LMFDB - Embedded newform 273.2.by.b.202.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(76,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("273.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.by (of order $12$, degree $4$, 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:	$4$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			202.1
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	273.202
Dual form			273.2.by.b.223.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.133975i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.36603 - 1.36603i) q^{5} +(-0.500000 - 0.133975i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-1.36603 + 1.36603i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.133975i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.36603 - 1.36603i) q^{5} +(-0.500000 - 0.133975i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-1.36603 + 1.36603i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.00000 - 3.73205i) q^{11} +1.73205 q^{12} +(3.23205 - 1.59808i) q^{13} +(0.0980762 - 1.36603i) q^{14} +(-1.86603 + 0.500000i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(0.366025 + 0.366025i) q^{18} +(-2.73205 - 0.732051i) q^{19} +(-0.866025 + 3.23205i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(5.36603 + 3.09808i) q^{23} +(1.86603 - 0.500000i) q^{24} +1.26795i q^{25} +(1.40192 - 1.23205i) q^{26} -1.00000i q^{27} +(0.866025 + 4.50000i) q^{28} +(3.50000 - 6.06218i) q^{29} +(-0.866025 + 0.500000i) q^{30} +(-3.26795 + 3.26795i) q^{31} +(1.33013 - 4.96410i) q^{32} +(-1.00000 + 3.73205i) q^{33} +(-1.90192 - 1.90192i) q^{34} +(-2.23205 - 4.59808i) q^{35} +(-1.50000 - 0.866025i) q^{36} +(2.50000 + 9.33013i) q^{37} -1.46410 q^{38} +(-3.59808 - 0.232051i) q^{39} +3.73205i q^{40} +(2.40192 + 8.96410i) q^{41} +(-0.767949 + 1.13397i) q^{42} +(-6.92820 + 4.00000i) q^{43} +(4.73205 + 4.73205i) q^{44} +(1.86603 + 0.500000i) q^{45} +(3.09808 + 0.830127i) q^{46} +(-2.53590 - 2.53590i) q^{47} +(-2.13397 + 1.23205i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(0.169873 + 0.633975i) q^{50} +5.19615i q^{51} +(-3.46410 + 5.19615i) q^{52} +7.73205 q^{53} +(-0.133975 - 0.500000i) q^{54} +(-6.46410 - 3.73205i) q^{55} +(2.23205 + 4.59808i) q^{56} +(2.00000 + 2.00000i) q^{57} +(0.937822 - 3.50000i) q^{58} +(-0.0980762 + 0.366025i) q^{59} +(2.36603 - 2.36603i) q^{60} +(5.59808 - 3.23205i) q^{61} +(-1.19615 + 2.07180i) q^{62} +(2.59808 - 0.500000i) q^{63} +2.26795i q^{64} +(2.23205 - 6.59808i) q^{65} +2.00000i q^{66} +(-10.5622 + 2.83013i) q^{67} +(7.79423 + 4.50000i) q^{68} +(-3.09808 - 5.36603i) q^{69} +(-1.73205 - 2.00000i) q^{70} +(1.46410 - 5.46410i) q^{71} +(-1.86603 - 0.500000i) q^{72} +(8.29423 + 8.29423i) q^{73} +(2.50000 + 4.33013i) q^{74} +(0.633975 - 1.09808i) q^{75} +(4.73205 - 1.26795i) q^{76} +(-10.1962 - 0.732051i) q^{77} +(-1.83013 + 0.366025i) q^{78} +15.6603 q^{79} +(-1.23205 - 4.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.40192 + 4.16025i) q^{82} +(6.92820 - 6.92820i) q^{83} +(1.50000 - 4.33013i) q^{84} +(-9.69615 - 2.59808i) q^{85} +(-2.92820 + 2.92820i) q^{86} +(-6.06218 + 3.50000i) q^{87} +(6.46410 + 3.73205i) q^{88} +(-9.83013 + 2.63397i) q^{89} +1.00000 q^{90} +(-1.19615 - 9.46410i) q^{91} -10.7321 q^{92} +(4.46410 - 1.19615i) q^{93} +(-1.60770 - 0.928203i) q^{94} +(-4.73205 + 2.73205i) q^{95} +(-3.63397 + 3.63397i) q^{96} +(-5.09808 - 1.36603i) q^{97} +(-3.33013 - 1.42820i) q^{98} +(2.73205 - 2.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 6 q^{13} - 10 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{19} - 8 q^{21} - 4 q^{22} + 18 q^{23} + 4 q^{24} + 16 q^{26} + 14 q^{29} - 20 q^{31} - 12 q^{32} - 4 q^{33} - 18 q^{34} - 2 q^{35} - 6 q^{36} + 10 q^{37} + 8 q^{38} - 4 q^{39} + 20 q^{41} - 10 q^{42} + 12 q^{44} + 4 q^{45} + 2 q^{46} - 24 q^{47} - 12 q^{48} - 22 q^{49} + 18 q^{50} + 24 q^{53} - 4 q^{54} - 12 q^{55} + 2 q^{56} + 8 q^{57} + 28 q^{58} + 10 q^{59} + 6 q^{60} + 12 q^{61} + 16 q^{62} + 2 q^{65} - 18 q^{67} - 2 q^{69} - 8 q^{71} - 4 q^{72} + 2 q^{73} + 10 q^{74} + 6 q^{75} + 12 q^{76} - 20 q^{77} + 10 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} + 20 q^{82} + 6 q^{84} - 18 q^{85} + 16 q^{86} + 12 q^{88} - 22 q^{89} + 4 q^{90} + 16 q^{91} - 36 q^{92} + 4 q^{93} - 48 q^{94} - 12 q^{95} - 18 q^{96} - 10 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 6 * q^13 - 10 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^19 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 4 * q^24 + 16 * q^26 + 14 * q^29 - 20 * q^31 - 12 * q^32 - 4 * q^33 - 18 * q^34 - 2 * q^35 - 6 * q^36 + 10 * q^37 + 8 * q^38 - 4 * q^39 + 20 * q^41 - 10 * q^42 + 12 * q^44 + 4 * q^45 + 2 * q^46 - 24 * q^47 - 12 * q^48 - 22 * q^49 + 18 * q^50 + 24 * q^53 - 4 * q^54 - 12 * q^55 + 2 * q^56 + 8 * q^57 + 28 * q^58 + 10 * q^59 + 6 * q^60 + 12 * q^61 + 16 * q^62 + 2 * q^65 - 18 * q^67 - 2 * q^69 - 8 * q^71 - 4 * q^72 + 2 * q^73 + 10 * q^74 + 6 * q^75 + 12 * q^76 - 20 * q^77 + 10 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 + 20 * q^82 + 6 * q^84 - 18 * q^85 + 16 * q^86 + 12 * q^88 - 22 * q^89 + 4 * q^90 + 16 * q^91 - 36 * q^92 + 4 * q^93 - 48 * q^94 - 12 * q^95 - 18 * q^96 - 10 * q^97 + 4 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$e\left(\frac{11}{12}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.500000	−	0.133975i	0.353553	−	0.0947343i	−0.0776710	−	0.996979i	$-0.524748\pi$
$2$	0.500000	−	0.133975i	0.353553	−	0.0947343i	0.431224	+	0.902245i	$0.358082\pi$
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−1.50000	+	0.866025i	−0.750000	+	0.433013i
$5$	1.36603	−	1.36603i	0.610905	−	0.610905i	−0.332277	−	0.943182i	$-0.607817\pi$
$5$	1.36603	−	1.36603i	0.610905	−	0.610905i	0.943182	+	0.332277i	$0.107817\pi$
$6$	−0.500000	−	0.133975i	−0.204124	−	0.0546949i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$7$	0.866025	−	2.50000i	0.327327	−	0.944911i
$8$	−1.36603	+	1.36603i	−0.482963	+	0.482963i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	−1.00000	−	3.73205i	−0.301511	−	1.12526i	−0.935907	−	0.352247i	$-0.885418\pi$
$11$	−1.00000	−	3.73205i	−0.301511	−	1.12526i	0.634396	−	0.773008i	$-0.281249\pi$
$12$	1.73205			0.500000
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$13$	3.23205	−	1.59808i	0.896410	−	0.443227i
$14$	0.0980762	−	1.36603i	0.0262120	−	0.365086i
$15$	−1.86603	+	0.500000i	−0.481806	+	0.129099i
$16$	1.23205	−	2.13397i	0.308013	−	0.533494i
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	−0.987526	−	0.157459i	$-0.949670\pi$
$17$	−2.59808	−	4.50000i	−0.630126	−	1.09141i	0.357400	−	0.933952i	$-0.383663\pi$
$18$	0.366025	+	0.366025i	0.0862730	+	0.0862730i
$19$	−2.73205	−	0.732051i	−0.626775	−	0.167944i	−0.0685694	−	0.997646i	$-0.521843\pi$
$19$	−2.73205	−	0.732051i	−0.626775	−	0.167944i	−0.558206	+	0.829702i	$0.688510\pi$
$20$	−0.866025	+	3.23205i	−0.193649	+	0.722709i
$21$	−2.00000	+	1.73205i	−0.436436	+	0.377964i
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	5.36603	+	3.09808i	1.11889	+	0.645994i	0.941118	−	0.338078i	$-0.109777\pi$
$23$	5.36603	+	3.09808i	1.11889	+	0.645994i	0.177775	+	0.984071i	$0.443110\pi$
$24$	1.86603	−	0.500000i	0.380901	−	0.102062i
$25$			1.26795i			0.253590i
$26$	1.40192	−	1.23205i	0.274940	−	0.241625i
$27$		−	1.00000i		−	0.192450i
$28$	0.866025	+	4.50000i	0.163663	+	0.850420i
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	−0.333205	−	0.942855i	$-0.608130\pi$
$29$	3.50000	−	6.06218i	0.649934	−	1.12572i	0.983138	−	0.182864i	$-0.0585367\pi$
$30$	−0.866025	+	0.500000i	−0.158114	+	0.0912871i
$31$	−3.26795	+	3.26795i	−0.586941	+	0.586941i	−0.936802	−	0.349861i	$-0.886229\pi$
$31$	−3.26795	+	3.26795i	−0.586941	+	0.586941i	0.349861	+	0.936802i	$0.386229\pi$
$32$	1.33013	−	4.96410i	0.235135	−	0.877537i
$33$	−1.00000	+	3.73205i	−0.174078	+	0.649667i
$34$	−1.90192	−	1.90192i	−0.326177	−	0.326177i
$35$	−2.23205	−	4.59808i	−0.377285	−	0.777217i
$36$	−1.50000	−	0.866025i	−0.250000	−	0.144338i
$37$	2.50000	+	9.33013i	0.410997	+	1.53386i	0.792720	+	0.609586i	$0.208664\pi$
$37$	2.50000	+	9.33013i	0.410997	+	1.53386i	−0.381722	+	0.924277i	$0.624669\pi$
$38$	−1.46410			−0.237509
$39$	−3.59808	−	0.232051i	−0.576153	−	0.0371579i
$40$			3.73205i			0.590089i
$41$	2.40192	+	8.96410i	0.375117	+	1.39996i	0.853173	+	0.521628i	$0.174675\pi$
$41$	2.40192	+	8.96410i	0.375117	+	1.39996i	−0.478056	+	0.878330i	$0.658658\pi$
$42$	−0.767949	+	1.13397i	−0.118497	+	0.174976i
$43$	−6.92820	+	4.00000i	−1.05654	+	0.609994i	−0.924473	−	0.381246i	$-0.875495\pi$
$43$	−6.92820	+	4.00000i	−1.05654	+	0.609994i	−0.132068	+	0.991241i	$0.542162\pi$
$44$	4.73205	+	4.73205i	0.713384	+	0.713384i
$45$	1.86603	+	0.500000i	0.278171	+	0.0745356i
$46$	3.09808	+	0.830127i	0.456786	+	0.122396i
$47$	−2.53590	−	2.53590i	−0.369899	−	0.369899i	0.497541	−	0.867440i	$-0.334236\pi$
$47$	−2.53590	−	2.53590i	−0.369899	−	0.369899i	−0.867440	+	0.497541i	$0.834236\pi$
$48$	−2.13397	+	1.23205i	−0.308013	+	0.177831i
$49$	−5.50000	−	4.33013i	−0.785714	−	0.618590i
$50$	0.169873	+	0.633975i	0.0240237	+	0.0896575i
$51$			5.19615i			0.727607i
$52$	−3.46410	+	5.19615i	−0.480384	+	0.720577i
$53$	7.73205			1.06208			0.531039	−	0.847347i	$-0.321802\pi$
$53$	7.73205			1.06208			0.531039	+	0.847347i	$0.321802\pi$
$54$	−0.133975	−	0.500000i	−0.0182316	−	0.0680414i
$55$	−6.46410	−	3.73205i	−0.871619	−	0.503230i
$56$	2.23205	+	4.59808i	0.298270	+	0.614444i
$57$	2.00000	+	2.00000i	0.264906	+	0.264906i
$58$	0.937822	−	3.50000i	0.123142	−	0.459573i
$59$	−0.0980762	+	0.366025i	−0.0127684	+	0.0476524i	−0.972016	−	0.234914i	$-0.924519\pi$
$59$	−0.0980762	+	0.366025i	−0.0127684	+	0.0476524i	0.959248	+	0.282567i	$0.0911858\pi$
$60$	2.36603	−	2.36603i	0.305453	−	0.305453i
$61$	5.59808	−	3.23205i	0.716760	−	0.413822i	−0.0967989	−	0.995304i	$-0.530860\pi$
$61$	5.59808	−	3.23205i	0.716760	−	0.413822i	0.813559	+	0.581482i	$0.197527\pi$
$62$	−1.19615	+	2.07180i	−0.151912	+	0.263118i
$63$	2.59808	−	0.500000i	0.327327	−	0.0629941i
$64$			2.26795i			0.283494i
$65$	2.23205	−	6.59808i	0.276852	−	0.818391i
$66$			2.00000i			0.246183i
$67$	−10.5622	+	2.83013i	−1.29038	+	0.345755i	−0.837803	−	0.545973i	$-0.816160\pi$
$67$	−10.5622	+	2.83013i	−1.29038	+	0.345755i	−0.452572	+	0.891728i	$0.649494\pi$
$68$	7.79423	+	4.50000i	0.945189	+	0.545705i
$69$	−3.09808	−	5.36603i	−0.372965	−	0.645994i
$70$	−1.73205	−	2.00000i	−0.207020	−	0.239046i
$71$	1.46410	−	5.46410i	0.173757	−	0.648470i	−0.823003	−	0.568037i	$-0.807703\pi$
$71$	1.46410	−	5.46410i	0.173757	−	0.648470i	0.996760	−	0.0804327i	$-0.0256302\pi$
$72$	−1.86603	−	0.500000i	−0.219913	−	0.0589256i
$73$	8.29423	+	8.29423i	0.970766	+	0.970766i	0.999585	−	0.0288186i	$-0.00917452\pi$
$73$	8.29423	+	8.29423i	0.970766	+	0.970766i	−0.0288186	+	0.999585i	$0.509175\pi$
$74$	2.50000	+	4.33013i	0.290619	+	0.503367i
$75$	0.633975	−	1.09808i	0.0732051	−	0.126795i
$76$	4.73205	−	1.26795i	0.542803	−	0.145444i
$77$	−10.1962	−	0.732051i	−1.16196	−	0.0834249i
$78$	−1.83013	+	0.366025i	−0.207221	+	0.0414442i
$79$	15.6603			1.76192			0.880958	−	0.473194i	$-0.156899\pi$
$79$	15.6603			1.76192			0.880958	+	0.473194i	$0.156899\pi$
$80$	−1.23205	−	4.59808i	−0.137747	−	0.514081i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	2.40192	+	4.16025i	0.265248	+	0.459423i
$83$	6.92820	−	6.92820i	0.760469	−	0.760469i	−0.215938	−	0.976407i	$-0.569281\pi$
$83$	6.92820	−	6.92820i	0.760469	−	0.760469i	0.976407	+	0.215938i	$0.0692809\pi$
$84$	1.50000	−	4.33013i	0.163663	−	0.472456i
$85$	−9.69615	−	2.59808i	−1.05170	−	0.281801i
$86$	−2.92820	+	2.92820i	−0.315756	+	0.315756i
$87$	−6.06218	+	3.50000i	−0.649934	+	0.375239i
$88$	6.46410	+	3.73205i	0.689076	+	0.397838i
$89$	−9.83013	+	2.63397i	−1.04199	+	0.279201i	−0.738938	−	0.673773i	$-0.764673\pi$
$89$	−9.83013	+	2.63397i	−1.04199	+	0.279201i	−0.303053	+	0.952974i	$0.598006\pi$
$90$	1.00000			0.105409
$91$	−1.19615	−	9.46410i	−0.125391	−	0.992107i
$92$	−10.7321			−1.11889
$93$	4.46410	−	1.19615i	0.462906	−	0.124035i
$94$	−1.60770	−	0.928203i	−0.165821	−	0.0957369i
$95$	−4.73205	+	2.73205i	−0.485498	+	0.280302i
$96$	−3.63397	+	3.63397i	−0.370891	+	0.370891i
$97$	−5.09808	−	1.36603i	−0.517631	−	0.138699i	−0.00946053	−	0.999955i	$-0.503011\pi$
$97$	−5.09808	−	1.36603i	−0.517631	−	0.138699i	−0.508171	+	0.861256i	$0.669678\pi$
$98$	−3.33013	−	1.42820i	−0.336394	−	0.144270i
$99$	2.73205	−	2.73205i	0.274581	−	0.274581i
$100$	−1.09808	−	1.90192i	−0.109808	−	0.190192i
$101$	1.96410	−	3.40192i	0.195435	−	0.338504i	−0.751608	−	0.659610i	$-0.770721\pi$
$101$	1.96410	−	3.40192i	0.195435	−	0.338504i	0.947043	+	0.321106i	$0.104055\pi$
$102$	0.696152	+	2.59808i	0.0689294	+	0.257248i
$103$	−6.92820			−0.682656			−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820			−0.682656			−0.341328	+	0.939944i	$0.610877\pi$
$104$	−2.23205	+	6.59808i	−0.218871	+	0.646995i
$105$	−0.366025	+	5.09808i	−0.0357204	+	0.497521i
$106$	3.86603	−	1.03590i	0.375502	−	0.100615i
$107$	3.73205	−	6.46410i	0.360791	−	0.624908i	−0.627300	−	0.778777i	$-0.715840\pi$
$107$	3.73205	−	6.46410i	0.360791	−	0.624908i	0.988091	+	0.153869i	$0.0491734\pi$
$108$	0.866025	+	1.50000i	0.0833333	+	0.144338i
$109$	7.73205	+	7.73205i	0.740596	+	0.740596i	0.972693	−	0.232097i	$-0.0745585\pi$
$109$	7.73205	+	7.73205i	0.740596	+	0.740596i	−0.232097	+	0.972693i	$0.574559\pi$
$110$	−3.73205	−	1.00000i	−0.355837	−	0.0953463i
$111$	2.50000	−	9.33013i	0.237289	−	0.885576i
$112$	−4.26795	−	4.92820i	−0.403283	−	0.465671i
$113$	−0.767949	−	1.33013i	−0.0722426	−	0.125128i	0.827641	−	0.561257i	$-0.189682\pi$
$113$	−0.767949	−	1.33013i	−0.0722426	−	0.125128i	−0.899884	+	0.436130i	$0.856349\pi$
$114$	1.26795	+	0.732051i	0.118754	+	0.0685628i
$115$	11.5622	−	3.09808i	1.07818	−	0.288897i
$116$			12.1244i			1.12572i
$117$	3.00000	+	2.00000i	0.277350	+	0.184900i
$118$			0.196152i			0.0180573i
$119$	−13.5000	+	2.59808i	−1.23754	+	0.238165i
$120$	1.86603	−	3.23205i	0.170344	−	0.295045i
$121$	−3.40192	+	1.96410i	−0.309266	+	0.178555i
$122$	2.36603	−	2.36603i	0.214210	−	0.214210i
$123$	2.40192	−	8.96410i	0.216574	−	0.808266i
$124$	2.07180	−	7.73205i	0.186053	−	0.694359i
$125$	8.56218	+	8.56218i	0.765824	+	0.765824i
$126$	1.23205	−	0.598076i	0.109760	−	0.0532809i
$127$	9.75833	+	5.63397i	0.865912	+	0.499934i	0.865988	−	0.500066i	$-0.166691\pi$
$127$	9.75833	+	5.63397i	0.865912	+	0.499934i	−7.57430e−5		1.00000i	$0.500024\pi$
$128$	2.96410	+	11.0622i	0.261992	+	0.977768i
$129$	8.00000			0.704361
$130$	0.232051	−	3.59808i	0.0203522	−	0.315572i
$131$		−	14.1962i		−	1.24032i	−0.784474	−	0.620162i	$-0.787067\pi$
$131$		−	14.1962i		−	1.24032i	0.784474	−	0.620162i	$-0.212933\pi$
$132$	−1.73205	−	6.46410i	−0.150756	−	0.562628i
$133$	−4.19615	+	6.19615i	−0.363853	+	0.537275i
$134$	−4.90192	+	2.83013i	−0.423462	+	0.244486i
$135$	−1.36603	−	1.36603i	−0.117569	−	0.117569i
$136$	9.69615	+	2.59808i	0.831438	+	0.222783i
$137$	−11.0622	−	2.96410i	−0.945106	−	0.253240i	−0.246821	−	0.969061i	$-0.579386\pi$
$137$	−11.0622	−	2.96410i	−0.945106	−	0.253240i	−0.698284	+	0.715821i	$0.746053\pi$
$138$	−2.26795	−	2.26795i	−0.193061	−	0.193061i
$139$	−7.09808	+	4.09808i	−0.602051	+	0.347594i	−0.769848	−	0.638227i	$-0.779668\pi$
$139$	−7.09808	+	4.09808i	−0.602051	+	0.347594i	0.167797	+	0.985822i	$0.446335\pi$
$140$	7.33013	+	4.96410i	0.619509	+	0.419543i
$141$	0.928203	+	3.46410i	0.0781688	+	0.291730i
$142$		−	2.92820i		−	0.245729i
$143$	−9.19615	−	10.4641i	−0.769021	−	0.875052i
$144$	2.46410			0.205342
$145$	−3.50000	−	13.0622i	−0.290659	−	1.08475i
$146$	5.25833	+	3.03590i	0.435183	+	0.251253i
$147$	2.59808	+	6.50000i	0.214286	+	0.536111i
$148$	−11.8301	−	11.8301i	−0.972430	−	0.972430i
$149$	0.526279	−	1.96410i	0.0431145	−	0.160905i	−0.941012	−	0.338372i	$-0.890124\pi$
$149$	0.526279	−	1.96410i	0.0431145	−	0.160905i	0.984127	+	0.177467i	$0.0567903\pi$
$150$	0.169873	−	0.633975i	0.0138701	−	0.0517638i
$151$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$151$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$152$	4.73205	−	2.73205i	0.383820	−	0.221599i
$153$	2.59808	−	4.50000i	0.210042	−	0.363803i
$154$	−5.19615	+	1.00000i	−0.418718	+	0.0805823i
$155$			8.92820i			0.717131i
$156$	5.59808	−	2.76795i	0.448205	−	0.221613i
$157$			1.33975i			0.106923i	0.998570	+	0.0534617i	$0.0170255\pi$
$157$			1.33975i			0.106923i	−0.998570	+	0.0534617i	$0.982975\pi$
$158$	7.83013	−	2.09808i	0.622931	−	0.166914i
$159$	−6.69615	−	3.86603i	−0.531039	−	0.306596i
$160$	−4.96410	−	8.59808i	−0.392447	−	0.679738i
$161$	12.3923	−	10.7321i	0.976650	−	0.845804i
$162$	−0.133975	+	0.500000i	−0.0105260	+	0.0392837i
$163$	−1.63397	−	0.437822i	−0.127983	−	0.0342929i	0.194259	−	0.980950i	$-0.437770\pi$
$163$	−1.63397	−	0.437822i	−0.127983	−	0.0342929i	−0.322242	+	0.946657i	$0.604436\pi$
$164$	−11.3660	−	11.3660i	−0.887537	−	0.887537i
$165$	3.73205	+	6.46410i	0.290540	+	0.503230i
$166$	2.53590	−	4.39230i	0.196824	−	0.340909i
$167$	0.633975	−	0.169873i	0.0490584	−	0.0131452i	−0.234206	−	0.972187i	$-0.575249\pi$
$167$	0.633975	−	0.169873i	0.0490584	−	0.0131452i	0.283265	+	0.959042i	$0.408582\pi$
$168$	0.366025	−	5.09808i	0.0282395	−	0.393325i
$169$	7.89230	−	10.3301i	0.607100	−	0.794625i
$170$	−5.19615			−0.398527
$171$	−0.732051	−	2.73205i	−0.0559813	−	0.208925i
$172$	6.92820	−	12.0000i	0.528271	−	0.914991i
$173$	11.6603	+	20.1962i	0.886513	+	1.53549i	0.843970	+	0.536390i	$0.180213\pi$
$173$	11.6603	+	20.1962i	0.886513	+	1.53549i	0.0425427	+	0.999095i	$0.486454\pi$
$174$	−2.56218	+	2.56218i	−0.194238	+	0.194238i
$175$	3.16987	+	1.09808i	0.239620	+	0.0830068i
$176$	−9.19615	−	2.46410i	−0.693186	−	0.185739i
$177$	0.267949	−	0.267949i	0.0201403	−	0.0201403i
$178$	−4.56218	+	2.63397i	−0.341950	+	0.197425i
$179$	9.63397	+	5.56218i	0.720077	+	0.415737i	0.814781	−	0.579769i	$-0.196857\pi$
$179$	9.63397	+	5.56218i	0.720077	+	0.415737i	−0.0947040	+	0.995505i	$0.530190\pi$
$180$	−3.23205	+	0.866025i	−0.240903	+	0.0645497i
$181$	7.92820			0.589299			0.294649	−	0.955605i	$-0.404797\pi$
$181$	7.92820			0.589299			0.294649	+	0.955605i	$0.404797\pi$
$182$	−1.86603	−	4.57180i	−0.138319	−	0.338884i
$183$	−6.46410			−0.477840
$184$	−11.5622	+	3.09808i	−0.852375	+	0.228393i
$185$	16.1603	+	9.33013i	1.18813	+	0.685965i
$186$	2.07180	−	1.19615i	0.151912	−	0.0877062i
$187$	−14.1962	+	14.1962i	−1.03813	+	1.03813i
$188$	6.00000	+	1.60770i	0.437595	+	0.117253i
$189$	−2.50000	−	0.866025i	−0.181848	−	0.0629941i
$190$	−2.00000	+	2.00000i	−0.145095	+	0.145095i
$191$	6.26795	+	10.8564i	0.453533	+	0.785542i	0.998603	−	0.0528488i	$-0.0168301\pi$
$191$	6.26795	+	10.8564i	0.453533	+	0.785542i	−0.545070	+	0.838391i	$0.683497\pi$
$192$	1.13397	−	1.96410i	0.0818376	−	0.141747i
$193$	−2.25833	−	8.42820i	−0.162558	−	0.606675i	−0.998339	−	0.0576122i	$-0.981651\pi$
$193$	−2.25833	−	8.42820i	−0.162558	−	0.606675i	0.835781	−	0.549063i	$-0.185015\pi$
$194$	−2.73205			−0.196150
$195$	−5.23205	+	4.59808i	−0.374675	+	0.329275i
$196$	12.0000	+	1.73205i	0.857143	+	0.123718i
$197$	−9.83013	+	2.63397i	−0.700368	+	0.187663i	−0.591395	−	0.806382i	$-0.701423\pi$
$197$	−9.83013	+	2.63397i	−0.700368	+	0.187663i	−0.108972	+	0.994045i	$0.534756\pi$
$198$	1.00000	−	1.73205i	0.0710669	−	0.123091i
$199$	−9.26795	−	16.0526i	−0.656987	−	1.13794i	−0.981392	−	0.192017i	$-0.938497\pi$
$199$	−9.26795	−	16.0526i	−0.656987	−	1.13794i	0.324404	−	0.945919i	$-0.394836\pi$
$200$	−1.73205	−	1.73205i	−0.122474	−	0.122474i
$201$	10.5622	+	2.83013i	0.744999	+	0.199622i
$202$	0.526279	−	1.96410i	0.0370289	−	0.138194i
$203$	−12.1244	−	14.0000i	−0.850963	−	0.982607i
$204$	−4.50000	−	7.79423i	−0.315063	−	0.545705i
$205$	15.5263	+	8.96410i	1.08440	+	0.626080i
$206$	−3.46410	+	0.928203i	−0.241355	+	0.0646710i
$207$			6.19615i			0.430662i
$208$	0.571797	−	8.86603i	0.0396470	−	0.614748i
$209$			10.9282i			0.755920i
$210$	0.500000	+	2.59808i	0.0345033	+	0.179284i
$211$	4.19615	−	7.26795i	0.288875	−	0.500346i	−0.684666	−	0.728857i	$-0.740052\pi$
$211$	4.19615	−	7.26795i	0.288875	−	0.500346i	0.973542	+	0.228510i	$0.0733855\pi$
$212$	−11.5981	+	6.69615i	−0.796559	+	0.459894i
$213$	−4.00000	+	4.00000i	−0.274075	+	0.274075i
$214$	1.00000	−	3.73205i	0.0683586	−	0.255118i
$215$	−4.00000	+	14.9282i	−0.272798	+	1.01810i
$216$	1.36603	+	1.36603i	0.0929463	+	0.0929463i
$217$	5.33975	+	11.0000i	0.362486	+	0.746729i
$218$	4.90192	+	2.83013i	0.332000	+	0.191680i
$219$	−3.03590	−	11.3301i	−0.205147	−	0.765619i
$220$	12.9282			0.871619
$221$	−15.5885	−	10.3923i	−1.04859	−	0.699062i
$222$		−	5.00000i		−	0.335578i
$223$	2.50962	+	9.36603i	0.168057	+	0.627195i	0.997631	+	0.0687987i	$0.0219166\pi$
$223$	2.50962	+	9.36603i	0.168057	+	0.627195i	−0.829574	+	0.558397i	$0.811417\pi$
$224$	−11.2583	−	7.62436i	−0.752229	−	0.509424i
$225$	−1.09808	+	0.633975i	−0.0732051	+	0.0422650i
$226$	−0.562178	−	0.562178i	−0.0373955	−	0.0373955i
$227$	−9.36603	−	2.50962i	−0.621645	−	0.166569i	−0.0657695	−	0.997835i	$-0.520950\pi$
$227$	−9.36603	−	2.50962i	−0.621645	−	0.166569i	−0.555875	+	0.831266i	$0.687617\pi$
$228$	−4.73205	−	1.26795i	−0.313388	−	0.0839720i
$229$	12.1244	+	12.1244i	0.801200	+	0.801200i	0.983283	−	0.182083i	$-0.0582840\pi$
$229$	12.1244	+	12.1244i	0.801200	+	0.801200i	−0.182083	+	0.983283i	$0.558284\pi$
$230$	5.36603	−	3.09808i	0.353825	−	0.204281i
$231$	8.46410	+	5.73205i	0.556897	+	0.377141i
$232$	3.50000	+	13.0622i	0.229786	+	0.857574i
$233$		−	2.00000i		−	0.131024i	−0.997852	−	0.0655122i	$-0.979132\pi$
$233$		−	2.00000i		−	0.131024i	0.997852	−	0.0655122i	$-0.0208681\pi$
$234$	1.76795	+	0.598076i	0.115574	+	0.0390975i
$235$	−6.92820			−0.451946
$236$	−0.169873	−	0.633975i	−0.0110578	−	0.0412682i
$237$	−13.5622	−	7.83013i	−0.880958	−	0.508621i
$238$	−6.40192	+	3.10770i	−0.414975	+	0.201442i
$239$	−0.339746	−	0.339746i	−0.0219763	−	0.0219763i	0.696033	−	0.718010i	$-0.254947\pi$
$239$	−0.339746	−	0.339746i	−0.0219763	−	0.0219763i	−0.718010	+	0.696033i	$0.754947\pi$
$240$	−1.23205	+	4.59808i	−0.0795285	+	0.296805i
$241$	−6.52628	+	24.3564i	−0.420395	+	1.56893i	0.353384	+	0.935478i	$0.385031\pi$
$241$	−6.52628	+	24.3564i	−0.420395	+	1.56893i	−0.773779	+	0.633456i	$0.781636\pi$
$242$	−1.43782	+	1.43782i	−0.0924267	+	0.0924267i
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	−5.59808	+	9.69615i	−0.358380	+	0.620733i
$245$	−13.4282	+	1.59808i	−0.857896	+	0.102097i
$246$		−	4.80385i		−	0.306282i
$247$	−10.0000	+	2.00000i	−0.636285	+	0.127257i
$248$		−	8.92820i		−	0.566941i
$249$	−9.46410	+	2.53590i	−0.599763	+	0.160706i
$250$	5.42820	+	3.13397i	0.343310	+	0.198210i
$251$	13.5622	+	23.4904i	0.856037	+	1.48270i	0.875680	+	0.482893i	$0.160414\pi$
$251$	13.5622	+	23.4904i	0.856037	+	1.48270i	−0.0196425	+	0.999807i	$0.506253\pi$
$252$	−3.46410	+	3.00000i	−0.218218	+	0.188982i
$253$	6.19615	−	23.1244i	0.389549	−	1.45382i
$254$	5.63397	+	1.50962i	0.353507	+	0.0947219i
$255$	7.09808	+	7.09808i	0.444499	+	0.444499i
$256$	0.696152	+	1.20577i	0.0435095	+	0.0753607i
$257$	−4.69615	+	8.13397i	−0.292938	+	0.507383i	−0.974503	−	0.224374i	$-0.927966\pi$
$257$	−4.69615	+	8.13397i	−0.292938	+	0.507383i	0.681565	+	0.731757i	$0.261300\pi$
$258$	4.00000	−	1.07180i	0.249029	−	0.0667272i
$259$	25.4904	+	1.83013i	1.58390	+	0.113719i
$260$	2.36603	+	11.8301i	0.146735	+	0.733673i
$261$	7.00000			0.433289
$262$	−1.90192	−	7.09808i	−0.117501	−	0.438521i
$263$	−11.6603	+	20.1962i	−0.719002	+	1.24535i	0.242393	+	0.970178i	$0.422068\pi$
$263$	−11.6603	+	20.1962i	−0.719002	+	1.24535i	−0.961396	+	0.275170i	$0.911266\pi$
$264$	−3.73205	−	6.46410i	−0.229692	−	0.397838i
$265$	10.5622	−	10.5622i	0.648829	−	0.648829i
$266$	−1.26795	+	3.66025i	−0.0777430	+	0.224425i
$267$	9.83013	+	2.63397i	0.601594	+	0.161197i
$268$	13.3923	−	13.3923i	0.818065	−	0.818065i
$269$	−0.928203	+	0.535898i	−0.0565935	+	0.0326743i	−0.528030	−	0.849226i	$-0.677069\pi$
$269$	−0.928203	+	0.535898i	−0.0565935	+	0.0326743i	0.471436	+	0.881900i	$0.343736\pi$
$270$	−0.866025	−	0.500000i	−0.0527046	−	0.0304290i
$271$	−4.09808	+	1.09808i	−0.248940	+	0.0667034i	−0.381131	−	0.924521i	$-0.624465\pi$
$271$	−4.09808	+	1.09808i	−0.248940	+	0.0667034i	0.132191	+	0.991224i	$0.457799\pi$
$272$	−12.8038			−0.776347
$273$	−3.69615	+	8.79423i	−0.223701	+	0.532251i
$274$	−5.92820			−0.358136
$275$	4.73205	−	1.26795i	0.285353	−	0.0764602i
$276$	9.29423	+	5.36603i	0.559447	+	0.322997i
$277$	15.2321	−	8.79423i	0.915205	−	0.528394i	0.0331030	−	0.999452i	$-0.489461\pi$
$277$	15.2321	−	8.79423i	0.915205	−	0.528394i	0.882102	+	0.471058i	$0.156128\pi$
$278$	−3.00000	+	3.00000i	−0.179928	+	0.179928i
$279$	−4.46410	−	1.19615i	−0.267259	−	0.0716118i
$280$	9.33013	+	3.23205i	0.557582	+	0.193152i
$281$	11.0263	−	11.0263i	0.657773	−	0.657773i	−0.297080	−	0.954853i	$-0.596013\pi$
$281$	11.0263	−	11.0263i	0.657773	−	0.657773i	0.954853	+	0.297080i	$0.0960128\pi$
$282$	0.928203	+	1.60770i	0.0552737	+	0.0957369i
$283$	−6.26795	+	10.8564i	−0.372591	+	0.645346i	−0.989963	−	0.141325i	$-0.954864\pi$
$283$	−6.26795	+	10.8564i	−0.372591	+	0.645346i	0.617372	+	0.786671i	$0.288197\pi$
$284$	2.53590	+	9.46410i	0.150478	+	0.561591i
$285$	5.46410			0.323665
$286$	−6.00000	−	4.00000i	−0.354787	−	0.236525i
$287$	24.4904	+	1.75833i	1.44562	+	0.103791i
$288$	4.96410	−	1.33013i	0.292512	−	0.0783785i
$289$	−5.00000	+	8.66025i	−0.294118	+	0.509427i
$290$	−3.50000	−	6.06218i	−0.205527	−	0.355983i
$291$	3.73205	+	3.73205i	0.218777	+	0.218777i
$292$	−19.6244	−	5.25833i	−1.14843	−	0.307721i
$293$	0.258330	−	0.964102i	0.0150918	−	0.0563234i	−0.957969	−	0.286871i	$-0.907385\pi$
$293$	0.258330	−	0.964102i	0.0150918	−	0.0563234i	0.973061	+	0.230547i	$0.0740516\pi$
$294$	2.16987	+	2.90192i	0.126550	+	0.169244i
$295$	0.366025	+	0.633975i	0.0213108	+	0.0369114i
$296$	−16.1603	−	9.33013i	−0.939296	−	0.542303i
$297$	−3.73205	+	1.00000i	−0.216556	+	0.0580259i
$298$		−	1.05256i		−	0.0609731i
$299$	22.2942	+	1.43782i	1.28931	+	0.0831514i
$300$			2.19615i			0.126795i
$301$	4.00000	+	20.7846i	0.230556	+	1.19800i
$302$		0			0
$303$	−3.40192	+	1.96410i	−0.195435	+	0.112835i
$304$	−4.92820	+	4.92820i	−0.282652	+	0.282652i
$305$	3.23205	−	12.0622i	0.185067	−	0.690678i
$306$	0.696152	−	2.59808i	0.0397964	−	0.148522i
$307$	−3.92820	−	3.92820i	−0.224194	−	0.224194i	0.586068	−	0.810262i	$-0.300675\pi$
$307$	−3.92820	−	3.92820i	−0.224194	−	0.224194i	−0.810262	+	0.586068i	$0.800675\pi$
$308$	15.9282	−	7.73205i	0.907594	−	0.440574i
$309$	6.00000	+	3.46410i	0.341328	+	0.197066i
$310$	1.19615	+	4.46410i	0.0679369	+	0.253544i
$311$	−13.6603			−0.774602			−0.387301	−	0.921953i	$-0.626593\pi$
$311$	−13.6603			−0.774602			−0.387301	+	0.921953i	$0.626593\pi$
$312$	5.23205	−	4.59808i	0.296207	−	0.260315i
$313$		−	9.60770i		−	0.543059i	−0.962430	−	0.271530i	$-0.912471\pi$
$313$		−	9.60770i		−	0.543059i	0.962430	−	0.271530i	$-0.0875295\pi$
$314$	0.179492	+	0.669873i	0.0101293	+	0.0378031i
$315$	2.86603	−	4.23205i	0.161482	−	0.238449i
$316$	−23.4904	+	13.5622i	−1.32144	+	0.762932i
$317$	−22.7583	−	22.7583i	−1.27824	−	1.27824i	−0.941655	−	0.336580i	$-0.890730\pi$
$317$	−22.7583	−	22.7583i	−1.27824	−	1.27824i	−0.336580	−	0.941655i	$-0.609270\pi$
$318$	−3.86603	−	1.03590i	−0.216796	−	0.0580903i
$319$	−26.1244	−	7.00000i	−1.46268	−	0.391925i
$320$	3.09808	+	3.09808i	0.173188	+	0.173188i
$321$	−6.46410	+	3.73205i	−0.360791	+	0.208303i
$322$	4.75833	−	7.02628i	0.265171	−	0.391559i
$323$	3.80385	+	14.1962i	0.211652	+	0.789895i
$324$		−	1.73205i		−	0.0962250i
$325$	2.02628	+	4.09808i	0.112398	+	0.227320i
$326$	−0.875644			−0.0484975
$327$	−2.83013	−	10.5622i	−0.156506	−	0.584090i
$328$	−15.5263	−	8.96410i	−0.857295	−	0.494960i
$329$	−8.53590	+	4.14359i	−0.470599	+	0.228444i
$330$	2.73205	+	2.73205i	0.150394	+	0.150394i
$331$	−1.75833	+	6.56218i	−0.0966466	+	0.360690i	−0.997264	−	0.0739229i	$-0.976448\pi$
$331$	−1.75833	+	6.56218i	−0.0966466	+	0.360690i	0.900617	+	0.434613i	$0.143115\pi$
$332$	−4.39230	+	16.3923i	−0.241059	+	0.899645i
$333$	−6.83013	+	6.83013i	−0.374289	+	0.374289i
$334$	0.294229	−	0.169873i	0.0160995	−	0.00929504i
$335$	−10.5622	+	18.2942i	−0.577073	+	0.999520i
$336$	1.23205	+	6.40192i	0.0672139	+	0.349254i
$337$			24.4641i			1.33264i	0.745664	+	0.666322i	$0.232132\pi$
$337$			24.4641i			1.33264i	−0.745664	+	0.666322i	$0.767868\pi$
$338$	2.56218	−	6.22243i	0.139364	−	0.338456i
$339$			1.53590i			0.0834185i
$340$	16.7942	−	4.50000i	0.910795	−	0.244047i
$341$	15.4641	+	8.92820i	0.837428	+	0.483489i
$342$	−0.732051	−	1.26795i	−0.0395848	−	0.0685628i
$343$	−15.5885	+	10.0000i	−0.841698	+	0.539949i
$344$	4.00000	−	14.9282i	0.215666	−	0.804875i
$345$	−11.5622	−	3.09808i	−0.622487	−	0.166795i
$346$	8.53590	+	8.53590i	0.458893	+	0.458893i
$347$	−2.83013	−	4.90192i	−0.151929	−	0.263149i	0.780007	−	0.625770i	$-0.215215\pi$
$347$	−2.83013	−	4.90192i	−0.151929	−	0.263149i	−0.931937	+	0.362621i	$0.881882\pi$
$348$	6.06218	−	10.5000i	0.324967	−	0.562859i
$349$	−4.56218	+	1.22243i	−0.244208	+	0.0654353i	−0.378847	−	0.925459i	$-0.623679\pi$
$349$	−4.56218	+	1.22243i	−0.244208	+	0.0654353i	0.134639	+	0.990895i	$0.457013\pi$
$350$	1.73205	+	0.124356i	0.0925820	+	0.00664709i
$351$	−1.59808	−	3.23205i	−0.0852990	−	0.172514i
$352$	−19.8564			−1.05835
$353$	−2.69615	−	10.0622i	−0.143502	−	0.535556i	−0.999818	−	0.0191031i	$-0.993919\pi$
$353$	−2.69615	−	10.0622i	−0.143502	−	0.535556i	0.856316	−	0.516453i	$-0.172748\pi$
$354$	0.0980762	−	0.169873i	0.00521269	−	0.00902865i
$355$	−5.46410	−	9.46410i	−0.290004	−	0.502302i
$356$	12.4641	−	12.4641i	0.660596	−	0.660596i
$357$	12.9904	+	4.50000i	0.687524	+	0.238165i
$358$	5.56218	+	1.49038i	0.293970	+	0.0787691i
$359$	−8.80385	+	8.80385i	−0.464649	+	0.464649i	−0.900176	−	0.435527i	$-0.856562\pi$
$359$	−8.80385	+	8.80385i	−0.464649	+	0.464649i	0.435527	+	0.900176i	$0.356562\pi$
$360$	−3.23205	+	1.86603i	−0.170344	+	0.0983482i
$361$	−9.52628	−	5.50000i	−0.501383	−	0.289474i
$362$	3.96410	−	1.06218i	0.208349	−	0.0558268i
$363$	3.92820			0.206177
$364$	9.99038	+	13.1603i	0.523638	+	0.689785i
$365$	22.6603			1.18609
$366$	−3.23205	+	0.866025i	−0.168942	+	0.0452679i
$367$	−10.2224	−	5.90192i	−0.533607	−	0.308078i	0.208877	−	0.977942i	$-0.433019\pi$
$367$	−10.2224	−	5.90192i	−0.533607	−	0.308078i	−0.742484	+	0.669864i	$0.766352\pi$
$368$	13.2224	−	7.63397i	0.689267	−	0.397948i
$369$	−6.56218	+	6.56218i	−0.341613	+	0.341613i
$370$	9.33013	+	2.50000i	0.485050	+	0.129969i
$371$	6.69615	−	19.3301i	0.347647	−	1.00357i
$372$	−5.66025	+	5.66025i	−0.293471	+	0.293471i
$373$	−12.1340	−	21.0167i	−0.628273	−	1.08820i	−0.987898	−	0.155104i	$-0.950429\pi$
$373$	−12.1340	−	21.0167i	−0.628273	−	1.08820i	0.359625	−	0.933097i	$-0.382905\pi$
$374$	−5.19615	+	9.00000i	−0.268687	+	0.465379i
$375$	−3.13397	−	11.6962i	−0.161838	−	0.603987i
$376$	6.92820			0.357295
$377$	1.62436	−	25.1865i	0.0836586	−	1.29717i
$378$	−1.36603	−	0.0980762i	−0.0702608	−	0.00504450i
$379$	27.1244	−	7.26795i	1.39328	−	0.373329i	0.517356	−	0.855770i	$-0.326916\pi$
$379$	27.1244	−	7.26795i	1.39328	−	0.373329i	0.875929	+	0.482441i	$0.160250\pi$
$380$	4.73205	−	8.19615i	0.242749	−	0.420454i
$381$	−5.63397	−	9.75833i	−0.288637	−	0.499934i
$382$	4.58846	+	4.58846i	0.234766	+	0.234766i
$383$	−16.7583	−	4.49038i	−0.856311	−	0.229448i	−0.196152	−	0.980574i	$-0.562844\pi$
$383$	−16.7583	−	4.49038i	−0.856311	−	0.229448i	−0.660159	+	0.751126i	$0.729511\pi$
$384$	2.96410	−	11.0622i	0.151261	−	0.564514i
$385$	−14.9282	+	12.9282i	−0.760812	+	0.658882i
$386$	−2.25833	−	3.91154i	−0.114946	−	0.199092i
$387$	−6.92820	−	4.00000i	−0.352180	−	0.203331i
$388$	8.83013	−	2.36603i	0.448282	−	0.120117i
$389$		−	26.2679i		−	1.33184i	−0.746024	−	0.665919i	$-0.768040\pi$
$389$		−	26.2679i		−	1.33184i	0.746024	−	0.665919i	$-0.231960\pi$
$390$	−2.00000	+	3.00000i	−0.101274	+	0.151911i
$391$		−	32.1962i		−	1.62823i
$392$	13.4282	−	1.59808i	0.678227	−	0.0807150i
$393$	−7.09808	+	12.2942i	−0.358051	+	0.620162i
$394$	−4.56218	+	2.63397i	−0.229839	+	0.132698i
$395$	21.3923	−	21.3923i	1.07636	−	1.07636i
$396$	−1.73205	+	6.46410i	−0.0870388	+	0.324833i
$397$	5.22243	−	19.4904i	0.262106	−	0.978194i	−0.701891	−	0.712284i	$-0.747661\pi$
$397$	5.22243	−	19.4904i	0.262106	−	0.978194i	0.963998	−	0.265910i	$-0.0856725\pi$
$398$	−6.78461	−	6.78461i	−0.340082	−	0.340082i
$399$	6.73205	−	3.26795i	0.337024	−	0.163602i
$400$	2.70577	+	1.56218i	0.135289	+	0.0781089i
$401$	−2.33013	−	8.69615i	−0.116361	−	0.434265i	0.883024	−	0.469328i	$-0.155504\pi$
$401$	−2.33013	−	8.69615i	−0.116361	−	0.434265i	−0.999385	+	0.0350625i	$0.988837\pi$
$402$	5.66025			0.282308
$403$	−5.33975	+	15.7846i	−0.265992	+	0.786287i
$404$			6.80385i			0.338504i
$405$	0.500000	+	1.86603i	0.0248452	+	0.0927235i
$406$	−7.93782	−	5.37564i	−0.393947	−	0.266789i
$407$	32.3205	−	18.6603i	1.60207	−	0.924954i
$408$	−7.09808	−	7.09808i	−0.351407	−	0.351407i
$409$	0.232051	+	0.0621778i	0.0114742	+	0.00307450i	0.264552	−	0.964372i	$-0.414776\pi$
$409$	0.232051	+	0.0621778i	0.0114742	+	0.00307450i	−0.253077	+	0.967446i	$0.581443\pi$
$410$	8.96410	+	2.40192i	0.442705	+	0.118623i
$411$	8.09808	+	8.09808i	0.399449	+	0.399449i
$412$	10.3923	−	6.00000i	0.511992	−	0.295599i
$413$	0.830127	+	0.562178i	0.0408479	+	0.0276630i
$414$	0.830127	+	3.09808i	0.0407985	+	0.152262i
$415$		−	18.9282i		−	0.929149i
$416$	−3.63397	−	18.1699i	−0.178170	−	0.890851i
$417$	8.19615			0.401367
$418$	1.46410	+	5.46410i	0.0716116	+	0.267258i
$419$	9.33975	+	5.39230i	0.456276	+	0.263431i	0.710477	−	0.703720i	$-0.248479\pi$
$419$	9.33975	+	5.39230i	0.456276	+	0.263431i	−0.254201	+	0.967151i	$0.581812\pi$
$420$	−3.86603	−	7.96410i	−0.188643	−	0.388608i
$421$	27.7583	+	27.7583i	1.35286	+	1.35286i	0.882448	+	0.470411i	$0.155894\pi$
$421$	27.7583	+	27.7583i	1.35286	+	1.35286i	0.470411	+	0.882448i	$0.344106\pi$
$422$	1.12436	−	4.19615i	0.0547328	−	0.204266i
$423$	0.928203	−	3.46410i	0.0451308	−	0.168430i
$424$	−10.5622	+	10.5622i	−0.512945	+	0.512945i
$425$	5.70577	−	3.29423i	0.276771	−	0.159794i
$426$	−1.46410	+	2.53590i	−0.0709360	+	0.122865i
$427$	−3.23205	−	16.7942i	−0.156410	−	0.812730i
$428$			12.9282i			0.624908i
$429$	2.73205	+	13.6603i	0.131905	+	0.659523i
$430$			8.00000i			0.385794i
$431$	−2.63397	+	0.705771i	−0.126874	+	0.0339958i	−0.321697	−	0.946843i	$-0.604253\pi$
$431$	−2.63397	+	0.705771i	−0.126874	+	0.0339958i	0.194823	+	0.980838i	$0.437587\pi$
$432$	−2.13397	−	1.23205i	−0.102671	−	0.0592771i
$433$	−5.06218	−	8.76795i	−0.243273	−	0.421361i	0.718372	−	0.695659i	$-0.244888\pi$
$433$	−5.06218	−	8.76795i	−0.243273	−	0.421361i	−0.961645	+	0.274299i	$0.911554\pi$
$434$	4.14359	+	4.78461i	0.198899	+	0.229669i
$435$	−3.50000	+	13.0622i	−0.167812	+	0.626283i
$436$	−18.2942	−	4.90192i	−0.876135	−	0.234760i
$437$	−12.3923	−	12.3923i	−0.592804	−	0.592804i
$438$	−3.03590	−	5.25833i	−0.145061	−	0.251253i
$439$	20.1244	−	34.8564i	0.960483	−	1.66361i	0.239193	−	0.970972i	$-0.423117\pi$
$439$	20.1244	−	34.8564i	0.960483	−	1.66361i	0.721290	−	0.692634i	$-0.243550\pi$
$440$	13.9282	−	3.73205i	0.664001	−	0.177919i
$441$	1.00000	−	6.92820i	0.0476190	−	0.329914i
$442$	−9.18653	−	3.10770i	−0.436959	−	0.147818i
$443$	10.3923			0.493753			0.246877	−	0.969047i	$-0.420596\pi$
$443$	10.3923			0.493753			0.246877	+	0.969047i	$0.420596\pi$
$444$	4.33013	+	16.1603i	0.205499	+	0.766932i
$445$	−9.83013	+	17.0263i	−0.465993	+	0.807123i
$446$	2.50962	+	4.34679i	0.118834	+	0.205826i
$447$	−1.43782	+	1.43782i	−0.0680067	+	0.0680067i
$448$	5.66987	+	1.96410i	0.267876	+	0.0927951i
$449$	5.83013	+	1.56218i	0.275141	+	0.0737237i	0.393751	−	0.919217i	$-0.371177\pi$
$449$	5.83013	+	1.56218i	0.275141	+	0.0737237i	−0.118610	+	0.992941i	$0.537844\pi$
$450$	−0.464102	+	0.464102i	−0.0218780	+	0.0218780i
$451$	31.0526	−	17.9282i	1.46221	−	0.844206i
$452$	2.30385	+	1.33013i	0.108364	+	0.0625639i
$453$		0			0
$454$	−5.01924			−0.235565
$455$	−14.5622	−	11.2942i	−0.682685	−	0.529482i
$456$	−5.46410			−0.255880
$457$	−27.5263	+	7.37564i	−1.28763	+	0.345018i	−0.836758	−	0.547573i	$-0.815552\pi$
$457$	−27.5263	+	7.37564i	−1.28763	+	0.345018i	−0.450867	+	0.892591i	$0.648885\pi$
$458$	7.68653	+	4.43782i	0.359168	+	0.207366i
$459$	−4.50000	+	2.59808i	−0.210042	+	0.121268i
$460$	−14.6603	+	14.6603i	−0.683538	+	0.683538i
$461$	2.03590	+	0.545517i	0.0948212	+	0.0254073i	0.305918	−	0.952058i	$-0.401037\pi$
$461$	2.03590	+	0.545517i	0.0948212	+	0.0254073i	−0.211096	+	0.977465i	$0.567703\pi$
$462$	5.00000	+	1.73205i	0.232621	+	0.0805823i
$463$	−8.19615	+	8.19615i	−0.380908	+	0.380908i	−0.871429	−	0.490522i	$-0.836806\pi$
$463$	−8.19615	+	8.19615i	−0.380908	+	0.380908i	0.490522	+	0.871429i	$0.336806\pi$
$464$	−8.62436	−	14.9378i	−0.400376	−	0.693471i
$465$	4.46410	−	7.73205i	0.207018	−	0.358565i
$466$	−0.267949	−	1.00000i	−0.0124125	−	0.0463241i
$467$	−30.7846			−1.42454			−0.712271	−	0.701905i	$-0.752333\pi$
$467$	−30.7846			−1.42454			−0.712271	+	0.701905i	$0.752333\pi$
$468$	−6.23205	−	0.401924i	−0.288077	−	0.0185789i
$469$	−2.07180	+	28.8564i	−0.0956667	+	1.33247i
$470$	−3.46410	+	0.928203i	−0.159787	+	0.0428148i
$471$	0.669873	−	1.16025i	0.0308661	−	0.0534617i
$472$	−0.366025	−	0.633975i	−0.0168477	−	0.0291810i
$473$	21.8564	+	21.8564i	1.00496	+	1.00496i
$474$	−7.83013	−	2.09808i	−0.359650	−	0.0963678i
$475$	0.928203	−	3.46410i	0.0425889	−	0.158944i
$476$	18.0000	−	15.5885i	0.825029	−	0.714496i
$477$	3.86603	+	6.69615i	0.177013	+	0.306596i
$478$	−0.215390	−	0.124356i	−0.00985172	−	0.00568790i
$479$	15.1962	−	4.07180i	0.694330	−	0.186045i	0.105640	−	0.994404i	$-0.466311\pi$
$479$	15.1962	−	4.07180i	0.694330	−	0.186045i	0.588689	+	0.808359i	$0.299644\pi$
$480$			9.92820i			0.453158i
$481$	22.9904	+	26.1603i	1.04827	+	1.19280i
$482$			13.0526i			0.594528i
$483$	−16.0981	+	3.09808i	−0.732488	+	0.140967i
$484$	3.40192	−	5.89230i	0.154633	−	0.267832i
$485$	−8.83013	+	5.09808i	−0.400955	+	0.231492i
$486$	0.366025	−	0.366025i	0.0166032	−	0.0166032i
$487$	0.954483	−	3.56218i	0.0432517	−	0.161418i	−0.940922	−	0.338623i	$-0.890039\pi$
$487$	0.954483	−	3.56218i	0.0432517	−	0.161418i	0.984174	+	0.177205i	$0.0567056\pi$
$488$	−3.23205	+	12.0622i	−0.146308	+	0.546029i
$489$	1.19615	+	1.19615i	0.0540919	+	0.0540919i
$490$	−6.50000	+	2.59808i	−0.293640	+	0.117369i
$491$	−10.9019	−	6.29423i	−0.491997	−	0.284055i	0.233406	−	0.972379i	$-0.425013\pi$
$491$	−10.9019	−	6.29423i	−0.491997	−	0.284055i	−0.725403	+	0.688325i	$0.758346\pi$
$492$	4.16025	+	15.5263i	0.187559	+	0.699979i
$493$	−36.3731			−1.63816
$494$	−4.73205	+	2.33975i	−0.212905	+	0.105270i
$495$		−	7.46410i		−	0.335486i
$496$	2.94744	+	11.0000i	0.132344	+	0.493915i
$497$	−12.3923	−	8.39230i	−0.555871	−	0.376446i
$498$	−4.39230	+	2.53590i	−0.196824	+	0.113636i
$499$	−2.39230	−	2.39230i	−0.107094	−	0.107094i	0.651529	−	0.758624i	$-0.274128\pi$
$499$	−2.39230	−	2.39230i	−0.107094	−	0.107094i	−0.758624	+	0.651529i	$0.774128\pi$
$500$	−20.2583	−	5.42820i	−0.905980	−	0.242757i
$501$	−0.633975	−	0.169873i	−0.0283239	−	0.00758937i
$502$	9.92820	+	9.92820i	0.443117	+	0.443117i
$503$	−26.5359	+	15.3205i	−1.18318	+	0.683108i	−0.956747	−	0.290920i	$-0.906039\pi$
$503$	−26.5359	+	15.3205i	−1.18318	+	0.683108i	−0.226430	+	0.974027i	$0.572705\pi$
$504$	−2.86603	+	4.23205i	−0.127663	+	0.188511i
$505$	−1.96410	−	7.33013i	−0.0874014	−	0.326186i
$506$		−	12.3923i		−	0.550905i
$507$	−12.0000	+	5.00000i	−0.532939	+	0.222058i
$508$	−19.5167			−0.865912
$509$	−8.79423	−	32.8205i	−0.389797	−	1.45474i	−0.830464	−	0.557073i	$-0.811925\pi$
$509$	−8.79423	−	32.8205i	−0.389797	−	1.45474i	0.440667	−	0.897671i	$-0.354742\pi$
$510$	4.50000	+	2.59808i	0.199263	+	0.115045i
$511$	27.9186	−	13.5526i	1.23505	−	0.599530i
$512$	−15.6865	−	15.6865i	−0.693253	−	0.693253i
$513$	−0.732051	+	2.73205i	−0.0323208	+	0.120623i
$514$	−1.25833	+	4.69615i	−0.0555026	+	0.207138i
$515$	−9.46410	+	9.46410i	−0.417038	+	0.417038i
$516$	−12.0000	+	6.92820i	−0.528271	+	0.304997i
$517$	−6.92820	+	12.0000i	−0.304702	+	0.527759i
$518$	12.9904	−	2.50000i	0.570765	−	0.109844i
$519$		−	23.3205i		−	1.02366i
$520$	5.96410	+	12.0622i	0.261543	+	0.528961i
$521$			27.3923i			1.20008i	0.799970	+	0.600039i	$0.204848\pi$
$521$			27.3923i			1.20008i	−0.799970	+	0.600039i	$0.795152\pi$
$522$	3.50000	−	0.937822i	0.153191	−	0.0410474i
$523$	21.7583	+	12.5622i	0.951425	+	0.549306i	0.893523	−	0.449017i	$-0.148226\pi$
$523$	21.7583	+	12.5622i	0.951425	+	0.549306i	0.0579019	+	0.998322i	$0.481559\pi$
$524$	12.2942	+	21.2942i	0.537076	+	0.930243i
$525$	−2.19615	−	2.53590i	−0.0958479	−	0.110676i
$526$	−3.12436	+	11.6603i	−0.136228	+	0.508411i
$527$	23.1962	+	6.21539i	1.01044	+	0.270747i
$528$	6.73205	+	6.73205i	0.292975	+	0.292975i
$529$	7.69615	+	13.3301i	0.334615	+	0.579571i
$530$	3.86603	−	6.69615i	0.167929	−	0.290862i
$531$	−0.366025	+	0.0980762i	−0.0158841	+	0.00425615i
$532$	0.928203	−	12.9282i	0.0402427	−	0.560509i
$533$	22.0885	+	25.1340i	0.956757	+	1.08867i
$534$	5.26795			0.227966
$535$	−3.73205	−	13.9282i	−0.161351	−	0.602169i
$536$	10.5622	−	18.2942i	0.456217	−	0.790190i
$537$	−5.56218	−	9.63397i	−0.240026	−	0.415737i
$538$	−0.392305	+	0.392305i	−0.0169135	+	0.0169135i
$539$	−10.6603	+	24.8564i	−0.459170	+	1.07064i
$540$	3.23205	+	0.866025i	0.139085	+	0.0372678i
$541$	−4.56218	+	4.56218i	−0.196143	+	0.196143i	−0.798344	−	0.602201i	$-0.794291\pi$
$541$	−4.56218	+	4.56218i	−0.196143	+	0.196143i	0.602201	+	0.798344i	$0.294291\pi$
$542$	−1.90192	+	1.09808i	−0.0816946	+	0.0471664i
$543$	−6.86603	−	3.96410i	−0.294649	−	0.170116i
$544$	−25.7942	+	6.91154i	−1.10592	+	0.296330i
$545$	21.1244			0.904868
$546$	−0.669873	+	4.89230i	−0.0286679	+	0.209371i
$547$	9.26795			0.396269			0.198134	−	0.980175i	$-0.436512\pi$
$547$	9.26795			0.396269			0.198134	+	0.980175i	$0.436512\pi$
$548$	19.1603	−	5.13397i	0.818485	−	0.219313i
$549$	5.59808	+	3.23205i	0.238920	+	0.137941i
$550$	2.19615	−	1.26795i	0.0936443	−	0.0540655i
$551$	−14.0000	+	14.0000i	−0.596420	+	0.596420i
$552$	11.5622	+	3.09808i	0.492119	+	0.131863i
$553$	13.5622	−	39.1506i	0.576722	−	1.66485i
$554$	6.43782	−	6.43782i	0.273517	−	0.273517i
$555$	−9.33013	−	16.1603i	−0.396042	−	0.685965i
$556$	7.09808	−	12.2942i	0.301025	−	0.521391i
$557$	−9.42820	−	35.1865i	−0.399486	−	1.49090i	−0.814003	−	0.580860i	$-0.802716\pi$
$557$	−9.42820	−	35.1865i	−0.399486	−	1.49090i	0.414518	−	0.910041i	$-0.363950\pi$
$558$	−2.39230			−0.101274
$559$	−16.0000	+	24.0000i	−0.676728	+	1.01509i
$560$	−12.5622	−	0.901924i	−0.530849	−	0.0381132i
$561$	19.3923	−	5.19615i	0.818744	−	0.219382i
$562$	4.03590	−	6.99038i	0.170244	−	0.294871i
$563$	21.9545	+	38.0263i	0.925271	+	1.60262i	0.791125	+	0.611655i	$0.209496\pi$
$563$	21.9545	+	38.0263i	0.925271	+	1.60262i	0.134147	+	0.990961i	$0.457171\pi$
$564$	−4.39230	−	4.39230i	−0.184949	−	0.184949i
$565$	−2.86603	−	0.767949i	−0.120575	−	0.0323079i
$566$	−1.67949	+	6.26795i	−0.0705943	+	0.263462i
$567$	1.73205	+	2.00000i	0.0727393	+	0.0839921i
$568$	5.46410	+	9.46410i	0.229269	+	0.397105i
$569$	−18.0000	−	10.3923i	−0.754599	−	0.435668i	0.0727541	−	0.997350i	$-0.476821\pi$
$569$	−18.0000	−	10.3923i	−0.754599	−	0.435668i	−0.827353	+	0.561682i	$0.810155\pi$
$570$	2.73205	−	0.732051i	0.114433	−	0.0306622i
$571$			5.41154i			0.226466i	0.993568	+	0.113233i	$0.0361207\pi$
$571$			5.41154i			0.226466i	−0.993568	+	0.113233i	$0.963879\pi$
$572$	22.8564	+	7.73205i	0.955674	+	0.323293i
$573$		−	12.5359i		−	0.523695i
$574$	12.4808	−	2.40192i	0.520937	−	0.100254i
$575$	−3.92820	+	6.80385i	−0.163817	+	0.283740i
$576$	−1.96410	+	1.13397i	−0.0818376	+	0.0472489i
$577$	−0.169873	+	0.169873i	−0.00707190	+	0.00707190i	−0.710634	−	0.703562i	$-0.751592\pi$
$577$	−0.169873	+	0.169873i	−0.00707190	+	0.00707190i	0.703562	+	0.710634i	$0.251592\pi$
$578$	−1.33975	+	5.00000i	−0.0557261	+	0.207973i
$579$	−2.25833	+	8.42820i	−0.0938530	+	0.350264i
$580$	16.5622	+	16.5622i	0.687707	+	0.687707i
$581$	−11.3205	−	23.3205i	−0.469654	−	0.967498i
$582$	2.36603	+	1.36603i	0.0980749	+	0.0566236i
$583$	−7.73205	−	28.8564i	−0.320229	−	1.19511i
$584$	−22.6603			−0.937688
$585$	6.83013	−	1.36603i	0.282391	−	0.0564782i
$586$		−	0.516660i		−	0.0213430i
$587$	8.07180	+	30.1244i	0.333159	+	1.24337i	0.905852	+	0.423595i	$0.139232\pi$
$587$	8.07180	+	30.1244i	0.333159	+	1.24337i	−0.572693	+	0.819770i	$0.694101\pi$
$588$	−9.52628	−	7.50000i	−0.392857	−	0.309295i
$589$	11.3205	−	6.53590i	0.466453	−	0.269307i
$590$	0.267949	+	0.267949i	0.0110313	+	0.0110313i
$591$	9.83013	+	2.63397i	0.404357	+	0.108347i
$592$	22.9904	+	6.16025i	0.944899	+	0.253185i
$593$	−17.0981	−	17.0981i	−0.702134	−	0.702134i	0.262734	−	0.964868i	$-0.415376\pi$
$593$	−17.0981	−	17.0981i	−0.702134	−	0.702134i	−0.964868	+	0.262734i	$0.915376\pi$
$594$	−1.73205	+	1.00000i	−0.0710669	+	0.0410305i
$595$	−14.8923	+	21.9904i	−0.610525	+	0.901518i
$596$	0.911543	+	3.40192i	0.0373382	+	0.139348i
$597$			18.5359i			0.758624i
$598$	11.3397	−	2.26795i	0.463717	−	0.0927433i
$599$	−25.8038			−1.05432			−0.527158	−	0.849767i	$-0.676743\pi$
$599$	−25.8038			−1.05432			−0.527158	+	0.849767i	$0.676743\pi$
$600$	0.633975	+	2.36603i	0.0258819	+	0.0965926i
$601$	−21.8205	−	12.5981i	−0.890077	−	0.513886i	−0.0161094	−	0.999870i	$-0.505128\pi$
$601$	−21.8205	−	12.5981i	−0.890077	−	0.513886i	−0.873968	+	0.485984i	$0.838461\pi$
$602$	4.78461	+	9.85641i	0.195006	+	0.401717i
$603$	−7.73205	−	7.73205i	−0.314873	−	0.314873i
$604$		0			0
$605$	−1.96410	+	7.33013i	−0.0798521	+	0.298012i
$606$	−1.43782	+	1.43782i	−0.0584075	+	0.0584075i
$607$	−35.9545	+	20.7583i	−1.45935	+	0.842555i	−0.998979	−	0.0451734i	$-0.985616\pi$
$607$	−35.9545	+	20.7583i	−1.45935	+	0.842555i	−0.460368	+	0.887728i	$0.652283\pi$
$608$	−7.26795	+	12.5885i	−0.294754	+	0.510529i
$609$	3.50000	+	18.1865i	0.141827	+	0.736956i
$610$		−	6.46410i		−	0.261724i
$611$	−12.2487	−	4.14359i	−0.495530	−	0.167632i
$612$			9.00000i			0.363803i
$613$	6.23205	−	1.66987i	0.251710	−	0.0674455i	−0.130758	−	0.991414i	$-0.541741\pi$
$613$	6.23205	−	1.66987i	0.251710	−	0.0674455i	0.382468	+	0.923969i	$0.375074\pi$
$614$	−2.49038	−	1.43782i	−0.100504	−	0.0580258i
$615$	−8.96410	−	15.5263i	−0.361467	−	0.626080i
$616$	14.9282	−	12.9282i	0.601474	−	0.520892i
$617$	−8.65064	+	32.2846i	−0.348261	+	1.29973i	0.540494	+	0.841348i	$0.318237\pi$
$617$	−8.65064	+	32.2846i	−0.348261	+	1.29973i	−0.888755	+	0.458382i	$0.848429\pi$
$618$	3.46410	+	0.928203i	0.139347	+	0.0373378i
$619$	−14.8564	−	14.8564i	−0.597129	−	0.597129i	0.342418	−	0.939548i	$-0.388754\pi$
$619$	−14.8564	−	14.8564i	−0.597129	−	0.597129i	−0.939548	+	0.342418i	$0.888754\pi$
$620$	−7.73205	−	13.3923i	−0.310527	−	0.537848i
$621$	3.09808	−	5.36603i	0.124322	−	0.215331i
$622$	−6.83013	+	1.83013i	−0.273863	+	0.0733814i
$623$	−1.92820	+	26.8564i	−0.0772518	+	1.07598i
$624$	−4.92820	+	7.39230i	−0.197286	+	0.295929i
$625$	17.0526			0.682102
$626$	−1.28719	−	4.80385i	−0.0514463	−	0.192000i
$627$	5.46410	−	9.46410i	0.218215	−	0.377960i
$628$	−1.16025	−	2.00962i	−0.0462992	−	0.0801925i
$629$	35.4904	−	35.4904i	1.41509	−	1.41509i
$630$	0.866025	−	2.50000i	0.0345033	−	0.0996024i
$631$	20.1962	+	5.41154i	0.803996	+	0.215430i	0.637338	−	0.770585i	$-0.280036\pi$
$631$	20.1962	+	5.41154i	0.803996	+	0.215430i	0.166658	+	0.986015i	$0.446702\pi$
$632$	−21.3923	+	21.3923i	−0.850940	+	0.850940i
$633$	−7.26795	+	4.19615i	−0.288875	+	0.166782i
$634$	−14.4282	−	8.33013i	−0.573017	−	0.330832i
$635$	21.0263	−	5.63397i	0.834402	−	0.223577i
$636$	13.3923			0.531039
$637$	−24.6962	−	5.20577i	−0.978497	−	0.206260i
$638$	−14.0000			−0.554265
$639$	5.46410	−	1.46410i	0.216157	−	0.0579190i
$640$	19.1603	+	11.0622i	0.757376	+	0.437271i
$641$	−19.7487	+	11.4019i	−0.780027	+	0.450349i	−0.836440	−	0.548059i	$-0.815367\pi$
$641$	−19.7487	+	11.4019i	−0.780027	+	0.450349i	0.0564127	+	0.998408i	$0.482034\pi$
$642$	−2.73205	+	2.73205i	−0.107825	+	0.107825i
$643$	21.9282	+	5.87564i	0.864764	+	0.231713i	0.663822	−	0.747890i	$-0.268933\pi$
$643$	21.9282	+	5.87564i	0.864764	+	0.231713i	0.200942	+	0.979603i	$0.435600\pi$
$644$	−9.29423	+	26.8301i	−0.366244	+	1.05726i
$645$	10.9282	−	10.9282i	0.430298	−	0.430298i
$646$	3.80385	+	6.58846i	0.149660	+	0.259219i
$647$	8.22243	−	14.2417i	0.323257	−	0.559898i	−0.657901	−	0.753104i	$-0.728555\pi$
$647$	8.22243	−	14.2417i	0.323257	−	0.559898i	0.981158	+	0.193207i	$0.0618888\pi$
$648$	−0.500000	−	1.86603i	−0.0196419	−	0.0733044i
$649$	1.46410			0.0574710
$650$	1.56218	+	1.77757i	0.0612737	+	0.0697220i
$651$	0.875644	−	12.1962i	0.0343192	−	0.478005i
$652$	2.83013	−	0.758330i	0.110836	−	0.0296985i
$653$	−16.7321	+	28.9808i	−0.654776	+	1.13410i	0.327174	+	0.944964i	$0.393904\pi$
$653$	−16.7321	+	28.9808i	−0.654776	+	1.13410i	−0.981950	+	0.189141i	$0.939430\pi$
$654$	−2.83013	−	4.90192i	−0.110667	−	0.191680i
$655$	−19.3923	−	19.3923i	−0.757720	−	0.757720i
$656$	22.0885	+	5.91858i	0.862409	+	0.231082i
$657$	−3.03590	+	11.3301i	−0.118442	+	0.442030i
$658$	−3.71281	+	3.21539i	−0.144741	+	0.125349i
$659$	16.3923	+	28.3923i	0.638554	+	1.10601i	0.985750	+	0.168215i	$0.0538002\pi$
$659$	16.3923	+	28.3923i	0.638554	+	1.10601i	−0.347197	+	0.937792i	$0.612866\pi$
$660$	−11.1962	−	6.46410i	−0.435810	−	0.251615i
$661$	8.79423	−	2.35641i	0.342056	−	0.0916536i	−0.0837017	−	0.996491i	$-0.526674\pi$
$661$	8.79423	−	2.35641i	0.342056	−	0.0916536i	0.425758	+	0.904837i	$0.360008\pi$
$662$			3.51666i			0.136679i
$663$	8.30385	+	16.7942i	0.322495	+	0.652234i
$664$			18.9282i			0.734557i
$665$	2.73205	+	14.1962i	0.105944	+	0.550503i
$666$	−2.50000	+	4.33013i	−0.0968730	+	0.167789i
$667$	37.5622	−	21.6865i	1.45441	−	0.839706i
$668$	−0.803848	+	0.803848i	−0.0311018	+	0.0311018i
$669$	2.50962	−	9.36603i	0.0970275	−	0.362111i
$670$	−2.83013	+	10.5622i	−0.109337	+	0.408053i
$671$	−17.6603	−	17.6603i	−0.681767	−	0.681767i
$672$	5.93782	+	12.2321i	0.229056	+	0.471862i
$673$	−32.0429	−	18.5000i	−1.23516	−	0.713123i	−0.267063	−	0.963679i	$-0.586053\pi$
$673$	−32.0429	−	18.5000i	−1.23516	−	0.713123i	−0.968102	+	0.250557i	$0.919386\pi$
$674$	3.27757	+	12.2321i	0.126247	+	0.471161i
$675$	1.26795			0.0488034
$676$	−2.89230	+	22.3301i	−0.111242	+	0.858851i
$677$		−	22.3923i		−	0.860606i	−0.902684	−	0.430303i	$-0.858407\pi$
$677$		−	22.3923i		−	0.860606i	0.902684	−	0.430303i	$-0.141593\pi$
$678$	0.205771	+	0.767949i	0.00790260	+	0.0294929i
$679$	−7.83013	+	11.5622i	−0.300493	+	0.443716i
$680$	16.7942	−	9.69615i	0.644029	−	0.371830i
$681$	6.85641	+	6.85641i	0.262738	+	0.262738i
$682$	8.92820	+	2.39230i	0.341879	+	0.0916061i
$683$	17.7583	+	4.75833i	0.679504	+	0.182072i	0.582032	−	0.813166i	$-0.302258\pi$
$683$	17.7583	+	4.75833i	0.679504	+	0.182072i	0.0974716	+	0.995238i	$0.468924\pi$
$684$	3.46410	+	3.46410i	0.132453	+	0.132453i
$685$	−19.1603	+	11.0622i	−0.732076	+	0.422664i
$686$	−6.45448	+	7.08846i	−0.246433	+	0.270639i
$687$	−4.43782	−	16.5622i	−0.169313	−	0.631886i
$688$			19.7128i			0.751544i
$689$	24.9904	−	12.3564i	0.952058	−	0.470742i
$690$	−6.19615			−0.235883
$691$	2.49038	+	9.29423i	0.0947386	+	0.353569i	0.996980	−	0.0776628i	$-0.0247457\pi$
$691$	2.49038	+	9.29423i	0.0947386	+	0.353569i	−0.902241	+	0.431232i	$0.858079\pi$
$692$	−34.9808	−	20.1962i	−1.32977	−	0.767743i
$693$	−4.46410	−	9.19615i	−0.169577	−	0.349333i
$694$	−2.07180	−	2.07180i	−0.0786443	−	0.0786443i
$695$	−4.09808	+	15.2942i	−0.155449	+	0.580143i
$696$	3.50000	−	13.0622i	0.132667	−	0.495121i
$697$	34.0981	−	34.0981i	1.29156	−	1.29156i
$698$	−2.11731	+	1.22243i	−0.0801415	+	0.0462697i
$699$	−1.00000	+	1.73205i	−0.0378235	+	0.0655122i
$700$	−5.70577	+	1.09808i	−0.215658	+	0.0415034i
$701$		−	34.9282i		−	1.31922i	−0.751608	−	0.659610i	$-0.770721\pi$
$701$		−	34.9282i		−	1.31922i	0.751608	−	0.659610i	$-0.229279\pi$
$702$	−1.23205	−	1.40192i	−0.0465008	−	0.0529122i
$703$		−	27.3205i		−	1.03041i
$704$	8.46410	−	2.26795i	0.319003	−	0.0854766i
$705$	6.00000	+	3.46410i	0.225973	+	0.130466i
$706$	−2.69615	−	4.66987i	−0.101471	−	0.175753i
$707$	−6.80385	−	7.85641i	−0.255885	−	0.295471i
$708$	−0.169873	+	0.633975i	−0.00638422	+	0.0238262i
$709$	5.69615	+	1.52628i	0.213923	+	0.0573206i	0.364189	−	0.931325i	$-0.381346\pi$
$709$	5.69615	+	1.52628i	0.213923	+	0.0573206i	−0.150266	+	0.988646i	$0.548013\pi$
$710$	−4.00000	−	4.00000i	−0.150117	−	0.150117i
$711$	7.83013	+	13.5622i	0.293653	+	0.508621i
$712$	9.83013	−	17.0263i	0.368400	−	0.638087i
$713$	−27.6603	+	7.41154i	−1.03588	+	0.277564i
$714$	7.09808	+	0.509619i	0.265639	+	0.0190720i
$715$	−26.8564	−	1.73205i	−1.00437	−	0.0647750i
$716$	−19.2679			−0.720077
$717$	0.124356	+	0.464102i	0.00464415	+	0.0173322i
$718$	−3.22243	+	5.58142i	−0.120260	+	0.208297i
$719$	−6.29423	−	10.9019i	−0.234735	−	0.406573i	0.724461	−	0.689316i	$-0.242089\pi$
$719$	−6.29423	−	10.9019i	−0.234735	−	0.406573i	−0.959196	+	0.282743i	$0.908756\pi$
$720$	3.36603	−	3.36603i	0.125444	−	0.125444i
$721$	−6.00000	+	17.3205i	−0.223452	+	0.645049i
$722$	−5.50000	−	1.47372i	−0.204689	−	0.0548462i
$723$	17.8301	−	17.8301i	0.663110	−	0.663110i
$724$	−11.8923	+	6.86603i	−0.441974	+	0.255174i
$725$	7.68653	+	4.43782i	0.285471	+	0.164817i
$726$	1.96410	−	0.526279i	0.0728946	−	0.0195321i
$727$	41.1244			1.52522			0.762609	−	0.646860i	$-0.223918\pi$
$727$	41.1244			1.52522			0.762609	+	0.646860i	$0.223918\pi$
$728$	14.5622	+	11.2942i	0.539710	+	0.418592i
$729$	−1.00000			−0.0370370
$730$	11.3301	−	3.03590i	0.419347	−	0.112364i
$731$	36.0000	+	20.7846i	1.33151	+	0.768747i
$732$	9.69615	−	5.59808i	0.358380	−	0.206911i
$733$	−21.6340	+	21.6340i	−0.799069	+	0.799069i	−0.982949	−	0.183880i	$-0.941134\pi$
$733$	−21.6340	+	21.6340i	−0.799069	+	0.799069i	0.183880	+	0.982949i	$0.441134\pi$
$734$	−5.90192	−	1.58142i	−0.217844	−	0.0583711i
$735$	12.4282	+	5.33013i	0.458421	+	0.196605i
$736$	22.5167	−	22.5167i	0.829975	−	0.829975i
$737$	21.1244	+	36.5885i	0.778126	+	1.34775i
$738$	−2.40192	+	4.16025i	−0.0884160	+	0.153141i
$739$	3.92820	+	14.6603i	0.144501	+	0.539286i	0.999777	+	0.0211131i	$0.00672101\pi$
$739$	3.92820	+	14.6603i	0.144501	+	0.539286i	−0.855276	+	0.518173i	$0.826612\pi$
$740$	−32.3205			−1.18813
$741$	9.66025	+	3.26795i	0.354878	+	0.120051i
$742$	0.758330	−	10.5622i	0.0278392	−	0.387750i
$743$	−33.0526	+	8.85641i	−1.21258	+	0.324910i	−0.807774	−	0.589492i	$-0.799328\pi$
$743$	−33.0526	+	8.85641i	−1.21258	+	0.324910i	−0.404807	+	0.914402i	$0.632661\pi$
$744$	−4.46410	+	7.73205i	−0.163662	+	0.283471i
$745$	−1.96410	−	3.40192i	−0.0719591	−	0.124637i
$746$	−8.88269	−	8.88269i	−0.325218	−	0.325218i
$747$	9.46410	+	2.53590i	0.346273	+	0.0927837i
$748$	9.00000	−	33.5885i	0.329073	−	1.22812i
$749$	−12.9282	−	14.9282i	−0.472386	−	0.545465i
$750$	−3.13397	−	5.42820i	−0.114437	−	0.198210i
$751$	−6.12436	−	3.53590i	−0.223481	−	0.129027i	0.384080	−	0.923300i	$-0.374519\pi$
$751$	−6.12436	−	3.53590i	−0.223481	−	0.129027i	−0.607561	+	0.794273i	$0.707852\pi$
$752$	−8.53590	+	2.28719i	−0.311272	+	0.0834051i
$753$		−	27.1244i		−	0.988466i
$754$	−2.56218	−	12.8109i	−0.0933090	−	0.466545i
$755$		0			0
$756$	4.50000	−	0.866025i	0.163663	−	0.0314970i
$757$	−8.00000	+	13.8564i	−0.290765	+	0.503620i	−0.973991	−	0.226587i	$-0.927243\pi$
$757$	−8.00000	+	13.8564i	−0.290765	+	0.503620i	0.683226	+	0.730207i	$0.260576\pi$
$758$	12.5885	−	7.26795i	0.457233	−	0.263984i
$759$	−16.9282	+	16.9282i	−0.614455	+	0.614455i
$760$	2.73205	−	10.1962i	0.0991019	−	0.369853i
$761$	−6.95448	+	25.9545i	−0.252100	+	0.940849i	0.717581	+	0.696475i	$0.245249\pi$
$761$	−6.95448	+	25.9545i	−0.252100	+	0.940849i	−0.969681	+	0.244374i	$0.921417\pi$
$762$	−4.12436	−	4.12436i	−0.149410	−	0.149410i
$763$	26.0263	−	12.6340i	0.942215	−	0.457381i
$764$	−18.8038	−	10.8564i	−0.680299	−	0.392771i
$765$	−2.59808	−	9.69615i	−0.0939336	−	0.350565i
$766$	−8.98076			−0.324488
$767$	0.267949	+	1.33975i	0.00967508	+	0.0483754i
$768$		−	1.39230i		−	0.0502405i
$769$	−7.43782	−	27.7583i	−0.268215	−	1.00099i	−0.960253	−	0.279130i	$-0.909954\pi$
$769$	−7.43782	−	27.7583i	−0.268215	−	1.00099i	0.692038	−	0.721861i	$-0.256713\pi$
$770$	−5.73205	+	8.46410i	−0.206569	+	0.305025i
$771$	8.13397	−	4.69615i	0.292938	−	0.169128i
$772$	10.6865	+	10.6865i	0.384617	+	0.384617i
$773$	−5.63397	−	1.50962i	−0.202640	−	0.0542972i	0.156071	−	0.987746i	$-0.450117\pi$
$773$	−5.63397	−	1.50962i	−0.202640	−	0.0542972i	−0.358711	+	0.933449i	$0.616784\pi$
$774$	−4.00000	−	1.07180i	−0.143777	−	0.0385249i
$775$	−4.14359	−	4.14359i	−0.148842	−	0.148842i
$776$	8.83013	−	5.09808i	0.316983	−	0.183010i
$777$	−21.1603	−	14.3301i	−0.759120	−	0.514090i
$778$	−3.51924	−	13.1340i	−0.126171	−	0.470876i
$779$		−	26.2487i		−	0.940458i
$780$	3.86603	−	11.4282i	0.138426	−	0.409195i
$781$	−21.8564			−0.782084
$782$	−4.31347	−	16.0981i	−0.154249	−	0.575666i
$783$	−6.06218	−	3.50000i	−0.216645	−	0.125080i
$784$	−16.0167	+	6.40192i	−0.572024	+	0.228640i
$785$	1.83013	+	1.83013i	0.0653200	+	0.0653200i
$786$	−1.90192	+	7.09808i	−0.0678394	+	0.253180i
$787$	−3.46410	+	12.9282i	−0.123482	+	0.460841i	−0.999781	−	0.0209267i	$-0.993338\pi$
$787$	−3.46410	+	12.9282i	−0.123482	+	0.460841i	0.876299	+	0.481767i	$0.160005\pi$
$788$	12.4641	−	12.4641i	0.444015	−	0.444015i
$789$	20.1962	−	11.6603i	0.719002	−	0.415116i
$790$	7.83013	−	13.5622i	0.278583	−	0.482521i
$791$	−3.99038	+	0.767949i	−0.141882	+	0.0273051i
$792$			7.46410i			0.265225i
$793$	12.9282	−	19.3923i	0.459094	−	0.688641i
$794$		−	10.4449i		−	0.370674i
$795$	−14.4282	+	3.86603i	−0.511716	+	0.137114i
$796$	27.8038	+	16.0526i	0.985481	+	0.568968i
$797$	1.33975	+	2.32051i	0.0474562	+	0.0821966i	0.888778	−	0.458338i	$-0.151555\pi$
$797$	1.33975	+	2.32051i	0.0474562	+	0.0821966i	−0.841322	+	0.540535i	$0.818222\pi$
$798$	2.92820	−	2.53590i	0.103657	−	0.0897698i
$799$	−4.82309	+	18.0000i	−0.170628	+	0.636794i
$800$	6.29423	+	1.68653i	0.222535	+	0.0596280i
$801$	−7.19615	−	7.19615i	−0.254264	−	0.254264i
$802$	−2.33013	−	4.03590i	−0.0822796	−	0.142513i
$803$	22.6603	−	39.2487i	0.799663	−	1.38506i
$804$	−18.2942	+	4.90192i	−0.645188	+	0.172878i
$805$	2.26795	−	31.5885i	0.0799347	−	1.11335i
$806$	−0.555136	+	8.60770i	−0.0195538	+	0.303193i
$807$	1.07180			0.0377290
$808$	1.96410	+	7.33013i	0.0690969	+	0.257873i
$809$	0.232051	−	0.401924i	0.00815847	−	0.0141309i	−0.861917	−	0.507049i	$-0.830736\pi$
$809$	0.232051	−	0.401924i	0.00815847	−	0.0141309i	0.870076	+	0.492918i	$0.164070\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	12.9282	−	12.9282i	0.453971	−	0.453971i	−0.442699	−	0.896670i	$-0.645979\pi$
$811$	12.9282	−	12.9282i	0.453971	−	0.453971i	0.896670	+	0.442699i	$0.145979\pi$
$812$	30.3109	+	10.5000i	1.06370	+	0.368478i
$813$	4.09808	+	1.09808i	0.143726	+	0.0385112i
$814$	13.6603	−	13.6603i	0.478792	−	0.478792i
$815$	−2.83013	+	1.63397i	−0.0991350	+	0.0572356i
$816$	11.0885	+	6.40192i	0.388174	+	0.224112i
$817$	21.8564	−	5.85641i	0.764659	−	0.204890i
$818$	0.124356			0.00434799
$819$	7.59808	−	5.76795i	0.265498	−	0.201548i
$820$	−31.0526			−1.08440
$821$	−6.56218	+	1.75833i	−0.229022	+	0.0613661i	−0.371505	−	0.928431i	$-0.621158\pi$
$821$	−6.56218	+	1.75833i	−0.229022	+	0.0613661i	0.142483	+	0.989797i	$0.454491\pi$
$822$	5.13397	+	2.96410i	0.179068	+	0.103385i
$823$	−0.215390	+	0.124356i	−0.00750803	+	0.00433477i	−0.503749	−	0.863850i	$-0.668046\pi$
$823$	−0.215390	+	0.124356i	−0.00750803	+	0.00433477i	0.496241	+	0.868185i	$0.334713\pi$
$824$	9.46410	−	9.46410i	0.329698	−	0.329698i
$825$	−4.73205	−	1.26795i	−0.164749	−	0.0441443i
$826$	0.490381	+	0.169873i	0.0170625	+	0.00591064i
$827$	−37.9282	+	37.9282i	−1.31889	+	1.31889i	−0.404240	+	0.914653i	$0.632464\pi$
$827$	−37.9282	+	37.9282i	−1.31889	+	1.31889i	−0.914653	+	0.404240i	$0.867536\pi$
$828$	−5.36603	−	9.29423i	−0.186482	−	0.322997i
$829$	6.99038	−	12.1077i	0.242786	−	0.420518i	−0.718721	−	0.695299i	$-0.755272\pi$
$829$	6.99038	−	12.1077i	0.242786	−	0.420518i	0.961507	+	0.274781i	$0.0886054\pi$
$830$	−2.53590	−	9.46410i	−0.0880223	−	0.328504i
$831$	−17.5885			−0.610137
$832$	3.62436	+	7.33013i	0.125652	+	0.254126i
$833$	−5.19615	+	36.0000i	−0.180036	+	1.24733i
$834$	4.09808	−	1.09808i	0.141905	−	0.0380233i
$835$	0.633975	−	1.09808i	0.0219396	−	0.0380005i
$836$	−9.46410	−	16.3923i	−0.327323	−	0.566940i
$837$	3.26795	+	3.26795i	0.112957	+	0.112957i
$838$	5.39230	+	1.44486i	0.186274	+	0.0499120i
$839$	6.43782	−	24.0263i	0.222258	−	0.829479i	−0.761226	−	0.648487i	$-0.775402\pi$
$839$	6.43782	−	24.0263i	0.222258	−	0.829479i	0.983484	−	0.180993i	$-0.0579311\pi$
$840$	−6.46410	−	7.46410i	−0.223033	−	0.257536i
$841$	−10.0000	−	17.3205i	−0.344828	−	0.597259i
$842$	17.5981	+	10.1603i	0.606470	+	0.350145i
$843$	−15.0622	+	4.03590i	−0.518769	+	0.139004i
$844$			14.5359i			0.500346i
$845$	−3.33013	−	24.8923i	−0.114560	−	0.856321i
$846$		−	1.85641i		−	0.0638246i
$847$	1.96410	+	10.2058i	0.0674873	+	0.350674i
$848$	9.52628	−	16.5000i	0.327134	−	0.566612i
$849$	10.8564	−	6.26795i	0.372591	−	0.215115i
$850$	2.41154	−	2.41154i	0.0827152	−	0.0827152i
$851$	−15.4904	+	57.8109i	−0.531003	+	1.98173i
$852$	2.53590	−	9.46410i	0.0868784	−	0.324235i
$853$	2.43782	+	2.43782i	0.0834694	+	0.0834694i	0.747609	−	0.664139i	$-0.231202\pi$
$853$	2.43782	+	2.43782i	0.0834694	+	0.0834694i	−0.664139	+	0.747609i	$0.731202\pi$
$854$	−3.86603	−	7.96410i	−0.132293	−	0.272526i
$855$	−4.73205	−	2.73205i	−0.161833	−	0.0934342i
$856$	3.73205	+	13.9282i	0.127559	+	0.476056i
$857$	21.6795			0.740557			0.370279	−	0.928921i	$-0.379262\pi$
$857$	21.6795			0.740557			0.370279	+	0.928921i	$0.379262\pi$
$858$	3.19615	+	6.46410i	0.109115	+	0.220681i
$859$		−	3.51666i		−	0.119987i	−0.998199	−	0.0599935i	$-0.980892\pi$
$859$		−	3.51666i		−	0.119987i	0.998199	−	0.0599935i	$-0.0191080\pi$
$860$	−6.92820	−	25.8564i	−0.236250	−	0.881696i
$861$	−20.3301	−	13.7679i	−0.692849	−	0.469210i
$862$	−1.22243	+	0.705771i	−0.0416362	+	0.0240387i
$863$	15.8564	+	15.8564i	0.539758	+	0.539758i	0.923458	−	0.383700i	$-0.125350\pi$
$863$	15.8564	+	15.8564i	0.539758	+	0.539758i	−0.383700	+	0.923458i	$0.625350\pi$
$864$	−4.96410	−	1.33013i	−0.168882	−	0.0452518i
$865$	43.5167	+	11.6603i	1.47961	+	0.396461i
$866$	−3.70577	−	3.70577i	−0.125927	−	0.125927i
$867$	8.66025	−	5.00000i	0.294118	−	0.169809i
$868$	−17.5359	−	11.8756i	−0.595207	−	0.403086i
$869$	−15.6603	−	58.4449i	−0.531238	−	1.98261i
$870$			7.00000i			0.237322i
$871$	−29.6147	+	26.0263i	−1.00346	+	0.881867i
$872$	−21.1244			−0.715361
$873$	−1.36603	−	5.09808i	−0.0462330	−	0.172544i
$874$	−7.85641	−	4.53590i	−0.265747	−	0.153429i
$875$	28.8205	−	13.9904i	0.974311	−	0.472961i
$876$	14.3660	+	14.3660i	0.485383	+	0.485383i
$877$	−13.8468	+	51.6769i	−0.467573	+	1.74501i	0.180643	+	0.983549i	$0.442182\pi$
$877$	−13.8468	+	51.6769i	−0.467573	+	1.74501i	−0.648216	+	0.761457i	$0.724485\pi$
$878$	5.39230	−	20.1244i	0.181981	−	0.679164i
$879$	−0.705771	+	0.705771i	−0.0238051	+	0.0238051i
$880$	−15.9282	+	9.19615i	−0.536940	+	0.310002i
$881$	−19.6244	+	33.9904i	−0.661161	+	1.14517i	0.319149	+	0.947704i	$0.396603\pi$
$881$	−19.6244	+	33.9904i	−0.661161	+	1.14517i	−0.980311	+	0.197461i	$0.936731\pi$
$882$	−0.428203	−	3.59808i	−0.0144184	−	0.121154i
$883$		−	27.0718i		−	0.911038i	−0.890226	−	0.455519i	$-0.849454\pi$
$883$		−	27.0718i		−	0.911038i	0.890226	−	0.455519i	$-0.150546\pi$
$884$	32.3827	+	2.08846i	1.08915	+	0.0702424i
$885$		−	0.732051i		−	0.0246076i
$886$	5.19615	−	1.39230i	0.174568	−	0.0467754i
$887$	41.1051	+	23.7321i	1.38017	+	0.796844i	0.992180	−	0.124817i	$-0.0398344\pi$
$887$	41.1051	+	23.7321i	1.38017	+	0.796844i	0.387995	+	0.921661i	$0.373168\pi$
$888$	9.33013	+	16.1603i	0.313099	+	0.542303i
$889$	22.5359	−	19.5167i	0.755830	−	0.654568i
$890$	−2.63397	+	9.83013i	−0.0882910	+	0.329507i
$891$	3.73205	+	1.00000i	0.125028	+	0.0335013i
$892$	−11.8756	−	11.8756i	−0.397626	−	0.397626i
$893$	5.07180	+	8.78461i	0.169721	+	0.293966i
$894$	−0.526279	+	0.911543i	−0.0176014	+	0.0304865i
$895$	20.7583	−	5.56218i	0.693874	−	0.185923i
$896$	30.2224	+	2.16987i	1.00966	+	0.0724904i
$897$	−18.5885	−	12.3923i	−0.620651	−	0.413767i
$898$	3.12436			0.104261
$899$	8.37307	+	31.2487i	0.279257	+	1.04220i
$900$	1.09808	−	1.90192i	0.0366025	−	0.0633975i
$901$	−20.0885	−	34.7942i	−0.669244	−	1.15916i
$902$	13.1244	−	13.1244i	0.436993	−	0.436993i
$903$	6.92820	−	20.0000i	0.230556	−	0.665558i
$904$	2.86603	+	0.767949i	0.0953226	+	0.0255416i
$905$	10.8301	−	10.8301i	0.360006	−	0.360006i
$906$		0			0
$907$	−21.0788	−	12.1699i	−0.699911	−	0.404094i	0.107403	−	0.994216i	$-0.465746\pi$
$907$	−21.0788	−	12.1699i	−0.699911	−	0.404094i	−0.807314	+	0.590122i	$0.799080\pi$
$908$	16.2224	−	4.34679i	0.538360	−	0.144253i
$909$	3.92820			0.130290
$910$	−8.79423	−	3.69615i	−0.291526	−	0.122526i
$911$	−5.07180			−0.168036			−0.0840181	−	0.996464i	$-0.526775\pi$
$911$	−5.07180			−0.168036			−0.0840181	+	0.996464i	$0.526775\pi$
$912$	6.73205	−	1.80385i	0.222920	−	0.0597314i
$913$	−32.7846	−	18.9282i	−1.08501	−	0.626432i
$914$	−12.7750	+	7.37564i	−0.422559	+	0.243965i
$915$	−8.83013	+	8.83013i	−0.291915	+	0.291915i
$916$	−28.6865	−	7.68653i	−0.947830	−	0.253970i
$917$	−35.4904	−	12.2942i	−1.17200	−	0.405991i
$918$	−1.90192	+	1.90192i	−0.0627728	+	0.0627728i
$919$	7.22243	+	12.5096i	0.238246	+	0.412654i	0.960211	−	0.279275i	$-0.0900942\pi$
$919$	7.22243	+	12.5096i	0.238246	+	0.412654i	−0.721965	+	0.691930i	$0.756761\pi$
$920$	−11.5622	+	20.0263i	−0.381194	+	0.660247i
$921$	1.43782	+	5.36603i	0.0473779	+	0.176817i
$922$	1.09103			0.0359313
$923$	−4.00000	−	20.0000i	−0.131662	−	0.658308i
$924$	−17.6603	−	1.26795i	−0.580980	−	0.0417125i
$925$	−11.8301	+	3.16987i	−0.388972	+	0.104225i
$926$	−3.00000	+	5.19615i	−0.0985861	+	0.170756i
$927$	−3.46410	−	6.00000i	−0.113776	−	0.197066i
$928$	−25.4378	−	25.4378i	−0.835037	−	0.835037i
$929$	−56.0429	−	15.0167i	−1.83871	−	0.492681i	−0.839958	−	0.542651i	$-0.817421\pi$
$929$	−56.0429	−	15.0167i	−1.83871	−	0.492681i	−0.998751	+	0.0499700i	$0.984087\pi$
$930$	1.19615	−	4.46410i	0.0392234	−	0.146384i
$931$	11.8564	+	15.8564i	0.388578	+	0.519673i
$932$	1.73205	+	3.00000i	0.0567352	+	0.0982683i
$933$	11.8301	+	6.83013i	0.387301	+	0.223608i
$934$	−15.3923	+	4.12436i	−0.503652	+	0.134953i
$935$			38.7846i			1.26839i
$936$	−6.83013	+	1.36603i	−0.223250	+	0.0446499i
$937$			47.1051i			1.53886i	0.638733	+	0.769429i	$0.279459\pi$
$937$			47.1051i			1.53886i	−0.638733	+	0.769429i	$0.720541\pi$
$938$	2.83013	+	14.7058i	0.0924069	+	0.480160i
$939$	−4.80385	+	8.32051i	−0.156768	+	0.271530i
$940$	10.3923	−	6.00000i	0.338960	−	0.195698i
$941$	−38.3205	+	38.3205i	−1.24921	+	1.24921i	−0.293145	+	0.956068i	$0.594702\pi$
$941$	−38.3205	+	38.3205i	−1.24921	+	1.24921i	−0.956068	+	0.293145i	$0.905298\pi$
$942$	0.179492	−	0.669873i	0.00584816	−	0.0218256i
$943$	−14.8827	+	55.5429i	−0.484647	+	1.80873i
$944$	0.660254	+	0.660254i	0.0214894	+	0.0214894i
$945$	−4.59808	+	2.23205i	−0.149575	+	0.0726086i
$946$	13.8564	+	8.00000i	0.450511	+	0.260102i
$947$	5.60770	+	20.9282i	0.182226	+	0.680075i	0.995207	+	0.0977862i	$0.0311761\pi$
$947$	5.60770	+	20.9282i	0.182226	+	0.680075i	−0.812982	+	0.582289i	$0.802157\pi$
$948$	27.1244			0.880958
$949$	40.0622	+	13.5526i	1.30047	+	0.439935i
$950$		−	1.85641i		−	0.0602298i
$951$	8.33013	+	31.0885i	0.270123	+	1.00811i
$952$	14.8923	−	21.9904i	0.482662	−	0.712712i
$953$	23.9090	−	13.8038i	0.774487	−	0.447150i	−0.0599857	−	0.998199i	$-0.519106\pi$
$953$	23.9090	−	13.8038i	0.774487	−	0.447150i	0.834473	+	0.551049i	$0.185772\pi$
$954$	2.83013	+	2.83013i	0.0916287	+	0.0916287i
$955$	23.3923	+	6.26795i	0.756957	+	0.202826i
$956$	0.803848	+	0.215390i	0.0259983	+	0.00696622i
$957$	19.1244	+	19.1244i	0.618203	+	0.618203i
$958$	7.05256	−	4.07180i	0.227858	−	0.131554i
$959$	−16.9904	+	25.0885i	−0.548648	+	0.810149i
$960$	−1.13397	−	4.23205i	−0.0365989	−	0.136589i
$961$			9.64102i			0.311001i
$962$	15.0000	+	10.0000i	0.483619	+	0.322413i
$963$	7.46410			0.240527
$964$	−11.3038	−	42.1865i	−0.364072	−	1.35874i
$965$	−14.5981	−	8.42820i	−0.469929	−	0.271313i
$966$	−7.63397	+	3.70577i	−0.245619	+	0.119231i
$967$	−8.85641	−	8.85641i	−0.284803	−	0.284803i	0.550218	−	0.835021i	$-0.314545\pi$
$967$	−8.85641	−	8.85641i	−0.284803	−	0.284803i	−0.835021	+	0.550218i	$0.814545\pi$
$968$	1.96410	−	7.33013i	0.0631286	−	0.235599i
$969$	3.80385	−	14.1962i	0.122197	−	0.456046i
$970$	−3.73205	+	3.73205i	−0.119829	+	0.119829i
$971$	21.8827	−	12.6340i	0.702249	−	0.405444i	−0.105936	−	0.994373i	$-0.533784\pi$
$971$	21.8827	−	12.6340i	0.702249	−	0.405444i	0.808184	+	0.588929i	$0.200450\pi$
$972$	−0.866025	+	1.50000i	−0.0277778	+	0.0481125i
$973$	4.09808	+	21.2942i	0.131378	+	0.682662i
$974$		−	1.90897i		−	0.0611672i
$975$	0.294229	−	4.56218i	0.00942286	−	0.146107i
$976$		−	15.9282i		−	0.509849i
$977$	49.8205	−	13.3494i	1.59390	−	0.427084i	0.650706	−	0.759330i	$-0.274473\pi$
$977$	49.8205	−	13.3494i	1.59390	−	0.427084i	0.943193	+	0.332245i	$0.107806\pi$
$978$	0.758330	+	0.437822i	0.0242487	+	0.0140000i
$979$	19.6603	+	34.0526i	0.628344	+	1.08832i
$980$	18.7583	−	14.0263i	0.599213	−	0.448053i
$981$	−2.83013	+	10.5622i	−0.0903590	+	0.337224i
$982$	−6.29423	−	1.68653i	−0.200857	−	0.0538194i
$983$	36.1244	+	36.1244i	1.15219	+	1.15219i	0.986113	+	0.166075i	$0.0531093\pi$
$983$	36.1244	+	36.1244i	1.15219	+	1.15219i	0.166075	+	0.986113i	$0.446891\pi$
$984$	8.96410	+	15.5263i	0.285765	+	0.494960i
$985$	−9.83013	+	17.0263i	−0.313214	+	0.542502i
$986$	−18.1865	+	4.87307i	−0.579177	+	0.155190i
$987$	9.46410	+	0.679492i	0.301246	+	0.0216285i
$988$	13.2679	−	11.6603i	0.422110	−	0.370962i
$989$	−49.5692			−1.57621
$990$	−1.00000	−	3.73205i	−0.0317821	−	0.118612i
$991$	8.36603	−	14.4904i	0.265756	−	0.460302i	−0.702006	−	0.712171i	$-0.747712\pi$
$991$	8.36603	−	14.4904i	0.265756	−	0.460302i	0.967761	+	0.251869i	$0.0810453\pi$
$992$	11.8756	+	20.5692i	0.377052	+	0.653073i
$993$	4.80385	−	4.80385i	0.152445	−	0.152445i
$994$	−7.32051	−	2.53590i	−0.232192	−	0.0804338i
$995$	−34.5885	−	9.26795i	−1.09653	−	0.293814i
$996$	12.0000	−	12.0000i	0.380235	−	0.380235i
$997$	27.8660	−	16.0885i	0.882526	−	0.509527i	0.0110355	−	0.999939i	$-0.496487\pi$
$997$	27.8660	−	16.0885i	0.882526	−	0.509527i	0.871490	+	0.490413i	$0.163154\pi$
$998$	−1.51666	−	0.875644i	−0.0480090	−	0.0277180i
$999$	9.33013	−	2.50000i	0.295192	−	0.0790965i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.by.b.202.1	yes	4
3.2	odd	2		819.2.fm.a.748.1		4
7.6	odd	2		273.2.by.a.202.1	✓	4
13.2	odd	12		273.2.by.a.223.1	yes	4
21.20	even	2		819.2.fm.b.748.1		4
39.2	even	12		819.2.fm.b.496.1		4
91.41	even	12	inner	273.2.by.b.223.1	yes	4
273.41	odd	12		819.2.fm.a.496.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.by.a.202.1	✓	4	7.6	odd	2
273.2.by.a.223.1	yes	4	13.2	odd	12
273.2.by.b.202.1	yes	4	1.1	even	1	trivial
273.2.by.b.223.1	yes	4	91.41	even	12	inner
819.2.fm.a.496.1		4	273.41	odd	12
819.2.fm.a.748.1		4	3.2	odd	2
819.2.fm.b.496.1		4	39.2	even	12
819.2.fm.b.748.1		4	21.20	even	2

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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.133975i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.36603 - 1.36603i) q^{5} +(-0.500000 - 0.133975i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-1.36603 + 1.36603i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.133975i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-1.50000 + 0.866025i) q^{4} +(1.36603 - 1.36603i) q^{5} +(-0.500000 - 0.133975i) q^{6} +(0.866025 - 2.50000i) q^{7} +(-1.36603 + 1.36603i) q^{8} +(0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(-1.00000 - 3.73205i) q^{11} +1.73205 q^{12} +(3.23205 - 1.59808i) q^{13} +(0.0980762 - 1.36603i) q^{14} +(-1.86603 + 0.500000i) q^{15} +(1.23205 - 2.13397i) q^{16} +(-2.59808 - 4.50000i) q^{17} +(0.366025 + 0.366025i) q^{18} +(-2.73205 - 0.732051i) q^{19} +(-0.866025 + 3.23205i) q^{20} +(-2.00000 + 1.73205i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(5.36603 + 3.09808i) q^{23} +(1.86603 - 0.500000i) q^{24} +1.26795i q^{25} +(1.40192 - 1.23205i) q^{26} -1.00000i q^{27} +(0.866025 + 4.50000i) q^{28} +(3.50000 - 6.06218i) q^{29} +(-0.866025 + 0.500000i) q^{30} +(-3.26795 + 3.26795i) q^{31} +(1.33013 - 4.96410i) q^{32} +(-1.00000 + 3.73205i) q^{33} +(-1.90192 - 1.90192i) q^{34} +(-2.23205 - 4.59808i) q^{35} +(-1.50000 - 0.866025i) q^{36} +(2.50000 + 9.33013i) q^{37} -1.46410 q^{38} +(-3.59808 - 0.232051i) q^{39} +3.73205i q^{40} +(2.40192 + 8.96410i) q^{41} +(-0.767949 + 1.13397i) q^{42} +(-6.92820 + 4.00000i) q^{43} +(4.73205 + 4.73205i) q^{44} +(1.86603 + 0.500000i) q^{45} +(3.09808 + 0.830127i) q^{46} +(-2.53590 - 2.53590i) q^{47} +(-2.13397 + 1.23205i) q^{48} +(-5.50000 - 4.33013i) q^{49} +(0.169873 + 0.633975i) q^{50} +5.19615i q^{51} +(-3.46410 + 5.19615i) q^{52} +7.73205 q^{53} +(-0.133975 - 0.500000i) q^{54} +(-6.46410 - 3.73205i) q^{55} +(2.23205 + 4.59808i) q^{56} +(2.00000 + 2.00000i) q^{57} +(0.937822 - 3.50000i) q^{58} +(-0.0980762 + 0.366025i) q^{59} +(2.36603 - 2.36603i) q^{60} +(5.59808 - 3.23205i) q^{61} +(-1.19615 + 2.07180i) q^{62} +(2.59808 - 0.500000i) q^{63} +2.26795i q^{64} +(2.23205 - 6.59808i) q^{65} +2.00000i q^{66} +(-10.5622 + 2.83013i) q^{67} +(7.79423 + 4.50000i) q^{68} +(-3.09808 - 5.36603i) q^{69} +(-1.73205 - 2.00000i) q^{70} +(1.46410 - 5.46410i) q^{71} +(-1.86603 - 0.500000i) q^{72} +(8.29423 + 8.29423i) q^{73} +(2.50000 + 4.33013i) q^{74} +(0.633975 - 1.09808i) q^{75} +(4.73205 - 1.26795i) q^{76} +(-10.1962 - 0.732051i) q^{77} +(-1.83013 + 0.366025i) q^{78} +15.6603 q^{79} +(-1.23205 - 4.59808i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(2.40192 + 4.16025i) q^{82} +(6.92820 - 6.92820i) q^{83} +(1.50000 - 4.33013i) q^{84} +(-9.69615 - 2.59808i) q^{85} +(-2.92820 + 2.92820i) q^{86} +(-6.06218 + 3.50000i) q^{87} +(6.46410 + 3.73205i) q^{88} +(-9.83013 + 2.63397i) q^{89} +1.00000 q^{90} +(-1.19615 - 9.46410i) q^{91} -10.7321 q^{92} +(4.46410 - 1.19615i) q^{93} +(-1.60770 - 0.928203i) q^{94} +(-4.73205 + 2.73205i) q^{95} +(-3.63397 + 3.63397i) q^{96} +(-5.09808 - 1.36603i) q^{97} +(-3.33013 - 1.42820i) q^{98} +(2.73205 - 2.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 6 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 4 q^{11} + 6 q^{13} - 10 q^{14} - 4 q^{15} - 2 q^{16} - 2 q^{18} - 4 q^{19} - 8 q^{21} - 4 q^{22} + 18 q^{23} + 4 q^{24} + 16 q^{26} + 14 q^{29} - 20 q^{31} - 12 q^{32} - 4 q^{33} - 18 q^{34} - 2 q^{35} - 6 q^{36} + 10 q^{37} + 8 q^{38} - 4 q^{39} + 20 q^{41} - 10 q^{42} + 12 q^{44} + 4 q^{45} + 2 q^{46} - 24 q^{47} - 12 q^{48} - 22 q^{49} + 18 q^{50} + 24 q^{53} - 4 q^{54} - 12 q^{55} + 2 q^{56} + 8 q^{57} + 28 q^{58} + 10 q^{59} + 6 q^{60} + 12 q^{61} + 16 q^{62} + 2 q^{65} - 18 q^{67} - 2 q^{69} - 8 q^{71} - 4 q^{72} + 2 q^{73} + 10 q^{74} + 6 q^{75} + 12 q^{76} - 20 q^{77} + 10 q^{78} + 28 q^{79} + 2 q^{80} - 2 q^{81} + 20 q^{82} + 6 q^{84} - 18 q^{85} + 16 q^{86} + 12 q^{88} - 22 q^{89} + 4 q^{90} + 16 q^{91} - 36 q^{92} + 4 q^{93} - 48 q^{94} - 12 q^{95} - 18 q^{96} - 10 q^{97} + 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 - 6 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 4 * q^11 + 6 * q^13 - 10 * q^14 - 4 * q^15 - 2 * q^16 - 2 * q^18 - 4 * q^19 - 8 * q^21 - 4 * q^22 + 18 * q^23 + 4 * q^24 + 16 * q^26 + 14 * q^29 - 20 * q^31 - 12 * q^32 - 4 * q^33 - 18 * q^34 - 2 * q^35 - 6 * q^36 + 10 * q^37 + 8 * q^38 - 4 * q^39 + 20 * q^41 - 10 * q^42 + 12 * q^44 + 4 * q^45 + 2 * q^46 - 24 * q^47 - 12 * q^48 - 22 * q^49 + 18 * q^50 + 24 * q^53 - 4 * q^54 - 12 * q^55 + 2 * q^56 + 8 * q^57 + 28 * q^58 + 10 * q^59 + 6 * q^60 + 12 * q^61 + 16 * q^62 + 2 * q^65 - 18 * q^67 - 2 * q^69 - 8 * q^71 - 4 * q^72 + 2 * q^73 + 10 * q^74 + 6 * q^75 + 12 * q^76 - 20 * q^77 + 10 * q^78 + 28 * q^79 + 2 * q^80 - 2 * q^81 + 20 * q^82 + 6 * q^84 - 18 * q^85 + 16 * q^86 + 12 * q^88 - 22 * q^89 + 4 * q^90 + 16 * q^91 - 36 * q^92 + 4 * q^93 - 48 * q^94 - 12 * q^95 - 18 * q^96 - 10 * q^97 + 4 * q^98 + 4 * q^99

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