LMFDB - Embedded newform 189.2.bd.a.47.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(47,189)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(189, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([7, 15]))

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

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

chi := DirichletCharacter("189.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.bd (of order $18$, degree $6$, 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:	$1.50917259820$
Analytic rank:	$0$
Dimension:	$132$
Relative dimension:	$22$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			47.13
Character	$\chi$	$=$	189.47
Dual form			189.2.bd.a.185.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.245063 + 0.0432112i) q^{2} +(1.36915 + 1.06086i) q^{3} +(-1.82120 - 0.662861i) q^{4} +(1.99870 + 0.727467i) q^{5} +(0.289688 + 0.319140i) q^{6} +(0.302346 + 2.62842i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(0.749157 + 2.90496i) q^{9} +O(q^{10})$	\(q+(0.245063 + 0.0432112i) q^{2} +(1.36915 + 1.06086i) q^{3} +(-1.82120 - 0.662861i) q^{4} +(1.99870 + 0.727467i) q^{5} +(0.289688 + 0.319140i) q^{6} +(0.302346 + 2.62842i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(0.749157 + 2.90496i) q^{9} +(0.458373 + 0.264642i) q^{10} +(-0.489168 - 1.34398i) q^{11} +(-1.79029 - 2.83959i) q^{12} +(1.30709 - 3.59121i) q^{13} +(-0.0394834 + 0.657193i) q^{14} +(1.96479 + 3.11635i) q^{15} +(2.78250 + 2.33479i) q^{16} +(0.109097 - 0.188961i) q^{17} +(0.0580640 + 0.744269i) q^{18} +(2.56992 - 1.48374i) q^{19} +(-3.15782 - 2.64972i) q^{20} +(-2.37442 + 3.91945i) q^{21} +(-0.0618021 - 0.350497i) q^{22} +(-7.61556 + 1.34283i) q^{23} +(-0.642162 - 1.57118i) q^{24} +(-0.364628 - 0.305959i) q^{25} +(0.475500 - 0.823590i) q^{26} +(-2.05604 + 4.77208i) q^{27} +(1.19165 - 4.98728i) q^{28} +(-1.78349 - 4.90009i) q^{29} +(0.346835 + 0.848603i) q^{30} +(1.32486 - 3.64001i) q^{31} +(1.84082 + 2.19380i) q^{32} +(0.756026 - 2.35905i) q^{33} +(0.0349009 - 0.0415932i) q^{34} +(-1.30779 + 5.47337i) q^{35} +(0.561220 - 5.78708i) q^{36} +6.01251 q^{37} +(0.693906 - 0.252561i) q^{38} +(5.59937 - 3.53027i) q^{39} +(-1.33980 - 1.59671i) q^{40} +(-10.0627 - 3.66253i) q^{41} +(-0.751248 + 0.857911i) q^{42} +(1.29579 - 7.34878i) q^{43} +2.77190i q^{44} +(-0.615920 + 6.35112i) q^{45} -1.92432 q^{46} +(-5.51793 + 2.00836i) q^{47} +(1.33278 + 6.14853i) q^{48} +(-6.81717 + 1.58938i) q^{49} +(-0.0761360 - 0.0907353i) q^{50} +(0.349832 - 0.142981i) q^{51} +(-4.76094 + 5.67387i) q^{52} +(12.1036 - 6.98800i) q^{53} +(-0.710066 + 1.08062i) q^{54} -3.04206i q^{55} +(1.03129 - 2.37882i) q^{56} +(5.09265 + 0.694850i) q^{57} +(-0.225328 - 1.27790i) q^{58} +(-1.21070 + 1.01590i) q^{59} +(-1.51255 - 6.97787i) q^{60} +(1.45500 + 3.99757i) q^{61} +(0.481963 - 0.834784i) q^{62} +(-7.40893 + 2.84740i) q^{63} +(-3.27598 - 5.67416i) q^{64} +(5.22497 - 6.22688i) q^{65} +(0.287211 - 0.545447i) q^{66} +(2.59043 + 14.6911i) q^{67} +(-0.323942 + 0.271820i) q^{68} +(-11.8514 - 6.24050i) q^{69} +(-0.557002 + 1.28481i) q^{70} +(-4.29452 + 2.47944i) q^{71} +(0.787586 - 2.83243i) q^{72} +2.46806i q^{73} +(1.47344 + 0.259808i) q^{74} +(-0.174652 - 0.805724i) q^{75} +(-5.66384 + 0.998688i) q^{76} +(3.38464 - 1.69209i) q^{77} +(1.52475 - 0.623182i) q^{78} +(-0.675969 + 3.83361i) q^{79} +(3.86290 + 6.69073i) q^{80} +(-7.87753 + 4.35254i) q^{81} +(-2.30773 - 1.33237i) q^{82} +(-0.141502 + 0.0515026i) q^{83} +(6.92235 - 5.56418i) q^{84} +(0.355515 - 0.298313i) q^{85} +(0.635099 - 1.74492i) q^{86} +(2.75644 - 8.60100i) q^{87} +(-0.243381 + 1.38028i) q^{88} +(3.40271 + 5.89366i) q^{89} +(-0.425379 + 1.52981i) q^{90} +(9.83439 + 2.34980i) q^{91} +(14.7595 + 2.60251i) q^{92} +(5.67547 - 3.57825i) q^{93} +(-1.43902 + 0.253739i) q^{94} +(6.21587 - 1.09603i) q^{95} +(0.193047 + 4.95649i) q^{96} +(12.2644 + 2.16255i) q^{97} +(-1.73932 + 0.0949204i) q^{98} +(3.53773 - 2.42786i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.245063	+	0.0432112i	0.173286	+	0.0305549i	0.259618	−	0.965711i	$-0.416403\pi$
$2$	0.245063	+	0.0432112i	0.173286	+	0.0305549i	−0.0863320	+	0.996266i	$0.527515\pi$
$3$	1.36915	+	1.06086i	0.790481	+	0.612487i
$3$	1.36915	+	1.06086i	0.790481	+	0.612487i
$4$	−1.82120	−	0.662861i	−0.910598	−	0.331431i
$5$	1.99870	+	0.727467i	0.893846	+	0.325333i	0.747784	−	0.663942i	$-0.231118\pi$
$5$	1.99870	+	0.727467i	0.893846	+	0.325333i	0.146062	+	0.989275i	$0.453340\pi$
$6$	0.289688	+	0.319140i	0.118264	+	0.130288i
$7$	0.302346	+	2.62842i	0.114276	+	0.993449i
$7$	0.302346	+	2.62842i	0.114276	+	0.993449i
$8$	−0.848674	−	0.489982i	−0.300052	−	0.173235i
$9$	0.749157	+	2.90496i	0.249719	+	0.968318i
$10$	0.458373	+	0.264642i	0.144950	+	0.0836870i
$11$	−0.489168	−	1.34398i	−0.147490	−	0.405225i	0.843845	−	0.536588i	$-0.180287\pi$
$11$	−0.489168	−	1.34398i	−0.147490	−	0.405225i	−0.991334	+	0.131363i	$0.958065\pi$
$12$	−1.79029	−	2.83959i	−0.516813	−	0.819719i
$13$	1.30709	−	3.59121i	0.362522	−	0.996021i	−0.615613	−	0.788049i	$-0.711091\pi$
$13$	1.30709	−	3.59121i	0.362522	−	0.996021i	0.978135	−	0.207972i	$-0.0666864\pi$
$14$	−0.0394834	+	0.657193i	−0.0105524	+	0.175642i
$15$	1.96479	+	3.11635i	0.507305	+	0.804639i
$16$	2.78250	+	2.33479i	0.695625	+	0.583699i
$17$	0.109097	−	0.188961i	0.0264599	−	0.0458299i	−0.852492	−	0.522740i	$-0.824910\pi$
$17$	0.109097	−	0.188961i	0.0264599	−	0.0458299i	0.878952	+	0.476910i	$0.158243\pi$
$18$	0.0580640	+	0.744269i	0.0136858	+	0.175426i
$19$	2.56992	−	1.48374i	0.589579	−	0.340394i	−0.175352	−	0.984506i	$-0.556106\pi$
$19$	2.56992	−	1.48374i	0.589579	−	0.340394i	0.764931	+	0.644112i	$0.222773\pi$
$20$	−3.15782	−	2.64972i	−0.706109	−	0.592496i
$21$	−2.37442	+	3.91945i	−0.518142	+	0.855295i
$22$	−0.0618021	−	0.350497i	−0.0131762	−	0.0747262i
$23$	−7.61556	+	1.34283i	−1.58795	+	0.279999i	−0.896709	−	0.442621i	$-0.854049\pi$
$23$	−7.61556	+	1.34283i	−1.58795	+	0.279999i	−0.691246	+	0.722620i	$0.742938\pi$
$24$	−0.642162	−	1.57118i	−0.131081	−	0.320717i
$25$	−0.364628	−	0.305959i	−0.0729256	−	0.0611919i
$26$	0.475500	−	0.823590i	0.0932532	−	0.161519i
$27$	−2.05604	+	4.77208i	−0.395684	+	0.918387i
$28$	1.19165	−	4.98728i	0.225200	−	0.942508i
$29$	−1.78349	−	4.90009i	−0.331185	−	0.909924i	−0.987804	−	0.155702i	$-0.950236\pi$
$29$	−1.78349	−	4.90009i	−0.331185	−	0.909924i	0.656619	−	0.754223i	$-0.271986\pi$
$30$	0.346835	+	0.848603i	0.0633231	+	0.154933i
$31$	1.32486	−	3.64001i	0.237951	−	0.653766i	−0.762029	−	0.647543i	$-0.775797\pi$
$31$	1.32486	−	3.64001i	0.237951	−	0.653766i	0.999981	−	0.00622334i	$-0.00198096\pi$
$32$	1.84082	+	2.19380i	0.325413	+	0.387813i
$33$	0.756026	−	2.35905i	0.131607	−	0.410658i
$34$	0.0349009	−	0.0415932i	0.00598545	−	0.00713318i
$35$	−1.30779	+	5.47337i	−0.221057	+	0.925168i
$36$	0.561220	−	5.78708i	0.0935367	−	0.964514i
$37$	6.01251			0.988450			0.494225	−	0.869334i	$-0.335452\pi$
$37$	6.01251			0.988450			0.494225	+	0.869334i	$0.335452\pi$
$38$	0.693906	−	0.252561i	0.112566	−	0.0409708i
$39$	5.59937	−	3.53027i	0.896617	−	0.565295i
$40$	−1.33980	−	1.59671i	−0.211841	−	0.252462i
$41$	−10.0627	−	3.66253i	−1.57153	−	0.571990i	−0.598190	−	0.801354i	$-0.704113\pi$
$41$	−10.0627	−	3.66253i	−1.57153	−	0.571990i	−0.973341	+	0.229364i	$0.926335\pi$
$42$	−0.751248	+	0.857911i	−0.115920	+	0.132379i
$43$	1.29579	−	7.34878i	0.197606	−	1.12068i	−0.711053	−	0.703139i	$-0.751781\pi$
$43$	1.29579	−	7.34878i	0.197606	−	1.12068i	0.908659	−	0.417540i	$-0.137108\pi$
$44$			2.77190i			0.417880i
$45$	−0.615920	+	6.35112i	−0.0918159	+	0.946769i
$46$	−1.92432			−0.283725
$47$	−5.51793	+	2.00836i	−0.804873	+	0.292950i	−0.711504	−	0.702682i	$-0.751986\pi$
$47$	−5.51793	+	2.00836i	−0.804873	+	0.292950i	−0.0933687	+	0.995632i	$0.529764\pi$
$48$	1.33278	+	6.14853i	0.192370	+	0.887464i
$49$	−6.81717	+	1.58938i	−0.973882	+	0.227055i
$50$	−0.0761360	−	0.0907353i	−0.0107673	−	0.0128319i
$51$	0.349832	−	0.142981i	0.0489862	−	0.0200213i
$52$	−4.76094	+	5.67387i	−0.660224	+	0.786824i
$53$	12.1036	−	6.98800i	1.66255	−	0.959875i	0.691063	−	0.722795i	$-0.257143\pi$
$53$	12.1036	−	6.98800i	1.66255	−	0.959875i	0.971490	−	0.237080i	$-0.0761904\pi$
$54$	−0.710066	+	1.08062i	−0.0966277	+	0.147053i
$55$		−	3.04206i		−	0.410192i
$56$	1.03129	−	2.37882i	0.137811	−	0.317883i
$57$	5.09265	+	0.694850i	0.674538	+	0.0920351i
$58$	−0.225328	−	1.27790i	−0.0295870	−	0.167796i
$59$	−1.21070	+	1.01590i	−0.157620	+	0.132259i	−0.718187	−	0.695850i	$-0.755028\pi$
$59$	−1.21070	+	1.01590i	−0.157620	+	0.132259i	0.560567	+	0.828109i	$0.310583\pi$
$60$	−1.51255	−	6.97787i	−0.195269	−	0.900839i
$61$	1.45500	+	3.99757i	0.186293	+	0.511837i	0.997319	−	0.0731735i	$-0.0233127\pi$
$61$	1.45500	+	3.99757i	0.186293	+	0.511837i	−0.811026	+	0.585010i	$0.801090\pi$
$62$	0.481963	−	0.834784i	0.0612093	−	0.106018i
$63$	−7.40893	+	2.84740i	−0.933438	+	0.358739i
$64$	−3.27598	−	5.67416i	−0.409497	−	0.709270i
$65$	5.22497	−	6.22688i	0.648078	−	0.772349i
$66$	0.287211	−	0.545447i	0.0353533	−	0.0671399i
$67$	2.59043	+	14.6911i	0.316471	+	1.79480i	0.563848	+	0.825879i	$0.309321\pi$
$67$	2.59043	+	14.6911i	0.316471	+	1.79480i	−0.247376	+	0.968920i	$0.579568\pi$
$68$	−0.323942	+	0.271820i	−0.0392838	+	0.0329630i
$69$	−11.8514	−	6.24050i	−1.42674	−	0.751268i
$70$	−0.557002	+	1.28481i	−0.0665745	+	0.153564i
$71$	−4.29452	+	2.47944i	−0.509666	+	0.294256i	−0.732696	−	0.680556i	$-0.761738\pi$
$71$	−4.29452	+	2.47944i	−0.509666	+	0.294256i	0.223031	+	0.974811i	$0.428405\pi$
$72$	0.787586	−	2.83243i	0.0928179	−	0.333806i
$73$			2.46806i			0.288864i	0.989515	+	0.144432i	$0.0461355\pi$
$73$			2.46806i			0.288864i	−0.989515	+	0.144432i	$0.953864\pi$
$74$	1.47344	+	0.259808i	0.171284	+	0.0302020i
$75$	−0.174652	−	0.805724i	−0.0201671	−	0.0930370i
$76$	−5.66384	+	0.998688i	−0.649687	+	0.114557i
$77$	3.38464	−	1.69209i	0.385716	−	0.192831i
$78$	1.52475	−	0.623182i	0.172643	−	0.0705615i
$79$	−0.675969	+	3.83361i	−0.0760524	+	0.431315i	0.922879	+	0.385091i	$0.125830\pi$
$79$	−0.675969	+	3.83361i	−0.0760524	+	0.431315i	−0.998931	+	0.0462239i	$0.985281\pi$
$80$	3.86290	+	6.69073i	0.431885	+	0.748047i
$81$	−7.87753	+	4.35254i	−0.875281	+	0.483615i
$82$	−2.30773	−	1.33237i	−0.254847	−	0.147136i
$83$	−0.141502	+	0.0515026i	−0.0155319	+	0.00565315i	−0.349774	−	0.936834i	$-0.613742\pi$
$83$	−0.141502	+	0.0515026i	−0.0155319	+	0.00565315i	0.334243	+	0.942487i	$0.391520\pi$
$84$	6.92235	−	5.56418i	0.755290	−	0.607102i
$85$	0.355515	−	0.298313i	0.0385610	−	0.0323566i
$86$	0.635099	−	1.74492i	0.0684845	−	0.188160i
$87$	2.75644	−	8.60100i	0.295521	−	0.922124i
$88$	−0.243381	+	1.38028i	−0.0259445	+	0.147139i
$89$	3.40271	+	5.89366i	0.360686	+	0.624727i	0.988074	−	0.153980i	$-0.0492092\pi$
$89$	3.40271	+	5.89366i	0.360686	+	0.624727i	−0.627388	+	0.778707i	$0.715876\pi$
$90$	−0.425379	+	1.52981i	−0.0448388	+	0.161256i
$91$	9.83439	+	2.34980i	1.03092	+	0.246326i
$92$	14.7595	+	2.60251i	1.53879	+	0.271330i
$93$	5.67547	−	3.57825i	0.588519	−	0.371047i
$94$	−1.43902	+	0.253739i	−0.148424	+	0.0261712i
$95$	6.21587	−	1.09603i	0.637735	−	0.112450i
$96$	0.193047	+	4.95649i	0.0197028	+	0.505870i
$97$	12.2644	+	2.16255i	1.24526	+	0.219573i	0.757169	−	0.653219i	$-0.226582\pi$
$97$	12.2644	+	2.16255i	1.24526	+	0.219573i	0.488092	+	0.872792i	$0.337693\pi$
$98$	−1.73932	+	0.0949204i	−0.175697	+	0.00958841i
$99$	3.53773	−	2.42786i	0.355556	−	0.244009i
$100$	0.461251	+	0.798910i	0.0461251	+	0.0798910i
$101$	−1.45464	+	8.24969i	−0.144742	+	0.820874i	0.822831	+	0.568286i	$0.192393\pi$
$101$	−1.45464	+	8.24969i	−0.144742	+	0.820874i	−0.967574	+	0.252589i	$0.918718\pi$
$102$	0.0919091	−	0.0199226i	0.00910036	−	0.00197263i
$103$	−0.0733066	+	0.201408i	−0.00722311	+	0.0198453i	−0.943252	−	0.332078i	$-0.892250\pi$
$103$	−0.0733066	+	0.201408i	−0.00722311	+	0.0198453i	0.936029	+	0.351924i	$0.114472\pi$
$104$	−2.86892	+	2.40731i	−0.281321	+	0.236056i
$105$	−7.59704	+	6.10649i	−0.741395	+	0.595933i
$106$	3.26809	−	1.18949i	0.317425	−	0.115533i
$107$	15.3166	+	8.84302i	1.48071	+	0.854887i	0.999761	−	0.0218632i	$-0.00695982\pi$
$107$	15.3166	+	8.84302i	1.48071	+	0.854887i	0.480946	+	0.876750i	$0.340293\pi$
$108$	6.90767	−	7.32802i	0.664691	−	0.705139i
$109$	−0.476343	−	0.825050i	−0.0456254	−	0.0790255i	0.842311	−	0.538992i	$-0.181195\pi$
$109$	−0.476343	−	0.825050i	−0.0456254	−	0.0790255i	−0.887936	+	0.459967i	$0.847861\pi$
$110$	0.131451	−	0.745497i	0.0125334	−	0.0710804i
$111$	8.23204	+	6.37842i	0.781351	+	0.605413i
$112$	−5.29554	+	8.01949i	−0.500382	+	0.757771i
$113$	−13.8921	+	2.44955i	−1.30686	+	0.230434i	−0.783346	−	0.621586i	$-0.786489\pi$
$113$	−13.8921	+	2.44955i	−1.30686	+	0.230434i	−0.523510	+	0.852020i	$0.675378\pi$
$114$	1.21799	+	0.390341i	0.114076	+	0.0365588i
$115$	−16.1981	−	2.85616i	−1.51048	−	0.266338i
$116$			10.1062i			0.938340i
$117$	11.4115	+	1.10667i	1.05499	+	0.102311i
$118$	−0.340597	+	0.196644i	−0.0313545	+	0.0181025i
$119$	0.529655	+	0.229621i	0.0485534	+	0.0210493i
$120$	−0.140505	−	3.60748i	−0.0128263	−	0.329316i
$121$	6.85950	−	5.75580i	0.623591	−	0.523255i
$122$	0.183826	+	1.04253i	0.0166428	+	0.0943862i
$123$	−9.89196	−	15.6897i	−0.891928	−	1.41469i
$124$	−4.82565	+	5.75099i	−0.433356	+	0.516454i
$125$	−5.82364	−	10.0868i	−0.520882	−	0.902194i
$126$	−1.93869	+	0.377643i	−0.172713	+	0.0336431i
$127$	−2.41898	+	4.18980i	−0.214650	+	0.371785i	−0.953164	−	0.302453i	$-0.902194\pi$
$127$	−2.41898	+	4.18980i	−0.214650	+	0.371785i	0.738514	+	0.674238i	$0.235528\pi$
$128$	−2.51659	−	6.91427i	−0.222437	−	0.611141i
$129$	9.57015	−	8.68695i	0.842605	−	0.764843i
$130$	1.54952	−	1.30020i	0.135902	−	0.114035i
$131$	0.622917	+	3.53274i	0.0544246	+	0.308657i	0.999853	−	0.0171742i	$-0.00546700\pi$
$131$	0.622917	+	3.53274i	0.0544246	+	0.308657i	−0.945428	+	0.325831i	$0.894356\pi$
$132$	−2.94059	+	3.79515i	−0.255946	+	0.330326i
$133$	4.67690	+	6.30622i	0.405539	+	0.546818i
$134$			3.71217i			0.320683i
$135$	−7.58093	+	8.04225i	−0.652463	+	0.692167i
$136$	−0.185175	+	0.106911i	−0.0158787	+	0.00916755i
$137$	2.29835	−	2.73907i	0.196361	−	0.234014i	−0.658875	−	0.752252i	$-0.728967\pi$
$137$	2.29835	−	2.73907i	0.196361	−	0.234014i	0.855236	+	0.518238i	$0.173412\pi$
$138$	−2.63468	−	2.04143i	−0.224279	−	0.173778i
$139$	−3.85722	−	4.59686i	−0.327165	−	0.389900i	0.577240	−	0.816574i	$-0.304130\pi$
$139$	−3.85722	−	4.59686i	−0.327165	−	0.389900i	−0.904405	+	0.426674i	$0.859685\pi$
$140$	6.00983	−	9.10120i	0.507923	−	0.769191i
$141$	−9.68548	−	3.10399i	−0.815664	−	0.261403i
$142$	−1.15957	+	0.422048i	−0.0973087	+	0.0354175i
$143$	−5.46589			−0.457081
$144$	−4.69794	+	9.83217i	−0.391495	+	0.819347i
$145$		−	11.0912i		−	0.921078i
$146$	−0.106648	+	0.604829i	−0.00882623	+	0.0500560i
$147$	−11.0199	−	5.05595i	−0.908903	−	0.417008i
$148$	−10.9500	−	3.98546i	−0.900081	−	0.327603i
$149$	3.58546	+	4.27298i	0.293732	+	0.350057i	0.892647	−	0.450756i	$-0.148846\pi$
$149$	3.58546	+	4.27298i	0.293732	+	0.350057i	−0.598915	+	0.800813i	$0.704401\pi$
$150$	−0.00798440	−	0.205000i	−0.000651923	−	0.0167382i
$151$	−1.49517	+	0.544196i	−0.121675	+	0.0442861i	−0.402140	−	0.915578i	$-0.631734\pi$
$151$	−1.49517	+	0.544196i	−0.121675	+	0.0442861i	0.280465	+	0.959864i	$0.409511\pi$
$152$	−2.90803			−0.235872
$153$	0.630655	+	0.175360i	0.0509854	+	0.0141770i
$154$	0.902567	−	0.268413i	0.0727309	−	0.0216293i
$155$	5.29598	−	6.31151i	0.425384	−	0.506952i
$156$	−12.5376	+	2.71771i	−1.00381	+	0.217591i
$157$	−15.9051	−	18.9549i	−1.26936	−	1.51277i	−0.755952	−	0.654627i	$-0.772826\pi$
$157$	−15.9051	−	18.9549i	−1.26936	−	1.51277i	−0.513412	−	0.858143i	$-0.671619\pi$
$158$	−0.331310	+	0.910266i	−0.0263576	+	0.0724169i
$159$	23.9849	+	3.27254i	1.90213	+	0.259529i
$160$	2.08332	+	5.72388i	0.164701	+	0.452513i
$161$	−5.83205	−	19.6109i	−0.459630	−	1.54555i
$162$	−2.11857	+	0.726248i	−0.166450	+	0.0570594i
$163$	−6.48707	+	11.2359i	−0.508107	+	0.880066i	0.491849	+	0.870680i	$0.336321\pi$
$163$	−6.48707	+	11.2359i	−0.508107	+	0.880066i	−0.999956	+	0.00938604i	$0.997012\pi$
$164$	15.8984	+	13.3404i	1.24146	+	1.04171i
$165$	3.22720	−	4.16505i	0.251237	−	0.324249i
$166$	−0.0369024	+	0.00650690i	−0.00286419	+	0.000505033i
$167$	1.43124	+	8.11696i	0.110753	+	0.628110i	0.988766	+	0.149473i	$0.0477577\pi$
$167$	1.43124	+	8.11696i	0.110753	+	0.628110i	−0.878013	+	0.478637i	$0.841131\pi$
$168$	3.93557	−	2.16291i	0.303636	−	0.166872i
$169$	−1.22969	−	1.03183i	−0.0945915	−	0.0793717i
$170$	0.100014	−	0.0577432i	0.00767073	−	0.00442870i
$171$	6.23548	+	6.35394i	0.476839	+	0.485898i
$172$	−7.23111	+	12.5246i	−0.551367	+	0.954995i
$173$	−18.0347	−	15.1329i	−1.37115	−	1.15053i	−0.972359	−	0.233491i	$-0.924985\pi$
$173$	−18.0347	−	15.1329i	−1.37115	−	1.15053i	−0.398793	−	0.917041i	$-0.630571\pi$
$174$	1.04716	−	1.98868i	0.0793851	−	0.150761i
$175$	0.693946	−	1.05090i	0.0524574	−	0.0794407i
$176$	1.77680	−	4.88173i	0.133932	−	0.367974i
$177$	−2.73537	+	0.106538i	−0.205603	+	0.00800787i
$178$	0.579205	+	1.59135i	0.0434133	+	0.119277i
$179$	−7.22926	−	4.17381i	−0.540340	−	0.311965i	0.204877	−	0.978788i	$-0.434321\pi$
$179$	−7.22926	−	4.17381i	−0.540340	−	0.311965i	−0.745217	+	0.666822i	$0.767654\pi$
$180$	5.33162	−	11.1584i	0.397396	−	0.831696i
$181$	−3.60525	−	2.08149i	−0.267976	−	0.154716i	0.359992	−	0.932956i	$-0.382780\pi$
$181$	−3.60525	−	2.08149i	−0.267976	−	0.154716i	−0.627967	+	0.778240i	$0.716113\pi$
$182$	2.30851	+	1.00080i	0.171118	+	0.0741846i
$183$	−2.24875	+	7.01684i	−0.166232	+	0.518699i
$184$	7.12109	+	2.59187i	0.524974	+	0.191075i
$185$	12.0172	+	4.37390i	0.883522	+	0.321576i
$186$	1.54547	−	0.631652i	0.113319	−	0.0463150i
$187$	−0.307327	−	0.0541900i	−0.0224740	−	0.00396277i
$188$	11.3805			0.830009
$189$	−13.1647	−	3.96131i	−0.957587	−	0.288143i
$190$	1.57064			0.113946
$191$	−0.952580	−	0.167966i	−0.0689263	−	0.0121536i	0.139079	−	0.990281i	$-0.455586\pi$
$191$	−0.952580	−	0.167966i	−0.0689263	−	0.0121536i	−0.208005	+	0.978128i	$0.566697\pi$
$192$	1.53417	−	11.2441i	0.110719	−	0.811476i
$193$	6.76620	+	2.46270i	0.487042	+	0.177269i	0.573857	−	0.818956i	$-0.305447\pi$
$193$	6.76620	+	2.46270i	0.487042	+	0.177269i	−0.0868148	+	0.996224i	$0.527669\pi$
$194$	2.91211	+	1.05992i	0.209077	+	0.0760978i
$195$	13.7596	−	2.98259i	0.985347	−	0.213588i
$196$	13.4690	+	1.62426i	0.962068	+	0.116019i
$197$	6.90426	+	3.98617i	0.491908	+	0.284003i	0.725366	−	0.688364i	$-0.241671\pi$
$197$	6.90426	+	3.98617i	0.491908	+	0.284003i	−0.233458	+	0.972367i	$0.575004\pi$
$198$	0.971878	−	0.442109i	0.0690684	−	0.0314193i
$199$	−3.69994	−	2.13616i	−0.262282	−	0.151428i	0.363093	−	0.931753i	$-0.381721\pi$
$199$	−3.69994	−	2.13616i	−0.262282	−	0.151428i	−0.625375	+	0.780324i	$0.715054\pi$
$200$	0.159536	+	0.438321i	0.0112809	+	0.0309940i
$201$	−12.0384	+	22.8624i	−0.849126	+	1.61259i
$202$	−0.712958	+	1.95884i	−0.0501635	+	0.137823i
$203$	12.3403	−	6.16927i	0.866117	−	0.432998i
$204$	−0.731889	+	0.0285058i	−0.0512424	+	0.00199580i
$205$	−17.4480	−	14.6406i	−1.21862	−	1.02254i
$206$	−0.0266678	+	0.0461900i	−0.00185804	+	0.00321821i
$207$	−9.60611	−	21.1169i	−0.667671	−	1.46772i
$208$	12.0217	−	6.94074i	0.833556	−	0.481254i
$209$	−3.25124	−	2.72811i	−0.224893	−	0.188708i
$210$	−2.12562	+	1.16820i	−0.146682	+	0.0806133i
$211$	3.70699	+	21.0234i	0.255199	+	1.44731i	0.795560	+	0.605875i	$0.207177\pi$
$211$	3.70699	+	21.0234i	0.255199	+	1.44731i	−0.540361	+	0.841433i	$0.681712\pi$
$212$	−26.6750	+	4.70353i	−1.83205	+	0.323040i
$213$	−8.51019	−	1.16114i	−0.583108	−	0.0795603i
$214$	3.37140	+	2.82894i	0.230464	+	0.193383i
$215$	7.93589	−	13.7454i	0.541223	−	0.937426i
$216$	4.08314	−	3.04252i	0.277822	−	0.207017i
$217$	9.96805	+	2.38174i	0.676675	+	0.161683i
$218$	−0.0810826	−	0.222773i	−0.00549161	−	0.0150881i
$219$	−2.61826	+	3.37915i	−0.176926	+	0.228342i
$220$	−2.01647	+	5.54020i	−0.135950	+	0.373520i
$221$	−0.536000	−	0.638779i	−0.0360552	−	0.0429689i
$222$	1.74175	+	1.91883i	0.116899	+	0.128784i
$223$	7.92110	−	9.44000i	0.530436	−	0.632149i	−0.432579	−	0.901596i	$-0.642396\pi$
$223$	7.92110	−	9.44000i	0.530436	−	0.632149i	0.963015	+	0.269447i	$0.0868408\pi$
$224$	−5.20966	+	5.50172i	−0.348085	+	0.367599i
$225$	0.615635	−	1.28844i	0.0410423	−	0.0858960i
$226$	−3.51028			−0.233500
$227$	−17.5438	+	6.38541i	−1.16442	+	0.423815i	−0.850675	−	0.525692i	$-0.823806\pi$
$227$	−17.5438	+	6.38541i	−1.16442	+	0.423815i	−0.313746	+	0.949507i	$0.601584\pi$
$228$	−8.81413	−	4.64118i	−0.583730	−	0.307370i
$229$	−12.4826	−	14.8762i	−0.824872	−	0.983044i	0.175127	−	0.984546i	$-0.443966\pi$
$229$	−12.4826	−	14.8762i	−0.824872	−	0.983044i	−0.999999	+	0.00150162i	$0.999522\pi$
$230$	−3.84613	−	1.39988i	−0.253607	−	0.0923052i
$231$	6.42915	+	1.27390i	0.423007	+	0.0838167i
$232$	−0.887358	+	5.03246i	−0.0582579	+	0.330397i
$233$		−	13.1872i		−	0.863923i	−0.901892	−	0.431961i	$-0.857822\pi$
$233$		−	13.1872i		−	0.863923i	0.901892	−	0.431961i	$-0.142178\pi$
$234$	2.74872	+	0.764308i	0.179689	+	0.0499644i
$235$	−12.4897			−0.814739
$236$	2.87833	−	1.04763i	0.187363	−	0.0681947i
$237$	−4.99242	+	4.53169i	−0.324293	+	0.294365i
$238$	0.119877	+	0.0791586i	0.00777044	+	0.00513109i
$239$	10.0464	+	11.9729i	0.649849	+	0.774460i	0.985891	−	0.167387i	$-0.0535330\pi$
$239$	10.0464	+	11.9729i	0.649849	+	0.774460i	−0.336043	+	0.941847i	$0.609089\pi$
$240$	−1.80903	+	13.2586i	−0.116772	+	0.855840i
$241$	4.17444	−	4.97490i	0.268899	−	0.320462i	−0.614650	−	0.788800i	$-0.710703\pi$
$241$	4.17444	−	4.97490i	0.268899	−	0.320462i	0.883549	+	0.468338i	$0.155147\pi$
$242$	1.92972	−	1.11413i	0.124047	−	0.0716187i
$243$	−15.4030	−	2.39766i	−0.988100	−	0.153810i
$244$		−	8.24483i		−	0.527821i
$245$	−14.7817	−	1.78257i	−0.944369	−	0.113884i
$246$	−1.74618	−	4.27240i	−0.111333	−	0.272398i
$247$	−1.96931	−	11.1685i	−0.125304	−	0.710634i
$248$	−2.90791	+	2.44003i	−0.184653	+	0.154942i
$249$	−0.248375	−	0.0795990i	−0.0157401	−	0.00504438i
$250$	−0.991293	−	2.72356i	−0.0626949	−	0.172253i
$251$	−11.9045	+	20.6191i	−0.751403	+	1.30147i	0.195740	+	0.980656i	$0.437289\pi$
$251$	−11.9045	+	20.6191i	−0.751403	+	1.30147i	−0.947143	+	0.320812i	$0.896044\pi$
$252$	15.3806	−	0.274578i	0.968884	−	0.0172968i
$253$	5.53002	+	9.57828i	0.347670	+	0.602182i
$254$	−0.773849	+	0.922238i	−0.0485556	+	0.0578663i
$255$	0.803222	−	0.0312841i	0.0502997	−	0.00195909i
$256$	1.95752	+	11.1017i	0.122345	+	0.693853i
$257$	−23.2700	+	19.5258i	−1.45154	+	1.21799i	−0.520096	+	0.854108i	$0.674104\pi$
$257$	−23.2700	+	19.5258i	−1.45154	+	1.21799i	−0.931446	+	0.363880i	$0.881452\pi$
$258$	2.72066	−	1.71531i	0.169381	−	0.106791i
$259$	1.81786	+	15.8034i	0.112956	+	0.981975i
$260$	−13.6433	+	7.87694i	−0.846119	+	0.488507i
$261$	12.8984	−	8.85189i	0.798393	−	0.547918i
$262$			0.892661i			0.0551488i
$263$	15.2337	+	2.68611i	0.939348	+	0.165632i	0.622302	−	0.782778i	$-0.286198\pi$
$263$	15.2337	+	2.68611i	0.939348	+	0.165632i	0.317047	+	0.948410i	$0.397309\pi$
$264$	−1.79751	+	1.63163i	−0.110629	+	0.100420i
$265$	29.2749	−	5.16196i	1.79835	−	0.317097i
$266$	0.873636	+	1.74751i	0.0535660	+	0.107147i
$267$	−1.59352	+	11.6791i	−0.0975217	+	0.714750i
$268$	5.02045	−	28.4724i	0.306673	−	1.73923i
$269$	0.343714	+	0.595329i	0.0209566	+	0.0362979i	0.876314	−	0.481741i	$-0.159995\pi$
$269$	0.343714	+	0.595329i	0.0209566	+	0.0362979i	−0.855357	+	0.518039i	$0.826662\pi$
$270$	−2.20532	+	1.64328i	−0.134212	+	0.100007i
$271$	6.24649	+	3.60641i	0.379447	+	0.219074i	0.677578	−	0.735451i	$-0.263030\pi$
$271$	6.24649	+	3.60641i	0.379447	+	0.219074i	−0.298131	+	0.954525i	$0.596363\pi$
$272$	0.744748	−	0.271066i	0.0451570	−	0.0164358i
$273$	10.9720	+	13.6501i	0.664054	+	0.826143i
$274$	0.681599	−	0.571929i	0.0411769	−	0.0345515i
$275$	−0.232838	+	0.639718i	−0.0140407	+	0.0385765i
$276$	17.4472	+	19.2210i	1.05020	+	1.15697i
$277$	2.15820	−	12.2398i	0.129674	−	0.735417i	−0.848748	−	0.528798i	$-0.822643\pi$
$277$	2.15820	−	12.2398i	0.129674	−	0.735417i	0.978421	−	0.206619i	$-0.0662461\pi$
$278$	−0.746626	−	1.29319i	−0.0447797	−	0.0775607i
$279$	11.5666	+	1.12171i	0.692474	+	0.0671548i
$280$	3.79174	−	4.00431i	0.226600	−	0.239303i
$281$	2.05517	+	0.362382i	0.122601	+	0.0216179i	0.234612	−	0.972089i	$-0.424618\pi$
$281$	2.05517	+	0.362382i	0.122601	+	0.0216179i	−0.112011	+	0.993707i	$0.535729\pi$
$282$	−2.23942	−	1.17919i	−0.133356	−	0.0702200i
$283$	19.9337	−	3.51484i	1.18493	−	0.208936i	0.453758	−	0.891125i	$-0.350083\pi$
$283$	19.9337	−	3.51484i	1.18493	−	0.208936i	0.731175	+	0.682189i	$0.238972\pi$
$284$	9.46469	−	1.66888i	0.561626	−	0.0990298i
$285$	9.67320	+	5.09353i	0.572991	+	0.301715i
$286$	−1.33949	−	0.236188i	−0.0792055	−	0.0139661i
$287$	6.58424	−	27.5564i	0.388655	−	1.62660i
$288$	−4.99383	+	6.99099i	−0.294264	+	0.411948i
$289$	8.47620	+	14.6812i	0.498600	+	0.863600i
$290$	0.479266	−	2.71805i	0.0281435	−	0.159610i
$291$	14.4977	+	15.9717i	0.849869	+	0.936275i
$292$	1.63598	−	4.49482i	0.0957384	−	0.263039i
$293$	21.6520	−	18.1682i	1.26493	−	1.06140i	0.269786	−	0.962920i	$-0.413047\pi$
$293$	21.6520	−	18.1682i	1.26493	−	1.06140i	0.995139	−	0.0984780i	$-0.0313974\pi$
$294$	−2.48209	−	1.71521i	−0.144758	−	0.100033i
$295$	−3.15887	+	1.14973i	−0.183916	+	0.0669401i
$296$	−5.10266	−	2.94602i	−0.296586	−	0.171234i
$297$	7.41932	+	0.428921i	0.430512	+	0.0248885i
$298$	0.694022	+	1.20208i	0.0402036	+	0.0696347i
$299$	−5.13186	+	29.1043i	−0.296783	+	1.68314i
$300$	−0.216008	+	1.58315i	−0.0124712	+	0.0914033i
$301$	19.7074	+	1.18400i	1.13592	+	0.0682448i
$302$	−0.389925	+	0.0687543i	−0.0224377	+	0.00395637i
$303$	−10.7434	+	9.75191i	−0.617191	+	0.560233i
$304$	10.6150	+	1.87172i	0.608814	+	0.107350i
$305$			9.04841i			0.518111i
$306$	0.146973	+	0.0702256i	0.00840187	+	0.00401453i
$307$	−1.71807	+	0.991927i	−0.0980553	+	0.0566122i	−0.548226	−	0.836330i	$-0.684697\pi$
$307$	−1.71807	+	0.991927i	−0.0980553	+	0.0566122i	0.450170	+	0.892943i	$0.351363\pi$
$308$	−7.28571	+	0.838072i	−0.415142	+	0.0477536i
$309$	−0.314034	+	0.197991i	−0.0178647	+	0.0112633i
$310$	1.57058	−	1.31787i	0.0892028	−	0.0748500i
$311$	−2.35895	−	13.3783i	−0.133764	−	0.758612i	−0.975713	−	0.219054i	$-0.929703\pi$
$311$	−2.35895	−	13.3783i	−0.133764	−	0.758612i	0.841949	−	0.539557i	$-0.181408\pi$
$312$	−6.48181	+	0.252455i	−0.366960	+	0.0142925i
$313$	−9.40882	+	11.2130i	−0.531818	+	0.633796i	−0.963333	−	0.268310i	$-0.913535\pi$
$313$	−9.40882	+	11.2130i	−0.531818	+	0.633796i	0.431515	+	0.902106i	$0.357979\pi$
$314$	−3.07868	−	5.33243i	−0.173740	−	0.300927i
$315$	−16.8796	+	0.301340i	−0.951059	+	0.0169786i
$316$	3.77222	−	6.53368i	0.212204	−	0.367548i
$317$	−6.46638	−	17.7662i	−0.363188	−	0.997850i	−0.977895	−	0.209095i	$-0.932948\pi$
$317$	−6.46638	−	17.7662i	−0.363188	−	0.997850i	0.614707	−	0.788755i	$-0.289274\pi$
$318$	5.73640	+	1.83840i	0.321681	+	0.103092i
$319$	−5.71319	+	4.79394i	−0.319877	+	0.268409i
$320$	−2.41993	−	13.7241i	−0.135278	−	0.767201i
$321$	11.5895	+	28.3561i	0.646863	+	1.58269i
$322$	−0.581809	−	5.05791i	−0.0324229	−	0.281866i
$323$		−	0.647487i		−	0.0360271i
$324$	17.2317	−	2.70511i	0.957314	−	0.150284i
$325$	−1.57537	+	0.909538i	−0.0873856	+	0.0504521i
$326$	−2.07526	+	2.47320i	−0.114938	+	0.136978i
$327$	0.223076	−	1.63495i	0.0123361	−	0.0904131i
$328$	6.74539	+	8.03884i	0.372452	+	0.443871i
$329$	−6.94714	−	13.8962i	−0.383008	−	0.766123i
$330$	0.970844	−	0.881248i	0.0534432	−	0.0485111i
$331$	−11.1300	+	4.05098i	−0.611760	+	0.222662i	−0.629273	−	0.777184i	$-0.716647\pi$
$331$	−11.1300	+	4.05098i	−0.611760	+	0.222662i	0.0175134	+	0.999847i	$0.494425\pi$
$332$	0.291842			0.0160169
$333$	4.50431	+	17.4661i	0.246835	+	0.957135i
$334$			2.05101i			0.112226i
$335$	−5.50977	+	31.2475i	−0.301031	+	1.70723i
$336$	−15.7580	+	5.36208i	−0.859667	+	0.292526i
$337$	19.6990	+	7.16984i	1.07307	+	0.390566i	0.817324	−	0.576178i	$-0.195456\pi$
$337$	19.6990	+	7.16984i	1.07307	+	0.390566i	0.255747	+	0.966744i	$0.417679\pi$
$338$	−0.256765	−	0.306000i	−0.0139662	−	0.0166442i
$339$	−21.6190	−	11.3837i	−1.17418	−	0.618279i
$340$	−0.845203	+	0.307629i	−0.0458376	+	0.0166835i
$341$	−5.54018			−0.300018
$342$	1.25352	+	1.82656i	0.0677827	+	0.0987689i
$343$	−6.23871	−	17.4378i	−0.336858	−	0.941555i
$344$	−4.70047	+	5.60181i	−0.253433	+	0.302029i
$345$	−19.1477	−	21.0944i	−1.03088	−	1.13568i
$346$	−3.76572	−	4.48781i	−0.202446	−	0.241266i
$347$	10.4749	−	28.7796i	0.562323	−	1.54497i	−0.253899	−	0.967231i	$-0.581713\pi$
$347$	10.4749	−	28.7796i	0.562323	−	1.54497i	0.816222	−	0.577738i	$-0.196065\pi$
$348$	−10.7213	+	13.8370i	−0.574721	+	0.741740i
$349$	−6.58819	−	18.1009i	−0.352658	−	0.968919i	−0.981513	−	0.191397i	$-0.938698\pi$
$349$	−6.58819	−	18.1009i	−0.352658	−	0.968919i	0.628855	−	0.777523i	$-0.283524\pi$
$350$	0.215471	−	0.227551i	0.0115174	−	0.0121631i
$351$	14.4501	+	13.6212i	0.771288	+	0.727045i
$352$	2.04795	−	3.54715i	0.109156	−	0.189064i
$353$	−14.1346	−	11.8604i	−0.752311	−	0.631264i	0.183802	−	0.982963i	$-0.441159\pi$
$353$	−14.1346	−	11.8604i	−0.752311	−	0.631264i	−0.936113	+	0.351700i	$0.885604\pi$
$354$	−0.674940	−	0.0920900i	−0.0358727	−	0.00489453i
$355$	−10.3872	+	1.83154i	−0.551294	+	0.0972079i
$356$	−2.29032	−	12.9890i	−0.121387	−	0.688418i
$357$	0.481583	+	0.876275i	0.0254881	+	0.0463774i
$358$	−1.59127	−	1.33523i	−0.0841011	−	0.0705692i
$359$	−0.675231	+	0.389845i	−0.0356373	+	0.0205752i	−0.517713	−	0.855554i	$-0.673216\pi$
$359$	−0.675231	+	0.389845i	−0.0356373	+	0.0205752i	0.482075	+	0.876130i	$0.339883\pi$
$360$	3.63465	−	5.08824i	0.191563	−	0.268174i
$361$	−5.09702	+	8.82829i	−0.268264	+	0.464647i
$362$	−0.793568	−	0.665883i	−0.0417090	−	0.0349980i
$363$	15.4978	−	0.603612i	0.813423	−	0.0316814i
$364$	−16.3528	−	10.7983i	−0.857118	−	0.565984i
$365$	−1.79543	+	4.93291i	−0.0939771	+	0.258200i
$366$	−0.854290	+	1.62240i	−0.0446545	+	0.0848039i
$367$	−8.50857	−	23.3771i	−0.444144	−	1.22027i	−0.936743	−	0.350018i	$-0.886175\pi$
$367$	−8.50857	−	23.3771i	−0.444144	−	1.22027i	0.492599	−	0.870256i	$-0.336047\pi$
$368$	−24.3255	−	14.0444i	−1.26806	−	0.732113i
$369$	3.10092	−	31.9755i	0.161428	−	1.66458i
$370$	2.75597	+	1.59116i	0.143276	+	0.0827205i
$371$	22.0268	+	29.7005i	1.14358	+	1.54197i
$372$	−12.7080	+	2.75464i	−0.658881	+	0.142822i
$373$	22.5973	+	8.22473i	1.17004	+	0.425860i	0.852675	−	0.522442i	$-0.174979\pi$
$373$	22.5973	+	8.22473i	1.17004	+	0.425860i	0.317367	+	0.948303i	$0.397201\pi$
$374$	−0.0729728	−	0.0265599i	−0.00377333	−	0.00137338i
$375$	2.72726	−	19.9885i	0.140835	−	1.03220i
$376$	5.66699	+	0.999243i	0.292253	+	0.0515320i
$377$	−19.9284			−1.02637
$378$	−3.05499	−	1.53963i	−0.157132	−	0.0791901i
$379$	−30.5872			−1.57116			−0.785579	−	0.618761i	$-0.787635\pi$
$379$	−30.5872			−1.57116			−0.785579	+	0.618761i	$0.787635\pi$
$380$	−12.0468	−	2.12418i	−0.617989	−	0.108968i
$381$	−7.75674	+	3.17028i	−0.397390	+	0.162418i
$382$	−0.226184	−	0.0823242i	−0.0115726	−	0.00421207i
$383$	33.8267	+	12.3119i	1.72846	+	0.629109i	0.998519	−	0.0543988i	$-0.0173242\pi$
$383$	33.8267	+	12.3119i	1.72846	+	0.629109i	0.729943	+	0.683508i	$0.239546\pi$
$384$	3.88947	−	12.1364i	0.198484	−	0.619335i
$385$	7.99582	−	0.919755i	0.407505	−	0.0468751i
$386$	1.55173	+	0.895891i	0.0789809	+	0.0455997i
$387$	22.3186	−	1.74118i	1.13452	−	0.0885094i
$388$	−20.9024	−	12.0680i	−1.06116	−	0.612661i
$389$	8.34439	+	22.9260i	0.423077	+	1.16240i	0.949937	+	0.312443i	$0.101147\pi$
$389$	8.34439	+	22.9260i	0.423077	+	1.16240i	−0.526859	+	0.849953i	$0.676631\pi$
$390$	3.50085	−	0.136352i	0.177273	−	0.00690446i
$391$	−0.577092	+	1.58555i	−0.0291848	+	0.0801845i
$392$	6.56433	+	1.99143i	0.331549	+	0.100582i
$393$	−2.89487	+	5.49769i	−0.146027	+	0.277322i
$394$	1.51973	+	1.27520i	0.0765629	+	0.0642439i
$395$	−4.13988	+	7.17049i	−0.208300	+	0.360786i
$396$	−8.05224	+	2.07659i	−0.404641	+	0.104353i
$397$	5.85723	−	3.38167i	0.293966	−	0.169721i	−0.345763	−	0.938322i	$-0.612380\pi$
$397$	5.85723	−	3.38167i	0.293966	−	0.169721i	0.639729	+	0.768601i	$0.279047\pi$
$398$	−0.814412	−	0.683373i	−0.0408228	−	0.0342544i
$399$	−0.286616	+	13.5957i	−0.0143487	+	0.680636i
$400$	−0.300226	−	1.70266i	−0.0150113	−	0.0851332i
$401$	−0.948178	+	0.167189i	−0.0473497	+	0.00834904i	−0.197273	−	0.980349i	$-0.563208\pi$
$401$	−0.948178	+	0.167189i	−0.0473497	+	0.00834904i	0.149923	+	0.988698i	$0.452097\pi$
$402$	−3.93809	+	5.08253i	−0.196414	+	0.253493i
$403$	−11.3403	−	9.51567i	−0.564902	−	0.474009i
$404$	8.11759	−	14.0601i	0.403865	−	0.699515i
$405$	−18.9111	+	2.96877i	−0.939702	+	0.147519i
$406$	3.29072	−	0.978623i	0.163316	−	0.0485682i
$407$	−2.94113	−	8.08068i	−0.145786	−	0.400545i
$408$	−0.366951	−	0.0500674i	−0.0181668	−	0.00247871i
$409$	−9.93846	+	27.3057i	−0.491425	+	1.35018i	0.407951	+	0.913004i	$0.366244\pi$
$409$	−9.93846	+	27.3057i	−0.491425	+	1.35018i	−0.899376	+	0.437176i	$0.855979\pi$
$410$	−3.64321	−	4.34181i	−0.179925	−	0.214427i
$411$	6.05255	−	1.31198i	0.298551	−	0.0647150i
$412$	0.267011	−	0.318212i	0.0131547	−	0.0156772i
$413$	−3.03626	−	2.87508i	−0.149405	−	0.141474i
$414$	−1.44162	−	5.59006i	−0.0708516	−	0.274736i
$415$	−0.320287			−0.0157223
$416$	10.2845	−	3.74325i	0.504239	−	0.183528i
$417$	−0.404508	−	10.3858i	−0.0198088	−	0.508593i
$418$	−0.678873	−	0.809050i	−0.0332048	−	0.0395719i
$419$	22.8869	+	8.33016i	1.11810	+	0.406955i	0.833958	−	0.551828i	$-0.186069\pi$
$419$	22.8869	+	8.33016i	1.11810	+	0.406955i	0.284141	+	0.958782i	$0.408292\pi$
$420$	17.8835	−	6.08535i	0.872623	−	0.296934i
$421$	2.03579	−	11.5455i	0.0992181	−	0.562694i	−0.894155	−	0.447758i	$-0.852223\pi$
$421$	2.03579	−	11.5455i	0.0992181	−	0.562694i	0.993373	−	0.114936i	$-0.0366663\pi$
$422$			5.31223i			0.258595i
$423$	−9.96800	−	14.5248i	−0.484661	−	0.706218i
$424$	−13.6960			−0.665135
$425$	−0.0975943	+	0.0355214i	−0.00473402	+	0.00172304i
$426$	−2.03536	−	0.652289i	−0.0986134	−	0.0316035i
$427$	−10.0674	+	5.03299i	−0.487195	+	0.243564i
$428$	−22.0328	−	26.2576i	−1.06499	−	1.26921i
$429$	−7.48364	−	5.79854i	−0.361313	−	0.279956i
$430$	2.53875	−	3.02556i	0.122429	−	0.145905i
$431$	−22.9443	+	13.2469i	−1.10519	+	0.638082i	−0.937579	−	0.347772i	$-0.886938\pi$
$431$	−22.9443	+	13.2469i	−1.10519	+	0.638082i	−0.167610	+	0.985853i	$0.553605\pi$
$432$	−16.8627	+	8.47788i	−0.811309	+	0.407892i
$433$			23.5474i			1.13161i	0.824538	+	0.565807i	$0.191435\pi$
$433$			23.5474i			1.13161i	−0.824538	+	0.565807i	$0.808565\pi$
$434$	2.33988	+	1.01441i	0.112318	+	0.0486931i
$435$	11.7662	−	15.1856i	0.564148	−	0.728094i
$436$	0.320620	+	1.81833i	0.0153549	+	0.0870821i
$437$	−17.5790	+	14.7505i	−0.840915	+	0.705612i
$438$	−0.787655	+	0.714965i	−0.0376356	+	0.0341624i
$439$	1.42802	+	3.92345i	0.0681557	+	0.187256i	0.969094	−	0.246690i	$-0.0793430\pi$
$439$	1.42802	+	3.92345i	0.0681557	+	0.187256i	−0.900939	+	0.433946i	$0.857121\pi$
$440$	−1.49056	+	2.58172i	−0.0710595	+	0.123079i
$441$	−9.72422	−	18.6129i	−0.463058	−	0.886328i
$442$	−0.103751	−	0.179702i	−0.00493494	−	0.00854757i
$443$	1.56064	−	1.85990i	0.0741482	−	0.0883663i	−0.727695	−	0.685901i	$-0.759408\pi$
$443$	1.56064	−	1.85990i	0.0741482	−	0.0883663i	0.801843	+	0.597534i	$0.203853\pi$
$444$	−10.7642	−	17.0731i	−0.510844	−	0.810252i
$445$	2.51355	+	14.2550i	0.119153	+	0.675753i
$446$	2.34908	−	1.97111i	0.111232	−	0.0933350i
$447$	0.376008	+	9.65403i	0.0177846	+	0.456620i
$448$	13.9236	−	10.3262i	0.657828	−	0.487867i
$449$	10.0967	−	5.82936i	0.476495	−	0.275104i	−0.242460	−	0.970161i	$-0.577954\pi$
$449$	10.0967	−	5.82936i	0.476495	−	0.275104i	0.718955	+	0.695057i	$0.244621\pi$
$450$	0.206544	−	0.289147i	0.00973659	−	0.0136305i
$451$			15.3157i			0.721186i
$452$	26.9239	+	4.74741i	1.26639	+	0.223299i
$453$	−2.62443	−	0.841073i	−0.123306	−	0.0395171i
$454$	−4.57525	+	0.806740i	−0.214727	+	0.0378622i
$455$	17.9466	+	11.8507i	0.841349	+	0.555571i
$456$	−3.98154	−	3.08501i	−0.186452	−	0.144469i
$457$	−3.68876	+	20.9200i	−0.172553	+	0.978597i	0.768377	+	0.639997i	$0.221064\pi$
$457$	−3.68876	+	20.9200i	−0.172553	+	0.978597i	−0.940930	+	0.338600i	$0.890047\pi$
$458$	−2.41620	−	4.18498i	−0.112902	−	0.195551i
$459$	0.677431	+	0.909130i	0.0316198	+	0.0424346i
$460$	27.6067	+	15.9387i	1.28717	+	0.743147i
$461$	25.2929	−	9.20586i	1.17801	−	0.428760i	0.322510	−	0.946566i	$-0.395473\pi$
$461$	25.2929	−	9.20586i	1.17801	−	0.428760i	0.855498	+	0.517806i	$0.173251\pi$
$462$	1.52050	+	0.589998i	0.0707401	+	0.0274492i
$463$	18.3826	−	15.4248i	0.854311	−	0.716852i	−0.106424	−	0.994321i	$-0.533940\pi$
$463$	18.3826	−	15.4248i	0.854311	−	0.716852i	0.960735	+	0.277469i	$0.0894956\pi$
$464$	6.47816	−	17.7986i	0.300741	−	0.826279i
$465$	13.9466	−	3.02313i	0.646759	−	0.140194i
$466$	0.569835	−	3.23170i	0.0263971	−	0.149705i
$467$	3.09488	+	5.36049i	0.143214	+	0.248054i	0.928705	−	0.370819i	$-0.120923\pi$
$467$	3.09488	+	5.36049i	0.143214	+	0.248054i	−0.785491	+	0.618873i	$0.787590\pi$
$468$	−20.0490	−	9.57970i	−0.926767	−	0.442822i
$469$	−37.8311	+	11.2505i	−1.74688	+	0.519500i
$470$	−3.06076	−	0.539695i	−0.141183	−	0.0248943i
$471$	−1.66797	−	42.8253i	−0.0768560	−	1.97328i
$472$	1.52527	−	0.268946i	0.0702061	−	0.0123792i
$473$	−10.5105	+	1.85328i	−0.483271	+	0.0852138i
$474$	−1.41928	+	0.894820i	−0.0651896	+	0.0411004i
$475$	−1.39103	−	0.245276i	−0.0638248	−	0.0112540i
$476$	−0.812399	−	0.769272i	−0.0372362	−	0.0352595i
$477$	29.3673	+	29.9252i	1.34464	+	1.37018i
$478$	1.94464	+	3.36822i	0.0889459	+	0.154059i
$479$	2.79921	−	15.8751i	0.127899	−	0.725353i	−0.851644	−	0.524121i	$-0.824394\pi$
$479$	2.79921	−	15.8751i	0.127899	−	0.725353i	0.979543	−	0.201233i	$-0.0644947\pi$
$480$	−3.21984	+	10.0470i	−0.146965	+	0.458580i
$481$	7.85890	−	21.5922i	0.358335	−	0.984518i
$482$	1.23797	−	1.03878i	0.0563881	−	0.0473152i
$483$	12.8194	−	33.0373i	0.583304	−	1.50325i
$484$	−16.3078	+	5.93555i	−0.741263	+	0.269798i
$485$	22.9397	+	13.2442i	1.04164	+	0.601390i
$486$	−3.67109	−	1.25316i	−0.166524	−	0.0568444i
$487$	−13.0260	−	22.5617i	−0.590265	−	1.02237i	−0.994196	−	0.107580i	$-0.965690\pi$
$487$	−13.0260	−	22.5617i	−0.590265	−	1.02237i	0.403931	−	0.914789i	$-0.367643\pi$
$488$	0.723921	−	4.10556i	0.0327704	−	0.185850i
$489$	−20.8015	+	8.50184i	−0.940678	+	0.384467i
$490$	−3.54542	−	1.07558i	−0.160166	−	0.0485897i
$491$	10.3899	−	1.83203i	0.468892	−	0.0826783i	0.0657902	−	0.997833i	$-0.479043\pi$
$491$	10.3899	−	1.83203i	0.468892	−	0.0826783i	0.403102	+	0.915155i	$0.367932\pi$
$492$	7.61513	+	35.1310i	0.343316	+	1.58383i
$493$	−1.12050	−	0.197575i	−0.0504648	−	0.00889831i
$494$		−	2.82208i		−	0.126971i
$495$	8.83706	−	2.27898i	0.397196	−	0.102433i
$496$	12.1851	−	7.03507i	0.547127	−	0.315884i
$497$	−7.81544	−	10.5381i	−0.350570	−	0.472700i
$498$	−0.0574280	−	0.0302393i	−0.00257341	−	0.00135506i
$499$	−6.18372	+	5.18876i	−0.276822	+	0.232281i	−0.770619	−	0.637296i	$-0.780053\pi$
$499$	−6.18372	+	5.18876i	−0.276822	+	0.232281i	0.493798	+	0.869577i	$0.335608\pi$
$500$	3.91982	+	22.2304i	0.175299	+	0.994173i
$501$	−6.65137	+	12.6317i	−0.297161	+	0.564343i
$502$	−3.80832	+	4.53858i	−0.169974	+	0.202567i
$503$	−15.6629	−	27.1289i	−0.698373	−	1.20962i	−0.969030	−	0.246941i	$-0.920575\pi$
$503$	−15.6629	−	27.1289i	−0.698373	−	1.20962i	0.270658	−	0.962676i	$-0.412759\pi$
$504$	7.68295	+	1.21373i	0.342226	+	0.0540639i
$505$	−8.90877	+	15.4304i	−0.396435	+	0.686646i
$506$	0.941315	+	2.58624i	0.0418465	+	0.114972i
$507$	−0.589004	−	2.71726i	−0.0261586	−	0.120678i
$508$	7.18270	−	6.02700i	0.318681	−	0.267405i
$509$	7.03911	+	39.9208i	0.312003	+	1.76946i	0.588555	+	0.808457i	$0.299697\pi$
$509$	7.03911	+	39.9208i	0.312003	+	1.76946i	−0.276552	+	0.960999i	$0.589192\pi$
$510$	0.198192	+	0.0270416i	0.00877608	+	0.00119742i
$511$	−6.48709	+	0.746206i	−0.286972	+	0.0330102i
$512$			17.5212i			0.774336i
$513$	1.79669	+	15.3145i	0.0793257	+	0.676150i
$514$	−6.54634	+	3.77953i	−0.288747	+	0.166708i
$515$	−0.293036	+	0.349227i	−0.0129127	+	0.0153888i
$516$	−23.1874	+	9.47696i	−1.02077	+	0.417200i
$517$	5.39839	+	6.43355i	0.237421	+	0.282947i
$518$	−0.237395	+	3.95138i	−0.0104305	+	0.173614i
$519$	−8.63836	−	39.8515i	−0.379182	−	1.74929i
$520$	−7.48536	+	2.72445i	−0.328255	+	0.119475i
$521$	23.4014			1.02523			0.512616	−	0.858618i	$-0.328676\pi$
$521$	23.4014			1.02523			0.512616	+	0.858618i	$0.328676\pi$
$522$	3.54343	−	1.61191i	0.155092	−	0.0705515i
$523$			14.0156i			0.612858i	0.951894	+	0.306429i	$0.0991342\pi$
$523$			14.0156i			0.612858i	−0.951894	+	0.306429i	$0.900866\pi$
$524$	1.20726	−	6.84672i	0.0527395	−	0.299100i
$525$	2.06498	−	0.702666i	0.0901229	−	0.0306668i
$526$	3.61714	+	1.31653i	0.157715	+	0.0574035i
$527$	−0.543284	−	0.647461i	−0.0236658	−	0.0282038i
$528$	7.61154	−	4.79889i	0.331250	−	0.208845i
$529$	34.5807	−	12.5863i	1.50351	−	0.547232i
$530$	7.39726			0.321316
$531$	−3.85815	−	2.75597i	−0.167430	−	0.119599i
$532$	−4.33741	−	14.5850i	−0.188050	−	0.632340i
$533$	−26.3058	+	31.3500i	−1.13943	+	1.35792i
$534$	−0.895181	+	2.79326i	−0.0387383	+	0.120876i
$535$	24.1802	+	28.8168i	1.04540	+	1.24586i
$536$	4.99993	−	13.7372i	0.215964	−	0.593356i
$537$	−5.47013	−	13.3838i	−0.236053	−	0.577554i
$538$	0.0585066	+	0.160745i	0.00252240	+	0.00693023i
$539$	5.47084	+	8.38466i	0.235646	+	0.361153i
$540$	19.1373	−	9.62141i	0.823537	−	0.414040i
$541$	−11.9247	+	20.6542i	−0.512683	+	0.887993i	0.487209	+	0.873285i	$0.338015\pi$
$541$	−11.9247	+	20.6542i	−0.512683	+	0.887993i	−0.999892	+	0.0147075i	$0.995318\pi$
$542$	1.37494	+	1.15372i	0.0590589	+	0.0495563i
$543$	−2.72796	−	6.67453i	−0.117068	−	0.286432i
$544$	0.615371	−	0.108506i	0.0263838	−	0.00465218i
$545$	−0.351870	−	1.99555i	−0.0150724	−	0.0854801i
$546$	2.09898	+	3.81925i	0.0898282	+	0.163449i
$547$	−0.534982	−	0.448903i	−0.0228742	−	0.0191937i	0.631279	−	0.775556i	$-0.282530\pi$
$547$	−0.534982	−	0.448903i	−0.0228742	−	0.0191937i	−0.654153	+	0.756362i	$0.726975\pi$
$548$	−6.00137	+	3.46489i	−0.256366	+	0.148013i
$549$	−10.5227	+	7.22151i	−0.449100	+	0.308207i
$550$	−0.0847030	+	0.146710i	−0.00361175	+	0.00625573i
$551$	−11.8539	−	9.94659i	−0.504993	−	0.423739i
$552$	7.00026	+	11.1031i	0.297951	+	0.472581i
$553$	−10.2807	−	0.617654i	−0.437180	−	0.0262653i
$554$	1.05779	−	2.90626i	0.0449413	−	0.123475i
$555$	11.8133	+	18.7371i	0.501446	+	0.795346i
$556$	3.97768	+	10.9286i	0.168691	+	0.463475i
$557$	9.63238	+	5.56126i	0.408137	+	0.235638i	0.689989	−	0.723820i	$-0.257615\pi$
$557$	9.63238	+	5.56126i	0.408137	+	0.235638i	−0.281852	+	0.959458i	$0.590949\pi$
$558$	2.78608	+	0.774696i	0.117944	+	0.0327955i
$559$	−24.6973	−	14.2590i	−1.04458	−	0.603090i
$560$	−16.4181	+	12.1762i	−0.693792	+	0.514539i
$561$	−0.363289	−	0.400225i	−0.0153381	−	0.0168975i
$562$	0.487987	+	0.177613i	0.0205845	+	0.00749214i
$563$	10.5579	+	3.84276i	0.444962	+	0.161953i	0.554777	−	0.831999i	$-0.312804\pi$
$563$	10.5579	+	3.84276i	0.444962	+	0.161953i	−0.109815	+	0.993952i	$0.535026\pi$
$564$	15.5816	+	12.0731i	0.656106	+	0.508370i
$565$	−29.5481	−	5.21012i	−1.24310	−	0.219191i
$566$	5.03688			0.211716
$567$	−13.8220	−	19.3895i	−0.580470	−	0.814281i
$568$	4.85953			0.203901
$569$	35.5984	+	6.27695i	1.49236	+	0.263143i	0.859505	−	0.511127i	$-0.170772\pi$
$569$	35.5984	+	6.27695i	1.49236	+	0.263143i	0.632855	+	0.774270i	$0.281883\pi$
$570$	2.15044	+	1.66623i	0.0900722	+	0.0697906i
$571$	−18.7772	−	6.83434i	−0.785802	−	0.286008i	−0.0822119	−	0.996615i	$-0.526198\pi$
$571$	−18.7772	−	6.83434i	−0.785802	−	0.286008i	−0.703590	+	0.710607i	$0.748421\pi$
$572$	9.95446	+	3.62313i	0.416217	+	0.151491i
$573$	−1.12604	−	1.24052i	−0.0470410	−	0.0518236i
$574$	2.80430	−	6.46853i	0.117049	−	0.269991i
$575$	3.18770	+	1.84042i	0.132936	+	0.0767508i
$576$	14.0290	−	13.7674i	0.584540	−	0.573642i
$577$	26.4773	+	15.2867i	1.10226	+	0.636393i	0.936815	−	0.349825i	$-0.113759\pi$
$577$	26.4773	+	15.2867i	1.10226	+	0.636393i	0.165450	+	0.986218i	$0.447092\pi$
$578$	1.44281	+	3.96408i	0.0600129	+	0.164884i
$579$	6.65139	+	10.5498i	0.276422	+	0.438434i
$580$	−7.35196	+	20.1993i	−0.305273	+	0.838732i
$581$	−0.178153	−	0.356356i	−0.00739103	−	0.0147841i
$582$	2.86269	+	4.54052i	0.118662	+	0.188211i
$583$	−15.3124	−	12.8486i	−0.634175	−	0.532136i
$584$	1.20930	−	2.09458i	0.0500414	−	0.0866742i
$585$	22.0031	+	10.5134i	0.909717	+	0.434675i
$586$	6.09118	−	3.51674i	0.251624	−	0.145275i
$587$	−23.6386	−	19.8352i	−0.975671	−	0.818685i	0.00775999	−	0.999970i	$-0.497530\pi$
$587$	−23.6386	−	19.8352i	−0.975671	−	0.818685i	−0.983431	+	0.181285i	$0.941974\pi$
$588$	16.7179	+	16.5125i	0.689436	+	0.680965i
$589$	−1.99607	−	11.3203i	−0.0822467	−	0.466444i
$590$	−0.823803	+	0.145259i	−0.0339154	+	0.00598021i
$591$	5.22421	+	12.7821i	0.214895	+	0.525786i
$592$	16.7298	+	14.0380i	0.687591	+	0.576957i
$593$	15.8362	−	27.4292i	0.650316	−	1.12638i	−0.332730	−	0.943022i	$-0.607970\pi$
$593$	15.8362	−	27.4292i	0.650316	−	1.12638i	0.983046	−	0.183358i	$-0.0586968\pi$
$594$	1.79967	+	0.425710i	0.0738412	+	0.0174671i
$595$	0.891579	+	0.844250i	0.0365512	+	0.0346109i
$596$	−3.69743	−	10.1586i	−0.151453	−	0.416113i
$597$	−2.79962	−	6.84984i	−0.114581	−	0.280345i
$598$	−2.51526	+	6.91062i	−0.102857	+	0.282596i
$599$	−9.55357	−	11.3855i	−0.390348	−	0.465199i	0.534703	−	0.845040i	$-0.320423\pi$
$599$	−9.55357	−	11.3855i	−0.390348	−	0.465199i	−0.925052	+	0.379841i	$0.875979\pi$
$600$	−0.246568	+	0.769374i	−0.0100661	+	0.0314095i
$601$	−11.0892	+	13.2156i	−0.452338	+	0.539075i	−0.943228	−	0.332146i	$-0.892227\pi$
$601$	−11.0892	+	13.2156i	−0.452338	+	0.539075i	0.490890	+	0.871221i	$0.336672\pi$
$602$	4.77840	+	1.14174i	0.194753	+	0.0465338i
$603$	−40.7362	+	18.5310i	−1.65891	+	0.754640i
$604$	3.08372			0.125475
$605$	17.8972	−	6.51406i	0.727626	−	0.264834i
$606$	−3.05420	+	1.92560i	−0.124068	+	0.0782220i
$607$	−26.1323	−	31.1432i	−1.06068	−	1.26407i	−0.963188	−	0.268829i	$-0.913363\pi$
$607$	−26.1323	−	31.1432i	−1.06068	−	1.26407i	−0.0974887	−	0.995237i	$-0.531081\pi$
$608$	7.98578	+	2.90659i	0.323866	+	0.117878i
$609$	23.4404	+	4.64460i	0.949854	+	0.188209i
$610$	−0.390993	+	2.21743i	−0.0158308	+	0.0897812i
$611$			22.4411i			0.907871i
$612$	−1.03231	−	0.737402i	−0.0417286	−	0.0298077i
$613$	28.1248			1.13595			0.567975	−	0.823046i	$-0.307727\pi$
$613$	28.1248			1.13595			0.567975	+	0.823046i	$0.307727\pi$
$614$	−0.463897	+	0.168845i	−0.0187214	+	0.00681402i
$615$	−8.35734	−	38.5550i	−0.337000	−	1.55469i
$616$	−3.70155	−	0.222385i	−0.149140	−	0.00896015i
$617$	2.77984	+	3.31289i	0.111912	+	0.133372i	0.819092	−	0.573661i	$-0.194477\pi$
$617$	2.77984	+	3.31289i	0.111912	+	0.133372i	−0.707180	+	0.707033i	$0.750033\pi$
$618$	−0.0855134	+	0.0349504i	−0.00343985	+	0.00140591i
$619$	9.94128	−	11.8476i	0.399574	−	0.476193i	−0.528316	−	0.849048i	$-0.677176\pi$
$619$	9.94128	−	11.8476i	0.399574	−	0.476193i	0.927890	+	0.372854i	$0.121621\pi$
$620$	−13.8287	+	7.98399i	−0.555373	+	0.320645i
$621$	9.24979	−	39.1030i	0.371181	−	1.56915i
$622$		−	3.38045i		−	0.135544i
$623$	−14.4622	+	10.7257i	−0.579417	+	0.429715i
$624$	23.8227	+	3.25041i	0.953671	+	0.130121i
$625$	−3.88859	−	22.0533i	−0.155544	−	0.882131i
$626$	−2.79028	+	2.34132i	−0.111522	+	0.0935781i
$627$	−1.55730	−	7.18431i	−0.0621925	−	0.286914i
$628$	16.4018	+	45.0635i	0.654503	+	1.79823i
$629$	0.655946	−	1.13613i	0.0261543	−	0.0453006i
$630$	−4.14959	−	0.655542i	−0.165324	−	0.0261174i
$631$	−17.0661	−	29.5593i	−0.679389	−	1.17674i	−0.975165	−	0.221479i	$-0.928911\pi$
$631$	−17.0661	−	29.5593i	−0.679389	−	1.17674i	0.295776	−	0.955257i	$-0.404422\pi$
$632$	2.45208	−	2.92227i	0.0975384	−	0.116242i
$633$	−17.2274	+	32.7168i	−0.684727	+	1.30038i
$634$	−0.816969	−	4.63326i	−0.0324460	−	0.184010i
$635$	−7.88276	+	6.61442i	−0.312818	+	0.262485i
$636$	−41.5120	−	21.8586i	−1.64606	−	0.866750i
$637$	−3.20287	+	26.5593i	−0.126903	+	1.05232i
$638$	−1.60724	+	0.927943i	−0.0636314	+	0.0367376i
$639$	−10.4199	−	10.6179i	−0.412206	−	0.420037i
$640$		−	15.6503i		−	0.618632i
$641$	3.26804	+	0.576243i	0.129080	+	0.0227602i	0.237815	−	0.971311i	$-0.423569\pi$
$641$	3.26804	+	0.576243i	0.129080	+	0.0227602i	−0.108735	+	0.994071i	$0.534680\pi$
$642$	1.61486	+	7.44984i	0.0637333	+	0.294022i
$643$	−24.9953	+	4.40734i	−0.985717	+	0.173808i	−0.643196	−	0.765702i	$-0.722392\pi$
$643$	−24.9953	+	4.40734i	−0.985717	+	0.173808i	−0.342521	+	0.939510i	$0.611281\pi$
$644$	−2.37799	+	39.5811i	−0.0937060	+	1.55972i
$645$	25.4473	−	10.4006i	1.00199	−	0.409525i
$646$	0.0279787	−	0.158675i	0.00110081	−	0.00624298i
$647$	0.170073	+	0.294574i	0.00668625	+	0.0115809i	0.869349	−	0.494198i	$-0.164538\pi$
$647$	0.170073	+	0.294574i	0.00668625	+	0.0115809i	−0.862663	+	0.505779i	$0.831205\pi$
$648$	8.81812	+	0.165964i	0.346408	+	0.00651969i
$649$	1.95759	+	1.13021i	0.0768420	+	0.0443648i
$650$	−0.425366	+	0.154821i	−0.0166842	+	0.00607256i
$651$	11.1211	+	13.8357i	0.435870	+	0.542262i
$652$	19.2621	−	16.1628i	0.754362	−	0.632985i
$653$	−9.61429	+	26.4150i	−0.376236	+	1.03370i	0.596667	+	0.802489i	$0.296491\pi$
$653$	−9.61429	+	26.4150i	−0.376236	+	1.03370i	−0.972903	+	0.231212i	$0.925731\pi$
$654$	0.125316	−	0.391027i	0.00490024	−	0.0152904i
$655$	−1.32493	+	7.51404i	−0.0517692	+	0.293598i
$656$	−19.4482	−	33.6853i	−0.759326	−	1.31519i
$657$	−7.16959	+	1.84896i	−0.279712	+	0.0721349i
$658$	−1.10201	−	3.70564i	−0.0429610	−	0.144461i
$659$	29.0041	+	5.11420i	1.12984	+	0.199221i	0.707157	−	0.707057i	$-0.249978\pi$
$659$	29.0041	+	5.11420i	1.12984	+	0.199221i	0.422682	+	0.906278i	$0.361089\pi$
$660$	−8.63822	+	5.44619i	−0.336242	+	0.211993i
$661$	−0.798762	+	0.140843i	−0.0310682	+	0.00547817i	−0.189161	−	0.981946i	$-0.560577\pi$
$661$	−0.798762	+	0.140843i	−0.0310682	+	0.00547817i	0.158092	+	0.987424i	$0.449466\pi$
$662$	−2.90260	+	0.511806i	−0.112813	+	0.0198919i
$663$	−0.0562104	−	1.44321i	−0.00218303	−	0.0560495i
$664$	0.145325	+	0.0256247i	0.00563969	+	0.000994430i
$665$	4.76015	+	16.0065i	0.184591	+	0.620707i
$666$	0.349111	+	4.47492i	0.0135278	+	0.173400i
$667$	20.1622	+	34.9220i	0.780685	+	1.35219i
$668$	2.77385	−	15.7313i	0.107324	−	0.608662i
$669$	20.8597	−	4.52163i	0.806483	−	0.174816i
$670$	−2.70048	+	7.41951i	−0.104329	+	0.286641i
$671$	4.66091	−	3.91097i	0.179933	−	0.150981i
$672$	−12.9694	+	2.00598i	−0.500304	+	0.0773824i
$673$	12.2309	−	4.45168i	0.471466	−	0.171600i	−0.0953502	−	0.995444i	$-0.530397\pi$
$673$	12.2309	−	4.45168i	0.471466	−	0.171600i	0.566816	+	0.823844i	$0.308175\pi$
$674$	4.51767	+	2.60828i	0.174014	+	0.100467i
$675$	2.20975	−	1.11097i	0.0850533	−	0.0427613i
$676$	1.55554	+	2.69428i	0.0598286	+	0.103626i
$677$	2.28800	−	12.9759i	0.0879349	−	0.498704i	−0.908750	−	0.417341i	$-0.862962\pi$
$677$	2.28800	−	12.9759i	0.0879349	−	0.498704i	0.996685	−	0.0813620i	$-0.0259270\pi$
$678$	−4.80611	−	3.72391i	−0.184577	−	0.143016i
$679$	−1.97599	+	32.8898i	−0.0758314	+	1.26220i
$680$	−0.447885	+	0.0789741i	−0.0171756	+	0.00302852i
$681$	−30.7941	−	9.86887i	−1.18003	−	0.378176i
$682$	−1.35769	−	0.239398i	−0.0519887	−	0.00916702i
$683$		−	6.25312i		−	0.239269i	−0.992818	−	0.119635i	$-0.961828\pi$
$683$		−	6.25312i		−	0.239269i	0.992818	−	0.119635i	$-0.0381723\pi$
$684$	−7.14425	−	15.7050i	−0.273167	−	0.600497i
$685$	6.58629	−	3.80260i	0.251649	−	0.145290i
$686$	−0.775365	−	4.54295i	−0.0296036	−	0.173451i
$687$	−1.30905	−	33.6100i	−0.0499434	−	1.28230i
$688$	20.7634	−	17.4226i	0.791598	−	0.664230i
$689$	−9.27486	−	52.6003i	−0.353344	−	2.00391i
$690$	−3.78087	−	5.99685i	−0.143935	−	0.228296i
$691$	−3.35901	+	4.00311i	−0.127783	+	0.152286i	−0.826142	−	0.563462i	$-0.809469\pi$
$691$	−3.35901	+	4.00311i	−0.127783	+	0.152286i	0.698359	+	0.715747i	$0.253914\pi$
$692$	22.8137	+	39.5145i	0.867246	+	1.50211i
$693$	7.45106	+	8.56459i	0.283042	+	0.325342i
$694$	3.81061	−	6.60018i	0.144649	−	0.250539i
$695$	−4.36537	−	11.9937i	−0.165588	−	0.454949i
$696$	−6.55366	+	5.94884i	−0.248416	+	0.225490i
$697$	−1.78989	+	1.50189i	−0.0677968	+	0.0568883i
$698$	−0.832360	−	4.72055i	−0.0315053	−	0.178675i
$699$	13.9898	−	18.0553i	0.529142	−	0.682914i
$700$	−1.96041	+	1.45391i	−0.0740967	+	0.0549526i
$701$		−	21.7945i		−	0.823166i	−0.911372	−	0.411583i	$-0.864976\pi$
$701$		−	21.7945i		−	0.823166i	0.911372	−	0.411583i	$-0.135024\pi$
$702$	2.95259	+	3.96245i	0.111438	+	0.149553i
$703$	15.4517	−	8.92101i	0.582770	−	0.336462i
$704$	−6.02344	+	7.17846i	−0.227017	+	0.270548i
$705$	−17.1003	−	13.2498i	−0.644035	−	0.499017i
$706$	−2.95137	−	3.51731i	−0.111076	−	0.132376i
$707$	−22.1234	−	1.32915i	−0.832038	−	0.0499879i
$708$	5.05226	+	1.61914i	0.189876	+	0.0608511i
$709$	−16.2367	+	5.90968i	−0.609783	+	0.221943i	−0.628408	−	0.777884i	$-0.716293\pi$
$709$	−16.2367	+	5.90968i	−0.609783	+	0.221943i	0.0186255	+	0.999827i	$0.494071\pi$
$710$	−2.62465			−0.0985015
$711$	−11.6429	+	0.908317i	−0.436642	+	0.0340645i
$712$		−	6.66907i		−	0.249934i
$713$	−5.20161	+	29.4998i	−0.194802	+	1.10478i
$714$	0.0801532	+	0.235552i	0.00299966	+	0.00881532i
$715$	−10.9247	−	3.97626i	−0.408560	−	0.148704i
$716$	10.3992	+	12.3933i	0.388638	+	0.463160i
$717$	1.05357	+	27.0505i	0.0393463	+	1.01022i
$718$	−0.182320	+	0.0663590i	−0.00680411	+	0.00247649i
$719$	24.2323			0.903713			0.451857	−	0.892091i	$-0.350762\pi$
$719$	24.2323			0.903713			0.451857	+	0.892091i	$0.350762\pi$
$720$	−16.5424	+	16.2340i	−0.616497	+	0.605004i
$721$	−0.551549	−	0.131786i	−0.0205408	−	0.00490795i
$722$	−1.63057	+	1.94324i	−0.0606836	+	0.0723199i
$723$	10.9931	−	2.38291i	0.408838	−	0.0886214i
$724$	5.18612	+	6.18058i	0.192741	+	0.229699i
$725$	−0.848919	+	2.33239i	−0.0315281	+	0.0866227i
$726$	3.82402	+	0.521755i	0.141923	+	0.0193642i
$727$	4.28953	+	11.7854i	0.159090	+	0.437095i	0.993470	−	0.114094i	$-0.0363965\pi$
$727$	4.28953	+	11.7854i	0.159090	+	0.437095i	−0.834380	+	0.551189i	$0.814174\pi$
$728$	−7.19483	−	6.81289i	−0.266658	−	0.252502i
$729$	−18.5454	−	19.6231i	−0.686868	−	0.726783i
$730$	−0.653150	+	1.13129i	−0.0241742	+	0.0418709i
$731$	−1.24727	−	1.04658i	−0.0461319	−	0.0387093i
$732$	8.74660	−	11.2884i	0.323284	−	0.417232i
$733$	−17.9357	+	3.16255i	−0.662471	+	0.116812i	−0.494767	−	0.869026i	$-0.664747\pi$
$733$	−17.9357	+	3.16255i	−0.662471	+	0.116812i	−0.167704	+	0.985837i	$0.553635\pi$
$734$	−1.07498	−	6.09652i	−0.0396783	−	0.225027i
$735$	−18.3474	−	18.1219i	−0.676753	−	0.668437i
$736$	−16.9648	−	14.2351i	−0.625329	−	0.524713i
$737$	18.4773	−	10.6679i	0.680621	−	0.392956i
$738$	2.14162	−	7.70202i	0.0788342	−	0.283515i
$739$	24.1785	−	41.8783i	0.889420	−	1.54052i	0.0488568	−	0.998806i	$-0.484442\pi$
$739$	24.1785	−	41.8783i	0.889420	−	1.54052i	0.840563	−	0.541714i	$-0.182224\pi$
$740$	−18.9864	−	15.9315i	−0.697954	−	0.585653i
$741$	9.15191	−	17.3805i	0.336204	−	0.638489i
$742$	4.11457	+	8.23029i	0.151051	+	0.302143i
$743$	11.3965	−	31.3117i	0.418098	−	1.14872i	−0.534682	−	0.845053i	$-0.679569\pi$
$743$	11.3965	−	31.3117i	0.418098	−	1.14872i	0.952780	−	0.303662i	$-0.0982092\pi$
$744$	−6.56990	+	0.255886i	−0.240864	+	0.00938125i
$745$	4.05780	+	11.1487i	0.148666	+	0.408457i
$746$	5.18235	+	2.99203i	0.189739	+	0.109546i
$747$	−0.255620	−	0.372474i	−0.00935265	−	0.0136281i
$748$	0.523782	+	0.302406i	0.0191514	+	0.0110570i
$749$	−18.6123	+	42.9320i	−0.680077	+	1.56870i
$750$	1.53208	−	4.78059i	0.0559435	−	0.174562i
$751$	−31.1058	−	11.3216i	−1.13507	−	0.413130i	−0.294937	−	0.955517i	$-0.595299\pi$
$751$	−31.1058	−	11.3216i	−1.13507	−	0.413130i	−0.840129	+	0.542387i	$0.817521\pi$
$752$	−20.0428	−	7.29497i	−0.730884	−	0.266020i
$753$	−38.1730	+	15.6018i	−1.39110	+	0.568561i
$754$	−4.88372	−	0.861131i	−0.177854	−	0.0313605i
$755$	−3.38427			−0.123166
$756$	21.3496	+	15.9407i	0.776478	+	0.579756i
$757$	37.7148			1.37077			0.685384	−	0.728182i	$-0.259635\pi$
$757$	37.7148			1.37077			0.685384	+	0.728182i	$0.259635\pi$
$758$	−7.49579	−	1.32171i	−0.272259	−	0.0480067i
$759$	−2.58976	+	18.9807i	−0.0940023	+	0.688956i
$760$	−5.81228	−	2.11550i	−0.210834	−	0.0767371i
$761$	5.51061	+	2.00570i	0.199760	+	0.0727065i	0.439962	−	0.898016i	$-0.354992\pi$
$761$	5.51061	+	2.00570i	0.199760	+	0.0727065i	−0.240203	+	0.970723i	$0.577214\pi$
$762$	−2.03788	+	0.441739i	−0.0738247	+	0.0160025i
$763$	2.02456	−	1.50148i	0.0732939	−	0.0543572i
$764$	1.62350	+	0.937327i	0.0587361	+	0.0339113i
$765$	1.13292	+	0.809273i	0.0409609	+	0.0292593i
$766$	7.75765	+	4.47888i	0.280295	+	0.161829i
$767$	2.06581	+	5.67576i	0.0745920	+	0.204940i
$768$	−9.09714	+	17.2765i	−0.328265	+	0.623412i
$769$	−6.33820	+	17.4141i	−0.228561	+	0.627967i	−0.999965	−	0.00837935i	$-0.997333\pi$
$769$	−6.33820	+	17.4141i	−0.228561	+	0.627967i	0.771404	+	0.636346i	$0.219555\pi$
$770$	1.99922	+	0.120111i	0.0720470	+	0.00432851i
$771$	−52.5743	+	2.04768i	−1.89342	+	0.0737453i
$772$	−10.6902	−	8.97011i	−0.384747	−	0.322841i
$773$	−3.16361	+	5.47954i	−0.113787	+	0.197085i	−0.917294	−	0.398210i	$-0.869632\pi$
$773$	−3.16361	+	5.47954i	−0.113787	+	0.197085i	0.803507	+	0.595295i	$0.202965\pi$
$774$	5.54471	+	0.537715i	0.199300	+	0.0193278i
$775$	−1.59678	+	0.921900i	−0.0573579	+	0.0331156i
$776$	−9.34888	−	7.84464i	−0.335605	−	0.281606i
$777$	−14.2762	+	23.5657i	−0.512158	+	0.845416i
$778$	1.05424	+	5.97889i	0.0377963	+	0.214354i
$779$	−31.2946	+	5.51808i	−1.12124	+	0.197706i
$780$	−27.0360	−	3.68884i	−0.968044	−	0.132082i
$781$	5.43306	+	4.55888i	0.194410	+	0.163129i
$782$	−0.209937	+	0.363622i	−0.00750733	+	0.0130031i
$783$	27.0505	+	1.56383i	0.966707	+	0.0558867i
$784$	−22.6797	−	11.4942i	−0.809988	−	0.410509i
$785$	−18.0004	−	49.4557i	−0.642462	−	1.76515i
$786$	−0.946987	+	1.22219i	−0.0337779	+	0.0435940i
$787$	16.1802	−	44.4547i	0.576762	−	1.58464i	−0.216843	−	0.976206i	$-0.569576\pi$
$787$	16.1802	−	44.4547i	0.576762	−	1.58464i	0.793605	−	0.608434i	$-0.208202\pi$
$788$	−9.93173	−	11.8362i	−0.353803	−	0.421646i
$789$	18.0076	+	19.8385i	0.641089	+	0.706268i
$790$	−1.32438	+	1.57833i	−0.0471192	+	0.0561545i
$791$	−10.6386	−	35.7736i	−0.378267	−	1.27196i
$792$	−4.19199	+	0.327038i	−0.148956	+	0.0116208i
$793$	16.2579			0.577336
$794$	1.58152	−	0.575625i	0.0561259	−	0.0204282i
$795$	45.5580	+	23.9891i	1.61577	+	0.850804i
$796$	5.32234	+	6.34291i	0.188645	+	0.224819i
$797$	−14.8436	−	5.40264i	−0.525788	−	0.191371i	0.0654686	−	0.997855i	$-0.479146\pi$
$797$	−14.8436	−	5.40264i	−0.525788	−	0.191371i	−0.591257	+	0.806483i	$0.701368\pi$
$798$	−0.657726	+	3.31942i	−0.0232832	+	0.117506i
$799$	−0.222486	+	1.26178i	−0.00787100	+	0.0446386i
$800$		−	1.36314i		−	0.0481942i
$801$	−14.5717	+	14.3000i	−0.514864	+	0.505265i
$802$	−0.239588			−0.00846013
$803$	3.31702	−	1.20729i	0.117055	−	0.0426045i
$804$	37.0790	−	33.6571i	1.30767	−	1.18699i
$805$	2.60976	−	43.4389i	0.0919821	−	1.53102i
$806$	−2.36791	−	2.82197i	−0.0834061	−	0.0993995i
$807$	−0.160964	+	1.17973i	−0.00566621	+	0.0415284i
$808$	5.27672	−	6.28855i	0.185634	−	0.221230i
$809$	−43.3139	+	25.0073i	−1.52284	+	0.879210i	−0.523200	+	0.852210i	$0.675262\pi$
$809$	−43.3139	+	25.0073i	−1.52284	+	0.879210i	−0.999635	+	0.0269998i	$0.991405\pi$
$810$	−4.76270	−	0.0896380i	−0.167344	−	0.00314956i
$811$		−	43.1499i		−	1.51520i	−0.652720	−	0.757600i	$-0.726372\pi$
$811$		−	43.1499i		−	1.51520i	0.652720	−	0.757600i	$-0.273628\pi$
$812$	−26.5634	+	3.05558i	−0.932193	+	0.107230i
$813$	4.72650	+	11.5644i	0.165766	+	0.405580i
$814$	−0.371585	−	2.10737i	−0.0130241	−	0.0738631i
$815$	−21.1395	+	17.7381i	−0.740484	+	0.621340i
$816$	1.30724	+	0.418942i	0.0457625	+	0.0146659i
$817$	−7.57363	−	20.8084i	−0.264968	−	0.727993i
$818$	−3.61546	+	6.26216i	−0.126412	+	0.218951i
$819$	0.541438	+	30.3288i	0.0189194	+	1.05977i
$820$	22.0715	+	38.2290i	0.770770	+	1.33501i
$821$	19.4758	−	23.2104i	0.679711	−	0.810048i	−0.310359	−	0.950619i	$-0.600449\pi$
$821$	19.4758	−	23.2104i	0.679711	−	0.810048i	0.990071	+	0.140571i	$0.0448938\pi$
$822$	1.53995	−	0.0599783i	0.0537119	−	0.00209198i
$823$	3.77527	+	21.4106i	0.131598	+	0.746327i	0.977169	+	0.212464i	$0.0681489\pi$
$823$	3.77527	+	21.4106i	0.131598	+	0.746327i	−0.845571	+	0.533862i	$0.820740\pi$
$824$	0.160900	−	0.135011i	0.00560521	−	0.00470333i
$825$	−0.997442	+	0.628863i	−0.0347265	+	0.0218942i
$826$	−0.619840	−	0.835777i	−0.0215670	−	0.0290804i
$827$	6.80237	−	3.92735i	0.236541	−	0.136567i	−0.377045	−	0.926195i	$-0.623060\pi$
$827$	6.80237	−	3.92735i	0.236541	−	0.136567i	0.613586	+	0.789628i	$0.289726\pi$
$828$	3.49706	+	44.8255i	0.121531	+	1.55779i
$829$			4.06084i			0.141039i	0.997510	+	0.0705193i	$0.0224656\pi$
$829$			4.06084i			0.141039i	−0.997510	+	0.0705193i	$0.977534\pi$
$830$	−0.0784905	−	0.0138400i	−0.00272444	−	0.000480393i
$831$	15.9396	−	14.4686i	0.552938	−	0.501909i
$832$	−24.6591	+	4.34806i	−0.854900	+	0.150742i
$833$	−0.443401	+	1.46158i	−0.0153629	+	0.0506407i
$834$	0.349652	−	2.56265i	0.0121074	−	0.0887372i
$835$	−3.04421	+	17.2646i	−0.105349	+	0.597465i
$836$	4.11279	+	7.12355i	0.142244	+	0.246373i
$837$	14.6465	+	13.8063i	0.506256	+	0.477216i
$838$	5.24878	+	3.03038i	0.181316	+	0.104683i
$839$	16.0171	−	5.82975i	0.552971	−	0.201265i	−0.0503948	−	0.998729i	$-0.516048\pi$
$839$	16.0171	−	5.82975i	0.552971	−	0.201265i	0.603366	+	0.797464i	$0.293826\pi$
$840$	9.43948	−	1.46001i	0.325693	−	0.0503752i
$841$	1.38521	−	1.16233i	0.0477660	−	0.0400804i
$842$	0.997791	−	2.74141i	0.0343862	−	0.0944752i
$843$	2.42941	+	2.67640i	0.0836732	+	0.0921802i
$844$	7.18442	−	40.7449i	0.247298	−	1.40250i
$845$	−1.70716	−	2.95688i	−0.0587280	−	0.101720i
$846$	−1.81515	−	3.99021i	−0.0624063	−	0.137186i
$847$	17.2026	+	16.2894i	0.591088	+	0.559710i
$848$	49.9937	+	8.81524i	1.71679	+	0.302717i
$849$	31.0210	+	16.3344i	1.06464	+	0.560597i
$850$	−0.0254517	+	0.00448782i	−0.000872985	+	0.000153931i
$851$	−45.7886	+	8.07377i	−1.56961	+	0.276765i
$852$	14.7290	+	7.75575i	0.504609	+	0.265707i
$853$	−23.9922	−	4.23048i	−0.821478	−	0.144849i	−0.252915	−	0.967488i	$-0.581389\pi$
$853$	−23.9922	−	4.23048i	−0.821478	−	0.144849i	−0.568563	+	0.822640i	$0.692500\pi$
$854$	−2.68462	+	0.798376i	−0.0918660	+	0.0273199i
$855$	7.84057	+	17.2357i	0.268142	+	0.589449i
$856$	−8.66584	−	15.0097i	−0.296192	−	0.513020i
$857$	9.37979	−	53.1954i	0.320407	−	1.81712i	−0.219749	−	0.975556i	$-0.570524\pi$
$857$	9.37979	−	53.1954i	0.320407	−	1.81712i	0.540157	−	0.841565i	$-0.318365\pi$
$858$	−1.58340	−	1.74438i	−0.0540564	−	0.0595523i
$859$	−9.38266	+	25.7786i	−0.320132	+	0.879556i	0.670366	+	0.742031i	$0.266137\pi$
$859$	−9.38266	+	25.7786i	−0.320132	+	0.879556i	−0.990498	+	0.137525i	$0.956085\pi$
$860$	−23.5641	+	19.7726i	−0.803529	+	0.674241i
$861$	38.2482	−	30.7439i	1.30350	−	1.04775i
$862$	−6.19522	+	2.25488i	−0.211010	+	0.0768014i
$863$	13.4069	+	7.74047i	0.456376	+	0.263489i	0.710519	−	0.703678i	$-0.248460\pi$
$863$	13.4069	+	7.74047i	0.456376	+	0.263489i	−0.254143	+	0.967167i	$0.581793\pi$
$864$	−14.2538	+	4.27398i	−0.484923	+	0.145404i
$865$	−25.0372	−	43.3658i	−0.851292	−	1.47448i
$866$	−1.01751	+	5.77059i	−0.0345764	+	0.196092i
$867$	−3.96948	+	29.0929i	−0.134811	+	0.988045i
$868$	−16.5750	−	10.9450i	−0.562593	−	0.371499i
$869$	5.48295	−	0.966792i	0.185996	−	0.0327962i
$870$	3.53966	−	3.21300i	0.120006	−	0.108931i
$871$	56.1445	+	9.89980i	1.90239	+	0.335442i
$872$			0.933598i			0.0316156i
$873$	2.90587	+	37.2476i	0.0983488	+	1.26064i
$874$	−4.94534	+	2.85519i	−0.167278	+	0.0965783i
$875$	24.7517	−	18.3567i	0.836760	−	0.620569i
$876$	7.00827	−	4.41855i	0.236788	−	0.149289i
$877$	27.8754	−	23.3902i	0.941285	−	0.789832i	−0.0365234	−	0.999333i	$-0.511628\pi$
$877$	27.8754	−	23.3902i	0.941285	−	0.789832i	0.977808	+	0.209501i	$0.0671839\pi$
$878$	0.180418	+	1.02320i	0.00608880	+	0.0345313i
$879$	48.9188	−	1.90530i	1.64999	−	0.0642643i
$880$	7.10260	−	8.46454i	0.239428	−	0.285340i
$881$	16.4076	+	28.4188i	0.552787	+	0.957455i	0.998072	+	0.0620663i	$0.0197690\pi$
$881$	16.4076	+	28.4188i	0.552787	+	0.957455i	−0.445285	+	0.895389i	$0.646898\pi$
$882$	−1.57876	−	4.98152i	−0.0531596	−	0.167737i
$883$	−4.24994	+	7.36111i	−0.143022	+	0.247721i	−0.928633	−	0.370999i	$-0.879015\pi$
$883$	−4.24994	+	7.36111i	−0.143022	+	0.247721i	0.785611	+	0.618720i	$0.212349\pi$
$884$	0.552738	+	1.51864i	0.0185906	+	0.0510773i
$885$	−5.54468	−	1.77695i	−0.186382	−	0.0597316i
$886$	0.462823	−	0.388355i	0.0155488	−	0.0130470i
$887$	−1.37491	−	7.79748i	−0.0461648	−	0.261814i	0.952986	−	0.303014i	$-0.0979929\pi$
$887$	−1.37491	−	7.79748i	−0.0461648	−	0.261814i	−0.999151	+	0.0412003i	$0.986882\pi$
$888$	−3.86101	−	9.44676i	−0.129567	−	0.317012i
$889$	−11.7439	−	5.09133i	−0.393878	−	0.170758i
$890$			3.60199i			0.120739i
$891$	9.70315	+	8.45811i	0.325068	+	0.283357i
$892$	−20.6833	+	11.9415i	−0.692528	+	0.399831i
$893$	−11.2007	+	13.3485i	−0.374818	+	0.446691i
$894$	−0.325017	+	2.38209i	−0.0108702	+	0.0796691i
$895$	−11.4128	−	13.6012i	−0.381488	−	0.454640i
$896$	17.4127	−	8.70515i	0.581718	−	0.290819i
$897$	−37.9018	+	34.4040i	−1.26550	+	1.14872i
$898$	2.72623	−	0.992267i	0.0909755	−	0.0331124i
$899$	−20.1993			−0.673683
$900$	−1.97525	+	1.93842i	−0.0658416	+	0.0646141i
$901$		−	3.04948i		−	0.101593i
$902$	−0.661808	+	3.75330i	−0.0220358	+	0.124971i
$903$	25.7264	+	22.5279i	0.856122	+	0.749682i
$904$	12.9901	+	4.72800i	0.432044	+	0.157251i
$905$	−5.69159	−	6.78297i	−0.189195	−	0.225474i
$906$	−0.606806	−	0.319520i	−0.0201598	−	0.0106154i
$907$	34.6469	−	12.6104i	1.15043	−	0.418722i	0.304761	−	0.952429i	$-0.401423\pi$
$907$	34.6469	−	12.6104i	1.15043	−	0.418722i	0.845670	+	0.533706i	$0.179201\pi$
$908$	36.1833			1.20079
$909$	−25.0547	+	1.95464i	−0.831013	+	0.0648313i
$910$	3.88596	+	3.67967i	0.128818	+	0.121980i
$911$	−3.62967	+	4.32568i	−0.120256	+	0.143316i	−0.822814	−	0.568311i	$-0.807597\pi$
$911$	−3.62967	+	4.32568i	−0.120256	+	0.143316i	0.702557	+	0.711627i	$0.252041\pi$
$912$	12.5480	+	13.8237i	0.415505	+	0.457749i
$913$	0.138437	+	0.164983i	0.00458159	+	0.00546013i
$914$	−1.80796	+	4.96732i	−0.0598019	+	0.164304i
$915$	−9.59909	+	12.3887i	−0.317336	+	0.409556i
$916$	12.8724	+	35.3666i	0.425316	+	1.16855i
$917$	−9.09719	+	2.70540i	−0.300416	+	0.0893401i
$918$	0.126729	+	0.252067i	0.00418267	+	0.00831944i
$919$	10.6179	−	18.3908i	0.350253	−	0.606655i	−0.636041	−	0.771655i	$-0.719429\pi$
$919$	10.6179	−	18.3908i	0.350253	−	0.606655i	0.986294	+	0.165000i	$0.0527624\pi$
$920$	12.3474	+	10.3607i	0.407083	+	0.341583i
$921$	−3.40459	−	0.464528i	−0.112185	−	0.0153067i
$922$	6.59615	−	1.16308i	0.217233	−	0.0383040i
$923$	3.29085	+	18.6634i	0.108320	+	0.614312i
$924$	−10.8643	−	6.58167i	−0.357410	−	0.216521i
$925$	−2.19233	−	1.83958i	−0.0720834	−	0.0604851i
$926$	5.17141	−	2.98572i	0.169943	−	0.0981167i
$927$	−0.640000	−	0.0620660i	−0.0210204	−	0.00203851i
$928$	7.46675	−	12.9328i	0.245108	−	0.424539i
$929$	−30.4946	−	25.5880i	−1.00050	−	0.839515i	−0.0134422	−	0.999910i	$-0.504279\pi$
$929$	−30.4946	−	25.5880i	−1.00050	−	0.839515i	−0.987053	+	0.160395i	$0.948723\pi$
$930$	3.54843	−	0.138205i	0.116358	−	0.00453193i
$931$	−15.1613	+	14.1995i	−0.496893	+	0.465370i
$932$	−8.74129	+	24.0165i	−0.286331	+	0.786687i
$933$	10.9627	−	20.8194i	0.358902	−	0.681596i
$934$	0.526807	+	1.44739i	0.0172376	+	0.0473600i
$935$	−0.574833	−	0.331880i	−0.0187990	−	0.0108536i
$936$	−9.14240	−	6.53063i	−0.298829	−	0.213460i
$937$	2.26157	+	1.30572i	0.0738824	+	0.0426560i	0.536486	−	0.843909i	$-0.319751\pi$
$937$	2.26157	+	1.30572i	0.0738824	+	0.0426560i	−0.462604	+	0.886565i	$0.653085\pi$
$938$	−9.75714	+	1.12236i	−0.318582	+	0.0366463i
$939$	−24.7775	+	5.37087i	−0.808584	+	0.175272i
$940$	22.7462	+	8.27895i	0.741900	+	0.270029i
$941$	−27.9161	−	10.1606i	−0.910038	−	0.331227i	−0.155770	−	0.987793i	$-0.549786\pi$
$941$	−27.9161	−	10.1606i	−0.910038	−	0.331227i	−0.754268	+	0.656566i	$0.772008\pi$
$942$	1.44177	−	10.5670i	0.0469755	−	0.344290i
$943$	81.5513	+	14.3797i	2.65568	+	0.468267i
$944$	−5.74070			−0.186844
$945$	−23.4305	−	17.4943i	−0.762193	−	0.569090i
$946$	−2.65581			−0.0863477
$947$	17.0572	+	3.00765i	0.554285	+	0.0977355i	0.443773	−	0.896139i	$-0.353640\pi$
$947$	17.0572	+	3.00765i	0.554285	+	0.0977355i	0.110513	+	0.993875i	$0.464751\pi$
$948$	12.0961	−	4.94381i	0.392862	−	0.160567i
$949$	8.86330	+	3.22598i	0.287715	+	0.104720i
$950$	−0.330291	−	0.120216i	−0.0107161	−	0.00390033i
$951$	9.99400	−	31.1846i	0.324078	−	1.01123i
$952$	−0.336994	−	0.454395i	−0.0109220	−	0.0147270i
$953$	−16.8568	−	9.73226i	−0.546044	−	0.315259i	0.201481	−	0.979492i	$-0.435425\pi$
$953$	−16.8568	−	9.73226i	−0.546044	−	0.315259i	−0.747525	+	0.664234i	$0.768758\pi$
$954$	5.90373	+	8.60255i	0.191140	+	0.278518i
$955$	−1.78173	−	1.02868i	−0.0576555	−	0.0332874i
$956$	−10.3602	−	28.4643i	−0.335071	−	0.920601i
$957$	−12.9079	+	0.502741i	−0.417254	+	0.0162513i
$958$	1.37197	−	3.76945i	0.0443262	−	0.121785i
$959$	7.89431	+	5.21288i	0.254921	+	0.168333i
$960$	11.2461	−	21.3576i	0.362966	−	0.689314i
$961$	12.2529	+	10.2814i	0.395255	+	0.331659i
$962$	2.85895	−	4.95184i	0.0921762	−	0.159654i
$963$	−14.2141	+	51.1187i	−0.458042	+	1.64728i
$964$	−10.9001	+	6.29320i	−0.351070	+	0.202690i
$965$	11.7321	+	9.84438i	0.377669	+	0.316902i
$966$	4.56915	−	7.54227i	0.147010	−	0.242669i
$967$	3.08674	+	17.5057i	0.0992627	+	0.562947i	0.993357	+	0.115069i	$0.0367089\pi$
$967$	3.08674	+	17.5057i	0.0992627	+	0.562947i	−0.894095	+	0.447878i	$0.852180\pi$
$968$	−8.64172	+	1.52377i	−0.277755	+	0.0489758i
$969$	0.686892	−	0.886508i	0.0220662	−	0.0284787i
$970$	5.04937	+	4.23692i	0.162125	+	0.136039i
$971$	−15.6634	+	27.1298i	−0.502662	+	0.870636i	0.497334	+	0.867559i	$0.334313\pi$
$971$	−15.6634	+	27.1298i	−0.502662	+	0.870636i	−0.999995	+	0.00307625i	$0.999021\pi$
$972$	26.4625	+	14.5766i	0.848785	+	0.467546i
$973$	10.9163	−	11.5282i	0.349959	−	0.369578i
$974$	−2.21727	−	6.09191i	−0.0710461	−	0.195197i
$975$	−3.12181	−	0.425945i	−0.0999778	−	0.0136411i
$976$	−5.28498	+	14.5204i	−0.169168	+	0.464786i
$977$	−0.137449	−	0.163806i	−0.00439739	−	0.00524061i	0.763841	−	0.645404i	$-0.223311\pi$
$977$	−0.137449	−	0.163806i	−0.00439739	−	0.00524061i	−0.768239	+	0.640164i	$0.778867\pi$
$978$	−5.46506	+	1.18463i	−0.174753	+	0.0378802i
$979$	6.25646	−	7.45616i	0.199957	−	0.238300i
$980$	25.7388	+	13.0446i	0.822196	+	0.416696i
$981$	2.03988	−	2.00185i	0.0651283	−	0.0639141i
$982$	2.62536			0.0837785
$983$	−18.2660	+	6.64828i	−0.582595	+	0.212047i	−0.616469	−	0.787379i	$-0.711438\pi$
$983$	−18.2660	+	6.64828i	−0.582595	+	0.212047i	0.0338747	+	0.999426i	$0.489215\pi$
$984$	0.707390	+	18.1623i	0.0225508	+	0.578993i
$985$	10.8997	+	12.9898i	0.347294	+	0.413889i
$986$	−0.266056	−	0.0968364i	−0.00847295	−	0.00308390i
$987$	5.23023	−	26.3960i	0.166480	−	0.840193i
$988$	−3.81667	+	21.6454i	−0.121424	+	0.688632i
$989$			57.7051i			1.83492i
$990$	2.26411	−	0.176635i	0.0719582	−	0.00561381i
$991$	−28.1667			−0.894746			−0.447373	−	0.894348i	$-0.647640\pi$
$991$	−28.1667			−0.894746			−0.447373	+	0.894348i	$0.647640\pi$
$992$	10.4243	−	3.79413i	0.330971	−	0.120464i
$993$	−19.5362	−	6.26093i	−0.619962	−	0.198685i
$994$	−1.45991	−	2.92022i	−0.0463055	−	0.0926239i
$995$	−5.84108	−	6.96113i	−0.185175	−	0.220683i
$996$	0.399577	+	0.309604i	0.0126611	+	0.00981017i
$997$	−21.5307	+	25.6593i	−0.681883	+	0.812637i	−0.990349	−	0.138599i	$-0.955740\pi$
$997$	−21.5307	+	25.6593i	−0.681883	+	0.812637i	0.308465	+	0.951236i	$0.400185\pi$
$998$	−1.73961	+	1.00437i	−0.0550665	+	0.0317927i
$999$	−12.3619	+	28.6922i	−0.391114	+	0.907780i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.47.13	yes	132
3.2	odd	2		567.2.bd.a.467.10		132
7.3	odd	6		189.2.ba.a.101.10	✓	132
21.17	even	6		567.2.ba.a.143.13		132
27.4	even	9		567.2.ba.a.341.13		132
27.23	odd	18		189.2.ba.a.131.10	yes	132
189.31	odd	18		567.2.bd.a.17.10		132
189.185	even	18	inner	189.2.bd.a.185.13	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.10	✓	132	7.3	odd	6
189.2.ba.a.131.10	yes	132	27.23	odd	18
189.2.bd.a.47.13	yes	132	1.1	even	1	trivial
189.2.bd.a.185.13	yes	132	189.185	even	18	inner
567.2.ba.a.143.13		132	21.17	even	6
567.2.ba.a.341.13		132	27.4	even	9
567.2.bd.a.17.10		132	189.31	odd	18
567.2.bd.a.467.10		132	3.2	odd	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:	\( N \)	\(=\)	\( 189 = 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	189.bd (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.245063 + 0.0432112i) q^{2} +(1.36915 + 1.06086i) q^{3} +(-1.82120 - 0.662861i) q^{4} +(1.99870 + 0.727467i) q^{5} +(0.289688 + 0.319140i) q^{6} +(0.302346 + 2.62842i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(0.749157 + 2.90496i) q^{9} +O(q^{10})\)	\(q+(0.245063 + 0.0432112i) q^{2} +(1.36915 + 1.06086i) q^{3} +(-1.82120 - 0.662861i) q^{4} +(1.99870 + 0.727467i) q^{5} +(0.289688 + 0.319140i) q^{6} +(0.302346 + 2.62842i) q^{7} +(-0.848674 - 0.489982i) q^{8} +(0.749157 + 2.90496i) q^{9} +(0.458373 + 0.264642i) q^{10} +(-0.489168 - 1.34398i) q^{11} +(-1.79029 - 2.83959i) q^{12} +(1.30709 - 3.59121i) q^{13} +(-0.0394834 + 0.657193i) q^{14} +(1.96479 + 3.11635i) q^{15} +(2.78250 + 2.33479i) q^{16} +(0.109097 - 0.188961i) q^{17} +(0.0580640 + 0.744269i) q^{18} +(2.56992 - 1.48374i) q^{19} +(-3.15782 - 2.64972i) q^{20} +(-2.37442 + 3.91945i) q^{21} +(-0.0618021 - 0.350497i) q^{22} +(-7.61556 + 1.34283i) q^{23} +(-0.642162 - 1.57118i) q^{24} +(-0.364628 - 0.305959i) q^{25} +(0.475500 - 0.823590i) q^{26} +(-2.05604 + 4.77208i) q^{27} +(1.19165 - 4.98728i) q^{28} +(-1.78349 - 4.90009i) q^{29} +(0.346835 + 0.848603i) q^{30} +(1.32486 - 3.64001i) q^{31} +(1.84082 + 2.19380i) q^{32} +(0.756026 - 2.35905i) q^{33} +(0.0349009 - 0.0415932i) q^{34} +(-1.30779 + 5.47337i) q^{35} +(0.561220 - 5.78708i) q^{36} +6.01251 q^{37} +(0.693906 - 0.252561i) q^{38} +(5.59937 - 3.53027i) q^{39} +(-1.33980 - 1.59671i) q^{40} +(-10.0627 - 3.66253i) q^{41} +(-0.751248 + 0.857911i) q^{42} +(1.29579 - 7.34878i) q^{43} +2.77190i q^{44} +(-0.615920 + 6.35112i) q^{45} -1.92432 q^{46} +(-5.51793 + 2.00836i) q^{47} +(1.33278 + 6.14853i) q^{48} +(-6.81717 + 1.58938i) q^{49} +(-0.0761360 - 0.0907353i) q^{50} +(0.349832 - 0.142981i) q^{51} +(-4.76094 + 5.67387i) q^{52} +(12.1036 - 6.98800i) q^{53} +(-0.710066 + 1.08062i) q^{54} -3.04206i q^{55} +(1.03129 - 2.37882i) q^{56} +(5.09265 + 0.694850i) q^{57} +(-0.225328 - 1.27790i) q^{58} +(-1.21070 + 1.01590i) q^{59} +(-1.51255 - 6.97787i) q^{60} +(1.45500 + 3.99757i) q^{61} +(0.481963 - 0.834784i) q^{62} +(-7.40893 + 2.84740i) q^{63} +(-3.27598 - 5.67416i) q^{64} +(5.22497 - 6.22688i) q^{65} +(0.287211 - 0.545447i) q^{66} +(2.59043 + 14.6911i) q^{67} +(-0.323942 + 0.271820i) q^{68} +(-11.8514 - 6.24050i) q^{69} +(-0.557002 + 1.28481i) q^{70} +(-4.29452 + 2.47944i) q^{71} +(0.787586 - 2.83243i) q^{72} +2.46806i q^{73} +(1.47344 + 0.259808i) q^{74} +(-0.174652 - 0.805724i) q^{75} +(-5.66384 + 0.998688i) q^{76} +(3.38464 - 1.69209i) q^{77} +(1.52475 - 0.623182i) q^{78} +(-0.675969 + 3.83361i) q^{79} +(3.86290 + 6.69073i) q^{80} +(-7.87753 + 4.35254i) q^{81} +(-2.30773 - 1.33237i) q^{82} +(-0.141502 + 0.0515026i) q^{83} +(6.92235 - 5.56418i) q^{84} +(0.355515 - 0.298313i) q^{85} +(0.635099 - 1.74492i) q^{86} +(2.75644 - 8.60100i) q^{87} +(-0.243381 + 1.38028i) q^{88} +(3.40271 + 5.89366i) q^{89} +(-0.425379 + 1.52981i) q^{90} +(9.83439 + 2.34980i) q^{91} +(14.7595 + 2.60251i) q^{92} +(5.67547 - 3.57825i) q^{93} +(-1.43902 + 0.253739i) q^{94} +(6.21587 - 1.09603i) q^{95} +(0.193047 + 4.95649i) q^{96} +(12.2644 + 2.16255i) q^{97} +(-1.73932 + 0.0949204i) q^{98} +(3.53773 - 2.42786i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 9 q^{3} - 3 q^{4} - 9 q^{5} + 18 q^{6} - 6 q^{7} - 18 q^{8} - 15 q^{9} - 9 q^{10} + 9 q^{11} - 9 q^{12} - 42 q^{14} - 24 q^{15} - 15 q^{16} - 9 q^{17} - 3 q^{18} - 9 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} + 30 q^{23} - 36 q^{24} - 3 q^{25} - 12 q^{28} + 6 q^{29} - 3 q^{30} - 9 q^{31} - 51 q^{32} - 9 q^{33} + 18 q^{34} - 9 q^{35} - 6 q^{37} - 9 q^{38} - 9 q^{39} - 9 q^{40} + 27 q^{42} - 12 q^{43} - 63 q^{45} - 6 q^{46} + 45 q^{47} + 30 q^{49} - 9 q^{50} + 33 q^{51} - 9 q^{52} + 45 q^{53} + 117 q^{54} - 51 q^{56} - 3 q^{58} - 9 q^{59} - 15 q^{60} - 63 q^{61} + 99 q^{62} - 33 q^{63} + 18 q^{64} - 102 q^{65} + 63 q^{66} - 3 q^{67} + 144 q^{68} - 108 q^{69} - 15 q^{70} + 18 q^{71} + 15 q^{72} - 33 q^{74} - 9 q^{75} - 36 q^{76} - 57 q^{77} + 66 q^{78} - 21 q^{79} - 72 q^{80} + 57 q^{81} - 18 q^{82} + 90 q^{83} + 51 q^{84} + 9 q^{85} - 33 q^{86} - 9 q^{87} + 45 q^{88} - 9 q^{89} - 81 q^{90} - 21 q^{91} + 150 q^{92} - 87 q^{93} - 9 q^{94} + 27 q^{95} - 9 q^{96} - 180 q^{98} + 96 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 9 * q^3 - 3 * q^4 - 9 * q^5 + 18 * q^6 - 6 * q^7 - 18 * q^8 - 15 * q^9 - 9 * q^10 + 9 * q^11 - 9 * q^12 - 42 * q^14 - 24 * q^15 - 15 * q^16 - 9 * q^17 - 3 * q^18 - 9 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 + 30 * q^23 - 36 * q^24 - 3 * q^25 - 12 * q^28 + 6 * q^29 - 3 * q^30 - 9 * q^31 - 51 * q^32 - 9 * q^33 + 18 * q^34 - 9 * q^35 - 6 * q^37 - 9 * q^38 - 9 * q^39 - 9 * q^40 + 27 * q^42 - 12 * q^43 - 63 * q^45 - 6 * q^46 + 45 * q^47 + 30 * q^49 - 9 * q^50 + 33 * q^51 - 9 * q^52 + 45 * q^53 + 117 * q^54 - 51 * q^56 - 3 * q^58 - 9 * q^59 - 15 * q^60 - 63 * q^61 + 99 * q^62 - 33 * q^63 + 18 * q^64 - 102 * q^65 + 63 * q^66 - 3 * q^67 + 144 * q^68 - 108 * q^69 - 15 * q^70 + 18 * q^71 + 15 * q^72 - 33 * q^74 - 9 * q^75 - 36 * q^76 - 57 * q^77 + 66 * q^78 - 21 * q^79 - 72 * q^80 + 57 * q^81 - 18 * q^82 + 90 * q^83 + 51 * q^84 + 9 * q^85 - 33 * q^86 - 9 * q^87 + 45 * q^88 - 9 * q^89 - 81 * q^90 - 21 * q^91 + 150 * q^92 - 87 * q^93 - 9 * q^94 + 27 * q^95 - 9 * q^96 - 180 * q^98 + 96 * q^99

Introduction

L-functions

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