LMFDB - Embedded newform 966.2.y.a.25.4

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			25.4
Character	$\chi$	$=$	966.25
Dual form			966.2.y.a.541.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0760992 + 0.313685i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64554 - 0.0334955i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})$	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0760992 + 0.313685i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64554 - 0.0334955i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.316951 + 0.0610872i) q^{10} +(-0.101308 - 2.12671i) q^{11} +(0.888835 + 0.458227i) q^{12} +(-4.17262 - 4.81546i) q^{13} +(-0.0924223 + 2.64414i) q^{14} +(0.0459369 - 0.319498i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.36310 + 1.91421i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-2.23561 + 3.13948i) q^{19} +(-0.0459369 - 0.319498i) q^{20} +(-2.46848 - 0.952151i) q^{21} +2.12912 q^{22} +(1.02894 - 4.68415i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.35157 - 2.24339i) q^{25} +(5.00855 - 3.93877i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-2.63674 - 0.218131i) q^{28} +(0.455867 - 0.998210i) q^{29} +(0.316951 + 0.0610872i) q^{30} +(-7.58035 - 5.96125i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-0.696367 + 2.01202i) q^{33} +(-1.97690 + 1.27048i) q^{34} +(0.211830 + 0.827317i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-2.50444 - 2.38798i) q^{37} +(-3.02955 - 2.38246i) q^{38} +(2.08400 + 6.02133i) q^{39} +(0.321322 - 0.0306826i) q^{40} +(4.43220 + 1.30141i) q^{41} +(1.06853 - 2.42038i) q^{42} +(-0.961020 - 6.68404i) q^{43} +(-0.101308 + 2.12671i) q^{44} +(-0.161392 + 0.279539i) q^{45} +(4.62989 + 1.25066i) q^{46} +(4.60971 + 7.98425i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(6.99776 - 0.177227i) q^{49} +(2.03379 + 4.45339i) q^{50} +(-0.554020 - 2.28370i) q^{51} +(3.69599 + 5.19029i) q^{52} +(-3.64707 - 10.5375i) q^{53} +(0.928368 - 0.371662i) q^{54} +(0.659407 - 0.193619i) q^{55} +(0.343345 - 2.62338i) q^{56} +(3.24230 - 2.08370i) q^{57} +(0.975389 + 0.502848i) q^{58} +(12.1400 - 2.33979i) q^{59} +(-0.0760992 + 0.313685i) q^{60} +(8.14998 - 3.26276i) q^{61} +(6.31519 - 7.28812i) q^{62} +(1.93778 + 1.80139i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.19301 - 1.67534i) q^{65} +(-1.97661 - 0.791314i) q^{66} +(2.66917 - 1.37605i) q^{67} +(-1.17497 - 2.03511i) q^{68} +(-2.69616 + 3.96620i) q^{69} +(-0.836459 + 0.172225i) q^{70} +(2.09525 + 1.34653i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-4.98072 - 0.475601i) q^{73} +(2.50444 - 2.38798i) q^{74} +(-4.87364 + 0.465376i) q^{75} +(2.52392 - 2.91276i) q^{76} +(-0.339248 - 5.62289i) q^{77} +(-6.11367 + 1.79514i) q^{78} +(3.07917 - 8.89669i) q^{79} +(0.0153587 + 0.322418i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-1.51083 + 4.36526i) q^{82} +(10.4797 - 3.07711i) q^{83} +(2.36680 + 1.18248i) q^{84} +(-0.496728 + 0.573254i) q^{85} +(6.72219 - 0.641892i) q^{86} +(-0.794210 + 0.757278i) q^{87} +(-2.11948 - 0.202386i) q^{88} +(-6.24257 + 4.90921i) q^{89} +(-0.271543 - 0.174510i) q^{90} +(-11.2001 - 12.5997i) q^{91} +(-1.46954 + 4.56514i) q^{92} +(4.82178 + 8.35157i) q^{93} +(-8.19454 + 4.22458i) q^{94} +(-1.15494 - 0.462367i) q^{95} +(0.580057 - 0.814576i) q^{96} +(14.9746 + 4.39693i) q^{97} +(-0.155940 + 6.99826i) q^{98} +(1.39428 - 1.60908i) 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	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 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 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$2$	−0.0475819	+	0.998867i	−0.0336455	+	0.706306i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$3$	−0.928368	−	0.371662i	−0.535993	−	0.214579i
$4$	−0.995472	−	0.0950560i	−0.497736	−	0.0475280i
$5$	0.0760992	+	0.313685i	0.0340326	+	0.140284i	0.986293	−	0.165002i	$-0.0527630\pi$
$5$	0.0760992	+	0.313685i	0.0340326	+	0.140284i	−0.952261	+	0.305286i	$0.901248\pi$
$6$	0.415415	−	0.909632i	0.169592	−	0.371356i
$7$	2.64554	−	0.0334955i	0.999920	−	0.0126601i
$7$	2.64554	−	0.0334955i	0.999920	−	0.0126601i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.723734	+	0.690079i	0.241245	+	0.230026i
$10$	−0.316951	+	0.0610872i	−0.100229	+	0.0193175i
$11$	−0.101308	−	2.12671i	−0.0305454	−	0.641226i	−0.961287	−	0.275549i	$-0.911140\pi$
$11$	−0.101308	−	2.12671i	−0.0305454	−	0.641226i	0.930742	−	0.365677i	$-0.119163\pi$
$12$	0.888835	+	0.458227i	0.256585	+	0.132279i
$13$	−4.17262	−	4.81546i	−1.15728	−	1.33557i	−0.932505	−	0.361158i	$-0.882382\pi$
$13$	−4.17262	−	4.81546i	−1.15728	−	1.33557i	−0.224772	−	0.974411i	$-0.572164\pi$
$14$	−0.0924223	+	2.64414i	−0.0247009	+	0.706675i
$15$	0.0459369	−	0.319498i	0.0118609	−	0.0824941i
$16$	0.981929	+	0.189251i	0.245482	+	0.0473128i
$17$	1.36310	+	1.91421i	0.330601	+	0.464264i	0.946100	−	0.323873i	$-0.104985\pi$
$17$	1.36310	+	1.91421i	0.330601	+	0.464264i	−0.615500	+	0.788137i	$0.711046\pi$
$18$	−0.723734	+	0.690079i	−0.170586	+	0.162653i
$19$	−2.23561	+	3.13948i	−0.512885	+	0.720246i	−0.987090	−	0.160168i	$-0.948796\pi$
$19$	−2.23561	+	3.13948i	−0.512885	+	0.720246i	0.474205	+	0.880415i	$0.342736\pi$
$20$	−0.0459369	−	0.319498i	−0.0102718	−	0.0714420i
$21$	−2.46848	−	0.952151i	−0.538667	−	0.207776i
$22$	2.12912			0.453930
$23$	1.02894	−	4.68415i	0.214549	−	0.976713i
$23$	1.02894	−	4.68415i	0.214549	−	0.976713i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	4.35157	−	2.24339i	0.870314	−	0.448678i
$26$	5.00855	−	3.93877i	0.982257	−	0.772456i
$27$	−0.415415	−	0.909632i	−0.0799467	−	0.175059i
$28$	−2.63674	−	0.218131i	−0.498298	−	0.0412228i
$29$	0.455867	−	0.998210i	0.0846524	−	0.185363i	−0.862572	−	0.505935i	$-0.831148\pi$
$29$	0.455867	−	0.998210i	0.0846524	−	0.185363i	0.947224	+	0.320572i	$0.103875\pi$
$30$	0.316951	+	0.0610872i	0.0578670	+	0.0111530i
$31$	−7.58035	−	5.96125i	−1.36147	−	1.07067i	−0.989824	−	0.142299i	$-0.954551\pi$
$31$	−7.58035	−	5.96125i	−1.36147	−	1.07067i	−0.371647	−	0.928374i	$-0.621207\pi$
$32$	−0.235759	+	0.971812i	−0.0416767	+	0.171794i
$33$	−0.696367	+	2.01202i	−0.121222	+	0.350248i
$34$	−1.97690	+	1.27048i	−0.339035	+	0.217885i
$35$	0.211830	+	0.827317i	0.0358059	+	0.139842i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	−2.50444	−	2.38798i	−0.411727	−	0.392581i	0.455710	−	0.890129i	$-0.349386\pi$
$37$	−2.50444	−	2.38798i	−0.411727	−	0.392581i	−0.867437	+	0.497547i	$0.834234\pi$
$38$	−3.02955	−	2.38246i	−0.491458	−	0.386487i
$39$	2.08400	+	6.02133i	0.333707	+	0.964184i
$40$	0.321322	−	0.0306826i	0.0508055	−	0.00485134i
$41$	4.43220	+	1.30141i	0.692194	+	0.203247i	0.608863	−	0.793275i	$-0.291626\pi$
$41$	4.43220	+	1.30141i	0.692194	+	0.203247i	0.0833311	+	0.996522i	$0.473444\pi$
$42$	1.06853	−	2.42038i	0.164877	−	0.373473i
$43$	−0.961020	−	6.68404i	−0.146554	−	1.01931i	−0.921805	−	0.387653i	$-0.873286\pi$
$43$	−0.961020	−	6.68404i	−0.146554	−	1.01931i	0.775251	−	0.631653i	$-0.217623\pi$
$44$	−0.101308	+	2.12671i	−0.0152727	+	0.320613i
$45$	−0.161392	+	0.279539i	−0.0240589	+	0.0416712i
$46$	4.62989	+	1.25066i	0.682640	+	0.184399i
$47$	4.60971	+	7.98425i	0.672395	+	1.16462i	0.977223	+	0.212215i	$0.0680676\pi$
$47$	4.60971	+	7.98425i	0.672395	+	1.16462i	−0.304828	+	0.952407i	$0.598599\pi$
$48$	−0.841254	−	0.540641i	−0.121424	−	0.0780348i
$49$	6.99776	−	0.177227i	0.999679	−	0.0253182i
$50$	2.03379	+	4.45339i	0.287622	+	0.629804i
$51$	−0.554020	−	2.28370i	−0.0775784	−	0.319782i
$52$	3.69599	+	5.19029i	0.512542	+	0.719764i
$53$	−3.64707	−	10.5375i	−0.500963	−	1.44744i	−0.858147	−	0.513405i	$-0.828384\pi$
$53$	−3.64707	−	10.5375i	−0.500963	−	1.44744i	0.357183	−	0.934034i	$-0.383737\pi$
$54$	0.928368	−	0.371662i	0.126335	−	0.0505769i
$55$	0.659407	−	0.193619i	0.0889144	−	0.0261076i
$56$	0.343345	−	2.62338i	0.0458814	−	0.350564i
$57$	3.24230	−	2.08370i	0.429453	−	0.275993i
$58$	0.975389	+	0.502848i	0.128075	+	0.0660271i
$59$	12.1400	−	2.33979i	1.58049	−	0.304615i	0.677914	−	0.735141i	$-0.262884\pi$
$59$	12.1400	−	2.33979i	1.58049	−	0.304615i	0.902578	+	0.430526i	$0.141672\pi$
$60$	−0.0760992	+	0.313685i	−0.00982436	+	0.0404966i
$61$	8.14998	−	3.26276i	1.04350	−	0.417754i	0.214335	−	0.976760i	$-0.431242\pi$
$61$	8.14998	−	3.26276i	1.04350	−	0.417754i	0.829163	+	0.559007i	$0.188817\pi$
$62$	6.31519	−	7.28812i	0.802030	−	0.925592i
$63$	1.93778	+	1.80139i	0.244138	+	0.226954i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	1.19301	−	1.67534i	0.147974	−	0.207801i
$66$	−1.97661	−	0.791314i	−0.243303	−	0.0974040i
$67$	2.66917	−	1.37605i	0.326091	−	0.168112i	−0.287405	−	0.957809i	$-0.592793\pi$
$67$	2.66917	−	1.37605i	0.326091	−	0.168112i	0.613497	+	0.789697i	$0.289762\pi$
$68$	−1.17497	−	2.03511i	−0.142486	−	0.246794i
$69$	−2.69616	+	3.96620i	−0.324579	+	0.477474i
$70$	−0.836459	+	0.172225i	−0.0999760	+	0.0205848i
$71$	2.09525	+	1.34653i	0.248660	+	0.159804i	0.659034	−	0.752113i	$-0.270965\pi$
$71$	2.09525	+	1.34653i	0.248660	+	0.159804i	−0.410374	+	0.911917i	$0.634602\pi$
$72$	0.786053	−	0.618159i	0.0926372	−	0.0728507i
$73$	−4.98072	−	0.475601i	−0.582949	−	0.0556649i	−0.200584	−	0.979676i	$-0.564284\pi$
$73$	−4.98072	−	0.475601i	−0.582949	−	0.0556649i	−0.382365	+	0.924012i	$0.624890\pi$
$74$	2.50444	−	2.38798i	0.291135	−	0.277597i
$75$	−4.87364	+	0.465376i	−0.562760	+	0.0537370i
$76$	2.52392	−	2.91276i	0.289513	−	0.334116i
$77$	−0.339248	−	5.62289i	−0.0386609	−	0.640788i
$78$	−6.11367	+	1.79514i	−0.692237	+	0.203259i
$79$	3.07917	−	8.89669i	0.346434	−	1.00096i	−0.628374	−	0.777911i	$-0.716279\pi$
$79$	3.07917	−	8.89669i	0.346434	−	1.00096i	0.974808	−	0.223044i	$-0.0715994\pi$
$80$	0.0153587	+	0.322418i	0.00171715	+	0.0360475i
$81$	0.0475819	+	0.998867i	0.00528688	+	0.110985i
$82$	−1.51083	+	4.36526i	−0.166843	+	0.482062i
$83$	10.4797	−	3.07711i	1.15029	−	0.337757i	0.349640	−	0.936884i	$-0.386304\pi$
$83$	10.4797	−	3.07711i	1.15029	−	0.337757i	0.800654	+	0.599127i	$0.204486\pi$
$84$	2.36680	+	1.18248i	0.258239	+	0.129020i
$85$	−0.496728	+	0.573254i	−0.0538777	+	0.0621782i
$86$	6.72219	−	0.641892i	0.724873	−	0.0692170i
$87$	−0.794210	+	0.757278i	−0.0851482	+	0.0811887i
$88$	−2.11948	−	0.202386i	−0.225937	−	0.0215744i
$89$	−6.24257	+	4.90921i	−0.661711	+	0.520375i	−0.891590	−	0.452844i	$-0.850410\pi$
$89$	−6.24257	+	4.90921i	−0.661711	+	0.520375i	0.229879	+	0.973219i	$0.426167\pi$
$90$	−0.271543	−	0.174510i	−0.0286231	−	0.0183950i
$91$	−11.2001	−	12.5997i	−1.17409	−	1.32081i
$92$	−1.46954	+	4.56514i	−0.153210	+	0.475948i
$93$	4.82178	+	8.35157i	0.499995	+	0.866017i
$94$	−8.19454	+	4.22458i	−0.845203	+	0.435732i
$95$	−1.15494	−	0.462367i	−0.118494	−	0.0474378i
$96$	0.580057	−	0.814576i	0.0592018	−	0.0831373i
$97$	14.9746	+	4.39693i	1.52044	+	0.446441i	0.932108	−	0.362180i	$-0.117968\pi$
$97$	14.9746	+	4.39693i	1.52044	+	0.446441i	0.588330	+	0.808621i	$0.299786\pi$
$98$	−0.155940	+	6.99826i	−0.0157523	+	0.706931i
$99$	1.39428	−	1.60908i	0.140130	−	0.161719i
$100$	−4.54511	+	1.81959i	−0.454511	+	0.181959i
$101$	−1.95372	+	8.05333i	−0.194402	+	0.801336i	0.788170	+	0.615457i	$0.211029\pi$
$101$	−1.95372	+	8.05333i	−0.194402	+	0.801336i	−0.982573	+	0.185879i	$0.940487\pi$
$102$	2.30748	−	0.444730i	0.228474	−	0.0440348i
$103$	−15.9160	−	8.20528i	−1.56825	−	0.808490i	−0.568355	−	0.822784i	$-0.692420\pi$
$103$	−15.9160	−	8.20528i	−1.56825	−	0.808490i	−0.999898	+	0.0142932i	$0.995450\pi$
$104$	−5.36027	+	3.44484i	−0.525618	+	0.337794i
$105$	0.110826	−	0.846784i	0.0108155	−	0.0826377i
$106$	10.6991	−	3.14154i	1.03919	−	0.305134i
$107$	1.36735	−	0.547404i	0.132187	−	0.0529195i	−0.304626	−	0.952472i	$-0.598532\pi$
$107$	1.36735	−	0.547404i	0.132187	−	0.0529195i	0.436813	+	0.899553i	$0.356107\pi$
$108$	0.327068	+	0.945001i	0.0314721	+	0.0909327i
$109$	−4.44703	−	6.24498i	−0.425948	−	0.598161i	0.544710	−	0.838625i	$-0.316640\pi$
$109$	−4.44703	−	6.24498i	−0.425948	−	0.598161i	−0.970658	+	0.240464i	$0.922700\pi$
$110$	0.162024	+	0.667873i	0.0154484	+	0.0636792i
$111$	1.43752	+	3.14773i	0.136443	+	0.298769i
$112$	2.60407	+	0.467781i	0.246061	+	0.0442012i
$113$	12.9033	+	8.29242i	1.21384	+	0.780085i	0.981297	−	0.192501i	$-0.0616600\pi$
$113$	12.9033	+	8.29242i	1.21384	+	0.780085i	0.232540	+	0.972587i	$0.425296\pi$
$114$	1.92706	+	3.33777i	0.180486	+	0.312611i
$115$	1.54765	−	0.0336969i	0.144319	−	0.00314225i
$116$	−0.548689	+	0.950357i	−0.0509445	+	0.0882385i
$117$	0.303181	−	6.36455i	0.0280291	−	0.588403i
$118$	1.75950	+	12.2376i	0.161975	+	1.12656i
$119$	3.67026	+	5.01846i	0.336452	+	0.460041i
$120$	−0.309709	−	0.0909387i	−0.0282724	−	0.00830153i
$121$	6.43757	−	0.614713i	0.585234	−	0.0558830i
$122$	2.87127	+	8.29600i	0.259953	+	0.751084i
$123$	−3.63103	−	2.85547i	−0.327399	−	0.257469i
$124$	6.97937	+	6.65482i	0.626766	+	0.597620i
$125$	2.09176	+	2.41402i	0.187093	+	0.215917i
$126$	−1.89155	+	1.84987i	−0.168513	+	0.164800i
$127$	−11.5152	+	7.40038i	−1.02181	+	0.656677i	−0.940423	−	0.340005i	$-0.889571\pi$
$127$	−11.5152	+	7.40038i	−1.02181	+	0.656677i	−0.0813862	+	0.996683i	$0.525935\pi$
$128$	0.327068	−	0.945001i	0.0289090	−	0.0835271i
$129$	−1.59203	+	6.56242i	−0.140170	+	0.577789i
$130$	1.61668	+	1.27137i	0.141792	+	0.111507i
$131$	−21.2894	−	4.10319i	−1.86006	−	0.358497i	−0.869319	−	0.494251i	$-0.835442\pi$
$131$	−21.2894	−	4.10319i	−1.86006	−	0.358497i	−0.990743	+	0.135754i	$0.956654\pi$
$132$	0.884468	−	1.93671i	0.0769831	−	0.168569i
$133$	−5.80925	+	8.38050i	−0.503726	+	0.726682i
$134$	1.24749	+	2.73162i	0.107767	+	0.235976i
$135$	0.253725	−	0.199532i	0.0218372	−	0.0171730i
$136$	2.08871	−	1.07681i	0.179106	−	0.0923354i
$137$	−5.24666	+	9.08748i	−0.448252	+	0.776396i	−0.998272	−	0.0587557i	$-0.981287\pi$
$137$	−5.24666	+	9.08748i	−0.448252	+	0.776396i	0.550020	+	0.835151i	$0.314620\pi$
$138$	−3.83342	−	2.88182i	−0.326322	−	0.245317i
$139$	−21.7255			−1.84274			−0.921368	−	0.388692i	$-0.872927\pi$
$139$	−21.7255			−1.84274			−0.921368	+	0.388692i	$0.872927\pi$
$140$	−0.132230	−	0.843707i	−0.0111755	−	0.0713062i
$141$	−1.31206	−	9.12557i	−0.110495	−	0.768512i
$142$	−1.44470	+	2.02880i	−0.121237	+	0.170253i
$143$	−9.81836	+	9.36179i	−0.821053	+	0.782872i
$144$	0.580057	+	0.814576i	0.0483381	+	0.0678813i
$145$	0.347815	+	0.0670358i	0.0288844	+	0.00556702i
$146$	0.712054	−	4.95245i	0.0589300	−	0.409867i
$147$	−6.56236	−	2.43627i	−0.541254	−	0.200940i
$148$	2.26611	+	2.61523i	0.186273	+	0.214970i
$149$	−6.71023	−	3.45936i	−0.549723	−	0.283402i	0.160905	−	0.986970i	$-0.448559\pi$
$149$	−6.71023	−	3.45936i	−0.549723	−	0.283402i	−0.710628	+	0.703568i	$0.751589\pi$
$150$	−0.232952	−	4.89027i	−0.0190205	−	0.399288i
$151$	−8.22227	+	1.58471i	−0.669119	+	0.128962i	−0.512487	−	0.858695i	$-0.671276\pi$
$151$	−8.22227	+	1.58471i	−0.669119	+	0.128962i	−0.156632	+	0.987657i	$0.550064\pi$
$152$	2.78936	+	2.65965i	0.226247	+	0.215726i
$153$	−0.334432	+	2.32603i	−0.0270372	+	0.188048i
$154$	5.63267	−	0.0713159i	0.453893	−	0.00574680i
$155$	1.29310	−	2.83149i	0.103864	−	0.227431i
$156$	−1.50220	−	6.19216i	−0.120272	−	0.495770i
$157$	−18.0587	−	1.72439i	−1.44124	−	0.137622i	−0.655040	−	0.755594i	$-0.727348\pi$
$157$	−18.0587	−	1.72439i	−1.44124	−	0.137622i	−0.786200	+	0.617973i	$0.787954\pi$
$158$	8.74010	+	3.49901i	0.695325	+	0.278366i
$159$	−0.530576	+	11.1382i	−0.0420774	+	0.883314i
$160$	−0.322784			−0.0255183
$161$	2.56520	−	12.4266i	0.202166	−	0.979351i
$162$	−1.00000			−0.0785674
$163$	0.496065	−	10.4137i	0.0388548	−	0.815664i	−0.892389	−	0.451267i	$-0.850972\pi$
$163$	0.496065	−	10.4137i	0.0388548	−	0.815664i	0.931244	−	0.364397i	$-0.118725\pi$
$164$	−4.28843	−	1.71683i	−0.334870	−	0.134062i
$165$	−0.684133	−	0.0653268i	−0.0532597	−	0.00508569i
$166$	2.57498	+	10.6142i	0.199857	+	0.823824i
$167$	8.41501	−	18.4263i	0.651173	−	1.42587i	−0.239351	−	0.970933i	$-0.576935\pi$
$167$	8.41501	−	18.4263i	0.651173	−	1.42587i	0.890524	−	0.454937i	$-0.150338\pi$
$168$	−1.29376	+	2.30785i	−0.0998159	+	0.178055i
$169$	−3.92781	+	27.3185i	−0.302139	+	2.10143i
$170$	−0.548970	−	0.523442i	−0.0421041	−	0.0401461i
$171$	−3.78448	+	0.729399i	−0.289406	+	0.0557785i
$172$	0.321310	+	6.74512i	0.0244996	+	0.514311i
$173$	10.5866	+	5.45779i	0.804887	+	0.414948i	0.811009	−	0.585033i	$-0.198918\pi$
$173$	10.5866	+	5.45779i	0.804887	+	0.414948i	−0.00612220	+	0.999981i	$0.501949\pi$
$174$	−0.718630	−	0.829343i	−0.0544792	−	0.0628723i
$175$	11.4371	−	6.08074i	0.864564	−	0.459660i
$176$	0.303005	−	2.10745i	0.0228399	−	0.158855i
$177$	−12.1400	−	2.33979i	−0.912497	−	0.175869i
$178$	−4.60662	−	6.46909i	−0.345281	−	0.484879i
$179$	12.9605	−	12.3578i	0.968710	−	0.923663i	−0.0284033	−	0.999597i	$-0.509042\pi$
$179$	12.9605	−	12.3578i	0.968710	−	0.923663i	0.997113	+	0.0759338i	$0.0241938\pi$
$180$	0.187233	−	0.262932i	0.0139555	−	0.0195978i
$181$	2.34818	+	16.3319i	0.174539	+	1.21394i	0.869146	+	0.494555i	$0.164669\pi$
$181$	2.34818	+	16.3319i	0.174539	+	1.21394i	−0.694608	+	0.719389i	$0.744422\pi$
$182$	13.1184	−	10.5879i	0.972399	−	0.784829i
$183$	−8.77882			−0.648949
$184$	−4.49004	−	1.68509i	−0.331010	−	0.124227i
$185$	0.558487	−	0.967328i	0.0410608	−	0.0711194i
$186$	−8.57154	+	4.41893i	−0.628496	+	0.324012i
$187$	3.93287	−	3.09284i	0.287600	−	0.226171i
$188$	−3.82988	−	8.38627i	−0.279323	−	0.611632i
$189$	−1.12947	−	2.39255i	−0.0821565	−	0.174033i
$190$	0.516797	−	1.13163i	0.0374924	−	0.0820969i
$191$	−6.85116	−	1.32045i	−0.495733	−	0.0955447i	−0.0647439	−	0.997902i	$-0.520623\pi$
$191$	−6.85116	−	1.32045i	−0.495733	−	0.0955447i	−0.430989	+	0.902357i	$0.641835\pi$
$192$	0.786053	+	0.618159i	0.0567285	+	0.0446118i
$193$	−0.721801	+	2.97530i	−0.0519564	+	0.214167i	−0.991872	−	0.127240i	$-0.959388\pi$
$193$	−0.721801	+	2.97530i	−0.0519564	+	0.214167i	0.939916	+	0.341407i	$0.110903\pi$
$194$	−5.10447	+	14.7484i	−0.366480	+	1.05887i
$195$	−1.73021	+	1.11194i	−0.123903	+	0.0796276i
$196$	−6.98292	−	0.488754i	−0.498780	−	0.0349110i
$197$	14.4807	+	16.7116i	1.03170	+	1.19065i	0.981412	+	0.191915i	$0.0614698\pi$
$197$	14.4807	+	16.7116i	1.03170	+	1.19065i	0.0502922	+	0.998735i	$0.483985\pi$
$198$	1.54092	+	1.46926i	0.109508	+	0.104416i
$199$	−2.82142	−	2.21879i	−0.200005	−	0.157286i	0.513133	−	0.858309i	$-0.328485\pi$
$199$	−2.82142	−	2.21879i	−0.200005	−	0.157286i	−0.713139	+	0.701023i	$0.752727\pi$
$200$	−1.60126	−	4.62655i	−0.113226	−	0.327146i
$201$	−2.98940	+	0.285453i	−0.210856	+	0.0201343i
$202$	−7.95125	−	2.33470i	−0.559448	−	0.164269i
$203$	1.17258	−	2.65607i	0.0822989	−	0.186420i
$204$	0.334432	+	2.32603i	0.0234149	+	0.162854i
$205$	−0.0709466	+	1.48935i	−0.00495513	+	0.104021i
$206$	8.95330	−	15.5076i	0.623806	−	1.08046i
$207$	3.97711	−	2.68003i	0.276429	−	0.186275i
$208$	−3.18589	−	5.51811i	−0.220901	−	0.382612i
$209$	6.90324	+	4.43644i	0.477507	+	0.306875i
$210$	0.840552	+	0.150992i	0.0580036	+	0.0104195i
$211$	5.65807	+	12.3895i	0.389518	+	0.852925i	0.998226	+	0.0595313i	$0.0189606\pi$
$211$	5.65807	+	12.3895i	0.389518	+	0.852925i	−0.608709	+	0.793394i	$0.708312\pi$
$212$	2.62890	+	10.8365i	0.180554	+	0.744252i
$213$	−1.44470	−	2.02880i	−0.0989894	−	0.139011i
$214$	0.481723	+	1.39185i	0.0329299	+	0.0951446i
$215$	2.02355	−	0.810107i	0.138005	−	0.0552489i
$216$	−0.959493	+	0.281733i	−0.0652852	+	0.0191695i
$217$	−20.2538	−	15.5168i	−1.37492	−	1.05335i
$218$	6.44951	−	4.14485i	0.436816	−	0.280724i
$219$	4.44718	+	2.29268i	0.300512	+	0.154925i
$220$	−0.674826	+	0.130062i	−0.0454967	+	0.00876878i
$221$	3.53009	−	14.5512i	0.237460	−	0.978822i
$222$	−3.21256	+	1.28612i	−0.215613	+	0.0863185i
$223$	−1.95222	+	2.25298i	−0.130730	+	0.150870i	−0.817340	−	0.576155i	$-0.804552\pi$
$223$	−1.95222	+	2.25298i	−0.130730	+	0.150870i	0.686610	+	0.727026i	$0.259098\pi$
$224$	−0.591158	+	2.57886i	−0.0394984	+	0.172308i
$225$	4.69750	+	1.37931i	0.313166	+	0.0919539i
$226$	−8.89699	+	12.4941i	−0.591819	+	0.831094i
$227$	−21.3753	−	8.55739i	−1.41873	−	0.567974i	−0.469606	−	0.882876i	$-0.655604\pi$
$227$	−21.3753	−	8.55739i	−1.41873	−	0.567974i	−0.949124	+	0.314902i	$0.898028\pi$
$228$	−3.42569	+	1.76606i	−0.226872	+	0.116960i
$229$	13.3082	+	23.0505i	0.879432	+	1.52322i	0.851965	+	0.523599i	$0.175411\pi$
$229$	13.3082	+	23.0505i	0.879432	+	1.52322i	0.0274674	+	0.999623i	$0.491256\pi$
$230$	−0.0399814	+	1.54750i	−0.00263630	+	0.102039i
$231$	−1.77487	+	5.34620i	−0.116778	+	0.351754i
$232$	−0.923173	−	0.593287i	−0.0606093	−	0.0389512i
$233$	8.97689	−	7.05950i	0.588095	−	0.462483i	−0.279230	−	0.960224i	$-0.590079\pi$
$233$	8.97689	−	7.05950i	0.588095	−	0.462483i	0.867326	+	0.497741i	$0.165837\pi$
$234$	6.34292	+	0.605675i	0.414650	+	0.0395942i
$235$	−2.15374	+	2.05359i	−0.140495	+	0.133961i
$236$	−12.3074	+	1.17522i	−0.801145	+	0.0765001i
$237$	−6.16517	+	7.11499i	−0.400471	+	0.462168i
$238$	−5.18741	+	3.42731i	−0.336250	+	0.222160i
$239$	−9.30272	+	2.73152i	−0.601743	+	0.176688i	−0.568394	−	0.822756i	$-0.692435\pi$
$239$	−9.30272	+	2.73152i	−0.601743	+	0.176688i	−0.0333482	+	0.999444i	$0.510617\pi$
$240$	0.105572	−	0.305031i	0.00681466	−	0.0196897i
$241$	0.329213	+	6.91104i	0.0212065	+	0.445179i	0.984354	+	0.176204i	$0.0563819\pi$
$241$	0.329213	+	6.91104i	0.0212065	+	0.445179i	−0.963147	+	0.268975i	$0.913315\pi$
$242$	0.307705	+	6.45953i	0.0197800	+	0.415234i
$243$	0.327068	−	0.945001i	0.0209814	−	0.0606218i
$244$	−8.42322	+	2.47328i	−0.539241	+	0.158336i
$245$	0.588117	+	2.18160i	0.0375734	+	0.139378i
$246$	3.02501	−	3.49105i	0.192868	−	0.222581i
$247$	24.4464	−	2.33435i	1.55549	−	0.148531i
$248$	−6.97937	+	6.65482i	−0.443191	+	0.422581i
$249$	−10.8726	−	1.03821i	−0.689026	−	0.0657940i
$250$	−2.51082	+	1.97453i	−0.158798	+	0.124880i
$251$	−6.01452	−	3.86530i	−0.379633	−	0.243975i	0.336882	−	0.941547i	$-0.390628\pi$
$251$	−6.01452	−	3.86530i	−0.379633	−	0.243975i	−0.716515	+	0.697571i	$0.754264\pi$
$252$	−1.75777	−	1.97743i	−0.110729	−	0.124566i
$253$	−10.0661	−	1.71371i	−0.632848	−	0.107740i
$254$	−6.84408	−	11.8543i	−0.429436	−	0.743804i
$255$	0.674203	−	0.347576i	0.0422202	−	0.0217660i
$256$	0.928368	+	0.371662i	0.0580230	+	0.0232289i
$257$	−9.52804	+	13.3803i	−0.594343	+	0.834638i	−0.996728	−	0.0808326i	$-0.974242\pi$
$257$	−9.52804	+	13.3803i	−0.594343	+	0.834638i	0.402385	+	0.915471i	$0.368181\pi$
$258$	−6.47924	−	1.90248i	−0.403380	−	0.118443i
$259$	−6.70558	−	6.23360i	−0.416664	−	0.387337i
$260$	−1.34685	+	1.55435i	−0.0835284	+	0.0963969i
$261$	1.01877	−	0.407854i	0.0630603	−	0.0252455i
$262$	5.11153	−	21.0700i	0.315792	−	1.30171i
$263$	24.6383	−	4.74864i	1.51926	−	0.292814i	0.639710	−	0.768616i	$-0.279054\pi$
$263$	24.6383	−	4.74864i	1.51926	−	0.292814i	0.879552	+	0.475803i	$0.157842\pi$
$264$	1.89244	+	0.975619i	0.116471	+	0.0600452i
$265$	3.02792	−	1.94593i	0.186004	−	0.119537i
$266$	−8.09460	−	6.20143i	−0.496312	−	0.380234i
$267$	7.61997	−	2.23743i	0.466335	−	0.136928i
$268$	−2.78789	+	1.11610i	−0.170297	+	0.0681768i
$269$	2.14315	+	6.19221i	0.130670	+	0.377546i	0.991289	−	0.131703i	$-0.0420445\pi$
$269$	2.14315	+	6.19221i	0.130670	+	0.377546i	−0.860619	+	0.509249i	$0.829923\pi$
$270$	0.187233	+	0.262932i	0.0113946	+	0.0160015i
$271$	−3.72976	−	15.3743i	−0.226567	−	0.933922i	−0.965554	−	0.260202i	$-0.916211\pi$
$271$	−3.72976	−	15.3743i	−0.226567	−	0.933922i	0.738987	−	0.673720i	$-0.235304\pi$
$272$	0.976202	+	2.13758i	0.0591910	+	0.129610i
$273$	5.71500	+	15.8599i	0.345887	+	0.959882i
$274$	−8.82754	−	5.67312i	−0.533291	−	0.342725i
$275$	−5.21188	−	9.02724i	−0.314288	−	0.544363i
$276$	3.06096	−	3.69195i	0.184248	−	0.222229i
$277$	5.50405	−	9.53329i	0.330706	−	0.572800i	−0.651944	−	0.758267i	$-0.726046\pi$
$277$	5.50405	−	9.53329i	0.330706	−	0.572800i	0.982651	+	0.185467i	$0.0593797\pi$
$278$	1.03374	−	21.7009i	0.0619998	−	1.30153i
$279$	−1.37242	−	9.54540i	−0.0821647	−	0.571468i
$280$	0.849043	−	0.0919348i	0.0507400	−	0.00549415i
$281$	5.98686	+	1.75790i	0.357146	+	0.104868i	0.455383	−	0.890295i	$-0.349502\pi$
$281$	5.98686	+	1.75790i	0.357146	+	0.104868i	−0.0982371	+	0.995163i	$0.531320\pi$
$282$	9.17767	−	0.876361i	0.546522	−	0.0521865i
$283$	6.39005	+	18.4628i	0.379849	+	1.09750i	0.959274	+	0.282477i	$0.0911560\pi$
$283$	6.39005	+	18.4628i	0.379849	+	1.09750i	−0.579425	+	0.815026i	$0.696723\pi$
$284$	−1.95776	−	1.53960i	−0.116172	−	0.0913585i
$285$	0.900362	+	0.858493i	0.0533328	+	0.0508528i
$286$	−8.88401	−	10.2527i	−0.525322	−	0.606254i
$287$	11.7692	+	3.29448i	0.694712	+	0.194467i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	3.75401	−	10.8465i	0.220824	−	0.638029i
$290$	−0.0835096	+	0.344231i	−0.00490385	+	0.0202139i
$291$	−12.2677	−	9.64746i	−0.719148	−	0.565544i
$292$	4.91296	+	0.946895i	0.287509	+	0.0554128i
$293$	−5.11794	+	11.2067i	−0.298993	+	0.654704i	−0.998184	−	0.0602306i	$-0.980816\pi$
$293$	−5.11794	+	11.2067i	−0.298993	+	0.654704i	0.699191	+	0.714935i	$0.253544\pi$
$294$	2.74576	−	6.43901i	0.160136	−	0.375530i
$295$	1.65780	+	3.63008i	0.0965209	+	0.211351i
$296$	−2.72009	+	2.13910i	−0.158102	+	0.124333i
$297$	−1.89244	+	0.975619i	−0.109810	+	0.0566111i
$298$	3.77473	−	6.53803i	0.218664	−	0.378738i
$299$	−26.8497	+	14.5904i	−1.55276	+	0.843783i
$300$	4.89581			0.282660
$301$	−2.76630	−	17.6507i	−0.159447	−	1.01737i
$302$	−1.19169	−	8.28836i	−0.0685739	−	0.476942i
$303$	4.80689	−	6.75033i	0.276149	−	0.387796i
$304$	−2.78936	+	2.65965i	−0.159981	+	0.152542i
$305$	1.64369	+	2.30823i	0.0941172	+	0.132169i
$306$	−2.30748	−	0.444730i	−0.131910	−	0.0254235i
$307$	0.957832	−	6.66187i	0.0546664	−	0.380213i	−0.944061	−	0.329772i	$-0.893028\pi$
$307$	0.957832	−	6.66187i	0.0546664	−	0.380213i	0.998727	−	0.0504412i	$-0.0160627\pi$
$308$	−0.196778	+	5.62968i	−0.0112125	+	0.320781i
$309$	11.7263	+	13.5329i	0.667088	+	0.769860i
$310$	2.76675	+	1.42636i	0.157141	+	0.0810118i
$311$	1.40856	+	29.5692i	0.0798718	+	1.67672i	0.582975	+	0.812490i	$0.301888\pi$
$311$	1.40856	+	29.5692i	0.0798718	+	1.67672i	−0.503103	+	0.864226i	$0.667809\pi$
$312$	6.25662	−	1.20587i	0.354212	−	0.0682687i
$313$	−3.64255	−	3.47316i	−0.205889	−	0.196315i	0.580118	−	0.814533i	$-0.303006\pi$
$313$	−3.64255	−	3.47316i	−0.205889	−	0.196315i	−0.786007	+	0.618218i	$0.787855\pi$
$314$	2.58171	−	17.9562i	0.145694	−	1.01333i
$315$	−0.417605	+	0.744937i	−0.0235294	+	0.0419725i
$316$	−3.91091	+	8.56371i	−0.220006	+	0.481746i
$317$	−2.82536	−	11.6463i	−0.158688	−	0.654122i	−0.994466	−	0.105055i	$-0.966498\pi$
$317$	−2.82536	−	11.6463i	−0.158688	−	0.654122i	0.835778	−	0.549067i	$-0.185017\pi$
$318$	−11.1003	−	1.05995i	−0.622474	−	0.0594391i
$319$	−2.16908	−	0.868370i	−0.121445	−	0.0486194i
$320$	0.0153587	−	0.322418i	0.000858576	−	0.0180237i
$321$	−1.47285			−0.0822065
$322$	12.2904	+	3.15358i	0.684920	+	0.175742i
$323$	−9.05699			−0.503944
$324$	0.0475819	−	0.998867i	0.00264344	−	0.0554926i
$325$	−28.9604	−	11.5940i	−1.60644	−	0.643120i
$326$	10.3783	+	0.991007i	0.574801	+	0.0548868i
$327$	1.80746	+	7.45044i	0.0999526	+	0.412010i
$328$	1.91893	−	4.20188i	0.105955	−	0.232010i
$329$	12.4626	+	20.9682i	0.687085	+	1.15602i
$330$	0.0978052	−	0.680250i	0.00538400	−	0.0374465i
$331$	2.90239	+	2.76742i	0.159530	+	0.152111i	0.765640	−	0.643269i	$-0.222422\pi$
$331$	2.90239	+	2.76742i	0.159530	+	0.152111i	−0.606110	+	0.795381i	$0.707271\pi$
$332$	−10.7247	+	2.06702i	−0.588596	+	0.113443i
$333$	−0.164654	−	3.45652i	−0.00902301	−	0.189416i
$334$	18.0050	+	9.28224i	0.985191	+	0.507901i
$335$	0.634769	+	0.732563i	0.0346811	+	0.0400242i
$336$	−2.24368	−	1.40211i	−0.122403	−	0.0764913i
$337$	0.461040	−	3.20660i	0.0251144	−	0.174675i	−0.973404	−	0.229097i	$-0.926423\pi$
$337$	0.461040	−	3.20660i	0.0251144	−	0.174675i	0.998518	+	0.0544223i	$0.0173317\pi$
$338$	−27.1007	−	5.22323i	−1.47408	−	0.284106i
$339$	−8.89699	−	12.4941i	−0.483218	−	0.678585i
$340$	0.548970	−	0.523442i	0.0297721	−	0.0283876i
$341$	−11.9099	+	16.7251i	−0.644957	+	0.905715i
$342$	−0.548500	−	3.81490i	−0.0296595	−	0.206286i
$343$	18.5069	−	0.703255i	0.999279	−	0.0379722i
$344$	−6.75277			−0.364085
$345$	−1.44931	−	0.543920i	−0.0780284	−	0.0292837i
$346$	−5.95534	+	10.3150i	−0.320161	+	0.554535i
$347$	−2.57169	+	1.32580i	−0.138055	+	0.0711725i	−0.525870	−	0.850565i	$-0.676260\pi$
$347$	−2.57169	+	1.32580i	−0.138055	+	0.0711725i	0.387815	+	0.921737i	$0.373230\pi$
$348$	0.862598	−	0.678354i	0.0462401	−	0.0363636i
$349$	0.501779	+	1.09874i	0.0268596	+	0.0588143i	0.922586	−	0.385791i	$-0.126071\pi$
$349$	0.501779	+	1.09874i	0.0268596	+	0.0588143i	−0.895727	+	0.444605i	$0.853344\pi$
$350$	5.52965	+	11.7135i	0.295572	+	0.626112i
$351$	−2.64693	+	5.79597i	−0.141283	+	0.309366i
$352$	2.09064	+	0.402938i	0.111432	+	0.0214767i
$353$	1.37668	+	1.08263i	0.0732732	+	0.0576227i	0.654124	−	0.756388i	$-0.273038\pi$
$353$	1.37668	+	1.08263i	0.0732732	+	0.0576227i	−0.580851	+	0.814010i	$0.697280\pi$
$354$	2.91478	−	12.0149i	0.154919	−	0.638585i
$355$	−0.262941	+	0.759717i	−0.0139554	+	0.0403216i
$356$	6.68096	−	4.29359i	0.354090	−	0.227560i
$357$	−1.54218	−	6.02307i	−0.0816206	−	0.318775i
$358$	11.7271	+	13.5338i	0.619796	+	0.715282i
$359$	1.60232	+	1.52781i	0.0845674	+	0.0806348i	0.731184	−	0.682180i	$-0.238968\pi$
$359$	1.60232	+	1.52781i	0.0845674	+	0.0806348i	−0.646617	+	0.762815i	$0.723817\pi$
$360$	0.253725	+	0.199532i	0.0133725	+	0.0105162i
$361$	1.35592	+	3.91768i	0.0713643	+	0.206194i
$362$	−16.4252	+	1.56841i	−0.863288	+	0.0824340i
$363$	−6.20490	−	1.82192i	−0.325673	−	0.0956261i
$364$	9.95174	+	13.6073i	0.521613	+	0.713217i
$365$	−0.229840	−	1.59857i	−0.0120304	−	0.0836730i
$366$	0.417713	−	8.76888i	0.0218342	−	0.458357i
$367$	3.20682	−	5.55438i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$367$	3.20682	−	5.55438i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$368$	1.89683	−	4.40478i	0.0988790	−	0.229615i
$369$	2.30966	+	4.00045i	0.120236	+	0.208255i
$370$	0.939659	+	0.603882i	0.0488505	+	0.0313943i
$371$	−10.0014	−	27.7552i	−0.519248	−	1.44098i
$372$	−4.00608	−	8.77209i	−0.207706	−	0.454812i
$373$	2.72888	+	11.2486i	0.141296	+	0.582429i	0.997800	+	0.0662900i	$0.0211162\pi$
$373$	2.72888	+	11.2486i	0.141296	+	0.582429i	−0.856505	+	0.516139i	$0.827369\pi$
$374$	2.90221	+	4.07558i	0.150069	+	0.210743i
$375$	−1.04472	−	3.01853i	−0.0539493	−	0.155876i
$376$	8.55901	−	3.42651i	0.441397	−	0.176709i
$377$	−6.70901	+	1.96994i	−0.345531	+	0.101457i
$378$	2.44358	−	1.01434i	0.125684	−	0.0521722i
$379$	−1.44876	+	0.931062i	−0.0744178	+	0.0478254i	−0.577321	−	0.816518i	$-0.695902\pi$
$379$	−1.44876	+	0.931062i	−0.0744178	+	0.0478254i	0.502903	+	0.864343i	$0.332265\pi$
$380$	1.10576	+	0.570057i	0.0567241	+	0.0292433i
$381$	13.4408	−	2.59050i	0.688593	−	0.132715i
$382$	1.64495	−	6.78057i	0.0841629	−	0.346924i
$383$	11.5122	−	4.60879i	0.588246	−	0.235498i	−0.0583938	−	0.998294i	$-0.518598\pi$
$383$	11.5122	−	4.60879i	0.588246	−	0.235498i	0.646640	+	0.762795i	$0.276174\pi$
$384$	−0.654861	+	0.755750i	−0.0334182	+	0.0385667i
$385$	1.73800	−	0.534315i	0.0885768	−	0.0272312i
$386$	−2.93759	−	0.862554i	−0.149519	−	0.0439029i
$387$	3.91699	−	5.50065i	0.199112	−	0.279613i
$388$	−14.4888	−	5.80045i	−0.735558	−	0.294473i
$389$	−2.42079	+	1.24800i	−0.122739	+	0.0632763i	−0.518502	−	0.855076i	$-0.673510\pi$
$389$	−2.42079	+	1.24800i	−0.122739	+	0.0632763i	0.395764	+	0.918352i	$0.370480\pi$
$390$	−1.02835	−	1.78116i	−0.0520726	−	0.0901925i
$391$	10.3690	−	4.41537i	0.524382	−	0.223295i
$392$	0.820461	−	6.95175i	0.0414395	−	0.351116i
$393$	18.2394	+	11.7217i	0.920055	+	0.591283i
$394$	−17.3817	+	13.6691i	−0.875675	+	0.688638i
$395$	3.02508	+	0.288860i	0.152208	+	0.0145341i
$396$	−1.54092	+	1.46926i	−0.0774339	+	0.0738331i
$397$	15.8595	−	1.51440i	0.795967	−	0.0760056i	0.310855	−	0.950457i	$-0.399385\pi$
$397$	15.8595	−	1.51440i	0.795967	−	0.0760056i	0.485112	+	0.874452i	$0.338779\pi$
$398$	2.35053	−	2.71265i	0.117821	−	0.135973i
$399$	8.50784	−	5.62111i	0.425925	−	0.281408i
$400$	4.69750	−	1.37931i	0.234875	−	0.0689655i
$401$	−5.14962	+	14.8789i	−0.257160	+	0.743015i	0.740332	+	0.672241i	$0.234668\pi$
$401$	−5.14962	+	14.8789i	−0.257160	+	0.743015i	−0.997492	+	0.0707738i	$0.977453\pi$
$402$	−0.142888	−	2.99960i	−0.00712663	−	0.149606i
$403$	2.92374	+	61.3769i	0.145642	+	3.05740i
$404$	2.71039	−	7.83115i	0.134847	−	0.389614i
$405$	−0.309709	+	0.0909387i	−0.0153896	+	0.00451878i
$406$	2.59727	+	1.29763i	0.128900	+	0.0644004i
$407$	−4.82481	+	5.56813i	−0.239157	+	0.276002i
$408$	−2.33930	+	0.223376i	−0.115813	+	0.0110588i
$409$	−1.92005	+	1.83076i	−0.0949403	+	0.0905254i	−0.736063	−	0.676913i	$-0.763317\pi$
$409$	−1.92005	+	1.83076i	−0.0949403	+	0.0905254i	0.641123	+	0.767438i	$0.278469\pi$
$410$	−1.48429	−	0.141733i	−0.0733039	−	0.00699967i
$411$	8.24830	−	6.48654i	0.406859	−	0.319957i
$412$	15.0640	+	9.68104i	0.742150	+	0.476951i
$413$	32.0384	−	6.59664i	1.57651	−	0.324600i
$414$	2.48776	+	4.10013i	0.122267	+	0.201510i
$415$	1.76274	+	3.05315i	0.0865295	+	0.149873i
$416$	5.66346	−	2.91971i	0.277674	−	0.143151i
$417$	20.1693	+	8.07456i	0.987694	+	0.395413i
$418$	−4.75989	+	6.68433i	−0.232814	+	0.326941i
$419$	−30.1640	−	8.85695i	−1.47361	−	0.432690i	−0.556338	−	0.830956i	$-0.687794\pi$
$419$	−30.1640	−	8.85695i	−1.47361	−	0.432690i	−0.917270	+	0.398265i	$0.869612\pi$
$420$	−0.190816	+	0.832415i	−0.00931088	+	0.0406177i
$421$	10.7405	−	12.3952i	0.523460	−	0.604105i	−0.431034	−	0.902336i	$-0.641851\pi$
$421$	10.7405	−	12.3952i	0.523460	−	0.604105i	0.954494	+	0.298231i	$0.0963965\pi$
$422$	−12.6446	+	5.06215i	−0.615532	+	0.246422i
$423$	−2.17356	+	8.95953i	−0.105682	+	0.435627i
$424$	−10.9493	+	2.11030i	−0.531745	+	0.102485i
$425$	10.2259	+	5.27184i	0.496031	+	0.255722i
$426$	2.09525	−	1.34653i	0.101515	−	0.0652397i
$427$	21.4518	−	8.90475i	1.03813	−	0.430931i
$428$	−1.41319	+	0.414950i	−0.0683091	+	0.0200574i
$429$	12.5945	−	5.04207i	0.608067	−	0.243433i
$430$	0.712905	+	2.05980i	0.0343793	+	0.0993326i
$431$	−12.7718	−	17.9354i	−0.615194	−	0.863919i	0.383015	−	0.923742i	$-0.374886\pi$
$431$	−12.7718	−	17.9354i	−0.615194	−	0.863919i	−0.998209	+	0.0598234i	$0.980946\pi$
$432$	−0.235759	−	0.971812i	−0.0113430	−	0.0467563i
$433$	−6.80556	−	14.9021i	−0.327054	−	0.716149i	0.672662	−	0.739949i	$-0.265151\pi$
$433$	−6.80556	−	14.9021i	−0.327054	−	0.716149i	−0.999717	+	0.0238005i	$0.992423\pi$
$434$	16.4630	−	19.4925i	0.790247	−	0.935671i
$435$	−0.297985	−	0.191504i	−0.0142873	−	0.00918189i
$436$	3.83327	+	6.63942i	0.183580	+	0.317971i
$437$	12.4055	+	13.7023i	0.593435	+	0.655470i
$438$	−2.50169	+	4.33305i	−0.119535	+	0.207041i
$439$	1.53018	−	32.1224i	0.0730315	−	1.53312i	−0.603892	−	0.797066i	$-0.706384\pi$
$439$	1.53018	−	32.1224i	0.0730315	−	1.53312i	0.676923	−	0.736054i	$-0.263313\pi$
$440$	−0.0978052	−	0.680250i	−0.00466268	−	0.0324296i
$441$	5.18682	+	4.70074i	0.246991	+	0.223845i
$442$	14.3668	+	4.21847i	0.683358	+	0.200652i
$443$	36.2152	−	3.45813i	1.72064	−	0.164301i	0.812496	−	0.582967i	$-0.198108\pi$
$443$	36.2152	−	3.45813i	1.72064	−	0.164301i	0.908140	+	0.418666i	$0.137502\pi$
$444$	−1.13180	−	3.27012i	−0.0537128	−	0.155193i
$445$	−2.01500	−	1.58461i	−0.0955202	−	0.0751179i
$446$	−2.15753	−	2.05721i	−0.102162	−	0.0974115i
$447$	4.94385	+	5.70550i	0.233836	+	0.269861i
$448$	−2.54781	−	0.713196i	−0.120373	−	0.0336953i
$449$	−14.8477	+	9.54202i	−0.700705	+	0.450316i	−0.841877	−	0.539669i	$-0.818549\pi$
$449$	−14.8477	+	9.54202i	−0.700705	+	0.450316i	0.141172	+	0.989985i	$0.454913\pi$
$450$	−1.60126	+	4.62655i	−0.0754843	+	0.218097i
$451$	2.31871	−	9.55785i	0.109184	−	0.450061i
$452$	−12.0566	−	9.48141i	−0.567094	−	0.445968i
$453$	8.22227	+	1.58471i	0.386316	+	0.0744563i
$454$	9.56478	−	20.9439i	0.448897	−	0.982948i
$455$	3.10003	−	4.47214i	0.145331	−	0.209657i
$456$	−1.60106	−	3.50584i	−0.0749767	−	0.164176i
$457$	28.1337	−	22.1246i	1.31604	−	1.03495i	0.319875	−	0.947460i	$-0.396359\pi$
$457$	28.1337	−	22.1246i	1.31604	−	1.03495i	0.996166	−	0.0874866i	$-0.0278835\pi$
$458$	−23.6576	+	12.1964i	−1.10545	+	0.569899i
$459$	1.17497	−	2.03511i	0.0548430	−	0.0949909i
$460$	−1.54385	−	0.113569i	−0.0719822	−	0.00529519i
$461$	6.36348			0.296377			0.148188	−	0.988959i	$-0.452656\pi$
$461$	6.36348			0.296377			0.148188	+	0.988959i	$0.452656\pi$
$462$	−5.25569	−	2.02724i	−0.244517	−	0.0943159i
$463$	4.57893	+	31.8472i	0.212801	+	1.48006i	0.763743	+	0.645520i	$0.223359\pi$
$463$	4.57893	+	31.8472i	0.212801	+	1.48006i	−0.550942	+	0.834544i	$0.685731\pi$
$464$	0.636542	−	0.893898i	0.0295507	−	0.0414982i
$465$	−2.25283	+	2.14807i	−0.104472	+	0.0996143i
$466$	6.62437	+	9.30262i	0.306868	+	0.430936i
$467$	1.26420	+	0.243655i	0.0585003	+	0.0112750i	0.218417	−	0.975855i	$-0.429911\pi$
$467$	1.26420	+	0.243655i	0.0585003	+	0.0112750i	−0.159917	+	0.987130i	$0.551123\pi$
$468$	−0.906797	+	6.30691i	−0.0419167	+	0.291537i
$469$	7.01531	−	3.72981i	0.323937	−	0.172227i
$470$	−1.94879	−	2.24902i	−0.0898908	−	0.103739i
$471$	16.1242	+	8.31261i	0.742964	+	0.383025i
$472$	−0.588275	−	12.3494i	−0.0270775	−	0.568428i
$473$	−14.1176	+	2.72095i	−0.649130	+	0.125109i
$474$	−6.81358	−	6.49673i	−0.312958	−	0.298405i
$475$	−2.68535	+	18.6770i	−0.123212	+	0.856961i
$476$	−3.17660	−	5.34461i	−0.145599	−	0.244970i
$477$	4.63221	−	10.1431i	0.212094	−	0.464422i
$478$	−2.28579	−	9.42215i	−0.104550	−	0.430959i
$479$	−8.92947	−	0.852661i	−0.407998	−	0.0389591i	−0.110960	−	0.993825i	$-0.535393\pi$
$479$	−8.92947	−	0.852661i	−0.407998	−	0.0389591i	−0.297038	+	0.954866i	$0.595999\pi$
$480$	0.299662	+	0.119967i	0.0136776	+	0.00547570i
$481$	−1.04914	+	22.0242i	−0.0478367	+	1.00422i
$482$	−6.91888			−0.315146
$483$	−6.99994	+	10.5830i	−0.318508	+	0.481545i
$484$	−6.46685			−0.293948
$485$	−0.239699	+	5.03190i	−0.0108842	+	0.228487i
$486$	0.928368	+	0.371662i	0.0421116	+	0.0168590i
$487$	−6.09371	−	0.581879i	−0.276133	−	0.0263675i	−0.0439289	−	0.999035i	$-0.513988\pi$
$487$	−6.09371	−	0.581879i	−0.276133	−	0.0263675i	−0.232204	+	0.972667i	$0.574594\pi$
$488$	−2.06969	−	8.53136i	−0.0936903	−	0.386197i
$489$	−4.33091	+	9.48337i	−0.195851	+	0.428853i
$490$	−2.20712	+	0.483646i	−0.0997074	+	0.0218489i
$491$	−4.22092	+	29.3572i	−0.190488	+	1.32487i	0.640233	+	0.768181i	$0.278838\pi$
$491$	−4.22092	+	29.3572i	−0.190488	+	1.32487i	−0.830721	+	0.556689i	$0.812071\pi$
$492$	3.34316	+	3.18770i	0.150721	+	0.143712i
$493$	2.53218	−	0.488037i	0.114043	−	0.0219801i
$494$	1.16850	+	24.5298i	0.0525733	+	1.10365i
$495$	0.610848	+	0.314914i	0.0274556	+	0.0141543i
$496$	−6.31519	−	7.28812i	−0.283560	−	0.327246i
$497$	5.58816	+	3.49212i	0.250663	+	0.156643i
$498$	1.55438	−	10.8109i	0.0696533	−	0.484449i
$499$	33.2143	+	6.40153i	1.48688	+	0.286572i	0.867071	−	0.498185i	$-0.166000\pi$
$499$	33.2143	+	6.40153i	1.48688	+	0.286572i	0.619804	+	0.784756i	$0.287212\pi$
$500$	−1.85282	−	2.60192i	−0.0828607	−	0.116362i
$501$	−14.6606	+	13.9788i	−0.654987	+	0.624529i
$502$	4.14710	−	5.82379i	0.185094	−	0.259928i
$503$	2.29225	+	15.9430i	0.102206	+	0.710861i	0.974908	+	0.222608i	$0.0714569\pi$
$503$	2.29225	+	15.9430i	0.102206	+	0.710861i	−0.872702	+	0.488254i	$0.837634\pi$
$504$	2.05883	−	1.66169i	0.0917075	−	0.0740177i
$505$	−2.67489			−0.119031
$506$	2.19074	−	9.97312i	0.0973901	−	0.443359i
$507$	13.7997	−	23.9018i	0.612867	−	1.06152i
$508$	12.1665	−	6.27228i	0.539802	−	0.278287i
$509$	6.42381	−	5.05174i	0.284731	−	0.223915i	−0.465571	−	0.885011i	$-0.654151\pi$
$509$	6.42381	−	5.05174i	0.284731	−	0.223915i	0.750301	+	0.661096i	$0.229908\pi$
$510$	0.315102	+	0.689978i	0.0139530	+	0.0305527i
$511$	−13.1926	−	1.09139i	−0.583607	−	0.0482802i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	3.78448	+	0.729399i	0.167089	+	0.0322037i
$514$	−12.9117	−	10.1539i	−0.569513	−	0.447870i
$515$	1.36268	−	5.61703i	0.0600468	−	0.247516i
$516$	2.20862	−	6.38137i	0.0972289	−	0.280924i
$517$	16.5132	−	10.6124i	0.726248	−	0.466731i
$518$	6.54561	−	6.40138i	0.287597	−	0.281260i
$519$	−7.79984	−	9.00150i	−0.342375	−	0.395122i
$520$	−1.48851	−	1.41929i	−0.0652754	−	0.0622399i
$521$	−13.1675	−	10.3550i	−0.576877	−	0.453661i	0.286600	−	0.958050i	$-0.407475\pi$
$521$	−13.1675	−	10.3550i	−0.576877	−	0.453661i	−0.863476	+	0.504390i	$0.831718\pi$
$522$	0.358917	+	1.03702i	0.0157094	+	0.0453893i
$523$	26.4168	−	2.52250i	1.15513	−	0.110301i	0.500142	−	0.865943i	$-0.333281\pi$
$523$	26.4168	−	2.52250i	1.15513	−	0.110301i	0.654985	+	0.755642i	$0.272675\pi$
$524$	20.8029	+	6.10830i	0.908781	+	0.266842i
$525$	−12.8778	+	1.39442i	−0.562034	+	0.0608573i
$526$	3.57093	+	24.8363i	0.155700	+	1.08292i
$527$	1.07829	−	22.6362i	0.0469712	−	0.986047i
$528$	−1.06456	+	1.84387i	−0.0463290	+	0.0802442i
$529$	−20.8826	−	9.63943i	−0.907938	−	0.419105i
$530$	1.79965	+	3.11708i	0.0781718	+	0.135397i
$531$	10.4008	+	6.68416i	0.451355	+	0.290068i
$532$	6.57956	−	7.79035i	0.285260	−	0.337755i
$533$	−12.2270	−	26.7734i	−0.529611	−	1.15969i
$534$	1.87232	+	7.71780i	0.0810232	+	0.333982i
$535$	0.275766	+	0.387260i	0.0119224	+	0.0167427i
$536$	−0.982185	−	2.83784i	−0.0424239	−	0.122576i
$537$	−16.6250	+	6.65564i	−0.717421	+	0.287212i
$538$	−6.28717	+	1.84608i	−0.271059	+	0.0795902i
$539$	−1.08584	−	14.8642i	−0.0467703	−	0.640248i
$540$	−0.271543	+	0.174510i	−0.0116854	+	0.00750972i
$541$	8.28832	+	4.27292i	0.356343	+	0.183707i	0.627097	−	0.778941i	$-0.284243\pi$
$541$	8.28832	+	4.27292i	0.356343	+	0.183707i	−0.270755	+	0.962648i	$0.587273\pi$
$542$	15.5344	−	2.99400i	0.667258	−	0.128603i
$543$	3.89000	−	16.0348i	0.166936	−	0.688118i
$544$	−2.18161	+	0.873386i	−0.0935359	+	0.0374461i
$545$	1.62054	−	1.87021i	0.0694164	−	0.0801108i
$546$	−16.1138	+	4.95388i	−0.689608	+	0.212007i
$547$	−12.4882	−	3.66686i	−0.533956	−	0.156784i	0.00362867	−	0.999993i	$-0.498845\pi$
$547$	−12.4882	−	3.66686i	−0.533956	−	0.156784i	−0.537585	+	0.843210i	$0.680663\pi$
$548$	6.08672	−	8.54760i	0.260012	−	0.365136i
$549$	8.14998	+	3.26276i	0.347833	+	0.139251i
$550$	9.26501	−	4.77644i	0.395061	−	0.203668i
$551$	2.11472	+	3.66280i	0.0900900	+	0.156041i
$552$	3.54212	+	3.23316i	0.150763	+	0.137613i
$553$	7.84807	−	23.6397i	0.333734	−	1.00526i
$554$	9.26060	+	5.95143i	0.393445	+	0.252852i
$555$	−0.878001	+	0.690468i	−0.0372691	+	0.0293087i
$556$	21.6272	+	2.06514i	0.917196	+	0.0875816i
$557$	−31.8565	+	30.3751i	−1.34980	+	1.28703i	−0.425713	+	0.904858i	$0.639977\pi$
$557$	−31.8565	+	30.3751i	−1.34980	+	1.28703i	−0.924090	+	0.382176i	$0.875175\pi$
$558$	9.59989	−	0.916679i	0.406396	−	0.0388061i
$559$	−28.1768	+	32.5177i	−1.19175	+	1.37535i
$560$	0.0514315	+	0.852456i	0.00217338	+	0.0360228i
$561$	−4.80064	+	1.40960i	−0.202683	+	0.0595132i
$562$	−2.04078	+	5.89644i	−0.0860850	+	0.248726i
$563$	1.17330	+	24.6305i	0.0494486	+	1.03805i	0.878157	+	0.478373i	$0.158773\pi$
$563$	1.17330	+	24.6305i	0.0494486	+	1.03805i	−0.828708	+	0.559681i	$0.810924\pi$
$564$	0.438677	+	9.20897i	0.0184717	+	0.387768i
$565$	−1.61928	+	4.67861i	−0.0681237	+	0.196830i
$566$	−18.7460	+	5.50432i	−0.787953	+	0.231364i
$567$	0.159337	+	2.64095i	0.00669154	+	0.110909i
$568$	1.63101	−	1.88229i	0.0684357	−	0.0789790i
$569$	−18.7542	+	1.79081i	−0.786216	+	0.0750745i	−0.480438	−	0.877028i	$-0.659522\pi$
$569$	−18.7542	+	1.79081i	−0.786216	+	0.0750745i	−0.305778	+	0.952103i	$0.598916\pi$
$570$	−0.900362	+	0.858493i	−0.0377120	+	0.0359583i
$571$	−39.4700	−	3.76893i	−1.65177	−	0.157725i	−0.772815	−	0.634632i	$-0.781152\pi$
$571$	−39.4700	−	3.76893i	−1.65177	−	0.157725i	−0.878954	+	0.476907i	$0.841758\pi$
$572$	10.6638	−	8.38610i	0.445876	−	0.350641i
$573$	5.86964	+	3.77219i	0.245208	+	0.157585i
$574$	−3.85075	+	11.5991i	−0.160727	+	0.484136i
$575$	−6.03088	−	22.6917i	−0.251505	−	0.946311i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	8.56403	−	4.41506i	0.356525	−	0.183801i	−0.270654	−	0.962677i	$-0.587240\pi$
$577$	8.56403	−	4.41506i	0.356525	−	0.183801i	0.627179	+	0.778875i	$0.284210\pi$
$578$	10.6556	+	4.26585i	0.443214	+	0.177436i
$579$	1.77591	−	2.49391i	0.0738041	−	0.103643i
$580$	−0.339868	−	0.0997942i	−0.0141122	−	0.00414373i
$581$	27.6213	−	8.49164i	1.14593	−	0.352293i
$582$	10.2203	−	11.7948i	0.423643	−	0.488910i
$583$	−22.0407	+	8.82378i	−0.912834	+	0.365444i
$584$	−1.17959	+	4.86234i	−0.0488118	+	0.201205i
$585$	2.01954	−	0.389234i	0.0834976	−	0.0160928i
$586$	−10.9505	−	5.64538i	−0.452362	−	0.233209i
$587$	21.2152	−	13.6342i	0.875644	−	0.562742i	−0.0238303	−	0.999716i	$-0.507586\pi$
$587$	21.2152	−	13.6342i	0.875644	−	0.562742i	0.899474	+	0.436974i	$0.143950\pi$
$588$	6.30106	+	3.04903i	0.259851	+	0.125740i
$589$	35.6620	−	10.4713i	1.46943	−	0.431462i
$590$	−3.70485	+	1.48320i	−0.152526	+	0.0610622i
$591$	−7.23231	−	20.8964i	−0.297498	−	0.859563i
$592$	−2.00725	−	2.81879i	−0.0824976	−	0.115852i
$593$	5.26194	+	21.6900i	0.216082	+	0.890702i	0.971800	+	0.235805i	$0.0757728\pi$
$593$	5.26194	+	21.6900i	0.216082	+	0.890702i	−0.755718	+	0.654897i	$0.772712\pi$
$594$	−0.884468	−	1.93671i	−0.0362902	−	0.0794644i
$595$	−1.29491	+	1.53320i	−0.0530862	+	0.0628553i
$596$	6.35101	+	4.08155i	0.260148	+	0.167187i
$597$	1.79468	+	3.10847i	0.0734513	+	0.127221i
$598$	−13.2963	−	27.5136i	−0.543726	−	1.12511i
$599$	−19.1704	+	33.2042i	−0.783283	+	1.35669i	0.146737	+	0.989176i	$0.453123\pi$
$599$	−19.1704	+	33.2042i	−0.783283	+	1.35669i	−0.930019	+	0.367510i	$0.880210\pi$
$600$	−0.232952	+	4.89027i	−0.00951023	+	0.199644i
$601$	−0.290427	−	2.01996i	−0.0118468	−	0.0823960i	0.983040	−	0.183390i	$-0.0587070\pi$
$601$	−0.290427	−	2.01996i	−0.0118468	−	0.0823960i	−0.994887	+	0.100994i	$0.967798\pi$
$602$	17.7623	−	1.92331i	0.723938	−	0.0783884i
$603$	2.88136	+	0.846043i	0.117338	+	0.0344535i
$604$	8.33568	−	0.795961i	0.339174	−	0.0323872i
$605$	0.682720	+	1.97259i	0.0277565	+	0.0801972i
$606$	6.51396	+	5.12264i	0.264612	+	0.208093i
$607$	9.96149	+	9.49826i	0.404324	+	0.385523i	0.864772	−	0.502164i	$-0.167463\pi$
$607$	9.96149	+	9.49826i	0.404324	+	0.385523i	−0.460448	+	0.887687i	$0.652311\pi$
$608$	−2.52392	−	2.91276i	−0.102358	−	0.118128i
$609$	−2.07575	+	2.03001i	−0.0841136	+	0.0822602i
$610$	−2.38383	+	1.53199i	−0.0965184	+	0.0620286i
$611$	19.2133	−	55.5131i	0.777286	−	2.24582i
$612$	0.554020	−	2.28370i	0.0223949	−	0.0923132i
$613$	18.2799	+	14.3755i	0.738318	+	0.580620i	0.914907	−	0.403665i	$-0.132264\pi$
$613$	18.2799	+	14.3755i	0.738318	+	0.580620i	−0.176589	+	0.984285i	$0.556506\pi$
$614$	6.60875	+	1.27373i	0.266707	+	0.0514036i
$615$	0.619401	−	1.35630i	0.0249767	−	0.0546913i
$616$	−5.61394	−	0.464426i	−0.226192	−	0.0187123i
$617$	11.0623	+	24.2230i	0.445350	+	0.975181i	0.990585	+	0.136897i	$0.0437131\pi$
$617$	11.0623	+	24.2230i	0.445350	+	0.975181i	−0.545235	+	0.838283i	$0.683560\pi$
$618$	−14.0755	+	11.0691i	−0.566201	+	0.445266i
$619$	32.1110	−	16.5544i	1.29065	−	0.665376i	0.330222	−	0.943903i	$-0.392876\pi$
$619$	32.1110	−	16.5544i	1.29065	−	0.665376i	0.960428	+	0.278527i	$0.0898461\pi$
$620$	−1.55639	+	2.69575i	−0.0625062	+	0.108264i
$621$	−4.68829	+	1.00991i	−0.188135	+	0.0405263i
$622$	−29.6027			−1.18696
$623$	−16.3505	+	13.1966i	−0.655070	+	0.528711i
$624$	0.906797	+	6.30691i	0.0363010	+	0.252479i
$625$	13.6012	−	19.1002i	0.544047	−	0.764008i
$626$	3.64255	−	3.47316i	0.145586	−	0.138816i
$627$	−4.75989	−	6.68433i	−0.190092	−	0.266946i
$628$	17.8130	+	3.43317i	0.710816	+	0.136999i
$629$	1.15728	−	8.04907i	0.0461439	−	0.320938i
$630$	−0.724223	−	0.452578i	−0.0288537	−	0.0180311i
$631$	−1.07649	−	1.24233i	−0.0428543	−	0.0494565i	0.733918	−	0.679238i	$-0.237690\pi$
$631$	−1.07649	−	1.24233i	−0.0428543	−	0.0494565i	−0.776772	+	0.629782i	$0.783144\pi$
$632$	−8.36792	−	4.31396i	−0.332858	−	0.171600i
$633$	−0.648080	−	13.6049i	−0.0257589	−	0.540745i
$634$	11.7676	−	2.26801i	0.467349	−	0.0900742i
$635$	−3.19769	−	3.04899i	−0.126896	−	0.120995i
$636$	1.58692	−	11.0373i	0.0629256	−	0.437657i
$637$	−30.0524	−	32.9579i	−1.19072	−	1.30584i
$638$	0.970596	−	2.12531i	0.0384263	−	0.0841418i
$639$	0.587187	+	2.42042i	0.0232287	+	0.0957502i
$640$	0.321322	+	0.0306826i	0.0127014	+	0.00121283i
$641$	−1.51872	−	0.608004i	−0.0599859	−	0.0240147i	0.341475	−	0.939891i	$-0.389073\pi$
$641$	−1.51872	−	0.608004i	−0.0599859	−	0.0240147i	−0.401461	+	0.915876i	$0.631498\pi$
$642$	0.0700811	−	1.47118i	0.00276588	−	0.0580630i
$643$	2.03784			0.0803644			0.0401822	−	0.999192i	$-0.487206\pi$
$643$	2.03784			0.0803644			0.0401822	+	0.999192i	$0.487206\pi$
$644$	−3.73481	+	12.1265i	−0.147172	+	0.477850i
$645$	−2.17969			−0.0858250
$646$	0.430949	−	9.04673i	0.0169555	−	0.355939i
$647$	32.9588	+	13.1947i	1.29574	+	0.518738i	0.914069	−	0.405559i	$-0.132923\pi$
$647$	32.9588	+	13.1947i	1.29574	+	0.518738i	0.381675	+	0.924297i	$0.375347\pi$
$648$	0.995472	+	0.0950560i	0.0391058	+	0.00373415i
$649$	−6.20592	−	25.5812i	−0.243604	−	1.00415i
$650$	12.9589	−	28.3760i	0.508288	−	1.11300i
$651$	13.0359	+	21.9329i	0.510919	+	0.859618i
$652$	−1.48370	+	10.3194i	−0.0581063	+	0.404138i
$653$	−6.11855	−	5.83402i	−0.239437	−	0.228303i	0.560854	−	0.827915i	$-0.310473\pi$
$653$	−6.11855	−	5.83402i	−0.239437	−	0.228303i	−0.800291	+	0.599612i	$0.795322\pi$
$654$	−7.52800	+	1.45090i	−0.294368	+	0.0567348i
$655$	−0.332994	−	6.99041i	−0.0130112	−	0.273138i
$656$	4.10582	+	2.11669i	0.160305	+	0.0826430i
$657$	−3.27651	−	3.78130i	−0.127829	−	0.147522i
$658$	−21.5375	+	11.4508i	−0.839618	+	0.446398i
$659$	−2.50622	+	17.4311i	−0.0976283	+	0.679020i	0.880960	+	0.473191i	$0.156898\pi$
$659$	−2.50622	+	17.4311i	−0.0976283	+	0.679020i	−0.978588	+	0.205829i	$0.934011\pi$
$660$	0.674826	+	0.130062i	0.0262676	+	0.00506266i
$661$	−15.7297	−	22.0892i	−0.611813	−	0.859171i	0.386185	−	0.922421i	$-0.373793\pi$
$661$	−15.7297	−	22.0892i	−0.611813	−	0.859171i	−0.997998	+	0.0632505i	$0.979853\pi$
$662$	−2.90239	+	2.76742i	−0.112805	+	0.107559i
$663$	−8.68537	+	12.1969i	−0.337312	+	0.473688i
$664$	−1.55438	−	10.8109i	−0.0603215	−	0.419546i
$665$	−3.07092	−	1.18452i	−0.119085	−	0.0459339i
$666$	3.46044			0.134089
$667$	−4.20671	−	3.16245i	−0.162884	−	0.122451i
$668$	−10.1284	+	17.5430i	−0.391881	+	0.678758i
$669$	2.64972	−	1.36603i	0.102444	−	0.0528136i
$670$	−0.761937	+	0.599194i	−0.0294362	+	0.0231489i
$671$	−7.76459	−	17.0021i	−0.299749	−	0.656358i
$672$	1.50728	−	2.17442i	0.0581445	−	0.0838801i
$673$	18.3294	−	40.1358i	0.706546	−	1.54712i	−0.125302	−	0.992119i	$-0.539990\pi$
$673$	18.3294	−	40.1358i	0.706546	−	1.54712i	0.831849	−	0.555002i	$-0.187283\pi$
$674$	3.18103	+	0.613094i	0.122529	+	0.0236155i
$675$	−3.84837	−	3.02639i	−0.148124	−	0.116486i
$676$	6.50682	−	26.8215i	0.250262	−	1.03160i
$677$	13.3270	−	38.5060i	0.512200	−	1.47990i	−0.331690	−	0.943388i	$-0.607619\pi$
$677$	13.3270	−	38.5060i	0.512200	−	1.47990i	0.843890	−	0.536516i	$-0.180260\pi$
$678$	12.9033	−	8.29242i	0.495547	−	0.318469i
$679$	39.7631	+	11.1307i	1.52597	+	0.427156i
$680$	0.496728	+	0.573254i	0.0190486	+	0.0219833i
$681$	16.6637	+	15.8888i	0.638555	+	0.608861i
$682$	−16.1395	−	12.6922i	−0.618012	−	0.486010i
$683$	−9.92164	−	28.6667i	−0.379641	−	1.09690i	−0.959385	−	0.282101i	$-0.908969\pi$
$683$	−9.92164	−	28.6667i	−0.379641	−	1.09690i	0.579744	−	0.814799i	$-0.303153\pi$
$684$	3.83668	−	0.366358i	0.146699	−	0.0140081i
$685$	−3.24987	−	0.954249i	−0.124171	−	0.0364600i
$686$	−0.178135	+	18.5194i	−0.00680123	+	0.707074i
$687$	−3.78792	−	26.3455i	−0.144518	−	1.00514i
$688$	0.321310	−	6.74512i	0.0122498	−	0.257155i
$689$	−35.5252	+	61.5314i	−1.35340	+	2.34416i
$690$	0.612265	−	1.42179i	0.0233085	−	0.0541266i
$691$	10.3159	+	17.8676i	0.392434	+	0.679715i	0.992770	−	0.120033i	$-0.0382999\pi$
$691$	10.3159	+	17.8676i	0.392434	+	0.679715i	−0.600336	+	0.799748i	$0.704967\pi$
$692$	−10.0199	−	6.43940i	−0.380900	−	0.244789i
$693$	3.63472	−	4.30359i	0.138071	−	0.163480i
$694$	−1.20193	−	2.63186i	−0.0456246	−	0.0999040i
$695$	−1.65330	−	6.81498i	−0.0627131	−	0.258507i
$696$	0.636542	+	0.893898i	0.0241281	+	0.0338831i
$697$	3.55037	+	10.2581i	0.134480	+	0.388554i
$698$	−1.12137	+	0.448930i	−0.0424446	+	0.0169922i
$699$	−10.9576	+	3.21744i	−0.414455	+	0.121695i
$700$	−11.9633	+	4.96604i	−0.452171	+	0.187698i
$701$	−16.0311	+	10.3025i	−0.605485	+	0.389122i	−0.807162	−	0.590331i	$-0.798997\pi$
$701$	−16.0311	+	10.3025i	−0.605485	+	0.389122i	0.201677	+	0.979452i	$0.435361\pi$
$702$	−5.66346	−	2.91971i	−0.213753	−	0.110198i
$703$	13.0960	−	2.52404i	0.493924	−	0.0951960i
$704$	−0.501959	+	2.06910i	−0.0189183	+	0.0779822i
$705$	2.76271	−	1.10602i	0.104050	−	0.0416552i
$706$	−1.14691	+	1.32361i	−0.0431646	+	0.0498146i
$707$	−4.89888	+	21.3708i	−0.184242	+	0.803733i
$708$	11.8626	+	3.48318i	0.445824	+	0.130906i
$709$	−18.8795	+	26.5125i	−0.709034	+	0.995699i	0.290215	+	0.956961i	$0.406273\pi$
$709$	−18.8795	+	26.5125i	−0.709034	+	0.995699i	−0.999249	+	0.0387377i	$0.987666\pi$
$710$	−0.746345	−	0.298792i	−0.0280098	−	0.0112135i
$711$	8.36792	−	4.31396i	0.313821	−	0.161786i
$712$	3.97083	+	6.87768i	0.148813	+	0.257752i
$713$	−35.7231	+	29.3737i	−1.33784	+	1.10006i
$714$	6.08963	−	1.25384i	0.227899	−	0.0469238i
$715$	−3.68382	−	2.36745i	−0.137767	−	0.0885376i
$716$	−14.0764	+	11.0698i	−0.526061	+	0.413699i
$717$	9.65155	+	0.921611i	0.360444	+	0.0344182i
$718$	−1.60232	+	1.52781i	−0.0597982	+	0.0570174i
$719$	−20.9957	+	2.00485i	−0.783009	+	0.0747683i	−0.478900	−	0.877869i	$-0.658965\pi$
$719$	−20.9957	+	2.00485i	−0.783009	+	0.0747683i	−0.304108	+	0.952637i	$0.598358\pi$
$720$	−0.211378	+	0.243944i	−0.00787761	+	0.00909125i
$721$	−42.3813	−	21.1743i	−1.57836	−	0.788571i
$722$	−3.97776	+	1.16797i	−0.148037	+	0.0434675i
$723$	2.26294	−	6.53834i	0.0841598	−	0.243164i
$724$	−0.785096	−	16.4812i	−0.0291779	−	0.612519i
$725$	−0.255636	−	5.36647i	−0.00949410	−	0.199306i
$726$	2.11510	−	6.11118i	0.0784987	−	0.226807i
$727$	2.43597	−	0.715265i	0.0903450	−	0.0265277i	−0.236248	−	0.971693i	$-0.575918\pi$
$727$	2.43597	−	0.715265i	0.0903450	−	0.0265277i	0.326593	+	0.945165i	$0.394099\pi$
$728$	−14.0654	+	9.29300i	−0.521300	+	0.344422i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	1.60770	−	0.153516i	0.0595035	−	0.00568189i
$731$	11.4847	−	10.9506i	0.424776	−	0.405023i
$732$	8.73907	+	0.834480i	0.323005	+	0.0308433i
$733$	−13.1678	+	10.3553i	−0.486365	+	0.382482i	−0.831016	−	0.556249i	$-0.812240\pi$
$733$	−13.1678	+	10.3553i	−0.486365	+	0.382482i	0.344650	+	0.938731i	$0.387998\pi$
$734$	5.39550	+	3.46748i	0.199152	+	0.127987i
$735$	0.264832	−	2.24391i	0.00976846	−	0.0827680i
$736$	4.30953	+	2.10427i	0.158851	+	0.0775643i
$737$	−3.19687	−	5.53714i	−0.117758	−	0.203963i
$738$	−4.10582	+	2.11669i	−0.151137	+	0.0779166i
$739$	25.2856	+	10.1228i	0.930145	+	0.372374i	0.786736	−	0.617290i	$-0.211769\pi$
$739$	25.2856	+	10.1228i	0.930145	+	0.372374i	0.143409	+	0.989664i	$0.454194\pi$
$740$	−0.647909	+	0.909861i	−0.0238176	+	0.0334471i
$741$	−23.5629	−	6.91868i	−0.865604	−	0.254164i
$742$	28.1997	−	8.66945i	1.03524	−	0.318265i
$743$	−0.139174	+	0.160616i	−0.00510581	+	0.00589242i	−0.758297	−	0.651910i	$-0.773968\pi$
$743$	−0.139174	+	0.160616i	−0.00510581	+	0.00589242i	0.753191	+	0.657802i	$0.228514\pi$
$744$	8.95277	−	3.58415i	0.328225	−	0.131401i
$745$	0.574508	−	2.36815i	0.0210483	−	0.0867624i
$746$	−11.3657	+	2.19056i	−0.416127	+	0.0802020i
$747$	9.70795	+	5.00480i	0.355195	+	0.183116i
$748$	−4.20905	+	2.70499i	−0.153898	+	0.0989044i
$749$	3.59904	−	1.49398i	0.131506	−	0.0545888i
$750$	3.06482	−	0.899912i	0.111911	−	0.0328602i
$751$	−39.5533	+	15.8347i	−1.44332	+	0.577818i	−0.955464	−	0.295107i	$-0.904645\pi$
$751$	−39.5533	+	15.8347i	−1.44332	+	0.577818i	−0.487855	+	0.872925i	$0.662220\pi$
$752$	3.01538	+	8.71235i	0.109959	+	0.317707i
$753$	4.14710	+	5.82379i	0.151129	+	0.212231i
$754$	−1.64848	−	6.79514i	−0.0600342	−	0.247464i
$755$	−1.12281	−	2.45861i	−0.0408632	−	0.0894779i
$756$	0.896924	+	2.48908i	0.0326208	+	0.0905270i
$757$	17.7287	+	11.3936i	0.644361	+	0.414106i	0.821602	−	0.570062i	$-0.193081\pi$
$757$	17.7287	+	11.3936i	0.644361	+	0.414106i	−0.177240	+	0.984168i	$0.556717\pi$
$758$	−0.861072	−	1.49142i	−0.0312756	−	0.0541709i
$759$	8.70808	+	5.33213i	0.316083	+	0.193544i
$760$	−0.622025	+	1.07738i	−0.0225632	+	0.0390807i
$761$	1.60615	−	33.7172i	0.0582228	−	1.22225i	−0.760992	−	0.648761i	$-0.775288\pi$
$761$	1.60615	−	33.7172i	0.0582228	−	1.22225i	0.819215	−	0.573486i	$-0.194409\pi$
$762$	1.94803	+	13.5488i	0.0705696	+	0.490822i
$763$	−11.9740	−	16.3724i	−0.433487	−	0.592720i
$764$	6.69462	+	1.96572i	0.242203	+	0.0711172i
$765$	−0.755089	+	0.0721023i	−0.0273003	+	0.00260686i
$766$	4.05580	+	11.7185i	0.146542	+	0.423405i
$767$	−61.9228	−	48.6966i	−2.23590	−	1.75833i
$768$	−0.723734	−	0.690079i	−0.0261155	−	0.0249011i
$769$	33.1434	+	38.2496i	1.19518	+	1.37931i	0.906671	+	0.421838i	$0.138615\pi$
$769$	33.1434	+	38.2496i	1.19518	+	1.37931i	0.288511	+	0.957477i	$0.406840\pi$
$770$	0.451012	+	1.76146i	0.0162533	+	0.0634785i
$771$	13.8185	−	8.88059i	0.497660	−	0.319827i
$772$	1.00135	−	2.89322i	0.0360395	−	0.104129i
$773$	−0.921423	+	3.79816i	−0.0331413	+	0.136610i	−0.985979	−	0.166871i	$-0.946634\pi$
$773$	−0.921423	+	3.79816i	−0.0331413	+	0.136610i	0.952838	+	0.303481i	$0.0981489\pi$
$774$	5.30804	+	4.17429i	0.190793	+	0.150042i
$775$	−46.3598	−	8.93513i	−1.66529	−	0.320959i
$776$	6.48328	−	14.1964i	0.232736	−	0.509621i
$777$	3.90845	+	8.27929i	0.140215	+	0.297018i
$778$	−1.13140	−	2.47743i	−0.0405628	−	0.0888201i
$779$	−13.9945	+	11.0054i	−0.501404	+	0.394308i
$780$	1.82807	−	0.942437i	0.0654555	−	0.0337446i
$781$	2.65142	−	4.59239i	0.0948751	−	0.164329i
$782$	3.91699	+	10.5673i	0.140071	+	0.377887i
$783$	−1.09738			−0.0392171
$784$	6.90484	+	1.15031i	0.246601	+	0.0410825i
$785$	−0.833334	−	5.79596i	−0.0297430	−	0.206867i
$786$	−12.5763	+	17.6610i	−0.448583	+	0.629946i
$787$	14.4941	−	13.8201i	0.516660	−	0.492634i	−0.386292	−	0.922377i	$-0.626244\pi$
$787$	14.4941	−	13.8201i	0.516660	−	0.492634i	0.902951	+	0.429743i	$0.141396\pi$
$788$	−12.8265	−	18.0124i	−0.456927	−	0.641664i
$789$	−24.6383	−	4.74864i	−0.877146	−	0.169056i
$790$	−0.432472	+	3.00791i	−0.0153867	+	0.107017i
$791$	34.4138	+	21.5057i	1.22362	+	0.764656i
$792$	−1.39428	−	1.60908i	−0.0495435	−	0.0571762i
$793$	−49.7185	−	25.6317i	−1.76556	−	0.910207i
$794$	0.758059	+	15.9136i	0.0269025	+	0.564753i
$795$	−3.53425	+	0.681172i	−0.125347	+	0.0241587i
$796$	2.59774	+	2.47694i	0.0920744	+	0.0877928i
$797$	7.42881	−	51.6685i	0.263142	−	1.83019i	−0.245716	−	0.969342i	$-0.579023\pi$
$797$	7.42881	−	51.6685i	0.263142	−	1.83019i	0.508858	−	0.860850i	$-0.330068\pi$
$798$	5.20993	+	8.76566i	0.184429	+	0.310301i
$799$	−9.00001	+	19.7073i	−0.318398	+	0.697193i
$800$	1.15423	+	4.75781i	0.0408082	+	0.168214i
$801$	−7.90571	−	0.754903i	−0.279334	−	0.0266732i
$802$	−14.6170	−	5.85175i	−0.516143	−	0.206633i
$803$	−0.506880	+	10.6407i	−0.0178874	+	0.375503i
$804$	3.00300			0.105908
$805$	4.09324	−	0.140986i	0.144268	−	0.00496910i
$806$	−61.4465			−2.16436
$807$	0.311785	−	6.54518i	0.0109754	−	0.230401i
$808$	7.69332	+	3.07994i	0.270650	+	0.108352i
$809$	43.4262	+	4.14670i	1.52678	+	0.145790i	0.824400	−	0.566008i	$-0.191513\pi$
$809$	43.4262	+	4.14670i	1.52678	+	0.145790i	0.702384	+	0.711798i	$0.252119\pi$
$810$	−0.0760992	−	0.313685i	−0.00267385	−	0.0110218i
$811$	−5.04612	+	11.0495i	−0.177193	+	0.387999i	−0.977301	−	0.211858i	$-0.932049\pi$
$811$	−5.04612	+	11.0495i	−0.177193	+	0.387999i	0.800107	+	0.599857i	$0.204776\pi$
$812$	−1.41975	+	2.53259i	−0.0498233	+	0.0888764i
$813$	−2.25146	+	15.6592i	−0.0789620	+	0.549193i
$814$	−5.33225	−	5.08429i	−0.186895	−	0.178204i
$815$	3.30437	−	0.636865i	0.115747	−	0.0223084i
$816$	−0.111815	−	2.34728i	−0.00391430	−	0.0821713i
$817$	23.1329	+	11.9258i	0.809317	+	0.417232i
$818$	−1.73733	−	2.00499i	−0.0607443	−	0.0701027i
$819$	0.588893	−	16.8478i	0.0205776	−	0.588711i
$820$	0.212197	−	1.47587i	0.00741025	−	0.0515394i
$821$	−1.43765	−	0.277085i	−0.0501745	−	0.00967033i	0.164102	−	0.986443i	$-0.447527\pi$
$821$	−1.43765	−	0.277085i	−0.0501745	−	0.00967033i	−0.214277	+	0.976773i	$0.568739\pi$
$822$	6.08672	+	8.54760i	0.212299	+	0.298132i
$823$	−10.1497	+	9.67774i	−0.353797	+	0.337345i	−0.846046	−	0.533110i	$-0.821023\pi$
$823$	−10.1497	+	9.67774i	−0.353797	+	0.337345i	0.492249	+	0.870454i	$0.336175\pi$
$824$	−10.3869	+	14.5863i	−0.361843	+	0.508137i
$825$	1.48346	+	10.3177i	0.0516473	+	0.359215i
$826$	5.06472	+	32.3160i	0.176224	+	1.12442i
$827$	7.36611			0.256145			0.128072	−	0.991765i	$-0.459121\pi$
$827$	7.36611			0.256145			0.128072	+	0.991765i	$0.459121\pi$
$828$	−4.21386	+	2.28985i	−0.146442	+	0.0795777i
$829$	0.816931	−	1.41497i	0.0283732	−	0.0491438i	−0.851490	−	0.524371i	$-0.824301\pi$
$829$	0.816931	−	1.41497i	0.0283732	−	0.0491438i	0.879863	+	0.475227i	$0.157634\pi$
$830$	−3.13357	+	1.61547i	−0.108768	+	0.0560737i
$831$	−8.65295	+	6.80475i	−0.300167	+	0.236054i
$832$	2.64693	+	5.79597i	0.0917658	+	0.200939i
$833$	9.87790	+	13.1536i	0.342249	+	0.455745i
$834$	−9.02511	+	19.7622i	−0.312514	+	0.684310i
$835$	6.42043	+	1.23744i	0.222188	+	0.0428233i
$836$	−6.45027	−	5.07255i	−0.223087	−	0.175438i
$837$	−2.27356	+	9.37172i	−0.0785856	+	0.323934i
$838$	10.2822	−	29.7084i	0.355192	−	1.02626i
$839$	3.65728	−	2.35039i	0.126263	−	0.0811445i	−0.475985	−	0.879454i	$-0.657908\pi$
$839$	3.65728	−	2.35039i	0.126263	−	0.0811445i	0.602248	+	0.798309i	$0.294272\pi$
$840$	−0.822393	−	0.230208i	−0.0283753	−	0.00794293i
$841$	18.2024	+	21.0066i	0.627667	+	0.724367i
$842$	11.8701	+	11.3181i	0.409071	+	0.390048i
$843$	−4.90467	−	3.85707i	−0.168926	−	0.132845i
$844$	−4.45476	−	12.8712i	−0.153339	−	0.443045i
$845$	−8.86832	+	0.846822i	−0.305079	+	0.0291316i
$846$	−8.84596	−	2.59741i	−0.304130	−	0.0893008i
$847$	17.0103	−	1.84188i	0.584479	−	0.0632877i
$848$	−1.58692	−	11.0373i	−0.0544952	−	0.379022i
$849$	0.929626	−	19.5153i	0.0319047	−	0.669762i
$850$	−5.75244	+	9.96352i	−0.197307	+	0.341746i
$851$	−13.7626	+	9.27409i	−0.471775	+	0.317912i
$852$	1.24531	+	2.15694i	0.0426637	+	0.0738956i
$853$	−17.0014	−	10.9261i	−0.582115	−	0.374103i	0.216194	−	0.976350i	$-0.430636\pi$
$853$	−17.0014	−	10.9261i	−0.582115	−	0.374103i	−0.798309	+	0.602248i	$0.794272\pi$
$854$	7.87394	+	21.8512i	0.269441	+	0.747733i
$855$	−0.516797	−	1.13163i	−0.0176741	−	0.0387009i
$856$	−0.347238	−	1.43133i	−0.0118683	−	0.0489220i
$857$	11.1610	+	15.6734i	0.381251	+	0.535392i	0.959958	−	0.280143i	$-0.0903819\pi$
$857$	11.1610	+	15.6734i	0.381251	+	0.535392i	−0.578707	+	0.815536i	$0.696443\pi$
$858$	4.43709	+	12.8201i	0.151480	+	0.437672i
$859$	−1.23086	+	0.492764i	−0.0419965	+	0.0168129i	−0.392566	−	0.919724i	$-0.628412\pi$
$859$	−1.23086	+	0.492764i	−0.0419965	+	0.0168129i	0.350569	+	0.936537i	$0.385988\pi$
$860$	−2.09139	+	0.614088i	−0.0713159	+	0.0209402i
$861$	−9.70168	−	7.43265i	−0.330632	−	0.253304i
$862$	18.5228	−	11.9039i	0.630889	−	0.405448i
$863$	−11.8526	−	6.11043i	−0.403467	−	0.208001i	0.244535	−	0.969640i	$-0.421365\pi$
$863$	−11.8526	−	6.11043i	−0.403467	−	0.208001i	−0.648002	+	0.761639i	$0.724395\pi$
$864$	0.981929	−	0.189251i	0.0334059	−	0.00643846i
$865$	−0.906393	+	3.73620i	−0.0308183	+	0.127035i
$866$	15.2090	−	6.08878i	0.516824	−	0.206905i
$867$	−7.51634	+	8.67431i	−0.255268	+	0.294595i
$868$	18.6871	+	17.3718i	0.634282	+	0.589637i
$869$	−19.2326	−	5.64720i	−0.652421	−	0.191568i
$870$	0.205465	−	0.288536i	0.00696593	−	0.00978228i
$871$	−17.7638	−	7.11155i	−0.601903	−	0.240966i
$872$	−6.81430	+	3.51301i	−0.230761	+	0.118966i
$873$	7.80338	+	13.5158i	0.264104	+	0.457442i
$874$	−14.2771	+	11.7395i	−0.482929	+	0.397093i
$875$	5.61470	+	6.31632i	0.189811	+	0.213531i
$876$	−4.20911	−	2.70503i	−0.142213	−	0.0913944i
$877$	17.0785	−	13.4306i	0.576699	−	0.453521i	−0.286716	−	0.958016i	$-0.592564\pi$
$877$	17.0785	−	13.4306i	0.576699	−	0.453521i	0.863415	+	0.504495i	$0.168321\pi$
$878$	32.0132	+	3.05689i	1.08039	+	0.103165i
$879$	8.91646	−	8.50182i	0.300745	−	0.286759i
$880$	0.684133	−	0.0653268i	0.0230621	−	0.00220217i
$881$	−20.6587	+	23.8414i	−0.696009	+	0.803237i	−0.988208	−	0.153120i	$-0.951068\pi$
$881$	−20.6587	+	23.8414i	−0.696009	+	0.803237i	0.292198	+	0.956358i	$0.405613\pi$
$882$	−4.94221	+	4.95727i	−0.166413	+	0.166920i
$883$	−33.4675	+	9.82694i	−1.12627	+	0.330703i	−0.791241	−	0.611505i	$-0.790565\pi$
$883$	−33.4675	+	9.82694i	−1.12627	+	0.330703i	−0.335030	+	0.942208i	$0.608746\pi$
$884$	−4.89729	+	14.1498i	−0.164714	+	0.475909i
$885$	−0.189886	−	3.98619i	−0.00638293	−	0.133994i
$886$	1.73103	+	36.3387i	0.0581550	+	1.22082i
$887$	4.01902	−	11.6122i	0.134945	−	0.389899i	−0.857201	−	0.514982i	$-0.827799\pi$
$887$	4.01902	−	11.6122i	0.134945	−	0.389899i	0.992146	+	0.125083i	$0.0399198\pi$
$888$	3.32027	−	0.974919i	0.111421	−	0.0327161i
$889$	−30.2161	+	19.9637i	−1.01341	+	0.669561i
$890$	1.67870	−	1.93732i	0.0562701	−	0.0649391i
$891$	2.11948	−	0.202386i	0.0710052	−	0.00678017i
$892$	2.15753	−	2.05721i	0.0722396	−	0.0688803i
$893$	−35.3719	−	3.37761i	−1.18368	−	0.113027i
$894$	−5.93428	+	4.66677i	−0.198472	+	0.156080i
$895$	4.86273	+	3.12508i	0.162543	+	0.104460i
$896$	0.833618	−	2.51099i	0.0278492	−	0.0838864i
$897$	30.3491	−	3.56619i	1.01333	−	0.119072i
$898$	−8.82473	−	15.2849i	−0.294485	−	0.510063i
$899$	−9.40622	+	4.84924i	−0.313715	+	0.161731i
$900$	−4.54511	−	1.81959i	−0.151504	−	0.0606530i
$901$	15.1997	−	21.3450i	0.506374	−	0.711103i
$902$	9.43669	+	2.77086i	0.314207	+	0.0922596i
$903$	−3.99196	+	17.4145i	−0.132844	+	0.579517i
$904$	10.0443	−	11.5918i	0.334070	−	0.385537i
$905$	−4.94439	+	1.97944i	−0.164357	+	0.0657987i
$906$	−1.97415	+	8.13756i	−0.0655867	+	0.270352i
$907$	6.48820	−	1.25050i	0.215437	−	0.0415221i	−0.0803905	−	0.996763i	$-0.525617\pi$
$907$	6.48820	−	1.25050i	0.215437	−	0.0415221i	0.295828	+	0.955241i	$0.404405\pi$
$908$	20.4651	+	10.5505i	0.679158	+	0.350130i
$909$	−6.97141	+	4.48025i	−0.231227	+	0.148601i
$910$	4.31957	+	3.30931i	0.143192	+	0.109703i
$911$	27.3356	−	8.02645i	0.905668	−	0.265928i	0.204452	−	0.978877i	$-0.434459\pi$
$911$	27.3356	−	8.02645i	0.905668	−	0.265928i	0.701216	+	0.712948i	$0.252641\pi$
$912$	3.57805	−	1.43244i	0.118481	−	0.0474327i
$913$	−7.60579	−	21.9755i	−0.251715	−	0.727282i
$914$	20.7609	+	29.1546i	0.686710	+	0.964349i
$915$	−0.668061	−	2.75379i	−0.0220854	−	0.0910374i
$916$	−11.0569	−	24.2112i	−0.365329	−	0.799960i
$917$	−56.4593	−	10.1421i	−1.86445	−	0.334920i
$918$	1.97690	+	1.27048i	0.0652474	+	0.0419320i
$919$	−15.0385	−	26.0475i	−0.496075	−	0.859228i	0.503914	−	0.863754i	$-0.331893\pi$
$919$	−15.0385	−	26.0475i	−0.496075	−	0.859228i	−0.999990	+	0.00452575i	$0.998559\pi$
$920$	0.186900	−	1.53669i	0.00616190	−	0.0506633i
$921$	−3.36519	+	5.82868i	−0.110887	+	0.192061i
$922$	−0.302786	+	6.35627i	−0.00997174	+	0.209333i
$923$	−2.25849	−	15.7081i	−0.0743391	−	0.517040i
$924$	2.27502	−	5.15328i	0.0748428	−	0.169530i
$925$	−16.2554	−	4.77302i	−0.534475	−	0.156936i
$926$	−32.0290	+	3.05840i	−1.05254	+	0.100505i
$927$	−5.85668	−	16.9218i	−0.192359	−	0.555783i
$928$	0.862598	+	0.678354i	0.0283162	+	0.0222681i
$929$	−31.5824	−	30.1138i	−1.03619	−	0.988001i	−0.0362504	−	0.999343i	$-0.511541\pi$
$929$	−31.5824	−	30.1138i	−1.03619	−	0.988001i	−0.999936	+	0.0113413i	$0.996390\pi$
$930$	−2.03844	−	2.35249i	−0.0668431	−	0.0771411i
$931$	−15.0879	+	22.3655i	−0.494485	+	0.733001i
$932$	−9.60729	+	6.17423i	−0.314697	+	0.202244i
$933$	9.68211	−	27.9746i	0.316978	−	0.915848i
$934$	−0.303532	+	1.25118i	−0.00993188	+	0.0409398i
$935$	1.26947	+	0.998319i	0.0415160	+	0.0326485i
$936$	−6.25662	−	1.20587i	−0.204504	−	0.0394149i
$937$	−4.24676	+	9.29910i	−0.138736	+	0.303788i	−0.966228	−	0.257688i	$-0.917039\pi$
$937$	−4.24676	+	9.29910i	−0.138736	+	0.303788i	0.827493	+	0.561477i	$0.189767\pi$
$938$	3.39178	+	7.18483i	0.110746	+	0.234593i
$939$	2.09078	+	4.57817i	0.0682301	+	0.149403i
$940$	2.33920	−	1.83957i	0.0762962	−	0.0600000i
$941$	30.4070	−	15.6759i	0.991241	−	0.511020i	0.115244	−	0.993337i	$-0.463235\pi$
$941$	30.4070	−	15.6759i	0.991241	−	0.511020i	0.875997	+	0.482317i	$0.160205\pi$
$942$	−9.07041	+	15.7104i	−0.295530	+	0.511873i
$943$	10.6565	−	19.4220i	0.347023	−	0.632469i
$944$	12.3634			0.402395
$945$	0.664557	−	0.536368i	0.0216180	−	0.0174480i
$946$	−2.04612	−	14.2311i	−0.0665253	−	0.462693i
$947$	−27.0083	+	37.9279i	−0.877652	+	1.23249i	0.0938807	+	0.995583i	$0.470073\pi$
$947$	−27.0083	+	37.9279i	−0.877652	+	1.23249i	−0.971533	+	0.236906i	$0.923867\pi$
$948$	6.81358	−	6.49673i	0.221295	−	0.211004i
$949$	18.4924	+	25.9690i	0.600289	+	0.842988i
$950$	−18.5281	−	3.57100i	−0.601131	−	0.115858i
$951$	−1.70552	+	11.8621i	−0.0553052	+	0.384656i
$952$	5.48971	−	2.91870i	0.177922	−	0.0945955i
$953$	27.3618	+	31.5772i	0.886335	+	1.02288i	0.999570	+	0.0293166i	$0.00933309\pi$
$953$	27.3618	+	31.5772i	0.886335	+	1.02288i	−0.113235	+	0.993568i	$0.536121\pi$
$954$	9.91123	+	5.10959i	0.320888	+	0.165429i
$955$	−0.107161	−	2.24959i	−0.00346766	−	0.0727951i
$956$	9.52024	−	1.83488i	0.307907	−	0.0593441i
$957$	1.69097	+	1.61233i	0.0546612	+	0.0521194i
$958$	1.27658	−	8.87879i	0.0412443	−	0.286861i
$959$	−13.5759	+	24.2170i	−0.438387	+	0.782008i
$960$	−0.134089	+	0.293615i	−0.00432771	+	0.00947637i
$961$	14.6166	+	60.2506i	0.471504	+	1.94357i
$962$	−21.9493	−	2.09590i	−0.707674	−	0.0675746i
$963$	1.36735	+	0.547404i	0.0440622	+	0.0176398i
$964$	0.329213	−	6.91104i	0.0106033	−	0.222590i
$965$	−0.988237			−0.0318125
$966$	−10.2380	−	7.49558i	−0.329402	−	0.241166i
$967$	45.6391			1.46765			0.733827	−	0.679337i	$-0.237732\pi$
$967$	45.6391			1.46765			0.733827	+	0.679337i	$0.237732\pi$
$968$	0.307705	−	6.45953i	0.00989002	−	0.207617i
$969$	8.40822	+	3.36614i	0.270111	+	0.108136i
$970$	−5.01480	−	0.478855i	−0.161015	−	0.0153751i
$971$	−5.12615	−	21.1303i	−0.164506	−	0.678103i	−0.993001	−	0.118107i	$-0.962318\pi$
$971$	−5.12615	−	21.1303i	−0.164506	−	0.678103i	0.828495	−	0.559997i	$-0.189198\pi$
$972$	−0.415415	+	0.909632i	−0.0133244	+	0.0291765i
$973$	−57.4757	+	0.727708i	−1.84259	+	0.0233292i
$974$	0.871171	−	6.05913i	0.0279141	−	0.194147i
$975$	22.5769	+	21.5270i	0.723038	+	0.689416i
$976$	8.62018	−	1.66140i	0.275925	−	0.0531802i
$977$	−2.82060	−	59.2117i	−0.0902390	−	1.89435i	−0.362287	−	0.932067i	$-0.618004\pi$
$977$	−2.82060	−	59.2117i	−0.0902390	−	1.89435i	0.272048	−	0.962284i	$-0.412299\pi$
$978$	−9.26656	−	4.77724i	−0.296312	−	0.152759i
$979$	11.0729	+	12.7788i	0.353891	+	0.408412i
$980$	−0.378079	−	2.22763i	−0.0120773	−	0.0711590i
$981$	1.09106	−	7.58851i	0.0348350	−	0.242282i
$982$	−29.1231	−	5.61301i	−0.929355	−	0.179118i
$983$	26.8003	+	37.6357i	0.854796	+	1.20039i	0.978123	+	0.208027i	$0.0667044\pi$
$983$	26.8003	+	37.6357i	0.854796	+	1.20039i	−0.123327	+	0.992366i	$0.539356\pi$
$984$	−3.34316	+	3.18770i	−0.106576	+	0.101620i
$985$	−4.14020	+	5.81410i	−0.131918	+	0.185253i
$986$	0.366998	+	2.55253i	0.0116876	+	0.0812891i
$987$	−3.77677	−	24.0981i	−0.120216	−	0.767052i
$988$	−24.5576			−0.781282
$989$	−32.2979	−	2.37591i	−1.02701	−	0.0755497i
$990$	−0.343623	+	0.595172i	−0.0109210	+	0.0189158i
$991$	−7.23033	+	3.72750i	−0.229679	+	0.118408i	−0.569225	−	0.822182i	$-0.692757\pi$
$991$	−7.23033	+	3.72750i	−0.229679	+	0.118408i	0.339546	+	0.940589i	$0.389727\pi$
$992$	7.58035	−	5.96125i	0.240676	−	0.189270i
$993$	−1.66594	−	3.64790i	−0.0528670	−	0.115762i
$994$	−3.75406	+	5.41567i	−0.119072	+	0.171774i
$995$	0.481294	−	1.05389i	0.0152580	−	0.0334105i
$996$	10.7247	+	2.06702i	0.339826	+	0.0654961i
$997$	−28.5322	−	22.4380i	−0.903625	−	0.710619i	0.0540291	−	0.998539i	$-0.482794\pi$
$997$	−28.5322	−	22.4380i	−0.903625	−	0.710619i	−0.957654	+	0.287921i	$0.907036\pi$
$998$	−7.97468	+	32.8721i	−0.252434	+	1.04055i
$999$	−1.13180	+	3.27012i	−0.0358086	+	0.103462i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.a.25.4	✓	160
7.2	even	3	inner	966.2.y.a.163.4	yes	160
23.12	even	11	inner	966.2.y.a.403.4	yes	160
161.58	even	33	inner	966.2.y.a.541.4	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.a.25.4	✓	160	1.1	even	1	trivial
966.2.y.a.163.4	yes	160	7.2	even	3	inner
966.2.y.a.403.4	yes	160	23.12	even	11	inner
966.2.y.a.541.4	yes	160	161.58	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)

\(f(q)\)	\(=\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0760992 + 0.313685i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64554 - 0.0334955i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +O(q^{10})\)	\(q+(-0.0475819 + 0.998867i) q^{2} +(-0.928368 - 0.371662i) q^{3} +(-0.995472 - 0.0950560i) q^{4} +(0.0760992 + 0.313685i) q^{5} +(0.415415 - 0.909632i) q^{6} +(2.64554 - 0.0334955i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.723734 + 0.690079i) q^{9} +(-0.316951 + 0.0610872i) q^{10} +(-0.101308 - 2.12671i) q^{11} +(0.888835 + 0.458227i) q^{12} +(-4.17262 - 4.81546i) q^{13} +(-0.0924223 + 2.64414i) q^{14} +(0.0459369 - 0.319498i) q^{15} +(0.981929 + 0.189251i) q^{16} +(1.36310 + 1.91421i) q^{17} +(-0.723734 + 0.690079i) q^{18} +(-2.23561 + 3.13948i) q^{19} +(-0.0459369 - 0.319498i) q^{20} +(-2.46848 - 0.952151i) q^{21} +2.12912 q^{22} +(1.02894 - 4.68415i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(4.35157 - 2.24339i) q^{25} +(5.00855 - 3.93877i) q^{26} +(-0.415415 - 0.909632i) q^{27} +(-2.63674 - 0.218131i) q^{28} +(0.455867 - 0.998210i) q^{29} +(0.316951 + 0.0610872i) q^{30} +(-7.58035 - 5.96125i) q^{31} +(-0.235759 + 0.971812i) q^{32} +(-0.696367 + 2.01202i) q^{33} +(-1.97690 + 1.27048i) q^{34} +(0.211830 + 0.827317i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(-2.50444 - 2.38798i) q^{37} +(-3.02955 - 2.38246i) q^{38} +(2.08400 + 6.02133i) q^{39} +(0.321322 - 0.0306826i) q^{40} +(4.43220 + 1.30141i) q^{41} +(1.06853 - 2.42038i) q^{42} +(-0.961020 - 6.68404i) q^{43} +(-0.101308 + 2.12671i) q^{44} +(-0.161392 + 0.279539i) q^{45} +(4.62989 + 1.25066i) q^{46} +(4.60971 + 7.98425i) q^{47} +(-0.841254 - 0.540641i) q^{48} +(6.99776 - 0.177227i) q^{49} +(2.03379 + 4.45339i) q^{50} +(-0.554020 - 2.28370i) q^{51} +(3.69599 + 5.19029i) q^{52} +(-3.64707 - 10.5375i) q^{53} +(0.928368 - 0.371662i) q^{54} +(0.659407 - 0.193619i) q^{55} +(0.343345 - 2.62338i) q^{56} +(3.24230 - 2.08370i) q^{57} +(0.975389 + 0.502848i) q^{58} +(12.1400 - 2.33979i) q^{59} +(-0.0760992 + 0.313685i) q^{60} +(8.14998 - 3.26276i) q^{61} +(6.31519 - 7.28812i) q^{62} +(1.93778 + 1.80139i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(1.19301 - 1.67534i) q^{65} +(-1.97661 - 0.791314i) q^{66} +(2.66917 - 1.37605i) q^{67} +(-1.17497 - 2.03511i) q^{68} +(-2.69616 + 3.96620i) q^{69} +(-0.836459 + 0.172225i) q^{70} +(2.09525 + 1.34653i) q^{71} +(0.786053 - 0.618159i) q^{72} +(-4.98072 - 0.475601i) q^{73} +(2.50444 - 2.38798i) q^{74} +(-4.87364 + 0.465376i) q^{75} +(2.52392 - 2.91276i) q^{76} +(-0.339248 - 5.62289i) q^{77} +(-6.11367 + 1.79514i) q^{78} +(3.07917 - 8.89669i) q^{79} +(0.0153587 + 0.322418i) q^{80} +(0.0475819 + 0.998867i) q^{81} +(-1.51083 + 4.36526i) q^{82} +(10.4797 - 3.07711i) q^{83} +(2.36680 + 1.18248i) q^{84} +(-0.496728 + 0.573254i) q^{85} +(6.72219 - 0.641892i) q^{86} +(-0.794210 + 0.757278i) q^{87} +(-2.11948 - 0.202386i) q^{88} +(-6.24257 + 4.90921i) q^{89} +(-0.271543 - 0.174510i) q^{90} +(-11.2001 - 12.5997i) q^{91} +(-1.46954 + 4.56514i) q^{92} +(4.82178 + 8.35157i) q^{93} +(-8.19454 + 4.22458i) q^{94} +(-1.15494 - 0.462367i) q^{95} +(0.580057 - 0.814576i) q^{96} +(14.9746 + 4.39693i) q^{97} +(-0.155940 + 6.99826i) q^{98} +(1.39428 - 1.60908i) 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	\( 160 q - 8 q^{2} - 8 q^{3} + 8 q^{4} + 2 q^{5} - 16 q^{6} - 2 q^{7} + 16 q^{8} + 8 q^{9} - 2 q^{10} + 4 q^{11} - 8 q^{12} + 4 q^{13} - 9 q^{14} - 18 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} + 18 q^{20} + 7 q^{21} + 52 q^{22} + 22 q^{23} - 80 q^{24} + 42 q^{25} + 2 q^{26} + 16 q^{27} - 18 q^{28} - 54 q^{29} + 2 q^{30} - 15 q^{31} - 8 q^{32} + 18 q^{33} + 84 q^{34} + 82 q^{35} - 16 q^{36} + 3 q^{37} + 11 q^{38} + 2 q^{39} - 13 q^{40} + 22 q^{41} - 2 q^{42} - 96 q^{43} + 4 q^{44} - 20 q^{45} - 26 q^{47} + 16 q^{48} - 2 q^{49} - 4 q^{50} + 13 q^{51} - 2 q^{52} + 16 q^{53} + 8 q^{54} - 34 q^{55} + 2 q^{56} - 22 q^{57} - 5 q^{58} - 6 q^{59} - 2 q^{60} + 40 q^{61} - 8 q^{62} - 2 q^{63} - 16 q^{64} - 82 q^{65} + 4 q^{66} + 10 q^{67} - 46 q^{68} - 22 q^{69} + 100 q^{70} + 92 q^{71} - 8 q^{72} + 68 q^{73} - 3 q^{74} + 2 q^{75} - 7 q^{77} - 18 q^{78} - 78 q^{79} + 2 q^{80} + 8 q^{81} + 55 q^{82} - 42 q^{83} - 9 q^{84} + 50 q^{85} + 40 q^{86} + 6 q^{87} + 7 q^{88} - 80 q^{89} + 4 q^{90} - 62 q^{91} + 66 q^{92} + 26 q^{93} + 4 q^{94} - 17 q^{95} + 8 q^{96} - 8 q^{97} - 3 q^{98} + 36 q^{99}+O(q^{100}) \) 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 + 4 * q^11 - 8 * q^12 + 4 * q^13 - 9 * q^14 - 18 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 + 18 * q^20 + 7 * q^21 + 52 * q^22 + 22 * q^23 - 80 * q^24 + 42 * q^25 + 2 * q^26 + 16 * q^27 - 18 * q^28 - 54 * q^29 + 2 * q^30 - 15 * q^31 - 8 * q^32 + 18 * q^33 + 84 * q^34 + 82 * q^35 - 16 * q^36 + 3 * q^37 + 11 * q^38 + 2 * q^39 - 13 * q^40 + 22 * q^41 - 2 * q^42 - 96 * q^43 + 4 * q^44 - 20 * q^45 - 26 * q^47 + 16 * q^48 - 2 * q^49 - 4 * q^50 + 13 * q^51 - 2 * q^52 + 16 * q^53 + 8 * q^54 - 34 * q^55 + 2 * q^56 - 22 * q^57 - 5 * q^58 - 6 * q^59 - 2 * q^60 + 40 * q^61 - 8 * q^62 - 2 * q^63 - 16 * q^64 - 82 * q^65 + 4 * q^66 + 10 * q^67 - 46 * q^68 - 22 * q^69 + 100 * q^70 + 92 * q^71 - 8 * q^72 + 68 * q^73 - 3 * q^74 + 2 * q^75 - 7 * q^77 - 18 * q^78 - 78 * q^79 + 2 * q^80 + 8 * q^81 + 55 * q^82 - 42 * q^83 - 9 * q^84 + 50 * q^85 + 40 * q^86 + 6 * q^87 + 7 * q^88 - 80 * q^89 + 4 * q^90 - 62 * q^91 + 66 * q^92 + 26 * q^93 + 4 * q^94 - 17 * q^95 + 8 * q^96 - 8 * q^97 - 3 * q^98 + 36 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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