LMFDB - Embedded newform 245.2.e.b.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,2,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.95633484952$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.2.e.b.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{12} -5.00000 q^{13} -1.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} -2.00000 q^{20} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{27} +3.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-1.50000 - 2.59808i) q^{33} +4.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-2.50000 + 4.33013i) q^{39} +12.0000 q^{41} -10.0000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.00000 - 1.73205i) q^{45} +(4.50000 + 7.79423i) q^{47} -4.00000 q^{48} +(-1.50000 - 2.59808i) q^{51} +(-5.00000 + 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-1.00000 + 1.73205i) q^{60} +(4.00000 + 6.92820i) q^{61} -8.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{69} +(1.00000 - 1.73205i) q^{73} +(0.500000 + 0.866025i) q^{75} +4.00000 q^{76} +(0.500000 + 0.866025i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} -3.00000 q^{85} +(1.50000 - 2.59808i) q^{87} +(-6.00000 - 10.3923i) q^{89} +12.0000 q^{92} +(2.00000 + 3.46410i) q^{93} +(1.00000 - 1.73205i) q^{95} +1.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{3} + 2 q^{4} - q^{5} + 2 q^{9}+O(q^{10}) $ 2 * q + q^3 + 2 * q^4 - q^5 + 2 * q^9	$ 2 q + q^{3} + 2 q^{4} - q^{5} + 2 q^{9} + 3 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{15} - 4 q^{16} + 3 q^{17} + 2 q^{19} - 4 q^{20} + 6 q^{23} - q^{25} + 10 q^{27} + 6 q^{29} - 4 q^{31} - 3 q^{33} + 8 q^{36} - 2 q^{37} - 5 q^{39} + 24 q^{41} - 20 q^{43} - 6 q^{44} + 2 q^{45} + 9 q^{47} - 8 q^{48} - 3 q^{51} - 10 q^{52} - 12 q^{53} - 6 q^{55} + 4 q^{57} - 2 q^{60} + 8 q^{61} - 16 q^{64} + 5 q^{65} + 4 q^{67} - 6 q^{68} + 12 q^{69} + 2 q^{73} + q^{75} + 8 q^{76} + q^{79} - 4 q^{80} - q^{81} - 24 q^{83} - 6 q^{85} + 3 q^{87} - 12 q^{89} + 24 q^{92} + 4 q^{93} + 2 q^{95} + 2 q^{97} + 12 q^{99}+O(q^{100}) $ 2 * q + q^3 + 2 * q^4 - q^5 + 2 * q^9 + 3 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^15 - 4 * q^16 + 3 * q^17 + 2 * q^19 - 4 * q^20 + 6 * q^23 - q^25 + 10 * q^27 + 6 * q^29 - 4 * q^31 - 3 * q^33 + 8 * q^36 - 2 * q^37 - 5 * q^39 + 24 * q^41 - 20 * q^43 - 6 * q^44 + 2 * q^45 + 9 * q^47 - 8 * q^48 - 3 * q^51 - 10 * q^52 - 12 * q^53 - 6 * q^55 + 4 * q^57 - 2 * q^60 + 8 * q^61 - 16 * q^64 + 5 * q^65 + 4 * q^67 - 6 * q^68 + 12 * q^69 + 2 * q^73 + q^75 + 8 * q^76 + q^79 - 4 * q^80 - q^81 - 24 * q^83 - 6 * q^85 + 3 * q^87 - 12 * q^89 + 24 * q^92 + 4 * q^93 + 2 * q^95 + 2 * q^97 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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			0		0.866025	−	0.500000i	$-0.166667\pi$
$2$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	−0.684819	−	0.728714i	$-0.740119\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i	0.973494	+	0.228714i	$0.0734519\pi$
$4$	1.00000	−	1.73205i	0.500000	−	0.866025i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$		0			0
$7$		0			0
$8$		0			0
$9$	1.00000	+	1.73205i	0.333333	+	0.577350i
$10$		0			0
$11$	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	$0.0172821\pi$
$12$	−1.00000	−	1.73205i	−0.288675	−	0.500000i
$13$	−5.00000			−1.38675			−0.693375	−	0.720577i	$-0.743877\pi$
$13$	−5.00000			−1.38675			−0.693375	+	0.720577i	$0.743877\pi$
$14$		0			0
$15$	−1.00000			−0.258199
$16$	−2.00000	−	3.46410i	−0.500000	−	0.866025i
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	−0.624780	−	0.780801i	$-0.714811\pi$
$17$	1.50000	−	2.59808i	0.363803	−	0.630126i	0.988583	+	0.150675i	$0.0481447\pi$
$18$		0			0
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	0.957635	−	0.287984i	$-0.0929851\pi$
$19$	1.00000	+	1.73205i	0.229416	+	0.397360i	−0.728219	+	0.685344i	$0.759652\pi$
$20$	−2.00000			−0.447214
$21$		0			0
$22$		0			0
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	0.988436	+	0.151642i	$0.0484560\pi$
$23$	3.00000	+	5.19615i	0.625543	+	1.08347i	−0.362892	+	0.931831i	$0.618211\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$		0			0
$27$	5.00000			0.962250
$28$		0			0
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	−0.987829	−	0.155543i	$-0.950287\pi$
$31$	−2.00000	+	3.46410i	−0.359211	+	0.622171i	0.628619	+	0.777714i	$0.283621\pi$
$32$		0			0
$33$	−1.50000	−	2.59808i	−0.261116	−	0.452267i
$34$		0			0
$35$		0			0
$36$	4.00000			0.666667
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	0.772043	−	0.635571i	$-0.219235\pi$
$37$	−1.00000	−	1.73205i	−0.164399	−	0.284747i	−0.936442	+	0.350823i	$0.885902\pi$
$38$		0			0
$39$	−2.50000	+	4.33013i	−0.400320	+	0.693375i
$40$		0			0
$41$	12.0000			1.87409			0.937043	−	0.349215i	$-0.113552\pi$
$41$	12.0000			1.87409			0.937043	+	0.349215i	$0.113552\pi$
$42$		0			0
$43$	−10.0000			−1.52499			−0.762493	−	0.646997i	$-0.776025\pi$
$43$	−10.0000			−1.52499			−0.762493	+	0.646997i	$0.776025\pi$
$44$	−3.00000	−	5.19615i	−0.452267	−	0.783349i
$45$	1.00000	−	1.73205i	0.149071	−	0.258199i
$46$		0			0
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	0.981543	+	0.191243i	$0.0612518\pi$
$47$	4.50000	+	7.79423i	0.656392	+	1.13691i	−0.325150	+	0.945662i	$0.605415\pi$
$48$	−4.00000			−0.577350
$49$		0			0
$50$		0			0
$51$	−1.50000	−	2.59808i	−0.210042	−	0.363803i
$52$	−5.00000	+	8.66025i	−0.693375	+	1.20096i
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	0.0783936	+	0.996922i	$0.475021\pi$
$53$	−6.00000	+	10.3923i	−0.824163	+	1.42749i	−0.902557	+	0.430570i	$0.858312\pi$
$54$		0			0
$55$	−3.00000			−0.404520
$56$		0			0
$57$	2.00000			0.264906
$58$		0			0
$59$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$59$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$60$	−1.00000	+	1.73205i	−0.129099	+	0.223607i
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	0.999901	+	0.0140840i	$0.00448323\pi$
$61$	4.00000	+	6.92820i	0.512148	+	0.887066i	−0.487753	+	0.872982i	$0.662183\pi$
$62$		0			0
$63$		0			0
$64$	−8.00000			−1.00000
$65$	2.50000	+	4.33013i	0.310087	+	0.537086i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	−3.00000	−	5.19615i	−0.363803	−	0.630126i
$69$	6.00000			0.722315
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	−0.801553	−	0.597924i	$-0.795992\pi$
$73$	1.00000	−	1.73205i	0.117041	−	0.202721i	0.918594	+	0.395203i	$0.129326\pi$
$74$		0			0
$75$	0.500000	+	0.866025i	0.0577350	+	0.100000i
$76$	4.00000			0.458831
$77$		0			0
$78$		0			0
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	0.892781	−	0.450490i	$-0.148751\pi$
$79$	0.500000	+	0.866025i	0.0562544	+	0.0974355i	−0.836527	+	0.547926i	$0.815418\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$		0			0
$83$	−12.0000			−1.31717			−0.658586	−	0.752506i	$-0.728845\pi$
$83$	−12.0000			−1.31717			−0.658586	+	0.752506i	$0.728845\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$		0			0
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$		0			0
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	−0.986303	−	0.164946i	$-0.947255\pi$
$89$	−6.00000	−	10.3923i	−0.635999	−	1.10158i	0.350304	−	0.936636i	$-0.386078\pi$
$90$		0			0
$91$		0			0
$92$	12.0000			1.25109
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$		0			0
$95$	1.00000	−	1.73205i	0.102598	−	0.177705i
$96$		0			0
$97$	1.00000			0.101535			0.0507673	−	0.998711i	$-0.483833\pi$
$97$	1.00000			0.101535			0.0507673	+	0.998711i	$0.483833\pi$
$98$		0			0
$99$	6.00000			0.603023
$100$	1.00000	+	1.73205i	0.100000	+	0.173205i
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$		0			0
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	0.962505	−	0.271263i	$-0.0874412\pi$
$103$	2.50000	+	4.33013i	0.246332	+	0.426660i	−0.716173	+	0.697923i	$0.754108\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	0.683793	−	0.729676i	$-0.260329\pi$
$107$	−3.00000	−	5.19615i	−0.290021	−	0.502331i	−0.973814	+	0.227345i	$0.926996\pi$
$108$	5.00000	−	8.66025i	0.481125	−	0.833333i
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	−0.648292	−	0.761392i	$-0.724516\pi$
$109$	3.50000	−	6.06218i	0.335239	−	0.580651i	0.983531	+	0.180741i	$0.0578495\pi$
$110$		0			0
$111$	−2.00000			−0.189832
$112$		0			0
$113$	6.00000			0.564433			0.282216	−	0.959351i	$-0.408930\pi$
$113$	6.00000			0.564433			0.282216	+	0.959351i	$0.408930\pi$
$114$		0			0
$115$	3.00000	−	5.19615i	0.279751	−	0.484544i
$116$	3.00000	−	5.19615i	0.278543	−	0.482451i
$117$	−5.00000	−	8.66025i	−0.462250	−	0.800641i
$118$		0			0
$119$		0			0
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$		0			0
$123$	6.00000	−	10.3923i	0.541002	−	0.937043i
$124$	4.00000	+	6.92820i	0.359211	+	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−16.0000			−1.41977			−0.709885	−	0.704317i	$-0.751253\pi$
$127$	−16.0000			−1.41977			−0.709885	+	0.704317i	$0.751253\pi$
$128$		0			0
$129$	−5.00000	+	8.66025i	−0.440225	+	0.762493i
$130$		0			0
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	0.704692	−	0.709514i	$-0.251085\pi$
$131$	−3.00000	−	5.19615i	−0.262111	−	0.453990i	−0.966803	+	0.255524i	$0.917752\pi$
$132$	−6.00000			−0.522233
$133$		0			0
$134$		0			0
$135$	−2.50000	−	4.33013i	−0.215166	−	0.372678i
$136$		0			0
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	−0.487278	−	0.873247i	$-0.662010\pi$
$137$	6.00000	−	10.3923i	0.512615	−	0.887875i	0.999893	−	0.0146279i	$-0.00465636\pi$
$138$		0			0
$139$	−14.0000			−1.18746			−0.593732	−	0.804663i	$-0.702346\pi$
$139$	−14.0000			−1.18746			−0.593732	+	0.804663i	$0.702346\pi$
$140$		0			0
$141$	9.00000			0.757937
$142$		0			0
$143$	−7.50000	+	12.9904i	−0.627182	+	1.08631i
$144$	4.00000	−	6.92820i	0.333333	−	0.577350i
$145$	−1.50000	−	2.59808i	−0.124568	−	0.215758i
$146$		0			0
$147$		0			0
$148$	−4.00000			−0.328798
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$		0			0
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	−0.844963	−	0.534824i	$-0.820378\pi$
$151$	0.500000	−	0.866025i	0.0406894	−	0.0704761i	0.885653	+	0.464348i	$0.153711\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	4.00000			0.321288
$156$	5.00000	+	8.66025i	0.400320	+	0.693375i
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	−0.438948	−	0.898513i	$-0.644649\pi$
$157$	7.00000	−	12.1244i	0.558661	−	0.967629i	0.997609	−	0.0691164i	$-0.0220180\pi$
$158$		0			0
$159$	6.00000	+	10.3923i	0.475831	+	0.824163i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	0.824202	−	0.566296i	$-0.191624\pi$
$163$	−1.00000	−	1.73205i	−0.0783260	−	0.135665i	−0.902528	+	0.430632i	$0.858291\pi$
$164$	12.0000	−	20.7846i	0.937043	−	1.62301i
$165$	−1.50000	+	2.59808i	−0.116775	+	0.202260i
$166$		0			0
$167$	3.00000			0.232147			0.116073	−	0.993241i	$-0.462969\pi$
$167$	3.00000			0.232147			0.116073	+	0.993241i	$0.462969\pi$
$168$		0			0
$169$	12.0000			0.923077
$170$		0			0
$171$	−2.00000	+	3.46410i	−0.152944	+	0.264906i
$172$	−10.0000	+	17.3205i	−0.762493	+	1.32068i
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	0.642699	−	0.766119i	$-0.277815\pi$
$173$	−4.50000	−	7.79423i	−0.342129	−	0.592584i	−0.984828	+	0.173534i	$0.944481\pi$
$174$		0			0
$175$		0			0
$176$	−12.0000			−0.904534
$177$		0			0
$178$		0			0
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	−0.998286	−	0.0585225i	$-0.981361\pi$
$179$	−6.00000	+	10.3923i	−0.448461	+	0.776757i	0.549825	+	0.835280i	$0.314694\pi$
$180$	−2.00000	−	3.46410i	−0.149071	−	0.258199i
$181$	−20.0000			−1.48659			−0.743294	−	0.668965i	$-0.766738\pi$
$181$	−20.0000			−1.48659			−0.743294	+	0.668965i	$0.766738\pi$
$182$		0			0
$183$	8.00000			0.591377
$184$		0			0
$185$	−1.00000	+	1.73205i	−0.0735215	+	0.127343i
$186$		0			0
$187$	−4.50000	−	7.79423i	−0.329073	−	0.569970i
$188$	18.0000			1.31278
$189$		0			0
$190$		0			0
$191$	−4.50000	−	7.79423i	−0.325609	−	0.563971i	0.656027	−	0.754738i	$-0.272236\pi$
$191$	−4.50000	−	7.79423i	−0.325609	−	0.563971i	−0.981635	+	0.190767i	$0.938902\pi$
$192$	−4.00000	+	6.92820i	−0.288675	+	0.500000i
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	−0.785022	−	0.619467i	$-0.787349\pi$
$193$	2.00000	−	3.46410i	0.143963	−	0.249351i	0.928986	+	0.370116i	$0.120682\pi$
$194$		0			0
$195$	5.00000			0.358057
$196$		0			0
$197$		0			0			−	1.00000i	$-0.5\pi$
$197$		0			0				1.00000i	$0.5\pi$
$198$		0			0
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	0.429745	+	0.902950i	$0.358603\pi$
$199$	−8.00000	+	13.8564i	−0.567105	+	0.982255i	−0.996850	+	0.0793045i	$0.974730\pi$
$200$		0			0
$201$	−2.00000	−	3.46410i	−0.141069	−	0.244339i
$202$		0			0
$203$		0			0
$204$	−6.00000			−0.420084
$205$	−6.00000	−	10.3923i	−0.419058	−	0.725830i
$206$		0			0
$207$	−6.00000	+	10.3923i	−0.417029	+	0.722315i
$208$	10.0000	+	17.3205i	0.693375	+	1.20096i
$209$	6.00000			0.415029
$210$		0			0
$211$	−13.0000			−0.894957			−0.447478	−	0.894295i	$-0.647678\pi$
$211$	−13.0000			−0.894957			−0.447478	+	0.894295i	$0.647678\pi$
$212$	12.0000	+	20.7846i	0.824163	+	1.42749i
$213$		0			0
$214$		0			0
$215$	5.00000	+	8.66025i	0.340997	+	0.590624i
$216$		0			0
$217$		0			0
$218$		0			0
$219$	−1.00000	−	1.73205i	−0.0675737	−	0.117041i
$220$	−3.00000	+	5.19615i	−0.202260	+	0.350325i
$221$	−7.50000	+	12.9904i	−0.504505	+	0.873828i
$222$		0			0
$223$	19.0000			1.27233			0.636167	−	0.771551i	$-0.280519\pi$
$223$	19.0000			1.27233			0.636167	+	0.771551i	$0.280519\pi$
$224$		0			0
$225$	−2.00000			−0.133333
$226$		0			0
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	−0.911502	−	0.411296i	$-0.865076\pi$
$227$	−1.50000	+	2.59808i	−0.0995585	+	0.172440i	0.811943	+	0.583736i	$0.198410\pi$
$228$	2.00000	−	3.46410i	0.132453	−	0.229416i
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	0.792347	−	0.610071i	$-0.208859\pi$
$229$	−2.00000	−	3.46410i	−0.132164	−	0.228914i	−0.924510	+	0.381157i	$0.875526\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	−0.928312	−	0.371802i	$-0.878740\pi$
$233$	−12.0000	−	20.7846i	−0.786146	−	1.36165i	0.142166	−	0.989843i	$-0.454593\pi$
$234$		0			0
$235$	4.50000	−	7.79423i	0.293548	−	0.508439i
$236$		0			0
$237$	1.00000			0.0649570
$238$		0			0
$239$	−21.0000			−1.35838			−0.679189	−	0.733964i	$-0.737668\pi$
$239$	−21.0000			−1.35838			−0.679189	+	0.733964i	$0.737668\pi$
$240$	2.00000	+	3.46410i	0.129099	+	0.223607i
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	−0.980917	−	0.194429i	$-0.937715\pi$
$241$	−5.00000	+	8.66025i	−0.322078	+	0.557856i	0.658838	+	0.752285i	$0.271048\pi$
$242$		0			0
$243$	8.00000	+	13.8564i	0.513200	+	0.888889i
$244$	16.0000			1.02430
$245$		0			0
$246$		0			0
$247$	−5.00000	−	8.66025i	−0.318142	−	0.551039i
$248$		0			0
$249$	−6.00000	+	10.3923i	−0.380235	+	0.658586i
$250$		0			0
$251$	−18.0000			−1.13615			−0.568075	−	0.822977i	$-0.692312\pi$
$251$	−18.0000			−1.13615			−0.568075	+	0.822977i	$0.692312\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$	−1.50000	+	2.59808i	−0.0939336	+	0.162698i
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.773427	+	0.633885i	$0.218541\pi$
$257$	15.0000	+	25.9808i	0.935674	+	1.62064i	0.162247	+	0.986750i	$0.448126\pi$
$258$		0			0
$259$		0			0
$260$	10.0000			0.620174
$261$	3.00000	+	5.19615i	0.185695	+	0.321634i
$262$		0			0
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	−0.943572	−	0.331166i	$-0.892558\pi$
$263$	−3.00000	+	5.19615i	−0.184988	+	0.320408i	0.758585	+	0.651575i	$0.225891\pi$
$264$		0			0
$265$	12.0000			0.737154
$266$		0			0
$267$	−12.0000			−0.734388
$268$	−4.00000	−	6.92820i	−0.244339	−	0.423207i
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	−0.942871	−	0.333157i	$-0.891886\pi$
$269$	−3.00000	+	5.19615i	−0.182913	+	0.316815i	0.759958	+	0.649972i	$0.225219\pi$
$270$		0			0
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	0.513905	−	0.857847i	$-0.328199\pi$
$271$	−8.00000	−	13.8564i	−0.485965	−	0.841717i	−0.999870	+	0.0161307i	$0.994865\pi$
$272$	−12.0000			−0.727607
$273$		0			0
$274$		0			0
$275$	1.50000	+	2.59808i	0.0904534	+	0.156670i
$276$	6.00000	−	10.3923i	0.361158	−	0.625543i
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	−0.675810	−	0.737075i	$-0.736206\pi$
$277$	5.00000	−	8.66025i	0.300421	−	0.520344i	0.976231	+	0.216731i	$0.0695395\pi$
$278$		0			0
$279$	−8.00000			−0.478947
$280$		0			0
$281$	3.00000			0.178965			0.0894825	−	0.995988i	$-0.471479\pi$
$281$	3.00000			0.178965			0.0894825	+	0.995988i	$0.471479\pi$
$282$		0			0
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	−0.991960	−	0.126550i	$-0.959610\pi$
$283$	−6.50000	+	11.2583i	−0.386385	+	0.669238i	0.605575	+	0.795788i	$0.292943\pi$
$284$		0			0
$285$	−1.00000	−	1.73205i	−0.0592349	−	0.102598i
$286$		0			0
$287$		0			0
$288$		0			0
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	0.500000	−	0.866025i	0.0293105	−	0.0507673i
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	21.0000			1.22683			0.613417	−	0.789760i	$-0.289795\pi$
$293$	21.0000			1.22683			0.613417	+	0.789760i	$0.289795\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	7.50000	−	12.9904i	0.435194	−	0.753778i
$298$		0			0
$299$	−15.0000	−	25.9808i	−0.867472	−	1.50251i
$300$	2.00000			0.115470
$301$		0			0
$302$		0			0
$303$	−3.00000	−	5.19615i	−0.172345	−	0.298511i
$304$	4.00000	−	6.92820i	0.229416	−	0.397360i
$305$	4.00000	−	6.92820i	0.229039	−	0.396708i
$306$		0			0
$307$	−11.0000			−0.627803			−0.313902	−	0.949456i	$-0.601636\pi$
$307$	−11.0000			−0.627803			−0.313902	+	0.949456i	$0.601636\pi$
$308$		0			0
$309$	5.00000			0.284440
$310$		0			0
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	−0.489585	−	0.871956i	$-0.662852\pi$
$311$	9.00000	−	15.5885i	0.510343	−	0.883940i	0.999928	−	0.0119847i	$-0.00381495\pi$
$312$		0			0
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	−0.999065	−	0.0432311i	$-0.986235\pi$
$313$	−9.50000	−	16.4545i	−0.536972	−	0.930062i	0.462093	−	0.886831i	$-0.347098\pi$
$314$		0			0
$315$		0			0
$316$	2.00000			0.112509
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	0.999980	+	0.00635137i	$0.00202172\pi$
$317$	9.00000	+	15.5885i	0.505490	+	0.875535i	−0.494489	+	0.869184i	$0.664645\pi$
$318$		0			0
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$	4.00000	+	6.92820i	0.223607	+	0.387298i
$321$	−6.00000			−0.334887
$322$		0			0
$323$	6.00000			0.333849
$324$	1.00000	+	1.73205i	0.0555556	+	0.0962250i
$325$	2.50000	−	4.33013i	0.138675	−	0.240192i
$326$		0			0
$327$	−3.50000	−	6.06218i	−0.193550	−	0.335239i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	0.937829	+	0.347097i	$0.112833\pi$
$331$	14.0000	+	24.2487i	0.769510	+	1.33283i	−0.168320	+	0.985732i	$0.553834\pi$
$332$	−12.0000	+	20.7846i	−0.658586	+	1.14070i
$333$	2.00000	−	3.46410i	0.109599	−	0.189832i
$334$		0			0
$335$	−4.00000			−0.218543
$336$		0			0
$337$	14.0000			0.762629			0.381314	−	0.924445i	$-0.375472\pi$
$337$	14.0000			0.762629			0.381314	+	0.924445i	$0.375472\pi$
$338$		0			0
$339$	3.00000	−	5.19615i	0.162938	−	0.282216i
$340$	−3.00000	+	5.19615i	−0.162698	+	0.281801i
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$		0			0
$343$		0			0
$344$		0			0
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$		0			0
$347$	9.00000	−	15.5885i	0.483145	−	0.836832i	−0.516667	−	0.856186i	$-0.672828\pi$
$347$	9.00000	−	15.5885i	0.483145	−	0.836832i	0.999813	+	0.0193540i	$0.00616095\pi$
$348$	−3.00000	−	5.19615i	−0.160817	−	0.278543i
$349$	−26.0000			−1.39175			−0.695874	−	0.718164i	$-0.744983\pi$
$349$	−26.0000			−1.39175			−0.695874	+	0.718164i	$0.744983\pi$
$350$		0			0
$351$	−25.0000			−1.33440
$352$		0			0
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	−0.594441	−	0.804139i	$-0.702627\pi$
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	0.993626	+	0.112731i	$0.0359599\pi$
$354$		0			0
$355$		0			0
$356$	−24.0000			−1.27200
$357$		0			0
$358$		0			0
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	−0.986865	−	0.161546i	$-0.948352\pi$
$359$	−12.0000	−	20.7846i	−0.633336	−	1.09697i	0.353529	−	0.935423i	$-0.384981\pi$
$360$		0			0
$361$	7.50000	−	12.9904i	0.394737	−	0.683704i
$362$		0			0
$363$	2.00000			0.104973
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	−0.554264	−	0.832341i	$-0.687000\pi$
$367$	8.50000	−	14.7224i	0.443696	−	0.768505i	0.997960	+	0.0638362i	$0.0203335\pi$
$368$	12.0000	−	20.7846i	0.625543	−	1.08347i
$369$	12.0000	+	20.7846i	0.624695	+	1.08200i
$370$		0			0
$371$		0			0
$372$	8.00000			0.414781
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	0.913147	−	0.407630i	$-0.133645\pi$
$373$	2.00000	+	3.46410i	0.103556	+	0.179364i	−0.809591	+	0.586994i	$0.800311\pi$
$374$		0			0
$375$	0.500000	−	0.866025i	0.0258199	−	0.0447214i
$376$		0			0
$377$	−15.0000			−0.772539
$378$		0			0
$379$	20.0000			1.02733			0.513665	−	0.857991i	$-0.328287\pi$
$379$	20.0000			1.02733			0.513665	+	0.857991i	$0.328287\pi$
$380$	−2.00000	−	3.46410i	−0.102598	−	0.177705i
$381$	−8.00000	+	13.8564i	−0.409852	+	0.709885i
$382$		0			0
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	0.977613	−	0.210411i	$-0.0674801\pi$
$383$	6.00000	+	10.3923i	0.306586	+	0.531022i	−0.671027	+	0.741433i	$0.734147\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−10.0000	−	17.3205i	−0.508329	−	0.880451i
$388$	1.00000	−	1.73205i	0.0507673	−	0.0879316i
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	−0.825491	−	0.564416i	$-0.809102\pi$
$389$	1.50000	−	2.59808i	0.0760530	−	0.131728i	0.901544	+	0.432688i	$0.142435\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$		0			0
$393$	−6.00000			−0.302660
$394$		0			0
$395$	0.500000	−	0.866025i	0.0251577	−	0.0435745i
$396$	6.00000	−	10.3923i	0.301511	−	0.522233i
$397$	−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
$399$		0			0
$400$	4.00000			0.200000
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	0.990257	−	0.139253i	$-0.0444700\pi$
$401$	7.50000	+	12.9904i	0.374532	+	0.648709i	−0.615725	+	0.787961i	$0.711137\pi$
$402$		0			0
$403$	10.0000	−	17.3205i	0.498135	−	0.862796i
$404$	−6.00000	−	10.3923i	−0.298511	−	0.517036i
$405$	1.00000			0.0496904
$406$		0			0
$407$	−6.00000			−0.297409
$408$		0			0
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$		0			0
$411$	−6.00000	−	10.3923i	−0.295958	−	0.512615i
$412$	10.0000			0.492665
$413$		0			0
$414$		0			0
$415$	6.00000	+	10.3923i	0.294528	+	0.510138i
$416$		0			0
$417$	−7.00000	+	12.1244i	−0.342791	+	0.593732i
$418$		0			0
$419$	12.0000			0.586238			0.293119	−	0.956076i	$-0.405307\pi$
$419$	12.0000			0.586238			0.293119	+	0.956076i	$0.405307\pi$
$420$		0			0
$421$	17.0000			0.828529			0.414265	−	0.910156i	$-0.364039\pi$
$421$	17.0000			0.828529			0.414265	+	0.910156i	$0.364039\pi$
$422$		0			0
$423$	−9.00000	+	15.5885i	−0.437595	+	0.757937i
$424$		0			0
$425$	1.50000	+	2.59808i	0.0727607	+	0.126025i
$426$		0			0
$427$		0			0
$428$	−12.0000			−0.580042
$429$	7.50000	+	12.9904i	0.362103	+	0.627182i
$430$		0			0
$431$	−10.5000	+	18.1865i	−0.505767	+	0.876014i	0.494211	+	0.869342i	$0.335457\pi$
$431$	−10.5000	+	18.1865i	−0.505767	+	0.876014i	−0.999978	+	0.00667224i	$0.997876\pi$
$432$	−10.0000	−	17.3205i	−0.481125	−	0.833333i
$433$	−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
$435$	−3.00000			−0.143839
$436$	−7.00000	−	12.1244i	−0.335239	−	0.580651i
$437$	−6.00000	+	10.3923i	−0.287019	+	0.497131i
$438$		0			0
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	0.989401	+	0.145210i	$0.0463858\pi$
$439$	13.0000	+	22.5167i	0.620456	+	1.07466i	−0.368945	+	0.929451i	$0.620281\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	9.00000	+	15.5885i	0.427603	+	0.740630i	0.996660	−	0.0816684i	$-0.0260248\pi$
$443$	9.00000	+	15.5885i	0.427603	+	0.740630i	−0.569057	+	0.822298i	$0.692691\pi$
$444$	−2.00000	+	3.46410i	−0.0949158	+	0.164399i
$445$	−6.00000	+	10.3923i	−0.284427	+	0.492642i
$446$		0			0
$447$	6.00000			0.283790
$448$		0			0
$449$	−9.00000			−0.424736			−0.212368	−	0.977190i	$-0.568118\pi$
$449$	−9.00000			−0.424736			−0.212368	+	0.977190i	$0.568118\pi$
$450$		0			0
$451$	18.0000	−	31.1769i	0.847587	−	1.46806i
$452$	6.00000	−	10.3923i	0.282216	−	0.488813i
$453$	−0.500000	−	0.866025i	−0.0234920	−	0.0406894i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	0.757174	−	0.653213i	$-0.226579\pi$
$457$	−4.00000	−	6.92820i	−0.187112	−	0.324088i	−0.944286	+	0.329125i	$0.893246\pi$
$458$		0			0
$459$	7.50000	−	12.9904i	0.350070	−	0.606339i
$460$	−6.00000	−	10.3923i	−0.279751	−	0.484544i
$461$	24.0000			1.11779			0.558896	−	0.829238i	$-0.311225\pi$
$461$	24.0000			1.11779			0.558896	+	0.829238i	$0.311225\pi$
$462$		0			0
$463$	32.0000			1.48717			0.743583	−	0.668644i	$-0.233125\pi$
$463$	32.0000			1.48717			0.743583	+	0.668644i	$0.233125\pi$
$464$	−6.00000	−	10.3923i	−0.278543	−	0.482451i
$465$	2.00000	−	3.46410i	0.0927478	−	0.160644i
$466$		0			0
$467$	7.50000	+	12.9904i	0.347059	+	0.601123i	0.985726	−	0.168360i	$-0.0538472\pi$
$467$	7.50000	+	12.9904i	0.347059	+	0.601123i	−0.638667	+	0.769483i	$0.720514\pi$
$468$	−20.0000			−0.924500
$469$		0			0
$470$		0			0
$471$	−7.00000	−	12.1244i	−0.322543	−	0.558661i
$472$		0			0
$473$	−15.0000	+	25.9808i	−0.689701	+	1.19460i
$474$		0			0
$475$	−2.00000			−0.0917663
$476$		0			0
$477$	−24.0000			−1.09888
$478$		0			0
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	0.287954	+	0.957644i	$0.407025\pi$
$479$	−15.0000	+	25.9808i	−0.685367	+	1.18709i	−0.973321	+	0.229447i	$0.926308\pi$
$480$		0			0
$481$	5.00000	+	8.66025i	0.227980	+	0.394874i
$482$		0			0
$483$		0			0
$484$	4.00000			0.181818
$485$	−0.500000	−	0.866025i	−0.0227038	−	0.0393242i
$486$		0			0
$487$	−19.0000	+	32.9090i	−0.860972	+	1.49125i	0.0100195	+	0.999950i	$0.496811\pi$
$487$	−19.0000	+	32.9090i	−0.860972	+	1.49125i	−0.870992	+	0.491298i	$0.836523\pi$
$488$		0			0
$489$	−2.00000			−0.0904431
$490$		0			0
$491$	15.0000			0.676941			0.338470	−	0.940977i	$-0.390091\pi$
$491$	15.0000			0.676941			0.338470	+	0.940977i	$0.390091\pi$
$492$	−12.0000	−	20.7846i	−0.541002	−	0.937043i
$493$	4.50000	−	7.79423i	0.202670	−	0.351034i
$494$		0			0
$495$	−3.00000	−	5.19615i	−0.134840	−	0.233550i
$496$	16.0000			0.718421
$497$		0			0
$498$		0			0
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	0.970558	+	0.240866i	$0.0774314\pi$
$499$	15.5000	+	26.8468i	0.693875	+	1.20183i	−0.276683	+	0.960961i	$0.589235\pi$
$500$	1.00000	−	1.73205i	0.0447214	−	0.0774597i
$501$	1.50000	−	2.59808i	0.0670151	−	0.116073i
$502$		0			0
$503$	−27.0000			−1.20387			−0.601935	−	0.798545i	$-0.705603\pi$
$503$	−27.0000			−1.20387			−0.601935	+	0.798545i	$0.705603\pi$
$504$		0			0
$505$	−6.00000			−0.266996
$506$		0			0
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$	−16.0000	+	27.7128i	−0.709885	+	1.22956i
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$		0			0
$512$		0			0
$513$	5.00000	+	8.66025i	0.220755	+	0.382360i
$514$		0			0
$515$	2.50000	−	4.33013i	0.110163	−	0.190808i
$516$	10.0000	+	17.3205i	0.440225	+	0.762493i
$517$	27.0000			1.18746
$518$		0			0
$519$	−9.00000			−0.395056
$520$		0			0
$521$	−21.0000	+	36.3731i	−0.920027	+	1.59353i	−0.120656	+	0.992694i	$0.538500\pi$
$521$	−21.0000	+	36.3731i	−0.920027	+	1.59353i	−0.799370	+	0.600839i	$0.794833\pi$
$522$		0			0
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	0.997478	−	0.0709788i	$-0.0226123\pi$
$523$	10.0000	+	17.3205i	0.437269	+	0.757373i	−0.560208	+	0.828352i	$0.689279\pi$
$524$	−12.0000			−0.524222
$525$		0			0
$526$		0			0
$527$	6.00000	+	10.3923i	0.261364	+	0.452696i
$528$	−6.00000	+	10.3923i	−0.261116	+	0.452267i
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−60.0000			−2.59889
$534$		0			0
$535$	−3.00000	+	5.19615i	−0.129701	+	0.224649i
$536$		0			0
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$		0			0
$539$		0			0
$540$	−10.0000			−0.430331
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	0.723234	−	0.690604i	$-0.242655\pi$
$541$	−5.50000	−	9.52628i	−0.236463	−	0.409567i	−0.959697	+	0.281037i	$0.909322\pi$
$542$		0			0
$543$	−10.0000	+	17.3205i	−0.429141	+	0.743294i
$544$		0			0
$545$	−7.00000			−0.299847
$546$		0			0
$547$	8.00000			0.342055			0.171028	−	0.985266i	$-0.445291\pi$
$547$	8.00000			0.342055			0.171028	+	0.985266i	$0.445291\pi$
$548$	−12.0000	−	20.7846i	−0.512615	−	0.887875i
$549$	−8.00000	+	13.8564i	−0.341432	+	0.591377i
$550$		0			0
$551$	3.00000	+	5.19615i	0.127804	+	0.221364i
$552$		0			0
$553$		0			0
$554$		0			0
$555$	1.00000	+	1.73205i	0.0424476	+	0.0735215i
$556$	−14.0000	+	24.2487i	−0.593732	+	1.02837i
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	−0.491496	−	0.870880i	$-0.663550\pi$
$557$	12.0000	−	20.7846i	0.508456	−	0.880672i	0.999952	−	0.00979220i	$-0.00311700\pi$
$558$		0			0
$559$	50.0000			2.11477
$560$		0			0
$561$	−9.00000			−0.379980
$562$		0			0
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	−0.184950	−	0.982748i	$-0.559212\pi$
$563$	18.0000	−	31.1769i	0.758610	−	1.31395i	0.943560	−	0.331202i	$-0.107454\pi$
$564$	9.00000	−	15.5885i	0.378968	−	0.656392i
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	0.613369	−	0.789797i	$-0.289814\pi$
$569$	−9.00000	−	15.5885i	−0.377300	−	0.653502i	−0.990668	+	0.136295i	$0.956481\pi$
$570$		0			0
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	−0.821138	−	0.570730i	$-0.806660\pi$
$571$	2.00000	−	3.46410i	0.0836974	−	0.144968i	0.904835	+	0.425762i	$0.139994\pi$
$572$	15.0000	+	25.9808i	0.627182	+	1.08631i
$573$	−9.00000			−0.375980
$574$		0			0
$575$	−6.00000			−0.250217
$576$	−8.00000	−	13.8564i	−0.333333	−	0.577350i
$577$	−3.50000	+	6.06218i	−0.145707	+	0.252372i	−0.929636	−	0.368478i	$-0.879879\pi$
$577$	−3.50000	+	6.06218i	−0.145707	+	0.252372i	0.783930	+	0.620850i	$0.213212\pi$
$578$		0			0
$579$	−2.00000	−	3.46410i	−0.0831172	−	0.143963i
$580$	−6.00000			−0.249136
$581$		0			0
$582$		0			0
$583$	18.0000	+	31.1769i	0.745484	+	1.29122i
$584$		0			0
$585$	−5.00000	+	8.66025i	−0.206725	+	0.358057i
$586$		0			0
$587$	24.0000			0.990586			0.495293	−	0.868726i	$-0.335061\pi$
$587$	24.0000			0.990586			0.495293	+	0.868726i	$0.335061\pi$
$588$		0			0
$589$	−8.00000			−0.329634
$590$		0			0
$591$		0			0
$592$	−4.00000	+	6.92820i	−0.164399	+	0.284747i
$593$	−19.5000	−	33.7750i	−0.800769	−	1.38697i	−0.919111	−	0.394000i	$-0.871091\pi$
$593$	−19.5000	−	33.7750i	−0.800769	−	1.38697i	0.118342	−	0.992973i	$-0.462242\pi$
$594$		0			0
$595$		0			0
$596$	12.0000			0.491539
$597$	8.00000	+	13.8564i	0.327418	+	0.567105i
$598$		0			0
$599$	−22.5000	+	38.9711i	−0.919325	+	1.59232i	−0.118882	+	0.992908i	$0.537931\pi$
$599$	−22.5000	+	38.9711i	−0.919325	+	1.59232i	−0.800443	+	0.599409i	$0.795402\pi$
$600$		0			0
$601$	10.0000			0.407909			0.203954	−	0.978980i	$-0.434621\pi$
$601$	10.0000			0.407909			0.203954	+	0.978980i	$0.434621\pi$
$602$		0			0
$603$	8.00000			0.325785
$604$	−1.00000	−	1.73205i	−0.0406894	−	0.0704761i
$605$	1.00000	−	1.73205i	0.0406558	−	0.0704179i
$606$		0			0
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	0.703429	−	0.710766i	$-0.251651\pi$
$607$	−6.50000	−	11.2583i	−0.263827	−	0.456962i	−0.967256	+	0.253804i	$0.918318\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−22.5000	−	38.9711i	−0.910253	−	1.57660i
$612$	6.00000	−	10.3923i	0.242536	−	0.420084i
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	−0.885514	−	0.464614i	$-0.846193\pi$
$613$	−1.00000	+	1.73205i	−0.0403896	+	0.0699569i	0.845124	+	0.534570i	$0.179527\pi$
$614$		0			0
$615$	−12.0000			−0.483887
$616$		0			0
$617$	42.0000			1.69086			0.845428	−	0.534089i	$-0.179345\pi$
$617$	42.0000			1.69086			0.845428	+	0.534089i	$0.179345\pi$
$618$		0			0
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	−0.477143	−	0.878826i	$-0.658328\pi$
$619$	13.0000	−	22.5167i	0.522514	−	0.905021i	0.999657	−	0.0261952i	$-0.00833914\pi$
$620$	4.00000	−	6.92820i	0.160644	−	0.278243i
$621$	15.0000	+	25.9808i	0.601929	+	1.04257i
$622$		0			0
$623$		0			0
$624$	20.0000			0.800641
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$		0			0
$627$	3.00000	−	5.19615i	0.119808	−	0.207514i
$628$	−14.0000	−	24.2487i	−0.558661	−	0.967629i
$629$	−6.00000			−0.239236
$630$		0			0
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$		0			0
$633$	−6.50000	+	11.2583i	−0.258352	+	0.447478i
$634$		0			0
$635$	8.00000	+	13.8564i	0.317470	+	0.549875i
$636$	24.0000			0.951662
$637$		0			0
$638$		0			0
$639$		0			0
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$		0			0
$643$	−41.0000			−1.61688			−0.808441	−	0.588577i	$-0.799688\pi$
$643$	−41.0000			−1.61688			−0.808441	+	0.588577i	$0.799688\pi$
$644$		0			0
$645$	10.0000			0.393750
$646$		0			0
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	−0.999478	−	0.0322975i	$-0.989718\pi$
$647$	−12.0000	+	20.7846i	−0.471769	+	0.817127i	0.527710	+	0.849425i	$0.323051\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$	−4.00000			−0.156652
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	0.918736	−	0.394872i	$-0.129211\pi$
$653$	3.00000	+	5.19615i	0.117399	+	0.203341i	−0.801337	+	0.598213i	$0.795878\pi$
$654$		0			0
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$	−24.0000	−	41.5692i	−0.937043	−	1.62301i
$657$	4.00000			0.156055
$658$		0			0
$659$	−15.0000			−0.584317			−0.292159	−	0.956370i	$-0.594373\pi$
$659$	−15.0000			−0.584317			−0.292159	+	0.956370i	$0.594373\pi$
$660$	3.00000	+	5.19615i	0.116775	+	0.202260i
$661$	16.0000	−	27.7128i	0.622328	−	1.07790i	−0.366723	−	0.930330i	$-0.619520\pi$
$661$	16.0000	−	27.7128i	0.622328	−	1.07790i	0.989051	−	0.147573i	$-0.0471463\pi$
$662$		0			0
$663$	7.50000	+	12.9904i	0.291276	+	0.504505i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	9.00000	+	15.5885i	0.348481	+	0.603587i
$668$	3.00000	−	5.19615i	0.116073	−	0.201045i
$669$	9.50000	−	16.4545i	0.367291	−	0.636167i
$670$		0			0
$671$	24.0000			0.926510
$672$		0			0
$673$	−28.0000			−1.07932			−0.539660	−	0.841883i	$-0.681447\pi$
$673$	−28.0000			−1.07932			−0.539660	+	0.841883i	$0.681447\pi$
$674$		0			0
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	12.0000	−	20.7846i	0.461538	−	0.799408i
$677$	22.5000	+	38.9711i	0.864745	+	1.49778i	0.867300	+	0.497786i	$0.165853\pi$
$677$	22.5000	+	38.9711i	0.864745	+	1.49778i	−0.00255466	+	0.999997i	$0.500813\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$	1.50000	+	2.59808i	0.0574801	+	0.0995585i
$682$		0			0
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	−0.539750	−	0.841825i	$-0.681481\pi$
$683$	12.0000	−	20.7846i	0.459167	−	0.795301i	0.998917	+	0.0465244i	$0.0148145\pi$
$684$	4.00000	+	6.92820i	0.152944	+	0.264906i
$685$	−12.0000			−0.458496
$686$		0			0
$687$	−4.00000			−0.152610
$688$	20.0000	+	34.6410i	0.762493	+	1.32068i
$689$	30.0000	−	51.9615i	1.14291	−	1.97958i
$690$		0			0
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	−0.999276	−	0.0380440i	$-0.987887\pi$
$691$	−14.0000	−	24.2487i	−0.532585	−	0.922464i	0.466691	−	0.884420i	$-0.345446\pi$
$692$	−18.0000			−0.684257
$693$		0			0
$694$		0			0
$695$	7.00000	+	12.1244i	0.265525	+	0.459903i
$696$		0			0
$697$	18.0000	−	31.1769i	0.681799	−	1.18091i
$698$		0			0
$699$	−24.0000			−0.907763
$700$		0			0
$701$	−9.00000			−0.339925			−0.169963	−	0.985451i	$-0.554365\pi$
$701$	−9.00000			−0.339925			−0.169963	+	0.985451i	$0.554365\pi$
$702$		0			0
$703$	2.00000	−	3.46410i	0.0754314	−	0.130651i
$704$	−12.0000	+	20.7846i	−0.452267	+	0.783349i
$705$	−4.50000	−	7.79423i	−0.169480	−	0.293548i
$706$		0			0
$707$		0			0
$708$		0			0
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	−0.981331	−	0.192328i	$-0.938396\pi$
$709$	−17.5000	−	30.3109i	−0.657226	−	1.13835i	0.324104	−	0.946021i	$-0.394937\pi$
$710$		0			0
$711$	−1.00000	+	1.73205i	−0.0375029	+	0.0649570i
$712$		0			0
$713$	−24.0000			−0.898807
$714$		0			0
$715$	15.0000			0.560968
$716$	12.0000	+	20.7846i	0.448461	+	0.776757i
$717$	−10.5000	+	18.1865i	−0.392130	+	0.679189i
$718$		0			0
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	−0.997546	−	0.0700124i	$-0.977696\pi$
$719$	−15.0000	−	25.9808i	−0.559406	−	0.968919i	0.438141	−	0.898906i	$-0.355637\pi$
$720$	−8.00000			−0.298142
$721$		0			0
$722$		0			0
$723$	5.00000	+	8.66025i	0.185952	+	0.322078i
$724$	−20.0000	+	34.6410i	−0.743294	+	1.28742i
$725$	−1.50000	+	2.59808i	−0.0557086	+	0.0964901i
$726$		0			0
$727$	−8.00000			−0.296704			−0.148352	−	0.988935i	$-0.547397\pi$
$727$	−8.00000			−0.296704			−0.148352	+	0.988935i	$0.547397\pi$
$728$		0			0
$729$	13.0000			0.481481
$730$		0			0
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$	8.00000	−	13.8564i	0.295689	−	0.512148i
$733$	−15.5000	−	26.8468i	−0.572506	−	0.991609i	−0.996308	−	0.0858539i	$-0.972638\pi$
$733$	−15.5000	−	26.8468i	−0.572506	−	0.991609i	0.423802	−	0.905755i	$-0.360695\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.00000	−	10.3923i	−0.221013	−	0.382805i
$738$		0			0
$739$	21.5000	−	37.2391i	0.790890	−	1.36986i	−0.134526	−	0.990910i	$-0.542951\pi$
$739$	21.5000	−	37.2391i	0.790890	−	1.36986i	0.925416	−	0.378952i	$-0.123715\pi$
$740$	2.00000	+	3.46410i	0.0735215	+	0.127343i
$741$	−10.0000			−0.367359
$742$		0			0
$743$	−12.0000			−0.440237			−0.220119	−	0.975473i	$-0.570644\pi$
$743$	−12.0000			−0.440237			−0.220119	+	0.975473i	$0.570644\pi$
$744$		0			0
$745$	3.00000	−	5.19615i	0.109911	−	0.190372i
$746$		0			0
$747$	−12.0000	−	20.7846i	−0.439057	−	0.760469i
$748$	−18.0000			−0.658145
$749$		0			0
$750$		0			0
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	0.576262	−	0.817265i	$-0.304511\pi$
$751$	−11.5000	−	19.9186i	−0.419641	−	0.726839i	−0.995903	+	0.0904254i	$0.971177\pi$
$752$	18.0000	−	31.1769i	0.656392	−	1.13691i
$753$	−9.00000	+	15.5885i	−0.327978	+	0.568075i
$754$		0			0
$755$	−1.00000			−0.0363937
$756$		0			0
$757$	−16.0000			−0.581530			−0.290765	−	0.956795i	$-0.593910\pi$
$757$	−16.0000			−0.581530			−0.290765	+	0.956795i	$0.593910\pi$
$758$		0			0
$759$	9.00000	−	15.5885i	0.326679	−	0.565825i
$760$		0			0
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	0.998684	+	0.0512772i	$0.0163292\pi$
$761$	15.0000	+	25.9808i	0.543750	+	0.941802i	−0.454935	+	0.890525i	$0.650337\pi$
$762$		0			0
$763$		0			0
$764$	−18.0000			−0.651217
$765$	−3.00000	−	5.19615i	−0.108465	−	0.187867i
$766$		0			0
$767$		0			0
$768$	8.00000	+	13.8564i	0.288675	+	0.500000i
$769$	−14.0000			−0.504853			−0.252426	−	0.967616i	$-0.581229\pi$
$769$	−14.0000			−0.504853			−0.252426	+	0.967616i	$0.581229\pi$
$770$		0			0
$771$	30.0000			1.08042
$772$	−4.00000	−	6.92820i	−0.143963	−	0.249351i
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	−0.613062	−	0.790034i	$-0.710063\pi$
$773$	10.5000	−	18.1865i	0.377659	−	0.654124i	0.990721	+	0.135910i	$0.0433959\pi$
$774$		0			0
$775$	−2.00000	−	3.46410i	−0.0718421	−	0.124434i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	12.0000	+	20.7846i	0.429945	+	0.744686i
$780$	5.00000	−	8.66025i	0.179029	−	0.310087i
$781$		0			0
$782$		0			0
$783$	15.0000			0.536056
$784$		0			0
$785$	−14.0000			−0.499681
$786$		0			0
$787$	2.50000	−	4.33013i	0.0891154	−	0.154352i	−0.818022	−	0.575187i	$-0.804929\pi$
$787$	2.50000	−	4.33013i	0.0891154	−	0.154352i	0.907137	+	0.420834i	$0.138263\pi$
$788$		0			0
$789$	3.00000	+	5.19615i	0.106803	+	0.184988i
$790$		0			0
$791$		0			0
$792$		0			0
$793$	−20.0000	−	34.6410i	−0.710221	−	1.23014i
$794$		0			0
$795$	6.00000	−	10.3923i	0.212798	−	0.368577i
$796$	16.0000	+	27.7128i	0.567105	+	0.982255i
$797$	−15.0000			−0.531327			−0.265664	−	0.964066i	$-0.585591\pi$
$797$	−15.0000			−0.531327			−0.265664	+	0.964066i	$0.585591\pi$
$798$		0			0
$799$	27.0000			0.955191
$800$		0			0
$801$	12.0000	−	20.7846i	0.423999	−	0.734388i
$802$		0			0
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$	−8.00000			−0.282138
$805$		0			0
$806$		0			0
$807$	3.00000	+	5.19615i	0.105605	+	0.182913i
$808$		0			0
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	−0.703533	−	0.710663i	$-0.748395\pi$
$809$	7.50000	−	12.9904i	0.263686	−	0.456717i	0.967219	+	0.253946i	$0.0817284\pi$
$810$		0			0
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$	−16.0000			−0.561144
$814$		0			0
$815$	−1.00000	+	1.73205i	−0.0350285	+	0.0606711i
$816$	−6.00000	+	10.3923i	−0.210042	+	0.363803i
$817$	−10.0000	−	17.3205i	−0.349856	−	0.605968i
$818$		0			0
$819$		0			0
$820$	−24.0000			−0.838116
$821$	13.5000	+	23.3827i	0.471153	+	0.816061i	0.999456	−	0.0329950i	$-0.0105045\pi$
$821$	13.5000	+	23.3827i	0.471153	+	0.816061i	−0.528302	+	0.849056i	$0.677171\pi$
$822$		0			0
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	−0.829060	−	0.559159i	$-0.811124\pi$
$823$	2.00000	−	3.46410i	0.0697156	−	0.120751i	0.898776	+	0.438408i	$0.144457\pi$
$824$		0			0
$825$	3.00000			0.104447
$826$		0			0
$827$	54.0000			1.87776			0.938882	−	0.344239i	$-0.111863\pi$
$827$	54.0000			1.87776			0.938882	+	0.344239i	$0.111863\pi$
$828$	12.0000	+	20.7846i	0.417029	+	0.722315i
$829$	−26.0000	+	45.0333i	−0.903017	+	1.56407i	−0.0794606	+	0.996838i	$0.525320\pi$
$829$	−26.0000	+	45.0333i	−0.903017	+	1.56407i	−0.823557	+	0.567234i	$0.808014\pi$
$830$		0			0
$831$	−5.00000	−	8.66025i	−0.173448	−	0.300421i
$832$	40.0000			1.38675
$833$		0			0
$834$		0			0
$835$	−1.50000	−	2.59808i	−0.0519096	−	0.0899101i
$836$	6.00000	−	10.3923i	0.207514	−	0.359425i
$837$	−10.0000	+	17.3205i	−0.345651	+	0.598684i
$838$		0			0
$839$	42.0000			1.45000			0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000			1.45000			0.725001	+	0.688748i	$0.241839\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$	1.50000	−	2.59808i	0.0516627	−	0.0894825i
$844$	−13.0000	+	22.5167i	−0.447478	+	0.775055i
$845$	−6.00000	−	10.3923i	−0.206406	−	0.357506i
$846$		0			0
$847$		0			0
$848$	48.0000			1.64833
$849$	6.50000	+	11.2583i	0.223079	+	0.386385i
$850$		0			0
$851$	6.00000	−	10.3923i	0.205677	−	0.356244i
$852$		0			0
$853$	10.0000			0.342393			0.171197	−	0.985237i	$-0.445237\pi$
$853$	10.0000			0.342393			0.171197	+	0.985237i	$0.445237\pi$
$854$		0			0
$855$	4.00000			0.136797
$856$		0			0
$857$	−15.0000	+	25.9808i	−0.512390	+	0.887486i	0.487507	+	0.873119i	$0.337907\pi$
$857$	−15.0000	+	25.9808i	−0.512390	+	0.887486i	−0.999897	+	0.0143666i	$0.995427\pi$
$858$		0			0
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	0.829887	−	0.557931i	$-0.188405\pi$
$859$	−2.00000	−	3.46410i	−0.0682391	−	0.118194i	−0.898126	+	0.439738i	$0.855071\pi$
$860$	20.0000			0.681994
$861$		0			0
$862$		0			0
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	0.586235	−	0.810141i	$-0.300609\pi$
$863$	−12.0000	−	20.7846i	−0.408485	−	0.707516i	−0.994720	+	0.102624i	$0.967276\pi$
$864$		0			0
$865$	−4.50000	+	7.79423i	−0.153005	+	0.265012i
$866$		0			0
$867$	8.00000			0.271694
$868$		0			0
$869$	3.00000			0.101768
$870$		0			0
$871$	−10.0000	+	17.3205i	−0.338837	+	0.586883i
$872$		0			0
$873$	1.00000	+	1.73205i	0.0338449	+	0.0586210i
$874$		0			0
$875$		0			0
$876$	−4.00000			−0.135147
$877$	−25.0000	−	43.3013i	−0.844190	−	1.46218i	−0.886323	−	0.463068i	$-0.846749\pi$
$877$	−25.0000	−	43.3013i	−0.844190	−	1.46218i	0.0421327	−	0.999112i	$-0.486585\pi$
$878$		0			0
$879$	10.5000	−	18.1865i	0.354156	−	0.613417i
$880$	6.00000	+	10.3923i	0.202260	+	0.350325i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$	20.0000			0.673054			0.336527	−	0.941674i	$-0.390748\pi$
$883$	20.0000			0.673054			0.336527	+	0.941674i	$0.390748\pi$
$884$	15.0000	+	25.9808i	0.504505	+	0.873828i
$885$		0			0
$886$		0			0
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	0.591156	−	0.806557i	$-0.298672\pi$
$887$	−12.0000	−	20.7846i	−0.402921	−	0.697879i	−0.994077	+	0.108678i	$0.965338\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	1.50000	+	2.59808i	0.0502519	+	0.0870388i
$892$	19.0000	−	32.9090i	0.636167	−	1.10187i
$893$	−9.00000	+	15.5885i	−0.301174	+	0.521648i
$894$		0			0
$895$	12.0000			0.401116
$896$		0			0
$897$	−30.0000			−1.00167
$898$		0			0
$899$	−6.00000	+	10.3923i	−0.200111	+	0.346603i
$900$	−2.00000	+	3.46410i	−0.0666667	+	0.115470i
$901$	18.0000	+	31.1769i	0.599667	+	1.03865i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.0000	+	17.3205i	0.332411	+	0.575753i
$906$		0			0
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	−0.997016	−	0.0771920i	$-0.975405\pi$
$907$	−13.0000	+	22.5167i	−0.431658	+	0.747653i	0.565358	+	0.824845i	$0.308738\pi$
$908$	3.00000	+	5.19615i	0.0995585	+	0.172440i
$909$	12.0000			0.398015
$910$		0			0
$911$	−24.0000			−0.795155			−0.397578	−	0.917568i	$-0.630149\pi$
$911$	−24.0000			−0.795155			−0.397578	+	0.917568i	$0.630149\pi$
$912$	−4.00000	−	6.92820i	−0.132453	−	0.229416i
$913$	−18.0000	+	31.1769i	−0.595713	+	1.03181i
$914$		0			0
$915$	−4.00000	−	6.92820i	−0.132236	−	0.229039i
$916$	−8.00000			−0.264327
$917$		0			0
$918$		0			0
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	0.760939	−	0.648824i	$-0.224739\pi$
$919$	−5.50000	−	9.52628i	−0.181428	−	0.314243i	−0.942367	+	0.334581i	$0.891405\pi$
$920$		0			0
$921$	−5.50000	+	9.52628i	−0.181231	+	0.313902i
$922$		0			0
$923$		0			0
$924$		0			0
$925$	2.00000			0.0657596
$926$		0			0
$927$	−5.00000	+	8.66025i	−0.164222	+	0.284440i
$928$		0			0
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	0.994157	+	0.107944i	$0.0344268\pi$
$929$	18.0000	+	31.1769i	0.590561	+	1.02288i	−0.403596	+	0.914937i	$0.632240\pi$
$930$		0			0
$931$		0			0
$932$	−48.0000			−1.57229
$933$	−9.00000	−	15.5885i	−0.294647	−	0.510343i
$934$		0			0
$935$	−4.50000	+	7.79423i	−0.147166	+	0.254899i
$936$		0			0
$937$	−47.0000			−1.53542			−0.767712	−	0.640796i	$-0.778605\pi$
$937$	−47.0000			−1.53542			−0.767712	+	0.640796i	$0.778605\pi$
$938$		0			0
$939$	−19.0000			−0.620042
$940$	−9.00000	−	15.5885i	−0.293548	−	0.508439i
$941$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$941$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$942$		0			0
$943$	36.0000	+	62.3538i	1.17232	+	2.03052i
$944$		0			0
$945$		0			0
$946$		0			0
$947$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$947$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$948$	1.00000	−	1.73205i	0.0324785	−	0.0562544i
$949$	−5.00000	+	8.66025i	−0.162307	+	0.281124i
$950$		0			0
$951$	18.0000			0.583690
$952$		0			0
$953$		0			0			−	1.00000i	$-0.5\pi$
$953$		0			0				1.00000i	$0.5\pi$
$954$		0			0
$955$	−4.50000	+	7.79423i	−0.145617	+	0.252215i
$956$	−21.0000	+	36.3731i	−0.679189	+	1.17639i
$957$	−4.50000	−	7.79423i	−0.145464	−	0.251952i
$958$		0			0
$959$		0			0
$960$	8.00000			0.258199
$961$	7.50000	+	12.9904i	0.241935	+	0.419045i
$962$		0			0
$963$	6.00000	−	10.3923i	0.193347	−	0.334887i
$964$	10.0000	+	17.3205i	0.322078	+	0.557856i
$965$	−4.00000			−0.128765
$966$		0			0
$967$	−22.0000			−0.707472			−0.353736	−	0.935345i	$-0.615089\pi$
$967$	−22.0000			−0.707472			−0.353736	+	0.935345i	$0.615089\pi$
$968$		0			0
$969$	3.00000	−	5.19615i	0.0963739	−	0.166924i
$970$		0			0
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	−0.937455	−	0.348107i	$-0.886825\pi$
$971$	−24.0000	−	41.5692i	−0.770197	−	1.33402i	0.167258	−	0.985913i	$-0.446509\pi$
$972$	32.0000			1.02640
$973$		0			0
$974$		0			0
$975$	−2.50000	−	4.33013i	−0.0800641	−	0.138675i
$976$	16.0000	−	27.7128i	0.512148	−	0.887066i
$977$	−27.0000	+	46.7654i	−0.863807	+	1.49616i	0.00442082	+	0.999990i	$0.498593\pi$
$977$	−27.0000	+	46.7654i	−0.863807	+	1.49616i	−0.868227	+	0.496167i	$0.834741\pi$
$978$		0			0
$979$	−36.0000			−1.15056
$980$		0			0
$981$	14.0000			0.446986
$982$		0			0
$983$	−10.5000	+	18.1865i	−0.334898	+	0.580060i	−0.983465	−	0.181097i	$-0.942035\pi$
$983$	−10.5000	+	18.1865i	−0.334898	+	0.580060i	0.648567	+	0.761157i	$0.275369\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		0			0
$988$	−20.0000			−0.636285
$989$	−30.0000	−	51.9615i	−0.953945	−	1.65228i
$990$		0			0
$991$	−28.0000	+	48.4974i	−0.889449	+	1.54057i	−0.0489218	+	0.998803i	$0.515578\pi$
$991$	−28.0000	+	48.4974i	−0.889449	+	1.54057i	−0.840528	+	0.541769i	$0.817755\pi$
$992$		0			0
$993$	28.0000			0.888553
$994$		0			0
$995$	16.0000			0.507234
$996$	12.0000	+	20.7846i	0.380235	+	0.658586i
$997$	−18.5000	+	32.0429i	−0.585901	+	1.01481i	0.408862	+	0.912596i	$0.365926\pi$
$997$	−18.5000	+	32.0429i	−0.585901	+	1.01481i	−0.994762	+	0.102214i	$0.967407\pi$
$998$		0			0
$999$	−5.00000	−	8.66025i	−0.158193	−	0.273998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.2.e.b.116.1		2
7.2	even	3	inner	245.2.e.b.226.1		2
7.3	odd	6		35.2.a.a.1.1	✓	1
7.4	even	3		245.2.a.c.1.1		1
7.5	odd	6		245.2.e.a.226.1		2
7.6	odd	2		245.2.e.a.116.1		2
21.11	odd	6		2205.2.a.e.1.1		1
21.17	even	6		315.2.a.b.1.1		1
28.3	even	6		560.2.a.b.1.1		1
28.11	odd	6		3920.2.a.ba.1.1		1
35.3	even	12		175.2.b.a.99.2		2
35.4	even	6		1225.2.a.e.1.1		1
35.17	even	12		175.2.b.a.99.1		2
35.18	odd	12		1225.2.b.d.99.1		2
35.24	odd	6		175.2.a.b.1.1		1
35.32	odd	12		1225.2.b.d.99.2		2
56.3	even	6		2240.2.a.u.1.1		1
56.45	odd	6		2240.2.a.k.1.1		1
77.10	even	6		4235.2.a.c.1.1		1
84.59	odd	6		5040.2.a.v.1.1		1
91.38	odd	6		5915.2.a.f.1.1		1
105.17	odd	12		1575.2.d.c.1324.2		2
105.38	odd	12		1575.2.d.c.1324.1		2
105.59	even	6		1575.2.a.f.1.1		1
140.3	odd	12		2800.2.g.l.449.1		2
140.59	even	6		2800.2.a.z.1.1		1
140.87	odd	12		2800.2.g.l.449.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.a.a.1.1	✓	1	7.3	odd	6
175.2.a.b.1.1		1	35.24	odd	6
175.2.b.a.99.1		2	35.17	even	12
175.2.b.a.99.2		2	35.3	even	12
245.2.a.c.1.1		1	7.4	even	3
245.2.e.a.116.1		2	7.6	odd	2
245.2.e.a.226.1		2	7.5	odd	6
245.2.e.b.116.1		2	1.1	even	1	trivial
245.2.e.b.226.1		2	7.2	even	3	inner
315.2.a.b.1.1		1	21.17	even	6
560.2.a.b.1.1		1	28.3	even	6
1225.2.a.e.1.1		1	35.4	even	6
1225.2.b.d.99.1		2	35.18	odd	12
1225.2.b.d.99.2		2	35.32	odd	12
1575.2.a.f.1.1		1	105.59	even	6
1575.2.d.c.1324.1		2	105.38	odd	12
1575.2.d.c.1324.2		2	105.17	odd	12
2205.2.a.e.1.1		1	21.11	odd	6
2240.2.a.k.1.1		1	56.45	odd	6
2240.2.a.u.1.1		1	56.3	even	6
2800.2.a.z.1.1		1	140.59	even	6
2800.2.g.l.449.1		2	140.3	odd	12
2800.2.g.l.449.2		2	140.87	odd	12
3920.2.a.ba.1.1		1	28.11	odd	6
4235.2.a.c.1.1		1	77.10	even	6
5040.2.a.v.1.1		1	84.59	odd	6
5915.2.a.f.1.1		1	91.38	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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{3} +(1.00000 - 1.73205i) q^{4} +(-0.500000 - 0.866025i) q^{5} +(1.00000 + 1.73205i) q^{9} +(1.50000 - 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{12} -5.00000 q^{13} -1.00000 q^{15} +(-2.00000 - 3.46410i) q^{16} +(1.50000 - 2.59808i) q^{17} +(1.00000 + 1.73205i) q^{19} -2.00000 q^{20} +(3.00000 + 5.19615i) q^{23} +(-0.500000 + 0.866025i) q^{25} +5.00000 q^{27} +3.00000 q^{29} +(-2.00000 + 3.46410i) q^{31} +(-1.50000 - 2.59808i) q^{33} +4.00000 q^{36} +(-1.00000 - 1.73205i) q^{37} +(-2.50000 + 4.33013i) q^{39} +12.0000 q^{41} -10.0000 q^{43} +(-3.00000 - 5.19615i) q^{44} +(1.00000 - 1.73205i) q^{45} +(4.50000 + 7.79423i) q^{47} -4.00000 q^{48} +(-1.50000 - 2.59808i) q^{51} +(-5.00000 + 8.66025i) q^{52} +(-6.00000 + 10.3923i) q^{53} -3.00000 q^{55} +2.00000 q^{57} +(-1.00000 + 1.73205i) q^{60} +(4.00000 + 6.92820i) q^{61} -8.00000 q^{64} +(2.50000 + 4.33013i) q^{65} +(2.00000 - 3.46410i) q^{67} +(-3.00000 - 5.19615i) q^{68} +6.00000 q^{69} +(1.00000 - 1.73205i) q^{73} +(0.500000 + 0.866025i) q^{75} +4.00000 q^{76} +(0.500000 + 0.866025i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-0.500000 + 0.866025i) q^{81} -12.0000 q^{83} -3.00000 q^{85} +(1.50000 - 2.59808i) q^{87} +(-6.00000 - 10.3923i) q^{89} +12.0000 q^{92} +(2.00000 + 3.46410i) q^{93} +(1.00000 - 1.73205i) q^{95} +1.00000 q^{97} +6.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{3} + 2 q^{4} - q^{5} + 2 q^{9}+O(q^{10}) \) 2 * q + q^3 + 2 * q^4 - q^5 + 2 * q^9	\( 2 q + q^{3} + 2 q^{4} - q^{5} + 2 q^{9} + 3 q^{11} - 2 q^{12} - 10 q^{13} - 2 q^{15} - 4 q^{16} + 3 q^{17} + 2 q^{19} - 4 q^{20} + 6 q^{23} - q^{25} + 10 q^{27} + 6 q^{29} - 4 q^{31} - 3 q^{33} + 8 q^{36} - 2 q^{37} - 5 q^{39} + 24 q^{41} - 20 q^{43} - 6 q^{44} + 2 q^{45} + 9 q^{47} - 8 q^{48} - 3 q^{51} - 10 q^{52} - 12 q^{53} - 6 q^{55} + 4 q^{57} - 2 q^{60} + 8 q^{61} - 16 q^{64} + 5 q^{65} + 4 q^{67} - 6 q^{68} + 12 q^{69} + 2 q^{73} + q^{75} + 8 q^{76} + q^{79} - 4 q^{80} - q^{81} - 24 q^{83} - 6 q^{85} + 3 q^{87} - 12 q^{89} + 24 q^{92} + 4 q^{93} + 2 q^{95} + 2 q^{97} + 12 q^{99}+O(q^{100}) \) 2 * q + q^3 + 2 * q^4 - q^5 + 2 * q^9 + 3 * q^11 - 2 * q^12 - 10 * q^13 - 2 * q^15 - 4 * q^16 + 3 * q^17 + 2 * q^19 - 4 * q^20 + 6 * q^23 - q^25 + 10 * q^27 + 6 * q^29 - 4 * q^31 - 3 * q^33 + 8 * q^36 - 2 * q^37 - 5 * q^39 + 24 * q^41 - 20 * q^43 - 6 * q^44 + 2 * q^45 + 9 * q^47 - 8 * q^48 - 3 * q^51 - 10 * q^52 - 12 * q^53 - 6 * q^55 + 4 * q^57 - 2 * q^60 + 8 * q^61 - 16 * q^64 + 5 * q^65 + 4 * q^67 - 6 * q^68 + 12 * q^69 + 2 * q^73 + q^75 + 8 * q^76 + q^79 - 4 * q^80 - q^81 - 24 * q^83 - 6 * q^85 + 3 * q^87 - 12 * q^89 + 24 * q^92 + 4 * q^93 + 2 * q^95 + 2 * q^97 + 12 * q^99

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