LMFDB - Embedded newform 525.2.r.d.499.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(424,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("525.424");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$525 = 3 \cdot 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	525.r (of order $6$ , 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$x^{4} - x^{2} + 1$ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			499.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.499
Dual form			525.2.r.d.424.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{2} +(0.866025 - 0.500000i) q^{3} +(1.00000 + 1.73205i) q^{4} -2.00000 q^{6} +(-2.59808 + 0.500000i) q^{7} +(0.500000 - 0.866025i) q^{9} +(3.00000 + 5.19615i) q^{11} +(1.73205 + 1.00000i) q^{12} -3.00000i q^{13} +(5.00000 + 1.73205i) q^{14} +(2.00000 - 3.46410i) q^{16} +(3.46410 - 2.00000i) q^{17} +(-1.73205 + 1.00000i) q^{18} +(0.500000 - 0.866025i) q^{19} +(-2.00000 + 1.73205i) q^{21} -12.0000i q^{22} +(3.46410 + 2.00000i) q^{23} +(-3.00000 + 5.19615i) q^{26} -1.00000i q^{27} +(-3.46410 - 4.00000i) q^{28} +8.00000 q^{29} +(-0.500000 - 0.866025i) q^{31} +(-6.92820 + 4.00000i) q^{32} +(5.19615 + 3.00000i) q^{33} -8.00000 q^{34} +2.00000 q^{36} +(6.06218 + 3.50000i) q^{37} +(-1.73205 + 1.00000i) q^{38} +(-1.50000 - 2.59808i) q^{39} -6.00000 q^{41} +(5.19615 - 1.00000i) q^{42} +1.00000i q^{43} +(-6.00000 + 10.3923i) q^{44} +(-4.00000 - 6.92820i) q^{46} +(1.73205 + 1.00000i) q^{47} -4.00000i q^{48} +(6.50000 - 2.59808i) q^{49} +(2.00000 - 3.46410i) q^{51} +(5.19615 - 3.00000i) q^{52} +(3.46410 - 2.00000i) q^{53} +(-1.00000 + 1.73205i) q^{54} -1.00000i q^{57} +(-13.8564 - 8.00000i) q^{58} +(-4.00000 - 6.92820i) q^{59} +(7.00000 - 12.1244i) q^{61} +2.00000i q^{62} +(-0.866025 + 2.50000i) q^{63} +8.00000 q^{64} +(-6.00000 - 10.3923i) q^{66} +(-6.06218 + 3.50000i) q^{67} +(6.92820 + 4.00000i) q^{68} +4.00000 q^{69} +6.00000 q^{71} +(0.866025 - 0.500000i) q^{73} +(-7.00000 - 12.1244i) q^{74} +2.00000 q^{76} +(-10.3923 - 12.0000i) q^{77} +6.00000i q^{78} +(-0.500000 + 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(10.3923 + 6.00000i) q^{82} +2.00000i q^{83} +(-5.00000 - 1.73205i) q^{84} +(1.00000 - 1.73205i) q^{86} +(6.92820 - 4.00000i) q^{87} +(-6.00000 + 10.3923i) q^{89} +(1.50000 + 7.79423i) q^{91} +8.00000i q^{92} +(-0.866025 - 0.500000i) q^{93} +(-2.00000 - 3.46410i) q^{94} +(-4.00000 + 6.92820i) q^{96} +6.00000i q^{97} +(-13.8564 - 2.00000i) q^{98} +6.00000 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 4 q^{4} - 8 q^{6} + 2 q^{9} + 12 q^{11} + 20 q^{14} + 8 q^{16} + 2 q^{19} - 8 q^{21} - 12 q^{26} + 32 q^{29} - 2 q^{31} - 32 q^{34} + 8 q^{36} - 6 q^{39} - 24 q^{41} - 24 q^{44} - 16 q^{46} + 26 q^{49}+ \cdots + 24 q^{99}+O(q^{100})$ 4 * q + 4 * q^4 - 8 * q^6 + 2 * q^9 + 12 * q^11 + 20 * q^14 + 8 * q^16 + 2 * q^19 - 8 * q^21 - 12 * q^26 + 32 * q^29 - 2 * q^31 - 32 * q^34 + 8 * q^36 - 6 * q^39 - 24 * q^41 - 24 * q^44 - 16 * q^46 + 26 * q^49 + 8 * q^51 - 4 * q^54 - 16 * q^59 + 28 * q^61 + 32 * q^64 - 24 * q^66 + 16 * q^69 + 24 * q^71 - 28 * q^74 + 8 * q^76 - 2 * q^79 - 2 * q^81 - 20 * q^84 + 4 * q^86 - 24 * q^89 + 6 * q^91 - 8 * q^94 - 16 * q^96 + 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$ .

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	−1.73205	−	1.00000i	−1.22474	−	0.707107i	−0.258819	−	0.965926i	$-0.583333\pi$
$2$	−1.73205	−	1.00000i	−1.22474	−	0.707107i	−0.965926	+	0.258819i	$0.916667\pi$
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$3$	0.866025	−	0.500000i	0.500000	−	0.288675i
$4$	1.00000	+	1.73205i	0.500000	+	0.866025i
$5$		0			0
$5$		0			0
$6$	−2.00000			−0.816497
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$7$	−2.59808	+	0.500000i	−0.981981	+	0.188982i
$8$		0			0
$9$	0.500000	−	0.866025i	0.166667	−	0.288675i
$10$		0			0
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$	1.73205	+	1.00000i	0.500000	+	0.288675i
$13$		−	3.00000i		−	0.832050i	−0.909353	−	0.416025i	$-0.863423\pi$
$13$		−	3.00000i		−	0.832050i	0.909353	−	0.416025i	$-0.136577\pi$
$14$	5.00000	+	1.73205i	1.33631	+	0.462910i
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	−0.0171533	−	0.999853i	$-0.505460\pi$
$17$	3.46410	−	2.00000i	0.840168	−	0.485071i	0.857321	+	0.514782i	$0.172127\pi$
$18$	−1.73205	+	1.00000i	−0.408248	+	0.235702i
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	−0.802955	−	0.596040i	$-0.796740\pi$
$19$	0.500000	−	0.866025i	0.114708	−	0.198680i	0.917663	+	0.397360i	$0.130073\pi$
$20$		0			0
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$		−	12.0000i		−	2.55841i
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	0.815604	−	0.578610i	$-0.196405\pi$
$23$	3.46410	+	2.00000i	0.722315	+	0.417029i	−0.0932891	+	0.995639i	$0.529738\pi$
$24$		0			0
$25$		0			0
$26$	−3.00000	+	5.19615i	−0.588348	+	1.01905i
$27$		−	1.00000i		−	0.192450i
$28$	−3.46410	−	4.00000i	−0.654654	−	0.755929i
$29$	8.00000			1.48556			0.742781	−	0.669534i	$-0.233506\pi$
$29$	8.00000			1.48556			0.742781	+	0.669534i	$0.233506\pi$
$30$		0			0
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	0.817625	−	0.575751i	$-0.195290\pi$
$31$	−0.500000	−	0.866025i	−0.0898027	−	0.155543i	−0.907428	+	0.420208i	$0.861957\pi$
$32$	−6.92820	+	4.00000i	−1.22474	+	0.707107i
$33$	5.19615	+	3.00000i	0.904534	+	0.522233i
$34$	−8.00000			−1.37199
$35$		0			0
$36$	2.00000			0.333333
$37$	6.06218	+	3.50000i	0.996616	+	0.575396i	0.907245	−	0.420602i	$-0.138181\pi$
$37$	6.06218	+	3.50000i	0.996616	+	0.575396i	0.0893706	+	0.995998i	$0.471514\pi$
$38$	−1.73205	+	1.00000i	−0.280976	+	0.162221i
$39$	−1.50000	−	2.59808i	−0.240192	−	0.416025i
$40$		0			0
$41$	−6.00000			−0.937043			−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000			−0.937043			−0.468521	+	0.883452i	$0.655213\pi$
$42$	5.19615	−	1.00000i	0.801784	−	0.154303i
$43$			1.00000i			0.152499i	0.997089	+	0.0762493i	$0.0242945\pi$
$43$			1.00000i			0.152499i	−0.997089	+	0.0762493i	$0.975706\pi$
$44$	−6.00000	+	10.3923i	−0.904534	+	1.56670i
$45$		0			0
$46$	−4.00000	−	6.92820i	−0.589768	−	1.02151i
$47$	1.73205	+	1.00000i	0.252646	+	0.145865i	0.620975	−	0.783830i	$-0.286737\pi$
$47$	1.73205	+	1.00000i	0.252646	+	0.145865i	−0.368329	+	0.929695i	$0.620070\pi$
$48$		−	4.00000i		−	0.577350i
$49$	6.50000	−	2.59808i	0.928571	−	0.371154i
$50$		0			0
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	5.19615	−	3.00000i	0.720577	−	0.416025i
$53$	3.46410	−	2.00000i	0.475831	−	0.274721i	−0.242846	−	0.970065i	$-0.578081\pi$
$53$	3.46410	−	2.00000i	0.475831	−	0.274721i	0.718677	+	0.695344i	$0.244748\pi$
$54$	−1.00000	+	1.73205i	−0.136083	+	0.235702i
$55$		0			0
$56$		0			0
$57$		−	1.00000i		−	0.132453i
$58$	−13.8564	−	8.00000i	−1.81944	−	1.05045i
$59$	−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	$-0.479608\pi$
$61$	7.00000	−	12.1244i	0.896258	−	1.55236i	0.832240	−	0.554416i	$-0.187058\pi$
$62$			2.00000i			0.254000i
$63$	−0.866025	+	2.50000i	−0.109109	+	0.314970i
$64$	8.00000			1.00000
$65$		0			0
$66$	−6.00000	−	10.3923i	−0.738549	−	1.27920i
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	−0.822292	−	0.569066i	$-0.807305\pi$
$67$	−6.06218	+	3.50000i	−0.740613	+	0.427593i	0.0816792	+	0.996659i	$0.473972\pi$
$68$	6.92820	+	4.00000i	0.840168	+	0.485071i
$69$	4.00000			0.481543
$70$		0			0
$71$	6.00000			0.712069			0.356034	−	0.934473i	$-0.384129\pi$
$71$	6.00000			0.712069			0.356034	+	0.934473i	$0.384129\pi$
$72$		0			0
$73$	0.866025	−	0.500000i	0.101361	−	0.0585206i	−0.448463	−	0.893801i	$-0.648028\pi$
$73$	0.866025	−	0.500000i	0.101361	−	0.0585206i	0.549823	+	0.835281i	$0.314695\pi$
$74$	−7.00000	−	12.1244i	−0.813733	−	1.40943i
$75$		0			0
$76$	2.00000			0.229416
$77$	−10.3923	−	12.0000i	−1.18431	−	1.36753i
$78$			6.00000i			0.679366i
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	10.3923	+	6.00000i	1.14764	+	0.662589i
$83$			2.00000i			0.219529i	0.993958	+	0.109764i	$0.0350096\pi$
$83$			2.00000i			0.219529i	−0.993958	+	0.109764i	$0.964990\pi$
$84$	−5.00000	−	1.73205i	−0.545545	−	0.188982i
$85$		0			0
$86$	1.00000	−	1.73205i	0.107833	−	0.186772i
$87$	6.92820	−	4.00000i	0.742781	−	0.428845i
$88$		0			0
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	0.350304	+	0.936636i	$0.386078\pi$
$89$	−6.00000	+	10.3923i	−0.635999	+	1.10158i	−0.986303	+	0.164946i	$0.947255\pi$
$90$		0			0
$91$	1.50000	+	7.79423i	0.157243	+	0.817057i
$92$			8.00000i			0.834058i
$93$	−0.866025	−	0.500000i	−0.0898027	−	0.0518476i
$94$	−2.00000	−	3.46410i	−0.206284	−	0.357295i
$95$		0			0
$96$	−4.00000	+	6.92820i	−0.408248	+	0.707107i
$97$			6.00000i			0.609208i	0.952479	+	0.304604i	$0.0985241\pi$
$97$			6.00000i			0.609208i	−0.952479	+	0.304604i	$0.901476\pi$
$98$	−13.8564	−	2.00000i	−1.39971	−	0.202031i
$99$	6.00000			0.603023
$100$		0			0
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	0.999996	−	0.00286291i	$-0.000911295\pi$
$101$	5.00000	+	8.66025i	0.497519	+	0.861727i	−0.502477	+	0.864590i	$0.667578\pi$
$102$	−6.92820	+	4.00000i	−0.685994	+	0.396059i
$103$	16.4545	+	9.50000i	1.62131	+	0.936063i	0.986571	+	0.163335i	$0.0522252\pi$
$103$	16.4545	+	9.50000i	1.62131	+	0.936063i	0.634738	+	0.772728i	$0.281108\pi$
$104$		0			0
$105$		0			0
$106$	−8.00000			−0.777029
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.909624	−	0.415432i	$-0.136370\pi$
$107$	10.3923	+	6.00000i	1.00466	+	0.580042i	0.0950377	+	0.995474i	$0.469703\pi$
$108$	1.73205	−	1.00000i	0.166667	−	0.0962250i
$109$	−7.50000	−	12.9904i	−0.718370	−	1.24425i	−0.961645	−	0.274296i	$-0.911555\pi$
$109$	−7.50000	−	12.9904i	−0.718370	−	1.24425i	0.243276	−	0.969957i	$-0.421778\pi$
$110$		0			0
$111$	7.00000			0.664411
$112$	−3.46410	+	10.0000i	−0.327327	+	0.944911i
$113$		−	6.00000i		−	0.564433i	−0.959351	−	0.282216i	$-0.908930\pi$
$113$		−	6.00000i		−	0.564433i	0.959351	−	0.282216i	$-0.0910696\pi$
$114$	−1.00000	+	1.73205i	−0.0936586	+	0.162221i
$115$		0			0
$116$	8.00000	+	13.8564i	0.742781	+	1.28654i
$117$	−2.59808	−	1.50000i	−0.240192	−	0.138675i
$118$			16.0000i			1.47292i
$119$	−8.00000	+	6.92820i	−0.733359	+	0.635107i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$	−24.2487	+	14.0000i	−2.19538	+	1.26750i
$123$	−5.19615	+	3.00000i	−0.468521	+	0.270501i
$124$	1.00000	−	1.73205i	0.0898027	−	0.155543i
$125$		0			0
$126$	4.00000	−	3.46410i	0.356348	−	0.308607i
$127$		−	5.00000i		−	0.443678i	−0.975083	−	0.221839i	$-0.928794\pi$
$127$		−	5.00000i		−	0.443678i	0.975083	−	0.221839i	$-0.0712060\pi$
$128$		0			0
$129$	0.500000	+	0.866025i	0.0440225	+	0.0762493i
$130$		0			0
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	−0.906399	−	0.422423i	$-0.861180\pi$
$131$	−1.00000	+	1.73205i	−0.0873704	+	0.151330i	0.819028	+	0.573753i	$0.194513\pi$
$132$			12.0000i			1.04447i
$133$	−0.866025	+	2.50000i	−0.0750939	+	0.216777i
$134$	14.0000			1.20942
$135$		0			0
$136$		0			0
$137$	−6.92820	+	4.00000i	−0.591916	+	0.341743i	−0.765855	−	0.643013i	$-0.777684\pi$
$137$	−6.92820	+	4.00000i	−0.591916	+	0.341743i	0.173939	+	0.984757i	$0.444351\pi$
$138$	−6.92820	−	4.00000i	−0.589768	−	0.340503i
$139$	−21.0000			−1.78120			−0.890598	−	0.454791i	$-0.849714\pi$
$139$	−21.0000			−1.78120			−0.890598	+	0.454791i	$0.849714\pi$
$140$		0			0
$141$	2.00000			0.168430
$142$	−10.3923	−	6.00000i	−0.872103	−	0.503509i
$143$	15.5885	−	9.00000i	1.30357	−	0.752618i
$144$	−2.00000	−	3.46410i	−0.166667	−	0.288675i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	4.33013	−	5.50000i	0.357143	−	0.453632i
$148$			14.0000i			1.15079i
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	−0.936245	−	0.351348i	$-0.885723\pi$
$149$	−2.00000	+	3.46410i	−0.163846	+	0.283790i	0.772399	+	0.635138i	$0.219057\pi$
$150$		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
$153$		−	4.00000i		−	0.323381i
$154$	6.00000	+	31.1769i	0.483494	+	2.51231i
$155$		0			0
$156$	3.00000	−	5.19615i	0.240192	−	0.416025i
$157$	−8.66025	+	5.00000i	−0.691164	+	0.399043i	−0.804048	−	0.594565i	$-0.797324\pi$
$157$	−8.66025	+	5.00000i	−0.691164	+	0.399043i	0.112884	+	0.993608i	$0.463991\pi$
$158$	1.73205	−	1.00000i	0.137795	−	0.0795557i
$159$	2.00000	−	3.46410i	0.158610	−	0.274721i
$160$		0			0
$161$	−10.0000	−	3.46410i	−0.788110	−	0.273009i
$162$			2.00000i			0.157135i
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	0.848339	−	0.529454i	$-0.177603\pi$
$163$	10.3923	+	6.00000i	0.813988	+	0.469956i	−0.0343508	+	0.999410i	$0.510936\pi$
$164$	−6.00000	−	10.3923i	−0.468521	−	0.811503i
$165$		0			0
$166$	2.00000	−	3.46410i	0.155230	−	0.268866i
$167$			10.0000i			0.773823i	0.922117	+	0.386912i	$0.126458\pi$
$167$			10.0000i			0.773823i	−0.922117	+	0.386912i	$0.873542\pi$
$168$		0			0
$169$	4.00000			0.307692
$170$		0			0
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	−1.73205	+	1.00000i	−0.132068	+	0.0762493i
$173$	−20.7846	−	12.0000i	−1.58022	−	0.912343i	−0.994826	−	0.101598i	$-0.967605\pi$
$173$	−20.7846	−	12.0000i	−1.58022	−	0.912343i	−0.585399	−	0.810745i	$-0.699062\pi$
$174$	−16.0000			−1.21296
$175$		0			0
$176$	24.0000			1.80907
$177$	−6.92820	−	4.00000i	−0.520756	−	0.300658i
$178$	20.7846	−	12.0000i	1.55787	−	0.899438i
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	0.977138	+	0.212607i	$0.0681952\pi$
$179$	9.00000	+	15.5885i	0.672692	+	1.16514i	−0.304446	+	0.952529i	$0.598471\pi$
$180$		0			0
$181$	13.0000			0.966282			0.483141	−	0.875542i	$-0.339496\pi$
$181$	13.0000			0.966282			0.483141	+	0.875542i	$0.339496\pi$
$182$	5.19615	−	15.0000i	0.385164	−	1.11187i
$183$		−	14.0000i		−	1.03491i
$184$		0			0
$185$		0			0
$186$	1.00000	+	1.73205i	0.0733236	+	0.127000i
$187$	20.7846	+	12.0000i	1.51992	+	0.877527i
$188$			4.00000i			0.291730i
$189$	0.500000	+	2.59808i	0.0363696	+	0.188982i
$190$		0			0
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	−0.988255	−	0.152813i	$-0.951167\pi$
$191$	−5.00000	+	8.66025i	−0.361787	+	0.626634i	0.626468	+	0.779447i	$0.284500\pi$
$192$	6.92820	−	4.00000i	0.500000	−	0.288675i
$193$	−7.79423	+	4.50000i	−0.561041	+	0.323917i	−0.753563	−	0.657376i	$-0.771667\pi$
$193$	−7.79423	+	4.50000i	−0.561041	+	0.323917i	0.192522	+	0.981293i	$0.438333\pi$
$194$	6.00000	−	10.3923i	0.430775	−	0.746124i
$195$		0			0
$196$	11.0000	+	8.66025i	0.785714	+	0.618590i
$197$		−	12.0000i		−	0.854965i	−0.904024	−	0.427482i	$-0.859401\pi$
$197$		−	12.0000i		−	0.854965i	0.904024	−	0.427482i	$-0.140599\pi$
$198$	−10.3923	−	6.00000i	−0.738549	−	0.426401i
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	0.972257	−	0.233915i	$-0.0751537\pi$
$199$	4.00000	+	6.92820i	0.283552	+	0.491127i	−0.688705	+	0.725042i	$0.741820\pi$
$200$		0			0
$201$	−3.50000	+	6.06218i	−0.246871	+	0.427593i
$202$		−	20.0000i		−	1.40720i
$203$	−20.7846	+	4.00000i	−1.45879	+	0.280745i
$204$	8.00000			0.560112
$205$		0			0
$206$	−19.0000	−	32.9090i	−1.32379	−	2.29288i
$207$	3.46410	−	2.00000i	0.240772	−	0.139010i
$208$	−10.3923	−	6.00000i	−0.720577	−	0.416025i
$209$	6.00000			0.415029
$210$		0			0
$211$	−20.0000			−1.37686			−0.688428	−	0.725304i	$-0.741699\pi$
$211$	−20.0000			−1.37686			−0.688428	+	0.725304i	$0.741699\pi$
$212$	6.92820	+	4.00000i	0.475831	+	0.274721i
$213$	5.19615	−	3.00000i	0.356034	−	0.205557i
$214$	−12.0000	−	20.7846i	−0.820303	−	1.42081i
$215$		0			0
$216$		0			0
$217$	1.73205	+	2.00000i	0.117579	+	0.135769i
$218$			30.0000i			2.03186i
$219$	0.500000	−	0.866025i	0.0337869	−	0.0585206i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−12.1244	−	7.00000i	−0.813733	−	0.469809i
$223$		−	24.0000i		−	1.60716i	−0.595198	−	0.803579i	$-0.702926\pi$
$223$		−	24.0000i		−	1.60716i	0.595198	−	0.803579i	$-0.297074\pi$
$224$	16.0000	−	13.8564i	1.06904	−	0.925820i
$225$		0			0
$226$	−6.00000	+	10.3923i	−0.399114	+	0.691286i
$227$	8.66025	−	5.00000i	0.574801	−	0.331862i	−0.184263	−	0.982877i	$-0.558990\pi$
$227$	8.66025	−	5.00000i	0.574801	−	0.331862i	0.759065	+	0.651015i	$0.225657\pi$
$228$	1.73205	−	1.00000i	0.114708	−	0.0662266i
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	−0.567300	−	0.823511i	$-0.692012\pi$
$229$	6.50000	−	11.2583i	0.429532	−	0.743971i	0.996832	+	0.0795401i	$0.0253452\pi$
$230$		0			0
$231$	−15.0000	−	5.19615i	−0.986928	−	0.341882i
$232$		0			0
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	0.320043	−	0.947403i	$-0.396303\pi$
$233$	−5.19615	−	3.00000i	−0.340411	−	0.196537i	−0.660454	+	0.750867i	$0.729636\pi$
$234$	3.00000	+	5.19615i	0.196116	+	0.339683i
$235$		0			0
$236$	8.00000	−	13.8564i	0.520756	−	0.901975i
$237$			1.00000i			0.0649570i
$238$	20.7846	−	4.00000i	1.34727	−	0.259281i
$239$	−14.0000			−0.905585			−0.452792	−	0.891616i	$-0.649572\pi$
$239$	−14.0000			−0.905585			−0.452792	+	0.891616i	$0.649572\pi$
$240$		0			0
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	0.995509	+	0.0946700i	$0.0301796\pi$
$241$	9.00000	+	15.5885i	0.579741	+	1.00414i	−0.415768	+	0.909471i	$0.636487\pi$
$242$	43.3013	−	25.0000i	2.78351	−	1.60706i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	28.0000			1.79252
$245$		0			0
$246$	12.0000			0.765092
$247$	−2.59808	−	1.50000i	−0.165312	−	0.0954427i
$248$		0			0
$249$	1.00000	+	1.73205i	0.0633724	+	0.109764i
$250$		0			0
$251$	12.0000			0.757433			0.378717	−	0.925513i	$-0.376365\pi$
$251$	12.0000			0.757433			0.378717	+	0.925513i	$0.376365\pi$
$252$	−5.19615	+	1.00000i	−0.327327	+	0.0629941i
$253$			24.0000i			1.50887i
$254$	−5.00000	+	8.66025i	−0.313728	+	0.543393i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−15.5885	−	9.00000i	−0.972381	−	0.561405i	−0.0724199	−	0.997374i	$-0.523072\pi$
$257$	−15.5885	−	9.00000i	−0.972381	−	0.561405i	−0.899961	+	0.435970i	$0.856405\pi$
$258$		−	2.00000i		−	0.124515i
$259$	−17.5000	−	6.06218i	−1.08740	−	0.376685i
$260$		0			0
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	3.46410	−	2.00000i	0.214013	−	0.123560i
$263$	3.46410	−	2.00000i	0.213606	−	0.123325i	−0.389380	−	0.921077i	$-0.627311\pi$
$263$	3.46410	−	2.00000i	0.213606	−	0.123325i	0.602986	+	0.797752i	$0.293977\pi$
$264$		0			0
$265$		0			0
$266$	4.00000	−	3.46410i	0.245256	−	0.212398i
$267$			12.0000i			0.734388i
$268$	−12.1244	−	7.00000i	−0.740613	−	0.427593i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$		0			0
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	−0.228380	−	0.973572i	$-0.573343\pi$
$271$	12.0000	−	20.7846i	0.728948	−	1.26258i	0.957328	−	0.289003i	$-0.0933238\pi$
$272$		−	16.0000i		−	0.970143i
$273$	5.19615	+	6.00000i	0.314485	+	0.363137i
$274$	16.0000			0.966595
$275$		0			0
$276$	4.00000	+	6.92820i	0.240772	+	0.417029i
$277$	6.06218	−	3.50000i	0.364241	−	0.210295i	−0.306699	−	0.951807i	$-0.599224\pi$
$277$	6.06218	−	3.50000i	0.364241	−	0.210295i	0.670940	+	0.741512i	$0.265891\pi$
$278$	36.3731	+	21.0000i	2.18151	+	1.25950i
$279$	−1.00000			−0.0598684
$280$		0			0
$281$	−12.0000			−0.715860			−0.357930	−	0.933748i	$-0.616517\pi$
$281$	−12.0000			−0.715860			−0.357930	+	0.933748i	$0.616517\pi$
$282$	−3.46410	−	2.00000i	−0.206284	−	0.119098i
$283$	−6.06218	+	3.50000i	−0.360359	+	0.208053i	−0.669238	−	0.743048i	$-0.733379\pi$
$283$	−6.06218	+	3.50000i	−0.360359	+	0.208053i	0.308879	+	0.951101i	$0.400046\pi$
$284$	6.00000	+	10.3923i	0.356034	+	0.616670i
$285$		0			0
$286$	−36.0000			−2.12872
$287$	15.5885	−	3.00000i	0.920158	−	0.177084i
$288$			8.00000i			0.471405i
$289$	−0.500000	+	0.866025i	−0.0294118	+	0.0509427i
$290$		0			0
$291$	3.00000	+	5.19615i	0.175863	+	0.304604i
$292$	1.73205	+	1.00000i	0.101361	+	0.0585206i
$293$		−	16.0000i		−	0.934730i	−0.884064	−	0.467365i	$-0.845203\pi$
$293$		−	16.0000i		−	0.934730i	0.884064	−	0.467365i	$-0.154797\pi$
$294$	−13.0000	+	5.19615i	−0.758175	+	0.303046i
$295$		0			0
$296$		0			0
$297$	5.19615	−	3.00000i	0.301511	−	0.174078i
$298$	6.92820	−	4.00000i	0.401340	−	0.231714i
$299$	6.00000	−	10.3923i	0.346989	−	0.601003i
$300$		0			0
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$			16.0000i			0.920697i
$303$	8.66025	+	5.00000i	0.497519	+	0.287242i
$304$	−2.00000	−	3.46410i	−0.114708	−	0.198680i
$305$		0			0
$306$	−4.00000	+	6.92820i	−0.228665	+	0.396059i
$307$		−	3.00000i		−	0.171219i	−0.996329	−	0.0856095i	$-0.972716\pi$
$307$		−	3.00000i		−	0.171219i	0.996329	−	0.0856095i	$-0.0272838\pi$
$308$	10.3923	−	30.0000i	0.592157	−	1.70941i
$309$	19.0000			1.08087
$310$		0			0
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	0.768345	−	0.640036i	$-0.221080\pi$
$311$	−3.00000	−	5.19615i	−0.170114	−	0.294647i	−0.938460	+	0.345389i	$0.887747\pi$
$312$		0			0
$313$	−9.52628	−	5.50000i	−0.538457	−	0.310878i	0.205996	−	0.978553i	$-0.433957\pi$
$313$	−9.52628	−	5.50000i	−0.538457	−	0.310878i	−0.744453	+	0.667674i	$0.767290\pi$
$314$	20.0000			1.12867
$315$		0			0
$316$	−2.00000			−0.112509
$317$	17.3205	+	10.0000i	0.972817	+	0.561656i	0.900094	−	0.435696i	$-0.143498\pi$
$317$	17.3205	+	10.0000i	0.972817	+	0.561656i	0.0727229	+	0.997352i	$0.476831\pi$
$318$	−6.92820	+	4.00000i	−0.388514	+	0.224309i
$319$	24.0000	+	41.5692i	1.34374	+	2.32743i
$320$		0			0
$321$	12.0000			0.669775
$322$	13.8564	+	16.0000i	0.772187	+	0.891645i
$323$		−	4.00000i		−	0.222566i
$324$	1.00000	−	1.73205i	0.0555556	−	0.0962250i
$325$		0			0
$326$	−12.0000	−	20.7846i	−0.664619	−	1.15115i
$327$	−12.9904	−	7.50000i	−0.718370	−	0.414751i
$328$		0			0
$329$	−5.00000	−	1.73205i	−0.275659	−	0.0954911i
$330$		0			0
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	−0.715445	−	0.698669i	$-0.753776\pi$
$331$	4.50000	−	7.79423i	0.247342	−	0.428410i	0.962788	+	0.270259i	$0.0871094\pi$
$332$	−3.46410	+	2.00000i	−0.190117	+	0.109764i
$333$	6.06218	−	3.50000i	0.332205	−	0.191799i
$334$	10.0000	−	17.3205i	0.547176	−	0.947736i
$335$		0			0
$336$	2.00000	+	10.3923i	0.109109	+	0.566947i
$337$		−	25.0000i		−	1.36184i	−0.732359	−	0.680918i	$-0.761581\pi$
$337$		−	25.0000i		−	1.36184i	0.732359	−	0.680918i	$-0.238419\pi$
$338$	−6.92820	−	4.00000i	−0.376845	−	0.217571i
$339$	−3.00000	−	5.19615i	−0.162938	−	0.282216i
$340$		0			0
$341$	3.00000	−	5.19615i	0.162459	−	0.281387i
$342$			2.00000i			0.108148i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$		0			0
$345$		0			0
$346$	24.0000	+	41.5692i	1.29025	+	2.23478i
$347$	−13.8564	+	8.00000i	−0.743851	+	0.429463i	−0.823468	−	0.567363i	$-0.807964\pi$
$347$	−13.8564	+	8.00000i	−0.743851	+	0.429463i	0.0796169	+	0.996826i	$0.474630\pi$
$348$	13.8564	+	8.00000i	0.742781	+	0.428845i
$349$	−2.00000			−0.107058			−0.0535288	−	0.998566i	$-0.517047\pi$
$349$	−2.00000			−0.107058			−0.0535288	+	0.998566i	$0.517047\pi$
$350$		0			0
$351$	−3.00000			−0.160128
$352$	−41.5692	−	24.0000i	−2.21565	−	1.27920i
$353$	−15.5885	+	9.00000i	−0.829690	+	0.479022i	−0.853746	−	0.520689i	$-0.825675\pi$
$353$	−15.5885	+	9.00000i	−0.829690	+	0.479022i	0.0240566	+	0.999711i	$0.492342\pi$
$354$	8.00000	+	13.8564i	0.425195	+	0.736460i
$355$		0			0
$356$	−24.0000			−1.27200
$357$	−3.46410	+	10.0000i	−0.183340	+	0.529256i
$358$		−	36.0000i		−	1.90266i
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	0.353529	+	0.935423i	$0.384981\pi$
$359$	−12.0000	+	20.7846i	−0.633336	+	1.09697i	−0.986865	+	0.161546i	$0.948352\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	−22.5167	−	13.0000i	−1.18345	−	0.683265i
$363$			25.0000i			1.31216i
$364$	−12.0000	+	10.3923i	−0.628971	+	0.544705i
$365$		0			0
$366$	−14.0000	+	24.2487i	−0.731792	+	1.26750i
$367$	−16.4545	+	9.50000i	−0.858917	+	0.495896i	−0.863649	−	0.504093i	$-0.831827\pi$
$367$	−16.4545	+	9.50000i	−0.858917	+	0.495896i	0.00473247	+	0.999989i	$0.498494\pi$
$368$	13.8564	−	8.00000i	0.722315	−	0.417029i
$369$	−3.00000	+	5.19615i	−0.156174	+	0.270501i
$370$		0			0
$371$	−8.00000	+	6.92820i	−0.415339	+	0.359694i
$372$		−	2.00000i		−	0.103695i
$373$	−9.52628	−	5.50000i	−0.493252	−	0.284779i	0.232671	−	0.972556i	$-0.425254\pi$
$373$	−9.52628	−	5.50000i	−0.493252	−	0.284779i	−0.725923	+	0.687776i	$0.758587\pi$
$374$	−24.0000	−	41.5692i	−1.24101	−	2.14949i
$375$		0			0
$376$		0			0
$377$		−	24.0000i		−	1.23606i
$378$	1.73205	−	5.00000i	0.0890871	−	0.257172i
$379$	−11.0000			−0.565032			−0.282516	−	0.959263i	$-0.591169\pi$
$379$	−11.0000			−0.565032			−0.282516	+	0.959263i	$0.591169\pi$
$380$		0			0
$381$	−2.50000	−	4.33013i	−0.128079	−	0.221839i
$382$	17.3205	−	10.0000i	0.886194	−	0.511645i
$383$	−24.2487	−	14.0000i	−1.23905	−	0.715367i	−0.270151	−	0.962818i	$-0.587074\pi$
$383$	−24.2487	−	14.0000i	−1.23905	−	0.715367i	−0.968900	+	0.247451i	$0.920407\pi$
$384$		0			0
$385$		0			0
$386$	18.0000			0.916176
$387$	0.866025	+	0.500000i	0.0440225	+	0.0254164i
$388$	−10.3923	+	6.00000i	−0.527589	+	0.304604i
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$		0			0
$393$			2.00000i			0.100887i
$394$	−12.0000	+	20.7846i	−0.604551	+	1.04711i
$395$		0			0
$396$	6.00000	+	10.3923i	0.301511	+	0.522233i
$397$	−32.0429	−	18.5000i	−1.60819	−	0.928488i	−0.989775	−	0.142636i	$-0.954442\pi$
$397$	−32.0429	−	18.5000i	−1.60819	−	0.928488i	−0.618414	−	0.785853i	$-0.712224\pi$
$398$		−	16.0000i		−	0.802008i
$399$	0.500000	+	2.59808i	0.0250313	+	0.130066i
$400$		0			0
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	−0.676425	−	0.736512i	$-0.736472\pi$
$401$	6.00000	−	10.3923i	0.299626	−	0.518967i	0.976050	+	0.217545i	$0.0698049\pi$
$402$	12.1244	−	7.00000i	0.604708	−	0.349128i
$403$	−2.59808	+	1.50000i	−0.129419	+	0.0747203i
$404$	−10.0000	+	17.3205i	−0.497519	+	0.861727i
$405$		0			0
$406$	40.0000	+	13.8564i	1.98517	+	0.687682i
$407$			42.0000i			2.08186i
$408$		0			0
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	0.921192	−	0.389109i	$-0.127217\pi$
$409$	2.50000	+	4.33013i	0.123617	+	0.214111i	−0.797574	+	0.603220i	$0.793884\pi$
$410$		0			0
$411$	−4.00000	+	6.92820i	−0.197305	+	0.341743i
$412$			38.0000i			1.87213i
$413$	13.8564	+	16.0000i	0.681829	+	0.787309i
$414$	−8.00000			−0.393179
$415$		0			0
$416$	12.0000	+	20.7846i	0.588348	+	1.01905i
$417$	−18.1865	+	10.5000i	−0.890598	+	0.514187i
$418$	−10.3923	−	6.00000i	−0.508304	−	0.293470i
$419$	−6.00000			−0.293119			−0.146560	−	0.989202i	$-0.546820\pi$
$419$	−6.00000			−0.293119			−0.146560	+	0.989202i	$0.546820\pi$
$420$		0			0
$421$	1.00000			0.0487370			0.0243685	−	0.999703i	$-0.492242\pi$
$421$	1.00000			0.0487370			0.0243685	+	0.999703i	$0.492242\pi$
$422$	34.6410	+	20.0000i	1.68630	+	0.973585i
$423$	1.73205	−	1.00000i	0.0842152	−	0.0486217i
$424$		0			0
$425$		0			0
$426$	−12.0000			−0.581402
$427$	−12.1244	+	35.0000i	−0.586739	+	1.69377i
$428$			24.0000i			1.16008i
$429$	9.00000	−	15.5885i	0.434524	−	0.752618i
$430$		0			0
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	0.889104	−	0.457705i	$-0.151328\pi$
$431$	1.00000	+	1.73205i	0.0481683	+	0.0834300i	−0.840936	+	0.541135i	$0.817995\pi$
$432$	−3.46410	−	2.00000i	−0.166667	−	0.0962250i
$433$		−	5.00000i		−	0.240285i	−0.992757	−	0.120142i	$-0.961665\pi$
$433$		−	5.00000i		−	0.240285i	0.992757	−	0.120142i	$-0.0383351\pi$
$434$	−1.00000	−	5.19615i	−0.0480015	−	0.249423i
$435$		0			0
$436$	15.0000	−	25.9808i	0.718370	−	1.24425i
$437$	3.46410	−	2.00000i	0.165710	−	0.0956730i
$438$	−1.73205	+	1.00000i	−0.0827606	+	0.0477818i
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	−0.609503	−	0.792784i	$-0.708631\pi$
$439$	8.00000	−	13.8564i	0.381819	−	0.661330i	0.991322	+	0.131453i	$0.0419644\pi$
$440$		0			0
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$			24.0000i			1.14156i
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.999774	−	0.0212481i	$-0.00676401\pi$
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.481486	+	0.876454i	$0.340097\pi$
$444$	7.00000	+	12.1244i	0.332205	+	0.575396i
$445$		0			0
$446$	−24.0000	+	41.5692i	−1.13643	+	1.96836i
$447$			4.00000i			0.189194i
$448$	−20.7846	+	4.00000i	−0.981981	+	0.188982i
$449$	−30.0000			−1.41579			−0.707894	−	0.706319i	$-0.750354\pi$
$449$	−30.0000			−1.41579			−0.707894	+	0.706319i	$0.750354\pi$
$450$		0			0
$451$	−18.0000	−	31.1769i	−0.847587	−	1.46806i
$452$	10.3923	−	6.00000i	0.488813	−	0.282216i
$453$	−6.92820	−	4.00000i	−0.325515	−	0.187936i
$454$	−20.0000			−0.938647
$455$		0			0
$456$		0			0
$457$	−12.9904	−	7.50000i	−0.607664	−	0.350835i	0.164386	−	0.986396i	$-0.447436\pi$
$457$	−12.9904	−	7.50000i	−0.607664	−	0.350835i	−0.772051	+	0.635561i	$0.780769\pi$
$458$	−22.5167	+	13.0000i	−1.05213	+	0.607450i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	−8.00000			−0.372597			−0.186299	−	0.982493i	$-0.559649\pi$
$461$	−8.00000			−0.372597			−0.186299	+	0.982493i	$0.559649\pi$
$462$	20.7846	+	24.0000i	0.966988	+	1.11658i
$463$			3.00000i			0.139422i	0.997567	+	0.0697109i	$0.0222077\pi$
$463$			3.00000i			0.139422i	−0.997567	+	0.0697109i	$0.977792\pi$
$464$	16.0000	−	27.7128i	0.742781	−	1.28654i
$465$		0			0
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$	19.0526	+	11.0000i	0.881647	+	0.509019i	0.871201	−	0.490926i	$-0.163342\pi$
$467$	19.0526	+	11.0000i	0.881647	+	0.509019i	0.0104461	+	0.999945i	$0.496675\pi$
$468$		−	6.00000i		−	0.277350i
$469$	14.0000	−	12.1244i	0.646460	−	0.559851i
$470$		0			0
$471$	−5.00000	+	8.66025i	−0.230388	+	0.399043i
$472$		0			0
$473$	−5.19615	+	3.00000i	−0.238919	+	0.137940i
$474$	1.00000	−	1.73205i	0.0459315	−	0.0795557i
$475$		0			0
$476$	−20.0000	−	6.92820i	−0.916698	−	0.317554i
$477$		−	4.00000i		−	0.183147i
$478$	24.2487	+	14.0000i	1.10911	+	0.640345i
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	0.816711	−	0.577047i	$-0.195795\pi$
$479$	−2.00000	−	3.46410i	−0.0913823	−	0.158279i	−0.908093	+	0.418769i	$0.862462\pi$
$480$		0			0
$481$	10.5000	−	18.1865i	0.478759	−	0.829235i
$482$		−	36.0000i		−	1.63976i
$483$	−10.3923	+	2.00000i	−0.472866	+	0.0910032i
$484$	−50.0000			−2.27273
$485$		0			0
$486$	1.00000	+	1.73205i	0.0453609	+	0.0785674i
$487$	11.2583	−	6.50000i	0.510164	−	0.294543i	−0.222737	−	0.974879i	$-0.571499\pi$
$487$	11.2583	−	6.50000i	0.510164	−	0.294543i	0.732901	+	0.680335i	$0.238166\pi$
$488$		0			0
$489$	12.0000			0.542659
$490$		0			0
$491$	−12.0000			−0.541552			−0.270776	−	0.962642i	$-0.587280\pi$
$491$	−12.0000			−0.541552			−0.270776	+	0.962642i	$0.587280\pi$
$492$	−10.3923	−	6.00000i	−0.468521	−	0.270501i
$493$	27.7128	−	16.0000i	1.24812	−	0.720604i
$494$	3.00000	+	5.19615i	0.134976	+	0.233786i
$495$		0			0
$496$	−4.00000			−0.179605
$497$	−15.5885	+	3.00000i	−0.699238	+	0.134568i
$498$		−	4.00000i		−	0.179244i
$499$	14.5000	−	25.1147i	0.649109	−	1.12429i	−0.334227	−	0.942493i	$-0.608475\pi$
$499$	14.5000	−	25.1147i	0.649109	−	1.12429i	0.983336	−	0.181797i	$-0.0581915\pi$
$500$		0			0
$501$	5.00000	+	8.66025i	0.223384	+	0.386912i
$502$	−20.7846	−	12.0000i	−0.927663	−	0.535586i
$503$		−	2.00000i		−	0.0891756i	−0.999005	−	0.0445878i	$-0.985803\pi$
$503$		−	2.00000i		−	0.0891756i	0.999005	−	0.0445878i	$-0.0141974\pi$
$504$		0			0
$505$		0			0
$506$	24.0000	−	41.5692i	1.06693	−	1.84798i
$507$	3.46410	−	2.00000i	0.153846	−	0.0888231i
$508$	8.66025	−	5.00000i	0.384237	−	0.221839i
$509$	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
$511$	−2.00000	+	1.73205i	−0.0884748	+	0.0766214i
$512$			32.0000i			1.41421i
$513$	−0.866025	−	0.500000i	−0.0382360	−	0.0220755i
$514$	18.0000	+	31.1769i	0.793946	+	1.37515i
$515$		0			0
$516$	−1.00000	+	1.73205i	−0.0440225	+	0.0762493i
$517$			12.0000i			0.527759i
$518$	24.2487	+	28.0000i	1.06543	+	1.23025i
$519$	−24.0000			−1.05348
$520$		0			0
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	0.818884	−	0.573959i	$-0.194593\pi$
$521$	−2.00000	−	3.46410i	−0.0876216	−	0.151765i	−0.906505	+	0.422194i	$0.861260\pi$
$522$	−13.8564	+	8.00000i	−0.606478	+	0.350150i
$523$	−9.52628	−	5.50000i	−0.416555	−	0.240498i	0.277047	−	0.960856i	$-0.410644\pi$
$523$	−9.52628	−	5.50000i	−0.416555	−	0.240498i	−0.693602	+	0.720358i	$0.743977\pi$
$524$	−4.00000			−0.174741
$525$		0			0
$526$	−8.00000			−0.348817
$527$	−3.46410	−	2.00000i	−0.150899	−	0.0871214i
$528$	20.7846	−	12.0000i	0.904534	−	0.522233i
$529$	−3.50000	−	6.06218i	−0.152174	−	0.263573i
$530$		0			0
$531$	−8.00000			−0.347170
$532$	−5.19615	+	1.00000i	−0.225282	+	0.0433555i
$533$			18.0000i			0.779667i
$534$	12.0000	−	20.7846i	0.519291	−	0.899438i
$535$		0			0
$536$		0			0
$537$	15.5885	+	9.00000i	0.672692	+	0.388379i
$538$			20.0000i			0.862261i
$539$	33.0000	+	25.9808i	1.42141	+	1.11907i
$540$		0			0
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	−0.831978	−	0.554809i	$-0.812791\pi$
$541$	1.50000	−	2.59808i	0.0644900	−	0.111700i	0.896468	+	0.443109i	$0.146125\pi$
$542$	−41.5692	+	24.0000i	−1.78555	+	1.03089i
$543$	11.2583	−	6.50000i	0.483141	−	0.278942i
$544$	−16.0000	+	27.7128i	−0.685994	+	1.18818i
$545$		0			0
$546$	−3.00000	−	15.5885i	−0.128388	−	0.667124i
$547$		−	36.0000i		−	1.53925i	−0.638497	−	0.769624i	$-0.720443\pi$
$547$		−	36.0000i		−	1.53925i	0.638497	−	0.769624i	$-0.279557\pi$
$548$	−13.8564	−	8.00000i	−0.591916	−	0.341743i
$549$	−7.00000	−	12.1244i	−0.298753	−	0.517455i
$550$		0			0
$551$	4.00000	−	6.92820i	0.170406	−	0.295151i
$552$		0			0
$553$	0.866025	−	2.50000i	0.0368271	−	0.106311i
$554$	−14.0000			−0.594803
$555$		0			0
$556$	−21.0000	−	36.3731i	−0.890598	−	1.54256i
$557$	8.66025	−	5.00000i	0.366947	−	0.211857i	−0.305177	−	0.952296i	$-0.598716\pi$
$557$	8.66025	−	5.00000i	0.366947	−	0.211857i	0.672124	+	0.740439i	$0.265382\pi$
$558$	1.73205	+	1.00000i	0.0733236	+	0.0423334i
$559$	3.00000			0.126886
$560$		0			0
$561$	24.0000			1.01328
$562$	20.7846	+	12.0000i	0.876746	+	0.506189i
$563$	−22.5167	+	13.0000i	−0.948964	+	0.547885i	−0.892759	−	0.450535i	$-0.851233\pi$
$563$	−22.5167	+	13.0000i	−0.948964	+	0.547885i	−0.0562051	+	0.998419i	$0.517900\pi$
$564$	2.00000	+	3.46410i	0.0842152	+	0.145865i
$565$		0			0
$566$	14.0000			0.588464
$567$	1.73205	+	2.00000i	0.0727393	+	0.0839921i
$568$		0			0
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	−0.613369	−	0.789797i	$-0.710186\pi$
$569$	9.00000	−	15.5885i	0.377300	−	0.653502i	0.990668	+	0.136295i	$0.0435194\pi$
$570$		0			0
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	0.895704	−	0.444651i	$-0.146672\pi$
$571$	1.50000	+	2.59808i	0.0627730	+	0.108726i	−0.832931	+	0.553377i	$0.813339\pi$
$572$	31.1769	+	18.0000i	1.30357	+	0.752618i
$573$			10.0000i			0.417756i
$574$	−30.0000	−	10.3923i	−1.25218	−	0.433766i
$575$		0			0
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	25.1147	−	14.5000i	1.04554	−	0.603643i	0.124143	−	0.992264i	$-0.460382\pi$
$577$	25.1147	−	14.5000i	1.04554	−	0.603643i	0.921397	+	0.388621i	$0.127049\pi$
$578$	1.73205	−	1.00000i	0.0720438	−	0.0415945i
$579$	−4.50000	+	7.79423i	−0.187014	+	0.323917i
$580$		0			0
$581$	−1.00000	−	5.19615i	−0.0414870	−	0.215573i
$582$		−	12.0000i		−	0.497416i
$583$	20.7846	+	12.0000i	0.860811	+	0.496989i
$584$		0			0
$585$		0			0
$586$	−16.0000	+	27.7128i	−0.660954	+	1.14481i
$587$		−	12.0000i		−	0.495293i	−0.968850	−	0.247647i	$-0.920343\pi$
$587$		−	12.0000i		−	0.495293i	0.968850	−	0.247647i	$-0.0796572\pi$
$588$	13.8564	+	2.00000i	0.571429	+	0.0824786i
$589$	−1.00000			−0.0412043
$590$		0			0
$591$	−6.00000	−	10.3923i	−0.246807	−	0.427482i
$592$	24.2487	−	14.0000i	0.996616	−	0.575396i
$593$	15.5885	+	9.00000i	0.640141	+	0.369586i	0.784669	−	0.619915i	$-0.212833\pi$
$593$	15.5885	+	9.00000i	0.640141	+	0.369586i	−0.144528	+	0.989501i	$0.546166\pi$
$594$	−12.0000			−0.492366
$595$		0			0
$596$	−8.00000			−0.327693
$597$	6.92820	+	4.00000i	0.283552	+	0.163709i
$598$	−20.7846	+	12.0000i	−0.849946	+	0.490716i
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	0.822270	−	0.569097i	$-0.192707\pi$
$599$	−2.00000	−	3.46410i	−0.0817178	−	0.141539i	−0.903988	+	0.427558i	$0.859374\pi$
$600$		0			0
$601$	−33.0000			−1.34610			−0.673049	−	0.739598i	$-0.735016\pi$
$601$	−33.0000			−1.34610			−0.673049	+	0.739598i	$0.735016\pi$
$602$	−1.73205	+	5.00000i	−0.0705931	+	0.203785i
$603$			7.00000i			0.285062i
$604$	8.00000	−	13.8564i	0.325515	−	0.563809i
$605$		0			0
$606$	−10.0000	−	17.3205i	−0.406222	−	0.703598i
$607$	30.3109	+	17.5000i	1.23028	+	0.710303i	0.967088	−	0.254440i	$-0.0818912\pi$
$607$	30.3109	+	17.5000i	1.23028	+	0.710303i	0.263193	+	0.964743i	$0.415225\pi$
$608$			8.00000i			0.324443i
$609$	−16.0000	+	13.8564i	−0.648353	+	0.561490i
$610$		0			0
$611$	3.00000	−	5.19615i	0.121367	−	0.210214i
$612$	6.92820	−	4.00000i	0.280056	−	0.161690i
$613$	−25.9808	+	15.0000i	−1.04935	+	0.605844i	−0.922468	−	0.386073i	$-0.873831\pi$
$613$	−25.9808	+	15.0000i	−1.04935	+	0.605844i	−0.126885	+	0.991917i	$0.540498\pi$
$614$	−3.00000	+	5.19615i	−0.121070	+	0.209700i
$615$		0			0
$616$		0			0
$617$		−	18.0000i		−	0.724653i	−0.932051	−	0.362326i	$-0.881983\pi$
$617$		−	18.0000i		−	0.724653i	0.932051	−	0.362326i	$-0.118017\pi$
$618$	−32.9090	−	19.0000i	−1.32379	−	0.764292i
$619$	1.50000	+	2.59808i	0.0602901	+	0.104425i	0.894595	−	0.446878i	$-0.147464\pi$
$619$	1.50000	+	2.59808i	0.0602901	+	0.104425i	−0.834305	+	0.551303i	$0.814131\pi$
$620$		0			0
$621$	2.00000	−	3.46410i	0.0802572	−	0.139010i
$622$			12.0000i			0.481156i
$623$	10.3923	−	30.0000i	0.416359	−	1.20192i
$624$	−12.0000			−0.480384
$625$		0			0
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$	5.19615	−	3.00000i	0.207514	−	0.119808i
$628$	−17.3205	−	10.0000i	−0.691164	−	0.399043i
$629$	28.0000			1.11643
$630$		0			0
$631$	24.0000			0.955425			0.477712	−	0.878516i	$-0.341466\pi$
$631$	24.0000			0.955425			0.477712	+	0.878516i	$0.341466\pi$
$632$		0			0
$633$	−17.3205	+	10.0000i	−0.688428	+	0.397464i
$634$	−20.0000	−	34.6410i	−0.794301	−	1.37577i
$635$		0			0
$636$	8.00000			0.317221
$637$	−7.79423	−	19.5000i	−0.308819	−	0.772618i
$638$		−	96.0000i		−	3.80068i
$639$	3.00000	−	5.19615i	0.118678	−	0.205557i
$640$		0			0
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	0.722862	−	0.690992i	$-0.242826\pi$
$641$	−6.00000	−	10.3923i	−0.236986	−	0.410471i	−0.959848	+	0.280521i	$0.909493\pi$
$642$	−20.7846	−	12.0000i	−0.820303	−	0.473602i
$643$			1.00000i			0.0394362i	0.999806	+	0.0197181i	$0.00627687\pi$
$643$			1.00000i			0.0394362i	−0.999806	+	0.0197181i	$0.993723\pi$
$644$	−4.00000	−	20.7846i	−0.157622	−	0.819028i
$645$		0			0
$646$	−4.00000	+	6.92820i	−0.157378	+	0.272587i
$647$	−25.9808	+	15.0000i	−1.02141	+	0.589711i	−0.914512	−	0.404559i	$-0.867425\pi$
$647$	−25.9808	+	15.0000i	−1.02141	+	0.589711i	−0.106897	+	0.994270i	$0.534092\pi$
$648$		0			0
$649$	24.0000	−	41.5692i	0.942082	−	1.63173i
$650$		0			0
$651$	2.50000	+	0.866025i	0.0979827	+	0.0339422i
$652$			24.0000i			0.939913i
$653$	−12.1244	−	7.00000i	−0.474463	−	0.273931i	0.243643	−	0.969865i	$-0.421657\pi$
$653$	−12.1244	−	7.00000i	−0.474463	−	0.273931i	−0.718106	+	0.695934i	$0.754991\pi$
$654$	15.0000	+	25.9808i	0.586546	+	1.01593i
$655$		0			0
$656$	−12.0000	+	20.7846i	−0.468521	+	0.811503i
$657$		−	1.00000i		−	0.0390137i
$658$	6.92820	+	8.00000i	0.270089	+	0.311872i
$659$	12.0000			0.467454			0.233727	−	0.972302i	$-0.424908\pi$
$659$	12.0000			0.467454			0.233727	+	0.972302i	$0.424908\pi$
$660$		0			0
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	0.550911	−	0.834564i	$-0.314280\pi$
$661$	−11.5000	−	19.9186i	−0.447298	−	0.774743i	−0.998209	+	0.0598209i	$0.980947\pi$
$662$	−15.5885	+	9.00000i	−0.605863	+	0.349795i
$663$	−10.3923	−	6.00000i	−0.403604	−	0.233021i
$664$		0			0
$665$		0			0
$666$	−14.0000			−0.542489
$667$	27.7128	+	16.0000i	1.07304	+	0.619522i
$668$	−17.3205	+	10.0000i	−0.670151	+	0.386912i
$669$	−12.0000	−	20.7846i	−0.463947	−	0.803579i
$670$		0			0
$671$	84.0000			3.24278
$672$	6.92820	−	20.0000i	0.267261	−	0.771517i
$673$		−	37.0000i		−	1.42625i	−0.701039	−	0.713123i	$-0.747280\pi$
$673$		−	37.0000i		−	1.42625i	0.701039	−	0.713123i	$-0.252720\pi$
$674$	−25.0000	+	43.3013i	−0.962964	+	1.66790i
$675$		0			0
$676$	4.00000	+	6.92820i	0.153846	+	0.266469i
$677$	13.8564	+	8.00000i	0.532545	+	0.307465i	0.742052	−	0.670342i	$-0.233853\pi$
$677$	13.8564	+	8.00000i	0.532545	+	0.307465i	−0.209507	+	0.977807i	$0.567186\pi$
$678$			12.0000i			0.460857i
$679$	−3.00000	−	15.5885i	−0.115129	−	0.598230i
$680$		0			0
$681$	5.00000	−	8.66025i	0.191600	−	0.331862i
$682$	−10.3923	+	6.00000i	−0.397942	+	0.229752i
$683$	−41.5692	+	24.0000i	−1.59060	+	0.918334i	−0.597398	+	0.801945i	$0.703799\pi$
$683$	−41.5692	+	24.0000i	−1.59060	+	0.918334i	−0.993204	+	0.116390i	$0.962868\pi$
$684$	1.00000	−	1.73205i	0.0382360	−	0.0662266i
$685$		0			0
$686$	37.0000	−	1.73205i	1.41267	−	0.0661300i
$687$		−	13.0000i		−	0.495981i
$688$	3.46410	+	2.00000i	0.132068	+	0.0762493i
$689$	−6.00000	−	10.3923i	−0.228582	−	0.395915i
$690$		0			0
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	0.486312	+	0.873785i	$0.338342\pi$
$691$	−13.5000	+	23.3827i	−0.513564	+	0.889519i	−0.999876	+	0.0157341i	$0.994991\pi$
$692$		−	48.0000i		−	1.82469i
$693$	−15.5885	+	3.00000i	−0.592157	+	0.113961i
$694$	32.0000			1.21470
$695$		0			0
$696$		0			0
$697$	−20.7846	+	12.0000i	−0.787273	+	0.454532i
$698$	3.46410	+	2.00000i	0.131118	+	0.0757011i
$699$	−6.00000			−0.226941
$700$		0			0
$701$	−44.0000			−1.66186			−0.830929	−	0.556379i	$-0.812190\pi$
$701$	−44.0000			−1.66186			−0.830929	+	0.556379i	$0.812190\pi$
$702$	5.19615	+	3.00000i	0.196116	+	0.113228i
$703$	6.06218	−	3.50000i	0.228639	−	0.132005i
$704$	24.0000	+	41.5692i	0.904534	+	1.56670i
$705$		0			0
$706$	36.0000			1.35488
$707$	−17.3205	−	20.0000i	−0.651405	−	0.752177i
$708$		−	16.0000i		−	0.601317i
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	−0.999908	−	0.0135434i	$-0.995689\pi$
$709$	−13.0000	+	22.5167i	−0.488225	+	0.845631i	0.511683	+	0.859174i	$0.329022\pi$
$710$		0			0
$711$	0.500000	+	0.866025i	0.0187515	+	0.0324785i
$712$		0			0
$713$		−	4.00000i		−	0.149801i
$714$	16.0000	−	13.8564i	0.598785	−	0.518563i
$715$		0			0
$716$	−18.0000	+	31.1769i	−0.672692	+	1.16514i
$717$	−12.1244	+	7.00000i	−0.452792	+	0.261420i
$718$	41.5692	−	24.0000i	1.55135	−	0.895672i
$719$	−17.0000	+	29.4449i	−0.633993	+	1.09811i	0.352735	+	0.935723i	$0.385252\pi$
$719$	−17.0000	+	29.4449i	−0.633993	+	1.09811i	−0.986728	+	0.162385i	$0.948081\pi$
$720$		0			0
$721$	−47.5000	−	16.4545i	−1.76899	−	0.612797i
$722$		−	36.0000i		−	1.33978i
$723$	15.5885	+	9.00000i	0.579741	+	0.334714i
$724$	13.0000	+	22.5167i	0.483141	+	0.836825i
$725$		0			0
$726$	25.0000	−	43.3013i	0.927837	−	1.60706i
$727$		−	7.00000i		−	0.259616i	−0.991539	−	0.129808i	$-0.958564\pi$
$727$		−	7.00000i		−	0.259616i	0.991539	−	0.129808i	$-0.0414360\pi$
$728$		0			0
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	2.00000	+	3.46410i	0.0739727	+	0.128124i
$732$	24.2487	−	14.0000i	0.896258	−	0.517455i
$733$	37.2391	+	21.5000i	1.37546	+	0.794121i	0.991609	−	0.129275i	$-0.0412651\pi$
$733$	37.2391	+	21.5000i	1.37546	+	0.794121i	0.383849	+	0.923396i	$0.374598\pi$
$734$	38.0000			1.40261
$735$		0			0
$736$	−32.0000			−1.17954
$737$	−36.3731	−	21.0000i	−1.33982	−	0.773545i
$738$	10.3923	−	6.00000i	0.382546	−	0.220863i
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	0.945818	+	0.324697i	$0.105262\pi$
$739$	20.5000	+	35.5070i	0.754105	+	1.30615i	−0.191714	+	0.981451i	$0.561404\pi$
$740$		0			0
$741$	−3.00000			−0.110208
$742$	20.7846	−	4.00000i	0.763027	−	0.146845i
$743$			6.00000i			0.220119i	0.993925	+	0.110059i	$0.0351041\pi$
$743$			6.00000i			0.220119i	−0.993925	+	0.110059i	$0.964896\pi$
$744$		0			0
$745$		0			0
$746$	11.0000	+	19.0526i	0.402739	+	0.697564i
$747$	1.73205	+	1.00000i	0.0633724	+	0.0365881i
$748$			48.0000i			1.75505i
$749$	−30.0000	−	10.3923i	−1.09618	−	0.379727i
$750$		0			0
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	0.470311	+	0.882501i	$0.344142\pi$
$751$	−14.5000	+	25.1147i	−0.529113	+	0.916450i	−0.999424	+	0.0339490i	$0.989192\pi$
$752$	6.92820	−	4.00000i	0.252646	−	0.145865i
$753$	10.3923	−	6.00000i	0.378717	−	0.218652i
$754$	−24.0000	+	41.5692i	−0.874028	+	1.51386i
$755$		0			0
$756$	−4.00000	+	3.46410i	−0.145479	+	0.125988i
$757$			22.0000i			0.799604i	0.916602	+	0.399802i	$0.130921\pi$
$757$			22.0000i			0.799604i	−0.916602	+	0.399802i	$0.869079\pi$
$758$	19.0526	+	11.0000i	0.692020	+	0.399538i
$759$	12.0000	+	20.7846i	0.435572	+	0.754434i
$760$		0			0
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	−0.736543	−	0.676391i	$-0.763543\pi$
$761$	6.00000	−	10.3923i	0.217500	−	0.376721i	0.954043	+	0.299670i	$0.0968765\pi$
$762$			10.0000i			0.362262i
$763$	25.9808	+	30.0000i	0.940567	+	1.08607i
$764$	−20.0000			−0.723575
$765$		0			0
$766$	28.0000	+	48.4974i	1.01168	+	1.75228i
$767$	−20.7846	+	12.0000i	−0.750489	+	0.433295i
$768$	−13.8564	−	8.00000i	−0.500000	−	0.288675i
$769$	49.0000			1.76699			0.883493	−	0.468445i	$-0.155186\pi$
$769$	49.0000			1.76699			0.883493	+	0.468445i	$0.155186\pi$
$770$		0			0
$771$	−18.0000			−0.648254
$772$	−15.5885	−	9.00000i	−0.561041	−	0.323917i
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	−0.192740	−	0.981250i	$-0.561737\pi$
$773$	15.5885	−	9.00000i	0.560678	−	0.323708i	0.753418	+	0.657542i	$0.228404\pi$
$774$	−1.00000	−	1.73205i	−0.0359443	−	0.0622573i
$775$		0			0
$776$		0			0
$777$	−18.1865	+	3.50000i	−0.652438	+	0.125562i
$778$		−	12.0000i		−	0.430221i
$779$	−3.00000	+	5.19615i	−0.107486	+	0.186171i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$	−27.7128	−	16.0000i	−0.991008	−	0.572159i
$783$		−	8.00000i		−	0.285897i
$784$	4.00000	−	27.7128i	0.142857	−	0.989743i
$785$		0			0
$786$	2.00000	−	3.46410i	0.0713376	−	0.123560i
$787$	27.7128	−	16.0000i	0.987855	−	0.570338i	0.0832226	−	0.996531i	$-0.473479\pi$
$787$	27.7128	−	16.0000i	0.987855	−	0.570338i	0.904632	+	0.426193i	$0.140145\pi$
$788$	20.7846	−	12.0000i	0.740421	−	0.427482i
$789$	2.00000	−	3.46410i	0.0712019	−	0.123325i
$790$		0			0
$791$	3.00000	+	15.5885i	0.106668	+	0.554262i
$792$		0			0
$793$	−36.3731	−	21.0000i	−1.29165	−	0.745732i
$794$	37.0000	+	64.0859i	1.31308	+	2.27432i
$795$		0			0
$796$	−8.00000	+	13.8564i	−0.283552	+	0.491127i
$797$			36.0000i			1.27519i	0.770374	+	0.637593i	$0.220070\pi$
$797$			36.0000i			1.27519i	−0.770374	+	0.637593i	$0.779930\pi$
$798$	1.73205	−	5.00000i	0.0613139	−	0.176998i
$799$	8.00000			0.283020
$800$		0			0
$801$	6.00000	+	10.3923i	0.212000	+	0.367194i
$802$	−20.7846	+	12.0000i	−0.733930	+	0.423735i
$803$	5.19615	+	3.00000i	0.183368	+	0.105868i
$804$	−14.0000			−0.493742
$805$		0			0
$806$	6.00000			0.211341
$807$	−8.66025	−	5.00000i	−0.304855	−	0.176008i
$808$		0			0
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	−0.953251	−	0.302180i	$-0.902286\pi$
$809$	−21.0000	−	36.3731i	−0.738321	−	1.27881i	0.214930	−	0.976629i	$-0.431048\pi$
$810$		0			0
$811$	−48.0000			−1.68551			−0.842754	−	0.538299i	$-0.819067\pi$
$811$	−48.0000			−1.68551			−0.842754	+	0.538299i	$0.819067\pi$
$812$	−27.7128	−	32.0000i	−0.972529	−	1.12298i
$813$		−	24.0000i		−	0.841717i
$814$	42.0000	−	72.7461i	1.47210	−	2.54975i
$815$		0			0
$816$	−8.00000	−	13.8564i	−0.280056	−	0.485071i
$817$	0.866025	+	0.500000i	0.0302984	+	0.0174928i
$818$		−	10.0000i		−	0.349642i
$819$	7.50000	+	2.59808i	0.262071	+	0.0907841i
$820$		0			0
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.181250	+	0.983437i	$0.558014\pi$
$821$	−27.0000	+	46.7654i	−0.942306	+	1.63212i	−0.761056	+	0.648686i	$0.775319\pi$
$822$	13.8564	−	8.00000i	0.483298	−	0.279032i
$823$	6.92820	−	4.00000i	0.241502	−	0.139431i	−0.374365	−	0.927281i	$-0.622139\pi$
$823$	6.92820	−	4.00000i	0.241502	−	0.139431i	0.615867	+	0.787850i	$0.288806\pi$
$824$		0			0
$825$		0			0
$826$	−8.00000	−	41.5692i	−0.278356	−	1.44638i
$827$			30.0000i			1.04320i	0.853189	+	0.521601i	$0.174665\pi$
$827$			30.0000i			1.04320i	−0.853189	+	0.521601i	$0.825335\pi$
$828$	6.92820	+	4.00000i	0.240772	+	0.139010i
$829$	28.5000	+	49.3634i	0.989846	+	1.71446i	0.618024	+	0.786159i	$0.287934\pi$
$829$	28.5000	+	49.3634i	0.989846	+	1.71446i	0.371822	+	0.928304i	$0.378733\pi$
$830$		0			0
$831$	3.50000	−	6.06218i	0.121414	−	0.210295i
$832$		−	24.0000i		−	0.832050i
$833$	17.3205	−	22.0000i	0.600120	−	0.762255i
$834$	42.0000			1.45434
$835$		0			0
$836$	6.00000	+	10.3923i	0.207514	+	0.359425i
$837$	−0.866025	+	0.500000i	−0.0299342	+	0.0172825i
$838$	10.3923	+	6.00000i	0.358996	+	0.207267i
$839$	−24.0000			−0.828572			−0.414286	−	0.910147i	$-0.635969\pi$
$839$	−24.0000			−0.828572			−0.414286	+	0.910147i	$0.635969\pi$
$840$		0			0
$841$	35.0000			1.20690
$842$	−1.73205	−	1.00000i	−0.0596904	−	0.0344623i
$843$	−10.3923	+	6.00000i	−0.357930	+	0.206651i
$844$	−20.0000	−	34.6410i	−0.688428	−	1.19239i
$845$		0			0
$846$	−4.00000			−0.137523
$847$	21.6506	−	62.5000i	0.743925	−	2.14753i
$848$		−	16.0000i		−	0.549442i
$849$	−3.50000	+	6.06218i	−0.120120	+	0.208053i
$850$		0			0
$851$	14.0000	+	24.2487i	0.479914	+	0.831235i
$852$	10.3923	+	6.00000i	0.356034	+	0.205557i
$853$		−	9.00000i		−	0.308154i	−0.988059	−	0.154077i	$-0.950760\pi$
$853$		−	9.00000i		−	0.308154i	0.988059	−	0.154077i	$-0.0492404\pi$
$854$	56.0000	−	48.4974i	1.91628	−	1.65955i
$855$		0			0
$856$		0			0
$857$	10.3923	−	6.00000i	0.354994	−	0.204956i	−0.311888	−	0.950119i	$-0.600962\pi$
$857$	10.3923	−	6.00000i	0.354994	−	0.204956i	0.666883	+	0.745163i	$0.267628\pi$
$858$	−31.1769	+	18.0000i	−1.06436	+	0.614510i
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	0.291858	+	0.956462i	$0.405727\pi$
$859$	−20.0000	+	34.6410i	−0.682391	+	1.18194i	−0.974249	+	0.225475i	$0.927607\pi$
$860$		0			0
$861$	12.0000	−	10.3923i	0.408959	−	0.354169i
$862$		−	4.00000i		−	0.136241i
$863$	5.19615	+	3.00000i	0.176879	+	0.102121i	0.585826	−	0.810437i	$-0.300770\pi$
$863$	5.19615	+	3.00000i	0.176879	+	0.102121i	−0.408946	+	0.912558i	$0.634104\pi$
$864$	4.00000	+	6.92820i	0.136083	+	0.235702i
$865$		0			0
$866$	−5.00000	+	8.66025i	−0.169907	+	0.294287i
$867$			1.00000i			0.0339618i
$868$	−1.73205	+	5.00000i	−0.0587896	+	0.169711i
$869$	−6.00000			−0.203536
$870$		0			0
$871$	10.5000	+	18.1865i	0.355779	+	0.616227i
$872$		0			0
$873$	5.19615	+	3.00000i	0.175863	+	0.101535i
$874$	−8.00000			−0.270604
$875$		0			0
$876$	2.00000			0.0675737
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	0.142548	−	0.989788i	$-0.454470\pi$
$877$	−19.0526	−	11.0000i	−0.643359	−	0.371444i	−0.785907	+	0.618344i	$0.787804\pi$
$878$	−27.7128	+	16.0000i	−0.935262	+	0.539974i
$879$	−8.00000	−	13.8564i	−0.269833	−	0.467365i
$880$		0			0
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$	−8.66025	+	11.0000i	−0.291606	+	0.370389i
$883$			7.00000i			0.235569i	0.993039	+	0.117784i	$0.0375792\pi$
$883$			7.00000i			0.235569i	−0.993039	+	0.117784i	$0.962421\pi$
$884$	12.0000	−	20.7846i	0.403604	−	0.699062i
$885$		0			0
$886$	−36.0000	−	62.3538i	−1.20944	−	2.09482i
$887$	8.66025	+	5.00000i	0.290783	+	0.167884i	0.638295	−	0.769792i	$-0.279640\pi$
$887$	8.66025	+	5.00000i	0.290783	+	0.167884i	−0.347512	+	0.937676i	$0.612973\pi$
$888$		0			0
$889$	2.50000	+	12.9904i	0.0838473	+	0.435683i
$890$		0			0
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$	41.5692	−	24.0000i	1.39184	−	0.803579i
$893$	1.73205	−	1.00000i	0.0579609	−	0.0334637i
$894$	4.00000	−	6.92820i	0.133780	−	0.231714i
$895$		0			0
$896$		0			0
$897$		−	12.0000i		−	0.400668i
$898$	51.9615	+	30.0000i	1.73398	+	1.00111i
$899$	−4.00000	−	6.92820i	−0.133407	−	0.231069i
$900$		0			0
$901$	8.00000	−	13.8564i	0.266519	−	0.461624i
$902$			72.0000i			2.39734i
$903$	−1.73205	−	2.00000i	−0.0576390	−	0.0665558i
$904$		0			0
$905$		0			0
$906$	8.00000	+	13.8564i	0.265782	+	0.460348i
$907$	−26.8468	+	15.5000i	−0.891433	+	0.514669i	−0.874411	−	0.485186i	$-0.838752\pi$
$907$	−26.8468	+	15.5000i	−0.891433	+	0.514669i	−0.0170220	+	0.999855i	$0.505419\pi$
$908$	17.3205	+	10.0000i	0.574801	+	0.331862i
$909$	10.0000			0.331679
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	−3.46410	−	2.00000i	−0.114708	−	0.0662266i
$913$	−10.3923	+	6.00000i	−0.343935	+	0.198571i
$914$	15.0000	+	25.9808i	0.496156	+	0.859367i
$915$		0			0
$916$	26.0000			0.859064
$917$	1.73205	−	5.00000i	0.0571974	−	0.165115i
$918$			8.00000i			0.264039i
$919$	−4.50000	+	7.79423i	−0.148441	+	0.257108i	−0.930652	−	0.365907i	$-0.880759\pi$
$919$	−4.50000	+	7.79423i	−0.148441	+	0.257108i	0.782210	+	0.623015i	$0.214092\pi$
$920$		0			0
$921$	−1.50000	−	2.59808i	−0.0494267	−	0.0856095i
$922$	13.8564	+	8.00000i	0.456336	+	0.263466i
$923$		−	18.0000i		−	0.592477i
$924$	−6.00000	−	31.1769i	−0.197386	−	1.02565i
$925$		0			0
$926$	3.00000	−	5.19615i	0.0985861	−	0.170756i
$927$	16.4545	−	9.50000i	0.540436	−	0.312021i
$928$	−55.4256	+	32.0000i	−1.81944	+	1.05045i
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	−0.957708	−	0.287742i	$-0.907096\pi$
$929$	−7.00000	+	12.1244i	−0.229663	+	0.397787i	0.728046	+	0.685529i	$0.240429\pi$
$930$		0			0
$931$	1.00000	−	6.92820i	0.0327737	−	0.227063i
$932$		−	12.0000i		−	0.393073i
$933$	−5.19615	−	3.00000i	−0.170114	−	0.0982156i
$934$	−22.0000	−	38.1051i	−0.719862	−	1.24684i
$935$		0			0
$936$		0			0
$937$			29.0000i			0.947389i	0.880689	+	0.473694i	$0.157080\pi$
$937$			29.0000i			0.947389i	−0.880689	+	0.473694i	$0.842920\pi$
$938$	−36.3731	+	7.00000i	−1.18762	+	0.228558i
$939$	−11.0000			−0.358971
$940$		0			0
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	17.3205	−	10.0000i	0.564333	−	0.325818i
$943$	−20.7846	−	12.0000i	−0.676840	−	0.390774i
$944$	−32.0000			−1.04151
$945$		0			0
$946$	12.0000			0.390154
$947$	22.5167	+	13.0000i	0.731693	+	0.422443i	0.819041	−	0.573735i	$-0.194506\pi$
$947$	22.5167	+	13.0000i	0.731693	+	0.422443i	−0.0873481	+	0.996178i	$0.527839\pi$
$948$	−1.73205	+	1.00000i	−0.0562544	+	0.0324785i
$949$	−1.50000	−	2.59808i	−0.0486921	−	0.0843371i
$950$		0			0
$951$	20.0000			0.648544
$952$		0			0
$953$			4.00000i			0.129573i	0.997899	+	0.0647864i	$0.0206366\pi$
$953$			4.00000i			0.129573i	−0.997899	+	0.0647864i	$0.979363\pi$
$954$	−4.00000	+	6.92820i	−0.129505	+	0.224309i
$955$		0			0
$956$	−14.0000	−	24.2487i	−0.452792	−	0.784259i
$957$	41.5692	+	24.0000i	1.34374	+	0.775810i
$958$			8.00000i			0.258468i
$959$	16.0000	−	13.8564i	0.516667	−	0.447447i
$960$		0			0
$961$	15.0000	−	25.9808i	0.483871	−	0.838089i
$962$	−36.3731	+	21.0000i	−1.17271	+	0.677067i
$963$	10.3923	−	6.00000i	0.334887	−	0.193347i
$964$	−18.0000	+	31.1769i	−0.579741	+	1.00414i
$965$		0			0
$966$	20.0000	+	6.92820i	0.643489	+	0.222911i
$967$		−	55.0000i		−	1.76868i	−0.466843	−	0.884340i	$-0.654609\pi$
$967$		−	55.0000i		−	1.76868i	0.466843	−	0.884340i	$-0.345391\pi$
$968$		0			0
$969$	−2.00000	−	3.46410i	−0.0642493	−	0.111283i
$970$		0			0
$971$	26.0000	−	45.0333i	0.834380	−	1.44519i	−0.0601548	−	0.998189i	$-0.519159\pi$
$971$	26.0000	−	45.0333i	0.834380	−	1.44519i	0.894534	−	0.446999i	$-0.147507\pi$
$972$		−	2.00000i		−	0.0641500i
$973$	54.5596	−	10.5000i	1.74910	−	0.336615i
$974$	−26.0000			−0.833094
$975$		0			0
$976$	−28.0000	−	48.4974i	−0.896258	−	1.55236i
$977$	19.0526	−	11.0000i	0.609545	−	0.351921i	−0.163242	−	0.986586i	$-0.552195\pi$
$977$	19.0526	−	11.0000i	0.609545	−	0.351921i	0.772787	+	0.634665i	$0.218862\pi$
$978$	−20.7846	−	12.0000i	−0.664619	−	0.383718i
$979$	−72.0000			−2.30113
$980$		0			0
$981$	−15.0000			−0.478913
$982$	20.7846	+	12.0000i	0.663264	+	0.382935i
$983$	27.7128	−	16.0000i	0.883901	−	0.510321i	0.0119587	−	0.999928i	$-0.496193\pi$
$983$	27.7128	−	16.0000i	0.883901	−	0.510321i	0.871943	+	0.489608i	$0.162860\pi$
$984$		0			0
$985$		0			0
$986$	−64.0000			−2.03818
$987$	−5.19615	+	1.00000i	−0.165395	+	0.0318304i
$988$		−	6.00000i		−	0.190885i
$989$	−2.00000	+	3.46410i	−0.0635963	+	0.110152i
$990$		0			0
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	0.960211	−	0.279276i	$-0.0900944\pi$
$991$	7.50000	+	12.9904i	0.238245	+	0.412653i	−0.721966	+	0.691929i	$0.756761\pi$
$992$	6.92820	+	4.00000i	0.219971	+	0.127000i
$993$		−	9.00000i		−	0.285606i
$994$	30.0000	+	10.3923i	0.951542	+	0.329624i
$995$		0			0
$996$	−2.00000	+	3.46410i	−0.0633724	+	0.109764i
$997$	21.6506	−	12.5000i	0.685682	−	0.395879i	−0.116310	−	0.993213i	$-0.537107\pi$
$997$	21.6506	−	12.5000i	0.685682	−	0.395879i	0.801993	+	0.597334i	$0.203773\pi$
$998$	−50.2295	+	29.0000i	−1.58999	+	0.917979i
$999$	3.50000	−	6.06218i	0.110735	−	0.191799i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.r.d.499.1		4
5.2	odd	4		105.2.i.b.16.1	✓	2
5.3	odd	4		525.2.i.a.226.1		2
5.4	even	2	inner	525.2.r.d.499.2		4
7.4	even	3	inner	525.2.r.d.424.2		4
15.2	even	4		315.2.j.a.226.1		2
20.7	even	4		1680.2.bg.l.961.1		2
35.2	odd	12		735.2.a.b.1.1		1
35.4	even	6	inner	525.2.r.d.424.1		4
35.12	even	12		735.2.a.a.1.1		1
35.17	even	12		735.2.i.f.361.1		2
35.18	odd	12		525.2.i.a.151.1		2
35.23	odd	12		3675.2.a.o.1.1		1
35.27	even	4		735.2.i.f.226.1		2
35.32	odd	12		105.2.i.b.46.1	yes	2
35.33	even	12		3675.2.a.p.1.1		1
105.2	even	12		2205.2.a.k.1.1		1
105.32	even	12		315.2.j.a.46.1		2
105.47	odd	12		2205.2.a.m.1.1		1
140.67	even	12		1680.2.bg.l.1201.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.i.b.16.1	✓	2	5.2	odd	4
105.2.i.b.46.1	yes	2	35.32	odd	12
315.2.j.a.46.1		2	105.32	even	12
315.2.j.a.226.1		2	15.2	even	4
525.2.i.a.151.1		2	35.18	odd	12
525.2.i.a.226.1		2	5.3	odd	4
525.2.r.d.424.1		4	35.4	even	6	inner
525.2.r.d.424.2		4	7.4	even	3	inner
525.2.r.d.499.1		4	1.1	even	1	trivial
525.2.r.d.499.2		4	5.4	even	2	inner
735.2.a.a.1.1		1	35.12	even	12
735.2.a.b.1.1		1	35.2	odd	12
735.2.i.f.226.1		2	35.27	even	4
735.2.i.f.361.1		2	35.17	even	12
1680.2.bg.l.961.1		2	20.7	even	4
1680.2.bg.l.1201.1		2	140.67	even	12
2205.2.a.k.1.1		1	105.2	even	12
2205.2.a.m.1.1		1	105.47	odd	12
3675.2.a.o.1.1		1	35.23	odd	12
3675.2.a.p.1.1		1	35.33	even	12

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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	525.2.r.d.499.1

Level	$525$
Weight	$2$
Character	525.499
Analytic conductor	$4.192$
Analytic rank	$0$
Dimension	$4$
Inner twists	$4$