LMFDB - Embedded newform 504.2.t.a.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(193,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 4]))

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

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

chi := DirichletCharacter("504.193");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.t (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$1$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			193.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	504.193
Dual form			504.2.t.a.457.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 0.866025i) q^{3} +1.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 0.866025i) q^{3} +1.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} -3.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(3.00000 - 3.46410i) q^{21} +1.00000 q^{23} -4.00000 q^{25} +5.19615i q^{27} +(-4.50000 - 7.79423i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(4.50000 - 2.59808i) q^{33} +(-2.50000 + 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} -1.73205i q^{39} +(-3.50000 + 6.06218i) q^{41} +(-1.50000 - 2.59808i) q^{43} +(1.50000 - 2.59808i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(5.50000 - 4.33013i) q^{49} -5.19615i q^{51} +(-4.50000 + 7.79423i) q^{53} -3.00000 q^{55} +(7.50000 + 4.33013i) q^{57} +(2.00000 + 3.46410i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-1.50000 + 7.79423i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(-6.00000 - 10.3923i) q^{67} +(-1.50000 + 0.866025i) q^{69} +8.00000 q^{71} +(6.50000 - 11.2583i) q^{73} +(6.00000 - 3.46410i) q^{75} +(7.50000 - 2.59808i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(6.50000 + 11.2583i) q^{83} +(-1.50000 + 2.59808i) q^{85} +(13.5000 + 7.79423i) q^{87} +(4.50000 + 7.79423i) q^{89} +(0.500000 - 2.59808i) q^{91} +(6.00000 + 3.46410i) q^{93} +(-2.50000 - 4.33013i) q^{95} +(8.50000 + 14.7224i) q^{97} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{3} + 2 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^3 + 2 * q^5 - 5 * q^7 + 3 * q^9	$ 2 q - 3 q^{3} + 2 q^{5} - 5 q^{7} + 3 q^{9} - 6 q^{11} - q^{13} - 3 q^{15} - 3 q^{17} - 5 q^{19} + 6 q^{21} + 2 q^{23} - 8 q^{25} - 9 q^{29} - 4 q^{31} + 9 q^{33} - 5 q^{35} - 5 q^{37} - 7 q^{41} - 3 q^{43} + 3 q^{45} - 8 q^{47} + 11 q^{49} - 9 q^{53} - 6 q^{55} + 15 q^{57} + 4 q^{59} - 2 q^{61} - 3 q^{63} - q^{65} - 12 q^{67} - 3 q^{69} + 16 q^{71} + 13 q^{73} + 12 q^{75} + 15 q^{77} - 8 q^{79} - 9 q^{81} + 13 q^{83} - 3 q^{85} + 27 q^{87} + 9 q^{89} + q^{91} + 12 q^{93} - 5 q^{95} + 17 q^{97} - 9 q^{99}+O(q^{100}) $ 2 * q - 3 * q^3 + 2 * q^5 - 5 * q^7 + 3 * q^9 - 6 * q^11 - q^13 - 3 * q^15 - 3 * q^17 - 5 * q^19 + 6 * q^21 + 2 * q^23 - 8 * q^25 - 9 * q^29 - 4 * q^31 + 9 * q^33 - 5 * q^35 - 5 * q^37 - 7 * q^41 - 3 * q^43 + 3 * q^45 - 8 * q^47 + 11 * q^49 - 9 * q^53 - 6 * q^55 + 15 * q^57 + 4 * q^59 - 2 * q^61 - 3 * q^63 - q^65 - 12 * q^67 - 3 * q^69 + 16 * q^71 + 13 * q^73 + 12 * q^75 + 15 * q^77 - 8 * q^79 - 9 * q^81 + 13 * q^83 - 3 * q^85 + 27 * q^87 + 9 * q^89 + q^91 + 12 * q^93 - 5 * q^95 + 17 * q^97 - 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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			0
$2$		0			0
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$3$	−1.50000	+	0.866025i	−0.866025	+	0.500000i
$4$		0			0
$5$	1.00000			0.447214			0.223607	−	0.974679i	$-0.428217\pi$
$5$	1.00000			0.447214			0.223607	+	0.974679i	$0.428217\pi$
$6$		0			0
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$7$	−2.50000	+	0.866025i	−0.944911	+	0.327327i
$8$		0			0
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$		0			0
$11$	−3.00000			−0.904534			−0.452267	−	0.891883i	$-0.649385\pi$
$11$	−3.00000			−0.904534			−0.452267	+	0.891883i	$0.649385\pi$
$12$		0			0
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	−0.926995	−	0.375073i	$-0.877618\pi$
$13$	−0.500000	+	0.866025i	−0.138675	+	0.240192i	0.788320	+	0.615265i	$0.210951\pi$
$14$		0			0
$15$	−1.50000	+	0.866025i	−0.387298	+	0.223607i
$16$		0			0
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$		0			0
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	−0.996199	−	0.0871106i	$-0.972237\pi$
$19$	−2.50000	−	4.33013i	−0.573539	−	0.993399i	0.422659	−	0.906289i	$-0.361097\pi$
$20$		0			0
$21$	3.00000	−	3.46410i	0.654654	−	0.755929i
$22$		0			0
$23$	1.00000			0.208514			0.104257	−	0.994550i	$-0.466753\pi$
$23$	1.00000			0.208514			0.104257	+	0.994550i	$0.466753\pi$
$24$		0			0
$25$	−4.00000			−0.800000
$26$		0			0
$27$			5.19615i			1.00000i
$28$		0			0
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	−0.893517	−	0.449029i	$-0.851770\pi$
$29$	−4.50000	−	7.79423i	−0.835629	−	1.44735i	0.0578882	−	0.998323i	$-0.481563\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$		0			0
$33$	4.50000	−	2.59808i	0.783349	−	0.452267i
$34$		0			0
$35$	−2.50000	+	0.866025i	−0.422577	+	0.146385i
$36$		0			0
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	0.584002	−	0.811752i	$-0.301486\pi$
$37$	−2.50000	−	4.33013i	−0.410997	−	0.711868i	−0.994999	+	0.0998840i	$0.968153\pi$
$38$		0			0
$39$		−	1.73205i		−	0.277350i
$40$		0			0
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	0.451896	+	0.892071i	$0.350748\pi$
$41$	−3.50000	+	6.06218i	−0.546608	+	0.946753i	−0.998504	+	0.0546823i	$0.982585\pi$
$42$		0			0
$43$	−1.50000	−	2.59808i	−0.228748	−	0.396203i	0.728689	−	0.684844i	$-0.240130\pi$
$43$	−1.50000	−	2.59808i	−0.228748	−	0.396203i	−0.957437	+	0.288641i	$0.906796\pi$
$44$		0			0
$45$	1.50000	−	2.59808i	0.223607	−	0.387298i
$46$		0			0
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	0.411606	+	0.911362i	$0.364968\pi$
$47$	−4.00000	+	6.92820i	−0.583460	+	1.01058i	−0.995066	+	0.0992202i	$0.968365\pi$
$48$		0			0
$49$	5.50000	−	4.33013i	0.785714	−	0.618590i
$50$		0			0
$51$		−	5.19615i		−	0.727607i
$52$		0			0
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	0.371706	+	0.928351i	$0.378773\pi$
$53$	−4.50000	+	7.79423i	−0.618123	+	1.07062i	−0.989828	+	0.142269i	$0.954560\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	7.50000	+	4.33013i	0.993399	+	0.573539i
$58$		0			0
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	0.966342	−	0.257260i	$-0.0828195\pi$
$59$	2.00000	+	3.46410i	0.260378	+	0.450988i	−0.705965	+	0.708247i	$0.749486\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$		0			0
$63$	−1.50000	+	7.79423i	−0.188982	+	0.981981i
$64$		0			0
$65$	−0.500000	+	0.866025i	−0.0620174	+	0.107417i
$66$		0			0
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$		0			0
$69$	−1.50000	+	0.866025i	−0.180579	+	0.104257i
$70$		0			0
$71$	8.00000			0.949425			0.474713	−	0.880141i	$-0.342552\pi$
$71$	8.00000			0.949425			0.474713	+	0.880141i	$0.342552\pi$
$72$		0			0
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	−0.181688	−	0.983356i	$-0.558156\pi$
$73$	6.50000	−	11.2583i	0.760767	−	1.31769i	0.942455	−	0.334332i	$-0.108511\pi$
$74$		0			0
$75$	6.00000	−	3.46410i	0.692820	−	0.400000i
$76$		0			0
$77$	7.50000	−	2.59808i	0.854704	−	0.296078i
$78$		0			0
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$		0			0
$83$	6.50000	+	11.2583i	0.713468	+	1.23576i	0.963548	+	0.267537i	$0.0862098\pi$
$83$	6.50000	+	11.2583i	0.713468	+	1.23576i	−0.250080	+	0.968225i	$0.580457\pi$
$84$		0			0
$85$	−1.50000	+	2.59808i	−0.162698	+	0.281801i
$86$		0			0
$87$	13.5000	+	7.79423i	1.44735	+	0.835629i
$88$		0			0
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	0.500000	−	2.59808i	0.0524142	−	0.272352i
$92$		0			0
$93$	6.00000	+	3.46410i	0.622171	+	0.359211i
$94$		0			0
$95$	−2.50000	−	4.33013i	−0.256495	−	0.444262i
$96$		0			0
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	0.868976	+	0.494854i	$0.164778\pi$
$97$	8.50000	+	14.7224i	0.863044	+	1.49484i	−0.00593185	+	0.999982i	$0.501888\pi$
$98$		0			0
$99$	−4.50000	+	7.79423i	−0.452267	+	0.783349i
$100$		0			0
$101$	−7.00000			−0.696526			−0.348263	−	0.937397i	$-0.613228\pi$
$101$	−7.00000			−0.696526			−0.348263	+	0.937397i	$0.613228\pi$
$102$		0			0
$103$	9.00000			0.886796			0.443398	−	0.896325i	$-0.353773\pi$
$103$	9.00000			0.886796			0.443398	+	0.896325i	$0.353773\pi$
$104$		0			0
$105$	3.00000	−	3.46410i	0.292770	−	0.338062i
$106$		0			0
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	0.984124	−	0.177482i	$-0.0567953\pi$
$107$	3.50000	+	6.06218i	0.338358	+	0.586053i	−0.645766	+	0.763535i	$0.723462\pi$
$108$		0			0
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	−0.960558	−	0.278078i	$-0.910303\pi$
$109$	−2.50000	+	4.33013i	−0.239457	+	0.414751i	0.721102	+	0.692829i	$0.243636\pi$
$110$		0			0
$111$	7.50000	+	4.33013i	0.711868	+	0.410997i
$112$		0			0
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	−0.841549	−	0.540181i	$-0.818356\pi$
$113$	0.500000	−	0.866025i	0.0470360	−	0.0814688i	0.888585	+	0.458712i	$0.151689\pi$
$114$		0			0
$115$	1.00000			0.0932505
$116$		0			0
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$		0			0
$119$	1.50000	−	7.79423i	0.137505	−	0.714496i
$120$		0			0
$121$	−2.00000			−0.181818
$122$		0			0
$123$		−	12.1244i		−	1.09322i
$124$		0			0
$125$	−9.00000			−0.804984
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$	4.50000	+	2.59808i	0.396203	+	0.228748i
$130$		0			0
$131$	3.00000			0.262111			0.131056	−	0.991375i	$-0.458163\pi$
$131$	3.00000			0.262111			0.131056	+	0.991375i	$0.458163\pi$
$132$		0			0
$133$	10.0000	+	8.66025i	0.867110	+	0.750939i
$134$		0			0
$135$			5.19615i			0.447214i
$136$		0			0
$137$	11.0000			0.939793			0.469897	−	0.882721i	$-0.344291\pi$
$137$	11.0000			0.939793			0.469897	+	0.882721i	$0.344291\pi$
$138$		0			0
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$		−	13.8564i		−	1.16692i
$142$		0			0
$143$	1.50000	−	2.59808i	0.125436	−	0.217262i
$144$		0			0
$145$	−4.50000	−	7.79423i	−0.373705	−	0.647275i
$146$		0			0
$147$	−4.50000	+	11.2583i	−0.371154	+	0.928571i
$148$		0			0
$149$	−15.0000			−1.22885			−0.614424	−	0.788976i	$-0.710612\pi$
$149$	−15.0000			−1.22885			−0.614424	+	0.788976i	$0.710612\pi$
$150$		0			0
$151$	−17.0000			−1.38344			−0.691720	−	0.722166i	$-0.743147\pi$
$151$	−17.0000			−1.38344			−0.691720	+	0.722166i	$0.743147\pi$
$152$		0			0
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$		0			0
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$		−	15.5885i		−	1.23625i
$160$		0			0
$161$	−2.50000	+	0.866025i	−0.197028	+	0.0682524i
$162$		0			0
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	−0.979076	−	0.203497i	$-0.934769\pi$
$163$	−8.50000	−	14.7224i	−0.665771	−	1.15315i	0.313304	−	0.949653i	$-0.398564\pi$
$164$		0			0
$165$	4.50000	−	2.59808i	0.350325	−	0.202260i
$166$		0			0
$167$	0.500000	−	0.866025i	0.0386912	−	0.0670151i	−0.846031	−	0.533133i	$-0.821014\pi$
$167$	0.500000	−	0.866025i	0.0386912	−	0.0670151i	0.884723	+	0.466118i	$0.154348\pi$
$168$		0			0
$169$	6.00000	+	10.3923i	0.461538	+	0.799408i
$170$		0			0
$171$	−15.0000			−1.14708
$172$		0			0
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	−0.825505	−	0.564396i	$-0.809109\pi$
$173$	1.00000	−	1.73205i	0.0760286	−	0.131685i	0.901533	+	0.432710i	$0.142443\pi$
$174$		0			0
$175$	10.0000	−	3.46410i	0.755929	−	0.261861i
$176$		0			0
$177$	−6.00000	−	3.46410i	−0.450988	−	0.260378i
$178$		0			0
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	−0.144308	−	0.989533i	$-0.546095\pi$
$179$	10.5000	−	18.1865i	0.784807	−	1.35933i	0.929114	−	0.369792i	$-0.120571\pi$
$180$		0			0
$181$	−18.0000			−1.33793			−0.668965	−	0.743294i	$-0.733262\pi$
$181$	−18.0000			−1.33793			−0.668965	+	0.743294i	$0.733262\pi$
$182$		0			0
$183$		−	3.46410i		−	0.256074i
$184$		0			0
$185$	−2.50000	−	4.33013i	−0.183804	−	0.318357i
$186$		0			0
$187$	4.50000	−	7.79423i	0.329073	−	0.569970i
$188$		0			0
$189$	−4.50000	−	12.9904i	−0.327327	−	0.944911i
$190$		0			0
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	−0.929267	−	0.369410i	$-0.879560\pi$
$191$	−2.00000	+	3.46410i	−0.144715	+	0.250654i	0.784552	+	0.620063i	$0.212893\pi$
$192$		0			0
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	0.983639	+	0.180150i	$0.0576584\pi$
$193$	9.00000	+	15.5885i	0.647834	+	1.12208i	−0.335805	+	0.941932i	$0.609008\pi$
$194$		0			0
$195$		−	1.73205i		−	0.124035i
$196$		0			0
$197$	−22.0000			−1.56744			−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000			−1.56744			−0.783718	+	0.621117i	$0.786679\pi$
$198$		0			0
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	0.206184	+	0.978513i	$0.433895\pi$
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	−0.950509	+	0.310696i	$0.899438\pi$
$200$		0			0
$201$	18.0000	+	10.3923i	1.26962	+	0.733017i
$202$		0			0
$203$	18.0000	+	15.5885i	1.26335	+	1.09410i
$204$		0			0
$205$	−3.50000	+	6.06218i	−0.244451	+	0.423401i
$206$		0			0
$207$	1.50000	−	2.59808i	0.104257	−	0.180579i
$208$		0			0
$209$	7.50000	+	12.9904i	0.518786	+	0.898563i
$210$		0			0
$211$	13.5000	−	23.3827i	0.929378	−	1.60973i	0.145014	−	0.989430i	$-0.453677\pi$
$211$	13.5000	−	23.3827i	0.929378	−	1.60973i	0.784364	−	0.620301i	$-0.212990\pi$
$212$		0			0
$213$	−12.0000	+	6.92820i	−0.822226	+	0.474713i
$214$		0			0
$215$	−1.50000	−	2.59808i	−0.102299	−	0.177187i
$216$		0			0
$217$	8.00000	+	6.92820i	0.543075	+	0.470317i
$218$		0			0
$219$			22.5167i			1.52153i
$220$		0			0
$221$	−1.50000	−	2.59808i	−0.100901	−	0.174766i
$222$		0			0
$223$	−6.50000	−	11.2583i	−0.435272	−	0.753914i	0.562046	−	0.827106i	$-0.310015\pi$
$223$	−6.50000	−	11.2583i	−0.435272	−	0.753914i	−0.997318	+	0.0731927i	$0.976681\pi$
$224$		0			0
$225$	−6.00000	+	10.3923i	−0.400000	+	0.692820i
$226$		0			0
$227$	−15.0000			−0.995585			−0.497792	−	0.867296i	$-0.665856\pi$
$227$	−15.0000			−0.995585			−0.497792	+	0.867296i	$0.665856\pi$
$228$		0			0
$229$	21.0000			1.38772			0.693860	−	0.720110i	$-0.255909\pi$
$229$	21.0000			1.38772			0.693860	+	0.720110i	$0.255909\pi$
$230$		0			0
$231$	−9.00000	+	10.3923i	−0.592157	+	0.683763i
$232$		0			0
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	0.812700	−	0.582683i	$-0.197997\pi$
$233$	−1.50000	−	2.59808i	−0.0982683	−	0.170206i	−0.910968	+	0.412477i	$0.864664\pi$
$234$		0			0
$235$	−4.00000	+	6.92820i	−0.260931	+	0.451946i
$236$		0			0
$237$		−	13.8564i		−	0.900070i
$238$		0			0
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	−0.682985	−	0.730433i	$-0.739318\pi$
$239$	4.50000	−	7.79423i	0.291081	−	0.504167i	0.974066	+	0.226266i	$0.0726518\pi$
$240$		0			0
$241$	−1.00000			−0.0644157			−0.0322078	−	0.999481i	$-0.510254\pi$
$241$	−1.00000			−0.0644157			−0.0322078	+	0.999481i	$0.510254\pi$
$242$		0			0
$243$	13.5000	+	7.79423i	0.866025	+	0.500000i
$244$		0			0
$245$	5.50000	−	4.33013i	0.351382	−	0.276642i
$246$		0			0
$247$	5.00000			0.318142
$248$		0			0
$249$	−19.5000	−	11.2583i	−1.23576	−	0.713468i
$250$		0			0
$251$	4.00000			0.252478			0.126239	−	0.992000i	$-0.459709\pi$
$251$	4.00000			0.252478			0.126239	+	0.992000i	$0.459709\pi$
$252$		0			0
$253$	−3.00000			−0.188608
$254$		0			0
$255$		−	5.19615i		−	0.325396i
$256$		0			0
$257$	−17.0000			−1.06043			−0.530215	−	0.847863i	$-0.677889\pi$
$257$	−17.0000			−1.06043			−0.530215	+	0.847863i	$0.677889\pi$
$258$		0			0
$259$	10.0000	+	8.66025i	0.621370	+	0.538122i
$260$		0			0
$261$	−27.0000			−1.67126
$262$		0			0
$263$	11.0000			0.678289			0.339145	−	0.940734i	$-0.389862\pi$
$263$	11.0000			0.678289			0.339145	+	0.940734i	$0.389862\pi$
$264$		0			0
$265$	−4.50000	+	7.79423i	−0.276433	+	0.478796i
$266$		0			0
$267$	−13.5000	−	7.79423i	−0.826187	−	0.476999i
$268$		0			0
$269$	3.50000	−	6.06218i	0.213399	−	0.369618i	−0.739377	−	0.673291i	$-0.764880\pi$
$269$	3.50000	−	6.06218i	0.213399	−	0.369618i	0.952776	+	0.303674i	$0.0982133\pi$
$270$		0			0
$271$	−15.5000	−	26.8468i	−0.941558	−	1.63083i	−0.762501	−	0.646988i	$-0.776029\pi$
$271$	−15.5000	−	26.8468i	−0.941558	−	1.63083i	−0.179057	−	0.983839i	$-0.557305\pi$
$272$		0			0
$273$	1.50000	+	4.33013i	0.0907841	+	0.262071i
$274$		0			0
$275$	12.0000			0.723627
$276$		0			0
$277$	−19.0000			−1.14160			−0.570800	−	0.821089i	$-0.693367\pi$
$277$	−19.0000			−1.14160			−0.570800	+	0.821089i	$0.693367\pi$
$278$		0			0
$279$	−12.0000			−0.718421
$280$		0			0
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	−0.916060	−	0.401042i	$-0.868648\pi$
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	0.110717	−	0.993852i	$-0.464685\pi$
$282$		0			0
$283$	12.0000	+	20.7846i	0.713326	+	1.23552i	0.963602	+	0.267342i	$0.0861454\pi$
$283$	12.0000	+	20.7846i	0.713326	+	1.23552i	−0.250276	+	0.968175i	$0.580521\pi$
$284$		0			0
$285$	7.50000	+	4.33013i	0.444262	+	0.256495i
$286$		0			0
$287$	3.50000	−	18.1865i	0.206598	−	1.07352i
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	−25.5000	−	14.7224i	−1.49484	−	0.863044i
$292$		0			0
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	−0.880261	−	0.474490i	$-0.842633\pi$
$293$	−0.500000	+	0.866025i	−0.0292103	+	0.0505937i	0.851051	+	0.525084i	$0.175966\pi$
$294$		0			0
$295$	2.00000	+	3.46410i	0.116445	+	0.201688i
$296$		0			0
$297$		−	15.5885i		−	0.904534i
$298$		0			0
$299$	−0.500000	+	0.866025i	−0.0289157	+	0.0500835i
$300$		0			0
$301$	6.00000	+	5.19615i	0.345834	+	0.299501i
$302$		0			0
$303$	10.5000	−	6.06218i	0.603209	−	0.348263i
$304$		0			0
$305$	−1.00000	+	1.73205i	−0.0572598	+	0.0991769i
$306$		0			0
$307$	−4.00000			−0.228292			−0.114146	−	0.993464i	$-0.536413\pi$
$307$	−4.00000			−0.228292			−0.114146	+	0.993464i	$0.536413\pi$
$308$		0			0
$309$	−13.5000	+	7.79423i	−0.767988	+	0.443398i
$310$		0			0
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	−0.938269	−	0.345907i	$-0.887571\pi$
$313$	−3.00000	+	5.19615i	−0.169570	+	0.293704i	0.768699	+	0.639611i	$0.220905\pi$
$314$		0			0
$315$	−1.50000	+	7.79423i	−0.0845154	+	0.439155i
$316$		0			0
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	−0.992864	−	0.119249i	$-0.961951\pi$
$317$	−7.00000	+	12.1244i	−0.393159	+	0.680972i	0.599705	+	0.800221i	$0.295285\pi$
$318$		0			0
$319$	13.5000	+	23.3827i	0.755855	+	1.30918i
$320$		0			0
$321$	−10.5000	−	6.06218i	−0.586053	−	0.338358i
$322$		0			0
$323$	15.0000			0.834622
$324$		0			0
$325$	2.00000	−	3.46410i	0.110940	−	0.192154i
$326$		0			0
$327$		−	8.66025i		−	0.478913i
$328$		0			0
$329$	4.00000	−	20.7846i	0.220527	−	1.14589i
$330$		0			0
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$		0			0
$333$	−15.0000			−0.821995
$334$		0			0
$335$	−6.00000	−	10.3923i	−0.327815	−	0.567792i
$336$		0			0
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	−0.994728	−	0.102552i	$-0.967299\pi$
$337$	−7.50000	+	12.9904i	−0.408551	+	0.707631i	0.586177	+	0.810183i	$0.300632\pi$
$338$		0			0
$339$			1.73205i			0.0940721i
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$	−10.0000	+	15.5885i	−0.539949	+	0.841698i
$344$		0			0
$345$	−1.50000	+	0.866025i	−0.0807573	+	0.0466252i
$346$		0			0
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$		0			0
$349$	−8.50000	−	14.7224i	−0.454995	−	0.788074i	0.543693	−	0.839284i	$-0.317025\pi$
$349$	−8.50000	−	14.7224i	−0.454995	−	0.788074i	−0.998688	+	0.0512103i	$0.983692\pi$
$350$		0			0
$351$	−4.50000	−	2.59808i	−0.240192	−	0.138675i
$352$		0			0
$353$	31.0000			1.64996			0.824982	−	0.565159i	$-0.191185\pi$
$353$	31.0000			1.64996			0.824982	+	0.565159i	$0.191185\pi$
$354$		0			0
$355$	8.00000			0.424596
$356$		0			0
$357$	4.50000	+	12.9904i	0.238165	+	0.687524i
$358$		0			0
$359$	−13.5000	−	23.3827i	−0.712503	−	1.23409i	−0.963915	−	0.266211i	$-0.914228\pi$
$359$	−13.5000	−	23.3827i	−0.712503	−	1.23409i	0.251412	−	0.967880i	$-0.419105\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$		0			0
$363$	3.00000	−	1.73205i	0.157459	−	0.0909091i
$364$		0			0
$365$	6.50000	−	11.2583i	0.340226	−	0.589288i
$366$		0			0
$367$	11.0000			0.574195			0.287098	−	0.957901i	$-0.407310\pi$
$367$	11.0000			0.574195			0.287098	+	0.957901i	$0.407310\pi$
$368$		0			0
$369$	10.5000	+	18.1865i	0.546608	+	0.946753i
$370$		0			0
$371$	4.50000	−	23.3827i	0.233628	−	1.21397i
$372$		0			0
$373$	13.0000			0.673114			0.336557	−	0.941663i	$-0.390737\pi$
$373$	13.0000			0.673114			0.336557	+	0.941663i	$0.390737\pi$
$374$		0			0
$375$	13.5000	−	7.79423i	0.697137	−	0.402492i
$376$		0			0
$377$	9.00000			0.463524
$378$		0			0
$379$	32.0000			1.64373			0.821865	−	0.569683i	$-0.192934\pi$
$379$	32.0000			1.64373			0.821865	+	0.569683i	$0.192934\pi$
$380$		0			0
$381$	−12.0000	+	6.92820i	−0.614779	+	0.354943i
$382$		0			0
$383$	−35.0000			−1.78842			−0.894208	−	0.447651i	$-0.852261\pi$
$383$	−35.0000			−1.78842			−0.894208	+	0.447651i	$0.852261\pi$
$384$		0			0
$385$	7.50000	−	2.59808i	0.382235	−	0.132410i
$386$		0			0
$387$	−9.00000			−0.457496
$388$		0			0
$389$	37.0000			1.87597			0.937987	−	0.346670i	$-0.112688\pi$
$389$	37.0000			1.87597			0.937987	+	0.346670i	$0.112688\pi$
$390$		0			0
$391$	−1.50000	+	2.59808i	−0.0758583	+	0.131390i
$392$		0			0
$393$	−4.50000	+	2.59808i	−0.226995	+	0.131056i
$394$		0			0
$395$	−4.00000	+	6.92820i	−0.201262	+	0.348596i
$396$		0			0
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	−0.988080	−	0.153941i	$-0.950803\pi$
$397$	−12.5000	−	21.6506i	−0.627357	−	1.08661i	0.360723	−	0.932673i	$-0.382530\pi$
$398$		0			0
$399$	−22.5000	−	4.33013i	−1.12641	−	0.216777i
$400$		0			0
$401$	−13.0000			−0.649189			−0.324595	−	0.945853i	$-0.605228\pi$
$401$	−13.0000			−0.649189			−0.324595	+	0.945853i	$0.605228\pi$
$402$		0			0
$403$	4.00000			0.199254
$404$		0			0
$405$	−4.50000	−	7.79423i	−0.223607	−	0.387298i
$406$		0			0
$407$	7.50000	+	12.9904i	0.371761	+	0.643909i
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$		0			0
$411$	−16.5000	+	9.52628i	−0.813885	+	0.469897i
$412$		0			0
$413$	−8.00000	−	6.92820i	−0.393654	−	0.340915i
$414$		0			0
$415$	6.50000	+	11.2583i	0.319072	+	0.552650i
$416$		0			0
$417$		−	8.66025i		−	0.424094i
$418$		0			0
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	0.486928	+	0.873442i	$0.338117\pi$
$419$	−10.5000	+	18.1865i	−0.512959	+	0.888470i	−0.999887	+	0.0150285i	$0.995216\pi$
$420$		0			0
$421$	1.50000	+	2.59808i	0.0731055	+	0.126622i	0.900261	−	0.435351i	$-0.143376\pi$
$421$	1.50000	+	2.59808i	0.0731055	+	0.126622i	−0.827155	+	0.561973i	$0.810042\pi$
$422$		0			0
$423$	12.0000	+	20.7846i	0.583460	+	1.01058i
$424$		0			0
$425$	6.00000	−	10.3923i	0.291043	−	0.504101i
$426$		0			0
$427$	1.00000	−	5.19615i	0.0483934	−	0.251459i
$428$		0			0
$429$			5.19615i			0.250873i
$430$		0			0
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	−0.626907	−	0.779094i	$-0.715679\pi$
$431$	7.50000	−	12.9904i	0.361262	−	0.625725i	0.988169	+	0.153370i	$0.0490126\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$	13.5000	+	7.79423i	0.647275	+	0.373705i
$436$		0			0
$437$	−2.50000	−	4.33013i	−0.119591	−	0.207138i
$438$		0			0
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	0.423556	+	0.905870i	$0.360782\pi$
$439$	−12.0000	+	20.7846i	−0.572729	+	0.991995i	−0.996284	+	0.0861252i	$0.972552\pi$
$440$		0			0
$441$	−3.00000	−	20.7846i	−0.142857	−	0.989743i
$442$		0			0
$443$	−8.00000	+	13.8564i	−0.380091	+	0.658338i	−0.991075	−	0.133306i	$-0.957441\pi$
$443$	−8.00000	+	13.8564i	−0.380091	+	0.658338i	0.610984	+	0.791643i	$0.290774\pi$
$444$		0			0
$445$	4.50000	+	7.79423i	0.213320	+	0.369482i
$446$		0			0
$447$	22.5000	−	12.9904i	1.06421	−	0.614424i
$448$		0			0
$449$	14.0000			0.660701			0.330350	−	0.943858i	$-0.392833\pi$
$449$	14.0000			0.660701			0.330350	+	0.943858i	$0.392833\pi$
$450$		0			0
$451$	10.5000	−	18.1865i	0.494426	−	0.856370i
$452$		0			0
$453$	25.5000	−	14.7224i	1.19809	−	0.691720i
$454$		0			0
$455$	0.500000	−	2.59808i	0.0234404	−	0.121800i
$456$		0			0
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	−0.383437	−	0.923567i	$-0.625260\pi$
$457$	13.0000	−	22.5167i	0.608114	−	1.05328i	0.991551	−	0.129718i	$-0.0414071\pi$
$458$		0			0
$459$	−13.5000	−	7.79423i	−0.630126	−	0.363803i
$460$		0			0
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	0.987801	+	0.155719i	$0.0497696\pi$
$461$	13.5000	+	23.3827i	0.628758	+	1.08904i	−0.359044	+	0.933321i	$0.616897\pi$
$462$		0			0
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	−0.854173	−	0.519989i	$-0.825936\pi$
$463$	0.500000	−	0.866025i	0.0232370	−	0.0402476i	0.877410	+	0.479741i	$0.159269\pi$
$464$		0			0
$465$	6.00000	+	3.46410i	0.278243	+	0.160644i
$466$		0			0
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	0.675530	−	0.737333i	$-0.263915\pi$
$467$	−6.50000	−	11.2583i	−0.300784	−	0.520973i	−0.976314	+	0.216359i	$0.930582\pi$
$468$		0			0
$469$	24.0000	+	20.7846i	1.10822	+	0.959744i
$470$		0			0
$471$	21.0000	+	12.1244i	0.967629	+	0.558661i
$472$		0			0
$473$	4.50000	+	7.79423i	0.206910	+	0.358379i
$474$		0			0
$475$	10.0000	+	17.3205i	0.458831	+	0.794719i
$476$		0			0
$477$	13.5000	+	23.3827i	0.618123	+	1.07062i
$478$		0			0
$479$	−21.0000			−0.959514			−0.479757	−	0.877401i	$-0.659275\pi$
$479$	−21.0000			−0.959514			−0.479757	+	0.877401i	$0.659275\pi$
$480$		0			0
$481$	5.00000			0.227980
$482$		0			0
$483$	3.00000	−	3.46410i	0.136505	−	0.157622i
$484$		0			0
$485$	8.50000	+	14.7224i	0.385965	+	0.668511i
$486$		0			0
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	0.0529875	+	0.998595i	$0.483126\pi$
$487$	−18.5000	+	32.0429i	−0.838315	+	1.45200i	−0.891303	+	0.453409i	$0.850208\pi$
$488$		0			0
$489$	25.5000	+	14.7224i	1.15315	+	0.665771i
$490$		0			0
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	−0.949520	−	0.313707i	$-0.898429\pi$
$491$	−4.50000	+	7.79423i	−0.203082	+	0.351749i	0.746438	+	0.665455i	$0.231763\pi$
$492$		0			0
$493$	27.0000			1.21602
$494$		0			0
$495$	−4.50000	+	7.79423i	−0.202260	+	0.350325i
$496$		0			0
$497$	−20.0000	+	6.92820i	−0.897123	+	0.310772i
$498$		0			0
$499$	−29.0000			−1.29822			−0.649109	−	0.760695i	$-0.724858\pi$
$499$	−29.0000			−1.29822			−0.649109	+	0.760695i	$0.724858\pi$
$500$		0			0
$501$			1.73205i			0.0773823i
$502$		0			0
$503$	12.0000			0.535054			0.267527	−	0.963550i	$-0.413794\pi$
$503$	12.0000			0.535054			0.267527	+	0.963550i	$0.413794\pi$
$504$		0			0
$505$	−7.00000			−0.311496
$506$		0			0
$507$	−18.0000	−	10.3923i	−0.799408	−	0.461538i
$508$		0			0
$509$	33.0000			1.46270			0.731350	−	0.682003i	$-0.238891\pi$
$509$	33.0000			1.46270			0.731350	+	0.682003i	$0.238891\pi$
$510$		0			0
$511$	−6.50000	+	33.7750i	−0.287543	+	1.49412i
$512$		0			0
$513$	22.5000	−	12.9904i	0.993399	−	0.573539i
$514$		0			0
$515$	9.00000			0.396587
$516$		0			0
$517$	12.0000	−	20.7846i	0.527759	−	0.914106i
$518$		0			0
$519$			3.46410i			0.152057i
$520$		0			0
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	−0.897011	−	0.442007i	$-0.854267\pi$
$521$	−1.50000	+	2.59808i	−0.0657162	+	0.113824i	0.831295	+	0.555831i	$0.187600\pi$
$522$		0			0
$523$	−16.5000	−	28.5788i	−0.721495	−	1.24967i	−0.960401	−	0.278623i	$-0.910122\pi$
$523$	−16.5000	−	28.5788i	−0.721495	−	1.24967i	0.238906	−	0.971043i	$-0.423211\pi$
$524$		0			0
$525$	−12.0000	+	13.8564i	−0.523723	+	0.604743i
$526$		0			0
$527$	12.0000			0.522728
$528$		0			0
$529$	−22.0000			−0.956522
$530$		0			0
$531$	12.0000			0.520756
$532$		0			0
$533$	−3.50000	−	6.06218i	−0.151602	−	0.262582i
$534$		0			0
$535$	3.50000	+	6.06218i	0.151318	+	0.262091i
$536$		0			0
$537$			36.3731i			1.56961i
$538$		0			0
$539$	−16.5000	+	12.9904i	−0.710705	+	0.559535i
$540$		0			0
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	0.959697	−	0.281037i	$-0.0906783\pi$
$541$	5.50000	+	9.52628i	0.236463	+	0.409567i	−0.723234	+	0.690604i	$0.757345\pi$
$542$		0			0
$543$	27.0000	−	15.5885i	1.15868	−	0.668965i
$544$		0			0
$545$	−2.50000	+	4.33013i	−0.107088	+	0.185482i
$546$		0			0
$547$	2.50000	+	4.33013i	0.106892	+	0.185143i	0.914510	−	0.404564i	$-0.132577\pi$
$547$	2.50000	+	4.33013i	0.106892	+	0.185143i	−0.807617	+	0.589707i	$0.799243\pi$
$548$		0			0
$549$	3.00000	+	5.19615i	0.128037	+	0.221766i
$550$		0			0
$551$	−22.5000	+	38.9711i	−0.958532	+	1.66023i
$552$		0			0
$553$	4.00000	−	20.7846i	0.170097	−	0.883852i
$554$		0			0
$555$	7.50000	+	4.33013i	0.318357	+	0.183804i
$556$		0			0
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	−0.0747252	−	0.997204i	$-0.523808\pi$
$557$	19.5000	−	33.7750i	0.826242	−	1.43109i	0.900967	−	0.433888i	$-0.142859\pi$
$558$		0			0
$559$	3.00000			0.126886
$560$		0			0
$561$			15.5885i			0.658145i
$562$		0			0
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	0.964315	−	0.264758i	$-0.0852922\pi$
$563$	6.00000	+	10.3923i	0.252870	+	0.437983i	−0.711445	+	0.702742i	$0.751959\pi$
$564$		0			0
$565$	0.500000	−	0.866025i	0.0210352	−	0.0364340i
$566$		0			0
$567$	18.0000	+	15.5885i	0.755929	+	0.654654i
$568$		0			0
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.0294311	−	0.999567i	$-0.490630\pi$
$569$	21.0000	−	36.3731i	0.880366	−	1.52484i	0.850935	−	0.525271i	$-0.176036\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$		0			0
$573$		−	6.92820i		−	0.289430i
$574$		0			0
$575$	−4.00000			−0.166812
$576$		0			0
$577$	−1.50000	+	2.59808i	−0.0624458	+	0.108159i	−0.895558	−	0.444945i	$-0.853223\pi$
$577$	−1.50000	+	2.59808i	−0.0624458	+	0.108159i	0.833112	+	0.553104i	$0.186557\pi$
$578$		0			0
$579$	−27.0000	−	15.5885i	−1.12208	−	0.647834i
$580$		0			0
$581$	−26.0000	−	22.5167i	−1.07866	−	0.934148i
$582$		0			0
$583$	13.5000	−	23.3827i	0.559113	−	0.968412i
$584$		0			0
$585$	1.50000	+	2.59808i	0.0620174	+	0.107417i
$586$		0			0
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	0.668708	−	0.743525i	$-0.266848\pi$
$587$	−7.50000	−	12.9904i	−0.309558	−	0.536170i	−0.978266	+	0.207355i	$0.933514\pi$
$588$		0			0
$589$	−10.0000	+	17.3205i	−0.412043	+	0.713679i
$590$		0			0
$591$	33.0000	−	19.0526i	1.35744	−	0.783718i
$592$		0			0
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	0.996976	−	0.0777165i	$-0.0247629\pi$
$593$	10.5000	+	18.1865i	0.431183	+	0.746831i	−0.565792	+	0.824548i	$0.691430\pi$
$594$		0			0
$595$	1.50000	−	7.79423i	0.0614940	−	0.319532i
$596$		0			0
$597$		−	36.3731i		−	1.48865i
$598$		0			0
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	0.999938	−	0.0111569i	$-0.00355143\pi$
$599$	12.0000	+	20.7846i	0.490307	+	0.849236i	−0.509631	+	0.860393i	$0.670218\pi$
$600$		0			0
$601$	−11.5000	−	19.9186i	−0.469095	−	0.812496i	0.530281	−	0.847822i	$-0.322086\pi$
$601$	−11.5000	−	19.9186i	−0.469095	−	0.812496i	−0.999376	+	0.0353259i	$0.988753\pi$
$602$		0			0
$603$	−36.0000			−1.46603
$604$		0			0
$605$	−2.00000			−0.0813116
$606$		0			0
$607$	−23.0000			−0.933541			−0.466771	−	0.884378i	$-0.654583\pi$
$607$	−23.0000			−0.933541			−0.466771	+	0.884378i	$0.654583\pi$
$608$		0			0
$609$	−40.5000	−	7.79423i	−1.64114	−	0.315838i
$610$		0			0
$611$	−4.00000	−	6.92820i	−0.161823	−	0.280285i
$612$		0			0
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	−0.912086	−	0.409998i	$-0.865529\pi$
$613$	−2.50000	+	4.33013i	−0.100974	+	0.174892i	0.811112	+	0.584891i	$0.198863\pi$
$614$		0			0
$615$		−	12.1244i		−	0.488901i
$616$		0			0
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	−0.894639	−	0.446790i	$-0.852567\pi$
$617$	−1.50000	+	2.59808i	−0.0603877	+	0.104595i	0.834251	+	0.551385i	$0.185900\pi$
$618$		0			0
$619$	21.0000			0.844061			0.422031	−	0.906582i	$-0.361317\pi$
$619$	21.0000			0.844061			0.422031	+	0.906582i	$0.361317\pi$
$620$		0			0
$621$			5.19615i			0.208514i
$622$		0			0
$623$	−18.0000	−	15.5885i	−0.721155	−	0.624538i
$624$		0			0
$625$	11.0000			0.440000
$626$		0			0
$627$	−22.5000	−	12.9904i	−0.898563	−	0.518786i
$628$		0			0
$629$	15.0000			0.598089
$630$		0			0
$631$	40.0000			1.59237			0.796187	−	0.605050i	$-0.206847\pi$
$631$	40.0000			1.59237			0.796187	+	0.605050i	$0.206847\pi$
$632$		0			0
$633$			46.7654i			1.85876i
$634$		0			0
$635$	8.00000			0.317470
$636$		0			0
$637$	1.00000	+	6.92820i	0.0396214	+	0.274505i
$638$		0			0
$639$	12.0000	−	20.7846i	0.474713	−	0.822226i
$640$		0			0
$641$	−5.00000			−0.197488			−0.0987441	−	0.995113i	$-0.531483\pi$
$641$	−5.00000			−0.197488			−0.0987441	+	0.995113i	$0.531483\pi$
$642$		0			0
$643$	−18.5000	+	32.0429i	−0.729569	+	1.26365i	0.227497	+	0.973779i	$0.426946\pi$
$643$	−18.5000	+	32.0429i	−0.729569	+	1.26365i	−0.957066	+	0.289871i	$0.906387\pi$
$644$		0			0
$645$	4.50000	+	2.59808i	0.177187	+	0.102299i
$646$		0			0
$647$	−20.5000	+	35.5070i	−0.805938	+	1.39593i	0.109718	+	0.993963i	$0.465005\pi$
$647$	−20.5000	+	35.5070i	−0.805938	+	1.39593i	−0.915656	+	0.401963i	$0.868328\pi$
$648$		0			0
$649$	−6.00000	−	10.3923i	−0.235521	−	0.407934i
$650$		0			0
$651$	−18.0000	−	3.46410i	−0.705476	−	0.135769i
$652$		0			0
$653$	−3.00000			−0.117399			−0.0586995	−	0.998276i	$-0.518695\pi$
$653$	−3.00000			−0.117399			−0.0586995	+	0.998276i	$0.518695\pi$
$654$		0			0
$655$	3.00000			0.117220
$656$		0			0
$657$	−19.5000	−	33.7750i	−0.760767	−	1.31769i
$658$		0			0
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	0.682161	−	0.731202i	$-0.261040\pi$
$659$	−7.50000	−	12.9904i	−0.292159	−	0.506033i	−0.974320	+	0.225168i	$0.927707\pi$
$660$		0			0
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	0.213925	−	0.976850i	$-0.431375\pi$
$662$		0			0
$663$	4.50000	+	2.59808i	0.174766	+	0.100901i
$664$		0			0
$665$	10.0000	+	8.66025i	0.387783	+	0.335830i
$666$		0			0
$667$	−4.50000	−	7.79423i	−0.174241	−	0.301794i
$668$		0			0
$669$	19.5000	+	11.2583i	0.753914	+	0.435272i
$670$		0			0
$671$	3.00000	−	5.19615i	0.115814	−	0.200595i
$672$		0			0
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	−0.976593	−	0.215096i	$-0.930993\pi$
$673$	−17.5000	−	30.3109i	−0.674575	−	1.16840i	0.302017	−	0.953302i	$-0.402340\pi$
$674$		0			0
$675$		−	20.7846i		−	0.800000i
$676$		0			0
$677$	−19.0000	+	32.9090i	−0.730229	+	1.26479i	0.226556	+	0.973998i	$0.427253\pi$
$677$	−19.0000	+	32.9090i	−0.730229	+	1.26479i	−0.956785	+	0.290796i	$0.906080\pi$
$678$		0			0
$679$	−34.0000	−	29.4449i	−1.30480	−	1.12999i
$680$		0			0
$681$	22.5000	−	12.9904i	0.862202	−	0.497792i
$682$		0			0
$683$	−15.5000	+	26.8468i	−0.593091	+	1.02726i	0.400722	+	0.916200i	$0.368759\pi$
$683$	−15.5000	+	26.8468i	−0.593091	+	1.02726i	−0.993813	+	0.111064i	$0.964574\pi$
$684$		0			0
$685$	11.0000			0.420288
$686$		0			0
$687$	−31.5000	+	18.1865i	−1.20180	+	0.693860i
$688$		0			0
$689$	−4.50000	−	7.79423i	−0.171436	−	0.296936i
$690$		0			0
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	−0.729039	−	0.684472i	$-0.760033\pi$
$691$	6.00000	−	10.3923i	0.228251	−	0.395342i	0.957290	+	0.289130i	$0.0933661\pi$
$692$		0			0
$693$	4.50000	−	23.3827i	0.170941	−	0.888235i
$694$		0			0
$695$	−2.50000	+	4.33013i	−0.0948304	+	0.164251i
$696$		0			0
$697$	−10.5000	−	18.1865i	−0.397716	−	0.688864i
$698$		0			0
$699$	4.50000	+	2.59808i	0.170206	+	0.0982683i
$700$		0			0
$701$	−26.0000			−0.982006			−0.491003	−	0.871158i	$-0.663370\pi$
$701$	−26.0000			−0.982006			−0.491003	+	0.871158i	$0.663370\pi$
$702$		0			0
$703$	−12.5000	+	21.6506i	−0.471446	+	0.816569i
$704$		0			0
$705$		−	13.8564i		−	0.521862i
$706$		0			0
$707$	17.5000	−	6.06218i	0.658155	−	0.227992i
$708$		0			0
$709$	9.00000	−	15.5885i	0.338002	−	0.585437i	−0.646055	−	0.763291i	$-0.723582\pi$
$709$	9.00000	−	15.5885i	0.338002	−	0.585437i	0.984057	+	0.177854i	$0.0569156\pi$
$710$		0			0
$711$	12.0000	+	20.7846i	0.450035	+	0.779484i
$712$		0			0
$713$	−2.00000	−	3.46410i	−0.0749006	−	0.129732i
$714$		0			0
$715$	1.50000	−	2.59808i	0.0560968	−	0.0971625i
$716$		0			0
$717$			15.5885i			0.582162i
$718$		0			0
$719$	−9.50000	−	16.4545i	−0.354290	−	0.613649i	0.632706	−	0.774392i	$-0.281944\pi$
$719$	−9.50000	−	16.4545i	−0.354290	−	0.613649i	−0.986996	+	0.160743i	$0.948611\pi$
$720$		0			0
$721$	−22.5000	+	7.79423i	−0.837944	+	0.290272i
$722$		0			0
$723$	1.50000	−	0.866025i	0.0557856	−	0.0322078i
$724$		0			0
$725$	18.0000	+	31.1769i	0.668503	+	1.15788i
$726$		0			0
$727$	−8.50000	−	14.7224i	−0.315248	−	0.546025i	0.664243	−	0.747517i	$-0.268754\pi$
$727$	−8.50000	−	14.7224i	−0.315248	−	0.546025i	−0.979490	+	0.201492i	$0.935421\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$		0			0
$731$	9.00000			0.332877
$732$		0			0
$733$	−43.0000			−1.58824			−0.794121	−	0.607760i	$-0.792068\pi$
$733$	−43.0000			−1.58824			−0.794121	+	0.607760i	$0.792068\pi$
$734$		0			0
$735$	−4.50000	+	11.2583i	−0.165985	+	0.415270i
$736$		0			0
$737$	18.0000	+	31.1769i	0.663039	+	1.14842i
$738$		0			0
$739$	8.50000	−	14.7224i	0.312678	−	0.541573i	−0.666264	−	0.745716i	$-0.732107\pi$
$739$	8.50000	−	14.7224i	0.312678	−	0.541573i	0.978941	+	0.204143i	$0.0654407\pi$
$740$		0			0
$741$	−7.50000	+	4.33013i	−0.275519	+	0.159071i
$742$		0			0
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	−0.856708	−	0.515802i	$-0.827494\pi$
$743$	0.500000	−	0.866025i	0.0183432	−	0.0317714i	0.875051	+	0.484030i	$0.160828\pi$
$744$		0			0
$745$	−15.0000			−0.549557
$746$		0			0
$747$	39.0000			1.42694
$748$		0			0
$749$	−14.0000	−	12.1244i	−0.511549	−	0.443014i
$750$		0			0
$751$	−15.0000			−0.547358			−0.273679	−	0.961821i	$-0.588241\pi$
$751$	−15.0000			−0.547358			−0.273679	+	0.961821i	$0.588241\pi$
$752$		0			0
$753$	−6.00000	+	3.46410i	−0.218652	+	0.126239i
$754$		0			0
$755$	−17.0000			−0.618693
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$		0			0
$759$	4.50000	−	2.59808i	0.163340	−	0.0943042i
$760$		0			0
$761$	−45.0000			−1.63125			−0.815624	−	0.578582i	$-0.803606\pi$
$761$	−45.0000			−1.63125			−0.815624	+	0.578582i	$0.803606\pi$
$762$		0			0
$763$	2.50000	−	12.9904i	0.0905061	−	0.470283i
$764$		0			0
$765$	4.50000	+	7.79423i	0.162698	+	0.281801i
$766$		0			0
$767$	−4.00000			−0.144432
$768$		0			0
$769$	20.5000	−	35.5070i	0.739249	−	1.28042i	−0.213585	−	0.976924i	$-0.568514\pi$
$769$	20.5000	−	35.5070i	0.739249	−	1.28042i	0.952834	−	0.303492i	$-0.0981526\pi$
$770$		0			0
$771$	25.5000	−	14.7224i	0.918360	−	0.530215i
$772$		0			0
$773$	3.50000	−	6.06218i	0.125886	−	0.218041i	−0.796193	−	0.605043i	$-0.793156\pi$
$773$	3.50000	−	6.06218i	0.125886	−	0.218041i	0.922079	+	0.387002i	$0.126489\pi$
$774$		0			0
$775$	8.00000	+	13.8564i	0.287368	+	0.497737i
$776$		0			0
$777$	−22.5000	−	4.33013i	−0.807183	−	0.155342i
$778$		0			0
$779$	35.0000			1.25401
$780$		0			0
$781$	−24.0000			−0.858788
$782$		0			0
$783$	40.5000	−	23.3827i	1.44735	−	0.835629i
$784$		0			0
$785$	−7.00000	−	12.1244i	−0.249841	−	0.432737i
$786$		0			0
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	0.630905	−	0.775860i	$-0.282684\pi$
$787$	−10.0000	−	17.3205i	−0.356462	−	0.617409i	−0.987367	+	0.158450i	$0.949350\pi$
$788$		0			0
$789$	−16.5000	+	9.52628i	−0.587416	+	0.339145i
$790$		0			0
$791$	−0.500000	+	2.59808i	−0.0177780	+	0.0923770i
$792$		0			0
$793$	−1.00000	−	1.73205i	−0.0355110	−	0.0615069i
$794$		0			0
$795$		−	15.5885i		−	0.552866i
$796$		0			0
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	−0.280875	−	0.959744i	$-0.590625\pi$
$797$	19.5000	−	33.7750i	0.690725	−	1.19637i	0.971601	−	0.236627i	$-0.0760420\pi$
$798$		0			0
$799$	−12.0000	−	20.7846i	−0.424529	−	0.735307i
$800$		0			0
$801$	27.0000			0.953998
$802$		0			0
$803$	−19.5000	+	33.7750i	−0.688140	+	1.19189i
$804$		0			0
$805$	−2.50000	+	0.866025i	−0.0881134	+	0.0305234i
$806$		0			0
$807$			12.1244i			0.426798i
$808$		0			0
$809$	−27.5000	+	47.6314i	−0.966849	+	1.67463i	−0.262284	+	0.964991i	$0.584476\pi$
$809$	−27.5000	+	47.6314i	−0.966849	+	1.67463i	−0.704564	+	0.709640i	$0.748858\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$		0			0
$813$	46.5000	+	26.8468i	1.63083	+	0.941558i
$814$		0			0
$815$	−8.50000	−	14.7224i	−0.297742	−	0.515704i
$816$		0			0
$817$	−7.50000	+	12.9904i	−0.262392	+	0.454476i
$818$		0			0
$819$	−6.00000	−	5.19615i	−0.209657	−	0.181568i
$820$		0			0
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	0.222731	+	0.974880i	$0.428503\pi$
$821$	−21.0000	+	36.3731i	−0.732905	+	1.26943i	−0.955636	+	0.294549i	$0.904831\pi$
$822$		0			0
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	0.969448	+	0.245295i	$0.0788849\pi$
$823$	20.0000	+	34.6410i	0.697156	+	1.20751i	−0.272292	+	0.962215i	$0.587782\pi$
$824$		0			0
$825$	−18.0000	+	10.3923i	−0.626680	+	0.361814i
$826$		0			0
$827$	−40.0000			−1.39094			−0.695468	−	0.718557i	$-0.744803\pi$
$827$	−40.0000			−1.39094			−0.695468	+	0.718557i	$0.744803\pi$
$828$		0			0
$829$	−2.50000	+	4.33013i	−0.0868286	+	0.150392i	−0.906169	−	0.422916i	$-0.861007\pi$
$829$	−2.50000	+	4.33013i	−0.0868286	+	0.150392i	0.819340	+	0.573307i	$0.194340\pi$
$830$		0			0
$831$	28.5000	−	16.4545i	0.988654	−	0.570800i
$832$		0			0
$833$	3.00000	+	20.7846i	0.103944	+	0.720144i
$834$		0			0
$835$	0.500000	−	0.866025i	0.0173032	−	0.0299700i
$836$		0			0
$837$	18.0000	−	10.3923i	0.622171	−	0.359211i
$838$		0			0
$839$	−22.5000	−	38.9711i	−0.776786	−	1.34543i	−0.933785	−	0.357834i	$-0.883515\pi$
$839$	−22.5000	−	38.9711i	−0.776786	−	1.34543i	0.156999	−	0.987599i	$-0.449818\pi$
$840$		0			0
$841$	−26.0000	+	45.0333i	−0.896552	+	1.55287i
$842$		0			0
$843$	40.5000	+	23.3827i	1.39489	+	0.805342i
$844$		0			0
$845$	6.00000	+	10.3923i	0.206406	+	0.357506i
$846$		0			0
$847$	5.00000	−	1.73205i	0.171802	−	0.0595140i
$848$		0			0
$849$	−36.0000	−	20.7846i	−1.23552	−	0.713326i
$850$		0			0
$851$	−2.50000	−	4.33013i	−0.0856989	−	0.148435i
$852$		0			0
$853$	−14.5000	−	25.1147i	−0.496471	−	0.859912i	0.503521	−	0.863983i	$-0.332038\pi$
$853$	−14.5000	−	25.1147i	−0.496471	−	0.859912i	−0.999992	+	0.00407068i	$0.998704\pi$
$854$		0			0
$855$	−15.0000			−0.512989
$856$		0			0
$857$	7.00000			0.239115			0.119558	−	0.992827i	$-0.461852\pi$
$857$	7.00000			0.239115			0.119558	+	0.992827i	$0.461852\pi$
$858$		0			0
$859$	19.0000			0.648272			0.324136	−	0.946011i	$-0.394927\pi$
$859$	19.0000			0.648272			0.324136	+	0.946011i	$0.394927\pi$
$860$		0			0
$861$	10.5000	+	30.3109i	0.357839	+	1.03299i
$862$		0			0
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	0.757101	−	0.653298i	$-0.226615\pi$
$863$	−5.50000	−	9.52628i	−0.187222	−	0.324278i	−0.944323	+	0.329020i	$0.893282\pi$
$864$		0			0
$865$	1.00000	−	1.73205i	0.0340010	−	0.0588915i
$866$		0			0
$867$	−12.0000	−	6.92820i	−0.407541	−	0.235294i
$868$		0			0
$869$	12.0000	−	20.7846i	0.407072	−	0.705070i
$870$		0			0
$871$	12.0000			0.406604
$872$		0			0
$873$	51.0000			1.72609
$874$		0			0
$875$	22.5000	−	7.79423i	0.760639	−	0.263493i
$876$		0			0
$877$	−23.0000			−0.776655			−0.388327	−	0.921521i	$-0.626947\pi$
$877$	−23.0000			−0.776655			−0.388327	+	0.921521i	$0.626947\pi$
$878$		0			0
$879$		−	1.73205i		−	0.0584206i
$880$		0			0
$881$	−18.0000			−0.606435			−0.303218	−	0.952921i	$-0.598061\pi$
$881$	−18.0000			−0.606435			−0.303218	+	0.952921i	$0.598061\pi$
$882$		0			0
$883$	52.0000			1.74994			0.874970	−	0.484178i	$-0.160881\pi$
$883$	52.0000			1.74994			0.874970	+	0.484178i	$0.160881\pi$
$884$		0			0
$885$	−6.00000	−	3.46410i	−0.201688	−	0.116445i
$886$		0			0
$887$	−27.0000			−0.906571			−0.453286	−	0.891365i	$-0.649748\pi$
$887$	−27.0000			−0.906571			−0.453286	+	0.891365i	$0.649748\pi$
$888$		0			0
$889$	−20.0000	+	6.92820i	−0.670778	+	0.232364i
$890$		0			0
$891$	13.5000	+	23.3827i	0.452267	+	0.783349i
$892$		0			0
$893$	40.0000			1.33855
$894$		0			0
$895$	10.5000	−	18.1865i	0.350976	−	0.607909i
$896$		0			0
$897$		−	1.73205i		−	0.0578315i
$898$		0			0
$899$	−18.0000	+	31.1769i	−0.600334	+	1.03981i
$900$		0			0
$901$	−13.5000	−	23.3827i	−0.449750	−	0.778990i
$902$		0			0
$903$	−13.5000	−	2.59808i	−0.449252	−	0.0864586i
$904$		0			0
$905$	−18.0000			−0.598340
$906$		0			0
$907$	−7.00000			−0.232431			−0.116216	−	0.993224i	$-0.537076\pi$
$907$	−7.00000			−0.232431			−0.116216	+	0.993224i	$0.537076\pi$
$908$		0			0
$909$	−10.5000	+	18.1865i	−0.348263	+	0.603209i
$910$		0			0
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	0.998208	−	0.0598468i	$-0.0190612\pi$
$911$	13.5000	+	23.3827i	0.447275	+	0.774703i	−0.550933	+	0.834550i	$0.685728\pi$
$912$		0			0
$913$	−19.5000	−	33.7750i	−0.645356	−	1.11779i
$914$		0			0
$915$		−	3.46410i		−	0.114520i
$916$		0			0
$917$	−7.50000	+	2.59808i	−0.247672	+	0.0857960i
$918$		0			0
$919$	6.50000	+	11.2583i	0.214415	+	0.371378i	0.953092	−	0.302682i	$-0.0978821\pi$
$919$	6.50000	+	11.2583i	0.214415	+	0.371378i	−0.738676	+	0.674060i	$0.764549\pi$
$920$		0			0
$921$	6.00000	−	3.46410i	0.197707	−	0.114146i
$922$		0			0
$923$	−4.00000	+	6.92820i	−0.131662	+	0.228045i
$924$		0			0
$925$	10.0000	+	17.3205i	0.328798	+	0.569495i
$926$		0			0
$927$	13.5000	−	23.3827i	0.443398	−	0.767988i
$928$		0			0
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	−0.679770	−	0.733426i	$-0.737920\pi$
$929$	9.00000	−	15.5885i	0.295280	−	0.511441i	0.975050	+	0.221985i	$0.0712536\pi$
$930$		0			0
$931$	−32.5000	−	12.9904i	−1.06514	−	0.425743i
$932$		0			0
$933$	36.0000	+	20.7846i	1.17859	+	0.680458i
$934$		0			0
$935$	4.50000	−	7.79423i	0.147166	−	0.254899i
$936$		0			0
$937$	−2.00000			−0.0653372			−0.0326686	−	0.999466i	$-0.510401\pi$
$937$	−2.00000			−0.0653372			−0.0326686	+	0.999466i	$0.510401\pi$
$938$		0			0
$939$		−	10.3923i		−	0.339140i
$940$		0			0
$941$	25.0000	+	43.3013i	0.814977	+	1.41158i	0.909345	+	0.416044i	$0.136584\pi$
$941$	25.0000	+	43.3013i	0.814977	+	1.41158i	−0.0943679	+	0.995537i	$0.530083\pi$
$942$		0			0
$943$	−3.50000	+	6.06218i	−0.113976	+	0.197412i
$944$		0			0
$945$	−4.50000	−	12.9904i	−0.146385	−	0.422577i
$946$		0			0
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	−0.409964	−	0.912102i	$-0.634459\pi$
$947$	18.0000	−	31.1769i	0.584921	−	1.01311i	0.994885	−	0.101012i	$-0.0322080\pi$
$948$		0			0
$949$	6.50000	+	11.2583i	0.210999	+	0.365461i
$950$		0			0
$951$		−	24.2487i		−	0.786318i
$952$		0			0
$953$	26.0000			0.842223			0.421111	−	0.907009i	$-0.361640\pi$
$953$	26.0000			0.842223			0.421111	+	0.907009i	$0.361640\pi$
$954$		0			0
$955$	−2.00000	+	3.46410i	−0.0647185	+	0.112096i
$956$		0			0
$957$	−40.5000	−	23.3827i	−1.30918	−	0.755855i
$958$		0			0
$959$	−27.5000	+	9.52628i	−0.888021	+	0.307620i
$960$		0			0
$961$	7.50000	−	12.9904i	0.241935	−	0.419045i
$962$		0			0
$963$	21.0000			0.676716
$964$		0			0
$965$	9.00000	+	15.5885i	0.289720	+	0.501810i
$966$		0			0
$967$	−13.5000	+	23.3827i	−0.434131	+	0.751936i	−0.997224	−	0.0744567i	$-0.976278\pi$
$967$	−13.5000	+	23.3827i	−0.434131	+	0.751936i	0.563094	+	0.826393i	$0.309611\pi$
$968$		0			0
$969$	−22.5000	+	12.9904i	−0.722804	+	0.417311i
$970$		0			0
$971$	21.5000	+	37.2391i	0.689968	+	1.19506i	0.971848	+	0.235610i	$0.0757087\pi$
$971$	21.5000	+	37.2391i	0.689968	+	1.19506i	−0.281880	+	0.959450i	$0.590958\pi$
$972$		0			0
$973$	2.50000	−	12.9904i	0.0801463	−	0.416452i
$974$		0			0
$975$			6.92820i			0.221880i
$976$		0			0
$977$	−11.0000	−	19.0526i	−0.351921	−	0.609545i	0.634665	−	0.772787i	$-0.281138\pi$
$977$	−11.0000	−	19.0526i	−0.351921	−	0.609545i	−0.986586	+	0.163242i	$0.947805\pi$
$978$		0			0
$979$	−13.5000	−	23.3827i	−0.431462	−	0.747314i
$980$		0			0
$981$	7.50000	+	12.9904i	0.239457	+	0.414751i
$982$		0			0
$983$	−41.0000			−1.30770			−0.653848	−	0.756626i	$-0.726847\pi$
$983$	−41.0000			−1.30770			−0.653848	+	0.756626i	$0.726847\pi$
$984$		0			0
$985$	−22.0000			−0.700978
$986$		0			0
$987$	12.0000	+	34.6410i	0.381964	+	1.10264i
$988$		0			0
$989$	−1.50000	−	2.59808i	−0.0476972	−	0.0826140i
$990$		0			0
$991$	7.50000	−	12.9904i	0.238245	−	0.412653i	−0.721966	−	0.691929i	$-0.756761\pi$
$991$	7.50000	−	12.9904i	0.238245	−	0.412653i	0.960211	+	0.279276i	$0.0900944\pi$
$992$		0			0
$993$		−	6.92820i		−	0.219860i
$994$		0			0
$995$	−10.5000	+	18.1865i	−0.332872	+	0.576552i
$996$		0			0
$997$	13.0000			0.411714			0.205857	−	0.978582i	$-0.434002\pi$
$997$	13.0000			0.411714			0.205857	+	0.978582i	$0.434002\pi$
$998$		0			0
$999$	22.5000	−	12.9904i	0.711868	−	0.410997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.t.a.193.1	yes	2
3.2	odd	2		1512.2.t.a.361.1		2
4.3	odd	2		1008.2.t.e.193.1		2
7.2	even	3		504.2.q.a.121.1	yes	2
9.2	odd	6		1512.2.q.b.1369.1		2
9.7	even	3		504.2.q.a.25.1	✓	2
12.11	even	2		3024.2.t.c.1873.1		2
21.2	odd	6		1512.2.q.b.793.1		2
28.23	odd	6		1008.2.q.b.625.1		2
36.7	odd	6		1008.2.q.b.529.1		2
36.11	even	6		3024.2.q.d.2881.1		2
63.2	odd	6		1512.2.t.a.289.1		2
63.16	even	3	inner	504.2.t.a.457.1	yes	2
84.23	even	6		3024.2.q.d.2305.1		2
252.79	odd	6		1008.2.t.e.961.1		2
252.191	even	6		3024.2.t.c.289.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.a.25.1	✓	2	9.7	even	3
504.2.q.a.121.1	yes	2	7.2	even	3
504.2.t.a.193.1	yes	2	1.1	even	1	trivial
504.2.t.a.457.1	yes	2	63.16	even	3	inner
1008.2.q.b.529.1		2	36.7	odd	6
1008.2.q.b.625.1		2	28.23	odd	6
1008.2.t.e.193.1		2	4.3	odd	2
1008.2.t.e.961.1		2	252.79	odd	6
1512.2.q.b.793.1		2	21.2	odd	6
1512.2.q.b.1369.1		2	9.2	odd	6
1512.2.t.a.289.1		2	63.2	odd	6
1512.2.t.a.361.1		2	3.2	odd	2
3024.2.q.d.2305.1		2	84.23	even	6
3024.2.q.d.2881.1		2	36.11	even	6
3024.2.t.c.289.1		2	252.191	even	6
3024.2.t.c.1873.1		2	12.11	even	2

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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.t (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 0.866025i) q^{3} +1.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 0.866025i) q^{3} +1.00000 q^{5} +(-2.50000 + 0.866025i) q^{7} +(1.50000 - 2.59808i) q^{9} -3.00000 q^{11} +(-0.500000 + 0.866025i) q^{13} +(-1.50000 + 0.866025i) q^{15} +(-1.50000 + 2.59808i) q^{17} +(-2.50000 - 4.33013i) q^{19} +(3.00000 - 3.46410i) q^{21} +1.00000 q^{23} -4.00000 q^{25} +5.19615i q^{27} +(-4.50000 - 7.79423i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(4.50000 - 2.59808i) q^{33} +(-2.50000 + 0.866025i) q^{35} +(-2.50000 - 4.33013i) q^{37} -1.73205i q^{39} +(-3.50000 + 6.06218i) q^{41} +(-1.50000 - 2.59808i) q^{43} +(1.50000 - 2.59808i) q^{45} +(-4.00000 + 6.92820i) q^{47} +(5.50000 - 4.33013i) q^{49} -5.19615i q^{51} +(-4.50000 + 7.79423i) q^{53} -3.00000 q^{55} +(7.50000 + 4.33013i) q^{57} +(2.00000 + 3.46410i) q^{59} +(-1.00000 + 1.73205i) q^{61} +(-1.50000 + 7.79423i) q^{63} +(-0.500000 + 0.866025i) q^{65} +(-6.00000 - 10.3923i) q^{67} +(-1.50000 + 0.866025i) q^{69} +8.00000 q^{71} +(6.50000 - 11.2583i) q^{73} +(6.00000 - 3.46410i) q^{75} +(7.50000 - 2.59808i) q^{77} +(-4.00000 + 6.92820i) q^{79} +(-4.50000 - 7.79423i) q^{81} +(6.50000 + 11.2583i) q^{83} +(-1.50000 + 2.59808i) q^{85} +(13.5000 + 7.79423i) q^{87} +(4.50000 + 7.79423i) q^{89} +(0.500000 - 2.59808i) q^{91} +(6.00000 + 3.46410i) q^{93} +(-2.50000 - 4.33013i) q^{95} +(8.50000 + 14.7224i) q^{97} +(-4.50000 + 7.79423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{3} + 2 q^{5} - 5 q^{7} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^3 + 2 * q^5 - 5 * q^7 + 3 * q^9	\( 2 q - 3 q^{3} + 2 q^{5} - 5 q^{7} + 3 q^{9} - 6 q^{11} - q^{13} - 3 q^{15} - 3 q^{17} - 5 q^{19} + 6 q^{21} + 2 q^{23} - 8 q^{25} - 9 q^{29} - 4 q^{31} + 9 q^{33} - 5 q^{35} - 5 q^{37} - 7 q^{41} - 3 q^{43} + 3 q^{45} - 8 q^{47} + 11 q^{49} - 9 q^{53} - 6 q^{55} + 15 q^{57} + 4 q^{59} - 2 q^{61} - 3 q^{63} - q^{65} - 12 q^{67} - 3 q^{69} + 16 q^{71} + 13 q^{73} + 12 q^{75} + 15 q^{77} - 8 q^{79} - 9 q^{81} + 13 q^{83} - 3 q^{85} + 27 q^{87} + 9 q^{89} + q^{91} + 12 q^{93} - 5 q^{95} + 17 q^{97} - 9 q^{99}+O(q^{100}) \) 2 * q - 3 * q^3 + 2 * q^5 - 5 * q^7 + 3 * q^9 - 6 * q^11 - q^13 - 3 * q^15 - 3 * q^17 - 5 * q^19 + 6 * q^21 + 2 * q^23 - 8 * q^25 - 9 * q^29 - 4 * q^31 + 9 * q^33 - 5 * q^35 - 5 * q^37 - 7 * q^41 - 3 * q^43 + 3 * q^45 - 8 * q^47 + 11 * q^49 - 9 * q^53 - 6 * q^55 + 15 * q^57 + 4 * q^59 - 2 * q^61 - 3 * q^63 - q^65 - 12 * q^67 - 3 * q^69 + 16 * q^71 + 13 * q^73 + 12 * q^75 + 15 * q^77 - 8 * q^79 - 9 * q^81 + 13 * q^83 - 3 * q^85 + 27 * q^87 + 9 * q^89 + q^91 + 12 * q^93 - 5 * q^95 + 17 * q^97 - 9 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more