LMFDB - Embedded newform 189.2.bd.a.185.6

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			185.6
Character	$\chi$	$=$	189.185
Dual form			189.2.bd.a.47.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.57155 + 0.277106i) q^{2} +(1.72554 - 0.149982i) q^{3} +(0.513586 - 0.186930i) q^{4} +(1.78318 - 0.649025i) q^{5} +(-2.67021 + 0.713863i) q^{6} +(-1.28547 + 2.31248i) q^{7} +(2.00866 - 1.15970i) q^{8} +(2.95501 - 0.517603i) q^{9} +O(q^{10})$	\(q+(-1.57155 + 0.277106i) q^{2} +(1.72554 - 0.149982i) q^{3} +(0.513586 - 0.186930i) q^{4} +(1.78318 - 0.649025i) q^{5} +(-2.67021 + 0.713863i) q^{6} +(-1.28547 + 2.31248i) q^{7} +(2.00866 - 1.15970i) q^{8} +(2.95501 - 0.517603i) q^{9} +(-2.62250 + 1.51410i) q^{10} +(0.432011 - 1.18694i) q^{11} +(0.858180 - 0.399585i) q^{12} +(0.326917 + 0.898197i) q^{13} +(1.37938 - 3.99038i) q^{14} +(2.97962 - 1.38737i) q^{15} +(-3.67271 + 3.08177i) q^{16} +(-2.00687 - 3.47600i) q^{17} +(-4.50051 + 1.63229i) q^{18} +(6.64640 + 3.83730i) q^{19} +(0.794495 - 0.666660i) q^{20} +(-1.87131 + 4.18309i) q^{21} +(-0.350017 + 1.98504i) q^{22} +(5.63807 + 0.994145i) q^{23} +(3.29211 - 2.30238i) q^{24} +(-1.07172 + 0.899282i) q^{25} +(-0.762661 - 1.32097i) q^{26} +(5.02137 - 1.33635i) q^{27} +(-0.227929 + 1.42795i) q^{28} +(-1.22870 + 3.37583i) q^{29} +(-4.29816 + 3.00598i) q^{30} +(-3.04428 - 8.36408i) q^{31} +(1.93608 - 2.30734i) q^{32} +(0.567434 - 2.11291i) q^{33} +(4.11711 + 4.90658i) q^{34} +(-0.791374 + 4.95787i) q^{35} +(1.42090 - 0.818214i) q^{36} -7.99870 q^{37} +(-11.5085 - 4.18874i) q^{38} +(0.698824 + 1.50085i) q^{39} +(2.82914 - 3.37163i) q^{40} +(-3.01647 + 1.09790i) q^{41} +(1.78169 - 7.09246i) q^{42} +(0.111496 + 0.632326i) q^{43} -0.690352i q^{44} +(4.93338 - 2.84085i) q^{45} -9.13598 q^{46} +(-8.03521 - 2.92458i) q^{47} +(-5.87521 + 5.86857i) q^{48} +(-3.69512 - 5.94526i) q^{49} +(1.43506 - 1.71024i) q^{50} +(-3.98428 - 5.69699i) q^{51} +(0.335800 + 0.400191i) q^{52} +(-11.3329 - 6.54305i) q^{53} +(-7.52101 + 3.49158i) q^{54} -2.39691i q^{55} +(0.0997058 + 6.13576i) q^{56} +(12.0442 + 5.62459i) q^{57} +(0.995499 - 5.64576i) q^{58} +(-1.65418 - 1.38802i) q^{59} +(1.27095 - 1.26951i) q^{60} +(-1.05430 + 2.89668i) q^{61} +(7.10196 + 12.3010i) q^{62} +(-2.60164 + 7.49876i) q^{63} +(2.39111 - 4.14152i) q^{64} +(1.16590 + 1.38947i) q^{65} +(-0.306248 + 3.47778i) q^{66} +(0.371427 - 2.10647i) q^{67} +(-1.68047 - 1.41008i) q^{68} +(9.87786 + 0.869829i) q^{69} +(-0.130175 - 8.01082i) q^{70} +(-0.154696 - 0.0893139i) q^{71} +(5.33536 - 4.46663i) q^{72} +11.5040i q^{73} +(12.5703 - 2.21649i) q^{74} +(-1.71443 + 1.71249i) q^{75} +(4.13081 + 0.728373i) q^{76} +(2.18944 + 2.52480i) q^{77} +(-1.51413 - 2.16500i) q^{78} +(-0.211994 - 1.20228i) q^{79} +(-4.54896 + 7.87903i) q^{80} +(8.46417 - 3.05904i) q^{81} +(4.43628 - 2.56129i) q^{82} +(-5.11532 - 1.86183i) q^{83} +(-0.179134 + 2.49818i) q^{84} +(-5.83462 - 4.89582i) q^{85} +(-0.350443 - 0.962834i) q^{86} +(-1.61386 + 6.00943i) q^{87} +(-0.508733 - 2.88517i) q^{88} +(2.81958 - 4.88366i) q^{89} +(-6.96582 + 5.83160i) q^{90} +(-2.49730 - 0.398619i) q^{91} +(3.08147 - 0.543347i) q^{92} +(-6.50750 - 13.9760i) q^{93} +(13.4381 + 2.36950i) q^{94} +(14.3422 + 2.52892i) q^{95} +(2.99474 - 4.27179i) q^{96} +(5.97585 - 1.05370i) q^{97} +(7.45452 + 8.31931i) q^{98} +(0.662233 - 3.73103i) 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 $

$2$	−1.57155	+	0.277106i	−1.11125	+	0.195944i	−0.698997	−	0.715125i	$-0.746370\pi$
$2$	−1.57155	+	0.277106i	−1.11125	+	0.195944i	−0.412255	+	0.911069i	$0.635259\pi$
$3$	1.72554	−	0.149982i	0.996244	−	0.0865924i
$3$	1.72554	−	0.149982i	0.996244	−	0.0865924i
$4$	0.513586	−	0.186930i	0.256793	−	0.0934650i
$5$	1.78318	−	0.649025i	0.797463	−	0.290253i	0.0890280	−	0.996029i	$-0.471624\pi$
$5$	1.78318	−	0.649025i	0.797463	−	0.290253i	0.708435	+	0.705776i	$0.249402\pi$
$6$	−2.67021	+	0.713863i	−1.09011	+	0.291434i
$7$	−1.28547	+	2.31248i	−0.485863	+	0.874035i
$7$	−1.28547	+	2.31248i	−0.485863	+	0.874035i
$8$	2.00866	−	1.15970i	0.710170	−	0.410017i
$9$	2.95501	−	0.517603i	0.985004	−	0.172534i
$10$	−2.62250	+	1.51410i	−0.829308	+	0.478801i
$11$	0.432011	−	1.18694i	0.130256	−	0.357876i	−0.857370	−	0.514700i	$-0.827903\pi$
$11$	0.432011	−	1.18694i	0.130256	−	0.357876i	0.987627	+	0.156824i	$0.0501256\pi$
$12$	0.858180	−	0.399585i	0.247735	−	0.115350i
$13$	0.326917	+	0.898197i	0.0906704	+	0.249115i	0.976736	−	0.214445i	$-0.0687942\pi$
$13$	0.326917	+	0.898197i	0.0906704	+	0.249115i	−0.886066	+	0.463560i	$0.846572\pi$
$14$	1.37938	−	3.99038i	0.368654	−	1.06647i
$15$	2.97962	−	1.38737i	0.769334	−	0.358217i
$16$	−3.67271	+	3.08177i	−0.918177	+	0.770442i
$17$	−2.00687	−	3.47600i	−0.486737	−	0.843053i	0.513147	−	0.858301i	$-0.328480\pi$
$17$	−2.00687	−	3.47600i	−0.486737	−	0.843053i	−0.999884	+	0.0152477i	$0.995146\pi$
$18$	−4.50051	+	1.63229i	−1.06078	+	0.384734i
$19$	6.64640	+	3.83730i	1.52479	+	0.880338i	0.999569	+	0.0293716i	$0.00935062\pi$
$19$	6.64640	+	3.83730i	1.52479	+	0.880338i	0.525221	+	0.850966i	$0.323983\pi$
$20$	0.794495	−	0.666660i	0.177654	−	0.149070i
$21$	−1.87131	+	4.18309i	−0.408353	+	0.912824i
$22$	−0.350017	+	1.98504i	−0.0746239	+	0.423213i
$23$	5.63807	+	0.994145i	1.17562	+	0.207293i	0.727133	−	0.686496i	$-0.240852\pi$
$23$	5.63807	+	0.994145i	1.17562	+	0.207293i	0.448486	+	0.893790i	$0.351963\pi$
$24$	3.29211	−	2.30238i	0.671998	−	0.469972i
$25$	−1.07172	+	0.899282i	−0.214344	+	0.179856i
$26$	−0.762661	−	1.32097i	−0.149570	−	0.259063i
$27$	5.02137	−	1.33635i	0.966364	−	0.257180i
$28$	−0.227929	+	1.42795i	−0.0430745	+	0.269857i
$29$	−1.22870	+	3.37583i	−0.228164	+	0.626876i	−0.999960	−	0.00899503i	$-0.997137\pi$
$29$	−1.22870	+	3.37583i	−0.228164	+	0.626876i	0.771795	+	0.635871i	$0.219359\pi$
$30$	−4.29816	+	3.00598i	−0.784733	+	0.548815i
$31$	−3.04428	−	8.36408i	−0.546768	−	1.50223i	−0.838048	−	0.545596i	$-0.816303\pi$
$31$	−3.04428	−	8.36408i	−0.546768	−	1.50223i	0.291280	−	0.956638i	$-0.405919\pi$
$32$	1.93608	−	2.30734i	0.342255	−	0.407883i
$33$	0.567434	−	2.11291i	0.0987776	−	0.367811i
$34$	4.11711	+	4.90658i	0.706078	+	0.841471i
$35$	−0.791374	+	4.95787i	−0.133767	+	0.838033i
$36$	1.42090	−	0.818214i	0.236816	−	0.136369i
$37$	−7.99870			−1.31498			−0.657489	−	0.753464i	$-0.728381\pi$
$37$	−7.99870			−1.31498			−0.657489	+	0.753464i	$0.728381\pi$
$38$	−11.5085	−	4.18874i	−1.86692	−	0.679504i
$39$	0.698824	+	1.50085i	0.111901	+	0.240328i
$40$	2.82914	−	3.37163i	0.447326	−	0.533102i
$41$	−3.01647	+	1.09790i	−0.471093	+	0.171464i	−0.566647	−	0.823960i	$-0.691760\pi$
$41$	−3.01647	+	1.09790i	−0.471093	+	0.171464i	0.0955544	+	0.995424i	$0.469538\pi$
$42$	1.78169	−	7.09246i	0.274921	−	1.09439i
$43$	0.111496	+	0.632326i	0.0170030	+	0.0964289i	0.992128	−	0.125226i	$-0.0399654\pi$
$43$	0.111496	+	0.632326i	0.0170030	+	0.0964289i	−0.975125	+	0.221654i	$0.928854\pi$
$44$		−	0.690352i		−	0.104074i
$45$	4.93338	−	2.84085i	0.735425	−	0.423490i
$46$	−9.13598			−1.34703
$47$	−8.03521	−	2.92458i	−1.17206	−	0.426593i	−0.318666	−	0.947867i	$-0.603235\pi$
$47$	−8.03521	−	2.92458i	−1.17206	−	0.426593i	−0.853389	+	0.521274i	$0.825457\pi$
$48$	−5.87521	+	5.86857i	−0.848014	+	0.847055i
$49$	−3.69512	−	5.94526i	−0.527874	−	0.849323i
$50$	1.43506	−	1.71024i	0.202949	−	0.241865i
$51$	−3.98428	−	5.69699i	−0.557911	−	0.797739i
$52$	0.335800	+	0.400191i	0.0465671	+	0.0554965i
$53$	−11.3329	−	6.54305i	−1.55669	−	0.898757i	−0.997570	−	0.0696726i	$-0.977805\pi$
$53$	−11.3329	−	6.54305i	−1.55669	−	0.898757i	−0.559123	−	0.829085i	$-0.688862\pi$
$54$	−7.52101	+	3.49158i	−1.02348	+	0.475144i
$55$		−	2.39691i		−	0.323200i
$56$	0.0997058	+	6.13576i	0.0133237	+	0.819926i
$57$	12.0442	+	5.62459i	1.59529	+	0.744996i
$58$	0.995499	−	5.64576i	0.130715	−	0.741324i
$59$	−1.65418	−	1.38802i	−0.215356	−	0.180705i	0.528728	−	0.848791i	$-0.322669\pi$
$59$	−1.65418	−	1.38802i	−0.215356	−	0.180705i	−0.744084	+	0.668086i	$0.767114\pi$
$60$	1.27095	−	1.26951i	0.164079	−	0.163893i
$61$	−1.05430	+	2.89668i	−0.134990	+	0.370882i	−0.988708	−	0.149853i	$-0.952120\pi$
$61$	−1.05430	+	2.89668i	−0.134990	+	0.370882i	0.853718	+	0.520735i	$0.174342\pi$
$62$	7.10196	+	12.3010i	0.901950	+	1.56222i
$63$	−2.60164	+	7.49876i	−0.327776	+	0.944756i
$64$	2.39111	−	4.14152i	0.298889	−	0.517690i
$65$	1.16590	+	1.38947i	0.144613	+	0.172343i
$66$	−0.306248	+	3.47778i	−0.0376965	+	0.428085i
$67$	0.371427	−	2.10647i	0.0453770	−	0.257346i	−0.953677	−	0.300833i	$-0.902735\pi$
$67$	0.371427	−	2.10647i	0.0453770	−	0.257346i	0.999054	+	0.0434866i	$0.0138466\pi$
$68$	−1.68047	−	1.41008i	−0.203787	−	0.170997i
$69$	9.87786	+	0.869829i	1.18915	+	0.104715i
$70$	−0.130175	−	8.01082i	−0.0155589	−	0.957476i
$71$	−0.154696	−	0.0893139i	−0.0183591	−	0.0105996i	0.490792	−	0.871277i	$-0.336707\pi$
$71$	−0.154696	−	0.0893139i	−0.0183591	−	0.0105996i	−0.509151	+	0.860677i	$0.670041\pi$
$72$	5.33536	−	4.46663i	0.628778	−	0.526397i
$73$			11.5040i			1.34644i	0.739443	+	0.673220i	$0.235089\pi$
$73$			11.5040i			1.34644i	−0.739443	+	0.673220i	$0.764911\pi$
$74$	12.5703	−	2.21649i	1.46127	−	0.257662i
$75$	−1.71443	+	1.71249i	−0.197965	+	0.197741i
$76$	4.13081	+	0.728373i	0.473836	+	0.0835501i
$77$	2.18944	+	2.52480i	0.249509	+	0.287727i
$78$	−1.51413	−	2.16500i	−0.171441	−	0.245138i
$79$	−0.211994	−	1.20228i	−0.0238512	−	0.135267i	0.970557	−	0.240872i	$-0.0774333\pi$
$79$	−0.211994	−	1.20228i	−0.0238512	−	0.135267i	−0.994408	+	0.105605i	$0.966322\pi$
$80$	−4.54896	+	7.87903i	−0.508589	+	0.880902i
$81$	8.46417	−	3.05904i	0.940464	−	0.339894i
$82$	4.43628	−	2.56129i	0.489906	−	0.282847i
$83$	−5.11532	−	1.86183i	−0.561480	−	0.204362i	0.0456599	−	0.998957i	$-0.485461\pi$
$83$	−5.11532	−	1.86183i	−0.561480	−	0.204362i	−0.607140	+	0.794595i	$0.707683\pi$
$84$	−0.179134	+	2.49818i	−0.0195452	+	0.272574i
$85$	−5.83462	−	4.89582i	−0.632853	−	0.531027i
$86$	−0.350443	−	0.962834i	−0.0377892	−	0.103825i
$87$	−1.61386	+	6.00943i	−0.173024	+	0.644279i
$88$	−0.508733	−	2.88517i	−0.0542311	−	0.307560i
$89$	2.81958	−	4.88366i	0.298875	−	0.517667i	−0.677004	−	0.735980i	$-0.736722\pi$
$89$	2.81958	−	4.88366i	0.298875	−	0.517667i	0.975879	+	0.218313i	$0.0700553\pi$
$90$	−6.96582	+	5.83160i	−0.734262	+	0.614705i
$91$	−2.49730	−	0.398619i	−0.261789	−	0.0417866i
$92$	3.08147	−	0.543347i	0.321266	−	0.0566478i
$93$	−6.50750	−	13.9760i	−0.674797	−	1.44925i
$94$	13.4381	+	2.36950i	1.38604	+	0.244396i
$95$	14.3422	+	2.52892i	1.47148	+	0.259462i
$96$	2.99474	−	4.27179i	0.305650	−	0.435988i
$97$	5.97585	−	1.05370i	0.606755	−	0.106987i	0.138174	−	0.990408i	$-0.455877\pi$
$97$	5.97585	−	1.05370i	0.606755	−	0.106987i	0.468581	+	0.883421i	$0.344765\pi$
$98$	7.45452	+	8.31931i	0.753020	+	0.840377i
$99$	0.662233	−	3.73103i	0.0665569	−	0.374983i
$100$	−0.382319	+	0.662196i	−0.0382319	+	0.0662196i
$101$	1.20524	+	6.83528i	0.119926	+	0.680136i	0.984193	+	0.177101i	$0.0566720\pi$
$101$	1.20524	+	6.83528i	0.119926	+	0.680136i	−0.864266	+	0.503034i	$0.832217\pi$
$102$	7.84015	+	7.84903i	0.776291	+	0.777169i
$103$	4.40696	+	12.1080i	0.434231	+	1.19304i	0.943192	+	0.332249i	$0.107808\pi$
$103$	4.40696	+	12.1080i	0.434231	+	1.19304i	−0.508961	+	0.860790i	$0.669970\pi$
$104$	1.69831	+	1.42505i	0.166533	+	0.139738i
$105$	−0.621958	+	8.67372i	−0.0606968	+	0.846469i
$106$	19.6233	+	7.14230i	1.90598	+	0.693721i
$107$	−1.24002	+	0.715923i	−0.119877	+	0.0692109i	−0.558739	−	0.829343i	$-0.688715\pi$
$107$	−1.24002	+	0.715923i	−0.119877	+	0.0692109i	0.438863	+	0.898554i	$0.355381\pi$
$108$	2.32910	−	1.62497i	0.224118	−	0.156363i
$109$	−0.946256	+	1.63896i	−0.0906349	+	0.156984i	−0.907778	−	0.419450i	$-0.862223\pi$
$109$	−0.946256	+	1.63896i	−0.0906349	+	0.156984i	0.817144	+	0.576434i	$0.195556\pi$
$110$	0.664200	+	3.76686i	0.0633289	+	0.359156i
$111$	−13.8021	+	1.19966i	−1.31004	+	0.113867i
$112$	−2.40536	−	12.4546i	−0.227285	−	1.17685i
$113$	0.855475	+	0.150843i	0.0804763	+	0.0141901i	0.213741	−	0.976890i	$-0.431435\pi$
$113$	0.855475	+	0.150843i	0.0804763	+	0.0141901i	−0.133265	+	0.991080i	$0.542546\pi$
$114$	−20.4866	−	5.50179i	−1.91875	−	0.515290i
$115$	10.6989	−	1.88651i	0.997680	−	0.175918i
$116$			1.96346i			0.182303i
$117$	1.43095	+	2.48497i	0.132292	+	0.229735i
$118$	2.98425	+	1.72296i	0.274723	+	0.158611i
$119$	10.6179	−	0.172541i	0.973345	−	0.0158168i
$120$	4.37612	−	6.24223i	0.399483	−	0.569835i
$121$	7.20430	+	6.04512i	0.654936	+	0.549557i
$122$	0.854202	−	4.84442i	0.0773358	−	0.438593i
$123$	−5.04038	+	2.34690i	−0.454476	+	0.211613i
$124$	−3.12700	−	3.72661i	−0.280813	−	0.334659i
$125$	−6.07147	+	10.5161i	−0.543049	+	0.940588i
$126$	2.01064	−	12.5056i	0.179122	−	1.11409i
$127$	−6.79273	−	11.7654i	−0.602757	−	1.04401i	−0.992402	−	0.123041i	$-0.960735\pi$
$127$	−6.79273	−	11.7654i	−0.602757	−	1.04401i	0.389644	−	0.920965i	$-0.372598\pi$
$128$	−4.67044	+	12.8319i	−0.412812	+	1.13419i
$129$	0.287230	+	1.07439i	0.0252892	+	0.0945943i
$130$	−2.21730	−	1.86054i	−0.194470	−	0.163180i
$131$	1.57513	−	8.93299i	0.137620	−	0.780479i	−0.835380	−	0.549673i	$-0.814752\pi$
$131$	1.57513	−	8.93299i	0.137620	−	0.780479i	0.973000	−	0.230807i	$-0.0741364\pi$
$132$	−0.103541	−	1.19123i	−0.00901205	−	0.103684i
$133$	−17.4175	+	10.4369i	−1.51028	+	0.904996i
$134$			3.41334i			0.294867i
$135$	8.08669	−	5.64194i	0.695992	−	0.485581i
$136$	−8.06225	−	4.65474i	−0.691332	−	0.399141i
$137$	−12.9124	−	15.3884i	−1.10318	−	1.31472i	−0.944914	−	0.327319i	$-0.893855\pi$
$137$	−12.9124	−	15.3884i	−1.10318	−	1.31472i	−0.158263	−	0.987397i	$-0.550590\pi$
$138$	−15.7645	+	1.37024i	−1.34197	+	0.116642i
$139$	4.91571	−	5.85831i	0.416945	−	0.496895i	−0.516164	−	0.856490i	$-0.672640\pi$
$139$	4.91571	−	5.85831i	0.416945	−	0.496895i	0.933109	+	0.359594i	$0.117085\pi$
$140$	0.520337	+	2.69423i	0.0439765	+	0.227704i
$141$	−14.3037	−	3.84135i	−1.20459	−	0.323500i
$142$	0.267862	+	0.0974937i	0.0224785	+	0.00818149i
$143$	1.20734			0.100963
$144$	−9.25776	+	11.0077i	−0.771480	+	0.917305i
$145$			6.81717i			0.566135i
$146$	−3.18782	−	18.0790i	−0.263826	−	1.49623i
$147$	−7.26778	−	9.70461i	−0.599436	−	0.800422i
$148$	−4.10802	+	1.49520i	−0.337677	+	0.122904i
$149$	4.75604	−	5.66803i	0.389630	−	0.464343i	−0.535199	−	0.844726i	$-0.679763\pi$
$149$	4.75604	−	5.66803i	0.389630	−	0.464343i	0.924829	+	0.380383i	$0.124208\pi$
$150$	2.21976	−	3.16634i	0.181243	−	0.258530i
$151$	5.79884	+	2.11061i	0.471903	+	0.171759i	0.567014	−	0.823708i	$-0.308098\pi$
$151$	5.79884	+	2.11061i	0.471903	+	0.171759i	−0.0951111	+	0.995467i	$0.530321\pi$
$152$	17.8005			1.44381
$153$	−7.72950	−	9.23285i	−0.624893	−	0.746432i
$154$	−4.14044	−	3.36113i	−0.333646	−	0.270847i
$155$	−10.8570	−	12.9389i	−0.872055	−	1.03927i
$156$	0.639460	+	0.640183i	0.0511977	+	0.0512557i
$157$	−12.2082	+	14.5492i	−0.974322	+	1.16115i	0.0125942	+	0.999921i	$0.495991\pi$
$157$	−12.2082	+	14.5492i	−0.974322	+	1.16115i	−0.986917	+	0.161232i	$0.948453\pi$
$158$	0.666317	+	1.83069i	0.0530093	+	0.145642i
$159$	−20.5368	−	9.59059i	−1.62867	−	0.760584i
$160$	1.95487	−	5.37096i	0.154546	−	0.424612i
$161$	−9.54653	+	11.7600i	−0.752372	+	0.926817i
$162$	−12.4542	+	7.15290i	−0.978492	+	0.561985i
$163$	−0.709039	−	1.22809i	−0.0555362	−	0.0961915i	0.836921	−	0.547324i	$-0.184353\pi$
$163$	−0.709039	−	1.22809i	−0.0555362	−	0.0961915i	−0.892457	+	0.451133i	$0.851020\pi$
$164$	−1.34398	+	1.12774i	−0.104948	+	0.0880615i
$165$	−0.359495	−	4.13598i	−0.0279866	−	0.321986i
$166$	8.55489	+	1.50846i	0.663989	+	0.117079i
$167$	−2.73878	+	15.5324i	−0.211933	+	1.20193i	0.674217	+	0.738533i	$0.264481\pi$
$167$	−2.73878	+	15.5324i	−0.211933	+	1.20193i	−0.886150	+	0.463398i	$0.846630\pi$
$168$	1.09230	+	10.5726i	0.0842730	+	0.815692i
$169$	9.25869	−	7.76897i	0.712207	−	0.597613i
$170$	10.5260	+	6.07721i	0.807310	+	0.466101i
$171$	21.6264	+	7.89907i	1.65381	+	0.604057i
$172$	0.175464	+	0.303912i	0.0133790	+	0.0231731i
$173$	−8.35696	+	7.01232i	−0.635368	+	0.533137i	−0.902592	−	0.430497i	$-0.858338\pi$
$173$	−8.35696	+	7.01232i	−0.635368	+	0.533137i	0.267224	+	0.963634i	$0.413894\pi$
$174$	0.871014	−	9.89131i	0.0660314	−	0.749859i
$175$	−0.701901	−	3.63434i	−0.0530587	−	0.274730i
$176$	2.07122	+	5.69064i	0.156124	+	0.428948i
$177$	−3.06254	−	2.14700i	−0.230195	−	0.161378i
$178$	−3.07781	+	8.45622i	−0.230692	+	0.633821i
$179$	20.4739	−	11.8206i	1.53029	−	0.883515i	0.530945	−	0.847406i	$-0.321837\pi$
$179$	20.4739	−	11.8206i	1.53029	−	0.883515i	0.999348	−	0.0361087i	$-0.0114963\pi$
$180$	2.00267	−	2.38122i	0.149271	−	0.177486i
$181$	18.7421	−	10.8208i	1.39309	−	0.804301i	0.399434	−	0.916762i	$-0.369207\pi$
$181$	18.7421	−	10.8208i	1.39309	−	0.804301i	0.993656	+	0.112461i	$0.0358733\pi$
$182$	4.03509	−	0.0655700i	0.299101	−	0.00486037i
$183$	−1.38480	+	5.15647i	−0.102367	+	0.381178i
$184$	12.4779	−	4.54159i	0.919884	−	0.334810i
$185$	−14.2631	+	5.19135i	−1.04865	+	0.381676i
$186$	14.0997	+	20.1607i	1.03384	+	1.47825i
$187$	−4.99279	+	0.880363i	−0.365109	+	0.0643786i
$188$	−4.67346			−0.340847
$189$	−3.36456	+	13.3297i	−0.244736	+	0.969590i
$190$	−23.2403			−1.68603
$191$	21.5750	−	3.80425i	1.56111	−	0.275266i	0.674675	−	0.738115i	$-0.264284\pi$
$191$	21.5750	−	3.80425i	1.56111	−	0.275266i	0.886437	+	0.462849i	$0.153173\pi$
$192$	3.50481	−	7.50501i	0.252938	−	0.541627i
$193$	−13.6881	+	4.98206i	−0.985290	+	0.358616i	−0.783895	−	0.620894i	$-0.786770\pi$
$193$	−13.6881	+	4.98206i	−0.985290	+	0.358616i	−0.201396	+	0.979510i	$0.564548\pi$
$194$	−9.09934	+	3.31189i	−0.653294	+	0.237780i
$195$	2.22022	+	2.22273i	0.158993	+	0.159173i
$196$	−3.00911	−	2.36267i	−0.214936	−	0.168762i
$197$	−2.06396	+	1.19163i	−0.147051	+	0.0849001i	−0.571720	−	0.820449i	$-0.693724\pi$
$197$	−2.06396	+	1.19163i	−0.147051	+	0.0849001i	0.424669	+	0.905349i	$0.360390\pi$
$198$	−0.00683910	+	6.04700i	−0.000486033	+	0.429741i
$199$	8.88525	−	5.12990i	0.629859	−	0.363649i	−0.150839	−	0.988558i	$-0.548197\pi$
$199$	8.88525	−	5.12990i	0.629859	−	0.363649i	0.780697	+	0.624909i	$0.214864\pi$
$200$	−1.10983	+	3.04923i	−0.0784769	+	0.215613i
$201$	0.324981	−	3.69051i	0.0229224	−	0.260309i
$202$	−3.78819	−	10.4080i	−0.266536	−	0.732303i
$203$	−6.22708	−	7.18089i	−0.437055	−	0.503999i
$204$	−3.11121	−	2.18112i	−0.217828	−	0.152709i
$205$	−4.66634	+	3.91552i	−0.325911	+	0.273472i
$206$	−10.2810	−	17.8071i	−0.716308	−	1.24068i
$207$	17.1751	+	0.0194249i	1.19375	+	0.00135013i
$208$	−3.96870	−	2.29133i	−0.275180	−	0.158875i
$209$	7.42597	−	6.23113i	0.513665	−	0.431016i
$210$	−1.42611	−	13.8035i	−0.0984107	−	0.952533i
$211$	−1.98228	+	11.2421i	−0.136466	+	0.773938i	0.837361	+	0.546650i	$0.184097\pi$
$211$	−1.98228	+	11.2421i	−0.136466	+	0.773938i	−0.973828	+	0.227288i	$0.927014\pi$
$212$	−7.04351	−	1.24196i	−0.483750	−	0.0852982i
$213$	−0.280331	−	0.130913i	−0.0192079	−	0.00897004i
$214$	1.75036	−	1.46872i	0.119652	−	0.100400i
$215$	0.609213	+	1.05519i	0.0415480	+	0.0719632i
$216$	8.53649	−	8.50757i	0.580834	−	0.578867i
$217$	23.2551	+	3.71197i	1.57866	+	0.251985i
$218$	1.03292	−	2.83792i	0.0699581	−	0.192208i
$219$	1.72540	+	19.8506i	0.116591	+	1.34138i
$220$	−0.448055	−	1.23102i	−0.0302079	−	0.0829955i
$221$	2.46605	−	2.93892i	0.165885	−	0.197693i
$222$	21.3582	−	5.70998i	1.43347	−	0.383229i
$223$	7.05545	+	8.40836i	0.472468	+	0.563065i	0.948669	−	0.316271i	$-0.102431\pi$
$223$	7.05545	+	8.40836i	0.472468	+	0.563065i	−0.476201	+	0.879336i	$0.657987\pi$
$224$	2.84688	+	7.44317i	0.190215	+	0.497318i
$225$	−2.70148	+	3.21211i	−0.180099	+	0.214141i
$226$	−1.38622			−0.0922098
$227$	14.1429	+	5.14758i	0.938695	+	0.341657i	0.765650	−	0.643257i	$-0.222417\pi$
$227$	14.1429	+	5.14758i	0.938695	+	0.341657i	0.173045	+	0.984914i	$0.444639\pi$
$228$	7.23714	+	0.637292i	0.479291	+	0.0422057i
$229$	−14.4445	+	17.2142i	−0.954517	+	1.13755i	0.0358884	+	0.999356i	$0.488574\pi$
$229$	−14.4445	+	17.2142i	−0.954517	+	1.13755i	−0.990405	+	0.138193i	$0.955871\pi$
$230$	−16.2911	+	5.92948i	−1.07420	+	0.390978i
$231$	4.15665	+	4.02827i	0.273487	+	0.265041i
$232$	1.44691	+	8.20584i	0.0949944	+	0.538740i
$233$		−	29.3420i		−	1.92226i	−0.276103	−	0.961128i	$-0.589043\pi$
$233$		−	29.3420i		−	1.92226i	0.276103	−	0.961128i	$-0.410957\pi$
$234$	−2.93741	−	3.50872i	−0.192024	−	0.229372i
$235$	−16.2263			−1.05849
$236$	−1.10903	−	0.403653i	−0.0721915	−	0.0262756i
$237$	−0.546126	−	2.04279i	−0.0354747	−	0.132693i
$238$	−16.6388	+	3.21345i	−1.07853	+	0.208297i
$239$	−17.8608	+	21.2856i	−1.15532	+	1.37685i	−0.241661	+	0.970361i	$0.577692\pi$
$239$	−17.8608	+	21.2856i	−1.15532	+	1.37685i	−0.913655	+	0.406491i	$0.866752\pi$
$240$	−6.66772	+	14.2779i	−0.430399	+	0.921633i
$241$	0.0482410	+	0.0574914i	0.00310747	+	0.00370334i	0.767596	−	0.640934i	$-0.221453\pi$
$241$	0.0482410	+	0.0574914i	0.00310747	+	0.00370334i	−0.764488	+	0.644637i	$0.777008\pi$
$242$	−12.9970	−	7.50384i	−0.835481	−	0.482365i
$243$	14.1465	−	6.54799i	0.907499	−	0.420054i
$244$			1.68477i			0.107857i
$245$	−10.4477	−	8.20324i	−0.667478	−	0.524086i
$246$	7.27086	−	5.08498i	0.463573	−	0.324207i
$247$	−1.27383	+	7.22426i	−0.0810519	+	0.459668i
$248$	−15.8148	−	13.2702i	−1.00424	−	0.842657i
$249$	−9.10596	−	2.44546i	−0.577067	−	0.154974i
$250$	6.62753	−	18.2090i	0.419162	−	1.15164i
$251$	9.64254	+	16.7014i	0.608632	+	1.05418i	0.991466	+	0.130364i	$0.0416147\pi$
$251$	9.64254	+	16.7014i	0.608632	+	1.05418i	−0.382834	+	0.923817i	$0.625052\pi$
$252$	0.0655786	+	4.33759i	0.00413106	+	0.273242i
$253$	3.61570	−	6.26258i	0.227317	−	0.393725i
$254$	13.9353	+	16.6075i	0.874381	+	1.04205i
$255$	−10.8022	−	7.57288i	−0.676459	−	0.474232i
$256$	2.12316	−	12.0410i	0.132697	−	0.752565i
$257$	2.39043	+	2.00581i	0.149111	+	0.125119i	0.714292	−	0.699848i	$-0.246749\pi$
$257$	2.39043	+	2.00581i	0.149111	+	0.125119i	−0.565180	+	0.824967i	$0.691193\pi$
$258$	−0.749113	−	1.60885i	−0.0466378	−	0.100163i
$259$	10.2821	−	18.4968i	0.638899	−	1.14934i
$260$	0.858526	+	0.495670i	0.0532435	+	0.0307402i
$261$	−1.88349	+	10.6116i	−0.116585	+	0.656841i
$262$			14.4751i			0.894274i
$263$	−4.30219	+	0.758592i	−0.265284	+	0.0467768i	−0.304708	−	0.952446i	$-0.598559\pi$
$263$	−4.30219	+	0.758592i	−0.265284	+	0.0467768i	0.0394238	+	0.999223i	$0.487448\pi$
$264$	−1.31057	−	4.90219i	−0.0806598	−	0.301709i
$265$	−24.4552	−	4.31211i	−1.50227	−	0.264891i
$266$	24.4802	−	21.2286i	1.50098	−	1.30161i
$267$	4.13285	−	8.84986i	0.252926	−	0.541603i
$268$	−0.203002	−	1.15128i	−0.0124003	−	0.0703258i
$269$	−0.429514	+	0.743940i	−0.0261879	+	0.0453588i	−0.878822	−	0.477149i	$-0.841670\pi$
$269$	−0.429514	+	0.743940i	−0.0261879	+	0.0453588i	0.852634	+	0.522508i	$0.175003\pi$
$270$	−11.1452	+	11.1074i	−0.678275	+	0.675978i
$271$	4.73193	−	2.73198i	0.287444	−	0.165956i	−0.349344	−	0.936994i	$-0.613596\pi$
$271$	4.73193	−	2.73198i	0.287444	−	0.165956i	0.636789	+	0.771038i	$0.280262\pi$
$272$	18.0829	+	6.58162i	1.09643	+	0.399069i
$273$	−4.36900	−	0.313283i	−0.264424	−	0.0189608i
$274$	24.5566	+	20.6054i	1.48352	+	1.24482i
$275$	0.604398	+	1.66057i	0.0364466	+	0.100136i
$276$	5.23573	−	1.39974i	0.315154	−	0.0842542i
$277$	−3.39626	−	19.2611i	−0.204061	−	1.15729i	−0.898910	−	0.438134i	$-0.855640\pi$
$277$	−3.39626	−	19.2611i	−0.204061	−	1.15729i	0.694848	−	0.719156i	$-0.255471\pi$
$278$	−6.10189	+	10.5688i	−0.365967	+	0.633873i
$279$	−13.3251	−	23.1402i	−0.797756	−	1.38537i
$280$	4.16005	+	10.8765i	0.248611	+	0.649993i
$281$	−13.1907	+	2.32587i	−0.786890	+	0.138750i	−0.552633	−	0.833425i	$-0.686377\pi$
$281$	−13.1907	+	2.32587i	−0.786890	+	0.138750i	−0.234257	+	0.972175i	$0.575266\pi$
$282$	23.5435	+	2.07320i	1.40199	+	0.123457i
$283$	10.5946	+	1.86812i	0.629786	+	0.111048i	0.479425	−	0.877583i	$-0.340845\pi$
$283$	10.5946	+	1.86812i	0.629786	+	0.111048i	0.150361	+	0.988631i	$0.451956\pi$
$284$	−0.0961453	−	0.0169530i	−0.00570517	−	0.00100598i
$285$	25.1275	+	2.21269i	1.48842	+	0.131068i
$286$	−1.89739	+	0.334561i	−0.112195	+	0.0197830i
$287$	1.33871	−	8.38684i	0.0790213	−	0.495060i
$288$	4.52687	−	7.82033i	0.266748	−	0.460817i
$289$	0.444961	−	0.770696i	0.0261742	−	0.0453350i
$290$	−1.88908	−	10.7135i	−0.110931	−	0.629119i
$291$	10.1536	−	2.71448i	0.595212	−	0.159126i
$292$	2.15044	+	5.90829i	0.125845	+	0.345756i
$293$	−6.87623	−	5.76984i	−0.401714	−	0.337078i	0.419442	−	0.907782i	$-0.362226\pi$
$293$	−6.87623	−	5.76984i	−0.401714	−	0.337078i	−0.821156	+	0.570704i	$0.806670\pi$
$294$	14.1109	+	13.2373i	0.822962	+	0.772015i
$295$	−3.85056	−	1.40149i	−0.224188	−	0.0815979i
$296$	−16.0667	+	9.27612i	−0.933858	+	0.539163i
$297$	0.583124	−	6.53738i	0.0338363	−	0.379337i
$298$	−5.90370	+	10.2255i	−0.341992	+	0.592348i
$299$	0.950244	+	5.38910i	0.0549540	+	0.311660i
$300$	−0.560391	+	1.19999i	−0.0323542	+	0.0692814i
$301$	−1.60557	−	0.555006i	−0.0925433	−	0.0319900i
$302$	−9.69802	−	1.71002i	−0.558058	−	0.0984007i
$303$	3.10487	+	11.6138i	0.178370	+	0.667196i
$304$	−36.2360	+	6.38938i	−2.07828	+	0.366456i
$305$			5.84957i			0.334945i
$306$	14.7058	+	12.3680i	0.840672	+	0.707029i
$307$	−17.4494	−	10.0744i	−0.995890	−	0.574977i	−0.0888603	−	0.996044i	$-0.528322\pi$
$307$	−17.4494	−	10.0744i	−0.995890	−	0.574977i	−0.907030	+	0.421067i	$0.861656\pi$
$308$	1.59642	+	0.887428i	0.0909647	+	0.0505659i
$309$	9.42040	+	20.2320i	0.535908	+	1.15096i
$310$	20.6477	+	17.3255i	1.17271	+	0.984021i
$311$	0.493149	−	2.79678i	0.0279639	−	0.158591i	−0.967628	−	0.252380i	$-0.918787\pi$
$311$	0.493149	−	2.79678i	0.0279639	−	0.158591i	0.995592	+	0.0937888i	$0.0298978\pi$
$312$	3.14424	+	2.20427i	0.178008	+	0.124792i
$313$	5.99493	+	7.14448i	0.338853	+	0.403830i	0.908382	−	0.418142i	$-0.137319\pi$
$313$	5.99493	+	7.14448i	0.338853	+	0.403830i	−0.569528	+	0.821972i	$0.692874\pi$
$314$	15.1541	−	26.2477i	0.855197	−	1.48124i
$315$	0.227690	+	15.0602i	0.0128289	+	0.848545i
$316$	−0.333619	−	0.577845i	−0.0187675	−	0.0325063i
$317$	−6.03103	+	16.5701i	−0.338736	+	0.930670i	0.647018	+	0.762475i	$0.276016\pi$
$317$	−6.03103	+	16.5701i	−0.338736	+	0.930670i	−0.985754	+	0.168195i	$0.946206\pi$
$318$	34.9321	+	9.38120i	1.95889	+	0.526072i
$319$	3.47610	+	2.91679i	0.194624	+	0.163309i
$320$	1.57583	−	8.93697i	0.0880915	−	0.499592i
$321$	−2.03233	+	1.42134i	−0.113433	+	0.0793314i
$322$	11.7441	−	21.1268i	0.654471	−	1.17735i
$323$		−	30.8038i		−	1.71397i
$324$	3.77526	−	3.15329i	0.209736	−	0.175183i
$325$	−1.15810	−	0.668627i	−0.0642396	−	0.0370887i
$326$	1.45460	+	1.73352i	0.0805628	+	0.0960110i
$327$	−1.38699	+	2.97003i	−0.0767008	+	0.164243i
$328$	−4.78583	+	5.70353i	−0.264253	+	0.314925i
$329$	17.0921	−	14.8218i	0.942316	−	0.817151i
$330$	1.71107	+	6.40027i	0.0941913	+	0.352323i
$331$	−25.7166	−	9.36008i	−1.41351	−	0.514476i	−0.481353	−	0.876527i	$-0.659855\pi$
$331$	−25.7166	−	9.36008i	−1.41351	−	0.514476i	−0.932159	+	0.362050i	$0.882077\pi$
$332$	−2.97519			−0.163285
$333$	−23.6362	+	4.14015i	−1.29526	+	0.226879i
$334$		−	25.1688i		−	1.37718i
$335$	−0.704828	−	3.99728i	−0.0385089	−	0.218395i
$336$	−6.01852	−	21.1302i	−0.328337	−	1.15275i
$337$	−14.1672	+	5.15645i	−0.771738	+	0.280889i	−0.697723	−	0.716368i	$-0.745803\pi$
$337$	−14.1672	+	5.15645i	−0.771738	+	0.280889i	−0.0740145	+	0.997257i	$0.523581\pi$
$338$	−12.3976	+	14.7749i	−0.674343	+	0.803651i
$339$	1.49878	+	0.131981i	0.0814028	+	0.00716821i
$340$	−3.91175	−	1.42376i	−0.212145	−	0.0772144i
$341$	−11.2428			−0.608833
$342$	−36.1758	−	6.42096i	−1.95616	−	0.347206i
$343$	18.4983	−	0.902423i	0.998812	−	0.0487262i
$344$	0.957269	+	1.14083i	0.0516125	+	0.0615094i
$345$	18.1785	−	4.85991i	0.978700	−	0.261649i
$346$	11.1902	−	13.3360i	0.601589	−	0.716946i
$347$	8.28375	+	22.7594i	0.444695	+	1.22179i	0.936371	+	0.351011i	$0.114162\pi$
$347$	8.28375	+	22.7594i	0.444695	+	1.22179i	−0.491677	+	0.870778i	$0.663616\pi$
$348$	0.294485	+	3.38804i	0.0157860	+	0.181618i
$349$	−1.92048	+	5.27647i	−0.102801	+	0.282443i	−0.980421	−	0.196914i	$-0.936908\pi$
$349$	−1.92048	+	5.27647i	−0.102801	+	0.282443i	0.877620	+	0.479357i	$0.159130\pi$
$350$	2.11017	+	5.51703i	0.112793	+	0.294898i
$351$	2.84187	+	4.07331i	0.151688	+	0.217417i
$352$	−1.90226	−	3.29481i	−0.101391	−	0.175614i
$353$	16.6130	−	13.9399i	0.884218	−	0.741947i	−0.0828238	−	0.996564i	$-0.526394\pi$
$353$	16.6130	−	13.9399i	0.884218	−	0.741947i	0.967042	+	0.254617i	$0.0819494\pi$
$354$	5.40787	+	2.52546i	0.287425	+	0.134226i
$355$	−0.333818	−	0.0588611i	−0.0177172	−	0.00312403i
$356$	0.535195	−	3.03524i	0.0283653	−	0.160868i
$357$	18.2959	−	1.89023i	0.968320	−	0.100042i
$358$	−28.9002	+	24.2501i	−1.52742	+	1.28166i
$359$	−19.0007	−	10.9700i	−1.00282	−	0.578976i	−0.0937359	−	0.995597i	$-0.529881\pi$
$359$	−19.0007	−	10.9700i	−1.00282	−	0.578976i	−0.909080	+	0.416621i	$0.863214\pi$
$360$	6.61496	−	11.4276i	0.348639	−	0.602286i
$361$	19.9498	+	34.5540i	1.04999	+	1.81863i
$362$	−26.4556	+	22.1989i	−1.39048	+	1.16675i
$363$	13.3380	+	9.35061i	0.700063	+	0.490780i
$364$	−1.35709	+	0.262096i	−0.0711311	+	0.0137376i
$365$	7.46637	+	20.5137i	0.390808	+	1.07374i
$366$	0.747386	−	8.48738i	0.0390665	−	0.443642i
$367$	−3.89839	+	10.7107i	−0.203494	+	0.559096i	−0.998895	−	0.0469871i	$-0.985038\pi$
$367$	−3.89839	+	10.7107i	−0.203494	+	0.559096i	0.795401	+	0.606083i	$0.207260\pi$
$368$	−23.7707	+	13.7240i	−1.23913	+	0.715415i
$369$	−8.34542	+	4.80565i	−0.434445	+	0.250172i
$370$	20.9766	−	12.1109i	1.09052	−	0.629613i
$371$	29.6988	−	17.7962i	1.54188	−	0.923931i
$372$	−5.95470	−	5.96144i	−0.308737	−	0.309086i
$373$	35.2170	−	12.8179i	1.82346	−	0.663687i	0.828921	−	0.559365i	$-0.188955\pi$
$373$	35.2170	−	12.8179i	1.82346	−	0.663687i	0.994544	−	0.104322i	$-0.0332672\pi$
$374$	7.60245	−	2.76706i	0.393113	−	0.143082i
$375$	−8.89937	+	19.0566i	−0.459561	+	0.984079i
$376$	−19.5317	+	3.44396i	−1.00727	+	0.177609i
$377$	−3.43384			−0.176852
$378$	1.59384	−	21.8805i	0.0819783	−	1.12541i
$379$	4.71335			0.242108			0.121054	−	0.992646i	$-0.461373\pi$
$379$	4.71335			0.242108			0.121054	+	0.992646i	$0.461373\pi$
$380$	7.83871	−	1.38218i	0.402117	−	0.0709041i
$381$	−13.4858	−	19.2829i	−0.690896	−	0.987890i
$382$	−32.8519	+	11.9571i	−1.68085	+	0.611780i
$383$	7.04901	−	2.56563i	0.360188	−	0.131098i	−0.155586	−	0.987822i	$-0.549727\pi$
$383$	7.04901	−	2.56563i	0.360188	−	0.131098i	0.515774	+	0.856725i	$0.327504\pi$
$384$	−6.13449	+	22.8425i	−0.313049	+	1.16568i
$385$	5.54281	+	3.08117i	0.282488	+	0.157031i
$386$	20.1309	−	11.6226i	1.02464	−	0.591574i
$387$	0.656766	+	1.81082i	0.0333853	+	0.0920492i
$388$	2.87214	−	1.65823i	0.145811	−	0.0841840i
$389$	7.89174	−	21.6824i	0.400127	−	1.09934i	−0.562094	−	0.827073i	$-0.690004\pi$
$389$	7.89174	−	21.6824i	0.400127	−	1.09934i	0.962222	−	0.272267i	$-0.0877735\pi$
$390$	−4.10510	−	2.87789i	−0.207870	−	0.145727i
$391$	−7.85923	−	21.5931i	−0.397458	−	1.09201i
$392$	−14.3170	−	7.65679i	−0.723117	−	0.386726i
$393$	1.37816	−	15.6505i	0.0695191	−	0.789464i
$394$	2.91341	−	2.44464i	0.146775	−	0.123159i
$395$	−1.15833	−	2.00629i	−0.0582820	−	0.100947i
$396$	−0.357328	−	2.04000i	−0.0179564	−	0.102514i
$397$	15.0855	+	8.70960i	0.757118	+	0.437122i	0.828260	−	0.560344i	$-0.189331\pi$
$397$	15.0855	+	8.70960i	0.757118	+	0.437122i	−0.0711419	+	0.997466i	$0.522664\pi$
$398$	−12.5421	+	10.5240i	−0.628677	+	0.527522i
$399$	−28.4892	+	20.6217i	−1.42625	+	1.03238i
$400$	1.16475	−	6.60560i	0.0582373	−	0.330280i
$401$	−21.1914	−	3.73662i	−1.05825	−	0.186598i	−0.382670	−	0.923885i	$-0.624995\pi$
$401$	−21.1914	−	3.73662i	−1.05825	−	0.186598i	−0.675579	+	0.737287i	$0.736106\pi$
$402$	0.511941	+	5.88987i	0.0255333	+	0.293760i
$403$	6.51737	−	5.46872i	0.324653	−	0.272416i
$404$	1.89672	+	3.28521i	0.0943651	+	0.163445i
$405$	13.1078	−	10.9483i	0.651330	−	0.544025i
$406$	11.7760	+	9.55954i	0.584433	+	0.474432i
$407$	−3.45553	+	9.49398i	−0.171284	+	0.470599i
$408$	−14.6099	−	6.82277i	−0.723298	−	0.337778i
$409$	9.10354	+	25.0118i	0.450141	+	1.23675i	0.932625	+	0.360847i	$0.117512\pi$
$409$	9.10354	+	25.0118i	0.450141	+	1.23675i	−0.482484	+	0.875905i	$0.660265\pi$
$410$	6.24836	−	7.44650i	0.308584	−	0.367756i
$411$	−24.5888	−	24.6167i	−1.21288	−	1.21425i
$412$	4.52671	+	5.39472i	0.223015	+	0.265779i
$413$	5.33618	−	2.04099i	0.262576	−	0.100431i
$414$	−26.9969	+	4.72881i	−1.32683	+	0.232408i
$415$	−10.3299			−0.507076
$416$	2.70538	+	0.984678i	0.132642	+	0.0482778i
$417$	7.60363	−	10.8460i	0.372351	−	0.531133i
$418$	−9.94357	+	11.8503i	−0.486356	+	0.579616i
$419$	5.47160	−	1.99150i	0.267305	−	0.0972911i	−0.204890	−	0.978785i	$-0.565684\pi$
$419$	5.47160	−	1.99150i	0.267305	−	0.0972911i	0.472196	+	0.881494i	$0.343462\pi$
$420$	1.30195	+	4.57097i	0.0635287	+	0.223040i
$421$	−0.858573	−	4.86921i	−0.0418443	−	0.237311i	0.956711	−	0.291039i	$-0.0940008\pi$
$421$	−0.858573	−	4.86921i	−0.0418443	−	0.237311i	−0.998556	+	0.0537277i	$0.982890\pi$
$422$		−	18.2168i		−	0.886779i
$423$	−25.2579	−	4.48311i	−1.22808	−	0.217976i
$424$	−30.3520			−1.47402
$425$	5.27670	+	1.92056i	0.255958	+	0.0931610i
$426$	0.476830	+	0.128055i	0.0231025	+	0.00620429i
$427$	−5.34323	−	6.16166i	−0.258577	−	0.298183i
$428$	−0.503027	+	0.599485i	−0.0243147	+	0.0289772i
$429$	2.08331	−	0.181079i	0.100583	−	0.00874259i
$430$	−1.24981	−	1.48946i	−0.0602710	−	0.0718282i
$431$	10.1898	+	5.88309i	0.490826	+	0.283378i	0.724917	−	0.688836i	$-0.241878\pi$
$431$	10.1898	+	5.88309i	0.490826	+	0.283378i	−0.234091	+	0.972215i	$0.575211\pi$
$432$	−14.3237	+	20.3827i	−0.689151	+	0.980664i
$433$			28.6389i			1.37630i	0.725569	+	0.688150i	$0.241577\pi$
$433$			28.6389i			1.37630i	−0.725569	+	0.688150i	$0.758423\pi$
$434$	−37.5751	+	0.610593i	−1.80366	+	0.0293094i
$435$	1.02246	+	11.7633i	0.0490230	+	0.564009i
$436$	−0.179612	+	1.01863i	−0.00860187	+	0.0487836i
$437$	33.6581	+	28.2425i	1.61008	+	1.35102i
$438$	−8.21227	−	30.7181i	−0.392398	−	1.46777i
$439$	3.67117	−	10.0865i	0.175216	−	0.481401i	−0.820734	−	0.571310i	$-0.806435\pi$
$439$	3.67117	−	10.0865i	0.175216	−	0.481401i	0.995950	+	0.0899091i	$0.0286577\pi$
$440$	−2.77971	−	4.81460i	−0.132517	−	0.229527i
$441$	−13.9964	−	15.6557i	−0.666495	−	0.745509i
$442$	−3.06112	+	5.30202i	−0.145603	+	0.252191i
$443$	10.3006	+	12.2757i	0.489394	+	0.583237i	0.953063	−	0.302771i	$-0.0979118\pi$
$443$	10.3006	+	12.2757i	0.489394	+	0.583237i	−0.463669	+	0.886008i	$0.653467\pi$
$444$	−6.86432	+	3.19616i	−0.325766	+	0.151683i
$445$	1.85821	−	10.5384i	0.0880875	−	0.499569i
$446$	−13.4180	−	11.2590i	−0.635360	−	0.533130i
$447$	7.35666	−	10.4938i	0.347958	−	0.496338i
$448$	6.50348	+	10.8532i	0.307261	+	0.512766i
$449$	−15.5368	−	8.97017i	−0.733226	−	0.423328i	0.0863750	−	0.996263i	$-0.472472\pi$
$449$	−15.5368	−	8.97017i	−0.733226	−	0.423328i	−0.819601	+	0.572934i	$0.805805\pi$
$450$	3.35540	−	5.79658i	0.158175	−	0.273253i
$451$			4.05467i			0.190927i
$452$	0.467557	−	0.0824429i	0.0219920	−	0.00387779i
$453$	10.3227	+	2.77222i	0.485004	+	0.130250i
$454$	−23.6526	−	4.17059i	−1.11007	−	0.195736i
$455$	−4.71186	+	0.910003i	−0.220895	+	0.0426616i
$456$	30.7156	−	2.66977i	1.43839	−	0.125023i
$457$	−3.98062	−	22.5752i	−0.186205	−	1.05602i	−0.924397	−	0.381432i	$-0.875431\pi$
$457$	−3.98062	−	22.5752i	−0.186205	−	1.05602i	0.738191	−	0.674591i	$-0.235680\pi$
$458$	17.9300	−	31.0556i	0.837813	−	1.45113i
$459$	−14.7224	−	14.7724i	−0.687181	−	0.689517i
$460$	5.14218	−	2.96884i	0.239755	−	0.138423i
$461$	11.2905	+	4.10942i	0.525852	+	0.191395i	0.591285	−	0.806462i	$-0.298621\pi$
$461$	11.2905	+	4.10942i	0.525852	+	0.191395i	−0.0654330	+	0.997857i	$0.520843\pi$
$462$	−7.64862	−	5.17878i	−0.355846	−	0.240939i
$463$	−0.859491	−	0.721198i	−0.0399439	−	0.0335169i	0.622597	−	0.782543i	$-0.286078\pi$
$463$	−0.859491	−	0.721198i	−0.0399439	−	0.0335169i	−0.662541	+	0.749026i	$0.730522\pi$
$464$	−5.89086	−	16.1850i	−0.273476	−	0.751370i
$465$	−20.6748	−	20.6982i	−0.958772	−	0.959857i
$466$	8.13084	+	46.1123i	0.376654	+	2.13611i
$467$	−6.58419	+	11.4042i	−0.304680	+	0.527721i	−0.977190	−	0.212367i	$-0.931883\pi$
$467$	−6.58419	+	11.4042i	−0.304680	+	0.527721i	0.672510	+	0.740088i	$0.265216\pi$
$468$	1.19943	+	1.00876i	0.0554438	+	0.0466298i
$469$	4.39370	+	3.56672i	0.202882	+	0.164696i
$470$	25.5005	−	4.49642i	1.17625	−	0.207404i
$471$	−18.8837	+	26.9363i	−0.870116	+	1.24116i
$472$	−4.93239	−	0.869713i	−0.227032	−	0.0400318i
$473$	0.798701	+	0.140833i	0.0367243	+	0.00647549i
$474$	1.42433	+	3.05900i	0.0654217	+	0.140505i
$475$	−10.5739	+	1.86447i	−0.485164	+	0.0855476i
$476$	5.42098	−	2.07343i	0.248470	−	0.0950354i
$477$	−36.8755	−	13.4688i	−1.68841	−	0.616696i
$478$	22.1706	−	38.4007i	1.01406	−	1.75641i
$479$	3.88749	+	22.0470i	0.177624	+	1.00736i	0.935071	+	0.354459i	$0.115335\pi$
$479$	3.88749	+	22.0470i	0.177624	+	1.00736i	−0.757448	+	0.652896i	$0.773554\pi$
$480$	2.56767	−	9.56104i	0.117197	−	0.436400i
$481$	−2.61491	−	7.18441i	−0.119230	−	0.327581i
$482$	−0.0917442	−	0.0769825i	−0.00417883	−	0.00350646i
$483$	−14.7092	+	21.7242i	−0.669291	+	0.988485i
$484$	4.83004	+	1.75799i	0.219547	+	0.0799087i
$485$	9.97214	−	5.75742i	0.452811	−	0.261431i
$486$	−20.4174	+	14.2106i	−0.926153	+	0.644604i
$487$	14.1370	−	24.4860i	0.640609	−	1.10957i	−0.344688	−	0.938717i	$-0.612015\pi$
$487$	14.1370	−	24.4860i	0.640609	−	1.10957i	0.985297	−	0.170850i	$-0.0546514\pi$
$488$	1.24154	+	7.04114i	0.0562020	+	0.318737i
$489$	−1.40767	−	2.01278i	−0.0636571	−	0.0910212i
$490$	18.6922	+	9.99666i	0.844427	+	0.451603i
$491$	36.4384	+	6.42508i	1.64444	+	0.289960i	0.917796	−	0.397052i	$-0.129967\pi$
$491$	36.4384	+	6.42508i	1.64444	+	0.289960i	0.726647	+	0.687012i	$0.241078\pi$
$492$	−2.14997	+	2.14753i	−0.0969279	+	0.0968184i
$493$	14.2002	−	2.50388i	0.639546	−	0.112769i
$494$		−	11.7062i		−	0.526689i
$495$	−1.24065	−	7.08291i	−0.0557630	−	0.318353i
$496$	36.9569	+	21.3371i	1.65941	+	0.958063i
$497$	0.405394	−	0.242921i	0.0181844	−	0.0108965i
$498$	14.9881	+	1.31983i	0.671633	+	0.0591430i
$499$	−12.5678	−	10.5456i	−0.562611	−	0.472087i	0.316573	−	0.948568i	$-0.397468\pi$
$499$	−12.5678	−	10.5456i	−0.562611	−	0.472087i	−0.879185	+	0.476481i	$0.841912\pi$
$500$	−1.15245	+	6.53586i	−0.0515391	+	0.292293i
$501$	−2.39630	+	27.2126i	−0.107059	+	1.21577i
$502$	−19.7818	−	23.5750i	−0.882903	−	1.05220i
$503$	−4.98173	+	8.62860i	−0.222124	+	0.384730i	−0.955453	−	0.295144i	$-0.904632\pi$
$503$	−4.98173	+	8.62860i	−0.222124	+	0.384730i	0.733329	+	0.679874i	$0.237966\pi$
$504$	3.47052	+	18.0796i	0.154589	+	0.805331i
$505$	6.58543	+	11.4063i	0.293048	+	0.507574i
$506$	−3.94684	+	10.8439i	−0.175459	+	0.482068i
$507$	14.8111	−	14.7943i	0.657783	−	0.657040i
$508$	−5.68795	−	4.77276i	−0.252362	−	0.211757i
$509$	1.19429	−	6.77313i	0.0529358	−	0.300214i	−0.946833	−	0.321726i	$-0.895737\pi$
$509$	1.19429	−	6.77313i	0.0529358	−	0.300214i	0.999769	+	0.0215123i	$0.00684812\pi$
$510$	19.0746	+	8.90778i	0.844638	+	0.394443i
$511$	−26.6027	−	14.7881i	−1.17684	−	0.654185i
$512$		−	7.79950i		−	0.344692i
$513$	38.5020	+	10.3866i	1.69991	+	0.458581i
$514$	−4.31250	−	2.48982i	−0.190216	−	0.109821i
$515$	15.7168	+	18.7306i	0.692566	+	0.825367i
$516$	0.348352	+	0.498097i	0.0153353	+	0.0219275i
$517$	−6.94259	+	8.27386i	−0.305335	+	0.363884i
$518$	−11.0332	+	31.9179i	−0.484772	+	1.40239i
$519$	−13.3686	+	13.3535i	−0.586816	+	0.586152i
$520$	3.95328	+	1.43888i	0.173363	+	0.0630989i
$521$	−13.4866			−0.590858			−0.295429	−	0.955365i	$-0.595463\pi$
$521$	−13.4866			−0.590858			−0.295429	+	0.955365i	$0.595463\pi$
$522$	0.0194514	−	17.1985i	0.000851364	−	0.752760i
$523$		−	34.9984i		−	1.53038i	−0.643807	−	0.765188i	$-0.722646\pi$
$523$		−	34.9984i		−	1.53038i	0.643807	−	0.765188i	$-0.277354\pi$
$524$	−0.860881	−	4.88230i	−0.0376078	−	0.213284i
$525$	−1.75625	−	6.16594i	−0.0766489	−	0.269104i
$526$	6.55088	−	2.38432i	0.285632	−	0.103961i
$527$	−22.9641	+	27.3675i	−1.00033	+	1.19215i
$528$	4.42749	+	9.50881i	0.192682	+	0.413818i
$529$	9.18663	+	3.34366i	0.399419	+	0.145377i
$530$	39.6274			1.72130
$531$	−5.60656	−	3.24541i	−0.243304	−	0.140839i
$532$	−6.99439	+	8.61610i	−0.303245	+	0.373555i
$533$	−1.97227	−	2.35046i	−0.0854284	−	0.101810i
$534$	−4.04262	+	15.0532i	−0.174941	+	0.651416i
$535$	−1.74652	+	2.08142i	−0.0755087	+	0.0899877i
$536$	−1.69680	−	4.66193i	−0.0732908	−	0.201365i
$537$	33.5558	−	23.4677i	1.44804	−	1.01271i
$538$	0.468851	−	1.28816i	0.0202136	−	0.0555364i
$539$	−8.65300	+	1.81747i	−0.372711	+	0.0782840i
$540$	3.09856	−	4.40927i	0.133341	−	0.189745i
$541$	0.619421	+	1.07287i	0.0266310	+	0.0461262i	0.879034	−	0.476760i	$-0.158189\pi$
$541$	0.619421	+	1.07287i	0.0266310	+	0.0461262i	−0.852403	+	0.522886i	$0.824855\pi$
$542$	−6.67940	+	5.60469i	−0.286905	+	0.240742i
$543$	30.7174	−	21.4827i	1.31821	−	0.921911i
$544$	−11.9058	−	2.09931i	−0.510455	−	0.0900070i
$545$	−0.623617	+	3.53671i	−0.0267128	+	0.151496i
$546$	6.95289	−	0.718336i	0.297556	−	0.0307420i
$547$	21.3784	−	17.9386i	0.914076	−	0.767000i	−0.0588145	−	0.998269i	$-0.518732\pi$
$547$	21.3784	−	17.9386i	0.914076	−	0.767000i	0.972890	+	0.231269i	$0.0742876\pi$
$548$	−9.50816	−	5.48954i	−0.406168	−	0.234501i
$549$	−1.61615	+	9.10542i	−0.0689757	+	0.388610i
$550$	−1.40999	−	2.44218i	−0.0601223	−	0.104135i
$551$	−21.1205	+	17.7222i	−0.899765	+	0.754992i
$552$	20.8500	−	9.70819i	0.887437	−	0.413208i
$553$	3.05275	+	1.05526i	0.129816	+	0.0448744i
$554$	10.6748	+	29.3287i	0.453527	+	1.24606i
$555$	−23.8331	+	11.0971i	−1.01166	+	0.471047i
$556$	1.42954	−	3.92764i	0.0606262	−	0.166569i
$557$	2.66791	−	1.54032i	0.113043	−	0.0652654i	−0.442412	−	0.896812i	$-0.645877\pi$
$557$	2.66791	−	1.54032i	0.113043	−	0.0652654i	0.555455	+	0.831546i	$0.312544\pi$
$558$	27.3534	+	32.6735i	1.15796	+	1.38318i
$559$	−0.531504	+	0.306864i	−0.0224802	+	0.0129790i
$560$	−12.3725	−	20.6476i	−0.522835	−	0.872522i
$561$	−8.48324	+	2.26794i	−0.358163	+	0.0957524i
$562$	20.0853	−	7.31043i	0.847245	−	0.308372i
$563$	−4.55950	+	1.65952i	−0.192160	+	0.0699406i	−0.436308	−	0.899798i	$-0.643714\pi$
$563$	−4.55950	+	1.65952i	−0.192160	+	0.0699406i	0.244148	+	0.969738i	$0.421492\pi$
$564$	−8.06427	+	0.700937i	−0.339567	+	0.0295148i
$565$	1.62337	−	0.286243i	0.0682956	−	0.0120423i
$566$	−17.1676			−0.721610
$567$	−3.80649	+	23.5055i	−0.159858	+	0.987140i
$568$	−0.414310			−0.0173841
$569$	−9.00123	+	1.58716i	−0.377351	+	0.0665372i	−0.359107	−	0.933296i	$-0.616919\pi$
$569$	−9.00123	+	1.58716i	−0.377351	+	0.0665372i	−0.0182441	+	0.999834i	$0.505808\pi$
$570$	−40.1022	+	3.48563i	−1.67969	+	0.145997i
$571$	39.9573	−	14.5433i	1.67216	−	0.608617i	0.679960	−	0.733250i	$-0.261997\pi$
$571$	39.9573	−	14.5433i	1.67216	−	0.608617i	0.992203	+	0.124632i	$0.0397750\pi$
$572$	0.620072	−	0.225688i	0.0259265	−	0.00943648i
$573$	36.6581	−	9.80028i	1.53141	−	0.409413i
$574$	0.220208	+	13.5513i	0.00919129	+	0.565620i
$575$	−6.93646	+	4.00477i	−0.289271	+	0.167010i
$576$	4.92209	−	13.4759i	0.205087	−	0.561495i
$577$	31.9551	−	18.4493i	1.33031	−	0.768053i	0.344961	−	0.938617i	$-0.387892\pi$
$577$	31.9551	−	18.4493i	1.33031	−	0.768053i	0.985347	+	0.170564i	$0.0545589\pi$
$578$	−0.485713	+	1.33449i	−0.0202030	+	0.0555073i
$579$	−22.8722	+	10.6497i	−0.950536	+	0.442588i
$580$	1.27433	+	3.50121i	0.0529139	+	0.145380i
$581$	10.8810	−	9.43576i	0.451422	−	0.391461i
$582$	−15.2046	+	7.07955i	−0.630251	+	0.293457i
$583$	−12.6621	+	10.6248i	−0.524412	+	0.440034i
$584$	13.3412	+	23.1076i	0.552063	+	0.956201i
$585$	4.16445	+	3.50242i	0.172179	+	0.144807i
$586$	12.4052	+	7.16213i	0.512453	+	0.295865i
$587$	−21.4793	+	18.0233i	−0.886545	+	0.743900i	−0.967514	−	0.252817i	$-0.918643\pi$
$587$	−21.4793	+	18.0233i	−0.886545	+	0.743900i	0.0809690	+	0.996717i	$0.474199\pi$
$588$	−5.54671	−	3.62558i	−0.228743	−	0.149517i
$589$	11.8620	−	67.2729i	0.488766	−	2.77193i
$590$	6.43970	+	1.13549i	0.265118	+	0.0467475i
$591$	−3.38274	+	2.36577i	−0.139147	+	0.0973147i
$592$	29.3769	−	24.6501i	1.20738	−	1.01311i
$593$	12.0746	+	20.9138i	0.495845	+	0.858828i	0.999989	−	0.00479135i	$-0.00152514\pi$
$593$	12.0746	+	20.9138i	0.495845	+	0.858828i	−0.504144	+	0.863620i	$0.668192\pi$
$594$	0.895142	+	10.4354i	0.0367281	+	0.428169i
$595$	18.8217	−	7.19898i	0.771616	−	0.295129i
$596$	1.38311	−	3.80007i	0.0566545	−	0.155657i
$597$	14.5625	−	10.1845i	0.596004	−	0.416824i
$598$	−2.98671	−	8.20591i	−0.122136	−	0.335565i
$599$	−23.4872	+	27.9909i	−0.959660	+	1.14368i	0.0298990	+	0.999553i	$0.490481\pi$
$599$	−23.4872	+	27.9909i	−0.959660	+	1.14368i	−0.989559	+	0.144126i	$0.953963\pi$
$600$	−1.45773	+	5.42805i	−0.0595116	+	0.221599i
$601$	−7.41347	−	8.83503i	−0.302402	−	0.360388i	0.593349	−	0.804945i	$-0.297805\pi$
$601$	−7.41347	−	8.83503i	−0.302402	−	0.360388i	−0.895750	+	0.444557i	$0.853361\pi$
$602$	2.67702	+	0.427305i	0.109107	+	0.0174156i
$603$	0.00725744	−	6.41689i	0.000295546	−	0.261316i
$604$	3.37274			0.137235
$605$	16.7700	+	6.10378i	0.681797	+	0.248154i
$606$	−8.09771	−	17.3913i	−0.328947	−	0.706472i
$607$	−15.4572	+	18.4212i	−0.627389	+	0.747693i	−0.982322	−	0.187199i	$-0.940059\pi$
$607$	−15.4572	+	18.4212i	−0.627389	+	0.747693i	0.354933	+	0.934892i	$0.384504\pi$
$608$	21.7219	−	7.90614i	0.880941	−	0.320636i
$609$	−11.8221	−	11.4570i	−0.479056	−	0.464261i
$610$	−1.62095	−	9.19287i	−0.0656304	−	0.372208i
$611$		−	8.17329i		−	0.330656i
$612$	−5.69566	−	3.29699i	−0.230233	−	0.133273i
$613$	−33.6863			−1.36058			−0.680289	−	0.732944i	$-0.738146\pi$
$613$	−33.6863			−1.36058			−0.680289	+	0.732944i	$0.738146\pi$
$614$	30.2142	+	10.9971i	1.21935	+	0.443806i
$615$	−7.46472	+	7.45628i	−0.301007	+	0.300666i
$616$	7.32586	+	2.53237i	0.295167	+	0.102032i
$617$	5.69508	−	6.78713i	0.229275	−	0.273240i	−0.639126	−	0.769102i	$-0.720704\pi$
$617$	5.69508	−	6.78713i	0.229275	−	0.273240i	0.868401	+	0.495863i	$0.165148\pi$
$618$	−20.4110	−	29.1850i	−0.821051	−	1.17399i
$619$	−2.57718	−	3.07137i	−0.103586	−	0.123449i	0.711761	−	0.702422i	$-0.247898\pi$
$619$	−2.57718	−	3.07137i	−0.103586	−	0.123449i	−0.815347	+	0.578973i	$0.803454\pi$
$620$	−7.99466	−	4.61572i	−0.321073	−	0.185372i
$621$	29.6394	−	2.54245i	1.18939	−	0.102025i
$622$			4.53193i			0.181714i
$623$	7.66886	+	12.7980i	0.307247	+	0.512742i
$624$	−7.19184	−	3.35856i	−0.287904	−	0.134450i
$625$	−2.78663	+	15.8037i	−0.111465	+	0.632150i
$626$	−11.4011	−	9.56665i	−0.455679	−	0.382360i
$627$	11.8793	−	11.8659i	0.474413	−	0.473876i
$628$	−3.55029	+	9.75435i	−0.141672	+	0.389241i
$629$	16.0523	+	27.8035i	0.640049	+	1.10860i
$630$	−4.53109	−	23.6047i	−0.180523	−	0.940433i
$631$	−6.55511	+	11.3538i	−0.260955	+	0.451987i	−0.966496	−	0.256682i	$-0.917371\pi$
$631$	−6.55511	+	11.3538i	−0.260955	+	0.451987i	0.705541	+	0.708669i	$0.250704\pi$
$632$	−1.82011	−	2.16912i	−0.0724001	−	0.0862831i
$633$	−1.73440	+	19.6960i	−0.0689364	+	0.782848i
$634$	4.88636	−	27.7119i	0.194062	−	1.10058i
$635$	−19.7487	−	16.5711i	−0.783702	−	0.657604i
$636$	−12.3402	−	1.08666i	−0.489320	−	0.0430887i
$637$	4.13201	−	5.26255i	0.163716	−	0.208510i
$638$	−6.27111	−	3.62063i	−0.248276	−	0.143342i
$639$	−0.503358	−	0.183852i	−0.0199125	−	0.00727308i
$640$			25.9129i			1.02430i
$641$	−7.86581	+	1.38695i	−0.310681	+	0.0547814i	−0.326815	−	0.945088i	$-0.605975\pi$
$641$	−7.86581	+	1.38695i	−0.310681	+	0.0547814i	0.0161339	+	0.999870i	$0.494864\pi$
$642$	2.80004	−	2.79687i	0.110509	−	0.110384i
$643$	38.0449	+	6.70834i	1.50034	+	0.264551i	0.862675	−	0.505759i	$-0.168787\pi$
$643$	38.0449	+	6.70834i	1.50034	+	0.264551i	0.637669	+	0.770310i	$0.279899\pi$
$644$	−2.70467	+	7.82430i	−0.106579	+	0.308321i
$645$	1.20948	+	1.72940i	0.0476234	+	0.0680952i
$646$	8.53593	+	48.4097i	0.335842	+	1.90465i
$647$	−19.9091	+	34.4836i	−0.782707	+	1.35569i	0.147652	+	0.989039i	$0.452829\pi$
$647$	−19.9091	+	34.4836i	−0.782707	+	1.35569i	−0.930359	+	0.366650i	$0.880505\pi$
$648$	13.4541	−	15.9605i	0.528527	−	0.626989i
$649$	−2.36212	+	1.36377i	−0.0927214	+	0.0535327i
$650$	2.00528	+	0.729863i	0.0786536	+	0.0286276i
$651$	40.6845	+	2.91732i	1.59455	+	0.114339i
$652$	−0.593720	−	0.498190i	−0.0232519	−	0.0195106i
$653$	−9.97502	−	27.4061i	−0.390353	−	1.07249i	−0.966841	−	0.255380i	$-0.917799\pi$
$653$	−9.97502	−	27.4061i	−0.390353	−	1.07249i	0.576488	−	0.817106i	$-0.304423\pi$
$654$	1.35671	−	5.05188i	0.0530515	−	0.197544i
$655$	−2.98900	−	16.9514i	−0.116790	−	0.662347i
$656$	7.69512	−	13.3283i	0.300444	−	0.520384i
$657$	5.95449	+	33.9944i	0.232307	+	1.32625i
$658$	−22.7538	+	28.0294i	−0.887034	+	1.09270i
$659$	20.9180	−	3.68841i	0.814851	−	0.143680i	0.249335	−	0.968417i	$-0.419788\pi$
$659$	20.9180	−	3.68841i	0.814851	−	0.143680i	0.565516	+	0.824737i	$0.308677\pi$
$660$	−0.957771	−	2.05698i	−0.0372812	−	0.0800680i
$661$	−21.8151	−	3.84658i	−0.848507	−	0.149615i	−0.267545	−	0.963545i	$-0.586212\pi$
$661$	−21.8151	−	3.84658i	−0.848507	−	0.149615i	−0.580962	+	0.813931i	$0.697324\pi$
$662$	43.0086	+	7.58357i	1.67158	+	0.294744i
$663$	3.81449	−	5.44111i	0.148143	−	0.211315i
$664$	−12.4341	+	2.19247i	−0.482538	+	0.0850845i
$665$	−24.2846	+	29.9153i	−0.941718	+	1.16006i
$666$	35.9982	−	13.0562i	1.39490	−	0.505917i
$667$	−10.2836	+	17.8117i	−0.398182	+	0.689671i
$668$	1.49687	+	8.48918i	0.0579157	+	0.328456i
$669$	13.4356	+	13.4508i	0.519450	+	0.520038i
$670$	2.21534	+	6.08660i	0.0855861	+	0.235146i
$671$	2.98271	+	2.50279i	0.115146	+	0.0966192i
$672$	6.02877	+	12.4165i	0.232565	+	0.478979i
$673$	15.9545	+	5.80696i	0.615000	+	0.223842i	0.630690	−	0.776035i	$-0.282772\pi$
$673$	15.9545	+	5.80696i	0.615000	+	0.223842i	−0.0156895	+	0.999877i	$0.504994\pi$
$674$	20.8356	−	12.0294i	0.802556	−	0.463356i
$675$	−4.17976	+	5.94782i	−0.160879	+	0.228932i
$676$	3.30288	−	5.72076i	0.127034	−	0.220029i
$677$	−7.28066	−	41.2907i	−0.279818	−	1.58693i	−0.723228	−	0.690610i	$-0.757342\pi$
$677$	−7.28066	−	41.2907i	−0.279818	−	1.58693i	0.443410	−	0.896319i	$-0.353769\pi$
$678$	−2.39198	+	0.207908i	−0.0918635	+	0.00798467i
$679$	−5.24512	+	15.1735i	−0.201289	+	0.582307i
$680$	−17.3975	−	3.06765i	−0.667163	−	0.117639i
$681$	25.1762	+	6.76120i	0.964754	+	0.259090i
$682$	17.6686	−	3.11546i	0.676567	−	0.119297i
$683$		−	1.56964i		−	0.0600606i	−0.999549	−	0.0300303i	$-0.990440\pi$
$683$		−	1.56964i		−	0.0600606i	0.999549	−	0.0300303i	$-0.00956038\pi$
$684$	12.5836	+	0.0142319i	0.481146	+	0.000544171i
$685$	−33.0125	−	19.0598i	−1.26134	−	0.728236i
$686$	−28.8208	+	6.54418i	−1.10038	+	0.249858i
$687$	−22.3427	+	31.8704i	−0.852428	+	1.21593i
$688$	−2.35818	−	1.97874i	−0.0899046	−	0.0754389i
$689$	2.17203	−	12.3182i	0.0827478	−	0.469286i
$690$	−27.2217	+	12.6750i	−1.03631	+	0.482527i
$691$	−23.8441	−	28.4163i	−0.907071	−	1.08101i	−0.996381	−	0.0850017i	$-0.972910\pi$
$691$	−23.8441	−	28.4163i	−0.907071	−	1.08101i	0.0893094	−	0.996004i	$-0.471534\pi$
$692$	−2.98121	+	5.16360i	−0.113328	+	0.196291i
$693$	7.77665	+	6.32754i	0.295410	+	0.240363i
$694$	−19.3251	−	33.4720i	−0.733569	−	1.27058i
$695$	4.96340	−	13.6368i	0.188273	−	0.517275i
$696$	3.72744	+	13.9425i	0.141288	+	0.528490i
$697$	9.86997	+	8.28188i	0.373852	+	0.313699i
$698$	1.55598	−	8.82439i	0.0588946	−	0.334008i
$699$	−4.40078	−	50.6309i	−0.166453	−	1.91504i
$700$	−1.03985	−	1.73534i	−0.0393028	−	0.0655896i
$701$			8.24161i			0.311281i	0.987814	+	0.155641i	$0.0497442\pi$
$701$			8.24161i			0.311281i	−0.987814	+	0.155641i	$0.950256\pi$
$702$	−5.59487	−	5.61389i	−0.211165	−	0.211883i
$703$	−53.1626	−	30.6934i	−2.00506	−	1.15762i
$704$	−3.88275	−	4.62729i	−0.146337	−	0.174397i
$705$	−27.9993	+	2.43367i	−1.05451	+	0.0916572i
$706$	−22.2452	+	26.5108i	−0.837209	+	0.997747i
$707$	−17.3557	−	5.99946i	−0.652730	−	0.225633i
$708$	−1.97422	−	0.530187i	−0.0741956	−	0.0199256i
$709$	−12.4403	−	4.52790i	−0.467206	−	0.170049i	0.0976805	−	0.995218i	$-0.468858\pi$
$709$	−12.4403	−	4.52790i	−0.467206	−	0.170049i	−0.564886	+	0.825169i	$0.691080\pi$
$710$	0.540922			0.0203004
$711$	−1.24875	−	3.44301i	−0.0468317	−	0.129123i
$712$		−	13.0795i		−	0.490175i
$713$	−8.84875	−	50.1838i	−0.331388	−	1.87940i
$714$	−28.2290	+	8.04048i	−1.05644	+	0.300908i
$715$	2.15290	−	0.783592i	0.0805139	−	0.0293047i
$716$	8.30549	−	9.89810i	0.310391	−	0.369909i
$717$	−27.6271	+	39.4081i	−1.03175	+	1.47172i
$718$	32.9003	+	11.9747i	1.22783	+	0.446893i
$719$	11.3474			0.423187			0.211594	−	0.977358i	$-0.432135\pi$
$719$	11.3474			0.423187			0.211594	+	0.977358i	$0.432135\pi$
$720$	−9.36401	+	25.6372i	−0.348976	+	0.955441i
$721$	−33.6646	−	5.37353i	−1.25373	−	0.200121i
$722$	−40.9271	−	48.7751i	−1.52315	−	1.81522i
$723$	0.0918647	+	0.0919686i	0.00341648	+	0.00342035i
$724$	7.60296	−	9.06086i	0.282562	−	0.336744i
$725$	−1.71900	−	4.72290i	−0.0638419	−	0.175404i
$726$	−23.5524	−	10.9989i	−0.874111	−	0.408207i
$727$	−7.94102	+	21.8178i	−0.294516	+	0.809176i	0.700876	+	0.713284i	$0.252793\pi$
$727$	−7.94102	+	21.8178i	−0.294516	+	0.809176i	−0.995392	+	0.0958928i	$0.969429\pi$
$728$	−5.47853	+	2.09544i	−0.203048	+	0.0776622i
$729$	23.4284	−	13.4206i	0.867717	−	0.497059i
$730$	−17.4182	−	30.1692i	−0.644677	−	1.11661i
$731$	1.97421	−	1.65656i	0.0730187	−	0.0612699i
$732$	0.252687	+	2.90715i	0.00933956	+	0.107452i
$733$	16.0347	+	2.82735i	0.592255	+	0.104431i	0.461739	−	0.887016i	$-0.347226\pi$
$733$	16.0347	+	2.82735i	0.592255	+	0.104431i	0.130516	+	0.991446i	$0.458337\pi$
$734$	3.15849	−	17.9127i	0.116582	−	0.661170i
$735$	−19.2583	−	12.5881i	−0.710353	−	0.464319i
$736$	13.2096	−	11.0842i	0.486913	−	0.408568i
$737$	−2.33979	−	1.35088i	−0.0861873	−	0.0497603i
$738$	11.7835	−	9.86487i	0.433758	−	0.363131i
$739$	5.44795	+	9.43613i	0.200406	+	0.347114i	0.948659	−	0.316300i	$-0.102440\pi$
$739$	5.44795	+	9.43613i	0.200406	+	0.347114i	−0.748253	+	0.663413i	$0.769107\pi$
$740$	−6.35492	+	5.33241i	−0.233612	+	0.196023i
$741$	−1.11454	+	12.6568i	−0.0409437	+	0.464960i
$742$	−41.7416	+	36.1972i	−1.53238	+	1.32884i
$743$	−16.4197	−	45.1128i	−0.602381	−	1.65503i	−0.746435	−	0.665458i	$-0.768236\pi$
$743$	−16.4197	−	45.1128i	−0.602381	−	1.65503i	0.144054	−	0.989570i	$-0.453986\pi$
$744$	−29.2794	−	20.5264i	−1.07344	−	0.752533i
$745$	4.80219	−	13.1939i	0.175939	−	0.483388i
$746$	−51.7932	+	29.9028i	−1.89628	+	1.09482i
$747$	−16.0795	−	2.85401i	−0.588319	−	0.104423i
$748$	−2.39966	+	1.38544i	−0.0877403	+	0.0506569i
$749$	−0.0615517	−	3.78781i	−0.00224905	−	0.138404i
$750$	8.70507	−	32.4144i	0.317864	−	1.18361i
$751$	−19.7103	+	7.17395i	−0.719237	+	0.261781i	−0.675602	−	0.737266i	$-0.736116\pi$
$751$	−19.7103	+	7.17395i	−0.719237	+	0.261781i	−0.0436354	+	0.999048i	$0.513894\pi$
$752$	38.5238	−	14.0215i	1.40482	−	0.511313i
$753$	19.1436	+	27.3728i	0.697630	+	0.997519i
$754$	5.39645	−	0.951539i	0.196527	−	0.0346530i
$755$	11.7102			0.426179
$756$	0.763720	+	7.47486i	0.0277762	+	0.271858i
$757$	−24.6333			−0.895314			−0.447657	−	0.894205i	$-0.647741\pi$
$757$	−24.6333			−0.895314			−0.447657	+	0.894205i	$0.647741\pi$
$758$	−7.40724	+	1.30610i	−0.269043	+	0.0474396i
$759$	5.29978	−	11.3486i	0.192370	−	0.411930i
$760$	31.7416	−	11.5530i	1.15139	−	0.419071i
$761$	−8.78216	+	3.19644i	−0.318353	+	0.115871i	−0.496254	−	0.868177i	$-0.665292\pi$
$761$	−8.78216	+	3.19644i	−0.318353	+	0.115871i	0.177901	+	0.984048i	$0.443069\pi$
$762$	26.5369	+	26.5669i	0.961330	+	0.962418i
$763$	−2.57368	−	4.29504i	−0.0931735	−	0.155491i
$764$	10.3695	−	5.98683i	0.375155	−	0.216596i
$765$	−19.7754	−	11.4472i	−0.714983	−	0.413874i
$766$	−10.3669	+	5.98533i	−0.374571	+	0.216259i
$767$	0.705937	−	1.93955i	0.0254899	−	0.0700330i
$768$	1.85766	−	21.0958i	0.0670327	−	0.761229i
$769$	3.02496	+	8.31100i	0.109083	+	0.299702i	0.982209	−	0.187792i	$-0.0601332\pi$
$769$	3.02496	+	8.31100i	0.109083	+	0.299702i	−0.873126	+	0.487494i	$0.837911\pi$
$770$	−9.56460	−	3.30625i	−0.344684	−	0.119149i
$771$	4.42564	+	3.10260i	0.159385	+	0.111737i
$772$	−6.09872	+	5.11743i	−0.219498	+	0.184180i
$773$	7.06558	+	12.2379i	0.254131	+	0.440168i	0.964659	−	0.263501i	$-0.0848771\pi$
$773$	7.06558	+	12.2379i	0.254131	+	0.440168i	−0.710528	+	0.703669i	$0.751544\pi$
$774$	−1.53393	−	2.66379i	−0.0551359	−	0.0957481i
$775$	10.7843	+	6.22631i	0.387383	+	0.223656i
$776$	10.7815	−	9.04675i	0.387033	−	0.324759i
$777$	14.9680	−	33.4592i	0.536976	−	1.20034i
$778$	−6.39392	+	36.2617i	−0.229233	+	1.30005i
$779$	−24.2617	−	4.27798i	−0.869264	−	0.153275i
$780$	1.55577	+	0.726537i	0.0557054	+	0.0260142i
$781$	−0.172841	+	0.145031i	−0.00618472	+	0.00518960i
$782$	18.3347	+	31.7566i	0.655648	+	1.13562i
$783$	−1.65849	+	18.5933i	−0.0592696	+	0.664469i
$784$	31.8930	+	10.4477i	1.13904	+	0.373132i
$785$	−12.3267	+	33.8673i	−0.439958	+	1.20878i
$786$	2.17101	+	24.9774i	0.0774373	+	0.890915i
$787$	−9.44389	−	25.9469i	−0.336638	−	0.924907i	−0.986341	−	0.164718i	$-0.947329\pi$
$787$	−9.44389	−	25.9469i	−0.336638	−	0.924907i	0.649702	−	0.760189i	$-0.274894\pi$
$788$	−0.837271	+	0.997821i	−0.0298265	+	0.0355459i
$789$	−7.30984	+	1.95424i	−0.260237	+	0.0695727i
$790$	2.37633	+	2.83200i	0.0845459	+	0.100758i
$791$	−1.44851	+	1.78436i	−0.0515031	+	0.0634446i
$792$	−2.99668	−	8.26238i	−0.106483	−	0.293591i
$793$	−2.94646			−0.104632
$794$	−26.1210	−	9.50727i	−0.927000	−	0.337400i
$795$	−42.8453	−	3.77289i	−1.51957	−	0.133811i
$796$	3.60441	−	4.29557i	0.127755	−	0.152252i
$797$	32.0647	−	11.6706i	1.13579	−	0.413394i	0.295399	−	0.955374i	$-0.404547\pi$
$797$	32.0647	−	11.6706i	1.13579	−	0.413394i	0.840391	+	0.541980i	$0.182325\pi$
$798$	39.0578	−	40.3025i	1.38263	−	1.42669i
$799$	5.95978	+	33.7996i	0.210842	+	1.19574i
$800$			4.21391i			0.148984i
$801$	5.80410	−	15.8907i	0.205078	−	0.561470i
$802$	34.3388			1.21254
$803$	13.6545	+	4.96985i	0.481858	+	0.175382i
$804$	−0.522962	−	1.95614i	−0.0184434	−	0.0689879i
$805$	−9.39067	+	27.1661i	−0.330978	+	0.957480i
$806$	−8.72693	+	10.4004i	−0.307393	+	0.366337i
$807$	−0.629567	+	1.34812i	−0.0221618	+	0.0474561i
$808$	10.3478	+	12.3321i	0.364035	+	0.433840i
$809$	−8.13629	−	4.69749i	−0.286057	−	0.165155i	0.350105	−	0.936710i	$-0.386146\pi$
$809$	−8.13629	−	4.69749i	−0.286057	−	0.165155i	−0.636162	+	0.771555i	$0.719479\pi$
$810$	−17.5656	+	20.8380i	−0.617193	+	0.732172i
$811$			31.3300i			1.10014i	0.835117	+	0.550072i	$0.185400\pi$
$811$			31.3300i			1.10014i	−0.835117	+	0.550072i	$0.814600\pi$
$812$	−4.54046	−	2.52398i	−0.159339	−	0.0885742i
$813$	7.75541	−	5.42387i	0.271994	−	0.190223i
$814$	2.79968	−	15.8778i	0.0981287	−	0.556516i
$815$	−2.06141	−	1.72972i	−0.0722079	−	0.0605896i
$816$	32.1899	+	8.64477i	1.12687	+	0.302628i
$817$	−1.68538	+	4.63054i	−0.0589639	+	0.162002i
$818$	−21.2375	−	36.7845i	−0.742554	−	1.28614i
$819$	−7.58589	+	0.114689i	−0.265072	+	0.00400754i
$820$	−1.66464	+	2.88324i	−0.0581317	+	0.100687i
$821$	4.21759	+	5.02633i	0.147195	+	0.175420i	0.834604	−	0.550850i	$-0.185696\pi$
$821$	4.21759	+	5.02633i	0.147195	+	0.175420i	−0.687409	+	0.726270i	$0.741252\pi$
$822$	45.4639	+	31.8725i	1.58574	+	1.11168i
$823$	−4.04297	+	22.9288i	−0.140929	+	0.799248i	0.829617	+	0.558333i	$0.188559\pi$
$823$	−4.04297	+	22.9288i	−0.140929	+	0.799248i	−0.970546	+	0.240915i	$0.922552\pi$
$824$	22.8938	+	19.2102i	0.797544	+	0.669219i
$825$	1.29197	+	2.77474i	0.0449807	+	0.0966040i
$826$	−7.82048	+	4.68620i	−0.272109	+	0.163054i
$827$	33.9354	+	19.5926i	1.18005	+	0.681302i	0.956026	−	0.293282i	$-0.0947476\pi$
$827$	33.9354	+	19.5926i	1.18005	+	0.681302i	0.224023	+	0.974584i	$0.428081\pi$
$828$	8.82455	−	3.20057i	0.306674	−	0.111228i
$829$		−	36.1621i		−	1.25596i	−0.778229	−	0.627981i	$-0.783882\pi$
$829$		−	36.1621i		−	1.25596i	0.778229	−	0.627981i	$-0.216118\pi$
$830$	16.2339	−	2.86248i	0.563489	−	0.0993582i
$831$	−8.74923	−	32.7266i	−0.303507	−	1.13527i
$832$	4.50160	+	0.793753i	0.156065	+	0.0275184i
$833$	−13.2501	+	24.7756i	−0.459088	+	0.858423i
$834$	−8.94395	+	19.1521i	−0.309704	+	0.663182i
$835$	5.19716	+	29.4746i	0.179855	+	1.02001i
$836$	2.64909	−	4.58836i	0.0916206	−	0.158692i
$837$	−26.4638	−	37.9310i	−0.914721	−	1.31109i
$838$	−8.04702	+	4.64595i	−0.277980	+	0.160492i
$839$	35.7513	+	13.0124i	1.23427	+	0.449238i	0.875058	−	0.484018i	$-0.160823\pi$
$839$	35.7513	+	13.0124i	1.23427	+	0.449238i	0.359212	+	0.933256i	$0.383045\pi$
$840$	8.80964	+	18.1439i	0.303961	+	0.626024i
$841$	12.3288	+	10.3451i	0.425130	+	0.356726i
$842$	2.69858	+	7.41428i	0.0929991	+	0.255513i
$843$	−22.4123	+	5.99177i	−0.771919	+	0.206367i
$844$	1.08341	+	6.14433i	0.0372926	+	0.211497i
$845$	11.4677	−	19.8626i	0.394500	−	0.683294i
$846$	40.9362	+	0.0462985i	1.40742	+	0.00159178i
$847$	−23.2401	+	8.88895i	−0.798541	+	0.305428i
$848$	61.7866	−	10.8946i	2.12176	−	0.374124i
$849$	18.5617	+	1.63452i	0.637036	+	0.0560965i
$850$	−8.82479	−	1.55605i	−0.302688	−	0.0533720i
$851$	−45.0973	−	7.95187i	−1.54591	−	0.272586i
$852$	−0.168446	−	0.0148331i	−0.00577085	−	0.000508173i
$853$	30.3259	−	5.34727i	1.03834	−	0.183087i	0.371611	−	0.928389i	$-0.378806\pi$
$853$	30.3259	−	5.34727i	1.03834	−	0.183087i	0.666728	+	0.745301i	$0.267694\pi$
$854$	10.1046	+	8.20269i	0.345771	+	0.280690i
$855$	43.6905	+	0.0494135i	1.49418	+	0.00168991i
$856$	−1.66052	+	2.87610i	−0.0567553	+	0.0983031i
$857$	−3.52209	−	19.9748i	−0.120312	−	0.682325i	−0.983982	−	0.178267i	$-0.942951\pi$
$857$	−3.52209	−	19.9748i	−0.120312	−	0.682325i	0.863670	−	0.504058i	$-0.168160\pi$
$858$	−3.22385	+	0.861874i	−0.110060	+	0.0294239i
$859$	11.8516	+	32.5620i	0.404371	+	1.11100i	0.960105	+	0.279640i	$0.0902153\pi$
$859$	11.8516	+	32.5620i	0.404371	+	1.11100i	−0.555734	+	0.831360i	$0.687563\pi$
$860$	0.510130	+	0.428050i	0.0173953	+	0.0145964i
$861$	1.05212	−	14.6727i	0.0358561	−	0.500043i
$862$	−17.6440	−	6.42189i	−0.600957	−	0.218731i
$863$	32.8141	−	18.9452i	1.11700	−	0.644902i	0.176369	−	0.984324i	$-0.443565\pi$
$863$	32.8141	−	18.9452i	1.11700	−	0.644902i	0.940634	+	0.339422i	$0.110231\pi$
$864$	6.63840	−	14.1733i	0.225843	−	0.482185i
$865$	−10.3508	+	17.9281i	−0.351938	+	0.609574i
$866$	−7.93603	−	45.0074i	−0.269677	−	1.52941i
$867$	0.652210	−	1.39661i	0.0221502	−	0.0474312i
$868$	12.6374	−	2.44066i	0.428941	−	0.0828414i
$869$	−1.51862	−	0.267773i	−0.0515155	−	0.00908357i
$870$	−4.86653	−	18.2033i	−0.164991	−	0.617150i
$871$	2.01345	−	0.355025i	0.0682231	−	0.0120296i
$872$			4.38950i			0.148647i
$873$	17.1133	−	6.20682i	0.579197	−	0.210069i
$874$	−60.7214	−	35.0575i	−2.05393	−	1.18584i
$875$	−16.5135	−	27.5583i	−0.558260	−	0.931641i
$876$	4.59682	+	9.87248i	0.155312	+	0.333560i
$877$	−9.10894	−	7.64331i	−0.307587	−	0.258096i	0.475907	−	0.879496i	$-0.342120\pi$
$877$	−9.10894	−	7.64331i	−0.307587	−	0.258096i	−0.783494	+	0.621399i	$0.786564\pi$
$878$	−2.97440	+	16.8687i	−0.100381	+	0.569290i
$879$	−12.7306	−	8.92481i	−0.429393	−	0.301026i
$880$	7.38673	+	8.80317i	0.249007	+	0.296755i
$881$	−19.8758	+	34.4258i	−0.669631	+	1.15984i	0.308376	+	0.951265i	$0.400215\pi$
$881$	−19.8758	+	34.4258i	−0.669631	+	1.15984i	−0.978007	+	0.208571i	$0.933119\pi$
$882$	26.3343	+	20.7252i	0.886722	+	0.697853i
$883$	25.4955	+	44.1595i	0.857992	+	1.48609i	0.873842	+	0.486211i	$0.161621\pi$
$883$	25.4955	+	44.1595i	0.857992	+	1.48609i	−0.0158499	+	0.999874i	$0.505045\pi$
$884$	0.717156	−	1.97037i	0.0241206	−	0.0662707i
$885$	−6.85452	−	1.84082i	−0.230412	−	0.0618784i
$886$	−19.5895	−	16.4375i	−0.658122	−	0.552230i
$887$	4.66549	−	26.4593i	0.156652	−	0.888416i	−0.800608	−	0.599188i	$-0.795490\pi$
$887$	4.66549	−	26.4593i	0.156652	−	0.888416i	0.957260	−	0.289228i	$-0.0933986\pi$
$888$	−26.3326	+	18.4161i	−0.883663	+	0.618003i
$889$	35.9390	−	0.584007i	1.20536	−	0.0195870i
$890$			17.0765i			0.572407i
$891$	0.0257142	−	11.3680i	0.000861460	−	0.380843i
$892$	5.19536	+	2.99954i	0.173953	+	0.100432i
$893$	−42.1827	−	50.2714i	−1.41159	−	1.68227i
$894$	−8.65345	+	18.5300i	−0.289415	+	0.619737i
$895$	28.8368	−	34.3664i	0.963909	−	1.14874i
$896$	−23.6698	−	27.2954i	−0.790754	−	0.911874i
$897$	2.44796	+	9.15662i	0.0817350	+	0.305731i
$898$	26.9025	+	9.79170i	0.897747	+	0.326753i
$899$	31.9762			1.06647
$900$	−0.787002	+	2.15468i	−0.0262334	+	0.0718228i
$901$			52.5242i			1.74983i
$902$	−1.12357	−	6.37211i	−0.0374109	−	0.212168i
$903$	−2.85372	−	0.716880i	−0.0949658	−	0.0238563i
$904$	1.89330	−	0.689103i	0.0629701	−	0.0229192i
$905$	26.3976	−	31.4595i	0.877487	−	1.04575i
$906$	−16.9908	−	1.49619i	−0.564483	−	0.0497075i
$907$	38.0140	+	13.8359i	1.26223	+	0.459415i	0.884518	−	0.466507i	$-0.154488\pi$
$907$	38.0140	+	13.8359i	1.26223	+	0.459415i	0.377715	+	0.925922i	$0.376710\pi$
$908$	8.22582			0.272983
$909$	7.09947	+	19.5745i	0.235474	+	0.649245i
$910$	7.15274	−	2.73580i	0.237111	−	0.0906908i
$911$	12.3517	+	14.7202i	0.409231	+	0.487702i	0.930811	−	0.365500i	$-0.119102\pi$
$911$	12.3517	+	14.7202i	0.409231	+	0.487702i	−0.521581	+	0.853202i	$0.674658\pi$
$912$	−61.5685	+	16.4599i	−2.03874	+	0.545042i
$913$	−4.41975	+	5.26725i	−0.146272	+	0.174321i
$914$	12.5115	+	34.3749i	0.413842	+	1.13702i
$915$	0.877333	+	10.0937i	0.0290037	+	0.333687i
$916$	−4.20062	+	11.5411i	−0.138792	+	0.381329i
$917$	18.6326	+	15.1256i	0.615302	+	0.499490i
$918$	27.2304	+	19.1359i	0.898738	+	0.631578i
$919$	1.00540	+	1.74140i	0.0331650	+	0.0574435i	0.882132	−	0.471003i	$-0.156108\pi$
$919$	1.00540	+	1.74140i	0.0331650	+	0.0574435i	−0.848966	+	0.528447i	$0.822775\pi$
$920$	19.3028	−	16.1970i	0.636394	−	0.533998i
$921$	−31.6207	−	14.7668i	−1.04194	−	0.486581i
$922$	−18.8823	−	3.32947i	−0.621857	−	0.109650i
$923$	0.0296486	−	0.168146i	0.000975897	−	0.00553459i
$924$	2.88780	+	1.29186i	0.0950017	+	0.0424991i
$925$	8.57238	−	7.19308i	0.281858	−	0.236507i
$926$	1.55058	+	0.895227i	0.0509552	+	0.0294190i
$927$	19.2898	+	33.4983i	0.633559	+	1.10023i
$928$	5.41030	+	9.37092i	0.177602	+	0.307616i
$929$	−2.67605	+	2.24547i	−0.0877982	+	0.0736714i	−0.685630	−	0.727950i	$-0.740473\pi$
$929$	−2.67605	+	2.24547i	−0.0877982	+	0.0736714i	0.597832	+	0.801621i	$0.296029\pi$
$930$	38.2271	+	26.7991i	1.25351	+	0.878777i
$931$	−1.74551	−	53.6939i	−0.0572066	−	1.75975i
$932$	−5.48490	−	15.0696i	−0.179664	−	0.493622i
$933$	0.431481	−	4.89994i	0.0141261	−	0.160417i
$934$	7.18720	−	19.7467i	0.235172	−	0.646131i
$935$	−8.33167	+	4.81029i	−0.272475	+	0.157313i
$936$	5.75613	+	3.33199i	0.188145	+	0.108909i
$937$	−29.0222	+	16.7560i	−0.948114	+	0.547394i	−0.892495	−	0.451058i	$-0.851047\pi$
$937$	−29.0222	+	16.7560i	−0.948114	+	0.547394i	−0.0556194	+	0.998452i	$0.517713\pi$
$938$	−7.89327	−	4.38775i	−0.257724	−	0.143265i
$939$	11.4161	+	11.4290i	0.372549	+	0.372971i
$940$	−8.33363	+	3.03319i	−0.271813	+	0.0989318i
$941$	−31.7471	+	11.5550i	−1.03493	+	0.376682i	−0.802955	−	0.596040i	$-0.796740\pi$
$941$	−31.7471	+	11.5550i	−1.03493	+	0.376682i	−0.231972	+	0.972722i	$0.574518\pi$
$942$	22.2124	−	47.5645i	0.723720	−	1.54973i
$943$	−18.0985	+	3.19126i	−0.589370	+	0.103922i
$944$	10.3529			0.336958
$945$	2.65165	+	25.9529i	0.0862582	+	0.844247i
$946$	−1.29422			−0.0420788
$947$	−1.54156	+	0.271818i	−0.0500939	+	0.00883291i	−0.198639	−	0.980073i	$-0.563652\pi$
$947$	−1.54156	+	0.271818i	−0.0500939	+	0.00883291i	0.148545	+	0.988906i	$0.452541\pi$
$948$	−0.662341	−	0.947061i	−0.0215118	−	0.0307591i
$949$	−10.3328	+	3.76085i	−0.335418	+	0.122082i
$950$	16.1007	−	5.86019i	0.522377	−	0.190130i
$951$	−7.92158	+	29.4970i	−0.256875	+	0.956506i
$952$	21.1278	−	12.6602i	0.684756	−	0.410321i
$953$	−13.8156	+	7.97645i	−0.447532	+	0.258383i	−0.706787	−	0.707426i	$-0.749856\pi$
$953$	−13.8156	+	7.97645i	−0.447532	+	0.258383i	0.259255	+	0.965809i	$0.416523\pi$
$954$	61.6839	+	10.9485i	1.99709	+	0.354470i
$955$	36.0031	−	20.7864i	1.16503	−	0.672631i
$956$	−5.19411	+	14.2707i	−0.167990	+	0.461548i
$957$	6.43563	+	4.51170i	0.208034	+	0.145843i
$958$	−12.2187	−	33.5707i	−0.394770	−	1.08462i
$959$	52.1837	−	10.0783i	1.68510	−	0.325444i
$960$	1.37878	−	15.6575i	0.0444998	−	0.505343i
$961$	−36.9429	+	30.9988i	−1.19171	+	0.999960i
$962$	6.10030	+	10.5660i	0.196681	+	0.340662i
$963$	−3.29370	+	2.75740i	−0.106138	+	0.0888559i
$964$	0.0355228	+	0.0205091i	0.00114411	+	0.000660553i
$965$	−21.1749	+	17.7678i	−0.681643	+	0.571966i
$966$	17.0962	−	38.2166i	0.550063	−	1.22960i
$967$	0.704391	−	3.99480i	0.0226517	−	0.128464i	−0.971385	−	0.237510i	$-0.923669\pi$
$967$	0.704391	−	3.99480i	0.0226517	−	0.128464i	0.994037	+	0.109046i	$0.0347797\pi$
$968$	21.4816	+	3.78778i	0.690444	+	0.121744i
$969$	−4.62003	−	53.1534i	−0.148417	−	1.70753i
$970$	−14.0763	+	11.8114i	−0.451962	+	0.379241i
$971$	−20.1944	−	34.9777i	−0.648068	−	1.12249i	−0.983584	−	0.180453i	$-0.942244\pi$
$971$	−20.1944	−	34.9777i	−0.648068	−	1.12249i	0.335515	−	0.942035i	$-0.391090\pi$
$972$	6.04144	−	6.00737i	0.193779	−	0.192686i
$973$	7.22821	+	18.8982i	0.231726	+	0.605847i
$974$	−15.4317	+	42.3984i	−0.494465	+	1.35853i
$975$	−2.09863	−	0.980052i	−0.0672099	−	0.0313868i
$976$	−5.05474	−	13.8878i	−0.161798	−	0.444537i
$977$	−5.59190	+	6.66416i	−0.178901	+	0.213205i	−0.848041	−	0.529931i	$-0.822218\pi$
$977$	−5.59190	+	6.66416i	−0.178901	+	0.213205i	0.669140	+	0.743136i	$0.266662\pi$
$978$	2.76997	+	2.77311i	0.0885740	+	0.0886742i
$979$	−4.57852	−	5.45647i	−0.146330	−	0.174389i
$980$	−6.89922	−	2.26009i	−0.220387	−	0.0721958i
$981$	−1.94786	+	5.33294i	−0.0621905	+	0.170268i
$982$	−59.0451			−1.88420
$983$	−31.7045	−	11.5395i	−1.01122	−	0.368053i	−0.217317	−	0.976101i	$-0.569731\pi$
$983$	−31.7045	−	11.5395i	−1.01122	−	0.368053i	−0.793900	+	0.608048i	$0.791953\pi$
$984$	−7.40273	+	10.5595i	−0.235991	+	0.336624i
$985$	−2.90702	+	3.46445i	−0.0926254	+	0.110387i
$986$	−21.6225	+	7.86994i	−0.688600	+	0.250630i
$987$	27.2701	−	28.1392i	0.868017	−	0.895679i
$988$	0.696209	+	3.94840i	0.0221493	+	0.125615i
$989$			3.67595i			0.116888i
$990$	3.91246	+	10.7873i	0.124346	+	0.342844i
$991$	−25.4615			−0.808810			−0.404405	−	0.914580i	$-0.632521\pi$
$991$	−25.4615			−0.808810			−0.404405	+	0.914580i	$0.632521\pi$
$992$	−25.1927	−	9.16940i	−0.799870	−	0.291129i
$993$	−45.7790	−	12.2942i	−1.45275	−	0.390144i
$994$	−0.569781	+	0.494099i	−0.0180724	+	0.0156719i
$995$	12.5146	−	14.9143i	0.396739	−	0.472815i
$996$	−5.13383	+	0.446226i	−0.162671	+	0.0141392i
$997$	5.62019	+	6.69788i	0.177993	+	0.212124i	0.847663	−	0.530535i	$-0.178009\pi$
$997$	5.62019	+	6.69788i	0.177993	+	0.212124i	−0.669670	+	0.742659i	$0.733564\pi$
$998$	22.6731	+	13.0903i	0.717705	+	0.414367i
$999$	−40.1644	+	10.6890i	−1.27075	+	0.338186i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.bd.a.185.6	yes	132
3.2	odd	2		567.2.bd.a.17.17		132
7.5	odd	6		189.2.ba.a.131.17	yes	132
21.5	even	6		567.2.ba.a.341.6		132
27.7	even	9		567.2.ba.a.143.6		132
27.20	odd	18		189.2.ba.a.101.17	✓	132
189.47	even	18	inner	189.2.bd.a.47.6	yes	132
189.61	odd	18		567.2.bd.a.467.17		132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.ba.a.101.17	✓	132	27.20	odd	18
189.2.ba.a.131.17	yes	132	7.5	odd	6
189.2.bd.a.47.6	yes	132	189.47	even	18	inner
189.2.bd.a.185.6	yes	132	1.1	even	1	trivial
567.2.ba.a.143.6		132	27.7	even	9
567.2.ba.a.341.6		132	21.5	even	6
567.2.bd.a.17.17		132	3.2	odd	2
567.2.bd.a.467.17		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)

\(f(q)\)	\(=\)	\(q+(-1.57155 + 0.277106i) q^{2} +(1.72554 - 0.149982i) q^{3} +(0.513586 - 0.186930i) q^{4} +(1.78318 - 0.649025i) q^{5} +(-2.67021 + 0.713863i) q^{6} +(-1.28547 + 2.31248i) q^{7} +(2.00866 - 1.15970i) q^{8} +(2.95501 - 0.517603i) q^{9} +O(q^{10})\)	\(q+(-1.57155 + 0.277106i) q^{2} +(1.72554 - 0.149982i) q^{3} +(0.513586 - 0.186930i) q^{4} +(1.78318 - 0.649025i) q^{5} +(-2.67021 + 0.713863i) q^{6} +(-1.28547 + 2.31248i) q^{7} +(2.00866 - 1.15970i) q^{8} +(2.95501 - 0.517603i) q^{9} +(-2.62250 + 1.51410i) q^{10} +(0.432011 - 1.18694i) q^{11} +(0.858180 - 0.399585i) q^{12} +(0.326917 + 0.898197i) q^{13} +(1.37938 - 3.99038i) q^{14} +(2.97962 - 1.38737i) q^{15} +(-3.67271 + 3.08177i) q^{16} +(-2.00687 - 3.47600i) q^{17} +(-4.50051 + 1.63229i) q^{18} +(6.64640 + 3.83730i) q^{19} +(0.794495 - 0.666660i) q^{20} +(-1.87131 + 4.18309i) q^{21} +(-0.350017 + 1.98504i) q^{22} +(5.63807 + 0.994145i) q^{23} +(3.29211 - 2.30238i) q^{24} +(-1.07172 + 0.899282i) q^{25} +(-0.762661 - 1.32097i) q^{26} +(5.02137 - 1.33635i) q^{27} +(-0.227929 + 1.42795i) q^{28} +(-1.22870 + 3.37583i) q^{29} +(-4.29816 + 3.00598i) q^{30} +(-3.04428 - 8.36408i) q^{31} +(1.93608 - 2.30734i) q^{32} +(0.567434 - 2.11291i) q^{33} +(4.11711 + 4.90658i) q^{34} +(-0.791374 + 4.95787i) q^{35} +(1.42090 - 0.818214i) q^{36} -7.99870 q^{37} +(-11.5085 - 4.18874i) q^{38} +(0.698824 + 1.50085i) q^{39} +(2.82914 - 3.37163i) q^{40} +(-3.01647 + 1.09790i) q^{41} +(1.78169 - 7.09246i) q^{42} +(0.111496 + 0.632326i) q^{43} -0.690352i q^{44} +(4.93338 - 2.84085i) q^{45} -9.13598 q^{46} +(-8.03521 - 2.92458i) q^{47} +(-5.87521 + 5.86857i) q^{48} +(-3.69512 - 5.94526i) q^{49} +(1.43506 - 1.71024i) q^{50} +(-3.98428 - 5.69699i) q^{51} +(0.335800 + 0.400191i) q^{52} +(-11.3329 - 6.54305i) q^{53} +(-7.52101 + 3.49158i) q^{54} -2.39691i q^{55} +(0.0997058 + 6.13576i) q^{56} +(12.0442 + 5.62459i) q^{57} +(0.995499 - 5.64576i) q^{58} +(-1.65418 - 1.38802i) q^{59} +(1.27095 - 1.26951i) q^{60} +(-1.05430 + 2.89668i) q^{61} +(7.10196 + 12.3010i) q^{62} +(-2.60164 + 7.49876i) q^{63} +(2.39111 - 4.14152i) q^{64} +(1.16590 + 1.38947i) q^{65} +(-0.306248 + 3.47778i) q^{66} +(0.371427 - 2.10647i) q^{67} +(-1.68047 - 1.41008i) q^{68} +(9.87786 + 0.869829i) q^{69} +(-0.130175 - 8.01082i) q^{70} +(-0.154696 - 0.0893139i) q^{71} +(5.33536 - 4.46663i) q^{72} +11.5040i q^{73} +(12.5703 - 2.21649i) q^{74} +(-1.71443 + 1.71249i) q^{75} +(4.13081 + 0.728373i) q^{76} +(2.18944 + 2.52480i) q^{77} +(-1.51413 - 2.16500i) q^{78} +(-0.211994 - 1.20228i) q^{79} +(-4.54896 + 7.87903i) q^{80} +(8.46417 - 3.05904i) q^{81} +(4.43628 - 2.56129i) q^{82} +(-5.11532 - 1.86183i) q^{83} +(-0.179134 + 2.49818i) q^{84} +(-5.83462 - 4.89582i) q^{85} +(-0.350443 - 0.962834i) q^{86} +(-1.61386 + 6.00943i) q^{87} +(-0.508733 - 2.88517i) q^{88} +(2.81958 - 4.88366i) q^{89} +(-6.96582 + 5.83160i) q^{90} +(-2.49730 - 0.398619i) q^{91} +(3.08147 - 0.543347i) q^{92} +(-6.50750 - 13.9760i) q^{93} +(13.4381 + 2.36950i) q^{94} +(14.3422 + 2.52892i) q^{95} +(2.99474 - 4.27179i) q^{96} +(5.97585 - 1.05370i) q^{97} +(7.45452 + 8.31931i) q^{98} +(0.662233 - 3.73103i) 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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