LMFDB - Embedded newform 189.2.bd.a.185.13

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			185.13
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.13

$q$-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 $\left(\mathbb{Z}/189\mathbb{Z}\right)^\times$.

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

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

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

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

$2$	0.245063	−	0.0432112i	0.173286	−	0.0305549i	−0.0863320	−	0.996266i	$-0.527515\pi$
$2$	0.245063	−	0.0432112i	0.173286	−	0.0305549i	0.259618	+	0.965711i	$0.416403\pi$
$3$	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	0.146062	−	0.989275i	$-0.453340\pi$
$5$	1.99870	−	0.727467i	0.893846	−	0.325333i	0.747784	+	0.663942i	$0.231118\pi$
$6$	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	−0.991334	−	0.131363i	$-0.958065\pi$
$11$	−0.489168	+	1.34398i	−0.147490	+	0.405225i	0.843845	+	0.536588i	$0.180287\pi$
$12$	−1.79029	+	2.83959i	−0.516813	+	0.819719i
$13$	1.30709	+	3.59121i	0.362522	+	0.996021i	0.978135	+	0.207972i	$0.0666864\pi$
$13$	1.30709	+	3.59121i	0.362522	+	0.996021i	−0.615613	+	0.788049i	$0.711091\pi$
$14$	−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	0.878952	−	0.476910i	$-0.158243\pi$
$17$	0.109097	+	0.188961i	0.0264599	+	0.0458299i	−0.852492	+	0.522740i	$0.824910\pi$
$18$	0.0580640	−	0.744269i	0.0136858	−	0.175426i
$19$	2.56992	+	1.48374i	0.589579	+	0.340394i	0.764931	−	0.644112i	$-0.222773\pi$
$19$	2.56992	+	1.48374i	0.589579	+	0.340394i	−0.175352	+	0.984506i	$0.556106\pi$
$20$	−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	−0.691246	−	0.722620i	$-0.742938\pi$
$23$	−7.61556	−	1.34283i	−1.58795	−	0.279999i	−0.896709	+	0.442621i	$0.854049\pi$
$24$	−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	0.656619	+	0.754223i	$0.271986\pi$
$29$	−1.78349	+	4.90009i	−0.331185	+	0.909924i	−0.987804	+	0.155702i	$0.950236\pi$
$30$	0.346835	−	0.848603i	0.0633231	−	0.154933i
$31$	1.32486	+	3.64001i	0.237951	+	0.653766i	0.999981	+	0.00622334i	$0.00198096\pi$
$31$	1.32486	+	3.64001i	0.237951	+	0.653766i	−0.762029	+	0.647543i	$0.775797\pi$
$32$	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	−0.973341	−	0.229364i	$-0.926335\pi$
$41$	−10.0627	+	3.66253i	−1.57153	+	0.571990i	−0.598190	+	0.801354i	$0.704113\pi$
$42$	−0.751248	−	0.857911i	−0.115920	−	0.132379i
$43$	1.29579	+	7.34878i	0.197606	+	1.12068i	0.908659	+	0.417540i	$0.137108\pi$
$43$	1.29579	+	7.34878i	0.197606	+	1.12068i	−0.711053	+	0.703139i	$0.751781\pi$
$44$		−	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	−0.0933687	−	0.995632i	$-0.529764\pi$
$47$	−5.51793	−	2.00836i	−0.804873	−	0.292950i	−0.711504	+	0.702682i	$0.751986\pi$
$48$	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	0.971490	+	0.237080i	$0.0761904\pi$
$53$	12.1036	+	6.98800i	1.66255	+	0.959875i	0.691063	+	0.722795i	$0.257143\pi$
$54$	−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	0.560567	−	0.828109i	$-0.310583\pi$
$59$	−1.21070	−	1.01590i	−0.157620	−	0.132259i	−0.718187	+	0.695850i	$0.755028\pi$
$60$	−1.51255	+	6.97787i	−0.195269	+	0.900839i
$61$	1.45500	−	3.99757i	0.186293	−	0.511837i	−0.811026	−	0.585010i	$-0.801090\pi$
$61$	1.45500	−	3.99757i	0.186293	−	0.511837i	0.997319	+	0.0731735i	$0.0233127\pi$
$62$	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	−0.247376	−	0.968920i	$-0.579568\pi$
$67$	2.59043	−	14.6911i	0.316471	−	1.79480i	0.563848	−	0.825879i	$-0.309321\pi$
$68$	−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	0.223031	−	0.974811i	$-0.428405\pi$
$71$	−4.29452	−	2.47944i	−0.509666	−	0.294256i	−0.732696	+	0.680556i	$0.761738\pi$
$72$	0.787586	+	2.83243i	0.0928179	+	0.333806i
$73$		−	2.46806i		−	0.288864i	−0.989515	−	0.144432i	$-0.953864\pi$
$73$		−	2.46806i		−	0.288864i	0.989515	−	0.144432i	$-0.0461355\pi$
$74$	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	−0.998931	−	0.0462239i	$-0.985281\pi$
$79$	−0.675969	−	3.83361i	−0.0760524	−	0.431315i	0.922879	−	0.385091i	$-0.125830\pi$
$80$	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	0.334243	−	0.942487i	$-0.391520\pi$
$83$	−0.141502	−	0.0515026i	−0.0155319	−	0.00565315i	−0.349774	+	0.936834i	$0.613742\pi$
$84$	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	−0.627388	−	0.778707i	$-0.715876\pi$
$89$	3.40271	−	5.89366i	0.360686	−	0.624727i	0.988074	+	0.153980i	$0.0492092\pi$
$90$	−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	0.488092	−	0.872792i	$-0.337693\pi$
$97$	12.2644	−	2.16255i	1.24526	−	0.219573i	0.757169	+	0.653219i	$0.226582\pi$
$98$	−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	−0.967574	−	0.252589i	$-0.918718\pi$
$101$	−1.45464	−	8.24969i	−0.144742	−	0.820874i	0.822831	−	0.568286i	$-0.192393\pi$
$102$	0.0919091	+	0.0199226i	0.00910036	+	0.00197263i
$103$	−0.0733066	−	0.201408i	−0.00722311	−	0.0198453i	0.936029	−	0.351924i	$-0.114472\pi$
$103$	−0.0733066	−	0.201408i	−0.00722311	−	0.0198453i	−0.943252	+	0.332078i	$0.892250\pi$
$104$	−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	0.480946	−	0.876750i	$-0.340293\pi$
$107$	15.3166	−	8.84302i	1.48071	−	0.854887i	0.999761	+	0.0218632i	$0.00695982\pi$
$108$	6.90767	+	7.32802i	0.664691	+	0.705139i
$109$	−0.476343	+	0.825050i	−0.0456254	+	0.0790255i	−0.887936	−	0.459967i	$-0.847861\pi$
$109$	−0.476343	+	0.825050i	−0.0456254	+	0.0790255i	0.842311	+	0.538992i	$0.181195\pi$
$110$	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	−0.523510	−	0.852020i	$-0.675378\pi$
$113$	−13.8921	−	2.44955i	−1.30686	−	0.230434i	−0.783346	+	0.621586i	$0.786489\pi$
$114$	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	0.738514	−	0.674238i	$-0.235528\pi$
$127$	−2.41898	−	4.18980i	−0.214650	−	0.371785i	−0.953164	+	0.302453i	$0.902194\pi$
$128$	−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	−0.945428	−	0.325831i	$-0.894356\pi$
$131$	0.622917	−	3.53274i	0.0544246	−	0.308657i	0.999853	+	0.0171742i	$0.00546700\pi$
$132$	−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	0.855236	−	0.518238i	$-0.173412\pi$
$137$	2.29835	+	2.73907i	0.196361	+	0.234014i	−0.658875	+	0.752252i	$0.728967\pi$
$138$	−2.63468	+	2.04143i	−0.224279	+	0.173778i
$139$	−3.85722	+	4.59686i	−0.327165	+	0.389900i	−0.904405	−	0.426674i	$-0.859685\pi$
$139$	−3.85722	+	4.59686i	−0.327165	+	0.389900i	0.577240	+	0.816574i	$0.304130\pi$
$140$	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	−0.598915	−	0.800813i	$-0.704401\pi$
$149$	3.58546	−	4.27298i	0.293732	−	0.350057i	0.892647	+	0.450756i	$0.148846\pi$
$150$	−0.00798440	+	0.205000i	−0.000651923	+	0.0167382i
$151$	−1.49517	−	0.544196i	−0.121675	−	0.0442861i	0.280465	−	0.959864i	$-0.409511\pi$
$151$	−1.49517	−	0.544196i	−0.121675	−	0.0442861i	−0.402140	+	0.915578i	$0.631734\pi$
$152$	−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	−0.513412	+	0.858143i	$0.671619\pi$
$157$	−15.9051	+	18.9549i	−1.26936	+	1.51277i	−0.755952	+	0.654627i	$0.772826\pi$
$158$	−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	−0.999956	−	0.00938604i	$-0.997012\pi$
$163$	−6.48707	−	11.2359i	−0.508107	−	0.880066i	0.491849	−	0.870680i	$-0.336321\pi$
$164$	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	−0.878013	−	0.478637i	$-0.841131\pi$
$167$	1.43124	−	8.11696i	0.110753	−	0.628110i	0.988766	−	0.149473i	$-0.0477577\pi$
$168$	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	−0.398793	+	0.917041i	$0.630571\pi$
$173$	−18.0347	+	15.1329i	−1.37115	+	1.15053i	−0.972359	+	0.233491i	$0.924985\pi$
$174$	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	−0.745217	−	0.666822i	$-0.767654\pi$
$179$	−7.22926	+	4.17381i	−0.540340	+	0.311965i	0.204877	+	0.978788i	$0.434321\pi$
$180$	5.33162	+	11.1584i	0.397396	+	0.831696i
$181$	−3.60525	+	2.08149i	−0.267976	+	0.154716i	−0.627967	−	0.778240i	$-0.716113\pi$
$181$	−3.60525	+	2.08149i	−0.267976	+	0.154716i	0.359992	+	0.932956i	$0.382780\pi$
$182$	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	−0.208005	−	0.978128i	$-0.566697\pi$
$191$	−0.952580	+	0.167966i	−0.0689263	+	0.0121536i	0.139079	+	0.990281i	$0.455586\pi$
$192$	1.53417	+	11.2441i	0.110719	+	0.811476i
$193$	6.76620	−	2.46270i	0.487042	−	0.177269i	−0.0868148	−	0.996224i	$-0.527669\pi$
$193$	6.76620	−	2.46270i	0.487042	−	0.177269i	0.573857	+	0.818956i	$0.305447\pi$
$194$	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	−0.233458	−	0.972367i	$-0.575004\pi$
$197$	6.90426	−	3.98617i	0.491908	−	0.284003i	0.725366	+	0.688364i	$0.241671\pi$
$198$	0.971878	+	0.442109i	0.0690684	+	0.0314193i
$199$	−3.69994	+	2.13616i	−0.262282	+	0.151428i	−0.625375	−	0.780324i	$-0.715054\pi$
$199$	−3.69994	+	2.13616i	−0.262282	+	0.151428i	0.363093	+	0.931753i	$0.381721\pi$
$200$	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	−0.540361	−	0.841433i	$-0.681712\pi$
$211$	3.70699	−	21.0234i	0.255199	−	1.44731i	0.795560	−	0.605875i	$-0.207177\pi$
$212$	−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	0.963015	−	0.269447i	$-0.0868408\pi$
$223$	7.92110	+	9.44000i	0.530436	+	0.632149i	−0.432579	+	0.901596i	$0.642396\pi$
$224$	−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	−0.313746	−	0.949507i	$-0.601584\pi$
$227$	−17.5438	−	6.38541i	−1.16442	−	0.423815i	−0.850675	+	0.525692i	$0.823806\pi$
$228$	−8.81413	+	4.64118i	−0.583730	+	0.307370i
$229$	−12.4826	+	14.8762i	−0.824872	+	0.983044i	−0.999999	−	0.00150162i	$-0.999522\pi$
$229$	−12.4826	+	14.8762i	−0.824872	+	0.983044i	0.175127	+	0.984546i	$0.443966\pi$
$230$	−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	$0.142178\pi$
$233$			13.1872i			0.863923i	−0.901892	+	0.431961i	$0.857822\pi$
$234$	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	−0.336043	−	0.941847i	$-0.609089\pi$
$239$	10.0464	−	11.9729i	0.649849	−	0.774460i	0.985891	+	0.167387i	$0.0535330\pi$
$240$	−1.80903	−	13.2586i	−0.116772	−	0.855840i
$241$	4.17444	+	4.97490i	0.268899	+	0.320462i	0.883549	−	0.468338i	$-0.155147\pi$
$241$	4.17444	+	4.97490i	0.268899	+	0.320462i	−0.614650	+	0.788800i	$0.710703\pi$
$242$	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	−0.947143	−	0.320812i	$-0.896044\pi$
$251$	−11.9045	−	20.6191i	−0.751403	−	1.30147i	0.195740	−	0.980656i	$-0.437289\pi$
$252$	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	−0.931446	−	0.363880i	$-0.881452\pi$
$257$	−23.2700	−	19.5258i	−1.45154	−	1.21799i	−0.520096	−	0.854108i	$-0.674104\pi$
$258$	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	0.317047	−	0.948410i	$-0.397309\pi$
$263$	15.2337	−	2.68611i	0.939348	−	0.165632i	0.622302	+	0.782778i	$0.286198\pi$
$264$	−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	−0.855357	−	0.518039i	$-0.826662\pi$
$269$	0.343714	−	0.595329i	0.0209566	−	0.0362979i	0.876314	+	0.481741i	$0.159995\pi$
$270$	−2.20532	−	1.64328i	−0.134212	−	0.100007i
$271$	6.24649	−	3.60641i	0.379447	−	0.219074i	−0.298131	−	0.954525i	$-0.596363\pi$
$271$	6.24649	−	3.60641i	0.379447	−	0.219074i	0.677578	+	0.735451i	$0.263030\pi$
$272$	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	0.978421	+	0.206619i	$0.0662461\pi$
$277$	2.15820	+	12.2398i	0.129674	+	0.735417i	−0.848748	+	0.528798i	$0.822643\pi$
$278$	−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	−0.112011	−	0.993707i	$-0.535729\pi$
$281$	2.05517	−	0.362382i	0.122601	−	0.0216179i	0.234612	+	0.972089i	$0.424618\pi$
$282$	−2.23942	+	1.17919i	−0.133356	+	0.0702200i
$283$	19.9337	+	3.51484i	1.18493	+	0.208936i	0.731175	−	0.682189i	$-0.238972\pi$
$283$	19.9337	+	3.51484i	1.18493	+	0.208936i	0.453758	+	0.891125i	$0.350083\pi$
$284$	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	0.995139	+	0.0984780i	$0.0313974\pi$
$293$	21.6520	+	18.1682i	1.26493	+	1.06140i	0.269786	+	0.962920i	$0.413047\pi$
$294$	−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	0.450170	−	0.892943i	$-0.351363\pi$
$307$	−1.71807	−	0.991927i	−0.0980553	−	0.0566122i	−0.548226	+	0.836330i	$0.684697\pi$
$308$	−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	0.841949	+	0.539557i	$0.181408\pi$
$311$	−2.35895	+	13.3783i	−0.133764	+	0.758612i	−0.975713	+	0.219054i	$0.929703\pi$
$312$	−6.48181	−	0.252455i	−0.366960	−	0.0142925i
$313$	−9.40882	−	11.2130i	−0.531818	−	0.633796i	0.431515	−	0.902106i	$-0.357979\pi$
$313$	−9.40882	−	11.2130i	−0.531818	−	0.633796i	−0.963333	+	0.268310i	$0.913535\pi$
$314$	−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	0.614707	+	0.788755i	$0.289274\pi$
$317$	−6.46638	+	17.7662i	−0.363188	+	0.997850i	−0.977895	+	0.209095i	$0.932948\pi$
$318$	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	0.0175134	−	0.999847i	$-0.494425\pi$
$331$	−11.1300	−	4.05098i	−0.611760	−	0.222662i	−0.629273	+	0.777184i	$0.716647\pi$
$332$	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	0.255747	−	0.966744i	$-0.417679\pi$
$337$	19.6990	−	7.16984i	1.07307	−	0.390566i	0.817324	+	0.576178i	$0.195456\pi$
$338$	−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	0.816222	+	0.577738i	$0.196065\pi$
$347$	10.4749	+	28.7796i	0.562323	+	1.54497i	−0.253899	+	0.967231i	$0.581713\pi$
$348$	−10.7213	−	13.8370i	−0.574721	−	0.741740i
$349$	−6.58819	+	18.1009i	−0.352658	+	0.968919i	0.628855	+	0.777523i	$0.283524\pi$
$349$	−6.58819	+	18.1009i	−0.352658	+	0.968919i	−0.981513	+	0.191397i	$0.938698\pi$
$350$	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	−0.936113	−	0.351700i	$-0.885604\pi$
$353$	−14.1346	+	11.8604i	−0.752311	+	0.631264i	0.183802	+	0.982963i	$0.441159\pi$
$354$	−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	0.482075	−	0.876130i	$-0.339883\pi$
$359$	−0.675231	−	0.389845i	−0.0356373	−	0.0205752i	−0.517713	+	0.855554i	$0.673216\pi$
$360$	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	0.492599	+	0.870256i	$0.336047\pi$
$367$	−8.50857	+	23.3771i	−0.444144	+	1.22027i	−0.936743	+	0.350018i	$0.886175\pi$
$368$	−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	0.317367	−	0.948303i	$-0.397201\pi$
$373$	22.5973	−	8.22473i	1.17004	−	0.425860i	0.852675	+	0.522442i	$0.174979\pi$
$374$	−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	0.729943	−	0.683508i	$-0.239546\pi$
$383$	33.8267	−	12.3119i	1.72846	−	0.629109i	0.998519	+	0.0543988i	$0.0173242\pi$
$384$	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	−0.526859	−	0.849953i	$-0.676631\pi$
$389$	8.34439	−	22.9260i	0.423077	−	1.16240i	0.949937	−	0.312443i	$-0.101147\pi$
$390$	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	0.639729	−	0.768601i	$-0.279047\pi$
$397$	5.85723	+	3.38167i	0.293966	+	0.169721i	−0.345763	+	0.938322i	$0.612380\pi$
$398$	−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	0.149923	−	0.988698i	$-0.452097\pi$
$401$	−0.948178	−	0.167189i	−0.0473497	−	0.00834904i	−0.197273	+	0.980349i	$0.563208\pi$
$402$	−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	−0.899376	−	0.437176i	$-0.855979\pi$
$409$	−9.93846	−	27.3057i	−0.491425	−	1.35018i	0.407951	−	0.913004i	$-0.366244\pi$
$410$	−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	0.284141	−	0.958782i	$-0.408292\pi$
$419$	22.8869	−	8.33016i	1.11810	−	0.406955i	0.833958	+	0.551828i	$0.186069\pi$
$420$	17.8835	+	6.08535i	0.872623	+	0.296934i
$421$	2.03579	+	11.5455i	0.0992181	+	0.562694i	0.993373	+	0.114936i	$0.0366663\pi$
$421$	2.03579	+	11.5455i	0.0992181	+	0.562694i	−0.894155	+	0.447758i	$0.852223\pi$
$422$		−	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	−0.167610	−	0.985853i	$-0.553605\pi$
$431$	−22.9443	−	13.2469i	−1.10519	−	0.638082i	−0.937579	+	0.347772i	$0.886938\pi$
$432$	−16.8627	−	8.47788i	−0.811309	−	0.407892i
$433$		−	23.5474i		−	1.13161i	−0.824538	−	0.565807i	$-0.808565\pi$
$433$		−	23.5474i		−	1.13161i	0.824538	−	0.565807i	$-0.191435\pi$
$434$	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	−0.900939	−	0.433946i	$-0.857121\pi$
$439$	1.42802	−	3.92345i	0.0681557	−	0.187256i	0.969094	+	0.246690i	$0.0793430\pi$
$440$	−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	0.801843	−	0.597534i	$-0.203853\pi$
$443$	1.56064	+	1.85990i	0.0741482	+	0.0883663i	−0.727695	+	0.685901i	$0.759408\pi$
$444$	−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	0.718955	−	0.695057i	$-0.244621\pi$
$449$	10.0967	+	5.82936i	0.476495	+	0.275104i	−0.242460	+	0.970161i	$0.577954\pi$
$450$	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	−0.940930	−	0.338600i	$-0.890047\pi$
$457$	−3.68876	−	20.9200i	−0.172553	−	0.978597i	0.768377	−	0.639997i	$-0.221064\pi$
$458$	−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	0.855498	−	0.517806i	$-0.173251\pi$
$461$	25.2929	+	9.20586i	1.17801	+	0.428760i	0.322510	+	0.946566i	$0.395473\pi$
$462$	1.52050	−	0.589998i	0.0707401	−	0.0274492i
$463$	18.3826	+	15.4248i	0.854311	+	0.716852i	0.960735	−	0.277469i	$-0.0894956\pi$
$463$	18.3826	+	15.4248i	0.854311	+	0.716852i	−0.106424	+	0.994321i	$0.533940\pi$
$464$	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	−0.785491	−	0.618873i	$-0.787590\pi$
$467$	3.09488	−	5.36049i	0.143214	−	0.248054i	0.928705	+	0.370819i	$0.120923\pi$
$468$	−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	0.979543	+	0.201233i	$0.0644947\pi$
$479$	2.79921	+	15.8751i	0.127899	+	0.725353i	−0.851644	+	0.524121i	$0.824394\pi$
$480$	−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	0.403931	+	0.914789i	$0.367643\pi$
$487$	−13.0260	+	22.5617i	−0.590265	+	1.02237i	−0.994196	+	0.107580i	$0.965690\pi$
$488$	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	0.403102	−	0.915155i	$-0.367932\pi$
$491$	10.3899	+	1.83203i	0.468892	+	0.0826783i	0.0657902	+	0.997833i	$0.479043\pi$
$492$	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	0.493798	−	0.869577i	$-0.335608\pi$
$499$	−6.18372	−	5.18876i	−0.276822	−	0.232281i	−0.770619	+	0.637296i	$0.780053\pi$
$500$	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	0.270658	+	0.962676i	$0.412759\pi$
$503$	−15.6629	+	27.1289i	−0.698373	+	1.20962i	−0.969030	+	0.246941i	$0.920575\pi$
$504$	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	−0.276552	−	0.960999i	$-0.589192\pi$
$509$	7.03911	−	39.9208i	0.312003	−	1.76946i	0.588555	−	0.808457i	$-0.299697\pi$
$510$	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	$-0.900866\pi$
$523$		−	14.0156i		−	0.612858i	0.951894	−	0.306429i	$-0.0991342\pi$
$524$	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	−0.999892	−	0.0147075i	$-0.995318\pi$
$541$	−11.9247	−	20.6542i	−0.512683	−	0.887993i	0.487209	−	0.873285i	$-0.338015\pi$
$542$	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	−0.654153	−	0.756362i	$-0.726975\pi$
$547$	−0.534982	+	0.448903i	−0.0228742	+	0.0191937i	0.631279	+	0.775556i	$0.282530\pi$
$548$	−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	−0.281852	−	0.959458i	$-0.590949\pi$
$557$	9.63238	−	5.56126i	0.408137	−	0.235638i	0.689989	+	0.723820i	$0.257615\pi$
$558$	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	−0.109815	−	0.993952i	$-0.535026\pi$
$563$	10.5579	−	3.84276i	0.444962	−	0.161953i	0.554777	+	0.831999i	$0.312804\pi$
$564$	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	0.632855	−	0.774270i	$-0.281883\pi$
$569$	35.5984	−	6.27695i	1.49236	−	0.263143i	0.859505	+	0.511127i	$0.170772\pi$
$570$	2.15044	−	1.66623i	0.0900722	−	0.0697906i
$571$	−18.7772	+	6.83434i	−0.785802	+	0.286008i	−0.703590	−	0.710607i	$-0.748421\pi$
$571$	−18.7772	+	6.83434i	−0.785802	+	0.286008i	−0.0822119	+	0.996615i	$0.526198\pi$
$572$	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	0.165450	−	0.986218i	$-0.447092\pi$
$577$	26.4773	−	15.2867i	1.10226	−	0.636393i	0.936815	+	0.349825i	$0.113759\pi$
$578$	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	−0.983431	−	0.181285i	$-0.941974\pi$
$587$	−23.6386	+	19.8352i	−0.975671	+	0.818685i	0.00775999	+	0.999970i	$0.497530\pi$
$588$	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	0.983046	+	0.183358i	$0.0586968\pi$
$593$	15.8362	+	27.4292i	0.650316	+	1.12638i	−0.332730	+	0.943022i	$0.607970\pi$
$594$	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	−0.925052	−	0.379841i	$-0.875979\pi$
$599$	−9.55357	+	11.3855i	−0.390348	+	0.465199i	0.534703	+	0.845040i	$0.320423\pi$
$600$	−0.246568	−	0.769374i	−0.0100661	−	0.0314095i
$601$	−11.0892	−	13.2156i	−0.452338	−	0.539075i	0.490890	−	0.871221i	$-0.336672\pi$
$601$	−11.0892	−	13.2156i	−0.452338	−	0.539075i	−0.943228	+	0.332146i	$0.892227\pi$
$602$	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	−0.0974887	+	0.995237i	$0.531081\pi$
$607$	−26.1323	+	31.1432i	−1.06068	+	1.26407i	−0.963188	+	0.268829i	$0.913363\pi$
$608$	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	−0.707180	−	0.707033i	$-0.750033\pi$
$617$	2.77984	−	3.31289i	0.111912	−	0.133372i	0.819092	+	0.573661i	$0.194477\pi$
$618$	−0.0855134	−	0.0349504i	−0.00343985	−	0.00140591i
$619$	9.94128	+	11.8476i	0.399574	+	0.476193i	0.927890	−	0.372854i	$-0.121621\pi$
$619$	9.94128	+	11.8476i	0.399574	+	0.476193i	−0.528316	+	0.849048i	$0.677176\pi$
$620$	−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	0.295776	+	0.955257i	$0.404422\pi$
$631$	−17.0661	+	29.5593i	−0.679389	+	1.17674i	−0.975165	+	0.221479i	$0.928911\pi$
$632$	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	−0.108735	−	0.994071i	$-0.534680\pi$
$641$	3.26804	−	0.576243i	0.129080	−	0.0227602i	0.237815	+	0.971311i	$0.423569\pi$
$642$	1.61486	−	7.44984i	0.0637333	−	0.294022i
$643$	−24.9953	−	4.40734i	−0.985717	−	0.173808i	−0.342521	−	0.939510i	$-0.611281\pi$
$643$	−24.9953	−	4.40734i	−0.985717	−	0.173808i	−0.643196	+	0.765702i	$0.722392\pi$
$644$	−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	−0.862663	−	0.505779i	$-0.831205\pi$
$647$	0.170073	−	0.294574i	0.00668625	−	0.0115809i	0.869349	+	0.494198i	$0.164538\pi$
$648$	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	−0.972903	−	0.231212i	$-0.925731\pi$
$653$	−9.61429	−	26.4150i	−0.376236	−	1.03370i	0.596667	−	0.802489i	$-0.296491\pi$
$654$	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	0.422682	−	0.906278i	$-0.361089\pi$
$659$	29.0041	−	5.11420i	1.12984	−	0.199221i	0.707157	+	0.707057i	$0.249978\pi$
$660$	−8.63822	−	5.44619i	−0.336242	−	0.211993i
$661$	−0.798762	−	0.140843i	−0.0310682	−	0.00547817i	0.158092	−	0.987424i	$-0.449466\pi$
$661$	−0.798762	−	0.140843i	−0.0310682	−	0.00547817i	−0.189161	+	0.981946i	$0.560577\pi$
$662$	−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	0.566816	−	0.823844i	$-0.308175\pi$
$673$	12.2309	+	4.45168i	0.471466	+	0.171600i	−0.0953502	+	0.995444i	$0.530397\pi$
$674$	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	0.996685	+	0.0813620i	$0.0259270\pi$
$677$	2.28800	+	12.9759i	0.0879349	+	0.498704i	−0.908750	+	0.417341i	$0.862962\pi$
$678$	−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	$0.0381723\pi$
$683$			6.25312i			0.239269i	−0.992818	+	0.119635i	$0.961828\pi$
$684$	−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	0.698359	−	0.715747i	$-0.253914\pi$
$691$	−3.35901	−	4.00311i	−0.127783	−	0.152286i	−0.826142	+	0.563462i	$0.809469\pi$
$692$	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	$0.135024\pi$
$701$			21.7945i			0.823166i	−0.911372	+	0.411583i	$0.864976\pi$
$702$	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	0.0186255	−	0.999827i	$-0.494071\pi$
$709$	−16.2367	−	5.90968i	−0.609783	−	0.221943i	−0.628408	+	0.777884i	$0.716293\pi$
$710$	−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	−0.834380	−	0.551189i	$-0.814174\pi$
$727$	4.28953	−	11.7854i	0.159090	−	0.437095i	0.993470	+	0.114094i	$0.0363965\pi$
$728$	−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	−0.167704	−	0.985837i	$-0.553635\pi$
$733$	−17.9357	−	3.16255i	−0.662471	−	0.116812i	−0.494767	+	0.869026i	$0.664747\pi$
$734$	−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	0.840563	+	0.541714i	$0.182224\pi$
$739$	24.1785	+	41.8783i	0.889420	+	1.54052i	0.0488568	+	0.998806i	$0.484442\pi$
$740$	−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	0.952780	+	0.303662i	$0.0982092\pi$
$743$	11.3965	+	31.3117i	0.418098	+	1.14872i	−0.534682	+	0.845053i	$0.679569\pi$
$744$	−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	−0.840129	−	0.542387i	$-0.817521\pi$
$751$	−31.1058	+	11.3216i	−1.13507	+	0.413130i	−0.294937	+	0.955517i	$0.595299\pi$
$752$	−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	−0.240203	−	0.970723i	$-0.577214\pi$
$761$	5.51061	−	2.00570i	0.199760	−	0.0727065i	0.439962	+	0.898016i	$0.354992\pi$
$762$	−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	0.771404	−	0.636346i	$-0.219555\pi$
$769$	−6.33820	−	17.4141i	−0.228561	−	0.627967i	−0.999965	+	0.00837935i	$0.997333\pi$
$770$	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	0.803507	−	0.595295i	$-0.202965\pi$
$773$	−3.16361	−	5.47954i	−0.113787	−	0.197085i	−0.917294	+	0.398210i	$0.869632\pi$
$774$	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	0.793605	+	0.608434i	$0.208202\pi$
$787$	16.1802	+	44.4547i	0.576762	+	1.58464i	−0.216843	+	0.976206i	$0.569576\pi$
$788$	−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	−0.591257	−	0.806483i	$-0.701368\pi$
$797$	−14.8436	+	5.40264i	−0.525788	+	0.191371i	0.0654686	+	0.997855i	$0.479146\pi$
$798$	−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	−0.999635	−	0.0269998i	$-0.991405\pi$
$809$	−43.3139	−	25.0073i	−1.52284	−	0.879210i	−0.523200	−	0.852210i	$-0.675262\pi$
$810$	−4.76270	+	0.0896380i	−0.167344	+	0.00314956i
$811$			43.1499i			1.51520i	0.652720	+	0.757600i	$0.273628\pi$
$811$			43.1499i			1.51520i	−0.652720	+	0.757600i	$0.726372\pi$
$812$	−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	0.990071	−	0.140571i	$-0.0448938\pi$
$821$	19.4758	+	23.2104i	0.679711	+	0.810048i	−0.310359	+	0.950619i	$0.600449\pi$
$822$	1.53995	+	0.0599783i	0.0537119	+	0.00209198i
$823$	3.77527	−	21.4106i	0.131598	−	0.746327i	−0.845571	−	0.533862i	$-0.820740\pi$
$823$	3.77527	−	21.4106i	0.131598	−	0.746327i	0.977169	−	0.212464i	$-0.0681489\pi$
$824$	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	0.613586	−	0.789628i	$-0.289726\pi$
$827$	6.80237	+	3.92735i	0.236541	+	0.136567i	−0.377045	+	0.926195i	$0.623060\pi$
$828$	3.49706	−	44.8255i	0.121531	−	1.55779i
$829$		−	4.06084i		−	0.141039i	−0.997510	−	0.0705193i	$-0.977534\pi$
$829$		−	4.06084i		−	0.141039i	0.997510	−	0.0705193i	$-0.0224656\pi$
$830$	−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	0.603366	−	0.797464i	$-0.293826\pi$
$839$	16.0171	+	5.82975i	0.552971	+	0.201265i	−0.0503948	+	0.998729i	$0.516048\pi$
$840$	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	−0.568563	−	0.822640i	$-0.692500\pi$
$853$	−23.9922	+	4.23048i	−0.821478	+	0.144849i	−0.252915	+	0.967488i	$0.581389\pi$
$854$	−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	0.540157	+	0.841565i	$0.318365\pi$
$857$	9.37979	+	53.1954i	0.320407	+	1.81712i	−0.219749	+	0.975556i	$0.570524\pi$
$858$	−1.58340	+	1.74438i	−0.0540564	+	0.0595523i
$859$	−9.38266	−	25.7786i	−0.320132	−	0.879556i	−0.990498	−	0.137525i	$-0.956085\pi$
$859$	−9.38266	−	25.7786i	−0.320132	−	0.879556i	0.670366	−	0.742031i	$-0.266137\pi$
$860$	−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	−0.254143	−	0.967167i	$-0.581793\pi$
$863$	13.4069	−	7.74047i	0.456376	−	0.263489i	0.710519	+	0.703678i	$0.248460\pi$
$864$	−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	0.977808	−	0.209501i	$-0.0671839\pi$
$877$	27.8754	+	23.3902i	0.941285	+	0.789832i	−0.0365234	+	0.999333i	$0.511628\pi$
$878$	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	−0.445285	−	0.895389i	$-0.646898\pi$
$881$	16.4076	−	28.4188i	0.552787	−	0.957455i	0.998072	−	0.0620663i	$-0.0197690\pi$
$882$	−1.57876	+	4.98152i	−0.0531596	+	0.167737i
$883$	−4.24994	−	7.36111i	−0.143022	−	0.247721i	0.785611	−	0.618720i	$-0.212349\pi$
$883$	−4.24994	−	7.36111i	−0.143022	−	0.247721i	−0.928633	+	0.370999i	$0.879015\pi$
$884$	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	−0.999151	−	0.0412003i	$-0.986882\pi$
$887$	−1.37491	+	7.79748i	−0.0461648	+	0.261814i	0.952986	+	0.303014i	$0.0979929\pi$
$888$	−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	0.845670	−	0.533706i	$-0.179201\pi$
$907$	34.6469	+	12.6104i	1.15043	+	0.418722i	0.304761	+	0.952429i	$0.401423\pi$
$908$	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	0.702557	−	0.711627i	$-0.252041\pi$
$911$	−3.62967	−	4.32568i	−0.120256	−	0.143316i	−0.822814	+	0.568311i	$0.807597\pi$
$912$	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	0.986294	−	0.165000i	$-0.0527624\pi$
$919$	10.6179	+	18.3908i	0.350253	+	0.606655i	−0.636041	+	0.771655i	$0.719429\pi$
$920$	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	−0.987053	−	0.160395i	$-0.948723\pi$
$929$	−30.4946	+	25.5880i	−1.00050	+	0.839515i	−0.0134422	+	0.999910i	$0.504279\pi$
$930$	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	−0.462604	−	0.886565i	$-0.653085\pi$
$937$	2.26157	−	1.30572i	0.0738824	−	0.0426560i	0.536486	+	0.843909i	$0.319751\pi$
$938$	−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	−0.754268	−	0.656566i	$-0.772008\pi$
$941$	−27.9161	+	10.1606i	−0.910038	+	0.331227i	−0.155770	+	0.987793i	$0.549786\pi$
$942$	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	0.110513	−	0.993875i	$-0.464751\pi$
$947$	17.0572	−	3.00765i	0.554285	−	0.0977355i	0.443773	+	0.896139i	$0.353640\pi$
$948$	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	−0.747525	−	0.664234i	$-0.768758\pi$
$953$	−16.8568	+	9.73226i	−0.546044	+	0.315259i	0.201481	+	0.979492i	$0.435425\pi$
$954$	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	−0.894095	−	0.447878i	$-0.852180\pi$
$967$	3.08674	−	17.5057i	0.0992627	−	0.562947i	0.993357	−	0.115069i	$-0.0367089\pi$
$968$	−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	−0.999995	−	0.00307625i	$-0.999021\pi$
$971$	−15.6634	−	27.1298i	−0.502662	−	0.870636i	0.497334	−	0.867559i	$-0.334313\pi$
$972$	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	−0.768239	−	0.640164i	$-0.778867\pi$
$977$	−0.137449	+	0.163806i	−0.00439739	+	0.00524061i	0.763841	+	0.645404i	$0.223311\pi$
$978$	−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	0.0338747	−	0.999426i	$-0.489215\pi$
$983$	−18.2660	−	6.64828i	−0.582595	−	0.212047i	−0.616469	+	0.787379i	$0.711438\pi$
$984$	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	0.308465	−	0.951236i	$-0.400185\pi$
$997$	−21.5307	−	25.6593i	−0.681883	−	0.812637i	−0.990349	+	0.138599i	$0.955740\pi$
$998$	−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.185.13	yes	132
3.2	odd	2		567.2.bd.a.17.10		132
7.5	odd	6		189.2.ba.a.131.10	yes	132
21.5	even	6		567.2.ba.a.341.13		132
27.7	even	9		567.2.ba.a.143.13		132
27.20	odd	18		189.2.ba.a.101.10	✓	132
189.47	even	18	inner	189.2.bd.a.47.13	yes	132
189.61	odd	18		567.2.bd.a.467.10		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.10	✓	132	27.20	odd	18
189.2.ba.a.131.10	yes	132	7.5	odd	6
189.2.bd.a.47.13	yes	132	189.47	even	18	inner
189.2.bd.a.185.13	yes	132	1.1	even	1	trivial
567.2.ba.a.143.13		132	27.7	even	9
567.2.ba.a.341.13		132	21.5	even	6
567.2.bd.a.17.10		132	3.2	odd	2
567.2.bd.a.467.10		132	189.61	odd	18

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

Modular forms

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