LMFDB - Embedded newform 189.2.u.a.16.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [189,2,Mod(4,189)]

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([2, 12]))

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

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

chi := DirichletCharacter("189.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 189 = 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	189.u (of order $9$, 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 $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			16.15
Character	$\chi$	$=$	189.16
Dual form			189.2.u.a.130.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.961357 - 0.349905i) q^{2} +(0.414250 - 1.68178i) q^{3} +(-0.730316 + 0.612808i) q^{4} +(1.57402 - 1.32076i) q^{5} +(-0.190223 - 1.76174i) q^{6} +(2.64575 - 0.00155053i) q^{7} +(-1.51072 + 2.61665i) q^{8} +(-2.65679 - 1.39336i) q^{9} +O(q^{10})$	\(q+(0.961357 - 0.349905i) q^{2} +(0.414250 - 1.68178i) q^{3} +(-0.730316 + 0.612808i) q^{4} +(1.57402 - 1.32076i) q^{5} +(-0.190223 - 1.76174i) q^{6} +(2.64575 - 0.00155053i) q^{7} +(-1.51072 + 2.61665i) q^{8} +(-2.65679 - 1.39336i) q^{9} +(1.05105 - 1.82048i) q^{10} +(-2.02055 - 1.69544i) q^{11} +(0.728077 + 1.48209i) q^{12} +(-0.698048 + 0.585732i) q^{13} +(2.54297 - 0.927253i) q^{14} +(-1.56919 - 3.19428i) q^{15} +(-0.205667 + 1.16639i) q^{16} +(0.580879 - 1.00611i) q^{17} +(-3.04167 - 0.409888i) q^{18} +(2.59011 + 4.48620i) q^{19} +(-0.340159 + 1.92914i) q^{20} +(1.09339 - 4.45022i) q^{21} +(-2.53571 - 0.922925i) q^{22} +(-0.912014 - 0.331946i) q^{23} +(3.77482 + 3.62466i) q^{24} +(-0.135111 + 0.766253i) q^{25} +(-0.466123 + 0.807348i) q^{26} +(-3.44390 + 3.89096i) q^{27} +(-1.93128 + 1.62247i) q^{28} +(7.72368 + 6.48094i) q^{29} +(-2.62625 - 2.52177i) q^{30} +(-7.47736 + 6.27425i) q^{31} +(-0.838930 - 4.75781i) q^{32} +(-3.68838 + 2.69579i) q^{33} +(0.206388 - 1.17048i) q^{34} +(4.16241 - 3.49683i) q^{35} +(2.79416 - 0.610513i) q^{36} -8.08953 q^{37} +(4.05977 + 3.40655i) q^{38} +(0.695908 + 1.41661i) q^{39} +(1.07805 + 6.11395i) q^{40} +(3.87706 - 3.25324i) q^{41} +(-0.506014 - 4.66084i) q^{42} +(4.96504 - 1.80713i) q^{43} +2.51462 q^{44} +(-6.02212 + 1.31581i) q^{45} -0.992920 q^{46} +(-1.84293 - 1.54640i) q^{47} +(1.87642 + 0.829066i) q^{48} +(7.00000 - 0.00820464i) q^{49} +(0.138226 + 0.783919i) q^{50} +(-1.45143 - 1.39369i) q^{51} +(0.150854 - 0.855538i) q^{52} +(-3.12093 - 5.40561i) q^{53} +(-1.94935 + 4.94564i) q^{54} -5.41965 q^{55} +(-3.99294 + 6.92535i) q^{56} +(8.61777 - 2.49760i) q^{57} +(9.69293 + 3.52794i) q^{58} +(-0.681969 - 3.86764i) q^{59} +(3.10348 + 1.37122i) q^{60} +(5.31960 + 4.46367i) q^{61} +(-4.99302 + 8.64816i) q^{62} +(-7.03138 - 3.68236i) q^{63} +(-3.65568 - 6.33182i) q^{64} +(-0.325130 + 1.84390i) q^{65} +(-2.60258 + 3.88220i) q^{66} +(-10.7266 - 3.90417i) q^{67} +(0.192328 + 1.09075i) q^{68} +(-0.936063 + 1.39630i) q^{69} +(2.77800 - 4.81815i) q^{70} +(-7.77877 - 13.4732i) q^{71} +(7.65961 - 4.84692i) q^{72} -0.0908330 q^{73} +(-7.77692 + 2.83057i) q^{74} +(1.23270 + 0.544648i) q^{75} +(-4.64078 - 1.68910i) q^{76} +(-5.34850 - 4.48259i) q^{77} +(1.16469 + 1.11836i) q^{78} +(-5.88546 + 2.14213i) q^{79} +(1.21680 + 2.10756i) q^{80} +(5.11711 + 7.40373i) q^{81} +(2.58892 - 4.48413i) q^{82} +(0.368342 + 0.309075i) q^{83} +(1.92861 + 3.92011i) q^{84} +(-0.414516 - 2.35083i) q^{85} +(4.14085 - 3.47459i) q^{86} +(14.0991 - 10.3048i) q^{87} +(7.48888 - 2.72573i) q^{88} +(0.746507 + 1.29299i) q^{89} +(-5.32900 + 3.37214i) q^{90} +(-1.84595 + 1.55078i) q^{91} +(0.869477 - 0.316464i) q^{92} +(7.45444 + 15.1744i) q^{93} +(-2.31281 - 0.841793i) q^{94} +(10.0021 + 3.64045i) q^{95} +(-8.34913 - 0.560023i) q^{96} +(14.3479 - 5.22221i) q^{97} +(6.72662 - 2.45722i) q^{98} +(3.00583 + 7.31979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) $ 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$29$	$136$
$\chi(n)$	$e\left(\frac{2}{9}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.961357	−	0.349905i	0.679782	−	0.247420i	0.0210280	−	0.999779i	$-0.493306\pi$
$2$	0.961357	−	0.349905i	0.679782	−	0.247420i	0.658754	+	0.752358i	$0.271084\pi$
$3$	0.414250	−	1.68178i	0.239167	−	0.970978i
$3$	0.414250	−	1.68178i	0.239167	−	0.970978i
$4$	−0.730316	+	0.612808i	−0.365158	+	0.306404i
$5$	1.57402	−	1.32076i	0.703922	−	0.590660i	−0.218965	−	0.975733i	$-0.570268\pi$
$5$	1.57402	−	1.32076i	0.703922	−	0.590660i	0.922886	+	0.385072i	$0.125824\pi$
$6$	−0.190223	−	1.76174i	−0.0776582	−	0.719228i
$7$	2.64575	−	0.00155053i	1.00000	−	0.000586046i
$7$	2.64575	−	0.00155053i	1.00000	−	0.000586046i
$8$	−1.51072	+	2.61665i	−0.534122	+	0.925126i
$9$	−2.65679	−	1.39336i	−0.885598	−	0.464453i
$10$	1.05105	−	1.82048i	0.332372	−	0.575685i
$11$	−2.02055	−	1.69544i	−0.609219	−	0.511195i	0.285175	−	0.958475i	$-0.407948\pi$
$11$	−2.02055	−	1.69544i	−0.609219	−	0.511195i	−0.894394	+	0.447280i	$0.852393\pi$
$12$	0.728077	+	1.48209i	0.210178	+	0.427842i
$13$	−0.698048	+	0.585732i	−0.193604	+	0.162453i	−0.734437	−	0.678677i	$-0.762554\pi$
$13$	−0.698048	+	0.585732i	−0.193604	+	0.162453i	0.540833	+	0.841130i	$0.318109\pi$
$14$	2.54297	−	0.927253i	0.679637	−	0.247819i
$15$	−1.56919	−	3.19428i	−0.405163	−	0.824759i
$16$	−0.205667	+	1.16639i	−0.0514167	+	0.291598i
$17$	0.580879	−	1.00611i	0.140884	−	0.244018i	−0.786946	−	0.617022i	$-0.788339\pi$
$17$	0.580879	−	1.00611i	0.140884	−	0.244018i	0.927830	+	0.373004i	$0.121672\pi$
$18$	−3.04167	−	0.409888i	−0.716929	−	0.0966115i
$19$	2.59011	+	4.48620i	0.594212	+	1.02921i	0.993658	+	0.112448i	$0.0358693\pi$
$19$	2.59011	+	4.48620i	0.594212	+	1.02921i	−0.399446	+	0.916757i	$0.630797\pi$
$20$	−0.340159	+	1.92914i	−0.0760619	+	0.431368i
$21$	1.09339	−	4.45022i	0.238598	−	0.971118i
$22$	−2.53571	−	0.922925i	−0.540616	−	0.196768i
$23$	−0.912014	−	0.331946i	−0.190168	−	0.0692155i	0.245181	−	0.969477i	$-0.421153\pi$
$23$	−0.912014	−	0.331946i	−0.190168	−	0.0692155i	−0.435349	+	0.900262i	$0.643375\pi$
$24$	3.77482	+	3.62466i	0.770533	+	0.739880i
$25$	−0.135111	+	0.766253i	−0.0270222	+	0.153251i
$26$	−0.466123	+	0.807348i	−0.0914141	+	0.158334i
$27$	−3.44390	+	3.89096i	−0.662779	+	0.748815i
$28$	−1.93128	+	1.62247i	−0.364978	+	0.306618i
$29$	7.72368	+	6.48094i	1.43425	+	1.20348i	0.943145	+	0.332381i	$0.107852\pi$
$29$	7.72368	+	6.48094i	1.43425	+	1.20348i	0.491107	+	0.871099i	$0.336592\pi$
$30$	−2.62625	−	2.52177i	−0.479485	−	0.460411i
$31$	−7.47736	+	6.27425i	−1.34297	+	1.12689i	−0.362122	+	0.932131i	$0.617948\pi$
$31$	−7.47736	+	6.27425i	−1.34297	+	1.12689i	−0.980851	+	0.194758i	$0.937608\pi$
$32$	−0.838930	−	4.75781i	−0.148303	−	0.841069i
$33$	−3.68838	+	2.69579i	−0.642065	+	0.469277i
$34$	0.206388	−	1.17048i	0.0353952	−	0.200736i
$35$	4.16241	−	3.49683i	0.703575	−	0.591073i
$36$	2.79416	−	0.610513i	0.465693	−	0.101752i
$37$	−8.08953			−1.32991			−0.664955	−	0.746883i	$-0.731549\pi$
$37$	−8.08953			−1.32991			−0.664955	+	0.746883i	$0.731549\pi$
$38$	4.05977	+	3.40655i	0.658581	+	0.552615i
$39$	0.695908	+	1.41661i	0.111434	+	0.226838i
$40$	1.07805	+	6.11395i	0.170455	+	0.966700i
$41$	3.87706	−	3.25324i	0.605496	−	0.508071i	−0.287711	−	0.957717i	$-0.592894\pi$
$41$	3.87706	−	3.25324i	0.605496	−	0.508071i	0.893207	+	0.449646i	$0.148450\pi$
$42$	−0.506014	−	4.66084i	−0.0780797	−	0.719183i
$43$	4.96504	−	1.80713i	0.757161	−	0.275584i	0.0655454	−	0.997850i	$-0.479121\pi$
$43$	4.96504	−	1.80713i	0.757161	−	0.275584i	0.691616	+	0.722265i	$0.256899\pi$
$44$	2.51462			0.379093
$45$	−6.02212	+	1.31581i	−0.897725	+	0.196149i
$46$	−0.992920			−0.146398
$47$	−1.84293	−	1.54640i	−0.268819	−	0.225566i	0.498406	−	0.866944i	$-0.333919\pi$
$47$	−1.84293	−	1.54640i	−0.268819	−	0.225566i	−0.767225	+	0.641378i	$0.778363\pi$
$48$	1.87642	+	0.829066i	0.270839	+	0.119665i
$49$	7.00000	−	0.00820464i	0.999999	−	0.00117209i
$50$	0.138226	+	0.783919i	0.0195481	+	0.110863i
$51$	−1.45143	−	1.39369i	−0.203241	−	0.195156i
$52$	0.150854	−	0.855538i	0.0209197	−	0.118642i
$53$	−3.12093	−	5.40561i	−0.428693	−	0.742518i	0.568064	−	0.822984i	$-0.307692\pi$
$53$	−3.12093	−	5.40561i	−0.428693	−	0.742518i	−0.996757	+	0.0804661i	$0.974359\pi$
$54$	−1.94935	+	4.94564i	−0.265274	+	0.673016i
$55$	−5.41965			−0.730785
$56$	−3.99294	+	6.92535i	−0.533579	+	0.925439i
$57$	8.61777	−	2.49760i	1.14145	−	0.330815i
$58$	9.69293	+	3.52794i	1.27274	+	0.463241i
$59$	−0.681969	−	3.86764i	−0.0887848	−	0.503524i	−0.996476	−	0.0838839i	$-0.973268\pi$
$59$	−0.681969	−	3.86764i	−0.0887848	−	0.503524i	0.907691	−	0.419640i	$-0.137844\pi$
$60$	3.10348	+	1.37122i	0.400658	+	0.177024i
$61$	5.31960	+	4.46367i	0.681104	+	0.571514i	0.916329	−	0.400427i	$-0.131138\pi$
$61$	5.31960	+	4.46367i	0.681104	+	0.571514i	−0.235224	+	0.971941i	$0.575583\pi$
$62$	−4.99302	+	8.64816i	−0.634114	+	1.09832i
$63$	−7.03138	−	3.68236i	−0.885870	−	0.463933i
$64$	−3.65568	−	6.33182i	−0.456960	−	0.791478i
$65$	−0.325130	+	1.84390i	−0.0403274	+	0.228708i
$66$	−2.60258	+	3.88220i	−0.320355	+	0.477866i
$67$	−10.7266	−	3.90417i	−1.31047	−	0.476970i	−0.410074	−	0.912052i	$-0.634497\pi$
$67$	−10.7266	−	3.90417i	−1.31047	−	0.476970i	−0.900391	+	0.435082i	$0.856720\pi$
$68$	0.192328	+	1.09075i	0.0233232	+	0.132272i
$69$	−0.936063	+	1.39630i	−0.112689	+	0.168095i
$70$	2.77800	−	4.81815i	0.332034	−	0.575879i
$71$	−7.77877	−	13.4732i	−0.923170	−	1.59898i	−0.794479	−	0.607292i	$-0.792256\pi$
$71$	−7.77877	−	13.4732i	−0.923170	−	1.59898i	−0.128691	−	0.991685i	$-0.541078\pi$
$72$	7.65961	−	4.84692i	0.902694	−	0.571215i
$73$	−0.0908330			−0.0106312			−0.00531560	−	0.999986i	$-0.501692\pi$
$73$	−0.0908330			−0.0106312			−0.00531560	+	0.999986i	$0.501692\pi$
$74$	−7.77692	+	2.83057i	−0.904049	+	0.329047i
$75$	1.23270	+	0.544648i	0.142340	+	0.0628905i
$76$	−4.64078	−	1.68910i	−0.532334	−	0.193754i
$77$	−5.34850	−	4.48259i	−0.609518	−	0.510838i
$78$	1.16469	+	1.11836i	0.131876	+	0.126629i
$79$	−5.88546	+	2.14213i	−0.662166	+	0.241009i	−0.651171	−	0.758931i	$-0.725722\pi$
$79$	−5.88546	+	2.14213i	−0.662166	+	0.241009i	−0.0109945	+	0.999940i	$0.503500\pi$
$80$	1.21680	+	2.10756i	0.136042	+	0.235632i
$81$	5.11711	+	7.40373i	0.568568	+	0.822637i
$82$	2.58892	−	4.48413i	0.285898	−	0.495190i
$83$	0.368342	+	0.309075i	0.0404307	+	0.0339254i	0.662779	−	0.748815i	$-0.269377\pi$
$83$	0.368342	+	0.309075i	0.0404307	+	0.0339254i	−0.622348	+	0.782740i	$0.713821\pi$
$84$	1.92861	+	3.92011i	0.210428	+	0.427719i
$85$	−0.414516	−	2.35083i	−0.0449605	−	0.254984i
$86$	4.14085	−	3.47459i	0.446520	−	0.374674i
$87$	14.0991	−	10.3048i	1.51158	−	1.10479i
$88$	7.48888	−	2.72573i	0.798317	−	0.290564i
$89$	0.746507	+	1.29299i	0.0791295	+	0.137056i	0.902875	−	0.429904i	$-0.141453\pi$
$89$	0.746507	+	1.29299i	0.0791295	+	0.137056i	−0.823745	+	0.566960i	$0.808119\pi$
$90$	−5.32900	+	3.37214i	−0.561726	+	0.355454i
$91$	−1.84595	+	1.55078i	−0.193508	+	0.162566i
$92$	0.869477	−	0.316464i	0.0906492	−	0.0329936i
$93$	7.45444	+	15.1744i	0.772989	+	1.57351i
$94$	−2.31281	−	0.841793i	−0.238548	−	0.0868244i
$95$	10.0021	+	3.64045i	1.02619	+	0.373502i
$96$	−8.34913	−	0.560023i	−0.852129	−	0.0571571i
$97$	14.3479	−	5.22221i	1.45681	−	0.530236i	0.512326	−	0.858791i	$-0.328784\pi$
$97$	14.3479	−	5.22221i	1.45681	−	0.530236i	0.944485	+	0.328556i	$0.106562\pi$
$98$	6.72662	−	2.45722i	0.679491	−	0.248217i
$99$	3.00583	+	7.31979i	0.302097	+	0.735667i
$100$	−0.370892	−	0.642403i	−0.0370892	−	0.0642403i
$101$	7.11265	−	2.58879i	0.707736	−	0.257595i	0.0370255	−	0.999314i	$-0.488212\pi$
$101$	7.11265	−	2.58879i	0.707736	−	0.257595i	0.670710	+	0.741720i	$0.265989\pi$
$102$	−1.88301	−	0.831973i	−0.186445	−	0.0823776i
$103$	4.37350	−	3.66981i	0.430934	−	0.361597i	−0.401370	−	0.915916i	$-0.631466\pi$
$103$	4.37350	−	3.66981i	0.430934	−	0.361597i	0.832304	+	0.554319i	$0.187021\pi$
$104$	−0.478098	−	2.71143i	−0.0468813	−	0.265877i
$105$	−4.15664	−	8.44883i	−0.405647	−	0.824522i
$106$	−4.89178	−	4.10469i	−0.475132	−	0.398683i
$107$	−2.90925	+	5.03897i	−0.281248	+	0.487135i	−0.971692	−	0.236250i	$-0.924082\pi$
$107$	−2.90925	+	5.03897i	−0.281248	+	0.487135i	0.690445	+	0.723385i	$0.257415\pi$
$108$	0.130730	−	4.95208i	0.0125795	−	0.476514i
$109$	−5.11278	−	8.85559i	−0.489715	−	0.848212i	0.510215	−	0.860047i	$-0.329566\pi$
$109$	−5.11278	−	8.85559i	−0.489715	−	0.848212i	−0.999930	+	0.0118352i	$0.996233\pi$
$110$	−5.21022	+	1.89636i	−0.496775	+	0.180811i
$111$	−3.35109	+	13.6048i	−0.318071	+	1.29131i
$112$	−0.542334	+	3.08631i	−0.0512458	+	0.291629i
$113$	−5.13595	−	1.86933i	−0.483150	−	0.175852i	0.0889502	−	0.996036i	$-0.471649\pi$
$113$	−5.13595	−	1.86933i	−0.483150	−	0.175852i	−0.572100	+	0.820184i	$0.693871\pi$
$114$	7.41083	−	5.41649i	0.694088	−	0.507300i
$115$	−1.87394	+	0.682060i	−0.174746	+	0.0636024i
$116$	−9.61230			−0.892479
$117$	2.67070	−	0.583538i	0.246907	−	0.0539481i
$118$	−2.00892	−	3.47956i	−0.184936	−	0.320319i
$119$	1.53530	−	2.66282i	0.140741	−	0.244100i
$120$	10.7289	+	0.719649i	0.979413	+	0.0656947i
$121$	−0.702033	−	3.98143i	−0.0638212	−	0.361948i
$122$	6.67589	+	2.42983i	0.604407	+	0.219986i
$123$	−3.86518	−	7.86804i	−0.348511	−	0.709437i
$124$	1.61592	−	9.16436i	0.145114	−	0.822984i
$125$	5.93620	+	10.2818i	0.530950	+	0.919632i
$126$	−8.04814	−	1.07974i	−0.716985	−	0.0961913i
$127$	1.98293	−	3.43454i	0.175957	−	0.304766i	−0.764535	−	0.644582i	$-0.777031\pi$
$127$	1.98293	−	3.43454i	0.175957	−	0.304766i	0.940492	+	0.339816i	$0.110365\pi$
$128$	1.67188	+	1.40288i	0.147775	+	0.123998i
$129$	−0.982429	−	9.09873i	−0.0864981	−	0.801098i
$130$	0.332626	+	1.88641i	0.0291732	+	0.165449i
$131$	−16.1051	−	5.86177i	−1.40711	−	0.512146i	−0.476829	−	0.878996i	$-0.658214\pi$
$131$	−16.1051	−	5.86177i	−1.40711	−	0.512146i	−0.930280	+	0.366851i	$0.880436\pi$
$132$	1.04168	−	4.22905i	0.0906667	−	0.368091i
$133$	6.85974	+	11.8654i	0.594815	+	1.02886i
$134$	−11.6782			−1.00884
$135$	−0.281756	+	10.6730i	−0.0242497	+	0.918584i
$136$	1.75509	+	3.03991i	0.150498	+	0.260670i
$137$	2.84479	−	16.1336i	0.243047	−	1.37839i	−0.581939	−	0.813233i	$-0.697706\pi$
$137$	2.84479	−	16.1336i	0.243047	−	1.37839i	0.824986	−	0.565154i	$-0.191183\pi$
$138$	−0.411317	+	1.66988i	−0.0350136	+	0.142149i
$139$	−0.00834926	−	0.0473510i	−0.000708175	−	0.00401626i	0.984452	−	0.175656i	$-0.0562046\pi$
$139$	−0.00834926	−	0.0473510i	−0.000708175	−	0.00401626i	−0.985160	+	0.171640i	$0.945094\pi$
$140$	−0.896985	+	5.10455i	−0.0758091	+	0.431413i
$141$	−3.36415	+	2.45881i	−0.283312	+	0.207069i
$142$	−12.1925	−	10.2307i	−1.02317	−	0.858545i
$143$	2.40352			0.200992
$144$	2.17162	−	2.81230i	0.180968	−	0.234358i
$145$	20.7170			1.72045
$146$	−0.0873229	+	0.0317830i	−0.00722690	+	0.00263038i
$147$	2.88595	−	11.7759i	0.238029	−	0.971258i
$148$	5.90791	−	4.95732i	0.485627	−	0.407489i
$149$	2.67479	+	15.1695i	0.219128	+	1.24273i	0.873598	+	0.486648i	$0.161780\pi$
$149$	2.67479	+	15.1695i	0.219128	+	1.24273i	−0.654471	+	0.756087i	$0.727108\pi$
$150$	1.37564	+	0.0922719i	0.112321	+	0.00753397i
$151$	3.21559	+	2.69820i	0.261681	+	0.219577i	0.764183	−	0.645000i	$-0.223142\pi$
$151$	3.21559	+	2.69820i	0.261681	+	0.219577i	−0.502502	+	0.864576i	$0.667587\pi$
$152$	−15.6518			−1.26953
$153$	−2.94515	+	1.86366i	−0.238101	+	0.150668i
$154$	−6.71030	−	2.43790i	−0.540731	−	0.196451i
$155$	−3.48273	+	19.7515i	−0.279740	+	1.58648i
$156$	−1.37634	−	0.608111i	−0.110195	−	0.0486879i
$157$	4.32926	+	24.5525i	0.345513	+	1.95950i	0.272442	+	0.962172i	$0.412169\pi$
$157$	4.32926	+	24.5525i	0.345513	+	1.95950i	0.0730704	+	0.997327i	$0.476720\pi$
$158$	−4.90848	+	4.11870i	−0.390498	+	0.327667i
$159$	−10.3839	+	3.00946i	−0.823498	+	0.238666i
$160$	−7.60439	−	6.38084i	−0.601180	−	0.504450i
$161$	−2.41348	−	0.876832i	−0.190209	−	0.0691040i
$162$	7.50997	+	5.32712i	0.590039	+	0.418538i
$163$	0.103346	−	0.179000i	0.00809466	−	0.0140204i	−0.861950	−	0.506994i	$-0.830757\pi$
$163$	0.103346	−	0.179000i	0.00809466	−	0.0140204i	0.870044	+	0.492973i	$0.164090\pi$
$164$	−0.837869	+	4.75179i	−0.0654265	+	0.371052i
$165$	−2.24509	+	9.11468i	−0.174780	+	0.709577i
$166$	0.462255	+	0.168247i	0.0358779	+	0.0130585i
$167$	−4.83612	−	1.76020i	−0.374230	−	0.136209i	0.148056	−	0.988979i	$-0.452698\pi$
$167$	−4.83612	−	1.76020i	−0.374230	−	0.136209i	−0.522286	+	0.852770i	$0.674921\pi$
$168$	9.99286	+	9.58409i	0.770966	+	0.739429i
$169$	−2.11324	+	11.9848i	−0.162557	+	0.921905i
$170$	−1.22107	−	2.11495i	−0.0936516	−	0.162209i
$171$	−0.630505	−	15.5279i	−0.0482159	−	1.18745i
$172$	−2.51863	+	4.36239i	−0.192043	+	0.332629i
$173$	1.35393	−	7.67851i	0.102937	−	0.583787i	−0.889087	−	0.457739i	$-0.848660\pi$
$173$	1.35393	−	7.67851i	0.102937	−	0.583787i	0.992024	−	0.126048i	$-0.0402293\pi$
$174$	9.94853	−	14.8400i	0.754196	−	1.12502i
$175$	−0.356282	+	2.02752i	−0.0269324	+	0.153266i
$176$	2.39311	−	2.00806i	0.180388	−	0.151363i
$177$	−6.78704	−	0.455244i	−0.510145	−	0.0342183i
$178$	1.17008	+	0.981816i	0.0877014	+	0.0735902i
$179$	−9.02234	+	15.6272i	−0.674362	+	1.16803i	0.302294	+	0.953215i	$0.402248\pi$
$179$	−9.02234	+	15.6272i	−0.674362	+	1.16803i	−0.976655	+	0.214814i	$0.931086\pi$
$180$	3.59171	−	4.65136i	0.267710	−	0.346692i
$181$	5.95289	−	10.3107i	0.442475	−	0.766389i	−0.555398	−	0.831585i	$-0.687434\pi$
$181$	5.95289	−	10.3107i	0.442475	−	0.766389i	0.997872	+	0.0651959i	$0.0207672\pi$
$182$	−1.23199	+	2.13676i	−0.0913213	+	0.158387i
$183$	9.71057	−	7.09733i	0.717826	−	0.524650i
$184$	2.24639	−	1.88494i	0.165606	−	0.138960i
$185$	−12.7331	+	10.6843i	−0.936152	+	0.785525i
$186$	12.4760	+	11.9797i	0.914783	+	0.878392i
$187$	−2.87950	+	1.04805i	−0.210570	+	0.0766411i
$188$	2.29357			0.167276
$189$	−9.10568	+	10.2998i	−0.662341	+	0.749203i
$190$	10.8894			0.789997
$191$	−1.60413	+	0.583855i	−0.116071	+	0.0422463i	−0.399403	−	0.916776i	$-0.630782\pi$
$191$	−1.60413	+	0.583855i	−0.116071	+	0.0422463i	0.283332	+	0.959022i	$0.408560\pi$
$192$	−12.1631	+	3.52511i	−0.877798	+	0.254403i
$193$	3.10853	−	2.60837i	0.223757	−	0.187754i	−0.524017	−	0.851708i	$-0.675567\pi$
$193$	3.10853	−	2.60837i	0.223757	−	0.187754i	0.747774	+	0.663953i	$0.231123\pi$
$194$	11.9662	−	10.0408i	0.859122	−	0.720889i
$195$	2.96636	+	1.31063i	0.212426	+	0.0938565i
$196$	−5.10718	+	4.29564i	−0.364798	+	0.306832i
$197$	−3.78159	+	6.54991i	−0.269427	+	0.466662i	−0.968714	−	0.248179i	$-0.920168\pi$
$197$	−3.78159	+	6.54991i	−0.269427	+	0.466662i	0.699287	+	0.714841i	$0.253501\pi$
$198$	5.45091	+	5.98518i	0.387379	+	0.425348i
$199$	9.27671	−	16.0677i	0.657609	−	1.13901i	−0.323624	−	0.946186i	$-0.604901\pi$
$199$	9.27671	−	16.0677i	0.657609	−	1.13901i	0.981233	−	0.192826i	$-0.0617652\pi$
$200$	−1.80090	−	1.51113i	−0.127343	−	0.106853i
$201$	−11.0095	+	16.4226i	−0.776548	+	1.15836i
$202$	5.93197	−	4.97751i	0.417372	−	0.350216i
$203$	20.4450	+	17.1350i	1.43496	+	1.20264i
$204$	1.91407	+	0.128387i	0.134012	+	0.00898891i
$205$	1.80582	−	10.2413i	0.126124	−	0.715285i
$206$	2.92041	−	5.05830i	0.203475	−	0.352429i
$207$	1.96051	+	2.15267i	0.136265	+	0.149621i
$208$	−0.539629	−	0.934664i	−0.0374165	−	0.0648073i
$209$	2.37265	−	13.4560i	0.164120	−	0.930770i
$210$	−6.95231	−	6.66791i	−0.479755	−	0.460130i
$211$	−7.77504	−	2.82988i	−0.535256	−	0.194817i	0.0602277	−	0.998185i	$-0.480817\pi$
$211$	−7.77504	−	2.82988i	−0.535256	−	0.194817i	−0.595484	+	0.803367i	$0.703040\pi$
$212$	5.59187	+	2.03527i	0.384051	+	0.139783i
$213$	−25.8814	+	7.50092i	−1.77336	+	0.513955i
$214$	−1.03367	+	5.86221i	−0.0706599	+	0.400732i
$215$	5.42828	−	9.40206i	0.370206	−	0.641215i
$216$	−4.97848	−	14.8896i	−0.338743	−	1.01311i
$217$	−19.7735	+	16.6117i	−1.34231	+	1.12768i
$218$	−8.01382	−	6.72440i	−0.542765	−	0.455434i
$219$	−0.0376276	+	0.152762i	−0.00254264	+	0.0103227i
$220$	3.95805	−	3.32120i	0.266852	−	0.223915i
$221$	0.183830	+	1.04255i	0.0123658	+	0.0701297i
$222$	1.53881	+	14.2517i	0.103278	+	0.956509i
$223$	−1.15146	+	6.53023i	−0.0771072	+	0.437297i	0.921675	+	0.387963i	$0.126821\pi$
$223$	−1.15146	+	6.53023i	−0.0771072	+	0.437297i	−0.998782	+	0.0493340i	$0.984290\pi$
$224$	−2.22698	−	12.5867i	−0.148796	−	0.840982i
$225$	1.42663	−	1.84752i	0.0951084	−	0.123168i
$226$	−5.59157			−0.371946
$227$	7.58196	+	6.36202i	0.503233	+	0.422262i	0.858740	−	0.512411i	$-0.171248\pi$
$227$	7.58196	+	6.36202i	0.503233	+	0.422262i	−0.355508	+	0.934673i	$0.615692\pi$
$228$	−4.76315	+	7.10507i	−0.315447	+	0.470545i
$229$	3.19233	+	18.1046i	0.210955	+	1.19639i	0.887789	+	0.460250i	$0.152240\pi$
$229$	3.19233	+	18.1046i	0.210955	+	1.19639i	−0.676834	+	0.736136i	$0.736649\pi$
$230$	−1.56287	+	1.31141i	−0.103053	+	0.0864716i
$231$	−9.75436	+	7.13811i	−0.641790	+	0.469653i
$232$	−28.6267	+	10.4193i	−1.87944	+	0.684059i
$233$	−0.135411			−0.00887105			−0.00443552	−	0.999990i	$-0.501412\pi$
$233$	−0.135411			−0.00887105			−0.00443552	+	0.999990i	$0.501412\pi$
$234$	2.36332	−	1.49548i	0.154495	−	0.0977627i
$235$	−4.94322			−0.322460
$236$	2.86817	+	2.40668i	0.186702	+	0.156662i
$237$	1.16455	+	10.7854i	0.0756457	+	0.700590i
$238$	0.544236	−	3.09713i	0.0352776	−	0.200757i
$239$	2.08152	+	11.8049i	0.134642	+	0.763594i	0.975108	+	0.221730i	$0.0711702\pi$
$239$	2.08152	+	11.8049i	0.134642	+	0.763594i	−0.840466	+	0.541864i	$0.817719\pi$
$240$	4.04852	−	1.17334i	0.261331	−	0.0757386i
$241$	−1.34492	+	7.62740i	−0.0866336	+	0.491324i	0.910358	+	0.413821i	$0.135806\pi$
$241$	−1.34492	+	7.62740i	−0.0866336	+	0.491324i	−0.996992	+	0.0775032i	$0.975305\pi$
$242$	−2.06803	−	3.58193i	−0.132938	−	0.230255i
$243$	14.5712	−	5.53888i	0.934745	−	0.355319i
$244$	−6.62035			−0.423825
$245$	11.0073	−	9.25820i	0.703229	−	0.591485i
$246$	−6.46888	−	6.21155i	−0.412441	−	0.396034i
$247$	−4.43573	−	1.61447i	−0.282239	−	0.102727i
$248$	−5.12129	−	29.0443i	−0.325202	−	1.84431i
$249$	0.672383	−	0.491437i	0.0426106	−	0.0311435i
$250$	9.30446	+	7.80737i	0.588466	+	0.493781i
$251$	10.4037	−	18.0197i	0.656674	−	1.13739i	−0.324798	−	0.945783i	$-0.605296\pi$
$251$	10.4037	−	18.0197i	0.656674	−	1.13739i	0.981471	−	0.191609i	$-0.0613704\pi$
$252$	7.39170	−	1.61960i	0.465633	−	0.102025i
$253$	1.27997	+	2.21698i	0.0804713	+	0.139380i
$254$	0.704542	−	3.99566i	0.0442069	−	0.250710i
$255$	−4.12531	−	0.276707i	−0.258337	−	0.0173281i
$256$	15.8390	+	5.76493i	0.989938	+	0.360308i
$257$	−4.35430	−	24.6945i	−0.271614	−	1.54040i	−0.749516	−	0.661987i	$-0.769714\pi$
$257$	−4.35430	−	24.6945i	−0.271614	−	1.54040i	0.477902	−	0.878413i	$-0.341398\pi$
$258$	−4.12816	−	8.40337i	−0.257008	−	0.523171i
$259$	−21.4029	+	0.0125431i	−1.32991	+	0.000779388i
$260$	−0.892510	−	1.54587i	−0.0553511	−	0.0958710i
$261$	−11.4900	−	27.9804i	−0.711211	−	1.73194i
$262$	−17.5338			−1.08324
$263$	12.2696	−	4.46575i	0.756573	−	0.275370i	0.0652043	−	0.997872i	$-0.479230\pi$
$263$	12.2696	−	4.46575i	0.756573	−	0.275370i	0.691369	+	0.722502i	$0.257008\pi$
$264$	−1.48182	−	13.7238i	−0.0911997	−	0.844642i
$265$	−12.0519	−	4.38653i	−0.740342	−	0.269463i
$266$	10.7464	+	9.00658i	0.658905	+	0.552229i
$267$	2.48377	−	0.719843i	0.152004	−	0.0440537i
$268$	10.2263	−	3.72208i	0.624672	−	0.227362i
$269$	11.0207	+	19.0884i	0.671943	+	1.16384i	0.977352	+	0.211619i	$0.0678735\pi$
$269$	11.0207	+	19.0884i	0.671943	+	1.16384i	−0.305409	+	0.952221i	$0.598793\pi$
$270$	3.46367	+	10.3591i	0.210792	+	0.630437i
$271$	10.4357	−	18.0752i	0.633924	−	1.09799i	−0.352818	−	0.935692i	$-0.614776\pi$
$271$	10.4357	−	18.0752i	0.633924	−	1.09799i	0.986742	−	0.162297i	$-0.0518902\pi$
$272$	1.05405	+	0.884457i	0.0639114	+	0.0536281i
$273$	1.84340	+	3.74691i	0.111567	+	0.226773i
$274$	−2.91037	−	16.5056i	−0.175822	−	0.997137i
$275$	1.57214	−	1.31918i	0.0948034	−	0.0795495i
$276$	−0.172043	−	1.59337i	−0.0103558	−	0.0959094i
$277$	28.1304	−	10.2386i	1.69019	−	0.615180i	0.695545	−	0.718483i	$-0.255163\pi$
$277$	28.1304	−	10.2386i	1.69019	−	0.615180i	0.994650	+	0.103303i	$0.0329410\pi$
$278$	−0.0245950	−	0.0425998i	−0.00147511	−	0.00255496i
$279$	28.6081	−	6.25075i	1.71272	−	0.374223i
$280$	2.86174	+	16.1743i	0.171022	+	0.966600i
$281$	−11.7853	+	4.28952i	−0.703055	+	0.255891i	−0.668715	−	0.743519i	$-0.733155\pi$
$281$	−11.7853	+	4.28952i	−0.703055	+	0.255891i	−0.0343403	+	0.999410i	$0.510933\pi$
$282$	−2.37380	+	3.54093i	−0.141357	+	0.210859i
$283$	−21.9474	−	7.98820i	−1.30464	−	0.474849i	−0.406133	−	0.913814i	$-0.633123\pi$
$283$	−21.9474	−	7.98820i	−1.30464	−	0.474849i	−0.898504	+	0.438965i	$0.855345\pi$
$284$	13.9374	+	5.07282i	0.827035	+	0.301016i
$285$	10.2658	−	15.3132i	0.608094	−	0.907078i
$286$	2.31064	−	0.841003i	0.136631	−	0.0497296i
$287$	10.2527	−	8.61328i	0.605198	−	0.508426i
$288$	−4.40046	+	13.8094i	−0.259300	+	0.813729i
$289$	7.82516	+	13.5536i	0.460304	+	0.797269i
$290$	19.9164	−	7.24897i	1.16953	−	0.425674i
$291$	−2.83901	−	26.2934i	−0.166426	−	1.54135i
$292$	0.0663368	−	0.0556632i	0.00388207	−	0.00325744i
$293$	2.30240	+	13.0576i	0.134508	+	0.762831i	0.975201	+	0.221320i	$0.0710366\pi$
$293$	2.30240	+	13.0576i	0.134508	+	0.762831i	−0.840693	+	0.541511i	$0.817852\pi$
$294$	−1.34601	−	12.3306i	−0.0785012	−	0.719137i
$295$	−6.18164	−	5.18701i	−0.359909	−	0.302000i
$296$	12.2210	−	21.1675i	0.710334	−	1.23033i
$297$	13.5555	−	2.02293i	0.786568	−	0.117382i
$298$	7.87932	+	13.6474i	0.456437	+	0.790572i
$299$	0.831061	−	0.302481i	0.0480615	−	0.0174929i
$300$	−1.23403	+	0.357644i	−0.0712465	+	0.0206486i
$301$	13.1335	−	4.78891i	0.757000	−	0.276028i
$302$	4.03545	+	1.46878i	0.232214	+	0.0845190i
$303$	−1.40738	−	13.0344i	−0.0808517	−	0.748804i
$304$	−5.76538	+	2.09843i	−0.330667	+	0.120353i
$305$	14.2686			0.817015
$306$	−2.17923	+	2.82216i	−0.124578	+	0.161332i
$307$	13.6884	+	23.7091i	0.781240	+	1.35315i	0.931220	+	0.364459i	$0.118746\pi$
$307$	13.6884	+	23.7091i	0.781240	+	1.35315i	−0.149979	+	0.988689i	$0.547921\pi$
$308$	6.65306	−	0.00389900i	0.379093	−	0.000222166i
$309$	−4.36010	−	8.87550i	−0.248037	−	0.504910i
$310$	3.56302	+	20.2069i	0.202366	+	1.14768i
$311$	−14.0693	−	5.12079i	−0.797795	−	0.290373i	−0.0892223	−	0.996012i	$-0.528438\pi$
$311$	−14.0693	−	5.12079i	−0.797795	−	0.290373i	−0.708572	+	0.705638i	$0.750660\pi$
$312$	−4.75809	−	0.319151i	−0.269374	−	0.0180684i
$313$	−2.88450	+	16.3588i	−0.163042	+	0.924656i	0.788019	+	0.615651i	$0.211107\pi$
$313$	−2.88450	+	16.3588i	−0.163042	+	0.924656i	−0.951060	+	0.309005i	$0.900004\pi$
$314$	12.7530	+	22.0888i	0.719693	+	1.24655i
$315$	−15.9310	+	3.49064i	−0.897610	+	0.196676i
$316$	2.98553	−	5.17108i	0.167949	−	0.290896i
$317$	−22.6537	−	19.0087i	−1.27236	−	1.06764i	−0.994250	−	0.107086i	$-0.965848\pi$
$317$	−22.6537	−	19.0087i	−1.27236	−	1.06764i	−0.278109	−	0.960550i	$-0.589708\pi$
$318$	−8.92963	+	6.52655i	−0.500749	+	0.365991i
$319$	−4.61803	−	26.1901i	−0.258560	−	1.46637i
$320$	−14.1169	−	5.13813i	−0.789159	−	0.287230i
$321$	7.26930	+	6.98012i	0.405733	+	0.389592i
$322$	−2.62702	+	0.00153955i	−0.146398	+	8.57960e-5i
$323$	6.01816			0.334859
$324$	−8.27417	−	2.27126i	−0.459676	−	0.126181i
$325$	−0.354505	−	0.614020i	−0.0196644	−	0.0340597i
$326$	0.0367191	−	0.208244i	0.00203368	−	0.0115336i
$327$	−17.0112	+	4.93016i	−0.940719	+	0.272638i
$328$	2.65543	+	15.0597i	0.146621	+	0.831531i
$329$	−4.87833	−	4.08854i	−0.268951	−	0.225408i
$330$	1.03094	+	9.54803i	0.0567515	+	0.525602i
$331$	−15.3697	−	12.8967i	−0.844797	−	0.708869i	0.113841	−	0.993499i	$-0.463685\pi$
$331$	−15.3697	−	12.8967i	−0.844797	−	0.708869i	−0.958637	+	0.284630i	$0.908129\pi$
$332$	−0.458409			−0.0251585
$333$	21.4922	+	11.2716i	1.17777	+	0.617680i
$334$	−5.26514			−0.288096
$335$	−22.0403	+	8.02203i	−1.20419	+	0.438290i
$336$	4.96584	+	2.19059i	0.270909	+	0.119507i
$337$	19.5952	−	16.4423i	1.06742	−	0.895671i	0.0726025	−	0.997361i	$-0.476870\pi$
$337$	19.5952	−	16.4423i	1.06742	−	0.895671i	0.994816	+	0.101690i	$0.0324251\pi$
$338$	2.16196	+	12.2611i	0.117595	+	0.666914i
$339$	−5.27138	+	7.86319i	−0.286302	+	0.427070i
$340$	1.74334	+	1.46283i	0.0945457	+	0.0793333i
$341$	25.7460			1.39423
$342$	−6.03942	−	14.7072i	−0.326575	−	0.795274i
$343$	18.5202	−	0.0325612i	0.999998	−	0.00175814i
$344$	−2.77219	+	15.7218i	−0.149466	+	0.847665i
$345$	0.370796	+	3.43411i	0.0199630	+	0.184886i
$346$	−1.38514	−	7.85554i	−0.0744658	−	0.422316i
$347$	−23.9467	+	20.0937i	−1.28553	+	1.07868i	−0.293068	+	0.956092i	$0.594676\pi$
$347$	−23.9467	+	20.0937i	−1.28553	+	1.07868i	−0.992457	+	0.122592i	$0.960879\pi$
$348$	−3.98189	+	16.1658i	−0.213452	+	0.866578i
$349$	−11.4708	−	9.62515i	−0.614018	−	0.515222i	0.281899	−	0.959444i	$-0.409036\pi$
$349$	−11.4708	−	9.62515i	−0.614018	−	0.515222i	−0.895917	+	0.444222i	$0.853480\pi$
$350$	0.366927	+	2.07384i	0.0196131	+	0.110851i
$351$	0.124954	−	4.73328i	0.00666953	−	0.252644i
$352$	−6.37149	+	11.0357i	−0.339602	+	0.588207i
$353$	2.67289	−	15.1587i	0.142264	−	0.806817i	−0.827260	−	0.561819i	$-0.810102\pi$
$353$	2.67289	−	15.1587i	0.142264	−	0.806817i	0.969524	−	0.244998i	$-0.0787872\pi$
$354$	−6.68406	+	1.93717i	−0.355254	+	0.102959i
$355$	−30.0388	−	10.9332i	−1.59429	−	0.580275i
$356$	−1.33754	−	0.486824i	−0.0708894	−	0.0258016i
$357$	−3.84229	−	3.68512i	−0.203356	−	0.195037i
$358$	−3.20567	+	18.1802i	−0.169425	+	0.960855i
$359$	12.7014	+	21.9995i	0.670356	+	1.16109i	0.977803	+	0.209526i	$0.0671920\pi$
$359$	12.7014	+	21.9995i	0.670356	+	1.16109i	−0.307447	+	0.951565i	$0.599475\pi$
$360$	5.65475	−	17.7456i	0.298032	−	0.935276i
$361$	−3.91734	+	6.78503i	−0.206176	+	0.357107i
$362$	2.11508	−	11.9952i	0.111166	−	0.630455i
$363$	−6.98672	−	0.468638i	−0.366707	−	0.0245971i
$364$	0.397797	−	2.26377i	0.0208502	−	0.118654i
$365$	−0.142973	+	0.119968i	−0.00748353	+	0.00627943i
$366$	6.85193	−	10.2209i	0.358156	−	0.534252i
$367$	21.6959	+	18.2050i	1.13252	+	0.950293i	0.999168	−	0.0407761i	$-0.0129830\pi$
$367$	21.6959	+	18.2050i	1.13252	+	0.950293i	0.133347	+	0.991069i	$0.457427\pi$
$368$	0.574750	−	0.995497i	0.0299609	−	0.0518939i
$369$	−14.8335	+	3.24106i	−0.772201	+	0.168723i
$370$	−8.50251	+	14.7268i	−0.442025	+	0.765609i
$371$	−8.26559	−	14.2971i	−0.429128	−	0.742267i
$372$	−14.7431	−	6.51397i	−0.764393	−	0.337734i
$373$	−2.38585	+	2.00197i	−0.123535	+	0.103658i	−0.702462	−	0.711721i	$-0.747916\pi$
$373$	−2.38585	+	2.00197i	−0.123535	+	0.103658i	0.578927	+	0.815379i	$0.303472\pi$
$374$	−2.40151	+	2.01510i	−0.124179	+	0.104199i
$375$	19.7508	−	5.72417i	1.01993	−	0.295595i
$376$	6.83055	−	2.48612i	0.352259	−	0.128212i
$377$	−9.18759			−0.473185
$378$	−5.14984	+	13.0879i	−0.264879	+	0.673171i
$379$	1.21116			0.0622130			0.0311065	−	0.999516i	$-0.490097\pi$
$379$	1.21116			0.0622130			0.0311065	+	0.999516i	$0.490097\pi$
$380$	−9.53555	+	3.47066i	−0.489164	+	0.178041i
$381$	−4.95472	−	4.75762i	−0.253838	−	0.243740i
$382$	−1.33785	+	1.12259i	−0.0684502	+	0.0574365i
$383$	15.9872	−	13.4149i	0.816909	−	0.685468i	−0.135337	−	0.990800i	$-0.543212\pi$
$383$	15.9872	−	13.4149i	0.816909	−	0.685468i	0.952246	+	0.305332i	$0.0987674\pi$
$384$	3.05191	−	2.23060i	0.155742	−	0.113830i
$385$	−14.3390	+	0.00840334i	−0.730785	+	0.000428274i
$386$	2.07573	−	3.59526i	0.105652	−	0.182994i
$387$	−15.7091	−	2.11691i	−0.798537	−	0.107609i
$388$	−7.27829	+	12.6064i	−0.369499	+	0.639992i
$389$	3.32274	+	2.78811i	0.168470	+	0.141363i	0.723125	−	0.690718i	$-0.242705\pi$
$389$	3.32274	+	2.78811i	0.168470	+	0.141363i	−0.554655	+	0.832081i	$0.687150\pi$
$390$	3.31033	+	0.222042i	0.167625	+	0.0112435i
$391$	−0.863744	+	0.724767i	−0.0436814	+	0.0366530i
$392$	−10.5536	+	18.3289i	−0.533037	+	0.925751i
$393$	−16.5298	+	24.6570i	−0.833817	+	1.24378i
$394$	−1.34361	+	7.62000i	−0.0676902	+	0.383890i
$395$	−6.43457	+	11.1450i	−0.323758	+	0.560766i
$396$	−6.68083	−	3.50377i	−0.335724	−	0.176071i
$397$	−3.74668	−	6.48945i	−0.188041	−	0.325696i	0.756556	−	0.653929i	$-0.226880\pi$
$397$	−3.74668	−	6.48945i	−0.188041	−	0.325696i	−0.944597	+	0.328233i	$0.893547\pi$
$398$	3.29604	−	18.6928i	0.165216	−	0.936985i
$399$	22.7966	−	6.62138i	1.14126	−	0.331484i
$400$	−0.865965	−	0.315185i	−0.0432982	−	0.0157593i
$401$	−16.2891	−	5.92877i	−0.813441	−	0.296068i	−0.0983967	−	0.995147i	$-0.531371\pi$
$401$	−16.2891	−	5.92877i	−0.813441	−	0.296068i	−0.715045	+	0.699079i	$0.753594\pi$
$402$	−4.83769	+	19.6402i	−0.241282	+	0.979565i
$403$	1.54453	−	8.75945i	0.0769384	−	0.436339i
$404$	−3.60805	+	6.24933i	−0.179507	+	0.310916i
$405$	17.8329	+	4.89514i	0.886126	+	0.243241i
$406$	25.6506	+	9.31902i	1.27302	+	0.462495i
$407$	16.3453	+	13.7153i	0.810207	+	0.679844i
$408$	5.83952	−	1.69241i	0.289099	−	0.0837866i
$409$	−0.425683	+	0.357191i	−0.0210487	+	0.0176619i	−0.653251	−	0.757141i	$-0.726595\pi$
$409$	−0.425683	+	0.357191i	−0.0210487	+	0.0176619i	0.632203	+	0.774803i	$0.282151\pi$
$410$	−1.84745	−	10.4774i	−0.0912392	−	0.517443i
$411$	−25.9548	−	11.4677i	−1.28025	−	0.565658i
$412$	−0.945154	+	5.36023i	−0.0465644	+	0.264080i
$413$	−1.81032	−	10.2318i	−0.0890799	−	0.503472i
$414$	2.63798	+	1.38349i	0.129650	+	0.0679950i
$415$	0.987989			0.0484985
$416$	3.37241	+	2.82979i	0.165346	+	0.138742i
$417$	−0.0830928	−	0.00557350i	−0.00406907	−	0.000272935i
$418$	−2.42735	−	13.7662i	−0.118726	−	0.673327i
$419$	−21.4377	+	17.9883i	−1.04730	+	0.878788i	−0.992807	−	0.119727i	$-0.961798\pi$
$419$	−21.4377	+	17.9883i	−1.04730	+	0.878788i	−0.0544914	+	0.998514i	$0.517354\pi$
$420$	8.21317	+	3.62309i	0.400762	+	0.176789i
$421$	−18.5174	+	6.73977i	−0.902481	+	0.328476i	−0.751247	−	0.660022i	$-0.770547\pi$
$421$	−18.5174	+	6.73977i	−0.902481	+	0.328476i	−0.151235	+	0.988498i	$0.548325\pi$
$422$	−8.46478			−0.412059
$423$	2.74160	+	6.67633i	0.133301	+	0.324614i
$424$	18.8595			0.915897
$425$	0.692452	+	0.581037i	0.0335889	+	0.0281844i
$426$	−22.2566	+	16.2671i	−1.07834	+	0.788144i
$427$	14.0812	+	11.8015i	0.681439	+	0.571115i
$428$	−0.963247	−	5.46285i	−0.0465603	−	0.264057i
$429$	0.995656	−	4.04220i	0.0480707	−	0.195159i
$430$	1.92868	−	10.9381i	0.0930094	−	0.527483i
$431$	16.2489	+	28.1440i	0.782683	+	1.35565i	0.930373	+	0.366613i	$0.119483\pi$
$431$	16.2489	+	28.1440i	0.782683	+	1.35565i	−0.147690	+	0.989034i	$0.547184\pi$
$432$	−3.83009	−	4.81719i	−0.184275	−	0.231767i
$433$	18.7301			0.900110			0.450055	−	0.893001i	$-0.351404\pi$
$433$	18.7301			0.900110			0.450055	+	0.893001i	$0.351404\pi$
$434$	−13.1969	+	22.8886i	−0.633470	+	1.09869i
$435$	8.58200	−	34.8414i	0.411475	−	1.67052i
$436$	9.16072	+	3.33423i	0.438719	+	0.159681i
$437$	−0.873040	−	4.95125i	−0.0417631	−	0.236851i
$438$	0.0172785	+	0.160024i	0.000825600	+	0.00764626i
$439$	−8.48328	−	7.11831i	−0.404885	−	0.339739i	0.417493	−	0.908680i	$-0.362909\pi$
$439$	−8.48328	−	7.11831i	−0.404885	−	0.339739i	−0.822378	+	0.568941i	$0.807353\pi$
$440$	8.18759	−	14.1813i	0.390328	−	0.676068i
$441$	−18.6090	−	9.73170i	−0.886142	−	0.463414i
$442$	0.541521	+	0.937942i	0.0257575	+	0.0446134i
$443$	−2.85884	+	16.2133i	−0.135828	+	0.770318i	0.838452	+	0.544976i	$0.183461\pi$
$443$	−2.85884	+	16.2133i	−0.135828	+	0.770318i	−0.974280	+	0.225342i	$0.927650\pi$
$444$	−5.88980	−	11.9894i	−0.279517	−	0.568992i
$445$	2.88274	+	1.04923i	0.136655	+	0.0497383i
$446$	1.17800	+	6.68078i	0.0557800	+	0.316344i
$447$	26.6199	+	1.78554i	1.25908	+	0.0844533i
$448$	−9.68183	−	16.7468i	−0.457424	−	0.791210i
$449$	−6.38906	−	11.0662i	−0.301519	−	0.522245i	0.674962	−	0.737853i	$-0.264160\pi$
$449$	−6.38906	−	11.0662i	−0.301519	−	0.522245i	−0.976480	+	0.215607i	$0.930827\pi$
$450$	0.725041	−	2.27531i	0.0341788	−	0.107259i
$451$	−13.3495			−0.628603
$452$	4.89641	−	1.78215i	0.230308	−	0.0838251i
$453$	5.86986	−	4.29020i	0.275790	−	0.201571i
$454$	9.51508	+	3.46321i	0.446565	+	0.162536i
$455$	−0.857354	+	4.87901i	−0.0401934	+	0.228732i
$456$	−6.48374	+	26.3229i	−0.303629	+	1.23268i
$457$	28.4864	−	10.3682i	1.33254	−	0.485004i	0.425082	−	0.905155i	$-0.360245\pi$
$457$	28.4864	−	10.3682i	1.33254	−	0.485004i	0.907454	+	0.420151i	$0.138023\pi$
$458$	9.40386	+	16.2880i	0.439414	+	0.761087i
$459$	1.91424	+	5.72512i	0.0893492	+	0.267226i
$460$	0.950599	−	1.64649i	0.0443219	−	0.0767678i
$461$	−11.3291	−	9.50624i	−0.527649	−	0.442750i	0.339640	−	0.940556i	$-0.389695\pi$
$461$	−11.3291	−	9.50624i	−0.527649	−	0.442750i	−0.867289	+	0.497806i	$0.834139\pi$
$462$	−6.87976	+	10.2754i	−0.320075	+	0.478054i
$463$	−2.92297	−	16.5770i	−0.135842	−	0.770398i	−0.974270	−	0.225385i	$-0.927636\pi$
$463$	−2.92297	−	16.5770i	−0.135842	−	0.770398i	0.838428	−	0.545013i	$-0.183475\pi$
$464$	−9.14783	+	7.67594i	−0.424678	+	0.356347i
$465$	31.7751	+	14.0393i	1.47354	+	0.651056i
$466$	−0.130178	+	0.0473809i	−0.00603038	+	0.00219488i
$467$	1.13339	+	1.96309i	0.0524470	+	0.0908409i	0.891057	−	0.453891i	$-0.149965\pi$
$467$	1.13339	+	1.96309i	0.0524470	+	0.0908409i	−0.838610	+	0.544732i	$0.816631\pi$
$468$	−1.59286	+	2.06279i	−0.0736300	+	0.0953527i
$469$	−28.3860	−	10.3128i	−1.31074	−	0.476202i
$470$	−4.75220	+	1.72966i	−0.219203	+	0.0797833i
$471$	43.0853	+	2.88997i	1.98527	+	0.133163i
$472$	11.1505	+	4.05846i	0.513245	+	0.186806i
$473$	−13.0960	−	4.76655i	−0.602155	−	0.219166i
$474$	4.89343	+	9.96118i	0.224763	+	0.457532i
$475$	−3.78752	+	1.37854i	−0.173783	+	0.0632519i
$476$	0.510543	+	2.88554i	0.0234007	+	0.132259i
$477$	0.759721	+	18.7102i	0.0347853	+	0.856680i
$478$	6.13167	+	10.6204i	0.280456	+	0.485764i
$479$	−16.9737	+	6.17792i	−0.775547	+	0.282276i	−0.699315	−	0.714814i	$-0.746511\pi$
$479$	−16.9737	+	6.17792i	−0.775547	+	0.282276i	−0.0762327	+	0.997090i	$0.524289\pi$
$480$	−13.8813	+	10.1457i	−0.633593	+	0.463085i
$481$	5.64688	−	4.73829i	0.257475	−	0.216048i
$482$	1.37592	+	7.80324i	0.0626715	+	0.355428i
$483$	−2.47442	+	3.69572i	−0.112590	+	0.168161i
$484$	2.95255	+	2.47749i	0.134207	+	0.112613i
$485$	15.6866	−	27.1700i	0.712291	−	1.23372i
$486$	12.0701	−	10.4234i	0.547510	−	0.472815i
$487$	2.74412	+	4.75296i	0.124348	+	0.215377i	0.921478	−	0.388431i	$-0.126983\pi$
$487$	2.74412	+	4.75296i	0.124348	+	0.215377i	−0.797130	+	0.603808i	$0.793649\pi$
$488$	−19.7163	+	7.17615i	−0.892515	+	0.324849i
$489$	−0.258228	−	0.247956i	−0.0116775	−	0.0112130i
$490$	7.34242	−	12.7519i	0.331697	−	0.576074i
$491$	22.2795	+	8.10907i	1.00546	+	0.365957i	0.791688	−	0.610926i	$-0.209203\pi$
$491$	22.2795	+	8.10907i	1.00546	+	0.365957i	0.213772	+	0.976884i	$0.431425\pi$
$492$	7.64439	+	3.37754i	0.344636	+	0.152271i
$493$	11.0071	−	4.00624i	0.495733	−	0.180432i
$494$	−4.82923			−0.217278
$495$	14.3989	+	7.55151i	0.647182	+	0.339415i
$496$	−5.78040	−	10.0120i	−0.259548	−	0.449550i
$497$	−20.6016	−	35.6347i	−0.924107	−	1.59844i
$498$	0.474444	−	0.707716i	0.0212603	−	0.0317135i
$499$	−5.72498	−	32.4680i	−0.256285	−	1.45347i	−0.792752	−	0.609545i	$-0.791352\pi$
$499$	−5.72498	−	32.4680i	−0.256285	−	1.45347i	0.536466	−	0.843922i	$-0.319759\pi$
$500$	−10.6361	−	3.87121i	−0.475659	−	0.173126i
$501$	−4.96364	+	7.40414i	−0.221759	+	0.330793i
$502$	3.69646	−	20.9636i	0.164981	−	0.935653i
$503$	−10.6738	−	18.4875i	−0.475919	−	0.824316i	0.523700	−	0.851903i	$-0.324551\pi$
$503$	−10.6738	−	18.4875i	−0.475919	−	0.824316i	−0.999619	+	0.0275864i	$0.991218\pi$
$504$	20.2579	−	12.8356i	0.902359	−	0.571744i
$505$	7.77627	−	13.4689i	0.346039	−	0.599358i
$506$	2.00625	+	1.68344i	0.0891885	+	0.0748380i
$507$	19.2804	+	8.51870i	0.856271	+	0.378329i
$508$	0.656545	+	3.72345i	0.0291295	+	0.165202i
$509$	30.6799	+	11.1666i	1.35986	+	0.494950i	0.916012	−	0.401151i	$-0.131390\pi$
$509$	30.6799	+	11.1666i	1.35986	+	0.494950i	0.443851	+	0.896100i	$0.353612\pi$
$510$	−4.06272	+	1.17745i	−0.179900	+	0.0521385i
$511$	−0.240322		0.000140839i	−0.0106312		6.23037e-6i
$512$	12.8791			0.569183
$513$	−26.3757	−	5.37204i	−1.16452	−	0.237182i
$514$	−12.8268	−	22.2166i	−0.565765	−	0.979933i
$515$	2.03705	−	11.5527i	0.0897630	−	0.509071i
$516$	6.29325	+	6.04290i	0.277045	+	0.266024i
$517$	1.10190	+	6.24917i	0.0484614	+	0.274838i
$518$	−20.5714	+	7.50104i	−0.903856	+	0.329577i
$519$	−12.3527	−	5.45784i	−0.542225	−	0.239573i
$520$	−4.33367	−	3.63638i	−0.190044	−	0.159466i
$521$	−14.0635			−0.616132			−0.308066	−	0.951365i	$-0.599682\pi$
$521$	−14.0635			−0.616132			−0.308066	+	0.951365i	$0.599682\pi$
$522$	−20.8364	−	22.8787i	−0.911986	−	1.00137i
$523$	5.35127			0.233995			0.116997	−	0.993132i	$-0.462673\pi$
$523$	5.35127			0.233995			0.116997	+	0.993132i	$0.462673\pi$
$524$	15.3539	−	5.58838i	0.670740	−	0.244129i
$525$	3.26227	+	1.43909i	0.142377	+	0.0628071i
$526$	10.2328	−	8.58637i	0.446173	−	0.374383i
$527$	1.96915	+	11.1676i	0.0857777	+	0.486470i
$528$	−2.38578	−	4.85654i	−0.103828	−	0.211354i
$529$	−16.8974	−	14.1786i	−0.734671	−	0.616462i
$530$	−13.1210			−0.569942
$531$	−3.57715	+	11.2257i	−0.155235	+	0.487156i
$532$	−12.2810	−	4.46175i	−0.532447	−	0.193442i
$533$	−0.800849	+	4.54184i	−0.0346886	+	0.196729i
$534$	2.13591	−	1.56111i	0.0924298	−	0.0675558i
$535$	2.07604	+	11.7738i	0.0897552	+	0.509027i
$536$	26.4208	−	22.1697i	1.14121	−	0.957585i
$537$	22.5440	+	21.6472i	0.972845	+	0.934145i
$538$	17.2739	+	14.4946i	0.744733	+	0.624905i
$539$	−14.1578	−	11.8515i	−0.609818	−	0.510481i
$540$	−6.33472	−	7.96731i	−0.272603	−	0.342858i
$541$	0.312793	−	0.541773i	0.0134480	−	0.0232926i	−0.859223	−	0.511601i	$-0.829053\pi$
$541$	0.312793	−	0.541773i	0.0134480	−	0.0232926i	0.872671	+	0.488308i	$0.162386\pi$
$542$	3.70784	−	21.0282i	0.159265	−	0.903239i
$543$	−14.8744	−	14.2827i	−0.638322	−	0.612929i
$544$	−5.27420	−	1.91965i	−0.226129	−	0.0823044i
$545$	−19.7437	−	7.18611i	−0.845726	−	0.307819i
$546$	3.08322	+	2.95710i	0.131950	+	0.126552i
$547$	−1.59634	+	9.05332i	−0.0682548	+	0.387092i	0.931474	+	0.363808i	$0.118523\pi$
$547$	−1.59634	+	9.05332i	−0.0682548	+	0.387092i	−0.999729	+	0.0232844i	$0.992588\pi$
$548$	7.80920	+	13.5259i	0.333592	+	0.577799i
$549$	−7.91358	−	19.2712i	−0.337743	−	0.822473i
$550$	1.04980	−	1.81830i	0.0447635	−	0.0775326i
$551$	−9.06962	+	51.4364i	−0.386379	+	2.19126i
$552$	−2.23950	−	4.55877i	−0.0953195	−	0.194034i
$553$	−15.5681	+	5.67667i	−0.662024	+	0.241397i
$554$	23.4608	−	19.6860i	0.996755	−	0.836377i
$555$	12.6940	+	25.8402i	0.538831	+	1.09686i
$556$	0.0351146	+	0.0294647i	0.00148919	+	0.00124958i
$557$	−5.78921	+	10.0272i	−0.245297	+	0.424867i	−0.962215	−	0.272291i	$-0.912219\pi$
$557$	−5.78921	+	10.0272i	−0.245297	+	0.424867i	0.716918	+	0.697157i	$0.245552\pi$
$558$	25.3154	−	16.0193i	1.07169	−	0.678152i
$559$	−2.40734	+	4.16964i	−0.101820	+	0.176357i
$560$	3.22262	+	5.57419i	0.136180	+	0.235552i
$561$	0.569765	+	5.27685i	0.0240555	+	0.222789i
$562$	−9.82900	+	8.24751i	−0.414611	+	0.347900i
$563$	−6.57406	+	5.51629i	−0.277063	+	0.232484i	−0.770721	−	0.637172i	$-0.780104\pi$
$563$	−6.57406	+	5.51629i	−0.277063	+	0.232484i	0.493658	+	0.869656i	$0.335659\pi$
$564$	0.950110	−	3.85729i	0.0400069	−	0.162421i
$565$	−10.5530	+	3.84098i	−0.443968	+	0.161591i
$566$	−23.8944			−1.00436
$567$	13.5501	+	19.5805i	0.569050	+	0.822303i
$568$	47.0063			1.97234
$569$	−12.5378	+	4.56338i	−0.525611	+	0.191307i	−0.591178	−	0.806541i	$-0.701337\pi$
$569$	−12.5378	+	4.56338i	−0.525611	+	0.191307i	0.0655665	+	0.997848i	$0.479115\pi$
$570$	4.51092	−	18.3135i	0.188941	−	0.767070i
$571$	−14.3197	+	12.0157i	−0.599262	+	0.502841i	−0.891208	−	0.453594i	$-0.850142\pi$
$571$	−14.3197	+	12.0157i	−0.599262	+	0.502841i	0.291946	+	0.956435i	$0.405697\pi$
$572$	−1.75533	+	1.47289i	−0.0733938	+	0.0615848i
$573$	0.317408	+	2.93966i	0.0132599	+	0.122806i
$574$	6.84267	−	11.8679i	0.285608	−	0.495357i
$575$	0.377578	−	0.653984i	0.0157461	−	0.0272730i
$576$	0.889894	+	21.9160i	0.0370789	+	0.913167i
$577$	9.25451	−	16.0293i	0.385270	−	0.667307i	−0.606537	−	0.795056i	$-0.707442\pi$
$577$	9.25451	−	16.0293i	0.385270	−	0.667307i	0.991807	+	0.127748i	$0.0407749\pi$
$578$	12.2652	+	10.2918i	0.510167	+	0.428081i
$579$	−3.09900	−	6.30840i	−0.128790	−	0.262168i
$580$	−15.1299	+	12.6955i	−0.628235	+	0.527152i
$581$	0.975019	+	0.817165i	0.0404506	+	0.0339017i
$582$	−11.9295	−	24.2839i	−0.494494	−	1.00660i
$583$	−2.85891	+	16.2137i	−0.118404	+	0.671502i
$584$	0.137224	−	0.237678i	0.00567835	−	0.00983520i
$585$	3.43302	−	4.44585i	0.141938	−	0.183813i
$586$	6.78234	+	11.7474i	0.280176	+	0.485279i
$587$	3.25536	−	18.4621i	0.134363	−	0.762011i	−0.840938	−	0.541131i	$-0.817996\pi$
$587$	3.25536	−	18.4621i	0.134363	−	0.762011i	0.975301	−	0.220879i	$-0.0708927\pi$
$588$	5.10869	+	10.3686i	0.210679	+	0.427595i
$589$	−47.5147	−	17.2939i	−1.95781	−	0.712585i
$590$	−7.75772	−	2.82358i	−0.319380	−	0.116245i
$591$	9.44901	+	9.07312i	0.388680	+	0.373218i
$592$	1.66375	−	9.43558i	0.0683796	−	0.387800i
$593$	−10.0735	+	17.4478i	−0.413670	+	0.716497i	−0.995288	−	0.0969652i	$-0.969086\pi$
$593$	−10.0735	+	17.4478i	−0.413670	+	0.716497i	0.581618	+	0.813462i	$0.302420\pi$
$594$	12.3238	−	6.68789i	0.505652	−	0.274407i
$595$	−1.10035	−	6.21908i	−0.0451100	−	0.254957i
$596$	−11.2494	−	9.43940i	−0.460795	−	0.386653i
$597$	−23.1796	−	22.2575i	−0.948677	−	0.910938i
$598$	0.693106	−	0.581585i	0.0283432	−	0.0237828i
$599$	1.14692	+	6.50449i	0.0468618	+	0.265766i	0.999232	−	0.0391769i	$-0.0124736\pi$
$599$	1.14692	+	6.50449i	0.0468618	+	0.265766i	−0.952371	+	0.304943i	$0.901362\pi$
$600$	−3.28743	+	2.40274i	−0.134209	+	0.0980914i
$601$	5.95018	−	33.7452i	0.242713	−	1.37649i	−0.583031	−	0.812450i	$-0.698133\pi$
$601$	5.95018	−	33.7452i	0.242713	−	1.37649i	0.825744	−	0.564045i	$-0.190755\pi$
$602$	10.9503	−	9.19931i	0.446300	−	0.374936i
$603$	23.0585	+	25.3186i	0.939015	+	1.03105i
$604$	−4.00188			−0.162834
$605$	−6.36351	−	5.33962i	−0.258713	−	0.217086i
$606$	−5.91378	−	12.0382i	−0.240231	−	0.489019i
$607$	0.876039	+	4.96827i	0.0355573	+	0.201656i	0.997411	−	0.0719078i	$-0.0229087\pi$
$607$	0.876039	+	4.96827i	0.0355573	+	0.201656i	−0.961854	+	0.273564i	$0.911798\pi$
$608$	19.1716	−	16.0868i	0.777509	−	0.652408i
$609$	37.2867	−	27.2859i	1.51093	−	1.10568i
$610$	13.7172	−	4.99264i	0.555392	−	0.202146i
$611$	2.19223			0.0886882
$612$	1.00882	−	3.16587i	0.0407793	−	0.127973i
$613$	−6.58525			−0.265976			−0.132988	−	0.991118i	$-0.542457\pi$
$613$	−6.58525			−0.265976			−0.132988	+	0.991118i	$0.542457\pi$
$614$	21.4554	+	18.0032i	0.865869	+	0.726551i
$615$	−16.4756	−	7.27946i	−0.664361	−	0.293536i
$616$	19.8095	−	7.22321i	0.798147	−	0.291031i
$617$	−3.97440	−	22.5400i	−0.160003	−	0.907425i	−0.954068	−	0.299591i	$-0.903150\pi$
$617$	−3.97440	−	22.5400i	−0.160003	−	0.907425i	0.794064	−	0.607834i	$-0.207961\pi$
$618$	−7.29719	−	7.00691i	−0.293536	−	0.281859i
$619$	1.91959	−	10.8865i	0.0771547	−	0.437566i	−0.921621	−	0.388092i	$-0.873134\pi$
$619$	1.91959	−	10.8865i	0.0771547	−	0.437566i	0.998775	−	0.0494742i	$-0.0157546\pi$
$620$	−9.56040	−	16.5591i	−0.383955	−	0.665030i
$621$	4.43247	−	2.40541i	0.177869	−	0.0965260i
$622$	−15.3174			−0.614171
$623$	1.97708	+	3.41976i	0.0792098	+	0.137010i
$624$	−1.79544	+	0.520354i	−0.0718753	+	0.0208308i
$625$	19.2677	+	7.01286i	0.770707	+	0.280514i
$626$	2.95101	+	16.7360i	0.117946	+	0.668904i
$627$	−21.6472	−	9.56443i	−0.864505	−	0.381967i
$628$	−18.2077	−	15.2780i	−0.726564	−	0.609660i
$629$	−4.69903	+	8.13896i	−0.187363	+	0.324522i
$630$	−14.0940	+	8.93010i	−0.561518	+	0.355784i
$631$	20.4895	+	35.4889i	0.815676	+	1.41279i	0.908842	+	0.417142i	$0.136968\pi$
$631$	20.4895	+	35.4889i	0.815676	+	1.41279i	−0.0931656	+	0.995651i	$0.529699\pi$
$632$	3.28609	−	18.6364i	0.130714	−	0.741314i
$633$	−7.98006	+	11.9037i	−0.317179	+	0.473128i
$634$	−28.4295	−	10.3475i	−1.12908	−	0.410952i
$635$	−1.41502	−	8.02499i	−0.0561535	−	0.318462i
$636$	5.73932	−	8.56120i	0.227579	−	0.339474i
$637$	−4.88153	+	4.10585i	−0.193413	+	0.162680i
$638$	−13.6036	−	23.5622i	−0.538573	−	0.932836i
$639$	1.89357	+	46.6342i	0.0749084	+	1.84482i
$640$	4.48443			0.177262
$641$	−14.1612	+	5.15426i	−0.559335	+	0.203581i	−0.606189	−	0.795321i	$-0.707303\pi$
$641$	−14.1612	+	5.15426i	−0.559335	+	0.203581i	0.0468544	+	0.998902i	$0.485080\pi$
$642$	9.43077	+	4.16682i	0.372203	+	0.164451i
$643$	32.7419	+	11.9171i	1.29122	+	0.469964i	0.894126	−	0.447816i	$-0.147798\pi$
$643$	32.7419	+	11.9171i	1.29122	+	0.469964i	0.397090	+	0.917780i	$0.370020\pi$
$644$	2.29993	−	0.838632i	0.0906299	−	0.0330467i
$645$	−13.5636	−	13.0240i	−0.534065	−	0.512819i
$646$	5.78560	−	2.10578i	0.227631	−	0.0828510i
$647$	24.5619	+	42.5424i	0.965627	+	1.67251i	0.707921	+	0.706291i	$0.249633\pi$
$647$	24.5619	+	42.5424i	0.965627	+	1.67251i	0.257705	+	0.966224i	$0.417034\pi$
$648$	−27.1035	+	2.20470i	−1.06473	+	0.0866086i
$649$	−5.17941	+	8.97100i	−0.203310	+	0.352143i
$650$	−0.555654	−	0.466249i	−0.0217946	−	0.0182878i
$651$	19.7461	+	40.1361i	0.773911	+	1.57306i
$652$	0.0342176	+	0.194058i	0.00134006	+	0.00759988i
$653$	−10.3921	+	8.72003i	−0.406676	+	0.341241i	−0.823067	−	0.567944i	$-0.807739\pi$
$653$	−10.3921	+	8.72003i	−0.406676	+	0.341241i	0.416392	+	0.909185i	$0.363295\pi$
$654$	−14.6287	+	10.6919i	−0.572028	+	0.418088i
$655$	−33.0917	+	12.0444i	−1.29300	+	0.470613i
$656$	2.99718	+	5.19127i	0.117020	+	0.202685i
$657$	0.241325	+	0.126563i	0.00941497	+	0.00493769i
$658$	−6.12042	−	2.22359i	−0.238599	−	0.0866845i
$659$	12.9747	−	4.72241i	0.505423	−	0.183959i	−0.0767086	−	0.997054i	$-0.524441\pi$
$659$	12.9747	−	4.72241i	0.505423	−	0.183959i	0.582131	+	0.813095i	$0.302219\pi$
$660$	−3.94592	−	8.03240i	−0.153595	−	0.312661i
$661$	4.53165	+	1.64939i	0.176261	+	0.0641537i	0.428643	−	0.903474i	$-0.358992\pi$
$661$	4.53165	+	1.64939i	0.176261	+	0.0641537i	−0.252382	+	0.967628i	$0.581214\pi$
$662$	−19.2884	−	7.02041i	−0.749666	−	0.272856i
$663$	1.82950	+	0.122715i	0.0710519	+	0.00476585i
$664$	−1.36520	+	0.496894i	−0.0529802	+	0.0192832i
$665$	26.4686	+	9.61622i	1.02641	+	0.372901i
$666$	24.6057	+	3.31580i	0.953451	+	0.128485i
$667$	−4.89278	−	8.47455i	−0.189449	−	0.328136i
$668$	4.61056	−	1.67811i	0.178388	−	0.0649279i
$669$	10.5054	+	4.64165i	0.406164	+	0.179456i
$670$	−18.3817	+	15.4241i	−0.710146	+	0.595884i
$671$	−3.18061	−	18.0381i	−0.122786	−	0.696355i
$672$	−22.0906	−	1.46873i	−0.852163	−	0.0566577i
$673$	17.0580	+	14.3133i	0.657536	+	0.551738i	0.909347	−	0.416038i	$-0.136582\pi$
$673$	17.0580	+	14.3133i	0.657536	+	0.551738i	−0.251811	+	0.967776i	$0.581026\pi$
$674$	13.0847	−	22.6634i	0.504005	−	0.872962i
$675$	−2.51615	−	3.16461i	−0.0968465	−	0.121806i
$676$	−5.80102	−	10.0477i	−0.223116	−	0.386449i
$677$	29.2022	−	10.6287i	1.12233	−	0.408495i	0.286829	−	0.957982i	$-0.407399\pi$
$677$	29.2022	−	10.6287i	1.12233	−	0.408495i	0.835503	+	0.549487i	$0.185177\pi$
$678$	−2.31631	+	9.40381i	−0.0889573	+	0.361151i
$679$	37.9529	−	13.8389i	1.45650	−	0.531089i
$680$	6.77753	+	2.46682i	0.259906	+	0.0945982i
$681$	13.8404	−	10.1158i	0.530364	−	0.387637i
$682$	24.7511	−	9.00867i	0.947769	−	0.344960i
$683$	−21.7508			−0.832272			−0.416136	−	0.909302i	$-0.636616\pi$
$683$	−21.7508			−0.832272			−0.416136	+	0.909302i	$0.636616\pi$
$684$	9.97606	+	10.9539i	0.381444	+	0.418831i
$685$	−16.8308	−	29.1518i	−0.643072	−	1.11383i
$686$	17.7932	−	6.51163i	0.679346	−	0.248615i
$687$	31.7705	+	2.13102i	1.21212	+	0.0813035i
$688$	1.08668	+	6.16286i	0.0414292	+	0.234957i
$689$	5.34480	+	1.94535i	0.203621	+	0.0741118i
$690$	1.55808	+	3.17166i	0.0593152	+	0.120743i
$691$	−7.33291	+	41.5870i	−0.278957	+	1.58204i	0.447148	+	0.894460i	$0.352440\pi$
$691$	−7.33291	+	41.5870i	−0.278957	+	1.58204i	−0.726105	+	0.687584i	$0.758671\pi$
$692$	3.71666	+	6.43744i	0.141286	+	0.244715i
$693$	7.96402	+	19.3617i	0.302528	+	0.735490i
$694$	−15.9904	+	27.6962i	−0.606989	+	1.05134i
$695$	−0.0756810	−	0.0635039i	−0.00287074	−	0.00240884i
$696$	5.66435	+	52.4601i	0.214707	+	1.98850i
$697$	−1.02102	−	5.79050i	−0.0386739	−	0.219331i
$698$	−14.3954	−	5.23951i	−0.544875	−	0.198318i
$699$	−0.0560939	+	0.227731i	−0.00212166	+	0.00861359i
$700$	−0.982283	−	1.69906i	−0.0371268	−	0.0642186i
$701$	−38.4657			−1.45283			−0.726415	−	0.687256i	$-0.758815\pi$
$701$	−38.4657			−1.45283			−0.726415	+	0.687256i	$0.758815\pi$
$702$	−1.53607	−	4.59409i	−0.0579754	−	0.173393i
$703$	−20.9528	−	36.2913i	−0.790249	−	1.36875i
$704$	−3.34876	+	18.9918i	−0.126211	+	0.715779i
$705$	−2.04773	+	8.31344i	−0.0771220	+	0.313102i
$706$	−2.73451	−	15.5082i	−0.102915	−	0.583659i
$707$	18.8143	−	6.86033i	0.707585	−	0.258009i
$708$	5.23566	−	3.82668i	0.196768	−	0.143815i
$709$	4.59569	+	3.85624i	0.172595	+	0.144824i	0.724993	−	0.688756i	$-0.241843\pi$
$709$	4.59569	+	3.85624i	0.172595	+	0.144824i	−0.552399	+	0.833580i	$0.686287\pi$
$710$	−32.7035			−1.22734
$711$	18.6212	+	2.50935i	0.698350	+	0.0941078i
$712$	−4.51106			−0.169059
$713$	8.90216	−	3.24012i	0.333389	−	0.121344i
$714$	−4.98325	−	2.19827i	−0.186494	−	0.0822683i
$715$	3.78317	−	3.17446i	0.141483	−	0.118718i
$716$	−2.98728	−	16.9417i	−0.111640	−	0.633142i
$717$	20.7155	+	1.38951i	0.773635	+	0.0518920i
$718$	19.9084	+	16.7051i	0.742974	+	0.623429i
$719$	−18.9028			−0.704954			−0.352477	−	0.935820i	$-0.614661\pi$
$719$	−18.9028			−0.704954			−0.352477	+	0.935820i	$0.614661\pi$
$720$	−0.296203	−	7.29479i	−0.0110388	−	0.271861i
$721$	11.5655	−	9.71617i	0.430722	−	0.361849i
$722$	−1.39184	+	7.89353i	−0.0517990	+	0.293767i
$723$	12.2705	+	5.42151i	0.456345	+	0.201628i
$724$	1.97099	+	11.1781i	0.0732513	+	0.415429i
$725$	−6.00959	+	5.04265i	−0.223191	+	0.187279i
$726$	−6.88071	+	1.99416i	−0.255367	+	0.0740102i
$727$	1.57062	+	1.31791i	0.0582512	+	0.0488786i	0.671448	−	0.741051i	$-0.265672\pi$
$727$	1.57062	+	1.31791i	0.0582512	+	0.0488786i	−0.613197	+	0.789930i	$0.710117\pi$
$728$	−1.26913	−	7.17302i	−0.0470371	−	0.265850i
$729$	−3.27906	−	26.8001i	−0.121447	−	0.992598i
$730$	−0.0954702	+	0.165359i	−0.00353351	+	0.00612022i
$731$	1.06591	−	6.04510i	0.0394243	−	0.223586i
$732$	−2.74248	+	11.1340i	−0.101365	+	0.411525i
$733$	−18.9122	−	6.88346i	−0.698537	−	0.254247i	−0.0317507	−	0.999496i	$-0.510108\pi$
$733$	−18.9122	−	6.88346i	−0.698537	−	0.254247i	−0.666786	+	0.745249i	$0.732330\pi$
$734$	27.2275	+	9.91000i	1.00499	+	0.365785i
$735$	−11.0105	−	22.3471i	−0.406130	−	0.824284i
$736$	−0.814219	+	4.61766i	−0.0300125	+	0.170209i
$737$	15.0544	+	26.0750i	0.554535	+	0.960483i
$738$	−13.1262	+	8.30613i	−0.483183	+	0.305753i
$739$	0.634992	−	1.09984i	0.0233586	−	0.0404582i	−0.854110	−	0.520093i	$-0.825897\pi$
$739$	0.634992	−	1.09984i	0.0233586	−	0.0404582i	0.877468	+	0.479634i	$0.159231\pi$
$740$	2.75173	−	15.6058i	0.101155	−	0.573681i
$741$	−4.55270	+	6.79115i	−0.167248	+	0.249479i
$742$	−12.9488	−	10.8524i	−0.475365	−	0.398404i
$743$	24.9523	−	20.9375i	0.915412	−	0.768122i	−0.0577289	−	0.998332i	$-0.518386\pi$
$743$	24.9523	−	20.9375i	0.915412	−	0.768122i	0.973141	+	0.230210i	$0.0739414\pi$
$744$	−50.9677	−	3.41869i	−1.86857	−	0.125335i
$745$	24.2454	+	20.3443i	0.888283	+	0.745358i
$746$	−1.59316	+	2.75943i	−0.0583297	+	0.101030i
$747$	−0.547955	−	1.33438i	−0.0200486	−	0.0488224i
$748$	1.46069	−	2.52999i	0.0534081	−	0.0925055i
$749$	−7.68933	+	13.3364i	−0.280962	+	0.487300i
$750$	16.9847	−	12.4139i	0.620193	−	0.453291i
$751$	10.5149	−	8.82303i	0.383693	−	0.321957i	−0.430457	−	0.902611i	$-0.641648\pi$
$751$	10.5149	−	8.82303i	0.383693	−	0.321957i	0.814150	+	0.580654i	$0.197203\pi$
$752$	2.18274	−	1.83154i	0.0795965	−	0.0667894i
$753$	−25.9955	−	24.9614i	−0.947328	−	0.909643i
$754$	−8.83256	+	3.21479i	−0.321663	+	0.117076i
$755$	8.62507			0.313898
$756$	0.338200	−	13.1022i	0.0123002	−	0.476521i
$757$	−25.8784			−0.940565			−0.470283	−	0.882516i	$-0.655848\pi$
$757$	−25.8784			−0.940565			−0.470283	+	0.882516i	$0.655848\pi$
$758$	1.16435	−	0.423790i	0.0422913	−	0.0153928i
$759$	4.25871	−	1.23426i	0.154581	−	0.0448007i
$760$	−24.6361	+	20.6722i	−0.893647	+	0.749858i
$761$	−29.1210	+	24.4354i	−1.05564	+	0.885783i	−0.993675	−	0.112296i	$-0.964180\pi$
$761$	−29.1210	+	24.4354i	−1.05564	+	0.885783i	−0.0619603	+	0.998079i	$0.519735\pi$
$762$	−6.42797	−	2.84009i	−0.232861	−	0.102886i
$763$	−13.5409	−	23.4218i	−0.490212	−	0.847925i
$764$	0.813730	−	1.40942i	0.0294397	−	0.0509911i
$765$	−2.17427	+	6.82325i	−0.0786109	+	0.246695i
$766$	10.6755	−	18.4905i	0.385721	−	0.668088i
$767$	2.74145	+	2.30035i	0.0989879	+	0.0830607i
$768$	16.2567	−	24.2497i	0.586612	−	0.875034i
$769$	−12.8819	+	10.8092i	−0.464534	+	0.389790i	−0.844796	−	0.535089i	$-0.820278\pi$
$769$	−12.8819	+	10.8092i	−0.464534	+	0.389790i	0.380262	+	0.924879i	$0.375834\pi$
$770$	−13.7820	+	5.02538i	−0.496669	+	0.181102i
$771$	−43.3346	−	2.90669i	−1.56066	−	0.104682i
$772$	−0.671782	+	3.80986i	−0.0241780	+	0.137120i
$773$	15.4749	−	26.8033i	0.556594	−	0.964049i	−0.441183	−	0.897417i	$-0.645441\pi$
$773$	15.4749	−	26.8033i	0.556594	−	0.964049i	0.997778	−	0.0666323i	$-0.0212255\pi$
$774$	−15.8427	+	3.46158i	−0.569455	+	0.124424i
$775$	−3.79739	−	6.57727i	−0.136406	−	0.236262i
$776$	−8.01103	+	45.4328i	−0.287579	+	1.63094i
$777$	−8.84504	+	36.0002i	−0.317314	+	1.29150i
$778$	4.16992	+	1.51773i	0.149499	+	0.0544131i
$779$	24.6367	+	8.96704i	0.882702	+	0.321277i
$780$	−2.96955	+	0.860632i	−0.106327	+	0.0308156i
$781$	−7.12569	+	40.4118i	−0.254977	+	1.44605i
$782$	−0.576766	+	0.998988i	−0.0206251	+	0.0357237i
$783$	−51.8167	+	7.73278i	−1.85178	+	0.276347i
$784$	−1.43010	+	8.16644i	−0.0510749	+	0.291659i
$785$	39.2421	+	32.9281i	1.40061	+	1.17525i
$786$	−7.26338	+	29.4881i	−0.259076	+	1.05180i
$787$	−7.02542	+	5.89503i	−0.250429	+	0.210135i	−0.759357	−	0.650674i	$-0.774486\pi$
$787$	−7.02542	+	5.89503i	−0.250429	+	0.210135i	0.508928	+	0.860809i	$0.330042\pi$
$788$	−1.25208	−	7.10089i	−0.0446035	−	0.252959i
$789$	−2.42777	−	22.4847i	−0.0864309	−	0.800476i
$790$	−2.28622	+	12.9658i	−0.0813402	+	0.461303i
$791$	−13.5913	−	4.93783i	−0.483253	−	0.175569i
$792$	−23.6943	−	3.19299i	−0.841941	−	0.113458i
$793$	−6.32785			−0.224708
$794$	−5.87259	−	4.92769i	−0.208410	−	0.174877i
$795$	−12.3697	+	18.4516i	−0.438708	+	0.654410i
$796$	3.07150	+	17.4194i	0.108867	+	0.617413i
$797$	−11.2510	+	9.44071i	−0.398531	+	0.334407i	−0.819925	−	0.572470i	$-0.805985\pi$
$797$	−11.2510	+	9.44071i	−0.398531	+	0.334407i	0.421395	+	0.906877i	$0.361541\pi$
$798$	19.5988	−	14.3422i	0.693791	−	0.507707i
$799$	−2.62637	+	0.955921i	−0.0929143	+	0.0338181i
$800$	3.75903			0.132902
$801$	−0.181720	−	4.47535i	−0.00642077	−	0.158129i
$802$	−17.7342			−0.626216
$803$	0.183533	+	0.154002i	0.00647673	+	0.00543462i
$804$	−2.02348	−	18.7403i	−0.0713625	−	0.660921i
$805$	−4.95693	+	1.80747i	−0.174709	+	0.0637048i
$806$	−1.58014	−	8.96140i	−0.0556579	−	0.315652i
$807$	36.6679	−	10.6271i	1.29077	−	0.374090i
$808$	−3.97129	+	22.5223i	−0.139709	+	0.792331i
$809$	−12.8233	−	22.2106i	−0.450844	−	0.780885i	0.547595	−	0.836744i	$-0.315544\pi$
$809$	−12.8233	−	22.2106i	−0.450844	−	0.780885i	−0.998439	+	0.0558590i	$0.982210\pi$
$810$	18.8567	−	1.53387i	0.662555	−	0.0538946i
$811$	−10.3038			−0.361815			−0.180908	−	0.983500i	$-0.557903\pi$
$811$	−10.3038			−0.361815			−0.180908	+	0.983500i	$0.557903\pi$
$812$	−25.4317	+	0.0149042i	−0.892479	+	0.000523034i
$813$	−26.0756	−	25.0382i	−0.914510	−	0.878130i
$814$	20.5127	+	7.46603i	0.718971	+	0.261684i
$815$	−0.0737476	−	0.418244i	−0.00258327	−	0.0146504i
$816$	1.92411	−	1.40631i	0.0673572	−	0.0492305i
$817$	20.9671	+	17.5935i	0.733547	+	0.615519i
$818$	−0.284251	+	0.492337i	−0.00993859	+	0.0172141i
$819$	7.06511	−	1.54804i	0.246875	−	0.0540928i
$820$	4.95714	+	8.58601i	0.173111	+	0.299837i
$821$	1.45384	−	8.24516i	0.0507395	−	0.287758i	−0.948871	−	0.315664i	$-0.897773\pi$
$821$	1.45384	−	8.24516i	0.0507395	−	0.287758i	0.999611	+	0.0279059i	$0.00888389\pi$
$822$	−28.9644	−	1.94280i	−1.01025	−	0.0677630i
$823$	43.4959	+	15.8312i	1.51617	+	0.551841i	0.960189	−	0.279352i	$-0.0901198\pi$
$823$	43.4959	+	15.8312i	1.51617	+	0.551841i	0.555983	+	0.831194i	$0.312342\pi$
$824$	2.99544	+	16.9880i	0.104351	+	0.591805i
$825$	−1.56732	−	3.19046i	−0.0545670	−	0.111078i
$826$	−5.32050	−	9.20292i	−0.185124	−	0.320211i
$827$	−20.8009	−	36.0283i	−0.723319	−	1.25283i	−0.959662	−	0.281156i	$-0.909282\pi$
$827$	−20.8009	−	36.0283i	−0.723319	−	1.25283i	0.236343	−	0.971670i	$-0.424051\pi$
$828$	−2.75097	−	0.370713i	−0.0956027	−	0.0128832i
$829$	36.6209			1.27190			0.635948	−	0.771732i	$-0.280609\pi$
$829$	36.6209			1.27190			0.635948	+	0.771732i	$0.280609\pi$
$830$	0.949810	−	0.345703i	0.0329684	−	0.0119995i
$831$	−5.56615	−	51.5507i	−0.193088	−	1.78827i
$832$	6.26059	+	2.27867i	0.217047	+	0.0789986i
$833$	4.05789	−	7.04754i	0.140598	−	0.244183i
$834$	−0.0818321	+	0.0237165i	−0.00283361	+	0.000821235i
$835$	−9.93693	+	3.61675i	−0.343882	+	0.125163i
$836$	6.51314	+	11.2811i	0.225262	+	0.390165i
$837$	1.33848	−	50.7020i	0.0462646	−	1.75252i
$838$	−14.3150	+	24.7944i	−0.494504	+	0.856507i
$839$	17.4518	+	14.6438i	0.602502	+	0.505559i	0.892249	−	0.451544i	$-0.149127\pi$
$839$	17.4518	+	14.6438i	0.602502	+	0.505559i	−0.289747	+	0.957103i	$0.593571\pi$
$840$	28.3872	+	1.88738i	0.979451	+	0.0651207i
$841$	12.6169	+	71.5540i	0.435066	+	2.46738i
$842$	−15.4435	+	12.9586i	−0.532219	+	0.446585i
$843$	2.33196	+	21.5973i	0.0803169	+	0.743852i
$844$	7.41241	−	2.69790i	0.255146	−	0.0928654i
$845$	12.5027	+	21.6553i	0.430105	+	0.744965i
$846$	4.97174	+	5.45904i	0.170932	+	0.187686i
$847$	−1.86358	−	10.5328i	−0.0640333	−	0.361910i
$848$	6.94695	−	2.52848i	0.238559	−	0.0868284i
$849$	−22.5261	+	33.6017i	−0.773095	+	1.15321i
$850$	0.869002	+	0.316291i	0.0298065	+	0.0108487i
$851$	7.37776	+	2.68529i	0.252906	+	0.0920504i
$852$	14.3050	−	21.3384i	0.490080	−	0.731040i
$853$	27.4631	−	9.99576i	0.940319	−	0.342248i	0.174027	−	0.984741i	$-0.444322\pi$
$853$	27.4631	−	9.99576i	0.940319	−	0.342248i	0.766292	+	0.642493i	$0.222100\pi$
$854$	17.6665	+	6.41836i	0.604536	+	0.219632i
$855$	−21.5010	−	23.6084i	−0.735317	−	0.807389i
$856$	−8.79014	−	15.2250i	−0.300441	−	0.520379i
$857$	14.8719	−	5.41293i	0.508014	−	0.184902i	−0.0752807	−	0.997162i	$-0.523985\pi$
$857$	14.8719	−	5.41293i	0.508014	−	0.184902i	0.583295	+	0.812260i	$0.301763\pi$
$858$	−0.457204	−	4.23438i	−0.0156087	−	0.144559i
$859$	3.23874	−	2.71763i	0.110505	−	0.0927243i	−0.585861	−	0.810411i	$-0.699244\pi$
$859$	3.23874	−	2.71763i	0.110505	−	0.0927243i	0.696366	+	0.717687i	$0.254799\pi$
$860$	1.79729	+	10.1930i	0.0612872	+	0.347577i
$861$	−10.2385	−	20.8109i	−0.348927	−	0.709233i
$862$	25.4687	+	21.3708i	0.867469	+	0.727893i
$863$	11.9821	−	20.7536i	0.407875	−	0.706461i	−0.586776	−	0.809749i	$-0.699603\pi$
$863$	11.9821	−	20.7536i	0.407875	−	0.706461i	0.994651	+	0.103288i	$0.0329365\pi$
$864$	21.4016	+	13.1212i	0.728097	+	0.446392i
$865$	−8.01034	−	13.8743i	−0.272360	−	0.471741i
$866$	18.0063	−	6.55375i	0.611878	−	0.222705i
$867$	26.0358	−	7.54566i	0.884221	−	0.256264i
$868$	4.26112	−	24.2491i	0.144632	−	0.823069i
$869$	15.5237	+	5.65017i	0.526606	+	0.191669i
$870$	−3.94084	−	36.4979i	−0.133607	−	1.23740i
$871$	9.77449	−	3.55762i	0.331196	−	0.120546i
$872$	30.8960			1.04627
$873$	−45.3959	−	6.11743i	−1.53642	−	0.207044i
$874$	−2.57177	−	4.45444i	−0.0869915	−	0.150674i
$875$	15.7216	+	27.1939i	0.531489	+	0.919321i
$876$	−0.0661334	−	0.134623i	−0.00223444	−	0.00454848i
$877$	5.19745	+	29.4762i	0.175505	+	0.995341i	0.937559	+	0.347827i	$0.113080\pi$
$877$	5.19745	+	29.4762i	0.175505	+	0.995341i	−0.762053	+	0.647514i	$0.775809\pi$
$878$	−10.6462	−	3.87490i	−0.359292	−	0.130771i
$879$	22.9138	+	1.53695i	0.772863	+	0.0518402i
$880$	1.11464	−	6.32144i	0.0375746	−	0.213096i
$881$	17.7623	+	30.7653i	0.598428	+	1.03651i	0.993053	+	0.117666i	$0.0375413\pi$
$881$	17.7623	+	30.7653i	0.598428	+	1.03651i	−0.394625	+	0.918842i	$0.629125\pi$
$882$	−21.2950	−	2.84426i	−0.717041	−	0.0957711i
$883$	6.01556	−	10.4193i	0.202440	−	0.350636i	−0.746874	−	0.664965i	$-0.768446\pi$
$883$	6.01556	−	10.4193i	0.202440	−	0.350636i	0.949314	+	0.314329i	$0.101780\pi$
$884$	−0.773138	−	0.648740i	−0.0260035	−	0.0218195i
$885$	−11.2842	+	8.24746i	−0.379313	+	0.277235i
$886$	2.92475	+	16.5871i	0.0982590	+	0.557255i
$887$	44.2145	+	16.0928i	1.48458	+	0.540342i	0.952016	−	0.306049i	$-0.0990072\pi$
$887$	44.2145	+	16.0928i	1.48458	+	0.540342i	0.532562	+	0.846391i	$0.321229\pi$
$888$	−30.5365	−	29.3218i	−1.02474	−	0.983974i
$889$	5.24102	−	9.09001i	0.175778	−	0.304869i
$890$	3.13847			0.105202
$891$	2.21322	−	23.6354i	0.0741458	−	0.791815i
$892$	−3.16085	−	5.47475i	−0.105833	−	0.183308i
$893$	2.16408	−	12.2731i	0.0724182	−	0.410704i
$894$	26.2160	−	7.59789i	0.876793	−	0.254111i
$895$	6.43835	+	36.5137i	0.215210	+	1.22052i
$896$	4.42556	+	3.70907i	0.147847	+	0.123911i
$897$	−0.164441	−	1.52297i	−0.00549054	−	0.0508504i
$898$	−10.0143	−	8.40298i	−0.334181	−	0.280411i
$899$	−98.4158			−3.28235
$900$	0.0902854	+	2.22352i	0.00300951	+	0.0741173i
$901$	−7.25153			−0.241583
$902$	−12.8336	+	4.67106i	−0.427313	+	0.155529i
$903$	−2.61337	−	24.0714i	−0.0869675	−	0.801047i
$904$	12.6504	−	10.6149i	0.420746	−	0.353048i
$905$	−4.24799	−	24.0916i	−0.141208	−	0.800830i
$906$	4.14186	−	6.17831i	0.137604	−	0.205261i
$907$	−17.4491	−	14.6415i	−0.579386	−	0.486163i	0.305359	−	0.952237i	$-0.401223\pi$
$907$	−17.4491	−	14.6415i	−0.579386	−	0.486163i	−0.884746	+	0.466074i	$0.845668\pi$
$908$	−9.43592			−0.313142
$909$	−22.5040	−	3.03258i	−0.746410	−	0.100584i
$910$	0.882969	+	4.99046i	0.0292701	+	0.165432i
$911$	0.736854	−	4.17891i	0.0244131	−	0.138453i	−0.970165	−	0.242445i	$-0.922051\pi$
$911$	0.736854	−	4.17891i	0.0244131	−	0.138453i	0.994578	+	0.103992i	$0.0331616\pi$
$912$	1.14079	+	10.5654i	0.0377754	+	0.349855i
$913$	−0.220233	−	1.24900i	−0.00728866	−	0.0413360i
$914$	23.7577	−	19.9351i	0.785834	−	0.659393i
$915$	5.91075	−	23.9966i	0.195403	−	0.793304i
$916$	−13.4260	−	11.2658i	−0.443609	−	0.372232i
$917$	−42.6192	−	15.4838i	−1.40741	−	0.511321i
$918$	3.84352	+	4.83408i	0.126855	+	0.159548i
$919$	−17.3324	+	30.0206i	−0.571744	+	0.990290i	0.424643	+	0.905361i	$0.360400\pi$
$919$	−17.3324	+	30.0206i	−0.571744	+	0.990290i	−0.996387	+	0.0849287i	$0.972934\pi$
$920$	1.04630	−	5.93386i	0.0344955	−	0.195634i
$921$	45.5440	−	13.1995i	1.50072	−	0.434939i
$922$	−14.2176	−	5.17478i	−0.468232	−	0.170422i
$923$	13.3216	+	4.84868i	0.438487	+	0.159596i
$924$	2.74947	−	11.1906i	0.0904510	−	0.368144i
$925$	1.09298	−	6.19862i	0.0359371	−	0.203809i
$926$	−8.61040	−	14.9136i	−0.282955	−	0.490093i
$927$	−16.7328	+	3.65606i	−0.549579	+	0.120081i
$928$	24.3554	−	42.1848i	0.799506	−	1.38479i
$929$	0.529327	−	3.00197i	0.0173667	−	0.0984913i	−0.974892	−	0.222677i	$-0.928521\pi$
$929$	0.529327	−	3.00197i	0.0173667	−	0.0984913i	0.992259	+	0.124185i	$0.0396317\pi$
$930$	35.4596	+	2.37848i	1.16277	+	0.0779933i
$931$	18.1676	+	31.3821i	0.595418	+	1.02851i
$932$	0.0988925	−	0.0829807i	0.00323933	−	0.00271812i
$933$	−14.4403	+	21.5402i	−0.472753	+	0.705193i
$934$	1.77649	+	1.49065i	0.0581284	+	0.0487755i
$935$	−3.14816	+	5.45277i	−0.102956	+	0.178325i
$936$	−2.50778	+	7.86986i	−0.0819694	+	0.257235i
$937$	−3.02253	+	5.23518i	−0.0987419	+	0.171026i	−0.911164	−	0.412044i	$-0.864815\pi$
$937$	−3.02253	+	5.23518i	−0.0987419	+	0.171026i	0.812422	+	0.583069i	$0.198148\pi$
$938$	−30.8976	+	0.0181074i	−1.00884	+	0.000591228i
$939$	26.3171	+	11.6278i	0.858827	+	0.379458i
$940$	3.61011	−	3.02925i	0.117749	−	0.0988031i
$941$	45.2653	−	37.9821i	1.47561	−	1.23818i	0.564876	−	0.825176i	$-0.308924\pi$
$941$	45.2653	−	37.9821i	1.47561	−	1.23818i	0.910729	−	0.413004i	$-0.135521\pi$
$942$	42.4316	−	12.2975i	1.38250	−	0.400674i
$943$	−4.61584	+	1.68003i	−0.150312	+	0.0547092i
$944$	4.65145			0.151392
$945$	−0.728906	+	28.2385i	−0.0237113	+	0.918598i
$946$	−14.2578			−0.463560
$947$	11.0992	−	4.03976i	0.360674	−	0.131275i	−0.155326	−	0.987863i	$-0.549643\pi$
$947$	11.0992	−	4.03976i	0.360674	−	0.131275i	0.516000	+	0.856589i	$0.327421\pi$
$948$	−7.45989	−	7.16313i	−0.242286	−	0.232648i
$949$	0.0634058	−	0.0532038i	0.00205824	−	0.00172707i
$950$	−3.15880	+	2.65054i	−0.102485	+	0.0859950i
$951$	−41.3528	+	30.2243i	−1.34096	+	0.980089i
$952$	4.64826	+	8.04013i	0.150651	+	0.260582i
$953$	5.75885	−	9.97463i	0.186548	−	0.323110i	−0.757549	−	0.652778i	$-0.773603\pi$
$953$	5.75885	−	9.97463i	0.186548	−	0.323110i	0.944097	+	0.329668i	$0.106937\pi$
$954$	7.27715	+	17.7213i	0.235606	+	0.573749i
$955$	−1.75379	+	3.03766i	−0.0567515	+	0.0982964i
$956$	−8.75428	−	7.34572i	−0.283134	−	0.237577i
$957$	−45.9592	−	3.08274i	−1.48565	−	0.0996507i
$958$	−14.1561	+	11.8784i	−0.457362	+	0.383772i
$959$	7.50159	−	42.6899i	0.242239	−	1.37853i
$960$	−14.4891	+	21.6131i	−0.467635	+	0.697560i
$961$	11.1616	−	63.3006i	0.360052	−	2.04195i
$962$	3.77071	−	6.53106i	0.121573	−	0.210570i
$963$	14.7504	−	9.33387i	0.475324	−	0.300780i
$964$	−3.69191	−	6.39458i	−0.118909	−	0.205956i
$965$	1.44786	−	8.21123i	0.0466083	−	0.264329i
$966$	−1.08565	+	4.41872i	−0.0349303	+	0.142170i
$967$	−10.6721	−	3.88432i	−0.343191	−	0.124911i	0.164674	−	0.986348i	$-0.447343\pi$
$967$	−10.6721	−	3.88432i	−0.343191	−	0.124911i	−0.507865	+	0.861437i	$0.669565\pi$
$968$	11.4786	+	4.17786i	0.368936	+	0.134282i
$969$	2.49302	−	10.1212i	0.0800874	−	0.325141i
$970$	5.57349	−	31.6088i	0.178954	−	1.01490i
$971$	6.23195	−	10.7940i	0.199993	−	0.346397i	−0.748533	−	0.663097i	$-0.769241\pi$
$971$	6.23195	−	10.7940i	0.199993	−	0.346397i	0.948526	+	0.316700i	$0.102575\pi$
$972$	−7.24733	+	12.9745i	−0.232458	+	0.416157i
$973$	−0.0221635	−	0.125266i	−0.000710528	−	0.00401584i
$974$	4.30116	+	3.60910i	0.137818	+	0.115643i
$975$	−1.17950	+	0.341842i	−0.0377743	+	0.0109477i
$976$	−6.30046	+	5.28671i	−0.201673	+	0.169224i
$977$	5.71361	+	32.4035i	0.182795	+	1.03668i	0.928756	+	0.370691i	$0.120879\pi$
$977$	5.71361	+	32.4035i	0.182795	+	1.03668i	−0.745962	+	0.665989i	$0.768010\pi$
$978$	−0.335011	−	0.148019i	−0.0107125	−	0.00473311i
$979$	0.683832	−	3.87821i	0.0218554	−	0.123948i
$980$	−2.36528	+	13.5068i	−0.0755562	+	0.431457i
$981$	1.24459	+	30.6514i	0.0397368	+	0.978624i
$982$	24.2560			0.774039
$983$	−11.1014	−	9.31517i	−0.354079	−	0.297108i	0.448346	−	0.893860i	$-0.352013\pi$
$983$	−11.1014	−	9.31517i	−0.354079	−	0.297108i	−0.802426	+	0.596752i	$0.796458\pi$
$984$	26.4271	+	1.77261i	0.842466	+	0.0565089i
$985$	2.69855	+	15.3042i	0.0859829	+	0.487633i
$986$	9.17991	−	7.70286i	0.292348	−	0.245309i
$987$	−8.89689	+	6.51063i	−0.283191	+	0.207235i
$988$	4.22885	−	1.53917i	0.134538	−	0.0489677i
$989$	−5.12805			−0.163063
$990$	16.4848	+	2.22145i	0.523921	+	0.0706022i
$991$	−25.8112			−0.819920			−0.409960	−	0.912103i	$-0.634457\pi$
$991$	−25.8112			−0.819920			−0.409960	+	0.912103i	$0.634457\pi$
$992$	36.1246	+	30.3122i	1.14696	+	0.962412i
$993$	−28.0564	+	20.5061i	−0.890344	+	0.650741i
$994$	−32.2742	−	27.0491i	−1.02368	−	0.857945i
$995$	−6.61987	−	37.5432i	−0.209864	−	1.19020i
$996$	−0.189896	+	0.770945i	−0.00601709	+	0.0244283i
$997$	4.52064	−	25.6378i	0.143170	−	0.811959i	−0.825648	−	0.564186i	$-0.809190\pi$
$997$	4.52064	−	25.6378i	0.143170	−	0.811959i	0.968818	−	0.247773i	$-0.0796987\pi$
$998$	−16.8645	−	29.2101i	−0.533836	−	0.924630i
$999$	27.8595	−	31.4760i	0.881437	−	0.995856i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	189.2.u.a.16.15	✓	132
3.2	odd	2		567.2.u.a.289.8		132
7.4	even	3		189.2.w.a.151.8	yes	132
21.11	odd	6		567.2.w.a.46.15		132
27.5	odd	18		567.2.w.a.37.15		132
27.22	even	9		189.2.w.a.184.8	yes	132
189.32	odd	18		567.2.u.a.361.8		132
189.130	even	9	inner	189.2.u.a.130.15	yes	132

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.u.a.16.15	✓	132	1.1	even	1	trivial
189.2.u.a.130.15	yes	132	189.130	even	9	inner
189.2.w.a.151.8	yes	132	7.4	even	3
189.2.w.a.184.8	yes	132	27.22	even	9
567.2.u.a.289.8		132	3.2	odd	2
567.2.u.a.361.8		132	189.32	odd	18
567.2.w.a.37.15		132	27.5	odd	18
567.2.w.a.46.15		132	21.11	odd	6

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.u (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.961357 - 0.349905i) q^{2} +(0.414250 - 1.68178i) q^{3} +(-0.730316 + 0.612808i) q^{4} +(1.57402 - 1.32076i) q^{5} +(-0.190223 - 1.76174i) q^{6} +(2.64575 - 0.00155053i) q^{7} +(-1.51072 + 2.61665i) q^{8} +(-2.65679 - 1.39336i) q^{9} +O(q^{10})\)	\(q+(0.961357 - 0.349905i) q^{2} +(0.414250 - 1.68178i) q^{3} +(-0.730316 + 0.612808i) q^{4} +(1.57402 - 1.32076i) q^{5} +(-0.190223 - 1.76174i) q^{6} +(2.64575 - 0.00155053i) q^{7} +(-1.51072 + 2.61665i) q^{8} +(-2.65679 - 1.39336i) q^{9} +(1.05105 - 1.82048i) q^{10} +(-2.02055 - 1.69544i) q^{11} +(0.728077 + 1.48209i) q^{12} +(-0.698048 + 0.585732i) q^{13} +(2.54297 - 0.927253i) q^{14} +(-1.56919 - 3.19428i) q^{15} +(-0.205667 + 1.16639i) q^{16} +(0.580879 - 1.00611i) q^{17} +(-3.04167 - 0.409888i) q^{18} +(2.59011 + 4.48620i) q^{19} +(-0.340159 + 1.92914i) q^{20} +(1.09339 - 4.45022i) q^{21} +(-2.53571 - 0.922925i) q^{22} +(-0.912014 - 0.331946i) q^{23} +(3.77482 + 3.62466i) q^{24} +(-0.135111 + 0.766253i) q^{25} +(-0.466123 + 0.807348i) q^{26} +(-3.44390 + 3.89096i) q^{27} +(-1.93128 + 1.62247i) q^{28} +(7.72368 + 6.48094i) q^{29} +(-2.62625 - 2.52177i) q^{30} +(-7.47736 + 6.27425i) q^{31} +(-0.838930 - 4.75781i) q^{32} +(-3.68838 + 2.69579i) q^{33} +(0.206388 - 1.17048i) q^{34} +(4.16241 - 3.49683i) q^{35} +(2.79416 - 0.610513i) q^{36} -8.08953 q^{37} +(4.05977 + 3.40655i) q^{38} +(0.695908 + 1.41661i) q^{39} +(1.07805 + 6.11395i) q^{40} +(3.87706 - 3.25324i) q^{41} +(-0.506014 - 4.66084i) q^{42} +(4.96504 - 1.80713i) q^{43} +2.51462 q^{44} +(-6.02212 + 1.31581i) q^{45} -0.992920 q^{46} +(-1.84293 - 1.54640i) q^{47} +(1.87642 + 0.829066i) q^{48} +(7.00000 - 0.00820464i) q^{49} +(0.138226 + 0.783919i) q^{50} +(-1.45143 - 1.39369i) q^{51} +(0.150854 - 0.855538i) q^{52} +(-3.12093 - 5.40561i) q^{53} +(-1.94935 + 4.94564i) q^{54} -5.41965 q^{55} +(-3.99294 + 6.92535i) q^{56} +(8.61777 - 2.49760i) q^{57} +(9.69293 + 3.52794i) q^{58} +(-0.681969 - 3.86764i) q^{59} +(3.10348 + 1.37122i) q^{60} +(5.31960 + 4.46367i) q^{61} +(-4.99302 + 8.64816i) q^{62} +(-7.03138 - 3.68236i) q^{63} +(-3.65568 - 6.33182i) q^{64} +(-0.325130 + 1.84390i) q^{65} +(-2.60258 + 3.88220i) q^{66} +(-10.7266 - 3.90417i) q^{67} +(0.192328 + 1.09075i) q^{68} +(-0.936063 + 1.39630i) q^{69} +(2.77800 - 4.81815i) q^{70} +(-7.77877 - 13.4732i) q^{71} +(7.65961 - 4.84692i) q^{72} -0.0908330 q^{73} +(-7.77692 + 2.83057i) q^{74} +(1.23270 + 0.544648i) q^{75} +(-4.64078 - 1.68910i) q^{76} +(-5.34850 - 4.48259i) q^{77} +(1.16469 + 1.11836i) q^{78} +(-5.88546 + 2.14213i) q^{79} +(1.21680 + 2.10756i) q^{80} +(5.11711 + 7.40373i) q^{81} +(2.58892 - 4.48413i) q^{82} +(0.368342 + 0.309075i) q^{83} +(1.92861 + 3.92011i) q^{84} +(-0.414516 - 2.35083i) q^{85} +(4.14085 - 3.47459i) q^{86} +(14.0991 - 10.3048i) q^{87} +(7.48888 - 2.72573i) q^{88} +(0.746507 + 1.29299i) q^{89} +(-5.32900 + 3.37214i) q^{90} +(-1.84595 + 1.55078i) q^{91} +(0.869477 - 0.316464i) q^{92} +(7.45444 + 15.1744i) q^{93} +(-2.31281 - 0.841793i) q^{94} +(10.0021 + 3.64045i) q^{95} +(-8.34913 - 0.560023i) q^{96} +(14.3479 - 5.22221i) q^{97} +(6.72662 - 2.45722i) q^{98} +(3.00583 + 7.31979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9}+O(q^{10}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9	\( 132 q - 3 q^{2} - 3 q^{3} - 3 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} - 6 q^{8} - 15 q^{9} + 3 q^{10} - 15 q^{11} - 3 q^{12} - 12 q^{13} - 30 q^{14} + 9 q^{16} + 27 q^{17} - 3 q^{18} + 3 q^{19} - 18 q^{20} + 15 q^{21} - 12 q^{22} - 36 q^{23} - 72 q^{24} - 3 q^{25} + 30 q^{26} - 12 q^{27} - 12 q^{28} - 30 q^{29} - 3 q^{30} - 3 q^{31} - 75 q^{32} + 15 q^{33} - 18 q^{34} + 15 q^{35} - 60 q^{36} - 6 q^{37} + 69 q^{38} + 51 q^{39} + 51 q^{40} - 39 q^{42} - 12 q^{43} - 6 q^{44} - 21 q^{45} - 6 q^{46} - 21 q^{47} + 90 q^{48} - 42 q^{49} - 39 q^{50} + 33 q^{51} + 9 q^{52} + 9 q^{53} - 9 q^{54} - 24 q^{55} + 111 q^{56} - 18 q^{57} - 3 q^{58} + 27 q^{59} - 63 q^{60} - 21 q^{61} + 75 q^{62} + 63 q^{63} - 30 q^{64} - 90 q^{65} - 3 q^{66} - 3 q^{67} - 30 q^{68} - 6 q^{69} + 39 q^{70} - 18 q^{71} + 183 q^{72} - 42 q^{73} + 51 q^{74} - 45 q^{75} - 24 q^{76} + 15 q^{77} - 30 q^{78} + 15 q^{79} + 102 q^{80} - 87 q^{81} - 6 q^{82} - 42 q^{83} + 135 q^{84} - 63 q^{85} - 93 q^{86} + 75 q^{87} - 51 q^{88} + 75 q^{89} - 39 q^{90} - 21 q^{91} - 66 q^{92} + 81 q^{93} + 33 q^{94} + 15 q^{95} - 171 q^{96} - 12 q^{97} - 36 q^{98} + 24 q^{99}+O(q^{100}) \) 132 * q - 3 * q^2 - 3 * q^3 - 3 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 - 6 * q^8 - 15 * q^9 + 3 * q^10 - 15 * q^11 - 3 * q^12 - 12 * q^13 - 30 * q^14 + 9 * q^16 + 27 * q^17 - 3 * q^18 + 3 * q^19 - 18 * q^20 + 15 * q^21 - 12 * q^22 - 36 * q^23 - 72 * q^24 - 3 * q^25 + 30 * q^26 - 12 * q^27 - 12 * q^28 - 30 * q^29 - 3 * q^30 - 3 * q^31 - 75 * q^32 + 15 * q^33 - 18 * q^34 + 15 * q^35 - 60 * q^36 - 6 * q^37 + 69 * q^38 + 51 * q^39 + 51 * q^40 - 39 * q^42 - 12 * q^43 - 6 * q^44 - 21 * q^45 - 6 * q^46 - 21 * q^47 + 90 * q^48 - 42 * q^49 - 39 * q^50 + 33 * q^51 + 9 * q^52 + 9 * q^53 - 9 * q^54 - 24 * q^55 + 111 * q^56 - 18 * q^57 - 3 * q^58 + 27 * q^59 - 63 * q^60 - 21 * q^61 + 75 * q^62 + 63 * q^63 - 30 * q^64 - 90 * q^65 - 3 * q^66 - 3 * q^67 - 30 * q^68 - 6 * q^69 + 39 * q^70 - 18 * q^71 + 183 * q^72 - 42 * q^73 + 51 * q^74 - 45 * q^75 - 24 * q^76 + 15 * q^77 - 30 * q^78 + 15 * q^79 + 102 * q^80 - 87 * q^81 - 6 * q^82 - 42 * q^83 + 135 * q^84 - 63 * q^85 - 93 * q^86 + 75 * q^87 - 51 * q^88 + 75 * q^89 - 39 * q^90 - 21 * q^91 - 66 * q^92 + 81 * q^93 + 33 * q^94 + 15 * q^95 - 171 * q^96 - 12 * q^97 - 36 * q^98 + 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more