LMFDB - Embedded newform 961.2.c.l.521.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [961,2,Mod(439,961)] 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("961.439"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(961, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 961 = 31^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	961.c (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [32,-16,0,16,16] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.67362363425$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			521.3
Character	$\chi$	$=$	961.521
Dual form			961.2.c.l.439.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.88954 q^{2} +(-0.934717 - 1.61898i) q^{3} +1.57037 q^{4} +(-1.24571 + 2.15763i) q^{5} +(1.76619 + 3.05913i) q^{6} +(1.95083 + 3.37894i) q^{7} +0.811809 q^{8} +(-0.247392 + 0.428495i) q^{9} +(2.35382 - 4.07693i) q^{10} +(-0.0228551 + 0.0395863i) q^{11} +(-1.46785 - 2.54239i) q^{12} +(2.52387 - 4.37148i) q^{13} +(-3.68617 - 6.38464i) q^{14} +4.65754 q^{15} -4.67468 q^{16} +(-0.202598 - 0.350910i) q^{17} +(0.467457 - 0.809660i) q^{18} +(2.82864 + 4.89935i) q^{19} +(-1.95622 + 3.38827i) q^{20} +(3.64695 - 6.31670i) q^{21} +(0.0431858 - 0.0747999i) q^{22} -0.710805 q^{23} +(-0.758812 - 1.31430i) q^{24} +(-0.603580 - 1.04543i) q^{25} +(-4.76896 + 8.26009i) q^{26} -4.68334 q^{27} +(3.06352 + 5.30617i) q^{28} -5.72084 q^{29} -8.80062 q^{30} +7.20939 q^{32} +0.0854524 q^{33} +(0.382817 + 0.663058i) q^{34} -9.72066 q^{35} +(-0.388496 + 0.672895i) q^{36} +(2.94974 + 5.10910i) q^{37} +(-5.34483 - 9.25752i) q^{38} -9.43643 q^{39} +(-1.01128 + 1.75158i) q^{40} +(0.441306 - 0.764364i) q^{41} +(-6.89106 + 11.9357i) q^{42} +(-1.49564 - 2.59052i) q^{43} +(-0.0358910 + 0.0621650i) q^{44} +(-0.616357 - 1.06756i) q^{45} +1.34310 q^{46} +3.20010 q^{47} +(4.36950 + 7.56820i) q^{48} +(-4.11148 + 7.12128i) q^{49} +(1.14049 + 1.97539i) q^{50} +(-0.378743 + 0.656002i) q^{51} +(3.96341 - 6.86482i) q^{52} +(-2.59392 + 4.49279i) q^{53} +8.84936 q^{54} +(-0.0569417 - 0.0986259i) q^{55} +(1.58370 + 2.74305i) q^{56} +(5.28796 - 9.15901i) q^{57} +10.8098 q^{58} +(-0.719926 - 1.24695i) q^{59} +7.31405 q^{60} +13.4661 q^{61} -1.93048 q^{63} -4.27307 q^{64} +(6.28802 + 10.8912i) q^{65} -0.161466 q^{66} +(1.10189 - 1.90853i) q^{67} +(-0.318153 - 0.551057i) q^{68} +(0.664402 + 1.15078i) q^{69} +18.3676 q^{70} +(4.50703 - 7.80641i) q^{71} +(-0.200835 + 0.347857i) q^{72} +(-1.11394 + 1.92939i) q^{73} +(-5.57366 - 9.65385i) q^{74} +(-1.12835 + 1.95437i) q^{75} +(4.44200 + 7.69378i) q^{76} -0.178346 q^{77} +17.8305 q^{78} +(1.56676 + 2.71372i) q^{79} +(5.82329 - 10.0862i) q^{80} +(5.11977 + 8.86770i) q^{81} +(-0.833865 + 1.44430i) q^{82} +(-7.54510 + 13.0685i) q^{83} +(5.72705 - 9.91954i) q^{84} +1.00951 q^{85} +(2.82607 + 4.89489i) q^{86} +(5.34736 + 9.26191i) q^{87} +(-0.0185540 + 0.0321365i) q^{88} +7.91106 q^{89} +(1.16463 + 2.01720i) q^{90} +19.6946 q^{91} -1.11623 q^{92} -6.04673 q^{94} -14.0947 q^{95} +(-6.73874 - 11.6718i) q^{96} +2.48466 q^{97} +(7.76880 - 13.4560i) q^{98} +(-0.0113084 - 0.0195867i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 16 q^{2} + 16 q^{4} + 16 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} - 16 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 16 q^{32} - 64 q^{33} - 32 q^{35} + 40 q^{36} + 24 q^{38} - 64 q^{39}+ \cdots - 16 q^{98}+O(q^{100}) $ 32 * q - 16 * q^2 + 16 * q^4 + 16 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 - 16 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 16 * q^32 - 64 * q^33 - 32 * q^35 + 40 * q^36 + 24 * q^38 - 64 * q^39 + 32 * q^41 + 16 * q^45 - 64 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 + 48 * q^56 + 64 * q^59 - 32 * q^63 - 32 * q^64 - 16 * q^67 + 32 * q^69 + 176 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 + 64 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 + 32 * q^87 - 40 * q^90 - 64 * q^94 - 96 * q^95 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/961\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.88954			−1.33611			−0.668054	−	0.744113i	$-0.732872\pi$
$2$	−1.88954			−1.33611			−0.668054	+	0.744113i	$0.732872\pi$
$3$	−0.934717	−	1.61898i	−0.539659	−	0.934717i	−0.998922	−	0.0464167i	$-0.985220\pi$
$3$	−0.934717	−	1.61898i	−0.539659	−	0.934717i	0.459263	−	0.888300i	$-0.348114\pi$
$4$	1.57037			0.785184
$5$	−1.24571	+	2.15763i	−0.557098	+	0.964922i	0.440639	+	0.897684i	$0.354752\pi$
$5$	−1.24571	+	2.15763i	−0.557098	+	0.964922i	−0.997737	+	0.0672375i	$0.978581\pi$
$6$	1.76619	+	3.05913i	0.721043	+	1.24888i
$7$	1.95083	+	3.37894i	0.737344	+	1.27712i	0.953687	+	0.300801i	$0.0972538\pi$
$7$	1.95083	+	3.37894i	0.737344	+	1.27712i	−0.216343	+	0.976318i	$0.569413\pi$
$8$	0.811809			0.287018
$9$	−0.247392	+	0.428495i	−0.0824640	+	0.142832i
$10$	2.35382	−	4.07693i	0.744343	−	1.28924i
$11$	−0.0228551	+	0.0395863i	−0.00689109	+	0.0119357i	−0.869450	−	0.494020i	$-0.835527\pi$
$11$	−0.0228551	+	0.0395863i	−0.00689109	+	0.0119357i	0.862559	+	0.505956i	$0.168860\pi$
$12$	−1.46785	−	2.54239i	−0.423731	−	0.733924i
$13$	2.52387	−	4.37148i	0.699997	−	1.21243i	−0.268470	−	0.963288i	$-0.586518\pi$
$13$	2.52387	−	4.37148i	0.699997	−	1.21243i	0.968467	−	0.249142i	$-0.0801485\pi$
$14$	−3.68617	−	6.38464i	−0.985172	−	1.70637i
$15$	4.65754			1.20257
$16$	−4.67468			−1.16867
$17$	−0.202598	−	0.350910i	−0.0491372	−	0.0851081i	0.840411	−	0.541950i	$-0.182314\pi$
$17$	−0.202598	−	0.350910i	−0.0491372	−	0.0851081i	−0.889548	+	0.456842i	$0.848980\pi$
$18$	0.467457	−	0.809660i	0.110181	−	0.190839i
$19$	2.82864	+	4.89935i	0.648935	+	1.12399i	0.983378	+	0.181572i	$0.0581185\pi$
$19$	2.82864	+	4.89935i	0.648935	+	1.12399i	−0.334443	+	0.942416i	$0.608548\pi$
$20$	−1.95622	+	3.38827i	−0.437424	+	0.757641i
$21$	3.64695	−	6.31670i	0.795829	−	1.37842i
$22$	0.0431858	−	0.0747999i	0.00920723	−	0.0159474i
$23$	−0.710805			−0.148213			−0.0741066	−	0.997250i	$-0.523611\pi$
$23$	−0.710805			−0.148213			−0.0741066	+	0.997250i	$0.523611\pi$
$24$	−0.758812	−	1.31430i	−0.154892	−	0.268281i
$25$	−0.603580	−	1.04543i	−0.120716	−	0.209086i
$26$	−4.76896	+	8.26009i	−0.935271	+	1.61994i
$27$	−4.68334			−0.901309
$28$	3.06352	+	5.30617i	0.578951	+	1.00277i
$29$	−5.72084			−1.06233			−0.531166	−	0.847268i	$-0.678246\pi$
$29$	−5.72084			−1.06233			−0.531166	+	0.847268i	$0.678246\pi$
$30$	−8.80062			−1.60677
$31$		0			0
$31$		0			0
$32$	7.20939			1.27445
$33$	0.0854524			0.0148754
$34$	0.382817	+	0.663058i	0.0656525	+	0.113714i
$35$	−9.72066			−1.64309
$36$	−0.388496	+	0.672895i	−0.0647494	+	0.112149i
$37$	2.94974	+	5.10910i	0.484934	+	0.839931i	0.999850	−	0.0173099i	$-0.00551020\pi$
$37$	2.94974	+	5.10910i	0.484934	+	0.839931i	−0.514916	+	0.857241i	$0.672177\pi$
$38$	−5.34483	−	9.25752i	−0.867047	−	1.50177i
$39$	−9.43643			−1.51104
$40$	−1.01128	+	1.75158i	−0.159897	+	0.276950i
$41$	0.441306	−	0.764364i	0.0689204	−	0.119374i	−0.829506	−	0.558498i	$-0.811378\pi$
$41$	0.441306	−	0.764364i	0.0689204	−	0.119374i	0.898426	+	0.439124i	$0.144711\pi$
$42$	−6.89106	+	11.9357i	−1.06331	+	1.84171i
$43$	−1.49564	−	2.59052i	−0.228083	−	0.395051i	0.729157	−	0.684346i	$-0.239912\pi$
$43$	−1.49564	−	2.59052i	−0.228083	−	0.395051i	−0.957240	+	0.289296i	$0.906579\pi$
$44$	−0.0358910	+	0.0621650i	−0.00541077	+	0.00937172i
$45$	−0.616357	−	1.06756i	−0.0918810	−	0.159143i
$46$	1.34310			0.198029
$47$	3.20010			0.466783			0.233391	−	0.972383i	$-0.425018\pi$
$47$	3.20010			0.466783			0.233391	+	0.972383i	$0.425018\pi$
$48$	4.36950	+	7.56820i	0.630684	+	1.09238i
$49$	−4.11148	+	7.12128i	−0.587354	+	1.01733i
$50$	1.14049	+	1.97539i	0.161290	+	0.279362i
$51$	−0.378743	+	0.656002i	−0.0530346	+	0.0918587i
$52$	3.96341	−	6.86482i	0.549626	−	0.951980i
$53$	−2.59392	+	4.49279i	−0.356302	+	0.617133i	−0.987340	−	0.158619i	$-0.949296\pi$
$53$	−2.59392	+	4.49279i	−0.356302	+	0.617133i	0.631038	+	0.775752i	$0.282629\pi$
$54$	8.84936			1.20425
$55$	−0.0569417	−	0.0986259i	−0.00767802	−	0.0132987i
$56$	1.58370	+	2.74305i	0.211631	+	0.366556i
$57$	5.28796	−	9.15901i	0.700407	−	1.21314i
$58$	10.8098			1.41939
$59$	−0.719926	−	1.24695i	−0.0937264	−	0.162339i	0.815350	−	0.578968i	$-0.196545\pi$
$59$	−0.719926	−	1.24695i	−0.0937264	−	0.162339i	−0.909076	+	0.416630i	$0.863211\pi$
$60$	7.31405			0.944240
$61$	13.4661			1.72416			0.862080	−	0.506772i	$-0.169161\pi$
$61$	13.4661			1.72416			0.862080	+	0.506772i	$0.169161\pi$
$62$		0			0
$63$	−1.93048			−0.243217
$64$	−4.27307			−0.534134
$65$	6.28802	+	10.8912i	0.779933	+	1.35088i
$66$	−0.161466			−0.0198751
$67$	1.10189	−	1.90853i	0.134617	−	0.233164i	−0.790834	−	0.612031i	$-0.790353\pi$
$67$	1.10189	−	1.90853i	0.134617	−	0.233164i	0.925451	+	0.378867i	$0.123686\pi$
$68$	−0.318153	−	0.551057i	−0.0385817	−	0.0668255i
$69$	0.664402	+	1.15078i	0.0799846	+	0.138537i
$70$	18.3676			2.19535
$71$	4.50703	−	7.80641i	0.534886	−	0.926450i	−0.464283	−	0.885687i	$-0.653688\pi$
$71$	4.50703	−	7.80641i	0.534886	−	0.926450i	0.999169	−	0.0407629i	$-0.0129788\pi$
$72$	−0.200835	+	0.347857i	−0.0236686	+	0.0409953i
$73$	−1.11394	+	1.92939i	−0.130376	+	0.225818i	−0.923822	−	0.382823i	$-0.874952\pi$
$73$	−1.11394	+	1.92939i	−0.130376	+	0.225818i	0.793445	+	0.608641i	$0.208285\pi$
$74$	−5.57366	−	9.65385i	−0.647924	−	1.12224i
$75$	−1.12835	+	1.95437i	−0.130291	+	0.225671i
$76$	4.44200	+	7.69378i	0.509533	+	0.882537i
$77$	−0.178346			−0.0203244
$78$	17.8305			2.01891
$79$	1.56676	+	2.71372i	0.176275	+	0.305317i	0.940602	−	0.339512i	$-0.110262\pi$
$79$	1.56676	+	2.71372i	0.176275	+	0.305317i	−0.764327	+	0.644829i	$0.776929\pi$
$80$	5.82329	−	10.0862i	0.651064	−	1.12768i
$81$	5.11977	+	8.86770i	0.568863	+	0.985300i
$82$	−0.833865	+	1.44430i	−0.0920850	+	0.159496i
$83$	−7.54510	+	13.0685i	−0.828183	+	1.43445i	0.0712799	+	0.997456i	$0.477292\pi$
$83$	−7.54510	+	13.0685i	−0.828183	+	1.43445i	−0.899462	+	0.436998i	$0.856042\pi$
$84$	5.72705	−	9.91954i	0.624872	−	1.08231i
$85$	1.00951			0.109497
$86$	2.82607	+	4.89489i	0.304743	+	0.527830i
$87$	5.34736	+	9.26191i	0.573298	+	0.992981i
$88$	−0.0185540	+	0.0321365i	−0.00197787	+	0.00342576i
$89$	7.91106			0.838571			0.419286	−	0.907854i	$-0.362281\pi$
$89$	7.91106			0.838571			0.419286	+	0.907854i	$0.362281\pi$
$90$	1.16463	+	2.01720i	0.122763	+	0.212632i
$91$	19.6946			2.06455
$92$	−1.11623			−0.116375
$93$		0			0
$94$	−6.04673			−0.623672
$95$	−14.0947			−1.44608
$96$	−6.73874	−	11.6718i	−0.687769	−	1.19125i
$97$	2.48466			0.252279			0.126140	−	0.992013i	$-0.459741\pi$
$97$	2.48466			0.252279			0.126140	+	0.992013i	$0.459741\pi$
$98$	7.76880	−	13.4560i	0.784768	−	1.35926i
$99$	−0.0113084	−	0.0195867i	−0.00113653	−	0.00196853i
$100$	−0.947843	−	1.64171i	−0.0947843	−	0.164171i
$101$	−13.6706			−1.36027			−0.680136	−	0.733086i	$-0.738079\pi$
$101$	−13.6706			−1.36027			−0.680136	+	0.733086i	$0.738079\pi$
$102$	0.715651	−	1.23954i	0.0708600	−	0.122733i
$103$	−2.48116	+	4.29749i	−0.244476	+	0.423445i	−0.961984	−	0.273105i	$-0.911949\pi$
$103$	−2.48116	+	4.29749i	−0.244476	+	0.423445i	0.717508	+	0.696550i	$0.245283\pi$
$104$	2.04890	−	3.54881i	0.200912	−	0.347989i
$105$	9.08607	+	15.7375i	0.886710	+	1.53583i
$106$	4.90131	−	8.48932i	0.476057	−	0.824556i
$107$	7.64522	+	13.2419i	0.739091	+	1.28014i	0.952905	+	0.303269i	$0.0980781\pi$
$107$	7.64522	+	13.2419i	0.739091	+	1.28014i	−0.213814	+	0.976874i	$0.568589\pi$
$108$	−7.35456			−0.707693
$109$	−12.8764			−1.23333			−0.616666	−	0.787225i	$-0.711517\pi$
$109$	−12.8764			−1.23333			−0.616666	+	0.787225i	$0.711517\pi$
$110$	0.107594	+	0.186358i	0.0102587	+	0.0177685i
$111$	5.51434	−	9.55112i	0.523398	−	0.906553i
$112$	−9.11951	−	15.7955i	−0.861713	−	1.49253i
$113$	0.810133	−	1.40319i	0.0762109	−	0.132001i	−0.825401	−	0.564546i	$-0.809051\pi$
$113$	0.810133	−	1.40319i	0.0762109	−	0.132001i	0.901612	+	0.432545i	$0.142384\pi$
$114$	−9.99182	+	17.3063i	−0.935819	+	1.62089i
$115$	0.885456	−	1.53366i	0.0825692	−	0.143014i
$116$	−8.98382			−0.834126
$117$	1.24877	+	2.16294i	0.115449	+	0.199964i
$118$	1.36033	+	2.35616i	0.125229	+	0.216902i
$119$	0.790467	−	1.36913i	0.0724620	−	0.125508i
$120$	3.78103			0.345160
$121$	5.49896	+	9.52447i	0.499905	+	0.865861i
$122$	−25.4448			−2.30366
$123$	−1.64998			−0.148774
$124$		0			0
$125$	−9.44955			−0.845193
$126$	3.64772			0.324965
$127$	9.18225	+	15.9041i	0.814793	+	1.41126i	0.909477	+	0.415755i	$0.136483\pi$
$127$	9.18225	+	15.9041i	0.814793	+	1.41126i	−0.0946843	+	0.995507i	$0.530184\pi$
$128$	−6.34463			−0.560791
$129$	−2.79599	+	4.84281i	−0.246174	+	0.426385i
$130$	−11.8815	−	20.5793i	−1.04207	−	1.80493i
$131$	7.30573	+	12.6539i	0.638304	+	1.10558i	0.985805	+	0.167896i	$0.0536972\pi$
$131$	7.30573	+	12.6539i	0.638304	+	1.10558i	−0.347500	+	0.937680i	$0.612969\pi$
$132$	0.134192			0.0116799
$133$	−11.0364	+	19.1156i	−0.956977	+	1.65753i
$134$	−2.08207	+	3.60624i	−0.179863	+	0.311532i
$135$	5.83407	−	10.1049i	0.502117	−	0.869692i
$136$	−0.164471	−	0.284872i	−0.0141032	−	0.0244275i
$137$	−10.8182	+	18.7376i	−0.924258	+	1.60086i	−0.131508	+	0.991315i	$0.541982\pi$
$137$	−10.8182	+	18.7376i	−0.924258	+	1.60086i	−0.792750	+	0.609547i	$0.791351\pi$
$138$	−1.25541	−	2.17444i	−0.106868	−	0.185101i
$139$	0.137919			0.0116981			0.00584906	−	0.999983i	$-0.498138\pi$
$139$	0.137919			0.0116981			0.00584906	+	0.999983i	$0.498138\pi$
$140$	−15.2650			−1.29013
$141$	−2.99119	−	5.18089i	−0.251904	−	0.436310i
$142$	−8.51622	+	14.7505i	−0.714665	+	1.23784i
$143$	0.115367	+	0.199822i	0.00964747	+	0.0167099i
$144$	1.15648	−	2.00308i	0.0963732	−	0.166923i
$145$	7.12650	−	12.3435i	0.591823	−	1.02507i
$146$	2.10483	−	3.64567i	0.174197	−	0.301718i
$147$	15.3723			1.26788
$148$	4.63217	+	8.02316i	0.380762	+	0.659500i
$149$	−7.50943	−	13.0067i	−0.615196	−	1.06555i	−0.990350	−	0.138589i	$-0.955743\pi$
$149$	−7.50943	−	13.0067i	−0.615196	−	1.06555i	0.375154	−	0.926963i	$-0.377590\pi$
$150$	2.13207	−	3.69286i	0.174083	−	0.301520i
$151$	−2.62149			−0.213334			−0.106667	−	0.994295i	$-0.534018\pi$
$151$	−2.62149			−0.213334			−0.106667	+	0.994295i	$0.534018\pi$
$152$	2.29632	+	3.97734i	0.186256	+	0.322605i
$153$	0.200484			0.0162082
$154$	0.336992			0.0271556
$155$		0			0
$156$	−14.8187			−1.18644
$157$	18.7778			1.49863			0.749316	−	0.662212i	$-0.230382\pi$
$157$	18.7778			1.49863			0.749316	+	0.662212i	$0.230382\pi$
$158$	−2.96047	−	5.12768i	−0.235522	−	0.407936i
$159$	9.69831			0.769126
$160$	−8.98080	+	15.5552i	−0.709994	+	1.22975i
$161$	−1.38666	−	2.40177i	−0.109284	−	0.189286i
$162$	−9.67402	−	16.7559i	−0.760063	−	1.31647i
$163$	4.50151			0.352585			0.176293	−	0.984338i	$-0.443590\pi$
$163$	4.50151			0.352585			0.176293	+	0.984338i	$0.443590\pi$
$164$	0.693012	−	1.20033i	0.0541151	−	0.0937302i
$165$	−0.106449	+	0.184375i	−0.00828703	+	0.0143536i
$166$	14.2568	−	24.6935i	1.10654	−	1.91659i
$167$	8.78332	+	15.2132i	0.679673	+	1.17723i	0.975079	+	0.221857i	$0.0712119\pi$
$167$	8.78332	+	15.2132i	0.679673	+	1.17723i	−0.295406	+	0.955372i	$0.595455\pi$
$168$	2.96063	−	5.12795i	0.228417	−	0.395630i
$169$	−6.23987	−	10.8078i	−0.479990	−	0.831368i
$170$	−1.90751			−0.146300
$171$	−2.79913			−0.214055
$172$	−2.34870	−	4.06807i	−0.179087	−	0.310187i
$173$	−5.69753	+	9.86842i	−0.433176	+	0.750282i	−0.997145	−	0.0755138i	$-0.975940\pi$
$173$	−5.69753	+	9.86842i	−0.433176	+	0.750282i	0.563969	+	0.825796i	$0.309274\pi$
$174$	−10.1041	−	17.5008i	−0.765987	−	1.32673i
$175$	2.35497	−	4.07892i	0.178019	−	0.308337i
$176$	0.106841	−	0.185053i	0.00805341	−	0.0139489i
$177$	−1.34585	+	2.33109i	−0.101161	+	0.175215i
$178$	−14.9483			−1.12042
$179$	2.49972	+	4.32964i	0.186838	+	0.323613i	0.944194	−	0.329389i	$-0.106843\pi$
$179$	2.49972	+	4.32964i	0.186838	+	0.323613i	−0.757356	+	0.653002i	$0.773509\pi$
$180$	−0.967906	−	1.67646i	−0.0721435	−	0.124956i
$181$	−2.36746	+	4.10056i	−0.175972	+	0.304792i	−0.940497	−	0.339802i	$-0.889640\pi$
$181$	−2.36746	+	4.10056i	−0.175972	+	0.304792i	0.764525	+	0.644594i	$0.222973\pi$
$182$	−37.2138			−2.75847
$183$	−12.5870	−	21.8014i	−0.930459	−	1.61160i
$184$	−0.577038			−0.0425398
$185$	−14.6981			−1.08062
$186$		0			0
$187$	0.0185216			0.00135443
$188$	5.02534			0.366510
$189$	−9.13639	−	15.8247i	−0.664575	−	1.15108i
$190$	26.6324			1.93212
$191$	7.31116	−	12.6633i	0.529017	−	0.916285i	−0.470410	−	0.882448i	$-0.655894\pi$
$191$	7.31116	−	12.6633i	0.529017	−	0.916285i	0.999427	−	0.0338369i	$-0.0107727\pi$
$192$	3.99411	+	6.91801i	0.288250	+	0.499264i
$193$	3.61831	+	6.26709i	0.260452	+	0.451115i	0.966362	−	0.257186i	$-0.0827952\pi$
$193$	3.61831	+	6.26709i	0.260452	+	0.451115i	−0.705910	+	0.708301i	$0.749462\pi$
$194$	−4.69487			−0.337072
$195$	11.7550	−	20.3603i	0.841796	−	1.45803i
$196$	−6.45653	+	11.1830i	−0.461180	+	0.798788i
$197$	−4.16402	+	7.21230i	−0.296674	+	0.513855i	−0.975373	−	0.220562i	$-0.929211\pi$
$197$	−4.16402	+	7.21230i	−0.296674	+	0.513855i	0.678699	+	0.734417i	$0.262544\pi$
$198$	0.0213676	+	0.0370098i	0.00151853	+	0.00263017i
$199$	−4.01850	+	6.96025i	−0.284864	+	0.493399i	−0.972576	−	0.232584i	$-0.925282\pi$
$199$	−4.01850	+	6.96025i	−0.284864	+	0.493399i	0.687712	+	0.725984i	$0.258615\pi$
$200$	−0.489992	−	0.848691i	−0.0346477	−	0.0600115i
$201$	−4.11982			−0.290590
$202$	25.8311			1.81747
$203$	−11.1604	−	19.3303i	−0.783305	−	1.35672i
$204$	−0.594766	+	1.03016i	−0.0416419	+	0.0721259i
$205$	1.09948	+	1.90435i	0.0767908	+	0.133006i
$206$	4.68825	−	8.12029i	0.326646	−	0.565767i
$207$	0.175848	−	0.304577i	0.0122222	−	0.0211696i
$208$	−11.7983	+	20.4353i	−0.818065	+	1.41693i
$209$	−0.258596			−0.0178875
$210$	−17.1685	−	29.7367i	−1.18474	−	2.05203i
$211$	7.95670	+	13.7814i	0.547762	+	0.948752i	0.998427	+	0.0560589i	$0.0178534\pi$
$211$	7.95670	+	13.7814i	0.547762	+	0.948752i	−0.450665	+	0.892693i	$0.648813\pi$
$212$	−4.07340	+	7.05533i	−0.279762	+	0.484562i
$213$	−16.8512			−1.15462
$214$	−14.4460	−	25.0211i	−0.987505	−	1.71041i
$215$	7.45251			0.508257
$216$	−3.80198			−0.258692
$217$		0			0
$218$	24.3304			1.64786
$219$	4.16486			0.281435
$220$	−0.0894194	−	0.154879i	−0.00602865	−	0.0104419i
$221$	−2.04532			−0.137583
$222$	−10.4196	+	18.0472i	−0.699317	+	1.21125i
$223$	8.24810	+	14.2861i	0.552334	+	0.956670i	0.998106	+	0.0615234i	$0.0195959\pi$
$223$	8.24810	+	14.2861i	0.552334	+	0.956670i	−0.445772	+	0.895147i	$0.647071\pi$
$224$	14.0643	+	24.3601i	0.939710	+	1.62762i
$225$	0.597284			0.0398189
$226$	−1.53078	+	2.65139i	−0.101826	+	0.176368i
$227$	0.199410	−	0.345388i	0.0132353	−	0.0229242i	−0.859332	−	0.511418i	$-0.829120\pi$
$227$	0.199410	−	0.345388i	0.0132353	−	0.0229242i	0.872567	+	0.488494i	$0.162454\pi$
$228$	8.30403	−	14.3830i	0.549948	−	0.952538i
$229$	−12.8769	−	22.3035i	−0.850931	−	1.47386i	−0.880369	−	0.474290i	$-0.842705\pi$
$229$	−12.8769	−	22.3035i	−0.850931	−	1.47386i	0.0294377	−	0.999567i	$-0.490628\pi$
$230$	−1.67311	+	2.89791i	−0.110321	+	0.191082i
$231$	0.166703	+	0.288738i	0.0109683	+	0.0189976i
$232$	−4.64423			−0.304909
$233$	−10.6201			−0.695744			−0.347872	−	0.937542i	$-0.613096\pi$
$233$	−10.6201			−0.695744			−0.347872	+	0.937542i	$0.613096\pi$
$234$	−2.35961	−	4.08696i	−0.154252	−	0.267173i
$235$	−3.98640	+	6.90464i	−0.260044	+	0.450409i
$236$	−1.13055	−	1.95817i	−0.0735924	−	0.127466i
$237$	2.92896	−	5.07311i	0.190257	−	0.329534i
$238$	−1.49362	+	2.58703i	−0.0968171	+	0.167692i
$239$	5.61240	−	9.72097i	0.363036	−	0.628797i	−0.625423	−	0.780286i	$-0.715073\pi$
$239$	5.61240	−	9.72097i	0.363036	−	0.628797i	0.988459	+	0.151489i	$0.0484068\pi$
$240$	−21.7725			−1.40541
$241$	−6.80597	−	11.7883i	−0.438411	−	0.759350i	0.559156	−	0.829062i	$-0.311125\pi$
$241$	−6.80597	−	11.7883i	−0.438411	−	0.759350i	−0.997567	+	0.0697124i	$0.977792\pi$
$242$	−10.3905	−	17.9969i	−0.667927	−	1.15688i
$243$	2.54607	−	4.40992i	0.163330	−	0.282896i
$244$	21.1468			1.35378
$245$	−10.2434	−	17.7421i	−0.654427	−	1.13350i
$246$	3.11771			0.198778
$247$	28.5565			1.81701
$248$		0			0
$249$	28.2101			1.78775
$250$	17.8553			1.12927
$251$	−7.13611	−	12.3601i	−0.450427	−	0.780163i	0.547985	−	0.836488i	$-0.315395\pi$
$251$	−7.13611	−	12.3601i	−0.450427	−	0.780163i	−0.998412	+	0.0563249i	$0.982062\pi$
$252$	−3.03156			−0.190970
$253$	0.0162456	−	0.0281381i	0.00102135	−	0.00176903i
$254$	−17.3502	−	30.0515i	−1.08865	−	1.88560i
$255$	−0.943607	−	1.63438i	−0.0590910	−	0.102349i
$256$	20.5346			1.28341
$257$	−3.44310	+	5.96362i	−0.214775	+	0.372000i	−0.953203	−	0.302332i	$-0.902235\pi$
$257$	−3.44310	+	5.96362i	−0.214775	+	0.372000i	0.738428	+	0.674332i	$0.235568\pi$
$258$	5.28315	−	9.15068i	0.328914	−	0.569697i
$259$	−11.5089	+	19.9340i	−0.715127	+	1.23864i
$260$	9.87450	+	17.1031i	0.612391	+	1.06069i
$261$	1.41529	−	2.45135i	0.0876042	−	0.151735i
$262$	−13.8045	−	23.9100i	−0.852843	−	1.47717i
$263$	19.5044			1.20269			0.601345	−	0.798989i	$-0.294632\pi$
$263$	19.5044			1.20269			0.601345	+	0.798989i	$0.294632\pi$
$264$	0.0693710			0.00426949
$265$	−6.46253	−	11.1934i	−0.396990	−	0.687606i
$266$	20.8537	−	36.1197i	1.27862	−	2.21464i
$267$	−7.39461	−	12.8078i	−0.452543	−	0.783827i
$268$	1.73037	−	2.99709i	0.105699	−	0.183076i
$269$	2.61307	−	4.52596i	0.159321	−	0.275953i	−0.775303	−	0.631590i	$-0.782403\pi$
$269$	2.61307	−	4.52596i	0.159321	−	0.275953i	0.934624	+	0.355637i	$0.115736\pi$
$270$	−11.0237	+	19.0936i	−0.670882	+	1.16200i
$271$	−21.1113			−1.28242			−0.641211	−	0.767364i	$-0.721568\pi$
$271$	−21.1113			−1.28242			−0.641211	+	0.767364i	$0.721568\pi$
$272$	0.947080	+	1.64039i	0.0574251	+	0.0994633i
$273$	−18.4089	−	31.8851i	−1.11416	−	1.92977i
$274$	20.4414	−	35.4055i	1.23491	−	2.13892i
$275$	0.0551797			0.00332746
$276$	1.04335	+	1.80714i	0.0628026	+	0.108777i
$277$	−29.6644			−1.78236			−0.891180	−	0.453649i	$-0.850122\pi$
$277$	−29.6644			−1.78236			−0.891180	+	0.453649i	$0.850122\pi$
$278$	−0.260603			−0.0156299
$279$		0			0
$280$	−7.89132			−0.471597
$281$	24.4213			1.45685			0.728427	−	0.685123i	$-0.240252\pi$
$281$	24.4213			1.45685			0.728427	+	0.685123i	$0.240252\pi$
$282$	5.65198	+	9.78951i	0.336570	+	0.582957i
$283$	17.8130			1.05888			0.529438	−	0.848349i	$-0.322403\pi$
$283$	17.8130			1.05888			0.529438	+	0.848349i	$0.322403\pi$
$284$	7.07769	−	12.2589i	0.419984	−	0.727433i
$285$	13.1745	+	22.8189i	0.780391	+	1.35168i
$286$	−0.217991	−	0.377571i	−0.0128901	−	0.0223262i
$287$	3.44365			0.203272
$288$	−1.78354	+	3.08919i	−0.105096	+	0.182032i
$289$	8.41791	−	14.5802i	0.495171	−	0.857661i
$290$	−13.4658	+	23.3235i	−0.790740	+	1.36960i
$291$	−2.32246	−	4.02261i	−0.136145	−	0.235810i
$292$	−1.74929	+	3.02985i	−0.102369	+	0.177309i
$293$	10.3943	+	18.0035i	0.607242	+	1.05177i	0.991693	+	0.128629i	$0.0410575\pi$
$293$	10.3943	+	18.0035i	0.607242	+	1.05177i	−0.384451	+	0.923146i	$0.625609\pi$
$294$	−29.0465			−1.69403
$295$	3.58727			0.208859
$296$	2.39463	+	4.14761i	0.139185	+	0.241075i
$297$	0.107038	−	0.185396i	0.00621100	−	0.0107578i
$298$	14.1894	+	24.5767i	0.821968	+	1.42369i
$299$	−1.79398	+	3.10727i	−0.103749	+	0.179698i
$300$	−1.77193	+	3.06907i	−0.102302	+	0.177193i
$301$	5.83547	−	10.1073i	0.336351	−	0.582577i
$302$	4.95341			0.285037
$303$	12.7781	+	22.1323i	0.734083	+	1.27147i
$304$	−13.2230	−	22.9029i	−0.758391	−	1.31357i
$305$	−16.7749	+	29.0549i	−0.960526	+	1.66368i
$306$	−0.378823			−0.0216559
$307$	6.01381	+	10.4162i	0.343227	+	0.594486i	0.985030	−	0.172383i	$-0.0551468\pi$
$307$	6.01381	+	10.4162i	0.343227	+	0.594486i	−0.641803	+	0.766869i	$0.721813\pi$
$308$	−0.280069			−0.0159584
$309$	9.27673			0.527734
$310$		0			0
$311$	−4.84477			−0.274722			−0.137361	−	0.990521i	$-0.543862\pi$
$311$	−4.84477			−0.274722			−0.137361	+	0.990521i	$0.543862\pi$
$312$	−7.66058			−0.433695
$313$	−13.5994	−	23.5549i	−0.768683	−	1.33140i	−0.938277	−	0.345885i	$-0.887579\pi$
$313$	−13.5994	−	23.5549i	−0.768683	−	1.33140i	0.169594	−	0.985514i	$-0.445755\pi$
$314$	−35.4815			−2.00233
$315$	2.40481	−	4.16526i	0.135496	−	0.234686i
$316$	2.46040	+	4.26153i	0.138408	+	0.239730i
$317$	−10.8215	−	18.7434i	−0.607796	−	1.05273i	−0.991603	−	0.129320i	$-0.958721\pi$
$317$	−10.8215	−	18.7434i	−0.607796	−	1.05273i	0.383807	−	0.923413i	$-0.374613\pi$
$318$	−18.3254			−1.02763
$319$	0.130751	−	0.226467i	0.00732063	−	0.0126797i
$320$	5.32300	−	9.21971i	0.297565	−	0.515397i
$321$	14.2922	−	24.7549i	0.797715	−	1.38168i
$322$	2.62015	+	4.53824i	0.146015	+	0.252906i
$323$	1.14615	−	1.98519i	0.0637736	−	0.110459i
$324$	8.03992	+	13.9255i	0.446662	+	0.773642i
$325$	−6.09344			−0.338003
$326$	−8.50578			−0.471092
$327$	12.0358	+	20.8465i	0.665579	+	1.15282i
$328$	0.358256	−	0.620518i	0.0197814	−	0.0342624i
$329$	6.24286	+	10.8129i	0.344180	+	0.596137i
$330$	0.201139	−	0.348384i	0.0110724	−	0.0191779i
$331$	1.84009	−	3.18713i	0.101140	−	0.175180i	−0.811014	−	0.585026i	$-0.801084\pi$
$331$	1.84009	−	3.18713i	0.101140	−	0.175180i	0.912155	+	0.409846i	$0.134418\pi$
$332$	−11.8486	+	20.5223i	−0.650275	+	1.12631i
$333$	−2.91897			−0.159958
$334$	−16.5964	−	28.7459i	−0.908117	−	1.57290i
$335$	2.74527	+	4.75494i	0.149990	+	0.259790i
$336$	−17.0483	+	29.5286i	−0.930062	+	1.61091i
$337$	11.6586			0.635085			0.317542	−	0.948244i	$-0.397142\pi$
$337$	11.6586			0.635085			0.317542	+	0.948244i	$0.397142\pi$
$338$	11.7905	+	20.4217i	0.641319	+	1.11080i
$339$	−3.02898			−0.164512
$340$	1.58530			0.0859751
$341$		0			0
$342$	5.28908			0.286000
$343$	−4.77154			−0.257639
$344$	−1.21417	−	2.10301i	−0.0654638	−	0.113387i
$345$	−3.31060			−0.178237
$346$	10.7657	−	18.6468i	0.578769	−	1.00246i
$347$	−16.7163	−	28.9534i	−0.897375	−	1.55430i	−0.830837	−	0.556516i	$-0.812138\pi$
$347$	−16.7163	−	28.9534i	−0.897375	−	1.55430i	−0.0665385	−	0.997784i	$-0.521196\pi$
$348$	8.39733	+	14.5446i	0.450144	+	0.779672i
$349$	−7.51065			−0.402036			−0.201018	−	0.979588i	$-0.564425\pi$
$349$	−7.51065			−0.402036			−0.201018	+	0.979588i	$0.564425\pi$
$350$	−4.44981	+	7.70729i	−0.237852	+	0.411972i
$351$	−11.8201	+	20.4731i	−0.630913	+	1.09277i
$352$	−0.164772	+	0.285393i	−0.00878236	+	0.0152115i
$353$	8.04477	+	13.9340i	0.428180	+	0.741630i	0.996712	−	0.0810319i	$-0.0258216\pi$
$353$	8.04477	+	13.9340i	0.428180	+	0.741630i	−0.568531	+	0.822662i	$0.692488\pi$
$354$	2.54305	−	4.40469i	0.135161	−	0.234107i
$355$	11.2289	+	19.4490i	0.595968	+	1.03225i
$356$	12.4233			0.658432
$357$	−2.95545			−0.156419
$358$	−4.72333	−	8.18104i	−0.249636	−	0.432382i
$359$	6.71698	−	11.6341i	0.354508	−	0.614027i	−0.632525	−	0.774540i	$-0.717982\pi$
$359$	6.71698	−	11.6341i	0.354508	−	0.614027i	0.987034	+	0.160513i	$0.0513149\pi$
$360$	−0.500364	−	0.866656i	−0.0263715	−	0.0456768i
$361$	−6.50242	+	11.2625i	−0.342233	+	0.592764i
$362$	4.47341	−	7.74818i	0.235117	−	0.407235i
$363$	10.2799	−	17.8054i	0.539557	−	0.934540i
$364$	30.9277			1.62105
$365$	−2.77528	−	4.80692i	−0.145265	−	0.251606i
$366$	23.7837	+	41.1946i	1.24319	+	2.15327i
$367$	4.27206	−	7.39942i	0.222999	−	0.386246i	−0.732718	−	0.680532i	$-0.761749\pi$
$367$	4.27206	−	7.39942i	0.222999	−	0.386246i	0.955717	+	0.294286i	$0.0950818\pi$
$368$	3.32279			0.173212
$369$	0.218351	+	0.378195i	0.0113669	+	0.0196880i
$370$	27.7726			1.44383
$371$	−20.2412			−1.05087
$372$		0			0
$373$	−21.0750			−1.09122			−0.545612	−	0.838038i	$-0.683703\pi$
$373$	−21.0750			−1.09122			−0.545612	+	0.838038i	$0.683703\pi$
$374$	−0.0349973			−0.00180967
$375$	8.83265	+	15.2986i	0.456116	+	0.790016i
$376$	2.59787			0.133975
$377$	−14.4387	+	25.0085i	−0.743629	+	1.28800i
$378$	17.2636	+	29.9014i	0.887943	+	1.53796i
$379$	−8.54759	−	14.8049i	−0.439060	−	0.760475i	0.558557	−	0.829466i	$-0.311355\pi$
$379$	−8.54759	−	14.8049i	−0.439060	−	0.760475i	−0.997617	+	0.0689913i	$0.978022\pi$
$380$	−22.1338			−1.13544
$381$	17.1656	−	29.7317i	0.879420	−	1.52320i
$382$	−13.8147	+	23.9278i	−0.706824	+	1.22426i
$383$	0.695115	−	1.20398i	0.0355187	−	0.0615203i	−0.847720	−	0.530445i	$-0.822025\pi$
$383$	0.695115	−	1.20398i	0.0355187	−	0.0615203i	0.883238	+	0.468924i	$0.155358\pi$
$384$	5.93043	+	10.2718i	0.302636	+	0.524181i
$385$	0.222167	−	0.384805i	0.0113227	−	0.0196115i
$386$	−6.83694	−	11.8419i	−0.347991	−	0.602739i
$387$	1.48003			0.0752344
$388$	3.90183			0.198085
$389$	8.01963	+	13.8904i	0.406611	+	0.704271i	0.994508	−	0.104665i	$-0.0333771\pi$
$389$	8.01963	+	13.8904i	0.406611	+	0.704271i	−0.587896	+	0.808936i	$0.700044\pi$
$390$	−22.2116	+	38.4717i	−1.12473	+	1.94809i
$391$	0.144008	+	0.249428i	0.00728277	+	0.0126141i
$392$	−3.33773	+	5.78112i	−0.168581	+	0.291991i
$393$	13.6576	−	23.6556i	0.688933	−	1.19327i
$394$	7.86809	−	13.6279i	0.396389	−	0.686565i
$395$	−7.80693			−0.392809
$396$	−0.0177583	−	0.0307582i	−0.000892387	−	0.00154566i
$397$	9.24716	+	16.0166i	0.464102	+	0.803848i	0.999160	−	0.0409672i	$-0.0130439\pi$
$397$	9.24716	+	16.0166i	0.464102	+	0.803848i	−0.535059	+	0.844815i	$0.679711\pi$
$398$	7.59313	−	13.1517i	0.380609	−	0.659234i
$399$	41.2636			2.06577
$400$	2.82155	+	4.88706i	0.141077	+	0.244353i
$401$	14.9769			0.747909			0.373955	−	0.927447i	$-0.378002\pi$
$401$	14.9769			0.747909			0.373955	+	0.927447i	$0.378002\pi$
$402$	7.78457			0.388259
$403$		0			0
$404$	−21.4678			−1.06806
$405$	−25.5110			−1.26765
$406$	21.0880	+	36.5255i	1.04658	+	1.81273i
$407$	−0.269667			−0.0133669
$408$	−0.307467	+	0.532549i	−0.0152219	+	0.0263651i
$409$	4.01325	+	6.95115i	0.198442	+	0.343712i	0.948024	−	0.318200i	$-0.103078\pi$
$409$	4.01325	+	6.95115i	0.198442	+	0.343712i	−0.749581	+	0.661912i	$0.769745\pi$
$410$	−2.07751	−	3.59835i	−0.102601	−	0.177710i
$411$	40.4477			1.99514
$412$	−3.89633	+	6.74864i	−0.191958	+	0.332482i
$413$	2.80891	−	4.86517i	0.138217	−	0.239399i
$414$	−0.332271	+	0.575511i	−0.0163302	+	0.0282848i
$415$	−18.7980	−	32.5591i	−0.922758	−	1.59826i
$416$	18.1956	−	31.5157i	0.892112	−	1.54518i
$417$	−0.128915	−	0.223287i	−0.00631300	−	0.0109344i
$418$	0.488628			0.0238996
$419$	1.45890			0.0712718			0.0356359	−	0.999365i	$-0.488654\pi$
$419$	1.45890			0.0712718			0.0356359	+	0.999365i	$0.488654\pi$
$420$	14.2685	+	24.7137i	0.696230	+	1.20591i
$421$	−6.36822	+	11.0301i	−0.310368	+	0.537574i	−0.978442	−	0.206521i	$-0.933786\pi$
$421$	−6.36822	+	11.0301i	−0.310368	+	0.537574i	0.668074	+	0.744095i	$0.267119\pi$
$422$	−15.0345	−	26.0406i	−0.731869	−	1.26763i
$423$	−0.791680	+	1.37123i	−0.0384928	+	0.0666715i
$424$	−2.10576	+	3.64729i	−0.102265	+	0.177128i
$425$	−0.244568	+	0.423604i	−0.0118633	+	0.0205478i
$426$	31.8410			1.54270
$427$	26.2701	+	45.5012i	1.27130	+	2.20196i
$428$	12.0058	+	20.7947i	0.580322	+	1.00515i
$429$	0.215671	−	0.373553i	0.0104127	−	0.0180353i
$430$	−14.0818			−0.679086
$431$	17.5775	+	30.4452i	0.846679	+	1.46649i	0.884155	+	0.467194i	$0.154735\pi$
$431$	17.5775	+	30.4452i	0.846679	+	1.46649i	−0.0374755	+	0.999298i	$0.511932\pi$
$432$	21.8931			1.05333
$433$	−29.5616			−1.42064			−0.710319	−	0.703880i	$-0.751449\pi$
$433$	−29.5616			−1.42064			−0.710319	+	0.703880i	$0.751449\pi$
$434$		0			0
$435$	−26.6450			−1.27753
$436$	−20.2206			−0.968392
$437$	−2.01061	−	3.48248i	−0.0961807	−	0.166590i
$438$	−7.86967			−0.376027
$439$	−9.28133	+	16.0757i	−0.442974	+	0.767253i	−0.997909	−	0.0646407i	$-0.979410\pi$
$439$	−9.28133	+	16.0757i	−0.442974	+	0.767253i	0.554935	+	0.831894i	$0.312743\pi$
$440$	−0.0462258	−	0.0800655i	−0.00220373	−	0.00381697i
$441$	−2.03429	−	3.52350i	−0.0968710	−	0.167786i
$442$	3.86472			0.183826
$443$	−12.4128	+	21.4997i	−0.589752	+	1.02148i	0.404513	+	0.914532i	$0.367441\pi$
$443$	−12.4128	+	21.4997i	−0.589752	+	1.02148i	−0.994265	+	0.106948i	$0.965892\pi$
$444$	8.65954	−	14.9988i	0.410964	−	0.711810i
$445$	−9.85488	+	17.0692i	−0.467166	+	0.809155i
$446$	−15.5851	−	26.9942i	−0.737977	−	1.27821i
$447$	−14.0384	+	24.3152i	−0.663993	+	1.15007i
$448$	−8.33604	−	14.4384i	−0.393841	−	0.682152i
$449$	12.6167			0.595417			0.297708	−	0.954657i	$-0.403778\pi$
$449$	12.6167			0.595417			0.297708	+	0.954657i	$0.403778\pi$
$450$	−1.12859			−0.0532024
$451$	0.0201722	+	0.0349393i	0.000949872	+	0.00164523i
$452$	1.27221	−	2.20353i	0.0598396	−	0.103645i
$453$	2.45035	+	4.24413i	0.115127	+	0.199407i
$454$	−0.376793	+	0.652625i	−0.0176838	+	0.0306292i
$455$	−24.5337	+	42.4937i	−1.15016	+	1.99213i
$456$	4.29281	−	7.43537i	0.201029	−	0.348193i
$457$	19.4392			0.909330			0.454665	−	0.890663i	$-0.349759\pi$
$457$	19.4392			0.909330			0.454665	+	0.890663i	$0.349759\pi$
$458$	24.3315	+	42.1434i	1.13694	+	1.96923i
$459$	0.948833	+	1.64343i	0.0442877	+	0.0767086i
$460$	1.39049	−	2.40840i	0.0648320	−	0.112292i
$461$	−34.6818			−1.61529			−0.807645	−	0.589669i	$-0.799258\pi$
$461$	−34.6818			−1.61529			−0.807645	+	0.589669i	$0.799258\pi$
$462$	−0.314992	−	0.545583i	−0.0146548	−	0.0253828i
$463$	12.2908			0.571200			0.285600	−	0.958349i	$-0.407807\pi$
$463$	12.2908			0.571200			0.285600	+	0.958349i	$0.407807\pi$
$464$	26.7431			1.24152
$465$		0			0
$466$	20.0671			0.929588
$467$	−37.7834			−1.74841			−0.874204	−	0.485558i	$-0.838616\pi$
$467$	−37.7834			−1.74841			−0.874204	+	0.485558i	$0.838616\pi$
$468$	1.96103	+	3.39660i	0.0906487	+	0.157008i
$469$	8.59840			0.397037
$470$	7.53246	−	13.0466i	0.347447	−	0.601795i
$471$	−17.5519	−	30.4009i	−0.808751	−	1.40080i
$472$	−0.584443	−	1.01228i	−0.0269012	−	0.0465942i
$473$	0.136732			0.00628695
$474$	−5.53440	+	9.58586i	−0.254203	+	0.440293i
$475$	3.41462	−	5.91430i	0.156674	−	0.271367i
$476$	1.24132	−	2.15004i	0.0568960	−	0.0985468i
$477$	−1.28343	−	2.22296i	−0.0587641	−	0.101782i
$478$	−10.6049	+	18.3682i	−0.485055	+	0.840141i
$479$	−3.20009	−	5.54272i	−0.146216	−	0.253253i	0.783610	−	0.621253i	$-0.213376\pi$
$479$	−3.20009	−	5.54272i	−0.146216	−	0.253253i	−0.929826	+	0.368000i	$0.880043\pi$
$480$	33.5780			1.53262
$481$	29.7791			1.35781
$482$	12.8602	+	22.2744i	0.585764	+	1.01457i
$483$	−2.59227	+	4.48994i	−0.117952	+	0.204300i
$484$	8.63538	+	14.9569i	0.392517	+	0.679860i
$485$	−3.09516	+	5.36098i	−0.140544	+	0.243430i
$486$	−4.81090	+	8.33273i	−0.218227	+	0.377980i
$487$	0.0226533	−	0.0392367i	0.00102652	−	0.00177798i	−0.865512	−	0.500889i	$-0.833007\pi$
$487$	0.0226533	−	0.0392367i	0.00102652	−	0.00177798i	0.866538	+	0.499111i	$0.166340\pi$
$488$	10.9319			0.494865
$489$	−4.20763	−	7.28784i	−0.190276	−	0.329567i
$490$	19.3553	+	33.5244i	0.874385	+	1.51448i
$491$	13.0362	−	22.5793i	0.588314	−	1.01899i	−0.406140	−	0.913811i	$-0.633125\pi$
$491$	13.0362	−	22.5793i	0.588314	−	1.01899i	0.994453	−	0.105178i	$-0.0335413\pi$
$492$	−2.59108			−0.116815
$493$	1.15903	+	2.00750i	0.0522000	+	0.0904131i
$494$	−53.9587			−2.42772
$495$	0.0563477			0.00253264
$496$		0			0
$497$	35.1698			1.57758
$498$	−53.3042			−2.38862
$499$	7.89826	+	13.6802i	0.353575	+	0.612409i	0.986873	−	0.161498i	$-0.0516327\pi$
$499$	7.89826	+	13.6802i	0.353575	+	0.612409i	−0.633298	+	0.773908i	$0.718299\pi$
$500$	−14.8393			−0.663632
$501$	16.4198	−	28.4400i	0.733584	−	1.27060i
$502$	13.4840	+	23.3549i	0.601820	+	1.04238i
$503$	−10.7592	−	18.6355i	−0.479731	−	0.830918i	0.519999	−	0.854167i	$-0.325932\pi$
$503$	−10.7592	−	18.6355i	−0.479731	−	0.830918i	−0.999730	+	0.0232491i	$0.992599\pi$
$504$	−1.56718			−0.0698078
$505$	17.0295	−	29.4960i	0.757804	−	1.31256i
$506$	−0.0306967	+	0.0531682i	−0.00136463	+	0.00236361i
$507$	−11.6650	+	20.2044i	−0.518062	+	0.897310i
$508$	14.4195	+	24.9753i	0.639762	+	1.10810i
$509$	8.24837	−	14.2866i	0.365602	−	0.633242i	−0.623270	−	0.782007i	$-0.714196\pi$
$509$	8.24837	−	14.2866i	0.365602	−	0.633242i	0.988873	+	0.148765i	$0.0475297\pi$
$510$	1.78298	+	3.08822i	0.0789519	+	0.136749i
$511$	−8.69239			−0.384529
$512$	−26.1117			−1.15398
$513$	−13.2475	−	22.9453i	−0.584890	−	1.01306i
$514$	6.50588	−	11.2685i	0.286962	−	0.497033i
$515$	−6.18160	−	10.7068i	−0.272394	−	0.471800i
$516$	−4.39074	+	7.60498i	−0.193291	+	0.334791i
$517$	−0.0731388	+	0.126680i	−0.00321664	+	0.00557139i
$518$	21.7465	−	37.6661i	0.955487	−	1.65495i
$519$	21.3023			0.935069
$520$	5.10467	+	8.84156i	0.223855	+	0.387728i
$521$	0.0891774	+	0.154460i	0.00390693	+	0.00676701i	0.867972	−	0.496613i	$-0.165423\pi$
$521$	0.0891774	+	0.154460i	0.00390693	+	0.00676701i	−0.864065	+	0.503380i	$0.832090\pi$
$522$	−2.67425	+	4.63193i	−0.117049	+	0.202734i
$523$	−1.27670			−0.0558263			−0.0279132	−	0.999610i	$-0.508886\pi$
$523$	−1.27670			−0.0558263			−0.0279132	+	0.999610i	$0.508886\pi$
$524$	11.4727	+	19.8713i	0.501186	+	0.868080i
$525$	−8.80491			−0.384278
$526$	−36.8543			−1.60692
$527$		0			0
$528$	−0.399463			−0.0173844
$529$	−22.4948			−0.978033
$530$	12.2112	+	21.1504i	0.530421	+	0.918716i
$531$	0.712416			0.0309162
$532$	−17.3312	+	30.0185i	−0.751402	+	1.30147i
$533$	−2.22760	−	3.85832i	−0.0964880	−	0.167122i
$534$	13.9724	+	24.2009i	0.604645	+	1.04728i
$535$	−38.0949			−1.64698
$536$	0.894524	−	1.54936i	0.0386376	−	0.0669222i
$537$	4.67306	−	8.09399i	0.201658	−	0.349281i
$538$	−4.93750	+	8.55200i	−0.212871	+	0.368703i
$539$	−0.187937	−	0.325516i	−0.00809501	−	0.0140210i
$540$	9.16164	−	15.8684i	0.394254	−	0.682868i
$541$	−9.35228	−	16.1986i	−0.402086	−	0.696433i	0.591891	−	0.806018i	$-0.298381\pi$
$541$	−9.35228	−	16.1986i	−0.402086	−	0.696433i	−0.993978	+	0.109584i	$0.965048\pi$
$542$	39.8908			1.71345
$543$	8.85162			0.379859
$544$	−1.46061	−	2.52984i	−0.0626229	−	0.108466i
$545$	16.0402	−	27.7824i	0.687086	−	1.19007i
$546$	34.7843	+	60.2482i	1.48863	+	2.57839i
$547$	11.5687	−	20.0376i	0.494641	−	0.856744i	−0.505339	−	0.862921i	$-0.668633\pi$
$547$	11.5687	−	20.0376i	0.494641	−	0.856744i	0.999981	+	0.00617649i	$0.00196605\pi$
$548$	−16.9885	+	29.4249i	−0.725712	+	1.25697i
$549$	−3.33141	+	5.77017i	−0.142181	+	0.246265i
$550$	−0.104264			−0.00444584
$551$	−16.1822	−	28.0284i	−0.689385	−	1.19405i
$552$	0.539368	+	0.934212i	0.0229570	+	0.0397627i
$553$	−6.11298	+	10.5880i	−0.259950	+	0.450247i
$554$	56.0521			2.38143
$555$	13.7385	+	23.7958i	0.583168	+	1.01008i
$556$	0.216583			0.00918517
$557$	−26.2162			−1.11082			−0.555408	−	0.831578i	$-0.687438\pi$
$557$	−26.2162			−1.11082			−0.555408	+	0.831578i	$0.687438\pi$
$558$		0			0
$559$	−15.0992			−0.638628
$560$	45.4410			1.92023
$561$	−0.0173125	−	0.0299861i	−0.000730933	−	0.00126601i
$562$	−46.1451			−1.94651
$563$	13.5215	−	23.4199i	0.569862	−	0.987031i	−0.426717	−	0.904385i	$-0.640330\pi$
$563$	13.5215	−	23.4199i	0.569862	−	0.987031i	0.996579	−	0.0826452i	$-0.0263368\pi$
$564$	−4.69727	−	8.13591i	−0.197791	−	0.342583i
$565$	2.01838	+	3.49594i	0.0849139	+	0.147075i
$566$	−33.6585			−1.41477
$567$	−19.9756	+	34.5988i	−0.838896	+	1.45301i
$568$	3.65885	−	6.33731i	0.153522	−	0.265908i
$569$	−6.27456	+	10.8679i	−0.263043	+	0.455604i	−0.967049	−	0.254590i	$-0.918060\pi$
$569$	−6.27456	+	10.8679i	−0.263043	+	0.455604i	0.704006	+	0.710194i	$0.251393\pi$
$570$	−24.8938	−	43.1173i	−1.04269	−	1.80598i
$571$	12.9699	−	22.4645i	0.542773	−	0.940111i	−0.455970	−	0.889995i	$-0.650708\pi$
$571$	12.9699	−	22.4645i	0.542773	−	0.940111i	0.998743	−	0.0501157i	$-0.0159590\pi$
$572$	0.181169	+	0.313793i	0.00757504	+	0.0131204i
$573$	−27.3355			−1.14196
$574$	−6.50692			−0.271594
$575$	0.429028	+	0.743099i	0.0178917	+	0.0309894i
$576$	1.05712	−	1.83099i	0.0440468	−	0.0762913i
$577$	−13.3108	−	23.0550i	−0.554135	−	0.959791i	−0.997970	−	0.0636821i	$-0.979716\pi$
$577$	−13.3108	−	23.0550i	−0.554135	−	0.959791i	0.443835	−	0.896109i	$-0.353618\pi$
$578$	−15.9060	+	27.5500i	−0.661602	+	1.14593i
$579$	6.76419	−	11.7159i	0.281110	−	0.486897i
$580$	11.1912	−	19.3838i	0.464690	−	0.804867i
$581$	−58.8769			−2.44262
$582$	4.38838	+	7.60089i	0.181904	+	0.315067i
$583$	−0.118569	−	0.205367i	−0.00491061	−	0.00850543i
$584$	−0.904303	+	1.56630i	−0.0374203	+	0.0648139i
$585$	−6.22242			−0.257266
$586$	−19.6405	−	34.0183i	−0.811341	−	1.40528i
$587$	23.0836			0.952762			0.476381	−	0.879239i	$-0.341948\pi$
$587$	23.0836			0.952762			0.476381	+	0.879239i	$0.341948\pi$
$588$	24.1401			0.995521
$589$		0			0
$590$	−6.77830			−0.279058
$591$	15.5687			0.640412
$592$	−13.7891	−	23.8834i	−0.566728	−	0.981602i
$593$	21.7001			0.891117			0.445559	−	0.895253i	$-0.353005\pi$
$593$	21.7001			0.891117			0.445559	+	0.895253i	$0.353005\pi$
$594$	−0.202253	+	0.350313i	−0.00829856	+	0.0143735i
$595$	1.96938	+	3.41107i	0.0807369	+	0.139840i
$596$	−11.7926	−	20.4253i	−0.483042	−	0.836653i
$597$	15.0247			0.614918
$598$	3.38980	−	5.87131i	0.138619	−	0.240096i
$599$	12.1868	−	21.1082i	0.497941	−	0.862459i	−0.502057	−	0.864835i	$-0.667423\pi$
$599$	12.1868	−	21.1082i	0.497941	−	0.862459i	0.999997	+	0.00237627i	$0.000756392\pi$
$600$	−0.916008	+	1.58657i	−0.0373959	+	0.0647715i
$601$	−4.23648	−	7.33780i	−0.172810	−	0.299315i	0.766591	−	0.642135i	$-0.221951\pi$
$601$	−4.23648	−	7.33780i	−0.172810	−	0.299315i	−0.939401	+	0.342820i	$0.888618\pi$
$602$	−11.0264	+	19.0982i	−0.449401	+	0.778385i
$603$	0.545197	+	0.944309i	0.0222021	+	0.0384552i
$604$	−4.11670			−0.167506
$605$	−27.4004			−1.11398
$606$	−24.1448	−	41.8200i	−0.980814	−	1.69882i
$607$	−20.8076	+	36.0398i	−0.844553	+	1.46281i	0.0414558	+	0.999140i	$0.486800\pi$
$607$	−20.8076	+	36.0398i	−0.844553	+	1.46281i	−0.886009	+	0.463668i	$0.846533\pi$
$608$	20.3928	+	35.3213i	0.827036	+	1.43247i
$609$	−20.8636	+	36.1368i	−0.845436	+	1.46434i
$610$	31.6968	−	54.9005i	1.28337	−	2.22286i
$611$	8.07665	−	13.9892i	0.326746	−	0.565941i
$612$	0.314834			0.0127264
$613$	−19.9582	−	34.5687i	−0.806106	−	1.39622i	−0.915542	−	0.402223i	$-0.868238\pi$
$613$	−19.9582	−	34.5687i	−0.806106	−	1.39622i	0.109436	−	0.993994i	$-0.465096\pi$
$614$	−11.3634	−	19.6819i	−0.458588	−	0.794297i
$615$	2.05540	−	3.56006i	0.0828817	−	0.143555i
$616$	−0.144783			−0.00583347
$617$	4.55839	+	7.89537i	0.183514	+	0.317855i	0.943075	−	0.332581i	$-0.107919\pi$
$617$	4.55839	+	7.89537i	0.183514	+	0.317855i	−0.759561	+	0.650436i	$0.774586\pi$
$618$	−17.5288			−0.705110
$619$	13.4807			0.541834			0.270917	−	0.962603i	$-0.412673\pi$
$619$	13.4807			0.541834			0.270917	+	0.962603i	$0.412673\pi$
$620$		0			0
$621$	3.32894			0.133586
$622$	9.15439			0.367058
$623$	15.4331	+	26.7310i	0.618316	+	1.07095i
$624$	44.1123			1.76591
$625$	14.7893	−	25.6158i	0.591571	−	1.02463i
$626$	25.6966	+	44.5079i	1.02704	+	1.77889i
$627$	0.241714	+	0.418661i	0.00965313	+	0.0167197i
$628$	29.4881			1.17670
$629$	1.19522	−	2.07018i	0.0476566	−	0.0825436i
$630$	−4.54400	+	7.87043i	−0.181037	+	0.313565i
$631$	12.9397	−	22.4123i	0.515123	−	0.892219i	−0.484723	−	0.874668i	$-0.661080\pi$
$631$	12.9397	−	22.4123i	0.515123	−	0.892219i	0.999846	−	0.0175512i	$-0.00558701\pi$
$632$	1.27191	+	2.20302i	0.0505940	+	0.0876314i
$633$	14.8745	−	25.7634i	0.591210	−	1.02401i
$634$	20.4477	+	35.4164i	0.812081	+	1.40657i
$635$	−45.7536			−1.81568
$636$	15.2299			0.603905
$637$	20.7537	+	35.9464i	0.822291	+	1.42425i
$638$	−0.247059	+	0.427918i	−0.00978115	+	0.0169414i
$639$	2.23001	+	3.86248i	0.0882177	+	0.152797i
$640$	7.90356	−	13.6894i	0.312415	−	0.541120i
$641$	18.2353	−	31.5845i	0.720251	−	1.24751i	−0.240648	−	0.970612i	$-0.577360\pi$
$641$	18.2353	−	31.5845i	0.720251	−	1.24751i	0.960899	−	0.276899i	$-0.0893067\pi$
$642$	−27.0058	+	46.7754i	−1.06583	+	1.84608i
$643$	36.1150			1.42424			0.712119	−	0.702059i	$-0.247736\pi$
$643$	36.1150			1.42424			0.712119	+	0.702059i	$0.247736\pi$
$644$	−2.17757	−	3.77165i	−0.0858081	−	0.148624i
$645$	−6.96599	−	12.0654i	−0.274286	−	0.475077i
$646$	−2.16570	+	3.75111i	−0.0852084	+	0.147585i
$647$	3.62208			0.142399			0.0711993	−	0.997462i	$-0.477317\pi$
$647$	3.62208			0.142399			0.0711993	+	0.997462i	$0.477317\pi$
$648$	4.15628	+	7.19888i	0.163274	+	0.282799i
$649$	0.0658161			0.00258351
$650$	11.5138			0.451609
$651$		0			0
$652$	7.06902			0.276844
$653$	26.4657			1.03568			0.517842	−	0.855476i	$-0.326735\pi$
$653$	26.4657			1.03568			0.517842	+	0.855476i	$0.326735\pi$
$654$	−22.7421	−	39.3904i	−0.889285	−	1.54029i
$655$	−36.4032			−1.42239
$656$	−2.06296	+	3.57316i	−0.0805452	+	0.139508i
$657$	−0.551157	−	0.954632i	−0.0215027	−	0.0372438i
$658$	−11.7961	−	20.4315i	−0.459861	−	0.796503i
$659$	23.6447			0.921067			0.460534	−	0.887642i	$-0.347658\pi$
$659$	23.6447			0.921067			0.460534	+	0.887642i	$0.347658\pi$
$660$	−0.167164	+	0.289536i	−0.00650684	+	0.0112702i
$661$	5.59538	−	9.69149i	0.217635	−	0.376955i	−0.736449	−	0.676493i	$-0.763499\pi$
$661$	5.59538	−	9.69149i	0.217635	−	0.376955i	0.954085	+	0.299537i	$0.0968324\pi$
$662$	−3.47692	+	6.02221i	−0.135134	+	0.234060i
$663$	1.91180	+	3.31133i	0.0742481	+	0.128602i
$664$	−6.12518	+	10.6091i	−0.237703	+	0.411714i
$665$	−27.4963	−	47.6249i	−1.06626	−	1.84682i
$666$	5.51551			0.213722
$667$	4.06640			0.157452
$668$	13.7930	+	23.8902i	0.533668	+	0.924341i
$669$	15.4193	−	26.7070i	0.596144	−	1.03255i
$670$	−5.18730	−	8.98466i	−0.200403	−	0.347108i
$671$	−0.307770	+	0.533074i	−0.0118813	+	0.0205791i
$672$	26.2923	−	45.5395i	1.01425	−	1.75673i
$673$	−25.7442	+	44.5903i	−0.992367	+	1.71883i	−0.389389	+	0.921074i	$0.627314\pi$
$673$	−25.7442	+	44.5903i	−0.992367	+	1.71883i	−0.602979	+	0.797757i	$0.706020\pi$
$674$	−22.0294			−0.848542
$675$	2.82677	+	4.89611i	0.108802	+	0.188451i
$676$	−9.79889	−	16.9722i	−0.376881	−	0.652776i
$677$	−14.8627	+	25.7430i	−0.571221	+	0.989383i	0.425220	+	0.905090i	$0.360197\pi$
$677$	−14.8627	+	25.7430i	−0.571221	+	0.989383i	−0.996441	+	0.0842935i	$0.973137\pi$
$678$	5.72339			0.219805
$679$	4.84715	+	8.39551i	0.186017	+	0.322190i
$680$	0.819530			0.0314276
$681$	−0.745567			−0.0285702
$682$		0			0
$683$	23.6925			0.906569			0.453285	−	0.891366i	$-0.350252\pi$
$683$	23.6925			0.906569			0.453285	+	0.891366i	$0.350252\pi$
$684$	−4.39566			−0.168072
$685$	−26.9526	−	46.6832i	−1.02980	−	1.78367i
$686$	9.01602			0.344233
$687$	−24.0726	+	41.6949i	−0.918426	+	1.59076i
$688$	6.99163	+	12.1099i	0.266553	+	0.461684i
$689$	13.0934	+	22.6785i	0.498820	+	0.863981i
$690$	6.25553			0.238144
$691$	8.44075	−	14.6198i	0.321101	−	0.556164i	−0.659614	−	0.751604i	$-0.729280\pi$
$691$	8.44075	−	14.6198i	0.321101	−	0.556164i	0.980716	+	0.195440i	$0.0626136\pi$
$692$	−8.94722	+	15.4970i	−0.340122	+	0.589109i
$693$	0.0441214	−	0.0764205i	0.00167603	−	0.00290297i
$694$	31.5861	+	54.7086i	1.19899	+	2.07671i
$695$	−0.171807	+	0.297578i	−0.00651700	+	0.0112878i
$696$	4.34104	+	7.51890i	0.164547	+	0.285003i
$697$	−0.357630			−0.0135462
$698$	14.1917			0.537163
$699$	9.92676	+	17.1936i	0.375464	+	0.650323i
$700$	3.69816	−	6.40540i	0.139777	−	0.242101i
$701$	10.9688	+	18.9985i	0.414286	+	0.717564i	0.995353	−	0.0962912i	$-0.0306980\pi$
$701$	10.9688	+	18.9985i	0.414286	+	0.717564i	−0.581067	+	0.813856i	$0.697365\pi$
$702$	22.3347	−	38.6848i	0.842967	−	1.46006i
$703$	−16.6875	+	28.9036i	−0.629381	+	1.09012i
$704$	0.0976617	−	0.169155i	0.00368076	−	0.00637527i
$705$	14.9046			0.561340
$706$	−15.2009	−	26.3288i	−0.572095	−	0.990897i
$707$	−26.6689	−	46.1920i	−1.00299	−	1.73723i
$708$	−2.11349	+	3.66066i	−0.0794297	+	0.137576i
$709$	−21.7591			−0.817181			−0.408591	−	0.912718i	$-0.633980\pi$
$709$	−21.7591			−0.817181			−0.408591	+	0.912718i	$0.633980\pi$
$710$	−21.2175	−	36.7497i	−0.796277	−	1.37919i
$711$	−1.55042			−0.0581453
$712$	6.42227			0.240685
$713$		0			0
$714$	5.58445			0.208993
$715$	−0.574855			−0.0214983
$716$	3.92548	+	6.79913i	0.146702	+	0.254095i
$717$	−20.9840			−0.783663
$718$	−12.6920	+	21.9832i	−0.473661	+	0.820406i
$719$	16.1068	+	27.8977i	0.600681	+	1.04041i	0.992718	+	0.120461i	$0.0384372\pi$
$719$	16.1068	+	27.8977i	0.600681	+	1.04041i	−0.392037	+	0.919949i	$0.628230\pi$
$720$	2.88127	+	4.99051i	0.107379	+	0.185985i
$721$	−19.3613			−0.721052
$722$	12.2866	−	21.2810i	0.457260	−	0.791997i
$723$	−12.7233	+	22.0374i	−0.473185	+	0.819580i
$724$	−3.71778	+	6.43938i	−0.138170	+	0.239318i
$725$	3.45299	+	5.98075i	0.128241	+	0.222119i
$726$	−19.4244	+	33.6440i	−0.720906	+	1.24865i
$727$	0.842615	+	1.45945i	0.0312508	+	0.0541281i	0.881228	−	0.472692i	$-0.156718\pi$
$727$	0.842615	+	1.45945i	0.0312508	+	0.0541281i	−0.849977	+	0.526820i	$0.823384\pi$
$728$	15.9883			0.592564
$729$	21.1992			0.785156
$730$	5.24400	+	9.08288i	0.194089	+	0.336172i
$731$	−0.606025	+	1.04967i	−0.0224147	+	0.0388233i
$732$	−19.7662	−	34.2361i	−0.730581	−	1.26540i
$733$	5.94658	−	10.2998i	0.219642	−	0.380431i	−0.735056	−	0.678006i	$-0.762844\pi$
$733$	5.94658	−	10.2998i	0.219642	−	0.380431i	0.954699	+	0.297575i	$0.0961777\pi$
$734$	−8.07223	+	13.9815i	−0.297951	+	0.516067i
$735$	−19.1494	+	33.1677i	−0.706335	+	1.22341i
$736$	−5.12447			−0.188890
$737$	0.0503677	+	0.0872394i	0.00185532	+	0.00321351i
$738$	−0.412583	−	0.714615i	−0.0151874	−	0.0263053i
$739$	−11.3806	+	19.7118i	−0.418643	+	0.725112i	−0.995803	−	0.0915195i	$-0.970828\pi$
$739$	−11.3806	+	19.7118i	−0.418643	+	0.725112i	0.577160	+	0.816631i	$0.304161\pi$
$740$	−23.0814			−0.848488
$741$	−26.6923	−	46.2324i	−0.980565	−	1.69839i
$742$	38.2465			1.40407
$743$	30.8079			1.13023			0.565116	−	0.825011i	$-0.308831\pi$
$743$	30.8079			1.13023			0.565116	+	0.825011i	$0.308831\pi$
$744$		0			0
$745$	37.4182			1.37090
$746$	39.8222			1.45799
$747$	−3.73320	−	6.46608i	−0.136590	−	0.236582i
$748$	0.0290857			0.00106348
$749$	−29.8290	+	51.6654i	−1.08993	+	1.88781i
$750$	−16.6897	−	28.9073i	−0.609420	−	1.05555i
$751$	8.16603	+	14.1440i	0.297983	+	0.516121i	0.975674	−	0.219225i	$-0.0703530\pi$
$751$	8.16603	+	14.1440i	0.297983	+	0.516121i	−0.677692	+	0.735346i	$0.737020\pi$
$752$	−14.9595			−0.545515
$753$	−13.3405	+	23.1064i	−0.486155	+	0.842044i
$754$	27.2825	−	47.2546i	0.993569	−	1.72091i
$755$	3.26561	−	5.65620i	0.118848	−	0.205850i
$756$	−14.3475	−	24.8506i	−0.521813	−	0.903807i
$757$	20.5817	−	35.6486i	0.748056	−	1.29567i	−0.200698	−	0.979653i	$-0.564321\pi$
$757$	20.5817	−	35.6486i	0.748056	−	1.29567i	0.948753	−	0.316017i	$-0.102346\pi$
$758$	16.1510	+	27.9744i	0.586632	+	1.01608i
$759$	−0.0607400			−0.00220472
$760$	−11.4422			−0.415051
$761$	−22.4539	−	38.8912i	−0.813952	−	1.40981i	−0.910078	−	0.414437i	$-0.863979\pi$
$761$	−22.4539	−	38.8912i	−0.813952	−	1.40981i	0.0961262	−	0.995369i	$-0.469355\pi$
$762$	−32.4351	+	56.1793i	−1.17500	+	2.03516i
$763$	−25.1196	−	43.5084i	−0.909390	−	1.57511i
$764$	11.4812	−	19.8860i	0.415376	−	0.719452i
$765$	−0.249745	+	0.432571i	−0.00902954	+	0.0156396i
$766$	−1.31345	+	2.27496i	−0.0474569	+	0.0821977i
$767$	−7.26801			−0.262433
$768$	−19.1940	−	33.2450i	−0.692605	−	1.19963i
$769$	−4.62630	−	8.01299i	−0.166829	−	0.288956i	0.770474	−	0.637471i	$-0.220019\pi$
$769$	−4.62630	−	8.01299i	−0.166829	−	0.288956i	−0.937303	+	0.348515i	$0.886686\pi$
$770$	−0.419794	+	0.727105i	−0.0151283	+	0.0262030i
$771$	12.8733			0.463620
$772$	5.68207	+	9.84164i	0.204502	+	0.354208i
$773$	−6.33144			−0.227726			−0.113863	−	0.993496i	$-0.536323\pi$
$773$	−6.33144			−0.227726			−0.113863	+	0.993496i	$0.536323\pi$
$774$	−2.79659			−0.100521
$775$		0			0
$776$	2.01707			0.0724086
$777$	43.0302			1.54370
$778$	−15.1534	−	26.2465i	−0.543276	−	0.940982i
$779$	4.99318			0.178899
$780$	18.4597	−	31.9732i	0.660964	−	1.14482i
$781$	0.206018	+	0.356833i	0.00737189	+	0.0127685i
$782$	−0.272108	−	0.471305i	−0.00973057	−	0.0168538i
$783$	26.7926			0.957490
$784$	19.2198	−	33.2897i	0.686423	−	1.18892i
$785$	−23.3917	+	40.5156i	−0.834885	+	1.44606i
$786$	−25.8066	+	44.6983i	−0.920489	+	1.59433i
$787$	9.39873	+	16.2791i	0.335028	+	0.580286i	0.983490	−	0.180961i	$-0.0579207\pi$
$787$	9.39873	+	16.2791i	0.335028	+	0.580286i	−0.648462	+	0.761247i	$0.724587\pi$
$788$	−6.53904	+	11.3260i	−0.232944	+	0.403470i
$789$	−18.2311	−	31.5771i	−0.649043	−	1.12418i
$790$	14.7515			0.524835
$791$	6.32173			0.224775
$792$	−0.00918023	−	0.0159006i	−0.000326205	−	0.000565004i
$793$	33.9868	−	58.8669i	1.20691	−	2.09042i
$794$	−17.4729	−	30.2639i	−0.620090	−	1.07403i
$795$	−12.0813	+	20.9254i	−0.428478	+	0.742146i
$796$	−6.31052	+	10.9301i	−0.223671	+	0.387409i
$797$	−8.60842	+	14.9102i	−0.304926	+	0.528147i	−0.977245	−	0.212115i	$-0.931965\pi$
$797$	−8.60842	+	14.9102i	−0.304926	+	0.528147i	0.672319	+	0.740262i	$0.265298\pi$
$798$	−77.9693			−2.76008
$799$	−0.648334	−	1.12295i	−0.0229364	−	0.0397270i
$800$	−4.35144	−	7.53692i	−0.153847	−	0.266470i
$801$	−1.95713	+	3.38985i	−0.0691519	+	0.119775i
$802$	−28.2994			−0.999287
$803$	−0.0509183	−	0.0881931i	−0.00179687	−	0.00311227i
$804$	−6.46963			−0.228166
$805$	6.90950			0.243528
$806$		0			0
$807$	−9.76991			−0.343917
$808$	−11.0979			−0.390422
$809$	21.7255	+	37.6296i	0.763827	+	1.32299i	0.940864	+	0.338784i	$0.110015\pi$
$809$	21.7255	+	37.6296i	0.763827	+	1.32299i	−0.177037	+	0.984204i	$0.556651\pi$
$810$	48.2040			1.69372
$811$	16.0099	−	27.7299i	0.562182	−	0.973728i	−0.435124	−	0.900371i	$-0.643295\pi$
$811$	16.0099	−	27.7299i	0.562182	−	0.973728i	0.997306	−	0.0733571i	$-0.0233713\pi$
$812$	−17.5259	−	30.3557i	−0.615038	−	1.06528i
$813$	19.7331	+	34.1788i	0.692071	+	1.19870i
$814$	0.509547			0.0178596
$815$	−5.60756	+	9.71259i	−0.196424	+	0.340217i
$816$	1.77050	−	3.06660i	0.0619800	−	0.107353i
$817$	8.46124	−	14.6553i	0.296021	−	0.512724i
$818$	−7.58320	−	13.1345i	−0.265140	−	0.459237i
$819$	−4.87228	+	8.43904i	−0.170251	+	0.294884i
$820$	1.72658	+	2.99053i	0.0602949	+	0.104434i
$821$	47.7531			1.66659			0.833297	−	0.552826i	$-0.186450\pi$
$821$	47.7531			1.66659			0.833297	+	0.552826i	$0.186450\pi$
$822$	−76.4276			−2.66572
$823$	7.42985	+	12.8689i	0.258988	+	0.448581i	0.965971	−	0.258650i	$-0.0832776\pi$
$823$	7.42985	+	12.8689i	0.258988	+	0.448581i	−0.706983	+	0.707231i	$0.749944\pi$
$824$	−2.01423	+	3.48874i	−0.0701689	+	0.121536i
$825$	−0.0515774	−	0.0893347i	−0.00179569	−	0.00311023i
$826$	−5.30755	+	9.19294i	−0.184673	+	0.319863i
$827$	10.0139	−	17.3446i	0.348219	−	0.603132i	−0.637715	−	0.770273i	$-0.720120\pi$
$827$	10.0139	−	17.3446i	0.348219	−	0.603132i	0.985933	+	0.167141i	$0.0534534\pi$
$828$	0.276145	−	0.478297i	0.00959671	−	0.0166220i
$829$	−55.7361			−1.93580			−0.967898	−	0.251344i	$-0.919128\pi$
$829$	−55.7361			−1.93580			−0.967898	+	0.251344i	$0.919128\pi$
$830$	35.5196	+	61.5218i	1.23290	+	2.13545i
$831$	27.7278	+	48.0260i	0.961867	+	1.66600i
$832$	−10.7847	+	18.6796i	−0.373892	+	0.647600i
$833$	3.33190			0.115444
$834$	0.243590	+	0.421911i	0.00843484	+	0.0146096i
$835$	−43.7658			−1.51458
$836$	−0.406091			−0.0140449
$837$		0			0
$838$	−2.75665			−0.0952268
$839$	−12.6727			−0.437509			−0.218755	−	0.975780i	$-0.570199\pi$
$839$	−12.6727			−0.437509			−0.218755	+	0.975780i	$0.570199\pi$
$840$	7.37616	+	12.7759i	0.254502	+	0.440810i
$841$	3.72798			0.128551
$842$	12.0330	−	20.8418i	0.414685	−	0.718256i
$843$	−22.8270	−	39.5376i	−0.786205	−	1.36175i
$844$	12.4949	+	21.6419i	0.430094	+	0.744944i
$845$	31.0923			1.06961
$846$	1.49591	−	2.59099i	0.0514305	−	0.0890802i
$847$	−21.4551	+	37.1612i	−0.737204	+	1.27688i
$848$	12.1257	−	21.0024i	0.416399	−	0.721225i
$849$	−16.6502	−	28.8389i	−0.571432	−	0.989749i
$850$	0.462121	−	0.800418i	0.0158506	−	0.0274541i
$851$	−2.09669	−	3.63157i	−0.0718736	−	0.124489i
$852$	−26.4626			−0.906592
$853$	5.65296			0.193554			0.0967768	−	0.995306i	$-0.469147\pi$
$853$	5.65296			0.193554			0.0967768	+	0.995306i	$0.469147\pi$
$854$	−49.6385	−	85.9764i	−1.69859	−	2.94205i
$855$	3.48690	−	6.03949i	0.119250	−	0.206546i
$856$	6.20646	+	10.7499i	0.212132	+	0.367424i
$857$	26.9489	−	46.6768i	0.920555	−	1.59445i	0.121998	−	0.992530i	$-0.461070\pi$
$857$	26.9489	−	46.6768i	0.920555	−	1.59445i	0.798558	−	0.601918i	$-0.205597\pi$
$858$	−0.407519	+	0.705844i	−0.0139125	+	0.0240971i
$859$	18.1130	−	31.3727i	0.618009	−	1.07042i	−0.371840	−	0.928297i	$-0.621273\pi$
$859$	18.1130	−	31.3727i	0.618009	−	1.07042i	0.989849	−	0.142126i	$-0.0453938\pi$
$860$	11.7032			0.399075
$861$	−3.21884	−	5.57519i	−0.109698	−	0.190002i
$862$	−33.2135	−	57.5274i	−1.13125	−	1.95939i
$863$	21.2228	−	36.7590i	0.722432	−	1.25129i	−0.237590	−	0.971366i	$-0.576357\pi$
$863$	21.2228	−	36.7590i	0.722432	−	1.25129i	0.960022	−	0.279924i	$-0.0903092\pi$
$864$	−33.7640			−1.14867
$865$	−14.1949	−	24.5864i	−0.482642	−	0.835961i
$866$	55.8578			1.89813
$867$	−31.4734			−1.06889
$868$		0			0
$869$	−0.143235			−0.00485890
$870$	50.3469			1.70692
$871$	−5.56206	−	9.63377i	−0.188463	−	0.326428i
$872$	−10.4531			−0.353988
$873$	−0.614685	+	1.06467i	−0.0208039	+	0.0360335i
$874$	3.79914	+	6.58030i	0.128508	+	0.222582i
$875$	−18.4345	−	31.9294i	−0.623198	−	1.07941i
$876$	6.54035			0.220978
$877$	−6.95447	+	12.0455i	−0.234836	+	0.406747i	−0.959225	−	0.282644i	$-0.908789\pi$
$877$	−6.95447	+	12.0455i	−0.234836	+	0.406747i	0.724389	+	0.689391i	$0.242122\pi$
$878$	17.5375	−	30.3758i	0.591861	−	1.02513i
$879$	19.4315	−	33.6563i	0.655408	−	1.13520i
$880$	0.266184	+	0.461045i	0.00897307	+	0.0155418i
$881$	−6.08660	+	10.5423i	−0.205063	+	0.355179i	−0.950153	−	0.311785i	$-0.899073\pi$
$881$	−6.08660	+	10.5423i	−0.205063	+	0.355179i	0.745090	+	0.666964i	$0.232407\pi$
$882$	3.84388	+	6.65779i	0.129430	+	0.224180i
$883$	−37.7754			−1.27124			−0.635622	−	0.772000i	$-0.719256\pi$
$883$	−37.7754			−1.27124			−0.635622	+	0.772000i	$0.719256\pi$
$884$	−3.21191			−0.108028
$885$	−3.35309	−	5.80771i	−0.112713	−	0.195224i
$886$	23.4546	−	40.6245i	0.787972	−	1.36481i
$887$	8.80309	+	15.2474i	0.295579	+	0.511958i	0.975119	−	0.221680i	$-0.0711541\pi$
$887$	8.80309	+	15.2474i	0.295579	+	0.511958i	−0.679540	+	0.733638i	$0.737821\pi$
$888$	4.47660	−	7.75369i	0.150225	−	0.260197i
$889$	−35.8260	+	62.0525i	−1.20157	+	2.08117i
$890$	18.6212	−	32.2529i	0.624184	−	1.08112i
$891$	−0.468052			−0.0156803
$892$	12.9525	+	22.4345i	0.433683	+	0.751161i
$893$	9.05194	+	15.6784i	0.302912	+	0.524658i
$894$	26.5261	−	45.9446i	0.887166	−	1.53662i
$895$	−12.4557			−0.416348
$896$	−12.3773	−	21.4381i	−0.413496	−	0.716196i
$897$	6.70747			0.223956
$898$	−23.8397			−0.795541
$899$		0			0
$900$	0.937955			0.0312652
$901$	2.10209			0.0700306
$902$	−0.0381162	−	0.0660193i	−0.00126913	−	0.00219820i
$903$	−21.8180			−0.726059
$904$	0.657674	−	1.13912i	0.0218739	−	0.0378867i
$905$	−5.89833	−	10.2162i	−0.196067	−	0.339598i
$906$	−4.63003	−	8.01946i	−0.153823	−	0.266429i
$907$	−48.3230			−1.60454			−0.802269	−	0.596962i	$-0.796374\pi$
$907$	−48.3230			−1.60454			−0.802269	+	0.596962i	$0.796374\pi$
$908$	0.313147	−	0.542386i	0.0103921	−	0.0179997i
$909$	3.38199	−	5.85777i	0.112173	−	0.194290i
$910$	46.3575	−	80.2935i	1.53674	−	2.66170i
$911$	28.2126	+	48.8656i	0.934725	+	1.61899i	0.775124	+	0.631809i	$0.217687\pi$
$911$	28.2126	+	48.8656i	0.934725	+	1.61899i	0.159601	+	0.987182i	$0.448979\pi$
$912$	−24.7195	+	42.8155i	−0.818545	+	1.41776i
$913$	−0.344889	−	0.597365i	−0.0114142	−	0.0197699i
$914$	−36.7313			−1.21496
$915$	62.7190			2.07343
$916$	−20.2215	−	35.0247i	−0.668137	−	1.15725i
$917$	−28.5045	+	49.3712i	−0.941300	+	1.63038i
$918$	−1.79286	−	3.10532i	−0.0591732	−	0.102491i
$919$	−18.9698	+	32.8567i	−0.625756	+	1.08384i	0.362638	+	0.931930i	$0.381876\pi$
$919$	−18.9698	+	32.8567i	−0.625756	+	1.08384i	−0.988394	+	0.151911i	$0.951457\pi$
$920$	0.718822	−	1.24504i	0.0236988	−	0.0410476i
$921$	11.2424	−	19.4725i	0.370451	−	0.641639i
$922$	65.5326			2.15820
$923$	−22.7503	−	39.4048i	−0.748837	−	1.29702i
$924$	0.261785	+	0.453425i	0.00861210	+	0.0149166i
$925$	3.56081	−	6.16750i	0.117079	−	0.202786i
$926$	−23.2239			−0.763185
$927$	−1.22764	−	2.12633i	−0.0403209	−	0.0698378i
$928$	−41.2437			−1.35389
$929$	18.3179			0.600990			0.300495	−	0.953783i	$-0.402848\pi$
$929$	18.3179			0.600990			0.300495	+	0.953783i	$0.402848\pi$
$930$		0			0
$931$	−46.5196			−1.52462
$932$	−16.6774			−0.546286
$933$	4.52849	+	7.84357i	0.148256	+	0.256787i
$934$	71.3934			2.33606
$935$	−0.0230725	+	0.0399628i	−0.000754552	+	0.00130692i
$936$	1.01376	+	1.75589i	0.0331359	+	0.0573931i
$937$	−0.424607	−	0.735441i	−0.0138713	−	0.0240258i	0.859006	−	0.511965i	$-0.171082\pi$
$937$	−0.424607	−	0.735441i	−0.0138713	−	0.0240258i	−0.872878	+	0.487939i	$0.837749\pi$
$938$	−16.2470			−0.530484
$939$	−25.4232	+	44.0342i	−0.829654	+	1.43700i
$940$	−6.26011	+	10.8428i	−0.204182	+	0.353654i
$941$	−2.18301	+	3.78108i	−0.0711640	+	0.123260i	−0.899412	−	0.437102i	$-0.856005\pi$
$941$	−2.18301	+	3.78108i	−0.0711640	+	0.123260i	0.828248	+	0.560362i	$0.189338\pi$
$942$	33.1651	+	57.4437i	1.08058	+	1.87162i
$943$	−0.313682	+	0.543314i	−0.0102149	+	0.0176927i
$944$	3.36543	+	5.82909i	0.109535	+	0.189721i
$945$	45.5251			1.48093
$946$	−0.258361			−0.00840004
$947$	13.1614	+	22.7962i	0.427688	+	0.740778i	0.996667	−	0.0815744i	$-0.0259948\pi$
$947$	13.1614	+	22.7962i	0.427688	+	0.740778i	−0.568979	+	0.822352i	$0.692661\pi$
$948$	4.59955	−	7.96665i	0.149386	−	0.258745i
$949$	5.62286	+	9.73909i	0.182526	+	0.316144i
$950$	−6.45207	+	11.1753i	−0.209333	+	0.362575i
$951$	−20.2301	+	35.0395i	−0.656005	+	1.13623i
$952$	0.641709	−	1.11147i	0.0207979	−	0.0360230i
$953$	24.0492			0.779031			0.389515	−	0.921020i	$-0.372642\pi$
$953$	24.0492			0.779031			0.389515	+	0.921020i	$0.372642\pi$
$954$	2.42509	+	4.20038i	0.0785152	+	0.135992i
$955$	18.2152	+	31.5496i	0.589429	+	1.02092i
$956$	8.81353	−	15.2655i	0.285050	−	0.493721i
$957$	−0.488859			−0.0158026
$958$	6.04670	+	10.4732i	0.195360	+	0.338374i
$959$	−84.4176			−2.72599
$960$	−19.9020			−0.642334
$961$		0			0
$962$	−56.2688			−1.81418
$963$	−7.56546			−0.243794
$964$	−10.6879	−	18.5119i	−0.344233	−	0.596229i
$965$	−18.0294			−0.580388
$966$	4.89820	−	8.48394i	0.157597	−	0.272966i
$967$	−4.57150	−	7.91808i	−0.147010	−	0.254628i	0.783111	−	0.621882i	$-0.213631\pi$
$967$	−4.57150	−	7.91808i	−0.147010	−	0.254628i	−0.930121	+	0.367253i	$0.880298\pi$
$968$	4.46410	+	7.73205i	0.143482	+	0.248518i
$969$	−4.28531			−0.137664
$970$	5.84844	−	10.1298i	0.187782	−	0.325248i
$971$	8.59880	−	14.8936i	0.275949	−	0.477957i	−0.694425	−	0.719565i	$-0.744341\pi$
$971$	8.59880	−	14.8936i	0.275949	−	0.477957i	0.970374	+	0.241608i	$0.0776747\pi$
$972$	3.99826	−	6.92519i	0.128244	−	0.222126i
$973$	0.269056	+	0.466019i	0.00862554	+	0.0149399i
$974$	−0.0428044	+	0.0741393i	−0.00137154	+	0.00237558i
$975$	5.69564	+	9.86515i	0.182407	+	0.315938i
$976$	−62.9498			−2.01498
$977$	−16.2134			−0.518712			−0.259356	−	0.965782i	$-0.583510\pi$
$977$	−16.2134			−0.518712			−0.259356	+	0.965782i	$0.583510\pi$
$978$	7.95050	+	13.7707i	0.254229	+	0.440337i
$979$	−0.180809	+	0.313170i	−0.00577867	+	0.0100089i
$980$	−16.0859	−	27.8616i	−0.513845	−	0.890006i
$981$	3.18551	−	5.51746i	0.101705	−	0.176159i
$982$	−24.6324	+	42.6645i	−0.786050	+	1.36148i
$983$	−8.64267	+	14.9695i	−0.275658	+	0.477454i	−0.970301	−	0.241901i	$-0.922229\pi$
$983$	−8.64267	+	14.9695i	−0.275658	+	0.477454i	0.694643	+	0.719355i	$0.255563\pi$
$984$	−1.33947			−0.0427008
$985$	−10.3743	−	17.9688i	−0.330553	−	0.572535i
$986$	−2.19003	−	3.79325i	−0.0697448	−	0.120802i
$987$	11.6706	−	20.2141i	0.371480	−	0.643422i
$988$	44.8442			1.42669
$989$	1.06311	+	1.84136i	0.0338048	+	0.0585517i
$990$	−0.106471			−0.00338388
$991$	−6.17867			−0.196272			−0.0981359	−	0.995173i	$-0.531288\pi$
$991$	−6.17867			−0.196272			−0.0981359	+	0.995173i	$0.531288\pi$
$992$		0			0
$993$	−6.87985			−0.218325
$994$	−66.4548			−2.10782
$995$	−10.0118	−	17.3409i	−0.317394	−	0.549743i
$996$	44.3003			1.40371
$997$	3.57139	−	6.18583i	0.113107	−	0.195907i	−0.803914	−	0.594745i	$-0.797253\pi$
$997$	3.57139	−	6.18583i	0.113107	−	0.195907i	0.917022	+	0.398838i	$0.130586\pi$
$998$	−14.9241	−	25.8493i	−0.472414	−	0.818245i
$999$	−13.8146	−	23.9276i	−0.437075	−	0.757037i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	961.2.c.l.521.3		32
31.2	even	5		961.2.g.w.844.3		128
31.3	odd	30		961.2.d.s.628.3		64
31.4	even	5		961.2.g.w.338.13		128
31.5	even	3	inner	961.2.c.l.439.3		32
31.6	odd	6		961.2.a.l.1.3	✓	16
31.7	even	15		961.2.d.s.388.13		64
31.8	even	5		961.2.g.w.732.14		128
31.9	even	15		961.2.g.w.816.13		128
31.10	even	15		961.2.g.w.547.4		128
31.11	odd	30		961.2.g.w.235.13		128
31.12	odd	30		961.2.d.s.531.3		64
31.13	odd	30		961.2.g.w.846.4		128
31.14	even	15		961.2.d.s.374.13		64
31.15	odd	10		961.2.g.w.448.3		128
31.16	even	5		961.2.g.w.448.4		128
31.17	odd	30		961.2.d.s.374.14		64
31.18	even	15		961.2.g.w.846.3		128
31.19	even	15		961.2.d.s.531.4		64
31.20	even	15		961.2.g.w.235.14		128
31.21	odd	30		961.2.g.w.547.3		128
31.22	odd	30		961.2.g.w.816.14		128
31.23	odd	10		961.2.g.w.732.13		128
31.24	odd	30		961.2.d.s.388.14		64
31.25	even	3		961.2.a.l.1.4	yes	16
31.26	odd	6	inner	961.2.c.l.439.4		32
31.27	odd	10		961.2.g.w.338.14		128
31.28	even	15		961.2.d.s.628.4		64
31.29	odd	10		961.2.g.w.844.4		128
31.30	odd	2	inner	961.2.c.l.521.4		32
93.56	odd	6		8649.2.a.bs.1.13		16
93.68	even	6		8649.2.a.bs.1.14		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
961.2.a.l.1.3	✓	16	31.6	odd	6
961.2.a.l.1.4	yes	16	31.25	even	3
961.2.c.l.439.3		32	31.5	even	3	inner
961.2.c.l.439.4		32	31.26	odd	6	inner
961.2.c.l.521.3		32	1.1	even	1	trivial
961.2.c.l.521.4		32	31.30	odd	2	inner
961.2.d.s.374.13		64	31.14	even	15
961.2.d.s.374.14		64	31.17	odd	30
961.2.d.s.388.13		64	31.7	even	15
961.2.d.s.388.14		64	31.24	odd	30
961.2.d.s.531.3		64	31.12	odd	30
961.2.d.s.531.4		64	31.19	even	15
961.2.d.s.628.3		64	31.3	odd	30
961.2.d.s.628.4		64	31.28	even	15
961.2.g.w.235.13		128	31.11	odd	30
961.2.g.w.235.14		128	31.20	even	15
961.2.g.w.338.13		128	31.4	even	5
961.2.g.w.338.14		128	31.27	odd	10
961.2.g.w.448.3		128	31.15	odd	10
961.2.g.w.448.4		128	31.16	even	5
961.2.g.w.547.3		128	31.21	odd	30
961.2.g.w.547.4		128	31.10	even	15
961.2.g.w.732.13		128	31.23	odd	10
961.2.g.w.732.14		128	31.8	even	5
961.2.g.w.816.13		128	31.9	even	15
961.2.g.w.816.14		128	31.22	odd	30
961.2.g.w.844.3		128	31.2	even	5
961.2.g.w.844.4		128	31.29	odd	10
961.2.g.w.846.3		128	31.18	even	15
961.2.g.w.846.4		128	31.13	odd	30
8649.2.a.bs.1.13		16	93.56	odd	6
8649.2.a.bs.1.14		16	93.68	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 961 = 31^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	961.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-1.88954 q^{2} +(-0.934717 - 1.61898i) q^{3} +1.57037 q^{4} +(-1.24571 + 2.15763i) q^{5} +(1.76619 + 3.05913i) q^{6} +(1.95083 + 3.37894i) q^{7} +0.811809 q^{8} +(-0.247392 + 0.428495i) q^{9} +(2.35382 - 4.07693i) q^{10} +(-0.0228551 + 0.0395863i) q^{11} +(-1.46785 - 2.54239i) q^{12} +(2.52387 - 4.37148i) q^{13} +(-3.68617 - 6.38464i) q^{14} +4.65754 q^{15} -4.67468 q^{16} +(-0.202598 - 0.350910i) q^{17} +(0.467457 - 0.809660i) q^{18} +(2.82864 + 4.89935i) q^{19} +(-1.95622 + 3.38827i) q^{20} +(3.64695 - 6.31670i) q^{21} +(0.0431858 - 0.0747999i) q^{22} -0.710805 q^{23} +(-0.758812 - 1.31430i) q^{24} +(-0.603580 - 1.04543i) q^{25} +(-4.76896 + 8.26009i) q^{26} -4.68334 q^{27} +(3.06352 + 5.30617i) q^{28} -5.72084 q^{29} -8.80062 q^{30} +7.20939 q^{32} +0.0854524 q^{33} +(0.382817 + 0.663058i) q^{34} -9.72066 q^{35} +(-0.388496 + 0.672895i) q^{36} +(2.94974 + 5.10910i) q^{37} +(-5.34483 - 9.25752i) q^{38} -9.43643 q^{39} +(-1.01128 + 1.75158i) q^{40} +(0.441306 - 0.764364i) q^{41} +(-6.89106 + 11.9357i) q^{42} +(-1.49564 - 2.59052i) q^{43} +(-0.0358910 + 0.0621650i) q^{44} +(-0.616357 - 1.06756i) q^{45} +1.34310 q^{46} +3.20010 q^{47} +(4.36950 + 7.56820i) q^{48} +(-4.11148 + 7.12128i) q^{49} +(1.14049 + 1.97539i) q^{50} +(-0.378743 + 0.656002i) q^{51} +(3.96341 - 6.86482i) q^{52} +(-2.59392 + 4.49279i) q^{53} +8.84936 q^{54} +(-0.0569417 - 0.0986259i) q^{55} +(1.58370 + 2.74305i) q^{56} +(5.28796 - 9.15901i) q^{57} +10.8098 q^{58} +(-0.719926 - 1.24695i) q^{59} +7.31405 q^{60} +13.4661 q^{61} -1.93048 q^{63} -4.27307 q^{64} +(6.28802 + 10.8912i) q^{65} -0.161466 q^{66} +(1.10189 - 1.90853i) q^{67} +(-0.318153 - 0.551057i) q^{68} +(0.664402 + 1.15078i) q^{69} +18.3676 q^{70} +(4.50703 - 7.80641i) q^{71} +(-0.200835 + 0.347857i) q^{72} +(-1.11394 + 1.92939i) q^{73} +(-5.57366 - 9.65385i) q^{74} +(-1.12835 + 1.95437i) q^{75} +(4.44200 + 7.69378i) q^{76} -0.178346 q^{77} +17.8305 q^{78} +(1.56676 + 2.71372i) q^{79} +(5.82329 - 10.0862i) q^{80} +(5.11977 + 8.86770i) q^{81} +(-0.833865 + 1.44430i) q^{82} +(-7.54510 + 13.0685i) q^{83} +(5.72705 - 9.91954i) q^{84} +1.00951 q^{85} +(2.82607 + 4.89489i) q^{86} +(5.34736 + 9.26191i) q^{87} +(-0.0185540 + 0.0321365i) q^{88} +7.91106 q^{89} +(1.16463 + 2.01720i) q^{90} +19.6946 q^{91} -1.11623 q^{92} -6.04673 q^{94} -14.0947 q^{95} +(-6.73874 - 11.6718i) q^{96} +2.48466 q^{97} +(7.76880 - 13.4560i) q^{98} +(-0.0113084 - 0.0195867i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 16 q^{2} + 16 q^{4} + 16 q^{5} + 16 q^{7} - 8 q^{10} + 8 q^{14} - 16 q^{16} + 24 q^{18} + 32 q^{19} + 24 q^{20} + 8 q^{28} - 16 q^{32} - 64 q^{33} - 32 q^{35} + 40 q^{36} + 24 q^{38} - 64 q^{39}+ \cdots - 16 q^{98}+O(q^{100}) \) 32 * q - 16 * q^2 + 16 * q^4 + 16 * q^5 + 16 * q^7 - 8 * q^10 + 8 * q^14 - 16 * q^16 + 24 * q^18 + 32 * q^19 + 24 * q^20 + 8 * q^28 - 16 * q^32 - 64 * q^33 - 32 * q^35 + 40 * q^36 + 24 * q^38 - 64 * q^39 + 32 * q^41 + 16 * q^45 - 64 * q^47 + 16 * q^49 + 32 * q^50 + 32 * q^51 + 48 * q^56 + 64 * q^59 - 32 * q^63 - 32 * q^64 - 16 * q^67 + 32 * q^69 + 176 * q^70 + 48 * q^71 - 48 * q^72 - 40 * q^76 + 64 * q^78 + 40 * q^80 + 16 * q^81 - 88 * q^82 + 32 * q^87 - 40 * q^90 - 64 * q^94 - 96 * q^95 - 16 * q^98

Introduction

L-functions

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