0.866025i	0.0460287	+	0.0797241i
$119$		0			0
$120$	1.00000	−	1.73205i	0.0912871	−	0.158114i
$121$	14.0000			1.27273
$122$	−2.00000			−0.181071
$123$	−10.0000	+	17.3205i	−0.901670	+	1.56174i
$124$	2.00000	+	3.46410i	0.179605	+	0.311086i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	−0.978487	−	0.206309i	$-0.933855\pi$
$127$	−3.50000	+	6.06218i	−0.310575	+	0.537931i	0.667912	+	0.744240i	$0.267188\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−6.00000	−	10.3923i	−0.528271	−	0.914991i
$130$	0.500000	+	0.866025i	0.0438529	+	0.0759555i
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	5.00000	−	8.66025i	0.435194	−	0.753778i
$133$		0			0
$134$	−8.00000			−0.691095
$135$	2.00000	+	3.46410i	0.172133	+	0.298142i
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	14.0000			1.19610			0.598050	−	0.801459i	$-0.295942\pi$
$137$	14.0000			1.19610			0.598050	+	0.801459i	$0.295942\pi$
$138$	−2.00000			−0.170251
$139$	−10.5000	+	18.1865i	−0.890598	+	1.54256i	−0.0514389	+	0.998676i	$0.516381\pi$
$139$	−10.5000	+	18.1865i	−0.890598	+	1.54256i	−0.839159	+	0.543885i	$0.816953\pi$
$140$		0			0
$141$	−9.00000	−	15.5885i	−0.757937	−	1.31278i
$142$	−14.0000			−1.17485
$143$	2.50000	+	4.33013i	0.209061	+	0.362103i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	1.00000	+	1.73205i	0.0830455	+	0.143839i
$146$	6.00000	−	10.3923i	0.496564	−	0.860073i
$147$	−14.0000			−1.15470
$148$	−5.00000	+	3.46410i	−0.410997	+	0.284747i
$149$	12.0000			0.983078			0.491539	−	0.870855i	$-0.336434\pi$
$149$	12.0000			0.983078			0.491539	+	0.870855i	$0.336434\pi$
$150$	1.00000	−	1.73205i	0.0816497	−	0.141421i
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$	−2.50000	−	4.33013i	−0.202777	−	0.351220i
$153$	2.00000	+	3.46410i	0.161690	+	0.280056i
$154$		0			0
$155$	2.00000	+	3.46410i	0.160644	+	0.278243i
$156$	2.00000			0.160128
$157$	−12.5000	+	21.6506i	−0.997609	+	1.72791i	−0.438948	+	0.898513i	$0.644649\pi$
$157$	−12.5000	+	21.6506i	−0.997609	+	1.72791i	−0.558661	+	0.829396i	$0.688685\pi$
$158$	8.00000			0.636446
$159$	−12.0000			−0.951662
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$		0			0
$162$	11.0000			0.864242
$163$	12.0000	−	20.7846i	0.939913	−	1.62798i	0.174282	−	0.984696i	$-0.444240\pi$
$163$	12.0000	−	20.7846i	0.939913	−	1.62798i	0.765631	−	0.643280i	$-0.222427\pi$
$164$	−5.00000	+	8.66025i	−0.390434	+	0.676252i
$165$	5.00000	−	8.66025i	0.389249	−	0.674200i
$166$	1.00000	+	1.73205i	0.0776151	+	0.134433i
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	0.668730	−	0.743505i	$-0.266838\pi$
$167$	−4.00000	−	6.92820i	−0.309529	−	0.536120i	−0.978259	+	0.207385i	$0.933505\pi$
$168$		0			0
$169$	6.00000	−	10.3923i	0.461538	−	0.799408i
$170$	−2.00000	+	3.46410i	−0.153393	+	0.265684i
$171$	−5.00000			−0.382360
$172$	−3.00000	−	5.19615i	−0.228748	−	0.396203i
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	−0.967851	−	0.251523i	$-0.919068\pi$
$173$	−3.50000	+	6.06218i	−0.266100	+	0.460899i	0.701751	+	0.712422i	$0.252402\pi$
$174$	4.00000			0.303239
$175$		0			0
$176$	2.50000	−	4.33013i	0.188445	−	0.326396i
$177$	2.00000			0.150329
$178$	0.500000	+	0.866025i	0.0374766	+	0.0649113i
$179$	3.00000			0.224231			0.112115	−	0.993695i	$-0.464237\pi$
$179$	3.00000			0.224231			0.112115	+	0.993695i	$0.464237\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	0.989819	−	0.142331i	$-0.0454598\pi$
$181$	5.00000	+	8.66025i	0.371647	+	0.643712i	−0.618172	+	0.786043i	$0.712126\pi$
$182$		0			0
$183$	−2.00000	+	3.46410i	−0.147844	+	0.256074i
$184$	−1.00000			−0.0737210
$185$	−5.00000	+	3.46410i	−0.367607	+	0.254686i
$186$	8.00000			0.586588
$187$	−10.0000	+	17.3205i	−0.731272	+	1.26660i
$188$	−4.50000	−	7.79423i	−0.328196	−	0.568453i
$189$		0			0
$190$	−2.50000	−	4.33013i	−0.181369	−	0.314140i
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$	−1.00000	−	1.73205i	−0.0721688	−	0.125000i
$193$	−10.0000			−0.719816			−0.359908	−	0.932988i	$-0.617192\pi$
$193$	−10.0000			−0.719816			−0.359908	+	0.932988i	$0.617192\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$	2.00000			0.143223
$196$	−7.00000			−0.500000
$197$	1.00000	−	1.73205i	0.0712470	−	0.123404i	−0.828201	−	0.560431i	$-0.810635\pi$
$197$	1.00000	−	1.73205i	0.0712470	−	0.123404i	0.899448	+	0.437028i	$0.143969\pi$
$198$	−2.50000	−	4.33013i	−0.177667	−	0.307729i
$199$	22.0000			1.55954			0.779769	−	0.626067i	$-0.215336\pi$
$199$	22.0000			1.55954			0.779769	+	0.626067i	$0.215336\pi$
$200$	0.500000	−	0.866025i	0.0353553	−	0.0612372i
$201$	−8.00000	+	13.8564i	−0.564276	+	0.977356i
$202$		0			0
$203$		0			0
$204$	4.00000	+	6.92820i	0.280056	+	0.485071i
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	−0.500000	+	0.866025i	−0.0348367	+	0.0603388i
$207$	−0.500000	+	0.866025i	−0.0347524	+	0.0601929i
$208$	1.00000			0.0693375
$209$	−12.5000	−	21.6506i	−0.864643	−	1.49761i
$210$		0			0
$211$	−19.0000			−1.30801			−0.654007	−	0.756489i	$-0.726913\pi$
$211$	−19.0000			−1.30801			−0.654007	+	0.756489i	$0.726913\pi$
$212$	−6.00000			−0.412082
$213$	−14.0000	+	24.2487i	−0.959264	+	1.66149i
$214$	−8.00000			−0.546869
$215$	−3.00000	−	5.19615i	−0.204598	−	0.354375i
$216$	4.00000			0.272166
$217$		0			0
$218$	4.00000	+	6.92820i	0.270914	+	0.469237i
$219$	−12.0000	−	20.7846i	−0.810885	−	1.40449i
$220$	2.50000	−	4.33013i	0.168550	−	0.291937i
$221$	−4.00000			−0.269069
$222$	1.00000	+	12.1244i	0.0671156	+	0.813733i
$223$	9.00000			0.602685			0.301342	−	0.953516i	$-0.402565\pi$
$223$	9.00000			0.602685			0.301342	+	0.953516i	$0.402565\pi$
$224$		0			0
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	2.00000	+	3.46410i	0.133038	+	0.230429i
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	0.830930	−	0.556378i	$-0.187809\pi$
$227$	−1.00000	−	1.73205i	−0.0663723	−	0.114960i	−0.897302	+	0.441417i	$0.854476\pi$
$228$	−10.0000			−0.662266
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	0.982592	−	0.185776i	$-0.0594799\pi$
$229$	5.00000	+	8.66025i	0.330409	+	0.572286i	−0.652183	+	0.758062i	$0.726147\pi$
$230$	−1.00000			−0.0659380
$231$		0			0
$232$	2.00000			0.131306
$233$	−8.00000			−0.524097			−0.262049	−	0.965055i	$-0.584398\pi$
$233$	−8.00000			−0.524097			−0.262049	+	0.965055i	$0.584398\pi$
$234$	0.500000	−	0.866025i	0.0326860	−	0.0566139i
$235$	−4.50000	−	7.79423i	−0.293548	−	0.508439i
$236$	1.00000			0.0650945
$237$	8.00000	−	13.8564i	0.519656	−	0.900070i
$238$		0			0
$239$	5.00000	−	8.66025i	0.323423	−	0.560185i	−0.657769	−	0.753220i	$-0.728500\pi$
$239$	5.00000	−	8.66025i	0.323423	−	0.560185i	0.981192	+	0.193035i	$0.0618330\pi$
$240$	−1.00000	−	1.73205i	−0.0645497	−	0.111803i
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	0.998443	+	0.0557856i	$0.0177663\pi$
$241$	8.50000	+	14.7224i	0.547533	+	0.948355i	−0.450910	+	0.892570i	$0.648900\pi$
$242$	7.00000	−	12.1244i	0.449977	−	0.779383i
$243$	5.00000	−	8.66025i	0.320750	−	0.555556i
$244$	−1.00000	+	1.73205i	−0.0640184	+	0.110883i
$245$	−7.00000			−0.447214
$246$	10.0000	+	17.3205i	0.637577	+	1.10432i
$247$	2.50000	−	4.33013i	0.159071	−	0.275519i
$248$	4.00000			0.254000
$249$	4.00000			0.253490
$250$	0.500000	−	0.866025i	0.0316228	−	0.0547723i
$251$	−15.0000			−0.946792			−0.473396	−	0.880850i	$-0.656972\pi$
$251$	−15.0000			−0.946792			−0.473396	+	0.880850i	$0.656972\pi$
$252$		0			0
$253$	−5.00000			−0.314347
$254$	3.50000	+	6.06218i	0.219610	+	0.380375i
$255$	4.00000	+	6.92820i	0.250490	+	0.433861i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	0.101305	+	0.994855i	$0.467698\pi$
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	−0.912222	+	0.409695i	$0.865635\pi$
$258$	−12.0000			−0.747087
$259$		0			0
$260$	1.00000			0.0620174
$261$	1.00000	−	1.73205i	0.0618984	−	0.107211i
$262$		0			0
$263$	−5.50000	−	9.52628i	−0.339145	−	0.587416i	0.645128	−	0.764075i	$-0.276804\pi$
$263$	−5.50000	−	9.52628i	−0.339145	−	0.587416i	−0.984272	+	0.176659i	$0.943471\pi$
$264$	−5.00000	−	8.66025i	−0.307729	−	0.533002i
$265$	−6.00000			−0.368577
$266$		0			0
$267$	2.00000			0.122398
$268$	−4.00000	+	6.92820i	−0.244339	+	0.423207i
$269$	16.0000			0.975537			0.487769	−	0.872973i	$-0.337811\pi$
$269$	16.0000			0.975537			0.487769	+	0.872973i	$0.337811\pi$
$270$	4.00000			0.243432
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	0.384201	+	0.923249i	$0.374477\pi$
$271$	−10.0000	+	17.3205i	−0.607457	+	1.05215i	−0.991658	+	0.128897i	$0.958856\pi$
$272$	2.00000	+	3.46410i	0.121268	+	0.210042i
$273$		0			0
$274$	7.00000	−	12.1244i	0.422885	−	0.732459i
$275$	2.50000	−	4.33013i	0.150756	−	0.261116i
$276$	−1.00000	+	1.73205i	−0.0601929	+	0.104257i
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	0.995997	−	0.0893846i	$-0.0284900\pi$
$277$	7.00000	+	12.1244i	0.420589	+	0.728482i	−0.575408	+	0.817867i	$0.695157\pi$
$278$	10.5000	+	18.1865i	0.629748	+	1.09076i
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$		0			0
$281$	11.5000	−	19.9186i	0.686032	−	1.18824i	−0.287079	−	0.957907i	$-0.592684\pi$
$281$	11.5000	−	19.9186i	0.686032	−	1.18824i	0.973111	−	0.230336i	$-0.0739826\pi$
$282$	−18.0000			−1.07188
$283$	−9.00000	−	15.5885i	−0.534994	−	0.926638i	−0.999164	−	0.0408910i	$-0.986980\pi$
$283$	−9.00000	−	15.5885i	−0.534994	−	0.926638i	0.464169	−	0.885747i	$-0.346353\pi$
$284$	−7.00000	+	12.1244i	−0.415374	+	0.719448i
$285$	−10.0000			−0.592349
$286$	5.00000			0.295656
$287$		0			0
$288$	−1.00000			−0.0589256
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$	2.00000			0.117444
$291$	−10.0000	−	17.3205i	−0.586210	−	1.01535i
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	−10.5000	−	18.1865i	−0.613417	−	1.06247i	−0.990660	−	0.136355i	$-0.956461\pi$
$293$	−10.5000	−	18.1865i	−0.613417	−	1.06247i	0.377244	−	0.926114i	$-0.376872\pi$
$294$	−7.00000	+	12.1244i	−0.408248	+	0.707107i
$295$	1.00000			0.0582223
$296$	0.500000	+	6.06218i	0.0290619	+	0.352357i
$297$	20.0000			1.16052
$298$	6.00000	−	10.3923i	0.347571	−	0.602010i
$299$	−0.500000	−	0.866025i	−0.0289157	−	0.0500835i
$300$	−1.00000	−	1.73205i	−0.0577350	−	0.100000i
$301$		0			0
$302$	8.00000			0.460348
$303$		0			0
$304$	−5.00000			−0.286770
$305$	−1.00000	+	1.73205i	−0.0572598	+	0.0991769i
$306$	4.00000			0.228665
$307$	18.0000			1.02731			0.513657	−	0.857996i	$-0.328290\pi$
$307$	18.0000			1.02731			0.513657	+	0.857996i	$0.328290\pi$
$308$		0			0
$309$	1.00000	+	1.73205i	0.0568880	+	0.0985329i
$310$	4.00000			0.227185
$311$	−15.0000	+	25.9808i	−0.850572	+	1.47323i	0.0301210	+	0.999546i	$0.490411\pi$
$311$	−15.0000	+	25.9808i	−0.850572	+	1.47323i	−0.880693	+	0.473688i	$0.842923\pi$
$312$	1.00000	−	1.73205i	0.0566139	−	0.0980581i
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	−0.546335	−	0.837567i	$-0.683977\pi$
$313$	8.00000	−	13.8564i	0.452187	−	0.783210i	0.998522	+	0.0543564i	$0.0173107\pi$
$314$	12.5000	+	21.6506i	0.705416	+	1.22182i
$315$		0			0
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$	10.5000	−	18.1865i	0.589739	−	1.02146i	−0.404528	−	0.914526i	$-0.632564\pi$
$317$	10.5000	−	18.1865i	0.589739	−	1.02146i	0.994266	−	0.106932i	$-0.0341026\pi$
$318$	−6.00000	+	10.3923i	−0.336463	+	0.582772i
$319$	10.0000			0.559893
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	−8.00000	+	13.8564i	−0.446516	+	0.773389i
$322$		0			0
$323$	20.0000			1.11283
$324$	5.50000	−	9.52628i	0.305556	−	0.529238i
$325$	1.00000			0.0554700
$326$	−12.0000	−	20.7846i	−0.664619	−	1.15115i
$327$	16.0000			0.884802
$328$	5.00000	+	8.66025i	0.276079	+	0.478183i
$329$		0			0
$330$	−5.00000	−	8.66025i	−0.275241	−	0.476731i
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	−0.209544	−	0.977799i	$-0.567198\pi$
$331$	13.5000	−	23.3827i	0.742027	−	1.28523i	0.951571	−	0.307429i	$-0.0994688\pi$
$332$	2.00000			0.109764
$333$	5.50000	+	2.59808i	0.301398	+	0.142374i
$334$	−8.00000			−0.437741
$335$	−4.00000	+	6.92820i	−0.218543	+	0.378528i
$336$		0			0
$337$	−4.00000	−	6.92820i	−0.217894	−	0.377403i	0.736270	−	0.676688i	$-0.236585\pi$
$337$	−4.00000	−	6.92820i	−0.217894	−	0.377403i	−0.954164	+	0.299285i	$0.903252\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	8.00000			0.434500
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	20.0000			1.08306
$342$	−2.50000	+	4.33013i	−0.135185	+	0.234146i
$343$		0			0
$344$	−6.00000			−0.323498
$345$	−1.00000	+	1.73205i	−0.0538382	+	0.0932505i
$346$	3.50000	+	6.06218i	0.188161	+	0.325905i
$347$	36.0000			1.93258			0.966291	−	0.257454i	$-0.0828835\pi$
$347$	36.0000			1.93258			0.966291	+	0.257454i	$0.0828835\pi$
$348$	2.00000	−	3.46410i	0.107211	−	0.185695i
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	0.274011	+	0.961727i	$0.411649\pi$
$349$	−13.0000	+	22.5167i	−0.695874	+	1.20529i	−0.969885	+	0.243563i	$0.921684\pi$
$350$		0			0
$351$	2.00000	+	3.46410i	0.106752	+	0.184900i
$352$	−2.50000	−	4.33013i	−0.133250	−	0.230797i
$353$	14.0000	−	24.2487i	0.745145	−	1.29063i	−0.204982	−	0.978766i	$-0.565714\pi$
$353$	14.0000	−	24.2487i	0.745145	−	1.29063i	0.950127	−	0.311863i	$-0.100953\pi$
$354$	1.00000	−	1.73205i	0.0531494	−	0.0920575i
$355$	−7.00000	+	12.1244i	−0.371521	+	0.643494i
$356$	1.00000			0.0529999
$357$		0			0
$358$	1.50000	−	2.59808i	0.0792775	−	0.137313i
$359$	16.0000			0.844448			0.422224	−	0.906492i	$-0.361250\pi$
$359$	16.0000			0.844448			0.422224	+	0.906492i	$0.361250\pi$
$360$	−1.00000			−0.0527046
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	10.0000			0.525588
$363$	−14.0000	−	24.2487i	−0.734809	−	1.27273i
$364$		0			0
$365$	−6.00000	−	10.3923i	−0.314054	−	0.543958i
$366$	2.00000	+	3.46410i	0.104542	+	0.181071i
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	0.554264	−	0.832341i	$-0.313000\pi$
$367$	−8.50000	−	14.7224i	−0.443696	−	0.768505i	−0.997960	+	0.0638362i	$0.979666\pi$
$368$	−0.500000	+	0.866025i	−0.0260643	+	0.0451447i
$369$	10.0000			0.520579
$370$	0.500000	+	6.06218i	0.0259938	+	0.315158i
$371$		0			0
$372$	4.00000	−	6.92820i	0.207390	−	0.359211i
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$	10.0000	+	17.3205i	0.517088	+	0.895622i
$375$	−1.00000	−	1.73205i	−0.0516398	−	0.0894427i
$376$	−9.00000			−0.464140
$377$	1.00000	+	1.73205i	0.0515026	+	0.0892052i
$378$		0			0
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$	−5.00000			−0.256495
$381$	14.0000			0.717242
$382$	4.00000	−	6.92820i	0.204658	−	0.354478i
$383$	−0.500000	−	0.866025i	−0.0255488	−	0.0442518i	0.852968	−	0.521963i	$-0.174800\pi$
$383$	−0.500000	−	0.866025i	−0.0255488	−	0.0442518i	−0.878517	+	0.477711i	$0.841467\pi$
$384$	−2.00000			−0.102062
$385$		0			0
$386$	−5.00000	+	8.66025i	−0.254493	+	0.440795i
$387$	−3.00000	+	5.19615i	−0.152499	+	0.264135i
$388$	−5.00000	−	8.66025i	−0.253837	−	0.439658i
$389$	−16.0000	−	27.7128i	−0.811232	−	1.40510i	−0.912002	−	0.410186i	$-0.865464\pi$
$389$	−16.0000	−	27.7128i	−0.811232	−	1.40510i	0.100770	−	0.994910i	$-0.467869\pi$
$390$	1.00000	−	1.73205i	0.0506370	−	0.0877058i
$391$	2.00000	−	3.46410i	0.101144	−	0.175187i
$392$	−3.50000	+	6.06218i	−0.176777	+	0.306186i
$393$		0			0
$394$	−1.00000	−	1.73205i	−0.0503793	−	0.0872595i
$395$	4.00000	−	6.92820i	0.201262	−	0.348596i
$396$	−5.00000			−0.251259
$397$	−25.0000			−1.25471			−0.627357	−	0.778732i	$-0.715863\pi$
$397$	−25.0000			−1.25471			−0.627357	+	0.778732i	$0.715863\pi$
$398$	11.0000	−	19.0526i	0.551380	−	0.955018i
$399$		0			0
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	−11.0000			−0.549314			−0.274657	−	0.961542i	$-0.588564\pi$
$401$	−11.0000			−0.549314			−0.274657	+	0.961542i	$0.588564\pi$
$402$	8.00000	+	13.8564i	0.399004	+	0.691095i
$403$	2.00000	+	3.46410i	0.0996271	+	0.172559i
$404$		0			0
$405$	5.50000	−	9.52628i	0.273297	−	0.473365i
$406$		0			0
$407$	2.50000	+	30.3109i	0.123920	+	1.50245i
$408$	8.00000			0.396059
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$	5.00000	+	8.66025i	0.246932	+	0.427699i
$411$	−14.0000	−	24.2487i	−0.690569	−	1.19610i
$412$	0.500000	+	0.866025i	0.0246332	+	0.0426660i
$413$		0			0
$414$	0.500000	+	0.866025i	0.0245737	+	0.0425628i
$415$	2.00000			0.0981761
$416$	0.500000	−	0.866025i	0.0245145	−	0.0424604i
$417$	42.0000			2.05675
$418$	−25.0000			−1.22279
$419$	−8.50000	+	14.7224i	−0.415252	+	0.719238i	−0.995455	−	0.0952342i	$-0.969640\pi$
$419$	−8.50000	+	14.7224i	−0.415252	+	0.719238i	0.580203	+	0.814472i	$0.302973\pi$
$420$		0			0
$421$	10.0000			0.487370			0.243685	−	0.969854i	$-0.421644\pi$
$421$	10.0000			0.487370			0.243685	+	0.969854i	$0.421644\pi$
$422$	−9.50000	+	16.4545i	−0.462453	+	0.800992i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	−3.00000	+	5.19615i	−0.145693	+	0.252347i
$425$	2.00000	+	3.46410i	0.0970143	+	0.168034i
$426$	14.0000	+	24.2487i	0.678302	+	1.17485i
$427$		0			0
$428$	−4.00000	+	6.92820i	−0.193347	+	0.334887i
$429$	5.00000	−	8.66025i	0.241402	−	0.418121i
$430$	−6.00000			−0.289346
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	2.00000	−	3.46410i	0.0962250	−	0.166667i
$433$	−16.0000			−0.768911			−0.384455	−	0.923144i	$-0.625611\pi$
$433$	−16.0000			−0.768911			−0.384455	+	0.923144i	$0.625611\pi$
$434$		0			0
$435$	2.00000	−	3.46410i	0.0958927	−	0.166091i
$436$	8.00000			0.383131
$437$	2.50000	+	4.33013i	0.119591	+	0.207138i
$438$	−24.0000			−1.14676
$439$	18.0000	+	31.1769i	0.859093	+	1.48799i	0.872795	+	0.488087i	$0.162305\pi$
$439$	18.0000	+	31.1769i	0.859093	+	1.48799i	−0.0137020	+	0.999906i	$0.504362\pi$
$440$	−2.50000	−	4.33013i	−0.119183	−	0.206431i
$441$	3.50000	+	6.06218i	0.166667	+	0.288675i
$442$	−2.00000	+	3.46410i	−0.0951303	+	0.164771i
$443$	−18.0000			−0.855206			−0.427603	−	0.903967i	$-0.640642\pi$
$443$	−18.0000			−0.855206			−0.427603	+	0.903967i	$0.640642\pi$
$444$	11.0000	+	5.19615i	0.522037	+	0.246598i
$445$	1.00000			0.0474045
$446$	4.50000	−	7.79423i	0.213081	−	0.369067i
$447$	−12.0000	−	20.7846i	−0.567581	−	0.983078i
$448$		0			0
$449$	3.00000	+	5.19615i	0.141579	+	0.245222i	0.928091	−	0.372353i	$-0.121449\pi$
$449$	3.00000	+	5.19615i	0.141579	+	0.245222i	−0.786513	+	0.617574i	$0.788115\pi$
$450$	−1.00000			−0.0471405
$451$	25.0000	+	43.3013i	1.17720	+	2.03898i
$452$	4.00000			0.188144
$453$	8.00000	−	13.8564i	0.375873	−	0.651031i
$454$	−2.00000			−0.0938647
$455$		0			0
$456$	−5.00000	+	8.66025i	−0.234146	+	0.405554i
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	0.787288	−	0.616585i	$-0.211484\pi$
$457$	−3.00000	−	5.19615i	−0.140334	−	0.243066i	−0.927622	+	0.373519i	$0.878151\pi$
$458$	10.0000			0.467269
$459$	−8.00000	+	13.8564i	−0.373408	+	0.646762i
$460$	−0.500000	+	0.866025i	−0.0233126	+	0.0403786i
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	−0.270326	−	0.962769i	$-0.587131\pi$
$461$	15.0000	−	25.9808i	0.698620	−	1.21004i	0.968945	−	0.247276i	$-0.0795353\pi$
$462$		0			0
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	−0.892778	−	0.450497i	$-0.851247\pi$
$463$	−18.0000	−	31.1769i	−0.836531	−	1.44891i	0.0562469	−	0.998417i	$-0.482087\pi$
$464$	1.00000	−	1.73205i	0.0464238	−	0.0804084i
$465$	4.00000	−	6.92820i	0.185496	−	0.321288i
$466$	−4.00000	+	6.92820i	−0.185296	+	0.320943i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$	−0.500000	−	0.866025i	−0.0231125	−	0.0400320i
$469$		0			0
$470$	−9.00000			−0.415139
$471$	50.0000			2.30388
$472$	0.500000	−	0.866025i	0.0230144	−	0.0398621i
$473$	−30.0000			−1.37940
$474$	−8.00000	−	13.8564i	−0.367452	−	0.636446i
$475$	−5.00000			−0.229416
$476$		0			0
$477$	3.00000	+	5.19615i	0.137361	+	0.237915i
$478$	−5.00000	−	8.66025i	−0.228695	−	0.396111i
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	−0.995023	−	0.0996406i	$-0.968231\pi$
$479$	−9.00000	+	15.5885i	−0.411220	+	0.712255i	0.583803	+	0.811895i	$0.301564\pi$
$480$	−2.00000			−0.0912871
$481$	−5.00000	+	3.46410i	−0.227980	+	0.157949i
$482$	17.0000			0.774329
$483$		0			0
$484$	−7.00000	−	12.1244i	−0.318182	−	0.551107i
$485$	−5.00000	−	8.66025i	−0.227038	−	0.393242i
$486$	−5.00000	−	8.66025i	−0.226805	−	0.392837i
$487$	12.0000			0.543772			0.271886	−	0.962329i	$-0.412353\pi$
$487$	12.0000			0.543772			0.271886	+	0.962329i	$0.412353\pi$
$488$	1.00000	+	1.73205i	0.0452679	+	0.0784063i
$489$	−48.0000			−2.17064
$490$	−3.50000	+	6.06218i	−0.158114	+	0.273861i
$491$	−11.0000			−0.496423			−0.248212	−	0.968706i	$-0.579843\pi$
$491$	−11.0000			−0.496423			−0.248212	+	0.968706i	$0.579843\pi$
$492$	20.0000			0.901670
$493$	−4.00000	+	6.92820i	−0.180151	+	0.312031i
$494$	−2.50000	−	4.33013i	−0.112480	−	0.194822i
$495$	−5.00000			−0.224733
$496$	2.00000	−	3.46410i	0.0898027	−	0.155543i
$497$		0			0
$498$	2.00000	−	3.46410i	0.0896221	−	0.155230i
$499$	−8.00000	−	13.8564i	−0.358129	−	0.620298i	0.629519	−	0.776985i	$-0.283252\pi$
$499$	−8.00000	−	13.8564i	−0.358129	−	0.620298i	−0.987648	+	0.156687i	$0.949919\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$	−8.00000	+	13.8564i	−0.357414	+	0.619059i
$502$	−7.50000	+	12.9904i	−0.334741	+	0.579789i
$503$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$503$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$504$		0			0
$505$		0			0
$506$	−2.50000	+	4.33013i	−0.111139	+	0.192498i
$507$	−24.0000			−1.06588
$508$	7.00000			0.310575
$509$	−20.0000	+	34.6410i	−0.886484	+	1.53544i	−0.0424816	+	0.999097i	$0.513526\pi$
$509$	−20.0000	+	34.6410i	−0.886484	+	1.53544i	−0.844003	+	0.536339i	$0.819807\pi$
$510$	8.00000			0.354246
$511$		0			0
$512$	−1.00000			−0.0441942
$513$	−10.0000	−	17.3205i	−0.441511	−	0.764719i
$514$	13.0000	+	22.5167i	0.573405	+	0.993167i
$515$	0.500000	+	0.866025i	0.0220326	+	0.0381616i
$516$	−6.00000	+	10.3923i	−0.264135	+	0.457496i
$517$	−45.0000			−1.97910
$518$		0			0
$519$	14.0000			0.614532
$520$	0.500000	−	0.866025i	0.0219265	−	0.0379777i
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	0.750454	−	0.660922i	$-0.229835\pi$
$521$	−4.50000	−	7.79423i	−0.197149	−	0.341471i	−0.947603	+	0.319451i	$0.896501\pi$
$522$	−1.00000	−	1.73205i	−0.0437688	−	0.0758098i
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	−0.950958	−	0.309320i	$-0.899899\pi$
$523$	−17.0000	−	29.4449i	−0.743358	−	1.28753i	0.207600	−	0.978214i	$-0.433435\pi$
$524$		0			0
$525$		0			0
$526$	−11.0000			−0.479623
$527$	−8.00000	+	13.8564i	−0.348485	+	0.603595i
$528$	−10.0000			−0.435194
$529$	−22.0000			−0.956522
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	−0.500000	−	0.866025i	−0.0216982	−	0.0375823i
$532$		0			0
$533$	−5.00000	+	8.66025i	−0.216574	+	0.375117i
$534$	1.00000	−	1.73205i	0.0432742	−	0.0749532i
$535$	−4.00000	+	6.92820i	−0.172935	+	0.299532i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$	−3.00000	−	5.19615i	−0.129460	−	0.224231i
$538$	8.00000	−	13.8564i	0.344904	−	0.597392i
$539$	−17.5000	+	30.3109i	−0.753778	+	1.30558i
$540$	2.00000	−	3.46410i	0.0860663	−	0.149071i
$541$	12.0000			0.515920			0.257960	−	0.966156i	$-0.416950\pi$
$541$	12.0000			0.515920			0.257960	+	0.966156i	$0.416950\pi$
$542$	10.0000	+	17.3205i	0.429537	+	0.743980i
$543$	10.0000	−	17.3205i	0.429141	−	0.743294i
$544$	4.00000			0.171499
$545$	8.00000			0.342682
$546$		0			0
$547$	−34.0000			−1.45374			−0.726868	−	0.686778i	$-0.759025\pi$
$547$	−34.0000			−1.45374			−0.726868	+	0.686778i	$0.759025\pi$
$548$	−7.00000	−	12.1244i	−0.299025	−	0.517927i
$549$	2.00000			0.0853579
$550$	−2.50000	−	4.33013i	−0.106600	−	0.184637i
$551$	−5.00000	−	8.66025i	−0.213007	−	0.368939i
$552$	1.00000	+	1.73205i	0.0425628	+	0.0737210i
$553$		0			0
$554$	14.0000			0.594803
$555$	11.0000	+	5.19615i	0.466924	+	0.220564i
$556$	21.0000			0.890598
$557$	−10.5000	+	18.1865i	−0.444899	+	0.770588i	−0.998045	−	0.0624962i	$-0.980094\pi$
$557$	−10.5000	+	18.1865i	−0.444899	+	0.770588i	0.553146	+	0.833084i	$0.313427\pi$
$558$	−2.00000	−	3.46410i	−0.0846668	−	0.146647i
$559$	−3.00000	−	5.19615i	−0.126886	−	0.219774i
$560$		0			0
$561$	40.0000			1.68880
$562$	−11.5000	−	19.9186i	−0.485098	−	0.840215i
$563$	−18.0000			−0.758610			−0.379305	−	0.925272i	$-0.623837\pi$
$563$	−18.0000			−0.758610			−0.379305	+	0.925272i	$0.623837\pi$
$564$	−9.00000	+	15.5885i	−0.378968	+	0.656392i
$565$	4.00000			0.168281
$566$	−18.0000			−0.756596
$567$		0			0
$568$	7.00000	+	12.1244i	0.293713	+	0.508727i
$569$	−31.0000			−1.29959			−0.649794	−	0.760111i	$-0.725145\pi$
$569$	−31.0000			−1.29959			−0.649794	+	0.760111i	$0.725145\pi$
$570$	−5.00000	+	8.66025i	−0.209427	+	0.362738i
$571$	22.5000	−	38.9711i	0.941596	−	1.63089i	0.179168	−	0.983819i	$-0.442660\pi$
$571$	22.5000	−	38.9711i	0.941596	−	1.63089i	0.762428	−	0.647073i	$-0.224007\pi$
$572$	2.50000	−	4.33013i	0.104530	−	0.181052i
$573$	−8.00000	−	13.8564i	−0.334205	−	0.578860i
$574$		0			0
$575$	−0.500000	+	0.866025i	−0.0208514	+	0.0361158i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−20.0000	+	34.6410i	−0.832611	+	1.44212i	0.0633500	+	0.997991i	$0.479822\pi$
$577$	−20.0000	+	34.6410i	−0.832611	+	1.44212i	−0.895961	+	0.444133i	$0.853512\pi$
$578$	1.00000			0.0415945
$579$	10.0000	+	17.3205i	0.415586	+	0.719816i
$580$	1.00000	−	1.73205i	0.0415227	−	0.0719195i
$581$		0			0
$582$	−20.0000			−0.829027
$583$	−15.0000	+	25.9808i	−0.621237	+	1.07601i
$584$	−12.0000			−0.496564
$585$	−0.500000	−	0.866025i	−0.0206725	−	0.0358057i
$586$	−21.0000			−0.867502
$587$	−15.0000	−	25.9808i	−0.619116	−	1.07234i	−0.989647	−	0.143521i	$-0.954158\pi$
$587$	−15.0000	−	25.9808i	−0.619116	−	1.07234i	0.370531	−	0.928820i	$-0.379176\pi$
$588$	7.00000	+	12.1244i	0.288675	+	0.500000i
$589$	−10.0000	−	17.3205i	−0.412043	−	0.713679i
$590$	0.500000	−	0.866025i	0.0205847	−	0.0356537i
$591$	−4.00000			−0.164538
$592$	5.50000	+	2.59808i	0.226049	+	0.106780i
$593$	−2.00000			−0.0821302			−0.0410651	−	0.999156i	$-0.513075\pi$
$593$	−2.00000			−0.0821302			−0.0410651	+	0.999156i	$0.513075\pi$
$594$	10.0000	−	17.3205i	0.410305	−	0.710669i
$595$		0			0
$596$	−6.00000	−	10.3923i	−0.245770	−	0.425685i
$597$	−22.0000	−	38.1051i	−0.900400	−	1.55954i
$598$	−1.00000			−0.0408930
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	0.989210	−	0.146503i	$-0.0468017\pi$
$599$	9.00000	+	15.5885i	0.367730	+	0.636927i	−0.621480	+	0.783430i	$0.713468\pi$
$600$	−2.00000			−0.0816497
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	−0.604601	−	0.796528i	$-0.706668\pi$
$601$	9.50000	−	16.4545i	0.387513	−	0.671192i	0.992114	+	0.125336i	$0.0400009\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$	4.00000	−	6.92820i	0.162758	−	0.281905i
$605$	−7.00000	−	12.1244i	−0.284590	−	0.492925i
$606$		0			0
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	−0.333842	−	0.942629i	$-0.608345\pi$
$607$	16.0000	−	27.7128i	0.649420	−	1.12483i	0.983262	−	0.182199i	$-0.0583216\pi$
$608$	−2.50000	+	4.33013i	−0.101388	+	0.175610i
$609$		0			0
$610$	1.00000	+	1.73205i	0.0404888	+	0.0701287i
$611$	−4.50000	−	7.79423i	−0.182051	−	0.315321i
$612$	2.00000	−	3.46410i	0.0808452	−	0.140028i
$613$	8.50000	−	14.7224i	0.343312	−	0.594633i	−0.641734	−	0.766927i	$-0.721785\pi$
$613$	8.50000	−	14.7224i	0.343312	−	0.594633i	0.985046	+	0.172294i	$0.0551179\pi$
$614$	9.00000	−	15.5885i	0.363210	−	0.629099i
$615$	20.0000			0.806478
$616$		0			0
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	−0.0398207	−	0.999207i	$-0.512679\pi$
$617$	21.0000	−	36.3731i	0.845428	−	1.46432i	0.885249	−	0.465118i	$-0.153988\pi$
$618$	2.00000			0.0804518
$619$	32.0000			1.28619			0.643094	−	0.765787i	$-0.277650\pi$
$619$	32.0000			1.28619			0.643094	+	0.765787i	$0.277650\pi$
$620$	2.00000	−	3.46410i	0.0803219	−	0.139122i
$621$	−4.00000			−0.160514
$622$	15.0000	+	25.9808i	0.601445	+	1.04173i
$623$		0			0
$624$	−1.00000	−	1.73205i	−0.0400320	−	0.0693375i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−8.00000	−	13.8564i	−0.319744	−	0.553813i
$627$	−25.0000	+	43.3013i	−0.998404	+	1.72929i
$628$	25.0000			0.997609
$629$	−22.0000	−	10.3923i	−0.877197	−	0.414368i
$630$		0			0
$631$	2.00000	−	3.46410i	0.0796187	−	0.137904i	−0.823467	−	0.567365i	$-0.807963\pi$
$631$	2.00000	−	3.46410i	0.0796187	−	0.137904i	0.903085	+	0.429461i	$0.141296\pi$
$632$	−4.00000	−	6.92820i	−0.159111	−	0.275589i
$633$	19.0000	+	32.9090i	0.755182	+	1.30801i
$634$	−10.5000	−	18.1865i	−0.417008	−	0.722280i
$635$	7.00000			0.277787
$636$	6.00000	+	10.3923i	0.237915	+	0.412082i
$637$	−7.00000			−0.277350
$638$	5.00000	−	8.66025i	0.197952	−	0.342863i
$639$	14.0000			0.553831
$640$	−1.00000			−0.0395285
$641$	−23.5000	+	40.7032i	−0.928194	+	1.60768i	−0.141852	+	0.989888i	$0.545306\pi$
$641$	−23.5000	+	40.7032i	−0.928194	+	1.60768i	−0.786342	+	0.617792i	$0.788027\pi$
$642$	8.00000	+	13.8564i	0.315735	+	0.546869i
$643$	8.00000			0.315489			0.157745	−	0.987480i	$-0.449578\pi$
$643$	8.00000			0.315489			0.157745	+	0.987480i	$0.449578\pi$
$644$		0			0
$645$	−6.00000	+	10.3923i	−0.236250	+	0.409197i
$646$	10.0000	−	17.3205i	0.393445	−	0.681466i
$647$	8.50000	+	14.7224i	0.334169	+	0.578799i	0.983325	−	0.181857i	$-0.0582109\pi$
$647$	8.50000	+	14.7224i	0.334169	+	0.578799i	−0.649155	+	0.760656i	$0.724878\pi$
$648$	−5.50000	−	9.52628i	−0.216060	−	0.374228i
$649$	2.50000	−	4.33013i	0.0981336	−	0.169972i
$650$	0.500000	−	0.866025i	0.0196116	−	0.0339683i
$651$		0			0
$652$	−24.0000			−0.939913
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	0.999456	+	0.0329874i	$0.0105021\pi$
$653$	13.5000	+	23.3827i	0.528296	+	0.915035i	−0.471160	+	0.882048i	$0.656165\pi$
$654$	8.00000	−	13.8564i	0.312825	−	0.541828i
$655$		0			0
$656$	10.0000			0.390434
$657$	−6.00000	+	10.3923i	−0.234082	+	0.405442i
$658$		0			0
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	0.999545	+	0.0301523i	$0.00959924\pi$
$659$	13.5000	+	23.3827i	0.525885	+	0.910860i	−0.473660	+	0.880708i	$0.657067\pi$
$660$	−10.0000			−0.389249
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	−0.980294	−	0.197542i	$-0.936704\pi$
$661$	−17.0000	−	29.4449i	−0.661223	−	1.14527i	0.319071	−	0.947731i	$-0.396629\pi$
$662$	−13.5000	−	23.3827i	−0.524692	−	0.908794i
$663$	4.00000	+	6.92820i	0.155347	+	0.269069i
$664$	1.00000	−	1.73205i	0.0388075	−	0.0672166i
$665$		0			0
$666$	5.00000	−	3.46410i	0.193746	−	0.134231i
$667$	−2.00000			−0.0774403
$668$	−4.00000	+	6.92820i	−0.154765	+	0.268060i
$669$	−9.00000	−	15.5885i	−0.347960	−	0.602685i
$670$	4.00000	+	6.92820i	0.154533	+	0.267660i
$671$	5.00000	+	8.66025i	0.193023	+	0.334325i
$672$		0			0
$673$	22.0000	+	38.1051i	0.848038	+	1.46884i	0.882957	+	0.469454i	$0.155549\pi$
$673$	22.0000	+	38.1051i	0.848038	+	1.46884i	−0.0349191	+	0.999390i	$0.511117\pi$
$674$	−8.00000			−0.308148
$675$	2.00000	−	3.46410i	0.0769800	−	0.133333i
$676$	−12.0000			−0.461538
$677$	33.0000			1.26829			0.634147	−	0.773213i	$-0.281352\pi$
$677$	33.0000			1.26829			0.634147	+	0.773213i	$0.281352\pi$
$678$	4.00000	−	6.92820i	0.153619	−	0.266076i
$679$		0			0
$680$	4.00000			0.153393
$681$	−2.00000	+	3.46410i	−0.0766402	+	0.132745i
$682$	10.0000	−	17.3205i	0.382920	−	0.663237i
$683$	−23.0000	+	39.8372i	−0.880071	+	1.52433i	−0.0288092	+	0.999585i	$0.509172\pi$
$683$	−23.0000	+	39.8372i	−0.880071	+	1.52433i	−0.851261	+	0.524742i	$0.824162\pi$
$684$	2.50000	+	4.33013i	0.0955899	+	0.165567i
$685$	−7.00000	−	12.1244i	−0.267456	−	0.463248i
$686$		0			0
$687$	10.0000	−	17.3205i	0.381524	−	0.660819i
$688$	−3.00000	+	5.19615i	−0.114374	+	0.198101i
$689$	−6.00000			−0.228582
$690$	1.00000	+	1.73205i	0.0380693	+	0.0659380i
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	−0.610704	−	0.791859i	$-0.709113\pi$
$691$	10.0000	−	17.3205i	0.380418	−	0.658903i	0.991122	+	0.132956i	$0.0424468\pi$
$692$	7.00000			0.266100
$693$		0			0
$694$	18.0000	−	31.1769i	0.683271	−	1.18346i
$695$	21.0000			0.796575
$696$	−2.00000	−	3.46410i	−0.0758098	−	0.131306i
$697$	−40.0000			−1.51511
$698$	13.0000	+	22.5167i	0.492057	+	0.852268i
$699$	8.00000	+	13.8564i	0.302588	+	0.524097i
$700$		0			0
$701$	−13.0000	+	22.5167i	−0.491003	+	0.850443i	−0.999946	−	0.0103576i	$-0.996703\pi$
$701$	−13.0000	+	22.5167i	−0.491003	+	0.850443i	0.508943	+	0.860800i	$0.330036\pi$
$702$	4.00000			0.150970
$703$	25.0000	−	17.3205i	0.942893	−	0.653255i
$704$	−5.00000			−0.188445
$705$	−9.00000	+	15.5885i	−0.338960	+	0.587095i
$706$	−14.0000	−	24.2487i	−0.526897	−	0.912612i
$707$		0			0
$708$	−1.00000	−	1.73205i	−0.0375823	−	0.0650945i
$709$	36.0000			1.35201			0.676004	−	0.736898i	$-0.263710\pi$
$709$	36.0000			1.35201			0.676004	+	0.736898i	$0.263710\pi$
$710$	7.00000	+	12.1244i	0.262705	+	0.455019i
$711$	−8.00000			−0.300023
$712$	0.500000	−	0.866025i	0.0187383	−	0.0324557i
$713$	−4.00000			−0.149801
$714$		0			0
$715$	2.50000	−	4.33013i	0.0934947	−	0.161938i
$716$	−1.50000	−	2.59808i	−0.0560576	−	0.0970947i
$717$	−20.0000			−0.746914
$718$	8.00000	−	13.8564i	0.298557	−	0.517116i
$719$	−23.0000	+	39.8372i	−0.857755	+	1.48568i	0.0163099	+	0.999867i	$0.494808\pi$
$719$	−23.0000	+	39.8372i	−0.857755	+	1.48568i	−0.874065	+	0.485809i	$0.838525\pi$
$720$	−0.500000	+	0.866025i	−0.0186339	+	0.0322749i
$721$		0			0
$722$	3.00000	+	5.19615i	0.111648	+	0.193381i
$723$	17.0000	−	29.4449i	0.632237	−	1.09507i
$724$	5.00000	−	8.66025i	0.185824	−	0.321856i
$725$	1.00000	−	1.73205i	0.0371391	−	0.0643268i
$726$	−28.0000			−1.03918
$727$	10.5000	+	18.1865i	0.389423	+	0.674501i	0.992372	−	0.123279i	$-0.0393409\pi$
$727$	10.5000	+	18.1865i	0.389423	+	0.674501i	−0.602949	+	0.797780i	$0.706008\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−12.0000			−0.444140
$731$	12.0000	−	20.7846i	0.443836	−	0.768747i
$732$	4.00000			0.147844
$733$	18.5000	+	32.0429i	0.683313	+	1.18353i	0.973964	+	0.226704i	$0.0727949\pi$
$733$	18.5000	+	32.0429i	0.683313	+	1.18353i	−0.290651	+	0.956829i	$0.593872\pi$
$734$	−17.0000			−0.627481
$735$	7.00000	+	12.1244i	0.258199	+	0.447214i
$736$	0.500000	+	0.866025i	0.0184302	+	0.0319221i
$737$	20.0000	+	34.6410i	0.736709	+	1.27602i
$738$	5.00000	−	8.66025i	0.184053	−	0.318788i
$739$	−15.0000			−0.551784			−0.275892	−	0.961189i	$-0.588973\pi$
$739$	−15.0000			−0.551784			−0.275892	+	0.961189i	$0.588973\pi$
$740$	5.50000	+	2.59808i	0.202184	+	0.0955072i
$741$	−10.0000			−0.367359
$742$		0			0
$743$	15.5000	+	26.8468i	0.568640	+	0.984913i	0.996701	+	0.0811633i	$0.0258635\pi$
$743$	15.5000	+	26.8468i	0.568640	+	0.984913i	−0.428061	+	0.903750i	$0.640803\pi$
$744$	−4.00000	−	6.92820i	−0.146647	−	0.254000i
$745$	−6.00000	−	10.3923i	−0.219823	−	0.380745i
$746$	23.0000			0.842090
$747$	−1.00000	−	1.73205i	−0.0365881	−	0.0633724i
$748$	20.0000			0.731272
$749$		0			0
$750$	−2.00000			−0.0730297
$751$	−46.0000			−1.67856			−0.839282	−	0.543696i	$-0.817024\pi$
$751$	−46.0000			−1.67856			−0.839282	+	0.543696i	$0.817024\pi$
$752$	−4.50000	+	7.79423i	−0.164098	+	0.284226i
$753$	15.0000	+	25.9808i	0.546630	+	0.946792i
$754$	2.00000			0.0728357
$755$	4.00000	−	6.92820i	0.145575	−	0.252143i
$756$		0			0
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	−0.669193	−	0.743089i	$-0.733360\pi$
$757$	8.50000	−	14.7224i	0.308938	−	0.535096i	0.978130	+	0.207993i	$0.0666932\pi$
$758$	−10.0000	−	17.3205i	−0.363216	−	0.629109i
$759$	5.00000	+	8.66025i	0.181489	+	0.314347i
$760$	−2.50000	+	4.33013i	−0.0906845	+	0.157070i
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	−0.874946	−	0.484221i	$-0.839103\pi$
$761$	−0.500000	+	0.866025i	−0.0181250	+	0.0313934i	0.856821	+	0.515615i	$0.172436\pi$
$762$	7.00000	−	12.1244i	0.253583	−	0.439219i
$763$		0			0
$764$	−4.00000	−	6.92820i	−0.144715	−	0.250654i
$765$	2.00000	−	3.46410i	0.0723102	−	0.125245i
$766$	−1.00000			−0.0361315
$767$	1.00000			0.0361079
$768$	−1.00000	+	1.73205i	−0.0360844	+	0.0625000i
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$	52.0000			1.87273
$772$	5.00000	+	8.66025i	0.179954	+	0.311689i
$773$	16.5000	+	28.5788i	0.593464	+	1.02791i	0.993762	+	0.111524i	$0.0355733\pi$
$773$	16.5000	+	28.5788i	0.593464	+	1.02791i	−0.400298	+	0.916385i	$0.631093\pi$
$774$	3.00000	+	5.19615i	0.107833	+	0.186772i
$775$	2.00000	−	3.46410i	0.0718421	−	0.124434i
$776$	−10.0000			−0.358979
$777$		0			0
$778$	−32.0000			−1.14726
$779$	25.0000	−	43.3013i	0.895718	−	1.55143i
$780$	−1.00000	−	1.73205i	−0.0358057	−	0.0620174i
$781$	35.0000	+	60.6218i	1.25240	+	2.16922i
$782$	−2.00000	−	3.46410i	−0.0715199	−	0.123876i
$783$	8.00000			0.285897
$784$	3.50000	+	6.06218i	0.125000	+	0.216506i
$785$	25.0000			0.892288
$786$		0			0
$787$	32.0000			1.14068			0.570338	−	0.821410i	$-0.306812\pi$
$787$	32.0000			1.14068			0.570338	+	0.821410i	$0.306812\pi$
$788$	−2.00000			−0.0712470
$789$	−11.0000	+	19.0526i	−0.391610	+	0.678289i
$790$	−4.00000	−	6.92820i	−0.142314	−	0.246494i
$791$		0			0
$792$	−2.50000	+	4.33013i	−0.0888336	+	0.153864i
$793$	−1.00000	+	1.73205i	−0.0355110	+	0.0615069i
$794$	−12.5000	+	21.6506i	−0.443608	+	0.768352i
$795$	6.00000	+	10.3923i	0.212798	+	0.368577i
$796$	−11.0000	−	19.0526i	−0.389885	−	0.675300i
$797$	6.50000	−	11.2583i	0.230242	−	0.398791i	−0.727637	−	0.685962i	$-0.759382\pi$
$797$	6.50000	−	11.2583i	0.230242	−	0.398791i	0.957879	+	0.287171i	$0.0927150\pi$
$798$		0			0
$799$	18.0000	−	31.1769i	0.636794	−	1.10296i
$800$	−1.00000			−0.0353553
$801$	−0.500000	−	0.866025i	−0.0176666	−	0.0305995i
$802$	−5.50000	+	9.52628i	−0.194212	+	0.336385i
$803$	−60.0000			−2.11735
$804$	16.0000			0.564276
$805$		0			0
$806$	4.00000			0.140894
$807$	−16.0000	−	27.7128i	−0.563227	−	0.975537i
$808$		0			0
$809$	−11.5000	−	19.9186i	−0.404318	−	0.700300i	0.589923	−	0.807459i	$-0.299158\pi$
$809$	−11.5000	−	19.9186i	−0.404318	−	0.700300i	−0.994242	+	0.107159i	$0.965825\pi$
$810$	−5.50000	−	9.52628i	−0.193250	−	0.334719i
$811$	3.50000	+	6.06218i	0.122902	+	0.212872i	0.920911	−	0.389774i	$-0.127447\pi$
$811$	3.50000	+	6.06218i	0.122902	+	0.212872i	−0.798009	+	0.602645i	$0.794113\pi$
$812$		0			0
$813$	40.0000			1.40286
$814$	27.5000	+	12.9904i	0.963875	+	0.455313i
$815$	−24.0000			−0.840683
$816$	4.00000	−	6.92820i	0.140028	−	0.242536i
$817$	15.0000	+	25.9808i	0.524784	+	0.908952i
$818$	−7.00000	−	12.1244i	−0.244749	−	0.423918i
$819$		0			0
$820$	10.0000			0.349215
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	0.979246	−	0.202674i	$-0.0649632\pi$
$821$	9.00000	+	15.5885i	0.314102	+	0.544041i	−0.665144	+	0.746715i	$0.731630\pi$
$822$	−28.0000			−0.976612
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	−0.971102	−	0.238664i	$-0.923291\pi$
$823$	−8.00000	+	13.8564i	−0.278862	+	0.483004i	0.692240	+	0.721668i	$0.256624\pi$
$824$	1.00000			0.0348367
$825$	−10.0000			−0.348155
$826$		0			0
$827$	3.00000	+	5.19615i	0.104320	+	0.180688i	0.913460	−	0.406928i	$-0.133400\pi$
$827$	3.00000	+	5.19615i	0.104320	+	0.180688i	−0.809140	+	0.587616i	$0.800067\pi$
$828$	1.00000			0.0347524
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	−0.403739	−	0.914874i	$-0.632290\pi$
$829$	17.0000	−	29.4449i	0.590434	−	1.02266i	0.994174	−	0.107788i	$-0.0343769\pi$
$830$	1.00000	−	1.73205i	0.0347105	−	0.0601204i
$831$	14.0000	−	24.2487i	0.485655	−	0.841178i
$832$	−0.500000	−	0.866025i	−0.0173344	−	0.0300240i
$833$	−14.0000	−	24.2487i	−0.485071	−	0.840168i
$834$	21.0000	−	36.3731i	0.727171	−	1.25950i
$835$	−4.00000	+	6.92820i	−0.138426	+	0.239760i
$836$	−12.5000	+	21.6506i	−0.432322	+	0.748803i
$837$	16.0000			0.553041
$838$	8.50000	+	14.7224i	0.293628	+	0.508578i
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	−0.233973	−	0.972243i	$-0.575173\pi$
$839$	21.0000	−	36.3731i	0.725001	−	1.25574i	0.958974	−	0.283495i	$-0.0914938\pi$
$840$		0			0
$841$	−25.0000			−0.862069
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$	−46.0000			−1.58432
$844$	9.50000	+	16.4545i	0.327003	+	0.566387i
$845$	−12.0000			−0.412813
$846$	4.50000	+	7.79423i	0.154713	+	0.267971i
$847$		0			0
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	−18.0000	+	31.1769i	−0.617758	+	1.06999i
$850$	4.00000			0.137199
$851$	−0.500000	−	6.06218i	−0.0171398	−	0.207809i
$852$	28.0000			0.959264
$853$	16.5000	−	28.5788i	0.564949	−	0.978521i	−0.432105	−	0.901823i	$-0.642229\pi$
$853$	16.5000	−	28.5788i	0.564949	−	0.978521i	0.997054	−	0.0766976i	$-0.0244376\pi$
$854$		0			0
$855$	2.50000	+	4.33013i	0.0854982	+	0.148087i
$856$	4.00000	+	6.92820i	0.136717	+	0.236801i
$857$	−54.0000			−1.84460			−0.922302	−	0.386469i	$-0.873695\pi$
$857$	−54.0000			−1.84460			−0.922302	+	0.386469i	$0.873695\pi$
$858$	−5.00000	−	8.66025i	−0.170697	−	0.295656i
$859$	45.0000			1.53538			0.767690	−	0.640821i	$-0.221406\pi$
$859$	45.0000			1.53538			0.767690	+	0.640821i	$0.221406\pi$
$860$	−3.00000	+	5.19615i	−0.102299	+	0.177187i
$861$		0			0
$862$	30.0000			1.02180
$863$	19.5000	−	33.7750i	0.663788	−	1.14971i	−0.315825	−	0.948818i	$-0.602281\pi$
$863$	19.5000	−	33.7750i	0.663788	−	1.14971i	0.979612	−	0.200897i	$-0.0643855\pi$
$864$	−2.00000	−	3.46410i	−0.0680414	−	0.117851i
$865$	7.00000			0.238007
$866$	−8.00000	+	13.8564i	−0.271851	+	0.470860i
$867$	1.00000	−	1.73205i	0.0339618	−	0.0588235i
$868$		0			0
$869$	−20.0000	−	34.6410i	−0.678454	−	1.17512i
$870$	−2.00000	−	3.46410i	−0.0678064	−	0.117444i
$871$	−4.00000	+	6.92820i	−0.135535	+	0.234753i
$872$	4.00000	−	6.92820i	0.135457	−	0.234619i
$873$	−5.00000	+	8.66025i	−0.169224	+	0.293105i
$874$	5.00000			0.169128
$875$		0			0
$876$	−12.0000	+	20.7846i	−0.405442	+	0.702247i
$877$	9.00000			0.303908			0.151954	−	0.988388i	$-0.451443\pi$
$877$	9.00000			0.303908			0.151954	+	0.988388i	$0.451443\pi$
$878$	36.0000			1.21494
$879$	−21.0000	+	36.3731i	−0.708312	+	1.22683i
$880$	−5.00000			−0.168550
$881$	−4.50000	−	7.79423i	−0.151609	−	0.262594i	0.780210	−	0.625517i	$-0.215112\pi$
$881$	−4.50000	−	7.79423i	−0.151609	−	0.262594i	−0.931819	+	0.362923i	$0.881779\pi$
$882$	7.00000			0.235702
$883$	5.00000	+	8.66025i	0.168263	+	0.291441i	0.937809	−	0.347151i	$-0.112851\pi$
$883$	5.00000	+	8.66025i	0.168263	+	0.291441i	−0.769546	+	0.638591i	$0.779517\pi$
$884$	2.00000	+	3.46410i	0.0672673	+	0.116510i
$885$	−1.00000	−	1.73205i	−0.0336146	−	0.0582223i
$886$	−9.00000	+	15.5885i	−0.302361	+	0.523704i
$887$		0			0			−	1.00000i	$-0.5\pi$
$887$		0			0				1.00000i	$0.5\pi$
$888$	10.0000	−	6.92820i	0.335578	−	0.232495i
$889$		0			0
$890$	0.500000	−	0.866025i	0.0167600	−	0.0290292i
$891$	−27.5000	−	47.6314i	−0.921285	−	1.59571i
$892$	−4.50000	−	7.79423i	−0.150671	−	0.260970i
$893$	22.5000	+	38.9711i	0.752934	+	1.30412i
$894$	−24.0000			−0.802680
$895$	−1.50000	−	2.59808i	−0.0501395	−	0.0868441i
$896$		0			0
$897$	−1.00000	+	1.73205i	−0.0333890	+	0.0578315i
$898$	6.00000			0.200223
$899$	8.00000			0.266815
$900$	−0.500000	+	0.866025i	−0.0166667	+	0.0288675i
$901$	−12.0000	−	20.7846i	−0.399778	−	0.692436i
$902$	50.0000			1.66482
$903$		0			0
$904$	2.00000	−	3.46410i	0.0665190	−	0.115214i
$905$	5.00000	−	8.66025i	0.166206	−	0.287877i
$906$	−8.00000	−	13.8564i	−0.265782	−	0.460348i
$907$	−21.0000	−	36.3731i	−0.697294	−	1.20775i	−0.969401	−	0.245481i	$-0.921054\pi$
$907$	−21.0000	−	36.3731i	−0.697294	−	1.20775i	0.272108	−	0.962267i	$-0.412279\pi$
$908$	−1.00000	+	1.73205i	−0.0331862	+	0.0574801i
$909$		0			0
$910$		0			0
$911$	2.00000			0.0662630			0.0331315	−	0.999451i	$-0.489452\pi$
$911$	2.00000			0.0662630			0.0331315	+	0.999451i	$0.489452\pi$
$912$	5.00000	+	8.66025i	0.165567	+	0.286770i
$913$	5.00000	−	8.66025i	0.165476	−	0.286613i
$914$	−6.00000			−0.198462
$915$	4.00000			0.132236
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$		0			0
$918$	8.00000	+	13.8564i	0.264039	+	0.457330i
$919$	24.0000			0.791687			0.395843	−	0.918318i	$-0.370452\pi$
$919$	24.0000			0.791687			0.395843	+	0.918318i	$0.370452\pi$
$920$	0.500000	+	0.866025i	0.0164845	+	0.0285520i
$921$	−18.0000	−	31.1769i	−0.593120	−	1.02731i
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	−7.00000	+	12.1244i	−0.230408	+	0.399078i
$924$		0			0
$925$	5.50000	+	2.59808i	0.180839	+	0.0854242i
$926$	−36.0000			−1.18303
$927$	0.500000	−	0.866025i	0.0164222	−	0.0284440i
$928$	−1.00000	−	1.73205i	−0.0328266	−	0.0568574i
$929$	−24.5000	−	42.4352i	−0.803819	−	1.39226i	−0.917086	−	0.398691i	$-0.869465\pi$
$929$	−24.5000	−	42.4352i	−0.803819	−	1.39226i	0.113267	−	0.993565i	$-0.463869\pi$
$930$	−4.00000	−	6.92820i	−0.131165	−	0.227185i
$931$	35.0000			1.14708
$932$	4.00000	+	6.92820i	0.131024	+	0.226941i
$933$	60.0000			1.96431
$934$	6.00000	−	10.3923i	0.196326	−	0.340047i
$935$	20.0000			0.654070
$936$	−1.00000			−0.0326860
$937$	−10.0000	+	17.3205i	−0.326686	+	0.565836i	−0.981852	−	0.189648i	$-0.939265\pi$
$937$	−10.0000	+	17.3205i	−0.326686	+	0.565836i	0.655166	+	0.755485i	$0.272599\pi$
$938$		0			0
$939$	−32.0000			−1.04428
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$	−18.0000	+	31.1769i	−0.586783	+	1.01634i	0.407867	+	0.913041i	$0.366273\pi$
$941$	−18.0000	+	31.1769i	−0.586783	+	1.01634i	−0.994651	+	0.103297i	$0.967061\pi$
$942$	25.0000	−	43.3013i	0.814544	−	1.41083i
$943$	−5.00000	−	8.66025i	−0.162822	−	0.282017i
$944$	−0.500000	−	0.866025i	−0.0162736	−	0.0281867i
$945$		0			0
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	−0.479801	−	0.877377i	$-0.659291\pi$
$947$	16.0000	−	27.7128i	0.519930	−	0.900545i	0.999732	−	0.0231683i	$-0.00737536\pi$
$948$	−16.0000			−0.519656
$949$	−6.00000	−	10.3923i	−0.194768	−	0.337348i
$950$	−2.50000	+	4.33013i	−0.0811107	+	0.140488i
$951$	−42.0000			−1.36194
$952$		0			0
$953$	2.00000	−	3.46410i	0.0647864	−	0.112213i	−0.831813	−	0.555056i	$-0.812697\pi$
$953$	2.00000	−	3.46410i	0.0647864	−	0.112213i	0.896599	+	0.442843i	$0.146030\pi$
$954$	6.00000			0.194257
$955$	−4.00000	−	6.92820i	−0.129437	−	0.224191i
$956$	−10.0000			−0.323423
$957$	−10.0000	−	17.3205i	−0.323254	−	0.559893i
$958$	9.00000	+	15.5885i	0.290777	+	0.503640i
$959$		0			0
$960$	−1.00000	+	1.73205i	−0.0322749	+	0.0559017i
$961$	−15.0000			−0.483871
$962$	0.500000	+	6.06218i	0.0161206	+	0.195452i
$963$	8.00000			0.257796
$964$	8.50000	−	14.7224i	0.273767	−	0.474178i
$965$	5.00000	+	8.66025i	0.160956	+	0.278783i
$966$		0			0
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	−0.980814	−	0.194946i	$-0.937547\pi$
$967$	−20.5000	−	35.5070i	−0.659236	−	1.14183i	0.321578	−	0.946883i	$-0.395787\pi$
$968$	−14.0000			−0.449977
$969$	−20.0000	−	34.6410i	−0.642493	−	1.11283i
$970$	−10.0000			−0.321081
$971$	6.50000	−	11.2583i	0.208595	−	0.361297i	−0.742677	−	0.669650i	$-0.766444\pi$
$971$	6.50000	−	11.2583i	0.208595	−	0.361297i	0.951272	+	0.308353i	$0.0997776\pi$
$972$	−10.0000			−0.320750
$973$		0			0
$974$	6.00000	−	10.3923i	0.192252	−	0.332991i
$975$	−1.00000	−	1.73205i	−0.0320256	−	0.0554700i
$976$	2.00000			0.0640184
$977$	−7.00000	+	12.1244i	−0.223950	+	0.387893i	−0.956004	−	0.293354i	$-0.905229\pi$
$977$	−7.00000	+	12.1244i	−0.223950	+	0.387893i	0.732054	+	0.681247i	$0.238562\pi$
$978$	−24.0000	+	41.5692i	−0.767435	+	1.32924i
$979$	2.50000	−	4.33013i	0.0799003	−	0.138391i
$980$	3.50000	+	6.06218i	0.111803	+	0.193649i
$981$	−4.00000	−	6.92820i	−0.127710	−	0.221201i
$982$	−5.50000	+	9.52628i	−0.175512	+	0.303996i
$983$	−25.5000	+	44.1673i	−0.813324	+	1.40872i	0.0972017	+	0.995265i	$0.469011\pi$
$983$	−25.5000	+	44.1673i	−0.813324	+	1.40872i	−0.910525	+	0.413453i	$0.864323\pi$
$984$	10.0000	−	17.3205i	0.318788	−	0.552158i
$985$	−2.00000			−0.0637253
$986$	4.00000	+	6.92820i	0.127386	+	0.220639i
$987$		0			0
$988$	−5.00000			−0.159071
$989$	6.00000			0.190789
$990$	−2.50000	+	4.33013i	−0.0794552	+	0.137620i
$991$	34.0000			1.08005			0.540023	−	0.841650i	$-0.318416\pi$
$991$	34.0000			1.08005			0.540023	+	0.841650i	$0.318416\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	−54.0000			−1.71364
$994$		0			0
$995$	−11.0000	−	19.0526i	−0.348723	−	0.604007i
$996$	−2.00000	−	3.46410i	−0.0633724	−	0.109764i
$997$	−16.5000	+	28.5788i	−0.522560	+	0.905101i	0.477095	+	0.878852i	$0.341690\pi$
$997$	−16.5000	+	28.5788i	−0.522560	+	0.905101i	−0.999655	+	0.0262493i	$0.991644\pi$
$998$	−16.0000			−0.506471
$999$	2.00000	+	24.2487i	0.0632772	+	0.767195i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.e.a.121.1	✓	2
37.26	even	3	inner	370.2.e.a.211.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.e.a.121.1	✓	2	1.1	even	1	trivial
370.2.e.a.211.1	yes	2	37.26	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-1.00000 - 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -1.00000 q^{10} -5.00000 q^{11} +(-1.00000 + 1.73205i) q^{12} +(-0.500000 - 0.866025i) q^{13} +(-1.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.00000 - 3.46410i) q^{17} +(0.500000 + 0.866025i) q^{18} +(2.50000 + 4.33013i) q^{19} +(-0.500000 + 0.866025i) q^{20} +(-2.50000 + 4.33013i) q^{22} +1.00000 q^{23} +(1.00000 + 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{25} -1.00000 q^{26} -4.00000 q^{27} -2.00000 q^{29} +(1.00000 + 1.73205i) q^{30} -4.00000 q^{31} +(0.500000 + 0.866025i) q^{32} +(5.00000 + 8.66025i) q^{33} +(-2.00000 - 3.46410i) q^{34} +1.00000 q^{36} +(-0.500000 - 6.06218i) q^{37} +5.00000 q^{38} +(-1.00000 + 1.73205i) q^{39} +(0.500000 + 0.866025i) q^{40} +(-5.00000 - 8.66025i) q^{41} +6.00000 q^{43} +(2.50000 + 4.33013i) q^{44} +1.00000 q^{45} +(0.500000 - 0.866025i) q^{46} +9.00000 q^{47} +2.00000 q^{48} +(3.50000 - 6.06218i) q^{49} +(0.500000 + 0.866025i) q^{50} -8.00000 q^{51} +(-0.500000 + 0.866025i) q^{52} +(3.00000 - 5.19615i) q^{53} +(-2.00000 + 3.46410i) q^{54} +(2.50000 + 4.33013i) q^{55} +(5.00000 - 8.66025i) q^{57} +(-1.00000 + 1.73205i) q^{58} +(-0.500000 + 0.866025i) q^{59} +2.00000 q^{60} +(-1.00000 - 1.73205i) q^{61} +(-2.00000 + 3.46410i) q^{62} +1.00000 q^{64} +(-0.500000 + 0.866025i) q^{65} +10.0000 q^{66} +(-4.00000 - 6.92820i) q^{67} -4.00000 q^{68} +(-1.00000 - 1.73205i) q^{69} +(-7.00000 - 12.1244i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-5.50000 - 2.59808i) q^{74} +2.00000 q^{75} +(2.50000 - 4.33013i) q^{76} +(1.00000 + 1.73205i) q^{78} +(4.00000 + 6.92820i) q^{79} +1.00000 q^{80} +(5.50000 + 9.52628i) q^{81} -10.0000 q^{82} +(-1.00000 + 1.73205i) q^{83} -4.00000 q^{85} +(3.00000 - 5.19615i) q^{86} +(2.00000 + 3.46410i) q^{87} +5.00000 q^{88} +(-0.500000 + 0.866025i) q^{89} +(0.500000 - 0.866025i) q^{90} +(-0.500000 - 0.866025i) q^{92} +(4.00000 + 6.92820i) q^{93} +(4.50000 - 7.79423i) q^{94} +(2.50000 - 4.33013i) q^{95} +(1.00000 - 1.73205i) q^{96} +10.0000 q^{97} +(-3.50000 - 6.06218i) q^{98} +(2.50000 - 4.33013i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - 4 q^{6} - 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - 4 * q^6 - 2 * q^8 - q^9	\( 2 q + q^{2} - 2 q^{3} - q^{4} - q^{5} - 4 q^{6} - 2 q^{8} - q^{9} - 2 q^{10} - 10 q^{11} - 2 q^{12} - q^{13} - 2 q^{15} - q^{16} + 4 q^{17} + q^{18} + 5 q^{19} - q^{20} - 5 q^{22} + 2 q^{23} + 2 q^{24} - q^{25} - 2 q^{26} - 8 q^{27} - 4 q^{29} + 2 q^{30} - 8 q^{31} + q^{32} + 10 q^{33} - 4 q^{34} + 2 q^{36} - q^{37} + 10 q^{38} - 2 q^{39} + q^{40} - 10 q^{41} + 12 q^{43} + 5 q^{44} + 2 q^{45} + q^{46} + 18 q^{47} + 4 q^{48} + 7 q^{49} + q^{50} - 16 q^{51} - q^{52} + 6 q^{53} - 4 q^{54} + 5 q^{55} + 10 q^{57} - 2 q^{58} - q^{59} + 4 q^{60} - 2 q^{61} - 4 q^{62} + 2 q^{64} - q^{65} + 20 q^{66} - 8 q^{67} - 8 q^{68} - 2 q^{69} - 14 q^{71} + q^{72} + 24 q^{73} - 11 q^{74} + 4 q^{75} + 5 q^{76} + 2 q^{78} + 8 q^{79} + 2 q^{80} + 11 q^{81} - 20 q^{82} - 2 q^{83} - 8 q^{85} + 6 q^{86} + 4 q^{87} + 10 q^{88} - q^{89} + q^{90} - q^{92} + 8 q^{93} + 9 q^{94} + 5 q^{95} + 2 q^{96} + 20 q^{97} - 7 q^{98} + 5 q^{99}+O(q^{100}) \) 2 * q + q^2 - 2 * q^3 - q^4 - q^5 - 4 * q^6 - 2 * q^8 - q^9 - 2 * q^10 - 10 * q^11 - 2 * q^12 - q^13 - 2 * q^15 - q^16 + 4 * q^17 + q^18 + 5 * q^19 - q^20 - 5 * q^22 + 2 * q^23 + 2 * q^24 - q^25 - 2 * q^26 - 8 * q^27 - 4 * q^29 + 2 * q^30 - 8 * q^31 + q^32 + 10 * q^33 - 4 * q^34 + 2 * q^36 - q^37 + 10 * q^38 - 2 * q^39 + q^40 - 10 * q^41 + 12 * q^43 + 5 * q^44 + 2 * q^45 + q^46 + 18 * q^47 + 4 * q^48 + 7 * q^49 + q^50 - 16 * q^51 - q^52 + 6 * q^53 - 4 * q^54 + 5 * q^55 + 10 * q^57 - 2 * q^58 - q^59 + 4 * q^60 - 2 * q^61 - 4 * q^62 + 2 * q^64 - q^65 + 20 * q^66 - 8 * q^67 - 8 * q^68 - 2 * q^69 - 14 * q^71 + q^72 + 24 * q^73 - 11 * q^74 + 4 * q^75 + 5 * q^76 + 2 * q^78 + 8 * q^79 + 2 * q^80 + 11 * q^81 - 20 * q^82 - 2 * q^83 - 8 * q^85 + 6 * q^86 + 4 * q^87 + 10 * q^88 - q^89 + q^90 - q^92 + 8 * q^93 + 9 * q^94 + 5 * q^95 + 2 * q^96 + 20 * q^97 - 7 * q^98 + 5 * q^99

Introduction

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