LMFDB - Embedded newform 546.2.bn.f.173.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(101,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 5]))

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

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

chi := DirichletCharacter("546.101");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bn (of order $6$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			173.17
Character	$\chi$	$=$	546.173
Dual form			546.2.bn.f.101.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.84717 + 1.64381i) q^{5} +(0.841952 + 1.51364i) q^{6} +(-0.683149 - 2.55603i) q^{7} -1.00000 q^{8} +(2.99847 + 0.0958395i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.84717 + 1.64381i) q^{5} +(0.841952 + 1.51364i) q^{6} +(-0.683149 - 2.55603i) q^{7} -1.00000 q^{8} +(2.99847 + 0.0958395i) q^{9} +3.28763i q^{10} +2.07020 q^{11} +(-0.889878 + 1.48597i) q^{12} +(-3.53365 - 0.716460i) q^{13} +(1.87202 - 1.86964i) q^{14} +(4.88532 + 2.92558i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.561810 - 0.973084i) q^{17} +(1.41623 + 2.64467i) q^{18} -1.01086 q^{19} +(-2.84717 + 1.64381i) q^{20} +(-1.11237 - 4.44552i) q^{21} +(1.03510 + 1.79285i) q^{22} +(-3.03183 + 1.75043i) q^{23} +(-1.73183 - 0.0276700i) q^{24} +(2.90424 + 5.03029i) q^{25} +(-1.14635 - 3.41846i) q^{26} +(5.19019 + 0.248945i) q^{27} +(2.55516 + 0.686393i) q^{28} +(-7.97573 - 4.60479i) q^{29} +(-0.0909687 + 5.69361i) q^{30} +(1.86666 + 3.23315i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.58524 + 0.0572825i) q^{33} +1.12362 q^{34} +(2.25660 - 8.40042i) q^{35} +(-1.58223 + 2.54883i) q^{36} +(-6.03816 + 3.48613i) q^{37} +(-0.505430 - 0.875431i) q^{38} +(-6.09986 - 1.33856i) q^{39} +(-2.84717 - 1.64381i) q^{40} +(-8.52566 - 4.92229i) q^{41} +(3.29375 - 3.18610i) q^{42} +(3.35600 + 5.81276i) q^{43} +(-1.03510 + 1.79285i) q^{44} +(8.37960 + 5.20179i) q^{45} +(-3.03183 - 1.75043i) q^{46} +(1.05515 + 0.609193i) q^{47} +(-0.841952 - 1.51364i) q^{48} +(-6.06662 + 3.49230i) q^{49} +(-2.90424 + 5.03029i) q^{50} +(0.999885 - 1.66967i) q^{51} +(2.38730 - 2.70200i) q^{52} +(5.05843 - 2.92049i) q^{53} +(2.37950 + 4.61931i) q^{54} +(5.89421 + 3.40302i) q^{55} +(0.683149 + 2.55603i) q^{56} +(-1.75064 - 0.0279705i) q^{57} -9.20958i q^{58} +(8.49492 + 4.90455i) q^{59} +(-4.97629 + 2.76802i) q^{60} -0.241991i q^{61} +(-1.86666 + 3.23315i) q^{62} +(-1.80343 - 7.72966i) q^{63} +1.00000 q^{64} +(-8.88317 - 7.84854i) q^{65} +(1.74301 + 3.13355i) q^{66} -11.8144i q^{67} +(0.561810 + 0.973084i) q^{68} +(-5.29905 + 2.94755i) q^{69} +(8.40328 - 2.24594i) q^{70} +(3.94585 + 6.83441i) q^{71} +(-2.99847 - 0.0958395i) q^{72} +(-0.878160 - 1.52102i) q^{73} +(-6.03816 - 3.48613i) q^{74} +(4.89046 + 8.79197i) q^{75} +(0.505430 - 0.875431i) q^{76} +(-1.41426 - 5.29150i) q^{77} +(-1.89070 - 5.95191i) q^{78} +(-2.48977 + 4.31240i) q^{79} -3.28763i q^{80} +(8.98163 + 0.574744i) q^{81} -9.84458i q^{82} -0.999900i q^{83} +(4.40612 + 1.25942i) q^{84} +(3.19914 - 1.84702i) q^{85} +(-3.35600 + 5.81276i) q^{86} +(-13.6852 - 8.19540i) q^{87} -2.07020 q^{88} +(6.59807 - 3.80940i) q^{89} +(-0.315084 + 9.85784i) q^{90} +(0.582714 + 9.52158i) q^{91} -3.50085i q^{92} +(3.14328 + 5.65092i) q^{93} +1.21839i q^{94} +(-2.87809 - 1.66167i) q^{95} +(0.889878 - 1.48597i) q^{96} +(3.21628 + 5.57077i) q^{97} +(-6.05773 - 3.50769i) q^{98} +(6.20743 + 0.198407i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	$ 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) $ 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	1.73183	+	0.0276700i	0.999872	+	0.0159753i
$3$	1.73183	+	0.0276700i	0.999872	+	0.0159753i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	2.84717	+	1.64381i	1.27329	+	0.735135i	0.975606	−	0.219529i	$-0.0704519\pi$
$5$	2.84717	+	1.64381i	1.27329	+	0.735135i	0.297686	+	0.954664i	$0.403785\pi$
$6$	0.841952	+	1.51364i	0.343725	+	0.617942i
$7$	−0.683149	−	2.55603i	−0.258206	−	0.966090i
$7$	−0.683149	−	2.55603i	−0.258206	−	0.966090i
$8$	−1.00000			−0.353553
$9$	2.99847	+	0.0958395i	0.999490	+	0.0319465i
$10$			3.28763i			1.03964i
$11$	2.07020			0.624189			0.312095	−	0.950051i	$-0.398969\pi$
$11$	2.07020			0.624189			0.312095	+	0.950051i	$0.398969\pi$
$12$	−0.889878	+	1.48597i	−0.256886	+	0.428964i
$13$	−3.53365	−	0.716460i	−0.980058	−	0.198710i
$13$	−3.53365	−	0.716460i	−0.980058	−	0.198710i
$14$	1.87202	−	1.86964i	0.500317	−	0.499683i
$15$	4.88532	+	2.92558i	1.26139	+	0.755383i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.561810	−	0.973084i	0.136259	−	0.236008i	−0.789819	−	0.613340i	$-0.789825\pi$
$17$	0.561810	−	0.973084i	0.136259	−	0.236008i	0.926078	+	0.377333i	$0.123159\pi$
$18$	1.41623	+	2.64467i	0.333810	+	0.623355i
$19$	−1.01086			−0.231907			−0.115954	−	0.993255i	$-0.536992\pi$
$19$	−1.01086			−0.231907			−0.115954	+	0.993255i	$0.536992\pi$
$20$	−2.84717	+	1.64381i	−0.636646	+	0.367568i
$21$	−1.11237	−	4.44552i	−0.242739	−	0.970092i
$22$	1.03510	+	1.79285i	0.220684	+	0.382236i
$23$	−3.03183	+	1.75043i	−0.632180	+	0.364989i	−0.781596	−	0.623785i	$-0.785594\pi$
$23$	−3.03183	+	1.75043i	−0.632180	+	0.364989i	0.149416	+	0.988774i	$0.452261\pi$
$24$	−1.73183	−	0.0276700i	−0.353508	−	0.00564812i
$25$	2.90424	+	5.03029i	0.580848	+	1.00606i
$26$	−1.14635	−	3.41846i	−0.224818	−	0.670415i
$27$	5.19019	+	0.248945i	0.998852	+	0.0479096i
$28$	2.55516	+	0.686393i	0.482881	+	0.129716i
$29$	−7.97573	−	4.60479i	−1.48106	−	0.855088i	−0.481287	−	0.876563i	$-0.659831\pi$
$29$	−7.97573	−	4.60479i	−1.48106	−	0.855088i	−0.999769	+	0.0214746i	$0.993164\pi$
$30$	−0.0909687	+	5.69361i	−0.0166085	+	1.03951i
$31$	1.86666	+	3.23315i	0.335262	+	0.580691i	0.983535	−	0.180717i	$-0.0578418\pi$
$31$	1.86666	+	3.23315i	0.335262	+	0.580691i	−0.648273	+	0.761408i	$0.724508\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	3.58524	+	0.0572825i	0.624109	+	0.00997160i
$34$	1.12362			0.192699
$35$	2.25660	−	8.40042i	0.381435	−	1.41993i
$36$	−1.58223	+	2.54883i	−0.263706	+	0.424805i
$37$	−6.03816	+	3.48613i	−0.992667	+	0.573116i	−0.906070	−	0.423127i	$-0.860932\pi$
$37$	−6.03816	+	3.48613i	−0.992667	+	0.573116i	−0.0865963	+	0.996243i	$0.527599\pi$
$38$	−0.505430	−	0.875431i	−0.0819916	−	0.142014i
$39$	−6.09986	−	1.33856i	−0.976759	−	0.214342i
$40$	−2.84717	−	1.64381i	−0.450177	−	0.259910i
$41$	−8.52566	−	4.92229i	−1.33148	−	0.768733i	−0.345957	−	0.938250i	$-0.612446\pi$
$41$	−8.52566	−	4.92229i	−1.33148	−	0.768733i	−0.985527	+	0.169517i	$0.945779\pi$
$42$	3.29375	−	3.18610i	0.508236	−	0.491626i
$43$	3.35600	+	5.81276i	0.511785	+	0.886438i	0.999907	+	0.0136621i	$0.00434890\pi$
$43$	3.35600	+	5.81276i	0.511785	+	0.886438i	−0.488122	+	0.872776i	$0.662318\pi$
$44$	−1.03510	+	1.79285i	−0.156047	+	0.270282i
$45$	8.37960	+	5.20179i	1.24916	+	0.775437i
$46$	−3.03183	−	1.75043i	−0.447019	−	0.258086i
$47$	1.05515	+	0.609193i	0.153910	+	0.0888599i	0.574977	−	0.818170i	$-0.305011\pi$
$47$	1.05515	+	0.609193i	0.153910	+	0.0888599i	−0.421067	+	0.907029i	$0.638344\pi$
$48$	−0.841952	−	1.51364i	−0.121525	−	0.218476i
$49$	−6.06662	+	3.49230i	−0.866659	+	0.498900i
$50$	−2.90424	+	5.03029i	−0.410722	+	0.711391i
$51$	0.999885	−	1.66967i	0.140012	−	0.233801i
$52$	2.38730	−	2.70200i	0.331059	−	0.374700i
$53$	5.05843	−	2.92049i	0.694829	−	0.401160i	−0.110589	−	0.993866i	$-0.535274\pi$
$53$	5.05843	−	2.92049i	0.694829	−	0.401160i	0.805419	+	0.592706i	$0.201941\pi$
$54$	2.37950	+	4.61931i	0.323809	+	0.628608i
$55$	5.89421	+	3.40302i	0.794775	+	0.458863i
$56$	0.683149	+	2.55603i	0.0912896	+	0.341564i
$57$	−1.75064	−	0.0279705i	−0.231878	−	0.00370479i
$58$		−	9.20958i		−	1.20928i
$59$	8.49492	+	4.90455i	1.10594	+	0.638517i	0.937776	−	0.347241i	$-0.112881\pi$
$59$	8.49492	+	4.90455i	1.10594	+	0.638517i	0.168169	+	0.985758i	$0.446215\pi$
$60$	−4.97629	+	2.76802i	−0.642437	+	0.357350i
$61$		−	0.241991i		−	0.0309838i	−0.999880	−	0.0154919i	$-0.995069\pi$
$61$		−	0.241991i		−	0.0309838i	0.999880	−	0.0154919i	$-0.00493142\pi$
$62$	−1.86666	+	3.23315i	−0.237066	+	0.410611i
$63$	−1.80343	−	7.72966i	−0.227211	−	0.973846i
$64$	1.00000			0.125000
$65$	−8.88317	−	7.84854i	−1.10182	−	0.973492i
$66$	1.74301	+	3.13355i	0.214550	+	0.385713i
$67$		−	11.8144i		−	1.44336i	−0.692226	−	0.721680i	$-0.743370\pi$
$67$		−	11.8144i		−	1.44336i	0.692226	−	0.721680i	$-0.256630\pi$
$68$	0.561810	+	0.973084i	0.0681295	+	0.118004i
$69$	−5.29905	+	2.94755i	−0.637930	+	0.354843i
$70$	8.40328	−	2.24594i	1.00438	−	0.268441i
$71$	3.94585	+	6.83441i	0.468286	+	0.811096i	0.999343	−	0.0362405i	$-0.0115383\pi$
$71$	3.94585	+	6.83441i	0.468286	+	0.811096i	−0.531057	+	0.847336i	$0.678205\pi$
$72$	−2.99847	−	0.0958395i	−0.353373	−	0.0112948i
$73$	−0.878160	−	1.52102i	−0.102781	−	0.178022i	0.810049	−	0.586363i	$-0.199441\pi$
$73$	−0.878160	−	1.52102i	−0.102781	−	0.178022i	−0.912829	+	0.408341i	$0.866107\pi$
$74$	−6.03816	−	3.48613i	−0.701921	−	0.405254i
$75$	4.89046	+	8.79197i	0.564702	+	1.01521i
$76$	0.505430	−	0.875431i	0.0579768	−	0.100419i
$77$	−1.41426	−	5.29150i	−0.161169	−	0.603023i
$78$	−1.89070	−	5.95191i	−0.214079	−	0.673921i
$79$	−2.48977	+	4.31240i	−0.280121	+	0.485183i	−0.971414	−	0.237391i	$-0.923708\pi$
$79$	−2.48977	+	4.31240i	−0.280121	+	0.485183i	0.691294	+	0.722574i	$0.257041\pi$
$80$		−	3.28763i		−	0.367568i
$81$	8.98163	+	0.574744i	0.997959	+	0.0638604i
$82$		−	9.84458i		−	1.08715i
$83$		−	0.999900i		−	0.109753i	−0.998493	−	0.0548767i	$-0.982523\pi$
$83$		−	0.999900i		−	0.109753i	0.998493	−	0.0548767i	$-0.0174766\pi$
$84$	4.40612	+	1.25942i	0.480747	+	0.137414i
$85$	3.19914	−	1.84702i	0.346995	−	0.200338i
$86$	−3.35600	+	5.81276i	−0.361887	+	0.626806i
$87$	−13.6852	−	8.19540i	−1.46721	−	0.878640i
$88$	−2.07020			−0.220684
$89$	6.59807	−	3.80940i	0.699394	−	0.403795i	−0.107728	−	0.994180i	$-0.534358\pi$
$89$	6.59807	−	3.80940i	0.699394	−	0.403795i	0.807122	+	0.590385i	$0.201024\pi$
$90$	−0.315084	+	9.85784i	−0.0332128	+	1.03911i
$91$	0.582714	+	9.52158i	0.0610850	+	0.998133i
$92$		−	3.50085i		−	0.364989i
$93$	3.14328	+	5.65092i	0.325943	+	0.585973i
$94$			1.21839i			0.125667i
$95$	−2.87809	−	1.66167i	−0.295286	−	0.170483i
$96$	0.889878	−	1.48597i	0.0908228	−	0.151662i
$97$	3.21628	+	5.57077i	0.326564	+	0.565626i	0.981828	−	0.189775i	$-0.0607757\pi$
$97$	3.21628	+	5.57077i	0.326564	+	0.565626i	−0.655264	+	0.755400i	$0.727442\pi$
$98$	−6.05773	−	3.50769i	−0.611923	−	0.354330i
$99$	6.20743	+	0.198407i	0.623870	+	0.0199407i
$100$	−5.80848			−0.580848
$101$	−19.3241			−1.92282			−0.961409	−	0.275123i	$-0.911281\pi$
$101$	−19.3241			−1.92282			−0.961409	+	0.275123i	$0.911281\pi$
$102$	1.94592	+	0.0310906i	0.192675	+	0.00307843i
$103$	−7.86720	−	4.54213i	−0.775178	−	0.447549i	0.0595405	−	0.998226i	$-0.481036\pi$
$103$	−7.86720	−	4.54213i	−0.775178	−	0.447549i	−0.834719	+	0.550677i	$0.814370\pi$
$104$	3.53365	+	0.716460i	0.346503	+	0.0702547i
$105$	4.14049	−	14.4857i	0.404070	−	1.41366i
$106$	5.05843	+	2.92049i	0.491318	+	0.283663i
$107$	3.25929	−	1.88175i	0.315088	−	0.181916i	−0.334113	−	0.942533i	$-0.608437\pi$
$107$	3.25929	−	1.88175i	0.315088	−	0.181916i	0.649201	+	0.760617i	$0.275103\pi$
$108$	−2.81069	+	4.37036i	−0.270458	+	0.420538i
$109$	2.43945	−	1.40841i	0.233657	−	0.134902i	−0.378601	−	0.925560i	$-0.623595\pi$
$109$	2.43945	−	1.40841i	0.233657	−	0.134902i	0.612258	+	0.790658i	$0.290261\pi$
$110$			6.80604i			0.648931i
$111$	−10.5535	+	5.87031i	−1.00170	+	0.557185i
$112$	−1.87202	+	1.86964i	−0.176889	+	0.176664i
$113$	4.57774	−	2.64296i	0.430637	−	0.248629i	−0.268981	−	0.963146i	$-0.586687\pi$
$113$	4.57774	−	2.64296i	0.430637	−	0.248629i	0.699618	+	0.714517i	$0.253354\pi$
$114$	−0.851096	−	1.53008i	−0.0797124	−	0.143305i
$115$	−11.5095			−1.07327
$116$	7.97573	−	4.60479i	0.740528	−	0.427544i
$117$	−10.5269	−	2.48695i	−0.973210	−	0.229918i
$118$			9.80909i			0.903000i
$119$	−2.87104	−	0.771245i	−0.263187	−	0.0706999i
$120$	−4.88532	−	2.92558i	−0.445967	−	0.267068i
$121$	−6.71427			−0.610388
$122$	0.209571	−	0.120996i	0.0189736	−	0.0109544i
$123$	−14.6288	−	8.76048i	−1.31903	−	0.789906i
$124$	−3.73332			−0.335262
$125$			2.65798i			0.237737i
$126$	5.79237	−	5.42665i	0.516025	−	0.483444i
$127$	9.40084	−	16.2827i	0.834190	−	1.44486i	−0.0604988	−	0.998168i	$-0.519269\pi$
$127$	9.40084	−	16.2827i	0.834190	−	1.44486i	0.894688	−	0.446691i	$-0.147398\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	5.65118	+	10.1596i	0.497559	+	0.894500i
$130$	2.35545	−	11.6173i	0.206587	−	1.01891i
$131$	1.45204	−	2.51500i	0.126865	−	0.219737i	−0.795595	−	0.605828i	$-0.792842\pi$
$131$	1.45204	−	2.51500i	0.126865	−	0.219737i	0.922460	+	0.386092i	$0.126175\pi$
$132$	−1.84223	+	3.07626i	−0.160345	+	0.267754i
$133$	0.690568	+	2.58379i	0.0598799	+	0.224043i
$134$	10.2316	−	5.90721i	0.883874	−	0.510305i
$135$	14.3681	+	9.24048i	1.23661	+	0.795294i
$136$	−0.561810	+	0.973084i	−0.0481748	+	0.0834413i
$137$	10.5895	−	18.3416i	0.904724	−	1.56703i	0.0834363	−	0.996513i	$-0.473410\pi$
$137$	10.5895	−	18.3416i	0.904724	−	1.56703i	0.821288	−	0.570515i	$-0.193256\pi$
$138$	−5.20218	−	3.11533i	−0.442839	−	0.265195i
$139$	−17.6205	+	10.1732i	−1.49455	+	0.862878i	−0.999980	−	0.00626156i	$-0.998007\pi$
$139$	−17.6205	+	10.1732i	−1.49455	+	0.862878i	−0.494568	+	0.869139i	$0.664674\pi$
$140$	6.14668	+	6.15449i	0.519489	+	0.520149i
$141$	1.81049	+	1.08421i	0.152471	+	0.0913073i
$142$	−3.94585	+	6.83441i	−0.331128	+	0.573531i
$143$	−7.31537	−	1.48322i	−0.611742	−	0.124033i
$144$	−1.41623	−	2.64467i	−0.118020	−	0.220389i
$145$	−15.1388	−	26.2212i	−1.25721	−	2.17755i
$146$	0.878160	−	1.52102i	0.0726770	−	0.125880i
$147$	−10.6030	+	5.88021i	−0.874519	+	0.484992i
$148$		−	6.97226i		−	0.573116i
$149$	13.2500			1.08549			0.542743	−	0.839899i	$-0.317386\pi$
$149$	13.2500			1.08549			0.542743	+	0.839899i	$0.317386\pi$
$150$	−5.16884	+	8.63125i	−0.422034	+	0.704738i
$151$	15.0137	−	8.66818i	1.22180	−	0.705407i	0.256499	−	0.966545i	$-0.417431\pi$
$151$	15.0137	−	8.66818i	1.22180	−	0.705407i	0.965301	+	0.261138i	$0.0840978\pi$
$152$	1.01086			0.0819916
$153$	1.77783	−	2.86392i	0.143729	−	0.231534i
$154$	3.87545	−	3.87053i	0.312293	−	0.311896i
$155$			12.2738i			0.985852i
$156$	4.20916	−	4.61335i	0.337002	−	0.369364i
$157$	12.2223	−	7.05652i	0.975442	−	0.563172i	0.0745511	−	0.997217i	$-0.476248\pi$
$157$	12.2223	−	7.05652i	0.975442	−	0.563172i	0.900891	+	0.434045i	$0.142914\pi$
$158$	−4.97953			−0.396150
$159$	8.84115	−	4.91782i	0.701149	−	0.390008i
$160$	2.84717	−	1.64381i	0.225088	−	0.129955i
$161$	6.54534	+	6.55365i	0.515845	+	0.516500i
$162$	3.99307	+	8.06569i	0.313725	+	0.633701i
$163$			10.3152i			0.807947i	0.914771	+	0.403974i	$0.132371\pi$
$163$			10.3152i			0.807947i	−0.914771	+	0.403974i	$0.867629\pi$
$164$	8.52566	−	4.92229i	0.665742	−	0.384366i
$165$	10.1136	+	6.05655i	0.787343	+	0.471502i
$166$	0.865939	−	0.499950i	0.0672099	−	0.0388037i
$167$	12.1099	+	6.99167i	0.937094	+	0.541032i	0.889048	−	0.457813i	$-0.151367\pi$
$167$	12.1099	+	6.99167i	0.937094	+	0.541032i	0.0480461	+	0.998845i	$0.484701\pi$
$168$	1.11237	+	4.44552i	0.0858214	+	0.342979i
$169$	11.9734	+	5.06344i	0.921028	+	0.389495i
$170$	3.19914	+	1.84702i	0.245363	+	0.141660i
$171$	−3.03103	−	0.0968804i	−0.231789	−	0.00740863i
$172$	−6.71200			−0.511785
$173$	−5.07795			−0.386069			−0.193035	−	0.981192i	$-0.561833\pi$
$173$	−5.07795			−0.386069			−0.193035	+	0.981192i	$0.561833\pi$
$174$	0.254829	−	15.9494i	0.0193186	−	1.20912i
$175$	10.8736	−	10.8598i	0.821964	−	0.820922i
$176$	−1.03510	−	1.79285i	−0.0780236	−	0.135141i
$177$	14.5760	+	8.72889i	1.09560	+	0.656104i
$178$	6.59807	+	3.80940i	0.494546	+	0.285526i
$179$		−	11.7132i		−	0.875486i	−0.899100	−	0.437743i	$-0.855778\pi$
$179$		−	11.7132i		−	0.875486i	0.899100	−	0.437743i	$-0.144222\pi$
$180$	−8.69468	+	4.65605i	−0.648063	+	0.347041i
$181$			22.6731i			1.68528i	0.538480	+	0.842638i	$0.318999\pi$
$181$			22.6731i			1.68528i	−0.538480	+	0.842638i	$0.681001\pi$
$182$	−7.95457	+	5.26543i	−0.589632	+	0.390300i
$183$	0.00669590	−	0.419088i	0.000494975	−	0.0309798i
$184$	3.03183	−	1.75043i	0.223509	−	0.129043i
$185$	−22.9222			−1.68527
$186$	−3.32220	+	5.54762i	−0.243596	+	0.406771i
$187$	1.16306	−	2.01448i	0.0850514	−	0.147313i
$188$	−1.05515	+	0.609193i	−0.0769549	+	0.0444299i
$189$	−2.90936	−	13.4364i	−0.211625	−	0.977351i
$190$		−	3.32333i		−	0.241100i
$191$		−	25.8552i		−	1.87082i	−0.353570	−	0.935408i	$-0.615032\pi$
$191$		−	25.8552i		−	1.87082i	0.353570	−	0.935408i	$-0.384968\pi$
$192$	1.73183	+	0.0276700i	0.124984	+	0.00199691i
$193$			21.8098i			1.56990i	0.619558	+	0.784951i	$0.287312\pi$
$193$			21.8098i			1.56990i	−0.619558	+	0.784951i	$0.712688\pi$
$194$	−3.21628	+	5.57077i	−0.230916	+	0.399958i
$195$	−15.1670	−	13.8381i	−1.08613	−	0.990969i
$196$	0.00888497	−	6.99999i	0.000634641	−	0.500000i
$197$	−3.51025	+	6.07993i	−0.250095	+	0.433177i	−0.963552	−	0.267522i	$-0.913795\pi$
$197$	−3.51025	+	6.07993i	−0.250095	+	0.433177i	0.713457	+	0.700699i	$0.247128\pi$
$198$	2.93189	+	5.47500i	0.208360	+	0.389091i
$199$	−13.0589	−	7.53954i	−0.925719	−	0.534464i	−0.0402638	−	0.999189i	$-0.512820\pi$
$199$	−13.0589	−	7.53954i	−0.925719	−	0.534464i	−0.885455	+	0.464725i	$0.846153\pi$
$200$	−2.90424	−	5.03029i	−0.205361	−	0.355695i
$201$	0.326905	−	20.4606i	0.0230581	−	1.44318i
$202$	−9.66204	−	16.7351i	−0.679819	−	1.17748i
$203$	−6.32139	+	23.5320i	−0.443675	+	1.65162i
$204$	0.946035	+	1.70076i	0.0662357	+	0.119077i
$205$	−16.1827	−	28.0292i	−1.13025	−	1.95764i
$206$		−	9.08426i		−	0.632930i
$207$	−9.25860	+	4.95803i	−0.643517	+	0.344607i
$208$	1.14635	+	3.41846i	0.0794853	+	0.237028i
$209$	−2.09268			−0.144754
$210$	14.6152	−	3.65706i	1.00854	−	0.252361i
$211$	−10.2101	+	17.6845i	−0.702895	+	1.21745i	0.264550	+	0.964372i	$0.414776\pi$
$211$	−10.2101	+	17.6845i	−0.702895	+	1.21745i	−0.967446	+	0.253079i	$0.918557\pi$
$212$			5.84097i			0.401160i
$213$	6.64443	+	11.9452i	0.455269	+	0.818473i
$214$	3.25929	+	1.88175i	0.222801	+	0.128634i
$215$			22.0665i			1.50493i
$216$	−5.19019	−	0.248945i	−0.353147	−	0.0169386i
$217$	6.98884	−	6.97997i	0.474433	−	0.473831i
$218$	2.43945	+	1.40841i	0.165220	+	0.0953899i
$219$	−1.47874	−	2.65844i	−0.0999238	−	0.179641i
$220$	−5.89421	+	3.40302i	−0.397387	+	0.229432i
$221$	−2.68242	+	3.03602i	−0.180439	+	0.204225i
$222$	−10.3606	−	6.20446i	−0.695358	−	0.416416i
$223$	−1.37326	+	2.37855i	−0.0919602	+	0.159280i	−0.908336	−	0.418241i	$-0.862647\pi$
$223$	−1.37326	+	2.37855i	−0.0919602	+	0.159280i	0.816376	+	0.577521i	$0.195980\pi$
$224$	−2.55516	−	0.686393i	−0.170724	−	0.0458615i
$225$	8.22617	+	15.3615i	0.548411	+	1.02410i
$226$	4.57774	+	2.64296i	0.304507	+	0.175807i
$227$	7.77691	+	4.49000i	0.516172	+	0.298012i	0.735367	−	0.677669i	$-0.237010\pi$
$227$	7.77691	+	4.49000i	0.516172	+	0.298012i	−0.219195	+	0.975681i	$0.570343\pi$
$228$	0.899542	−	1.50211i	0.0595736	−	0.0994798i
$229$	−8.23500	+	14.2634i	−0.544184	+	0.942554i	0.454474	+	0.890760i	$0.349827\pi$
$229$	−8.23500	+	14.2634i	−0.544184	+	0.942554i	−0.998658	+	0.0517940i	$0.983506\pi$
$230$	−5.75475	−	9.96752i	−0.379457	−	0.657239i
$231$	−2.30283	−	9.20311i	−0.151515	−	0.605521i
$232$	7.97573	+	4.60479i	0.523633	+	0.302319i
$233$	−4.79194	−	2.76663i	−0.313931	−	0.181248i	0.334753	−	0.942306i	$-0.391347\pi$
$233$	−4.79194	−	2.76663i	−0.313931	−	0.181248i	−0.648684	+	0.761058i	$0.724680\pi$
$234$	−3.10968	−	10.3600i	−0.203286	−	0.677255i
$235$	2.00280	+	3.46895i	0.130648	+	0.226289i
$236$	−8.49492	+	4.90455i	−0.552972	+	0.319259i
$237$	−4.43118	+	7.39946i	−0.287836	+	0.480646i
$238$	−0.767600	−	2.87201i	−0.0497561	−	0.186165i
$239$	−4.33497			−0.280406			−0.140203	−	0.990123i	$-0.544776\pi$
$239$	−4.33497			−0.280406			−0.140203	+	0.990123i	$0.544776\pi$
$240$	0.0909687	−	5.69361i	0.00587200	−	0.367521i
$241$	2.10349	−	3.64335i	0.135498	−	0.234689i	−0.790290	−	0.612733i	$-0.790070\pi$
$241$	2.10349	−	3.64335i	0.135498	−	0.234689i	0.925787	+	0.378044i	$0.123403\pi$
$242$	−3.35713	−	5.81473i	−0.215805	−	0.373785i
$243$	15.5388	+	1.24388i	0.996811	+	0.0797949i
$244$	0.209571	+	0.120996i	0.0134164	+	0.00774595i
$245$	−23.0134	−	0.0292105i	−1.47027	−	0.00186619i
$246$	0.272400	−	17.0491i	0.0173676	−	1.08701i
$247$	3.57203	+	0.724241i	0.227283	+	0.0460824i
$248$	−1.86666	−	3.23315i	−0.118533	−	0.205305i
$249$	0.0276673	−	1.73166i	0.00175334	−	0.109739i
$250$	−2.30188	+	1.32899i	−0.145583	+	0.0840526i
$251$	9.79168	+	16.9597i	0.618045	+	1.07049i	0.989842	+	0.142172i	$0.0454086\pi$
$251$	9.79168	+	16.9597i	0.618045	+	1.07049i	−0.371797	+	0.928314i	$0.621258\pi$
$252$	7.59580	+	2.30301i	0.478490	+	0.145076i
$253$	−6.27649	+	3.62374i	−0.394600	+	0.227822i
$254$	18.8017			1.17972
$255$	5.59147	−	3.11021i	0.350151	−	0.194769i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−8.97486	−	15.5449i	−0.559837	−	0.969665i	−0.997510	−	0.0705311i	$-0.977531\pi$
$257$	−8.97486	−	15.5449i	−0.559837	−	0.969665i	0.437673	−	0.899134i	$-0.355803\pi$
$258$	−5.97286	+	9.97385i	−0.371854	+	0.620945i
$259$	13.0356	+	13.0522i	0.809994	+	0.811023i
$260$	11.2386	−	3.76878i	0.696990	−	0.233730i
$261$	−23.4737	−	14.5717i	−1.45298	−	0.901967i
$262$	2.90408			0.179414
$263$			27.8469i			1.71711i	0.512717	+	0.858557i	$0.328639\pi$
$263$			27.8469i			1.71711i	−0.512717	+	0.858557i	$0.671361\pi$
$264$	−3.58524	−	0.0572825i	−0.220656	−	0.00352549i
$265$	19.2029			1.17963
$266$	−1.89235	+	1.88995i	−0.116027	+	0.115880i
$267$	11.5321	−	6.41466i	0.705755	−	0.392571i
$268$	10.2316	+	5.90721i	0.624994	+	0.360840i
$269$	−14.1534	+	24.5145i	−0.862951	+	1.49467i	0.00611690	+	0.999981i	$0.498053\pi$
$269$	−14.1534	+	24.5145i	−0.862951	+	1.49467i	−0.869068	+	0.494693i	$0.835280\pi$
$270$	−0.818439	+	17.0634i	−0.0498086	+	1.03844i
$271$	12.6519	+	21.9137i	0.768546	+	1.33116i	0.938352	+	0.345682i	$0.112353\pi$
$271$	12.6519	+	21.9137i	0.768546	+	1.33116i	−0.169806	+	0.985478i	$0.554314\pi$
$272$	−1.12362			−0.0681295
$273$	0.745698	+	16.5059i	0.0451317	+	0.998981i
$274$	21.1790			1.27947
$275$	6.01236	+	10.4137i	0.362559	+	0.627970i
$276$	0.0968687	−	6.06288i	0.00583081	−	0.364943i
$277$	6.54676	−	11.3393i	0.393356	−	0.681313i	−0.599533	−	0.800350i	$-0.704647\pi$
$277$	6.54676	−	11.3393i	0.393356	−	0.681313i	0.992890	+	0.119036i	$0.0379805\pi$
$278$	−17.6205	−	10.1732i	−1.05680	−	0.610147i
$279$	5.28726	+	9.87340i	0.316540	+	0.591105i
$280$	−2.25660	+	8.40042i	−0.134858	+	0.502021i
$281$	16.5616			0.987980			0.493990	−	0.869468i	$-0.335538\pi$
$281$	16.5616			0.987980			0.493990	+	0.869468i	$0.335538\pi$
$282$	−0.0337127	+	2.11004i	−0.00200756	+	0.125651i
$283$			18.3919i			1.09328i	0.837367	+	0.546642i	$0.184094\pi$
$283$			18.3919i			1.09328i	−0.837367	+	0.546642i	$0.815906\pi$
$284$	−7.89170			−0.468286
$285$	−4.93838	−	2.95736i	−0.292524	−	0.175179i
$286$	−2.37318	−	7.07690i	−0.140329	−	0.418466i
$287$	−6.75725	+	25.1545i	−0.398868	+	1.48483i
$288$	1.58223	−	2.54883i	0.0932340	−	0.150191i
$289$	7.86874	+	13.6291i	0.462867	+	0.801709i
$290$	15.1388	−	26.2212i	0.888983	−	1.53976i
$291$	5.41591	+	9.73662i	0.317486	+	0.570771i
$292$	1.75632			0.102781
$293$	−7.37759	+	4.25945i	−0.431003	+	0.248840i	−0.699774	−	0.714364i	$-0.746716\pi$
$293$	−7.37759	+	4.25945i	−0.431003	+	0.248840i	0.268771	+	0.963204i	$0.413383\pi$
$294$	−10.3939	−	6.24234i	−0.606185	−	0.364061i
$295$	16.1243	+	27.9281i	0.938793	+	1.62604i
$296$	6.03816	−	3.48613i	0.350961	−	0.202627i
$297$	10.7447	+	0.515367i	0.623472	+	0.0299046i
$298$	6.62502	+	11.4749i	0.383777	+	0.664721i
$299$	11.9675	−	4.01321i	0.692100	−	0.232090i
$300$	−10.0593	−	0.160721i	−0.580774	−	0.00927922i
$301$	12.5650	−	12.5490i	0.724233	−	0.723314i
$302$	15.0137	+	8.66818i	0.863943	+	0.498798i
$303$	−33.4660	−	0.534698i	−1.92257	−	0.0307176i
$304$	0.505430	+	0.875431i	0.0289884	+	0.0502094i
$305$	0.397788	−	0.688989i	0.0227773	−	0.0394514i
$306$	3.36914	+	0.107687i	0.192601	+	0.00615607i
$307$	21.3161			1.21658			0.608288	−	0.793716i	$-0.291857\pi$
$307$	21.3161			1.21658			0.608288	+	0.793716i	$0.291857\pi$
$308$	5.28970	+	1.42097i	0.301409	+	0.0809673i
$309$	−13.4990	−	8.08388i	−0.767930	−	0.459876i
$310$	−10.6294	+	6.13688i	−0.603709	+	0.348551i
$311$	7.40693	+	12.8292i	0.420008	+	0.727476i	0.995940	−	0.0900223i	$-0.0286938\pi$
$311$	7.40693	+	12.8292i	0.420008	+	0.727476i	−0.575931	+	0.817498i	$0.695361\pi$
$312$	6.09986	+	1.33856i	0.345336	+	0.0757812i
$313$	−22.7031	−	13.1077i	−1.28326	−	0.740889i	−0.305814	−	0.952091i	$-0.598929\pi$
$313$	−22.7031	−	13.1077i	−1.28326	−	0.740889i	−0.977442	+	0.211203i	$0.932262\pi$
$314$	12.2223	+	7.05652i	0.689742	+	0.398223i
$315$	7.57144	−	24.9721i	0.426602	−	1.40702i
$316$	−2.48977	−	4.31240i	−0.140060	−	0.242592i
$317$	9.80532	−	16.9833i	0.550722	−	0.953878i	−0.447501	−	0.894283i	$-0.647686\pi$
$317$	9.80532	−	16.9833i	0.550722	−	0.953878i	0.998223	−	0.0595945i	$-0.0189808\pi$
$318$	8.67953	+	5.19775i	0.486724	+	0.291476i
$319$	−16.5114	−	9.53284i	−0.924459	−	0.533737i
$320$	2.84717	+	1.64381i	0.159161	+	0.0918919i
$321$	5.69661	−	3.16869i	0.317954	−	0.176859i
$322$	−2.40296	+	8.94526i	−0.133912	+	0.498500i
$323$	−0.567912	+	0.983652i	−0.0315995	+	0.0547319i
$324$	−4.98856	+	7.49095i	−0.277142	+	0.416164i
$325$	−6.65857	−	19.8561i	−0.369351	−	1.10142i
$326$	−8.93321	+	5.15759i	−0.494765	+	0.285652i
$327$	4.26368	−	2.37163i	0.235782	−	0.131152i
$328$	8.52566	+	4.92229i	0.470751	+	0.271788i
$329$	0.836291	−	3.11317i	0.0461062	−	0.171635i
$330$	−0.188323	+	11.7869i	−0.0103669	+	0.648848i
$331$		−	26.0774i		−	1.43334i	−0.697412	−	0.716671i	$-0.745665\pi$
$331$		−	26.0774i		−	1.43334i	0.697412	−	0.716671i	$-0.254335\pi$
$332$	0.865939	+	0.499950i	0.0475246	+	0.0274383i
$333$	−18.4393	+	9.87436i	−1.01047	+	0.541112i
$334$			13.9833i			0.765134i
$335$	19.4207	−	33.6376i	1.06107	−	1.83782i
$336$	−3.29375	+	3.18610i	−0.179689	+	0.173816i
$337$	−13.5184			−0.736394			−0.368197	−	0.929748i	$-0.620025\pi$
$337$	−13.5184			−0.736394			−0.368197	+	0.929748i	$0.620025\pi$
$338$	1.60162	+	12.9010i	0.0871166	+	0.701720i
$339$	8.00099	−	4.45049i	0.434554	−	0.241717i
$340$			3.69404i			0.200338i
$341$	3.86436	+	6.69327i	0.209267	+	0.362461i
$342$	−1.43162	−	2.67339i	−0.0774129	−	0.144561i
$343$	13.0708	+	13.1207i	0.705759	+	0.708452i
$344$	−3.35600	−	5.81276i	−0.180943	−	0.313403i
$345$	−19.9325	−	0.318468i	−1.07313	−	0.0171457i
$346$	−2.53897	−	4.39763i	−0.136496	−	0.236418i
$347$	29.0781	+	16.7882i	1.56099	+	0.901239i	0.997157	+	0.0753519i	$0.0240080\pi$
$347$	29.0781	+	16.7882i	1.56099	+	0.901239i	0.563835	+	0.825887i	$0.309325\pi$
$348$	13.9400	−	7.75403i	0.747264	−	0.415659i
$349$	−11.8845	+	20.5845i	−0.636161	+	1.10186i	0.350107	+	0.936710i	$0.386145\pi$
$349$	−11.8845	+	20.5845i	−0.636161	+	1.10186i	−0.986268	+	0.165153i	$0.947188\pi$
$350$	14.8416	+	3.98690i	0.793318	+	0.213109i
$351$	−18.1619	−	4.59825i	−0.969413	−	0.245436i
$352$	1.03510	−	1.79285i	0.0551710	−	0.0955590i
$353$		−	10.7207i		−	0.570608i	−0.958437	−	0.285304i	$-0.907905\pi$
$353$		−	10.7207i		−	0.570608i	0.958437	−	0.285304i	$-0.0920945\pi$
$354$	−0.271418	+	16.9877i	−0.0144257	+	0.902885i
$355$			25.9450i			1.37702i
$356$			7.61879i			0.403795i
$357$	−4.95081	−	1.41511i	−0.262024	−	0.0748954i
$358$	10.1439	−	5.85660i	0.536123	−	0.309531i
$359$	7.26878	−	12.5899i	0.383632	−	0.664469i	−0.607947	−	0.793978i	$-0.708007\pi$
$359$	7.26878	−	12.5899i	0.383632	−	0.664469i	0.991578	+	0.129508i	$0.0413399\pi$
$360$	−8.37960	−	5.20179i	−0.441644	−	0.274159i
$361$	−17.9782			−0.946219
$362$	−19.6355	+	11.3365i	−1.03202	+	0.595835i
$363$	−11.6280	−	0.185784i	−0.610310	−	0.00975113i
$364$	−8.53729	−	4.25614i	−0.447475	−	0.223083i
$365$		−	5.77412i		−	0.302231i
$366$	0.366288	−	0.203745i	0.0191462	−	0.0106499i
$367$			17.4965i			0.913308i	0.889644	+	0.456654i	$0.150952\pi$
$367$			17.4965i			0.913308i	−0.889644	+	0.456654i	$0.849048\pi$
$368$	3.03183	+	1.75043i	0.158045	+	0.0912473i
$369$	−25.0922	−	15.5764i	−1.30625	−	0.810877i
$370$	−11.4611	−	19.8512i	−0.595834	−	1.03201i
$371$	−10.9205	−	10.9344i	−0.566965	−	0.567686i
$372$	−6.46548	−	0.103301i	−0.335219	−	0.00535591i
$373$	−11.8665			−0.614423			−0.307211	−	0.951641i	$-0.599396\pi$
$373$	−11.8665			−0.614423			−0.307211	+	0.951641i	$0.599396\pi$
$374$	2.32612			0.120281
$375$	−0.0735463	+	4.60316i	−0.00379791	+	0.237706i
$376$	−1.05515	−	0.609193i	−0.0544153	−	0.0314167i
$377$	24.8843	+	21.9860i	1.28161	+	1.13234i
$378$	10.1815	−	9.23775i	0.523682	−	0.475139i
$379$	10.9141	+	6.30127i	0.560620	+	0.323674i	0.753394	−	0.657569i	$-0.228415\pi$
$379$	10.9141	+	6.30127i	0.560620	+	0.323674i	−0.192774	+	0.981243i	$0.561748\pi$
$380$	2.87809	−	1.66167i	0.147643	−	0.0852416i
$381$	16.7312	−	27.9388i	0.857165	−	1.43135i
$382$	22.3913	−	12.9276i	1.14564	−	0.661433i
$383$		−	1.06335i		−	0.0543345i	−0.999631	−	0.0271672i	$-0.991351\pi$
$383$		−	1.06335i		−	0.0543345i	0.999631	−	0.0271672i	$-0.00864866\pi$
$384$	0.841952	+	1.51364i	0.0429657	+	0.0772428i
$385$	4.67162	−	17.3906i	0.238088	−	0.886305i
$386$	−18.8878	+	10.9049i	−0.961364	+	0.555044i
$387$	9.50577	+	17.7510i	0.483205	+	0.902335i
$388$	−6.43257			−0.326564
$389$	2.28039	−	1.31658i	0.115620	−	0.0667534i	−0.441075	−	0.897470i	$-0.645403\pi$
$389$	2.28039	−	1.31658i	0.115620	−	0.0667534i	0.556695	+	0.830717i	$0.312069\pi$
$390$	4.40069	−	20.0540i	0.222838	−	1.01548i
$391$			3.93363i			0.198932i
$392$	6.06662	−	3.49230i	0.306410	−	0.176388i
$393$	2.58427	−	4.31538i	0.130359	−	0.217682i
$394$	−7.02050			−0.353688
$395$	−14.1776	+	8.18542i	−0.713351	+	0.411853i
$396$	−3.27554	+	5.27659i	−0.164602	+	0.265159i
$397$	−8.54714			−0.428969			−0.214484	−	0.976727i	$-0.568807\pi$
$397$	−8.54714			−0.428969			−0.214484	+	0.976727i	$0.568807\pi$
$398$		−	15.0791i		−	0.755846i
$399$	1.12445	+	4.49380i	0.0562931	+	0.224971i
$400$	2.90424	−	5.03029i	0.145212	−	0.251515i
$401$	7.78768	+	13.4887i	0.388898	+	0.673592i	0.992302	−	0.123845i	$-0.0395224\pi$
$401$	7.78768	+	13.4887i	0.388898	+	0.673592i	−0.603403	+	0.797436i	$0.706189\pi$
$402$	17.8828	−	9.94717i	0.891914	−	0.496120i
$403$	−4.27970	−	12.7622i	−0.213187	−	0.635731i
$404$	9.66204	−	16.7351i	0.480705	−	0.832605i
$405$	24.6274	+	16.4005i	1.22375	+	0.814948i
$406$	−23.5400	+	6.29152i	−1.16827	+	0.312243i
$407$	−12.5002	+	7.21699i	−0.619612	+	0.357733i
$408$	−0.999885	+	1.66967i	−0.0495017	+	0.0826610i
$409$	5.40484	−	9.36145i	0.267252	−	0.462894i	−0.700899	−	0.713260i	$-0.747218\pi$
$409$	5.40484	−	9.36145i	0.267252	−	0.462894i	0.968151	+	0.250366i	$0.0805511\pi$
$410$	16.1827	−	28.0292i	0.799204	−	1.38426i
$411$	18.8468	−	31.4715i	0.929642	−	1.55237i
$412$	7.86720	−	4.54213i	0.387589	−	0.223775i
$413$	6.73289	−	25.0638i	0.331304	−	1.23331i
$414$	−8.92308	−	5.53917i	−0.438546	−	0.272235i
$415$	1.64365	−	2.84688i	0.0806836	−	0.139748i
$416$	−2.38730	+	2.70200i	−0.117047	+	0.132477i
$417$	−30.7971	+	17.1307i	−1.50814	+	0.838892i
$418$	−1.04634	−	1.81232i	−0.0511783	−	0.0886434i
$419$	7.13932	−	12.3657i	0.348779	−	0.604102i	−0.637254	−	0.770654i	$-0.719930\pi$
$419$	7.13932	−	12.3657i	0.348779	−	0.604102i	0.986033	+	0.166551i	$0.0532632\pi$
$420$	10.4747	+	10.8286i	0.511113	+	0.528382i
$421$		−	31.1553i		−	1.51842i	−0.650848	−	0.759208i	$-0.725586\pi$
$421$		−	31.1553i		−	1.51842i	0.650848	−	0.759208i	$-0.274414\pi$
$422$	−20.4203			−0.994044
$423$	3.10546	+	1.92777i	0.150993	+	0.0937314i
$424$	−5.05843	+	2.92049i	−0.245659	+	0.141831i
$425$	6.52653			0.316583
$426$	−7.02265	+	11.7269i	−0.340249	+	0.568168i
$427$	−0.618538	+	0.165316i	−0.0299331	+	0.00800020i
$428$			3.76351i			0.181916i
$429$	−12.6279	−	2.77109i	−0.609682	−	0.133790i
$430$	−19.1102	+	11.0333i	−0.921575	+	0.532071i
$431$	−21.5902			−1.03996			−0.519981	−	0.854178i	$-0.674061\pi$
$431$	−21.5902			−1.03996			−0.519981	+	0.854178i	$0.674061\pi$
$432$	−2.37950	−	4.61931i	−0.114484	−	0.222246i
$433$	−16.2009	+	9.35358i	−0.778565	+	0.449505i	−0.835921	−	0.548849i	$-0.815066\pi$
$433$	−16.2009	+	9.35358i	−0.778565	+	0.449505i	0.0573567	+	0.998354i	$0.481733\pi$
$434$	9.53925	+	2.56252i	0.457899	+	0.123005i
$435$	−25.4923	−	45.8296i	−1.22226	−	2.19736i
$436$			2.81683i			0.134902i
$437$	3.06476	−	1.76944i	0.146607	−	0.0846437i
$438$	1.56291	−	2.60985i	0.0746787	−	0.124703i
$439$	−12.4456	+	7.18545i	−0.593994	+	0.342943i	−0.766675	−	0.642035i	$-0.778090\pi$
$439$	−12.4456	+	7.18545i	−0.593994	+	0.342943i	0.172681	+	0.984978i	$0.444757\pi$
$440$	−5.89421	−	3.40302i	−0.280995	−	0.162233i
$441$	−18.5253	+	9.89014i	−0.882155	+	0.470959i
$442$	−3.97048	−	0.805029i	−0.188857	−	0.0382913i
$443$	−1.21594	−	0.702023i	−0.0577711	−	0.0333541i	0.470836	−	0.882221i	$-0.343952\pi$
$443$	−1.21594	−	0.702023i	−0.0577711	−	0.0333541i	−0.528607	+	0.848866i	$0.677286\pi$
$444$	0.192923	−	12.0748i	0.00915570	−	0.573043i
$445$	25.0477			1.18738
$446$	−2.74652			−0.130051
$447$	22.9468	+	0.366629i	1.08535	+	0.0173409i
$448$	−0.683149	−	2.55603i	−0.0322757	−	0.120761i
$449$	11.0266	+	19.0987i	0.520379	+	0.901323i	0.999719	+	0.0236937i	$0.00754264\pi$
$449$	11.0266	+	19.0987i	0.520379	+	0.901323i	−0.479340	+	0.877629i	$0.659124\pi$
$450$	−9.19037	+	14.8048i	−0.433238	+	0.697906i
$451$	−17.6498	−	10.1901i	−0.831098	−	0.479835i
$452$			5.28591i			0.248629i
$453$	26.2411	−	14.5964i	1.23291	−	0.685798i
$454$			8.98000i			0.421453i
$455$	−13.9926	+	28.0674i	−0.655984	+	1.31582i
$456$	1.75064	+	0.0279705i	0.0819812	+	0.00130984i
$457$	36.6548	−	21.1627i	1.71464	−	0.989948i	0.786604	−	0.617457i	$-0.211837\pi$
$457$	36.6548	−	21.1627i	1.71464	−	0.989948i	0.928036	−	0.372491i	$-0.121496\pi$
$458$	−16.4700			−0.769592
$459$	3.15815	−	4.91063i	0.147410	−	0.229208i
$460$	5.75475	−	9.96752i	0.268317	−	0.464738i
$461$	−10.2913	+	5.94166i	−0.479312	+	0.276731i	−0.720130	−	0.693839i	$-0.755918\pi$
$461$	−10.2913	+	5.94166i	−0.479312	+	0.276731i	0.240818	+	0.970570i	$0.422584\pi$
$462$	6.81871	−	6.59587i	0.317235	−	0.306868i
$463$		−	3.56440i		−	0.165652i	−0.996564	−	0.0828258i	$-0.973605\pi$
$463$		−	3.56440i		−	0.165652i	0.996564	−	0.0828258i	$-0.0263945\pi$
$464$			9.20958i			0.427544i
$465$	−0.339615	+	21.2561i	−0.0157493	+	0.985727i
$466$		−	5.53326i		−	0.256323i
$467$	3.56143	−	6.16858i	0.164803	−	0.285448i	−0.771782	−	0.635887i	$-0.780634\pi$
$467$	3.56143	−	6.16858i	0.164803	−	0.285448i	0.936585	+	0.350439i	$0.113968\pi$
$468$	7.41720	−	7.87307i	0.342860	−	0.363933i
$469$	−30.1981	+	8.07101i	−1.39442	+	0.372684i
$470$	−2.00280	+	3.46895i	−0.0923821	+	0.160011i
$471$	21.3621	−	11.8825i	0.984314	−	0.547517i
$472$	−8.49492	−	4.90455i	−0.391010	−	0.225750i
$473$	6.94759	+	12.0336i	0.319451	+	0.553305i
$474$	−8.62370	−	0.137784i	−0.396100	−	0.00632862i
$475$	−2.93578	−	5.08492i	−0.134703	−	0.233312i
$476$	2.10344	−	2.10077i	0.0964108	−	0.0962885i
$477$	15.4474	−	8.27219i	0.707290	−	0.378758i
$478$	−2.16749	−	3.75420i	−0.0991386	−	0.171713i
$479$		−	30.5472i		−	1.39574i	−0.716225	−	0.697870i	$-0.754132\pi$
$479$		−	30.5472i		−	1.39574i	0.716225	−	0.697870i	$-0.245868\pi$
$480$	4.97629	−	2.76802i	0.227136	−	0.126342i
$481$	23.8344	−	7.99267i	1.08676	−	0.364434i
$482$	4.20698			0.191623
$483$	11.1541	+	11.5309i	0.507528	+	0.524675i
$484$	3.35713	−	5.81473i	0.152597	−	0.264306i
$485$			21.1479i			0.960275i
$486$	6.69214	+	14.0789i	0.303562	+	0.638632i
$487$	−27.7303	−	16.0101i	−1.25658	−	0.725488i	−0.284173	−	0.958773i	$-0.591719\pi$
$487$	−27.7303	−	16.0101i	−1.25658	−	0.725488i	−0.972408	+	0.233285i	$0.925052\pi$
$488$			0.241991i			0.0109544i
$489$	−0.285421	+	17.8641i	−0.0129072	+	0.807844i
$490$	−11.4814	−	19.9448i	−0.518676	−	0.901012i
$491$	13.0865	+	7.55549i	0.590585	+	0.340975i	0.765329	−	0.643639i	$-0.222576\pi$
$491$	13.0865	+	7.55549i	0.590585	+	0.340975i	−0.174744	+	0.984614i	$0.555910\pi$
$492$	14.9012	−	8.28867i	0.671798	−	0.373682i
$493$	−8.96170	+	5.17404i	−0.403615	+	0.233027i
$494$	1.15880	+	3.45559i	0.0521370	+	0.155474i
$495$	17.3475	+	10.7688i	0.779710	+	0.484019i
$496$	1.86666	−	3.23315i	0.0838156	−	0.145173i
$497$	14.7734	−	14.7546i	0.662677	−	0.661836i
$498$	1.51349	−	0.841868i	0.0678212	−	0.0377250i
$499$	4.18606	+	2.41682i	0.187394	+	0.108192i	0.590762	−	0.806846i	$-0.298827\pi$
$499$	4.18606	+	2.41682i	0.187394	+	0.108192i	−0.403368	+	0.915038i	$0.632161\pi$
$500$	−2.30188	−	1.32899i	−0.102943	−	0.0594342i
$501$	20.7789	+	12.4435i	0.928332	+	0.555933i
$502$	−9.79168	+	16.9597i	−0.437024	+	0.756948i
$503$	−13.7946	−	23.8930i	−0.615073	−	1.06534i	−0.990372	−	0.138433i	$-0.955793\pi$
$503$	−13.7946	−	23.8930i	−0.615073	−	1.06534i	0.375299	−	0.926904i	$-0.377540\pi$
$504$	1.80343	+	7.72966i	0.0803312	+	0.344306i
$505$	−55.0189	−	31.7652i	−2.44831	−	1.41353i
$506$	−6.27649	−	3.62374i	−0.279024	−	0.161095i
$507$	20.5957	+	9.10032i	0.914689	+	0.404159i
$508$	9.40084	+	16.2827i	0.417095	+	0.722429i
$509$	−27.1836	+	15.6945i	−1.20489	+	0.695645i	−0.961639	−	0.274318i	$-0.911548\pi$
$509$	−27.1836	+	15.6945i	−1.20489	+	0.695645i	−0.243253	+	0.969963i	$0.578214\pi$
$510$	5.48925	+	3.28725i	0.243068	+	0.145562i
$511$	−3.28786	+	3.28369i	−0.145446	+	0.145262i
$512$	−1.00000			−0.0441942
$513$	−5.24655	−	0.251649i	−0.231641	−	0.0111106i
$514$	8.97486	−	15.5449i	0.395864	−	0.685657i
$515$	−14.9328	−	25.8644i	−0.658019	−	1.13972i
$516$	−11.6240	−	0.185721i	−0.511720	−	0.00817592i
$517$	2.18438	+	1.26115i	0.0960688	+	0.0554654i
$518$	−4.78571	+	17.8153i	−0.210272	+	0.782758i
$519$	−8.79414	−	0.140507i	−0.386020	−	0.00616757i
$520$	8.88317	+	7.84854i	0.389553	+	0.344181i
$521$	−0.178115	−	0.308505i	−0.00780338	−	0.0135159i	0.862097	−	0.506743i	$-0.169151\pi$
$521$	−0.178115	−	0.308505i	−0.00780338	−	0.0135159i	−0.869901	+	0.493227i	$0.835817\pi$
$522$	0.882642	−	27.6146i	0.0386322	−	1.20866i
$523$	21.5730	−	12.4552i	0.943320	−	0.544626i	0.0523207	−	0.998630i	$-0.483338\pi$
$523$	21.5730	−	12.4552i	0.943320	−	0.544626i	0.891000	+	0.454004i	$0.150005\pi$
$524$	1.45204	+	2.51500i	0.0634326	+	0.109868i
$525$	19.1317	−	18.5064i	0.834974	−	0.807686i
$526$	−24.1161	+	13.9235i	−1.05151	+	0.607092i
$527$	4.19484			0.182730
$528$	−1.74301	−	3.13355i	−0.0758548	−	0.136370i
$529$	−5.37201	+	9.30459i	−0.233566	+	0.404548i
$530$	9.60147	+	16.6302i	0.417061	+	0.722371i
$531$	25.0017	+	15.5203i	1.08498	+	0.673523i
$532$	−2.58291	−	0.693847i	−0.111984	−	0.0300821i
$533$	26.6001	+	23.5020i	1.15218	+	1.01798i
$534$	11.3213	+	6.77979i	0.489922	+	0.293390i
$535$	12.3730			0.534931
$536$			11.8144i			0.510305i
$537$	0.324105	−	20.2853i	0.0139861	−	0.875374i
$538$	−28.3069			−1.22040
$539$	−12.5591	+	7.22977i	−0.540959	+	0.311408i
$540$	−15.1865	+	7.82290i	−0.653525	+	0.336644i
$541$	−17.5713	−	10.1448i	−0.755447	−	0.436158i	0.0722115	−	0.997389i	$-0.476994\pi$
$541$	−17.5713	−	10.1448i	−0.755447	−	0.436158i	−0.827659	+	0.561232i	$0.810328\pi$
$542$	−12.6519	+	21.9137i	−0.543444	+	0.941272i
$543$	−0.627364	+	39.2659i	−0.0269228	+	1.68506i
$544$	−0.561810	−	0.973084i	−0.0240874	−	0.0417206i
$545$	9.26068			0.396684
$546$	−13.9217	+	8.89873i	−0.595792	+	0.380831i
$547$	−18.3443			−0.784344			−0.392172	−	0.919892i	$-0.628276\pi$
$547$	−18.3443			−0.784344			−0.392172	+	0.919892i	$0.628276\pi$
$548$	10.5895	+	18.3416i	0.452362	+	0.783514i
$549$	0.0231923	−	0.725603i	0.000989824	−	0.0309680i
$550$	−6.01236	+	10.4137i	−0.256368	+	0.444042i
$551$	8.06235	+	4.65480i	0.343468	+	0.198301i
$552$	5.29905	−	2.94755i	0.225542	−	0.125456i
$553$	12.7235	+	3.41791i	0.541059	+	0.145345i
$554$	13.0935			0.556290
$555$	−39.6973	−	0.634257i	−1.68506	−	0.0269227i
$556$		−	20.3464i		−	0.862878i
$557$	12.1781			0.516004			0.258002	−	0.966144i	$-0.416936\pi$
$557$	12.1781			0.516004			0.258002	+	0.966144i	$0.416936\pi$
$558$	−5.90699	+	9.51560i	−0.250063	+	0.402828i
$559$	−7.69432	−	22.9447i	−0.325435	−	0.970457i
$560$	−8.40328	+	2.24594i	−0.355103	+	0.0949082i
$561$	2.06996	−	3.45655i	0.0873939	−	0.145936i
$562$	8.28078	+	14.3427i	0.349304	+	0.605012i
$563$	5.68587	−	9.84822i	0.239631	−	0.415053i	−0.720978	−	0.692958i	$-0.756307\pi$
$563$	5.68587	−	9.84822i	0.239631	−	0.415053i	0.960608	+	0.277906i	$0.0896403\pi$
$564$	−1.84420	+	1.02582i	−0.0776549	+	0.0431949i
$565$	17.3781			0.731102
$566$	−15.9278	+	9.19594i	−0.669497	+	0.386534i
$567$	−4.66673	−	23.3500i	−0.195984	−	0.980607i
$568$	−3.94585	−	6.83441i	−0.165564	−	0.286766i
$569$	20.8276	−	12.0248i	0.873140	−	0.504108i	0.00474984	−	0.999989i	$-0.498488\pi$
$569$	20.8276	−	12.0248i	0.873140	−	0.504108i	0.868391	+	0.495881i	$0.165155\pi$
$570$	0.0919566	−	5.75544i	0.00385164	−	0.241069i
$571$	3.64194	+	6.30802i	0.152410	+	0.263983i	0.932113	−	0.362167i	$-0.117963\pi$
$571$	3.64194	+	6.30802i	0.152410	+	0.263983i	−0.779703	+	0.626150i	$0.784630\pi$
$572$	4.94219	−	5.59369i	0.206643	−	0.233884i
$573$	0.715414	−	44.7768i	0.0298868	−	1.87058i
$574$	−25.1631	+	6.72532i	−1.05029	+	0.280709i
$575$	−17.6103	−	10.1673i	−0.734401	−	0.424007i
$576$	2.99847	+	0.0958395i	0.124936	+	0.00399331i
$577$	2.11186	+	3.65785i	0.0879179	+	0.152278i	0.906631	−	0.421925i	$-0.138645\pi$
$577$	2.11186	+	3.65785i	0.0879179	+	0.152278i	−0.818713	+	0.574203i	$0.805312\pi$
$578$	−7.86874	+	13.6291i	−0.327296	+	0.566894i
$579$	−0.603477	+	37.7708i	−0.0250796	+	1.56970i
$580$	30.2777			1.25721
$581$	−2.55578	+	0.683081i	−0.106032	+	0.0283390i
$582$	−5.72420	+	9.55863i	−0.237276	+	0.396218i
$583$	10.4720	−	6.04600i	0.433705	−	0.250400i
$584$	0.878160	+	1.52102i	0.0363385	+	0.0629402i
$585$	−25.8837	−	24.3850i	−1.07016	−	1.00819i
$586$	−7.37759	−	4.25945i	−0.304765	−	0.175956i
$587$	−39.5103	−	22.8113i	−1.63077	−	0.941523i	−0.983857	−	0.178954i	$-0.942729\pi$
$587$	−39.5103	−	22.8113i	−1.63077	−	0.941523i	−0.646908	−	0.762568i	$-0.723938\pi$
$588$	0.209077	−	12.1226i	0.00862220	−	0.499926i
$589$	−1.88693	−	3.26827i	−0.0777498	−	0.134667i
$590$	−16.1243	+	27.9281i	−0.663827	+	1.14978i
$591$	−6.24738	+	10.4323i	−0.256983	+	0.429126i
$592$	6.03816	+	3.48613i	0.248167	+	0.143279i
$593$	21.1653	+	12.2198i	0.869154	+	0.501807i	0.867067	−	0.498191i	$-0.166002\pi$
$593$	21.1653	+	12.2198i	0.869154	+	0.501807i	0.00208732	+	0.999998i	$0.499336\pi$
$594$	4.92604	+	9.56289i	0.202118	+	0.392370i
$595$	−6.90654	−	6.91531i	−0.283140	−	0.283500i
$596$	−6.62502	+	11.4749i	−0.271371	+	0.470029i
$597$	−22.4071	−	13.4185i	−0.917062	−	0.549184i
$598$	9.45931	+	8.35758i	0.386820	+	0.341767i
$599$	11.4214	−	6.59416i	0.466667	−	0.269430i	−0.248177	−	0.968715i	$-0.579831\pi$
$599$	11.4214	−	6.59416i	0.466667	−	0.269430i	0.714843	+	0.699285i	$0.246498\pi$
$600$	−4.89046	−	8.79197i	−0.199652	−	0.358931i
$601$	−34.6176	−	19.9865i	−1.41208	−	0.815266i	−0.416497	−	0.909137i	$-0.636742\pi$
$601$	−34.6176	−	19.9865i	−1.41208	−	0.815266i	−0.995584	+	0.0938714i	$0.970076\pi$
$602$	17.1503	+	4.60707i	0.698992	+	0.187770i
$603$	1.13229	−	35.4252i	0.0461103	−	1.44262i
$604$			17.3364i			0.705407i
$605$	−19.1166	−	11.0370i	−0.777202	−	0.448718i
$606$	−16.2699	−	29.2498i	−0.660922	−	1.18819i
$607$		−	20.1780i		−	0.819000i	−0.912310	−	0.409500i	$-0.865703\pi$
$607$		−	20.1780i		−	0.819000i	0.912310	−	0.409500i	$-0.134297\pi$
$608$	−0.505430	+	0.875431i	−0.0204979	+	0.0355034i
$609$	−11.5987	+	40.5785i	−0.470003	+	1.64432i
$610$	0.795576			0.0322119
$611$	−3.29208	−	2.90865i	−0.133183	−	0.117671i
$612$	1.59131	+	2.97161i	0.0643249	+	0.120120i
$613$			24.9422i			1.00741i	0.863877	+	0.503703i	$0.168030\pi$
$613$			24.9422i			1.00741i	−0.863877	+	0.503703i	$0.831970\pi$
$614$	10.6581	+	18.4603i	0.430124	+	0.744997i
$615$	−27.2500	−	48.9895i	−1.09883	−	1.97545i
$616$	1.41426	+	5.29150i	0.0569820	+	0.213201i
$617$	−1.22499	−	2.12175i	−0.0493164	−	0.0854185i	0.840313	−	0.542101i	$-0.182371\pi$
$617$	−1.22499	−	2.12175i	−0.0493164	−	0.0854185i	−0.889630	+	0.456682i	$0.849038\pi$
$618$	0.251362	−	15.7324i	0.0101112	−	0.632850i
$619$	11.9145	+	20.6365i	0.478883	+	0.829449i	0.999707	−	0.0242147i	$-0.00770853\pi$
$619$	11.9145	+	20.6365i	0.478883	+	0.829449i	−0.520824	+	0.853664i	$0.674375\pi$
$620$	−10.6294	−	6.13688i	−0.426887	−	0.246463i
$621$	−16.1715	+	8.33028i	−0.648941	+	0.334283i
$622$	−7.40693	+	12.8292i	−0.296991	+	0.514403i
$623$	−14.2444	−	14.2625i	−0.570690	−	0.571415i
$624$	1.89070	+	5.95191i	0.0756885	+	0.238267i
$625$	10.1520	−	17.5837i	0.406079	−	0.703350i
$626$		−	26.2153i		−	1.04777i
$627$	−3.62417	−	0.0579046i	−0.144736	−	0.00231249i
$628$			14.1130i			0.563172i
$629$			7.83418i			0.312369i
$630$	25.4122	−	5.92901i	1.01245	−	0.236217i
$631$	−17.5516	+	10.1334i	−0.698718	+	0.403405i	−0.806870	−	0.590729i	$-0.798840\pi$
$631$	−17.5516	+	10.1334i	−0.698718	+	0.403405i	0.108152	+	0.994134i	$0.465507\pi$
$632$	2.48977	−	4.31240i	0.0990376	−	0.171538i
$633$	−18.1716	+	30.3440i	−0.722255	+	1.20607i
$634$	19.6106			0.778838
$635$	53.5315	−	30.9064i	2.12433	−	1.22648i
$636$	−0.161620	+	10.1156i	−0.00640865	+	0.401109i
$637$	23.9394	−	7.99409i	0.948513	−	0.316737i
$638$		−	19.0657i		−	0.754818i
$639$	11.1765	+	20.8709i	0.442136	+	0.825642i
$640$			3.28763i			0.129955i
$641$	−28.8080	−	16.6323i	−1.13785	−	0.656938i	−0.191952	−	0.981404i	$-0.561482\pi$
$641$	−28.8080	−	16.6323i	−1.13785	−	0.656938i	−0.945897	+	0.324467i	$0.894815\pi$
$642$	5.59247	+	3.34906i	0.220717	+	0.132177i
$643$	3.65734	+	6.33469i	0.144231	+	0.249816i	0.929086	−	0.369864i	$-0.120596\pi$
$643$	3.65734	+	6.33469i	0.144231	+	0.249816i	−0.784855	+	0.619680i	$0.787262\pi$
$644$	−8.94830	+	2.39160i	−0.352612	+	0.0942424i
$645$	−0.610581	+	38.2155i	−0.0240416	+	1.50473i
$646$	−1.13582			−0.0446884
$647$	−32.0372			−1.25951			−0.629757	−	0.776792i	$-0.716846\pi$
$647$	−32.0372			−1.25951			−0.629757	+	0.776792i	$0.716846\pi$
$648$	−8.98163	−	0.574744i	−0.352832	−	0.0225781i
$649$	17.5862	+	10.1534i	0.690319	+	0.398556i
$650$	13.8666	−	15.6945i	0.543892	−	0.615590i
$651$	12.2966	−	11.8947i	0.481942	−	0.466192i
$652$	−8.93321	−	5.15759i	−0.349851	−	0.201987i
$653$	29.1377	−	16.8227i	1.14025	−	0.658321i	0.193754	−	0.981050i	$-0.437934\pi$
$653$	29.1377	−	16.8227i	1.14025	−	0.658321i	0.946491	+	0.322729i	$0.104600\pi$
$654$	4.18573	+	2.50663i	0.163675	+	0.0980171i
$655$	8.26839	−	4.77376i	0.323073	−	0.186526i
$656$			9.84458i			0.384366i
$657$	−2.48736	−	4.64489i	−0.0970412	−	0.181214i
$658$	3.11423	−	0.832338i	0.121405	−	0.0324479i
$659$	−21.1966	+	12.2379i	−0.825704	+	0.476720i	−0.852379	−	0.522924i	$-0.824841\pi$
$659$	−21.1966	+	12.2379i	−0.825704	+	0.476720i	0.0266755	+	0.999644i	$0.491508\pi$
$660$	−10.3019	+	5.73036i	−0.401002	+	0.223054i
$661$	5.55570			0.216092			0.108046	−	0.994146i	$-0.465541\pi$
$661$	5.55570			0.216092			0.108046	+	0.994146i	$0.465541\pi$
$662$	22.5837	−	13.0387i	0.877739	−	0.506763i
$663$	−4.72950	+	5.18366i	−0.183678	+	0.201317i
$664$			0.999900i			0.0388037i
$665$	−2.28111	+	8.49166i	−0.0884576	+	0.329292i
$666$	−17.7711	−	11.0317i	−0.688617	−	0.427472i
$667$	32.2414			1.24839
$668$	−12.1099	+	6.99167i	−0.468547	+	0.270516i
$669$	−2.44407	+	4.08125i	−0.0944930	+	0.157790i
$670$	38.8414			1.50057
$671$		−	0.500970i		−	0.0193397i
$672$	−4.40612	−	1.25942i	−0.169970	−	0.0485830i
$673$	9.31475	−	16.1336i	0.359057	−	0.621905i	−0.628746	−	0.777610i	$-0.716432\pi$
$673$	9.31475	−	16.1336i	0.359057	−	0.621905i	0.987804	+	0.155705i	$0.0497649\pi$
$674$	−6.75920	−	11.7073i	−0.260355	−	0.450947i
$675$	13.8213	+	26.8311i	0.531981	+	1.03273i
$676$	−10.3718	+	7.83752i	−0.398913	+	0.301443i
$677$	13.4512	−	23.2982i	0.516972	−	0.895422i	−0.482833	−	0.875712i	$-0.660392\pi$
$677$	13.4512	−	23.2982i	0.516972	−	0.895422i	0.999806	−	0.0197102i	$-0.00627434\pi$
$678$	7.85473	+	4.70382i	0.301659	+	0.180649i
$679$	12.0419	−	12.0266i	0.462124	−	0.461538i
$680$	−3.19914	+	1.84702i	−0.122681	+	0.0708301i
$681$	13.3440	+	7.99111i	0.511345	+	0.306220i
$682$	−3.86436	+	6.69327i	−0.147974	+	0.256299i
$683$	20.3836	−	35.3055i	0.779958	−	1.35093i	−0.152007	−	0.988379i	$-0.548574\pi$
$683$	20.3836	−	35.3055i	0.779958	−	1.35093i	0.931965	−	0.362548i	$-0.118093\pi$
$684$	1.59942	−	2.57651i	0.0611553	−	0.0985154i
$685$	60.3003	−	34.8144i	2.30395	−	1.33019i
$686$	−4.82745	+	17.8800i	−0.184313	+	0.682663i
$687$	−14.6563	+	24.4740i	−0.559172	+	0.933740i
$688$	3.35600	−	5.81276i	0.127946	−	0.221609i
$689$	−19.9671	+	6.69582i	−0.760688	+	0.255090i
$690$	−9.69044	−	17.4213i	−0.368909	−	0.663217i
$691$	6.89853	+	11.9486i	0.262432	+	0.454546i	0.966888	−	0.255202i	$-0.0821420\pi$
$691$	6.89853	+	11.9486i	0.262432	+	0.454546i	−0.704455	+	0.709748i	$0.748809\pi$
$692$	2.53897	−	4.39763i	0.0965173	−	0.167173i
$693$	−3.73347	−	16.0019i	−0.141823	−	0.607864i
$694$			33.5765i			1.27454i
$695$	−66.8912			−2.53733
$696$	13.6852	+	8.19540i	0.518736	+	0.310646i
$697$	−9.57961	+	5.53079i	−0.362854	+	0.209494i
$698$	−23.7689			−0.899667
$699$	−8.22228	−	4.92393i	−0.310995	−	0.186240i
$700$	3.96806	+	14.8467i	0.149978	+	0.561151i
$701$			9.30649i			0.351501i	0.984435	+	0.175751i	$0.0562352\pi$
$701$			9.30649i			0.351501i	−0.984435	+	0.175751i	$0.943765\pi$
$702$	−5.09877	−	18.0278i	−0.192441	−	0.680416i
$703$	6.10373	−	3.52399i	0.230207	−	0.132910i
$704$	2.07020			0.0780236
$705$	3.37252	+	6.06304i	0.127016	+	0.228347i
$706$	9.28444	−	5.36037i	0.349425	−	0.201740i
$707$	13.2012	+	49.3930i	0.496483	+	1.85762i
$708$	−14.8475	+	8.25878i	−0.558002	+	0.310384i
$709$			3.09917i			0.116392i	0.998305	+	0.0581958i	$0.0185348\pi$
$709$			3.09917i			0.116392i	−0.998305	+	0.0581958i	$0.981465\pi$
$710$	−22.4690	+	12.9725i	−0.843246	+	0.486848i
$711$	−7.87879	+	12.6920i	−0.295478	+	0.475987i
$712$	−6.59807	+	3.80940i	−0.247273	+	0.142763i
$713$	−11.3188	−	6.53491i	−0.423892	−	0.244734i
$714$	−1.24988	−	4.99508i	−0.0467757	−	0.186936i
$715$	−18.3899	−	16.2481i	−0.687745	−	0.607643i
$716$	10.1439	+	5.85660i	0.379097	+	0.218871i
$717$	−7.50744	−	0.119949i	−0.280370	−	0.00447957i
$718$	14.5376			0.542537
$719$	−11.7740			−0.439098			−0.219549	−	0.975602i	$-0.570459\pi$
$719$	−11.7740			−0.439098			−0.219549	+	0.975602i	$0.570459\pi$
$720$	0.315084	−	9.85784i	0.0117425	−	0.367380i
$721$	−6.23537	+	23.2118i	−0.232217	+	0.864452i
$722$	−8.98908	−	15.5695i	−0.334539	−	0.579438i
$723$	3.74370	−	6.25146i	0.139230	−	0.232494i
$724$	−19.6355	−	11.3365i	−0.729746	−	0.421319i
$725$		−	53.4937i		−	1.98671i
$726$	−5.65309	−	10.1630i	−0.209806	−	0.377185i
$727$		−	13.8729i		−	0.514518i	−0.966342	−	0.257259i	$-0.917181\pi$
$727$		−	13.8729i		−	0.514518i	0.966342	−	0.257259i	$-0.0828194\pi$
$728$	−0.582714	−	9.52158i	−0.0215968	−	0.352893i
$729$	26.8761	+	2.58415i	0.995409	+	0.0957091i
$730$	5.00054	−	2.88706i	0.185078	−	0.106855i
$731$	7.54174			0.278941
$732$	0.359592	+	0.215343i	0.0132909	+	0.00795929i
$733$	−21.6003	+	37.4129i	−0.797827	+	1.38188i	0.123202	+	0.992382i	$0.460684\pi$
$733$	−21.6003	+	37.4129i	−0.797827	+	1.38188i	−0.921029	+	0.389495i	$0.872650\pi$
$734$	−15.1524	+	8.74823i	−0.559284	+	0.322903i
$735$	−39.8544	−	0.687368i	−1.47005	−	0.0253539i
$736$			3.50085i			0.129043i
$737$		−	24.4582i		−	0.900930i
$738$	0.943500	−	29.5187i	0.0347307	−	1.08660i
$739$		−	34.1756i		−	1.25717i	−0.777741	−	0.628585i	$-0.783635\pi$
$739$		−	34.1756i		−	1.25717i	0.777741	−	0.628585i	$-0.216365\pi$
$740$	11.4611	−	19.8512i	0.421318	−	0.729744i
$741$	6.16610	+	1.35310i	0.226517	+	0.0497074i
$742$	4.00920	−	14.9247i	0.147182	−	0.547901i
$743$	15.6321	−	27.0755i	0.573484	−	0.993304i	−0.422720	−	0.906260i	$-0.638925\pi$
$743$	15.6321	−	27.0755i	0.573484	−	0.993304i	0.996204	−	0.0870439i	$-0.0277420\pi$
$744$	−3.14328	−	5.65092i	−0.115238	−	0.207173i
$745$	37.7251	+	21.7806i	1.38214	+	0.797978i
$746$	−5.93324	−	10.2767i	−0.217231	−	0.376256i
$747$	0.0958300	−	2.99817i	0.00350624	−	0.109697i
$748$	1.16306	+	2.01448i	0.0425257	+	0.0736567i
$749$	−7.03641	−	7.04534i	−0.257105	−	0.257431i
$750$	−4.02323	+	2.23789i	−0.146908	+	0.0817162i
$751$	−1.05163	−	1.82147i	−0.0383744	−	0.0664664i	0.846200	−	0.532865i	$-0.178885\pi$
$751$	−1.05163	−	1.82147i	−0.0383744	−	0.0664664i	−0.884575	+	0.466398i	$0.845551\pi$
$752$		−	1.21839i		−	0.0444299i
$753$	16.4883	+	29.6422i	0.600865	+	1.08022i
$754$	−6.59830	+	32.5434i	−0.240296	+	1.18516i
$755$	56.9955			2.07428
$756$	13.0909	+	4.19860i	0.476112	+	0.152702i
$757$	16.8638	−	29.2089i	0.612924	−	1.06162i	−0.377821	−	0.925879i	$-0.623326\pi$
$757$	16.8638	−	29.2089i	0.612924	−	1.06162i	0.990745	−	0.135737i	$-0.0433402\pi$
$758$			12.6025i			0.457745i
$759$	−10.9701	+	6.10202i	−0.398189	+	0.221489i
$760$	2.87809	+	1.66167i	0.104399	+	0.0602749i
$761$			19.2154i			0.696556i	0.937391	+	0.348278i	$0.113233\pi$
$761$			19.2154i			0.696556i	−0.937391	+	0.348278i	$0.886767\pi$
$762$	32.5613	+	0.520243i	1.17957	+	0.0188464i
$763$	−5.26646	−	5.27315i	−0.190659	−	0.190901i
$764$	22.3913	+	12.9276i	0.810087	+	0.467704i
$765$	9.76953	−	5.23163i	0.353218	−	0.189150i
$766$	0.920885	−	0.531673i	0.0332729	−	0.0192101i
$767$	−26.5042	−	23.4172i	−0.957010	−	0.845547i
$768$	−0.889878	+	1.48597i	−0.0321107	+	0.0536205i
$769$	−19.1381	+	33.1482i	−0.690139	+	1.19536i	0.281653	+	0.959516i	$0.409117\pi$
$769$	−19.1381	+	33.1482i	−0.690139	+	1.19536i	−0.971792	+	0.235840i	$0.924216\pi$
$770$	17.3965	−	4.64954i	0.626926	−	0.167558i
$771$	−15.1128	−	27.1695i	−0.544274	−	0.978485i
$772$	−18.8878	−	10.9049i	−0.679787	−	0.392475i
$773$	2.18604	+	1.26211i	0.0786263	+	0.0453949i	0.538798	−	0.842435i	$-0.318879\pi$
$773$	2.18604	+	1.26211i	0.0786263	+	0.0453949i	−0.460171	+	0.887830i	$0.652212\pi$
$774$	−10.6199	+	17.1077i	−0.381726	+	0.614925i
$775$	−10.8425	+	18.7797i	−0.389473	+	0.674587i
$776$	−3.21628	−	5.57077i	−0.115458	−	0.199979i
$777$	22.2143	+	22.9649i	0.796935	+	0.823860i
$778$	2.28039	+	1.31658i	0.0817558	+	0.0472018i
$779$	8.61825	+	4.97575i	0.308781	+	0.178275i
$780$	19.5677	−	6.21591i	0.700634	−	0.222565i
$781$	8.16870	+	14.1486i	0.292299	+	0.506277i
$782$	−3.40663	+	1.96682i	−0.121821	+	0.0703332i
$783$	−40.2492	−	25.8852i	−1.43839	−	0.925063i
$784$	6.05773	+	3.50769i	0.216348	+	0.125275i
$785$	46.3984			1.65603
$786$	5.02937	+	0.0803559i	0.179392	+	0.00286620i
$787$	−0.882459	+	1.52846i	−0.0314563	+	0.0544839i	−0.881325	−	0.472511i	$-0.843348\pi$
$787$	−0.882459	+	1.52846i	−0.0314563	+	0.0544839i	0.849869	+	0.526995i	$0.176681\pi$
$788$	−3.51025	−	6.07993i	−0.125047	−	0.216588i
$789$	−0.770525	+	48.2261i	−0.0274314	+	1.71690i
$790$	−14.1776	−	8.18542i	−0.504415	−	0.291224i
$791$	−9.88276	−	9.89532i	−0.351391	−	0.351837i
$792$	−6.20743	−	0.198407i	−0.220572	−	0.00705009i
$793$	−0.173377	+	0.855112i	−0.00615680	+	0.0303659i
$794$	−4.27357	−	7.40204i	−0.151663	−	0.262689i
$795$	33.2562	+	0.531346i	1.17948	+	0.0188449i
$796$	13.0589	−	7.53954i	0.462859	−	0.267232i
$797$	5.40206	+	9.35664i	0.191351	+	0.331429i	0.945698	−	0.325046i	$-0.105380\pi$
$797$	5.40206	+	9.35664i	0.191351	+	0.331429i	−0.754347	+	0.656476i	$0.772047\pi$
$798$	−3.32952	+	3.22070i	−0.117864	+	0.114012i
$799$	1.18559	−	0.684502i	0.0419432	−	0.0242159i
$800$	5.80848			0.205361
$801$	20.1492	−	10.7900i	0.711937	−	0.381246i
$802$	−7.78768	+	13.4887i	−0.274993	+	0.476301i
$803$	−1.81797	−	3.14881i	−0.0641547	−	0.111119i
$804$	17.5559	+	10.5134i	0.619149	+	0.370779i
$805$	7.86270	+	29.4187i	0.277124	+	1.03687i
$806$	8.91255	−	10.0874i	0.313931	−	0.355315i
$807$	−25.1897	+	42.0633i	−0.886718	+	1.48070i
$808$	19.3241			0.679819
$809$			16.6138i			0.584110i	0.956402	+	0.292055i	$0.0943390\pi$
$809$			16.6138i			0.584110i	−0.956402	+	0.292055i	$0.905661\pi$
$810$	−1.88954	+	29.5282i	−0.0663917	+	1.03752i
$811$	7.44633			0.261476			0.130738	−	0.991417i	$-0.458265\pi$
$811$	7.44633			0.261476			0.130738	+	0.991417i	$0.458265\pi$
$812$	−17.2186	−	17.2405i	−0.604255	−	0.605022i
$813$	21.3045	+	38.3008i	0.747182	+	1.34327i
$814$	−12.5002	−	7.21699i	−0.438132	−	0.252955i
$815$	−16.9562	+	29.3690i	−0.593951	+	1.02875i
$816$	−1.94592	−	0.0310906i	−0.0681208	−	0.00108839i
$817$	−3.39245	−	5.87589i	−0.118687	−	0.205571i
$818$	10.8097			0.377951
$819$	0.834705	+	28.6060i	0.0291669	+	0.999575i
$820$	32.3653			1.13025
$821$	−1.71387	−	2.96850i	−0.0598143	−	0.103601i	0.834568	−	0.550905i	$-0.185718\pi$
$821$	−1.71387	−	2.96850i	−0.0598143	−	0.103601i	−0.894382	+	0.447304i	$0.852384\pi$
$822$	36.6785	+	0.586025i	1.27931	+	0.0204400i
$823$	−19.8190	+	34.3275i	−0.690847	+	1.19658i	0.280713	+	0.959792i	$0.409429\pi$
$823$	−19.8190	+	34.3275i	−0.690847	+	1.19658i	−0.971561	+	0.236791i	$0.923904\pi$
$824$	7.86720	+	4.54213i	0.274067	+	0.158233i
$825$	10.1242	+	18.2011i	0.352481	+	0.633682i
$826$	25.0724	−	6.70107i	0.872379	−	0.233160i
$827$	−0.211856			−0.00736695			−0.00368347	−	0.999993i	$-0.501172\pi$
$827$	−0.211856			−0.00736695			−0.00368347	+	0.999993i	$0.501172\pi$
$828$	0.335520	−	10.4972i	0.0116601	−	0.364803i
$829$		−	31.5116i		−	1.09444i	−0.836988	−	0.547221i	$-0.815686\pi$
$829$		−	31.5116i		−	1.09444i	0.836988	−	0.547221i	$-0.184314\pi$
$830$	3.28730			0.114104
$831$	11.6516	−	19.4566i	0.404190	−	0.674942i
$832$	−3.53365	−	0.716460i	−0.122507	−	0.0248388i
$833$	−0.00998334	+	7.86534i	−0.000345902	+	0.272518i
$834$	−30.2341	−	18.1058i	−1.04692	−	0.626952i
$835$	22.9860	+	39.8129i	0.795463	+	1.37778i
$836$	1.04634	−	1.81232i	0.0361885	−	0.0626803i
$837$	8.88344	+	17.2454i	0.307057	+	0.596087i
$838$	14.2786			0.493248
$839$	−13.7645	+	7.94694i	−0.475204	+	0.274359i	−0.718416	−	0.695614i	$-0.755132\pi$
$839$	−13.7645	+	7.94694i	−0.475204	+	0.274359i	0.243212	+	0.969973i	$0.421799\pi$
$840$	−4.14049	+	14.4857i	−0.142860	+	0.499803i
$841$	27.9082	+	48.3384i	0.962352	+	1.66684i
$842$	26.9813	−	15.5776i	0.929836	−	0.536841i
$843$	28.6818	+	0.458259i	0.987854	+	0.0157833i
$844$	−10.2101	−	17.6845i	−0.351448	−	0.608725i
$845$	25.7668	+	34.0984i	0.886406	+	1.17302i
$846$	−0.116769	+	3.65329i	−0.00401462	+	0.125603i
$847$	4.58684	+	17.1619i	0.157606	+	0.589690i
$848$	−5.05843	−	2.92049i	−0.173707	−	0.100290i
$849$	−0.508904	+	31.8516i	−0.0174655	+	1.09314i
$850$	3.26326	+	5.65214i	0.111929	+	0.193867i
$851$	12.2044	−	21.1387i	0.418363	−	0.724625i
$852$	−13.6671	−	0.218364i	−0.468227	−	0.00748101i
$853$	8.80214			0.301379			0.150690	−	0.988581i	$-0.451851\pi$
$853$	8.80214			0.301379			0.150690	+	0.988581i	$0.451851\pi$
$854$	−0.452437	−	0.453011i	−0.0154821	−	0.0155017i
$855$	−8.47061	−	5.25829i	−0.289689	−	0.179830i
$856$	−3.25929	+	1.88175i	−0.111400	+	0.0643170i
$857$	−2.96296	−	5.13199i	−0.101213	−	0.175305i	0.810972	−	0.585085i	$-0.198939\pi$
$857$	−2.96296	−	5.13199i	−0.101213	−	0.175305i	−0.912185	+	0.409780i	$0.865606\pi$
$858$	−3.91413	−	12.3217i	−0.133626	−	0.420654i
$859$	21.0079	+	12.1289i	0.716781	+	0.413834i	0.813567	−	0.581472i	$-0.197523\pi$
$859$	21.0079	+	12.1289i	0.716781	+	0.413834i	−0.0967860	+	0.995305i	$0.530856\pi$
$860$	−19.1102	−	11.0333i	−0.651652	−	0.376231i
$861$	−12.3984	+	43.3764i	−0.422537	+	1.47826i
$862$	−10.7951	−	18.6976i	−0.367682	−	0.636844i
$863$	−9.92236	+	17.1860i	−0.337761	+	0.585019i	−0.984011	−	0.178106i	$-0.943003\pi$
$863$	−9.92236	+	17.1860i	−0.337761	+	0.585019i	0.646250	+	0.763126i	$0.276336\pi$
$864$	2.81069	−	4.37036i	0.0956215	−	0.148683i
$865$	−14.4578	−	8.34719i	−0.491579	−	0.283813i
$866$	−16.2009	−	9.35358i	−0.550528	−	0.317848i
$867$	13.2502	+	23.8209i	0.450000	+	0.809001i
$868$	2.55041	+	9.54250i	0.0865667	+	0.323893i
$869$	−5.15432	+	8.92754i	−0.174848	+	0.302846i
$870$	26.9434	−	44.9918i	0.913467	−	1.52536i
$871$	−8.46456	+	41.7480i	−0.286811	+	1.41458i
$872$	−2.43945	+	1.40841i	−0.0826101	+	0.0476949i
$873$	9.11003	+	17.0120i	0.308328	+	0.575770i
$874$	3.06476	+	1.76944i	0.103667	+	0.0598521i
$875$	6.79388	−	1.81579i	0.229675	−	0.0613850i
$876$	3.04165	+	0.0485974i	0.102768	+	0.00164195i
$877$			8.82826i			0.298109i	0.988829	+	0.149055i	$0.0476230\pi$
$877$			8.82826i			0.298109i	−0.988829	+	0.149055i	$0.952377\pi$
$878$	−12.4456	−	7.18545i	−0.420017	−	0.242497i
$879$	−12.8946	+	7.17251i	−0.434923	+	0.241923i
$880$		−	6.80604i		−	0.229432i
$881$	−9.51336	+	16.4776i	−0.320513	+	0.555145i	−0.980594	−	0.196049i	$-0.937189\pi$
$881$	−9.51336	+	16.4776i	−0.320513	+	0.555145i	0.660081	+	0.751195i	$0.270522\pi$
$882$	−17.8277	−	11.0983i	−0.600291	−	0.373698i
$883$	−30.8587			−1.03848			−0.519239	−	0.854629i	$-0.673785\pi$
$883$	−30.8587			−1.03848			−0.519239	+	0.854629i	$0.673785\pi$
$884$	−1.28807	−	3.84105i	−0.0433223	−	0.129189i
$885$	27.1518	+	48.8129i	0.912697	+	1.64083i
$886$		−	1.40405i		−	0.0471699i
$887$	6.57095	+	11.3812i	0.220631	+	0.382144i	0.955000	−	0.296607i	$-0.0958551\pi$
$887$	6.57095	+	11.3812i	0.220631	+	0.382144i	−0.734369	+	0.678751i	$0.762522\pi$
$888$	10.5535	−	5.87031i	0.354153	−	0.196995i
$889$	−48.0414	−	12.9053i	−1.61126	−	0.432831i
$890$	12.5239	+	21.6920i	0.419801	+	0.727116i
$891$	18.5938	+	1.18983i	0.622915	+	0.0398610i
$892$	−1.37326	−	2.37855i	−0.0459801	−	0.0796399i
$893$	−1.06661	−	0.615809i	−0.0356928	−	0.0206073i
$894$	11.1559	+	20.0558i	0.373109	+	0.670767i
$895$	19.2543	−	33.3494i	0.643601	−	1.11475i
$896$	1.87202	−	1.86964i	0.0625397	−	0.0624603i
$897$	20.8368	−	6.61906i	0.695720	−	0.221004i
$898$	−11.0266	+	19.0987i	−0.367963	+	0.637331i
$899$		−	34.3823i		−	1.14672i
$900$	−17.4165	−	0.556682i	−0.580551	−	0.0185561i
$901$		−	6.56304i		−	0.218647i
$902$		−	20.3803i		−	0.678589i
$903$	22.1076	−	21.3851i	0.735695	−	0.711652i
$904$	−4.57774	+	2.64296i	−0.152253	+	0.0879035i
$905$	−37.2703	+	64.5540i	−1.23891	+	2.14585i
$906$	25.7614	+	15.4272i	0.855864	+	0.512536i
$907$	48.7067			1.61728			0.808640	−	0.588303i	$-0.200204\pi$
$907$	48.7067			1.61728			0.808640	+	0.588303i	$0.200204\pi$
$908$	−7.77691	+	4.49000i	−0.258086	+	0.149006i
$909$	−57.9427	−	1.85201i	−1.92184	−	0.0614273i
$910$	−31.3034	+	1.91574i	−1.03770	+	0.0635063i
$911$			7.94598i			0.263262i	0.991299	+	0.131631i	$0.0420214\pi$
$911$			7.94598i			0.263262i	−0.991299	+	0.131631i	$0.957979\pi$
$912$	0.851096	+	1.53008i	0.0281826	+	0.0506661i
$913$		−	2.06999i		−	0.0685068i
$914$	36.6548	+	21.1627i	1.21243	+	0.699999i
$915$	0.707966	−	1.18221i	0.0234046	−	0.0390825i
$916$	−8.23500	−	14.2634i	−0.272092	−	0.471277i
$917$	−7.42039	−	1.99334i	−0.245043	−	0.0658258i
$918$	5.83180	+	0.279720i	0.192478	+	0.00923215i
$919$	−27.1660			−0.896124			−0.448062	−	0.894002i	$-0.647886\pi$
$919$	−27.1660			−0.896124			−0.448062	+	0.894002i	$0.647886\pi$
$920$	11.5095			0.379457
$921$	36.9159	+	0.589818i	1.21642	+	0.0194352i
$922$	−10.2913	−	5.94166i	−0.338925	−	0.195678i
$923$	−9.04667	−	26.9775i	−0.297775	−	0.887974i
$924$	9.12155	+	2.60725i	0.300077	+	0.0857721i
$925$	−35.0725	−	20.2491i	−1.15318	−	0.665787i
$926$	3.08686	−	1.78220i	0.101441	−	0.0585667i
$927$	−23.1542	−	14.3734i	−0.760485	−	0.472085i
$928$	−7.97573	+	4.60479i	−0.261816	+	0.151160i
$929$		−	23.7500i		−	0.779211i	−0.920982	−	0.389605i	$-0.872611\pi$
$929$		−	23.7500i		−	0.779211i	0.920982	−	0.389605i	$-0.127389\pi$
$930$	−18.5781	+	10.3339i	−0.609200	+	0.338863i
$931$	6.13250	−	3.53023i	0.200985	−	0.115699i
$932$	4.79194	−	2.76663i	0.156965	−	0.0906240i
$933$	12.4726	+	22.4229i	0.408333	+	0.734093i
$934$	7.12287			0.233067
$935$	6.62285	−	3.82371i	0.216591	−	0.125049i
$936$	10.5269	+	2.48695i	0.344082	+	0.0812884i
$937$		−	44.8244i		−	1.46435i	−0.681116	−	0.732175i	$-0.738505\pi$
$937$		−	44.8244i		−	1.46435i	0.681116	−	0.732175i	$-0.261495\pi$
$938$	−22.0887	−	22.1168i	−0.721222	−	0.722138i
$939$	−38.9553	−	23.3284i	−1.27126	−	0.761294i
$940$	−4.00559			−0.130648
$941$	26.3318	−	15.2027i	0.858393	−	0.495593i	−0.00508113	−	0.999987i	$-0.501617\pi$
$941$	26.3318	−	15.2027i	0.858393	−	0.495593i	0.863474	+	0.504394i	$0.168284\pi$
$942$	20.9716	+	12.5589i	0.683292	+	0.409191i
$943$	34.4645			1.12232
$944$		−	9.80909i		−	0.319259i
$945$	13.8034	−	43.0380i	0.449026	−	1.40003i
$946$	−6.94759	+	12.0336i	−0.225886	+	0.391245i
$947$	4.00703	+	6.94038i	0.130211	+	0.225532i	0.923758	−	0.382977i	$-0.125101\pi$
$947$	4.00703	+	6.94038i	0.130211	+	0.225532i	−0.793547	+	0.608509i	$0.791768\pi$
$948$	−4.19253	−	7.53724i	−0.136167	−	0.244798i
$949$	2.01336	+	6.00391i	0.0653565	+	0.194895i
$950$	2.93578	−	5.08492i	0.0952493	−	0.164977i
$951$	17.4511	−	29.1409i	0.565890	−	0.944958i
$952$	2.87104	+	0.771245i	0.0930508	+	0.0249962i
$953$	−4.48194	+	2.58765i	−0.145184	+	0.0838222i	−0.570833	−	0.821067i	$-0.693379\pi$
$953$	−4.48194	+	2.58765i	−0.145184	+	0.0838222i	0.425648	+	0.904889i	$0.360046\pi$
$954$	14.8877	+	9.24179i	0.482006	+	0.299214i
$955$	42.5011	−	73.6140i	1.37530	−	2.38209i
$956$	2.16749	−	3.75420i	0.0701016	−	0.121419i
$957$	−28.3311	−	16.9661i	−0.915815	−	0.548437i
$958$	26.4547	−	15.2736i	0.854712	−	0.493468i
$959$	−54.1159	−	14.5371i	−1.74749	−	0.469429i
$960$	4.88532	+	2.92558i	0.157673	+	0.0944228i
$961$	8.53115	−	14.7764i	0.275199	−	0.476658i
$962$	18.8391	+	16.6449i	0.607396	+	0.536652i
$963$	9.95323	−	5.33001i	0.320738	−	0.171757i
$964$	2.10349	+	3.64335i	0.0677488	+	0.117344i
$965$	−35.8512	+	62.0960i	−1.15409	+	1.99894i
$966$	−4.40903	+	15.4252i	−0.141858	+	0.496297i
$967$			14.4231i			0.463816i	0.972738	+	0.231908i	$0.0744968\pi$
$967$			14.4231i			0.463816i	−0.972738	+	0.231908i	$0.925503\pi$
$968$	6.71427			0.215805
$969$	−1.01074	+	1.68780i	−0.0324698	+	0.0542201i
$970$	−18.3146	+	10.5739i	−0.588046	+	0.339509i
$971$	−1.42967			−0.0458802			−0.0229401	−	0.999737i	$-0.507303\pi$
$971$	−1.42967			−0.0458802			−0.0229401	+	0.999737i	$0.507303\pi$
$972$	−8.84661	+	12.8350i	−0.283755	+	0.411683i
$973$	38.0404	+	38.0887i	1.21952	+	1.22107i
$974$		−	32.0202i		−	1.02599i
$975$	−10.9821	−	34.5716i	−0.351708	−	1.10718i
$976$	−0.209571	+	0.120996i	−0.00670819	+	0.00387297i
$977$	−14.9269			−0.477552			−0.238776	−	0.971075i	$-0.576746\pi$
$977$	−14.9269			−0.477552			−0.238776	+	0.971075i	$0.576746\pi$
$978$	−15.6135	+	8.68489i	−0.499265	+	0.277712i
$979$	13.6593	−	7.88621i	0.436554	−	0.252044i
$980$	11.5320	−	19.9155i	0.368375	−	0.636179i
$981$	7.44958	−	3.98929i	0.237847	−	0.127368i
$982$			15.1110i			0.482211i
$983$	−2.34938	+	1.35641i	−0.0749334	+	0.0432628i	−0.536999	−	0.843583i	$-0.680442\pi$
$983$	−2.34938	+	1.35641i	−0.0749334	+	0.0432628i	0.462065	+	0.886846i	$0.347109\pi$
$984$	14.6288	+	8.76048i	0.466349	+	0.279274i
$985$	−19.9885	+	11.5404i	−0.636887	+	0.367707i
$986$	−8.96170	−	5.17404i	−0.285399	−	0.164775i
$987$	1.53445	−	5.36835i	0.0488422	−	0.170876i
$988$	−2.41322	+	2.73135i	−0.0767749	+	0.0868957i
$989$	−20.3496	−	11.7489i	−0.647080	−	0.373592i
$990$	−0.652288	+	20.4077i	−0.0207311	+	0.648600i
$991$	−6.57676			−0.208918			−0.104459	−	0.994529i	$-0.533311\pi$
$991$	−6.57676			−0.208918			−0.104459	+	0.994529i	$0.533311\pi$
$992$	3.73332			0.118533
$993$	0.721561	−	45.1615i	0.0228980	−	1.43316i
$994$	20.1646	+	5.41681i	0.639582	+	0.171811i
$995$	−24.7872	−	42.9327i	−0.785807	−	1.36106i
$996$	1.48583	+	0.889789i	0.0470802	+	0.0281941i
$997$	19.9103	+	11.4952i	0.630565	+	0.364057i	0.780971	−	0.624568i	$-0.214725\pi$
$997$	19.9103	+	11.4952i	0.630565	+	0.364057i	−0.150406	+	0.988624i	$0.548058\pi$
$998$			4.83365i			0.153007i
$999$	−32.2070	+	16.5905i	−1.01898	+	0.524900i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bn.f.173.17	yes	34
3.2	odd	2		546.2.bn.e.173.1	yes	34
7.3	odd	6		546.2.bi.e.17.12	✓	34
13.10	even	6		546.2.bi.f.257.6	yes	34
21.17	even	6		546.2.bi.f.17.6	yes	34
39.23	odd	6		546.2.bi.e.257.12	yes	34
91.10	odd	6		546.2.bn.e.101.1	yes	34
273.101	even	6	inner	546.2.bn.f.101.17	yes	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bi.e.17.12	✓	34	7.3	odd	6
546.2.bi.e.257.12	yes	34	39.23	odd	6
546.2.bi.f.17.6	yes	34	21.17	even	6
546.2.bi.f.257.6	yes	34	13.10	even	6
546.2.bn.e.101.1	yes	34	91.10	odd	6
546.2.bn.e.173.1	yes	34	3.2	odd	2
546.2.bn.f.101.17	yes	34	273.101	even	6	inner
546.2.bn.f.173.17	yes	34	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bn (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.84717 + 1.64381i) q^{5} +(0.841952 + 1.51364i) q^{6} +(-0.683149 - 2.55603i) q^{7} -1.00000 q^{8} +(2.99847 + 0.0958395i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(1.73183 + 0.0276700i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(2.84717 + 1.64381i) q^{5} +(0.841952 + 1.51364i) q^{6} +(-0.683149 - 2.55603i) q^{7} -1.00000 q^{8} +(2.99847 + 0.0958395i) q^{9} +3.28763i q^{10} +2.07020 q^{11} +(-0.889878 + 1.48597i) q^{12} +(-3.53365 - 0.716460i) q^{13} +(1.87202 - 1.86964i) q^{14} +(4.88532 + 2.92558i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(0.561810 - 0.973084i) q^{17} +(1.41623 + 2.64467i) q^{18} -1.01086 q^{19} +(-2.84717 + 1.64381i) q^{20} +(-1.11237 - 4.44552i) q^{21} +(1.03510 + 1.79285i) q^{22} +(-3.03183 + 1.75043i) q^{23} +(-1.73183 - 0.0276700i) q^{24} +(2.90424 + 5.03029i) q^{25} +(-1.14635 - 3.41846i) q^{26} +(5.19019 + 0.248945i) q^{27} +(2.55516 + 0.686393i) q^{28} +(-7.97573 - 4.60479i) q^{29} +(-0.0909687 + 5.69361i) q^{30} +(1.86666 + 3.23315i) q^{31} +(0.500000 - 0.866025i) q^{32} +(3.58524 + 0.0572825i) q^{33} +1.12362 q^{34} +(2.25660 - 8.40042i) q^{35} +(-1.58223 + 2.54883i) q^{36} +(-6.03816 + 3.48613i) q^{37} +(-0.505430 - 0.875431i) q^{38} +(-6.09986 - 1.33856i) q^{39} +(-2.84717 - 1.64381i) q^{40} +(-8.52566 - 4.92229i) q^{41} +(3.29375 - 3.18610i) q^{42} +(3.35600 + 5.81276i) q^{43} +(-1.03510 + 1.79285i) q^{44} +(8.37960 + 5.20179i) q^{45} +(-3.03183 - 1.75043i) q^{46} +(1.05515 + 0.609193i) q^{47} +(-0.841952 - 1.51364i) q^{48} +(-6.06662 + 3.49230i) q^{49} +(-2.90424 + 5.03029i) q^{50} +(0.999885 - 1.66967i) q^{51} +(2.38730 - 2.70200i) q^{52} +(5.05843 - 2.92049i) q^{53} +(2.37950 + 4.61931i) q^{54} +(5.89421 + 3.40302i) q^{55} +(0.683149 + 2.55603i) q^{56} +(-1.75064 - 0.0279705i) q^{57} -9.20958i q^{58} +(8.49492 + 4.90455i) q^{59} +(-4.97629 + 2.76802i) q^{60} -0.241991i q^{61} +(-1.86666 + 3.23315i) q^{62} +(-1.80343 - 7.72966i) q^{63} +1.00000 q^{64} +(-8.88317 - 7.84854i) q^{65} +(1.74301 + 3.13355i) q^{66} -11.8144i q^{67} +(0.561810 + 0.973084i) q^{68} +(-5.29905 + 2.94755i) q^{69} +(8.40328 - 2.24594i) q^{70} +(3.94585 + 6.83441i) q^{71} +(-2.99847 - 0.0958395i) q^{72} +(-0.878160 - 1.52102i) q^{73} +(-6.03816 - 3.48613i) q^{74} +(4.89046 + 8.79197i) q^{75} +(0.505430 - 0.875431i) q^{76} +(-1.41426 - 5.29150i) q^{77} +(-1.89070 - 5.95191i) q^{78} +(-2.48977 + 4.31240i) q^{79} -3.28763i q^{80} +(8.98163 + 0.574744i) q^{81} -9.84458i q^{82} -0.999900i q^{83} +(4.40612 + 1.25942i) q^{84} +(3.19914 - 1.84702i) q^{85} +(-3.35600 + 5.81276i) q^{86} +(-13.6852 - 8.19540i) q^{87} -2.07020 q^{88} +(6.59807 - 3.80940i) q^{89} +(-0.315084 + 9.85784i) q^{90} +(0.582714 + 9.52158i) q^{91} -3.50085i q^{92} +(3.14328 + 5.65092i) q^{93} +1.21839i q^{94} +(-2.87809 - 1.66167i) q^{95} +(0.889878 - 1.48597i) q^{96} +(3.21628 + 5.57077i) q^{97} +(-6.05773 - 3.50769i) q^{98} +(6.20743 + 0.198407i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9}+O(q^{10}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9	\( 34 q + 17 q^{2} - 3 q^{3} - 17 q^{4} - 9 q^{5} + 3 q^{6} + 5 q^{7} - 34 q^{8} + 7 q^{9} + 18 q^{11} + 6 q^{12} - 8 q^{13} + 4 q^{14} - 4 q^{15} - 17 q^{16} - 6 q^{17} - 4 q^{18} - 10 q^{19} + 9 q^{20} + 7 q^{21} + 9 q^{22} - 6 q^{23} + 3 q^{24} + 16 q^{25} - 13 q^{26} - 18 q^{27} - q^{28} - 27 q^{29} + 13 q^{30} + q^{31} + 17 q^{32} + 21 q^{33} - 12 q^{34} + 3 q^{35} - 11 q^{36} + 6 q^{37} - 5 q^{38} - 2 q^{39} + 9 q^{40} - 3 q^{41} + 8 q^{42} - 3 q^{43} - 9 q^{44} + 9 q^{45} - 6 q^{46} + 27 q^{47} - 3 q^{48} - 5 q^{49} - 16 q^{50} - 36 q^{51} - 5 q^{52} - 21 q^{53} + 57 q^{55} - 5 q^{56} + 17 q^{57} + 6 q^{59} + 17 q^{60} - q^{62} + 34 q^{64} - 33 q^{65} - 6 q^{68} - 42 q^{69} + 3 q^{70} + 15 q^{71} - 7 q^{72} + 19 q^{73} + 6 q^{74} - 9 q^{75} + 5 q^{76} + 9 q^{77} - 7 q^{78} - 9 q^{79} - 5 q^{81} + q^{84} - 42 q^{85} + 3 q^{86} + 6 q^{87} - 18 q^{88} + 18 q^{89} + 9 q^{90} - 27 q^{91} + 8 q^{93} + 3 q^{95} - 6 q^{96} - 19 q^{97} - 7 q^{98} + 27 q^{99}+O(q^{100}) \) 34 * q + 17 * q^2 - 3 * q^3 - 17 * q^4 - 9 * q^5 + 3 * q^6 + 5 * q^7 - 34 * q^8 + 7 * q^9 + 18 * q^11 + 6 * q^12 - 8 * q^13 + 4 * q^14 - 4 * q^15 - 17 * q^16 - 6 * q^17 - 4 * q^18 - 10 * q^19 + 9 * q^20 + 7 * q^21 + 9 * q^22 - 6 * q^23 + 3 * q^24 + 16 * q^25 - 13 * q^26 - 18 * q^27 - q^28 - 27 * q^29 + 13 * q^30 + q^31 + 17 * q^32 + 21 * q^33 - 12 * q^34 + 3 * q^35 - 11 * q^36 + 6 * q^37 - 5 * q^38 - 2 * q^39 + 9 * q^40 - 3 * q^41 + 8 * q^42 - 3 * q^43 - 9 * q^44 + 9 * q^45 - 6 * q^46 + 27 * q^47 - 3 * q^48 - 5 * q^49 - 16 * q^50 - 36 * q^51 - 5 * q^52 - 21 * q^53 + 57 * q^55 - 5 * q^56 + 17 * q^57 + 6 * q^59 + 17 * q^60 - q^62 + 34 * q^64 - 33 * q^65 - 6 * q^68 - 42 * q^69 + 3 * q^70 + 15 * q^71 - 7 * q^72 + 19 * q^73 + 6 * q^74 - 9 * q^75 + 5 * q^76 + 9 * q^77 - 7 * q^78 - 9 * q^79 - 5 * q^81 + q^84 - 42 * q^85 + 3 * q^86 + 6 * q^87 - 18 * q^88 + 18 * q^89 + 9 * q^90 - 27 * q^91 + 8 * q^93 + 3 * q^95 - 6 * q^96 - 19 * q^97 - 7 * q^98 + 27 * q^99

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