LMFDB - Embedded newform 121.3.d.e.94.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [121,3,Mod(40,121)] 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("121.40"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(121, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([7])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 121 = 11^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	121.d (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$3.29701119876$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{10})$
Coefficient field:	8.0.64000000.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{6} + 4x^{4} - 8x^{2} + 16 $ x^8 - 2x^6 + 4x^4 - 8*x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			94.1
Root			$-1.34500 + 0.437016i$ of defining polynomial
Character	$\chi$	$=$	121.94
Dual form			121.3.d.e.112.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34500 + 0.437016i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-2.16312 + 6.65740i) q^{5} +(-1.34500 - 0.437016i) q^{6} +(-4.15627 - 5.72061i) q^{7} +(4.98752 - 6.86474i) q^{8} +(-2.47214 - 7.60845i) q^{9} -9.89949i q^{10} -2.00000 q^{12} +(-16.1400 + 5.24419i) q^{13} +(8.09017 + 5.87785i) q^{14} +(-5.66312 + 4.11450i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-4.03499 - 1.31105i) q^{17} +(6.65003 + 9.15298i) q^{18} +(-9.97505 + 13.7295i) q^{19} +(-4.32624 - 13.3148i) q^{20} -7.07107i q^{21} -9.00000 q^{23} +(8.06998 - 2.62210i) q^{24} +(-19.4164 - 14.1068i) q^{25} +(19.4164 - 14.1068i) q^{26} +(5.25329 - 16.1680i) q^{27} +(13.4500 + 4.37016i) q^{28} +(-13.3001 - 18.3060i) q^{29} +(5.81878 - 8.00886i) q^{30} +(15.1418 + 46.6018i) q^{31} +28.2843i q^{32} +6.00000 q^{34} +(47.0749 - 15.2956i) q^{35} +(12.9443 + 9.40456i) q^{36} +(-13.7533 + 9.99235i) q^{37} +(7.41641 - 22.8254i) q^{38} +(-16.1400 - 5.24419i) q^{39} +(34.9127 + 48.0532i) q^{40} +(-9.97505 + 13.7295i) q^{41} +(3.09017 + 9.51057i) q^{42} +46.6690i q^{43} +56.0000 q^{45} +(12.1050 - 3.93314i) q^{46} +(-25.8885 - 18.8091i) q^{47} +(-3.23607 + 2.35114i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(32.2799 + 10.4884i) q^{50} +(-2.49376 - 3.43237i) q^{51} +(19.9501 - 27.4589i) q^{52} +(4.94427 + 15.2169i) q^{53} +24.0416i q^{54} -60.0000 q^{56} +(-16.1400 + 5.24419i) q^{57} +(25.8885 + 18.8091i) q^{58} +(57.4402 - 41.7328i) q^{59} +(4.32624 - 13.3148i) q^{60} +(10.7600 + 3.49613i) q^{61} +(-40.7314 - 56.0620i) q^{62} +(-33.2502 + 45.7649i) q^{63} +(-17.3050 - 53.2592i) q^{64} -118.794i q^{65} -31.0000 q^{67} +(8.06998 - 2.62210i) q^{68} +(-7.28115 - 5.29007i) q^{69} +(-56.6312 + 41.1450i) q^{70} +(-22.5582 + 69.4271i) q^{71} +(-64.5599 - 20.9768i) q^{72} +(23.2751 + 32.0354i) q^{73} +(14.1313 - 19.4501i) q^{74} +(-7.41641 - 22.8254i) q^{75} -33.9411i q^{76} +24.0000 q^{78} +(-149.295 + 48.5088i) q^{79} +(-22.6525 - 16.4580i) q^{80} +(-44.4959 + 32.3282i) q^{81} +(7.41641 - 22.8254i) q^{82} +(-33.6249 - 10.9254i) q^{83} +(8.31254 + 11.4412i) q^{84} +(17.4563 - 24.0266i) q^{85} +(-20.3951 - 62.7697i) q^{86} -22.6274i q^{87} -9.00000 q^{89} +(-75.3198 + 24.4729i) q^{90} +(97.0820 + 70.5342i) q^{91} +(14.5623 - 10.5801i) q^{92} +(-15.1418 + 46.6018i) q^{93} +(43.0399 + 13.9845i) q^{94} +(-69.8253 - 96.1063i) q^{95} +(-16.6251 + 22.8825i) q^{96} +(-5.25329 - 16.1680i) q^{97} -1.41421i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9} - 16 q^{12} + 20 q^{14} - 14 q^{15} + 8 q^{16} + 28 q^{20} - 72 q^{23} - 48 q^{25} + 48 q^{26} - 34 q^{27} - 98 q^{31} + 48 q^{34} + 32 q^{36} - 34 q^{37} - 48 q^{38}+ \cdots + 34 q^{97}+O(q^{100}) $ 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9 - 16 * q^12 + 20 * q^14 - 14 * q^15 + 8 * q^16 + 28 * q^20 - 72 * q^23 - 48 * q^25 + 48 * q^26 - 34 * q^27 - 98 * q^31 + 48 * q^34 + 32 * q^36 - 34 * q^37 - 48 * q^38 - 20 * q^42 + 448 * q^45 - 64 * q^47 - 8 * q^48 + 2 * q^49 - 32 * q^53 - 480 * q^56 + 64 * q^58 + 142 * q^59 - 28 * q^60 + 112 * q^64 - 248 * q^67 - 18 * q^69 - 140 * q^70 + 146 * q^71 + 48 * q^75 + 192 * q^78 - 56 * q^80 - 110 * q^81 - 48 * q^82 + 132 * q^86 - 72 * q^89 + 240 * q^91 + 36 * q^92 + 98 * q^93 + 34 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/121\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	−1.34500	+	0.437016i	−0.672499	+	0.218508i	−0.625308	−	0.780378i	$-0.715027\pi$
$2$	−1.34500	+	0.437016i	−0.672499	+	0.218508i	−0.0471903	+	0.998886i	$0.515027\pi$
$3$	0.809017	+	0.587785i	0.269672	+	0.195928i	0.714400	−	0.699737i	$-0.246700\pi$
$3$	0.809017	+	0.587785i	0.269672	+	0.195928i	−0.444728	+	0.895666i	$0.646700\pi$
$4$	−1.61803	+	1.17557i	−0.404508	+	0.293893i
$5$	−2.16312	+	6.65740i	−0.432624	+	1.33148i	0.462878	+	0.886422i	$0.346817\pi$
$5$	−2.16312	+	6.65740i	−0.432624	+	1.33148i	−0.895502	+	0.445057i	$0.853183\pi$
$6$	−1.34500	−	0.437016i	−0.224166	−	0.0728360i
$7$	−4.15627	−	5.72061i	−0.593753	−	0.817231i	0.401366	−	0.915918i	$-0.368536\pi$
$7$	−4.15627	−	5.72061i	−0.593753	−	0.817231i	−0.995118	+	0.0986873i	$0.968536\pi$
$8$	4.98752	−	6.86474i	0.623440	−	0.858092i
$9$	−2.47214	−	7.60845i	−0.274682	−	0.845384i
$10$		−	9.89949i		−	0.989949i
$11$		0			0
$11$		0			0
$12$	−2.00000			−0.166667
$13$	−16.1400	+	5.24419i	−1.24154	+	0.403399i	−0.854881	−	0.518825i	$-0.826370\pi$
$13$	−16.1400	+	5.24419i	−1.24154	+	0.403399i	−0.386655	+	0.922224i	$0.626370\pi$
$14$	8.09017	+	5.87785i	0.577869	+	0.419847i
$15$	−5.66312	+	4.11450i	−0.377541	+	0.274300i
$16$	−1.23607	+	3.80423i	−0.0772542	+	0.237764i
$17$	−4.03499	−	1.31105i	−0.237352	−	0.0771205i	0.187926	−	0.982183i	$-0.439824\pi$
$17$	−4.03499	−	1.31105i	−0.237352	−	0.0771205i	−0.425278	+	0.905063i	$0.639824\pi$
$18$	6.65003	+	9.15298i	0.369446	+	0.508499i
$19$	−9.97505	+	13.7295i	−0.525002	+	0.722604i	−0.986359	−	0.164611i	$-0.947363\pi$
$19$	−9.97505	+	13.7295i	−0.525002	+	0.722604i	0.461356	+	0.887215i	$0.347363\pi$
$20$	−4.32624	−	13.3148i	−0.216312	−	0.665740i
$21$		−	7.07107i		−	0.336718i
$22$		0			0
$23$	−9.00000			−0.391304			−0.195652	−	0.980673i	$-0.562682\pi$
$23$	−9.00000			−0.391304			−0.195652	+	0.980673i	$0.562682\pi$
$24$	8.06998	−	2.62210i	0.336249	−	0.109254i
$25$	−19.4164	−	14.1068i	−0.776656	−	0.564274i
$26$	19.4164	−	14.1068i	0.746785	−	0.542571i
$27$	5.25329	−	16.1680i	0.194566	−	0.598813i
$28$	13.4500	+	4.37016i	0.480356	+	0.156077i
$29$	−13.3001	−	18.3060i	−0.458623	−	0.631240i	0.515600	−	0.856830i	$-0.327569\pi$
$29$	−13.3001	−	18.3060i	−0.458623	−	0.631240i	−0.974222	+	0.225589i	$0.927569\pi$
$30$	5.81878	−	8.00886i	0.193959	−	0.266962i
$31$	15.1418	+	46.6018i	0.488446	+	1.50328i	0.826927	+	0.562310i	$0.190087\pi$
$31$	15.1418	+	46.6018i	0.488446	+	1.50328i	−0.338481	+	0.940973i	$0.609913\pi$
$32$			28.2843i			0.883883i
$33$		0			0
$34$	6.00000			0.176471
$35$	47.0749	−	15.2956i	1.34500	−	0.437016i
$36$	12.9443	+	9.40456i	0.359563	+	0.261238i
$37$	−13.7533	+	9.99235i	−0.371711	+	0.270063i	−0.757920	−	0.652348i	$-0.773784\pi$
$37$	−13.7533	+	9.99235i	−0.371711	+	0.270063i	0.386209	+	0.922411i	$0.373784\pi$
$38$	7.41641	−	22.8254i	0.195169	−	0.600667i
$39$	−16.1400	−	5.24419i	−0.413845	−	0.134466i
$40$	34.9127	+	48.0532i	0.872817	+	1.20133i
$41$	−9.97505	+	13.7295i	−0.243294	+	0.334865i	−0.913149	−	0.407627i	$-0.866356\pi$
$41$	−9.97505	+	13.7295i	−0.243294	+	0.334865i	0.669855	+	0.742492i	$0.266356\pi$
$42$	3.09017	+	9.51057i	0.0735755	+	0.226442i
$43$			46.6690i			1.08533i	0.839950	+	0.542663i	$0.182584\pi$
$43$			46.6690i			1.08533i	−0.839950	+	0.542663i	$0.817416\pi$
$44$		0			0
$45$	56.0000			1.24444
$46$	12.1050	−	3.93314i	0.263152	−	0.0855031i
$47$	−25.8885	−	18.8091i	−0.550820	−	0.400194i	0.277268	−	0.960793i	$-0.410571\pi$
$47$	−25.8885	−	18.8091i	−0.550820	−	0.400194i	−0.828088	+	0.560598i	$0.810571\pi$
$48$	−3.23607	+	2.35114i	−0.0674181	+	0.0489821i
$49$	−0.309017	+	0.951057i	−0.00630647	+	0.0194093i
$50$	32.2799	+	10.4884i	0.645599	+	0.209768i
$51$	−2.49376	−	3.43237i	−0.0488973	−	0.0673013i
$52$	19.9501	−	27.4589i	0.383656	−	0.528057i
$53$	4.94427	+	15.2169i	0.0932881	+	0.287111i	0.986804	−	0.161921i	$-0.0517689\pi$
$53$	4.94427	+	15.2169i	0.0932881	+	0.287111i	−0.893516	+	0.449032i	$0.851769\pi$
$54$			24.0416i			0.445215i
$55$		0			0
$56$	−60.0000			−1.07143
$57$	−16.1400	+	5.24419i	−0.283157	+	0.0920034i
$58$	25.8885	+	18.8091i	0.446354	+	0.324295i
$59$	57.4402	−	41.7328i	0.973563	−	0.707335i	0.0173020	−	0.999850i	$-0.494492\pi$
$59$	57.4402	−	41.7328i	0.973563	−	0.707335i	0.956261	+	0.292516i	$0.0944923\pi$
$60$	4.32624	−	13.3148i	0.0721040	−	0.221913i
$61$	10.7600	+	3.49613i	0.176393	+	0.0573136i	0.395882	−	0.918301i	$-0.370439\pi$
$61$	10.7600	+	3.49613i	0.176393	+	0.0573136i	−0.219489	+	0.975615i	$0.570439\pi$
$62$	−40.7314	−	56.0620i	−0.656959	−	0.904226i
$63$	−33.2502	+	45.7649i	−0.527780	+	0.726427i
$64$	−17.3050	−	53.2592i	−0.270390	−	0.832174i
$65$		−	118.794i		−	1.82760i
$66$		0			0
$67$	−31.0000			−0.462687			−0.231343	−	0.972872i	$-0.574312\pi$
$67$	−31.0000			−0.462687			−0.231343	+	0.972872i	$0.574312\pi$
$68$	8.06998	−	2.62210i	0.118676	−	0.0385602i
$69$	−7.28115	−	5.29007i	−0.105524	−	0.0766676i
$70$	−56.6312	+	41.1450i	−0.809017	+	0.587785i
$71$	−22.5582	+	69.4271i	−0.317722	+	0.977847i	0.656898	+	0.753980i	$0.271868\pi$
$71$	−22.5582	+	69.4271i	−0.317722	+	0.977847i	−0.974620	+	0.223867i	$0.928132\pi$
$72$	−64.5599	−	20.9768i	−0.896665	−	0.291344i
$73$	23.2751	+	32.0354i	0.318837	+	0.438842i	0.938112	−	0.346333i	$-0.112573\pi$
$73$	23.2751	+	32.0354i	0.318837	+	0.438842i	−0.619275	+	0.785174i	$0.712573\pi$
$74$	14.1313	−	19.4501i	0.190964	−	0.262839i
$75$	−7.41641	−	22.8254i	−0.0988854	−	0.304338i
$76$		−	33.9411i		−	0.446594i
$77$		0			0
$78$	24.0000			0.307692
$79$	−149.295	+	48.5088i	−1.88981	+	0.614035i	−0.909807	+	0.415031i	$0.863771\pi$
$79$	−149.295	+	48.5088i	−1.88981	+	0.614035i	−0.979999	+	0.199004i	$0.936229\pi$
$80$	−22.6525	−	16.4580i	−0.283156	−	0.205725i
$81$	−44.4959	+	32.3282i	−0.549333	+	0.399113i
$82$	7.41641	−	22.8254i	0.0904440	−	0.278358i
$83$	−33.6249	−	10.9254i	−0.405120	−	0.131631i	0.0993670	−	0.995051i	$-0.468318\pi$
$83$	−33.6249	−	10.9254i	−0.405120	−	0.131631i	−0.504487	+	0.863420i	$0.668318\pi$
$84$	8.31254	+	11.4412i	0.0989588	+	0.136205i
$85$	17.4563	−	24.0266i	0.205369	−	0.282666i
$86$	−20.3951	−	62.7697i	−0.237153	−	0.729881i
$87$		−	22.6274i		−	0.260085i
$88$		0			0
$89$	−9.00000			−0.101124			−0.0505618	−	0.998721i	$-0.516101\pi$
$89$	−9.00000			−0.101124			−0.0505618	+	0.998721i	$0.516101\pi$
$90$	−75.3198	+	24.4729i	−0.836887	+	0.271921i
$91$	97.0820	+	70.5342i	1.06684	+	0.775101i
$92$	14.5623	−	10.5801i	0.158286	−	0.115001i
$93$	−15.1418	+	46.6018i	−0.162815	+	0.501094i
$94$	43.0399	+	13.9845i	0.457871	+	0.148771i
$95$	−69.8253	−	96.1063i	−0.735003	−	1.01165i
$96$	−16.6251	+	22.8825i	−0.173178	+	0.238359i
$97$	−5.25329	−	16.1680i	−0.0541576	−	0.166680i	0.920319	−	0.391168i	$-0.127929\pi$
$97$	−5.25329	−	16.1680i	−0.0541576	−	0.166680i	−0.974477	+	0.224488i	$0.927929\pi$
$98$		−	1.41421i		−	0.0144308i
$99$		0			0
$100$	48.0000			0.480000
$101$	146.605	−	47.6347i	1.45153	−	0.471631i	0.526060	−	0.850448i	$-0.323669\pi$
$101$	146.605	−	47.6347i	1.45153	−	0.471631i	0.925472	+	0.378817i	$0.123669\pi$
$102$	4.85410	+	3.52671i	0.0475892	+	0.0345756i
$103$	12.9443	−	9.40456i	0.125673	−	0.0913064i	−0.523173	−	0.852226i	$-0.675252\pi$
$103$	12.9443	−	9.40456i	0.125673	−	0.0913064i	0.648846	+	0.760920i	$0.275252\pi$
$104$	−44.4984	+	136.952i	−0.427870	+	1.31685i
$105$	47.0749	+	15.2956i	0.448332	+	0.145672i
$106$	−13.3001	−	18.3060i	−0.125472	−	0.172698i
$107$	108.894	−	149.880i	1.01770	−	1.40075i	0.103902	−	0.994588i	$-0.466867\pi$
$107$	108.894	−	149.880i	1.01770	−	1.40075i	0.913802	−	0.406161i	$-0.133133\pi$
$108$	10.5066	+	32.3359i	0.0972831	+	0.299407i
$109$			46.6690i			0.428156i	0.976817	+	0.214078i	$0.0686747\pi$
$109$			46.6690i			0.428156i	−0.976817	+	0.214078i	$0.931325\pi$
$110$		0			0
$111$	−17.0000			−0.153153
$112$	26.8999	−	8.74032i	0.240178	−	0.0780386i
$113$	−52.5861	−	38.2060i	−0.465364	−	0.338107i	0.330268	−	0.943887i	$-0.392861\pi$
$113$	−52.5861	−	38.2060i	−0.465364	−	0.338107i	−0.795632	+	0.605781i	$0.792861\pi$
$114$	19.4164	−	14.1068i	0.170319	−	0.123744i
$115$	19.4681	−	59.9166i	0.169288	−	0.521014i
$116$	43.0399	+	13.9845i	0.371034	+	0.120556i
$117$	79.8004	+	109.836i	0.682054	+	0.938767i
$118$	−59.0190	+	81.2327i	−0.500161	+	0.688413i
$119$	9.27051	+	28.5317i	0.0779034	+	0.239762i
$120$			59.3970i			0.494975i
$121$		0			0
$122$	−16.0000			−0.131148
$123$	−16.1400	+	5.24419i	−0.131219	+	0.0426357i
$124$	−79.2837	−	57.6030i	−0.639384	−	0.464540i
$125$	−5.66312	+	4.11450i	−0.0453050	+	0.0329160i
$126$	24.7214	−	76.0845i	0.196201	−	0.603845i
$127$	−166.780	−	54.1900i	−1.31323	−	0.426693i	−0.433062	−	0.901364i	$-0.642567\pi$
$127$	−166.780	−	54.1900i	−1.31323	−	0.426693i	−0.880163	+	0.474671i	$0.842567\pi$
$128$	−19.9501	−	27.4589i	−0.155860	−	0.214523i
$129$	−27.4314	+	37.7561i	−0.212646	+	0.292683i
$130$	51.9149	+	159.777i	0.399345	+	1.22906i
$131$			140.007i			1.06876i	0.845245	+	0.534378i	$0.179454\pi$
$131$			140.007i			1.06876i	−0.845245	+	0.534378i	$0.820546\pi$
$132$		0			0
$133$	120.000			0.902256
$134$	41.6949	−	13.5475i	0.311156	−	0.101101i
$135$	96.2730	+	69.9464i	0.713133	+	0.518122i
$136$	−29.1246	+	21.1603i	−0.214152	+	0.155590i
$137$	79.4174	−	244.422i	0.579689	−	1.78410i	−0.0399380	−	0.999202i	$-0.512716\pi$
$137$	79.4174	−	244.422i	0.579689	−	1.78410i	0.619627	−	0.784897i	$-0.287284\pi$
$138$	12.1050	+	3.93314i	0.0877172	+	0.0285010i
$139$	50.7065	+	69.7915i	0.364795	+	0.502097i	0.951477	−	0.307720i	$-0.0995661\pi$
$139$	50.7065	+	69.7915i	0.364795	+	0.502097i	−0.586682	+	0.809817i	$0.699566\pi$
$140$	−58.1878	+	80.0886i	−0.415627	+	0.572061i
$141$	−9.88854	−	30.4338i	−0.0701315	−	0.215843i
$142$		−	103.238i		−	0.727025i
$143$		0			0
$144$	32.0000			0.222222
$145$	150.640	−	48.9458i	1.03889	−	0.337557i
$146$	−45.3050	−	32.9160i	−0.310308	−	0.225452i
$147$	−0.809017	+	0.587785i	−0.00550352	+	0.00399854i
$148$	10.5066	−	32.3359i	0.0709904	−	0.218486i
$149$	262.274	+	85.2181i	1.76023	+	0.571934i	0.997224	−	0.0744568i	$-0.0237223\pi$
$149$	262.274	+	85.2181i	1.76023	+	0.571934i	0.763007	+	0.646391i	$0.223722\pi$
$150$	19.9501	+	27.4589i	0.133001	+	0.183060i
$151$	−92.2692	+	126.998i	−0.611054	+	0.841044i	−0.996664	−	0.0816182i	$-0.973991\pi$
$151$	−92.2692	+	126.998i	−0.611054	+	0.841044i	0.385609	+	0.922662i	$0.373991\pi$
$152$	44.4984	+	136.952i	0.292753	+	0.901001i
$153$			33.9411i			0.221837i
$154$		0			0
$155$	−343.000			−2.21290
$156$	32.2799	−	10.4884i	0.206923	−	0.0672332i
$157$	−141.578	−	102.862i	−0.901771	−	0.655175i	0.0371496	−	0.999310i	$-0.488172\pi$
$157$	−141.578	−	102.862i	−0.901771	−	0.655175i	−0.938920	+	0.344135i	$0.888172\pi$
$158$	179.602	−	130.488i	1.13672	−	0.825875i
$159$	−4.94427	+	15.2169i	−0.0310960	+	0.0957038i
$160$	−188.300	−	61.1822i	−1.17687	−	0.382389i
$161$	37.4064	+	51.4855i	0.232338	+	0.319786i
$162$	45.7190	−	62.9268i	0.282216	−	0.388437i
$163$	−49.4427	−	152.169i	−0.303330	−	0.933552i	−0.980295	−	0.197538i	$-0.936705\pi$
$163$	−49.4427	−	152.169i	−0.303330	−	0.933552i	0.676966	−	0.736015i	$-0.263295\pi$
$164$		−	33.9411i		−	0.206958i
$165$		0			0
$166$	50.0000			0.301205
$167$	−16.1400	+	5.24419i	−0.0966465	+	0.0314023i	−0.356941	−	0.934127i	$-0.616180\pi$
$167$	−16.1400	+	5.24419i	−0.0966465	+	0.0314023i	0.260295	+	0.965529i	$0.416180\pi$
$168$	−48.5410	−	35.2671i	−0.288935	−	0.209923i
$169$	96.2730	−	69.9464i	0.569663	−	0.413884i
$170$	−12.9787	+	39.9444i	−0.0763454	+	0.234967i
$171$	129.120	+	41.9535i	0.755086	+	0.245342i
$172$	−54.8628	−	75.5121i	−0.318970	−	0.439024i
$173$	72.3191	−	99.5387i	0.418029	−	0.575368i	−0.547124	−	0.837051i	$-0.684278\pi$
$173$	72.3191	−	99.5387i	0.418029	−	0.575368i	0.965154	+	0.261683i	$0.0842776\pi$
$174$	9.88854	+	30.4338i	0.0568307	+	0.174907i
$175$			169.706i			0.969746i
$176$		0			0
$177$	71.0000			0.401130
$178$	12.1050	−	3.93314i	0.0680055	−	0.0220963i
$179$	160.994	+	116.969i	0.899410	+	0.653460i	0.938314	−	0.345783i	$-0.112387\pi$
$179$	160.994	+	116.969i	0.899410	+	0.653460i	−0.0389044	+	0.999243i	$0.512387\pi$
$180$	−90.6099	+	65.8319i	−0.503388	+	0.365733i
$181$	−22.5582	+	69.4271i	−0.124631	+	0.383575i	−0.993834	−	0.110881i	$-0.964633\pi$
$181$	−22.5582	+	69.4271i	−0.124631	+	0.383575i	0.869203	+	0.494456i	$0.164633\pi$
$182$	−161.400	−	52.4419i	−0.886811	−	0.288142i
$183$	6.65003	+	9.15298i	0.0363390	+	0.0500163i
$184$	−44.8877	+	61.7826i	−0.243955	+	0.335775i
$185$	−36.7730	−	113.176i	−0.198773	−	0.611761i
$186$		−	69.2965i		−	0.372562i
$187$		0			0
$188$	64.0000			0.340426
$189$	−114.325	+	37.1464i	−0.604893	+	0.196542i
$190$	135.915	+	98.7479i	0.715341	+	0.519726i
$191$	−173.939	+	126.374i	−0.910674	+	0.661643i	−0.941185	−	0.337891i	$-0.890286\pi$
$191$	−173.939	+	126.374i	−0.910674	+	0.661643i	0.0305116	+	0.999534i	$0.490286\pi$
$192$	17.3050	−	53.2592i	0.0901300	−	0.277391i
$193$	129.120	+	41.9535i	0.669014	+	0.217376i	0.623779	−	0.781601i	$-0.285596\pi$
$193$	129.120	+	41.9535i	0.669014	+	0.217376i	0.0452348	+	0.998976i	$0.485596\pi$
$194$	14.1313	+	19.4501i	0.0728418	+	0.100258i
$195$	69.8253	−	96.1063i	0.358079	−	0.492853i
$196$	−0.618034	−	1.90211i	−0.00315323	−	0.00970466i
$197$		−	202.233i		−	1.02656i	−0.858221	−	0.513281i	$-0.828430\pi$
$197$		−	202.233i		−	1.02656i	0.858221	−	0.513281i	$-0.171570\pi$
$198$		0			0
$199$	200.000			1.00503			0.502513	−	0.864570i	$-0.332409\pi$
$199$	200.000			1.00503			0.502513	+	0.864570i	$0.332409\pi$
$200$	−193.680	+	62.9303i	−0.968398	+	0.314652i
$201$	−25.0795	−	18.2213i	−0.124774	−	0.0906534i
$202$	−176.366	+	128.137i	−0.873098	+	0.634342i
$203$	−49.4427	+	152.169i	−0.243560	+	0.749601i
$204$	8.06998	+	2.62210i	0.0395587	+	0.0128534i
$205$	−69.8253	−	96.1063i	−0.340611	−	0.468811i
$206$	−13.3001	+	18.3060i	−0.0645634	+	0.0888639i
$207$	22.2492	+	68.4761i	0.107484	+	0.330802i
$208$		−	67.8823i		−	0.326357i
$209$		0			0
$210$	−70.0000			−0.333333
$211$	−75.3198	+	24.4729i	−0.356966	+	0.115985i	−0.482010	−	0.876166i	$-0.660093\pi$
$211$	−75.3198	+	24.4729i	−0.356966	+	0.115985i	0.125044	+	0.992151i	$0.460093\pi$
$212$	−25.8885	−	18.8091i	−0.122116	−	0.0887223i
$213$	−59.0582	+	42.9083i	−0.277269	+	0.201448i
$214$	−80.9625	+	249.177i	−0.378329	+	1.16438i
$215$	−310.694	−	100.951i	−1.44509	−	0.469538i
$216$	−84.7879	−	116.701i	−0.392537	−	0.540280i
$217$	203.657	−	280.310i	0.938512	−	1.29175i
$218$	−20.3951	−	62.7697i	−0.0935556	−	0.287935i
$219$			39.5980i			0.180813i
$220$		0			0
$221$	72.0000			0.325792
$222$	22.8649	−	7.42927i	0.102995	−	0.0334652i
$223$	89.8009	+	65.2442i	0.402695	+	0.292575i	0.770638	−	0.637274i	$-0.219938\pi$
$223$	89.8009	+	65.2442i	0.402695	+	0.292575i	−0.367943	+	0.929848i	$0.619938\pi$
$224$	161.803	−	117.557i	0.722337	−	0.524808i
$225$	−59.3313	+	182.603i	−0.263695	+	0.811568i
$226$	87.4248	+	28.4060i	0.386835	+	0.125690i
$227$	−77.3066	−	106.403i	−0.340558	−	0.468738i	0.604046	−	0.796949i	$-0.293554\pi$
$227$	−77.3066	−	106.403i	−0.340558	−	0.468738i	−0.944604	+	0.328212i	$0.893554\pi$
$228$	19.9501	−	27.4589i	0.0875004	−	0.120434i
$229$	−93.6321	−	288.170i	−0.408874	−	1.25838i	−0.917617	−	0.397466i	$-0.869890\pi$
$229$	−93.6321	−	288.170i	−0.408874	−	1.25838i	0.508743	−	0.860919i	$-0.330110\pi$
$230$			89.0955i			0.387372i
$231$		0			0
$232$	−192.000			−0.827586
$233$	−75.3198	+	24.4729i	−0.323261	+	0.105034i	−0.466152	−	0.884705i	$-0.654360\pi$
$233$	−75.3198	+	24.4729i	−0.323261	+	0.105034i	0.142891	+	0.989738i	$0.454360\pi$
$234$	−155.331	−	112.855i	−0.663809	−	0.482285i
$235$	181.220	−	131.664i	0.771148	−	0.560272i
$236$	−43.8804	+	135.050i	−0.185934	+	0.572246i
$237$	−149.295	−	48.5088i	−0.629935	−	0.204678i
$238$	−24.9376	−	34.3237i	−0.104780	−	0.144217i
$239$	−165.420	+	227.680i	−0.692132	+	0.952638i	0.307867	+	0.951429i	$0.400385\pi$
$239$	−165.420	+	227.680i	−0.692132	+	0.952638i	−0.999999	+	0.00120854i	$0.999615\pi$
$240$	−8.65248	−	26.6296i	−0.0360520	−	0.110957i
$241$		−	373.352i		−	1.54918i	−0.632464	−	0.774590i	$-0.717956\pi$
$241$		−	373.352i		−	1.54918i	0.632464	−	0.774590i	$-0.282044\pi$
$242$		0			0
$243$	−208.000			−0.855967
$244$	−21.5200	+	6.99226i	−0.0881965	+	0.0286568i
$245$	−5.66312	−	4.11450i	−0.0231148	−	0.0167939i
$246$	19.4164	−	14.1068i	0.0789285	−	0.0573449i
$247$	88.9969	−	273.904i	0.360311	−	1.10892i
$248$	395.429	+	128.483i	1.59447	+	0.518075i
$249$	−20.7813	−	28.6031i	−0.0834592	−	0.114872i
$250$	5.81878	−	8.00886i	0.0232751	−	0.0320354i
$251$	69.5288	+	213.988i	0.277007	+	0.852541i	0.988681	+	0.150031i	$0.0479373\pi$
$251$	69.5288	+	213.988i	0.277007	+	0.852541i	−0.711674	+	0.702510i	$0.752063\pi$
$252$		−	113.137i		−	0.448957i
$253$		0			0
$254$	248.000			0.976378
$255$	28.2449	−	9.17734i	0.110764	−	0.0359896i
$256$	220.053	+	159.878i	0.859581	+	0.624522i
$257$	−343.023	+	249.221i	−1.33472	+	0.969731i	−0.335100	+	0.942183i	$0.608770\pi$
$257$	−343.023	+	249.221i	−1.33472	+	0.969731i	−0.999620	+	0.0275488i	$0.991230\pi$
$258$	20.3951	−	62.7697i	0.0790509	−	0.243294i
$259$	114.325	+	37.1464i	0.441408	+	0.143422i
$260$	139.651	+	192.213i	0.537118	+	0.739279i
$261$	−106.400	+	146.448i	−0.407665	+	0.561102i
$262$	−61.1854	−	188.309i	−0.233532	−	0.718737i
$263$			140.007i			0.532347i	0.963925	+	0.266173i	$0.0857593\pi$
$263$			140.007i			0.532347i	−0.963925	+	0.266173i	$0.914241\pi$
$264$		0			0
$265$	−112.000			−0.422642
$266$	−161.400	+	52.4419i	−0.606766	+	0.197150i
$267$	−7.28115	−	5.29007i	−0.0272702	−	0.0198130i
$268$	50.1591	−	36.4427i	0.187161	−	0.135980i
$269$	42.0263	−	129.344i	0.156232	−	0.480832i	−0.842052	−	0.539396i	$-0.818652\pi$
$269$	42.0263	−	129.344i	0.156232	−	0.480832i	0.998284	+	0.0585649i	$0.0186524\pi$
$270$	−160.055	−	52.0049i	−0.592795	−	0.192611i
$271$	169.576	+	233.401i	0.625741	+	0.861258i	0.997755	−	0.0669686i	$-0.0213327\pi$
$271$	169.576	+	233.401i	0.625741	+	0.861258i	−0.372014	+	0.928227i	$0.621333\pi$
$272$	9.97505	−	13.7295i	0.0366730	−	0.0504760i
$273$	37.0820	+	114.127i	0.135832	+	0.418047i
$274$			363.453i			1.32647i
$275$		0			0
$276$	18.0000			0.0652174
$277$	117.015	−	38.0204i	0.422436	−	0.137258i	−0.0900819	−	0.995934i	$-0.528713\pi$
$277$	117.015	−	38.0204i	0.422436	−	0.137258i	0.512518	+	0.858677i	$0.328713\pi$
$278$	−98.7001	−	71.7098i	−0.355036	−	0.257949i
$279$	317.135	−	230.412i	1.13668	−	0.825849i
$280$	129.787	−	399.444i	0.463525	−	1.42658i
$281$	−270.344	−	87.8402i	−0.962080	−	0.312599i	−0.214465	−	0.976732i	$-0.568801\pi$
$281$	−270.344	−	87.8402i	−0.962080	−	0.312599i	−0.747614	+	0.664133i	$0.768801\pi$
$282$	26.6001	+	36.6119i	0.0943267	+	0.129830i
$283$	−46.5502	+	64.0709i	−0.164488	+	0.226399i	−0.883302	−	0.468803i	$-0.844685\pi$
$283$	−46.5502	+	64.0709i	−0.164488	+	0.226399i	0.718814	+	0.695202i	$0.244685\pi$
$284$	−45.1165	−	138.854i	−0.158861	−	0.488923i
$285$		−	118.794i		−	0.416821i
$286$		0			0
$287$	120.000			0.418118
$288$	215.200	−	69.9226i	0.747221	−	0.242787i
$289$	−219.244	−	159.290i	−0.758628	−	0.551176i
$290$	−181.220	+	131.664i	−0.624896	+	0.454013i
$291$	5.25329	−	16.1680i	0.0180525	−	0.0555600i
$292$	−75.3198	−	24.4729i	−0.257945	−	0.0838113i
$293$	96.4254	+	132.718i	0.329097	+	0.452963i	0.941217	−	0.337801i	$-0.109683\pi$
$293$	96.4254	+	132.718i	0.329097	+	0.452963i	−0.612120	+	0.790765i	$0.709683\pi$
$294$	0.831254	−	1.14412i	0.00282739	−	0.00389157i
$295$	153.581	+	472.675i	0.520615	+	1.60229i
$296$			144.250i			0.487330i
$297$		0			0
$298$	−390.000			−1.30872
$299$	145.260	−	47.1977i	0.485818	−	0.157852i
$300$	38.8328	+	28.2137i	0.129443	+	0.0940456i
$301$	266.976	−	193.969i	0.886962	−	0.644416i
$302$	68.6018	−	211.135i	0.227158	−	0.699121i
$303$	146.605	+	47.6347i	0.483844	+	0.157210i
$304$	−39.9002	−	54.9179i	−0.131251	−	0.180651i
$305$	−46.5502	+	64.0709i	−0.152624	+	0.210068i
$306$	−14.8328	−	45.6507i	−0.0484733	−	0.149185i
$307$			186.676i			0.608066i	0.952662	+	0.304033i	$0.0983333\pi$
$307$			186.676i			0.608066i	−0.952662	+	0.304033i	$0.901667\pi$
$308$		0			0
$309$	16.0000			0.0517799
$310$	461.334	−	149.896i	1.48817	−	0.483537i
$311$	−114.880	−	83.4655i	−0.369390	−	0.268378i	0.387568	−	0.921841i	$-0.373315\pi$
$311$	−114.880	−	83.4655i	−0.369390	−	0.268378i	−0.756958	+	0.653463i	$0.773315\pi$
$312$	−116.498	+	84.6411i	−0.373392	+	0.271286i
$313$	−138.131	+	425.122i	−0.441312	+	1.35822i	0.445166	+	0.895448i	$0.353145\pi$
$313$	−138.131	+	425.122i	−0.441312	+	1.35822i	−0.886478	+	0.462770i	$0.846855\pi$
$314$	235.374	+	76.4778i	0.749600	+	0.243560i
$315$	−232.751	−	320.354i	−0.738892	−	1.01700i
$316$	184.538	−	253.995i	0.583982	−	0.803782i
$317$	130.714	+	402.297i	0.412348	+	1.26908i	0.914602	+	0.404355i	$0.132504\pi$
$317$	130.714	+	402.297i	0.412348	+	1.26908i	−0.502254	+	0.864720i	$0.667496\pi$
$318$		−	22.6274i		−	0.0711554i
$319$		0			0
$320$	392.000			1.22500
$321$	176.195	−	57.2491i	0.548893	−	0.178346i
$322$	−72.8115	−	52.9007i	−0.226123	−	0.164288i
$323$	58.2492	−	42.3205i	0.180338	−	0.131023i
$324$	33.9919	−	104.616i	0.104913	−	0.322890i
$325$	387.359	+	125.861i	1.19187	+	0.387263i
$326$	133.001	+	183.060i	0.407977	+	0.561533i
$327$	−27.4314	+	37.7561i	−0.0838880	+	0.115462i
$328$	44.4984	+	136.952i	0.135666	+	0.417537i
$329$			226.274i			0.687763i
$330$		0			0
$331$	145.000			0.438066			0.219033	−	0.975717i	$-0.429710\pi$
$331$	145.000			0.438066			0.219033	+	0.975717i	$0.429710\pi$
$332$	67.2499	−	21.8508i	0.202560	−	0.0658157i
$333$	110.026	+	79.9388i	0.330409	+	0.240056i
$334$	19.4164	−	14.1068i	0.0581330	−	0.0422361i
$335$	67.0567	−	206.379i	0.200169	−	0.616058i
$336$	26.8999	+	8.74032i	0.0800593	+	0.0260129i
$337$	−150.457	−	207.086i	−0.446460	−	0.614499i	0.525173	−	0.850996i	$-0.324001\pi$
$337$	−150.457	−	207.086i	−0.446460	−	0.614499i	−0.971632	+	0.236497i	$0.924001\pi$
$338$	−98.9192	+	136.151i	−0.292660	+	0.402812i
$339$	−20.0861	−	61.8187i	−0.0592510	−	0.182356i
$340$			59.3970i			0.174697i
$341$		0			0
$342$	−192.000			−0.561404
$343$	−322.799	+	104.884i	−0.941106	+	0.305784i
$344$	320.371	+	232.763i	0.931310	+	0.676637i
$345$	50.9681	−	37.0305i	0.147734	−	0.107335i
$346$	−53.7690	+	165.484i	−0.155402	+	0.478277i
$347$	−521.859	−	169.562i	−1.50392	−	0.488652i	−0.562759	−	0.826621i	$-0.690260\pi$
$347$	−521.859	−	169.562i	−1.50392	−	0.488652i	−0.941157	+	0.337969i	$0.890260\pi$
$348$	26.6001	+	36.6119i	0.0764371	+	0.105207i
$349$	−256.857	+	353.534i	−0.735981	+	1.01299i	0.262859	+	0.964834i	$0.415335\pi$
$349$	−256.857	+	353.534i	−0.735981	+	1.01299i	−0.998840	+	0.0481569i	$0.984665\pi$
$350$	−74.1641	−	228.254i	−0.211897	−	0.652153i
$351$			288.500i			0.821936i
$352$		0			0
$353$	585.000			1.65722			0.828612	−	0.559823i	$-0.189131\pi$
$353$	585.000			1.65722			0.828612	+	0.559823i	$0.189131\pi$
$354$	−95.4948	+	31.0281i	−0.269759	+	0.0876501i
$355$	−413.408	−	300.358i	−1.16453	−	0.846080i
$356$	14.5623	−	10.5801i	0.0409054	−	0.0297195i
$357$	−9.27051	+	28.5317i	−0.0259678	+	0.0799207i
$358$	−267.654	−	86.9662i	−0.747638	−	0.242922i
$359$	242.726	+	334.084i	0.676117	+	0.930596i	0.999879	−	0.0155429i	$-0.00494766\pi$
$359$	242.726	+	334.084i	0.676117	+	0.930596i	−0.323762	+	0.946139i	$0.604948\pi$
$360$	279.301	−	384.425i	0.775837	−	1.06785i
$361$	22.5582	+	69.4271i	0.0624882	+	0.192319i
$362$		−	103.238i		−	0.285187i
$363$		0			0
$364$	−240.000			−0.659341
$365$	−263.619	+	85.6551i	−0.722245	+	0.234672i
$366$	−12.9443	−	9.40456i	−0.0353669	−	0.0256955i
$367$	−440.914	+	320.343i	−1.20140	+	0.872869i	−0.994422	−	0.105476i	$-0.966363\pi$
$367$	−440.914	+	320.343i	−1.20140	+	0.872869i	−0.206979	+	0.978345i	$0.566363\pi$
$368$	11.1246	−	34.2380i	0.0302299	−	0.0930381i
$369$	129.120	+	41.9535i	0.349918	+	0.113695i
$370$	98.9192	+	136.151i	0.267349	+	0.367975i
$371$	66.5003	−	91.5298i	0.179246	−	0.246711i
$372$	−30.2837	−	93.2035i	−0.0814077	−	0.250547i
$373$		−	233.345i		−	0.625590i	−0.949821	−	0.312795i	$-0.898735\pi$
$373$		−	233.345i		−	0.625590i	0.949821	−	0.312795i	$-0.101265\pi$
$374$		0			0
$375$	−7.00000			−0.0186667
$376$	−258.239	+	83.9071i	−0.686807	+	0.223157i
$377$	310.663	+	225.710i	0.824039	+	0.598699i
$378$	137.533	−	99.9235i	0.363844	−	0.264348i
$379$	−138.131	+	425.122i	−0.364461	+	1.12169i	0.585857	+	0.810414i	$0.300758\pi$
$379$	−138.131	+	425.122i	−0.364461	+	1.12169i	−0.950318	+	0.311280i	$0.899242\pi$
$380$	225.960	+	73.4187i	0.594630	+	0.193207i
$381$	−103.075	−	141.871i	−0.270539	−	0.372365i
$382$	178.720	−	245.986i	0.467852	−	0.643943i
$383$	−168.414	−	518.326i	−0.439724	−	1.35333i	−0.888167	−	0.459520i	$-0.848021\pi$
$383$	−168.414	−	518.326i	−0.439724	−	1.35333i	0.448444	−	0.893811i	$-0.351979\pi$
$384$		−	33.9411i		−	0.0883883i
$385$		0			0
$386$	−192.000			−0.497409
$387$	355.079	−	115.372i	0.917517	−	0.298119i
$388$	27.5066	+	19.9847i	0.0708932	+	0.0515070i
$389$	−173.939	+	126.374i	−0.447143	+	0.324868i	−0.788467	−	0.615077i	$-0.789125\pi$
$389$	−173.939	+	126.374i	−0.447143	+	0.324868i	0.341324	+	0.939946i	$0.389125\pi$
$390$	−51.9149	+	159.777i	−0.133115	+	0.409686i
$391$	36.3149	+	11.7994i	0.0928770	+	0.0301776i
$392$	4.98752	+	6.86474i	0.0127233	+	0.0175121i
$393$	−82.2941	+	113.268i	−0.209400	+	0.288214i
$394$	88.3789	+	272.002i	0.224312	+	0.690361i
$395$		−	1098.84i		−	2.78188i
$396$		0			0
$397$	−592.000			−1.49118			−0.745592	−	0.666403i	$-0.767833\pi$
$397$	−592.000			−1.49118			−0.745592	+	0.666403i	$0.767833\pi$
$398$	−268.999	+	87.4032i	−0.675878	+	0.219606i
$399$	97.0820	+	70.5342i	0.243313	+	0.176778i
$400$	77.6656	−	56.4274i	0.194164	−	0.141068i
$401$	150.800	−	464.116i	0.376061	−	1.15740i	−0.566700	−	0.823924i	$-0.691780\pi$
$401$	150.800	−	464.116i	0.376061	−	1.15740i	0.942760	−	0.333471i	$-0.108220\pi$
$402$	41.6949	+	13.5475i	0.103719	+	0.0337002i
$403$	−488.777	−	672.744i	−1.21285	−	1.66934i
$404$	−181.213	+	249.419i	−0.448548	+	0.617373i
$405$	−118.972	−	366.157i	−0.293757	−	0.904091i
$406$		−	226.274i		−	0.557326i
$407$		0			0
$408$	−36.0000			−0.0882353
$409$	−149.295	+	48.5088i	−0.365024	+	0.118603i	−0.485785	−	0.874078i	$-0.661466\pi$
$409$	−149.295	+	48.5088i	−0.365024	+	0.118603i	0.120762	+	0.992682i	$0.461466\pi$
$410$	135.915	+	98.7479i	0.331500	+	0.240849i
$411$	207.917	−	151.061i	0.505882	−	0.367545i
$412$	−9.88854	+	30.4338i	−0.0240013	+	0.0738685i
$413$	−477.474	−	155.141i	−1.15611	−	0.375643i
$414$	−59.8503	−	82.3768i	−0.144566	−	0.198978i
$415$	145.469	−	200.221i	0.350529	−	0.482461i
$416$	−148.328	−	456.507i	−0.356558	−	1.09737i
$417$			86.2670i			0.206875i
$418$		0			0
$419$	−328.000			−0.782816			−0.391408	−	0.920217i	$-0.628012\pi$
$419$	−328.000			−0.782816			−0.391408	+	0.920217i	$0.628012\pi$
$420$	−94.1498	+	30.5911i	−0.224166	+	0.0728360i
$421$	−168.276	−	122.259i	−0.399704	−	0.290402i	0.369716	−	0.929145i	$-0.379455\pi$
$421$	−168.276	−	122.259i	−0.399704	−	0.290402i	−0.769421	+	0.638743i	$0.779455\pi$
$422$	90.6099	−	65.8319i	0.214715	−	0.156000i
$423$	−79.1084	+	243.470i	−0.187017	+	0.575580i
$424$	129.120	+	41.9535i	0.304528	+	0.0989470i
$425$	59.8503	+	82.3768i	0.140824	+	0.193828i
$426$	60.6815	−	83.5210i	0.142445	−	0.196059i
$427$	−24.7214	−	76.0845i	−0.0578955	−	0.178184i
$428$			370.524i			0.865710i
$429$		0			0
$430$	462.000			1.07442
$431$	−533.964	+	173.495i	−1.23890	+	0.402541i	−0.853929	−	0.520389i	$-0.825787\pi$
$431$	−533.964	+	173.495i	−1.23890	+	0.402541i	−0.384966	+	0.922931i	$0.625787\pi$
$432$	55.0132	+	39.9694i	0.127345	+	0.0925218i
$433$	−31.5517	+	22.9236i	−0.0728676	+	0.0529414i	−0.623623	−	0.781725i	$-0.714340\pi$
$433$	−31.5517	+	22.9236i	−0.0728676	+	0.0529414i	0.550755	+	0.834667i	$0.314340\pi$
$434$	−151.418	+	466.018i	−0.348890	+	1.07377i
$435$	150.640	+	48.9458i	0.346298	+	0.112519i
$436$	−54.8628	−	75.5121i	−0.125832	−	0.173193i
$437$	89.7754	−	123.565i	0.205436	−	0.282758i
$438$	−17.3050	−	53.2592i	−0.0395090	−	0.121596i
$439$		−	248.902i		−	0.566974i	−0.958976	−	0.283487i	$-0.908509\pi$
$439$		−	248.902i		−	0.566974i	0.958976	−	0.283487i	$-0.0914913\pi$
$440$		0			0
$441$	8.00000			0.0181406
$442$	−96.8398	+	31.4652i	−0.219095	+	0.0711881i
$443$	−141.578	−	102.862i	−0.319589	−	0.232195i	0.416411	−	0.909176i	$-0.363288\pi$
$443$	−141.578	−	102.862i	−0.319589	−	0.232195i	−0.736000	+	0.676981i	$0.763288\pi$
$444$	27.5066	−	19.9847i	0.0619518	−	0.0450106i
$445$	19.4681	−	59.9166i	0.0437485	−	0.134644i
$446$	−149.295	−	48.5088i	−0.334741	−	0.108764i
$447$	162.095	+	223.104i	0.362628	+	0.499114i
$448$	−232.751	+	320.354i	−0.519534	+	0.715077i
$449$	96.7223	+	297.681i	0.215417	+	0.662986i	0.999124	+	0.0418546i	$0.0133266\pi$
$449$	96.7223	+	297.681i	0.215417	+	0.662986i	−0.783707	+	0.621131i	$0.786673\pi$
$450$		−	271.529i		−	0.603398i
$451$		0			0
$452$	130.000			0.287611
$453$	−149.295	+	48.5088i	−0.329569	+	0.107083i
$454$	150.477	+	109.328i	0.331447	+	0.240811i
$455$	−679.574	+	493.740i	−1.49357	+	1.08514i
$456$	−44.4984	+	136.952i	−0.0975843	+	0.300334i
$457$	10.7600	+	3.49613i	0.0235448	+	0.00765017i	0.320766	−	0.947159i	$-0.396060\pi$
$457$	10.7600	+	3.49613i	0.0235448	+	0.00765017i	−0.297221	+	0.954809i	$0.596060\pi$
$458$	251.870	+	346.669i	0.549934	+	0.756920i
$459$	−42.3939	+	58.3503i	−0.0923615	+	0.127125i
$460$	38.9361	+	119.833i	0.0846438	+	0.260507i
$461$			871.156i			1.88971i	0.327491	+	0.944854i	$0.393797\pi$
$461$			871.156i			1.88971i	−0.327491	+	0.944854i	$0.606203\pi$
$462$		0			0
$463$	321.000			0.693305			0.346652	−	0.937994i	$-0.387318\pi$
$463$	321.000			0.693305			0.346652	+	0.937994i	$0.387318\pi$
$464$	86.0798	−	27.9690i	0.185517	−	0.0602781i
$465$	−277.493	−	201.610i	−0.596759	−	0.433571i
$466$	90.6099	−	65.8319i	0.194442	−	0.141270i
$467$	−49.7517	+	153.120i	−0.106535	+	0.327880i	−0.990088	−	0.140451i	$-0.955145\pi$
$467$	−49.7517	+	153.120i	−0.106535	+	0.327880i	0.883553	+	0.468331i	$0.155145\pi$
$468$	−258.239	−	83.9071i	−0.551794	−	0.179289i
$469$	128.844	+	177.339i	0.274721	+	0.378122i
$470$	−186.201	+	256.284i	−0.396172	+	0.545284i
$471$	−54.0780	−	166.435i	−0.114815	−	0.353365i
$472$		−	602.455i		−	1.27639i
$473$		0			0
$474$	222.000			0.468354
$475$	387.359	−	125.861i	0.815493	−	0.264970i
$476$	−48.5410	−	35.2671i	−0.101977	−	0.0740906i
$477$	103.554	−	75.2365i	0.217095	−	0.157729i
$478$	122.989	−	378.520i	0.257299	−	0.791884i
$479$	425.019	+	138.097i	0.887305	+	0.288303i	0.716987	−	0.697086i	$-0.245521\pi$
$479$	425.019	+	138.097i	0.887305	+	0.288303i	0.170318	+	0.985389i	$0.445521\pi$
$480$	−116.376	−	160.177i	−0.242449	−	0.333702i
$481$	169.576	−	233.401i	0.352548	−	0.485241i
$482$	163.161	+	502.158i	0.338508	+	1.04182i
$483$			63.6396i			0.131759i
$484$		0			0
$485$	119.000			0.245361
$486$	279.759	−	90.8993i	0.575637	−	0.187036i
$487$	588.155	+	427.320i	1.20771	+	0.877454i	0.995021	−	0.0996661i	$-0.0317775\pi$
$487$	588.155	+	427.320i	1.20771	+	0.877454i	0.212690	+	0.977120i	$0.431777\pi$
$488$	77.6656	−	56.4274i	0.159151	−	0.115630i
$489$	49.4427	−	152.169i	0.101110	−	0.311184i
$490$	9.41498	+	3.05911i	0.0192142	+	0.00624309i
$491$	−305.901	−	421.037i	−0.623017	−	0.857510i	0.374551	−	0.927206i	$-0.377797\pi$
$491$	−305.901	−	421.037i	−0.623017	−	0.857510i	−0.997568	+	0.0696967i	$0.977797\pi$
$492$	19.9501	−	27.4589i	0.0405490	−	0.0558109i
$493$	29.6656	+	91.3014i	0.0601737	+	0.185196i
$494$			407.294i			0.824481i
$495$		0			0
$496$	−196.000			−0.395161
$497$	490.924	−	159.511i	0.987774	−	0.320947i
$498$	40.4508	+	29.3893i	0.0812266	+	0.0590146i
$499$	297.718	−	216.305i	0.596630	−	0.433477i	−0.248051	−	0.968747i	$-0.579790\pi$
$499$	297.718	−	216.305i	0.596630	−	0.433477i	0.844681	+	0.535270i	$0.179790\pi$
$500$	4.32624	−	13.3148i	0.00865248	−	0.0266296i
$501$	−16.1400	−	5.24419i	−0.0322155	−	0.0104674i
$502$	−187.032	−	257.428i	−0.372574	−	0.512804i
$503$	273.483	−	376.416i	0.543703	−	0.748343i	−0.445438	−	0.895313i	$-0.646952\pi$
$503$	273.483	−	376.416i	0.543703	−	0.748343i	0.989141	+	0.146970i	$0.0469521\pi$
$504$	148.328	+	456.507i	0.294302	+	0.905768i
$505$			1079.04i			2.13672i
$506$		0			0
$507$	119.000			0.234714
$508$	333.559	−	108.380i	0.656613	−	0.213346i
$509$	89.8009	+	65.2442i	0.176426	+	0.128181i	0.672494	−	0.740103i	$-0.265223\pi$
$509$	89.8009	+	65.2442i	0.176426	+	0.128181i	−0.496068	+	0.868284i	$0.665223\pi$
$510$	−33.9787	+	24.6870i	−0.0666249	+	0.0484058i
$511$	86.5248	−	266.296i	0.169324	−	0.521127i
$512$	−236.719	−	76.9148i	−0.462343	−	0.150224i
$513$	169.576	+	233.401i	0.330557	+	0.454973i
$514$	352.452	−	485.108i	0.685704	−	0.943790i
$515$	34.6099	+	106.518i	0.0672037	+	0.206832i
$516$		−	93.3381i		−	0.180888i
$517$		0			0
$518$	−170.000			−0.328185
$519$	117.015	−	38.0204i	0.225462	−	0.0732570i
$520$	−815.489	−	592.488i	−1.56825	−	1.13940i
$521$	413.408	−	300.358i	0.793489	−	0.576503i	−0.115508	−	0.993307i	$-0.536850\pi$
$521$	413.408	−	300.358i	0.793489	−	0.576503i	0.908997	+	0.416803i	$0.136850\pi$
$522$	79.1084	−	243.470i	0.151549	−	0.466419i
$523$	661.739	+	215.012i	1.26527	+	0.411113i	0.863371	−	0.504569i	$-0.168349\pi$
$523$	661.739	+	215.012i	1.26527	+	0.411113i	0.401903	+	0.915682i	$0.368349\pi$
$524$	−164.588	−	226.536i	−0.314100	−	0.432321i
$525$	−99.7505	+	137.295i	−0.190001	+	0.261514i
$526$	−61.1854	−	188.309i	−0.116322	−	0.358002i
$527$		−	207.889i		−	0.394477i
$528$		0			0
$529$	−448.000			−0.846881
$530$	150.640	−	48.9458i	0.284226	−	0.0923506i
$531$	−459.522	−	333.862i	−0.865389	−	0.628742i
$532$	−194.164	+	141.068i	−0.364970	+	0.265166i
$533$	88.9969	−	273.904i	0.166974	−	0.513892i
$534$	12.1050	+	3.93314i	0.0226685	+	0.00736544i
$535$	762.260	+	1049.16i	1.42478	+	1.96105i
$536$	−154.613	+	212.807i	−0.288458	+	0.397028i
$537$	61.4944	+	189.260i	0.114515	+	0.352440i
$538$			192.333i			0.357496i
$539$		0			0
$540$	−238.000			−0.440741
$541$	220.580	−	71.6706i	0.407726	−	0.132478i	−0.0979715	−	0.995189i	$-0.531235\pi$
$541$	220.580	−	71.6706i	0.407726	−	0.132478i	0.505697	+	0.862711i	$0.331235\pi$
$542$	−330.079	−	239.816i	−0.609002	−	0.442466i
$543$	−59.0582	+	42.9083i	−0.108763	+	0.0790209i
$544$	37.0820	−	114.127i	0.0681655	−	0.209792i
$545$	−310.694	−	100.951i	−0.570081	−	0.185231i
$546$	−99.7505	−	137.295i	−0.182693	−	0.251456i
$547$	−412.302	+	567.485i	−0.753751	+	1.03745i	0.243957	+	0.969786i	$0.421554\pi$
$547$	−412.302	+	567.485i	−0.753751	+	1.03745i	−0.997708	+	0.0676635i	$0.978446\pi$
$548$	158.835	+	488.843i	0.289844	+	0.892049i
$549$		−	90.5097i		−	0.164863i
$550$		0			0
$551$	384.000			0.696915
$552$	−72.6298	+	23.5989i	−0.131576	+	0.0427516i
$553$	898.009	+	652.442i	1.62389	+	1.17982i
$554$	−140.769	+	102.275i	−0.254096	+	0.184611i
$555$	36.7730	−	113.176i	0.0662577	−	0.203920i
$556$	−164.090	−	53.3160i	−0.295125	−	0.0958920i
$557$	123.857	+	170.474i	0.222364	+	0.306058i	0.905594	−	0.424145i	$-0.139425\pi$
$557$	123.857	+	170.474i	0.222364	+	0.306058i	−0.683230	+	0.730203i	$0.739425\pi$
$558$	−325.852	+	448.496i	−0.583963	+	0.803757i
$559$	−244.741	−	753.237i	−0.437820	−	1.34747i
$560$			197.990i			0.353553i
$561$		0			0
$562$	402.000			0.715302
$563$	516.479	−	167.814i	0.917369	−	0.298071i	0.187982	−	0.982172i	$-0.439805\pi$
$563$	516.479	−	167.814i	0.917369	−	0.298071i	0.729387	+	0.684101i	$0.239805\pi$
$564$	51.7771	+	37.6183i	0.0918033	+	0.0666990i
$565$	368.103	−	267.442i	0.651509	−	0.473349i
$566$	34.6099	−	106.518i	0.0611482	−	0.188195i
$567$	369.874	+	120.179i	0.652335	+	0.211957i
$568$	364.089	+	501.126i	0.641002	+	0.882264i
$569$	−46.5502	+	64.0709i	−0.0818106	+	0.112603i	−0.847961	−	0.530059i	$-0.822170\pi$
$569$	−46.5502	+	64.0709i	−0.0818106	+	0.112603i	0.766150	+	0.642661i	$0.222170\pi$
$570$	51.9149	+	159.777i	0.0910787	+	0.280311i
$571$			124.451i			0.217952i	0.994044	+	0.108976i	$0.0347572\pi$
$571$			124.451i			0.217952i	−0.994044	+	0.108976i	$0.965243\pi$
$572$		0			0
$573$	−215.000			−0.375218
$574$	−161.400	+	52.4419i	−0.281184	+	0.0913622i
$575$	174.748	+	126.962i	0.303909	+	0.220803i
$576$	−362.440	+	263.328i	−0.629235	+	0.457166i
$577$	31.8288	−	97.9588i	0.0551625	−	0.169773i	−0.919679	−	0.392670i	$-0.871551\pi$
$577$	31.8288	−	97.9588i	0.0551625	−	0.169773i	0.974842	+	0.222897i	$0.0715515\pi$
$578$	364.494	+	118.431i	0.630613	+	0.204899i
$579$	79.8004	+	109.836i	0.137824	+	0.189699i
$580$	−186.201	+	256.284i	−0.321036	+	0.441868i
$581$	77.2542	+	237.764i	0.132968	+	0.409233i
$582$			24.0416i			0.0413086i
$583$		0			0
$584$	336.000			0.575342
$585$	−903.838	+	293.675i	−1.54502	+	0.502008i
$586$	−187.692	−	136.366i	−0.320293	−	0.232707i
$587$	511.299	−	371.480i	0.871037	−	0.632845i	−0.0598280	−	0.998209i	$-0.519055\pi$
$587$	511.299	−	371.480i	0.871037	−	0.632845i	0.930865	+	0.365363i	$0.119055\pi$
$588$	0.618034	−	1.90211i	0.00105108	−	0.00323489i
$589$	−790.858	−	256.965i	−1.34271	−	0.436274i
$590$	−413.133	−	568.629i	−0.700226	−	0.963778i
$591$	118.869	−	163.610i	0.201132	−	0.276835i
$592$	−21.0132	−	64.6718i	−0.0354952	−	0.109243i
$593$		−	497.803i		−	0.839466i	−0.907648	−	0.419733i	$-0.862124\pi$
$593$		−	497.803i		−	0.839466i	0.907648	−	0.419733i	$-0.137876\pi$
$594$		0			0
$595$	−210.000			−0.352941
$596$	−524.549	+	170.436i	−0.880116	+	0.285967i
$597$	161.803	+	117.557i	0.271027	+	0.196913i
$598$	−174.748	+	126.962i	−0.292220	+	0.212310i
$599$	96.4133	−	296.730i	0.160957	−	0.495375i	−0.837759	−	0.546041i	$-0.816134\pi$
$599$	96.4133	−	296.730i	0.160957	−	0.495375i	0.998716	+	0.0506658i	$0.0161343\pi$
$600$	−193.680	−	62.9303i	−0.322799	−	0.104884i
$601$	−241.895	−	332.940i	−0.402487	−	0.553976i	0.558879	−	0.829249i	$-0.311232\pi$
$601$	−241.895	−	332.940i	−0.402487	−	0.553976i	−0.961366	+	0.275273i	$0.911232\pi$
$602$	−274.314	+	377.561i	−0.455671	+	0.627177i
$603$	76.6362	+	235.862i	0.127092	+	0.391148i
$604$		−	313.955i		−	0.519794i
$605$		0			0
$606$	−218.000			−0.359736
$607$	117.015	−	38.0204i	0.192776	−	0.0626366i	−0.211038	−	0.977478i	$-0.567684\pi$
$607$	117.015	−	38.0204i	0.192776	−	0.0626366i	0.403814	+	0.914841i	$0.367684\pi$
$608$	−388.328	−	282.137i	−0.638698	−	0.464041i
$609$	−129.443	+	94.0456i	−0.212550	+	0.154426i
$610$	34.6099	−	106.518i	0.0567375	−	0.174620i
$611$	516.479	+	167.814i	0.845301	+	0.274655i
$612$	−39.9002	−	54.9179i	−0.0651964	−	0.0897351i
$613$	319.201	−	439.343i	0.520720	−	0.716710i	−0.464961	−	0.885331i	$-0.653932\pi$
$613$	319.201	−	439.343i	0.520720	−	0.716710i	0.985681	+	0.168621i	$0.0539315\pi$
$614$	−81.5805	−	251.079i	−0.132867	−	0.408923i
$615$		−	118.794i		−	0.193161i
$616$		0			0
$617$	−1120.00			−1.81524			−0.907618	−	0.419798i	$-0.862101\pi$
$617$	−1120.00			−1.81524			−0.907618	+	0.419798i	$0.862101\pi$
$618$	−21.5200	+	6.99226i	−0.0348219	+	0.0113143i
$619$	−568.739	−	413.213i	−0.918803	−	0.667549i	0.0244229	−	0.999702i	$-0.492225\pi$
$619$	−568.739	−	413.213i	−0.918803	−	0.667549i	−0.943226	+	0.332152i	$0.892225\pi$
$620$	554.986	−	403.221i	0.895138	−	0.650356i
$621$	−47.2796	+	145.512i	−0.0761346	+	0.234318i
$622$	190.990	+	62.0563i	0.307057	+	0.0997689i
$623$	37.4064	+	51.4855i	0.0600424	+	0.0826413i
$624$	39.9002	−	54.9179i	0.0639426	−	0.0880094i
$625$	−200.552	−	617.236i	−0.320883	−	0.987577i
$626$		−	632.153i		−	1.00983i
$627$		0			0
$628$	350.000			0.557325
$629$	68.5948	−	22.2878i	0.109054	−	0.0354337i
$630$	453.050	+	329.160i	0.719126	+	0.522476i
$631$	−316.326	+	229.824i	−0.501308	+	0.364222i	−0.809517	−	0.587097i	$-0.800271\pi$
$631$	−316.326	+	229.824i	−0.501308	+	0.364222i	0.308208	+	0.951319i	$0.400271\pi$
$632$	−411.611	+	1266.81i	−0.651283	+	2.00444i
$633$	−75.3198	−	24.4729i	−0.118989	−	0.0386618i
$634$	−351.620	−	483.964i	−0.554606	−	0.763350i
$635$	721.528	−	993.099i	1.13627	−	1.56393i
$636$	−9.88854	−	30.4338i	−0.0155480	−	0.0478519i
$637$		−	16.9706i		−	0.0266414i
$638$		0			0
$639$	584.000			0.913928
$640$	225.960	−	73.4187i	0.353062	−	0.114717i
$641$	18.6074	+	13.5191i	0.0290287	+	0.0210906i	0.602205	−	0.798341i	$-0.294289\pi$
$641$	18.6074	+	13.5191i	0.0290287	+	0.0210906i	−0.573176	+	0.819432i	$0.694289\pi$
$642$	−211.962	+	154.000i	−0.330160	+	0.239875i
$643$	−138.131	+	425.122i	−0.214822	+	0.661154i	0.784344	+	0.620326i	$0.213000\pi$
$643$	−138.131	+	425.122i	−0.214822	+	0.661154i	−0.999166	+	0.0408284i	$0.987000\pi$
$644$	−121.050	−	39.3314i	−0.187965	−	0.0610737i
$645$	−192.020	−	264.292i	−0.297705	−	0.409756i
$646$	−59.8503	+	82.3768i	−0.0926475	+	0.127518i
$647$	−148.019	−	455.556i	−0.228778	−	0.704105i	−0.997886	−	0.0649869i	$-0.979299\pi$
$647$	−148.019	−	455.556i	−0.228778	−	0.704105i	0.769108	−	0.639118i	$-0.220701\pi$
$648$			466.690i			0.720201i
$649$		0			0
$650$	−576.000			−0.886154
$651$	329.524	−	107.069i	0.506182	−	0.164468i
$652$	258.885	+	188.091i	0.397064	+	0.288484i
$653$	−583.301	+	423.793i	−0.893264	+	0.648994i	−0.936727	−	0.350061i	$-0.886161\pi$
$653$	−583.301	+	423.793i	−0.893264	+	0.648994i	0.0434632	+	0.999055i	$0.486161\pi$
$654$	20.3951	−	62.7697i	0.0311852	−	0.0959782i
$655$	−932.083	−	302.852i	−1.42303	−	0.462370i
$656$	−39.9002	−	54.9179i	−0.0608235	−	0.0837163i
$657$	186.201	−	256.284i	0.283411	−	0.390081i
$658$	−98.8854	−	304.338i	−0.150282	−	0.462520i
$659$		−	700.036i		−	1.06227i	−0.847287	−	0.531135i	$-0.821766\pi$
$659$		−	700.036i		−	1.06227i	0.847287	−	0.531135i	$-0.178234\pi$
$660$		0			0
$661$	607.000			0.918306			0.459153	−	0.888357i	$-0.348153\pi$
$661$	607.000			0.918306			0.459153	+	0.888357i	$0.348153\pi$
$662$	−195.025	+	63.3673i	−0.294599	+	0.0957210i
$663$	58.2492	+	42.3205i	0.0878570	+	0.0638319i
$664$	−242.705	+	176.336i	−0.365520	+	0.265566i
$665$	−259.574	+	798.887i	−0.390337	+	1.20133i
$666$	−182.920	−	59.4342i	−0.274654	−	0.0892405i
$667$	119.701	+	164.754i	0.179461	+	0.247007i
$668$	19.9501	−	27.4589i	0.0298654	−	0.0411062i
$669$	34.3009	+	105.567i	0.0512719	+	0.157799i
$670$			306.884i			0.458036i
$671$		0			0
$672$	200.000			0.297619
$673$	−948.223	+	308.096i	−1.40895	+	0.457795i	−0.912074	−	0.410026i	$-0.865519\pi$
$673$	−948.223	+	308.096i	−1.40895	+	0.457795i	−0.496876	+	0.867822i	$0.665519\pi$
$674$	292.864	+	212.778i	0.434517	+	0.315695i
$675$	−330.079	+	239.816i	−0.489006	+	0.355284i
$676$	−73.5460	+	226.351i	−0.108796	+	0.334839i
$677$	735.713	+	239.048i	1.08673	+	0.353099i	0.796980	−	0.604005i	$-0.206429\pi$
$677$	735.713	+	239.048i	1.08673	+	0.353099i	0.289745	+	0.957104i	$0.406429\pi$
$678$	54.0315	+	74.3680i	0.0796925	+	0.109687i
$679$	−70.6566	+	97.2504i	−0.104060	+	0.143226i
$680$	−77.8723	−	239.666i	−0.114518	−	0.352450i
$681$		−	131.522i		−	0.193130i
$682$		0			0
$683$	−218.000			−0.319180			−0.159590	−	0.987183i	$-0.551017\pi$
$683$	−218.000			−0.319180			−0.159590	+	0.987183i	$0.551017\pi$
$684$	−258.239	+	83.9071i	−0.377543	+	0.122671i
$685$	1455.42	+	1057.43i	2.12470	+	1.54369i
$686$	388.328	−	282.137i	0.566076	−	0.411278i
$687$	93.6321	−	288.170i	0.136291	−	0.419462i
$688$	−177.540	−	57.6861i	−0.258052	−	0.0838461i
$689$	−159.601	−	219.672i	−0.231641	−	0.318827i
$690$	−52.3690	+	72.0797i	−0.0758971	+	0.104463i
$691$	266.682	+	820.762i	0.385936	+	1.18779i	0.935799	+	0.352534i	$0.114680\pi$
$691$	266.682	+	820.762i	0.385936	+	1.18779i	−0.549863	+	0.835255i	$0.685320\pi$
$692$			246.073i			0.355597i
$693$		0			0
$694$	776.000			1.11816
$695$	−574.314	+	186.606i	−0.826351	+	0.268498i
$696$	−155.331	−	112.855i	−0.223177	−	0.162148i
$697$	58.2492	−	42.3205i	0.0835713	−	0.0607181i
$698$	190.973	−	587.753i	0.273600	−	0.842053i
$699$	−75.3198	−	24.4729i	−0.107754	−	0.0350113i
$700$	−199.501	−	274.589i	−0.285001	−	0.392271i
$701$	236.907	−	326.075i	0.337956	−	0.465157i	−0.605887	−	0.795551i	$-0.707182\pi$
$701$	236.907	−	326.075i	0.337956	−	0.465157i	0.943843	+	0.330394i	$0.107182\pi$
$702$	−126.079	−	388.031i	−0.179600	−	0.552751i
$703$		−	288.500i		−	0.410383i
$704$		0			0
$705$	224.000			0.317730
$706$	−786.823	+	255.654i	−1.11448	+	0.362117i
$707$	−881.829	−	640.686i	−1.24728	−	0.906204i
$708$	−114.880	+	83.4655i	−0.162260	+	0.117889i
$709$	−192.518	+	592.508i	−0.271534	+	0.835696i	0.718582	+	0.695443i	$0.244792\pi$
$709$	−192.518	+	592.508i	−0.271534	+	0.835696i	−0.990116	+	0.140253i	$0.955208\pi$
$710$	687.293	+	223.315i	0.968019	+	0.314528i
$711$	738.153	+	1015.98i	1.03819	+	1.42895i
$712$	−44.8877	+	61.7826i	−0.0630445	+	0.0867734i
$713$	−136.276	−	419.416i	−0.191131	−	0.588241i
$714$		−	42.4264i		−	0.0594207i
$715$		0			0
$716$	−398.000			−0.555866
$717$	−267.654	+	86.9662i	−0.373298	+	0.121292i
$718$	−472.466	−	343.267i	−0.658031	−	0.478087i
$719$	−227.334	+	165.168i	−0.316180	+	0.229719i	−0.734544	−	0.678561i	$-0.762604\pi$
$719$	−227.334	+	165.168i	−0.316180	+	0.229719i	0.418363	+	0.908280i	$0.362604\pi$
$720$	−69.2198	+	213.037i	−0.0961386	+	0.295884i
$721$	−107.600	−	34.9613i	−0.149237	−	0.0484900i
$722$	−60.6815	−	83.5210i	−0.0840464	−	0.115680i
$723$	219.451	−	302.048i	0.303528	−	0.417771i
$724$	−45.1165	−	138.854i	−0.0623156	−	0.191788i
$725$			543.058i			0.749046i
$726$		0			0
$727$	1223.00			1.68226			0.841128	−	0.540836i	$-0.181892\pi$
$727$	1223.00			1.68226			0.841128	+	0.540836i	$0.181892\pi$
$728$	968.398	−	314.652i	1.33022	−	0.432214i
$729$	232.188	+	168.694i	0.318502	+	0.231405i
$730$	317.135	−	230.412i	0.434431	−	0.315633i
$731$	61.1854	−	188.309i	0.0837009	−	0.257605i
$732$	−21.5200	−	6.99226i	−0.0293988	−	0.00955226i
$733$	−525.352	−	723.086i	−0.716715	−	0.986474i	−0.999627	−	0.0273281i	$-0.991300\pi$
$733$	−525.352	−	723.086i	−0.716715	−	0.986474i	0.282911	−	0.959146i	$-0.408700\pi$
$734$	453.033	−	623.547i	0.617212	−	0.849519i
$735$	−2.16312	−	6.65740i	−0.00294302	−	0.00905768i
$736$		−	254.558i		−	0.345867i
$737$		0			0
$738$	−192.000			−0.260163
$739$	915.943	−	297.608i	1.23944	−	0.402717i	0.385312	−	0.922786i	$-0.374094\pi$
$739$	915.943	−	297.608i	1.23944	−	0.402717i	0.854124	+	0.520069i	$0.174094\pi$
$740$	192.546	+	139.893i	0.260197	+	0.189044i
$741$	232.997	−	169.282i	0.314436	−	0.228451i
$742$	−49.4427	+	152.169i	−0.0666344	+	0.205080i
$743$	10.7600	+	3.49613i	0.0144818	+	0.00470542i	0.316249	−	0.948676i	$-0.397577\pi$
$743$	10.7600	+	3.49613i	0.0144818	+	0.00470542i	−0.301767	+	0.953382i	$0.597577\pi$
$744$	244.389	+	336.372i	0.328479	+	0.452113i
$745$	−1134.66	+	1561.73i	−1.52304	+	2.09628i
$746$	101.976	+	313.849i	0.136697	+	0.420709i
$747$			282.843i			0.378638i
$748$		0			0
$749$	−1310.00			−1.74900
$750$	9.41498	−	3.05911i	0.0125533	−	0.00407882i
$751$	−426.352	−	309.763i	−0.567712	−	0.412467i	0.266561	−	0.963818i	$-0.414113\pi$
$751$	−426.352	−	309.763i	−0.567712	−	0.412467i	−0.834273	+	0.551351i	$0.814113\pi$
$752$	103.554	−	75.2365i	0.137705	−	0.100049i
$753$	−69.5288	+	213.988i	−0.0923358	+	0.284180i
$754$	−516.479	−	167.814i	−0.684985	−	0.222565i
$755$	−645.884	−	888.983i	−0.855476	−	1.17746i
$756$	141.313	−	194.501i	0.186922	−	0.257276i
$757$	11.7426	+	36.1401i	0.0155121	+	0.0477413i	0.958513	−	0.285049i	$-0.0920099\pi$
$757$	11.7426	+	36.1401i	0.0155121	+	0.0477413i	−0.943001	+	0.332790i	$0.892010\pi$
$758$		−	632.153i		−	0.833976i
$759$		0			0
$760$	−1008.00			−1.32632
$761$	1167.46	−	379.330i	1.53411	−	0.498462i	0.584366	−	0.811490i	$-0.301343\pi$
$761$	1167.46	−	379.330i	1.53411	−	0.498462i	0.949744	+	0.313028i	$0.101343\pi$
$762$	200.636	+	145.771i	0.263302	+	0.191300i
$763$	266.976	−	193.969i	0.349903	−	0.254219i
$764$	132.877	−	408.954i	0.173923	−	0.535281i
$765$	−225.960	−	73.4187i	−0.295372	−	0.0959721i
$766$	453.033	+	623.547i	0.591427	+	0.814030i
$767$	−708.228	+	974.793i	−0.923375	+	1.27092i
$768$	84.0526	+	258.687i	0.109444	+	0.336833i
$769$		−	311.127i		−	0.404586i	−0.979325	−	0.202293i	$-0.935161\pi$
$769$		−	311.127i		−	0.404586i	0.979325	−	0.202293i	$-0.0648394\pi$
$770$		0			0
$771$	−424.000			−0.549935
$772$	−258.239	+	83.9071i	−0.334507	+	0.108688i
$773$	−951.404	−	691.235i	−1.23079	−	0.894224i	−0.233845	−	0.972274i	$-0.575131\pi$
$773$	−951.404	−	691.235i	−1.23079	−	0.894224i	−0.996949	+	0.0780495i	$0.975131\pi$
$774$	−427.161	+	310.351i	−0.551888	+	0.400970i
$775$	363.404	−	1118.44i	0.468908	−	1.44315i
$776$	−137.190	−	44.5756i	−0.176791	−	0.0574428i
$777$	70.6566	+	97.2504i	0.0909351	+	0.125161i
$778$	178.720	−	245.986i	0.229717	−	0.316178i
$779$	−88.9969	−	273.904i	−0.114245	−	0.351610i
$780$			237.588i			0.304600i
$781$		0			0
$782$	−54.0000			−0.0690537
$783$	−365.839	+	118.868i	−0.467228	+	0.151811i
$784$	−3.23607	−	2.35114i	−0.00412764	−	0.00299890i
$785$	991.046	−	720.037i	1.26248	−	0.917245i
$786$	61.1854	−	188.309i	0.0778440	−	0.239579i
$787$	1194.36	+	388.070i	1.51761	+	0.493101i	0.945095	−	0.326795i	$-0.105969\pi$
$787$	1194.36	+	388.070i	1.51761	+	0.493101i	0.572513	+	0.819896i	$0.305969\pi$
$788$	237.739	+	327.219i	0.301699	+	0.415253i
$789$	−82.2941	+	113.268i	−0.104302	+	0.143559i
$790$	480.212	+	1477.94i	0.607864	+	1.87081i
$791$			459.619i			0.581061i
$792$		0			0
$793$	−192.000			−0.242119
$794$	796.238	−	258.713i	1.00282	−	0.325836i
$795$	−90.6099	−	65.8319i	−0.113975	−	0.0828075i
$796$	−323.607	+	235.114i	−0.406541	+	0.295369i
$797$	59.0222	−	181.652i	0.0740555	−	0.227919i	−0.907176	−	0.420750i	$-0.861767\pi$
$797$	59.0222	−	181.652i	0.0740555	−	0.227919i	0.981232	+	0.192831i	$0.0617669\pi$
$798$	−161.400	−	52.4419i	−0.202255	−	0.0657167i
$799$	79.8004	+	109.836i	0.0998753	+	0.137467i
$800$	399.002	−	549.179i	0.498752	−	0.686474i
$801$	22.2492	+	68.4761i	0.0277768	+	0.0854882i
$802$			690.136i			0.860519i
$803$		0			0
$804$	62.0000			0.0771144
$805$	−423.674	+	137.660i	−0.526303	+	0.171006i
$806$	951.404	+	691.235i	1.18040	+	0.857612i
$807$	110.026	−	79.9388i	0.136340	−	0.0990567i
$808$	404.194	−	1243.98i	0.500240	−	1.53958i
$809$	−521.859	−	169.562i	−0.645067	−	0.209595i	−0.0318290	−	0.999493i	$-0.510133\pi$
$809$	−521.859	−	169.562i	−0.645067	−	0.209595i	−0.613238	+	0.789899i	$0.710133\pi$
$810$	320.033	+	440.487i	0.395102	+	0.543811i
$811$	−238.570	+	328.363i	−0.294168	+	0.404887i	−0.930362	−	0.366642i	$-0.880508\pi$
$811$	−238.570	+	328.363i	−0.294168	+	0.404887i	0.636195	+	0.771529i	$0.280508\pi$
$812$	−98.8854	−	304.338i	−0.121780	−	0.374801i
$813$			288.500i			0.354858i
$814$		0			0
$815$	1120.00			1.37423
$816$	16.1400	−	5.24419i	0.0197794	−	0.00642671i
$817$	−640.741	−	465.526i	−0.784261	−	0.569799i
$818$	179.602	−	130.488i	0.219562	−	0.159521i
$819$	296.656	−	913.014i	0.362218	−	1.11479i
$820$	225.960	+	73.4187i	0.275560	+	0.0895350i
$821$	32.4189	+	44.6208i	0.0394871	+	0.0543493i	0.828304	−	0.560279i	$-0.189306\pi$
$821$	32.4189	+	44.6208i	0.0394871	+	0.0543493i	−0.788817	+	0.614628i	$0.789306\pi$
$822$	−213.632	+	294.040i	−0.259893	+	0.357712i
$823$	212.295	+	653.376i	0.257952	+	0.793895i	0.993234	+	0.116133i	$0.0370500\pi$
$823$	212.295	+	653.376i	0.257952	+	0.793895i	−0.735281	+	0.677762i	$0.762950\pi$
$824$		−	135.765i		−	0.164763i
$825$		0			0
$826$	710.000			0.859564
$827$	−16.1400	+	5.24419i	−0.0195163	+	0.00634122i	−0.318759	−	0.947836i	$-0.603266\pi$
$827$	−16.1400	+	5.24419i	−0.0195163	+	0.00634122i	0.299243	+	0.954177i	$0.403266\pi$
$828$	−116.498	−	84.6411i	−0.140699	−	0.102224i
$829$	−796.882	+	578.968i	−0.961257	+	0.698394i	−0.953442	−	0.301576i	$-0.902487\pi$
$829$	−796.882	+	578.968i	−0.961257	+	0.698394i	−0.00781437	+	0.999969i	$0.502487\pi$
$830$	−108.156	+	332.870i	−0.130308	+	0.401048i
$831$	117.015	+	38.0204i	0.140812	+	0.0457526i
$832$	558.603	+	768.851i	0.671397	+	0.924099i
$833$	2.49376	−	3.43237i	0.00299371	−	0.00412049i
$834$	−37.7001	−	116.029i	−0.0452039	−	0.139123i
$835$		−	118.794i		−	0.142268i
$836$		0			0
$837$	833.000			0.995221
$838$	441.159	−	143.341i	0.526443	−	0.171052i
$839$	−70.3845	−	51.1373i	−0.0838909	−	0.0609503i	0.545049	−	0.838404i	$-0.316511\pi$
$839$	−70.3845	−	51.1373i	−0.0838909	−	0.0609503i	−0.628940	+	0.777454i	$0.716511\pi$
$840$	339.787	−	246.870i	0.404508	−	0.293893i
$841$	101.667	−	312.898i	0.120888	−	0.372054i
$842$	279.759	+	90.8993i	0.332256	+	0.107956i
$843$	−167.082	−	229.969i	−0.198199	−	0.272798i
$844$	93.1004	−	128.142i	0.110309	−	0.151827i
$845$	257.411	+	792.230i	0.304629	+	0.937550i
$846$		−	362.039i		−	0.427942i
$847$		0			0
$848$	−64.0000			−0.0754717
$849$	−75.3198	+	24.4729i	−0.0887159	+	0.0288256i
$850$	−116.498	−	84.6411i	−0.137057	−	0.0995777i
$851$	123.780	−	89.9311i	0.145452	−	0.105677i
$852$	45.1165	−	138.854i	0.0529536	−	0.162974i
$853$	−507.064	−	164.755i	−0.594448	−	0.193148i	−0.00368511	−	0.999993i	$-0.501173\pi$
$853$	−507.064	−	164.755i	−0.594448	−	0.193148i	−0.590763	+	0.806845i	$0.701173\pi$
$854$	66.5003	+	91.5298i	0.0778692	+	0.107178i
$855$	−558.603	+	768.851i	−0.653336	+	0.899240i
$856$	−485.775	−	1495.06i	−0.567494	−	1.74657i
$857$			1368.96i			1.59738i	0.601740	+	0.798692i	$0.294475\pi$
$857$			1368.96i			1.59738i	−0.601740	+	0.798692i	$0.705525\pi$
$858$		0			0
$859$	−977.000			−1.13737			−0.568685	−	0.822556i	$-0.692547\pi$
$859$	−977.000			−1.13737			−0.568685	+	0.822556i	$0.692547\pi$
$860$	621.389	−	201.901i	0.722545	−	0.234769i
$861$	97.0820	+	70.5342i	0.112755	+	0.0819213i
$862$	642.359	−	466.701i	0.745197	−	0.541417i
$863$	−393.070	+	1209.74i	−0.455469	+	1.40179i	0.415115	+	0.909769i	$0.363741\pi$
$863$	−393.070	+	1209.74i	−0.455469	+	1.40179i	−0.870584	+	0.492020i	$0.836259\pi$
$864$	457.299	+	148.585i	0.529281	+	0.171974i
$865$	506.234	+	696.771i	0.585241	+	0.805515i
$866$	32.4189	−	44.6208i	0.0374352	−	0.0515252i
$867$	−83.7436	−	257.736i	−0.0965901	−	0.297274i
$868$			692.965i			0.798346i
$869$		0			0
$870$	−224.000			−0.257471
$871$	500.339	−	162.570i	0.574442	−	0.186647i
$872$	320.371	+	232.763i	0.367398	+	0.266930i
$873$	−110.026	+	79.9388i	−0.126032	+	0.0915679i
$874$	−66.7477	+	205.428i	−0.0763703	+	0.235044i
$875$	47.0749	+	15.2956i	0.0537999	+	0.0174806i
$876$	−46.5502	−	64.0709i	−0.0531395	−	0.0731403i
$877$	355.777	−	489.685i	0.405675	−	0.558363i	−0.556482	−	0.830860i	$-0.687849\pi$
$877$	355.777	−	489.685i	0.405675	−	0.558363i	0.962157	+	0.272496i	$0.0878493\pi$
$878$	108.774	+	334.772i	0.123888	+	0.381289i
$879$			164.049i			0.186631i
$880$		0			0
$881$	−295.000			−0.334847			−0.167423	−	0.985885i	$-0.553545\pi$
$881$	−295.000			−0.334847			−0.167423	+	0.985885i	$0.553545\pi$
$882$	−10.7600	+	3.49613i	−0.0121995	+	0.00396386i
$883$	472.466	+	343.267i	0.535069	+	0.388750i	0.822250	−	0.569126i	$-0.192718\pi$
$883$	472.466	+	343.267i	0.535069	+	0.388750i	−0.287181	+	0.957876i	$0.592718\pi$
$884$	−116.498	+	84.6411i	−0.131786	+	0.0957478i
$885$	−153.581	+	472.675i	−0.173538	+	0.534096i
$886$	235.374	+	76.4778i	0.265660	+	0.0863181i
$887$	−571.071	−	786.012i	−0.643823	−	0.886147i	0.354989	−	0.934871i	$-0.384485\pi$
$887$	−571.071	−	786.012i	−0.643823	−	0.886147i	−0.998812	+	0.0487236i	$0.984485\pi$
$888$	−84.7879	+	116.701i	−0.0954819	+	0.131420i
$889$	383.181	+	1179.31i	0.431025	+	1.32656i
$890$			89.0955i			0.100107i
$891$		0			0
$892$	−222.000			−0.248879
$893$	516.479	−	167.814i	0.578364	−	0.187922i
$894$	−315.517	−	229.236i	−0.352927	−	0.256416i
$895$	−1126.96	+	818.785i	−1.25917	+	0.914843i
$896$	−74.1641	+	228.254i	−0.0827724	+	0.254747i
$897$	145.260	+	47.1977i	0.161939	+	0.0526173i
$898$	−260.182	−	358.110i	−0.289735	−	0.398787i
$899$	651.703	−	896.992i	0.724920	−	0.997767i
$900$	−118.663	−	365.206i	−0.131847	−	0.405784i
$901$		−	67.8823i		−	0.0753410i
$902$		0			0
$903$	330.000			0.365449
$904$	−524.549	+	170.436i	−0.580253	+	0.188536i
$905$	−413.408	−	300.358i	−0.456804	−	0.331888i
$906$	179.602	−	130.488i	0.198236	−	0.144027i
$907$	−474.650	+	1460.82i	−0.523319	+	1.61061i	0.244298	+	0.969700i	$0.421443\pi$
$907$	−474.650	+	1460.82i	−0.523319	+	1.61061i	−0.767617	+	0.640909i	$0.778557\pi$
$908$	250.169	+	81.2850i	0.275517	+	0.0895209i
$909$	−724.853	−	997.675i	−0.797418	−	1.09755i
$910$	698.253	−	961.063i	0.767311	−	1.05611i
$911$	256.484	+	789.377i	0.281541	+	0.866495i	0.987414	+	0.158156i	$0.0505550\pi$
$911$	256.484	+	789.377i	0.281541	+	0.866495i	−0.705873	+	0.708339i	$0.749445\pi$
$912$		−	67.8823i		−	0.0744323i
$913$		0			0
$914$	−16.0000			−0.0175055
$915$	−75.3198	+	24.4729i	−0.0823168	+	0.0267463i
$916$	490.264	+	356.198i	0.535223	+	0.388862i
$917$	800.927	−	581.907i	0.873421	−	0.634577i
$918$	31.5197	−	97.0078i	0.0343352	−	0.105673i
$919$	−536.654	−	174.369i	−0.583954	−	0.189738i	0.00211708	−	0.999998i	$-0.499326\pi$
$919$	−536.654	−	174.369i	−0.583954	−	0.189738i	−0.586071	+	0.810260i	$0.699326\pi$
$920$	−314.214	−	432.478i	−0.341537	−	0.470085i
$921$	−109.726	+	151.024i	−0.119137	+	0.163979i
$922$	−380.709	−	1171.70i	−0.412916	−	1.27083i
$923$		−	1238.85i		−	1.34220i
$924$		0			0
$925$	408.000			0.441081
$926$	−431.744	+	140.282i	−0.466246	+	0.151493i
$927$	−103.554	−	75.2365i	−0.111709	−	0.0811613i
$928$	517.771	−	376.183i	0.557943	−	0.405369i
$929$	477.122	−	1468.43i	0.513587	−	1.58066i	−0.272252	−	0.962226i	$-0.587768\pi$
$929$	477.122	−	1468.43i	0.513587	−	1.58066i	0.785838	−	0.618432i	$-0.212232\pi$
$930$	461.334	+	149.896i	0.496058	+	0.161179i
$931$	−9.97505	−	13.7295i	−0.0107143	−	0.0147470i
$932$	93.1004	−	128.142i	0.0998932	−	0.137491i
$933$	−43.8804	−	135.050i	−0.0470315	−	0.144748i
$934$		−	227.688i		−	0.243778i
$935$		0			0
$936$	1152.00			1.23077
$937$	−844.658	+	274.446i	−0.901449	+	0.292899i	−0.722835	−	0.691020i	$-0.757161\pi$
$937$	−844.658	+	274.446i	−0.901449	+	0.292899i	−0.178614	+	0.983919i	$0.557161\pi$
$938$	−250.795	−	182.213i	−0.267372	−	0.194257i
$939$	−361.631	+	262.740i	−0.385123	+	0.279808i
$940$	−138.440	+	426.073i	−0.147276	+	0.453269i
$941$	−773.373	−	251.284i	−0.821863	−	0.267040i	−0.132249	−	0.991217i	$-0.542220\pi$
$941$	−773.373	−	251.284i	−0.821863	−	0.267040i	−0.689614	+	0.724177i	$0.742220\pi$
$942$	145.469	+	200.221i	0.154426	+	0.212549i
$943$	89.7754	−	123.565i	0.0952019	−	0.131034i
$944$	87.7608	+	270.100i	0.0929670	+	0.286123i
$945$		−	841.457i		−	0.890431i
$946$		0			0
$947$	145.000			0.153115			0.0765576	−	0.997065i	$-0.475607\pi$
$947$	145.000			0.153115			0.0765576	+	0.997065i	$0.475607\pi$
$948$	298.589	−	97.0176i	0.314968	−	0.102339i
$949$	−543.659	−	394.992i	−0.572876	−	0.416219i
$950$	−465.994	+	338.564i	−0.490520	+	0.356383i
$951$	−130.714	+	402.297i	−0.137449	+	0.423025i
$952$	242.099	+	78.6629i	0.254306	+	0.0826291i
$953$	−369.908	−	509.135i	−0.388151	−	0.534244i	0.569570	−	0.821943i	$-0.307110\pi$
$953$	−369.908	−	509.135i	−0.388151	−	0.534244i	−0.957721	+	0.287699i	$0.907110\pi$
$954$	−106.400	+	146.448i	−0.111531	+	0.153509i
$955$	−465.071	−	1431.34i	−0.486985	−	1.49879i
$956$		−	562.857i		−	0.588763i
$957$		0			0
$958$	−632.000			−0.659708
$959$	−1728.32	+	561.566i	−1.80221	+	0.585574i
$960$	317.135	+	230.412i	0.330349	+	0.240012i
$961$	−1164.98	+	846.411i	−1.21226	+	0.880760i
$962$	−126.079	+	388.031i	−0.131059	+	0.403359i
$963$	−1409.56	−	457.993i	−1.46371	−	0.475590i
$964$	438.902	+	604.097i	0.455293	+	0.626656i
$965$	−558.603	+	768.851i	−0.578863	+	0.796736i
$966$	−27.8115	−	85.5951i	−0.0287904	−	0.0886077i
$967$		−	373.352i		−	0.386093i	−0.981190	−	0.193047i	$-0.938163\pi$
$967$		−	373.352i		−	0.386093i	0.981190	−	0.193047i	$-0.0618369\pi$
$968$		0			0
$969$	72.0000			0.0743034
$970$	−160.055	+	52.0049i	−0.165005	+	0.0536133i
$971$	1371.28	+	996.296i	1.41224	+	1.02605i	0.992992	+	0.118179i	$0.0377057\pi$
$971$	1371.28	+	996.296i	1.41224	+	1.02605i	0.419246	+	0.907872i	$0.362294\pi$
$972$	336.551	−	244.519i	0.346246	−	0.251562i
$973$	188.500	−	580.144i	0.193731	−	0.596243i
$974$	−977.813	−	317.711i	−1.00391	−	0.326192i
$975$	239.401	+	329.507i	0.245540	+	0.337956i
$976$	−26.6001	+	36.6119i	−0.0272542	+	0.0375122i
$977$	−114.027	−	350.940i	−0.116712	−	0.359201i	0.875589	−	0.483058i	$-0.160474\pi$
$977$	−114.027	−	350.940i	−0.116712	−	0.359201i	−0.992300	+	0.123856i	$0.960474\pi$
$978$			226.274i			0.231364i
$979$		0			0
$980$	14.0000			0.0142857
$981$	355.079	−	115.372i	0.361956	−	0.117607i
$982$	595.437	+	432.610i	0.606351	+	0.440540i
$983$	−369.721	+	268.618i	−0.376115	+	0.273263i	−0.759742	−	0.650225i	$-0.774675\pi$
$983$	−369.721	+	268.618i	−0.376115	+	0.273263i	0.383627	+	0.923488i	$0.374675\pi$
$984$	−44.4984	+	136.952i	−0.0452220	+	0.139179i
$985$	1346.34	+	437.453i	1.36684	+	0.444115i
$986$	−79.8004	−	109.836i	−0.0809334	−	0.111395i
$987$	−133.001	+	183.060i	−0.134752	+	0.185471i
$988$	177.994	+	547.809i	0.180156	+	0.554462i
$989$		−	420.021i		−	0.424693i
$990$		0			0
$991$	−1032.00			−1.04137			−0.520686	−	0.853748i	$-0.674324\pi$
$991$	−1032.00			−1.04137			−0.520686	+	0.853748i	$0.674324\pi$
$992$	−1318.10	+	428.276i	−1.32873	+	0.431730i
$993$	117.307	+	85.2289i	0.118134	+	0.0858297i
$994$	−590.582	+	429.083i	−0.594147	+	0.431673i
$995$	−432.624	+	1331.48i	−0.434798	+	1.33817i
$996$	67.2499	+	21.8508i	0.0675199	+	0.0219386i
$997$	416.458	+	573.206i	0.417711	+	0.574930i	0.965078	−	0.261963i	$-0.0843697\pi$
$997$	416.458	+	573.206i	0.417711	+	0.574930i	−0.547367	+	0.836893i	$0.684370\pi$
$998$	−305.901	+	421.037i	−0.306514	+	0.421881i
$999$	89.3059	+	274.855i	0.0893953	+	0.275130i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	121.3.d.e.94.1		8
11.2	odd	10	inner	121.3.d.e.112.1		8
11.3	even	5		121.3.b.a.120.2	yes	2
11.4	even	5	inner	121.3.d.e.118.1		8
11.5	even	5	inner	121.3.d.e.40.2		8
11.6	odd	10	inner	121.3.d.e.40.1		8
11.7	odd	10	inner	121.3.d.e.118.2		8
11.8	odd	10		121.3.b.a.120.1	✓	2
11.9	even	5	inner	121.3.d.e.112.2		8
11.10	odd	2	inner	121.3.d.e.94.2		8
33.8	even	10		1089.3.c.a.604.2		2
33.14	odd	10		1089.3.c.a.604.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
121.3.b.a.120.1	✓	2	11.8	odd	10
121.3.b.a.120.2	yes	2	11.3	even	5
121.3.d.e.40.1		8	11.6	odd	10	inner
121.3.d.e.40.2		8	11.5	even	5	inner
121.3.d.e.94.1		8	1.1	even	1	trivial
121.3.d.e.94.2		8	11.10	odd	2	inner
121.3.d.e.112.1		8	11.2	odd	10	inner
121.3.d.e.112.2		8	11.9	even	5	inner
121.3.d.e.118.1		8	11.4	even	5	inner
121.3.d.e.118.2		8	11.7	odd	10	inner
1089.3.c.a.604.1		2	33.14	odd	10
1089.3.c.a.604.2		2	33.8	even	10

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:	\( N \)	\(=\)	\( 121 = 11^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	121.d (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.34500 + 0.437016i) q^{2} +(0.809017 + 0.587785i) q^{3} +(-1.61803 + 1.17557i) q^{4} +(-2.16312 + 6.65740i) q^{5} +(-1.34500 - 0.437016i) q^{6} +(-4.15627 - 5.72061i) q^{7} +(4.98752 - 6.86474i) q^{8} +(-2.47214 - 7.60845i) q^{9} -9.89949i q^{10} -2.00000 q^{12} +(-16.1400 + 5.24419i) q^{13} +(8.09017 + 5.87785i) q^{14} +(-5.66312 + 4.11450i) q^{15} +(-1.23607 + 3.80423i) q^{16} +(-4.03499 - 1.31105i) q^{17} +(6.65003 + 9.15298i) q^{18} +(-9.97505 + 13.7295i) q^{19} +(-4.32624 - 13.3148i) q^{20} -7.07107i q^{21} -9.00000 q^{23} +(8.06998 - 2.62210i) q^{24} +(-19.4164 - 14.1068i) q^{25} +(19.4164 - 14.1068i) q^{26} +(5.25329 - 16.1680i) q^{27} +(13.4500 + 4.37016i) q^{28} +(-13.3001 - 18.3060i) q^{29} +(5.81878 - 8.00886i) q^{30} +(15.1418 + 46.6018i) q^{31} +28.2843i q^{32} +6.00000 q^{34} +(47.0749 - 15.2956i) q^{35} +(12.9443 + 9.40456i) q^{36} +(-13.7533 + 9.99235i) q^{37} +(7.41641 - 22.8254i) q^{38} +(-16.1400 - 5.24419i) q^{39} +(34.9127 + 48.0532i) q^{40} +(-9.97505 + 13.7295i) q^{41} +(3.09017 + 9.51057i) q^{42} +46.6690i q^{43} +56.0000 q^{45} +(12.1050 - 3.93314i) q^{46} +(-25.8885 - 18.8091i) q^{47} +(-3.23607 + 2.35114i) q^{48} +(-0.309017 + 0.951057i) q^{49} +(32.2799 + 10.4884i) q^{50} +(-2.49376 - 3.43237i) q^{51} +(19.9501 - 27.4589i) q^{52} +(4.94427 + 15.2169i) q^{53} +24.0416i q^{54} -60.0000 q^{56} +(-16.1400 + 5.24419i) q^{57} +(25.8885 + 18.8091i) q^{58} +(57.4402 - 41.7328i) q^{59} +(4.32624 - 13.3148i) q^{60} +(10.7600 + 3.49613i) q^{61} +(-40.7314 - 56.0620i) q^{62} +(-33.2502 + 45.7649i) q^{63} +(-17.3050 - 53.2592i) q^{64} -118.794i q^{65} -31.0000 q^{67} +(8.06998 - 2.62210i) q^{68} +(-7.28115 - 5.29007i) q^{69} +(-56.6312 + 41.1450i) q^{70} +(-22.5582 + 69.4271i) q^{71} +(-64.5599 - 20.9768i) q^{72} +(23.2751 + 32.0354i) q^{73} +(14.1313 - 19.4501i) q^{74} +(-7.41641 - 22.8254i) q^{75} -33.9411i q^{76} +24.0000 q^{78} +(-149.295 + 48.5088i) q^{79} +(-22.6525 - 16.4580i) q^{80} +(-44.4959 + 32.3282i) q^{81} +(7.41641 - 22.8254i) q^{82} +(-33.6249 - 10.9254i) q^{83} +(8.31254 + 11.4412i) q^{84} +(17.4563 - 24.0266i) q^{85} +(-20.3951 - 62.7697i) q^{86} -22.6274i q^{87} -9.00000 q^{89} +(-75.3198 + 24.4729i) q^{90} +(97.0820 + 70.5342i) q^{91} +(14.5623 - 10.5801i) q^{92} +(-15.1418 + 46.6018i) q^{93} +(43.0399 + 13.9845i) q^{94} +(-69.8253 - 96.1063i) q^{95} +(-16.6251 + 22.8825i) q^{96} +(-5.25329 - 16.1680i) q^{97} -1.41421i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9} - 16 q^{12} + 20 q^{14} - 14 q^{15} + 8 q^{16} + 28 q^{20} - 72 q^{23} - 48 q^{25} + 48 q^{26} - 34 q^{27} - 98 q^{31} + 48 q^{34} + 32 q^{36} - 34 q^{37} - 48 q^{38}+ \cdots + 34 q^{97}+O(q^{100}) \) 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9 - 16 * q^12 + 20 * q^14 - 14 * q^15 + 8 * q^16 + 28 * q^20 - 72 * q^23 - 48 * q^25 + 48 * q^26 - 34 * q^27 - 98 * q^31 + 48 * q^34 + 32 * q^36 - 34 * q^37 - 48 * q^38 - 20 * q^42 + 448 * q^45 - 64 * q^47 - 8 * q^48 + 2 * q^49 - 32 * q^53 - 480 * q^56 + 64 * q^58 + 142 * q^59 - 28 * q^60 + 112 * q^64 - 248 * q^67 - 18 * q^69 - 140 * q^70 + 146 * q^71 + 48 * q^75 + 192 * q^78 - 56 * q^80 - 110 * q^81 - 48 * q^82 + 132 * q^86 - 72 * q^89 + 240 * q^91 + 36 * q^92 + 98 * q^93 + 34 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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