LMFDB - Embedded newform 338.4.e.f.147.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(23,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (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:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.45979465625856.49
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 109x^{6} + 8965x^{4} - 317844x^{2} + 8503056 $ x^8 - 109x^6 + 8965x^4 - 317844*x^2 + 8503056
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 26)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			147.2
Root			$-6.81169 + 3.93273i$ of defining polynomial
Character	$\chi$	$=$	338.147
Dual form			338.4.e.f.23.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{2} +(4.43273 - 7.67771i) q^{3} +(2.00000 + 3.46410i) q^{4} +3.86546i q^{5} +(-15.3554 + 8.86546i) q^{6} +(13.1069 - 7.56727i) q^{7} -8.00000i q^{8} +(-25.7982 - 44.6838i) q^{9} +O(q^{10})$	\(q+(-1.73205 - 1.00000i) q^{2} +(4.43273 - 7.67771i) q^{3} +(2.00000 + 3.46410i) q^{4} +3.86546i q^{5} +(-15.3554 + 8.86546i) q^{6} +(13.1069 - 7.56727i) q^{7} -8.00000i q^{8} +(-25.7982 - 44.6838i) q^{9} +(3.86546 - 6.69517i) q^{10} +(46.8158 + 27.0291i) q^{11} +35.4618 q^{12} -30.2691 q^{14} +(29.6779 + 17.1345i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-61.9618 - 107.321i) q^{17} +103.193i q^{18} +(7.67771 - 4.43273i) q^{19} +(-13.3903 + 7.73092i) q^{20} -134.175i q^{21} +(-54.0582 - 93.6316i) q^{22} +(19.2982 - 33.4254i) q^{23} +(-61.4217 - 35.4618i) q^{24} +110.058 q^{25} -218.058 q^{27} +(52.4276 + 30.2691i) q^{28} +(93.6928 - 162.281i) q^{29} +(-34.2691 - 59.3558i) q^{30} -36.7710i q^{31} +(27.7128 - 16.0000i) q^{32} +(415.044 - 239.625i) q^{33} +247.847i q^{34} +(29.2510 + 50.6642i) q^{35} +(103.193 - 178.735i) q^{36} +(-278.460 - 160.769i) q^{37} -17.7309 q^{38} +30.9237 q^{40} +(22.7844 + 13.1546i) q^{41} +(-134.175 + 232.397i) q^{42} +(68.8182 + 119.197i) q^{43} +216.233i q^{44} +(172.723 - 99.7219i) q^{45} +(-66.8509 + 38.5964i) q^{46} +300.466i q^{47} +(70.9237 + 122.843i) q^{48} +(-56.9728 + 98.6799i) q^{49} +(-190.626 - 110.058i) q^{50} -1098.64 q^{51} -260.135 q^{53} +(377.688 + 218.058i) q^{54} +(-104.480 + 180.965i) q^{55} +(-60.5382 - 104.855i) q^{56} -78.5964i q^{57} +(-324.561 + 187.386i) q^{58} +(213.093 - 123.029i) q^{59} +137.076i q^{60} +(-45.6526 - 79.0727i) q^{61} +(-36.7710 + 63.6893i) q^{62} +(-676.268 - 390.444i) q^{63} -64.0000 q^{64} -958.502 q^{66} +(-355.524 - 205.262i) q^{67} +(247.847 - 429.284i) q^{68} +(-171.087 - 296.332i) q^{69} -117.004i q^{70} +(-367.579 + 212.222i) q^{71} +(-357.470 + 206.386i) q^{72} +421.982i q^{73} +(321.538 + 556.920i) q^{74} +(487.858 - 844.995i) q^{75} +(30.7109 + 17.7309i) q^{76} +818.146 q^{77} +733.542 q^{79} +(-53.5614 - 30.9237i) q^{80} +(-270.042 + 467.727i) q^{81} +(-26.3092 - 45.5689i) q^{82} -616.843i q^{83} +(464.795 - 268.349i) q^{84} +(414.845 - 239.511i) q^{85} -275.273i q^{86} +(-830.629 - 1438.69i) q^{87} +(216.233 - 374.526i) q^{88} +(-179.415 - 103.585i) q^{89} -398.887 q^{90} +154.386 q^{92} +(-282.317 - 162.996i) q^{93} +(300.466 - 520.422i) q^{94} +(17.1345 + 29.6779i) q^{95} -283.695i q^{96} +(-642.144 + 370.742i) q^{97} +(197.360 - 113.946i) q^{98} -2789.21i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 6 q^{3} + 16 q^{4} - 118 q^{9}+O(q^{10}) $ 8 * q + 6 * q^3 + 16 * q^4 - 118 * q^9	$ 8 q + 6 q^{3} + 16 q^{4} - 118 q^{9} - 28 q^{10} + 48 q^{12} - 360 q^{14} - 64 q^{16} - 260 q^{17} - 20 q^{22} + 66 q^{23} + 468 q^{25} - 1332 q^{27} + 396 q^{29} - 392 q^{30} - 532 q^{35} + 472 q^{36} - 24 q^{38} - 224 q^{40} + 164 q^{42} - 186 q^{43} + 96 q^{48} + 870 q^{49} - 4252 q^{51} - 2140 q^{53} - 1484 q^{55} - 720 q^{56} - 1308 q^{61} + 1120 q^{62} - 512 q^{64} - 6136 q^{66} + 1040 q^{68} - 750 q^{69} + 2808 q^{74} + 1870 q^{75} - 2588 q^{77} + 3040 q^{79} + 668 q^{81} + 968 q^{82} - 3198 q^{87} + 80 q^{88} - 952 q^{90} + 528 q^{92} - 896 q^{94} + 196 q^{95}+O(q^{100}) $ 8 * q + 6 * q^3 + 16 * q^4 - 118 * q^9 - 28 * q^10 + 48 * q^12 - 360 * q^14 - 64 * q^16 - 260 * q^17 - 20 * q^22 + 66 * q^23 + 468 * q^25 - 1332 * q^27 + 396 * q^29 - 392 * q^30 - 532 * q^35 + 472 * q^36 - 24 * q^38 - 224 * q^40 + 164 * q^42 - 186 * q^43 + 96 * q^48 + 870 * q^49 - 4252 * q^51 - 2140 * q^53 - 1484 * q^55 - 720 * q^56 - 1308 * q^61 + 1120 * q^62 - 512 * q^64 - 6136 * q^66 + 1040 * q^68 - 750 * q^69 + 2808 * q^74 + 1870 * q^75 - 2588 * q^77 + 3040 * q^79 + 668 * q^81 + 968 * q^82 - 3198 * q^87 + 80 * q^88 - 952 * q^90 + 528 * q^92 - 896 * q^94 + 196 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	4.43273	−	7.67771i	0.853079	−	1.47758i	−0.0253362	−	0.999679i	$-0.508066\pi$
$3$	4.43273	−	7.67771i	0.853079	−	1.47758i	0.878416	−	0.477898i	$-0.158601\pi$
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$			3.86546i			0.345737i	0.984945	+	0.172869i	$0.0553036\pi$
$5$			3.86546i			0.345737i	−0.984945	+	0.172869i	$0.944696\pi$
$6$	−15.3554	+	8.86546i	−1.04480	+	0.603218i
$7$	13.1069	−	7.56727i	0.707706	−	0.408594i	−0.102505	−	0.994732i	$-0.532686\pi$
$7$	13.1069	−	7.56727i	0.707706	−	0.408594i	0.810211	+	0.586138i	$0.199352\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−25.7982	−	44.6838i	−0.955489	−	1.65495i
$10$	3.86546	−	6.69517i	0.122237	−	0.211720i
$11$	46.8158	+	27.0291i	1.28323	+	0.740871i	0.977437	−	0.211228i	$-0.0677462\pi$
$11$	46.8158	+	27.0291i	1.28323	+	0.740871i	0.305790	+	0.952099i	$0.401080\pi$
$12$	35.4618			0.853079
$13$		0			0
$13$		0			0
$14$	−30.2691			−0.577839
$15$	29.6779	+	17.1345i	0.510853	+	0.294941i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−61.9618	−	107.321i	−0.883997	−	1.53113i	−0.846859	−	0.531818i	$-0.821509\pi$
$17$	−61.9618	−	107.321i	−0.883997	−	1.53113i	−0.0371386	−	0.999310i	$-0.511824\pi$
$18$			103.193i			1.35126i
$19$	7.67771	−	4.43273i	0.0927046	−	0.0535231i	−0.452931	−	0.891546i	$-0.649622\pi$
$19$	7.67771	−	4.43273i	0.0927046	−	0.0535231i	0.545636	+	0.838023i	$0.316288\pi$
$20$	−13.3903	+	7.73092i	−0.149709	+	0.0864343i
$21$		−	134.175i		−	1.39425i
$22$	−54.0582	−	93.6316i	−0.523875	−	0.907378i
$23$	19.2982	−	33.4254i	0.174954	−	0.303030i	−0.765191	−	0.643803i	$-0.777356\pi$
$23$	19.2982	−	33.4254i	0.174954	−	0.303030i	0.940145	+	0.340773i	$0.110689\pi$
$24$	−61.4217	−	35.4618i	−0.522402	−	0.301609i
$25$	110.058			0.880466
$26$		0			0
$27$	−218.058			−1.55427
$28$	52.4276	+	30.2691i	0.353853	+	0.204297i
$29$	93.6928	−	162.281i	0.599942	−	1.03913i	−0.392887	−	0.919587i	$-0.628524\pi$
$29$	93.6928	−	162.281i	0.599942	−	1.03913i	0.992829	−	0.119543i	$-0.0381429\pi$
$30$	−34.2691	−	59.3558i	−0.208555	−	0.361228i
$31$		−	36.7710i		−	0.213041i	−0.994311	−	0.106521i	$-0.966029\pi$
$31$		−	36.7710i		−	0.213041i	0.994311	−	0.106521i	$-0.0339710\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	415.044	−	239.625i	2.18939	−	1.26404i
$34$			247.847i			1.25016i
$35$	29.2510	+	50.6642i	0.141266	+	0.244680i
$36$	103.193	−	178.735i	0.477744	−	0.827477i
$37$	−278.460	−	160.769i	−1.23726	−	0.714332i	−0.268726	−	0.963217i	$-0.586603\pi$
$37$	−278.460	−	160.769i	−1.23726	−	0.714332i	−0.968533	+	0.248885i	$0.919936\pi$
$38$	−17.7309			−0.0756930
$39$		0			0
$40$	30.9237			0.122237
$41$	22.7844	+	13.1546i	0.0867886	+	0.0501074i	0.542766	−	0.839884i	$-0.317377\pi$
$41$	22.7844	+	13.1546i	0.0867886	+	0.0501074i	−0.455978	+	0.889991i	$0.650710\pi$
$42$	−134.175	+	232.397i	−0.492943	+	0.853802i
$43$	68.8182	+	119.197i	0.244062	+	0.422729i	0.961868	−	0.273515i	$-0.0881865\pi$
$43$	68.8182	+	119.197i	0.244062	+	0.422729i	−0.717805	+	0.696244i	$0.754853\pi$
$44$			216.233i			0.740871i
$45$	172.723	−	99.7219i	0.572179	−	0.330348i
$46$	−66.8509	+	38.5964i	−0.214274	+	0.123711i
$47$			300.466i			0.932499i	0.884653	+	0.466249i	$0.154395\pi$
$47$			300.466i			0.932499i	−0.884653	+	0.466249i	$0.845605\pi$
$48$	70.9237	+	122.843i	0.213270	+	0.369394i
$49$	−56.9728	+	98.6799i	−0.166102	+	0.287696i
$50$	−190.626	−	110.058i	−0.539173	−	0.311292i
$51$	−1098.64			−3.01648
$52$		0			0
$53$	−260.135			−0.674193			−0.337096	−	0.941470i	$-0.609445\pi$
$53$	−260.135			−0.674193			−0.337096	+	0.941470i	$0.609445\pi$
$54$	377.688	+	218.058i	0.951793	+	0.549518i
$55$	−104.480	+	180.965i	−0.256147	+	0.443659i
$56$	−60.5382	−	104.855i	−0.144460	−	0.250212i
$57$		−	78.5964i		−	0.182638i
$58$	−324.561	+	187.386i	−0.734775	+	0.424223i
$59$	213.093	−	123.029i	0.470209	−	0.271475i	−0.246118	−	0.969240i	$-0.579155\pi$
$59$	213.093	−	123.029i	0.470209	−	0.271475i	0.716327	+	0.697765i	$0.245822\pi$
$60$			137.076i			0.294941i
$61$	−45.6526	−	79.0727i	−0.0958233	−	0.165971i	0.814129	−	0.580685i	$-0.197215\pi$
$61$	−45.6526	−	79.0727i	−0.0958233	−	0.165971i	−0.909952	+	0.414714i	$0.863882\pi$
$62$	−36.7710	+	63.6893i	−0.0753214	+	0.130460i
$63$	−676.268	−	390.444i	−1.35241	−	0.780814i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−958.502			−1.78763
$67$	−355.524	−	205.262i	−0.648272	−	0.374280i	0.139522	−	0.990219i	$-0.455443\pi$
$67$	−355.524	−	205.262i	−0.648272	−	0.374280i	−0.787794	+	0.615939i	$0.788777\pi$
$68$	247.847	−	429.284i	0.441999	−	0.765564i
$69$	−171.087	−	296.332i	−0.298500	−	0.517017i
$70$		−	117.004i		−	0.199781i
$71$	−367.579	+	212.222i	−0.614417	+	0.354734i	−0.774692	−	0.632339i	$-0.782095\pi$
$71$	−367.579	+	212.222i	−0.614417	+	0.354734i	0.160275	+	0.987072i	$0.448762\pi$
$72$	−357.470	+	206.386i	−0.585115	+	0.337816i
$73$			421.982i			0.676565i	0.941045	+	0.338283i	$0.109846\pi$
$73$			421.982i			0.676565i	−0.941045	+	0.338283i	$0.890154\pi$
$74$	321.538	+	556.920i	0.505109	+	0.874874i
$75$	487.858	−	844.995i	0.751107	−	1.30096i
$76$	30.7109	+	17.7309i	0.0463523	+	0.0267615i
$77$	818.146			1.21086
$78$		0			0
$79$	733.542			1.04468			0.522341	−	0.852736i	$-0.325059\pi$
$79$	733.542			1.04468			0.522341	+	0.852736i	$0.325059\pi$
$80$	−53.5614	−	30.9237i	−0.0748543	−	0.0432172i
$81$	−270.042	+	467.727i	−0.370428	+	0.641600i
$82$	−26.3092	−	45.5689i	−0.0354313	−	0.0613688i
$83$		−	616.843i		−	0.815751i	−0.913037	−	0.407876i	$-0.866270\pi$
$83$		−	616.843i		−	0.815751i	0.913037	−	0.407876i	$-0.133730\pi$
$84$	464.795	−	268.349i	0.603729	−	0.348563i
$85$	414.845	−	239.511i	0.529368	−	0.305631i
$86$		−	275.273i		−	0.345156i
$87$	−830.629	−	1438.69i	−1.02360	−	1.77292i
$88$	216.233	−	374.526i	0.261938	−	0.453689i
$89$	−179.415	−	103.585i	−0.213685	−	0.123371i	0.389338	−	0.921095i	$-0.372704\pi$
$89$	−179.415	−	103.585i	−0.213685	−	0.123371i	−0.603023	+	0.797724i	$0.706037\pi$
$90$	−398.887			−0.467183
$91$		0			0
$92$	154.386			0.174954
$93$	−282.317	−	162.996i	−0.314785	−	0.181741i
$94$	300.466	−	520.422i	0.329688	−	0.571036i
$95$	17.1345	+	29.6779i	0.0185049	+	0.0320514i
$96$		−	283.695i		−	0.301609i
$97$	−642.144	+	370.742i	−0.672163	+	0.388074i	−0.796896	−	0.604117i	$-0.793526\pi$
$97$	−642.144	+	370.742i	−0.672163	+	0.388074i	0.124733	+	0.992190i	$0.460193\pi$
$98$	197.360	−	113.946i	0.203432	−	0.117452i
$99$		−	2789.21i		−	2.83158i
$100$	220.116	+	381.253i	0.220116	+	0.381253i
$101$	−206.653	+	357.933i	−0.203591	+	0.352630i	−0.949683	−	0.313213i	$-0.898595\pi$
$101$	−206.653	+	357.933i	−0.203591	+	0.352630i	0.746092	+	0.665843i	$0.231928\pi$
$102$	1902.90	+	1098.64i	1.84721	+	1.06649i
$103$	3.76712			0.00360374			0.00180187	−	0.999998i	$-0.499426\pi$
$103$	3.76712			0.00360374			0.00180187	+	0.999998i	$0.499426\pi$
$104$		0			0
$105$	518.647			0.482045
$106$	450.566	+	260.135i	0.412857	+	0.238363i
$107$	−56.9127	+	98.5756i	−0.0514201	+	0.0890623i	−0.890590	−	0.454807i	$-0.849708\pi$
$107$	−56.9127	+	98.5756i	−0.0514201	+	0.0890623i	0.839170	+	0.543870i	$0.183041\pi$
$108$	−436.116	−	755.376i	−0.388568	−	0.673019i
$109$			1935.63i			1.70092i	0.526044	+	0.850458i	$0.323675\pi$
$109$			1935.63i			1.70092i	−0.526044	+	0.850458i	$0.676325\pi$
$110$	361.929	−	208.960i	0.313714	−	0.181123i
$111$	−2468.68	+	1425.29i	−2.11096	+	1.21876i
$112$			242.153i			0.204297i
$113$	−949.391	−	1644.39i	−0.790365	−	1.36895i	−0.925741	−	0.378158i	$-0.876558\pi$
$113$	−949.391	−	1644.39i	−0.790365	−	1.36895i	0.135376	−	0.990794i	$-0.456776\pi$
$114$	−78.5964	+	136.133i	−0.0645722	+	0.111842i
$115$	129.205	+	74.5964i	0.104769	+	0.0604882i
$116$	749.542			0.599942
$117$		0			0
$118$	−492.116			−0.383924
$119$	−1624.25	−	937.764i	−1.25122	−	0.722392i
$120$	137.076	−	237.423i	0.104277	−	0.180614i
$121$	795.646	+	1378.10i	0.597780	+	1.03539i
$122$			182.611i			0.135515i
$123$	201.994	−	116.622i	0.148075	−	0.0854912i
$124$	127.379	−	73.5421i	0.0922495	−	0.0532603i
$125$			908.608i			0.650147i
$126$	780.887	+	1352.54i	0.552119	+	0.956298i
$127$	122.302	−	211.833i	0.0854532	−	0.148009i	−0.820131	−	0.572176i	$-0.806100\pi$
$127$	122.302	−	211.833i	0.0854532	−	0.148009i	0.905584	+	0.424166i	$0.139433\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	1220.21			0.832818
$130$		0			0
$131$	1615.62			1.07754			0.538769	−	0.842453i	$-0.318889\pi$
$131$	1615.62			1.07754			0.538769	+	0.842453i	$0.318889\pi$
$132$	1660.17	+	958.502i	1.09469	+	0.632022i
$133$	67.0873	−	116.199i	0.0437384	−	0.0757572i
$134$	410.524	+	711.048i	0.264656	+	0.458397i
$135$		−	842.895i		−	0.537369i
$136$	−858.568	+	495.695i	−0.541336	+	0.312540i
$137$	1993.54	−	1150.97i	1.24321	−	0.717769i	0.273465	−	0.961882i	$-0.411830\pi$
$137$	1993.54	−	1150.97i	1.24321	−	0.717769i	0.969747	+	0.244113i	$0.0784969\pi$
$138$			684.349i			0.422143i
$139$	1404.53	+	2432.73i	0.857058	+	1.48447i	0.874722	+	0.484625i	$0.161044\pi$
$139$	1404.53	+	2432.73i	0.857058	+	1.48447i	−0.0176640	+	0.999844i	$0.505623\pi$
$140$	−117.004	+	202.657i	−0.0706331	+	0.122340i
$141$	2306.89	+	1331.88i	1.37784	+	0.795495i
$142$	848.887			0.501669
$143$		0			0
$144$	825.542			0.477744
$145$	627.289	+	362.166i	0.359266	+	0.207422i
$146$	421.982	−	730.894i	0.239202	−	0.414310i
$147$	505.091	+	874.842i	0.283396	+	0.490856i
$148$		−	1286.15i		−	0.714332i
$149$	2193.79	−	1266.58i	1.20619	−	0.696393i	0.244264	−	0.969709i	$-0.421454\pi$
$149$	2193.79	−	1266.58i	1.20619	−	0.696393i	0.961925	+	0.273315i	$0.0881202\pi$
$150$	−1689.99	+	975.717i	−0.919915	+	0.531113i
$151$			2391.10i			1.28864i	0.764755	+	0.644321i	$0.222860\pi$
$151$			2391.10i			1.28864i	−0.764755	+	0.644321i	$0.777140\pi$
$152$	−35.4618	−	61.4217i	−0.0189233	−	0.0327760i
$153$	−3197.01	+	5537.38i	−1.68930	+	2.92595i
$154$	−1417.07	−	818.146i	−0.741499	−	0.428105i
$155$	142.137			0.0736562
$156$		0			0
$157$	1927.49			0.979811			0.489905	−	0.871776i	$-0.337031\pi$
$157$	1927.49			0.979811			0.489905	+	0.871776i	$0.337031\pi$
$158$	−1270.53	−	733.542i	−0.639735	−	0.369351i
$159$	−1153.11	+	1997.24i	−0.575140	+	0.996172i
$160$	61.8474	+	107.123i	0.0305591	+	0.0529300i
$161$		−	584.138i		−	0.285941i
$162$	935.453	−	540.084i	0.453680	−	0.261932i
$163$	1921.30	−	1109.26i	0.923237	−	0.533031i	0.0385709	−	0.999256i	$-0.487719\pi$
$163$	1921.30	−	1109.26i	0.923237	−	0.533031i	0.884666	+	0.466225i	$0.154386\pi$
$164$			105.237i			0.0501074i
$165$	926.263	+	1604.33i	0.437027	+	0.756953i
$166$	−616.843	+	1068.40i	−0.288412	+	0.499544i
$167$	−1306.20	−	754.135i	−0.605251	−	0.349442i	0.165854	−	0.986150i	$-0.446962\pi$
$167$	−1306.20	−	754.135i	−0.605251	−	0.349442i	−0.771104	+	0.636709i	$0.780295\pi$
$168$	−1073.40			−0.492943
$169$		0			0
$170$	−958.044			−0.432227
$171$	−396.142	−	228.713i	−0.177156	−	0.102281i
$172$	−275.273	+	476.787i	−0.122031	+	0.211364i
$173$	−853.236	−	1477.85i	−0.374973	−	0.649472i	0.615350	−	0.788254i	$-0.289015\pi$
$173$	−853.236	−	1477.85i	−0.374973	−	0.649472i	−0.990323	+	0.138782i	$0.955681\pi$
$174$			3322.52i			1.44758i
$175$	1442.52	−	832.840i	0.623111	−	0.359753i
$176$	−749.053	+	432.466i	−0.320807	+	0.185218i
$177$		−	2181.42i		−	0.926359i
$178$	207.171	+	358.830i	0.0872365	+	0.151098i
$179$	297.611	−	515.478i	0.124271	−	0.215244i	−0.797177	−	0.603746i	$-0.793674\pi$
$179$	297.611	−	515.478i	0.124271	−	0.215244i	0.921448	+	0.388502i	$0.127007\pi$
$180$	690.893	+	398.887i	0.286090	+	0.165174i
$181$	−403.006			−0.165498			−0.0827492	−	0.996570i	$-0.526370\pi$
$181$	−403.006			−0.165498			−0.0827492	+	0.996570i	$0.526370\pi$
$182$		0			0
$183$	−809.463			−0.326980
$184$	−267.404	−	154.386i	−0.107137	−	0.0618557i
$185$	621.446	−	1076.38i	0.246971	−	0.427766i
$186$	325.992	+	564.635i	0.128510	+	0.222586i
$187$		−	6699.09i		−	2.61971i
$188$	−1040.84	+	600.932i	−0.403784	+	0.233125i
$189$	−2858.07	+	1650.11i	−1.09997	+	0.635066i
$190$		−	68.5382i		−	0.0261699i
$191$	306.848	+	531.476i	0.116245	+	0.201342i	0.918277	−	0.395939i	$-0.129581\pi$
$191$	306.848	+	531.476i	0.116245	+	0.201342i	−0.802032	+	0.597281i	$0.796248\pi$
$192$	−283.695	+	491.374i	−0.106635	+	0.184697i
$193$	1736.67	+	1002.66i	0.647709	+	0.373955i	0.787578	−	0.616215i	$-0.211335\pi$
$193$	1736.67	+	1002.66i	0.647709	+	0.373955i	−0.139869	+	0.990170i	$0.544668\pi$
$194$	1482.97			0.548819
$195$		0			0
$196$	−455.783			−0.166102
$197$	482.809	+	278.750i	0.174613	+	0.100813i	0.584759	−	0.811207i	$-0.301189\pi$
$197$	482.809	+	278.750i	0.174613	+	0.100813i	−0.410146	+	0.912020i	$0.634522\pi$
$198$	−2789.21	+	4831.05i	−1.00111	+	1.73398i
$199$	2766.99	+	4792.56i	0.985661	+	1.70721i	0.638963	+	0.769237i	$0.279364\pi$
$199$	2766.99	+	4792.56i	0.985661	+	1.70721i	0.346698	+	0.937977i	$0.387303\pi$
$200$		−	880.466i		−	0.311292i
$201$	−3151.89	+	1819.74i	−1.10605	+	0.638581i
$202$	715.866	−	413.305i	0.249347	−	0.143961i
$203$		−	2835.99i		−	0.980531i
$204$	−2197.28	−	3805.80i	−0.754120	−	1.30617i
$205$	−50.8486	+	88.0723i	−0.0173240	+	0.0300060i
$206$	−6.52485	−	3.76712i	−0.00220683	−	0.00127412i
$207$	−1991.43			−0.668668
$208$		0			0
$209$	479.251			0.158615
$210$	−898.323	−	518.647i	−0.295191	−	0.170429i
$211$	2341.87	−	4056.23i	0.764079	−	1.32342i	−0.176653	−	0.984273i	$-0.556527\pi$
$211$	2341.87	−	4056.23i	0.764079	−	1.32342i	0.940732	−	0.339151i	$-0.110140\pi$
$212$	−520.269	−	901.132i	−0.168548	−	0.291934i
$213$			3762.89i			1.21046i
$214$	197.151	−	113.825i	0.0629766	−	0.0363595i
$215$	−460.750	+	266.014i	−0.146153	+	0.0843815i
$216$			1744.47i			0.549518i
$217$	−278.256	−	481.954i	−0.0870473	−	0.150770i
$218$	1935.63	−	3352.61i	0.601364	−	1.04159i
$219$	3239.86	+	1870.53i	0.999677	+	0.577164i
$220$	−835.840			−0.256147
$221$		0			0
$222$	5701.17			1.72359
$223$	2064.48	+	1191.93i	0.619947	+	0.357926i	0.776848	−	0.629688i	$-0.216817\pi$
$223$	2064.48	+	1191.93i	0.619947	+	0.357926i	−0.156902	+	0.987614i	$0.550151\pi$
$224$	242.153	−	419.421i	0.0722299	−	0.125106i
$225$	−2839.30	−	4917.82i	−0.841275	−	1.45713i
$226$			3797.57i			1.11774i
$227$	−1345.87	+	777.037i	−0.393517	+	0.227197i	−0.683683	−	0.729779i	$-0.739623\pi$
$227$	−1345.87	+	777.037i	−0.393517	+	0.227197i	0.290166	+	0.956976i	$0.406290\pi$
$228$	272.266	−	157.193i	0.0790844	−	0.0456594i
$229$			2915.60i			0.841346i	0.907212	+	0.420673i	$0.138206\pi$
$229$			2915.60i			0.841346i	−0.907212	+	0.420673i	$0.861794\pi$
$230$	−149.193	−	258.409i	−0.0427716	−	0.0740827i
$231$	3626.62	−	6281.49i	1.03296	−	1.78914i
$232$	−1298.24	−	749.542i	−0.367388	−	0.212111i
$233$	4233.93			1.19045			0.595223	−	0.803561i	$-0.297064\pi$
$233$	4233.93			1.19045			0.595223	+	0.803561i	$0.297064\pi$
$234$		0			0
$235$	−1161.44			−0.322400
$236$	852.371	+	492.116i	0.235104	+	0.135738i
$237$	3251.59	−	5631.93i	0.891197	−	1.54360i
$238$	1875.53	+	3248.51i	0.510808	+	0.884746i
$239$			2372.55i			0.642124i	0.947058	+	0.321062i	$0.104040\pi$
$239$			2372.55i			0.642124i	−0.947058	+	0.321062i	$0.895960\pi$
$240$	−474.846	+	274.153i	−0.127713	+	0.0737353i
$241$	−282.119	+	162.882i	−0.0754062	+	0.0435358i	−0.537229	−	0.843436i	$-0.680529\pi$
$241$	−282.119	+	162.882i	−0.0754062	+	0.0435358i	0.461823	+	0.886972i	$0.347196\pi$
$242$		−	3182.58i		−	0.845389i
$243$	−549.739	−	952.175i	−0.145127	−	0.251367i
$244$	182.611	−	316.291i	0.0479117	−	0.0829854i
$245$	−381.443	−	220.226i	−0.0994674	−	0.0574275i
$246$	−466.486			−0.120903
$247$		0			0
$248$	−294.168			−0.0753214
$249$	−4735.95	−	2734.30i	−1.20534	−	0.695901i
$250$	908.608	−	1573.76i	0.229862	−	0.398132i
$251$	−1300.88	−	2253.20i	−0.327136	−	0.566616i	0.654806	−	0.755797i	$-0.272750\pi$
$251$	−1300.88	−	2253.20i	−0.327136	−	0.566616i	−0.981942	+	0.189181i	$0.939417\pi$
$252$		−	3123.55i		−	0.780814i
$253$	1806.92	−	1043.23i	0.449012	−	0.259237i
$254$	−423.667	+	244.604i	−0.104658	+	0.0604245i
$255$		−	4246.75i		−	1.04291i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	2108.55	−	3652.11i	0.511781	−	0.886430i	−0.488126	−	0.872773i	$-0.662319\pi$
$257$	2108.55	−	3652.11i	0.511781	−	0.886430i	0.999907	−	0.0136569i	$-0.00434725\pi$
$258$	−2113.47	−	1220.21i	−0.509995	−	0.294446i
$259$	−4866.33			−1.16749
$260$		0			0
$261$	−9668.41			−2.29295
$262$	−2798.34	−	1615.62i	−0.659855	−	0.380967i
$263$	−3237.16	+	5606.93i	−0.758981	+	1.31459i	0.184390	+	0.982853i	$0.440969\pi$
$263$	−3237.16	+	5606.93i	−0.758981	+	1.31459i	−0.943371	+	0.331740i	$0.892364\pi$
$264$	−1917.00	−	3320.35i	−0.446907	−	0.774066i
$265$		−	1005.54i		−	0.233094i
$266$	−232.397	+	134.175i	−0.0535684	+	0.0309277i
$267$	−1590.60	+	918.332i	−0.364580	+	0.210491i
$268$		−	1642.10i		−	0.374280i
$269$	650.517	+	1126.73i	0.147445	+	0.255382i	0.930282	−	0.366844i	$-0.119562\pi$
$269$	650.517	+	1126.73i	0.147445	+	0.255382i	−0.782837	+	0.622226i	$0.786228\pi$
$270$	−842.895	+	1459.94i	−0.189989	+	0.329070i
$271$	−2667.05	−	1539.82i	−0.597829	−	0.345157i	0.170358	−	0.985382i	$-0.445508\pi$
$271$	−2667.05	−	1539.82i	−0.597829	−	0.345157i	−0.768187	+	0.640225i	$0.778841\pi$
$272$	1982.78			0.441999
$273$		0			0
$274$	−4603.89			−1.01508
$275$	5152.46	+	2974.78i	1.12984	+	0.652312i
$276$	684.349	−	1185.33i	0.149250	−	0.258509i
$277$	−3143.95	−	5445.48i	−0.681955	−	1.18118i	−0.974383	−	0.224894i	$-0.927797\pi$
$277$	−3143.95	−	5445.48i	−0.681955	−	1.18118i	0.292428	−	0.956288i	$-0.405537\pi$
$278$		−	5618.14i		−	1.21206i
$279$	−1643.07	+	948.626i	−0.352573	+	0.203558i
$280$	405.313	−	234.008i	0.0865075	−	0.0499452i
$281$			3226.00i			0.684864i	0.939543	+	0.342432i	$0.111251\pi$
$281$			3226.00i			0.684864i	−0.939543	+	0.342432i	$0.888749\pi$
$282$	−2663.77	−	4613.78i	−0.562500	−	0.974279i
$283$	−193.292	+	334.791i	−0.0406007	+	0.0703225i	−0.885612	−	0.464426i	$-0.846261\pi$
$283$	−193.292	+	334.791i	−0.0406007	+	0.0703225i	0.845011	+	0.534749i	$0.179594\pi$
$284$	−1470.32	−	848.887i	−0.307209	−	0.177367i
$285$	303.811			0.0631446
$286$		0			0
$287$	398.178			0.0818944
$288$	−1429.88	−	825.542i	−0.292557	−	0.168908i
$289$	−5222.04	+	9044.84i	−1.06290	+	1.84100i
$290$	−724.331	−	1254.58i	−0.146670	−	0.254039i
$291$			6573.60i			1.32423i
$292$	−1461.79	+	843.964i	−0.292961	+	0.169141i
$293$	−1899.04	+	1096.41i	−0.378645	+	0.218611i	−0.677229	−	0.735773i	$-0.736819\pi$
$293$	−1899.04	+	1096.41i	−0.378645	+	0.218611i	0.298583	+	0.954384i	$0.403486\pi$
$294$		−	2020.36i		−	0.400782i
$295$	475.564	+	823.701i	0.0938590	+	0.162569i
$296$	−1286.15	+	2227.68i	−0.252554	+	0.437437i
$297$	−10208.6	−	5893.92i	−1.99448	−	1.15151i
$298$	−5066.34			−0.984849
$299$		0			0
$300$	3902.87			0.751107
$301$	1803.99	+	1041.53i	0.345449	+	0.199445i
$302$	2391.10	−	4141.51i	0.455604	−	0.789129i
$303$	1832.07	+	3173.24i	0.347359	+	0.601643i
$304$			141.847i			0.0267615i
$305$	305.652	−	176.468i	0.0573823	−	0.0331297i
$306$	11074.8	−	6394.01i	2.06896	−	1.19451i
$307$			8083.96i			1.50285i	0.659817	+	0.751427i	$0.270634\pi$
$307$			8083.96i			1.50285i	−0.659817	+	0.751427i	$0.729366\pi$
$308$	1636.29	+	2834.14i	0.302716	+	0.524319i
$309$	16.6986	−	28.9229i	0.00307428	−	0.00532481i
$310$	−246.188	−	142.137i	−0.0451050	−	0.0260414i
$311$	−244.409			−0.0445632			−0.0222816	−	0.999752i	$-0.507093\pi$
$311$	−244.409			−0.0445632			−0.0222816	+	0.999752i	$0.507093\pi$
$312$		0			0
$313$	4444.13			0.802546			0.401273	−	0.915958i	$-0.368568\pi$
$313$	4444.13			0.802546			0.401273	+	0.915958i	$0.368568\pi$
$314$	−3338.51	−	1927.49i	−0.600009	−	0.346415i
$315$	1509.24	−	2614.09i	0.269957	−	0.467578i
$316$	1467.08	+	2541.06i	0.261171	+	0.452361i
$317$			930.597i			0.164882i	0.996596	+	0.0824409i	$0.0262716\pi$
$317$			930.597i			0.164882i	−0.996596	+	0.0824409i	$0.973728\pi$
$318$	3994.48	−	2306.21i	0.704400	−	0.406685i
$319$	8772.60	−	5064.86i	1.53972	−	0.888959i
$320$		−	247.389i		−	0.0432172i
$321$	504.557	+	873.918i	0.0877309	+	0.151954i
$322$	−584.138	+	1011.76i	−0.101096	+	0.175103i
$323$	−951.451	−	549.320i	−0.163901	−	0.0946285i
$324$	−2160.34			−0.370428
$325$		0			0
$326$	−4437.05			−0.753820
$327$	14861.2	+	8580.13i	2.51323	+	1.45102i
$328$	105.237	−	182.275i	0.0177156	−	0.0306844i
$329$	2273.71	+	3938.17i	0.381014	+	0.659935i
$330$		−	3705.05i		−	0.618050i
$331$	4180.61	−	2413.68i	0.694221	−	0.400809i	−0.110970	−	0.993824i	$-0.535396\pi$
$331$	4180.61	−	2413.68i	0.694221	−	0.400809i	0.805191	+	0.593015i	$0.202063\pi$
$332$	2136.81	−	1233.69i	0.353231	−	0.203938i
$333$			16590.2i			2.73014i
$334$	1508.27	+	2612.40i	0.247092	+	0.427977i
$335$	793.432	−	1374.26i	0.129402	−	0.224132i
$336$	1859.18	+	1073.40i	0.301865	+	0.174282i
$337$	−10709.7			−1.73115			−0.865573	−	0.500782i	$-0.833046\pi$
$337$	−10709.7			−1.73115			−0.865573	+	0.500782i	$0.833046\pi$
$338$		0			0
$339$	−16833.6			−2.69698
$340$	1659.38	+	958.044i	0.264684	+	0.152815i
$341$	993.888	−	1721.47i	0.157836	−	0.273380i
$342$	457.426	+	792.284i	0.0723238	+	0.125269i
$343$			6915.66i			1.08866i
$344$	953.574	−	550.546i	0.149457	−	0.0862891i
$345$	1145.46	−	661.331i	0.178752	−	0.103203i
$346$			3412.94i			0.530292i
$347$	−3200.54	−	5543.51i	−0.495142	−	0.857611i	0.504842	−	0.863211i	$-0.331551\pi$
$347$	−3200.54	−	5543.51i	−0.495142	−	0.857611i	−0.999984	+	0.00560066i	$0.998217\pi$
$348$	3322.52	−	5754.77i	0.511798	−	0.886460i
$349$	−2104.46	−	1215.01i	−0.322777	−	0.186355i	0.329853	−	0.944032i	$-0.393001\pi$
$349$	−2104.46	−	1215.01i	−0.322777	−	0.186355i	−0.652630	+	0.757677i	$0.726334\pi$
$350$	−3331.36			−0.508768
$351$		0			0
$352$	1729.86			0.261938
$353$	−6997.51	−	4040.01i	−1.05507	−	0.609145i	−0.131006	−	0.991382i	$-0.541821\pi$
$353$	−6997.51	−	4040.01i	−1.05507	−	0.609145i	−0.924064	+	0.382237i	$0.875154\pi$
$354$	−2181.42	+	3778.33i	−0.327517	+	0.567277i
$355$	−820.335	−	1420.86i	−0.122645	−	0.212427i
$356$		−	828.683i		−	0.123371i
$357$	−14399.8	+	8313.71i	−2.13478	+	1.23252i
$358$	−1030.96	+	595.223i	−0.152200	+	0.0878729i
$359$		−	8715.23i		−	1.28126i	−0.767850	−	0.640630i	$-0.778673\pi$
$359$		−	8715.23i		−	1.28126i	0.767850	−	0.640630i	$-0.221327\pi$
$360$	−797.775	−	1381.79i	−0.116796	−	0.202296i
$361$	−3390.20	+	5872.00i	−0.494271	+	0.856102i
$362$	698.027	+	403.006i	0.101347	+	0.0585126i
$363$	14107.5			2.03982
$364$		0			0
$365$	−1631.15			−0.233914
$366$	1402.03	+	809.463i	0.200233	+	0.115605i
$367$	−1410.44	+	2442.95i	−0.200611	+	0.347469i	−0.948726	−	0.316101i	$-0.897626\pi$
$367$	−1410.44	+	2442.95i	−0.200611	+	0.347469i	0.748114	+	0.663570i	$0.230959\pi$
$368$	308.771	+	534.807i	0.0437386	+	0.0757575i
$369$		−	1357.46i		−	0.191508i
$370$	−2152.75	+	1242.89i	−0.302477	+	0.174635i
$371$	−3409.56	+	1968.51i	−0.477130	+	0.275471i
$372$		−	1303.97i		−	0.181741i
$373$	6464.84	+	11197.4i	0.897418	+	1.55437i	0.830783	+	0.556596i	$0.187893\pi$
$373$	6464.84	+	11197.4i	0.897418	+	1.55437i	0.0666351	+	0.997777i	$0.478774\pi$
$374$	−6699.09	+	11603.2i	−0.926208	+	1.60424i
$375$	6976.03	+	4027.61i	0.960642	+	0.554627i
$376$	2403.73			0.329688
$377$		0			0
$378$	6600.42			0.898119
$379$	1981.51	+	1144.02i	0.268557	+	0.155052i	0.628232	−	0.778026i	$-0.283779\pi$
$379$	1981.51	+	1144.02i	0.268557	+	0.155052i	−0.359675	+	0.933078i	$0.617112\pi$
$380$	−68.5382	+	118.712i	−0.00925246	+	0.0160257i
$381$	−1084.26	−	1878.00i	−0.145797	−	0.252527i
$382$		−	1227.39i		−	0.164395i
$383$	10527.6	−	6078.10i	1.40453	−	0.810904i	0.409674	−	0.912232i	$-0.365642\pi$
$383$	10527.6	−	6078.10i	1.40453	−	0.810904i	0.994853	+	0.101328i	$0.0323090\pi$
$384$	982.747	−	567.389i	0.130601	−	0.0754023i
$385$			3162.51i			0.418640i
$386$	−2005.33	−	3473.33i	−0.264426	−	0.458000i
$387$	3550.77	−	6150.12i	0.466398	−	0.807825i
$388$	−2568.58	−	1482.97i	−0.336082	−	0.194037i
$389$	1479.71			0.192864			0.0964322	−	0.995340i	$-0.469257\pi$
$389$	1479.71			0.192864			0.0964322	+	0.995340i	$0.469257\pi$
$390$		0			0
$391$	−4783.01			−0.618637
$392$	789.439	+	455.783i	0.101716	+	0.0587258i
$393$	7161.62	−	12404.3i	0.919226	−	1.59215i
$394$	−557.500	−	965.617i	−0.0712853	−	0.123470i
$395$			2835.48i			0.361186i
$396$	9662.10	−	5578.42i	1.22611	−	0.707894i
$397$	−13225.3	+	7635.63i	−1.67194	+	0.965292i	−0.705382	+	0.708827i	$0.749225\pi$
$397$	−13225.3	+	7635.63i	−1.67194	+	0.965292i	−0.966554	+	0.256465i	$0.917442\pi$
$398$		−	11067.9i		−	1.39393i
$399$	−594.760	−	1030.15i	−0.0746247	−	0.129254i
$400$	−880.466	+	1525.01i	−0.110058	+	0.190626i
$401$	2220.96	+	1282.27i	0.276582	+	0.159685i	0.631875	−	0.775070i	$-0.282286\pi$
$401$	2220.96	+	1282.27i	0.276582	+	0.159685i	−0.355293	+	0.934755i	$0.615619\pi$
$402$	7278.97			0.903089
$403$		0			0
$404$	−1653.22			−0.203591
$405$	−1807.98	−	1043.84i	−0.221825	−	0.128071i
$406$	−2835.99	+	4912.09i	−0.346670	+	0.600450i
$407$	−8690.89	−	15053.1i	−1.05846	−	1.83330i
$408$			8789.12i			1.06649i
$409$	911.465	−	526.235i	0.110193	−	0.0636201i	−0.443890	−	0.896081i	$-0.646402\pi$
$409$	911.465	−	526.235i	0.110193	−	0.0636201i	0.554084	+	0.832461i	$0.313069\pi$
$410$	176.145	−	101.697i	0.0212175	−	0.0122499i
$411$		−	20407.8i		−	2.44925i
$412$	7.53424	+	13.0497i	0.000900936	+	0.00156047i
$413$	1861.99	−	3225.06i	0.221846	−	0.384249i
$414$	3449.26	+	1991.43i	0.409474	+	0.236410i
$415$	2384.38			0.282036
$416$		0			0
$417$	24903.7			2.92455
$418$	−830.087	−	479.251i	−0.0971313	−	0.0560788i
$419$	−4355.81	+	7544.48i	−0.507864	+	0.879647i	0.492094	+	0.870542i	$0.336232\pi$
$419$	−4355.81	+	7544.48i	−0.507864	+	0.879647i	−0.999959	+	0.00910485i	$0.997102\pi$
$420$	1037.29	+	1796.65i	0.120511	+	0.208732i
$421$			213.335i			0.0246967i	0.999924	+	0.0123484i	$0.00393070\pi$
$421$			213.335i			0.0246967i	−0.999924	+	0.0123484i	$0.996069\pi$
$422$	−8112.46	+	4683.73i	−0.935802	+	0.540286i
$423$	13425.9	−	7751.47i	1.54324	−	0.890992i
$424$			2081.08i			0.238363i
$425$	−6819.41	−	11811.6i	−0.778329	−	1.34811i
$426$	3762.89	−	6517.51i	0.427964	−	0.741255i
$427$	−1196.73	−	690.932i	−0.135629	−	0.0783057i
$428$	−455.301			−0.0514201
$429$		0			0
$430$	1064.06			0.119333
$431$	−7753.91	−	4476.72i	−0.866573	−	0.500316i	−0.000364932	−	1.00000i	$-0.500116\pi$
$431$	−7753.91	−	4476.72i	−0.866573	−	0.500316i	−0.866208	+	0.499684i	$0.833449\pi$
$432$	1744.47	−	3021.50i	0.194284	−	0.336510i
$433$	2930.72	+	5076.16i	0.325269	+	0.563382i	0.981567	−	0.191120i	$-0.0612118\pi$
$433$	2930.72	+	5076.16i	0.325269	+	0.563382i	−0.656298	+	0.754502i	$0.727878\pi$
$434$			1113.03i			0.123104i
$435$	5561.21	−	3210.76i	0.612964	−	0.353895i
$436$	−6705.22	+	3871.26i	−0.736518	+	0.425229i
$437$		−	342.175i		−	0.0374564i
$438$	−3741.06	−	6479.71i	−0.408116	−	0.706878i
$439$	−5221.77	+	9044.36i	−0.567702	+	0.983289i	0.429090	+	0.903262i	$0.358834\pi$
$439$	−5221.77	+	9044.36i	−0.567702	+	0.983289i	−0.996793	+	0.0800275i	$0.974499\pi$
$440$	1447.72	+	835.840i	0.156857	+	0.0905616i
$441$	5879.19			0.634833
$442$		0			0
$443$	8789.73			0.942692			0.471346	−	0.881948i	$-0.343768\pi$
$443$	8789.73			0.942692			0.471346	+	0.881948i	$0.343768\pi$
$444$	−9874.71	−	5701.17i	−1.05548	−	0.609382i
$445$	400.405	−	693.522i	0.0426540	−	0.0738789i
$446$	−2383.86	−	4128.97i	−0.253092	−	0.438369i
$447$		−	22457.7i		−	2.37632i
$448$	−838.841	+	484.305i	−0.0884632	+	0.0510743i
$449$	−7479.09	+	4318.06i	−0.786103	+	0.453857i	−0.838589	−	0.544765i	$-0.816619\pi$
$449$	−7479.09	+	4318.06i	−0.786103	+	0.453857i	0.0524857	+	0.998622i	$0.483286\pi$
$450$			11357.2i			1.18974i
$451$	711.114	+	1231.69i	0.0742463	+	0.128598i
$452$	3797.57	−	6577.58i	0.395182	−	0.684476i
$453$	18358.2	+	10599.1i	1.90407	+	1.09931i
$454$	3108.15			0.321305
$455$		0			0
$456$	−628.771			−0.0645722
$457$	−4223.57	−	2438.48i	−0.432320	−	0.249600i	0.268014	−	0.963415i	$-0.413633\pi$
$457$	−4223.57	−	2438.48i	−0.432320	−	0.249600i	−0.700335	+	0.713815i	$0.746966\pi$
$458$	2915.60	−	5049.97i	0.297461	−	0.515217i
$459$	13511.3	+	23402.2i	1.37397	+	2.37979i
$460$			596.771i			0.0604882i
$461$	−10222.5	+	5901.96i	−1.03277	+	0.596272i	−0.917778	−	0.397094i	$-0.870019\pi$
$461$	−10222.5	+	5901.96i	−1.03277	+	0.596272i	−0.114996	+	0.993366i	$0.536685\pi$
$462$	−12563.0	+	7253.24i	−1.26511	+	0.730414i
$463$			4797.53i			0.481555i	0.970580	+	0.240777i	$0.0774024\pi$
$463$			4797.53i			0.481555i	−0.970580	+	0.240777i	$0.922598\pi$
$464$	1499.08	+	2596.49i	0.149985	+	0.259782i
$465$	630.055	−	1091.29i	0.0628346	−	0.108833i
$466$	−7333.38	−	4233.93i	−0.728996	−	0.420886i
$467$	13188.7			1.30686			0.653428	−	0.756989i	$-0.273330\pi$
$467$	13188.7			1.30686			0.653428	+	0.756989i	$0.273330\pi$
$468$		0			0
$469$	−6213.09			−0.611714
$470$	2011.67	+	1161.44i	0.197429	+	0.113985i
$471$	8544.03	−	14798.7i	0.835856	−	1.44775i
$472$	−984.233	−	1704.74i	−0.0959809	−	0.166244i
$473$			7440.38i			0.723275i
$474$	−11263.9	+	6503.19i	−1.09149	+	0.630172i
$475$	844.995	−	487.858i	0.0816233	−	0.0471252i
$476$		−	7502.11i		−	0.722392i
$477$	6711.00	+	11623.8i	0.644184	+	1.11576i
$478$	2372.55	−	4109.38i	0.227025	−	0.393219i
$479$	15630.7	+	9024.41i	1.49100	+	0.860827i	0.999947	−	0.0103054i	$-0.00328038\pi$
$479$	15630.7	+	9024.41i	1.49100	+	0.860827i	0.491049	+	0.871132i	$0.336614\pi$
$480$	1096.61			0.104277
$481$		0			0
$482$	651.526			0.0615689
$483$	−4484.85	−	2589.33i	−0.422500	−	0.243931i
$484$	−3182.58	+	5512.39i	−0.298890	+	0.517693i
$485$	−1433.09	−	2482.18i	−0.134171	−	0.232392i
$486$			2198.96i			0.205240i
$487$	9960.37	−	5750.62i	0.926792	−	0.535084i	0.0409963	−	0.999159i	$-0.486947\pi$
$487$	9960.37	−	5750.62i	0.926792	−	0.535084i	0.885796	+	0.464076i	$0.153613\pi$
$488$	−632.582	+	365.221i	−0.0586796	+	0.0338787i
$489$		−	19668.2i		−	1.81887i
$490$	440.453	+	762.886i	0.0406074	+	0.0703340i
$491$	−2000.33	+	3464.67i	−0.183856	+	0.318449i	−0.943191	−	0.332252i	$-0.892191\pi$
$491$	−2000.33	+	3464.67i	−0.183856	+	0.318449i	0.759334	+	0.650701i	$0.225525\pi$
$492$	807.978	+	466.486i	0.0740375	+	0.0427456i
$493$	−23221.5			−2.12139
$494$		0			0
$495$	10781.6			0.978981
$496$	509.514	+	294.168i	0.0461247	+	0.0266301i
$497$	−3211.88	+	5563.14i	−0.289884	+	0.502094i
$498$	5468.60	+	9471.89i	0.492076	+	0.852301i
$499$		−	8322.72i		−	0.746645i	−0.927702	−	0.373323i	$-0.878218\pi$
$499$		−	8322.72i		−	0.746645i	0.927702	−	0.373323i	$-0.121782\pi$
$500$	−3147.51	+	1817.22i	−0.281522	+	0.162537i
$501$	−11580.1	+	6685.76i	−1.03265	+	0.596203i
$502$			5203.54i			0.462640i
$503$	3563.74	+	6172.58i	0.315903	+	0.547160i	0.979629	−	0.200816i	$-0.0643592\pi$
$503$	3563.74	+	6172.58i	0.315903	+	0.547160i	−0.663726	+	0.747976i	$0.731026\pi$
$504$	−3123.55	+	5410.15i	−0.276059	+	0.478149i
$505$	−1383.58	−	798.808i	−0.121917	−	0.0703890i
$506$	−4172.90			−0.366617
$507$		0			0
$508$	978.417			0.0854532
$509$	12426.5	+	7174.46i	1.08211	+	0.624759i	0.931466	−	0.363828i	$-0.118530\pi$
$509$	12426.5	+	7174.46i	1.08211	+	0.624759i	0.150649	+	0.988587i	$0.451864\pi$
$510$	−4246.75	+	7355.59i	−0.368724	+	0.638649i
$511$	3193.25	+	5530.87i	0.276441	+	0.478809i
$512$			512.000i			0.0441942i
$513$	−1674.19	+	966.593i	−0.144088	+	0.0831893i
$514$	−7304.22	+	4217.10i	−0.626801	+	0.361884i
$515$			14.5617i			0.00124595i
$516$	2440.42	+	4226.93i	0.208205	+	0.360621i
$517$	−8121.32	+	14066.5i	−0.690861	+	1.19661i
$518$	8428.73	+	4866.33i	0.714937	+	0.412769i
$519$	−15128.7			−1.27953
$520$		0			0
$521$	3535.86			0.297329			0.148665	−	0.988888i	$-0.452502\pi$
$521$	3535.86			0.297329			0.148665	+	0.988888i	$0.452502\pi$
$522$	16746.2	+	9668.41i	1.40414	+	0.810680i
$523$	−6982.44	+	12093.9i	−0.583787	+	1.01115i	0.411238	+	0.911528i	$0.365096\pi$
$523$	−6982.44	+	12093.9i	−0.583787	+	1.01115i	−0.995025	+	0.0996211i	$0.968237\pi$
$524$	3231.24	+	5596.68i	0.269385	+	0.466588i
$525$		−	14767.0i		−	1.22759i
$526$	11213.9	−	6474.32i	0.929558	−	0.536680i
$527$	−3946.31	+	2278.40i	−0.326193	+	0.188328i
$528$			7668.02i			0.632022i
$529$	5338.66	+	9246.83i	0.438782	+	0.759993i
$530$	−1005.54	+	1741.65i	−0.0824110	+	0.142740i
$531$	−10994.8	−	6347.86i	−0.898558	−	0.518783i
$532$	536.699			0.0437384
$533$		0			0
$534$	3673.33			0.297679
$535$	−381.040	−	219.994i	−0.0307922	−	0.0177779i
$536$	−1642.10	+	2844.19i	−0.132328	+	0.229199i
$537$	−2638.46	−	4569.95i	−0.212026	−	0.367240i
$538$		−	2602.07i		−	0.208519i
$539$	−5334.46	+	3079.85i	−0.426292	+	0.246120i
$540$	2919.88	−	1685.79i	0.232688	−	0.134342i
$541$			10661.6i			0.847277i	0.905831	+	0.423638i	$0.139247\pi$
$541$			10661.6i			0.847277i	−0.905831	+	0.423638i	$0.860753\pi$
$542$	3079.64	+	5334.10i	0.244063	+	0.422729i
$543$	−1786.42	+	3094.17i	−0.141183	+	0.244537i
$544$	−3434.27	−	1982.78i	−0.270668	−	0.156270i
$545$	−7482.10			−0.588070
$546$		0			0
$547$	−3393.59			−0.265264			−0.132632	−	0.991165i	$-0.542343\pi$
$547$	−3393.59			−0.265264			−0.132632	+	0.991165i	$0.542343\pi$
$548$	7974.18	+	4603.89i	0.621606	+	0.358884i
$549$	−2355.51	+	4079.86i	−0.183116	+	0.317166i
$550$	−5949.55	−	10304.9i	−0.461254	−	0.798915i
$551$		−	1661.26i		−	0.128443i
$552$	−2370.66	+	1368.70i	−0.182793	+	0.105536i
$553$	9614.46	−	5550.91i	0.739328	−	0.426851i
$554$			12575.8i			0.964430i
$555$	−5509.41	−	9542.58i	−0.421372	−	0.729837i
$556$	−5618.14	+	9730.90i	−0.428529	+	0.742234i
$557$	−7143.87	−	4124.51i	−0.543439	−	0.313754i	0.203033	−	0.979172i	$-0.434920\pi$
$557$	−7143.87	−	4124.51i	−0.543439	−	0.313754i	−0.746471	+	0.665418i	$0.768254\pi$
$558$	3794.50			0.287875
$559$		0			0
$560$	−936.031			−0.0706331
$561$	−51433.7	−	29695.3i	−3.87083	−	2.23482i
$562$	3226.00	−	5587.59i	0.242136	−	0.419392i
$563$	4434.39	+	7680.59i	0.331949	+	0.574953i	0.982894	−	0.184172i	$-0.0589604\pi$
$563$	4434.39	+	7680.59i	0.331949	+	0.574953i	−0.650945	+	0.759125i	$0.725627\pi$
$564$			10655.1i			0.795495i
$565$	6356.34	−	3669.83i	0.473298	−	0.273259i
$566$	669.583	−	386.584i	0.0497255	−	0.0287091i
$567$			8173.93i			0.605419i
$568$	1697.77	+	2940.63i	0.125417	+	0.217229i
$569$	−3204.24	+	5549.91i	−0.236079	+	0.408901i	−0.959586	−	0.281417i	$-0.909196\pi$
$569$	−3204.24	+	5549.91i	−0.236079	+	0.408901i	0.723507	+	0.690317i	$0.242529\pi$
$570$	−526.216	−	303.811i	−0.0386680	−	0.0223250i
$571$	−10045.2			−0.736212			−0.368106	−	0.929784i	$-0.619994\pi$
$571$	−10045.2			−0.736212			−0.368106	+	0.929784i	$0.619994\pi$
$572$		0			0
$573$	5440.70			0.396664
$574$	−689.664	−	398.178i	−0.0501498	−	0.0289540i
$575$	2123.92	−	3678.75i	0.154041	−	0.266807i
$576$	1651.08	+	2859.76i	0.119436	+	0.206869i
$577$		−	24528.9i		−	1.76976i	−0.465818	−	0.884880i	$-0.654240\pi$
$577$		−	24528.9i		−	1.76976i	0.465818	−	0.884880i	$-0.345760\pi$
$578$	18089.7	−	10444.1i	1.30178	−	0.751585i
$579$	15396.3	−	8889.08i	1.10510	−	0.638027i
$580$			2897.32i			0.207422i
$581$	−4667.82	−	8084.90i	−0.333311	−	0.577312i
$582$	6573.60	−	11385.8i	0.468186	−	0.810922i
$583$	−12178.4	−	7031.21i	−0.865142	−	0.499490i
$584$	3375.86			0.239202
$585$		0			0
$586$	4385.64			0.309163
$587$	13773.1	+	7951.88i	0.968441	+	0.559130i	0.898761	−	0.438440i	$-0.144469\pi$
$587$	13773.1	+	7951.88i	0.968441	+	0.559130i	0.0696803	+	0.997569i	$0.477802\pi$
$588$	−2020.36	+	3499.37i	−0.141698	+	0.245428i
$589$	−162.996	−	282.317i	−0.0114026	−	0.0197499i
$590$		−	1902.26i		−	0.132737i
$591$	4280.32	−	2471.24i	0.297917	−	0.172002i
$592$	4455.36	−	2572.31i	0.309315	−	0.178583i
$593$			5436.51i			0.376477i	0.982123	+	0.188238i	$0.0602778\pi$
$593$			5436.51i			0.376477i	−0.982123	+	0.188238i	$0.939722\pi$
$594$	11787.8	+	20417.1i	0.814244	+	1.41031i
$595$	3624.89	−	6278.49i	0.249758	−	0.432593i
$596$	8775.15	+	5066.34i	0.603094	+	0.348197i
$597$	49061.2			3.36339
$598$		0			0
$599$	6872.46			0.468783			0.234392	−	0.972142i	$-0.424690\pi$
$599$	6872.46			0.468783			0.234392	+	0.972142i	$0.424690\pi$
$600$	−6759.96	−	3902.87i	−0.459957	−	0.265556i
$601$	708.911	−	1227.87i	0.0481149	−	0.0833375i	−0.840965	−	0.541090i	$-0.818012\pi$
$601$	708.911	−	1227.87i	0.0481149	−	0.0833375i	0.889080	+	0.457752i	$0.151345\pi$
$602$	−2083.07	−	3607.97i	−0.141029	−	0.244269i
$603$			21181.6i			1.43048i
$604$	−8283.01	+	4782.20i	−0.557998	+	0.322161i
$605$	−5326.98	+	3075.54i	−0.357971	+	0.206675i
$606$		−	7328.28i		−	0.491240i
$607$	6796.67	+	11772.2i	0.454478	+	0.787180i	0.998658	−	0.0517890i	$-0.0164923\pi$
$607$	6796.67	+	11772.2i	0.454478	+	0.787180i	−0.544180	+	0.838969i	$0.683159\pi$
$608$	141.847	−	245.687i	0.00946163	−	0.0163880i
$609$	−21773.9	−	12571.2i	−1.44881	−	0.836470i
$610$	−705.874			−0.0468525
$611$		0			0
$612$	−25576.1			−1.68930
$613$	14964.4	+	8639.71i	0.985982	+	0.569257i	0.904071	−	0.427383i	$-0.140564\pi$
$613$	14964.4	+	8639.71i	0.985982	+	0.569257i	0.0819112	+	0.996640i	$0.473898\pi$
$614$	8083.96	−	14001.8i	0.531339	−	0.920306i
$615$	450.796	+	780.802i	0.0295575	+	0.0511951i
$616$		−	6545.17i		−	0.428105i
$617$	−1885.40	+	1088.54i	−0.123020	+	0.0710256i	−0.560247	−	0.828325i	$-0.689294\pi$
$617$	−1885.40	+	1088.54i	−0.123020	+	0.0710256i	0.437227	+	0.899351i	$0.355961\pi$
$618$	−57.8458	+	33.3973i	−0.00376521	+	0.00217384i
$619$		−	17067.5i		−	1.10824i	−0.832436	−	0.554121i	$-0.813055\pi$
$619$		−	17067.5i		−	1.10824i	0.832436	−	0.554121i	$-0.186945\pi$
$620$	284.274	+	492.377i	0.0184141	+	0.0318941i
$621$	−4208.13	+	7288.69i	−0.271927	+	0.470991i
$622$	423.329	+	244.409i	0.0272893	+	0.0157555i
$623$	−3135.43			−0.201635
$624$		0			0
$625$	10245.1			0.655686
$626$	−7697.45	−	4444.13i	−0.491457	−	0.283743i
$627$	2124.39	−	3679.55i	0.135311	−	0.234365i
$628$	3854.98	+	6677.01i	0.244953	+	0.424270i
$629$			39846.2i			2.52587i
$630$	−5228.18	+	3018.49i	−0.330628	+	0.190888i
$631$	6867.55	−	3964.98i	0.433269	−	0.250148i	−0.267469	−	0.963566i	$-0.586187\pi$
$631$	6867.55	−	3964.98i	0.433269	−	0.250148i	0.700738	+	0.713418i	$0.252854\pi$
$632$		−	5868.34i		−	0.369351i
$633$	−20761.7	−	35960.4i	−1.30364	−	2.25797i
$634$	930.597	−	1611.84i	0.0582945	−	0.100969i
$635$	818.834	+	472.754i	0.0511723	+	0.0295444i
$636$	−9224.85			−0.575140
$637$		0			0
$638$	−20259.5			−1.25718
$639$	18965.7	+	10949.9i	1.17414	+	0.677888i
$640$	−247.389	+	428.491i	−0.0152796	+	0.0264650i
$641$	−2919.53	−	5056.77i	−0.179898	−	0.311592i	0.761948	−	0.647639i	$-0.224243\pi$
$641$	−2919.53	−	5056.77i	−0.179898	−	0.311592i	−0.941845	+	0.336047i	$0.890910\pi$
$642$		−	2018.23i		−	0.124070i
$643$	−14742.2	+	8511.42i	−0.904161	+	0.522018i	−0.878548	−	0.477654i	$-0.841487\pi$
$643$	−14742.2	+	8511.42i	−0.904161	+	0.522018i	−0.0256134	+	0.999672i	$0.508154\pi$
$644$	2023.51	−	1168.28i	0.123816	−	0.0714853i
$645$			4716.68i			0.287936i
$646$	1098.64	+	1902.90i	0.0669124	+	0.115896i
$647$	10889.6	−	18861.4i	0.661694	−	1.14609i	−0.318476	−	0.947931i	$-0.603171\pi$
$647$	10889.6	−	18861.4i	0.661694	−	1.14609i	0.980170	−	0.198157i	$-0.0634956\pi$
$648$	3741.81	+	2160.34i	0.226840	+	0.130966i
$649$	13301.5			0.804512
$650$		0			0
$651$	−4933.74			−0.297033
$652$	7685.19	+	4437.05i	0.461619	+	0.266516i
$653$	−8520.81	+	14758.5i	−0.510636	+	0.884447i	0.489288	+	0.872122i	$0.337257\pi$
$653$	−8520.81	+	14758.5i	−0.510636	+	0.884447i	−0.999924	+	0.0123250i	$0.996077\pi$
$654$	−17160.3	−	29722.4i	−1.02602	−	1.77712i
$655$			6245.12i			0.372545i
$656$	−364.551	+	210.474i	−0.0216971	+	0.0125268i
$657$	18855.7	−	10886.4i	1.11968	−	0.646450i
$658$		−	9094.82i		−	0.538834i
$659$	−15382.9	−	26644.0i	−0.909306	−	1.57496i	−0.815030	−	0.579419i	$-0.803280\pi$
$659$	−15382.9	−	26644.0i	−0.909306	−	1.57496i	−0.0942763	−	0.995546i	$-0.530054\pi$
$660$	−3705.05	+	6417.34i	−0.218514	+	0.378476i
$661$	6707.11	+	3872.35i	0.394669	+	0.227862i	0.684181	−	0.729312i	$-0.260160\pi$
$661$	6707.11	+	3872.35i	0.394669	+	0.227862i	−0.289512	+	0.957174i	$0.593493\pi$
$662$	−9654.71			−0.566829
$663$		0			0
$664$	−4934.75			−0.288412
$665$	449.161	+	259.323i	0.0261921	+	0.0151220i
$666$	16590.2	−	28735.1i	0.965251	−	1.67186i
$667$	−3616.20	−	6263.44i	−0.209925	−	0.363601i
$668$		−	6033.08i		−	0.349442i
$669$	18302.6	−	10567.0i	1.05773	−	0.610679i
$670$	−2748.53	+	1586.86i	−0.158485	+	0.0915013i
$671$		−	4935.80i		−	0.283971i
$672$	−2146.79	−	3718.36i	−0.123236	−	0.213451i
$673$	−1151.23	+	1993.98i	−0.0659384	+	0.114209i	−0.897110	−	0.441808i	$-0.854337\pi$
$673$	−1151.23	+	1993.98i	−0.0659384	+	0.114209i	0.831171	+	0.556016i	$0.187671\pi$
$674$	18549.8	+	10709.7i	1.06011	+	0.612053i
$675$	−23999.1			−1.36848
$676$		0			0
$677$	−15932.6			−0.904488			−0.452244	−	0.891894i	$-0.649376\pi$
$677$	−15932.6			−0.904488			−0.452244	+	0.891894i	$0.649376\pi$
$678$	29156.6	+	16833.6i	1.65155	+	0.953525i
$679$	−5611.01	+	9718.55i	−0.317129	+	0.549284i
$680$	−1916.09	−	3318.76i	−0.108057	−	0.187160i
$681$			13777.6i			0.775269i
$682$	−3442.93	+	1987.78i	−0.193309	+	0.111607i
$683$	−15985.6	+	9229.29i	−0.895566	+	0.517055i	−0.875759	−	0.482748i	$-0.839639\pi$
$683$	−15985.6	+	9229.29i	−0.895566	+	0.517055i	−0.0198072	+	0.999804i	$0.506305\pi$
$684$		−	1829.70i		−	0.102281i
$685$	4449.04	+	7705.97i	0.248159	+	0.429825i
$686$	6915.66	−	11978.3i	0.384900	−	0.666666i
$687$	22385.1	+	12924.1i	1.24315	+	0.717735i
$688$	−2202.18			−0.122031
$689$		0			0
$690$	−2645.32			−0.145950
$691$	−19900.7	−	11489.7i	−1.09560	−	0.632544i	−0.160537	−	0.987030i	$-0.551323\pi$
$691$	−19900.7	−	11489.7i	−1.09560	−	0.632544i	−0.935061	+	0.354486i	$0.884656\pi$
$692$	3412.94	−	5911.39i	0.187487	−	0.324736i
$693$	−21106.7	−	36557.9i	−1.15697	−	2.00392i
$694$			12802.2i			0.700236i
$695$	−9403.60	+	5429.17i	−0.513236	+	0.296317i
$696$	−11509.5	+	6645.04i	−0.626822	+	0.361896i
$697$		−	3260.33i		−	0.177179i
$698$	2430.02	+	4208.92i	0.131773	+	0.228238i
$699$	18767.9	−	32506.9i	1.01554	−	1.75897i
$700$	5770.09	+	3331.36i	0.311555	+	0.179877i
$701$	−8633.81			−0.465185			−0.232592	−	0.972574i	$-0.574721\pi$
$701$	−8633.81			−0.465185			−0.232592	+	0.972574i	$0.574721\pi$
$702$		0			0
$703$	−2850.58			−0.152933
$704$	−2996.21	−	1729.86i	−0.160403	−	0.0926089i
$705$	−5148.34	+	8917.19i	−0.275032	+	0.476370i
$706$	8080.03	+	13995.0i	0.430731	+	0.746047i
$707$			6255.19i			0.332745i
$708$	7556.66	−	4362.84i	0.401125	−	0.231590i
$709$	22189.7	−	12811.2i	1.17539	−	0.678612i	0.220447	−	0.975399i	$-0.429249\pi$
$709$	22189.7	−	12811.2i	1.17539	−	0.678612i	0.954944	+	0.296787i	$0.0959152\pi$
$710$			3281.34i			0.173446i
$711$	−18924.1	−	32777.4i	−0.998182	−	1.72890i
$712$	−828.683	+	1435.32i	−0.0436183	+	0.0755491i
$713$	−1229.09	−	709.614i	−0.0645578	−	0.0372725i
$714$	33254.8			1.74304
$715$		0			0
$716$	2380.89			0.124271
$717$	18215.8	+	10516.9i	0.948788	+	0.547783i
$718$	−8715.23	+	15095.2i	−0.452994	+	0.784608i
$719$	17477.4	+	30271.7i	0.906532	+	1.57016i	0.818847	+	0.574011i	$0.194613\pi$
$719$	17477.4	+	30271.7i	0.906532	+	1.57016i	0.0876845	+	0.996148i	$0.472053\pi$
$720$			3191.10i			0.165174i
$721$	49.3753	−	28.5068i	0.00255039	−	0.00147247i
$722$	11744.0	−	6780.40i	0.605355	−	0.349502i
$723$			2888.04i			0.148558i
$724$	−806.013	−	1396.05i	−0.0413746	−	0.0716629i
$725$	10311.7	−	17860.3i	0.528228	−	0.914918i
$726$	−24435.0	−	14107.5i	−1.24913	−	0.721184i
$727$	23397.0			1.19360			0.596800	−	0.802390i	$-0.296438\pi$
$727$	23397.0			1.19360			0.596800	+	0.802390i	$0.296438\pi$
$728$		0			0
$729$	−24329.6			−1.23607
$730$	2825.24	+	1631.15i	0.143242	+	0.0827010i
$731$	8528.21	−	14771.3i	0.431501	−	0.747382i
$732$	−1618.93	−	2804.06i	−0.0817449	−	0.141586i
$733$		−	3541.17i		−	0.178440i	−0.996012	−	0.0892198i	$-0.971563\pi$
$733$		−	3541.17i		−	0.178440i	0.996012	−	0.0892198i	$-0.0284374\pi$
$734$	4885.90	−	2820.88i	0.245698	−	0.141854i
$735$	−3381.67	+	1952.41i	−0.169707	+	0.0979804i
$736$		−	1235.08i		−	0.0618557i
$737$	−11096.1	−	19219.0i	−0.554586	−	0.960571i
$738$	−1357.46	+	2351.19i	−0.0677084	+	0.117274i
$739$	−33976.8	−	19616.5i	−1.69128	−	0.976460i	−0.953488	−	0.301431i	$-0.902536\pi$
$739$	−33976.8	−	19616.5i	−1.69128	−	0.976460i	−0.737791	−	0.675029i	$-0.764131\pi$
$740$	4971.57			0.246971
$741$		0			0
$742$	7874.03			0.389575
$743$	−33081.1	−	19099.4i	−1.63341	−	0.943052i	−0.983030	−	0.183446i	$-0.941275\pi$
$743$	−33081.1	−	19099.4i	−1.63341	−	0.943052i	−0.650383	−	0.759606i	$-0.725392\pi$
$744$	−1303.97	+	2258.54i	−0.0642551	+	0.111293i
$745$	4895.93	+	8480.00i	0.240769	+	0.417024i
$746$		−	25859.4i		−	1.26914i
$747$	−27562.9	+	15913.4i	−1.35003	+	0.779441i
$748$	23206.3	−	13398.2i	1.13437	−	0.654928i
$749$			1722.69i			0.0840399i
$750$	−8055.23	−	13952.1i	−0.392180	−	0.679277i
$751$	−835.377	+	1446.92i	−0.0405903	+	0.0703045i	−0.885607	−	0.464436i	$-0.846257\pi$
$751$	−835.377	+	1446.92i	−0.0405903	+	0.0703045i	0.845017	+	0.534740i	$0.179591\pi$
$752$	−4163.38	−	2403.73i	−0.201892	−	0.116562i
$753$	−23065.9			−1.11629
$754$		0			0
$755$	−9242.70			−0.445532
$756$	−11432.3	−	6600.42i	−0.549983	−	0.317533i
$757$	18974.3	−	32864.4i	0.911007	−	1.57791i	0.0983617	−	0.995151i	$-0.468640\pi$
$757$	18974.3	−	32864.4i	0.911007	−	1.57791i	0.812645	−	0.582759i	$-0.198027\pi$
$758$	−2288.05	−	3963.01i	−0.109638	−	0.189899i
$759$		−	18497.4i		−	0.884600i
$760$	237.423	−	137.076i	0.0113319	−	0.00654247i
$761$	32712.1	−	18886.4i	1.55823	−	0.899645i	0.560805	−	0.827948i	$-0.310492\pi$
$761$	32712.1	−	18886.4i	1.55823	−	0.899645i	0.997426	−	0.0716969i	$-0.0228414\pi$
$762$			4337.06i			0.206188i
$763$	14647.4	+	25370.1i	0.694984	+	1.20375i
$764$	−1227.39	+	2125.91i	−0.0581224	+	0.100671i
$765$	−21404.5	−	12357.9i	−1.01161	−	0.584053i
$766$	−24312.4			−1.14679
$767$		0			0
$768$	−2269.56			−0.106635
$769$	11321.8	+	6536.64i	0.530916	+	0.306524i	0.741389	−	0.671075i	$-0.234167\pi$
$769$	11321.8	+	6536.64i	0.530916	+	0.306524i	−0.210474	+	0.977600i	$0.567501\pi$
$770$	3162.51	−	5477.63i	0.148012	−	0.256364i
$771$	−18693.2	−	32377.7i	−0.873179	−	1.51239i
$772$			8021.32i			0.373955i
$773$	−21774.6	+	12571.5i	−1.01316	+	0.584951i	−0.912117	−	0.409931i	$-0.865553\pi$
$773$	−21774.6	+	12571.5i	−1.01316	+	0.584951i	−0.101048	+	0.994882i	$0.532220\pi$
$774$	−12300.2	+	7101.55i	−0.571218	+	0.329793i
$775$		−	4046.96i		−	0.187575i
$776$	2965.94	+	5137.15i	0.137205	+	0.237646i
$777$	−21571.1	+	37362.3i	−0.995959	+	1.72505i
$778$	−2562.93	−	1479.71i	−0.118105	−	0.0681879i
$779$	233.243			0.0107276
$780$		0			0
$781$	−22944.7			−1.05125
$782$	8284.41	+	4783.01i	0.378836	+	0.218721i
$783$	−20430.5	+	35386.6i	−0.932472	+	1.61509i
$784$	−911.566	−	1578.88i	−0.0415254	−	0.0719241i
$785$			7450.63i			0.338757i
$786$	−24808.6	+	14323.2i	−1.12582	+	0.649991i
$787$	−16597.0	+	9582.29i	−0.751740	+	0.434017i	−0.826322	−	0.563197i	$-0.809571\pi$
$787$	−16597.0	+	9582.29i	−0.751740	+	0.434017i	0.0745822	+	0.997215i	$0.476238\pi$
$788$			2230.00i			0.100813i
$789$	28698.9	+	49708.0i	1.29494	+	2.24290i
$790$	2835.48	−	4911.19i	0.127698	−	0.221180i
$791$	−24887.1	−	14368.6i	−1.11869	−	0.645877i
$792$	−22313.7			−1.00111
$793$		0			0
$794$	30542.5			1.36513
$795$	−7720.25	−	4457.29i	−0.344414	−	0.198847i
$796$	−11067.9	+	19170.2i	−0.492830	+	0.853607i
$797$	14495.7	+	25107.3i	0.644246	+	1.11587i	0.984475	+	0.175525i	$0.0561622\pi$
$797$	14495.7	+	25107.3i	0.644246	+	1.11587i	−0.340229	+	0.940343i	$0.610504\pi$
$798$			2379.04i			0.105535i
$799$	32246.3	−	18617.4i	1.42777	−	0.824326i
$800$	3050.02	−	1760.93i	0.134793	−	0.0778229i
$801$			10689.3i			0.471519i
$802$	−2564.54	−	4441.92i	−0.112914	−	0.195573i
$803$	−11405.8	+	19755.4i	−0.501248	+	0.868186i
$804$	−12607.5	−	7278.97i	−0.553027	−	0.319290i
$805$	2257.96			0.0988606
$806$		0			0
$807$	11534.3			0.503129
$808$	2863.46	+	1653.22i	0.124674	+	0.0719803i
$809$	8446.41	−	14629.6i	0.367070	−	0.635784i	−0.622036	−	0.782989i	$-0.713694\pi$
$809$	8446.41	−	14629.6i	0.367070	−	0.635784i	0.989106	+	0.147204i	$0.0470275\pi$
$810$	2087.67	+	3615.96i	0.0905597	+	0.156854i
$811$		−	42182.9i		−	1.82644i	−0.407466	−	0.913220i	$-0.633587\pi$
$811$		−	42182.9i		−	1.82644i	0.407466	−	0.913220i	$-0.366413\pi$
$812$	9824.17	−	5671.99i	0.424582	−	0.245133i
$813$	−23644.6	+	13651.2i	−1.01999	+	0.588892i
$814$			34763.6i			1.49688i
$815$	4287.81	+	7426.70i	0.184289	+	0.319198i
$816$	8789.12	−	15223.2i	0.377060	−	0.653087i
$817$	1056.73	+	610.105i	0.0452514	+	0.0261259i
$818$	−2104.94			−0.0899725
$819$		0			0
$820$	−406.789			−0.0173240
$821$	16022.1	+	9250.39i	0.681092	+	0.393229i	0.800266	−	0.599645i	$-0.204691\pi$
$821$	16022.1	+	9250.39i	0.681092	+	0.393229i	−0.119174	+	0.992873i	$0.538025\pi$
$822$	−20407.8	+	35347.4i	−0.865942	+	1.49986i
$823$	−13934.4	−	24135.0i	−0.590184	−	1.02223i	−0.994207	−	0.107480i	$-0.965722\pi$
$823$	−13934.4	−	24135.0i	−0.590184	−	1.02223i	0.404024	−	0.914749i	$-0.367611\pi$
$824$		−	30.1370i		−	0.00127412i
$825$	45679.0	−	26372.8i	1.92768	−	1.11295i
$826$	−6450.12	+	3723.98i	−0.271705	+	0.156869i
$827$		−	2541.96i		−	0.106884i	−0.998571	−	0.0534418i	$-0.982981\pi$
$827$		−	2541.96i		−	0.106884i	0.998571	−	0.0534418i	$-0.0170192\pi$
$828$	−3982.87	−	6898.53i	−0.167167	−	0.289542i
$829$	14785.0	−	25608.4i	0.619427	−	1.07288i	−0.370164	−	0.928967i	$-0.620698\pi$
$829$	14785.0	−	25608.4i	0.619427	−	1.07288i	0.989590	−	0.143912i	$-0.0459682\pi$
$830$	−4129.87	−	2384.38i	−0.172711	−	0.0997147i
$831$	−55745.1			−2.32705
$832$		0			0
$833$	14120.6			0.587333
$834$	−43134.5	−	24903.7i	−1.79092	−	1.03399i
$835$	2915.08	−	5049.07i	0.120815	−	0.209258i
$836$	958.502	+	1660.17i	0.0396537	+	0.0686822i
$837$			8018.23i			0.331124i
$838$	15089.0	−	8711.62i	0.622004	−	0.359114i
$839$	−18712.6	+	10803.7i	−0.770002	+	0.444561i	−0.832875	−	0.553460i	$-0.813307\pi$
$839$	−18712.6	+	10803.7i	−0.770002	+	0.444561i	0.0628731	+	0.998022i	$0.479974\pi$
$840$		−	4149.17i		−	0.170429i
$841$	−5362.17	−	9287.54i	−0.219860	−	0.380809i
$842$	213.335	−	369.507i	0.00873161	−	0.0151236i
$843$	24768.3	+	14300.0i	1.01194	+	0.584244i
$844$	18734.9			0.764079
$845$		0			0
$846$	−31005.9			−1.26005
$847$	20856.9	+	12041.7i	0.846105	+	0.488499i
$848$	2081.08	−	3604.53i	0.0842741	−	0.145967i
$849$	1713.62	+	2968.08i	0.0692713	+	0.119981i
$850$			27277.6i			1.10072i
$851$	−10747.6	+	6205.10i	−0.432928	+	0.249951i
$852$	−13035.0	+	7525.78i	−0.524146	+	0.302616i
$853$			28695.1i			1.15182i	0.817513	+	0.575910i	$0.195352\pi$
$853$			28695.1i			1.15182i	−0.817513	+	0.575910i	$0.804648\pi$
$854$	1381.86	+	2393.46i	0.0553705	+	0.0959045i
$855$	884.080	−	1531.27i	0.0353625	−	0.0612496i
$856$	788.605	+	455.301i	0.0314883	+	0.0181798i
$857$	−8720.01			−0.347573			−0.173786	−	0.984783i	$-0.555600\pi$
$857$	−8720.01			−0.347573			−0.173786	+	0.984783i	$0.555600\pi$
$858$		0			0
$859$	−1750.23			−0.0695191			−0.0347596	−	0.999396i	$-0.511067\pi$
$859$	−1750.23			−0.0695191			−0.0347596	+	0.999396i	$0.511067\pi$
$860$	−1843.00	−	1064.06i	−0.0730765	−	0.0421907i
$861$	1765.01	−	3057.09i	0.0698624	−	0.121005i
$862$	8953.45	+	15507.8i	0.353777	+	0.612759i
$863$		−	35493.3i		−	1.40001i	−0.714139	−	0.700004i	$-0.753181\pi$
$863$		−	35493.3i		−	1.40001i	0.714139	−	0.700004i	$-0.246819\pi$
$864$	−6043.01	+	3488.93i	−0.237948	+	0.137379i
$865$	5712.56	−	3298.15i	0.224547	−	0.129642i
$866$		−	11722.9i		−	0.460000i
$867$	46295.8	+	80186.6i	1.81348	+	3.14104i
$868$	1113.03	−	1927.82i	0.0435237	−	0.0753852i
$869$	34341.4	+	19827.0i	1.34056	+	0.773975i
$870$	−12843.1			−0.500483
$871$		0			0
$872$	15485.0			0.601364
$873$	33132.3	+	19128.9i	1.28449	+	0.741600i
$874$	−342.175	+	592.664i	−0.0132428	+	0.0229372i
$875$	6875.68	+	11909.0i	0.265646	+	0.460113i
$876$			14964.3i			0.577164i
$877$	−22887.2	+	13213.9i	−0.881237	+	0.508782i	−0.871066	−	0.491166i	$-0.836571\pi$
$877$	−22887.2	+	13213.9i	−0.881237	+	0.508782i	−0.0101709	+	0.999948i	$0.503238\pi$
$878$	18088.7	−	10443.5i	0.695290	−	0.401426i
$879$			19440.4i			0.745970i
$880$	−1671.68	−	2895.43i	−0.0640367	−	0.110915i
$881$	383.063	−	663.484i	0.0146489	−	0.0253727i	−0.858608	−	0.512633i	$-0.828670\pi$
$881$	383.063	−	663.484i	0.0146489	−	0.0253727i	0.873257	+	0.487260i	$0.162004\pi$
$882$	−10183.0	−	5879.19i	−0.388754	−	0.224447i
$883$	−6521.89			−0.248561			−0.124280	−	0.992247i	$-0.539662\pi$
$883$	−6521.89			−0.248561			−0.124280	+	0.992247i	$0.539662\pi$
$884$		0			0
$885$	8432.19			0.320277
$886$	−15224.3	−	8789.73i	−0.577279	−	0.333292i
$887$	−12675.8	+	21955.2i	−0.479834	+	0.831097i	−0.999732	−	0.0231313i	$-0.992636\pi$
$887$	−12675.8	+	21955.2i	−0.479834	+	0.831097i	0.519899	+	0.854228i	$0.325970\pi$
$888$	11402.3	+	19749.4i	0.430898	+	0.746337i
$889$		−	3701.97i		−	0.139663i
$890$	−1387.04	+	800.810i	−0.0522402	+	0.0301609i
$891$	−25284.5	+	14598.0i	−0.950686	+	0.548879i
$892$			9535.45i			0.357926i
$893$	1331.88	+	2306.89i	0.0499102	+	0.0864470i
$894$	−22457.7	+	38897.9i	−0.840154	+	1.45519i
$895$	1992.56	+	1150.40i	0.0744178	+	0.0429651i
$896$	1937.22			0.0722299
$897$		0			0
$898$	17272.2			0.641851
$899$	−5967.23	−	3445.18i	−0.221377	−	0.127812i
$900$	11357.2	−	19671.3i	0.420637	−	0.728565i
$901$	16118.4	+	27917.9i	0.595985	+	1.03228i
$902$		−	2844.46i		−	0.105000i
$903$	15993.2	−	9233.67i	0.589390	−	0.340285i
$904$	−13155.2	+	7595.13i	−0.483998	+	0.279436i
$905$		−	1557.80i		−	0.0572190i
$906$	−21198.2	−	36716.4i	−0.777332	−	1.34638i
$907$	−4752.28	+	8231.20i	−0.173977	+	0.301337i	−0.939807	−	0.341707i	$-0.888995\pi$
$907$	−4752.28	+	8231.20i	−0.173977	+	0.301337i	0.765830	+	0.643043i	$0.222328\pi$
$908$	−5383.47	−	3108.15i	−0.196759	−	0.113599i
$909$	21325.1			0.778116
$910$		0			0
$911$	6435.82			0.234059			0.117030	−	0.993128i	$-0.462663\pi$
$911$	6435.82			0.234059			0.117030	+	0.993128i	$0.462663\pi$
$912$	1089.06	+	628.771i	0.0395422	+	0.0228297i
$913$	16672.7	−	28878.0i	0.604367	−	1.04679i
$914$	4876.96	+	8447.14i	0.176494	+	0.305697i
$915$		−	3128.95i		−	0.113049i
$916$	−10099.9	+	5831.20i	−0.364313	+	0.210336i
$917$	21175.8	−	12225.9i	0.762581	−	0.440276i
$918$		−	54045.2i		−	1.94309i
$919$	−7476.96	−	12950.5i	−0.268381	−	0.464849i	0.700063	−	0.714081i	$-0.253155\pi$
$919$	−7476.96	−	12950.5i	−0.268381	−	0.464849i	−0.968444	+	0.249232i	$0.919822\pi$
$920$	596.771	−	1033.64i	0.0213858	−	0.0370413i
$921$	62066.3	+	35834.0i	2.22058	+	1.28205i
$922$	23607.8			0.843256
$923$		0			0
$924$	29013.0			1.03296
$925$	−30646.8	−	17694.0i	−1.08936	−	0.628945i
$926$	4797.53	−	8309.56i	0.170255	−	0.294891i
$927$	−97.1849	−	168.329i	−0.00344334	−	0.00596403i
$928$		−	5996.34i		−	0.212111i
$929$	−32962.5	+	19030.9i	−1.16412	+	0.672103i	−0.952287	−	0.305204i	$-0.901275\pi$
$929$	−32962.5	+	19030.9i	−1.16412	+	0.672103i	−0.211829	+	0.977307i	$0.567942\pi$
$930$	−2182.57	+	1260.11i	−0.0769564	+	0.0444308i
$931$			1010.18i			0.0355611i
$932$	8467.86	+	14666.8i	0.297611	+	0.515478i
$933$	−1083.40	+	1876.50i	−0.0380160	+	0.0658456i
$934$	−22843.6	−	13188.7i	−0.800282	−	0.462043i
$935$	25895.1			0.905732
$936$		0			0
$937$	14572.5			0.508072			0.254036	−	0.967195i	$-0.418242\pi$
$937$	14572.5			0.508072			0.254036	+	0.967195i	$0.418242\pi$
$938$	10761.4	+	6213.09i	0.374597	+	0.216274i
$939$	19699.6	−	34120.7i	0.684635	−	1.18582i
$940$	−2322.88	−	4023.34i	−0.0805999	−	0.139603i
$941$			32190.2i			1.11516i	0.830122	+	0.557582i	$0.188271\pi$
$941$			32190.2i			1.11516i	−0.830122	+	0.557582i	$0.811729\pi$
$942$	−29597.4	+	17088.1i	−1.02371	+	0.591040i
$943$	879.397	−	507.720i	0.0303681	−	0.0175330i
$944$			3936.93i			0.135738i
$945$	−6378.42	−	11047.7i	−0.219566	−	0.380300i
$946$	7440.38	−	12887.1i	0.255716	−	0.442914i
$947$	−36573.1	−	21115.5i	−1.25498	−	0.724563i	−0.282886	−	0.959154i	$-0.591292\pi$
$947$	−36573.1	−	21115.5i	−1.25498	−	0.724563i	−0.972094	+	0.234590i	$0.924625\pi$
$948$	26012.8			0.891197
$949$		0			0
$950$	−1951.43			−0.0666451
$951$	7144.86	+	4125.09i	0.243626	+	0.140657i
$952$	−7502.11	+	12994.0i	−0.255404	+	0.442373i
$953$	−4084.22	−	7074.07i	−0.138826	−	0.240453i	0.788227	−	0.615385i	$-0.210999\pi$
$953$	−4084.22	−	7074.07i	−0.138826	−	0.240453i	−0.927052	+	0.374932i	$0.877666\pi$
$954$		−	26844.0i		−	0.911013i
$955$	−2054.40	+	1186.11i	−0.0696114	+	0.0401901i
$956$	−8218.77	+	4745.11i	−0.278048	+	0.160531i
$957$		−	89804.7i		−	3.03341i
$958$	−18048.8	−	31261.5i	−0.608696	−	1.05429i
$959$	17419.5	−	30171.4i	0.586552	−	1.01594i
$960$	−1899.39	−	1096.61i	−0.0638567	−	0.0368677i
$961$	28438.9			0.954613
$962$		0			0
$963$	5872.98			0.196525
$964$	−1128.48	−	651.526i	−0.0377031	−	0.0217679i
$965$	−3875.76	+	6713.01i	−0.129290	+	0.223937i
$966$	5178.66	+	8969.70i	0.172485	+	0.298753i
$967$			52022.1i			1.73001i	0.501766	+	0.865003i	$0.332684\pi$
$967$			52022.1i			1.73001i	−0.501766	+	0.865003i	$0.667316\pi$
$968$	11024.8	−	6365.16i	0.366064	−	0.211347i
$969$	−8435.05	+	4869.98i	−0.279642	+	0.161451i
$970$			5732.35i			0.189747i
$971$	5972.47	+	10344.6i	0.197390	+	0.341890i	0.947681	−	0.319218i	$-0.103420\pi$
$971$	5972.47	+	10344.6i	0.197390	+	0.341890i	−0.750291	+	0.661107i	$0.770087\pi$
$972$	2198.96	−	3808.70i	0.0725633	−	0.125683i
$973$	36818.2	+	21257.0i	1.21309	+	0.700378i
$974$	−23002.5			−0.756722
$975$		0			0
$976$	1460.88			0.0479117
$977$	−16445.7	−	9494.95i	−0.538532	−	0.310922i	0.205952	−	0.978562i	$-0.433971\pi$
$977$	−16445.7	−	9494.95i	−0.538532	−	0.310922i	−0.744484	+	0.667640i	$0.767304\pi$
$978$	−19668.2	+	34066.4i	−0.643068	+	1.11383i
$979$	−5599.64	−	9698.86i	−0.182804	−	0.316626i
$980$		−	1761.81i		−	0.0574275i
$981$	86491.3	−	49935.8i	2.81494	−	1.62520i
$982$	6929.34	−	4000.65i	0.225177	−	0.130006i
$983$			47187.4i			1.53107i	0.643392	+	0.765537i	$0.277526\pi$
$983$			47187.4i			1.53107i	−0.643392	+	0.765537i	$0.722474\pi$
$984$	−932.973	−	1615.96i	−0.0302257	−	0.0523524i
$985$	−1077.50	+	1866.28i	−0.0348547	+	0.0603701i
$986$	40220.8	+	23221.5i	1.29908	+	0.750024i
$987$	40314.9			1.30014
$988$		0			0
$989$	5312.27			0.170799
$990$	−18674.2	−	10781.6i	−0.599501	−	0.346122i
$991$	15379.7	−	26638.5i	0.492991	−	0.853885i	−0.506977	−	0.861960i	$-0.669237\pi$
$991$	15379.7	−	26638.5i	0.492991	−	0.853885i	0.999967	+	0.00807499i	$0.00257038\pi$
$992$	−588.337	−	1019.03i	−0.0188303	−	0.0326151i
$993$		−	42796.7i		−	1.36769i
$994$	11126.3	−	6423.76i	0.355034	−	0.204979i
$995$	−18525.5	+	10695.7i	−0.590248	+	0.340780i
$996$		−	21874.4i		−	0.695901i
$997$	−24666.1	−	42722.9i	−0.783533	−	1.35712i	−0.929871	−	0.367885i	$-0.880082\pi$
$997$	−24666.1	−	42722.9i	−0.783533	−	1.35712i	0.146338	−	0.989235i	$-0.453251\pi$
$998$	−8322.72	+	14415.4i	−0.263979	+	0.457225i
$999$	60720.5	+	35057.0i	1.92304	+	1.11027i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.f.147.2		8
13.2	odd	12		26.4.c.b.3.2	✓	4
13.3	even	3	inner	338.4.e.f.23.4		8
13.4	even	6		338.4.b.e.337.1		4
13.5	odd	4		26.4.c.b.9.2	yes	4
13.6	odd	12		338.4.a.h.1.1		2
13.7	odd	12		338.4.a.g.1.1		2
13.8	odd	4		338.4.c.j.191.2		4
13.9	even	3		338.4.b.e.337.3		4
13.10	even	6	inner	338.4.e.f.23.2		8
13.11	odd	12		338.4.c.j.315.2		4
13.12	even	2	inner	338.4.e.f.147.4		8
39.2	even	12		234.4.h.h.55.1		4
39.5	even	4		234.4.h.h.217.1		4
52.15	even	12		208.4.i.d.81.1		4
52.31	even	4		208.4.i.d.113.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
26.4.c.b.3.2	✓	4	13.2	odd	12
26.4.c.b.9.2	yes	4	13.5	odd	4
208.4.i.d.81.1		4	52.15	even	12
208.4.i.d.113.1		4	52.31	even	4
234.4.h.h.55.1		4	39.2	even	12
234.4.h.h.217.1		4	39.5	even	4
338.4.a.g.1.1		2	13.7	odd	12
338.4.a.h.1.1		2	13.6	odd	12
338.4.b.e.337.1		4	13.4	even	6
338.4.b.e.337.3		4	13.9	even	3
338.4.c.j.191.2		4	13.8	odd	4
338.4.c.j.315.2		4	13.11	odd	12
338.4.e.f.23.2		8	13.10	even	6	inner
338.4.e.f.23.4		8	13.3	even	3	inner
338.4.e.f.147.2		8	1.1	even	1	trivial
338.4.e.f.147.4		8	13.12	even	2	inner

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(4.43273 - 7.67771i) q^{3} +(2.00000 + 3.46410i) q^{4} +3.86546i q^{5} +(-15.3554 + 8.86546i) q^{6} +(13.1069 - 7.56727i) q^{7} -8.00000i q^{8} +(-25.7982 - 44.6838i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.00000i) q^{2} +(4.43273 - 7.67771i) q^{3} +(2.00000 + 3.46410i) q^{4} +3.86546i q^{5} +(-15.3554 + 8.86546i) q^{6} +(13.1069 - 7.56727i) q^{7} -8.00000i q^{8} +(-25.7982 - 44.6838i) q^{9} +(3.86546 - 6.69517i) q^{10} +(46.8158 + 27.0291i) q^{11} +35.4618 q^{12} -30.2691 q^{14} +(29.6779 + 17.1345i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-61.9618 - 107.321i) q^{17} +103.193i q^{18} +(7.67771 - 4.43273i) q^{19} +(-13.3903 + 7.73092i) q^{20} -134.175i q^{21} +(-54.0582 - 93.6316i) q^{22} +(19.2982 - 33.4254i) q^{23} +(-61.4217 - 35.4618i) q^{24} +110.058 q^{25} -218.058 q^{27} +(52.4276 + 30.2691i) q^{28} +(93.6928 - 162.281i) q^{29} +(-34.2691 - 59.3558i) q^{30} -36.7710i q^{31} +(27.7128 - 16.0000i) q^{32} +(415.044 - 239.625i) q^{33} +247.847i q^{34} +(29.2510 + 50.6642i) q^{35} +(103.193 - 178.735i) q^{36} +(-278.460 - 160.769i) q^{37} -17.7309 q^{38} +30.9237 q^{40} +(22.7844 + 13.1546i) q^{41} +(-134.175 + 232.397i) q^{42} +(68.8182 + 119.197i) q^{43} +216.233i q^{44} +(172.723 - 99.7219i) q^{45} +(-66.8509 + 38.5964i) q^{46} +300.466i q^{47} +(70.9237 + 122.843i) q^{48} +(-56.9728 + 98.6799i) q^{49} +(-190.626 - 110.058i) q^{50} -1098.64 q^{51} -260.135 q^{53} +(377.688 + 218.058i) q^{54} +(-104.480 + 180.965i) q^{55} +(-60.5382 - 104.855i) q^{56} -78.5964i q^{57} +(-324.561 + 187.386i) q^{58} +(213.093 - 123.029i) q^{59} +137.076i q^{60} +(-45.6526 - 79.0727i) q^{61} +(-36.7710 + 63.6893i) q^{62} +(-676.268 - 390.444i) q^{63} -64.0000 q^{64} -958.502 q^{66} +(-355.524 - 205.262i) q^{67} +(247.847 - 429.284i) q^{68} +(-171.087 - 296.332i) q^{69} -117.004i q^{70} +(-367.579 + 212.222i) q^{71} +(-357.470 + 206.386i) q^{72} +421.982i q^{73} +(321.538 + 556.920i) q^{74} +(487.858 - 844.995i) q^{75} +(30.7109 + 17.7309i) q^{76} +818.146 q^{77} +733.542 q^{79} +(-53.5614 - 30.9237i) q^{80} +(-270.042 + 467.727i) q^{81} +(-26.3092 - 45.5689i) q^{82} -616.843i q^{83} +(464.795 - 268.349i) q^{84} +(414.845 - 239.511i) q^{85} -275.273i q^{86} +(-830.629 - 1438.69i) q^{87} +(216.233 - 374.526i) q^{88} +(-179.415 - 103.585i) q^{89} -398.887 q^{90} +154.386 q^{92} +(-282.317 - 162.996i) q^{93} +(300.466 - 520.422i) q^{94} +(17.1345 + 29.6779i) q^{95} -283.695i q^{96} +(-642.144 + 370.742i) q^{97} +(197.360 - 113.946i) q^{98} -2789.21i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 6 q^{3} + 16 q^{4} - 118 q^{9}+O(q^{10}) \) 8 * q + 6 * q^3 + 16 * q^4 - 118 * q^9	\( 8 q + 6 q^{3} + 16 q^{4} - 118 q^{9} - 28 q^{10} + 48 q^{12} - 360 q^{14} - 64 q^{16} - 260 q^{17} - 20 q^{22} + 66 q^{23} + 468 q^{25} - 1332 q^{27} + 396 q^{29} - 392 q^{30} - 532 q^{35} + 472 q^{36} - 24 q^{38} - 224 q^{40} + 164 q^{42} - 186 q^{43} + 96 q^{48} + 870 q^{49} - 4252 q^{51} - 2140 q^{53} - 1484 q^{55} - 720 q^{56} - 1308 q^{61} + 1120 q^{62} - 512 q^{64} - 6136 q^{66} + 1040 q^{68} - 750 q^{69} + 2808 q^{74} + 1870 q^{75} - 2588 q^{77} + 3040 q^{79} + 668 q^{81} + 968 q^{82} - 3198 q^{87} + 80 q^{88} - 952 q^{90} + 528 q^{92} - 896 q^{94} + 196 q^{95}+O(q^{100}) \) 8 * q + 6 * q^3 + 16 * q^4 - 118 * q^9 - 28 * q^10 + 48 * q^12 - 360 * q^14 - 64 * q^16 - 260 * q^17 - 20 * q^22 + 66 * q^23 + 468 * q^25 - 1332 * q^27 + 396 * q^29 - 392 * q^30 - 532 * q^35 + 472 * q^36 - 24 * q^38 - 224 * q^40 + 164 * q^42 - 186 * q^43 + 96 * q^48 + 870 * q^49 - 4252 * q^51 - 2140 * q^53 - 1484 * q^55 - 720 * q^56 - 1308 * q^61 + 1120 * q^62 - 512 * q^64 - 6136 * q^66 + 1040 * q^68 - 750 * q^69 + 2808 * q^74 + 1870 * q^75 - 2588 * q^77 + 3040 * q^79 + 668 * q^81 + 968 * q^82 - 3198 * q^87 + 80 * q^88 - 952 * q^90 + 528 * q^92 - 896 * q^94 + 196 * q^95

Introduction

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