LMFDB - Embedded newform 61.2.c.a.47.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [61,2,Mod(13,61)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(61, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("61.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 61 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	61.c (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.487087452330$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.310217769.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 4x^{6} - 2x^{5} + 15x^{4} - 4x^{3} + 5x^{2} + x + 1 $ x^8 + 4x^6 - 2x^5 + 15x^4 - 4x^3 + 5*x^2 + x + 1
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			47.3
Root			$-0.198169 - 0.343239i$ of defining polynomial
Character	$\chi$	$=$	61.47
Dual form			61.2.c.a.13.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.198169 + 0.343239i) q^{2} -0.716159 q^{3} +(0.921458 - 1.59601i) q^{4} +(1.82493 + 3.16087i) q^{5} +(-0.141921 - 0.245814i) q^{6} +(-1.26155 - 2.18506i) q^{7} +1.52310 q^{8} -2.48712 q^{9} +O(q^{10})$	\(q+(0.198169 + 0.343239i) q^{2} -0.716159 q^{3} +(0.921458 - 1.59601i) q^{4} +(1.82493 + 3.16087i) q^{5} +(-0.141921 - 0.245814i) q^{6} +(-1.26155 - 2.18506i) q^{7} +1.52310 q^{8} -2.48712 q^{9} +(-0.723289 + 1.25277i) q^{10} -4.36601 q^{11} +(-0.659910 + 1.14300i) q^{12} +(0.443751 + 0.768600i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-1.30694 - 2.26368i) q^{15} +(-1.54109 - 2.66924i) q^{16} +(2.14475 - 3.71481i) q^{17} +(-0.492870 - 0.853676i) q^{18} +(-2.69014 + 4.65945i) q^{19} +6.72637 q^{20} +(0.903468 + 1.56485i) q^{21} +(-0.865209 - 1.49859i) q^{22} +4.92509 q^{23} -1.09078 q^{24} +(-4.16071 + 7.20656i) q^{25} +(-0.175876 + 0.304626i) q^{26} +3.92965 q^{27} -4.64985 q^{28} +(-3.71413 + 6.43307i) q^{29} +(0.517989 - 0.897184i) q^{30} +(3.66502 - 6.34799i) q^{31} +(2.13389 - 3.69600i) q^{32} +3.12676 q^{33} +1.70009 q^{34} +(4.60446 - 7.97516i) q^{35} +(-2.29177 + 3.96947i) q^{36} +5.30716 q^{37} -2.13241 q^{38} +(-0.317796 - 0.550440i) q^{39} +(2.77954 + 4.81430i) q^{40} +0.964021 q^{41} +(-0.358079 + 0.620212i) q^{42} +(-0.230419 - 0.399097i) q^{43} +(-4.02310 + 6.96821i) q^{44} +(-4.53880 - 7.86144i) q^{45} +(0.976001 + 1.69048i) q^{46} +(-2.23755 + 3.87555i) q^{47} +(1.10366 + 1.91160i) q^{48} +(0.316994 - 0.549050i) q^{49} -3.29810 q^{50} +(-1.53598 + 2.66039i) q^{51} +1.63559 q^{52} -0.555027 q^{53} +(0.778735 + 1.34881i) q^{54} +(-7.96765 - 13.8004i) q^{55} +(-1.92146 - 3.32806i) q^{56} +(1.92656 - 3.33691i) q^{57} -2.94411 q^{58} +(1.91715 + 3.32061i) q^{59} -4.81715 q^{60} +(-1.48882 - 7.66703i) q^{61} +2.90517 q^{62} +(3.13762 + 5.43451i) q^{63} -4.47286 q^{64} +(-1.61963 + 2.80528i) q^{65} +(0.619627 + 1.07323i) q^{66} +(1.15586 + 2.00201i) q^{67} +(-3.95259 - 6.84608i) q^{68} -3.52714 q^{69} +3.64985 q^{70} +(-1.47600 + 2.55651i) q^{71} -3.78812 q^{72} +(-5.96254 + 10.3274i) q^{73} +(1.05172 + 1.82163i) q^{74} +(2.97973 - 5.16104i) q^{75} +(4.95769 + 8.58698i) q^{76} +(5.50793 + 9.54002i) q^{77} +(0.125955 - 0.218160i) q^{78} +(-1.20903 - 2.09410i) q^{79} +(5.62473 - 9.74232i) q^{80} +4.64710 q^{81} +(0.191039 + 0.330890i) q^{82} +(0.751592 + 1.30180i) q^{83} +3.33003 q^{84} +15.6560 q^{85} +(0.0913237 - 0.158177i) q^{86} +(2.65991 - 4.60710i) q^{87} -6.64985 q^{88} +3.10048 q^{89} +(1.79890 - 3.11579i) q^{90} +(1.11963 - 1.93925i) q^{91} +(4.53826 - 7.86050i) q^{92} +(-2.62473 + 4.54617i) q^{93} -1.77365 q^{94} -19.6372 q^{95} +(-1.52820 + 2.64692i) q^{96} +(9.54529 - 16.5329i) q^{97} +0.251274 q^{98} +10.8588 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 2 q^{5} - q^{6} - q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) $ 8 * q - 6 * q^3 - 2 * q^5 - q^6 - q^7 - 6 * q^8 + 2 * q^9	\( 8 q - 6 q^{3} - 2 q^{5} - q^{6} - q^{7} - 6 q^{8} + 2 q^{9} - 2 q^{11} - 7 q^{12} + 5 q^{13} + 4 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 10 q^{18} + q^{19} + 14 q^{20} - 2 q^{21} - q^{22} - 8 q^{23} + 10 q^{24} - 8 q^{25} + 9 q^{26} - 30 q^{27} - 4 q^{28} - 16 q^{29} + 6 q^{30} + 11 q^{31} - 4 q^{32} + 10 q^{33} - 28 q^{34} + 13 q^{35} + 15 q^{36} + 4 q^{37} + 24 q^{38} + 8 q^{39} + 15 q^{40} + 4 q^{41} - 3 q^{42} + 10 q^{43} - 14 q^{44} - 27 q^{45} - q^{46} + 12 q^{48} + 19 q^{49} - 14 q^{50} - 16 q^{51} - 8 q^{52} + 38 q^{53} + 26 q^{54} - 20 q^{55} - 8 q^{56} - 12 q^{57} - 58 q^{58} + q^{59} + 20 q^{60} + 10 q^{61} + 14 q^{62} + 18 q^{63} - 26 q^{64} - 4 q^{65} - 4 q^{66} - 17 q^{67} - 27 q^{68} - 38 q^{69} - 4 q^{70} - 3 q^{71} - 38 q^{72} - 24 q^{73} + 20 q^{74} + 29 q^{75} + 15 q^{76} + 11 q^{77} + 13 q^{78} - 16 q^{79} + 16 q^{80} + 72 q^{81} + 6 q^{82} + 16 q^{83} - 10 q^{84} + 24 q^{85} - 24 q^{86} + 23 q^{87} - 20 q^{88} + 8 q^{89} - 25 q^{90} + 33 q^{92} + 8 q^{93} + 74 q^{94} - 82 q^{95} + 26 q^{96} + 13 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 2 * q^5 - q^6 - q^7 - 6 * q^8 + 2 * q^9 - 2 * q^11 - 7 * q^12 + 5 * q^13 + 4 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 10 * q^18 + q^19 + 14 * q^20 - 2 * q^21 - q^22 - 8 * q^23 + 10 * q^24 - 8 * q^25 + 9 * q^26 - 30 * q^27 - 4 * q^28 - 16 * q^29 + 6 * q^30 + 11 * q^31 - 4 * q^32 + 10 * q^33 - 28 * q^34 + 13 * q^35 + 15 * q^36 + 4 * q^37 + 24 * q^38 + 8 * q^39 + 15 * q^40 + 4 * q^41 - 3 * q^42 + 10 * q^43 - 14 * q^44 - 27 * q^45 - q^46 + 12 * q^48 + 19 * q^49 - 14 * q^50 - 16 * q^51 - 8 * q^52 + 38 * q^53 + 26 * q^54 - 20 * q^55 - 8 * q^56 - 12 * q^57 - 58 * q^58 + q^59 + 20 * q^60 + 10 * q^61 + 14 * q^62 + 18 * q^63 - 26 * q^64 - 4 * q^65 - 4 * q^66 - 17 * q^67 - 27 * q^68 - 38 * q^69 - 4 * q^70 - 3 * q^71 - 38 * q^72 - 24 * q^73 + 20 * q^74 + 29 * q^75 + 15 * q^76 + 11 * q^77 + 13 * q^78 - 16 * q^79 + 16 * q^80 + 72 * q^81 + 6 * q^82 + 16 * q^83 - 10 * q^84 + 24 * q^85 - 24 * q^86 + 23 * q^87 - 20 * q^88 + 8 * q^89 - 25 * q^90 + 33 * q^92 + 8 * q^93 + 74 * q^94 - 82 * q^95 + 26 * q^96 + 13 * q^97 - 2 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/61\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.198169	+	0.343239i	0.140127	+	0.242707i	0.927544	−	0.373713i	$-0.121916\pi$
$2$	0.198169	+	0.343239i	0.140127	+	0.242707i	−0.787417	+	0.616420i	$0.788582\pi$
$3$	−0.716159			−0.413474			−0.206737	−	0.978397i	$-0.566285\pi$
$3$	−0.716159			−0.413474			−0.206737	+	0.978397i	$0.566285\pi$
$4$	0.921458	−	1.59601i	0.460729	−	0.798006i
$5$	1.82493	+	3.16087i	0.816132	+	1.41358i	0.908512	+	0.417858i	$0.137219\pi$
$5$	1.82493	+	3.16087i	0.816132	+	1.41358i	−0.0923805	+	0.995724i	$0.529448\pi$
$6$	−0.141921	−	0.245814i	−0.0579389	−	0.100353i
$7$	−1.26155	−	2.18506i	−0.476820	−	0.825877i	0.522827	−	0.852439i	$-0.324877\pi$
$7$	−1.26155	−	2.18506i	−0.476820	−	0.825877i	−0.999647	+	0.0265620i	$0.991544\pi$
$8$	1.52310			0.538496
$9$	−2.48712			−0.829039
$10$	−0.723289	+	1.25277i	−0.228724	+	0.396161i
$11$	−4.36601			−1.31640			−0.658201	−	0.752842i	$-0.728682\pi$
$11$	−4.36601			−1.31640			−0.658201	+	0.752842i	$0.728682\pi$
$12$	−0.659910	+	1.14300i	−0.190500	+	0.329955i
$13$	0.443751	+	0.768600i	0.123074	+	0.213171i	0.920979	−	0.389613i	$-0.127391\pi$
$13$	0.443751	+	0.768600i	0.123074	+	0.213171i	−0.797904	+	0.602784i	$0.794058\pi$
$14$	0.500000	−	0.866025i	0.133631	−	0.231455i
$15$	−1.30694	−	2.26368i	−0.337450	−	0.584480i
$16$	−1.54109	−	2.66924i	−0.385271	−	0.667309i
$17$	2.14475	−	3.71481i	0.520177	−	0.900974i	−0.479547	−	0.877516i	$-0.659199\pi$
$17$	2.14475	−	3.71481i	0.520177	−	0.900974i	0.999725	−	0.0234578i	$-0.00746752\pi$
$18$	−0.492870	−	0.853676i	−0.116171	−	0.201213i
$19$	−2.69014	+	4.65945i	−0.617159	+	1.06895i	0.372842	+	0.927895i	$0.378383\pi$
$19$	−2.69014	+	4.65945i	−0.617159	+	1.06895i	−0.990002	+	0.141057i	$0.954950\pi$
$20$	6.72637			1.50406
$21$	0.903468	+	1.56485i	0.197153	+	0.341479i
$22$	−0.865209	−	1.49859i	−0.184463	−	0.319500i
$23$	4.92509			1.02695			0.513476	−	0.858104i	$-0.328358\pi$
$23$	4.92509			1.02695			0.513476	+	0.858104i	$0.328358\pi$
$24$	−1.09078			−0.222654
$25$	−4.16071	+	7.20656i	−0.832142	+	1.44131i
$26$	−0.175876	+	0.304626i	−0.0344921	+	0.0597420i
$27$	3.92965			0.756261
$28$	−4.64985			−0.878740
$29$	−3.71413	+	6.43307i	−0.689698	+	1.19459i	0.282238	+	0.959344i	$0.408923\pi$
$29$	−3.71413	+	6.43307i	−0.689698	+	1.19459i	−0.971936	+	0.235247i	$0.924410\pi$
$30$	0.517989	−	0.897184i	0.0945715	−	0.163803i
$31$	3.66502	−	6.34799i	0.658256	−	1.14013i	−0.322810	−	0.946464i	$-0.604628\pi$
$31$	3.66502	−	6.34799i	0.658256	−	1.14013i	0.981067	−	0.193670i	$-0.0620390\pi$
$32$	2.13389	−	3.69600i	0.377221	−	0.653367i
$33$	3.12676			0.544299
$34$	1.70009			0.291563
$35$	4.60446	−	7.97516i	0.778296	−	1.34805i
$36$	−2.29177	+	3.96947i	−0.381962	+	0.661578i
$37$	5.30716			0.872492			0.436246	−	0.899827i	$-0.356308\pi$
$37$	5.30716			0.872492			0.436246	+	0.899827i	$0.356308\pi$
$38$	−2.13241			−0.345922
$39$	−0.317796	−	0.550440i	−0.0508882	−	0.0881409i
$40$	2.77954	+	4.81430i	0.439483	+	0.761208i
$41$	0.964021			0.150555			0.0752774	−	0.997163i	$-0.476016\pi$
$41$	0.964021			0.150555			0.0752774	+	0.997163i	$0.476016\pi$
$42$	−0.358079	+	0.620212i	−0.0552528	+	0.0957007i
$43$	−0.230419	−	0.399097i	−0.0351385	−	0.0608617i	0.847921	−	0.530122i	$-0.177854\pi$
$43$	−0.230419	−	0.399097i	−0.0351385	−	0.0608617i	−0.883060	+	0.469260i	$0.844521\pi$
$44$	−4.02310	+	6.96821i	−0.606504	+	1.05050i
$45$	−4.53880	−	7.86144i	−0.676605	−	1.17191i
$46$	0.976001	+	1.69048i	0.143903	+	0.249248i
$47$	−2.23755	+	3.87555i	−0.326380	+	0.565307i	−0.981791	−	0.189966i	$-0.939162\pi$
$47$	−2.23755	+	3.87555i	−0.326380	+	0.565307i	0.655411	+	0.755273i	$0.272496\pi$
$48$	1.10366	+	1.91160i	0.159300	+	0.275915i
$49$	0.316994	−	0.549050i	0.0452849	−	0.0784358i
$50$	−3.29810			−0.466422
$51$	−1.53598	+	2.66039i	−0.215080	+	0.372530i
$52$	1.63559			0.226816
$53$	−0.555027			−0.0762388			−0.0381194	−	0.999273i	$-0.512137\pi$
$53$	−0.555027			−0.0762388			−0.0381194	+	0.999273i	$0.512137\pi$
$54$	0.778735	+	1.34881i	0.105972	+	0.183550i
$55$	−7.96765	−	13.8004i	−1.07436	−	1.86084i
$56$	−1.92146	−	3.32806i	−0.256766	−	0.444731i
$57$	1.92656	−	3.33691i	0.255180	−	0.441984i
$58$	−2.94411			−0.386581
$59$	1.91715	+	3.32061i	0.249592	+	0.432306i	0.963413	−	0.268022i	$-0.0863701\pi$
$59$	1.91715	+	3.32061i	0.249592	+	0.432306i	−0.713821	+	0.700329i	$0.753037\pi$
$60$	−4.81715			−0.621891
$61$	−1.48882	−	7.66703i	−0.190624	−	0.981663i
$61$	−1.48882	−	7.66703i	−0.190624	−	0.981663i
$62$	2.90517			0.368958
$63$	3.13762	+	5.43451i	0.395303	+	0.684684i
$64$	−4.47286			−0.559107
$65$	−1.61963	+	2.80528i	−0.200890	+	0.347952i
$66$	0.619627	+	1.07323i	0.0762708	+	0.132105i
$67$	1.15586	+	2.00201i	0.141211	+	0.244585i	0.927953	−	0.372697i	$-0.121567\pi$
$67$	1.15586	+	2.00201i	0.141211	+	0.244585i	−0.786742	+	0.617282i	$0.788234\pi$
$68$	−3.95259	−	6.84608i	−0.479322	−	0.830209i
$69$	−3.52714			−0.424618
$70$	3.64985			0.436241
$71$	−1.47600	+	2.55651i	−0.175169	+	0.303402i	−0.940220	−	0.340568i	$-0.889381\pi$
$71$	−1.47600	+	2.55651i	−0.175169	+	0.303402i	0.765051	+	0.643970i	$0.222714\pi$
$72$	−3.78812			−0.446434
$73$	−5.96254	+	10.3274i	−0.697863	+	1.20873i	0.271343	+	0.962483i	$0.412532\pi$
$73$	−5.96254	+	10.3274i	−0.697863	+	1.20873i	−0.969206	+	0.246251i	$0.920801\pi$
$74$	1.05172	+	1.82163i	0.122260	+	0.211760i
$75$	2.97973	−	5.16104i	0.344070	−	0.595946i
$76$	4.95769	+	8.58698i	0.568686	+	0.984994i
$77$	5.50793	+	9.54002i	0.627687	+	1.08719i
$78$	0.125955	−	0.218160i	0.0142616	−	0.0247018i
$79$	−1.20903	−	2.09410i	−0.136026	−	0.235605i	0.789963	−	0.613155i	$-0.210100\pi$
$79$	−1.20903	−	2.09410i	−0.136026	−	0.235605i	−0.925989	+	0.377550i	$0.876767\pi$
$80$	5.62473	−	9.74232i	0.628864	−	1.08922i
$81$	4.64710			0.516344
$82$	0.191039	+	0.330890i	0.0210968	+	0.0365407i
$83$	0.751592	+	1.30180i	0.0824979	+	0.142891i	0.904322	−	0.426850i	$-0.140377\pi$
$83$	0.751592	+	1.30180i	0.0824979	+	0.142891i	−0.821824	+	0.569741i	$0.807044\pi$
$84$	3.33003			0.363336
$85$	15.6560			1.69813
$86$	0.0913237	−	0.158177i	0.00984769	−	0.0170567i
$87$	2.65991	−	4.60710i	0.285172	−	0.493933i
$88$	−6.64985			−0.708877
$89$	3.10048			0.328650			0.164325	−	0.986406i	$-0.447455\pi$
$89$	3.10048			0.328650			0.164325	+	0.986406i	$0.447455\pi$
$90$	1.79890	−	3.11579i	0.189621	−	0.328433i
$91$	1.11963	−	1.93925i	0.117369	−	0.203289i
$92$	4.53826	−	7.86050i	0.473146	−	0.819513i
$93$	−2.62473	+	4.54617i	−0.272172	+	0.471416i
$94$	−1.77365			−0.182938
$95$	−19.6372			−2.01473
$96$	−1.52820	+	2.64692i	−0.155971	+	0.270150i
$97$	9.54529	−	16.5329i	0.969177	−	1.67866i	0.271230	−	0.962515i	$-0.412570\pi$
$97$	9.54529	−	16.5329i	0.969177	−	1.67866i	0.697947	−	0.716149i	$-0.254097\pi$
$98$	0.251274			0.0253825
$99$	10.8588			1.09135
$100$	7.66784	+	13.2811i	0.766784	+	1.32811i
$101$	0.796725	+	1.37997i	0.0792771	+	0.137312i	0.902938	−	0.429770i	$-0.141405\pi$
$101$	0.796725	+	1.37997i	0.0792771	+	0.137312i	−0.823661	+	0.567082i	$0.808072\pi$
$102$	−1.21754			−0.120554
$103$	−5.51021	+	9.54397i	−0.542937	+	0.940395i	0.455796	+	0.890084i	$0.349355\pi$
$103$	−5.51021	+	9.54397i	−0.542937	+	0.940395i	−0.998734	+	0.0503109i	$0.983979\pi$
$104$	0.675876	+	1.17065i	0.0662751	+	0.114792i
$105$	−3.29753	+	5.71148i	−0.321806	+	0.557384i
$106$	−0.109989	−	0.190507i	−0.0106831	−	0.0185037i
$107$	−3.76235	−	6.51658i	−0.363720	−	0.629982i	0.624850	−	0.780745i	$-0.285160\pi$
$107$	−3.76235	−	6.51658i	−0.363720	−	0.629982i	−0.988570	+	0.150763i	$0.951827\pi$
$108$	3.62100	−	6.27176i	0.348431	−	0.603501i
$109$	−0.285547	−	0.494582i	−0.0273505	−	0.0473724i	0.852026	−	0.523499i	$-0.175374\pi$
$109$	−0.285547	−	0.494582i	−0.0273505	−	0.0473724i	−0.879377	+	0.476127i	$0.842040\pi$
$110$	3.15789	−	5.46962i	0.301093	−	0.521508i
$111$	−3.80077			−0.360753
$112$	−3.88830	+	6.73474i	−0.367410	+	0.636373i
$113$	−14.5333			−1.36718			−0.683589	−	0.729867i	$-0.739582\pi$
$113$	−14.5333			−1.36718			−0.683589	+	0.729867i	$0.739582\pi$
$114$	1.52714			0.143030
$115$	8.98792	+	15.5675i	0.838128	+	1.45168i
$116$	6.84484	+	11.8556i	0.635527	+	1.10077i
$117$	−1.10366	−	1.91160i	−0.102034	−	0.176727i
$118$	−0.759842	+	1.31608i	−0.0699491	+	0.121155i
$119$	−10.8228			−0.992125
$120$	−1.99059	−	3.44780i	−0.181715	−	0.314740i
$121$	8.06206			0.732914
$122$	2.33659	−	2.03039i	0.211545	−	0.183823i
$123$	−0.690392			−0.0622506
$124$	−6.75432	−	11.6988i	−0.606556	−	1.05058i
$125$	−12.1227			−1.08429
$126$	−1.24356	+	2.15391i	−0.110785	+	0.191885i
$127$	−8.66662	−	15.0110i	−0.769038	−	1.33201i	−0.938085	−	0.346405i	$-0.887402\pi$
$127$	−8.66662	−	15.0110i	−0.769038	−	1.33201i	0.169047	−	0.985608i	$-0.445931\pi$
$128$	−5.15416	−	8.92726i	−0.455567	−	0.789066i
$129$	0.165016	+	0.285817i	0.0145289	+	0.0251647i
$130$	−1.28384			−0.112600
$131$	−1.53055			−0.133725			−0.0668626	−	0.997762i	$-0.521299\pi$
$131$	−1.53055			−0.133725			−0.0668626	+	0.997762i	$0.521299\pi$
$132$	2.88117	−	4.99034i	0.250774	−	0.434353i
$133$	13.5749			1.17710
$134$	−0.458113	+	0.793475i	−0.0395749	+	0.0685458i
$135$	7.17132	+	12.4211i	0.617209	+	1.06904i
$136$	3.26665	−	5.65801i	0.280113	−	0.485170i
$137$	6.57764	+	11.3928i	0.561966	+	0.973353i	0.997325	+	0.0730961i	$0.0232880\pi$
$137$	6.57764	+	11.3928i	0.561966	+	0.973353i	−0.435359	+	0.900257i	$0.643379\pi$
$138$	−0.698971	−	1.21065i	−0.0595004	−	0.103058i
$139$	0.602859	−	1.04418i	0.0511339	−	0.0885665i	−0.839326	−	0.543629i	$-0.817050\pi$
$139$	0.602859	−	1.04418i	0.0511339	−	0.0885665i	0.890459	+	0.455063i	$0.150383\pi$
$140$	−8.48564	−	14.6976i	−0.717167	−	1.24217i
$141$	1.60244	−	2.77551i	0.134950	−	0.233740i
$142$	−1.16999			−0.0981835
$143$	−1.93742	−	3.35572i	−0.162015	−	0.280619i
$144$	3.83286	+	6.63871i	0.319405	+	0.553225i
$145$	−27.1121			−2.25154
$146$	−4.72637			−0.391157
$147$	−0.227018	+	0.393207i	−0.0187241	+	0.0324312i
$148$	4.89033	−	8.47030i	0.401983	−	0.696254i
$149$	−19.1768			−1.57102			−0.785512	−	0.618846i	$-0.787600\pi$
$149$	−19.1768			−1.57102			−0.785512	+	0.618846i	$0.787600\pi$
$150$	2.36196			0.192854
$151$	−10.2515	+	17.7561i	−0.834254	+	1.44497i	0.0603815	+	0.998175i	$0.480768\pi$
$151$	−10.2515	+	17.7561i	−0.834254	+	1.44497i	−0.894636	+	0.446796i	$0.852565\pi$
$152$	−4.09733	+	7.09679i	−0.332338	+	0.575626i
$153$	−5.33423	+	9.23917i	−0.431247	+	0.746942i
$154$	−2.18301	+	3.78108i	−0.175912	+	0.304688i
$155$	26.7535			2.14890
$156$	−1.17134			−0.0937826
$157$	2.37835	−	4.11942i	0.189813	−	0.328766i	−0.755375	−	0.655293i	$-0.772545\pi$
$157$	2.37835	−	4.11942i	0.189813	−	0.328766i	0.945188	+	0.326527i	$0.105879\pi$
$158$	0.479185	−	0.829972i	0.0381219	−	0.0660290i
$159$	0.397487			0.0315228
$160$	15.5767			1.23145
$161$	−6.21323	−	10.7616i	−0.489671	−	0.848135i
$162$	0.920912	+	1.59507i	0.0723537	+	0.125320i
$163$	14.1426			1.10774			0.553868	−	0.832605i	$-0.313151\pi$
$163$	14.1426			1.10774			0.553868	+	0.832605i	$0.313151\pi$
$164$	0.888305	−	1.53859i	0.0693650	−	0.120144i
$165$	5.70610	+	9.88326i	0.444219	+	0.769411i
$166$	−0.297885	+	0.515952i	−0.0231204	+	0.0400456i
$167$	−0.521748	−	0.903694i	−0.0403741	−	0.0699299i	0.845132	−	0.534557i	$-0.179522\pi$
$167$	−0.521748	−	0.903694i	−0.0403741	−	0.0699299i	−0.885506	+	0.464627i	$0.846188\pi$
$168$	1.37607	+	2.38342i	0.106166	+	0.183885i
$169$	6.10617	−	10.5762i	0.469705	−	0.813554i
$170$	3.10254	+	5.37376i	0.237954	+	0.412149i
$171$	6.69068	−	11.5886i	0.511649	−	0.886202i
$172$	−0.849284			−0.0647573
$173$	8.36884	−	14.4953i	0.636271	−	1.10205i	−0.349973	−	0.936760i	$-0.613809\pi$
$173$	8.36884	−	14.4953i	0.636271	−	1.10205i	0.986244	−	0.165294i	$-0.0528573\pi$
$174$	2.10845			0.159841
$175$	20.9957			1.58713
$176$	6.72839	+	11.6539i	0.507172	+	0.878447i
$177$	−1.37299	−	2.37808i	−0.103200	−	0.178748i
$178$	0.614419	+	1.06421i	0.0460527	+	0.0797656i
$179$	−3.69467	+	6.39935i	−0.276152	+	0.478310i	−0.970425	−	0.241402i	$-0.922393\pi$
$179$	−3.69467	+	6.39935i	−0.276152	+	0.478310i	0.694273	+	0.719712i	$0.255726\pi$
$180$	−16.7293			−1.24693
$181$	−10.1720	−	17.6185i	−0.756082	−	1.30957i	−0.944835	−	0.327548i	$-0.893778\pi$
$181$	−10.1720	−	17.6185i	−0.756082	−	1.30957i	0.188752	−	0.982025i	$-0.439556\pi$
$182$	0.887503			0.0657861
$183$	1.06623	+	5.49081i	0.0788182	+	0.405893i
$184$	7.50138			0.553009
$185$	9.68518	+	16.7752i	0.712069	+	1.23334i
$186$	−2.08057			−0.152554
$187$	−9.36399	+	16.2189i	−0.684763	+	1.18604i
$188$	4.12361	+	7.14231i	0.300745	+	0.520906i
$189$	−4.95744	−	8.58653i	−0.360600	−	0.624578i
$190$	−3.89149	−	6.74026i	−0.282318	−	0.488990i
$191$	−24.7981			−1.79433			−0.897165	−	0.441696i	$-0.854377\pi$
$191$	−24.7981			−1.79433			−0.897165	+	0.441696i	$0.854377\pi$
$192$	3.20328			0.231176
$193$	4.84792	−	8.39684i	0.348961	−	0.604418i	−0.637104	−	0.770778i	$-0.719868\pi$
$193$	4.84792	−	8.39684i	0.348961	−	0.604418i	0.986065	+	0.166360i	$0.0532013\pi$
$194$	7.56633			0.543231
$195$	1.15991	−	2.00902i	0.0830629	−	0.143869i
$196$	−0.584194	−	1.01185i	−0.0417281	−	0.0722752i
$197$	−2.16864	+	3.75620i	−0.154510	+	0.267618i	−0.932880	−	0.360186i	$-0.882713\pi$
$197$	−2.16864	+	3.75620i	−0.154510	+	0.267618i	0.778371	+	0.627805i	$0.216046\pi$
$198$	2.15188	+	3.72716i	0.152927	+	0.264878i
$199$	5.94398	+	10.2953i	0.421358	+	0.729813i	0.996073	−	0.0885410i	$-0.0282204\pi$
$199$	5.94398	+	10.2953i	0.421358	+	0.729813i	−0.574715	+	0.818354i	$0.694887\pi$
$200$	−6.33716	+	10.9763i	−0.448105	+	0.776141i
$201$	−0.827781	−	1.43376i	−0.0583872	−	0.101130i
$202$	−0.315773	+	0.546934i	−0.0222177	+	0.0384822i
$203$	18.7422			1.31545
$204$	2.83068	+	4.90288i	0.198187	+	0.343270i
$205$	1.75927	+	3.04714i	0.122873	+	0.212822i
$206$	−4.36782			−0.304320
$207$	−12.2493			−0.851383
$208$	1.36772	−	2.36896i	0.0948341	−	0.164258i
$209$	11.7452	−	20.3432i	0.812430	−	1.40717i
$210$	−2.61387			−0.180374
$211$	5.73093			0.394534			0.197267	−	0.980350i	$-0.436793\pi$
$211$	5.73093			0.394534			0.197267	+	0.980350i	$0.436793\pi$
$212$	−0.511434	+	0.885830i	−0.0351254	+	0.0608390i
$213$	1.05705	−	1.83087i	0.0724279	−	0.125449i
$214$	1.49116	−	2.58277i	0.101934	−	0.176555i
$215$	0.840994	−	1.45664i	0.0573553	−	0.0993423i
$216$	5.98523			0.407243
$217$	−18.4944			−1.25548
$218$	0.113173	−	0.196022i	0.00766507	−	0.0132763i
$219$	4.27013	−	7.39608i	0.288548	−	0.499781i
$220$	−29.3674			−1.97995
$221$	3.80694			0.256082
$222$	−0.753196	−	1.30457i	−0.0505512	−	0.0875573i
$223$	6.40969	+	11.1019i	0.429225	+	0.743439i	0.996805	−	0.0798792i	$-0.0254534\pi$
$223$	6.40969	+	11.1019i	0.429225	+	0.743439i	−0.567580	+	0.823318i	$0.692120\pi$
$224$	−10.7680			−0.719467
$225$	10.3482	−	17.9236i	0.689878	−	1.19490i
$226$	−2.88005	−	4.98840i	−0.191578	−	0.331824i
$227$	7.61465	−	13.1890i	0.505402	−	0.875382i	−0.494579	−	0.869133i	$-0.664678\pi$
$227$	7.61465	−	13.1890i	0.505402	−	0.875382i	0.999980	−	0.00624882i	$-0.00198907\pi$
$228$	−3.55050	−	6.14964i	−0.235137	−	0.407270i
$229$	7.66151	+	13.2701i	0.506287	+	0.876915i	0.999974	+	0.00727501i	$0.00231573\pi$
$229$	7.66151	+	13.2701i	0.506287	+	0.876915i	−0.493686	+	0.869640i	$0.664351\pi$
$230$	−3.56226	+	6.17001i	−0.234888	+	0.406839i
$231$	−3.94455	−	6.83217i	−0.259533	−	0.449524i
$232$	−5.65698	+	9.79818i	−0.371399	+	0.643282i
$233$	−10.8456			−0.710520			−0.355260	−	0.934768i	$-0.615608\pi$
$233$	−10.8456			−0.710520			−0.355260	+	0.934768i	$0.615608\pi$
$234$	0.437424	−	0.757640i	0.0285953	−	0.0495285i
$235$	−16.3334			−1.06548
$236$	7.06631			0.459977
$237$	0.865857	+	1.49971i	0.0562434	+	0.0974165i
$238$	−2.14475	−	3.71481i	−0.139023	−	0.240795i
$239$	3.56428	+	6.17352i	0.230554	+	0.399332i	0.957971	−	0.286864i	$-0.0926127\pi$
$239$	3.56428	+	6.17352i	0.230554	+	0.399332i	−0.727417	+	0.686196i	$0.759279\pi$
$240$	−4.02820	+	6.97705i	−0.260019	+	0.450367i
$241$	1.81086			0.116648			0.0583239	−	0.998298i	$-0.481424\pi$
$241$	1.81086			0.116648			0.0583239	+	0.998298i	$0.481424\pi$
$242$	1.59765	+	2.76721i	0.102701	+	0.177883i
$243$	−15.1170			−0.969756
$244$	−13.6086	−	4.68867i	−0.871199	−	0.300161i
$245$	2.31397			0.147834
$246$	−0.136814	−	0.236970i	−0.00872297	−	0.0151086i
$247$	−4.77501			−0.303826
$248$	5.58217	−	9.66860i	0.354468	−	0.613957i
$249$	−0.538259	−	0.932292i	−0.0341108	−	0.0590816i
$250$	−2.40235	−	4.16099i	−0.151938	−	0.263164i
$251$	5.13155	+	8.88810i	0.323900	+	0.561012i	0.981289	−	0.192540i	$-0.0616724\pi$
$251$	5.13155	+	8.88810i	0.323900	+	0.561012i	−0.657389	+	0.753551i	$0.728339\pi$
$252$	11.5647			0.728509
$253$	−21.5030			−1.35188
$254$	3.43492	−	5.94945i	0.215526	−	0.373302i
$255$	−11.2122			−0.702135
$256$	−2.43007	+	4.20900i	−0.151879	+	0.263062i
$257$	15.1940	+	26.3168i	0.947777	+	1.64160i	0.750093	+	0.661332i	$0.230009\pi$
$257$	15.1940	+	26.3168i	0.947777	+	1.64160i	0.197684	+	0.980266i	$0.436658\pi$
$258$	−0.0654023	+	0.113280i	−0.00407177	+	0.00705251i
$259$	−6.69524	−	11.5965i	−0.416022	−	0.720571i
$260$	2.98484	+	5.16989i	0.185112	+	0.320623i
$261$	9.23749	−	15.9998i	0.571786	−	0.990363i
$262$	−0.303309	−	0.525346i	−0.0187385	−	0.0324560i
$263$	3.29177	−	5.70152i	0.202979	−	0.351571i	−0.746508	−	0.665377i	$-0.768271\pi$
$263$	3.29177	−	5.70152i	0.202979	−	0.351571i	0.949487	+	0.313806i	$0.101604\pi$
$264$	4.76235			0.293102
$265$	−1.01288	−	1.75437i	−0.0622209	−	0.107770i
$266$	2.69014	+	4.65945i	0.164943	+	0.285689i
$267$	−2.22043			−0.135888
$268$	4.26031			0.260240
$269$	−3.01654	+	5.22480i	−0.183922	+	0.318562i	−0.943213	−	0.332190i	$-0.892213\pi$
$269$	−3.01654	+	5.22480i	−0.183922	+	0.318562i	0.759291	+	0.650751i	$0.225546\pi$
$270$	−2.84227	+	4.92295i	−0.172975	+	0.299601i
$271$	26.7289			1.62366			0.811831	−	0.583892i	$-0.198471\pi$
$271$	26.7289			1.62366			0.811831	+	0.583892i	$0.198471\pi$
$272$	−13.2209			−0.801638
$273$	−0.801831	+	1.38881i	−0.0485290	+	0.0840547i
$274$	−2.60697	+	4.51541i	−0.157493	+	0.272786i
$275$	18.1657	−	31.4639i	1.09543	−	1.89735i
$276$	−3.25011	+	5.62936i	−0.195634	+	0.338848i
$277$	−12.7372			−0.765305			−0.382653	−	0.923892i	$-0.624989\pi$
$277$	−12.7372			−0.765305			−0.382653	+	0.923892i	$0.624989\pi$
$278$	0.477873			0.0286609
$279$	−9.11532	+	15.7882i	−0.545720	+	0.945215i
$280$	7.01304	−	12.1469i	0.419109	−	0.725918i
$281$	3.70819			0.221212			0.110606	−	0.993864i	$-0.464721\pi$
$281$	3.70819			0.221212			0.110606	+	0.993864i	$0.464721\pi$
$282$	1.27022			0.0756403
$283$	9.62294	+	16.6674i	0.572024	+	0.990775i	0.996358	+	0.0852692i	$0.0271750\pi$
$283$	9.62294	+	16.6674i	0.572024	+	0.990775i	−0.424334	+	0.905506i	$0.639492\pi$
$284$	2.72014	+	4.71143i	0.161411	+	0.279572i
$285$	14.0633			0.833041
$286$	0.767876	−	1.33000i	0.0454054	−	0.0786445i
$287$	−1.21616	−	2.10645i	−0.0717876	−	0.124340i
$288$	−5.30723	+	9.19238i	−0.312731	+	0.541666i
$289$	−0.699875	−	1.21222i	−0.0411691	−	0.0713070i
$290$	−5.37278	−	9.30593i	−0.315501	−	0.546463i
$291$	−6.83594	+	11.8402i	−0.400730	+	0.694085i
$292$	10.9885	+	19.0326i	0.643051	+	1.11380i
$293$	6.29665	−	10.9061i	0.367854	−	0.637142i	−0.621376	−	0.783513i	$-0.713426\pi$
$293$	6.29665	−	10.9061i	0.367854	−	0.637142i	0.989230	+	0.146371i	$0.0467592\pi$
$294$	−0.179952			−0.0104950
$295$	−6.99733	+	12.1197i	−0.407400	+	0.705638i
$296$	8.08332			0.469833
$297$	−17.1569			−0.995543
$298$	−3.80025	−	6.58223i	−0.220143	−	0.381298i
$299$	2.18551	+	3.78542i	0.126392	+	0.218917i
$300$	−5.49139	−	9.51137i	−0.317046	−	0.549139i
$301$	−0.581368	+	1.00696i	−0.0335095	+	0.0580401i
$302$	−8.12612			−0.467606
$303$	−0.570581	−	0.988276i	−0.0327790	−	0.0567750i
$304$	16.5829			0.951095
$305$	21.5175	−	18.6977i	1.23209	−	1.07063i
$306$	−4.22833			−0.241717
$307$	1.40671	+	2.43650i	0.0802854	+	0.139058i	0.903373	−	0.428857i	$-0.141083\pi$
$307$	1.40671	+	2.43650i	0.0802854	+	0.139058i	−0.823087	+	0.567915i	$0.807750\pi$
$308$	20.3013			1.15677
$309$	3.94619	−	6.83500i	0.224491	−	0.388829i
$310$	5.30173	+	9.18286i	0.301118	+	0.521552i
$311$	−6.33026	−	10.9643i	−0.358956	−	0.621730i	0.628831	−	0.777542i	$-0.283534\pi$
$311$	−6.33026	−	10.9643i	−0.358956	−	0.621730i	−0.987787	+	0.155812i	$0.950201\pi$
$312$	−0.484034	−	0.838372i	−0.0274030	−	0.0474635i
$313$	12.1666			0.687696			0.343848	−	0.939025i	$-0.388270\pi$
$313$	12.1666			0.687696			0.343848	+	0.939025i	$0.388270\pi$
$314$	1.88526			0.106392
$315$	−11.4518	+	19.8352i	−0.645238	+	1.11758i
$316$	−4.45628			−0.250685
$317$	−2.58818	+	4.48286i	−0.145367	+	0.251782i	−0.929510	−	0.368798i	$-0.879770\pi$
$317$	−2.58818	+	4.48286i	−0.145367	+	0.251782i	0.784143	+	0.620580i	$0.213103\pi$
$318$	0.0787698	+	0.136433i	0.00441719	+	0.00765080i
$319$	16.2160	−	28.0869i	0.907919	−	1.57256i
$320$	−8.16263	−	14.1381i	−0.456305	−	0.790344i
$321$	2.69444	+	4.66691i	0.150389	+	0.260481i
$322$	2.46254	−	4.26525i	0.137232	−	0.237693i
$323$	11.5393	+	19.9867i	0.642065	+	1.11209i
$324$	4.28211	−	7.41683i	0.237895	−	0.412046i
$325$	−7.38529			−0.409662
$326$	2.80263	+	4.85430i	0.155223	+	0.268855i
$327$	0.204497	+	0.354199i	0.0113087	+	0.0195873i
$328$	1.46830			0.0810731
$329$	11.2911			0.622498
$330$	−2.26155	+	3.91712i	−0.124494	+	0.215630i
$331$	−6.74603	+	11.6845i	−0.370795	+	0.642236i	−0.989688	−	0.143239i	$-0.954248\pi$
$331$	−6.74603	+	11.6845i	−0.370795	+	0.642236i	0.618893	+	0.785475i	$0.287581\pi$
$332$	2.77024			0.152037
$333$	−13.1995			−0.723330
$334$	0.206789	−	0.358169i	0.0113150	−	0.0195981i
$335$	−4.21873	+	7.30705i	−0.230494	+	0.399227i
$336$	2.78464	−	4.82314i	0.151915	−	0.263124i
$337$	13.8008	−	23.9038i	0.751779	−	1.30212i	−0.195180	−	0.980767i	$-0.562529\pi$
$337$	13.8008	−	23.9038i	0.751779	−	1.30212i	0.946960	−	0.321353i	$-0.104138\pi$
$338$	4.84022			0.263273
$339$	10.4082			0.565293
$340$	14.4264	−	24.9872i	0.782379	−	1.35512i
$341$	−16.0015	+	27.7154i	−0.866530	+	1.50087i
$342$	5.30355			0.286783
$343$	−19.2613			−1.04001
$344$	−0.350949	−	0.607862i	−0.0189219	−	0.0327737i
$345$	−6.43678	−	11.1488i	−0.346544	−	0.600232i
$346$	6.63379			0.356635
$347$	−16.6106	+	28.7704i	−0.891703	+	1.54448i	−0.0538704	+	0.998548i	$0.517156\pi$
$347$	−16.6106	+	28.7704i	−0.891703	+	1.54448i	−0.837833	+	0.545927i	$0.816178\pi$
$348$	−4.90199	−	8.49050i	−0.262774	−	0.455138i
$349$	−7.89906	+	13.6816i	−0.422827	+	0.732358i	−0.996215	−	0.0869261i	$-0.972296\pi$
$349$	−7.89906	+	13.6816i	−0.422827	+	0.732358i	0.573388	+	0.819284i	$0.305629\pi$
$350$	4.16071	+	7.20656i	0.222399	+	0.385207i
$351$	1.74379	+	3.02033i	0.0930764	+	0.161213i
$352$	−9.31657	+	16.1368i	−0.496575	+	0.860093i
$353$	8.04577	+	13.9357i	0.428233	+	0.741722i	0.996716	−	0.0809733i	$-0.0258028\pi$
$353$	8.04577	+	13.9357i	0.428233	+	0.741722i	−0.568483	+	0.822695i	$0.692470\pi$
$354$	0.544167	−	0.942526i	0.0289222	−	0.0500947i
$355$	−10.7744			−0.571844
$356$	2.85696	−	4.94840i	0.151419	−	0.262265i
$357$	7.75084			0.410218
$358$	−2.92868			−0.154785
$359$	−12.7646	−	22.1090i	−0.673691	−	1.16687i	−0.976850	−	0.213927i	$-0.931374\pi$
$359$	−12.7646	−	22.1090i	−0.673691	−	1.16687i	0.303158	−	0.952940i	$-0.401959\pi$
$360$	−6.91303	−	11.9737i	−0.364349	−	0.631071i
$361$	−4.97366	−	8.61463i	−0.261772	−	0.453402i
$362$	4.03157	−	6.98289i	0.211895	−	0.367013i
$363$	−5.77371			−0.303041
$364$	−2.06338	−	3.57388i	−0.108150	−	0.187322i
$365$	−43.5248			−2.27819
$366$	−1.67337	+	1.45408i	−0.0874683	+	0.0760062i
$367$	4.77673			0.249343			0.124672	−	0.992198i	$-0.460212\pi$
$367$	4.77673			0.249343			0.124672	+	0.992198i	$0.460212\pi$
$368$	−7.58998	−	13.1462i	−0.395655	−	0.685294i
$369$	−2.39763			−0.124816
$370$	−3.83861	+	6.64867i	−0.199560	+	0.345648i
$371$	0.700193	+	1.21277i	0.0363522	+	0.0629639i
$372$	4.83716	+	8.37821i	0.250795	+	0.434390i
$373$	−12.0480	−	20.8678i	−0.623822	−	1.08049i	−0.988767	−	0.149463i	$-0.952246\pi$
$373$	−12.0480	−	20.8678i	−0.623822	−	1.08049i	0.364945	−	0.931029i	$-0.381088\pi$
$374$	−7.42262			−0.383814
$375$	8.68178			0.448325
$376$	−3.40800	+	5.90283i	−0.175754	+	0.304415i
$377$	−6.59261			−0.339537
$378$	1.96482	−	3.40317i	0.101060	−	0.175040i
$379$	−2.84484	−	4.92740i	−0.146130	−	0.253104i	0.783664	−	0.621185i	$-0.213348\pi$
$379$	−2.84484	−	4.92740i	−0.146130	−	0.253104i	−0.929794	+	0.368081i	$0.880015\pi$
$380$	−18.0949	+	31.3412i	−0.928246	+	1.60777i
$381$	6.20668	+	10.7503i	0.317978	+	0.550753i
$382$	−4.91423	−	8.51169i	−0.251434	−	0.435496i
$383$	9.23399	−	15.9937i	0.471835	−	0.817241i	−0.527646	−	0.849464i	$-0.676925\pi$
$383$	9.23399	−	15.9937i	0.471835	−	0.817241i	0.999481	+	0.0322228i	$0.0102586\pi$
$384$	3.69119	+	6.39334i	0.188365	+	0.326259i
$385$	−20.1031	+	34.8197i	−1.02455	+	1.77457i
$386$	3.84284			0.195595
$387$	0.573078	+	0.992600i	0.0291312	+	0.0504567i
$388$	−17.5912	−	30.4688i	−0.893056	−	1.54682i
$389$	24.7174			1.25322			0.626610	−	0.779333i	$-0.284442\pi$
$389$	24.7174			1.25322			0.626610	+	0.779333i	$0.284442\pi$
$390$	0.919434			0.0465574
$391$	10.5631	−	18.2958i	0.534197	−	0.925256i
$392$	0.482813	−	0.836256i	0.0243857	−	0.0422373i
$393$	1.09612			0.0552919
$394$	−1.71903			−0.0866037
$395$	4.41278	−	7.64315i	0.222031	−	0.384569i
$396$	10.0059	−	17.3307i	0.502816	−	0.870903i
$397$	−3.37064	+	5.83813i	−0.169168	+	0.293007i	−0.938128	−	0.346290i	$-0.887441\pi$
$397$	−3.37064	+	5.83813i	−0.169168	+	0.293007i	0.768960	+	0.639297i	$0.220775\pi$
$398$	−2.35583	+	4.08041i	−0.118087	+	0.204533i
$399$	−9.72181			−0.486699
$400$	25.6480			1.28240
$401$	6.28327	−	10.8829i	0.313771	−	0.543468i	−0.665404	−	0.746483i	$-0.731741\pi$
$401$	6.28327	−	10.8829i	0.313771	−	0.543468i	0.979176	+	0.203015i	$0.0650741\pi$
$402$	0.328082	−	0.568254i	0.0163632	−	0.0283419i
$403$	6.50542			0.324058
$404$	2.93659			0.146101
$405$	8.48061	+	14.6889i	0.421405	+	0.729895i
$406$	3.71413	+	6.43307i	0.184329	+	0.319268i
$407$	−23.1711			−1.14855
$408$	−2.33944	+	4.05203i	−0.115820	+	0.200606i
$409$	1.94953	+	3.37669i	0.0963982	+	0.166967i	0.910191	−	0.414188i	$-0.135934\pi$
$409$	1.94953	+	3.37669i	0.0963982	+	0.166967i	−0.813793	+	0.581155i	$0.802601\pi$
$410$	−0.697265	+	1.20770i	−0.0344355	+	0.0596440i
$411$	−4.71063	−	8.15906i	−0.232358	−	0.402457i
$412$	10.1549	+	17.5887i	0.500294	+	0.866534i
$413$	4.83716	−	8.37821i	0.238021	−	0.412265i
$414$	−2.42743	−	4.20443i	−0.119302	−	0.206636i
$415$	−2.74320	+	4.75136i	−0.134658	+	0.233235i
$416$	3.78766			0.185705
$417$	−0.431743	+	0.747801i	−0.0211425	+	0.0366200i
$418$	9.31012			0.455373
$419$	18.9331			0.924940			0.462470	−	0.886635i	$-0.346963\pi$
$419$	18.9331			0.924940			0.462470	+	0.886635i	$0.346963\pi$
$420$	6.07706	+	10.5258i	0.296530	+	0.513606i
$421$	−12.9581	−	22.4442i	−0.631541	−	1.09386i	−0.987237	−	0.159259i	$-0.949089\pi$
$421$	−12.9581	−	22.4442i	−0.631541	−	1.09386i	0.355696	−	0.934602i	$-0.384244\pi$
$422$	1.13569	+	1.96708i	0.0552847	+	0.0957560i
$423$	5.56504	−	9.63894i	0.270582	−	0.468661i
$424$	−0.845359			−0.0410543
$425$	17.8473	+	30.9125i	0.865723	+	1.49948i
$426$	0.837900			0.0405964
$427$	−14.8747	+	12.9255i	−0.719839	+	0.625509i
$428$	−13.8674			−0.670305
$429$	1.38750	+	2.40323i	0.0669893	+	0.116029i
$430$	0.666636			0.0321481
$431$	12.9904	−	22.5001i	0.625727	−	1.08379i	−0.362673	−	0.931916i	$-0.618136\pi$
$431$	12.9904	−	22.5001i	0.625727	−	1.08379i	0.988400	−	0.151874i	$-0.0485309\pi$
$432$	−6.05592	−	10.4892i	−0.291366	−	0.504660i
$433$	11.2528	+	19.4905i	0.540777	+	0.936653i	0.998860	+	0.0477435i	$0.0152030\pi$
$433$	11.2528	+	19.4905i	0.540777	+	0.936653i	−0.458083	+	0.888910i	$0.651464\pi$
$434$	−3.66502	−	6.34799i	−0.175926	−	0.304713i
$435$	19.4166			0.930953
$436$	−1.05248			−0.0504046
$437$	−13.2491	+	22.9482i	−0.633793	+	1.09776i
$438$	3.38483			0.161734
$439$	0.480952	−	0.833033i	0.0229546	−	0.0397585i	−0.854320	−	0.519748i	$-0.826026\pi$
$439$	0.480952	−	0.833033i	0.0229546	−	0.0397585i	0.877275	+	0.479989i	$0.159359\pi$
$440$	−12.1355	−	21.0193i	−0.578537	−	1.00206i
$441$	−0.788402	+	1.36555i	−0.0375429	+	0.0650263i
$442$	0.754418	+	1.30669i	0.0358840	+	0.0621529i
$443$	−3.43492	−	5.94945i	−0.163198	−	0.282667i	0.772816	−	0.634630i	$-0.218848\pi$
$443$	−3.43492	−	5.94945i	−0.163198	−	0.282667i	−0.936014	+	0.351963i	$0.885514\pi$
$444$	−3.50225	+	6.06608i	−0.166209	+	0.287883i
$445$	5.65814	+	9.80019i	0.268222	+	0.464574i
$446$	−2.54041	+	4.40012i	−0.120292	+	0.208352i
$447$	13.7336			0.649578
$448$	5.64272	+	9.77348i	0.266594	+	0.461754i
$449$	−5.34079	−	9.25052i	−0.252047	−	0.436559i	0.712042	−	0.702137i	$-0.247771\pi$
$449$	−5.34079	−	9.25052i	−0.252047	−	0.436559i	−0.964089	+	0.265578i	$0.914437\pi$
$450$	8.20276			0.386682
$451$	−4.20893			−0.198191
$452$	−13.3918	+	23.1953i	−0.629899	+	1.09102i
$453$	7.34169	−	12.7162i	0.344943	−	0.597459i
$454$	6.03596			0.283281
$455$	8.17295			0.383154
$456$	2.93434	−	5.08243i	0.137413	−	0.238006i
$457$	−3.49945	+	6.06123i	−0.163698	+	0.283533i	−0.936192	−	0.351489i	$-0.885675\pi$
$457$	−3.49945	+	6.06123i	−0.163698	+	0.283533i	0.772494	+	0.635022i	$0.219009\pi$
$458$	−3.03655	+	5.25946i	−0.141889	+	0.245759i
$459$	8.42810	−	14.5979i	0.393390	−	0.681371i
$460$	33.1280			1.54460
$461$	5.77526			0.268981			0.134490	−	0.990915i	$-0.457060\pi$
$461$	5.77526			0.268981			0.134490	+	0.990915i	$0.457060\pi$
$462$	1.56338	−	2.70785i	0.0727350	−	0.125981i
$463$	−5.60187	+	9.70272i	−0.260341	+	0.450923i	−0.966332	−	0.257297i	$-0.917168\pi$
$463$	−5.60187	+	9.70272i	−0.260341	+	0.450923i	0.705992	+	0.708220i	$0.250502\pi$
$464$	22.8952			1.06288
$465$	−19.1598			−0.888514
$466$	−2.14927	−	3.72264i	−0.0995629	−	0.172448i
$467$	−17.0665	−	29.5600i	−0.789742	−	1.36787i	−0.926125	−	0.377217i	$-0.876881\pi$
$467$	−17.0665	−	29.5600i	−0.789742	−	1.36787i	0.136383	−	0.990656i	$-0.456452\pi$
$468$	−4.06791			−0.188039
$469$	2.91635	−	5.05127i	0.134665	−	0.233246i
$470$	−3.23679	−	5.60628i	−0.149302	−	0.258598i
$471$	−1.70328	+	2.95016i	−0.0784828	+	0.135936i
$472$	2.92001	+	5.05760i	0.134404	+	0.232795i
$473$	1.00601	+	1.74246i	0.0462564	+	0.0801184i
$474$	−0.343172	+	0.594392i	−0.0157624	+	0.0273013i
$475$	−22.3858	−	38.7733i	−1.02713	−	1.77904i
$476$	−9.97276	+	17.2733i	−0.457100	+	0.791721i
$477$	1.38042			0.0632049
$478$	−1.41266	+	2.44680i	−0.0646137	+	0.111914i
$479$	−21.6236			−0.988006			−0.494003	−	0.869460i	$-0.664467\pi$
$479$	−21.6236			−0.988006			−0.494003	+	0.869460i	$0.664467\pi$
$480$	−11.1554			−0.509173
$481$	2.35506	+	4.07909i	0.107382	+	0.185990i
$482$	0.358857	+	0.621559i	0.0163455	+	0.0283112i
$483$	4.44966	+	7.70704i	0.202467	+	0.350682i
$484$	7.42884	−	12.8671i	0.337675	−	0.584870i
$485$	69.6778			3.16391
$486$	−2.99572	−	5.18875i	−0.135889	−	0.235366i
$487$	43.4768			1.97012			0.985062	−	0.172202i	$-0.0550883\pi$
$487$	43.4768			1.97012			0.985062	+	0.172202i	$0.0550883\pi$
$488$	−2.26762	−	11.6776i	−0.102650	−	0.528621i
$489$	−10.1284			−0.458020
$490$	0.458557	+	0.794244i	0.0207155	+	0.0358803i
$491$	−12.6884			−0.572619			−0.286309	−	0.958137i	$-0.592428\pi$
$491$	−12.6884			−0.572619			−0.286309	+	0.958137i	$0.592428\pi$
$492$	−0.636167	+	1.10187i	−0.0286806	+	0.0496763i
$493$	15.9318	+	27.5946i	0.717530	+	1.24280i
$494$	−0.946259	−	1.63897i	−0.0425742	−	0.0737407i
$495$	19.8165	+	34.3231i	0.890684	+	1.54271i
$496$	−22.5924			−1.01443
$497$	7.44818			0.334097
$498$	0.213333	−	0.369503i	0.00955967	−	0.0165578i
$499$	8.93711			0.400080			0.200040	−	0.979788i	$-0.435893\pi$
$499$	8.93711			0.400080			0.200040	+	0.979788i	$0.435893\pi$
$500$	−11.1706	+	19.3480i	−0.499563	+	0.865268i
$501$	0.373654	+	0.647188i	0.0166936	+	0.0289142i
$502$	−2.03383	+	3.52270i	−0.0907742	+	0.157226i
$503$	−0.305015	−	0.528301i	−0.0135999	−	0.0235558i	0.859145	−	0.511732i	$-0.170996\pi$
$503$	−0.305015	−	0.528301i	−0.0135999	−	0.0235558i	−0.872745	+	0.488176i	$0.837662\pi$
$504$	4.77889	+	8.27728i	0.212869	+	0.368699i
$505$	−2.90793	+	5.03668i	−0.129401	+	0.224129i
$506$	−4.26123	−	7.38067i	−0.189435	−	0.328111i
$507$	−4.37299	+	7.57423i	−0.194211	+	0.336384i
$508$	−31.9437			−1.41727
$509$	−10.1083	−	17.5081i	−0.448043	−	0.776034i	0.550215	−	0.835023i	$-0.314546\pi$
$509$	−10.1083	−	17.5081i	−0.448043	−	0.776034i	−0.998259	+	0.0589890i	$0.981212\pi$
$510$	−2.22191	−	3.84846i	−0.0983879	−	0.170413i
$511$	30.0881			1.33102
$512$	−22.5429			−0.996264
$513$	−10.5713	+	18.3100i	−0.466733	+	0.808406i
$514$	−6.02198	+	10.4304i	−0.265618	+	0.460064i
$515$	−40.2229			−1.77243
$516$	0.608222			0.0267755
$517$	9.76916	−	16.9207i	0.429647	−	0.744171i
$518$	2.65358	−	4.59614i	0.116592	−	0.201943i
$519$	−5.99342	+	10.3809i	−0.263082	+	0.455671i
$520$	−2.46685	+	4.27270i	−0.108178	+	0.187370i
$521$	−35.3195			−1.54738			−0.773688	−	0.633567i	$-0.781590\pi$
$521$	−35.3195			−1.54738			−0.773688	+	0.633567i	$0.781590\pi$
$522$	7.32234			0.320490
$523$	−9.79155	+	16.9595i	−0.428154	+	0.741585i	−0.996709	−	0.0810602i	$-0.974169\pi$
$523$	−9.79155	+	16.9595i	−0.428154	+	0.741585i	0.568555	+	0.822645i	$0.307503\pi$
$524$	−1.41034	+	2.44278i	−0.0616111	+	0.106714i
$525$	−15.0363			−0.656237
$526$	2.60931			0.113771
$527$	−15.7211	−	27.2297i	−0.684820	−	1.18614i
$528$	−4.81860	−	8.34606i	−0.209703	−	0.363216i
$529$	1.25647			0.0546292
$530$	0.401445	−	0.695323i	0.0174376	−	0.0302029i
$531$	−4.76819	−	8.25874i	−0.206922	−	0.358399i
$532$	12.5087	−	21.6658i	0.542322	−	0.939330i
$533$	0.427786	+	0.740947i	0.0185295	+	0.0320940i
$534$	−0.440022	−	0.762140i	−0.0190416	−	0.0329810i
$535$	13.7320	−	23.7846i	0.593687	−	1.02830i
$536$	1.76049	+	3.04926i	0.0760416	+	0.131708i
$537$	2.64597	−	4.58295i	0.114182	−	0.197769i
$538$	−2.39114			−0.103089
$539$	−1.38400	+	2.39716i	−0.0596131	+	0.103253i
$540$	26.4323			1.13746
$541$	−14.7092			−0.632396			−0.316198	−	0.948693i	$-0.602406\pi$
$541$	−14.7092			−0.632396			−0.316198	+	0.948693i	$0.602406\pi$
$542$	5.29684	+	9.17439i	0.227519	+	0.394074i
$543$	7.28480	+	12.6176i	0.312621	+	0.541475i
$544$	−9.15329	−	15.8540i	−0.392444	−	0.679733i
$545$	1.04221	−	1.80515i	0.0446432	−	0.0773242i
$546$	−0.635593			−0.0272009
$547$	−6.47999	−	11.2237i	−0.277064	−	0.479889i	0.693590	−	0.720370i	$-0.256028\pi$
$547$	−6.47999	−	11.2237i	−0.277064	−	0.479889i	−0.970654	+	0.240481i	$0.922695\pi$
$548$	24.2441			1.03566
$549$	3.70288	+	19.0688i	0.158035	+	0.813837i
$550$	14.3995			0.613999
$551$	−19.9831	−	34.6117i	−0.851307	−	1.47451i
$552$	−5.37218			−0.228655
$553$	−3.05050	+	5.28361i	−0.129720	+	0.224682i
$554$	−2.52413	−	4.37191i	−0.107240	−	0.185745i
$555$	−6.93613	−	12.0137i	−0.294422	−	0.509954i
$556$	−1.11102	−	1.92434i	−0.0471177	−	0.0816103i
$557$	26.5978			1.12699			0.563493	−	0.826121i	$-0.309457\pi$
$557$	26.5978			1.12699			0.563493	+	0.826121i	$0.309457\pi$
$558$	−7.22551			−0.305880
$559$	0.204497	−	0.354199i	0.00864930	−	0.0149810i
$560$	−28.3835			−1.19942
$561$	6.70610	−	11.6153i	0.283132	−	0.490399i
$562$	0.734849	+	1.27280i	0.0309977	+	0.0536896i
$563$	12.5730	−	21.7772i	0.529891	−	0.917798i	−0.469501	−	0.882932i	$-0.655566\pi$
$563$	12.5730	−	21.7772i	0.529891	−	0.917798i	0.999392	−	0.0348658i	$-0.0111004\pi$
$564$	−2.95316	−	5.11503i	−0.124351	−	0.215381i
$565$	−26.5222	−	45.9378i	−1.11580	−	1.93262i
$566$	−3.81394	+	6.60594i	−0.160312	+	0.277668i
$567$	−5.86254	−	10.1542i	−0.246203	−	0.426437i
$568$	−2.24809	+	3.89381i	−0.0943278	+	0.163380i
$569$	−27.3135			−1.14504			−0.572520	−	0.819891i	$-0.694034\pi$
$569$	−27.3135			−1.14504			−0.572520	+	0.819891i	$0.694034\pi$
$570$	2.78692	+	4.82709i	0.116731	+	0.202185i
$571$	22.9754	+	39.7945i	0.961490	+	1.66535i	0.718764	+	0.695254i	$0.244708\pi$
$571$	22.9754	+	39.7945i	0.961490	+	1.66535i	0.242725	+	0.970095i	$0.421959\pi$
$572$	−7.14102			−0.298581
$573$	17.7594			0.741909
$574$	0.482011	−	0.834867i	0.0201187	−	0.0348467i
$575$	−20.4919	+	35.4930i	−0.854570	+	1.48016i
$576$	11.1245			0.463522
$577$	29.2224			1.21654			0.608272	−	0.793728i	$-0.291863\pi$
$577$	29.2224			1.21654			0.608272	+	0.793728i	$0.291863\pi$
$578$	0.277387	−	0.480449i	0.0115378	−	0.0199841i
$579$	−3.47188	+	6.01347i	−0.144286	+	0.249911i
$580$	−24.9826	+	43.2712i	−1.03735	+	1.79674i
$581$	1.89634	−	3.28455i	0.0786734	−	0.136266i
$582$	−5.41869			−0.224612
$583$	2.42325			0.100361
$584$	−9.08152	+	15.7297i	−0.375796	+	0.650898i
$585$	4.02820	−	6.97705i	0.166546	−	0.288466i
$586$	4.99121			0.206185
$587$	−1.54502			−0.0637697			−0.0318849	−	0.999492i	$-0.510151\pi$
$587$	−1.54502			−0.0637697			−0.0318849	+	0.999492i	$0.510151\pi$
$588$	0.418376	+	0.724648i	0.0172535	+	0.0298840i
$589$	19.7188	+	34.1539i	0.812498	+	1.40729i
$590$	−5.54662			−0.228351
$591$	1.55309	−	2.69004i	0.0638857	−	0.110653i
$592$	−8.17879	−	14.1661i	−0.336146	−	0.582222i
$593$	−1.44160	+	2.49692i	−0.0591993	+	0.102536i	−0.894106	−	0.447855i	$-0.852188\pi$
$593$	−1.44160	+	2.49692i	−0.0591993	+	0.102536i	0.834907	+	0.550391i	$0.185521\pi$
$594$	−3.39997	−	5.88891i	−0.139502	−	0.241625i
$595$	−19.7508	−	34.2094i	−0.809704	−	1.40245i
$596$	−17.6706	+	30.6064i	−0.723816	+	1.25369i
$597$	−4.25683	−	7.37305i	−0.174221	−	0.301759i
$598$	−0.866203	+	1.50031i	−0.0354217	+	0.0613522i
$599$	25.0351			1.02291			0.511454	−	0.859311i	$-0.329107\pi$
$599$	25.0351			1.02291			0.511454	+	0.859311i	$0.329107\pi$
$600$	4.53841	−	7.86076i	0.185280	−	0.320914i
$601$	−0.684105			−0.0279052			−0.0139526	−	0.999903i	$-0.504441\pi$
$601$	−0.684105			−0.0279052			−0.0139526	+	0.999903i	$0.504441\pi$
$602$	−0.460837			−0.0187823
$603$	−2.87477	−	4.97924i	−0.117069	−	0.202770i
$604$	18.8926	+	32.7230i	0.768730	+	1.33148i
$605$	14.7127	+	25.4831i	0.598155	+	1.03603i
$606$	0.226143	−	0.391692i	0.00918645	−	0.0159114i
$607$	−0.503559			−0.0204388			−0.0102194	−	0.999948i	$-0.503253\pi$
$607$	−0.503559			−0.0204388			−0.0102194	+	0.999948i	$0.503253\pi$
$608$	11.4809	+	19.8855i	0.465612	+	0.806463i
$609$	−13.4224			−0.543904
$610$	10.6819	+	3.68032i	0.432497	+	0.149012i
$611$	−3.97166			−0.160676
$612$	9.83055	+	17.0270i	0.397376	+	0.688276i
$613$	23.4050			0.945319			0.472659	−	0.881245i	$-0.343294\pi$
$613$	23.4050			0.945319			0.472659	+	0.881245i	$0.343294\pi$
$614$	−0.557535	+	0.965679i	−0.0225003	+	0.0389716i
$615$	−1.25991	−	2.18224i	−0.0508047	−	0.0879963i
$616$	8.38911	+	14.5304i	0.338007	+	0.585445i
$617$	−6.43742	−	11.1499i	−0.259161	−	0.448880i	0.706856	−	0.707357i	$-0.250113\pi$
$617$	−6.43742	−	11.1499i	−0.259161	−	0.448880i	−0.966017	+	0.258477i	$0.916779\pi$
$618$	3.12805			0.125829
$619$	22.2499			0.894299			0.447149	−	0.894459i	$-0.352439\pi$
$619$	22.2499			0.894299			0.447149	+	0.894459i	$0.352439\pi$
$620$	24.6523	−	42.6990i	0.990059	−	1.71483i
$621$	19.3538			0.776643
$622$	2.50893	−	4.34559i	0.100599	−	0.174242i
$623$	−3.91140	−	6.77474i	−0.156707	−	0.271424i
$624$	−0.979503	+	1.69655i	−0.0392115	+	0.0679163i
$625$	−1.31949	−	2.28543i	−0.0527796	−	0.0914170i
$626$	2.41104	+	4.17605i	0.0963646	+	0.166908i
$627$	−8.41140	+	14.5690i	−0.335919	+	0.581829i
$628$	−4.38310	−	7.59175i	−0.174905	−	0.302944i
$629$	11.3825	−	19.7151i	0.453851	−	0.786093i
$630$	−9.07761			−0.361661
$631$	0.756926	+	1.31103i	0.0301327	+	0.0521914i	0.880699	−	0.473677i	$-0.157074\pi$
$631$	0.756926	+	1.31103i	0.0301327	+	0.0521914i	−0.850566	+	0.525869i	$0.823740\pi$
$632$	−1.84147	−	3.18951i	−0.0732496	−	0.126872i
$633$	−4.10426			−0.163130
$634$	−2.05159			−0.0814791
$635$	31.6319	−	54.7880i	1.25527	−	2.17420i
$636$	0.366268	−	0.634395i	0.0145235	−	0.0251554i
$637$	0.562667			0.0222937
$638$	12.8540			0.508895
$639$	3.67099	−	6.35833i	0.145222	−	0.251532i
$640$	18.8119	−	32.5832i	0.743606	−	1.28796i
$641$	−11.3234	+	19.6127i	−0.447246	+	0.774654i	−0.998206	−	0.0598786i	$-0.980929\pi$
$641$	−11.3234	+	19.6127i	−0.447246	+	0.774654i	0.550959	+	0.834532i	$0.314262\pi$
$642$	−1.06791	+	1.84967i	−0.0421471	+	0.0730008i
$643$	−46.7934			−1.84535			−0.922675	−	0.385579i	$-0.874002\pi$
$643$	−46.7934			−1.84535			−0.922675	+	0.385579i	$0.874002\pi$
$644$	−22.9009			−0.902423
$645$	−0.602285	+	1.04319i	−0.0237149	+	0.0410755i
$646$	−4.57348	+	7.92149i	−0.179941	+	0.311667i
$647$	14.1047			0.554514			0.277257	−	0.960796i	$-0.410575\pi$
$647$	14.1047			0.554514			0.277257	+	0.960796i	$0.410575\pi$
$648$	7.07798			0.278049
$649$	−8.37032	−	14.4978i	−0.328564	−	0.569089i
$650$	−1.46354	−	2.53492i	−0.0574046	−	0.0994278i
$651$	13.2449			0.519109
$652$	13.0318	−	22.5718i	0.510366	−	0.883980i
$653$	13.6009	+	23.5574i	0.532244	+	0.921873i	0.999291	+	0.0376412i	$0.0119844\pi$
$653$	13.6009	+	23.5574i	0.532244	+	0.921873i	−0.467047	+	0.884232i	$0.654682\pi$
$654$	−0.0810501	+	0.140383i	−0.00316931	+	0.00548940i
$655$	−2.79315	−	4.83788i	−0.109137	−	0.189032i
$656$	−1.48564	−	2.57320i	−0.0580044	−	0.100467i
$657$	14.8295	−	25.6855i	0.578555	−	1.00209i
$658$	2.23755	+	3.87555i	0.0872287	+	0.151085i
$659$	−7.33662	+	12.7074i	−0.285794	+	0.495010i	−0.972801	−	0.231641i	$-0.925591\pi$
$659$	−7.33662	+	12.7074i	−0.285794	+	0.495010i	0.687007	+	0.726650i	$0.258924\pi$
$660$	21.0317			0.818659
$661$	−5.65695	+	9.79813i	−0.220030	+	0.381103i	−0.954817	−	0.297195i	$-0.903949\pi$
$661$	−5.65695	+	9.79813i	−0.220030	+	0.381103i	0.734787	+	0.678298i	$0.237282\pi$
$662$	−5.34742			−0.207833
$663$	−2.72637			−0.105883
$664$	1.14475	+	1.98276i	0.0444248	+	0.0769460i
$665$	24.7733	+	42.9085i	0.960666	+	1.66392i
$666$	−2.61574	−	4.53060i	−0.101358	−	0.175557i
$667$	−18.2924	+	31.6834i	−0.708286	+	1.22679i
$668$	−1.92307			−0.0744060
$669$	−4.59036	−	7.95073i	−0.177474	−	0.307393i
$670$	−3.34409			−0.129193
$671$	6.50022	+	33.4744i	0.250938	+	1.29226i
$672$	7.71160			0.297481
$673$	12.0184	+	20.8165i	0.463277	+	0.802419i	0.999122	−	0.0418976i	$-0.0133403\pi$
$673$	12.0184	+	20.8165i	0.463277	+	0.802419i	−0.535845	+	0.844316i	$0.680007\pi$
$674$	10.9396			0.421378
$675$	−16.3501	+	28.3193i	−0.629317	+	1.09001i
$676$	−11.2532	−	19.4910i	−0.432814	−	0.749655i
$677$	10.7838	+	18.6780i	0.414453	+	0.717854i	0.995371	−	0.0961083i	$-0.0306395\pi$
$677$	10.7838	+	18.6780i	0.414453	+	0.717854i	−0.580918	+	0.813962i	$0.697306\pi$
$678$	2.06258	+	3.57249i	0.0792128	+	0.137201i
$679$	−48.1673			−1.84849
$680$	23.8456			0.914437
$681$	−5.45330	+	9.44539i	−0.208971	+	0.361948i
$682$	−12.6840			−0.485696
$683$	22.7142	−	39.3421i	0.869134	−	1.50538i	0.00625155	−	0.999980i	$-0.498010\pi$
$683$	22.7142	−	39.3421i	0.869134	−	1.50538i	0.862883	−	0.505404i	$-0.168657\pi$
$684$	−12.3304	−	21.3568i	−0.471463	−	0.816598i
$685$	−24.0074	+	41.5821i	−0.917276	+	1.58877i
$686$	−3.81699	−	6.61123i	−0.145734	−	0.252418i
$687$	−5.48686	−	9.50352i	−0.209337	−	0.362582i
$688$	−0.710189	+	1.23008i	−0.0270757	+	0.0468965i
$689$	−0.246294	−	0.426594i	−0.00938305	−	0.0162519i
$690$	2.55114	−	4.41871i	0.0971203	−	0.168217i
$691$	−4.01839			−0.152867			−0.0764333	−	0.997075i	$-0.524353\pi$
$691$	−4.01839			−0.152867			−0.0764333	+	0.997075i	$0.524353\pi$
$692$	−15.4231	−	26.7135i	−0.586297	−	1.01550i
$693$	−13.6989	−	23.7271i	−0.520377	−	0.901319i
$694$	−13.1668			−0.499806
$695$	4.40070			0.166928
$696$	4.05130	−	7.01705i	0.153564	−	0.265981i
$697$	2.06758	−	3.58116i	0.0783152	−	0.135646i
$698$	−6.26141			−0.236998
$699$	7.76718			0.293782
$700$	19.3467	−	33.5095i	0.731236	−	1.26654i
$701$	−17.8368	+	30.8943i	−0.673687	+	1.16686i	0.303164	+	0.952938i	$0.401957\pi$
$701$	−17.8368	+	30.8943i	−0.673687	+	1.16686i	−0.976851	+	0.213921i	$0.931376\pi$
$702$	−0.691130	+	1.19707i	−0.0260850	+	0.0451806i
$703$	−14.2770	+	24.7285i	−0.538467	+	0.932652i
$704$	19.5285			0.736010
$705$	11.6973			0.440547
$706$	−3.18885	+	5.52325i	−0.120014	+	0.207870i
$707$	2.01021	−	3.48179i	0.0756018	−	0.130946i
$708$	−5.06060			−0.190189
$709$	−21.7635			−0.817345			−0.408673	−	0.912681i	$-0.634008\pi$
$709$	−21.7635			−0.817345			−0.408673	+	0.912681i	$0.634008\pi$
$710$	−2.13515	−	3.69819i	−0.0801307	−	0.138790i
$711$	3.00700	+	5.20827i	0.112771	+	0.195325i
$712$	4.72232			0.176977
$713$	18.0505	−	31.2644i	0.675997	−	1.17086i
$714$	1.53598	+	2.66039i	0.0574826	+	0.0995627i
$715$	7.07131	−	12.2479i	0.264452	−	0.458044i
$716$	6.80896	+	11.7935i	0.254463	+	0.440743i
$717$	−2.55259	−	4.42122i	−0.0953283	−	0.165113i
$718$	5.05911	−	8.76264i	0.188804	−	0.327019i
$719$	9.09666	+	15.7559i	0.339248	+	0.587595i	0.984291	−	0.176551i	$-0.0564941\pi$
$719$	9.09666	+	15.7559i	0.339248	+	0.587595i	−0.645043	+	0.764146i	$0.723161\pi$
$720$	−13.9894	+	24.2303i	−0.521353	+	0.903010i
$721$	27.8056			1.03553
$722$	1.97125	−	3.41431i	0.0733624	−	0.127067i
$723$	−1.29686			−0.0482309
$724$	−37.4924			−1.39340
$725$	−30.9069	−	53.5323i	−1.14785	−	1.98814i
$726$	−1.14417	−	1.98176i	−0.0424642	−	0.0735502i
$727$	14.5942	+	25.2779i	0.541268	+	0.937504i	0.998832	+	0.0483269i	$0.0153889\pi$
$727$	14.5942	+	25.2779i	0.541268	+	0.937504i	−0.457563	+	0.889177i	$0.651278\pi$
$728$	1.70530	−	2.95366i	0.0632026	−	0.109470i
$729$	−3.11513			−0.115375
$730$	−8.62528	−	14.9394i	−0.319236	−	0.552933i
$731$	−1.97676			−0.0731130
$732$	9.74589	+	3.35783i	0.360219	+	0.124109i
$733$	−44.9718			−1.66107			−0.830536	−	0.556964i	$-0.811966\pi$
$733$	−44.9718			−1.66107			−0.830536	+	0.556964i	$0.811966\pi$
$734$	0.946602	+	1.63956i	0.0349397	+	0.0605173i
$735$	−1.65717			−0.0611255
$736$	10.5096	−	18.2031i	0.387388	−	0.670976i
$737$	−5.04651	−	8.74081i	−0.185891	−	0.321972i
$738$	−0.475137	−	0.822962i	−0.0174900	−	0.0302936i
$739$	26.1675	+	45.3234i	0.962586	+	1.66725i	0.715964	+	0.698137i	$0.245987\pi$
$739$	26.1675	+	45.3234i	0.962586	+	1.66725i	0.246622	+	0.969112i	$0.420679\pi$
$740$	35.6980			1.31228
$741$	3.41966			0.125624
$742$	−0.277513	+	0.480667i	−0.0101878	+	0.0176459i
$743$	7.44457			0.273115			0.136557	−	0.990632i	$-0.456396\pi$
$743$	7.44457			0.273115			0.136557	+	0.990632i	$0.456396\pi$
$744$	−3.99772	+	6.92425i	−0.146564	+	0.253855i
$745$	−34.9962	−	60.6153i	−1.28216	−	2.22077i
$746$	4.77509	−	8.27070i	0.174829	−	0.302812i
$747$	−1.86930	−	3.23772i	−0.0683940	−	0.118462i
$748$	17.2570	+	29.8901i	0.630980	+	1.09289i
$749$	−9.49277	+	16.4420i	−0.346858	+	0.600776i
$750$	1.72046	+	2.97993i	0.0628224	+	0.108812i
$751$	18.9022	−	32.7395i	0.689750	−	1.19468i	−0.282169	−	0.959365i	$-0.591054\pi$
$751$	18.9022	−	32.7395i	0.689750	−	1.19468i	0.971919	−	0.235317i	$-0.0756129\pi$
$752$	13.7930			0.502979
$753$	−3.67500	−	6.36529i	−0.133924	−	0.231964i
$754$	−1.30645	−	2.26284i	−0.0475782	−	0.0824079i
$755$	−74.8329			−2.72345
$756$	−18.2723			−0.664556
$757$	16.3204	−	28.2678i	0.593176	−	1.02741i	−0.400626	−	0.916242i	$-0.631207\pi$
$757$	16.3204	−	28.2678i	0.593176	−	1.02741i	0.993802	−	0.111169i	$-0.0354594\pi$
$758$	1.12752	−	1.95292i	0.0409533	−	0.0709332i
$759$	15.3995			0.558968
$760$	−29.9093			−1.08493
$761$	−18.6822	+	32.3585i	−0.677228	+	1.17299i	0.298584	+	0.954383i	$0.403486\pi$
$761$	−18.6822	+	32.3585i	−0.677228	+	1.17299i	−0.975812	+	0.218610i	$0.929848\pi$
$762$	−2.45994	+	4.26075i	−0.0891144	+	0.154351i
$763$	−0.720463	+	1.24788i	−0.0260825	+	0.0451762i
$764$	−22.8504	+	39.5781i	−0.826699	+	1.43189i
$765$	−38.9383			−1.40782
$766$	7.31957			0.264467
$767$	−1.70148	+	2.94705i	−0.0614369	+	0.106412i
$768$	1.74031	−	3.01431i	0.0627981	−	0.108770i
$769$	−8.84174			−0.318841			−0.159421	−	0.987211i	$-0.550963\pi$
$769$	−8.84174			−0.318841			−0.159421	+	0.987211i	$0.550963\pi$
$770$	−15.9353			−0.574268
$771$	−10.8813	−	18.8470i	−0.391882	−	0.678759i
$772$	−8.93431	−	15.4747i	−0.321553	−	0.556946i
$773$	−35.5776			−1.27964			−0.639819	−	0.768525i	$-0.720991\pi$
$773$	−35.5776			−1.27964			−0.639819	+	0.768525i	$0.720991\pi$
$774$	−0.227133	+	0.393406i	−0.00816412	+	0.0141407i
$775$	30.4982	+	52.8244i	1.09553	+	1.89751i
$776$	14.5384	−	25.1812i	0.521898	−	0.903953i
$777$	4.79486	+	8.30493i	0.172014	+	0.297938i
$778$	4.89822	+	8.48397i	0.175610	+	0.304165i
$779$	−2.59335	+	4.49181i	−0.0929163	+	0.160936i
$780$	−2.13762	−	3.70246i	−0.0765390	−	0.132569i
$781$	6.44424	−	11.1617i	0.230593	−	0.399399i
$782$	8.37310			0.299421
$783$	−14.5952	+	25.2797i	−0.521591	+	0.903422i
$784$	−1.95406			−0.0697879
$785$	17.3612			0.619649
$786$	0.217217	+	0.376231i	0.00774789	+	0.0134197i
$787$	−5.27494	−	9.13647i	−0.188031	−	0.325680i	0.756562	−	0.653922i	$-0.226877\pi$
$787$	−5.27494	−	9.13647i	−0.188031	−	0.325680i	−0.944594	+	0.328241i	$0.893544\pi$
$788$	3.99663	+	6.92236i	0.142374	+	0.246599i
$789$	−2.35743	+	4.08319i	−0.0839268	+	0.145365i
$790$	3.49791			0.124450
$791$	18.3345	+	31.7562i	0.651898	+	1.12912i
$792$	16.5390			0.587686
$793$	5.23221	−	4.54657i	0.185801	−	0.161453i
$794$	−2.67183			−0.0948198
$795$	0.725385	+	1.25640i	0.0257268	+	0.0445601i
$796$	21.9085			0.776526
$797$	−1.54938	+	2.68360i	−0.0548817	+	0.0950579i	−0.892161	−	0.451717i	$-0.850811\pi$
$797$	−1.54938	+	2.68360i	−0.0548817	+	0.0950579i	0.837279	+	0.546775i	$0.184145\pi$
$798$	−1.92656	−	3.33691i	−0.0681996	−	0.118125i
$799$	9.59795	+	16.6241i	0.339551	+	0.588120i
$800$	17.7570	+	30.7560i	0.627804	+	1.08739i
$801$	−7.71125			−0.272464
$802$	4.98060			0.175871
$803$	26.0325	−	45.0897i	0.918668	−	1.59118i
$804$	−3.05106			−0.107603
$805$	22.6774	−	39.2784i	0.799273	−	1.38438i
$806$	1.28918	+	2.23292i	0.0454093	+	0.0786511i
$807$	2.16032	−	3.74179i	0.0760469	−	0.131717i
$808$	1.21349	+	2.10182i	0.0426903	+	0.0739419i
$809$	−10.1630	−	17.6028i	−0.357312	−	0.618882i	0.630199	−	0.776434i	$-0.282973\pi$
$809$	−10.1630	−	17.6028i	−0.357312	−	0.618882i	−0.987511	+	0.157551i	$0.949640\pi$
$810$	−3.36119	+	5.82176i	−0.118100	+	0.204556i
$811$	1.67725	+	2.90509i	0.0588963	+	0.102011i	0.893970	−	0.448126i	$-0.147909\pi$
$811$	1.67725	+	2.90509i	0.0588963	+	0.102011i	−0.835074	+	0.550138i	$0.814575\pi$
$812$	17.2702	−	29.9128i	0.606065	−	1.04973i
$813$	−19.1421			−0.671343
$814$	−4.59181	−	7.95324i	−0.160943	−	0.278761i
$815$	25.8092	+	44.7029i	0.904058	+	1.56587i
$816$	9.46830			0.331457
$817$	2.47943			0.0867442
$818$	−0.772675	+	1.33831i	−0.0270160	+	0.0467930i
$819$	−2.78464	+	4.82314i	−0.0973033	+	0.168534i
$820$	6.48436			0.226444
$821$	−8.33953			−0.291052			−0.145526	−	0.989354i	$-0.546487\pi$
$821$	−8.33953			−0.291052			−0.145526	+	0.989354i	$0.546487\pi$
$822$	1.86701	−	3.23375i	0.0651193	−	0.112790i
$823$	8.64872	−	14.9800i	0.301475	−	0.522171i	−0.674995	−	0.737822i	$-0.735854\pi$
$823$	8.64872	−	14.9800i	0.301475	−	0.522171i	0.976470	+	0.215652i	$0.0691875\pi$
$824$	−8.39258	+	14.5364i	−0.292369	+	0.506399i
$825$	−13.0095	+	22.5332i	−0.452934	+	0.784505i
$826$	3.83431			0.133413
$827$	42.9127			1.49222			0.746111	−	0.665822i	$-0.231919\pi$
$827$	42.9127			1.49222			0.746111	+	0.665822i	$0.231919\pi$
$828$	−11.2872	+	19.5500i	−0.392257	+	0.679408i
$829$	−0.435747	+	0.754735i	−0.0151341	+	0.0262130i	−0.873493	−	0.486836i	$-0.838151\pi$
$829$	−0.435747	+	0.754735i	−0.0151341	+	0.0262130i	0.858359	+	0.513049i	$0.171484\pi$
$830$	−2.17447			−0.0754770
$831$	9.12187			0.316434
$832$	−1.98484	−	3.43784i	−0.0688118	−	0.119186i
$833$	−1.35974	−	2.35515i	−0.0471124	−	0.0816010i
$834$	−0.342233			−0.0118506
$835$	1.90430	−	3.29835i	0.0659011	−	0.114144i
$836$	−21.6453	−	37.4908i	−0.748620	−	1.29665i
$837$	14.4022	−	24.9454i	0.497813	−	0.862238i
$838$	3.75195	+	6.49857i	0.129609	+	0.224489i
$839$	14.3433	+	24.8433i	0.495185	+	0.857686i	0.999985	−	0.00555070i	$-0.00176685\pi$
$839$	14.3433	+	24.8433i	0.495185	+	0.857686i	−0.504799	+	0.863237i	$0.668434\pi$
$840$	−5.02245	+	8.69914i	−0.173291	+	0.300149i
$841$	−13.0896	−	22.6718i	−0.451365	−	0.781788i
$842$	5.13581	−	8.89548i	0.176992	−	0.306559i
$843$	−2.65565			−0.0914654
$844$	5.28081	−	9.14663i	0.181773	−	0.314840i
$845$	44.5732			1.53337
$846$	4.41128			0.151663
$847$	−10.1707	−	17.6161i	−0.349468	−	0.605297i
$848$	0.855344	+	1.48150i	0.0293726	+	0.0508749i
$849$	−6.89155	−	11.9365i	−0.236517	−	0.409660i
$850$	−7.07359	+	12.2518i	−0.242622	+	0.420234i
$851$	26.1382			0.896007
$852$	−1.94806	−	3.37413i	−0.0667393	−	0.115596i
$853$	−18.8522			−0.645487			−0.322744	−	0.946486i	$-0.604605\pi$
$853$	−18.8522			−0.645487			−0.322744	+	0.946486i	$0.604605\pi$
$854$	−7.38426	−	2.54416i	−0.252684	−	0.0870593i
$855$	48.8400			1.67029
$856$	−5.73042	−	9.92538i	−0.195862	−	0.339242i
$857$	13.3248			0.455167			0.227583	−	0.973759i	$-0.426918\pi$
$857$	13.3248			0.455167			0.227583	+	0.973759i	$0.426918\pi$
$858$	−0.549921	+	0.952491i	−0.0187740	+	0.0325175i
$859$	−17.6435	−	30.5595i	−0.601990	−	1.04268i	−0.992519	−	0.122087i	$-0.961041\pi$
$859$	−17.6435	−	30.5595i	−0.601990	−	1.04268i	0.390529	−	0.920591i	$-0.372292\pi$
$860$	−1.54988	−	2.68447i	−0.0528505	−	0.0915397i
$861$	0.870963	+	1.50855i	0.0296823	+	0.0514113i
$862$	10.2972			0.350724
$863$	−30.9955			−1.05510			−0.527549	−	0.849524i	$-0.676889\pi$
$863$	−30.9955			−1.05510			−0.527549	+	0.849524i	$0.676889\pi$
$864$	8.38542	−	14.5240i	0.285278	−	0.494116i
$865$	61.0900			2.07712
$866$	−4.45993	+	7.72483i	−0.151555	+	0.262500i
$867$	0.501222	+	0.868141i	0.0170224	+	0.0294836i
$868$	−17.0418	+	29.5172i	−0.578436	+	1.00188i
$869$	5.27863	+	9.14286i	0.179065	+	0.310150i
$870$	3.84777	+	6.66453i	0.130451	+	0.225949i
$871$	−1.02583	+	1.77679i	−0.0347590	+	0.0602043i
$872$	−0.434916	−	0.753296i	−0.0147281	−	0.0255098i
$873$	−23.7402	+	41.1193i	−0.803486	+	1.39168i
$874$	−10.5023			−0.355245
$875$	15.2934	+	26.4889i	0.517011	+	0.895488i
$876$	−7.86948	−	13.6303i	−0.265885	−	0.460527i
$877$	54.4698			1.83932			0.919658	−	0.392721i	$-0.128466\pi$
$877$	54.4698			1.83932			0.919658	+	0.392721i	$0.128466\pi$
$878$	0.381240			0.0128662
$879$	−4.50940	+	7.81051i	−0.152098	+	0.263442i
$880$	−24.5576	+	42.5351i	−0.827838	+	1.43386i
$881$	13.7004			0.461579			0.230790	−	0.973004i	$-0.425869\pi$
$881$	13.7004			0.461579			0.230790	+	0.973004i	$0.425869\pi$
$882$	−0.624948			−0.0210431
$883$	0.553452	−	0.958606i	0.0186251	−	0.0322597i	−0.856563	−	0.516043i	$-0.827404\pi$
$883$	0.553452	−	0.958606i	0.0186251	−	0.0322597i	0.875188	+	0.483783i	$0.160738\pi$
$884$	3.50793	−	6.07592i	0.117985	−	0.204355i
$885$	5.01120	−	8.67965i	0.168450	−	0.291763i
$886$	1.36139	−	2.35800i	0.0457368	−	0.0792184i
$887$	−11.5750			−0.388650			−0.194325	−	0.980937i	$-0.562252\pi$
$887$	−11.5750			−0.388650			−0.194325	+	0.980937i	$0.562252\pi$
$888$	−5.78894			−0.194264
$889$	−21.8667	+	37.8743i	−0.733386	+	1.27026i
$890$	−2.24254	+	3.88419i	−0.0751701	+	0.130198i
$891$	−20.2893			−0.679717
$892$	23.6251			0.791025
$893$	−12.0386	−	20.8515i	−0.402857	−	0.697769i
$894$	2.72158	+	4.71392i	0.0910233	+	0.157657i
$895$	−26.9700			−0.901507
$896$	−13.0044	+	22.5243i	−0.434448	+	0.752485i
$897$	−1.56517	−	2.71096i	−0.0522597	−	0.0905164i
$898$	2.11676	−	3.66634i	0.0706372	−	0.122347i
$899$	27.2247	+	47.1546i	0.907996	+	1.57269i
$900$	−19.0708	−	33.0316i	−0.635694	−	1.10105i
$901$	−1.19039	+	2.06182i	−0.0396577	+	0.0686892i
$902$	−0.834080	−	1.44467i	−0.0277718	−	0.0481022i
$903$	0.416352	−	0.721142i	0.0138553	−	0.0239981i
$904$	−22.1356			−0.736220
$905$	37.1265	−	64.3049i	1.23413	−	2.13757i
$906$	5.81959			0.193343
$907$	−44.8586			−1.48951			−0.744753	−	0.667340i	$-0.767433\pi$
$907$	−44.8586			−1.48951			−0.744753	+	0.667340i	$0.767433\pi$
$908$	−14.0332	−	24.3061i	−0.465707	−	0.806627i
$909$	−1.98155	−	3.43214i	−0.0657238	−	0.113837i
$910$	1.61963	+	2.80528i	0.0536901	+	0.0929940i
$911$	4.60716	−	7.97984i	0.152642	−	0.264384i	−0.779556	−	0.626333i	$-0.784555\pi$
$911$	4.60716	−	7.97984i	0.152642	−	0.264384i	0.932198	+	0.361949i	$0.117888\pi$
$912$	−11.8760			−0.393254
$913$	−3.28146	−	5.68365i	−0.108600	−	0.188102i
$914$	−2.77394			−0.0917537
$915$	−15.4099	+	13.3905i	−0.509436	+	0.442678i
$916$	28.2391			0.933045
$917$	1.93087	+	3.34436i	0.0637629	+	0.110441i
$918$	6.68076			0.220498
$919$	12.9221	−	22.3818i	0.426262	−	0.738308i	−0.570275	−	0.821454i	$-0.693163\pi$
$919$	12.9221	−	22.3818i	0.426262	−	0.738308i	0.996537	+	0.0831458i	$0.0264967\pi$
$920$	13.6895	+	23.7108i	0.451328	+	0.781723i
$921$	−1.00743	−	1.74492i	−0.0331960	−	0.0574971i
$922$	1.14448	+	1.98229i	0.0376914	+	0.0652834i
$923$	−2.61991			−0.0862354
$924$	−14.5390			−0.478297
$925$	−22.0816	+	38.2464i	−0.726038	+	1.25753i
$926$	−4.44047			−0.145923
$927$	13.7045	−	23.7370i	0.450116	−	0.779624i
$928$	15.8511	+	27.4549i	0.520337	+	0.901251i
$929$	12.1935	−	21.1198i	0.400057	−	0.692920i	−0.593675	−	0.804705i	$-0.702324\pi$
$929$	12.1935	−	21.1198i	0.400057	−	0.692920i	0.993732	+	0.111785i	$0.0356569\pi$
$930$	−3.79688	−	6.57639i	−0.124505	−	0.215648i
$931$	1.70552	+	2.95404i	0.0558960	+	0.0968147i
$932$	−9.99377	+	17.3097i	−0.327357	+	0.566999i
$933$	4.53347	+	7.85220i	0.148419	+	0.257070i
$934$	6.76410	−	11.7158i	0.221328	−	0.383351i
$935$	−68.3543			−2.23543
$936$	−1.68098	−	2.91155i	−0.0549446	−	0.0951669i
$937$	7.91847	+	13.7152i	0.258685	+	0.448056i	0.965890	−	0.258953i	$-0.0833775\pi$
$937$	7.91847	+	13.7152i	0.258685	+	0.448056i	−0.707205	+	0.707009i	$0.750044\pi$
$938$	2.31173			0.0754805
$939$	−8.71320			−0.284345
$940$	−15.0506	+	26.0684i	−0.490896	+	0.850257i
$941$	−5.21809	+	9.03800i	−0.170105	+	0.294630i	−0.938456	−	0.345398i	$-0.887744\pi$
$941$	−5.21809	+	9.03800i	−0.170105	+	0.294630i	0.768351	+	0.640028i	$0.221077\pi$
$942$	−1.35015			−0.0439902
$943$	4.74789			0.154612
$944$	5.90899	−	10.2347i	0.192321	−	0.333110i
$945$	18.0939	−	31.3396i	0.588595	−	1.01948i
$946$	−0.398720	+	0.690604i	−0.0129635	+	0.0224535i
$947$	16.1386	−	27.9529i	0.524435	−	0.908348i	−0.475160	−	0.879899i	$-0.657610\pi$
$947$	16.1386	−	27.9529i	0.524435	−	0.908348i	0.999595	−	0.0284490i	$-0.00905682\pi$
$948$	3.19140			0.103652
$949$	−10.5835			−0.343556
$950$	8.87234	−	15.3673i	0.287857	−	0.498582i
$951$	1.85355	−	3.21044i	0.0601054	−	0.104106i
$952$	−16.4842			−0.534255
$953$	−40.4644			−1.31077			−0.655385	−	0.755295i	$-0.727493\pi$
$953$	−40.4644			−1.31077			−0.655385	+	0.755295i	$0.727493\pi$
$954$	0.273556	+	0.473813i	0.00885671	+	0.0153403i
$955$	−45.2548	−	78.3835i	−1.46441	−	2.53643i
$956$	13.1373			0.424892
$957$	−11.6132	+	20.1146i	−0.375401	+	0.650214i
$958$	−4.28513	−	7.42206i	−0.138446	−	0.239796i
$959$	16.5960	−	28.7451i	0.535913	−	0.928229i
$960$	5.84574	+	10.1251i	0.188670	+	0.326787i
$961$	−11.3647	−	19.6842i	−0.366603	−	0.634975i
$962$	−0.933402	+	1.61670i	−0.0300941	+	0.0521245i
$963$	9.35740	+	16.2075i	0.301538	+	0.522279i
$964$	1.66863	−	2.89016i	0.0537430	−	0.0930857i
$965$	35.3884			1.13919
$966$	−1.76357	+	3.05460i	−0.0567420	+	0.0982800i
$967$	7.76447			0.249688			0.124844	−	0.992176i	$-0.460157\pi$
$967$	7.76447			0.249688			0.124844	+	0.992176i	$0.460157\pi$
$968$	12.2793			0.394671
$969$	−8.26398	−	14.3136i	−0.265477	−	0.459820i
$970$	13.8080	+	23.9161i	0.443348	+	0.767901i
$971$	12.5352	+	21.7116i	0.402274	+	0.696759i	0.994000	−	0.109380i	$-0.0348866\pi$
$971$	12.5352	+	21.7116i	0.402274	+	0.696759i	−0.591726	+	0.806139i	$0.701553\pi$
$972$	−13.9297	+	24.1269i	−0.446795	+	0.773871i
$973$	−3.04214			−0.0975266
$974$	8.61577	+	14.9230i	0.276067	+	0.478162i
$975$	5.28904			0.169385
$976$	−18.1707	+	15.7896i	−0.581631	+	0.505412i
$977$	−36.2003			−1.15815			−0.579075	−	0.815274i	$-0.696586\pi$
$977$	−36.2003			−1.15815			−0.579075	+	0.815274i	$0.696586\pi$
$978$	−2.00713	−	3.47645i	−0.0641809	−	0.111165i
$979$	−13.5367			−0.432635
$980$	2.13222	−	3.69312i	0.0681113	−	0.117972i
$981$	0.710189	+	1.23008i	0.0226746	+	0.0392735i
$982$	−2.51445	−	4.35515i	−0.0802392	−	0.138978i
$983$	−16.8261	−	29.1437i	−0.536670	−	0.929539i	−0.999081	−	0.0428733i	$-0.986349\pi$
$983$	−16.8261	−	29.1437i	−0.536670	−	0.929539i	0.462411	−	0.886666i	$-0.346985\pi$
$984$	−1.05153			−0.0335217
$985$	−15.8305			−0.504401
$986$	−6.31437	+	10.9368i	−0.201090	+	0.348299i
$987$	−8.08622			−0.257387
$988$	−4.39997	+	7.62097i	−0.139982	+	0.242455i
$989$	−1.13483	−	1.96559i	−0.0360855	−	0.0625020i
$990$	−7.85403	+	13.6036i	−0.249618	+	0.432350i
$991$	−15.4271	−	26.7205i	−0.490057	−	0.848804i	0.509878	−	0.860247i	$-0.329691\pi$
$991$	−15.4271	−	26.7205i	−0.490057	−	0.848804i	−0.999935	+	0.0114434i	$0.996357\pi$
$992$	−15.6415	−	27.0918i	−0.496617	−	0.860166i
$993$	4.83123	−	8.36793i	0.153314	−	0.265548i
$994$	1.47600	+	2.55651i	0.0468159	+	0.0810875i
$995$	−21.6946	+	37.5762i	−0.687767	+	1.19125i
$996$	−1.98393			−0.0628633
$997$	−5.14169	−	8.90567i	−0.162839	−	0.282046i	0.773047	−	0.634349i	$-0.218732\pi$
$997$	−5.14169	−	8.90567i	−0.162839	−	0.282046i	−0.935886	+	0.352304i	$0.885398\pi$
$998$	1.77106	+	3.06757i	0.0560619	+	0.0971021i
$999$	20.8553			0.659832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	61.2.c.a.47.3	yes	8
3.2	odd	2		549.2.e.g.352.2		8
4.3	odd	2		976.2.i.g.657.3		8
61.13	even	3	inner	61.2.c.a.13.3	✓	8
61.14	even	6		3721.2.a.d.1.3		4
61.47	even	3		3721.2.a.e.1.2		4
183.74	odd	6		549.2.e.g.379.2		8
244.135	odd	6		976.2.i.g.257.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
61.2.c.a.13.3	✓	8	61.13	even	3	inner
61.2.c.a.47.3	yes	8	1.1	even	1	trivial
549.2.e.g.352.2		8	3.2	odd	2
549.2.e.g.379.2		8	183.74	odd	6
976.2.i.g.257.3		8	244.135	odd	6
976.2.i.g.657.3		8	4.3	odd	2
3721.2.a.d.1.3		4	61.14	even	6
3721.2.a.e.1.2		4	61.47	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 61 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	61.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.198169 + 0.343239i) q^{2} -0.716159 q^{3} +(0.921458 - 1.59601i) q^{4} +(1.82493 + 3.16087i) q^{5} +(-0.141921 - 0.245814i) q^{6} +(-1.26155 - 2.18506i) q^{7} +1.52310 q^{8} -2.48712 q^{9} +O(q^{10})\)	\(q+(0.198169 + 0.343239i) q^{2} -0.716159 q^{3} +(0.921458 - 1.59601i) q^{4} +(1.82493 + 3.16087i) q^{5} +(-0.141921 - 0.245814i) q^{6} +(-1.26155 - 2.18506i) q^{7} +1.52310 q^{8} -2.48712 q^{9} +(-0.723289 + 1.25277i) q^{10} -4.36601 q^{11} +(-0.659910 + 1.14300i) q^{12} +(0.443751 + 0.768600i) q^{13} +(0.500000 - 0.866025i) q^{14} +(-1.30694 - 2.26368i) q^{15} +(-1.54109 - 2.66924i) q^{16} +(2.14475 - 3.71481i) q^{17} +(-0.492870 - 0.853676i) q^{18} +(-2.69014 + 4.65945i) q^{19} +6.72637 q^{20} +(0.903468 + 1.56485i) q^{21} +(-0.865209 - 1.49859i) q^{22} +4.92509 q^{23} -1.09078 q^{24} +(-4.16071 + 7.20656i) q^{25} +(-0.175876 + 0.304626i) q^{26} +3.92965 q^{27} -4.64985 q^{28} +(-3.71413 + 6.43307i) q^{29} +(0.517989 - 0.897184i) q^{30} +(3.66502 - 6.34799i) q^{31} +(2.13389 - 3.69600i) q^{32} +3.12676 q^{33} +1.70009 q^{34} +(4.60446 - 7.97516i) q^{35} +(-2.29177 + 3.96947i) q^{36} +5.30716 q^{37} -2.13241 q^{38} +(-0.317796 - 0.550440i) q^{39} +(2.77954 + 4.81430i) q^{40} +0.964021 q^{41} +(-0.358079 + 0.620212i) q^{42} +(-0.230419 - 0.399097i) q^{43} +(-4.02310 + 6.96821i) q^{44} +(-4.53880 - 7.86144i) q^{45} +(0.976001 + 1.69048i) q^{46} +(-2.23755 + 3.87555i) q^{47} +(1.10366 + 1.91160i) q^{48} +(0.316994 - 0.549050i) q^{49} -3.29810 q^{50} +(-1.53598 + 2.66039i) q^{51} +1.63559 q^{52} -0.555027 q^{53} +(0.778735 + 1.34881i) q^{54} +(-7.96765 - 13.8004i) q^{55} +(-1.92146 - 3.32806i) q^{56} +(1.92656 - 3.33691i) q^{57} -2.94411 q^{58} +(1.91715 + 3.32061i) q^{59} -4.81715 q^{60} +(-1.48882 - 7.66703i) q^{61} +2.90517 q^{62} +(3.13762 + 5.43451i) q^{63} -4.47286 q^{64} +(-1.61963 + 2.80528i) q^{65} +(0.619627 + 1.07323i) q^{66} +(1.15586 + 2.00201i) q^{67} +(-3.95259 - 6.84608i) q^{68} -3.52714 q^{69} +3.64985 q^{70} +(-1.47600 + 2.55651i) q^{71} -3.78812 q^{72} +(-5.96254 + 10.3274i) q^{73} +(1.05172 + 1.82163i) q^{74} +(2.97973 - 5.16104i) q^{75} +(4.95769 + 8.58698i) q^{76} +(5.50793 + 9.54002i) q^{77} +(0.125955 - 0.218160i) q^{78} +(-1.20903 - 2.09410i) q^{79} +(5.62473 - 9.74232i) q^{80} +4.64710 q^{81} +(0.191039 + 0.330890i) q^{82} +(0.751592 + 1.30180i) q^{83} +3.33003 q^{84} +15.6560 q^{85} +(0.0913237 - 0.158177i) q^{86} +(2.65991 - 4.60710i) q^{87} -6.64985 q^{88} +3.10048 q^{89} +(1.79890 - 3.11579i) q^{90} +(1.11963 - 1.93925i) q^{91} +(4.53826 - 7.86050i) q^{92} +(-2.62473 + 4.54617i) q^{93} -1.77365 q^{94} -19.6372 q^{95} +(-1.52820 + 2.64692i) q^{96} +(9.54529 - 16.5329i) q^{97} +0.251274 q^{98} +10.8588 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 2 q^{5} - q^{6} - q^{7} - 6 q^{8} + 2 q^{9}+O(q^{10}) \) 8 * q - 6 * q^3 - 2 * q^5 - q^6 - q^7 - 6 * q^8 + 2 * q^9	\( 8 q - 6 q^{3} - 2 q^{5} - q^{6} - q^{7} - 6 q^{8} + 2 q^{9} - 2 q^{11} - 7 q^{12} + 5 q^{13} + 4 q^{14} + 8 q^{15} + 4 q^{16} + 4 q^{17} - 10 q^{18} + q^{19} + 14 q^{20} - 2 q^{21} - q^{22} - 8 q^{23} + 10 q^{24} - 8 q^{25} + 9 q^{26} - 30 q^{27} - 4 q^{28} - 16 q^{29} + 6 q^{30} + 11 q^{31} - 4 q^{32} + 10 q^{33} - 28 q^{34} + 13 q^{35} + 15 q^{36} + 4 q^{37} + 24 q^{38} + 8 q^{39} + 15 q^{40} + 4 q^{41} - 3 q^{42} + 10 q^{43} - 14 q^{44} - 27 q^{45} - q^{46} + 12 q^{48} + 19 q^{49} - 14 q^{50} - 16 q^{51} - 8 q^{52} + 38 q^{53} + 26 q^{54} - 20 q^{55} - 8 q^{56} - 12 q^{57} - 58 q^{58} + q^{59} + 20 q^{60} + 10 q^{61} + 14 q^{62} + 18 q^{63} - 26 q^{64} - 4 q^{65} - 4 q^{66} - 17 q^{67} - 27 q^{68} - 38 q^{69} - 4 q^{70} - 3 q^{71} - 38 q^{72} - 24 q^{73} + 20 q^{74} + 29 q^{75} + 15 q^{76} + 11 q^{77} + 13 q^{78} - 16 q^{79} + 16 q^{80} + 72 q^{81} + 6 q^{82} + 16 q^{83} - 10 q^{84} + 24 q^{85} - 24 q^{86} + 23 q^{87} - 20 q^{88} + 8 q^{89} - 25 q^{90} + 33 q^{92} + 8 q^{93} + 74 q^{94} - 82 q^{95} + 26 q^{96} + 13 q^{97} - 2 q^{98} + 6 q^{99}+O(q^{100}) \) 8 * q - 6 * q^3 - 2 * q^5 - q^6 - q^7 - 6 * q^8 + 2 * q^9 - 2 * q^11 - 7 * q^12 + 5 * q^13 + 4 * q^14 + 8 * q^15 + 4 * q^16 + 4 * q^17 - 10 * q^18 + q^19 + 14 * q^20 - 2 * q^21 - q^22 - 8 * q^23 + 10 * q^24 - 8 * q^25 + 9 * q^26 - 30 * q^27 - 4 * q^28 - 16 * q^29 + 6 * q^30 + 11 * q^31 - 4 * q^32 + 10 * q^33 - 28 * q^34 + 13 * q^35 + 15 * q^36 + 4 * q^37 + 24 * q^38 + 8 * q^39 + 15 * q^40 + 4 * q^41 - 3 * q^42 + 10 * q^43 - 14 * q^44 - 27 * q^45 - q^46 + 12 * q^48 + 19 * q^49 - 14 * q^50 - 16 * q^51 - 8 * q^52 + 38 * q^53 + 26 * q^54 - 20 * q^55 - 8 * q^56 - 12 * q^57 - 58 * q^58 + q^59 + 20 * q^60 + 10 * q^61 + 14 * q^62 + 18 * q^63 - 26 * q^64 - 4 * q^65 - 4 * q^66 - 17 * q^67 - 27 * q^68 - 38 * q^69 - 4 * q^70 - 3 * q^71 - 38 * q^72 - 24 * q^73 + 20 * q^74 + 29 * q^75 + 15 * q^76 + 11 * q^77 + 13 * q^78 - 16 * q^79 + 16 * q^80 + 72 * q^81 + 6 * q^82 + 16 * q^83 - 10 * q^84 + 24 * q^85 - 24 * q^86 + 23 * q^87 - 20 * q^88 + 8 * q^89 - 25 * q^90 + 33 * q^92 + 8 * q^93 + 74 * q^94 - 82 * q^95 + 26 * q^96 + 13 * q^97 - 2 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

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