LMFDB - Embedded newform 966.2.y.b.193.8

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			193.8
Character	$\chi$	$=$	966.193
Dual form			966.2.y.b.961.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.723734 - 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(2.30813 - 1.81513i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-2.63458 + 0.242856i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})$	\(q+(-0.723734 - 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(2.30813 - 1.81513i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-2.63458 + 0.242856i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +(-2.92306 - 0.279118i) q^{10} +(2.65585 - 2.53235i) q^{11} +(0.235759 + 0.971812i) q^{12} +(1.50952 + 3.30539i) q^{13} +(2.07433 + 1.64231i) q^{14} +(1.92290 - 2.21915i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(1.58873 - 0.819046i) q^{17} +(-0.928368 - 0.371662i) q^{18} +(2.11407 + 1.08988i) q^{19} +(1.92290 + 2.21915i) q^{20} +(-2.54101 + 0.737065i) q^{21} -3.66966 q^{22} +(2.69606 - 3.96626i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.853960 - 3.52007i) q^{25} +(1.18849 - 3.43391i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.367939 - 2.62004i) q^{28} +(-6.06561 - 3.89813i) q^{29} +(-2.92306 + 0.279118i) q^{30} +(-0.452844 - 1.30841i) q^{31} +(0.786053 + 0.618159i) q^{32} +(2.12861 - 2.98921i) q^{33} +(-1.71502 - 0.503576i) q^{34} +(-5.64014 + 5.34266i) q^{35} +(0.415415 + 0.909632i) q^{36} +(4.97638 - 1.99224i) q^{37} +(-0.777922 - 2.24766i) q^{38} +(2.10779 + 2.95998i) q^{39} +(0.139717 - 2.93303i) q^{40} +(0.177696 + 1.23591i) q^{41} +(2.34765 + 1.22006i) q^{42} +(-7.52251 - 8.68144i) q^{43} +(2.65585 + 2.53235i) q^{44} +(1.46818 - 2.54296i) q^{45} +(-4.68827 + 1.01002i) q^{46} +(1.59260 + 2.75846i) q^{47} +(-0.959493 + 0.281733i) q^{48} +(6.88204 - 1.27965i) q^{49} +(-3.04717 + 1.95829i) q^{50} +(1.40501 - 1.10491i) q^{51} +(-3.22982 + 1.66509i) q^{52} +(7.61906 + 10.6995i) q^{53} +(-0.981929 - 0.189251i) q^{54} +(1.53350 - 10.6657i) q^{55} +(-1.54175 + 2.15012i) q^{56} +(2.28213 + 0.670093i) q^{57} +(1.69987 + 7.00696i) q^{58} +(3.59561 + 0.343339i) q^{59} +(2.30813 + 1.81513i) q^{60} +(-7.12722 - 1.37366i) q^{61} +(-0.575166 + 1.25944i) q^{62} +(-2.35560 + 1.20463i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(9.48390 + 4.88929i) q^{65} +(-3.60334 + 0.694487i) q^{66} +(1.54914 - 6.38565i) q^{67} +(0.893713 + 1.54796i) q^{68} +(1.89672 - 4.40482i) q^{69} +(7.76882 + 0.0254779i) q^{70} +(-7.41919 + 2.17847i) q^{71} +(0.327068 - 0.945001i) q^{72} +(-0.0129741 - 0.272359i) q^{73} +(-4.97638 - 1.99224i) q^{74} +(0.172350 - 3.61807i) q^{75} +(-0.988053 + 2.16353i) q^{76} +(-6.38207 + 7.31668i) q^{77} +(0.517139 - 3.59678i) q^{78} +(-3.21045 + 4.50845i) q^{79} +(-2.12514 + 2.02632i) q^{80} +(0.723734 - 0.690079i) q^{81} +(0.724268 - 1.01709i) q^{82} +(1.78220 - 12.3955i) q^{83} +(-0.857136 - 2.50306i) q^{84} +(2.18031 - 4.77422i) q^{85} +(-0.546583 + 11.4742i) q^{86} +(-6.69373 - 2.67976i) q^{87} +(-0.174609 - 3.66550i) q^{88} +(-0.505095 + 1.45938i) q^{89} +(-2.81741 + 0.827266i) q^{90} +(-4.77969 - 8.34173i) q^{91} +(4.09005 + 2.50429i) q^{92} +(-0.692279 - 1.19906i) q^{93} +(0.750939 - 3.09541i) q^{94} +(6.85783 - 1.32174i) q^{95} +(0.888835 + 0.458227i) q^{96} +(2.03190 + 14.1322i) q^{97} +(-5.86383 - 3.82303i) q^{98} +(1.52443 - 3.33804i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) $ 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−0.723734	−	0.690079i	−0.511757	−	0.487960i
$2$	−0.723734	−	0.690079i	−0.511757	−	0.487960i
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$3$	0.981929	−	0.189251i	0.566917	−	0.109264i
$4$	0.0475819	+	0.998867i	0.0237910	+	0.499434i
$5$	2.30813	−	1.81513i	1.03223	−	0.811752i	0.0498679	−	0.998756i	$-0.484120\pi$
$5$	2.30813	−	1.81513i	1.03223	−	0.811752i	0.982359	+	0.187003i	$0.0598776\pi$
$6$	−0.841254	−	0.540641i	−0.343440	−	0.220716i
$7$	−2.63458	+	0.242856i	−0.995778	+	0.0917909i
$7$	−2.63458	+	0.242856i	−0.995778	+	0.0917909i
$8$	0.654861	−	0.755750i	0.231528	−	0.267198i
$9$	0.928368	−	0.371662i	0.309456	−	0.123887i
$10$	−2.92306	−	0.279118i	−0.924352	−	0.0882649i
$11$	2.65585	−	2.53235i	0.800770	−	0.763533i	−0.174474	−	0.984662i	$-0.555823\pi$
$11$	2.65585	−	2.53235i	0.800770	−	0.763533i	0.975245	+	0.221129i	$0.0709741\pi$
$12$	0.235759	+	0.971812i	0.0680577	+	0.280538i
$13$	1.50952	+	3.30539i	0.418666	+	0.916750i	0.995032	+	0.0995586i	$0.0317431\pi$
$13$	1.50952	+	3.30539i	0.418666	+	0.916750i	−0.576366	+	0.817192i	$0.695530\pi$
$14$	2.07433	+	1.64231i	0.554387	+	0.438925i
$15$	1.92290	−	2.21915i	0.496491	−	0.572982i
$16$	−0.995472	+	0.0950560i	−0.248868	+	0.0237640i
$17$	1.58873	−	0.819046i	0.385323	−	0.198648i	−0.254671	−	0.967028i	$-0.581967\pi$
$17$	1.58873	−	0.819046i	0.385323	−	0.198648i	0.639994	+	0.768380i	$0.278937\pi$
$18$	−0.928368	−	0.371662i	−0.218818	−	0.0876017i
$19$	2.11407	+	1.08988i	0.485001	+	0.250035i	0.683343	−	0.730097i	$-0.260525\pi$
$19$	2.11407	+	1.08988i	0.485001	+	0.250035i	−0.198342	+	0.980133i	$0.563556\pi$
$20$	1.92290	+	2.21915i	0.429974	+	0.496217i
$21$	−2.54101	+	0.737065i	−0.554494	+	0.160841i
$22$	−3.66966			−0.782373
$23$	2.69606	−	3.96626i	0.562168	−	0.827023i
$23$	2.69606	−	3.96626i	0.562168	−	0.827023i
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	0.853960	−	3.52007i	0.170792	−	0.704014i
$26$	1.18849	−	3.43391i	0.233082	−	0.673446i
$27$	0.841254	−	0.540641i	0.161899	−	0.104046i
$28$	−0.367939	−	2.62004i	−0.0695340	−	0.495141i
$29$	−6.06561	−	3.89813i	−1.12636	−	0.723865i	−0.161560	−	0.986863i	$-0.551652\pi$
$29$	−6.06561	−	3.89813i	−1.12636	−	0.723865i	−0.964796	+	0.262998i	$0.915289\pi$
$30$	−2.92306	+	0.279118i	−0.533675	+	0.0509598i
$31$	−0.452844	−	1.30841i	−0.0813333	−	0.234997i	0.897001	−	0.442028i	$-0.145741\pi$
$31$	−0.452844	−	1.30841i	−0.0813333	−	0.234997i	−0.978334	+	0.207031i	$0.933620\pi$
$32$	0.786053	+	0.618159i	0.138956	+	0.109276i
$33$	2.12861	−	2.98921i	0.370543	−	0.520355i
$34$	−1.71502	−	0.503576i	−0.294124	−	0.0863625i
$35$	−5.64014	+	5.34266i	−0.953358	+	0.903074i
$36$	0.415415	+	0.909632i	0.0692358	+	0.151605i
$37$	4.97638	−	1.99224i	0.818112	−	0.327523i	0.0754167	−	0.997152i	$-0.475971\pi$
$37$	4.97638	−	1.99224i	0.818112	−	0.327523i	0.742695	+	0.669629i	$0.233547\pi$
$38$	−0.777922	−	2.24766i	−0.126196	−	0.364618i
$39$	2.10779	+	2.95998i	0.337517	+	0.473976i
$40$	0.139717	−	2.93303i	0.0220913	−	0.463752i
$41$	0.177696	+	1.23591i	0.0277515	+	0.193016i	0.998981	−	0.0451288i	$-0.0143698\pi$
$41$	0.177696	+	1.23591i	0.0277515	+	0.193016i	−0.971230	+	0.238145i	$0.923461\pi$
$42$	2.34765	+	1.22006i	0.362250	+	0.188259i
$43$	−7.52251	−	8.68144i	−1.14717	−	1.32391i	−0.938243	−	0.345977i	$-0.887548\pi$
$43$	−7.52251	−	8.68144i	−1.14717	−	1.32391i	−0.208929	−	0.977931i	$-0.566998\pi$
$44$	2.65585	+	2.53235i	0.400385	+	0.381766i
$45$	1.46818	−	2.54296i	0.218863	−	0.379082i
$46$	−4.68827	+	1.01002i	−0.691247	+	0.148920i
$47$	1.59260	+	2.75846i	0.232304	+	0.402363i	0.958486	−	0.285140i	$-0.0920401\pi$
$47$	1.59260	+	2.75846i	0.232304	+	0.402363i	−0.726181	+	0.687503i	$0.758707\pi$
$48$	−0.959493	+	0.281733i	−0.138491	+	0.0406646i
$49$	6.88204	−	1.27965i	0.983149	−	0.182807i
$50$	−3.04717	+	1.95829i	−0.430934	+	0.276945i
$51$	1.40501	−	1.10491i	0.196741	−	0.154719i
$52$	−3.22982	+	1.66509i	−0.447896	+	0.230906i
$53$	7.61906	+	10.6995i	1.04656	+	1.46968i	0.874762	+	0.484552i	$0.161017\pi$
$53$	7.61906	+	10.6995i	1.04656	+	1.46968i	0.171795	+	0.985133i	$0.445043\pi$
$54$	−0.981929	−	0.189251i	−0.133624	−	0.0257538i
$55$	1.53350	−	10.6657i	0.206777	−	1.43817i
$56$	−1.54175	+	2.15012i	−0.206024	+	0.287322i
$57$	2.28213	+	0.670093i	0.302275	+	0.0887560i
$58$	1.69987	+	7.00696i	0.223204	+	0.920060i
$59$	3.59561	+	0.343339i	0.468108	+	0.0446989i	0.326445	−	0.945216i	$-0.394149\pi$
$59$	3.59561	+	0.343339i	0.468108	+	0.0446989i	0.141663	+	0.989915i	$0.454755\pi$
$60$	2.30813	+	1.81513i	0.297978	+	0.234333i
$61$	−7.12722	−	1.37366i	−0.912546	−	0.175879i	−0.288694	−	0.957421i	$-0.593221\pi$
$61$	−7.12722	−	1.37366i	−0.912546	−	0.175879i	−0.623852	+	0.781542i	$0.714433\pi$
$62$	−0.575166	+	1.25944i	−0.0730462	+	0.159949i
$63$	−2.35560	+	1.20463i	−0.296778	+	0.151770i
$64$	−0.142315	−	0.989821i	−0.0177894	−	0.123728i
$65$	9.48390	+	4.88929i	1.17633	+	0.606442i
$66$	−3.60334	+	0.694487i	−0.443540	+	0.0854854i
$67$	1.54914	−	6.38565i	0.189258	−	0.780131i	−0.795465	−	0.606000i	$-0.792773\pi$
$67$	1.54914	−	6.38565i	0.189258	−	0.780131i	0.984722	−	0.174131i	$-0.0557116\pi$
$68$	0.893713	+	1.54796i	0.108379	+	0.187717i
$69$	1.89672	−	4.40482i	0.228339	−	0.530278i
$70$	7.76882	+	0.0254779i	0.928552	+	0.00304520i
$71$	−7.41919	+	2.17847i	−0.880496	+	0.258537i	−0.690574	−	0.723262i	$-0.742642\pi$
$71$	−7.41919	+	2.17847i	−0.880496	+	0.258537i	−0.189922	+	0.981799i	$0.560824\pi$
$72$	0.327068	−	0.945001i	0.0385453	−	0.111369i
$73$	−0.0129741	−	0.272359i	−0.00151850	−	0.0318772i	0.997981	−	0.0635145i	$-0.0202309\pi$
$73$	−0.0129741	−	0.272359i	−0.00151850	−	0.0318772i	−0.999499	+	0.0316372i	$0.989928\pi$
$74$	−4.97638	−	1.99224i	−0.578493	−	0.231593i
$75$	0.172350	−	3.61807i	0.0199013	−	0.417779i
$76$	−0.988053	+	2.16353i	−0.113337	+	0.248174i
$77$	−6.38207	+	7.31668i	−0.727304	+	0.833813i
$78$	0.517139	−	3.59678i	0.0585545	−	0.407255i
$79$	−3.21045	+	4.50845i	−0.361204	+	0.507240i	−0.954689	−	0.297605i	$-0.903812\pi$
$79$	−3.21045	+	4.50845i	−0.361204	+	0.507240i	0.593485	+	0.804845i	$0.297752\pi$
$80$	−2.12514	+	2.02632i	−0.237598	+	0.226549i
$81$	0.723734	−	0.690079i	0.0804149	−	0.0766754i
$82$	0.724268	−	1.01709i	0.0799820	−	0.112319i
$83$	1.78220	−	12.3955i	0.195622	−	1.36058i	−0.621183	−	0.783665i	$-0.713348\pi$
$83$	1.78220	−	12.3955i	0.195622	−	1.36058i	0.816805	−	0.576914i	$-0.195743\pi$
$84$	−0.857136	−	2.50306i	−0.0935212	−	0.273106i
$85$	2.18031	−	4.77422i	0.236488	−	0.517836i
$86$	−0.546583	+	11.4742i	−0.0589395	+	1.23729i
$87$	−6.69373	−	2.67976i	−0.717643	−	0.287301i
$88$	−0.174609	−	3.66550i	−0.0186134	−	0.390743i
$89$	−0.505095	+	1.45938i	−0.0535399	+	0.154693i	−0.968600	−	0.248624i	$-0.920022\pi$
$89$	−0.505095	+	1.45938i	−0.0535399	+	0.154693i	0.915060	+	0.403317i	$0.132143\pi$
$90$	−2.81741	+	0.827266i	−0.296981	+	0.0872015i
$91$	−4.77969	−	8.34173i	−0.501048	−	0.874450i
$92$	4.09005	+	2.50429i	0.426418	+	0.261090i
$93$	−0.692279	−	1.19906i	−0.0717860	−	0.124337i
$94$	0.750939	−	3.09541i	0.0774534	−	0.319267i
$95$	6.85783	−	1.32174i	0.703598	−	0.135607i
$96$	0.888835	+	0.458227i	0.0907164	+	0.0467675i
$97$	2.03190	+	14.1322i	0.206308	+	1.43491i	0.785068	+	0.619409i	$0.212628\pi$
$97$	2.03190	+	14.1322i	0.206308	+	1.43491i	−0.578760	+	0.815498i	$0.696463\pi$
$98$	−5.86383	−	3.82303i	−0.592336	−	0.386184i
$99$	1.52443	−	3.33804i	0.153211	−	0.335485i
$100$	3.55672	+	0.685501i	0.355672	+	0.0685501i
$101$	−3.62077	−	2.84741i	−0.360280	−	0.283327i	0.421567	−	0.906797i	$-0.361480\pi$
$101$	−3.62077	−	2.84741i	−0.360280	−	0.283327i	−0.781848	+	0.623470i	$0.785723\pi$
$102$	−1.77933	−	0.169906i	−0.176180	−	0.0168232i
$103$	−2.24724	−	9.26326i	−0.221427	−	0.912736i	−0.968703	−	0.248222i	$-0.920154\pi$
$103$	−2.24724	−	9.26326i	−0.221427	−	0.912736i	0.747276	−	0.664514i	$-0.231361\pi$
$104$	3.48657	+	1.02375i	0.341887	+	0.100387i
$105$	−4.52711	+	6.31352i	−0.441801	+	0.616136i
$106$	1.86931	−	13.0013i	0.181563	−	1.26280i
$107$	10.8124	+	2.08391i	1.04527	+	0.201459i	0.682852	−	0.730557i	$-0.260739\pi$
$107$	10.8124	+	2.08391i	1.04527	+	0.201459i	0.362418	+	0.932016i	$0.381951\pi$
$108$	0.580057	+	0.814576i	0.0558160	+	0.0783826i
$109$	8.74988	−	4.51088i	0.838086	−	0.432064i	0.0149369	−	0.999888i	$-0.495245\pi$
$109$	8.74988	−	4.51088i	0.838086	−	0.432064i	0.823149	+	0.567825i	$0.192215\pi$
$110$	−8.47004	+	6.66091i	−0.807587	+	0.635093i
$111$	4.50942	−	2.89803i	0.428015	−	0.275068i
$112$	2.59957	−	0.492189i	0.245636	−	0.0465075i
$113$	−6.02466	+	1.76900i	−0.566752	+	0.166413i	−0.552541	−	0.833486i	$-0.686342\pi$
$113$	−6.02466	+	1.76900i	−0.566752	+	0.166413i	−0.0142110	+	0.999899i	$0.504524\pi$
$114$	−1.18924	−	2.05982i	−0.111382	−	0.192920i
$115$	−0.976430	−	14.0484i	−0.0910526	−	1.31002i
$116$	3.60510	−	6.24422i	0.334726	−	0.579762i
$117$	2.62988	+	2.50759i	0.243133	+	0.231826i
$118$	−2.36533	−	2.72974i	−0.217746	−	0.251293i
$119$	−3.98672	+	2.54367i	−0.365462	+	0.233178i
$120$	−0.417887	−	2.90647i	−0.0381477	−	0.265323i
$121$	0.117355	−	2.46357i	0.0106686	−	0.223961i
$122$	4.21028	+	5.91250i	0.381180	+	0.535293i
$123$	0.408382	+	1.17994i	0.0368225	+	0.106392i
$124$	1.28538	−	0.514588i	0.115430	−	0.0462114i
$125$	1.68068	+	3.68018i	0.150325	+	0.329165i
$126$	2.53612	+	0.753716i	0.225936	+	0.0671463i
$127$	−0.512053	−	0.150352i	−0.0454374	−	0.0133416i	0.258935	−	0.965895i	$-0.416628\pi$
$127$	−0.512053	−	0.150352i	−0.0454374	−	0.0133416i	−0.304372	+	0.952553i	$0.598447\pi$
$128$	−0.580057	+	0.814576i	−0.0512703	+	0.0719990i
$129$	−9.02954	−	7.10091i	−0.795007	−	0.625200i
$130$	−3.48982	−	10.0832i	−0.306078	−	0.884354i
$131$	−10.5327	+	1.00575i	−0.920249	+	0.0878731i	−0.544417	−	0.838815i	$-0.683249\pi$
$131$	−10.5327	+	1.00575i	−0.920249	+	0.0878731i	−0.375832	+	0.926688i	$0.622643\pi$
$132$	3.08711	+	1.98397i	0.268698	+	0.172682i
$133$	−5.83438	−	2.35796i	−0.505905	−	0.204461i
$134$	−5.52777	+	3.55248i	−0.477526	+	0.306888i
$135$	0.960387	−	2.77486i	0.0826570	−	0.238822i
$136$	0.421401	−	1.73704i	0.0361349	−	0.148950i
$137$	−1.32656	+	2.29768i	−0.113336	+	0.196304i	−0.917113	−	0.398627i	$-0.869487\pi$
$137$	−1.32656	+	2.29768i	−0.113336	+	0.196304i	0.803777	+	0.594930i	$0.202820\pi$
$138$	−4.41240	+	1.87903i	−0.375608	+	0.159954i
$139$	−2.17291			−0.184304			−0.0921520	−	0.995745i	$-0.529375\pi$
$139$	−2.17291			−0.184304			−0.0921520	+	0.995745i	$0.529375\pi$
$140$	−5.60498	−	5.37954i	−0.473707	−	0.454654i
$141$	2.08586	+	2.40721i	0.175661	+	0.202724i
$142$	6.87284	+	3.54319i	0.576756	+	0.297338i
$143$	12.3795	+	4.95600i	1.03522	+	0.414441i
$144$	−0.888835	+	0.458227i	−0.0740696	+	0.0381855i
$145$	−21.0759	+	2.01250i	−1.75025	+	0.167129i
$146$	−0.178560	+	0.206069i	−0.0147777	+	0.0170544i
$147$	6.51550	−	2.55896i	0.537389	−	0.211059i
$148$	2.22677	+	4.87595i	0.183040	+	0.400801i
$149$	0.248334	+	1.02365i	0.0203443	+	0.0838605i	0.981079	−	0.193609i	$-0.0620194\pi$
$149$	0.248334	+	1.02365i	0.0203443	+	0.0838605i	−0.960734	+	0.277470i	$0.910504\pi$
$150$	−2.62149	+	2.49959i	−0.214044	+	0.204090i
$151$	−10.5947	−	1.01167i	−0.862183	−	0.0823285i	−0.345411	−	0.938452i	$-0.612260\pi$
$151$	−10.5947	−	1.01167i	−0.862183	−	0.0823285i	−0.516772	+	0.856123i	$0.672866\pi$
$152$	2.20810	−	0.883989i	0.179100	−	0.0717010i
$153$	1.17051	−	1.35085i	0.0946305	−	0.109209i
$154$	9.66801	−	0.891197i	0.779070	−	0.0718147i
$155$	−3.42016	−	2.19800i	−0.274714	−	0.176548i
$156$	−2.85633	+	2.24625i	−0.228690	+	0.179844i
$157$	0.707233	+	14.8467i	0.0564434	+	1.18489i	0.832425	+	0.554137i	$0.186952\pi$
$157$	0.707233	+	14.8467i	0.0564434	+	1.18489i	−0.775982	+	0.630755i	$0.782745\pi$
$158$	5.43470	−	1.04745i	0.432361	−	0.0833308i
$159$	9.50626	+	9.06420i	0.753895	+	0.718838i
$160$	2.93635			0.232139
$161$	−6.13977	+	11.1042i	−0.483882	+	0.875133i
$162$	−1.00000			−0.0785674
$163$	13.4059	+	12.7825i	1.05003	+	1.00120i	0.999997	+	0.00245168i	$0.000780396\pi$
$163$	13.4059	+	12.7825i	1.05003	+	1.00120i	0.0500307	+	0.998748i	$0.484068\pi$
$164$	−1.22605	+	0.236302i	−0.0957385	+	0.0184521i
$165$	−0.512714	−	10.7632i	−0.0399148	−	0.837914i
$166$	−9.84369	+	7.74116i	−0.764018	+	0.600831i
$167$	−10.4682	−	6.72750i	−0.810053	−	0.520590i	0.0688290	−	0.997628i	$-0.478074\pi$
$167$	−10.4682	−	6.72750i	−0.810053	−	0.520590i	−0.878882	+	0.477039i	$0.841710\pi$
$168$	−1.10697	+	2.40304i	−0.0854047	+	0.185399i
$169$	−0.133762	+	0.154370i	−0.0102894	+	0.0118746i
$170$	−4.87255	+	1.95068i	−0.373708	+	0.149610i
$171$	2.36770	+	0.226088i	0.181063	+	0.0172894i
$172$	8.31367	−	7.92707i	0.633912	−	0.604433i
$173$	1.51559	+	6.24735i	0.115228	+	0.474977i	0.999961	+	0.00887763i	$0.00282587\pi$
$173$	1.51559	+	6.24735i	0.115228	+	0.474977i	−0.884732	+	0.466099i	$0.845659\pi$
$174$	2.99523	+	6.55864i	0.227068	+	0.497209i
$175$	−1.39496	+	9.48130i	−0.105449	+	0.716719i
$176$	−2.40311	+	2.77334i	−0.181141	+	0.209048i
$177$	3.59561	−	0.343339i	0.270262	−	0.0258069i
$178$	1.37264	−	0.707644i	0.102884	−	0.0530402i
$179$	18.1933	+	7.28350i	1.35983	+	0.544394i	0.932980	−	0.359927i	$-0.117199\pi$
$179$	18.1933	+	7.28350i	1.35983	+	0.544394i	0.426851	+	0.904322i	$0.359623\pi$
$180$	2.60994	+	1.34552i	0.194533	+	0.100289i
$181$	1.25395	+	1.44713i	0.0932051	+	0.107564i	0.800436	−	0.599418i	$-0.204601\pi$
$181$	1.25395	+	1.44713i	0.0932051	+	0.107564i	−0.707231	+	0.706983i	$0.750056\pi$
$182$	−2.29722	+	9.33555i	−0.170282	+	0.691997i
$183$	−7.25838			−0.536555
$184$	−1.23195	−	4.63490i	−0.0908209	−	0.341689i
$185$	7.86995	−	13.6312i	0.578610	−	1.00218i
$186$	−0.326422	+	1.34553i	−0.0239344	+	0.0986590i
$187$	2.14532	−	6.19848i	0.156881	−	0.453278i
$188$	−2.67956	+	1.72205i	−0.195427	+	0.125593i
$189$	−2.08505	+	1.62867i	−0.151665	+	0.118468i
$190$	−5.87535	−	3.77586i	−0.426242	−	0.273929i
$191$	−26.3635	+	2.51741i	−1.90760	+	0.182153i	−0.981014	−	0.193939i	$-0.937874\pi$
$191$	−26.3635	+	2.51741i	−1.90760	+	0.182153i	−0.926582	+	0.376092i	$0.877268\pi$
$192$	−0.327068	−	0.945001i	−0.0236041	−	0.0681996i
$193$	−1.59232	−	1.25222i	−0.114618	−	0.0901364i	0.559205	−	0.829029i	$-0.311106\pi$
$193$	−1.59232	−	1.25222i	−0.114618	−	0.0901364i	−0.673823	+	0.738893i	$0.735349\pi$
$194$	8.28177	−	11.6301i	0.594597	−	0.834994i
$195$	10.2378	+	3.00609i	0.733145	+	0.215271i
$196$	1.60566	+	6.81336i	0.114690	+	0.486668i
$197$	1.41707	+	3.10296i	0.100962	+	0.221076i	0.953372	−	0.301798i	$-0.0975869\pi$
$197$	1.41707	+	3.10296i	0.100962	+	0.221076i	−0.852410	+	0.522875i	$0.824860\pi$
$198$	−3.40679	+	1.36387i	−0.242110	+	0.0969262i
$199$	7.54648	+	21.8041i	0.534956	+	1.54565i	0.811322	+	0.584600i	$0.198749\pi$
$199$	7.54648	+	21.8041i	0.534956	+	1.54565i	−0.276366	+	0.961052i	$0.589130\pi$
$200$	−2.10107	−	2.95054i	−0.148568	−	0.208634i
$201$	0.312655	−	6.56343i	0.0220529	−	0.462948i
$202$	0.655540	+	4.55938i	0.0461236	+	0.320797i
$203$	16.9270	+	8.79688i	1.18805	+	0.617420i
$204$	1.17051	+	1.35085i	0.0819524	+	0.0945781i
$205$	2.65348	+	2.53009i	0.185327	+	0.176709i
$206$	−4.76598	+	8.25491i	−0.332061	+	0.575147i
$207$	1.02883	−	4.68418i	0.0715085	−	0.325573i
$208$	−1.81688	−	3.14693i	−0.125978	−	0.218201i
$209$	8.37462	−	2.45901i	0.579285	−	0.170093i
$210$	7.63325	−	1.44524i	0.526744	−	0.0997311i
$211$	−16.6077	+	10.6731i	−1.14332	+	0.734770i	−0.968299	−	0.249795i	$-0.919637\pi$
$211$	−16.6077	+	10.6731i	−1.14332	+	0.734770i	−0.175025	+	0.984564i	$0.556001\pi$
$212$	−10.3248	+	8.11953i	−0.709111	+	0.557651i
$213$	−6.87284	+	3.54319i	−0.470919	+	0.242776i
$214$	−6.38721	−	8.96957i	−0.436620	−	0.613148i
$215$	−33.1209	−	6.38353i	−2.25883	−	0.435353i
$216$	0.142315	−	0.989821i	0.00968330	−	0.0673488i
$217$	1.51081	+	3.33713i	0.102560	+	0.226539i
$218$	−9.44544	−	2.77343i	−0.639726	−	0.187841i
$219$	−0.0642839	−	0.264982i	−0.00434390	−	0.0179058i
$220$	10.7266	+	1.02427i	0.723188	+	0.0690561i
$221$	5.10548	+	4.01500i	0.343432	+	0.270078i
$222$	−5.26349	−	1.01445i	−0.353262	−	0.0680857i
$223$	−9.87927	+	21.6326i	−0.661565	+	1.44863i	0.219491	+	0.975614i	$0.429560\pi$
$223$	−9.87927	+	21.6326i	−0.661565	+	1.44863i	−0.881057	+	0.473011i	$0.843167\pi$
$224$	−2.22104	−	1.43769i	−0.148400	−	0.0960599i
$225$	−0.515489	−	3.58531i	−0.0343659	−	0.239020i
$226$	5.58100	+	2.87721i	0.371243	+	0.191389i
$227$	24.0155	−	4.62860i	1.59396	−	0.307211i	0.686431	−	0.727195i	$-0.259177\pi$
$227$	24.0155	−	4.62860i	1.59396	−	0.307211i	0.907531	+	0.419984i	$0.137964\pi$
$228$	−0.560746	+	2.31143i	−0.0371363	+	0.153078i
$229$	10.8474	+	18.7883i	0.716820	+	1.24157i	0.962254	+	0.272155i	$0.0877362\pi$
$229$	10.8474	+	18.7883i	0.716820	+	1.24157i	−0.245434	+	0.969413i	$0.578930\pi$
$230$	−8.98781	+	10.8411i	−0.592638	+	0.714841i
$231$	−4.88205	+	8.39227i	−0.321215	+	0.552171i
$232$	−6.91815	+	2.03135i	−0.454198	+	0.133365i
$233$	−3.45856	+	9.99284i	−0.226578	+	0.654653i	0.773212	+	0.634147i	$0.218649\pi$
$233$	−3.45856	+	9.99284i	−0.226578	+	0.654653i	−0.999790	+	0.0205055i	$0.993472\pi$
$234$	−0.172902	−	3.62965i	−0.0113029	−	0.237278i
$235$	8.68290	+	3.47611i	0.566410	+	0.226756i
$236$	−0.171864	+	3.60787i	−0.0111874	+	0.234852i
$237$	−2.29920	+	5.03455i	−0.149349	+	0.327029i
$238$	4.64066	+	0.910209i	0.300809	+	0.0590001i
$239$	−2.47319	+	17.2014i	−0.159977	+	1.11267i	0.738693	+	0.674042i	$0.235443\pi$
$239$	−2.47319	+	17.2014i	−0.159977	+	1.11267i	−0.898670	+	0.438625i	$0.855466\pi$
$240$	−1.70325	+	2.39188i	−0.109944	+	0.154395i
$241$	2.82594	−	2.69453i	0.182035	−	0.173570i	−0.593583	−	0.804773i	$-0.702287\pi$
$241$	2.82594	−	2.69453i	0.182035	−	0.173570i	0.775618	+	0.631203i	$0.217439\pi$
$242$	−1.78499	+	1.70199i	−0.114744	+	0.109408i
$243$	0.580057	−	0.814576i	0.0372107	−	0.0522551i
$244$	1.03298	−	7.18450i	0.0661295	−	0.459941i
$245$	13.5619	−	15.4454i	0.866439	−	0.986772i
$246$	0.518693	−	1.13578i	0.0330707	−	0.0724147i
$247$	−0.411242	+	8.63302i	−0.0261667	+	0.549306i
$248$	−1.28538	−	0.514588i	−0.0816216	−	0.0326764i
$249$	−0.595865	−	12.5087i	−0.0377614	−	0.792710i
$250$	1.32325	−	3.82327i	0.0836895	−	0.241805i
$251$	2.99563	−	0.879595i	0.189082	−	0.0555196i	−0.185820	−	0.982584i	$-0.559494\pi$
$251$	2.99563	−	0.879595i	0.189082	−	0.0555196i	0.374903	+	0.927064i	$0.377676\pi$
$252$	−1.31535	−	2.29561i	−0.0828595	−	0.144610i
$253$	−2.88362	−	17.3612i	−0.181292	−	1.09149i
$254$	0.266835	+	0.462172i	0.0167427	+	0.0289993i
$255$	1.23738	−	5.10057i	0.0774880	−	0.319410i
$256$	0.981929	−	0.189251i	0.0613705	−	0.0118282i
$257$	15.2909	+	7.88299i	0.953818	+	0.491727i	0.863590	−	0.504194i	$-0.168210\pi$
$257$	15.2909	+	7.88299i	0.953818	+	0.491727i	0.0902272	+	0.995921i	$0.471241\pi$
$258$	1.63480	+	11.3703i	0.101778	+	0.707882i
$259$	−12.6269	+	6.45727i	−0.784595	+	0.401235i
$260$	−4.43249	+	9.70580i	−0.274891	+	0.601928i
$261$	−7.07991	−	1.36454i	−0.438236	−	0.0844630i
$262$	8.31694	+	6.54052i	0.513823	+	0.404075i
$263$	9.43475	+	0.900909i	0.581772	+	0.0555524i	0.381793	−	0.924248i	$-0.375307\pi$
$263$	9.43475	+	0.900909i	0.581772	+	0.0555524i	0.199979	+	0.979800i	$0.435913\pi$
$264$	−0.865154	−	3.56621i	−0.0532465	−	0.219485i
$265$	37.0067	+	10.8662i	2.27331	+	0.667503i
$266$	2.59536	+	5.73272i	0.159132	+	0.351495i
$267$	−0.219778	+	1.52859i	−0.0134502	+	0.0935483i
$268$	6.45212	+	1.24355i	0.394126	+	0.0759616i
$269$	−3.22474	−	4.52851i	−0.196616	−	0.276108i	0.704484	−	0.709720i	$-0.251178\pi$
$269$	−3.22474	−	4.52851i	−0.196616	−	0.276108i	−0.901100	+	0.433611i	$0.857239\pi$
$270$	−2.60994	+	1.34552i	−0.158836	+	0.0818854i
$271$	−3.49620	+	2.74944i	−0.212379	+	0.167017i	−0.718682	−	0.695339i	$-0.755254\pi$
$271$	−3.49620	+	2.74944i	−0.212379	+	0.167017i	0.506303	+	0.862356i	$0.331012\pi$
$272$	−1.50368	+	0.966355i	−0.0911739	+	0.0585939i
$273$	−6.27200	−	7.28642i	−0.379599	−	0.440994i
$274$	2.54566	−	0.747472i	0.153789	−	0.0451564i
$275$	−6.64606	−	11.5113i	−0.400773	−	0.694159i
$276$	4.49008	+	1.68498i	0.270271	+	0.101424i
$277$	3.73603	−	6.47099i	0.224476	−	0.388804i	−0.731686	−	0.681642i	$-0.761266\pi$
$277$	3.73603	−	6.47099i	0.224476	−	0.388804i	0.956162	+	0.292838i	$0.0945996\pi$
$278$	1.57261	+	1.49948i	0.0943189	+	0.0899329i
$279$	−0.906692	−	1.04638i	−0.0542823	−	0.0626451i
$280$	0.344206	+	7.76123i	0.0205703	+	0.463822i
$281$	1.71245	+	11.9103i	0.102156	+	0.710511i	0.974950	+	0.222423i	$0.0713965\pi$
$281$	1.71245	+	11.9103i	0.102156	+	0.710511i	−0.872794	+	0.488088i	$0.837694\pi$
$282$	0.151558	−	3.18159i	0.00902514	−	0.189461i
$283$	−12.3983	−	17.4110i	−0.737002	−	1.03497i	−0.997580	−	0.0695218i	$-0.977853\pi$
$283$	−12.3983	−	17.4110i	−0.737002	−	1.03497i	0.260578	−	0.965453i	$-0.416087\pi$
$284$	−2.52902	−	7.30713i	−0.150070	−	0.433598i
$285$	6.48376	−	2.59570i	0.384065	−	0.153756i
$286$	−5.53942	−	12.1296i	−0.327553	−	0.717241i
$287$	−0.768303	−	3.21294i	−0.0453515	−	0.189654i
$288$	0.959493	+	0.281733i	0.0565387	+	0.0166013i
$289$	−8.00775	+	11.2453i	−0.471044	+	0.661489i
$290$	16.6421	+	13.0875i	0.977258	+	0.768524i
$291$	4.66972	+	13.4923i	0.273744	+	0.790931i
$292$	0.271433	−	0.0259187i	0.0158844	−	0.00151678i
$293$	19.3489	+	12.4348i	1.13037	+	0.726447i	0.965638	−	0.259891i	$-0.0836867\pi$
$293$	19.3489	+	12.4348i	1.13037	+	0.726447i	0.164735	+	0.986338i	$0.447323\pi$
$294$	−6.48137	−	2.64421i	−0.378001	−	0.154213i
$295$	8.92233	−	5.73404i	0.519478	−	0.333849i
$296$	1.75320	−	5.06554i	0.101903	−	0.294428i
$297$	0.865154	−	3.56621i	0.0502013	−	0.206933i
$298$	0.526670	−	0.912219i	0.0305092	−	0.0528435i
$299$	17.1798	+	2.92439i	0.993534	+	0.169122i
$300$	3.62217			0.209126
$301$	21.9270	+	21.0451i	1.26385	+	1.21302i
$302$	6.96960	+	8.04334i	0.401055	+	0.462842i
$303$	−4.09421	−	2.11071i	−0.235206	−	0.121257i
$304$	−2.20810	−	0.883989i	−0.126643	−	0.0507002i
$305$	−18.9439	+	9.76627i	−1.08473	+	0.559215i
$306$	−1.77933	+	0.169906i	−0.101718	+	0.00971285i
$307$	7.66265	−	8.84317i	0.437330	−	0.504706i	−0.493708	−	0.869628i	$-0.664359\pi$
$307$	7.66265	−	8.84317i	0.437330	−	0.504706i	0.931038	+	0.364922i	$0.118904\pi$
$308$	−7.61206	−	6.02670i	−0.433737	−	0.343403i
$309$	−3.95972	−	8.67057i	−0.225260	−	0.493252i
$310$	0.958490	+	3.95095i	0.0544386	+	0.224399i
$311$	19.8016	−	18.8808i	1.12285	−	1.07063i	0.125939	−	0.992038i	$-0.459806\pi$
$311$	19.8016	−	18.8808i	1.12285	−	1.07063i	0.996907	−	0.0785935i	$-0.0250429\pi$
$312$	3.61731	+	0.345411i	0.204790	+	0.0195551i
$313$	−5.34032	+	2.13794i	−0.301852	+	0.120844i	−0.517644	−	0.855596i	$-0.673191\pi$
$313$	−5.34032	+	2.13794i	−0.301852	+	0.120844i	0.215792	+	0.976439i	$0.430767\pi$
$314$	9.73351	−	11.2331i	0.549294	−	0.633919i
$315$	−3.25046	+	7.05618i	−0.183143	+	0.397571i
$316$	−4.65610	−	2.99229i	−0.261926	−	0.168330i
$317$	−18.4231	+	14.4881i	−1.03474	+	0.813732i	−0.982754	−	0.184916i	$-0.940799\pi$
$317$	−18.4231	+	14.4881i	−1.03474	+	0.813732i	−0.0519900	+	0.998648i	$0.516556\pi$
$318$	−0.624989	−	13.1201i	−0.0350477	−	0.735741i
$319$	−25.9808	+	5.00740i	−1.45465	+	0.280360i
$320$	−2.12514	−	2.02632i	−0.118799	−	0.113275i
$321$	11.0113			0.614593
$322$	12.1063	−	3.79956i	0.674660	−	0.211741i
$323$	4.25134			0.236551
$324$	0.723734	+	0.690079i	0.0402074	+	0.0383377i
$325$	12.9243	−	2.49095i	0.716910	−	0.138173i
$326$	−0.881368	−	18.5022i	−0.0488145	−	1.02474i
$327$	7.73807	−	6.08528i	0.427916	−	0.336517i
$328$	1.05040	+	0.675052i	0.0579987	+	0.0372735i
$329$	−4.86574	−	6.88062i	−0.268257	−	0.379341i
$330$	−7.05639	+	8.14351i	−0.388441	+	0.448285i
$331$	−14.4586	+	5.78833i	−0.794714	+	0.318156i	−0.733255	−	0.679954i	$-0.762000\pi$
$331$	−14.4586	+	5.78833i	−0.794714	+	0.318156i	−0.0614594	+	0.998110i	$0.519575\pi$
$332$	12.4662	+	1.19038i	0.684173	+	0.0653306i
$333$	3.87947	−	3.69907i	0.212594	−	0.202708i
$334$	2.93368	+	12.0928i	0.160524	+	0.661689i
$335$	−8.01518	−	17.5508i	−0.437916	−	0.958903i
$336$	2.45944	−	0.975266i	0.134174	−	0.0532051i
$337$	−21.7526	+	25.1038i	−1.18494	+	1.36749i	−0.270523	+	0.962713i	$0.587197\pi$
$337$	−21.7526	+	25.1038i	−1.18494	+	1.36749i	−0.914415	+	0.404778i	$0.867349\pi$
$338$	0.203336	−	0.0194162i	0.0110600	−	0.00105610i
$339$	−5.58100	+	2.87721i	−0.303118	+	0.156268i
$340$	4.87255	+	1.95068i	0.264251	+	0.105790i
$341$	−4.51604	−	2.32818i	−0.244557	−	0.126078i
$342$	−1.55757	−	1.79753i	−0.0842236	−	0.0971993i
$343$	−17.8205	+	5.04268i	−0.962218	+	0.272279i
$344$	−11.4872			−0.619348
$345$	−3.61746	−	13.6097i	−0.194757	−	0.732722i
$346$	3.21428	−	5.56729i	0.172801	−	0.299300i
$347$	−4.54598	+	18.7388i	−0.244041	+	1.00595i	0.709504	+	0.704701i	$0.248919\pi$
$347$	−4.54598	+	18.7388i	−0.244041	+	1.00595i	−0.953545	+	0.301250i	$0.902596\pi$
$348$	2.35823	−	6.81365i	0.126414	−	0.365250i
$349$	−15.5390	+	9.98628i	−0.831781	+	0.534553i	−0.885844	−	0.463984i	$-0.846419\pi$
$349$	−15.5390	+	9.98628i	−0.831781	+	0.534553i	0.0540621	+	0.998538i	$0.482783\pi$
$350$	7.55243	−	5.89931i	0.403694	−	0.315331i
$351$	3.05692	+	1.96456i	0.163166	+	0.104861i
$352$	3.65304	−	0.348823i	0.194708	−	0.0185923i
$353$	−11.1164	−	32.1188i	−0.591668	−	1.70951i	−0.698846	−	0.715273i	$-0.746303\pi$
$353$	−11.1164	−	32.1188i	−0.591668	−	1.70951i	0.107178	−	0.994240i	$-0.465819\pi$
$354$	−2.83919	−	2.23277i	−0.150901	−	0.118670i
$355$	−13.1702	+	18.4950i	−0.699004	+	0.981613i
$356$	−1.48176	−	0.435083i	−0.0785329	−	0.0230593i
$357$	−3.43328	+	3.25220i	−0.181709	+	0.172125i
$358$	−8.14092	−	17.8261i	−0.430261	−	0.942141i
$359$	−17.6329	+	7.05914i	−0.930628	+	0.372567i	−0.786921	−	0.617053i	$-0.788326\pi$
$359$	−17.6329	+	7.05914i	−0.930628	+	0.372567i	−0.143706	+	0.989620i	$0.545902\pi$
$360$	−0.960387	−	2.77486i	−0.0506169	−	0.146248i
$361$	−7.73962	−	10.8688i	−0.407349	−	0.572041i
$362$	0.0911113	−	1.91266i	0.00478870	−	0.100527i
$363$	−0.351001	−	2.44126i	−0.0184228	−	0.128133i
$364$	8.10485	−	5.17119i	0.424810	−	0.271044i
$365$	−0.524314	−	0.605090i	−0.0274438	−	0.0316719i
$366$	5.25314	+	5.00886i	0.274586	+	0.261817i
$367$	4.08708	−	7.07904i	0.213344	−	0.369523i	−0.739415	−	0.673250i	$-0.764898\pi$
$367$	4.08708	−	7.07904i	0.213344	−	0.369523i	0.952759	+	0.303727i	$0.0982311\pi$
$368$	−2.30684	+	4.20458i	−0.120252	+	0.219179i
$369$	0.624307	+	1.08133i	0.0325001	+	0.0562919i
$370$	−15.1023	+	4.43444i	−0.785132	+	0.230536i
$371$	−22.6715	−	26.3383i	−1.17704	−	1.36742i
$372$	1.16476	−	0.748548i	0.0603902	−	0.0388104i
$373$	21.4870	−	16.8976i	1.11255	−	0.874922i	0.119529	−	0.992831i	$-0.461861\pi$
$373$	21.4870	−	16.8976i	1.11255	−	0.874922i	0.993024	+	0.117909i	$0.0376190\pi$
$374$	−5.83008	+	3.00561i	−0.301466	+	0.155417i
$375$	2.34679	+	3.29560i	0.121187	+	0.170184i
$376$	3.12764	+	0.602803i	0.161296	+	0.0310872i
$377$	3.72868	−	25.9335i	0.192037	−	1.33565i
$378$	2.63293	+	0.260131i	0.135423	+	0.0133797i
$379$	−27.3005	−	8.01615i	−1.40233	−	0.411762i	−0.508848	−	0.860857i	$-0.669928\pi$
$379$	−27.3005	−	8.01615i	−1.40233	−	0.411762i	−0.893484	+	0.449095i	$0.851747\pi$
$380$	1.64655	+	6.78717i	0.0844662	+	0.348174i
$381$	−0.531254	−	0.0507286i	−0.0272170	−	0.00259891i
$382$	20.8174	+	16.3710i	1.06511	+	0.837611i
$383$	24.1796	+	4.66024i	1.23552	+	0.238127i	0.764865	−	0.644190i	$-0.222805\pi$
$383$	24.1796	+	4.66024i	1.23552	+	0.238127i	0.470655	+	0.882317i	$0.344018\pi$
$384$	−0.415415	+	0.909632i	−0.0211991	+	0.0464195i
$385$	−1.44990	+	28.4722i	−0.0738936	+	1.45108i
$386$	0.288290	+	2.00510i	0.0146736	+	0.102057i
$387$	−10.2102	−	5.26374i	−0.519015	−	0.267571i
$388$	−14.0195	+	2.70204i	−0.711733	+	0.137175i
$389$	−3.81791	+	15.7376i	−0.193576	+	0.797929i	0.789353	+	0.613940i	$0.210416\pi$
$389$	−3.81791	+	15.7376i	−0.193576	+	0.797929i	−0.982928	+	0.183989i	$0.941099\pi$
$390$	−5.33501	−	9.24051i	−0.270149	−	0.467912i
$391$	1.03476	−	8.50951i	0.0523300	−	0.430344i
$392$	3.53969	−	6.03909i	0.178781	−	0.305020i
$393$	−10.1520	+	2.98091i	−0.512103	+	0.150367i
$394$	1.11570	−	3.22361i	0.0562082	−	0.162403i
$395$	0.773296	+	16.2335i	0.0389087	+	0.816795i
$396$	3.40679	+	1.36387i	0.171198	+	0.0685372i
$397$	1.48982	−	31.2752i	0.0747720	−	1.56966i	−0.580497	−	0.814262i	$-0.697142\pi$
$397$	1.48982	−	31.2752i	0.0747720	−	1.56966i	0.655269	−	0.755395i	$-0.272555\pi$
$398$	9.58492	−	20.9880i	0.480449	−	1.05204i
$399$	−6.17519	−	1.21119i	−0.309146	−	0.0606352i
$400$	−0.515489	+	3.58531i	−0.0257745	+	0.179265i
$401$	−0.425501	+	0.597533i	−0.0212485	+	0.0298394i	−0.825064	−	0.565040i	$-0.808861\pi$
$401$	−0.425501	+	0.597533i	−0.0212485	+	0.0298394i	0.803815	+	0.594879i	$0.202800\pi$
$402$	−4.75556	+	4.53442i	−0.237186	+	0.226156i
$403$	3.64122	−	3.47190i	0.181382	−	0.172948i
$404$	2.67190	−	3.75215i	0.132932	−	0.186677i
$405$	0.417887	−	2.90647i	0.0207650	−	0.144423i
$406$	−6.18013	−	18.0476i	−0.306715	−	0.895687i
$407$	8.17148	−	17.8931i	0.405045	−	0.886926i
$408$	0.0850491	−	1.78540i	0.00421056	−	0.0883905i
$409$	−9.04676	−	3.62177i	−0.447333	−	0.179085i	0.137048	−	0.990564i	$-0.456239\pi$
$409$	−9.04676	−	3.62177i	−0.447333	−	0.179085i	−0.584381	+	0.811479i	$0.698663\pi$
$410$	−0.174453	−	3.66222i	−0.00861562	−	0.180864i
$411$	−0.867753	+	2.50721i	−0.0428031	+	0.123671i
$412$	9.14584	−	2.68546i	0.450583	−	0.132303i
$413$	−9.55630	−	0.0313400i	−0.470235	−	0.00154214i
$414$	−3.97705	+	2.68013i	−0.195461	+	0.131721i
$415$	−18.3859	−	31.8453i	−0.902527	−	1.56322i
$416$	−0.856693	+	3.53134i	−0.0420028	+	0.173138i
$417$	−2.13365	+	0.411226i	−0.104485	+	0.0201378i
$418$	−7.75791	−	3.99948i	−0.379452	−	0.195621i
$419$	3.87708	+	26.9657i	0.189408	+	1.31736i	0.833545	+	0.552451i	$0.186307\pi$
$419$	3.87708	+	26.9657i	0.189408	+	1.31736i	−0.644137	+	0.764910i	$0.722783\pi$
$420$	−6.52177	−	4.22157i	−0.318230	−	0.205992i
$421$	−8.26449	+	18.0967i	−0.402786	+	0.881979i	0.594194	+	0.804322i	$0.297471\pi$
$421$	−8.26449	+	18.0967i	−0.402786	+	0.881979i	−0.996980	+	0.0776573i	$0.975256\pi$
$422$	19.3849	+	3.73613i	0.943642	+	0.181872i
$423$	2.50373	+	1.96896i	0.121736	+	0.0957340i
$424$	13.0755	+	1.24856i	0.635004	+	0.0606356i
$425$	−1.52639	−	6.29186i	−0.0740408	−	0.305200i
$426$	7.41919	+	2.17847i	0.359461	+	0.105547i
$427$	19.1108	+	1.88813i	0.924838	+	0.0913730i
$428$	−1.56708	+	10.8993i	−0.0757475	+	0.526836i
$429$	13.0937	+	2.52360i	0.632170	+	0.121841i
$430$	19.5656	+	27.4760i	0.943536	+	1.32501i
$431$	−35.3403	+	18.2192i	−1.70228	+	0.877587i	−0.719112	+	0.694894i	$0.755451\pi$
$431$	−35.3403	+	18.2192i	−1.70228	+	0.877587i	−0.983170	+	0.182693i	$0.941518\pi$
$432$	−0.786053	+	0.618159i	−0.0378190	+	0.0297412i
$433$	−10.2057	+	6.55878i	−0.490453	+	0.315195i	−0.762387	−	0.647121i	$-0.775973\pi$
$433$	−10.2057	+	6.55878i	−0.490453	+	0.315195i	0.271935	+	0.962316i	$0.412337\pi$
$434$	1.20946	−	3.45777i	0.0580559	−	0.165978i
$435$	−20.3141	+	5.96476i	−0.973988	+	0.285989i
$436$	4.92210	+	8.52533i	0.235726	+	0.408289i
$437$	10.0224	−	5.44658i	0.479437	−	0.260545i
$438$	−0.136334	+	0.236137i	−0.00651429	+	0.0112831i
$439$	29.7505	+	28.3670i	1.41991	+	1.35389i	0.843963	+	0.536401i	$0.180217\pi$
$439$	29.7505	+	28.3670i	1.41991	+	1.35389i	0.575951	+	0.817484i	$0.304632\pi$
$440$	−7.05639	−	8.14351i	−0.336400	−	0.388227i
$441$	5.91347	−	3.74578i	0.281594	−	0.178370i
$442$	−0.924347	−	6.42898i	−0.0439667	−	0.305795i
$443$	1.64262	−	34.4829i	0.0780433	−	1.63833i	−0.532558	−	0.846393i	$-0.678769\pi$
$443$	1.64262	−	34.4829i	0.0780433	−	1.63833i	0.610602	−	0.791938i	$-0.290928\pi$
$444$	3.10931	+	4.36642i	0.147561	+	0.207221i
$445$	1.48314	+	4.28524i	0.0703074	+	0.203140i
$446$	22.0782	−	8.83876i	1.04543	−	0.418528i
$447$	0.437573	+	0.958152i	0.0206965	+	0.0453190i
$448$	0.615324	+	2.57320i	0.0290713	+	0.121572i
$449$	22.9752	+	6.74612i	1.08427	+	0.318369i	0.774584	−	0.632471i	$-0.217959\pi$
$449$	22.9752	+	6.74612i	1.08427	+	0.318369i	0.309682	+	0.950840i	$0.399778\pi$
$450$	−2.10107	+	2.95054i	−0.0990452	+	0.139090i
$451$	3.60168	+	2.83240i	0.169597	+	0.133372i
$452$	−2.05366	−	5.93366i	−0.0965961	−	0.279096i
$453$	−10.5947	+	1.01167i	−0.497781	+	0.0475324i
$454$	−20.5749	−	13.2227i	−0.965628	−	0.620571i
$455$	−26.1735	−	10.5780i	−1.22703	−	0.495905i
$456$	2.00090	−	1.28590i	0.0937007	−	0.0602178i
$457$	6.90934	−	19.9632i	0.323205	−	0.933840i	−0.659989	−	0.751276i	$-0.729439\pi$
$457$	6.90934	−	19.9632i	0.323205	−	0.933840i	0.983194	−	0.182565i	$-0.0584399\pi$
$458$	5.11477	−	21.0834i	0.238997	−	0.985160i
$459$	0.893713	−	1.54796i	0.0417149	−	0.0722524i
$460$	13.9860	−	1.64377i	0.652100	−	0.0766413i
$461$	−7.41526			−0.345363			−0.172681	−	0.984978i	$-0.555243\pi$
$461$	−7.41526			−0.345363			−0.172681	+	0.984978i	$0.555243\pi$
$462$	9.32463	−	2.70477i	0.433821	−	0.125837i
$463$	−11.0273	−	12.7261i	−0.512480	−	0.591434i	0.439252	−	0.898364i	$-0.355244\pi$
$463$	−11.0273	−	12.7261i	−0.512480	−	0.591434i	−0.951732	+	0.306930i	$0.900698\pi$
$464$	6.40869	+	3.30391i	0.297516	+	0.153380i
$465$	−3.77433	−	1.51101i	−0.175030	−	0.0700715i
$466$	9.39893	−	4.84548i	0.435397	−	0.224463i
$467$	−18.5147	+	1.76794i	−0.856759	+	0.0818106i	−0.514184	−	0.857680i	$-0.671905\pi$
$467$	−18.5147	+	1.76794i	−0.856759	+	0.0818106i	−0.342575	+	0.939490i	$0.611299\pi$
$468$	−2.37961	+	2.74622i	−0.109998	+	0.126944i
$469$	−2.53055	+	17.1997i	−0.116850	+	0.794209i
$470$	−3.88532	−	8.50767i	−0.179217	−	0.392429i
$471$	3.50420	+	14.4445i	0.161465	+	0.665568i
$472$	2.61410	−	2.49254i	0.120324	−	0.114728i
$473$	−41.9632	−	4.00700i	−1.92947	−	0.184242i
$474$	5.13825	−	2.05705i	0.236008	−	0.0944833i
$475$	5.64178	−	6.51096i	0.258863	−	0.298744i
$476$	−2.73049	−	3.86117i	−0.125152	−	0.176977i
$477$	11.0499	+	7.10132i	0.505939	+	0.325147i
$478$	13.6603	−	10.7426i	0.624806	−	0.491353i
$479$	0.290557	+	6.09954i	0.0132759	+	0.278695i	0.995738	+	0.0922310i	$0.0293998\pi$
$479$	0.290557	+	6.09954i	0.0132759	+	0.278695i	−0.982462	+	0.186464i	$0.940297\pi$
$480$	2.88329	−	0.555709i	0.131604	−	0.0253645i
$481$	14.0971	+	13.4416i	0.642772	+	0.612882i
$482$	−3.90467			−0.177853
$483$	−3.92733	+	12.0655i	−0.178700	+	0.548999i
$484$	2.46637			0.112108
$485$	30.3417	+	28.9308i	1.37775	+	1.31368i
$486$	−0.981929	+	0.189251i	−0.0445412	+	0.00858461i
$487$	−0.582791	−	12.2343i	−0.0264088	−	0.554388i	−0.972839	−	0.231481i	$-0.925643\pi$
$487$	−0.582791	−	12.2343i	−0.0264088	−	0.554388i	0.946431	−	0.322907i	$-0.104660\pi$
$488$	−5.70547	+	4.48684i	−0.258275	+	0.203109i
$489$	15.5827	+	10.0144i	0.704674	+	0.452866i
$490$	−20.4738	+	1.81958i	−0.924911	+	0.0822002i
$491$	27.6352	−	31.8927i	1.24716	−	1.43930i	0.392794	−	0.919627i	$-0.371509\pi$
$491$	27.6352	−	31.8927i	1.24716	−	1.43930i	0.854366	−	0.519672i	$-0.173946\pi$
$492$	−1.15917	+	0.464063i	−0.0522596	+	0.0209216i
$493$	−12.8294	−	1.22505i	−0.577805	−	0.0551737i
$494$	6.25510	−	5.96422i	0.281430	−	0.268343i
$495$	−2.54040	−	10.4717i	−0.114182	−	0.470666i
$496$	0.575166	+	1.25944i	0.0258257	+	0.0565504i
$497$	19.0174	−	7.54115i	0.853047	−	0.338267i
$498$	−8.20078	+	9.46420i	−0.367486	+	0.424101i
$499$	−7.30809	+	0.697838i	−0.327155	+	0.0312395i	−0.257342	−	0.966321i	$-0.582847\pi$
$499$	−7.30809	+	0.697838i	−0.327155	+	0.0312395i	−0.0698137	+	0.997560i	$0.522240\pi$
$500$	−3.59604	+	1.85389i	−0.160820	+	0.0829083i
$501$	−11.5522	−	4.62481i	−0.516115	−	0.206621i
$502$	−2.77503	−	1.43063i	−0.123856	−	0.0638520i
$503$	−6.95459	−	8.02603i	−0.310090	−	0.357863i	0.579217	−	0.815173i	$-0.303358\pi$
$503$	−6.95459	−	8.02603i	−0.310090	−	0.357863i	−0.889307	+	0.457310i	$0.848813\pi$
$504$	−0.632188	+	2.56911i	−0.0281599	+	0.114437i
$505$	−13.5256			−0.601883
$506$	−9.89362	+	14.5548i	−0.439825	+	0.647040i
$507$	−0.102130	+	0.176895i	−0.00453577	+	0.00785619i
$508$	0.125818	−	0.518627i	0.00558226	−	0.0230104i
$509$	10.9928	−	31.7615i	0.487245	−	1.40780i	−0.386893	−	0.922125i	$-0.626452\pi$
$509$	10.9928	−	31.7615i	0.487245	−	1.40780i	0.874138	−	0.485678i	$-0.161427\pi$
$510$	−4.41533	+	2.83756i	−0.195514	+	0.125649i
$511$	0.100325	+	0.714401i	0.00443813	+	0.0316033i
$512$	−0.841254	−	0.540641i	−0.0371785	−	0.0238932i
$513$	2.36770	−	0.226088i	0.104537	−	0.00998204i
$514$	−5.62663	−	16.2571i	−0.248180	−	0.717069i
$515$	−22.0010	−	17.3018i	−0.969479	−	0.762407i
$516$	6.66323	−	9.35719i	0.293332	−	0.411927i
$517$	11.2151	+	3.29305i	0.493240	+	0.144828i
$518$	13.5945	+	4.04018i	0.597309	+	0.177515i
$519$	2.67052	+	5.84762i	0.117223	+	0.256682i
$520$	9.90571	−	3.96565i	0.434394	−	0.173905i
$521$	−9.01619	−	26.0506i	−0.395006	−	1.14130i	−0.950754	−	0.309945i	$-0.899689\pi$
$521$	−9.01619	−	26.0506i	−0.395006	−	1.14130i	0.555748	−	0.831351i	$-0.312432\pi$
$522$	4.18233	+	5.87326i	0.183056	+	0.257066i
$523$	1.81417	−	38.0842i	0.0793283	−	1.66531i	−0.512083	−	0.858936i	$-0.671126\pi$
$523$	1.81417	−	38.0842i	0.0793283	−	1.66531i	0.591412	−	0.806370i	$-0.298571\pi$
$524$	−1.50578	−	10.4729i	−0.0657804	−	0.457513i
$525$	0.424600	+	9.57396i	0.0185310	+	0.417842i
$526$	−6.20655	−	7.16274i	−0.270618	−	0.312310i
$527$	−1.79109	−	1.70780i	−0.0780212	−	0.0743931i
$528$	−1.83483	+	3.17801i	−0.0798506	+	0.138305i
$529$	−8.46248	−	21.3866i	−0.367934	−	0.929852i
$530$	−19.2845	−	33.4018i	−0.837666	−	1.45088i
$531$	3.46565	−	1.01761i	0.150397	−	0.0441604i
$532$	2.07768	−	5.93996i	0.0900788	−	0.257530i
$533$	−3.81691	+	2.45298i	−0.165329	+	0.106250i
$534$	1.21391	−	0.954630i	0.0525311	−	0.0413109i
$535$	28.7389	−	14.8159i	1.24249	−	0.640548i
$536$	−3.81148	−	5.35247i	−0.164631	−	0.231192i
$537$	19.2429	+	3.70877i	0.830394	+	0.160045i
$538$	−0.791178	+	5.50276i	−0.0341101	+	0.237241i
$539$	15.0372	−	20.8263i	0.647697	−	0.897053i
$540$	2.81741	+	0.827266i	0.121242	+	0.0355999i
$541$	−0.812015	−	3.34717i	−0.0349112	−	0.143906i	0.951689	−	0.307065i	$-0.0993469\pi$
$541$	−0.812015	−	3.34717i	−0.0349112	−	0.143906i	−0.986600	+	0.163159i	$0.947832\pi$
$542$	4.42766	+	0.422790i	0.190184	+	0.0181604i
$543$	1.50516	+	1.18367i	0.0645925	+	0.0507961i
$544$	1.75512	+	0.338272i	0.0752503	+	0.0145033i
$545$	12.0080	−	26.2939i	0.514367	−	1.12631i
$546$	−0.488946	+	9.60160i	−0.0209249	+	0.410911i
$547$	−1.91242	−	13.3012i	−0.0817693	−	0.568718i	−0.988981	−	0.148043i	$-0.952702\pi$
$547$	−1.91242	−	13.3012i	−0.0817693	−	0.568718i	0.907212	−	0.420675i	$-0.138207\pi$
$548$	−2.35819	−	1.21573i	−0.100737	−	0.0519335i
$549$	−7.12722	+	1.37366i	−0.304182	+	0.0586263i
$550$	−3.13374	+	12.9174i	−0.133623	+	0.550802i
$551$	−8.57464	−	14.8517i	−0.365292	−	0.632704i
$552$	−2.08685	−	4.31799i	−0.0888223	−	0.183786i
$553$	7.36329	−	12.6575i	0.313119	−	0.538254i
$554$	−7.16939	+	2.10512i	−0.304598	+	0.0894381i
$555$	5.14802	−	14.8742i	0.218521	−	0.631375i
$556$	−0.103391	−	2.17045i	−0.00438477	−	0.0920476i
$557$	30.3325	+	12.1433i	1.28523	+	0.514528i	0.910846	−	0.412746i	$-0.135430\pi$
$557$	30.3325	+	12.1433i	1.28523	+	0.514528i	0.374383	+	0.927274i	$0.377854\pi$
$558$	−0.0658799	+	1.38299i	−0.00278892	+	0.0585466i
$559$	17.3402	−	37.9697i	0.733411	−	1.60595i
$560$	5.10675	−	5.85460i	0.215800	−	0.247402i
$561$	0.933476	−	6.49247i	0.0394114	−	0.274112i
$562$	6.97972	−	9.80164i	0.294422	−	0.413457i
$563$	1.70628	−	1.62694i	0.0719112	−	0.0685672i	−0.653271	−	0.757124i	$-0.726604\pi$
$563$	1.70628	−	1.62694i	0.0719112	−	0.0685672i	0.725182	+	0.688557i	$0.241755\pi$
$564$	−2.30524	+	2.19804i	−0.0970679	+	0.0925541i
$565$	−10.6947	+	15.0186i	−0.449930	+	0.631839i
$566$	−3.04188	+	21.1567i	−0.127860	+	0.889283i
$567$	−1.73915	+	1.99383i	−0.0730373	+	0.0837331i
$568$	−3.21216	+	7.03364i	−0.134779	+	0.295125i
$569$	−0.667166	+	14.0055i	−0.0279690	+	0.587142i	0.940768	+	0.339052i	$0.110106\pi$
$569$	−0.667166	+	14.0055i	−0.0279690	+	0.587142i	−0.968737	+	0.248091i	$0.920197\pi$
$570$	−6.48376	−	2.59570i	−0.271575	−	0.108722i
$571$	1.08241	+	22.7226i	0.0452976	+	0.950913i	0.901100	+	0.433611i	$0.142761\pi$
$571$	1.08241	+	22.7226i	0.0452976	+	0.950913i	−0.855803	+	0.517302i	$0.826936\pi$
$572$	−4.36134	+	12.6013i	−0.182357	+	0.526886i
$573$	−25.4107	+	7.46124i	−1.06155	+	0.311698i
$574$	−1.66114	+	2.85550i	−0.0693344	+	0.119186i
$575$	−11.6592	−	12.8774i	−0.486222	−	0.537023i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	9.31427	−	38.3940i	0.387758	−	1.59836i	−0.359048	−	0.933319i	$-0.616899\pi$
$577$	9.31427	−	38.3940i	0.387758	−	1.59836i	0.746806	−	0.665042i	$-0.231586\pi$
$578$	13.5556	−	2.61263i	0.563840	−	0.108671i
$579$	−1.80053	−	0.928238i	−0.0748275	−	0.0385762i
$580$	−3.01305	−	20.9562i	−0.125110	−	0.870160i
$581$	−1.68504	+	33.0897i	−0.0699071	+	1.37279i
$582$	5.93110	−	12.9873i	0.245852	−	0.538340i
$583$	47.3299	+	9.12209i	1.96020	+	0.377799i
$584$	−0.214331	−	0.168552i	−0.00886910	−	0.00697474i
$585$	10.6217	+	1.01425i	0.439154	+	0.0419341i
$586$	−5.42247	−	22.3517i	−0.224000	−	0.923341i
$587$	1.59069	+	0.467068i	0.0656547	+	0.0192780i	0.314395	−	0.949292i	$-0.398198\pi$
$587$	1.59069	+	0.467068i	0.0656547	+	0.0192780i	−0.248740	+	0.968570i	$0.580017\pi$
$588$	2.86608	+	6.38636i	0.118195	+	0.263369i
$589$	0.468662	−	3.25961i	0.0193109	−	0.134310i
$590$	−10.4143	−	2.00720i	−0.428751	−	0.0826351i
$591$	1.97870	+	2.77870i	0.0813929	+	0.114300i
$592$	−4.76447	+	2.45626i	−0.195819	+	0.100952i
$593$	−17.1230	+	13.4657i	−0.703156	+	0.552968i	−0.904459	−	0.426561i	$-0.859725\pi$
$593$	−17.1230	+	13.4657i	−0.703156	+	0.552968i	0.201303	+	0.979529i	$0.435483\pi$
$594$	−3.08711	+	1.98397i	−0.126666	+	0.0814031i
$595$	−4.58476	+	13.1076i	−0.187957	+	0.537358i
$596$	−1.01067	+	0.296760i	−0.0413988	+	0.0121558i
$597$	11.5366	+	19.9819i	0.472160	+	0.817805i
$598$	−10.4156	−	13.9719i	−0.425924	−	0.571354i
$599$	10.2970	−	17.8349i	0.420723	−	0.728714i	−0.575287	−	0.817952i	$-0.695110\pi$
$599$	10.2970	−	17.8349i	0.420723	−	0.728714i	0.996010	+	0.0892374i	$0.0284430\pi$
$600$	−2.62149	−	2.49959i	−0.107022	−	0.102045i
$601$	20.4104	+	23.5549i	0.832558	+	0.960823i	0.999685	−	0.0251121i	$-0.00799426\pi$
$601$	20.4104	+	23.5549i	0.832558	+	0.960823i	−0.167126	+	0.985935i	$0.553449\pi$
$602$	−1.34656	−	30.3624i	−0.0548815	−	1.23748i
$603$	−0.935132	−	6.50399i	−0.0380815	−	0.264863i
$604$	0.506408	−	10.6308i	0.0206055	−	0.432562i
$605$	−4.20085	−	5.89927i	−0.170789	−	0.239839i
$606$	1.50656	+	4.35293i	0.0611999	+	0.176826i
$607$	−10.3081	+	4.12675i	−0.418394	+	0.167500i	−0.571301	−	0.820741i	$-0.693561\pi$
$607$	−10.3081	+	4.12675i	−0.418394	+	0.167500i	0.152906	+	0.988241i	$0.451137\pi$
$608$	0.988053	+	2.16353i	0.0400708	+	0.0877429i
$609$	18.2860	+	5.43445i	0.740985	+	0.220215i
$610$	20.4498	+	6.00462i	0.827990	+	0.243120i
$611$	−6.71373	+	9.42812i	−0.271609	+	0.381421i
$612$	1.40501	+	1.10491i	0.0567942	+	0.0446635i
$613$	14.4914	+	41.8700i	0.585300	+	1.69111i	0.714621	+	0.699512i	$0.246599\pi$
$613$	14.4914	+	41.8700i	0.585300	+	1.69111i	−0.129321	+	0.991603i	$0.541280\pi$
$614$	−11.6482	+	1.11227i	−0.470083	+	0.0448875i
$615$	3.08435	+	1.98219i	0.124373	+	0.0799297i
$616$	1.35021	+	9.61465i	0.0544015	+	0.387385i
$617$	−13.8844	+	8.92297i	−0.558965	+	0.359225i	−0.789416	−	0.613859i	$-0.789616\pi$
$617$	−13.8844	+	8.92297i	−0.558965	+	0.359225i	0.230450	+	0.973084i	$0.425980\pi$
$618$	−3.11760	+	9.00770i	−0.125408	+	0.362343i
$619$	−2.29885	+	9.47600i	−0.0923987	+	0.380873i	−0.999169	−	0.0407517i	$-0.987025\pi$
$619$	−2.29885	+	9.47600i	−0.0923987	+	0.380873i	0.906771	+	0.421624i	$0.138540\pi$
$620$	2.03278	−	3.52087i	0.0816382	−	0.141402i
$621$	0.123750	−	4.79423i	0.00496591	−	0.192386i
$622$	−27.3603			−1.09705
$623$	0.976296	−	3.96751i	0.0391145	−	0.158955i
$624$	−2.37961	−	2.74622i	−0.0952607	−	0.109937i
$625$	26.6568	+	13.7425i	1.06627	+	0.549702i
$626$	5.34032	+	2.13794i	0.213442	+	0.0854493i
$627$	7.75791	−	3.99948i	0.309821	−	0.159724i
$628$	−14.7962	+	1.41286i	−0.590432	+	0.0563794i
$629$	6.27437	−	7.24101i	0.250176	−	0.288718i
$630$	7.22179	−	2.86373i	0.287723	−	0.114094i
$631$	−19.0362	−	41.6834i	−0.757819	−	1.65939i	−0.751784	−	0.659410i	$-0.770806\pi$
$631$	−19.0362	−	41.6834i	−0.757819	−	1.65939i	−0.00603495	−	0.999982i	$-0.501921\pi$
$632$	1.30486	+	5.37870i	0.0519045	+	0.213953i
$633$	−14.2877	+	13.6233i	−0.567885	+	0.541478i
$634$	23.3313	+	2.22787i	0.926606	+	0.0884802i
$635$	−1.45480	+	0.582412i	−0.0577318	+	0.0231123i
$636$	−8.60161	+	9.92678i	−0.341076	+	0.393622i
$637$	14.6183	+	20.8162i	0.579199	+	0.824767i
$638$	22.2587	+	14.3048i	0.881231	+	0.566333i
$639$	−6.07808	+	4.77986i	−0.240445	+	0.189088i
$640$	0.139717	+	2.93303i	0.00552281	+	0.115938i
$641$	35.5439	−	6.85052i	1.40390	−	0.270579i	0.569614	−	0.821912i	$-0.307093\pi$
$641$	35.5439	−	6.85052i	1.40390	−	0.270579i	0.834285	+	0.551333i	$0.185881\pi$
$642$	−7.96928	−	7.59870i	−0.314523	−	0.299897i
$643$	11.7648			0.463960			0.231980	−	0.972721i	$-0.425480\pi$
$643$	11.7648			0.463960			0.231980	+	0.972721i	$0.425480\pi$
$644$	−11.3838	−	5.60446i	−0.448583	−	0.220847i
$645$	−33.7305			−1.32814
$646$	−3.07684	−	2.93376i	−0.121057	−	0.115427i
$647$	24.4803	−	4.71819i	0.962419	−	0.185491i	0.316242	−	0.948679i	$-0.397579\pi$
$647$	24.4803	−	4.71819i	0.962419	−	0.185491i	0.646177	+	0.763188i	$0.276367\pi$
$648$	−0.0475819	−	0.998867i	−0.00186919	−	0.0392392i
$649$	10.4189	−	8.19348i	0.408976	−	0.321622i
$650$	−11.0727	−	7.11599i	−0.434307	−	0.279112i
$651$	2.11506	+	2.99090i	0.0828959	+	0.117223i
$652$	−12.1301	+	13.9989i	−0.475052	+	0.548239i
$653$	2.60468	−	1.04275i	0.101929	−	0.0408061i	−0.320138	−	0.947371i	$-0.603729\pi$
$653$	2.60468	−	1.04275i	0.101929	−	0.0408061i	0.422066	+	0.906565i	$0.361305\pi$
$654$	−9.79963	−	0.935751i	−0.383196	−	0.0365908i
$655$	−22.4853	+	21.4397i	−0.878575	+	0.837719i
$656$	−0.294372	−	1.21342i	−0.0114933	−	0.0473760i
$657$	−0.113270	−	0.248027i	−0.00441910	−	0.00967647i
$658$	−1.22667	+	8.33749i	−0.0478206	+	0.325029i
$659$	30.1262	−	34.7675i	1.17355	−	1.35435i	0.251231	−	0.967927i	$-0.419165\pi$
$659$	30.1262	−	34.7675i	1.17355	−	1.35435i	0.922321	−	0.386424i	$-0.126290\pi$
$660$	10.7266	−	1.02427i	0.417533	−	0.0398696i
$661$	−24.0171	+	12.3817i	−0.934157	+	0.481591i	−0.856936	−	0.515423i	$-0.827635\pi$
$661$	−24.0171	+	12.3817i	−0.934157	+	0.481591i	−0.0772210	+	0.997014i	$0.524605\pi$
$662$	14.4586	+	5.78833i	0.561948	+	0.224970i
$663$	5.77306	+	2.97622i	0.224207	+	0.115587i
$664$	−8.20078	−	9.46420i	−0.318252	−	0.367282i
$665$	−17.7465	+	5.14769i	−0.688180	+	0.199619i
$666$	−5.36035			−0.207710
$667$	−31.8143	+	13.5482i	−1.23185	+	0.524588i
$668$	6.22178	−	10.7764i	0.240728	−	0.416953i
$669$	−5.60675	+	23.1113i	−0.216769	+	0.893536i
$670$	−6.31058	+	18.2332i	−0.243799	+	0.704411i
$671$	−22.4074	+	14.4004i	−0.865029	+	0.555921i
$672$	−2.45299	−	0.991376i	−0.0946262	−	0.0382432i
$673$	18.5791	+	11.9401i	0.716171	+	0.460255i	0.847303	−	0.531110i	$-0.178225\pi$
$673$	18.5791	+	11.9401i	0.716171	+	0.460255i	−0.131132	+	0.991365i	$0.541861\pi$
$674$	33.0667	−	3.15749i	1.27368	−	0.121622i
$675$	−1.18470	−	3.42296i	−0.0455990	−	0.131750i
$676$	−0.160560	−	0.126266i	−0.00617538	−	0.00485637i
$677$	15.1417	−	21.2636i	0.581945	−	0.817227i	−0.413704	−	0.910411i	$-0.635765\pi$
$677$	15.1417	−	21.2636i	0.581945	−	0.817227i	0.995649	+	0.0931846i	$0.0297047\pi$
$678$	6.02466	+	1.76900i	0.231376	+	0.0679380i
$679$	−8.78530	−	36.7390i	−0.337149	−	1.40991i
$680$	−2.18031	−	4.77422i	−0.0836111	−	0.183083i
$681$	22.7055	−	9.08991i	0.870077	−	0.348326i
$682$	1.66178	+	4.80141i	0.0636330	+	0.183855i
$683$	−25.9913	−	36.4997i	−0.994530	−	1.39662i	−0.916665	−	0.399658i	$-0.869129\pi$
$683$	−25.9913	−	36.4997i	−0.994530	−	1.39662i	−0.0778651	−	0.996964i	$-0.524810\pi$
$684$	−0.113172	+	2.37578i	−0.00432725	+	0.0908402i
$685$	1.10871	+	7.71122i	0.0423615	+	0.294631i
$686$	16.3772	+	8.64802i	0.625283	+	0.330183i
$687$	14.2071	+	16.3959i	0.542036	+	0.625543i
$688$	8.31367	+	7.92707i	0.316956	+	0.302217i
$689$	−23.8648	+	41.3350i	−0.909176	+	1.57474i
$690$	−6.77369	+	12.3461i	−0.257870	+	0.470009i
$691$	−13.3387	−	23.1033i	−0.507429	−	0.878893i	−0.999963	−	0.00859947i	$-0.997263\pi$
$691$	−13.3387	−	23.1033i	−0.507429	−	0.878893i	0.492534	−	0.870293i	$-0.336071\pi$
$692$	−6.16815	+	1.81113i	−0.234478	+	0.0688490i
$693$	−3.20557	+	9.16454i	−0.121770	+	0.348132i
$694$	16.2213	−	10.4248i	0.615754	−	0.395721i
$695$	−5.01536	+	3.94413i	−0.190244	+	0.149609i
$696$	−6.40869	+	3.30391i	−0.242921	+	0.125234i
$697$	1.29457	+	1.81797i	0.0490355	+	0.0688607i
$698$	18.1374	+	3.49570i	0.686511	+	0.132314i
$699$	−1.50490	+	10.4668i	−0.0569205	+	0.395891i
$700$	−9.53694	−	0.942239i	−0.360462	−	0.0356133i
$701$	−28.9900	−	8.51222i	−1.09494	−	0.321502i	−0.316098	−	0.948727i	$-0.602373\pi$
$701$	−28.9900	−	8.51222i	−1.09494	−	0.321502i	−0.778839	+	0.627224i	$0.784191\pi$
$702$	−0.856693	−	3.53134i	−0.0323338	−	0.133282i
$703$	12.6917	+	1.21191i	0.478677	+	0.0457082i
$704$	−2.88454	−	2.26843i	−0.108715	−	0.0854947i
$705$	9.18385	+	1.77004i	0.345884	+	0.0666636i
$706$	−14.1192	+	30.9167i	−0.531383	+	1.16357i
$707$	10.2307	+	6.62240i	0.384766	+	0.249061i
$708$	0.514036	+	3.57520i	0.0193187	+	0.134364i
$709$	−41.4791	−	21.3839i	−1.55778	−	0.803091i	−0.558134	−	0.829751i	$-0.688482\pi$
$709$	−41.4791	−	21.3839i	−1.55778	−	0.803091i	−0.999645	+	0.0266602i	$0.991513\pi$
$710$	22.2948	−	4.29697i	0.836708	−	0.161262i
$711$	−1.30486	+	5.37870i	−0.0489360	+	0.201717i
$712$	0.772156	+	1.33741i	0.0289378	+	0.0501217i
$713$	−6.41039	−	1.73145i	−0.240071	−	0.0648434i
$714$	4.72906	+	0.0155090i	0.176981	+	0.000580410i
$715$	37.5692	−	11.0313i	1.40501	−	0.412548i
$716$	−6.40958	+	18.5193i	−0.239537	+	0.692097i
$717$	0.826893	+	17.3586i	0.0308809	+	0.648269i
$718$	17.6329	+	7.05914i	0.658053	+	0.263445i
$719$	−2.27142	+	47.6830i	−0.0847097	+	1.77828i	0.412804	+	0.910820i	$0.364549\pi$
$719$	−2.27142	+	47.6830i	−0.0847097	+	1.77828i	−0.497514	+	0.867456i	$0.665754\pi$
$720$	−1.21981	+	2.67100i	−0.0454595	+	0.0995423i
$721$	8.17018	+	23.8591i	0.304274	+	0.888558i
$722$	−1.89889	+	13.2071i	−0.0706693	+	0.491516i
$723$	2.26493	−	3.18065i	0.0842336	−	0.118290i
$724$	−1.38583	+	1.32138i	−0.0515039	+	0.0491088i
$725$	−18.9015	+	18.0225i	−0.701984	+	0.669340i
$726$	−1.43063	+	2.00904i	−0.0530958	+	0.0745626i
$727$	−6.68840	+	46.5188i	−0.248059	+	1.72529i	0.361349	+	0.932431i	$0.382316\pi$
$727$	−6.68840	+	46.5188i	−0.248059	+	1.72529i	−0.609408	+	0.792857i	$0.708593\pi$
$728$	−9.43429	−	1.85042i	−0.349658	−	0.0685811i
$729$	0.415415	−	0.909632i	0.0153857	−	0.0336901i
$730$	−0.0380964	+	0.799743i	−0.00141001	+	0.0295998i
$731$	−19.0617	−	7.63116i	−0.705023	−	0.282249i
$732$	−0.345368	−	7.25016i	−0.0127652	−	0.267974i
$733$	−0.819240	+	2.36704i	−0.0302593	+	0.0874286i	−0.959119	−	0.283004i	$-0.908669\pi$
$733$	−0.819240	+	2.36704i	−0.0302593	+	0.0874286i	0.928860	+	0.370432i	$0.120790\pi$
$734$	−7.84306	+	2.30293i	−0.289493	+	0.0850027i
$735$	10.3938	−	17.7329i	0.383380	−	0.654088i
$736$	4.57103	−	1.45110i	0.168490	−	0.0534881i
$737$	−12.0564	−	20.8823i	−0.444104	−	0.769210i
$738$	0.294372	−	1.21342i	0.0108360	−	0.0446665i
$739$	−40.4505	+	7.79619i	−1.48799	+	0.286788i	−0.867506	−	0.497427i	$-0.834278\pi$
$739$	−40.4505	+	7.79619i	−1.48799	+	0.286788i	−0.620489	+	0.784215i	$0.713066\pi$
$740$	13.9902	+	7.21244i	0.514289	+	0.265135i
$741$	1.23000	+	8.55484i	0.0451852	+	0.314270i
$742$	−1.76740	+	34.7070i	−0.0648832	+	1.27413i
$743$	−18.1381	+	39.7170i	−0.665423	+	1.45707i	0.211957	+	0.977279i	$0.432016\pi$
$743$	−18.1381	+	39.7170i	−0.665423	+	1.45707i	−0.877381	+	0.479795i	$0.840711\pi$
$744$	−1.35954	−	0.262029i	−0.0498430	−	0.00960646i
$745$	2.43125	+	1.91195i	0.0890740	+	0.0700485i
$746$	−27.2115	−	2.59838i	−0.996284	−	0.0951336i
$747$	−2.95239	−	12.1699i	−0.108022	−	0.445274i
$748$	6.29354	+	1.84795i	0.230115	+	0.0675677i
$749$	−28.9921	−	2.86439i	−1.05935	−	0.104662i
$750$	0.575775	−	4.00461i	0.0210243	−	0.146227i
$751$	−8.06122	−	1.55367i	−0.294158	−	0.0566943i	0.0400372	−	0.999198i	$-0.487252\pi$
$751$	−8.06122	−	1.55367i	−0.294158	−	0.0566943i	−0.334195	+	0.942504i	$0.608464\pi$
$752$	−1.84760	−	2.59459i	−0.0673749	−	0.0946148i
$753$	2.77503	−	1.43063i	0.101128	−	0.0521349i
$754$	−20.5948	+	16.1959i	−0.750017	+	0.589820i
$755$	−26.2902	+	16.8957i	−0.956799	+	0.614897i
$756$	−1.72603	−	2.00520i	−0.0627752	−	0.0729283i
$757$	−7.50923	+	2.20491i	−0.272928	+	0.0801388i	−0.415332	−	0.909670i	$-0.636335\pi$
$757$	−7.50923	+	2.20491i	−0.272928	+	0.0801388i	0.142405	+	0.989809i	$0.454517\pi$
$758$	14.2265	+	24.6410i	0.516730	+	0.895003i
$759$	−6.11714	−	16.5017i	−0.222038	−	0.598975i
$760$	3.49202	−	6.04835i	0.126669	−	0.219397i
$761$	3.61283	+	3.44482i	0.130965	+	0.124875i	0.752731	−	0.658328i	$-0.228736\pi$
$761$	3.61283	+	3.44482i	0.130965	+	0.124875i	−0.621766	+	0.783203i	$0.713585\pi$
$762$	0.349480	+	0.403321i	0.0126603	+	0.0146108i
$763$	−21.9568	+	14.0092i	−0.794889	+	0.507168i
$764$	−3.76898	−	26.2139i	−0.136357	−	0.948384i
$765$	0.249734	−	5.24257i	0.00902916	−	0.189545i
$766$	−14.2837	−	20.0586i	−0.516090	−	0.724747i
$767$	4.29278	+	12.4032i	0.155003	+	0.447852i
$768$	0.928368	−	0.371662i	0.0334996	−	0.0134112i
$769$	21.5201	+	47.1225i	0.776035	+	1.69928i	0.712890	+	0.701276i	$0.247386\pi$
$769$	21.5201	+	47.1225i	0.776035	+	1.69928i	0.0631453	+	0.998004i	$0.479887\pi$
$770$	20.6974	−	19.6057i	0.745882	−	0.706541i
$771$	16.5064	+	4.84672i	0.594463	+	0.174550i
$772$	1.17503	−	1.65010i	0.0422903	−	0.0593884i
$773$	4.49599	+	3.53569i	0.161710	+	0.127170i	0.695735	−	0.718299i	$-0.255079\pi$
$773$	4.49599	+	3.53569i	0.161710	+	0.127170i	−0.534025	+	0.845469i	$0.679321\pi$
$774$	3.75709	+	10.8554i	0.135046	+	0.390190i
$775$	−4.99240	+	0.476716i	−0.179332	+	0.0171242i
$776$	12.0110	+	7.71901i	0.431170	+	0.277096i
$777$	−11.1766	+	8.73023i	−0.400959	+	0.313195i
$778$	13.6234	−	8.75520i	0.488421	−	0.313889i
$779$	−0.971325	+	2.80646i	−0.0348013	+	0.100552i
$780$	−2.51555	+	10.3693i	−0.0900713	+	0.371279i
$781$	−14.1876	+	24.5737i	−0.507673	+	0.879316i
$782$	−6.62112	+	5.44455i	−0.236771	+	0.194697i
$783$	−7.21021			−0.257672
$784$	−6.72924	+	1.92803i	−0.240330	+	0.0688583i
$785$	28.5810	+	32.9843i	1.02010	+	1.17726i
$786$	9.40445	+	4.84833i	0.335446	+	0.172934i
$787$	−31.5965	−	12.6493i	−1.12629	−	0.450900i	−0.267672	−	0.963510i	$-0.586254\pi$
$787$	−31.5965	−	12.6493i	−1.12629	−	0.450900i	−0.858622	+	0.512610i	$0.828679\pi$
$788$	−3.03201	+	1.56311i	−0.108011	+	0.0556835i
$789$	9.43475	−	0.900909i	0.335886	−	0.0320732i
$790$	10.6427	−	12.2824i	0.378651	−	0.436987i
$791$	15.4428	−	6.12370i	0.549084	−	0.217734i
$792$	−1.52443	−	3.33804i	−0.0541683	−	0.118612i
$793$	−6.21821	−	25.6318i	−0.220815	−	0.910212i
$794$	−22.6606	+	21.6068i	−0.804195	+	0.766798i
$795$	38.3944	+	3.66622i	1.36171	+	0.130027i
$796$	−21.4203	+	8.57541i	−0.759224	+	0.303947i
$797$	11.0918	−	12.8006i	0.392891	−	0.453420i	−0.524498	−	0.851411i	$-0.675747\pi$
$797$	11.0918	−	12.8006i	0.392891	−	0.453420i	0.917389	+	0.397991i	$0.130293\pi$
$798$	3.63338	+	5.13794i	0.128620	+	0.181881i
$799$	4.78951	+	3.07803i	0.169441	+	0.108893i
$800$	2.84722	−	2.23908i	0.100664	−	0.0791634i
$801$	0.0734813	+	1.54256i	0.00259633	+	0.0545038i
$802$	0.720295	−	0.138825i	0.0254345	−	0.00490210i
$803$	−0.724166	−	0.690491i	−0.0255553	−	0.0243669i
$804$	6.57087			0.231737
$805$	5.98421	+	36.7744i	0.210916	+	1.29613i
$806$	−5.03116			−0.177215
$807$	−4.02349	−	3.83639i	−0.141634	−	0.135047i
$808$	−4.52303	+	0.871742i	−0.159120	+	0.0306678i
$809$	−1.37189	−	28.7994i	−0.0482329	−	1.01253i	−0.885180	−	0.465249i	$-0.845965\pi$
$809$	−1.37189	−	28.7994i	−0.0482329	−	1.01253i	0.836947	−	0.547284i	$-0.184338\pi$
$810$	−2.30813	+	1.81513i	−0.0810994	+	0.0637773i
$811$	−14.4904	−	9.31241i	−0.508826	−	0.327003i	0.260912	−	0.965363i	$-0.415977\pi$
$811$	−14.4904	−	9.31241i	−0.508826	−	0.327003i	−0.769738	+	0.638360i	$0.779613\pi$
$812$	−7.98150	+	17.3264i	−0.280096	+	0.608039i
$813$	−2.91269	+	3.36142i	−0.102152	+	0.117890i
$814$	−18.2616	+	7.31084i	−0.640069	+	0.256245i
$815$	54.1443	+	5.17016i	1.89659	+	0.181103i
$816$	−1.29362	+	1.23346i	−0.0452858	+	0.0431799i
$817$	−6.44140	−	26.5518i	−0.225356	−	0.928930i
$818$	4.04813	+	8.86418i	0.141540	+	0.309929i
$819$	−7.53762	−	5.96776i	−0.263386	−	0.208530i
$820$	−2.40096	+	2.77086i	−0.0838453	+	0.0967627i
$821$	−38.4547	+	3.67198i	−1.34208	+	0.128153i	−0.741252	−	0.671226i	$-0.765768\pi$
$821$	−38.4547	+	3.67198i	−1.34208	+	0.128153i	−0.600827	+	0.799379i	$0.705162\pi$
$822$	2.35819	−	1.21573i	0.0822514	−	0.0424036i
$823$	−24.5199	−	9.81630i	−0.854711	−	0.342175i	−0.0974128	−	0.995244i	$-0.531057\pi$
$823$	−24.5199	−	9.81630i	−0.854711	−	0.342175i	−0.757298	+	0.653070i	$0.773481\pi$
$824$	−8.47234	−	4.36779i	−0.295148	−	0.152159i
$825$	−8.70449	−	10.0455i	−0.303052	−	0.349740i
$826$	6.89459	+	6.61729i	0.239894	+	0.230245i
$827$	35.1052			1.22073			0.610364	−	0.792121i	$-0.291023\pi$
$827$	35.1052			1.22073			0.610364	+	0.792121i	$0.291023\pi$
$828$	4.72782	+	0.804781i	0.164303	+	0.0279681i
$829$	6.53530	−	11.3195i	0.226980	−	0.393142i	−0.729931	−	0.683521i	$-0.760448\pi$
$829$	6.53530	−	11.3195i	0.226980	−	0.393142i	0.956912	+	0.290379i	$0.0937813\pi$
$830$	−8.66927	+	35.7352i	−0.300915	+	1.24039i
$831$	2.44387	−	7.06110i	0.0847769	−	0.244947i
$832$	3.05692	−	1.96456i	0.105980	−	0.0681090i
$833$	9.88560	−	7.66972i	0.342516	−	0.265740i
$834$	1.82797	+	1.17477i	0.0632974	+	0.0406788i
$835$	−36.3733	+	3.47323i	−1.25875	+	0.120196i
$836$	2.85471	+	8.24813i	0.0987321	+	0.285268i
$837$	−1.08834	−	0.855877i	−0.0376184	−	0.0295834i
$838$	15.8025	−	22.1915i	0.545888	−	0.766593i
$839$	−34.2762	−	10.0644i	−1.18335	−	0.347462i	−0.369883	−	0.929079i	$-0.620602\pi$
$839$	−34.2762	−	10.0644i	−1.18335	−	0.347462i	−0.813463	+	0.581617i	$0.802420\pi$
$840$	1.80681	+	7.55584i	0.0623408	+	0.260701i
$841$	9.54919	+	20.9098i	0.329283	+	0.721028i
$842$	18.4694	−	7.39405i	0.636499	−	0.254816i
$843$	3.93555	+	11.3710i	0.135547	+	0.391639i
$844$	−11.4513	−	16.0811i	−0.394169	−	0.553533i
$845$	−0.0285388	+	0.599103i	−0.000981764	+	0.0206098i
$846$	−0.453301	−	3.15278i	−0.0155848	−	0.108395i
$847$	0.289113	+	6.51899i	0.00993406	+	0.223995i
$848$	−8.60161	−	9.92678i	−0.295380	−	0.340887i
$849$	−15.4693	−	14.7499i	−0.530905	−	0.506216i
$850$	−3.23718	+	5.60696i	−0.111034	+	0.192317i
$851$	5.51488	−	25.1088i	0.189048	−	0.860720i
$852$	−3.86620	−	6.69646i	−0.132454	−	0.229417i
$853$	−7.30259	+	2.14423i	−0.250036	+	0.0734172i	−0.404349	−	0.914605i	$-0.632502\pi$
$853$	−7.30259	+	2.14423i	−0.250036	+	0.0734172i	0.154313	+	0.988022i	$0.450684\pi$
$854$	−12.5282	−	14.5545i	−0.428706	−	0.498044i
$855$	5.87535	−	3.77586i	0.200933	−	0.129132i
$856$	8.65550	−	6.80676i	0.295839	−	0.232650i
$857$	26.0754	−	13.4428i	0.890720	−	0.459198i	0.0488050	−	0.998808i	$-0.484459\pi$
$857$	26.0754	−	13.4428i	0.890720	−	0.459198i	0.841915	+	0.539610i	$0.181428\pi$
$858$	−7.73487	−	10.8621i	−0.264064	−	0.370826i
$859$	23.8617	+	4.59897i	0.814152	+	0.156915i	0.579298	−	0.815116i	$-0.303327\pi$
$859$	23.8617	+	4.59897i	0.814152	+	0.156915i	0.234854	+	0.972031i	$0.424539\pi$
$860$	4.80035	−	33.3871i	0.163690	−	1.13849i
$861$	−1.36247	−	3.00948i	−0.0464329	−	0.102563i
$862$	38.1497	+	11.2017i	1.29938	+	0.381533i
$863$	7.37242	+	30.3895i	0.250960	+	1.03447i	0.948210	+	0.317644i	$0.102892\pi$
$863$	7.37242	+	30.3895i	0.250960	+	1.03447i	−0.697250	+	0.716828i	$0.745593\pi$
$864$	0.995472	+	0.0950560i	0.0338666	+	0.00323387i
$865$	14.8379	+	11.6687i	0.504505	+	0.396747i
$866$	11.9123	+	2.29590i	0.404795	+	0.0780179i
$867$	−5.73485	+	12.5576i	−0.194766	+	0.426477i
$868$	−3.26147	+	1.66789i	−0.110701	+	0.0566117i
$869$	2.89049	+	20.1038i	0.0980530	+	0.681974i
$870$	18.8182	+	9.70145i	0.637996	+	0.328910i
$871$	23.4455	−	4.51875i	0.794421	−	0.153112i
$872$	2.32086	−	9.56671i	0.0785942	−	0.323970i
$873$	7.13876	+	12.3647i	0.241610	+	0.418482i
$874$	−11.0121	−	2.97439i	−0.372491	−	0.100610i
$875$	−5.32164	−	9.28756i	−0.179904	−	0.313977i
$876$	0.261623	−	0.0768194i	0.00883942	−	0.00259549i
$877$	−0.110847	+	0.320272i	−0.00374304	+	0.0108148i	−0.946857	−	0.321655i	$-0.895761\pi$
$877$	−0.110847	+	0.320272i	−0.00374304	+	0.0108148i	0.943114	+	0.332470i	$0.107882\pi$
$878$	−1.95595	−	41.0604i	−0.0660100	−	1.38572i
$879$	21.3525	+	8.54825i	0.720202	+	0.288325i
$880$	−0.512714	+	10.7632i	−0.0172836	+	0.362827i
$881$	19.4037	−	42.4882i	0.653728	−	1.43146i	−0.234525	−	0.972110i	$-0.575353\pi$
$881$	19.4037	−	42.4882i	0.653728	−	1.43146i	0.888253	−	0.459355i	$-0.151919\pi$
$882$	−6.86466	−	1.36981i	−0.231145	−	0.0461240i
$883$	−0.803452	+	5.58813i	−0.0270383	+	0.188056i	−0.998864	−	0.0476434i	$-0.984829\pi$
$883$	−0.803452	+	5.58813i	−0.0270383	+	0.188056i	0.971826	+	0.235699i	$0.0757380\pi$
$884$	−3.76752	+	5.29074i	−0.126715	+	0.177947i
$885$	7.67592	−	7.31898i	0.258023	−	0.246025i
$886$	−24.9847	+	23.8229i	−0.839379	+	0.800346i
$887$	12.9595	−	18.1991i	0.435138	−	0.611066i	−0.537536	−	0.843241i	$-0.680645\pi$
$887$	12.9595	−	18.1991i	0.435138	−	0.611066i	0.972674	+	0.232175i	$0.0745842\pi$
$888$	0.762858	−	5.30579i	0.0255998	−	0.178051i
$889$	1.38556	+	0.271761i	0.0464702	+	0.00911456i
$890$	1.88376	−	4.12486i	0.0631438	−	0.138266i
$891$	0.174609	−	3.66550i	0.00584963	−	0.122799i
$892$	−22.0782	−	8.83876i	−0.739232	−	0.295944i
$893$	0.360476	+	7.56732i	0.0120629	+	0.253231i
$894$	0.344514	−	0.995407i	0.0115223	−	0.0332914i
$895$	55.2130	−	16.2120i	1.84557	−	0.541908i
$896$	1.33038	−	2.28694i	0.0444450	−	0.0764012i
$897$	17.4228	−	0.379762i	0.581730	−	0.0126799i
$898$	−11.9726	−	20.7371i	−0.399529	−	0.692005i
$899$	−2.35357	+	9.70155i	−0.0784959	+	0.323565i
$900$	3.55672	−	0.685501i	0.118557	−	0.0228500i
$901$	20.8679	+	10.7582i	0.695212	+	0.358407i
$902$	−0.652084	−	4.53535i	−0.0217120	−	0.151011i
$903$	25.5136	+	16.5151i	0.849038	+	0.549587i
$904$	−2.60839	+	5.71158i	−0.0867538	+	0.189964i
$905$	5.52101	+	1.06409i	0.183525	+	0.0353715i
$906$	8.36586	+	6.57899i	0.277937	+	0.218572i
$907$	18.7391	+	1.78937i	0.622222	+	0.0594150i	0.401406	−	0.915900i	$-0.368522\pi$
$907$	18.7391	+	1.78937i	0.622222	+	0.0594150i	0.220816	+	0.975315i	$0.429128\pi$
$908$	5.76606	+	23.7680i	0.191353	+	0.788769i
$909$	−4.41968	−	1.29774i	−0.146592	−	0.0430432i
$910$	11.6430	+	25.7174i	0.385961	+	0.852525i
$911$	−5.67551	+	39.4740i	−0.188038	+	1.30783i	0.649042	+	0.760753i	$0.275170\pi$
$911$	−5.67551	+	39.4740i	−0.188038	+	1.30783i	−0.837080	+	0.547081i	$0.815739\pi$
$912$	−2.33549	−	0.450129i	−0.0773358	−	0.0149053i
$913$	−26.6564	−	37.4337i	−0.882199	−	1.23887i
$914$	−18.7767	+	9.68008i	−0.621079	+	0.320188i
$915$	−16.7533	+	13.1749i	−0.553847	+	0.435550i
$916$	−18.2509	+	11.7291i	−0.603027	+	0.387542i
$917$	27.5051	−	5.20768i	0.908298	−	0.171973i
$918$	−1.71502	+	0.503576i	−0.0566042	+	0.0166205i
$919$	−16.3885	−	28.3858i	−0.540608	−	0.936361i	−0.998869	−	0.0475433i	$-0.984861\pi$
$919$	−16.3885	−	28.3858i	−0.540608	−	0.936361i	0.458261	−	0.888818i	$-0.348473\pi$
$920$	−11.2565	−	8.46179i	−0.371115	−	0.278977i
$921$	5.85059	−	10.1335i	0.192784	−	0.333911i
$922$	5.36667	+	5.11711i	0.176742	+	0.168523i
$923$	−18.4001	−	21.2349i	−0.605647	−	0.698954i
$924$	−8.61506	−	4.47720i	−0.283415	−	0.147289i
$925$	−2.76320	−	19.2185i	−0.0908536	−	0.631901i
$926$	−0.801237	+	16.8200i	−0.0263303	+	0.552740i
$927$	−5.52908	−	7.76450i	−0.181599	−	0.255020i
$928$	−2.35823	−	6.81365i	−0.0774126	−	0.223669i
$929$	−4.28497	+	1.71544i	−0.140585	+	0.0562819i	−0.440888	−	0.897562i	$-0.645337\pi$
$929$	−4.28497	+	1.71544i	−0.140585	+	0.0562819i	0.300303	+	0.953844i	$0.402912\pi$
$930$	1.68889	+	3.69816i	0.0553809	+	0.121267i
$931$	15.9438	+	4.79533i	0.522536	+	0.157161i
$932$	−10.1461	−	2.97916i	−0.332346	−	0.0975856i
$933$	15.8706	−	22.2871i	0.519579	−	0.729646i
$934$	14.6198	+	11.4971i	0.478373	+	0.376197i
$935$	−6.29940	−	18.2009i	−0.206013	−	0.595234i
$936$	3.61731	−	0.345411i	0.118236	−	0.0112901i
$937$	41.8956	+	26.9247i	1.36867	+	0.879590i	0.998775	−	0.0494838i	$-0.0157576\pi$
$937$	41.8956	+	26.9247i	1.36867	+	0.879590i	0.369894	+	0.929074i	$0.379394\pi$
$938$	13.7006	−	10.7017i	0.447341	−	0.349424i
$939$	−4.83920	+	3.10997i	−0.157921	+	0.101490i
$940$	−3.05902	+	8.83847i	−0.0997743	+	0.288279i
$941$	7.98390	−	32.9101i	0.260268	−	1.07284i	−0.680219	−	0.733008i	$-0.738116\pi$
$941$	7.98390	−	32.9101i	0.260268	−	1.07284i	0.940487	−	0.339829i	$-0.110369\pi$
$942$	7.43174	−	12.8722i	0.242139	−	0.419398i
$943$	5.38101	+	2.62729i	0.175230	+	0.0855563i
$944$	−3.61196			−0.117559
$945$	−1.85633	+	7.54382i	−0.0603864	+	0.245401i
$946$	27.6050	+	31.8579i	0.897517	+	1.03579i
$947$	19.8849	+	10.2514i	0.646172	+	0.333125i	0.749968	−	0.661474i	$-0.230069\pi$
$947$	19.8849	+	10.2514i	0.646172	+	0.333125i	−0.103796	+	0.994599i	$0.533099\pi$
$948$	−5.13825	−	2.05705i	−0.166883	−	0.0668098i
$949$	0.880668	−	0.454016i	0.0285877	−	0.0147380i
$950$	−8.57623	+	0.818931i	−0.278250	+	0.0265696i
$951$	−15.3483	+	17.7129i	−0.497702	+	0.574379i
$952$	−0.688366	+	4.67871i	−0.0223101	+	0.151638i
$953$	−1.98832	−	4.35381i	−0.0644080	−	0.141034i	0.874691	−	0.484682i	$-0.161065\pi$
$953$	−1.98832	−	4.35381i	−0.0644080	−	0.141034i	−0.939099	+	0.343648i	$0.888337\pi$
$954$	−3.09670	−	12.7648i	−0.100259	−	0.413274i
$955$	−56.2810	+	53.6638i	−1.82121	+	1.73652i
$956$	−17.2996	−	1.65191i	−0.559509	−	0.0534267i
$957$	−24.5637	+	9.83381i	−0.794031	+	0.317882i
$958$	3.99888	−	4.61495i	0.129198	−	0.149102i
$959$	2.93694	−	6.37558i	0.0948386	−	0.205878i
$960$	−2.47022	−	1.58751i	−0.0797259	−	0.0512368i
$961$	22.8608	−	17.9779i	0.737445	−	0.579933i
$962$	−0.926814	−	19.4562i	−0.0298817	−	0.627294i
$963$	10.8124	−	2.08391i	0.348423	−	0.0671531i
$964$	2.82594	+	2.69453i	0.0910174	+	0.0867850i
$965$	−5.94822			−0.191480
$966$	11.1685	−	6.02204i	0.359340	−	0.193756i
$967$	−5.22811			−0.168125			−0.0840623	−	0.996460i	$-0.526789\pi$
$967$	−5.22811			−0.168125			−0.0840623	+	0.996460i	$0.526789\pi$
$968$	−1.78499	−	1.70199i	−0.0573719	−	0.0547040i
$969$	4.17451	−	0.804572i	0.134105	−	0.0258466i
$970$	−1.99482	−	41.8764i	−0.0640497	−	1.34457i
$971$	36.3347	−	28.5740i	1.16604	−	0.916982i	0.168402	−	0.985718i	$-0.446139\pi$
$971$	36.3347	−	28.5740i	1.16604	−	0.916982i	0.997635	+	0.0687366i	$0.0218968\pi$
$972$	0.841254	+	0.540641i	0.0269832	+	0.0173411i
$973$	5.72472	−	0.527705i	0.183526	−	0.0169174i
$974$	−8.02084	+	9.25654i	−0.257004	+	0.296599i
$975$	12.2193	−	4.89187i	0.391331	−	0.156665i
$976$	7.22552	+	0.689953i	0.231283	+	0.0220849i
$977$	26.8033	−	25.5569i	0.857514	−	0.817637i	−0.127190	−	0.991878i	$-0.540596\pi$
$977$	26.8033	−	25.5569i	0.857514	−	0.817637i	0.984703	+	0.174241i	$0.0557472\pi$
$978$	−4.36701	−	18.0010i	−0.139641	−	0.575610i
$979$	2.35419	+	5.15497i	0.0752404	+	0.164753i
$980$	16.0732	+	12.8116i	0.513440	+	0.409253i
$981$	6.44658	−	7.43975i	0.205824	−	0.237533i
$982$	−42.0090	+	4.01138i	−1.34056	+	0.128008i
$983$	−9.94263	+	5.12578i	−0.317121	+	0.163487i	−0.609437	−	0.792835i	$-0.708604\pi$
$983$	−9.94263	+	5.12578i	−0.317121	+	0.163487i	0.292316	+	0.956322i	$0.405574\pi$
$984$	1.15917	+	0.464063i	0.0369531	+	0.0147938i
$985$	8.90306	+	4.58985i	0.283675	+	0.146245i
$986$	8.43965	+	9.73988i	0.268773	+	0.310181i
$987$	−6.07998	−	5.83543i	−0.193528	−	0.185744i
$988$	−8.64281			−0.274965
$989$	−54.7140	+	6.43054i	−1.73981	+	0.204479i
$990$	−5.38770	+	9.33178i	−0.171232	+	0.296583i
$991$	−0.793243	+	3.26979i	−0.0251982	+	0.103868i	−0.983022	−	0.183488i	$-0.941261\pi$
$991$	−0.793243	+	3.26979i	−0.0251982	+	0.103868i	0.957824	+	0.287356i	$0.0927764\pi$
$992$	0.452844	−	1.30841i	0.0143778	−	0.0415420i
$993$	−13.1018	+	8.42003i	−0.415774	+	0.267202i
$994$	−18.9675	−	7.66573i	−0.601614	−	0.243142i
$995$	56.9956	+	36.6289i	1.80688	+	1.16121i
$996$	12.4662	−	1.19038i	0.395008	−	0.0377186i
$997$	−1.77041	−	5.11526i	−0.0560694	−	0.162002i	0.913488	−	0.406865i	$-0.133378\pi$
$997$	−1.77041	−	5.11526i	−0.0560694	−	0.162002i	−0.969558	+	0.244863i	$0.921257\pi$
$998$	5.77068	+	4.53811i	0.182668	+	0.143651i
$999$	3.10931	−	4.36642i	0.0983742	−	0.138147i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.193.8	✓	160
7.2	even	3	inner	966.2.y.b.331.1	yes	160
23.18	even	11	inner	966.2.y.b.823.1	yes	160
161.156	even	33	inner	966.2.y.b.961.8	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.193.8	✓	160	1.1	even	1	trivial
966.2.y.b.331.1	yes	160	7.2	even	3	inner
966.2.y.b.823.1	yes	160	23.18	even	11	inner
966.2.y.b.961.8	yes	160	161.156	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)

\(f(q)\)	\(=\)	\(q+(-0.723734 - 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(2.30813 - 1.81513i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-2.63458 + 0.242856i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +O(q^{10})\)	\(q+(-0.723734 - 0.690079i) q^{2} +(0.981929 - 0.189251i) q^{3} +(0.0475819 + 0.998867i) q^{4} +(2.30813 - 1.81513i) q^{5} +(-0.841254 - 0.540641i) q^{6} +(-2.63458 + 0.242856i) q^{7} +(0.654861 - 0.755750i) q^{8} +(0.928368 - 0.371662i) q^{9} +(-2.92306 - 0.279118i) q^{10} +(2.65585 - 2.53235i) q^{11} +(0.235759 + 0.971812i) q^{12} +(1.50952 + 3.30539i) q^{13} +(2.07433 + 1.64231i) q^{14} +(1.92290 - 2.21915i) q^{15} +(-0.995472 + 0.0950560i) q^{16} +(1.58873 - 0.819046i) q^{17} +(-0.928368 - 0.371662i) q^{18} +(2.11407 + 1.08988i) q^{19} +(1.92290 + 2.21915i) q^{20} +(-2.54101 + 0.737065i) q^{21} -3.66966 q^{22} +(2.69606 - 3.96626i) q^{23} +(0.500000 - 0.866025i) q^{24} +(0.853960 - 3.52007i) q^{25} +(1.18849 - 3.43391i) q^{26} +(0.841254 - 0.540641i) q^{27} +(-0.367939 - 2.62004i) q^{28} +(-6.06561 - 3.89813i) q^{29} +(-2.92306 + 0.279118i) q^{30} +(-0.452844 - 1.30841i) q^{31} +(0.786053 + 0.618159i) q^{32} +(2.12861 - 2.98921i) q^{33} +(-1.71502 - 0.503576i) q^{34} +(-5.64014 + 5.34266i) q^{35} +(0.415415 + 0.909632i) q^{36} +(4.97638 - 1.99224i) q^{37} +(-0.777922 - 2.24766i) q^{38} +(2.10779 + 2.95998i) q^{39} +(0.139717 - 2.93303i) q^{40} +(0.177696 + 1.23591i) q^{41} +(2.34765 + 1.22006i) q^{42} +(-7.52251 - 8.68144i) q^{43} +(2.65585 + 2.53235i) q^{44} +(1.46818 - 2.54296i) q^{45} +(-4.68827 + 1.01002i) q^{46} +(1.59260 + 2.75846i) q^{47} +(-0.959493 + 0.281733i) q^{48} +(6.88204 - 1.27965i) q^{49} +(-3.04717 + 1.95829i) q^{50} +(1.40501 - 1.10491i) q^{51} +(-3.22982 + 1.66509i) q^{52} +(7.61906 + 10.6995i) q^{53} +(-0.981929 - 0.189251i) q^{54} +(1.53350 - 10.6657i) q^{55} +(-1.54175 + 2.15012i) q^{56} +(2.28213 + 0.670093i) q^{57} +(1.69987 + 7.00696i) q^{58} +(3.59561 + 0.343339i) q^{59} +(2.30813 + 1.81513i) q^{60} +(-7.12722 - 1.37366i) q^{61} +(-0.575166 + 1.25944i) q^{62} +(-2.35560 + 1.20463i) q^{63} +(-0.142315 - 0.989821i) q^{64} +(9.48390 + 4.88929i) q^{65} +(-3.60334 + 0.694487i) q^{66} +(1.54914 - 6.38565i) q^{67} +(0.893713 + 1.54796i) q^{68} +(1.89672 - 4.40482i) q^{69} +(7.76882 + 0.0254779i) q^{70} +(-7.41919 + 2.17847i) q^{71} +(0.327068 - 0.945001i) q^{72} +(-0.0129741 - 0.272359i) q^{73} +(-4.97638 - 1.99224i) q^{74} +(0.172350 - 3.61807i) q^{75} +(-0.988053 + 2.16353i) q^{76} +(-6.38207 + 7.31668i) q^{77} +(0.517139 - 3.59678i) q^{78} +(-3.21045 + 4.50845i) q^{79} +(-2.12514 + 2.02632i) q^{80} +(0.723734 - 0.690079i) q^{81} +(0.724268 - 1.01709i) q^{82} +(1.78220 - 12.3955i) q^{83} +(-0.857136 - 2.50306i) q^{84} +(2.18031 - 4.77422i) q^{85} +(-0.546583 + 11.4742i) q^{86} +(-6.69373 - 2.67976i) q^{87} +(-0.174609 - 3.66550i) q^{88} +(-0.505095 + 1.45938i) q^{89} +(-2.81741 + 0.827266i) q^{90} +(-4.77969 - 8.34173i) q^{91} +(4.09005 + 2.50429i) q^{92} +(-0.692279 - 1.19906i) q^{93} +(0.750939 - 3.09541i) q^{94} +(6.85783 - 1.32174i) q^{95} +(0.888835 + 0.458227i) q^{96} +(2.03190 + 14.1322i) q^{97} +(-5.86383 - 3.82303i) q^{98} +(1.52443 - 3.33804i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more