LMFDB - Embedded newform 1638.2.r.l.1387.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(757,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1638.757");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.r (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:	$13.0794958511$
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 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			1387.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1638.1387
Dual form			1638.2.r.l.757.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{10} +(1.50000 - 2.59808i) q^{11} +(3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-1.00000 - 1.73205i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} -1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(0.500000 - 0.866025i) q^{28} +(2.50000 - 4.33013i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +7.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 - 1.73205i) q^{37} -5.00000 q^{38} +2.00000 q^{40} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 - 1.73205i) q^{43} -3.00000 q^{44} +(3.00000 + 5.19615i) q^{46} +1.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.50000 - 2.59808i) q^{52} -3.00000 q^{53} +(3.00000 - 5.19615i) q^{55} +(0.500000 + 0.866025i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(7.00000 - 1.73205i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-3.50000 + 6.06218i) q^{68} -2.00000 q^{70} +(4.00000 + 6.92820i) q^{71} +12.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{76} +3.00000 q^{77} +3.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(-2.50000 - 4.33013i) q^{82} +8.00000 q^{83} +(-7.00000 - 12.1244i) q^{85} +2.00000 q^{86} +(1.50000 - 2.59808i) q^{88} +(-5.50000 + 9.52628i) q^{89} +(2.50000 + 2.59808i) q^{91} -6.00000 q^{92} +(-0.500000 + 0.866025i) q^{94} +(5.00000 + 8.66025i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8}+O(q^{10}) $ 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8	$ 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8} - 2 q^{10} + 3 q^{11} + 7 q^{13} - 2 q^{14} - q^{16} - 7 q^{17} + 5 q^{19} - 2 q^{20} + 3 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} + q^{28} + 5 q^{29} - 4 q^{31} - q^{32} + 14 q^{34} + 2 q^{35} + 2 q^{37} - 10 q^{38} + 4 q^{40} - 5 q^{41} - 2 q^{43} - 6 q^{44} + 6 q^{46} + 2 q^{47} - q^{49} + q^{50} - 5 q^{52} - 6 q^{53} + 6 q^{55} + q^{56} + 5 q^{58} - 6 q^{59} - 7 q^{61} + 2 q^{62} + 2 q^{64} + 14 q^{65} - 2 q^{67} - 7 q^{68} - 4 q^{70} + 8 q^{71} + 24 q^{73} + 2 q^{74} + 5 q^{76} + 6 q^{77} + 6 q^{79} - 2 q^{80} - 5 q^{82} + 16 q^{83} - 14 q^{85} + 4 q^{86} + 3 q^{88} - 11 q^{89} + 5 q^{91} - 12 q^{92} - q^{94} + 10 q^{95} + 2 q^{97} - q^{98}+O(q^{100}) $ 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8 - 2 * q^10 + 3 * q^11 + 7 * q^13 - 2 * q^14 - q^16 - 7 * q^17 + 5 * q^19 - 2 * q^20 + 3 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 + q^28 + 5 * q^29 - 4 * q^31 - q^32 + 14 * q^34 + 2 * q^35 + 2 * q^37 - 10 * q^38 + 4 * q^40 - 5 * q^41 - 2 * q^43 - 6 * q^44 + 6 * q^46 + 2 * q^47 - q^49 + q^50 - 5 * q^52 - 6 * q^53 + 6 * q^55 + q^56 + 5 * q^58 - 6 * q^59 - 7 * q^61 + 2 * q^62 + 2 * q^64 + 14 * q^65 - 2 * q^67 - 7 * q^68 - 4 * q^70 + 8 * q^71 + 24 * q^73 + 2 * q^74 + 5 * q^76 + 6 * q^77 + 6 * q^79 - 2 * q^80 - 5 * q^82 + 16 * q^83 - 14 * q^85 + 4 * q^86 + 3 * q^88 - 11 * q^89 + 5 * q^91 - 12 * q^92 - q^94 + 10 * q^95 + 2 * q^97 - q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	2.00000			0.894427			0.447214	−	0.894427i	$-0.352416\pi$
$5$	2.00000			0.894427			0.447214	+	0.894427i	$0.352416\pi$
$6$		0			0
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$		0			0
$10$	−1.00000	+	1.73205i	−0.316228	+	0.547723i
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	−0.546259	−	0.837616i	$-0.683949\pi$
$11$	1.50000	−	2.59808i	0.452267	−	0.783349i	0.998526	+	0.0542666i	$0.0172821\pi$
$12$		0			0
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$13$	3.50000	−	0.866025i	0.970725	−	0.240192i
$14$	−1.00000			−0.267261
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	−0.882213	−	0.470850i	$-0.843947\pi$
$17$	−3.50000	−	6.06218i	−0.848875	−	1.47029i	0.0333386	−	0.999444i	$-0.489386\pi$
$18$		0			0
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	0.996199	+	0.0871106i	$0.0277634\pi$
$19$	2.50000	+	4.33013i	0.573539	+	0.993399i	−0.422659	+	0.906289i	$0.638903\pi$
$20$	−1.00000	−	1.73205i	−0.223607	−	0.387298i
$21$		0			0
$22$	1.50000	+	2.59808i	0.319801	+	0.553912i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$		0			0
$25$	−1.00000			−0.200000
$26$	−1.00000	+	3.46410i	−0.196116	+	0.679366i
$27$		0			0
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	−0.534928	−	0.844897i	$-0.679661\pi$
$29$	2.50000	−	4.33013i	0.464238	−	0.804084i	0.999167	+	0.0408130i	$0.0129948\pi$
$30$		0			0
$31$	−2.00000			−0.359211			−0.179605	−	0.983739i	$-0.557482\pi$
$31$	−2.00000			−0.359211			−0.179605	+	0.983739i	$0.557482\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	7.00000			1.20049
$35$	1.00000	+	1.73205i	0.169031	+	0.292770i
$36$		0			0
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	−0.772043	−	0.635571i	$-0.780765\pi$
$37$	1.00000	−	1.73205i	0.164399	−	0.284747i	0.936442	+	0.350823i	$0.114098\pi$
$38$	−5.00000			−0.811107
$39$		0			0
$40$	2.00000			0.316228
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	−0.992507	−	0.122189i	$-0.961009\pi$
$41$	−2.50000	+	4.33013i	−0.390434	+	0.676252i	0.602072	+	0.798441i	$0.294342\pi$
$42$		0			0
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	0.779647	−	0.626219i	$-0.215399\pi$
$43$	−1.00000	−	1.73205i	−0.152499	−	0.264135i	−0.932145	+	0.362084i	$0.882065\pi$
$44$	−3.00000			−0.452267
$45$		0			0
$46$	3.00000	+	5.19615i	0.442326	+	0.766131i
$47$	1.00000			0.145865			0.0729325	−	0.997337i	$-0.476764\pi$
$47$	1.00000			0.145865			0.0729325	+	0.997337i	$0.476764\pi$
$48$		0			0
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$		0			0
$52$	−2.50000	−	2.59808i	−0.346688	−	0.360288i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$		0			0
$55$	3.00000	−	5.19615i	0.404520	−	0.700649i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$		0			0
$58$	2.50000	+	4.33013i	0.328266	+	0.568574i
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	0.550135	−	0.835076i	$-0.314576\pi$
$61$	−3.50000	−	6.06218i	−0.448129	−	0.776182i	−0.998264	+	0.0588933i	$0.981243\pi$
$62$	1.00000	−	1.73205i	0.127000	−	0.219971i
$63$		0			0
$64$	1.00000			0.125000
$65$	7.00000	−	1.73205i	0.868243	−	0.214834i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$	−3.50000	+	6.06218i	−0.424437	+	0.735147i
$69$		0			0
$70$	−2.00000			−0.239046
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	0.999581	−	0.0289572i	$-0.00921865\pi$
$71$	4.00000	+	6.92820i	0.474713	+	0.822226i	−0.524868	+	0.851184i	$0.675885\pi$
$72$		0			0
$73$	12.0000			1.40449			0.702247	−	0.711934i	$-0.252180\pi$
$73$	12.0000			1.40449			0.702247	+	0.711934i	$0.252180\pi$
$74$	1.00000	+	1.73205i	0.116248	+	0.201347i
$75$		0			0
$76$	2.50000	−	4.33013i	0.286770	−	0.496700i
$77$	3.00000			0.341882
$78$		0			0
$79$	3.00000			0.337526			0.168763	−	0.985657i	$-0.446023\pi$
$79$	3.00000			0.337526			0.168763	+	0.985657i	$0.446023\pi$
$80$	−1.00000	+	1.73205i	−0.111803	+	0.193649i
$81$		0			0
$82$	−2.50000	−	4.33013i	−0.276079	−	0.478183i
$83$	8.00000			0.878114			0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000			0.878114			0.439057	+	0.898459i	$0.355313\pi$
$84$		0			0
$85$	−7.00000	−	12.1244i	−0.759257	−	1.31507i
$86$	2.00000			0.215666
$87$		0			0
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−5.50000	+	9.52628i	−0.582999	+	1.00978i	0.412123	+	0.911128i	$0.364787\pi$
$89$	−5.50000	+	9.52628i	−0.582999	+	1.00978i	−0.995122	+	0.0986553i	$0.968546\pi$
$90$		0			0
$91$	2.50000	+	2.59808i	0.262071	+	0.272352i
$92$	−6.00000			−0.625543
$93$		0			0
$94$	−0.500000	+	0.866025i	−0.0515711	+	0.0893237i
$95$	5.00000	+	8.66025i	0.512989	+	0.888523i
$96$		0			0
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$		0			0
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	−0.273138	−	0.961975i	$-0.588061\pi$
$101$	7.00000	−	12.1244i	0.696526	−	1.20642i	0.969664	−	0.244443i	$-0.0786053\pi$
$102$		0			0
$103$	10.0000			0.985329			0.492665	−	0.870219i	$-0.336023\pi$
$103$	10.0000			0.985329			0.492665	+	0.870219i	$0.336023\pi$
$104$	3.50000	−	0.866025i	0.343203	−	0.0849208i
$105$		0			0
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	−0.233900	−	0.972261i	$-0.575149\pi$
$107$	7.50000	−	12.9904i	0.725052	−	1.25583i	0.958952	−	0.283567i	$-0.0915178\pi$
$108$		0			0
$109$	−16.0000			−1.53252			−0.766261	−	0.642529i	$-0.777885\pi$
$109$	−16.0000			−1.53252			−0.766261	+	0.642529i	$0.777885\pi$
$110$	3.00000	+	5.19615i	0.286039	+	0.495434i
$111$		0			0
$112$	−1.00000			−0.0944911
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	0.971930	−	0.235269i	$-0.0755971\pi$
$113$	3.00000	+	5.19615i	0.282216	+	0.488813i	−0.689714	+	0.724082i	$0.742264\pi$
$114$		0			0
$115$	6.00000	−	10.3923i	0.559503	−	0.969087i
$116$	−5.00000			−0.464238
$117$		0			0
$118$	6.00000			0.552345
$119$	3.50000	−	6.06218i	0.320844	−	0.555719i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	7.00000			0.633750
$123$		0			0
$124$	1.00000	+	1.73205i	0.0898027	+	0.155543i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	−0.466870	−	0.884326i	$-0.654618\pi$
$127$	6.00000	−	10.3923i	0.532414	−	0.922168i	0.999284	−	0.0378419i	$-0.0120483\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−2.00000	+	6.92820i	−0.175412	+	0.607644i
$131$	−8.00000			−0.698963			−0.349482	−	0.936943i	$-0.613642\pi$
$131$	−8.00000			−0.698963			−0.349482	+	0.936943i	$0.613642\pi$
$132$		0			0
$133$	−2.50000	+	4.33013i	−0.216777	+	0.375470i
$134$	−1.00000	−	1.73205i	−0.0863868	−	0.149626i
$135$		0			0
$136$	−3.50000	−	6.06218i	−0.300123	−	0.519827i
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	0.938148	+	0.346235i	$0.112540\pi$
$137$	9.00000	+	15.5885i	0.768922	+	1.33181i	−0.169226	+	0.985577i	$0.554127\pi$
$138$		0			0
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	0.915764	+	0.401718i	$0.131587\pi$
$139$	9.50000	+	16.4545i	0.805779	+	1.39565i	−0.109984	+	0.993933i	$0.535080\pi$
$140$	1.00000	−	1.73205i	0.0845154	−	0.146385i
$141$		0			0
$142$	−8.00000			−0.671345
$143$	3.00000	−	10.3923i	0.250873	−	0.869048i
$144$		0			0
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$	−6.00000	+	10.3923i	−0.496564	+	0.860073i
$147$		0			0
$148$	−2.00000			−0.164399
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	0.996207	+	0.0870170i	$0.0277334\pi$
$149$	7.00000	+	12.1244i	0.573462	+	0.993266i	−0.422744	+	0.906249i	$0.638933\pi$
$150$		0			0
$151$	13.0000			1.05792			0.528962	−	0.848645i	$-0.322581\pi$
$151$	13.0000			1.05792			0.528962	+	0.848645i	$0.322581\pi$
$152$	2.50000	+	4.33013i	0.202777	+	0.351220i
$153$		0			0
$154$	−1.50000	+	2.59808i	−0.120873	+	0.209359i
$155$	−4.00000			−0.321288
$156$		0			0
$157$	−18.0000			−1.43656			−0.718278	−	0.695756i	$-0.755069\pi$
$157$	−18.0000			−1.43656			−0.718278	+	0.695756i	$0.755069\pi$
$158$	−1.50000	+	2.59808i	−0.119334	+	0.206692i
$159$		0			0
$160$	−1.00000	−	1.73205i	−0.0790569	−	0.136931i
$161$	6.00000			0.472866
$162$		0			0
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	0.998392	+	0.0566798i	$0.0180514\pi$
$163$	7.00000	+	12.1244i	0.548282	+	0.949653i	−0.450110	+	0.892973i	$0.648615\pi$
$164$	5.00000			0.390434
$165$		0			0
$166$	−4.00000	+	6.92820i	−0.310460	+	0.537733i
$167$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$167$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$168$		0			0
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$	14.0000			1.07375
$171$		0			0
$172$	−1.00000	+	1.73205i	−0.0762493	+	0.132068i
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$		0			0
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	1.50000	+	2.59808i	0.113067	+	0.195837i
$177$		0			0
$178$	−5.50000	−	9.52628i	−0.412242	−	0.714025i
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	−0.201613	−	0.979465i	$-0.564618\pi$
$179$	10.0000	−	17.3205i	0.747435	−	1.29460i	0.949048	−	0.315130i	$-0.102048\pi$
$180$		0			0
$181$	−9.00000			−0.668965			−0.334482	−	0.942402i	$-0.608561\pi$
$181$	−9.00000			−0.668965			−0.334482	+	0.942402i	$0.608561\pi$
$182$	−3.50000	+	0.866025i	−0.259437	+	0.0641941i
$183$		0			0
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$		0			0
$187$	−21.0000			−1.53567
$188$	−0.500000	−	0.866025i	−0.0364662	−	0.0631614i
$189$		0			0
$190$	−10.0000			−0.725476
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	0.784552	−	0.620063i	$-0.212893\pi$
$191$	−2.00000	−	3.46410i	−0.144715	−	0.250654i	−0.929267	+	0.369410i	$0.879560\pi$
$192$		0			0
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	−0.999326	−	0.0366998i	$-0.988315\pi$
$193$	−6.50000	+	11.2583i	−0.467880	+	0.810392i	0.531446	+	0.847092i	$0.321649\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	1.00000			0.0714286
$197$	−4.50000	+	7.79423i	−0.320612	+	0.555316i	−0.980614	−	0.195947i	$-0.937222\pi$
$197$	−4.50000	+	7.79423i	−0.320612	+	0.555316i	0.660003	+	0.751263i	$0.270555\pi$
$198$		0			0
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.797025	+	0.603947i	$0.206406\pi$
$199$	13.0000	+	22.5167i	0.921546	+	1.59616i	0.124521	+	0.992217i	$0.460261\pi$
$200$	−1.00000			−0.0707107
$201$		0			0
$202$	7.00000	+	12.1244i	0.492518	+	0.853067i
$203$	5.00000			0.350931
$204$		0			0
$205$	−5.00000	+	8.66025i	−0.349215	+	0.604858i
$206$	−5.00000	+	8.66025i	−0.348367	+	0.603388i
$207$		0			0
$208$	−1.00000	+	3.46410i	−0.0693375	+	0.240192i
$209$	15.0000			1.03757
$210$		0			0
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	−0.640996	−	0.767544i	$-0.721479\pi$
$211$	5.00000	−	8.66025i	0.344214	−	0.596196i	0.985211	+	0.171347i	$0.0548120\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$		0			0
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	−2.00000	−	3.46410i	−0.136399	−	0.236250i
$216$		0			0
$217$	−1.00000	−	1.73205i	−0.0678844	−	0.117579i
$218$	8.00000	−	13.8564i	0.541828	−	0.938474i
$219$		0			0
$220$	−6.00000			−0.404520
$221$	−17.5000	−	18.1865i	−1.17718	−	1.22336i
$222$		0			0
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	−0.791258	−	0.611482i	$-0.790574\pi$
$223$	2.00000	−	3.46410i	0.133930	−	0.231973i	0.925188	+	0.379509i	$0.123907\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$		0			0
$226$	−6.00000			−0.399114
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	0.999184	−	0.0403978i	$-0.0128625\pi$
$227$	7.00000	+	12.1244i	0.464606	+	0.804722i	−0.534577	+	0.845120i	$0.679529\pi$
$228$		0			0
$229$	27.0000			1.78421			0.892105	−	0.451828i	$-0.149228\pi$
$229$	27.0000			1.78421			0.892105	+	0.451828i	$0.149228\pi$
$230$	6.00000	+	10.3923i	0.395628	+	0.685248i
$231$		0			0
$232$	2.50000	−	4.33013i	0.164133	−	0.284287i
$233$	−26.0000			−1.70332			−0.851658	−	0.524097i	$-0.824403\pi$
$233$	−26.0000			−1.70332			−0.851658	+	0.524097i	$0.824403\pi$
$234$		0			0
$235$	2.00000			0.130466
$236$	−3.00000	+	5.19615i	−0.195283	+	0.338241i
$237$		0			0
$238$	3.50000	+	6.06218i	0.226871	+	0.392953i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	−14.0000	−	24.2487i	−0.901819	−	1.56200i	−0.825131	−	0.564942i	$-0.808899\pi$
$241$	−14.0000	−	24.2487i	−0.901819	−	1.56200i	−0.0766885	−	0.997055i	$-0.524435\pi$
$242$	−2.00000			−0.128565
$243$		0			0
$244$	−3.50000	+	6.06218i	−0.224065	+	0.388091i
$245$	−1.00000	+	1.73205i	−0.0638877	+	0.110657i
$246$		0			0
$247$	12.5000	+	12.9904i	0.795356	+	0.826558i
$248$	−2.00000			−0.127000
$249$		0			0
$250$	6.00000	−	10.3923i	0.379473	−	0.657267i
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	0.612159	−	0.790735i	$-0.290301\pi$
$251$	−6.00000	−	10.3923i	−0.378717	−	0.655956i	−0.990876	+	0.134778i	$0.956968\pi$
$252$		0			0
$253$	−9.00000	−	15.5885i	−0.565825	−	0.980038i
$254$	6.00000	+	10.3923i	0.376473	+	0.652071i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	−0.999325	−	0.0367485i	$-0.988300\pi$
$257$	−7.50000	+	12.9904i	−0.467837	+	0.810318i	0.531487	+	0.847066i	$0.321633\pi$
$258$		0			0
$259$	2.00000			0.124274
$260$	−5.00000	−	5.19615i	−0.310087	−	0.322252i
$261$		0			0
$262$	4.00000	−	6.92820i	0.247121	−	0.428026i
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	0.212565	+	0.977147i	$0.431818\pi$
$263$	−12.0000	+	20.7846i	−0.739952	+	1.28163i	−0.952517	+	0.304487i	$0.901515\pi$
$264$		0			0
$265$	−6.00000			−0.368577
$266$	−2.50000	−	4.33013i	−0.153285	−	0.265497i
$267$		0			0
$268$	2.00000			0.122169
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	−0.956176	−	0.292791i	$-0.905416\pi$
$269$	−12.0000	−	20.7846i	−0.731653	−	1.26726i	0.224523	−	0.974469i	$-0.427917\pi$
$270$		0			0
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	−0.894799	−	0.446469i	$-0.852681\pi$
$271$	−1.00000	+	1.73205i	−0.0607457	+	0.105215i	0.834053	+	0.551684i	$0.186015\pi$
$272$	7.00000			0.424437
$273$		0			0
$274$	−18.0000			−1.08742
$275$	−1.50000	+	2.59808i	−0.0904534	+	0.156670i
$276$		0			0
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	0.761714	−	0.647913i	$-0.224358\pi$
$277$	−3.00000	−	5.19615i	−0.180253	−	0.312207i	−0.941966	+	0.335707i	$0.891025\pi$
$278$	−19.0000			−1.13954
$279$		0			0
$280$	1.00000	+	1.73205i	0.0597614	+	0.103510i
$281$	−16.0000			−0.954480			−0.477240	−	0.878773i	$-0.658363\pi$
$281$	−16.0000			−0.954480			−0.477240	+	0.878773i	$0.658363\pi$
$282$		0			0
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	0.0640654	+	0.997946i	$0.479593\pi$
$283$	−14.0000	+	24.2487i	−0.832214	+	1.44144i	−0.896279	+	0.443491i	$0.853740\pi$
$284$	4.00000	−	6.92820i	0.237356	−	0.411113i
$285$		0			0
$286$	7.50000	+	7.79423i	0.443484	+	0.460882i
$287$	−5.00000			−0.295141
$288$		0			0
$289$	−16.0000	+	27.7128i	−0.941176	+	1.63017i
$290$	5.00000	+	8.66025i	0.293610	+	0.508548i
$291$		0			0
$292$	−6.00000	−	10.3923i	−0.351123	−	0.608164i
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	0.986341	−	0.164714i	$-0.0526703\pi$
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	−0.635818	+	0.771839i	$0.719337\pi$
$294$		0			0
$295$	−6.00000	−	10.3923i	−0.349334	−	0.605063i
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$		0			0
$298$	−14.0000			−0.810998
$299$	6.00000	−	20.7846i	0.346989	−	1.20201i
$300$		0			0
$301$	1.00000	−	1.73205i	0.0576390	−	0.0998337i
$302$	−6.50000	+	11.2583i	−0.374033	+	0.647844i
$303$		0			0
$304$	−5.00000			−0.286770
$305$	−7.00000	−	12.1244i	−0.400819	−	0.694239i
$306$		0			0
$307$	9.00000			0.513657			0.256829	−	0.966457i	$-0.417322\pi$
$307$	9.00000			0.513657			0.256829	+	0.966457i	$0.417322\pi$
$308$	−1.50000	−	2.59808i	−0.0854704	−	0.148039i
$309$		0			0
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$	−23.0000			−1.30421			−0.652105	−	0.758129i	$-0.726114\pi$
$311$	−23.0000			−1.30421			−0.652105	+	0.758129i	$0.726114\pi$
$312$		0			0
$313$	28.0000			1.58265			0.791327	−	0.611393i	$-0.209391\pi$
$313$	28.0000			1.58265			0.791327	+	0.611393i	$0.209391\pi$
$314$	9.00000	−	15.5885i	0.507899	−	0.879708i
$315$		0			0
$316$	−1.50000	−	2.59808i	−0.0843816	−	0.146153i
$317$	−30.0000			−1.68497			−0.842484	−	0.538721i	$-0.818908\pi$
$317$	−30.0000			−1.68497			−0.842484	+	0.538721i	$0.818908\pi$
$318$		0			0
$319$	−7.50000	−	12.9904i	−0.419919	−	0.727322i
$320$	2.00000			0.111803
$321$		0			0
$322$	−3.00000	+	5.19615i	−0.167183	+	0.289570i
$323$	17.5000	−	30.3109i	0.973726	−	1.68654i
$324$		0			0
$325$	−3.50000	+	0.866025i	−0.194145	+	0.0480384i
$326$	−14.0000			−0.775388
$327$		0			0
$328$	−2.50000	+	4.33013i	−0.138039	+	0.239091i
$329$	0.500000	+	0.866025i	0.0275659	+	0.0477455i
$330$		0			0
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	−0.992112	−	0.125353i	$-0.959994\pi$
$331$	−11.0000	−	19.0526i	−0.604615	−	1.04722i	0.387498	−	0.921871i	$-0.373340\pi$
$332$	−4.00000	−	6.92820i	−0.219529	−	0.380235i
$333$		0			0
$334$		0			0
$335$	−2.00000	+	3.46410i	−0.109272	+	0.189264i
$336$		0			0
$337$	−17.0000			−0.926049			−0.463025	−	0.886345i	$-0.653236\pi$
$337$	−17.0000			−0.926049			−0.463025	+	0.886345i	$0.653236\pi$
$338$	−0.500000	+	12.9904i	−0.0271964	+	0.706584i
$339$		0			0
$340$	−7.00000	+	12.1244i	−0.379628	+	0.657536i
$341$	−3.00000	+	5.19615i	−0.162459	+	0.281387i
$342$		0			0
$343$	−1.00000			−0.0539949
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	−12.0000			−0.645124
$347$	8.50000	+	14.7224i	0.456304	+	0.790342i	0.998762	−	0.0497412i	$-0.0158397\pi$
$347$	8.50000	+	14.7224i	0.456304	+	0.790342i	−0.542458	+	0.840083i	$0.682506\pi$
$348$		0			0
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	−0.518022	−	0.855367i	$-0.673331\pi$
$349$	9.00000	−	15.5885i	0.481759	−	0.834431i	0.999781	+	0.0209364i	$0.00666475\pi$
$350$	1.00000			0.0534522
$351$		0			0
$352$	−3.00000			−0.159901
$353$	7.00000	−	12.1244i	0.372572	−	0.645314i	−0.617388	−	0.786659i	$-0.711809\pi$
$353$	7.00000	−	12.1244i	0.372572	−	0.645314i	0.989960	+	0.141344i	$0.0451425\pi$
$354$		0			0
$355$	8.00000	+	13.8564i	0.424596	+	0.735422i
$356$	11.0000			0.582999
$357$		0			0
$358$	10.0000	+	17.3205i	0.528516	+	0.915417i
$359$	−18.0000			−0.950004			−0.475002	−	0.879985i	$-0.657553\pi$
$359$	−18.0000			−0.950004			−0.475002	+	0.879985i	$0.657553\pi$
$360$		0			0
$361$	−3.00000	+	5.19615i	−0.157895	+	0.273482i
$362$	4.50000	−	7.79423i	0.236515	−	0.409656i
$363$		0			0
$364$	1.00000	−	3.46410i	0.0524142	−	0.181568i
$365$	24.0000			1.25622
$366$		0			0
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	−0.705509	−	0.708700i	$-0.749282\pi$
$367$	5.00000	−	8.66025i	0.260998	−	0.452062i	0.966507	+	0.256639i	$0.0826151\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$		0			0
$370$	2.00000	+	3.46410i	0.103975	+	0.180090i
$371$	−1.50000	−	2.59808i	−0.0778761	−	0.134885i
$372$		0			0
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	10.5000	−	18.1865i	0.542942	−	0.940403i
$375$		0			0
$376$	1.00000			0.0515711
$377$	5.00000	−	17.3205i	0.257513	−	0.892052i
$378$		0			0
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	−0.486209	−	0.873843i	$-0.661621\pi$
$379$	10.0000	−	17.3205i	0.513665	−	0.889695i	0.999874	−	0.0158521i	$-0.00504609\pi$
$380$	5.00000	−	8.66025i	0.256495	−	0.444262i
$381$		0			0
$382$	4.00000			0.204658
$383$	15.5000	+	26.8468i	0.792013	+	1.37181i	0.924719	+	0.380651i	$0.124300\pi$
$383$	15.5000	+	26.8468i	0.792013	+	1.37181i	−0.132706	+	0.991155i	$0.542367\pi$
$384$		0			0
$385$	6.00000			0.305788
$386$	−6.50000	−	11.2583i	−0.330841	−	0.573034i
$387$		0			0
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	−42.0000			−2.12403
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$		0			0
$394$	−4.50000	−	7.79423i	−0.226707	−	0.392668i
$395$	6.00000			0.301893
$396$		0			0
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	0.990538	−	0.137241i	$-0.0438236\pi$
$397$	7.50000	+	12.9904i	0.376414	+	0.651969i	−0.614123	+	0.789210i	$0.710490\pi$
$398$	−26.0000			−1.30326
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	−0.548911	−	0.835881i	$-0.684957\pi$
$401$	9.00000	−	15.5885i	0.449439	−	0.778450i	0.998350	+	0.0574304i	$0.0182907\pi$
$402$		0			0
$403$	−7.00000	+	1.73205i	−0.348695	+	0.0862796i
$404$	−14.0000			−0.696526
$405$		0			0
$406$	−2.50000	+	4.33013i	−0.124073	+	0.214901i
$407$	−3.00000	−	5.19615i	−0.148704	−	0.257564i
$408$		0			0
$409$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$409$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$410$	−5.00000	−	8.66025i	−0.246932	−	0.427699i
$411$		0			0
$412$	−5.00000	−	8.66025i	−0.246332	−	0.426660i
$413$	3.00000	−	5.19615i	0.147620	−	0.255686i
$414$		0			0
$415$	16.0000			0.785409
$416$	−2.50000	−	2.59808i	−0.122573	−	0.127381i
$417$		0			0
$418$	−7.50000	+	12.9904i	−0.366837	+	0.635380i
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	−0.813029	−	0.582224i	$-0.802183\pi$
$419$	2.00000	−	3.46410i	0.0977064	−	0.169232i	0.910735	+	0.412991i	$0.135516\pi$
$420$		0			0
$421$	−22.0000			−1.07221			−0.536107	−	0.844150i	$-0.680106\pi$
$421$	−22.0000			−1.07221			−0.536107	+	0.844150i	$0.680106\pi$
$422$	5.00000	+	8.66025i	0.243396	+	0.421575i
$423$		0			0
$424$	−3.00000			−0.145693
$425$	3.50000	+	6.06218i	0.169775	+	0.294059i
$426$		0			0
$427$	3.50000	−	6.06218i	0.169377	−	0.293369i
$428$	−15.0000			−0.725052
$429$		0			0
$430$	4.00000			0.192897
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	−0.946135	−	0.323772i	$-0.895049\pi$
$431$	−4.00000	+	6.92820i	−0.192673	+	0.333720i	0.753462	+	0.657491i	$0.228382\pi$
$432$		0			0
$433$	−13.0000	−	22.5167i	−0.624740	−	1.08208i	−0.988591	−	0.150624i	$-0.951872\pi$
$433$	−13.0000	−	22.5167i	−0.624740	−	1.08208i	0.363851	−	0.931457i	$-0.381462\pi$
$434$	2.00000			0.0960031
$435$		0			0
$436$	8.00000	+	13.8564i	0.383131	+	0.663602i
$437$	30.0000			1.43509
$438$		0			0
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	−0.909798	−	0.415051i	$-0.863764\pi$
$439$	−2.00000	+	3.46410i	−0.0954548	+	0.165333i	0.814344	+	0.580383i	$0.197097\pi$
$440$	3.00000	−	5.19615i	0.143019	−	0.247717i
$441$		0			0
$442$	24.5000	−	6.06218i	1.16535	−	0.288348i
$443$	−15.0000			−0.712672			−0.356336	−	0.934358i	$-0.615974\pi$
$443$	−15.0000			−0.712672			−0.356336	+	0.934358i	$0.615974\pi$
$444$		0			0
$445$	−11.0000	+	19.0526i	−0.521450	+	0.903178i
$446$	2.00000	+	3.46410i	0.0947027	+	0.164030i
$447$		0			0
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	−19.0000	−	32.9090i	−0.896665	−	1.55307i	−0.831730	−	0.555181i	$-0.812649\pi$
$449$	−19.0000	−	32.9090i	−0.896665	−	1.55307i	−0.0649356	−	0.997889i	$-0.520684\pi$
$450$		0			0
$451$	7.50000	+	12.9904i	0.353161	+	0.611693i
$452$	3.00000	−	5.19615i	0.141108	−	0.244406i
$453$		0			0
$454$	−14.0000			−0.657053
$455$	5.00000	+	5.19615i	0.234404	+	0.243599i
$456$		0			0
$457$	−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	$0.958593\pi$
$458$	−13.5000	+	23.3827i	−0.630814	+	1.09260i
$459$		0			0
$460$	−12.0000			−0.559503
$461$	4.00000	+	6.92820i	0.186299	+	0.322679i	0.944013	−	0.329907i	$-0.107017\pi$
$461$	4.00000	+	6.92820i	0.186299	+	0.322679i	−0.757715	+	0.652586i	$0.773684\pi$
$462$		0			0
$463$	−31.0000			−1.44069			−0.720346	−	0.693615i	$-0.756017\pi$
$463$	−31.0000			−1.44069			−0.720346	+	0.693615i	$0.756017\pi$
$464$	2.50000	+	4.33013i	0.116060	+	0.201021i
$465$		0			0
$466$	13.0000	−	22.5167i	0.602213	−	1.04306i
$467$	12.0000			0.555294			0.277647	−	0.960683i	$-0.410445\pi$
$467$	12.0000			0.555294			0.277647	+	0.960683i	$0.410445\pi$
$468$		0			0
$469$	−2.00000			−0.0923514
$470$	−1.00000	+	1.73205i	−0.0461266	+	0.0798935i
$471$		0			0
$472$	−3.00000	−	5.19615i	−0.138086	−	0.239172i
$473$	−6.00000			−0.275880
$474$		0			0
$475$	−2.50000	−	4.33013i	−0.114708	−	0.198680i
$476$	−7.00000			−0.320844
$477$		0			0
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	−0.519973	−	0.854183i	$-0.674058\pi$
$479$	10.5000	−	18.1865i	0.479757	−	0.830964i	0.999730	+	0.0232187i	$0.00739140\pi$
$480$		0			0
$481$	2.00000	−	6.92820i	0.0911922	−	0.315899i
$482$	28.0000			1.27537
$483$		0			0
$484$	1.00000	−	1.73205i	0.0454545	−	0.0787296i
$485$	2.00000	+	3.46410i	0.0908153	+	0.157297i
$486$		0			0
$487$	−17.5000	−	30.3109i	−0.793001	−	1.37352i	−0.924101	−	0.382148i	$-0.875184\pi$
$487$	−17.5000	−	30.3109i	−0.793001	−	1.37352i	0.131100	−	0.991369i	$-0.458149\pi$
$488$	−3.50000	−	6.06218i	−0.158438	−	0.274422i
$489$		0			0
$490$	−1.00000	−	1.73205i	−0.0451754	−	0.0782461i
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	−0.942057	−	0.335453i	$-0.891111\pi$
$491$	−4.00000	+	6.92820i	−0.180517	+	0.312665i	0.761539	+	0.648119i	$0.224444\pi$
$492$		0			0
$493$	−35.0000			−1.57632
$494$	−17.5000	+	4.33013i	−0.787362	+	0.194822i
$495$		0			0
$496$	1.00000	−	1.73205i	0.0449013	−	0.0777714i
$497$	−4.00000	+	6.92820i	−0.179425	+	0.310772i
$498$		0			0
$499$	14.0000			0.626726			0.313363	−	0.949633i	$-0.398544\pi$
$499$	14.0000			0.626726			0.313363	+	0.949633i	$0.398544\pi$
$500$	6.00000	+	10.3923i	0.268328	+	0.464758i
$501$		0			0
$502$	12.0000			0.535586
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	0.999161	+	0.0409609i	$0.0130419\pi$
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	−0.464107	+	0.885779i	$0.653625\pi$
$504$		0			0
$505$	14.0000	−	24.2487i	0.622992	−	1.07905i
$506$	18.0000			0.800198
$507$		0			0
$508$	−12.0000			−0.532414
$509$	−20.0000	+	34.6410i	−0.886484	+	1.53544i	−0.0424816	+	0.999097i	$0.513526\pi$
$509$	−20.0000	+	34.6410i	−0.886484	+	1.53544i	−0.844003	+	0.536339i	$0.819807\pi$
$510$		0			0
$511$	6.00000	+	10.3923i	0.265424	+	0.459728i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−7.50000	−	12.9904i	−0.330811	−	0.572981i
$515$	20.0000			0.881305
$516$		0			0
$517$	1.50000	−	2.59808i	0.0659699	−	0.114263i
$518$	−1.00000	+	1.73205i	−0.0439375	+	0.0761019i
$519$		0			0
$520$	7.00000	−	1.73205i	0.306970	−	0.0759555i
$521$	−21.0000			−0.920027			−0.460013	−	0.887912i	$-0.652155\pi$
$521$	−21.0000			−0.920027			−0.460013	+	0.887912i	$0.652155\pi$
$522$		0			0
$523$	−19.5000	+	33.7750i	−0.852675	+	1.47688i	0.0261094	+	0.999659i	$0.491688\pi$
$523$	−19.5000	+	33.7750i	−0.852675	+	1.47688i	−0.878785	+	0.477218i	$0.841645\pi$
$524$	4.00000	+	6.92820i	0.174741	+	0.302660i
$525$		0			0
$526$	−12.0000	−	20.7846i	−0.523225	−	0.906252i
$527$	7.00000	+	12.1244i	0.304925	+	0.528145i
$528$		0			0
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	3.00000	−	5.19615i	0.130312	−	0.225706i
$531$		0			0
$532$	5.00000			0.216777
$533$	−5.00000	+	17.3205i	−0.216574	+	0.750234i
$534$		0			0
$535$	15.0000	−	25.9808i	0.648507	−	1.12325i
$536$	−1.00000	+	1.73205i	−0.0431934	+	0.0748132i
$537$		0			0
$538$	24.0000			1.03471
$539$	1.50000	+	2.59808i	0.0646096	+	0.111907i
$540$		0			0
$541$	20.0000			0.859867			0.429934	−	0.902861i	$-0.358537\pi$
$541$	20.0000			0.859867			0.429934	+	0.902861i	$0.358537\pi$
$542$	−1.00000	−	1.73205i	−0.0429537	−	0.0743980i
$543$		0			0
$544$	−3.50000	+	6.06218i	−0.150061	+	0.259914i
$545$	−32.0000			−1.37073
$546$		0			0
$547$	−32.0000			−1.36822			−0.684111	−	0.729378i	$-0.739809\pi$
$547$	−32.0000			−1.36822			−0.684111	+	0.729378i	$0.739809\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$		0			0
$550$	−1.50000	−	2.59808i	−0.0639602	−	0.110782i
$551$	25.0000			1.06504
$552$		0			0
$553$	1.50000	+	2.59808i	0.0637865	+	0.110481i
$554$	6.00000			0.254916
$555$		0			0
$556$	9.50000	−	16.4545i	0.402890	−	0.697826i
$557$	−7.50000	+	12.9904i	−0.317785	+	0.550420i	−0.980026	−	0.198871i	$-0.936272\pi$
$557$	−7.50000	+	12.9904i	−0.317785	+	0.550420i	0.662240	+	0.749291i	$0.269606\pi$
$558$		0			0
$559$	−5.00000	−	5.19615i	−0.211477	−	0.219774i
$560$	−2.00000			−0.0845154
$561$		0			0
$562$	8.00000	−	13.8564i	0.337460	−	0.584497i
$563$	15.0000	+	25.9808i	0.632175	+	1.09496i	0.987106	+	0.160066i	$0.0511708\pi$
$563$	15.0000	+	25.9808i	0.632175	+	1.09496i	−0.354932	+	0.934892i	$0.615496\pi$
$564$		0			0
$565$	6.00000	+	10.3923i	0.252422	+	0.437208i
$566$	−14.0000	−	24.2487i	−0.588464	−	1.01925i
$567$		0			0
$568$	4.00000	+	6.92820i	0.167836	+	0.290701i
$569$	−22.0000	+	38.1051i	−0.922288	+	1.59745i	−0.126422	+	0.991977i	$0.540349\pi$
$569$	−22.0000	+	38.1051i	−0.922288	+	1.59745i	−0.795866	+	0.605473i	$0.792984\pi$
$570$		0			0
$571$	−12.0000			−0.502184			−0.251092	−	0.967963i	$-0.580790\pi$
$571$	−12.0000			−0.502184			−0.251092	+	0.967963i	$0.580790\pi$
$572$	−10.5000	+	2.59808i	−0.439027	+	0.108631i
$573$		0			0
$574$	2.50000	−	4.33013i	0.104348	−	0.180736i
$575$	−3.00000	+	5.19615i	−0.125109	+	0.216695i
$576$		0			0
$577$	20.0000			0.832611			0.416305	−	0.909225i	$-0.363325\pi$
$577$	20.0000			0.832611			0.416305	+	0.909225i	$0.363325\pi$
$578$	−16.0000	−	27.7128i	−0.665512	−	1.15270i
$579$		0			0
$580$	−10.0000			−0.415227
$581$	4.00000	+	6.92820i	0.165948	+	0.287430i
$582$		0			0
$583$	−4.50000	+	7.79423i	−0.186371	+	0.322804i
$584$	12.0000			0.496564
$585$		0			0
$586$	−12.0000			−0.495715
$587$	5.00000	−	8.66025i	0.206372	−	0.357447i	−0.744197	−	0.667960i	$-0.767168\pi$
$587$	5.00000	−	8.66025i	0.206372	−	0.357447i	0.950569	+	0.310513i	$0.100501\pi$
$588$		0			0
$589$	−5.00000	−	8.66025i	−0.206021	−	0.356840i
$590$	12.0000			0.494032
$591$		0			0
$592$	1.00000	+	1.73205i	0.0410997	+	0.0711868i
$593$	13.0000			0.533846			0.266923	−	0.963718i	$-0.413993\pi$
$593$	13.0000			0.533846			0.266923	+	0.963718i	$0.413993\pi$
$594$		0			0
$595$	7.00000	−	12.1244i	0.286972	−	0.497050i
$596$	7.00000	−	12.1244i	0.286731	−	0.496633i
$597$		0			0
$598$	15.0000	+	15.5885i	0.613396	+	0.637459i
$599$	26.0000			1.06233			0.531166	−	0.847268i	$-0.321754\pi$
$599$	26.0000			1.06233			0.531166	+	0.847268i	$0.321754\pi$
$600$		0			0
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	0.159754	+	0.987157i	$0.448930\pi$
$601$	−19.0000	+	32.9090i	−0.775026	+	1.34238i	−0.934780	+	0.355228i	$0.884403\pi$
$602$	1.00000	+	1.73205i	0.0407570	+	0.0705931i
$603$		0			0
$604$	−6.50000	−	11.2583i	−0.264481	−	0.458095i
$605$	2.00000	+	3.46410i	0.0813116	+	0.140836i
$606$		0			0
$607$	15.0000	+	25.9808i	0.608831	+	1.05453i	0.991433	+	0.130613i	$0.0416947\pi$
$607$	15.0000	+	25.9808i	0.608831	+	1.05453i	−0.382602	+	0.923913i	$0.624972\pi$
$608$	2.50000	−	4.33013i	0.101388	−	0.175610i
$609$		0			0
$610$	14.0000			0.566843
$611$	3.50000	−	0.866025i	0.141595	−	0.0350356i
$612$		0			0
$613$	14.0000	−	24.2487i	0.565455	−	0.979396i	−0.431553	−	0.902088i	$-0.642034\pi$
$613$	14.0000	−	24.2487i	0.565455	−	0.979396i	0.997007	−	0.0773084i	$-0.0246326\pi$
$614$	−4.50000	+	7.79423i	−0.181605	+	0.314549i
$615$		0			0
$616$	3.00000			0.120873
$617$	−10.0000	−	17.3205i	−0.402585	−	0.697297i	0.591452	−	0.806340i	$-0.298555\pi$
$617$	−10.0000	−	17.3205i	−0.402585	−	0.697297i	−0.994037	+	0.109043i	$0.965221\pi$
$618$		0			0
$619$	41.0000			1.64793			0.823965	−	0.566641i	$-0.191757\pi$
$619$	41.0000			1.64793			0.823965	+	0.566641i	$0.191757\pi$
$620$	2.00000	+	3.46410i	0.0803219	+	0.139122i
$621$		0			0
$622$	11.5000	−	19.9186i	0.461108	−	0.798662i
$623$	−11.0000			−0.440706
$624$		0			0
$625$	−19.0000			−0.760000
$626$	−14.0000	+	24.2487i	−0.559553	+	0.969173i
$627$		0			0
$628$	9.00000	+	15.5885i	0.359139	+	0.622047i
$629$	−14.0000			−0.558217
$630$		0			0
$631$	−7.50000	−	12.9904i	−0.298570	−	0.517139i	0.677239	−	0.735763i	$-0.263176\pi$
$631$	−7.50000	−	12.9904i	−0.298570	−	0.517139i	−0.975809	+	0.218624i	$0.929843\pi$
$632$	3.00000			0.119334
$633$		0			0
$634$	15.0000	−	25.9808i	0.595726	−	1.03183i
$635$	12.0000	−	20.7846i	0.476205	−	0.824812i
$636$		0			0
$637$	−1.00000	+	3.46410i	−0.0396214	+	0.137253i
$638$	15.0000			0.593856
$639$		0			0
$640$	−1.00000	+	1.73205i	−0.0395285	+	0.0684653i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$		0			0
$643$	24.5000	+	42.4352i	0.966186	+	1.67348i	0.706395	+	0.707818i	$0.250320\pi$
$643$	24.5000	+	42.4352i	0.966186	+	1.67348i	0.259791	+	0.965665i	$0.416346\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$		0			0
$646$	17.5000	+	30.3109i	0.688528	+	1.19257i
$647$	0.500000	−	0.866025i	0.0196570	−	0.0340470i	−0.856030	−	0.516927i	$-0.827076\pi$
$647$	0.500000	−	0.866025i	0.0196570	−	0.0340470i	0.875687	+	0.482880i	$0.160409\pi$
$648$		0			0
$649$	−18.0000			−0.706562
$650$	1.00000	−	3.46410i	0.0392232	−	0.135873i
$651$		0			0
$652$	7.00000	−	12.1244i	0.274141	−	0.474826i
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	−0.471160	−	0.882048i	$-0.656165\pi$
$653$	13.5000	−	23.3827i	0.528296	−	0.915035i	0.999456	−	0.0329874i	$-0.0105021\pi$
$654$		0			0
$655$	−16.0000			−0.625172
$656$	−2.50000	−	4.33013i	−0.0976086	−	0.169063i
$657$		0			0
$658$	−1.00000			−0.0389841
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	−0.999545	−	0.0301523i	$-0.990401\pi$
$659$	−13.5000	−	23.3827i	−0.525885	−	0.910860i	0.473660	−	0.880708i	$-0.342933\pi$
$660$		0			0
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	−0.697174	−	0.716902i	$-0.745559\pi$
$661$	7.00000	−	12.1244i	0.272268	−	0.471583i	0.969442	+	0.245319i	$0.0788928\pi$
$662$	22.0000			0.855054
$663$		0			0
$664$	8.00000			0.310460
$665$	−5.00000	+	8.66025i	−0.193892	+	0.335830i
$666$		0			0
$667$	−15.0000	−	25.9808i	−0.580802	−	1.00598i
$668$		0			0
$669$		0			0
$670$	−2.00000	−	3.46410i	−0.0772667	−	0.133830i
$671$	−21.0000			−0.810696
$672$		0			0
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	−0.997932	−	0.0642860i	$-0.979523\pi$
$673$	−11.5000	+	19.9186i	−0.443292	+	0.767805i	0.554639	+	0.832091i	$0.312856\pi$
$674$	8.50000	−	14.7224i	0.327408	−	0.567087i
$675$		0			0
$676$	−11.0000	−	6.92820i	−0.423077	−	0.266469i
$677$		0			0			−	1.00000i	$-0.5\pi$
$677$		0			0				1.00000i	$0.5\pi$
$678$		0			0
$679$	−1.00000	+	1.73205i	−0.0383765	+	0.0664700i
$680$	−7.00000	−	12.1244i	−0.268438	−	0.464948i
$681$		0			0
$682$	−3.00000	−	5.19615i	−0.114876	−	0.198971i
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	0.972242	+	0.233977i	$0.0751739\pi$
$683$	18.0000	+	31.1769i	0.688751	+	1.19295i	−0.283491	+	0.958975i	$0.591493\pi$
$684$		0			0
$685$	18.0000	+	31.1769i	0.687745	+	1.19121i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$		0			0
$688$	2.00000			0.0762493
$689$	−10.5000	+	2.59808i	−0.400018	+	0.0989788i
$690$		0			0
$691$	−20.0000	+	34.6410i	−0.760836	+	1.31781i	0.181584	+	0.983375i	$0.441877\pi$
$691$	−20.0000	+	34.6410i	−0.760836	+	1.31781i	−0.942420	+	0.334431i	$0.891456\pi$
$692$	6.00000	−	10.3923i	0.228086	−	0.395056i
$693$		0			0
$694$	−17.0000			−0.645311
$695$	19.0000	+	32.9090i	0.720711	+	1.24831i
$696$		0			0
$697$	35.0000			1.32572
$698$	9.00000	+	15.5885i	0.340655	+	0.590032i
$699$		0			0
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−13.0000			−0.491003			−0.245502	−	0.969396i	$-0.578953\pi$
$701$	−13.0000			−0.491003			−0.245502	+	0.969396i	$0.578953\pi$
$702$		0			0
$703$	10.0000			0.377157
$704$	1.50000	−	2.59808i	0.0565334	−	0.0979187i
$705$		0			0
$706$	7.00000	+	12.1244i	0.263448	+	0.456306i
$707$	14.0000			0.526524
$708$		0			0
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	0.999549	+	0.0300298i	$0.00956021\pi$
$709$	14.0000	+	24.2487i	0.525781	+	0.910679i	−0.473768	+	0.880650i	$0.657106\pi$
$710$	−16.0000			−0.600469
$711$		0			0
$712$	−5.50000	+	9.52628i	−0.206121	+	0.357012i
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$		0			0
$715$	6.00000	−	20.7846i	0.224387	−	0.777300i
$716$	−20.0000			−0.747435
$717$		0			0
$718$	9.00000	−	15.5885i	0.335877	−	0.581756i
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	0.691608	−	0.722273i	$-0.256903\pi$
$719$	−7.50000	−	12.9904i	−0.279703	−	0.484459i	−0.971311	+	0.237814i	$0.923569\pi$
$720$		0			0
$721$	5.00000	+	8.66025i	0.186210	+	0.322525i
$722$	−3.00000	−	5.19615i	−0.111648	−	0.193381i
$723$		0			0
$724$	4.50000	+	7.79423i	0.167241	+	0.289670i
$725$	−2.50000	+	4.33013i	−0.0928477	+	0.160817i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	2.50000	+	2.59808i	0.0926562	+	0.0962911i
$729$		0			0
$730$	−12.0000	+	20.7846i	−0.444140	+	0.769273i
$731$	−7.00000	+	12.1244i	−0.258904	+	0.448435i
$732$		0			0
$733$	−7.00000			−0.258551			−0.129275	−	0.991609i	$-0.541265\pi$
$733$	−7.00000			−0.258551			−0.129275	+	0.991609i	$0.541265\pi$
$734$	5.00000	+	8.66025i	0.184553	+	0.319656i
$735$		0			0
$736$	−6.00000			−0.221163
$737$	3.00000	+	5.19615i	0.110506	+	0.191403i
$738$		0			0
$739$	7.00000	−	12.1244i	0.257499	−	0.446002i	−0.708072	−	0.706140i	$-0.750435\pi$
$739$	7.00000	−	12.1244i	0.257499	−	0.446002i	0.965571	+	0.260138i	$0.0837682\pi$
$740$	−4.00000			−0.147043
$741$		0			0
$742$	3.00000			0.110133
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	−0.915794	−	0.401648i	$-0.868437\pi$
$743$	−3.00000	+	5.19615i	−0.110059	+	0.190628i	0.805735	+	0.592277i	$0.201771\pi$
$744$		0			0
$745$	14.0000	+	24.2487i	0.512920	+	0.888404i
$746$	4.00000			0.146450
$747$		0			0
$748$	10.5000	+	18.1865i	0.383918	+	0.664966i
$749$	15.0000			0.548088
$750$		0			0
$751$	16.5000	−	28.5788i	0.602094	−	1.04286i	−0.390410	−	0.920641i	$-0.627667\pi$
$751$	16.5000	−	28.5788i	0.602094	−	1.04286i	0.992504	−	0.122216i	$-0.0389999\pi$
$752$	−0.500000	+	0.866025i	−0.0182331	+	0.0315807i
$753$		0			0
$754$	12.5000	+	12.9904i	0.455223	+	0.473082i
$755$	26.0000			0.946237
$756$		0			0
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	0.413768	+	0.910382i	$0.364212\pi$
$757$	−16.0000	+	27.7128i	−0.581530	+	1.00724i	−0.995298	+	0.0968571i	$0.969121\pi$
$758$	10.0000	+	17.3205i	0.363216	+	0.629109i
$759$		0			0
$760$	5.00000	+	8.66025i	0.181369	+	0.314140i
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$		0			0
$763$	−8.00000	−	13.8564i	−0.289619	−	0.501636i
$764$	−2.00000	+	3.46410i	−0.0723575	+	0.125327i
$765$		0			0
$766$	−31.0000			−1.12008
$767$	−15.0000	−	15.5885i	−0.541619	−	0.562867i
$768$		0			0
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	0.0691074	+	0.997609i	$0.477985\pi$
$769$	−23.0000	+	39.8372i	−0.829401	+	1.43657i	−0.898509	+	0.438956i	$0.855348\pi$
$770$	−3.00000	+	5.19615i	−0.108112	+	0.187256i
$771$		0			0
$772$	13.0000			0.467880
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	0.761987	−	0.647592i	$-0.224224\pi$
$773$	−5.00000	−	8.66025i	−0.179838	−	0.311488i	−0.941825	+	0.336104i	$0.890891\pi$
$774$		0			0
$775$	2.00000			0.0718421
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$		0			0
$778$	3.00000	−	5.19615i	0.107555	−	0.186291i
$779$	−25.0000			−0.895718
$780$		0			0
$781$	24.0000			0.858788
$782$	21.0000	−	36.3731i	0.750958	−	1.30070i
$783$		0			0
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−36.0000			−1.28490
$786$		0			0
$787$	−12.5000	−	21.6506i	−0.445577	−	0.771762i	0.552515	−	0.833503i	$-0.313668\pi$
$787$	−12.5000	−	21.6506i	−0.445577	−	0.771762i	−0.998092	+	0.0617409i	$0.980335\pi$
$788$	9.00000			0.320612
$789$		0			0
$790$	−3.00000	+	5.19615i	−0.106735	+	0.184871i
$791$	−3.00000	+	5.19615i	−0.106668	+	0.184754i
$792$		0			0
$793$	−17.5000	−	18.1865i	−0.621443	−	0.645823i
$794$	−15.0000			−0.532330
$795$		0			0
$796$	13.0000	−	22.5167i	0.460773	−	0.798082i
$797$	28.0000	+	48.4974i	0.991811	+	1.71787i	0.606510	+	0.795076i	$0.292569\pi$
$797$	28.0000	+	48.4974i	0.991811	+	1.71787i	0.385301	+	0.922791i	$0.374098\pi$
$798$		0			0
$799$	−3.50000	−	6.06218i	−0.123821	−	0.214464i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$		0			0
$802$	9.00000	+	15.5885i	0.317801	+	0.550448i
$803$	18.0000	−	31.1769i	0.635206	−	1.10021i
$804$		0			0
$805$	12.0000			0.422944
$806$	2.00000	−	6.92820i	0.0704470	−	0.244036i
$807$		0			0
$808$	7.00000	−	12.1244i	0.246259	−	0.426533i
$809$	26.0000	−	45.0333i	0.914111	−	1.58329i	0.105914	−	0.994375i	$-0.466223\pi$
$809$	26.0000	−	45.0333i	0.914111	−	1.58329i	0.808197	−	0.588912i	$-0.200444\pi$
$810$		0			0
$811$	−4.00000			−0.140459			−0.0702295	−	0.997531i	$-0.522373\pi$
$811$	−4.00000			−0.140459			−0.0702295	+	0.997531i	$0.522373\pi$
$812$	−2.50000	−	4.33013i	−0.0877328	−	0.151958i
$813$		0			0
$814$	6.00000			0.210300
$815$	14.0000	+	24.2487i	0.490399	+	0.849395i
$816$		0			0
$817$	5.00000	−	8.66025i	0.174928	−	0.302984i
$818$		0			0
$819$		0			0
$820$	10.0000			0.349215
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	−0.704956	−	0.709251i	$-0.749033\pi$
$821$	7.50000	−	12.9904i	0.261752	−	0.453367i	0.966708	+	0.255884i	$0.0823665\pi$
$822$		0			0
$823$	24.0000	+	41.5692i	0.836587	+	1.44901i	0.892731	+	0.450589i	$0.148786\pi$
$823$	24.0000	+	41.5692i	0.836587	+	1.44901i	−0.0561440	+	0.998423i	$0.517881\pi$
$824$	10.0000			0.348367
$825$		0			0
$826$	3.00000	+	5.19615i	0.104383	+	0.180797i
$827$	8.00000			0.278187			0.139094	−	0.990279i	$-0.455581\pi$
$827$	8.00000			0.278187			0.139094	+	0.990279i	$0.455581\pi$
$828$		0			0
$829$	3.50000	−	6.06218i	0.121560	−	0.210548i	−0.798823	−	0.601566i	$-0.794544\pi$
$829$	3.50000	−	6.06218i	0.121560	−	0.210548i	0.920383	+	0.391018i	$0.127877\pi$
$830$	−8.00000	+	13.8564i	−0.277684	+	0.480963i
$831$		0			0
$832$	3.50000	−	0.866025i	0.121341	−	0.0300240i
$833$	7.00000			0.242536
$834$		0			0
$835$		0			0
$836$	−7.50000	−	12.9904i	−0.259393	−	0.449282i
$837$		0			0
$838$	2.00000	+	3.46410i	0.0690889	+	0.119665i
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	0.581067	−	0.813856i	$-0.302635\pi$
$839$	−12.0000	−	20.7846i	−0.414286	−	0.717564i	−0.995353	+	0.0962912i	$0.969302\pi$
$840$		0			0
$841$	2.00000	+	3.46410i	0.0689655	+	0.119452i
$842$	11.0000	−	19.0526i	0.379085	−	0.656595i
$843$		0			0
$844$	−10.0000			−0.344214
$845$	23.0000	−	12.1244i	0.791224	−	0.417091i
$846$		0			0
$847$	−1.00000	+	1.73205i	−0.0343604	+	0.0595140i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$		0			0
$850$	−7.00000			−0.240098
$851$	−6.00000	−	10.3923i	−0.205677	−	0.356244i
$852$		0			0
$853$	41.0000			1.40381			0.701907	−	0.712269i	$-0.252332\pi$
$853$	41.0000			1.40381			0.701907	+	0.712269i	$0.252332\pi$
$854$	3.50000	+	6.06218i	0.119768	+	0.207443i
$855$		0			0
$856$	7.50000	−	12.9904i	0.256345	−	0.444002i
$857$	−6.00000			−0.204956			−0.102478	−	0.994735i	$-0.532677\pi$
$857$	−6.00000			−0.204956			−0.102478	+	0.994735i	$0.532677\pi$
$858$		0			0
$859$	35.0000			1.19418			0.597092	−	0.802173i	$-0.296323\pi$
$859$	35.0000			1.19418			0.597092	+	0.802173i	$0.296323\pi$
$860$	−2.00000	+	3.46410i	−0.0681994	+	0.118125i
$861$		0			0
$862$	−4.00000	−	6.92820i	−0.136241	−	0.235976i
$863$	−34.0000			−1.15737			−0.578687	−	0.815550i	$-0.696435\pi$
$863$	−34.0000			−1.15737			−0.578687	+	0.815550i	$0.696435\pi$
$864$		0			0
$865$	12.0000	+	20.7846i	0.408012	+	0.706698i
$866$	26.0000			0.883516
$867$		0			0
$868$	−1.00000	+	1.73205i	−0.0339422	+	0.0587896i
$869$	4.50000	−	7.79423i	0.152652	−	0.264401i
$870$		0			0
$871$	−2.00000	+	6.92820i	−0.0677674	+	0.234753i
$872$	−16.0000			−0.541828
$873$		0			0
$874$	−15.0000	+	25.9808i	−0.507383	+	0.878812i
$875$	−6.00000	−	10.3923i	−0.202837	−	0.351324i
$876$		0			0
$877$	−20.0000	−	34.6410i	−0.675352	−	1.16974i	−0.976366	−	0.216124i	$-0.930658\pi$
$877$	−20.0000	−	34.6410i	−0.675352	−	1.16974i	0.301014	−	0.953620i	$-0.402675\pi$
$878$	−2.00000	−	3.46410i	−0.0674967	−	0.116908i
$879$		0			0
$880$	3.00000	+	5.19615i	0.101130	+	0.175162i
$881$	−13.0000	+	22.5167i	−0.437981	+	0.758606i	−0.997534	−	0.0701893i	$-0.977640\pi$
$881$	−13.0000	+	22.5167i	−0.437981	+	0.758606i	0.559553	+	0.828795i	$0.310973\pi$
$882$		0			0
$883$	−14.0000			−0.471138			−0.235569	−	0.971858i	$-0.575695\pi$
$883$	−14.0000			−0.471138			−0.235569	+	0.971858i	$0.575695\pi$
$884$	−7.00000	+	24.2487i	−0.235435	+	0.815572i
$885$		0			0
$886$	7.50000	−	12.9904i	0.251967	−	0.436420i
$887$	18.5000	−	32.0429i	0.621169	−	1.07590i	−0.368099	−	0.929787i	$-0.619991\pi$
$887$	18.5000	−	32.0429i	0.621169	−	1.07590i	0.989268	−	0.146110i	$-0.0466754\pi$
$888$		0			0
$889$	12.0000			0.402467
$890$	−11.0000	−	19.0526i	−0.368721	−	0.638643i
$891$		0			0
$892$	−4.00000			−0.133930
$893$	2.50000	+	4.33013i	0.0836593	+	0.144902i
$894$		0			0
$895$	20.0000	−	34.6410i	0.668526	−	1.15792i
$896$	−1.00000			−0.0334077
$897$		0			0
$898$	38.0000			1.26808
$899$	−5.00000	+	8.66025i	−0.166759	+	0.288836i
$900$		0			0
$901$	10.5000	+	18.1865i	0.349806	+	0.605881i
$902$	−15.0000			−0.499445
$903$		0			0
$904$	3.00000	+	5.19615i	0.0997785	+	0.172821i
$905$	−18.0000			−0.598340
$906$		0			0
$907$	19.0000	−	32.9090i	0.630885	−	1.09272i	−0.356487	−	0.934300i	$-0.616025\pi$
$907$	19.0000	−	32.9090i	0.630885	−	1.09272i	0.987371	−	0.158424i	$-0.0506412\pi$
$908$	7.00000	−	12.1244i	0.232303	−	0.402361i
$909$		0			0
$910$	−7.00000	+	1.73205i	−0.232048	+	0.0574169i
$911$	52.0000			1.72284			0.861418	−	0.507896i	$-0.169577\pi$
$911$	52.0000			1.72284			0.861418	+	0.507896i	$0.169577\pi$
$912$		0			0
$913$	12.0000	−	20.7846i	0.397142	−	0.687870i
$914$	−13.0000	−	22.5167i	−0.430002	−	0.744785i
$915$		0			0
$916$	−13.5000	−	23.3827i	−0.446053	−	0.772586i
$917$	−4.00000	−	6.92820i	−0.132092	−	0.228789i
$918$		0			0
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	0.942367	−	0.334581i	$-0.108595\pi$
$919$	5.50000	+	9.52628i	0.181428	+	0.314243i	−0.760939	+	0.648824i	$0.775261\pi$
$920$	6.00000	−	10.3923i	0.197814	−	0.342624i
$921$		0			0
$922$	−8.00000			−0.263466
$923$	20.0000	+	20.7846i	0.658308	+	0.684134i
$924$		0			0
$925$	−1.00000	+	1.73205i	−0.0328798	+	0.0569495i
$926$	15.5000	−	26.8468i	0.509362	−	0.882240i
$927$		0			0
$928$	−5.00000			−0.164133
$929$	−6.50000	−	11.2583i	−0.213258	−	0.369374i	0.739474	−	0.673185i	$-0.235074\pi$
$929$	−6.50000	−	11.2583i	−0.213258	−	0.369374i	−0.952732	+	0.303811i	$0.901741\pi$
$930$		0			0
$931$	−5.00000			−0.163868
$932$	13.0000	+	22.5167i	0.425829	+	0.737558i
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	−42.0000			−1.37355
$936$		0			0
$937$	52.0000			1.69877			0.849383	−	0.527777i	$-0.176974\pi$
$937$	52.0000			1.69877			0.849383	+	0.527777i	$0.176974\pi$
$938$	1.00000	−	1.73205i	0.0326512	−	0.0565535i
$939$		0			0
$940$	−1.00000	−	1.73205i	−0.0326164	−	0.0564933i
$941$		0			0			−	1.00000i	$-0.5\pi$
$941$		0			0				1.00000i	$0.5\pi$
$942$		0			0
$943$	15.0000	+	25.9808i	0.488467	+	0.846050i
$944$	6.00000			0.195283
$945$		0			0
$946$	3.00000	−	5.19615i	0.0975384	−	0.168941i
$947$	−15.5000	+	26.8468i	−0.503682	+	0.872403i	0.496309	+	0.868146i	$0.334688\pi$
$947$	−15.5000	+	26.8468i	−0.503682	+	0.872403i	−0.999991	+	0.00425721i	$0.998645\pi$
$948$		0			0
$949$	42.0000	−	10.3923i	1.36338	−	0.337348i
$950$	5.00000			0.162221
$951$		0			0
$952$	3.50000	−	6.06218i	0.113436	−	0.196476i
$953$	−7.00000	−	12.1244i	−0.226752	−	0.392746i	0.730091	−	0.683349i	$-0.239477\pi$
$953$	−7.00000	−	12.1244i	−0.226752	−	0.392746i	−0.956844	+	0.290603i	$0.906144\pi$
$954$		0			0
$955$	−4.00000	−	6.92820i	−0.129437	−	0.224191i
$956$	6.00000	+	10.3923i	0.194054	+	0.336111i
$957$		0			0
$958$	10.5000	+	18.1865i	0.339240	+	0.587580i
$959$	−9.00000	+	15.5885i	−0.290625	+	0.503378i
$960$		0			0
$961$	−27.0000			−0.870968
$962$	5.00000	+	5.19615i	0.161206	+	0.167531i
$963$		0			0
$964$	−14.0000	+	24.2487i	−0.450910	+	0.780998i
$965$	−13.0000	+	22.5167i	−0.418485	+	0.724837i
$966$		0			0
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	+	1.73205i	0.0321412	+	0.0556702i
$969$		0			0
$970$	−4.00000			−0.128432
$971$	11.0000	+	19.0526i	0.353007	+	0.611426i	0.986775	−	0.162098i	$-0.0518259\pi$
$971$	11.0000	+	19.0526i	0.353007	+	0.611426i	−0.633768	+	0.773523i	$0.718493\pi$
$972$		0			0
$973$	−9.50000	+	16.4545i	−0.304556	+	0.527506i
$974$	35.0000			1.12147
$975$		0			0
$976$	7.00000			0.224065
$977$	4.00000	−	6.92820i	0.127971	−	0.221653i	−0.794919	−	0.606715i	$-0.792487\pi$
$977$	4.00000	−	6.92820i	0.127971	−	0.221653i	0.922890	+	0.385063i	$0.125820\pi$
$978$		0			0
$979$	16.5000	+	28.5788i	0.527342	+	0.913384i
$980$	2.00000			0.0638877
$981$		0			0
$982$	−4.00000	−	6.92820i	−0.127645	−	0.221088i
$983$	32.0000			1.02064			0.510321	−	0.859984i	$-0.329527\pi$
$983$	32.0000			1.02064			0.510321	+	0.859984i	$0.329527\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$	17.5000	−	30.3109i	0.557314	−	0.965295i
$987$		0			0
$988$	5.00000	−	17.3205i	0.159071	−	0.551039i
$989$	−12.0000			−0.381578
$990$		0			0
$991$	1.50000	−	2.59808i	0.0476491	−	0.0825306i	−0.841217	−	0.540697i	$-0.818160\pi$
$991$	1.50000	−	2.59808i	0.0476491	−	0.0825306i	0.888866	+	0.458167i	$0.151494\pi$
$992$	1.00000	+	1.73205i	0.0317500	+	0.0549927i
$993$		0			0
$994$	−4.00000	−	6.92820i	−0.126872	−	0.219749i
$995$	26.0000	+	45.0333i	0.824255	+	1.42765i
$996$		0			0
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	0.805266	−	0.592914i	$-0.202023\pi$
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	−0.916112	+	0.400923i	$0.868689\pi$
$998$	−7.00000	+	12.1244i	−0.221581	+	0.383790i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.r.l.1387.1		2
3.2	odd	2		546.2.l.c.295.1	yes	2
13.3	even	3	inner	1638.2.r.l.757.1		2
39.17	odd	6		7098.2.a.bd.1.1		1
39.29	odd	6		546.2.l.c.211.1	✓	2
39.35	odd	6		7098.2.a.i.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.c.211.1	✓	2	39.29	odd	6
546.2.l.c.295.1	yes	2	3.2	odd	2
1638.2.r.l.757.1		2	13.3	even	3	inner
1638.2.r.l.1387.1		2	1.1	even	1	trivial
7098.2.a.i.1.1		1	39.35	odd	6
7098.2.a.bd.1.1		1	39.17	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.r (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{5} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-1.00000 + 1.73205i) q^{10} +(1.50000 - 2.59808i) q^{11} +(3.50000 - 0.866025i) q^{13} -1.00000 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.50000 - 6.06218i) q^{17} +(2.50000 + 4.33013i) q^{19} +(-1.00000 - 1.73205i) q^{20} +(1.50000 + 2.59808i) q^{22} +(3.00000 - 5.19615i) q^{23} -1.00000 q^{25} +(-1.00000 + 3.46410i) q^{26} +(0.500000 - 0.866025i) q^{28} +(2.50000 - 4.33013i) q^{29} -2.00000 q^{31} +(-0.500000 - 0.866025i) q^{32} +7.00000 q^{34} +(1.00000 + 1.73205i) q^{35} +(1.00000 - 1.73205i) q^{37} -5.00000 q^{38} +2.00000 q^{40} +(-2.50000 + 4.33013i) q^{41} +(-1.00000 - 1.73205i) q^{43} -3.00000 q^{44} +(3.00000 + 5.19615i) q^{46} +1.00000 q^{47} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} +(-2.50000 - 2.59808i) q^{52} -3.00000 q^{53} +(3.00000 - 5.19615i) q^{55} +(0.500000 + 0.866025i) q^{56} +(2.50000 + 4.33013i) q^{58} +(-3.00000 - 5.19615i) q^{59} +(-3.50000 - 6.06218i) q^{61} +(1.00000 - 1.73205i) q^{62} +1.00000 q^{64} +(7.00000 - 1.73205i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-3.50000 + 6.06218i) q^{68} -2.00000 q^{70} +(4.00000 + 6.92820i) q^{71} +12.0000 q^{73} +(1.00000 + 1.73205i) q^{74} +(2.50000 - 4.33013i) q^{76} +3.00000 q^{77} +3.00000 q^{79} +(-1.00000 + 1.73205i) q^{80} +(-2.50000 - 4.33013i) q^{82} +8.00000 q^{83} +(-7.00000 - 12.1244i) q^{85} +2.00000 q^{86} +(1.50000 - 2.59808i) q^{88} +(-5.50000 + 9.52628i) q^{89} +(2.50000 + 2.59808i) q^{91} -6.00000 q^{92} +(-0.500000 + 0.866025i) q^{94} +(5.00000 + 8.66025i) q^{95} +(1.00000 + 1.73205i) q^{97} +(-0.500000 - 0.866025i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8}+O(q^{10}) \) 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8	\( 2 q - q^{2} - q^{4} + 4 q^{5} + q^{7} + 2 q^{8} - 2 q^{10} + 3 q^{11} + 7 q^{13} - 2 q^{14} - q^{16} - 7 q^{17} + 5 q^{19} - 2 q^{20} + 3 q^{22} + 6 q^{23} - 2 q^{25} - 2 q^{26} + q^{28} + 5 q^{29} - 4 q^{31} - q^{32} + 14 q^{34} + 2 q^{35} + 2 q^{37} - 10 q^{38} + 4 q^{40} - 5 q^{41} - 2 q^{43} - 6 q^{44} + 6 q^{46} + 2 q^{47} - q^{49} + q^{50} - 5 q^{52} - 6 q^{53} + 6 q^{55} + q^{56} + 5 q^{58} - 6 q^{59} - 7 q^{61} + 2 q^{62} + 2 q^{64} + 14 q^{65} - 2 q^{67} - 7 q^{68} - 4 q^{70} + 8 q^{71} + 24 q^{73} + 2 q^{74} + 5 q^{76} + 6 q^{77} + 6 q^{79} - 2 q^{80} - 5 q^{82} + 16 q^{83} - 14 q^{85} + 4 q^{86} + 3 q^{88} - 11 q^{89} + 5 q^{91} - 12 q^{92} - q^{94} + 10 q^{95} + 2 q^{97} - q^{98}+O(q^{100}) \) 2 * q - q^2 - q^4 + 4 * q^5 + q^7 + 2 * q^8 - 2 * q^10 + 3 * q^11 + 7 * q^13 - 2 * q^14 - q^16 - 7 * q^17 + 5 * q^19 - 2 * q^20 + 3 * q^22 + 6 * q^23 - 2 * q^25 - 2 * q^26 + q^28 + 5 * q^29 - 4 * q^31 - q^32 + 14 * q^34 + 2 * q^35 + 2 * q^37 - 10 * q^38 + 4 * q^40 - 5 * q^41 - 2 * q^43 - 6 * q^44 + 6 * q^46 + 2 * q^47 - q^49 + q^50 - 5 * q^52 - 6 * q^53 + 6 * q^55 + q^56 + 5 * q^58 - 6 * q^59 - 7 * q^61 + 2 * q^62 + 2 * q^64 + 14 * q^65 - 2 * q^67 - 7 * q^68 - 4 * q^70 + 8 * q^71 + 24 * q^73 + 2 * q^74 + 5 * q^76 + 6 * q^77 + 6 * q^79 - 2 * q^80 - 5 * q^82 + 16 * q^83 - 14 * q^85 + 4 * q^86 + 3 * q^88 - 11 * q^89 + 5 * q^91 - 12 * q^92 - q^94 + 10 * q^95 + 2 * q^97 - q^98

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