LMFDB - Embedded newform 121.3.d.e.112.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [121,3,Mod(40,121)]

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

lf = mfeigenbasis(mf)

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")

//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);

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: f = N[0] # Warning: the index may be different

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			112.1
Root			$-1.34500 - 0.437016i$ of defining polynomial
Character	$\chi$	$=$	121.112
Dual form			121.3.d.e.94.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.34500 - 0.437016i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(-2.16312 - 6.65740i) q^{5} +(-1.34500 + 0.437016i) q^{6} +(-4.15627 + 5.72061i) q^{7} +(4.98752 + 6.86474i) q^{8} +(-2.47214 + 7.60845i) q^{9} +O(q^{10})$	\(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}+O(q^{10}) $ 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{10}\right)$

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	−0.0471903	−	0.998886i	$-0.515027\pi$
$2$	−1.34500	−	0.437016i	−0.672499	−	0.218508i	−0.625308	+	0.780378i	$0.715027\pi$
$3$	0.809017	−	0.587785i	0.269672	−	0.195928i	−0.444728	−	0.895666i	$-0.646700\pi$
$3$	0.809017	−	0.587785i	0.269672	−	0.195928i	0.714400	+	0.699737i	$0.246700\pi$
$4$	−1.61803	−	1.17557i	−0.404508	−	0.293893i
$5$	−2.16312	−	6.65740i	−0.432624	−	1.33148i	−0.895502	−	0.445057i	$-0.853183\pi$
$5$	−2.16312	−	6.65740i	−0.432624	−	1.33148i	0.462878	−	0.886422i	$-0.346817\pi$
$6$	−1.34500	+	0.437016i	−0.224166	+	0.0728360i
$7$	−4.15627	+	5.72061i	−0.593753	+	0.817231i	−0.995118	−	0.0986873i	$-0.968536\pi$
$7$	−4.15627	+	5.72061i	−0.593753	+	0.817231i	0.401366	+	0.915918i	$0.368536\pi$
$8$	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	−0.386655	−	0.922224i	$-0.626370\pi$
$13$	−16.1400	−	5.24419i	−1.24154	−	0.403399i	−0.854881	+	0.518825i	$0.826370\pi$
$14$	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	−0.425278	−	0.905063i	$-0.639824\pi$
$17$	−4.03499	+	1.31105i	−0.237352	+	0.0771205i	0.187926	+	0.982183i	$0.439824\pi$
$18$	6.65003	−	9.15298i	0.369446	−	0.508499i
$19$	−9.97505	−	13.7295i	−0.525002	−	0.722604i	0.461356	−	0.887215i	$-0.347363\pi$
$19$	−9.97505	−	13.7295i	−0.525002	−	0.722604i	−0.986359	+	0.164611i	$0.947363\pi$
$20$	−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	−0.974222	−	0.225589i	$-0.927569\pi$
$29$	−13.3001	+	18.3060i	−0.458623	+	0.631240i	0.515600	+	0.856830i	$0.327569\pi$
$30$	5.81878	+	8.00886i	0.193959	+	0.266962i
$31$	15.1418	−	46.6018i	0.488446	−	1.50328i	−0.338481	−	0.940973i	$-0.609913\pi$
$31$	15.1418	−	46.6018i	0.488446	−	1.50328i	0.826927	−	0.562310i	$-0.190087\pi$
$32$		−	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	0.386209	−	0.922411i	$-0.373784\pi$
$37$	−13.7533	−	9.99235i	−0.371711	−	0.270063i	−0.757920	+	0.652348i	$0.773784\pi$
$38$	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	0.669855	−	0.742492i	$-0.266356\pi$
$41$	−9.97505	−	13.7295i	−0.243294	−	0.334865i	−0.913149	+	0.407627i	$0.866356\pi$
$42$	3.09017	−	9.51057i	0.0735755	−	0.226442i
$43$		−	46.6690i		−	1.08533i	−0.839950	−	0.542663i	$-0.817416\pi$
$43$		−	46.6690i		−	1.08533i	0.839950	−	0.542663i	$-0.182584\pi$
$44$		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	−0.828088	−	0.560598i	$-0.810571\pi$
$47$	−25.8885	+	18.8091i	−0.550820	+	0.400194i	0.277268	+	0.960793i	$0.410571\pi$
$48$	−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	−0.893516	−	0.449032i	$-0.851769\pi$
$53$	4.94427	−	15.2169i	0.0932881	−	0.287111i	0.986804	+	0.161921i	$0.0517689\pi$
$54$		−	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	0.956261	−	0.292516i	$-0.0944923\pi$
$59$	57.4402	+	41.7328i	0.973563	+	0.707335i	0.0173020	+	0.999850i	$0.494492\pi$
$60$	4.32624	+	13.3148i	0.0721040	+	0.221913i
$61$	10.7600	−	3.49613i	0.176393	−	0.0573136i	−0.219489	−	0.975615i	$-0.570439\pi$
$61$	10.7600	−	3.49613i	0.176393	−	0.0573136i	0.395882	+	0.918301i	$0.370439\pi$
$62$	−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	−0.974620	−	0.223867i	$-0.928132\pi$
$71$	−22.5582	−	69.4271i	−0.317722	−	0.977847i	0.656898	−	0.753980i	$-0.271868\pi$
$72$	−64.5599	+	20.9768i	−0.896665	+	0.291344i
$73$	23.2751	−	32.0354i	0.318837	−	0.438842i	−0.619275	−	0.785174i	$-0.712573\pi$
$73$	23.2751	−	32.0354i	0.318837	−	0.438842i	0.938112	+	0.346333i	$0.112573\pi$
$74$	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	−0.979999	−	0.199004i	$-0.936229\pi$
$79$	−149.295	−	48.5088i	−1.88981	−	0.614035i	−0.909807	−	0.415031i	$-0.863771\pi$
$80$	−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	−0.504487	−	0.863420i	$-0.668318\pi$
$83$	−33.6249	+	10.9254i	−0.405120	+	0.131631i	0.0993670	+	0.995051i	$0.468318\pi$
$84$	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	−0.974477	−	0.224488i	$-0.927929\pi$
$97$	−5.25329	+	16.1680i	−0.0541576	+	0.166680i	0.920319	+	0.391168i	$0.127929\pi$
$98$			1.41421i			0.0144308i
$99$		0			0
$100$	48.0000			0.480000
$101$	146.605	+	47.6347i	1.45153	+	0.471631i	0.925472	−	0.378817i	$-0.123669\pi$
$101$	146.605	+	47.6347i	1.45153	+	0.471631i	0.526060	+	0.850448i	$0.323669\pi$
$102$	4.85410	−	3.52671i	0.0475892	−	0.0345756i
$103$	12.9443	+	9.40456i	0.125673	+	0.0913064i	0.648846	−	0.760920i	$-0.275252\pi$
$103$	12.9443	+	9.40456i	0.125673	+	0.0913064i	−0.523173	+	0.852226i	$0.675252\pi$
$104$	−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	0.913802	+	0.406161i	$0.133133\pi$
$107$	108.894	+	149.880i	1.01770	+	1.40075i	0.103902	+	0.994588i	$0.466867\pi$
$108$	10.5066	−	32.3359i	0.0972831	−	0.299407i
$109$		−	46.6690i		−	0.428156i	−0.976817	−	0.214078i	$-0.931325\pi$
$109$		−	46.6690i		−	0.428156i	0.976817	−	0.214078i	$-0.0686747\pi$
$110$		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	−0.795632	−	0.605781i	$-0.792861\pi$
$113$	−52.5861	+	38.2060i	−0.465364	+	0.338107i	0.330268	+	0.943887i	$0.392861\pi$
$114$	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	−0.880163	−	0.474671i	$-0.842567\pi$
$127$	−166.780	+	54.1900i	−1.31323	+	0.426693i	−0.433062	+	0.901364i	$0.642567\pi$
$128$	−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	$-0.820546\pi$
$131$		−	140.007i		−	1.06876i	0.845245	−	0.534378i	$-0.179454\pi$
$132$		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	0.619627	+	0.784897i	$0.287284\pi$
$137$	79.4174	+	244.422i	0.579689	+	1.78410i	−0.0399380	+	0.999202i	$0.512716\pi$
$138$	12.1050	−	3.93314i	0.0877172	−	0.0285010i
$139$	50.7065	−	69.7915i	0.364795	−	0.502097i	−0.586682	−	0.809817i	$-0.699566\pi$
$139$	50.7065	−	69.7915i	0.364795	−	0.502097i	0.951477	+	0.307720i	$0.0995661\pi$
$140$	−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	0.763007	−	0.646391i	$-0.223722\pi$
$149$	262.274	−	85.2181i	1.76023	−	0.571934i	0.997224	+	0.0744568i	$0.0237223\pi$
$150$	19.9501	−	27.4589i	0.133001	−	0.183060i
$151$	−92.2692	−	126.998i	−0.611054	−	0.841044i	0.385609	−	0.922662i	$-0.373991\pi$
$151$	−92.2692	−	126.998i	−0.611054	−	0.841044i	−0.996664	+	0.0816182i	$0.973991\pi$
$152$	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	−0.938920	−	0.344135i	$-0.888172\pi$
$157$	−141.578	+	102.862i	−0.901771	+	0.655175i	0.0371496	+	0.999310i	$0.488172\pi$
$158$	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	0.676966	+	0.736015i	$0.263295\pi$
$163$	−49.4427	+	152.169i	−0.303330	+	0.933552i	−0.980295	+	0.197538i	$0.936705\pi$
$164$			33.9411i			0.206958i
$165$		0			0
$166$	50.0000			0.301205
$167$	−16.1400	−	5.24419i	−0.0966465	−	0.0314023i	0.260295	−	0.965529i	$-0.416180\pi$
$167$	−16.1400	−	5.24419i	−0.0966465	−	0.0314023i	−0.356941	+	0.934127i	$0.616180\pi$
$168$	−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	0.965154	−	0.261683i	$-0.0842776\pi$
$173$	72.3191	+	99.5387i	0.418029	+	0.575368i	−0.547124	+	0.837051i	$0.684278\pi$
$174$	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	−0.0389044	−	0.999243i	$-0.512387\pi$
$179$	160.994	−	116.969i	0.899410	−	0.653460i	0.938314	+	0.345783i	$0.112387\pi$
$180$	−90.6099	−	65.8319i	−0.503388	−	0.365733i
$181$	−22.5582	−	69.4271i	−0.124631	−	0.383575i	0.869203	−	0.494456i	$-0.164633\pi$
$181$	−22.5582	−	69.4271i	−0.124631	−	0.383575i	−0.993834	+	0.110881i	$0.964633\pi$
$182$	−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	0.0305116	−	0.999534i	$-0.490286\pi$
$191$	−173.939	−	126.374i	−0.910674	−	0.661643i	−0.941185	+	0.337891i	$0.890286\pi$
$192$	17.3050	+	53.2592i	0.0901300	+	0.277391i
$193$	129.120	−	41.9535i	0.669014	−	0.217376i	0.0452348	−	0.998976i	$-0.485596\pi$
$193$	129.120	−	41.9535i	0.669014	−	0.217376i	0.623779	+	0.781601i	$0.285596\pi$
$194$	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	$0.171570\pi$
$197$			202.233i			1.02656i	−0.858221	+	0.513281i	$0.828430\pi$
$198$		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	0.125044	−	0.992151i	$-0.460093\pi$
$211$	−75.3198	−	24.4729i	−0.356966	−	0.115985i	−0.482010	+	0.876166i	$0.660093\pi$
$212$	−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	−0.367943	−	0.929848i	$-0.619938\pi$
$223$	89.8009	−	65.2442i	0.402695	−	0.292575i	0.770638	+	0.637274i	$0.219938\pi$
$224$	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	−0.944604	−	0.328212i	$-0.893554\pi$
$227$	−77.3066	+	106.403i	−0.340558	+	0.468738i	0.604046	+	0.796949i	$0.293554\pi$
$228$	19.9501	+	27.4589i	0.0875004	+	0.120434i
$229$	−93.6321	+	288.170i	−0.408874	+	1.25838i	0.508743	+	0.860919i	$0.330110\pi$
$229$	−93.6321	+	288.170i	−0.408874	+	1.25838i	−0.917617	+	0.397466i	$0.869890\pi$
$230$		−	89.0955i		−	0.387372i
$231$		0			0
$232$	−192.000			−0.827586
$233$	−75.3198	−	24.4729i	−0.323261	−	0.105034i	0.142891	−	0.989738i	$-0.454360\pi$
$233$	−75.3198	−	24.4729i	−0.323261	−	0.105034i	−0.466152	+	0.884705i	$0.654360\pi$
$234$	−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	−0.999999	−	0.00120854i	$-0.999615\pi$
$239$	−165.420	−	227.680i	−0.692132	−	0.952638i	0.307867	−	0.951429i	$-0.400385\pi$
$240$	−8.65248	+	26.6296i	−0.0360520	+	0.110957i
$241$			373.352i			1.54918i	0.632464	+	0.774590i	$0.282044\pi$
$241$			373.352i			1.54918i	−0.632464	+	0.774590i	$0.717956\pi$
$242$		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	−0.711674	−	0.702510i	$-0.752063\pi$
$251$	69.5288	−	213.988i	0.277007	−	0.852541i	0.988681	−	0.150031i	$-0.0479373\pi$
$252$			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	−0.999620	−	0.0275488i	$-0.991230\pi$
$257$	−343.023	−	249.221i	−1.33472	−	0.969731i	−0.335100	−	0.942183i	$-0.608770\pi$
$258$	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	$-0.914241\pi$
$263$		−	140.007i		−	0.532347i	0.963925	−	0.266173i	$-0.0857593\pi$
$264$		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	0.998284	−	0.0585649i	$-0.0186524\pi$
$269$	42.0263	+	129.344i	0.156232	+	0.480832i	−0.842052	+	0.539396i	$0.818652\pi$
$270$	−160.055	+	52.0049i	−0.592795	+	0.192611i
$271$	169.576	−	233.401i	0.625741	−	0.861258i	−0.372014	−	0.928227i	$-0.621333\pi$
$271$	169.576	−	233.401i	0.625741	−	0.861258i	0.997755	+	0.0669686i	$0.0213327\pi$
$272$	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	0.512518	−	0.858677i	$-0.328713\pi$
$277$	117.015	+	38.0204i	0.422436	+	0.137258i	−0.0900819	+	0.995934i	$0.528713\pi$
$278$	−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	−0.747614	−	0.664133i	$-0.768801\pi$
$281$	−270.344	+	87.8402i	−0.962080	+	0.312599i	−0.214465	+	0.976732i	$0.568801\pi$
$282$	26.6001	−	36.6119i	0.0943267	−	0.129830i
$283$	−46.5502	−	64.0709i	−0.164488	−	0.226399i	0.718814	−	0.695202i	$-0.244685\pi$
$283$	−46.5502	−	64.0709i	−0.164488	−	0.226399i	−0.883302	+	0.468803i	$0.844685\pi$
$284$	−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	−0.612120	−	0.790765i	$-0.709683\pi$
$293$	96.4254	−	132.718i	0.329097	−	0.452963i	0.941217	+	0.337801i	$0.109683\pi$
$294$	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	$-0.901667\pi$
$307$		−	186.676i		−	0.608066i	0.952662	−	0.304033i	$-0.0983333\pi$
$308$		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	−0.756958	−	0.653463i	$-0.773315\pi$
$311$	−114.880	+	83.4655i	−0.369390	+	0.268378i	0.387568	+	0.921841i	$0.373315\pi$
$312$	−116.498	−	84.6411i	−0.373392	−	0.271286i
$313$	−138.131	−	425.122i	−0.441312	−	1.35822i	−0.886478	−	0.462770i	$-0.846855\pi$
$313$	−138.131	−	425.122i	−0.441312	−	1.35822i	0.445166	−	0.895448i	$-0.353145\pi$
$314$	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	−0.502254	−	0.864720i	$-0.667496\pi$
$317$	130.714	−	402.297i	0.412348	−	1.26908i	0.914602	−	0.404355i	$-0.132504\pi$
$318$			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	−0.971632	−	0.236497i	$-0.924001\pi$
$337$	−150.457	+	207.086i	−0.446460	+	0.614499i	0.525173	+	0.850996i	$0.324001\pi$
$338$	−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	−0.941157	−	0.337969i	$-0.890260\pi$
$347$	−521.859	+	169.562i	−1.50392	+	0.488652i	−0.562759	+	0.826621i	$0.690260\pi$
$348$	26.6001	−	36.6119i	0.0764371	−	0.105207i
$349$	−256.857	−	353.534i	−0.735981	−	1.01299i	−0.998840	−	0.0481569i	$-0.984665\pi$
$349$	−256.857	−	353.534i	−0.735981	−	1.01299i	0.262859	−	0.964834i	$-0.415335\pi$
$350$	−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	−0.323762	−	0.946139i	$-0.604948\pi$
$359$	242.726	−	334.084i	0.676117	−	0.930596i	0.999879	+	0.0155429i	$0.00494766\pi$
$360$	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	−0.206979	−	0.978345i	$-0.566363\pi$
$367$	−440.914	−	320.343i	−1.20140	−	0.872869i	−0.994422	+	0.105476i	$0.966363\pi$
$368$	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	$0.101265\pi$
$373$			233.345i			0.625590i	−0.949821	+	0.312795i	$0.898735\pi$
$374$		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	−0.950318	−	0.311280i	$-0.899242\pi$
$379$	−138.131	−	425.122i	−0.364461	−	1.12169i	0.585857	−	0.810414i	$-0.300758\pi$
$380$	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	0.448444	+	0.893811i	$0.351979\pi$
$383$	−168.414	+	518.326i	−0.439724	+	1.35333i	−0.888167	+	0.459520i	$0.848021\pi$
$384$			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	0.341324	−	0.939946i	$-0.389125\pi$
$389$	−173.939	−	126.374i	−0.447143	−	0.324868i	−0.788467	+	0.615077i	$0.789125\pi$
$390$	−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	0.942760	+	0.333471i	$0.108220\pi$
$401$	150.800	+	464.116i	0.376061	+	1.15740i	−0.566700	+	0.823924i	$0.691780\pi$
$402$	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	0.120762	−	0.992682i	$-0.461466\pi$
$409$	−149.295	−	48.5088i	−0.365024	−	0.118603i	−0.485785	+	0.874078i	$0.661466\pi$
$410$	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	−0.769421	−	0.638743i	$-0.779455\pi$
$421$	−168.276	+	122.259i	−0.399704	+	0.290402i	0.369716	+	0.929145i	$0.379455\pi$
$422$	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	−0.384966	−	0.922931i	$-0.625787\pi$
$431$	−533.964	−	173.495i	−1.23890	−	0.402541i	−0.853929	+	0.520389i	$0.825787\pi$
$432$	55.0132	−	39.9694i	0.127345	−	0.0925218i
$433$	−31.5517	−	22.9236i	−0.0728676	−	0.0529414i	0.550755	−	0.834667i	$-0.314340\pi$
$433$	−31.5517	−	22.9236i	−0.0728676	−	0.0529414i	−0.623623	+	0.781725i	$0.714340\pi$
$434$	−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	$0.0914913\pi$
$439$			248.902i			0.566974i	−0.958976	+	0.283487i	$0.908509\pi$
$440$		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	−0.736000	−	0.676981i	$-0.763288\pi$
$443$	−141.578	+	102.862i	−0.319589	+	0.232195i	0.416411	+	0.909176i	$0.363288\pi$
$444$	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	−0.783707	−	0.621131i	$-0.786673\pi$
$449$	96.7223	−	297.681i	0.215417	−	0.662986i	0.999124	−	0.0418546i	$-0.0133266\pi$
$450$			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	−0.297221	−	0.954809i	$-0.596060\pi$
$457$	10.7600	−	3.49613i	0.0235448	−	0.00765017i	0.320766	+	0.947159i	$0.396060\pi$
$458$	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	$-0.606203\pi$
$461$		−	871.156i		−	1.88971i	0.327491	−	0.944854i	$-0.393797\pi$
$462$		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	0.883553	−	0.468331i	$-0.155145\pi$
$467$	−49.7517	−	153.120i	−0.106535	−	0.327880i	−0.990088	+	0.140451i	$0.955145\pi$
$468$	−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	0.170318	−	0.985389i	$-0.445521\pi$
$479$	425.019	−	138.097i	0.887305	−	0.288303i	0.716987	+	0.697086i	$0.245521\pi$
$480$	−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	0.212690	−	0.977120i	$-0.431777\pi$
$487$	588.155	−	427.320i	1.20771	−	0.877454i	0.995021	+	0.0996661i	$0.0317775\pi$
$488$	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	−0.997568	−	0.0696967i	$-0.977797\pi$
$491$	−305.901	+	421.037i	−0.623017	+	0.857510i	0.374551	+	0.927206i	$0.377797\pi$
$492$	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	0.844681	−	0.535270i	$-0.179790\pi$
$499$	297.718	+	216.305i	0.596630	+	0.433477i	−0.248051	+	0.968747i	$0.579790\pi$
$500$	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	0.989141	−	0.146970i	$-0.0469521\pi$
$503$	273.483	+	376.416i	0.543703	+	0.748343i	−0.445438	+	0.895313i	$0.646952\pi$
$504$	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	−0.496068	−	0.868284i	$-0.665223\pi$
$509$	89.8009	−	65.2442i	0.176426	−	0.128181i	0.672494	+	0.740103i	$0.265223\pi$
$510$	−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	0.908997	−	0.416803i	$-0.136850\pi$
$521$	413.408	+	300.358i	0.793489	+	0.576503i	−0.115508	+	0.993307i	$0.536850\pi$
$522$	79.1084	+	243.470i	0.151549	+	0.466419i
$523$	661.739	−	215.012i	1.26527	−	0.411113i	0.401903	−	0.915682i	$-0.368349\pi$
$523$	661.739	−	215.012i	1.26527	−	0.411113i	0.863371	+	0.504569i	$0.168349\pi$
$524$	−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	0.505697	−	0.862711i	$-0.331235\pi$
$541$	220.580	+	71.6706i	0.407726	+	0.132478i	−0.0979715	+	0.995189i	$0.531235\pi$
$542$	−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	−0.997708	−	0.0676635i	$-0.978446\pi$
$547$	−412.302	−	567.485i	−0.753751	−	1.03745i	0.243957	−	0.969786i	$-0.421554\pi$
$548$	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	−0.683230	−	0.730203i	$-0.739425\pi$
$557$	123.857	−	170.474i	0.222364	−	0.306058i	0.905594	+	0.424145i	$0.139425\pi$
$558$	−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	0.729387	−	0.684101i	$-0.239805\pi$
$563$	516.479	+	167.814i	0.917369	+	0.298071i	0.187982	+	0.982172i	$0.439805\pi$
$564$	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	0.766150	−	0.642661i	$-0.222170\pi$
$569$	−46.5502	−	64.0709i	−0.0818106	−	0.112603i	−0.847961	+	0.530059i	$0.822170\pi$
$570$	51.9149	−	159.777i	0.0910787	−	0.280311i
$571$		−	124.451i		−	0.217952i	−0.994044	−	0.108976i	$-0.965243\pi$
$571$		−	124.451i		−	0.217952i	0.994044	−	0.108976i	$-0.0347572\pi$
$572$		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	0.974842	−	0.222897i	$-0.0715515\pi$
$577$	31.8288	+	97.9588i	0.0551625	+	0.169773i	−0.919679	+	0.392670i	$0.871551\pi$
$578$	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	0.930865	−	0.365363i	$-0.119055\pi$
$587$	511.299	+	371.480i	0.871037	+	0.632845i	−0.0598280	+	0.998209i	$0.519055\pi$
$588$	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	$0.137876\pi$
$593$			497.803i			0.839466i	−0.907648	+	0.419733i	$0.862124\pi$
$594$		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	0.998716	−	0.0506658i	$-0.0161343\pi$
$599$	96.4133	+	296.730i	0.160957	+	0.495375i	−0.837759	+	0.546041i	$0.816134\pi$
$600$	−193.680	+	62.9303i	−0.322799	+	0.104884i
$601$	−241.895	+	332.940i	−0.402487	+	0.553976i	−0.961366	−	0.275273i	$-0.911232\pi$
$601$	−241.895	+	332.940i	−0.402487	+	0.553976i	0.558879	+	0.829249i	$0.311232\pi$
$602$	−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	0.403814	−	0.914841i	$-0.367684\pi$
$607$	117.015	+	38.0204i	0.192776	+	0.0626366i	−0.211038	+	0.977478i	$0.567684\pi$
$608$	−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	0.985681	−	0.168621i	$-0.0539315\pi$
$613$	319.201	+	439.343i	0.520720	+	0.716710i	−0.464961	+	0.885331i	$0.653932\pi$
$614$	−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	−0.943226	−	0.332152i	$-0.892225\pi$
$619$	−568.739	+	413.213i	−0.918803	+	0.667549i	0.0244229	+	0.999702i	$0.492225\pi$
$620$	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	0.308208	−	0.951319i	$-0.400271\pi$
$631$	−316.326	−	229.824i	−0.501308	−	0.364222i	−0.809517	+	0.587097i	$0.800271\pi$
$632$	−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	−0.573176	−	0.819432i	$-0.694289\pi$
$641$	18.6074	−	13.5191i	0.0290287	−	0.0210906i	0.602205	+	0.798341i	$0.294289\pi$
$642$	−211.962	−	154.000i	−0.330160	−	0.239875i
$643$	−138.131	−	425.122i	−0.214822	−	0.661154i	−0.999166	−	0.0408284i	$-0.987000\pi$
$643$	−138.131	−	425.122i	−0.214822	−	0.661154i	0.784344	−	0.620326i	$-0.213000\pi$
$644$	−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	0.769108	+	0.639118i	$0.220701\pi$
$647$	−148.019	+	455.556i	−0.228778	+	0.704105i	−0.997886	+	0.0649869i	$0.979299\pi$
$648$		−	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	0.0434632	−	0.999055i	$-0.486161\pi$
$653$	−583.301	−	423.793i	−0.893264	−	0.648994i	−0.936727	+	0.350061i	$0.886161\pi$
$654$	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	$0.178234\pi$
$659$			700.036i			1.06227i	−0.847287	+	0.531135i	$0.821766\pi$
$660$		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	−0.496876	−	0.867822i	$-0.665519\pi$
$673$	−948.223	−	308.096i	−1.40895	−	0.457795i	−0.912074	+	0.410026i	$0.865519\pi$
$674$	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	0.289745	−	0.957104i	$-0.406429\pi$
$677$	735.713	−	239.048i	1.08673	−	0.353099i	0.796980	+	0.604005i	$0.206429\pi$
$678$	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	−0.549863	−	0.835255i	$-0.685320\pi$
$691$	266.682	−	820.762i	0.385936	−	1.18779i	0.935799	−	0.352534i	$-0.114680\pi$
$692$		−	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	0.943843	−	0.330394i	$-0.107182\pi$
$701$	236.907	+	326.075i	0.337956	+	0.465157i	−0.605887	+	0.795551i	$0.707182\pi$
$702$	−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	−0.990116	−	0.140253i	$-0.955208\pi$
$709$	−192.518	−	592.508i	−0.271534	−	0.835696i	0.718582	−	0.695443i	$-0.244792\pi$
$710$	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	0.418363	−	0.908280i	$-0.362604\pi$
$719$	−227.334	−	165.168i	−0.316180	−	0.229719i	−0.734544	+	0.678561i	$0.762604\pi$
$720$	−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	0.282911	+	0.959146i	$0.408700\pi$
$733$	−525.352	+	723.086i	−0.716715	+	0.986474i	−0.999627	+	0.0273281i	$0.991300\pi$
$734$	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	0.854124	−	0.520069i	$-0.174094\pi$
$739$	915.943	+	297.608i	1.23944	+	0.402717i	0.385312	+	0.922786i	$0.374094\pi$
$740$	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	−0.301767	−	0.953382i	$-0.597577\pi$
$743$	10.7600	−	3.49613i	0.0144818	−	0.00470542i	0.316249	+	0.948676i	$0.397577\pi$
$744$	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	−0.834273	−	0.551351i	$-0.814113\pi$
$751$	−426.352	+	309.763i	−0.567712	+	0.412467i	0.266561	+	0.963818i	$0.414113\pi$
$752$	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	−0.943001	−	0.332790i	$-0.892010\pi$
$757$	11.7426	−	36.1401i	0.0155121	−	0.0477413i	0.958513	+	0.285049i	$0.0920099\pi$
$758$			632.153i			0.833976i
$759$		0			0
$760$	−1008.00			−1.32632
$761$	1167.46	+	379.330i	1.53411	+	0.498462i	0.949744	−	0.313028i	$-0.101343\pi$
$761$	1167.46	+	379.330i	1.53411	+	0.498462i	0.584366	+	0.811490i	$0.301343\pi$
$762$	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	$0.0648394\pi$
$769$			311.127i			0.404586i	−0.979325	+	0.202293i	$0.935161\pi$
$770$		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	−0.996949	−	0.0780495i	$-0.975131\pi$
$773$	−951.404	+	691.235i	−1.23079	+	0.894224i	−0.233845	+	0.972274i	$0.575131\pi$
$774$	−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	0.572513	−	0.819896i	$-0.305969\pi$
$787$	1194.36	−	388.070i	1.51761	−	0.493101i	0.945095	+	0.326795i	$0.105969\pi$
$788$	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	0.981232	−	0.192831i	$-0.0617669\pi$
$797$	59.0222	+	181.652i	0.0740555	+	0.227919i	−0.907176	+	0.420750i	$0.861767\pi$
$798$	−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	−0.613238	−	0.789899i	$-0.710133\pi$
$809$	−521.859	+	169.562i	−0.645067	+	0.209595i	−0.0318290	+	0.999493i	$0.510133\pi$
$810$	320.033	−	440.487i	0.395102	−	0.543811i
$811$	−238.570	−	328.363i	−0.294168	−	0.404887i	0.636195	−	0.771529i	$-0.280508\pi$
$811$	−238.570	−	328.363i	−0.294168	−	0.404887i	−0.930362	+	0.366642i	$0.880508\pi$
$812$	−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	−0.788817	−	0.614628i	$-0.789306\pi$
$821$	32.4189	−	44.6208i	0.0394871	−	0.0543493i	0.828304	+	0.560279i	$0.189306\pi$
$822$	−213.632	−	294.040i	−0.259893	−	0.357712i
$823$	212.295	−	653.376i	0.257952	−	0.793895i	−0.735281	−	0.677762i	$-0.762950\pi$
$823$	212.295	−	653.376i	0.257952	−	0.793895i	0.993234	−	0.116133i	$-0.0370500\pi$
$824$			135.765i			0.164763i
$825$		0			0
$826$	710.000			0.859564
$827$	−16.1400	−	5.24419i	−0.0195163	−	0.00634122i	0.299243	−	0.954177i	$-0.403266\pi$
$827$	−16.1400	−	5.24419i	−0.0195163	−	0.00634122i	−0.318759	+	0.947836i	$0.603266\pi$
$828$	−116.498	+	84.6411i	−0.140699	+	0.102224i
$829$	−796.882	−	578.968i	−0.961257	−	0.698394i	−0.00781437	−	0.999969i	$-0.502487\pi$
$829$	−796.882	−	578.968i	−0.961257	−	0.698394i	−0.953442	+	0.301576i	$0.902487\pi$
$830$	−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	−0.628940	−	0.777454i	$-0.716511\pi$
$839$	−70.3845	+	51.1373i	−0.0838909	+	0.0609503i	0.545049	+	0.838404i	$0.316511\pi$
$840$	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	−0.590763	−	0.806845i	$-0.701173\pi$
$853$	−507.064	+	164.755i	−0.594448	+	0.193148i	−0.00368511	+	0.999993i	$0.501173\pi$
$854$	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	$-0.705525\pi$
$857$		−	1368.96i		−	1.59738i	0.601740	−	0.798692i	$-0.294475\pi$
$858$		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	−0.870584	−	0.492020i	$-0.836259\pi$
$863$	−393.070	−	1209.74i	−0.455469	−	1.40179i	0.415115	−	0.909769i	$-0.363741\pi$
$864$	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	0.962157	−	0.272496i	$-0.0878493\pi$
$877$	355.777	+	489.685i	0.405675	+	0.558363i	−0.556482	+	0.830860i	$0.687849\pi$
$878$	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	−0.287181	−	0.957876i	$-0.592718\pi$
$883$	472.466	−	343.267i	0.535069	−	0.388750i	0.822250	+	0.569126i	$0.192718\pi$
$884$	−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	−0.998812	−	0.0487236i	$-0.984485\pi$
$887$	−571.071	+	786.012i	−0.643823	+	0.886147i	0.354989	+	0.934871i	$0.384485\pi$
$888$	−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	−0.767617	−	0.640909i	$-0.778557\pi$
$907$	−474.650	−	1460.82i	−0.523319	−	1.61061i	0.244298	−	0.969700i	$-0.421443\pi$
$908$	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	−0.705873	−	0.708339i	$-0.749445\pi$
$911$	256.484	−	789.377i	0.281541	−	0.866495i	0.987414	−	0.158156i	$-0.0505550\pi$
$912$			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	−0.586071	−	0.810260i	$-0.699326\pi$
$919$	−536.654	+	174.369i	−0.583954	+	0.189738i	0.00211708	+	0.999998i	$0.499326\pi$
$920$	−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	0.785838	+	0.618432i	$0.212232\pi$
$929$	477.122	+	1468.43i	0.513587	+	1.58066i	−0.272252	+	0.962226i	$0.587768\pi$
$930$	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	−0.178614	−	0.983919i	$-0.557161\pi$
$937$	−844.658	−	274.446i	−0.901449	−	0.292899i	−0.722835	+	0.691020i	$0.757161\pi$
$938$	−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	−0.689614	−	0.724177i	$-0.742220\pi$
$941$	−773.373	+	251.284i	−0.821863	+	0.267040i	−0.132249	+	0.991217i	$0.542220\pi$
$942$	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	−0.957721	−	0.287699i	$-0.907110\pi$
$953$	−369.908	+	509.135i	−0.388151	+	0.534244i	0.569570	+	0.821943i	$0.307110\pi$
$954$	−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	$0.0618369\pi$
$967$			373.352i			0.386093i	−0.981190	+	0.193047i	$0.938163\pi$
$968$		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	0.419246	−	0.907872i	$-0.362294\pi$
$971$	1371.28	−	996.296i	1.41224	−	1.02605i	0.992992	−	0.118179i	$-0.0377057\pi$
$972$	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	−0.992300	−	0.123856i	$-0.960474\pi$
$977$	−114.027	+	350.940i	−0.116712	+	0.359201i	0.875589	+	0.483058i	$0.160474\pi$
$978$		−	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	0.383627	−	0.923488i	$-0.374675\pi$
$983$	−369.721	−	268.618i	−0.376115	−	0.273263i	−0.759742	+	0.650225i	$0.774675\pi$
$984$	−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	−0.547367	−	0.836893i	$-0.684370\pi$
$997$	416.458	−	573.206i	0.417711	−	0.574930i	0.965078	+	0.261963i	$0.0843697\pi$
$998$	−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.112.1		8
11.2	odd	10	inner	121.3.d.e.118.1		8
11.3	even	5	inner	121.3.d.e.40.1		8
11.4	even	5		121.3.b.a.120.1	✓	2
11.5	even	5	inner	121.3.d.e.94.2		8
11.6	odd	10	inner	121.3.d.e.94.1		8
11.7	odd	10		121.3.b.a.120.2	yes	2
11.8	odd	10	inner	121.3.d.e.40.2		8
11.9	even	5	inner	121.3.d.e.118.2		8
11.10	odd	2	inner	121.3.d.e.112.2		8
33.26	odd	10		1089.3.c.a.604.2		2
33.29	even	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	11.4	even	5
121.3.b.a.120.2	yes	2	11.7	odd	10
121.3.d.e.40.1		8	11.3	even	5	inner
121.3.d.e.40.2		8	11.8	odd	10	inner
121.3.d.e.94.1		8	11.6	odd	10	inner
121.3.d.e.94.2		8	11.5	even	5	inner
121.3.d.e.112.1		8	1.1	even	1	trivial
121.3.d.e.112.2		8	11.10	odd	2	inner
121.3.d.e.118.1		8	11.2	odd	10	inner
121.3.d.e.118.2		8	11.9	even	5	inner
1089.3.c.a.604.1		2	33.29	even	10
1089.3.c.a.604.2		2	33.26	odd	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-1.34500 - 0.437016i) q^{2} +(0.809017 - 0.587785i) q^{3} +(-1.61803 - 1.17557i) q^{4} +(-2.16312 - 6.65740i) q^{5} +(-1.34500 + 0.437016i) q^{6} +(-4.15627 + 5.72061i) q^{7} +(4.98752 + 6.86474i) q^{8} +(-2.47214 + 7.60845i) q^{9} +O(q^{10})\)	\(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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9}+O(q^{10}) \) 8 * q + 2 * q^3 - 4 * q^4 + 14 * q^5 + 16 * q^9	\( 8 q + 2 q^{3} - 4 q^{4} + 14 q^{5} + 16 q^{9} - 16 q^{12} + 20 q^{14} - 14 q^{15} + 8 q^{16} + 28 q^{20} - 72 q^{23} - 48 q^{25} + 48 q^{26} - 34 q^{27} - 98 q^{31} + 48 q^{34} + 32 q^{36} - 34 q^{37} - 48 q^{38} - 20 q^{42} + 448 q^{45} - 64 q^{47} - 8 q^{48} + 2 q^{49} - 32 q^{53} - 480 q^{56} + 64 q^{58} + 142 q^{59} - 28 q^{60} + 112 q^{64} - 248 q^{67} - 18 q^{69} - 140 q^{70} + 146 q^{71} + 48 q^{75} + 192 q^{78} - 56 q^{80} - 110 q^{81} - 48 q^{82} + 132 q^{86} - 72 q^{89} + 240 q^{91} + 36 q^{92} + 98 q^{93} + 34 q^{97}+O(q^{100}) \) 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

Fields

Representations

Groups

Database

Properties

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