LMFDB - Embedded newform 490.2.e.c.471.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [490,2,Mod(361,490)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(490, 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("490.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 490 = 2 \cdot 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	490.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:	$3.91266969904$
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 70)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			471.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	490.471
Dual form			490.2.e.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +6.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(1.50000 + 2.59808i) q^{18} +1.00000 q^{20} +4.00000 q^{22} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} +6.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -2.00000 q^{34} -3.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} +4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.50000 + 2.59808i) q^{45} +(4.00000 - 6.92820i) q^{47} +1.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(1.00000 + 1.73205i) q^{53} +4.00000 q^{55} +(-3.00000 + 5.19615i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-7.00000 + 12.1244i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(6.00000 + 10.3923i) q^{67} +(1.00000 - 1.73205i) q^{68} -16.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(1.00000 + 1.73205i) q^{73} +(5.00000 + 8.66025i) q^{74} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.00000 - 1.73205i) q^{82} -8.00000 q^{83} -2.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{88} +(5.00000 - 8.66025i) q^{89} -3.00000 q^{90} +(4.00000 + 6.92820i) q^{94} -2.00000 q^{97} -12.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{4} - q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - q^2 - q^4 - q^5 + 2 * q^8 + 3 * q^9	$ 2 q - q^{2} - q^{4} - q^{5} + 2 q^{8} + 3 q^{9} - q^{10} - 4 q^{11} + 12 q^{13} - q^{16} + 2 q^{17} + 3 q^{18} + 2 q^{20} + 8 q^{22} - q^{25} - 6 q^{26} + 12 q^{29} + 8 q^{31} - q^{32} - 4 q^{34} - 6 q^{36} + 10 q^{37} - q^{40} - 4 q^{41} + 8 q^{43} - 4 q^{44} + 3 q^{45} + 8 q^{47} + 2 q^{50} - 6 q^{52} + 2 q^{53} + 8 q^{55} - 6 q^{58} - 8 q^{59} - 14 q^{61} - 16 q^{62} + 2 q^{64} - 6 q^{65} + 12 q^{67} + 2 q^{68} - 32 q^{71} + 3 q^{72} + 2 q^{73} + 10 q^{74} + 8 q^{79} - q^{80} - 9 q^{81} + 2 q^{82} - 16 q^{83} - 4 q^{85} - 4 q^{86} - 4 q^{88} + 10 q^{89} - 6 q^{90} + 8 q^{94} - 4 q^{97} - 24 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^4 - q^5 + 2 * q^8 + 3 * q^9 - q^10 - 4 * q^11 + 12 * q^13 - q^16 + 2 * q^17 + 3 * q^18 + 2 * q^20 + 8 * q^22 - q^25 - 6 * q^26 + 12 * q^29 + 8 * q^31 - q^32 - 4 * q^34 - 6 * q^36 + 10 * q^37 - q^40 - 4 * q^41 + 8 * q^43 - 4 * q^44 + 3 * q^45 + 8 * q^47 + 2 * q^50 - 6 * q^52 + 2 * q^53 + 8 * q^55 - 6 * q^58 - 8 * q^59 - 14 * q^61 - 16 * q^62 + 2 * q^64 - 6 * q^65 + 12 * q^67 + 2 * q^68 - 32 * q^71 + 3 * q^72 + 2 * q^73 + 10 * q^74 + 8 * q^79 - q^80 - 9 * q^81 + 2 * q^82 - 16 * q^83 - 4 * q^85 - 4 * q^86 - 4 * q^88 + 10 * q^89 - 6 * q^90 + 8 * q^94 - 4 * q^97 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/490\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−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
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	−0.500000	−	0.866025i	−0.158114	−	0.273861i
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	−0.992361	−	0.123371i	$-0.960630\pi$
$11$	−2.00000	−	3.46410i	−0.603023	−	1.04447i	0.389338	−	0.921095i	$-0.372704\pi$
$12$		0			0
$13$	6.00000			1.66410			0.832050	−	0.554700i	$-0.187167\pi$
$13$	6.00000			1.66410			0.832050	+	0.554700i	$0.187167\pi$
$14$		0			0
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	1.50000	+	2.59808i	0.353553	+	0.612372i
$19$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$19$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$20$	1.00000			0.223607
$21$		0			0
$22$	4.00000			0.852803
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$		0			0
$28$		0			0
$29$	6.00000			1.11417			0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000			1.11417			0.557086	+	0.830455i	$0.311919\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−2.00000			−0.342997
$35$		0			0
$36$	−3.00000			−0.500000
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	−0.0821995	−	0.996616i	$-0.526194\pi$
$37$	5.00000	−	8.66025i	0.821995	−	1.42374i	0.904194	−	0.427121i	$-0.140472\pi$
$38$		0			0
$39$		0			0
$40$	−0.500000	+	0.866025i	−0.0790569	+	0.136931i
$41$	−2.00000			−0.312348			−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000			−0.312348			−0.156174	+	0.987730i	$0.549916\pi$
$42$		0			0
$43$	4.00000			0.609994			0.304997	−	0.952353i	$-0.401344\pi$
$43$	4.00000			0.609994			0.304997	+	0.952353i	$0.401344\pi$
$44$	−2.00000	+	3.46410i	−0.301511	+	0.522233i
$45$	1.50000	+	2.59808i	0.223607	+	0.387298i
$46$		0			0
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	−0.411606	−	0.911362i	$-0.635032\pi$
$47$	4.00000	−	6.92820i	0.583460	−	1.01058i	0.995066	−	0.0992202i	$-0.0316348\pi$
$48$		0			0
$49$		0			0
$50$	1.00000			0.141421
$51$		0			0
$52$	−3.00000	−	5.19615i	−0.416025	−	0.720577i
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	0.926497	−	0.376303i	$-0.122805\pi$
$53$	1.00000	+	1.73205i	0.137361	+	0.237915i	−0.789136	+	0.614218i	$0.789471\pi$
$54$		0			0
$55$	4.00000			0.539360
$56$		0			0
$57$		0			0
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	−0.999709	−	0.0241347i	$-0.992317\pi$
$59$	−4.00000	−	6.92820i	−0.520756	−	0.901975i	0.478953	−	0.877841i	$-0.341016\pi$
$60$		0			0
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.0640184	+	0.997949i	$0.520392\pi$
$61$	−7.00000	+	12.1244i	−0.896258	+	1.55236i	−0.832240	+	0.554416i	$0.812942\pi$
$62$	−8.00000			−1.01600
$63$		0			0
$64$	1.00000			0.125000
$65$	−3.00000	+	5.19615i	−0.372104	+	0.644503i
$66$		0			0
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	0.955588	+	0.294706i	$0.0952216\pi$
$67$	6.00000	+	10.3923i	0.733017	+	1.26962i	−0.222571	+	0.974916i	$0.571445\pi$
$68$	1.00000	−	1.73205i	0.121268	−	0.210042i
$69$		0			0
$70$		0			0
$71$	−16.0000			−1.89885			−0.949425	−	0.313993i	$-0.898333\pi$
$71$	−16.0000			−1.89885			−0.949425	+	0.313993i	$0.898333\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	0.918594	−	0.395203i	$-0.129326\pi$
$73$	1.00000	+	1.73205i	0.117041	+	0.202721i	−0.801553	+	0.597924i	$0.795992\pi$
$74$	5.00000	+	8.66025i	0.581238	+	1.00673i
$75$		0			0
$76$		0			0
$77$		0			0
$78$		0			0
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	−0.548352	−	0.836247i	$-0.684745\pi$
$79$	4.00000	−	6.92820i	0.450035	−	0.779484i	0.998388	+	0.0567635i	$0.0180781\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	−8.00000			−0.878114			−0.439057	−	0.898459i	$-0.644687\pi$
$83$	−8.00000			−0.878114			−0.439057	+	0.898459i	$0.644687\pi$
$84$		0			0
$85$	−2.00000			−0.216930
$86$	−2.00000	+	3.46410i	−0.215666	+	0.373544i
$87$		0			0
$88$	−2.00000	−	3.46410i	−0.213201	−	0.369274i
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	−0.469389	−	0.882992i	$-0.655526\pi$
$89$	5.00000	−	8.66025i	0.529999	−	0.917985i	0.999388	−	0.0349934i	$-0.0111410\pi$
$90$	−3.00000			−0.316228
$91$		0			0
$92$		0			0
$93$		0			0
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$		0			0
$96$		0			0
$97$	−2.00000			−0.203069			−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000			−0.203069			−0.101535	+	0.994832i	$0.532375\pi$
$98$		0			0
$99$	−12.0000			−1.20605
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$		0			0
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	−0.138767	−	0.990325i	$-0.544314\pi$
$103$	8.00000	−	13.8564i	0.788263	−	1.36531i	0.927030	−	0.374987i	$-0.122353\pi$
$104$	6.00000			0.588348
$105$		0			0
$106$	−2.00000			−0.194257
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	0.415432	+	0.909624i	$0.363630\pi$
$107$	−6.00000	+	10.3923i	−0.580042	+	1.00466i	−0.995474	+	0.0950377i	$0.969703\pi$
$108$		0			0
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$	−2.00000	+	3.46410i	−0.190693	+	0.330289i
$111$		0			0
$112$		0			0
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$		0			0
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	9.00000	−	15.5885i	0.832050	−	1.44115i
$118$	8.00000			0.736460
$119$		0			0
$120$		0			0
$121$	−2.50000	+	4.33013i	−0.227273	+	0.393648i
$122$	−7.00000	−	12.1244i	−0.633750	−	1.09769i
$123$		0			0
$124$	4.00000	−	6.92820i	0.359211	−	0.622171i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−8.00000			−0.709885			−0.354943	−	0.934888i	$-0.615500\pi$
$127$	−8.00000			−0.709885			−0.354943	+	0.934888i	$0.615500\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−3.00000	−	5.19615i	−0.263117	−	0.455733i
$131$	−8.00000	+	13.8564i	−0.698963	+	1.21064i	0.269863	+	0.962899i	$0.413022\pi$
$131$	−8.00000	+	13.8564i	−0.698963	+	1.21064i	−0.968826	+	0.247741i	$0.920312\pi$
$132$		0			0
$133$		0			0
$134$	−12.0000			−1.03664
$135$		0			0
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	0.965250	−	0.261329i	$-0.0841608\pi$
$137$	3.00000	+	5.19615i	0.256307	+	0.443937i	−0.708942	+	0.705266i	$0.750827\pi$
$138$		0			0
$139$	−16.0000			−1.35710			−0.678551	−	0.734553i	$-0.737392\pi$
$139$	−16.0000			−1.35710			−0.678551	+	0.734553i	$0.737392\pi$
$140$		0			0
$141$		0			0
$142$	8.00000	−	13.8564i	0.671345	−	1.16280i
$143$	−12.0000	−	20.7846i	−1.00349	−	1.73810i
$144$	1.50000	+	2.59808i	0.125000	+	0.216506i
$145$	−3.00000	+	5.19615i	−0.249136	+	0.431517i
$146$	−2.00000			−0.165521
$147$		0			0
$148$	−10.0000			−0.821995
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$		0			0
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	0.656101	−	0.754673i	$-0.272204\pi$
$151$	−4.00000	−	6.92820i	−0.325515	−	0.563809i	−0.981617	+	0.190864i	$0.938871\pi$
$152$		0			0
$153$	6.00000			0.485071
$154$		0			0
$155$	−8.00000			−0.642575
$156$		0			0
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	0.993608	−	0.112884i	$-0.0360089\pi$
$157$	5.00000	+	8.66025i	0.399043	+	0.691164i	−0.594565	+	0.804048i	$0.702676\pi$
$158$	4.00000	+	6.92820i	0.318223	+	0.551178i
$159$		0			0
$160$	1.00000			0.0790569
$161$		0			0
$162$	9.00000			0.707107
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	−0.777007	−	0.629492i	$-0.783263\pi$
$163$	2.00000	−	3.46410i	0.156652	−	0.271329i	0.933659	+	0.358162i	$0.116597\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$		0			0
$166$	4.00000	−	6.92820i	0.310460	−	0.537733i
$167$		0			0			−	1.00000i	$-0.5\pi$
$167$		0			0				1.00000i	$0.5\pi$
$168$		0			0
$169$	23.0000			1.76923
$170$	1.00000	−	1.73205i	0.0766965	−	0.132842i
$171$		0			0
$172$	−2.00000	−	3.46410i	−0.152499	−	0.264135i
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	0.0566411	+	0.998395i	$0.481961\pi$
$173$	−11.0000	+	19.0526i	−0.836315	+	1.44854i	−0.892956	+	0.450145i	$0.851372\pi$
$174$		0			0
$175$		0			0
$176$	4.00000			0.301511
$177$		0			0
$178$	5.00000	+	8.66025i	0.374766	+	0.649113i
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	0.998286	−	0.0585225i	$-0.0186389\pi$
$179$	6.00000	+	10.3923i	0.448461	+	0.776757i	−0.549825	+	0.835280i	$0.685306\pi$
$180$	1.50000	−	2.59808i	0.111803	−	0.193649i
$181$	14.0000			1.04061			0.520306	−	0.853980i	$-0.325818\pi$
$181$	14.0000			1.04061			0.520306	+	0.853980i	$0.325818\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	5.00000	+	8.66025i	0.367607	+	0.636715i
$186$		0			0
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$	−8.00000			−0.583460
$189$		0			0
$190$		0			0
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$		0			0
$196$		0			0
$197$	14.0000			0.997459			0.498729	−	0.866758i	$-0.333800\pi$
$197$	14.0000			0.997459			0.498729	+	0.866758i	$0.333800\pi$
$198$	6.00000	−	10.3923i	0.426401	−	0.738549i
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	−0.996850	−	0.0793045i	$-0.974730\pi$
$199$	−8.00000	−	13.8564i	−0.567105	−	0.982255i	0.429745	−	0.902950i	$-0.358603\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	6.00000			0.422159
$203$		0			0
$204$		0			0
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	8.00000	+	13.8564i	0.557386	+	0.965422i
$207$		0			0
$208$	−3.00000	+	5.19615i	−0.208013	+	0.360288i
$209$		0			0
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	1.00000	−	1.73205i	0.0686803	−	0.118958i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	−2.00000	+	3.46410i	−0.136399	+	0.236250i
$216$		0			0
$217$		0			0
$218$	6.00000			0.406371
$219$		0			0
$220$	−2.00000	−	3.46410i	−0.134840	−	0.233550i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	−16.0000			−1.07144			−0.535720	−	0.844396i	$-0.679960\pi$
$223$	−16.0000			−1.07144			−0.535720	+	0.844396i	$0.679960\pi$
$224$		0			0
$225$	−3.00000			−0.200000
$226$	−1.00000	+	1.73205i	−0.0665190	+	0.115214i
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	0.967692	−	0.252136i	$-0.0811332\pi$
$227$	4.00000	+	6.92820i	0.265489	+	0.459841i	−0.702202	+	0.711977i	$0.747800\pi$
$228$		0			0
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	−0.999088	−	0.0426906i	$-0.986407\pi$
$229$	−7.00000	+	12.1244i	−0.462573	+	0.801200i	0.536515	+	0.843891i	$0.319740\pi$
$230$		0			0
$231$		0			0
$232$	6.00000			0.393919
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	9.00000	+	15.5885i	0.588348	+	1.01905i
$235$	4.00000	+	6.92820i	0.260931	+	0.451946i
$236$	−4.00000	+	6.92820i	−0.260378	+	0.450988i
$237$		0			0
$238$		0			0
$239$	16.0000			1.03495			0.517477	−	0.855697i	$-0.326871\pi$
$239$	16.0000			1.03495			0.517477	+	0.855697i	$0.326871\pi$
$240$		0			0
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	0.980917	−	0.194429i	$-0.0622852\pi$
$241$	5.00000	+	8.66025i	0.322078	+	0.557856i	−0.658838	+	0.752285i	$0.728952\pi$
$242$	−2.50000	−	4.33013i	−0.160706	−	0.278351i
$243$		0			0
$244$	14.0000			0.896258
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.00000	+	6.92820i	0.254000	+	0.439941i
$249$		0			0
$250$	−0.500000	+	0.866025i	−0.0316228	+	0.0547723i
$251$		0			0			−	1.00000i	$-0.5\pi$
$251$		0			0				1.00000i	$0.5\pi$
$252$		0			0
$253$		0			0
$254$	4.00000	−	6.92820i	0.250982	−	0.434714i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	0.286909	+	0.957958i	$0.407372\pi$
$257$	−11.0000	+	19.0526i	−0.686161	+	1.18847i	−0.973070	+	0.230508i	$0.925961\pi$
$258$		0			0
$259$		0			0
$260$	6.00000			0.372104
$261$	9.00000	−	15.5885i	0.557086	−	0.964901i
$262$	−8.00000	−	13.8564i	−0.494242	−	0.856052i
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	0.715944	−	0.698158i	$-0.245997\pi$
$263$	−4.00000	−	6.92820i	−0.246651	−	0.427211i	−0.962594	+	0.270947i	$0.912663\pi$
$264$		0			0
$265$	−2.00000			−0.122859
$266$		0			0
$267$		0			0
$268$	6.00000	−	10.3923i	0.366508	−	0.634811i
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	0.759958	−	0.649972i	$-0.225219\pi$
$269$	−3.00000	−	5.19615i	−0.182913	−	0.316815i	−0.942871	+	0.333157i	$0.891886\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−2.00000			−0.121268
$273$		0			0
$274$	−6.00000			−0.362473
$275$	−2.00000	+	3.46410i	−0.120605	+	0.208893i
$276$		0			0
$277$	9.00000	+	15.5885i	0.540758	+	0.936620i	0.998861	+	0.0477206i	$0.0151957\pi$
$277$	9.00000	+	15.5885i	0.540758	+	0.936620i	−0.458103	+	0.888899i	$0.651471\pi$
$278$	8.00000	−	13.8564i	0.479808	−	0.831052i
$279$	24.0000			1.43684
$280$		0			0
$281$	26.0000			1.55103			0.775515	−	0.631329i	$-0.217490\pi$
$281$	26.0000			1.55103			0.775515	+	0.631329i	$0.217490\pi$
$282$		0			0
$283$	16.0000	+	27.7128i	0.951101	+	1.64736i	0.743048	+	0.669238i	$0.233379\pi$
$283$	16.0000	+	27.7128i	0.951101	+	1.64736i	0.208053	+	0.978117i	$0.433287\pi$
$284$	8.00000	+	13.8564i	0.474713	+	0.822226i
$285$		0			0
$286$	24.0000			1.41915
$287$		0			0
$288$	−3.00000			−0.176777
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−3.00000	−	5.19615i	−0.176166	−	0.305129i
$291$		0			0
$292$	1.00000	−	1.73205i	0.0585206	−	0.101361i
$293$	−10.0000			−0.584206			−0.292103	−	0.956387i	$-0.594355\pi$
$293$	−10.0000			−0.584206			−0.292103	+	0.956387i	$0.594355\pi$
$294$		0			0
$295$	8.00000			0.465778
$296$	5.00000	−	8.66025i	0.290619	−	0.503367i
$297$		0			0
$298$	−3.00000	−	5.19615i	−0.173785	−	0.301005i
$299$		0			0
$300$		0			0
$301$		0			0
$302$	8.00000			0.460348
$303$		0			0
$304$		0			0
$305$	−7.00000	−	12.1244i	−0.400819	−	0.694239i
$306$	−3.00000	+	5.19615i	−0.171499	+	0.297044i
$307$	8.00000			0.456584			0.228292	−	0.973593i	$-0.426686\pi$
$307$	8.00000			0.456584			0.228292	+	0.973593i	$0.426686\pi$
$308$		0			0
$309$		0			0
$310$	4.00000	−	6.92820i	0.227185	−	0.393496i
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	−0.974841	−	0.222900i	$-0.928448\pi$
$311$	−12.0000	−	20.7846i	−0.680458	−	1.17859i	0.294384	−	0.955687i	$-0.404886\pi$
$312$		0			0
$313$	−11.0000	+	19.0526i	−0.621757	+	1.07691i	0.367402	+	0.930062i	$0.380247\pi$
$313$	−11.0000	+	19.0526i	−0.621757	+	1.07691i	−0.989158	+	0.146852i	$0.953086\pi$
$314$	−10.0000			−0.564333
$315$		0			0
$316$	−8.00000			−0.450035
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	0.372061	+	0.928208i	$0.378651\pi$
$317$	−11.0000	+	19.0526i	−0.617822	+	1.07010i	−0.989882	+	0.141890i	$0.954682\pi$
$318$		0			0
$319$	−12.0000	−	20.7846i	−0.671871	−	1.16371i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	−4.50000	+	7.79423i	−0.250000	+	0.433013i
$325$	−3.00000	−	5.19615i	−0.166410	−	0.288231i
$326$	2.00000	+	3.46410i	0.110770	+	0.191859i
$327$		0			0
$328$	−2.00000			−0.110432
$329$		0			0
$330$		0			0
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	−0.915742	−	0.401768i	$-0.868396\pi$
$331$	−2.00000	+	3.46410i	−0.109930	+	0.190404i	0.805812	+	0.592172i	$0.201729\pi$
$332$	4.00000	+	6.92820i	0.219529	+	0.380235i
$333$	−15.0000	−	25.9808i	−0.821995	−	1.42374i
$334$		0			0
$335$	−12.0000			−0.655630
$336$		0			0
$337$	−14.0000			−0.762629			−0.381314	−	0.924445i	$-0.624528\pi$
$337$	−14.0000			−0.762629			−0.381314	+	0.924445i	$0.624528\pi$
$338$	−11.5000	+	19.9186i	−0.625518	+	1.08343i
$339$		0			0
$340$	1.00000	+	1.73205i	0.0542326	+	0.0939336i
$341$	16.0000	−	27.7128i	0.866449	−	1.50073i
$342$		0			0
$343$		0			0
$344$	4.00000			0.215666
$345$		0			0
$346$	−11.0000	−	19.0526i	−0.591364	−	1.02427i
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	0.807337	−	0.590091i	$-0.200908\pi$
$347$	−2.00000	−	3.46410i	−0.107366	−	0.185963i	−0.914702	+	0.404128i	$0.867575\pi$
$348$		0			0
$349$	−10.0000			−0.535288			−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000			−0.535288			−0.267644	+	0.963518i	$0.586245\pi$
$350$		0			0
$351$		0			0
$352$	−2.00000	+	3.46410i	−0.106600	+	0.184637i
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	0.775077	−	0.631867i	$-0.217711\pi$
$353$	−3.00000	−	5.19615i	−0.159674	−	0.276563i	−0.934751	+	0.355303i	$0.884378\pi$
$354$		0			0
$355$	8.00000	−	13.8564i	0.424596	−	0.735422i
$356$	−10.0000			−0.529999
$357$		0			0
$358$	−12.0000			−0.634220
$359$	−4.00000	+	6.92820i	−0.211112	+	0.365657i	−0.952063	−	0.305903i	$-0.901042\pi$
$359$	−4.00000	+	6.92820i	−0.211112	+	0.365657i	0.740951	+	0.671559i	$0.234375\pi$
$360$	1.50000	+	2.59808i	0.0790569	+	0.136931i
$361$	9.50000	+	16.4545i	0.500000	+	0.866025i
$362$	−7.00000	+	12.1244i	−0.367912	+	0.637242i
$363$		0			0
$364$		0			0
$365$	−2.00000			−0.104685
$366$		0			0
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	0.995697	−	0.0926670i	$-0.0295392\pi$
$367$	8.00000	+	13.8564i	0.417597	+	0.723299i	−0.578101	+	0.815966i	$0.696206\pi$
$368$		0			0
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$	−10.0000			−0.519875
$371$		0			0
$372$		0			0
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$		0			0
$376$	4.00000	−	6.92820i	0.206284	−	0.357295i
$377$	36.0000			1.85409
$378$		0			0
$379$	−12.0000			−0.616399			−0.308199	−	0.951322i	$-0.599726\pi$
$379$	−12.0000			−0.616399			−0.308199	+	0.951322i	$0.599726\pi$
$380$		0			0
$381$		0			0
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	−0.377531	−	0.925997i	$-0.623227\pi$
$383$	12.0000	−	20.7846i	0.613171	−	1.06204i	0.990702	−	0.136047i	$-0.0434398\pi$
$384$		0			0
$385$		0			0
$386$	2.00000			0.101797
$387$	6.00000	−	10.3923i	0.304997	−	0.528271i
$388$	1.00000	+	1.73205i	0.0507673	+	0.0879316i
$389$	−7.00000	−	12.1244i	−0.354914	−	0.614729i	0.632189	−	0.774814i	$-0.282157\pi$
$389$	−7.00000	−	12.1244i	−0.354914	−	0.614729i	−0.987103	+	0.160085i	$0.948823\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$		0			0
$394$	−7.00000	+	12.1244i	−0.352655	+	0.610816i
$395$	4.00000	+	6.92820i	0.201262	+	0.348596i
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	−0.712843	−	0.701324i	$-0.752593\pi$
$397$	5.00000	−	8.66025i	0.250943	−	0.434646i	0.963786	+	0.266678i	$0.0859261\pi$
$398$	16.0000			0.802008
$399$		0			0
$400$	1.00000			0.0500000
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	−0.636609	−	0.771187i	$-0.719663\pi$
$401$	7.00000	−	12.1244i	0.349563	−	0.605461i	0.986172	+	0.165726i	$0.0529966\pi$
$402$		0			0
$403$	24.0000	+	41.5692i	1.19553	+	2.07071i
$404$	−3.00000	+	5.19615i	−0.149256	+	0.258518i
$405$	9.00000			0.447214
$406$		0			0
$407$	−40.0000			−1.98273
$408$		0			0
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	−0.951720	−	0.306968i	$-0.900685\pi$
$409$	−15.0000	−	25.9808i	−0.741702	−	1.28467i	0.210017	−	0.977698i	$-0.432648\pi$
$410$	1.00000	+	1.73205i	0.0493865	+	0.0855399i
$411$		0			0
$412$	−16.0000			−0.788263
$413$		0			0
$414$		0			0
$415$	4.00000	−	6.92820i	0.196352	−	0.340092i
$416$	−3.00000	−	5.19615i	−0.147087	−	0.254762i
$417$		0			0
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	−2.00000	+	3.46410i	−0.0973585	+	0.168630i
$423$	−12.0000	−	20.7846i	−0.583460	−	1.01058i
$424$	1.00000	+	1.73205i	0.0485643	+	0.0841158i
$425$	1.00000	−	1.73205i	0.0485071	−	0.0840168i
$426$		0			0
$427$		0			0
$428$	12.0000			0.580042
$429$		0			0
$430$	−2.00000	−	3.46410i	−0.0964486	−	0.167054i
$431$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$431$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$432$		0			0
$433$	−2.00000			−0.0961139			−0.0480569	−	0.998845i	$-0.515303\pi$
$433$	−2.00000			−0.0961139			−0.0480569	+	0.998845i	$0.515303\pi$
$434$		0			0
$435$		0			0
$436$	−3.00000	+	5.19615i	−0.143674	+	0.248851i
$437$		0			0
$438$		0			0
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	−0.945552	−	0.325471i	$-0.894477\pi$
$439$	−4.00000	+	6.92820i	−0.190910	+	0.330665i	0.754642	+	0.656136i	$0.227810\pi$
$440$	4.00000			0.190693
$441$		0			0
$442$	−12.0000			−0.570782
$443$	10.0000	−	17.3205i	0.475114	−	0.822922i	−0.524479	−	0.851423i	$-0.675740\pi$
$443$	10.0000	−	17.3205i	0.475114	−	0.822922i	0.999594	+	0.0285009i	$0.00907336\pi$
$444$		0			0
$445$	5.00000	+	8.66025i	0.237023	+	0.410535i
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$		0			0
$448$		0			0
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$	1.50000	−	2.59808i	0.0707107	−	0.122474i
$451$	4.00000	+	6.92820i	0.188353	+	0.326236i
$452$	−1.00000	−	1.73205i	−0.0470360	−	0.0814688i
$453$		0			0
$454$	−8.00000			−0.375459
$455$		0			0
$456$		0			0
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	−0.958950	−	0.283577i	$-0.908479\pi$
$457$	−5.00000	+	8.66025i	−0.233890	+	0.405110i	0.725059	+	0.688686i	$0.241812\pi$
$458$	−7.00000	−	12.1244i	−0.327089	−	0.566534i
$459$		0			0
$460$		0			0
$461$	−10.0000			−0.465746			−0.232873	−	0.972507i	$-0.574813\pi$
$461$	−10.0000			−0.465746			−0.232873	+	0.972507i	$0.574813\pi$
$462$		0			0
$463$	−16.0000			−0.743583			−0.371792	−	0.928316i	$-0.621256\pi$
$463$	−16.0000			−0.743583			−0.371792	+	0.928316i	$0.621256\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−20.0000	+	34.6410i	−0.925490	+	1.60300i	−0.134718	+	0.990884i	$0.543013\pi$
$467$	−20.0000	+	34.6410i	−0.925490	+	1.60300i	−0.790772	+	0.612111i	$0.790321\pi$
$468$	−18.0000			−0.832050
$469$		0			0
$470$	−8.00000			−0.369012
$471$		0			0
$472$	−4.00000	−	6.92820i	−0.184115	−	0.318896i
$473$	−8.00000	−	13.8564i	−0.367840	−	0.637118i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	6.00000			0.274721
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	0.998392	+	0.0566937i	$0.0180558\pi$
$479$	12.0000	+	20.7846i	0.548294	+	0.949673i	−0.450098	+	0.892979i	$0.648611\pi$
$480$		0			0
$481$	30.0000	−	51.9615i	1.36788	−	2.36924i
$482$	−10.0000			−0.455488
$483$		0			0
$484$	5.00000			0.227273
$485$	1.00000	−	1.73205i	0.0454077	−	0.0786484i
$486$		0			0
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	−0.958962	−	0.283535i	$-0.908493\pi$
$487$	−16.0000	−	27.7128i	−0.725029	−	1.25579i	0.233933	−	0.972253i	$-0.424840\pi$
$488$	−7.00000	+	12.1244i	−0.316875	+	0.548844i
$489$		0			0
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$		0			0
$493$	6.00000	+	10.3923i	0.270226	+	0.468046i
$494$		0			0
$495$	6.00000	−	10.3923i	0.269680	−	0.467099i
$496$	−8.00000			−0.359211
$497$		0			0
$498$		0			0
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	−0.699903	−	0.714238i	$-0.746773\pi$
$499$	6.00000	−	10.3923i	0.268597	−	0.465223i	0.968500	+	0.249015i	$0.0801067\pi$
$500$	−0.500000	−	0.866025i	−0.0223607	−	0.0387298i
$501$		0			0
$502$		0			0
$503$	24.0000			1.07011			0.535054	−	0.844818i	$-0.320291\pi$
$503$	24.0000			1.07011			0.535054	+	0.844818i	$0.320291\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$		0			0
$507$		0			0
$508$	4.00000	+	6.92820i	0.177471	+	0.307389i
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	−0.733679	−	0.679496i	$-0.762199\pi$
$509$	5.00000	−	8.66025i	0.221621	−	0.383859i	0.955300	+	0.295637i	$0.0955319\pi$
$510$		0			0
$511$		0			0
$512$	1.00000			0.0441942
$513$		0			0
$514$	−11.0000	−	19.0526i	−0.485189	−	0.840372i
$515$	8.00000	+	13.8564i	0.352522	+	0.610586i
$516$		0			0
$517$	−32.0000			−1.40736
$518$		0			0
$519$		0			0
$520$	−3.00000	+	5.19615i	−0.131559	+	0.227866i
$521$	1.00000	+	1.73205i	0.0438108	+	0.0758825i	0.887099	−	0.461579i	$-0.152717\pi$
$521$	1.00000	+	1.73205i	0.0438108	+	0.0758825i	−0.843288	+	0.537461i	$0.819383\pi$
$522$	9.00000	+	15.5885i	0.393919	+	0.682288i
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	−0.636401	−	0.771358i	$-0.719578\pi$
$523$	8.00000	−	13.8564i	0.349816	−	0.605898i	0.986216	+	0.165460i	$0.0529109\pi$
$524$	16.0000			0.698963
$525$		0			0
$526$	8.00000			0.348817
$527$	−8.00000	+	13.8564i	−0.348485	+	0.603595i
$528$		0			0
$529$	11.5000	+	19.9186i	0.500000	+	0.866025i
$530$	1.00000	−	1.73205i	0.0434372	−	0.0752355i
$531$	−24.0000			−1.04151
$532$		0			0
$533$	−12.0000			−0.519778
$534$		0			0
$535$	−6.00000	−	10.3923i	−0.259403	−	0.449299i
$536$	6.00000	+	10.3923i	0.259161	+	0.448879i
$537$		0			0
$538$	6.00000			0.258678
$539$		0			0
$540$		0			0
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	−0.605096	−	0.796152i	$-0.706865\pi$
$541$	9.00000	−	15.5885i	0.386940	−	0.670200i	0.992036	+	0.125952i	$0.0401986\pi$
$542$		0			0
$543$		0			0
$544$	1.00000	−	1.73205i	0.0428746	−	0.0742611i
$545$	6.00000			0.257012
$546$		0			0
$547$	12.0000			0.513083			0.256541	−	0.966533i	$-0.417417\pi$
$547$	12.0000			0.513083			0.256541	+	0.966533i	$0.417417\pi$
$548$	3.00000	−	5.19615i	0.128154	−	0.221969i
$549$	21.0000	+	36.3731i	0.896258	+	1.55236i
$550$	−2.00000	−	3.46410i	−0.0852803	−	0.147710i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	−18.0000			−0.764747
$555$		0			0
$556$	8.00000	+	13.8564i	0.339276	+	0.587643i
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	0.533165	−	0.846011i	$-0.321003\pi$
$557$	−11.0000	−	19.0526i	−0.466085	−	0.807283i	−0.999250	+	0.0387286i	$0.987669\pi$
$558$	−12.0000	+	20.7846i	−0.508001	+	0.879883i
$559$	24.0000			1.01509
$560$		0			0
$561$		0			0
$562$	−13.0000	+	22.5167i	−0.548372	+	0.949808i
$563$	−8.00000	−	13.8564i	−0.337160	−	0.583978i	0.646737	−	0.762713i	$-0.276133\pi$
$563$	−8.00000	−	13.8564i	−0.337160	−	0.583978i	−0.983897	+	0.178735i	$0.942800\pi$
$564$		0			0
$565$	−1.00000	+	1.73205i	−0.0420703	+	0.0728679i
$566$	−32.0000			−1.34506
$567$		0			0
$568$	−16.0000			−0.671345
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	6.00000	+	10.3923i	0.251092	+	0.434904i	0.963827	−	0.266529i	$-0.0858769\pi$
$571$	6.00000	+	10.3923i	0.251092	+	0.434904i	−0.712735	+	0.701434i	$0.752544\pi$
$572$	−12.0000	+	20.7846i	−0.501745	+	0.869048i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	5.00000	+	8.66025i	0.208153	+	0.360531i	0.951133	−	0.308783i	$-0.0999216\pi$
$577$	5.00000	+	8.66025i	0.208153	+	0.360531i	−0.742980	+	0.669314i	$0.766588\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$		0			0
$580$	6.00000			0.249136
$581$		0			0
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	1.00000	+	1.73205i	0.0413803	+	0.0716728i
$585$	9.00000	+	15.5885i	0.372104	+	0.644503i
$586$	5.00000	−	8.66025i	0.206548	−	0.357752i
$587$	−8.00000			−0.330195			−0.165098	−	0.986277i	$-0.552794\pi$
$587$	−8.00000			−0.330195			−0.165098	+	0.986277i	$0.552794\pi$
$588$		0			0
$589$		0			0
$590$	−4.00000	+	6.92820i	−0.164677	+	0.285230i
$591$		0			0
$592$	5.00000	+	8.66025i	0.205499	+	0.355934i
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	−0.921026	−	0.389501i	$-0.872647\pi$
$593$	−3.00000	+	5.19615i	−0.123195	+	0.213380i	0.797831	+	0.602881i	$0.205981\pi$
$594$		0			0
$595$		0			0
$596$	6.00000			0.245770
$597$		0			0
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−42.0000			−1.71322			−0.856608	−	0.515968i	$-0.827432\pi$
$601$	−42.0000			−1.71322			−0.856608	+	0.515968i	$0.827432\pi$
$602$		0			0
$603$	36.0000			1.46603
$604$	−4.00000	+	6.92820i	−0.162758	+	0.281905i
$605$	−2.50000	−	4.33013i	−0.101639	−	0.176045i
$606$		0			0
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	0.333842	+	0.942629i	$0.391655\pi$
$607$	−16.0000	+	27.7128i	−0.649420	+	1.12483i	−0.983262	+	0.182199i	$0.941678\pi$
$608$		0			0
$609$		0			0
$610$	14.0000			0.566843
$611$	24.0000	−	41.5692i	0.970936	−	1.68171i
$612$	−3.00000	−	5.19615i	−0.121268	−	0.210042i
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	0.799060	−	0.601251i	$-0.205331\pi$
$613$	−3.00000	−	5.19615i	−0.121169	−	0.209871i	−0.920229	+	0.391381i	$0.871998\pi$
$614$	−4.00000	+	6.92820i	−0.161427	+	0.279600i
$615$		0			0
$616$		0			0
$617$	−22.0000			−0.885687			−0.442843	−	0.896599i	$-0.646030\pi$
$617$	−22.0000			−0.885687			−0.442843	+	0.896599i	$0.646030\pi$
$618$		0			0
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	0.935146	−	0.354262i	$-0.115268\pi$
$619$	4.00000	+	6.92820i	0.160774	+	0.278468i	−0.774373	+	0.632730i	$0.781934\pi$
$620$	4.00000	+	6.92820i	0.160644	+	0.278243i
$621$		0			0
$622$	24.0000			0.962312
$623$		0			0
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−11.0000	−	19.0526i	−0.439648	−	0.761493i
$627$		0			0
$628$	5.00000	−	8.66025i	0.199522	−	0.345582i
$629$	20.0000			0.797452
$630$		0			0
$631$	−16.0000			−0.636950			−0.318475	−	0.947931i	$-0.603171\pi$
$631$	−16.0000			−0.636950			−0.318475	+	0.947931i	$0.603171\pi$
$632$	4.00000	−	6.92820i	0.159111	−	0.275589i
$633$		0			0
$634$	−11.0000	−	19.0526i	−0.436866	−	0.756674i
$635$	4.00000	−	6.92820i	0.158735	−	0.274937i
$636$		0			0
$637$		0			0
$638$	24.0000			0.950169
$639$	−24.0000	+	41.5692i	−0.949425	+	1.64445i
$640$	−0.500000	−	0.866025i	−0.0197642	−	0.0342327i
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	0.845601	−	0.533816i	$-0.179242\pi$
$641$	−1.00000	−	1.73205i	−0.0394976	−	0.0684119i	−0.885098	+	0.465404i	$0.845909\pi$
$642$		0			0
$643$	32.0000			1.26196			0.630978	−	0.775800i	$-0.282654\pi$
$643$	32.0000			1.26196			0.630978	+	0.775800i	$0.282654\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	8.00000	+	13.8564i	0.314512	+	0.544752i	0.979334	−	0.202251i	$-0.0648256\pi$
$647$	8.00000	+	13.8564i	0.314512	+	0.544752i	−0.664821	+	0.747002i	$0.731492\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−16.0000	+	27.7128i	−0.628055	+	1.08782i
$650$	6.00000			0.235339
$651$		0			0
$652$	−4.00000			−0.156652
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	−0.969865	−	0.243643i	$-0.921657\pi$
$653$	−7.00000	+	12.1244i	−0.273931	+	0.474463i	0.695934	+	0.718106i	$0.254991\pi$
$654$		0			0
$655$	−8.00000	−	13.8564i	−0.312586	−	0.541415i
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	6.00000			0.234082
$658$		0			0
$659$	28.0000			1.09073			0.545363	−	0.838200i	$-0.316392\pi$
$659$	28.0000			1.09073			0.545363	+	0.838200i	$0.316392\pi$
$660$		0			0
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	0.213925	−	0.976850i	$-0.431375\pi$
$662$	−2.00000	−	3.46410i	−0.0777322	−	0.134636i
$663$		0			0
$664$	−8.00000			−0.310460
$665$		0			0
$666$	30.0000			1.16248
$667$		0			0
$668$		0			0
$669$		0			0
$670$	6.00000	−	10.3923i	0.231800	−	0.401490i
$671$	56.0000			2.16186
$672$		0			0
$673$	−14.0000			−0.539660			−0.269830	−	0.962908i	$-0.586968\pi$
$673$	−14.0000			−0.539660			−0.269830	+	0.962908i	$0.586968\pi$
$674$	7.00000	−	12.1244i	0.269630	−	0.467013i
$675$		0			0
$676$	−11.5000	−	19.9186i	−0.442308	−	0.766099i
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	−0.639618	−	0.768693i	$-0.720908\pi$
$677$	9.00000	−	15.5885i	0.345898	−	0.599113i	0.985517	+	0.169580i	$0.0542410\pi$
$678$		0			0
$679$		0			0
$680$	−2.00000			−0.0766965
$681$		0			0
$682$	16.0000	+	27.7128i	0.612672	+	1.06118i
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	0.901750	−	0.432259i	$-0.142283\pi$
$683$	2.00000	+	3.46410i	0.0765279	+	0.132550i	−0.825222	+	0.564809i	$0.808950\pi$
$684$		0			0
$685$	−6.00000			−0.229248
$686$		0			0
$687$		0			0
$688$	−2.00000	+	3.46410i	−0.0762493	+	0.132068i
$689$	6.00000	+	10.3923i	0.228582	+	0.395915i
$690$		0			0
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	0.382791	+	0.923835i	$0.374963\pi$
$691$	−16.0000	+	27.7128i	−0.608669	+	1.05425i	−0.991460	+	0.130410i	$0.958371\pi$
$692$	22.0000			0.836315
$693$		0			0
$694$	4.00000			0.151838
$695$	8.00000	−	13.8564i	0.303457	−	0.525603i
$696$		0			0
$697$	−2.00000	−	3.46410i	−0.0757554	−	0.131212i
$698$	5.00000	−	8.66025i	0.189253	−	0.327795i
$699$		0			0
$700$		0			0
$701$	22.0000			0.830929			0.415464	−	0.909610i	$-0.363619\pi$
$701$	22.0000			0.830929			0.415464	+	0.909610i	$0.363619\pi$
$702$		0			0
$703$		0			0
$704$	−2.00000	−	3.46410i	−0.0753778	−	0.130558i
$705$		0			0
$706$	6.00000			0.225813
$707$		0			0
$708$		0			0
$709$	1.00000	−	1.73205i	0.0375558	−	0.0650485i	−0.846637	−	0.532172i	$-0.821376\pi$
$709$	1.00000	−	1.73205i	0.0375558	−	0.0650485i	0.884192	+	0.467123i	$0.154709\pi$
$710$	8.00000	+	13.8564i	0.300235	+	0.520022i
$711$	−12.0000	−	20.7846i	−0.450035	−	0.779484i
$712$	5.00000	−	8.66025i	0.187383	−	0.324557i
$713$		0			0
$714$		0			0
$715$	24.0000			0.897549
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$		0			0
$718$	−4.00000	−	6.92820i	−0.149279	−	0.258558i
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	−0.550700	−	0.834703i	$-0.685639\pi$
$719$	12.0000	−	20.7846i	0.447524	−	0.775135i	0.998224	+	0.0595683i	$0.0189724\pi$
$720$	−3.00000			−0.111803
$721$		0			0
$722$	−19.0000			−0.707107
$723$		0			0
$724$	−7.00000	−	12.1244i	−0.260153	−	0.450598i
$725$	−3.00000	−	5.19615i	−0.111417	−	0.192980i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$		0			0
$729$	−27.0000			−1.00000
$730$	1.00000	−	1.73205i	0.0370117	−	0.0641061i
$731$	4.00000	+	6.92820i	0.147945	+	0.256249i
$732$		0			0
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$	−16.0000			−0.590571
$735$		0			0
$736$		0			0
$737$	24.0000	−	41.5692i	0.884051	−	1.53122i
$738$	−3.00000	−	5.19615i	−0.110432	−	0.191273i
$739$	−14.0000	−	24.2487i	−0.514998	−	0.892003i	−0.999849	−	0.0174060i	$-0.994459\pi$
$739$	−14.0000	−	24.2487i	−0.514998	−	0.892003i	0.484850	−	0.874597i	$-0.338874\pi$
$740$	5.00000	−	8.66025i	0.183804	−	0.318357i
$741$		0			0
$742$		0			0
$743$	48.0000			1.76095			0.880475	−	0.474093i	$-0.157224\pi$
$743$	48.0000			1.76095			0.880475	+	0.474093i	$0.157224\pi$
$744$		0			0
$745$	−3.00000	−	5.19615i	−0.109911	−	0.190372i
$746$	−7.00000	−	12.1244i	−0.256288	−	0.443904i
$747$	−12.0000	+	20.7846i	−0.439057	+	0.760469i
$748$	−8.00000			−0.292509
$749$		0			0
$750$		0			0
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	−0.682341	−	0.731034i	$-0.739038\pi$
$751$	8.00000	−	13.8564i	0.291924	−	0.505627i	0.974265	+	0.225407i	$0.0723712\pi$
$752$	4.00000	+	6.92820i	0.145865	+	0.252646i
$753$		0			0
$754$	−18.0000	+	31.1769i	−0.655521	+	1.13540i
$755$	8.00000			0.291150
$756$		0			0
$757$	22.0000			0.799604			0.399802	−	0.916602i	$-0.369079\pi$
$757$	22.0000			0.799604			0.399802	+	0.916602i	$0.369079\pi$
$758$	6.00000	−	10.3923i	0.217930	−	0.377466i
$759$		0			0
$760$		0			0
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	−0.655515	−	0.755182i	$-0.727548\pi$
$761$	9.00000	−	15.5885i	0.326250	−	0.565081i	0.981764	+	0.190101i	$0.0608816\pi$
$762$		0			0
$763$		0			0
$764$	24.0000			0.868290
$765$	−3.00000	+	5.19615i	−0.108465	+	0.187867i
$766$	12.0000	+	20.7846i	0.433578	+	0.750978i
$767$	−24.0000	−	41.5692i	−0.866590	−	1.50098i
$768$		0			0
$769$	−10.0000			−0.360609			−0.180305	−	0.983611i	$-0.557708\pi$
$769$	−10.0000			−0.360609			−0.180305	+	0.983611i	$0.557708\pi$
$770$		0			0
$771$		0			0
$772$	−1.00000	+	1.73205i	−0.0359908	+	0.0623379i
$773$	21.0000	+	36.3731i	0.755318	+	1.30825i	0.945216	+	0.326445i	$0.105851\pi$
$773$	21.0000	+	36.3731i	0.755318	+	1.30825i	−0.189899	+	0.981804i	$0.560816\pi$
$774$	6.00000	+	10.3923i	0.215666	+	0.373544i
$775$	4.00000	−	6.92820i	0.143684	−	0.248868i
$776$	−2.00000			−0.0717958
$777$		0			0
$778$	14.0000			0.501924
$779$		0			0
$780$		0			0
$781$	32.0000	+	55.4256i	1.14505	+	1.98328i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−10.0000			−0.356915
$786$		0			0
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	0.785885	−	0.618373i	$-0.212208\pi$
$787$	−4.00000	−	6.92820i	−0.142585	−	0.246964i	−0.928469	+	0.371409i	$0.878875\pi$
$788$	−7.00000	−	12.1244i	−0.249365	−	0.431912i
$789$		0			0
$790$	−8.00000			−0.284627
$791$		0			0
$792$	−12.0000			−0.426401
$793$	−42.0000	+	72.7461i	−1.49146	+	2.58329i
$794$	5.00000	+	8.66025i	0.177443	+	0.307341i
$795$		0			0
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$	6.00000			0.212531			0.106265	−	0.994338i	$-0.466111\pi$
$797$	6.00000			0.212531			0.106265	+	0.994338i	$0.466111\pi$
$798$		0			0
$799$	16.0000			0.566039
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−15.0000	−	25.9808i	−0.529999	−	0.917985i
$802$	7.00000	+	12.1244i	0.247179	+	0.428126i
$803$	4.00000	−	6.92820i	0.141157	−	0.244491i
$804$		0			0
$805$		0			0
$806$	−48.0000			−1.69073
$807$		0			0
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	0.913932	−	0.405868i	$-0.133031\pi$
$809$	3.00000	+	5.19615i	0.105474	+	0.182687i	−0.808458	+	0.588555i	$0.799697\pi$
$810$	−4.50000	+	7.79423i	−0.158114	+	0.273861i
$811$	−8.00000			−0.280918			−0.140459	−	0.990086i	$-0.544858\pi$
$811$	−8.00000			−0.280918			−0.140459	+	0.990086i	$0.544858\pi$
$812$		0			0
$813$		0			0
$814$	20.0000	−	34.6410i	0.701000	−	1.21417i
$815$	2.00000	+	3.46410i	0.0700569	+	0.121342i
$816$		0			0
$817$		0			0
$818$	30.0000			1.04893
$819$		0			0
$820$	−2.00000			−0.0698430
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	−0.913616	−	0.406578i	$-0.866722\pi$
$821$	−3.00000	+	5.19615i	−0.104701	+	0.181347i	0.808915	+	0.587925i	$0.200055\pi$
$822$		0			0
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	0.927281	−	0.374365i	$-0.122139\pi$
$823$	4.00000	+	6.92820i	0.139431	+	0.241502i	−0.787850	+	0.615867i	$0.788806\pi$
$824$	8.00000	−	13.8564i	0.278693	−	0.482711i
$825$		0			0
$826$		0			0
$827$	44.0000			1.53003			0.765015	−	0.644013i	$-0.222732\pi$
$827$	44.0000			1.53003			0.765015	+	0.644013i	$0.222732\pi$
$828$		0			0
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	−0.920383	−	0.391018i	$-0.872123\pi$
$829$	−23.0000	−	39.8372i	−0.798823	−	1.38360i	0.121560	−	0.992584i	$-0.461210\pi$
$830$	4.00000	+	6.92820i	0.138842	+	0.240481i
$831$		0			0
$832$	6.00000			0.208013
$833$		0			0
$834$		0			0
$835$		0			0
$836$		0			0
$837$		0			0
$838$	12.0000	−	20.7846i	0.414533	−	0.717992i
$839$	16.0000			0.552381			0.276191	−	0.961103i	$-0.410928\pi$
$839$	16.0000			0.552381			0.276191	+	0.961103i	$0.410928\pi$
$840$		0			0
$841$	7.00000			0.241379
$842$	5.00000	−	8.66025i	0.172311	−	0.298452i
$843$		0			0
$844$	−2.00000	−	3.46410i	−0.0688428	−	0.119239i
$845$	−11.5000	+	19.9186i	−0.395612	+	0.685220i
$846$	24.0000			0.825137
$847$		0			0
$848$	−2.00000			−0.0686803
$849$		0			0
$850$	1.00000	+	1.73205i	0.0342997	+	0.0594089i
$851$		0			0
$852$		0			0
$853$	46.0000			1.57501			0.787505	−	0.616308i	$-0.211372\pi$
$853$	46.0000			1.57501			0.787505	+	0.616308i	$0.211372\pi$
$854$		0			0
$855$		0			0
$856$	−6.00000	+	10.3923i	−0.205076	+	0.355202i
$857$	−27.0000	−	46.7654i	−0.922302	−	1.59747i	−0.795843	−	0.605503i	$-0.792972\pi$
$857$	−27.0000	−	46.7654i	−0.922302	−	1.59747i	−0.126459	−	0.991972i	$-0.540361\pi$
$858$		0			0
$859$	−24.0000	+	41.5692i	−0.818869	+	1.41832i	0.0876464	+	0.996152i	$0.472065\pi$
$859$	−24.0000	+	41.5692i	−0.818869	+	1.41832i	−0.906516	+	0.422172i	$0.861268\pi$
$860$	4.00000			0.136399
$861$		0			0
$862$		0			0
$863$	16.0000	−	27.7128i	0.544646	−	0.943355i	−0.453983	−	0.891010i	$-0.649997\pi$
$863$	16.0000	−	27.7128i	0.544646	−	0.943355i	0.998629	−	0.0523446i	$-0.0166694\pi$
$864$		0			0
$865$	−11.0000	−	19.0526i	−0.374011	−	0.647806i
$866$	1.00000	−	1.73205i	0.0339814	−	0.0588575i
$867$		0			0
$868$		0			0
$869$	−32.0000			−1.08553
$870$		0			0
$871$	36.0000	+	62.3538i	1.21981	+	2.11278i
$872$	−3.00000	−	5.19615i	−0.101593	−	0.175964i
$873$	−3.00000	+	5.19615i	−0.101535	+	0.175863i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	−0.959671	−	0.281126i	$-0.909292\pi$
$877$	−7.00000	+	12.1244i	−0.236373	+	0.409410i	0.723298	+	0.690536i	$0.242625\pi$
$878$	−4.00000	−	6.92820i	−0.134993	−	0.233816i
$879$		0			0
$880$	−2.00000	+	3.46410i	−0.0674200	+	0.116775i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	−12.0000			−0.403832			−0.201916	−	0.979403i	$-0.564717\pi$
$883$	−12.0000			−0.403832			−0.201916	+	0.979403i	$0.564717\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$		0			0
$886$	10.0000	+	17.3205i	0.335957	+	0.581894i
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	−0.968504	−	0.248998i	$-0.919899\pi$
$887$	−8.00000	+	13.8564i	−0.268614	+	0.465253i	0.699890	+	0.714250i	$0.253232\pi$
$888$		0			0
$889$		0			0
$890$	−10.0000			−0.335201
$891$	−18.0000	+	31.1769i	−0.603023	+	1.04447i
$892$	8.00000	+	13.8564i	0.267860	+	0.463947i
$893$		0			0
$894$		0			0
$895$	−12.0000			−0.401116
$896$		0			0
$897$		0			0
$898$	15.0000	−	25.9808i	0.500556	−	0.866989i
$899$	24.0000	+	41.5692i	0.800445	+	1.38641i
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$	−2.00000	+	3.46410i	−0.0666297	+	0.115406i
$902$	−8.00000			−0.266371
$903$		0			0
$904$	2.00000			0.0665190
$905$	−7.00000	+	12.1244i	−0.232688	+	0.403027i
$906$		0			0
$907$	26.0000	+	45.0333i	0.863316	+	1.49531i	0.868710	+	0.495321i	$0.164950\pi$
$907$	26.0000	+	45.0333i	0.863316	+	1.49531i	−0.00539395	+	0.999985i	$0.501717\pi$
$908$	4.00000	−	6.92820i	0.132745	−	0.229920i
$909$	−18.0000			−0.597022
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	16.0000	+	27.7128i	0.529523	+	0.917160i
$914$	−5.00000	−	8.66025i	−0.165385	−	0.286456i
$915$		0			0
$916$	14.0000			0.462573
$917$		0			0
$918$		0			0
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	−0.703378	−	0.710816i	$-0.748326\pi$
$919$	8.00000	−	13.8564i	0.263896	−	0.457081i	0.967274	+	0.253735i	$0.0816592\pi$
$920$		0			0
$921$		0			0
$922$	5.00000	−	8.66025i	0.164666	−	0.285210i
$923$	−96.0000			−3.15988
$924$		0			0
$925$	−10.0000			−0.328798
$926$	8.00000	−	13.8564i	0.262896	−	0.455350i
$927$	−24.0000	−	41.5692i	−0.788263	−	1.36531i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	29.0000	−	50.2295i	0.951459	−	1.64798i	0.209189	−	0.977875i	$-0.432918\pi$
$929$	29.0000	−	50.2295i	0.951459	−	1.64798i	0.742271	−	0.670100i	$-0.233749\pi$
$930$		0			0
$931$		0			0
$932$	−6.00000			−0.196537
$933$		0			0
$934$	−20.0000	−	34.6410i	−0.654420	−	1.13349i
$935$	4.00000	+	6.92820i	0.130814	+	0.226576i
$936$	9.00000	−	15.5885i	0.294174	−	0.509525i
$937$	−50.0000			−1.63343			−0.816714	−	0.577042i	$-0.804207\pi$
$937$	−50.0000			−1.63343			−0.816714	+	0.577042i	$0.804207\pi$
$938$		0			0
$939$		0			0
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	1.00000	+	1.73205i	0.0325991	+	0.0564632i	0.881865	−	0.471503i	$-0.156288\pi$
$941$	1.00000	+	1.73205i	0.0325991	+	0.0564632i	−0.849266	+	0.527966i	$0.822955\pi$
$942$		0			0
$943$		0			0
$944$	8.00000			0.260378
$945$		0			0
$946$	16.0000			0.520205
$947$	−22.0000	+	38.1051i	−0.714904	+	1.23825i	0.248093	+	0.968736i	$0.420196\pi$
$947$	−22.0000	+	38.1051i	−0.714904	+	1.23825i	−0.962997	+	0.269514i	$0.913137\pi$
$948$		0			0
$949$	6.00000	+	10.3923i	0.194768	+	0.337348i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−54.0000			−1.74923			−0.874616	−	0.484817i	$-0.838886\pi$
$953$	−54.0000			−1.74923			−0.874616	+	0.484817i	$0.838886\pi$
$954$	−3.00000	+	5.19615i	−0.0971286	+	0.168232i
$955$	−12.0000	−	20.7846i	−0.388311	−	0.672574i
$956$	−8.00000	−	13.8564i	−0.258738	−	0.448148i
$957$		0			0
$958$	−24.0000			−0.775405
$959$		0			0
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$	30.0000	+	51.9615i	0.967239	+	1.67531i
$963$	18.0000	+	31.1769i	0.580042	+	1.00466i
$964$	5.00000	−	8.66025i	0.161039	−	0.278928i
$965$	2.00000			0.0643823
$966$		0			0
$967$	16.0000			0.514525			0.257263	−	0.966342i	$-0.417179\pi$
$967$	16.0000			0.514525			0.257263	+	0.966342i	$0.417179\pi$
$968$	−2.50000	+	4.33013i	−0.0803530	+	0.139176i
$969$		0			0
$970$	1.00000	+	1.73205i	0.0321081	+	0.0556128i
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	−0.991783	−	0.127933i	$-0.959166\pi$
$971$	−12.0000	+	20.7846i	−0.385098	+	0.667010i	0.606685	+	0.794943i	$0.292499\pi$
$972$		0			0
$973$		0			0
$974$	32.0000			1.02535
$975$		0			0
$976$	−7.00000	−	12.1244i	−0.224065	−	0.388091i
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	0.999734	−	0.0230645i	$-0.00734232\pi$
$977$	15.0000	+	25.9808i	0.479893	+	0.831198i	−0.519841	+	0.854263i	$0.674009\pi$
$978$		0			0
$979$	−40.0000			−1.27841
$980$		0			0
$981$	−18.0000			−0.574696
$982$	−6.00000	+	10.3923i	−0.191468	+	0.331632i
$983$	−8.00000	−	13.8564i	−0.255160	−	0.441951i	0.709779	−	0.704425i	$-0.248795\pi$
$983$	−8.00000	−	13.8564i	−0.255160	−	0.441951i	−0.964939	+	0.262474i	$0.915462\pi$
$984$		0			0
$985$	−7.00000	+	12.1244i	−0.223039	+	0.386314i
$986$	−12.0000			−0.382158
$987$		0			0
$988$		0			0
$989$		0			0
$990$	6.00000	+	10.3923i	0.190693	+	0.330289i
$991$	−20.0000	−	34.6410i	−0.635321	−	1.10041i	−0.986447	−	0.164080i	$-0.947534\pi$
$991$	−20.0000	−	34.6410i	−0.635321	−	1.10041i	0.351126	−	0.936328i	$-0.385799\pi$
$992$	4.00000	−	6.92820i	0.127000	−	0.219971i
$993$		0			0
$994$		0			0
$995$	16.0000			0.507234
$996$		0			0
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	0.637587	−	0.770378i	$-0.279933\pi$
$997$	−11.0000	−	19.0526i	−0.348373	−	0.603401i	−0.985961	+	0.166978i	$0.946599\pi$
$998$	6.00000	+	10.3923i	0.189927	+	0.328963i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	490.2.e.c.471.1		2
7.2	even	3		490.2.a.h.1.1		1
7.3	odd	6		490.2.e.d.361.1		2
7.4	even	3	inner	490.2.e.c.361.1		2
7.5	odd	6		70.2.a.a.1.1	✓	1
7.6	odd	2		490.2.e.d.471.1		2
21.2	odd	6		4410.2.a.b.1.1		1
21.5	even	6		630.2.a.d.1.1		1
28.19	even	6		560.2.a.d.1.1		1
28.23	odd	6		3920.2.a.t.1.1		1
35.2	odd	12		2450.2.c.k.99.2		2
35.9	even	6		2450.2.a.l.1.1		1
35.12	even	12		350.2.c.b.99.2		2
35.19	odd	6		350.2.a.b.1.1		1
35.23	odd	12		2450.2.c.k.99.1		2
35.33	even	12		350.2.c.b.99.1		2
56.5	odd	6		2240.2.a.n.1.1		1
56.19	even	6		2240.2.a.q.1.1		1
77.54	even	6		8470.2.a.j.1.1		1
84.47	odd	6		5040.2.a.bm.1.1		1
105.47	odd	12		3150.2.g.c.2899.1		2
105.68	odd	12		3150.2.g.c.2899.2		2
105.89	even	6		3150.2.a.bj.1.1		1
140.19	even	6		2800.2.a.m.1.1		1
140.47	odd	12		2800.2.g.n.449.2		2
140.103	odd	12		2800.2.g.n.449.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
70.2.a.a.1.1	✓	1	7.5	odd	6
350.2.a.b.1.1		1	35.19	odd	6
350.2.c.b.99.1		2	35.33	even	12
350.2.c.b.99.2		2	35.12	even	12
490.2.a.h.1.1		1	7.2	even	3
490.2.e.c.361.1		2	7.4	even	3	inner
490.2.e.c.471.1		2	1.1	even	1	trivial
490.2.e.d.361.1		2	7.3	odd	6
490.2.e.d.471.1		2	7.6	odd	2
560.2.a.d.1.1		1	28.19	even	6
630.2.a.d.1.1		1	21.5	even	6
2240.2.a.n.1.1		1	56.5	odd	6
2240.2.a.q.1.1		1	56.19	even	6
2450.2.a.l.1.1		1	35.9	even	6
2450.2.c.k.99.1		2	35.23	odd	12
2450.2.c.k.99.2		2	35.2	odd	12
2800.2.a.m.1.1		1	140.19	even	6
2800.2.g.n.449.1		2	140.103	odd	12
2800.2.g.n.449.2		2	140.47	odd	12
3150.2.a.bj.1.1		1	105.89	even	6
3150.2.g.c.2899.1		2	105.47	odd	12
3150.2.g.c.2899.2		2	105.68	odd	12
3920.2.a.t.1.1		1	28.23	odd	6
4410.2.a.b.1.1		1	21.2	odd	6
5040.2.a.bm.1.1		1	84.47	odd	6
8470.2.a.j.1.1		1	77.54	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	490.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-0.500000 - 0.866025i) q^{10} +(-2.00000 - 3.46410i) q^{11} +6.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(1.50000 + 2.59808i) q^{18} +1.00000 q^{20} +4.00000 q^{22} +(-0.500000 - 0.866025i) q^{25} +(-3.00000 + 5.19615i) q^{26} +6.00000 q^{29} +(4.00000 + 6.92820i) q^{31} +(-0.500000 - 0.866025i) q^{32} -2.00000 q^{34} -3.00000 q^{36} +(5.00000 - 8.66025i) q^{37} +(-0.500000 + 0.866025i) q^{40} -2.00000 q^{41} +4.00000 q^{43} +(-2.00000 + 3.46410i) q^{44} +(1.50000 + 2.59808i) q^{45} +(4.00000 - 6.92820i) q^{47} +1.00000 q^{50} +(-3.00000 - 5.19615i) q^{52} +(1.00000 + 1.73205i) q^{53} +4.00000 q^{55} +(-3.00000 + 5.19615i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(-7.00000 + 12.1244i) q^{61} -8.00000 q^{62} +1.00000 q^{64} +(-3.00000 + 5.19615i) q^{65} +(6.00000 + 10.3923i) q^{67} +(1.00000 - 1.73205i) q^{68} -16.0000 q^{71} +(1.50000 - 2.59808i) q^{72} +(1.00000 + 1.73205i) q^{73} +(5.00000 + 8.66025i) q^{74} +(4.00000 - 6.92820i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(1.00000 - 1.73205i) q^{82} -8.00000 q^{83} -2.00000 q^{85} +(-2.00000 + 3.46410i) q^{86} +(-2.00000 - 3.46410i) q^{88} +(5.00000 - 8.66025i) q^{89} -3.00000 q^{90} +(4.00000 + 6.92820i) q^{94} -2.00000 q^{97} -12.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{4} - q^{5} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - q^2 - q^4 - q^5 + 2 * q^8 + 3 * q^9	\( 2 q - q^{2} - q^{4} - q^{5} + 2 q^{8} + 3 q^{9} - q^{10} - 4 q^{11} + 12 q^{13} - q^{16} + 2 q^{17} + 3 q^{18} + 2 q^{20} + 8 q^{22} - q^{25} - 6 q^{26} + 12 q^{29} + 8 q^{31} - q^{32} - 4 q^{34} - 6 q^{36} + 10 q^{37} - q^{40} - 4 q^{41} + 8 q^{43} - 4 q^{44} + 3 q^{45} + 8 q^{47} + 2 q^{50} - 6 q^{52} + 2 q^{53} + 8 q^{55} - 6 q^{58} - 8 q^{59} - 14 q^{61} - 16 q^{62} + 2 q^{64} - 6 q^{65} + 12 q^{67} + 2 q^{68} - 32 q^{71} + 3 q^{72} + 2 q^{73} + 10 q^{74} + 8 q^{79} - q^{80} - 9 q^{81} + 2 q^{82} - 16 q^{83} - 4 q^{85} - 4 q^{86} - 4 q^{88} + 10 q^{89} - 6 q^{90} + 8 q^{94} - 4 q^{97} - 24 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^4 - q^5 + 2 * q^8 + 3 * q^9 - q^10 - 4 * q^11 + 12 * q^13 - q^16 + 2 * q^17 + 3 * q^18 + 2 * q^20 + 8 * q^22 - q^25 - 6 * q^26 + 12 * q^29 + 8 * q^31 - q^32 - 4 * q^34 - 6 * q^36 + 10 * q^37 - q^40 - 4 * q^41 + 8 * q^43 - 4 * q^44 + 3 * q^45 + 8 * q^47 + 2 * q^50 - 6 * q^52 + 2 * q^53 + 8 * q^55 - 6 * q^58 - 8 * q^59 - 14 * q^61 - 16 * q^62 + 2 * q^64 - 6 * q^65 + 12 * q^67 + 2 * q^68 - 32 * q^71 + 3 * q^72 + 2 * q^73 + 10 * q^74 + 8 * q^79 - q^80 - 9 * q^81 + 2 * q^82 - 16 * q^83 - 4 * q^85 - 4 * q^86 - 4 * q^88 + 10 * q^89 - 6 * q^90 + 8 * q^94 - 4 * q^97 - 24 * q^99

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