LMFDB - Embedded newform 392.3.k.l.67.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(67,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("392.67");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.k (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:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4 x^{10} + 3 x^{9} + 86 x^{8} - 163 x^{7} + 155 x^{6} - 166 x^{5} + 164 x^{4} + \cdots + 4 $ x^12 - 3x^11 - 4x^10 + 3x^9 + 86x^8 - 163x^7 + 155x^6 - 166x^5 + 164x^4 - 116x^3 + 60x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			67.5
Root			$2.79733 - 1.03769i$ of defining polynomial
Character	$\chi$	$=$	392.67
Dual form			392.3.k.l.275.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.51615 + 1.30434i) q^{2} +(0.824388 - 1.42788i) q^{3} +(0.597396 + 3.95514i) q^{4} +(-3.95004 + 2.28056i) q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} +(3.14077 + 5.43997i) q^{9} +O(q^{10})$	\(q+(1.51615 + 1.30434i) q^{2} +(0.824388 - 1.42788i) q^{3} +(0.597396 + 3.95514i) q^{4} +(-3.95004 + 2.28056i) q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} +(3.14077 + 5.43997i) q^{9} +(-8.96346 - 1.69454i) q^{10} +(6.18983 - 10.7211i) q^{11} +(6.13996 + 2.40756i) q^{12} +18.3741i q^{13} +7.52026i q^{15} +(-15.2862 + 4.72557i) q^{16} +(-6.51422 + 11.2830i) q^{17} +(-2.33371 + 12.3444i) q^{18} +(-1.51262 - 2.61993i) q^{19} +(-11.3797 - 14.2606i) q^{20} +(23.3686 - 8.18111i) q^{22} +(-26.2611 + 15.1619i) q^{23} +(6.16880 + 11.6588i) q^{24} +(-2.09812 + 3.63405i) q^{25} +(-23.9661 + 27.8579i) q^{26} +25.1958 q^{27} +22.7701i q^{29} +(-9.80897 + 11.4018i) q^{30} +(-19.5382 - 11.2804i) q^{31} +(-29.3399 - 12.7738i) q^{32} +(-10.2056 - 17.6767i) q^{33} +(-24.5933 + 8.60985i) q^{34} +(-19.6396 + 15.6720i) q^{36} +(11.9335 - 6.88983i) q^{37} +(1.12393 - 5.94517i) q^{38} +(26.2361 + 15.1474i) q^{39} +(1.34740 - 36.4640i) q^{40} +60.5026 q^{41} +39.0188 q^{43} +(46.1012 + 18.0769i) q^{44} +(-24.8123 - 14.3254i) q^{45} +(-59.5919 - 11.2658i) q^{46} +(17.6115 - 10.1680i) q^{47} +(-5.85424 + 25.7226i) q^{48} +(-7.92109 + 2.77309i) q^{50} +(10.7405 + 18.6031i) q^{51} +(-72.6723 + 10.9766i) q^{52} +(4.12744 + 2.38298i) q^{53} +(38.2006 + 32.8639i) q^{54} +56.4650i q^{55} -4.98794 q^{57} +(-29.6999 + 34.5228i) q^{58} +(5.86884 - 10.1651i) q^{59} +(-29.7437 + 4.49257i) q^{60} +(94.3137 - 54.4520i) q^{61} +(-14.9093 - 42.5872i) q^{62} +(-27.8222 - 57.6361i) q^{64} +(-41.9033 - 72.5786i) q^{65} +(7.58317 - 40.1121i) q^{66} +(39.5997 - 68.5887i) q^{67} +(-48.5172 - 19.0242i) q^{68} +49.9970i q^{69} -12.9952i q^{71} +(-50.2180 - 1.85563i) q^{72} +(-49.2909 + 85.3744i) q^{73} +(27.0797 + 5.11940i) q^{74} +(3.45933 + 5.99173i) q^{75} +(9.45857 - 7.54776i) q^{76} +(20.0204 + 57.1865i) q^{78} +(113.644 - 65.6123i) q^{79} +(49.6043 - 53.5273i) q^{80} +(-7.49577 + 12.9831i) q^{81} +(91.7308 + 78.9160i) q^{82} -28.3732 q^{83} -59.4242i q^{85} +(59.1582 + 50.8938i) q^{86} +(32.5130 + 18.7714i) q^{87} +(46.3177 + 87.5388i) q^{88} +(-78.7090 - 136.328i) q^{89} +(-18.9339 - 54.0831i) q^{90} +(-75.6555 - 94.8087i) q^{92} +(-32.2141 + 18.5988i) q^{93} +(39.9642 + 7.55521i) q^{94} +(11.9498 + 6.89923i) q^{95} +(-42.4269 + 31.3634i) q^{96} +39.6175 q^{97} +77.7633 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) $ 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9	$ 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9} + 6 q^{10} + 30 q^{11} - 32 q^{12} + 16 q^{16} - 30 q^{17} - 16 q^{18} - 78 q^{19} - 48 q^{20} + 24 q^{22} + 76 q^{24} - 92 q^{25} + 128 q^{26} - 156 q^{27} - 16 q^{30} + 112 q^{32} + 78 q^{33} - 76 q^{34} - 248 q^{36} - 80 q^{38} - 44 q^{40} + 232 q^{41} - 200 q^{43} + 132 q^{44} - 156 q^{46} - 176 q^{48} + 48 q^{50} + 10 q^{51} - 132 q^{52} + 36 q^{54} + 332 q^{57} + 4 q^{58} + 110 q^{59} + 84 q^{60} + 96 q^{62} - 160 q^{64} - 32 q^{65} + 138 q^{66} + 434 q^{67} - 96 q^{68} - 328 q^{72} - 102 q^{73} - 34 q^{74} + 60 q^{75} + 168 q^{76} + 720 q^{78} + 256 q^{80} - 82 q^{81} + 24 q^{82} + 536 q^{83} + 240 q^{86} - 204 q^{88} - 214 q^{89} - 440 q^{90} + 160 q^{92} + 16 q^{94} - 48 q^{96} + 152 q^{97} + 504 q^{99}+O(q^{100}) $ 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9 + 6 * q^10 + 30 * q^11 - 32 * q^12 + 16 * q^16 - 30 * q^17 - 16 * q^18 - 78 * q^19 - 48 * q^20 + 24 * q^22 + 76 * q^24 - 92 * q^25 + 128 * q^26 - 156 * q^27 - 16 * q^30 + 112 * q^32 + 78 * q^33 - 76 * q^34 - 248 * q^36 - 80 * q^38 - 44 * q^40 + 232 * q^41 - 200 * q^43 + 132 * q^44 - 156 * q^46 - 176 * q^48 + 48 * q^50 + 10 * q^51 - 132 * q^52 + 36 * q^54 + 332 * q^57 + 4 * q^58 + 110 * q^59 + 84 * q^60 + 96 * q^62 - 160 * q^64 - 32 * q^65 + 138 * q^66 + 434 * q^67 - 96 * q^68 - 328 * q^72 - 102 * q^73 - 34 * q^74 + 60 * q^75 + 168 * q^76 + 720 * q^78 + 256 * q^80 - 82 * q^81 + 24 * q^82 + 536 * q^83 + 240 * q^86 - 204 * q^88 - 214 * q^89 - 440 * q^90 + 160 * q^92 + 16 * q^94 - 48 * q^96 + 152 * q^97 + 504 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.51615	+	1.30434i	0.758073	+	0.652170i
$2$	1.51615	+	1.30434i	0.758073	+	0.652170i
$3$	0.824388	−	1.42788i	0.274796	−	0.475961i	−0.695288	−	0.718732i	$-0.744723\pi$
$3$	0.824388	−	1.42788i	0.274796	−	0.475961i	0.970084	+	0.242771i	$0.0780563\pi$
$4$	0.597396	+	3.95514i	0.149349	+	0.988785i
$5$	−3.95004	+	2.28056i	−0.790008	+	0.456111i	−0.839965	−	0.542640i	$-0.817425\pi$
$5$	−3.95004	+	2.28056i	−0.790008	+	0.456111i	0.0499573	+	0.998751i	$0.484091\pi$
$6$	3.11234	−	1.08960i	0.518723	−	0.181599i
$7$		0			0
$7$		0			0
$8$	−4.25310	+	6.77577i	−0.531638	+	0.846972i
$9$	3.14077	+	5.43997i	0.348974	+	0.604441i
$10$	−8.96346	−	1.69454i	−0.896346	−	0.169454i
$11$	6.18983	−	10.7211i	0.562712	−	0.974645i	−0.434547	−	0.900649i	$-0.643091\pi$
$11$	6.18983	−	10.7211i	0.562712	−	0.974645i	0.997259	−	0.0739960i	$-0.0235752\pi$
$12$	6.13996	+	2.40756i	0.511663	+	0.200630i
$13$			18.3741i			1.41340i	0.707516	+	0.706698i	$0.249816\pi$
$13$			18.3741i			1.41340i	−0.707516	+	0.706698i	$0.750184\pi$
$14$		0			0
$15$			7.52026i			0.501350i
$16$	−15.2862	+	4.72557i	−0.955390	+	0.295348i
$17$	−6.51422	+	11.2830i	−0.383189	+	0.663703i	−0.991516	−	0.129983i	$-0.958508\pi$
$17$	−6.51422	+	11.2830i	−0.383189	+	0.663703i	0.608327	+	0.793687i	$0.291841\pi$
$18$	−2.33371	+	12.3444i	−0.129650	+	0.685801i
$19$	−1.51262	−	2.61993i	−0.0796115	−	0.137891i	0.823471	−	0.567359i	$-0.192035\pi$
$19$	−1.51262	−	2.61993i	−0.0796115	−	0.137891i	−0.903082	+	0.429467i	$0.858701\pi$
$20$	−11.3797	−	14.2606i	−0.568983	−	0.713028i
$21$		0			0
$22$	23.3686	−	8.18111i	1.06221	−	0.371869i
$23$	−26.2611	+	15.1619i	−1.14179	+	0.659211i	−0.946873	−	0.321609i	$-0.895776\pi$
$23$	−26.2611	+	15.1619i	−1.14179	+	0.659211i	−0.194915	+	0.980820i	$0.562443\pi$
$24$	6.16880	+	11.6588i	0.257033	+	0.485783i
$25$	−2.09812	+	3.63405i	−0.0839248	+	0.145362i
$26$	−23.9661	+	27.8579i	−0.921774	+	1.07146i
$27$	25.1958			0.933179
$28$		0			0
$29$			22.7701i			0.785176i	0.919714	+	0.392588i	$0.128420\pi$
$29$			22.7701i			0.785176i	−0.919714	+	0.392588i	$0.871580\pi$
$30$	−9.80897	+	11.4018i	−0.326966	+	0.380060i
$31$	−19.5382	−	11.2804i	−0.630264	−	0.363883i	0.150590	−	0.988596i	$-0.451883\pi$
$31$	−19.5382	−	11.2804i	−0.630264	−	0.363883i	−0.780855	+	0.624713i	$0.785216\pi$
$32$	−29.3399	−	12.7738i	−0.916872	−	0.399181i
$33$	−10.2056	−	17.6767i	−0.309262	−	0.535657i
$34$	−24.5933	+	8.60985i	−0.723333	+	0.253231i
$35$		0			0
$36$	−19.6396	+	15.6720i	−0.545543	+	0.435333i
$37$	11.9335	−	6.88983i	0.322528	−	0.186212i	−0.329991	−	0.943984i	$-0.607046\pi$
$37$	11.9335	−	6.88983i	0.322528	−	0.186212i	0.652519	+	0.757772i	$0.273712\pi$
$38$	1.12393	−	5.94517i	0.0295772	−	0.156452i
$39$	26.2361	+	15.1474i	0.672721	+	0.388395i
$40$	1.34740	−	36.4640i	0.0336849	−	0.911601i
$41$	60.5026			1.47567			0.737837	−	0.674979i	$-0.235847\pi$
$41$	60.5026			1.47567			0.737837	+	0.674979i	$0.235847\pi$
$42$		0			0
$43$	39.0188			0.907414			0.453707	−	0.891151i	$-0.350101\pi$
$43$	39.0188			0.907414			0.453707	+	0.891151i	$0.350101\pi$
$44$	46.1012	+	18.0769i	1.04775	+	0.410838i
$45$	−24.8123	−	14.3254i	−0.551385	−	0.318342i
$46$	−59.5919	−	11.2658i	−1.29548	−	0.244909i
$47$	17.6115	−	10.1680i	0.374713	−	0.216341i	−0.300802	−	0.953686i	$-0.597254\pi$
$47$	17.6115	−	10.1680i	0.374713	−	0.216341i	0.675516	+	0.737346i	$0.263921\pi$
$48$	−5.85424	+	25.7226i	−0.121963	+	0.535888i
$49$		0			0
$50$	−7.92109	+	2.77309i	−0.158422	+	0.0554618i
$51$	10.7405	+	18.6031i	0.210598	+	0.364766i
$52$	−72.6723	+	10.9766i	−1.39754	+	0.211089i
$53$	4.12744	+	2.38298i	0.0778762	+	0.0449619i	0.538432	−	0.842669i	$-0.319017\pi$
$53$	4.12744	+	2.38298i	0.0778762	+	0.0449619i	−0.460556	+	0.887631i	$0.652350\pi$
$54$	38.2006	+	32.8639i	0.707418	+	0.608591i
$55$			56.4650i			1.02664i
$56$		0			0
$57$	−4.98794			−0.0875077
$58$	−29.6999	+	34.5228i	−0.512068	+	0.595221i
$59$	5.86884	−	10.1651i	0.0994718	−	0.172290i	−0.811994	−	0.583665i	$-0.801618\pi$
$59$	5.86884	−	10.1651i	0.0994718	−	0.172290i	0.911466	+	0.411375i	$0.134951\pi$
$60$	−29.7437	+	4.49257i	−0.495728	+	0.0748762i
$61$	94.3137	−	54.4520i	1.54613	−	0.892656i	0.547694	−	0.836679i	$-0.315506\pi$
$61$	94.3137	−	54.4520i	1.54613	−	0.892656i	0.998432	−	0.0559779i	$-0.0178276\pi$
$62$	−14.9093	−	42.5872i	−0.240473	−	0.686890i
$63$		0			0
$64$	−27.8222	−	57.6361i	−0.434722	−	0.900565i
$65$	−41.9033	−	72.5786i	−0.644666	−	1.11659i
$66$	7.58317	−	40.1121i	0.114896	−	0.607759i
$67$	39.5997	−	68.5887i	0.591041	−	1.02371i	−0.403052	−	0.915177i	$-0.632051\pi$
$67$	39.5997	−	68.5887i	0.591041	−	1.02371i	0.994093	−	0.108535i	$-0.0346160\pi$
$68$	−48.5172	−	19.0242i	−0.713488	−	0.279768i
$69$			49.9970i			0.724595i
$70$		0			0
$71$		−	12.9952i		−	0.183031i	−0.995804	−	0.0915157i	$-0.970829\pi$
$71$		−	12.9952i		−	0.183031i	0.995804	−	0.0915157i	$-0.0291712\pi$
$72$	−50.2180	−	1.85563i	−0.697473	−	0.0257726i
$73$	−49.2909	+	85.3744i	−0.675218	+	1.16951i	0.301187	+	0.953565i	$0.402617\pi$
$73$	−49.2909	+	85.3744i	−0.675218	+	1.16951i	−0.976405	+	0.215947i	$0.930716\pi$
$74$	27.0797	+	5.11940i	0.365942	+	0.0691811i
$75$	3.45933	+	5.99173i	0.0461244	+	0.0798898i
$76$	9.45857	−	7.54776i	0.124455	−	0.0993126i
$77$		0			0
$78$	20.0204	+	57.1865i	0.256671	+	0.733160i
$79$	113.644	−	65.6123i	1.43853	−	0.830535i	0.440781	−	0.897615i	$-0.354701\pi$
$79$	113.644	−	65.6123i	1.43853	−	0.830535i	0.997748	+	0.0670794i	$0.0213681\pi$
$80$	49.6043	−	53.5273i	0.620054	−	0.669091i
$81$	−7.49577	+	12.9831i	−0.0925404	+	0.160285i
$82$	91.7308	+	78.9160i	1.11867	+	0.962390i
$83$	−28.3732			−0.341846			−0.170923	−	0.985284i	$-0.554675\pi$
$83$	−28.3732			−0.341846			−0.170923	+	0.985284i	$0.554675\pi$
$84$		0			0
$85$		−	59.4242i		−	0.699108i
$86$	59.1582	+	50.8938i	0.687886	+	0.591788i
$87$	32.5130	+	18.7714i	0.373713	+	0.215763i
$88$	46.3177	+	87.5388i	0.526338	+	0.994759i
$89$	−78.7090	−	136.328i	−0.884371	−	1.53178i	−0.846433	−	0.532495i	$-0.821254\pi$
$89$	−78.7090	−	136.328i	−0.884371	−	1.53178i	−0.0379380	−	0.999280i	$-0.512079\pi$
$90$	−18.9339	−	54.0831i	−0.210377	−	0.600923i
$91$		0			0
$92$	−75.6555	−	94.8087i	−0.822343	−	1.03053i
$93$	−32.2141	+	18.5988i	−0.346388	+	0.199987i
$94$	39.9642	+	7.55521i	0.425151	+	0.0803746i
$95$	11.9498	+	6.89923i	0.125788	+	0.0726235i
$96$	−42.4269	+	31.3634i	−0.441947	+	0.326702i
$97$	39.6175			0.408428			0.204214	−	0.978926i	$-0.434536\pi$
$97$	39.6175			0.408428			0.204214	+	0.978926i	$0.434536\pi$
$98$		0			0
$99$	77.7633			0.785488
$100$	−15.6266	−	6.12739i	−0.156266	−	0.0612739i
$101$	−37.7745	−	21.8091i	−0.374005	−	0.215932i	0.301202	−	0.953560i	$-0.402612\pi$
$101$	−37.7745	−	21.8091i	−0.374005	−	0.215932i	−0.675207	+	0.737628i	$0.735946\pi$
$102$	−7.98058	+	42.2142i	−0.0782409	+	0.413865i
$103$	−54.4748	+	31.4510i	−0.528881	+	0.305350i	−0.740561	−	0.671989i	$-0.765440\pi$
$103$	−54.4748	+	31.4510i	−0.528881	+	0.305350i	0.211679	+	0.977339i	$0.432107\pi$
$104$	−124.499	−	78.1471i	−1.19711	−	0.751415i
$105$		0			0
$106$	3.14959	+	8.99653i	0.0297131	+	0.0848729i
$107$	−22.1133	−	38.3014i	−0.206667	−	0.357957i	0.743996	−	0.668184i	$-0.232928\pi$
$107$	−22.1133	−	38.3014i	−0.206667	−	0.357957i	−0.950663	+	0.310227i	$0.899595\pi$
$108$	15.0519	+	99.6530i	0.139369	+	0.922713i
$109$	7.63419	+	4.40760i	0.0700384	+	0.0404367i	0.534610	−	0.845099i	$-0.320458\pi$
$109$	7.63419	+	4.40760i	0.0700384	+	0.0404367i	−0.464572	+	0.885535i	$0.653792\pi$
$110$	−73.6496	+	85.6092i	−0.669542	+	0.778266i
$111$		−	22.7196i		−	0.204681i
$112$		0			0
$113$	−121.408			−1.07440			−0.537202	−	0.843454i	$-0.680519\pi$
$113$	−121.408			−1.07440			−0.537202	+	0.843454i	$0.680519\pi$
$114$	−7.56245	−	6.50597i	−0.0663373	−	0.0570699i
$115$	69.1550	−	119.780i	0.601347	−	1.04156i
$116$	−90.0589	+	13.6028i	−0.776370	+	0.117265i
$117$	−99.9548	+	57.7089i	−0.854314	+	0.493239i
$118$	22.1568	−	7.75685i	0.187769	−	0.0657360i
$119$		0			0
$120$	−50.9556	−	31.9844i	−0.424630	−	0.266537i
$121$	−16.1279	−	27.9344i	−0.133289	−	0.230863i
$122$	214.017	+	40.4599i	1.75424	+	0.331638i
$123$	49.8776	−	86.3906i	0.405509	−	0.702363i
$124$	32.9434	−	84.0151i	0.265673	−	0.677541i
$125$		−	133.167i		−	1.06534i
$126$		0			0
$127$			222.845i			1.75468i	0.479868	+	0.877341i	$0.340685\pi$
$127$			222.845i			1.75468i	−0.479868	+	0.877341i	$0.659315\pi$
$128$	32.9946	−	123.674i	0.257770	−	0.966206i
$129$	32.1666	−	55.7143i	0.249354	−	0.431893i
$130$	31.1357	−	164.696i	0.239505	−	1.26689i
$131$	118.527	+	205.294i	0.904785	+	1.56713i	0.821206	+	0.570632i	$0.193302\pi$
$131$	118.527	+	205.294i	0.904785	+	1.56713i	0.0835786	+	0.996501i	$0.473365\pi$
$132$	63.8169	−	50.9247i	0.483462	−	0.385793i
$133$		0			0
$134$	149.502	−	52.3390i	1.11569	−	0.390590i
$135$	−99.5246	+	57.4605i	−0.737219	+	0.425634i
$136$	−48.7451	−	92.1264i	−0.358420	−	0.677400i
$137$	4.83138	−	8.36820i	0.0352656	−	0.0610818i	−0.847854	−	0.530230i	$-0.822106\pi$
$137$	4.83138	−	8.36820i	0.0352656	−	0.0610818i	0.883119	+	0.469148i	$0.155439\pi$
$138$	−65.2131	+	75.8028i	−0.472559	+	0.549295i
$139$	63.0621			0.453684			0.226842	−	0.973932i	$-0.427160\pi$
$139$	63.0621			0.453684			0.226842	+	0.973932i	$0.427160\pi$
$140$		0			0
$141$		−	33.5296i		−	0.237798i
$142$	16.9502	−	19.7027i	0.119368	−	0.138751i
$143$	196.991	+	113.733i	1.37756	+	0.795334i
$144$	−73.7175	−	68.3148i	−0.511927	−	0.474408i
$145$	−51.9285	−	89.9428i	−0.358128	−	0.620295i
$146$	−186.089	+	65.1479i	−1.27459	+	0.446219i
$147$		0			0
$148$	34.3793	+	43.0829i	0.232293	+	0.291100i
$149$	233.751	−	134.956i	1.56880	−	0.905746i	0.572489	−	0.819912i	$-0.305978\pi$
$149$	233.751	−	134.956i	1.56880	−	0.905746i	0.996309	−	0.0858343i	$-0.0273556\pi$
$150$	−2.57041	+	13.5965i	−0.0171361	+	0.0906432i
$151$	93.6846	+	54.0888i	0.620428	+	0.358204i	0.777036	−	0.629457i	$-0.216723\pi$
$151$	93.6846	+	54.0888i	0.620428	+	0.358204i	−0.156608	+	0.987661i	$0.550056\pi$
$152$	24.1854	+	0.893685i	0.159114	+	0.00587951i
$153$	−81.8386			−0.534893
$154$		0			0
$155$	102.902			0.663885
$156$	−44.2368	+	112.816i	−0.283569	+	0.723182i
$157$	102.565	+	59.2159i	0.653280	+	0.377171i	0.789712	−	0.613478i	$-0.210230\pi$
$157$	102.565	+	59.2159i	0.653280	+	0.377171i	−0.136432	+	0.990649i	$0.543563\pi$
$158$	257.881	+	48.7523i	1.63216	+	0.308559i
$159$	6.80523	−	3.92900i	0.0428002	−	0.0247107i
$160$	145.025	−	16.4543i	0.906407	−	0.102839i
$161$		0			0
$162$	−28.2990	+	9.90717i	−0.174685	+	0.0611554i
$163$	41.0142	+	71.0387i	0.251621	+	0.435820i	0.963972	−	0.266003i	$-0.0857031\pi$
$163$	41.0142	+	71.0387i	0.251621	+	0.435820i	−0.712351	+	0.701823i	$0.752370\pi$
$164$	36.1440	+	239.296i	0.220390	+	1.45912i
$165$	80.6254	+	46.5491i	0.488639	+	0.282116i
$166$	−43.0179	−	37.0083i	−0.259144	−	0.222942i
$167$		−	131.596i		−	0.788002i	−0.919110	−	0.394001i	$-0.871091\pi$
$167$		−	131.596i		−	0.788002i	0.919110	−	0.394001i	$-0.128909\pi$
$168$		0			0
$169$	−168.609			−0.997687
$170$	77.5093	−	90.0957i	0.455937	−	0.529975i
$171$	9.50157	−	16.4572i	0.0555648	−	0.0962410i
$172$	23.3097	+	154.325i	0.135521	+	0.897237i
$173$	95.3611	−	55.0568i	0.551220	−	0.318247i	−0.198394	−	0.980122i	$-0.563572\pi$
$173$	95.3611	−	55.0568i	0.551220	−	0.318247i	0.749614	+	0.661875i	$0.230239\pi$
$174$	24.8102	+	70.8682i	0.142587	+	0.407289i
$175$		0			0
$176$	−43.9559	+	193.136i	−0.249749	+	1.09736i
$177$	−9.67640	−	16.7600i	−0.0546689	−	0.0946893i
$178$	58.4837	−	309.356i	0.328560	−	1.73796i
$179$	−76.9263	+	133.240i	−0.429756	+	0.744359i	−0.996851	−	0.0792929i	$-0.974734\pi$
$179$	−76.9263	+	133.240i	−0.429756	+	0.744359i	0.567095	+	0.823652i	$0.308067\pi$
$180$	41.8362	−	106.694i	0.232423	−	0.592745i
$181$			227.511i			1.25697i	0.777823	+	0.628484i	$0.216324\pi$
$181$			227.511i			1.25697i	−0.777823	+	0.628484i	$0.783676\pi$
$182$		0			0
$183$		−	179.558i		−	0.981194i
$184$	8.95792	−	242.424i	0.0486844	−	1.31752i
$185$	−31.4253	+	54.4303i	−0.169867	+	0.294218i
$186$	−73.1005	−	13.8196i	−0.393013	−	0.0742990i
$187$	80.6438	+	139.679i	0.431250	+	0.746947i
$188$	50.7370	+	63.5817i	0.269877	+	0.338200i
$189$		0			0
$190$	9.11872	+	26.0469i	0.0479933	+	0.137089i
$191$	−105.262	+	60.7728i	−0.551107	+	0.318182i	−0.749569	−	0.661927i	$-0.769739\pi$
$191$	−105.262	+	60.7728i	−0.551107	+	0.318182i	0.198461	+	0.980109i	$0.436406\pi$
$192$	−105.234	−	7.78772i	−0.548093	−	0.0405610i
$193$	−42.7276	+	74.0064i	−0.221386	+	0.383453i	−0.955229	−	0.295867i	$-0.904392\pi$
$193$	−42.7276	+	74.0064i	−0.221386	+	0.383453i	0.733843	+	0.679319i	$0.237725\pi$
$194$	60.0659	+	51.6747i	0.309618	+	0.266364i
$195$	−138.178			−0.708606
$196$		0			0
$197$		−	214.100i		−	1.08680i	−0.839474	−	0.543400i	$-0.817137\pi$
$197$		−	214.100i		−	1.08680i	0.839474	−	0.543400i	$-0.182863\pi$
$198$	117.900	+	101.430i	0.595457	+	0.512271i
$199$	−214.968	−	124.112i	−1.08024	−	0.623677i	−0.149279	−	0.988795i	$-0.547695\pi$
$199$	−214.968	−	124.112i	−1.08024	−	0.623677i	−0.930961	+	0.365118i	$0.881029\pi$
$200$	−15.7000	−	29.6724i	−0.0784999	−	0.148362i
$201$	−65.2911	−	113.087i	−0.324831	−	0.562624i
$202$	−28.8252	−	82.3366i	−0.142699	−	0.407607i
$203$		0			0
$204$	−67.1614	+	53.5935i	−0.329222	+	0.262713i
$205$	−238.988	+	137.980i	−1.16579	+	0.673071i
$206$	−123.615	−	23.3693i	−0.600070	−	0.113443i
$207$	−164.960	−	95.2398i	−0.796909	−	0.460096i
$208$	−86.8282	−	280.871i	−0.417443	−	1.35034i
$209$	−37.4514			−0.179193
$210$		0			0
$211$	191.753			0.908783			0.454392	−	0.890802i	$-0.349857\pi$
$211$	191.753			0.908783			0.454392	+	0.890802i	$0.349857\pi$
$212$	−6.95929	+	17.7482i	−0.0328269	+	0.0837178i
$213$	−18.5557	−	10.7131i	−0.0871157	−	0.0502963i
$214$	16.4310	−	86.9139i	0.0767805	−	0.406140i
$215$	−154.126	+	88.9846i	−0.716864	+	0.413882i
$216$	−107.161	+	170.721i	−0.496113	+	0.790376i
$217$		0			0
$218$	5.82553	+	16.6401i	0.0267226	+	0.0763309i
$219$	81.2697	+	140.763i	0.371095	+	0.642755i
$220$	−223.327	+	33.7320i	−1.01512	+	0.153327i
$221$	−207.315	−	119.693i	−0.938075	−	0.541598i
$222$	29.6341	−	34.4462i	0.133487	−	0.155163i
$223$			41.2269i			0.184874i	0.995719	+	0.0924370i	$0.0294657\pi$
$223$			41.2269i			0.184874i	−0.995719	+	0.0924370i	$0.970534\pi$
$224$		0			0
$225$	−26.3588			−0.117150
$226$	−184.072	−	158.357i	−0.814477	−	0.700694i
$227$	35.2219	−	61.0060i	0.155162	−	0.268749i	−0.777956	−	0.628319i	$-0.783743\pi$
$227$	35.2219	−	61.0060i	0.155162	−	0.268749i	0.933118	+	0.359570i	$0.117077\pi$
$228$	−2.97978	−	19.7280i	−0.0130692	−	0.0865263i
$229$	81.8558	−	47.2595i	0.357449	−	0.206373i	−0.310512	−	0.950569i	$-0.600501\pi$
$229$	81.8558	−	47.2595i	0.357449	−	0.206373i	0.667961	+	0.744196i	$0.267167\pi$
$230$	261.083	−	91.4022i	1.13514	−	0.397401i
$231$		0			0
$232$	−154.285	−	96.8436i	−0.665022	−	0.417429i
$233$	68.1434	+	118.028i	0.292461	+	0.506557i	0.974391	−	0.224860i	$-0.0721925\pi$
$233$	68.1434	+	118.028i	0.292461	+	0.506557i	−0.681930	+	0.731417i	$0.738859\pi$
$234$	−226.818	−	42.8799i	−0.969308	−	0.183247i
$235$	−46.3775	+	80.3281i	−0.197351	+	0.341822i
$236$	43.7105	+	17.1395i	0.185214	+	0.0726248i
$237$		−	216.360i		−	0.912911i
$238$		0			0
$239$		−	173.230i		−	0.724813i	−0.932020	−	0.362406i	$-0.881955\pi$
$239$		−	173.230i		−	0.724813i	0.932020	−	0.362406i	$-0.118045\pi$
$240$	−35.5375	−	114.956i	−0.148073	−	0.478985i
$241$	−164.461	+	284.856i	−0.682413	+	1.18197i	0.291830	+	0.956470i	$0.405736\pi$
$241$	−164.461	+	284.856i	−0.682413	+	1.18197i	−0.974242	+	0.225503i	$0.927597\pi$
$242$	11.9837	−	63.3890i	0.0495193	−	0.261938i
$243$	125.740	+	217.788i	0.517449	+	0.896248i
$244$	271.708	+	340.494i	1.11356	+	1.39547i
$245$		0			0
$246$	188.304	−	65.9234i	0.765465	−	0.267981i
$247$	48.1390	−	27.7931i	0.194895	−	0.112523i
$248$	159.531	−	84.4098i	0.643271	−	0.340362i
$249$	−23.3905	+	40.5136i	−0.0939379	+	0.162705i
$250$	173.695	−	201.901i	0.694782	−	0.807605i
$251$	−160.255			−0.638466			−0.319233	−	0.947676i	$-0.603425\pi$
$251$	−160.255			−0.638466			−0.319233	+	0.947676i	$0.603425\pi$
$252$		0			0
$253$			375.397i			1.48378i
$254$	−290.665	+	337.865i	−1.14435	+	1.33018i
$255$	−84.8507	−	48.9886i	−0.332748	−	0.192112i
$256$	211.338	−	144.472i	0.825539	−	0.564345i
$257$	72.7208	+	125.956i	0.282960	+	0.490102i	0.972113	−	0.234515i	$-0.0753502\pi$
$257$	72.7208	+	125.956i	0.282960	+	0.490102i	−0.689152	+	0.724617i	$0.742017\pi$
$258$	121.440	−	42.5147i	0.470696	−	0.164786i
$259$		0			0
$260$	262.026	−	209.091i	1.00779	−	0.804198i
$261$	−123.869	+	71.5156i	−0.474593	+	0.274006i
$262$	−88.0698	+	465.855i	−0.336144	+	1.77807i
$263$	−175.617	−	101.392i	−0.667745	−	0.385523i	0.127477	−	0.991842i	$-0.459312\pi$
$263$	−175.617	−	101.392i	−0.667745	−	0.385523i	−0.795222	+	0.606319i	$0.792645\pi$
$264$	163.179	+	6.02969i	0.618102	+	0.0228397i
$265$	−21.7381			−0.0820305
$266$		0			0
$267$	−259.547			−0.972087
$268$	294.935	+	115.648i	1.10050	+	0.431521i
$269$	−191.662	−	110.656i	−0.712497	−	0.411360i	0.0994882	−	0.995039i	$-0.468279\pi$
$269$	−191.662	−	110.656i	−0.712497	−	0.411360i	−0.811985	+	0.583679i	$0.801613\pi$
$270$	−225.842	−	42.6953i	−0.836451	−	0.158131i
$271$	−101.651	+	58.6880i	−0.375095	+	0.216561i	−0.675682	−	0.737193i	$-0.736151\pi$
$271$	−101.651	+	58.6880i	−0.375095	+	0.216561i	0.300587	+	0.953754i	$0.402817\pi$
$272$	46.2595	−	203.257i	0.170072	−	0.747269i
$273$		0			0
$274$	18.2401	−	6.38565i	0.0665695	−	0.0233053i
$275$	25.9740	+	44.9883i	0.0944509	+	0.163594i
$276$	−197.745	+	29.8680i	−0.716468	+	0.108217i
$277$	−221.277	−	127.755i	−0.798835	−	0.461208i	0.0442283	−	0.999021i	$-0.485917\pi$
$277$	−221.277	−	127.755i	−0.798835	−	0.461208i	−0.843064	+	0.537814i	$0.819250\pi$
$278$	95.6113	+	82.2544i	0.343926	+	0.295879i
$279$		−	141.716i		−	0.507944i
$280$		0			0
$281$	−278.004			−0.989336			−0.494668	−	0.869082i	$-0.664710\pi$
$281$	−278.004			−0.989336			−0.494668	+	0.869082i	$0.664710\pi$
$282$	43.7339	−	50.8357i	0.155085	−	0.180268i
$283$	28.3448	−	49.0947i	0.100158	−	0.173479i	−0.811591	−	0.584225i	$-0.801398\pi$
$283$	28.3448	−	49.0947i	0.100158	−	0.173479i	0.911750	+	0.410746i	$0.134732\pi$
$284$	51.3979	−	7.76330i	0.180979	−	0.0273356i
$285$	19.7026	−	11.3753i	0.0691318	−	0.0399133i
$286$	150.321	+	429.379i	0.525597	+	1.50132i
$287$		0			0
$288$	−22.6608	−	199.728i	−0.0786833	−	0.693499i
$289$	59.6300	+	103.282i	0.206332	+	0.357378i
$290$	38.5848	−	204.099i	0.133051	−	0.703789i
$291$	32.6602	−	56.5691i	0.112234	−	0.194396i
$292$	−367.114	−	143.950i	−1.25724	−	0.492980i
$293$		−	287.871i		−	0.982493i	−0.871020	−	0.491247i	$-0.836541\pi$
$293$		−	287.871i		−	0.982493i	0.871020	−	0.491247i	$-0.163459\pi$
$294$		0			0
$295$			53.5369i			0.181481i
$296$	−4.07065	+	110.162i	−0.0137522	+	0.372169i
$297$	155.958	−	270.127i	0.525111	−	0.909518i
$298$	530.429	+	100.277i	1.77996	+	0.336501i
$299$	−278.586	−	482.525i	−0.931726	−	1.61380i
$300$	−21.6315	+	17.2616i	−0.0721052	+	0.0575385i
$301$		0			0
$302$	71.4893	+	204.203i	0.236720	+	0.676169i
$303$	−62.2817	+	35.9584i	−0.205550	+	0.118675i
$304$	35.5029	+	32.9009i	0.116786	+	0.108227i
$305$	−248.362	+	430.176i	−0.814302	+	1.41041i
$306$	−124.079	−	106.745i	−0.405488	−	0.348841i
$307$	−53.6483			−0.174750			−0.0873750	−	0.996175i	$-0.527848\pi$
$307$	−53.6483			−0.174750			−0.0873750	+	0.996175i	$0.527848\pi$
$308$		0			0
$309$			103.711i			0.335636i
$310$	156.015	+	134.219i	0.503274	+	0.432966i
$311$	−91.0263	−	52.5541i	−0.292689	−	0.168984i	0.346465	−	0.938063i	$-0.387382\pi$
$311$	−91.0263	−	52.5541i	−0.292689	−	0.168984i	−0.639154	+	0.769079i	$0.720715\pi$
$312$	−214.220	+	113.346i	−0.686604	+	0.363290i
$313$	105.245	+	182.290i	0.336246	+	0.582395i	0.983723	−	0.179690i	$-0.0575093\pi$
$313$	105.245	+	182.290i	0.336246	+	0.582395i	−0.647477	+	0.762085i	$0.724176\pi$
$314$	78.2657	+	223.559i	0.249254	+	0.711973i
$315$		0			0
$316$	327.396	+	410.280i	1.03606	+	1.29836i
$317$	54.4626	−	31.4440i	0.171806	−	0.0991925i	−0.411631	−	0.911351i	$-0.635041\pi$
$317$	54.4626	−	31.4440i	0.171806	−	0.0991925i	0.583437	+	0.812158i	$0.301707\pi$
$318$	15.4425	+	2.91939i	0.0485612	+	0.00918047i
$319$	244.120	+	140.943i	0.765268	+	0.441828i
$320$	241.341	+	164.215i	0.754192	+	0.513172i
$321$	−72.9199			−0.227165
$322$		0			0
$323$	39.4141			0.122025
$324$	−55.8277	−	21.8908i	−0.172308	−	0.0675641i
$325$	−66.7725	−	38.5511i	−0.205454	−	0.118619i
$326$	−30.4751	+	161.201i	−0.0934818	+	0.494483i
$327$	12.5871	−	7.26715i	0.0384926	−	0.0222237i
$328$	−257.324	+	409.952i	−0.784524	+	1.24985i
$329$		0			0
$330$	61.5240	+	175.738i	0.186436	+	0.532540i
$331$	−98.2893	−	170.242i	−0.296947	−	0.514327i	0.678489	−	0.734610i	$-0.262635\pi$
$331$	−98.2893	−	170.242i	−0.296947	−	0.514327i	−0.975436	+	0.220284i	$0.929302\pi$
$332$	−16.9500	−	112.220i	−0.0510544	−	0.338012i
$333$	74.9610	+	43.2787i	0.225108	+	0.129966i
$334$	171.646	−	199.519i	0.513911	−	0.597363i
$335$			361.238i			1.07832i
$336$		0			0
$337$	591.516			1.75524			0.877620	−	0.479358i	$-0.159130\pi$
$337$	591.516			1.75524			0.877620	+	0.479358i	$0.159130\pi$
$338$	−255.636	−	219.923i	−0.756319	−	0.650661i
$339$	−100.087	+	173.356i	−0.295242	+	0.511374i
$340$	235.031	−	35.4998i	0.691267	−	0.104411i
$341$	−241.876	+	139.647i	−0.709314	+	0.409523i
$342$	35.8716	−	12.5582i	0.104888	−	0.0367200i
$343$		0			0
$344$	−165.951	+	264.383i	−0.482416	+	0.768554i
$345$	−114.021	−	197.490i	−0.330496	−	0.572436i
$346$	216.394	+	40.9092i	0.625416	+	0.118235i
$347$	−123.770	+	214.376i	−0.356685	+	0.617797i	−0.987405	−	0.158214i	$-0.949427\pi$
$347$	−123.770	+	214.376i	−0.356685	+	0.617797i	0.630719	+	0.776011i	$0.282760\pi$
$348$	−54.8203	+	139.807i	−0.157530	+	0.401746i
$349$			288.749i			0.827362i	0.910422	+	0.413681i	$0.135757\pi$
$349$			288.749i			0.827362i	−0.910422	+	0.413681i	$0.864243\pi$
$350$		0			0
$351$			462.952i			1.31895i
$352$	−318.558	+	235.488i	−0.904995	+	0.669001i
$353$	−0.634830	+	1.09956i	−0.00179839	+	0.00311490i	−0.866923	−	0.498442i	$-0.833906\pi$
$353$	−0.634830	+	1.09956i	−0.00179839	+	0.00311490i	0.865125	+	0.501557i	$0.167239\pi$
$354$	7.18992	−	38.0319i	0.0203105	−	0.107435i
$355$	29.6364	+	51.3317i	0.0834827	+	0.144596i
$356$	492.176	−	392.747i	1.38252	−	1.10322i
$357$		0			0
$358$	−290.422	+	101.674i	−0.811235	+	0.284005i
$359$	−15.0707	+	8.70105i	−0.0419796	+	0.0242369i	−0.520843	−	0.853653i	$-0.674382\pi$
$359$	−15.0707	+	8.70105i	−0.0419796	+	0.0242369i	0.478863	+	0.877889i	$0.341049\pi$
$360$	202.595	−	107.195i	0.562764	−	0.297765i
$361$	175.924	−	304.709i	0.487324	−	0.844070i
$362$	−296.752	+	344.940i	−0.819756	+	0.952873i
$363$	−53.1828			−0.146509
$364$		0			0
$365$		−	449.643i		−	1.23190i
$366$	234.205	−	272.237i	0.639905	−	0.743816i
$367$	459.021	+	265.016i	1.25074	+	0.722115i	0.971256	−	0.238036i	$-0.0765036\pi$
$367$	459.021	+	265.016i	1.25074	+	0.722115i	0.279483	+	0.960151i	$0.409837\pi$
$368$	329.785	−	355.866i	0.896155	−	0.967028i
$369$	190.025	+	329.132i	0.514972	+	0.891958i
$370$	−118.641	+	41.5349i	−0.320651	+	0.112256i
$371$		0			0
$372$	−92.8055	−	116.300i	−0.249477	−	0.312636i
$373$	−102.722	+	59.3066i	−0.275394	+	0.158999i	−0.631337	−	0.775509i	$-0.717493\pi$
$373$	−102.722	+	59.3066i	−0.275394	+	0.158999i	0.355942	+	0.934508i	$0.384160\pi$
$374$	−59.9213	+	316.961i	−0.160217	+	0.847489i
$375$	−190.147	−	109.782i	−0.507059	−	0.292751i
$376$	−6.00746	+	162.577i	−0.0159773	+	0.432386i
$377$	−418.381			−1.10976
$378$		0			0
$379$	−345.947			−0.912790			−0.456395	−	0.889777i	$-0.650860\pi$
$379$	−345.947			−0.912790			−0.456395	+	0.889777i	$0.650860\pi$
$380$	−20.1486	+	51.3847i	−0.0530227	+	0.135223i
$381$	318.196	+	183.710i	0.835160	+	0.482180i
$382$	−238.860	−	45.1564i	−0.625288	−	0.118210i
$383$	350.630	−	202.436i	0.915483	−	0.528555i	0.0332920	−	0.999446i	$-0.489401\pi$
$383$	350.630	−	202.436i	0.915483	−	0.528555i	0.882191	+	0.470891i	$0.156068\pi$
$384$	−149.392	−	149.068i	−0.389042	−	0.388198i
$385$		0			0
$386$	−161.311	+	56.4731i	−0.417903	+	0.146303i
$387$	122.549	+	212.261i	0.316664	+	0.548478i
$388$	23.6673	+	156.693i	0.0609983	+	0.403847i
$389$	116.391	+	67.1985i	0.299206	+	0.172747i	0.642086	−	0.766632i	$-0.278069\pi$
$389$	116.391	+	67.1985i	0.299206	+	0.172747i	−0.342880	+	0.939379i	$0.611402\pi$
$390$	−209.498	−	180.231i	−0.537175	−	0.462132i
$391$		−	395.070i		−	1.01041i
$392$		0			0
$393$	390.848			0.994525
$394$	279.259	−	324.606i	0.708779	−	0.823874i
$395$	−299.265	+	518.342i	−0.757633	+	1.31226i
$396$	46.4555	+	307.564i	0.117312	+	0.776678i
$397$	−530.424	+	306.240i	−1.33608	+	0.771386i	−0.986224	−	0.165417i	$-0.947103\pi$
$397$	−530.424	+	306.240i	−1.33608	+	0.771386i	−0.349857	+	0.936803i	$0.613770\pi$
$398$	−164.039	−	468.563i	−0.412158	−	1.17729i
$399$		0			0
$400$	14.8994	−	65.4657i	0.0372485	−	0.163664i
$401$	63.1234	+	109.333i	0.157415	+	0.272651i	0.933936	−	0.357441i	$-0.116351\pi$
$401$	63.1234	+	109.333i	0.157415	+	0.272651i	−0.776521	+	0.630092i	$0.783017\pi$
$402$	48.5137	−	256.619i	0.120681	−	0.638355i
$403$	207.267	−	358.998i	0.514311	−	0.890813i
$404$	63.6918	−	162.432i	0.157653	−	0.402060i
$405$		−	68.3781i		−	0.168835i
$406$		0			0
$407$		−	170.588i		−	0.419134i
$408$	−171.731	−	6.34569i	−0.420908	−	0.0155532i
$409$	171.259	−	296.630i	0.418727	−	0.725257i	−0.577084	−	0.816685i	$-0.695810\pi$
$409$	171.259	−	296.630i	0.418727	−	0.725257i	0.995812	+	0.0914275i	$0.0291430\pi$
$410$	−542.313	−	102.524i	−1.32271	−	0.250058i
$411$	−7.96587	−	13.7973i	−0.0193817	−	0.0335700i
$412$	−156.936	−	196.667i	−0.380913	−	0.477346i
$413$		0			0
$414$	−125.879	−	359.561i	−0.304055	−	0.868506i
$415$	112.075	−	64.7068i	0.270061	−	0.155920i
$416$	234.708	−	539.096i	0.564201	−	1.29590i
$417$	51.9876	−	90.0452i	0.124671	−	0.215936i
$418$	−56.7818	−	48.8494i	−0.135842	−	0.116865i
$419$	376.392			0.898311			0.449155	−	0.893454i	$-0.351725\pi$
$419$	376.392			0.898311			0.449155	+	0.893454i	$0.351725\pi$
$420$		0			0
$421$		−	111.135i		−	0.263978i	−0.991251	−	0.131989i	$-0.957864\pi$
$421$		−	111.135i		−	0.263978i	0.991251	−	0.131989i	$-0.0421363\pi$
$422$	290.726	+	250.111i	0.688924	+	0.592681i
$423$	110.627	+	63.8708i	0.261531	+	0.150995i
$424$	−33.7010	+	17.8315i	−0.0794834	+	0.0420555i
$425$	−27.3352	−	47.3460i	−0.0643181	−	0.111402i
$426$	−14.1595	−	40.4455i	−0.0332384	−	0.0949425i
$427$		0			0
$428$	138.277	−	110.342i	0.323077	−	0.257810i
$429$	324.794	−	187.520i	0.757096	−	0.437109i
$430$	−349.743	−	66.1188i	−0.813357	−	0.153765i
$431$	−35.7481	−	20.6392i	−0.0829422	−	0.0478867i	0.457955	−	0.888975i	$-0.348582\pi$
$431$	−35.7481	−	20.6392i	−0.0829422	−	0.0478867i	−0.540898	+	0.841089i	$0.681915\pi$
$432$	−385.149	+	119.065i	−0.891550	+	0.275613i
$433$	675.176			1.55930			0.779649	−	0.626217i	$-0.215397\pi$
$433$	675.176			1.55930			0.779649	+	0.626217i	$0.215397\pi$
$434$		0			0
$435$	−171.237			−0.393648
$436$	−12.8720	+	32.8273i	−0.0295230	+	0.0752921i
$437$	79.4461	+	45.8682i	0.181799	+	0.104962i
$438$	−60.3864	+	319.421i	−0.137868	+	0.729272i
$439$	459.215	−	265.128i	1.04605	−	0.603936i	0.124508	−	0.992219i	$-0.460265\pi$
$439$	459.215	−	265.128i	1.04605	−	0.603936i	0.921541	+	0.388282i	$0.126931\pi$
$440$	−382.594	−	240.152i	−0.869532	−	0.545799i
$441$		0			0
$442$	−158.199	−	451.881i	−0.357915	−	1.02235i
$443$	−166.016	−	287.549i	−0.374755	−	0.649094i	0.615535	−	0.788109i	$-0.288940\pi$
$443$	−166.016	−	287.549i	−0.374755	−	0.649094i	−0.990290	+	0.139015i	$0.955606\pi$
$444$	89.8591	−	13.5726i	0.202385	−	0.0305689i
$445$	621.808	+	359.001i	1.39732	+	0.806743i
$446$	−53.7739	+	62.5060i	−0.120569	+	0.140148i
$447$		−	445.025i		−	0.995582i
$448$		0			0
$449$	−19.4200			−0.0432517			−0.0216259	−	0.999766i	$-0.506884\pi$
$449$	−19.4200			−0.0432517			−0.0216259	+	0.999766i	$0.506884\pi$
$450$	−39.9638	−	34.3809i	−0.0888085	−	0.0764019i
$451$	374.501	−	648.654i	0.830379	−	1.43826i
$452$	−72.5285	−	480.184i	−0.160461	−	1.06235i
$453$	154.465	−	89.1804i	0.340982	−	0.196866i
$454$	132.974	−	46.5528i	0.292894	−	0.102539i
$455$		0			0
$456$	21.2142	−	33.7972i	0.0465224	−	0.0741166i
$457$	88.9796	+	154.117i	0.194704	+	0.337237i	0.946803	−	0.321813i	$-0.104292\pi$
$457$	88.9796	+	154.117i	0.194704	+	0.337237i	−0.752100	+	0.659049i	$0.770959\pi$
$458$	185.748	+	35.1155i	0.405563	+	0.0766715i
$459$	−164.131	+	284.283i	−0.357584	+	0.619354i
$460$	515.059	+	201.961i	1.11969	+	0.439047i
$461$			299.341i			0.649329i	0.945829	+	0.324664i	$0.105251\pi$
$461$			299.341i			0.649329i	−0.945829	+	0.324664i	$0.894749\pi$
$462$		0			0
$463$		−	505.213i		−	1.09117i	−0.838055	−	0.545586i	$-0.816307\pi$
$463$		−	505.213i		−	1.09117i	0.838055	−	0.545586i	$-0.183693\pi$
$464$	−107.602	−	348.069i	−0.231900	−	0.750149i
$465$	84.8314	−	146.932i	0.182433	−	0.315983i
$466$	−50.6330	+	267.829i	−0.108655	+	0.574741i
$467$	−325.162	−	563.197i	−0.696278	−	1.20599i	−0.969748	−	0.244108i	$-0.921505\pi$
$467$	−325.162	−	563.197i	−0.696278	−	1.20599i	0.273470	−	0.961881i	$-0.411829\pi$
$468$	−287.959	−	360.860i	−0.615298	−	0.771068i
$469$		0			0
$470$	−175.090	+	61.2972i	−0.372532	+	0.130420i
$471$	169.107	−	97.6338i	0.359037	−	0.207290i
$472$	43.9158	+	82.9992i	0.0930419	+	0.175846i
$473$	241.520	−	418.324i	0.510612	−	0.884407i
$474$	282.207	−	328.033i	0.595373	−	0.692053i
$475$	12.6946			0.0267255
$476$		0			0
$477$			29.9375i			0.0627621i
$478$	225.951	−	262.642i	0.472701	−	0.549461i
$479$	−572.400	−	330.475i	−1.19499	−	0.689928i	−0.235556	−	0.971861i	$-0.575691\pi$
$479$	−572.400	−	330.475i	−1.19499	−	0.689928i	−0.959434	+	0.281933i	$0.909024\pi$
$480$	96.0622	−	220.644i	0.200130	−	0.459674i
$481$	126.595	+	219.269i	0.263191	+	0.455860i
$482$	−620.896	+	217.369i	−1.28817	+	0.450973i
$483$		0			0
$484$	100.850	−	80.4762i	0.208367	−	0.166273i
$485$	−156.491	+	90.3500i	−0.322661	+	0.186289i
$486$	−93.4295	+	494.207i	−0.192242	+	1.01689i
$487$	334.373	+	193.050i	0.686597	+	0.396407i	0.802336	−	0.596873i	$-0.203590\pi$
$487$	334.373	+	193.050i	0.686597	+	0.396407i	−0.115739	+	0.993280i	$0.536924\pi$
$488$	−32.1713	+	870.639i	−0.0659248	+	1.78410i
$489$	135.246			0.276578
$490$		0			0
$491$	−898.359			−1.82965			−0.914826	−	0.403848i	$-0.867672\pi$
$491$	−898.359			−1.82965			−0.914826	+	0.403848i	$0.867672\pi$
$492$	371.483	+	145.664i	0.755048	+	0.296064i
$493$	−256.914	−	148.329i	−0.521124	−	0.300871i
$494$	109.237	+	20.6513i	0.221128	+	0.0418042i
$495$	−307.168	+	177.344i	−0.620542	+	0.358270i
$496$	351.972	+	80.1055i	0.709620	+	0.161503i
$497$		0			0
$498$	−88.3070	+	30.9153i	−0.177323	+	0.0620790i
$499$	−395.588	−	685.178i	−0.792761	−	1.37310i	−0.924251	−	0.381785i	$-0.875309\pi$
$499$	−395.588	−	685.178i	−0.792761	−	1.37310i	0.131490	−	0.991318i	$-0.458024\pi$
$500$	526.695	−	79.5537i	1.05339	−	0.159107i
$501$	−187.904	−	108.486i	−0.375058	−	0.216540i
$502$	−242.970	−	209.027i	−0.484004	−	0.416389i
$503$			798.990i			1.58845i	0.607624	+	0.794225i	$0.292123\pi$
$503$			798.990i			1.58845i	−0.607624	+	0.794225i	$0.707877\pi$
$504$		0			0
$505$	198.948			0.393956
$506$	−489.645	+	569.157i	−0.967679	+	1.12482i
$507$	−138.999	+	240.754i	−0.274160	+	0.474860i
$508$	−881.381	+	133.126i	−1.73500	+	0.262060i
$509$	477.272	−	275.553i	0.937666	−	0.541362i	0.0484379	−	0.998826i	$-0.484576\pi$
$509$	477.272	−	275.553i	0.937666	−	0.541362i	0.889228	+	0.457465i	$0.151242\pi$
$510$	−64.7483	−	184.948i	−0.126957	−	0.362643i
$511$		0			0
$512$	508.860	+	56.6155i	0.993868	+	0.110577i
$513$	−38.1117	−	66.0114i	−0.0742918	−	0.128677i
$514$	−54.0342	+	285.820i	−0.105125	+	0.556071i
$515$	143.452	−	248.466i	0.278547	−	0.482458i
$516$	239.574	+	93.9400i	0.464290	+	0.182054i
$517$		−	251.753i		−	0.486950i
$518$		0			0
$519$		−	181.553i		−	0.349812i
$520$	669.995	+	24.7573i	1.28845	+	0.0476101i
$521$	71.3914	−	123.654i	0.137028	−	0.237339i	−0.789343	−	0.613953i	$-0.789578\pi$
$521$	71.3914	−	123.654i	0.137028	−	0.237339i	0.926370	+	0.376614i	$0.122912\pi$
$522$	−281.084	−	53.1387i	−0.538474	−	0.101798i
$523$	−416.255	−	720.976i	−0.795900	−	1.37854i	−0.922266	−	0.386555i	$-0.873665\pi$
$523$	−416.255	−	720.976i	−0.795900	−	1.37854i	0.126367	−	0.991984i	$-0.459668\pi$
$524$	−741.160	+	591.432i	−1.41443	+	1.12869i
$525$		0			0
$526$	−134.011	−	382.790i	−0.254773	−	0.727737i
$527$	254.552	−	146.966i	0.483021	−	0.278872i
$528$	239.538	+	221.983i	0.453671	+	0.420422i
$529$	195.264	−	338.207i	0.369119	−	0.639333i
$530$	−32.9581	−	28.3538i	−0.0621851	−	0.0534978i
$531$	73.7306			0.138852
$532$		0			0
$533$			1111.68i			2.08571i
$534$	−393.511	−	338.538i	−0.736912	−	0.633966i
$535$	174.697	+	100.862i	0.326537	+	0.188526i
$536$	296.320	+	560.034i	0.552836	+	1.04484i
$537$	126.834	+	219.683i	0.236191	+	0.409094i
$538$	−146.254	−	417.762i	−0.271848	−	0.776510i
$539$		0			0
$540$	−286.720	−	359.307i	−0.530963	−	0.665383i
$541$	533.874	−	308.232i	0.986829	−	0.569746i	0.0825038	−	0.996591i	$-0.473708\pi$
$541$	533.874	−	308.232i	0.986829	−	0.569746i	0.904325	+	0.426845i	$0.140375\pi$
$542$	−230.666	−	43.6074i	−0.425584	−	0.0804564i
$543$	324.859	+	187.557i	0.598267	+	0.345410i
$544$	335.253	−	247.830i	0.616273	−	0.455569i
$545$	−40.2071			−0.0737746
$546$		0			0
$547$	577.704			1.05613			0.528065	−	0.849204i	$-0.322918\pi$
$547$	577.704			1.05613			0.528065	+	0.849204i	$0.322918\pi$
$548$	35.9836	+	14.1097i	0.0656636	+	0.0257475i
$549$	592.435	+	342.043i	1.07912	+	0.623028i
$550$	−19.2996	+	102.088i	−0.0350903	+	0.185614i
$551$	59.6562	−	34.4425i	0.108269	−	0.0625091i
$552$	−338.768	−	212.643i	−0.613711	−	0.385222i
$553$		0			0
$554$	−168.853	−	482.316i	−0.304790	−	0.870606i
$555$	51.8133	+	89.7433i	0.0933573	+	0.161700i
$556$	37.6730	+	249.419i	0.0677573	+	0.448596i
$557$	−445.752	−	257.355i	−0.800273	−	0.462038i	0.0432939	−	0.999062i	$-0.486215\pi$
$557$	−445.752	−	257.355i	−0.800273	−	0.462038i	−0.843566	+	0.537025i	$0.819548\pi$
$558$	184.846	−	214.863i	0.331266	−	0.385058i
$559$			716.937i			1.28253i
$560$		0			0
$561$	265.927			0.474023
$562$	−421.494	−	362.611i	−0.749989	−	0.645215i
$563$	−304.360	+	527.166i	−0.540603	+	0.936352i	0.458266	+	0.888815i	$0.348471\pi$
$563$	−304.360	+	527.166i	−0.540603	+	0.936352i	−0.998869	+	0.0475374i	$0.984863\pi$
$564$	132.614	−	20.0304i	0.235131	−	0.0355149i
$565$	479.565	−	276.877i	0.848788	−	0.490048i
$566$	107.011	−	37.4634i	0.189065	−	0.0661897i
$567$		0			0
$568$	88.0527	+	55.2701i	0.155022	+	0.0973064i
$569$	−93.1872	−	161.405i	−0.163774	−	0.283664i	0.772445	−	0.635081i	$-0.219033\pi$
$569$	−93.1872	−	161.405i	−0.163774	−	0.283664i	−0.936219	+	0.351417i	$0.885700\pi$
$570$	44.7092	+	8.45226i	0.0784372	+	0.0148285i
$571$	−91.8878	+	159.154i	−0.160924	+	0.278729i	−0.935200	−	0.354119i	$-0.884781\pi$
$571$	−91.8878	+	159.154i	−0.160924	+	0.278729i	0.774276	+	0.632848i	$0.218114\pi$
$572$	−332.147	+	847.070i	−0.580677	+	1.48089i
$573$			200.401i			0.349741i
$574$		0			0
$575$		−	127.246i		−	0.221297i
$576$	226.156	−	332.374i	0.392632	−	0.577038i
$577$	67.2281	−	116.442i	0.116513	−	0.201807i	−0.801870	−	0.597498i	$-0.796162\pi$
$577$	67.2281	−	116.442i	0.116513	−	0.201807i	0.918384	+	0.395691i	$0.129495\pi$
$578$	−44.3073	+	234.369i	−0.0766562	+	0.405482i
$579$	70.4482	+	122.020i	0.121672	+	0.210743i
$580$	324.714	−	259.116i	0.559852	−	0.446752i
$581$		0			0
$582$	123.303	−	43.1670i	0.211861	−	0.0741702i
$583$	51.0963	−	29.5005i	0.0876437	−	0.0506011i
$584$	−368.838	−	697.091i	−0.631572	−	1.19365i
$585$	263.217	−	455.905i	0.449944	−	0.779325i
$586$	375.481	−	436.454i	0.640753	−	0.744802i
$587$	921.405			1.56968			0.784842	−	0.619696i	$-0.212744\pi$
$587$	921.405			1.56968			0.784842	+	0.619696i	$0.212744\pi$
$588$		0			0
$589$			68.2517i			0.115877i
$590$	−69.8303	+	81.1697i	−0.118356	+	0.137576i
$591$	−305.709	−	176.501i	−0.517274	−	0.298648i
$592$	−149.861	+	161.712i	−0.253143	+	0.273163i
$593$	48.1873	+	83.4628i	0.0812602	+	0.140747i	0.903791	−	0.427973i	$-0.140772\pi$
$593$	48.1873	+	83.4628i	0.0812602	+	0.140747i	−0.822531	+	0.568720i	$0.807439\pi$
$594$	588.792	−	206.130i	0.991233	−	0.347020i
$595$		0			0
$596$	673.412	+	843.895i	1.12989	+	1.41593i
$597$	−354.434	+	204.632i	−0.593692	+	0.342768i
$598$	207.000	−	1094.95i	0.346153	−	1.83102i
$599$	−144.711	−	83.5489i	−0.241587	−	0.139481i	0.374319	−	0.927300i	$-0.377877\pi$
$599$	−144.711	−	83.5489i	−0.241587	−	0.139481i	−0.615906	+	0.787820i	$0.711210\pi$
$600$	−55.3115	−	2.04384i	−0.0921859	−	0.00340640i
$601$	−88.4635			−0.147194			−0.0735969	−	0.997288i	$-0.523448\pi$
$601$	−88.4635			−0.147194			−0.0735969	+	0.997288i	$0.523448\pi$
$602$		0			0
$603$	497.494			0.825032
$604$	−157.962	+	402.848i	−0.261526	+	0.666967i
$605$	127.412	+	73.5614i	0.210598	+	0.121589i
$606$	−141.330	−	26.7184i	−0.233218	−	0.0440898i
$607$	−48.1243	+	27.7846i	−0.0792822	+	0.0457736i	−0.539117	−	0.842231i	$-0.681242\pi$
$607$	−48.1243	+	27.7846i	−0.0792822	+	0.0457736i	0.459835	+	0.888004i	$0.347909\pi$
$608$	10.9136	+	96.1905i	0.0179500	+	0.158208i
$609$		0			0
$610$	−937.648	+	328.260i	−1.53713	+	0.538132i
$611$	186.829	+	323.597i	0.305775	+	0.529618i
$612$	−48.8900	−	323.683i	−0.0798857	−	0.528894i
$613$	752.678	+	434.559i	1.22786	+	0.708905i	0.966582	−	0.256359i	$-0.0825229\pi$
$613$	752.678	+	434.559i	1.22786	+	0.708905i	0.261278	+	0.965264i	$0.415856\pi$
$614$	−81.3386	−	69.9756i	−0.132473	−	0.113967i
$615$			454.995i			0.739829i
$616$		0			0
$617$	−249.359			−0.404147			−0.202074	−	0.979370i	$-0.564768\pi$
$617$	−249.359			−0.404147			−0.202074	+	0.979370i	$0.564768\pi$
$618$	−135.275	+	157.242i	−0.218891	+	0.254436i
$619$	−248.837	+	430.998i	−0.401998	+	0.696280i	−0.993967	−	0.109680i	$-0.965017\pi$
$619$	−248.837	+	430.998i	−0.401998	+	0.696280i	0.591969	+	0.805961i	$0.298351\pi$
$620$	61.4734	+	406.993i	0.0991506	+	0.656440i
$621$	−661.671	+	382.016i	−1.06549	+	0.615162i
$622$	−69.4608	−	198.409i	−0.111673	−	0.318985i
$623$		0			0
$624$	−472.631	−	107.567i	−0.757422	−	0.172382i
$625$	251.243	+	435.165i	0.401988	+	0.696264i
$626$	−78.2009	+	413.653i	−0.124922	+	0.660787i
$627$	−30.8745	+	53.4762i	−0.0492416	+	0.0852890i
$628$	−172.935	+	441.034i	−0.275374	+	0.702283i
$629$			179.527i			0.285417i
$630$		0			0
$631$			172.763i			0.273792i	0.990585	+	0.136896i	$0.0437126\pi$
$631$			172.763i			0.273792i	−0.990585	+	0.136896i	$0.956287\pi$
$632$	−38.7650	+	1049.08i	−0.0613370	+	1.65994i
$633$	158.079	−	273.801i	0.249730	−	0.432545i
$634$	123.587	+	23.3641i	0.194932	+	0.0368518i
$635$	−508.210	−	880.245i	−0.800330	−	1.38621i
$636$	19.6051	+	24.5684i	0.0308257	+	0.0386296i
$637$		0			0
$638$	186.285	+	532.106i	0.291982	+	0.834022i
$639$	70.6937	−	40.8150i	0.110632	−	0.0638732i
$640$	151.717	+	563.765i	0.237057	+	0.880883i
$641$	213.949	−	370.570i	0.333774	−	0.578113i	−0.649475	−	0.760383i	$-0.725011\pi$
$641$	213.949	−	370.570i	0.333774	−	0.578113i	0.983248	+	0.182270i	$0.0583446\pi$
$642$	−110.557	−	95.1124i	−0.172208	−	0.148150i
$643$	15.9463			0.0247998			0.0123999	−	0.999923i	$-0.496053\pi$
$643$	15.9463			0.0247998			0.0123999	+	0.999923i	$0.496053\pi$
$644$		0			0
$645$			293.431i			0.454932i
$646$	59.7575	+	51.4094i	0.0925039	+	0.0795811i
$647$	−450.510	−	260.102i	−0.696306	−	0.402012i	0.109664	−	0.993969i	$-0.465022\pi$
$647$	−450.510	−	260.102i	−0.696306	−	0.402012i	−0.805970	+	0.591956i	$0.798356\pi$
$648$	−56.0899	−	106.008i	−0.0865586	−	0.163592i
$649$	−72.6542	−	125.841i	−0.111948	−	0.193899i
$650$	−50.9531	−	145.543i	−0.0783894	−	0.223913i
$651$		0			0
$652$	−256.466	+	204.655i	−0.393353	+	0.313888i
$653$	−367.687	+	212.284i	−0.563074	+	0.325091i	−0.754378	−	0.656440i	$-0.772061\pi$
$653$	−367.687	+	212.284i	−0.563074	+	0.325091i	0.191305	+	0.981531i	$0.438728\pi$
$654$	28.5627	+	5.39976i	0.0436738	+	0.00825651i
$655$	−936.371	−	540.614i	−1.42957	−	0.825365i
$656$	−924.857	+	285.909i	−1.40984	+	0.435837i
$657$	−619.246			−0.942535
$658$		0			0
$659$	304.044			0.461372			0.230686	−	0.973028i	$-0.425903\pi$
$659$	304.044			0.461372			0.230686	+	0.973028i	$0.425903\pi$
$660$	−135.943	+	346.693i	−0.205974	+	0.525292i
$661$	−155.112	−	89.5542i	−0.234663	−	0.135483i	0.378058	−	0.925782i	$-0.376592\pi$
$661$	−155.112	−	89.5542i	−0.234663	−	0.135483i	−0.612722	+	0.790299i	$0.709925\pi$
$662$	73.0326	−	386.315i	0.110321	−	0.583557i
$663$	−341.815	+	197.347i	−0.515559	+	0.297658i
$664$	120.674	−	192.251i	0.181738	−	0.289534i
$665$		0			0
$666$	57.2016	+	163.391i	0.0858883	+	0.245333i
$667$	−345.237	−	597.968i	−0.517597	−	0.896504i
$668$	520.482	−	78.6151i	0.779164	−	0.117687i
$669$	58.8671	+	33.9870i	0.0879927	+	0.0508026i
$670$	−471.177	+	547.689i	−0.703249	+	0.817446i
$671$		−	1348.20i		−	2.00923i
$672$		0			0
$673$	544.352			0.808844			0.404422	−	0.914573i	$-0.367473\pi$
$673$	544.352			0.808844			0.404422	+	0.914573i	$0.367473\pi$
$674$	896.824	+	771.537i	1.33060	+	1.14471i
$675$	−52.8639	+	91.5629i	−0.0783168	+	0.135649i
$676$	−100.726	−	666.872i	−0.149004	−	0.986497i
$677$	471.416	−	272.172i	0.696330	−	0.402027i	−0.109649	−	0.993970i	$-0.534973\pi$
$677$	471.416	−	272.172i	0.696330	−	0.402027i	0.805979	+	0.591944i	$0.201639\pi$
$678$	−377.861	+	132.285i	−0.557318	+	0.195111i
$679$		0			0
$680$	402.645	+	252.737i	0.592125	+	0.371672i
$681$	−58.0730	−	100.585i	−0.0852760	−	0.147702i
$682$	−548.867	−	103.763i	−0.804790	−	0.152145i
$683$	−443.494	+	768.154i	−0.649332	+	1.12468i	0.333951	+	0.942591i	$0.391618\pi$
$683$	−443.494	+	768.154i	−0.649332	+	1.12468i	−0.983283	+	0.182086i	$0.941715\pi$
$684$	70.7667	+	27.7486i	0.103460	+	0.0405681i
$685$			44.0730i			0.0643401i
$686$		0			0
$687$		−	155.841i		−	0.226842i
$688$	−596.451	+	184.386i	−0.866934	+	0.268003i
$689$	−43.7852	+	75.8382i	−0.0635489	+	0.110070i
$690$	84.7218	−	448.146i	0.122785	−	0.649487i
$691$	589.242	+	1020.60i	0.852738	+	1.47698i	0.878728	+	0.477323i	$0.158393\pi$
$691$	589.242	+	1020.60i	0.852738	+	1.47698i	−0.0259906	+	0.999662i	$0.508274\pi$
$692$	274.725	+	344.276i	0.397002	+	0.497508i
$693$		0			0
$694$	−467.272	+	163.587i	−0.673302	+	0.235716i
$695$	−249.098	+	143.817i	−0.358414	+	0.206930i
$696$	−265.472	+	140.464i	−0.381425	+	0.201816i
$697$	−394.127	+	682.648i	−0.565462	+	0.979409i
$698$	−376.627	+	437.786i	−0.539580	+	0.627200i
$699$	224.706			0.321468
$700$		0			0
$701$		−	901.601i		−	1.28616i	−0.765797	−	0.643082i	$-0.777655\pi$
$701$		−	901.601i		−	1.28616i	0.765797	−	0.643082i	$-0.222345\pi$
$702$	−603.846	+	701.902i	−0.860180	+	0.999861i
$703$	−36.1018	−	20.8434i	−0.0513539	−	0.0296492i
$704$	−790.137	−	58.4732i	−1.12235	−	0.0830586i
$705$	76.4661	+	132.443i	0.108463	+	0.187863i
$706$	−2.39669	+	0.839056i	−0.00339475	+	0.00118846i
$707$		0			0
$708$	60.5075	−	48.2839i	0.0854626	−	0.0681975i
$709$	−288.215	+	166.401i	−0.406510	+	0.234698i	−0.689289	−	0.724487i	$-0.742077\pi$
$709$	−288.215	+	166.401i	−0.406510	+	0.234698i	0.282779	+	0.959185i	$0.408744\pi$
$710$	−22.0209	+	116.482i	−0.0310154	+	0.164059i
$711$	713.858	+	412.146i	1.00402	+	0.579671i
$712$	1258.49	+	46.5028i	1.76754	+	0.0653129i
$713$	684.126			0.959504
$714$		0			0
$715$	−1037.50			−1.45104
$716$	−572.939	−	224.657i	−0.800195	−	0.313767i
$717$	−247.352	−	142.809i	−0.344982	−	0.199176i
$718$	−34.1985	−	6.46520i	−0.0476302	−	0.00900446i
$719$	1026.20	−	592.475i	1.42726	−	0.824027i	0.430353	−	0.902661i	$-0.358389\pi$
$719$	1026.20	−	592.475i	1.42726	−	0.824027i	0.996904	+	0.0786341i	$0.0250559\pi$
$720$	446.983	+	101.729i	0.620809	+	0.141291i
$721$		0			0
$722$	664.171	−	232.519i	0.919904	−	0.322049i
$723$	271.160	+	469.663i	0.375049	+	0.649603i
$724$	−899.838	+	135.914i	−1.24287	+	0.187727i
$725$	−82.7477	−	47.7744i	−0.114135	−	0.0658957i
$726$	−80.6328	−	69.3684i	−0.111064	−	0.0955487i
$727$			19.9398i			0.0274275i	0.999906	+	0.0137138i	$0.00436536\pi$
$727$			19.9398i			0.0274275i	−0.999906	+	0.0137138i	$0.995635\pi$
$728$		0			0
$729$	279.711			0.383691
$730$	586.487	−	681.725i	0.803407	−	0.933869i
$731$	−254.177	+	440.247i	−0.347711	+	0.602254i
$732$	710.179	−	107.268i	0.970189	−	0.146540i
$733$	−898.325	+	518.648i	−1.22555	+	0.707569i	−0.966095	−	0.258188i	$-0.916875\pi$
$733$	−898.325	+	518.648i	−1.22555	+	0.707569i	−0.259450	+	0.965756i	$0.583541\pi$
$734$	350.272	+	1000.52i	0.477210	+	1.36311i
$735$		0			0
$736$	964.173	−	109.393i	1.31002	−	0.148632i
$737$	−490.231	−	849.105i	−0.665171	−	1.15211i
$738$	−141.195	+	746.869i	−0.191322	+	1.01202i
$739$	209.986	−	363.706i	0.284148	−	0.492160i	−0.688254	−	0.725470i	$-0.741622\pi$
$739$	209.986	−	363.706i	0.284148	−	0.492160i	0.972402	+	0.233310i	$0.0749558\pi$
$740$	−234.053	−	91.7751i	−0.316287	−	0.124020i
$741$		−	91.6491i		−	0.123683i
$742$		0			0
$743$			1241.67i			1.67116i	0.549370	+	0.835579i	$0.314868\pi$
$743$			1241.67i			1.67116i	−0.549370	+	0.835579i	$0.685132\pi$
$744$	10.9886	−	297.378i	0.0147696	−	0.399702i
$745$	−615.551	+	1066.17i	−0.826243	+	1.43109i
$746$	−233.098	−	44.0670i	−0.312463	−	0.0590711i
$747$	−89.1137	−	154.349i	−0.119295	−	0.206626i
$748$	−504.274	+	402.401i	−0.674163	+	0.537969i
$749$		0			0
$750$	−145.099	−	414.462i	−0.193465	−	0.552615i
$751$	−561.008	+	323.898i	−0.747015	+	0.431289i	−0.824614	−	0.565695i	$-0.808608\pi$
$751$	−561.008	+	323.898i	−0.747015	+	0.431289i	0.0775992	+	0.996985i	$0.475275\pi$
$752$	−221.164	+	238.655i	−0.294101	+	0.317360i
$753$	−132.112	+	228.825i	−0.175448	+	0.303885i
$754$	−634.327	−	545.711i	−0.841282	−	0.723755i
$755$	−493.411			−0.653524
$756$		0			0
$757$			105.310i			0.139116i	0.997578	+	0.0695578i	$0.0221588\pi$
$757$			105.310i			0.139116i	−0.997578	+	0.0695578i	$0.977841\pi$
$758$	−524.507	−	451.233i	−0.691961	−	0.595294i
$759$	536.023	+	309.473i	0.706223	+	0.407738i
$760$	−97.5714	+	51.6261i	−0.128383	+	0.0679291i
$761$	−210.942	−	365.362i	−0.277190	−	0.480108i	0.693495	−	0.720461i	$-0.256070\pi$
$761$	−210.942	−	365.362i	−0.277190	−	0.480108i	−0.970685	+	0.240354i	$0.922737\pi$
$762$	242.810	+	693.567i	0.318649	+	0.910193i
$763$		0			0
$764$	−303.247	−	380.018i	−0.396921	−	0.497406i
$765$	323.266	−	186.638i	0.422570	−	0.243971i
$766$	795.652	+	150.418i	1.03871	+	0.196368i
$767$	186.775	+	107.835i	0.243514	+	0.140593i
$768$	−32.0648	−	420.867i	−0.0417511	−	0.548004i
$769$	189.767			0.246772			0.123386	−	0.992359i	$-0.460625\pi$
$769$	189.767			0.246772			0.123386	+	0.992359i	$0.460625\pi$
$770$		0			0
$771$	239.801			0.311025
$772$	−318.231	−	124.782i	−0.412216	−	0.161635i
$773$	−729.875	−	421.394i	−0.944211	−	0.545141i	−0.0529334	−	0.998598i	$-0.516857\pi$
$773$	−729.875	−	421.394i	−0.944211	−	0.545141i	−0.891278	+	0.453457i	$0.850190\pi$
$774$	−91.0584	+	481.664i	−0.117647	+	0.622305i
$775$	81.9870	−	47.3352i	0.105790	−	0.0610777i
$776$	−168.497	+	268.439i	−0.217136	+	0.345927i
$777$		0			0
$778$	88.8164	+	253.696i	0.114160	+	0.326088i
$779$	−91.5174	−	158.513i	−0.117481	−	0.203482i
$780$	−82.5471	−	546.514i	−0.105830	−	0.700659i
$781$	−139.323	−	80.4382i	−0.178391	−	0.102994i
$782$	515.306	−	598.984i	0.658959	−	0.765965i
$783$			573.712i			0.732710i
$784$		0			0
$785$	−540.181			−0.688128
$786$	592.583	+	509.799i	0.753922	+	0.648599i
$787$	747.098	−	1294.01i	0.949298	−	1.64423i	0.202391	−	0.979305i	$-0.435129\pi$
$787$	747.098	−	1294.01i	0.949298	−	1.64423i	0.746907	−	0.664928i	$-0.231538\pi$
$788$	846.794	−	127.902i	1.07461	−	0.162313i
$789$	−289.553	+	167.173i	−0.366987	+	0.211880i
$790$	−1129.82	+	395.539i	−1.43016	+	0.500682i
$791$		0			0
$792$	−330.735	+	526.906i	−0.417595	+	0.665286i
$793$	1000.51	+	1732.93i	1.26168	+	2.18529i
$794$	−1203.64	−	227.548i	−1.51592	−	0.286584i
$795$	−17.9206	+	31.0394i	−0.0225417	+	0.0390433i
$796$	362.458	−	924.371i	0.455349	−	1.16127i
$797$			292.040i			0.366424i	0.983073	+	0.183212i	$0.0586494\pi$
$797$			292.040i			0.366424i	−0.983073	+	0.183212i	$0.941351\pi$
$798$		0			0
$799$			264.947i			0.331598i
$800$	107.979	−	79.8217i	0.134974	−	0.0997772i
$801$	494.414	−	856.349i	0.617245	−	1.06910i
$802$	−46.9030	+	248.099i	−0.0584825	+	0.309350i
$803$	610.205	+	1056.91i	0.759906	+	1.31620i
$804$	408.272	−	325.793i	0.507801	−	0.405215i
$805$		0			0
$806$	782.502	−	273.946i	0.970847	−	0.339883i
$807$	−316.007	+	182.447i	−0.391582	+	0.226080i
$808$	308.433	−	163.195i	0.381724	−	0.201974i
$809$	−78.4531	+	135.885i	−0.0969754	+	0.167966i	−0.910431	−	0.413660i	$-0.864250\pi$
$809$	−78.4531	+	135.885i	−0.0969754	+	0.167966i	0.813456	+	0.581627i	$0.197583\pi$
$810$	89.1883	−	103.671i	0.110109	−	0.127989i
$811$	−1183.00			−1.45869			−0.729347	−	0.684144i	$-0.760176\pi$
$811$	−1183.00			−1.45869			−0.729347	+	0.684144i	$0.760176\pi$
$812$		0			0
$813$			193.527i			0.238040i
$814$	222.504	−	258.636i	0.273347	−	0.317734i
$815$	−324.015	−	187.070i	−0.397565	−	0.229534i
$816$	−252.092	−	233.616i	−0.308936	−	0.286294i
$817$	−59.0206	−	102.227i	−0.0722406	−	0.125124i
$818$	646.561	−	226.354i	0.790417	−	0.276716i
$819$		0			0
$820$	−688.499	−	862.801i	−0.839633	−	1.05220i
$821$	160.574	−	92.7074i	0.195583	−	0.112920i	−0.399010	−	0.916946i	$-0.630646\pi$
$821$	160.574	−	92.7074i	0.195583	−	0.112920i	0.594594	+	0.804026i	$0.297313\pi$
$822$	5.91893	−	31.3089i	0.00720065	−	0.0380887i
$823$	−564.922	−	326.158i	−0.686418	−	0.396304i	0.115850	−	0.993267i	$-0.463041\pi$
$823$	−564.922	−	326.158i	−0.686418	−	0.396304i	−0.802269	+	0.596963i	$0.796374\pi$
$824$	18.5819	−	502.873i	0.0225508	−	0.610283i
$825$	85.6506			0.103819
$826$		0			0
$827$	−829.430			−1.00294			−0.501469	−	0.865176i	$-0.667207\pi$
$827$	−829.430			−1.00294			−0.501469	+	0.865176i	$0.667207\pi$
$828$	278.140	−	709.336i	0.335918	−	0.856686i
$829$	−653.961	−	377.565i	−0.788856	−	0.455446i	0.0507039	−	0.998714i	$-0.483854\pi$
$829$	−653.961	−	377.565i	−0.788856	−	0.455446i	−0.839560	+	0.543268i	$0.817187\pi$
$830$	254.322	+	48.0795i	0.306412	+	0.0579271i
$831$	−364.837	+	210.639i	−0.439034	+	0.253476i
$832$	1059.01	−	511.209i	1.27285	−	0.614434i
$833$		0			0
$834$	196.270	−	68.7122i	0.235336	−	0.0823887i
$835$	300.113	+	519.811i	0.359417	+	0.622528i
$836$	−22.3733	−	148.126i	−0.0267624	−	0.177184i
$837$	−492.281	−	284.219i	−0.588150	−	0.339568i
$838$	570.665	+	490.943i	0.680985	+	0.585851i
$839$		−	88.6147i		−	0.105619i	−0.998605	−	0.0528097i	$-0.983182\pi$
$839$		−	88.6147i		−	0.105619i	0.998605	−	0.0528097i	$-0.0168177\pi$
$840$		0			0
$841$	322.522			0.383499
$842$	144.957	−	168.496i	0.172158	−	0.200114i
$843$	−229.183	+	396.956i	−0.271866	+	0.470885i
$844$	114.553	+	758.411i	0.135726	+	0.898591i
$845$	666.013	−	384.523i	0.788181	−	0.455056i
$846$	84.4181	+	241.133i	0.0997850	+	0.285027i
$847$		0			0
$848$	−74.3540	−	16.9223i	−0.0876816	−	0.0199555i
$849$	−46.7343	−	80.9461i	−0.0550462	−	0.0953429i
$850$	20.3111	−	107.438i	0.0238954	−	0.126397i
$851$	−208.925	+	361.869i	−0.245506	+	0.425228i
$852$	31.2868	−	79.7901i	0.0367216	−	0.0936504i
$853$		−	367.466i		−	0.430792i	−0.976527	−	0.215396i	$-0.930896\pi$
$853$		−	367.466i		−	0.430792i	0.976527	−	0.215396i	$-0.0691042\pi$
$854$		0			0
$855$			86.6755i			0.101375i
$856$	353.572	+	13.0650i	0.413052	+	0.0152628i
$857$	−82.6698	+	143.188i	−0.0964642	+	0.167081i	−0.910219	−	0.414128i	$-0.864087\pi$
$857$	−82.6698	+	143.188i	−0.0964642	+	0.167081i	0.813755	+	0.581209i	$0.197420\pi$
$858$	737.025	+	139.334i	0.859003	+	0.162394i
$859$	−325.486	−	563.758i	−0.378913	−	0.656296i	0.611992	−	0.790864i	$-0.290369\pi$
$859$	−325.486	−	563.758i	−0.378913	−	0.656296i	−0.990904	+	0.134568i	$0.957035\pi$
$860$	−444.021	−	556.430i	−0.516303	−	0.647012i
$861$		0			0
$862$	−27.2788	−	77.9197i	−0.0316460	−	0.0903941i
$863$	118.417	−	68.3679i	0.137215	−	0.0792212i	−0.429821	−	0.902914i	$-0.641423\pi$
$863$	118.417	−	68.3679i	0.137215	−	0.0792212i	0.567036	+	0.823693i	$0.308090\pi$
$864$	−739.243	−	321.846i	−0.855606	−	0.372507i
$865$	−251.120	+	434.953i	−0.290312	+	0.502836i
$866$	1023.67	+	880.659i	1.18206	+	1.01693i
$867$	196.633			0.226797
$868$		0			0
$869$		−	1624.51i		−	1.86941i
$870$	−259.620	−	223.351i	−0.298414	−	0.256726i
$871$	1260.26	+	727.611i	1.44691	+	0.835374i
$872$	−62.3339	+	32.9815i	−0.0714838	+	0.0378229i
$873$	124.429	+	215.518i	0.142531	+	0.246871i
$874$	60.6241	+	173.168i	0.0693640	+	0.198132i
$875$		0			0
$876$	−508.188	+	405.524i	−0.580123	+	0.462927i
$877$	152.855	−	88.2509i	0.174293	−	0.100628i	−0.410316	−	0.911944i	$-0.634581\pi$
$877$	152.855	−	88.2509i	0.174293	−	0.100628i	0.584609	+	0.811315i	$0.301248\pi$
$878$	1042.05	+	197.000i	1.18685	+	0.224374i
$879$	−411.045	−	237.317i	−0.467628	−	0.269985i
$880$	−266.829	−	863.138i	−0.303215	−	0.980838i
$881$	−734.879			−0.834142			−0.417071	−	0.908874i	$-0.636943\pi$
$881$	−734.879			−0.834142			−0.417071	+	0.908874i	$0.636943\pi$
$882$		0			0
$883$	872.637			0.988264			0.494132	−	0.869387i	$-0.335486\pi$
$883$	872.637			0.988264			0.494132	+	0.869387i	$0.335486\pi$
$884$	349.554	−	891.462i	0.395423	−	1.00844i
$885$	76.4443	+	44.1352i	0.0863778	+	0.0498702i
$886$	123.356	−	652.508i	0.139228	−	0.736465i
$887$	−20.8696	+	12.0490i	−0.0235282	+	0.0135840i	−0.511718	−	0.859153i	$-0.670991\pi$
$887$	−20.8696	+	12.0490i	−0.0235282	+	0.0135840i	0.488190	+	0.872738i	$0.337657\pi$
$888$	153.943	+	96.6288i	0.173359	+	0.108816i
$889$		0			0
$890$	474.492	+	1355.35i	0.533137	+	1.52286i
$891$	92.7951	+	160.726i	0.104147	+	0.180388i
$892$	−163.058	+	24.6288i	−0.182801	+	0.0276107i
$893$	−53.2790	−	30.7607i	−0.0596630	−	0.0344464i
$894$	580.464	−	674.723i	0.649289	−	0.754724i
$895$		−	701.740i		−	0.784067i
$896$		0			0
$897$	−918.652			−1.02414
$898$	−29.4436	−	25.3303i	−0.0327880	−	0.0282075i
$899$	256.855	−	444.887i	0.285712	−	0.494868i
$900$	−15.7467	−	104.253i	−0.0174963	−	0.115836i
$901$	−53.7741	+	31.0465i	−0.0596827	+	0.0344578i
$902$	1413.86	−	494.978i	1.56748	−	0.548756i
$903$		0			0
$904$	516.360	−	822.631i	0.571194	−	0.909990i
$905$	−518.852	−	898.678i	−0.573317	−	0.993014i
$906$	350.513	+	66.2643i	0.386880	+	0.0731394i
$907$	706.653	−	1223.96i	0.779110	−	1.34946i	−0.153345	−	0.988173i	$-0.549005\pi$
$907$	706.653	−	1223.96i	0.779110	−	1.34946i	0.932455	−	0.361285i	$-0.117662\pi$
$908$	262.329	+	102.863i	0.288908	+	0.113285i
$909$		−	273.990i		−	0.301419i
$910$		0			0
$911$		−	1778.28i		−	1.95201i	−0.217746	−	0.976005i	$-0.569871\pi$
$911$		−	1778.28i		−	1.95201i	0.217746	−	0.976005i	$-0.430129\pi$
$912$	76.2469	−	23.5709i	0.0836040	−	0.0258452i
$913$	−175.625	+	304.192i	−0.192361	+	0.333179i
$914$	−66.1151	+	349.724i	−0.0723360	+	0.382630i
$915$	409.493	+	709.263i	0.447534	+	0.775151i
$916$	235.818	+	295.518i	0.257443	+	0.322618i
$917$		0			0
$918$	−619.649	+	216.932i	−0.674999	+	0.236310i
$919$	774.089	−	446.921i	0.842317	−	0.486312i	−0.0157340	−	0.999876i	$-0.505009\pi$
$919$	774.089	−	446.921i	0.842317	−	0.486312i	0.858051	+	0.513564i	$0.171675\pi$
$920$	517.478	+	978.015i	0.562476	+	1.06306i
$921$	−44.2270	+	76.6034i	−0.0480206	+	0.0831742i
$922$	−390.442	+	453.844i	−0.423473	+	0.492239i
$923$	238.776			0.258696
$924$		0			0
$925$			57.8228i			0.0625111i
$926$	658.969	−	765.977i	0.711630	−	0.827188i
$927$	−342.185	−	197.561i	−0.369132	−	0.213118i
$928$	290.861	−	668.073i	0.313427	−	0.719906i
$929$	−364.730	−	631.731i	−0.392605	−	0.680012i	0.600187	−	0.799859i	$-0.295093\pi$
$929$	−364.730	−	631.731i	−0.392605	−	0.680012i	−0.992792	+	0.119848i	$0.961759\pi$
$930$	320.266	−	112.122i	0.344372	−	0.120561i
$931$		0			0
$932$	−426.108	+	340.026i	−0.457197	+	0.364835i
$933$	−150.082	+	86.6499i	−0.160860	+	0.0928724i
$934$	241.607	−	1278.01i	0.258680	−	1.36832i
$935$	−637.092	−	367.825i	−0.681382	−	0.393396i
$936$	34.0956	−	922.713i	0.0364269	−	0.985805i
$937$	−637.240			−0.680085			−0.340042	−	0.940410i	$-0.610441\pi$
$937$	−637.240			−0.680085			−0.340042	+	0.940410i	$0.610441\pi$
$938$		0			0
$939$	347.051			0.369596
$940$	−345.415	−	135.442i	−0.367462	−	0.144087i
$941$	1518.64	+	876.787i	1.61386	+	0.931761i	0.988465	+	0.151451i	$0.0483947\pi$
$941$	1518.64	+	876.787i	1.61386	+	0.931761i	0.625393	+	0.780310i	$0.284939\pi$
$942$	383.738	+	72.5455i	0.407365	+	0.0770122i
$943$	−1588.87	+	917.332i	−1.68491	+	0.972780i
$944$	−41.6764	+	183.120i	−0.0441488	+	0.193983i
$945$		0			0
$946$	911.816	−	319.217i	0.963865	−	0.337439i
$947$	436.996	+	756.900i	0.461453	+	0.799261i	0.999034	−	0.0439519i	$-0.0139948\pi$
$947$	436.996	+	756.900i	0.461453	+	0.799261i	−0.537580	+	0.843213i	$0.680661\pi$
$948$	855.733	−	129.253i	0.902672	−	0.136342i
$949$	−1568.68	−	905.679i	−1.65298	−	0.954351i
$950$	19.2469	+	16.5581i	0.0202599	+	0.0174296i
$951$		−	103.688i		−	0.109031i
$952$		0			0
$953$	−880.208			−0.923618			−0.461809	−	0.886979i	$-0.652800\pi$
$953$	−880.208			−0.923618			−0.461809	+	0.886979i	$0.652800\pi$
$954$	−39.0487	+	45.3897i	−0.0409316	+	0.0475783i
$955$	277.191	−	480.110i	0.290253	−	0.502733i
$956$	685.149	−	103.487i	0.716684	−	0.108250i
$957$	402.500	−	232.383i	0.420585	−	0.242825i
$958$	−436.790	−	1247.65i	−0.455939	−	1.30235i
$959$		0			0
$960$	433.439	−	209.230i	0.451498	−	0.217948i
$961$	−226.006	−	391.454i	−0.235178	−	0.407340i
$962$	−94.0646	+	497.566i	−0.0977802	+	0.517220i
$963$	138.906	−	240.592i	0.144243	−	0.249836i
$964$	−1224.89	−	480.296i	−1.27063	−	0.498233i
$965$		−	389.771i		−	0.403908i
$966$		0			0
$967$		−	259.016i		−	0.267855i	−0.990991	−	0.133928i	$-0.957241\pi$
$967$		−	259.016i		−	0.267855i	0.990991	−	0.133928i	$-0.0427590\pi$
$968$	257.871	+	9.52870i	0.266396	+	0.00984370i
$969$	32.4925	−	56.2787i	0.0335320	−	0.0580792i
$970$	−355.110	−	67.1334i	−0.366093	−	0.0692097i
$971$	−216.325	−	374.686i	−0.222786	−	0.385877i	0.732867	−	0.680372i	$-0.238182\pi$
$971$	−216.325	−	374.686i	−0.222786	−	0.385877i	−0.955653	+	0.294495i	$0.904848\pi$
$972$	−786.266	+	627.425i	−0.808916	+	0.645499i
$973$		0			0
$974$	255.155	+	728.827i	0.261966	+	0.748283i
$975$	−110.093	+	63.5622i	−0.112916	+	0.0651920i
$976$	−1184.38	+	1278.05i	−1.21351	+	1.30948i
$977$	−407.755	+	706.252i	−0.417354	+	0.722878i	−0.995672	−	0.0929330i	$-0.970376\pi$
$977$	−407.755	+	706.252i	−0.417354	+	0.722878i	0.578319	+	0.815811i	$0.303709\pi$
$978$	205.053	+	176.407i	0.209666	+	0.180376i
$979$	−1948.78			−1.99058
$980$		0			0
$981$			55.3730i			0.0564455i
$982$	−1362.04	−	1171.77i	−1.38701	−	1.19324i
$983$	−120.735	−	69.7061i	−0.122822	−	0.0709116i	0.437330	−	0.899301i	$-0.355924\pi$
$983$	−120.735	−	69.7061i	−0.122822	−	0.0709116i	−0.560153	+	0.828389i	$0.689257\pi$
$984$	373.228	+	705.388i	0.379297	+	0.716857i
$985$	488.267	+	845.702i	0.495702	+	0.858581i
$986$	−196.047	−	559.992i	−0.198831	−	0.567943i
$987$		0			0
$988$	138.684	+	173.793i	0.140368	+	0.175904i
$989$	−1024.68	+	591.598i	−1.03607	+	0.598178i
$990$	−697.028	−	131.773i	−0.704069	−	0.133104i
$991$	1341.28	+	774.390i	1.35346	+	0.781423i	0.988733	−	0.149690i	$-0.0478276\pi$
$991$	1341.28	+	774.390i	1.35346	+	0.781423i	0.364731	+	0.931113i	$0.381161\pi$
$992$	429.156	+	580.542i	0.432617	+	0.585224i
$993$	−324.114			−0.326399
$994$		0			0
$995$	1132.18			1.13786
$996$	−174.210	−	68.3102i	−0.174910	−	0.0685845i
$997$	1110.67	+	641.248i	1.11402	+	0.643178i	0.939867	−	0.341541i	$-0.110949\pi$
$997$	1110.67	+	641.248i	1.11402	+	0.643178i	0.174150	+	0.984719i	$0.444282\pi$
$998$	293.936	−	1554.81i	0.294525	−	1.55793i
$999$	300.676	−	173.595i	0.300977	−	0.173769i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.k.l.67.5		12
7.2	even	3	inner	392.3.k.l.275.4		12
7.3	odd	6		392.3.g.j.99.2		6
7.4	even	3		392.3.g.i.99.2		6
7.5	odd	6		56.3.k.d.51.4	yes	12
7.6	odd	2		56.3.k.d.11.5	yes	12
8.3	odd	2	inner	392.3.k.l.67.4		12
28.3	even	6		1568.3.g.j.687.4		6
28.11	odd	6		1568.3.g.l.687.3		6
28.19	even	6		224.3.o.d.79.3		12
28.27	even	2		224.3.o.d.207.4		12
56.3	even	6		392.3.g.j.99.1		6
56.5	odd	6		224.3.o.d.79.4		12
56.11	odd	6		392.3.g.i.99.1		6
56.13	odd	2		224.3.o.d.207.3		12
56.19	even	6		56.3.k.d.51.5	yes	12
56.27	even	2		56.3.k.d.11.4	✓	12
56.45	odd	6		1568.3.g.j.687.3		6
56.51	odd	6	inner	392.3.k.l.275.5		12
56.53	even	6		1568.3.g.l.687.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.k.d.11.4	✓	12	56.27	even	2
56.3.k.d.11.5	yes	12	7.6	odd	2
56.3.k.d.51.4	yes	12	7.5	odd	6
56.3.k.d.51.5	yes	12	56.19	even	6
224.3.o.d.79.3		12	28.19	even	6
224.3.o.d.79.4		12	56.5	odd	6
224.3.o.d.207.3		12	56.13	odd	2
224.3.o.d.207.4		12	28.27	even	2
392.3.g.i.99.1		6	56.11	odd	6
392.3.g.i.99.2		6	7.4	even	3
392.3.g.j.99.1		6	56.3	even	6
392.3.g.j.99.2		6	7.3	odd	6
392.3.k.l.67.4		12	8.3	odd	2	inner
392.3.k.l.67.5		12	1.1	even	1	trivial
392.3.k.l.275.4		12	7.2	even	3	inner
392.3.k.l.275.5		12	56.51	odd	6	inner
1568.3.g.j.687.3		6	56.45	odd	6
1568.3.g.j.687.4		6	28.3	even	6
1568.3.g.l.687.3		6	28.11	odd	6
1568.3.g.l.687.4		6	56.53	even	6

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.51615 + 1.30434i) q^{2} +(0.824388 - 1.42788i) q^{3} +(0.597396 + 3.95514i) q^{4} +(-3.95004 + 2.28056i) q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} +(3.14077 + 5.43997i) q^{9} +O(q^{10})\)	\(q+(1.51615 + 1.30434i) q^{2} +(0.824388 - 1.42788i) q^{3} +(0.597396 + 3.95514i) q^{4} +(-3.95004 + 2.28056i) q^{5} +(3.11234 - 1.08960i) q^{6} +(-4.25310 + 6.77577i) q^{8} +(3.14077 + 5.43997i) q^{9} +(-8.96346 - 1.69454i) q^{10} +(6.18983 - 10.7211i) q^{11} +(6.13996 + 2.40756i) q^{12} +18.3741i q^{13} +7.52026i q^{15} +(-15.2862 + 4.72557i) q^{16} +(-6.51422 + 11.2830i) q^{17} +(-2.33371 + 12.3444i) q^{18} +(-1.51262 - 2.61993i) q^{19} +(-11.3797 - 14.2606i) q^{20} +(23.3686 - 8.18111i) q^{22} +(-26.2611 + 15.1619i) q^{23} +(6.16880 + 11.6588i) q^{24} +(-2.09812 + 3.63405i) q^{25} +(-23.9661 + 27.8579i) q^{26} +25.1958 q^{27} +22.7701i q^{29} +(-9.80897 + 11.4018i) q^{30} +(-19.5382 - 11.2804i) q^{31} +(-29.3399 - 12.7738i) q^{32} +(-10.2056 - 17.6767i) q^{33} +(-24.5933 + 8.60985i) q^{34} +(-19.6396 + 15.6720i) q^{36} +(11.9335 - 6.88983i) q^{37} +(1.12393 - 5.94517i) q^{38} +(26.2361 + 15.1474i) q^{39} +(1.34740 - 36.4640i) q^{40} +60.5026 q^{41} +39.0188 q^{43} +(46.1012 + 18.0769i) q^{44} +(-24.8123 - 14.3254i) q^{45} +(-59.5919 - 11.2658i) q^{46} +(17.6115 - 10.1680i) q^{47} +(-5.85424 + 25.7226i) q^{48} +(-7.92109 + 2.77309i) q^{50} +(10.7405 + 18.6031i) q^{51} +(-72.6723 + 10.9766i) q^{52} +(4.12744 + 2.38298i) q^{53} +(38.2006 + 32.8639i) q^{54} +56.4650i q^{55} -4.98794 q^{57} +(-29.6999 + 34.5228i) q^{58} +(5.86884 - 10.1651i) q^{59} +(-29.7437 + 4.49257i) q^{60} +(94.3137 - 54.4520i) q^{61} +(-14.9093 - 42.5872i) q^{62} +(-27.8222 - 57.6361i) q^{64} +(-41.9033 - 72.5786i) q^{65} +(7.58317 - 40.1121i) q^{66} +(39.5997 - 68.5887i) q^{67} +(-48.5172 - 19.0242i) q^{68} +49.9970i q^{69} -12.9952i q^{71} +(-50.2180 - 1.85563i) q^{72} +(-49.2909 + 85.3744i) q^{73} +(27.0797 + 5.11940i) q^{74} +(3.45933 + 5.99173i) q^{75} +(9.45857 - 7.54776i) q^{76} +(20.0204 + 57.1865i) q^{78} +(113.644 - 65.6123i) q^{79} +(49.6043 - 53.5273i) q^{80} +(-7.49577 + 12.9831i) q^{81} +(91.7308 + 78.9160i) q^{82} -28.3732 q^{83} -59.4242i q^{85} +(59.1582 + 50.8938i) q^{86} +(32.5130 + 18.7714i) q^{87} +(46.3177 + 87.5388i) q^{88} +(-78.7090 - 136.328i) q^{89} +(-18.9339 - 54.0831i) q^{90} +(-75.6555 - 94.8087i) q^{92} +(-32.2141 + 18.5988i) q^{93} +(39.9642 + 7.55521i) q^{94} +(11.9498 + 6.89923i) q^{95} +(-42.4269 + 31.3634i) q^{96} +39.6175 q^{97} +77.7633 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9}+O(q^{10}) \) 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9	\( 12 q + 2 q^{2} + 6 q^{3} - 4 q^{4} + 56 q^{6} + 8 q^{8} - 40 q^{9} + 6 q^{10} + 30 q^{11} - 32 q^{12} + 16 q^{16} - 30 q^{17} - 16 q^{18} - 78 q^{19} - 48 q^{20} + 24 q^{22} + 76 q^{24} - 92 q^{25} + 128 q^{26} - 156 q^{27} - 16 q^{30} + 112 q^{32} + 78 q^{33} - 76 q^{34} - 248 q^{36} - 80 q^{38} - 44 q^{40} + 232 q^{41} - 200 q^{43} + 132 q^{44} - 156 q^{46} - 176 q^{48} + 48 q^{50} + 10 q^{51} - 132 q^{52} + 36 q^{54} + 332 q^{57} + 4 q^{58} + 110 q^{59} + 84 q^{60} + 96 q^{62} - 160 q^{64} - 32 q^{65} + 138 q^{66} + 434 q^{67} - 96 q^{68} - 328 q^{72} - 102 q^{73} - 34 q^{74} + 60 q^{75} + 168 q^{76} + 720 q^{78} + 256 q^{80} - 82 q^{81} + 24 q^{82} + 536 q^{83} + 240 q^{86} - 204 q^{88} - 214 q^{89} - 440 q^{90} + 160 q^{92} + 16 q^{94} - 48 q^{96} + 152 q^{97} + 504 q^{99}+O(q^{100}) \) 12 * q + 2 * q^2 + 6 * q^3 - 4 * q^4 + 56 * q^6 + 8 * q^8 - 40 * q^9 + 6 * q^10 + 30 * q^11 - 32 * q^12 + 16 * q^16 - 30 * q^17 - 16 * q^18 - 78 * q^19 - 48 * q^20 + 24 * q^22 + 76 * q^24 - 92 * q^25 + 128 * q^26 - 156 * q^27 - 16 * q^30 + 112 * q^32 + 78 * q^33 - 76 * q^34 - 248 * q^36 - 80 * q^38 - 44 * q^40 + 232 * q^41 - 200 * q^43 + 132 * q^44 - 156 * q^46 - 176 * q^48 + 48 * q^50 + 10 * q^51 - 132 * q^52 + 36 * q^54 + 332 * q^57 + 4 * q^58 + 110 * q^59 + 84 * q^60 + 96 * q^62 - 160 * q^64 - 32 * q^65 + 138 * q^66 + 434 * q^67 - 96 * q^68 - 328 * q^72 - 102 * q^73 - 34 * q^74 + 60 * q^75 + 168 * q^76 + 720 * q^78 + 256 * q^80 - 82 * q^81 + 24 * q^82 + 536 * q^83 + 240 * q^86 - 204 * q^88 - 214 * q^89 - 440 * q^90 + 160 * q^92 + 16 * q^94 - 48 * q^96 + 152 * q^97 + 504 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more