LMFDB - Embedded newform 525.3.s.d.199.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [525,3,Mod(124,525)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("525.124"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(525, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 3, 5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	525.s (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [4,0,0,0,0,0,0,0,-6,0,-20,0,0,-28] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

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

Self dual:	no
Analytic conductor:	$14.3052138789$
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 21)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	525.199
Dual form			525.3.s.d.124.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(0.866025 - 1.50000i) q^{3} -3.46410i q^{6} +(-6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.00000 + 8.66025i) q^{11} -12.1244 q^{13} +(-7.00000 + 12.1244i) q^{14} +(8.00000 + 13.8564i) q^{16} +(-3.46410 + 6.00000i) q^{17} +(-5.19615 - 3.00000i) q^{18} +(-28.5000 + 16.4545i) q^{19} +12.1244i q^{21} +20.0000i q^{22} +(34.6410 - 20.0000i) q^{23} +(12.0000 + 6.92820i) q^{24} +(-21.0000 + 12.1244i) q^{26} -5.19615 q^{27} -16.0000 q^{29} +(4.50000 + 2.59808i) q^{31} +(8.66025 + 15.0000i) q^{33} +13.8564i q^{34} +(-4.33013 + 2.50000i) q^{37} +(-32.9090 + 57.0000i) q^{38} +(-10.5000 + 18.1865i) q^{39} +24.2487i q^{41} +(12.1244 + 21.0000i) q^{42} -19.0000i q^{43} +(40.0000 - 69.2820i) q^{46} +(25.9808 + 45.0000i) q^{47} +27.7128 q^{48} +(24.5000 - 42.4352i) q^{49} +(6.00000 + 10.3923i) q^{51} +(27.7128 + 16.0000i) q^{53} +(-9.00000 + 5.19615i) q^{54} +(-28.0000 - 48.4974i) q^{56} +57.0000i q^{57} +(-27.7128 + 16.0000i) q^{58} +(-36.0000 - 20.7846i) q^{59} +(18.0000 - 10.3923i) q^{61} +10.3923 q^{62} +(18.1865 + 10.5000i) q^{63} -64.0000 q^{64} +(30.0000 + 17.3205i) q^{66} +(51.0955 + 29.5000i) q^{67} -69.2820i q^{69} -26.0000 q^{71} +(20.7846 - 12.0000i) q^{72} +(9.52628 - 16.5000i) q^{73} +(-5.00000 + 8.66025i) q^{74} -70.0000i q^{77} +42.0000i q^{78} +(23.5000 + 40.7032i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(24.2487 + 42.0000i) q^{82} +24.2487 q^{83} +(-19.0000 - 32.9090i) q^{86} +(-13.8564 + 24.0000i) q^{87} +(-69.2820 - 40.0000i) q^{88} +(-102.000 + 58.8897i) q^{89} +(73.5000 - 42.4352i) q^{91} +(7.79423 - 4.50000i) q^{93} +(90.0000 + 51.9615i) q^{94} -48.4974 q^{97} -98.0000i q^{98} +30.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{9} - 20 q^{11} - 28 q^{14} + 32 q^{16} - 114 q^{19} + 48 q^{24} - 84 q^{26} - 64 q^{29} + 18 q^{31} - 42 q^{39} + 160 q^{46} + 98 q^{49} + 24 q^{51} - 36 q^{54} - 112 q^{56} - 144 q^{59} + 72 q^{61}+ \cdots + 120 q^{99}+O(q^{100}) $ 4 * q - 6 * q^9 - 20 * q^11 - 28 * q^14 + 32 * q^16 - 114 * q^19 + 48 * q^24 - 84 * q^26 - 64 * q^29 + 18 * q^31 - 42 * q^39 + 160 * q^46 + 98 * q^49 + 24 * q^51 - 36 * q^54 - 112 * q^56 - 144 * q^59 + 72 * q^61 - 256 * q^64 + 120 * q^66 - 104 * q^71 - 20 * q^74 + 94 * q^79 - 18 * q^81 - 76 * q^86 - 408 * q^89 + 294 * q^91 + 360 * q^94 + 120 * q^99

Character values

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

$n$	$127$	$176$	$451$
$\chi(n)$	$-1$	$1$	$e\left(\frac{1}{6}\right)$

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	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$2$	1.73205	−	1.00000i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$		0			0
$5$		0			0
$5$		0			0
$6$		−	3.46410i		−	0.577350i
$7$	−6.06218	+	3.50000i	−0.866025	+	0.500000i
$7$	−6.06218	+	3.50000i	−0.866025	+	0.500000i
$8$			8.00000i			1.00000i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	−5.00000	+	8.66025i	−0.454545	+	0.787296i	−0.998662	−	0.0517139i	$-0.983532\pi$
$11$	−5.00000	+	8.66025i	−0.454545	+	0.787296i	0.544116	+	0.839010i	$0.316865\pi$
$12$		0			0
$13$	−12.1244			−0.932643			−0.466321	−	0.884615i	$-0.654421\pi$
$13$	−12.1244			−0.932643			−0.466321	+	0.884615i	$0.654421\pi$
$14$	−7.00000	+	12.1244i	−0.500000	+	0.866025i
$15$		0			0
$16$	8.00000	+	13.8564i	0.500000	+	0.866025i
$17$	−3.46410	+	6.00000i	−0.203771	+	0.352941i	−0.949740	−	0.313039i	$-0.898653\pi$
$17$	−3.46410	+	6.00000i	−0.203771	+	0.352941i	0.745970	+	0.665980i	$0.231986\pi$
$18$	−5.19615	−	3.00000i	−0.288675	−	0.166667i
$19$	−28.5000	+	16.4545i	−1.50000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$19$	−28.5000	+	16.4545i	−1.50000	+	0.866025i	−1.00000			$\pi$
$20$		0			0
$21$			12.1244i			0.577350i
$22$			20.0000i			0.909091i
$23$	34.6410	−	20.0000i	1.50613	−	0.869565i	0.506157	−	0.862442i	$-0.331066\pi$
$23$	34.6410	−	20.0000i	1.50613	−	0.869565i	0.999975	−	0.00712357i	$-0.00226752\pi$
$24$	12.0000	+	6.92820i	0.500000	+	0.288675i
$25$		0			0
$26$	−21.0000	+	12.1244i	−0.807692	+	0.466321i
$27$	−5.19615			−0.192450
$28$		0			0
$29$	−16.0000			−0.551724			−0.275862	−	0.961197i	$-0.588963\pi$
$29$	−16.0000			−0.551724			−0.275862	+	0.961197i	$0.588963\pi$
$30$		0			0
$31$	4.50000	+	2.59808i	0.145161	+	0.0838089i	0.570822	−	0.821074i	$-0.306625\pi$
$31$	4.50000	+	2.59808i	0.145161	+	0.0838089i	−0.425660	+	0.904883i	$0.639958\pi$
$32$		0			0
$33$	8.66025	+	15.0000i	0.262432	+	0.454545i
$34$			13.8564i			0.407541i
$35$		0			0
$36$		0			0
$37$	−4.33013	+	2.50000i	−0.117030	+	0.0675676i	−0.557373	−	0.830262i	$-0.688190\pi$
$37$	−4.33013	+	2.50000i	−0.117030	+	0.0675676i	0.440342	+	0.897830i	$0.354857\pi$
$38$	−32.9090	+	57.0000i	−0.866025	+	1.50000i
$39$	−10.5000	+	18.1865i	−0.269231	+	0.466321i
$40$		0			0
$41$			24.2487i			0.591432i	0.955276	+	0.295716i	$0.0955582\pi$
$41$			24.2487i			0.591432i	−0.955276	+	0.295716i	$0.904442\pi$
$42$	12.1244	+	21.0000i	0.288675	+	0.500000i
$43$		−	19.0000i		−	0.441860i	−0.975290	−	0.220930i	$-0.929091\pi$
$43$		−	19.0000i		−	0.441860i	0.975290	−	0.220930i	$-0.0709093\pi$
$44$		0			0
$45$		0			0
$46$	40.0000	−	69.2820i	0.869565	−	1.50613i
$47$	25.9808	+	45.0000i	0.552782	+	0.957447i	0.998072	+	0.0620605i	$0.0197672\pi$
$47$	25.9808	+	45.0000i	0.552782	+	0.957447i	−0.445290	+	0.895386i	$0.646899\pi$
$48$	27.7128			0.577350
$49$	24.5000	−	42.4352i	0.500000	−	0.866025i
$50$		0			0
$51$	6.00000	+	10.3923i	0.117647	+	0.203771i
$52$		0			0
$53$	27.7128	+	16.0000i	0.522883	+	0.301887i	0.738114	−	0.674677i	$-0.235717\pi$
$53$	27.7128	+	16.0000i	0.522883	+	0.301887i	−0.215230	+	0.976563i	$0.569050\pi$
$54$	−9.00000	+	5.19615i	−0.166667	+	0.0962250i
$55$		0			0
$56$	−28.0000	−	48.4974i	−0.500000	−	0.866025i
$57$			57.0000i			1.00000i
$58$	−27.7128	+	16.0000i	−0.477807	+	0.275862i
$59$	−36.0000	−	20.7846i	−0.610169	−	0.352282i	0.162862	−	0.986649i	$-0.447927\pi$
$59$	−36.0000	−	20.7846i	−0.610169	−	0.352282i	−0.773032	+	0.634367i	$0.781261\pi$
$60$		0			0
$61$	18.0000	−	10.3923i	0.295082	−	0.170366i	−0.345149	−	0.938548i	$-0.612172\pi$
$61$	18.0000	−	10.3923i	0.295082	−	0.170366i	0.640231	+	0.768182i	$0.278838\pi$
$62$	10.3923			0.167618
$63$	18.1865	+	10.5000i	0.288675	+	0.166667i
$64$	−64.0000			−1.00000
$65$		0			0
$66$	30.0000	+	17.3205i	0.454545	+	0.262432i
$67$	51.0955	+	29.5000i	0.762619	+	0.440299i	0.830235	−	0.557413i	$-0.188206\pi$
$67$	51.0955	+	29.5000i	0.762619	+	0.440299i	−0.0676160	+	0.997711i	$0.521539\pi$
$68$		0			0
$69$		−	69.2820i		−	1.00409i
$70$		0			0
$71$	−26.0000			−0.366197			−0.183099	−	0.983095i	$-0.558613\pi$
$71$	−26.0000			−0.366197			−0.183099	+	0.983095i	$0.558613\pi$
$72$	20.7846	−	12.0000i	0.288675	−	0.166667i
$73$	9.52628	−	16.5000i	0.130497	−	0.226027i	−0.793371	−	0.608738i	$-0.791676\pi$
$73$	9.52628	−	16.5000i	0.130497	−	0.226027i	0.923868	+	0.382711i	$0.125009\pi$
$74$	−5.00000	+	8.66025i	−0.0675676	+	0.117030i
$75$		0			0
$76$		0			0
$77$		−	70.0000i		−	0.909091i
$78$			42.0000i			0.538462i
$79$	23.5000	+	40.7032i	0.297468	+	0.515230i	0.975556	−	0.219751i	$-0.0705244\pi$
$79$	23.5000	+	40.7032i	0.297468	+	0.515230i	−0.678088	+	0.734981i	$0.737191\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	24.2487	+	42.0000i	0.295716	+	0.512195i
$83$	24.2487			0.292153			0.146077	−	0.989273i	$-0.453335\pi$
$83$	24.2487			0.292153			0.146077	+	0.989273i	$0.453335\pi$
$84$		0			0
$85$		0			0
$86$	−19.0000	−	32.9090i	−0.220930	−	0.382662i
$87$	−13.8564	+	24.0000i	−0.159269	+	0.275862i
$88$	−69.2820	−	40.0000i	−0.787296	−	0.454545i
$89$	−102.000	+	58.8897i	−1.14607	+	0.661682i	−0.947926	−	0.318491i	$-0.896824\pi$
$89$	−102.000	+	58.8897i	−1.14607	+	0.661682i	−0.198142	+	0.980173i	$0.563491\pi$
$90$		0			0
$91$	73.5000	−	42.4352i	0.807692	−	0.466321i
$92$		0			0
$93$	7.79423	−	4.50000i	0.0838089	−	0.0483871i
$94$	90.0000	+	51.9615i	0.957447	+	0.552782i
$95$		0			0
$96$		0			0
$97$	−48.4974			−0.499973			−0.249987	−	0.968249i	$-0.580426\pi$
$97$	−48.4974			−0.499973			−0.249987	+	0.968249i	$0.580426\pi$
$98$		−	98.0000i		−	1.00000i
$99$	30.0000			0.303030
$100$		0			0
$101$	−111.000	−	64.0859i	−1.09901	−	0.634514i	−0.163049	−	0.986618i	$-0.552133\pi$
$101$	−111.000	−	64.0859i	−1.09901	−	0.634514i	−0.935961	+	0.352104i	$0.885466\pi$
$102$	20.7846	+	12.0000i	0.203771	+	0.117647i
$103$	4.33013	+	7.50000i	0.0420401	+	0.0728155i	0.886280	−	0.463150i	$-0.153281\pi$
$103$	4.33013	+	7.50000i	0.0420401	+	0.0728155i	−0.844240	+	0.535966i	$0.819948\pi$
$104$		−	96.9948i		−	0.932643i
$105$		0			0
$106$	64.0000			0.603774
$107$	183.597	−	106.000i	1.71586	−	0.990654i	0.789733	−	0.613451i	$-0.210219\pi$
$107$	183.597	−	106.000i	1.71586	−	0.990654i	0.926130	−	0.377204i	$-0.123114\pi$
$108$		0			0
$109$	8.50000	−	14.7224i	0.0779817	−	0.135068i	−0.824397	−	0.566011i	$-0.808486\pi$
$109$	8.50000	−	14.7224i	0.0779817	−	0.135068i	0.902379	+	0.430943i	$0.141819\pi$
$110$		0			0
$111$			8.66025i			0.0780203i
$112$	−96.9948	−	56.0000i	−0.866025	−	0.500000i
$113$			142.000i			1.25664i	0.777956	+	0.628319i	$0.216257\pi$
$113$			142.000i			1.25664i	−0.777956	+	0.628319i	$0.783743\pi$
$114$	57.0000	+	98.7269i	0.500000	+	0.866025i
$115$		0			0
$116$		0			0
$117$	18.1865	+	31.5000i	0.155440	+	0.269231i
$118$	−83.1384			−0.704563
$119$		−	48.4974i		−	0.407541i
$120$		0			0
$121$	10.5000	+	18.1865i	0.0867769	+	0.150302i
$122$	20.7846	−	36.0000i	0.170366	−	0.295082i
$123$	36.3731	+	21.0000i	0.295716	+	0.170732i
$124$		0			0
$125$		0			0
$126$	42.0000			0.333333
$127$			145.000i			1.14173i	0.821043	+	0.570866i	$0.193392\pi$
$127$			145.000i			1.14173i	−0.821043	+	0.570866i	$0.806608\pi$
$128$	−110.851	+	64.0000i	−0.866025	+	0.500000i
$129$	−28.5000	−	16.4545i	−0.220930	−	0.127554i
$130$		0			0
$131$	−129.000	+	74.4782i	−0.984733	+	0.568536i	−0.903696	−	0.428175i	$-0.859157\pi$
$131$	−129.000	+	74.4782i	−0.984733	+	0.568536i	−0.0810371	+	0.996711i	$0.525823\pi$
$132$		0			0
$133$	115.181	−	199.500i	0.866025	−	1.50000i
$134$	118.000			0.880597
$135$		0			0
$136$	−48.0000	−	27.7128i	−0.352941	−	0.203771i
$137$	−100.459	−	58.0000i	−0.733277	−	0.423358i	0.0863428	−	0.996265i	$-0.472482\pi$
$137$	−100.459	−	58.0000i	−0.733277	−	0.423358i	−0.819620	+	0.572908i	$0.805815\pi$
$138$	−69.2820	−	120.000i	−0.502044	−	0.869565i
$139$		−	84.8705i		−	0.610579i	−0.952260	−	0.305290i	$-0.901247\pi$
$139$		−	84.8705i		−	0.610579i	0.952260	−	0.305290i	$-0.0987532\pi$
$140$		0			0
$141$	90.0000			0.638298
$142$	−45.0333	+	26.0000i	−0.317136	+	0.183099i
$143$	60.6218	−	105.000i	0.423929	−	0.734266i
$144$	24.0000	−	41.5692i	0.166667	−	0.288675i
$145$		0			0
$146$		−	38.1051i		−	0.260994i
$147$	−42.4352	−	73.5000i	−0.288675	−	0.500000i
$148$		0			0
$149$	62.0000	+	107.387i	0.416107	+	0.720719i	0.995544	−	0.0942982i	$-0.0300607\pi$
$149$	62.0000	+	107.387i	0.416107	+	0.720719i	−0.579437	+	0.815017i	$0.696727\pi$
$150$		0			0
$151$	23.0000	−	39.8372i	0.152318	−	0.263822i	−0.779761	−	0.626077i	$-0.784660\pi$
$151$	23.0000	−	39.8372i	0.152318	−	0.263822i	0.932079	+	0.362255i	$0.117993\pi$
$152$	−131.636	−	228.000i	−0.866025	−	1.50000i
$153$	20.7846			0.135847
$154$	−70.0000	−	121.244i	−0.454545	−	0.787296i
$155$		0			0
$156$		0			0
$157$	93.5307	−	162.000i	0.595737	−	1.03185i	−0.397705	−	0.917513i	$-0.630193\pi$
$157$	93.5307	−	162.000i	0.595737	−	1.03185i	0.993442	−	0.114334i	$-0.0364734\pi$
$158$	81.4064	+	47.0000i	0.515230	+	0.297468i
$159$	48.0000	−	27.7128i	0.301887	−	0.174294i
$160$		0			0
$161$	−140.000	+	242.487i	−0.869565	+	1.50613i
$162$			18.0000i			0.111111i
$163$	−50.2295	+	29.0000i	−0.308156	+	0.177914i	−0.646101	−	0.763252i	$-0.723602\pi$
$163$	−50.2295	+	29.0000i	−0.308156	+	0.177914i	0.337945	+	0.941166i	$0.390268\pi$
$164$		0			0
$165$		0			0
$166$	42.0000	−	24.2487i	0.253012	−	0.146077i
$167$	−266.736			−1.59722			−0.798610	−	0.601849i	$-0.794431\pi$
$167$	−266.736			−1.59722			−0.798610	+	0.601849i	$0.794431\pi$
$168$	−96.9948			−0.577350
$169$	−22.0000			−0.130178
$170$		0			0
$171$	85.5000	+	49.3634i	0.500000	+	0.288675i
$172$		0			0
$173$	−62.3538	−	108.000i	−0.360427	−	0.624277i	0.627604	−	0.778532i	$-0.284036\pi$
$173$	−62.3538	−	108.000i	−0.360427	−	0.624277i	−0.988031	+	0.154255i	$0.950702\pi$
$174$			55.4256i			0.318538i
$175$		0			0
$176$	−160.000			−0.909091
$177$	−62.3538	+	36.0000i	−0.352282	+	0.203390i
$178$	−117.779	+	204.000i	−0.661682	+	1.14607i
$179$	5.00000	−	8.66025i	0.0279330	−	0.0483813i	−0.851721	−	0.523996i	$-0.824441\pi$
$179$	5.00000	−	8.66025i	0.0279330	−	0.0483813i	0.879654	+	0.475614i	$0.157774\pi$
$180$		0			0
$181$			327.358i			1.80861i	0.426892	+	0.904303i	$0.359609\pi$
$181$			327.358i			1.80861i	−0.426892	+	0.904303i	$0.640391\pi$
$182$	84.8705	−	147.000i	0.466321	−	0.807692i
$183$		−	36.0000i		−	0.196721i
$184$	160.000	+	277.128i	0.869565	+	1.50613i
$185$		0			0
$186$	9.00000	−	15.5885i	0.0483871	−	0.0838089i
$187$	−34.6410	−	60.0000i	−0.185246	−	0.320856i
$188$		0			0
$189$	31.5000	−	18.1865i	0.166667	−	0.0962250i
$190$		0			0
$191$	1.00000	+	1.73205i	0.00523560	+	0.00906833i	0.868631	−	0.495459i	$-0.165000\pi$
$191$	1.00000	+	1.73205i	0.00523560	+	0.00906833i	−0.863396	+	0.504527i	$0.831667\pi$
$192$	−55.4256	+	96.0000i	−0.288675	+	0.500000i
$193$	203.516	+	117.500i	1.05449	+	0.608808i	0.923902	−	0.382629i	$-0.124981\pi$
$193$	203.516	+	117.500i	1.05449	+	0.608808i	0.130585	+	0.991437i	$0.458315\pi$
$194$	−84.0000	+	48.4974i	−0.432990	+	0.249987i
$195$		0			0
$196$		0			0
$197$		−	100.000i		−	0.507614i	−0.967255	−	0.253807i	$-0.918317\pi$
$197$		−	100.000i		−	0.507614i	0.967255	−	0.253807i	$-0.0816828\pi$
$198$	51.9615	−	30.0000i	0.262432	−	0.151515i
$199$	174.000	+	100.459i	0.874372	+	0.504819i	0.868799	−	0.495166i	$-0.164893\pi$
$199$	174.000	+	100.459i	0.874372	+	0.504819i	0.00557327	+	0.999984i	$0.498226\pi$
$200$		0			0
$201$	88.5000	−	51.0955i	0.440299	−	0.254206i
$202$	−256.344			−1.26903
$203$	96.9948	−	56.0000i	0.477807	−	0.275862i
$204$		0			0
$205$		0			0
$206$	15.0000	+	8.66025i	0.0728155	+	0.0420401i
$207$	−103.923	−	60.0000i	−0.502044	−	0.289855i
$208$	−96.9948	−	168.000i	−0.466321	−	0.807692i
$209$		−	329.090i		−	1.57459i
$210$		0			0
$211$	2.00000			0.00947867			0.00473934	−	0.999989i	$-0.498491\pi$
$211$	2.00000			0.00947867			0.00473934	+	0.999989i	$0.498491\pi$
$212$		0			0
$213$	−22.5167	+	39.0000i	−0.105712	+	0.183099i
$214$	212.000	−	367.195i	0.990654	−	1.71586i
$215$		0			0
$216$		−	41.5692i		−	0.192450i
$217$	−36.3731			−0.167618
$218$		−	34.0000i		−	0.155963i
$219$	−16.5000	−	28.5788i	−0.0753425	−	0.130497i
$220$		0			0
$221$	42.0000	−	72.7461i	0.190045	−	0.329168i
$222$	8.66025	+	15.0000i	0.0390102	+	0.0675676i
$223$	339.482			1.52234			0.761170	−	0.648552i	$-0.224625\pi$
$223$	339.482			1.52234			0.761170	+	0.648552i	$0.224625\pi$
$224$		0			0
$225$		0			0
$226$	142.000	+	245.951i	0.628319	+	1.08828i
$227$	81.4064	−	141.000i	0.358618	−	0.621145i	−0.629112	−	0.777315i	$-0.716581\pi$
$227$	81.4064	−	141.000i	0.358618	−	0.621145i	0.987730	+	0.156169i	$0.0499146\pi$
$228$		0			0
$229$	−7.50000	+	4.33013i	−0.0327511	+	0.0189089i	−0.516286	−	0.856416i	$-0.672686\pi$
$229$	−7.50000	+	4.33013i	−0.0327511	+	0.0189089i	0.483535	+	0.875325i	$0.339353\pi$
$230$		0			0
$231$	−105.000	−	60.6218i	−0.454545	−	0.262432i
$232$		−	128.000i		−	0.551724i
$233$	−147.224	+	85.0000i	−0.631864	+	0.364807i	−0.781474	−	0.623938i	$-0.785532\pi$
$233$	−147.224	+	85.0000i	−0.631864	+	0.364807i	0.149610	+	0.988745i	$0.452198\pi$
$234$	63.0000	+	36.3731i	0.269231	+	0.155440i
$235$		0			0
$236$		0			0
$237$	81.4064			0.343487
$238$	−48.4974	−	84.0000i	−0.203771	−	0.352941i
$239$	−142.000			−0.594142			−0.297071	−	0.954855i	$-0.596010\pi$
$239$	−142.000			−0.594142			−0.297071	+	0.954855i	$0.596010\pi$
$240$		0			0
$241$	−132.000	−	76.2102i	−0.547718	−	0.316225i	0.200483	−	0.979697i	$-0.435749\pi$
$241$	−132.000	−	76.2102i	−0.547718	−	0.316225i	−0.748201	+	0.663472i	$0.769082\pi$
$242$	36.3731	+	21.0000i	0.150302	+	0.0867769i
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$		0			0
$245$		0			0
$246$	84.0000			0.341463
$247$	345.544	−	199.500i	1.39896	−	0.807692i
$248$	−20.7846	+	36.0000i	−0.0838089	+	0.145161i
$249$	21.0000	−	36.3731i	0.0843373	−	0.146077i
$250$		0			0
$251$		−	290.985i		−	1.15930i	−0.814865	−	0.579650i	$-0.803189\pi$
$251$		−	290.985i		−	1.15930i	0.814865	−	0.579650i	$-0.196811\pi$
$252$		0			0
$253$			400.000i			1.58103i
$254$	145.000	+	251.147i	0.570866	+	0.988769i
$255$		0			0
$256$		0			0
$257$	219.970	+	381.000i	0.855916	+	1.48249i	0.875792	+	0.482688i	$0.160339\pi$
$257$	219.970	+	381.000i	0.855916	+	1.48249i	−0.0198763	+	0.999802i	$0.506327\pi$
$258$	−65.8179			−0.255108
$259$	17.5000	−	30.3109i	0.0675676	−	0.117030i
$260$		0			0
$261$	24.0000	+	41.5692i	0.0919540	+	0.159269i
$262$	−148.956	+	258.000i	−0.568536	+	0.984733i
$263$	−117.779	−	68.0000i	−0.447831	−	0.258555i	0.259083	−	0.965855i	$-0.416580\pi$
$263$	−117.779	−	68.0000i	−0.447831	−	0.258555i	−0.706914	+	0.707300i	$0.749913\pi$
$264$	−120.000	+	69.2820i	−0.454545	+	0.262432i
$265$		0			0
$266$		−	460.726i		−	1.73205i
$267$			204.000i			0.764045i
$268$		0			0
$269$	195.000	+	112.583i	0.724907	+	0.418525i	0.816556	−	0.577266i	$-0.195880\pi$
$269$	195.000	+	112.583i	0.724907	+	0.418525i	−0.0916490	+	0.995791i	$0.529214\pi$
$270$		0			0
$271$	−318.000	+	183.597i	−1.17343	+	0.677481i	−0.954486	−	0.298256i	$-0.903595\pi$
$271$	−318.000	+	183.597i	−1.17343	+	0.677481i	−0.218946	+	0.975737i	$0.570262\pi$
$272$	−110.851			−0.407541
$273$		−	147.000i		−	0.538462i
$274$	−232.000			−0.846715
$275$		0			0
$276$		0			0
$277$	342.080	+	197.500i	1.23495	+	0.712996i	0.968057	−	0.250731i	$-0.0806709\pi$
$277$	342.080	+	197.500i	1.23495	+	0.712996i	0.266889	+	0.963727i	$0.414004\pi$
$278$	−84.8705	−	147.000i	−0.305290	−	0.528777i
$279$		−	15.5885i		−	0.0558726i
$280$		0			0
$281$	100.000			0.355872			0.177936	−	0.984042i	$-0.443058\pi$
$281$	100.000			0.355872			0.177936	+	0.984042i	$0.443058\pi$
$282$	155.885	−	90.0000i	0.552782	−	0.319149i
$283$	179.267	−	310.500i	0.633453	−	1.09717i	−0.353387	−	0.935477i	$-0.614970\pi$
$283$	179.267	−	310.500i	0.633453	−	1.09717i	0.986841	−	0.161696i	$-0.0516964\pi$
$284$		0			0
$285$		0			0
$286$		−	242.487i		−	0.847857i
$287$	−84.8705	−	147.000i	−0.295716	−	0.512195i
$288$		0			0
$289$	120.500	+	208.712i	0.416955	+	0.722187i
$290$		0			0
$291$	−42.0000	+	72.7461i	−0.144330	+	0.249987i
$292$		0			0
$293$	−242.487			−0.827601			−0.413801	−	0.910368i	$-0.635799\pi$
$293$	−242.487			−0.827601			−0.413801	+	0.910368i	$0.635799\pi$
$294$	−147.000	−	84.8705i	−0.500000	−	0.288675i
$295$		0			0
$296$	−20.0000	−	34.6410i	−0.0675676	−	0.117030i
$297$	25.9808	−	45.0000i	0.0874773	−	0.151515i
$298$	214.774	+	124.000i	0.720719	+	0.416107i
$299$	−420.000	+	242.487i	−1.40468	+	0.810994i
$300$		0			0
$301$	66.5000	+	115.181i	0.220930	+	0.382662i
$302$		−	92.0000i		−	0.304636i
$303$	−192.258	+	111.000i	−0.634514	+	0.366337i
$304$	−456.000	−	263.272i	−1.50000	−	0.866025i
$305$		0			0
$306$	36.0000	−	20.7846i	0.117647	−	0.0679236i
$307$	181.865			0.592395			0.296198	−	0.955127i	$-0.404281\pi$
$307$	181.865			0.592395			0.296198	+	0.955127i	$0.404281\pi$
$308$		0			0
$309$	15.0000			0.0485437
$310$		0			0
$311$	477.000	+	275.396i	1.53376	+	0.885518i	0.999184	+	0.0403991i	$0.0128629\pi$
$311$	477.000	+	275.396i	1.53376	+	0.885518i	0.534578	+	0.845119i	$0.320470\pi$
$312$	−145.492	−	84.0000i	−0.466321	−	0.269231i
$313$	101.325	+	175.500i	0.323722	+	0.560703i	0.981253	−	0.192725i	$-0.0617324\pi$
$313$	101.325	+	175.500i	0.323722	+	0.560703i	−0.657531	+	0.753428i	$0.728399\pi$
$314$		−	374.123i		−	1.19147i
$315$		0			0
$316$		0			0
$317$	−252.879	+	146.000i	−0.797727	+	0.460568i	−0.842676	−	0.538421i	$-0.819021\pi$
$317$	−252.879	+	146.000i	−0.797727	+	0.460568i	0.0449488	+	0.998989i	$0.485688\pi$
$318$	55.4256	−	96.0000i	0.174294	−	0.301887i
$319$	80.0000	−	138.564i	0.250784	−	0.434370i
$320$		0			0
$321$		−	367.195i		−	1.14391i
$322$			560.000i			1.73913i
$323$		−	228.000i		−	0.705882i
$324$		0			0
$325$		0			0
$326$	−58.0000	+	100.459i	−0.177914	+	0.308156i
$327$	−14.7224	−	25.5000i	−0.0450227	−	0.0779817i
$328$	−193.990			−0.591432
$329$	−315.000	−	181.865i	−0.957447	−	0.552782i
$330$		0			0
$331$	−2.50000	−	4.33013i	−0.00755287	−	0.0130820i	0.862224	−	0.506527i	$-0.169071\pi$
$331$	−2.50000	−	4.33013i	−0.00755287	−	0.0130820i	−0.869777	+	0.493445i	$0.835738\pi$
$332$		0			0
$333$	12.9904	+	7.50000i	0.0390102	+	0.0225225i
$334$	−462.000	+	266.736i	−1.38323	+	0.798610i
$335$		0			0
$336$	−168.000	+	96.9948i	−0.500000	+	0.288675i
$337$			439.000i			1.30267i	0.758790	+	0.651335i	$0.225791\pi$
$337$			439.000i			1.30267i	−0.758790	+	0.651335i	$0.774209\pi$
$338$	−38.1051	+	22.0000i	−0.112737	+	0.0650888i
$339$	213.000	+	122.976i	0.628319	+	0.362760i
$340$		0			0
$341$	−45.0000	+	25.9808i	−0.131965	+	0.0761899i
$342$	197.454			0.577350
$343$			343.000i			1.00000i
$344$	152.000			0.441860
$345$		0			0
$346$	−216.000	−	124.708i	−0.624277	−	0.360427i
$347$	190.526	+	110.000i	0.549065	+	0.317003i	0.748745	−	0.662858i	$-0.230657\pi$
$347$	190.526	+	110.000i	0.549065	+	0.317003i	−0.199680	+	0.979861i	$0.563990\pi$
$348$		0			0
$349$			339.482i			0.972728i	0.873756	+	0.486364i	$0.161677\pi$
$349$			339.482i			0.972728i	−0.873756	+	0.486364i	$0.838323\pi$
$350$		0			0
$351$	63.0000			0.179487
$352$		0			0
$353$	−154.153	+	267.000i	−0.436693	+	0.756374i	−0.997432	−	0.0716184i	$-0.977184\pi$
$353$	−154.153	+	267.000i	−0.436693	+	0.756374i	0.560739	+	0.827992i	$0.310517\pi$
$354$	−72.0000	+	124.708i	−0.203390	+	0.352282i
$355$		0			0
$356$		0			0
$357$	−72.7461	−	42.0000i	−0.203771	−	0.117647i
$358$		−	20.0000i		−	0.0558659i
$359$	146.000	+	252.879i	0.406685	+	0.704399i	0.994516	−	0.104584i	$-0.0333512\pi$
$359$	146.000	+	252.879i	0.406685	+	0.704399i	−0.587831	+	0.808984i	$0.700018\pi$
$360$		0			0
$361$	361.000	−	625.270i	1.00000	−	1.73205i
$362$	327.358	+	567.000i	0.904303	+	1.56630i
$363$	36.3731			0.100201
$364$		0			0
$365$		0			0
$366$	−36.0000	−	62.3538i	−0.0983607	−	0.170366i
$367$	269.334	−	466.500i	0.733880	−	1.27112i	−0.221333	−	0.975198i	$-0.571041\pi$
$367$	269.334	−	466.500i	0.733880	−	1.27112i	0.955213	−	0.295919i	$-0.0956258\pi$
$368$	554.256	+	320.000i	1.50613	+	0.869565i
$369$	63.0000	−	36.3731i	0.170732	−	0.0985720i
$370$		0			0
$371$	−224.000			−0.603774
$372$		0			0
$373$	−177.535	+	102.500i	−0.475966	+	0.274799i	−0.718734	−	0.695285i	$-0.755278\pi$
$373$	−177.535	+	102.500i	−0.475966	+	0.274799i	0.242768	+	0.970084i	$0.421945\pi$
$374$	−120.000	−	69.2820i	−0.320856	−	0.185246i
$375$		0			0
$376$	−360.000	+	207.846i	−0.957447	+	0.552782i
$377$	193.990			0.514562
$378$	36.3731	−	63.0000i	0.0962250	−	0.166667i
$379$	523.000			1.37995			0.689974	−	0.723835i	$-0.257622\pi$
$379$	523.000			1.37995			0.689974	+	0.723835i	$0.257622\pi$
$380$		0			0
$381$	217.500	+	125.574i	0.570866	+	0.329590i
$382$	3.46410	+	2.00000i	0.00906833	+	0.00523560i
$383$	−38.1051	−	66.0000i	−0.0994912	−	0.172324i	0.811983	−	0.583681i	$-0.198388\pi$
$383$	−38.1051	−	66.0000i	−0.0994912	−	0.172324i	−0.911474	+	0.411357i	$0.865055\pi$
$384$			221.703i			0.577350i
$385$		0			0
$386$	470.000			1.21762
$387$	−49.3634	+	28.5000i	−0.127554	+	0.0736434i
$388$		0			0
$389$	−37.0000	+	64.0859i	−0.0951157	+	0.164745i	−0.909657	−	0.415361i	$-0.863655\pi$
$389$	−37.0000	+	64.0859i	−0.0951157	+	0.164745i	0.814541	+	0.580106i	$0.196989\pi$
$390$		0			0
$391$			277.128i			0.708768i
$392$	339.482	+	196.000i	0.866025	+	0.500000i
$393$			258.000i			0.656489i
$394$	−100.000	−	173.205i	−0.253807	−	0.439607i
$395$		0			0
$396$		0			0
$397$	−161.947	−	280.500i	−0.407926	−	0.706549i	0.586731	−	0.809782i	$-0.300415\pi$
$397$	−161.947	−	280.500i	−0.407926	−	0.706549i	−0.994657	+	0.103233i	$0.967081\pi$
$398$	401.836			1.00964
$399$	−199.500	−	345.544i	−0.500000	−	0.866025i
$400$		0			0
$401$	64.0000	+	110.851i	0.159601	+	0.276437i	0.934725	−	0.355372i	$-0.115646\pi$
$401$	64.0000	+	110.851i	0.159601	+	0.276437i	−0.775124	+	0.631809i	$0.782313\pi$
$402$	102.191	−	177.000i	0.254206	−	0.440299i
$403$	−54.5596	−	31.5000i	−0.135384	−	0.0781638i
$404$		0			0
$405$		0			0
$406$	112.000	−	193.990i	0.275862	−	0.477807i
$407$		−	50.0000i		−	0.122850i
$408$	−83.1384	+	48.0000i	−0.203771	+	0.117647i
$409$	−256.500	−	148.090i	−0.627139	−	0.362079i	0.152504	−	0.988303i	$-0.451266\pi$
$409$	−256.500	−	148.090i	−0.627139	−	0.362079i	−0.779643	+	0.626224i	$0.784600\pi$
$410$		0			0
$411$	−174.000	+	100.459i	−0.423358	+	0.244426i
$412$		0			0
$413$	290.985			0.704563
$414$	−240.000			−0.579710
$415$		0			0
$416$		0			0
$417$	−127.306	−	73.5000i	−0.305290	−	0.176259i
$418$	−329.090	−	570.000i	−0.787296	−	1.36364i
$419$			412.228i			0.983838i	0.870641	+	0.491919i	$0.163704\pi$
$419$			412.228i			0.983838i	−0.870641	+	0.491919i	$0.836296\pi$
$420$		0			0
$421$	107.000			0.254157			0.127078	−	0.991893i	$-0.459440\pi$
$421$	107.000			0.254157			0.127078	+	0.991893i	$0.459440\pi$
$422$	3.46410	−	2.00000i	0.00820877	−	0.00473934i
$423$	77.9423	−	135.000i	0.184261	−	0.319149i
$424$	−128.000	+	221.703i	−0.301887	+	0.522883i
$425$		0			0
$426$			90.0666i			0.211424i
$427$	−72.7461	+	126.000i	−0.170366	+	0.295082i
$428$		0			0
$429$	−105.000	−	181.865i	−0.244755	−	0.423929i
$430$		0			0
$431$	−131.000	+	226.899i	−0.303944	+	0.526447i	−0.977026	−	0.213121i	$-0.931637\pi$
$431$	−131.000	+	226.899i	−0.303944	+	0.526447i	0.673081	+	0.739568i	$0.264970\pi$
$432$	−41.5692	−	72.0000i	−0.0962250	−	0.166667i
$433$	36.3731			0.0840025			0.0420012	−	0.999118i	$-0.486627\pi$
$433$	36.3731			0.0840025			0.0420012	+	0.999118i	$0.486627\pi$
$434$	−63.0000	+	36.3731i	−0.145161	+	0.0838089i
$435$		0			0
$436$		0			0
$437$	−658.179	+	1140.00i	−1.50613	+	2.60870i
$438$	−57.1577	−	33.0000i	−0.130497	−	0.0753425i
$439$	−270.000	+	155.885i	−0.615034	+	0.355090i	−0.774933	−	0.632043i	$-0.782216\pi$
$439$	−270.000	+	155.885i	−0.615034	+	0.355090i	0.159899	+	0.987133i	$0.448883\pi$
$440$		0			0
$441$	−147.000			−0.333333
$442$		−	168.000i		−	0.380090i
$443$	−183.597	+	106.000i	−0.414441	+	0.239278i	−0.692696	−	0.721230i	$-0.743577\pi$
$443$	−183.597	+	106.000i	−0.414441	+	0.239278i	0.278255	+	0.960507i	$0.410244\pi$
$444$		0			0
$445$		0			0
$446$	588.000	−	339.482i	1.31839	−	0.761170i
$447$	214.774			0.480479
$448$	387.979	−	224.000i	0.866025	−	0.500000i
$449$	782.000			1.74165			0.870824	−	0.491595i	$-0.163586\pi$
$449$	782.000			1.74165			0.870824	+	0.491595i	$0.163586\pi$
$450$		0			0
$451$	−210.000	−	121.244i	−0.465632	−	0.268833i
$452$		0			0
$453$	−39.8372	−	69.0000i	−0.0879408	−	0.152318i
$454$		−	325.626i		−	0.717237i
$455$		0			0
$456$	−456.000			−1.00000
$457$	−586.299	+	338.500i	−1.28293	+	0.740700i	−0.977383	−	0.211477i	$-0.932173\pi$
$457$	−586.299	+	338.500i	−1.28293	+	0.740700i	−0.305547	+	0.952177i	$0.598839\pi$
$458$	−8.66025	+	15.0000i	−0.0189089	+	0.0327511i
$459$	18.0000	−	31.1769i	0.0392157	−	0.0679236i
$460$		0			0
$461$			484.974i			1.05200i	0.850483	+	0.526002i	$0.176310\pi$
$461$			484.974i			1.05200i	−0.850483	+	0.526002i	$0.823690\pi$
$462$	−242.487			−0.524864
$463$			443.000i			0.956803i	0.878141	+	0.478402i	$0.158784\pi$
$463$			443.000i			0.956803i	−0.878141	+	0.478402i	$0.841216\pi$
$464$	−128.000	−	221.703i	−0.275862	−	0.477807i
$465$		0			0
$466$	−170.000	+	294.449i	−0.364807	+	0.631864i
$467$	−22.5167	−	39.0000i	−0.0482155	−	0.0835118i	0.840910	−	0.541174i	$-0.182020\pi$
$467$	−22.5167	−	39.0000i	−0.0482155	−	0.0835118i	−0.889126	+	0.457663i	$0.848687\pi$
$468$		0			0
$469$	−413.000			−0.880597
$470$		0			0
$471$	−162.000	−	280.592i	−0.343949	−	0.595737i
$472$	166.277	−	288.000i	0.352282	−	0.610169i
$473$	164.545	+	95.0000i	0.347875	+	0.200846i
$474$	141.000	−	81.4064i	0.297468	−	0.171743i
$475$		0			0
$476$		0			0
$477$		−	96.0000i		−	0.201258i
$478$	−245.951	+	142.000i	−0.514542	+	0.297071i
$479$	48.0000	+	27.7128i	0.100209	+	0.0578556i	0.549267	−	0.835647i	$-0.314907\pi$
$479$	48.0000	+	27.7128i	0.100209	+	0.0578556i	−0.449058	+	0.893503i	$0.648240\pi$
$480$		0			0
$481$	52.5000	−	30.3109i	0.109148	−	0.0630164i
$482$	−304.841			−0.632450
$483$	242.487	+	420.000i	0.502044	+	0.869565i
$484$		0			0
$485$		0			0
$486$	27.0000	+	15.5885i	0.0555556	+	0.0320750i
$487$	−58.0237	−	33.5000i	−0.119145	−	0.0687885i	0.439243	−	0.898368i	$-0.355247\pi$
$487$	−58.0237	−	33.5000i	−0.119145	−	0.0687885i	−0.558388	+	0.829580i	$0.688580\pi$
$488$	83.1384	+	144.000i	0.170366	+	0.295082i
$489$			100.459i			0.205438i
$490$		0			0
$491$	−68.0000			−0.138493			−0.0692464	−	0.997600i	$-0.522059\pi$
$491$	−68.0000			−0.138493			−0.0692464	+	0.997600i	$0.522059\pi$
$492$		0			0
$493$	55.4256	−	96.0000i	0.112425	−	0.194726i
$494$	399.000	−	691.088i	0.807692	−	1.39896i
$495$		0			0
$496$			83.1384i			0.167618i
$497$	157.617	−	91.0000i	0.317136	−	0.183099i
$498$		−	84.0000i		−	0.168675i
$499$	254.500	+	440.807i	0.510020	+	0.883381i	0.999933	+	0.0116091i	$0.00369536\pi$
$499$	254.500	+	440.807i	0.510020	+	0.883381i	−0.489913	+	0.871772i	$0.662971\pi$
$500$		0			0
$501$	−231.000	+	400.104i	−0.461078	+	0.798610i
$502$	−290.985	−	504.000i	−0.579650	−	1.00398i
$503$	−654.715			−1.30162			−0.650810	−	0.759240i	$-0.725571\pi$
$503$	−654.715			−1.30162			−0.650810	+	0.759240i	$0.725571\pi$
$504$	−84.0000	+	145.492i	−0.166667	+	0.288675i
$505$		0			0
$506$	400.000	+	692.820i	0.790514	+	1.36921i
$507$	−19.0526	+	33.0000i	−0.0375790	+	0.0650888i
$508$		0			0
$509$	−753.000	+	434.745i	−1.47937	+	0.854115i	−0.999727	−	0.0233478i	$-0.992567\pi$
$509$	−753.000	+	434.745i	−1.47937	+	0.854115i	−0.479644	+	0.877463i	$0.659234\pi$
$510$		0			0
$511$			133.368i			0.260994i
$512$		−	512.000i		−	1.00000i
$513$	148.090	−	85.5000i	0.288675	−	0.166667i
$514$	762.000	+	439.941i	1.48249	+	0.855916i
$515$		0			0
$516$		0			0
$517$	−519.615			−1.00506
$518$		−	70.0000i		−	0.135135i
$519$	−216.000			−0.416185
$520$		0			0
$521$	372.000	+	214.774i	0.714012	+	0.412235i	0.812545	−	0.582899i	$-0.198082\pi$
$521$	372.000	+	214.774i	0.714012	+	0.412235i	−0.0985331	+	0.995134i	$0.531415\pi$
$522$	83.1384	+	48.0000i	0.159269	+	0.0919540i
$523$	−492.768	−	853.500i	−0.942196	−	1.63193i	−0.761271	−	0.648434i	$-0.775424\pi$
$523$	−492.768	−	853.500i	−0.942196	−	1.63193i	−0.180925	−	0.983497i	$-0.557909\pi$
$524$		0			0
$525$		0			0
$526$	−272.000			−0.517110
$527$	−31.1769	+	18.0000i	−0.0591592	+	0.0341556i
$528$	−138.564	+	240.000i	−0.262432	+	0.454545i
$529$	535.500	−	927.513i	1.01229	−	1.75333i
$530$		0			0
$531$			124.708i			0.234854i
$532$		0			0
$533$		−	294.000i		−	0.551595i
$534$	204.000	+	353.338i	0.382022	+	0.661682i
$535$		0			0
$536$	−236.000	+	408.764i	−0.440299	+	0.762619i
$537$	−8.66025	−	15.0000i	−0.0161271	−	0.0279330i
$538$	450.333			0.837051
$539$	245.000	+	424.352i	0.454545	+	0.787296i
$540$		0			0
$541$	60.5000	+	104.789i	0.111830	+	0.193695i	0.916508	−	0.400016i	$-0.130995\pi$
$541$	60.5000	+	104.789i	0.111830	+	0.193695i	−0.804678	+	0.593711i	$0.797662\pi$
$542$	−367.195	+	636.000i	−0.677481	+	1.17343i
$543$	491.036	+	283.500i	0.904303	+	0.522099i
$544$		0			0
$545$		0			0
$546$	−147.000	−	254.611i	−0.269231	−	0.466321i
$547$		−	926.000i		−	1.69287i	−0.532492	−	0.846435i	$-0.678744\pi$
$547$		−	926.000i		−	1.69287i	0.532492	−	0.846435i	$-0.321256\pi$
$548$		0			0
$549$	−54.0000	−	31.1769i	−0.0983607	−	0.0567886i
$550$		0			0
$551$	456.000	−	263.272i	0.827586	−	0.477807i
$552$	554.256			1.00409
$553$	−284.922	−	164.500i	−0.515230	−	0.297468i
$554$	790.000			1.42599
$555$		0			0
$556$		0			0
$557$	−573.309	−	331.000i	−1.02928	−	0.594255i	−0.112502	−	0.993652i	$-0.535886\pi$
$557$	−573.309	−	331.000i	−1.02928	−	0.594255i	−0.916778	+	0.399397i	$0.869220\pi$
$558$	−15.5885	−	27.0000i	−0.0279363	−	0.0483871i
$559$			230.363i			0.412098i
$560$		0			0
$561$	−120.000			−0.213904
$562$	173.205	−	100.000i	0.308194	−	0.177936i
$563$	161.081	−	279.000i	0.286111	−	0.495560i	−0.686767	−	0.726878i	$-0.740971\pi$
$563$	161.081	−	279.000i	0.286111	−	0.495560i	0.972878	+	0.231318i	$0.0743039\pi$
$564$		0			0
$565$		0			0
$566$		−	717.069i		−	1.26691i
$567$		−	63.0000i		−	0.111111i
$568$		−	208.000i		−	0.366197i
$569$	−379.000	−	656.447i	−0.666081	−	1.15369i	−0.978991	−	0.203903i	$-0.934637\pi$
$569$	−379.000	−	656.447i	−0.666081	−	1.15369i	0.312910	−	0.949783i	$-0.398696\pi$
$570$		0			0
$571$	432.500	−	749.112i	0.757443	−	1.31193i	−0.186707	−	0.982416i	$-0.559782\pi$
$571$	432.500	−	749.112i	0.757443	−	1.31193i	0.944151	−	0.329514i	$-0.106885\pi$
$572$		0			0
$573$	3.46410			0.00604555
$574$	−294.000	−	169.741i	−0.512195	−	0.295716i
$575$		0			0
$576$	96.0000	+	166.277i	0.166667	+	0.288675i
$577$	536.070	−	928.500i	0.929064	−	1.60919i	0.144172	−	0.989553i	$-0.453948\pi$
$577$	536.070	−	928.500i	0.929064	−	1.60919i	0.784892	−	0.619633i	$-0.212718\pi$
$578$	417.424	+	241.000i	0.722187	+	0.416955i
$579$	352.500	−	203.516i	0.608808	−	0.351496i
$580$		0			0
$581$	−147.000	+	84.8705i	−0.253012	+	0.146077i
$582$			168.000i			0.288660i
$583$	−277.128	+	160.000i	−0.475348	+	0.274443i
$584$	132.000	+	76.2102i	0.226027	+	0.130497i
$585$		0			0
$586$	−420.000	+	242.487i	−0.716724	+	0.413801i
$587$	339.482			0.578334			0.289167	−	0.957279i	$-0.406622\pi$
$587$	339.482			0.578334			0.289167	+	0.957279i	$0.406622\pi$
$588$		0			0
$589$	−171.000			−0.290323
$590$		0			0
$591$	−150.000	−	86.6025i	−0.253807	−	0.146536i
$592$	−69.2820	−	40.0000i	−0.117030	−	0.0675676i
$593$	−122.976	−	213.000i	−0.207379	−	0.359191i	0.743509	−	0.668726i	$-0.233160\pi$
$593$	−122.976	−	213.000i	−0.207379	−	0.359191i	−0.950888	+	0.309535i	$0.899827\pi$
$594$		−	103.923i		−	0.174955i
$595$		0			0
$596$		0			0
$597$	301.377	−	174.000i	0.504819	−	0.291457i
$598$	−484.974	+	840.000i	−0.810994	+	1.40468i
$599$	−142.000	+	245.951i	−0.237062	+	0.410603i	−0.959870	−	0.280446i	$-0.909518\pi$
$599$	−142.000	+	245.951i	−0.237062	+	0.410603i	0.722808	+	0.691049i	$0.242851\pi$
$600$		0			0
$601$		−	594.093i		−	0.988508i	−0.869317	−	0.494254i	$-0.835441\pi$
$601$		−	594.093i		−	0.988508i	0.869317	−	0.494254i	$-0.164559\pi$
$602$	230.363	+	133.000i	0.382662	+	0.220930i
$603$		−	177.000i		−	0.293532i
$604$		0			0
$605$		0			0
$606$	−222.000	+	384.515i	−0.366337	+	0.634514i
$607$	−4.33013	−	7.50000i	−0.00713365	−	0.0123558i	0.862437	−	0.506165i	$-0.168937\pi$
$607$	−4.33013	−	7.50000i	−0.00713365	−	0.0123558i	−0.869570	+	0.493809i	$0.835604\pi$
$608$		0			0
$609$		−	193.990i		−	0.318538i
$610$		0			0
$611$	−315.000	−	545.596i	−0.515548	−	0.892956i
$612$		0			0
$613$	−760.370	−	439.000i	−1.24041	−	0.716150i	−0.271231	−	0.962514i	$-0.587431\pi$
$613$	−760.370	−	439.000i	−1.24041	−	0.716150i	−0.969177	+	0.246364i	$0.920764\pi$
$614$	315.000	−	181.865i	0.513029	−	0.296198i
$615$		0			0
$616$	560.000			0.909091
$617$			194.000i			0.314425i	0.987565	+	0.157212i	$0.0502507\pi$
$617$			194.000i			0.314425i	−0.987565	+	0.157212i	$0.949749\pi$
$618$	25.9808	−	15.0000i	0.0420401	−	0.0242718i
$619$	−529.500	−	305.707i	−0.855412	−	0.493872i	0.00706124	−	0.999975i	$-0.497752\pi$
$619$	−529.500	−	305.707i	−0.855412	−	0.493872i	−0.862473	+	0.506103i	$0.831086\pi$
$620$		0			0
$621$	−180.000	+	103.923i	−0.289855	+	0.167348i
$622$	1101.58			1.77104
$623$	412.228	−	714.000i	0.661682	−	1.14607i
$624$	−336.000			−0.538462
$625$		0			0
$626$	351.000	+	202.650i	0.560703	+	0.323722i
$627$	−493.634	−	285.000i	−0.787296	−	0.454545i
$628$		0			0
$629$		−	34.6410i		−	0.0550732i
$630$		0			0
$631$	−250.000			−0.396197			−0.198098	−	0.980182i	$-0.563477\pi$
$631$	−250.000			−0.396197			−0.198098	+	0.980182i	$0.563477\pi$
$632$	−325.626	+	188.000i	−0.515230	+	0.297468i
$633$	1.73205	−	3.00000i	0.00273626	−	0.00473934i
$634$	−292.000	+	505.759i	−0.460568	+	0.797727i
$635$		0			0
$636$		0			0
$637$	−297.047	+	514.500i	−0.466321	+	0.807692i
$638$		−	320.000i		−	0.501567i
$639$	39.0000	+	67.5500i	0.0610329	+	0.105712i
$640$		0			0
$641$	562.000	−	973.413i	0.876755	−	1.51858i	0.0218737	−	0.999761i	$-0.493037\pi$
$641$	562.000	−	973.413i	0.876755	−	1.51858i	0.854881	−	0.518824i	$-0.173630\pi$
$642$	−367.195	−	636.000i	−0.571954	−	0.990654i
$643$	569.845			0.886228			0.443114	−	0.896465i	$-0.353874\pi$
$643$	569.845			0.886228			0.443114	+	0.896465i	$0.353874\pi$
$644$		0			0
$645$		0			0
$646$	−228.000	−	394.908i	−0.352941	−	0.611312i
$647$	542.132	−	939.000i	0.837916	−	1.45131i	−0.0537173	−	0.998556i	$-0.517107\pi$
$647$	542.132	−	939.000i	0.837916	−	1.45131i	0.891634	−	0.452758i	$-0.149560\pi$
$648$	−62.3538	−	36.0000i	−0.0962250	−	0.0555556i
$649$	360.000	−	207.846i	0.554700	−	0.320256i
$650$		0			0
$651$	−31.5000	+	54.5596i	−0.0483871	+	0.0838089i
$652$		0			0
$653$	−874.686	+	505.000i	−1.33949	+	0.773354i	−0.986731	−	0.162361i	$-0.948089\pi$
$653$	−874.686	+	505.000i	−1.33949	+	0.773354i	−0.352757	+	0.935715i	$0.614756\pi$
$654$	−51.0000	−	29.4449i	−0.0779817	−	0.0450227i
$655$		0			0
$656$	−336.000	+	193.990i	−0.512195	+	0.295716i
$657$	−57.1577			−0.0869980
$658$	−727.461			−1.10556
$659$	908.000			1.37785			0.688923	−	0.724835i	$-0.258084\pi$
$659$	908.000			1.37785			0.688923	+	0.724835i	$0.258084\pi$
$660$		0			0
$661$	−625.500	−	361.133i	−0.946293	−	0.546343i	−0.0543659	−	0.998521i	$-0.517314\pi$
$661$	−625.500	−	361.133i	−0.946293	−	0.546343i	−0.891928	+	0.452178i	$0.850647\pi$
$662$	−8.66025	−	5.00000i	−0.0130820	−	0.00755287i
$663$	−72.7461	−	126.000i	−0.109723	−	0.190045i
$664$			193.990i			0.292153i
$665$		0			0
$666$	30.0000			0.0450450
$667$	−554.256	+	320.000i	−0.830969	+	0.479760i
$668$		0			0
$669$	294.000	−	509.223i	0.439462	−	0.761170i
$670$		0			0
$671$			207.846i			0.309756i
$672$		0			0
$673$		−	1027.00i		−	1.52600i	−0.646397	−	0.763001i	$-0.723725\pi$
$673$		−	1027.00i		−	1.52600i	0.646397	−	0.763001i	$-0.276275\pi$
$674$	439.000	+	760.370i	0.651335	+	1.12815i
$675$		0			0
$676$		0			0
$677$	280.592	+	486.000i	0.414464	+	0.717873i	0.995372	−	0.0960963i	$-0.0306357\pi$
$677$	280.592	+	486.000i	0.414464	+	0.717873i	−0.580908	+	0.813969i	$0.697302\pi$
$678$	491.902			0.725520
$679$	294.000	−	169.741i	0.432990	−	0.249987i
$680$		0			0
$681$	−141.000	−	244.219i	−0.207048	−	0.358618i
$682$	−51.9615	+	90.0000i	−0.0761899	+	0.131965i
$683$	−845.241	−	488.000i	−1.23754	−	0.714495i	−0.268950	−	0.963154i	$-0.586677\pi$
$683$	−845.241	−	488.000i	−1.23754	−	0.714495i	−0.968591	+	0.248659i	$0.920010\pi$
$684$		0			0
$685$		0			0
$686$	343.000	+	594.093i	0.500000	+	0.866025i
$687$			15.0000i			0.0218341i
$688$	263.272	−	152.000i	0.382662	−	0.220930i
$689$	−336.000	−	193.990i	−0.487663	−	0.281553i
$690$		0			0
$691$	490.500	−	283.190i	0.709841	−	0.409827i	−0.101161	−	0.994870i	$-0.532256\pi$
$691$	490.500	−	283.190i	0.709841	−	0.409827i	0.811002	+	0.585043i	$0.198922\pi$
$692$		0			0
$693$	−181.865	+	105.000i	−0.262432	+	0.151515i
$694$	440.000			0.634006
$695$		0			0
$696$	−192.000	−	110.851i	−0.275862	−	0.159269i
$697$	−145.492	−	84.0000i	−0.208741	−	0.120516i
$698$	339.482	+	588.000i	0.486364	+	0.842407i
$699$			294.449i			0.421243i
$700$		0			0
$701$	352.000			0.502140			0.251070	−	0.967969i	$-0.419218\pi$
$701$	352.000			0.502140			0.251070	+	0.967969i	$0.419218\pi$
$702$	109.119	−	63.0000i	0.155440	−	0.0897436i
$703$	82.2724	−	142.500i	0.117030	−	0.202703i
$704$	320.000	−	554.256i	0.454545	−	0.787296i
$705$		0			0
$706$			616.610i			0.873385i
$707$	897.202			1.26903
$708$		0			0
$709$	−575.000	−	995.929i	−0.811001	−	1.40470i	−0.912164	−	0.409826i	$-0.865590\pi$
$709$	−575.000	−	995.929i	−0.811001	−	1.40470i	0.101162	−	0.994870i	$-0.467744\pi$
$710$		0			0
$711$	70.5000	−	122.110i	0.0991561	−	0.171743i
$712$	−471.118	−	816.000i	−0.661682	−	1.14607i
$713$	207.846			0.291509
$714$	−168.000			−0.235294
$715$		0			0
$716$		0			0
$717$	−122.976	+	213.000i	−0.171514	+	0.297071i
$718$	505.759	+	292.000i	0.704399	+	0.406685i
$719$	843.000	−	486.706i	1.17246	−	0.676921i	0.218203	−	0.975903i	$-0.429980\pi$
$719$	843.000	−	486.706i	1.17246	−	0.676921i	0.954259	+	0.298982i	$0.0966471\pi$
$720$		0			0
$721$	−52.5000	−	30.3109i	−0.0728155	−	0.0420401i
$722$		−	1444.00i		−	2.00000i
$723$	−228.631	+	132.000i	−0.316225	+	0.182573i
$724$		0			0
$725$		0			0
$726$	63.0000	−	36.3731i	0.0867769	−	0.0501006i
$727$	206.114			0.283513			0.141757	−	0.989902i	$-0.454725\pi$
$727$	206.114			0.283513			0.141757	+	0.989902i	$0.454725\pi$
$728$	339.482	+	588.000i	0.466321	+	0.807692i
$729$	27.0000			0.0370370
$730$		0			0
$731$	114.000	+	65.8179i	0.155951	+	0.0900382i
$732$		0			0
$733$	622.672	+	1078.50i	0.849485	+	1.47135i	0.881669	+	0.471869i	$0.156420\pi$
$733$	622.672	+	1078.50i	0.849485	+	1.47135i	−0.0321842	+	0.999482i	$0.510246\pi$
$734$		−	1077.34i		−	1.46776i
$735$		0			0
$736$		0			0
$737$	−510.955	+	295.000i	−0.693290	+	0.400271i
$738$	72.7461	−	126.000i	0.0985720	−	0.170732i
$739$	155.500	−	269.334i	0.210419	−	0.364457i	−0.741426	−	0.671034i	$-0.765850\pi$
$739$	155.500	−	269.334i	0.210419	−	0.364457i	0.951846	+	0.306577i	$0.0991837\pi$
$740$		0			0
$741$		−	691.088i		−	0.932643i
$742$	−387.979	+	224.000i	−0.522883	+	0.301887i
$743$			394.000i			0.530283i	0.964210	+	0.265141i	$0.0854186\pi$
$743$			394.000i			0.530283i	−0.964210	+	0.265141i	$0.914581\pi$
$744$	36.0000	+	62.3538i	0.0483871	+	0.0838089i
$745$		0			0
$746$	−205.000	+	355.070i	−0.274799	+	0.475966i
$747$	−36.3731	−	63.0000i	−0.0486922	−	0.0843373i
$748$		0			0
$749$	−742.000	+	1285.18i	−0.990654	+	1.71586i
$750$		0			0
$751$	39.5000	+	68.4160i	0.0525965	+	0.0910999i	0.891125	−	0.453758i	$-0.149917\pi$
$751$	39.5000	+	68.4160i	0.0525965	+	0.0910999i	−0.838528	+	0.544858i	$0.816584\pi$
$752$	−415.692	+	720.000i	−0.552782	+	0.957447i
$753$	−436.477	−	252.000i	−0.579650	−	0.334661i
$754$	336.000	−	193.990i	0.445623	−	0.257281i
$755$		0			0
$756$		0			0
$757$			250.000i			0.330251i	0.986273	+	0.165125i	$0.0528029\pi$
$757$			250.000i			0.330251i	−0.986273	+	0.165125i	$0.947197\pi$
$758$	905.863	−	523.000i	1.19507	−	0.689974i
$759$	600.000	+	346.410i	0.790514	+	0.456403i
$760$		0			0
$761$	−822.000	+	474.582i	−1.08016	+	0.623629i	−0.930939	−	0.365175i	$-0.881009\pi$
$761$	−822.000	+	474.582i	−1.08016	+	0.623629i	−0.149219	+	0.988804i	$0.547676\pi$
$762$	502.295			0.659179
$763$			119.000i			0.155963i
$764$		0			0
$765$		0			0
$766$	−132.000	−	76.2102i	−0.172324	−	0.0994912i
$767$	436.477	+	252.000i	0.569070	+	0.328553i
$768$		0			0
$769$			860.829i			1.11941i	0.828691	+	0.559707i	$0.189086\pi$
$769$			860.829i			1.11941i	−0.828691	+	0.559707i	$0.810914\pi$
$770$		0			0
$771$	762.000			0.988327
$772$		0			0
$773$	112.583	−	195.000i	0.145645	−	0.252264i	−0.783969	−	0.620800i	$-0.786808\pi$
$773$	112.583	−	195.000i	0.145645	−	0.252264i	0.929613	+	0.368537i	$0.120141\pi$
$774$	−57.0000	+	98.7269i	−0.0736434	+	0.127554i
$775$		0			0
$776$		−	387.979i		−	0.499973i
$777$	−30.3109	−	52.5000i	−0.0390102	−	0.0675676i
$778$			148.000i			0.190231i
$779$	−399.000	−	691.088i	−0.512195	−	0.887148i
$780$		0			0
$781$	130.000	−	225.167i	0.166453	−	0.288306i
$782$	277.128	+	480.000i	0.354384	+	0.613811i
$783$	83.1384			0.106179
$784$	784.000			1.00000
$785$		0			0
$786$	258.000	+	446.869i	0.328244	+	0.568536i
$787$	−124.708	+	216.000i	−0.158460	+	0.274460i	−0.934313	−	0.356453i	$-0.883986\pi$
$787$	−124.708	+	216.000i	−0.158460	+	0.274460i	0.775854	+	0.630913i	$0.217319\pi$
$788$		0			0
$789$	−204.000	+	117.779i	−0.258555	+	0.149277i
$790$		0			0
$791$	−497.000	−	860.829i	−0.628319	−	1.08828i
$792$			240.000i			0.303030i
$793$	−218.238	+	126.000i	−0.275206	+	0.158890i
$794$	−561.000	−	323.894i	−0.706549	−	0.407926i
$795$		0			0
$796$		0			0
$797$	−1357.93			−1.70380			−0.851900	−	0.523705i	$-0.824549\pi$
$797$	−1357.93			−1.70380			−0.851900	+	0.523705i	$0.824549\pi$
$798$	−691.088	−	399.000i	−0.866025	−	0.500000i
$799$	−360.000			−0.450563
$800$		0			0
$801$	306.000	+	176.669i	0.382022	+	0.220561i
$802$	221.703	+	128.000i	0.276437	+	0.159601i
$803$	95.2628	+	165.000i	0.118634	+	0.205479i
$804$		0			0
$805$		0			0
$806$	−126.000			−0.156328
$807$	337.750	−	195.000i	0.418525	−	0.241636i
$808$	512.687	−	888.000i	0.634514	−	1.09901i
$809$	−709.000	+	1228.02i	−0.876391	+	1.51795i	−0.0211166	+	0.999777i	$0.506722\pi$
$809$	−709.000	+	1228.02i	−0.876391	+	1.51795i	−0.855274	+	0.518176i	$0.826611\pi$
$810$		0			0
$811$			872.954i			1.07639i	0.842820	+	0.538196i	$0.180894\pi$
$811$			872.954i			1.07639i	−0.842820	+	0.538196i	$0.819106\pi$
$812$		0			0
$813$			636.000i			0.782288i
$814$	−50.0000	−	86.6025i	−0.0614251	−	0.106391i
$815$		0			0
$816$	−96.0000	+	166.277i	−0.117647	+	0.203771i
$817$	312.635	+	541.500i	0.382662	+	0.662791i
$818$	−592.361			−0.724158
$819$	−220.500	−	127.306i	−0.269231	−	0.155440i
$820$		0			0
$821$	−125.000	−	216.506i	−0.152253	−	0.263711i	0.779802	−	0.626026i	$-0.215320\pi$
$821$	−125.000	−	216.506i	−0.152253	−	0.263711i	−0.932056	+	0.362315i	$0.881986\pi$
$822$	−200.918	+	348.000i	−0.244426	+	0.423358i
$823$	−178.401	−	103.000i	−0.216769	−	0.125152i	0.387684	−	0.921792i	$-0.373275\pi$
$823$	−178.401	−	103.000i	−0.216769	−	0.125152i	−0.604454	+	0.796640i	$0.706608\pi$
$824$	−60.0000	+	34.6410i	−0.0728155	+	0.0420401i
$825$		0			0
$826$	504.000	−	290.985i	0.610169	−	0.352282i
$827$		−	1234.00i		−	1.49214i	−0.665867	−	0.746070i	$-0.731938\pi$
$827$		−	1234.00i		−	1.49214i	0.665867	−	0.746070i	$-0.268062\pi$
$828$		0			0
$829$	−298.500	−	172.339i	−0.360072	−	0.207888i	0.309040	−	0.951049i	$-0.399992\pi$
$829$	−298.500	−	172.339i	−0.360072	−	0.207888i	−0.669113	+	0.743161i	$0.733326\pi$
$830$		0			0
$831$	592.500	−	342.080i	0.712996	−	0.411649i
$832$	775.959			0.932643
$833$	169.741	+	294.000i	0.203771	+	0.352941i
$834$	−294.000			−0.352518
$835$		0			0
$836$		0			0
$837$	−23.3827	−	13.5000i	−0.0279363	−	0.0161290i
$838$	412.228	+	714.000i	0.491919	+	0.852029i
$839$		−	484.974i		−	0.578038i	−0.957323	−	0.289019i	$-0.906671\pi$
$839$		−	484.974i		−	0.578038i	0.957323	−	0.289019i	$-0.0933291\pi$
$840$		0			0
$841$	−585.000			−0.695600
$842$	185.329	−	107.000i	0.220106	−	0.127078i
$843$	86.6025	−	150.000i	0.102731	−	0.177936i
$844$		0			0
$845$		0			0
$846$		−	311.769i		−	0.368521i
$847$	−127.306	−	73.5000i	−0.150302	−	0.0867769i
$848$			512.000i			0.603774i
$849$	−310.500	−	537.802i	−0.365724	−	0.633453i
$850$		0			0
$851$	−100.000	+	173.205i	−0.117509	+	0.203531i
$852$		0			0
$853$	−278.860			−0.326917			−0.163458	−	0.986550i	$-0.552265\pi$
$853$	−278.860			−0.326917			−0.163458	+	0.986550i	$0.552265\pi$
$854$			290.985i			0.340731i
$855$		0			0
$856$	848.000	+	1468.78i	0.990654	+	1.71586i
$857$	−318.697	+	552.000i	−0.371876	+	0.644107i	−0.989854	−	0.142088i	$-0.954619\pi$
$857$	−318.697	+	552.000i	−0.371876	+	0.644107i	0.617979	+	0.786195i	$0.287952\pi$
$858$	−363.731	−	210.000i	−0.423929	−	0.244755i
$859$	528.000	−	304.841i	0.614668	−	0.354879i	−0.160122	−	0.987097i	$-0.551189\pi$
$859$	528.000	−	304.841i	0.614668	−	0.354879i	0.774790	+	0.632218i	$0.217855\pi$
$860$		0			0
$861$	−294.000			−0.341463
$862$			524.000i			0.607889i
$863$	580.237	−	335.000i	0.672349	−	0.388181i	−0.124617	−	0.992205i	$-0.539770\pi$
$863$	580.237	−	335.000i	0.672349	−	0.388181i	0.796966	+	0.604024i	$0.206437\pi$
$864$		0			0
$865$		0			0
$866$	63.0000	−	36.3731i	0.0727483	−	0.0420012i
$867$	417.424			0.481458
$868$		0			0
$869$	−470.000			−0.540852
$870$		0			0
$871$	−619.500	−	357.668i	−0.711251	−	0.410641i
$872$	117.779	+	68.0000i	0.135068	+	0.0779817i
$873$	72.7461	+	126.000i	0.0833289	+	0.144330i
$874$			2632.72i			3.01226i
$875$		0			0
$876$		0			0
$877$	341.214	−	197.000i	0.389070	−	0.224629i	−0.292687	−	0.956208i	$-0.594550\pi$
$877$	341.214	−	197.000i	0.389070	−	0.224629i	0.681757	+	0.731579i	$0.261216\pi$
$878$	−311.769	+	540.000i	−0.355090	+	0.615034i
$879$	−210.000	+	363.731i	−0.238908	+	0.413801i
$880$		0			0
$881$			1163.94i			1.32116i	0.750758	+	0.660578i	$0.229689\pi$
$881$			1163.94i			1.32116i	−0.750758	+	0.660578i	$0.770311\pi$
$882$	−254.611	+	147.000i	−0.288675	+	0.166667i
$883$			737.000i			0.834655i	0.908756	+	0.417327i	$0.137033\pi$
$883$			737.000i			0.834655i	−0.908756	+	0.417327i	$0.862967\pi$
$884$		0			0
$885$		0			0
$886$	−212.000	+	367.195i	−0.239278	+	0.414441i
$887$	365.463	+	633.000i	0.412021	+	0.713641i	0.995111	−	0.0987664i	$-0.0314897\pi$
$887$	365.463	+	633.000i	0.412021	+	0.713641i	−0.583090	+	0.812408i	$0.698156\pi$
$888$	−69.2820			−0.0780203
$889$	−507.500	−	879.016i	−0.570866	−	0.988769i
$890$		0			0
$891$	−45.0000	−	77.9423i	−0.0505051	−	0.0874773i
$892$		0			0
$893$	−1480.90	−	855.000i	−1.65835	−	0.957447i
$894$	372.000	−	214.774i	0.416107	−	0.240240i
$895$		0			0
$896$	448.000	−	775.959i	0.500000	−	0.866025i
$897$			840.000i			0.936455i
$898$	1354.46	−	782.000i	1.50831	−	0.870824i
$899$	−72.0000	−	41.5692i	−0.0800890	−	0.0462394i
$900$		0			0
$901$	−192.000	+	110.851i	−0.213097	+	0.123031i
$902$	−484.974			−0.537665
$903$	230.363			0.255108
$904$	−1136.00			−1.25664
$905$		0			0
$906$	−138.000	−	79.6743i	−0.152318	−	0.0879408i
$907$	−203.516	−	117.500i	−0.224384	−	0.129548i	0.383595	−	0.923502i	$-0.374686\pi$
$907$	−203.516	−	117.500i	−0.224384	−	0.129548i	−0.607978	+	0.793954i	$0.708019\pi$
$908$		0			0
$909$			384.515i			0.423009i
$910$		0			0
$911$	−740.000			−0.812294			−0.406147	−	0.913808i	$-0.633128\pi$
$911$	−740.000			−0.812294			−0.406147	+	0.913808i	$0.633128\pi$
$912$	−789.815	+	456.000i	−0.866025	+	0.500000i
$913$	−121.244	+	210.000i	−0.132797	+	0.230011i
$914$	−677.000	+	1172.60i	−0.740700	+	1.28293i
$915$		0			0
$916$		0			0
$917$	521.347	−	903.000i	0.568536	−	0.984733i
$918$		−	72.0000i		−	0.0784314i
$919$	758.500	+	1313.76i	0.825354	+	1.42955i	0.901649	+	0.432469i	$0.142358\pi$
$919$	758.500	+	1313.76i	0.825354	+	1.42955i	−0.0762951	+	0.997085i	$0.524309\pi$
$920$		0			0
$921$	157.500	−	272.798i	0.171010	−	0.296198i
$922$	484.974	+	840.000i	0.526002	+	0.911063i
$923$	315.233			0.341531
$924$		0			0
$925$		0			0
$926$	443.000	+	767.299i	0.478402	+	0.828616i
$927$	12.9904	−	22.5000i	0.0140134	−	0.0242718i
$928$		0			0
$929$	−963.000	+	555.988i	−1.03660	+	0.598480i	−0.918868	−	0.394565i	$-0.870895\pi$
$929$	−963.000	+	555.988i	−1.03660	+	0.598480i	−0.117731	+	0.993046i	$0.537562\pi$
$930$		0			0
$931$			1612.54i			1.73205i
$932$		0			0
$933$	826.188	−	477.000i	0.885518	−	0.511254i
$934$	−78.0000	−	45.0333i	−0.0835118	−	0.0482155i
$935$		0			0
$936$	−252.000	+	145.492i	−0.269231	+	0.155440i
$937$	−836.581			−0.892829			−0.446414	−	0.894826i	$-0.647299\pi$
$937$	−836.581			−0.892829			−0.446414	+	0.894826i	$0.647299\pi$
$938$	−715.337	+	413.000i	−0.762619	+	0.440299i
$939$	351.000			0.373802
$940$		0			0
$941$	−342.000	−	197.454i	−0.363443	−	0.209834i	0.307147	−	0.951662i	$-0.400626\pi$
$941$	−342.000	−	197.454i	−0.363443	−	0.209834i	−0.670590	+	0.741828i	$0.733959\pi$
$942$	−561.184	−	324.000i	−0.595737	−	0.343949i
$943$	484.974	+	840.000i	0.514289	+	0.890774i
$944$		−	665.108i		−	0.704563i
$945$		0			0
$946$	380.000			0.401691
$947$	292.717	−	169.000i	0.309099	−	0.178458i	−0.337424	−	0.941353i	$-0.609556\pi$
$947$	292.717	−	169.000i	0.309099	−	0.178458i	0.646523	+	0.762894i	$0.276222\pi$
$948$		0			0
$949$	−115.500	+	200.052i	−0.121707	+	0.210803i
$950$		0			0
$951$			505.759i			0.531818i
$952$	387.979			0.407541
$953$		−	1244.00i		−	1.30535i	−0.757637	−	0.652676i	$-0.773646\pi$
$953$		−	1244.00i		−	1.30535i	0.757637	−	0.652676i	$-0.226354\pi$
$954$	−96.0000	−	166.277i	−0.100629	−	0.174294i
$955$		0			0
$956$		0			0
$957$	−138.564	−	240.000i	−0.144790	−	0.250784i
$958$	110.851			0.115711
$959$	812.000			0.846715
$960$		0			0
$961$	−467.000	−	808.868i	−0.485952	−	0.841694i
$962$	60.6218	−	105.000i	0.0630164	−	0.109148i
$963$	−550.792	−	318.000i	−0.571954	−	0.330218i
$964$		0			0
$965$		0			0
$966$	840.000	+	484.974i	0.869565	+	0.502044i
$967$			1741.00i			1.80041i	0.435463	+	0.900207i	$0.356585\pi$
$967$			1741.00i			1.80041i	−0.435463	+	0.900207i	$0.643415\pi$
$968$	−145.492	+	84.0000i	−0.150302	+	0.0867769i
$969$	−342.000	−	197.454i	−0.352941	−	0.203771i
$970$		0			0
$971$	1110.00	−	640.859i	1.14315	−	0.659999i	0.195942	−	0.980615i	$-0.437223\pi$
$971$	1110.00	−	640.859i	1.14315	−	0.659999i	0.947209	+	0.320617i	$0.103890\pi$
$972$		0			0
$973$	297.047	+	514.500i	0.305290	+	0.528777i
$974$	−134.000			−0.137577
$975$		0			0
$976$	288.000	+	166.277i	0.295082	+	0.170366i
$977$	226.899	+	131.000i	0.232240	+	0.134084i	0.611605	−	0.791163i	$-0.290524\pi$
$977$	226.899	+	131.000i	0.232240	+	0.134084i	−0.379365	+	0.925247i	$0.623857\pi$
$978$	100.459	+	174.000i	0.102719	+	0.177914i
$979$		−	1177.79i		−	1.20306i
$980$		0			0
$981$	−51.0000			−0.0519878
$982$	−117.779	+	68.0000i	−0.119938	+	0.0692464i
$983$	−554.256	+	960.000i	−0.563842	+	0.976602i	0.433315	+	0.901243i	$0.357344\pi$
$983$	−554.256	+	960.000i	−0.563842	+	0.976602i	−0.997156	+	0.0753596i	$0.975990\pi$
$984$	−168.000	+	290.985i	−0.170732	+	0.295716i
$985$		0			0
$986$		−	221.703i		−	0.224850i
$987$	−545.596	+	315.000i	−0.552782	+	0.319149i
$988$		0			0
$989$	−380.000	−	658.179i	−0.384226	−	0.665500i
$990$		0			0
$991$	33.5000	−	58.0237i	0.0338042	−	0.0585507i	−0.848628	−	0.528990i	$-0.822571\pi$
$991$	33.5000	−	58.0237i	0.0338042	−	0.0585507i	0.882433	+	0.470439i	$0.155904\pi$
$992$		0			0
$993$	−8.66025			−0.00872130
$994$	182.000	−	315.233i	0.183099	−	0.317136i
$995$		0			0
$996$		0			0
$997$	−494.501	+	856.500i	−0.495988	+	0.859077i	−0.999989	−	0.00462594i	$-0.998528\pi$
$997$	−494.501	+	856.500i	−0.495988	+	0.859077i	0.504001	+	0.863703i	$0.331861\pi$
$998$	881.614	+	509.000i	0.883381	+	0.510020i
$999$	22.5000	−	12.9904i	0.0225225	−	0.0130034i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.s.d.199.2		4
5.2	odd	4		21.3.f.c.10.1	✓	2
5.3	odd	4		525.3.o.b.451.1		2
5.4	even	2	inner	525.3.s.d.199.1		4
7.5	odd	6	inner	525.3.s.d.124.1		4
15.2	even	4		63.3.m.a.10.1		2
20.7	even	4		336.3.bh.c.241.1		2
35.2	odd	12		147.3.f.e.19.1		2
35.12	even	12		21.3.f.c.19.1	yes	2
35.17	even	12		147.3.d.a.97.1		2
35.19	odd	6	inner	525.3.s.d.124.2		4
35.27	even	4		147.3.f.e.31.1		2
35.32	odd	12		147.3.d.a.97.2		2
35.33	even	12		525.3.o.b.376.1		2
60.47	odd	4		1008.3.cg.f.577.1		2
105.2	even	12		441.3.m.b.19.1		2
105.17	odd	12		441.3.d.d.244.1		2
105.32	even	12		441.3.d.d.244.2		2
105.47	odd	12		63.3.m.a.19.1		2
105.62	odd	4		441.3.m.b.325.1		2
140.47	odd	12		336.3.bh.c.145.1		2
140.67	even	12		2352.3.f.b.97.1		2
140.87	odd	12		2352.3.f.b.97.2		2
420.47	even	12		1008.3.cg.f.145.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.c.10.1	✓	2	5.2	odd	4
21.3.f.c.19.1	yes	2	35.12	even	12
63.3.m.a.10.1		2	15.2	even	4
63.3.m.a.19.1		2	105.47	odd	12
147.3.d.a.97.1		2	35.17	even	12
147.3.d.a.97.2		2	35.32	odd	12
147.3.f.e.19.1		2	35.2	odd	12
147.3.f.e.31.1		2	35.27	even	4
336.3.bh.c.145.1		2	140.47	odd	12
336.3.bh.c.241.1		2	20.7	even	4
441.3.d.d.244.1		2	105.17	odd	12
441.3.d.d.244.2		2	105.32	even	12
441.3.m.b.19.1		2	105.2	even	12
441.3.m.b.325.1		2	105.62	odd	4
525.3.o.b.376.1		2	35.33	even	12
525.3.o.b.451.1		2	5.3	odd	4
525.3.s.d.124.1		4	7.5	odd	6	inner
525.3.s.d.124.2		4	35.19	odd	6	inner
525.3.s.d.199.1		4	5.4	even	2	inner
525.3.s.d.199.2		4	1.1	even	1	trivial
1008.3.cg.f.145.1		2	420.47	even	12
1008.3.cg.f.577.1		2	60.47	odd	4
2352.3.f.b.97.1		2	140.67	even	12
2352.3.f.b.97.2		2	140.87	odd	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	525.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(0.866025 - 1.50000i) q^{3} -3.46410i q^{6} +(-6.06218 + 3.50000i) q^{7} +8.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(-5.00000 + 8.66025i) q^{11} -12.1244 q^{13} +(-7.00000 + 12.1244i) q^{14} +(8.00000 + 13.8564i) q^{16} +(-3.46410 + 6.00000i) q^{17} +(-5.19615 - 3.00000i) q^{18} +(-28.5000 + 16.4545i) q^{19} +12.1244i q^{21} +20.0000i q^{22} +(34.6410 - 20.0000i) q^{23} +(12.0000 + 6.92820i) q^{24} +(-21.0000 + 12.1244i) q^{26} -5.19615 q^{27} -16.0000 q^{29} +(4.50000 + 2.59808i) q^{31} +(8.66025 + 15.0000i) q^{33} +13.8564i q^{34} +(-4.33013 + 2.50000i) q^{37} +(-32.9090 + 57.0000i) q^{38} +(-10.5000 + 18.1865i) q^{39} +24.2487i q^{41} +(12.1244 + 21.0000i) q^{42} -19.0000i q^{43} +(40.0000 - 69.2820i) q^{46} +(25.9808 + 45.0000i) q^{47} +27.7128 q^{48} +(24.5000 - 42.4352i) q^{49} +(6.00000 + 10.3923i) q^{51} +(27.7128 + 16.0000i) q^{53} +(-9.00000 + 5.19615i) q^{54} +(-28.0000 - 48.4974i) q^{56} +57.0000i q^{57} +(-27.7128 + 16.0000i) q^{58} +(-36.0000 - 20.7846i) q^{59} +(18.0000 - 10.3923i) q^{61} +10.3923 q^{62} +(18.1865 + 10.5000i) q^{63} -64.0000 q^{64} +(30.0000 + 17.3205i) q^{66} +(51.0955 + 29.5000i) q^{67} -69.2820i q^{69} -26.0000 q^{71} +(20.7846 - 12.0000i) q^{72} +(9.52628 - 16.5000i) q^{73} +(-5.00000 + 8.66025i) q^{74} -70.0000i q^{77} +42.0000i q^{78} +(23.5000 + 40.7032i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(24.2487 + 42.0000i) q^{82} +24.2487 q^{83} +(-19.0000 - 32.9090i) q^{86} +(-13.8564 + 24.0000i) q^{87} +(-69.2820 - 40.0000i) q^{88} +(-102.000 + 58.8897i) q^{89} +(73.5000 - 42.4352i) q^{91} +(7.79423 - 4.50000i) q^{93} +(90.0000 + 51.9615i) q^{94} -48.4974 q^{97} -98.0000i q^{98} +30.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{9} - 20 q^{11} - 28 q^{14} + 32 q^{16} - 114 q^{19} + 48 q^{24} - 84 q^{26} - 64 q^{29} + 18 q^{31} - 42 q^{39} + 160 q^{46} + 98 q^{49} + 24 q^{51} - 36 q^{54} - 112 q^{56} - 144 q^{59} + 72 q^{61}+ \cdots + 120 q^{99}+O(q^{100}) \) 4 * q - 6 * q^9 - 20 * q^11 - 28 * q^14 + 32 * q^16 - 114 * q^19 + 48 * q^24 - 84 * q^26 - 64 * q^29 + 18 * q^31 - 42 * q^39 + 160 * q^46 + 98 * q^49 + 24 * q^51 - 36 * q^54 - 112 * q^56 - 144 * q^59 + 72 * q^61 - 256 * q^64 + 120 * q^66 - 104 * q^71 - 20 * q^74 + 94 * q^79 - 18 * q^81 - 76 * q^86 - 408 * q^89 + 294 * q^91 + 360 * q^94 + 120 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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