LMFDB - Embedded newform 525.3.s.c.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,3,Mod(124,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

N = Newforms(chi, 3, names="a")

//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);

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

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:	$\Z[a_1, a_2]$
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.c.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+(0.866025 - 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.50000 + 2.59808i) q^{4} -1.73205i q^{6} +(-6.06218 - 3.50000i) q^{7} +7.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.50000 - 9.52628i) q^{11} +(2.59808 + 4.50000i) q^{12} -6.92820 q^{13} -7.00000 q^{14} +(-2.50000 - 4.33013i) q^{16} +(-12.1244 + 21.0000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-10.5000 + 6.06218i) q^{21} -11.0000i q^{22} +(-24.2487 + 14.0000i) q^{23} +(10.5000 + 6.06218i) q^{24} +(-6.00000 + 3.46410i) q^{26} -5.19615 q^{27} +(18.1865 - 10.5000i) q^{28} -25.0000 q^{29} +(-28.5000 - 16.4545i) q^{31} +(-28.5788 - 16.5000i) q^{32} +(-9.52628 - 16.5000i) q^{33} +24.2487i q^{34} +9.00000 q^{36} +(-50.2295 + 29.0000i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-6.00000 + 10.3923i) q^{39} -3.46410i q^{41} +(-6.06218 + 10.5000i) q^{42} -26.0000i q^{43} +(16.5000 + 28.5788i) q^{44} +(-14.0000 + 24.2487i) q^{46} +(-38.1051 - 66.0000i) q^{47} -8.66025 q^{48} +(24.5000 + 42.4352i) q^{49} +(21.0000 + 36.3731i) q^{51} +(10.3923 - 18.0000i) q^{52} +(26.8468 + 15.5000i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(24.5000 - 42.4352i) q^{56} -6.00000i q^{57} +(-21.6506 + 12.5000i) q^{58} +(7.50000 + 4.33013i) q^{59} +(12.0000 - 6.92820i) q^{61} -32.9090 q^{62} +21.0000i q^{63} -13.0000 q^{64} +(-16.5000 - 9.52628i) q^{66} +(45.0333 + 26.0000i) q^{67} +(-36.3731 - 63.0000i) q^{68} +48.4974i q^{69} +64.0000 q^{71} +(18.1865 - 10.5000i) q^{72} +(3.46410 - 6.00000i) q^{73} +(-29.0000 + 50.2295i) q^{74} +10.3923i q^{76} +(-66.6840 + 38.5000i) q^{77} +12.0000i q^{78} +(8.50000 + 14.7224i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.73205 - 3.00000i) q^{82} -53.6936 q^{83} -36.3731i q^{84} +(-13.0000 - 22.5167i) q^{86} +(-21.6506 + 37.5000i) q^{87} +(66.6840 + 38.5000i) q^{88} +(69.0000 - 39.8372i) q^{89} +(42.0000 + 24.2487i) q^{91} -84.0000i q^{92} +(-49.3634 + 28.5000i) q^{93} +(-66.0000 - 38.1051i) q^{94} +(-49.5000 + 28.5788i) q^{96} +91.7987 q^{97} +(42.4352 + 24.5000i) q^{98} -33.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{4} - 6 q^{9} + 22 q^{11} - 28 q^{14} - 10 q^{16} + 12 q^{19} - 42 q^{21} + 42 q^{24} - 24 q^{26} - 100 q^{29} - 114 q^{31} + 36 q^{36} - 24 q^{39} + 66 q^{44} - 56 q^{46} + 98 q^{49} + 84 q^{51}+ \cdots - 132 q^{99}+O(q^{100}) $ 4 * q - 6 * q^4 - 6 * q^9 + 22 * q^11 - 28 * q^14 - 10 * q^16 + 12 * q^19 - 42 * q^21 + 42 * q^24 - 24 * q^26 - 100 * q^29 - 114 * q^31 + 36 * q^36 - 24 * q^39 + 66 * q^44 - 56 * q^46 + 98 * q^49 + 84 * q^51 - 18 * q^54 + 98 * q^56 + 30 * q^59 + 48 * q^61 - 52 * q^64 - 66 * q^66 + 256 * q^71 - 116 * q^74 + 34 * q^79 - 18 * q^81 - 52 * q^86 + 276 * q^89 + 168 * q^91 - 264 * q^94 - 198 * q^96 - 132 * 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 $

$2$	0.866025	−	0.500000i	0.433013	−	0.250000i	−0.267617	−	0.963525i	$-0.586236\pi$
$2$	0.866025	−	0.500000i	0.433013	−	0.250000i	0.700629	+	0.713525i	$0.252903\pi$
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$3$	0.866025	−	1.50000i	0.288675	−	0.500000i
$4$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$5$		0			0
$5$		0			0
$6$		−	1.73205i		−	0.288675i
$7$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$7$	−6.06218	−	3.50000i	−0.866025	−	0.500000i
$8$			7.00000i			0.875000i
$9$	−1.50000	−	2.59808i	−0.166667	−	0.288675i
$10$		0			0
$11$	5.50000	−	9.52628i	0.500000	−	0.866025i	−0.500000	−	0.866025i	$-0.666667\pi$
$11$	5.50000	−	9.52628i	0.500000	−	0.866025i	1.00000			$0$
$12$	2.59808	+	4.50000i	0.216506	+	0.375000i
$13$	−6.92820			−0.532939			−0.266469	−	0.963843i	$-0.585857\pi$
$13$	−6.92820			−0.532939			−0.266469	+	0.963843i	$0.585857\pi$
$14$	−7.00000			−0.500000
$15$		0			0
$16$	−2.50000	−	4.33013i	−0.156250	−	0.270633i
$17$	−12.1244	+	21.0000i	−0.713197	+	1.23529i	0.250453	+	0.968129i	$0.419420\pi$
$17$	−12.1244	+	21.0000i	−0.713197	+	1.23529i	−0.963651	+	0.267165i	$0.913913\pi$
$18$	−2.59808	−	1.50000i	−0.144338	−	0.0833333i
$19$	3.00000	−	1.73205i	0.157895	−	0.0911606i	−0.418971	−	0.908000i	$-0.637609\pi$
$19$	3.00000	−	1.73205i	0.157895	−	0.0911606i	0.576865	+	0.816839i	$0.304276\pi$
$20$		0			0
$21$	−10.5000	+	6.06218i	−0.500000	+	0.288675i
$22$		−	11.0000i		−	0.500000i
$23$	−24.2487	+	14.0000i	−1.05429	+	0.608696i	−0.923848	−	0.382760i	$-0.874974\pi$
$23$	−24.2487	+	14.0000i	−1.05429	+	0.608696i	−0.130444	+	0.991456i	$0.541640\pi$
$24$	10.5000	+	6.06218i	0.437500	+	0.252591i
$25$		0			0
$26$	−6.00000	+	3.46410i	−0.230769	+	0.133235i
$27$	−5.19615			−0.192450
$28$	18.1865	−	10.5000i	0.649519	−	0.375000i
$29$	−25.0000			−0.862069			−0.431034	−	0.902335i	$-0.641851\pi$
$29$	−25.0000			−0.862069			−0.431034	+	0.902335i	$0.641851\pi$
$30$		0			0
$31$	−28.5000	−	16.4545i	−0.919355	−	0.530790i	−0.0359257	−	0.999354i	$-0.511438\pi$
$31$	−28.5000	−	16.4545i	−0.919355	−	0.530790i	−0.883429	+	0.468565i	$0.844771\pi$
$32$	−28.5788	−	16.5000i	−0.893089	−	0.515625i
$33$	−9.52628	−	16.5000i	−0.288675	−	0.500000i
$34$			24.2487i			0.713197i
$35$		0			0
$36$	9.00000			0.250000
$37$	−50.2295	+	29.0000i	−1.35755	+	0.783784i	−0.989294	−	0.145939i	$-0.953380\pi$
$37$	−50.2295	+	29.0000i	−1.35755	+	0.783784i	−0.368260	+	0.929723i	$0.620046\pi$
$38$	1.73205	−	3.00000i	0.0455803	−	0.0789474i
$39$	−6.00000	+	10.3923i	−0.153846	+	0.266469i
$40$		0			0
$41$		−	3.46410i		−	0.0844903i	−0.999107	−	0.0422451i	$-0.986549\pi$
$41$		−	3.46410i		−	0.0844903i	0.999107	−	0.0422451i	$-0.0134510\pi$
$42$	−6.06218	+	10.5000i	−0.144338	+	0.250000i
$43$		−	26.0000i		−	0.604651i	−0.953205	−	0.302326i	$-0.902237\pi$
$43$		−	26.0000i		−	0.604651i	0.953205	−	0.302326i	$-0.0977630\pi$
$44$	16.5000	+	28.5788i	0.375000	+	0.649519i
$45$		0			0
$46$	−14.0000	+	24.2487i	−0.304348	+	0.527146i
$47$	−38.1051	−	66.0000i	−0.810747	−	1.40426i	−0.912342	−	0.409429i	$-0.865728\pi$
$47$	−38.1051	−	66.0000i	−0.810747	−	1.40426i	0.101595	−	0.994826i	$-0.467606\pi$
$48$	−8.66025			−0.180422
$49$	24.5000	+	42.4352i	0.500000	+	0.866025i
$50$		0			0
$51$	21.0000	+	36.3731i	0.411765	+	0.713197i
$52$	10.3923	−	18.0000i	0.199852	−	0.346154i
$53$	26.8468	+	15.5000i	0.506543	+	0.292453i	0.731412	−	0.681936i	$-0.238862\pi$
$53$	26.8468	+	15.5000i	0.506543	+	0.292453i	−0.224868	+	0.974389i	$0.572195\pi$
$54$	−4.50000	+	2.59808i	−0.0833333	+	0.0481125i
$55$		0			0
$56$	24.5000	−	42.4352i	0.437500	−	0.757772i
$57$		−	6.00000i		−	0.105263i
$58$	−21.6506	+	12.5000i	−0.373287	+	0.215517i
$59$	7.50000	+	4.33013i	0.127119	+	0.0733920i	0.562211	−	0.826994i	$-0.309951\pi$
$59$	7.50000	+	4.33013i	0.127119	+	0.0733920i	−0.435092	+	0.900386i	$0.643284\pi$
$60$		0			0
$61$	12.0000	−	6.92820i	0.196721	−	0.113577i	−0.398404	−	0.917210i	$-0.630436\pi$
$61$	12.0000	−	6.92820i	0.196721	−	0.113577i	0.595125	+	0.803633i	$0.297102\pi$
$62$	−32.9090			−0.530790
$63$			21.0000i			0.333333i
$64$	−13.0000			−0.203125
$65$		0			0
$66$	−16.5000	−	9.52628i	−0.250000	−	0.144338i
$67$	45.0333	+	26.0000i	0.672139	+	0.388060i	0.796887	−	0.604129i	$-0.206479\pi$
$67$	45.0333	+	26.0000i	0.672139	+	0.388060i	−0.124748	+	0.992189i	$0.539812\pi$
$68$	−36.3731	−	63.0000i	−0.534898	−	0.926471i
$69$			48.4974i			0.702861i
$70$		0			0
$71$	64.0000			0.901408			0.450704	−	0.892673i	$-0.351173\pi$
$71$	64.0000			0.901408			0.450704	+	0.892673i	$0.351173\pi$
$72$	18.1865	−	10.5000i	0.252591	−	0.145833i
$73$	3.46410	−	6.00000i	0.0474534	−	0.0821918i	−0.841323	−	0.540533i	$-0.818223\pi$
$73$	3.46410	−	6.00000i	0.0474534	−	0.0821918i	0.888777	+	0.458341i	$0.151556\pi$
$74$	−29.0000	+	50.2295i	−0.391892	+	0.678777i
$75$		0			0
$76$			10.3923i			0.136741i
$77$	−66.6840	+	38.5000i	−0.866025	+	0.500000i
$78$			12.0000i			0.153846i
$79$	8.50000	+	14.7224i	0.107595	+	0.186360i	0.914795	−	0.403917i	$-0.132352\pi$
$79$	8.50000	+	14.7224i	0.107595	+	0.186360i	−0.807200	+	0.590277i	$0.799018\pi$
$80$		0			0
$81$	−4.50000	+	7.79423i	−0.0555556	+	0.0962250i
$82$	−1.73205	−	3.00000i	−0.0211226	−	0.0365854i
$83$	−53.6936			−0.646911			−0.323455	−	0.946243i	$-0.604845\pi$
$83$	−53.6936			−0.646911			−0.323455	+	0.946243i	$0.604845\pi$
$84$		−	36.3731i		−	0.433013i
$85$		0			0
$86$	−13.0000	−	22.5167i	−0.151163	−	0.261822i
$87$	−21.6506	+	37.5000i	−0.248858	+	0.431034i
$88$	66.6840	+	38.5000i	0.757772	+	0.437500i
$89$	69.0000	−	39.8372i	0.775281	−	0.447609i	−0.0594743	−	0.998230i	$-0.518942\pi$
$89$	69.0000	−	39.8372i	0.775281	−	0.447609i	0.834755	+	0.550621i	$0.185609\pi$
$90$		0			0
$91$	42.0000	+	24.2487i	0.461538	+	0.266469i
$92$		−	84.0000i		−	0.913043i
$93$	−49.3634	+	28.5000i	−0.530790	+	0.306452i
$94$	−66.0000	−	38.1051i	−0.702128	−	0.405374i
$95$		0			0
$96$	−49.5000	+	28.5788i	−0.515625	+	0.297696i
$97$	91.7987			0.946378			0.473189	−	0.880961i	$-0.343103\pi$
$97$	91.7987			0.946378			0.473189	+	0.880961i	$0.343103\pi$
$98$	42.4352	+	24.5000i	0.433013	+	0.250000i
$99$	−33.0000			−0.333333
$100$		0			0
$101$	−18.0000	−	10.3923i	−0.178218	−	0.102894i	0.408237	−	0.912876i	$-0.366144\pi$
$101$	−18.0000	−	10.3923i	−0.178218	−	0.102894i	−0.586455	+	0.809982i	$0.699477\pi$
$102$	36.3731	+	21.0000i	0.356599	+	0.205882i
$103$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$103$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$104$		−	48.4974i		−	0.466321i
$105$		0			0
$106$	31.0000			0.292453
$107$	26.8468	−	15.5000i	0.250905	−	0.144860i	−0.369274	−	0.929321i	$-0.620394\pi$
$107$	26.8468	−	15.5000i	0.250905	−	0.144860i	0.620178	+	0.784461i	$0.287060\pi$
$108$	7.79423	−	13.5000i	0.0721688	−	0.125000i
$109$	−68.0000	+	117.779i	−0.623853	+	1.08055i	0.364908	+	0.931043i	$0.381100\pi$
$109$	−68.0000	+	117.779i	−0.623853	+	1.08055i	−0.988761	+	0.149502i	$0.952233\pi$
$110$		0			0
$111$			100.459i			0.905036i
$112$			35.0000i			0.312500i
$113$			74.0000i			0.654867i	0.944874	+	0.327434i	$0.106184\pi$
$113$			74.0000i			0.654867i	−0.944874	+	0.327434i	$0.893816\pi$
$114$	−3.00000	−	5.19615i	−0.0263158	−	0.0455803i
$115$		0			0
$116$	37.5000	−	64.9519i	0.323276	−	0.559930i
$117$	10.3923	+	18.0000i	0.0888231	+	0.153846i
$118$	8.66025			0.0733920
$119$	147.000	−	84.8705i	1.23529	−	0.713197i
$120$		0			0
$121$		0			0
$122$	6.92820	−	12.0000i	0.0567886	−	0.0983607i
$123$	−5.19615	−	3.00000i	−0.0422451	−	0.0243902i
$124$	85.5000	−	49.3634i	0.689516	−	0.398092i
$125$		0			0
$126$	10.5000	+	18.1865i	0.0833333	+	0.144338i
$127$		−	1.00000i		−	0.00787402i	−0.999992	−	0.00393701i	$-0.998747\pi$
$127$		−	1.00000i		−	0.00787402i	0.999992	−	0.00393701i	$-0.00125319\pi$
$128$	103.057	−	59.5000i	0.805133	−	0.464844i
$129$	−39.0000	−	22.5167i	−0.302326	−	0.174548i
$130$		0			0
$131$	157.500	−	90.9327i	1.20229	−	0.694142i	0.241226	−	0.970469i	$-0.422450\pi$
$131$	157.500	−	90.9327i	1.20229	−	0.694142i	0.961064	+	0.276326i	$0.0891171\pi$
$132$	57.1577			0.433013
$133$	−24.2487			−0.182321
$134$	52.0000			0.388060
$135$		0			0
$136$	−147.000	−	84.8705i	−1.08088	−	0.624048i
$137$	−76.2102	−	44.0000i	−0.556279	−	0.321168i	0.195372	−	0.980729i	$-0.437409\pi$
$137$	−76.2102	−	44.0000i	−0.556279	−	0.321168i	−0.751651	+	0.659561i	$0.770742\pi$
$138$	24.2487	+	42.0000i	0.175715	+	0.304348i
$139$		−	190.526i		−	1.37069i	−0.728220	−	0.685344i	$-0.759652\pi$
$139$		−	190.526i		−	1.37069i	0.728220	−	0.685344i	$-0.240348\pi$
$140$		0			0
$141$	−132.000			−0.936170
$142$	55.4256	−	32.0000i	0.390321	−	0.225352i
$143$	−38.1051	+	66.0000i	−0.266469	+	0.461538i
$144$	−7.50000	+	12.9904i	−0.0520833	+	0.0902110i
$145$		0			0
$146$		−	6.92820i		−	0.0474534i
$147$	84.8705			0.577350
$148$		−	174.000i		−	1.17568i
$149$	−115.000	−	199.186i	−0.771812	−	1.33682i	−0.936569	−	0.350484i	$-0.886017\pi$
$149$	−115.000	−	199.186i	−0.771812	−	1.33682i	0.164757	−	0.986334i	$-0.447316\pi$
$150$		0			0
$151$	−113.500	+	196.588i	−0.751656	+	1.30191i	0.195364	+	0.980731i	$0.437411\pi$
$151$	−113.500	+	196.588i	−0.751656	+	1.30191i	−0.947020	+	0.321175i	$0.895922\pi$
$152$	12.1244	+	21.0000i	0.0797655	+	0.138158i
$153$	72.7461			0.475465
$154$	−38.5000	+	66.6840i	−0.250000	+	0.433013i
$155$		0			0
$156$	−18.0000	−	31.1769i	−0.115385	−	0.199852i
$157$	24.2487	−	42.0000i	0.154450	−	0.267516i	−0.778408	−	0.627758i	$-0.783973\pi$
$157$	24.2487	−	42.0000i	0.154450	−	0.267516i	0.932859	+	0.360242i	$0.117306\pi$
$158$	14.7224	+	8.50000i	0.0931799	+	0.0537975i
$159$	46.5000	−	26.8468i	0.292453	−	0.168848i
$160$		0			0
$161$	196.000			1.21739
$162$			9.00000i			0.0555556i
$163$	−183.597	+	106.000i	−1.12636	+	0.650307i	−0.943018	−	0.332742i	$-0.892026\pi$
$163$	−183.597	+	106.000i	−1.12636	+	0.650307i	−0.183346	+	0.983048i	$0.558693\pi$
$164$	9.00000	+	5.19615i	0.0548780	+	0.0316839i
$165$		0			0
$166$	−46.5000	+	26.8468i	−0.280120	+	0.161728i
$167$	96.9948			0.580807			0.290404	−	0.956904i	$-0.406210\pi$
$167$	96.9948			0.580807			0.290404	+	0.956904i	$0.406210\pi$
$168$	−42.4352	−	73.5000i	−0.252591	−	0.437500i
$169$	−121.000			−0.715976
$170$		0			0
$171$	−9.00000	−	5.19615i	−0.0526316	−	0.0303869i
$172$	67.5500	+	39.0000i	0.392732	+	0.226744i
$173$	−107.387	−	186.000i	−0.620735	−	1.07514i	−0.989349	−	0.145562i	$-0.953501\pi$
$173$	−107.387	−	186.000i	−0.620735	−	1.07514i	0.368614	−	0.929582i	$-0.379832\pi$
$174$			43.3013i			0.248858i
$175$		0			0
$176$	−55.0000			−0.312500
$177$	12.9904	−	7.50000i	0.0733920	−	0.0423729i
$178$	39.8372	−	69.0000i	0.223804	−	0.387640i
$179$	23.0000	−	39.8372i	0.128492	−	0.222554i	−0.794601	−	0.607132i	$-0.792320\pi$
$179$	23.0000	−	39.8372i	0.128492	−	0.222554i	0.923092	+	0.384578i	$0.125653\pi$
$180$		0			0
$181$			31.1769i			0.172248i	0.996284	+	0.0861241i	$0.0274481\pi$
$181$			31.1769i			0.172248i	−0.996284	+	0.0861241i	$0.972552\pi$
$182$	48.4974			0.266469
$183$		−	24.0000i		−	0.131148i
$184$	−98.0000	−	169.741i	−0.532609	−	0.922505i
$185$		0			0
$186$	−28.5000	+	49.3634i	−0.153226	+	0.265395i
$187$	133.368	+	231.000i	0.713197	+	1.23529i
$188$	228.631			1.21612
$189$	31.5000	+	18.1865i	0.166667	+	0.0962250i
$190$		0			0
$191$	−104.000	−	180.133i	−0.544503	−	0.943106i	−0.998638	−	0.0521735i	$-0.983385\pi$
$191$	−104.000	−	180.133i	−0.544503	−	0.943106i	0.454135	−	0.890933i	$-0.349948\pi$
$192$	−11.2583	+	19.5000i	−0.0586371	+	0.101562i
$193$	206.980	+	119.500i	1.07244	+	0.619171i	0.928846	−	0.370466i	$-0.120802\pi$
$193$	206.980	+	119.500i	1.07244	+	0.619171i	0.143590	+	0.989637i	$0.454135\pi$
$194$	79.5000	−	45.8993i	0.409794	−	0.236595i
$195$		0			0
$196$	−147.000			−0.750000
$197$		−	26.0000i		−	0.131980i	−0.997820	−	0.0659898i	$-0.978980\pi$
$197$		−	26.0000i		−	0.131980i	0.997820	−	0.0659898i	$-0.0210205\pi$
$198$	−28.5788	+	16.5000i	−0.144338	+	0.0833333i
$199$	210.000	+	121.244i	1.05528	+	0.609264i	0.924122	−	0.382098i	$-0.124798\pi$
$199$	210.000	+	121.244i	1.05528	+	0.609264i	0.131155	+	0.991362i	$0.458132\pi$
$200$		0			0
$201$	78.0000	−	45.0333i	0.388060	−	0.224046i
$202$	−20.7846			−0.102894
$203$	151.554	+	87.5000i	0.746574	+	0.431034i
$204$	−126.000			−0.617647
$205$		0			0
$206$		0			0
$207$	72.7461	+	42.0000i	0.351431	+	0.202899i
$208$	17.3205	+	30.0000i	0.0832717	+	0.144231i
$209$		−	38.1051i		−	0.182321i
$210$		0			0
$211$	−52.0000			−0.246445			−0.123223	−	0.992379i	$-0.539323\pi$
$211$	−52.0000			−0.246445			−0.123223	+	0.992379i	$0.539323\pi$
$212$	−80.5404	+	46.5000i	−0.379907	+	0.219340i
$213$	55.4256	−	96.0000i	0.260214	−	0.450704i
$214$	15.5000	−	26.8468i	0.0724299	−	0.125452i
$215$		0			0
$216$		−	36.3731i		−	0.168394i
$217$	115.181	+	199.500i	0.530790	+	0.919355i
$218$			136.000i			0.623853i
$219$	−6.00000	−	10.3923i	−0.0273973	−	0.0474534i
$220$		0			0
$221$	84.0000	−	145.492i	0.380090	−	0.658336i
$222$	50.2295	+	87.0000i	0.226259	+	0.391892i
$223$	22.5167			0.100972			0.0504858	−	0.998725i	$-0.483923\pi$
$223$	22.5167			0.100972			0.0504858	+	0.998725i	$0.483923\pi$
$224$	115.500	+	200.052i	0.515625	+	0.893089i
$225$		0			0
$226$	37.0000	+	64.0859i	0.163717	+	0.283566i
$227$	−33.7750	+	58.5000i	−0.148789	+	0.257709i	−0.930780	−	0.365580i	$-0.880871\pi$
$227$	−33.7750	+	58.5000i	−0.148789	+	0.257709i	0.781991	+	0.623289i	$0.214204\pi$
$228$	15.5885	+	9.00000i	0.0683704	+	0.0394737i
$229$	27.0000	−	15.5885i	0.117904	−	0.0680719i	−0.439888	−	0.898053i	$-0.644982\pi$
$229$	27.0000	−	15.5885i	0.117904	−	0.0680719i	0.557792	+	0.829981i	$0.311649\pi$
$230$		0			0
$231$			133.368i			0.577350i
$232$		−	175.000i		−	0.754310i
$233$	−226.899	+	131.000i	−0.973814	+	0.562232i	−0.900397	−	0.435070i	$-0.856724\pi$
$233$	−226.899	+	131.000i	−0.973814	+	0.562232i	−0.0734171	+	0.997301i	$0.523390\pi$
$234$	18.0000	+	10.3923i	0.0769231	+	0.0444116i
$235$		0			0
$236$	−22.5000	+	12.9904i	−0.0953390	+	0.0550440i
$237$	29.4449			0.124240
$238$	84.8705	−	147.000i	0.356599	−	0.617647i
$239$	−160.000			−0.669456			−0.334728	−	0.942315i	$-0.608644\pi$
$239$	−160.000			−0.669456			−0.334728	+	0.942315i	$0.608644\pi$
$240$		0			0
$241$	409.500	+	236.425i	1.69917	+	0.981016i	0.946548	+	0.322564i	$0.104545\pi$
$241$	409.500	+	236.425i	1.69917	+	0.981016i	0.752622	+	0.658452i	$0.228789\pi$
$242$		0			0
$243$	7.79423	+	13.5000i	0.0320750	+	0.0555556i
$244$			41.5692i			0.170366i
$245$		0			0
$246$	−6.00000			−0.0243902
$247$	−20.7846	+	12.0000i	−0.0841482	+	0.0485830i
$248$	115.181	−	199.500i	0.464441	−	0.804435i
$249$	−46.5000	+	80.5404i	−0.186747	+	0.323455i
$250$		0			0
$251$			67.5500i			0.269123i	0.990905	+	0.134562i	$0.0429626\pi$
$251$			67.5500i			0.269123i	−0.990905	+	0.134562i	$0.957037\pi$
$252$	−54.5596	−	31.5000i	−0.216506	−	0.125000i
$253$			308.000i			1.21739i
$254$	−0.500000	−	0.866025i	−0.00196850	−	0.00340955i
$255$		0			0
$256$	85.5000	−	148.090i	0.333984	−	0.578478i
$257$	−202.650	−	351.000i	−0.788521	−	1.36576i	−0.926873	−	0.375376i	$-0.877514\pi$
$257$	−202.650	−	351.000i	−0.788521	−	1.36576i	0.138352	−	0.990383i	$-0.455820\pi$
$258$	−45.0333			−0.174548
$259$	406.000			1.56757
$260$		0			0
$261$	37.5000	+	64.9519i	0.143678	+	0.248858i
$262$	90.9327	−	157.500i	0.347071	−	0.601145i
$263$	91.7987	+	53.0000i	0.349044	+	0.201521i	0.664264	−	0.747498i	$-0.268745\pi$
$263$	91.7987	+	53.0000i	0.349044	+	0.201521i	−0.315220	+	0.949019i	$0.602078\pi$
$264$	115.500	−	66.6840i	0.437500	−	0.252591i
$265$		0			0
$266$	−21.0000	+	12.1244i	−0.0789474	+	0.0455803i
$267$		−	138.000i		−	0.516854i
$268$	−135.100	+	78.0000i	−0.504104	+	0.291045i
$269$	−376.500	−	217.372i	−1.39963	−	0.808076i	−0.405275	−	0.914195i	$-0.632824\pi$
$269$	−376.500	−	217.372i	−1.39963	−	0.808076i	−0.994353	+	0.106119i	$0.966158\pi$
$270$		0			0
$271$	109.500	−	63.2199i	0.404059	−	0.233284i	−0.284175	−	0.958772i	$-0.591720\pi$
$271$	109.500	−	63.2199i	0.404059	−	0.233284i	0.688234	+	0.725489i	$0.258386\pi$
$272$	121.244			0.445748
$273$	72.7461	−	42.0000i	0.266469	−	0.153846i
$274$	−88.0000			−0.321168
$275$		0			0
$276$	−126.000	−	72.7461i	−0.456522	−	0.263573i
$277$	−204.382	−	118.000i	−0.737841	−	0.425993i	0.0834427	−	0.996513i	$-0.473408\pi$
$277$	−204.382	−	118.000i	−0.737841	−	0.425993i	−0.821284	+	0.570520i	$0.806742\pi$
$278$	−95.2628	−	165.000i	−0.342672	−	0.593525i
$279$			98.7269i			0.353860i
$280$		0			0
$281$	−116.000			−0.412811			−0.206406	−	0.978466i	$-0.566177\pi$
$281$	−116.000			−0.412811			−0.206406	+	0.978466i	$0.566177\pi$
$282$	−114.315	+	66.0000i	−0.405374	+	0.234043i
$283$	−185.329	+	321.000i	−0.654874	+	1.13428i	0.327051	+	0.945007i	$0.393945\pi$
$283$	−185.329	+	321.000i	−0.654874	+	1.13428i	−0.981925	+	0.189269i	$0.939388\pi$
$284$	−96.0000	+	166.277i	−0.338028	+	0.585482i
$285$		0			0
$286$			76.2102i			0.266469i
$287$	−12.1244	+	21.0000i	−0.0422451	+	0.0731707i
$288$			99.0000i			0.343750i
$289$	−149.500	−	258.942i	−0.517301	−	0.895992i
$290$		0			0
$291$	79.5000	−	137.698i	0.273196	−	0.473189i
$292$	10.3923	+	18.0000i	0.0355901	+	0.0616438i
$293$	−19.0526			−0.0650258			−0.0325129	−	0.999471i	$-0.510351\pi$
$293$	−19.0526			−0.0650258			−0.0325129	+	0.999471i	$0.510351\pi$
$294$	73.5000	−	42.4352i	0.250000	−	0.144338i
$295$		0			0
$296$	−203.000	−	351.606i	−0.685811	−	1.18786i
$297$	−28.5788	+	49.5000i	−0.0962250	+	0.166667i
$298$	−199.186	−	115.000i	−0.668409	−	0.385906i
$299$	168.000	−	96.9948i	0.561873	−	0.324397i
$300$		0			0
$301$	−91.0000	+	157.617i	−0.302326	+	0.523643i
$302$			227.000i			0.751656i
$303$	−31.1769	+	18.0000i	−0.102894	+	0.0594059i
$304$	−15.0000	−	8.66025i	−0.0493421	−	0.0284877i
$305$		0			0
$306$	63.0000	−	36.3731i	0.205882	−	0.118866i
$307$	−457.261			−1.48945			−0.744725	−	0.667371i	$-0.767420\pi$
$307$	−457.261			−1.48945			−0.744725	+	0.667371i	$0.767420\pi$
$308$		−	231.000i		−	0.750000i
$309$		0			0
$310$		0			0
$311$	285.000	+	164.545i	0.916399	+	0.529083i	0.882484	−	0.470342i	$-0.155869\pi$
$311$	285.000	+	164.545i	0.916399	+	0.529083i	0.0339143	+	0.999425i	$0.489203\pi$
$312$	−72.7461	−	42.0000i	−0.233161	−	0.134615i
$313$	−274.530	−	475.500i	−0.877093	−	1.51917i	−0.854517	−	0.519424i	$-0.826146\pi$
$313$	−274.530	−	475.500i	−0.877093	−	1.51917i	−0.0225763	−	0.999745i	$-0.507187\pi$
$314$		−	48.4974i		−	0.154450i
$315$		0			0
$316$	−51.0000			−0.161392
$317$	161.947	−	93.5000i	0.510873	−	0.294953i	−0.222319	−	0.974974i	$-0.571363\pi$
$317$	161.947	−	93.5000i	0.510873	−	0.294953i	0.733192	+	0.680021i	$0.238029\pi$
$318$	26.8468	−	46.5000i	0.0844239	−	0.146226i
$319$	−137.500	+	238.157i	−0.431034	+	0.746574i
$320$		0			0
$321$		−	53.6936i		−	0.167270i
$322$	169.741	−	98.0000i	0.527146	−	0.304348i
$323$			84.0000i			0.260062i
$324$	−13.5000	−	23.3827i	−0.0416667	−	0.0721688i
$325$		0			0
$326$	−106.000	+	183.597i	−0.325153	+	0.563182i
$327$	117.779	+	204.000i	0.360182	+	0.623853i
$328$	24.2487			0.0739290
$329$			533.472i			1.62149i
$330$		0			0
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	0.877857	−	0.478923i	$-0.158973\pi$
$331$	8.00000	+	13.8564i	0.0241692	+	0.0418623i	−0.853688	+	0.520785i	$0.825639\pi$
$332$	80.5404	−	139.500i	0.242591	−	0.420181i
$333$	150.688	+	87.0000i	0.452518	+	0.261261i
$334$	84.0000	−	48.4974i	0.251497	−	0.145202i
$335$		0			0
$336$	52.5000	+	30.3109i	0.156250	+	0.0902110i
$337$			83.0000i			0.246291i	0.992389	+	0.123145i	$0.0392982\pi$
$337$			83.0000i			0.246291i	−0.992389	+	0.123145i	$0.960702\pi$
$338$	−104.789	+	60.5000i	−0.310027	+	0.178994i
$339$	111.000	+	64.0859i	0.327434	+	0.189044i
$340$		0			0
$341$	−313.500	+	180.999i	−0.919355	+	0.530790i
$342$	−10.3923			−0.0303869
$343$		−	343.000i		−	1.00000i
$344$	182.000			0.529070
$345$		0			0
$346$	−186.000	−	107.387i	−0.537572	−	0.310367i
$347$	−310.037	−	179.000i	−0.893479	−	0.515850i	−0.0183999	−	0.999831i	$-0.505857\pi$
$347$	−310.037	−	179.000i	−0.893479	−	0.515850i	−0.875079	+	0.483981i	$0.839191\pi$
$348$	−64.9519	−	112.500i	−0.186643	−	0.323276i
$349$			678.964i			1.94546i	0.231950	+	0.972728i	$0.425489\pi$
$349$			678.964i			1.94546i	−0.231950	+	0.972728i	$0.574511\pi$
$350$		0			0
$351$	36.0000			0.102564
$352$	−314.367	+	181.500i	−0.893089	+	0.515625i
$353$	−322.161	+	558.000i	−0.912639	+	1.58074i	−0.102317	+	0.994752i	$0.532625\pi$
$353$	−322.161	+	558.000i	−0.912639	+	1.58074i	−0.810322	+	0.585985i	$0.800708\pi$
$354$	7.50000	−	12.9904i	0.0211864	−	0.0366960i
$355$		0			0
$356$			239.023i			0.671413i
$357$		−	294.000i		−	0.823529i
$358$		−	46.0000i		−	0.128492i
$359$	−142.000	−	245.951i	−0.395543	−	0.685101i	0.597627	−	0.801774i	$-0.296110\pi$
$359$	−142.000	−	245.951i	−0.395543	−	0.685101i	−0.993170	+	0.116673i	$0.962777\pi$
$360$		0			0
$361$	−174.500	+	302.243i	−0.483380	+	0.837238i
$362$	15.5885	+	27.0000i	0.0430620	+	0.0745856i
$363$		0			0
$364$	−126.000	+	72.7461i	−0.346154	+	0.199852i
$365$		0			0
$366$	−12.0000	−	20.7846i	−0.0327869	−	0.0567886i
$367$	−137.698	+	238.500i	−0.375199	+	0.649864i	−0.990357	−	0.138540i	$-0.955759\pi$
$367$	−137.698	+	238.500i	−0.375199	+	0.649864i	0.615158	+	0.788404i	$0.289092\pi$
$368$	121.244	+	70.0000i	0.329466	+	0.190217i
$369$	−9.00000	+	5.19615i	−0.0243902	+	0.0140817i
$370$		0			0
$371$	−108.500	−	187.928i	−0.292453	−	0.506543i
$372$		−	171.000i		−	0.459677i
$373$	−43.3013	+	25.0000i	−0.116089	+	0.0670241i	−0.556920	−	0.830566i	$-0.688017\pi$
$373$	−43.3013	+	25.0000i	−0.116089	+	0.0670241i	0.440831	+	0.897590i	$0.354684\pi$
$374$	231.000	+	133.368i	0.617647	+	0.356599i
$375$		0			0
$376$	462.000	−	266.736i	1.22872	−	0.709404i
$377$	173.205			0.459430
$378$	36.3731			0.0962250
$379$	−458.000			−1.20844			−0.604222	−	0.796816i	$-0.706516\pi$
$379$	−458.000			−1.20844			−0.604222	+	0.796816i	$0.706516\pi$
$380$		0			0
$381$	−1.50000	−	0.866025i	−0.00393701	−	0.00227303i
$382$	−180.133	−	104.000i	−0.471553	−	0.272251i
$383$	−202.650	−	351.000i	−0.529112	−	0.916449i	−0.999424	−	0.0339486i	$-0.989192\pi$
$383$	−202.650	−	351.000i	−0.529112	−	0.916449i	0.470311	−	0.882501i	$-0.344142\pi$
$384$		−	206.114i		−	0.536755i
$385$		0			0
$386$	239.000			0.619171
$387$	−67.5500	+	39.0000i	−0.174548	+	0.100775i
$388$	−137.698	+	238.500i	−0.354892	+	0.614691i
$389$	−349.000	+	604.486i	−0.897172	+	1.55395i	−0.0660793	+	0.997814i	$0.521049\pi$
$389$	−349.000	+	604.486i	−0.897172	+	1.55395i	−0.831093	+	0.556134i	$0.812284\pi$
$390$		0			0
$391$		−	678.964i		−	1.73648i
$392$	−297.047	+	171.500i	−0.757772	+	0.437500i
$393$		−	315.000i		−	0.801527i
$394$	−13.0000	−	22.5167i	−0.0329949	−	0.0571489i
$395$		0			0
$396$	49.5000	−	85.7365i	0.125000	−	0.216506i
$397$	−287.520	−	498.000i	−0.724233	−	1.25441i	−0.959289	−	0.282426i	$-0.908861\pi$
$397$	−287.520	−	498.000i	−0.724233	−	1.25441i	0.235056	−	0.971982i	$-0.424473\pi$
$398$	242.487			0.609264
$399$	−21.0000	+	36.3731i	−0.0526316	+	0.0911606i
$400$		0			0
$401$	142.000	+	245.951i	0.354115	+	0.613345i	0.986966	−	0.160929i	$-0.0514489\pi$
$401$	142.000	+	245.951i	0.354115	+	0.613345i	−0.632851	+	0.774273i	$0.718116\pi$
$402$	45.0333	−	78.0000i	0.112023	−	0.194030i
$403$	197.454	+	114.000i	0.489960	+	0.282878i
$404$	54.0000	−	31.1769i	0.133663	−	0.0771706i
$405$		0			0
$406$	175.000			0.431034
$407$			638.000i			1.56757i
$408$	−254.611	+	147.000i	−0.624048	+	0.360294i
$409$	181.500	+	104.789i	0.443765	+	0.256208i	0.705193	−	0.709015i	$-0.250860\pi$
$409$	181.500	+	104.789i	0.443765	+	0.256208i	−0.261428	+	0.965223i	$0.584193\pi$
$410$		0			0
$411$	−132.000	+	76.2102i	−0.321168	+	0.185426i
$412$		0			0
$413$	−30.3109	−	52.5000i	−0.0733920	−	0.127119i
$414$	84.0000			0.202899
$415$		0			0
$416$	198.000	+	114.315i	0.475962	+	0.274797i
$417$	−285.788	−	165.000i	−0.685344	−	0.395683i
$418$	−19.0526	−	33.0000i	−0.0455803	−	0.0789474i
$419$		−	131.636i		−	0.314167i	−0.987585	−	0.157083i	$-0.949791\pi$
$419$		−	131.636i		−	0.314167i	0.987585	−	0.157083i	$-0.0502091\pi$
$420$		0			0
$421$	−28.0000			−0.0665083			−0.0332542	−	0.999447i	$-0.510587\pi$
$421$	−28.0000			−0.0665083			−0.0332542	+	0.999447i	$0.510587\pi$
$422$	−45.0333	+	26.0000i	−0.106714	+	0.0616114i
$423$	−114.315	+	198.000i	−0.270249	+	0.468085i
$424$	−108.500	+	187.928i	−0.255896	+	0.443225i
$425$		0			0
$426$		−	110.851i		−	0.260214i
$427$	−96.9948			−0.227154
$428$			93.0000i			0.217290i
$429$	66.0000	+	114.315i	0.153846	+	0.266469i
$430$		0			0
$431$	−59.0000	+	102.191i	−0.136891	+	0.237102i	−0.926318	−	0.376742i	$-0.877044\pi$
$431$	−59.0000	+	102.191i	−0.136891	+	0.237102i	0.789427	+	0.613844i	$0.210378\pi$
$432$	12.9904	+	22.5000i	0.0300703	+	0.0520833i
$433$	561.184			1.29604			0.648019	−	0.761624i	$-0.275598\pi$
$433$	561.184			1.29604			0.648019	+	0.761624i	$0.275598\pi$
$434$	199.500	+	115.181i	0.459677	+	0.265395i
$435$		0			0
$436$	−204.000	−	353.338i	−0.467890	−	0.810409i
$437$	−48.4974	+	84.0000i	−0.110978	+	0.192220i
$438$	−10.3923	−	6.00000i	−0.0237267	−	0.0136986i
$439$	640.500	−	369.793i	1.45900	−	0.842353i	0.460036	−	0.887900i	$-0.347837\pi$
$439$	640.500	−	369.793i	1.45900	−	0.842353i	0.998962	+	0.0455478i	$0.0145033\pi$
$440$		0			0
$441$	73.5000	−	127.306i	0.166667	−	0.288675i
$442$		−	168.000i		−	0.380090i
$443$	134.234	−	77.5000i	0.303011	−	0.174944i	−0.340784	−	0.940142i	$-0.610692\pi$
$443$	134.234	−	77.5000i	0.303011	−	0.174944i	0.643795	+	0.765198i	$0.277359\pi$
$444$	−261.000	−	150.688i	−0.587838	−	0.339388i
$445$		0			0
$446$	19.5000	−	11.2583i	0.0437220	−	0.0252429i
$447$	−398.372			−0.891212
$448$	78.8083	+	45.5000i	0.175911	+	0.101562i
$449$	368.000			0.819599			0.409800	−	0.912176i	$-0.365599\pi$
$449$	368.000			0.819599			0.409800	+	0.912176i	$0.365599\pi$
$450$		0			0
$451$	−33.0000	−	19.0526i	−0.0731707	−	0.0422451i
$452$	−192.258	−	111.000i	−0.425349	−	0.245575i
$453$	196.588	+	340.500i	0.433969	+	0.751656i
$454$			67.5500i			0.148789i
$455$		0			0
$456$	42.0000			0.0921053
$457$	295.315	−	170.500i	0.646203	−	0.373085i	−0.140797	−	0.990038i	$-0.544967\pi$
$457$	295.315	−	170.500i	0.646203	−	0.373085i	0.787000	+	0.616953i	$0.211633\pi$
$458$	15.5885	−	27.0000i	0.0340359	−	0.0589520i
$459$	63.0000	−	109.119i	0.137255	−	0.237732i
$460$		0			0
$461$			55.4256i			0.120229i	0.998191	+	0.0601146i	$0.0191466\pi$
$461$			55.4256i			0.120229i	−0.998191	+	0.0601146i	$0.980853\pi$
$462$	66.6840	+	115.500i	0.144338	+	0.250000i
$463$			178.000i			0.384449i	0.981351	+	0.192225i	$0.0615702\pi$
$463$			178.000i			0.384449i	−0.981351	+	0.192225i	$0.938430\pi$
$464$	62.5000	+	108.253i	0.134698	+	0.233304i
$465$		0			0
$466$	−131.000	+	226.899i	−0.281116	+	0.486907i
$467$	329.090	+	570.000i	0.704689	+	1.22056i	0.966804	+	0.255520i	$0.0822467\pi$
$467$	329.090	+	570.000i	0.704689	+	1.22056i	−0.262115	+	0.965037i	$0.584420\pi$
$468$	−62.3538			−0.133235
$469$	−182.000	−	315.233i	−0.388060	−	0.672139i
$470$		0			0
$471$	−42.0000	−	72.7461i	−0.0891720	−	0.154450i
$472$	−30.3109	+	52.5000i	−0.0642180	+	0.111229i
$473$	−247.683	−	143.000i	−0.523643	−	0.302326i
$474$	25.5000	−	14.7224i	0.0537975	−	0.0310600i
$475$		0			0
$476$			509.223i			1.06980i
$477$		−	93.0000i		−	0.194969i
$478$	−138.564	+	80.0000i	−0.289883	+	0.167364i
$479$	−441.000	−	254.611i	−0.920668	−	0.531548i	−0.0368199	−	0.999322i	$-0.511723\pi$
$479$	−441.000	−	254.611i	−0.920668	−	0.531548i	−0.883848	+	0.467774i	$0.845056\pi$
$480$		0			0
$481$	348.000	−	200.918i	0.723493	−	0.417709i
$482$	472.850			0.981016
$483$	169.741	−	294.000i	0.351431	−	0.608696i
$484$		0			0
$485$		0			0
$486$	13.5000	+	7.79423i	0.0277778	+	0.0160375i
$487$	728.327	+	420.500i	1.49554	+	0.863450i	0.999987	−	0.00512864i	$-0.00163251\pi$
$487$	728.327	+	420.500i	1.49554	+	0.863450i	0.495552	+	0.868578i	$0.334966\pi$
$488$	48.4974	+	84.0000i	0.0993800	+	0.172131i
$489$			367.195i			0.750910i
$490$		0			0
$491$	−959.000			−1.95316			−0.976578	−	0.215162i	$-0.930972\pi$
$491$	−959.000			−1.95316			−0.976578	+	0.215162i	$0.930972\pi$
$492$	15.5885	−	9.00000i	0.0316839	−	0.0182927i
$493$	303.109	−	525.000i	0.614825	−	1.06491i
$494$	−12.0000	+	20.7846i	−0.0242915	+	0.0420741i
$495$		0			0
$496$			164.545i			0.331744i
$497$	−387.979	−	224.000i	−0.780643	−	0.450704i
$498$			93.0000i			0.186747i
$499$	−59.0000	−	102.191i	−0.118236	−	0.204792i	0.800832	−	0.598889i	$-0.204391\pi$
$499$	−59.0000	−	102.191i	−0.118236	−	0.204792i	−0.919069	+	0.394097i	$0.871057\pi$
$500$		0			0
$501$	84.0000	−	145.492i	0.167665	−	0.290404i
$502$	33.7750	+	58.5000i	0.0672809	+	0.116534i
$503$	−363.731			−0.723123			−0.361561	−	0.932348i	$-0.617756\pi$
$503$	−363.731			−0.723123			−0.361561	+	0.932348i	$0.617756\pi$
$504$	−147.000			−0.291667
$505$		0			0
$506$	154.000	+	266.736i	0.304348	+	0.527146i
$507$	−104.789	+	181.500i	−0.206685	+	0.357988i
$508$	2.59808	+	1.50000i	0.00511432	+	0.00295276i
$509$	−382.500	+	220.836i	−0.751473	+	0.433863i	−0.826226	−	0.563339i	$-0.809517\pi$
$509$	−382.500	+	220.836i	−0.751473	+	0.433863i	0.0747526	+	0.997202i	$0.476183\pi$
$510$		0			0
$511$	−42.0000	+	24.2487i	−0.0821918	+	0.0474534i
$512$			305.000i			0.595703i
$513$	−15.5885	+	9.00000i	−0.0303869	+	0.0175439i
$514$	−351.000	−	202.650i	−0.682879	−	0.394261i
$515$		0			0
$516$	117.000	−	67.5500i	0.226744	−	0.130911i
$517$	−838.313			−1.62149
$518$	351.606	−	203.000i	0.678777	−	0.391892i
$519$	−372.000			−0.716763
$520$		0			0
$521$	−843.000	−	486.706i	−1.61804	−	0.934177i	−0.987426	−	0.158082i	$-0.949469\pi$
$521$	−843.000	−	486.706i	−1.61804	−	0.934177i	−0.630616	−	0.776095i	$-0.717198\pi$
$522$	64.9519	+	37.5000i	0.124429	+	0.0718391i
$523$	235.559	+	408.000i	0.450399	+	0.780115i	0.998411	−	0.0563562i	$-0.0179483\pi$
$523$	235.559	+	408.000i	0.450399	+	0.780115i	−0.548011	+	0.836471i	$0.684615\pi$
$524$			545.596i			1.04121i
$525$		0			0
$526$	106.000			0.201521
$527$	691.088	−	399.000i	1.31136	−	0.757116i
$528$	−47.6314	+	82.5000i	−0.0902110	+	0.156250i
$529$	127.500	−	220.836i	0.241021	−	0.417460i
$530$		0			0
$531$		−	25.9808i		−	0.0489280i
$532$	36.3731	−	63.0000i	0.0683704	−	0.118421i
$533$			24.0000i			0.0450281i
$534$	−69.0000	−	119.512i	−0.129213	−	0.223804i
$535$		0			0
$536$	−182.000	+	315.233i	−0.339552	+	0.588122i
$537$	−39.8372	−	69.0000i	−0.0741847	−	0.128492i
$538$	−434.745			−0.808076
$539$	539.000			1.00000
$540$		0			0
$541$	−403.000	−	698.016i	−0.744917	−	1.29023i	−0.950234	−	0.311538i	$-0.899156\pi$
$541$	−403.000	−	698.016i	−0.744917	−	1.29023i	0.205317	−	0.978696i	$-0.434178\pi$
$542$	63.2199	−	109.500i	0.116642	−	0.202030i
$543$	46.7654	+	27.0000i	0.0861241	+	0.0497238i
$544$	693.000	−	400.104i	1.27390	−	0.735485i
$545$		0			0
$546$	42.0000	−	72.7461i	0.0769231	−	0.133235i
$547$		−	154.000i		−	0.281536i	−0.990043	−	0.140768i	$-0.955043\pi$
$547$		−	154.000i		−	0.281536i	0.990043	−	0.140768i	$-0.0449571\pi$
$548$	228.631	−	132.000i	0.417209	−	0.240876i
$549$	−36.0000	−	20.7846i	−0.0655738	−	0.0378590i
$550$		0			0
$551$	−75.0000	+	43.3013i	−0.136116	+	0.0785867i
$552$	−339.482			−0.615004
$553$		−	119.000i		−	0.215190i
$554$	−236.000			−0.425993
$555$		0			0
$556$	495.000	+	285.788i	0.890288	+	0.514008i
$557$	736.988	+	425.500i	1.32314	+	0.763914i	0.984228	−	0.176905i	$-0.0566086\pi$
$557$	736.988	+	425.500i	1.32314	+	0.763914i	0.338910	+	0.940819i	$0.389942\pi$
$558$	49.3634	+	85.5000i	0.0884650	+	0.153226i
$559$			180.133i			0.322242i
$560$		0			0
$561$	462.000			0.823529
$562$	−100.459	+	58.0000i	−0.178753	+	0.103203i
$563$	213.908	−	370.500i	0.379944	−	0.658082i	−0.611110	−	0.791546i	$-0.709277\pi$
$563$	213.908	−	370.500i	0.379944	−	0.658082i	0.991054	+	0.133464i	$0.0426100\pi$
$564$	198.000	−	342.946i	0.351064	−	0.608060i
$565$		0			0
$566$			370.659i			0.654874i
$567$	54.5596	−	31.5000i	0.0962250	−	0.0555556i
$568$			448.000i			0.788732i
$569$	−409.000	−	708.409i	−0.718805	−	1.24501i	−0.961474	−	0.274897i	$-0.911356\pi$
$569$	−409.000	−	708.409i	−0.718805	−	1.24501i	0.242669	−	0.970109i	$-0.421977\pi$
$570$		0			0
$571$	−142.000	+	245.951i	−0.248687	+	0.430738i	−0.963162	−	0.268923i	$-0.913332\pi$
$571$	−142.000	+	245.951i	−0.248687	+	0.430738i	0.714475	+	0.699661i	$0.246666\pi$
$572$	−114.315	−	198.000i	−0.199852	−	0.346154i
$573$	−360.267			−0.628737
$574$			24.2487i			0.0422451i
$575$		0			0
$576$	19.5000	+	33.7750i	0.0338542	+	0.0586371i
$577$	378.453	−	655.500i	0.655898	−	1.13605i	−0.325770	−	0.945449i	$-0.605623\pi$
$577$	378.453	−	655.500i	0.655898	−	1.13605i	0.981668	−	0.190599i	$-0.0610432\pi$
$578$	−258.942	−	149.500i	−0.447996	−	0.258651i
$579$	358.500	−	206.980i	0.619171	−	0.357479i
$580$		0			0
$581$	325.500	+	187.928i	0.560241	+	0.323455i
$582$		−	159.000i		−	0.273196i
$583$	295.315	−	170.500i	0.506543	−	0.292453i
$584$	42.0000	+	24.2487i	0.0719178	+	0.0415218i
$585$		0			0
$586$	−16.5000	+	9.52628i	−0.0281570	+	0.0162564i
$587$	947.432			1.61402			0.807012	−	0.590535i	$-0.201083\pi$
$587$	947.432			1.61402			0.807012	+	0.590535i	$0.201083\pi$
$588$	−127.306	+	220.500i	−0.216506	+	0.375000i
$589$	−114.000			−0.193548
$590$		0			0
$591$	−39.0000	−	22.5167i	−0.0659898	−	0.0380993i
$592$	251.147	+	145.000i	0.424235	+	0.244932i
$593$	−204.382	−	354.000i	−0.344658	−	0.596965i	0.640634	−	0.767847i	$-0.278672\pi$
$593$	−204.382	−	354.000i	−0.344658	−	0.596965i	−0.985292	+	0.170882i	$0.945338\pi$
$594$			57.1577i			0.0962250i
$595$		0			0
$596$	690.000			1.15772
$597$	363.731	−	210.000i	0.609264	−	0.351759i
$598$	96.9948	−	168.000i	0.162199	−	0.280936i
$599$	278.000	−	481.510i	0.464107	−	0.803857i	−0.535054	−	0.844818i	$-0.679709\pi$
$599$	278.000	−	481.510i	0.464107	−	0.803857i	0.999161	+	0.0409613i	$0.0130420\pi$
$600$		0			0
$601$		−	580.237i		−	0.965453i	−0.875771	−	0.482726i	$-0.839647\pi$
$601$		−	580.237i		−	0.965453i	0.875771	−	0.482726i	$-0.160353\pi$
$602$			182.000i			0.302326i
$603$		−	156.000i		−	0.258706i
$604$	−340.500	−	589.763i	−0.563742	−	0.976429i
$605$		0			0
$606$	−18.0000	+	31.1769i	−0.0297030	+	0.0514471i
$607$	329.956	+	571.500i	0.543584	+	0.941516i	0.998695	+	0.0510805i	$0.0162665\pi$
$607$	329.956	+	571.500i	0.543584	+	0.941516i	−0.455110	+	0.890435i	$0.650400\pi$
$608$	−114.315			−0.188019
$609$	262.500	−	151.554i	0.431034	−	0.248858i
$610$		0			0
$611$	264.000	+	457.261i	0.432079	+	0.748382i
$612$	−109.119	+	189.000i	−0.178299	+	0.308824i
$613$	277.128	+	160.000i	0.452085	+	0.261011i	0.708710	−	0.705500i	$-0.249277\pi$
$613$	277.128	+	160.000i	0.452085	+	0.261011i	−0.256625	+	0.966511i	$0.582611\pi$
$614$	−396.000	+	228.631i	−0.644951	+	0.372363i
$615$		0			0
$616$	−269.500	−	466.788i	−0.437500	−	0.757772i
$617$			652.000i			1.05673i	0.849019	+	0.528363i	$0.177194\pi$
$617$			652.000i			1.05673i	−0.849019	+	0.528363i	$0.822806\pi$
$618$		0			0
$619$	558.000	+	322.161i	0.901454	+	0.520455i	0.877672	−	0.479262i	$-0.159096\pi$
$619$	558.000	+	322.161i	0.901454	+	0.520455i	0.0237823	+	0.999717i	$0.492429\pi$
$620$		0			0
$621$	126.000	−	72.7461i	0.202899	−	0.117144i
$622$	329.090			0.529083
$623$	−557.720			−0.895217
$624$	60.0000			0.0961538
$625$		0			0
$626$	−475.500	−	274.530i	−0.759585	−	0.438546i
$627$	−57.1577	−	33.0000i	−0.0911606	−	0.0526316i
$628$	72.7461	+	126.000i	0.115838	+	0.200637i
$629$		−	1406.43i		−	2.23597i
$630$		0			0
$631$	−97.0000			−0.153724			−0.0768621	−	0.997042i	$-0.524490\pi$
$631$	−97.0000			−0.153724			−0.0768621	+	0.997042i	$0.524490\pi$
$632$	−103.057	+	59.5000i	−0.163065	+	0.0941456i
$633$	−45.0333	+	78.0000i	−0.0711427	+	0.123223i
$634$	93.5000	−	161.947i	0.147476	−	0.255437i
$635$		0			0
$636$			161.081i			0.253272i
$637$	−169.741	−	294.000i	−0.266469	−	0.461538i
$638$			275.000i			0.431034i
$639$	−96.0000	−	166.277i	−0.150235	−	0.260214i
$640$		0			0
$641$	−350.000	+	606.218i	−0.546022	+	0.945738i	0.452520	+	0.891754i	$0.350525\pi$
$641$	−350.000	+	606.218i	−0.546022	+	0.945738i	−0.998542	+	0.0539833i	$0.982808\pi$
$642$	−26.8468	−	46.5000i	−0.0418174	−	0.0724299i
$643$	325.626			0.506416			0.253208	−	0.967412i	$-0.418514\pi$
$643$	325.626			0.506416			0.253208	+	0.967412i	$0.418514\pi$
$644$	−294.000	+	509.223i	−0.456522	+	0.790719i
$645$		0			0
$646$	42.0000	+	72.7461i	0.0650155	+	0.112610i
$647$	180.133	−	312.000i	0.278413	−	0.482226i	−0.692577	−	0.721344i	$-0.743525\pi$
$647$	180.133	−	312.000i	0.278413	−	0.482226i	0.970991	+	0.239118i	$0.0768582\pi$
$648$	−54.5596	−	31.5000i	−0.0841969	−	0.0486111i
$649$	82.5000	−	47.6314i	0.127119	−	0.0733920i
$650$		0			0
$651$	399.000			0.612903
$652$		−	636.000i		−	0.975460i
$653$	−323.027	+	186.500i	−0.494682	+	0.285605i	−0.726515	−	0.687151i	$-0.758861\pi$
$653$	−323.027	+	186.500i	−0.494682	+	0.285605i	0.231833	+	0.972756i	$0.425528\pi$
$654$	204.000	+	117.779i	0.311927	+	0.180091i
$655$		0			0
$656$	−15.0000	+	8.66025i	−0.0228659	+	0.0132016i
$657$	−20.7846			−0.0316356
$658$	266.736	+	462.000i	0.405374	+	0.702128i
$659$	818.000			1.24127			0.620637	−	0.784098i	$-0.286874\pi$
$659$	818.000			1.24127			0.620637	+	0.784098i	$0.286874\pi$
$660$		0			0
$661$	327.000	+	188.794i	0.494705	+	0.285618i	0.726524	−	0.687141i	$-0.241134\pi$
$661$	327.000	+	188.794i	0.494705	+	0.285618i	−0.231819	+	0.972759i	$0.574468\pi$
$662$	13.8564	+	8.00000i	0.0209311	+	0.0120846i
$663$	−145.492	−	252.000i	−0.219445	−	0.380090i
$664$		−	375.855i		−	0.566047i
$665$		0			0
$666$	174.000			0.261261
$667$	606.218	−	350.000i	0.908872	−	0.524738i
$668$	−145.492	+	252.000i	−0.217803	+	0.377246i
$669$	19.5000	−	33.7750i	0.0291480	−	0.0504858i
$670$		0			0
$671$		−	152.420i		−	0.227154i
$672$	400.104			0.595392
$673$		−	1205.00i		−	1.79049i	−0.445574	−	0.895245i	$-0.647000\pi$
$673$		−	1205.00i		−	1.79049i	0.445574	−	0.895245i	$-0.353000\pi$
$674$	41.5000	+	71.8801i	0.0615727	+	0.106647i
$675$		0			0
$676$	181.500	−	314.367i	0.268491	−	0.465040i
$677$	−269.334	−	466.500i	−0.397834	−	0.689069i	0.595624	−	0.803263i	$-0.296905\pi$
$677$	−269.334	−	466.500i	−0.397834	−	0.689069i	−0.993458	+	0.114194i	$0.963571\pi$
$678$	128.172			0.189044
$679$	−556.500	−	321.295i	−0.819588	−	0.473189i
$680$		0			0
$681$	58.5000	+	101.325i	0.0859031	+	0.148789i
$682$	−180.999	+	313.500i	−0.265395	+	0.459677i
$683$	821.858	+	474.500i	1.20331	+	0.694729i	0.961289	−	0.275543i	$-0.0888576\pi$
$683$	821.858	+	474.500i	1.20331	+	0.694729i	0.242017	+	0.970272i	$0.422191\pi$
$684$	27.0000	−	15.5885i	0.0394737	−	0.0227901i
$685$		0			0
$686$	−171.500	−	297.047i	−0.250000	−	0.433013i
$687$		−	54.0000i		−	0.0786026i
$688$	−112.583	+	65.0000i	−0.163639	+	0.0944767i
$689$	−186.000	−	107.387i	−0.269956	−	0.155859i
$690$		0			0
$691$	−267.000	+	154.153i	−0.386397	+	0.223086i	−0.680598	−	0.732657i	$-0.738280\pi$
$691$	−267.000	+	154.153i	−0.386397	+	0.223086i	0.294201	+	0.955744i	$0.404946\pi$
$692$	644.323			0.931102
$693$	200.052	+	115.500i	0.288675	+	0.166667i
$694$	−358.000			−0.515850
$695$		0			0
$696$	−262.500	−	151.554i	−0.377155	−	0.217751i
$697$	72.7461	+	42.0000i	0.104370	+	0.0602582i
$698$	339.482	+	588.000i	0.486364	+	0.842407i
$699$			453.797i			0.649209i
$700$		0			0
$701$	−413.000			−0.589158			−0.294579	−	0.955627i	$-0.595179\pi$
$701$	−413.000			−0.589158			−0.294579	+	0.955627i	$0.595179\pi$
$702$	31.1769	−	18.0000i	0.0444116	−	0.0256410i
$703$	−100.459	+	174.000i	−0.142900	+	0.247511i
$704$	−71.5000	+	123.842i	−0.101562	+	0.175911i
$705$		0			0
$706$			644.323i			0.912639i
$707$	72.7461	+	126.000i	0.102894	+	0.178218i
$708$			45.0000i			0.0635593i
$709$	445.000	+	770.763i	0.627645	+	1.08711i	0.988023	+	0.154306i	$0.0493142\pi$
$709$	445.000	+	770.763i	0.627645	+	1.08711i	−0.360379	+	0.932806i	$0.617352\pi$
$710$		0			0
$711$	25.5000	−	44.1673i	0.0358650	−	0.0621200i
$712$	278.860	+	483.000i	0.391658	+	0.678371i
$713$	921.451			1.29236
$714$	−147.000	−	254.611i	−0.205882	−	0.356599i
$715$		0			0
$716$	69.0000	+	119.512i	0.0963687	+	0.166916i
$717$	−138.564	+	240.000i	−0.193255	+	0.334728i
$718$	−245.951	−	142.000i	−0.342550	−	0.197772i
$719$	−579.000	+	334.286i	−0.805285	+	0.464932i	−0.845316	−	0.534267i	$-0.820588\pi$
$719$	−579.000	+	334.286i	−0.805285	+	0.464932i	0.0400307	+	0.999198i	$0.487254\pi$
$720$		0			0
$721$		0			0
$722$			349.000i			0.483380i
$723$	709.275	−	409.500i	0.981016	−	0.566390i
$724$	−81.0000	−	46.7654i	−0.111878	−	0.0645931i
$725$		0			0
$726$		0			0
$727$	−417.424			−0.574174			−0.287087	−	0.957905i	$-0.592687\pi$
$727$	−417.424			−0.574174			−0.287087	+	0.957905i	$0.592687\pi$
$728$	−169.741	+	294.000i	−0.233161	+	0.403846i
$729$	27.0000			0.0370370
$730$		0			0
$731$	546.000	+	315.233i	0.746922	+	0.431236i
$732$	62.3538	+	36.0000i	0.0851828	+	0.0491803i
$733$	−98.7269	−	171.000i	−0.134689	−	0.233288i	0.790790	−	0.612088i	$-0.209670\pi$
$733$	−98.7269	−	171.000i	−0.134689	−	0.233288i	−0.925479	+	0.378800i	$0.876337\pi$
$734$			275.396i			0.375199i
$735$		0			0
$736$	924.000			1.25543
$737$	495.367	−	286.000i	0.672139	−	0.388060i
$738$	−5.19615	+	9.00000i	−0.00704086	+	0.0121951i
$739$	−155.000	+	268.468i	−0.209743	+	0.363285i	−0.951633	−	0.307236i	$-0.900596\pi$
$739$	−155.000	+	268.468i	−0.209743	+	0.363285i	0.741891	+	0.670521i	$0.233929\pi$
$740$		0			0
$741$			41.5692i			0.0560988i
$742$	−187.928	−	108.500i	−0.253272	−	0.146226i
$743$			812.000i			1.09287i	0.837503	+	0.546433i	$0.184015\pi$
$743$			812.000i			1.09287i	−0.837503	+	0.546433i	$0.815985\pi$
$744$	−199.500	−	345.544i	−0.268145	−	0.464441i
$745$		0			0
$746$	−25.0000	+	43.3013i	−0.0335121	+	0.0580446i
$747$	80.5404	+	139.500i	0.107818	+	0.186747i
$748$	−800.207			−1.06980
$749$	−217.000			−0.289720
$750$		0			0
$751$	537.500	+	930.977i	0.715712	+	1.23965i	0.962684	+	0.270628i	$0.0872312\pi$
$751$	537.500	+	930.977i	0.715712	+	1.23965i	−0.246972	+	0.969023i	$0.579435\pi$
$752$	−190.526	+	330.000i	−0.253358	+	0.438830i
$753$	101.325	+	58.5000i	0.134562	+	0.0776892i
$754$	150.000	−	86.6025i	0.198939	−	0.114857i
$755$		0			0
$756$	−94.5000	+	54.5596i	−0.125000	+	0.0721688i
$757$		−	484.000i		−	0.639366i	−0.947525	−	0.319683i	$-0.896424\pi$
$757$		−	484.000i		−	0.639366i	0.947525	−	0.319683i	$-0.103576\pi$
$758$	−396.640	+	229.000i	−0.523271	+	0.302111i
$759$	462.000	+	266.736i	0.608696	+	0.351431i
$760$		0			0
$761$	144.000	−	83.1384i	0.189225	−	0.109249i	−0.402395	−	0.915466i	$-0.631822\pi$
$761$	144.000	−	83.1384i	0.189225	−	0.109249i	0.591620	+	0.806217i	$0.298489\pi$
$762$	−1.73205			−0.00227303
$763$	824.456	−	476.000i	1.08055	−	0.623853i
$764$	624.000			0.816754
$765$		0			0
$766$	−351.000	−	202.650i	−0.458225	−	0.264556i
$767$	−51.9615	−	30.0000i	−0.0677464	−	0.0391134i
$768$	−148.090	−	256.500i	−0.192826	−	0.333984i
$769$			594.093i			0.772553i	0.922383	+	0.386277i	$0.126239\pi$
$769$			594.093i			0.772553i	−0.922383	+	0.386277i	$0.873761\pi$
$770$		0			0
$771$	−702.000			−0.910506
$772$	−620.940	+	358.500i	−0.804327	+	0.464378i
$773$	516.151	−	894.000i	0.667725	−	1.15653i	−0.310814	−	0.950471i	$-0.600602\pi$
$773$	516.151	−	894.000i	0.667725	−	1.15653i	0.978539	−	0.206062i	$-0.0660650\pi$
$774$	−39.0000	+	67.5500i	−0.0503876	+	0.0872739i
$775$		0			0
$776$			642.591i			0.828081i
$777$	351.606	−	609.000i	0.452518	−	0.783784i
$778$			698.000i			0.897172i
$779$	−6.00000	−	10.3923i	−0.00770218	−	0.0133406i
$780$		0			0
$781$	352.000	−	609.682i	0.450704	−	0.780643i
$782$	−339.482	−	588.000i	−0.434120	−	0.751918i
$783$	129.904			0.165905
$784$	122.500	−	212.176i	0.156250	−	0.270633i
$785$		0			0
$786$	−157.500	−	272.798i	−0.200382	−	0.347071i
$787$	−204.382	+	354.000i	−0.259698	+	0.449809i	−0.966161	−	0.257940i	$-0.916956\pi$
$787$	−204.382	+	354.000i	−0.259698	+	0.449809i	0.706463	+	0.707750i	$0.250290\pi$
$788$	67.5500	+	39.0000i	0.0857233	+	0.0494924i
$789$	159.000	−	91.7987i	0.201521	−	0.116348i
$790$		0			0
$791$	259.000	−	448.601i	0.327434	−	0.567132i
$792$		−	231.000i		−	0.291667i
$793$	−83.1384	+	48.0000i	−0.104840	+	0.0605296i
$794$	−498.000	−	287.520i	−0.627204	−	0.362116i
$795$		0			0
$796$	−630.000	+	363.731i	−0.791457	+	0.456948i
$797$	−625.270			−0.784530			−0.392265	−	0.919852i	$-0.628308\pi$
$797$	−625.270			−0.784530			−0.392265	+	0.919852i	$0.628308\pi$
$798$			42.0000i			0.0526316i
$799$	1848.00			2.31289
$800$		0			0
$801$	−207.000	−	119.512i	−0.258427	−	0.149203i
$802$	245.951	+	142.000i	0.306672	+	0.177057i
$803$	−38.1051	−	66.0000i	−0.0474534	−	0.0821918i
$804$			270.200i			0.336070i
$805$		0			0
$806$	228.000			0.282878
$807$	−652.117	+	376.500i	−0.808076	+	0.466543i
$808$	72.7461	−	126.000i	0.0900323	−	0.155941i
$809$	−376.000	+	651.251i	−0.464771	+	0.805008i	−0.999191	−	0.0402116i	$-0.987197\pi$
$809$	−376.000	+	651.251i	−0.464771	+	0.805008i	0.534420	+	0.845219i	$0.320530\pi$
$810$		0			0
$811$		−	270.200i		−	0.333169i	−0.986027	−	0.166584i	$-0.946726\pi$
$811$		−	270.200i		−	0.333169i	0.986027	−	0.166584i	$-0.0532738\pi$
$812$	−454.663	+	262.500i	−0.559930	+	0.323276i
$813$		−	219.000i		−	0.269373i
$814$	319.000	+	552.524i	0.391892	+	0.678777i
$815$		0			0
$816$	105.000	−	181.865i	0.128676	−	0.222874i
$817$	−45.0333	−	78.0000i	−0.0551203	−	0.0954712i
$818$	209.578			0.256208
$819$		−	145.492i		−	0.177646i
$820$		0			0
$821$	−441.500	−	764.700i	−0.537759	−	0.931426i	−0.999024	−	0.0441635i	$-0.985938\pi$
$821$	−441.500	−	764.700i	−0.537759	−	0.931426i	0.461265	−	0.887262i	$-0.347396\pi$
$822$	−76.2102	+	132.000i	−0.0927132	+	0.160584i
$823$	−424.352	−	245.000i	−0.515617	−	0.297691i	0.219523	−	0.975607i	$-0.429550\pi$
$823$	−424.352	−	245.000i	−0.515617	−	0.297691i	−0.735139	+	0.677916i	$0.762883\pi$
$824$		0			0
$825$		0			0
$826$	−52.5000	−	30.3109i	−0.0635593	−	0.0366960i
$827$			1279.00i			1.54655i	0.634068	+	0.773277i	$0.281384\pi$
$827$			1279.00i			1.54655i	−0.634068	+	0.773277i	$0.718616\pi$
$828$	−218.238	+	126.000i	−0.263573	+	0.152174i
$829$	−1311.00	−	756.906i	−1.58142	−	0.913035i	−0.994652	−	0.103283i	$-0.967065\pi$
$829$	−1311.00	−	756.906i	−1.58142	−	0.913035i	−0.586771	−	0.809753i	$-0.699601\pi$
$830$		0			0
$831$	−354.000	+	204.382i	−0.425993	+	0.245947i
$832$	90.0666			0.108253
$833$	−1188.19			−1.42639
$834$	−330.000			−0.395683
$835$		0			0
$836$	99.0000	+	57.1577i	0.118421	+	0.0683704i
$837$	148.090	+	85.5000i	0.176930	+	0.102151i
$838$	−65.8179	−	114.000i	−0.0785417	−	0.136038i
$839$		−	523.079i		−	0.623456i	−0.950171	−	0.311728i	$-0.899092\pi$
$839$		−	523.079i		−	0.623456i	0.950171	−	0.311728i	$-0.100908\pi$
$840$		0			0
$841$	−216.000			−0.256837
$842$	−24.2487	+	14.0000i	−0.0287989	+	0.0166271i
$843$	−100.459	+	174.000i	−0.119168	+	0.206406i
$844$	78.0000	−	135.100i	0.0924171	−	0.160071i
$845$		0			0
$846$			228.631i			0.270249i
$847$		0			0
$848$		−	155.000i		−	0.182783i
$849$	321.000	+	555.988i	0.378092	+	0.654874i
$850$		0			0
$851$	812.000	−	1406.43i	0.954172	−	1.65267i
$852$	166.277	+	288.000i	0.195161	+	0.338028i
$853$	−387.979			−0.454841			−0.227421	−	0.973797i	$-0.573029\pi$
$853$	−387.979			−0.454841			−0.227421	+	0.973797i	$0.573029\pi$
$854$	−84.0000	+	48.4974i	−0.0983607	+	0.0567886i
$855$		0			0
$856$	108.500	+	187.928i	0.126752	+	0.219541i
$857$	415.692	−	720.000i	0.485055	−	0.840140i	−0.514797	−	0.857312i	$-0.672133\pi$
$857$	415.692	−	720.000i	0.485055	−	0.840140i	0.999853	+	0.0171718i	$0.00546622\pi$
$858$	114.315	+	66.0000i	0.133235	+	0.0769231i
$859$	−981.000	+	566.381i	−1.14203	+	0.659349i	−0.946931	−	0.321436i	$-0.895835\pi$
$859$	−981.000	+	566.381i	−1.14203	+	0.659349i	−0.195094	+	0.980785i	$0.562501\pi$
$860$		0			0
$861$	21.0000	+	36.3731i	0.0243902	+	0.0422451i
$862$			118.000i			0.136891i
$863$	−19.0526	+	11.0000i	−0.0220771	+	0.0127462i	−0.510998	−	0.859582i	$-0.670724\pi$
$863$	−19.0526	+	11.0000i	−0.0220771	+	0.0127462i	0.488921	+	0.872328i	$0.337391\pi$
$864$	148.500	+	85.7365i	0.171875	+	0.0992321i
$865$		0			0
$866$	486.000	−	280.592i	0.561201	−	0.324010i
$867$	−517.883			−0.597328
$868$	−691.088			−0.796185
$869$	187.000			0.215190
$870$		0			0
$871$	−312.000	−	180.133i	−0.358209	−	0.206812i
$872$	−824.456	−	476.000i	−0.945477	−	0.545872i
$873$	−137.698	−	238.500i	−0.157730	−	0.273196i
$874$			96.9948i			0.110978i
$875$		0			0
$876$	36.0000			0.0410959
$877$	−34.6410	+	20.0000i	−0.0394994	+	0.0228050i	−0.519620	−	0.854398i	$-0.673926\pi$
$877$	−34.6410	+	20.0000i	−0.0394994	+	0.0228050i	0.480120	+	0.877203i	$0.340593\pi$
$878$	369.793	−	640.500i	0.421176	−	0.729499i
$879$	−16.5000	+	28.5788i	−0.0187713	+	0.0325129i
$880$		0			0
$881$		−	20.7846i		−	0.0235921i	−0.999930	−	0.0117960i	$-0.996245\pi$
$881$		−	20.7846i		−	0.0235921i	0.999930	−	0.0117960i	$-0.00375488\pi$
$882$		−	147.000i		−	0.166667i
$883$		−	386.000i		−	0.437146i	−0.975821	−	0.218573i	$-0.929860\pi$
$883$		−	386.000i		−	0.437146i	0.975821	−	0.218573i	$-0.0701402\pi$
$884$	252.000	+	436.477i	0.285068	+	0.493752i
$885$		0			0
$886$	77.5000	−	134.234i	0.0874718	−	0.151506i
$887$	−862.561	−	1494.00i	−0.972448	−	1.68433i	−0.688112	−	0.725604i	$-0.741560\pi$
$887$	−862.561	−	1494.00i	−0.972448	−	1.68433i	−0.284336	−	0.958725i	$-0.591773\pi$
$888$	−703.213			−0.791906
$889$	−3.50000	+	6.06218i	−0.00393701	+	0.00681910i
$890$		0			0
$891$	49.5000	+	85.7365i	0.0555556	+	0.0962250i
$892$	−33.7750	+	58.5000i	−0.0378643	+	0.0655830i
$893$	−228.631	−	132.000i	−0.256025	−	0.147816i
$894$	−345.000	+	199.186i	−0.385906	+	0.222803i
$895$		0			0
$896$	−833.000			−0.929688
$897$		−	336.000i		−	0.374582i
$898$	318.697	−	184.000i	0.354897	−	0.204900i
$899$	712.500	+	411.362i	0.792547	+	0.457577i
$900$		0			0
$901$	−651.000	+	375.855i	−0.722531	+	0.417153i
$902$	−38.1051			−0.0422451
$903$	157.617	+	273.000i	0.174548	+	0.302326i
$904$	−518.000			−0.573009
$905$		0			0
$906$	340.500	+	196.588i	0.375828	+	0.216984i
$907$	512.687	+	296.000i	0.565256	+	0.326351i	0.755252	−	0.655434i	$-0.227514\pi$
$907$	512.687	+	296.000i	0.565256	+	0.326351i	−0.189996	+	0.981785i	$0.560848\pi$
$908$	−101.325	−	175.500i	−0.111591	−	0.193282i
$909$			62.3538i			0.0685961i
$910$		0			0
$911$	−416.000			−0.456641			−0.228321	−	0.973586i	$-0.573323\pi$
$911$	−416.000			−0.456641			−0.228321	+	0.973586i	$0.573323\pi$
$912$	−25.9808	+	15.0000i	−0.0284877	+	0.0164474i
$913$	−295.315	+	511.500i	−0.323455	+	0.560241i
$914$	170.500	−	295.315i	0.186543	−	0.323101i
$915$		0			0
$916$			93.5307i			0.102108i
$917$	−1273.06			−1.38828
$918$		−	126.000i		−	0.137255i
$919$	25.0000	+	43.3013i	0.0272035	+	0.0471178i	0.879307	−	0.476256i	$-0.158006\pi$
$919$	25.0000	+	43.3013i	0.0272035	+	0.0471178i	−0.852103	+	0.523374i	$0.824673\pi$
$920$		0			0
$921$	−396.000	+	685.892i	−0.429967	+	0.744725i
$922$	27.7128	+	48.0000i	0.0300573	+	0.0520607i
$923$	−443.405			−0.480395
$924$	−346.500	−	200.052i	−0.375000	−	0.216506i
$925$		0			0
$926$	89.0000	+	154.153i	0.0961123	+	0.166471i
$927$		0			0
$928$	714.471	+	412.500i	0.769904	+	0.444504i
$929$	−357.000	+	206.114i	−0.384284	+	0.221867i	−0.679681	−	0.733508i	$-0.737882\pi$
$929$	−357.000	+	206.114i	−0.384284	+	0.221867i	0.295396	+	0.955375i	$0.404548\pi$
$930$		0			0
$931$	147.000	+	84.8705i	0.157895	+	0.0911606i
$932$		−	786.000i		−	0.843348i
$933$	493.634	−	285.000i	0.529083	−	0.305466i
$934$	570.000	+	329.090i	0.610278	+	0.352344i
$935$		0			0
$936$	−126.000	+	72.7461i	−0.134615	+	0.0777202i
$937$	−1605.61			−1.71357			−0.856783	−	0.515677i	$-0.827540\pi$
$937$	−1605.61			−1.71357			−0.856783	+	0.515677i	$0.827540\pi$
$938$	−315.233	−	182.000i	−0.336070	−	0.194030i
$939$	−951.000			−1.01278
$940$		0			0
$941$	−1150.50	−	664.241i	−1.22264	−	0.705889i	−0.257156	−	0.966370i	$-0.582786\pi$
$941$	−1150.50	−	664.241i	−1.22264	−	0.705889i	−0.965479	+	0.260481i	$0.916119\pi$
$942$	−72.7461	−	42.0000i	−0.0772252	−	0.0445860i
$943$	48.4974	+	84.0000i	0.0514289	+	0.0890774i
$944$		−	43.3013i		−	0.0458700i
$945$		0			0
$946$	−286.000			−0.302326
$947$	−1186.45	+	685.000i	−1.25286	+	0.723337i	−0.971676	−	0.236318i	$-0.924059\pi$
$947$	−1186.45	+	685.000i	−1.25286	+	0.723337i	−0.281180	+	0.959655i	$0.590726\pi$
$948$	−44.1673	+	76.5000i	−0.0465900	+	0.0806962i
$949$	−24.0000	+	41.5692i	−0.0252898	+	0.0438032i
$950$		0			0
$951$		−	323.894i		−	0.340582i
$952$	594.093	+	1029.00i	0.624048	+	1.08088i
$953$		−	1150.00i		−	1.20672i	−0.797471	−	0.603358i	$-0.793829\pi$
$953$		−	1150.00i		−	1.20672i	0.797471	−	0.603358i	$-0.206171\pi$
$954$	−46.5000	−	80.5404i	−0.0487421	−	0.0844239i
$955$		0			0
$956$	240.000	−	415.692i	0.251046	−	0.434824i
$957$	238.157	+	412.500i	0.248858	+	0.431034i
$958$	−509.223			−0.531548
$959$	308.000	+	533.472i	0.321168	+	0.556279i
$960$		0			0
$961$	61.0000	+	105.655i	0.0634755	+	0.109943i
$962$	200.918	−	348.000i	0.208854	−	0.361746i
$963$	−80.5404	−	46.5000i	−0.0836349	−	0.0482866i
$964$	−1228.50	+	709.275i	−1.27438	+	0.735762i
$965$		0			0
$966$		−	339.482i		−	0.351431i
$967$			5.00000i			0.00517063i	0.999997	+	0.00258532i	$0.000822932\pi$
$967$			5.00000i			0.00517063i	−0.999997	+	0.00258532i	$0.999177\pi$
$968$		0			0
$969$	126.000	+	72.7461i	0.130031	+	0.0750734i
$970$		0			0
$971$	385.500	−	222.569i	0.397013	−	0.229216i	−0.288181	−	0.957576i	$-0.593051\pi$
$971$	385.500	−	222.569i	0.397013	−	0.229216i	0.685195	+	0.728360i	$0.259717\pi$
$972$	−46.7654			−0.0481125
$973$	−666.840	+	1155.00i	−0.685344	+	1.18705i
$974$	841.000			0.863450
$975$		0			0
$976$	−60.0000	−	34.6410i	−0.0614754	−	0.0354928i
$977$	−829.652	−	479.000i	−0.849184	−	0.490276i	0.0111917	−	0.999937i	$-0.496437\pi$
$977$	−829.652	−	479.000i	−0.849184	−	0.490276i	−0.860375	+	0.509661i	$0.829771\pi$
$978$	183.597	+	318.000i	0.187727	+	0.325153i
$979$		−	876.418i		−	0.895217i
$980$		0			0
$981$	408.000			0.415902
$982$	−830.518	+	479.500i	−0.845742	+	0.488289i
$983$	140.296	−	243.000i	0.142722	−	0.247202i	−0.785798	−	0.618483i	$-0.787748\pi$
$983$	140.296	−	243.000i	0.142722	−	0.247202i	0.928521	+	0.371280i	$0.121081\pi$
$984$	21.0000	−	36.3731i	0.0213415	−	0.0369645i
$985$		0			0
$986$		−	606.218i		−	0.614825i
$987$	800.207	+	462.000i	0.810747	+	0.468085i
$988$		−	72.0000i		−	0.0728745i
$989$	364.000	+	630.466i	0.368049	+	0.637479i
$990$		0			0
$991$	−461.500	+	799.341i	−0.465691	+	0.806601i	−0.999232	−	0.0391732i	$-0.987528\pi$
$991$	−461.500	+	799.341i	−0.465691	+	0.806601i	0.533541	+	0.845774i	$0.320861\pi$
$992$	542.998	+	940.500i	0.547377	+	0.948085i
$993$	27.7128			0.0279082
$994$	−448.000			−0.450704
$995$		0			0
$996$	−139.500	−	241.621i	−0.140060	−	0.242591i
$997$	−10.3923	+	18.0000i	−0.0104236	+	0.0180542i	−0.871190	−	0.490946i	$-0.836651\pi$
$997$	−10.3923	+	18.0000i	−0.0104236	+	0.0180542i	0.860767	+	0.509000i	$0.169985\pi$
$998$	−102.191	−	59.0000i	−0.102396	−	0.0591182i
$999$	261.000	−	150.688i	0.261261	−	0.150839i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.3.s.c.199.2		4
5.2	odd	4		525.3.o.g.451.1		2
5.3	odd	4		21.3.f.b.10.1	✓	2
5.4	even	2	inner	525.3.s.c.199.1		4
7.5	odd	6	inner	525.3.s.c.124.1		4
15.8	even	4		63.3.m.c.10.1		2
20.3	even	4		336.3.bh.a.241.1		2
35.3	even	12		147.3.d.b.97.2		2
35.12	even	12		525.3.o.g.376.1		2
35.13	even	4		147.3.f.c.31.1		2
35.18	odd	12		147.3.d.b.97.1		2
35.19	odd	6	inner	525.3.s.c.124.2		4
35.23	odd	12		147.3.f.c.19.1		2
35.33	even	12		21.3.f.b.19.1	yes	2
60.23	odd	4		1008.3.cg.g.577.1		2
105.23	even	12		441.3.m.e.19.1		2
105.38	odd	12		441.3.d.b.244.1		2
105.53	even	12		441.3.d.b.244.2		2
105.68	odd	12		63.3.m.c.19.1		2
105.83	odd	4		441.3.m.e.325.1		2
140.3	odd	12		2352.3.f.d.97.1		2
140.103	odd	12		336.3.bh.a.145.1		2
140.123	even	12		2352.3.f.d.97.2		2
420.383	even	12		1008.3.cg.g.145.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.b.10.1	✓	2	5.3	odd	4
21.3.f.b.19.1	yes	2	35.33	even	12
63.3.m.c.10.1		2	15.8	even	4
63.3.m.c.19.1		2	105.68	odd	12
147.3.d.b.97.1		2	35.18	odd	12
147.3.d.b.97.2		2	35.3	even	12
147.3.f.c.19.1		2	35.23	odd	12
147.3.f.c.31.1		2	35.13	even	4
336.3.bh.a.145.1		2	140.103	odd	12
336.3.bh.a.241.1		2	20.3	even	4
441.3.d.b.244.1		2	105.38	odd	12
441.3.d.b.244.2		2	105.53	even	12
441.3.m.e.19.1		2	105.23	even	12
441.3.m.e.325.1		2	105.83	odd	4
525.3.o.g.376.1		2	35.12	even	12
525.3.o.g.451.1		2	5.2	odd	4
525.3.s.c.124.1		4	7.5	odd	6	inner
525.3.s.c.124.2		4	35.19	odd	6	inner
525.3.s.c.199.1		4	5.4	even	2	inner
525.3.s.c.199.2		4	1.1	even	1	trivial
1008.3.cg.g.145.1		2	420.383	even	12
1008.3.cg.g.577.1		2	60.23	odd	4
2352.3.f.d.97.1		2	140.3	odd	12
2352.3.f.d.97.2		2	140.123	even	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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+(0.866025 - 0.500000i) q^{2} +(0.866025 - 1.50000i) q^{3} +(-1.50000 + 2.59808i) q^{4} -1.73205i q^{6} +(-6.06218 - 3.50000i) q^{7} +7.00000i q^{8} +(-1.50000 - 2.59808i) q^{9} +(5.50000 - 9.52628i) q^{11} +(2.59808 + 4.50000i) q^{12} -6.92820 q^{13} -7.00000 q^{14} +(-2.50000 - 4.33013i) q^{16} +(-12.1244 + 21.0000i) q^{17} +(-2.59808 - 1.50000i) q^{18} +(3.00000 - 1.73205i) q^{19} +(-10.5000 + 6.06218i) q^{21} -11.0000i q^{22} +(-24.2487 + 14.0000i) q^{23} +(10.5000 + 6.06218i) q^{24} +(-6.00000 + 3.46410i) q^{26} -5.19615 q^{27} +(18.1865 - 10.5000i) q^{28} -25.0000 q^{29} +(-28.5000 - 16.4545i) q^{31} +(-28.5788 - 16.5000i) q^{32} +(-9.52628 - 16.5000i) q^{33} +24.2487i q^{34} +9.00000 q^{36} +(-50.2295 + 29.0000i) q^{37} +(1.73205 - 3.00000i) q^{38} +(-6.00000 + 10.3923i) q^{39} -3.46410i q^{41} +(-6.06218 + 10.5000i) q^{42} -26.0000i q^{43} +(16.5000 + 28.5788i) q^{44} +(-14.0000 + 24.2487i) q^{46} +(-38.1051 - 66.0000i) q^{47} -8.66025 q^{48} +(24.5000 + 42.4352i) q^{49} +(21.0000 + 36.3731i) q^{51} +(10.3923 - 18.0000i) q^{52} +(26.8468 + 15.5000i) q^{53} +(-4.50000 + 2.59808i) q^{54} +(24.5000 - 42.4352i) q^{56} -6.00000i q^{57} +(-21.6506 + 12.5000i) q^{58} +(7.50000 + 4.33013i) q^{59} +(12.0000 - 6.92820i) q^{61} -32.9090 q^{62} +21.0000i q^{63} -13.0000 q^{64} +(-16.5000 - 9.52628i) q^{66} +(45.0333 + 26.0000i) q^{67} +(-36.3731 - 63.0000i) q^{68} +48.4974i q^{69} +64.0000 q^{71} +(18.1865 - 10.5000i) q^{72} +(3.46410 - 6.00000i) q^{73} +(-29.0000 + 50.2295i) q^{74} +10.3923i q^{76} +(-66.6840 + 38.5000i) q^{77} +12.0000i q^{78} +(8.50000 + 14.7224i) q^{79} +(-4.50000 + 7.79423i) q^{81} +(-1.73205 - 3.00000i) q^{82} -53.6936 q^{83} -36.3731i q^{84} +(-13.0000 - 22.5167i) q^{86} +(-21.6506 + 37.5000i) q^{87} +(66.6840 + 38.5000i) q^{88} +(69.0000 - 39.8372i) q^{89} +(42.0000 + 24.2487i) q^{91} -84.0000i q^{92} +(-49.3634 + 28.5000i) q^{93} +(-66.0000 - 38.1051i) q^{94} +(-49.5000 + 28.5788i) q^{96} +91.7987 q^{97} +(42.4352 + 24.5000i) q^{98} -33.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{4} - 6 q^{9} + 22 q^{11} - 28 q^{14} - 10 q^{16} + 12 q^{19} - 42 q^{21} + 42 q^{24} - 24 q^{26} - 100 q^{29} - 114 q^{31} + 36 q^{36} - 24 q^{39} + 66 q^{44} - 56 q^{46} + 98 q^{49} + 84 q^{51}+ \cdots - 132 q^{99}+O(q^{100}) \) 4 * q - 6 * q^4 - 6 * q^9 + 22 * q^11 - 28 * q^14 - 10 * q^16 + 12 * q^19 - 42 * q^21 + 42 * q^24 - 24 * q^26 - 100 * q^29 - 114 * q^31 + 36 * q^36 - 24 * q^39 + 66 * q^44 - 56 * q^46 + 98 * q^49 + 84 * q^51 - 18 * q^54 + 98 * q^56 + 30 * q^59 + 48 * q^61 - 52 * q^64 - 66 * q^66 + 256 * q^71 - 116 * q^74 + 34 * q^79 - 18 * q^81 - 52 * q^86 + 276 * q^89 + 168 * q^91 - 264 * q^94 - 198 * q^96 - 132 * q^99

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