LMFDB - Embedded newform 185.2.e.a.26.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [185,2,Mod(26,185)] 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("185.26"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(185, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 185 = 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	185.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [14,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$1.47723243739$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 11 x^{12} - 2 x^{11} + 86 x^{10} - 18 x^{9} + 332 x^{8} - 110 x^{7} + 935 x^{6} - 290 x^{5} + \cdots + 81 $ x^14 + 11x^12 - 2x^11 + 86x^10 - 18x^9 + 332x^8 - 110x^7 + 935x^6 - 290x^5 + 985x^4 - 441x^3 + 792x^2 - 243x + 81
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			26.3
Root			$-0.560420 + 0.970676i$ of defining polynomial
Character	$\chi$	$=$	185.26
Dual form			185.2.e.a.121.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.560420 - 0.970676i) q^{2} +(-1.67000 + 2.89252i) q^{3} +(0.371859 - 0.644078i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.74360 q^{6} +(-0.612087 + 1.06017i) q^{7} -3.07527 q^{8} +(-4.07778 - 7.06292i) q^{9} +1.12084 q^{10} -3.59983 q^{11} +(1.24201 + 2.15122i) q^{12} +(-0.349805 + 0.605879i) q^{13} +1.37210 q^{14} +(-1.67000 - 2.89252i) q^{15} +(0.979724 + 1.69693i) q^{16} +(-0.289385 - 0.501229i) q^{17} +(-4.57054 + 7.91640i) q^{18} +(-3.87804 + 6.71697i) q^{19} +(0.371859 + 0.644078i) q^{20} +(-2.04437 - 3.54094i) q^{21} +(2.01742 + 3.49427i) q^{22} -4.47887 q^{23} +(5.13569 - 8.89527i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.784150 q^{26} +17.2195 q^{27} +(0.455220 + 0.788464i) q^{28} +3.04867 q^{29} +(-1.87180 + 3.24205i) q^{30} +7.98457 q^{31} +(-1.97715 + 3.42453i) q^{32} +(6.01171 - 10.4126i) q^{33} +(-0.324354 + 0.561797i) q^{34} +(-0.612087 - 1.06017i) q^{35} -6.06543 q^{36} +(-1.32431 - 5.93685i) q^{37} +8.69333 q^{38} +(-1.16835 - 2.02363i) q^{39} +(1.53763 - 2.66326i) q^{40} +(-2.79335 + 4.83822i) q^{41} +(-2.29141 + 3.96883i) q^{42} +4.02235 q^{43} +(-1.33863 + 2.31857i) q^{44} +8.15556 q^{45} +(2.51005 + 4.34753i) q^{46} -8.09571 q^{47} -6.54454 q^{48} +(2.75070 + 4.76435i) q^{49} +(-0.560420 + 0.970676i) q^{50} +1.93309 q^{51} +(0.260156 + 0.450603i) q^{52} +(4.96979 + 8.60794i) q^{53} +(-9.65017 - 16.7146i) q^{54} +(1.79992 - 3.11755i) q^{55} +(1.88233 - 3.26029i) q^{56} +(-12.9526 - 22.4346i) q^{57} +(-1.70853 - 2.95927i) q^{58} +(-0.242678 - 0.420330i) q^{59} -2.48401 q^{60} +(0.459736 - 0.796287i) q^{61} +(-4.47471 - 7.75043i) q^{62} +9.98382 q^{63} +8.35104 q^{64} +(-0.349805 - 0.605879i) q^{65} -13.4763 q^{66} +(-5.62845 + 9.74876i) q^{67} -0.430441 q^{68} +(7.47970 - 12.9552i) q^{69} +(-0.686051 + 1.18828i) q^{70} +(0.253677 - 0.439381i) q^{71} +(12.5403 + 21.7204i) q^{72} -3.55519 q^{73} +(-5.02059 + 4.61261i) q^{74} +3.33999 q^{75} +(2.88417 + 4.99553i) q^{76} +(2.20341 - 3.81642i) q^{77} +(-1.30953 + 2.26817i) q^{78} +(1.90707 - 3.30314i) q^{79} -1.95945 q^{80} +(-16.5232 + 28.6191i) q^{81} +6.26179 q^{82} +(5.80544 + 10.0553i) q^{83} -3.04086 q^{84} +0.578769 q^{85} +(-2.25421 - 3.90440i) q^{86} +(-5.09126 + 8.81833i) q^{87} +11.0705 q^{88} +(-7.19183 - 12.4566i) q^{89} +(-4.57054 - 7.91640i) q^{90} +(-0.428221 - 0.741701i) q^{91} +(-1.66551 + 2.88475i) q^{92} +(-13.3342 + 23.0955i) q^{93} +(4.53700 + 7.85831i) q^{94} +(-3.87804 - 6.71697i) q^{95} +(-6.60368 - 11.4379i) q^{96} -10.2579 q^{97} +(3.08309 - 5.34008i) q^{98} +(14.6793 + 25.4253i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{3} - 8 q^{4} - 7 q^{5} - 4 q^{6} + 6 q^{8} - 13 q^{9} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 20 q^{14} - 2 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 14 q^{19} - 8 q^{20} + q^{21} + 7 q^{22} + 15 q^{24}+ \cdots + 56 q^{99}+O(q^{100}) $ 14 * q - 2 * q^3 - 8 * q^4 - 7 * q^5 - 4 * q^6 + 6 * q^8 - 13 * q^9 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 20 * q^14 - 2 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 14 * q^19 - 8 * q^20 + q^21 + 7 * q^22 + 15 * q^24 - 7 * q^25 - 22 * q^26 - 14 * q^27 + 9 * q^28 - 12 * q^29 + 2 * q^30 + 4 * q^32 - 11 * q^33 + 33 * q^34 + 40 * q^36 + 18 * q^37 - 4 * q^38 - 25 * q^39 - 3 * q^40 - 7 * q^41 - 29 * q^42 + 38 * q^43 - 19 * q^44 + 26 * q^45 - 14 * q^46 + 8 * q^47 + 36 * q^48 + 5 * q^49 + 58 * q^51 - 8 * q^52 - 6 * q^53 - 9 * q^54 + q^55 - 25 * q^56 - 44 * q^57 - 12 * q^58 + 2 * q^59 - 12 * q^60 - 4 * q^61 - 25 * q^62 + 10 * q^63 - 62 * q^64 + 4 * q^65 - 2 * q^66 - 8 * q^67 + 26 * q^68 - 11 * q^69 - 10 * q^70 + 33 * q^71 + 43 * q^72 + 18 * q^74 + 4 * q^75 - 12 * q^76 - 5 * q^77 - 22 * q^78 - 9 * q^79 - 4 * q^80 - 35 * q^81 + 152 * q^82 - 11 * q^83 - 80 * q^84 + 6 * q^85 + 17 * q^86 - 29 * q^87 + 40 * q^88 - 12 * q^89 - 6 * q^90 - 24 * q^91 - 7 * q^92 - 47 * q^93 + 10 * q^94 - 14 * q^95 - 15 * q^96 + 30 * q^97 + 54 * q^98 + 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/185\mathbb{Z}\right)^\times$.

$n$	$76$	$112$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.560420	−	0.970676i	−0.396277	−	0.686372i	0.596986	−	0.802251i	$-0.296365\pi$
$2$	−0.560420	−	0.970676i	−0.396277	−	0.686372i	−0.993263	+	0.115880i	$0.963031\pi$
$3$	−1.67000	+	2.89252i	−0.964173	+	1.67000i	−0.252353	+	0.967635i	$0.581204\pi$
$3$	−1.67000	+	2.89252i	−0.964173	+	1.67000i	−0.711821	+	0.702361i	$0.752129\pi$
$4$	0.371859	−	0.644078i	0.185929	−	0.322039i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$	3.74360			1.52832
$7$	−0.612087	+	1.06017i	−0.231347	+	0.400705i	−0.958205	−	0.286083i	$-0.907647\pi$
$7$	−0.612087	+	1.06017i	−0.231347	+	0.400705i	0.726858	+	0.686788i	$0.240980\pi$
$8$	−3.07527			−1.08727
$9$	−4.07778	−	7.06292i	−1.35926	−	2.35431i
$10$	1.12084			0.354441
$11$	−3.59983			−1.08539			−0.542695	−	0.839930i	$-0.682596\pi$
$11$	−3.59983			−1.08539			−0.542695	+	0.839930i	$0.682596\pi$
$12$	1.24201	+	2.15122i	0.358536	+	0.621003i
$13$	−0.349805	+	0.605879i	−0.0970183	+	0.168041i	−0.910449	−	0.413621i	$-0.864264\pi$
$13$	−0.349805	+	0.605879i	−0.0970183	+	0.168041i	0.813431	+	0.581662i	$0.197597\pi$
$14$	1.37210			0.366710
$15$	−1.67000	−	2.89252i	−0.431191	−	0.746845i
$16$	0.979724	+	1.69693i	0.244931	+	0.424233i
$17$	−0.289385	−	0.501229i	−0.0701861	−	0.121566i	0.828797	−	0.559550i	$-0.189026\pi$
$17$	−0.289385	−	0.501229i	−0.0701861	−	0.121566i	−0.898983	+	0.437984i	$0.855693\pi$
$18$	−4.57054	+	7.91640i	−1.07729	+	1.86591i
$19$	−3.87804	+	6.71697i	−0.889684	+	1.54098i	−0.0494348	+	0.998777i	$0.515742\pi$
$19$	−3.87804	+	6.71697i	−0.889684	+	1.54098i	−0.840249	+	0.542200i	$0.817591\pi$
$20$	0.371859	+	0.644078i	0.0831502	+	0.144020i
$21$	−2.04437	−	3.54094i	−0.446117	−	0.772698i
$22$	2.01742	+	3.49427i	0.430115	+	0.744981i
$23$	−4.47887			−0.933910			−0.466955	−	0.884281i	$-0.654649\pi$
$23$	−4.47887			−0.933910			−0.466955	+	0.884281i	$0.654649\pi$
$24$	5.13569	−	8.89527i	1.04832	−	1.81574i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	0.784150			0.153784
$27$	17.2195			3.31390
$28$	0.455220	+	0.788464i	0.0860284	+	0.149006i
$29$	3.04867			0.566123			0.283062	−	0.959102i	$-0.408650\pi$
$29$	3.04867			0.566123			0.283062	+	0.959102i	$0.408650\pi$
$30$	−1.87180	+	3.24205i	−0.341742	+	0.591915i
$31$	7.98457			1.43407			0.717035	−	0.697037i	$-0.245499\pi$
$31$	7.98457			1.43407			0.717035	+	0.697037i	$0.245499\pi$
$32$	−1.97715	+	3.42453i	−0.349515	+	0.605377i
$33$	6.01171	−	10.4126i	1.04650	−	1.81260i
$34$	−0.324354	+	0.561797i	−0.0556262	+	0.0963474i
$35$	−0.612087	−	1.06017i	−0.103462	−	0.179201i
$36$	−6.06543			−1.01091
$37$	−1.32431	−	5.93685i	−0.217715	−	0.976012i
$37$	−1.32431	−	5.93685i	−0.217715	−	0.976012i
$38$	8.69333			1.41024
$39$	−1.16835	−	2.02363i	−0.187085	−	0.324041i
$40$	1.53763	−	2.66326i	0.243121	−	0.421098i
$41$	−2.79335	+	4.83822i	−0.436247	+	0.755603i	−0.997397	−	0.0721120i	$-0.977026\pi$
$41$	−2.79335	+	4.83822i	−0.436247	+	0.755603i	0.561149	+	0.827715i	$0.310359\pi$
$42$	−2.29141	+	3.96883i	−0.353572	+	0.612404i
$43$	4.02235			0.613403			0.306701	−	0.951806i	$-0.400775\pi$
$43$	4.02235			0.613403			0.306701	+	0.951806i	$0.400775\pi$
$44$	−1.33863	+	2.31857i	−0.201806	+	0.349538i
$45$	8.15556			1.21576
$46$	2.51005	+	4.34753i	0.370087	+	0.641009i
$47$	−8.09571			−1.18088			−0.590440	−	0.807081i	$-0.701046\pi$
$47$	−8.09571			−1.18088			−0.590440	+	0.807081i	$0.701046\pi$
$48$	−6.54454			−0.944624
$49$	2.75070	+	4.76435i	0.392957	+	0.680622i
$50$	−0.560420	+	0.970676i	−0.0792554	+	0.137274i
$51$	1.93309			0.270686
$52$	0.260156	+	0.450603i	0.0360771	+	0.0624874i
$53$	4.96979	+	8.60794i	0.682654	+	1.18239i	0.974168	+	0.225824i	$0.0725075\pi$
$53$	4.96979	+	8.60794i	0.682654	+	1.18239i	−0.291514	+	0.956566i	$0.594159\pi$
$54$	−9.65017	−	16.7146i	−1.31322	−	2.27457i
$55$	1.79992	−	3.11755i	0.242701	−	0.420370i
$56$	1.88233	−	3.26029i	0.251537	−	0.435675i
$57$	−12.9526	−	22.4346i	−1.71562	−	2.97154i
$58$	−1.70853	−	2.95927i	−0.224341	−	0.388571i
$59$	−0.242678	−	0.420330i	−0.0315940	−	0.0547224i	0.849796	−	0.527112i	$-0.176725\pi$
$59$	−0.242678	−	0.420330i	−0.0315940	−	0.0547224i	−0.881390	+	0.472389i	$0.843392\pi$
$60$	−2.48401			−0.320685
$61$	0.459736	−	0.796287i	0.0588632	−	0.101954i	−0.835092	−	0.550110i	$-0.814586\pi$
$61$	0.459736	−	0.796287i	0.0588632	−	0.101954i	0.893955	+	0.448156i	$0.147919\pi$
$62$	−4.47471	−	7.75043i	−0.568289	−	0.984305i
$63$	9.98382			1.25784
$64$	8.35104			1.04388
$65$	−0.349805	−	0.605879i	−0.0433879	−	0.0751501i
$66$	−13.4763			−1.65882
$67$	−5.62845	+	9.74876i	−0.687624	+	1.19100i	0.284980	+	0.958533i	$0.408013\pi$
$67$	−5.62845	+	9.74876i	−0.687624	+	1.19100i	−0.972604	+	0.232467i	$0.925320\pi$
$68$	−0.430441			−0.0521986
$69$	7.47970	−	12.9552i	0.900451	−	1.55963i
$70$	−0.686051	+	1.18828i	−0.0819988	+	0.142026i
$71$	0.253677	−	0.439381i	0.0301059	−	0.0521450i	−0.850580	−	0.525846i	$-0.823749\pi$
$71$	0.253677	−	0.439381i	0.0301059	−	0.0521450i	0.880686	+	0.473701i	$0.157082\pi$
$72$	12.5403	+	21.7204i	1.47788	+	2.55977i
$73$	−3.55519			−0.416104			−0.208052	−	0.978118i	$-0.566712\pi$
$73$	−3.55519			−0.416104			−0.208052	+	0.978118i	$0.566712\pi$
$74$	−5.02059	+	4.61261i	−0.583632	+	0.536204i
$75$	3.33999			0.385669
$76$	2.88417	+	4.99553i	0.330837	+	0.573026i
$77$	2.20341	−	3.81642i	0.251102	−	0.434921i
$78$	−1.30953	+	2.26817i	−0.148275	+	0.256820i
$79$	1.90707	−	3.30314i	0.214562	−	0.371633i	−0.738575	−	0.674172i	$-0.764501\pi$
$79$	1.90707	−	3.30314i	0.214562	−	0.371633i	0.953137	+	0.302539i	$0.0978342\pi$
$80$	−1.95945			−0.219073
$81$	−16.5232	+	28.6191i	−1.83591	+	3.17989i
$82$	6.26179			0.691499
$83$	5.80544	+	10.0553i	0.637230	+	1.10371i	0.986038	+	0.166521i	$0.0532532\pi$
$83$	5.80544	+	10.0553i	0.637230	+	1.10371i	−0.348808	+	0.937194i	$0.613413\pi$
$84$	−3.04086			−0.331785
$85$	0.578769			0.0627763
$86$	−2.25421	−	3.90440i	−0.243077	−	0.421022i
$87$	−5.09126	+	8.81833i	−0.545841	+	0.945424i
$88$	11.0705			1.18011
$89$	−7.19183	−	12.4566i	−0.762333	−	1.32040i	−0.941645	−	0.336607i	$-0.890721\pi$
$89$	−7.19183	−	12.4566i	−0.762333	−	1.32040i	0.179312	−	0.983792i	$-0.442613\pi$
$90$	−4.57054	−	7.91640i	−0.481777	−	0.834462i
$91$	−0.428221	−	0.741701i	−0.0448898	−	0.0777514i
$92$	−1.66551	+	2.88475i	−0.173641	+	0.300756i
$93$	−13.3342	+	23.0955i	−1.38269	+	2.39489i
$94$	4.53700	+	7.85831i	0.467956	+	0.810523i
$95$	−3.87804	−	6.71697i	−0.397879	−	0.689146i
$96$	−6.60368	−	11.4379i	−0.673986	−	1.16738i
$97$	−10.2579			−1.04154			−0.520768	−	0.853698i	$-0.674354\pi$
$97$	−10.2579			−1.04154			−0.520768	+	0.853698i	$0.674354\pi$
$98$	3.08309	−	5.34008i	0.311440	−	0.539429i
$99$	14.6793	+	25.4253i	1.47533	+	2.55534i
$100$	−0.743718			−0.0743718
$101$	−5.50183			−0.547452			−0.273726	−	0.961808i	$-0.588256\pi$
$101$	−5.50183			−0.547452			−0.273726	+	0.961808i	$0.588256\pi$
$102$	−1.08334	−	1.87640i	−0.107267	−	0.185791i
$103$	6.24169			0.615012			0.307506	−	0.951546i	$-0.400506\pi$
$103$	6.24169			0.615012			0.307506	+	0.951546i	$0.400506\pi$
$104$	1.07574	−	1.86324i	0.105485	−	0.182706i
$105$	4.08873			0.399019
$106$	5.57034	−	9.64812i	0.541040	−	0.937108i
$107$	0.185069	−	0.320549i	0.0178913	−	0.0309886i	−0.856941	−	0.515414i	$-0.827638\pi$
$107$	0.185069	−	0.320549i	0.0178913	−	0.0309886i	0.874832	+	0.484426i	$0.160971\pi$
$108$	6.40323	−	11.0907i	0.616151	−	1.06721i
$109$	−1.55541	−	2.69404i	−0.148981	−	0.258043i	0.781870	−	0.623441i	$-0.214266\pi$
$109$	−1.55541	−	2.69404i	−0.148981	−	0.258043i	−0.930851	+	0.365399i	$0.880933\pi$
$110$	−4.03484			−0.384707
$111$	19.3840	+	6.08393i	1.83985	+	0.577461i
$112$	−2.39870			−0.226656
$113$	−5.84618	−	10.1259i	−0.549962	−	0.952562i	−0.998276	−	0.0586863i	$-0.981309\pi$
$113$	−5.84618	−	10.1259i	−0.549962	−	0.952562i	0.448314	−	0.893876i	$-0.352025\pi$
$114$	−14.5178	+	25.1456i	−1.35972	+	2.35510i
$115$	2.23944	−	3.87882i	0.208829	−	0.361702i
$116$	1.13367	−	1.96358i	0.105259	−	0.182314i
$117$	5.70570			0.527492
$118$	−0.272003	+	0.471123i	−0.0250399	+	0.0433704i
$119$	0.708514			0.0649494
$120$	5.13569	+	8.89527i	0.468822	+	0.812024i
$121$	1.95880			0.178072
$122$	−1.03058			−0.0933045
$123$	−9.32976	−	16.1596i	−0.841236	−	1.45706i
$124$	2.96913	−	5.14269i	0.266636	−	0.461827i
$125$	1.00000			0.0894427
$126$	−5.59513	−	9.69105i	−0.498454	−	0.863347i
$127$	−8.87482	−	15.3716i	−0.787513	−	1.36401i	−0.927486	−	0.373857i	$-0.878035\pi$
$127$	−8.87482	−	15.3716i	−0.787513	−	1.36401i	0.139973	−	0.990155i	$-0.455298\pi$
$128$	−0.725783	−	1.25709i	−0.0641508	−	0.111112i
$129$	−6.71731	+	11.6347i	−0.591426	+	1.02438i
$130$	−0.392075	+	0.679094i	−0.0343872	+	0.0595605i
$131$	0.575328	+	0.996498i	0.0502667	+	0.0870644i	0.890064	−	0.455836i	$-0.150660\pi$
$131$	0.575328	+	0.996498i	0.0502667	+	0.0870644i	−0.839797	+	0.542900i	$0.817326\pi$
$132$	−4.47101	−	7.74402i	−0.389152	−	0.674031i
$133$	−4.74740	−	8.22273i	−0.411651	−	0.713001i
$134$	12.6172			1.08996
$135$	−8.60976	+	14.9125i	−0.741010	+	1.28347i
$136$	0.889935	+	1.54141i	0.0763113	+	0.132175i
$137$	1.91138			0.163301			0.0816503	−	0.996661i	$-0.473981\pi$
$137$	1.91138			0.163301			0.0816503	+	0.996661i	$0.473981\pi$
$138$	−16.7671			−1.42731
$139$	1.89002	+	3.27360i	0.160309	+	0.277663i	0.934980	−	0.354702i	$-0.115418\pi$
$139$	1.89002	+	3.27360i	0.160309	+	0.277663i	−0.774670	+	0.632365i	$0.782084\pi$
$140$	−0.910439			−0.0769462
$141$	13.5198	−	23.4170i	1.13857	−	1.97207i
$142$	−0.568663			−0.0477211
$143$	1.25924	−	2.18106i	0.105303	−	0.182390i
$144$	7.99020	−	13.8394i	0.665850	−	1.15329i
$145$	−1.52433	+	2.64022i	−0.126589	+	0.219259i
$146$	1.99240	+	3.45094i	0.164892	+	0.285602i
$147$	−18.3746			−1.51551
$148$	−4.31625	−	1.35471i	−0.354794	−	0.111357i
$149$	−0.552510			−0.0452633			−0.0226317	−	0.999744i	$-0.507205\pi$
$149$	−0.552510			−0.0452633			−0.0226317	+	0.999744i	$0.507205\pi$
$150$	−1.87180	−	3.24205i	−0.152832	−	0.264712i
$151$	−4.57907	+	7.93118i	−0.372639	+	0.645430i	−0.989971	−	0.141273i	$-0.954880\pi$
$151$	−4.57907	+	7.93118i	−0.372639	+	0.645430i	0.617331	+	0.786703i	$0.288214\pi$
$152$	11.9260	−	20.6565i	0.967328	−	1.67546i
$153$	−2.36009	+	4.08780i	−0.190802	+	0.330479i
$154$	−4.93934			−0.398023
$155$	−3.99228	+	6.91484i	−0.320668	+	0.555413i
$156$	−1.73784			−0.139138
$157$	1.37082	+	2.37433i	0.109403	+	0.189492i	0.915529	−	0.402253i	$-0.131773\pi$
$157$	1.37082	+	2.37433i	0.109403	+	0.189492i	−0.806125	+	0.591745i	$0.798439\pi$
$158$	−4.27504			−0.340104
$159$	−33.1982			−2.63279
$160$	−1.97715	−	3.42453i	−0.156308	−	0.270733i
$161$	2.74146	−	4.74835i	0.216057	−	0.374222i
$162$	37.0398			2.91012
$163$	−10.5345	−	18.2462i	−0.825123	−	1.42915i	−0.901826	−	0.432100i	$-0.857773\pi$
$163$	−10.5345	−	18.2462i	−0.825123	−	1.42915i	0.0767030	−	0.997054i	$-0.475561\pi$
$164$	2.07746	+	3.59827i	0.162222	+	0.280978i
$165$	6.01171	+	10.4126i	0.468011	+	0.810619i
$166$	6.50697	−	11.2704i	0.505039	−	0.874753i
$167$	5.01447	−	8.68532i	0.388031	−	0.672090i	−0.604153	−	0.796868i	$-0.706489\pi$
$167$	5.01447	−	8.68532i	0.388031	−	0.672090i	0.992185	+	0.124778i	$0.0398219\pi$
$168$	6.28697	+	10.8894i	0.485050	+	0.840132i
$169$	6.25527	+	10.8345i	0.481175	+	0.833419i
$170$	−0.324354	−	0.561797i	−0.0248768	−	0.0430879i
$171$	63.2552			4.83725
$172$	1.49575	−	2.59071i	0.114050	−	0.197540i
$173$	6.65162	+	11.5209i	0.505714	+	0.875922i	0.999978	+	0.00661007i	$0.00210407\pi$
$173$	6.65162	+	11.5209i	0.505714	+	0.875922i	−0.494265	+	0.869312i	$0.664563\pi$
$174$	11.4130			0.865216
$175$	1.22417			0.0925388
$176$	−3.52684	−	6.10867i	−0.265846	−	0.460458i
$177$	1.62109			0.121848
$178$	−8.06089	+	13.9619i	−0.604190	+	1.04649i
$179$	9.15637			0.684379			0.342190	−	0.939631i	$-0.388832\pi$
$179$	9.15637			0.684379			0.342190	+	0.939631i	$0.388832\pi$
$180$	3.03272	−	5.25282i	0.226045	−	0.391522i
$181$	−10.5528	+	18.2780i	−0.784382	+	1.35859i	0.144986	+	0.989434i	$0.453686\pi$
$181$	−10.5528	+	18.2780i	−0.784382	+	1.35859i	−0.929368	+	0.369156i	$0.879647\pi$
$182$	−0.479968	+	0.831328i	−0.0355776	+	0.0616222i
$183$	1.53552	+	2.65959i	0.113509	+	0.196603i
$184$	13.7737			1.01541
$185$	5.80362	+	1.82154i	0.426691	+	0.133922i
$186$	29.8910			2.19172
$187$	1.04174	+	1.80434i	0.0761793	+	0.131946i
$188$	−3.01046	+	5.21427i	−0.219561	+	0.380290i
$189$	−10.5398	+	18.2555i	−0.766661	+	1.32790i
$190$	−4.34667	+	7.52864i	−0.315340	+	0.546185i
$191$	−7.51240			−0.543578			−0.271789	−	0.962357i	$-0.587615\pi$
$191$	−7.51240			−0.543578			−0.271789	+	0.962357i	$0.587615\pi$
$192$	−13.9462	+	24.1556i	−1.00648	+	1.74328i
$193$	16.5435			1.19083			0.595415	−	0.803418i	$-0.296988\pi$
$193$	16.5435			1.19083			0.595415	+	0.803418i	$0.296988\pi$
$194$	5.74876	+	9.95714i	0.412737	+	0.714881i
$195$	2.33669			0.167334
$196$	4.09149			0.292249
$197$	−0.873381	−	1.51274i	−0.0622259	−	0.107778i	0.833234	−	0.552920i	$-0.186487\pi$
$197$	−0.873381	−	1.51274i	−0.0622259	−	0.107778i	−0.895460	+	0.445142i	$0.853153\pi$
$198$	16.4532	−	28.4977i	1.16928	−	2.02525i
$199$	−14.8223			−1.05073			−0.525364	−	0.850878i	$-0.676071\pi$
$199$	−14.8223			−1.05073			−0.525364	+	0.850878i	$0.676071\pi$
$200$	1.53763	+	2.66326i	0.108727	+	0.188321i
$201$	−18.7990	−	32.5608i	−1.32598	−	2.29666i
$202$	3.08334	+	5.34049i	0.216943	+	0.375756i
$203$	−1.86605	+	3.23209i	−0.130971	+	0.226848i
$204$	0.718835	−	1.24506i	0.0503285	−	0.0871715i
$205$	−2.79335	−	4.83822i	−0.195096	−	0.337916i
$206$	−3.49797	−	6.05866i	−0.243715	−	0.422127i
$207$	18.2639	+	31.6339i	1.26943	+	2.19871i
$208$	−1.37085			−0.0950512
$209$	13.9603	−	24.1800i	0.965654	−	1.67256i
$210$	−2.29141	−	3.96883i	−0.158122	−	0.273875i
$211$	−18.1359			−1.24853			−0.624264	−	0.781214i	$-0.714601\pi$
$211$	−18.1359			−1.24853			−0.624264	+	0.781214i	$0.714601\pi$
$212$	7.39225			0.507702
$213$	0.847279	+	1.46753i	0.0580546	+	0.100554i
$214$	−0.414866			−0.0283596
$215$	−2.01117	+	3.48346i	−0.137161	+	0.237570i
$216$	−52.9547			−3.60311
$217$	−4.88725	+	8.46496i	−0.331768	+	0.574639i
$218$	−1.74336	+	3.01959i	−0.118075	+	0.204513i
$219$	5.93716	−	10.2835i	0.401196	−	0.694892i
$220$	−1.33863	−	2.31857i	−0.0902504	−	0.156318i
$221$	0.404912			0.0272373
$222$	−4.95768	−	22.2252i	−0.332738	−	1.49166i
$223$	−3.84578			−0.257532			−0.128766	−	0.991675i	$-0.541102\pi$
$223$	−3.84578			−0.257532			−0.128766	+	0.991675i	$0.541102\pi$
$224$	−2.42038	−	4.19222i	−0.161718	−	0.280105i
$225$	−4.07778	+	7.06292i	−0.271852	+	0.470861i
$226$	−6.55263	+	11.3495i	−0.435874	+	0.754957i
$227$	6.90676	−	11.9629i	0.458418	−	0.794003i	−0.540460	−	0.841370i	$-0.681750\pi$
$227$	6.90676	−	11.9629i	0.458418	−	0.794003i	0.998878	+	0.0473671i	$0.0150831\pi$
$228$	−19.2662			−1.27594
$229$	−0.301499	+	0.522211i	−0.0199236	+	0.0345087i	−0.875815	−	0.482646i	$-0.839676\pi$
$229$	−0.301499	+	0.522211i	−0.0199236	+	0.0345087i	0.855892	+	0.517155i	$0.173009\pi$
$230$	−5.02010			−0.331016
$231$	7.35937	+	12.7468i	0.484211	+	0.838679i
$232$	−9.37547			−0.615530
$233$	23.3424			1.52921			0.764605	−	0.644499i	$-0.222934\pi$
$233$	23.3424			1.52921			0.764605	+	0.644499i	$0.222934\pi$
$234$	−3.19759	−	5.53839i	−0.209033	−	0.362056i
$235$	4.04786	−	7.01109i	0.264053	−	0.457353i
$236$	−0.360968			−0.0234970
$237$	6.36961	+	11.0325i	0.413750	+	0.716637i
$238$	−0.397065	−	0.687737i	−0.0257379	−	0.0445794i
$239$	14.0468	+	24.3297i	0.908610	+	1.57376i	0.815997	+	0.578057i	$0.196189\pi$
$239$	14.0468	+	24.3297i	0.908610	+	1.57376i	0.0926135	+	0.995702i	$0.470478\pi$
$240$	3.27227	−	5.66774i	0.211224	−	0.365851i
$241$	−0.0182021	+	0.0315270i	−0.00117250	+	0.00203084i	−0.866611	−	0.498984i	$-0.833707\pi$
$241$	−0.0182021	+	0.0315270i	−0.00117250	+	0.00203084i	0.865439	+	0.501015i	$0.167040\pi$
$242$	−1.09775	−	1.90136i	−0.0705659	−	0.122224i
$243$	−29.3582	−	50.8498i	−1.88333	−	3.26202i
$244$	−0.341914	−	0.592213i	−0.0218888	−	0.0379125i
$245$	−5.50140			−0.351472
$246$	−10.4572	+	18.1123i	−0.666725	+	1.15480i
$247$	−2.71311	−	4.69925i	−0.172631	−	0.299006i
$248$	−24.5547			−1.55922
$249$	−38.7803			−2.45760
$250$	−0.560420	−	0.970676i	−0.0354441	−	0.0613909i
$251$	−21.4173			−1.35185			−0.675924	−	0.736971i	$-0.736255\pi$
$251$	−21.4173			−1.35185			−0.675924	+	0.736971i	$0.736255\pi$
$252$	3.71257	−	6.43036i	0.233870	−	0.405075i
$253$	16.1232			1.01366
$254$	−9.94726	+	17.2292i	−0.624146	+	1.08105i
$255$	−0.966543	+	1.67410i	−0.0605273	+	0.104836i
$256$	7.53756	−	13.0554i	0.471097	−	0.815965i
$257$	0.403879	+	0.699538i	0.0251933	+	0.0436360i	0.878347	−	0.478023i	$-0.158647\pi$
$257$	0.403879	+	0.699538i	0.0251933	+	0.0436360i	−0.853154	+	0.521659i	$0.825313\pi$
$258$	15.0581			0.937474
$259$	7.10464	+	2.22988i	0.441461	+	0.138558i
$260$	−0.520312			−0.0322684
$261$	−12.4318	−	21.5325i	−0.769508	−	1.33283i
$262$	0.644851	−	1.11691i	0.0398390	−	0.0690032i
$263$	−1.21933	+	2.11194i	−0.0751871	+	0.130228i	−0.901168	−	0.433471i	$-0.857289\pi$
$263$	−1.21933	+	2.11194i	−0.0751871	+	0.130228i	0.825981	+	0.563699i	$0.190622\pi$
$264$	−18.4876	+	32.0215i	−1.13783	+	1.97079i
$265$	−9.93959			−0.610584
$266$	−5.32107	+	9.21637i	−0.326256	+	0.565092i
$267$	48.0414			2.94008
$268$	4.18598	+	7.25032i	0.255699	+	0.442884i
$269$	12.1567			0.741208			0.370604	−	0.928791i	$-0.379151\pi$
$269$	12.1567			0.741208			0.370604	+	0.928791i	$0.379151\pi$
$270$	19.3003			1.17458
$271$	15.6514	+	27.1090i	0.950755	+	1.64676i	0.743797	+	0.668405i	$0.233023\pi$
$271$	15.6514	+	27.1090i	0.950755	+	1.64676i	0.206957	+	0.978350i	$0.433644\pi$
$272$	0.567034	−	0.982132i	0.0343815	−	0.0595505i
$273$	2.86051			0.173126
$274$	−1.07118	−	1.85533i	−0.0647122	−	0.112085i
$275$	1.79992	+	3.11755i	0.108539	+	0.187995i
$276$	−5.56279	−	9.63503i	−0.334841	−	0.579961i
$277$	−11.5959	+	20.0847i	−0.696732	+	1.20678i	0.272861	+	0.962053i	$0.412030\pi$
$277$	−11.5959	+	20.0847i	−0.696732	+	1.20678i	−0.969593	+	0.244722i	$0.921303\pi$
$278$	2.11841	−	3.66919i	0.127053	−	0.220063i
$279$	−32.5593	−	56.3944i	−1.94927	−	3.37624i
$280$	1.88233	+	3.26029i	0.112491	+	0.194840i
$281$	10.7114	+	18.5527i	0.638988	+	1.10676i	0.985655	+	0.168771i	$0.0539799\pi$
$281$	10.7114	+	18.5527i	0.638988	+	1.10676i	−0.346668	+	0.937988i	$0.612687\pi$
$282$	−30.3071			−1.80476
$283$	6.90784	−	11.9647i	0.410628	−	0.711229i	−0.584330	−	0.811516i	$-0.698643\pi$
$283$	6.90784	−	11.9647i	0.410628	−	0.711229i	0.994959	+	0.100287i	$0.0319761\pi$
$284$	−0.188664	−	0.326776i	−0.0111952	−	0.0193906i
$285$	25.9053			1.53450
$286$	−2.82281			−0.166916
$287$	−3.41954	−	5.92282i	−0.201849	−	0.349613i
$288$	32.2496			1.90033
$289$	8.33251	−	14.4323i	0.490148	−	0.848961i
$290$	3.41707			0.200657
$291$	17.1307	−	29.6713i	1.00422	−	1.73936i
$292$	−1.32203	+	2.28982i	−0.0773659	+	0.134002i
$293$	3.55370	−	6.15518i	0.207609	−	0.359589i	−0.743352	−	0.668901i	$-0.766765\pi$
$293$	3.55370	−	6.15518i	0.207609	−	0.359589i	0.950961	+	0.309311i	$0.100098\pi$
$294$	10.2975	+	17.8358i	0.600563	+	1.04021i
$295$	0.485356			0.0282585
$296$	4.07261	+	18.2574i	0.236715	+	1.06119i
$297$	−61.9874			−3.59687
$298$	0.309637	+	0.536308i	0.0179368	+	0.0310675i
$299$	1.56673	−	2.71366i	0.0906064	−	0.156935i
$300$	1.24201	−	2.15122i	0.0717073	−	0.124201i
$301$	−2.46203	+	4.26436i	−0.141909	+	0.245793i
$302$	10.2648			0.590673
$303$	9.18804	−	15.9141i	0.527839	−	0.914244i
$304$	−15.1976			−0.871645
$305$	0.459736	+	0.796287i	0.0263244	+	0.0455952i
$306$	5.29057			0.302442
$307$	−23.6385			−1.34912			−0.674560	−	0.738220i	$-0.735667\pi$
$307$	−23.6385			−1.34912			−0.674560	+	0.738220i	$0.735667\pi$
$308$	−1.63871	−	2.83834i	−0.0933744	−	0.161729i
$309$	−10.4236	+	18.0542i	−0.592978	+	1.02707i
$310$	8.94942			0.508293
$311$	9.68043	+	16.7670i	0.548927	+	0.950769i	0.998348	+	0.0574494i	$0.0182968\pi$
$311$	9.68043	+	16.7670i	0.548927	+	0.950769i	−0.449422	+	0.893320i	$0.648370\pi$
$312$	3.59297	+	6.22321i	0.203412	+	0.352320i
$313$	−3.05523	−	5.29181i	−0.172692	−	0.299111i	0.766668	−	0.642043i	$-0.221913\pi$
$313$	−3.05523	−	5.29181i	−0.172692	−	0.299111i	−0.939360	+	0.342932i	$0.888580\pi$
$314$	1.53647	−	2.66124i	0.0867079	−	0.150183i
$315$	−4.99191	+	8.64624i	−0.281262	+	0.487160i
$316$	−1.41832	−	2.45661i	−0.0797869	−	0.138195i
$317$	16.6203	+	28.7872i	0.933490	+	1.61685i	0.777304	+	0.629125i	$0.216586\pi$
$317$	16.6203	+	28.7872i	0.933490	+	1.61685i	0.156186	+	0.987728i	$0.450080\pi$
$318$	18.6049	+	32.2247i	1.04331	+	1.80707i
$319$	−10.9747			−0.614465
$320$	−4.17552	+	7.23222i	−0.233419	+	0.404293i
$321$	0.618129	+	1.07063i	0.0345006	+	0.0597568i
$322$	−6.14547			−0.342474
$323$	4.48898			0.249774
$324$	12.2886	+	21.2845i	0.682701	+	1.18247i
$325$	0.699609			0.0388073
$326$	−11.8074	+	20.4511i	−0.653954	+	1.13268i
$327$	10.3901			0.574574
$328$	8.59029	−	14.8788i	0.474319	−	0.821545i
$329$	4.95528	−	8.58279i	0.273193	−	0.473185i
$330$	6.73816	−	11.6708i	0.370924	−	0.642459i
$331$	−0.693675	−	1.20148i	−0.0381278	−	0.0660394i	0.846332	−	0.532656i	$-0.178806\pi$
$331$	−0.693675	−	1.20148i	−0.0381278	−	0.0660394i	−0.884460	+	0.466617i	$0.845473\pi$
$332$	8.63522			0.473919
$333$	−36.5313	+	33.5627i	−2.00190	+	1.83922i
$334$	−11.2408			−0.615071
$335$	−5.62845	−	9.74876i	−0.307515	−	0.532631i
$336$	4.00583	−	6.93830i	0.218536	−	0.378515i
$337$	−7.65489	+	13.2587i	−0.416989	+	0.722245i	−0.995635	−	0.0933332i	$-0.970248\pi$
$337$	−7.65489	+	13.2587i	−0.416989	+	0.722245i	0.578646	+	0.815579i	$0.303581\pi$
$338$	7.01116	−	12.1437i	0.381357	−	0.660529i
$339$	39.0524			2.12103
$340$	0.215220	−	0.372773i	0.0116720	−	0.0202164i
$341$	−28.7431			−1.55653
$342$	−35.4495	−	61.4003i	−1.91689	−	3.32015i
$343$	−15.3039			−0.826332
$344$	−12.3698			−0.666935
$345$	7.47970	+	12.9552i	0.402694	+	0.697486i
$346$	7.45541	−	12.9131i	0.400805	−	0.694215i
$347$	27.0099			1.44997			0.724983	−	0.688767i	$-0.241848\pi$
$347$	27.0099			1.44997			0.724983	+	0.688767i	$0.241848\pi$
$348$	3.78646	+	6.55835i	0.202976	+	0.351564i
$349$	10.1591	+	17.5961i	0.543806	+	0.941900i	0.998681	+	0.0513447i	$0.0163507\pi$
$349$	10.1591	+	17.5961i	0.543806	+	0.941900i	−0.454875	+	0.890555i	$0.650316\pi$
$350$	−0.686051	−	1.18828i	−0.0366710	−	0.0635160i
$351$	−6.02347	+	10.4330i	−0.321509	+	0.556870i
$352$	7.11743	−	12.3277i	0.379360	−	0.657071i
$353$	2.23510	+	3.87131i	0.118962	+	0.206049i	0.919357	−	0.393425i	$-0.128710\pi$
$353$	2.23510	+	3.87131i	0.118962	+	0.206049i	−0.800394	+	0.599474i	$0.795377\pi$
$354$	−0.908489	−	1.57355i	−0.0482856	−	0.0836332i
$355$	0.253677	+	0.439381i	0.0134638	+	0.0233199i
$356$	−10.6974			−0.566960
$357$	−1.18322	+	2.04939i	−0.0626224	+	0.108465i
$358$	−5.13141	−	8.88786i	−0.271204	−	0.469738i
$359$	−31.2742			−1.65059			−0.825295	−	0.564702i	$-0.808991\pi$
$359$	−31.2742			−1.65059			−0.825295	+	0.564702i	$0.808991\pi$
$360$	−25.0805			−1.32186
$361$	−20.5784	−	35.6429i	−1.08308	−	1.87594i
$362$	23.6560			1.24333
$363$	−3.27118	+	5.66585i	−0.171693	+	0.297380i
$364$	−0.636952			−0.0333853
$365$	1.77760	−	3.07889i	0.0930436	−	0.161156i
$366$	1.72107	−	2.98098i	0.0899617	−	0.155818i
$367$	8.06325	−	13.9660i	0.420898	−	0.729017i	−0.575130	−	0.818062i	$-0.695048\pi$
$367$	8.06325	−	13.9660i	0.420898	−	0.729017i	0.996028	+	0.0890456i	$0.0283817\pi$
$368$	−4.38806	−	7.60034i	−0.228743	−	0.396195i
$369$	45.5626			2.37189
$370$	−1.48434	−	6.65426i	−0.0771671	−	0.345939i
$371$	−12.1678			−0.631720
$372$	9.91688	+	17.1765i	0.514166	+	0.890562i
$373$	5.12016	−	8.86838i	0.265112	−	0.459187i	−0.702481	−	0.711703i	$-0.747924\pi$
$373$	5.12016	−	8.86838i	0.265112	−	0.459187i	0.967593	+	0.252515i	$0.0812577\pi$
$374$	1.16762	−	2.02238i	0.0603762	−	0.104575i
$375$	−1.67000	+	2.89252i	−0.0862383	+	0.149369i
$376$	24.8965			1.28394
$377$	−1.06644	+	1.84712i	−0.0549243	+	0.0951317i
$378$	23.6270			1.21524
$379$	−8.28107	−	14.3432i	−0.425370	−	0.736763i	0.571085	−	0.820891i	$-0.306523\pi$
$379$	−8.28107	−	14.3432i	−0.425370	−	0.736763i	−0.996455	+	0.0841283i	$0.973189\pi$
$380$	−5.76834			−0.295910
$381$	59.2837			3.03720
$382$	4.21010	+	7.29211i	0.215408	+	0.373097i
$383$	−9.15069	+	15.8495i	−0.467578	+	0.809869i	−0.999314	−	0.0370411i	$-0.988207\pi$
$383$	−9.15069	+	15.8495i	−0.467578	+	0.809869i	0.531735	+	0.846911i	$0.321540\pi$
$384$	4.84822			0.247410
$385$	2.20341	+	3.81642i	0.112296	+	0.194503i
$386$	−9.27133	−	16.0584i	−0.471898	−	0.817352i
$387$	−16.4023	−	28.4095i	−0.833773	−	1.44414i
$388$	−3.81451	+	6.60692i	−0.193652	+	0.335416i
$389$	7.33608	−	12.7065i	0.371954	−	0.644243i	−0.617912	−	0.786247i	$-0.712021\pi$
$389$	7.33608	−	12.7065i	0.371954	−	0.644243i	0.989866	+	0.142004i	$0.0453546\pi$
$390$	−1.30953	−	2.26817i	−0.0663105	−	0.114853i
$391$	1.29612	+	2.24494i	0.0655474	+	0.113532i
$392$	−8.45914	−	14.6517i	−0.427251	−	0.740021i
$393$	−3.84319			−0.193863
$394$	−0.978921	+	1.69554i	−0.0493173	+	0.0854201i
$395$	1.90707	+	3.30314i	0.0959552	+	0.166199i
$396$	21.8345			1.09723
$397$	−2.00229			−0.100492			−0.0502460	−	0.998737i	$-0.516001\pi$
$397$	−2.00229			−0.100492			−0.0502460	+	0.998737i	$0.516001\pi$
$398$	8.30673	+	14.3877i	0.416379	+	0.721189i
$399$	31.7125			1.58761
$400$	0.979724	−	1.69693i	0.0489862	−	0.0848466i
$401$	−22.8854			−1.14284			−0.571422	−	0.820656i	$-0.693608\pi$
$401$	−22.8854			−1.14284			−0.571422	+	0.820656i	$0.693608\pi$
$402$	−21.0706	+	36.4954i	−1.05091	+	1.82023i
$403$	−2.79304	+	4.83768i	−0.139131	+	0.240982i
$404$	−2.04590	+	3.54361i	−0.101788	+	0.176301i
$405$	−16.5232	−	28.6191i	−0.821045	−	1.42209i
$406$	4.18308			0.207603
$407$	4.76729	+	21.3717i	0.236306	+	1.05935i
$408$	−5.94476			−0.294309
$409$	−4.55814	−	7.89494i	−0.225386	−	0.390380i	0.731049	−	0.682325i	$-0.239031\pi$
$409$	−4.55814	−	7.89494i	−0.225386	−	0.390380i	−0.956435	+	0.291945i	$0.905698\pi$
$410$	−3.13089	+	5.42287i	−0.154624	+	0.267816i
$411$	−3.19200	+	5.52871i	−0.157450	+	0.272711i
$412$	2.32103	−	4.02014i	0.114349	−	0.198058i
$413$	0.594160			0.0292367
$414$	20.4709	−	35.4566i	1.00609	−	1.74259i
$415$	−11.6109			−0.569956
$416$	−1.38324	−	2.39583i	−0.0678187	−	0.117465i
$417$	−12.6253			−0.618263
$418$	−31.2945			−1.53067
$419$	4.25529	+	7.37039i	0.207885	+	0.360067i	0.951048	−	0.309043i	$-0.100009\pi$
$419$	4.25529	+	7.37039i	0.207885	+	0.360067i	−0.743163	+	0.669110i	$0.766675\pi$
$420$	1.52043	−	2.63346i	0.0741894	−	0.128500i
$421$	−8.83588			−0.430635			−0.215317	−	0.976544i	$-0.569079\pi$
$421$	−8.83588			−0.430635			−0.215317	+	0.976544i	$0.569079\pi$
$422$	10.1637	+	17.6041i	0.494762	+	0.856953i
$423$	33.0125	+	57.1794i	1.60512	+	2.78016i
$424$	−15.2834	−	26.4717i	−0.742230	−	1.28558i
$425$	−0.289385	+	0.501229i	−0.0140372	+	0.0243132i
$426$	0.949665	−	1.64487i	0.0460114	−	0.0796941i
$427$	0.562797	+	0.974793i	0.0272357	+	0.0471735i
$428$	−0.137639	−	0.238398i	−0.00665304	−	0.0115234i
$429$	4.20585	+	7.28474i	0.203060	+	0.351711i
$430$	4.50841			0.217415
$431$	−0.755326	+	1.30826i	−0.0363828	+	0.0630168i	−0.883643	−	0.468161i	$-0.844917\pi$
$431$	−0.755326	+	1.30826i	−0.0363828	+	0.0630168i	0.847261	+	0.531177i	$0.178250\pi$
$432$	16.8704	+	29.2204i	0.811677	+	1.40587i
$433$	6.85824			0.329586			0.164793	−	0.986328i	$-0.447304\pi$
$433$	6.85824			0.329586			0.164793	+	0.986328i	$0.447304\pi$
$434$	10.9556			0.525888
$435$	−5.09126	−	8.81833i	−0.244107	−	0.422806i
$436$	−2.31357			−0.110800
$437$	17.3693	−	30.0844i	0.830884	−	1.43913i
$438$	−13.3092			−0.635938
$439$	−9.56891	+	16.5738i	−0.456699	+	0.791026i	−0.998784	−	0.0492976i	$-0.984302\pi$
$439$	−9.56891	+	16.5738i	−0.456699	+	0.791026i	0.542085	+	0.840324i	$0.317635\pi$
$440$	−5.53523	+	9.58729i	−0.263882	+	0.457056i
$441$	22.4335	−	38.8559i	1.06826	−	1.85028i
$442$	−0.226921	−	0.393039i	−0.0107935	−	0.0186949i
$443$	−2.25690			−0.107229			−0.0536144	−	0.998562i	$-0.517074\pi$
$443$	−2.25690			−0.107229			−0.0536144	+	0.998562i	$0.517074\pi$
$444$	11.1267	−	10.2225i	0.528048	−	0.485138i
$445$	14.3837			0.681851
$446$	2.15525	+	3.73300i	0.102054	+	0.176763i
$447$	0.922689	−	1.59814i	0.0436417	−	0.0755896i
$448$	−5.11156	+	8.85349i	−0.241499	+	0.418288i
$449$	12.1889	−	21.1119i	0.575232	−	0.996330i	−0.420785	−	0.907160i	$-0.638245\pi$
$449$	12.1889	−	21.1119i	0.575232	−	0.996330i	0.996016	−	0.0891698i	$-0.0284214\pi$
$450$	9.14107			0.430914
$451$	10.0556	−	17.4168i	0.473499	−	0.820124i
$452$	−8.69581			−0.409017
$453$	−15.2941	−	26.4901i	−0.718578	−	1.24461i
$454$	−15.4827			−0.726641
$455$	0.856443			0.0401507
$456$	39.8328	+	68.9925i	1.86534	+	3.23087i
$457$	7.02629	−	12.1699i	0.328676	−	0.569283i	−0.653574	−	0.756863i	$-0.726731\pi$
$457$	7.02629	−	12.1699i	0.328676	−	0.569283i	0.982249	+	0.187580i	$0.0600643\pi$
$458$	0.675864			0.0315810
$459$	−4.98307	−	8.63092i	−0.232590	−	0.402857i
$460$	−1.66551	−	2.88475i	−0.0776547	−	0.134502i
$461$	13.2088	+	22.8783i	0.615195	+	1.06555i	0.990350	+	0.138587i	$0.0442559\pi$
$461$	13.2088	+	22.8783i	0.615195	+	1.06555i	−0.375156	+	0.926962i	$0.622411\pi$
$462$	8.24868	−	14.2871i	0.383763	−	0.664698i
$463$	−12.5712	+	21.7739i	−0.584233	+	1.01192i	0.410738	+	0.911753i	$0.365271\pi$
$463$	−12.5712	+	21.7739i	−0.584233	+	1.01192i	−0.994971	+	0.100167i	$0.968062\pi$
$464$	2.98685	+	5.17338i	0.138661	+	0.240168i
$465$	−13.3342	−	23.0955i	−0.618359	−	1.07103i
$466$	−13.0815	−	22.6579i	−0.605991	−	1.04961i
$467$	−14.0309			−0.649271			−0.324635	−	0.945839i	$-0.605242\pi$
$467$	−14.0309			−0.649271			−0.324635	+	0.945839i	$0.605242\pi$
$468$	2.12172	−	3.67492i	0.0980764	−	0.169873i
$469$	−6.89019	−	11.9342i	−0.318160	−	0.551069i
$470$	−9.07400			−0.418552
$471$	−9.15705			−0.421935
$472$	0.746300	+	1.29263i	0.0343512	+	0.0594981i
$473$	−14.4798			−0.665781
$474$	7.13931	−	12.3656i	0.327919	−	0.567973i
$475$	7.75609			0.355874
$476$	0.263467	−	0.456339i	0.0120760	−	0.0209162i
$477$	40.5314	−	70.2025i	1.85581	−	3.21435i
$478$	15.7442	−	27.2697i	0.720122	−	1.24729i
$479$	3.34106	+	5.78689i	0.152657	+	0.264410i	0.932203	−	0.361935i	$-0.117884\pi$
$479$	3.34106	+	5.78689i	0.152657	+	0.264410i	−0.779546	+	0.626344i	$0.784550\pi$
$480$	13.2074			0.602831
$481$	4.06026	+	1.27437i	0.185132	+	0.0581061i
$482$	0.0408034			0.00185854
$483$	9.15645	+	15.8594i	0.416633	+	0.721630i
$484$	0.728396	−	1.26162i	0.0331089	−	0.0573463i
$485$	5.12897	−	8.88364i	0.232895	−	0.403385i
$486$	−32.9058	+	56.9945i	−1.49264	+	2.58532i
$487$	−7.26544			−0.329229			−0.164614	−	0.986358i	$-0.552638\pi$
$487$	−7.26544			−0.329229			−0.164614	+	0.986358i	$0.552638\pi$
$488$	−1.41381	+	2.44880i	−0.0640003	+	0.110852i
$489$	70.3701			3.18224
$490$	3.08309	+	5.34008i	0.139280	+	0.241240i
$491$	0.446623			0.0201558			0.0100779	−	0.999949i	$-0.496792\pi$
$491$	0.446623			0.0201558			0.0100779	+	0.999949i	$0.496792\pi$
$492$	−13.8774			−0.625642
$493$	−0.882237	−	1.52808i	−0.0397340	−	0.0688212i
$494$	−3.04097	+	5.26711i	−0.136820	+	0.236978i
$495$	−29.3586			−1.31957
$496$	7.82267	+	13.5493i	0.351248	+	0.608380i
$497$	0.310545	+	0.537879i	0.0139298	+	0.0241272i
$498$	21.7332	+	37.6431i	0.973890	+	1.68683i
$499$	5.30225	−	9.18376i	0.237361	−	0.411122i	−0.722595	−	0.691272i	$-0.757051\pi$
$499$	5.30225	−	9.18376i	0.237361	−	0.411122i	0.959956	+	0.280150i	$0.0903842\pi$
$500$	0.371859	−	0.644078i	0.0166300	−	0.0288041i
$501$	16.7483	+	29.0089i	0.748259	+	1.29602i
$502$	12.0027	+	20.7893i	0.535706	+	0.927870i
$503$	−6.98478	−	12.0980i	−0.311436	−	0.539423i	0.667237	−	0.744845i	$-0.267477\pi$
$503$	−6.98478	−	12.0980i	−0.311436	−	0.539423i	−0.978673	+	0.205422i	$0.934143\pi$
$504$	−30.7029			−1.36762
$505$	2.75091	−	4.76472i	0.122414	−	0.212027i
$506$	−9.03576	−	15.6504i	−0.401689	−	0.695745i
$507$	−41.7851			−1.85574
$508$	−13.2007			−0.585687
$509$	−19.8167	−	34.3235i	−0.878360	−	1.52136i	−0.853140	−	0.521682i	$-0.825305\pi$
$509$	−19.8167	−	34.3235i	−0.878360	−	1.52136i	−0.0252198	−	0.999682i	$-0.508029\pi$
$510$	2.16668			0.0959422
$511$	2.17609	−	3.76909i	0.0962643	−	0.166735i
$512$	−19.7999			−0.875041
$513$	−66.7781	+	115.663i	−2.94832	+	5.10665i
$514$	0.452683	−	0.784070i	0.0199670	−	0.0345839i
$515$	−3.12085	+	5.40547i	−0.137521	+	0.238193i
$516$	4.99578	+	8.65295i	0.219927	+	0.380925i
$517$	29.1432			1.28172
$518$	−1.81709	−	8.14597i	−0.0798383	−	0.357913i
$519$	−44.4328			−1.95038
$520$	1.07574	+	1.86324i	0.0471745	+	0.0817085i
$521$	15.7148	−	27.2188i	0.688477	−	1.19248i	−0.283854	−	0.958868i	$-0.591613\pi$
$521$	15.7148	−	27.2188i	0.688477	−	1.19248i	0.972331	−	0.233609i	$-0.0750537\pi$
$522$	−13.9340	+	24.1345i	−0.609877	+	1.05634i
$523$	−7.17472	+	12.4270i	−0.313729	+	0.543394i	−0.979166	−	0.203059i	$-0.934912\pi$
$523$	−7.17472	+	12.4270i	−0.313729	+	0.543394i	0.665438	+	0.746453i	$0.268245\pi$
$524$	0.855764			0.0373842
$525$	−2.04437	+	3.54094i	−0.0892234	+	0.154540i
$526$	2.73335			0.119180
$527$	−2.31061	−	4.00210i	−0.100652	−	0.174334i
$528$	23.5593			1.02529
$529$	−2.93969			−0.127813
$530$	5.57034	+	9.64812i	0.241960	+	0.419087i
$531$	−1.97917	+	3.42803i	−0.0858888	+	0.148764i
$532$	−7.06145			−0.306153
$533$	−1.95425	−	3.38486i	−0.0846480	−	0.146615i
$534$	−26.9233	−	46.6326i	−1.16509	−	2.01799i
$535$	0.185069	+	0.320549i	0.00800123	+	0.0138585i
$536$	17.3090	−	29.9800i	0.747634	−	1.29494i
$537$	−15.2911	+	26.4850i	−0.659860	+	1.14291i
$538$	−6.81287	−	11.8002i	−0.293723	−	0.508744i
$539$	−9.90206	−	17.1509i	−0.426512	−	0.738740i
$540$	6.40323	+	11.0907i	0.275551	+	0.477269i
$541$	14.4219			0.620046			0.310023	−	0.950729i	$-0.399663\pi$
$541$	14.4219			0.620046			0.310023	+	0.950729i	$0.399663\pi$
$542$	17.5427	−	30.3849i	0.753524	−	1.30514i
$543$	−35.2462	−	61.0482i	−1.51256	−	2.61983i
$544$	2.28863			0.0981243
$545$	3.11081			0.133253
$546$	−1.60309	−	2.77663i	−0.0686059	−	0.118829i
$547$	4.85582			0.207620			0.103810	−	0.994597i	$-0.466897\pi$
$547$	4.85582			0.207620			0.103810	+	0.994597i	$0.466897\pi$
$548$	0.710765	−	1.23108i	0.0303624	−	0.0525892i
$549$	−7.49881			−0.320041
$550$	2.01742	−	3.49427i	0.0860230	−	0.148996i
$551$	−11.8229	+	20.4778i	−0.503671	+	0.872383i
$552$	−23.0021	+	39.8408i	−0.979034	+	1.69574i
$553$	2.33459	+	4.04362i	0.0992767	+	0.171952i
$554$	25.9944			1.10439
$555$	−14.9609	+	13.7451i	−0.635053	+	0.583448i
$556$	2.81128			0.119225
$557$	2.37410	+	4.11206i	0.100594	+	0.174233i	0.911929	−	0.410347i	$-0.134592\pi$
$557$	2.37410	+	4.11206i	0.100594	+	0.174233i	−0.811336	+	0.584581i	$0.801259\pi$
$558$	−36.4938	+	63.2091i	−1.54490	+	2.67585i
$559$	−1.40704	+	2.43706i	−0.0595113	+	0.103077i
$560$	1.19935	−	2.07734i	0.0506819	−	0.0877836i
$561$	−6.95878			−0.293800
$562$	12.0057	−	20.7946i	0.506432	−	0.877166i
$563$	12.4349			0.524069			0.262035	−	0.965058i	$-0.415607\pi$
$563$	12.4349			0.524069			0.262035	+	0.965058i	$0.415607\pi$
$564$	−10.0549	−	17.4156i	−0.423389	−	0.733331i
$565$	11.6924			0.491901
$566$	−15.4852			−0.650890
$567$	−20.2273	−	35.0347i	−0.849466	−	1.47132i
$568$	−0.780125	+	1.35122i	−0.0327333	+	0.0566958i
$569$	11.9189			0.499666			0.249833	−	0.968289i	$-0.419624\pi$
$569$	11.9189			0.499666			0.249833	+	0.968289i	$0.419624\pi$
$570$	−14.5178	−	25.1456i	−0.608085	−	1.05323i
$571$	13.7047	+	23.7372i	0.573522	+	0.993369i	0.996201	+	0.0870894i	$0.0277566\pi$
$571$	13.7047	+	23.7372i	0.573522	+	0.993369i	−0.422679	+	0.906280i	$0.638910\pi$
$572$	−0.936518	−	1.62210i	−0.0391578	−	0.0678232i
$573$	12.5457	−	21.7298i	0.524104	−	0.907774i
$574$	−3.83276	+	6.63853i	−0.159976	+	0.277087i
$575$	2.23944	+	3.87882i	0.0933910	+	0.161758i
$576$	−34.0537	−	58.9828i	−1.41890	−	2.45761i
$577$	3.23957	+	5.61111i	0.134865	+	0.233593i	0.925546	−	0.378635i	$-0.123607\pi$
$577$	3.23957	+	5.61111i	0.134865	+	0.233593i	−0.790681	+	0.612229i	$0.790273\pi$
$578$	−18.6788			−0.776937
$579$	−27.6277	+	47.8525i	−1.14817	+	1.98868i
$580$	1.13367	+	1.96358i	0.0470732	+	0.0815332i
$581$	−14.2137			−0.589685
$582$	−38.4016			−1.59180
$583$	−17.8904	−	30.9871i	−0.740946	−	1.28336i
$584$	10.9332			0.452418
$585$	−2.85285	+	4.94128i	−0.117951	+	0.204297i
$586$	−7.96625			−0.329083
$587$	−19.4315	+	33.6563i	−0.802022	+	1.38914i	0.116261	+	0.993219i	$0.462909\pi$
$587$	−19.4315	+	33.6563i	−0.802022	+	1.38914i	−0.918283	+	0.395924i	$0.870424\pi$
$588$	−6.83277	+	11.8347i	−0.281779	+	0.488055i
$589$	−30.9645	+	53.6321i	−1.27587	+	2.20987i
$590$	−0.272003	−	0.471123i	−0.0111982	−	0.0193958i
$591$	5.83418			0.239986
$592$	8.77698	−	8.06374i	0.360731	−	0.331418i
$593$	35.6076			1.46223			0.731115	−	0.682254i	$-0.239000\pi$
$593$	35.6076			1.46223			0.731115	+	0.682254i	$0.239000\pi$
$594$	34.7390	+	60.1697i	1.42536	+	2.46879i
$595$	−0.354257	+	0.613591i	−0.0145231	+	0.0251548i
$596$	−0.205456	+	0.355859i	−0.00841579	+	0.0145766i
$597$	24.7532	−	42.8739i	1.01308	−	1.75471i
$598$	−3.51211			−0.143621
$599$	−8.46167	+	14.6560i	−0.345735	+	0.598830i	−0.985487	−	0.169751i	$-0.945704\pi$
$599$	−8.46167	+	14.6560i	−0.345735	+	0.598830i	0.639752	+	0.768581i	$0.279037\pi$
$600$	−10.2714			−0.419327
$601$	6.62845	+	11.4808i	0.270380	+	0.468312i	0.968959	−	0.247221i	$-0.0795173\pi$
$601$	6.62845	+	11.4808i	0.270380	+	0.468312i	−0.698579	+	0.715533i	$0.746184\pi$
$602$	5.51908			0.224941
$603$	91.8062			3.73864
$604$	3.40553	+	5.89856i	0.138569	+	0.240009i
$605$	−0.979398	+	1.69637i	−0.0398182	+	0.0689671i
$606$	−20.5966			−0.836681
$607$	2.88086	+	4.98980i	0.116931	+	0.202530i	0.918550	−	0.395305i	$-0.129361\pi$
$607$	2.88086	+	4.98980i	0.116931	+	0.202530i	−0.801619	+	0.597835i	$0.796028\pi$
$608$	−15.3350	−	26.5610i	−0.621916	−	1.07719i
$609$	−6.23259	−	10.7952i	−0.252557	−	0.437442i
$610$	0.515291	−	0.892510i	0.0208635	−	0.0361367i
$611$	2.83192	−	4.90502i	0.114567	−	0.198436i
$612$	1.75524	+	3.04017i	0.0709515	+	0.122892i
$613$	16.6927	+	28.9125i	0.674210	+	1.16777i	0.976699	+	0.214613i	$0.0688491\pi$
$613$	16.6927	+	28.9125i	0.674210	+	1.16777i	−0.302489	+	0.953153i	$0.597818\pi$
$614$	13.2475	+	22.9453i	0.534625	+	0.925998i
$615$	18.6595			0.752424
$616$	−6.77608	+	11.7365i	−0.273016	+	0.472877i
$617$	16.8377	+	29.1637i	0.677860	+	1.17409i	0.975624	+	0.219448i	$0.0704256\pi$
$617$	16.8377	+	29.1637i	0.677860	+	1.17409i	−0.297765	+	0.954639i	$0.596241\pi$
$618$	23.3664			0.939934
$619$	28.0530			1.12755			0.563774	−	0.825929i	$-0.309349\pi$
$619$	28.0530			1.12755			0.563774	+	0.825929i	$0.309349\pi$
$620$	2.96913	+	5.14269i	0.119243	+	0.206535i
$621$	−77.1241			−3.09488
$622$	10.8502	−	18.7931i	0.435054	−	0.753535i
$623$	17.6081			0.705454
$624$	2.28931	−	3.96520i	0.0916458	−	0.158735i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−3.42442	+	5.93127i	−0.136867	+	0.237061i
$627$	46.6273	+	80.7609i	1.86212	+	3.22528i
$628$	2.03900			0.0813652
$629$	−2.59249	+	2.38182i	−0.103369	+	0.0949692i
$630$	11.1903			0.445831
$631$	−15.8300	−	27.4183i	−0.630181	−	1.09151i	−0.987514	−	0.157528i	$-0.949647\pi$
$631$	−15.8300	−	27.4183i	−0.630181	−	1.09151i	0.357334	−	0.933977i	$-0.383686\pi$
$632$	−5.86476	+	10.1581i	−0.233288	+	0.404066i
$633$	30.2869	−	52.4585i	1.20380	−	2.08504i
$634$	18.6287	−	32.2659i	0.739841	−	1.28144i
$635$	17.7496			0.704373
$636$	−12.3450	+	21.3822i	−0.489512	+	0.847860i
$637$	−3.84883			−0.152496
$638$	6.15044	+	10.6529i	0.243498	+	0.421751i
$639$	−4.13775			−0.163687
$640$	1.45157			0.0573782
$641$	1.04348	+	1.80736i	0.0412149	+	0.0713864i	0.885897	−	0.463882i	$-0.153544\pi$
$641$	1.04348	+	1.80736i	0.0412149	+	0.0713864i	−0.844682	+	0.535268i	$0.820210\pi$
$642$	0.692824	−	1.20001i	0.0273436	−	0.0473605i
$643$	1.07099			0.0422359			0.0211179	−	0.999777i	$-0.493277\pi$
$643$	1.07099			0.0422359			0.0211179	+	0.999777i	$0.493277\pi$
$644$	−2.03887	−	3.53143i	−0.0803428	−	0.139158i
$645$	−6.71731	−	11.6347i	−0.264494	−	0.458117i
$646$	−2.51572	−	4.35735i	−0.0989795	−	0.171438i
$647$	17.4463	−	30.2179i	0.685886	−	1.18799i	−0.287271	−	0.957849i	$-0.592748\pi$
$647$	17.4463	−	30.2179i	0.685886	−	1.18799i	0.973157	−	0.230141i	$-0.0739186\pi$
$648$	50.8133	−	88.0113i	1.99614	−	3.45741i
$649$	0.873600	+	1.51312i	0.0342918	+	0.0593951i
$650$	−0.392075	−	0.679094i	−0.0153784	−	0.0266362i
$651$	−16.3234	−	28.2729i	−0.639764	−	1.10810i
$652$	−15.6693			−0.613658
$653$	0.981744	−	1.70043i	0.0384186	−	0.0665430i	−0.846177	−	0.532902i	$-0.821101\pi$
$653$	0.981744	−	1.70043i	0.0384186	−	0.0665430i	0.884595	+	0.466359i	$0.154435\pi$
$654$	−5.82282	−	10.0854i	−0.227690	−	0.394371i
$655$	−1.15066			−0.0449599
$656$	−10.9468			−0.427402
$657$	14.4973	+	25.1100i	0.565593	+	0.979635i
$658$	−11.1081			−0.433041
$659$	−9.77811	+	16.9362i	−0.380901	+	0.659740i	−0.991191	−	0.132438i	$-0.957720\pi$
$659$	−9.77811	+	16.9362i	−0.380901	+	0.659740i	0.610290	+	0.792178i	$0.291053\pi$
$660$	8.94203			0.348068
$661$	−0.987098	+	1.70970i	−0.0383937	+	0.0664998i	−0.884584	−	0.466381i	$-0.845557\pi$
$661$	−0.987098	+	1.70970i	−0.0383937	+	0.0664998i	0.846190	+	0.532881i	$0.178891\pi$
$662$	−0.777499	+	1.34667i	−0.0302184	+	0.0523397i
$663$	−0.676202	+	1.17122i	−0.0262615	+	0.0454863i
$664$	−17.8533	−	30.9228i	−0.692842	−	1.20004i
$665$	9.49479			0.368192
$666$	53.0513	+	16.6508i	2.05570	+	0.645207i
$667$	−13.6546			−0.528708
$668$	−3.72935	−	6.45942i	−0.144293	−	0.249923i
$669$	6.42244	−	11.1240i	0.248306	−	0.430078i
$670$	−6.30859	+	10.9268i	−0.243722	+	0.422139i
$671$	−1.65497	+	2.86650i	−0.0638896	+	0.110660i
$672$	16.1681			0.623698
$673$	−10.3326	+	17.8966i	−0.398292	+	0.689861i	−0.993515	−	0.113699i	$-0.963730\pi$
$673$	−10.3326	+	17.8966i	−0.398292	+	0.689861i	0.595224	+	0.803560i	$0.297063\pi$
$674$	17.1598			0.660971
$675$	−8.60976	−	14.9125i	−0.331390	−	0.573984i
$676$	9.30432			0.357858
$677$	−10.7458			−0.412994			−0.206497	−	0.978447i	$-0.566206\pi$
$677$	−10.7458			−0.412994			−0.206497	+	0.978447i	$0.566206\pi$
$678$	−21.8857	−	37.9072i	−0.840517	−	1.45582i
$679$	6.27875	−	10.8751i	0.240956	−	0.417349i
$680$	−1.77987			−0.0682549
$681$	23.0685	+	39.9559i	0.883988	+	1.53111i
$682$	16.1082	+	27.9002i	0.616815	+	1.06836i
$683$	−6.02617	−	10.4376i	−0.230585	−	0.399385i	0.727396	−	0.686218i	$-0.240731\pi$
$683$	−6.02617	−	10.4376i	−0.230585	−	0.399385i	−0.957980	+	0.286834i	$0.907397\pi$
$684$	23.5220	−	40.7413i	0.899386	−	1.55778i
$685$	−0.955692	+	1.65531i	−0.0365151	+	0.0632460i
$686$	8.57660	+	14.8551i	0.327456	+	0.567171i
$687$	−1.00700	−	1.74418i	−0.0384196	−	0.0665447i
$688$	3.94079	+	6.82565i	0.150241	+	0.260226i
$689$	−6.95383			−0.264920
$690$	8.38355	−	14.5207i	0.319156	−	0.552795i
$691$	−5.15674	−	8.93174i	−0.196172	−	0.339779i	0.751112	−	0.660175i	$-0.229518\pi$
$691$	−5.15674	−	8.93174i	−0.196172	−	0.339779i	−0.947284	+	0.320395i	$0.896184\pi$
$692$	9.89386			0.376108
$693$	−35.9401			−1.36525
$694$	−15.1369	−	26.2178i	−0.574587	−	0.995215i
$695$	−3.78003			−0.143385
$696$	15.6570	−	27.1187i	0.593477	−	1.02793i
$697$	3.23341			0.122474
$698$	11.3868	−	19.7225i	0.430996	−	0.746506i
$699$	−38.9817	+	67.5183i	−1.47442	+	2.55378i
$700$	0.455220	−	0.788464i	0.0172057	−	0.0298011i
$701$	−17.7577	−	30.7573i	−0.670699	−	1.16169i	−0.977706	−	0.209978i	$-0.932661\pi$
$701$	−17.7577	−	30.7573i	−0.670699	−	1.16169i	0.307007	−	0.951707i	$-0.400673\pi$
$702$	13.5027			0.509626
$703$	45.0134	+	14.1280i	1.69771	+	0.532848i
$704$	−30.0624			−1.13302
$705$	13.5198	+	23.4170i	0.509186	+	0.881935i
$706$	2.50519	−	4.33912i	0.0942841	−	0.163305i
$707$	3.36760	−	5.83285i	0.126652	−	0.219367i
$708$	0.602815	−	1.04411i	0.0226552	−	0.0392399i
$709$	−32.6695			−1.22693			−0.613465	−	0.789722i	$-0.710225\pi$
$709$	−32.6695			−1.22693			−0.613465	+	0.789722i	$0.710225\pi$
$710$	0.284331	−	0.492476i	0.0106708	−	0.0184823i
$711$	−31.1065			−1.16658
$712$	22.1168	+	38.3075i	0.828863	+	1.43563i
$713$	−35.7619			−1.33929
$714$	2.65239			0.0992632
$715$	1.25924	+	2.18106i	0.0470928	+	0.0815672i
$716$	3.40488	−	5.89742i	0.127246	−	0.220397i
$717$	−93.8323			−3.50423
$718$	17.5267	+	30.3571i	0.654090	+	1.13292i
$719$	−16.3243	−	28.2746i	−0.608794	−	1.05446i	−0.991439	−	0.130567i	$-0.958320\pi$
$719$	−16.3243	−	28.2746i	−0.608794	−	1.05446i	0.382645	−	0.923895i	$-0.375013\pi$
$720$	7.99020	+	13.8394i	0.297777	+	0.515765i
$721$	−3.82046	+	6.61723i	−0.142281	+	0.246438i
$722$	−23.0651	+	39.9500i	−0.858395	+	1.48678i
$723$	−0.0607951	−	0.105300i	−0.00226099	−	0.00391615i
$724$	7.84829	+	13.5936i	0.291679	+	0.505204i
$725$	−1.52433	−	2.64022i	−0.0566123	−	0.0980554i
$726$	7.33294			0.272151
$727$	7.09098	−	12.2819i	0.262990	−	0.455512i	−0.704045	−	0.710155i	$-0.748625\pi$
$727$	7.09098	−	12.2819i	0.262990	−	0.455512i	0.967035	+	0.254643i	$0.0819581\pi$
$728$	1.31690	+	2.28093i	0.0488074	+	0.0845369i
$729$	96.9728			3.59158
$730$	−3.98480			−0.147484
$731$	−1.16401	−	2.01612i	−0.0430523	−	0.0745688i
$732$	2.28398			0.0844184
$733$	−9.72667	+	16.8471i	−0.359263	+	0.622261i	−0.987838	−	0.155488i	$-0.950305\pi$
$733$	−9.72667	+	16.8471i	−0.359263	+	0.622261i	0.628575	+	0.777749i	$0.283638\pi$
$734$	−18.0752			−0.667168
$735$	9.18732	−	15.9129i	0.338879	−	0.586956i
$736$	8.85542	−	15.3380i	0.326415	−	0.565368i
$737$	20.2615	−	35.0939i	0.746341	−	1.29270i
$738$	−25.5342	−	44.2265i	−0.939926	−	1.62800i
$739$	−52.1774			−1.91938			−0.959689	−	0.281063i	$-0.909313\pi$
$739$	−52.1774			−1.91938			−0.959689	+	0.281063i	$0.909313\pi$
$740$	3.33134	−	3.06063i	0.122463	−	0.112511i
$741$	18.1236			0.665786
$742$	6.81907	+	11.8110i	0.250336	+	0.433594i
$743$	−6.68363	+	11.5764i	−0.245198	+	0.424696i	−0.962187	−	0.272388i	$-0.912186\pi$
$743$	−6.68363	+	11.5764i	−0.245198	+	0.424696i	0.716989	+	0.697085i	$0.245520\pi$
$744$	41.0063	−	71.0249i	1.50336	−	2.60390i
$745$	0.276255	−	0.478487i	0.0101212	−	0.0175304i
$746$	−11.4778			−0.420231
$747$	47.3466	−	82.0067i	1.73232	−	3.00047i
$748$	1.54952			0.0566559
$749$	0.226557	+	0.392408i	0.00827820	+	0.0143383i
$750$	3.74360			0.136697
$751$	16.7410			0.610887			0.305443	−	0.952210i	$-0.401195\pi$
$751$	16.7410			0.610887			0.305443	+	0.952210i	$0.401195\pi$
$752$	−7.93156	−	13.7379i	−0.289234	−	0.500969i
$753$	35.7668	−	61.9500i	1.30342	−	2.25758i
$754$	2.39061			0.0870609
$755$	−4.57907	−	7.93118i	−0.166649	−	0.288645i
$756$	7.83867	+	13.5770i	0.285090	+	0.493790i
$757$	5.63936	+	9.76765i	0.204966	+	0.355011i	0.950122	−	0.311879i	$-0.100958\pi$
$757$	5.63936	+	9.76765i	0.204966	+	0.355011i	−0.745156	+	0.666890i	$0.767625\pi$
$758$	−9.28176	+	16.0765i	−0.337129	+	0.583924i
$759$	−26.9257	+	46.6367i	−0.977340	+	1.69280i
$760$	11.9260	+	20.6565i	0.432602	+	0.749289i
$761$	23.3731	+	40.4834i	0.847275	+	1.46752i	0.883631	+	0.468184i	$0.155092\pi$
$761$	23.3731	+	40.4834i	0.847275	+	1.46752i	−0.0363559	+	0.999339i	$0.511575\pi$
$762$	−33.2238	−	57.5453i	−1.20357	−	2.08464i
$763$	3.80818			0.137865
$764$	−2.79355	+	4.83858i	−0.101067	+	0.175054i
$765$	−2.36009	−	4.08780i	−0.0853293	−	0.147795i
$766$	20.5129			0.741162
$767$	0.339559			0.0122608
$768$	25.1754	+	43.6051i	0.908439	+	1.57346i
$769$	37.8487			1.36486			0.682430	−	0.730951i	$-0.260923\pi$
$769$	37.8487			1.36486			0.682430	+	0.730951i	$0.260923\pi$
$770$	2.46967	−	4.27759i	0.0890007	−	0.154154i
$771$	−2.69790			−0.0971626
$772$	6.15186	−	10.6553i	0.221410	−	0.383494i
$773$	2.07440	−	3.59297i	0.0746110	−	0.129230i	−0.826306	−	0.563221i	$-0.809562\pi$
$773$	2.07440	−	3.59297i	0.0746110	−	0.129230i	0.900917	+	0.433991i	$0.142895\pi$
$774$	−18.3843	+	31.8425i	−0.660810	+	1.14456i
$775$	−3.99228	−	6.91484i	−0.143407	−	0.248388i
$776$	31.5459			1.13243
$777$	−18.3147	+	16.8264i	−0.657036	+	0.603644i
$778$	−16.4451			−0.589587
$779$	−21.6654	−	37.5256i	−0.776245	−	1.34450i
$780$	0.868919	−	1.50501i	0.0311123	−	0.0538881i
$781$	−0.913195	+	1.58170i	−0.0326767	+	0.0565977i
$782$	1.45274	−	2.51622i	0.0519499	−	0.0899798i
$783$	52.4966			1.87608
$784$	−5.38985	+	9.33550i	−0.192495	+	0.333411i
$785$	−2.74164			−0.0978533
$786$	2.15380	+	3.73049i	0.0768234	+	0.133062i
$787$	−42.8205			−1.52639			−0.763193	−	0.646170i	$-0.776370\pi$
$787$	−42.8205			−1.52639			−0.763193	+	0.646170i	$0.776370\pi$
$788$	−1.29910			−0.0462785
$789$	−4.07256	−	7.05387i	−0.144987	−	0.251125i
$790$	2.13752	−	3.70230i	0.0760496	−	0.131722i
$791$	14.3135			0.508928
$792$	−45.1429	−	78.1897i	−1.60408	−	2.77835i
$793$	0.321636	+	0.557089i	0.0114216	+	0.0197828i
$794$	1.12212	+	1.94357i	0.0398226	+	0.0689748i
$795$	16.5991	−	28.7504i	0.588709	−	1.01967i
$796$	−5.51182	+	9.54674i	−0.195361	+	0.338375i
$797$	18.8156	+	32.5896i	0.666482	+	1.15438i	0.978881	+	0.204430i	$0.0655341\pi$
$797$	18.8156	+	32.5896i	0.666482	+	1.15438i	−0.312399	+	0.949951i	$0.601133\pi$
$798$	−17.7723	−	30.7826i	−0.629134	−	1.08969i
$799$	2.34277	+	4.05780i	0.0828814	+	0.143555i
$800$	3.95431			0.139806
$801$	−58.6534	+	101.591i	−2.07242	+	3.58953i
$802$	12.8255	+	22.2143i	0.452883	+	0.784416i
$803$	12.7981			0.451635
$804$	−27.9623			−0.986153
$805$	2.74146	+	4.74835i	0.0966237	+	0.167357i
$806$	6.26110			0.220538
$807$	−20.3017	+	35.1635i	−0.714653	+	1.23781i
$808$	16.9196			0.595230
$809$	11.7837	−	20.4099i	0.414292	−	0.717576i	−0.581061	−	0.813860i	$-0.697362\pi$
$809$	11.7837	−	20.4099i	0.414292	−	0.717576i	0.995354	+	0.0962841i	$0.0306957\pi$
$810$	−18.5199	+	32.0774i	−0.650722	+	1.12708i
$811$	24.7159	−	42.8093i	0.867894	−	1.50324i	0.00374948	−	0.999993i	$-0.498807\pi$
$811$	24.7159	−	42.8093i	0.867894	−	1.50324i	0.864145	−	0.503244i	$-0.167860\pi$
$812$	1.38781	+	2.40376i	0.0487027	+	0.0843555i
$813$	−104.551			−3.66677
$814$	18.0733	−	16.6046i	0.633468	−	0.581991i
$815$	21.0689			0.738012
$816$	1.89389	+	3.28031i	0.0662994	+	0.114834i
$817$	−15.5988	+	27.0180i	−0.545734	+	0.945240i
$818$	−5.10895	+	8.84896i	−0.178630	+	0.309397i
$819$	−3.49238	+	6.04899i	−0.122034	+	0.211369i
$820$	−4.15492			−0.145096
$821$	−12.6853	+	21.9716i	−0.442721	+	0.766815i	−0.997890	−	0.0649222i	$-0.979320\pi$
$821$	−12.6853	+	21.9716i	−0.442721	+	0.766815i	0.555169	+	0.831737i	$0.312653\pi$
$822$	7.15545			0.249575
$823$	4.08512	+	7.07564i	0.142398	+	0.246641i	0.928399	−	0.371584i	$-0.121185\pi$
$823$	4.08512	+	7.07564i	0.142398	+	0.246641i	−0.786001	+	0.618225i	$0.787852\pi$
$824$	−19.1949			−0.668686
$825$	−12.0234			−0.418602
$826$	−0.332979	−	0.576736i	−0.0115858	−	0.0200672i
$827$	0.495060	−	0.857468i	0.0172149	−	0.0298171i	−0.857290	−	0.514834i	$-0.827853\pi$
$827$	0.495060	−	0.857468i	0.0172149	−	0.0298171i	0.874505	+	0.485017i	$0.161187\pi$
$828$	27.1663			0.944094
$829$	13.0618	+	22.6237i	0.453654	+	0.785752i	0.998610	−	0.0527126i	$-0.0167867\pi$
$829$	13.0618	+	22.6237i	0.453654	+	0.785752i	−0.544955	+	0.838465i	$0.683453\pi$
$830$	6.50697	+	11.2704i	0.225860	+	0.391201i
$831$	−38.7303	−	67.0829i	−1.34354	−	2.32708i
$832$	−2.92123	+	5.05972i	−0.101276	+	0.175414i
$833$	1.59202	−	2.75746i	0.0551602	−	0.0955403i
$834$	7.07546	+	12.2551i	0.245003	+	0.424358i
$835$	5.01447	+	8.68532i	0.173533	+	0.300568i
$836$	−10.3825	−	17.9831i	−0.359087	−	0.621957i
$837$	137.490			4.75237
$838$	4.76950	−	8.26102i	0.164760	−	0.285372i
$839$	20.0623	+	34.7490i	0.692629	+	1.19967i	0.970973	+	0.239187i	$0.0768810\pi$
$839$	20.0623	+	34.7490i	0.692629	+	1.19967i	−0.278344	+	0.960481i	$0.589786\pi$
$840$	−12.5739			−0.433842
$841$	−19.7056			−0.679505
$842$	4.95181	+	8.57678i	0.170650	+	0.295575i
$843$	−71.5519			−2.46438
$844$	−6.74400	+	11.6809i	−0.232138	+	0.402075i
$845$	−12.5105			−0.430376
$846$	37.0017	−	64.0889i	1.27215	−	2.20342i
$847$	−1.19895	+	2.07665i	−0.0411965	+	0.0713544i
$848$	−9.73805	+	16.8668i	−0.334406	+	0.579208i
$849$	23.0721	+	39.9621i	0.791833	+	1.37150i
$850$	0.648708			0.0222505
$851$	5.93141	+	26.5904i	0.203326	+	0.911507i
$852$	1.26027			0.0431763
$853$	16.3382	+	28.2985i	0.559408	+	0.968923i	0.997546	+	0.0700154i	$0.0223048\pi$
$853$	16.3382	+	28.2985i	0.559408	+	0.968923i	−0.438138	+	0.898908i	$0.644362\pi$
$854$	0.630805	−	1.09259i	0.0215857	−	0.0373876i
$855$	−31.6276	+	54.7806i	−1.08164	+	1.87346i
$856$	−0.569137	+	0.985774i	−0.0194527	+	0.0336931i
$857$	−9.95029			−0.339896			−0.169948	−	0.985453i	$-0.554360\pi$
$857$	−9.95029			−0.339896			−0.169948	+	0.985453i	$0.554360\pi$
$858$	4.71408	−	8.16503i	0.160936	−	0.278749i
$859$	4.53739			0.154814			0.0774068	−	0.997000i	$-0.475336\pi$
$859$	4.53739			0.154814			0.0774068	+	0.997000i	$0.475336\pi$
$860$	1.49575	+	2.59071i	0.0510045	+	0.0883424i
$861$	22.8425			0.778470
$862$	1.69320			0.0576706
$863$	−1.72742	−	2.99198i	−0.0588020	−	0.101848i	0.835126	−	0.550059i	$-0.185395\pi$
$863$	−1.72742	−	2.99198i	−0.0588020	−	0.101848i	−0.893928	+	0.448211i	$0.852061\pi$
$864$	−34.0457	+	58.9688i	−1.15826	+	2.00616i
$865$	−13.3032			−0.452324
$866$	−3.84349	−	6.65712i	−0.130607	−	0.226218i
$867$	27.8305	+	48.2039i	0.945175	+	1.63709i
$868$	3.63473	+	6.29554i	0.123371	+	0.213685i
$869$	−6.86514	+	11.8908i	−0.232884	+	0.403367i
$870$	−5.70649	+	9.88393i	−0.193468	+	0.335097i
$871$	−3.93771	−	6.82032i	−0.133424	−	0.231098i
$872$	4.78330	+	8.28491i	0.161983	+	0.280562i
$873$	41.8296	+	72.4510i	1.41572	+	2.45210i
$874$	−38.9363			−1.31704
$875$	−0.612087	+	1.06017i	−0.0206923	+	0.0358401i
$876$	−4.41557	−	7.64799i	−0.149188	−	0.258402i
$877$	−23.2726			−0.785861			−0.392931	−	0.919568i	$-0.628539\pi$
$877$	−23.2726			−0.785861			−0.392931	+	0.919568i	$0.628539\pi$
$878$	21.4504			0.723917
$879$	11.8693	+	20.5583i	0.400342	+	0.693413i
$880$	7.05369			0.237780
$881$	−6.16226	+	10.6733i	−0.207612	+	0.359594i	−0.950962	−	0.309309i	$-0.899902\pi$
$881$	−6.16226	+	10.6733i	−0.207612	+	0.359594i	0.743350	+	0.668903i	$0.233236\pi$
$882$	−50.2887			−1.69331
$883$	−8.82778	+	15.2902i	−0.297078	+	0.514555i	−0.975466	−	0.220149i	$-0.929346\pi$
$883$	−8.82778	+	15.2902i	−0.297078	+	0.514555i	0.678388	+	0.734704i	$0.262679\pi$
$884$	0.150570	−	0.260795i	0.00506422	−	0.00877149i
$885$	−0.810543	+	1.40390i	−0.0272461	+	0.0471916i
$886$	1.26481	+	2.19072i	0.0424922	+	0.0735987i
$887$	40.8268			1.37083			0.685415	−	0.728153i	$-0.259621\pi$
$887$	40.8268			1.37083			0.685415	+	0.728153i	$0.259621\pi$
$888$	−59.6112	−	18.7097i	−2.00042	−	0.627857i
$889$	21.7286			0.728755
$890$	−8.06089	−	13.9619i	−0.270202	−	0.468003i
$891$	59.4808	−	103.024i	1.99268	−	3.45143i
$892$	−1.43009	+	2.47698i	−0.0478828	+	0.0829355i
$893$	31.3955	−	54.3786i	1.05061	−	1.81971i
$894$	−2.06837			−0.0691768
$895$	−4.57818	+	7.92965i	−0.153032	+	0.265059i
$896$	1.77697			0.0593644
$897$	5.23287	+	9.06360i	0.174720	+	0.302625i
$898$	−27.3237			−0.911804
$899$	24.3423			0.811861
$900$	3.03272	+	5.25282i	0.101091	+	0.175094i
$901$	2.87636	−	4.98201i	0.0958256	−	0.165975i
$902$	−22.5414			−0.750546
$903$	−8.22315	−	14.2429i	−0.273649	−	0.473975i
$904$	17.9786	+	31.1398i	0.597958	+	1.03569i
$905$	−10.5528	−	18.2780i	−0.350786	−	0.607580i
$906$	−17.1422	+	29.6912i	−0.569511	+	0.986422i
$907$	28.6551	−	49.6320i	0.951475	−	1.64800i	0.209240	−	0.977864i	$-0.432901\pi$
$907$	28.6551	−	49.6320i	0.951475	−	1.64800i	0.742235	−	0.670139i	$-0.233766\pi$
$908$	−5.13668	−	8.89699i	−0.170467	−	0.295257i
$909$	22.4352	+	38.8590i	0.744130	+	1.28887i
$910$	−0.479968	−	0.831328i	−0.0159108	−	0.0275583i
$911$	−21.6237			−0.716426			−0.358213	−	0.933640i	$-0.616614\pi$
$911$	−21.6237			−0.716426			−0.358213	+	0.933640i	$0.616614\pi$
$912$	25.3800	−	43.9595i	0.840417	−	1.45564i
$913$	−20.8986	−	36.1975i	−0.691643	−	1.19796i
$914$	−15.7507			−0.520986
$915$	−3.07103			−0.101525
$916$	0.224230	+	0.388378i	0.00740877	+	0.0128324i
$917$	−1.40860			−0.0465162
$918$	−5.58522	+	9.67388i	−0.184340	+	0.319286i
$919$	30.6901			1.01237			0.506186	−	0.862424i	$-0.331055\pi$
$919$	30.6901			1.01237			0.506186	+	0.862424i	$0.331055\pi$
$920$	−6.88687	+	11.9284i	−0.227053	+	0.393268i
$921$	39.4762	−	68.3748i	1.30079	−	2.25303i
$922$	14.8049	−	25.6429i	0.487575	−	0.844504i
$923$	0.177475	+	0.307395i	0.00584165	+	0.0101180i
$924$	10.9466			0.360117
$925$	−4.47931	+	4.11531i	−0.147279	+	0.135311i
$926$	28.1806			0.926071
$927$	−25.4522	−	44.0846i	−0.835961	−	1.44793i
$928$	−6.02768	+	10.4403i	−0.197868	+	0.342718i
$929$	4.44146	−	7.69284i	0.145720	−	0.252394i	−0.783922	−	0.620860i	$-0.786784\pi$
$929$	4.44146	−	7.69284i	0.145720	−	0.252394i	0.929641	+	0.368466i	$0.120117\pi$
$930$	−14.9455	+	25.8864i	−0.490083	+	0.848848i
$931$	−42.6693			−1.39843
$932$	8.68007	−	15.0343i	0.284325	−	0.492466i
$933$	−64.6652			−2.11704
$934$	7.86317	+	13.6194i	0.257291	+	0.445641i
$935$	−2.08347			−0.0681368
$936$	−17.5466			−0.573527
$937$	−0.306294	−	0.530517i	−0.0100062	−	0.0173312i	0.860979	−	0.508641i	$-0.169852\pi$
$937$	−0.306294	−	0.530517i	−0.0100062	−	0.0173312i	−0.870985	+	0.491309i	$0.836518\pi$
$938$	−7.72281	+	13.3763i	−0.252159	+	0.436751i
$939$	20.4089			0.666019
$940$	−3.01046	−	5.21427i	−0.0981904	−	0.170071i
$941$	−16.6946	−	28.9159i	−0.544229	−	0.942632i	−0.998655	−	0.0518474i	$-0.983489\pi$
$941$	−16.6946	−	28.9159i	−0.544229	−	0.942632i	0.454426	−	0.890784i	$-0.349844\pi$
$942$	5.13180	+	8.88853i	0.167203	+	0.289604i
$943$	12.5110	−	21.6698i	0.407416	−	0.705665i
$944$	0.475515	−	0.823616i	0.0154767	−	0.0268064i
$945$	−10.5398	−	18.2555i	−0.342861	−	0.593853i
$946$	8.11476	+	14.0552i	0.263834	+	0.456973i
$947$	5.18210	+	8.97566i	0.168396	+	0.291670i	0.937856	−	0.347025i	$-0.112808\pi$
$947$	5.18210	+	8.97566i	0.168396	+	0.291670i	−0.769460	+	0.638695i	$0.779475\pi$
$948$	9.47438			0.307714
$949$	1.24362	−	2.15402i	0.0403697	−	0.0699223i
$950$	−4.34667	−	7.52864i	−0.141024	−	0.244261i
$951$	−111.024			−3.60018
$952$	−2.17887			−0.0706176
$953$	−7.44472	−	12.8946i	−0.241158	−	0.417698i	0.719886	−	0.694092i	$-0.244194\pi$
$953$	−7.44472	−	12.8946i	−0.241158	−	0.417698i	−0.961044	+	0.276394i	$0.910861\pi$
$954$	−90.8585			−2.94165
$955$	3.75620	−	6.50593i	0.121548	−	0.210527i
$956$	20.8937			0.675749
$957$	18.3277	−	31.7445i	0.592450	−	1.02615i
$958$	3.74479	−	6.48617i	0.120989	−	0.209559i
$959$	−1.16993	+	2.02638i	−0.0377791	+	0.0654353i
$960$	−13.9462	−	24.1556i	−0.450112	−	0.779617i
$961$	32.7533			1.05656
$962$	−1.03846	−	4.65538i	−0.0334812	−	0.150096i
$963$	−3.01868			−0.0972757
$964$	0.0135373	+	0.0234472i	0.000436006	+	0.000755184i
$965$	−8.27177	+	14.3271i	−0.266278	+	0.461206i
$966$	10.2629	−	17.7759i	0.330204	−	0.571930i
$967$	−21.6538	+	37.5055i	−0.696339	+	1.20609i	0.273389	+	0.961904i	$0.411855\pi$
$967$	−21.6538	+	37.5055i	−0.696339	+	1.20609i	−0.969727	+	0.244190i	$0.921478\pi$
$968$	−6.02382			−0.193613
$969$	−7.49659	+	12.9845i	−0.240825	+	0.417121i
$970$	−11.4975			−0.369163
$971$	−4.45691	−	7.71960i	−0.143029	−	0.247734i	0.785607	−	0.618726i	$-0.212351\pi$
$971$	−4.45691	−	7.71960i	−0.143029	−	0.247734i	−0.928636	+	0.370992i	$0.879018\pi$
$972$	−43.6684			−1.40066
$973$	−4.62741			−0.148348
$974$	4.07170	+	7.05239i	0.130466	+	0.225973i
$975$	−1.16835	+	2.02363i	−0.0374170	+	0.0648081i
$976$	1.80166			0.0576697
$977$	−6.68632	−	11.5810i	−0.213914	−	0.370511i	0.739022	−	0.673681i	$-0.235288\pi$
$977$	−6.68632	−	11.5810i	−0.213914	−	0.370511i	−0.952936	+	0.303171i	$0.901955\pi$
$978$	−39.4368	−	68.3065i	−1.26105	−	2.18420i
$979$	25.8894	+	44.8418i	0.827429	+	1.43315i
$980$	−2.04574	+	3.54333i	−0.0653489	+	0.113188i
$981$	−12.6852	+	21.9714i	−0.405008	+	0.701494i
$982$	−0.250296	−	0.433526i	−0.00798728	−	0.0138344i
$983$	11.5659	+	20.0327i	0.368894	+	0.638944i	0.989393	−	0.145264i	$-0.0464031\pi$
$983$	11.5659	+	20.0327i	0.368894	+	0.638944i	−0.620499	+	0.784208i	$0.713070\pi$
$984$	28.6915	+	49.6952i	0.914652	+	1.58422i
$985$	1.74676			0.0556565
$986$	−0.988847	+	1.71273i	−0.0314913	+	0.0545445i
$987$	16.5506	+	28.6665i	0.526811	+	0.912464i
$988$	−4.03558			−0.128389
$989$	−18.0156			−0.572863
$990$	16.4532	+	28.4977i	0.522916	+	0.905717i
$991$	14.4144			0.457887			0.228944	−	0.973440i	$-0.426473\pi$
$991$	14.4144			0.457887			0.228944	+	0.973440i	$0.426473\pi$
$992$	−15.7867	+	27.3434i	−0.501229	+	0.868154i
$993$	4.63374			0.147047
$994$	0.348071	−	0.602876i	0.0110401	−	0.0191221i
$995$	7.41117	−	12.8365i	0.234950	−	0.406945i
$996$	−14.4208	+	24.9775i	−0.456940	+	0.791444i
$997$	0.509477	+	0.882439i	0.0161353	+	0.0279471i	0.873980	−	0.485961i	$-0.161530\pi$
$997$	0.509477	+	0.882439i	0.0161353	+	0.0279471i	−0.857845	+	0.513908i	$0.828197\pi$
$998$	−11.8859			−0.376243
$999$	−22.8040	−	102.230i	−0.721486	−	3.23441i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	185.2.e.a.26.3	✓	14
5.2	odd	4		925.2.o.b.174.10		28
5.3	odd	4		925.2.o.b.174.5		28
5.4	even	2		925.2.e.c.26.5		14
37.10	even	3	inner	185.2.e.a.121.3	yes	14
37.11	even	6		6845.2.a.k.1.3		7
37.26	even	3		6845.2.a.l.1.5		7
185.47	odd	12		925.2.o.b.824.5		28
185.84	even	6		925.2.e.c.676.5		14
185.158	odd	12		925.2.o.b.824.10		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
185.2.e.a.26.3	✓	14	1.1	even	1	trivial
185.2.e.a.121.3	yes	14	37.10	even	3	inner
925.2.e.c.26.5		14	5.4	even	2
925.2.e.c.676.5		14	185.84	even	6
925.2.o.b.174.5		28	5.3	odd	4
925.2.o.b.174.10		28	5.2	odd	4
925.2.o.b.824.5		28	185.47	odd	12
925.2.o.b.824.10		28	185.158	odd	12
6845.2.a.k.1.3		7	37.11	even	6
6845.2.a.l.1.5		7	37.26	even	3

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:	\( N \)	\(=\)	\( 185 = 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	185.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.560420 - 0.970676i) q^{2} +(-1.67000 + 2.89252i) q^{3} +(0.371859 - 0.644078i) q^{4} +(-0.500000 + 0.866025i) q^{5} +3.74360 q^{6} +(-0.612087 + 1.06017i) q^{7} -3.07527 q^{8} +(-4.07778 - 7.06292i) q^{9} +1.12084 q^{10} -3.59983 q^{11} +(1.24201 + 2.15122i) q^{12} +(-0.349805 + 0.605879i) q^{13} +1.37210 q^{14} +(-1.67000 - 2.89252i) q^{15} +(0.979724 + 1.69693i) q^{16} +(-0.289385 - 0.501229i) q^{17} +(-4.57054 + 7.91640i) q^{18} +(-3.87804 + 6.71697i) q^{19} +(0.371859 + 0.644078i) q^{20} +(-2.04437 - 3.54094i) q^{21} +(2.01742 + 3.49427i) q^{22} -4.47887 q^{23} +(5.13569 - 8.89527i) q^{24} +(-0.500000 - 0.866025i) q^{25} +0.784150 q^{26} +17.2195 q^{27} +(0.455220 + 0.788464i) q^{28} +3.04867 q^{29} +(-1.87180 + 3.24205i) q^{30} +7.98457 q^{31} +(-1.97715 + 3.42453i) q^{32} +(6.01171 - 10.4126i) q^{33} +(-0.324354 + 0.561797i) q^{34} +(-0.612087 - 1.06017i) q^{35} -6.06543 q^{36} +(-1.32431 - 5.93685i) q^{37} +8.69333 q^{38} +(-1.16835 - 2.02363i) q^{39} +(1.53763 - 2.66326i) q^{40} +(-2.79335 + 4.83822i) q^{41} +(-2.29141 + 3.96883i) q^{42} +4.02235 q^{43} +(-1.33863 + 2.31857i) q^{44} +8.15556 q^{45} +(2.51005 + 4.34753i) q^{46} -8.09571 q^{47} -6.54454 q^{48} +(2.75070 + 4.76435i) q^{49} +(-0.560420 + 0.970676i) q^{50} +1.93309 q^{51} +(0.260156 + 0.450603i) q^{52} +(4.96979 + 8.60794i) q^{53} +(-9.65017 - 16.7146i) q^{54} +(1.79992 - 3.11755i) q^{55} +(1.88233 - 3.26029i) q^{56} +(-12.9526 - 22.4346i) q^{57} +(-1.70853 - 2.95927i) q^{58} +(-0.242678 - 0.420330i) q^{59} -2.48401 q^{60} +(0.459736 - 0.796287i) q^{61} +(-4.47471 - 7.75043i) q^{62} +9.98382 q^{63} +8.35104 q^{64} +(-0.349805 - 0.605879i) q^{65} -13.4763 q^{66} +(-5.62845 + 9.74876i) q^{67} -0.430441 q^{68} +(7.47970 - 12.9552i) q^{69} +(-0.686051 + 1.18828i) q^{70} +(0.253677 - 0.439381i) q^{71} +(12.5403 + 21.7204i) q^{72} -3.55519 q^{73} +(-5.02059 + 4.61261i) q^{74} +3.33999 q^{75} +(2.88417 + 4.99553i) q^{76} +(2.20341 - 3.81642i) q^{77} +(-1.30953 + 2.26817i) q^{78} +(1.90707 - 3.30314i) q^{79} -1.95945 q^{80} +(-16.5232 + 28.6191i) q^{81} +6.26179 q^{82} +(5.80544 + 10.0553i) q^{83} -3.04086 q^{84} +0.578769 q^{85} +(-2.25421 - 3.90440i) q^{86} +(-5.09126 + 8.81833i) q^{87} +11.0705 q^{88} +(-7.19183 - 12.4566i) q^{89} +(-4.57054 - 7.91640i) q^{90} +(-0.428221 - 0.741701i) q^{91} +(-1.66551 + 2.88475i) q^{92} +(-13.3342 + 23.0955i) q^{93} +(4.53700 + 7.85831i) q^{94} +(-3.87804 - 6.71697i) q^{95} +(-6.60368 - 11.4379i) q^{96} -10.2579 q^{97} +(3.08309 - 5.34008i) q^{98} +(14.6793 + 25.4253i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{3} - 8 q^{4} - 7 q^{5} - 4 q^{6} + 6 q^{8} - 13 q^{9} - 2 q^{11} + 6 q^{12} + 4 q^{13} + 20 q^{14} - 2 q^{15} + 2 q^{16} - 3 q^{17} - 6 q^{18} - 14 q^{19} - 8 q^{20} + q^{21} + 7 q^{22} + 15 q^{24}+ \cdots + 56 q^{99}+O(q^{100}) \) 14 * q - 2 * q^3 - 8 * q^4 - 7 * q^5 - 4 * q^6 + 6 * q^8 - 13 * q^9 - 2 * q^11 + 6 * q^12 + 4 * q^13 + 20 * q^14 - 2 * q^15 + 2 * q^16 - 3 * q^17 - 6 * q^18 - 14 * q^19 - 8 * q^20 + q^21 + 7 * q^22 + 15 * q^24 - 7 * q^25 - 22 * q^26 - 14 * q^27 + 9 * q^28 - 12 * q^29 + 2 * q^30 + 4 * q^32 - 11 * q^33 + 33 * q^34 + 40 * q^36 + 18 * q^37 - 4 * q^38 - 25 * q^39 - 3 * q^40 - 7 * q^41 - 29 * q^42 + 38 * q^43 - 19 * q^44 + 26 * q^45 - 14 * q^46 + 8 * q^47 + 36 * q^48 + 5 * q^49 + 58 * q^51 - 8 * q^52 - 6 * q^53 - 9 * q^54 + q^55 - 25 * q^56 - 44 * q^57 - 12 * q^58 + 2 * q^59 - 12 * q^60 - 4 * q^61 - 25 * q^62 + 10 * q^63 - 62 * q^64 + 4 * q^65 - 2 * q^66 - 8 * q^67 + 26 * q^68 - 11 * q^69 - 10 * q^70 + 33 * q^71 + 43 * q^72 + 18 * q^74 + 4 * q^75 - 12 * q^76 - 5 * q^77 - 22 * q^78 - 9 * q^79 - 4 * q^80 - 35 * q^81 + 152 * q^82 - 11 * q^83 - 80 * q^84 + 6 * q^85 + 17 * q^86 - 29 * q^87 + 40 * q^88 - 12 * q^89 - 6 * q^90 - 24 * q^91 - 7 * q^92 - 47 * q^93 + 10 * q^94 - 14 * q^95 - 15 * q^96 + 30 * q^97 + 54 * q^98 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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