LMFDB - Embedded newform 338.2.e.a.23.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,2,Mod(23,338)]

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([5]))

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

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	338.23
Dual form			338.2.e.a.147.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	0.684819	−	0.728714i	$-0.259881\pi$
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i	−0.973494	+	0.228714i	$0.926548\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$			3.00000i			1.34164i	0.741620	+	0.670820i	$0.234058\pi$
$5$			3.00000i			1.34164i	−0.741620	+	0.670820i	$0.765942\pi$
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	0.866025	+	0.500000i	0.327327	+	0.188982i	−0.327327	+	0.944911i	$0.606148\pi$
$8$		−	1.00000i		−	0.353553i
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$	1.50000	+	2.59808i	0.474342	+	0.821584i
$11$	5.19615	−	3.00000i	1.56670	−	0.904534i	0.570149	−	0.821541i	$-0.306886\pi$
$11$	5.19615	−	3.00000i	1.56670	−	0.904534i	0.996550	−	0.0829925i	$-0.0264478\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	1.00000			0.267261
$15$	2.59808	−	1.50000i	0.670820	−	0.387298i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		−	2.00000i		−	0.471405i
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	0.685344	−	0.728219i	$-0.259652\pi$
$19$	1.73205	+	1.00000i	0.397360	+	0.229416i	−0.287984	+	0.957635i	$0.592985\pi$
$20$	2.59808	+	1.50000i	0.580948	+	0.335410i
$21$		−	1.00000i		−	0.218218i
$22$	3.00000	−	5.19615i	0.639602	−	1.10782i
$23$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$23$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$	−4.00000			−0.800000
$26$		0			0
$27$	−5.00000			−0.962250
$28$	0.866025	−	0.500000i	0.163663	−	0.0944911i
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	−0.997738	−	0.0672232i	$-0.978586\pi$
$29$	−3.00000	−	5.19615i	−0.557086	−	0.964901i	0.440652	−	0.897678i	$-0.354747\pi$
$30$	1.50000	−	2.59808i	0.273861	−	0.474342i
$31$			4.00000i			0.718421i	0.933257	+	0.359211i	$0.116954\pi$
$31$			4.00000i			0.718421i	−0.933257	+	0.359211i	$0.883046\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−5.19615	−	3.00000i	−0.904534	−	0.522233i
$34$			3.00000i			0.514496i
$35$	−1.50000	+	2.59808i	−0.253546	+	0.439155i
$36$	−1.00000	−	1.73205i	−0.166667	−	0.288675i
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.907245	−	0.420602i	$-0.861819\pi$
$37$	−6.06218	+	3.50000i	−0.996616	+	0.575396i	−0.0893706	+	0.995998i	$0.528486\pi$
$38$	2.00000			0.324443
$39$		0			0
$40$	3.00000			0.474342
$41$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$41$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	−0.901629	−	0.432511i	$-0.857628\pi$
$43$	−0.500000	+	0.866025i	−0.0762493	+	0.132068i	0.825380	+	0.564578i	$0.190961\pi$
$44$		−	6.00000i		−	0.904534i
$45$	5.19615	+	3.00000i	0.774597	+	0.447214i
$46$		0			0
$47$			3.00000i			0.437595i	0.975770	+	0.218797i	$0.0702134\pi$
$47$			3.00000i			0.437595i	−0.975770	+	0.218797i	$0.929787\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−3.00000	−	5.19615i	−0.428571	−	0.742307i
$50$	−3.46410	+	2.00000i	−0.489898	+	0.282843i
$51$	3.00000			0.420084
$52$		0			0
$53$		0			0			−	1.00000i	$-0.5\pi$
$53$		0			0				1.00000i	$0.5\pi$
$54$	−4.33013	+	2.50000i	−0.589256	+	0.340207i
$55$	9.00000	+	15.5885i	1.21356	+	2.10195i
$56$	0.500000	−	0.866025i	0.0668153	−	0.115728i
$57$		−	2.00000i		−	0.264906i
$58$	−5.19615	−	3.00000i	−0.682288	−	0.393919i
$59$	5.19615	+	3.00000i	0.676481	+	0.390567i	0.798528	−	0.601958i	$-0.205612\pi$
$59$	5.19615	+	3.00000i	0.676481	+	0.390567i	−0.122047	+	0.992524i	$0.538946\pi$
$60$		−	3.00000i		−	0.387298i
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	0.487753	+	0.872982i	$0.337817\pi$
$61$	−4.00000	+	6.92820i	−0.512148	+	0.887066i	−0.999901	+	0.0140840i	$0.995517\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	1.73205	−	1.00000i	0.218218	−	0.125988i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	−12.1244	+	7.00000i	−1.48123	+	0.855186i	−0.999773	−	0.0212861i	$-0.993224\pi$
$67$	−12.1244	+	7.00000i	−1.48123	+	0.855186i	−0.481452	+	0.876472i	$0.659891\pi$
$68$	1.50000	+	2.59808i	0.181902	+	0.315063i
$69$		0			0
$70$			3.00000i			0.358569i
$71$	−2.59808	−	1.50000i	−0.308335	−	0.178017i	0.337846	−	0.941201i	$-0.390302\pi$
$71$	−2.59808	−	1.50000i	−0.308335	−	0.178017i	−0.646181	+	0.763184i	$0.723635\pi$
$72$	−1.73205	−	1.00000i	−0.204124	−	0.117851i
$73$			2.00000i			0.234082i	0.993127	+	0.117041i	$0.0373409\pi$
$73$			2.00000i			0.234082i	−0.993127	+	0.117041i	$0.962659\pi$
$74$	−3.50000	+	6.06218i	−0.406867	+	0.704714i
$75$	2.00000	+	3.46410i	0.230940	+	0.400000i
$76$	1.73205	−	1.00000i	0.198680	−	0.114708i
$77$	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	$0.351411\pi$
$80$	2.59808	−	1.50000i	0.290474	−	0.167705i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$		0			0
$83$		−	12.0000i		−	1.31717i	−0.752506	−	0.658586i	$-0.771155\pi$
$83$		−	12.0000i		−	1.31717i	0.752506	−	0.658586i	$-0.228845\pi$
$84$	−0.866025	−	0.500000i	−0.0944911	−	0.0545545i
$85$	−7.79423	−	4.50000i	−0.845403	−	0.488094i
$86$			1.00000i			0.107833i
$87$	−3.00000	+	5.19615i	−0.321634	+	0.557086i
$88$	−3.00000	−	5.19615i	−0.319801	−	0.553912i
$89$	−5.19615	+	3.00000i	−0.550791	+	0.317999i	−0.749441	−	0.662071i	$-0.769678\pi$
$89$	−5.19615	+	3.00000i	−0.550791	+	0.317999i	0.198650	+	0.980071i	$0.436344\pi$
$90$	6.00000			0.632456
$91$		0			0
$92$		0			0
$93$	3.46410	−	2.00000i	0.359211	−	0.207390i
$94$	1.50000	+	2.59808i	0.154713	+	0.267971i
$95$	−3.00000	+	5.19615i	−0.307794	+	0.533114i
$96$			1.00000i			0.102062i
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.00888289	−	0.999961i	$-0.502828\pi$
$97$	−8.66025	−	5.00000i	−0.879316	−	0.507673i	−0.870433	+	0.492287i	$0.836161\pi$
$98$	−5.19615	−	3.00000i	−0.524891	−	0.303046i
$99$		−	12.0000i		−	1.20605i
$100$	−2.00000	+	3.46410i	−0.200000	+	0.346410i
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	−0.993258	−	0.115924i	$-0.963017\pi$
$101$	−6.00000	−	10.3923i	−0.597022	−	1.03407i	0.396236	−	0.918149i	$-0.370316\pi$
$102$	2.59808	−	1.50000i	0.257248	−	0.148522i
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$	3.00000			0.292770
$106$		0			0
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	−0.995474	−	0.0950377i	$-0.969703\pi$
$107$	−6.00000	−	10.3923i	−0.580042	−	1.00466i	0.415432	−	0.909624i	$-0.363630\pi$
$108$	−2.50000	+	4.33013i	−0.240563	+	0.416667i
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$	15.5885	+	9.00000i	1.48630	+	0.858116i
$111$	6.06218	+	3.50000i	0.575396	+	0.332205i
$112$		−	1.00000i		−	0.0944911i
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	−0.689714	−	0.724082i	$-0.742264\pi$
$113$	3.00000	−	5.19615i	0.282216	−	0.488813i	0.971930	+	0.235269i	$0.0755971\pi$
$114$	−1.00000	−	1.73205i	−0.0936586	−	0.162221i
$115$		0			0
$116$	−6.00000			−0.557086
$117$		0			0
$118$	6.00000			0.552345
$119$	−2.59808	+	1.50000i	−0.238165	+	0.137505i
$120$	−1.50000	−	2.59808i	−0.136931	−	0.237171i
$121$	12.5000	−	21.6506i	1.13636	−	1.96824i
$122$			8.00000i			0.724286i
$123$		0			0
$124$	3.46410	+	2.00000i	0.311086	+	0.179605i
$125$			3.00000i			0.268328i
$126$	1.00000	−	1.73205i	0.0890871	−	0.154303i
$127$	10.0000	+	17.3205i	0.887357	+	1.53695i	0.842989	+	0.537931i	$0.180794\pi$
$127$	10.0000	+	17.3205i	0.887357	+	1.53695i	0.0443678	+	0.999015i	$0.485873\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	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	$0.869707\pi$
$132$	−5.19615	+	3.00000i	−0.452267	+	0.261116i
$133$	1.00000	+	1.73205i	0.0867110	+	0.150188i
$134$	−7.00000	+	12.1244i	−0.604708	+	1.04738i
$135$		−	15.0000i		−	1.29099i
$136$	2.59808	+	1.50000i	0.222783	+	0.128624i
$137$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$137$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$138$		0			0
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$	1.50000	+	2.59808i	0.126773	+	0.219578i
$141$	2.59808	−	1.50000i	0.218797	−	0.126323i
$142$	−3.00000			−0.251754
$143$		0			0
$144$	−2.00000			−0.166667
$145$	15.5885	−	9.00000i	1.29455	−	0.747409i
$146$	1.00000	+	1.73205i	0.0827606	+	0.143346i
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$			7.00000i			0.575396i
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	0.271821	−	0.962348i	$-0.412374\pi$
$149$	−5.19615	−	3.00000i	−0.425685	−	0.245770i	−0.697507	+	0.716578i	$0.745707\pi$
$150$	3.46410	+	2.00000i	0.282843	+	0.163299i
$151$			17.0000i			1.38344i	0.722166	+	0.691720i	$0.243147\pi$
$151$			17.0000i			1.38344i	−0.722166	+	0.691720i	$0.756853\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$	3.00000	+	5.19615i	0.242536	+	0.420084i
$154$	5.19615	−	3.00000i	0.418718	−	0.241747i
$155$	−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	$0.311315\pi$
$158$	6.92820	−	4.00000i	0.551178	−	0.318223i
$159$		0			0
$160$	1.50000	−	2.59808i	0.118585	−	0.205396i
$161$		0			0
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.932326	−	0.361619i	$-0.117776\pi$
$163$	13.8564	+	8.00000i	1.08532	+	0.626608i	0.152992	+	0.988227i	$0.451109\pi$
$164$		0			0
$165$	9.00000	−	15.5885i	0.700649	−	1.21356i
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$167$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$168$	−1.00000			−0.0771517
$169$		0			0
$170$	−9.00000			−0.690268
$171$	3.46410	−	2.00000i	0.264906	−	0.152944i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$			6.00000i			0.454859i
$175$	−3.46410	−	2.00000i	−0.261861	−	0.151186i
$176$	−5.19615	−	3.00000i	−0.391675	−	0.226134i
$177$		−	6.00000i		−	0.450988i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	0.916623	−	0.399753i	$-0.130904\pi$
$179$	1.50000	+	2.59808i	0.112115	+	0.194189i	−0.804508	+	0.593942i	$0.797571\pi$
$180$	5.19615	−	3.00000i	0.387298	−	0.223607i
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$		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
$187$			18.0000i			1.31629i
$188$	2.59808	+	1.50000i	0.189484	+	0.109399i
$189$	−4.33013	−	2.50000i	−0.314970	−	0.181848i
$190$			6.00000i			0.435286i
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	−0.331611	−	0.943416i	$-0.607592\pi$
$191$	9.00000	−	15.5885i	0.651217	−	1.12794i	0.982828	−	0.184525i	$-0.0590746\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	−0.619467	−	0.785022i	$-0.712651\pi$
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	0.370116	+	0.928986i	$0.379318\pi$
$194$	−10.0000			−0.717958
$195$		0			0
$196$	−6.00000			−0.428571
$197$	−2.59808	+	1.50000i	−0.185105	+	0.106871i	−0.589689	−	0.807630i	$-0.700750\pi$
$197$	−2.59808	+	1.50000i	−0.185105	+	0.106871i	0.404584	+	0.914501i	$0.367416\pi$
$198$	−6.00000	−	10.3923i	−0.426401	−	0.738549i
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	−0.828403	−	0.560133i	$-0.810750\pi$
$199$	1.00000	−	1.73205i	0.0708881	−	0.122782i	0.899291	+	0.437351i	$0.144083\pi$
$200$			4.00000i			0.282843i
$201$	12.1244	+	7.00000i	0.855186	+	0.493742i
$202$	−10.3923	−	6.00000i	−0.731200	−	0.422159i
$203$		−	6.00000i		−	0.421117i
$204$	1.50000	−	2.59808i	0.105021	−	0.181902i
$205$		0			0
$206$	3.46410	−	2.00000i	0.241355	−	0.139347i
$207$		0			0
$208$		0			0
$209$	12.0000			0.830057
$210$	2.59808	−	1.50000i	0.179284	−	0.103510i
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	0.998221	−	0.0596196i	$-0.0189888\pi$
$211$	6.50000	+	11.2583i	0.447478	+	0.775055i	−0.550743	+	0.834675i	$0.685655\pi$
$212$		0			0
$213$			3.00000i			0.205557i
$214$	−10.3923	−	6.00000i	−0.710403	−	0.410152i
$215$	−2.59808	−	1.50000i	−0.177187	−	0.102299i
$216$			5.00000i			0.340207i
$217$	−2.00000	+	3.46410i	−0.135769	+	0.235159i
$218$	3.50000	+	6.06218i	0.237050	+	0.410582i
$219$	1.73205	−	1.00000i	0.117041	−	0.0675737i
$220$	18.0000			1.21356
$221$		0			0
$222$	7.00000			0.469809
$223$	16.4545	−	9.50000i	1.10187	−	0.636167i	0.165161	−	0.986267i	$-0.447186\pi$
$223$	16.4545	−	9.50000i	1.10187	−	0.636167i	0.936713	+	0.350100i	$0.113852\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	−4.00000	+	6.92820i	−0.266667	+	0.461880i
$226$		−	6.00000i		−	0.399114i
$227$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$227$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$228$	−1.73205	−	1.00000i	−0.114708	−	0.0662266i
$229$		−	13.0000i		−	0.859064i	−0.903052	−	0.429532i	$-0.858679\pi$
$229$		−	13.0000i		−	0.859064i	0.903052	−	0.429532i	$-0.141321\pi$
$230$		0			0
$231$	−3.00000	−	5.19615i	−0.197386	−	0.341882i
$232$	−5.19615	+	3.00000i	−0.341144	+	0.196960i
$233$	27.0000			1.76883			0.884414	−	0.466702i	$-0.154558\pi$
$233$	27.0000			1.76883			0.884414	+	0.466702i	$0.154558\pi$
$234$		0			0
$235$	−9.00000			−0.587095
$236$	5.19615	−	3.00000i	0.338241	−	0.195283i
$237$	−4.00000	−	6.92820i	−0.259828	−	0.450035i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$		−	15.0000i		−	0.970269i	−0.874439	−	0.485135i	$-0.838771\pi$
$239$		−	15.0000i		−	0.970269i	0.874439	−	0.485135i	$-0.161229\pi$
$240$	−2.59808	−	1.50000i	−0.167705	−	0.0968246i
$241$	8.66025	+	5.00000i	0.557856	+	0.322078i	0.752285	−	0.658838i	$-0.228952\pi$
$241$	8.66025	+	5.00000i	0.557856	+	0.322078i	−0.194429	+	0.980917i	$0.562285\pi$
$242$		−	25.0000i		−	1.60706i
$243$	−8.00000	+	13.8564i	−0.513200	+	0.888889i
$244$	4.00000	+	6.92820i	0.256074	+	0.443533i
$245$	15.5885	−	9.00000i	0.995910	−	0.574989i
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$	−10.3923	+	6.00000i	−0.658586	+	0.380235i
$250$	1.50000	+	2.59808i	0.0948683	+	0.164317i
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	−0.186722	−	0.982413i	$-0.559786\pi$
$251$	12.0000	−	20.7846i	0.757433	−	1.31191i	0.944156	−	0.329500i	$-0.106880\pi$
$252$		−	2.00000i		−	0.125988i
$253$		0			0
$254$	17.3205	+	10.0000i	1.08679	+	0.627456i
$255$			9.00000i			0.563602i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.50000	+	7.79423i	0.280702	+	0.486191i	0.971558	−	0.236802i	$-0.0760993\pi$
$257$	4.50000	+	7.79423i	0.280702	+	0.486191i	−0.690856	+	0.722993i	$0.742766\pi$
$258$	0.866025	−	0.500000i	0.0539164	−	0.0311286i
$259$	−7.00000			−0.434959
$260$		0			0
$261$	−12.0000			−0.742781
$262$	−18.1865	+	10.5000i	−1.12357	+	0.648692i
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	0.989561	−	0.144112i	$-0.0460326\pi$
$263$	6.00000	+	10.3923i	0.369976	+	0.640817i	−0.619586	+	0.784929i	$0.712699\pi$
$264$	−3.00000	+	5.19615i	−0.184637	+	0.319801i
$265$		0			0
$266$	1.73205	+	1.00000i	0.106199	+	0.0613139i
$267$	5.19615	+	3.00000i	0.317999	+	0.183597i
$268$			14.0000i			0.855186i
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$	−7.50000	−	12.9904i	−0.456435	−	0.790569i
$271$	9.52628	−	5.50000i	0.578680	−	0.334101i	−0.181928	−	0.983312i	$-0.558234\pi$
$271$	9.52628	−	5.50000i	0.578680	−	0.334101i	0.760609	+	0.649211i	$0.224901\pi$
$272$	3.00000			0.181902
$273$		0			0
$274$		0			0
$275$	−20.7846	+	12.0000i	−1.25336	+	0.723627i
$276$		0			0
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	0.0477206	+	0.998861i	$0.484804\pi$
$277$	−14.0000	+	24.2487i	−0.841178	+	1.45696i	−0.888899	+	0.458103i	$0.848529\pi$
$278$		−	13.0000i		−	0.779688i
$279$	6.92820	+	4.00000i	0.414781	+	0.239474i
$280$	2.59808	+	1.50000i	0.155265	+	0.0896421i
$281$		−	6.00000i		−	0.357930i	−0.983855	−	0.178965i	$-0.942725\pi$
$281$		−	6.00000i		−	0.357930i	0.983855	−	0.178965i	$-0.0572749\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	0.800439	−	0.599414i	$-0.204600\pi$
$283$	−2.00000	−	3.46410i	−0.118888	−	0.205919i	−0.919327	+	0.393494i	$0.871266\pi$
$284$	−2.59808	+	1.50000i	−0.154167	+	0.0890086i
$285$	6.00000			0.355409
$286$		0			0
$287$		0			0
$288$	−1.73205	+	1.00000i	−0.102062	+	0.0589256i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	9.00000	−	15.5885i	0.528498	−	0.915386i
$291$			10.0000i			0.586210i
$292$	1.73205	+	1.00000i	0.101361	+	0.0585206i
$293$	−18.1865	−	10.5000i	−1.06247	−	0.613417i	−0.136355	−	0.990660i	$-0.543539\pi$
$293$	−18.1865	−	10.5000i	−1.06247	−	0.613417i	−0.926114	+	0.377244i	$0.876872\pi$
$294$			6.00000i			0.349927i
$295$	−9.00000	+	15.5885i	−0.524000	+	0.907595i
$296$	3.50000	+	6.06218i	0.203433	+	0.352357i
$297$	−25.9808	+	15.0000i	−1.50756	+	0.870388i
$298$	−6.00000			−0.347571
$299$		0			0
$300$	4.00000			0.230940
$301$	−0.866025	+	0.500000i	−0.0499169	+	0.0288195i
$302$	8.50000	+	14.7224i	0.489120	+	0.847181i
$303$	−6.00000	+	10.3923i	−0.344691	+	0.597022i
$304$		−	2.00000i		−	0.114708i
$305$	−20.7846	−	12.0000i	−1.19012	−	0.687118i
$306$	5.19615	+	3.00000i	0.297044	+	0.171499i
$307$			2.00000i			0.114146i	0.998370	+	0.0570730i	$0.0181768\pi$
$307$			2.00000i			0.114146i	−0.998370	+	0.0570730i	$0.981823\pi$
$308$	3.00000	−	5.19615i	0.170941	−	0.296078i
$309$	−2.00000	−	3.46410i	−0.113776	−	0.197066i
$310$	−10.3923	+	6.00000i	−0.590243	+	0.340777i
$311$	30.0000			1.70114			0.850572	−	0.525859i	$-0.176256\pi$
$311$	30.0000			1.70114			0.850572	+	0.525859i	$0.176256\pi$
$312$		0			0
$313$	−1.00000			−0.0565233			−0.0282617	−	0.999601i	$-0.508997\pi$
$313$	−1.00000			−0.0565233			−0.0282617	+	0.999601i	$0.508997\pi$
$314$	12.1244	−	7.00000i	0.684217	−	0.395033i
$315$	3.00000	+	5.19615i	0.169031	+	0.292770i
$316$	4.00000	−	6.92820i	0.225018	−	0.389742i
$317$			6.00000i			0.336994i	0.985702	+	0.168497i	$0.0538913\pi$
$317$			6.00000i			0.336994i	−0.985702	+	0.168497i	$0.946109\pi$
$318$		0			0
$319$	−31.1769	−	18.0000i	−1.74557	−	1.00781i
$320$		−	3.00000i		−	0.167705i
$321$	−6.00000	+	10.3923i	−0.334887	+	0.580042i
$322$		0			0
$323$	−5.19615	+	3.00000i	−0.289122	+	0.166924i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	16.0000			0.886158
$327$	6.06218	−	3.50000i	0.335239	−	0.193550i
$328$		0			0
$329$	−1.50000	+	2.59808i	−0.0826977	+	0.143237i
$330$		−	18.0000i		−	0.990867i
$331$	6.92820	+	4.00000i	0.380808	+	0.219860i	0.678170	−	0.734905i	$-0.262773\pi$
$331$	6.92820	+	4.00000i	0.380808	+	0.219860i	−0.297361	+	0.954765i	$0.596107\pi$
$332$	−10.3923	−	6.00000i	−0.570352	−	0.329293i
$333$			14.0000i			0.767195i
$334$		0			0
$335$	−21.0000	−	36.3731i	−1.14735	−	1.98727i
$336$	−0.866025	+	0.500000i	−0.0472456	+	0.0272772i
$337$	−23.0000			−1.25289			−0.626445	−	0.779466i	$-0.715491\pi$
$337$	−23.0000			−1.25289			−0.626445	+	0.779466i	$0.715491\pi$
$338$		0			0
$339$	−6.00000			−0.325875
$340$	−7.79423	+	4.50000i	−0.422701	+	0.244047i
$341$	12.0000	+	20.7846i	0.649836	+	1.12555i
$342$	2.00000	−	3.46410i	0.108148	−	0.187317i
$343$		−	13.0000i		−	0.701934i
$344$	0.866025	+	0.500000i	0.0466930	+	0.0269582i
$345$		0			0
$346$		0			0
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	−0.903475	−	0.428640i	$-0.858993\pi$
$347$	−1.50000	+	2.59808i	−0.0805242	+	0.139472i	0.822951	+	0.568112i	$0.192326\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−16.4545	+	9.50000i	−0.880788	+	0.508523i	−0.870918	−	0.491428i	$-0.836475\pi$
$349$	−16.4545	+	9.50000i	−0.880788	+	0.508523i	−0.00987003	+	0.999951i	$0.503142\pi$
$350$	−4.00000			−0.213809
$351$		0			0
$352$	−6.00000			−0.319801
$353$	−20.7846	+	12.0000i	−1.10625	+	0.638696i	−0.937856	−	0.347024i	$-0.887192\pi$
$353$	−20.7846	+	12.0000i	−1.10625	+	0.638696i	−0.168397	+	0.985719i	$0.553859\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$	4.50000	−	7.79423i	0.238835	−	0.413675i
$356$			6.00000i			0.317999i
$357$	2.59808	+	1.50000i	0.137505	+	0.0793884i
$358$	2.59808	+	1.50000i	0.137313	+	0.0792775i
$359$		0			0		1.00000			$0$
$359$		0			0		−1.00000			$\pi$
$360$	3.00000	−	5.19615i	0.158114	−	0.273861i
$361$	−7.50000	−	12.9904i	−0.394737	−	0.683704i
$362$	−17.3205	+	10.0000i	−0.910346	+	0.525588i
$363$	−25.0000			−1.31216
$364$		0			0
$365$	−6.00000			−0.314054
$366$	6.92820	−	4.00000i	0.362143	−	0.209083i
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	−0.975404	−	0.220423i	$-0.929256\pi$
$367$	−13.0000	−	22.5167i	−0.678594	−	1.17536i	0.296810	−	0.954937i	$-0.404077\pi$
$368$		0			0
$369$		0			0
$370$	−18.1865	−	10.5000i	−0.945473	−	0.545869i
$371$		0			0
$372$		−	4.00000i		−	0.207390i
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	−0.809591	−	0.586994i	$-0.800311\pi$
$373$	2.00000	−	3.46410i	0.103556	−	0.179364i	0.913147	+	0.407630i	$0.133645\pi$
$374$	9.00000	+	15.5885i	0.465379	+	0.806060i
$375$	2.59808	−	1.50000i	0.134164	−	0.0774597i
$376$	3.00000			0.154713
$377$		0			0
$378$	−5.00000			−0.257172
$379$	−17.3205	+	10.0000i	−0.889695	+	0.513665i	−0.873843	−	0.486209i	$-0.838379\pi$
$379$	−17.3205	+	10.0000i	−0.889695	+	0.513665i	−0.0158521	+	0.999874i	$0.505046\pi$
$380$	3.00000	+	5.19615i	0.153897	+	0.266557i
$381$	10.0000	−	17.3205i	0.512316	−	0.887357i
$382$		−	18.0000i		−	0.920960i
$383$	18.1865	+	10.5000i	0.929288	+	0.536525i	0.886586	−	0.462563i	$-0.153070\pi$
$383$	18.1865	+	10.5000i	0.929288	+	0.536525i	0.0427020	+	0.999088i	$0.486403\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$			18.0000i			0.917365i
$386$	−2.00000	+	3.46410i	−0.101797	+	0.176318i
$387$	1.00000	+	1.73205i	0.0508329	+	0.0880451i
$388$	−8.66025	+	5.00000i	−0.439658	+	0.253837i
$389$	6.00000			0.304212			0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000			0.304212			0.152106	+	0.988364i	$0.451394\pi$
$390$		0			0
$391$		0			0
$392$	−5.19615	+	3.00000i	−0.262445	+	0.151523i
$393$	10.5000	+	18.1865i	0.529655	+	0.917389i
$394$	−1.50000	+	2.59808i	−0.0755689	+	0.130889i
$395$			24.0000i			1.20757i
$396$	−10.3923	−	6.00000i	−0.522233	−	0.301511i
$397$	29.4449	+	17.0000i	1.47780	+	0.853206i	0.999685	−	0.0250943i	$-0.00798860\pi$
$397$	29.4449	+	17.0000i	1.47780	+	0.853206i	0.478110	+	0.878300i	$0.341322\pi$
$398$		−	2.00000i		−	0.100251i
$399$	1.00000	−	1.73205i	0.0500626	−	0.0867110i
$400$	2.00000	+	3.46410i	0.100000	+	0.173205i
$401$	31.1769	−	18.0000i	1.55690	−	0.898877i	0.559350	−	0.828932i	$-0.311051\pi$
$401$	31.1769	−	18.0000i	1.55690	−	0.898877i	0.997551	−	0.0699455i	$-0.0222825\pi$
$402$	14.0000			0.698257
$403$		0			0
$404$	−12.0000			−0.597022
$405$	2.59808	−	1.50000i	0.129099	−	0.0745356i
$406$	−3.00000	−	5.19615i	−0.148888	−	0.257881i
$407$	−21.0000	+	36.3731i	−1.04093	+	1.80295i
$408$		−	3.00000i		−	0.148522i
$409$	27.7128	+	16.0000i	1.37031	+	0.791149i	0.990967	−	0.134107i	$-0.0428165\pi$
$409$	27.7128	+	16.0000i	1.37031	+	0.791149i	0.379344	+	0.925256i	$0.376150\pi$
$410$		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
$418$	10.3923	−	6.00000i	0.508304	−	0.293470i
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	0.734919	−	0.678155i	$-0.237220\pi$
$419$	−4.50000	−	7.79423i	−0.219839	−	0.380773i	−0.954759	+	0.297382i	$0.903887\pi$
$420$	1.50000	−	2.59808i	0.0731925	−	0.126773i
$421$		−	17.0000i		−	0.828529i	−0.910156	−	0.414265i	$-0.864039\pi$
$421$		−	17.0000i		−	0.828529i	0.910156	−	0.414265i	$-0.135961\pi$
$422$	11.2583	+	6.50000i	0.548047	+	0.316415i
$423$	5.19615	+	3.00000i	0.252646	+	0.145865i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$	1.50000	+	2.59808i	0.0726752	+	0.125877i
$427$	−6.92820	+	4.00000i	−0.335279	+	0.193574i
$428$	−12.0000			−0.580042
$429$		0			0
$430$	−3.00000			−0.144673
$431$	28.5788	−	16.5000i	1.37659	−	0.794777i	0.384846	−	0.922981i	$-0.374254\pi$
$431$	28.5788	−	16.5000i	1.37659	−	0.794777i	0.991748	+	0.128204i	$0.0409211\pi$
$432$	2.50000	+	4.33013i	0.120281	+	0.208333i
$433$	−12.5000	+	21.6506i	−0.600712	+	1.04046i	0.392002	+	0.919964i	$0.371783\pi$
$433$	−12.5000	+	21.6506i	−0.600712	+	1.04046i	−0.992713	+	0.120499i	$0.961551\pi$
$434$			4.00000i			0.192006i
$435$	−15.5885	−	9.00000i	−0.747409	−	0.431517i
$436$	6.06218	+	3.50000i	0.290326	+	0.167620i
$437$		0			0
$438$	1.00000	−	1.73205i	0.0477818	−	0.0827606i
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	0.989401	+	0.145210i	$0.0463858\pi$
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	−0.368945	+	0.929451i	$0.620281\pi$
$440$	15.5885	−	9.00000i	0.743151	−	0.429058i
$441$	−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	$0.333748\pi$
$444$	6.06218	−	3.50000i	0.287698	−	0.166103i
$445$	−9.00000	−	15.5885i	−0.426641	−	0.738964i
$446$	9.50000	−	16.4545i	0.449838	−	0.779142i
$447$			6.00000i			0.283790i
$448$	−0.866025	−	0.500000i	−0.0409159	−	0.0236228i
$449$	−5.19615	−	3.00000i	−0.245222	−	0.141579i	0.372353	−	0.928091i	$-0.378551\pi$
$449$	−5.19615	−	3.00000i	−0.245222	−	0.141579i	−0.617574	+	0.786513i	$0.711885\pi$
$450$			8.00000i			0.377124i
$451$		0			0
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$	14.7224	−	8.50000i	0.691720	−	0.399365i
$454$		0			0
$455$		0			0
$456$	−2.00000			−0.0936586
$457$	8.66025	−	5.00000i	0.405110	−	0.233890i	−0.283577	−	0.958950i	$-0.591521\pi$
$457$	8.66025	−	5.00000i	0.405110	−	0.233890i	0.688686	+	0.725059i	$0.258188\pi$
$458$	−6.50000	−	11.2583i	−0.303725	−	0.526067i
$459$	7.50000	−	12.9904i	0.350070	−	0.606339i
$460$		0			0
$461$	7.79423	+	4.50000i	0.363013	+	0.209586i	0.670402	−	0.741998i	$-0.266122\pi$
$461$	7.79423	+	4.50000i	0.363013	+	0.209586i	−0.307388	+	0.951584i	$0.599455\pi$
$462$	−5.19615	−	3.00000i	−0.241747	−	0.139573i
$463$		−	40.0000i		−	1.85896i	−0.368875	−	0.929479i	$-0.620257\pi$
$463$		−	40.0000i		−	1.85896i	0.368875	−	0.929479i	$-0.379743\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$	6.00000	+	10.3923i	0.278243	+	0.481932i
$466$	23.3827	−	13.5000i	1.08318	−	0.625375i
$467$	−36.0000			−1.66588			−0.832941	−	0.553362i	$-0.813345\pi$
$467$	−36.0000			−1.66588			−0.832941	+	0.553362i	$0.813345\pi$
$468$		0			0
$469$	−14.0000			−0.646460
$470$	−7.79423	+	4.50000i	−0.359521	+	0.207570i
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$			6.00000i			0.275880i
$474$	−6.92820	−	4.00000i	−0.318223	−	0.183726i
$475$	−6.92820	−	4.00000i	−0.317888	−	0.183533i
$476$			3.00000i			0.137505i
$477$		0			0
$478$	−7.50000	−	12.9904i	−0.343042	−	0.594166i
$479$	−18.1865	+	10.5000i	−0.830964	+	0.479757i	−0.854183	−	0.519973i	$-0.825942\pi$
$479$	−18.1865	+	10.5000i	−0.830964	+	0.479757i	0.0232187	+	0.999730i	$0.492609\pi$
$480$	−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
$486$			16.0000i			0.725775i
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	0.152042	−	0.988374i	$-0.451415\pi$
$487$	−13.8564	−	8.00000i	−0.627894	−	0.362515i	−0.779936	+	0.625859i	$0.784748\pi$
$488$	6.92820	+	4.00000i	0.313625	+	0.181071i
$489$		−	16.0000i		−	0.723545i
$490$	9.00000	−	15.5885i	0.406579	−	0.704215i
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	0.746438	−	0.665455i	$-0.231763\pi$
$491$	−4.50000	−	7.79423i	−0.203082	−	0.351749i	−0.949520	+	0.313707i	$0.898429\pi$
$492$		0			0
$493$	18.0000			0.810679
$494$		0			0
$495$	36.0000			1.61808
$496$	3.46410	−	2.00000i	0.155543	−	0.0898027i
$497$	−1.50000	−	2.59808i	−0.0672842	−	0.116540i
$498$	−6.00000	+	10.3923i	−0.268866	+	0.465690i
$499$			40.0000i			1.79065i	0.445418	+	0.895323i	$0.353055\pi$
$499$			40.0000i			1.79065i	−0.445418	+	0.895323i	$0.646945\pi$
$500$	2.59808	+	1.50000i	0.116190	+	0.0670820i
$501$		0			0
$502$		−	24.0000i		−	1.07117i
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	−0.309418	−	0.950926i	$-0.600134\pi$
$503$	15.0000	−	25.9808i	0.668817	−	1.15842i	0.978235	−	0.207499i	$-0.0665323\pi$
$504$	−1.00000	−	1.73205i	−0.0445435	−	0.0771517i
$505$	31.1769	−	18.0000i	1.38735	−	0.800989i
$506$		0			0
$507$		0			0
$508$	20.0000			0.887357
$509$	15.5885	−	9.00000i	0.690946	−	0.398918i	−0.113020	−	0.993593i	$-0.536052\pi$
$509$	15.5885	−	9.00000i	0.690946	−	0.398918i	0.803966	+	0.594675i	$0.202719\pi$
$510$	4.50000	+	7.79423i	0.199263	+	0.345134i
$511$	−1.00000	+	1.73205i	−0.0442374	+	0.0766214i
$512$			1.00000i			0.0441942i
$513$	−8.66025	−	5.00000i	−0.382360	−	0.220755i
$514$	7.79423	+	4.50000i	0.343789	+	0.198486i
$515$			12.0000i			0.528783i
$516$	0.500000	−	0.866025i	0.0220113	−	0.0381246i
$517$	9.00000	+	15.5885i	0.395820	+	0.685580i
$518$	−6.06218	+	3.50000i	−0.266357	+	0.153781i
$519$		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	$0.563168\pi$
$522$	−10.3923	+	6.00000i	−0.454859	+	0.262613i
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	0.560208	−	0.828352i	$-0.310721\pi$
$523$	−10.0000	−	17.3205i	−0.437269	−	0.757373i	−0.997478	+	0.0709788i	$0.977388\pi$
$524$	−10.5000	+	18.1865i	−0.458695	+	0.794482i
$525$			4.00000i			0.174574i
$526$	10.3923	+	6.00000i	0.453126	+	0.261612i
$527$	−10.3923	−	6.00000i	−0.452696	−	0.261364i
$528$			6.00000i			0.261116i
$529$	11.5000	−	19.9186i	0.500000	−	0.866025i
$530$		0			0
$531$	10.3923	−	6.00000i	0.450988	−	0.260378i
$532$	2.00000			0.0867110
$533$		0			0
$534$	6.00000			0.259645
$535$	31.1769	−	18.0000i	1.34790	−	0.778208i
$536$	7.00000	+	12.1244i	0.302354	+	0.523692i
$537$	1.50000	−	2.59808i	0.0647298	−	0.112115i
$538$			24.0000i			1.03471i
$539$	−31.1769	−	18.0000i	−1.34288	−	0.775315i
$540$	−12.9904	−	7.50000i	−0.559017	−	0.322749i
$541$			11.0000i			0.472927i	0.971640	+	0.236463i	$0.0759884\pi$
$541$			11.0000i			0.472927i	−0.971640	+	0.236463i	$0.924012\pi$
$542$	5.50000	−	9.52628i	0.236245	−	0.409189i
$543$	10.0000	+	17.3205i	0.429141	+	0.743294i
$544$	2.59808	−	1.50000i	0.111392	−	0.0643120i
$545$	−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
$551$		−	12.0000i		−	0.511217i
$552$		0			0
$553$	6.92820	+	4.00000i	0.294617	+	0.170097i
$554$			28.0000i			1.18961i
$555$	−10.5000	+	18.1865i	−0.445700	+	0.771975i
$556$	−6.50000	−	11.2583i	−0.275661	−	0.477460i
$557$	2.59808	−	1.50000i	0.110084	−	0.0635570i	−0.443947	−	0.896053i	$-0.646422\pi$
$557$	2.59808	−	1.50000i	0.110084	−	0.0635570i	0.554031	+	0.832496i	$0.313089\pi$
$558$	8.00000			0.338667
$559$		0			0
$560$	3.00000			0.126773
$561$	15.5885	−	9.00000i	0.658145	−	0.379980i
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	−0.0824933	−	0.996592i	$-0.526288\pi$
$563$	19.5000	−	33.7750i	0.821827	−	1.42345i	0.904320	−	0.426855i	$-0.140378\pi$
$564$		−	3.00000i		−	0.126323i
$565$	15.5885	+	9.00000i	0.655811	+	0.378633i
$566$	−3.46410	−	2.00000i	−0.145607	−	0.0840663i
$567$		−	1.00000i		−	0.0419961i
$568$	−1.50000	+	2.59808i	−0.0629386	+	0.109013i
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	0.979313	−	0.202350i	$-0.0648579\pi$
$569$	7.50000	+	12.9904i	0.314416	+	0.544585i	−0.664897	+	0.746935i	$0.731525\pi$
$570$	5.19615	−	3.00000i	0.217643	−	0.125656i
$571$	−5.00000			−0.209243			−0.104622	−	0.994512i	$-0.533363\pi$
$571$	−5.00000			−0.209243			−0.104622	+	0.994512i	$0.533363\pi$
$572$		0			0
$573$	−18.0000			−0.751961
$574$		0			0
$575$		0			0
$576$	−1.00000	+	1.73205i	−0.0416667	+	0.0721688i
$577$		−	38.0000i		−	1.58196i	−0.611842	−	0.790980i	$-0.709571\pi$
$577$		−	38.0000i		−	1.58196i	0.611842	−	0.790980i	$-0.290429\pi$
$578$	6.92820	+	4.00000i	0.288175	+	0.166378i
$579$	3.46410	+	2.00000i	0.143963	+	0.0831172i
$580$		−	18.0000i		−	0.747409i
$581$	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
$587$	−20.7846	+	12.0000i	−0.857873	+	0.495293i	−0.863299	−	0.504692i	$-0.831606\pi$
$587$	−20.7846	+	12.0000i	−0.857873	+	0.495293i	0.00542667	+	0.999985i	$0.498273\pi$
$588$	3.00000	+	5.19615i	0.123718	+	0.214286i
$589$	−4.00000	+	6.92820i	−0.164817	+	0.285472i
$590$			18.0000i			0.741048i
$591$	2.59808	+	1.50000i	0.106871	+	0.0617018i
$592$	6.06218	+	3.50000i	0.249154	+	0.143849i
$593$			18.0000i			0.739171i	0.929197	+	0.369586i	$0.120500\pi$
$593$			18.0000i			0.739171i	−0.929197	+	0.369586i	$0.879500\pi$
$594$	−15.0000	+	25.9808i	−0.615457	+	1.06600i
$595$	−4.50000	−	7.79423i	−0.184482	−	0.319532i
$596$	−5.19615	+	3.00000i	−0.212843	+	0.122885i
$597$	−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	$0.460884\pi$
$600$	3.46410	−	2.00000i	0.141421	−	0.0816497i
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	0.992114	−	0.125336i	$-0.0400009\pi$
$601$	9.50000	+	16.4545i	0.387513	+	0.671192i	−0.604601	+	0.796528i	$0.706668\pi$
$602$	−0.500000	+	0.866025i	−0.0203785	+	0.0352966i
$603$			28.0000i			1.14025i
$604$	14.7224	+	8.50000i	0.599047	+	0.345860i
$605$	64.9519	+	37.5000i	2.64067	+	1.52459i
$606$			12.0000i			0.487467i
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	−0.972396	−	0.233338i	$-0.925035\pi$
$607$	−7.00000	+	12.1244i	−0.284121	+	0.492112i	0.688274	+	0.725450i	$0.258368\pi$
$608$	−1.00000	−	1.73205i	−0.0405554	−	0.0702439i
$609$	−5.19615	+	3.00000i	−0.210559	+	0.121566i
$610$	−24.0000			−0.971732
$611$		0			0
$612$	6.00000			0.242536
$613$	−32.9090	+	19.0000i	−1.32918	+	0.767403i	−0.985173	−	0.171564i	$-0.945118\pi$
$613$	−32.9090	+	19.0000i	−1.32918	+	0.767403i	−0.344008	+	0.938967i	$0.611785\pi$
$614$	1.00000	+	1.73205i	0.0403567	+	0.0698999i
$615$		0			0
$616$		−	6.00000i		−	0.241747i
$617$	−20.7846	−	12.0000i	−0.836757	−	0.483102i	0.0194037	−	0.999812i	$-0.493823\pi$
$617$	−20.7846	−	12.0000i	−0.836757	−	0.483102i	−0.856161	+	0.516710i	$0.827157\pi$
$618$	−3.46410	−	2.00000i	−0.139347	−	0.0804518i
$619$		−	28.0000i		−	1.12542i	−0.826656	−	0.562708i	$-0.809760\pi$
$619$		−	28.0000i		−	1.12542i	0.826656	−	0.562708i	$-0.190240\pi$
$620$	−6.00000	+	10.3923i	−0.240966	+	0.417365i
$621$		0			0
$622$	25.9808	−	15.0000i	1.04173	−	0.601445i
$623$	−6.00000			−0.240385
$624$		0			0
$625$	−29.0000			−1.16000
$626$	−0.866025	+	0.500000i	−0.0346133	+	0.0199840i
$627$	−6.00000	−	10.3923i	−0.239617	−	0.415029i
$628$	7.00000	−	12.1244i	0.279330	−	0.483814i
$629$		−	21.0000i		−	0.837325i
$630$	5.19615	+	3.00000i	0.207020	+	0.119523i
$631$	−25.1147	−	14.5000i	−0.999802	−	0.577236i	−0.0916122	−	0.995795i	$-0.529202\pi$
$631$	−25.1147	−	14.5000i	−0.999802	−	0.577236i	−0.908190	+	0.418559i	$0.862535\pi$
$632$		−	8.00000i		−	0.318223i
$633$	6.50000	−	11.2583i	0.258352	−	0.447478i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$	−51.9615	+	30.0000i	−2.06203	+	1.19051i
$636$		0			0
$637$		0			0
$638$	−36.0000			−1.42525
$639$	−5.19615	+	3.00000i	−0.205557	+	0.118678i
$640$	−1.50000	−	2.59808i	−0.0592927	−	0.102698i
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	−0.987200	−	0.159489i	$-0.949015\pi$
$641$	−9.00000	+	15.5885i	−0.355479	+	0.615707i	0.631721	+	0.775196i	$0.282349\pi$
$642$			12.0000i			0.473602i
$643$	12.1244	+	7.00000i	0.478138	+	0.276053i	0.719640	−	0.694347i	$-0.244307\pi$
$643$	12.1244	+	7.00000i	0.478138	+	0.276053i	−0.241502	+	0.970400i	$0.577640\pi$
$644$		0			0
$645$			3.00000i			0.118125i
$646$	−3.00000	+	5.19615i	−0.118033	+	0.204440i
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	0.801010	−	0.598651i	$-0.204296\pi$
$647$	−3.00000	−	5.19615i	−0.117942	−	0.204282i	−0.918952	+	0.394369i	$0.870963\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	36.0000			1.41312
$650$		0			0
$651$	4.00000			0.156772
$652$	13.8564	−	8.00000i	0.542659	−	0.313304i
$653$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$653$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$654$	3.50000	−	6.06218i	0.136861	−	0.237050i
$655$		−	63.0000i		−	2.46161i
$656$		0			0
$657$	3.46410	+	2.00000i	0.135147	+	0.0780274i
$658$			3.00000i			0.116952i
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	−0.266872	−	0.963732i	$-0.585990\pi$
$659$	18.0000	−	31.1769i	0.701180	−	1.21448i	0.968052	−	0.250748i	$-0.0806766\pi$
$660$	−9.00000	−	15.5885i	−0.350325	−	0.606780i
$661$	−19.0526	+	11.0000i	−0.741059	+	0.427850i	−0.822454	−	0.568831i	$-0.807396\pi$
$661$	−19.0526	+	11.0000i	−0.741059	+	0.427850i	0.0813955	+	0.996682i	$0.474062\pi$
$662$	8.00000			0.310929
$663$		0			0
$664$	−12.0000			−0.465690
$665$	−5.19615	+	3.00000i	−0.201498	+	0.116335i
$666$	7.00000	+	12.1244i	0.271244	+	0.469809i
$667$		0			0
$668$		0			0
$669$	−16.4545	−	9.50000i	−0.636167	−	0.367291i
$670$	−36.3731	−	21.0000i	−1.40521	−	0.811301i
$671$			48.0000i			1.85302i
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	0.622770	−	0.782405i	$-0.286007\pi$
$673$	−9.50000	−	16.4545i	−0.366198	−	0.634274i	−0.988968	+	0.148132i	$0.952674\pi$
$674$	−19.9186	+	11.5000i	−0.767235	+	0.442963i
$675$	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	$0.126229\pi$
$678$	−5.19615	+	3.00000i	−0.199557	+	0.115214i
$679$	−5.00000	−	8.66025i	−0.191882	−	0.332350i
$680$	−4.50000	+	7.79423i	−0.172567	+	0.298895i
$681$		0			0
$682$	20.7846	+	12.0000i	0.795884	+	0.459504i
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	0.0465244	−	0.998917i	$-0.485185\pi$
$683$	−20.7846	−	12.0000i	−0.795301	−	0.459167i	−0.841825	+	0.539750i	$0.818519\pi$
$684$		−	4.00000i		−	0.152944i
$685$		0			0
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	−11.2583	+	6.50000i	−0.429532	+	0.247990i
$688$	1.00000			0.0381246
$689$		0			0
$690$		0			0
$691$	−6.92820	+	4.00000i	−0.263561	+	0.152167i	−0.625958	−	0.779857i	$-0.715292\pi$
$691$	−6.92820	+	4.00000i	−0.263561	+	0.152167i	0.362397	+	0.932024i	$0.381959\pi$
$692$		0			0
$693$	6.00000	−	10.3923i	0.227921	−	0.394771i
$694$			3.00000i			0.113878i
$695$	33.7750	+	19.5000i	1.28116	+	0.739677i
$696$	5.19615	+	3.00000i	0.196960	+	0.113715i
$697$		0			0
$698$	−9.50000	+	16.4545i	−0.359580	+	0.622811i
$699$	−13.5000	−	23.3827i	−0.510617	−	0.884414i
$700$	−3.46410	+	2.00000i	−0.130931	+	0.0755929i
$701$		0			0			−	1.00000i	$-0.5\pi$
$701$		0			0				1.00000i	$0.5\pi$
$702$		0			0
$703$	−14.0000			−0.528020
$704$	−5.19615	+	3.00000i	−0.195837	+	0.113067i
$705$	4.50000	+	7.79423i	0.169480	+	0.293548i
$706$	−12.0000	+	20.7846i	−0.451626	+	0.782239i
$707$		−	12.0000i		−	0.451306i
$708$	−5.19615	−	3.00000i	−0.195283	−	0.112747i
$709$	−22.5167	−	13.0000i	−0.845631	−	0.488225i	0.0135434	−	0.999908i	$-0.495689\pi$
$709$	−22.5167	−	13.0000i	−0.845631	−	0.488225i	−0.859174	+	0.511683i	$0.829022\pi$
$710$		−	9.00000i		−	0.337764i
$711$	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
$717$	−12.9904	+	7.50000i	−0.485135	+	0.280093i
$718$		0			0
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	−0.804648	−	0.593753i	$-0.797646\pi$
$719$	3.00000	−	5.19615i	0.111881	−	0.193784i	0.916529	+	0.399969i	$0.130979\pi$
$720$		−	6.00000i		−	0.223607i
$721$	3.46410	+	2.00000i	0.129010	+	0.0744839i
$722$	−12.9904	−	7.50000i	−0.483452	−	0.279121i
$723$		−	10.0000i		−	0.371904i
$724$	−10.0000	+	17.3205i	−0.371647	+	0.643712i
$725$	12.0000	+	20.7846i	0.445669	+	0.771921i
$726$	−21.6506	+	12.5000i	−0.803530	+	0.463919i
$727$	10.0000			0.370879			0.185440	−	0.982656i	$-0.440629\pi$
$727$	10.0000			0.370879			0.185440	+	0.982656i	$0.440629\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$	−5.19615	+	3.00000i	−0.192318	+	0.111035i
$731$	−1.50000	−	2.59808i	−0.0554795	−	0.0960933i
$732$	4.00000	−	6.92820i	0.147844	−	0.256074i
$733$		−	23.0000i		−	0.849524i	−0.905305	−	0.424762i	$-0.860358\pi$
$733$		−	23.0000i		−	0.849524i	0.905305	−	0.424762i	$-0.139642\pi$
$734$	−22.5167	−	13.0000i	−0.831105	−	0.479839i
$735$	−15.5885	−	9.00000i	−0.574989	−	0.331970i
$736$		0			0
$737$	−42.0000	+	72.7461i	−1.54709	+	2.67964i
$738$		0			0
$739$	17.3205	−	10.0000i	0.637145	−	0.367856i	−0.146369	−	0.989230i	$-0.546759\pi$
$739$	17.3205	−	10.0000i	0.637145	−	0.367856i	0.783514	+	0.621374i	$0.213425\pi$
$740$	−21.0000			−0.771975
$741$		0			0
$742$		0			0
$743$	7.79423	−	4.50000i	0.285943	−	0.165089i	−0.350168	−	0.936687i	$-0.613876\pi$
$743$	7.79423	−	4.50000i	0.285943	−	0.165089i	0.636111	+	0.771598i	$0.280542\pi$
$744$	−2.00000	−	3.46410i	−0.0733236	−	0.127000i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$		−	4.00000i		−	0.146450i
$747$	−20.7846	−	12.0000i	−0.760469	−	0.439057i
$748$	15.5885	+	9.00000i	0.569970	+	0.329073i
$749$		−	12.0000i		−	0.438470i
$750$	1.50000	−	2.59808i	0.0547723	−	0.0948683i
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	−0.956963	−	0.290209i	$-0.906275\pi$
$751$	−20.0000	−	34.6410i	−0.729810	−	1.26407i	0.227153	−	0.973859i	$-0.427058\pi$
$752$	2.59808	−	1.50000i	0.0947421	−	0.0546994i
$753$	−24.0000			−0.874609
$754$		0			0
$755$	−51.0000			−1.85608
$756$	−4.33013	+	2.50000i	−0.157485	+	0.0909241i
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	0.973991	−	0.226587i	$-0.0727569\pi$
$757$	8.00000	+	13.8564i	0.290765	+	0.503620i	−0.683226	+	0.730207i	$0.739424\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$		0			0
$760$	5.19615	+	3.00000i	0.188484	+	0.108821i
$761$	5.19615	+	3.00000i	0.188360	+	0.108750i	0.591215	−	0.806514i	$-0.298649\pi$
$761$	5.19615	+	3.00000i	0.188360	+	0.108750i	−0.402854	+	0.915264i	$0.631982\pi$
$762$		−	20.0000i		−	0.724524i
$763$	−3.50000	+	6.06218i	−0.126709	+	0.219466i
$764$	−9.00000	−	15.5885i	−0.325609	−	0.563971i
$765$	−15.5885	+	9.00000i	−0.563602	+	0.325396i
$766$	21.0000			0.758761
$767$		0			0
$768$	1.00000			0.0360844
$769$	−27.7128	+	16.0000i	−0.999350	+	0.576975i	−0.908056	−	0.418849i	$-0.862434\pi$
$769$	−27.7128	+	16.0000i	−0.999350	+	0.576975i	−0.0912938	+	0.995824i	$0.529100\pi$
$770$	9.00000	+	15.5885i	0.324337	+	0.561769i
$771$	4.50000	−	7.79423i	0.162064	−	0.280702i
$772$			4.00000i			0.143963i
$773$	−33.7750	−	19.5000i	−1.21480	−	0.701366i	−0.251000	−	0.967987i	$-0.580760\pi$
$773$	−33.7750	−	19.5000i	−1.21480	−	0.701366i	−0.963802	+	0.266621i	$0.914093\pi$
$774$	1.73205	+	1.00000i	0.0622573	+	0.0359443i
$775$		−	16.0000i		−	0.574737i
$776$	−5.00000	+	8.66025i	−0.179490	+	0.310885i
$777$	3.50000	+	6.06218i	0.125562	+	0.217479i
$778$	5.19615	−	3.00000i	0.186291	−	0.107555i
$779$		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
$785$			42.0000i			1.49904i
$786$	18.1865	+	10.5000i	0.648692	+	0.374523i
$787$	34.6410	+	20.0000i	1.23482	+	0.712923i	0.968031	−	0.250832i	$-0.0807042\pi$
$787$	34.6410	+	20.0000i	1.23482	+	0.712923i	0.266788	+	0.963755i	$0.414038\pi$
$788$			3.00000i			0.106871i
$789$	6.00000	−	10.3923i	0.213606	−	0.369976i
$790$	12.0000	+	20.7846i	0.426941	+	0.739483i
$791$	5.19615	−	3.00000i	0.184754	−	0.106668i
$792$	−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	0.206868	+	0.978369i	$0.433673\pi$
$797$	−21.0000	+	36.3731i	−0.743858	+	1.28840i	−0.950726	+	0.310031i	$0.899660\pi$
$798$		−	2.00000i		−	0.0707992i
$799$	−7.79423	−	4.50000i	−0.275740	−	0.159199i
$800$	3.46410	+	2.00000i	0.122474	+	0.0707107i
$801$			12.0000i			0.423999i
$802$	18.0000	−	31.1769i	0.635602	−	1.10090i
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$	12.1244	−	7.00000i	0.427593	−	0.246871i
$805$		0			0
$806$		0			0
$807$	24.0000			0.844840
$808$	−10.3923	+	6.00000i	−0.365600	+	0.211079i
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	0.995466	+	0.0951198i	$0.0303234\pi$
$809$	16.5000	+	28.5788i	0.580109	+	1.00478i	−0.415357	+	0.909659i	$0.636343\pi$
$810$	1.50000	−	2.59808i	0.0527046	−	0.0912871i
$811$		−	20.0000i		−	0.702295i	−0.936320	−	0.351147i	$-0.885792\pi$
$811$		−	20.0000i		−	0.702295i	0.936320	−	0.351147i	$-0.114208\pi$
$812$	−5.19615	−	3.00000i	−0.182349	−	0.105279i
$813$	−9.52628	−	5.50000i	−0.334101	−	0.192893i
$814$			42.0000i			1.47210i
$815$	−24.0000	+	41.5692i	−0.840683	+	1.45611i
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−1.73205	+	1.00000i	−0.0605968	+	0.0349856i
$818$	32.0000			1.11885
$819$		0			0
$820$		0			0
$821$	2.59808	−	1.50000i	0.0906735	−	0.0523504i	−0.453978	−	0.891013i	$-0.649995\pi$
$821$	2.59808	−	1.50000i	0.0906735	−	0.0523504i	0.544651	+	0.838663i	$0.316662\pi$
$822$		0			0
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	−0.717847	−	0.696201i	$-0.754872\pi$
$823$	7.00000	−	12.1244i	0.244005	−	0.422628i	0.961851	+	0.273573i	$0.0882054\pi$
$824$		−	4.00000i		−	0.139347i
$825$	20.7846	+	12.0000i	0.723627	+	0.417786i
$826$	5.19615	+	3.00000i	0.180797	+	0.104383i
$827$			18.0000i			0.625921i	0.949766	+	0.312961i	$0.101321\pi$
$827$			18.0000i			0.625921i	−0.949766	+	0.312961i	$0.898679\pi$
$828$		0			0
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	0.980642	+	0.195810i	$0.0627335\pi$
$829$	19.0000	+	32.9090i	0.659897	+	1.14298i	−0.320745	+	0.947166i	$0.603933\pi$
$830$	31.1769	−	18.0000i	1.08217	−	0.624789i
$831$	28.0000			0.971309
$832$		0			0
$833$	18.0000			0.623663
$834$	−11.2583	+	6.50000i	−0.389844	+	0.225077i
$835$		0			0
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$		−	20.0000i		−	0.691301i
$838$	−7.79423	−	4.50000i	−0.269247	−	0.155450i
$839$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$839$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$840$		−	3.00000i		−	0.103510i
$841$	−3.50000	+	6.06218i	−0.120690	+	0.209041i
$842$	−8.50000	−	14.7224i	−0.292929	−	0.507369i
$843$	−5.19615	+	3.00000i	−0.178965	+	0.103325i
$844$	13.0000			0.447478
$845$		0			0
$846$	6.00000			0.206284
$847$	21.6506	−	12.5000i	0.743925	−	0.429505i
$848$		0			0
$849$	−2.00000	+	3.46410i	−0.0686398	+	0.118888i
$850$		−	12.0000i		−	0.411597i
$851$		0			0
$852$	2.59808	+	1.50000i	0.0890086	+	0.0513892i
$853$		−	37.0000i		−	1.26686i	−0.773802	−	0.633428i	$-0.781647\pi$
$853$		−	37.0000i		−	1.26686i	0.773802	−	0.633428i	$-0.218353\pi$
$854$	−4.00000	+	6.92820i	−0.136877	+	0.237078i
$855$	6.00000	+	10.3923i	0.205196	+	0.355409i
$856$	−10.3923	+	6.00000i	−0.355202	+	0.205076i
$857$	42.0000			1.43469			0.717346	−	0.696717i	$-0.245357\pi$
$857$	42.0000			1.43469			0.717346	+	0.696717i	$0.245357\pi$
$858$		0			0
$859$	−4.00000			−0.136478			−0.0682391	−	0.997669i	$-0.521738\pi$
$859$	−4.00000			−0.136478			−0.0682391	+	0.997669i	$0.521738\pi$
$860$	−2.59808	+	1.50000i	−0.0885937	+	0.0511496i
$861$		0			0
$862$	16.5000	−	28.5788i	0.561992	−	0.973399i
$863$			45.0000i			1.53182i	0.642949	+	0.765909i	$0.277711\pi$
$863$			45.0000i			1.53182i	−0.642949	+	0.765909i	$0.722289\pi$
$864$	4.33013	+	2.50000i	0.147314	+	0.0850517i
$865$		0			0
$866$			25.0000i			0.849535i
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	41.5692	−	24.0000i	1.41014	−	0.814144i
$870$	−18.0000			−0.610257
$871$		0			0
$872$	7.00000			0.237050
$873$	−17.3205	+	10.0000i	−0.586210	+	0.338449i
$874$		0			0
$875$	−1.50000	+	2.59808i	−0.0507093	+	0.0878310i
$876$		−	2.00000i		−	0.0675737i
$877$	−11.2583	−	6.50000i	−0.380167	−	0.219489i	0.297724	−	0.954652i	$-0.403772\pi$
$877$	−11.2583	−	6.50000i	−0.380167	−	0.219489i	−0.677891	+	0.735163i	$0.737106\pi$
$878$	22.5167	+	13.0000i	0.759900	+	0.438729i
$879$			21.0000i			0.708312i
$880$	9.00000	−	15.5885i	0.303390	−	0.525487i
$881$	10.5000	+	18.1865i	0.353754	+	0.612720i	0.986904	−	0.161309i	$-0.0515717\pi$
$881$	10.5000	+	18.1865i	0.353754	+	0.612720i	−0.633150	+	0.774029i	$0.718238\pi$
$882$	−10.3923	+	6.00000i	−0.349927	+	0.202031i
$883$	−29.0000			−0.975928			−0.487964	−	0.872864i	$-0.662260\pi$
$883$	−29.0000			−0.975928			−0.487964	+	0.872864i	$0.662260\pi$
$884$		0			0
$885$	18.0000			0.605063
$886$	18.1865	−	10.5000i	0.610989	−	0.352754i
$887$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$887$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$888$	3.50000	−	6.06218i	0.117452	−	0.203433i
$889$			20.0000i			0.670778i
$890$	−15.5885	−	9.00000i	−0.522526	−	0.301681i
$891$	−5.19615	−	3.00000i	−0.174078	−	0.100504i
$892$		−	19.0000i		−	0.636167i
$893$	−3.00000	+	5.19615i	−0.100391	+	0.173883i
$894$	3.00000	+	5.19615i	0.100335	+	0.173785i
$895$	−7.79423	+	4.50000i	−0.260532	+	0.150418i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	−6.00000			−0.200223
$899$	20.7846	−	12.0000i	0.693206	−	0.400222i
$900$	4.00000	+	6.92820i	0.133333	+	0.230940i
$901$		0			0
$902$		0			0
$903$	0.866025	+	0.500000i	0.0288195	+	0.0166390i
$904$	−5.19615	−	3.00000i	−0.172821	−	0.0997785i
$905$		−	60.0000i		−	1.99447i
$906$	8.50000	−	14.7224i	0.282394	−	0.489120i
$907$	−18.5000	−	32.0429i	−0.614282	−	1.06397i	−0.990510	−	0.137441i	$-0.956112\pi$
$907$	−18.5000	−	32.0429i	−0.614282	−	1.06397i	0.376228	−	0.926527i	$-0.377221\pi$
$908$		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	$0.334445\pi$
$912$	−1.73205	+	1.00000i	−0.0573539	+	0.0331133i
$913$	−36.0000	−	62.3538i	−1.19143	−	2.06361i
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$			24.0000i			0.793416i
$916$	−11.2583	−	6.50000i	−0.371986	−	0.214766i
$917$	−18.1865	−	10.5000i	−0.600572	−	0.346741i
$918$		−	15.0000i		−	0.495074i
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$	1.73205	−	1.00000i	0.0570730	−	0.0329511i
$922$	9.00000			0.296399
$923$		0			0
$924$	−6.00000			−0.197386
$925$	24.2487	−	14.0000i	0.797293	−	0.460317i
$926$	−20.0000	−	34.6410i	−0.657241	−	1.13837i
$927$	4.00000	−	6.92820i	0.131377	−	0.227552i
$928$			6.00000i			0.196960i
$929$	31.1769	+	18.0000i	1.02288	+	0.590561i	0.914937	−	0.403596i	$-0.132240\pi$
$929$	31.1769	+	18.0000i	1.02288	+	0.590561i	0.107944	+	0.994157i	$0.465573\pi$
$930$	10.3923	+	6.00000i	0.340777	+	0.196748i
$931$		−	12.0000i		−	0.393284i
$932$	13.5000	−	23.3827i	0.442207	−	0.765925i
$933$	−15.0000	−	25.9808i	−0.491078	−	0.850572i
$934$	−31.1769	+	18.0000i	−1.02014	+	0.588978i
$935$	−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	$0.687422\pi$
$938$	−12.1244	+	7.00000i	−0.395874	+	0.228558i
$939$	0.500000	+	0.866025i	0.0163169	+	0.0282617i
$940$	−4.50000	+	7.79423i	−0.146774	+	0.254220i
$941$			21.0000i			0.684580i	0.939594	+	0.342290i	$0.111203\pi$
$941$			21.0000i			0.684580i	−0.939594	+	0.342290i	$0.888797\pi$
$942$	−12.1244	−	7.00000i	−0.395033	−	0.228072i
$943$		0			0
$944$		−	6.00000i		−	0.195283i
$945$	7.50000	−	12.9904i	0.243975	−	0.422577i
$946$	3.00000	+	5.19615i	0.0975384	+	0.168941i
$947$	5.19615	−	3.00000i	0.168852	−	0.0974869i	−0.413192	−	0.910644i	$-0.635586\pi$
$947$	5.19615	−	3.00000i	0.168852	−	0.0974869i	0.582045	+	0.813157i	$0.302253\pi$
$948$	−8.00000			−0.259828
$949$		0			0
$950$	−8.00000			−0.259554
$951$	5.19615	−	3.00000i	0.168497	−	0.0972817i
$952$	1.50000	+	2.59808i	0.0486153	+	0.0842041i
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	−0.718604	−	0.695419i	$-0.755219\pi$
$953$	7.50000	−	12.9904i	0.242949	−	0.420800i	0.961553	+	0.274620i	$0.0885520\pi$
$954$		0			0
$955$	46.7654	+	27.0000i	1.51329	+	0.873699i
$956$	−12.9904	−	7.50000i	−0.420139	−	0.242567i
$957$			36.0000i			1.16371i
$958$	−10.5000	+	18.1865i	−0.339240	+	0.587580i
$959$		0			0
$960$	−2.59808	+	1.50000i	−0.0838525	+	0.0484123i
$961$	15.0000			0.483871
$962$		0			0
$963$	−24.0000			−0.773389
$964$	8.66025	−	5.00000i	0.278928	−	0.161039i
$965$	−6.00000	−	10.3923i	−0.193147	−	0.334540i
$966$		0			0
$967$			31.0000i			0.996893i	0.866921	+	0.498446i	$0.166096\pi$
$967$			31.0000i			0.996893i	−0.866921	+	0.498446i	$0.833904\pi$
$968$	−21.6506	−	12.5000i	−0.695878	−	0.401765i
$969$	5.19615	+	3.00000i	0.166924	+	0.0963739i
$970$		−	30.0000i		−	0.963242i
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	−0.840953	−	0.541108i	$-0.818005\pi$
$971$	1.50000	−	2.59808i	0.0481373	−	0.0833762i	0.889090	+	0.457732i	$0.151338\pi$
$972$	8.00000	+	13.8564i	0.256600	+	0.444444i
$973$	11.2583	−	6.50000i	0.360925	−	0.208380i
$974$	−16.0000			−0.512673
$975$		0			0
$976$	8.00000			0.256074
$977$	46.7654	−	27.0000i	1.49616	−	0.863807i	0.496167	−	0.868227i	$-0.334741\pi$
$977$	46.7654	−	27.0000i	1.49616	−	0.863807i	0.999990	+	0.00442082i	$0.00140720\pi$
$978$	−8.00000	−	13.8564i	−0.255812	−	0.443079i
$979$	−18.0000	+	31.1769i	−0.575282	+	0.996419i
$980$		−	18.0000i		−	0.574989i
$981$	12.1244	+	7.00000i	0.387101	+	0.223493i
$982$	−7.79423	−	4.50000i	−0.248724	−	0.143601i
$983$			39.0000i			1.24391i	0.783054	+	0.621953i	$0.213661\pi$
$983$			39.0000i			1.24391i	−0.783054	+	0.621953i	$0.786339\pi$
$984$		0			0
$985$	−4.50000	−	7.79423i	−0.143382	−	0.248345i
$986$	15.5885	−	9.00000i	0.496438	−	0.286618i
$987$	3.00000			0.0954911
$988$		0			0
$989$		0			0
$990$	31.1769	−	18.0000i	0.990867	−	0.572078i
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	0.849705	−	0.527258i	$-0.176780\pi$
$991$	−1.00000	−	1.73205i	−0.0317660	−	0.0550204i	−0.881471	+	0.472237i	$0.843446\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$		−	8.00000i		−	0.253872i
$994$	−2.59808	−	1.50000i	−0.0824060	−	0.0475771i
$995$	5.19615	+	3.00000i	0.164729	+	0.0951064i
$996$			12.0000i			0.380235i
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	−0.229135	−	0.973395i	$-0.573590\pi$
$997$	23.0000	−	39.8372i	0.728417	−	1.26166i	0.957552	−	0.288261i	$-0.0930771\pi$
$998$	20.0000	+	34.6410i	0.633089	+	1.09654i
$999$	30.3109	−	17.5000i	0.958994	−	0.553675i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.2.e.a.23.2		4
13.2	odd	12		338.2.a.f.1.1		1
13.3	even	3		338.2.b.c.337.2		2
13.4	even	6	inner	338.2.e.a.147.2		4
13.5	odd	4		338.2.c.a.315.1		2
13.6	odd	12		338.2.c.a.191.1		2
13.7	odd	12		338.2.c.d.191.1		2
13.8	odd	4		338.2.c.d.315.1		2
13.9	even	3	inner	338.2.e.a.147.1		4
13.10	even	6		338.2.b.c.337.1		2
13.11	odd	12		26.2.a.a.1.1	✓	1
13.12	even	2	inner	338.2.e.a.23.1		4
39.2	even	12		3042.2.a.a.1.1		1
39.11	even	12		234.2.a.e.1.1		1
39.23	odd	6		3042.2.b.a.1351.2		2
39.29	odd	6		3042.2.b.a.1351.1		2
52.3	odd	6		2704.2.f.d.337.2		2
52.11	even	12		208.2.a.a.1.1		1
52.15	even	12		2704.2.a.f.1.1		1
52.23	odd	6		2704.2.f.d.337.1		2
65.24	odd	12		650.2.a.j.1.1		1
65.37	even	12		650.2.b.d.599.1		2
65.54	odd	12		8450.2.a.c.1.1		1
65.63	even	12		650.2.b.d.599.2		2
91.11	odd	12		1274.2.f.p.79.1		2
91.24	even	12		1274.2.f.r.79.1		2
91.37	odd	12		1274.2.f.p.1145.1		2
91.76	even	12		1274.2.a.d.1.1		1
91.89	even	12		1274.2.f.r.1145.1		2
104.11	even	12		832.2.a.i.1.1		1
104.37	odd	12		832.2.a.d.1.1		1
117.11	even	12		2106.2.e.b.1405.1		2
117.50	even	12		2106.2.e.b.703.1		2
117.76	odd	12		2106.2.e.ba.703.1		2
117.115	odd	12		2106.2.e.ba.1405.1		2
143.76	even	12		3146.2.a.n.1.1		1
156.11	odd	12		1872.2.a.q.1.1		1
195.89	even	12		5850.2.a.p.1.1		1
195.128	odd	12		5850.2.e.a.5149.1		2
195.167	odd	12		5850.2.e.a.5149.2		2
208.11	even	12		3328.2.b.j.1665.2		2
208.37	odd	12		3328.2.b.m.1665.1		2
208.115	even	12		3328.2.b.j.1665.1		2
208.141	odd	12		3328.2.b.m.1665.2		2
221.50	odd	12		7514.2.a.c.1.1		1
247.37	even	12		9386.2.a.j.1.1		1
260.219	even	12		5200.2.a.x.1.1		1
312.11	odd	12		7488.2.a.h.1.1		1
312.245	even	12		7488.2.a.g.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.2.a.a.1.1	✓	1	13.11	odd	12
208.2.a.a.1.1		1	52.11	even	12
234.2.a.e.1.1		1	39.11	even	12
338.2.a.f.1.1		1	13.2	odd	12
338.2.b.c.337.1		2	13.10	even	6
338.2.b.c.337.2		2	13.3	even	3
338.2.c.a.191.1		2	13.6	odd	12
338.2.c.a.315.1		2	13.5	odd	4
338.2.c.d.191.1		2	13.7	odd	12
338.2.c.d.315.1		2	13.8	odd	4
338.2.e.a.23.1		4	13.12	even	2	inner
338.2.e.a.23.2		4	1.1	even	1	trivial
338.2.e.a.147.1		4	13.9	even	3	inner
338.2.e.a.147.2		4	13.4	even	6	inner
650.2.a.j.1.1		1	65.24	odd	12
650.2.b.d.599.1		2	65.37	even	12
650.2.b.d.599.2		2	65.63	even	12
832.2.a.d.1.1		1	104.37	odd	12
832.2.a.i.1.1		1	104.11	even	12
1274.2.a.d.1.1		1	91.76	even	12
1274.2.f.p.79.1		2	91.11	odd	12
1274.2.f.p.1145.1		2	91.37	odd	12
1274.2.f.r.79.1		2	91.24	even	12
1274.2.f.r.1145.1		2	91.89	even	12
1872.2.a.q.1.1		1	156.11	odd	12
2106.2.e.b.703.1		2	117.50	even	12
2106.2.e.b.1405.1		2	117.11	even	12
2106.2.e.ba.703.1		2	117.76	odd	12
2106.2.e.ba.1405.1		2	117.115	odd	12
2704.2.a.f.1.1		1	52.15	even	12
2704.2.f.d.337.1		2	52.23	odd	6
2704.2.f.d.337.2		2	52.3	odd	6
3042.2.a.a.1.1		1	39.2	even	12
3042.2.b.a.1351.1		2	39.29	odd	6
3042.2.b.a.1351.2		2	39.23	odd	6
3146.2.a.n.1.1		1	143.76	even	12
3328.2.b.j.1665.1		2	208.115	even	12
3328.2.b.j.1665.2		2	208.11	even	12
3328.2.b.m.1665.1		2	208.37	odd	12
3328.2.b.m.1665.2		2	208.141	odd	12
5200.2.a.x.1.1		1	260.219	even	12
5850.2.a.p.1.1		1	195.89	even	12
5850.2.e.a.5149.1		2	195.128	odd	12
5850.2.e.a.5149.2		2	195.167	odd	12
7488.2.a.g.1.1		1	312.245	even	12
7488.2.a.h.1.1		1	312.11	odd	12
7514.2.a.c.1.1		1	221.50	odd	12
8450.2.a.c.1.1		1	65.54	odd	12
9386.2.a.j.1.1		1	247.37	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

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

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