LMFDB - Embedded newform 39.3.l.b.37.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,3,Mod(7,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 11]))

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

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

chi := DirichletCharacter("39.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	39.l (of order $12$, degree $4$, 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:	$1.06267303101$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
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} - 4 x^{11} + 8 x^{10} + 8 x^{9} + 178 x^{8} - 620 x^{7} + 1088 x^{6} + 640 x^{5} + 7921 x^{4} + \cdots + 5184 $ x^12 - 4x^11 + 8x^10 + 8x^9 + 178x^8 - 620x^7 + 1088x^6 + 640x^5 + 7921x^4 - 22128x^3 + 28800x^2 - 17280*x + 5184
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			37.3
Root			$2.74087 + 2.74087i$ of defining polynomial
Character	$\chi$	$=$	39.37
Dual form			39.3.l.b.19.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00323 - 3.74409i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-9.54767 - 5.51235i) q^{4} +(3.30327 + 3.30327i) q^{5} +(6.48496 - 1.73764i) q^{6} +(0.235277 + 0.878067i) q^{7} +(-19.2537 + 19.2537i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})$	\(q+(1.00323 - 3.74409i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-9.54767 - 5.51235i) q^{4} +(3.30327 + 3.30327i) q^{5} +(6.48496 - 1.73764i) q^{6} +(0.235277 + 0.878067i) q^{7} +(-19.2537 + 19.2537i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(15.6817 - 9.05381i) q^{10} +(5.60803 + 1.50267i) q^{11} -19.0953i q^{12} +(-3.44589 - 12.5350i) q^{13} +3.52360 q^{14} +(-2.09419 + 7.81561i) q^{15} +(30.7226 + 53.2130i) q^{16} +(6.85933 + 3.96024i) q^{17} +(8.22260 + 8.22260i) q^{18} +(-27.7306 + 7.43040i) q^{19} +(-13.3297 - 49.7472i) q^{20} +(-1.11334 + 1.11334i) q^{21} +(11.2522 - 19.4895i) q^{22} +(-9.29823 + 5.36834i) q^{23} +(-45.5549 - 12.2064i) q^{24} -3.17685i q^{25} +(-50.3892 + 0.326284i) q^{26} -5.19615 q^{27} +(2.59386 - 9.68042i) q^{28} +(7.56721 + 13.1068i) q^{29} +(27.1614 + 15.6817i) q^{30} +(-13.6593 - 13.6593i) q^{31} +(124.852 - 33.4539i) q^{32} +(2.60270 + 9.71339i) q^{33} +(21.7090 - 21.7090i) q^{34} +(-2.12331 + 3.67768i) q^{35} +(28.6430 - 16.5370i) q^{36} +(-2.46101 - 0.659427i) q^{37} +111.280i q^{38} +(15.8183 - 16.0244i) q^{39} -127.201 q^{40} +(11.4567 - 42.7572i) q^{41} +(3.05153 + 5.28540i) q^{42} +(-3.74071 - 2.15970i) q^{43} +(-45.2604 - 45.2604i) q^{44} +(-13.5370 + 3.62724i) q^{45} +(10.7713 + 40.1991i) q^{46} +(18.4764 - 18.4764i) q^{47} +(-53.2130 + 92.1677i) q^{48} +(41.7196 - 24.0868i) q^{49} +(-11.8944 - 3.18710i) q^{50} +13.7187i q^{51} +(-36.1970 + 138.675i) q^{52} +81.0078 q^{53} +(-5.21292 + 19.4549i) q^{54} +(13.5611 + 23.4885i) q^{55} +(-21.4361 - 12.3761i) q^{56} +(-35.1610 - 35.1610i) q^{57} +(56.6647 - 15.1832i) q^{58} +(3.85460 + 14.3856i) q^{59} +(63.0770 - 63.0770i) q^{60} +(17.7204 - 30.6926i) q^{61} +(-64.8452 + 37.4384i) q^{62} +(-2.63420 - 0.705832i) q^{63} -255.238i q^{64} +(30.0237 - 52.7891i) q^{65} +38.9789 q^{66} +(-24.9466 + 93.1019i) q^{67} +(-43.6604 - 75.6220i) q^{68} +(-16.1050 - 9.29823i) q^{69} +(11.6394 + 11.6394i) q^{70} +(-94.0489 + 25.2003i) q^{71} +(-21.1421 - 78.9033i) q^{72} +(3.74695 - 3.74695i) q^{73} +(-4.93791 + 8.55271i) q^{74} +(4.76528 - 2.75123i) q^{75} +(305.722 + 81.9179i) q^{76} +5.27777i q^{77} +(-44.1277 - 75.3012i) q^{78} +43.6772 q^{79} +(-74.2920 + 277.262i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-148.593 - 85.7902i) q^{82} +(-29.7042 - 29.7042i) q^{83} +(16.7670 - 4.49270i) q^{84} +(9.57649 + 35.7399i) q^{85} +(-11.8389 + 11.8389i) q^{86} +(-13.1068 + 22.7016i) q^{87} +(-136.908 + 79.0436i) q^{88} +(-27.1548 - 7.27610i) q^{89} +54.3229i q^{90} +(10.1958 - 5.97492i) q^{91} +118.369 q^{92} +(8.65967 - 32.3183i) q^{93} +(-50.6414 - 87.7135i) q^{94} +(-116.146 - 67.0571i) q^{95} +(158.306 + 158.306i) q^{96} +(-129.936 + 34.8163i) q^{97} +(-48.3291 - 180.367i) q^{98} +(-12.3161 + 12.3161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9}+O(q^{10}) $ 12 * q - 2 * q^2 - 12 * q^4 + 4 * q^5 + 6 * q^6 - 32 * q^7 - 24 * q^8 - 18 * q^9	\( 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9} + 30 q^{10} + 22 q^{11} + 2 q^{13} + 92 q^{14} + 52 q^{16} - 6 q^{17} + 12 q^{18} + 4 q^{19} - 208 q^{20} + 54 q^{21} - 98 q^{22} - 18 q^{23} - 54 q^{24} - 44 q^{26} - 78 q^{28} + 128 q^{29} + 6 q^{30} - 66 q^{31} + 358 q^{32} - 6 q^{33} + 336 q^{34} + 14 q^{35} + 36 q^{36} - 36 q^{37} - 18 q^{39} - 12 q^{40} - 326 q^{41} - 6 q^{42} + 60 q^{43} - 236 q^{44} - 24 q^{45} - 138 q^{46} + 40 q^{47} - 144 q^{48} + 78 q^{49} - 40 q^{50} - 392 q^{52} + 80 q^{53} - 18 q^{54} + 166 q^{55} - 102 q^{56} + 250 q^{58} - 164 q^{59} + 396 q^{60} - 98 q^{61} + 228 q^{62} + 66 q^{63} + 514 q^{65} + 60 q^{66} - 230 q^{67} + 78 q^{68} - 54 q^{69} - 92 q^{70} + 70 q^{71} - 18 q^{72} + 106 q^{73} - 16 q^{74} - 150 q^{75} + 534 q^{76} - 456 q^{78} + 16 q^{79} + 124 q^{80} - 54 q^{81} - 156 q^{82} - 176 q^{83} - 30 q^{84} + 90 q^{85} - 612 q^{86} + 48 q^{87} - 318 q^{88} - 476 q^{89} + 106 q^{91} + 228 q^{92} + 66 q^{93} - 374 q^{94} - 234 q^{95} + 384 q^{96} - 306 q^{97} - 350 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 12 * q^4 + 4 * q^5 + 6 * q^6 - 32 * q^7 - 24 * q^8 - 18 * q^9 + 30 * q^10 + 22 * q^11 + 2 * q^13 + 92 * q^14 + 52 * q^16 - 6 * q^17 + 12 * q^18 + 4 * q^19 - 208 * q^20 + 54 * q^21 - 98 * q^22 - 18 * q^23 - 54 * q^24 - 44 * q^26 - 78 * q^28 + 128 * q^29 + 6 * q^30 - 66 * q^31 + 358 * q^32 - 6 * q^33 + 336 * q^34 + 14 * q^35 + 36 * q^36 - 36 * q^37 - 18 * q^39 - 12 * q^40 - 326 * q^41 - 6 * q^42 + 60 * q^43 - 236 * q^44 - 24 * q^45 - 138 * q^46 + 40 * q^47 - 144 * q^48 + 78 * q^49 - 40 * q^50 - 392 * q^52 + 80 * q^53 - 18 * q^54 + 166 * q^55 - 102 * q^56 + 250 * q^58 - 164 * q^59 + 396 * q^60 - 98 * q^61 + 228 * q^62 + 66 * q^63 + 514 * q^65 + 60 * q^66 - 230 * q^67 + 78 * q^68 - 54 * q^69 - 92 * q^70 + 70 * q^71 - 18 * q^72 + 106 * q^73 - 16 * q^74 - 150 * q^75 + 534 * q^76 - 456 * q^78 + 16 * q^79 + 124 * q^80 - 54 * q^81 - 156 * q^82 - 176 * q^83 - 30 * q^84 + 90 * q^85 - 612 * q^86 + 48 * q^87 - 318 * q^88 - 476 * q^89 + 106 * q^91 + 228 * q^92 + 66 * q^93 - 374 * q^94 - 234 * q^95 + 384 * q^96 - 306 * q^97 - 350 * q^98 - 24 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	1.00323	−	3.74409i	0.501613	−	1.87205i	0.0123254	−	0.999924i	$-0.496077\pi$
$2$	1.00323	−	3.74409i	0.501613	−	1.87205i	0.489288	−	0.872122i	$-0.337257\pi$
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$3$	0.866025	+	1.50000i	0.288675	+	0.500000i
$4$	−9.54767	−	5.51235i	−2.38692	−	1.37809i
$5$	3.30327	+	3.30327i	0.660653	+	0.660653i	0.955534	−	0.294881i	$-0.0952799\pi$
$5$	3.30327	+	3.30327i	0.660653	+	0.660653i	−0.294881	+	0.955534i	$0.595280\pi$
$6$	6.48496	−	1.73764i	1.08083	−	0.289607i
$7$	0.235277	+	0.878067i	0.0336111	+	0.125438i	0.980693	−	0.195554i	$-0.0626504\pi$
$7$	0.235277	+	0.878067i	0.0336111	+	0.125438i	−0.947082	+	0.320992i	$0.895984\pi$
$8$	−19.2537	+	19.2537i	−2.40672	+	2.40672i
$9$	−1.50000	+	2.59808i	−0.166667	+	0.288675i
$10$	15.6817	−	9.05381i	1.56817	−	0.905381i
$11$	5.60803	+	1.50267i	0.509821	+	0.136606i	0.504554	−	0.863380i	$-0.331657\pi$
$11$	5.60803	+	1.50267i	0.509821	+	0.136606i	0.00526673	+	0.999986i	$0.498324\pi$
$12$		−	19.0953i		−	1.59128i
$13$	−3.44589	−	12.5350i	−0.265068	−	0.964230i
$13$	−3.44589	−	12.5350i	−0.265068	−	0.964230i
$14$	3.52360			0.251686
$15$	−2.09419	+	7.81561i	−0.139613	+	0.521041i
$16$	30.7226	+	53.2130i	1.92016	+	3.32581i
$17$	6.85933	+	3.96024i	0.403490	+	0.232955i	0.687989	−	0.725721i	$-0.258494\pi$
$17$	6.85933	+	3.96024i	0.403490	+	0.232955i	−0.284499	+	0.958676i	$0.591827\pi$
$18$	8.22260	+	8.22260i	0.456811	+	0.456811i
$19$	−27.7306	+	7.43040i	−1.45951	+	0.391074i	−0.899320	−	0.437292i	$-0.855938\pi$
$19$	−27.7306	+	7.43040i	−1.45951	+	0.391074i	−0.560188	+	0.828366i	$0.689271\pi$
$20$	−13.3297	−	49.7472i	−0.666487	−	2.48736i
$21$	−1.11334	+	1.11334i	−0.0530164	+	0.0530164i
$22$	11.2522	−	19.4895i	0.511466	−	0.885885i
$23$	−9.29823	+	5.36834i	−0.404271	+	0.233406i	−0.688325	−	0.725402i	$-0.741654\pi$
$23$	−9.29823	+	5.36834i	−0.404271	+	0.233406i	0.284054	+	0.958808i	$0.408320\pi$
$24$	−45.5549	−	12.2064i	−1.89812	−	0.508599i
$25$		−	3.17685i		−	0.127074i
$26$	−50.3892	+	0.326284i	−1.93804	+	0.0125494i
$27$	−5.19615			−0.192450
$28$	2.59386	−	9.68042i	0.0926379	−	0.345729i
$29$	7.56721	+	13.1068i	0.260938	+	0.451958i	0.966491	−	0.256699i	$-0.0826348\pi$
$29$	7.56721	+	13.1068i	0.260938	+	0.451958i	−0.705553	+	0.708657i	$0.749301\pi$
$30$	27.1614	+	15.6817i	0.905381	+	0.522722i
$31$	−13.6593	−	13.6593i	−0.440624	−	0.440624i	0.451598	−	0.892222i	$-0.350854\pi$
$31$	−13.6593	−	13.6593i	−0.440624	−	0.440624i	−0.892222	+	0.451598i	$0.850854\pi$
$32$	124.852	−	33.4539i	3.90162	−	1.04544i
$33$	2.60270	+	9.71339i	0.0788696	+	0.294345i
$34$	21.7090	−	21.7090i	0.638499	−	0.638499i
$35$	−2.12331	+	3.67768i	−0.0606659	+	0.105076i
$36$	28.6430	−	16.5370i	0.795639	−	0.459362i
$37$	−2.46101	−	0.659427i	−0.0665139	−	0.0178223i	0.225409	−	0.974264i	$-0.427628\pi$
$37$	−2.46101	−	0.659427i	−0.0665139	−	0.0178223i	−0.291923	+	0.956442i	$0.594295\pi$
$38$			111.280i			2.92843i
$39$	15.8183	−	16.0244i	0.405596	−	0.410883i
$40$	−127.201			−3.18001
$41$	11.4567	−	42.7572i	0.279433	−	1.04286i	−0.673379	−	0.739297i	$-0.735158\pi$
$41$	11.4567	−	42.7572i	0.279433	−	1.04286i	0.952812	−	0.303560i	$-0.0981754\pi$
$42$	3.05153	+	5.28540i	0.0726554	+	0.125843i
$43$	−3.74071	−	2.15970i	−0.0869932	−	0.0502255i	0.455872	−	0.890045i	$-0.349327\pi$
$43$	−3.74071	−	2.15970i	−0.0869932	−	0.0502255i	−0.542866	+	0.839820i	$0.682661\pi$
$44$	−45.2604	−	45.2604i	−1.02864	−	1.02864i
$45$	−13.5370	+	3.62724i	−0.300823	+	0.0806053i
$46$	10.7713	+	40.1991i	0.234159	+	0.873893i
$47$	18.4764	−	18.4764i	0.393115	−	0.393115i	−0.482681	−	0.875796i	$-0.660337\pi$
$47$	18.4764	−	18.4764i	0.393115	−	0.393115i	0.875796	+	0.482681i	$0.160337\pi$
$48$	−53.2130	+	92.1677i	−1.10860	+	1.92016i
$49$	41.7196	−	24.0868i	0.851420	−	0.491568i
$50$	−11.8944	−	3.18710i	−0.237888	−	0.0637420i
$51$			13.7187i			0.268993i
$52$	−36.1970	+	138.675i	−0.696097	+	2.66682i
$53$	81.0078			1.52845			0.764224	−	0.644951i	$-0.223122\pi$
$53$	81.0078			1.52845			0.764224	+	0.644951i	$0.223122\pi$
$54$	−5.21292	+	19.4549i	−0.0965355	+	0.360275i
$55$	13.5611	+	23.4885i	0.246566	+	0.427064i
$56$	−21.4361	−	12.3761i	−0.382787	−	0.221002i
$57$	−35.1610	−	35.1610i	−0.616861	−	0.616861i
$58$	56.6647	−	15.1832i	0.976977	−	0.261780i
$59$	3.85460	+	14.3856i	0.0653322	+	0.243823i	0.990868	−	0.134838i	$-0.0430514\pi$
$59$	3.85460	+	14.3856i	0.0653322	+	0.243823i	−0.925536	+	0.378661i	$0.876385\pi$
$60$	63.0770	−	63.0770i	1.05128	−	1.05128i
$61$	17.7204	−	30.6926i	0.290498	−	0.503158i	−0.683429	−	0.730017i	$-0.739512\pi$
$61$	17.7204	−	30.6926i	0.290498	−	0.503158i	0.973928	+	0.226859i	$0.0728456\pi$
$62$	−64.8452	+	37.4384i	−1.04589	+	0.603845i
$63$	−2.63420	−	0.705832i	−0.0418127	−	0.0112037i
$64$		−	255.238i		−	3.98809i
$65$	30.0237	−	52.7891i	0.461903	−	0.812140i
$66$	38.9789			0.590590
$67$	−24.9466	+	93.1019i	−0.372337	+	1.38958i	0.484860	+	0.874592i	$0.338871\pi$
$67$	−24.9466	+	93.1019i	−0.372337	+	1.38958i	−0.857197	+	0.514989i	$0.827796\pi$
$68$	−43.6604	−	75.6220i	−0.642065	−	1.11209i
$69$	−16.1050	−	9.29823i	−0.233406	−	0.134757i
$70$	11.6394	+	11.6394i	0.166277	+	0.166277i
$71$	−94.0489	+	25.2003i	−1.32463	+	0.354934i	−0.850711	−	0.525633i	$-0.823828\pi$
$71$	−94.0489	+	25.2003i	−1.32463	+	0.354934i	−0.473921	+	0.880567i	$0.657162\pi$
$72$	−21.1421	−	78.9033i	−0.293640	−	1.09588i
$73$	3.74695	−	3.74695i	0.0513281	−	0.0513281i	−0.680977	−	0.732305i	$-0.738445\pi$
$73$	3.74695	−	3.74695i	0.0513281	−	0.0513281i	0.732305	+	0.680977i	$0.238445\pi$
$74$	−4.93791	+	8.55271i	−0.0667285	+	0.115577i
$75$	4.76528	−	2.75123i	0.0635370	−	0.0366831i
$76$	305.722	+	81.9179i	4.02266	+	1.07787i
$77$			5.27777i			0.0685425i
$78$	−44.1277	−	75.3012i	−0.565740	−	0.965399i
$79$	43.6772			0.552876			0.276438	−	0.961032i	$-0.410846\pi$
$79$	43.6772			0.552876			0.276438	+	0.961032i	$0.410846\pi$
$80$	−74.2920	+	277.262i	−0.928650	+	3.46577i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−148.593	−	85.7902i	−1.81211	−	1.04622i
$83$	−29.7042	−	29.7042i	−0.357882	−	0.357882i	0.505150	−	0.863032i	$-0.331437\pi$
$83$	−29.7042	−	29.7042i	−0.357882	−	0.357882i	−0.863032	+	0.505150i	$0.831437\pi$
$84$	16.7670	−	4.49270i	0.199607	−	0.0534845i
$85$	9.57649	+	35.7399i	0.112665	+	0.420470i
$86$	−11.8389	+	11.8389i	−0.137661	+	0.137661i
$87$	−13.1068	+	22.7016i	−0.150653	+	0.260938i
$88$	−136.908	+	79.0436i	−1.55577	+	0.898223i
$89$	−27.1548	−	7.27610i	−0.305110	−	0.0817540i	0.103016	−	0.994680i	$-0.467151\pi$
$89$	−27.1548	−	7.27610i	−0.305110	−	0.0817540i	−0.408126	+	0.912926i	$0.633817\pi$
$90$			54.3229i			0.603588i
$91$	10.1958	−	5.97492i	0.112042	−	0.0656584i
$92$	118.369			1.28661
$93$	8.65967	−	32.3183i	0.0931148	−	0.347509i
$94$	−50.6414	−	87.7135i	−0.538738	−	0.933122i
$95$	−116.146	−	67.0571i	−1.22259	−	0.705864i
$96$	158.306	+	158.306i	1.64902	+	1.64902i
$97$	−129.936	+	34.8163i	−1.33955	+	0.358930i	−0.856266	−	0.516535i	$-0.827222\pi$
$97$	−129.936	+	34.8163i	−1.33955	+	0.358930i	−0.483281	+	0.875465i	$0.660555\pi$
$98$	−48.3291	−	180.367i	−0.493154	−	1.84048i
$99$	−12.3161	+	12.3161i	−0.124405	+	0.124405i
$100$	−17.5119	+	30.3315i	−0.175119	+	0.303315i
$101$	85.7700	−	49.5193i	0.849208	−	0.490290i	−0.0111758	−	0.999938i	$-0.503557\pi$
$101$	85.7700	−	49.5193i	0.849208	−	0.490290i	0.860383	+	0.509647i	$0.170224\pi$
$102$	51.3640	+	13.7629i	0.503568	+	0.134931i
$103$			132.264i			1.28412i	0.766655	+	0.642059i	$0.221920\pi$
$103$			132.264i			1.28412i	−0.766655	+	0.642059i	$0.778080\pi$
$104$	307.692	+	174.999i	2.95857	+	1.68268i
$105$	−7.35535			−0.0700510
$106$	81.2692	−	303.301i	0.766690	−	2.86133i
$107$	69.0289	+	119.561i	0.645130	+	1.11740i	0.984272	+	0.176662i	$0.0565299\pi$
$107$	69.0289	+	119.561i	0.645130	+	1.11740i	−0.339142	+	0.940735i	$0.610137\pi$
$108$	49.6111	+	28.6430i	0.459362	+	0.265213i
$109$	26.2463	+	26.2463i	0.240792	+	0.240792i	0.817178	−	0.576386i	$-0.195538\pi$
$109$	26.2463	+	26.2463i	0.240792	+	0.240792i	−0.576386	+	0.817178i	$0.695538\pi$
$110$	101.548	−	27.2097i	0.923165	−	0.247361i
$111$	−1.14216	−	4.26260i	−0.0102897	−	0.0384018i
$112$	−39.4963	+	39.4963i	−0.352645	+	0.352645i
$113$	−90.5319	+	156.806i	−0.801167	+	1.38766i	0.117681	+	0.993051i	$0.462454\pi$
$113$	−90.5319	+	156.806i	−0.801167	+	1.38766i	−0.918848	+	0.394611i	$0.870879\pi$
$114$	−166.921	+	96.3717i	−1.46422	+	0.845366i
$115$	−48.4476	−	12.9815i	−0.421283	−	0.112883i
$116$		−	166.852i		−	1.43838i
$117$	37.7357	+	9.84980i	0.322527	+	0.0841864i
$118$	57.7279			0.489219
$119$	−1.86351	+	6.95471i	−0.0156597	+	0.0584429i
$120$	−110.159	−	190.801i	−0.917991	−	1.59001i
$121$	−75.5971	−	43.6460i	−0.624769	−	0.360711i
$122$	−97.1385	−	97.1385i	−0.796217	−	0.796217i
$123$	74.0576	−	19.8437i	0.602094	−	0.161331i
$124$	55.1198	+	205.710i	0.444514	+	1.65895i
$125$	93.0757	−	93.0757i	0.744605	−	0.744605i
$126$	−5.28540	+	9.15459i	−0.0419476	+	0.0726554i
$127$	188.451	−	108.802i	1.48387	−	0.856710i	0.484034	−	0.875049i	$-0.339171\pi$
$127$	188.451	−	108.802i	1.48387	−	0.856710i	0.999832	+	0.0183386i	$0.00583769\pi$
$128$	−456.228	−	122.246i	−3.56428	−	0.955045i
$129$		−	7.48141i		−	0.0579954i
$130$	−167.527	−	165.371i	−1.28867	−	1.27208i
$131$	−158.787			−1.21212			−0.606058	−	0.795421i	$-0.707250\pi$
$131$	−158.787			−1.21212			−0.606058	+	0.795421i	$0.707250\pi$
$132$	28.6939	−	107.087i	0.217378	−	0.811267i
$133$	−13.0488	−	22.6012i	−0.0981112	−	0.169934i
$134$	323.555	+	186.805i	2.41459	+	1.39406i
$135$	−17.1643	−	17.1643i	−0.127143	−	0.127143i
$136$	−208.317	+	55.8184i	−1.53174	+	0.410430i
$137$	62.8465	+	234.546i	0.458733	+	1.71202i	0.676874	+	0.736098i	$0.263334\pi$
$137$	62.8465	+	234.546i	0.458733	+	1.71202i	−0.218141	+	0.975917i	$0.569999\pi$
$138$	−50.9704	+	50.9704i	−0.369351	+	0.369351i
$139$	39.8702	−	69.0573i	0.286836	−	0.496815i	−0.686217	−	0.727397i	$-0.740730\pi$
$139$	39.8702	−	69.0573i	0.286836	−	0.496815i	0.973053	+	0.230582i	$0.0740631\pi$
$140$	40.5452	−	23.4088i	0.289609	−	0.167206i
$141$	43.7157	+	11.7136i	0.310040	+	0.0830751i
$142$			377.409i			2.65781i
$143$	−0.488720	−	75.4746i	−0.00341762	−	0.527794i
$144$	−184.335			−1.28011
$145$	−18.2987	+	68.2917i	−0.126198	+	0.470978i
$146$	−10.2699	−	17.7880i	−0.0703418	−	0.121836i
$147$	72.2605	+	41.7196i	0.491568	+	0.283807i
$148$	19.8619	+	19.8619i	0.134202	+	0.134202i
$149$	−46.6353	+	12.4959i	−0.312988	+	0.0838650i	−0.411894	−	0.911232i	$-0.635133\pi$
$149$	−46.6353	+	12.4959i	−0.312988	+	0.0838650i	0.0989054	+	0.995097i	$0.468466\pi$
$150$	−5.52022	−	20.6017i	−0.0368015	−	0.137345i
$151$	181.386	−	181.386i	1.20123	−	1.20123i	0.227437	−	0.973793i	$-0.426965\pi$
$151$	181.386	−	181.386i	1.20123	−	1.20123i	0.973793	−	0.227437i	$-0.0730346\pi$
$152$	390.856	−	676.982i	2.57142	−	4.45383i
$153$	−20.5780	+	11.8807i	−0.134497	+	0.0776517i
$154$	19.7605	+	5.29480i	0.128315	+	0.0343818i
$155$		−	90.2409i		−	0.582199i
$156$	−239.360	+	65.8003i	−1.53436	+	0.421797i
$157$	80.3793			0.511970			0.255985	−	0.966681i	$-0.417600\pi$
$157$	80.3793			0.511970			0.255985	+	0.966681i	$0.417600\pi$
$158$	43.8181	−	163.531i	0.277330	−	1.03501i
$159$	70.1548	+	121.512i	0.441225	+	0.764224i
$160$	522.926	+	301.911i	3.26829	+	1.88695i
$161$	−6.90142	−	6.90142i	−0.0428660	−	0.0428660i
$162$	−33.6968	+	9.02904i	−0.208005	+	0.0557348i
$163$	−45.5771	−	170.096i	−0.279614	−	1.04353i	−0.952686	−	0.303956i	$-0.901692\pi$
$163$	−45.5771	−	170.096i	−0.279614	−	1.04353i	0.673072	−	0.739577i	$-0.264974\pi$
$164$	−345.077	+	345.077i	−2.10413	+	2.10413i
$165$	−23.4885	+	40.6833i	−0.142355	+	0.246566i
$166$	−141.015	+	81.4153i	−0.849490	+	0.490453i
$167$	−140.594	−	37.6720i	−0.841880	−	0.225581i	−0.187990	−	0.982171i	$-0.560197\pi$
$167$	−140.594	−	37.6720i	−0.841880	−	0.225581i	−0.653890	+	0.756590i	$0.726864\pi$
$168$		−	42.8721i		−	0.255191i
$169$	−145.252	+	86.3883i	−0.859478	+	0.511173i
$170$	143.421			0.843653
$171$	22.2912	−	83.1919i	0.130358	−	0.486503i
$172$	23.8100	+	41.2401i	0.138430	+	0.239768i
$173$	136.733	+	78.9429i	0.790364	+	0.456317i	0.840091	−	0.542446i	$-0.182502\pi$
$173$	136.733	+	78.9429i	0.790364	+	0.456317i	−0.0497264	+	0.998763i	$0.515835\pi$
$174$	71.8479	+	71.8479i	0.412919	+	0.412919i
$175$	2.78949	−	0.747441i	0.0159399	−	0.00427109i
$176$	92.3315	+	344.586i	0.524611	+	1.95787i
$177$	−18.2402	+	18.2402i	−0.103052	+	0.103052i
$178$	−54.4848	+	94.3705i	−0.306094	+	0.530171i
$179$	−82.5165	+	47.6409i	−0.460986	+	0.266150i	−0.712459	−	0.701714i	$-0.752418\pi$
$179$	−82.5165	+	47.6409i	−0.460986	+	0.266150i	0.251473	+	0.967864i	$0.419085\pi$
$180$	149.242	+	39.9892i	0.829121	+	0.222162i
$181$		−	169.256i		−	0.935116i	−0.883962	−	0.467558i	$-0.845134\pi$
$181$		−	169.256i		−	0.935116i	0.883962	−	0.467558i	$-0.154866\pi$
$182$	−12.1419	−	44.1683i	−0.0667139	−	0.242683i
$183$	61.3853			0.335439
$184$	75.6652	−	282.386i	0.411224	−	1.53471i
$185$	−5.95112	−	10.3076i	−0.0321682	−	0.0557170i
$186$	−112.315	−	64.8452i	−0.603845	−	0.348630i
$187$	32.5164	+	32.5164i	0.173885	+	0.173885i
$188$	−278.255	+	74.5582i	−1.48008	+	0.396586i
$189$	−1.22254	−	4.56257i	−0.00646845	−	0.0241406i
$190$	−367.589	+	367.589i	−1.93468	+	1.93468i
$191$	46.3432	−	80.2688i	0.242635	−	0.420256i	−0.718829	−	0.695187i	$-0.755322\pi$
$191$	46.3432	−	80.2688i	0.242635	−	0.420256i	0.961464	+	0.274931i	$0.0886550\pi$
$192$	382.857	−	221.043i	1.99405	−	1.15126i
$193$	−310.573	−	83.2179i	−1.60919	−	0.431181i	−0.661388	−	0.750044i	$-0.730032\pi$
$193$	−310.573	−	83.2179i	−1.60919	−	0.431181i	−0.947801	+	0.318863i	$0.896699\pi$
$194$			521.421i			2.68774i
$195$	105.185	−	0.681103i	0.539410	−	0.00349283i
$196$	−531.100			−2.70969
$197$	−29.0041	+	108.245i	−0.147229	+	0.549466i	0.852417	+	0.522863i	$0.175136\pi$
$197$	−29.0041	+	108.245i	−0.147229	+	0.549466i	−0.999646	+	0.0266038i	$0.991531\pi$
$198$	33.7567	+	58.4684i	0.170489	+	0.295295i
$199$	−59.4497	−	34.3233i	−0.298742	−	0.172479i	0.343136	−	0.939286i	$-0.388511\pi$
$199$	−59.4497	−	34.3233i	−0.298742	−	0.172479i	−0.641878	+	0.766807i	$0.721844\pi$
$200$	61.1663	+	61.1663i	0.305831	+	0.305831i
$201$	−161.257	+	43.2087i	−0.802275	+	0.214969i
$202$	−99.3582	−	370.810i	−0.491872	−	1.83569i
$203$	−9.72825	+	9.72825i	−0.0479224	+	0.0479224i
$204$	75.6220	−	130.981i	0.370696	−	0.642065i
$205$	179.083	−	103.394i	0.873576	−	0.504359i
$206$	495.209	+	132.691i	2.40393	+	0.644131i
$207$		−	32.2100i		−	0.155604i
$208$	561.158	−	568.473i	2.69788	−	2.73304i
$209$	−166.680			−0.797511
$210$	−7.37908	+	27.5391i	−0.0351385	+	0.131139i
$211$	−22.2146	−	38.4768i	−0.105282	−	0.182355i	0.808571	−	0.588398i	$-0.200241\pi$
$211$	−22.2146	−	38.4768i	−0.105282	−	0.182355i	−0.913854	+	0.406044i	$0.866908\pi$
$212$	−773.435	−	446.543i	−3.64828	−	2.10633i
$213$	−119.249	−	119.249i	−0.559856	−	0.559856i
$214$	516.901	−	138.503i	2.41542	−	0.647211i
$215$	−5.22249	−	19.4906i	−0.0242907	−	0.0906540i
$216$	100.045	−	100.045i	0.463173	−	0.463173i
$217$	8.78009	−	15.2076i	0.0404612	−	0.0700809i
$218$	124.599	−	71.9375i	0.571557	−	0.329989i
$219$	8.86539	+	2.37547i	0.0404812	+	0.0108469i
$220$		−	299.014i		−	1.35916i
$221$	26.0050	−	99.6282i	0.117670	−	0.450806i
$222$	−17.1054			−0.0770514
$223$	−78.3280	+	292.324i	−0.351247	+	1.31087i	0.533896	+	0.845550i	$0.320727\pi$
$223$	−78.3280	+	292.324i	−0.351247	+	1.31087i	−0.885142	+	0.465320i	$0.845939\pi$
$224$	58.7496	+	101.757i	0.262275	+	0.454274i
$225$	8.25370	+	4.76528i	0.0366831	+	0.0211790i
$226$	496.272	+	496.272i	2.19589	+	2.19589i
$227$	302.517	−	81.0591i	1.33267	−	0.357088i	0.478962	−	0.877836i	$-0.341013\pi$
$227$	302.517	−	81.0591i	1.33267	−	0.357088i	0.853711	+	0.520747i	$0.174347\pi$
$228$	141.886	+	529.526i	0.622307	+	2.32248i
$229$	−113.873	+	113.873i	−0.497260	+	0.497260i	−0.910584	−	0.413324i	$-0.864368\pi$
$229$	−113.873	+	113.873i	−0.497260	+	0.497260i	0.413324	+	0.910584i	$0.364368\pi$
$230$	−97.2078	+	168.369i	−0.422643	+	0.732039i
$231$	−7.91666	+	4.57068i	−0.0342712	+	0.0197865i
$232$	−398.052	−	106.658i	−1.71574	−	0.459731i
$233$		−	191.488i		−	0.821838i	−0.911672	−	0.410919i	$-0.865208\pi$
$233$		−	191.488i		−	0.821838i	0.911672	−	0.410919i	$-0.134792\pi$
$234$	74.7360	−	131.404i	0.319385	−	0.561557i
$235$	122.065			0.519426
$236$	42.4958	−	158.596i	0.180067	−	0.672018i
$237$	37.8255	+	65.5158i	0.159601	+	0.276438i
$238$	24.1696	+	13.9543i	0.101553	+	0.0586315i
$239$	−173.094	−	173.094i	−0.724244	−	0.724244i	0.245223	−	0.969467i	$-0.421139\pi$
$239$	−173.094	−	173.094i	−0.724244	−	0.724244i	−0.969467	+	0.245223i	$0.921139\pi$
$240$	−480.231	+	128.678i	−2.00096	+	0.536157i
$241$	15.1870	+	56.6788i	0.0630167	+	0.235182i	0.990250	−	0.139303i	$-0.0444863\pi$
$241$	15.1870	+	56.6788i	0.0630167	+	0.235182i	−0.927233	+	0.374485i	$0.877820\pi$
$242$	−239.256	+	239.256i	−0.988660	+	0.988660i
$243$	7.79423	−	13.5000i	0.0320750	−	0.0555556i
$244$	−338.377	+	195.362i	−1.38679	+	0.800664i
$245$	217.376	+	58.2458i	0.887250	+	0.237738i
$246$		−	297.186i		−	1.20807i
$247$	188.697	+	321.999i	0.763954	+	1.30364i
$248$	525.987			2.12091
$249$	18.8317	−	70.2809i	0.0756294	−	0.282253i
$250$	−255.108	−	441.860i	−1.02043	−	1.76744i
$251$	98.6857	+	56.9762i	0.393170	+	0.226997i	0.683533	−	0.729920i	$-0.260443\pi$
$251$	98.6857	+	56.9762i	0.393170	+	0.226997i	−0.290363	+	0.956917i	$0.593776\pi$
$252$	21.2597	+	21.2597i	0.0843638	+	0.0843638i
$253$	−60.2116	+	16.1336i	−0.237990	+	0.0637693i
$254$	−218.307	−	814.731i	−0.859475	−	3.20760i
$255$	−45.3164	+	45.3164i	−0.177711	+	0.177711i
$256$	−404.923	+	701.348i	−1.58173	+	2.73964i
$257$	−324.407	+	187.297i	−1.26229	+	0.728781i	−0.973516	−	0.228618i	$-0.926579\pi$
$257$	−324.407	+	187.297i	−1.26229	+	0.728781i	−0.288769	+	0.957399i	$0.593246\pi$
$258$	−28.0111	−	7.50555i	−0.108570	−	0.0290913i
$259$		−	2.31608i		−	0.00894241i
$260$	−577.648	+	338.511i	−2.22172	+	1.30197i
$261$	−45.4033			−0.173959
$262$	−159.300	+	594.514i	−0.608013	+	2.26914i
$263$	57.8742	+	100.241i	0.220054	+	0.381145i	0.954824	−	0.297171i	$-0.0960433\pi$
$263$	57.8742	+	100.241i	0.220054	+	0.381145i	−0.734770	+	0.678316i	$0.762710\pi$
$264$	−237.131	−	136.908i	−0.898223	−	0.518589i
$265$	267.590	+	267.590i	1.00977	+	1.00977i
$266$	−97.7118	+	26.1818i	−0.367337	+	0.0984278i
$267$	−12.6026	−	47.0335i	−0.0472007	−	0.176155i
$268$	751.392	−	751.392i	2.80370	−	2.80370i
$269$	51.2997	−	88.8537i	0.190705	−	0.330311i	−0.754779	−	0.655979i	$-0.772256\pi$
$269$	51.2997	−	88.8537i	0.190705	−	0.330311i	0.945484	+	0.325668i	$0.105589\pi$
$270$	−81.4843	+	47.0450i	−0.301794	+	0.174241i
$271$	−89.8030	−	24.0626i	−0.331376	−	0.0887920i	0.0892948	−	0.996005i	$-0.471539\pi$
$271$	−89.8030	−	24.0626i	−0.331376	−	0.0887920i	−0.420671	+	0.907213i	$0.638205\pi$
$272$			486.674i			1.78924i
$273$	17.7922	+	10.1193i	0.0651730	+	0.0370670i
$274$	941.212			3.43508
$275$	4.77375	−	17.8159i	0.0173591	−	0.0647850i
$276$	102.510	+	177.553i	0.371414	+	0.643307i
$277$	366.341	+	211.507i	1.32253	+	0.763563i	0.984132	−	0.177441i	$-0.0567818\pi$
$277$	366.341	+	211.507i	1.32253	+	0.763563i	0.338398	+	0.941003i	$0.390115\pi$
$278$	−218.558	−	218.558i	−0.786179	−	0.786179i
$279$	55.9770	−	14.9990i	0.200634	−	0.0537598i
$280$	−29.9274	−	111.691i	−0.106884	−	0.398895i
$281$	6.57627	−	6.57627i	0.0234031	−	0.0234031i	−0.695308	−	0.718712i	$-0.744732\pi$
$281$	6.57627	−	6.57627i	0.0234031	−	0.0234031i	0.718712	+	0.695308i	$0.244732\pi$
$282$	87.7135	−	151.924i	0.311041	−	0.538738i
$283$	48.9456	−	28.2588i	0.172953	−	0.0998543i	−0.411025	−	0.911624i	$-0.634829\pi$
$283$	48.9456	−	28.2588i	0.172953	−	0.0998543i	0.583977	+	0.811770i	$0.301496\pi$
$284$	1036.86	+	277.826i	3.65092	+	0.978260i
$285$		−	232.293i		−	0.815062i
$286$	−283.074	−	73.8883i	−0.989770	−	0.258351i
$287$	40.2392			0.140206
$288$	−100.362	+	374.555i	−0.348478	+	1.30054i
$289$	−113.133	−	195.952i	−0.391464	−	0.678035i
$290$	237.333	+	137.024i	0.818389	+	0.472497i
$291$	−164.752	−	164.752i	−0.566159	−	0.566159i
$292$	−56.4292	+	15.1202i	−0.193251	+	0.0517813i
$293$	53.0538	+	197.999i	0.181071	+	0.675766i	0.995438	+	0.0954150i	$0.0304178\pi$
$293$	53.0538	+	197.999i	0.181071	+	0.675766i	−0.814367	+	0.580351i	$0.802916\pi$
$294$	228.696	−	228.696i	0.777876	−	0.777876i
$295$	−34.7866	+	60.2521i	−0.117921	+	0.204244i
$296$	60.0802	−	34.6873i	0.202973	−	0.117187i
$297$	−29.1402	−	7.80809i	−0.0981151	−	0.0262899i
$298$			187.143i			0.627997i
$299$	99.3326	+	98.0545i	0.332216	+	0.327942i
$300$	−60.6630			−0.202210
$301$	1.01626	−	3.79272i	0.00337627	−	0.0126004i
$302$	−497.154	−	861.096i	−1.64621	−	2.85131i
$303$	148.558	+	85.7700i	0.490290	+	0.283069i
$304$	−1247.35	−	1247.35i	−4.10313	−	4.10313i
$305$	159.921	−	42.8507i	0.524332	−	0.140494i
$306$	23.8381	+	88.9650i	0.0779023	+	0.290735i
$307$	−21.2456	+	21.2456i	−0.0692039	+	0.0692039i	−0.740862	−	0.671658i	$-0.765583\pi$
$307$	−21.2456	+	21.2456i	−0.0692039	+	0.0692039i	0.671658	+	0.740862i	$0.265583\pi$
$308$	29.0929	−	50.3904i	0.0944575	−	0.163605i
$309$	−198.396	+	114.544i	−0.642059	+	0.370693i
$310$	−337.870	−	90.5321i	−1.08990	−	0.292039i
$311$		−	328.015i		−	1.05471i	−0.849645	−	0.527355i	$-0.823184\pi$
$311$		−	328.015i		−	1.05471i	0.849645	−	0.527355i	$-0.176816\pi$
$312$	3.96994	+	613.091i	0.0127242	+	1.96504i
$313$	−572.183			−1.82806			−0.914030	−	0.405647i	$-0.867046\pi$
$313$	−572.183			−1.82806			−0.914030	+	0.405647i	$0.867046\pi$
$314$	80.6387	−	300.948i	0.256811	−	0.958432i
$315$	−6.36992	−	11.0330i	−0.0202220	−	0.0350255i
$316$	−417.015	−	240.764i	−1.31967	−	0.761911i
$317$	263.833	+	263.833i	0.832280	+	0.832280i	0.987828	−	0.155548i	$-0.0497143\pi$
$317$	263.833	+	263.833i	0.832280	+	0.832280i	−0.155548	+	0.987828i	$0.549714\pi$
$318$	525.332	−	140.762i	1.65199	−	0.442649i
$319$	22.7420	+	84.8743i	0.0712915	+	0.266064i
$320$	843.119	−	843.119i	2.63475	−	2.63475i
$321$	−119.561	+	207.087i	−0.372466	+	0.645130i
$322$	−32.7633	+	18.9159i	−0.101749	+	0.0587450i
$323$	−219.640	−	58.8523i	−0.680000	−	0.182205i
$324$			99.2222i			0.306241i
$325$	−39.8218	+	10.9471i	−0.122529	+	0.0336833i
$326$	−682.579			−2.09380
$327$	−16.6395	+	62.0994i	−0.0508852	+	0.189906i
$328$	602.650	+	1043.82i	1.83735	+	3.18238i
$329$	20.5706	+	11.8765i	0.0625247	+	0.0360987i
$330$	128.758	+	128.758i	0.390175	+	0.390175i
$331$	82.4800	−	22.1005i	0.249184	−	0.0667688i	−0.132065	−	0.991241i	$-0.542161\pi$
$331$	82.4800	−	22.1005i	0.249184	−	0.0667688i	0.381249	+	0.924472i	$0.375494\pi$
$332$	119.866	+	447.346i	0.361042	+	1.34743i
$333$	5.40476	−	5.40476i	0.0162305	−	0.0162305i
$334$	−282.095	+	488.603i	−0.844596	+	1.46288i
$335$	−389.946	+	225.135i	−1.16402	+	0.672046i
$336$	−93.4492	−	25.0396i	−0.278123	−	0.0745228i
$337$			151.474i			0.449476i	0.974419	+	0.224738i	$0.0721527\pi$
$337$			151.474i			0.449476i	−0.974419	+	0.224738i	$0.927847\pi$
$338$	177.725	+	630.503i	0.525814	+	1.86539i
$339$	−313.612			−0.925108
$340$	105.578	−	394.022i	0.310523	−	1.15889i
$341$	−56.0765	−	97.1274i	−0.164447	−	0.284831i
$342$	−289.115	−	166.921i	−0.845366	−	0.488072i
$343$	62.4622	+	62.4622i	0.182106	+	0.182106i
$344$	113.605	−	30.4403i	0.330247	−	0.0884893i
$345$	−22.4846	−	83.9137i	−0.0651728	−	0.243228i
$346$	432.744	−	432.744i	1.25070	−	1.25070i
$347$	68.0738	−	117.907i	0.196178	−	0.339790i	−0.751108	−	0.660179i	$-0.770480\pi$
$347$	68.0738	−	117.907i	0.196178	−	0.339790i	0.947286	+	0.320389i	$0.103814\pi$
$348$	250.278	−	144.498i	0.719191	−	0.415225i
$349$	−162.066	−	43.4254i	−0.464371	−	0.124428i	0.0190447	−	0.999819i	$-0.493938\pi$
$349$	−162.066	−	43.4254i	−0.464371	−	0.124428i	−0.483416	+	0.875391i	$0.660604\pi$
$350$		−	11.1940i		−	0.0319827i
$351$	17.9053	+	65.1337i	0.0510124	+	0.185566i
$352$	750.442			2.13194
$353$	82.1005	−	306.403i	0.232579	−	0.867998i	−0.746646	−	0.665222i	$-0.768337\pi$
$353$	82.1005	−	306.403i	0.232579	−	0.867998i	0.979225	−	0.202776i	$-0.0649963\pi$
$354$	49.9938	+	86.5918i	0.141225	+	0.244610i
$355$	−393.912	−	227.425i	−1.10961	−	0.640634i
$356$	219.156	+	219.156i	0.615608	+	0.615608i
$357$	−12.0459	+	3.22769i	−0.0337421	+	0.00904116i
$358$	95.5892	+	356.744i	0.267009	+	0.996491i
$359$	−61.9541	+	61.9541i	−0.172574	+	0.172574i	−0.788109	−	0.615535i	$-0.788940\pi$
$359$	−61.9541	+	61.9541i	−0.172574	+	0.172574i	0.615535	+	0.788109i	$0.288940\pi$
$360$	190.801	−	330.477i	0.530002	−	0.917991i
$361$	401.143	−	231.600i	1.11120	−	0.641551i
$362$	−633.710	−	169.802i	−1.75058	−	0.469067i
$363$		−	151.194i		−	0.416513i
$364$	−130.282	+	0.843614i	−0.357918	+	0.00231762i
$365$	24.7544			0.0678202
$366$	61.5833	−	229.832i	0.168260	−	0.627956i
$367$	−232.100	−	402.010i	−0.632426	−	1.09539i	−0.987054	−	0.160387i	$-0.948726\pi$
$367$	−232.100	−	402.010i	−0.632426	−	1.09539i	0.354628	−	0.935007i	$-0.384607\pi$
$368$	−571.331	−	329.858i	−1.55253	−	0.896353i
$369$	93.9012	+	93.9012i	0.254475	+	0.254475i
$370$	−44.5631	+	11.9406i	−0.120441	+	0.0322720i
$371$	19.0593	+	71.1303i	0.0513728	+	0.191726i
$372$	−260.830	+	260.830i	−0.701155	+	0.701155i
$373$	28.9854	−	50.2042i	0.0777088	−	0.134596i	−0.824552	−	0.565786i	$-0.808573\pi$
$373$	28.9854	−	50.2042i	0.0777088	−	0.134596i	0.902261	+	0.431190i	$0.141906\pi$
$374$	154.366	−	89.1232i	0.412743	−	0.238297i
$375$	220.219	+	59.0076i	0.587252	+	0.157354i
$376$			711.481i			1.89224i
$377$	138.218	−	140.019i	0.366625	−	0.371404i
$378$	−18.3092			−0.0484370
$379$	−18.1969	+	67.9119i	−0.0480130	+	0.179187i	−0.985768	−	0.168110i	$-0.946234\pi$
$379$	−18.1969	+	67.9119i	−0.0480130	+	0.179187i	0.937755	+	0.347297i	$0.112900\pi$
$380$	739.284	+	1280.48i	1.94548	+	3.36968i
$381$	326.407	+	188.451i	0.856710	+	0.494622i
$382$	−254.041	−	254.041i	−0.665029	−	0.665029i
$383$	201.339	−	53.9485i	0.525688	−	0.140858i	0.0137918	−	0.999905i	$-0.495610\pi$
$383$	201.339	−	53.9485i	0.525688	−	0.140858i	0.511896	+	0.859047i	$0.328943\pi$
$384$	−211.736	−	790.209i	−0.551396	−	2.05784i
$385$	−17.4339	+	17.4339i	−0.0452828	+	0.0452828i
$386$	−623.151	+	1079.33i	−1.61438	+	2.79619i
$387$	11.2221	−	6.47909i	0.0289977	−	0.0167418i
$388$	1432.51	+	383.839i	3.69202	+	0.989275i
$389$		−	459.988i		−	1.18249i	−0.806492	−	0.591245i	$-0.798637\pi$
$389$		−	459.988i		−	1.18249i	0.806492	−	0.591245i	$-0.201363\pi$
$390$	102.974	−	394.505i	0.264036	−	1.01155i
$391$	−85.0395			−0.217492
$392$	−339.497	+	1267.02i	−0.866064	+	3.23219i
$393$	−137.514	−	238.181i	−0.349908	−	0.606058i
$394$	376.181	+	217.188i	0.954775	+	0.551239i
$395$	144.277	+	144.277i	0.365259	+	0.365259i
$396$	185.480	−	49.6993i	0.468385	−	0.125503i
$397$	−149.364	−	557.434i	−0.376232	−	1.40412i	−0.851537	−	0.524295i	$-0.824329\pi$
$397$	−149.364	−	557.434i	−0.376232	−	1.40412i	0.475305	−	0.879821i	$-0.342338\pi$
$398$	−188.151	+	188.151i	−0.472741	+	0.472741i
$399$	22.6012	−	39.1464i	0.0566445	−	0.0981112i
$400$	169.050	−	97.6010i	0.422625	−	0.244002i
$401$	141.512	+	37.9181i	0.352898	+	0.0945588i	0.430913	−	0.902393i	$-0.358192\pi$
$401$	141.512	+	37.9181i	0.352898	+	0.0945588i	−0.0780149	+	0.996952i	$0.524858\pi$
$402$			647.110i			1.60973i
$403$	−124.151	+	218.288i	−0.308067	+	0.541658i
$404$	−1091.87			−2.70265
$405$	10.8817	−	40.6111i	0.0268684	−	0.100274i
$406$	26.6638	+	46.1831i	0.0656745	+	0.113752i
$407$	−12.8105	−	7.39617i	−0.0314755	−	0.0181724i
$408$	−264.136	−	264.136i	−0.647391	−	0.647391i
$409$	220.136	−	58.9852i	0.538230	−	0.144218i	0.0205438	−	0.999789i	$-0.493460\pi$
$409$	220.136	−	58.9852i	0.538230	−	0.144218i	0.517686	+	0.855571i	$0.326794\pi$
$410$	−207.454	−	774.231i	−0.505986	−	1.88837i
$411$	−297.393	+	297.393i	−0.723583	+	0.723583i
$412$	729.086	−	1262.81i	1.76963	−	3.06508i
$413$	−11.7246	+	6.76919i	−0.0283888	+	0.0163903i
$414$	−120.597	−	32.3139i	−0.291298	−	0.0780530i
$415$		−	196.242i		−	0.472872i
$416$	−849.569	−	1449.74i	−2.04223	−	3.48494i
$417$	138.115			0.331210
$418$	−167.218	+	624.064i	−0.400042	+	1.49298i
$419$	206.102	+	356.979i	0.491889	+	0.851977i	0.999956	−	0.00934013i	$-0.00297310\pi$
$419$	206.102	+	356.979i	0.491889	+	0.851977i	−0.508067	+	0.861318i	$0.669640\pi$
$420$	70.2264	+	40.5452i	0.167206	+	0.0965363i
$421$	516.646	+	516.646i	1.22719	+	1.22719i	0.965024	+	0.262163i	$0.0844358\pi$
$421$	516.646	+	516.646i	1.22719	+	1.22719i	0.262163	+	0.965024i	$0.415564\pi$
$422$	−166.347	+	44.5725i	−0.394187	+	0.105622i
$423$	20.2885	+	75.7178i	0.0479634	+	0.179002i
$424$	−1559.70	+	1559.70i	−3.67855	+	3.67855i
$425$	12.5811	−	21.7911i	0.0296026	−	0.0512731i
$426$	−566.114	+	326.846i	−1.32891	+	0.767245i
$427$	31.1194	+	8.33842i	0.0728792	+	0.0195279i
$428$		−	1522.04i		−	3.55618i
$429$	112.789	−	66.0960i	0.262911	−	0.154070i
$430$	−78.2140			−0.181893
$431$	−22.6165	+	84.4059i	−0.0524745	+	0.195837i	−0.987187	−	0.159567i	$-0.948990\pi$
$431$	−22.6165	+	84.4059i	−0.0524745	+	0.195837i	0.934713	+	0.355404i	$0.115657\pi$
$432$	−159.639	−	276.503i	−0.369535	−	0.640053i
$433$	−270.622	−	156.244i	−0.624994	−	0.360840i	0.153817	−	0.988099i	$-0.450843\pi$
$433$	−270.622	−	156.244i	−0.624994	−	0.360840i	−0.778811	+	0.627259i	$0.784177\pi$
$434$	−48.1301	−	48.1301i	−0.110899	−	0.110899i
$435$	−118.285	+	31.6943i	−0.271919	+	0.0728605i
$436$	−105.912	−	395.269i	−0.242918	−	0.906581i
$437$	217.957	−	217.957i	0.498757	−	0.498757i
$438$	17.7880	−	30.8097i	0.0406118	−	0.0703418i
$439$	114.773	−	66.2644i	0.261443	−	0.150944i	−0.363550	−	0.931575i	$-0.618435\pi$
$439$	114.773	−	66.2644i	0.261443	−	0.150944i	0.624992	+	0.780631i	$0.285102\pi$
$440$	−713.344	−	191.140i	−1.62124	−	0.434409i
$441$			144.521i			0.327712i
$442$	−346.928	−	197.315i	−0.784905	−	0.446414i
$443$	762.677			1.72162			0.860809	−	0.508928i	$-0.169958\pi$
$443$	762.677			1.72162			0.860809	+	0.508928i	$0.169958\pi$
$444$	−12.5920	+	46.9939i	−0.0283603	+	0.105842i
$445$	−65.6646	−	113.734i	−0.147561	−	0.255583i
$446$	1015.91	+	586.535i	2.27782	+	1.31510i
$447$	−59.1312	−	59.1312i	−0.132284	−	0.132284i
$448$	224.116	−	60.0517i	0.500259	−	0.134044i
$449$	71.2323	+	265.843i	0.158647	+	0.592077i	0.998765	+	0.0496748i	$0.0158185\pi$
$449$	71.2323	+	265.843i	0.158647	+	0.592077i	−0.840119	+	0.542402i	$0.817515\pi$
$450$	26.1220	−	26.1220i	0.0580488	−	0.0580488i
$451$	128.500	−	222.568i	0.284921	−	0.493498i
$452$	1728.74	−	998.086i	3.82464	−	2.20816i
$453$	429.163	+	114.994i	0.947380	+	0.253850i
$454$		−	1213.97i		−	2.67394i
$455$	53.4163	+	13.9428i	0.117398	+	0.0306435i
$456$	1353.96			2.96922
$457$	147.457	−	550.316i	0.322662	−	1.20419i	−0.593979	−	0.804481i	$-0.702444\pi$
$457$	147.457	−	550.316i	0.322662	−	1.20419i	0.916641	−	0.399711i	$-0.130890\pi$
$458$	312.110	+	540.590i	0.681462	+	1.18033i
$459$	−35.6421	−	20.5780i	−0.0776517	−	0.0448322i
$460$	391.003	+	391.003i	0.850006	+	0.850006i
$461$	−131.737	+	35.2989i	−0.285764	+	0.0765704i	−0.398854	−	0.917014i	$-0.630592\pi$
$461$	−131.737	+	35.2989i	−0.285764	+	0.0765704i	0.113090	+	0.993585i	$0.463925\pi$
$462$	9.17086	+	34.2261i	0.0198504	+	0.0740825i
$463$	−555.943	+	555.943i	−1.20074	+	1.20074i	−0.226798	+	0.973942i	$0.572826\pi$
$463$	−555.943	+	555.943i	−1.20074	+	1.20074i	−0.973942	+	0.226798i	$0.927174\pi$
$464$	−464.968	+	805.348i	−1.00209	+	1.73566i
$465$	135.361	−	78.1509i	0.291100	−	0.168066i
$466$	−716.950	−	192.106i	−1.53852	−	0.412245i
$467$			684.656i			1.46607i	0.680189	+	0.733037i	$0.261898\pi$
$467$			684.656i			1.46607i	−0.680189	+	0.733037i	$0.738102\pi$
$468$	−305.992	−	302.055i	−0.653829	−	0.645416i
$469$	−87.6191			−0.186821
$470$	122.459	−	457.023i	0.260551	−	0.972390i
$471$	69.6105	+	120.569i	0.147793	+	0.255985i
$472$	−351.191	−	202.760i	−0.744049	−	0.429577i
$473$	−17.7327	−	17.7327i	−0.0374898	−	0.0374898i
$474$	283.245	−	75.8952i	0.597563	−	0.160116i
$475$	23.6053	+	88.0961i	0.0496953	+	0.185466i
$476$	56.1289	−	56.1289i	0.117918	−	0.117918i
$477$	−121.512	+	210.464i	−0.254741	+	0.441225i
$478$	−821.733	+	474.428i	−1.71911	+	0.992527i
$479$	−808.391	−	216.608i	−1.68766	−	0.452208i	−0.717879	−	0.696168i	$-0.754887\pi$
$479$	−808.391	−	216.608i	−1.68766	−	0.452208i	−0.969785	+	0.243960i	$0.921554\pi$
$480$			1045.85i			2.17886i
$481$	0.214468	+	33.1211i	0.000445880	+	0.0688588i
$482$	227.447			0.471881
$483$	4.37533	−	16.3289i	0.00905865	−	0.0338073i
$484$	481.184	+	833.435i	0.994181	+	1.72197i
$485$	−544.221	−	314.206i	−1.12210	−	0.647848i
$486$	−42.7259	−	42.7259i	−0.0879133	−	0.0879133i
$487$	421.775	−	113.014i	0.866068	−	0.232062i	0.201681	−	0.979451i	$-0.435359\pi$
$487$	421.775	−	113.014i	0.866068	−	0.232062i	0.664387	+	0.747389i	$0.268693\pi$
$488$	249.764	+	932.132i	0.511812	+	1.91011i
$489$	215.673	−	215.673i	0.441049	−	0.441049i
$490$	436.155	−	755.443i	0.890113	−	1.54172i
$491$	−384.073	+	221.744i	−0.782226	+	0.451618i	−0.837218	−	0.546869i	$-0.815820\pi$
$491$	−384.073	+	221.744i	−0.782226	+	0.451618i	0.0549929	+	0.998487i	$0.482486\pi$
$492$	−816.462	−	218.770i	−1.65948	−	0.444655i
$493$			119.872i			0.243148i
$494$	1394.90	−	383.460i	2.82368	−	0.776234i
$495$	−81.3667			−0.164377
$496$	307.205	−	1146.50i	0.619365	−	2.31150i
$497$	−44.2552	−	76.6522i	−0.0890446	−	0.154230i
$498$	−244.246	−	141.015i	−0.490453	−	0.283163i
$499$	−453.730	−	453.730i	−0.909279	−	0.909279i	0.0869354	−	0.996214i	$-0.472293\pi$
$499$	−453.730	−	453.730i	−0.909279	−	0.909279i	−0.996214	+	0.0869354i	$0.972293\pi$
$500$	−1401.72	+	375.590i	−2.80344	+	0.751180i
$501$	−65.2499	−	243.516i	−0.130239	−	0.486059i
$502$	312.328	−	312.328i	0.622168	−	0.622168i
$503$	163.827	−	283.757i	0.325700	−	0.564129i	−0.655954	−	0.754801i	$-0.727733\pi$
$503$	163.827	−	283.757i	0.325700	−	0.564129i	0.981654	+	0.190672i	$0.0610666\pi$
$504$	64.3082	−	37.1283i	0.127596	−	0.0736673i
$505$	446.897	+	119.746i	0.884944	+	0.237120i
$506$			241.623i			0.477517i
$507$	−255.374	−	143.063i	−0.503696	−	0.282176i
$508$	−2399.02			−4.72249
$509$	−97.4223	+	363.585i	−0.191399	+	0.714312i	0.801770	+	0.597632i	$0.203892\pi$
$509$	−97.4223	+	363.585i	−0.191399	+	0.714312i	−0.993170	+	0.116680i	$0.962775\pi$
$510$	124.206	+	215.132i	0.243542	+	0.421827i
$511$	4.17165	+	2.40850i	0.00816370	+	0.00471332i
$512$	883.754	+	883.754i	1.72608	+	1.72608i
$513$	144.093	−	38.6095i	0.280882	−	0.0752622i
$514$	375.802	+	1402.51i	0.731132	+	2.72862i
$515$	−436.904	+	436.904i	−0.848357	+	0.848357i
$516$	−41.2401	+	71.4300i	−0.0799228	+	0.138430i
$517$	131.380	−	75.8524i	0.254120	−	0.146716i
$518$	−8.67163	−	2.32356i	−0.0167406	−	0.00448563i
$519$			273.466i			0.526910i
$520$	438.319	+	1594.46i	0.842920	+	3.06626i
$521$	−615.884			−1.18212			−0.591060	−	0.806628i	$-0.701290\pi$
$521$	−615.884			−1.18212			−0.591060	+	0.806628i	$0.701290\pi$
$522$	−45.5497	+	169.994i	−0.0872601	+	0.325659i
$523$	−122.231	−	211.711i	−0.233712	−	0.404801i	0.725185	−	0.688554i	$-0.241754\pi$
$523$	−122.231	−	211.711i	−0.233712	−	0.404801i	−0.958898	+	0.283752i	$0.908421\pi$
$524$	1516.05	+	875.290i	2.89322	+	1.67040i
$525$	3.53693	+	3.53693i	0.00673701	+	0.00673701i
$526$	433.373	−	116.122i	0.823903	−	0.220764i
$527$	−39.5997	−	147.788i	−0.0751418	−	0.280433i
$528$	−436.918	+	436.918i	−0.827495	+	0.827495i
$529$	−206.862	+	358.295i	−0.391043	+	0.677307i
$530$	1270.34	−	733.429i	2.39686	−	1.38383i
$531$	−43.1567	−	11.5638i	−0.0812743	−	0.0217774i
$532$			287.718i			0.540823i
$533$	−575.439	+	3.72613i	−1.07962	+	0.00699087i
$534$	−188.741			−0.353447
$535$	−166.923	+	622.964i	−0.312005	+	1.16442i
$536$	−1312.25	−	2272.88i	−2.44822	−	4.24044i
$537$	−142.923	−	82.5165i	−0.266150	−	0.153662i
$538$	−281.211	−	281.211i	−0.522698	−	0.522698i
$539$	270.159	−	72.3889i	0.501223	−	0.134302i
$540$	69.2633	+	258.494i	0.128265	+	0.478693i
$541$	264.659	−	264.659i	0.489204	−	0.489204i	−0.418851	−	0.908055i	$-0.637567\pi$
$541$	264.659	−	264.659i	0.489204	−	0.489204i	0.908055	+	0.418851i	$0.137567\pi$
$542$	−180.185	+	312.090i	−0.332446	+	0.575813i
$543$	253.884	−	146.580i	0.467558	−	0.269945i
$544$	988.885	+	264.971i	1.81780	+	0.487079i
$545$			173.397i			0.318160i
$546$	55.7372	−	56.4638i	0.102083	−	0.103413i
$547$	439.360			0.803218			0.401609	−	0.915811i	$-0.368451\pi$
$547$	439.360			0.803218			0.401609	+	0.915811i	$0.368451\pi$
$548$	692.863	−	2585.80i	1.26435	−	4.71861i
$549$	53.1612	+	92.0779i	0.0968328	+	0.167719i
$550$	−61.9151	−	35.7467i	−0.112573	−	0.0649940i
$551$	−307.232	−	307.232i	−0.557590	−	0.557590i
$552$	489.107	−	131.056i	0.886064	−	0.237420i
$553$	10.2763	+	38.3515i	0.0185827	+	0.0693517i
$554$	1159.42	−	1159.42i	2.09282	−	2.09282i
$555$	10.3076	−	17.8534i	0.0185723	−	0.0321682i
$556$	−761.335	+	439.557i	−1.36931	+	0.790570i
$557$	81.7290	+	21.8992i	0.146731	+	0.0393164i	0.331437	−	0.943477i	$-0.392467\pi$
$557$	81.7290	+	21.8992i	0.146731	+	0.0393164i	−0.184706	+	0.982794i	$0.559133\pi$
$558$		−	224.631i		−	0.402564i
$559$	−14.1817	+	54.3318i	−0.0253698	+	0.0971946i
$560$	−260.934			−0.465953
$561$	−20.6146	+	76.9347i	−0.0367461	+	0.137138i
$562$	−18.0247	−	31.2197i	−0.0320724	−	0.0555510i
$563$	131.716	+	76.0461i	0.233953	+	0.135073i	0.612394	−	0.790552i	$-0.290206\pi$
$563$	131.716	+	76.0461i	0.233953	+	0.135073i	−0.378441	+	0.925625i	$0.623540\pi$
$564$	−352.813	−	352.813i	−0.625556	−	0.625556i
$565$	−817.023	+	218.921i	−1.44606	+	0.387470i
$566$	−56.6999	−	211.607i	−0.100176	−	0.373864i
$567$	5.78511	−	5.78511i	0.0102030	−	0.0102030i
$568$	1325.59	−	2295.99i	2.33379	−	4.04224i
$569$	−634.451	+	366.300i	−1.11503	+	0.643761i	−0.940127	−	0.340825i	$-0.889294\pi$
$569$	−634.451	+	366.300i	−1.11503	+	0.643761i	−0.174901	+	0.984586i	$0.555960\pi$
$570$	−869.725	−	233.042i	−1.52583	−	0.408846i
$571$			965.471i			1.69084i	0.534100	+	0.845421i	$0.320651\pi$
$571$			965.471i			1.69084i	−0.534100	+	0.845421i	$0.679349\pi$
$572$	−411.376	+	723.300i	−0.719189	+	1.26451i
$573$	160.538			0.280170
$574$	40.3690	−	150.659i	0.0703293	−	0.262472i
$575$	17.0544	+	29.5391i	0.0296598	+	0.0513723i
$576$	663.128	+	382.857i	1.15126	+	0.664682i
$577$	232.745	+	232.745i	0.403371	+	0.403371i	0.879419	−	0.476048i	$-0.157931\pi$
$577$	232.745	+	232.745i	0.403371	+	0.403371i	−0.476048	+	0.879419i	$0.657931\pi$
$578$	−847.161	+	226.996i	−1.46568	+	0.392727i
$579$	−144.138	−	537.929i	−0.248942	−	0.929065i
$580$	551.158	−	551.158i	0.950272	−	0.950272i
$581$	19.0936	−	33.0710i	0.0328633	−	0.0569209i
$582$	−782.132	+	451.564i	−1.34387	+	0.775883i
$583$	454.294	+	121.728i	0.779235	+	0.208795i
$584$			144.286i			0.247065i
$585$	92.1145	+	157.188i	0.157461	+	0.268697i
$586$	794.553			1.35589
$587$	−34.0511	+	127.081i	−0.0580087	+	0.216492i	−0.988846	−	0.148943i	$-0.952413\pi$
$587$	−34.0511	+	127.081i	−0.0580087	+	0.216492i	0.930837	+	0.365435i	$0.119080\pi$
$588$	−459.946	−	796.649i	−0.782221	−	1.35485i
$589$	480.277	+	277.288i	0.815410	+	0.470777i
$590$	190.691	+	190.691i	0.323204	+	0.323204i
$591$	−187.486	+	50.2366i	−0.317235	+	0.0850028i
$592$	−40.5185	−	151.217i	−0.0684435	−	0.255434i
$593$	310.017	−	310.017i	0.522794	−	0.522794i	−0.395620	−	0.918414i	$-0.629470\pi$
$593$	310.017	−	310.017i	0.522794	−	0.522794i	0.918414	+	0.395620i	$0.129470\pi$
$594$	−58.4684	+	101.270i	−0.0984317	+	0.170489i
$595$	−29.1289	+	16.8176i	−0.0489562	+	0.0282649i
$596$	514.140	+	137.763i	0.862650	+	0.231146i
$597$		−	118.899i		−	0.199161i
$598$	466.778	−	273.540i	0.780566	−	0.457424i
$599$	934.777			1.56056			0.780281	−	0.625429i	$-0.215076\pi$
$599$	934.777			1.56056			0.780281	+	0.625429i	$0.215076\pi$
$600$	−38.7779	+	144.721i	−0.0646298	+	0.241202i
$601$	479.955	+	831.307i	0.798595	+	1.38321i	0.920531	+	0.390669i	$0.127756\pi$
$601$	479.955	+	831.307i	0.798595	+	1.38321i	−0.121937	+	0.992538i	$0.538910\pi$
$602$	−13.1808	−	7.60992i	−0.0218950	−	0.0126411i
$603$	−204.466	−	204.466i	−0.339081	−	0.339081i
$604$	−2731.67	+	731.949i	−4.52263	+	1.21184i
$605$	−105.543	−	393.892i	−0.174451	−	0.651061i
$606$	470.168	−	470.168i	0.775855	−	0.775855i
$607$	137.053	−	237.384i	0.225788	−	0.391077i	−0.730767	−	0.682627i	$-0.760838\pi$
$607$	137.053	−	237.384i	0.225788	−	0.391077i	0.956556	+	0.291550i	$0.0941709\pi$
$608$	−3213.64	+	1855.40i	−5.28560	+	3.05164i
$609$	−23.0173	−	6.16746i	−0.0377952	−	0.0101272i
$610$		−	641.749i		−	1.05205i
$611$	−295.269	−	167.934i	−0.483256	−	0.274851i
$612$	261.962			0.428043
$613$	97.1779	−	362.673i	0.158528	−	0.591636i	−0.840249	−	0.542201i	$-0.817591\pi$
$613$	97.1779	−	362.673i	0.158528	−	0.591636i	0.998777	−	0.0494352i	$-0.0157421\pi$
$614$	58.2314	+	100.860i	0.0948394	+	0.164267i
$615$	310.181	+	179.083i	0.504359	+	0.291192i
$616$	−101.617	−	101.617i	−0.164962	−	0.164962i
$617$	236.820	−	63.4556i	0.383824	−	0.102845i	−0.0617470	−	0.998092i	$-0.519667\pi$
$617$	236.820	−	63.4556i	0.383824	−	0.102845i	0.445571	+	0.895246i	$0.353001\pi$
$618$	229.828	+	857.728i	0.371889	+	1.38791i
$619$	334.351	−	334.351i	0.540147	−	0.540147i	−0.383425	−	0.923572i	$-0.625256\pi$
$619$	334.351	−	334.351i	0.540147	−	0.540147i	0.923572	+	0.383425i	$0.125256\pi$
$620$	−497.439	+	861.590i	−0.802321	+	1.38966i
$621$	48.3150	−	27.8947i	0.0778020	−	0.0449190i
$622$	−1228.12	−	329.073i	−1.97446	−	0.529056i
$623$		−	25.5556i		−	0.0410203i
$624$	1338.69	+	349.425i	2.14533	+	0.559976i
$625$	535.486			0.856778
$626$	−574.029	+	2142.30i	−0.916979	+	3.42221i
$627$	−144.349	−	250.020i	−0.230221	−	0.398755i
$628$	−767.435	−	443.079i	−1.22203	−	0.705539i
$629$	−14.2694	−	14.2694i	−0.0226859	−	0.0226859i
$630$	−47.6991	+	12.7809i	−0.0757129	+	0.0202872i
$631$	−16.9296	−	63.1822i	−0.0268298	−	0.100130i	0.951213	−	0.308536i	$-0.0998391\pi$
$631$	−16.9296	−	63.1822i	−0.0268298	−	0.100130i	−0.978042	+	0.208406i	$0.933172\pi$
$632$	−840.949	+	840.949i	−1.33062	+	1.33062i
$633$	38.4768	−	66.6438i	0.0607848	−	0.105282i
$634$	1252.50	−	723.131i	1.97555	−	1.14058i
$635$	981.907	+	263.101i	1.54631	+	0.414332i
$636$		−	1546.87i		−	2.43219i
$637$	−445.689	−	439.954i	−0.699669	−	0.690666i
$638$	340.592			0.533844
$639$	75.6010	−	282.147i	0.118311	−	0.441544i
$640$	−1103.23	−	1910.85i	−1.72380	−	2.98571i
$641$	−404.577	−	233.583i	−0.631166	−	0.364404i	0.150037	−	0.988680i	$-0.452061\pi$
$641$	−404.577	−	233.583i	−0.631166	−	0.364404i	−0.781204	+	0.624276i	$0.785394\pi$
$642$	655.404	+	655.404i	1.02088	+	1.02088i
$643$	−535.165	+	143.397i	−0.832294	+	0.223012i	−0.649714	−	0.760179i	$-0.725111\pi$
$643$	−535.165	+	143.397i	−0.832294	+	0.223012i	−0.182580	+	0.983191i	$0.558445\pi$
$644$	27.8494	+	103.936i	0.0432445	+	0.161391i
$645$	24.7131	−	24.7131i	0.0383149	−	0.0383149i
$646$	−440.697	+	763.310i	−0.682194	+	1.18159i
$647$	365.279	−	210.894i	0.564573	−	0.325956i	−0.190406	−	0.981705i	$-0.560980\pi$
$647$	365.279	−	210.894i	0.564573	−	0.325956i	0.754979	+	0.655749i	$0.227647\pi$
$648$	236.710	+	63.4262i	0.365293	+	0.0978800i
$649$			86.4668i			0.133231i
$650$	1.03656	+	160.079i	0.00159470	+	0.246275i
$651$	30.4151			0.0467206
$652$	−502.473	+	1875.26i	−0.770665	+	2.87616i
$653$	−182.251	−	315.668i	−0.279098	−	0.483412i	0.692063	−	0.721837i	$-0.256702\pi$
$653$	−182.251	−	315.668i	−0.279098	−	0.483412i	−0.971161	+	0.238425i	$0.923369\pi$
$654$	215.813	+	124.599i	0.329989	+	0.190519i
$655$	−524.516	−	524.516i	−0.800788	−	0.800788i
$656$	2627.22	−	703.961i	4.00490	−	1.07311i
$657$	4.11444	+	15.3553i	0.00626247	+	0.0233718i
$658$	65.1036	−	65.1036i	0.0989416	−	0.0989416i
$659$	286.379	−	496.022i	0.434565	−	0.752689i	−0.562695	−	0.826665i	$-0.690235\pi$
$659$	286.379	−	496.022i	0.434565	−	0.752689i	0.997260	+	0.0739756i	$0.0235687\pi$
$660$	448.521	−	258.954i	0.679578	−	0.392354i
$661$	849.859	+	227.719i	1.28572	+	0.344507i	0.836032	−	0.548681i	$-0.184870\pi$
$661$	849.859	+	227.719i	1.28572	+	0.344507i	0.449685	+	0.893187i	$0.351536\pi$
$662$		−	330.985i		−	0.499977i
$663$	171.963	−	47.2730i	0.259371	−	0.0713016i
$664$	1143.83			1.72264
$665$	31.5541	−	117.761i	0.0474497	−	0.177085i
$666$	−14.8137	−	25.6581i	−0.0222428	−	0.0385257i
$667$	−140.723	−	81.2466i	−0.210979	−	0.121809i
$668$	1134.68	+	1134.68i	1.69863	+	1.69863i
$669$	−506.320	+	135.668i	−0.756831	+	0.202792i
$670$	451.723	+	1685.85i	0.674214	+	2.51620i
$671$	145.497	−	145.497i	0.216837	−	0.216837i
$672$	−101.757	+	176.249i	−0.151425	+	0.262275i
$673$	44.2409	−	25.5425i	0.0657369	−	0.0379532i	−0.466771	−	0.884378i	$-0.654583\pi$
$673$	44.2409	−	25.5425i	0.0657369	−	0.0379532i	0.532508	+	0.846425i	$0.321250\pi$
$674$	567.131	+	151.962i	0.841441	+	0.225463i
$675$			16.5074i			0.0244554i
$676$	1863.02	−	24.1282i	2.75594	−	0.0356925i
$677$	−1045.92			−1.54494			−0.772469	−	0.635053i	$-0.780978\pi$
$677$	−1045.92			−1.54494			−0.772469	+	0.635053i	$0.780978\pi$
$678$	−314.624	+	1174.19i	−0.464047	+	1.73185i
$679$	−61.1420	−	105.901i	−0.0900472	−	0.155966i
$680$	−872.511	−	503.744i	−1.28310	−	0.740801i
$681$	383.576	+	383.576i	0.563254	+	0.563254i
$682$	−419.912	+	112.515i	−0.615706	+	0.164978i
$683$	161.532	+	602.846i	0.236504	+	0.882644i	0.977465	+	0.211096i	$0.0677034\pi$
$683$	161.532	+	602.846i	0.236504	+	0.882644i	−0.740962	+	0.671547i	$0.765630\pi$
$684$	−671.412	+	671.412i	−0.981596	+	0.981596i
$685$	−567.170	+	982.367i	−0.827985	+	1.43411i
$686$	296.528	−	171.201i	0.432257	−	0.249564i
$687$	−269.426	−	72.1923i	−0.392177	−	0.105083i
$688$		−	265.406i		−	0.385764i
$689$	−279.144	−	1015.43i	−0.405143	−	1.47378i
$690$	−336.738			−0.488026
$691$	138.390	−	516.478i	0.200275	−	0.747436i	−0.790563	−	0.612380i	$-0.790212\pi$
$691$	138.390	−	516.478i	0.200275	−	0.747436i	0.990838	−	0.135055i	$-0.0431213\pi$
$692$	−870.321	−	1507.44i	−1.25769	−	2.17838i
$693$	−13.7121	−	7.91666i	−0.0197865	−	0.0114237i
$694$	−373.162	−	373.162i	−0.537698	−	0.537698i
$695$	359.817	−	96.4126i	0.517722	−	0.138723i
$696$	−184.737	−	689.446i	−0.265426	−	0.990583i
$697$	247.914	−	247.914i	0.355687	−	0.355687i
$698$	−325.177	+	563.223i	−0.465870	+	0.806910i
$699$	287.232	−	165.834i	0.410919	−	0.237244i
$700$	−30.7533	−	8.24031i	−0.0439332	−	0.0117719i
$701$			1086.67i			1.55017i	0.631854	+	0.775087i	$0.282294\pi$
$701$			1086.67i			1.55017i	−0.631854	+	0.775087i	$0.717706\pi$
$702$	261.830	−	1.69542i	0.372977	−	0.00241513i
$703$	73.1453			0.104047
$704$	383.538	−	1431.38i	0.544798	−	2.03321i
$705$	105.712	+	183.098i	0.149945	+	0.259713i
$706$	−1064.84	−	614.784i	−1.50827	−	0.870798i
$707$	63.6610	+	63.6610i	0.0900439	+	0.0900439i
$708$	274.697	−	73.6048i	0.387990	−	0.103962i
$709$	−115.524	−	431.140i	−0.162939	−	0.608096i	−0.998294	−	0.0583855i	$-0.981405\pi$
$709$	−115.524	−	431.140i	−0.162939	−	0.608096i	0.835355	−	0.549710i	$-0.185262\pi$
$710$	−1246.68	+	1246.68i	−1.75589	+	1.75589i
$711$	−65.5158	+	113.477i	−0.0921460	+	0.159601i
$712$	662.924	−	382.739i	0.931073	−	0.537555i
$713$	200.336	+	53.6798i	0.280976	+	0.0752872i
$714$			48.3391i			0.0677018i
$715$	247.698	−	250.927i	0.346431	−	0.350947i
$716$	1050.45			1.46711
$717$	109.737	−	409.545i	0.153051	−	0.571193i
$718$	169.808	+	294.116i	0.236501	+	0.409632i
$719$	−905.624	−	522.862i	−1.25956	−	0.727207i	−0.286571	−	0.958059i	$-0.592516\pi$
$719$	−905.624	−	522.862i	−1.25956	−	0.727207i	−0.972989	+	0.230851i	$0.925849\pi$
$720$	−608.909	−	608.909i	−0.845707	−	0.845707i
$721$	−116.137	+	31.1188i	−0.161077	+	0.0431606i
$722$	−464.694	−	1734.26i	−0.643621	−	2.40203i
$723$	−71.8658	+	71.8658i	−0.0993994	+	0.0993994i
$724$	−932.998	+	1616.00i	−1.28867	+	2.23204i
$725$	41.6383	−	24.0399i	0.0574322	−	0.0331585i
$726$	−566.085	−	151.682i	−0.779731	−	0.208928i
$727$		−	346.434i		−	0.476525i	−0.971201	−	0.238263i	$-0.923422\pi$
$727$		−	346.434i		−	0.476525i	0.971201	−	0.238263i	$-0.0765779\pi$
$728$	−81.2682	+	311.347i	−0.111632	+	0.427675i
$729$	27.0000			0.0370370
$730$	24.8343	−	92.6827i	0.0340195	−	0.126963i
$731$	−17.1058	−	29.6282i	−0.0234006	−	0.0405310i
$732$	−586.086	−	338.377i	−0.800664	−	0.462263i
$733$	−632.247	−	632.247i	−0.862547	−	0.862547i	0.129087	−	0.991633i	$-0.458796\pi$
$733$	−632.247	−	632.247i	−0.862547	−	0.862547i	−0.991633	+	0.129087i	$0.958796\pi$
$734$	−1738.01	+	465.698i	−2.36786	+	0.634467i
$735$	100.885	+	376.507i	0.137258	+	0.512254i
$736$	−981.308	+	981.308i	−1.33330	+	1.33330i
$737$	−279.802	+	484.632i	−0.379650	+	0.657574i
$738$	445.779	−	257.371i	0.604037	−	0.348741i
$739$	31.2351	+	8.36942i	0.0422667	+	0.0113253i	0.279890	−	0.960032i	$-0.409702\pi$
$739$	31.2351	+	8.36942i	0.0422667	+	0.0113253i	−0.237624	+	0.971357i	$0.576369\pi$
$740$			131.219i			0.177322i
$741$	−319.582	+	561.904i	−0.431285	+	0.758305i
$742$	285.439			0.384689
$743$	192.884	−	719.854i	0.259602	−	0.968847i	−0.705870	−	0.708341i	$-0.749444\pi$
$743$	192.884	−	719.854i	0.259602	−	0.968847i	0.965472	−	0.260506i	$-0.0838895\pi$
$744$	455.518	+	788.980i	0.612255	+	1.06046i
$745$	−195.326	−	112.772i	−0.262183	−	0.151371i
$746$	−158.890	−	158.890i	−0.212989	−	0.212989i
$747$	121.730	−	32.6175i	0.162959	−	0.0436646i
$748$	−131.214	−	489.698i	−0.175420	−	0.654676i
$749$	−88.7421	+	88.7421i	−0.118481	+	0.118481i
$750$	441.860	−	765.324i	0.589147	−	1.02043i
$751$	−894.943	+	516.695i	−1.19167	+	0.688010i	−0.958685	−	0.284471i	$-0.908182\pi$
$751$	−894.943	+	516.695i	−1.19167	+	0.688010i	−0.232983	+	0.972481i	$0.574849\pi$
$752$	1550.83	+	415.543i	2.06227	+	0.552584i
$753$			197.371i			0.262114i
$754$	−385.582	−	657.971i	−0.511382	−	0.872641i
$755$	1198.33			1.58719
$756$	−13.4781	+	50.3010i	−0.0178282	+	0.0665357i
$757$	378.681	+	655.895i	0.500240	+	0.866440i	1.00000		0.000276678i	$8.80693e-5\pi$
$757$	378.681	+	655.895i	0.500240	+	0.866440i	−0.499760	+	0.866164i	$0.666579\pi$
$758$	236.013	+	136.262i	0.311362	+	0.179765i
$759$	−76.3452	−	76.3452i	−0.100587	−	0.100587i
$760$	3527.35	−	945.151i	4.64125	−	1.24362i
$761$	215.400	+	803.884i	0.283049	+	1.05635i	0.950253	+	0.311478i	$0.100824\pi$
$761$	215.400	+	803.884i	0.283049	+	1.05635i	−0.667205	+	0.744874i	$0.732509\pi$
$762$	1033.04	−	1033.04i	1.35569	−	1.35569i
$763$	−16.8708	+	29.2212i	−0.0221112	+	0.0382977i
$764$	−884.939	+	510.920i	−1.15830	+	0.668743i
$765$	−107.220	−	28.7295i	−0.140157	−	0.0375548i
$766$		−	807.953i		−	1.05477i
$767$	167.040	−	97.8883i	0.217784	−	0.127625i
$768$	−1402.70			−1.82643
$769$	251.358	−	938.081i	0.326864	−	1.21987i	−0.585562	−	0.810628i	$-0.699126\pi$
$769$	251.358	−	938.081i	0.326864	−	1.21987i	0.912425	−	0.409243i	$-0.134207\pi$
$770$	47.7840	+	82.7642i	0.0620571	+	0.107486i
$771$	−561.890	−	324.407i	−0.728781	−	0.420762i
$772$	2506.52	+	2506.52i	3.24679	+	3.24679i
$773$	−657.402	+	176.150i	−0.850456	+	0.227879i	−0.657618	−	0.753352i	$-0.728436\pi$
$773$	−657.402	+	176.150i	−0.850456	+	0.227879i	−0.192838	+	0.981231i	$0.561769\pi$
$774$	−13.0000	−	48.5167i	−0.0167959	−	0.0626830i
$775$	−43.3937	+	43.3937i	−0.0559919	+	0.0559919i
$776$	1831.41	−	3172.10i	2.36007	−	4.08776i
$777$	3.47413	−	2.00579i	0.00447120	−	0.00258145i
$778$	−1722.24	−	461.473i	−2.21367	−	0.593152i
$779$			1270.81i			1.63134i
$780$	−1008.03	−	573.313i	−1.29234	−	0.735017i
$781$	−565.297			−0.723811
$782$	−85.3139	+	318.396i	−0.109097	+	0.407156i
$783$	−39.3204	−	68.1049i	−0.0502176	−	0.0869794i
$784$	2563.46	+	1480.02i	3.26973	+	1.88778i
$785$	265.514	+	265.514i	0.338235	+	0.338235i
$786$	−1029.73	+	275.915i	−1.31009	+	0.351037i
$787$	−193.341	−	721.557i	−0.245668	−	0.916845i	−0.973047	−	0.230609i	$-0.925928\pi$
$787$	−193.341	−	721.557i	−0.245668	−	0.916845i	0.727379	−	0.686236i	$-0.240738\pi$
$788$	873.605	−	873.605i	1.10864	−	1.10864i
$789$	−100.241	+	173.623i	−0.127048	+	0.220054i
$790$	684.931	−	395.445i	0.867001	−	0.500563i
$791$	−158.986	−	42.6002i	−0.200994	−	0.0538562i
$792$		−	474.262i		−	0.598815i
$793$	−445.794	−	116.362i	−0.562162	−	0.146736i
$794$	−2236.93			−2.81729
$795$	−169.645	+	633.126i	−0.213391	+	0.796384i
$796$	378.404	+	655.415i	0.475382	+	0.823385i
$797$	431.093	+	248.892i	0.540895	+	0.312286i	0.745442	−	0.666571i	$-0.232239\pi$
$797$	431.093	+	248.892i	0.540895	+	0.312286i	−0.204547	+	0.978857i	$0.565572\pi$
$798$	−123.894	−	123.894i	−0.155255	−	0.155255i
$799$	199.907	−	53.5649i	0.250196	−	0.0670399i
$800$	−106.278	−	396.635i	−0.132848	−	0.495794i
$801$	59.6361	−	59.6361i	0.0744520	−	0.0744520i
$802$	283.938	−	491.794i	0.354037	−	0.613210i
$803$	26.6435	−	15.3826i	0.0331799	−	0.0191564i
$804$	1777.81	+	476.363i	2.21121	+	0.592492i
$805$		−	45.5945i		−	0.0566391i
$806$	692.739	+	683.826i	0.859478	+	0.848419i
$807$	177.707			0.220208
$808$	−697.961	+	2604.83i	−0.863813	+	3.22379i
$809$	26.3804	+	45.6922i	0.0326087	+	0.0564799i	0.881869	−	0.471494i	$-0.156285\pi$
$809$	26.3804	+	45.6922i	0.0326087	+	0.0564799i	−0.849261	+	0.527974i	$0.822952\pi$
$810$	−141.135	−	81.4843i	−0.174241	−	0.100598i
$811$	−883.046	−	883.046i	−1.08884	−	1.08884i	−0.995649	−	0.0931873i	$-0.970294\pi$
$811$	−883.046	−	883.046i	−1.08884	−	1.08884i	−0.0931873	−	0.995649i	$-0.529706\pi$
$812$	146.508	−	39.2566i	0.180428	−	0.0483455i
$813$	−41.6777	−	155.543i	−0.0512641	−	0.191320i
$814$	−40.5438	+	40.5438i	−0.0498081	+	0.0498081i
$815$	411.319	−	712.426i	0.504686	−	0.874142i
$816$	−730.012	+	421.472i	−0.894622	+	0.516510i
$817$	119.780	+	32.0949i	0.146609	+	0.0392838i
$818$		−	883.385i		−	1.07993i
$819$	0.229561	+	35.4519i	0.000280295	+	0.0432868i
$820$	−2279.77			−2.78020
$821$	−150.881	+	563.097i	−0.183778	+	0.685867i	0.811111	+	0.584892i	$0.198863\pi$
$821$	−150.881	+	563.097i	−0.183778	+	0.685867i	−0.994889	+	0.100976i	$0.967804\pi$
$822$	815.113	+	1411.82i	0.991622	+	1.71754i
$823$	1096.00	+	632.773i	1.33171	+	0.768862i	0.985561	−	0.169319i	$-0.0541567\pi$
$823$	1096.00	+	632.773i	1.33171	+	0.768862i	0.346147	+	0.938180i	$0.387490\pi$
$824$	−2546.58	−	2546.58i	−3.09051	−	3.09051i
$825$	30.8580	−	8.26838i	0.0374036	−	0.0100223i
$826$	13.5821	+	50.6890i	0.0164432	+	0.0613668i
$827$	513.651	−	513.651i	0.621102	−	0.621102i	−0.324712	−	0.945813i	$-0.605267\pi$
$827$	513.651	−	513.651i	0.621102	−	0.621102i	0.945813	+	0.324712i	$0.105267\pi$
$828$	−177.553	+	307.530i	−0.214436	+	0.371414i
$829$	−759.340	+	438.405i	−0.915972	+	0.528836i	−0.882348	−	0.470598i	$-0.844038\pi$
$829$	−759.340	+	438.405i	−0.915972	+	0.528836i	−0.0336239	+	0.999435i	$0.510705\pi$
$830$	−734.748	−	196.875i	−0.885238	−	0.237199i
$831$			732.681i			0.881686i
$832$	−3199.40	+	879.521i	−3.84544	+	1.05712i
$833$	381.558			0.458053
$834$	138.560	−	517.114i	0.166139	−	0.620040i
$835$	−339.978	−	588.860i	−0.407160	−	0.705222i
$836$	1591.40	+	918.796i	1.90359	+	1.09904i
$837$	70.9760	+	70.9760i	0.0847981	+	0.0847981i
$838$	1543.33	−	413.533i	1.84168	−	0.493477i
$839$	122.684	+	457.864i	0.146227	+	0.545726i	0.999698	+	0.0245853i	$0.00782652\pi$
$839$	122.684	+	457.864i	0.146227	+	0.545726i	−0.853471	+	0.521140i	$0.825507\pi$
$840$	141.618	−	141.618i	0.168593	−	0.168593i
$841$	305.975	−	529.964i	0.363822	−	0.630159i
$842$	2452.68	−	1416.06i	2.91292	−	1.68178i
$843$	15.5596	+	4.16919i	0.0184574	+	0.00494566i
$844$			489.818i			0.580353i
$845$	−765.169	−	194.442i	−0.905525	−	0.230109i
$846$	303.848			0.359159
$847$	20.5378	−	76.6482i	0.0242477	−	0.0904938i
$848$	2488.77	+	4310.67i	2.93486	+	5.08334i
$849$	84.7763	+	48.9456i	0.0998543	+	0.0576509i
$850$	−68.9661	−	68.9661i	−0.0811366	−	0.0811366i
$851$	26.4231	−	7.08005i	0.0310495	−	0.00831968i
$852$	481.209	+	1795.89i	0.564799	+	2.10786i
$853$	−703.767	+	703.767i	−0.825049	+	0.825049i	−0.986827	−	0.161778i	$-0.948277\pi$
$853$	−703.767	+	703.767i	−0.825049	+	0.825049i	0.161778	+	0.986827i	$0.448277\pi$
$854$	62.4396	−	108.149i	0.0731143	−	0.126638i
$855$	348.439	−	201.171i	0.407531	−	0.235288i
$856$	−3631.07	−	972.942i	−4.24190	−	1.13661i
$857$		−	12.6753i		−	0.0147903i	−0.999973	−	0.00739514i	$-0.997646\pi$
$857$		−	12.6753i		−	0.0147903i	0.999973	−	0.00739514i	$-0.00235397\pi$
$858$	−134.317	−	488.600i	−0.156547	−	0.569464i
$859$	317.200			0.369266			0.184633	−	0.982808i	$-0.440890\pi$
$859$	317.200			0.369266			0.184633	+	0.982808i	$0.440890\pi$
$860$	−57.5764	+	214.878i	−0.0669493	+	0.249858i
$861$	34.8481	+	60.3588i	0.0404740	+	0.0701031i
$862$	293.334	+	169.357i	0.340295	+	0.196469i
$863$	−26.7486	−	26.7486i	−0.0309949	−	0.0309949i	0.691439	−	0.722434i	$-0.256977\pi$
$863$	−26.7486	−	26.7486i	−0.0309949	−	0.0309949i	−0.722434	+	0.691439i	$0.756977\pi$
$864$	−648.749	+	173.832i	−0.750866	+	0.201194i
$865$	190.896	+	712.435i	0.220690	+	0.823625i
$866$	−856.487	+	856.487i	−0.989015	+	0.989015i
$867$	195.952	−	339.399i	0.226012	−	0.391464i
$868$	−167.659	+	96.7978i	−0.193155	+	0.111518i
$869$	244.943	+	65.6323i	0.281868	+	0.0755262i
$870$			474.666i			0.545593i
$871$	1252.99	−	8.11350i	1.43857	−	0.00931515i
$872$	−1010.68			−1.15903
$873$	104.449	−	389.808i	0.119643	−	0.446516i
$874$	−597.391	−	1034.71i	−0.683514	−	1.18388i
$875$	103.625	+	59.8281i	0.118429	+	0.0683750i
$876$	−71.5493	−	71.5493i	−0.0816773	−	0.0816773i
$877$	−445.096	+	119.263i	−0.507521	+	0.135990i	−0.503488	−	0.864002i	$-0.667950\pi$
$877$	−445.096	+	119.263i	−0.507521	+	0.135990i	−0.00403275	+	0.999992i	$0.501284\pi$
$878$	−132.956	−	496.200i	−0.151431	−	0.565148i
$879$	−251.053	+	251.053i	−0.285612	+	0.285612i
$880$	−833.264	+	1443.26i	−0.946891	+	1.64006i
$881$	1118.08	−	645.522i	1.26910	−	0.732715i	0.294283	−	0.955718i	$-0.404919\pi$
$881$	1118.08	−	645.522i	1.26910	−	0.732715i	0.974818	+	0.223003i	$0.0715860\pi$
$882$	541.100	+	144.987i	0.613492	+	0.164385i
$883$			721.384i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$883$			721.384i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$884$	−797.473	+	807.868i	−0.902118	+	0.913877i
$885$	−120.504			−0.136163
$886$	765.138	−	2855.53i	0.863587	−	3.22295i
$887$	300.489	+	520.463i	0.338770	+	0.586767i	0.984202	−	0.177051i	$-0.0566557\pi$
$887$	300.489	+	520.463i	0.338770	+	0.586767i	−0.645431	+	0.763818i	$0.723322\pi$
$888$	104.062	+	60.0802i	0.117187	+	0.0676578i
$889$	139.874	+	139.874i	0.157339	+	0.157339i
$890$	−491.709	+	131.753i	−0.552482	+	0.148037i
$891$	−13.5240	−	50.4723i	−0.0151785	−	0.0566468i
$892$	2359.24	−	2359.24i	2.64489	−	2.64489i
$893$	−375.076	+	649.650i	−0.420018	+	0.727492i
$894$	−280.715	+	162.071i	−0.313998	+	0.181287i
$895$	−429.945	−	115.203i	−0.480385	−	0.128719i
$896$		−	429.360i		−	0.479197i
$897$	−61.0572	+	233.917i	−0.0680682	+	0.260777i
$898$	1066.80			1.18798
$899$	75.6670	−	282.393i	0.0841680	−	0.314119i
$900$	−52.5357	−	90.9945i	−0.0583730	−	0.101105i
$901$	555.659	+	320.810i	0.616714	+	0.356060i
$902$	−704.400	−	704.400i	−0.780931	−	0.780931i
$903$	6.56918	−	1.76021i	0.00727484	−	0.00194929i
$904$	−1276.02	−	4762.18i	−1.41153	−	5.26790i
$905$	559.098	−	559.098i	0.617788	−	0.617788i
$906$	861.096	−	1491.46i	0.950437	−	1.64621i
$907$	−281.007	+	162.240i	−0.309820	+	0.178875i	−0.646846	−	0.762621i	$-0.723912\pi$
$907$	−281.007	+	162.240i	−0.309820	+	0.178875i	0.337026	+	0.941495i	$0.390579\pi$
$908$	−3335.15	−	893.652i	−3.67308	−	0.984198i
$909$			297.116i			0.326860i
$910$	105.792	−	186.008i	0.116255	−	0.204404i
$911$	−894.435			−0.981817			−0.490908	−	0.871211i	$-0.663335\pi$
$911$	−894.435			−0.981817			−0.490908	+	0.871211i	$0.663335\pi$
$912$	790.788	−	2951.26i	0.867093	−	3.23603i
$913$	−121.947	−	211.218i	−0.133567	−	0.231345i
$914$	−1912.50	−	1104.18i	−2.09245	−	1.20808i
$915$	202.772	+	202.772i	0.221609	+	0.221609i
$916$	1714.92	−	459.512i	1.87219	−	0.501651i
$917$	−37.3590	−	139.426i	−0.0407405	−	0.152046i
$918$	−112.803	+	112.803i	−0.122879	+	0.122879i
$919$	160.850	−	278.600i	0.175027	−	0.303155i	−0.765144	−	0.643860i	$-0.777332\pi$
$919$	160.850	−	278.600i	0.175027	−	0.303155i	0.940171	+	0.340704i	$0.110665\pi$
$920$	1182.74	−	682.855i	1.28559	−	0.742234i
$921$	−50.2676	−	13.4692i	−0.0545794	−	0.0146245i
$922$			528.650i			0.573373i
$923$	639.968	+	1092.06i	0.693356	+	1.18317i
$924$	100.781			0.109070
$925$	−2.09490	+	7.81827i	−0.00226476	+	0.00845219i
$926$	1523.76	+	2639.24i	1.64553	+	2.85015i
$927$	−343.632	−	198.396i	−0.370693	−	0.214020i
$928$	1383.25	+	1383.25i	1.49057	+	1.49057i
$929$	1606.59	−	430.484i	1.72937	−	0.463384i	0.749336	−	0.662190i	$-0.230373\pi$
$929$	1606.59	−	430.484i	1.72937	−	0.463384i	0.980039	+	0.198806i	$0.0637064\pi$
$930$	−156.806	−	585.209i	−0.168609	−	0.629256i
$931$	−977.937	+	977.937i	−1.05042	+	1.05042i
$932$	−1055.55	+	1828.27i	−1.13256	+	1.96166i
$933$	492.022	−	284.069i	0.527355	−	0.304468i
$934$	2563.42	+	686.865i	2.74456	+	0.735402i
$935$			214.821i			0.229755i
$936$	−916.199	+	536.907i	−0.978845	+	0.573619i
$937$	34.1401			0.0364355			0.0182178	−	0.999834i	$-0.494201\pi$
$937$	34.1401			0.0364355			0.0182178	+	0.999834i	$0.494201\pi$
$938$	−87.9018	+	328.054i	−0.0937120	+	0.349738i
$939$	−495.525	−	858.274i	−0.527715	−	0.914030i
$940$	−1165.44	−	672.865i	−1.23983	−	0.715814i
$941$	135.813	+	135.813i	0.144328	+	0.144328i	0.775579	−	0.631251i	$-0.217458\pi$
$941$	135.813	+	135.813i	0.144328	+	0.144328i	−0.631251	+	0.775579i	$0.717458\pi$
$942$	521.257	−	139.670i	0.553351	−	0.148270i
$943$	123.007	+	459.069i	0.130443	+	0.486818i
$944$	−647.076	+	647.076i	−0.685462	+	0.685462i
$945$	11.0330	−	19.1098i	0.0116752	−	0.0202220i
$946$	−84.1827	+	48.6029i	−0.0889881	+	0.0513773i
$947$	−1083.44	−	290.306i	−1.14407	−	0.306554i	−0.363486	−	0.931600i	$-0.618414\pi$
$947$	−1083.44	−	290.306i	−1.14407	−	0.306554i	−0.780588	+	0.625046i	$0.785080\pi$
$948$		−	834.030i		−	0.879779i
$949$	−59.8796	−	34.0564i	−0.0630976	−	0.0358867i
$950$	353.522			0.372128
$951$	−167.263	+	624.235i	−0.175882	+	0.656399i
$952$	−98.0247	−	169.784i	−0.102967	−	0.178344i
$953$	−310.812	−	179.447i	−0.326140	−	0.188297i	0.327986	−	0.944683i	$-0.393630\pi$
$953$	−310.812	−	179.447i	−0.326140	−	0.188297i	−0.654126	+	0.756385i	$0.726963\pi$
$954$	666.094	+	666.094i	0.698212	+	0.698212i
$955$	418.233	−	112.065i	0.437941	−	0.117346i
$956$	698.490	+	2606.80i	0.730638	+	2.72678i
$957$	−107.616	+	107.616i	−0.112452	+	0.112452i
$958$	−1622.00	+	2809.38i	−1.69311	+	2.93255i
$959$	−191.161	+	110.367i	−0.199334	+	0.115085i
$960$	1994.84	+	534.516i	2.07796	+	0.556788i
$961$		−	587.845i		−	0.611701i
$962$	124.224	+	32.4250i	0.129130	+	0.0337058i
$963$	−414.173			−0.430086
$964$	167.432	−	624.866i	0.173685	−	0.648201i
$965$	−751.016	−	1300.80i	−0.778255	−	1.34798i
$966$	−56.7476	−	32.7633i	−0.0587450	−	0.0339164i
$967$	139.945	+	139.945i	0.144721	+	0.144721i	0.775755	−	0.631034i	$-0.217369\pi$
$967$	139.945	+	139.945i	0.144721	+	0.144721i	−0.631034	+	0.775755i	$0.717369\pi$
$968$	2295.88	−	615.178i	2.37177	−	0.635515i
$969$	−101.935	−	380.427i	−0.105196	−	0.392598i
$970$	−1722.39	+	1722.39i	−1.77566	+	1.77566i
$971$	711.780	−	1232.84i	0.733038	−	1.26966i	−0.222541	−	0.974923i	$-0.571435\pi$
$971$	711.780	−	1232.84i	0.733038	−	1.26966i	0.955579	−	0.294736i	$-0.0952316\pi$
$972$	−148.833	+	85.9290i	−0.153121	+	0.0884043i
$973$	70.0175	+	18.7611i	0.0719604	+	0.0192817i
$974$		−	1692.54i		−	1.73773i
$975$	−50.9073	−	50.2522i	−0.0522126	−	0.0515408i
$976$	2177.66			2.23121
$977$	−8.38753	+	31.3027i	−0.00858499	+	0.0320396i	−0.970085	−	0.242764i	$-0.921946\pi$
$977$	−8.38753	+	31.3027i	−0.00858499	+	0.0320396i	0.961500	+	0.274803i	$0.0886127\pi$
$978$	−591.131	−	1023.87i	−0.604428	−	1.04690i
$979$	−141.351	−	81.6092i	−0.144383	−	0.0833598i
$980$	−1754.36	−	1754.36i	−1.79017	−	1.79017i
$981$	−107.559	+	28.8204i	−0.109642	+	0.0293786i
$982$	444.920	+	1660.46i	0.453075	+	1.69090i
$983$	−370.965	+	370.965i	−0.377381	+	0.377381i	−0.870156	−	0.492776i	$-0.835982\pi$
$983$	−370.965	+	370.965i	−0.377381	+	0.377381i	0.492776	+	0.870156i	$0.335982\pi$
$984$	−1043.82	+	1807.95i	−1.06079	+	1.83735i
$985$	−453.370	+	261.753i	−0.460274	+	0.265739i
$986$	448.811	+	120.259i	0.455184	+	0.121966i
$987$			41.1413i			0.0416831i
$988$	−26.6426	−	4114.50i	−0.0269662	−	4.16447i
$989$	46.3759			0.0468917
$990$	−81.6292	+	304.644i	−0.0824537	+	0.307722i
$991$	600.773	+	1040.57i	0.606229	+	1.05002i	0.991856	+	0.127365i	$0.0406518\pi$
$991$	600.773	+	1040.57i	0.606229	+	1.05002i	−0.385627	+	0.922655i	$0.626015\pi$
$992$	−2162.35	−	1248.43i	−2.17979	−	1.25850i
$993$	104.580	+	104.580i	0.105318	+	0.105318i
$994$	−331.391	+	88.7959i	−0.333391	+	0.0893319i
$995$	−82.9992	−	309.757i	−0.0834163	−	0.311314i
$996$	−567.212	+	567.212i	−0.569490	+	0.569490i
$997$	−523.573	+	906.855i	−0.525148	+	0.909584i	0.474423	+	0.880297i	$0.342657\pi$
$997$	−523.573	+	906.855i	−0.525148	+	0.909584i	−0.999571	+	0.0292865i	$0.990676\pi$
$998$	−2154.00	+	1243.61i	−2.15832	+	1.24611i
$999$	12.7878	+	3.42648i	0.0128006	+	0.00342991i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.3.l.b.37.3	yes	12
3.2	odd	2		117.3.bd.d.37.1		12
13.6	odd	12	inner	39.3.l.b.19.3	✓	12
39.32	even	12		117.3.bd.d.19.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.3.l.b.19.3	✓	12	13.6	odd	12	inner
39.3.l.b.37.3	yes	12	1.1	even	1	trivial
117.3.bd.d.19.1		12	39.32	even	12
117.3.bd.d.37.1		12	3.2	odd	2

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:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	39.l (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00323 - 3.74409i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-9.54767 - 5.51235i) q^{4} +(3.30327 + 3.30327i) q^{5} +(6.48496 - 1.73764i) q^{6} +(0.235277 + 0.878067i) q^{7} +(-19.2537 + 19.2537i) q^{8} +(-1.50000 + 2.59808i) q^{9} +O(q^{10})\)	\(q+(1.00323 - 3.74409i) q^{2} +(0.866025 + 1.50000i) q^{3} +(-9.54767 - 5.51235i) q^{4} +(3.30327 + 3.30327i) q^{5} +(6.48496 - 1.73764i) q^{6} +(0.235277 + 0.878067i) q^{7} +(-19.2537 + 19.2537i) q^{8} +(-1.50000 + 2.59808i) q^{9} +(15.6817 - 9.05381i) q^{10} +(5.60803 + 1.50267i) q^{11} -19.0953i q^{12} +(-3.44589 - 12.5350i) q^{13} +3.52360 q^{14} +(-2.09419 + 7.81561i) q^{15} +(30.7226 + 53.2130i) q^{16} +(6.85933 + 3.96024i) q^{17} +(8.22260 + 8.22260i) q^{18} +(-27.7306 + 7.43040i) q^{19} +(-13.3297 - 49.7472i) q^{20} +(-1.11334 + 1.11334i) q^{21} +(11.2522 - 19.4895i) q^{22} +(-9.29823 + 5.36834i) q^{23} +(-45.5549 - 12.2064i) q^{24} -3.17685i q^{25} +(-50.3892 + 0.326284i) q^{26} -5.19615 q^{27} +(2.59386 - 9.68042i) q^{28} +(7.56721 + 13.1068i) q^{29} +(27.1614 + 15.6817i) q^{30} +(-13.6593 - 13.6593i) q^{31} +(124.852 - 33.4539i) q^{32} +(2.60270 + 9.71339i) q^{33} +(21.7090 - 21.7090i) q^{34} +(-2.12331 + 3.67768i) q^{35} +(28.6430 - 16.5370i) q^{36} +(-2.46101 - 0.659427i) q^{37} +111.280i q^{38} +(15.8183 - 16.0244i) q^{39} -127.201 q^{40} +(11.4567 - 42.7572i) q^{41} +(3.05153 + 5.28540i) q^{42} +(-3.74071 - 2.15970i) q^{43} +(-45.2604 - 45.2604i) q^{44} +(-13.5370 + 3.62724i) q^{45} +(10.7713 + 40.1991i) q^{46} +(18.4764 - 18.4764i) q^{47} +(-53.2130 + 92.1677i) q^{48} +(41.7196 - 24.0868i) q^{49} +(-11.8944 - 3.18710i) q^{50} +13.7187i q^{51} +(-36.1970 + 138.675i) q^{52} +81.0078 q^{53} +(-5.21292 + 19.4549i) q^{54} +(13.5611 + 23.4885i) q^{55} +(-21.4361 - 12.3761i) q^{56} +(-35.1610 - 35.1610i) q^{57} +(56.6647 - 15.1832i) q^{58} +(3.85460 + 14.3856i) q^{59} +(63.0770 - 63.0770i) q^{60} +(17.7204 - 30.6926i) q^{61} +(-64.8452 + 37.4384i) q^{62} +(-2.63420 - 0.705832i) q^{63} -255.238i q^{64} +(30.0237 - 52.7891i) q^{65} +38.9789 q^{66} +(-24.9466 + 93.1019i) q^{67} +(-43.6604 - 75.6220i) q^{68} +(-16.1050 - 9.29823i) q^{69} +(11.6394 + 11.6394i) q^{70} +(-94.0489 + 25.2003i) q^{71} +(-21.1421 - 78.9033i) q^{72} +(3.74695 - 3.74695i) q^{73} +(-4.93791 + 8.55271i) q^{74} +(4.76528 - 2.75123i) q^{75} +(305.722 + 81.9179i) q^{76} +5.27777i q^{77} +(-44.1277 - 75.3012i) q^{78} +43.6772 q^{79} +(-74.2920 + 277.262i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-148.593 - 85.7902i) q^{82} +(-29.7042 - 29.7042i) q^{83} +(16.7670 - 4.49270i) q^{84} +(9.57649 + 35.7399i) q^{85} +(-11.8389 + 11.8389i) q^{86} +(-13.1068 + 22.7016i) q^{87} +(-136.908 + 79.0436i) q^{88} +(-27.1548 - 7.27610i) q^{89} +54.3229i q^{90} +(10.1958 - 5.97492i) q^{91} +118.369 q^{92} +(8.65967 - 32.3183i) q^{93} +(-50.6414 - 87.7135i) q^{94} +(-116.146 - 67.0571i) q^{95} +(158.306 + 158.306i) q^{96} +(-129.936 + 34.8163i) q^{97} +(-48.3291 - 180.367i) q^{98} +(-12.3161 + 12.3161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9}+O(q^{10}) \) 12 * q - 2 * q^2 - 12 * q^4 + 4 * q^5 + 6 * q^6 - 32 * q^7 - 24 * q^8 - 18 * q^9	\( 12 q - 2 q^{2} - 12 q^{4} + 4 q^{5} + 6 q^{6} - 32 q^{7} - 24 q^{8} - 18 q^{9} + 30 q^{10} + 22 q^{11} + 2 q^{13} + 92 q^{14} + 52 q^{16} - 6 q^{17} + 12 q^{18} + 4 q^{19} - 208 q^{20} + 54 q^{21} - 98 q^{22} - 18 q^{23} - 54 q^{24} - 44 q^{26} - 78 q^{28} + 128 q^{29} + 6 q^{30} - 66 q^{31} + 358 q^{32} - 6 q^{33} + 336 q^{34} + 14 q^{35} + 36 q^{36} - 36 q^{37} - 18 q^{39} - 12 q^{40} - 326 q^{41} - 6 q^{42} + 60 q^{43} - 236 q^{44} - 24 q^{45} - 138 q^{46} + 40 q^{47} - 144 q^{48} + 78 q^{49} - 40 q^{50} - 392 q^{52} + 80 q^{53} - 18 q^{54} + 166 q^{55} - 102 q^{56} + 250 q^{58} - 164 q^{59} + 396 q^{60} - 98 q^{61} + 228 q^{62} + 66 q^{63} + 514 q^{65} + 60 q^{66} - 230 q^{67} + 78 q^{68} - 54 q^{69} - 92 q^{70} + 70 q^{71} - 18 q^{72} + 106 q^{73} - 16 q^{74} - 150 q^{75} + 534 q^{76} - 456 q^{78} + 16 q^{79} + 124 q^{80} - 54 q^{81} - 156 q^{82} - 176 q^{83} - 30 q^{84} + 90 q^{85} - 612 q^{86} + 48 q^{87} - 318 q^{88} - 476 q^{89} + 106 q^{91} + 228 q^{92} + 66 q^{93} - 374 q^{94} - 234 q^{95} + 384 q^{96} - 306 q^{97} - 350 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q - 2 * q^2 - 12 * q^4 + 4 * q^5 + 6 * q^6 - 32 * q^7 - 24 * q^8 - 18 * q^9 + 30 * q^10 + 22 * q^11 + 2 * q^13 + 92 * q^14 + 52 * q^16 - 6 * q^17 + 12 * q^18 + 4 * q^19 - 208 * q^20 + 54 * q^21 - 98 * q^22 - 18 * q^23 - 54 * q^24 - 44 * q^26 - 78 * q^28 + 128 * q^29 + 6 * q^30 - 66 * q^31 + 358 * q^32 - 6 * q^33 + 336 * q^34 + 14 * q^35 + 36 * q^36 - 36 * q^37 - 18 * q^39 - 12 * q^40 - 326 * q^41 - 6 * q^42 + 60 * q^43 - 236 * q^44 - 24 * q^45 - 138 * q^46 + 40 * q^47 - 144 * q^48 + 78 * q^49 - 40 * q^50 - 392 * q^52 + 80 * q^53 - 18 * q^54 + 166 * q^55 - 102 * q^56 + 250 * q^58 - 164 * q^59 + 396 * q^60 - 98 * q^61 + 228 * q^62 + 66 * q^63 + 514 * q^65 + 60 * q^66 - 230 * q^67 + 78 * q^68 - 54 * q^69 - 92 * q^70 + 70 * q^71 - 18 * q^72 + 106 * q^73 - 16 * q^74 - 150 * q^75 + 534 * q^76 - 456 * q^78 + 16 * q^79 + 124 * q^80 - 54 * q^81 - 156 * q^82 - 176 * q^83 - 30 * q^84 + 90 * q^85 - 612 * q^86 + 48 * q^87 - 318 * q^88 - 476 * q^89 + 106 * q^91 + 228 * q^92 + 66 * q^93 - 374 * q^94 - 234 * q^95 + 384 * q^96 - 306 * q^97 - 350 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more