LMFDB - Embedded newform 169.3.f.d.80.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [169,3,Mod(19,169)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("169.19"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(169, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 169 = 13^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	169.f (of order $12$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,-4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$4.60491646769$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	8.0.3317760000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 25x^{4} + 625 $ x^8 - 25*x^4 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 13)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			80.1
Root			$2.15988 - 0.578737i$ of defining polynomial
Character	$\chi$	$=$	169.80
Dual form			169.3.f.d.150.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-3.52590 - 0.944762i) q^{2} +(-1.08114 - 1.87259i) q^{3} +(8.07530 + 4.66228i) q^{4} +(-0.418861 + 0.418861i) q^{5} +(2.04284 + 7.62398i) q^{6} +(-1.93820 + 0.519339i) q^{7} +(-13.7434 - 13.7434i) q^{8} +(2.16228 - 3.74517i) q^{9} +(1.87259 - 1.08114i) q^{10} +(2.68097 - 10.0055i) q^{11} -20.1623i q^{12} +7.32456 q^{14} +(1.23720 + 0.331507i) q^{15} +(16.8246 + 29.1410i) q^{16} +(-13.8336 - 7.98683i) q^{17} +(-11.1623 + 11.1623i) q^{18} +(1.15747 + 4.31975i) q^{19} +(-5.33528 + 1.42958i) q^{20} +(3.06797 + 3.06797i) q^{21} +(-18.9057 + 32.7456i) q^{22} +(-23.8043 + 13.7434i) q^{23} +(-10.8772 + 40.5943i) q^{24} +24.6491i q^{25} -28.8114 q^{27} +(-18.0729 - 4.84261i) q^{28} +(-12.9057 - 22.3533i) q^{29} +(-4.04905 - 2.33772i) q^{30} +(-19.4868 + 19.4868i) q^{31} +(-11.6687 - 43.5480i) q^{32} +(-21.6347 + 5.79701i) q^{33} +(41.2302 + 41.2302i) q^{34} +(0.594306 - 1.02937i) q^{35} +(34.9221 - 20.1623i) q^{36} +(1.54838 - 5.77863i) q^{37} -16.3246i q^{38} +11.5132 q^{40} +(15.2480 + 4.08568i) q^{41} +(-7.91886 - 13.7159i) q^{42} +(-9.97070 - 5.75658i) q^{43} +(68.2982 - 68.2982i) q^{44} +(0.663014 + 2.47440i) q^{45} +(96.9159 - 25.9685i) q^{46} +(-35.3662 - 35.3662i) q^{47} +(36.3794 - 63.0109i) q^{48} +(-38.9483 + 22.4868i) q^{49} +(23.2876 - 86.9103i) q^{50} +34.5395i q^{51} -4.18861 q^{53} +(101.586 + 27.2199i) q^{54} +(3.06797 + 5.31388i) q^{55} +(33.7750 + 19.5000i) q^{56} +(6.83772 - 6.83772i) q^{57} +(24.3856 + 91.0084i) q^{58} +(-41.3522 + 11.0803i) q^{59} +(8.44520 + 8.44520i) q^{60} +(33.8377 - 58.6087i) q^{61} +(87.1191 - 50.2982i) q^{62} +(-2.24591 + 8.38185i) q^{63} +29.9737i q^{64} +81.7587 q^{66} +(-110.762 - 29.6785i) q^{67} +(-74.4737 - 128.992i) q^{68} +(51.4715 + 29.7171i) q^{69} +(-3.06797 + 3.06797i) q^{70} +(-18.4642 - 68.9094i) q^{71} +(-81.1886 + 21.7544i) q^{72} +(31.6228 + 31.6228i) q^{73} +(-10.9189 + 18.9120i) q^{74} +(46.1576 - 26.6491i) q^{75} +(-10.7929 + 40.2798i) q^{76} +20.7851i q^{77} +50.7851 q^{79} +(-19.2532 - 5.15887i) q^{80} +(11.6886 + 20.2453i) q^{81} +(-49.9028 - 28.8114i) q^{82} +(-18.6228 + 18.6228i) q^{83} +(10.4711 + 39.0785i) q^{84} +(9.13973 - 2.44898i) q^{85} +(29.7171 + 29.7171i) q^{86} +(-27.9057 + 48.3341i) q^{87} +(-174.356 + 100.664i) q^{88} +(-33.3484 + 124.458i) q^{89} -9.35089i q^{90} -256.302 q^{92} +(57.5588 + 15.4228i) q^{93} +(91.2851 + 158.110i) q^{94} +(-2.29420 - 1.32456i) q^{95} +(-68.9320 + 68.9320i) q^{96} +(-31.9742 - 119.329i) q^{97} +(158.573 - 42.4894i) q^{98} +(-31.6754 - 31.6754i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 4 q^{3} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 72 q^{8} - 8 q^{9} - 4 q^{11} + 8 q^{14} - 28 q^{15} + 84 q^{16} - 64 q^{18} + 16 q^{20} - 64 q^{21} - 88 q^{22} + 24 q^{24} - 104 q^{27} + 4 q^{28}+ \cdots - 304 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 4 * q^3 - 16 * q^5 - 16 * q^6 - 12 * q^7 - 72 * q^8 - 8 * q^9 - 4 * q^11 + 8 * q^14 - 28 * q^15 + 84 * q^16 - 64 * q^18 + 16 * q^20 - 64 * q^21 - 88 * q^22 + 24 * q^24 - 104 * q^27 + 4 * q^28 - 40 * q^29 - 80 * q^31 + 20 * q^32 - 76 * q^33 + 216 * q^34 + 68 * q^35 + 40 * q^37 + 168 * q^40 + 32 * q^41 - 76 * q^42 + 344 * q^44 + 56 * q^45 + 132 * q^46 + 8 * q^47 + 76 * q^48 - 128 * q^50 - 160 * q^53 + 152 * q^54 - 64 * q^55 + 80 * q^57 - 140 * q^58 + 56 * q^59 + 232 * q^60 + 296 * q^61 - 64 * q^63 + 224 * q^66 - 84 * q^67 - 444 * q^68 + 64 * q^70 + 284 * q^71 - 48 * q^72 - 100 * q^74 + 80 * q^76 + 128 * q^79 - 88 * q^80 + 220 * q^81 + 104 * q^83 - 184 * q^84 - 144 * q^85 + 48 * q^86 - 160 * q^87 + 200 * q^89 - 912 * q^92 + 80 * q^93 + 452 * q^94 - 640 * q^96 - 68 * q^97 + 224 * q^98 - 304 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/169\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{12}\right)$

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 $

$2$	−3.52590	−	0.944762i	−1.76295	−	0.472381i	−0.775639	−	0.631177i	$-0.782572\pi$
$2$	−3.52590	−	0.944762i	−1.76295	−	0.472381i	−0.987312	+	0.158795i	$0.949239\pi$
$3$	−1.08114	−	1.87259i	−0.360380	−	0.624196i	0.627644	−	0.778501i	$-0.284020\pi$
$3$	−1.08114	−	1.87259i	−0.360380	−	0.624196i	−0.988023	+	0.154305i	$0.950686\pi$
$4$	8.07530	+	4.66228i	2.01883	+	1.16557i
$5$	−0.418861	+	0.418861i	−0.0837722	+	0.0837722i	−0.747751	−	0.663979i	$-0.768866\pi$
$5$	−0.418861	+	0.418861i	−0.0837722	+	0.0837722i	0.663979	+	0.747751i	$0.268866\pi$
$6$	2.04284	+	7.62398i	0.340473	+	1.27066i
$7$	−1.93820	+	0.519339i	−0.276886	+	0.0741913i	−0.394590	−	0.918857i	$-0.629113\pi$
$7$	−1.93820	+	0.519339i	−0.276886	+	0.0741913i	0.117704	+	0.993049i	$0.462447\pi$
$8$	−13.7434	−	13.7434i	−1.71793	−	1.71793i
$9$	2.16228	−	3.74517i	0.240253	−	0.416131i
$10$	1.87259	−	1.08114i	0.187259	−	0.108114i
$11$	2.68097	−	10.0055i	0.243725	−	0.909594i	−0.730295	−	0.683132i	$-0.760617\pi$
$11$	2.68097	−	10.0055i	0.243725	−	0.909594i	0.974020	−	0.226462i	$-0.0727158\pi$
$12$		−	20.1623i		−	1.68019i
$13$		0			0
$13$		0			0
$14$	7.32456			0.523183
$15$	1.23720	+	0.331507i	0.0824801	+	0.0221005i
$16$	16.8246	+	29.1410i	1.05153	+	1.82131i
$17$	−13.8336	−	7.98683i	−0.813741	−	0.469814i	0.0345122	−	0.999404i	$-0.489012\pi$
$17$	−13.8336	−	7.98683i	−0.813741	−	0.469814i	−0.848253	+	0.529591i	$0.822346\pi$
$18$	−11.1623	+	11.1623i	−0.620127	+	0.620127i
$19$	1.15747	+	4.31975i	0.0609197	+	0.227355i	0.989673	−	0.143343i	$-0.0457851\pi$
$19$	1.15747	+	4.31975i	0.0609197	+	0.227355i	−0.928753	+	0.370698i	$0.879118\pi$
$20$	−5.33528	+	1.42958i	−0.266764	+	0.0714792i
$21$	3.06797	+	3.06797i	0.146094	+	0.146094i
$22$	−18.9057	+	32.7456i	−0.859350	+	1.48844i
$23$	−23.8043	+	13.7434i	−1.03497	+	0.597540i	−0.918404	−	0.395643i	$-0.870522\pi$
$23$	−23.8043	+	13.7434i	−1.03497	+	0.597540i	−0.116565	+	0.993183i	$0.537188\pi$
$24$	−10.8772	+	40.5943i	−0.453217	+	1.69143i
$25$			24.6491i			0.985964i
$26$		0			0
$27$	−28.8114			−1.06709
$28$	−18.0729	−	4.84261i	−0.645459	−	0.172950i
$29$	−12.9057	−	22.3533i	−0.445024	−	0.770804i	0.553030	−	0.833161i	$-0.313472\pi$
$29$	−12.9057	−	22.3533i	−0.445024	−	0.770804i	−0.998054	+	0.0623573i	$0.980138\pi$
$30$	−4.04905	−	2.33772i	−0.134968	−	0.0779241i
$31$	−19.4868	+	19.4868i	−0.628608	+	0.628608i	−0.947718	−	0.319110i	$-0.896616\pi$
$31$	−19.4868	+	19.4868i	−0.628608	+	0.628608i	0.319110	+	0.947718i	$0.396616\pi$
$32$	−11.6687	−	43.5480i	−0.364645	−	1.36088i
$33$	−21.6347	+	5.79701i	−0.655598	+	0.175667i
$34$	41.2302	+	41.2302i	1.21265	+	1.21265i
$35$	0.594306	−	1.02937i	0.0169802	−	0.0294105i
$36$	34.9221	−	20.1623i	0.970058	−	0.560063i
$37$	1.54838	−	5.77863i	0.0418481	−	0.156179i	−0.941840	−	0.336061i	$-0.890905\pi$
$37$	1.54838	−	5.77863i	0.0418481	−	0.156179i	0.983688	+	0.179882i	$0.0575717\pi$
$38$		−	16.3246i		−	0.429594i
$39$		0			0
$40$	11.5132			0.287829
$41$	15.2480	+	4.08568i	0.371901	+	0.0996507i	0.439928	−	0.898033i	$-0.355004\pi$
$41$	15.2480	+	4.08568i	0.371901	+	0.0996507i	−0.0680272	+	0.997683i	$0.521670\pi$
$42$	−7.91886	−	13.7159i	−0.188544	−	0.326568i
$43$	−9.97070	−	5.75658i	−0.231877	−	0.133874i	0.379561	−	0.925167i	$-0.376075\pi$
$43$	−9.97070	−	5.75658i	−0.231877	−	0.133874i	−0.611437	+	0.791293i	$0.709408\pi$
$44$	68.2982	−	68.2982i	1.55223	−	1.55223i
$45$	0.663014	+	2.47440i	0.0147336	+	0.0549867i
$46$	96.9159	−	25.9685i	2.10687	−	0.564533i
$47$	−35.3662	−	35.3662i	−0.752472	−	0.752472i	0.222468	−	0.974940i	$-0.428589\pi$
$47$	−35.3662	−	35.3662i	−0.752472	−	0.752472i	−0.974940	+	0.222468i	$0.928589\pi$
$48$	36.3794	−	63.0109i	0.757903	−	1.31273i
$49$	−38.9483	+	22.4868i	−0.794864	+	0.458915i
$50$	23.2876	−	86.9103i	0.465751	−	1.73821i
$51$			34.5395i			0.677245i
$52$		0			0
$53$	−4.18861			−0.0790304			−0.0395152	−	0.999219i	$-0.512581\pi$
$53$	−4.18861			−0.0790304			−0.0395152	+	0.999219i	$0.512581\pi$
$54$	101.586	+	27.2199i	1.88122	+	0.504073i
$55$	3.06797	+	5.31388i	0.0557813	+	0.0966161i
$56$	33.7750	+	19.5000i	0.603125	+	0.348214i
$57$	6.83772	−	6.83772i	0.119960	−	0.119960i
$58$	24.3856	+	91.0084i	0.420442	+	1.56911i
$59$	−41.3522	+	11.0803i	−0.700884	+	0.187801i	−0.591627	−	0.806212i	$-0.701514\pi$
$59$	−41.3522	+	11.0803i	−0.700884	+	0.187801i	−0.109258	+	0.994013i	$0.534847\pi$
$60$	8.44520	+	8.44520i	0.140753	+	0.140753i
$61$	33.8377	−	58.6087i	0.554717	−	0.960798i	−0.443209	−	0.896418i	$-0.646160\pi$
$61$	33.8377	−	58.6087i	0.554717	−	0.960798i	0.997926	−	0.0643792i	$-0.0205067\pi$
$62$	87.1191	−	50.2982i	1.40515	−	0.811262i
$63$	−2.24591	+	8.38185i	−0.0356494	+	0.133045i
$64$			29.9737i			0.468339i
$65$		0			0
$66$	81.7587			1.23877
$67$	−110.762	−	29.6785i	−1.65316	−	0.442963i	−0.692666	−	0.721259i	$-0.743564\pi$
$67$	−110.762	−	29.6785i	−1.65316	−	0.442963i	−0.960496	+	0.278295i	$0.910231\pi$
$68$	−74.4737	−	128.992i	−1.09520	−	1.89694i
$69$	51.4715	+	29.7171i	0.745964	+	0.430682i
$70$	−3.06797	+	3.06797i	−0.0438282	+	0.0438282i
$71$	−18.4642	−	68.9094i	−0.260059	−	0.970555i	−0.965205	−	0.261493i	$-0.915785\pi$
$71$	−18.4642	−	68.9094i	−0.260059	−	0.970555i	0.705146	−	0.709062i	$-0.250881\pi$
$72$	−81.1886	+	21.7544i	−1.12762	+	0.302145i
$73$	31.6228	+	31.6228i	0.433189	+	0.433189i	0.889712	−	0.456523i	$-0.150905\pi$
$73$	31.6228	+	31.6228i	0.433189	+	0.433189i	−0.456523	+	0.889712i	$0.650905\pi$
$74$	−10.9189	+	18.9120i	−0.147552	+	0.255568i
$75$	46.1576	−	26.6491i	0.615435	−	0.355321i
$76$	−10.7929	+	40.2798i	−0.142012	+	0.529997i
$77$			20.7851i			0.269936i
$78$		0			0
$79$	50.7851			0.642849			0.321424	−	0.946935i	$-0.395838\pi$
$79$	50.7851			0.642849			0.321424	+	0.946935i	$0.395838\pi$
$80$	−19.2532	−	5.15887i	−0.240665	−	0.0644859i
$81$	11.6886	+	20.2453i	0.144304	+	0.249942i
$82$	−49.9028	−	28.8114i	−0.608571	−	0.351358i
$83$	−18.6228	+	18.6228i	−0.224371	+	0.224371i	−0.810336	−	0.585965i	$-0.800715\pi$
$83$	−18.6228	+	18.6228i	−0.224371	+	0.224371i	0.585965	+	0.810336i	$0.300715\pi$
$84$	10.4711	+	39.0785i	0.124655	+	0.465221i
$85$	9.13973	−	2.44898i	0.107526	−	0.0288116i
$86$	29.7171	+	29.7171i	0.345547	+	0.345547i
$87$	−27.9057	+	48.3341i	−0.320755	+	0.555564i
$88$	−174.356	+	100.664i	−1.98132	+	1.14391i
$89$	−33.3484	+	124.458i	−0.374701	+	1.39840i	0.479079	+	0.877772i	$0.340971\pi$
$89$	−33.3484	+	124.458i	−0.374701	+	1.39840i	−0.853780	+	0.520633i	$0.825696\pi$
$90$		−	9.35089i		−	0.103899i
$91$		0			0
$92$	−256.302			−2.78590
$93$	57.5588	+	15.4228i	0.618911	+	0.165837i
$94$	91.2851	+	158.110i	0.971118	+	1.68203i
$95$	−2.29420	−	1.32456i	−0.0241494	−	0.0139427i
$96$	−68.9320	+	68.9320i	−0.718042	+	0.718042i
$97$	−31.9742	−	119.329i	−0.329631	−	1.23020i	−0.909574	−	0.415542i	$-0.863592\pi$
$97$	−31.9742	−	119.329i	−0.329631	−	1.23020i	0.579943	−	0.814657i	$-0.303075\pi$
$98$	158.573	−	42.4894i	1.61809	−	0.433566i
$99$	−31.6754	−	31.6754i	−0.319954	−	0.319954i
$100$	−114.921	+	199.049i	−1.14921	+	1.99049i
$101$	7.72581	−	4.46050i	0.0764932	−	0.0441634i	−0.461266	−	0.887262i	$-0.652604\pi$
$101$	7.72581	−	4.46050i	0.0764932	−	0.0441634i	0.537759	+	0.843099i	$0.319271\pi$
$102$	32.6316	−	121.783i	0.319918	−	1.19395i
$103$		−	59.4342i		−	0.577031i	−0.957475	−	0.288515i	$-0.906838\pi$
$103$		−	59.4342i		−	0.577031i	0.957475	−	0.288515i	$-0.0931616\pi$
$104$		0			0
$105$	−2.57011			−0.0244772
$106$	14.7686	+	3.95724i	0.139327	+	0.0373325i
$107$	71.7851	+	124.335i	0.670888	+	1.16201i	0.977653	+	0.210227i	$0.0674204\pi$
$107$	71.7851	+	124.335i	0.670888	+	1.16201i	−0.306764	+	0.951786i	$0.599246\pi$
$108$	−232.661	−	134.327i	−2.15427	−	1.24377i
$109$	84.7740	−	84.7740i	0.777743	−	0.777743i	−0.201703	−	0.979447i	$-0.564648\pi$
$109$	84.7740	−	84.7740i	0.777743	−	0.777743i	0.979447	+	0.201703i	$0.0646477\pi$
$110$	−5.79701	−	21.6347i	−0.0527001	−	0.196679i
$111$	−12.4950	+	3.34802i	−0.112568	+	0.0301624i
$112$	−47.7434	−	47.7434i	−0.426281	−	0.426281i
$113$	54.2719	−	94.0017i	0.480282	−	0.831873i	−0.519462	−	0.854494i	$-0.673868\pi$
$113$	54.2719	−	94.0017i	0.480282	−	0.831873i	0.999744	+	0.0226204i	$0.00720092\pi$
$114$	−30.5692	+	17.6491i	−0.268150	+	0.154817i
$115$	4.21411	−	15.7273i	0.0366444	−	0.136759i
$116$		−	240.680i		−	2.07483i
$117$		0			0
$118$	156.272			1.32434
$119$	30.9602	+	8.29575i	0.260169	+	0.0697122i
$120$	−12.4473	−	21.5594i	−0.103728	−	0.179662i
$121$	11.8661	+	6.85089i	0.0980668	+	0.0566189i
$122$	−174.680	+	174.680i	−1.43180	+	1.43180i
$123$	−8.83437	−	32.9703i	−0.0718241	−	0.268051i
$124$	−248.215	+	66.5090i	−2.00173	+	0.536363i
$125$	−20.7961	−	20.7961i	−0.166369	−	0.166369i
$126$	15.8377	−	27.4317i	0.125696	−	0.217712i
$127$	82.1319	−	47.4189i	0.646708	−	0.373377i	−0.140486	−	0.990083i	$-0.544867\pi$
$127$	82.1319	−	47.4189i	0.646708	−	0.373377i	0.787194	+	0.616706i	$0.211533\pi$
$128$	−18.3566	+	68.5079i	−0.143411	+	0.535218i
$129$			24.8947i			0.192982i
$130$		0			0
$131$	−112.268			−0.857005			−0.428502	−	0.903541i	$-0.640959\pi$
$131$	−112.268			−0.857005			−0.428502	+	0.903541i	$0.640959\pi$
$132$	−201.734	−	54.0545i	−1.52829	−	0.409504i
$133$	−4.48683	−	7.77142i	−0.0337356	−	0.0584317i
$134$	362.496	+	209.287i	2.70519	+	1.56184i
$135$	12.0680	−	12.0680i	0.0893924	−	0.0893924i
$136$	80.3546	+	299.887i	0.590842	+	2.20505i
$137$	118.473	−	31.7447i	0.864765	−	0.231713i	0.200942	−	0.979603i	$-0.435600\pi$
$137$	118.473	−	31.7447i	0.864765	−	0.231713i	0.663823	+	0.747890i	$0.268933\pi$
$138$	−153.408	−	153.408i	−1.11165	−	1.11165i
$139$	−39.2698	+	68.0172i	−0.282516	+	0.489332i	−0.972004	−	0.234965i	$-0.924502\pi$
$139$	−39.2698	+	68.0172i	−0.282516	+	0.489332i	0.689488	+	0.724297i	$0.257836\pi$
$140$	9.59840	−	5.54164i	0.0685600	−	0.0395831i
$141$	−27.9905	+	104.462i	−0.198514	+	0.740866i
$142$			260.412i			1.83389i
$143$		0			0
$144$	145.517			1.01054
$145$	14.7686	+	3.95724i	0.101853	+	0.0272913i
$146$	−81.6228	−	141.375i	−0.559060	−	0.968321i
$147$	84.2171	+	48.6228i	0.572906	+	0.330767i
$148$	39.4452	−	39.4452i	0.266522	−	0.266522i
$149$	46.9315	+	175.151i	0.314976	+	1.17551i	0.924011	+	0.382365i	$0.124890\pi$
$149$	46.9315	+	175.151i	0.314976	+	1.17551i	−0.609035	+	0.793143i	$0.708443\pi$
$150$	−187.924	+	50.3542i	−1.25283	+	0.335694i
$151$	−29.1776	−	29.1776i	−0.193229	−	0.193229i	0.603861	−	0.797090i	$-0.293628\pi$
$151$	−29.1776	−	29.1776i	−0.193229	−	0.193229i	−0.797090	+	0.603861i	$0.793628\pi$
$152$	43.4605	−	75.2758i	0.285924	−	0.495235i
$153$	−59.8242	+	34.5395i	−0.391008	+	0.225748i
$154$	19.6369	−	73.2860i	0.127513	−	0.475883i
$155$		−	16.3246i		−	0.105320i
$156$		0			0
$157$	232.544			1.48117			0.740585	−	0.671962i	$-0.234548\pi$
$157$	232.544			1.48117			0.740585	+	0.671962i	$0.234548\pi$
$158$	−179.063	−	47.9798i	−1.13331	−	0.303670i
$159$	4.52847	+	7.84354i	0.0284809	+	0.0493304i
$160$	23.1281	+	13.3530i	0.144551	+	0.0834564i
$161$	39.0000	−	39.0000i	0.242236	−	0.242236i
$162$	−22.0859	−	82.4258i	−0.136333	−	0.508801i
$163$	15.6553	−	4.19483i	0.0960450	−	0.0257352i	−0.210476	−	0.977599i	$-0.567502\pi$
$163$	15.6553	−	4.19483i	0.0960450	−	0.0257352i	0.306521	+	0.951864i	$0.400835\pi$
$164$	104.083	+	104.083i	0.634654	+	0.634654i
$165$	6.63381	−	11.4901i	0.0402049	−	0.0696369i
$166$	83.2562	−	48.0680i	0.501543	−	0.289566i
$167$	75.6886	−	282.474i	0.453225	−	1.69146i	−0.240029	−	0.970766i	$-0.577157\pi$
$167$	75.6886	−	282.474i	0.453225	−	1.69146i	0.693254	−	0.720693i	$-0.256176\pi$
$168$		−	84.3288i		−	0.501957i
$169$		0			0
$170$	−34.5395			−0.203174
$171$	18.6810	+	5.00556i	0.109246	+	0.0292723i
$172$	−53.6776	−	92.9723i	−0.312079	−	0.540537i
$173$	−79.1387	−	45.6907i	−0.457449	−	0.264108i	0.253522	−	0.967330i	$-0.418411\pi$
$173$	−79.1387	−	45.6907i	−0.457449	−	0.264108i	−0.710971	+	0.703221i	$0.751744\pi$
$174$	144.057	−	144.057i	0.827913	−	0.827913i
$175$	−12.8013	−	47.7749i	−0.0731500	−	0.273000i
$176$	336.677	−	90.2124i	1.91294	−	0.512570i
$177$	65.4562	+	65.4562i	0.369809	+	0.369809i
$178$	235.167	−	407.320i	1.32116	−	2.28832i
$179$	62.0691	−	35.8356i	0.346754	−	0.200199i	−0.316500	−	0.948592i	$-0.602508\pi$
$179$	62.0691	−	35.8356i	0.346754	−	0.200199i	0.663255	+	0.748394i	$0.269175\pi$
$180$	−6.18231	+	23.0727i	−0.0343462	+	0.128182i
$181$		−	274.144i		−	1.51461i	−0.653061	−	0.757305i	$-0.726516\pi$
$181$		−	274.144i		−	1.51461i	0.653061	−	0.757305i	$-0.273484\pi$
$182$		0			0
$183$	−146.333			−0.799634
$184$	516.034	+	138.271i	2.80453	+	0.751472i
$185$	1.77189	+	3.06900i	0.00957777	+	0.0165892i
$186$	−188.376	−	108.759i	−1.01277	−	0.584724i
$187$	−117.000	+	117.000i	−0.625668	+	0.625668i
$188$	−120.706	−	450.480i	−0.642051	−	2.39617i
$189$	55.8422	−	14.9629i	0.295462	−	0.0791687i
$190$	6.83772	+	6.83772i	0.0359880	+	0.0359880i
$191$	−89.8530	+	155.630i	−0.470435	+	0.814817i	−0.999428	−	0.0338090i	$-0.989236\pi$
$191$	−89.8530	+	155.630i	−0.470435	+	0.814817i	0.528994	+	0.848626i	$0.322570\pi$
$192$	56.1283	−	32.4057i	0.292335	−	0.168780i
$193$	0.415784	−	1.55173i	0.00215432	−	0.00804004i	−0.964840	−	0.262837i	$-0.915342\pi$
$193$	0.415784	−	1.55173i	0.00215432	−	0.00804004i	0.966995	+	0.254797i	$0.0820086\pi$
$194$			450.952i			2.32449i
$195$		0			0
$196$	−419.359			−2.13959
$197$	193.847	+	51.9411i	0.983994	+	0.263660i	0.714726	−	0.699405i	$-0.246552\pi$
$197$	193.847	+	51.9411i	0.983994	+	0.263660i	0.269268	+	0.963065i	$0.413218\pi$
$198$	81.7587	+	141.610i	0.412923	+	0.715203i
$199$	−224.958	−	129.879i	−1.13044	−	0.652660i	−0.186395	−	0.982475i	$-0.559680\pi$
$199$	−224.958	−	129.879i	−1.13044	−	0.652660i	−0.944046	+	0.329815i	$0.893014\pi$
$200$	338.763	−	338.763i	1.69381	−	1.69381i
$201$	64.1732	+	239.498i	0.319270	+	1.19153i
$202$	−31.4546	+	8.42822i	−0.155716	+	0.0417239i
$203$	36.6228	+	36.6228i	0.180408	+	0.180408i
$204$	−161.033	+	278.917i	−0.789376	+	1.36724i
$205$	−8.09811	+	4.67544i	−0.0395030	+	0.0228070i
$206$	−56.1512	+	209.559i	−0.272578	+	1.01728i
$207$			118.868i			0.574243i
$208$		0			0
$209$	46.3246			0.221649
$210$	9.06195	+	2.42814i	0.0431521	+	0.0115626i
$211$	−162.787	−	281.956i	−0.771503	−	1.33628i	−0.936739	−	0.350029i	$-0.886172\pi$
$211$	−162.787	−	281.956i	−0.771503	−	1.33628i	0.165236	−	0.986254i	$-0.447162\pi$
$212$	−33.8243	−	19.5285i	−0.159549	−	0.0921154i
$213$	−109.077	+	109.077i	−0.512096	+	0.512096i
$214$	−135.640	−	506.214i	−0.633830	−	2.36549i
$215$	6.58755	−	1.76513i	0.0306398	−	0.00820990i
$216$	395.967	+	395.967i	1.83318	+	1.83318i
$217$	27.6491	−	47.8897i	0.127415	−	0.220690i
$218$	−378.996	+	218.814i	−1.73851	+	1.00373i
$219$	25.0278	−	93.4050i	0.114282	−	0.426507i
$220$			57.2149i			0.260068i
$221$		0			0
$222$	47.2192			0.212699
$223$	−333.002	−	89.2275i	−1.49328	−	0.400123i	−0.582437	−	0.812876i	$-0.697901\pi$
$223$	−333.002	−	89.2275i	−1.49328	−	0.400123i	−0.910843	+	0.412753i	$0.864567\pi$
$224$	45.2324	+	78.3448i	0.201930	+	0.349754i
$225$	92.3152	+	53.2982i	0.410290	+	0.236881i
$226$	−280.167	+	280.167i	−1.23968	+	1.23968i
$227$	36.8706	+	137.603i	0.162426	+	0.606181i	0.998355	+	0.0573429i	$0.0182628\pi$
$227$	36.8706	+	137.603i	0.162426	+	0.606181i	−0.835929	+	0.548838i	$0.815070\pi$
$228$	87.0960	−	23.3373i	0.382000	−	0.102357i
$229$	240.366	+	240.366i	1.04963	+	1.04963i	0.998702	+	0.0509319i	$0.0162191\pi$
$229$	240.366	+	240.366i	1.04963	+	1.04963i	0.0509319	+	0.998702i	$0.483781\pi$
$230$	−29.7171	+	51.4715i	−0.129205	+	0.223789i
$231$	38.9218	−	22.4715i	0.168493	−	0.0972793i
$232$	−129.843	+	484.579i	−0.559667	+	2.08870i
$233$			10.7893i			0.0463061i	0.999732	+	0.0231531i	$0.00737051\pi$
$233$			10.7893i			0.0463061i	−0.999732	+	0.0231531i	$0.992629\pi$
$234$		0			0
$235$	29.6271			0.126073
$236$	−385.591	−	103.319i	−1.63386	−	0.437791i
$237$	−54.9057	−	95.0995i	−0.231670	−	0.401264i
$238$	−101.325	−	58.5000i	−0.425735	−	0.245798i
$239$	98.0153	−	98.0153i	0.410106	−	0.410106i	−0.471670	−	0.881775i	$-0.656348\pi$
$239$	98.0153	−	98.0153i	0.410106	−	0.410106i	0.881775	+	0.471670i	$0.156348\pi$
$240$	11.1549	+	41.6307i	0.0464788	+	0.173461i
$241$	−268.010	+	71.8131i	−1.11208	+	0.297980i	−0.767673	−	0.640842i	$-0.778585\pi$
$241$	−268.010	+	71.8131i	−1.11208	+	0.297980i	−0.344403	+	0.938822i	$0.611919\pi$
$242$	−35.3662	−	35.3662i	−0.146141	−	0.146141i
$243$	−104.377	+	180.787i	−0.429536	+	0.743978i
$244$	546.500	−	315.522i	2.23975	−	1.29312i
$245$	6.89508	−	25.7328i	0.0281432	−	0.105032i
$246$			124.596i			0.506490i
$247$		0			0
$248$	535.631			2.15980
$249$	55.0066	+	14.7390i	0.220910	+	0.0591926i
$250$	53.6776	+	92.9723i	0.214710	+	0.371889i
$251$	−83.0016	−	47.9210i	−0.330684	−	0.190920i	0.325461	−	0.945555i	$-0.394481\pi$
$251$	−83.0016	−	47.9210i	−0.330684	−	0.190920i	−0.656145	+	0.754635i	$0.727814\pi$
$252$	−57.2149	+	57.2149i	−0.227043	+	0.227043i
$253$	73.6915	+	275.020i	0.291271	+	1.08704i
$254$	−334.388	+	89.5991i	−1.31649	+	0.352752i
$255$	−14.4673	−	14.4673i	−0.0567343	−	0.0567343i
$256$	189.395	−	328.041i	0.739823	−	1.28141i
$257$	−390.213	+	225.289i	−1.51834	+	0.876612i	−0.518570	+	0.855035i	$0.673535\pi$
$257$	−390.213	+	225.289i	−1.51834	+	0.876612i	−0.999767	+	0.0215768i	$0.993131\pi$
$258$	23.5195	−	87.7761i	0.0911610	−	0.340218i
$259$			12.0043i			0.0463485i
$260$		0			0
$261$	−111.623			−0.427673
$262$	395.845	+	106.066i	1.51086	+	0.404833i
$263$	−83.4911	−	144.611i	−0.317457	−	0.549851i	0.662500	−	0.749062i	$-0.269495\pi$
$263$	−83.4911	−	144.611i	−0.317457	−	0.549851i	−0.979957	+	0.199211i	$0.936162\pi$
$264$	377.006	+	217.664i	1.42805	+	0.824486i
$265$	1.75445	−	1.75445i	0.00662055	−	0.00662055i
$266$	8.47798	+	31.6403i	0.0318721	+	0.118948i
$267$	269.113	−	72.1086i	1.00791	−	0.270070i
$268$	−756.065	−	756.065i	−2.82114	−	2.82114i
$269$	−85.0306	+	147.277i	−0.316099	+	0.547499i	−0.979670	−	0.200613i	$-0.935706\pi$
$269$	−85.0306	+	147.277i	−0.316099	+	0.547499i	0.663572	+	0.748113i	$0.269040\pi$
$270$	−53.9518	+	31.1491i	−0.199822	+	0.115367i
$271$	79.4540	−	296.526i	0.293188	−	1.09419i	−0.649458	−	0.760398i	$-0.725004\pi$
$271$	79.4540	−	296.526i	0.293188	−	1.09419i	0.942646	−	0.333795i	$-0.108329\pi$
$272$		−	537.500i		−	1.97610i
$273$		0			0
$274$	−447.715			−1.63399
$275$	246.627	+	66.0836i	0.896827	+	0.240304i
$276$	277.099	+	479.949i	1.00398	+	1.73894i
$277$	162.767	+	93.9737i	0.587607	+	0.339255i	0.764151	−	0.645038i	$-0.223158\pi$
$277$	162.767	+	93.9737i	0.587607	+	0.339255i	−0.176544	+	0.984293i	$0.556492\pi$
$278$	202.721	−	202.721i	0.729214	−	0.729214i
$279$	30.8457	+	115.118i	0.110558	+	0.412608i
$280$	−22.3148	+	5.97924i	−0.0796958	+	0.0213544i
$281$	−286.846	−	286.846i	−1.02081	−	1.02081i	−0.999779	−	0.0210263i	$-0.993307\pi$
$281$	−286.846	−	286.846i	−1.02081	−	1.02081i	−0.0210263	−	0.999779i	$-0.506693\pi$
$282$	197.384	−	341.878i	0.699942	−	1.21234i
$283$	345.719	−	199.601i	1.22162	−	0.705303i	0.256357	−	0.966582i	$-0.417478\pi$
$283$	345.719	−	199.601i	1.22162	−	0.705303i	0.965263	+	0.261279i	$0.0841443\pi$
$284$	172.171	−	642.550i	0.606235	−	2.26250i
$285$			5.72811i			0.0200986i
$286$		0			0
$287$	−31.6754			−0.110367
$288$	−188.326	−	50.4617i	−0.653909	−	0.175214i
$289$	−16.9210	−	29.3080i	−0.0585502	−	0.101412i
$290$	−48.3341	−	27.9057i	−0.166669	−	0.0962265i
$291$	−188.886	+	188.886i	−0.649093	+	0.649093i
$292$	107.929	+	402.798i	0.369621	+	1.37944i
$293$	185.992	−	49.8364i	0.634785	−	0.170090i	0.0729447	−	0.997336i	$-0.476760\pi$
$293$	185.992	−	49.8364i	0.634785	−	0.170090i	0.561840	+	0.827246i	$0.310094\pi$
$294$	−251.004	−	251.004i	−0.853756	−	0.853756i
$295$	12.6797	−	21.9619i	0.0429821	−	0.0744472i
$296$	−100.698	+	58.1381i	−0.340196	+	0.196412i
$297$	−77.2426	+	288.273i	−0.260076	+	0.970617i
$298$		−	661.903i		−	2.22115i
$299$		0			0
$300$	496.982			1.65661
$301$	22.3148	+	5.97924i	0.0741356	+	0.0198646i
$302$	75.3114	+	130.443i	0.249375	+	0.431931i
$303$	−16.7053	−	9.64484i	−0.0551332	−	0.0318311i
$304$	−106.408	+	106.408i	−0.350026	+	0.350026i
$305$	10.3756	+	38.7222i	0.0340183	+	0.126958i
$306$	243.566	−	65.2632i	0.795966	−	0.213279i
$307$	235.684	+	235.684i	0.767700	+	0.767700i	0.977701	−	0.210001i	$-0.0673467\pi$
$307$	235.684	+	235.684i	0.767700	+	0.767700i	−0.210001	+	0.977701i	$0.567347\pi$
$308$	−96.9057	+	167.846i	−0.314629	+	0.544953i
$309$	−111.296	+	64.2566i	−0.360180	+	0.207950i
$310$	−15.4228	+	57.5588i	−0.0497511	+	0.185673i
$311$			113.684i			0.365543i	0.983155	+	0.182772i	$0.0585069\pi$
$311$			113.684i			0.365543i	−0.983155	+	0.182772i	$0.941493\pi$
$312$		0			0
$313$	223.483			0.714002			0.357001	−	0.934104i	$-0.383799\pi$
$313$	223.483			0.714002			0.357001	+	0.934104i	$0.383799\pi$
$314$	−819.926	−	219.699i	−2.61123	−	0.699677i
$315$	−2.57011	−	4.45156i	−0.00815907	−	0.0141319i
$316$	410.105	+	236.774i	1.29780	+	0.749285i
$317$	125.140	−	125.140i	0.394764	−	0.394764i	−0.481617	−	0.876382i	$-0.659951\pi$
$317$	125.140	−	125.140i	0.394764	−	0.394764i	0.876382	+	0.481617i	$0.159951\pi$
$318$	−8.55666	−	31.9339i	−0.0269077	−	0.100421i
$319$	−258.257	+	69.1996i	−0.809582	+	0.216927i
$320$	−12.5548	−	12.5548i	−0.0392338	−	0.0392338i
$321$	155.219	−	268.848i	0.483549	−	0.837531i
$322$	−174.356	+	100.664i	−0.541478	+	0.312622i
$323$	18.4891	−	69.0023i	0.0572418	−	0.213629i
$324$			217.982i			0.672785i
$325$		0			0
$326$	−59.1623			−0.181479
$327$	−250.399	−	67.0943i	−0.765747	−	0.205181i
$328$	−153.408	−	265.710i	−0.467707	−	0.810092i
$329$	86.9138	+	50.1797i	0.264176	+	0.152522i
$330$	−34.2456	+	34.2456i	−0.103774	+	0.103774i
$331$	−113.461	−	423.444i	−0.342784	−	1.27929i	−0.895180	−	0.445704i	$-0.852953\pi$
$331$	−113.461	−	423.444i	−0.342784	−	1.27929i	0.552397	−	0.833581i	$-0.313713\pi$
$332$	−237.209	+	63.5600i	−0.714485	+	0.191446i
$333$	−18.2939	−	18.2939i	−0.0549368	−	0.0549368i
$334$	−533.741	+	924.466i	−1.59803	+	2.76786i
$335$	58.8250	−	33.9626i	0.175597	−	0.101381i
$336$	−37.7865	+	141.021i	−0.112460	+	0.419705i
$337$		−	5.32456i		−	0.0157999i	−0.999969	−	0.00789993i	$-0.997485\pi$
$337$		−	5.32456i		−	0.0157999i	0.999969	−	0.00789993i	$-0.00251465\pi$
$338$		0			0
$339$	−234.702			−0.692336
$340$	85.2239	+	22.8357i	0.250659	+	0.0671638i
$341$	142.732	+	247.220i	0.418570	+	0.724985i
$342$	−61.1383	−	35.2982i	−0.178767	−	0.103211i
$343$	133.336	−	133.336i	0.388733	−	0.388733i
$344$	57.9163	+	216.147i	0.168361	+	0.628333i
$345$	−34.0067	+	9.11208i	−0.0985703	+	0.0264118i
$346$	235.868	+	235.868i	0.681700	+	0.681700i
$347$	23.6206	−	40.9121i	0.0680710	−	0.117902i	−0.829981	−	0.557791i	$-0.811649\pi$
$347$	23.6206	−	40.9121i	0.0680710	−	0.117902i	0.898052	+	0.439889i	$0.144982\pi$
$348$	−450.694	+	260.208i	−1.29510	+	0.747725i
$349$	−81.8364	+	305.418i	−0.234488	+	0.875122i	0.743891	+	0.668301i	$0.232978\pi$
$349$	−81.8364	+	305.418i	−0.234488	+	0.875122i	−0.978379	+	0.206821i	$0.933688\pi$
$350$			180.544i			0.515839i
$351$		0			0
$352$	−467.004			−1.32672
$353$	150.700	+	40.3800i	0.426913	+	0.114391i	0.465877	−	0.884850i	$-0.345739\pi$
$353$	150.700	+	40.3800i	0.426913	+	0.114391i	−0.0389637	+	0.999241i	$0.512406\pi$
$354$	−168.952	−	292.633i	−0.477264	−	0.826646i
$355$	36.5974	+	21.1295i	0.103091	+	0.0595198i
$356$	−849.557	+	849.557i	−2.38639	+	2.38639i
$357$	−17.9377	−	66.9445i	−0.0502457	−	0.187520i
$358$	−252.705	+	67.7122i	−0.705881	+	0.189140i
$359$	−63.2149	−	63.2149i	−0.176086	−	0.176086i	0.613561	−	0.789647i	$-0.289736\pi$
$359$	−63.2149	−	63.2149i	−0.176086	−	0.176086i	−0.789647	+	0.613561i	$0.789736\pi$
$360$	24.8947	−	43.1188i	0.0691518	−	0.119775i
$361$	295.315	−	170.500i	0.818046	−	0.472299i
$362$	−259.001	+	966.606i	−0.715473	+	2.67018i
$363$		−	29.6271i		−	0.0816172i
$364$		0			0
$365$	−26.4911			−0.0725784
$366$	515.956	+	138.250i	1.40972	+	0.377732i
$367$	159.208	+	275.757i	0.433810	+	0.751381i	0.997198	−	0.0748120i	$-0.0238357\pi$
$367$	159.208	+	275.757i	0.433810	+	0.751381i	−0.563388	+	0.826193i	$0.690502\pi$
$368$	−800.993	−	462.454i	−2.17661	−	1.25667i
$369$	48.2719	−	48.2719i	0.130818	−	0.130818i
$370$	−3.34802	−	12.4950i	−0.00904872	−	0.0337703i
$371$	8.11837	−	2.17531i	0.0218824	−	0.00586337i
$372$	392.899	+	392.899i	1.05618	+	1.05618i
$373$	−4.43844	+	7.68760i	−0.0118993	+	0.0206102i	−0.871914	−	0.489660i	$-0.837121\pi$
$373$	−4.43844	+	7.68760i	−0.0118993	+	0.0206102i	0.860014	+	0.510270i	$0.170454\pi$
$374$	523.068	−	301.993i	1.39858	−	0.807469i
$375$	−16.4590	+	61.4259i	−0.0438907	+	0.163803i
$376$			972.105i			2.58538i
$377$		0			0
$378$	−211.031			−0.558282
$379$	−197.660	−	52.9630i	−0.521532	−	0.139744i	−0.0115566	−	0.999933i	$-0.503679\pi$
$379$	−197.660	−	52.9630i	−0.521532	−	0.139744i	−0.509975	+	0.860189i	$0.670345\pi$
$380$	−12.3509	−	21.3924i	−0.0325023	−	0.0562957i
$381$	−177.592	−	102.533i	−0.466121	−	0.269115i
$382$	463.846	−	463.846i	1.21426	−	1.21426i
$383$	−130.767	−	488.027i	−0.341427	−	1.27422i	−0.896731	−	0.442576i	$-0.854065\pi$
$383$	−130.767	−	488.027i	−0.341427	−	1.27422i	0.555304	−	0.831647i	$-0.312602\pi$
$384$	148.133	−	39.6921i	0.385763	−	0.103365i
$385$	−8.70605	−	8.70605i	−0.0226131	−	0.0226131i
$386$	−2.93203	+	5.07842i	−0.00759593	+	0.0131565i
$387$	−43.1188	+	24.8947i	−0.111418	+	0.0643273i
$388$	298.145	−	1112.69i	0.768416	−	2.86777i
$389$		−	438.342i		−	1.12684i	−0.826170	−	0.563421i	$-0.809485\pi$
$389$		−	438.342i		−	1.12684i	0.826170	−	0.563421i	$-0.190515\pi$
$390$		0			0
$391$	439.065			1.12293
$392$	844.329	+	226.237i	2.15390	+	0.577136i
$393$	121.377	+	210.231i	0.308847	+	0.534939i
$394$	−634.413	−	366.278i	−1.61018	−	0.929640i
$395$	−21.2719	+	21.2719i	−0.0538529	+	0.0538529i
$396$	−108.109	−	403.468i	−0.273003	−	1.01886i
$397$	341.590	−	91.5288i	0.860428	−	0.230551i	0.198484	−	0.980104i	$-0.436398\pi$
$397$	341.590	−	91.5288i	0.860428	−	0.230551i	0.661944	+	0.749553i	$0.269732\pi$
$398$	670.473	+	670.473i	1.68461	+	1.68461i
$399$	−9.70178	+	16.8040i	−0.0243152	+	0.0421152i
$400$	−718.299	+	414.710i	−1.79575	+	1.03678i
$401$	−34.2972	+	127.999i	−0.0855293	+	0.319200i	−0.995414	−	0.0956618i	$-0.969503\pi$
$401$	−34.2972	+	127.999i	−0.0855293	+	0.319200i	0.909885	+	0.414861i	$0.136170\pi$
$402$		−	905.074i		−	2.25143i
$403$		0			0
$404$	83.1843			0.205902
$405$	−13.3759	−	3.58405i	−0.0330268	−	0.00884951i
$406$	−94.5285	−	163.728i	−0.232829	−	0.403271i
$407$	−53.6671	−	30.9847i	−0.131860	−	0.0761295i
$408$	474.691	−	474.691i	1.16346	−	1.16346i
$409$	−135.481	−	505.621i	−0.331249	−	1.23624i	−0.907879	−	0.419232i	$-0.862299\pi$
$409$	−135.481	−	505.621i	−0.331249	−	1.23624i	0.576630	−	0.817005i	$-0.304367\pi$
$410$	32.9703	−	8.83437i	0.0804154	−	0.0215472i
$411$	−187.530	−	187.530i	−0.456278	−	0.456278i
$412$	277.099	−	479.949i	0.672569	−	1.16492i
$413$	74.3944	−	42.9516i	0.180132	−	0.103999i
$414$	112.302	−	419.118i	0.271262	−	1.01236i
$415$		−	15.6007i		−	0.0375921i
$416$		0			0
$417$	169.824			0.407252
$418$	−163.336	−	43.7657i	−0.390756	−	0.104703i
$419$	329.384	+	570.509i	0.786118	+	1.36160i	0.928329	+	0.371761i	$0.121246\pi$
$419$	329.384	+	570.509i	0.786118	+	1.36160i	−0.142210	+	0.989836i	$0.545421\pi$
$420$	−20.7544	−	11.9826i	−0.0494152	−	0.0285299i
$421$	80.3135	−	80.3135i	0.190768	−	0.190768i	−0.605260	−	0.796028i	$-0.706931\pi$
$421$	80.3135	−	80.3135i	0.190768	−	0.190768i	0.796028	+	0.605260i	$0.206931\pi$
$422$	307.590	+	1147.94i	0.728887	+	2.72024i
$423$	−208.924	+	55.9810i	−0.493910	+	0.132343i
$424$	57.5658	+	57.5658i	0.135768	+	0.135768i
$425$	196.868	−	340.986i	0.463220	−	0.802320i
$426$	487.644	−	281.542i	1.14471	−	0.660896i
$427$	−35.1465	+	131.169i	−0.0823103	+	0.307186i
$428$			1338.73i			3.12787i
$429$		0			0
$430$	−24.8947			−0.0578946
$431$	404.395	+	108.357i	0.938270	+	0.251409i	0.695378	−	0.718644i	$-0.255237\pi$
$431$	404.395	+	108.357i	0.938270	+	0.251409i	0.242893	+	0.970053i	$0.421904\pi$
$432$	−484.739	−	839.592i	−1.12208	−	1.94350i
$433$	135.221	+	78.0701i	0.312290	+	0.180300i	0.647951	−	0.761682i	$-0.275626\pi$
$433$	135.221	+	78.0701i	0.312290	+	0.180300i	−0.335661	+	0.941983i	$0.608960\pi$
$434$	−142.732	+	142.732i	−0.328876	+	0.328876i
$435$	−8.55666	−	31.9339i	−0.0196705	−	0.0734112i
$436$	1079.82	−	289.336i	2.47664	−	0.663614i
$437$	−86.9210	−	86.9210i	−0.198904	−	0.198904i
$438$	−176.491	+	305.692i	−0.402948	+	0.697926i
$439$	−388.595	+	224.355i	−0.885181	+	0.511060i	−0.872363	−	0.488858i	$-0.837414\pi$
$439$	−388.595	+	224.355i	−0.885181	+	0.511060i	−0.0128180	+	0.999918i	$0.504080\pi$
$440$	30.8665	−	115.195i	0.0701511	−	0.261808i
$441$			194.491i			0.441023i
$442$		0			0
$443$	−577.372			−1.30332			−0.651662	−	0.758510i	$-0.725928\pi$
$443$	−577.372			−1.30332			−0.651662	+	0.758510i	$0.725928\pi$
$444$	−116.510	−	31.2188i	−0.262411	−	0.0703127i
$445$	−38.1623	−	66.0990i	−0.0857579	−	0.148537i
$446$	1089.83	+	629.215i	2.44357	+	1.41080i
$447$	277.246	−	277.246i	0.620236	−	0.620236i
$448$	−15.5665	−	58.0950i	−0.0347467	−	0.129676i
$449$	−146.339	+	39.2113i	−0.325921	+	0.0873304i	−0.418070	−	0.908415i	$-0.637293\pi$
$449$	−146.339	+	39.2113i	−0.325921	+	0.0873304i	0.0921484	+	0.995745i	$0.470627\pi$
$450$	−275.140	−	275.140i	−0.611423	−	0.611423i
$451$	81.7587	−	141.610i	0.181283	−	0.313992i
$452$	876.524	−	506.061i	1.93921	−	1.11960i
$453$	−23.0926	+	86.1826i	−0.0509769	+	0.190249i
$454$		−	520.009i		−	1.14539i
$455$		0			0
$456$	−187.947			−0.412165
$457$	−486.430	−	130.339i	−1.06440	−	0.285205i	−0.316209	−	0.948689i	$-0.602410\pi$
$457$	−486.430	−	130.339i	−1.06440	−	0.285205i	−0.748190	+	0.663485i	$0.769077\pi$
$458$	−620.419	−	1074.60i	−1.35463	−	2.34628i
$459$	398.565	+	230.112i	0.868334	+	0.501333i
$460$	107.355	−	107.355i	0.233381	−	0.233381i
$461$	−12.3525	−	46.1002i	−0.0267950	−	0.100000i	0.951233	−	0.308472i	$-0.0998177\pi$
$461$	−12.3525	−	46.1002i	−0.0267950	−	0.100000i	−0.978028	+	0.208472i	$0.933151\pi$
$462$	−158.465	+	42.4605i	−0.342997	+	0.0919059i
$463$	−336.355	−	336.355i	−0.726469	−	0.726469i	0.243446	−	0.969915i	$-0.421722\pi$
$463$	−336.355	−	336.355i	−0.726469	−	0.726469i	−0.969915	+	0.243446i	$0.921722\pi$
$464$	434.265	−	752.169i	0.935916	−	1.62105i
$465$	−30.5692	+	17.6491i	−0.0657401	+	0.0379551i
$466$	10.1934	−	38.0421i	0.0218741	−	0.0816354i
$467$			308.263i			0.660093i	0.943965	+	0.330046i	$0.107064\pi$
$467$			308.263i			0.660093i	−0.943965	+	0.330046i	$0.892936\pi$
$468$		0			0
$469$	230.092			0.490601
$470$	−104.462	−	27.9905i	−0.222260	−	0.0595543i
$471$	−251.412	−	435.459i	−0.533784	−	0.924540i
$472$	720.601	+	416.039i	1.52670	+	0.881439i
$473$	−84.3288	+	84.3288i	−0.178285	+	0.178285i
$474$	103.746	+	387.184i	0.218873	+	0.816844i
$475$	−106.478	+	28.5307i	−0.224164	+	0.0600646i
$476$	211.336	+	211.336i	0.443982	+	0.443982i
$477$	−9.05694	+	15.6871i	−0.0189873	+	0.0328870i
$478$	−438.193	+	252.991i	−0.916723	+	0.529270i
$479$	−28.0530	+	104.695i	−0.0585659	+	0.218571i	−0.989007	−	0.147872i	$-0.952758\pi$
$479$	−28.0530	+	104.695i	−0.0585659	+	0.218571i	0.930441	+	0.366443i	$0.119424\pi$
$480$		−	57.7459i		−	0.120304i
$481$		0			0
$482$	1012.82			2.10130
$483$	−115.195	−	30.8665i	−0.238500	−	0.0639058i
$484$	63.8815	+	110.646i	0.131987	+	0.228607i
$485$	63.3752	+	36.5897i	0.130671	+	0.0754427i
$486$	538.824	−	538.824i	1.10869	−	1.10869i
$487$	25.2797	+	94.3452i	0.0519091	+	0.193727i	0.987011	−	0.160651i	$-0.0513593\pi$
$487$	25.2797	+	94.3452i	0.0519091	+	0.193727i	−0.935102	+	0.354378i	$0.884693\pi$
$488$	−1270.53	+	340.437i	−2.60354	+	0.697617i
$489$	−24.7808	−	24.7808i	−0.0506764	−	0.0506764i
$490$	−48.6228	+	84.2171i	−0.0992302	+	0.171872i
$491$	593.489	−	342.651i	1.20874	−	0.697864i	0.246253	−	0.969206i	$-0.420801\pi$
$491$	593.489	−	342.651i	1.20874	−	0.697864i	0.962483	+	0.271342i	$0.0874673\pi$
$492$	82.3766	−	307.433i	0.167432	−	0.624865i
$493$			412.302i			0.836313i
$494$		0			0
$495$	26.5352			0.0536065
$496$	−895.723	−	240.008i	−1.80589	−	0.483888i
$497$	71.5747	+	123.971i	0.144014	+	0.249439i
$498$	−180.023	−	103.936i	−0.361492	−	0.208707i
$499$	−349.329	+	349.329i	−0.700058	+	0.700058i	−0.964423	−	0.264365i	$-0.914838\pi$
$499$	−349.329	+	349.329i	−0.700058	+	0.700058i	0.264365	+	0.964423i	$0.414838\pi$
$500$	−70.9775	−	264.892i	−0.141955	−	0.529784i
$501$	−610.786	+	163.660i	−1.21913	+	0.326666i
$502$	247.381	+	247.381i	0.492792	+	0.492792i
$503$	−21.1359	+	36.6085i	−0.0420198	+	0.0727804i	−0.886270	−	0.463168i	$-0.846713\pi$
$503$	−21.1359	+	36.6085i	−0.0420198	+	0.0727804i	0.844251	+	0.535949i	$0.180046\pi$
$504$	146.062	−	84.3288i	0.289805	−	0.167319i
$505$	−1.36771	+	5.10437i	−0.00270834	+	0.0101077i
$506$		−	1039.32i		−	2.05398i
$507$		0			0
$508$	884.320			1.74079
$509$	251.732	+	67.4513i	0.494561	+	0.132517i	0.497475	−	0.867478i	$-0.334261\pi$
$509$	251.732	+	67.4513i	0.494561	+	0.132517i	−0.00291340	+	0.999996i	$0.500927\pi$
$510$	37.3420	+	64.6782i	0.0732196	+	0.126820i
$511$	−77.7142	−	44.8683i	−0.152083	−	0.0878050i
$512$	−777.103	+	777.103i	−1.51778	+	1.51778i
$513$	−33.3484	−	124.458i	−0.0650067	−	0.242608i
$514$	1588.70	−	425.690i	3.09085	−	0.828190i
$515$	24.8947	+	24.8947i	0.0483392	+	0.0483392i
$516$	−116.066	+	201.032i	−0.224934	+	0.389597i
$517$	−448.673	+	259.042i	−0.867840	+	0.501048i
$518$	11.3412	−	42.3259i	0.0218942	−	0.0817102i
$519$			197.592i			0.380717i
$520$		0			0
$521$	−757.122			−1.45321			−0.726605	−	0.687055i	$-0.758903\pi$
$521$	−757.122			−1.45321			−0.726605	+	0.687055i	$0.758903\pi$
$522$	393.571	+	105.457i	0.753967	+	0.202025i
$523$	110.925	+	192.128i	0.212094	+	0.367358i	0.952370	−	0.304946i	$-0.0986383\pi$
$523$	110.925	+	192.128i	0.212094	+	0.367358i	−0.740276	+	0.672304i	$0.765305\pi$
$524$	−906.595	−	523.423i	−1.73014	−	0.998898i
$525$	−75.6228	+	75.6228i	−0.144043	+	0.144043i
$526$	157.759	+	588.763i	0.299921	+	1.11932i
$527$	425.211	−	113.935i	0.806852	−	0.216195i
$528$	−532.925	−	532.925i	−1.00933	−	1.00933i
$529$	113.263	−	196.177i	0.214108	−	0.370845i
$530$	−7.84354	+	4.52847i	−0.0147991	+	0.00854428i
$531$	−47.9173	+	178.830i	−0.0902397	+	0.336779i
$532$		−	83.6754i		−	0.157285i
$533$		0			0
$534$	−1016.99			−1.90448
$535$	−82.1472	−	22.0113i	−0.153546	−	0.0411426i
$536$	1114.36	+	1930.13i	2.07903	+	3.60099i
$537$	−134.211	−	77.4865i	−0.249927	−	0.144295i
$538$	438.952	−	438.952i	0.815895	−	0.815895i
$539$	120.573	+	449.985i	0.223698	+	0.834852i
$540$	153.717	−	41.1883i	0.284661	−	0.0762746i
$541$	243.379	+	243.379i	0.449869	+	0.449869i	0.895311	−	0.445442i	$-0.146953\pi$
$541$	243.379	+	243.379i	0.449869	+	0.449869i	−0.445442	+	0.895311i	$0.646953\pi$
$542$	−560.294	+	970.457i	−1.03375	+	1.79051i
$543$	−513.360	+	296.388i	−0.945413	+	0.545835i
$544$	−186.391	+	695.621i	−0.342631	+	1.27872i
$545$			71.0171i			0.130307i
$546$		0			0
$547$	−317.777			−0.580944			−0.290472	−	0.956883i	$-0.593812\pi$
$547$	−317.777			−0.580944			−0.290472	+	0.956883i	$0.593812\pi$
$548$	1104.71	+	296.005i	2.01589	+	0.540155i
$549$	−146.333	−	253.456i	−0.266545	−	0.461669i
$550$	−807.150	−	466.009i	−1.46755	−	0.847288i
$551$	81.6228	−	81.6228i	0.148136	−	0.148136i
$552$	−298.980	−	1115.81i	−0.541630	−	2.02139i
$553$	−98.4316	+	26.3747i	−0.177996	+	0.0476938i
$554$	−485.118	−	485.118i	−0.875665	−	0.875665i
$555$	3.83131	−	6.63603i	0.00690327	−	0.0119568i
$556$	−634.230	+	366.173i	−1.14070	+	0.658584i
$557$	175.481	−	654.904i	0.315047	−	1.17577i	−0.608899	−	0.793248i	$-0.708389\pi$
$557$	175.481	−	654.904i	0.315047	−	1.17577i	0.923946	−	0.382523i	$-0.124945\pi$
$558$		−	435.035i		−	0.779632i
$559$		0			0
$560$	39.9957			0.0714209
$561$	345.586	+	92.5995i	0.616018	+	0.165061i
$562$	740.390	+	1282.39i	1.31742	+	2.28184i
$563$	−399.819	−	230.836i	−0.710158	−	0.410010i	0.100962	−	0.994890i	$-0.467808\pi$
$563$	−399.819	−	230.836i	−0.710158	−	0.410010i	−0.811120	+	0.584880i	$0.801141\pi$
$564$	−713.063	+	713.063i	−1.26430	+	1.26430i
$565$	16.6413	+	62.1060i	0.0294536	+	0.109922i
$566$	−1407.54	+	377.150i	−2.48683	+	0.666344i
$567$	−33.1690	−	33.1690i	−0.0584992	−	0.0584992i
$568$	−693.289	+	1200.81i	−1.22058	+	2.11411i
$569$	−453.273	+	261.697i	−0.796613	+	0.459925i	−0.842285	−	0.539032i	$-0.818790\pi$
$569$	−453.273	+	261.697i	−0.796613	+	0.459925i	0.0456725	+	0.998956i	$0.485457\pi$
$570$	5.41171	−	20.1968i	0.00949422	−	0.0354329i
$571$		−	115.715i		−	0.202654i	−0.994853	−	0.101327i	$-0.967691\pi$
$571$		−	115.715i		−	0.202654i	0.994853	−	0.101327i	$-0.0323088\pi$
$572$		0			0
$573$	388.574			0.678140
$574$	111.684	+	29.9258i	0.194572	+	0.0521355i
$575$	−338.763	−	586.755i	−0.589153	−	1.02044i
$576$	112.257	+	64.8114i	0.194890	+	0.112520i
$577$	−130.158	+	130.158i	−0.225577	+	0.225577i	−0.810842	−	0.585265i	$-0.800990\pi$
$577$	−130.158	+	130.158i	−0.225577	+	0.225577i	0.585265	+	0.810842i	$0.300990\pi$
$578$	31.9726	+	119.324i	0.0553160	+	0.206442i
$579$	−3.35527	+	0.899041i	−0.00579493	+	0.00155275i
$580$	100.811	+	100.811i	0.173813	+	0.173813i
$581$	26.4231	−	45.7662i	0.0454787	−	0.0787714i
$582$	844.446	−	487.541i	1.45094	−	0.837700i
$583$	−11.2296	+	41.9093i	−0.0192617	+	0.0718855i
$584$		−	869.210i		−	1.48837i
$585$		0			0
$586$	−702.873			−1.19944
$587$	−474.436	−	127.125i	−0.808238	−	0.216567i	−0.169040	−	0.985609i	$-0.554067\pi$
$587$	−474.436	−	127.125i	−0.808238	−	0.216567i	−0.639198	+	0.769042i	$0.720733\pi$
$588$	453.386	+	785.287i	0.771064	+	1.33552i
$589$	−106.734	−	61.6228i	−0.181212	−	0.104623i
$590$	−65.4562	+	65.4562i	−0.110943	+	0.110943i
$591$	−112.311	−	419.151i	−0.190036	−	0.709223i
$592$	194.446	−	52.1016i	0.328456	−	0.0880094i
$593$	240.285	+	240.285i	0.405202	+	0.405202i	0.880062	−	0.474860i	$-0.157501\pi$
$593$	240.285	+	240.285i	0.405202	+	0.405202i	−0.474860	+	0.880062i	$0.657501\pi$
$594$	544.699	−	943.447i	0.917002	−	1.58829i
$595$	−16.4428	+	9.49324i	−0.0276349	+	0.0159550i
$596$	−437.615	+	1633.20i	−0.734254	+	2.74027i
$597$			561.670i			0.940822i
$598$		0			0
$599$	1044.77			1.74419			0.872096	−	0.489334i	$-0.162760\pi$
$599$	1044.77			1.74419			0.872096	+	0.489334i	$0.162760\pi$
$600$	−1000.61	−	268.113i	−1.66769	−	0.446856i
$601$	−466.649	−	808.259i	−0.776454	−	1.34486i	−0.933974	−	0.357342i	$-0.883683\pi$
$601$	−466.649	−	808.259i	−0.776454	−	1.34486i	0.157520	−	0.987516i	$-0.449650\pi$
$602$	−73.0309	−	42.1644i	−0.121314	−	0.0700406i
$603$	−350.649	+	350.649i	−0.581508	+	0.581508i
$604$	−99.5838	−	371.652i	−0.164874	−	0.615317i
$605$	−7.83982	+	2.10067i	−0.0129584	+	0.00347219i
$606$	49.7893	+	49.7893i	0.0821606	+	0.0821606i
$607$	−289.956	+	502.218i	−0.477687	+	0.827378i	−0.999673	−	0.0255762i	$-0.991858\pi$
$607$	−289.956	+	502.218i	−0.477687	+	0.827378i	0.521986	+	0.852954i	$0.325191\pi$
$608$	174.610	−	100.811i	0.287188	−	0.165808i
$609$	28.9850	−	108.174i	0.0475945	−	0.177625i
$610$		−	146.333i		−	0.239890i
$611$		0			0
$612$	−644.131			−1.05250
$613$	−394.044	−	105.584i	−0.642813	−	0.172241i	−0.0773357	−	0.997005i	$-0.524641\pi$
$613$	−394.044	−	105.584i	−0.642813	−	0.172241i	−0.565477	+	0.824764i	$0.691308\pi$
$614$	−608.333	−	1053.66i	−0.990771	−	1.71606i
$615$	17.5104	+	10.1096i	0.0284721	+	0.0164384i
$616$	285.658	−	285.658i	0.463730	−	0.463730i
$617$	−34.9233	−	130.335i	−0.0566017	−	0.211240i	0.931833	−	0.362887i	$-0.118209\pi$
$617$	−34.9233	−	130.335i	−0.0566017	−	0.211240i	−0.988435	+	0.151647i	$0.951542\pi$
$618$	453.125	−	121.414i	0.733212	−	0.196463i
$619$	544.952	+	544.952i	0.880374	+	0.880374i	0.993572	−	0.113198i	$-0.0361095\pi$
$619$	544.952	+	544.952i	0.880374	+	0.880374i	−0.113198	+	0.993572i	$0.536110\pi$
$620$	76.1096	−	131.826i	0.122757	−	0.212622i
$621$	685.835	−	395.967i	1.10440	−	0.637628i
$622$	107.404	−	400.839i	0.172676	−	0.644435i
$623$		−	258.544i		−	0.414998i
$624$		0			0
$625$	−598.806			−0.958090
$626$	−787.977	−	211.138i	−1.25875	−	0.337281i
$627$	−50.0833	−	86.7468i	−0.0798776	−	0.138352i
$628$	1877.86	+	1084.18i	2.99022	+	1.72641i
$629$	−67.5726	+	67.5726i	−0.107429	+	0.107429i
$630$	4.85628	+	18.1239i	0.00770839	+	0.0287681i
$631$	−877.722	+	235.185i	−1.39100	+	0.372718i	−0.875105	−	0.483933i	$-0.839208\pi$
$631$	−877.722	+	235.185i	−1.39100	+	0.372718i	−0.515896	+	0.856651i	$0.672541\pi$
$632$	−697.960	−	697.960i	−1.10437	−	1.10437i
$633$	−351.991	+	609.666i	−0.556068	+	0.963138i
$634$	−559.460	+	323.004i	−0.882429	+	0.509470i
$635$	−14.5399	+	54.2638i	−0.0228975	+	0.0854548i
$636$			84.4520i			0.132786i
$637$		0			0
$638$	975.964			1.52972
$639$	−298.003	−	79.8496i	−0.466358	−	0.124960i
$640$	−21.0064	−	36.3842i	−0.0328225	−	0.0568503i
$641$	−422.005	−	243.645i	−0.658355	−	0.380101i	0.133295	−	0.991076i	$-0.457444\pi$
$641$	−422.005	−	243.645i	−0.658355	−	0.380101i	−0.791650	+	0.610975i	$0.790777\pi$
$642$	−801.285	+	801.285i	−1.24811	+	1.24811i
$643$	291.974	+	1089.66i	0.454081	+	1.69465i	0.690775	+	0.723070i	$0.257269\pi$
$643$	291.974	+	1089.66i	0.454081	+	1.69465i	−0.236694	+	0.971584i	$0.576064\pi$
$644$	496.766	−	133.108i	0.771375	−	0.206689i
$645$	−10.4274	−	10.4274i	−0.0161665	−	0.0161665i
$646$	−130.381	+	225.827i	−0.201829	+	0.349578i
$647$	−856.955	+	494.763i	−1.32450	+	0.764703i	−0.984444	−	0.175700i	$-0.943781\pi$
$647$	−856.955	+	494.763i	−1.32450	+	0.764703i	−0.340061	+	0.940403i	$0.610448\pi$
$648$	117.598	−	438.881i	0.181478	−	0.677285i
$649$			443.456i			0.683292i
$650$		0			0
$651$	−119.570			−0.183671
$652$	145.979	+	39.1150i	0.223894	+	0.0599923i
$653$	43.1537	+	74.7445i	0.0660853	+	0.114463i	0.897175	−	0.441675i	$-0.145616\pi$
$653$	43.1537	+	74.7445i	0.0660853	+	0.114463i	−0.831090	+	0.556139i	$0.812282\pi$
$654$	819.495	+	473.136i	1.25305	+	0.723449i
$655$	47.0245	−	47.0245i	0.0717932	−	0.0717932i
$656$	137.479	+	513.080i	0.209572	+	0.782134i
$657$	186.810	−	50.0556i	0.284338	−	0.0761881i
$658$	−259.042	−	259.042i	−0.393680	−	0.393680i
$659$	592.495	−	1026.23i	0.899083	−	1.55726i	0.0704134	−	0.997518i	$-0.477568\pi$
$659$	592.495	−	1026.23i	0.899083	−	1.55726i	0.828669	−	0.559739i	$-0.189098\pi$
$660$	107.140	−	61.8573i	0.162333	−	0.0937232i
$661$	71.1582	−	265.566i	0.107652	−	0.401764i	−0.890980	−	0.454042i	$-0.849982\pi$
$661$	71.1582	−	265.566i	0.107652	−	0.401764i	0.998633	+	0.0522781i	$0.0166482\pi$
$662$			1600.21i			2.41724i
$663$		0			0
$664$	511.881			0.770905
$665$	5.13451	+	1.37579i	0.00772106	+	0.00206885i
$666$	47.2192	+	81.7861i	0.0708997	+	0.122802i
$667$	614.422	+	354.737i	0.921172	+	0.531839i
$668$	1928.18	−	1928.18i	2.88650	−	2.88650i
$669$	192.935	+	720.042i	0.288393	+	1.07630i
$670$	−239.498	+	64.1732i	−0.357459	+	0.0957810i
$671$	−495.693	−	495.693i	−0.738737	−	0.738737i
$672$	97.8050	−	169.403i	0.145543	−	0.252088i
$673$	533.038	−	307.750i	0.792033	−	0.457281i	−0.0486446	−	0.998816i	$-0.515490\pi$
$673$	533.038	−	307.750i	0.792033	−	0.457281i	0.840678	+	0.541536i	$0.182157\pi$
$674$	−5.03044	+	18.7739i	−0.00746356	+	0.0278544i
$675$		−	710.175i		−	1.05211i
$676$		0			0
$677$	−412.031			−0.608612			−0.304306	−	0.952574i	$-0.598425\pi$
$677$	−412.031			−0.608612			−0.304306	+	0.952574i	$0.598425\pi$
$678$	827.535	+	221.737i	1.22055	+	0.327046i
$679$	123.945	+	214.679i	0.182540	+	0.316169i
$680$	−159.269	−	91.9537i	−0.234218	−	0.135226i
$681$	217.811	−	217.811i	0.319841	−	0.319841i
$682$	−269.696	−	1006.52i	−0.395449	−	1.47584i
$683$	176.278	−	47.2334i	0.258093	−	0.0691558i	−0.127452	−	0.991845i	$-0.540680\pi$
$683$	176.278	−	47.2334i	0.258093	−	0.0691558i	0.385545	+	0.922689i	$0.374013\pi$
$684$	127.517	+	127.517i	0.186429	+	0.186429i
$685$	−36.3270	+	62.9203i	−0.0530322	+	0.0918544i
$686$	−596.099	+	344.158i	−0.868948	+	0.501688i
$687$	190.237	−	709.976i	0.276910	−	1.03344i
$688$		−	387.408i		−	0.563093i
$689$		0			0
$690$	128.513			0.186251
$691$	993.243	+	266.139i	1.43740	+	0.385150i	0.891622	−	0.452780i	$-0.149568\pi$
$691$	993.243	+	266.139i	1.43740	+	0.385150i	0.545778	+	0.837930i	$0.316234\pi$
$692$	−426.046	−	737.933i	−0.615673	−	1.06638i
$693$	77.8437	+	44.9431i	0.112329	+	0.0648529i
$694$	−121.936	+	121.936i	−0.175701	+	0.175701i
$695$	−12.0412	−	44.9383i	−0.0173255	−	0.0646595i
$696$	1047.79	−	280.756i	1.50545	−	0.403385i
$697$	−178.302	−	178.302i	−0.255814	−	0.255814i
$698$	577.094	−	999.556i	0.826782	−	1.43203i
$699$	20.2040	−	11.6648i	0.0289041	−	0.0166878i
$700$	119.366	−	445.480i	0.170523	−	0.636400i
$701$		−	635.934i		−	0.907181i	−0.891210	−	0.453590i	$-0.850143\pi$
$701$		−	635.934i		−	0.907181i	0.891210	−	0.453590i	$-0.149857\pi$
$702$		0			0
$703$	26.7544			0.0380575
$704$	299.902	+	80.3586i	0.425998	+	0.114146i
$705$	−32.0310	−	55.4792i	−0.0454340	−	0.0786940i
$706$	−493.205	−	284.752i	−0.698590	−	0.403331i
$707$	−12.6577	+	12.6577i	−0.0179033	+	0.0179033i
$708$	223.404	+	833.754i	0.315542	+	1.17762i
$709$	949.818	−	254.503i	1.33966	−	0.358961i	0.483351	−	0.875426i	$-0.339419\pi$
$709$	949.818	−	254.503i	1.33966	−	0.358961i	0.856308	+	0.516466i	$0.172753\pi$
$710$	−109.077	−	109.077i	−0.153629	−	0.153629i
$711$	109.811	−	190.199i	0.154446	−	0.267509i
$712$	2168.80	−	1252.16i	3.04607	−	1.75865i
$713$	196.055	−	731.686i	0.274971	−	1.02621i
$714$			252.986i			0.354323i
$715$		0			0
$716$	668.302			0.933382
$717$	−289.510	−	77.5741i	−0.403780	−	0.108193i
$718$	163.167	+	282.613i	0.227251	+	0.393611i
$719$	−744.405	−	429.783i	−1.03533	−	0.597750i	−0.116826	−	0.993152i	$-0.537272\pi$
$719$	−744.405	−	429.783i	−1.03533	−	0.597750i	−0.918508	+	0.395402i	$0.870605\pi$
$720$	−60.9516	+	60.9516i	−0.0846550	+	0.0846550i
$721$	30.8665	+	115.195i	0.0428107	+	0.159772i
$722$	−1202.33	+	322.164i	−1.66528	+	0.446210i
$723$	424.233	+	424.233i	0.586767	+	0.586767i
$724$	1278.14	−	2213.80i	1.76538	−	3.05773i
$725$	550.989	−	318.114i	0.759985	−	0.438778i
$726$	−27.9905	+	104.462i	−0.0385544	+	0.143887i
$727$		−	437.337i		−	0.601564i	−0.953693	−	0.300782i	$-0.902752\pi$
$727$		−	437.337i		−	0.601564i	0.953693	−	0.300782i	$-0.0972477\pi$
$728$		0			0
$729$	661.780			0.907792
$730$	93.4050	+	25.0278i	0.127952	+	0.0342847i
$731$	91.9537	+	159.269i	0.125792	+	0.217878i
$732$	−1181.68	−	682.246i	−1.61432	−	0.932029i
$733$	−39.5591	+	39.5591i	−0.0539687	+	0.0539687i	−0.733576	−	0.679607i	$-0.762150\pi$
$733$	−39.5591	+	39.5591i	−0.0539687	+	0.0539687i	0.679607	+	0.733576i	$0.262150\pi$
$734$	−300.828	−	1122.70i	−0.409847	−	1.52957i
$735$	−55.6415	+	14.9091i	−0.0757027	+	0.0202845i
$736$	876.263	+	876.263i	1.19057	+	1.19057i
$737$	−593.899	+	1028.66i	−0.805833	+	1.39574i
$738$	−215.807	+	124.596i	−0.292422	+	0.168830i
$739$	−336.645	+	1256.38i	−0.455541	+	1.70010i	0.230950	+	0.972966i	$0.425817\pi$
$739$	−336.645	+	1256.38i	−0.455541	+	1.70010i	−0.686491	+	0.727138i	$0.740850\pi$
$740$			33.0441i			0.0446542i
$741$		0			0
$742$	−30.6797			−0.0413473
$743$	998.076	+	267.434i	1.34331	+	0.359938i	0.857660	−	0.514218i	$-0.171918\pi$
$743$	998.076	+	267.434i	1.34331	+	0.359938i	0.485646	+	0.874156i	$0.338584\pi$
$744$	−579.092	−	1003.02i	−0.778349	−	1.34814i
$745$	−93.0216	−	53.7061i	−0.124861	−	0.0720887i
$746$	22.9125	−	22.9125i	0.0307137	−	0.0307137i
$747$	29.4779	+	110.013i	0.0394618	+	0.147273i
$748$	−1490.30	+	399.324i	−1.99238	+	0.533855i
$749$	−203.706	−	203.706i	−0.271971	−	0.271971i
$750$	116.066	−	201.032i	0.154754	−	0.268043i
$751$	−173.000	+	99.8818i	−0.230360	+	0.132998i	−0.610738	−	0.791833i	$-0.709127\pi$
$751$	−173.000	+	99.8818i	−0.230360	+	0.132998i	0.380378	+	0.924831i	$0.375794\pi$
$752$	435.585	−	1625.63i	0.579236	−	2.16174i
$753$			207.237i			0.275215i
$754$		0			0
$755$	24.4427			0.0323745
$756$	520.704	+	139.522i	0.688762	+	0.184553i
$757$	−62.2744	−	107.862i	−0.0822647	−	0.142487i	0.821958	−	0.569549i	$-0.192882\pi$
$757$	−62.2744	−	107.862i	−0.0822647	−	0.142487i	−0.904222	+	0.427062i	$0.859549\pi$
$758$	646.894	+	373.484i	0.853422	+	0.492723i
$759$	435.329	−	435.329i	0.573556	−	0.573556i
$760$	13.3262	+	49.7340i	0.0175345	+	0.0654395i
$761$	220.493	−	59.0809i	0.289741	−	0.0776359i	−0.111021	−	0.993818i	$-0.535412\pi$
$761$	220.493	−	59.0809i	0.289741	−	0.0776359i	0.400762	+	0.916182i	$0.368745\pi$
$762$	529.302	+	529.302i	0.694623	+	0.694623i
$763$	−120.283	+	208.336i	−0.157644	+	0.273048i
$764$	−1451.18	+	837.840i	−1.89945	+	1.09665i
$765$	10.5908	−	39.5253i	0.0138441	−	0.0516670i
$766$			1844.28i			2.40768i
$767$		0			0
$768$	−819.048			−1.06647
$769$	188.440	+	50.4922i	0.245045	+	0.0656596i	0.379251	−	0.925294i	$-0.376182\pi$
$769$	188.440	+	50.4922i	0.245045	+	0.0656596i	−0.134206	+	0.990953i	$0.542848\pi$
$770$	22.4715	+	38.9218i	0.0291838	+	0.0505478i
$771$	843.748	+	487.138i	1.09436	+	0.631826i
$772$	10.5922	−	10.5922i	0.0137204	−	0.0137204i
$773$	−201.612	−	752.425i	−0.260817	−	0.973383i	−0.964761	−	0.263127i	$-0.915246\pi$
$773$	−201.612	−	752.425i	−0.260817	−	0.973383i	0.703944	−	0.710255i	$-0.251421\pi$
$774$	175.552	−	47.0391i	0.226812	−	0.0607740i
$775$	−480.333	−	480.333i	−0.619785	−	0.619785i
$776$	−1200.56	+	2079.43i	−1.54711	+	2.67968i
$777$	22.4791	−	12.9783i	0.0289306	−	0.0167031i
$778$	−414.129	+	1545.55i	−0.532299	+	1.98657i
$779$			70.5964i			0.0906244i
$780$		0			0
$781$	−738.977			−0.946194
$782$	−1548.10	−	414.813i	−1.97967	−	0.530451i
$783$	371.831	+	644.030i	0.474880	+	0.822516i
$784$	−1310.58	−	756.662i	−1.67165	−	0.965130i
$785$	−97.4036	+	97.4036i	−0.124081	+	0.124081i
$786$	−229.345	−	855.926i	−0.291787	−	1.08896i
$787$	996.426	−	266.991i	1.26611	−	0.339252i	0.437568	−	0.899185i	$-0.355840\pi$
$787$	996.426	−	266.991i	1.26611	−	0.339252i	0.828538	+	0.559933i	$0.189173\pi$
$788$	1323.21	+	1323.21i	1.67920	+	1.67920i
$789$	−180.531	+	312.689i	−0.228810	+	0.396310i
$790$	95.0995	−	54.9057i	0.120379	−	0.0695009i
$791$	−56.3710	+	210.380i	−0.0712655	+	0.265967i
$792$			870.658i			1.09932i
$793$		0			0
$794$	−1290.89			−1.62580
$795$	−5.18216	−	1.38855i	−0.00651843	−	0.00174661i
$796$	−1211.07	−	2097.63i	−1.52144	−	2.63521i
$797$	385.358	+	222.487i	0.483511	+	0.279155i	0.721879	−	0.692020i	$-0.243279\pi$
$797$	385.358	+	222.487i	0.483511	+	0.279155i	−0.238367	+	0.971175i	$0.576612\pi$
$798$	50.0833	−	50.0833i	0.0627610	−	0.0627610i
$799$	206.778	+	771.706i	0.258796	+	0.965839i
$800$	1073.42	−	287.622i	1.34177	−	0.359527i
$801$	394.009	+	394.009i	0.491896	+	0.491896i
$802$	241.857	−	418.909i	0.301568	−	0.522331i
$803$	401.182	−	231.623i	0.499605	−	0.288447i
$804$	−598.387	+	2233.21i	−0.744262	+	2.77762i
$805$			32.6712i			0.0405853i
$806$		0			0
$807$	367.720			0.455662
$808$	−167.482	−	44.8765i	−0.207279	−	0.0555403i
$809$	545.180	+	944.279i	0.673893	+	1.16722i	0.976791	+	0.214194i	$0.0687126\pi$
$809$	545.180	+	944.279i	0.673893	+	1.16722i	−0.302898	+	0.953023i	$0.597954\pi$
$810$	43.7759	+	25.2740i	0.0540443	+	0.0312025i
$811$	−445.614	+	445.614i	−0.549463	+	0.549463i	−0.926285	−	0.376823i	$-0.877017\pi$
$811$	−445.614	+	445.614i	−0.549463	+	0.549463i	0.376823	+	0.926285i	$0.377017\pi$
$812$	124.994	+	466.486i	0.153934	+	0.574490i
$813$	−641.172	+	171.802i	−0.788649	+	0.211318i
$814$	159.952	+	159.952i	0.196501	+	0.196501i
$815$	−4.80036	+	8.31446i	−0.00589001	+	0.0102018i
$816$	−1006.52	+	581.112i	−1.23347	+	0.712147i
$817$	13.3262	−	49.7340i	0.0163111	−	0.0608740i
$818$			1910.77i			2.33590i
$819$		0			0
$820$	−87.1929			−0.106333
$821$	−330.832	−	88.6463i	−0.402963	−	0.107974i	0.0516445	−	0.998666i	$-0.483554\pi$
$821$	−330.832	−	88.6463i	−0.402963	−	0.107974i	−0.454607	+	0.890692i	$0.650220\pi$
$822$	484.042	+	838.385i	0.588858	+	1.01993i
$823$	86.2376	+	49.7893i	0.104785	+	0.0604974i	0.551476	−	0.834190i	$-0.314065\pi$
$823$	86.2376	+	49.7893i	0.104785	+	0.0604974i	−0.446692	+	0.894688i	$0.647398\pi$
$824$	−816.828	+	816.828i	−0.991297	+	0.991297i
$825$	−142.891	−	533.277i	−0.173201	−	0.646396i
$826$	−302.886	+	81.1581i	−0.366690	+	0.0982544i
$827$	899.548	+	899.548i	1.08772	+	1.08772i	0.995763	+	0.0919618i	$0.0293138\pi$
$827$	899.548	+	899.548i	1.08772	+	1.08772i	0.0919618	+	0.995763i	$0.470686\pi$
$828$	−554.197	+	959.898i	−0.669320	+	1.15930i
$829$	27.8083	−	16.0552i	0.0335444	−	0.0193669i	−0.483134	−	0.875546i	$-0.660502\pi$
$829$	27.8083	−	16.0552i	0.0335444	−	0.0193669i	0.516678	+	0.856180i	$0.327168\pi$
$830$	−14.7390	+	55.0066i	−0.0177578	+	0.0662730i
$831$		−	406.394i		−	0.489042i
$832$		0			0
$833$	718.394			0.862418
$834$	−598.783	−	160.444i	−0.717966	−	0.192378i
$835$	86.6142	+	150.020i	0.103730	+	0.179665i
$836$	374.085	+	215.978i	0.447470	+	0.258347i
$837$	561.443	−	561.443i	0.670780	−	0.670780i
$838$	−622.379	−	2322.75i	−0.742695	−	2.77178i
$839$	558.422	−	149.629i	0.665581	−	0.178342i	0.0898176	−	0.995958i	$-0.471372\pi$
$839$	558.422	−	149.629i	0.665581	−	0.178342i	0.575763	+	0.817616i	$0.304705\pi$
$840$	35.3221	+	35.3221i	0.0420501	+	0.0420501i
$841$	87.3861	−	151.357i	0.103907	−	0.179973i
$842$	−359.055	+	207.300i	−0.426431	+	0.246200i
$843$	−227.024	+	847.265i	−0.269305	+	1.00506i
$844$		−	3035.84i		−	3.59696i
$845$		0			0
$846$	789.535			0.933256
$847$	−26.5568	−	7.11587i	−0.0313539	−	0.00840126i
$848$	−70.4715	−	122.060i	−0.0831032	−	0.143939i
$849$	−747.540	−	431.592i	−0.880494	−	0.508354i
$850$	−1016.29	+	1016.29i	−1.19563	+	1.19563i
$851$	42.5600	+	158.836i	0.0500118	+	0.186647i
$852$	−1389.37	+	372.281i	−1.63072	+	0.436949i
$853$	−529.546	−	529.546i	−0.620804	−	0.620804i	0.324933	−	0.945737i	$-0.394658\pi$
$853$	−529.546	−	529.546i	−0.620804	−	0.620804i	−0.945737	+	0.324933i	$0.894658\pi$
$854$	247.846	−	429.282i	0.290218	−	0.502673i
$855$	−9.92138	+	5.72811i	−0.0116040	+	0.00669955i
$856$	722.221	−	2695.36i	0.843716	−	3.14879i
$857$		−	1586.76i		−	1.85153i	−0.378097	−	0.925766i	$-0.623421\pi$
$857$		−	1586.76i		−	1.85153i	0.378097	−	0.925766i	$-0.376579\pi$
$858$		0			0
$859$	145.062			0.168873			0.0844365	−	0.996429i	$-0.473091\pi$
$859$	145.062			0.168873			0.0844365	+	0.996429i	$0.473091\pi$
$860$	61.4259	+	16.4590i	0.0714255	+	0.0191384i
$861$	34.2456	+	59.3150i	0.0397742	+	0.0688909i
$862$	−1323.48	−	764.114i	−1.53536	−	0.886443i
$863$	1005.80	−	1005.80i	1.16547	−	1.16547i	0.182216	−	0.983258i	$-0.441673\pi$
$863$	1005.80	−	1005.80i	1.16547	−	1.16547i	0.983258	−	0.182216i	$-0.0583271\pi$
$864$	336.190	+	1254.68i	0.389109	+	1.45217i
$865$	52.2862	−	14.0100i	0.0604465	−	0.0161966i
$866$	−403.020	−	403.020i	−0.465381	−	0.465381i
$867$	−36.5879	+	63.3721i	−0.0422006	+	0.0730935i
$868$	446.550	−	257.816i	0.514458	−	0.297023i
$869$	136.153	−	508.131i	0.156678	−	0.584731i
$870$			120.680i			0.138712i
$871$		0			0
$872$	−2330.17			−2.67221
$873$	−516.046	−	138.274i	−0.591119	−	0.158390i
$874$	224.355	+	388.595i	0.256699	+	0.444616i
$875$	51.1072	+	29.5068i	0.0584082	+	0.0337220i
$876$	637.587	−	637.587i	0.727839	−	0.727839i
$877$	−252.386	−	941.918i	−0.287784	−	1.07402i	−0.946781	−	0.321878i	$-0.895686\pi$
$877$	−252.386	−	941.918i	−0.287784	−	1.07402i	0.658998	−	0.752145i	$-0.270981\pi$
$878$	1582.11	−	423.925i	1.80195	−	0.482830i
$879$	−294.406	−	294.406i	−0.334933	−	0.334933i
$880$	−103.235	+	178.807i	−0.117312	+	0.203190i
$881$	1391.98	−	803.657i	1.57999	−	0.912210i	0.585136	−	0.810935i	$-0.301041\pi$
$881$	1391.98	−	803.657i	1.57999	−	0.912210i	0.994858	−	0.101275i	$-0.0322923\pi$
$882$	183.748	−	685.756i	0.208331	−	0.777502i
$883$			153.969i			0.174370i	0.996192	+	0.0871850i	$0.0277871\pi$
$883$			153.969i			0.174370i	−0.996192	+	0.0871850i	$0.972213\pi$
$884$		0			0
$885$	−54.8341			−0.0619595
$886$	2035.76	+	545.480i	2.29769	+	0.615665i
$887$	−62.6363	−	108.489i	−0.0706159	−	0.122310i	0.828555	−	0.559907i	$-0.189163\pi$
$887$	−62.6363	−	108.489i	−0.0706159	−	0.122310i	−0.899171	+	0.437597i	$0.855830\pi$
$888$	217.737	+	125.711i	0.245200	+	0.141566i
$889$	−134.562	+	134.562i	−0.151363	+	0.151363i
$890$	72.1086	+	269.113i	0.0810209	+	0.302374i
$891$	233.901	−	62.6737i	0.262516	−	0.0703409i
$892$	−2273.08	−	2273.08i	−2.54830	−	2.54830i
$893$	111.838	−	193.709i	0.125238	−	0.216919i
$894$	−1239.47	+	715.609i	−1.38643	+	0.800458i
$895$	−10.9882	+	41.0085i	−0.0122773	+	0.0458195i
$896$		−	142.315i		−	0.158834i
$897$		0			0
$898$	553.021			0.615837
$899$	687.086	+	184.104i	0.764279	+	0.204788i
$900$	496.982	+	860.798i	0.552202	+	0.956443i
$901$	57.9436	+	33.4537i	0.0643103	+	0.0371296i
$902$	−422.061	+	422.061i	−0.467917	+	0.467917i
$903$	−12.9288	−	48.2508i	−0.0143176	−	0.0534339i
$904$	−2037.79	+	546.023i	−2.25419	+	0.604008i
$905$	114.828	+	114.828i	0.126882	+	0.126882i
$906$	162.844	−	282.054i	0.179740	−	0.311318i
$907$	307.070	−	177.287i	0.338555	−	0.195465i	−0.321078	−	0.947053i	$-0.604045\pi$
$907$	307.070	−	177.287i	0.338555	−	0.195465i	0.659633	+	0.751588i	$0.270712\pi$
$908$	−343.802	+	1283.09i	−0.378637	+	1.41309i
$909$		−	38.5793i		−	0.0424415i
$910$		0			0
$911$	1040.31			1.14194			0.570972	−	0.820970i	$-0.306566\pi$
$911$	1040.31			1.14194			0.570972	+	0.820970i	$0.306566\pi$
$912$	314.300	+	84.2163i	0.344627	+	0.0923425i
$913$	136.404	+	236.258i	0.149401	+	0.258771i
$914$	1591.97	+	919.122i	1.74176	+	1.00560i
$915$	61.2933	−	61.2933i	0.0669872	−	0.0669872i
$916$	820.376	+	3061.68i	0.895607	+	3.34245i
$917$	217.597	−	58.3050i	0.237292	−	0.0635823i
$918$	−1187.90	−	1187.90i	−1.29401	−	1.29401i
$919$	208.100	−	360.440i	0.226442	−	0.392209i	−0.730309	−	0.683117i	$-0.760624\pi$
$919$	208.100	−	360.440i	0.226442	−	0.392209i	0.956751	+	0.290908i	$0.0939572\pi$
$920$	−274.063	+	158.230i	−0.297894	+	0.171989i
$921$	186.532	−	696.146i	0.202532	−	0.755859i
$922$			174.215i			0.188953i
$923$		0			0
$924$	419.074			0.453543
$925$	142.438	+	38.1662i	0.153987	+	0.0412607i
$926$	868.179	+	1503.73i	0.937559	+	1.62390i
$927$	−222.591	−	128.513i	−0.240120	−	0.138633i
$928$	−822.851	+	822.851i	−0.886692	+	0.886692i
$929$	156.806	+	585.209i	0.168790	+	0.629935i	0.997526	+	0.0702945i	$0.0223939\pi$
$929$	156.806	+	585.209i	0.168790	+	0.629935i	−0.828736	+	0.559640i	$0.810939\pi$
$930$	124.458	−	33.3484i	0.133826	−	0.0358585i
$931$	−142.219	−	142.219i	−0.152760	−	0.152760i
$932$	−50.3028	+	87.1271i	−0.0539730	+	0.0934840i
$933$	212.883	−	122.908i	0.228171	−	0.131734i
$934$	291.236	−	1086.91i	0.311815	−	1.16371i
$935$		−	98.0135i		−	0.104827i
$936$		0			0
$937$	−990.702			−1.05731			−0.528656	−	0.848836i	$-0.677304\pi$
$937$	−990.702			−1.05731			−0.528656	+	0.848836i	$0.677304\pi$
$938$	−811.281	−	217.382i	−0.864905	−	0.231751i
$939$	−241.616	−	418.491i	−0.257312	−	0.445677i
$940$	239.247	+	138.130i	0.254518	+	0.146946i
$941$	−974.392	+	974.392i	−1.03549	+	1.03549i	−0.0361387	+	0.999347i	$0.511506\pi$
$941$	−974.392	+	974.392i	−1.03549	+	1.03549i	−0.999347	+	0.0361387i	$0.988494\pi$
$942$	475.049	+	1772.91i	0.504299	+	1.88207i
$943$	−419.118	+	112.302i	−0.444452	+	0.119090i
$944$	−1018.62	−	1018.62i	−1.07905	−	1.07905i
$945$	−17.1228	+	29.6575i	−0.0181193	+	0.0313836i
$946$	377.006	−	217.664i	0.398526	−	0.230089i
$947$	−328.533	+	1226.10i	−0.346920	+	1.29472i	0.543433	+	0.839452i	$0.317124\pi$
$947$	−328.533	+	1226.10i	−0.346920	+	1.29472i	−0.890353	+	0.455271i	$0.849543\pi$
$948$		−	1023.94i		−	1.08011i
$949$		0			0
$950$	402.386			0.423564
$951$	−369.630	−	99.0420i	−0.388675	−	0.104145i
$952$	−311.486	−	539.510i	−0.327192	−	0.566713i
$953$	962.769	+	555.855i	1.01025	+	0.583269i	0.911265	−	0.411820i	$-0.135107\pi$
$953$	962.769	+	555.855i	1.01025	+	0.583269i	0.0989860	+	0.995089i	$0.468440\pi$
$954$	46.7544	−	46.7544i	0.0490089	−	0.0490089i
$955$	−27.5514	−	102.823i	−0.0288497	−	0.107668i
$956$	1248.48	−	334.529i	1.30594	−	0.349925i
$957$	408.794	+	408.794i	0.427162	+	0.427162i
$958$	197.825	−	342.642i	0.206497	−	0.357664i
$959$	−213.138	+	123.055i	−0.222250	+	0.128316i
$960$	−9.93648	+	37.0835i	−0.0103505	+	0.0386286i
$961$			201.527i			0.209705i
$962$		0			0
$963$	620.877			0.644732
$964$	−2499.08	−	669.626i	−2.59240	−	0.694632i
$965$	0.475803	+	0.824114i	0.000493060	+	0.000854005i
$966$	377.006	+	217.664i	0.390275	+	0.225325i
$967$	1333.92	−	1333.92i	1.37944	−	1.37944i	0.533879	−	0.845561i	$-0.320734\pi$
$967$	1333.92	−	1333.92i	1.37944	−	1.37944i	0.845561	−	0.533879i	$-0.179266\pi$
$968$	−68.9260	−	257.235i	−0.0712045	−	0.265739i
$969$	−149.202	+	39.9786i	−0.153975	+	0.0412576i
$970$	−188.886	−	188.886i	−0.194728	−	0.194728i
$971$	278.055	−	481.605i	0.286359	−	0.495989i	−0.686579	−	0.727056i	$-0.740888\pi$
$971$	278.055	−	481.605i	0.286359	−	0.495989i	0.972938	+	0.231067i	$0.0742216\pi$
$972$	−1685.76	+	973.271i	−1.73432	+	1.00131i
$973$	40.7886	−	152.225i	0.0419205	−	0.156449i
$974$		−	356.535i		−	0.366053i
$975$		0			0
$976$	2277.22			2.33322
$977$	−1507.49	−	403.931i	−1.54298	−	0.413440i	−0.615753	−	0.787939i	$-0.711148\pi$
$977$	−1507.49	−	403.931i	−1.54298	−	0.413440i	−0.927227	+	0.374499i	$0.877815\pi$
$978$	63.9626	+	110.787i	0.0654015	+	0.113279i
$979$	1155.86	+	667.337i	1.18066	+	0.681652i
$980$	175.653	−	175.653i	0.179238	−	0.179238i
$981$	−134.189	−	500.799i	−0.136788	−	0.510498i
$982$	−2416.31	+	647.448i	−2.46060	+	0.659316i
$983$	901.475	+	901.475i	0.917065	+	0.917065i	0.996815	−	0.0797497i	$-0.0254121\pi$
$983$	901.475	+	901.475i	0.917065	+	0.917065i	−0.0797497	+	0.996815i	$0.525412\pi$
$984$	−331.710	+	574.539i	−0.337104	+	0.583881i
$985$	−102.951	+	59.4388i	−0.104519	+	0.0603439i
$986$	389.528	−	1453.74i	0.395059	−	1.47438i
$987$		−	217.005i		−	0.219863i
$988$		0			0
$989$	316.460			0.319980
$990$	−93.5606	−	25.0695i	−0.0945056	−	0.0253227i
$991$	−382.670	−	662.805i	−0.386146	−	0.668824i	0.605782	−	0.795631i	$-0.292861\pi$
$991$	−382.670	−	662.805i	−0.386146	−	0.668824i	−0.991927	+	0.126807i	$0.959527\pi$
$992$	1076.00	+	621.228i	1.08468	+	0.626238i
$993$	−670.268	+	670.268i	−0.674993	+	0.674993i
$994$	−135.242	−	504.731i	−0.136059	−	0.507778i
$995$	148.627	−	39.8246i	0.149374	−	0.0400247i
$996$	375.478	+	375.478i	0.376986	+	0.376986i
$997$	−537.699	+	931.322i	−0.539317	+	0.934125i	0.459624	+	0.888114i	$0.347984\pi$
$997$	−537.699	+	931.322i	−0.539317	+	0.934125i	−0.998941	+	0.0460111i	$0.985349\pi$
$998$	1561.73	−	901.666i	1.56486	−	0.903473i
$999$	−44.6109	+	166.490i	−0.0446556	+	0.166657i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	169.3.f.d.80.1		8
13.2	odd	12		13.3.d.a.8.1	yes	4
13.3	even	3		169.3.d.d.70.2		4
13.4	even	6		169.3.f.f.19.1		8
13.5	odd	4		169.3.f.f.89.1		8
13.6	odd	12		169.3.f.f.150.2		8
13.7	odd	12	inner	169.3.f.d.150.1		8
13.8	odd	4	inner	169.3.f.d.89.2		8
13.9	even	3	inner	169.3.f.d.19.2		8
13.10	even	6		13.3.d.a.5.1	✓	4
13.11	odd	12		169.3.d.d.99.2		4
13.12	even	2		169.3.f.f.80.2		8
39.2	even	12		117.3.j.a.73.2		4
39.23	odd	6		117.3.j.a.109.2		4
52.15	even	12		208.3.t.c.177.1		4
52.23	odd	6		208.3.t.c.161.1		4
65.2	even	12		325.3.g.b.99.2		4
65.23	odd	12		325.3.g.b.174.2		4
65.28	even	12		325.3.g.a.99.1		4
65.49	even	6		325.3.j.a.226.2		4
65.54	odd	12		325.3.j.a.151.2		4
65.62	odd	12		325.3.g.a.174.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
13.3.d.a.5.1	✓	4	13.10	even	6
13.3.d.a.8.1	yes	4	13.2	odd	12
117.3.j.a.73.2		4	39.2	even	12
117.3.j.a.109.2		4	39.23	odd	6
169.3.d.d.70.2		4	13.3	even	3
169.3.d.d.99.2		4	13.11	odd	12
169.3.f.d.19.2		8	13.9	even	3	inner
169.3.f.d.80.1		8	1.1	even	1	trivial
169.3.f.d.89.2		8	13.8	odd	4	inner
169.3.f.d.150.1		8	13.7	odd	12	inner
169.3.f.f.19.1		8	13.4	even	6
169.3.f.f.80.2		8	13.12	even	2
169.3.f.f.89.1		8	13.5	odd	4
169.3.f.f.150.2		8	13.6	odd	12
208.3.t.c.161.1		4	52.23	odd	6
208.3.t.c.177.1		4	52.15	even	12
325.3.g.a.99.1		4	65.28	even	12
325.3.g.a.174.1		4	65.62	odd	12
325.3.g.b.99.2		4	65.2	even	12
325.3.g.b.174.2		4	65.23	odd	12
325.3.j.a.151.2		4	65.54	odd	12
325.3.j.a.226.2		4	65.49	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 169 = 13^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	169.f (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.52590 - 0.944762i) q^{2} +(-1.08114 - 1.87259i) q^{3} +(8.07530 + 4.66228i) q^{4} +(-0.418861 + 0.418861i) q^{5} +(2.04284 + 7.62398i) q^{6} +(-1.93820 + 0.519339i) q^{7} +(-13.7434 - 13.7434i) q^{8} +(2.16228 - 3.74517i) q^{9} +(1.87259 - 1.08114i) q^{10} +(2.68097 - 10.0055i) q^{11} -20.1623i q^{12} +7.32456 q^{14} +(1.23720 + 0.331507i) q^{15} +(16.8246 + 29.1410i) q^{16} +(-13.8336 - 7.98683i) q^{17} +(-11.1623 + 11.1623i) q^{18} +(1.15747 + 4.31975i) q^{19} +(-5.33528 + 1.42958i) q^{20} +(3.06797 + 3.06797i) q^{21} +(-18.9057 + 32.7456i) q^{22} +(-23.8043 + 13.7434i) q^{23} +(-10.8772 + 40.5943i) q^{24} +24.6491i q^{25} -28.8114 q^{27} +(-18.0729 - 4.84261i) q^{28} +(-12.9057 - 22.3533i) q^{29} +(-4.04905 - 2.33772i) q^{30} +(-19.4868 + 19.4868i) q^{31} +(-11.6687 - 43.5480i) q^{32} +(-21.6347 + 5.79701i) q^{33} +(41.2302 + 41.2302i) q^{34} +(0.594306 - 1.02937i) q^{35} +(34.9221 - 20.1623i) q^{36} +(1.54838 - 5.77863i) q^{37} -16.3246i q^{38} +11.5132 q^{40} +(15.2480 + 4.08568i) q^{41} +(-7.91886 - 13.7159i) q^{42} +(-9.97070 - 5.75658i) q^{43} +(68.2982 - 68.2982i) q^{44} +(0.663014 + 2.47440i) q^{45} +(96.9159 - 25.9685i) q^{46} +(-35.3662 - 35.3662i) q^{47} +(36.3794 - 63.0109i) q^{48} +(-38.9483 + 22.4868i) q^{49} +(23.2876 - 86.9103i) q^{50} +34.5395i q^{51} -4.18861 q^{53} +(101.586 + 27.2199i) q^{54} +(3.06797 + 5.31388i) q^{55} +(33.7750 + 19.5000i) q^{56} +(6.83772 - 6.83772i) q^{57} +(24.3856 + 91.0084i) q^{58} +(-41.3522 + 11.0803i) q^{59} +(8.44520 + 8.44520i) q^{60} +(33.8377 - 58.6087i) q^{61} +(87.1191 - 50.2982i) q^{62} +(-2.24591 + 8.38185i) q^{63} +29.9737i q^{64} +81.7587 q^{66} +(-110.762 - 29.6785i) q^{67} +(-74.4737 - 128.992i) q^{68} +(51.4715 + 29.7171i) q^{69} +(-3.06797 + 3.06797i) q^{70} +(-18.4642 - 68.9094i) q^{71} +(-81.1886 + 21.7544i) q^{72} +(31.6228 + 31.6228i) q^{73} +(-10.9189 + 18.9120i) q^{74} +(46.1576 - 26.6491i) q^{75} +(-10.7929 + 40.2798i) q^{76} +20.7851i q^{77} +50.7851 q^{79} +(-19.2532 - 5.15887i) q^{80} +(11.6886 + 20.2453i) q^{81} +(-49.9028 - 28.8114i) q^{82} +(-18.6228 + 18.6228i) q^{83} +(10.4711 + 39.0785i) q^{84} +(9.13973 - 2.44898i) q^{85} +(29.7171 + 29.7171i) q^{86} +(-27.9057 + 48.3341i) q^{87} +(-174.356 + 100.664i) q^{88} +(-33.3484 + 124.458i) q^{89} -9.35089i q^{90} -256.302 q^{92} +(57.5588 + 15.4228i) q^{93} +(91.2851 + 158.110i) q^{94} +(-2.29420 - 1.32456i) q^{95} +(-68.9320 + 68.9320i) q^{96} +(-31.9742 - 119.329i) q^{97} +(158.573 - 42.4894i) q^{98} +(-31.6754 - 31.6754i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 4 q^{3} - 16 q^{5} - 16 q^{6} - 12 q^{7} - 72 q^{8} - 8 q^{9} - 4 q^{11} + 8 q^{14} - 28 q^{15} + 84 q^{16} - 64 q^{18} + 16 q^{20} - 64 q^{21} - 88 q^{22} + 24 q^{24} - 104 q^{27} + 4 q^{28}+ \cdots - 304 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 4 * q^3 - 16 * q^5 - 16 * q^6 - 12 * q^7 - 72 * q^8 - 8 * q^9 - 4 * q^11 + 8 * q^14 - 28 * q^15 + 84 * q^16 - 64 * q^18 + 16 * q^20 - 64 * q^21 - 88 * q^22 + 24 * q^24 - 104 * q^27 + 4 * q^28 - 40 * q^29 - 80 * q^31 + 20 * q^32 - 76 * q^33 + 216 * q^34 + 68 * q^35 + 40 * q^37 + 168 * q^40 + 32 * q^41 - 76 * q^42 + 344 * q^44 + 56 * q^45 + 132 * q^46 + 8 * q^47 + 76 * q^48 - 128 * q^50 - 160 * q^53 + 152 * q^54 - 64 * q^55 + 80 * q^57 - 140 * q^58 + 56 * q^59 + 232 * q^60 + 296 * q^61 - 64 * q^63 + 224 * q^66 - 84 * q^67 - 444 * q^68 + 64 * q^70 + 284 * q^71 - 48 * q^72 - 100 * q^74 + 80 * q^76 + 128 * q^79 - 88 * q^80 + 220 * q^81 + 104 * q^83 - 184 * q^84 - 144 * q^85 + 48 * q^86 - 160 * q^87 + 200 * q^89 - 912 * q^92 + 80 * q^93 + 452 * q^94 - 640 * q^96 - 68 * q^97 + 224 * q^98 - 304 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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