LMFDB - Embedded newform 273.2.i.e.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(79,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("273.79");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.i (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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - x^{9} + 7x^{8} - 8x^{7} + 41x^{6} - 40x^{5} + 59x^{4} - 10x^{3} + 18x^{2} - 4x + 4 $ x^10 - x^9 + 7x^8 - 8x^7 + 41x^6 - 40x^5 + 59x^4 - 10x^3 + 18x^2 - 4x + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$0.253637 - 0.439313i$ of defining polynomial
Character	$\chi$	$=$	273.235
Dual form			273.2.i.e.79.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.26840 - 2.19693i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.21768 + 3.84114i) q^{4} +(1.26113 + 2.18434i) q^{5} -2.53680 q^{6} +(1.47427 + 2.19693i) q^{7} +6.17804 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-1.26840 - 2.19693i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.21768 + 3.84114i) q^{4} +(1.26113 + 2.18434i) q^{5} -2.53680 q^{6} +(1.47427 + 2.19693i) q^{7} +6.17804 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.19923 - 5.54123i) q^{10} +(2.98608 - 5.17205i) q^{11} +(2.21768 + 3.84114i) q^{12} -1.00000 q^{13} +(2.95656 - 6.02547i) q^{14} +2.52225 q^{15} +(-3.40086 - 5.89047i) q^{16} +(1.39706 - 2.41979i) q^{17} +(-1.26840 + 2.19693i) q^{18} +(1.00727 + 1.74465i) q^{19} -11.1871 q^{20} +(2.63974 - 0.178289i) q^{21} -15.1502 q^{22} +(3.53830 + 6.12851i) q^{23} +(3.08902 - 5.35034i) q^{24} +(-0.680880 + 1.17932i) q^{25} +(1.26840 + 2.19693i) q^{26} -1.00000 q^{27} +(-11.7082 + 0.790778i) q^{28} +4.59586 q^{29} +(-3.19923 - 5.54123i) q^{30} +(-1.18318 + 2.04933i) q^{31} +(-2.44928 + 4.24228i) q^{32} +(-2.98608 - 5.17205i) q^{33} -7.08815 q^{34} +(-2.93960 + 5.99092i) q^{35} +4.43536 q^{36} +(-1.59870 - 2.76903i) q^{37} +(2.55526 - 4.42583i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(7.79129 + 13.4949i) q^{40} -8.19259 q^{41} +(-3.73994 - 5.57319i) q^{42} +3.59125 q^{43} +(13.2444 + 22.9399i) q^{44} +(1.26113 - 2.18434i) q^{45} +(8.97597 - 15.5468i) q^{46} +(-5.04284 - 8.73445i) q^{47} -6.80173 q^{48} +(-2.65305 + 6.47776i) q^{49} +3.45452 q^{50} +(-1.39706 - 2.41979i) q^{51} +(2.21768 - 3.84114i) q^{52} +(5.40647 - 9.36428i) q^{53} +(1.26840 + 2.19693i) q^{54} +15.0633 q^{55} +(9.10810 + 13.5727i) q^{56} +2.01455 q^{57} +(-5.82939 - 10.0968i) q^{58} +(-5.74480 + 9.95029i) q^{59} +(-5.59356 + 9.68832i) q^{60} +(2.39706 + 4.15184i) q^{61} +6.00300 q^{62} +(1.16547 - 2.37522i) q^{63} -1.17677 q^{64} +(-1.26113 - 2.18434i) q^{65} +(-7.57510 + 13.1205i) q^{66} +(-2.65515 + 4.59886i) q^{67} +(6.19649 + 10.7326i) q^{68} +7.07660 q^{69} +(16.8902 - 1.14078i) q^{70} -8.35181 q^{71} +(-3.08902 - 5.35034i) q^{72} +(1.66093 - 2.87681i) q^{73} +(-4.05559 + 7.02448i) q^{74} +(0.680880 + 1.17932i) q^{75} -8.93526 q^{76} +(15.7649 - 1.06477i) q^{77} +2.53680 q^{78} +(6.14080 + 10.6362i) q^{79} +(8.57784 - 14.8573i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(10.3915 + 17.9986i) q^{82} -11.8547 q^{83} +(-5.16926 + 10.5350i) q^{84} +7.04750 q^{85} +(-4.55515 - 7.88975i) q^{86} +(2.29793 - 3.98013i) q^{87} +(18.4481 - 31.9531i) q^{88} +(1.84181 + 3.19011i) q^{89} -6.39846 q^{90} +(-1.47427 - 2.19693i) q^{91} -31.3873 q^{92} +(1.18318 + 2.04933i) q^{93} +(-12.7927 + 22.1576i) q^{94} +(-2.54060 + 4.40045i) q^{95} +(2.44928 + 4.24228i) q^{96} +1.29736 q^{97} +(17.5963 - 2.38782i) q^{98} -5.97217 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} - 10 q^{13} + 23 q^{14} + 6 q^{15} + 13 q^{17} + 7 q^{19} - 26 q^{20} + 2 q^{21} - 38 q^{22} + 4 q^{23} + 3 q^{24} - 16 q^{25} - 10 q^{27} - 4 q^{28} - 24 q^{29} - 2 q^{30} + 6 q^{31} - 21 q^{32} - q^{33} - 14 q^{34} - 3 q^{35} + 12 q^{36} - 11 q^{37} + 14 q^{38} - 5 q^{39} + 11 q^{40} - 20 q^{41} - 2 q^{42} + 20 q^{43} + 29 q^{44} + 3 q^{45} - q^{46} - 4 q^{47} + 22 q^{49} - 58 q^{50} - 13 q^{51} + 6 q^{52} + 9 q^{53} + 24 q^{55} + 42 q^{56} + 14 q^{57} - 34 q^{58} + 7 q^{59} - 13 q^{60} + 23 q^{61} + 48 q^{62} - 2 q^{63} - 26 q^{64} - 3 q^{65} - 19 q^{66} - 25 q^{67} + 20 q^{68} + 8 q^{69} + 73 q^{70} - 54 q^{71} - 3 q^{72} + 18 q^{73} - 15 q^{74} + 16 q^{75} - 4 q^{76} + 27 q^{77} - 8 q^{79} + 41 q^{80} - 5 q^{81} + 26 q^{82} - 24 q^{83} - 5 q^{84} + 20 q^{85} + 19 q^{86} - 12 q^{87} + 36 q^{88} + 29 q^{89} - 4 q^{90} - 4 q^{91} - 100 q^{92} - 6 q^{93} - 2 q^{94} + 33 q^{95} + 21 q^{96} - 26 q^{97} + 15 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + q^11 + 6 * q^12 - 10 * q^13 + 23 * q^14 + 6 * q^15 + 13 * q^17 + 7 * q^19 - 26 * q^20 + 2 * q^21 - 38 * q^22 + 4 * q^23 + 3 * q^24 - 16 * q^25 - 10 * q^27 - 4 * q^28 - 24 * q^29 - 2 * q^30 + 6 * q^31 - 21 * q^32 - q^33 - 14 * q^34 - 3 * q^35 + 12 * q^36 - 11 * q^37 + 14 * q^38 - 5 * q^39 + 11 * q^40 - 20 * q^41 - 2 * q^42 + 20 * q^43 + 29 * q^44 + 3 * q^45 - q^46 - 4 * q^47 + 22 * q^49 - 58 * q^50 - 13 * q^51 + 6 * q^52 + 9 * q^53 + 24 * q^55 + 42 * q^56 + 14 * q^57 - 34 * q^58 + 7 * q^59 - 13 * q^60 + 23 * q^61 + 48 * q^62 - 2 * q^63 - 26 * q^64 - 3 * q^65 - 19 * q^66 - 25 * q^67 + 20 * q^68 + 8 * q^69 + 73 * q^70 - 54 * q^71 - 3 * q^72 + 18 * q^73 - 15 * q^74 + 16 * q^75 - 4 * q^76 + 27 * q^77 - 8 * q^79 + 41 * q^80 - 5 * q^81 + 26 * q^82 - 24 * q^83 - 5 * q^84 + 20 * q^85 + 19 * q^86 - 12 * q^87 + 36 * q^88 + 29 * q^89 - 4 * q^90 - 4 * q^91 - 100 * q^92 - 6 * q^93 - 2 * q^94 + 33 * q^95 + 21 * q^96 - 26 * q^97 + 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.26840	−	2.19693i	−0.896895	−	1.55347i	−0.831442	−	0.555612i	$-0.812484\pi$
$2$	−1.26840	−	2.19693i	−0.896895	−	1.55347i	−0.0654532	−	0.997856i	$-0.520849\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−2.21768	+	3.84114i	−1.10884	+	1.92057i
$5$	1.26113	+	2.18434i	0.563993	+	0.976864i	0.997143	+	0.0755424i	$0.0240688\pi$
$5$	1.26113	+	2.18434i	0.563993	+	0.976864i	−0.433150	+	0.901322i	$0.642598\pi$
$6$	−2.53680			−1.03565
$7$	1.47427	+	2.19693i	0.557222	+	0.830363i
$7$	1.47427	+	2.19693i	0.557222	+	0.830363i
$8$	6.17804			2.18427
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	3.19923	−	5.54123i	1.01168	−	1.75229i
$11$	2.98608	−	5.17205i	0.900338	−	1.55943i	0.0732821	−	0.997311i	$-0.476653\pi$
$11$	2.98608	−	5.17205i	0.900338	−	1.55943i	0.827056	−	0.562120i	$-0.190014\pi$
$12$	2.21768	+	3.84114i	0.640190	+	1.10884i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	2.95656	−	6.02547i	0.790173	−	1.61038i
$15$	2.52225			0.651243
$16$	−3.40086	−	5.89047i	−0.850216	−	1.47262i
$17$	1.39706	−	2.41979i	0.338838	−	0.586885i	−0.645376	−	0.763865i	$-0.723299\pi$
$17$	1.39706	−	2.41979i	0.338838	−	0.586885i	0.984214	+	0.176980i	$0.0566328\pi$
$18$	−1.26840	+	2.19693i	−0.298965	+	0.517823i
$19$	1.00727	+	1.74465i	0.231085	+	0.400250i	0.958128	−	0.286342i	$-0.0924392\pi$
$19$	1.00727	+	1.74465i	0.231085	+	0.400250i	−0.727043	+	0.686592i	$0.759106\pi$
$20$	−11.1871			−2.50151
$21$	2.63974	−	0.178289i	0.576038	−	0.0389059i
$22$	−15.1502			−3.23003
$23$	3.53830	+	6.12851i	0.737786	+	1.27788i	0.953490	+	0.301425i	$0.0974622\pi$
$23$	3.53830	+	6.12851i	0.737786	+	1.27788i	−0.215704	+	0.976459i	$0.569204\pi$
$24$	3.08902	−	5.35034i	0.630543	−	1.09213i
$25$	−0.680880	+	1.17932i	−0.136176	+	0.235864i
$26$	1.26840	+	2.19693i	0.248754	+	0.430854i
$27$	−1.00000			−0.192450
$28$	−11.7082	+	0.790778i	−2.21264	+	0.149443i
$29$	4.59586			0.853429			0.426715	−	0.904386i	$-0.359671\pi$
$29$	4.59586			0.853429			0.426715	+	0.904386i	$0.359671\pi$
$30$	−3.19923	−	5.54123i	−0.584096	−	1.01168i
$31$	−1.18318	+	2.04933i	−0.212506	+	0.368071i	−0.952498	−	0.304545i	$-0.901496\pi$
$31$	−1.18318	+	2.04933i	−0.212506	+	0.368071i	0.739992	+	0.672615i	$0.234829\pi$
$32$	−2.44928	+	4.24228i	−0.432976	+	0.749936i
$33$	−2.98608	−	5.17205i	−0.519810	−	0.900338i
$34$	−7.08815			−1.21561
$35$	−2.93960	+	5.99092i	−0.496883	+	1.01265i
$36$	4.43536			0.739227
$37$	−1.59870	−	2.76903i	−0.262825	−	0.455226i	0.704167	−	0.710035i	$-0.251321\pi$
$37$	−1.59870	−	2.76903i	−0.262825	−	0.455226i	−0.966991	+	0.254809i	$0.917987\pi$
$38$	2.55526	−	4.42583i	0.414517	−	0.717965i
$39$	−0.500000	+	0.866025i	−0.0800641	+	0.138675i
$40$	7.79129	+	13.4949i	1.23191	+	2.13373i
$41$	−8.19259			−1.27947			−0.639733	−	0.768597i	$-0.720955\pi$
$41$	−8.19259			−1.27947			−0.639733	+	0.768597i	$0.720955\pi$
$42$	−3.73994	−	5.57319i	−0.577085	−	0.859962i
$43$	3.59125			0.547661			0.273831	−	0.961778i	$-0.411709\pi$
$43$	3.59125			0.547661			0.273831	+	0.961778i	$0.411709\pi$
$44$	13.2444	+	22.9399i	1.99666	+	3.45832i
$45$	1.26113	−	2.18434i	0.187998	−	0.325621i
$46$	8.97597	−	15.5468i	1.32343	−	2.29225i
$47$	−5.04284	−	8.73445i	−0.735573	−	1.27405i	−0.954471	−	0.298303i	$-0.903580\pi$
$47$	−5.04284	−	8.73445i	−0.735573	−	1.27405i	0.218898	−	0.975748i	$-0.429754\pi$
$48$	−6.80173			−0.981745
$49$	−2.65305	+	6.47776i	−0.379007	+	0.925394i
$50$	3.45452			0.488542
$51$	−1.39706	−	2.41979i	−0.195628	−	0.338838i
$52$	2.21768	−	3.84114i	0.307537	−	0.532670i
$53$	5.40647	−	9.36428i	0.742636	−	1.28628i	−0.208656	−	0.977989i	$-0.566909\pi$
$53$	5.40647	−	9.36428i	0.742636	−	1.28628i	0.951291	−	0.308293i	$-0.0997579\pi$
$54$	1.26840	+	2.19693i	0.172608	+	0.298965i
$55$	15.0633			2.03114
$56$	9.10810	+	13.5727i	1.21712	+	1.81373i
$57$	2.01455			0.266834
$58$	−5.82939	−	10.0968i	−0.765436	−	1.32577i
$59$	−5.74480	+	9.95029i	−0.747910	+	1.29542i	0.200913	+	0.979609i	$0.435609\pi$
$59$	−5.74480	+	9.95029i	−0.747910	+	1.29542i	−0.948823	+	0.315808i	$0.897724\pi$
$60$	−5.59356	+	9.68832i	−0.722125	+	1.25076i
$61$	2.39706	+	4.15184i	0.306913	+	0.531588i	0.977685	−	0.210075i	$-0.0673707\pi$
$61$	2.39706	+	4.15184i	0.306913	+	0.531588i	−0.670773	+	0.741663i	$0.734037\pi$
$62$	6.00300			0.762381
$63$	1.16547	−	2.37522i	0.146835	−	0.299250i
$64$	−1.17677			−0.147097
$65$	−1.26113	−	2.18434i	−0.156423	−	0.270933i
$66$	−7.57510	+	13.1205i	−0.932431	+	1.61502i
$67$	−2.65515	+	4.59886i	−0.324378	+	0.561840i	−0.981386	−	0.192044i	$-0.938488\pi$
$67$	−2.65515	+	4.59886i	−0.324378	+	0.561840i	0.657008	+	0.753884i	$0.271822\pi$
$68$	6.19649	+	10.7326i	0.751435	+	1.30152i
$69$	7.07660			0.851922
$70$	16.8902	−	1.14078i	2.01877	−	0.136349i
$71$	−8.35181			−0.991178			−0.495589	−	0.868557i	$-0.665048\pi$
$71$	−8.35181			−0.991178			−0.495589	+	0.868557i	$0.665048\pi$
$72$	−3.08902	−	5.35034i	−0.364044	−	0.630543i
$73$	1.66093	−	2.87681i	0.194397	−	0.336705i	−0.752306	−	0.658814i	$-0.771058\pi$
$73$	1.66093	−	2.87681i	0.194397	−	0.336705i	0.946703	+	0.322109i	$0.104392\pi$
$74$	−4.05559	+	7.02448i	−0.471452	+	0.816579i
$75$	0.680880	+	1.17932i	0.0786213	+	0.136176i
$76$	−8.93526			−1.02494
$77$	15.7649	−	1.06477i	1.79658	−	0.121342i
$78$	2.53680			0.287236
$79$	6.14080	+	10.6362i	0.690894	+	1.19666i	0.971545	+	0.236854i	$0.0761162\pi$
$79$	6.14080	+	10.6362i	0.690894	+	1.19666i	−0.280652	+	0.959810i	$0.590551\pi$
$80$	8.57784	−	14.8573i	0.959032	−	1.66109i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	10.3915	+	17.9986i	1.14755	+	1.98761i
$83$	−11.8547			−1.30122			−0.650611	−	0.759411i	$-0.725487\pi$
$83$	−11.8547			−1.30122			−0.650611	+	0.759411i	$0.725487\pi$
$84$	−5.16926	+	10.5350i	−0.564013	+	1.14946i
$85$	7.04750			0.764409
$86$	−4.55515	−	7.88975i	−0.491194	−	0.850774i
$87$	2.29793	−	3.98013i	0.246364	−	0.426715i
$88$	18.4481	−	31.9531i	1.96658	−	3.40621i
$89$	1.84181	+	3.19011i	0.195231	+	0.338151i	0.946976	−	0.321303i	$-0.104121\pi$
$89$	1.84181	+	3.19011i	0.195231	+	0.338151i	−0.751745	+	0.659454i	$0.770788\pi$
$90$	−6.39846			−0.674457
$91$	−1.47427	−	2.19693i	−0.154546	−	0.230301i
$92$	−31.3873			−3.27235
$93$	1.18318	+	2.04933i	0.122690	+	0.212506i
$94$	−12.7927	+	22.1576i	−1.31946	+	2.28538i
$95$	−2.54060	+	4.40045i	−0.260660	+	0.451477i
$96$	2.44928	+	4.24228i	0.249979	+	0.432976i
$97$	1.29736			0.131727			0.0658636	−	0.997829i	$-0.479020\pi$
$97$	1.29736			0.131727			0.0658636	+	0.997829i	$0.479020\pi$
$98$	17.5963	−	2.38782i	1.77750	−	0.241207i
$99$	−5.97217			−0.600225
$100$	−3.01995	−	5.23071i	−0.301995	−	0.523071i
$101$	−1.01982	+	1.76639i	−0.101476	+	0.175762i	−0.912293	−	0.409538i	$-0.865690\pi$
$101$	−1.01982	+	1.76639i	−0.101476	+	0.175762i	0.810817	+	0.585300i	$0.199023\pi$
$102$	−3.54408	+	6.13852i	−0.350916	+	0.607804i
$103$	−2.61774	−	4.53406i	−0.257934	−	0.446754i	0.707754	−	0.706459i	$-0.249708\pi$
$103$	−2.61774	−	4.53406i	−0.257934	−	0.446754i	−0.965688	+	0.259704i	$0.916375\pi$
$104$	−6.17804			−0.605806
$105$	3.71849	+	5.54123i	0.362887	+	0.540768i
$106$	−27.4303			−2.66426
$107$	−8.93676	−	15.4789i	−0.863949	−	1.49640i	−0.868087	−	0.496412i	$-0.834651\pi$
$107$	−8.93676	−	15.4789i	−0.863949	−	1.49640i	0.00413835	−	0.999991i	$-0.498683\pi$
$108$	2.21768	−	3.84114i	0.213397	−	0.369614i
$109$	−0.468495	+	0.811457i	−0.0448737	+	0.0777235i	−0.887590	−	0.460635i	$-0.847622\pi$
$109$	−0.468495	+	0.811457i	−0.0448737	+	0.0777235i	0.842716	+	0.538358i	$0.180955\pi$
$110$	−19.1063	−	33.0931i	−1.82172	−	3.15531i
$111$	−3.19740			−0.303484
$112$	7.92718	−	16.1556i	0.749048	−	1.52656i
$113$	−15.5090			−1.45896			−0.729481	−	0.684002i	$-0.760238\pi$
$113$	−15.5090			−1.45896			−0.729481	+	0.684002i	$0.760238\pi$
$114$	−2.55526	−	4.42583i	−0.239322	−	0.414517i
$115$	−8.92449	+	15.4577i	−0.832213	+	1.44143i
$116$	−10.1921	+	17.6533i	−0.946317	+	1.63907i
$117$	0.500000	+	0.866025i	0.0462250	+	0.0800641i
$118$	29.1469			2.68319
$119$	7.37577	−	0.498163i	0.676135	−	0.0456665i
$120$	15.5826			1.42249
$121$	−12.3334	−	21.3620i	−1.12122	−	1.94200i
$122$	6.08088	−	10.5324i	0.550537	−	0.953558i
$123$	−4.09629	+	7.09499i	−0.369350	+	0.639733i
$124$	−5.24784	−	9.08953i	−0.471270	−	0.816264i
$125$	9.17656			0.820777
$126$	−6.69649	+	0.452284i	−0.596571	+	0.0402927i
$127$	−5.29002			−0.469414			−0.234707	−	0.972066i	$-0.575413\pi$
$127$	−5.29002			−0.469414			−0.234707	+	0.972066i	$0.575413\pi$
$128$	6.39118	+	11.0699i	0.564906	+	0.978446i
$129$	1.79563	−	3.11012i	0.158096	−	0.273831i
$130$	−3.19923	+	5.54123i	−0.280591	+	0.485998i
$131$	6.32349	+	10.9526i	0.552485	+	0.956933i	0.998094	+	0.0617052i	$0.0196538\pi$
$131$	6.32349	+	10.9526i	0.552485	+	0.956933i	−0.445609	+	0.895228i	$0.647013\pi$
$132$	26.4887			2.30555
$133$	−2.34789	+	4.78501i	−0.203588	+	0.414913i
$134$	13.4712			1.16373
$135$	−1.26113	−	2.18434i	−0.108540	−	0.187998i
$136$	8.63112	−	14.9495i	0.740112	−	1.28191i
$137$	3.57373	−	6.18988i	0.305324	−	0.528838i	−0.672009	−	0.740543i	$-0.734568\pi$
$137$	3.57373	−	6.18988i	0.305324	−	0.528838i	0.977334	+	0.211705i	$0.0679017\pi$
$138$	−8.97597	−	15.5468i	−0.764085	−	1.32343i
$139$	19.7543			1.67554			0.837768	−	0.546027i	$-0.183860\pi$
$139$	19.7543			1.67554			0.837768	+	0.546027i	$0.183860\pi$
$140$	−16.4928	−	24.5774i	−1.39390	−	2.07717i
$141$	−10.0857			−0.849367
$142$	10.5934	+	18.3484i	0.888983	+	1.53976i
$143$	−2.98608	+	5.17205i	−0.249709	+	0.432508i
$144$	−3.40086	+	5.89047i	−0.283405	+	0.490872i
$145$	5.79596	+	10.0389i	0.481328	+	0.833685i
$146$	−8.42689			−0.697415
$147$	4.28338	+	5.53648i	0.353287	+	0.456642i
$148$	14.1816			1.16572
$149$	−6.85318	−	11.8701i	−0.561435	−	0.972433i	−0.997372	−	0.0724562i	$-0.976916\pi$
$149$	−6.85318	−	11.8701i	−0.561435	−	0.972433i	0.435937	−	0.899977i	$-0.356417\pi$
$150$	1.72726	−	2.99170i	0.141030	−	0.244271i
$151$	−1.57204	+	2.72285i	−0.127931	+	0.221583i	−0.922875	−	0.385100i	$-0.874167\pi$
$151$	−1.57204	+	2.72285i	−0.127931	+	0.221583i	0.794944	+	0.606683i	$0.207500\pi$
$152$	6.22298	+	10.7785i	0.504750	+	0.874253i
$153$	−2.79413			−0.225892
$154$	−22.3355	−	33.2840i	−1.79985	−	2.68210i
$155$	−5.96857			−0.479407
$156$	−2.21768	−	3.84114i	−0.177557	−	0.307537i
$157$	−2.21390	+	3.83460i	−0.176689	+	0.306034i	−0.940744	−	0.339116i	$-0.889872\pi$
$157$	−2.21390	+	3.83460i	−0.176689	+	0.306034i	0.764056	+	0.645150i	$0.223205\pi$
$158$	15.5780	−	26.9819i	1.23932	−	2.14656i
$159$	−5.40647	−	9.36428i	−0.428761	−	0.742636i
$160$	−12.3554			−0.976781
$161$	−8.24753	+	16.8085i	−0.649997	+	1.32470i
$162$	2.53680			0.199310
$163$	−9.20501	−	15.9435i	−0.720992	−	1.24879i	−0.960603	−	0.277925i	$-0.910353\pi$
$163$	−9.20501	−	15.9435i	−0.720992	−	1.24879i	0.239611	−	0.970869i	$-0.422980\pi$
$164$	18.1686	−	31.4689i	1.41873	−	2.45730i
$165$	7.53166	−	13.0452i	0.586339	−	1.01557i
$166$	15.0365	+	26.0440i	1.16706	+	2.02141i
$167$	−8.78236			−0.679600			−0.339800	−	0.940498i	$-0.610359\pi$
$167$	−8.78236			−0.679600			−0.339800	+	0.940498i	$0.610359\pi$
$168$	16.3084	−	1.10148i	1.25822	−	0.0849808i
$169$	1.00000			0.0769231
$170$	−8.93906	−	15.4829i	−0.685594	−	1.18748i
$171$	1.00727	−	1.74465i	0.0770282	−	0.133417i
$172$	−7.96426	+	13.7945i	−0.607269	+	1.05182i
$173$	4.97080	+	8.60967i	0.377923	+	0.654581i	0.990760	−	0.135628i	$-0.0433052\pi$
$173$	4.97080	+	8.60967i	0.377923	+	0.654581i	−0.612837	+	0.790209i	$0.709972\pi$
$174$	−11.6588			−0.883850
$175$	−3.59469	+	0.242787i	−0.271733	+	0.0183530i
$176$	−40.6210			−3.06193
$177$	5.74480	+	9.95029i	0.431806	+	0.747910i
$178$	4.67230	−	8.09267i	0.350204	−	0.606571i
$179$	−8.29646	+	14.3699i	−0.620106	+	1.07406i	0.369359	+	0.929287i	$0.379577\pi$
$179$	−8.29646	+	14.3699i	−0.620106	+	1.07406i	−0.989466	+	0.144769i	$0.953756\pi$
$180$	5.59356	+	9.68832i	0.416919	+	0.722125i
$181$	−17.8813			−1.32911			−0.664554	−	0.747240i	$-0.731378\pi$
$181$	−17.8813			−1.32911			−0.664554	+	0.747240i	$0.731378\pi$
$182$	−2.95656	+	6.02547i	−0.219154	+	0.446638i
$183$	4.79413			0.354392
$184$	21.8597	+	37.8622i	1.61152	+	2.79124i
$185$	4.03233	−	6.98419i	0.296463	−	0.513488i
$186$	3.00150	−	5.19875i	0.220080	−	0.381191i
$187$	−8.34350	−	14.4514i	−0.610137	−	1.05679i
$188$	44.7336			3.26254
$189$	−1.47427	−	2.19693i	−0.107237	−	0.159804i
$190$	12.8900			0.935139
$191$	−0.341936	−	0.592251i	−0.0247417	−	0.0428538i	0.853389	−	0.521274i	$-0.174543\pi$
$191$	−0.341936	−	0.592251i	−0.0247417	−	0.0428538i	−0.878131	+	0.478420i	$0.841210\pi$
$192$	−0.588386	+	1.01912i	−0.0424631	+	0.0735483i
$193$	1.43306	−	2.48214i	0.103154	−	0.178668i	−0.809828	−	0.586667i	$-0.800440\pi$
$193$	1.43306	−	2.48214i	0.103154	−	0.178668i	0.912983	+	0.407999i	$0.133773\pi$
$194$	−1.64558	−	2.85022i	−0.118145	−	0.204634i
$195$	−2.52225			−0.180622
$196$	−18.9983	−	24.5563i	−1.35702	−	1.75402i
$197$	3.63963			0.259313			0.129656	−	0.991559i	$-0.458613\pi$
$197$	3.63963			0.259313			0.129656	+	0.991559i	$0.458613\pi$
$198$	7.57510	+	13.1205i	0.538339	+	0.932431i
$199$	−5.65396	+	9.79294i	−0.400798	+	0.694203i	−0.993822	−	0.110982i	$-0.964601\pi$
$199$	−5.65396	+	9.79294i	−0.400798	+	0.694203i	0.593024	+	0.805185i	$0.297934\pi$
$200$	−4.20650	+	7.28588i	−0.297445	+	0.515189i
$201$	2.65515	+	4.59886i	0.187280	+	0.324378i
$202$	5.17418			0.364054
$203$	6.77554	+	10.0968i	0.475550	+	0.708656i
$204$	12.3930			0.867682
$205$	−10.3319	−	17.8954i	−0.721610	−	1.24987i
$206$	−6.64069	+	11.5020i	−0.462679	+	0.801384i
$207$	3.53830	−	6.12851i	0.245929	−	0.425961i
$208$	3.40086	+	5.89047i	0.235807	+	0.408431i
$209$	12.0312			0.832217
$210$	7.45718	−	15.1978i	0.514594	−	1.04875i
$211$	−3.67632			−0.253089			−0.126544	−	0.991961i	$-0.540389\pi$
$211$	−3.67632			−0.253089			−0.126544	+	0.991961i	$0.540389\pi$
$212$	23.9797	+	41.5340i	1.64693	+	2.85257i
$213$	−4.17591	+	7.23288i	−0.286128	+	0.495589i
$214$	−22.6708	+	39.2669i	−1.54974	+	2.68423i
$215$	4.52903	+	7.84450i	0.308877	+	0.534991i
$216$	−6.17804			−0.420362
$217$	−6.24658	+	0.421897i	−0.424045	+	0.0286402i
$218$	2.37696			0.160988
$219$	−1.66093	−	2.87681i	−0.112235	−	0.194397i
$220$	−33.4056	+	57.8603i	−2.25221	+	3.90094i
$221$	−1.39706	+	2.41979i	−0.0939767	+	0.162772i
$222$	4.05559	+	7.02448i	0.272193	+	0.471452i
$223$	−12.1311			−0.812355			−0.406178	−	0.913794i	$-0.633139\pi$
$223$	−12.1311			−0.812355			−0.406178	+	0.913794i	$0.633139\pi$
$224$	−12.9309	+	0.873361i	−0.863983	+	0.0583539i
$225$	1.36176			0.0907840
$226$	19.6716	+	34.0722i	1.30853	+	2.26645i
$227$	−8.63129	+	14.9498i	−0.572879	+	0.992255i	0.423390	+	0.905948i	$0.360840\pi$
$227$	−8.63129	+	14.9498i	−0.572879	+	0.992255i	−0.996269	+	0.0863075i	$0.972493\pi$
$228$	−4.46763	+	7.73816i	−0.295876	+	0.512472i
$229$	0.687087	+	1.19007i	0.0454040	+	0.0786420i	0.887834	−	0.460163i	$-0.152209\pi$
$229$	0.687087	+	1.19007i	0.0454040	+	0.0786420i	−0.842430	+	0.538805i	$0.818876\pi$
$230$	45.2793			2.98563
$231$	6.96035	−	14.1852i	0.457958	−	0.933320i
$232$	28.3934			1.86412
$233$	2.81788	+	4.88071i	0.184605	+	0.319746i	0.943444	−	0.331533i	$-0.107566\pi$
$233$	2.81788	+	4.88071i	0.184605	+	0.319746i	−0.758838	+	0.651279i	$0.774233\pi$
$234$	1.26840	−	2.19693i	0.0829180	−	0.143618i
$235$	12.7193	−	22.0305i	0.829716	−	1.43711i
$236$	−25.4803	−	44.1332i	−1.65863	−	2.87282i
$237$	12.2816			0.797776
$238$	−10.4499	−	15.5722i	−0.677364	−	1.00940i
$239$	10.3028			0.666430			0.333215	−	0.942851i	$-0.391867\pi$
$239$	10.3028			0.666430			0.333215	+	0.942851i	$0.391867\pi$
$240$	−8.57784	−	14.8573i	−0.553697	−	0.959032i
$241$	9.88781	−	17.1262i	0.636930	−	1.10320i	−0.349173	−	0.937058i	$-0.613537\pi$
$241$	9.88781	−	17.1262i	0.636930	−	1.10320i	0.986103	−	0.166137i	$-0.0531293\pi$
$242$	−31.2874	+	54.1913i	−2.01123	+	3.48355i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−21.2637			−1.36127
$245$	−17.4954	+	2.37413i	−1.11774	+	0.151678i
$246$	20.7830			1.32507
$247$	−1.00727	−	1.74465i	−0.0640913	−	0.111009i
$248$	−7.30974	+	12.6608i	−0.464169	+	0.803964i
$249$	−5.92735	+	10.2665i	−0.375631	+	0.650611i
$250$	−11.6396	−	20.1603i	−0.736150	−	1.27505i
$251$	−8.30123			−0.523969			−0.261984	−	0.965072i	$-0.584377\pi$
$251$	−8.30123			−0.523969			−0.261984	+	0.965072i	$0.584377\pi$
$252$	6.53893	+	9.74421i	0.411914	+	0.613827i
$253$	42.2626			2.65703
$254$	6.70987	+	11.6218i	0.421015	+	0.729219i
$255$	3.52375	−	6.10332i	0.220666	−	0.382204i
$256$	15.0364	−	26.0438i	0.939774	−	1.62774i
$257$	−13.2214	−	22.9001i	−0.824727	−	1.42847i	−0.902128	−	0.431469i	$-0.857996\pi$
$257$	−13.2214	−	22.9001i	−0.824727	−	1.42847i	0.0774012	−	0.997000i	$-0.475338\pi$
$258$	−9.11030			−0.567183
$259$	3.72646	−	7.59454i	0.231551	−	0.471902i
$260$	11.1871			0.693795
$261$	−2.29793	−	3.98013i	−0.142238	−	0.246364i
$262$	16.0414	−	27.7846i	0.991043	−	1.71654i
$263$	4.89146	−	8.47226i	0.301620	−	0.522422i	−0.674883	−	0.737925i	$-0.735806\pi$
$263$	4.89146	−	8.47226i	0.301620	−	0.522422i	0.976503	+	0.215503i	$0.0691392\pi$
$264$	−18.4481	−	31.9531i	−1.13540	−	1.96658i
$265$	27.2730			1.67536
$266$	13.4904	−	0.911149i	0.827150	−	0.0558661i
$267$	3.68362			0.225434
$268$	−11.7766	−	20.3976i	−0.719368	−	1.24598i
$269$	10.1461	−	17.5736i	0.618621	−	1.07148i	−0.371116	−	0.928586i	$-0.621025\pi$
$269$	10.1461	−	17.5736i	0.618621	−	1.07148i	0.989738	−	0.142897i	$-0.0456419\pi$
$270$	−3.19923	+	5.54123i	−0.194699	+	0.337228i
$271$	11.2066	+	19.4105i	0.680754	+	1.17910i	0.974751	+	0.223295i	$0.0716813\pi$
$271$	11.2066	+	19.4105i	0.680754	+	1.17910i	−0.293996	+	0.955806i	$0.594985\pi$
$272$	−19.0049			−1.15234
$273$	−2.63974	+	0.178289i	−0.159764	+	0.0107906i
$274$	−18.1317			−1.09538
$275$	4.06633	+	7.04309i	0.245209	+	0.424714i
$276$	−15.6936	+	27.1822i	−0.944647	+	1.63618i
$277$	−2.53620	+	4.39283i	−0.152386	+	0.263939i	−0.932104	−	0.362191i	$-0.882029\pi$
$277$	−2.53620	+	4.39283i	−0.152386	+	0.263939i	0.779718	+	0.626130i	$0.215362\pi$
$278$	−25.0563	−	43.3989i	−1.50278	−	2.60289i
$279$	2.36636			0.141670
$280$	−18.1610	+	37.0121i	−1.08532	+	2.21190i
$281$	−4.18893			−0.249891			−0.124945	−	0.992164i	$-0.539876\pi$
$281$	−4.18893			−0.249891			−0.124945	+	0.992164i	$0.539876\pi$
$282$	12.7927	+	22.1576i	0.761793	+	1.31946i
$283$	−4.05923	+	7.03080i	−0.241296	+	0.417938i	−0.961084	−	0.276257i	$-0.910906\pi$
$283$	−4.05923	+	7.03080i	−0.241296	+	0.417938i	0.719787	+	0.694195i	$0.244239\pi$
$284$	18.5217	−	32.0805i	1.09906	−	1.90363i
$285$	2.54060	+	4.40045i	0.150492	+	0.260660i
$286$	15.1502			0.895850
$287$	−12.0781	−	17.9986i	−0.712948	−	1.06242i
$288$	4.89856			0.288651
$289$	4.59642	+	7.96123i	0.270378	+	0.468308i
$290$	14.7032	−	25.4667i	0.863401	−	1.49546i
$291$	0.648681	−	1.12355i	0.0380264	−	0.0658636i
$292$	7.36682	+	12.7597i	0.431111	+	0.746706i
$293$	2.53093			0.147859			0.0739294	−	0.997263i	$-0.476446\pi$
$293$	2.53093			0.147859			0.0739294	+	0.997263i	$0.476446\pi$
$294$	6.73025	−	16.4328i	0.392516	−	0.958380i
$295$	−28.9797			−1.68726
$296$	−9.87683	−	17.1072i	−0.574079	−	0.994334i
$297$	−2.98608	+	5.17205i	−0.173270	+	0.300113i
$298$	−17.3852	+	30.1120i	−1.00710	+	1.74434i
$299$	−3.53830	−	6.12851i	−0.204625	−	0.354421i
$300$	−6.03990			−0.348714
$301$	5.29448	+	7.88975i	0.305169	+	0.454758i
$302$	7.97591			0.458962
$303$	1.01982	+	1.76639i	0.0585874	+	0.101476i
$304$	6.85121	−	11.8666i	0.392944	−	0.680598i
$305$	−6.04600	+	10.4720i	−0.346193	+	0.599624i
$306$	3.54408	+	6.13852i	0.202601	+	0.350916i
$307$	−18.2289			−1.04038			−0.520190	−	0.854050i	$-0.674139\pi$
$307$	−18.2289			−1.04038			−0.520190	+	0.854050i	$0.674139\pi$
$308$	−30.8717	+	62.9167i	−1.75908	+	3.58501i
$309$	−5.23548			−0.297836
$310$	7.57054	+	13.1126i	0.429978	+	0.744743i
$311$	−2.39363	+	4.14589i	−0.135731	+	0.235092i	−0.925876	−	0.377827i	$-0.876671\pi$
$311$	−2.39363	+	4.14589i	−0.135731	+	0.235092i	0.790146	+	0.612919i	$0.210005\pi$
$312$	−3.08902	+	5.35034i	−0.174881	+	0.302903i
$313$	−2.64968	−	4.58939i	−0.149769	−	0.259407i	0.781373	−	0.624064i	$-0.214520\pi$
$313$	−2.64968	−	4.58939i	−0.149769	−	0.259407i	−0.931142	+	0.364657i	$0.881186\pi$
$314$	11.2325			0.633885
$315$	6.65809	−	0.449690i	0.375141	−	0.0253372i
$316$	−54.4734			−3.06437
$317$	−5.37099	−	9.30282i	−0.301665	−	0.522498i	0.674849	−	0.737956i	$-0.264209\pi$
$317$	−5.37099	−	9.30282i	−0.301665	−	0.522498i	−0.976513	+	0.215458i	$0.930876\pi$
$318$	−13.7151	+	23.7553i	−0.769107	+	1.33213i
$319$	13.7236	−	23.7700i	0.768375	−	1.33086i
$320$	−1.48406	−	2.57047i	−0.0829614	−	0.143693i
$321$	−17.8735			−0.997602
$322$	47.3884	−	3.20064i	2.64085	−	0.178364i
$323$	5.62891			0.313201
$324$	−2.21768	−	3.84114i	−0.123205	−	0.213397i
$325$	0.680880	−	1.17932i	0.0377684	−	0.0654168i
$326$	−23.3513	+	40.4456i	−1.29331	+	2.24007i
$327$	0.468495	+	0.811457i	0.0259078	+	0.0448737i
$328$	−50.6141			−2.79470
$329$	11.7545	−	23.9557i	0.648047	−	1.32072i
$330$	−38.2126			−2.10354
$331$	−1.67832	−	2.90694i	−0.0922489	−	0.159780i	0.816208	−	0.577758i	$-0.196072\pi$
$331$	−1.67832	−	2.90694i	−0.0922489	−	0.159780i	−0.908457	+	0.417978i	$0.862739\pi$
$332$	26.2900	−	45.5356i	1.44285	−	2.49909i
$333$	−1.59870	+	2.76903i	−0.0876082	+	0.151742i
$334$	11.1396	+	19.2943i	0.609530	+	1.05574i
$335$	−13.3939			−0.731789
$336$	−10.0276	−	14.9430i	−0.547050	−	0.815205i
$337$	9.95736			0.542412			0.271206	−	0.962521i	$-0.412578\pi$
$337$	9.95736			0.542412			0.271206	+	0.962521i	$0.412578\pi$
$338$	−1.26840	−	2.19693i	−0.0689919	−	0.119498i
$339$	−7.75448	+	13.4312i	−0.421166	+	0.729481i
$340$	−15.6291	+	27.0704i	−0.847608	+	1.46810i
$341$	7.06616	+	12.2389i	0.382654	+	0.662776i
$342$	−5.11051			−0.276345
$343$	−18.1425	+	3.72140i	−0.979604	+	0.200937i
$344$	22.1869			1.19624
$345$	8.92449	+	15.4577i	0.480478	+	0.832213i
$346$	12.6099	−	21.8410i	0.677914	−	1.17418i
$347$	11.0289	−	19.1026i	0.592063	−	1.02548i	−0.401891	−	0.915688i	$-0.631647\pi$
$347$	11.0289	−	19.1026i	0.592063	−	1.02548i	0.993954	−	0.109796i	$-0.0350198\pi$
$348$	10.1921	+	17.6533i	0.546357	+	0.946317i
$349$	10.4865			0.561331			0.280665	−	0.959806i	$-0.409445\pi$
$349$	10.4865			0.561331			0.280665	+	0.959806i	$0.409445\pi$
$350$	5.09290	+	7.58935i	0.272227	+	0.405668i
$351$	1.00000			0.0533761
$352$	14.6275	+	25.3356i	0.779649	+	1.35039i
$353$	−3.02695	+	5.24283i	−0.161108	+	0.279048i	−0.935266	−	0.353945i	$-0.884840\pi$
$353$	−3.02695	+	5.24283i	−0.161108	+	0.279048i	0.774158	+	0.632992i	$0.218173\pi$
$354$	14.5734	−	25.2419i	0.774569	−	1.34159i
$355$	−10.5327	−	18.2432i	−0.559017	−	0.968247i
$356$	−16.3382			−0.865922
$357$	3.25646	−	6.63668i	0.172350	−	0.351251i
$358$	42.0929			2.22468
$359$	−5.41978	−	9.38733i	−0.286045	−	0.495444i	0.686817	−	0.726830i	$-0.259007\pi$
$359$	−5.41978	−	9.38733i	−0.286045	−	0.495444i	−0.972862	+	0.231386i	$0.925674\pi$
$360$	7.79129	−	13.4949i	0.410637	−	0.711244i
$361$	7.47080	−	12.9398i	0.393200	−	0.681042i
$362$	22.6807	+	39.2841i	1.19207	+	2.06473i
$363$	−24.6668			−1.29467
$364$	11.7082	−	0.790778i	0.613676	−	0.0414480i
$365$	8.37856			0.438554
$366$	−6.08088	−	10.5324i	−0.317853	−	0.550537i
$367$	17.8967	−	30.9980i	0.934199	−	1.61808i	0.158142	−	0.987416i	$-0.449449\pi$
$367$	17.8967	−	30.9980i	0.934199	−	1.61808i	0.776056	−	0.630664i	$-0.217217\pi$
$368$	24.0665	−	41.6845i	1.25456	−	2.17295i
$369$	4.09629	+	7.09499i	0.213244	+	0.369350i
$370$	−20.4584			−1.06358
$371$	28.5433	−	1.92783i	1.48190	−	0.100088i
$372$	−10.4957			−0.544176
$373$	13.4619	+	23.3167i	0.697030	+	1.20729i	0.969492	+	0.245124i	$0.0788287\pi$
$373$	13.4619	+	23.3167i	0.697030	+	1.20729i	−0.272462	+	0.962166i	$0.587838\pi$
$374$	−21.1658	+	36.6603i	−1.09446	+	1.89566i
$375$	4.58828	−	7.94713i	0.236938	−	0.410388i
$376$	−31.1548	−	53.9617i	−1.60669	−	2.78286i
$377$	−4.59586			−0.236699
$378$	−2.95656	+	6.02547i	−0.152069	+	0.309917i
$379$	−25.0182			−1.28510			−0.642550	−	0.766243i	$-0.722124\pi$
$379$	−25.0182			−1.28510			−0.642550	+	0.766243i	$0.722124\pi$
$380$	−11.2685	−	19.5176i	−0.578061	−	1.00123i
$381$	−2.64501	+	4.58130i	−0.135508	+	0.234707i
$382$	−0.867425	+	1.50242i	−0.0443813	+	0.0768707i
$383$	9.52835	+	16.5036i	0.486876	+	0.843294i	0.999886	−	0.0150884i	$-0.00480298\pi$
$383$	9.52835	+	16.5036i	0.486876	+	0.843294i	−0.513010	+	0.858383i	$0.671470\pi$
$384$	12.7824			0.652297
$385$	22.2074	+	33.0931i	1.13179	+	1.68658i
$386$	−7.27079			−0.370074
$387$	−1.79563	−	3.11012i	−0.0912768	−	0.158096i
$388$	−2.87714	+	4.98335i	−0.146065	+	0.252991i
$389$	11.0361	−	19.1151i	0.559553	−	0.969174i	−0.437981	−	0.898984i	$-0.644306\pi$
$389$	11.0361	−	19.1151i	0.559553	−	0.969174i	0.997534	−	0.0701897i	$-0.0223605\pi$
$390$	3.19923	+	5.54123i	0.161999	+	0.280591i
$391$	19.7729			0.999960
$392$	−16.3906	+	40.0198i	−0.827851	+	2.02131i
$393$	12.6470			0.637955
$394$	−4.61651	−	7.99602i	−0.232576	−	0.402834i
$395$	−15.4886	+	26.8271i	−0.779318	+	1.34982i
$396$	13.2444	−	22.9399i	0.665554	−	1.15277i
$397$	−10.7946	−	18.6968i	−0.541765	−	0.938364i	−0.998803	−	0.0489172i	$-0.984423\pi$
$397$	−10.7946	−	18.6968i	−0.541765	−	0.938364i	0.457038	−	0.889447i	$-0.348910\pi$
$398$	28.6859			1.43790
$399$	2.96999	+	4.42583i	0.148686	+	0.221569i
$400$	9.26232			0.463116
$401$	−1.68536	−	2.91912i	−0.0841626	−	0.145774i	0.820871	−	0.571113i	$-0.193488\pi$
$401$	−1.68536	−	2.91912i	−0.0841626	−	0.145774i	−0.905034	+	0.425339i	$0.860155\pi$
$402$	6.73559	−	11.6664i	0.335941	−	0.581867i
$403$	1.18318	−	2.04933i	0.0589385	−	0.102084i
$404$	−4.52329	−	7.83457i	−0.225042	−	0.389784i
$405$	−2.52225			−0.125332
$406$	13.5879	−	27.6922i	0.674356	−	1.37434i
$407$	−19.0954			−0.946524
$408$	−8.63112	−	14.9495i	−0.427304	−	0.740112i
$409$	11.8530	−	20.5299i	0.586091	−	1.01514i	−0.408648	−	0.912692i	$-0.634000\pi$
$409$	11.8530	−	20.5299i	0.586091	−	1.01514i	0.994738	−	0.102447i	$-0.0326671\pi$
$410$	−26.2100	+	45.3970i	−1.29442	+	2.24200i
$411$	−3.57373	−	6.18988i	−0.176279	−	0.305324i
$412$	23.2213			1.14403
$413$	−30.3295	+	2.04847i	−1.49242	+	0.100799i
$414$	−17.9519			−0.882289
$415$	−14.9503	−	25.8946i	−0.733880	−	1.27112i
$416$	2.44928	−	4.24228i	0.120086	−	0.207995i
$417$	9.87714	−	17.1077i	0.483686	−	0.837768i
$418$	−15.2604	−	26.4318i	−0.746411	−	1.29282i
$419$	−4.59074			−0.224272			−0.112136	−	0.993693i	$-0.535769\pi$
$419$	−4.59074			−0.224272			−0.112136	+	0.993693i	$0.535769\pi$
$420$	−29.5310	+	1.99454i	−1.44097	+	0.0973236i
$421$	−17.8939			−0.872095			−0.436047	−	0.899924i	$-0.643622\pi$
$421$	−17.8939			−0.872095			−0.436047	+	0.899924i	$0.643622\pi$
$422$	4.66305	+	8.07664i	0.226994	+	0.393165i
$423$	−5.04284	+	8.73445i	−0.245191	+	0.424683i
$424$	33.4014	−	57.8529i	1.62211	−	2.80958i
$425$	1.90247	+	3.29517i	0.0922832	+	0.159839i
$426$	21.1869			1.02651
$427$	−5.58739	+	11.3871i	−0.270393	+	0.551062i
$428$	79.2755			3.83193
$429$	2.98608	+	5.17205i	0.144169	+	0.249709i
$430$	11.4892	−	19.8999i	0.554060	−	0.959661i
$431$	−2.41567	+	4.18406i	−0.116359	+	0.201539i	−0.918322	−	0.395834i	$-0.870456\pi$
$431$	−2.41567	+	4.18406i	−0.116359	+	0.201539i	0.801963	+	0.597373i	$0.203789\pi$
$432$	3.40086	+	5.89047i	0.163624	+	0.283405i
$433$	3.59798			0.172908			0.0864539	−	0.996256i	$-0.472446\pi$
$433$	3.59798			0.172908			0.0864539	+	0.996256i	$0.472446\pi$
$434$	8.85005	+	13.1882i	0.424816	+	0.633053i
$435$	11.5919			0.555790
$436$	−2.07794	−	3.59911i	−0.0995155	−	0.172366i
$437$	−7.12808	+	12.3462i	−0.340982	+	0.590598i
$438$	−4.21345	+	7.29790i	−0.201326	+	0.348707i
$439$	7.97399	+	13.8114i	0.380578	+	0.659180i	0.991145	−	0.132784i	$-0.0423917\pi$
$439$	7.97399	+	13.8114i	0.380578	+	0.659180i	−0.610567	+	0.791965i	$0.709058\pi$
$440$	93.0617			4.43654
$441$	6.93643	−	0.941273i	0.330306	−	0.0448225i
$442$	7.08815			0.337149
$443$	20.1699	+	34.9353i	0.958302	+	1.65983i	0.726625	+	0.687035i	$0.241088\pi$
$443$	20.1699	+	34.9353i	0.958302	+	1.65983i	0.231677	+	0.972793i	$0.425579\pi$
$444$	7.09082	−	12.2817i	0.336515	−	0.582862i
$445$	−4.64551	+	8.04626i	−0.220218	+	0.381429i
$446$	15.3870	+	26.6511i	0.728597	+	1.26197i
$447$	−13.7064			−0.648289
$448$	−1.73488	−	2.58529i	−0.0819655	−	0.122144i
$449$	−15.1341			−0.714224			−0.357112	−	0.934062i	$-0.616239\pi$
$449$	−15.1341			−0.714224			−0.357112	+	0.934062i	$0.616239\pi$
$450$	−1.72726	−	2.99170i	−0.0814237	−	0.141030i
$451$	−24.4637	+	42.3724i	−1.15195	+	1.99524i
$452$	34.3940	−	59.5721i	1.61776	−	2.80204i
$453$	1.57204	+	2.72285i	0.0738609	+	0.127931i
$454$	43.7917			2.05525
$455$	2.93960	−	5.99092i	0.137811	−	0.280858i
$456$	12.4460			0.582835
$457$	−7.73158	−	13.3915i	−0.361668	−	0.626427i	0.626567	−	0.779367i	$-0.284459\pi$
$457$	−7.73158	−	13.3915i	−0.361668	−	0.626427i	−0.988236	+	0.152940i	$0.951126\pi$
$458$	1.74300	−	3.01897i	0.0814452	−	0.141067i
$459$	−1.39706	+	2.41979i	−0.0652094	+	0.112946i
$460$	−39.5833	−	68.5604i	−1.84558	−	3.19664i
$461$	24.2726			1.13049			0.565244	−	0.824924i	$-0.308782\pi$
$461$	24.2726			1.13049			0.565244	+	0.824924i	$0.308782\pi$
$462$	−39.9926	+	2.70112i	−1.86062	+	0.125667i
$463$	14.1845			0.659211			0.329605	−	0.944119i	$-0.393084\pi$
$463$	14.1845			0.659211			0.329605	+	0.944119i	$0.393084\pi$
$464$	−15.6299	−	27.0718i	−0.725599	−	1.25677i
$465$	−2.98428	+	5.16893i	−0.138393	+	0.239703i
$466$	7.14840	−	12.3814i	0.331143	−	0.573557i
$467$	18.3890	+	31.8506i	0.850940	+	1.47387i	0.880361	+	0.474304i	$0.157300\pi$
$467$	18.3890	+	31.8506i	0.850940	+	1.47387i	−0.0294209	+	0.999567i	$0.509366\pi$
$468$	−4.43536			−0.205025
$469$	−14.0178	+	0.946770i	−0.647282	+	0.0437178i
$470$	−64.5327			−2.97667
$471$	2.21390	+	3.83460i	0.102011	+	0.176689i
$472$	−35.4916	+	61.4733i	−1.63363	+	2.82954i
$473$	10.7238	−	18.5741i	0.493080	−	0.854040i
$474$	−15.5780	−	26.9819i	−0.715521	−	1.23932i
$475$	−2.74333			−0.125873
$476$	−14.4436	+	29.4361i	−0.662021	+	1.34920i
$477$	−10.8129			−0.495090
$478$	−13.0680	−	22.6345i	−0.597717	−	1.03528i
$479$	−19.3503	+	33.5157i	−0.884138	+	1.53137i	−0.0374388	+	0.999299i	$0.511920\pi$
$479$	−19.3503	+	33.5157i	−0.884138	+	1.53137i	−0.846699	+	0.532072i	$0.821413\pi$
$480$	−6.17771	+	10.7001i	−0.281972	+	0.488391i
$481$	1.59870	+	2.76903i	0.0728945	+	0.126257i
$482$	−50.1668			−2.28504
$483$	10.4328	+	15.5468i	0.474710	+	0.707405i
$484$	109.406			4.97300
$485$	1.63614	+	2.83387i	0.0742932	+	0.128680i
$486$	1.26840	−	2.19693i	0.0575358	−	0.0996550i
$487$	−2.41602	+	4.18467i	−0.109480	+	0.189626i	−0.915560	−	0.402182i	$-0.868252\pi$
$487$	−2.41602	+	4.18467i	−0.109480	+	0.189626i	0.806080	+	0.591807i	$0.201585\pi$
$488$	14.8092	+	25.6502i	0.670379	+	1.16113i
$489$	−18.4100			−0.832529
$490$	27.4070	+	35.4250i	1.23812	+	1.60034i
$491$	22.2550			1.00435			0.502177	−	0.864765i	$-0.332533\pi$
$491$	22.2550			1.00435			0.502177	+	0.864765i	$0.332533\pi$
$492$	−18.1686	−	31.4689i	−0.819102	−	1.41873i
$493$	6.42071	−	11.1210i	0.289174	−	0.500864i
$494$	−2.55526	+	4.42583i	−0.114966	+	0.199128i
$495$	−7.53166	−	13.0452i	−0.338523	−	0.586339i
$496$	16.0954			0.722703
$497$	−12.3128	−	18.3484i	−0.552306	−	0.823038i
$498$	30.0730			1.34760
$499$	−8.57102	−	14.8454i	−0.383691	−	0.664573i	0.607895	−	0.794017i	$-0.292014\pi$
$499$	−8.57102	−	14.8454i	−0.383691	−	0.664573i	−0.991587	+	0.129444i	$0.958681\pi$
$500$	−20.3507	+	35.2484i	−0.910111	+	1.57636i
$501$	−4.39118	+	7.60575i	−0.196184	+	0.339800i
$502$	10.5293	+	18.2373i	0.469945	+	0.813969i
$503$	−22.1597			−0.988051			−0.494025	−	0.869447i	$-0.664475\pi$
$503$	−22.1597			−0.988051			−0.494025	+	0.869447i	$0.664475\pi$
$504$	7.20029	−	14.6742i	0.320726	−	0.653642i
$505$	−5.14451			−0.228928
$506$	−53.6060	−	92.8482i	−2.38308	−	4.12761i
$507$	0.500000	−	0.866025i	0.0222058	−	0.0384615i
$508$	11.7316	−	20.3197i	0.520505	−	0.901542i
$509$	7.24391	+	12.5468i	0.321081	+	0.556128i	0.980711	−	0.195462i	$-0.0626206\pi$
$509$	7.24391	+	12.5468i	0.321081	+	0.556128i	−0.659631	+	0.751590i	$0.729287\pi$
$510$	−17.8781			−0.791656
$511$	8.76883	−	0.592251i	0.387910	−	0.0261997i
$512$	−50.7240			−2.24170
$513$	−1.00727	−	1.74465i	−0.0444723	−	0.0770282i
$514$	−33.5400	+	58.0930i	−1.47939	+	2.56237i
$515$	6.60261	−	11.4361i	0.290946	−	0.503933i
$516$	7.96426	+	13.7945i	0.350607	+	0.607269i
$517$	−60.2333			−2.64906
$518$	−21.4114	+	1.44613i	−0.940761	+	0.0635395i
$519$	9.94159			0.436387
$520$	−7.79129	−	13.4949i	−0.341670	−	0.591791i
$521$	9.95651	−	17.2452i	0.436202	−	0.755525i	−0.561191	−	0.827687i	$-0.689657\pi$
$521$	9.95651	−	17.2452i	0.436202	−	0.755525i	0.997393	+	0.0721619i	$0.0229898\pi$
$522$	−5.82939	+	10.0968i	−0.255145	+	0.441925i
$523$	13.9589	+	24.1775i	0.610379	+	1.05721i	0.991176	+	0.132549i	$0.0423163\pi$
$523$	13.9589	+	24.1775i	0.610379	+	1.05721i	−0.380797	+	0.924659i	$0.624350\pi$
$524$	−56.0939			−2.45047
$525$	−1.58708	+	3.23449i	−0.0692661	+	0.141165i
$526$	−24.8173			−1.08209
$527$	3.30596	+	5.72610i	0.144010	+	0.249433i
$528$	−20.3105	+	35.1789i	−0.883902	+	1.53096i
$529$	−13.5391	+	23.4505i	−0.588658	+	1.01959i
$530$	−34.5931	−	59.9169i	−1.50263	−	2.60263i
$531$	11.4896			0.498606
$532$	−13.1730	−	19.6302i	−0.571122	−	0.851076i
$533$	8.19259			0.354860
$534$	−4.67230	−	8.09267i	−0.202190	−	0.350204i
$535$	22.5408	−	39.0417i	0.974522	−	1.68792i
$536$	−16.4036	+	28.4119i	−0.708529	+	1.22721i
$537$	8.29646	+	14.3699i	0.358018	+	0.620106i
$538$	−51.4775			−2.21935
$539$	25.5811	+	33.0648i	1.10185	+	1.42420i
$540$	11.1871			0.481417
$541$	13.3986	+	23.2070i	0.576050	+	0.997748i	0.995927	+	0.0901670i	$0.0287401\pi$
$541$	13.3986	+	23.2070i	0.576050	+	0.997748i	−0.419876	+	0.907581i	$0.637927\pi$
$542$	28.4290	−	49.2405i	1.22113	−	2.11506i
$543$	−8.94066	+	15.4857i	−0.383680	+	0.664554i
$544$	6.84361	+	11.8535i	0.293417	+	0.508214i
$545$	−2.36332			−0.101234
$546$	3.73994	+	5.57319i	0.160054	+	0.238510i
$547$	33.4428			1.42991			0.714955	−	0.699170i	$-0.246447\pi$
$547$	33.4428			1.42991			0.714955	+	0.699170i	$0.246447\pi$
$548$	15.8508	+	27.4544i	0.677113	+	1.17279i
$549$	2.39706	−	4.15184i	0.102304	−	0.177196i
$550$	10.3155	−	17.8669i	0.439853	−	0.761848i
$551$	4.62929	+	8.01816i	0.197214	+	0.341585i
$552$	43.7195			1.86083
$553$	−14.3138	+	29.1715i	−0.608684	+	1.24050i
$554$	12.8677			0.546695
$555$	−4.03233	−	6.98419i	−0.171163	−	0.296463i
$556$	−43.8087	+	75.8789i	−1.85790	+	3.21798i
$557$	3.89570	−	6.74755i	0.165066	−	0.285903i	−0.771613	−	0.636093i	$-0.780550\pi$
$557$	3.89570	−	6.74755i	0.165066	−	0.285903i	0.936679	+	0.350190i	$0.113883\pi$
$558$	−3.00150	−	5.19875i	−0.127064	−	0.220080i
$559$	−3.59125			−0.151894
$560$	45.2865	−	3.05867i	1.91370	−	0.129252i
$561$	−16.6870			−0.704526
$562$	5.31324	+	9.20281i	0.224126	+	0.388197i
$563$	−3.96760	+	6.87208i	−0.167214	+	0.289624i	−0.937439	−	0.348148i	$-0.886811\pi$
$563$	−3.96760	+	6.87208i	−0.167214	+	0.289624i	0.770225	+	0.637772i	$0.220144\pi$
$564$	22.3668	−	38.7405i	0.941813	−	1.63127i
$565$	−19.5588	−	33.8768i	−0.822844	−	1.42521i
$566$	20.5949			0.865670
$567$	−2.63974	+	0.178289i	−0.110859	+	0.00748744i
$568$	−51.5978			−2.16500
$569$	12.4955	+	21.6428i	0.523837	+	0.907312i	0.999615	+	0.0277468i	$0.00883320\pi$
$569$	12.4955	+	21.6428i	0.523837	+	0.907312i	−0.475778	+	0.879565i	$0.657833\pi$
$570$	6.44500	−	11.1631i	0.269951	−	0.467570i
$571$	−14.7876	+	25.6129i	−0.618843	+	1.07187i	0.370854	+	0.928691i	$0.379065\pi$
$571$	−14.7876	+	25.6129i	−0.618843	+	1.07187i	−0.989697	+	0.143177i	$0.954268\pi$
$572$	−13.2444	−	22.9399i	−0.553775	−	0.959166i
$573$	−0.683873			−0.0285692
$574$	−24.2218	+	49.3642i	−1.01100	+	2.06042i
$575$	−9.63663			−0.401875
$576$	0.588386	+	1.01912i	0.0245161	+	0.0424631i
$577$	13.5953	−	23.5477i	0.565979	−	0.980305i	−0.430978	−	0.902362i	$-0.641831\pi$
$577$	13.5953	−	23.5477i	0.565979	−	0.980305i	0.996958	−	0.0779429i	$-0.0248352\pi$
$578$	11.6602	−	20.1961i	0.485001	−	0.840046i
$579$	−1.43306	−	2.48214i	−0.0595561	−	0.103154i
$580$	−51.4144			−2.13487
$581$	−17.4771	−	26.0440i	−0.725070	−	1.08049i
$582$	−3.29115			−0.136423
$583$	−32.2883	−	55.9250i	−1.33725	−	2.31618i
$584$	10.2613	−	17.7731i	0.424615	−	0.735454i
$585$	−1.26113	+	2.18434i	−0.0521412	+	0.0903111i
$586$	−3.21024	−	5.56030i	−0.132614	−	0.229694i
$587$	20.6366			0.851762			0.425881	−	0.904779i	$-0.359964\pi$
$587$	20.6366			0.851762			0.425881	+	0.904779i	$0.359964\pi$
$588$	−30.7656	+	4.17489i	−1.26875	+	0.172170i
$589$	−4.76715			−0.196427
$590$	36.7579	+	63.6665i	1.51330	+	2.62111i
$591$	1.81981	−	3.15201i	0.0748571	−	0.129656i
$592$	−10.8739	+	18.8342i	−0.446916	+	0.774080i
$593$	−5.67474	−	9.82893i	−0.233033	−	0.403626i	0.725666	−	0.688047i	$-0.241532\pi$
$593$	−5.67474	−	9.82893i	−0.233033	−	0.403626i	−0.958699	+	0.284421i	$0.908199\pi$
$594$	15.1502			0.621620
$595$	10.3899	+	15.4829i	0.425946	+	0.634737i
$596$	60.7927			2.49017
$597$	5.65396	+	9.79294i	0.231401	+	0.400798i
$598$	−8.97597	+	15.5468i	−0.367055	+	0.635757i
$599$	19.3274	−	33.4760i	0.789696	−	1.36779i	−0.136457	−	0.990646i	$-0.543572\pi$
$599$	19.3274	−	33.4760i	0.789696	−	1.36779i	0.926153	−	0.377148i	$-0.123095\pi$
$600$	4.20650	+	7.28588i	0.171730	+	0.297445i
$601$	−31.6162			−1.28965			−0.644825	−	0.764330i	$-0.723070\pi$
$601$	−31.6162			−1.28965			−0.644825	+	0.764330i	$0.723070\pi$
$602$	10.6177	−	21.6390i	0.432747	−	0.881940i
$603$	5.31030			0.216252
$604$	−6.97257	−	12.0768i	−0.283710	−	0.491400i
$605$	31.1079	−	53.8805i	1.26472	−	2.19055i
$606$	2.58709	−	4.48097i	0.105093	−	0.182027i
$607$	−14.2547	−	24.6899i	−0.578582	−	1.00213i	−0.995642	−	0.0932550i	$-0.970273\pi$
$607$	−14.2547	−	24.6899i	−0.578582	−	1.00213i	0.417060	−	0.908879i	$-0.363061\pi$
$608$	−9.86839			−0.400216
$609$	12.1319	−	0.819392i	0.491608	−	0.0332034i
$610$	30.6750			1.24200
$611$	5.04284	+	8.73445i	0.204011	+	0.353358i
$612$	6.19649	−	10.7326i	0.250478	−	0.433841i
$613$	−13.6589	+	23.6579i	−0.551677	+	0.955533i	0.446476	+	0.894795i	$0.352679\pi$
$613$	−13.6589	+	23.6579i	−0.551677	+	0.955533i	−0.998154	+	0.0607378i	$0.980655\pi$
$614$	23.1216	+	40.0478i	0.933112	+	1.61620i
$615$	−20.6638			−0.833244
$616$	97.3964	−	6.57821i	3.92421	−	0.265043i
$617$	−18.5656			−0.747423			−0.373711	−	0.927545i	$-0.621915\pi$
$617$	−18.5656			−0.747423			−0.373711	+	0.927545i	$0.621915\pi$
$618$	6.64069	+	11.5020i	0.267128	+	0.462679i
$619$	−2.29395	+	3.97324i	−0.0922016	+	0.159698i	−0.908437	−	0.418021i	$-0.862724\pi$
$619$	−2.29395	+	3.97324i	−0.0922016	+	0.159698i	0.816236	+	0.577719i	$0.196057\pi$
$620$	13.2364	−	22.9261i	0.531586	−	0.920734i
$621$	−3.53830	−	6.12851i	−0.141987	−	0.245929i
$622$	12.1443			0.486944
$623$	−4.29313	+	8.74942i	−0.172001	+	0.350538i
$624$	6.80173			0.272287
$625$	14.9772	+	25.9413i	0.599088	+	1.03765i
$626$	−6.72172	+	11.6424i	−0.268654	+	0.465322i
$627$	6.01561	−	10.4193i	0.240240	−	0.416108i
$628$	−9.81947	−	17.0078i	−0.391840	−	0.678686i
$629$	−8.93395			−0.356220
$630$	−9.43306	−	14.0570i	−0.375822	−	0.560044i
$631$	40.7776			1.62333			0.811665	−	0.584123i	$-0.198562\pi$
$631$	40.7776			1.62333			0.811665	+	0.584123i	$0.198562\pi$
$632$	37.9381	+	65.7107i	1.50910	+	2.61383i
$633$	−1.83816	+	3.18379i	−0.0730604	+	0.126544i
$634$	−13.6251	+	23.5994i	−0.541123	+	0.937253i
$635$	−6.67139	−	11.5552i	−0.264746	−	0.458554i
$636$	47.9593			1.90171
$637$	2.65305	−	6.47776i	0.105118	−	0.256658i
$638$	−69.6282			−2.75661
$639$	4.17591	+	7.23288i	0.165196	+	0.286128i
$640$	−16.1202	+	27.9210i	−0.637206	+	1.10367i
$641$	15.1277	−	26.2019i	0.597508	−	1.03491i	−0.395680	−	0.918389i	$-0.629491\pi$
$641$	15.1277	−	26.2019i	0.597508	−	1.03491i	0.993188	−	0.116526i	$-0.0371757\pi$
$642$	22.6708	+	39.2669i	0.894744	+	1.54974i
$643$	4.56130			0.179880			0.0899400	−	0.995947i	$-0.471332\pi$
$643$	4.56130			0.179880			0.0899400	+	0.995947i	$0.471332\pi$
$644$	−46.2734	−	68.9558i	−1.82343	−	2.71724i
$645$	9.05805			0.356660
$646$	−7.13972	−	12.3664i	−0.280908	−	0.486548i
$647$	9.92924	−	17.1980i	0.390359	−	0.676121i	−0.602138	−	0.798392i	$-0.705684\pi$
$647$	9.92924	−	17.1980i	0.390359	−	0.676121i	0.992497	+	0.122271i	$0.0390176\pi$
$648$	−3.08902	+	5.35034i	−0.121348	+	0.210181i
$649$	34.3089	+	59.4248i	1.34674	+	2.33263i
$650$	−3.45452			−0.135497
$651$	−2.75792	+	5.62064i	−0.108091	+	0.220290i
$652$	81.6551			3.19786
$653$	0.390528	+	0.676415i	0.0152825	+	0.0264701i	0.873566	−	0.486707i	$-0.161802\pi$
$653$	0.390528	+	0.676415i	0.0152825	+	0.0264701i	−0.858283	+	0.513177i	$0.828469\pi$
$654$	1.18848	−	2.05850i	0.0464732	−	0.0804939i
$655$	−15.9494	+	27.6252i	−0.623196	+	1.07941i
$656$	27.8619	+	48.2582i	1.08782	+	1.88417i
$657$	−3.32186			−0.129598
$658$	−67.5386	+	4.56159i	−2.63293	+	0.177829i
$659$	−7.97960			−0.310841			−0.155420	−	0.987848i	$-0.549673\pi$
$659$	−7.97960			−0.310841			−0.155420	+	0.987848i	$0.549673\pi$
$660$	33.4056	+	57.8603i	1.30031	+	2.25221i
$661$	3.32932	−	5.76656i	0.129496	−	0.224293i	−0.793986	−	0.607937i	$-0.791997\pi$
$661$	3.32932	−	5.76656i	0.129496	−	0.224293i	0.923481	+	0.383643i	$0.125331\pi$
$662$	−4.25757	+	7.37432i	−0.165475	+	0.286611i
$663$	1.39706	+	2.41979i	0.0542575	+	0.0939767i
$664$	−73.2388			−2.84222
$665$	−13.4130	+	0.905923i	−0.520135	+	0.0351302i
$666$	8.11117			0.314302
$667$	16.2615	+	28.1658i	0.629649	+	1.09058i
$668$	19.4765	−	33.7343i	0.753568	−	1.30522i
$669$	−6.06553	+	10.5058i	−0.234507	+	0.406178i
$670$	16.9889	+	29.4256i	0.656337	+	1.13681i
$671$	28.6313			1.10530
$672$	−5.70911	+	11.6352i	−0.220234	+	0.448837i
$673$	23.9858			0.924587			0.462293	−	0.886727i	$-0.347027\pi$
$673$	23.9858			0.924587			0.462293	+	0.886727i	$0.347027\pi$
$674$	−12.6299	−	21.8757i	−0.486487	−	0.842620i
$675$	0.680880	−	1.17932i	0.0262071	−	0.0453920i
$676$	−2.21768	+	3.84114i	−0.0852955	+	0.147736i
$677$	14.0498	+	24.3350i	0.539979	+	0.935271i	0.998904	+	0.0467960i	$0.0149011\pi$
$677$	14.0498	+	24.3350i	0.539979	+	0.935271i	−0.458926	+	0.888475i	$0.651766\pi$
$678$	39.3432			1.51097
$679$	1.91266	+	2.85022i	0.0734013	+	0.109381i
$680$	43.5397			1.66967
$681$	8.63129	+	14.9498i	0.330752	+	0.572879i
$682$	17.9254	−	31.0478i	0.686401	−	1.18888i
$683$	−7.60630	+	13.1745i	−0.291047	+	0.504108i	−0.974058	−	0.226300i	$-0.927337\pi$
$683$	−7.60630	+	13.1745i	−0.291047	+	0.504108i	0.683011	+	0.730408i	$0.260670\pi$
$684$	4.46763	+	7.73816i	0.170824	+	0.295876i
$685$	18.0277			0.688803
$686$	31.1877	+	35.1377i	1.19075	+	1.34156i
$687$	1.37417			0.0524280
$688$	−12.2134	−	21.1542i	−0.465630	−	0.806495i
$689$	−5.40647	+	9.36428i	−0.205970	+	0.356751i
$690$	22.6397	−	39.2130i	0.861877	−	1.49281i
$691$	9.09631	+	15.7553i	0.346040	+	0.599359i	0.985542	−	0.169431i	$-0.0541929\pi$
$691$	9.09631	+	15.7553i	0.346040	+	0.599359i	−0.639502	+	0.768789i	$0.720860\pi$
$692$	−44.0946			−1.67622
$693$	−8.80460	−	13.1205i	−0.334459	−	0.498405i
$694$	−55.9564			−2.12407
$695$	24.9126	+	43.1500i	0.944990	+	1.63677i
$696$	14.1967	−	24.5894i	0.538124	−	0.932058i
$697$	−11.4456	+	19.8243i	−0.433532	+	0.750899i
$698$	−13.3011	−	23.0382i	−0.503455	−	0.872009i
$699$	5.63576			0.213164
$700$	7.03930	−	14.3461i	0.266061	−	0.542233i
$701$	−49.3716			−1.86474			−0.932369	−	0.361507i	$-0.882262\pi$
$701$	−49.3716			−1.86474			−0.932369	+	0.361507i	$0.882262\pi$
$702$	−1.26840	−	2.19693i	−0.0478727	−	0.0829180i
$703$	3.22066	−	5.57835i	0.121469	−	0.210391i
$704$	−3.51394	+	6.08632i	−0.132437	+	0.229387i
$705$	−12.7193	−	22.0305i	−0.479037	−	0.829716i
$706$	15.3575			0.577989
$707$	−5.38413	+	0.363647i	−0.202491	+	0.0136764i
$708$	−50.9606			−1.91522
$709$	−8.35427	−	14.4700i	−0.313751	−	0.543433i	0.665420	−	0.746469i	$-0.268252\pi$
$709$	−8.35427	−	14.4700i	−0.313751	−	0.543433i	−0.979171	+	0.203036i	$0.934919\pi$
$710$	−26.7194	+	46.2793i	−1.00276	+	1.73683i
$711$	6.14080	−	10.6362i	0.230298	−	0.398888i
$712$	11.3788	+	19.7086i	0.426437	+	0.738611i
$713$	−16.7458			−0.627135
$714$	−18.7109	+	1.26374i	−0.700236	+	0.0472943i
$715$	−15.0633			−0.563336
$716$	−36.7978	−	63.7357i	−1.37520	−	2.38191i
$717$	5.15138	−	8.92245i	0.192382	−	0.333215i
$718$	−13.7489	+	23.8138i	−0.513105	+	0.888723i
$719$	−9.84040	−	17.0441i	−0.366985	−	0.635636i	0.622108	−	0.782932i	$-0.286277\pi$
$719$	−9.84040	−	17.0441i	−0.366985	−	0.635636i	−0.989093	+	0.147295i	$0.952943\pi$
$720$	−17.1557			−0.639354
$721$	6.10178	−	12.4354i	0.227242	−	0.463120i
$722$	−37.9039			−1.41064
$723$	−9.88781	−	17.1262i	−0.367732	−	0.636930i
$724$	39.6551	−	68.6846i	1.47377	−	2.55264i
$725$	−3.12923	+	5.41998i	−0.116217	+	0.201293i
$726$	31.2874	+	54.1913i	1.16118	+	2.01123i
$727$	27.9233			1.03562			0.517810	−	0.855496i	$-0.326748\pi$
$727$	27.9233			1.03562			0.517810	+	0.855496i	$0.326748\pi$
$728$	−9.10810	−	13.5727i	−0.337569	−	0.503039i
$729$	1.00000			0.0370370
$730$	−10.6274	−	18.4072i	−0.393337	−	0.681280i
$731$	5.01721	−	8.69007i	0.185568	−	0.321414i
$732$	−10.6319	+	18.4149i	−0.392965	+	0.680635i
$733$	8.03222	+	13.9122i	0.296677	+	0.513860i	0.975374	−	0.220559i	$-0.0707882\pi$
$733$	8.03222	+	13.9122i	0.296677	+	0.513860i	−0.678697	+	0.734419i	$0.737455\pi$
$734$	−90.8006			−3.35151
$735$	−6.69165	+	16.3385i	−0.246825	+	0.602656i
$736$	−34.6652			−1.27777
$737$	15.8570	+	27.4651i	0.584100	+	1.01169i
$738$	10.3915	−	17.9986i	0.382516	−	0.662537i
$739$	−5.61989	+	9.73394i	−0.206731	+	0.358069i	−0.950683	−	0.310165i	$-0.899616\pi$
$739$	−5.61989	+	9.73394i	−0.206731	+	0.358069i	0.743952	+	0.668233i	$0.232949\pi$
$740$	17.8848	+	30.9774i	0.657460	+	1.13875i
$741$	−2.01455			−0.0740063
$742$	−40.4397	−	60.2625i	−1.48459	−	2.21231i
$743$	29.0034			1.06403			0.532016	−	0.846734i	$-0.321434\pi$
$743$	29.0034			1.06403			0.532016	+	0.846734i	$0.321434\pi$
$744$	7.30974	+	12.6608i	0.267988	+	0.464169i
$745$	17.2855	−	29.9393i	0.633290	−	1.09689i
$746$	34.1501	−	59.1497i	1.25032	−	2.16563i
$747$	5.92735	+	10.2665i	0.216870	+	0.375631i
$748$	74.0129			2.70618
$749$	20.8310	−	42.4536i	0.761147	−	1.55122i
$750$	−23.2791			−0.850033
$751$	−4.59513	−	7.95900i	−0.167679	−	0.290428i	0.769925	−	0.638135i	$-0.220294\pi$
$751$	−4.59513	−	7.95900i	−0.167679	−	0.290428i	−0.937603	+	0.347707i	$0.886960\pi$
$752$	−34.3000	+	59.4093i	−1.25079	+	2.16644i
$753$	−4.15061	+	7.18908i	−0.151257	+	0.261984i
$754$	5.82939	+	10.0968i	0.212294	+	0.367704i
$755$	−7.93017			−0.288608
$756$	11.7082	−	0.790778i	0.425823	−	0.0287603i
$757$	21.6191			0.785760			0.392880	−	0.919590i	$-0.371479\pi$
$757$	21.6191			0.785760			0.392880	+	0.919590i	$0.371479\pi$
$758$	31.7332	+	54.9634i	1.15260	+	1.99636i
$759$	21.1313	−	36.6005i	0.767018	−	1.32851i
$760$	−15.6959	+	27.1861i	−0.569351	+	0.986145i
$761$	−17.7229	−	30.6970i	−0.642456	−	1.11277i	−0.984883	−	0.173222i	$-0.944582\pi$
$761$	−17.7229	−	30.6970i	−0.642456	−	1.11277i	0.342427	−	0.939544i	$-0.388751\pi$
$762$	13.4197			0.486146
$763$	−2.47341	+	0.167055i	−0.0895433	+	0.00604780i
$764$	3.03323			0.109738
$765$	−3.52375	−	6.10332i	−0.127401	−	0.220666i
$766$	24.1715	−	41.8663i	0.873353	−	1.51269i
$767$	5.74480	−	9.95029i	0.207433	−	0.359284i
$768$	−15.0364	−	26.0438i	−0.542579	−	0.939774i
$769$	5.80265			0.209249			0.104624	−	0.994512i	$-0.466636\pi$
$769$	5.80265			0.209249			0.104624	+	0.994512i	$0.466636\pi$
$770$	44.5355	−	90.7636i	1.60495	−	3.27089i
$771$	−26.4428			−0.952312
$772$	6.35616	+	11.0092i	0.228763	+	0.396229i
$773$	−4.58311	+	7.93819i	−0.164843	+	0.285517i	−0.936600	−	0.350402i	$-0.886045\pi$
$773$	−4.58311	+	7.93819i	−0.164843	+	0.285517i	0.771756	+	0.635918i	$0.219378\pi$
$774$	−4.55515	+	7.88975i	−0.163731	+	0.283591i
$775$	−1.61121	−	2.79070i	−0.0578764	−	0.100245i
$776$	8.01515			0.287727
$777$	−4.71384	−	7.02448i	−0.169108	−	0.252002i
$778$	−55.9928			−2.00744
$779$	−8.25218	−	14.2932i	−0.295665	−	0.512107i
$780$	5.59356	−	9.68832i	0.200281	−	0.346898i
$781$	−24.9392	+	43.1960i	−0.892395	+	1.54567i
$782$	−25.0800	−	43.4398i	−0.896859	−	1.55341i
$783$	−4.59586			−0.164243
$784$	47.1797	−	6.40228i	1.68499	−	0.228653i
$785$	−11.1681			−0.398605
$786$	−16.0414	−	27.7846i	−0.572179	−	0.991043i
$787$	19.4153	−	33.6283i	0.692081	−	1.19872i	−0.279074	−	0.960270i	$-0.590028\pi$
$787$	19.4153	−	33.6283i	0.692081	−	1.19872i	0.971155	−	0.238449i	$-0.0766391\pi$
$788$	−8.07154	+	13.9803i	−0.287537	+	0.498028i
$789$	−4.89146	−	8.47226i	−0.174141	−	0.301620i
$790$	78.5833			2.79587
$791$	−22.8644	−	34.0722i	−0.812966	−	1.21147i
$792$	−36.8963			−1.31105
$793$	−2.39706	−	4.15184i	−0.0851223	−	0.147436i
$794$	−27.3837	+	47.4300i	−0.971812	+	1.68323i
$795$	13.6365	−	23.6191i	0.483636	−	0.837682i
$796$	−25.0774	−	43.4353i	−0.888843	−	1.53952i
$797$	36.0515			1.27701			0.638505	−	0.769617i	$-0.279553\pi$
$797$	36.0515			1.27701			0.638505	+	0.769617i	$0.279553\pi$
$798$	5.95613	−	12.1386i	0.210845	−	0.429702i
$799$	−28.1807			−0.996961
$800$	−3.33533	−	5.77697i	−0.117922	−	0.204247i
$801$	1.84181	−	3.19011i	0.0650771	−	0.112717i
$802$	−4.27541	+	7.40523i	−0.150970	+	0.261488i
$803$	−9.91934	−	17.1808i	−0.350046	−	0.606297i
$804$	−23.5531			−0.830655
$805$	−47.1166	+	3.18228i	−1.66064	+	0.112161i
$806$	−6.00300			−0.211446
$807$	−10.1461	−	17.5736i	−0.357161	−	0.618621i
$808$	−6.30051	+	10.9128i	−0.221651	+	0.383911i
$809$	−23.0492	+	39.9224i	−0.810367	+	1.40360i	0.102240	+	0.994760i	$0.467399\pi$
$809$	−23.0492	+	39.9224i	−0.810367	+	1.40360i	−0.912607	+	0.408837i	$0.865934\pi$
$810$	3.19923	+	5.54123i	0.112409	+	0.194699i
$811$	55.2134			1.93880			0.969402	−	0.245480i	$-0.0789457\pi$
$811$	55.2134			1.93880			0.969402	+	0.245480i	$0.0789457\pi$
$812$	−53.8092	+	3.63430i	−1.88833	+	0.127539i
$813$	22.4133			0.786068
$814$	24.2206	+	41.9514i	0.848933	+	1.47039i
$815$	23.2174	−	40.2136i	0.813268	−	1.40862i
$816$	−9.50245	+	16.4587i	−0.332652	+	0.576171i
$817$	3.61738	+	6.26548i	0.126556	+	0.219202i
$818$	−60.1372			−2.10265
$819$	−1.16547	+	2.37522i	−0.0407247	+	0.0829970i
$820$	91.6514			3.20060
$821$	11.0843	+	19.1986i	0.386845	+	0.670035i	0.992023	−	0.126055i	$-0.0402315\pi$
$821$	11.0843	+	19.1986i	0.386845	+	0.670035i	−0.605178	+	0.796090i	$0.706898\pi$
$822$	−9.06585	+	15.7025i	−0.316208	+	0.547688i
$823$	22.0031	−	38.1106i	0.766981	−	1.32845i	−0.172211	−	0.985060i	$-0.555091\pi$
$823$	22.0031	−	38.1106i	0.766981	−	1.32845i	0.939193	−	0.343391i	$-0.111576\pi$
$824$	−16.1725	−	28.0116i	−0.563396	−	0.975830i
$825$	8.13266			0.283143
$826$	42.9704	+	64.0337i	1.49513	+	2.22802i
$827$	34.1440			1.18730			0.593652	−	0.804722i	$-0.297685\pi$
$827$	34.1440			1.18730			0.593652	+	0.804722i	$0.297685\pi$
$828$	15.6936	+	27.1822i	0.545392	+	0.944647i
$829$	−5.46552	+	9.46656i	−0.189825	+	0.328787i	−0.945192	−	0.326515i	$-0.894126\pi$
$829$	−5.46552	+	9.46656i	−0.189825	+	0.328787i	0.755366	+	0.655303i	$0.227459\pi$
$830$	−37.9259	+	65.6896i	−1.31643	+	2.28012i
$831$	2.53620	+	4.39283i	0.0879798	+	0.152386i
$832$	1.17677			0.0407973
$833$	11.9683	+	15.4697i	0.414678	+	0.535992i
$834$	−50.1127			−1.73526
$835$	−11.0757	−	19.1836i	−0.383289	−	0.663877i
$836$	−26.6814	+	46.2136i	−0.922796	+	1.59833i
$837$	1.18318	−	2.04933i	0.0408967	−	0.0708352i
$838$	5.82290	+	10.0856i	0.201149	+	0.348400i
$839$	−48.3195			−1.66817			−0.834087	−	0.551634i	$-0.814005\pi$
$839$	−48.3195			−1.66817			−0.834087	+	0.551634i	$0.814005\pi$
$840$	22.9729	+	34.2339i	0.792642	+	1.18118i
$841$	−7.87810			−0.271659
$842$	22.6966	+	39.3117i	0.782177	+	1.35477i
$843$	−2.09447	+	3.62772i	−0.0721372	+	0.124945i
$844$	8.15292	−	14.1213i	0.280635	−	0.486074i
$845$	1.26113	+	2.18434i	0.0433841	+	0.0751434i
$846$	25.5854			0.879643
$847$	28.7483	−	58.5891i	0.987802	−	2.01315i
$848$	−73.5467			−2.52560
$849$	4.05923	+	7.03080i	0.139313	+	0.241296i
$850$	4.82618	−	8.35919i	0.165537	−	0.286718i
$851$	11.3134	−	19.5953i	0.387817	−	0.671719i
$852$	−18.5217	−	32.0805i	−0.634542	−	1.09906i
$853$	−35.7709			−1.22477			−0.612387	−	0.790558i	$-0.709790\pi$
$853$	−35.7709			−1.22477			−0.612387	+	0.790558i	$0.709790\pi$
$854$	32.1038	−	2.16831i	1.09857	−	0.0741980i
$855$	5.08120			0.173773
$856$	−55.2116	−	95.6293i	−1.88709	−	3.26854i
$857$	18.4358	−	31.9317i	0.629753	−	1.09076i	−0.357848	−	0.933780i	$-0.616489\pi$
$857$	18.4358	−	31.9317i	0.629753	−	1.09076i	0.987601	−	0.156985i	$-0.0501774\pi$
$858$	7.57510	−	13.1205i	0.258610	−	0.447925i
$859$	9.95545	+	17.2433i	0.339675	+	0.588335i	0.984372	−	0.176104i	$-0.0563494\pi$
$859$	9.95545	+	17.2433i	0.339675	+	0.588335i	−0.644696	+	0.764439i	$0.723016\pi$
$860$	−40.1758			−1.36998
$861$	−21.6263	+	1.46065i	−0.737021	+	0.0497788i
$862$	12.2562			0.417446
$863$	−4.03708	−	6.99243i	−0.137424	−	0.238025i	0.789097	−	0.614269i	$-0.210549\pi$
$863$	−4.03708	−	6.99243i	−0.137424	−	0.238025i	−0.926521	+	0.376244i	$0.877216\pi$
$864$	2.44928	−	4.24228i	0.0833262	−	0.144325i
$865$	−12.5376	+	21.7158i	−0.426291	+	0.738358i
$866$	−4.56368	−	7.90453i	−0.155080	−	0.268607i
$867$	9.19284			0.312205
$868$	12.2324	−	24.9296i	0.415193	−	0.846166i
$869$	73.3477			2.48815
$870$	−14.7032	−	25.4667i	−0.498485	−	0.863401i
$871$	2.65515	−	4.59886i	0.0899664	−	0.155826i
$872$	−2.89438	+	5.01321i	−0.0980160	+	0.169769i
$873$	−0.648681	−	1.12355i	−0.0219545	−	0.0380264i
$874$	36.1650			1.22330
$875$	13.5287	+	20.1603i	0.457355	+	0.681543i
$876$	14.7336			0.497804
$877$	5.70221	+	9.87651i	0.192550	+	0.333506i	0.946095	−	0.323891i	$-0.104991\pi$
$877$	5.70221	+	9.87651i	0.192550	+	0.333506i	−0.753545	+	0.657397i	$0.771658\pi$
$878$	20.2284	−	35.0367i	0.682677	−	1.18243i
$879$	1.26547	−	2.19185i	0.0426832	−	0.0739294i
$880$	−51.2283	−	88.7300i	−1.72690	−	2.99109i
$881$	−10.6226			−0.357884			−0.178942	−	0.983860i	$-0.557267\pi$
$881$	−10.6226			−0.357884			−0.178942	+	0.983860i	$0.557267\pi$
$882$	−10.8661	−	14.0450i	−0.365880	−	0.472919i
$883$	10.7754			0.362620			0.181310	−	0.983426i	$-0.441966\pi$
$883$	10.7754			0.362620			0.181310	+	0.983426i	$0.441966\pi$
$884$	−6.19649	−	10.7326i	−0.208411	−	0.360978i
$885$	−14.4898	+	25.0971i	−0.487071	+	0.843631i
$886$	51.1671	−	88.6240i	1.71899	−	2.97738i
$887$	15.4452	+	26.7519i	0.518600	+	0.898242i	0.999766	+	0.0216128i	$0.00688012\pi$
$887$	15.4452	+	26.7519i	0.518600	+	0.898242i	−0.481166	+	0.876630i	$0.659787\pi$
$888$	−19.7537			−0.662889
$889$	−7.79893	−	11.6218i	−0.261568	−	0.389784i
$890$	23.5695			0.790050
$891$	2.98608	+	5.17205i	0.100038	+	0.173270i
$892$	26.9028	−	46.5970i	0.900773	−	1.56018i
$893$	10.1590	−	17.5960i	0.339959	−	0.588827i
$894$	17.3852	+	30.1120i	0.581447	+	1.00710i
$895$	−41.8515			−1.39894
$896$	−14.8974	+	30.3610i	−0.497687	+	1.01429i
$897$	−7.07660			−0.236281
$898$	19.1962	+	33.2487i	0.640584	+	1.10952i
$899$	−5.43773	+	9.41843i	−0.181359	+	0.314122i
$900$	−3.01995	+	5.23071i	−0.100665	+	0.174357i
$901$	−15.1064	−	26.1650i	−0.503266	−	0.871683i
$902$	124.119			4.13272
$903$	9.47997	−	0.640282i	0.315474	−	0.0213072i
$904$	−95.8150			−3.18676
$905$	−22.5506	−	39.0588i	−0.749608	−	1.29836i
$906$	3.98796	−	6.90734i	0.132491	−	0.229481i
$907$	−30.1088	+	52.1500i	−0.999746	+	1.73161i	−0.480353	+	0.877075i	$0.659492\pi$
$907$	−30.1088	+	52.1500i	−0.999746	+	1.73161i	−0.519393	+	0.854536i	$0.673842\pi$
$908$	−38.2829	−	66.3079i	−1.27046	−	2.20051i
$909$	2.03965			0.0676508
$910$	−16.8902	+	1.14078i	−0.559906	+	0.0378163i
$911$	3.15553			0.104547			0.0522737	−	0.998633i	$-0.483353\pi$
$911$	3.15553			0.104547			0.0522737	+	0.998633i	$0.483353\pi$
$912$	−6.85121	−	11.8666i	−0.226866	−	0.392944i
$913$	−35.3991	+	61.3131i	−1.17154	+	2.02917i
$914$	−19.6135	+	33.9716i	−0.648756	+	1.12368i
$915$	6.04600	+	10.4720i	0.199875	+	0.346193i
$916$	−6.09496			−0.201383
$917$	−14.7396	+	30.0394i	−0.486745	+	0.991988i
$918$	7.08815			0.233944
$919$	−15.6121	−	27.0409i	−0.514995	−	0.891998i	−0.999849	−	0.0174022i	$-0.994460\pi$
$919$	−15.6121	−	27.0409i	−0.514995	−	0.891998i	0.484854	−	0.874595i	$-0.338873\pi$
$920$	−55.1358	+	95.4980i	−1.81777	+	3.14848i
$921$	−9.11447	+	15.7867i	−0.300332	+	0.520190i
$922$	−30.7874	−	53.3254i	−1.01393	−	1.75618i
$923$	8.35181			0.274903
$924$	39.0516	+	58.1940i	1.28470	+	1.91444i
$925$	4.35409			0.143162
$926$	−17.9917	−	31.1625i	−0.591243	−	1.02406i
$927$	−2.61774	+	4.53406i	−0.0859779	+	0.148918i
$928$	−11.2565	+	19.4969i	−0.369514	+	0.640017i
$929$	−4.11676	−	7.13044i	−0.135067	−	0.233942i	0.790556	−	0.612389i	$-0.209792\pi$
$929$	−4.11676	−	7.13044i	−0.135067	−	0.233942i	−0.925623	+	0.378447i	$0.876458\pi$
$930$	15.1411			0.496495
$931$	−13.9738	+	1.89624i	−0.457972	+	0.0621468i
$932$	−24.9966			−0.818792
$933$	2.39363	+	4.14589i	0.0783640	+	0.135731i
$934$	46.6492	−	80.7987i	1.52641	−	2.64382i
$935$	21.0444	−	36.4500i	0.688226	−	1.19204i
$936$	3.08902	+	5.35034i	0.100968	+	0.174881i
$937$	−21.6093			−0.705944			−0.352972	−	0.935634i	$-0.614829\pi$
$937$	−21.6093			−0.705944			−0.352972	+	0.935634i	$0.614829\pi$
$938$	19.8602	+	29.5953i	0.648458	+	0.966322i
$939$	−5.29937			−0.172938
$940$	56.4148	+	97.7133i	1.84005	+	3.18705i
$941$	−14.8945	+	25.7981i	−0.485548	+	0.840994i	−0.999862	−	0.0166080i	$-0.994713\pi$
$941$	−14.8945	+	25.7981i	−0.485548	+	0.840994i	0.514314	+	0.857602i	$0.328047\pi$
$942$	5.61624	−	9.72761i	0.182987	−	0.316943i
$943$	−28.9878	−	50.2084i	−0.943973	−	1.63501i
$944$	78.1492			2.54354
$945$	2.93960	−	5.99092i	0.0956252	−	0.194885i
$946$	−54.4082			−1.76896
$947$	9.29709	+	16.1030i	0.302115	+	0.523278i	0.976615	−	0.214997i	$-0.0689741\pi$
$947$	9.29709	+	16.1030i	0.302115	+	0.523278i	−0.674500	+	0.738275i	$0.735641\pi$
$948$	−27.2367	+	47.1753i	−0.884606	+	1.53218i
$949$	−1.66093	+	2.87681i	−0.0539160	+	0.0933853i
$950$	3.47965	+	6.02692i	0.112895	+	0.195539i
$951$	−10.7420			−0.348332
$952$	45.5678	−	3.07767i	1.47686	−	0.0997479i
$953$	−12.3033			−0.398543			−0.199272	−	0.979944i	$-0.563858\pi$
$953$	−12.3033			−0.398543			−0.199272	+	0.979944i	$0.563858\pi$
$954$	13.7151	+	23.7553i	0.444044	+	0.769107i
$955$	0.862450	−	1.49381i	0.0279082	−	0.0483385i
$956$	−22.8482	+	39.5743i	−0.738965	+	1.27992i
$957$	−13.7236	−	23.7700i	−0.443621	−	0.768375i
$958$	98.1757			3.17191
$959$	18.8674	−	1.27432i	0.609261	−	0.0411498i
$960$	−2.96812			−0.0957956
$961$	12.7002	+	21.9973i	0.409683	+	0.709591i
$962$	4.05559	−	7.02448i	0.130757	−	0.226478i
$963$	−8.93676	+	15.4789i	−0.287983	+	0.498801i
$964$	43.8560	+	75.9609i	1.41251	+	2.44654i
$965$	7.22909			0.232713
$966$	20.9224	−	42.6399i	0.673166	−	1.37191i
$967$	−3.28572			−0.105662			−0.0528308	−	0.998603i	$-0.516824\pi$
$967$	−3.28572			−0.105662			−0.0528308	+	0.998603i	$0.516824\pi$
$968$	−76.1961	−	131.976i	−2.44904	−	4.24185i
$969$	2.81446	−	4.87478i	0.0904133	−	0.156600i
$970$	4.15056	−	7.18898i	0.133266	−	0.230824i
$971$	−9.36949	−	16.2284i	−0.300681	−	0.520795i	0.675609	−	0.737260i	$-0.263881\pi$
$971$	−9.36949	−	16.2284i	−0.300681	−	0.520795i	−0.976290	+	0.216465i	$0.930547\pi$
$972$	−4.43536			−0.142264
$973$	29.1232	+	43.3989i	0.933646	+	1.39130i
$974$	12.2579			0.392769
$975$	−0.680880	−	1.17932i	−0.0218056	−	0.0377684i
$976$	16.3042	−	28.2397i	0.521884	−	0.903930i
$977$	0.357961	−	0.620007i	0.0114522	−	0.0198358i	−0.860243	−	0.509885i	$-0.829688\pi$
$977$	0.357961	−	0.620007i	0.0114522	−	0.0198358i	0.871695	+	0.490049i	$0.163021\pi$
$978$	23.3513	+	40.4456i	0.746691	+	1.29331i
$979$	21.9992			0.703097
$980$	29.6799	−	72.4674i	0.948090	−	2.31489i
$981$	0.936989			0.0299158
$982$	−28.2282	−	48.8928i	−0.900799	−	1.56023i
$983$	−19.3804	+	33.5679i	−0.618140	+	1.07065i	0.371685	+	0.928359i	$0.378780\pi$
$983$	−19.3804	+	33.5679i	−0.618140	+	1.07065i	−0.989825	+	0.142291i	$0.954553\pi$
$984$	−25.3070	+	43.8331i	−0.806759	+	1.39735i
$985$	4.59003	+	7.95017i	0.146251	+	0.253313i
$986$	−32.5761			−1.03744
$987$	−14.8690	−	22.1576i	−0.473286	−	0.705283i
$988$	8.93526			0.284268
$989$	12.7069	+	22.0091i	0.404057	+	0.699847i
$990$	−19.1063	+	33.0931i	−0.607239	+	1.05177i
$991$	−1.12865	+	1.95489i	−0.0358529	+	0.0620990i	−0.883395	−	0.468629i	$-0.844748\pi$
$991$	−1.12865	+	1.95489i	−0.0358529	+	0.0620990i	0.847542	+	0.530728i	$0.178081\pi$
$992$	−5.79589	−	10.0388i	−0.184020	−	0.318731i
$993$	−3.35664			−0.106520
$994$	−24.6926	+	50.3236i	−0.783202	+	1.59617i
$995$	−28.5214			−0.904190
$996$	−26.2900	−	45.5356i	−0.833029	−	1.44285i
$997$	−14.1059	+	24.4321i	−0.446737	+	0.773772i	−0.998171	−	0.0604468i	$-0.980747\pi$
$997$	−14.1059	+	24.4321i	−0.446737	+	0.773772i	0.551434	+	0.834218i	$0.314081\pi$
$998$	−21.7430	+	37.6599i	−0.688262	+	1.19210i
$999$	1.59870	+	2.76903i	0.0505806	+	0.0876082i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.i.e.235.1	yes	10
3.2	odd	2		819.2.j.g.235.5		10
7.2	even	3	inner	273.2.i.e.79.1	✓	10
7.3	odd	6		1911.2.a.u.1.5		5
7.4	even	3		1911.2.a.t.1.5		5
21.2	odd	6		819.2.j.g.352.5		10
21.11	odd	6		5733.2.a.bq.1.1		5
21.17	even	6		5733.2.a.bp.1.1		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.i.e.79.1	✓	10	7.2	even	3	inner
273.2.i.e.235.1	yes	10	1.1	even	1	trivial
819.2.j.g.235.5		10	3.2	odd	2
819.2.j.g.352.5		10	21.2	odd	6
1911.2.a.t.1.5		5	7.4	even	3
1911.2.a.u.1.5		5	7.3	odd	6
5733.2.a.bp.1.1		5	21.17	even	6
5733.2.a.bq.1.1		5	21.11	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.26840 - 2.19693i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.21768 + 3.84114i) q^{4} +(1.26113 + 2.18434i) q^{5} -2.53680 q^{6} +(1.47427 + 2.19693i) q^{7} +6.17804 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-1.26840 - 2.19693i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-2.21768 + 3.84114i) q^{4} +(1.26113 + 2.18434i) q^{5} -2.53680 q^{6} +(1.47427 + 2.19693i) q^{7} +6.17804 q^{8} +(-0.500000 - 0.866025i) q^{9} +(3.19923 - 5.54123i) q^{10} +(2.98608 - 5.17205i) q^{11} +(2.21768 + 3.84114i) q^{12} -1.00000 q^{13} +(2.95656 - 6.02547i) q^{14} +2.52225 q^{15} +(-3.40086 - 5.89047i) q^{16} +(1.39706 - 2.41979i) q^{17} +(-1.26840 + 2.19693i) q^{18} +(1.00727 + 1.74465i) q^{19} -11.1871 q^{20} +(2.63974 - 0.178289i) q^{21} -15.1502 q^{22} +(3.53830 + 6.12851i) q^{23} +(3.08902 - 5.35034i) q^{24} +(-0.680880 + 1.17932i) q^{25} +(1.26840 + 2.19693i) q^{26} -1.00000 q^{27} +(-11.7082 + 0.790778i) q^{28} +4.59586 q^{29} +(-3.19923 - 5.54123i) q^{30} +(-1.18318 + 2.04933i) q^{31} +(-2.44928 + 4.24228i) q^{32} +(-2.98608 - 5.17205i) q^{33} -7.08815 q^{34} +(-2.93960 + 5.99092i) q^{35} +4.43536 q^{36} +(-1.59870 - 2.76903i) q^{37} +(2.55526 - 4.42583i) q^{38} +(-0.500000 + 0.866025i) q^{39} +(7.79129 + 13.4949i) q^{40} -8.19259 q^{41} +(-3.73994 - 5.57319i) q^{42} +3.59125 q^{43} +(13.2444 + 22.9399i) q^{44} +(1.26113 - 2.18434i) q^{45} +(8.97597 - 15.5468i) q^{46} +(-5.04284 - 8.73445i) q^{47} -6.80173 q^{48} +(-2.65305 + 6.47776i) q^{49} +3.45452 q^{50} +(-1.39706 - 2.41979i) q^{51} +(2.21768 - 3.84114i) q^{52} +(5.40647 - 9.36428i) q^{53} +(1.26840 + 2.19693i) q^{54} +15.0633 q^{55} +(9.10810 + 13.5727i) q^{56} +2.01455 q^{57} +(-5.82939 - 10.0968i) q^{58} +(-5.74480 + 9.95029i) q^{59} +(-5.59356 + 9.68832i) q^{60} +(2.39706 + 4.15184i) q^{61} +6.00300 q^{62} +(1.16547 - 2.37522i) q^{63} -1.17677 q^{64} +(-1.26113 - 2.18434i) q^{65} +(-7.57510 + 13.1205i) q^{66} +(-2.65515 + 4.59886i) q^{67} +(6.19649 + 10.7326i) q^{68} +7.07660 q^{69} +(16.8902 - 1.14078i) q^{70} -8.35181 q^{71} +(-3.08902 - 5.35034i) q^{72} +(1.66093 - 2.87681i) q^{73} +(-4.05559 + 7.02448i) q^{74} +(0.680880 + 1.17932i) q^{75} -8.93526 q^{76} +(15.7649 - 1.06477i) q^{77} +2.53680 q^{78} +(6.14080 + 10.6362i) q^{79} +(8.57784 - 14.8573i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(10.3915 + 17.9986i) q^{82} -11.8547 q^{83} +(-5.16926 + 10.5350i) q^{84} +7.04750 q^{85} +(-4.55515 - 7.88975i) q^{86} +(2.29793 - 3.98013i) q^{87} +(18.4481 - 31.9531i) q^{88} +(1.84181 + 3.19011i) q^{89} -6.39846 q^{90} +(-1.47427 - 2.19693i) q^{91} -31.3873 q^{92} +(1.18318 + 2.04933i) q^{93} +(-12.7927 + 22.1576i) q^{94} +(-2.54060 + 4.40045i) q^{95} +(2.44928 + 4.24228i) q^{96} +1.29736 q^{97} +(17.5963 - 2.38782i) q^{98} -5.97217 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9	\( 10 q + 5 q^{3} - 6 q^{4} + 3 q^{5} + 4 q^{7} + 6 q^{8} - 5 q^{9} + 2 q^{10} + q^{11} + 6 q^{12} - 10 q^{13} + 23 q^{14} + 6 q^{15} + 13 q^{17} + 7 q^{19} - 26 q^{20} + 2 q^{21} - 38 q^{22} + 4 q^{23} + 3 q^{24} - 16 q^{25} - 10 q^{27} - 4 q^{28} - 24 q^{29} - 2 q^{30} + 6 q^{31} - 21 q^{32} - q^{33} - 14 q^{34} - 3 q^{35} + 12 q^{36} - 11 q^{37} + 14 q^{38} - 5 q^{39} + 11 q^{40} - 20 q^{41} - 2 q^{42} + 20 q^{43} + 29 q^{44} + 3 q^{45} - q^{46} - 4 q^{47} + 22 q^{49} - 58 q^{50} - 13 q^{51} + 6 q^{52} + 9 q^{53} + 24 q^{55} + 42 q^{56} + 14 q^{57} - 34 q^{58} + 7 q^{59} - 13 q^{60} + 23 q^{61} + 48 q^{62} - 2 q^{63} - 26 q^{64} - 3 q^{65} - 19 q^{66} - 25 q^{67} + 20 q^{68} + 8 q^{69} + 73 q^{70} - 54 q^{71} - 3 q^{72} + 18 q^{73} - 15 q^{74} + 16 q^{75} - 4 q^{76} + 27 q^{77} - 8 q^{79} + 41 q^{80} - 5 q^{81} + 26 q^{82} - 24 q^{83} - 5 q^{84} + 20 q^{85} + 19 q^{86} - 12 q^{87} + 36 q^{88} + 29 q^{89} - 4 q^{90} - 4 q^{91} - 100 q^{92} - 6 q^{93} - 2 q^{94} + 33 q^{95} + 21 q^{96} - 26 q^{97} + 15 q^{98} - 2 q^{99}+O(q^{100}) \) 10 * q + 5 * q^3 - 6 * q^4 + 3 * q^5 + 4 * q^7 + 6 * q^8 - 5 * q^9 + 2 * q^10 + q^11 + 6 * q^12 - 10 * q^13 + 23 * q^14 + 6 * q^15 + 13 * q^17 + 7 * q^19 - 26 * q^20 + 2 * q^21 - 38 * q^22 + 4 * q^23 + 3 * q^24 - 16 * q^25 - 10 * q^27 - 4 * q^28 - 24 * q^29 - 2 * q^30 + 6 * q^31 - 21 * q^32 - q^33 - 14 * q^34 - 3 * q^35 + 12 * q^36 - 11 * q^37 + 14 * q^38 - 5 * q^39 + 11 * q^40 - 20 * q^41 - 2 * q^42 + 20 * q^43 + 29 * q^44 + 3 * q^45 - q^46 - 4 * q^47 + 22 * q^49 - 58 * q^50 - 13 * q^51 + 6 * q^52 + 9 * q^53 + 24 * q^55 + 42 * q^56 + 14 * q^57 - 34 * q^58 + 7 * q^59 - 13 * q^60 + 23 * q^61 + 48 * q^62 - 2 * q^63 - 26 * q^64 - 3 * q^65 - 19 * q^66 - 25 * q^67 + 20 * q^68 + 8 * q^69 + 73 * q^70 - 54 * q^71 - 3 * q^72 + 18 * q^73 - 15 * q^74 + 16 * q^75 - 4 * q^76 + 27 * q^77 - 8 * q^79 + 41 * q^80 - 5 * q^81 + 26 * q^82 - 24 * q^83 - 5 * q^84 + 20 * q^85 + 19 * q^86 - 12 * q^87 + 36 * q^88 + 29 * q^89 - 4 * q^90 - 4 * q^91 - 100 * q^92 - 6 * q^93 - 2 * q^94 + 33 * q^95 + 21 * q^96 - 26 * q^97 + 15 * q^98 - 2 * q^99

Introduction

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