LMFDB - Embedded newform 966.2.y.c.151.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(25,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(66))

chi = DirichletCharacter(H, H._module([0, 44, 6]))

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.y (of order $33$, degree $20$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			151.2
Character	$\chi$	$=$	966.151
Dual form			966.2.y.c.499.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.327068 + 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.78783 + 0.266206i) q^{5} +(0.142315 + 0.989821i) q^{6} +(2.46897 - 0.950880i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})$	\(q+(-0.327068 + 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.78783 + 0.266206i) q^{5} +(0.142315 + 0.989821i) q^{6} +(2.46897 - 0.950880i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.660246 - 2.72157i) q^{10} +(-0.0624518 - 0.180443i) q^{11} +(-0.981929 - 0.189251i) q^{12} +(0.0600493 - 0.0176321i) q^{13} +(0.0910606 + 2.64418i) q^{14} +(-2.35594 + 1.51407i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-2.04740 - 0.819657i) q^{17} +(0.580057 + 0.814576i) q^{18} +(2.41401 - 0.966423i) q^{19} +(2.35594 + 1.51407i) q^{20} +(1.75879 - 1.97652i) q^{21} +0.190944 q^{22} +(-2.83650 - 3.86707i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.79149 - 0.538016i) q^{25} +(-0.00297789 + 0.0625136i) q^{26} +(0.142315 - 0.989821i) q^{27} +(-2.52854 - 0.778775i) q^{28} +(-0.695962 - 4.84052i) q^{29} +(-0.660246 - 2.72157i) q^{30} +(-0.161249 - 3.38504i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-0.138193 - 0.131767i) q^{33} +(1.44422 - 1.66671i) q^{34} +(-6.62995 + 3.30815i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(6.74162 - 9.46728i) q^{37} +(0.123726 + 2.59733i) q^{38} +(0.0452945 - 0.0431882i) q^{39} +(-2.20135 + 1.73116i) q^{40} +(1.02760 - 2.25012i) q^{41} +(1.29257 + 2.30852i) q^{42} +(1.44456 + 0.928361i) q^{43} +(-0.0624518 + 0.180443i) q^{44} +(-1.40026 + 2.42531i) q^{45} +(4.58212 - 1.41570i) q^{46} +(3.97232 + 6.88027i) q^{47} +(0.654861 + 0.755750i) q^{48} +(5.19165 - 4.69539i) q^{49} +(-0.404582 + 2.81393i) q^{50} +(-2.19539 + 0.209635i) q^{51} +(-0.0581014 - 0.0232603i) q^{52} +(6.66207 - 6.35227i) q^{53} +(0.888835 + 0.458227i) q^{54} +(0.222140 + 0.486419i) q^{55} +(1.56295 - 2.13476i) q^{56} +(1.70282 - 1.96515i) q^{57} +(4.80192 + 0.925494i) q^{58} +(1.68959 - 6.96458i) q^{59} +(2.78783 + 0.266206i) q^{60} +(6.58470 + 3.39465i) q^{61} +(3.25161 + 0.954758i) q^{62} +(0.657581 - 2.56273i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.162714 + 0.0651407i) q^{65} +(0.169718 - 0.0874958i) q^{66} +(-2.61006 + 0.503049i) q^{67} +(1.10269 + 1.90991i) q^{68} +(-4.29318 - 2.13743i) q^{69} +(-0.957758 - 7.34730i) q^{70} +(0.221991 + 0.256191i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-7.24113 - 5.69449i) q^{73} +(6.74162 + 9.46728i) q^{74} +(2.23464 - 1.75734i) q^{75} +(-2.49494 - 0.732581i) q^{76} +(-0.325771 - 0.386124i) q^{77} +(0.0259985 + 0.0569288i) q^{78} +(1.31342 + 1.25235i) q^{79} +(-0.915958 - 2.64649i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(1.79027 + 1.70702i) q^{82} +(0.814445 + 1.78339i) q^{83} +(-2.60431 + 0.466440i) q^{84} +(5.92601 + 1.74003i) q^{85} +(-1.34977 + 1.06147i) q^{86} +(-2.83665 - 3.98352i) q^{87} +(-0.150093 - 0.118034i) q^{88} +(0.0282373 - 0.592773i) q^{89} +(-1.83395 - 2.11649i) q^{90} +(0.131494 - 0.100633i) q^{91} +(-0.160824 + 4.79313i) q^{92} +(-1.69444 - 2.93486i) q^{93} +(-7.80108 + 1.50353i) q^{94} +(-6.47258 + 3.33685i) q^{95} +(-0.928368 + 0.371662i) q^{96} +(-4.73445 + 10.3670i) q^{97} +(2.73913 + 6.44183i) q^{98} +(-0.183210 - 0.0537953i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{7}{11}\right)$

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 $

$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$2$	−0.327068	+	0.945001i	−0.231272	+	0.668216i
$3$	0.888835	−	0.458227i	0.513169	−	0.264557i
$3$	0.888835	−	0.458227i	0.513169	−	0.264557i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−2.78783	+	0.266206i	−1.24676	+	0.119051i	−0.697488	−	0.716596i	$-0.745699\pi$
$5$	−2.78783	+	0.266206i	−1.24676	+	0.119051i	−0.549267	+	0.835647i	$0.685093\pi$
$6$	0.142315	+	0.989821i	0.0580998	+	0.404093i
$7$	2.46897	−	0.950880i	0.933184	−	0.359399i
$7$	2.46897	−	0.950880i	0.933184	−	0.359399i
$8$	0.841254	−	0.540641i	0.297428	−	0.191145i
$9$	0.580057	−	0.814576i	0.193352	−	0.271525i
$10$	0.660246	−	2.72157i	0.208788	−	0.860636i
$11$	−0.0624518	−	0.180443i	−0.0188299	−	0.0544055i	0.935194	−	0.354135i	$-0.115225\pi$
$11$	−0.0624518	−	0.180443i	−0.0188299	−	0.0544055i	−0.954024	+	0.299730i	$0.903104\pi$
$12$	−0.981929	−	0.189251i	−0.283458	−	0.0546321i
$13$	0.0600493	−	0.0176321i	0.0166547	−	0.00489026i	−0.273395	−	0.961902i	$-0.588146\pi$
$13$	0.0600493	−	0.0176321i	0.0166547	−	0.00489026i	0.290049	+	0.957012i	$0.406328\pi$
$14$	0.0910606	+	2.64418i	0.0243370	+	0.706688i
$15$	−2.35594	+	1.51407i	−0.608301	+	0.390931i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	−2.04740	−	0.819657i	−0.496568	−	0.198796i	0.109840	−	0.993949i	$-0.464966\pi$
$17$	−2.04740	−	0.819657i	−0.496568	−	0.198796i	−0.606408	+	0.795153i	$0.707390\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	2.41401	−	0.966423i	0.553812	−	0.221713i	−0.0778390	−	0.996966i	$-0.524802\pi$
$19$	2.41401	−	0.966423i	0.553812	−	0.221713i	0.631651	+	0.775253i	$0.282378\pi$
$20$	2.35594	+	1.51407i	0.526804	+	0.338557i
$21$	1.75879	−	1.97652i	0.383800	−	0.431313i
$22$	0.190944			0.0407095
$23$	−2.83650	−	3.86707i	−0.591452	−	0.806340i
$23$	−2.83650	−	3.86707i	−0.591452	−	0.806340i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	2.79149	−	0.538016i	0.558298	−	0.107603i
$26$	−0.00297789	+	0.0625136i	−0.000584012	+	0.0122599i
$27$	0.142315	−	0.989821i	0.0273885	−	0.190491i
$28$	−2.52854	−	0.778775i	−0.477849	−	0.147175i
$29$	−0.695962	−	4.84052i	−0.129237	−	0.898862i	−0.946525	−	0.322632i	$-0.895432\pi$
$29$	−0.695962	−	4.84052i	−0.129237	−	0.898862i	0.817288	−	0.576230i	$-0.195477\pi$
$30$	−0.660246	−	2.72157i	−0.120544	−	0.496888i
$31$	−0.161249	−	3.38504i	−0.0289613	−	0.607972i	−0.965968	−	0.258661i	$-0.916719\pi$
$31$	−0.161249	−	3.38504i	−0.0289613	−	0.607972i	0.937007	−	0.349311i	$-0.113584\pi$
$32$	−0.995472	−	0.0950560i	−0.175976	−	0.0168037i
$33$	−0.138193	−	0.131767i	−0.0240563	−	0.0229377i
$34$	1.44422	−	1.66671i	0.247681	−	0.285839i
$35$	−6.62995	+	3.30815i	−1.12067	+	0.559179i
$36$	−0.959493	+	0.281733i	−0.159915	+	0.0469554i
$37$	6.74162	−	9.46728i	1.10832	−	1.55641i	0.313472	−	0.949597i	$-0.398508\pi$
$37$	6.74162	−	9.46728i	1.10832	−	1.55641i	0.794844	−	0.606814i	$-0.207553\pi$
$38$	0.123726	+	2.59733i	0.0200710	+	0.421342i
$39$	0.0452945	−	0.0431882i	0.00725292	−	0.00691565i
$40$	−2.20135	+	1.73116i	−0.348064	+	0.273721i
$41$	1.02760	−	2.25012i	0.160484	−	0.351410i	−0.812259	−	0.583297i	$-0.801763\pi$
$41$	1.02760	−	2.25012i	0.160484	−	0.351410i	0.972743	+	0.231887i	$0.0744898\pi$
$42$	1.29257	+	2.30852i	0.199448	+	0.356212i
$43$	1.44456	+	0.928361i	0.220293	+	0.141574i	0.646133	−	0.763225i	$-0.276385\pi$
$43$	1.44456	+	0.928361i	0.220293	+	0.141574i	−0.425840	+	0.904798i	$0.640021\pi$
$44$	−0.0624518	+	0.180443i	−0.00941497	+	0.0272028i
$45$	−1.40026	+	2.42531i	−0.208738	+	0.361544i
$46$	4.58212	−	1.41570i	0.675596	−	0.208734i
$47$	3.97232	+	6.88027i	0.579423	+	1.00359i	0.995546	+	0.0942814i	$0.0300553\pi$
$47$	3.97232	+	6.88027i	0.579423	+	1.00359i	−0.416123	+	0.909308i	$0.636611\pi$
$48$	0.654861	+	0.755750i	0.0945210	+	0.109083i
$49$	5.19165	−	4.69539i	0.741665	−	0.670771i
$50$	−0.404582	+	2.81393i	−0.0572165	+	0.397950i
$51$	−2.19539	+	0.209635i	−0.307416	+	0.0293547i
$52$	−0.0581014	−	0.0232603i	−0.00805721	−	0.00322562i
$53$	6.66207	−	6.35227i	0.915106	−	0.872552i	−0.0771174	−	0.997022i	$-0.524572\pi$
$53$	6.66207	−	6.35227i	0.915106	−	0.872552i	0.992223	+	0.124470i	$0.0397231\pi$
$54$	0.888835	+	0.458227i	0.120955	+	0.0623567i
$55$	0.222140	+	0.486419i	0.0299533	+	0.0655887i
$56$	1.56295	−	2.13476i	0.208858	−	0.285269i
$57$	1.70282	−	1.96515i	0.225543	−	0.260291i
$58$	4.80192	+	0.925494i	0.630523	+	0.121523i
$59$	1.68959	−	6.96458i	0.219966	−	0.906711i	−0.749602	−	0.661889i	$-0.769755\pi$
$59$	1.68959	−	6.96458i	0.219966	−	0.906711i	0.969568	−	0.244823i	$-0.0787297\pi$
$60$	2.78783	+	0.266206i	0.359907	+	0.0343670i
$61$	6.58470	+	3.39465i	0.843084	+	0.434640i	0.824957	−	0.565195i	$-0.191199\pi$
$61$	6.58470	+	3.39465i	0.843084	+	0.434640i	0.0181274	+	0.999836i	$0.494230\pi$
$62$	3.25161	+	0.954758i	0.412955	+	0.121254i
$63$	0.657581	−	2.56273i	0.0828474	−	0.322874i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	−0.162714	+	0.0651407i	−0.0201821	+	0.00807971i
$66$	0.169718	−	0.0874958i	0.0208909	−	0.0107700i
$67$	−2.61006	+	0.503049i	−0.318870	+	0.0614572i	−0.346175	−	0.938170i	$-0.612520\pi$
$67$	−2.61006	+	0.503049i	−0.318870	+	0.0614572i	0.0273048	+	0.999627i	$0.491308\pi$
$68$	1.10269	+	1.90991i	0.133721	+	0.231611i
$69$	−4.29318	−	2.13743i	−0.516838	−	0.257316i
$70$	−0.957758	−	7.34730i	−0.114474	−	0.878170i
$71$	0.221991	+	0.256191i	0.0263455	+	0.0304043i	0.768769	−	0.639526i	$-0.220869\pi$
$71$	0.221991	+	0.256191i	0.0263455	+	0.0304043i	−0.742424	+	0.669930i	$0.766324\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	−7.24113	−	5.69449i	−0.847510	−	0.666490i	0.0968871	−	0.995295i	$-0.469111\pi$
$73$	−7.24113	−	5.69449i	−0.847510	−	0.666490i	−0.944398	+	0.328806i	$0.893354\pi$
$74$	6.74162	+	9.46728i	0.783698	+	1.10055i
$75$	2.23464	−	1.75734i	0.258034	−	0.202920i
$76$	−2.49494	−	0.732581i	−0.286190	−	0.0840328i
$77$	−0.325771	−	0.386124i	−0.0371251	−	0.0440029i
$78$	0.0259985	+	0.0569288i	0.00294375	+	0.00644592i
$79$	1.31342	+	1.25235i	0.147772	+	0.140900i	0.760359	−	0.649503i	$-0.225023\pi$
$79$	1.31342	+	1.25235i	0.147772	+	0.140900i	−0.612588	+	0.790403i	$0.709871\pi$
$80$	−0.915958	−	2.64649i	−0.102407	−	0.295886i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	1.79027	+	1.70702i	0.197703	+	0.188509i
$83$	0.814445	+	1.78339i	0.0893970	+	0.195752i	0.949049	−	0.315127i	$-0.102047\pi$
$83$	0.814445	+	1.78339i	0.0893970	+	0.195752i	−0.859652	+	0.510879i	$0.829320\pi$
$84$	−2.60431	+	0.466440i	−0.284154	+	0.0508928i
$85$	5.92601	+	1.74003i	0.642766	+	0.188733i
$86$	−1.34977	+	1.06147i	−0.145550	+	0.114461i
$87$	−2.83665	−	3.98352i	−0.304121	−	0.427078i
$88$	−0.150093	−	0.118034i	−0.0159999	−	0.0125825i
$89$	0.0282373	−	0.592773i	0.00299314	−	0.0628338i	−0.996877	−	0.0789753i	$-0.974835\pi$
$89$	0.0282373	−	0.592773i	0.00299314	−	0.0628338i	0.999870	+	0.0161415i	$0.00513821\pi$
$90$	−1.83395	−	2.11649i	−0.193315	−	0.223097i
$91$	0.131494	−	0.100633i	0.0137843	−	0.0105492i
$92$	−0.160824	+	4.79313i	−0.0167670	+	0.499719i
$93$	−1.69444	−	2.93486i	−0.175705	−	0.304331i
$94$	−7.80108	+	1.50353i	−0.804620	+	0.155078i
$95$	−6.47258	+	3.33685i	−0.664073	+	0.342353i
$96$	−0.928368	+	0.371662i	−0.0947512	+	0.0379326i
$97$	−4.73445	+	10.3670i	−0.480711	+	1.05261i	0.501557	+	0.865125i	$0.332761\pi$
$97$	−4.73445	+	10.3670i	−0.480711	+	1.05261i	−0.982267	+	0.187485i	$0.939966\pi$
$98$	2.73913	+	6.44183i	0.276694	+	0.650723i
$99$	−0.183210	−	0.0537953i	−0.0184133	−	0.00540663i
$100$	−2.52684	−	1.30268i	−0.252684	−	0.130268i
$101$	−17.4035	−	1.66184i	−1.73172	−	0.165359i	−0.818957	−	0.573854i	$-0.805448\pi$
$101$	−17.4035	−	1.66184i	−1.73172	−	0.165359i	−0.912760	+	0.408495i	$0.866054\pi$
$102$	0.519938	−	2.14321i	0.0514815	−	0.212210i
$103$	1.27283	+	0.245317i	0.125415	+	0.0241718i	0.251573	−	0.967838i	$-0.419052\pi$
$103$	1.27283	+	0.245317i	0.125415	+	0.0241718i	−0.126157	+	0.992010i	$0.540264\pi$
$104$	0.0409841	−	0.0472982i	0.00401882	−	0.00463797i
$105$	−4.37705	+	5.97842i	−0.427157	+	0.583434i
$106$	3.82395	+	8.37329i	0.371415	+	0.813286i
$107$	−7.68501	−	3.96190i	−0.742938	−	0.383011i	0.0448207	−	0.998995i	$-0.485728\pi$
$107$	−7.68501	−	3.96190i	−0.742938	−	0.383011i	−0.787759	+	0.615984i	$0.788759\pi$
$108$	−0.723734	+	0.690079i	−0.0696413	+	0.0664029i
$109$	−5.63921	−	2.25760i	−0.540139	−	0.216239i	0.0855191	−	0.996337i	$-0.472745\pi$
$109$	−5.63921	−	2.25760i	−0.540139	−	0.216239i	−0.625658	+	0.780098i	$0.715169\pi$
$110$	−0.532321	+	0.0508305i	−0.0507548	+	0.00484650i
$111$	1.65403	−	11.5040i	0.156994	−	1.09192i
$112$	1.50616	+	2.17520i	0.142319	+	0.205537i
$113$	−1.06079	−	1.22422i	−0.0997910	−	0.115165i	0.703657	−	0.710540i	$-0.251549\pi$
$113$	−1.06079	−	1.22422i	−0.0997910	−	0.115165i	−0.803448	+	0.595375i	$0.797004\pi$
$114$	1.30014	+	2.25190i	0.121769	+	0.210910i
$115$	8.93713	+	10.0257i	0.833391	+	0.934897i
$116$	−2.44515	+	4.23512i	−0.227026	+	0.393221i
$117$	0.0204694	−	0.0591424i	0.00189239	−	0.00546771i
$118$	6.02893	+	3.87456i	0.555008	+	0.356682i
$119$	−5.83438	−	0.0768747i	−0.534837	−	0.00704710i
$120$	−1.16337	+	2.54743i	−0.106201	+	0.232548i
$121$	8.61792	−	6.77721i	0.783448	−	0.616110i
$122$	−5.36159	+	5.11227i	−0.485416	+	0.462843i
$123$	−0.117702	−	2.47086i	−0.0106128	−	0.222790i
$124$	−1.96574	+	2.76050i	−0.176529	+	0.247900i
$125$	5.79638	−	1.70197i	0.518444	−	0.152229i
$126$	2.20671	+	1.45960i	0.196589	+	0.130032i
$127$	−0.768770	+	0.887208i	−0.0682173	+	0.0787270i	−0.788832	−	0.614608i	$-0.789314\pi$
$127$	−0.768770	+	0.887208i	−0.0682173	+	0.0787270i	0.720615	+	0.693335i	$0.243860\pi$
$128$	0.723734	+	0.690079i	0.0639697	+	0.0609949i
$129$	1.70937	+	0.163225i	0.150502	+	0.0143712i
$130$	−0.00833961	−	0.175070i	−0.000731432	−	0.0153547i
$131$	4.76758	+	19.6522i	0.416545	+	1.71702i	0.663657	+	0.748037i	$0.269003\pi$
$131$	4.76758	+	19.6522i	0.416545	+	1.71702i	−0.247112	+	0.968987i	$0.579482\pi$
$132$	0.0271742	+	0.189001i	0.00236521	+	0.0164504i
$133$	5.04117	−	4.68151i	0.437125	−	0.405938i
$134$	0.378287	−	2.63104i	0.0326790	−	0.227288i
$135$	−0.133254	+	2.79734i	−0.0114687	+	0.240757i
$136$	−2.16552	+	0.417371i	−0.185692	+	0.0357892i
$137$	−6.03157	+	10.4470i	−0.515312	+	0.892546i	0.484530	+	0.874775i	$0.338991\pi$
$137$	−6.03157	+	10.4470i	−0.515312	+	0.892546i	−0.999842	+	0.0177718i	$0.994343\pi$
$138$	3.42403	−	3.35797i	0.291473	−	0.285850i
$139$	−16.7333			−1.41930			−0.709648	−	0.704556i	$-0.751146\pi$
$139$	−16.7333			−1.41930			−0.709648	+	0.704556i	$0.751146\pi$
$140$	7.25645	+	1.49798i	0.613282	+	0.126603i
$141$	6.68346	+	4.29520i	0.562849	+	0.361721i
$142$	−0.314707	+	0.125990i	−0.0264096	+	0.0105728i
$143$	−0.00693177	−	0.00973431i	−0.000579664	−	0.000814024i
$144$	0.928368	+	0.371662i	0.0773640	+	0.0309719i
$145$	3.22880	+	13.3093i	0.268137	+	1.10528i
$146$	7.74964	−	4.98039i	0.641365	−	0.412180i
$147$	2.46297	−	6.55239i	0.203142	−	0.540432i
$148$	−11.1516	+	3.27439i	−0.916652	+	0.269153i
$149$	10.8969	+	2.10021i	0.892712	+	0.172056i	0.614924	−	0.788586i	$-0.289187\pi$
$149$	10.8969	+	2.10021i	0.892712	+	0.172056i	0.277788	+	0.960642i	$0.410399\pi$
$150$	0.929810	+	2.68651i	0.0759187	+	0.219353i
$151$	2.97000	−	12.2425i	0.241695	−	0.996281i	−0.713583	−	0.700571i	$-0.752929\pi$
$151$	2.97000	−	12.2425i	0.241695	−	0.996281i	0.955278	−	0.295710i	$-0.0955562\pi$
$152$	1.50831	−	2.11812i	0.122340	−	0.171802i
$153$	−1.85528	+	1.19232i	−0.149991	+	0.0963932i
$154$	0.471437	−	0.181565i	0.0379895	−	0.0146310i
$155$	1.35065	+	9.39400i	0.108487	+	0.754544i
$156$	−0.0623011	+	0.00594903i	−0.00498808	+	0.000476304i
$157$	12.2182	+	9.60849i	0.975118	+	0.766841i	0.972439	−	0.233155i	$-0.0749051\pi$
$157$	12.2182	+	9.60849i	0.975118	+	0.766841i	0.00267822	+	0.999996i	$0.499147\pi$
$158$	−1.61305	+	0.831584i	−0.128327	+	0.0661573i
$159$	3.01071	−	8.69886i	0.238765	−	0.689865i
$160$	2.80051			0.221400
$161$	−10.6804	−	6.85052i	−0.841731	−	0.539897i
$162$	1.00000			0.0785674
$163$	2.16069	−	6.24290i	0.169238	−	0.488982i	−0.828207	−	0.560423i	$-0.810639\pi$
$163$	2.16069	−	6.24290i	0.169238	−	0.488982i	0.997445	+	0.0714412i	$0.0227598\pi$
$164$	−2.19868	+	1.13350i	−0.171688	+	0.0885113i
$165$	0.420336	+	0.330556i	0.0327231	+	0.0257337i
$166$	−1.95168	+	0.186363i	−0.151480	+	0.0144646i
$167$	0.0719267	+	0.500261i	0.00556585	+	0.0387113i	0.992415	−	0.122932i	$-0.0392297\pi$
$167$	0.0719267	+	0.500261i	0.00556585	+	0.0387113i	−0.986849	+	0.161643i	$0.948321\pi$
$168$	0.411000	−	2.61363i	0.0317093	−	0.201646i
$169$	−10.9330	+	7.02621i	−0.841000	+	0.540478i
$170$	−3.58254	+	5.03098i	−0.274768	+	0.385858i
$171$	0.613037	−	2.52697i	0.0468801	−	0.193243i
$172$	−0.561625	−	1.62271i	−0.0428235	−	0.123730i
$173$	22.3445	+	4.30655i	1.69882	+	0.327421i	0.944357	−	0.328921i	$-0.106685\pi$
$173$	22.3445	+	4.30655i	1.69882	+	0.327421i	0.754463	+	0.656342i	$0.227897\pi$
$174$	4.69220	−	1.37776i	0.355715	−	0.104447i
$175$	6.38053	−	3.98272i	0.482322	−	0.301065i
$176$	0.160633	−	0.103232i	0.0121081	−	0.00778143i
$177$	−1.68959	−	6.96458i	−0.126997	−	0.523490i
$178$	0.550935	+	0.220561i	0.0412943	+	0.0165318i
$179$	−7.40092	−	10.3931i	−0.553171	−	0.776819i	0.439426	−	0.898279i	$-0.355182\pi$
$179$	−7.40092	−	10.3931i	−0.553171	−	0.776819i	−0.992596	+	0.121460i	$0.961243\pi$
$180$	2.59991	−	1.04084i	0.193785	−	0.0775800i
$181$	−6.47076	−	4.15850i	−0.480968	−	0.309099i	0.277596	−	0.960698i	$-0.410462\pi$
$181$	−6.47076	−	4.15850i	−0.480968	−	0.309099i	−0.758564	+	0.651599i	$0.774099\pi$
$182$	0.0520906	+	0.157176i	0.00386121	+	0.0116507i
$183$	7.40823			0.547632
$184$	−4.47692	−	1.71966i	−0.330043	−	0.126775i
$185$	−16.2743	+	28.1878i	−1.19651	+	2.07241i
$186$	3.32764	−	0.641350i	0.243994	−	0.0470261i
$187$	−0.0200370	+	0.420628i	−0.00146525	+	0.0307594i
$188$	1.13064	−	7.86378i	0.0824605	−	0.573525i
$189$	−0.589830	−	2.57917i	−0.0429038	−	0.187607i
$190$	−1.03635	−	7.20797i	−0.0751847	−	0.522921i
$191$	4.25645	+	17.5453i	0.307986	+	1.26954i	0.889851	+	0.456251i	$0.150808\pi$
$191$	4.25645	+	17.5453i	0.307986	+	1.26954i	−0.581865	+	0.813286i	$0.697677\pi$
$192$	−0.0475819	−	0.998867i	−0.00343393	−	0.0720870i
$193$	−5.39947	−	0.515587i	−0.388662	−	0.0371127i	−0.101104	−	0.994876i	$-0.532237\pi$
$193$	−5.39947	−	0.515587i	−0.388662	−	0.0371127i	−0.287558	+	0.957763i	$0.592844\pi$
$194$	−8.24834	−	7.86478i	−0.592196	−	0.564658i
$195$	−0.114776	+	0.132459i	−0.00821931	+	0.00948559i
$196$	−6.98342	+	0.481562i	−0.498815	+	0.0343973i
$197$	4.29436	−	1.26094i	0.305960	−	0.0898380i	−0.125148	−	0.992138i	$-0.539941\pi$
$197$	4.29436	−	1.26094i	0.305960	−	0.0898380i	0.431109	+	0.902300i	$0.358123\pi$
$198$	0.110759	−	0.155539i	0.00787128	−	0.0110537i
$199$	0.401414	+	8.42672i	0.0284555	+	0.597354i	0.967395	+	0.253272i	$0.0815068\pi$
$199$	0.401414	+	8.42672i	0.0284555	+	0.597354i	−0.938940	+	0.344082i	$0.888190\pi$
$200$	2.05748	−	1.96180i	0.145486	−	0.138720i
$201$	−2.08941	+	1.64313i	−0.147375	+	0.115897i
$202$	7.26258	−	15.9028i	0.510993	−	1.11892i
$203$	−6.32106	−	11.2893i	−0.443652	−	0.792356i
$204$	1.85528	+	1.19232i	0.129896	+	0.0834789i
$205$	−2.26577	+	6.54651i	−0.158248	+	0.457228i
$206$	−0.648126	+	1.12259i	−0.0451571	+	0.0782144i
$207$	−4.79536	+	0.0674251i	−0.333300	+	0.00468637i
$208$	0.0312922	+	0.0541997i	0.00216973	+	0.00375807i
$209$	−0.325143	−	0.375235i	−0.0224906	−	0.0259556i
$210$	−4.21802	−	6.09167i	−0.291071	−	0.420365i
$211$	0.729719	−	5.07531i	0.0502359	−	0.349399i	−0.949165	−	0.314780i	$-0.898069\pi$
$211$	0.729719	−	5.07531i	0.0502359	−	0.349399i	0.999401	−	0.0346187i	$-0.0110217\pi$
$212$	−9.16346	+	0.875004i	−0.629349	+	0.0600955i
$213$	0.314707	+	0.125990i	0.0215634	+	0.00863268i
$214$	6.25752	−	5.96653i	0.427755	−	0.407864i
$215$	−4.27432	−	2.20356i	−0.291506	−	0.150282i
$216$	−0.415415	−	0.909632i	−0.0282654	−	0.0618926i
$217$	−3.61689	−	8.20425i	−0.245531	−	0.556941i
$218$	3.97784	−	4.59067i	0.269413	−	0.310920i
$219$	−9.04554	−	1.74339i	−0.611241	−	0.117807i
$220$	0.126070	−	0.519669i	0.00849966	−	0.0350361i
$221$	−0.137397	−	0.0131199i	−0.00924235	−	0.000882538i
$222$	10.3304	+	5.32567i	0.693328	+	0.357435i
$223$	−13.3652	−	3.92437i	−0.894999	−	0.262796i	−0.198285	−	0.980144i	$-0.563537\pi$
$223$	−13.3652	−	3.92437i	−0.894999	−	0.262796i	−0.696714	+	0.717349i	$0.745355\pi$
$224$	−2.54818	+	0.711884i	−0.170257	+	0.0475647i
$225$	1.18097	−	2.58596i	0.0787312	−	0.172397i
$226$	1.50384	−	0.602047i	0.100034	−	0.0400476i
$227$	−1.22427	+	0.631157i	−0.0812579	+	0.0418914i	−0.498377	−	0.866961i	$-0.666070\pi$
$227$	−1.22427	+	0.631157i	−0.0812579	+	0.0418914i	0.417119	+	0.908852i	$0.363040\pi$
$228$	−2.55328	+	0.492105i	−0.169095	+	0.0325904i
$229$	5.89154	+	10.2045i	0.389324	+	0.674329i	0.992359	−	0.123386i	$-0.0393753\pi$
$229$	5.89154	+	10.2045i	0.389324	+	0.674329i	−0.603035	+	0.797715i	$0.706042\pi$
$230$	−12.3973	+	5.16652i	−0.817453	+	0.340670i
$231$	−0.466489	−	0.193924i	−0.0306927	−	0.0127592i
$232$	−3.20246	−	3.69584i	−0.210252	−	0.242644i
$233$	0.594025	−	12.4701i	0.0389159	−	0.816945i	−0.892072	−	0.451894i	$-0.850749\pi$
$233$	0.594025	−	12.4701i	0.0389159	−	0.816945i	0.930988	−	0.365051i	$-0.118948\pi$
$234$	0.0491947	+	0.0386871i	0.00321596	+	0.00252906i
$235$	−12.9057	−	18.1236i	−0.841877	−	1.18225i
$236$	−5.63333	+	4.43010i	−0.366698	+	0.288375i
$237$	1.74128	+	0.511285i	0.113108	+	0.0332115i
$238$	1.98088	−	5.48835i	0.128402	−	0.355757i
$239$	7.49579	+	16.4135i	0.484862	+	1.06170i	0.981098	+	0.193513i	$0.0619880\pi$
$239$	7.49579	+	16.4135i	0.484862	+	1.06170i	−0.496235	+	0.868188i	$0.665285\pi$
$240$	−2.02683	−	1.93257i	−0.130831	−	0.124747i
$241$	3.86282	+	11.1609i	0.248826	+	0.718936i	0.998375	+	0.0569871i	$0.0181494\pi$
$241$	3.86282	+	11.1609i	0.248826	+	0.718936i	−0.749549	+	0.661949i	$0.769729\pi$
$242$	3.58582	+	10.3606i	0.230505	+	0.666002i
$243$	−0.723734	−	0.690079i	−0.0464276	−	0.0442686i
$244$	−3.07749	−	6.73877i	−0.197016	−	0.431405i
$245$	−13.2235	+	14.4720i	−0.844819	+	0.924583i
$246$	2.37346	+	0.696911i	0.151326	+	0.0444334i
$247$	0.127920	−	0.100597i	0.00813933	−	0.00640084i
$248$	−1.96574	−	2.76050i	−0.124825	−	0.175292i
$249$	1.54110	+	1.21194i	0.0976634	+	0.0768034i
$250$	−0.287446	+	6.03424i	−0.0181797	+	0.381639i
$251$	15.7889	+	18.2214i	0.996586	+	1.15012i	0.988663	+	0.150153i	$0.0479766\pi$
$251$	15.7889	+	18.2214i	0.996586	+	1.15012i	0.00792308	+	0.999969i	$0.497478\pi$
$252$	−2.10107	+	1.60795i	−0.132355	+	0.101292i
$253$	−0.520640	+	0.753332i	−0.0327324	+	0.0473616i
$254$	−0.586972	−	1.01667i	−0.0368299	−	0.0637913i
$255$	6.06458	−	1.16885i	0.379779	−	0.0731963i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−22.2480	+	8.90674i	−1.38779	+	0.555587i	−0.940803	−	0.338954i	$-0.889927\pi$
$257$	−22.2480	+	8.90674i	−1.38779	+	0.555587i	−0.446986	+	0.894541i	$0.647503\pi$
$258$	−0.713330	+	1.56197i	−0.0444100	+	0.0972443i
$259$	7.64263	−	29.7849i	0.474890	−	1.85075i
$260$	0.168169	+	0.0493788i	0.0104294	+	0.00306235i
$261$	−4.34667	−	2.24086i	−0.269052	−	0.138706i
$262$	−20.1307	−	1.92225i	−1.24368	−	0.118757i
$263$	2.86092	−	11.7929i	0.176412	−	0.727180i	−0.813027	−	0.582227i	$-0.802182\pi$
$263$	2.86092	−	11.7929i	0.176412	−	0.727180i	0.989439	−	0.144953i	$-0.0463032\pi$
$264$	−0.187494	−	0.0361365i	−0.0115395	−	0.00222405i
$265$	−16.8817	+	19.4825i	−1.03704	+	1.19680i
$266$	2.77522	+	6.29508i	0.170160	+	0.385976i
$267$	−0.246526	−	0.539817i	−0.0150871	−	0.0330362i
$268$	2.36261	+	1.21801i	0.144320	+	0.0744019i
$269$	−17.1840	+	16.3849i	−1.04773	+	0.999004i	−0.0477253	+	0.998860i	$0.515197\pi$
$269$	−17.1840	+	16.3849i	−1.04773	+	0.999004i	−1.00000		0.000143524i	$0.999954\pi$
$270$	−2.59991	−	1.04084i	−0.158225	−	0.0633438i
$271$	−4.32018	+	0.412527i	−0.262432	+	0.0250592i	−0.225443	−	0.974256i	$-0.572383\pi$
$271$	−4.32018	+	0.412527i	−0.262432	+	0.0250592i	−0.0369894	+	0.999316i	$0.511777\pi$
$272$	0.313858	−	2.18293i	0.0190304	−	0.132360i
$273$	0.0707641	−	0.149700i	0.00428284	−	0.00906027i
$274$	−7.89968	−	9.11671i	−0.477237	−	0.550761i
$275$	−0.271415	−	0.470104i	−0.0163669	−	0.0283483i
$276$	2.05340	+	4.33400i	0.123600	+	0.260876i
$277$	−8.58362	+	14.8673i	−0.515740	+	0.893288i	0.484093	+	0.875016i	$0.339150\pi$
$277$	−8.58362	+	14.8673i	−0.515740	+	0.893288i	−0.999833	+	0.0182712i	$0.994184\pi$
$278$	5.47291	−	15.8129i	0.328244	−	0.948398i
$279$	−2.85091	−	1.83217i	−0.170679	−	0.109689i
$280$	−3.78895	+	6.36741i	−0.226433	+	0.380526i
$281$	1.00791	−	2.20702i	0.0601270	−	0.131660i	−0.877183	−	0.480156i	$-0.840580\pi$
$281$	1.00791	−	2.20702i	0.0601270	−	0.131660i	0.937310	+	0.348496i	$0.113307\pi$
$282$	−6.24491	+	4.91105i	−0.371879	+	0.292449i
$283$	16.3897	−	15.6276i	0.974269	−	0.928963i	−0.0232241	−	0.999730i	$-0.507393\pi$
$283$	16.3897	−	15.6276i	0.974269	−	0.928963i	0.997493	+	0.0707669i	$0.0225446\pi$
$284$	−0.0161298	−	0.338606i	−0.000957127	−	0.0200926i
$285$	−4.22403	+	5.93182i	−0.250210	+	0.351370i
$286$	0.0114661	−	0.00336675i	0.000678004	−	0.000199080i
$287$	0.397511	−	6.53261i	0.0234643	−	0.385608i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	−8.78346	−	8.37501i	−0.516674	−	0.492648i
$290$	−13.6333	−	1.30182i	−0.800576	−	0.0764457i
$291$	0.542287	+	11.3840i	0.0317894	+	0.667343i
$292$	2.17181	+	8.95234i	0.127096	+	0.523896i
$293$	−0.450175	−	3.13104i	−0.0262995	−	0.182917i	0.972437	−	0.233165i	$-0.0749081\pi$
$293$	−0.450175	−	3.13104i	−0.0262995	−	0.182917i	−0.998737	+	0.0502475i	$0.983999\pi$
$294$	5.38645	+	4.47059i	0.314144	+	0.260730i
$295$	−2.85628	+	19.8659i	−0.166299	+	1.15663i
$296$	0.553013	−	11.6092i	0.0321433	−	0.674770i
$297$	−0.187494	+	0.0361365i	−0.0108795	+	0.00209685i
$298$	−5.54874	+	9.61070i	−0.321430	+	0.556733i
$299$	−0.238515	−	0.182202i	−0.0137937	−	0.0105370i
$300$	−2.84286			−0.164133
$301$	4.44933	+	0.918497i	0.256455	+	0.0529413i
$302$	10.5978	+	6.81078i	0.609834	+	0.391917i
$303$	−16.2304	+	6.49767i	−0.932411	+	0.373281i
$304$	1.50831	+	2.11812i	0.0865073	+	0.121482i
$305$	−19.2607	−	7.71082i	−1.10286	−	0.441520i
$306$	−0.519938	−	2.14321i	−0.0297229	−	0.122519i
$307$	1.92320	−	1.23597i	0.109763	−	0.0705405i	−0.484608	−	0.874732i	$-0.661038\pi$
$307$	1.92320	−	1.23597i	0.109763	−	0.0705405i	0.594371	+	0.804191i	$0.297401\pi$
$308$	0.0173875	+	0.504892i	0.000990746	+	0.0287689i
$309$	1.24374	−	0.365196i	0.0707542	−	0.0207753i
$310$	−9.31910	−	1.79611i	−0.529289	−	0.102012i
$311$	1.22777	+	3.54741i	0.0696204	+	0.201155i	0.974443	−	0.224633i	$-0.0721182\pi$
$311$	1.22777	+	3.54741i	0.0696204	+	0.201155i	−0.904823	+	0.425788i	$0.859997\pi$
$312$	0.0147548	−	0.0608203i	0.000835329	−	0.00344327i
$313$	−16.7892	+	23.5771i	−0.948981	+	1.33266i	−0.00594010	+	0.999982i	$0.501891\pi$
$313$	−16.7892	+	23.5771i	−0.948981	+	1.33266i	−0.943041	+	0.332676i	$0.892049\pi$
$314$	−13.0762	+	8.40357i	−0.737933	+	0.474241i
$315$	−1.15101	+	7.31951i	−0.0648521	+	0.412408i
$316$	−0.258271	−	1.79632i	−0.0145289	−	0.101051i
$317$	0.981102	−	0.0936839i	0.0551042	−	0.00526181i	−0.0674675	−	0.997721i	$-0.521492\pi$
$317$	0.981102	−	0.0936839i	0.0551042	−	0.00526181i	0.122572	+	0.992460i	$0.460886\pi$
$318$	7.23573	+	5.69024i	0.405759	+	0.319093i
$319$	−0.829972	+	0.427880i	−0.0464695	+	0.0239567i
$320$	−0.915958	+	2.64649i	−0.0512036	+	0.147943i
$321$	−8.64616			−0.482581
$322$	9.96696	−	7.85237i	0.555437	−	0.437596i
$323$	−5.73458			−0.319081
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	0.158141	−	0.0815273i	0.00877208	−	0.00452232i
$326$	5.19285	+	4.08371i	0.287606	+	0.226176i
$327$	−6.04683	+	0.577402i	−0.334390	+	0.0319304i
$328$	−0.352039	−	2.44848i	−0.0194381	−	0.135195i
$329$	16.3499	+	13.2100i	0.901397	+	0.728290i
$330$	−0.449854	+	0.289103i	−0.0247636	+	0.0159146i
$331$	5.68920	−	7.98936i	0.312707	−	0.439135i	−0.628073	−	0.778155i	$-0.716156\pi$
$331$	5.68920	−	7.98936i	0.312707	−	0.439135i	0.940779	+	0.339020i	$0.110095\pi$
$332$	0.462219	−	1.90529i	0.0253676	−	0.104567i
$333$	−3.80130	−	10.9831i	−0.208310	−	0.601872i
$334$	−0.496272	−	0.0956486i	−0.0271548	−	0.00523366i
$335$	7.14250	−	2.09723i	0.390237	−	0.114584i
$336$	2.33546	+	1.24323i	0.127410	+	0.0678238i
$337$	−11.0122	+	7.07713i	−0.599874	+	0.385516i	−0.805048	−	0.593210i	$-0.797860\pi$
$337$	−11.0122	+	7.07713i	−0.599874	+	0.385516i	0.205174	+	0.978726i	$0.434224\pi$
$338$	−3.06394	−	12.6297i	−0.166657	−	0.686968i
$339$	−1.50384	−	0.602047i	−0.0816774	−	0.0326987i
$340$	−3.58254	−	5.03098i	−0.194291	−	0.272843i
$341$	−0.600736	+	0.240498i	−0.0325317	+	0.0130237i
$342$	2.18749	+	1.40581i	0.118286	+	0.0760177i
$343$	8.35329	−	16.5294i	0.451036	−	0.892506i
$344$	1.71715			0.0925825
$345$	12.5377	+	4.81592i	0.675005	+	0.259281i
$346$	−11.3779	+	19.7070i	−0.611678	+	1.05946i
$347$	17.2988	−	3.33407i	0.928647	−	0.178982i	0.297568	−	0.954701i	$-0.403825\pi$
$347$	17.2988	−	3.33407i	0.928647	−	0.178982i	0.631079	+	0.775719i	$0.282612\pi$
$348$	−0.232690	+	4.88476i	−0.0124735	+	0.261850i
$349$	0.736705	−	5.12389i	0.0394349	−	0.274276i	−0.960558	−	0.278080i	$-0.910302\pi$
$349$	0.736705	−	5.12389i	0.0394349	−	0.274276i	0.999993	+	0.00380441i	$0.00121098\pi$
$350$	1.67681	+	7.33222i	0.0896291	+	0.391924i
$351$	−0.00890670	−	0.0619474i	−0.000475404	−	0.00330651i
$352$	0.0450169	+	0.185562i	0.00239941	+	0.00989049i
$353$	0.178699	+	3.75135i	0.00951119	+	0.199664i	0.998622	+	0.0524885i	$0.0167153\pi$
$353$	0.178699	+	3.75135i	0.00951119	+	0.199664i	−0.989110	+	0.147176i	$0.952982\pi$
$354$	7.13415	+	0.681228i	0.379176	+	0.0362069i
$355$	−0.687073	−	0.655123i	−0.0364661	−	0.0347703i
$356$	−0.388624	+	0.448496i	−0.0205970	+	0.0237702i
$357$	−5.22103	+	2.60514i	−0.276326	+	0.137879i
$358$	12.2421	−	3.59461i	0.647016	−	0.189981i
$359$	10.9090	−	15.3196i	0.575757	−	0.808538i	−0.419299	−	0.907848i	$-0.637724\pi$
$359$	10.9090	−	15.3196i	0.575757	−	0.808538i	0.995057	+	0.0993099i	$0.0316635\pi$
$360$	0.133254	+	2.79734i	0.00702309	+	0.147433i
$361$	−8.85748	+	8.44559i	−0.466183	+	0.444505i
$362$	6.04617	−	4.75476i	0.317779	−	0.249905i
$363$	4.55442	−	9.97279i	0.239045	−	0.523436i
$364$	−0.165569	−	0.00218156i	−0.00867815	−	0.000114345i
$365$	21.7030	+	13.9476i	1.13598	+	0.730053i
$366$	−2.42300	+	7.00079i	−0.126652	+	0.365937i
$367$	10.4799	−	18.1517i	0.547045	−	0.947509i	−0.451430	−	0.892306i	$-0.649086\pi$
$367$	10.4799	−	18.1517i	0.547045	−	0.947509i	0.998475	−	0.0552029i	$-0.0175806\pi$
$368$	3.08933	−	3.66824i	0.161043	−	0.191220i
$369$	−1.23683	−	2.14225i	−0.0643869	−	0.111521i
$370$	−21.3147	−	24.5985i	−1.10810	−	1.27882i
$371$	10.4082	−	22.0184i	0.540368	−	1.14314i
$372$	−0.482288	+	3.35439i	−0.0250055	+	0.173917i
$373$	26.8167	−	2.56068i	1.38851	−	0.132587i	0.626134	−	0.779716i	$-0.284636\pi$
$373$	26.8167	−	2.56068i	1.38851	−	0.132587i	0.762381	+	0.647129i	$0.224030\pi$
$374$	−0.390940	−	0.156509i	−0.0202150	−	0.00809288i
$375$	4.37214	−	4.16882i	0.225776	−	0.215277i
$376$	7.06148	+	3.64045i	0.364168	+	0.187742i
$377$	−0.127140	−	0.278399i	−0.00654807	−	0.0143383i
$378$	2.63023	+	0.286173i	0.135284	+	0.0147191i
$379$	−4.92054	+	5.67861i	−0.252751	+	0.291690i	−0.867919	−	0.496706i	$-0.834543\pi$
$379$	−4.92054	+	5.67861i	−0.252751	+	0.291690i	0.615168	+	0.788396i	$0.289088\pi$
$380$	7.15049	+	1.37814i	0.366813	+	0.0706973i
$381$	−0.276768	+	1.14085i	−0.0141792	+	0.0584477i
$382$	−17.9725	−	1.71617i	−0.919554	−	0.0878068i
$383$	−23.1064	−	11.9122i	−1.18068	−	0.608684i	−0.247781	−	0.968816i	$-0.579701\pi$
$383$	−23.1064	−	11.9122i	−1.18068	−	0.608684i	−0.932901	+	0.360132i	$0.882732\pi$
$384$	0.959493	+	0.281733i	0.0489639	+	0.0143771i
$385$	1.01098	+	0.989726i	0.0515245	+	0.0504411i
$386$	2.25322	−	4.93387i	0.114686	−	0.251127i
$387$	1.59415	−	0.638200i	0.0810350	−	0.0324415i
$388$	10.1300	−	5.22237i	0.514272	−	0.265126i
$389$	23.6710	−	4.56222i	1.20017	−	0.231314i	0.450286	−	0.892884i	$-0.351322\pi$
$389$	23.6710	−	4.56222i	1.20017	−	0.231314i	0.749883	+	0.661571i	$0.230110\pi$
$390$	−0.0876342	−	0.151787i	−0.00443753	−	0.00768603i
$391$	2.63779	+	10.2424i	0.133399	+	0.517981i
$392$	1.82898	−	6.75684i	0.0923772	−	0.341272i
$393$	13.2428	+	15.2830i	0.668009	+	0.770924i
$394$	−0.212960	+	4.47058i	−0.0107288	+	0.225225i
$395$	−3.99499	−	3.14169i	−0.201010	−	0.158076i
$396$	0.110759	+	0.155539i	0.00556583	+	0.00781612i
$397$	12.3176	−	9.68670i	0.618205	−	0.486162i	−0.259257	−	0.965808i	$-0.583478\pi$
$397$	12.3176	−	9.68670i	0.618205	−	0.486162i	0.877462	+	0.479647i	$0.159235\pi$
$398$	−8.09454	−	2.37677i	−0.405743	−	0.119137i
$399$	2.33558	−	6.47109i	0.116925	−	0.323959i
$400$	1.18097	+	2.58596i	0.0590484	+	0.129298i
$401$	−11.1953	−	10.6747i	−0.559065	−	0.533068i	0.356996	−	0.934106i	$-0.383801\pi$
$401$	−11.1953	−	10.6747i	−0.559065	−	0.533068i	−0.916061	+	0.401038i	$0.868649\pi$
$402$	−0.869379	−	2.51191i	−0.0433607	−	0.125283i
$403$	−0.0693683	−	0.200426i	−0.00345548	−	0.00998395i
$404$	12.6528	+	12.0645i	0.629502	+	0.600229i
$405$	1.16337	+	2.54743i	0.0578085	+	0.126583i
$406$	12.7358	−	2.28103i	0.632069	−	0.113206i
$407$	−2.12933	−	0.625227i	−0.105547	−	0.0309914i
$408$	−1.73354	+	1.36327i	−0.0858233	+	0.0674922i
$409$	15.9370	+	22.3804i	0.788036	+	1.10664i	0.991822	+	0.127626i	$0.0407357\pi$
$409$	15.9370	+	22.3804i	0.788036	+	1.10664i	−0.203787	+	0.979015i	$0.565325\pi$
$410$	−5.44540	−	4.28231i	−0.268929	−	0.211488i
$411$	−0.573987	+	12.0495i	−0.0283127	+	0.594357i
$412$	−0.848865	−	0.979642i	−0.0418206	−	0.0482635i
$413$	−2.45093	−	18.8020i	−0.120603	−	0.925184i
$414$	1.50469	−	4.55367i	0.0739515	−	0.223801i
$415$	−2.74528	−	4.75497i	−0.134761	−	0.233412i
$416$	−0.0614535	+	0.0118442i	−0.00301300	+	0.000580709i
$417$	−14.8731	+	7.66763i	−0.728340	+	0.375485i
$418$	0.460942	−	0.184533i	0.0225454	−	0.00902581i
$419$	12.8609	−	28.1613i	0.628294	−	1.37577i	−0.281036	−	0.959697i	$-0.590678\pi$
$419$	12.8609	−	28.1613i	0.628294	−	1.37577i	0.909330	−	0.416075i	$-0.136595\pi$
$420$	7.13621	−	1.99364i	0.348211	−	0.0972796i
$421$	28.2327	+	8.28987i	1.37598	+	0.404024i	0.884368	−	0.466791i	$-0.154590\pi$
$421$	28.2327	+	8.28987i	1.37598	+	0.404024i	0.491611	+	0.870815i	$0.336408\pi$
$422$	4.55750	+	2.34956i	0.221856	+	0.114375i
$423$	7.90867	+	0.755187i	0.384533	+	0.0367184i
$424$	2.17019	−	8.94566i	0.105394	−	0.434440i
$425$	−6.15629	−	1.18653i	−0.298624	−	0.0575551i
$426$	−0.221991	+	0.256191i	−0.0107555	+	0.0124125i
$427$	19.4853	+	2.12003i	0.942962	+	0.102596i
$428$	3.59174	+	7.86482i	0.173613	+	0.380161i
$429$	−0.0106217	−	0.00547588i	−0.000512822	−	0.000264378i
$430$	3.48036	−	3.31852i	0.167838	−	0.160033i
$431$	1.26814	+	0.507687i	0.0610842	+	0.0244544i	0.402003	−	0.915638i	$-0.368314\pi$
$431$	1.26814	+	0.507687i	0.0610842	+	0.0244544i	−0.340919	+	0.940093i	$0.610738\pi$
$432$	0.995472	−	0.0950560i	0.0478947	−	0.00457339i
$433$	−5.13304	+	35.7011i	−0.246678	+	1.71568i	0.370476	+	0.928842i	$0.379194\pi$
$433$	−5.13304	+	35.7011i	−0.246678	+	1.71568i	−0.617154	+	0.786842i	$0.711715\pi$
$434$	8.93599	−	0.734617i	0.428941	−	0.0352628i
$435$	8.96853	+	10.3502i	0.430008	+	0.496256i
$436$	3.03717	+	5.26053i	0.145454	+	0.251933i
$437$	−10.5846	−	6.59388i	−0.506329	−	0.315428i
$438$	4.60601	−	7.97784i	0.220084	−	0.381196i
$439$	5.09246	−	14.7137i	0.243050	−	0.702247i	−0.755823	−	0.654776i	$-0.772763\pi$
$439$	5.09246	−	14.7137i	0.243050	−	0.702247i	0.998873	−	0.0474703i	$-0.0151160\pi$
$440$	0.449854	+	0.289103i	0.0214459	+	0.0137825i
$441$	−0.813301	−	6.95259i	−0.0387286	−	0.331076i
$442$	0.0573366	−	0.125550i	0.00272722	−	0.00597179i
$443$	29.6536	−	23.3199i	1.40889	−	1.10796i	0.430169	−	0.902748i	$-0.358454\pi$
$443$	29.6536	−	23.3199i	1.40889	−	1.10796i	0.978718	−	0.205212i	$-0.0657884\pi$
$444$	−8.41149	+	8.02034i	−0.399191	+	0.380628i
$445$	0.0790787	+	1.66007i	0.00374869	+	0.0786947i
$446$	8.07986	−	11.3466i	0.382593	−	0.537276i
$447$	10.6480	−	3.12652i	0.503631	−	0.147879i
$448$	0.160697	−	2.64087i	0.00759224	−	0.124769i
$449$	−0.268525	+	0.309895i	−0.0126725	+	0.0146248i	−0.762050	−	0.647518i	$-0.775807\pi$
$449$	−0.268525	+	0.309895i	−0.0126725	+	0.0146248i	0.749378	+	0.662142i	$0.230353\pi$
$450$	2.05748	+	1.96180i	0.0969904	+	0.0924802i
$451$	−0.470193	−	0.0448980i	−0.0221405	−	0.00211417i
$452$	0.0770768	+	1.61804i	0.00362539	+	0.0761062i
$453$	−2.97000	−	12.2425i	−0.139543	−	0.575203i
$454$	−0.196023	−	1.36337i	−0.00919983	−	0.0639862i
$455$	−0.339795	+	0.315552i	−0.0159298	+	0.0147933i
$456$	0.370057	−	2.57380i	0.0173295	−	0.120529i
$457$	−1.43042	+	30.0281i	−0.0669120	+	1.40466i	0.676805	+	0.736162i	$0.263364\pi$
$457$	−1.43042	+	30.0281i	−0.0669120	+	1.40466i	−0.743717	+	0.668494i	$0.766939\pi$
$458$	−11.5701	+	2.22996i	−0.540638	+	0.104199i
$459$	−1.10269	+	1.90991i	−0.0514691	+	0.0891472i
$460$	−0.827610	−	13.4053i	−0.0385875	−	0.625023i
$461$	14.6175			0.680804			0.340402	−	0.940280i	$-0.389437\pi$
$461$	14.6175			0.680804			0.340402	+	0.940280i	$0.389437\pi$
$462$	0.335832	−	0.377407i	0.0156243	−	0.0175585i
$463$	16.1668	+	10.3898i	0.751337	+	0.482855i	0.859409	−	0.511288i	$-0.170832\pi$
$463$	16.1668	+	10.3898i	0.751337	+	0.482855i	−0.108073	+	0.994143i	$0.534468\pi$
$464$	4.53999	−	1.81754i	0.210764	−	0.0843771i
$465$	5.50509	+	7.73082i	0.255292	+	0.358508i
$466$	11.5900	+	4.63993i	0.536896	+	0.214941i
$467$	4.12739	+	17.0133i	0.190993	+	0.787282i	0.984014	+	0.178089i	$0.0569915\pi$
$467$	4.12739	+	17.0133i	0.190993	+	0.787282i	−0.793022	+	0.609193i	$0.791493\pi$
$468$	−0.0526494	+	0.0338357i	−0.00243372	+	0.00156406i
$469$	−5.96584	+	3.72387i	−0.275477	+	0.171952i
$470$	21.3478	−	6.26829i	0.984702	−	0.289135i
$471$	15.2628	+	2.94167i	0.703274	+	0.135545i
$472$	−2.34396	−	6.77244i	−0.107890	−	0.311727i
$473$	0.0773007	−	0.318638i	0.00355429	−	0.0146510i
$474$	−1.05268	+	1.47828i	−0.0483512	+	0.0678998i
$475$	6.21873	−	3.99654i	0.285335	−	0.183374i
$476$	4.53861	+	3.66700i	0.208027	+	0.168077i
$477$	−1.31003	−	9.11144i	−0.0599821	−	0.417184i
$478$	−17.9624	+	1.71520i	−0.821581	+	0.0784515i
$479$	−5.23816	−	4.11934i	−0.239338	−	0.188217i	0.491285	−	0.870999i	$-0.336528\pi$
$479$	−5.23816	−	4.11934i	−0.239338	−	0.188217i	−0.730622	+	0.682782i	$0.760770\pi$
$480$	2.48919	−	1.28327i	0.113616	−	0.0585729i
$481$	0.237902	−	0.687373i	0.0108474	−	0.0313415i
$482$	−11.8105			−0.537952
$483$	−12.6322	−	1.19496i	−0.574784	−	0.0543724i
$484$	−10.9635			−0.498343
$485$	10.4391	−	30.1618i	0.474015	−	1.36958i
$486$	0.888835	−	0.458227i	0.0403184	−	0.0207856i
$487$	−7.40314	−	5.82190i	−0.335468	−	0.263815i	0.436187	−	0.899856i	$-0.356329\pi$
$487$	−7.40314	−	5.82190i	−0.335468	−	0.263815i	−0.771656	+	0.636041i	$0.780571\pi$
$488$	7.37469	−	0.704197i	0.333836	−	0.0318775i
$489$	−0.940166	−	6.53900i	−0.0425158	−	0.295704i
$490$	−9.35108	−	17.2296i	−0.422439	−	0.778352i
$491$	19.6726	−	12.6428i	0.887813	−	0.570563i	−0.0153399	−	0.999882i	$-0.504883\pi$
$491$	19.6726	−	12.6428i	0.887813	−	0.570563i	0.903153	+	0.429320i	$0.141247\pi$
$492$	−1.43487	+	2.01499i	−0.0646887	+	0.0908426i
$493$	−2.54265	+	10.4809i	−0.114515	+	0.472038i
$494$	0.0532259	+	0.153786i	0.00239475	+	0.00691917i
$495$	0.525079	+	0.101201i	0.0236005	+	0.00454863i
$496$	3.25161	−	0.954758i	0.146002	−	0.0428699i
$497$	0.791697	+	0.421443i	0.0355125	+	0.0189043i
$498$	−1.64933	+	1.05996i	−0.0739081	+	0.0474978i
$499$	−5.52159	−	22.7603i	−0.247181	−	1.01889i	−0.951167	−	0.308678i	$-0.900113\pi$
$499$	−5.52159	−	22.7603i	−0.247181	−	1.01889i	0.703986	−	0.710214i	$-0.251402\pi$
$500$	−5.60835	−	2.24524i	−0.250813	−	0.100410i
$501$	0.293164	+	0.411691i	0.0130976	+	0.0183930i
$502$	−22.3832	+	8.96089i	−0.999012	+	0.399944i
$503$	13.0139	+	8.36354i	0.580262	+	0.372912i	0.797602	−	0.603184i	$-0.206102\pi$
$503$	13.0139	+	8.36354i	0.580262	+	0.372912i	−0.217340	+	0.976096i	$0.569738\pi$
$504$	−0.832325	−	2.51142i	−0.0370747	−	0.111868i
$505$	48.9605			2.17872
$506$	−0.541615	−	0.738396i	−0.0240777	−	0.0328257i
$507$	−6.49804	+	11.2549i	−0.288588	+	0.499849i
$508$	1.15273	−	0.222170i	0.0511441	−	0.00985722i
$509$	1.13375	−	23.8003i	0.0502524	−	1.05493i	−0.823118	−	0.567871i	$-0.807767\pi$
$509$	1.13375	−	23.8003i	0.0502524	−	1.05493i	0.873370	−	0.487057i	$-0.161930\pi$
$510$	−0.878963	+	6.11332i	−0.0389212	+	0.270703i
$511$	−23.2929	−	7.17409i	−1.03042	−	0.317363i
$512$	−0.142315	−	0.989821i	−0.00628949	−	0.0437443i
$513$	−0.613037	−	2.52697i	−0.0270663	−	0.111569i
$514$	−1.14028	−	23.9374i	−0.0502956	−	1.05584i
$515$	−3.61373	−	0.345069i	−0.159240	−	0.0152056i
$516$	−1.24276	−	1.18497i	−0.0547094	−	0.0521653i
$517$	0.993415	−	1.14646i	0.0436903	−	0.0504213i
$518$	25.6471	+	16.9640i	1.12687	+	0.745355i
$519$	21.8340	−	6.41103i	0.958404	−	0.281413i
$520$	−0.101666	+	0.142769i	−0.00445834	+	0.00626086i
$521$	−0.825982	−	17.3395i	−0.0361869	−	0.759657i	−0.941926	−	0.335821i	$-0.890986\pi$
$521$	−0.825982	−	17.3395i	−0.0361869	−	0.759657i	0.905739	−	0.423836i	$-0.139317\pi$
$522$	3.53927	−	3.37469i	0.154910	−	0.147706i
$523$	−20.8426	+	16.3908i	−0.911384	+	0.716721i	−0.959377	−	0.282127i	$-0.908960\pi$
$523$	−20.8426	+	16.3908i	−0.911384	+	0.716721i	0.0479926	+	0.998848i	$0.484718\pi$
$524$	8.40063	−	18.3948i	0.366983	−	0.803581i
$525$	3.84625	−	6.46371i	0.167864	−	0.282099i
$526$	10.2086	+	6.56064i	0.445114	+	0.286058i
$527$	−2.44443	+	7.06272i	−0.106481	+	0.307657i
$528$	0.0954722	−	0.165363i	0.00415490	−	0.00719649i
$529$	−6.90850	+	21.9379i	−0.300370	+	0.953823i
$530$	−12.8895	−	22.3254i	−0.559886	−	0.969751i
$531$	−4.69312	−	5.41615i	−0.203664	−	0.235041i
$532$	−6.85654	+	0.563668i	−0.297269	+	0.0244381i
$533$	0.0220322	−	0.153237i	0.000954319	−	0.00663743i
$534$	0.590758	−	0.0564105i	0.0255646	−	0.00244112i
$535$	22.4792	+	8.99931i	0.971860	+	0.389074i
$536$	−1.92376	+	1.83430i	−0.0830937	+	0.0792296i
$537$	−11.3406	−	5.84649i	−0.489383	−	0.252295i
$538$	−9.86340	−	21.5978i	−0.425241	−	0.931149i
$539$	−1.17148	−	0.643560i	−0.0504591	−	0.0277201i
$540$	1.83395	−	2.11649i	0.0789204	−	0.0910790i
$541$	−26.6504	−	5.13644i	−1.14579	−	0.220833i	−0.419192	−	0.907897i	$-0.637687\pi$
$541$	−26.6504	−	5.13644i	−1.14579	−	0.220833i	−0.726596	+	0.687065i	$0.758899\pi$
$542$	1.02315	−	4.21750i	0.0439482	−	0.181157i
$543$	−7.65697	−	0.731152i	−0.328592	−	0.0313768i
$544$	1.96022	+	1.01056i	0.0840437	+	0.0433275i
$545$	16.3222	+	4.79262i	0.699165	+	0.205293i
$546$	0.118322	+	0.115834i	0.00506372	+	0.00495725i
$547$	−11.3684	+	24.8934i	−0.486078	+	1.06436i	0.494669	+	0.869081i	$0.335289\pi$
$547$	−11.3684	+	24.8934i	−0.486078	+	1.06436i	−0.980747	+	0.195281i	$0.937438\pi$
$548$	11.1990	−	4.48342i	0.478399	−	0.191522i
$549$	6.58470	−	3.39465i	0.281028	−	0.144880i
$550$	0.533020	−	0.102731i	0.0227280	−	0.00438047i
$551$	−6.35805	−	11.0125i	−0.270862	−	0.469147i
$552$	−4.76723	+	0.522948i	−0.202907	+	0.0222581i
$553$	4.43364	+	1.84310i	0.188538	+	0.0783767i
$554$	−11.2422	−	12.9741i	−0.477633	−	0.551218i
$555$	−1.54872	+	32.5116i	−0.0657395	+	1.38004i
$556$	13.1532	+	10.3438i	0.557821	+	0.438676i
$557$	14.2046	+	19.9475i	0.601867	+	0.845204i	0.997311	−	0.0732861i	$-0.0233486\pi$
$557$	14.2046	+	19.9475i	0.601867	+	0.845204i	−0.395444	+	0.918490i	$0.629409\pi$
$558$	2.66384	−	2.09487i	0.112769	−	0.0886828i
$559$	0.103114	+	0.0302769i	0.00436124	+	0.00128058i
$560$	−4.77797	−	5.66314i	−0.201906	−	0.239311i
$561$	0.174933	+	0.383051i	0.00738569	+	0.0161724i
$562$	1.75598	+	1.67432i	0.0740715	+	0.0706270i
$563$	−3.41539	−	9.86813i	−0.143942	−	0.415892i	0.849867	−	0.526997i	$-0.176682\pi$
$563$	−3.41539	−	9.86813i	−0.143942	−	0.415892i	−0.993809	+	0.111105i	$0.964561\pi$
$564$	−2.59844	−	7.50770i	−0.109414	−	0.316131i
$565$	3.28320	+	3.13053i	0.138125	+	0.131702i
$566$	9.40752	+	20.5996i	0.395428	+	0.865866i
$567$	−1.70610	−	2.02218i	−0.0716497	−	0.0849235i
$568$	0.325258	+	0.0955045i	0.0136475	+	0.00400728i
$569$	28.9405	−	22.7591i	1.21325	−	0.954110i	0.213511	−	0.976941i	$-0.431510\pi$
$569$	28.9405	−	22.7591i	1.21325	−	0.954110i	0.999739	+	0.0228303i	$0.00726774\pi$
$570$	−4.22403	−	5.93182i	−0.176925	−	0.248456i
$571$	25.9042	+	20.3713i	1.08406	+	0.852513i	0.989719	−	0.143027i	$-0.0456835\pi$
$571$	25.9042	+	20.3713i	1.08406	+	0.852513i	0.0943401	+	0.995540i	$0.469926\pi$
$572$	−0.000568611		0.0119366i	−2.37748e−5		0.000499095i
$573$	11.8230	+	13.6445i	0.493914	+	0.570007i
$574$	6.04331	+	2.51226i	0.252243	+	0.104860i
$575$	−9.99862	−	9.26881i	−0.416971	−	0.386536i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−46.5560	+	8.97293i	−1.93815	+	0.373548i	−0.938555	+	0.345130i	$0.887835\pi$
$577$	−46.5560	+	8.97293i	−1.93815	+	0.373548i	−0.999596	+	0.0284176i	$0.990953\pi$
$578$	10.7872	−	5.56118i	0.448687	−	0.231314i
$579$	−5.03549	+	2.01591i	−0.209268	+	0.0837783i
$580$	5.68924	−	12.4577i	0.236233	−	0.517278i
$581$	3.70663	+	3.62869i	0.153777	+	0.150544i
$582$	−10.9353	−	3.21088i	−0.453281	−	0.133095i
$583$	−1.56228	−	0.805411i	−0.0647030	−	0.0333567i
$584$	−9.17030	−	0.875658i	−0.379470	−	0.0362350i
$585$	−0.0413211	+	0.170328i	−0.00170842	+	0.00704219i
$586$	3.10607	+	0.598646i	0.128311	+	0.0247298i
$587$	−20.6802	+	23.8663i	−0.853564	+	0.985066i	−0.999991	−	0.00415573i	$-0.998677\pi$
$587$	−20.6802	+	23.8663i	−0.853564	+	0.985066i	0.146427	+	0.989221i	$0.453223\pi$
$588$	−5.98644	+	3.62802i	−0.246877	+	0.149617i
$589$	−3.66064	−	8.01569i	−0.150834	−	0.330281i
$590$	−17.8391	−	9.19667i	−0.734422	−	0.378621i
$591$	3.23918	−	3.08855i	0.133242	−	0.127046i
$592$	10.7898	+	4.31959i	0.443459	+	0.177534i
$593$	−10.4324	+	0.996171i	−0.428406	+	0.0409079i	−0.307033	−	0.951699i	$-0.599336\pi$
$593$	−10.4324	+	0.996171i	−0.428406	+	0.0409079i	−0.121374	+	0.992607i	$0.538730\pi$
$594$	0.0271742	−	0.189001i	0.00111497	−	0.00775480i
$595$	16.2857	−	1.33883i	0.667649	−	0.0548867i
$596$	−7.26730	−	8.38692i	−0.297680	−	0.343542i
$597$	4.21814	+	7.30602i	0.172637	+	0.299016i
$598$	0.250191	−	0.165804i	0.0102311	−	0.00678024i
$599$	−19.9130	+	34.4903i	−0.813623	+	1.40924i	0.0966902	+	0.995315i	$0.469174\pi$
$599$	−19.9130	+	34.4903i	−0.813623	+	1.40924i	−0.910313	+	0.413921i	$0.864159\pi$
$600$	0.929810	−	2.68651i	0.0379593	−	0.109676i
$601$	29.6686	+	19.0669i	1.21021	+	0.777754i	0.980694	−	0.195551i	$-0.0626494\pi$
$601$	29.6686	+	19.0669i	1.21021	+	0.777754i	0.229516	+	0.973305i	$0.426286\pi$
$602$	−2.32321	+	3.90421i	−0.0946872	+	0.159124i
$603$	−1.10421	+	2.41789i	−0.0449671	+	0.0984642i
$604$	−9.90239	+	7.78733i	−0.402923	+	0.316862i
$605$	−22.2212	+	21.1879i	−0.903420	+	0.861409i
$606$	−0.831861	−	17.4629i	−0.0337920	−	0.709382i
$607$	2.83098	−	3.97555i	0.114906	−	0.161363i	−0.753118	−	0.657886i	$-0.771451\pi$
$607$	2.83098	−	3.97555i	0.114906	−	0.161363i	0.868023	+	0.496523i	$0.165390\pi$
$608$	−2.49494	+	0.732581i	−0.101183	+	0.0297101i
$609$	−10.7915	−	7.13788i	−0.437292	−	0.289242i
$610$	13.5863	−	15.6794i	0.550093	−	0.634841i
$611$	0.359849	+	0.343115i	0.0145579	+	0.0138810i
$612$	2.19539	+	0.209635i	0.0887435	+	0.00847398i
$613$	0.858300	+	18.0179i	0.0346664	+	0.727738i	0.947567	+	0.319556i	$0.103534\pi$
$613$	0.858300	+	18.0179i	0.0346664	+	0.727738i	−0.912901	+	0.408181i	$0.866163\pi$
$614$	0.538973	+	2.22168i	0.0217512	+	0.0896595i
$615$	0.985889	+	6.85701i	0.0397549	+	0.276501i
$616$	−0.482811	−	0.148703i	−0.0194530	−	0.00599141i
$617$	−4.02150	+	27.9702i	−0.161900	+	1.12604i	0.733149	+	0.680068i	$0.238050\pi$
$617$	−4.02150	+	27.9702i	−0.161900	+	1.12604i	−0.895049	+	0.445969i	$0.852859\pi$
$618$	−0.0616782	+	1.29478i	−0.00248106	+	0.0520838i
$619$	7.97625	−	1.53730i	0.320593	−	0.0617892i	−0.0264162	−	0.999651i	$-0.508410\pi$
$619$	7.97625	−	1.53730i	0.320593	−	0.0617892i	0.347009	+	0.937862i	$0.387197\pi$
$620$	4.74530	−	8.21910i	0.190576	−	0.330087i
$621$	−4.23139	+	2.25729i	−0.169800	+	0.0905819i
$622$	−3.75387			−0.150516
$623$	−0.493939	−	1.49039i	−0.0197892	−	0.0597112i
$624$	0.0526494	+	0.0338357i	0.00210766	+	0.00135451i
$625$	−28.9024	+	11.5708i	−1.15609	+	0.462830i
$626$	−16.7892	−	23.5771i	−0.671031	−	0.942331i
$627$	−0.460942	−	0.184533i	−0.0184082	−	0.00736955i
$628$	−3.66457	−	15.1056i	−0.146232	−	0.602778i
$629$	−21.5627	+	13.8575i	−0.859763	+	0.552536i
$630$	−6.54048	−	3.48168i	−0.260579	−	0.138714i
$631$	9.35364	−	2.74648i	0.372362	−	0.109335i	−0.0901965	−	0.995924i	$-0.528750\pi$
$631$	9.35364	−	2.74648i	0.372362	−	0.109335i	0.462559	+	0.886589i	$0.346931\pi$
$632$	1.78199	+	0.343451i	0.0708839	+	0.0136617i
$633$	−1.67704	−	4.84549i	−0.0666564	−	0.192591i
$634$	−0.232356	+	0.957783i	−0.00922803	+	0.0380384i
$635$	1.90702	−	2.67804i	0.0756778	−	0.106275i
$636$	−7.74386	+	4.97667i	−0.307064	+	0.197338i
$637$	0.228966	−	0.373495i	0.00907196	−	0.0147984i
$638$	−0.132890	−	0.924270i	−0.00526117	−	0.0365922i
$639$	0.337455	−	0.0322230i	0.0133495	−	0.00127472i
$640$	−2.20135	−	1.73116i	−0.0870160	−	0.0684302i
$641$	33.0861	−	17.0570i	1.30682	−	0.673713i	0.342767	−	0.939420i	$-0.388636\pi$
$641$	33.0861	−	17.0570i	1.30682	−	0.673713i	0.964054	+	0.265707i	$0.0856055\pi$
$642$	2.82788	−	8.17063i	0.111608	−	0.322469i
$643$	4.22735			0.166710			0.0833551	−	0.996520i	$-0.473436\pi$
$643$	4.22735			0.166710			0.0833551	+	0.996520i	$0.473436\pi$
$644$	4.16063	+	11.9870i	0.163952	+	0.472356i
$645$	−4.80890			−0.189350
$646$	1.87560	−	5.41919i	0.0737944	−	0.213215i
$647$	4.56946	−	2.35572i	0.179644	−	0.0926130i	−0.366059	−	0.930592i	$-0.619293\pi$
$647$	4.56946	−	2.35572i	0.179644	−	0.0926130i	0.545703	+	0.837979i	$0.316263\pi$
$648$	−0.786053	−	0.618159i	−0.0308791	−	0.0242836i
$649$	−1.36223	+	0.130077i	−0.0534720	+	0.00510596i
$650$	0.0253205	+	0.176108i	0.000993153	+	0.00690753i
$651$	−6.97423	−	5.63487i	−0.273341	−	0.220848i
$652$	−5.55752	+	3.57160i	−0.217649	+	0.139875i
$653$	13.7488	−	19.3074i	0.538030	−	0.755558i	−0.452661	−	0.891683i	$-0.649525\pi$
$653$	13.7488	−	19.3074i	0.538030	−	0.755558i	0.990692	+	0.136125i	$0.0434647\pi$
$654$	1.43208	−	5.90311i	0.0559987	−	0.230830i
$655$	−18.5227	−	53.5179i	−0.723743	−	2.09112i
$656$	2.42896	+	0.468144i	0.0948350	+	0.0182779i
$657$	−8.83886	+	2.59532i	−0.344837	+	0.101253i
$658$	−17.8310	+	11.1301i	−0.695123	+	0.433895i
$659$	−15.5534	+	9.99556i	−0.605874	+	0.389372i	−0.807308	−	0.590131i	$-0.799076\pi$
$659$	−15.5534	+	9.99556i	−0.605874	+	0.389372i	0.201434	+	0.979502i	$0.435440\pi$
$660$	−0.126070	−	0.519669i	−0.00490728	−	0.0202281i
$661$	29.7666	+	11.9167i	1.15778	+	0.463507i	0.869449	−	0.494022i	$-0.164474\pi$
$661$	29.7666	+	11.9167i	1.15778	+	0.463507i	0.288336	+	0.957529i	$0.406898\pi$
$662$	5.68920	+	7.98936i	0.221117	+	0.310515i
$663$	−0.128136	+	0.0512978i	−0.00497637	+	0.00199224i
$664$	1.64933	+	1.05996i	0.0640063	+	0.0411343i
$665$	−12.8077	+	14.3932i	−0.496661	+	0.558146i
$666$	11.6223			0.450357
$667$	−16.7445	+	16.4215i	−0.648351	+	0.635842i
$668$	0.252703	−	0.437694i	0.00977736	−	0.0169349i
$669$	−13.6777	+	2.63616i	−0.528811	+	0.101920i
$670$	−0.354202	+	7.43561i	−0.0136840	+	0.287263i
$671$	0.201313	−	1.40016i	0.00777160	−	0.0540527i
$672$	−1.93871	+	1.80039i	−0.0747873	+	0.0694516i
$673$	−3.75890	−	26.1437i	−0.144895	−	1.00777i	−0.924415	−	0.381388i	$-0.875446\pi$
$673$	−3.75890	−	26.1437i	−0.144895	−	1.00777i	0.779520	−	0.626377i	$-0.215463\pi$
$674$	−3.08615	−	12.7213i	−0.118874	−	0.490005i
$675$	−0.135269	−	2.83964i	−0.00520650	−	0.109298i
$676$	12.9372	+	1.23536i	0.497586	+	0.0475137i
$677$	−28.3205	−	27.0036i	−1.08845	−	1.03783i	−0.999125	−	0.0418294i	$-0.986681\pi$
$677$	−28.3205	−	27.0036i	−1.08845	−	1.03783i	−0.0893223	−	0.996003i	$-0.528470\pi$
$678$	1.06079	−	1.22422i	0.0407395	−	0.0470159i
$679$	−1.83146	+	30.0978i	−0.0702848	+	1.15505i
$680$	5.92601	−	1.74003i	0.227252	−	0.0667272i
$681$	−0.798965	+	1.12199i	−0.0306164	+	0.0429947i
$682$	−0.0307897	−	0.646355i	−0.00117900	−	0.0247502i
$683$	33.0003	−	31.4657i	1.26272	−	1.20400i	0.294011	−	0.955802i	$-0.405010\pi$
$683$	33.0003	−	31.4657i	1.26272	−	1.20400i	0.968709	−	0.248199i	$-0.0798386\pi$
$684$	−2.04395	+	1.60738i	−0.0781524	+	0.0614598i
$685$	14.0340	−	30.7301i	0.536210	−	1.17414i
$686$	12.8882	+	13.3001i	0.492075	+	0.507801i
$687$	9.91256	+	6.37042i	0.378188	+	0.243047i
$688$	−0.561625	+	1.62271i	−0.0214117	+	0.0618651i
$689$	0.288049	−	0.498916i	0.0109738	−	0.0190072i
$690$	−8.65172	+	10.2730i	−0.329365	+	0.391085i
$691$	0.589165	+	1.02046i	0.0224129	+	0.0388203i	0.877014	−	0.480464i	$-0.159532\pi$
$691$	0.589165	+	1.02046i	0.0224129	+	0.0388203i	−0.854601	+	0.519285i	$0.826198\pi$
$692$	−14.9018	−	17.1976i	−0.566482	−	0.653756i
$693$	−0.503493	+	0.0413916i	−0.0191261	+	0.00157234i
$694$	−2.50718	+	17.4378i	−0.0951713	+	0.661931i
$695$	46.6495	−	4.45449i	1.76952	−	0.168968i
$696$	−4.53999	−	1.81754i	−0.172088	−	0.0688936i
$697$	−3.94823	+	3.76463i	−0.149550	+	0.142596i
$698$	4.60113	+	2.37205i	0.174155	+	0.0897834i
$699$	−5.18615	−	11.3561i	−0.196158	−	0.429527i
$700$	−7.47739	−	0.813551i	−0.282619	−	0.0307493i
$701$	19.4286	−	22.4217i	0.733806	−	0.846858i	−0.259088	−	0.965854i	$-0.583422\pi$
$701$	19.4286	−	22.4217i	0.733806	−	0.846858i	0.992895	+	0.118996i	$0.0379676\pi$
$702$	0.0614535	+	0.0118442i	0.00231941	+	0.000447030i
$703$	7.12493	−	29.3694i	0.268722	−	1.10769i
$704$	−0.190080	−	0.0181504i	−0.00716391	−	0.000684070i
$705$	−19.7758	−	10.1951i	−0.744798	−	0.383970i
$706$	−3.60348	−	1.05808i	−0.135619	−	0.0398212i
$707$	−44.5491	+	12.4457i	−1.67544	+	0.468067i
$708$	−2.97711	+	6.51897i	−0.111887	+	0.244998i
$709$	32.6925	−	13.0881i	1.22779	−	0.491534i	0.335092	−	0.942185i	$-0.391233\pi$
$709$	32.6925	−	13.0881i	1.22779	−	0.491534i	0.892700	+	0.450651i	$0.148808\pi$
$710$	0.843811	−	0.435015i	0.0316677	−	0.0163258i
$711$	1.78199	−	0.343451i	0.0668299	−	0.0128804i
$712$	−0.296723	−	0.513938i	−0.0111201	−	0.0192607i
$713$	−12.6328	+	10.2252i	−0.473103	+	0.382939i
$714$	−0.754226	−	5.78593i	−0.0282262	−	0.216533i
$715$	0.0219159	+	0.0252923i	0.000819609	+	0.000945880i
$716$	−0.607095	+	12.7445i	−0.0226882	+	0.476284i
$717$	14.1836	+	11.1541i	0.529697	+	0.416558i
$718$	10.9090	+	15.3196i	0.407122	+	0.571723i
$719$	12.8157	−	10.0784i	0.477944	−	0.375859i	−0.349928	−	0.936777i	$-0.613794\pi$
$719$	12.8157	−	10.0784i	0.477944	−	0.375859i	0.827872	+	0.560917i	$0.189551\pi$
$720$	−2.68707	−	0.788995i	−0.100141	−	0.0294041i
$721$	3.37584	−	0.604624i	0.125723	−	0.0225174i
$722$	−5.08409	−	11.1326i	−0.189210	−	0.414313i
$723$	8.54763	+	8.15015i	0.317890	+	0.303107i
$724$	2.51574	+	7.26876i	0.0934968	+	0.270141i
$725$	−4.54705	−	13.1378i	−0.168873	−	0.487927i
$726$	7.93469	+	7.56571i	0.294484	+	0.280790i
$727$	4.08611	+	8.94732i	0.151545	+	0.331838i	0.970145	−	0.242527i	$-0.0779763\pi$
$727$	4.08611	+	8.94732i	0.151545	+	0.331838i	−0.818599	+	0.574365i	$0.805249\pi$
$728$	0.0562137	−	0.155749i	0.00208342	−	0.00577244i
$729$	−0.959493	−	0.281733i	−0.0355368	−	0.0104345i
$730$	−20.2789	+	15.9475i	−0.750555	+	0.590243i
$731$	−2.19666	−	3.08477i	−0.0812462	−	0.114094i
$732$	−5.82326	−	4.57947i	−0.215234	−	0.169262i
$733$	−1.55373	+	32.6168i	−0.0573883	+	1.20473i	0.768108	+	0.640321i	$0.221198\pi$
$733$	−1.55373	+	32.6168i	−0.0573883	+	1.20473i	−0.825496	+	0.564408i	$0.809105\pi$
$734$	13.7257	+	15.8403i	0.506625	+	0.584677i
$735$	−5.12207	+	18.9226i	−0.188930	+	0.697971i
$736$	2.45607	+	4.11919i	0.0905320	+	0.151835i
$737$	0.253775	+	0.439551i	0.00934791	+	0.0161911i
$738$	2.42896	−	0.468144i	0.0894113	−	0.0172326i
$739$	−30.7440	+	15.8496i	−1.13094	+	0.583038i	−0.919005	−	0.394246i	$-0.871006\pi$
$739$	−30.7440	+	15.8496i	−1.13094	+	0.583038i	−0.211932	+	0.977285i	$0.567975\pi$
$740$	30.2170	−	12.0971i	1.11080	−	0.444697i
$741$	0.0676032	−	0.148030i	0.00248347	−	0.00543803i
$742$	17.4032	+	17.0373i	0.638893	+	0.625459i
$743$	−0.525799	−	0.154389i	−0.0192897	−	0.00566397i	0.272073	−	0.962276i	$-0.412291\pi$
$743$	−0.525799	−	0.154389i	−0.0192897	−	0.00566397i	−0.291363	+	0.956613i	$0.594109\pi$
$744$	−3.01216	−	1.55288i	−0.110431	−	0.0569312i
$745$	−30.9379	−	2.95421i	−1.13348	−	0.108234i
$746$	−6.35103	+	26.1793i	−0.232528	+	0.958492i
$747$	1.92513	+	0.371038i	0.0704368	+	0.0135756i
$748$	0.275765	−	0.318250i	0.0100830	−	0.0116364i
$749$	−22.7414	−	2.47430i	−0.830952	−	0.0904088i
$750$	2.50956	+	5.49516i	0.0916360	+	0.200655i
$751$	−11.1940	−	5.77093i	−0.408477	−	0.210584i	0.241727	−	0.970344i	$-0.422286\pi$
$751$	−11.1940	−	5.77093i	−0.408477	−	0.210584i	−0.650204	+	0.759760i	$0.725316\pi$
$752$	−5.74981	+	5.48243i	−0.209674	+	0.199924i
$753$	22.3832	+	8.96089i	0.815690	+	0.326553i
$754$	0.304671	−	0.0290925i	0.0110954	−	0.00105949i
$755$	−5.02083	+	34.9207i	−0.182727	+	1.27089i
$756$	−1.13070	+	2.39197i	−0.0411231	+	0.0869951i
$757$	−15.0426	−	17.3601i	−0.546734	−	0.630965i	0.413385	−	0.910556i	$-0.364346\pi$
$757$	−15.0426	−	17.3601i	−0.546734	−	0.630965i	−0.960119	+	0.279592i	$0.909801\pi$
$758$	−3.75694	−	6.50721i	−0.136458	−	0.236352i
$759$	−0.117567	+	0.908159i	−0.00426740	+	0.0329641i
$760$	−3.64105	+	6.30648i	−0.132075	+	0.228760i
$761$	12.3017	−	35.5436i	0.445938	−	1.28845i	−0.468406	−	0.883514i	$-0.655171\pi$
$761$	12.3017	−	35.5436i	0.445938	−	1.28845i	0.914344	−	0.404939i	$-0.132707\pi$
$762$	−0.987585	−	0.634682i	−0.0357764	−	0.0229921i
$763$	−16.0698	−	0.211738i	−0.581765	−	0.00766543i
$764$	7.50001	−	16.4227i	0.271341	−	0.594154i
$765$	4.85481	−	3.81787i	0.175526	−	0.138035i
$766$	18.8144	−	17.9395i	0.679792	−	0.648180i
$767$	−0.0213413	−	0.448010i	−0.000770591	−	0.0161767i
$768$	−0.580057	+	0.814576i	−0.0209310	+	0.0293935i
$769$	−5.21701	+	1.53185i	−0.188130	+	0.0552400i	−0.374440	−	0.927251i	$-0.622165\pi$
$769$	−5.21701	+	1.53185i	−0.188130	+	0.0552400i	0.186310	+	0.982491i	$0.440347\pi$
$770$	−1.26595	+	0.631672i	−0.0456218	+	0.0227639i
$771$	−15.6935	+	18.1112i	−0.565186	+	0.652260i
$772$	3.92555	+	3.74301i	0.141284	+	0.134714i
$773$	−28.4491	−	2.71656i	−1.02324	−	0.0977077i	−0.430080	−	0.902791i	$-0.641515\pi$
$773$	−28.4491	−	2.71656i	−1.02324	−	0.0977077i	−0.593162	+	0.805083i	$0.702121\pi$
$774$	0.0817053	+	1.71520i	0.00293683	+	0.0616517i
$775$	−2.27133	−	9.36256i	−0.0815887	−	0.336313i
$776$	1.62195	+	11.2809i	0.0582247	+	0.404961i
$777$	−6.85521	−	29.9760i	−0.245929	−	1.07538i
$778$	−3.43074	+	23.8613i	−0.122998	+	0.855469i
$779$	0.306056	−	6.42491i	0.0109656	−	0.230196i
$780$	0.172101	−	0.0331698i	0.00616221	−	0.00118767i
$781$	0.0323641	−	0.0560563i	0.00115808	−	0.00200585i
$782$	−10.5418	−	0.857248i	−0.376975	−	0.0306551i
$783$	−4.89030			−0.174765
$784$	5.78702	+	3.93833i	0.206679	+	0.140655i
$785$	−36.6201	−	23.5343i	−1.30703	−	0.839975i
$786$	−18.7737	+	7.51586i	−0.669636	+	0.268082i
$787$	−27.6288	−	38.7992i	−0.984860	−	1.38304i	−0.922932	−	0.384962i	$-0.874214\pi$
$787$	−27.6288	−	38.7992i	−0.984860	−	1.38304i	−0.0619282	−	0.998081i	$-0.519725\pi$
$788$	−4.15505	−	1.66343i	−0.148018	−	0.0592573i
$789$	−2.86092	−	11.7929i	−0.101851	−	0.419837i
$790$	4.27553	−	2.74772i	0.152117	−	0.0977594i
$791$	−3.78315	−	2.01388i	−0.134513	−	0.0716053i
$792$	−0.183210	+	0.0537953i	−0.00651008	+	0.00191153i
$793$	0.455262	+	0.0877445i	0.0161668	+	0.00311590i
$794$	5.12523	+	14.8084i	0.181888	+	0.525530i
$795$	−6.07765	+	25.0524i	−0.215552	+	0.888518i
$796$	4.89352	−	6.87198i	0.173446	−	0.243571i
$797$	−24.0512	+	15.4568i	−0.851937	+	0.547507i	−0.892178	−	0.451683i	$-0.850824\pi$
$797$	−24.0512	+	15.4568i	−0.851937	+	0.547507i	0.0402413	+	0.999190i	$0.487187\pi$
$798$	5.35129	+	4.32361i	0.189434	+	0.153054i
$799$	−2.49349	−	17.3426i	−0.0882134	−	0.613538i
$800$	−2.82999	+	0.270231i	−0.100055	+	0.00955413i
$801$	−0.466479	−	0.366843i	−0.0164822	−	0.0129618i
$802$	13.7492	−	7.08820i	0.485501	−	0.250293i
$803$	−0.575307	+	1.66224i	−0.0203021	+	0.0586592i
$804$	2.65810			0.0937440
$805$	31.5987	+	16.2549i	1.11371	+	0.572911i
$806$	0.212091			0.00747060
$807$	−7.76573	+	22.4376i	−0.273367	+	0.789842i
$808$	−15.5393	+	8.01104i	−0.546669	+	0.281827i
$809$	40.0245	+	31.4756i	1.40719	+	1.10662i	0.979213	+	0.202834i	$0.0650151\pi$
$809$	40.0245	+	31.4756i	1.40719	+	1.10662i	0.427974	+	0.903791i	$0.359227\pi$
$810$	−2.78783	+	0.266206i	−0.0979544	+	0.00935351i
$811$	−3.37095	−	23.4455i	−0.118370	−	0.823282i	−0.959351	−	0.282217i	$-0.908930\pi$
$811$	−3.37095	−	23.4455i	−0.118370	−	0.823282i	0.840980	−	0.541065i	$-0.181979\pi$
$812$	−2.00991	+	12.7814i	−0.0705341	+	0.448541i
$813$	−3.65090	+	2.34629i	−0.128043	+	0.0822879i
$814$	1.28728	−	1.80773i	0.0451190	−	0.0633607i
$815$	−4.36174	+	17.9793i	−0.152785	+	0.629789i
$816$	−0.721309	−	2.08408i	−0.0252509	−	0.0729576i
$817$	4.38437	+	0.845017i	0.153390	+	0.0295634i
$818$	−26.3620	+	7.74059i	−0.921727	+	0.270643i
$819$	−0.00569898	−	0.165485i	−0.000199138	−	0.00578251i
$820$	5.82780	−	3.74530i	0.203516	−	0.130792i
$821$	−9.99810	−	41.2127i	−0.348936	−	1.43833i	−0.828086	−	0.560601i	$-0.810570\pi$
$821$	−9.99810	−	41.2127i	−0.348936	−	1.43833i	0.479150	−	0.877733i	$-0.340945\pi$
$822$	−11.1990	−	4.48342i	−0.390611	−	0.156377i
$823$	18.1475	+	25.4846i	0.632582	+	0.888337i	0.999115	−	0.0420682i	$-0.0133947\pi$
$823$	18.1475	+	25.4846i	0.632582	+	0.888337i	−0.366533	+	0.930405i	$0.619455\pi$
$824$	1.20340	−	0.481768i	0.0419224	−	0.0167832i
$825$	−0.456657	−	0.293476i	−0.0158988	−	0.0102175i
$826$	18.5695	+	3.83339i	0.646115	+	0.133381i
$827$	−12.9831			−0.451466			−0.225733	−	0.974189i	$-0.572478\pi$
$827$	−12.9831			−0.451466			−0.225733	+	0.974189i	$0.572478\pi$
$828$	3.81109	+	2.91129i	0.132444	+	0.101174i
$829$	21.5827	−	37.3823i	0.749598	−	1.29834i	−0.198418	−	0.980117i	$-0.563580\pi$
$829$	21.5827	−	37.3823i	0.749598	−	1.29834i	0.948016	−	0.318224i	$-0.103086\pi$
$830$	5.39134	−	1.03910i	0.187136	−	0.0360676i
$831$	−0.816850	+	17.1478i	−0.0283362	+	0.594851i
$832$	0.00890670	−	0.0619474i	0.000308784	−	0.00214764i
$833$	−14.4780	+	5.35799i	−0.501634	+	0.185643i
$834$	−2.38139	−	16.5629i	−0.0824609	−	0.573528i
$835$	−0.333692	−	1.37550i	−0.0115479	−	0.0476010i
$836$	0.0236248	+	0.495945i	0.000817080	+	0.0171526i
$837$	−3.37354	−	0.322134i	−0.116606	−	0.0111346i
$838$	22.4061	+	21.3642i	0.774007	+	0.738014i
$839$	−0.549915	+	0.634636i	−0.0189852	+	0.0219101i	−0.765163	−	0.643837i	$-0.777342\pi$
$839$	−0.549915	+	0.634636i	−0.0189852	+	0.0219101i	0.746178	+	0.665747i	$0.231887\pi$
$840$	−0.450035	+	7.39578i	−0.0155277	+	0.255179i
$841$	4.87904	−	1.43261i	0.168243	−	0.0494005i
$842$	−17.0680	+	23.9686i	−0.588201	+	0.826012i
$843$	−0.115447	−	2.42353i	−0.00397620	−	0.0834707i
$844$	−3.71095	+	3.53838i	−0.127736	+	0.121796i
$845$	28.6089	−	22.4983i	0.984177	−	0.773966i
$846$	−3.30033	+	7.22670i	−0.113468	+	0.248459i
$847$	14.8331	−	24.9274i	0.509672	−	0.856514i
$848$	7.74386	+	4.97667i	0.265925	+	0.170900i
$849$	7.40681	−	21.4006i	0.254201	−	0.734465i
$850$	3.13480	−	5.42963i	0.107523	−	0.186235i
$851$	−55.7333	+	0.783638i	−1.91051	+	0.0268628i
$852$	−0.169495	−	0.293574i	−0.00580680	−	0.0100577i
$853$	−31.0815	−	35.8699i	−1.06421	−	1.22816i	−0.972629	−	0.232366i	$-0.925353\pi$
$853$	−31.0815	−	35.8699i	−1.06421	−	1.22816i	−0.0915810	−	0.995798i	$-0.529192\pi$
$854$	−8.37647	+	17.7203i	−0.286637	+	0.606375i
$855$	−1.03635	+	7.20797i	−0.0354424	+	0.246507i
$856$	−8.60701	+	0.821870i	−0.294181	+	0.0280909i
$857$	−35.2311	−	14.1044i	−1.20347	−	0.481797i	−0.318714	−	0.947851i	$-0.603251\pi$
$857$	−35.2311	−	14.1044i	−1.20347	−	0.481797i	−0.884756	+	0.466054i	$0.845675\pi$
$858$	0.00864873	−	0.00824655i	0.000295263	−	0.000281533i
$859$	39.5994	+	20.4149i	1.35111	+	0.696548i	0.973344	−	0.229351i	$-0.0736604\pi$
$859$	39.5994	+	20.4149i	1.35111	+	0.696548i	0.377771	+	0.925899i	$0.376691\pi$
$860$	1.99769	+	4.37433i	0.0681206	+	0.149163i
$861$	−2.64009	−	5.98857i	−0.0899742	−	0.204090i
$862$	−0.894533	+	1.03235i	−0.0304679	+	0.0351618i
$863$	38.5966	+	7.43889i	1.31384	+	0.253223i	0.797583	−	0.603209i	$-0.206111\pi$
$863$	38.5966	+	7.43889i	1.31384	+	0.253223i	0.516261	+	0.856431i	$0.327323\pi$
$864$	−0.235759	+	0.971812i	−0.00802068	+	0.0330617i
$865$	−63.4391	−	6.05770i	−2.15699	−	0.205968i
$866$	−32.0587	−	16.5274i	−1.08940	−	0.561624i
$867$	−11.6447	−	3.41919i	−0.395475	−	0.116122i
$868$	−2.22846	+	8.68479i	−0.0756390	+	0.294781i
$869$	0.143951	−	0.315209i	0.00488321	−	0.0106927i
$870$	−12.7143	+	5.09004i	−0.431055	+	0.172568i
$871$	−0.147863	+	0.0762286i	−0.00501014	+	0.00258291i
$872$	−5.96456	+	1.14957i	−0.201985	+	0.0389295i
$873$	5.69846	+	9.87002i	0.192864	+	0.334050i
$874$	9.69310	−	7.84578i	0.327874	−	0.265388i
$875$	12.6927	−	9.71377i	0.429092	−	0.328386i
$876$	6.03259	+	6.96198i	0.203822	+	0.235223i
$877$	−1.01771	+	21.3644i	−0.0343657	+	0.721424i	0.914280	+	0.405083i	$0.132757\pi$
$877$	−1.01771	+	21.3644i	−0.0343657	+	0.721424i	−0.948645	+	0.316341i	$0.897546\pi$
$878$	12.2389	+	9.62476i	0.413042	+	0.324820i
$879$	−1.83486	−	2.57669i	−0.0618882	−	0.0869098i
$880$	−0.420336	+	0.330556i	−0.0141695	+	0.0111430i
$881$	5.53609	+	1.62554i	0.186516	+	0.0547659i	0.373656	−	0.927567i	$-0.378104\pi$
$881$	5.53609	+	1.62554i	0.186516	+	0.0547659i	−0.187141	+	0.982333i	$0.559922\pi$
$882$	6.83621	+	1.50540i	0.230187	+	0.0506895i
$883$	−21.0527	−	46.0990i	−0.708479	−	1.55135i	−0.829378	−	0.558689i	$-0.811305\pi$
$883$	−21.0527	−	46.0990i	−0.708479	−	1.55135i	0.120898	−	0.992665i	$-0.461423\pi$
$884$	0.0998915	+	0.0952464i	0.00335972	+	0.00320348i
$885$	6.56430	+	18.9663i	0.220657	+	0.637545i
$886$	12.3385	+	35.6499i	0.414522	+	1.19768i
$887$	−12.1468	−	11.5819i	−0.407850	−	0.388884i	0.458194	−	0.888852i	$-0.348496\pi$
$887$	−12.1468	−	11.5819i	−0.407850	−	0.388884i	−0.866044	+	0.499968i	$0.833345\pi$
$888$	−4.82810	−	10.5721i	−0.162020	−	0.354775i
$889$	−1.05444	+	2.92150i	−0.0353649	+	0.0979840i
$890$	−1.59463	−	0.468225i	−0.0534521	−	0.0156949i
$891$	−0.150093	+	0.118034i	−0.00502829	+	0.00395429i
$892$	8.07986	+	11.3466i	0.270534	+	0.379912i
$893$	16.2385	+	12.7701i	0.543400	+	0.427334i
$894$	−0.528039	+	11.0849i	−0.0176603	+	0.370735i
$895$	23.3992	+	27.0041i	0.782150	+	0.902649i
$896$	2.44306	+	1.01560i	0.0816170	+	0.0339289i
$897$	−0.295490	−	0.0526536i	−0.00986612	−	0.00175805i
$898$	−0.205025	−	0.355113i	−0.00684176	−	0.0118503i
$899$	−16.2731	+	3.13639i	−0.542740	+	0.104605i
$900$	−2.52684	+	1.30268i	−0.0842280	+	0.0434225i
$901$	−18.8466	+	7.54505i	−0.627872	+	0.251362i
$902$	0.196214	−	0.429649i	0.00653321	−	0.0143057i
$903$	4.37561	−	1.22241i	0.145611	−	0.0406793i
$904$	−1.55426	−	0.456372i	−0.0516939	−	0.0151787i
$905$	19.1464	+	9.87065i	0.636448	+	0.328112i
$906$	12.5406	+	1.19748i	0.416633	+	0.0397836i
$907$	−6.44904	+	26.5833i	−0.214137	+	0.882684i	0.758746	+	0.651386i	$0.225812\pi$
$907$	−6.44904	+	26.5833i	−0.214137	+	0.882684i	−0.972883	+	0.231298i	$0.925703\pi$
$908$	1.35250	+	0.260673i	0.0448843	+	0.00865074i
$909$	−11.4487	+	13.2126i	−0.379731	+	0.438233i
$910$	−0.187061	−	0.424313i	−0.00620101	−	0.0140658i
$911$	−15.0698	−	32.9982i	−0.499285	−	1.09328i	−0.976701	−	0.214604i	$-0.931154\pi$
$911$	−15.0698	−	32.9982i	−0.499285	−	1.09328i	0.477417	−	0.878677i	$-0.341573\pi$
$912$	2.31121	+	1.19151i	0.0765319	+	0.0394550i
$913$	0.270936	−	0.258336i	0.00896666	−	0.00854969i
$914$	−27.9088	−	11.1730i	−0.923140	−	0.369569i
$915$	−20.6529	+	1.97211i	−0.682764	+	0.0651960i
$916$	1.67691	−	11.6632i	0.0554066	−	0.385361i
$917$	30.4579	+	43.9874i	1.00581	+	1.45259i
$918$	−1.44422	−	1.66671i	−0.0476662	−	0.0550098i
$919$	−24.9937	−	43.2904i	−0.824467	−	1.42802i	−0.902326	−	0.431054i	$-0.858142\pi$
$919$	−24.9937	−	43.2904i	−0.824467	−	1.42802i	0.0778593	−	0.996964i	$-0.475191\pi$
$920$	12.9387	+	3.60234i	0.426575	+	0.118766i
$921$	1.14306	−	1.97984i	0.0376651	−	0.0652378i
$922$	−4.78091	+	13.8135i	−0.157451	+	0.454924i
$923$	0.0178476	+	0.0114700i	0.000587461	+	0.000377538i
$924$	0.246810	+	0.440799i	0.00811944	+	0.0145012i
$925$	13.7256	−	30.0549i	0.451296	−	0.988200i
$926$	−15.1060	+	11.8795i	−0.496415	+	0.390385i
$927$	0.938142	−	0.894516i	0.0308126	−	0.0293798i
$928$	0.232690	+	4.88476i	0.00763841	+	0.160350i
$929$	−4.28548	+	6.01811i	−0.140602	+	0.197448i	−0.878872	−	0.477057i	$-0.841703\pi$
$929$	−4.28548	+	6.01811i	−0.140602	+	0.197448i	0.738270	+	0.674505i	$0.235643\pi$
$930$	−9.10617	+	2.67381i	−0.298603	+	0.0876777i
$931$	7.99496	−	16.3521i	0.262024	−	0.535917i
$932$	−8.17545	+	9.43498i	−0.267796	+	0.309053i
$933$	2.71680	+	2.59046i	0.0889441	+	0.0848080i
$934$	−17.4275	−	1.66413i	−0.570246	−	0.0544519i
$935$	−0.0561138	−	1.17797i	−0.00183512	−	0.0385239i
$936$	−0.0147548	−	0.0608203i	−0.000482277	−	0.00198797i
$937$	0.944337	+	6.56801i	0.0308501	+	0.214567i	0.999415	−	0.0341927i	$-0.0108860\pi$
$937$	0.944337	+	6.56801i	0.0308501	+	0.214567i	−0.968565	+	0.248760i	$0.919977\pi$
$938$	−1.56783	−	6.85568i	−0.0511914	−	0.223846i
$939$	−4.11917	+	28.6494i	−0.134424	+	0.934939i
$940$	−1.05865	+	22.2239i	−0.0345295	+	0.724863i
$941$	5.45497	−	1.05136i	0.177827	−	0.0342733i	−0.0995603	−	0.995032i	$-0.531744\pi$
$941$	5.45497	−	1.05136i	0.177827	−	0.0342733i	0.277387	+	0.960758i	$0.410532\pi$
$942$	−7.77186	+	13.4613i	−0.253221	+	0.438591i
$943$	−11.6162	+	2.40869i	−0.378274	+	0.0784377i
$944$	7.16660			0.233253
$945$	2.33093	+	7.03326i	0.0758253	+	0.228792i
$946$	0.275830	+	0.177265i	0.00896802	+	0.00576340i
$947$	−30.5663	+	12.2369i	−0.993271	+	0.397646i	−0.810646	−	0.585537i	$-0.800884\pi$
$947$	−30.5663	+	12.2369i	−0.993271	+	0.397646i	−0.182625	+	0.983183i	$0.558460\pi$
$948$	−1.05268	−	1.47828i	−0.0341895	−	0.0480124i
$949$	−0.535231	−	0.214274i	−0.0173743	−	0.00695563i
$950$	1.74278	+	7.18385i	0.0565433	+	0.233075i
$951$	0.829110	−	0.532837i	0.0268857	−	0.0172784i
$952$	−4.94975	+	3.08963i	−0.160422	+	0.100136i
$953$	17.7408	−	5.20918i	0.574682	−	0.168742i	0.0185383	−	0.999828i	$-0.494099\pi$
$953$	17.7408	−	5.20918i	0.574682	−	0.168742i	0.556143	+	0.831086i	$0.312281\pi$
$954$	9.03879	+	1.74208i	0.292642	+	0.0564020i
$955$	−16.5369	−	47.7804i	−0.535123	−	1.54614i
$956$	4.25406	−	17.5355i	0.137586	−	0.567138i
$957$	−0.541643	+	0.760631i	−0.0175088	+	0.0245877i
$958$	5.60601	−	3.60277i	0.181122	−	0.116400i
$959$	−4.95795	+	31.5286i	−0.160101	+	1.01811i
$960$	0.398554	+	2.77201i	0.0128633	+	0.0894661i
$961$	19.4271	−	1.85506i	0.626681	−	0.0598408i
$962$	0.571758	+	0.449635i	0.0184342	+	0.0144968i
$963$	−7.68501	+	3.96190i	−0.247646	+	0.127670i
$964$	3.86282	−	11.1609i	0.124413	−	0.359468i
$965$	15.1901			0.488985
$966$	5.26082	−	11.5466i	0.169264	−	0.371506i
$967$	−23.9987			−0.771746			−0.385873	−	0.922552i	$-0.626100\pi$
$967$	−23.9987			−0.771746			−0.385873	+	0.922552i	$0.626100\pi$
$968$	3.58582	−	10.3606i	0.115253	−	0.333001i
$969$	−5.09710	+	2.62774i	−0.163742	+	0.0844151i
$970$	25.0886	+	19.7299i	0.805547	+	0.633489i
$971$	22.1520	−	2.11526i	0.710893	−	0.0678820i	0.266656	−	0.963792i	$-0.414081\pi$
$971$	22.1520	−	2.11526i	0.710893	−	0.0678820i	0.444236	+	0.895910i	$0.353475\pi$
$972$	0.142315	+	0.989821i	0.00456475	+	0.0317485i
$973$	−41.3140	+	15.9113i	−1.32447	+	0.510094i
$974$	7.92303	−	5.09182i	0.253870	−	0.163152i
$975$	0.103203	−	0.144929i	0.00330515	−	0.00464143i
$976$	−1.74656	+	7.19941i	−0.0559059	+	0.230447i
$977$	3.58010	+	10.3440i	0.114538	+	0.330935i	0.987670	−	0.156548i	$-0.0500365\pi$
$977$	3.58010	+	10.3440i	0.114538	+	0.330935i	−0.873133	+	0.487483i	$0.837915\pi$
$978$	6.48686	+	1.25024i	0.207427	+	0.0399782i
$979$	−0.108725	+	0.0319245i	−0.00347487	+	0.00102031i
$980$	19.3404	−	3.20154i	0.617806	−	0.102269i
$981$	−5.11005	+	3.28403i	−0.163151	+	0.104851i
$982$	5.51319	+	22.7257i	0.175933	+	0.725206i
$983$	24.4257	+	9.77858i	0.779059	+	0.311888i	0.726893	−	0.686750i	$-0.240963\pi$
$983$	24.4257	+	9.77858i	0.779059	+	0.311888i	0.0521655	+	0.998638i	$0.483388\pi$
$984$	−1.43487	−	2.01499i	−0.0457418	−	0.0642354i
$985$	−11.6363	+	4.65846i	−0.370762	+	0.148431i
$986$	−9.07288	−	5.83079i	−0.288939	−	0.185690i
$987$	20.5855	+	4.24956i	0.655244	+	0.135265i
$988$	−0.162737			−0.00517734
$989$	−0.507454	−	8.21951i	−0.0161361	−	0.261365i
$990$	−0.267371	+	0.463100i	−0.00849761	+	0.0147183i
$991$	−11.9327	+	2.29983i	−0.379053	+	0.0730566i	−0.375219	−	0.926936i	$-0.622433\pi$
$991$	−11.9327	+	2.29983i	−0.379053	+	0.0730566i	−0.00383419	+	0.999993i	$0.501220\pi$
$992$	−0.161249	+	3.38504i	−0.00511968	+	0.107475i
$993$	1.39582	−	9.70817i	0.0442951	−	0.308079i
$994$	−0.657203	+	0.610314i	−0.0208452	+	0.0193580i
$995$	−3.36231	−	23.3854i	−0.106592	−	0.741367i
$996$	−0.462219	−	1.90529i	−0.0146460	−	0.0603715i
$997$	1.29675	+	27.2221i	0.0410685	+	0.862134i	0.921599	+	0.388144i	$0.126884\pi$
$997$	1.29675	+	27.2221i	0.0410685	+	0.862134i	−0.880530	+	0.473990i	$0.842813\pi$
$998$	23.3145	+	2.22626i	0.738006	+	0.0704711i
$999$	−8.41149	−	8.02034i	−0.266128	−	0.253752i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.c.151.2	✓	160
7.2	even	3	inner	966.2.y.c.289.7	yes	160
23.16	even	11	inner	966.2.y.c.361.7	yes	160
161.16	even	33	inner	966.2.y.c.499.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.c.151.2	✓	160	1.1	even	1	trivial
966.2.y.c.289.7	yes	160	7.2	even	3	inner
966.2.y.c.361.7	yes	160	23.16	even	11	inner
966.2.y.c.499.2	yes	160	161.16	even	33	inner

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.y (of order \(33\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.78783 + 0.266206i) q^{5} +(0.142315 + 0.989821i) q^{6} +(2.46897 - 0.950880i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +O(q^{10})\)	\(q+(-0.327068 + 0.945001i) q^{2} +(0.888835 - 0.458227i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-2.78783 + 0.266206i) q^{5} +(0.142315 + 0.989821i) q^{6} +(2.46897 - 0.950880i) q^{7} +(0.841254 - 0.540641i) q^{8} +(0.580057 - 0.814576i) q^{9} +(0.660246 - 2.72157i) q^{10} +(-0.0624518 - 0.180443i) q^{11} +(-0.981929 - 0.189251i) q^{12} +(0.0600493 - 0.0176321i) q^{13} +(0.0910606 + 2.64418i) q^{14} +(-2.35594 + 1.51407i) q^{15} +(0.235759 + 0.971812i) q^{16} +(-2.04740 - 0.819657i) q^{17} +(0.580057 + 0.814576i) q^{18} +(2.41401 - 0.966423i) q^{19} +(2.35594 + 1.51407i) q^{20} +(1.75879 - 1.97652i) q^{21} +0.190944 q^{22} +(-2.83650 - 3.86707i) q^{23} +(0.500000 - 0.866025i) q^{24} +(2.79149 - 0.538016i) q^{25} +(-0.00297789 + 0.0625136i) q^{26} +(0.142315 - 0.989821i) q^{27} +(-2.52854 - 0.778775i) q^{28} +(-0.695962 - 4.84052i) q^{29} +(-0.660246 - 2.72157i) q^{30} +(-0.161249 - 3.38504i) q^{31} +(-0.995472 - 0.0950560i) q^{32} +(-0.138193 - 0.131767i) q^{33} +(1.44422 - 1.66671i) q^{34} +(-6.62995 + 3.30815i) q^{35} +(-0.959493 + 0.281733i) q^{36} +(6.74162 - 9.46728i) q^{37} +(0.123726 + 2.59733i) q^{38} +(0.0452945 - 0.0431882i) q^{39} +(-2.20135 + 1.73116i) q^{40} +(1.02760 - 2.25012i) q^{41} +(1.29257 + 2.30852i) q^{42} +(1.44456 + 0.928361i) q^{43} +(-0.0624518 + 0.180443i) q^{44} +(-1.40026 + 2.42531i) q^{45} +(4.58212 - 1.41570i) q^{46} +(3.97232 + 6.88027i) q^{47} +(0.654861 + 0.755750i) q^{48} +(5.19165 - 4.69539i) q^{49} +(-0.404582 + 2.81393i) q^{50} +(-2.19539 + 0.209635i) q^{51} +(-0.0581014 - 0.0232603i) q^{52} +(6.66207 - 6.35227i) q^{53} +(0.888835 + 0.458227i) q^{54} +(0.222140 + 0.486419i) q^{55} +(1.56295 - 2.13476i) q^{56} +(1.70282 - 1.96515i) q^{57} +(4.80192 + 0.925494i) q^{58} +(1.68959 - 6.96458i) q^{59} +(2.78783 + 0.266206i) q^{60} +(6.58470 + 3.39465i) q^{61} +(3.25161 + 0.954758i) q^{62} +(0.657581 - 2.56273i) q^{63} +(0.415415 - 0.909632i) q^{64} +(-0.162714 + 0.0651407i) q^{65} +(0.169718 - 0.0874958i) q^{66} +(-2.61006 + 0.503049i) q^{67} +(1.10269 + 1.90991i) q^{68} +(-4.29318 - 2.13743i) q^{69} +(-0.957758 - 7.34730i) q^{70} +(0.221991 + 0.256191i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(-7.24113 - 5.69449i) q^{73} +(6.74162 + 9.46728i) q^{74} +(2.23464 - 1.75734i) q^{75} +(-2.49494 - 0.732581i) q^{76} +(-0.325771 - 0.386124i) q^{77} +(0.0259985 + 0.0569288i) q^{78} +(1.31342 + 1.25235i) q^{79} +(-0.915958 - 2.64649i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(1.79027 + 1.70702i) q^{82} +(0.814445 + 1.78339i) q^{83} +(-2.60431 + 0.466440i) q^{84} +(5.92601 + 1.74003i) q^{85} +(-1.34977 + 1.06147i) q^{86} +(-2.83665 - 3.98352i) q^{87} +(-0.150093 - 0.118034i) q^{88} +(0.0282373 - 0.592773i) q^{89} +(-1.83395 - 2.11649i) q^{90} +(0.131494 - 0.100633i) q^{91} +(-0.160824 + 4.79313i) q^{92} +(-1.69444 - 2.93486i) q^{93} +(-7.80108 + 1.50353i) q^{94} +(-6.47258 + 3.33685i) q^{95} +(-0.928368 + 0.371662i) q^{96} +(-4.73445 + 10.3670i) q^{97} +(2.73913 + 6.44183i) q^{98} +(-0.183210 - 0.0537953i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9	\( 160 q + 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} + 16 q^{6} - 2 q^{7} - 16 q^{8} + 8 q^{9} + 2 q^{10} + 8 q^{11} - 8 q^{12} - 4 q^{13} + 9 q^{14} - 18 q^{15} + 8 q^{16} - 21 q^{17} + 8 q^{18} + 4 q^{19} + 18 q^{20} - 15 q^{21} + 116 q^{22} + 14 q^{23} + 80 q^{24} + 2 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 46 q^{29} - 2 q^{30} + q^{31} + 8 q^{32} - 8 q^{33} - 68 q^{34} - 84 q^{35} - 16 q^{36} + 19 q^{37} - 7 q^{38} - 2 q^{39} - 9 q^{40} + 38 q^{41} + 2 q^{42} + 28 q^{43} + 8 q^{44} + 24 q^{45} - 8 q^{46} - 26 q^{47} + 16 q^{48} - 6 q^{49} - 4 q^{50} + 21 q^{51} + 2 q^{52} - 20 q^{53} - 8 q^{54} + 46 q^{55} - 2 q^{56} - 14 q^{57} - 21 q^{58} + 36 q^{59} - 2 q^{60} + 40 q^{61} - 24 q^{62} - 2 q^{63} - 16 q^{64} - 10 q^{65} - 8 q^{66} + 6 q^{67} + 34 q^{68} + 6 q^{69} - 20 q^{70} + 132 q^{71} + 8 q^{72} - 36 q^{73} + 19 q^{74} - 2 q^{75} - 8 q^{76} - 75 q^{77} - 18 q^{78} + 34 q^{79} + 2 q^{80} + 8 q^{81} + 47 q^{82} + 74 q^{83} + 13 q^{84} + 2 q^{85} + 30 q^{86} + 10 q^{87} - 3 q^{88} - 12 q^{89} - 4 q^{90} - 30 q^{91} - 50 q^{92} + 10 q^{93} - 4 q^{94} + 27 q^{95} - 8 q^{96} + 24 q^{97} + 7 q^{98} - 16 q^{99}+O(q^{100}) \) 160 * q + 8 * q^2 - 8 * q^3 + 8 * q^4 + 2 * q^5 + 16 * q^6 - 2 * q^7 - 16 * q^8 + 8 * q^9 + 2 * q^10 + 8 * q^11 - 8 * q^12 - 4 * q^13 + 9 * q^14 - 18 * q^15 + 8 * q^16 - 21 * q^17 + 8 * q^18 + 4 * q^19 + 18 * q^20 - 15 * q^21 + 116 * q^22 + 14 * q^23 + 80 * q^24 + 2 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 46 * q^29 - 2 * q^30 + q^31 + 8 * q^32 - 8 * q^33 - 68 * q^34 - 84 * q^35 - 16 * q^36 + 19 * q^37 - 7 * q^38 - 2 * q^39 - 9 * q^40 + 38 * q^41 + 2 * q^42 + 28 * q^43 + 8 * q^44 + 24 * q^45 - 8 * q^46 - 26 * q^47 + 16 * q^48 - 6 * q^49 - 4 * q^50 + 21 * q^51 + 2 * q^52 - 20 * q^53 - 8 * q^54 + 46 * q^55 - 2 * q^56 - 14 * q^57 - 21 * q^58 + 36 * q^59 - 2 * q^60 + 40 * q^61 - 24 * q^62 - 2 * q^63 - 16 * q^64 - 10 * q^65 - 8 * q^66 + 6 * q^67 + 34 * q^68 + 6 * q^69 - 20 * q^70 + 132 * q^71 + 8 * q^72 - 36 * q^73 + 19 * q^74 - 2 * q^75 - 8 * q^76 - 75 * q^77 - 18 * q^78 + 34 * q^79 + 2 * q^80 + 8 * q^81 + 47 * q^82 + 74 * q^83 + 13 * q^84 + 2 * q^85 + 30 * q^86 + 10 * q^87 - 3 * q^88 - 12 * q^89 - 4 * q^90 - 30 * q^91 - 50 * q^92 + 10 * q^93 - 4 * q^94 + 27 * q^95 - 8 * q^96 + 24 * q^97 + 7 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more