LMFDB - Embedded newform 1274.2.f.i.79.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1274,2,Mod(79,1274)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1274, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1274.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1274 = 2 \cdot 7^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1274.f (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:	$10.1729412175$
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 182)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1274.79
Dual form			1274.2.f.i.1145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} -3.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} +5.00000 q^{27} +(2.50000 + 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} -3.00000 q^{41} +8.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-1.50000 + 2.59808i) q^{47} -1.00000 q^{48} -5.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{54} +2.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(-0.500000 + 0.866025i) q^{61} -5.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} +3.00000 q^{69} +12.0000 q^{71} +(1.00000 - 1.73205i) q^{72} +(5.50000 + 9.52628i) q^{73} +(3.50000 + 6.06218i) q^{74} +(-2.50000 + 4.33013i) q^{75} -2.00000 q^{76} +1.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} -12.0000 q^{83} +(-4.00000 + 6.92820i) q^{86} +(1.50000 + 2.59808i) q^{88} +(-9.00000 + 15.5885i) q^{89} -3.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} -17.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 3 q^{11} + q^{12} - 2 q^{13} - q^{16} + 2 q^{18} + 2 q^{19} - 6 q^{22} + 3 q^{23} + q^{24} + 5 q^{25} + q^{26} + 10 q^{27} + 5 q^{31} - q^{32} - 3 q^{33} - 4 q^{36} + 7 q^{37} + 2 q^{38} - q^{39} - 6 q^{41} + 16 q^{43} + 3 q^{44} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 10 q^{50} + q^{52} + 12 q^{53} - 5 q^{54} + 4 q^{57} + 6 q^{59} - q^{61} - 10 q^{62} + 2 q^{64} - 3 q^{66} - 5 q^{67} + 6 q^{69} + 24 q^{71} + 2 q^{72} + 11 q^{73} + 7 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{78} + q^{79} - q^{81} + 3 q^{82} - 24 q^{83} - 8 q^{86} + 3 q^{88} - 18 q^{89} - 6 q^{92} - 5 q^{93} - 3 q^{94} + q^{96} - 34 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 3 * q^11 + q^12 - 2 * q^13 - q^16 + 2 * q^18 + 2 * q^19 - 6 * q^22 + 3 * q^23 + q^24 + 5 * q^25 + q^26 + 10 * q^27 + 5 * q^31 - q^32 - 3 * q^33 - 4 * q^36 + 7 * q^37 + 2 * q^38 - q^39 - 6 * q^41 + 16 * q^43 + 3 * q^44 + 3 * q^46 - 3 * q^47 - 2 * q^48 - 10 * q^50 + q^52 + 12 * q^53 - 5 * q^54 + 4 * q^57 + 6 * q^59 - q^61 - 10 * q^62 + 2 * q^64 - 3 * q^66 - 5 * q^67 + 6 * q^69 + 24 * q^71 + 2 * q^72 + 11 * q^73 + 7 * q^74 - 5 * q^75 - 4 * q^76 + 2 * q^78 + q^79 - q^81 + 3 * q^82 - 24 * q^83 - 8 * q^86 + 3 * q^88 - 18 * q^89 - 6 * q^92 - 5 * q^93 - 3 * q^94 + q^96 - 34 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1274\mathbb{Z}\right)^\times$.

$n$	$197$	$885$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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	$-0.0734519\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i	−0.684819	+	0.728714i	$0.740119\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	−1.00000			−0.408248
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	1.00000	−	1.73205i	0.333333	−	0.577350i
$10$		0			0
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	0.998526	−	0.0542666i	$-0.0172821\pi$
$11$	1.50000	+	2.59808i	0.452267	+	0.783349i	−0.546259	+	0.837616i	$0.683949\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$	1.00000	+	1.73205i	0.235702	+	0.408248i
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	−0.728219	−	0.685344i	$-0.759652\pi$
$19$	1.00000	−	1.73205i	0.229416	−	0.397360i	0.957635	+	0.287984i	$0.0929851\pi$
$20$		0			0
$21$		0			0
$22$	−3.00000			−0.639602
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	0.500000	−	0.866025i	0.0980581	−	0.169842i
$27$	5.00000			0.962250
$28$		0			0
$29$		0			0			−	1.00000i	$-0.5\pi$
$29$		0			0				1.00000i	$0.5\pi$
$30$		0			0
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	0.998322	−	0.0579057i	$-0.0184423\pi$
$31$	2.50000	+	4.33013i	0.449013	+	0.777714i	−0.549309	+	0.835619i	$0.685109\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$		0			0
$35$		0			0
$36$	−2.00000			−0.333333
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	−0.420602	−	0.907245i	$-0.638181\pi$
$37$	3.50000	−	6.06218i	0.575396	−	0.996616i	0.995998	−	0.0893706i	$-0.0284856\pi$
$38$	1.00000	+	1.73205i	0.162221	+	0.280976i
$39$	−0.500000	−	0.866025i	−0.0800641	−	0.138675i
$40$		0			0
$41$	−3.00000			−0.468521			−0.234261	−	0.972174i	$-0.575267\pi$
$41$	−3.00000			−0.468521			−0.234261	+	0.972174i	$0.575267\pi$
$42$		0			0
$43$	8.00000			1.21999			0.609994	−	0.792406i	$-0.291172\pi$
$43$	8.00000			1.21999			0.609994	+	0.792406i	$0.291172\pi$
$44$	1.50000	−	2.59808i	0.226134	−	0.391675i
$45$		0			0
$46$	1.50000	+	2.59808i	0.221163	+	0.383065i
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	−0.954441	−	0.298401i	$-0.903547\pi$
$47$	−1.50000	+	2.59808i	−0.218797	+	0.378968i	0.735643	+	0.677369i	$0.236880\pi$
$48$	−1.00000			−0.144338
$49$		0			0
$50$	−5.00000			−0.707107
$51$		0			0
$52$	0.500000	+	0.866025i	0.0693375	+	0.120096i
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$	−2.50000	+	4.33013i	−0.340207	+	0.589256i
$55$		0			0
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	0.992524	−	0.122047i	$-0.0389457\pi$
$59$	3.00000	+	5.19615i	0.390567	+	0.676481i	−0.601958	+	0.798528i	$0.705612\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$	−5.00000			−0.635001
$63$		0			0
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.50000	−	2.59808i	−0.184637	−	0.319801i
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	0.671932	−	0.740613i	$-0.265465\pi$
$67$	−2.50000	−	4.33013i	−0.305424	−	0.529009i	−0.977356	+	0.211604i	$0.932131\pi$
$68$		0			0
$69$	3.00000			0.361158
$70$		0			0
$71$	12.0000			1.42414			0.712069	−	0.702109i	$-0.247758\pi$
$71$	12.0000			1.42414			0.712069	+	0.702109i	$0.247758\pi$
$72$	1.00000	−	1.73205i	0.117851	−	0.204124i
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$	−2.50000	+	4.33013i	−0.288675	+	0.500000i
$76$	−2.00000			−0.229416
$77$		0			0
$78$	1.00000			0.113228
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	−0.836527	−	0.547926i	$-0.815418\pi$
$79$	0.500000	−	0.866025i	0.0562544	−	0.0974355i	0.892781	+	0.450490i	$0.148751\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	−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			0
$85$		0			0
$86$	−4.00000	+	6.92820i	−0.431331	+	0.747087i
$87$		0			0
$88$	1.50000	+	2.59808i	0.159901	+	0.276956i
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.217354	+	0.976093i	$0.569742\pi$
$89$	−9.00000	+	15.5885i	−0.953998	+	1.65237i	−0.736644	+	0.676280i	$0.763591\pi$
$90$		0			0
$91$		0			0
$92$	−3.00000			−0.312772
$93$	−2.50000	+	4.33013i	−0.259238	+	0.449013i
$94$	−1.50000	−	2.59808i	−0.154713	−	0.267971i
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−17.0000			−1.72609			−0.863044	−	0.505128i	$-0.831445\pi$
$97$	−17.0000			−1.72609			−0.863044	+	0.505128i	$0.831445\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$	−1.00000			−0.0980581
$105$		0			0
$106$	−12.0000			−1.16554
$107$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$107$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$108$	−2.50000	−	4.33013i	−0.240563	−	0.416667i
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	0.814152	−	0.580651i	$-0.197202\pi$
$109$	−1.00000	−	1.73205i	−0.0957826	−	0.165900i	−0.909935	+	0.414751i	$0.863869\pi$
$110$		0			0
$111$	7.00000			0.664411
$112$		0			0
$113$	9.00000			0.846649			0.423324	−	0.905978i	$-0.360863\pi$
$113$	9.00000			0.846649			0.423324	+	0.905978i	$0.360863\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$		0			0
$117$	−1.00000	+	1.73205i	−0.0924500	+	0.160128i
$118$	−6.00000			−0.552345
$119$		0			0
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	−0.500000	−	0.866025i	−0.0452679	−	0.0784063i
$123$	−1.50000	−	2.59808i	−0.135250	−	0.234261i
$124$	2.50000	−	4.33013i	0.224507	−	0.388857i
$125$		0			0
$126$		0			0
$127$	−7.00000			−0.621150			−0.310575	−	0.950549i	$-0.600522\pi$
$127$	−7.00000			−0.621150			−0.310575	+	0.950549i	$0.600522\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	4.00000	+	6.92820i	0.352180	+	0.609994i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	3.00000			0.261116
$133$		0			0
$134$	5.00000			0.431934
$135$		0			0
$136$		0			0
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$	−1.50000	+	2.59808i	−0.127688	+	0.221163i
$139$	4.00000			0.339276			0.169638	−	0.985506i	$-0.445740\pi$
$139$	4.00000			0.339276			0.169638	+	0.985506i	$0.445740\pi$
$140$		0			0
$141$	−3.00000			−0.252646
$142$	−6.00000	+	10.3923i	−0.503509	+	0.872103i
$143$	−1.50000	−	2.59808i	−0.125436	−	0.217262i
$144$	1.00000	+	1.73205i	0.0833333	+	0.144338i
$145$		0			0
$146$	−11.0000			−0.910366
$147$		0			0
$148$	−7.00000			−0.575396
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	−0.376061	−	0.926595i	$-0.622722\pi$
$149$	7.50000	−	12.9904i	0.614424	−	1.06421i	0.990485	−	0.137619i	$-0.0439449\pi$
$150$	−2.50000	−	4.33013i	−0.204124	−	0.353553i
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$	1.00000	−	1.73205i	0.0811107	−	0.140488i
$153$		0			0
$154$		0			0
$155$		0			0
$156$	−0.500000	+	0.866025i	−0.0400320	+	0.0693375i
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	−0.999762	−	0.0217953i	$-0.993062\pi$
$157$	−6.50000	−	11.2583i	−0.518756	−	0.898513i	0.481006	−	0.876717i	$-0.340272\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$	−6.00000	+	10.3923i	−0.475831	+	0.824163i
$160$		0			0
$161$		0			0
$162$	1.00000			0.0785674
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$	1.50000	+	2.59808i	0.117130	+	0.202876i
$165$		0			0
$166$	6.00000	−	10.3923i	0.465690	−	0.806599i
$167$	24.0000			1.85718			0.928588	−	0.371113i	$-0.121024\pi$
$167$	24.0000			1.85718			0.928588	+	0.371113i	$0.121024\pi$
$168$		0			0
$169$	1.00000			0.0769231
$170$		0			0
$171$	−2.00000	−	3.46410i	−0.152944	−	0.264906i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$		0			0
$175$		0			0
$176$	−3.00000			−0.226134
$177$	−3.00000	+	5.19615i	−0.225494	+	0.390567i
$178$	−9.00000	−	15.5885i	−0.674579	−	1.16840i
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	0.956088	−	0.293079i	$-0.0946798\pi$
$179$	3.00000	+	5.19615i	0.224231	+	0.388379i	−0.731858	+	0.681457i	$0.761346\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$		0			0
$183$	−1.00000			−0.0739221
$184$	1.50000	−	2.59808i	0.110581	−	0.191533i
$185$		0			0
$186$	−2.50000	−	4.33013i	−0.183309	−	0.317500i
$187$		0			0
$188$	3.00000			0.218797
$189$		0			0
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	0.928986	−	0.370116i	$-0.120682\pi$
$193$	2.00000	+	3.46410i	0.143963	+	0.249351i	−0.785022	+	0.619467i	$0.787349\pi$
$194$	8.50000	−	14.7224i	0.610264	−	1.05701i
$195$		0			0
$196$		0			0
$197$	−3.00000			−0.213741			−0.106871	−	0.994273i	$-0.534083\pi$
$197$	−3.00000			−0.213741			−0.106871	+	0.994273i	$0.534083\pi$
$198$	−3.00000	+	5.19615i	−0.213201	+	0.369274i
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$	2.50000	+	4.33013i	0.176777	+	0.306186i
$201$	2.50000	−	4.33013i	0.176336	−	0.305424i
$202$	3.00000			0.211079
$203$		0			0
$204$		0			0
$205$		0			0
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	−3.00000	−	5.19615i	−0.208514	−	0.361158i
$208$	0.500000	−	0.866025i	0.0346688	−	0.0600481i
$209$	6.00000			0.415029
$210$		0			0
$211$	−22.0000			−1.51454			−0.757271	−	0.653101i	$-0.773468\pi$
$211$	−22.0000			−1.51454			−0.757271	+	0.653101i	$0.773468\pi$
$212$	6.00000	−	10.3923i	0.412082	−	0.713746i
$213$	6.00000	+	10.3923i	0.411113	+	0.712069i
$214$		0			0
$215$		0			0
$216$	5.00000			0.340207
$217$		0			0
$218$	2.00000			0.135457
$219$	−5.50000	+	9.52628i	−0.371656	+	0.643726i
$220$		0			0
$221$		0			0
$222$	−3.50000	+	6.06218i	−0.234905	+	0.406867i
$223$	1.00000			0.0669650			0.0334825	−	0.999439i	$-0.489340\pi$
$223$	1.00000			0.0669650			0.0334825	+	0.999439i	$0.489340\pi$
$224$		0			0
$225$	10.0000			0.666667
$226$	−4.50000	+	7.79423i	−0.299336	+	0.518464i
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	−0.921903	−	0.387421i	$-0.873366\pi$
$227$	−12.0000	−	20.7846i	−0.796468	−	1.37952i	0.125435	−	0.992102i	$-0.459967\pi$
$228$	−1.00000	−	1.73205i	−0.0662266	−	0.114708i
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	−0.924510	−	0.381157i	$-0.875526\pi$
$229$	−2.00000	+	3.46410i	−0.132164	+	0.228914i	0.792347	+	0.610071i	$0.208859\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	−0.910968	−	0.412477i	$-0.864664\pi$
$233$	−1.50000	+	2.59808i	−0.0982683	+	0.170206i	0.812700	+	0.582683i	$0.197997\pi$
$234$	−1.00000	−	1.73205i	−0.0653720	−	0.113228i
$235$		0			0
$236$	3.00000	−	5.19615i	0.195283	−	0.338241i
$237$	1.00000			0.0649570
$238$		0			0
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	0.892058	+	0.451920i	$0.149261\pi$
$241$	13.0000	+	22.5167i	0.837404	+	1.45043i	−0.0546547	+	0.998505i	$0.517406\pi$
$242$	1.00000	+	1.73205i	0.0642824	+	0.111340i
$243$	8.00000	−	13.8564i	0.513200	−	0.888889i
$244$	1.00000			0.0640184
$245$		0			0
$246$	3.00000			0.191273
$247$	−1.00000	+	1.73205i	−0.0636285	+	0.110208i
$248$	2.50000	+	4.33013i	0.158750	+	0.274963i
$249$	−6.00000	−	10.3923i	−0.380235	−	0.658586i
$250$		0			0
$251$	15.0000			0.946792			0.473396	−	0.880850i	$-0.343028\pi$
$251$	15.0000			0.946792			0.473396	+	0.880850i	$0.343028\pi$
$252$		0			0
$253$	9.00000			0.565825
$254$	3.50000	−	6.06218i	0.219610	−	0.380375i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.0000	−	20.7846i	0.748539	−	1.29651i	−0.199983	−	0.979799i	$-0.564089\pi$
$257$	12.0000	−	20.7846i	0.748539	−	1.29651i	0.948523	−	0.316709i	$-0.102578\pi$
$258$	−8.00000			−0.498058
$259$		0			0
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	−0.952517	−	0.304487i	$-0.901515\pi$
$263$	−12.0000	−	20.7846i	−0.739952	−	1.28163i	0.212565	−	0.977147i	$-0.431818\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$		0			0
$267$	−18.0000			−1.10158
$268$	−2.50000	+	4.33013i	−0.152712	+	0.264505i
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	0.695606	−	0.718423i	$-0.255136\pi$
$269$	−4.50000	−	7.79423i	−0.274370	−	0.475223i	−0.969976	+	0.243201i	$0.921803\pi$
$270$		0			0
$271$	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	$0.0582339\pi$
$272$		0			0
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−7.50000	+	12.9904i	−0.452267	+	0.783349i
$276$	−1.50000	−	2.59808i	−0.0902894	−	0.156386i
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−13.0000	−	22.5167i	−0.781094	−	1.35290i	0.150210	−	0.988654i	$-0.452005\pi$
$278$	−2.00000	+	3.46410i	−0.119952	+	0.207763i
$279$	10.0000			0.598684
$280$		0			0
$281$	12.0000			0.715860			0.357930	−	0.933748i	$-0.383483\pi$
$281$	12.0000			0.715860			0.357930	+	0.933748i	$0.383483\pi$
$282$	1.50000	−	2.59808i	0.0893237	−	0.154713i
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.797283	−	0.603606i	$-0.793730\pi$
$283$	−15.5000	−	26.8468i	−0.921379	−	1.59588i	−0.124096	−	0.992270i	$-0.539603\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	3.00000			0.177394
$287$		0			0
$288$	−2.00000			−0.117851
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$		0			0
$291$	−8.50000	−	14.7224i	−0.498279	−	0.863044i
$292$	5.50000	−	9.52628i	0.321863	−	0.557483i
$293$	−18.0000			−1.05157			−0.525786	−	0.850617i	$-0.676229\pi$
$293$	−18.0000			−1.05157			−0.525786	+	0.850617i	$0.676229\pi$
$294$		0			0
$295$		0			0
$296$	3.50000	−	6.06218i	0.203433	−	0.352357i
$297$	7.50000	+	12.9904i	0.435194	+	0.753778i
$298$	7.50000	+	12.9904i	0.434463	+	0.752513i
$299$	−1.50000	+	2.59808i	−0.0867472	+	0.150251i
$300$	5.00000			0.288675
$301$		0			0
$302$	8.00000			0.460348
$303$	1.50000	−	2.59808i	0.0861727	−	0.149256i
$304$	1.00000	+	1.73205i	0.0573539	+	0.0993399i
$305$		0			0
$306$		0			0
$307$	16.0000			0.913168			0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000			0.913168			0.456584	+	0.889680i	$0.349073\pi$
$308$		0			0
$309$	14.0000			0.796432
$310$		0			0
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	−0.500000	−	0.866025i	−0.0283069	−	0.0490290i
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	−0.220006	−	0.975499i	$-0.570608\pi$
$313$	13.0000	−	22.5167i	0.734803	−	1.27272i	0.954810	−	0.297218i	$-0.0960589\pi$
$314$	13.0000			0.733632
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	−0.820822	−	0.571184i	$-0.806484\pi$
$317$	1.50000	−	2.59808i	0.0842484	−	0.145922i	0.905071	+	0.425261i	$0.139818\pi$
$318$	−6.00000	−	10.3923i	−0.336463	−	0.582772i
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	−2.50000	−	4.33013i	−0.138675	−	0.240192i
$326$	−10.0000	−	17.3205i	−0.553849	−	0.959294i
$327$	1.00000	−	1.73205i	0.0553001	−	0.0957826i
$328$	−3.00000			−0.165647
$329$		0			0
$330$		0			0
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	−0.477500	−	0.878632i	$-0.658457\pi$
$331$	9.50000	−	16.4545i	0.522167	−	0.904420i	0.999667	−	0.0257885i	$-0.00820965\pi$
$332$	6.00000	+	10.3923i	0.329293	+	0.570352i
$333$	−7.00000	−	12.1244i	−0.383598	−	0.664411i
$334$	−12.0000	+	20.7846i	−0.656611	+	1.13728i
$335$		0			0
$336$		0			0
$337$	−31.0000			−1.68868			−0.844339	−	0.535810i	$-0.820006\pi$
$337$	−31.0000			−1.68868			−0.844339	+	0.535810i	$0.820006\pi$
$338$	−0.500000	+	0.866025i	−0.0271964	+	0.0471056i
$339$	4.50000	+	7.79423i	0.244406	+	0.423324i
$340$		0			0
$341$	−7.50000	+	12.9904i	−0.406148	+	0.703469i
$342$	4.00000			0.216295
$343$		0			0
$344$	8.00000			0.431331
$345$		0			0
$346$	−9.00000	−	15.5885i	−0.483843	−	0.838041i
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	−0.984487	−	0.175457i	$-0.943860\pi$
$347$	−12.0000	−	20.7846i	−0.644194	−	1.11578i	0.340293	−	0.940319i	$-0.389474\pi$
$348$		0			0
$349$	10.0000			0.535288			0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000			0.535288			0.267644	+	0.963518i	$0.413755\pi$
$350$		0			0
$351$	−5.00000			−0.266880
$352$	1.50000	−	2.59808i	0.0799503	−	0.138478i
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	0.993626	−	0.112731i	$-0.0359599\pi$
$353$	7.50000	+	12.9904i	0.399185	+	0.691408i	−0.594441	+	0.804139i	$0.702627\pi$
$354$	−3.00000	−	5.19615i	−0.159448	−	0.276172i
$355$		0			0
$356$	18.0000			0.953998
$357$		0			0
$358$	−6.00000			−0.317110
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	−0.353529	−	0.935423i	$-0.615019\pi$
$359$	12.0000	−	20.7846i	0.633336	−	1.09697i	0.986865	−	0.161546i	$-0.0516481\pi$
$360$		0			0
$361$	7.50000	+	12.9904i	0.394737	+	0.683704i
$362$	−3.50000	+	6.06218i	−0.183956	+	0.318621i
$363$	2.00000			0.104973
$364$		0			0
$365$		0			0
$366$	0.500000	−	0.866025i	0.0261354	−	0.0452679i
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	−0.956544	−	0.291587i	$-0.905817\pi$
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	0.225750	−	0.974185i	$-0.427517\pi$
$368$	1.50000	+	2.59808i	0.0781929	+	0.135434i
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$		0			0
$371$		0			0
$372$	5.00000			0.259238
$373$	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	$0.133645\pi$
$374$		0			0
$375$		0			0
$376$	−1.50000	+	2.59808i	−0.0773566	+	0.133986i
$377$		0			0
$378$		0			0
$379$	−16.0000			−0.821865			−0.410932	−	0.911666i	$-0.634797\pi$
$379$	−16.0000			−0.821865			−0.410932	+	0.911666i	$0.634797\pi$
$380$		0			0
$381$	−3.50000	−	6.06218i	−0.179310	−	0.310575i
$382$		0			0
$383$	1.50000	−	2.59808i	0.0766464	−	0.132755i	−0.825155	−	0.564907i	$-0.808912\pi$
$383$	1.50000	−	2.59808i	0.0766464	−	0.132755i	0.901801	+	0.432151i	$0.142245\pi$
$384$	−1.00000			−0.0510310
$385$		0			0
$386$	−4.00000			−0.203595
$387$	8.00000	−	13.8564i	0.406663	−	0.704361i
$388$	8.50000	+	14.7224i	0.431522	+	0.747418i
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.810326	+	0.585980i	$0.199290\pi$
$389$	18.0000	+	31.1769i	0.912636	+	1.58073i	0.102311	+	0.994753i	$0.467376\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	1.50000	−	2.59808i	0.0755689	−	0.130889i
$395$		0			0
$396$	−3.00000	−	5.19615i	−0.150756	−	0.261116i
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	−0.498112	−	0.867113i	$-0.665973\pi$
$397$	10.0000	−	17.3205i	0.501886	−	0.869291i	0.999998	−	0.00217869i	$-0.000693499\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	−5.00000			−0.250000
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	0.393680	+	0.919247i	$0.371202\pi$
$401$	−12.0000	+	20.7846i	−0.599251	+	1.03793i	−0.992932	+	0.118686i	$0.962132\pi$
$402$	2.50000	+	4.33013i	0.124689	+	0.215967i
$403$	−2.50000	−	4.33013i	−0.124534	−	0.215699i
$404$	−1.50000	+	2.59808i	−0.0746278	+	0.129259i
$405$		0			0
$406$		0			0
$407$	21.0000			1.04093
$408$		0			0
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	−0.998674	−	0.0514740i	$-0.983608\pi$
$409$	−11.0000	−	19.0526i	−0.543915	−	0.942088i	0.454759	−	0.890614i	$-0.349725\pi$
$410$		0			0
$411$	−3.00000	+	5.19615i	−0.147979	+	0.256307i
$412$	−14.0000			−0.689730
$413$		0			0
$414$	6.00000			0.294884
$415$		0			0
$416$	0.500000	+	0.866025i	0.0245145	+	0.0424604i
$417$	2.00000	+	3.46410i	0.0979404	+	0.169638i
$418$	−3.00000	+	5.19615i	−0.146735	+	0.254152i
$419$	−21.0000			−1.02592			−0.512959	−	0.858413i	$-0.671451\pi$
$419$	−21.0000			−1.02592			−0.512959	+	0.858413i	$0.671451\pi$
$420$		0			0
$421$	−37.0000			−1.80327			−0.901635	−	0.432498i	$-0.857632\pi$
$421$	−37.0000			−1.80327			−0.901635	+	0.432498i	$0.857632\pi$
$422$	11.0000	−	19.0526i	0.535472	−	0.927464i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	6.00000	+	10.3923i	0.291386	+	0.504695i
$425$		0			0
$426$	−12.0000			−0.581402
$427$		0			0
$428$		0			0
$429$	1.50000	−	2.59808i	0.0724207	−	0.125436i
$430$		0			0
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	0.929188	−	0.369607i	$-0.120508\pi$
$431$	3.00000	+	5.19615i	0.144505	+	0.250290i	−0.784683	+	0.619897i	$0.787174\pi$
$432$	−2.50000	+	4.33013i	−0.120281	+	0.208333i
$433$	−38.0000			−1.82616			−0.913082	−	0.407777i	$-0.866304\pi$
$433$	−38.0000			−1.82616			−0.913082	+	0.407777i	$0.866304\pi$
$434$		0			0
$435$		0			0
$436$	−1.00000	+	1.73205i	−0.0478913	+	0.0829502i
$437$	−3.00000	−	5.19615i	−0.143509	−	0.248566i
$438$	−5.50000	−	9.52628i	−0.262800	−	0.455183i
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	−0.368945	−	0.929451i	$-0.620281\pi$
$439$	13.0000	−	22.5167i	0.620456	−	1.07466i	0.989401	−	0.145210i	$-0.0463858\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	0.426414	+	0.904528i	$0.359777\pi$
$443$	−12.0000	+	20.7846i	−0.570137	+	0.987507i	−0.996551	+	0.0829786i	$0.973557\pi$
$444$	−3.50000	−	6.06218i	−0.166103	−	0.287698i
$445$		0			0
$446$	−0.500000	+	0.866025i	−0.0236757	+	0.0410075i
$447$	15.0000			0.709476
$448$		0			0
$449$	−6.00000			−0.283158			−0.141579	−	0.989927i	$-0.545218\pi$
$449$	−6.00000			−0.283158			−0.141579	+	0.989927i	$0.545218\pi$
$450$	−5.00000	+	8.66025i	−0.235702	+	0.408248i
$451$	−4.50000	−	7.79423i	−0.211897	−	0.367016i
$452$	−4.50000	−	7.79423i	−0.211662	−	0.366610i
$453$	4.00000	−	6.92820i	0.187936	−	0.325515i
$454$	24.0000			1.12638
$455$		0			0
$456$	2.00000			0.0936586
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	0.383437	+	0.923567i	$0.374740\pi$
$457$	−13.0000	+	22.5167i	−0.608114	+	1.05328i	−0.991551	+	0.129718i	$0.958593\pi$
$458$	−2.00000	−	3.46410i	−0.0934539	−	0.161867i
$459$		0			0
$460$		0			0
$461$	−24.0000			−1.11779			−0.558896	−	0.829238i	$-0.688775\pi$
$461$	−24.0000			−1.11779			−0.558896	+	0.829238i	$0.688775\pi$
$462$		0			0
$463$	−40.0000			−1.85896			−0.929479	−	0.368875i	$-0.879743\pi$
$463$	−40.0000			−1.85896			−0.929479	+	0.368875i	$0.879743\pi$
$464$		0			0
$465$		0			0
$466$	−1.50000	−	2.59808i	−0.0694862	−	0.120354i
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	−0.693153	−	0.720791i	$-0.743779\pi$
$467$	6.00000	−	10.3923i	0.277647	−	0.480899i	0.970799	+	0.239892i	$0.0771121\pi$
$468$	2.00000			0.0924500
$469$		0			0
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	12.0000	+	20.7846i	0.551761	+	0.955677i
$474$	−0.500000	+	0.866025i	−0.0229658	+	0.0397779i
$475$	10.0000			0.458831
$476$		0			0
$477$	24.0000			1.09888
$478$	−3.00000	+	5.19615i	−0.137217	+	0.237666i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	−3.50000	+	6.06218i	−0.159586	+	0.276412i
$482$	−26.0000			−1.18427
$483$		0			0
$484$	−2.00000			−0.0909091
$485$		0			0
$486$	8.00000	+	13.8564i	0.362887	+	0.628539i
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	0.842479	−	0.538730i	$-0.181096\pi$
$487$	−1.00000	−	1.73205i	−0.0453143	−	0.0784867i	−0.887793	+	0.460243i	$0.847762\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$	−20.0000			−0.904431
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	−1.50000	+	2.59808i	−0.0676252	+	0.117130i
$493$		0			0
$494$	−1.00000	−	1.73205i	−0.0449921	−	0.0779287i
$495$		0			0
$496$	−5.00000			−0.224507
$497$		0			0
$498$	12.0000			0.537733
$499$	−11.5000	+	19.9186i	−0.514811	+	0.891678i	0.485042	+	0.874491i	$0.338804\pi$
$499$	−11.5000	+	19.9186i	−0.514811	+	0.891678i	−0.999852	+	0.0171872i	$0.994529\pi$
$500$		0			0
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$	−7.50000	+	12.9904i	−0.334741	+	0.579789i
$503$	−12.0000			−0.535054			−0.267527	−	0.963550i	$-0.586206\pi$
$503$	−12.0000			−0.535054			−0.267527	+	0.963550i	$0.586206\pi$
$504$		0			0
$505$		0			0
$506$	−4.50000	+	7.79423i	−0.200049	+	0.346496i
$507$	0.500000	+	0.866025i	0.0222058	+	0.0384615i
$508$	3.50000	+	6.06218i	0.155287	+	0.268966i
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	0.314459	+	0.949271i	$0.398177\pi$
$509$	−15.0000	+	25.9808i	−0.664863	+	1.15158i	−0.979322	+	0.202306i	$0.935156\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$	5.00000	−	8.66025i	0.220755	−	0.382360i
$514$	12.0000	+	20.7846i	0.529297	+	0.916770i
$515$		0			0
$516$	4.00000	−	6.92820i	0.176090	−	0.304997i
$517$	−9.00000			−0.395820
$518$		0			0
$519$	−18.0000			−0.790112
$520$		0			0
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	0.924229	−	0.381839i	$-0.124709\pi$
$521$	3.00000	+	5.19615i	0.131432	+	0.227648i	−0.792797	+	0.609486i	$0.791376\pi$
$522$		0			0
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	−0.932345	−	0.361569i	$-0.882241\pi$
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	0.779301	+	0.626650i	$0.215574\pi$
$524$		0			0
$525$		0			0
$526$	24.0000			1.04645
$527$		0			0
$528$	−1.50000	−	2.59808i	−0.0652791	−	0.113067i
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$	3.00000			0.129944
$534$	9.00000	−	15.5885i	0.389468	−	0.674579i
$535$		0			0
$536$	−2.50000	−	4.33013i	−0.107984	−	0.187033i
$537$	−3.00000	+	5.19615i	−0.129460	+	0.224231i
$538$	9.00000			0.388018
$539$		0			0
$540$		0			0
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	−0.225617	−	0.974216i	$-0.572440\pi$
$541$	17.0000	−	29.4449i	0.730887	−	1.26593i	0.956504	−	0.291718i	$-0.0942267\pi$
$542$	5.50000	+	9.52628i	0.236245	+	0.409189i
$543$	3.50000	+	6.06218i	0.150199	+	0.260153i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	1.00000	+	1.73205i	0.0426790	+	0.0739221i
$550$	−7.50000	−	12.9904i	−0.319801	−	0.553912i
$551$		0			0
$552$	3.00000			0.127688
$553$		0			0
$554$	26.0000			1.10463
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	0.980026	−	0.198871i	$-0.0637276\pi$
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	−0.662240	+	0.749291i	$0.730394\pi$
$558$	−5.00000	+	8.66025i	−0.211667	+	0.366618i
$559$	−8.00000			−0.338364
$560$		0			0
$561$		0			0
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	−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	$-0.473712\pi$
$564$	1.50000	+	2.59808i	0.0631614	+	0.109399i
$565$		0			0
$566$	31.0000			1.30303
$567$		0			0
$568$	12.0000			0.503509
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	−0.997703	−	0.0677445i	$-0.978420\pi$
$569$	−10.5000	+	18.1865i	−0.440183	+	0.762419i	0.557520	+	0.830164i	$0.311753\pi$
$570$		0			0
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	0.998978	−	0.0452101i	$-0.0143957\pi$
$571$	11.0000	+	19.0526i	0.460336	+	0.797325i	−0.538642	+	0.842535i	$0.681062\pi$
$572$	−1.50000	+	2.59808i	−0.0627182	+	0.108631i
$573$		0			0
$574$		0			0
$575$	15.0000			0.625543
$576$	1.00000	−	1.73205i	0.0416667	−	0.0721688i
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	0.886090	−	0.463513i	$-0.153411\pi$
$577$	1.00000	+	1.73205i	0.0416305	+	0.0721062i	−0.844459	+	0.535620i	$0.820078\pi$
$578$	8.50000	+	14.7224i	0.353553	+	0.612372i
$579$	−2.00000	+	3.46410i	−0.0831172	+	0.143963i
$580$		0			0
$581$		0			0
$582$	17.0000			0.704673
$583$	−18.0000	+	31.1769i	−0.745484	+	1.29122i
$584$	5.50000	+	9.52628i	0.227592	+	0.394200i
$585$		0			0
$586$	9.00000	−	15.5885i	0.371787	−	0.643953i
$587$	−18.0000			−0.742940			−0.371470	−	0.928445i	$-0.621146\pi$
$587$	−18.0000			−0.742940			−0.371470	+	0.928445i	$0.621146\pi$
$588$		0			0
$589$	10.0000			0.412043
$590$		0			0
$591$	−1.50000	−	2.59808i	−0.0617018	−	0.106871i
$592$	3.50000	+	6.06218i	0.143849	+	0.249154i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$	−15.0000			−0.615457
$595$		0			0
$596$	−15.0000			−0.614424
$597$	8.00000	−	13.8564i	0.327418	−	0.567105i
$598$	−1.50000	−	2.59808i	−0.0613396	−	0.106243i
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	−0.921723	−	0.387849i	$-0.873218\pi$
$599$	−19.5000	−	33.7750i	−0.796748	−	1.38001i	0.124975	−	0.992160i	$-0.460115\pi$
$600$	−2.50000	+	4.33013i	−0.102062	+	0.176777i
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	−10.0000			−0.407231
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$		0			0
$606$	1.50000	+	2.59808i	0.0609333	+	0.105540i
$607$	7.00000	−	12.1244i	0.284121	−	0.492112i	−0.688274	−	0.725450i	$-0.741632\pi$
$607$	7.00000	−	12.1244i	0.284121	−	0.492112i	0.972396	+	0.233338i	$0.0749648\pi$
$608$	−2.00000			−0.0811107
$609$		0			0
$610$		0			0
$611$	1.50000	−	2.59808i	0.0606835	−	0.105107i
$612$		0			0
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	0.999984	+	0.00563283i	$0.00179300\pi$
$613$	12.5000	+	21.6506i	0.504870	+	0.874461i	−0.495114	+	0.868828i	$0.664874\pi$
$614$	−8.00000	+	13.8564i	−0.322854	+	0.559199i
$615$		0			0
$616$		0			0
$617$	18.0000			0.724653			0.362326	−	0.932051i	$-0.381983\pi$
$617$	18.0000			0.724653			0.362326	+	0.932051i	$0.381983\pi$
$618$	−7.00000	+	12.1244i	−0.281581	+	0.487713i
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	0.747873	−	0.663842i	$-0.231075\pi$
$619$	−5.00000	−	8.66025i	−0.200967	−	0.348085i	−0.948840	+	0.315757i	$0.897742\pi$
$620$		0			0
$621$	7.50000	−	12.9904i	0.300965	−	0.521286i
$622$	−30.0000			−1.20289
$623$		0			0
$624$	1.00000			0.0400320
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	13.0000	+	22.5167i	0.519584	+	0.899947i
$627$	3.00000	+	5.19615i	0.119808	+	0.207514i
$628$	−6.50000	+	11.2583i	−0.259378	+	0.449256i
$629$		0			0
$630$		0			0
$631$	−34.0000			−1.35352			−0.676759	−	0.736204i	$-0.736616\pi$
$631$	−34.0000			−1.35352			−0.676759	+	0.736204i	$0.736616\pi$
$632$	0.500000	−	0.866025i	0.0198889	−	0.0344486i
$633$	−11.0000	−	19.0526i	−0.437211	−	0.757271i
$634$	1.50000	+	2.59808i	0.0595726	+	0.103183i
$635$		0			0
$636$	12.0000			0.475831
$637$		0			0
$638$		0			0
$639$	12.0000	−	20.7846i	0.474713	−	0.822226i
$640$		0			0
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	0.982708	+	0.185164i	$0.0592817\pi$
$641$	16.5000	+	28.5788i	0.651711	+	1.12880i	−0.330997	+	0.943632i	$0.607385\pi$
$642$		0			0
$643$	−32.0000			−1.26196			−0.630978	−	0.775800i	$-0.717346\pi$
$643$	−32.0000			−1.26196			−0.630978	+	0.775800i	$0.717346\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	0.959529	−	0.281609i	$-0.0908680\pi$
$647$	6.00000	+	10.3923i	0.235884	+	0.408564i	−0.723645	+	0.690172i	$0.757535\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−9.00000	+	15.5885i	−0.353281	+	0.611900i
$650$	5.00000			0.196116
$651$		0			0
$652$	20.0000			0.783260
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	−0.999396	−	0.0347583i	$-0.988934\pi$
$653$	−12.0000	+	20.7846i	−0.469596	+	0.813365i	0.529799	+	0.848123i	$0.322267\pi$
$654$	1.00000	+	1.73205i	0.0391031	+	0.0677285i
$655$		0			0
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$	22.0000			0.858302
$658$		0			0
$659$	42.0000			1.63609			0.818044	−	0.575156i	$-0.195059\pi$
$659$	42.0000			1.63609			0.818044	+	0.575156i	$0.195059\pi$
$660$		0			0
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	0.989051	+	0.147573i	$0.0471463\pi$
$661$	16.0000	+	27.7128i	0.622328	+	1.07790i	−0.366723	+	0.930330i	$0.619520\pi$
$662$	9.50000	+	16.4545i	0.369228	+	0.639522i
$663$		0			0
$664$	−12.0000			−0.465690
$665$		0			0
$666$	14.0000			0.542489
$667$		0			0
$668$	−12.0000	−	20.7846i	−0.464294	−	0.804181i
$669$	0.500000	+	0.866025i	0.0193311	+	0.0334825i
$670$		0			0
$671$	−3.00000			−0.115814
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	15.5000	−	26.8468i	0.597038	−	1.03410i
$675$	12.5000	+	21.6506i	0.481125	+	0.833333i
$676$	−0.500000	−	0.866025i	−0.0192308	−	0.0333087i
$677$	−19.5000	+	33.7750i	−0.749446	+	1.29808i	0.198643	+	0.980072i	$0.436347\pi$
$677$	−19.5000	+	33.7750i	−0.749446	+	1.29808i	−0.948089	+	0.318006i	$0.896987\pi$
$678$	−9.00000			−0.345643
$679$		0			0
$680$		0			0
$681$	12.0000	−	20.7846i	0.459841	−	0.796468i
$682$	−7.50000	−	12.9904i	−0.287190	−	0.497427i
$683$	13.5000	+	23.3827i	0.516563	+	0.894714i	0.999815	+	0.0192323i	$0.00612219\pi$
$683$	13.5000	+	23.3827i	0.516563	+	0.894714i	−0.483252	+	0.875481i	$0.660544\pi$
$684$	−2.00000	+	3.46410i	−0.0764719	+	0.132453i
$685$		0			0
$686$		0			0
$687$	−4.00000			−0.152610
$688$	−4.00000	+	6.92820i	−0.152499	+	0.264135i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		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	$0.118041\pi$
$692$	18.0000			0.684257
$693$		0			0
$694$	24.0000			0.911028
$695$		0			0
$696$		0			0
$697$		0			0
$698$	−5.00000	+	8.66025i	−0.189253	+	0.327795i
$699$	−3.00000			−0.113470
$700$		0			0
$701$	−36.0000			−1.35970			−0.679851	−	0.733351i	$-0.737955\pi$
$701$	−36.0000			−1.35970			−0.679851	+	0.733351i	$0.737955\pi$
$702$	2.50000	−	4.33013i	0.0943564	−	0.163430i
$703$	−7.00000	−	12.1244i	−0.264010	−	0.457279i
$704$	1.50000	+	2.59808i	0.0565334	+	0.0979187i
$705$		0			0
$706$	−15.0000			−0.564532
$707$		0			0
$708$	6.00000			0.225494
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	0.324104	+	0.946021i	$0.394937\pi$
$709$	−17.5000	+	30.3109i	−0.657226	+	1.13835i	−0.981331	+	0.192328i	$0.938396\pi$
$710$		0			0
$711$	−1.00000	−	1.73205i	−0.0375029	−	0.0649570i
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$	15.0000			0.561754
$714$		0			0
$715$		0			0
$716$	3.00000	−	5.19615i	0.112115	−	0.194189i
$717$	3.00000	+	5.19615i	0.112037	+	0.194054i
$718$	12.0000	+	20.7846i	0.447836	+	0.775675i
$719$	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	$0.130979\pi$
$720$		0			0
$721$		0			0
$722$	−15.0000			−0.558242
$723$	−13.0000	+	22.5167i	−0.483475	+	0.837404i
$724$	−3.50000	−	6.06218i	−0.130076	−	0.225299i
$725$		0			0
$726$	−1.00000	+	1.73205i	−0.0371135	+	0.0642824i
$727$	−26.0000			−0.964287			−0.482143	−	0.876092i	$-0.660142\pi$
$727$	−26.0000			−0.964287			−0.482143	+	0.876092i	$0.660142\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$		0			0
$732$	0.500000	+	0.866025i	0.0184805	+	0.0320092i
$733$	−2.00000	+	3.46410i	−0.0738717	+	0.127950i	−0.900595	−	0.434659i	$-0.856869\pi$
$733$	−2.00000	+	3.46410i	−0.0738717	+	0.127950i	0.826723	+	0.562609i	$0.190202\pi$
$734$	28.0000			1.03350
$735$		0			0
$736$	−3.00000			−0.110581
$737$	7.50000	−	12.9904i	0.276266	−	0.478507i
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	0.974818	−	0.223001i	$-0.0715853\pi$
$739$	8.00000	+	13.8564i	0.294285	+	0.509716i	−0.680534	+	0.732717i	$0.738252\pi$
$740$		0			0
$741$	−2.00000			−0.0734718
$742$		0			0
$743$	−24.0000			−0.880475			−0.440237	−	0.897881i	$-0.645106\pi$
$743$	−24.0000			−0.880475			−0.440237	+	0.897881i	$0.645106\pi$
$744$	−2.50000	+	4.33013i	−0.0916544	+	0.158750i
$745$		0			0
$746$	2.00000	+	3.46410i	0.0732252	+	0.126830i
$747$	−12.0000	+	20.7846i	−0.439057	+	0.760469i
$748$		0			0
$749$		0			0
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$	−1.50000	−	2.59808i	−0.0546994	−	0.0947421i
$753$	7.50000	+	12.9904i	0.273315	+	0.473396i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	38.0000			1.38113			0.690567	−	0.723269i	$-0.257361\pi$
$757$	38.0000			1.38113			0.690567	+	0.723269i	$0.257361\pi$
$758$	8.00000	−	13.8564i	0.290573	−	0.503287i
$759$	4.50000	+	7.79423i	0.163340	+	0.282913i
$760$		0			0
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	−0.837557	−	0.546350i	$-0.816017\pi$
$761$	1.50000	−	2.59808i	0.0543750	−	0.0941802i	0.891932	+	0.452170i	$0.149350\pi$
$762$	7.00000			0.253583
$763$		0			0
$764$		0			0
$765$		0			0
$766$	1.50000	+	2.59808i	0.0541972	+	0.0938723i
$767$	−3.00000	−	5.19615i	−0.108324	−	0.187622i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	13.0000			0.468792			0.234396	−	0.972141i	$-0.424689\pi$
$769$	13.0000			0.468792			0.234396	+	0.972141i	$0.424689\pi$
$770$		0			0
$771$	24.0000			0.864339
$772$	2.00000	−	3.46410i	0.0719816	−	0.124676i
$773$	−27.0000	−	46.7654i	−0.971123	−	1.68203i	−0.692179	−	0.721726i	$-0.743349\pi$
$773$	−27.0000	−	46.7654i	−0.971123	−	1.68203i	−0.278944	−	0.960307i	$-0.589984\pi$
$774$	8.00000	+	13.8564i	0.287554	+	0.498058i
$775$	−12.5000	+	21.6506i	−0.449013	+	0.777714i
$776$	−17.0000			−0.610264
$777$		0			0
$778$	−36.0000			−1.29066
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$		0			0
$784$		0			0
$785$		0			0
$786$		0			0
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	0.996531	+	0.0832226i	$0.0265213\pi$
$787$	16.0000	+	27.7128i	0.570338	+	0.987855i	−0.426193	+	0.904632i	$0.640145\pi$
$788$	1.50000	+	2.59808i	0.0534353	+	0.0925526i
$789$	12.0000	−	20.7846i	0.427211	−	0.739952i
$790$		0			0
$791$		0			0
$792$	6.00000			0.213201
$793$	0.500000	−	0.866025i	0.0177555	−	0.0307535i
$794$	10.0000	+	17.3205i	0.354887	+	0.614682i
$795$		0			0
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	−9.00000			−0.318796			−0.159398	−	0.987214i	$-0.550955\pi$
$797$	−9.00000			−0.318796			−0.159398	+	0.987214i	$0.550955\pi$
$798$		0			0
$799$		0			0
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	18.0000	+	31.1769i	0.635999	+	1.10158i
$802$	−12.0000	−	20.7846i	−0.423735	−	0.733930i
$803$	−16.5000	+	28.5788i	−0.582272	+	1.00853i
$804$	−5.00000			−0.176336
$805$		0			0
$806$	5.00000			0.176117
$807$	4.50000	−	7.79423i	0.158408	−	0.274370i
$808$	−1.50000	−	2.59808i	−0.0527698	−	0.0914000i
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	−0.999491	−	0.0319002i	$-0.989844\pi$
$809$	−15.0000	−	25.9808i	−0.527372	−	0.913435i	0.472119	−	0.881535i	$-0.343489\pi$
$810$		0			0
$811$	−20.0000			−0.702295			−0.351147	−	0.936320i	$-0.614208\pi$
$811$	−20.0000			−0.702295			−0.351147	+	0.936320i	$0.614208\pi$
$812$		0			0
$813$	11.0000			0.385787
$814$	−10.5000	+	18.1865i	−0.368025	+	0.637438i
$815$		0			0
$816$		0			0
$817$	8.00000	−	13.8564i	0.279885	−	0.484774i
$818$	22.0000			0.769212
$819$		0			0
$820$		0			0
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	−0.808915	−	0.587925i	$-0.799945\pi$
$821$	3.00000	−	5.19615i	0.104701	−	0.181347i	0.913616	+	0.406578i	$0.133278\pi$
$822$	−3.00000	−	5.19615i	−0.104637	−	0.181237i
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	−0.963119	−	0.269075i	$-0.913282\pi$
$823$	−20.5000	−	35.5070i	−0.714585	−	1.23770i	0.248534	−	0.968623i	$-0.420051\pi$
$824$	7.00000	−	12.1244i	0.243857	−	0.422372i
$825$	−15.0000			−0.522233
$826$		0			0
$827$	−36.0000			−1.25184			−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000			−1.25184			−0.625921	+	0.779886i	$0.715277\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	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	$0.603933\pi$
$830$		0			0
$831$	13.0000	−	22.5167i	0.450965	−	0.781094i
$832$	−1.00000			−0.0346688
$833$		0			0
$834$	−4.00000			−0.138509
$835$		0			0
$836$	−3.00000	−	5.19615i	−0.103757	−	0.179713i
$837$	12.5000	+	21.6506i	0.432063	+	0.748355i
$838$	10.5000	−	18.1865i	0.362716	−	0.628243i
$839$	21.0000			0.725001			0.362500	−	0.931984i	$-0.381923\pi$
$839$	21.0000			0.725001			0.362500	+	0.931984i	$0.381923\pi$
$840$		0			0
$841$	−29.0000			−1.00000
$842$	18.5000	−	32.0429i	0.637552	−	1.10427i
$843$	6.00000	+	10.3923i	0.206651	+	0.357930i
$844$	11.0000	+	19.0526i	0.378636	+	0.655816i
$845$		0			0
$846$	−6.00000			−0.206284
$847$		0			0
$848$	−12.0000			−0.412082
$849$	15.5000	−	26.8468i	0.531959	−	0.921379i
$850$		0			0
$851$	−10.5000	−	18.1865i	−0.359935	−	0.623426i
$852$	6.00000	−	10.3923i	0.205557	−	0.356034i
$853$	−44.0000			−1.50653			−0.753266	−	0.657716i	$-0.771523\pi$
$853$	−44.0000			−1.50653			−0.753266	+	0.657716i	$0.771523\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.795843	+	0.605503i	$0.207028\pi$
$857$	27.0000	+	46.7654i	0.922302	+	1.59747i	0.126459	+	0.991972i	$0.459639\pi$
$858$	1.50000	+	2.59808i	0.0512092	+	0.0886969i
$859$	11.5000	−	19.9186i	0.392375	−	0.679613i	−0.600387	−	0.799709i	$-0.704987\pi$
$859$	11.5000	−	19.9186i	0.392375	−	0.679613i	0.992762	+	0.120096i	$0.0383202\pi$
$860$		0			0
$861$		0			0
$862$	−6.00000			−0.204361
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	−0.949891	−	0.312581i	$-0.898806\pi$
$863$	−6.00000	+	10.3923i	−0.204242	+	0.353758i	0.745649	+	0.666339i	$0.232140\pi$
$864$	−2.50000	−	4.33013i	−0.0850517	−	0.147314i
$865$		0			0
$866$	19.0000	−	32.9090i	0.645646	−	1.11829i
$867$	17.0000			0.577350
$868$		0			0
$869$	3.00000			0.101768
$870$		0			0
$871$	2.50000	+	4.33013i	0.0847093	+	0.146721i
$872$	−1.00000	−	1.73205i	−0.0338643	−	0.0586546i
$873$	−17.0000	+	29.4449i	−0.575363	+	0.996558i
$874$	6.00000			0.202953
$875$		0			0
$876$	11.0000			0.371656
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	−0.735163	−	0.677891i	$-0.762894\pi$
$877$	6.50000	−	11.2583i	0.219489	−	0.380167i	0.954652	+	0.297724i	$0.0962275\pi$
$878$	13.0000	+	22.5167i	0.438729	+	0.759900i
$879$	−9.00000	−	15.5885i	−0.303562	−	0.525786i
$880$		0			0
$881$	−6.00000			−0.202145			−0.101073	−	0.994879i	$-0.532227\pi$
$881$	−6.00000			−0.202145			−0.101073	+	0.994879i	$0.532227\pi$
$882$		0			0
$883$	2.00000			0.0673054			0.0336527	−	0.999434i	$-0.489286\pi$
$883$	2.00000			0.0673054			0.0336527	+	0.999434i	$0.489286\pi$
$884$		0			0
$885$		0			0
$886$	−12.0000	−	20.7846i	−0.403148	−	0.698273i
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	−0.261540	−	0.965193i	$-0.584230\pi$
$887$	21.0000	−	36.3731i	0.705111	−	1.22129i	0.966651	−	0.256096i	$-0.0824362\pi$
$888$	7.00000			0.234905
$889$		0			0
$890$		0			0
$891$	1.50000	−	2.59808i	0.0502519	−	0.0870388i
$892$	−0.500000	−	0.866025i	−0.0167412	−	0.0289967i
$893$	3.00000	+	5.19615i	0.100391	+	0.173883i
$894$	−7.50000	+	12.9904i	−0.250838	+	0.434463i
$895$		0			0
$896$		0			0
$897$	−3.00000			−0.100167
$898$	3.00000	−	5.19615i	0.100111	−	0.173398i
$899$		0			0
$900$	−5.00000	−	8.66025i	−0.166667	−	0.288675i
$901$		0			0
$902$	9.00000			0.299667
$903$		0			0
$904$	9.00000			0.299336
$905$		0			0
$906$	4.00000	+	6.92820i	0.132891	+	0.230174i
$907$	−13.0000	−	22.5167i	−0.431658	−	0.747653i	0.565358	−	0.824845i	$-0.308738\pi$
$907$	−13.0000	−	22.5167i	−0.431658	−	0.747653i	−0.997016	+	0.0771920i	$0.975405\pi$
$908$	−12.0000	+	20.7846i	−0.398234	+	0.689761i
$909$	−6.00000			−0.199007
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−1.00000	+	1.73205i	−0.0331133	+	0.0573539i
$913$	−18.0000	−	31.1769i	−0.595713	−	1.03181i
$914$	−13.0000	−	22.5167i	−0.430002	−	0.744785i
$915$		0			0
$916$	4.00000			0.132164
$917$		0			0
$918$		0			0
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	−0.582808	−	0.812610i	$-0.698046\pi$
$919$	12.5000	−	21.6506i	0.412337	−	0.714189i	0.995145	+	0.0984214i	$0.0313793\pi$
$920$		0			0
$921$	8.00000	+	13.8564i	0.263609	+	0.456584i
$922$	12.0000	−	20.7846i	0.395199	−	0.684505i
$923$	−12.0000			−0.394985
$924$		0			0
$925$	35.0000			1.15079
$926$	20.0000	−	34.6410i	0.657241	−	1.13837i
$927$	−14.0000	−	24.2487i	−0.459820	−	0.796432i
$928$		0			0
$929$	−4.50000	+	7.79423i	−0.147640	+	0.255720i	−0.930355	−	0.366660i	$-0.880501\pi$
$929$	−4.50000	+	7.79423i	−0.147640	+	0.255720i	0.782715	+	0.622381i	$0.213834\pi$
$930$		0			0
$931$		0			0
$932$	3.00000			0.0982683
$933$	−15.0000	+	25.9808i	−0.491078	+	0.850572i
$934$	6.00000	+	10.3923i	0.196326	+	0.340047i
$935$		0			0
$936$	−1.00000	+	1.73205i	−0.0326860	+	0.0566139i
$937$	52.0000			1.69877			0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000			1.69877			0.849383	+	0.527777i	$0.176974\pi$
$938$		0			0
$939$	26.0000			0.848478
$940$		0			0
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	0.999920	−	0.0126715i	$-0.00403357\pi$
$941$	15.0000	+	25.9808i	0.488986	+	0.846949i	−0.510934	+	0.859620i	$0.670700\pi$
$942$	6.50000	+	11.2583i	0.211781	+	0.366816i
$943$	−4.50000	+	7.79423i	−0.146540	+	0.253815i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−24.0000			−0.780307
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	0.152106	+	0.988364i	$0.451394\pi$
$947$	−24.0000	+	41.5692i	−0.779895	+	1.35082i	−0.932002	+	0.362454i	$0.881939\pi$
$948$	−0.500000	−	0.866025i	−0.0162392	−	0.0281272i
$949$	−5.50000	−	9.52628i	−0.178538	−	0.309236i
$950$	−5.00000	+	8.66025i	−0.162221	+	0.280976i
$951$	3.00000			0.0972817
$952$		0			0
$953$	−42.0000			−1.36051			−0.680257	−	0.732974i	$-0.738132\pi$
$953$	−42.0000			−1.36051			−0.680257	+	0.732974i	$0.738132\pi$
$954$	−12.0000	+	20.7846i	−0.388514	+	0.672927i
$955$		0			0
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$		0			0
$958$	−24.0000			−0.775405
$959$		0			0
$960$		0			0
$961$	3.00000	−	5.19615i	0.0967742	−	0.167618i
$962$	−3.50000	−	6.06218i	−0.112845	−	0.195452i
$963$		0			0
$964$	13.0000	−	22.5167i	0.418702	−	0.725213i
$965$		0			0
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$		0			0
$970$		0			0
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	−0.983860	−	0.178942i	$-0.942732\pi$
$971$	−10.5000	+	18.1865i	−0.336961	+	0.583634i	0.646899	+	0.762576i	$0.276066\pi$
$972$	−16.0000			−0.513200
$973$		0			0
$974$	2.00000			0.0640841
$975$	2.50000	−	4.33013i	0.0800641	−	0.138675i
$976$	−0.500000	−	0.866025i	−0.0160046	−	0.0277208i
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	0.685381	−	0.728184i	$-0.259636\pi$
$977$	−9.00000	−	15.5885i	−0.287936	−	0.498719i	−0.973317	+	0.229465i	$0.926302\pi$
$978$	10.0000	−	17.3205i	0.319765	−	0.553849i
$979$	−54.0000			−1.72585
$980$		0			0
$981$	−4.00000			−0.127710
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$983$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$984$	−1.50000	−	2.59808i	−0.0478183	−	0.0828236i
$985$		0			0
$986$		0			0
$987$		0			0
$988$	2.00000			0.0636285
$989$	12.0000	−	20.7846i	0.381578	−	0.660912i
$990$		0			0
$991$	−5.50000	−	9.52628i	−0.174713	−	0.302612i	0.765349	−	0.643616i	$-0.222567\pi$
$991$	−5.50000	−	9.52628i	−0.174713	−	0.302612i	−0.940062	+	0.341004i	$0.889233\pi$
$992$	2.50000	−	4.33013i	0.0793751	−	0.137482i
$993$	19.0000			0.602947
$994$		0			0
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	−18.5000	−	32.0429i	−0.585901	−	1.01481i	−0.994762	−	0.102214i	$-0.967407\pi$
$997$	−18.5000	−	32.0429i	−0.585901	−	1.01481i	0.408862	−	0.912596i	$-0.365926\pi$
$998$	−11.5000	−	19.9186i	−0.364026	−	0.630512i
$999$	17.5000	−	30.3109i	0.553675	−	0.958994i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1274.2.f.i.79.1		2
7.2	even	3		1274.2.a.j.1.1		1
7.3	odd	6		1274.2.f.d.1145.1		2
7.4	even	3	inner	1274.2.f.i.1145.1		2
7.5	odd	6		182.2.a.d.1.1	✓	1
7.6	odd	2		1274.2.f.d.79.1		2
21.5	even	6		1638.2.a.f.1.1		1
28.19	even	6		1456.2.a.d.1.1		1
35.19	odd	6		4550.2.a.c.1.1		1
56.5	odd	6		5824.2.a.k.1.1		1
56.19	even	6		5824.2.a.x.1.1		1
91.5	even	12		2366.2.d.e.337.1		2
91.12	odd	6		2366.2.a.e.1.1		1
91.47	even	12		2366.2.d.e.337.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
182.2.a.d.1.1	✓	1	7.5	odd	6
1274.2.a.j.1.1		1	7.2	even	3
1274.2.f.d.79.1		2	7.6	odd	2
1274.2.f.d.1145.1		2	7.3	odd	6
1274.2.f.i.79.1		2	1.1	even	1	trivial
1274.2.f.i.1145.1		2	7.4	even	3	inner
1456.2.a.d.1.1		1	28.19	even	6
1638.2.a.f.1.1		1	21.5	even	6
2366.2.a.e.1.1		1	91.12	odd	6
2366.2.d.e.337.1		2	91.5	even	12
2366.2.d.e.337.2		2	91.47	even	12
4550.2.a.c.1.1		1	35.19	odd	6
5824.2.a.k.1.1		1	56.5	odd	6
5824.2.a.x.1.1		1	56.19	even	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:	\( N \)	\(=\)	\( 1274 = 2 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1274.f (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -1.00000 q^{6} +1.00000 q^{8} +(1.00000 - 1.73205i) q^{9} +(1.50000 + 2.59808i) q^{11} +(0.500000 - 0.866025i) q^{12} -1.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{18} +(1.00000 - 1.73205i) q^{19} -3.00000 q^{22} +(1.50000 - 2.59808i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 + 4.33013i) q^{25} +(0.500000 - 0.866025i) q^{26} +5.00000 q^{27} +(2.50000 + 4.33013i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} -2.00000 q^{36} +(3.50000 - 6.06218i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-0.500000 - 0.866025i) q^{39} -3.00000 q^{41} +8.00000 q^{43} +(1.50000 - 2.59808i) q^{44} +(1.50000 + 2.59808i) q^{46} +(-1.50000 + 2.59808i) q^{47} -1.00000 q^{48} -5.00000 q^{50} +(0.500000 + 0.866025i) q^{52} +(6.00000 + 10.3923i) q^{53} +(-2.50000 + 4.33013i) q^{54} +2.00000 q^{57} +(3.00000 + 5.19615i) q^{59} +(-0.500000 + 0.866025i) q^{61} -5.00000 q^{62} +1.00000 q^{64} +(-1.50000 - 2.59808i) q^{66} +(-2.50000 - 4.33013i) q^{67} +3.00000 q^{69} +12.0000 q^{71} +(1.00000 - 1.73205i) q^{72} +(5.50000 + 9.52628i) q^{73} +(3.50000 + 6.06218i) q^{74} +(-2.50000 + 4.33013i) q^{75} -2.00000 q^{76} +1.00000 q^{78} +(0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} -12.0000 q^{83} +(-4.00000 + 6.92820i) q^{86} +(1.50000 + 2.59808i) q^{88} +(-9.00000 + 15.5885i) q^{89} -3.00000 q^{92} +(-2.50000 + 4.33013i) q^{93} +(-1.50000 - 2.59808i) q^{94} +(0.500000 - 0.866025i) q^{96} -17.0000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} + q^{3} - q^{4} - 2 q^{6} + 2 q^{8} + 2 q^{9} + 3 q^{11} + q^{12} - 2 q^{13} - q^{16} + 2 q^{18} + 2 q^{19} - 6 q^{22} + 3 q^{23} + q^{24} + 5 q^{25} + q^{26} + 10 q^{27} + 5 q^{31} - q^{32} - 3 q^{33} - 4 q^{36} + 7 q^{37} + 2 q^{38} - q^{39} - 6 q^{41} + 16 q^{43} + 3 q^{44} + 3 q^{46} - 3 q^{47} - 2 q^{48} - 10 q^{50} + q^{52} + 12 q^{53} - 5 q^{54} + 4 q^{57} + 6 q^{59} - q^{61} - 10 q^{62} + 2 q^{64} - 3 q^{66} - 5 q^{67} + 6 q^{69} + 24 q^{71} + 2 q^{72} + 11 q^{73} + 7 q^{74} - 5 q^{75} - 4 q^{76} + 2 q^{78} + q^{79} - q^{81} + 3 q^{82} - 24 q^{83} - 8 q^{86} + 3 q^{88} - 18 q^{89} - 6 q^{92} - 5 q^{93} - 3 q^{94} + q^{96} - 34 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 - q^4 - 2 * q^6 + 2 * q^8 + 2 * q^9 + 3 * q^11 + q^12 - 2 * q^13 - q^16 + 2 * q^18 + 2 * q^19 - 6 * q^22 + 3 * q^23 + q^24 + 5 * q^25 + q^26 + 10 * q^27 + 5 * q^31 - q^32 - 3 * q^33 - 4 * q^36 + 7 * q^37 + 2 * q^38 - q^39 - 6 * q^41 + 16 * q^43 + 3 * q^44 + 3 * q^46 - 3 * q^47 - 2 * q^48 - 10 * q^50 + q^52 + 12 * q^53 - 5 * q^54 + 4 * q^57 + 6 * q^59 - q^61 - 10 * q^62 + 2 * q^64 - 3 * q^66 - 5 * q^67 + 6 * q^69 + 24 * q^71 + 2 * q^72 + 11 * q^73 + 7 * q^74 - 5 * q^75 - 4 * q^76 + 2 * q^78 + q^79 - q^81 + 3 * q^82 - 24 * q^83 - 8 * q^86 + 3 * q^88 - 18 * q^89 - 6 * q^92 - 5 * q^93 - 3 * q^94 + q^96 - 34 * q^97 + 12 * q^99

Introduction

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