LMFDB - Embedded newform 975.2.w.b.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$975 = 3 \cdot 5^{2} \cdot 13$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	975.w (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:	$7.78541419707$
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:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.199
Dual form			975.2.w.b.49.2

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 1.50000i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-1.50000 + 0.866025i) q^{6} +(-0.866025 - 1.50000i) q^{7} +1.73205 q^{8} +(0.500000 + 0.866025i) q^{9} +(3.00000 + 1.73205i) q^{11} +1.00000i q^{12} +(3.46410 + 1.00000i) q^{13} -3.00000 q^{14} +(2.50000 - 4.33013i) q^{16} +(5.19615 - 3.00000i) q^{17} +1.73205 q^{18} +(-1.50000 + 0.866025i) q^{19} +1.73205i q^{21} +(5.19615 - 3.00000i) q^{22} +(-5.19615 - 3.00000i) q^{23} +(-1.50000 - 0.866025i) q^{24} +(4.50000 - 4.33013i) q^{26} -1.00000i q^{27} +(-0.866025 + 1.50000i) q^{28} +(-3.00000 + 5.19615i) q^{29} -3.46410i q^{31} +(-2.59808 - 4.50000i) q^{32} +(-1.73205 - 3.00000i) q^{33} -10.3923i q^{34} +(0.500000 - 0.866025i) q^{36} +(3.46410 - 6.00000i) q^{37} +3.00000i q^{38} +(-2.50000 - 2.59808i) q^{39} +(-3.00000 - 1.73205i) q^{41} +(2.59808 + 1.50000i) q^{42} +(-4.33013 + 2.50000i) q^{43} -3.46410i q^{44} +(-9.00000 + 5.19615i) q^{46} +6.92820 q^{47} +(-4.33013 + 2.50000i) q^{48} +(2.00000 - 3.46410i) q^{49} -6.00000 q^{51} +(-0.866025 - 3.50000i) q^{52} -12.0000i q^{53} +(-1.50000 - 0.866025i) q^{54} +(-1.50000 - 2.59808i) q^{56} +1.73205 q^{57} +(5.19615 + 9.00000i) q^{58} +(-9.00000 + 5.19615i) q^{59} +(1.00000 + 1.73205i) q^{61} +(-5.19615 - 3.00000i) q^{62} +(0.866025 - 1.50000i) q^{63} +1.00000 q^{64} -6.00000 q^{66} +(-4.33013 + 7.50000i) q^{67} +(-5.19615 - 3.00000i) q^{68} +(3.00000 + 5.19615i) q^{69} +(3.00000 - 1.73205i) q^{71} +(0.866025 + 1.50000i) q^{72} +8.66025 q^{73} +(-6.00000 - 10.3923i) q^{74} +(1.50000 + 0.866025i) q^{76} -6.00000i q^{77} +(-6.06218 + 1.50000i) q^{78} +11.0000 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-5.19615 + 3.00000i) q^{82} -3.46410 q^{83} +(1.50000 - 0.866025i) q^{84} +8.66025i q^{86} +(5.19615 - 3.00000i) q^{87} +(5.19615 + 3.00000i) q^{88} +(3.00000 + 1.73205i) q^{89} +(-1.50000 - 6.06218i) q^{91} +6.00000i q^{92} +(-1.73205 + 3.00000i) q^{93} +(6.00000 - 10.3923i) q^{94} +5.19615i q^{96} +(3.46410 + 6.00000i) q^{97} +(-3.46410 - 6.00000i) q^{98} +3.46410i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q - 2 q^{4} - 6 q^{6} + 2 q^{9} + 12 q^{11} - 12 q^{14} + 10 q^{16} - 6 q^{19} - 6 q^{24} + 18 q^{26} - 12 q^{29} + 2 q^{36} - 10 q^{39} - 12 q^{41} - 36 q^{46} + 8 q^{49} - 24 q^{51} - 6 q^{54} - 6 q^{56}+ \cdots + 24 q^{94}+O(q^{100})$ 4 * q - 2 * q^4 - 6 * q^6 + 2 * q^9 + 12 * q^11 - 12 * q^14 + 10 * q^16 - 6 * q^19 - 6 * q^24 + 18 * q^26 - 12 * q^29 + 2 * q^36 - 10 * q^39 - 12 * q^41 - 36 * q^46 + 8 * q^49 - 24 * q^51 - 6 * q^54 - 6 * q^56 - 36 * q^59 + 4 * q^61 + 4 * q^64 - 24 * q^66 + 12 * q^69 + 12 * q^71 - 24 * q^74 + 6 * q^76 + 44 * q^79 - 2 * q^81 + 6 * q^84 + 12 * q^89 - 6 * q^91 + 24 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$ .

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

Display

a_p

with

p

up to: 50 250 1000 (See

a_n

instead) (See

a_n

instead) (See

a_n

instead) Display

a_n

with

n

up to: 50 250 1000 (See only

a_p

) (See only

a_p

) (See only

a_p

)

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

$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	−0.378467	−	0.925615i	$-0.623549\pi$
$2$	0.866025	−	1.50000i	0.612372	−	1.06066i	0.990839	−	0.135045i	$-0.0431180\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.50000	+	0.866025i	−0.612372	+	0.353553i
$7$	−0.866025	−	1.50000i	−0.327327	−	0.566947i	0.654654	−	0.755929i	$-0.272814\pi$
$7$	−0.866025	−	1.50000i	−0.327327	−	0.566947i	−0.981981	+	0.188982i	$0.939481\pi$
$8$	1.73205			0.612372
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.878668	−	0.477432i	$-0.158432\pi$
$11$	3.00000	+	1.73205i	0.904534	+	0.522233i	0.0258656	+	0.999665i	$0.491766\pi$
$12$			1.00000i			0.288675i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$13$	3.46410	+	1.00000i	0.960769	+	0.277350i
$14$	−3.00000			−0.801784
$15$		0			0
$16$	2.50000	−	4.33013i	0.625000	−	1.08253i
$17$	5.19615	−	3.00000i	1.26025	−	0.727607i	0.287129	−	0.957892i	$-0.407299\pi$
$17$	5.19615	−	3.00000i	1.26025	−	0.727607i	0.973123	+	0.230285i	$0.0739659\pi$
$18$	1.73205			0.408248
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	−0.662094	−	0.749421i	$-0.730332\pi$
$19$	−1.50000	+	0.866025i	−0.344124	+	0.198680i	0.317970	+	0.948101i	$0.396999\pi$
$20$		0			0
$21$			1.73205i			0.377964i
$22$	5.19615	−	3.00000i	1.10782	−	0.639602i
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.151642	−	0.988436i	$-0.548456\pi$
$23$	−5.19615	−	3.00000i	−1.08347	−	0.625543i	−0.931831	+	0.362892i	$0.881789\pi$
$24$	−1.50000	−	0.866025i	−0.306186	−	0.176777i
$25$		0			0
$26$	4.50000	−	4.33013i	0.882523	−	0.849208i
$27$		−	1.00000i		−	0.192450i
$28$	−0.866025	+	1.50000i	−0.163663	+	0.283473i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$		−	3.46410i		−	0.622171i	−0.950382	−	0.311086i	$-0.899307\pi$
$31$		−	3.46410i		−	0.622171i	0.950382	−	0.311086i	$-0.100693\pi$
$32$	−2.59808	−	4.50000i	−0.459279	−	0.795495i
$33$	−1.73205	−	3.00000i	−0.301511	−	0.522233i
$34$		−	10.3923i		−	1.78227i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.46410	−	6.00000i	0.569495	−	0.986394i	−0.427121	−	0.904194i	$-0.640472\pi$
$37$	3.46410	−	6.00000i	0.569495	−	0.986394i	0.996616	−	0.0821995i	$-0.0261945\pi$
$38$			3.00000i			0.486664i
$39$	−2.50000	−	2.59808i	−0.400320	−	0.416025i
$40$		0			0
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	0.247099	−	0.968990i	$-0.420523\pi$
$41$	−3.00000	−	1.73205i	−0.468521	−	0.270501i	−0.715621	+	0.698489i	$0.753856\pi$
$42$	2.59808	+	1.50000i	0.400892	+	0.231455i
$43$	−4.33013	+	2.50000i	−0.660338	+	0.381246i	−0.792406	−	0.609994i	$-0.791172\pi$
$43$	−4.33013	+	2.50000i	−0.660338	+	0.381246i	0.132068	+	0.991241i	$0.457838\pi$
$44$		−	3.46410i		−	0.522233i
$45$		0			0
$46$	−9.00000	+	5.19615i	−1.32698	+	0.766131i
$47$	6.92820			1.01058			0.505291	−	0.862949i	$-0.331385\pi$
$47$	6.92820			1.01058			0.505291	+	0.862949i	$0.331385\pi$
$48$	−4.33013	+	2.50000i	−0.625000	+	0.360844i
$49$	2.00000	−	3.46410i	0.285714	−	0.494872i
$50$		0			0
$51$	−6.00000			−0.840168
$52$	−0.866025	−	3.50000i	−0.120096	−	0.485363i
$53$		−	12.0000i		−	1.64833i	−0.566352	−	0.824163i	$-0.691646\pi$
$53$		−	12.0000i		−	1.64833i	0.566352	−	0.824163i	$-0.308354\pi$
$54$	−1.50000	−	0.866025i	−0.204124	−	0.117851i
$55$		0			0
$56$	−1.50000	−	2.59808i	−0.200446	−	0.347183i
$57$	1.73205			0.229416
$58$	5.19615	+	9.00000i	0.682288	+	1.18176i
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.954080	−	0.299552i	$-0.903163\pi$
$59$	−9.00000	+	5.19615i	−1.17170	+	0.676481i	−0.217620	+	0.976034i	$0.569829\pi$
$60$		0			0
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	0.922916	−	0.385002i	$-0.125799\pi$
$61$	1.00000	+	1.73205i	0.128037	+	0.221766i	−0.794879	+	0.606768i	$0.792466\pi$
$62$	−5.19615	−	3.00000i	−0.659912	−	0.381000i
$63$	0.866025	−	1.50000i	0.109109	−	0.188982i
$64$	1.00000			0.125000
$65$		0			0
$66$	−6.00000			−0.738549
$67$	−4.33013	+	7.50000i	−0.529009	+	0.916271i	0.470418	+	0.882443i	$0.344103\pi$
$67$	−4.33013	+	7.50000i	−0.529009	+	0.916271i	−0.999428	+	0.0338274i	$0.989230\pi$
$68$	−5.19615	−	3.00000i	−0.630126	−	0.363803i
$69$	3.00000	+	5.19615i	0.361158	+	0.625543i
$70$		0			0
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	−0.311305	−	0.950310i	$-0.600766\pi$
$71$	3.00000	−	1.73205i	0.356034	−	0.205557i	0.667340	+	0.744753i	$0.267433\pi$
$72$	0.866025	+	1.50000i	0.102062	+	0.176777i
$73$	8.66025			1.01361			0.506803	−	0.862062i	$-0.330827\pi$
$73$	8.66025			1.01361			0.506803	+	0.862062i	$0.330827\pi$
$74$	−6.00000	−	10.3923i	−0.697486	−	1.20808i
$75$		0			0
$76$	1.50000	+	0.866025i	0.172062	+	0.0993399i
$77$		−	6.00000i		−	0.683763i
$78$	−6.06218	+	1.50000i	−0.686406	+	0.169842i
$79$	11.0000			1.23760			0.618798	−	0.785550i	$-0.287620\pi$
$79$	11.0000			1.23760			0.618798	+	0.785550i	$0.287620\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−5.19615	+	3.00000i	−0.573819	+	0.331295i
$83$	−3.46410			−0.380235			−0.190117	−	0.981761i	$-0.560887\pi$
$83$	−3.46410			−0.380235			−0.190117	+	0.981761i	$0.560887\pi$
$84$	1.50000	−	0.866025i	0.163663	−	0.0944911i
$85$		0			0
$86$			8.66025i			0.933859i
$87$	5.19615	−	3.00000i	0.557086	−	0.321634i
$88$	5.19615	+	3.00000i	0.553912	+	0.319801i
$89$	3.00000	+	1.73205i	0.317999	+	0.183597i	0.650500	−	0.759506i	$-0.274559\pi$
$89$	3.00000	+	1.73205i	0.317999	+	0.183597i	−0.332501	+	0.943103i	$0.607893\pi$
$90$		0			0
$91$	−1.50000	−	6.06218i	−0.157243	−	0.635489i
$92$			6.00000i			0.625543i
$93$	−1.73205	+	3.00000i	−0.179605	+	0.311086i
$94$	6.00000	−	10.3923i	0.618853	−	1.07188i
$95$		0			0
$96$			5.19615i			0.530330i
$97$	3.46410	+	6.00000i	0.351726	+	0.609208i	0.986552	−	0.163448i	$-0.0522615\pi$
$97$	3.46410	+	6.00000i	0.351726	+	0.609208i	−0.634826	+	0.772655i	$0.718928\pi$
$98$	−3.46410	−	6.00000i	−0.349927	−	0.606092i
$99$			3.46410i			0.348155i
$100$		0			0
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	−0.677284	−	0.735721i	$-0.736843\pi$
$101$	3.00000	−	5.19615i	0.298511	−	0.517036i	0.975796	+	0.218685i	$0.0701767\pi$
$102$	−5.19615	+	9.00000i	−0.514496	+	0.891133i
$103$			13.0000i			1.28093i	0.767988	+	0.640464i	$0.221258\pi$
$103$			13.0000i			1.28093i	−0.767988	+	0.640464i	$0.778742\pi$
$104$	6.00000	+	1.73205i	0.588348	+	0.169842i
$105$		0			0
$106$	−18.0000	−	10.3923i	−1.74831	−	1.00939i
$107$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$107$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$			13.8564i			1.32720i	0.748086	+	0.663602i	$0.230973\pi$
$109$			13.8564i			1.32720i	−0.748086	+	0.663602i	$0.769027\pi$
$110$		0			0
$111$	−6.00000	+	3.46410i	−0.569495	+	0.328798i
$112$	−8.66025			−0.818317
$113$	−10.3923	+	6.00000i	−0.977626	+	0.564433i	−0.901553	−	0.432670i	$-0.857572\pi$
$113$	−10.3923	+	6.00000i	−0.977626	+	0.564433i	−0.0760733	+	0.997102i	$0.524238\pi$
$114$	1.50000	−	2.59808i	0.140488	−	0.243332i
$115$		0			0
$116$	6.00000			0.557086
$117$	0.866025	+	3.50000i	0.0800641	+	0.323575i
$118$			18.0000i			1.65703i
$119$	−9.00000	−	5.19615i	−0.825029	−	0.476331i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	3.46410			0.313625
$123$	1.73205	+	3.00000i	0.156174	+	0.270501i
$124$	−3.00000	+	1.73205i	−0.269408	+	0.155543i
$125$		0			0
$126$	−1.50000	−	2.59808i	−0.133631	−	0.231455i
$127$	−0.866025	−	0.500000i	−0.0768473	−	0.0443678i	0.461084	−	0.887357i	$-0.347461\pi$
$127$	−0.866025	−	0.500000i	−0.0768473	−	0.0443678i	−0.537931	+	0.842989i	$0.680794\pi$
$128$	6.06218	−	10.5000i	0.535826	−	0.928078i
$129$	5.00000			0.440225
$130$		0			0
$131$	−12.0000			−1.04844			−0.524222	−	0.851581i	$-0.675644\pi$
$131$	−12.0000			−1.04844			−0.524222	+	0.851581i	$0.675644\pi$
$132$	−1.73205	+	3.00000i	−0.150756	+	0.261116i
$133$	2.59808	+	1.50000i	0.225282	+	0.130066i
$134$	7.50000	+	12.9904i	0.647901	+	1.12220i
$135$		0			0
$136$	9.00000	−	5.19615i	0.771744	−	0.445566i
$137$	−5.19615	−	9.00000i	−0.443937	−	0.768922i	0.554040	−	0.832490i	$-0.313085\pi$
$137$	−5.19615	−	9.00000i	−0.443937	−	0.768922i	−0.997978	+	0.0635680i	$0.979752\pi$
$138$	10.3923			0.884652
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	0.952355	−	0.304991i	$-0.0986536\pi$
$139$	2.50000	+	4.33013i	0.212047	+	0.367277i	−0.740308	+	0.672268i	$0.765320\pi$
$140$		0			0
$141$	−6.00000	−	3.46410i	−0.505291	−	0.291730i
$142$		−	6.00000i		−	0.503509i
$143$	8.66025	+	9.00000i	0.724207	+	0.752618i
$144$	5.00000			0.416667
$145$		0			0
$146$	7.50000	−	12.9904i	0.620704	−	1.07509i
$147$	−3.46410	+	2.00000i	−0.285714	+	0.164957i
$148$	−6.92820			−0.569495
$149$	−3.00000	+	1.73205i	−0.245770	+	0.141895i	−0.617826	−	0.786315i	$-0.711986\pi$
$149$	−3.00000	+	1.73205i	−0.245770	+	0.141895i	0.372056	+	0.928210i	$0.378653\pi$
$150$		0			0
$151$			8.66025i			0.704761i	0.935857	+	0.352381i	$0.114628\pi$
$151$			8.66025i			0.704761i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	−2.59808	+	1.50000i	−0.210732	+	0.121666i
$153$	5.19615	+	3.00000i	0.420084	+	0.242536i
$154$	−9.00000	−	5.19615i	−0.725241	−	0.418718i
$155$		0			0
$156$	−1.00000	+	3.46410i	−0.0800641	+	0.277350i
$157$			23.0000i			1.83560i	0.397043	+	0.917800i	$0.370036\pi$
$157$			23.0000i			1.83560i	−0.397043	+	0.917800i	$0.629964\pi$
$158$	9.52628	−	16.5000i	0.757870	−	1.31267i
$159$	−6.00000	+	10.3923i	−0.475831	+	0.824163i
$160$		0			0
$161$			10.3923i			0.819028i
$162$	0.866025	+	1.50000i	0.0680414	+	0.117851i
$163$	−12.1244	−	21.0000i	−0.949653	−	1.64485i	−0.746156	−	0.665771i	$-0.768103\pi$
$163$	−12.1244	−	21.0000i	−0.949653	−	1.64485i	−0.203497	−	0.979076i	$-0.565231\pi$
$164$			3.46410i			0.270501i
$165$		0			0
$166$	−3.00000	+	5.19615i	−0.232845	+	0.403300i
$167$	−1.73205	+	3.00000i	−0.134030	+	0.232147i	−0.925227	−	0.379415i	$-0.876125\pi$
$167$	−1.73205	+	3.00000i	−0.134030	+	0.232147i	0.791196	+	0.611562i	$0.209459\pi$
$168$			3.00000i			0.231455i
$169$	11.0000	+	6.92820i	0.846154	+	0.532939i
$170$		0			0
$171$	−1.50000	−	0.866025i	−0.114708	−	0.0662266i
$172$	4.33013	+	2.50000i	0.330169	+	0.190623i
$173$	−20.7846	+	12.0000i	−1.58022	+	0.912343i	−0.585399	+	0.810745i	$0.699062\pi$
$173$	−20.7846	+	12.0000i	−1.58022	+	0.912343i	−0.994826	+	0.101598i	$0.967605\pi$
$174$		−	10.3923i		−	0.787839i
$175$		0			0
$176$	15.0000	−	8.66025i	1.13067	−	0.652791i
$177$	10.3923			0.781133
$178$	5.19615	−	3.00000i	0.389468	−	0.224860i
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	−0.549825	−	0.835280i	$-0.685306\pi$
$179$	6.00000	−	10.3923i	0.448461	−	0.776757i	0.998286	+	0.0585225i	$0.0186389\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	−10.3923	−	3.00000i	−0.770329	−	0.222375i
$183$		−	2.00000i		−	0.147844i
$184$	−9.00000	−	5.19615i	−0.663489	−	0.383065i
$185$		0			0
$186$	3.00000	+	5.19615i	0.219971	+	0.381000i
$187$	20.7846			1.51992
$188$	−3.46410	−	6.00000i	−0.252646	−	0.437595i
$189$	−1.50000	+	0.866025i	−0.109109	+	0.0629941i
$190$		0			0
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	0.953912	−	0.300088i	$-0.0970159\pi$
$191$	3.00000	+	5.19615i	0.217072	+	0.375980i	−0.736839	+	0.676068i	$0.763683\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	11.2583	−	19.5000i	0.810392	−	1.40364i	−0.102197	−	0.994764i	$-0.532587\pi$
$193$	11.2583	−	19.5000i	0.810392	−	1.40364i	0.912590	−	0.408877i	$-0.134079\pi$
$194$	12.0000			0.861550
$195$		0			0
$196$	−4.00000			−0.285714
$197$	−10.3923	+	18.0000i	−0.740421	+	1.28245i	0.211883	+	0.977295i	$0.432041\pi$
$197$	−10.3923	+	18.0000i	−0.740421	+	1.28245i	−0.952304	+	0.305152i	$0.901293\pi$
$198$	5.19615	+	3.00000i	0.369274	+	0.213201i
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.844446	+	0.535641i	$0.179930\pi$
$199$	12.5000	+	21.6506i	0.886102	+	1.53477i	0.0416556	+	0.999132i	$0.486737\pi$
$200$		0			0
$201$	7.50000	−	4.33013i	0.529009	−	0.305424i
$202$	−5.19615	−	9.00000i	−0.365600	−	0.633238i
$203$	10.3923			0.729397
$204$	3.00000	+	5.19615i	0.210042	+	0.363803i
$205$		0			0
$206$	19.5000	+	11.2583i	1.35863	+	0.784405i
$207$		−	6.00000i		−	0.417029i
$208$	12.9904	−	12.5000i	0.900721	−	0.866719i
$209$	−6.00000			−0.415029
$210$		0			0
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	0.447478	+	0.894295i	$0.352322\pi$
$211$	−8.00000	+	13.8564i	−0.550743	+	0.953914i	−0.998221	+	0.0596196i	$0.981011\pi$
$212$	−10.3923	+	6.00000i	−0.713746	+	0.412082i
$213$	−3.46410			−0.237356
$214$		0			0
$215$		0			0
$216$		−	1.73205i		−	0.117851i
$217$	−5.19615	+	3.00000i	−0.352738	+	0.203653i
$218$	20.7846	+	12.0000i	1.40771	+	0.812743i
$219$	−7.50000	−	4.33013i	−0.506803	−	0.292603i
$220$		0			0
$221$	21.0000	−	5.19615i	1.41261	−	0.349531i
$222$			12.0000i			0.805387i
$223$	−4.33013	+	7.50000i	−0.289967	+	0.502237i	−0.973801	−	0.227400i	$-0.926978\pi$
$223$	−4.33013	+	7.50000i	−0.289967	+	0.502237i	0.683835	+	0.729637i	$0.260311\pi$
$224$	−4.50000	+	7.79423i	−0.300669	+	0.520774i
$225$		0			0
$226$			20.7846i			1.38257i
$227$	−13.8564	−	24.0000i	−0.919682	−	1.59294i	−0.799898	−	0.600136i	$-0.795113\pi$
$227$	−13.8564	−	24.0000i	−0.919682	−	1.59294i	−0.119784	−	0.992800i	$-0.538220\pi$
$228$	−0.866025	−	1.50000i	−0.0573539	−	0.0993399i
$229$		−	1.73205i		−	0.114457i	−0.998361	−	0.0572286i	$-0.981774\pi$
$229$		−	1.73205i		−	0.114457i	0.998361	−	0.0572286i	$-0.0182264\pi$
$230$		0			0
$231$	−3.00000	+	5.19615i	−0.197386	+	0.341882i
$232$	−5.19615	+	9.00000i	−0.341144	+	0.590879i
$233$		−	24.0000i		−	1.57229i	−0.618041	−	0.786146i	$-0.712073\pi$
$233$		−	24.0000i		−	1.57229i	0.618041	−	0.786146i	$-0.287927\pi$
$234$	6.00000	+	1.73205i	0.392232	+	0.113228i
$235$		0			0
$236$	9.00000	+	5.19615i	0.585850	+	0.338241i
$237$	−9.52628	−	5.50000i	−0.618798	−	0.357263i
$238$	−15.5885	+	9.00000i	−1.01045	+	0.583383i
$239$			10.3923i			0.672222i	0.941822	+	0.336111i	$0.109112\pi$
$239$			10.3923i			0.672222i	−0.941822	+	0.336111i	$0.890888\pi$
$240$		0			0
$241$	−16.5000	+	9.52628i	−1.06286	+	0.613642i	−0.926222	−	0.376980i	$-0.876963\pi$
$241$	−16.5000	+	9.52628i	−1.06286	+	0.613642i	−0.136637	+	0.990621i	$0.543629\pi$
$242$	1.73205			0.111340
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	1.00000	−	1.73205i	0.0640184	−	0.110883i
$245$		0			0
$246$	6.00000			0.382546
$247$	−6.06218	+	1.50000i	−0.385727	+	0.0954427i
$248$		−	6.00000i		−	0.381000i
$249$	3.00000	+	1.73205i	0.190117	+	0.109764i
$250$		0			0
$251$	12.0000	+	20.7846i	0.757433	+	1.31191i	0.944156	+	0.329500i	$0.106880\pi$
$251$	12.0000	+	20.7846i	0.757433	+	1.31191i	−0.186722	+	0.982413i	$0.559786\pi$
$252$	−1.73205			−0.109109
$253$	−10.3923	−	18.0000i	−0.653359	−	1.13165i
$254$	−1.50000	+	0.866025i	−0.0941184	+	0.0543393i
$255$		0			0
$256$	−9.50000	−	16.4545i	−0.593750	−	1.02841i
$257$	10.3923	+	6.00000i	0.648254	+	0.374270i	0.787787	−	0.615948i	$-0.211227\pi$
$257$	10.3923	+	6.00000i	0.648254	+	0.374270i	−0.139533	+	0.990217i	$0.544560\pi$
$258$	4.33013	−	7.50000i	0.269582	−	0.466930i
$259$	−12.0000			−0.745644
$260$		0			0
$261$	−6.00000			−0.371391
$262$	−10.3923	+	18.0000i	−0.642039	+	1.11204i
$263$	−5.19615	−	3.00000i	−0.320408	−	0.184988i	0.331166	−	0.943572i	$-0.392558\pi$
$263$	−5.19615	−	3.00000i	−0.320408	−	0.184988i	−0.651575	+	0.758585i	$0.725891\pi$
$264$	−3.00000	−	5.19615i	−0.184637	−	0.319801i
$265$		0			0
$266$	4.50000	−	2.59808i	0.275913	−	0.159298i
$267$	−1.73205	−	3.00000i	−0.106000	−	0.183597i
$268$	8.66025			0.529009
$269$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$269$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$270$		0			0
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	0.710189	−	0.704011i	$-0.248609\pi$
$271$	7.50000	+	4.33013i	0.455593	+	0.263036i	−0.254597	+	0.967047i	$0.581943\pi$
$272$		−	30.0000i		−	1.81902i
$273$	−1.73205	+	6.00000i	−0.104828	+	0.363137i
$274$	−18.0000			−1.08742
$275$		0			0
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	14.7224	−	8.50000i	0.884585	−	0.510716i	0.0124177	−	0.999923i	$-0.496047\pi$
$277$	14.7224	−	8.50000i	0.884585	−	0.510716i	0.872167	+	0.489207i	$0.162714\pi$
$278$	8.66025			0.519408
$279$	3.00000	−	1.73205i	0.179605	−	0.103695i
$280$		0			0
$281$		−	3.46410i		−	0.206651i	−0.994648	−	0.103325i	$-0.967052\pi$
$281$		−	3.46410i		−	0.206651i	0.994648	−	0.103325i	$-0.0329483\pi$
$282$	−10.3923	+	6.00000i	−0.618853	+	0.357295i
$283$	3.46410	+	2.00000i	0.205919	+	0.118888i	0.599414	−	0.800439i	$-0.295400\pi$
$283$	3.46410	+	2.00000i	0.205919	+	0.118888i	−0.393494	+	0.919327i	$0.628734\pi$
$284$	−3.00000	−	1.73205i	−0.178017	−	0.102778i
$285$		0			0
$286$	21.0000	−	5.19615i	1.24176	−	0.307255i
$287$			6.00000i			0.354169i
$288$	2.59808	−	4.50000i	0.153093	−	0.265165i
$289$	9.50000	−	16.4545i	0.558824	−	0.967911i
$290$		0			0
$291$		−	6.92820i		−	0.406138i
$292$	−4.33013	−	7.50000i	−0.253402	−	0.438904i
$293$	−3.46410	−	6.00000i	−0.202375	−	0.350524i	0.746918	−	0.664916i	$-0.231533\pi$
$293$	−3.46410	−	6.00000i	−0.202375	−	0.350524i	−0.949293	+	0.314392i	$0.898199\pi$
$294$			6.92820i			0.404061i
$295$		0			0
$296$	6.00000	−	10.3923i	0.348743	−	0.604040i
$297$	1.73205	−	3.00000i	0.100504	−	0.174078i
$298$			6.00000i			0.347571i
$299$	−15.0000	−	15.5885i	−0.867472	−	0.901504i
$300$		0			0
$301$	7.50000	+	4.33013i	0.432293	+	0.249584i
$302$	12.9904	+	7.50000i	0.747512	+	0.431577i
$303$	−5.19615	+	3.00000i	−0.298511	+	0.172345i
$304$			8.66025i			0.496700i
$305$		0			0
$306$	9.00000	−	5.19615i	0.514496	−	0.297044i
$307$	−10.3923			−0.593120			−0.296560	−	0.955014i	$-0.595840\pi$
$307$	−10.3923			−0.593120			−0.296560	+	0.955014i	$0.595840\pi$
$308$	−5.19615	+	3.00000i	−0.296078	+	0.170941i
$309$	6.50000	−	11.2583i	0.369772	−	0.640464i
$310$		0			0
$311$	12.0000			0.680458			0.340229	−	0.940343i	$-0.389495\pi$
$311$	12.0000			0.680458			0.340229	+	0.940343i	$0.389495\pi$
$312$	−4.33013	−	4.50000i	−0.245145	−	0.254762i
$313$		−	25.0000i		−	1.41308i	−0.707671	−	0.706542i	$-0.750254\pi$
$313$		−	25.0000i		−	1.41308i	0.707671	−	0.706542i	$-0.249746\pi$
$314$	34.5000	+	19.9186i	1.94695	+	1.12407i
$315$		0			0
$316$	−5.50000	−	9.52628i	−0.309399	−	0.535895i
$317$	6.92820			0.389127			0.194563	−	0.980890i	$-0.437671\pi$
$317$	6.92820			0.389127			0.194563	+	0.980890i	$0.437671\pi$
$318$	10.3923	+	18.0000i	0.582772	+	1.00939i
$319$	−18.0000	+	10.3923i	−1.00781	+	0.581857i
$320$		0			0
$321$		0			0
$322$	15.5885	+	9.00000i	0.868711	+	0.501550i
$323$	−5.19615	+	9.00000i	−0.289122	+	0.500773i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−42.0000			−2.32616
$327$	6.92820	−	12.0000i	0.383131	−	0.663602i
$328$	−5.19615	−	3.00000i	−0.286910	−	0.165647i
$329$	−6.00000	−	10.3923i	−0.330791	−	0.572946i
$330$		0			0
$331$	4.50000	−	2.59808i	0.247342	−	0.142803i	−0.371204	−	0.928551i	$-0.621055\pi$
$331$	4.50000	−	2.59808i	0.247342	−	0.142803i	0.618547	+	0.785748i	$0.287722\pi$
$332$	1.73205	+	3.00000i	0.0950586	+	0.164646i
$333$	6.92820			0.379663
$334$	3.00000	+	5.19615i	0.164153	+	0.284321i
$335$		0			0
$336$	7.50000	+	4.33013i	0.409159	+	0.236228i
$337$			19.0000i			1.03500i	0.855684	+	0.517498i	$0.173136\pi$
$337$			19.0000i			1.03500i	−0.855684	+	0.517498i	$0.826864\pi$
$338$	19.9186	−	10.5000i	1.08343	−	0.571125i
$339$	12.0000			0.651751
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	−2.59808	+	1.50000i	−0.140488	+	0.0811107i
$343$	−19.0526			−1.02874
$344$	−7.50000	+	4.33013i	−0.404373	+	0.233465i
$345$		0			0
$346$			41.5692i			2.23478i
$347$	−20.7846	+	12.0000i	−1.11578	+	0.644194i	−0.940319	−	0.340293i	$-0.889474\pi$
$347$	−20.7846	+	12.0000i	−1.11578	+	0.644194i	−0.175457	+	0.984487i	$0.556140\pi$
$348$	−5.19615	−	3.00000i	−0.278543	−	0.160817i
$349$	10.5000	+	6.06218i	0.562052	+	0.324501i	0.753969	−	0.656910i	$-0.228137\pi$
$349$	10.5000	+	6.06218i	0.562052	+	0.324501i	−0.191917	+	0.981411i	$0.561470\pi$
$350$		0			0
$351$	1.00000	−	3.46410i	0.0533761	−	0.184900i
$352$		−	18.0000i		−	0.959403i
$353$	−12.1244	+	21.0000i	−0.645314	+	1.11772i	0.338914	+	0.940817i	$0.389940\pi$
$353$	−12.1244	+	21.0000i	−0.645314	+	1.11772i	−0.984229	+	0.176900i	$0.943393\pi$
$354$	9.00000	−	15.5885i	0.478345	−	0.828517i
$355$		0			0
$356$		−	3.46410i		−	0.183597i
$357$	5.19615	+	9.00000i	0.275010	+	0.476331i
$358$	−10.3923	−	18.0000i	−0.549250	−	0.951330i
$359$		−	27.7128i		−	1.46263i	−0.682042	−	0.731313i	$-0.738908\pi$
$359$		−	27.7128i		−	1.46263i	0.682042	−	0.731313i	$-0.261092\pi$
$360$		0			0
$361$	−8.00000	+	13.8564i	−0.421053	+	0.729285i
$362$	14.7224	−	25.5000i	0.773794	−	1.34025i
$363$		−	1.00000i		−	0.0524864i
$364$	−4.50000	+	4.33013i	−0.235864	+	0.226960i
$365$		0			0
$366$	−3.00000	−	1.73205i	−0.156813	−	0.0905357i
$367$	−30.3109	−	17.5000i	−1.58222	−	0.913493i	−0.994535	−	0.104399i	$-0.966708\pi$
$367$	−30.3109	−	17.5000i	−1.58222	−	0.913493i	−0.587680	−	0.809093i	$-0.699959\pi$
$368$	−25.9808	+	15.0000i	−1.35434	+	0.781929i
$369$		−	3.46410i		−	0.180334i
$370$		0			0
$371$	−18.0000	+	10.3923i	−0.934513	+	0.539542i
$372$	3.46410			0.179605
$373$	−32.0429	+	18.5000i	−1.65912	+	0.957894i	−0.685999	+	0.727603i	$0.740634\pi$
$373$	−32.0429	+	18.5000i	−1.65912	+	0.957894i	−0.973122	+	0.230291i	$0.926032\pi$
$374$	18.0000	−	31.1769i	0.930758	−	1.61212i
$375$		0			0
$376$	12.0000			0.618853
$377$	−15.5885	+	15.0000i	−0.802846	+	0.772539i
$378$			3.00000i			0.154303i
$379$	−22.5000	−	12.9904i	−1.15575	−	0.667271i	−0.205466	−	0.978664i	$-0.565871\pi$
$379$	−22.5000	−	12.9904i	−1.15575	−	0.667271i	−0.950281	+	0.311393i	$0.899204\pi$
$380$		0			0
$381$	0.500000	+	0.866025i	0.0256158	+	0.0443678i
$382$	10.3923			0.531717
$383$	13.8564	+	24.0000i	0.708029	+	1.22634i	0.965587	+	0.260080i	$0.0837489\pi$
$383$	13.8564	+	24.0000i	0.708029	+	1.22634i	−0.257558	+	0.966263i	$0.582918\pi$
$384$	−10.5000	+	6.06218i	−0.535826	+	0.309359i
$385$		0			0
$386$	−19.5000	−	33.7750i	−0.992524	−	1.71910i
$387$	−4.33013	−	2.50000i	−0.220113	−	0.127082i
$388$	3.46410	−	6.00000i	0.175863	−	0.304604i
$389$	12.0000			0.608424			0.304212	−	0.952604i	$-0.401607\pi$
$389$	12.0000			0.608424			0.304212	+	0.952604i	$0.401607\pi$
$390$		0			0
$391$	−36.0000			−1.82060
$392$	3.46410	−	6.00000i	0.174964	−	0.303046i
$393$	10.3923	+	6.00000i	0.524222	+	0.302660i
$394$	18.0000	+	31.1769i	0.906827	+	1.57067i
$395$		0			0
$396$	3.00000	−	1.73205i	0.150756	−	0.0870388i
$397$	12.9904	+	22.5000i	0.651969	+	1.12924i	0.982645	+	0.185498i	$0.0593899\pi$
$397$	12.9904	+	22.5000i	0.651969	+	1.12924i	−0.330676	+	0.943744i	$0.607277\pi$
$398$	43.3013			2.17050
$399$	−1.50000	−	2.59808i	−0.0750939	−	0.130066i
$400$		0			0
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	0.342649	−	0.939463i	$-0.388676\pi$
$401$	−6.00000	−	3.46410i	−0.299626	−	0.172989i	−0.642275	+	0.766475i	$0.722009\pi$
$402$		−	15.0000i		−	0.748132i
$403$	3.46410	−	12.0000i	0.172559	−	0.597763i
$404$	−6.00000			−0.298511
$405$		0			0
$406$	9.00000	−	15.5885i	0.446663	−	0.773642i
$407$	20.7846	−	12.0000i	1.03025	−	0.594818i
$408$	−10.3923			−0.514496
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.483582	−	0.875299i	$-0.339335\pi$
$409$	30.0000	−	17.3205i	1.48340	−	0.856444i	0.999822	+	0.0188549i	$0.00600205\pi$
$410$		0			0
$411$			10.3923i			0.512615i
$412$	11.2583	−	6.50000i	0.554658	−	0.320232i
$413$	15.5885	+	9.00000i	0.767058	+	0.442861i
$414$	−9.00000	−	5.19615i	−0.442326	−	0.255377i
$415$		0			0
$416$	−4.50000	−	18.1865i	−0.220631	−	0.891668i
$417$		−	5.00000i		−	0.244851i
$418$	−5.19615	+	9.00000i	−0.254152	+	0.440204i
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	−0.974546	−	0.224189i	$-0.928027\pi$
$419$	−6.00000	+	10.3923i	−0.293119	+	0.507697i	0.681426	+	0.731887i	$0.261360\pi$
$420$		0			0
$421$		−	5.19615i		−	0.253245i	−0.991951	−	0.126622i	$-0.959586\pi$
$421$		−	5.19615i		−	0.253245i	0.991951	−	0.126622i	$-0.0404137\pi$
$422$	13.8564	+	24.0000i	0.674519	+	1.16830i
$423$	3.46410	+	6.00000i	0.168430	+	0.291730i
$424$		−	20.7846i		−	1.00939i
$425$		0			0
$426$	−3.00000	+	5.19615i	−0.145350	+	0.251754i
$427$	1.73205	−	3.00000i	0.0838198	−	0.145180i
$428$		0			0
$429$	−3.00000	−	12.1244i	−0.144841	−	0.585369i
$430$		0			0
$431$	−24.0000	−	13.8564i	−1.15604	−	0.667440i	−0.205688	−	0.978618i	$-0.565943\pi$
$431$	−24.0000	−	13.8564i	−1.15604	−	0.667440i	−0.950352	+	0.311178i	$0.899276\pi$
$432$	−4.33013	−	2.50000i	−0.208333	−	0.120281i
$433$	1.73205	−	1.00000i	0.0832370	−	0.0480569i	−0.457804	−	0.889053i	$-0.651364\pi$
$433$	1.73205	−	1.00000i	0.0832370	−	0.0480569i	0.541041	+	0.840996i	$0.318030\pi$
$434$			10.3923i			0.498847i
$435$		0			0
$436$	12.0000	−	6.92820i	0.574696	−	0.331801i
$437$	10.3923			0.497131
$438$	−12.9904	+	7.50000i	−0.620704	+	0.358364i
$439$	−15.5000	+	26.8468i	−0.739775	+	1.28133i	0.212822	+	0.977091i	$0.431735\pi$
$439$	−15.5000	+	26.8468i	−0.739775	+	1.28133i	−0.952597	+	0.304236i	$0.901599\pi$
$440$		0			0
$441$	4.00000			0.190476
$442$	10.3923	−	36.0000i	0.494312	−	1.71235i
$443$			18.0000i			0.855206i	0.903967	+	0.427603i	$0.140642\pi$
$443$			18.0000i			0.855206i	−0.903967	+	0.427603i	$0.859358\pi$
$444$	6.00000	+	3.46410i	0.284747	+	0.164399i
$445$		0			0
$446$	7.50000	+	12.9904i	0.355135	+	0.615112i
$447$	3.46410			0.163846
$448$	−0.866025	−	1.50000i	−0.0409159	−	0.0708683i
$449$	−24.0000	+	13.8564i	−1.13263	+	0.653924i	−0.944595	−	0.328238i	$-0.893545\pi$
$449$	−24.0000	+	13.8564i	−1.13263	+	0.653924i	−0.188035	+	0.982162i	$0.560212\pi$
$450$		0			0
$451$	−6.00000	−	10.3923i	−0.282529	−	0.489355i
$452$	10.3923	+	6.00000i	0.488813	+	0.282216i
$453$	4.33013	−	7.50000i	0.203447	−	0.352381i
$454$	−48.0000			−2.25275
$455$		0			0
$456$	3.00000			0.140488
$457$	0.866025	−	1.50000i	0.0405110	−	0.0701670i	−0.845059	−	0.534673i	$-0.820435\pi$
$457$	0.866025	−	1.50000i	0.0405110	−	0.0701670i	0.885570	+	0.464506i	$0.153768\pi$
$458$	−2.59808	−	1.50000i	−0.121400	−	0.0700904i
$459$	−3.00000	−	5.19615i	−0.140028	−	0.242536i
$460$		0			0
$461$	−21.0000	+	12.1244i	−0.978068	+	0.564688i	−0.901686	−	0.432391i	$-0.857670\pi$
$461$	−21.0000	+	12.1244i	−0.978068	+	0.564688i	−0.0763814	+	0.997079i	$0.524337\pi$
$462$	5.19615	+	9.00000i	0.241747	+	0.418718i
$463$	−15.5885			−0.724457			−0.362229	−	0.932089i	$-0.617984\pi$
$463$	−15.5885			−0.724457			−0.362229	+	0.932089i	$0.617984\pi$
$464$	15.0000	+	25.9808i	0.696358	+	1.20613i
$465$		0			0
$466$	−36.0000	−	20.7846i	−1.66767	−	0.962828i
$467$			18.0000i			0.832941i	0.909149	+	0.416470i	$0.136733\pi$
$467$			18.0000i			0.832941i	−0.909149	+	0.416470i	$0.863267\pi$
$468$	2.59808	−	2.50000i	0.120096	−	0.115563i
$469$	15.0000			0.692636
$470$		0			0
$471$	11.5000	−	19.9186i	0.529892	−	0.917800i
$472$	−15.5885	+	9.00000i	−0.717517	+	0.414259i
$473$	−17.3205			−0.796398
$474$	−16.5000	+	9.52628i	−0.757870	+	0.437557i
$475$		0			0
$476$			10.3923i			0.476331i
$477$	10.3923	−	6.00000i	0.475831	−	0.274721i
$478$	15.5885	+	9.00000i	0.712999	+	0.411650i
$479$	−18.0000	−	10.3923i	−0.822441	−	0.474837i	0.0288165	−	0.999585i	$-0.490826\pi$
$479$	−18.0000	−	10.3923i	−0.822441	−	0.474837i	−0.851258	+	0.524748i	$0.824159\pi$
$480$		0			0
$481$	18.0000	−	17.3205i	0.820729	−	0.789747i
$482$			33.0000i			1.50311i
$483$	5.19615	−	9.00000i	0.236433	−	0.409514i
$484$	0.500000	−	0.866025i	0.0227273	−	0.0393648i
$485$		0			0
$486$		−	1.73205i		−	0.0785674i
$487$	−12.9904	−	22.5000i	−0.588650	−	1.01957i	−0.994410	−	0.105592i	$-0.966326\pi$
$487$	−12.9904	−	22.5000i	−0.588650	−	1.01957i	0.405759	−	0.913980i	$-0.367007\pi$
$488$	1.73205	+	3.00000i	0.0784063	+	0.135804i
$489$			24.2487i			1.09656i
$490$		0			0
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	0.298957	+	0.954267i	$0.403361\pi$
$491$	−15.0000	+	25.9808i	−0.676941	+	1.17250i	−0.975898	+	0.218229i	$0.929972\pi$
$492$	1.73205	−	3.00000i	0.0780869	−	0.135250i
$493$			36.0000i			1.62136i
$494$	−3.00000	+	10.3923i	−0.134976	+	0.467572i
$495$		0			0
$496$	−15.0000	−	8.66025i	−0.673520	−	0.388857i
$497$	−5.19615	−	3.00000i	−0.233079	−	0.134568i
$498$	5.19615	−	3.00000i	0.232845	−	0.134433i
$499$		−	32.9090i		−	1.47321i	−0.676325	−	0.736604i	$-0.736428\pi$
$499$		−	32.9090i		−	1.47321i	0.676325	−	0.736604i	$-0.263572\pi$
$500$		0			0
$501$	3.00000	−	1.73205i	0.134030	−	0.0773823i
$502$	41.5692			1.85533
$503$	5.19615	−	3.00000i	0.231685	−	0.133763i	−0.379664	−	0.925124i	$-0.623960\pi$
$503$	5.19615	−	3.00000i	0.231685	−	0.133763i	0.611349	+	0.791361i	$0.290627\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	−36.0000			−1.60040
$507$	−6.06218	−	11.5000i	−0.269231	−	0.510733i
$508$			1.00000i			0.0443678i
$509$	9.00000	+	5.19615i	0.398918	+	0.230315i	0.686017	−	0.727586i	$-0.259358\pi$
$509$	9.00000	+	5.19615i	0.398918	+	0.230315i	−0.287099	+	0.957901i	$0.592691\pi$
$510$		0			0
$511$	−7.50000	−	12.9904i	−0.331780	−	0.574661i
$512$	−8.66025			−0.382733
$513$	0.866025	+	1.50000i	0.0382360	+	0.0662266i
$514$	18.0000	−	10.3923i	0.793946	−	0.458385i
$515$		0			0
$516$	−2.50000	−	4.33013i	−0.110056	−	0.190623i
$517$	20.7846	+	12.0000i	0.914106	+	0.527759i
$518$	−10.3923	+	18.0000i	−0.456612	+	0.790875i
$519$	24.0000			1.05348
$520$		0			0
$521$	−6.00000			−0.262865			−0.131432	−	0.991325i	$-0.541958\pi$
$521$	−6.00000			−0.262865			−0.131432	+	0.991325i	$0.541958\pi$
$522$	−5.19615	+	9.00000i	−0.227429	+	0.393919i
$523$	25.1147	+	14.5000i	1.09819	+	0.634041i	0.935745	−	0.352677i	$-0.114728\pi$
$523$	25.1147	+	14.5000i	1.09819	+	0.634041i	0.162446	+	0.986718i	$0.448062\pi$
$524$	6.00000	+	10.3923i	0.262111	+	0.453990i
$525$		0			0
$526$	−9.00000	+	5.19615i	−0.392419	+	0.226563i
$527$	−10.3923	−	18.0000i	−0.452696	−	0.784092i
$528$	−17.3205			−0.753778
$529$	6.50000	+	11.2583i	0.282609	+	0.489493i
$530$		0			0
$531$	−9.00000	−	5.19615i	−0.390567	−	0.225494i
$532$		−	3.00000i		−	0.130066i
$533$	−8.66025	−	9.00000i	−0.375117	−	0.389833i
$534$	−6.00000			−0.259645
$535$		0			0
$536$	−7.50000	+	12.9904i	−0.323951	+	0.561099i
$537$	−10.3923	+	6.00000i	−0.448461	+	0.258919i
$538$		0			0
$539$	12.0000	−	6.92820i	0.516877	−	0.298419i
$540$		0			0
$541$			6.92820i			0.297867i	0.988847	+	0.148933i	$0.0475840\pi$
$541$			6.92820i			0.297867i	−0.988847	+	0.148933i	$0.952416\pi$
$542$	12.9904	−	7.50000i	0.557985	−	0.322153i
$543$	−14.7224	−	8.50000i	−0.631800	−	0.364770i
$544$	−27.0000	−	15.5885i	−1.15762	−	0.668350i
$545$		0			0
$546$	7.50000	+	7.79423i	0.320970	+	0.333562i
$547$			17.0000i			0.726868i	0.931620	+	0.363434i	$0.118396\pi$
$547$			17.0000i			0.726868i	−0.931620	+	0.363434i	$0.881604\pi$
$548$	−5.19615	+	9.00000i	−0.221969	+	0.384461i
$549$	−1.00000	+	1.73205i	−0.0426790	+	0.0739221i
$550$		0			0
$551$		−	10.3923i		−	0.442727i
$552$	5.19615	+	9.00000i	0.221163	+	0.383065i
$553$	−9.52628	−	16.5000i	−0.405099	−	0.701651i
$554$		−	29.4449i		−	1.25099i
$555$		0			0
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	−19.0526	+	33.0000i	−0.807283	+	1.39825i	0.107456	+	0.994210i	$0.465729\pi$
$557$	−19.0526	+	33.0000i	−0.807283	+	1.39825i	−0.914739	+	0.404045i	$0.867604\pi$
$558$		−	6.00000i		−	0.254000i
$559$	−17.5000	+	4.33013i	−0.740171	+	0.183145i
$560$		0			0
$561$	−18.0000	−	10.3923i	−0.759961	−	0.438763i
$562$	−5.19615	−	3.00000i	−0.219186	−	0.126547i
$563$	−31.1769	+	18.0000i	−1.31395	+	0.758610i	−0.982748	−	0.184950i	$-0.940788\pi$
$563$	−31.1769	+	18.0000i	−1.31395	+	0.758610i	−0.331202	+	0.943560i	$0.607454\pi$
$564$			6.92820i			0.291730i
$565$		0			0
$566$	6.00000	−	3.46410i	0.252199	−	0.145607i
$567$	1.73205			0.0727393
$568$	5.19615	−	3.00000i	0.218026	−	0.125877i
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	−0.796266	−	0.604947i	$-0.793194\pi$
$569$	3.00000	−	5.19615i	0.125767	−	0.217834i	0.922032	+	0.387113i	$0.126528\pi$
$570$		0			0
$571$	19.0000			0.795125			0.397563	−	0.917575i	$-0.369856\pi$
$571$	19.0000			0.795125			0.397563	+	0.917575i	$0.369856\pi$
$572$	3.46410	−	12.0000i	0.144841	−	0.501745i
$573$		−	6.00000i		−	0.250654i
$574$	9.00000	+	5.19615i	0.375653	+	0.216883i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	1.73205			0.0721062			0.0360531	−	0.999350i	$-0.488521\pi$
$577$	1.73205			0.0721062			0.0360531	+	0.999350i	$0.488521\pi$
$578$	−16.4545	−	28.5000i	−0.684416	−	1.18544i
$579$	−19.5000	+	11.2583i	−0.810392	+	0.467880i
$580$		0			0
$581$	3.00000	+	5.19615i	0.124461	+	0.215573i
$582$	−10.3923	−	6.00000i	−0.430775	−	0.248708i
$583$	20.7846	−	36.0000i	0.860811	−	1.49097i
$584$	15.0000			0.620704
$585$		0			0
$586$	−12.0000			−0.495715
$587$	20.7846	−	36.0000i	0.857873	−	1.48588i	−0.0160815	−	0.999871i	$-0.505119\pi$
$587$	20.7846	−	36.0000i	0.857873	−	1.48588i	0.873954	−	0.486008i	$-0.161548\pi$
$588$	3.46410	+	2.00000i	0.142857	+	0.0824786i
$589$	3.00000	+	5.19615i	0.123613	+	0.214104i
$590$		0			0
$591$	18.0000	−	10.3923i	0.740421	−	0.427482i
$592$	−17.3205	−	30.0000i	−0.711868	−	1.23299i
$593$	27.7128			1.13803			0.569014	−	0.822328i	$-0.307325\pi$
$593$	27.7128			1.13803			0.569014	+	0.822328i	$0.307325\pi$
$594$	−3.00000	−	5.19615i	−0.123091	−	0.213201i
$595$		0			0
$596$	3.00000	+	1.73205i	0.122885	+	0.0709476i
$597$		−	25.0000i		−	1.02318i
$598$	−36.3731	+	9.00000i	−1.48741	+	0.368037i
$599$	−12.0000			−0.490307			−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000			−0.490307			−0.245153	+	0.969484i	$0.578838\pi$
$600$		0			0
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	−0.731774	−	0.681547i	$-0.761308\pi$
$601$	5.50000	−	9.52628i	0.224350	−	0.388585i	0.956124	+	0.292962i	$0.0946409\pi$
$602$	12.9904	−	7.50000i	0.529448	−	0.305677i
$603$	−8.66025			−0.352673
$604$	7.50000	−	4.33013i	0.305171	−	0.176190i
$605$		0			0
$606$			10.3923i			0.422159i
$607$	−3.46410	+	2.00000i	−0.140604	+	0.0811775i	−0.568652	−	0.822578i	$-0.692535\pi$
$607$	−3.46410	+	2.00000i	−0.140604	+	0.0811775i	0.428048	+	0.903756i	$0.359201\pi$
$608$	7.79423	+	4.50000i	0.316098	+	0.182499i
$609$	−9.00000	−	5.19615i	−0.364698	−	0.210559i
$610$		0			0
$611$	24.0000	+	6.92820i	0.970936	+	0.280285i
$612$		−	6.00000i		−	0.242536i
$613$	0.866025	−	1.50000i	0.0349784	−	0.0605844i	−0.848006	−	0.529986i	$-0.822197\pi$
$613$	0.866025	−	1.50000i	0.0349784	−	0.0605844i	0.882985	+	0.469402i	$0.155530\pi$
$614$	−9.00000	+	15.5885i	−0.363210	+	0.629099i
$615$		0			0
$616$		−	10.3923i		−	0.418718i
$617$	12.1244	+	21.0000i	0.488108	+	0.845428i	0.999906	−	0.0136775i	$-0.00435381\pi$
$617$	12.1244	+	21.0000i	0.488108	+	0.845428i	−0.511798	+	0.859106i	$0.671020\pi$
$618$	−11.2583	−	19.5000i	−0.452876	−	0.784405i
$619$		−	19.0526i		−	0.765787i	−0.923792	−	0.382893i	$-0.874928\pi$
$619$		−	19.0526i		−	0.765787i	0.923792	−	0.382893i	$-0.125072\pi$
$620$		0			0
$621$	−3.00000	+	5.19615i	−0.120386	+	0.208514i
$622$	10.3923	−	18.0000i	0.416693	−	0.721734i
$623$		−	6.00000i		−	0.240385i
$624$	−17.5000	+	4.33013i	−0.700561	+	0.173344i
$625$		0			0
$626$	−37.5000	−	21.6506i	−1.49880	−	0.865333i
$627$	5.19615	+	3.00000i	0.207514	+	0.119808i
$628$	19.9186	−	11.5000i	0.794838	−	0.458900i
$629$		−	41.5692i		−	1.65747i
$630$		0			0
$631$	31.5000	−	18.1865i	1.25400	−	0.723994i	0.282095	−	0.959387i	$-0.408971\pi$
$631$	31.5000	−	18.1865i	1.25400	−	0.723994i	0.971900	+	0.235392i	$0.0756374\pi$
$632$	19.0526			0.757870
$633$	13.8564	−	8.00000i	0.550743	−	0.317971i
$634$	6.00000	−	10.3923i	0.238290	−	0.412731i
$635$		0			0
$636$	12.0000			0.475831
$637$	10.3923	−	10.0000i	0.411758	−	0.396214i
$638$			36.0000i			1.42525i
$639$	3.00000	+	1.73205i	0.118678	+	0.0685189i
$640$		0			0
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	−0.898470	−	0.439034i	$-0.855321\pi$
$641$	−21.0000	−	36.3731i	−0.829450	−	1.43665i	0.0690201	−	0.997615i	$-0.478013\pi$
$642$		0			0
$643$	11.2583	+	19.5000i	0.443985	+	0.769005i	0.997981	−	0.0635146i	$-0.0202309\pi$
$643$	11.2583	+	19.5000i	0.443985	+	0.769005i	−0.553996	+	0.832520i	$0.686898\pi$
$644$	9.00000	−	5.19615i	0.354650	−	0.204757i
$645$		0			0
$646$	9.00000	+	15.5885i	0.354100	+	0.613320i
$647$	−10.3923	−	6.00000i	−0.408564	−	0.235884i	0.281609	−	0.959529i	$-0.409132\pi$
$647$	−10.3923	−	6.00000i	−0.408564	−	0.235884i	−0.690172	+	0.723645i	$0.742465\pi$
$648$	−0.866025	+	1.50000i	−0.0340207	+	0.0589256i
$649$	−36.0000			−1.41312
$650$		0			0
$651$	6.00000			0.235159
$652$	−12.1244	+	21.0000i	−0.474826	+	0.822423i
$653$	−10.3923	−	6.00000i	−0.406682	−	0.234798i	0.282681	−	0.959214i	$-0.408776\pi$
$653$	−10.3923	−	6.00000i	−0.406682	−	0.234798i	−0.689363	+	0.724416i	$0.742110\pi$
$654$	−12.0000	−	20.7846i	−0.469237	−	0.812743i
$655$		0			0
$656$	−15.0000	+	8.66025i	−0.585652	+	0.338126i
$657$	4.33013	+	7.50000i	0.168934	+	0.292603i
$658$	−20.7846			−0.810268
$659$	−9.00000	−	15.5885i	−0.350590	−	0.607240i	0.635763	−	0.771885i	$-0.280686\pi$
$659$	−9.00000	−	15.5885i	−0.350590	−	0.607240i	−0.986353	+	0.164644i	$0.947352\pi$
$660$		0			0
$661$	37.5000	+	21.6506i	1.45858	+	0.842112i	0.998942	−	0.0459936i	$-0.0146454\pi$
$661$	37.5000	+	21.6506i	1.45858	+	0.842112i	0.459639	+	0.888106i	$0.347979\pi$
$662$		−	9.00000i		−	0.349795i
$663$	−20.7846	−	6.00000i	−0.807207	−	0.233021i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	6.00000	−	10.3923i	0.232495	−	0.402694i
$667$	31.1769	−	18.0000i	1.20717	−	0.696963i
$668$	3.46410			0.134030
$669$	7.50000	−	4.33013i	0.289967	−	0.167412i
$670$		0			0
$671$			6.92820i			0.267460i
$672$	7.79423	−	4.50000i	0.300669	−	0.173591i
$673$	40.7032	+	23.5000i	1.56899	+	0.905858i	0.996287	+	0.0860977i	$0.0274397\pi$
$673$	40.7032	+	23.5000i	1.56899	+	0.905858i	0.572706	+	0.819761i	$0.305894\pi$
$674$	28.5000	+	16.4545i	1.09778	+	0.633803i
$675$		0			0
$676$	0.500000	−	12.9904i	0.0192308	−	0.499630i
$677$		−	24.0000i		−	0.922395i	−0.887298	−	0.461197i	$-0.847420\pi$
$677$		−	24.0000i		−	0.922395i	0.887298	−	0.461197i	$-0.152580\pi$
$678$	10.3923	−	18.0000i	0.399114	−	0.691286i
$679$	6.00000	−	10.3923i	0.230259	−	0.398820i
$680$		0			0
$681$			27.7128i			1.06196i
$682$	−10.3923	−	18.0000i	−0.397942	−	0.689256i
$683$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$683$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$684$			1.73205i			0.0662266i
$685$		0			0
$686$	−16.5000	+	28.5788i	−0.629973	+	1.09115i
$687$	−0.866025	+	1.50000i	−0.0330409	+	0.0572286i
$688$			25.0000i			0.953116i
$689$	12.0000	−	41.5692i	0.457164	−	1.58366i
$690$		0			0
$691$	−4.50000	−	2.59808i	−0.171188	−	0.0988355i	0.411958	−	0.911203i	$-0.364845\pi$
$691$	−4.50000	−	2.59808i	−0.171188	−	0.0988355i	−0.583146	+	0.812367i	$0.698178\pi$
$692$	20.7846	+	12.0000i	0.790112	+	0.456172i
$693$	5.19615	−	3.00000i	0.197386	−	0.113961i
$694$			41.5692i			1.57795i
$695$		0			0
$696$	9.00000	−	5.19615i	0.341144	−	0.196960i
$697$	−20.7846			−0.787273
$698$	18.1865	−	10.5000i	0.688370	−	0.397431i
$699$	−12.0000	+	20.7846i	−0.453882	+	0.786146i
$700$		0			0
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	−4.33013	−	4.50000i	−0.163430	−	0.169842i
$703$			12.0000i			0.452589i
$704$	3.00000	+	1.73205i	0.113067	+	0.0652791i
$705$		0			0
$706$	21.0000	+	36.3731i	0.790345	+	1.36892i
$707$	−10.3923			−0.390843
$708$	−5.19615	−	9.00000i	−0.195283	−	0.338241i
$709$	31.5000	−	18.1865i	1.18301	−	0.683010i	0.226299	−	0.974058i	$-0.427337\pi$
$709$	31.5000	−	18.1865i	1.18301	−	0.683010i	0.956708	+	0.291048i	$0.0940040\pi$
$710$		0			0
$711$	5.50000	+	9.52628i	0.206266	+	0.357263i
$712$	5.19615	+	3.00000i	0.194734	+	0.112430i
$713$	−10.3923	+	18.0000i	−0.389195	+	0.674105i
$714$	18.0000			0.673633
$715$		0			0
$716$	−12.0000			−0.448461
$717$	5.19615	−	9.00000i	0.194054	−	0.336111i
$718$	−41.5692	−	24.0000i	−1.55135	−	0.895672i
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	0.804648	−	0.593753i	$-0.202354\pi$
$719$	−3.00000	−	5.19615i	−0.111881	−	0.193784i	−0.916529	+	0.399969i	$0.869021\pi$
$720$		0			0
$721$	19.5000	−	11.2583i	0.726218	−	0.419282i
$722$	13.8564	+	24.0000i	0.515682	+	0.893188i
$723$	19.0526			0.708572
$724$	−8.50000	−	14.7224i	−0.315900	−	0.547155i
$725$		0			0
$726$	−1.50000	−	0.866025i	−0.0556702	−	0.0321412i
$727$		−	17.0000i		−	0.630495i	−0.949009	−	0.315248i	$-0.897912\pi$
$727$		−	17.0000i		−	0.630495i	0.949009	−	0.315248i	$-0.102088\pi$
$728$	−2.59808	−	10.5000i	−0.0962911	−	0.389156i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−15.0000	+	25.9808i	−0.554795	+	0.960933i
$732$	−1.73205	+	1.00000i	−0.0640184	+	0.0369611i
$733$	46.7654			1.72732			0.863659	−	0.504076i	$-0.168167\pi$
$733$	46.7654			1.72732			0.863659	+	0.504076i	$0.168167\pi$
$734$	−52.5000	+	30.3109i	−1.93781	+	1.11880i
$735$		0			0
$736$			31.1769i			1.14920i
$737$	−25.9808	+	15.0000i	−0.957014	+	0.552532i
$738$	−5.19615	−	3.00000i	−0.191273	−	0.110432i
$739$	21.0000	+	12.1244i	0.772497	+	0.446002i	0.833765	−	0.552120i	$-0.186181\pi$
$739$	21.0000	+	12.1244i	0.772497	+	0.446002i	−0.0612673	+	0.998121i	$0.519514\pi$
$740$		0			0
$741$	6.00000	+	1.73205i	0.220416	+	0.0636285i
$742$			36.0000i			1.32160i
$743$	−1.73205	+	3.00000i	−0.0635428	+	0.110059i	−0.896047	−	0.443960i	$-0.853573\pi$
$743$	−1.73205	+	3.00000i	−0.0635428	+	0.110059i	0.832504	+	0.554019i	$0.186907\pi$
$744$	−3.00000	+	5.19615i	−0.109985	+	0.190500i
$745$		0			0
$746$			64.0859i			2.34635i
$747$	−1.73205	−	3.00000i	−0.0633724	−	0.109764i
$748$	−10.3923	−	18.0000i	−0.379980	−	0.658145i
$749$		0			0
$750$		0			0
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	−0.227153	−	0.973859i	$-0.572942\pi$
$751$	20.0000	−	34.6410i	0.729810	−	1.26407i	0.956963	−	0.290209i	$-0.0937250\pi$
$752$	17.3205	−	30.0000i	0.631614	−	1.09399i
$753$		−	24.0000i		−	0.874609i
$754$	9.00000	+	36.3731i	0.327761	+	1.32463i
$755$		0			0
$756$	1.50000	+	0.866025i	0.0545545	+	0.0314970i
$757$	−37.2391	−	21.5000i	−1.35348	−	0.781431i	−0.364743	−	0.931108i	$-0.618843\pi$
$757$	−37.2391	−	21.5000i	−1.35348	−	0.781431i	−0.988735	+	0.149677i	$0.952176\pi$
$758$	−38.9711	+	22.5000i	−1.41550	+	0.817237i
$759$			20.7846i			0.754434i
$760$		0			0
$761$	39.0000	−	22.5167i	1.41375	−	0.816228i	0.418010	−	0.908443i	$-0.362728\pi$
$761$	39.0000	−	22.5167i	1.41375	−	0.816228i	0.995739	+	0.0922143i	$0.0293945\pi$
$762$	1.73205			0.0627456
$763$	20.7846	−	12.0000i	0.752453	−	0.434429i
$764$	3.00000	−	5.19615i	0.108536	−	0.187990i
$765$		0			0
$766$	48.0000			1.73431
$767$	−36.3731	+	9.00000i	−1.31336	+	0.324971i
$768$			19.0000i			0.685603i
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	0.236433	−	0.971648i	$-0.424022\pi$
$769$	−13.5000	−	7.79423i	−0.486822	−	0.281067i	−0.723255	+	0.690581i	$0.757355\pi$
$770$		0			0
$771$	−6.00000	−	10.3923i	−0.216085	−	0.374270i
$772$	−22.5167			−0.810392
$773$	−13.8564	−	24.0000i	−0.498380	−	0.863220i	0.501618	−	0.865089i	$-0.332738\pi$
$773$	−13.8564	−	24.0000i	−0.498380	−	0.863220i	−0.999998	+	0.00186926i	$0.999405\pi$
$774$	−7.50000	+	4.33013i	−0.269582	+	0.155643i
$775$		0			0
$776$	6.00000	+	10.3923i	0.215387	+	0.373062i
$777$	10.3923	+	6.00000i	0.372822	+	0.215249i
$778$	10.3923	−	18.0000i	0.372582	−	0.645331i
$779$	6.00000			0.214972
$780$		0			0
$781$	12.0000			0.429394
$782$	−31.1769	+	54.0000i	−1.11488	+	1.93104i
$783$	5.19615	+	3.00000i	0.185695	+	0.107211i
$784$	−10.0000	−	17.3205i	−0.357143	−	0.618590i
$785$		0			0
$786$	18.0000	−	10.3923i	0.642039	−	0.370681i
$787$	−25.9808	−	45.0000i	−0.926114	−	1.60408i	−0.789759	−	0.613417i	$-0.789795\pi$
$787$	−25.9808	−	45.0000i	−0.926114	−	1.60408i	−0.136355	−	0.990660i	$-0.543539\pi$
$788$	20.7846			0.740421
$789$	3.00000	+	5.19615i	0.106803	+	0.184988i
$790$		0			0
$791$	18.0000	+	10.3923i	0.640006	+	0.369508i
$792$			6.00000i			0.213201i
$793$	1.73205	+	7.00000i	0.0615069	+	0.248577i
$794$	45.0000			1.59699
$795$		0			0
$796$	12.5000	−	21.6506i	0.443051	−	0.767386i
$797$	−25.9808	+	15.0000i	−0.920286	+	0.531327i	−0.883726	−	0.468004i	$-0.844973\pi$
$797$	−25.9808	+	15.0000i	−0.920286	+	0.531327i	−0.0365596	+	0.999331i	$0.511640\pi$
$798$	−5.19615			−0.183942
$799$	36.0000	−	20.7846i	1.27359	−	0.735307i
$800$		0			0
$801$			3.46410i			0.122398i
$802$	−10.3923	+	6.00000i	−0.366965	+	0.211867i
$803$	25.9808	+	15.0000i	0.916841	+	0.529339i
$804$	−7.50000	−	4.33013i	−0.264505	−	0.152712i
$805$		0			0
$806$	−15.0000	−	15.5885i	−0.528352	−	0.549080i
$807$		0			0
$808$	5.19615	−	9.00000i	0.182800	−	0.316619i
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	−0.996125	−	0.0879478i	$-0.971969\pi$
$809$	−12.0000	+	20.7846i	−0.421898	+	0.730748i	0.574228	+	0.818696i	$0.305302\pi$
$810$		0			0
$811$		−	5.19615i		−	0.182462i	−0.995830	−	0.0912308i	$-0.970920\pi$
$811$		−	5.19615i		−	0.182462i	0.995830	−	0.0912308i	$-0.0290801\pi$
$812$	−5.19615	−	9.00000i	−0.182349	−	0.315838i
$813$	−4.33013	−	7.50000i	−0.151864	−	0.263036i
$814$		−	41.5692i		−	1.45700i
$815$		0			0
$816$	−15.0000	+	25.9808i	−0.525105	+	0.909509i
$817$	4.33013	−	7.50000i	0.151492	−	0.262392i
$818$		−	60.0000i		−	2.09785i
$819$	4.50000	−	4.33013i	0.157243	−	0.151307i
$820$		0			0
$821$	6.00000	+	3.46410i	0.209401	+	0.120898i	0.601033	−	0.799224i	$-0.294756\pi$
$821$	6.00000	+	3.46410i	0.209401	+	0.120898i	−0.391632	+	0.920122i	$0.628089\pi$
$822$	15.5885	+	9.00000i	0.543710	+	0.313911i
$823$	32.0429	−	18.5000i	1.11695	−	0.644869i	0.176327	−	0.984332i	$-0.443578\pi$
$823$	32.0429	−	18.5000i	1.11695	−	0.644869i	0.940620	+	0.339462i	$0.110245\pi$
$824$			22.5167i			0.784405i
$825$		0			0
$826$	27.0000	−	15.5885i	0.939450	−	0.542392i
$827$	48.4974			1.68642			0.843210	−	0.537584i	$-0.180663\pi$
$827$	48.4974			1.68642			0.843210	+	0.537584i	$0.180663\pi$
$828$	−5.19615	+	3.00000i	−0.180579	+	0.104257i
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	0.252113	+	0.967698i	$0.418875\pi$
$829$	−20.5000	+	35.5070i	−0.711994	+	1.23321i	−0.964107	+	0.265513i	$0.914459\pi$
$830$		0			0
$831$	−17.0000			−0.589723
$832$	3.46410	+	1.00000i	0.120096	+	0.0346688i
$833$		−	24.0000i		−	0.831551i
$834$	−7.50000	−	4.33013i	−0.259704	−	0.149940i
$835$		0			0
$836$	3.00000	+	5.19615i	0.103757	+	0.179713i
$837$	−3.46410			−0.119737
$838$	10.3923	+	18.0000i	0.358996	+	0.621800i
$839$	−12.0000	+	6.92820i	−0.414286	+	0.239188i	−0.692630	−	0.721293i	$-0.743548\pi$
$839$	−12.0000	+	6.92820i	−0.414286	+	0.239188i	0.278344	+	0.960482i	$0.410215\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−7.79423	−	4.50000i	−0.268607	−	0.155080i
$843$	−1.73205	+	3.00000i	−0.0596550	+	0.103325i
$844$	16.0000			0.550743
$845$		0			0
$846$	12.0000			0.412568
$847$	0.866025	−	1.50000i	0.0297570	−	0.0515406i
$848$	−51.9615	−	30.0000i	−1.78437	−	1.03020i
$849$	−2.00000	−	3.46410i	−0.0686398	−	0.118888i
$850$		0			0
$851$	−36.0000	+	20.7846i	−1.23406	+	0.712487i
$852$	1.73205	+	3.00000i	0.0593391	+	0.102778i
$853$		0			0			−	1.00000i	$-0.5\pi$
$853$		0			0				1.00000i	$0.5\pi$
$854$	−3.00000	−	5.19615i	−0.102658	−	0.177809i
$855$		0			0
$856$		0			0
$857$			42.0000i			1.43469i	0.696717	+	0.717346i	$0.254643\pi$
$857$			42.0000i			1.43469i	−0.696717	+	0.717346i	$0.745357\pi$
$858$	−20.7846	−	6.00000i	−0.709575	−	0.204837i
$859$	−1.00000			−0.0341196			−0.0170598	−	0.999854i	$-0.505431\pi$
$859$	−1.00000			−0.0341196			−0.0170598	+	0.999854i	$0.505431\pi$
$860$		0			0
$861$	3.00000	−	5.19615i	0.102240	−	0.177084i
$862$	−41.5692	+	24.0000i	−1.41585	+	0.817443i
$863$	20.7846			0.707516			0.353758	−	0.935337i	$-0.384904\pi$
$863$	20.7846			0.707516			0.353758	+	0.935337i	$0.384904\pi$
$864$	−4.50000	+	2.59808i	−0.153093	+	0.0883883i
$865$		0			0
$866$		−	3.46410i		−	0.117715i
$867$	−16.4545	+	9.50000i	−0.558824	+	0.322637i
$868$	5.19615	+	3.00000i	0.176369	+	0.101827i
$869$	33.0000	+	19.0526i	1.11945	+	0.646314i
$870$		0			0
$871$	−22.5000	+	21.6506i	−0.762383	+	0.733604i
$872$			24.0000i			0.812743i
$873$	−3.46410	+	6.00000i	−0.117242	+	0.203069i
$874$	9.00000	−	15.5885i	0.304430	−	0.527287i
$875$		0			0
$876$			8.66025i			0.292603i
$877$	−7.79423	−	13.5000i	−0.263192	−	0.455863i	0.703896	−	0.710303i	$-0.251442\pi$
$877$	−7.79423	−	13.5000i	−0.263192	−	0.455863i	−0.967088	+	0.254440i	$0.918109\pi$
$878$	26.8468	+	46.5000i	0.906035	+	1.56930i
$879$			6.92820i			0.233682i
$880$		0			0
$881$	6.00000	−	10.3923i	0.202145	−	0.350126i	−0.747074	−	0.664741i	$-0.768542\pi$
$881$	6.00000	−	10.3923i	0.202145	−	0.350126i	0.949219	+	0.314615i	$0.101875\pi$
$882$	3.46410	−	6.00000i	0.116642	−	0.202031i
$883$		−	16.0000i		−	0.538443i	−0.963078	−	0.269221i	$-0.913234\pi$
$883$		−	16.0000i		−	0.538443i	0.963078	−	0.269221i	$-0.0867663\pi$
$884$	−15.0000	−	15.5885i	−0.504505	−	0.524297i
$885$		0			0
$886$	27.0000	+	15.5885i	0.907083	+	0.523704i
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	0.806557	−	0.591156i	$-0.201328\pi$
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	−0.108678	+	0.994077i	$0.534662\pi$
$888$	−10.3923	+	6.00000i	−0.348743	+	0.201347i
$889$			1.73205i			0.0580911i
$890$		0			0
$891$	−3.00000	+	1.73205i	−0.100504	+	0.0580259i
$892$	8.66025			0.289967
$893$	−10.3923	+	6.00000i	−0.347765	+	0.200782i
$894$	3.00000	−	5.19615i	0.100335	−	0.173785i
$895$		0			0
$896$	−21.0000			−0.701561
$897$	5.19615	+	21.0000i	0.173494	+	0.701170i
$898$			48.0000i			1.60178i
$899$	18.0000	+	10.3923i	0.600334	+	0.346603i
$900$		0			0
$901$	−36.0000	−	62.3538i	−1.19933	−	2.07731i
$902$	−20.7846			−0.692052
$903$	−4.33013	−	7.50000i	−0.144098	−	0.249584i
$904$	−18.0000	+	10.3923i	−0.598671	+	0.345643i
$905$		0			0
$906$	−7.50000	−	12.9904i	−0.249171	−	0.431577i
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	0.610594	−	0.791944i	$-0.290931\pi$
$907$	6.92820	+	4.00000i	0.230047	+	0.132818i	−0.380547	+	0.924762i	$0.624264\pi$
$908$	−13.8564	+	24.0000i	−0.459841	+	0.796468i
$909$	6.00000			0.199007
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$	4.33013	−	7.50000i	0.143385	−	0.248350i
$913$	−10.3923	−	6.00000i	−0.343935	−	0.198571i
$914$	−1.50000	−	2.59808i	−0.0496156	−	0.0859367i
$915$		0			0
$916$	−1.50000	+	0.866025i	−0.0495614	+	0.0286143i
$917$	10.3923	+	18.0000i	0.343184	+	0.594412i
$918$	−10.3923			−0.342997
$919$	21.5000	+	37.2391i	0.709220	+	1.22840i	0.965147	+	0.261708i	$0.0842858\pi$
$919$	21.5000	+	37.2391i	0.709220	+	1.22840i	−0.255927	+	0.966696i	$0.582381\pi$
$920$		0			0
$921$	9.00000	+	5.19615i	0.296560	+	0.171219i
$922$			42.0000i			1.38320i
$923$	12.1244	−	3.00000i	0.399078	−	0.0987462i
$924$	6.00000			0.197386
$925$		0			0
$926$	−13.5000	+	23.3827i	−0.443638	+	0.768403i
$927$	−11.2583	+	6.50000i	−0.369772	+	0.213488i
$928$	31.1769			1.02343
$929$	−27.0000	+	15.5885i	−0.885841	+	0.511441i	−0.872580	−	0.488471i	$-0.837555\pi$
$929$	−27.0000	+	15.5885i	−0.885841	+	0.511441i	−0.0132613	+	0.999912i	$0.504221\pi$
$930$		0			0
$931$			6.92820i			0.227063i
$932$	−20.7846	+	12.0000i	−0.680823	+	0.393073i
$933$	−10.3923	−	6.00000i	−0.340229	−	0.196431i
$934$	27.0000	+	15.5885i	0.883467	+	0.510070i
$935$		0			0
$936$	1.50000	+	6.06218i	0.0490290	+	0.198148i
$937$			13.0000i			0.424691i	0.977195	+	0.212346i	$0.0681103\pi$
$937$			13.0000i			0.424691i	−0.977195	+	0.212346i	$0.931890\pi$
$938$	12.9904	−	22.5000i	0.424151	−	0.734651i
$939$	−12.5000	+	21.6506i	−0.407922	+	0.706542i
$940$		0			0
$941$		0			0		1.00000			$0$
$941$		0			0		−1.00000			$\pi$
$942$	−19.9186	−	34.5000i	−0.648983	−	1.12407i
$943$	10.3923	+	18.0000i	0.338420	+	0.586161i
$944$			51.9615i			1.69120i
$945$		0			0
$946$	−15.0000	+	25.9808i	−0.487692	+	0.844707i
$947$	15.5885	−	27.0000i	0.506557	−	0.877382i	−0.493414	−	0.869794i	$-0.664251\pi$
$947$	15.5885	−	27.0000i	0.506557	−	0.877382i	0.999971	−	0.00758776i	$-0.00241528\pi$
$948$			11.0000i			0.357263i
$949$	30.0000	+	8.66025i	0.973841	+	0.281124i
$950$		0			0
$951$	−6.00000	−	3.46410i	−0.194563	−	0.112331i
$952$	−15.5885	−	9.00000i	−0.505225	−	0.291692i
$953$	46.7654	−	27.0000i	1.51488	−	0.874616i	0.515031	−	0.857171i	$-0.327780\pi$
$953$	46.7654	−	27.0000i	1.51488	−	0.874616i	0.999848	−	0.0174443i	$-0.00555298\pi$
$954$		−	20.7846i		−	0.672927i
$955$		0			0
$956$	9.00000	−	5.19615i	0.291081	−	0.168056i
$957$	20.7846			0.671871
$958$	−31.1769	+	18.0000i	−1.00728	+	0.581554i
$959$	−9.00000	+	15.5885i	−0.290625	+	0.503378i
$960$		0			0
$961$	19.0000			0.612903
$962$	−10.3923	−	42.0000i	−0.335061	−	1.35413i
$963$		0			0
$964$	16.5000	+	9.52628i	0.531429	+	0.306821i
$965$		0			0
$966$	−9.00000	−	15.5885i	−0.289570	−	0.501550i
$967$	−10.3923			−0.334194			−0.167097	−	0.985940i	$-0.553439\pi$
$967$	−10.3923			−0.334194			−0.167097	+	0.985940i	$0.553439\pi$
$968$	0.866025	+	1.50000i	0.0278351	+	0.0482118i
$969$	9.00000	−	5.19615i	0.289122	−	0.166924i
$970$		0			0
$971$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$971$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	4.33013	−	7.50000i	0.138817	−	0.240439i
$974$	−45.0000			−1.44189
$975$		0			0
$976$	10.0000			0.320092
$977$	3.46410	−	6.00000i	0.110826	−	0.191957i	−0.805277	−	0.592898i	$-0.797984\pi$
$977$	3.46410	−	6.00000i	0.110826	−	0.191957i	0.916104	+	0.400941i	$0.131317\pi$
$978$	36.3731	+	21.0000i	1.16308	+	0.671506i
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$		0			0
$981$	−12.0000	+	6.92820i	−0.383131	+	0.221201i
$982$	25.9808	+	45.0000i	0.829079	+	1.43601i
$983$	31.1769			0.994389			0.497195	−	0.867639i	$-0.334364\pi$
$983$	31.1769			0.994389			0.497195	+	0.867639i	$0.334364\pi$
$984$	3.00000	+	5.19615i	0.0956365	+	0.165647i
$985$		0			0
$986$	54.0000	+	31.1769i	1.71971	+	0.992875i
$987$			12.0000i			0.381964i
$988$	4.33013	+	4.50000i	0.137760	+	0.143164i
$989$	30.0000			0.953945
$990$		0			0
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$	−15.5885	+	9.00000i	−0.494934	+	0.285750i
$993$	−5.19615			−0.164895
$994$	−9.00000	+	5.19615i	−0.285463	+	0.164812i
$995$		0			0
$996$		−	3.46410i		−	0.109764i
$997$	−0.866025	+	0.500000i	−0.0274273	+	0.0158352i	−0.513651	−	0.857999i	$-0.671707\pi$
$997$	−0.866025	+	0.500000i	−0.0274273	+	0.0158352i	0.486224	+	0.873834i	$0.338374\pi$
$998$	−49.3634	−	28.5000i	−1.56257	−	0.902152i
$999$	−6.00000	−	3.46410i	−0.189832	−	0.109599i

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	975.2.w.b.199.2		4
5.2	odd	4		975.2.bc.f.901.1	yes	2
5.3	odd	4		975.2.bc.b.901.1	yes	2
5.4	even	2	inner	975.2.w.b.199.1		4
13.10	even	6	inner	975.2.w.b.49.1		4
65.23	odd	12		975.2.bc.b.751.1	✓	2
65.49	even	6	inner	975.2.w.b.49.2		4
65.62	odd	12		975.2.bc.f.751.1	yes	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
975.2.w.b.49.1		4	13.10	even	6	inner
975.2.w.b.49.2		4	65.49	even	6	inner
975.2.w.b.199.1		4	5.4	even	2	inner
975.2.w.b.199.2		4	1.1	even	1	trivial
975.2.bc.b.751.1	✓	2	65.23	odd	12
975.2.bc.b.901.1	yes	2	5.3	odd	4
975.2.bc.f.751.1	yes	2	65.62	odd	12
975.2.bc.f.901.1	yes	2	5.2	odd	4

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 $\F_{q}$
Belyi maps

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	975.2.w.b.199.2

Level	$975$
Weight	$2$
Character	975.199
Analytic conductor	$7.785$
Analytic rank	$0$
Dimension	$4$
Inner twists	$4$