LMFDB - Embedded newform 338.2.c.a.191.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,2,Mod(191,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("338.191");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not 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:	$2.69894358832$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	338.191
Dual form			338.2.c.a.315.1

$q$-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} +3.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{12} +1.00000 q^{14} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} -2.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +(-1.50000 - 2.59808i) q^{20} +1.00000 q^{21} +(3.00000 + 5.19615i) q^{22} +(-0.500000 + 0.866025i) q^{24} +4.00000 q^{25} -5.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(-1.50000 - 2.59808i) q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} -3.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(1.00000 - 1.73205i) q^{36} +(-3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +3.00000 q^{40} +(-0.500000 + 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} -6.00000 q^{44} +(3.00000 + 5.19615i) q^{45} -3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.00000 + 3.46410i) q^{50} -3.00000 q^{51} +(2.50000 - 4.33013i) q^{54} +(9.00000 - 15.5885i) q^{55} +(-0.500000 - 0.866025i) q^{56} -2.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(-3.00000 - 5.19615i) q^{59} +3.00000 q^{60} +(-4.00000 - 6.92820i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(7.00000 - 12.1244i) q^{67} +(1.50000 - 2.59808i) q^{68} +3.00000 q^{70} +(-1.50000 - 2.59808i) q^{71} +(1.00000 + 1.73205i) q^{72} -2.00000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(1.00000 - 1.73205i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} +(-0.500000 - 0.866025i) q^{84} +(4.50000 + 7.79423i) q^{85} -1.00000 q^{86} +(-3.00000 - 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(-3.00000 + 5.19615i) q^{89} -6.00000 q^{90} +(-2.00000 + 3.46410i) q^{93} +(1.50000 - 2.59808i) q^{94} +(3.00000 + 5.19615i) q^{95} +1.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(3.00000 + 5.19615i) q^{98} +12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} + 6 q^{5} - q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + 6 q^{11} + 2 q^{12} + 2 q^{14} - 3 q^{15} - q^{16} + 3 q^{17} - 4 q^{18} + 2 q^{19} - 3 q^{20} + 2 q^{21} + 6 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 + 6 * q^5 - q^6 - q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + 6 * q^11 + 2 * q^12 + 2 * q^14 - 3 * q^15 - q^16 + 3 * q^17 - 4 * q^18 + 2 * q^19 - 3 * q^20 + 2 * q^21 + 6 * q^22 - q^24 + 8 * q^25 - 10 * q^27 - q^28 - 6 * q^29 - 3 * q^30 + 8 * q^31 - q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 2 * q^36 - 7 * q^37 - 4 * q^38 + 6 * q^40 - q^42 + q^43 - 12 * q^44 + 6 * q^45 - 6 * q^47 - q^48 + 6 * q^49 - 4 * q^50 - 6 * q^51 + 5 * q^54 + 18 * q^55 - q^56 - 4 * q^57 - 6 * q^58 - 6 * q^59 + 6 * q^60 - 8 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 - 12 * q^66 + 14 * q^67 + 3 * q^68 + 6 * q^70 - 3 * q^71 + 2 * q^72 - 4 * q^73 - 7 * q^74 - 4 * q^75 + 2 * q^76 - 12 * q^77 + 16 * q^79 - 3 * q^80 - q^81 - 24 * q^83 - q^84 + 9 * q^85 - 2 * q^86 - 6 * q^87 + 6 * q^88 - 6 * q^89 - 12 * q^90 - 4 * q^93 + 3 * q^94 + 6 * q^95 + 2 * q^96 - 10 * q^97 + 6 * q^98 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	−0.973494	−	0.228714i	$-0.926548\pi$
$3$	−0.500000	+	0.866025i	−0.288675	+	0.500000i	0.684819	+	0.728714i	$0.259881\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	3.00000			1.34164			0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.00000			1.34164			0.670820	+	0.741620i	$0.265942\pi$
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	0.755929	−	0.654654i	$-0.227186\pi$
$7$	−0.500000	−	0.866025i	−0.188982	−	0.327327i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$	−1.50000	+	2.59808i	−0.474342	+	0.821584i
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	1.00000			0.288675
$13$		0			0
$13$		0			0
$14$	1.00000			0.267261
$15$	−1.50000	+	2.59808i	−0.387298	+	0.670820i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	0.988583	−	0.150675i	$-0.0481447\pi$
$17$	1.50000	+	2.59808i	0.363803	+	0.630126i	−0.624780	+	0.780801i	$0.714811\pi$
$18$	−2.00000			−0.471405
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−1.50000	−	2.59808i	−0.335410	−	0.580948i
$21$	1.00000			0.218218
$22$	3.00000	+	5.19615i	0.639602	+	1.10782i
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	4.00000			0.800000
$26$		0			0
$27$	−5.00000			−0.962250
$28$	−0.500000	+	0.866025i	−0.0944911	+	0.163663i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$	−1.50000	−	2.59808i	−0.273861	−	0.474342i
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	3.00000	+	5.19615i	0.522233	+	0.904534i
$34$	−3.00000			−0.514496
$35$	−1.50000	−	2.59808i	−0.253546	−	0.439155i
$36$	1.00000	−	1.73205i	0.166667	−	0.288675i
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	0.420602	+	0.907245i	$0.361819\pi$
$37$	−3.50000	+	6.06218i	−0.575396	+	0.996616i	−0.995998	+	0.0893706i	$0.971514\pi$
$38$	−2.00000			−0.324443
$39$		0			0
$40$	3.00000			0.474342
$41$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$41$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−6.00000			−0.904534
$45$	3.00000	+	5.19615i	0.447214	+	0.774597i
$46$		0			0
$47$	−3.00000			−0.437595			−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000			−0.437595			−0.218797	+	0.975770i	$0.570213\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	−2.00000	+	3.46410i	−0.282843	+	0.489898i
$51$	−3.00000			−0.420084
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	2.50000	−	4.33013i	0.340207	−	0.589256i
$55$	9.00000	−	15.5885i	1.21356	−	2.10195i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−2.00000			−0.264906
$58$	−3.00000	−	5.19615i	−0.393919	−	0.682288i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$	3.00000			0.387298
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	−0.999901	−	0.0140840i	$-0.995517\pi$
$61$	−4.00000	−	6.92820i	−0.512148	−	0.887066i	0.487753	−	0.872982i	$-0.337817\pi$
$62$	−2.00000	+	3.46410i	−0.254000	+	0.439941i
$63$	1.00000	−	1.73205i	0.125988	−	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	−0.0212861	−	0.999773i	$-0.506776\pi$
$67$	7.00000	−	12.1244i	0.855186	−	1.48123i	0.876472	−	0.481452i	$-0.159891\pi$
$68$	1.50000	−	2.59808i	0.181902	−	0.315063i
$69$		0			0
$70$	3.00000			0.358569
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	0.763184	−	0.646181i	$-0.223635\pi$
$71$	−1.50000	−	2.59808i	−0.178017	−	0.308335i	−0.941201	+	0.337846i	$0.890302\pi$
$72$	1.00000	+	1.73205i	0.117851	+	0.204124i
$73$	−2.00000			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$73$	−2.00000			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$74$	−3.50000	−	6.06218i	−0.406867	−	0.704714i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	1.00000	−	1.73205i	0.114708	−	0.198680i
$77$	−6.00000			−0.683763
$78$		0			0
$79$	8.00000			0.900070			0.450035	−	0.893011i	$-0.351411\pi$
$79$	8.00000			0.900070			0.450035	+	0.893011i	$0.351411\pi$
$80$	−1.50000	+	2.59808i	−0.167705	+	0.290474i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$	−0.500000	−	0.866025i	−0.0545545	−	0.0944911i
$85$	4.50000	+	7.79423i	0.488094	+	0.845403i
$86$	−1.00000			−0.107833
$87$	−3.00000	−	5.19615i	−0.321634	−	0.557086i
$88$	3.00000	−	5.19615i	0.319801	−	0.553912i
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	−0.980071	−	0.198650i	$-0.936344\pi$
$89$	−3.00000	+	5.19615i	−0.317999	+	0.550791i	0.662071	+	0.749441i	$0.269678\pi$
$90$	−6.00000			−0.632456
$91$		0			0
$92$		0			0
$93$	−2.00000	+	3.46410i	−0.207390	+	0.359211i
$94$	1.50000	−	2.59808i	0.154713	−	0.267971i
$95$	3.00000	+	5.19615i	0.307794	+	0.533114i
$96$	1.00000			0.102062
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	12.0000			1.20605
$100$	−2.00000	−	3.46410i	−0.200000	−	0.346410i
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	−0.396236	−	0.918149i	$-0.629684\pi$
$101$	6.00000	−	10.3923i	0.597022	−	1.03407i	0.993258	−	0.115924i	$-0.0369830\pi$
$102$	1.50000	−	2.59808i	0.148522	−	0.257248i
$103$	−4.00000			−0.394132			−0.197066	−	0.980390i	$-0.563141\pi$
$103$	−4.00000			−0.394132			−0.197066	+	0.980390i	$0.563141\pi$
$104$		0			0
$105$	3.00000			0.292770
$106$		0			0
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$	2.50000	+	4.33013i	0.240563	+	0.416667i
$109$	7.00000			0.670478			0.335239	−	0.942133i	$-0.391183\pi$
$109$	7.00000			0.670478			0.335239	+	0.942133i	$0.391183\pi$
$110$	9.00000	+	15.5885i	0.858116	+	1.48630i
$111$	−3.50000	−	6.06218i	−0.332205	−	0.575396i
$112$	1.00000			0.0944911
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$	1.00000	−	1.73205i	0.0936586	−	0.162221i
$115$		0			0
$116$	6.00000			0.557086
$117$		0			0
$118$	6.00000			0.552345
$119$	1.50000	−	2.59808i	0.137505	−	0.238165i
$120$	−1.50000	+	2.59808i	−0.136931	+	0.237171i
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	8.00000			0.724286
$123$		0			0
$124$	−2.00000	−	3.46410i	−0.179605	−	0.311086i
$125$	−3.00000			−0.268328
$126$	1.00000	+	1.73205i	0.0890871	+	0.154303i
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.0443678	+	0.999015i	$0.514127\pi$
$127$	−10.0000	+	17.3205i	−0.887357	+	1.53695i	−0.842989	+	0.537931i	$0.819206\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−1.00000			−0.0880451
$130$		0			0
$131$	−21.0000			−1.83478			−0.917389	−	0.397991i	$-0.869707\pi$
$131$	−21.0000			−1.83478			−0.917389	+	0.397991i	$0.869707\pi$
$132$	3.00000	−	5.19615i	0.261116	−	0.452267i
$133$	1.00000	−	1.73205i	0.0867110	−	0.150188i
$134$	7.00000	+	12.1244i	0.604708	+	1.04738i
$135$	−15.0000			−1.29099
$136$	1.50000	+	2.59808i	0.128624	+	0.222783i
$137$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$137$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$138$		0			0
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	0.998179	+	0.0603135i	$0.0192101\pi$
$139$	6.50000	+	11.2583i	0.551323	+	0.954919i	−0.446857	+	0.894606i	$0.647457\pi$
$140$	−1.50000	+	2.59808i	−0.126773	+	0.219578i
$141$	1.50000	−	2.59808i	0.126323	−	0.218797i
$142$	3.00000			0.251754
$143$		0			0
$144$	−2.00000			−0.166667
$145$	−9.00000	+	15.5885i	−0.747409	+	1.29455i
$146$	1.00000	−	1.73205i	0.0827606	−	0.143346i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	7.00000			0.575396
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	0.716578	−	0.697507i	$-0.245707\pi$
$149$	−3.00000	−	5.19615i	−0.245770	−	0.425685i	−0.962348	+	0.271821i	$0.912374\pi$
$150$	−2.00000	−	3.46410i	−0.163299	−	0.282843i
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$	1.00000	+	1.73205i	0.0811107	+	0.140488i
$153$	−3.00000	+	5.19615i	−0.242536	+	0.420084i
$154$	3.00000	−	5.19615i	0.241747	−	0.418718i
$155$	12.0000			0.963863
$156$		0			0
$157$	14.0000			1.11732			0.558661	−	0.829396i	$-0.311315\pi$
$157$	14.0000			1.11732			0.558661	+	0.829396i	$0.311315\pi$
$158$	−4.00000	+	6.92820i	−0.318223	+	0.551178i
$159$		0			0
$160$	−1.50000	−	2.59808i	−0.118585	−	0.205396i
$161$		0			0
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	−0.988227	−	0.152992i	$-0.951109\pi$
$163$	−8.00000	−	13.8564i	−0.626608	−	1.08532i	0.361619	−	0.932326i	$-0.382224\pi$
$164$		0			0
$165$	9.00000	+	15.5885i	0.700649	+	1.21356i
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$	1.00000			0.0771517
$169$		0			0
$170$	−9.00000			−0.690268
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	0.500000	−	0.866025i	0.0381246	−	0.0660338i
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	6.00000			0.454859
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	3.00000	+	5.19615i	0.226134	+	0.391675i
$177$	6.00000			0.450988
$178$	−3.00000	−	5.19615i	−0.224860	−	0.389468i
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	−0.916623	−	0.399753i	$-0.869096\pi$
$179$	−1.50000	+	2.59808i	−0.112115	+	0.194189i	0.804508	+	0.593942i	$0.202429\pi$
$180$	3.00000	−	5.19615i	0.223607	−	0.387298i
$181$	20.0000			1.48659			0.743294	−	0.668965i	$-0.233262\pi$
$181$	20.0000			1.48659			0.743294	+	0.668965i	$0.233262\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$		0			0
$185$	−10.5000	+	18.1865i	−0.771975	+	1.33710i
$186$	−2.00000	−	3.46410i	−0.146647	−	0.254000i
$187$	18.0000			1.31629
$188$	1.50000	+	2.59808i	0.109399	+	0.189484i
$189$	2.50000	+	4.33013i	0.181848	+	0.314970i
$190$	−6.00000			−0.435286
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$	−0.500000	+	0.866025i	−0.0360844	+	0.0625000i
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	−0.928986	−	0.370116i	$-0.879318\pi$
$193$	−2.00000	+	3.46410i	−0.143963	+	0.249351i	0.785022	+	0.619467i	$0.212651\pi$
$194$	10.0000			0.717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	−0.807630	−	0.589689i	$-0.799250\pi$
$197$	1.50000	−	2.59808i	0.106871	−	0.185105i	0.914501	+	0.404584i	$0.132584\pi$
$198$	−6.00000	+	10.3923i	−0.426401	+	0.738549i
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	0.828403	−	0.560133i	$-0.189250\pi$
$199$	−1.00000	−	1.73205i	−0.0708881	−	0.122782i	−0.899291	+	0.437351i	$0.855917\pi$
$200$	4.00000			0.282843
$201$	7.00000	+	12.1244i	0.493742	+	0.855186i
$202$	6.00000	+	10.3923i	0.422159	+	0.731200i
$203$	6.00000			0.421117
$204$	1.50000	+	2.59808i	0.105021	+	0.181902i
$205$		0			0
$206$	2.00000	−	3.46410i	0.139347	−	0.241355i
$207$		0			0
$208$		0			0
$209$	12.0000			0.830057
$210$	−1.50000	+	2.59808i	−0.103510	+	0.179284i
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	−0.550743	−	0.834675i	$-0.685655\pi$
$211$	6.50000	−	11.2583i	0.447478	−	0.775055i	0.998221	+	0.0596196i	$0.0189888\pi$
$212$		0			0
$213$	3.00000			0.205557
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	1.50000	+	2.59808i	0.102299	+	0.177187i
$216$	−5.00000			−0.340207
$217$	−2.00000	−	3.46410i	−0.135769	−	0.235159i
$218$	−3.50000	+	6.06218i	−0.237050	+	0.410582i
$219$	1.00000	−	1.73205i	0.0675737	−	0.117041i
$220$	−18.0000			−1.21356
$221$		0			0
$222$	7.00000			0.469809
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	0.350100	+	0.936713i	$0.386148\pi$
$223$	−9.50000	+	16.4545i	−0.636167	+	1.10187i	−0.986267	+	0.165161i	$0.947186\pi$
$224$	−0.500000	+	0.866025i	−0.0334077	+	0.0578638i
$225$	4.00000	+	6.92820i	0.266667	+	0.461880i
$226$	−6.00000			−0.399114
$227$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$227$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$228$	1.00000	+	1.73205i	0.0662266	+	0.114708i
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$	3.00000	−	5.19615i	0.197386	−	0.341882i
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	−27.0000			−1.76883			−0.884414	−	0.466702i	$-0.845442\pi$
$233$	−27.0000			−1.76883			−0.884414	+	0.466702i	$0.845442\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$	−4.00000	+	6.92820i	−0.259828	+	0.450035i
$238$	1.50000	+	2.59808i	0.0972306	+	0.168408i
$239$	−15.0000			−0.970269			−0.485135	−	0.874439i	$-0.661229\pi$
$239$	−15.0000			−0.970269			−0.485135	+	0.874439i	$0.661229\pi$
$240$	−1.50000	−	2.59808i	−0.0968246	−	0.167705i
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	25.0000			1.60706
$243$	−8.00000	−	13.8564i	−0.513200	−	0.888889i
$244$	−4.00000	+	6.92820i	−0.256074	+	0.443533i
$245$	9.00000	−	15.5885i	0.574989	−	0.995910i
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$	6.00000	−	10.3923i	0.380235	−	0.658586i
$250$	1.50000	−	2.59808i	0.0948683	−	0.164317i
$251$	−12.0000	−	20.7846i	−0.757433	−	1.31191i	−0.944156	−	0.329500i	$-0.893120\pi$
$251$	−12.0000	−	20.7846i	−0.757433	−	1.31191i	0.186722	−	0.982413i	$-0.440214\pi$
$252$	−2.00000			−0.125988
$253$		0			0
$254$	−10.0000	−	17.3205i	−0.627456	−	1.08679i
$255$	−9.00000			−0.563602
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	−0.971558	−	0.236802i	$-0.923901\pi$
$257$	−4.50000	+	7.79423i	−0.280702	+	0.486191i	0.690856	+	0.722993i	$0.257234\pi$
$258$	0.500000	−	0.866025i	0.0311286	−	0.0539164i
$259$	7.00000			0.434959
$260$		0			0
$261$	−12.0000			−0.742781
$262$	10.5000	−	18.1865i	0.648692	−	1.12357i
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	1.00000	+	1.73205i	0.0613139	+	0.106199i
$267$	−3.00000	−	5.19615i	−0.183597	−	0.317999i
$268$	−14.0000			−0.855186
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$	7.50000	−	12.9904i	0.456435	−	0.790569i
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	−0.649211	−	0.760609i	$-0.724901\pi$
$271$	5.50000	−	9.52628i	0.334101	−	0.578680i	0.983312	+	0.181928i	$0.0582339\pi$
$272$	−3.00000			−0.181902
$273$		0			0
$274$		0			0
$275$	12.0000	−	20.7846i	0.723627	−	1.25336i
$276$		0			0
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	0.888899	+	0.458103i	$0.151471\pi$
$277$	14.0000	+	24.2487i	0.841178	+	1.45696i	−0.0477206	+	0.998861i	$0.515196\pi$
$278$	−13.0000			−0.779688
$279$	4.00000	+	6.92820i	0.239474	+	0.414781i
$280$	−1.50000	−	2.59808i	−0.0896421	−	0.155265i
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	1.50000	+	2.59808i	0.0893237	+	0.154713i
$283$	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	$0.128734\pi$
$284$	−1.50000	+	2.59808i	−0.0890086	+	0.154167i
$285$	−6.00000			−0.355409
$286$		0			0
$287$		0			0
$288$	1.00000	−	1.73205i	0.0589256	−	0.102062i
$289$	4.00000	−	6.92820i	0.235294	−	0.407541i
$290$	−9.00000	−	15.5885i	−0.528498	−	0.915386i
$291$	10.0000			0.586210
$292$	1.00000	+	1.73205i	0.0585206	+	0.101361i
$293$	10.5000	+	18.1865i	0.613417	+	1.06247i	0.990660	+	0.136355i	$0.0435386\pi$
$293$	10.5000	+	18.1865i	0.613417	+	1.06247i	−0.377244	+	0.926114i	$0.623128\pi$
$294$	−6.00000			−0.349927
$295$	−9.00000	−	15.5885i	−0.524000	−	0.907595i
$296$	−3.50000	+	6.06218i	−0.203433	+	0.352357i
$297$	−15.0000	+	25.9808i	−0.870388	+	1.50756i
$298$	6.00000			0.347571
$299$		0			0
$300$	4.00000			0.230940
$301$	0.500000	−	0.866025i	0.0288195	−	0.0499169i
$302$	8.50000	−	14.7224i	0.489120	−	0.847181i
$303$	6.00000	+	10.3923i	0.344691	+	0.597022i
$304$	−2.00000			−0.114708
$305$	−12.0000	−	20.7846i	−0.687118	−	1.19012i
$306$	−3.00000	−	5.19615i	−0.171499	−	0.297044i
$307$	−2.00000			−0.114146			−0.0570730	−	0.998370i	$-0.518177\pi$
$307$	−2.00000			−0.114146			−0.0570730	+	0.998370i	$0.518177\pi$
$308$	3.00000	+	5.19615i	0.170941	+	0.296078i
$309$	2.00000	−	3.46410i	0.113776	−	0.197066i
$310$	−6.00000	+	10.3923i	−0.340777	+	0.590243i
$311$	−30.0000			−1.70114			−0.850572	−	0.525859i	$-0.823744\pi$
$311$	−30.0000			−1.70114			−0.850572	+	0.525859i	$0.823744\pi$
$312$		0			0
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	−7.00000	+	12.1244i	−0.395033	+	0.684217i
$315$	3.00000	−	5.19615i	0.169031	−	0.292770i
$316$	−4.00000	−	6.92820i	−0.225018	−	0.389742i
$317$	6.00000			0.336994			0.168497	−	0.985702i	$-0.446109\pi$
$317$	6.00000			0.336994			0.168497	+	0.985702i	$0.446109\pi$
$318$		0			0
$319$	18.0000	+	31.1769i	1.00781	+	1.74557i
$320$	3.00000			0.167705
$321$	−6.00000	−	10.3923i	−0.334887	−	0.580042i
$322$		0			0
$323$	−3.00000	+	5.19615i	−0.166924	+	0.289122i
$324$	1.00000			0.0555556
$325$		0			0
$326$	16.0000			0.886158
$327$	−3.50000	+	6.06218i	−0.193550	+	0.335239i
$328$		0			0
$329$	1.50000	+	2.59808i	0.0826977	+	0.143237i
$330$	−18.0000			−0.990867
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	−14.0000			−0.767195
$334$		0			0
$335$	21.0000	−	36.3731i	1.14735	−	1.98727i
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	23.0000			1.25289			0.626445	−	0.779466i	$-0.284509\pi$
$337$	23.0000			1.25289			0.626445	+	0.779466i	$0.284509\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$	4.50000	−	7.79423i	0.244047	−	0.422701i
$341$	12.0000	−	20.7846i	0.649836	−	1.12555i
$342$	−2.00000	−	3.46410i	−0.108148	−	0.187317i
$343$	−13.0000			−0.701934
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$		0			0
$346$		0			0
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	0.822951	−	0.568112i	$-0.192326\pi$
$347$	−1.50000	−	2.59808i	−0.0805242	−	0.139472i	−0.903475	+	0.428640i	$0.858993\pi$
$348$	−3.00000	+	5.19615i	−0.160817	+	0.278543i
$349$	−9.50000	+	16.4545i	−0.508523	+	0.880788i	0.491428	+	0.870918i	$0.336475\pi$
$349$	−9.50000	+	16.4545i	−0.508523	+	0.880788i	−0.999951	+	0.00987003i	$0.996858\pi$
$350$	4.00000			0.213809
$351$		0			0
$352$	−6.00000			−0.319801
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	−0.347024	−	0.937856i	$-0.612808\pi$
$353$	12.0000	−	20.7846i	0.638696	−	1.10625i	0.985719	−	0.168397i	$-0.0538590\pi$
$354$	−3.00000	+	5.19615i	−0.159448	+	0.276172i
$355$	−4.50000	−	7.79423i	−0.238835	−	0.413675i
$356$	6.00000			0.317999
$357$	1.50000	+	2.59808i	0.0793884	+	0.137505i
$358$	−1.50000	−	2.59808i	−0.0792775	−	0.137313i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$	3.00000	+	5.19615i	0.158114	+	0.273861i
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$	−10.0000	+	17.3205i	−0.525588	+	0.910346i
$363$	25.0000			1.31216
$364$		0			0
$365$	−6.00000			−0.314054
$366$	−4.00000	+	6.92820i	−0.209083	+	0.362143i
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	0.296810	+	0.954937i	$0.404077\pi$
$367$	−13.0000	+	22.5167i	−0.678594	+	1.17536i	−0.975404	+	0.220423i	$0.929256\pi$
$368$		0			0
$369$		0			0
$370$	−10.5000	−	18.1865i	−0.545869	−	0.945473i
$371$		0			0
$372$	4.00000			0.207390
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$	−9.00000	+	15.5885i	−0.465379	+	0.806060i
$375$	1.50000	−	2.59808i	0.0774597	−	0.134164i
$376$	−3.00000			−0.154713
$377$		0			0
$378$	−5.00000			−0.257172
$379$	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	$-0.00504609\pi$
$380$	3.00000	−	5.19615i	0.153897	−	0.266557i
$381$	−10.0000	−	17.3205i	−0.512316	−	0.887357i
$382$	−18.0000			−0.920960
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	0.999088	+	0.0427020i	$0.0135966\pi$
$383$	10.5000	+	18.1865i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−18.0000			−0.917365
$386$	−2.00000	−	3.46410i	−0.101797	−	0.176318i
$387$	−1.00000	+	1.73205i	−0.0508329	+	0.0880451i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$		0			0
$392$	3.00000	−	5.19615i	0.151523	−	0.262445i
$393$	10.5000	−	18.1865i	0.529655	−	0.917389i
$394$	1.50000	+	2.59808i	0.0755689	+	0.130889i
$395$	24.0000			1.20757
$396$	−6.00000	−	10.3923i	−0.301511	−	0.522233i
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−17.0000	−	29.4449i	−0.853206	−	1.47780i	0.0250943	−	0.999685i	$-0.492011\pi$
$398$	2.00000			0.100251
$399$	1.00000	+	1.73205i	0.0500626	+	0.0867110i
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.0699455	−	0.997551i	$-0.477717\pi$
$401$	18.0000	−	31.1769i	0.898877	−	1.55690i	0.828932	−	0.559350i	$-0.188949\pi$
$402$	−14.0000			−0.698257
$403$		0			0
$404$	−12.0000			−0.597022
$405$	−1.50000	+	2.59808i	−0.0745356	+	0.129099i
$406$	−3.00000	+	5.19615i	−0.148888	+	0.257881i
$407$	21.0000	+	36.3731i	1.04093	+	1.80295i
$408$	−3.00000			−0.148522
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	0.925256	+	0.379344i	$0.123850\pi$
$409$	16.0000	+	27.7128i	0.791149	+	1.37031i	−0.134107	+	0.990967i	$0.542817\pi$
$410$		0			0
$411$		0			0
$412$	2.00000	+	3.46410i	0.0985329	+	0.170664i
$413$	−3.00000	+	5.19615i	−0.147620	+	0.255686i
$414$		0			0
$415$	−36.0000			−1.76717
$416$		0			0
$417$	−13.0000			−0.636613
$418$	−6.00000	+	10.3923i	−0.293470	+	0.508304i
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	−0.954759	−	0.297382i	$-0.903887\pi$
$419$	−4.50000	+	7.79423i	−0.219839	+	0.380773i	0.734919	+	0.678155i	$0.237220\pi$
$420$	−1.50000	−	2.59808i	−0.0731925	−	0.126773i
$421$	−17.0000			−0.828529			−0.414265	−	0.910156i	$-0.635961\pi$
$421$	−17.0000			−0.828529			−0.414265	+	0.910156i	$0.635961\pi$
$422$	6.50000	+	11.2583i	0.316415	+	0.548047i
$423$	−3.00000	−	5.19615i	−0.145865	−	0.252646i
$424$		0			0
$425$	6.00000	+	10.3923i	0.291043	+	0.504101i
$426$	−1.50000	+	2.59808i	−0.0726752	+	0.125877i
$427$	−4.00000	+	6.92820i	−0.193574	+	0.335279i
$428$	12.0000			0.580042
$429$		0			0
$430$	−3.00000			−0.144673
$431$	−16.5000	+	28.5788i	−0.794777	+	1.37659i	0.128204	+	0.991748i	$0.459079\pi$
$431$	−16.5000	+	28.5788i	−0.794777	+	1.37659i	−0.922981	+	0.384846i	$0.874254\pi$
$432$	2.50000	−	4.33013i	0.120281	−	0.208333i
$433$	12.5000	+	21.6506i	0.600712	+	1.04046i	0.992713	+	0.120499i	$0.0384494\pi$
$433$	12.5000	+	21.6506i	0.600712	+	1.04046i	−0.392002	+	0.919964i	$0.628217\pi$
$434$	4.00000			0.192006
$435$	−9.00000	−	15.5885i	−0.431517	−	0.747409i
$436$	−3.50000	−	6.06218i	−0.167620	−	0.290326i
$437$		0			0
$438$	1.00000	+	1.73205i	0.0477818	+	0.0827606i
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	0.368945	+	0.929451i	$0.379719\pi$
$439$	−13.0000	+	22.5167i	−0.620456	+	1.07466i	−0.989401	+	0.145210i	$0.953614\pi$
$440$	9.00000	−	15.5885i	0.429058	−	0.743151i
$441$	12.0000			0.571429
$442$		0			0
$443$	21.0000			0.997740			0.498870	−	0.866677i	$-0.333748\pi$
$443$	21.0000			0.997740			0.498870	+	0.866677i	$0.333748\pi$
$444$	−3.50000	+	6.06218i	−0.166103	+	0.287698i
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	−9.50000	−	16.4545i	−0.449838	−	0.779142i
$447$	6.00000			0.283790
$448$	−0.500000	−	0.866025i	−0.0236228	−	0.0409159i
$449$	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	$0.788115\pi$
$450$	−8.00000			−0.377124
$451$		0			0
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$	8.50000	−	14.7224i	0.399365	−	0.691720i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	−6.50000	+	11.2583i	−0.303725	+	0.526067i
$459$	−7.50000	−	12.9904i	−0.350070	−	0.606339i
$460$		0			0
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	0.951584	−	0.307388i	$-0.0994551\pi$
$461$	4.50000	+	7.79423i	0.209586	+	0.363013i	−0.741998	+	0.670402i	$0.766122\pi$
$462$	3.00000	+	5.19615i	0.139573	+	0.241747i
$463$	40.0000			1.85896			0.929479	−	0.368875i	$-0.120257\pi$
$463$	40.0000			1.85896			0.929479	+	0.368875i	$0.120257\pi$
$464$	−3.00000	−	5.19615i	−0.139272	−	0.241225i
$465$	−6.00000	+	10.3923i	−0.278243	+	0.481932i
$466$	13.5000	−	23.3827i	0.625375	−	1.08318i
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−14.0000			−0.646460
$470$	4.50000	−	7.79423i	0.207570	−	0.359521i
$471$	−7.00000	+	12.1244i	−0.322543	+	0.558661i
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	6.00000			0.275880
$474$	−4.00000	−	6.92820i	−0.183726	−	0.318223i
$475$	4.00000	+	6.92820i	0.183533	+	0.317888i
$476$	−3.00000			−0.137505
$477$		0			0
$478$	7.50000	−	12.9904i	0.343042	−	0.594166i
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	−0.999730	−	0.0232187i	$-0.992609\pi$
$479$	−10.5000	+	18.1865i	−0.479757	+	0.830964i	0.519973	+	0.854183i	$0.325942\pi$
$480$	3.00000			0.136931
$481$		0			0
$482$	10.0000			0.455488
$483$		0			0
$484$	−12.5000	+	21.6506i	−0.568182	+	0.984120i
$485$	−15.0000	−	25.9808i	−0.681115	−	1.17973i
$486$	16.0000			0.725775
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	0.625859	−	0.779936i	$-0.284748\pi$
$487$	−8.00000	−	13.8564i	−0.362515	−	0.627894i	−0.988374	+	0.152042i	$0.951415\pi$
$488$	−4.00000	−	6.92820i	−0.181071	−	0.313625i
$489$	16.0000			0.723545
$490$	9.00000	+	15.5885i	0.406579	+	0.704215i
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	−0.746438	−	0.665455i	$-0.768237\pi$
$491$	4.50000	−	7.79423i	0.203082	−	0.351749i	0.949520	+	0.313707i	$0.101571\pi$
$492$		0			0
$493$	−18.0000			−0.810679
$494$		0			0
$495$	36.0000			1.61808
$496$	−2.00000	+	3.46410i	−0.0898027	+	0.155543i
$497$	−1.50000	+	2.59808i	−0.0672842	+	0.116540i
$498$	6.00000	+	10.3923i	0.268866	+	0.465690i
$499$	40.0000			1.79065			0.895323	−	0.445418i	$-0.146945\pi$
$499$	40.0000			1.79065			0.895323	+	0.445418i	$0.146945\pi$
$500$	1.50000	+	2.59808i	0.0670820	+	0.116190i
$501$		0			0
$502$	24.0000			1.07117
$503$	15.0000	+	25.9808i	0.668817	+	1.15842i	0.978235	+	0.207499i	$0.0665323\pi$
$503$	15.0000	+	25.9808i	0.668817	+	1.15842i	−0.309418	+	0.950926i	$0.600134\pi$
$504$	1.00000	−	1.73205i	0.0445435	−	0.0771517i
$505$	18.0000	−	31.1769i	0.800989	−	1.38735i
$506$		0			0
$507$		0			0
$508$	20.0000			0.887357
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	−0.993593	−	0.113020i	$-0.963948\pi$
$509$	−9.00000	+	15.5885i	−0.398918	+	0.690946i	0.594675	+	0.803966i	$0.297281\pi$
$510$	4.50000	−	7.79423i	0.199263	−	0.345134i
$511$	1.00000	+	1.73205i	0.0442374	+	0.0766214i
$512$	1.00000			0.0441942
$513$	−5.00000	−	8.66025i	−0.220755	−	0.382360i
$514$	−4.50000	−	7.79423i	−0.198486	−	0.343789i
$515$	−12.0000			−0.528783
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$	−9.00000	+	15.5885i	−0.395820	+	0.685580i
$518$	−3.50000	+	6.06218i	−0.153781	+	0.266357i
$519$		0			0
$520$		0			0
$521$	−9.00000			−0.394297			−0.197149	−	0.980374i	$-0.563168\pi$
$521$	−9.00000			−0.394297			−0.197149	+	0.980374i	$0.563168\pi$
$522$	6.00000	−	10.3923i	0.262613	−	0.454859i
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	−0.997478	−	0.0709788i	$-0.977388\pi$
$523$	−10.0000	+	17.3205i	−0.437269	+	0.757373i	0.560208	+	0.828352i	$0.310721\pi$
$524$	10.5000	+	18.1865i	0.458695	+	0.794482i
$525$	4.00000			0.174574
$526$	6.00000	+	10.3923i	0.261612	+	0.453126i
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	−6.00000			−0.261116
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$		0			0
$531$	6.00000	−	10.3923i	0.260378	−	0.450988i
$532$	−2.00000			−0.0867110
$533$		0			0
$534$	6.00000			0.259645
$535$	−18.0000	+	31.1769i	−0.778208	+	1.34790i
$536$	7.00000	−	12.1244i	0.302354	−	0.523692i
$537$	−1.50000	−	2.59808i	−0.0647298	−	0.112115i
$538$	24.0000			1.03471
$539$	−18.0000	−	31.1769i	−0.775315	−	1.34288i
$540$	7.50000	+	12.9904i	0.322749	+	0.559017i
$541$	−11.0000			−0.472927			−0.236463	−	0.971640i	$-0.575988\pi$
$541$	−11.0000			−0.472927			−0.236463	+	0.971640i	$0.575988\pi$
$542$	5.50000	+	9.52628i	0.236245	+	0.409189i
$543$	−10.0000	+	17.3205i	−0.429141	+	0.743294i
$544$	1.50000	−	2.59808i	0.0643120	−	0.111392i
$545$	21.0000			0.899541
$546$		0			0
$547$	17.0000			0.726868			0.363434	−	0.931620i	$-0.381604\pi$
$547$	17.0000			0.726868			0.363434	+	0.931620i	$0.381604\pi$
$548$		0			0
$549$	8.00000	−	13.8564i	0.341432	−	0.591377i
$550$	12.0000	+	20.7846i	0.511682	+	0.886259i
$551$	−12.0000			−0.511217
$552$		0			0
$553$	−4.00000	−	6.92820i	−0.170097	−	0.294617i
$554$	−28.0000			−1.18961
$555$	−10.5000	−	18.1865i	−0.445700	−	0.771975i
$556$	6.50000	−	11.2583i	0.275661	−	0.477460i
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	−0.832496	−	0.554031i	$-0.813089\pi$
$557$	1.50000	−	2.59808i	0.0635570	−	0.110084i	0.896053	+	0.443947i	$0.146422\pi$
$558$	−8.00000			−0.338667
$559$		0			0
$560$	3.00000			0.126773
$561$	−9.00000	+	15.5885i	−0.379980	+	0.658145i
$562$	−3.00000	+	5.19615i	−0.126547	+	0.219186i
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	−0.904320	−	0.426855i	$-0.859622\pi$
$563$	−19.5000	−	33.7750i	−0.821827	−	1.42345i	0.0824933	−	0.996592i	$-0.473712\pi$
$564$	−3.00000			−0.126323
$565$	9.00000	+	15.5885i	0.378633	+	0.655811i
$566$	2.00000	+	3.46410i	0.0840663	+	0.145607i
$567$	1.00000			0.0419961
$568$	−1.50000	−	2.59808i	−0.0629386	−	0.109013i
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	−0.979313	−	0.202350i	$-0.935142\pi$
$569$	−7.50000	+	12.9904i	−0.314416	+	0.544585i	0.664897	+	0.746935i	$0.268475\pi$
$570$	3.00000	−	5.19615i	0.125656	−	0.217643i
$571$	5.00000			0.209243			0.104622	−	0.994512i	$-0.466637\pi$
$571$	5.00000			0.209243			0.104622	+	0.994512i	$0.466637\pi$
$572$		0			0
$573$	−18.0000			−0.751961
$574$		0			0
$575$		0			0
$576$	1.00000	+	1.73205i	0.0416667	+	0.0721688i
$577$	−38.0000			−1.58196			−0.790980	−	0.611842i	$-0.790429\pi$
$577$	−38.0000			−1.58196			−0.790980	+	0.611842i	$0.790429\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$	18.0000			0.747409
$581$	6.00000	+	10.3923i	0.248922	+	0.431145i
$582$	−5.00000	+	8.66025i	−0.207257	+	0.358979i
$583$		0			0
$584$	−2.00000			−0.0827606
$585$		0			0
$586$	−21.0000			−0.867502
$587$	12.0000	−	20.7846i	0.495293	−	0.857873i	−0.504692	−	0.863299i	$-0.668394\pi$
$587$	12.0000	−	20.7846i	0.495293	−	0.857873i	0.999985	+	0.00542667i	$0.00172737\pi$
$588$	3.00000	−	5.19615i	0.123718	−	0.214286i
$589$	4.00000	+	6.92820i	0.164817	+	0.285472i
$590$	18.0000			0.741048
$591$	1.50000	+	2.59808i	0.0617018	+	0.106871i
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	−18.0000			−0.739171			−0.369586	−	0.929197i	$-0.620500\pi$
$593$	−18.0000			−0.739171			−0.369586	+	0.929197i	$0.620500\pi$
$594$	−15.0000	−	25.9808i	−0.615457	−	1.06600i
$595$	4.50000	−	7.79423i	0.184482	−	0.319532i
$596$	−3.00000	+	5.19615i	−0.122885	+	0.212843i
$597$	2.00000			0.0818546
$598$		0			0
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$	−2.00000	+	3.46410i	−0.0816497	+	0.141421i
$601$	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	$0.0400009\pi$
$602$	0.500000	+	0.866025i	0.0203785	+	0.0352966i
$603$	28.0000			1.14025
$604$	8.50000	+	14.7224i	0.345860	+	0.599047i
$605$	−37.5000	−	64.9519i	−1.52459	−	2.64067i
$606$	−12.0000			−0.487467
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	0.688274	−	0.725450i	$-0.258368\pi$
$607$	−7.00000	−	12.1244i	−0.284121	−	0.492112i	−0.972396	+	0.233338i	$0.925035\pi$
$608$	1.00000	−	1.73205i	0.0405554	−	0.0702439i
$609$	−3.00000	+	5.19615i	−0.121566	+	0.210559i
$610$	24.0000			0.971732
$611$		0			0
$612$	6.00000			0.242536
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	−0.171564	−	0.985173i	$-0.554882\pi$
$613$	19.0000	−	32.9090i	0.767403	−	1.32918i	0.938967	−	0.344008i	$-0.111785\pi$
$614$	1.00000	−	1.73205i	0.0403567	−	0.0698999i
$615$		0			0
$616$	−6.00000			−0.241747
$617$	−12.0000	−	20.7846i	−0.483102	−	0.836757i	0.516710	−	0.856161i	$-0.327157\pi$
$617$	−12.0000	−	20.7846i	−0.483102	−	0.836757i	−0.999812	+	0.0194037i	$0.993823\pi$
$618$	2.00000	+	3.46410i	0.0804518	+	0.139347i
$619$	28.0000			1.12542			0.562708	−	0.826656i	$-0.309760\pi$
$619$	28.0000			1.12542			0.562708	+	0.826656i	$0.309760\pi$
$620$	−6.00000	−	10.3923i	−0.240966	−	0.417365i
$621$		0			0
$622$	15.0000	−	25.9808i	0.601445	−	1.04173i
$623$	6.00000			0.240385
$624$		0			0
$625$	−29.0000			−1.16000
$626$	0.500000	−	0.866025i	0.0199840	−	0.0346133i
$627$	−6.00000	+	10.3923i	−0.239617	+	0.415029i
$628$	−7.00000	−	12.1244i	−0.279330	−	0.483814i
$629$	−21.0000			−0.837325
$630$	3.00000	+	5.19615i	0.119523	+	0.207020i
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	0.995795	+	0.0916122i	$0.0292020\pi$
$631$	14.5000	+	25.1147i	0.577236	+	0.999802i	−0.418559	+	0.908190i	$0.637465\pi$
$632$	8.00000			0.318223
$633$	6.50000	+	11.2583i	0.258352	+	0.447478i
$634$	−3.00000	+	5.19615i	−0.119145	+	0.206366i
$635$	−30.0000	+	51.9615i	−1.19051	+	2.06203i
$636$		0			0
$637$		0			0
$638$	−36.0000			−1.42525
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$	−1.50000	+	2.59808i	−0.0592927	+	0.102698i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$	12.0000			0.473602
$643$	7.00000	+	12.1244i	0.276053	+	0.478138i	0.970400	−	0.241502i	$-0.0776401\pi$
$643$	7.00000	+	12.1244i	0.276053	+	0.478138i	−0.694347	+	0.719640i	$0.744307\pi$
$644$		0			0
$645$	−3.00000			−0.118125
$646$	−3.00000	−	5.19615i	−0.118033	−	0.204440i
$647$	3.00000	−	5.19615i	0.117942	−	0.204282i	−0.801010	−	0.598651i	$-0.795704\pi$
$647$	3.00000	−	5.19615i	0.117942	−	0.204282i	0.918952	+	0.394369i	$0.129037\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	−36.0000			−1.41312
$650$		0			0
$651$	4.00000			0.156772
$652$	−8.00000	+	13.8564i	−0.313304	+	0.542659i
$653$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$653$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$654$	−3.50000	−	6.06218i	−0.136861	−	0.237050i
$655$	−63.0000			−2.46161
$656$		0			0
$657$	−2.00000	−	3.46410i	−0.0780274	−	0.135147i
$658$	−3.00000			−0.116952
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$	9.00000	−	15.5885i	0.350325	−	0.606780i
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	−0.996682	−	0.0813955i	$-0.974062\pi$
$661$	−11.0000	+	19.0526i	−0.427850	+	0.741059i	0.568831	+	0.822454i	$0.307396\pi$
$662$	−8.00000			−0.310929
$663$		0			0
$664$	−12.0000			−0.465690
$665$	3.00000	−	5.19615i	0.116335	−	0.201498i
$666$	7.00000	−	12.1244i	0.271244	−	0.469809i
$667$		0			0
$668$		0			0
$669$	−9.50000	−	16.4545i	−0.367291	−	0.636167i
$670$	21.0000	+	36.3731i	0.811301	+	1.40521i
$671$	−48.0000			−1.85302
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	9.50000	−	16.4545i	0.366198	−	0.634274i	−0.622770	−	0.782405i	$-0.713993\pi$
$673$	9.50000	−	16.4545i	0.366198	−	0.634274i	0.988968	+	0.148132i	$0.0473259\pi$
$674$	−11.5000	+	19.9186i	−0.442963	+	0.767235i
$675$	−20.0000			−0.769800
$676$		0			0
$677$	48.0000			1.84479			0.922395	−	0.386248i	$-0.126229\pi$
$677$	48.0000			1.84479			0.922395	+	0.386248i	$0.126229\pi$
$678$	3.00000	−	5.19615i	0.115214	−	0.199557i
$679$	−5.00000	+	8.66025i	−0.191882	+	0.332350i
$680$	4.50000	+	7.79423i	0.172567	+	0.298895i
$681$		0			0
$682$	12.0000	+	20.7846i	0.459504	+	0.795884i
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	0.998917	−	0.0465244i	$-0.0148145\pi$
$683$	12.0000	+	20.7846i	0.459167	+	0.795301i	−0.539750	+	0.841825i	$0.681481\pi$
$684$	4.00000			0.152944
$685$		0			0
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	−6.50000	+	11.2583i	−0.247990	+	0.429532i
$688$	−1.00000			−0.0381246
$689$		0			0
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$		0			0
$693$	−6.00000	−	10.3923i	−0.227921	−	0.394771i
$694$	3.00000			0.113878
$695$	19.5000	+	33.7750i	0.739677	+	1.28116i
$696$	−3.00000	−	5.19615i	−0.113715	−	0.196960i
$697$		0			0
$698$	−9.50000	−	16.4545i	−0.359580	−	0.622811i
$699$	13.5000	−	23.3827i	0.510617	−	0.884414i
$700$	−2.00000	+	3.46410i	−0.0755929	+	0.130931i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	3.00000	−	5.19615i	0.113067	−	0.195837i
$705$	4.50000	−	7.79423i	0.169480	−	0.293548i
$706$	12.0000	+	20.7846i	0.451626	+	0.782239i
$707$	−12.0000			−0.451306
$708$	−3.00000	−	5.19615i	−0.112747	−	0.195283i
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	0.999908	−	0.0135434i	$-0.00431112\pi$
$709$	13.0000	+	22.5167i	0.488225	+	0.845631i	−0.511683	+	0.859174i	$0.670978\pi$
$710$	9.00000			0.337764
$711$	8.00000	+	13.8564i	0.300023	+	0.519656i
$712$	−3.00000	+	5.19615i	−0.112430	+	0.194734i
$713$		0			0
$714$	−3.00000			−0.112272
$715$		0			0
$716$	3.00000			0.112115
$717$	7.50000	−	12.9904i	0.280093	−	0.485135i
$718$		0			0
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$	−6.00000			−0.223607
$721$	2.00000	+	3.46410i	0.0744839	+	0.129010i
$722$	7.50000	+	12.9904i	0.279121	+	0.483452i
$723$	10.0000			0.371904
$724$	−10.0000	−	17.3205i	−0.371647	−	0.643712i
$725$	−12.0000	+	20.7846i	−0.445669	+	0.771921i
$726$	−12.5000	+	21.6506i	−0.463919	+	0.803530i
$727$	−10.0000			−0.370879			−0.185440	−	0.982656i	$-0.559371\pi$
$727$	−10.0000			−0.370879			−0.185440	+	0.982656i	$0.559371\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	3.00000	−	5.19615i	0.111035	−	0.192318i
$731$	−1.50000	+	2.59808i	−0.0554795	+	0.0960933i
$732$	−4.00000	−	6.92820i	−0.147844	−	0.256074i
$733$	−23.0000			−0.849524			−0.424762	−	0.905305i	$-0.639642\pi$
$733$	−23.0000			−0.849524			−0.424762	+	0.905305i	$0.639642\pi$
$734$	−13.0000	−	22.5167i	−0.479839	−	0.831105i
$735$	9.00000	+	15.5885i	0.331970	+	0.574989i
$736$		0			0
$737$	−42.0000	−	72.7461i	−1.54709	−	2.67964i
$738$		0			0
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	−0.621374	−	0.783514i	$-0.713425\pi$
$739$	10.0000	−	17.3205i	0.367856	−	0.637145i	0.989230	+	0.146369i	$0.0467586\pi$
$740$	21.0000			0.771975
$741$		0			0
$742$		0			0
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	−0.936687	−	0.350168i	$-0.886124\pi$
$743$	−4.50000	+	7.79423i	−0.165089	+	0.285943i	0.771598	+	0.636111i	$0.219458\pi$
$744$	−2.00000	+	3.46410i	−0.0733236	+	0.127000i
$745$	−9.00000	−	15.5885i	−0.329734	−	0.571117i
$746$	−4.00000			−0.146450
$747$	−12.0000	−	20.7846i	−0.439057	−	0.760469i
$748$	−9.00000	−	15.5885i	−0.329073	−	0.569970i
$749$	12.0000			0.438470
$750$	1.50000	+	2.59808i	0.0547723	+	0.0948683i
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	1.50000	−	2.59808i	0.0546994	−	0.0947421i
$753$	24.0000			0.874609
$754$		0			0
$755$	−51.0000			−1.85608
$756$	2.50000	−	4.33013i	0.0909241	−	0.157485i
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	−0.683226	−	0.730207i	$-0.739424\pi$
$757$	8.00000	−	13.8564i	0.290765	−	0.503620i	0.973991	+	0.226587i	$0.0727569\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$		0			0
$760$	3.00000	+	5.19615i	0.108821	+	0.188484i
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	0.806514	−	0.591215i	$-0.201351\pi$
$761$	−3.00000	−	5.19615i	−0.108750	−	0.188360i	−0.915264	+	0.402854i	$0.868018\pi$
$762$	20.0000			0.724524
$763$	−3.50000	−	6.06218i	−0.126709	−	0.219466i
$764$	9.00000	−	15.5885i	0.325609	−	0.563971i
$765$	−9.00000	+	15.5885i	−0.325396	+	0.563602i
$766$	−21.0000			−0.758761
$767$		0			0
$768$	1.00000			0.0360844
$769$	16.0000	−	27.7128i	0.576975	−	0.999350i	−0.418849	−	0.908056i	$-0.637566\pi$
$769$	16.0000	−	27.7128i	0.576975	−	0.999350i	0.995824	−	0.0912938i	$-0.0291002\pi$
$770$	9.00000	−	15.5885i	0.324337	−	0.561769i
$771$	−4.50000	−	7.79423i	−0.162064	−	0.280702i
$772$	4.00000			0.143963
$773$	−19.5000	−	33.7750i	−0.701366	−	1.21480i	−0.967987	−	0.251000i	$-0.919240\pi$
$773$	−19.5000	−	33.7750i	−0.701366	−	1.21480i	0.266621	−	0.963802i	$-0.414093\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$	16.0000			0.574737
$776$	−5.00000	−	8.66025i	−0.179490	−	0.310885i
$777$	−3.50000	+	6.06218i	−0.125562	+	0.217479i
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$		0			0
$780$		0			0
$781$	−18.0000			−0.644091
$782$		0			0
$783$	15.0000	−	25.9808i	0.536056	−	0.928477i
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	42.0000			1.49904
$786$	10.5000	+	18.1865i	0.374523	+	0.648692i
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	−0.963755	−	0.266788i	$-0.914038\pi$
$787$	−20.0000	−	34.6410i	−0.712923	−	1.23482i	0.250832	−	0.968031i	$-0.419296\pi$
$788$	−3.00000			−0.106871
$789$	6.00000	+	10.3923i	0.213606	+	0.369976i
$790$	−12.0000	+	20.7846i	−0.426941	+	0.739483i
$791$	3.00000	−	5.19615i	0.106668	−	0.184754i
$792$	12.0000			0.426401
$793$		0			0
$794$	34.0000			1.20661
$795$		0			0
$796$	−1.00000	+	1.73205i	−0.0354441	+	0.0613909i
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	0.950726	+	0.310031i	$0.100340\pi$
$797$	21.0000	+	36.3731i	0.743858	+	1.28840i	−0.206868	+	0.978369i	$0.566327\pi$
$798$	−2.00000			−0.0707992
$799$	−4.50000	−	7.79423i	−0.159199	−	0.275740i
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	−12.0000			−0.423999
$802$	18.0000	+	31.1769i	0.635602	+	1.10090i
$803$	−6.00000	+	10.3923i	−0.211735	+	0.366736i
$804$	7.00000	−	12.1244i	0.246871	−	0.427593i
$805$		0			0
$806$		0			0
$807$	24.0000			0.844840
$808$	6.00000	−	10.3923i	0.211079	−	0.365600i
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	−0.415357	−	0.909659i	$-0.636343\pi$
$809$	16.5000	−	28.5788i	0.580109	−	1.00478i	0.995466	−	0.0951198i	$-0.0303234\pi$
$810$	−1.50000	−	2.59808i	−0.0527046	−	0.0912871i
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$	−3.00000	−	5.19615i	−0.105279	−	0.182349i
$813$	5.50000	+	9.52628i	0.192893	+	0.334101i
$814$	−42.0000			−1.47210
$815$	−24.0000	−	41.5692i	−0.840683	−	1.45611i
$816$	1.50000	−	2.59808i	0.0525105	−	0.0909509i
$817$	−1.00000	+	1.73205i	−0.0349856	+	0.0605968i
$818$	−32.0000			−1.11885
$819$		0			0
$820$		0			0
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	−0.891013	−	0.453978i	$-0.850005\pi$
$821$	−1.50000	+	2.59808i	−0.0523504	+	0.0906735i	0.838663	+	0.544651i	$0.183338\pi$
$822$		0			0
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	0.717847	−	0.696201i	$-0.245128\pi$
$823$	−7.00000	−	12.1244i	−0.244005	−	0.422628i	−0.961851	+	0.273573i	$0.911795\pi$
$824$	−4.00000			−0.139347
$825$	12.0000	+	20.7846i	0.417786	+	0.723627i
$826$	−3.00000	−	5.19615i	−0.104383	−	0.180797i
$827$	−18.0000			−0.625921			−0.312961	−	0.949766i	$-0.601321\pi$
$827$	−18.0000			−0.625921			−0.312961	+	0.949766i	$0.601321\pi$
$828$		0			0
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	0.320745	+	0.947166i	$0.396067\pi$
$829$	−19.0000	+	32.9090i	−0.659897	+	1.14298i	−0.980642	+	0.195810i	$0.937266\pi$
$830$	18.0000	−	31.1769i	0.624789	−	1.08217i
$831$	−28.0000			−0.971309
$832$		0			0
$833$	18.0000			0.623663
$834$	6.50000	−	11.2583i	0.225077	−	0.389844i
$835$		0			0
$836$	−6.00000	−	10.3923i	−0.207514	−	0.359425i
$837$	−20.0000			−0.691301
$838$	−4.50000	−	7.79423i	−0.155450	−	0.269247i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	3.00000			0.103510
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	8.50000	−	14.7224i	0.292929	−	0.507369i
$843$	−3.00000	+	5.19615i	−0.103325	+	0.178965i
$844$	−13.0000			−0.447478
$845$		0			0
$846$	6.00000			0.206284
$847$	−12.5000	+	21.6506i	−0.429505	+	0.743925i
$848$		0			0
$849$	2.00000	+	3.46410i	0.0686398	+	0.118888i
$850$	−12.0000			−0.411597
$851$		0			0
$852$	−1.50000	−	2.59808i	−0.0513892	−	0.0890086i
$853$	37.0000			1.26686			0.633428	−	0.773802i	$-0.281647\pi$
$853$	37.0000			1.26686			0.633428	+	0.773802i	$0.281647\pi$
$854$	−4.00000	−	6.92820i	−0.136877	−	0.237078i
$855$	−6.00000	+	10.3923i	−0.205196	+	0.355409i
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−42.0000			−1.43469			−0.717346	−	0.696717i	$-0.754643\pi$
$857$	−42.0000			−1.43469			−0.717346	+	0.696717i	$0.754643\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	1.50000	−	2.59808i	0.0511496	−	0.0885937i
$861$		0			0
$862$	−16.5000	−	28.5788i	−0.561992	−	0.973399i
$863$	45.0000			1.53182			0.765909	−	0.642949i	$-0.222289\pi$
$863$	45.0000			1.53182			0.765909	+	0.642949i	$0.222289\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	−25.0000			−0.849535
$867$	4.00000	+	6.92820i	0.135847	+	0.235294i
$868$	−2.00000	+	3.46410i	−0.0678844	+	0.117579i
$869$	24.0000	−	41.5692i	0.814144	−	1.41014i
$870$	18.0000			0.610257
$871$		0			0
$872$	7.00000			0.237050
$873$	10.0000	−	17.3205i	0.338449	−	0.586210i
$874$		0			0
$875$	1.50000	+	2.59808i	0.0507093	+	0.0878310i
$876$	−2.00000			−0.0675737
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	0.735163	−	0.677891i	$-0.237106\pi$
$877$	−6.50000	−	11.2583i	−0.219489	−	0.380167i	−0.954652	+	0.297724i	$0.903772\pi$
$878$	−13.0000	−	22.5167i	−0.438729	−	0.759900i
$879$	−21.0000			−0.708312
$880$	9.00000	+	15.5885i	0.303390	+	0.525487i
$881$	−10.5000	+	18.1865i	−0.353754	+	0.612720i	−0.986904	−	0.161309i	$-0.948428\pi$
$881$	−10.5000	+	18.1865i	−0.353754	+	0.612720i	0.633150	+	0.774029i	$0.281762\pi$
$882$	−6.00000	+	10.3923i	−0.202031	+	0.349927i
$883$	29.0000			0.975928			0.487964	−	0.872864i	$-0.337740\pi$
$883$	29.0000			0.975928			0.487964	+	0.872864i	$0.337740\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$	−10.5000	+	18.1865i	−0.352754	+	0.610989i
$887$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$887$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$888$	−3.50000	−	6.06218i	−0.117452	−	0.203433i
$889$	20.0000			0.670778
$890$	−9.00000	−	15.5885i	−0.301681	−	0.522526i
$891$	3.00000	+	5.19615i	0.100504	+	0.174078i
$892$	19.0000			0.636167
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$	−3.00000	+	5.19615i	−0.100335	+	0.173785i
$895$	−4.50000	+	7.79423i	−0.150418	+	0.260532i
$896$	1.00000			0.0334077
$897$		0			0
$898$	−6.00000			−0.200223
$899$	−12.0000	+	20.7846i	−0.400222	+	0.693206i
$900$	4.00000	−	6.92820i	0.133333	−	0.230940i
$901$		0			0
$902$		0			0
$903$	0.500000	+	0.866025i	0.0166390	+	0.0288195i
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	60.0000			1.99447
$906$	8.50000	+	14.7224i	0.282394	+	0.489120i
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	−0.376228	−	0.926527i	$-0.622779\pi$
$907$	18.5000	−	32.0429i	0.614282	−	1.06397i	0.990510	−	0.137441i	$-0.0438878\pi$
$908$		0			0
$909$	24.0000			0.796030
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	1.00000	−	1.73205i	0.0331133	−	0.0573539i
$913$	−36.0000	+	62.3538i	−1.19143	+	2.06361i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$	24.0000			0.793416
$916$	−6.50000	−	11.2583i	−0.214766	−	0.371986i
$917$	10.5000	+	18.1865i	0.346741	+	0.600572i
$918$	15.0000			0.495074
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	0.967274	−	0.253735i	$-0.0816592\pi$
$919$	8.00000	+	13.8564i	0.263896	+	0.457081i	−0.703378	+	0.710816i	$0.748326\pi$
$920$		0			0
$921$	1.00000	−	1.73205i	0.0329511	−	0.0570730i
$922$	−9.00000			−0.296399
$923$		0			0
$924$	−6.00000			−0.197386
$925$	−14.0000	+	24.2487i	−0.460317	+	0.797293i
$926$	−20.0000	+	34.6410i	−0.657241	+	1.13837i
$927$	−4.00000	−	6.92820i	−0.131377	−	0.227552i
$928$	6.00000			0.196960
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	0.994157	+	0.107944i	$0.0344268\pi$
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	−0.403596	+	0.914937i	$0.632240\pi$
$930$	−6.00000	−	10.3923i	−0.196748	−	0.340777i
$931$	12.0000			0.393284
$932$	13.5000	+	23.3827i	0.442207	+	0.765925i
$933$	15.0000	−	25.9808i	0.491078	−	0.850572i
$934$	−18.0000	+	31.1769i	−0.588978	+	1.02014i
$935$	54.0000			1.76599
$936$		0			0
$937$	−34.0000			−1.11073			−0.555366	−	0.831606i	$-0.687422\pi$
$937$	−34.0000			−1.11073			−0.555366	+	0.831606i	$0.687422\pi$
$938$	7.00000	−	12.1244i	0.228558	−	0.395874i
$939$	0.500000	−	0.866025i	0.0163169	−	0.0282617i
$940$	4.50000	+	7.79423i	0.146774	+	0.254220i
$941$	21.0000			0.684580			0.342290	−	0.939594i	$-0.388797\pi$
$941$	21.0000			0.684580			0.342290	+	0.939594i	$0.388797\pi$
$942$	−7.00000	−	12.1244i	−0.228072	−	0.395033i
$943$		0			0
$944$	6.00000			0.195283
$945$	7.50000	+	12.9904i	0.243975	+	0.422577i
$946$	−3.00000	+	5.19615i	−0.0975384	+	0.168941i
$947$	3.00000	−	5.19615i	0.0974869	−	0.168852i	−0.813157	−	0.582045i	$-0.802253\pi$
$947$	3.00000	−	5.19615i	0.0974869	−	0.168852i	0.910644	+	0.413192i	$0.135586\pi$
$948$	8.00000			0.259828
$949$		0			0
$950$	−8.00000			−0.259554
$951$	−3.00000	+	5.19615i	−0.0972817	+	0.168497i
$952$	1.50000	−	2.59808i	0.0486153	−	0.0842041i
$953$	−7.50000	−	12.9904i	−0.242949	−	0.420800i	0.718604	−	0.695419i	$-0.244781\pi$
$953$	−7.50000	−	12.9904i	−0.242949	−	0.420800i	−0.961553	+	0.274620i	$0.911448\pi$
$954$		0			0
$955$	27.0000	+	46.7654i	0.873699	+	1.51329i
$956$	7.50000	+	12.9904i	0.242567	+	0.420139i
$957$	−36.0000			−1.16371
$958$	−10.5000	−	18.1865i	−0.339240	−	0.587580i
$959$		0			0
$960$	−1.50000	+	2.59808i	−0.0484123	+	0.0838525i
$961$	−15.0000			−0.483871
$962$		0			0
$963$	−24.0000			−0.773389
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$	−6.00000	+	10.3923i	−0.193147	+	0.334540i
$966$		0			0
$967$	31.0000			0.996893			0.498446	−	0.866921i	$-0.333904\pi$
$967$	31.0000			0.996893			0.498446	+	0.866921i	$0.333904\pi$
$968$	−12.5000	−	21.6506i	−0.401765	−	0.695878i
$969$	−3.00000	−	5.19615i	−0.0963739	−	0.166924i
$970$	30.0000			0.963242
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	0.889090	−	0.457732i	$-0.151338\pi$
$971$	1.50000	+	2.59808i	0.0481373	+	0.0833762i	−0.840953	+	0.541108i	$0.818005\pi$
$972$	−8.00000	+	13.8564i	−0.256600	+	0.444444i
$973$	6.50000	−	11.2583i	0.208380	−	0.360925i
$974$	16.0000			0.512673
$975$		0			0
$976$	8.00000			0.256074
$977$	−27.0000	+	46.7654i	−0.863807	+	1.49616i	0.00442082	+	0.999990i	$0.498593\pi$
$977$	−27.0000	+	46.7654i	−0.863807	+	1.49616i	−0.868227	+	0.496167i	$0.834741\pi$
$978$	−8.00000	+	13.8564i	−0.255812	+	0.443079i
$979$	18.0000	+	31.1769i	0.575282	+	0.996419i
$980$	−18.0000			−0.574989
$981$	7.00000	+	12.1244i	0.223493	+	0.387101i
$982$	4.50000	+	7.79423i	0.143601	+	0.248724i
$983$	−39.0000			−1.24391			−0.621953	−	0.783054i	$-0.713661\pi$
$983$	−39.0000			−1.24391			−0.621953	+	0.783054i	$0.713661\pi$
$984$		0			0
$985$	4.50000	−	7.79423i	0.143382	−	0.248345i
$986$	9.00000	−	15.5885i	0.286618	−	0.496438i
$987$	−3.00000			−0.0954911
$988$		0			0
$989$		0			0
$990$	−18.0000	+	31.1769i	−0.572078	+	0.990867i
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	−0.881471	−	0.472237i	$-0.843446\pi$
$991$	−1.00000	+	1.73205i	−0.0317660	+	0.0550204i	0.849705	+	0.527258i	$0.176780\pi$
$992$	−2.00000	−	3.46410i	−0.0635001	−	0.109985i
$993$	−8.00000			−0.253872
$994$	−1.50000	−	2.59808i	−0.0475771	−	0.0824060i
$995$	−3.00000	−	5.19615i	−0.0951064	−	0.164729i
$996$	−12.0000			−0.380235
$997$	23.0000	+	39.8372i	0.728417	+	1.26166i	0.957552	+	0.288261i	$0.0930771\pi$
$997$	23.0000	+	39.8372i	0.728417	+	1.26166i	−0.229135	+	0.973395i	$0.573590\pi$
$998$	−20.0000	+	34.6410i	−0.633089	+	1.09654i
$999$	17.5000	−	30.3109i	0.553675	−	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.c.a.191.1		2
13.2	odd	12		338.2.e.a.23.1		4
13.3	even	3	inner	338.2.c.a.315.1		2
13.4	even	6		26.2.a.a.1.1	✓	1
13.5	odd	4		338.2.e.a.147.2		4
13.6	odd	12		338.2.b.c.337.1		2
13.7	odd	12		338.2.b.c.337.2		2
13.8	odd	4		338.2.e.a.147.1		4
13.9	even	3		338.2.a.f.1.1		1
13.10	even	6		338.2.c.d.315.1		2
13.11	odd	12		338.2.e.a.23.2		4
13.12	even	2		338.2.c.d.191.1		2
39.17	odd	6		234.2.a.e.1.1		1
39.20	even	12		3042.2.b.a.1351.1		2
39.32	even	12		3042.2.b.a.1351.2		2
39.35	odd	6		3042.2.a.a.1.1		1
52.7	even	12		2704.2.f.d.337.2		2
52.19	even	12		2704.2.f.d.337.1		2
52.35	odd	6		2704.2.a.f.1.1		1
52.43	odd	6		208.2.a.a.1.1		1
65.4	even	6		650.2.a.j.1.1		1
65.9	even	6		8450.2.a.c.1.1		1
65.17	odd	12		650.2.b.d.599.1		2
65.43	odd	12		650.2.b.d.599.2		2
91.4	even	6		1274.2.f.p.79.1		2
91.17	odd	6		1274.2.f.r.79.1		2
91.30	even	6		1274.2.f.p.1145.1		2
91.69	odd	6		1274.2.a.d.1.1		1
91.82	odd	6		1274.2.f.r.1145.1		2
104.43	odd	6		832.2.a.i.1.1		1
104.69	even	6		832.2.a.d.1.1		1
117.4	even	6		2106.2.e.ba.703.1		2
117.43	even	6		2106.2.e.ba.1405.1		2
117.56	odd	6		2106.2.e.b.1405.1		2
117.95	odd	6		2106.2.e.b.703.1		2
143.43	odd	6		3146.2.a.n.1.1		1
156.95	even	6		1872.2.a.q.1.1		1
195.17	even	12		5850.2.e.a.5149.2		2
195.134	odd	6		5850.2.a.p.1.1		1
195.173	even	12		5850.2.e.a.5149.1		2
208.43	odd	12		3328.2.b.j.1665.2		2
208.69	even	12		3328.2.b.m.1665.1		2
208.147	odd	12		3328.2.b.j.1665.1		2
208.173	even	12		3328.2.b.m.1665.2		2
221.186	even	6		7514.2.a.c.1.1		1
247.56	odd	6		9386.2.a.j.1.1		1
260.199	odd	6		5200.2.a.x.1.1		1
312.173	odd	6		7488.2.a.g.1.1		1
312.251	even	6		7488.2.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.a.a.1.1	✓	1	13.4	even	6
208.2.a.a.1.1		1	52.43	odd	6
234.2.a.e.1.1		1	39.17	odd	6
338.2.a.f.1.1		1	13.9	even	3
338.2.b.c.337.1		2	13.6	odd	12
338.2.b.c.337.2		2	13.7	odd	12
338.2.c.a.191.1		2	1.1	even	1	trivial
338.2.c.a.315.1		2	13.3	even	3	inner
338.2.c.d.191.1		2	13.12	even	2
338.2.c.d.315.1		2	13.10	even	6
338.2.e.a.23.1		4	13.2	odd	12
338.2.e.a.23.2		4	13.11	odd	12
338.2.e.a.147.1		4	13.8	odd	4
338.2.e.a.147.2		4	13.5	odd	4
650.2.a.j.1.1		1	65.4	even	6
650.2.b.d.599.1		2	65.17	odd	12
650.2.b.d.599.2		2	65.43	odd	12
832.2.a.d.1.1		1	104.69	even	6
832.2.a.i.1.1		1	104.43	odd	6
1274.2.a.d.1.1		1	91.69	odd	6
1274.2.f.p.79.1		2	91.4	even	6
1274.2.f.p.1145.1		2	91.30	even	6
1274.2.f.r.79.1		2	91.17	odd	6
1274.2.f.r.1145.1		2	91.82	odd	6
1872.2.a.q.1.1		1	156.95	even	6
2106.2.e.b.703.1		2	117.95	odd	6
2106.2.e.b.1405.1		2	117.56	odd	6
2106.2.e.ba.703.1		2	117.4	even	6
2106.2.e.ba.1405.1		2	117.43	even	6
2704.2.a.f.1.1		1	52.35	odd	6
2704.2.f.d.337.1		2	52.19	even	12
2704.2.f.d.337.2		2	52.7	even	12
3042.2.a.a.1.1		1	39.35	odd	6
3042.2.b.a.1351.1		2	39.20	even	12
3042.2.b.a.1351.2		2	39.32	even	12
3146.2.a.n.1.1		1	143.43	odd	6
3328.2.b.j.1665.1		2	208.147	odd	12
3328.2.b.j.1665.2		2	208.43	odd	12
3328.2.b.m.1665.1		2	208.69	even	12
3328.2.b.m.1665.2		2	208.173	even	12
5200.2.a.x.1.1		1	260.199	odd	6
5850.2.a.p.1.1		1	195.134	odd	6
5850.2.e.a.5149.1		2	195.173	even	12
5850.2.e.a.5149.2		2	195.17	even	12
7488.2.a.g.1.1		1	312.173	odd	6
7488.2.a.h.1.1		1	312.251	even	6
7514.2.a.c.1.1		1	221.186	even	6
8450.2.a.c.1.1		1	65.9	even	6
9386.2.a.j.1.1		1	247.56	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +3.00000 q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.500000 - 0.866025i) q^{7} +1.00000 q^{8} +(1.00000 + 1.73205i) q^{9} +(-1.50000 + 2.59808i) q^{10} +(3.00000 - 5.19615i) q^{11} +1.00000 q^{12} +1.00000 q^{14} +(-1.50000 + 2.59808i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.50000 + 2.59808i) q^{17} -2.00000 q^{18} +(1.00000 + 1.73205i) q^{19} +(-1.50000 - 2.59808i) q^{20} +1.00000 q^{21} +(3.00000 + 5.19615i) q^{22} +(-0.500000 + 0.866025i) q^{24} +4.00000 q^{25} -5.00000 q^{27} +(-0.500000 + 0.866025i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(-1.50000 - 2.59808i) q^{30} +4.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +(3.00000 + 5.19615i) q^{33} -3.00000 q^{34} +(-1.50000 - 2.59808i) q^{35} +(1.00000 - 1.73205i) q^{36} +(-3.50000 + 6.06218i) q^{37} -2.00000 q^{38} +3.00000 q^{40} +(-0.500000 + 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} -6.00000 q^{44} +(3.00000 + 5.19615i) q^{45} -3.00000 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.00000 - 5.19615i) q^{49} +(-2.00000 + 3.46410i) q^{50} -3.00000 q^{51} +(2.50000 - 4.33013i) q^{54} +(9.00000 - 15.5885i) q^{55} +(-0.500000 - 0.866025i) q^{56} -2.00000 q^{57} +(-3.00000 - 5.19615i) q^{58} +(-3.00000 - 5.19615i) q^{59} +3.00000 q^{60} +(-4.00000 - 6.92820i) q^{61} +(-2.00000 + 3.46410i) q^{62} +(1.00000 - 1.73205i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(7.00000 - 12.1244i) q^{67} +(1.50000 - 2.59808i) q^{68} +3.00000 q^{70} +(-1.50000 - 2.59808i) q^{71} +(1.00000 + 1.73205i) q^{72} -2.00000 q^{73} +(-3.50000 - 6.06218i) q^{74} +(-2.00000 + 3.46410i) q^{75} +(1.00000 - 1.73205i) q^{76} -6.00000 q^{77} +8.00000 q^{79} +(-1.50000 + 2.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} +(-0.500000 - 0.866025i) q^{84} +(4.50000 + 7.79423i) q^{85} -1.00000 q^{86} +(-3.00000 - 5.19615i) q^{87} +(3.00000 - 5.19615i) q^{88} +(-3.00000 + 5.19615i) q^{89} -6.00000 q^{90} +(-2.00000 + 3.46410i) q^{93} +(1.50000 - 2.59808i) q^{94} +(3.00000 + 5.19615i) q^{95} +1.00000 q^{96} +(-5.00000 - 8.66025i) q^{97} +(3.00000 + 5.19615i) q^{98} +12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + 6 q^{5} - q^{6} - q^{7} + 2 q^{8} + 2 q^{9} - 3 q^{10} + 6 q^{11} + 2 q^{12} + 2 q^{14} - 3 q^{15} - q^{16} + 3 q^{17} - 4 q^{18} + 2 q^{19} - 3 q^{20} + 2 q^{21} + 6 q^{22}+ \cdots + 24 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + 6 * q^5 - q^6 - q^7 + 2 * q^8 + 2 * q^9 - 3 * q^10 + 6 * q^11 + 2 * q^12 + 2 * q^14 - 3 * q^15 - q^16 + 3 * q^17 - 4 * q^18 + 2 * q^19 - 3 * q^20 + 2 * q^21 + 6 * q^22 - q^24 + 8 * q^25 - 10 * q^27 - q^28 - 6 * q^29 - 3 * q^30 + 8 * q^31 - q^32 + 6 * q^33 - 6 * q^34 - 3 * q^35 + 2 * q^36 - 7 * q^37 - 4 * q^38 + 6 * q^40 - q^42 + q^43 - 12 * q^44 + 6 * q^45 - 6 * q^47 - q^48 + 6 * q^49 - 4 * q^50 - 6 * q^51 + 5 * q^54 + 18 * q^55 - q^56 - 4 * q^57 - 6 * q^58 - 6 * q^59 + 6 * q^60 - 8 * q^61 - 4 * q^62 + 2 * q^63 + 2 * q^64 - 12 * q^66 + 14 * q^67 + 3 * q^68 + 6 * q^70 - 3 * q^71 + 2 * q^72 - 4 * q^73 - 7 * q^74 - 4 * q^75 + 2 * q^76 - 12 * q^77 + 16 * q^79 - 3 * q^80 - q^81 - 24 * q^83 - q^84 + 9 * q^85 - 2 * q^86 - 6 * q^87 + 6 * q^88 - 6 * q^89 - 12 * q^90 - 4 * q^93 + 3 * q^94 + 6 * q^95 + 2 * q^96 - 10 * q^97 + 6 * q^98 + 24 * q^99

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