LMFDB - Embedded newform 430.2.e.c.251.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(221,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, 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("430.221");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.43356728692$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			251.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	430.251
Dual form			430.2.e.c.221.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +5.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{14} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.500000 + 0.866025i) q^{20} +5.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-2.00000 + 3.46410i) q^{28} +(4.00000 - 6.92820i) q^{29} +1.00000 q^{32} +(-1.50000 + 2.59808i) q^{34} -4.00000 q^{35} +(1.50000 - 2.59808i) q^{36} +(-5.00000 - 8.66025i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(0.500000 + 0.866025i) q^{40} -7.00000 q^{41} +(-2.50000 - 6.06218i) q^{43} +5.00000 q^{44} +3.00000 q^{45} +(2.00000 + 3.46410i) q^{46} +6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(2.50000 + 4.33013i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(4.00000 - 6.92820i) q^{58} -3.00000 q^{59} +(-7.00000 + 12.1244i) q^{61} +(6.00000 + 10.3923i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(1.50000 + 2.59808i) q^{67} +(-1.50000 + 2.59808i) q^{68} -4.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.50000 - 2.59808i) q^{72} +(5.50000 - 9.52628i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-0.500000 - 0.866025i) q^{76} +(-10.0000 + 17.3205i) q^{77} +(3.00000 - 5.19615i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} -7.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} -3.00000 q^{85} +(-2.50000 - 6.06218i) q^{86} +5.00000 q^{88} +(-7.50000 - 12.9904i) q^{89} +3.00000 q^{90} +(-4.00000 - 6.92820i) q^{91} +(2.00000 + 3.46410i) q^{92} +6.00000 q^{94} +(0.500000 - 0.866025i) q^{95} +7.00000 q^{97} +(-4.50000 - 7.79423i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + 2 q^{4} + q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + 2 * q^4 + q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9	$ 2 q + 2 q^{2} + 2 q^{4} + q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{14} + 2 q^{16} - 3 q^{17} + 3 q^{18} - q^{19} + q^{20} + 10 q^{22} + 4 q^{23} - q^{25} - 2 q^{26} - 4 q^{28} + 8 q^{29} + 2 q^{32} - 3 q^{34} - 8 q^{35} + 3 q^{36} - 10 q^{37} - q^{38} + q^{40} - 14 q^{41} - 5 q^{43} + 10 q^{44} + 6 q^{45} + 4 q^{46} + 12 q^{47} - 9 q^{49} - q^{50} - 2 q^{52} - 4 q^{53} + 5 q^{55} - 4 q^{56} + 8 q^{58} - 6 q^{59} - 14 q^{61} + 12 q^{63} + 2 q^{64} - 4 q^{65} + 3 q^{67} - 3 q^{68} - 8 q^{70} - 6 q^{71} + 3 q^{72} + 11 q^{73} - 10 q^{74} - q^{76} - 20 q^{77} + 6 q^{79} + q^{80} - 9 q^{81} - 14 q^{82} - 12 q^{83} - 6 q^{85} - 5 q^{86} + 10 q^{88} - 15 q^{89} + 6 q^{90} - 8 q^{91} + 4 q^{92} + 12 q^{94} + q^{95} + 14 q^{97} - 9 q^{98} + 15 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + 2 * q^4 + q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - 4 * q^14 + 2 * q^16 - 3 * q^17 + 3 * q^18 - q^19 + q^20 + 10 * q^22 + 4 * q^23 - q^25 - 2 * q^26 - 4 * q^28 + 8 * q^29 + 2 * q^32 - 3 * q^34 - 8 * q^35 + 3 * q^36 - 10 * q^37 - q^38 + q^40 - 14 * q^41 - 5 * q^43 + 10 * q^44 + 6 * q^45 + 4 * q^46 + 12 * q^47 - 9 * q^49 - q^50 - 2 * q^52 - 4 * q^53 + 5 * q^55 - 4 * q^56 + 8 * q^58 - 6 * q^59 - 14 * q^61 + 12 * q^63 + 2 * q^64 - 4 * q^65 + 3 * q^67 - 3 * q^68 - 8 * q^70 - 6 * q^71 + 3 * q^72 + 11 * q^73 - 10 * q^74 - q^76 - 20 * q^77 + 6 * q^79 + q^80 - 9 * q^81 - 14 * q^82 - 12 * q^83 - 6 * q^85 - 5 * q^86 + 10 * q^88 - 15 * q^89 + 6 * q^90 - 8 * q^91 + 4 * q^92 + 12 * q^94 + q^95 + 14 * q^97 - 9 * q^98 + 15 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/430\mathbb{Z}\right)^\times$.

$n$	$87$	$261$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$3$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$4$	1.00000			0.500000
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$		0			0
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	0.188982	+	0.981981i	$0.439481\pi$
$7$	−2.00000	+	3.46410i	−0.755929	+	1.30931i	−0.944911	+	0.327327i	$0.893852\pi$
$8$	1.00000			0.353553
$9$	1.50000	−	2.59808i	0.500000	−	0.866025i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	5.00000			1.50756			0.753778	−	0.657129i	$-0.228229\pi$
$11$	5.00000			1.50756			0.753778	+	0.657129i	$0.228229\pi$
$12$		0			0
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−1.00000	+	1.73205i	−0.277350	+	0.480384i	0.693375	+	0.720577i	$0.256123\pi$
$14$	−2.00000	+	3.46410i	−0.534522	+	0.925820i
$15$		0			0
$16$	1.00000			0.250000
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	1.50000	−	2.59808i	0.353553	−	0.612372i
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	0.802955	−	0.596040i	$-0.203260\pi$
$19$	−0.500000	−	0.866025i	−0.114708	−	0.198680i	−0.917663	+	0.397360i	$0.869927\pi$
$20$	0.500000	+	0.866025i	0.111803	+	0.193649i
$21$		0			0
$22$	5.00000			1.06600
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−1.00000	+	1.73205i	−0.196116	+	0.339683i
$27$		0			0
$28$	−2.00000	+	3.46410i	−0.377964	+	0.654654i
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	−0.208443	−	0.978035i	$-0.566840\pi$
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	0.951224	−	0.308500i	$-0.0998271\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	1.00000			0.176777
$33$		0			0
$34$	−1.50000	+	2.59808i	−0.257248	+	0.445566i
$35$	−4.00000			−0.676123
$36$	1.50000	−	2.59808i	0.250000	−	0.433013i
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−5.00000	−	8.66025i	−0.821995	−	1.42374i	0.0821995	−	0.996616i	$-0.473806\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$		0			0
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−7.00000			−1.09322			−0.546608	−	0.837389i	$-0.684081\pi$
$41$	−7.00000			−1.09322			−0.546608	+	0.837389i	$0.684081\pi$
$42$		0			0
$43$	−2.50000	−	6.06218i	−0.381246	−	0.924473i
$43$	−2.50000	−	6.06218i	−0.381246	−	0.924473i
$44$	5.00000			0.753778
$45$	3.00000			0.447214
$46$	2.00000	+	3.46410i	0.294884	+	0.510754i
$47$	6.00000			0.875190			0.437595	−	0.899172i	$-0.355830\pi$
$47$	6.00000			0.875190			0.437595	+	0.899172i	$0.355830\pi$
$48$		0			0
$49$	−4.50000	−	7.79423i	−0.642857	−	1.11346i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−1.00000	+	1.73205i	−0.138675	+	0.240192i
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	0.695344	−	0.718677i	$-0.255252\pi$
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	−0.970065	+	0.242846i	$0.921919\pi$
$54$		0			0
$55$	2.50000	+	4.33013i	0.337100	+	0.583874i
$56$	−2.00000	+	3.46410i	−0.267261	+	0.462910i
$57$		0			0
$58$	4.00000	−	6.92820i	0.525226	−	0.909718i
$59$	−3.00000			−0.390567			−0.195283	−	0.980747i	$-0.562563\pi$
$59$	−3.00000			−0.390567			−0.195283	+	0.980747i	$0.562563\pi$
$60$		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	$0.812942\pi$
$62$		0			0
$63$	6.00000	+	10.3923i	0.755929	+	1.30931i
$64$	1.00000			0.125000
$65$	−2.00000			−0.248069
$66$		0			0
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	0.942987	−	0.332830i	$-0.108004\pi$
$67$	1.50000	+	2.59808i	0.183254	+	0.317406i	−0.759733	+	0.650236i	$0.774670\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$		0			0
$70$	−4.00000			−0.478091
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$	−5.00000	−	8.66025i	−0.581238	−	1.00673i
$75$		0			0
$76$	−0.500000	−	0.866025i	−0.0573539	−	0.0993399i
$77$	−10.0000	+	17.3205i	−1.13961	+	1.97386i
$78$		0			0
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	−0.646440	−	0.762964i	$-0.723743\pi$
$79$	3.00000	−	5.19615i	0.337526	−	0.584613i	0.983967	+	0.178352i	$0.0570765\pi$
$80$	0.500000	+	0.866025i	0.0559017	+	0.0968246i
$81$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$82$	−7.00000			−0.773021
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	−0.980982	−	0.194099i	$-0.937822\pi$
$83$	−6.00000	−	10.3923i	−0.658586	−	1.14070i	0.322396	−	0.946605i	$-0.395512\pi$
$84$		0			0
$85$	−3.00000			−0.325396
$86$	−2.50000	−	6.06218i	−0.269582	−	0.653701i
$87$		0			0
$88$	5.00000			0.533002
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	−0.922840	−	0.385183i	$-0.874138\pi$
$89$	−7.50000	−	12.9904i	−0.794998	−	1.37698i	0.127842	−	0.991795i	$-0.459195\pi$
$90$	3.00000			0.316228
$91$	−4.00000	−	6.92820i	−0.419314	−	0.726273i
$92$	2.00000	+	3.46410i	0.208514	+	0.361158i
$93$		0			0
$94$	6.00000			0.618853
$95$	0.500000	−	0.866025i	0.0512989	−	0.0888523i
$96$		0			0
$97$	7.00000			0.710742			0.355371	−	0.934725i	$-0.384354\pi$
$97$	7.00000			0.710742			0.355371	+	0.934725i	$0.384354\pi$
$98$	−4.50000	−	7.79423i	−0.454569	−	0.787336i
$99$	7.50000	−	12.9904i	0.753778	−	1.30558i
$100$	−0.500000	+	0.866025i	−0.0500000	+	0.0866025i
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	−0.999996	−	0.00286291i	$-0.999089\pi$
$101$	−5.00000	+	8.66025i	−0.497519	+	0.861727i	0.502477	+	0.864590i	$0.332422\pi$
$102$		0			0
$103$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$103$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$104$	−1.00000	+	1.73205i	−0.0980581	+	0.169842i
$105$		0			0
$106$	−2.00000	−	3.46410i	−0.194257	−	0.336463i
$107$	3.00000			0.290021			0.145010	−	0.989430i	$-0.453678\pi$
$107$	3.00000			0.290021			0.145010	+	0.989430i	$0.453678\pi$
$108$		0			0
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	0.999708	−	0.0241802i	$-0.00769755\pi$
$109$	5.00000	+	8.66025i	0.478913	+	0.829502i	−0.520794	+	0.853682i	$0.674364\pi$
$110$	2.50000	+	4.33013i	0.238366	+	0.412861i
$111$		0			0
$112$	−2.00000	+	3.46410i	−0.188982	+	0.327327i
$113$	−19.0000			−1.78737			−0.893685	−	0.448695i	$-0.851889\pi$
$113$	−19.0000			−1.78737			−0.893685	+	0.448695i	$0.851889\pi$
$114$		0			0
$115$	−2.00000	+	3.46410i	−0.186501	+	0.323029i
$116$	4.00000	−	6.92820i	0.371391	−	0.643268i
$117$	3.00000	+	5.19615i	0.277350	+	0.480384i
$118$	−3.00000			−0.276172
$119$	−6.00000	−	10.3923i	−0.550019	−	0.952661i
$120$		0			0
$121$	14.0000			1.27273
$122$	−7.00000	+	12.1244i	−0.633750	+	1.09769i
$123$		0			0
$124$		0			0
$125$	−1.00000			−0.0894427
$126$	6.00000	+	10.3923i	0.534522	+	0.925820i
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$	1.00000			0.0883883
$129$		0			0
$130$	−2.00000			−0.175412
$131$	13.0000			1.13582			0.567908	−	0.823092i	$-0.307753\pi$
$131$	13.0000			1.13582			0.567908	+	0.823092i	$0.307753\pi$
$132$		0			0
$133$	4.00000			0.346844
$134$	1.50000	+	2.59808i	0.129580	+	0.224440i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	−2.00000			−0.170872			−0.0854358	−	0.996344i	$-0.527228\pi$
$137$	−2.00000			−0.170872			−0.0854358	+	0.996344i	$0.527228\pi$
$138$		0			0
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	0.991303	−	0.131597i	$-0.0420106\pi$
$139$	4.50000	+	7.79423i	0.381685	+	0.661098i	−0.609618	+	0.792695i	$0.708677\pi$
$140$	−4.00000			−0.338062
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−5.00000	+	8.66025i	−0.418121	+	0.724207i
$144$	1.50000	−	2.59808i	0.125000	−	0.216506i
$145$	8.00000			0.664364
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$		0			0
$148$	−5.00000	−	8.66025i	−0.410997	−	0.711868i
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	0.585231	−	0.810867i	$-0.301004\pi$
$149$	−5.00000	−	8.66025i	−0.409616	−	0.709476i	−0.994847	+	0.101391i	$0.967671\pi$
$150$		0			0
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	−0.500000	−	0.866025i	−0.0405554	−	0.0702439i
$153$	4.50000	+	7.79423i	0.363803	+	0.630126i
$154$	−10.0000	+	17.3205i	−0.805823	+	1.39573i
$155$		0			0
$156$		0			0
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	−0.775113	−	0.631822i	$-0.782307\pi$
$157$	2.00000	−	3.46410i	0.159617	−	0.276465i	0.934731	+	0.355357i	$0.115641\pi$
$158$	3.00000	−	5.19615i	0.238667	−	0.413384i
$159$		0			0
$160$	0.500000	+	0.866025i	0.0395285	+	0.0684653i
$161$	−16.0000			−1.26098
$162$	−4.50000	−	7.79423i	−0.353553	−	0.612372i
$163$	−0.500000	+	0.866025i	−0.0391630	+	0.0678323i	−0.884943	−	0.465700i	$-0.845802\pi$
$163$	−0.500000	+	0.866025i	−0.0391630	+	0.0678323i	0.845780	+	0.533533i	$0.179136\pi$
$164$	−7.00000			−0.546608
$165$		0			0
$166$	−6.00000	−	10.3923i	−0.465690	−	0.806599i
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	0.989658	+	0.143448i	$0.0458190\pi$
$167$	8.00000	+	13.8564i	0.619059	+	1.07224i	−0.370599	+	0.928793i	$0.620848\pi$
$168$		0			0
$169$	4.50000	+	7.79423i	0.346154	+	0.599556i
$170$	−3.00000			−0.230089
$171$	−3.00000			−0.229416
$172$	−2.50000	−	6.06218i	−0.190623	−	0.462237i
$173$	20.0000			1.52057			0.760286	−	0.649589i	$-0.225059\pi$
$173$	20.0000			1.52057			0.760286	+	0.649589i	$0.225059\pi$
$174$		0			0
$175$	−2.00000	−	3.46410i	−0.151186	−	0.261861i
$176$	5.00000			0.376889
$177$		0			0
$178$	−7.50000	−	12.9904i	−0.562149	−	0.973670i
$179$	−2.50000	+	4.33013i	−0.186859	+	0.323649i	−0.944201	−	0.329369i	$-0.893164\pi$
$179$	−2.50000	+	4.33013i	−0.186859	+	0.323649i	0.757343	+	0.653018i	$0.226497\pi$
$180$	3.00000			0.223607
$181$	13.0000	−	22.5167i	0.966282	−	1.67365i	0.260153	−	0.965567i	$-0.416227\pi$
$181$	13.0000	−	22.5167i	0.966282	−	1.67365i	0.706129	−	0.708083i	$-0.250440\pi$
$182$	−4.00000	−	6.92820i	−0.296500	−	0.513553i
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	5.00000	−	8.66025i	0.367607	−	0.636715i
$186$		0			0
$187$	−7.50000	+	12.9904i	−0.548454	+	0.949951i
$188$	6.00000			0.437595
$189$		0			0
$190$	0.500000	−	0.866025i	0.0362738	−	0.0628281i
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	0.982828	+	0.184525i	$0.0590746\pi$
$191$	9.00000	+	15.5885i	0.651217	+	1.12794i	−0.331611	+	0.943416i	$0.607592\pi$
$192$		0			0
$193$	−2.00000			−0.143963			−0.0719816	−	0.997406i	$-0.522932\pi$
$193$	−2.00000			−0.143963			−0.0719816	+	0.997406i	$0.522932\pi$
$194$	7.00000			0.502571
$195$		0			0
$196$	−4.50000	−	7.79423i	−0.321429	−	0.556731i
$197$	−10.0000	+	17.3205i	−0.712470	+	1.23404i	0.251457	+	0.967869i	$0.419090\pi$
$197$	−10.0000	+	17.3205i	−0.712470	+	1.23404i	−0.963927	+	0.266167i	$0.914243\pi$
$198$	7.50000	−	12.9904i	0.533002	−	0.923186i
$199$	−10.0000			−0.708881			−0.354441	−	0.935079i	$-0.615329\pi$
$199$	−10.0000			−0.708881			−0.354441	+	0.935079i	$0.615329\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$		0			0
$202$	−5.00000	+	8.66025i	−0.351799	+	0.609333i
$203$	16.0000	+	27.7128i	1.12298	+	1.94506i
$204$		0			0
$205$	−3.50000	−	6.06218i	−0.244451	−	0.423401i
$206$		0			0
$207$	12.0000			0.834058
$208$	−1.00000	+	1.73205i	−0.0693375	+	0.120096i
$209$	−2.50000	−	4.33013i	−0.172929	−	0.299521i
$210$		0			0
$211$	16.0000			1.10149			0.550743	−	0.834675i	$-0.314345\pi$
$211$	16.0000			1.10149			0.550743	+	0.834675i	$0.314345\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$		0			0
$214$	3.00000			0.205076
$215$	4.00000	−	5.19615i	0.272798	−	0.354375i
$216$		0			0
$217$		0			0
$218$	5.00000	+	8.66025i	0.338643	+	0.586546i
$219$		0			0
$220$	2.50000	+	4.33013i	0.168550	+	0.291937i
$221$	−3.00000	−	5.19615i	−0.201802	−	0.349531i
$222$		0			0
$223$	−28.0000			−1.87502			−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000			−1.87502			−0.937509	+	0.347960i	$0.886874\pi$
$224$	−2.00000	+	3.46410i	−0.133631	+	0.231455i
$225$	1.50000	+	2.59808i	0.100000	+	0.173205i
$226$	−19.0000			−1.26386
$227$	−3.50000	−	6.06218i	−0.232303	−	0.402361i	0.726182	−	0.687502i	$-0.241293\pi$
$227$	−3.50000	−	6.06218i	−0.232303	−	0.402361i	−0.958485	+	0.285141i	$0.907959\pi$
$228$		0			0
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	−0.536515	−	0.843891i	$-0.680260\pi$
$229$	7.00000	−	12.1244i	0.462573	−	0.801200i	0.999088	+	0.0426906i	$0.0135930\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$		0			0
$232$	4.00000	−	6.92820i	0.262613	−	0.454859i
$233$	−0.500000	+	0.866025i	−0.0327561	+	0.0567352i	−0.881939	−	0.471364i	$-0.843762\pi$
$233$	−0.500000	+	0.866025i	−0.0327561	+	0.0567352i	0.849183	+	0.528099i	$0.177095\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$	3.00000	+	5.19615i	0.195698	+	0.338960i
$236$	−3.00000			−0.195283
$237$		0			0
$238$	−6.00000	−	10.3923i	−0.388922	−	0.673633i
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	0.752536	−	0.658551i	$-0.228830\pi$
$239$	−3.00000	−	5.19615i	−0.194054	−	0.336111i	−0.946590	+	0.322440i	$0.895497\pi$
$240$		0			0
$241$	−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	$0.271048\pi$
$242$	14.0000			0.899954
$243$		0			0
$244$	−7.00000	+	12.1244i	−0.448129	+	0.776182i
$245$	4.50000	−	7.79423i	0.287494	−	0.497955i
$246$		0			0
$247$	2.00000			0.127257
$248$		0			0
$249$		0			0
$250$	−1.00000			−0.0632456
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	0.232740	+	0.972539i	$0.425231\pi$
$251$	−11.5000	+	19.9186i	−0.725874	+	1.25725i	−0.958613	+	0.284711i	$0.908102\pi$
$252$	6.00000	+	10.3923i	0.377964	+	0.654654i
$253$	10.0000	+	17.3205i	0.628695	+	1.08893i
$254$	2.00000			0.125491
$255$		0			0
$256$	1.00000			0.0625000
$257$	−15.0000			−0.935674			−0.467837	−	0.883815i	$-0.654967\pi$
$257$	−15.0000			−0.935674			−0.467837	+	0.883815i	$0.654967\pi$
$258$		0			0
$259$	40.0000			2.48548
$260$	−2.00000			−0.124035
$261$	−12.0000	−	20.7846i	−0.742781	−	1.28654i
$262$	13.0000			0.803143
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	0.952517	+	0.304487i	$0.0984850\pi$
$263$	12.0000	+	20.7846i	0.739952	+	1.28163i	−0.212565	+	0.977147i	$0.568182\pi$
$264$		0			0
$265$	2.00000	−	3.46410i	0.122859	−	0.212798i
$266$	4.00000			0.245256
$267$		0			0
$268$	1.50000	+	2.59808i	0.0916271	+	0.158703i
$269$	4.00000			0.243884			0.121942	−	0.992537i	$-0.461088\pi$
$269$	4.00000			0.243884			0.121942	+	0.992537i	$0.461088\pi$
$270$		0			0
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	−0.996441	−	0.0842940i	$-0.973137\pi$
$271$	−7.00000	+	12.1244i	−0.425220	+	0.736502i	0.571221	+	0.820796i	$0.306470\pi$
$272$	−1.50000	+	2.59808i	−0.0909509	+	0.157532i
$273$		0			0
$274$	−2.00000			−0.120824
$275$	−2.50000	+	4.33013i	−0.150756	+	0.261116i
$276$		0			0
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	0.976231	−	0.216731i	$-0.0695395\pi$
$277$	5.00000	+	8.66025i	0.300421	+	0.520344i	−0.675810	+	0.737075i	$0.736206\pi$
$278$	4.50000	+	7.79423i	0.269892	+	0.467467i
$279$		0			0
$280$	−4.00000			−0.239046
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	−0.916060	−	0.401042i	$-0.868648\pi$
$281$	−13.5000	−	23.3827i	−0.805342	−	1.39489i	0.110717	−	0.993852i	$-0.464685\pi$
$282$		0			0
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	−0.208053	−	0.978117i	$-0.566713\pi$
$283$	12.5000	−	21.6506i	0.743048	−	1.28700i	0.951101	−	0.308879i	$-0.0999539\pi$
$284$	−3.00000	+	5.19615i	−0.178017	+	0.308335i
$285$		0			0
$286$	−5.00000	+	8.66025i	−0.295656	+	0.512092i
$287$	14.0000	−	24.2487i	0.826394	−	1.43136i
$288$	1.50000	−	2.59808i	0.0883883	−	0.153093i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$	8.00000			0.469776
$291$		0			0
$292$	5.50000	−	9.52628i	0.321863	−	0.557483i
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$		0			0
$295$	−1.50000	−	2.59808i	−0.0873334	−	0.151266i
$296$	−5.00000	−	8.66025i	−0.290619	−	0.503367i
$297$		0			0
$298$	−5.00000	−	8.66025i	−0.289642	−	0.501675i
$299$	−8.00000			−0.462652
$300$		0			0
$301$	26.0000	+	3.46410i	1.49862	+	0.199667i
$302$	12.0000			0.690522
$303$		0			0
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$	−14.0000			−0.801638
$306$	4.50000	+	7.79423i	0.257248	+	0.445566i
$307$	11.5000	+	19.9186i	0.656340	+	1.13681i	0.981556	+	0.191174i	$0.0612295\pi$
$307$	11.5000	+	19.9186i	0.656340	+	1.13681i	−0.325216	+	0.945640i	$0.605437\pi$
$308$	−10.0000	+	17.3205i	−0.569803	+	0.986928i
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	0.367402	−	0.930062i	$-0.380247\pi$
$314$	2.00000	−	3.46410i	0.112867	−	0.195491i
$315$	−6.00000	+	10.3923i	−0.338062	+	0.585540i
$316$	3.00000	−	5.19615i	0.168763	−	0.292306i
$317$	−4.00000			−0.224662			−0.112331	−	0.993671i	$-0.535832\pi$
$317$	−4.00000			−0.224662			−0.112331	+	0.993671i	$0.535832\pi$
$318$		0			0
$319$	20.0000	−	34.6410i	1.11979	−	1.93952i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$		0			0
$322$	−16.0000			−0.891645
$323$	3.00000			0.166924
$324$	−4.50000	−	7.79423i	−0.250000	−	0.433013i
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$	−0.500000	+	0.866025i	−0.0276924	+	0.0479647i
$327$		0			0
$328$	−7.00000			−0.386510
$329$	−12.0000	+	20.7846i	−0.661581	+	1.14589i
$330$		0			0
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	−0.995134	−	0.0985303i	$-0.968586\pi$
$331$	−7.50000	+	12.9904i	−0.412237	+	0.714016i	0.582897	+	0.812546i	$0.301919\pi$
$332$	−6.00000	−	10.3923i	−0.329293	−	0.570352i
$333$	−30.0000			−1.64399
$334$	8.00000	+	13.8564i	0.437741	+	0.758189i
$335$	−1.50000	+	2.59808i	−0.0819538	+	0.141948i
$336$		0			0
$337$	7.50000	−	12.9904i	0.408551	−	0.707631i	−0.586177	−	0.810183i	$-0.699368\pi$
$337$	7.50000	−	12.9904i	0.408551	−	0.707631i	0.994728	+	0.102552i	$0.0327009\pi$
$338$	4.50000	+	7.79423i	0.244768	+	0.423950i
$339$		0			0
$340$	−3.00000			−0.162698
$341$		0			0
$342$	−3.00000			−0.162221
$343$	8.00000			0.431959
$344$	−2.50000	−	6.06218i	−0.134791	−	0.326851i
$345$		0			0
$346$	20.0000			1.07521
$347$	−5.50000	−	9.52628i	−0.295255	−	0.511397i	0.679789	−	0.733408i	$-0.262071\pi$
$347$	−5.50000	−	9.52628i	−0.295255	−	0.511397i	−0.975044	+	0.222010i	$0.928738\pi$
$348$		0			0
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	0.891548	−	0.452926i	$-0.149620\pi$
$349$	1.00000	+	1.73205i	0.0535288	+	0.0927146i	−0.838019	+	0.545640i	$0.816286\pi$
$350$	−2.00000	−	3.46410i	−0.106904	−	0.185164i
$351$		0			0
$352$	5.00000			0.266501
$353$	−8.50000	+	14.7224i	−0.452409	+	0.783596i	−0.998535	−	0.0541072i	$-0.982769\pi$
$353$	−8.50000	+	14.7224i	−0.452409	+	0.783596i	0.546126	+	0.837703i	$0.316102\pi$
$354$		0			0
$355$	−6.00000			−0.318447
$356$	−7.50000	−	12.9904i	−0.397499	−	0.688489i
$357$		0			0
$358$	−2.50000	+	4.33013i	−0.132129	+	0.228854i
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.204595	+	0.978847i	$0.565588\pi$
$359$	−18.0000	+	31.1769i	−0.950004	+	1.64545i	−0.745409	+	0.666608i	$0.767746\pi$
$360$	3.00000			0.158114
$361$	9.00000	−	15.5885i	0.473684	−	0.820445i
$362$	13.0000	−	22.5167i	0.683265	−	1.18345i
$363$		0			0
$364$	−4.00000	−	6.92820i	−0.209657	−	0.363137i
$365$	11.0000			0.575766
$366$		0			0
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	−0.956544	−	0.291587i	$-0.905817\pi$
$367$	−14.0000	−	24.2487i	−0.730794	−	1.26577i	0.225750	−	0.974185i	$-0.427517\pi$
$368$	2.00000	+	3.46410i	0.104257	+	0.180579i
$369$	−10.5000	+	18.1865i	−0.546608	+	0.946753i
$370$	5.00000	−	8.66025i	0.259938	−	0.450225i
$371$	16.0000			0.830679
$372$		0			0
$373$	−18.0000	+	31.1769i	−0.932005	+	1.61428i	−0.152115	+	0.988363i	$0.548608\pi$
$373$	−18.0000	+	31.1769i	−0.932005	+	1.61428i	−0.779890	+	0.625917i	$0.784725\pi$
$374$	−7.50000	+	12.9904i	−0.387816	+	0.671717i
$375$		0			0
$376$	6.00000			0.309426
$377$	8.00000	+	13.8564i	0.412021	+	0.713641i
$378$		0			0
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$	0.500000	−	0.866025i	0.0256495	−	0.0444262i
$381$		0			0
$382$	9.00000	+	15.5885i	0.460480	+	0.797575i
$383$	−8.00000			−0.408781			−0.204390	−	0.978889i	$-0.565521\pi$
$383$	−8.00000			−0.408781			−0.204390	+	0.978889i	$0.565521\pi$
$384$		0			0
$385$	−20.0000			−1.01929
$386$	−2.00000			−0.101797
$387$	−19.5000	−	2.59808i	−0.991241	−	0.132068i
$388$	7.00000			0.355371
$389$	−30.0000			−1.52106			−0.760530	−	0.649303i	$-0.775061\pi$
$389$	−30.0000			−1.52106			−0.760530	+	0.649303i	$0.775061\pi$
$390$		0			0
$391$	−12.0000			−0.606866
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$		0			0
$394$	−10.0000	+	17.3205i	−0.503793	+	0.872595i
$395$	6.00000			0.301893
$396$	7.50000	−	12.9904i	0.376889	−	0.652791i
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	0.999998	+	0.00217869i	$0.000693499\pi$
$397$	10.0000	+	17.3205i	0.501886	+	0.869291i	−0.498112	+	0.867113i	$0.665973\pi$
$398$	−10.0000			−0.501255
$399$		0			0
$400$	−0.500000	+	0.866025i	−0.0250000	+	0.0433013i
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$		0			0
$403$		0			0
$404$	−5.00000	+	8.66025i	−0.248759	+	0.430864i
$405$	4.50000	−	7.79423i	0.223607	−	0.387298i
$406$	16.0000	+	27.7128i	0.794067	+	1.37536i
$407$	−25.0000	−	43.3013i	−1.23920	−	2.14636i
$408$		0			0
$409$	−3.00000			−0.148340			−0.0741702	−	0.997246i	$-0.523631\pi$
$409$	−3.00000			−0.148340			−0.0741702	+	0.997246i	$0.523631\pi$
$410$	−3.50000	−	6.06218i	−0.172853	−	0.299390i
$411$		0			0
$412$		0			0
$413$	6.00000	−	10.3923i	0.295241	−	0.511372i
$414$	12.0000			0.589768
$415$	6.00000	−	10.3923i	0.294528	−	0.510138i
$416$	−1.00000	+	1.73205i	−0.0490290	+	0.0849208i
$417$		0			0
$418$	−2.50000	−	4.33013i	−0.122279	−	0.211793i
$419$	28.0000			1.36789			0.683945	−	0.729534i	$-0.260263\pi$
$419$	28.0000			1.36789			0.683945	+	0.729534i	$0.260263\pi$
$420$		0			0
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.0229375	−	0.999737i	$-0.492698\pi$
$421$	18.0000	−	31.1769i	0.877266	−	1.51947i	0.854329	−	0.519733i	$-0.173969\pi$
$422$	16.0000			0.778868
$423$	9.00000	−	15.5885i	0.437595	−	0.757937i
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$	−1.50000	−	2.59808i	−0.0727607	−	0.126025i
$426$		0			0
$427$	−28.0000	−	48.4974i	−1.35501	−	2.34695i
$428$	3.00000			0.145010
$429$		0			0
$430$	4.00000	−	5.19615i	0.192897	−	0.250581i
$431$	−30.0000			−1.44505			−0.722525	−	0.691345i	$-0.757018\pi$
$431$	−30.0000			−1.44505			−0.722525	+	0.691345i	$0.757018\pi$
$432$		0			0
$433$	1.00000	+	1.73205i	0.0480569	+	0.0832370i	0.889053	−	0.457804i	$-0.151364\pi$
$433$	1.00000	+	1.73205i	0.0480569	+	0.0832370i	−0.840996	+	0.541041i	$0.818030\pi$
$434$		0			0
$435$		0			0
$436$	5.00000	+	8.66025i	0.239457	+	0.414751i
$437$	2.00000	−	3.46410i	0.0956730	−	0.165710i
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	2.50000	+	4.33013i	0.119183	+	0.206431i
$441$	−27.0000			−1.28571
$442$	−3.00000	−	5.19615i	−0.142695	−	0.247156i
$443$	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
$445$	7.50000	−	12.9904i	0.355534	−	0.615803i
$446$	−28.0000			−1.32584
$447$		0			0
$448$	−2.00000	+	3.46410i	−0.0944911	+	0.163663i
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	0.986937	−	0.161106i	$-0.0515060\pi$
$449$	7.50000	+	12.9904i	0.353947	+	0.613054i	−0.632990	+	0.774160i	$0.718173\pi$
$450$	1.50000	+	2.59808i	0.0707107	+	0.122474i
$451$	−35.0000			−1.64809
$452$	−19.0000			−0.893685
$453$		0			0
$454$	−3.50000	−	6.06218i	−0.164263	−	0.284512i
$455$	4.00000	−	6.92820i	0.187523	−	0.324799i
$456$		0			0
$457$	3.00000			0.140334			0.0701670	−	0.997535i	$-0.477647\pi$
$457$	3.00000			0.140334			0.0701670	+	0.997535i	$0.477647\pi$
$458$	7.00000	−	12.1244i	0.327089	−	0.566534i
$459$		0			0
$460$	−2.00000	+	3.46410i	−0.0932505	+	0.161515i
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	0.968945	+	0.247276i	$0.0795353\pi$
$461$	15.0000	+	25.9808i	0.698620	+	1.21004i	−0.270326	+	0.962769i	$0.587131\pi$
$462$		0			0
$463$	−17.0000	−	29.4449i	−0.790057	−	1.36842i	−0.925931	−	0.377693i	$-0.876718\pi$
$463$	−17.0000	−	29.4449i	−0.790057	−	1.36842i	0.135874	−	0.990726i	$-0.456616\pi$
$464$	4.00000	−	6.92820i	0.185695	−	0.321634i
$465$		0			0
$466$	−0.500000	+	0.866025i	−0.0231621	+	0.0401179i
$467$	−14.5000	−	25.1147i	−0.670980	−	1.16217i	−0.977627	−	0.210348i	$-0.932540\pi$
$467$	−14.5000	−	25.1147i	−0.670980	−	1.16217i	0.306647	−	0.951823i	$-0.400793\pi$
$468$	3.00000	+	5.19615i	0.138675	+	0.240192i
$469$	−12.0000			−0.554109
$470$	3.00000	+	5.19615i	0.138380	+	0.239681i
$471$		0			0
$472$	−3.00000			−0.138086
$473$	−12.5000	−	30.3109i	−0.574751	−	1.39370i
$474$		0			0
$475$	1.00000			0.0458831
$476$	−6.00000	−	10.3923i	−0.275010	−	0.476331i
$477$	−12.0000			−0.549442
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	−0.985504	−	0.169654i	$-0.945735\pi$
$479$	−14.0000	−	24.2487i	−0.639676	−	1.10795i	0.345827	−	0.938298i	$-0.387598\pi$
$480$		0			0
$481$	20.0000			0.911922
$482$	−5.00000	+	8.66025i	−0.227744	+	0.394464i
$483$		0			0
$484$	14.0000			0.636364
$485$	3.50000	+	6.06218i	0.158927	+	0.275269i
$486$		0			0
$487$	15.0000	−	25.9808i	0.679715	−	1.17730i	−0.295352	−	0.955389i	$-0.595437\pi$
$487$	15.0000	−	25.9808i	0.679715	−	1.17730i	0.975067	−	0.221912i	$-0.0712298\pi$
$488$	−7.00000	+	12.1244i	−0.316875	+	0.548844i
$489$		0			0
$490$	4.50000	−	7.79423i	0.203289	−	0.352107i
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	0.382118	+	0.924113i	$0.375195\pi$
$491$	−13.5000	+	23.3827i	−0.609246	+	1.05525i	−0.991365	+	0.131132i	$0.958139\pi$
$492$		0			0
$493$	12.0000	+	20.7846i	0.540453	+	0.936092i
$494$	2.00000			0.0899843
$495$	15.0000			0.674200
$496$		0			0
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	−21.5000	+	37.2391i	−0.962472	+	1.66705i	−0.246214	+	0.969216i	$0.579187\pi$
$499$	−21.5000	+	37.2391i	−0.962472	+	1.66705i	−0.716258	+	0.697835i	$0.754147\pi$
$500$	−1.00000			−0.0447214
$501$		0			0
$502$	−11.5000	+	19.9186i	−0.513270	+	0.889010i
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.322151	+	0.946688i	$0.604406\pi$
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.658781	+	0.752335i	$0.728928\pi$
$504$	6.00000	+	10.3923i	0.267261	+	0.462910i
$505$	−10.0000			−0.444994
$506$	10.0000	+	17.3205i	0.444554	+	0.769991i
$507$		0			0
$508$	2.00000			0.0887357
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	−0.978421	−	0.206623i	$-0.933753\pi$
$509$	−7.00000	+	12.1244i	−0.310270	+	0.537403i	0.668151	+	0.744026i	$0.267086\pi$
$510$		0			0
$511$	22.0000	+	38.1051i	0.973223	+	1.68567i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−15.0000			−0.661622
$515$		0			0
$516$		0			0
$517$	30.0000			1.31940
$518$	40.0000			1.75750
$519$		0			0
$520$	−2.00000			−0.0877058
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	0.538948	−	0.842339i	$-0.318822\pi$
$521$	−10.5000	−	18.1865i	−0.460013	−	0.796766i	−0.998961	+	0.0455727i	$0.985489\pi$
$522$	−12.0000	−	20.7846i	−0.525226	−	0.909718i
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	−0.932345	−	0.361569i	$-0.882241\pi$
$523$	−3.50000	+	6.06218i	−0.153044	+	0.265081i	0.779301	+	0.626650i	$0.215574\pi$
$524$	13.0000			0.567908
$525$		0			0
$526$	12.0000	+	20.7846i	0.523225	+	0.906252i
$527$		0			0
$528$		0			0
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$	2.00000	−	3.46410i	0.0868744	−	0.150471i
$531$	−4.50000	+	7.79423i	−0.195283	+	0.338241i
$532$	4.00000			0.173422
$533$	7.00000	−	12.1244i	0.303204	−	0.525164i
$534$		0			0
$535$	1.50000	+	2.59808i	0.0648507	+	0.112325i
$536$	1.50000	+	2.59808i	0.0647901	+	0.112220i
$537$		0			0
$538$	4.00000			0.172452
$539$	−22.5000	−	38.9711i	−0.969144	−	1.67861i
$540$		0			0
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	−0.999520	−	0.0309841i	$-0.990136\pi$
$541$	−11.0000	+	19.0526i	−0.472927	+	0.819133i	0.526593	+	0.850118i	$0.323469\pi$
$542$	−7.00000	+	12.1244i	−0.300676	+	0.520786i
$543$		0			0
$544$	−1.50000	+	2.59808i	−0.0643120	+	0.111392i
$545$	−5.00000	+	8.66025i	−0.214176	+	0.370965i
$546$		0			0
$547$	18.0000	+	31.1769i	0.769624	+	1.33303i	0.937767	+	0.347266i	$0.112890\pi$
$547$	18.0000	+	31.1769i	0.769624	+	1.33303i	−0.168142	+	0.985763i	$0.553777\pi$
$548$	−2.00000			−0.0854358
$549$	21.0000	+	36.3731i	0.896258	+	1.55236i
$550$	−2.50000	+	4.33013i	−0.106600	+	0.184637i
$551$	−8.00000			−0.340811
$552$		0			0
$553$	12.0000	+	20.7846i	0.510292	+	0.883852i
$554$	5.00000	+	8.66025i	0.212430	+	0.367939i
$555$		0			0
$556$	4.50000	+	7.79423i	0.190843	+	0.330549i
$557$	12.0000			0.508456			0.254228	−	0.967144i	$-0.418179\pi$
$557$	12.0000			0.508456			0.254228	+	0.967144i	$0.418179\pi$
$558$		0			0
$559$	13.0000	+	1.73205i	0.549841	+	0.0732579i
$560$	−4.00000			−0.169031
$561$		0			0
$562$	−13.5000	−	23.3827i	−0.569463	−	0.986339i
$563$	4.00000			0.168580			0.0842900	−	0.996441i	$-0.473138\pi$
$563$	4.00000			0.168580			0.0842900	+	0.996441i	$0.473138\pi$
$564$		0			0
$565$	−9.50000	−	16.4545i	−0.399668	−	0.692245i
$566$	12.5000	−	21.6506i	0.525414	−	0.910044i
$567$	36.0000			1.51186
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	5.50000	+	9.52628i	0.230572	+	0.399362i	0.957977	−	0.286846i	$-0.0926069\pi$
$569$	5.50000	+	9.52628i	0.230572	+	0.399362i	−0.727405	+	0.686209i	$0.759274\pi$
$570$		0			0
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	0.821138	−	0.570730i	$-0.193340\pi$
$571$	−2.00000	−	3.46410i	−0.0836974	−	0.144968i	−0.904835	+	0.425762i	$0.860006\pi$
$572$	−5.00000	+	8.66025i	−0.209061	+	0.362103i
$573$		0			0
$574$	14.0000	−	24.2487i	0.584349	−	1.01212i
$575$	−4.00000			−0.166812
$576$	1.50000	−	2.59808i	0.0625000	−	0.108253i
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	−0.615603	−	0.788056i	$-0.711088\pi$
$577$	9.00000	−	15.5885i	0.374675	−	0.648956i	0.990278	+	0.139100i	$0.0444210\pi$
$578$	4.00000	+	6.92820i	0.166378	+	0.288175i
$579$		0			0
$580$	8.00000			0.332182
$581$	48.0000			1.99138
$582$		0			0
$583$	−10.0000	−	17.3205i	−0.414158	−	0.717342i
$584$	5.50000	−	9.52628i	0.227592	−	0.394200i
$585$	−3.00000	+	5.19615i	−0.124035	+	0.214834i
$586$	14.0000			0.578335
$587$	−11.5000	+	19.9186i	−0.474656	+	0.822128i	−0.999579	−	0.0290218i	$-0.990761\pi$
$587$	−11.5000	+	19.9186i	−0.474656	+	0.822128i	0.524923	+	0.851150i	$0.324094\pi$
$588$		0			0
$589$		0			0
$590$	−1.50000	−	2.59808i	−0.0617540	−	0.106961i
$591$		0			0
$592$	−5.00000	−	8.66025i	−0.205499	−	0.355934i
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	−0.996976	−	0.0777165i	$-0.975237\pi$
$593$	−10.5000	+	18.1865i	−0.431183	+	0.746831i	0.565792	+	0.824548i	$0.308570\pi$
$594$		0			0
$595$	6.00000	−	10.3923i	0.245976	−	0.426043i
$596$	−5.00000	−	8.66025i	−0.204808	−	0.354738i
$597$		0			0
$598$	−8.00000			−0.327144
$599$	−16.0000	−	27.7128i	−0.653742	−	1.13231i	−0.982208	−	0.187799i	$-0.939865\pi$
$599$	−16.0000	−	27.7128i	−0.653742	−	1.13231i	0.328465	−	0.944516i	$-0.393469\pi$
$600$		0			0
$601$	−21.0000			−0.856608			−0.428304	−	0.903635i	$-0.640889\pi$
$601$	−21.0000			−0.856608			−0.428304	+	0.903635i	$0.640889\pi$
$602$	26.0000	+	3.46410i	1.05968	+	0.141186i
$603$	9.00000			0.366508
$604$	12.0000			0.488273
$605$	7.00000	+	12.1244i	0.284590	+	0.492925i
$606$		0			0
$607$	3.00000	+	5.19615i	0.121766	+	0.210905i	0.920464	−	0.390827i	$-0.127811\pi$
$607$	3.00000	+	5.19615i	0.121766	+	0.210905i	−0.798698	+	0.601732i	$0.794478\pi$
$608$	−0.500000	−	0.866025i	−0.0202777	−	0.0351220i
$609$		0			0
$610$	−14.0000			−0.566843
$611$	−6.00000	+	10.3923i	−0.242734	+	0.420428i
$612$	4.50000	+	7.79423i	0.181902	+	0.315063i
$613$	−44.0000			−1.77714			−0.888572	−	0.458738i	$-0.848302\pi$
$613$	−44.0000			−1.77714			−0.888572	+	0.458738i	$0.848302\pi$
$614$	11.5000	+	19.9186i	0.464102	+	0.803849i
$615$		0			0
$616$	−10.0000	+	17.3205i	−0.402911	+	0.697863i
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$		0			0
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	60.0000			2.40385
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	−11.0000	−	19.0526i	−0.439648	−	0.761493i
$627$		0			0
$628$	2.00000	−	3.46410i	0.0798087	−	0.138233i
$629$	30.0000			1.19618
$630$	−6.00000	+	10.3923i	−0.239046	+	0.414039i
$631$	−3.00000	+	5.19615i	−0.119428	+	0.206856i	−0.919541	−	0.392994i	$-0.871439\pi$
$631$	−3.00000	+	5.19615i	−0.119428	+	0.206856i	0.800113	+	0.599849i	$0.204773\pi$
$632$	3.00000	−	5.19615i	0.119334	−	0.206692i
$633$		0			0
$634$	−4.00000			−0.158860
$635$	1.00000	+	1.73205i	0.0396838	+	0.0687343i
$636$		0			0
$637$	18.0000			0.713186
$638$	20.0000	−	34.6410i	0.791808	−	1.37145i
$639$	9.00000	+	15.5885i	0.356034	+	0.616670i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	33.0000			1.30342			0.651711	−	0.758468i	$-0.274052\pi$
$641$	33.0000			1.30342			0.651711	+	0.758468i	$0.274052\pi$
$642$		0			0
$643$	−21.0000			−0.828159			−0.414080	−	0.910241i	$-0.635896\pi$
$643$	−21.0000			−0.828159			−0.414080	+	0.910241i	$0.635896\pi$
$644$	−16.0000			−0.630488
$645$		0			0
$646$	3.00000			0.118033
$647$	32.0000			1.25805			0.629025	−	0.777385i	$-0.283454\pi$
$647$	32.0000			1.25805			0.629025	+	0.777385i	$0.283454\pi$
$648$	−4.50000	−	7.79423i	−0.176777	−	0.306186i
$649$	−15.0000			−0.588802
$650$	−1.00000	−	1.73205i	−0.0392232	−	0.0679366i
$651$		0			0
$652$	−0.500000	+	0.866025i	−0.0195815	+	0.0339162i
$653$	24.0000			0.939193			0.469596	−	0.882881i	$-0.344399\pi$
$653$	24.0000			0.939193			0.469596	+	0.882881i	$0.344399\pi$
$654$		0			0
$655$	6.50000	+	11.2583i	0.253976	+	0.439899i
$656$	−7.00000			−0.273304
$657$	−16.5000	−	28.5788i	−0.643726	−	1.11497i
$658$	−12.0000	+	20.7846i	−0.467809	+	0.810268i
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	−0.992388	−	0.123148i	$-0.960701\pi$
$659$	−10.0000	+	17.3205i	−0.389545	+	0.674711i	0.602844	+	0.797859i	$0.294034\pi$
$660$		0			0
$661$	32.0000			1.24466			0.622328	−	0.782757i	$-0.286187\pi$
$661$	32.0000			1.24466			0.622328	+	0.782757i	$0.286187\pi$
$662$	−7.50000	+	12.9904i	−0.291496	+	0.504885i
$663$		0			0
$664$	−6.00000	−	10.3923i	−0.232845	−	0.403300i
$665$	2.00000	+	3.46410i	0.0775567	+	0.134332i
$666$	−30.0000			−1.16248
$667$	32.0000			1.23904
$668$	8.00000	+	13.8564i	0.309529	+	0.536120i
$669$		0			0
$670$	−1.50000	+	2.59808i	−0.0579501	+	0.100372i
$671$	−35.0000	+	60.6218i	−1.35116	+	2.34028i
$672$		0			0
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$	7.50000	−	12.9904i	0.288889	−	0.500371i
$675$		0			0
$676$	4.50000	+	7.79423i	0.173077	+	0.299778i
$677$	−8.00000			−0.307465			−0.153732	−	0.988113i	$-0.549129\pi$
$677$	−8.00000			−0.307465			−0.153732	+	0.988113i	$0.549129\pi$
$678$		0			0
$679$	−14.0000	+	24.2487i	−0.537271	+	0.930580i
$680$	−3.00000			−0.115045
$681$		0			0
$682$		0			0
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	0.825222	−	0.564809i	$-0.191050\pi$
$683$	−2.00000	−	3.46410i	−0.0765279	−	0.132550i	−0.901750	+	0.432259i	$0.857717\pi$
$684$	−3.00000			−0.114708
$685$	−1.00000	−	1.73205i	−0.0382080	−	0.0661783i
$686$	8.00000			0.305441
$687$		0			0
$688$	−2.50000	−	6.06218i	−0.0953116	−	0.231118i
$689$	8.00000			0.304776
$690$		0			0
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	0.856358	−	0.516382i	$-0.172722\pi$
$691$	−0.500000	−	0.866025i	−0.0190209	−	0.0329452i	−0.875379	+	0.483437i	$0.839388\pi$
$692$	20.0000			0.760286
$693$	30.0000	+	51.9615i	1.13961	+	1.97386i
$694$	−5.50000	−	9.52628i	−0.208777	−	0.361613i
$695$	−4.50000	+	7.79423i	−0.170695	+	0.295652i
$696$		0			0
$697$	10.5000	−	18.1865i	0.397716	−	0.688864i
$698$	1.00000	+	1.73205i	0.0378506	+	0.0655591i
$699$		0			0
$700$	−2.00000	−	3.46410i	−0.0755929	−	0.130931i
$701$	18.0000	−	31.1769i	0.679851	−	1.17754i	−0.295175	−	0.955443i	$-0.595378\pi$
$701$	18.0000	−	31.1769i	0.679851	−	1.17754i	0.975026	−	0.222093i	$-0.0712887\pi$
$702$		0			0
$703$	−5.00000	+	8.66025i	−0.188579	+	0.326628i
$704$	5.00000			0.188445
$705$		0			0
$706$	−8.50000	+	14.7224i	−0.319902	+	0.554086i
$707$	−20.0000	−	34.6410i	−0.752177	−	1.30281i
$708$		0			0
$709$	38.0000			1.42712			0.713560	−	0.700594i	$-0.247082\pi$
$709$	38.0000			1.42712			0.713560	+	0.700594i	$0.247082\pi$
$710$	−6.00000			−0.225176
$711$	−9.00000	−	15.5885i	−0.337526	−	0.584613i
$712$	−7.50000	−	12.9904i	−0.281074	−	0.486835i
$713$		0			0
$714$		0			0
$715$	−10.0000			−0.373979
$716$	−2.50000	+	4.33013i	−0.0934294	+	0.161824i
$717$		0			0
$718$	−18.0000	+	31.1769i	−0.671754	+	1.16351i
$719$	17.0000	+	29.4449i	0.633993	+	1.09811i	0.986728	+	0.162385i	$0.0519185\pi$
$719$	17.0000	+	29.4449i	0.633993	+	1.09811i	−0.352735	+	0.935723i	$0.614748\pi$
$720$	3.00000			0.111803
$721$		0			0
$722$	9.00000	−	15.5885i	0.334945	−	0.580142i
$723$		0			0
$724$	13.0000	−	22.5167i	0.483141	−	0.836825i
$725$	4.00000	+	6.92820i	0.148556	+	0.257307i
$726$		0			0
$727$		0			0			−	1.00000i	$-0.5\pi$
$727$		0			0				1.00000i	$0.5\pi$
$728$	−4.00000	−	6.92820i	−0.148250	−	0.256776i
$729$	−27.0000			−1.00000
$730$	11.0000			0.407128
$731$	19.5000	+	2.59808i	0.721234	+	0.0960933i
$732$		0			0
$733$	34.0000			1.25582			0.627909	−	0.778287i	$-0.283911\pi$
$733$	34.0000			1.25582			0.627909	+	0.778287i	$0.283911\pi$
$734$	−14.0000	−	24.2487i	−0.516749	−	0.895036i
$735$		0			0
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	7.50000	+	12.9904i	0.276266	+	0.478507i
$738$	−10.5000	+	18.1865i	−0.386510	+	0.669456i
$739$	40.0000			1.47142			0.735712	−	0.677295i	$-0.236848\pi$
$739$	40.0000			1.47142			0.735712	+	0.677295i	$0.236848\pi$
$740$	5.00000	−	8.66025i	0.183804	−	0.318357i
$741$		0			0
$742$	16.0000			0.587378
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$		0			0
$745$	5.00000	−	8.66025i	0.183186	−	0.317287i
$746$	−18.0000	+	31.1769i	−0.659027	+	1.14147i
$747$	−36.0000			−1.31717
$748$	−7.50000	+	12.9904i	−0.274227	+	0.474975i
$749$	−6.00000	+	10.3923i	−0.219235	+	0.379727i
$750$		0			0
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	0.760263	−	0.649616i	$-0.225070\pi$
$751$	−5.00000	−	8.66025i	−0.182453	−	0.316017i	−0.942715	+	0.333599i	$0.891737\pi$
$752$	6.00000			0.218797
$753$		0			0
$754$	8.00000	+	13.8564i	0.291343	+	0.504621i
$755$	6.00000	+	10.3923i	0.218362	+	0.378215i
$756$		0			0
$757$	−10.0000	+	17.3205i	−0.363456	+	0.629525i	−0.988527	−	0.151043i	$-0.951737\pi$
$757$	−10.0000	+	17.3205i	−0.363456	+	0.629525i	0.625071	+	0.780568i	$0.285070\pi$
$758$	−5.00000			−0.181608
$759$		0			0
$760$	0.500000	−	0.866025i	0.0181369	−	0.0314140i
$761$	7.00000	−	12.1244i	0.253750	−	0.439508i	−0.710805	−	0.703389i	$-0.751669\pi$
$761$	7.00000	−	12.1244i	0.253750	−	0.439508i	0.964555	+	0.263881i	$0.0850027\pi$
$762$		0			0
$763$	−40.0000			−1.44810
$764$	9.00000	+	15.5885i	0.325609	+	0.563971i
$765$	−4.50000	+	7.79423i	−0.162698	+	0.281801i
$766$	−8.00000			−0.289052
$767$	3.00000	−	5.19615i	0.108324	−	0.187622i
$768$		0			0
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	0.995397	−	0.0958377i	$-0.0305530\pi$
$769$	11.5000	+	19.9186i	0.414701	+	0.718283i	−0.580696	+	0.814120i	$0.697220\pi$
$770$	−20.0000			−0.720750
$771$		0			0
$772$	−2.00000			−0.0719816
$773$	−24.0000			−0.863220			−0.431610	−	0.902060i	$-0.642054\pi$
$773$	−24.0000			−0.863220			−0.431610	+	0.902060i	$0.642054\pi$
$774$	−19.5000	−	2.59808i	−0.700913	−	0.0933859i
$775$		0			0
$776$	7.00000			0.251285
$777$		0			0
$778$	−30.0000			−1.07555
$779$	3.50000	+	6.06218i	0.125401	+	0.217200i
$780$		0			0
$781$	−15.0000	+	25.9808i	−0.536742	+	0.929665i
$782$	−12.0000			−0.429119
$783$		0			0
$784$	−4.50000	−	7.79423i	−0.160714	−	0.278365i
$785$	4.00000			0.142766
$786$		0			0
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	−0.828176	−	0.560469i	$-0.810621\pi$
$787$	2.00000	−	3.46410i	0.0712923	−	0.123482i	0.899468	+	0.436987i	$0.143954\pi$
$788$	−10.0000	+	17.3205i	−0.356235	+	0.617018i
$789$		0			0
$790$	6.00000			0.213470
$791$	38.0000	−	65.8179i	1.35112	−	2.34022i
$792$	7.50000	−	12.9904i	0.266501	−	0.461593i
$793$	−14.0000	−	24.2487i	−0.497155	−	0.861097i
$794$	10.0000	+	17.3205i	0.354887	+	0.614682i
$795$		0			0
$796$	−10.0000			−0.354441
$797$	8.00000	+	13.8564i	0.283375	+	0.490819i	0.972214	−	0.234095i	$-0.0752127\pi$
$797$	8.00000	+	13.8564i	0.283375	+	0.490819i	−0.688839	+	0.724914i	$0.741879\pi$
$798$		0			0
$799$	−9.00000	+	15.5885i	−0.318397	+	0.551480i
$800$	−0.500000	+	0.866025i	−0.0176777	+	0.0306186i
$801$	−45.0000			−1.59000
$802$	3.00000	−	5.19615i	0.105934	−	0.183483i
$803$	27.5000	−	47.6314i	0.970454	−	1.68088i
$804$		0			0
$805$	−8.00000	−	13.8564i	−0.281963	−	0.488374i
$806$		0			0
$807$		0			0
$808$	−5.00000	+	8.66025i	−0.175899	+	0.304667i
$809$	26.0000			0.914111			0.457056	−	0.889438i	$-0.348904\pi$
$809$	26.0000			0.914111			0.457056	+	0.889438i	$0.348904\pi$
$810$	4.50000	−	7.79423i	0.158114	−	0.273861i
$811$	4.50000	+	7.79423i	0.158016	+	0.273692i	0.934153	−	0.356872i	$-0.116157\pi$
$811$	4.50000	+	7.79423i	0.158016	+	0.273692i	−0.776137	+	0.630564i	$0.782823\pi$
$812$	16.0000	+	27.7128i	0.561490	+	0.972529i
$813$		0			0
$814$	−25.0000	−	43.3013i	−0.876250	−	1.51771i
$815$	−1.00000			−0.0350285
$816$		0			0
$817$	−4.00000	+	5.19615i	−0.139942	+	0.181790i
$818$	−3.00000			−0.104893
$819$	−24.0000			−0.838628
$820$	−3.50000	−	6.06218i	−0.122225	−	0.211700i
$821$	−18.0000			−0.628204			−0.314102	−	0.949389i	$-0.601703\pi$
$821$	−18.0000			−0.628204			−0.314102	+	0.949389i	$0.601703\pi$
$822$		0			0
$823$	−23.0000	−	39.8372i	−0.801730	−	1.38864i	−0.918477	−	0.395475i	$-0.870580\pi$
$823$	−23.0000	−	39.8372i	−0.801730	−	1.38864i	0.116747	−	0.993162i	$-0.462753\pi$
$824$		0			0
$825$		0			0
$826$	6.00000	−	10.3923i	0.208767	−	0.361595i
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	0.529949	−	0.848030i	$-0.322211\pi$
$827$	−13.5000	−	23.3827i	−0.469441	−	0.813096i	−0.999390	+	0.0349341i	$0.988878\pi$
$828$	12.0000			0.417029
$829$	−14.0000	−	24.2487i	−0.486240	−	0.842193i	0.513635	−	0.858009i	$-0.328299\pi$
$829$	−14.0000	−	24.2487i	−0.486240	−	0.842193i	−0.999875	+	0.0158163i	$0.994965\pi$
$830$	6.00000	−	10.3923i	0.208263	−	0.360722i
$831$		0			0
$832$	−1.00000	+	1.73205i	−0.0346688	+	0.0600481i
$833$	27.0000			0.935495
$834$		0			0
$835$	−8.00000	+	13.8564i	−0.276851	+	0.479521i
$836$	−2.50000	−	4.33013i	−0.0864643	−	0.149761i
$837$		0			0
$838$	28.0000			0.967244
$839$	−42.0000			−1.45000			−0.725001	−	0.688748i	$-0.758161\pi$
$839$	−42.0000			−1.45000			−0.725001	+	0.688748i	$0.758161\pi$
$840$		0			0
$841$	−17.5000	−	30.3109i	−0.603448	−	1.04520i
$842$	18.0000	−	31.1769i	0.620321	−	1.07443i
$843$		0			0
$844$	16.0000			0.550743
$845$	−4.50000	+	7.79423i	−0.154805	+	0.268130i
$846$	9.00000	−	15.5885i	0.309426	−	0.535942i
$847$	−28.0000	+	48.4974i	−0.962091	+	1.66639i
$848$	−2.00000	−	3.46410i	−0.0686803	−	0.118958i
$849$		0			0
$850$	−1.50000	−	2.59808i	−0.0514496	−	0.0891133i
$851$	20.0000	−	34.6410i	0.685591	−	1.18748i
$852$		0			0
$853$	−8.00000	+	13.8564i	−0.273915	+	0.474434i	−0.969861	−	0.243660i	$-0.921652\pi$
$853$	−8.00000	+	13.8564i	−0.273915	+	0.474434i	0.695946	+	0.718094i	$0.254985\pi$
$854$	−28.0000	−	48.4974i	−0.958140	−	1.65955i
$855$	−1.50000	−	2.59808i	−0.0512989	−	0.0888523i
$856$	3.00000			0.102538
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	−1.00000			−0.0341196			−0.0170598	−	0.999854i	$-0.505431\pi$
$859$	−1.00000			−0.0341196			−0.0170598	+	0.999854i	$0.505431\pi$
$860$	4.00000	−	5.19615i	0.136399	−	0.177187i
$861$		0			0
$862$	−30.0000			−1.02180
$863$	23.0000	+	39.8372i	0.782929	+	1.35607i	0.930228	+	0.366981i	$0.119609\pi$
$863$	23.0000	+	39.8372i	0.782929	+	1.35607i	−0.147299	+	0.989092i	$0.547058\pi$
$864$		0			0
$865$	10.0000	+	17.3205i	0.340010	+	0.588915i
$866$	1.00000	+	1.73205i	0.0339814	+	0.0588575i
$867$		0			0
$868$		0			0
$869$	15.0000	−	25.9808i	0.508840	−	0.881337i
$870$		0			0
$871$	−6.00000			−0.203302
$872$	5.00000	+	8.66025i	0.169321	+	0.293273i
$873$	10.5000	−	18.1865i	0.355371	−	0.615521i
$874$	2.00000	−	3.46410i	0.0676510	−	0.117175i
$875$	2.00000	−	3.46410i	0.0676123	−	0.117108i
$876$		0			0
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	−0.989788	−	0.142548i	$-0.954470\pi$
$877$	−11.0000	+	19.0526i	−0.371444	+	0.643359i	0.618344	+	0.785907i	$0.287804\pi$
$878$		0			0
$879$		0			0
$880$	2.50000	+	4.33013i	0.0842750	+	0.145969i
$881$	7.00000			0.235836			0.117918	−	0.993023i	$-0.462378\pi$
$881$	7.00000			0.235836			0.117918	+	0.993023i	$0.462378\pi$
$882$	−27.0000			−0.909137
$883$	18.0000	+	31.1769i	0.605748	+	1.04919i	0.991933	+	0.126765i	$0.0404595\pi$
$883$	18.0000	+	31.1769i	0.605748	+	1.04919i	−0.386185	+	0.922422i	$0.626207\pi$
$884$	−3.00000	−	5.19615i	−0.100901	−	0.174766i
$885$		0			0
$886$	10.0000	−	17.3205i	0.335957	−	0.581894i
$887$	−22.0000			−0.738688			−0.369344	−	0.929293i	$-0.620418\pi$
$887$	−22.0000			−0.738688			−0.369344	+	0.929293i	$0.620418\pi$
$888$		0			0
$889$	−4.00000	+	6.92820i	−0.134156	+	0.232364i
$890$	7.50000	−	12.9904i	0.251401	−	0.435439i
$891$	−22.5000	−	38.9711i	−0.753778	−	1.30558i
$892$	−28.0000			−0.937509
$893$	−3.00000	−	5.19615i	−0.100391	−	0.173883i
$894$		0			0
$895$	−5.00000			−0.167132
$896$	−2.00000	+	3.46410i	−0.0668153	+	0.115728i
$897$		0			0
$898$	7.50000	+	12.9904i	0.250278	+	0.433495i
$899$		0			0
$900$	1.50000	+	2.59808i	0.0500000	+	0.0866025i
$901$	12.0000			0.399778
$902$	−35.0000			−1.16537
$903$		0			0
$904$	−19.0000			−0.631931
$905$	26.0000			0.864269
$906$		0			0
$907$	−23.0000			−0.763702			−0.381851	−	0.924224i	$-0.624713\pi$
$907$	−23.0000			−0.763702			−0.381851	+	0.924224i	$0.624713\pi$
$908$	−3.50000	−	6.06218i	−0.116152	−	0.201180i
$909$	15.0000	+	25.9808i	0.497519	+	0.861727i
$910$	4.00000	−	6.92820i	0.132599	−	0.229668i
$911$	58.0000			1.92163			0.960813	−	0.277198i	$-0.0894057\pi$
$911$	58.0000			1.92163			0.960813	+	0.277198i	$0.0894057\pi$
$912$		0			0
$913$	−30.0000	−	51.9615i	−0.992855	−	1.71968i
$914$	3.00000			0.0992312
$915$		0			0
$916$	7.00000	−	12.1244i	0.231287	−	0.400600i
$917$	−26.0000	+	45.0333i	−0.858596	+	1.48713i
$918$		0			0
$919$	−32.0000			−1.05558			−0.527791	−	0.849374i	$-0.676980\pi$
$919$	−32.0000			−1.05558			−0.527791	+	0.849374i	$0.676980\pi$
$920$	−2.00000	+	3.46410i	−0.0659380	+	0.114208i
$921$		0			0
$922$	15.0000	+	25.9808i	0.493999	+	0.855631i
$923$	−6.00000	−	10.3923i	−0.197492	−	0.342067i
$924$		0			0
$925$	10.0000			0.328798
$926$	−17.0000	−	29.4449i	−0.558655	−	0.967618i
$927$		0			0
$928$	4.00000	−	6.92820i	0.131306	−	0.227429i
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	−0.985262	−	0.171054i	$-0.945283\pi$
$929$	−10.5000	+	18.1865i	−0.344494	+	0.596681i	0.640768	+	0.767735i	$0.278616\pi$
$930$		0			0
$931$	−4.50000	+	7.79423i	−0.147482	+	0.255446i
$932$	−0.500000	+	0.866025i	−0.0163780	+	0.0283676i
$933$		0			0
$934$	−14.5000	−	25.1147i	−0.474454	−	0.821779i
$935$	−15.0000			−0.490552
$936$	3.00000	+	5.19615i	0.0980581	+	0.169842i
$937$	−18.5000	+	32.0429i	−0.604369	+	1.04680i	0.387782	+	0.921751i	$0.373241\pi$
$937$	−18.5000	+	32.0429i	−0.604369	+	1.04680i	−0.992151	+	0.125046i	$0.960092\pi$
$938$	−12.0000			−0.391814
$939$		0			0
$940$	3.00000	+	5.19615i	0.0978492	+	0.169480i
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	0.998767	−	0.0496480i	$-0.0158099\pi$
$941$	14.0000	+	24.2487i	0.456387	+	0.790485i	−0.542380	+	0.840133i	$0.682477\pi$
$942$		0			0
$943$	−14.0000	−	24.2487i	−0.455903	−	0.789647i
$944$	−3.00000			−0.0976417
$945$		0			0
$946$	−12.5000	−	30.3109i	−0.406410	−	0.985492i
$947$	17.0000			0.552426			0.276213	−	0.961096i	$-0.410921\pi$
$947$	17.0000			0.552426			0.276213	+	0.961096i	$0.410921\pi$
$948$		0			0
$949$	11.0000	+	19.0526i	0.357075	+	0.618472i
$950$	1.00000			0.0324443
$951$		0			0
$952$	−6.00000	−	10.3923i	−0.194461	−	0.336817i
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	−0.631019	−	0.775768i	$-0.717363\pi$
$953$	11.0000	−	19.0526i	0.356325	−	0.617173i	0.987344	+	0.158595i	$0.0506963\pi$
$954$	−12.0000			−0.388514
$955$	−9.00000	+	15.5885i	−0.291233	+	0.504431i
$956$	−3.00000	−	5.19615i	−0.0970269	−	0.168056i
$957$		0			0
$958$	−14.0000	−	24.2487i	−0.452319	−	0.783440i
$959$	4.00000	−	6.92820i	0.129167	−	0.223723i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	20.0000			0.644826
$963$	4.50000	−	7.79423i	0.145010	−	0.251166i
$964$	−5.00000	+	8.66025i	−0.161039	+	0.278928i
$965$	−1.00000	−	1.73205i	−0.0321911	−	0.0557567i
$966$		0			0
$967$	−12.0000			−0.385894			−0.192947	−	0.981209i	$-0.561805\pi$
$967$	−12.0000			−0.385894			−0.192947	+	0.981209i	$0.561805\pi$
$968$	14.0000			0.449977
$969$		0			0
$970$	3.50000	+	6.06218i	0.112378	+	0.194645i
$971$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$971$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$972$		0			0
$973$	−36.0000			−1.15411
$974$	15.0000	−	25.9808i	0.480631	−	0.832477i
$975$		0			0
$976$	−7.00000	+	12.1244i	−0.224065	+	0.388091i
$977$	8.50000	+	14.7224i	0.271939	+	0.471012i	0.969358	−	0.245651i	$-0.0790017\pi$
$977$	8.50000	+	14.7224i	0.271939	+	0.471012i	−0.697419	+	0.716663i	$0.745668\pi$
$978$		0			0
$979$	−37.5000	−	64.9519i	−1.19851	−	2.07587i
$980$	4.50000	−	7.79423i	0.143747	−	0.248978i
$981$	30.0000			0.957826
$982$	−13.5000	+	23.3827i	−0.430802	+	0.746171i
$983$	−28.0000	−	48.4974i	−0.893061	−	1.54683i	−0.836186	−	0.548446i	$-0.815220\pi$
$983$	−28.0000	−	48.4974i	−0.893061	−	1.54683i	−0.0568755	−	0.998381i	$-0.518114\pi$
$984$		0			0
$985$	−20.0000			−0.637253
$986$	12.0000	+	20.7846i	0.382158	+	0.661917i
$987$		0			0
$988$	2.00000			0.0636285
$989$	16.0000	−	20.7846i	0.508770	−	0.660912i
$990$	15.0000			0.476731
$991$	−2.00000			−0.0635321			−0.0317660	−	0.999495i	$-0.510113\pi$
$991$	−2.00000			−0.0635321			−0.0317660	+	0.999495i	$0.510113\pi$
$992$		0			0
$993$		0			0
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$	−5.00000	−	8.66025i	−0.158511	−	0.274549i
$996$		0			0
$997$	32.0000			1.01345			0.506725	−	0.862108i	$-0.330856\pi$
$997$	32.0000			1.01345			0.506725	+	0.862108i	$0.330856\pi$
$998$	−21.5000	+	37.2391i	−0.680571	+	1.17878i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.e.c.251.1	yes	2
43.6	even	3	inner	430.2.e.c.221.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.e.c.221.1	✓	2	43.6	even	3	inner
430.2.e.c.251.1	yes	2	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{5} +(-2.00000 + 3.46410i) q^{7} +1.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(0.500000 + 0.866025i) q^{10} +5.00000 q^{11} +(-1.00000 + 1.73205i) q^{13} +(-2.00000 + 3.46410i) q^{14} +1.00000 q^{16} +(-1.50000 + 2.59808i) q^{17} +(1.50000 - 2.59808i) q^{18} +(-0.500000 - 0.866025i) q^{19} +(0.500000 + 0.866025i) q^{20} +5.00000 q^{22} +(2.00000 + 3.46410i) q^{23} +(-0.500000 + 0.866025i) q^{25} +(-1.00000 + 1.73205i) q^{26} +(-2.00000 + 3.46410i) q^{28} +(4.00000 - 6.92820i) q^{29} +1.00000 q^{32} +(-1.50000 + 2.59808i) q^{34} -4.00000 q^{35} +(1.50000 - 2.59808i) q^{36} +(-5.00000 - 8.66025i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(0.500000 + 0.866025i) q^{40} -7.00000 q^{41} +(-2.50000 - 6.06218i) q^{43} +5.00000 q^{44} +3.00000 q^{45} +(2.00000 + 3.46410i) q^{46} +6.00000 q^{47} +(-4.50000 - 7.79423i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.00000 + 1.73205i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(2.50000 + 4.33013i) q^{55} +(-2.00000 + 3.46410i) q^{56} +(4.00000 - 6.92820i) q^{58} -3.00000 q^{59} +(-7.00000 + 12.1244i) q^{61} +(6.00000 + 10.3923i) q^{63} +1.00000 q^{64} -2.00000 q^{65} +(1.50000 + 2.59808i) q^{67} +(-1.50000 + 2.59808i) q^{68} -4.00000 q^{70} +(-3.00000 + 5.19615i) q^{71} +(1.50000 - 2.59808i) q^{72} +(5.50000 - 9.52628i) q^{73} +(-5.00000 - 8.66025i) q^{74} +(-0.500000 - 0.866025i) q^{76} +(-10.0000 + 17.3205i) q^{77} +(3.00000 - 5.19615i) q^{79} +(0.500000 + 0.866025i) q^{80} +(-4.50000 - 7.79423i) q^{81} -7.00000 q^{82} +(-6.00000 - 10.3923i) q^{83} -3.00000 q^{85} +(-2.50000 - 6.06218i) q^{86} +5.00000 q^{88} +(-7.50000 - 12.9904i) q^{89} +3.00000 q^{90} +(-4.00000 - 6.92820i) q^{91} +(2.00000 + 3.46410i) q^{92} +6.00000 q^{94} +(0.500000 - 0.866025i) q^{95} +7.00000 q^{97} +(-4.50000 - 7.79423i) q^{98} +(7.50000 - 12.9904i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + 2 q^{4} + q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + 2 * q^4 + q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9	\( 2 q + 2 q^{2} + 2 q^{4} + q^{5} - 4 q^{7} + 2 q^{8} + 3 q^{9} + q^{10} + 10 q^{11} - 2 q^{13} - 4 q^{14} + 2 q^{16} - 3 q^{17} + 3 q^{18} - q^{19} + q^{20} + 10 q^{22} + 4 q^{23} - q^{25} - 2 q^{26} - 4 q^{28} + 8 q^{29} + 2 q^{32} - 3 q^{34} - 8 q^{35} + 3 q^{36} - 10 q^{37} - q^{38} + q^{40} - 14 q^{41} - 5 q^{43} + 10 q^{44} + 6 q^{45} + 4 q^{46} + 12 q^{47} - 9 q^{49} - q^{50} - 2 q^{52} - 4 q^{53} + 5 q^{55} - 4 q^{56} + 8 q^{58} - 6 q^{59} - 14 q^{61} + 12 q^{63} + 2 q^{64} - 4 q^{65} + 3 q^{67} - 3 q^{68} - 8 q^{70} - 6 q^{71} + 3 q^{72} + 11 q^{73} - 10 q^{74} - q^{76} - 20 q^{77} + 6 q^{79} + q^{80} - 9 q^{81} - 14 q^{82} - 12 q^{83} - 6 q^{85} - 5 q^{86} + 10 q^{88} - 15 q^{89} + 6 q^{90} - 8 q^{91} + 4 q^{92} + 12 q^{94} + q^{95} + 14 q^{97} - 9 q^{98} + 15 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + 2 * q^4 + q^5 - 4 * q^7 + 2 * q^8 + 3 * q^9 + q^10 + 10 * q^11 - 2 * q^13 - 4 * q^14 + 2 * q^16 - 3 * q^17 + 3 * q^18 - q^19 + q^20 + 10 * q^22 + 4 * q^23 - q^25 - 2 * q^26 - 4 * q^28 + 8 * q^29 + 2 * q^32 - 3 * q^34 - 8 * q^35 + 3 * q^36 - 10 * q^37 - q^38 + q^40 - 14 * q^41 - 5 * q^43 + 10 * q^44 + 6 * q^45 + 4 * q^46 + 12 * q^47 - 9 * q^49 - q^50 - 2 * q^52 - 4 * q^53 + 5 * q^55 - 4 * q^56 + 8 * q^58 - 6 * q^59 - 14 * q^61 + 12 * q^63 + 2 * q^64 - 4 * q^65 + 3 * q^67 - 3 * q^68 - 8 * q^70 - 6 * q^71 + 3 * q^72 + 11 * q^73 - 10 * q^74 - q^76 - 20 * q^77 + 6 * q^79 + q^80 - 9 * q^81 - 14 * q^82 - 12 * q^83 - 6 * q^85 - 5 * q^86 + 10 * q^88 - 15 * q^89 + 6 * q^90 - 8 * q^91 + 4 * q^92 + 12 * q^94 + q^95 + 14 * q^97 - 9 * q^98 + 15 * q^99

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