LMFDB - Embedded newform 966.2.y.b.121.1

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			121.1
Character	$\chi$	$=$	966.121
Dual form			966.2.y.b.487.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.204977 - 4.30300i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.384103 - 2.61772i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.204977 - 4.30300i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.384103 - 2.61772i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-3.38622 + 2.66296i) q^{10} +(2.20529 - 3.09689i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.163559 - 1.13758i) q^{13} +(-1.90953 + 1.83131i) q^{14} +(4.13338 - 1.21367i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(2.31105 + 0.445418i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-3.84100 + 0.740293i) q^{19} +(4.13338 + 1.21367i) q^{20} +(2.45338 - 0.990427i) q^{21} -3.80184 q^{22} +(2.77878 + 3.90875i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-13.4965 + 1.28875i) q^{25} +(-0.831770 + 0.793091i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(2.59938 + 0.493195i) q^{28} +(-4.08824 + 4.71808i) q^{29} +(-3.38622 - 2.66296i) q^{30} +(-3.96417 - 3.77983i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(3.52951 + 1.41300i) q^{33} +(-0.977713 - 2.14089i) q^{34} +(-11.1853 + 2.18937i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(6.29205 - 3.24378i) q^{37} +(2.83102 + 2.69938i) q^{38} +(1.06695 - 0.427143i) q^{39} +(-1.40897 - 4.07095i) q^{40} +(-6.55138 + 4.21031i) q^{41} +(-2.22988 - 1.42396i) q^{42} +(5.55144 + 1.63005i) q^{43} +(2.20529 + 3.09689i) q^{44} +(2.15394 + 3.73073i) q^{45} +(1.57212 - 4.53083i) q^{46} +(2.27292 - 3.93682i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-6.70493 + 2.01095i) q^{49} +(8.87850 + 10.2463i) q^{50} +(0.111988 + 2.35091i) q^{51} +(1.12851 + 0.217502i) q^{52} +(4.24066 - 1.69771i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-13.7780 - 8.85456i) q^{55} +(-1.10604 - 2.40347i) q^{56} +(-1.62498 - 3.55820i) q^{57} +(6.21464 + 0.593427i) q^{58} +(2.46713 - 1.94017i) q^{59} +(-0.204977 + 4.30300i) q^{60} +(1.23918 - 5.10796i) q^{61} +(-0.779514 + 5.42164i) q^{62} +(1.54091 + 2.15072i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-4.86148 + 0.936973i) q^{65} +(-0.896319 - 3.69468i) q^{66} +(-12.7277 + 1.21535i) q^{67} +(-1.17679 + 2.03826i) q^{68} +(-3.14345 + 3.62198i) q^{69} +(8.27154 + 7.84134i) q^{70} +(6.00359 - 13.1460i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(-1.48382 + 4.28723i) q^{73} +(-6.29205 - 3.24378i) q^{74} +(-4.43434 - 12.8122i) q^{75} +(0.556692 - 3.87188i) q^{76} +(-8.95385 - 4.58330i) q^{77} +(-0.966833 - 0.621346i) q^{78} +(1.66302 + 0.665772i) q^{79} +(-2.49882 + 3.50910i) q^{80} +(0.580057 - 0.814576i) q^{81} +(7.22979 + 2.89437i) q^{82} +(-8.63318 - 5.54821i) q^{83} +(0.133534 + 2.64238i) q^{84} +(1.44292 - 10.0357i) q^{85} +(-1.89235 - 5.46760i) q^{86} +(-5.54892 - 2.86067i) q^{87} +(1.24346 - 3.59275i) q^{88} +(12.4224 - 11.8447i) q^{89} +(1.78956 - 3.91859i) q^{90} +(-2.91504 + 0.865100i) q^{91} +(-4.60263 + 1.34753i) q^{92} +(2.73869 - 4.74356i) q^{93} +(-4.52526 + 0.432110i) q^{94} +(3.97280 + 16.3761i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-0.798183 + 0.512961i) q^{97} +(5.52731 + 4.29521i) q^{98} +(-0.541059 + 3.76315i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{11}\right)$

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 $

$2$	−0.580057	−	0.814576i	−0.410162	−	0.575992i
$2$	−0.580057	−	0.814576i	−0.410162	−	0.575992i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$3$	0.235759	+	0.971812i	0.136115	+	0.561076i
$4$	−0.327068	+	0.945001i	−0.163534	+	0.472500i
$5$	−0.204977	−	4.30300i	−0.0916686	−	1.92436i	−0.314059	−	0.949403i	$-0.601689\pi$
$5$	−0.204977	−	4.30300i	−0.0916686	−	1.92436i	0.222391	−	0.974958i	$-0.428614\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−0.384103	−	2.61772i	−0.145177	−	0.989406i
$7$	−0.384103	−	2.61772i	−0.145177	−	0.989406i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−3.38622	+	2.66296i	−1.07082	+	0.842100i
$11$	2.20529	−	3.09689i	0.664919	−	0.933748i	−0.335046	−	0.942202i	$-0.608752\pi$
$11$	2.20529	−	3.09689i	0.664919	−	0.933748i	0.999964	+	0.00845420i	$0.00269109\pi$
$12$	−0.995472	−	0.0950560i	−0.287368	−	0.0274403i
$13$	−0.163559	−	1.13758i	−0.0453631	−	0.315507i	−0.999851	−	0.0172579i	$-0.994506\pi$
$13$	−0.163559	−	1.13758i	−0.0453631	−	0.315507i	0.954488	−	0.298249i	$-0.0964027\pi$
$14$	−1.90953	+	1.83131i	−0.510344	+	0.489438i
$15$	4.13338	−	1.21367i	1.06723	−	0.313368i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	2.31105	+	0.445418i	0.560511	+	0.108030i	0.461635	−	0.887070i	$-0.347263\pi$
$17$	2.31105	+	0.445418i	0.560511	+	0.108030i	0.0988765	+	0.995100i	$0.468475\pi$
$18$	0.888835	+	0.458227i	0.209501	+	0.108005i
$19$	−3.84100	+	0.740293i	−0.881186	+	0.169835i	−0.609724	−	0.792614i	$-0.708720\pi$
$19$	−3.84100	+	0.740293i	−0.881186	+	0.169835i	−0.271463	+	0.962449i	$0.587507\pi$
$20$	4.13338	+	1.21367i	0.924252	+	0.271385i
$21$	2.45338	−	0.990427i	0.535371	−	0.216129i
$22$	−3.80184			−0.810556
$23$	2.77878	+	3.90875i	0.579417	+	0.815031i
$23$	2.77878	+	3.90875i	0.579417	+	0.815031i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−13.4965	+	1.28875i	−2.69929	+	0.257751i
$26$	−0.831770	+	0.793091i	−0.163124	+	0.155538i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	2.59938	+	0.493195i	0.491236	+	0.0932050i
$29$	−4.08824	+	4.71808i	−0.759167	+	0.876125i	−0.995423	−	0.0955656i	$-0.969534\pi$
$29$	−4.08824	+	4.71808i	−0.759167	+	0.876125i	0.236256	+	0.971691i	$0.424079\pi$
$30$	−3.38622	−	2.66296i	−0.618237	−	0.486187i
$31$	−3.96417	−	3.77983i	−0.711986	−	0.678878i	0.244832	−	0.969566i	$-0.421267\pi$
$31$	−3.96417	−	3.77983i	−0.711986	−	0.678878i	−0.956818	+	0.290688i	$0.906116\pi$
$32$	−0.0475819	+	0.998867i	−0.00841137	+	0.176576i
$33$	3.52951	+	1.41300i	0.614409	+	0.245972i
$34$	−0.977713	−	2.14089i	−0.167676	−	0.367160i
$35$	−11.1853	+	2.18937i	−1.89067	+	0.370071i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	6.29205	−	3.24378i	1.03441	−	0.533273i	0.144542	−	0.989499i	$-0.453829\pi$
$37$	6.29205	−	3.24378i	1.03441	−	0.533273i	0.889864	+	0.456225i	$0.150799\pi$
$38$	2.83102	+	2.69938i	0.459253	+	0.437897i
$39$	1.06695	−	0.427143i	0.170849	−	0.0683976i
$40$	−1.40897	−	4.07095i	−0.222778	−	0.643674i
$41$	−6.55138	+	4.21031i	−1.02315	+	0.657540i	−0.940765	−	0.339060i	$-0.889891\pi$
$41$	−6.55138	+	4.21031i	−1.02315	+	0.657540i	−0.0823882	+	0.996600i	$0.526255\pi$
$42$	−2.22988	−	1.42396i	−0.344077	−	0.219721i
$43$	5.55144	+	1.63005i	0.846587	+	0.248580i	0.676128	−	0.736784i	$-0.263657\pi$
$43$	5.55144	+	1.63005i	0.846587	+	0.248580i	0.170459	+	0.985365i	$0.445475\pi$
$44$	2.20529	+	3.09689i	0.332459	+	0.466874i
$45$	2.15394	+	3.73073i	0.321091	+	0.556145i
$46$	1.57212	−	4.53083i	0.231797	−	0.668035i
$47$	2.27292	−	3.93682i	0.331540	−	0.574244i	−0.651274	−	0.758842i	$-0.725765\pi$
$47$	2.27292	−	3.93682i	0.331540	−	0.574244i	0.982814	+	0.184599i	$0.0590986\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−6.70493	+	2.01095i	−0.957847	+	0.287279i
$50$	8.87850	+	10.2463i	1.25561	+	1.44905i
$51$	0.111988	+	2.35091i	0.0156814	+	0.329194i
$52$	1.12851	+	0.217502i	0.156496	+	0.0301621i
$53$	4.24066	−	1.69771i	0.582500	−	0.233198i	−0.0616490	−	0.998098i	$-0.519636\pi$
$53$	4.24066	−	1.69771i	0.582500	−	0.233198i	0.644149	+	0.764900i	$0.277212\pi$
$54$	−0.235759	+	0.971812i	−0.0320827	+	0.132247i
$55$	−13.7780	−	8.85456i	−1.85782	−	1.19395i
$56$	−1.10604	−	2.40347i	−0.147801	−	0.321177i
$57$	−1.62498	−	3.55820i	−0.215233	−	0.471295i
$58$	6.21464	+	0.593427i	0.816023	+	0.0779207i
$59$	2.46713	−	1.94017i	0.321193	−	0.252589i	−0.444524	−	0.895767i	$-0.646627\pi$
$59$	2.46713	−	1.94017i	0.321193	−	0.252589i	0.765716	+	0.643178i	$0.222385\pi$
$60$	−0.204977	+	4.30300i	−0.0264624	+	0.555515i
$61$	1.23918	−	5.10796i	0.158661	−	0.654008i	−0.835812	−	0.549015i	$-0.815003\pi$
$61$	1.23918	−	5.10796i	0.158661	−	0.654008i	0.994473	−	0.104993i	$-0.0334819\pi$
$62$	−0.779514	+	5.42164i	−0.0989983	+	0.688548i
$63$	1.54091	+	2.15072i	0.194137	+	0.270965i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	−4.86148	+	0.936973i	−0.602992	+	0.116217i
$66$	−0.896319	−	3.69468i	−0.110329	−	0.454783i
$67$	−12.7277	+	1.21535i	−1.55494	+	0.148479i	−0.836834	−	0.547457i	$-0.815596\pi$
$67$	−12.7277	+	1.21535i	−1.55494	+	0.148479i	−0.718104	+	0.695936i	$0.754990\pi$
$68$	−1.17679	+	2.03826i	−0.142707	+	0.247175i
$69$	−3.14345	+	3.62198i	−0.378427	+	0.436035i
$70$	8.27154	+	7.84134i	0.988638	+	0.937219i
$71$	6.00359	−	13.1460i	0.712495	−	1.56015i	−0.111638	−	0.993749i	$-0.535610\pi$
$71$	6.00359	−	13.1460i	0.712495	−	1.56015i	0.824133	−	0.566397i	$-0.191663\pi$
$72$	−0.723734	+	0.690079i	−0.0852929	+	0.0813266i
$73$	−1.48382	+	4.28723i	−0.173668	+	0.501782i	−0.997922	−	0.0644394i	$-0.979474\pi$
$73$	−1.48382	+	4.28723i	−0.173668	+	0.501782i	0.824253	+	0.566221i	$0.191595\pi$
$74$	−6.29205	−	3.24378i	−0.731436	−	0.377081i
$75$	−4.43434	−	12.8122i	−0.512033	−	1.47942i
$76$	0.556692	−	3.87188i	0.0638569	−	0.444135i
$77$	−8.95385	−	4.58330i	−1.02039	−	0.522315i
$78$	−0.966833	−	0.621346i	−0.109472	−	0.0703535i
$79$	1.66302	+	0.665772i	0.187104	+	0.0749052i	0.463323	−	0.886190i	$-0.346657\pi$
$79$	1.66302	+	0.665772i	0.187104	+	0.0749052i	−0.276219	+	0.961095i	$0.589081\pi$
$80$	−2.49882	+	3.50910i	−0.279376	+	0.392329i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	7.22979	+	2.89437i	0.798397	+	0.319630i
$83$	−8.63318	−	5.54821i	−0.947615	−	0.608995i	−0.0270706	−	0.999634i	$-0.508618\pi$
$83$	−8.63318	−	5.54821i	−0.947615	−	0.608995i	−0.920544	+	0.390639i	$0.872254\pi$
$84$	0.133534	+	2.64238i	0.0145697	+	0.288307i
$85$	1.44292	−	10.0357i	0.156507	−	1.08853i
$86$	−1.89235	−	5.46760i	−0.204058	−	0.589586i
$87$	−5.54892	−	2.86067i	−0.594907	−	0.306696i
$88$	1.24346	−	3.59275i	0.132553	−	0.382988i
$89$	12.4224	−	11.8447i	1.31677	−	1.25554i	0.371829	−	0.928301i	$-0.378731\pi$
$89$	12.4224	−	11.8447i	1.31677	−	1.25554i	0.944942	−	0.327238i	$-0.106118\pi$
$90$	1.78956	−	3.91859i	0.188636	−	0.413055i
$91$	−2.91504	+	0.865100i	−0.305579	+	0.0906871i
$92$	−4.60263	+	1.34753i	−0.479857	+	0.140489i
$93$	2.73869	−	4.74356i	0.283989	−	0.491884i
$94$	−4.52526	+	0.432110i	−0.466745	+	0.0445687i
$95$	3.97280	+	16.3761i	0.407601	+	1.68015i
$96$	−0.981929	+	0.189251i	−0.100218	+	0.0193154i
$97$	−0.798183	+	0.512961i	−0.0810432	+	0.0520833i	−0.580535	−	0.814235i	$-0.697157\pi$
$97$	−0.798183	+	0.512961i	−0.0810432	+	0.0520833i	0.499492	+	0.866319i	$0.333520\pi$
$98$	5.52731	+	4.29521i	0.558343	+	0.433882i
$99$	−0.541059	+	3.76315i	−0.0543785	+	0.378211i
$100$	3.19638	−	13.1757i	0.319638	−	1.31757i
$101$	−0.485045	+	10.1824i	−0.0482638	+	1.01318i	0.836741	+	0.547599i	$0.184458\pi$
$101$	−0.485045	+	10.1824i	−0.0482638	+	1.01318i	−0.885005	+	0.465582i	$0.845845\pi$
$102$	1.85004	−	1.45489i	0.183181	−	0.144055i
$103$	−13.4813	−	1.28731i	−1.32835	−	0.126842i	−0.593369	−	0.804930i	$-0.702203\pi$
$103$	−13.4813	−	1.28731i	−1.32835	−	0.126842i	−0.734981	+	0.678088i	$0.762809\pi$
$104$	−0.477427	−	1.04542i	−0.0468155	−	0.102512i
$105$	−4.76470	−	10.3539i	−0.464987	−	1.01043i
$106$	−3.84274	−	2.46958i	−0.373240	−	0.239866i
$107$	−0.596448	+	2.45859i	−0.0576608	+	0.237681i	−0.993348	−	0.115149i	$-0.963265\pi$
$107$	−0.596448	+	2.45859i	−0.0576608	+	0.237681i	0.935687	+	0.352830i	$0.114781\pi$
$108$	0.928368	−	0.371662i	0.0893322	−	0.0357632i
$109$	18.2299	+	3.51352i	1.74611	+	0.336534i	0.959668	−	0.281134i	$-0.0907106\pi$
$109$	18.2299	+	3.51352i	1.74611	+	0.336534i	0.786438	+	0.617669i	$0.211923\pi$
$110$	0.779292	+	16.3593i	0.0743025	+	1.55980i
$111$	4.63574	+	5.34993i	0.440005	+	0.507793i
$112$	−1.31624	+	2.29510i	−0.124373	+	0.216867i
$113$	−4.26839	+	9.34647i	−0.401536	+	0.879242i	0.595576	+	0.803299i	$0.296924\pi$
$113$	−4.26839	+	9.34647i	−0.401536	+	0.879242i	−0.997112	+	0.0759427i	$0.975803\pi$
$114$	−1.95585	+	3.38762i	−0.183182	+	0.317280i
$115$	16.2498	−	12.7583i	1.51530	−	1.18972i
$116$	−3.12146	−	5.40652i	−0.289820	−	0.501983i
$117$	0.666646	+	0.936173i	0.0616314	+	0.0865492i
$118$	−3.01149	−	0.884254i	−0.277230	−	0.0814022i
$119$	0.278299	−	6.22077i	0.0255116	−	0.570257i
$120$	3.62402	−	2.32902i	0.330826	−	0.212609i
$121$	−1.12970	−	3.26405i	−0.102700	−	0.296732i
$122$	−4.87962	+	1.95350i	−0.441780	+	0.176862i
$123$	−5.63618	−	5.37408i	−0.508197	−	0.484565i
$124$	4.86850	−	2.50988i	0.437204	−	0.225394i
$125$	5.24660	+	36.4909i	0.469270	+	3.26385i
$126$	0.858105	−	2.50273i	0.0764460	−	0.222961i
$127$	−8.78701	−	19.2409i	−0.779721	−	1.70735i	−0.703975	−	0.710225i	$-0.748593\pi$
$127$	−8.78701	−	19.2409i	−0.779721	−	1.70735i	−0.0757465	−	0.997127i	$-0.524134\pi$
$128$	−0.928368	−	0.371662i	−0.0820569	−	0.0328506i
$129$	−0.275300	+	5.77926i	−0.0242388	+	0.508835i
$130$	3.58317	+	3.41654i	0.314265	+	0.299651i
$131$	7.26232	+	5.71115i	0.634512	+	0.498986i	0.882830	−	0.469693i	$-0.155635\pi$
$131$	7.26232	+	5.71115i	0.634512	+	0.498986i	−0.248318	+	0.968679i	$0.579878\pi$
$132$	−2.48968	+	2.87324i	−0.216699	+	0.250084i
$133$	3.41322	+	9.77033i	0.295964	+	0.847195i
$134$	8.37279	+	9.66272i	0.723299	+	0.834732i
$135$	−3.11776	+	2.97278i	−0.268334	+	0.255856i
$136$	2.34292	−	0.223722i	0.200904	−	0.0191840i
$137$	−2.37192	−	4.10828i	−0.202647	−	0.350994i	0.746734	−	0.665123i	$-0.231621\pi$
$137$	−2.37192	−	4.10828i	−0.202647	−	0.350994i	−0.949380	+	0.314129i	$0.898288\pi$
$138$	4.77376	+	0.459624i	0.406369	+	0.0391258i
$139$	1.36156			0.115486			0.0577430	−	0.998331i	$-0.481610\pi$
$139$	1.36156			0.115486			0.0577430	+	0.998331i	$0.481610\pi$
$140$	1.58940	−	11.2862i	0.134329	−	0.953859i
$141$	4.36170	+	1.28071i	0.367322	+	0.107855i
$142$	−14.1909	+	2.73506i	−1.19087	+	0.229521i
$143$	−3.88365	−	2.00216i	−0.324767	−	0.167429i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	21.1399	+	16.6246i	1.75557	+	1.38060i
$146$	4.35298	−	1.27815i	0.360255	−	0.105780i
$147$	−3.53501	−	6.04183i	−0.291563	−	0.498322i
$148$	1.00744	+	7.00692i	0.0828114	+	0.575966i
$149$	−12.7573	−	1.21818i	−1.04512	−	0.0997968i	−0.441654	−	0.897186i	$-0.645608\pi$
$149$	−12.7573	−	1.21818i	−1.04512	−	0.0997968i	−0.603466	+	0.797389i	$0.706214\pi$
$150$	−7.86432	+	11.0439i	−0.642119	+	0.901730i
$151$	−0.695540	+	0.546979i	−0.0566022	+	0.0445125i	−0.646059	−	0.763287i	$-0.723584\pi$
$151$	−0.695540	+	0.546979i	−0.0566022	+	0.0445125i	0.589457	+	0.807800i	$0.299342\pi$
$152$	−3.47685	+	1.79244i	−0.282010	+	0.145386i
$153$	−2.25824	+	0.663080i	−0.182568	+	0.0536069i
$154$	1.46030	+	9.95217i	0.117674	+	0.801969i
$155$	−15.4521	+	17.8326i	−1.24114	+	1.43235i
$156$	0.0546848	+	1.14797i	0.00437828	+	0.0919115i
$157$	−2.73453	+	7.90091i	−0.218239	+	0.630561i	0.781736	+	0.623609i	$0.214334\pi$
$157$	−2.73453	+	7.90091i	−0.218239	+	0.630561i	−0.999976	+	0.00695239i	$0.997787\pi$
$158$	−0.422323	−	1.74084i	−0.0335982	−	0.138494i
$159$	2.64962	+	3.72088i	0.210129	+	0.295085i
$160$	4.30788			0.340568
$161$	9.16469	−	8.77545i	0.722279	−	0.691602i
$162$	−1.00000			−0.0785674
$163$	−0.276819	−	0.388737i	−0.0216821	−	0.0304483i	0.803593	−	0.595180i	$-0.202919\pi$
$163$	−0.276819	−	0.388737i	−0.0216821	−	0.0304483i	−0.825275	+	0.564731i	$0.808980\pi$
$164$	−1.83600	−	7.56811i	−0.143368	−	0.590970i
$165$	5.35668	−	15.4771i	0.417017	−	1.20489i
$166$	0.488299	+	10.2507i	0.0378994	+	0.795605i
$167$	4.50222	−	5.19584i	0.348392	−	0.402066i	−0.554325	−	0.832300i	$-0.687024\pi$
$167$	4.50222	−	5.19584i	0.348392	−	0.402066i	0.902717	+	0.430234i	$0.141569\pi$
$168$	2.07496	−	1.64150i	0.160087	−	0.126645i
$169$	11.2061	−	3.29040i	0.862006	−	0.253108i
$170$	−9.01185	+	4.64593i	−0.691178	+	0.356327i
$171$	3.07480	−	2.41805i	0.235136	−	0.184913i
$172$	−3.35610	+	4.71298i	−0.255900	+	0.359361i
$173$	18.6750	+	1.78325i	1.41984	+	0.135578i	0.776553	−	0.630052i	$-0.216966\pi$
$173$	18.6750	+	1.78325i	1.41984	+	0.135578i	0.643282	+	0.765629i	$0.277572\pi$
$174$	0.888459	+	6.17937i	0.0673539	+	0.468457i
$175$	8.55763	+	34.8349i	0.646896	+	2.63327i
$176$	−3.64784	+	1.07110i	−0.274967	+	0.0807374i
$177$	2.46713	+	1.94017i	0.185441	+	0.145832i
$178$	−16.8541	−	3.24837i	−1.26327	−	0.243475i
$179$	17.1424	+	8.83752i	1.28128	+	0.660547i	0.958275	−	0.285849i	$-0.0922756\pi$
$179$	17.1424	+	8.83752i	1.28128	+	0.660547i	0.323008	+	0.946396i	$0.395306\pi$
$180$	−4.23003	+	0.815272i	−0.315288	+	0.0607668i
$181$	−6.49847	−	1.90812i	−0.483027	−	0.141830i	0.0311478	−	0.999515i	$-0.490084\pi$
$181$	−6.49847	−	1.90812i	−0.483027	−	0.141830i	−0.514175	+	0.857685i	$0.671902\pi$
$182$	2.39558	+	1.87271i	0.177572	+	0.138815i
$183$	5.25613			0.388544
$184$	3.76745	+	2.96755i	0.277740	+	0.218771i
$185$	−15.2477	−	26.4098i	−1.12103	−	1.94169i
$186$	−5.45259	+	0.520659i	−0.399803	+	0.0381766i
$187$	6.47593	−	6.17479i	0.473567	−	0.451545i
$188$	2.97689	+	3.43552i	0.217112	+	0.250561i
$189$	−1.72681	+	2.00453i	−0.125607	+	0.145808i
$190$	11.0351	−	12.7352i	0.800572	−	0.923910i
$191$	9.27976	+	7.29769i	0.671460	+	0.528042i	0.894670	−	0.446728i	$-0.147411\pi$
$191$	9.27976	+	7.29769i	0.671460	+	0.528042i	−0.223210	+	0.974770i	$0.571653\pi$
$192$	0.723734	+	0.690079i	0.0522310	+	0.0498022i
$193$	−0.384900	+	8.08004i	−0.0277057	+	0.581614i	0.941745	+	0.336328i	$0.109185\pi$
$193$	−0.384900	+	8.08004i	−0.0277057	+	0.581614i	−0.969451	+	0.245286i	$0.921118\pi$
$194$	0.880838	+	0.352634i	0.0632405	+	0.0253177i
$195$	−2.05670	−	4.50354i	−0.147283	−	0.322505i
$196$	0.292617	−	6.99388i	0.0209012	−	0.499563i
$197$	0.317714	+	2.20975i	0.0226362	+	0.157438i	0.998004	−	0.0631449i	$-0.0201130\pi$
$197$	0.317714	+	2.20975i	0.0226362	+	0.157438i	−0.975368	+	0.220583i	$0.929204\pi$
$198$	3.37921	−	1.74211i	0.240150	−	0.123806i
$199$	−15.5096	−	14.7883i	−1.09944	−	1.04832i	−0.998572	−	0.0534179i	$-0.982988\pi$
$199$	−15.5096	−	14.7883i	−1.09944	−	1.04832i	−0.100871	−	0.994899i	$-0.532163\pi$
$200$	−12.5867	+	5.03894i	−0.890012	+	0.356307i
$201$	−4.18176	−	12.0824i	−0.294959	−	0.852228i
$202$	8.57565	−	5.51124i	0.603381	−	0.387769i
$203$	13.9209	+	8.88964i	0.977057	+	0.623930i
$204$	−2.25824	−	0.663080i	−0.158109	−	0.0464249i
$205$	19.4599	+	27.3276i	1.35914	+	1.90864i
$206$	6.77130	+	11.7282i	0.471779	+	0.817145i
$207$	−4.26098	−	2.20093i	−0.296158	−	0.152975i
$208$	−0.574638	+	0.995302i	−0.0398440	+	0.0690118i
$209$	−6.17790	+	13.5277i	−0.427335	+	0.935732i
$210$	−5.67022	+	9.88704i	−0.391282	+	0.682271i
$211$	−3.63644	−	4.19668i	−0.250343	−	0.288911i	0.616644	−	0.787242i	$-0.288492\pi$
$211$	−3.63644	−	4.19668i	−0.250343	−	0.288911i	−0.866987	+	0.498331i	$0.833946\pi$
$212$	0.217348	+	4.56270i	0.0149275	+	0.313367i
$213$	14.1909	+	2.73506i	0.972341	+	0.187403i
$214$	2.34868	−	0.940271i	0.160553	−	0.0642756i
$215$	5.87619	−	24.2220i	0.400753	−	1.65193i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−8.37189	+	11.8289i	−0.568321	+	0.803001i
$218$	−7.71234	−	16.8877i	−0.522346	−	1.14378i
$219$	−4.51620	−	0.431245i	−0.305177	−	0.0291408i
$220$	12.8739	−	10.1241i	0.867958	−	0.682570i
$221$	0.128705	−	2.70185i	0.00865763	−	0.181746i
$222$	1.66893	−	6.87943i	0.112011	−	0.461717i
$223$	0.742732	−	5.16582i	0.0497370	−	0.345929i	−0.949724	−	0.313090i	$-0.898636\pi$
$223$	0.742732	−	5.16582i	0.0497370	−	0.345929i	0.999461	−	0.0328391i	$-0.0104549\pi$
$224$	2.63303	−	0.259112i	0.175927	−	0.0173127i
$225$	11.4056	−	7.32992i	0.760372	−	0.488662i
$226$	10.0893	−	1.94456i	0.671131	−	0.129350i
$227$	−6.64293	−	27.3825i	−0.440907	−	1.81744i	−0.564901	−	0.825159i	$-0.691086\pi$
$227$	−6.64293	−	27.3825i	−0.440907	−	1.81744i	0.123995	−	0.992283i	$-0.460429\pi$
$228$	3.89398	−	0.371830i	0.257885	−	0.0246250i
$229$	4.89845	−	8.48437i	0.323699	−	0.560663i	−0.657549	−	0.753412i	$-0.728407\pi$
$229$	4.89845	−	8.48437i	0.323699	−	0.560663i	0.981248	+	0.192749i	$0.0617402\pi$
$230$	−19.8184	−	5.83613i	−1.30679	−	0.384823i
$231$	2.34315	−	9.78201i	0.154168	−	0.643609i
$232$	−2.59340	+	5.67875i	−0.170265	+	0.372828i
$233$	1.86468	−	1.77796i	0.122159	−	0.116478i	−0.626538	−	0.779391i	$-0.715529\pi$
$233$	1.86468	−	1.77796i	0.122159	−	0.116478i	0.748697	+	0.662913i	$0.230680\pi$
$234$	0.375891	−	1.08607i	0.0245728	−	0.0709984i
$235$	−17.4060	−	8.97343i	−1.13544	−	0.585362i
$236$	1.02654	+	2.96601i	0.0668224	+	0.193071i
$237$	−0.254933	+	1.77310i	−0.0165597	+	0.115175i
$238$	−5.22872	+	3.38170i	−0.338927	+	0.219203i
$239$	11.7433	+	7.54693i	0.759608	+	0.488170i	0.862209	−	0.506552i	$-0.169080\pi$
$239$	11.7433	+	7.54693i	0.759608	+	0.488170i	−0.102601	+	0.994723i	$0.532717\pi$
$240$	−3.99930	−	1.60108i	−0.258154	−	0.103349i
$241$	14.2519	−	20.0139i	0.918043	−	1.28921i	−0.0389929	−	0.999239i	$-0.512415\pi$
$241$	14.2519	−	20.0139i	0.918043	−	1.28921i	0.957035	−	0.289971i	$-0.0936456\pi$
$242$	−2.00353	+	2.81356i	−0.128792	+	0.180863i
$243$	0.928368	+	0.371662i	0.0595548	+	0.0238422i
$244$	4.42173	+	2.84168i	0.283073	+	0.181920i
$245$	10.0275	+	28.4391i	0.640632	+	1.81691i
$246$	−1.10830	+	7.70837i	−0.0706624	+	0.491468i
$247$	1.47037	+	4.24836i	0.0935575	+	0.270317i
$248$	−4.86850	−	2.50988i	−0.309150	−	0.159378i
$249$	3.35646	−	9.69786i	0.212707	−	0.614577i
$250$	26.6813	−	25.4406i	1.68747	−	1.60900i
$251$	10.2169	−	22.3718i	0.644883	−	1.41210i	−0.251078	−	0.967967i	$-0.580785\pi$
$251$	10.2169	−	22.3718i	0.644883	−	1.41210i	0.895962	−	0.444131i	$-0.146488\pi$
$252$	−2.53641	+	0.752734i	−0.159779	+	0.0474178i
$253$	18.2330	+	0.0143264i	1.14630	+	0.000900692i
$254$	−10.5762	+	18.3185i	−0.663609	+	1.14940i
$255$	10.0930	−	0.963768i	0.632050	−	0.0603535i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	−8.82993	+	1.70183i	−0.550796	+	0.106157i	−0.457053	−	0.889439i	$-0.651095\pi$
$257$	−8.82993	+	1.70183i	−0.550796	+	0.106157i	−0.0937425	+	0.995596i	$0.529883\pi$
$258$	4.86733	−	3.12805i	0.303027	−	0.194744i
$259$	−10.9081	−	15.2249i	−0.677796	−	0.946028i
$260$	0.704593	−	4.90055i	0.0436970	−	0.303919i
$261$	1.47182	−	6.06693i	0.0911035	−	0.375534i
$262$	0.439608	−	9.22850i	0.0271591	−	0.570139i
$263$	−14.6540	+	11.5240i	−0.903604	+	0.710602i	−0.957650	−	0.287936i	$-0.907031\pi$
$263$	−14.6540	+	11.5240i	−0.903604	+	0.710602i	0.0540452	+	0.998538i	$0.482788\pi$
$264$	3.78463	+	0.361388i	0.232928	+	0.0222419i
$265$	−8.17447	−	17.8996i	−0.502154	−	1.09956i
$266$	5.97881	−	8.44767i	0.366584	−	0.517960i
$267$	14.4395	+	9.27973i	0.883685	+	0.567910i
$268$	3.01432	−	12.4252i	0.184129	−	0.758990i
$269$	24.1397	−	9.66408i	1.47182	−	0.589229i	0.509339	−	0.860566i	$-0.329890\pi$
$269$	24.1397	−	9.66408i	1.47182	−	0.589229i	0.962485	+	0.271336i	$0.0874656\pi$
$270$	4.23003	+	0.815272i	0.257432	+	0.0496159i
$271$	0.686539	+	14.4122i	0.0417043	+	0.875480i	0.918694	+	0.394971i	$0.129245\pi$
$271$	0.686539	+	14.4122i	0.0417043	+	0.875480i	−0.876989	+	0.480510i	$0.840452\pi$
$272$	−1.54127	−	1.77872i	−0.0934531	−	0.107851i
$273$	−1.52796	−	2.62891i	−0.0924764	−	0.159109i
$274$	−1.97066	+	4.31514i	−0.119052	+	0.260687i
$275$	−25.7724	+	44.6391i	−1.55413	+	2.69184i
$276$	−2.39465	−	4.15519i	−0.144141	−	0.250113i
$277$	5.32163	+	9.21734i	0.319746	+	0.553816i	0.980435	−	0.196844i	$-0.0630691\pi$
$277$	5.32163	+	9.21734i	0.319746	+	0.553816i	−0.660689	+	0.750660i	$0.729736\pi$
$278$	−0.789782	−	1.10909i	−0.0473680	−	0.0665190i
$279$	5.25552	+	1.54316i	0.314639	+	0.0923865i
$280$	−10.1154	+	5.25196i	−0.604512	+	0.313864i
$281$	27.2628	−	17.5207i	1.62636	−	1.04520i	0.674684	−	0.738107i	$-0.264280\pi$
$281$	27.2628	−	17.5207i	1.62636	−	1.04520i	0.951679	−	0.307094i	$-0.0993565\pi$
$282$	−1.48680	−	4.29582i	−0.0885376	−	0.255813i
$283$	−0.903363	+	0.361652i	−0.0536994	+	0.0214980i	−0.398357	−	0.917231i	$-0.630419\pi$
$283$	−0.903363	+	0.361652i	−0.0536994	+	0.0214980i	0.344657	+	0.938729i	$0.387995\pi$
$284$	10.4594	+	9.97304i	0.620652	+	0.591791i
$285$	−14.9779	+	7.72162i	−0.887212	+	0.457390i
$286$	0.621826	+	4.32489i	0.0367693	+	0.255736i
$287$	13.5378	+	15.5325i	0.799113	+	0.916853i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	−10.6397	−	4.25950i	−0.625865	−	0.250559i
$290$	1.27966	−	26.8633i	0.0751439	−	1.57747i
$291$	−0.686681	−	0.654749i	−0.0402539	−	0.0383820i
$292$	−3.56612	−	2.80443i	−0.208692	−	0.164117i
$293$	13.9043	−	16.0465i	0.812300	−	0.937444i	−0.186688	−	0.982419i	$-0.559775\pi$
$293$	13.9043	−	16.0465i	0.812300	−	0.937444i	0.998988	+	0.0449754i	$0.0143209\pi$
$294$	−2.87102	+	6.38414i	−0.167441	+	0.372331i
$295$	−8.85427	−	10.2184i	−0.515515	−	0.594936i
$296$	5.12330	−	4.88505i	0.297786	−	0.283938i
$297$	−3.78463	+	0.361388i	−0.219606	+	0.0209699i
$298$	6.40767	+	11.0984i	0.371186	+	0.642914i
$299$	3.99202	−	3.80040i	0.230864	−	0.219783i
$300$	13.5578			0.782762
$301$	2.13469	−	15.1582i	0.123042	−	0.873707i
$302$	0.849008	+	0.249291i	0.0488549	+	0.0143451i
$303$	−10.0097	+	1.92921i	−0.575041	+	0.110830i
$304$	3.47685	+	1.79244i	0.199411	+	0.102804i
$305$	−22.2336	−	4.28517i	−1.27309	−	0.245368i
$306$	1.85004	+	1.45489i	0.105760	+	0.0831703i
$307$	1.28565	−	0.377500i	0.0733757	−	0.0215450i	−0.244839	−	0.969564i	$-0.578735\pi$
$307$	1.28565	−	0.377500i	0.0733757	−	0.0215450i	0.318214	+	0.948019i	$0.396917\pi$
$308$	7.25974	−	6.96235i	0.413662	−	0.396717i
$309$	−1.92731	−	13.4048i	−0.109641	−	0.762570i
$310$	23.4891	+	2.24294i	1.33409	+	0.127390i
$311$	9.14928	−	12.8484i	0.518808	−	0.728564i	−0.469179	−	0.883103i	$-0.655450\pi$
$311$	9.14928	−	12.8484i	0.518808	−	0.728564i	0.987987	+	0.154539i	$0.0493893\pi$
$312$	0.903392	−	0.710435i	0.0511445	−	0.0402205i
$313$	9.40246	−	4.84731i	0.531459	−	0.273986i	−0.171540	−	0.985177i	$-0.554874\pi$
$313$	9.40246	−	4.84731i	0.531459	−	0.273986i	0.702999	+	0.711191i	$0.251844\pi$
$314$	8.02208	−	2.35549i	0.452712	−	0.132928i
$315$	8.93869	−	7.07140i	0.503638	−	0.398428i
$316$	−1.17307	+	1.35380i	−0.0659906	+	0.0761572i
$317$	0.916665	+	19.2432i	0.0514850	+	1.08080i	0.865803	+	0.500385i	$0.166808\pi$
$317$	0.916665	+	19.2432i	0.0514850	+	1.08080i	−0.814318	+	0.580419i	$0.802889\pi$
$318$	1.49400	−	4.31664i	0.0837796	−	0.242065i
$319$	5.59564	+	23.0655i	0.313296	+	1.29142i
$320$	−2.49882	−	3.50910i	−0.139688	−	0.196164i
$321$	−2.52991			−0.141206
$322$	−12.4643	−	2.37507i	−0.694609	−	0.132358i
$323$	−9.20648			−0.512262
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	3.67353	+	15.1425i	0.203771	+	0.839954i
$326$	−0.156086	+	0.450980i	−0.00864478	+	0.0249775i
$327$	0.883377	+	18.5444i	0.0488509	+	1.02551i
$328$	−5.09982	+	5.88550i	−0.281590	+	0.324972i
$329$	−11.1785	−	4.43773i	−0.616292	−	0.244660i
$330$	−15.7145	+	4.61419i	−0.865053	+	0.254003i
$331$	−19.2220	+	9.90961i	−1.05653	+	0.544681i	−0.896781	−	0.442476i	$-0.854100\pi$
$331$	−19.2220	+	9.90961i	−1.05653	+	0.544681i	−0.159754	+	0.987157i	$0.551070\pi$
$332$	8.06670	−	6.34372i	0.442718	−	0.348157i
$333$	−4.10621	+	5.76636i	−0.225019	+	0.315995i
$334$	−6.84395	−	0.653518i	−0.374484	−	0.0357589i
$335$	7.83854	+	54.5183i	0.428265	+	2.97865i
$336$	−2.54073	−	0.738048i	−0.138608	−	0.0402638i
$337$	15.5541	−	4.56709i	0.847285	−	0.248785i	0.170859	−	0.985296i	$-0.445346\pi$
$337$	15.5541	−	4.56709i	0.847285	−	0.248785i	0.676426	+	0.736510i	$0.263528\pi$
$338$	−9.18044	−	7.21958i	−0.499350	−	0.392693i
$339$	−10.0893	−	1.94456i	−0.547976	−	0.105614i
$340$	9.01185	+	4.64593i	0.488736	+	0.251961i
$341$	−20.4479	+	3.94100i	−1.10731	+	0.213417i
$342$	−3.75324	−	1.10205i	−0.202952	−	0.0595921i
$343$	7.83950	+	16.7792i	0.423293	+	0.905993i
$344$	5.78581			0.311950
$345$	16.2297	+	12.7838i	0.873779	+	0.688259i
$346$	−9.37998	−	16.2466i	−0.504271	−	0.873423i
$347$	2.05394	−	0.196128i	0.110261	−	0.0105287i	−0.0397795	−	0.999208i	$-0.512666\pi$
$347$	2.05394	−	0.196128i	0.110261	−	0.0105287i	0.150041	+	0.988680i	$0.452059\pi$
$348$	4.51821	−	4.30810i	0.242201	−	0.230939i
$349$	−22.2558	−	25.6845i	−1.19132	−	1.37486i	−0.909663	−	0.415348i	$-0.863660\pi$
$349$	−22.2558	−	25.6845i	−1.19132	−	1.37486i	−0.281662	−	0.959514i	$-0.590886\pi$
$350$	23.4118	−	27.1771i	1.25141	−	1.45268i
$351$	−0.752616	+	0.868565i	−0.0401717	+	0.0463606i
$352$	2.98845	+	2.35014i	0.159285	+	0.125263i
$353$	−13.2959	−	12.6777i	−0.707671	−	0.674763i	0.248147	−	0.968722i	$-0.420179\pi$
$353$	−13.2959	−	12.6777i	−0.707671	−	0.674763i	−0.955818	+	0.293959i	$0.905027\pi$
$354$	0.149342	−	3.13507i	0.00793743	−	0.166627i
$355$	−57.7980	−	23.1388i	−3.06760	−	1.22808i
$356$	7.13031	+	15.6132i	0.377906	+	0.827498i
$357$	6.11102	−	1.19615i	0.323430	−	0.0633068i
$358$	−2.74473	−	19.0900i	−0.145064	−	1.00894i
$359$	0.302667	−	0.156036i	0.0159741	−	0.00823525i	−0.450221	−	0.892917i	$-0.648655\pi$
$359$	0.302667	−	0.156036i	0.0159741	−	0.00823525i	0.466195	+	0.884682i	$0.345624\pi$
$360$	3.11776	+	2.97278i	0.164320	+	0.156679i
$361$	−3.43372	+	1.37465i	−0.180722	+	0.0723502i
$362$	2.21517	+	6.40032i	0.116427	+	0.336393i
$363$	2.90571	−	1.86738i	0.152510	−	0.0980122i
$364$	0.135896	−	3.03766i	0.00712289	−	0.159217i
$365$	18.7521	+	5.50611i	0.981530	+	0.288203i
$366$	−3.04885	−	4.28151i	−0.159366	−	0.223798i
$367$	9.17928	+	15.8990i	0.479155	+	0.829920i	0.999714	−	0.0239050i	$-0.00760993\pi$
$367$	9.17928	+	15.8990i	0.479155	+	0.829920i	−0.520559	+	0.853825i	$0.674277\pi$
$368$	0.231959	−	4.79022i	0.0120917	−	0.249707i
$369$	3.89382	−	6.74429i	0.202704	−	0.351094i
$370$	−12.6682	+	27.7396i	−0.658591	+	1.44211i
$371$	−6.07297	−	10.4488i	−0.315293	−	0.542474i
$372$	3.58693	+	4.13953i	0.185973	+	0.214625i
$373$	−1.03471	−	21.7212i	−0.0535751	−	1.12468i	−0.852323	−	0.523015i	$-0.824807\pi$
$373$	−1.03471	−	21.7212i	−0.0535751	−	1.12468i	0.798748	−	0.601665i	$-0.205496\pi$
$374$	−8.78624	−	1.69341i	−0.454326	−	0.0875641i
$375$	−34.2254	+	13.7018i	−1.76739	+	0.707556i
$376$	1.07172	−	4.41770i	0.0552699	−	0.227826i
$377$	6.03585	+	3.87901i	0.310862	+	0.199779i
$378$	2.63449	+	0.243875i	0.135503	+	0.0125436i
$379$	11.6240	+	25.4530i	0.597085	+	1.30743i	0.931065	+	0.364854i	$0.118881\pi$
$379$	11.6240	+	25.4530i	0.597085	+	1.30743i	−0.333979	+	0.942580i	$0.608392\pi$
$380$	−16.7748	−	1.60180i	−0.860529	−	0.0821706i
$381$	16.6269	−	13.0755i	0.851821	−	0.669880i
$382$	0.561729	−	11.7921i	0.0287406	−	0.603339i
$383$	3.09050	−	12.7392i	0.157917	−	0.650944i	−0.836730	−	0.547616i	$-0.815536\pi$
$383$	3.09050	−	12.7392i	0.157917	−	0.650944i	0.994647	−	0.103328i	$-0.0329492\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	−17.8866	+	39.4679i	−0.911586	+	2.01147i
$386$	6.80507	−	4.37335i	0.346369	−	0.222598i
$387$	−5.68125	+	1.09497i	−0.288794	+	0.0556605i
$388$	−0.223689	−	0.922057i	−0.0113561	−	0.0468104i
$389$	−2.28437	+	0.218131i	−0.115822	+	0.0110597i	−0.152806	−	0.988256i	$-0.548831\pi$
$389$	−2.28437	+	0.218131i	−0.115822	+	0.0110597i	0.0369839	+	0.999316i	$0.488225\pi$
$390$	−2.47547	+	4.28764i	−0.125350	+	0.217113i
$391$	4.68088	+	10.2710i	0.236722	+	0.519429i
$392$	−5.86678	+	3.81849i	−0.296317	+	0.192863i
$393$	−3.83801	+	8.40406i	−0.193602	+	0.423929i
$394$	1.61572	−	1.54058i	0.0813987	−	0.0776135i
$395$	2.52394	−	7.29243i	0.126993	−	0.366922i
$396$	−3.37921	−	1.74211i	−0.169812	−	0.0875441i
$397$	10.3385	+	29.8712i	0.518875	+	1.49919i	0.834879	+	0.550433i	$0.185537\pi$
$397$	10.3385	+	29.8712i	0.518875	+	1.49919i	−0.316004	+	0.948758i	$0.602341\pi$
$398$	−3.04980	+	21.2118i	−0.152872	+	1.06325i
$399$	−8.69022	+	5.62045i	−0.435055	+	0.281374i
$400$	11.4056	+	7.32992i	0.570279	+	0.366496i
$401$	15.1359	+	6.05948i	0.755849	+	0.302596i	0.717397	−	0.696664i	$-0.245333\pi$
$401$	15.1359	+	6.05948i	0.755849	+	0.302596i	0.0384514	+	0.999260i	$0.487758\pi$
$402$	−7.41638	+	10.4149i	−0.369896	+	0.519446i
$403$	−3.65148	+	5.12778i	−0.181893	+	0.255433i
$404$	−9.46369	−	3.78869i	−0.470836	−	0.188494i
$405$	−3.62402	−	2.32902i	−0.180079	−	0.115730i
$406$	−0.833640	−	16.4961i	−0.0413729	−	0.818690i
$407$	3.83014	−	26.6392i	0.189853	−	1.32046i
$408$	0.769781	+	2.22414i	0.0381098	+	0.110111i
$409$	4.37818	+	2.25711i	0.216487	+	0.111607i	0.563060	−	0.826416i	$-0.309624\pi$
$409$	4.37818	+	2.25711i	0.216487	+	0.111607i	−0.346572	+	0.938023i	$0.612654\pi$
$410$	10.9725	−	31.7031i	0.541895	−	1.56570i
$411$	3.43327	−	3.27362i	0.169351	−	0.161476i
$412$	5.62580	−	12.3188i	0.277163	−	0.606903i
$413$	−6.02646	−	5.71303i	−0.296543	−	0.281120i
$414$	0.678788	+	4.74755i	0.0333606	+	0.233329i
$415$	−22.1043	+	38.2859i	−1.08506	+	1.87938i
$416$	1.14407	−	0.109246i	0.0560928	−	0.00535621i
$417$	0.321000	+	1.32318i	0.0157194	+	0.0647964i
$418$	14.6029	−	2.81448i	0.714251	−	0.137661i
$419$	16.9127	−	10.8691i	0.826240	−	0.530992i	−0.0578411	−	0.998326i	$-0.518422\pi$
$419$	16.9127	−	10.8691i	0.826240	−	0.530992i	0.884081	+	0.467334i	$0.154785\pi$
$420$	11.3428	−	1.11622i	0.553472	−	0.0544662i
$421$	−2.67949	+	18.6362i	−0.130590	+	0.908275i	0.814197	+	0.580589i	$0.197178\pi$
$421$	−2.67949	+	18.6362i	−0.130590	+	0.908275i	−0.944787	+	0.327686i	$0.893731\pi$
$422$	−1.30917	+	5.39647i	−0.0637294	+	0.262696i
$423$	−0.216300	+	4.54069i	−0.0105169	+	0.220776i
$424$	3.59059	−	2.82367i	0.174374	−	0.137130i
$425$	−31.7650	−	3.03319i	−1.54083	−	0.147131i
$426$	−6.00359	−	13.1460i	−0.290875	−	0.636927i
$427$	−13.8472	−	1.28184i	−0.670113	−	0.0620325i
$428$	−2.12829	−	1.36777i	−0.102875	−	0.0661137i
$429$	1.03012	−	4.24620i	0.0497346	−	0.205009i
$430$	−23.1392	+	9.26353i	−1.11587	+	0.446727i
$431$	9.90481	+	1.90900i	0.477098	+	0.0919531i	0.422130	−	0.906535i	$-0.361282\pi$
$431$	9.90481	+	1.90900i	0.477098	+	0.0919531i	0.0549673	+	0.998488i	$0.482495\pi$
$432$	0.0475819	+	0.998867i	0.00228929	+	0.0480580i
$433$	−5.52720	−	6.37872i	−0.265620	−	0.306542i	0.607234	−	0.794523i	$-0.292279\pi$
$433$	−5.52720	−	6.37872i	−0.265620	−	0.306542i	−0.872854	+	0.487981i	$0.837734\pi$
$434$	14.4917	−	0.0419194i	0.695626	−	0.00201220i
$435$	−11.1721	+	24.4634i	−0.535659	+	1.17293i
$436$	−9.28270	+	16.0781i	−0.444560	+	0.770001i
$437$	−13.5669	−	12.9564i	−0.648995	−	0.619790i
$438$	2.26837	+	3.92894i	0.108387	+	0.187732i
$439$	4.25332	+	5.97295i	0.203000	+	0.285073i	0.903508	−	0.428571i	$-0.140983\pi$
$439$	4.25332	+	5.97295i	0.203000	+	0.285073i	−0.700508	+	0.713644i	$0.747043\pi$
$440$	−15.7145	−	4.61419i	−0.749158	−	0.219973i
$441$	5.03811	−	4.85978i	0.239910	−	0.231418i
$442$	−2.27552	+	1.46239i	−0.108235	+	0.0695586i
$443$	2.13079	+	6.15650i	0.101237	+	0.292504i	0.984233	−	0.176875i	$-0.0565989\pi$
$443$	2.13079	+	6.15650i	0.101237	+	0.292504i	−0.882997	+	0.469379i	$0.844478\pi$
$444$	−6.57190	+	2.63099i	−0.311888	+	0.124861i
$445$	−53.5142	−	51.0257i	−2.53682	−	2.41885i
$446$	−4.63878	+	2.39146i	−0.219652	+	0.113239i
$447$	−1.82381	−	12.6849i	−0.0862634	−	0.599975i
$448$	−1.73838	−	1.99451i	−0.0821305	−	0.0942315i
$449$	−3.19135	−	6.98808i	−0.150609	−	0.329788i	0.819257	−	0.573427i	$-0.194386\pi$
$449$	−3.19135	−	6.98808i	−0.150609	−	0.329788i	−0.969866	+	0.243639i	$0.921659\pi$
$450$	−12.5867	−	5.03894i	−0.593341	−	0.237538i
$451$	−1.40878	+	29.5738i	−0.0663367	+	1.39258i
$452$	−7.43637	−	7.09056i	−0.349777	−	0.333512i
$453$	−0.695540	−	0.546979i	−0.0326793	−	0.0256993i
$454$	−18.4519	+	21.2946i	−0.865989	+	0.999404i
$455$	4.32004	+	12.3661i	0.202527	+	0.579731i
$456$	−2.56161	−	2.95626i	−0.119959	−	0.138440i
$457$	−9.93943	+	9.47722i	−0.464947	+	0.443326i	−0.885983	−	0.463718i	$-0.846515\pi$
$457$	−9.93943	+	9.47722i	−0.464947	+	0.443326i	0.421036	+	0.907044i	$0.361667\pi$
$458$	−9.75255	+	0.931255i	−0.455707	+	0.0435147i
$459$	−1.17679	−	2.03826i	−0.0549279	−	0.0951378i
$460$	6.74184	+	19.5289i	0.314340	+	0.910540i
$461$	10.9772			0.511258			0.255629	−	0.966775i	$-0.417717\pi$
$461$	10.9772			0.511258			0.255629	+	0.966775i	$0.417717\pi$
$462$	−9.32735	+	3.76545i	−0.433948	+	0.175185i
$463$	−19.1617	−	5.62637i	−0.890518	−	0.261480i	−0.195698	−	0.980664i	$-0.562697\pi$
$463$	−19.1617	−	5.62637i	−0.890518	−	0.261480i	−0.694819	+	0.719185i	$0.744516\pi$
$464$	6.13010	−	1.18148i	0.284583	−	0.0548488i
$465$	−20.9729	−	10.8123i	−0.972595	−	0.501408i
$466$	−2.52990	−	0.487599i	−0.117196	−	0.0225876i
$467$	−20.6381	−	16.2300i	−0.955017	−	0.751033i	0.0135189	−	0.999909i	$-0.495697\pi$
$467$	−20.6381	−	16.2300i	−0.955017	−	0.751033i	−0.968536	+	0.248875i	$0.919939\pi$
$468$	−1.10272	+	0.323789i	−0.0509734	+	0.0149671i
$469$	8.07021	+	32.8508i	0.372647	+	1.51691i
$470$	2.78694	+	19.3836i	0.128552	+	0.894100i
$471$	−8.32289	−	0.794739i	−0.383498	−	0.0366197i
$472$	1.82058	−	2.55665i	0.0837991	−	0.117679i
$473$	17.2906	−	13.5975i	0.795023	−	0.625213i
$474$	1.59220	−	0.820837i	0.0731322	−	0.0377023i
$475$	50.8859	−	14.9414i	2.33480	−	0.685560i
$476$	5.78761	+	2.29761i	0.265275	+	0.105311i
$477$	−2.99132	+	3.45217i	−0.136963	+	0.158064i
$478$	−0.664207	−	13.9434i	−0.0303801	−	0.637757i
$479$	−6.54037	+	18.8972i	−0.298837	+	0.863433i	0.691204	+	0.722659i	$0.257080\pi$
$479$	−6.54037	+	18.8972i	−0.298837	+	0.863433i	−0.990042	+	0.140774i	$0.955041\pi$
$480$	1.01562	+	4.18645i	0.0463566	+	0.191084i
$481$	−4.71917	−	6.62715i	−0.215176	−	0.302172i
$482$	−24.5698			−1.11912
$483$	10.6887	+	6.83746i	0.486355	+	0.311115i
$484$	3.45402			0.157001
$485$	2.37088	+	3.32944i	0.107656	+	0.151182i
$486$	−0.235759	−	0.971812i	−0.0106942	−	0.0440823i
$487$	2.31626	−	6.69241i	0.104960	−	0.303262i	−0.880276	−	0.474461i	$-0.842643\pi$
$487$	2.31626	−	6.69241i	0.104960	−	0.303262i	0.985236	+	0.171199i	$0.0547642\pi$
$488$	−0.250097	−	5.25017i	−0.0113213	−	0.237664i
$489$	0.312517	−	0.360664i	0.0141325	−	0.0163098i
$490$	17.3493	−	24.6645i	0.783762	−	1.11423i
$491$	−0.264993	+	0.0778090i	−0.0119590	+	0.00351147i	−0.287707	−	0.957719i	$-0.592893\pi$
$491$	−0.264993	+	0.0778090i	−0.0119590	+	0.00351147i	0.275748	+	0.961230i	$0.411075\pi$
$492$	6.92193	−	3.56850i	0.312065	−	0.160880i
$493$	−11.5496	+	9.08273i	−0.520169	+	0.409066i
$494$	2.60771	−	3.66202i	0.117327	−	0.164762i
$495$	16.3037	+	1.55682i	0.732798	+	0.0699738i
$496$	0.779514	+	5.42164i	0.0350012	+	0.243439i
$497$	−36.7186	−	10.6663i	−1.64706	−	0.478448i
$498$	−9.84659	+	2.89122i	−0.441236	+	0.129559i
$499$	−25.6823	−	20.1968i	−1.14970	−	0.904132i	−0.153236	−	0.988190i	$-0.548970\pi$
$499$	−25.6823	−	20.1968i	−1.14970	−	0.904132i	−0.996461	+	0.0840578i	$0.973212\pi$
$500$	−36.1999	−	6.97697i	−1.61891	−	0.312019i
$501$	6.11082	+	3.15035i	0.273011	+	0.140747i
$502$	−24.1499	+	4.65452i	−1.07786	+	0.207741i
$503$	13.4620	+	3.95280i	0.600241	+	0.176247i	0.567716	−	0.823224i	$-0.307827\pi$
$503$	13.4620	+	3.95280i	0.600241	+	0.176247i	0.0325245	+	0.999471i	$0.489645\pi$
$504$	2.08442	+	1.62947i	0.0928476	+	0.0725825i
$505$	43.9141			1.95415
$506$	−10.5645	−	14.8605i	−0.469650	−	0.660629i
$507$	5.83958	+	10.1145i	0.259345	+	0.449199i
$508$	21.0566	−	2.01066i	0.934235	−	0.0892087i
$509$	7.23770	−	6.90113i	0.320805	−	0.305887i	−0.512514	−	0.858679i	$-0.671286\pi$
$509$	7.23770	−	6.90113i	0.320805	−	0.305887i	0.833320	+	0.552791i	$0.186437\pi$
$510$	−6.63960	−	7.66250i	−0.294006	−	0.339301i
$511$	11.7927	+	2.23750i	0.521679	+	0.0989811i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	3.07480	+	2.41805i	0.135756	+	0.106759i
$514$	6.50813	+	6.20549i	0.287061	+	0.273712i
$515$	−2.77593	+	58.2738i	−0.122322	+	2.56785i
$516$	−5.37136	−	2.15037i	−0.236461	−	0.0946647i
$517$	−7.17945	−	15.7208i	−0.315752	−	0.691400i
$518$	−6.07450	+	17.7168i	−0.266898	+	0.778430i
$519$	2.66982	+	18.5690i	0.117192	+	0.815089i
$520$	−4.40058	+	2.26865i	−0.192978	+	0.0994871i
$521$	−3.11453	−	2.96970i	−0.136450	−	0.130105i	0.618781	−	0.785564i	$-0.287627\pi$
$521$	−3.11453	−	2.96970i	−0.136450	−	0.130105i	−0.755231	+	0.655459i	$0.772475\pi$
$522$	−5.79572	+	2.32026i	−0.253672	+	0.101555i
$523$	8.36279	+	24.1627i	0.365679	+	1.05656i	0.966387	+	0.257092i	$0.0827645\pi$
$523$	8.36279	+	24.1627i	0.365679	+	1.05656i	−0.600707	+	0.799469i	$0.705114\pi$
$524$	−7.77231	+	4.99496i	−0.339535	+	0.218206i
$525$	−31.8355	+	16.5291i	−1.38941	+	0.721387i
$526$	17.8874	+	5.25220i	0.779926	+	0.229007i
$527$	−7.47779	−	10.5011i	−0.325738	−	0.457434i
$528$	−1.90092	−	3.29249i	−0.0827270	−	0.143287i
$529$	−7.55671	+	21.7232i	−0.328553	+	0.944486i
$530$	−9.83892	+	17.0415i	−0.427375	+	0.740236i
$531$	−1.30383	+	2.85500i	−0.0565815	+	0.123896i
$532$	−10.3493	+	0.0299369i	−0.448700	+	0.00129793i
$533$	5.86110	+	6.76407i	0.253872	+	0.292984i
$534$	−0.816711	−	17.1449i	−0.0353425	−	0.741931i
$535$	10.7016	+	2.06256i	0.462670	+	0.0891723i
$536$	−11.8698	+	4.75193i	−0.512695	+	0.205252i
$537$	−4.54693	+	18.7427i	−0.196214	+	0.808807i
$538$	−21.8745	−	14.0579i	−0.943078	−	0.606079i
$539$	−8.55859	+	25.1992i	−0.368645	+	1.08540i
$540$	−1.78956	−	3.91859i	−0.0770103	−	0.168629i
$541$	20.8168	+	1.98777i	0.894985	+	0.0854607i	0.532403	−	0.846491i	$-0.321289\pi$
$541$	20.8168	+	1.98777i	0.894985	+	0.0854607i	0.362582	+	0.931952i	$0.381895\pi$
$542$	11.3416	−	8.91915i	0.487164	−	0.383110i
$543$	0.322264	−	6.76514i	0.0138297	−	0.290320i
$544$	−0.554878	+	2.28724i	−0.0237902	+	0.0980645i
$545$	11.3820	−	79.1634i	0.487551	−	3.39099i
$546$	−1.25515	+	2.76956i	−0.0537153	+	0.118526i
$547$	−12.2797	+	7.89171i	−0.525044	+	0.337425i	−0.776164	−	0.630531i	$-0.782837\pi$
$547$	−12.2797	+	7.89171i	−0.525044	+	0.337425i	0.251120	+	0.967956i	$0.419201\pi$
$548$	4.65811	−	0.897776i	0.198984	−	0.0383511i
$549$	1.23918	+	5.10796i	0.0528869	+	0.218003i
$550$	51.3114	−	4.89965i	2.18793	−	0.208922i
$551$	12.2102	−	21.1486i	0.520171	−	0.900963i
$552$	−1.99569	+	4.36088i	−0.0849421	+	0.185611i
$553$	1.10403	−	4.60904i	0.0469483	−	0.195996i
$554$	4.42137	−	9.68145i	0.187846	−	0.411326i
$555$	22.0706	−	21.0442i	0.936843	−	0.893278i
$556$	−0.445322	+	1.28667i	−0.0188859	+	0.0545672i
$557$	2.71733	+	1.40088i	0.115137	+	0.0593572i	0.514833	−	0.857291i	$-0.327854\pi$
$557$	2.71733	+	1.40088i	0.115137	+	0.0593572i	−0.399696	+	0.916648i	$0.630884\pi$
$558$	−1.79148	−	5.17614i	−0.0758393	−	0.219123i
$559$	0.946322	−	6.58181i	0.0400251	−	0.278381i
$560$	10.1456	+	5.19335i	0.428732	+	0.219459i
$561$	7.52749	+	4.83762i	0.317811	+	0.204245i
$562$	−30.0860	−	12.0446i	−1.26910	−	0.508071i
$563$	6.20981	−	8.72045i	0.261712	−	0.367523i	−0.662722	−	0.748866i	$-0.730599\pi$
$563$	6.20981	−	8.72045i	0.261712	−	0.367523i	0.924434	+	0.381343i	$0.124538\pi$
$564$	−2.63685	+	3.70293i	−0.111031	+	0.155922i
$565$	41.0928	+	16.4511i	1.72879	+	0.692102i
$566$	0.818595	+	0.526079i	0.0344081	+	0.0221128i
$567$	−2.35513	−	1.20555i	−0.0989064	−	0.0506282i
$568$	2.05674	−	14.3049i	0.0862988	−	0.600221i
$569$	−5.11485	−	14.7784i	−0.214425	−	0.619542i	−1.00000		0.000774284i	$-0.999754\pi$
$569$	−5.11485	−	14.7784i	−0.214425	−	0.619542i	0.785574	−	0.618767i	$-0.212368\pi$
$570$	14.9779	+	7.72162i	0.627354	+	0.323423i
$571$	14.7096	−	42.5005i	0.615576	−	1.77859i	−0.0118696	−	0.999930i	$-0.503778\pi$
$571$	14.7096	−	42.5005i	0.615576	−	1.77859i	0.627446	−	0.778660i	$-0.284100\pi$
$572$	3.16226	−	3.01521i	0.132221	−	0.126072i
$573$	−4.90419	+	10.7387i	−0.204875	+	0.448615i
$574$	4.79967	−	20.0373i	0.200334	−	0.836341i
$575$	−42.5412	−	49.1731i	−1.77409	−	2.05066i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−9.40156	+	0.897740i	−0.391392	+	0.0373734i	−0.288897	−	0.957360i	$-0.593289\pi$
$577$	−9.40156	+	0.897740i	−0.391392	+	0.0373734i	−0.102495	+	0.994734i	$0.532683\pi$
$578$	2.70195	+	11.1376i	0.112386	+	0.463263i
$579$	−7.94302	+	1.53089i	−0.330101	+	0.0636217i
$580$	−22.6244	+	14.5398i	−0.939429	+	0.603734i
$581$	−11.2076	+	24.7303i	−0.464971	+	1.02599i
$582$	−0.135029	+	0.939145i	−0.00559712	+	0.0389288i
$583$	4.09427	−	16.8768i	0.169567	−	0.698966i
$584$	−0.215867	+	4.53161i	−0.00893264	+	0.187519i
$585$	3.89171	−	3.06047i	0.160902	−	0.126535i
$586$	−21.1364	−	2.01828i	−0.873135	−	0.0833743i
$587$	−2.45264	−	5.37053i	−0.101231	−	0.221665i	0.852239	−	0.523153i	$-0.175244\pi$
$587$	−2.45264	−	5.37053i	−0.101231	−	0.221665i	−0.953470	+	0.301487i	$0.902517\pi$
$588$	6.86572	−	1.36450i	0.283138	−	0.0562711i
$589$	18.0246	+	11.5837i	0.742690	+	0.477298i
$590$	−3.18766	+	13.1397i	−0.131234	+	0.540953i
$591$	−2.07256	+	0.829727i	−0.0852537	+	0.0341304i
$592$	−6.95105	−	1.33971i	−0.285686	−	0.0550616i
$593$	−0.826944	−	17.3597i	−0.0339585	−	0.712877i	−0.950086	−	0.311989i	$-0.899005\pi$
$593$	−0.826944	−	17.3597i	−0.0339585	−	0.712877i	0.916127	−	0.400888i	$-0.131298\pi$
$594$	2.48968	+	2.87324i	0.102153	+	0.117891i
$595$	−26.8250	+	0.0775951i	−1.09972	+	0.00318109i
$596$	5.32369	−	11.6572i	0.218067	−	0.477499i
$597$	10.7150	−	18.5589i	0.438534	−	0.759563i
$598$	−5.41131	−	1.04735i	−0.221285	−	0.0428295i
$599$	−13.1493	−	22.7752i	−0.537265	−	0.930571i	−0.999050	−	0.0435788i	$-0.986124\pi$
$599$	−13.1493	−	22.7752i	−0.537265	−	0.930571i	0.461785	−	0.886992i	$-0.347209\pi$
$600$	−7.86432	−	11.0439i	−0.321060	−	0.450865i
$601$	−3.11273	−	0.913979i	−0.126971	−	0.0372820i	0.217630	−	0.976031i	$-0.430167\pi$
$601$	−3.11273	−	0.913979i	−0.126971	−	0.0372820i	−0.344601	+	0.938749i	$0.611986\pi$
$602$	−13.5858	+	7.05377i	−0.553715	+	0.287490i
$603$	10.7559	−	6.91242i	0.438016	−	0.281496i
$604$	−0.289406	−	0.836185i	−0.0117758	−	0.0340239i
$605$	−13.8137	+	5.53015i	−0.561605	+	0.224833i
$606$	7.37767	+	7.03459i	0.299697	+	0.285761i
$607$	15.2907	−	7.88292i	0.620632	−	0.319958i	−0.119077	−	0.992885i	$-0.537994\pi$
$607$	15.2907	−	7.88292i	0.620632	−	0.319958i	0.739709	+	0.672927i	$0.234963\pi$
$608$	−0.556692	−	3.87188i	−0.0225768	−	0.157025i
$609$	−5.35707	+	15.6243i	−0.217080	+	0.633130i
$610$	9.40614	+	20.5966i	0.380844	+	0.833931i
$611$	−4.85019	−	1.94172i	−0.196218	−	0.0785537i
$612$	0.111988	−	2.35091i	0.00452684	−	0.0950301i
$613$	12.9093	+	12.3090i	0.521401	+	0.497154i	0.904454	−	0.426572i	$-0.140279\pi$
$613$	12.9093	+	12.3090i	0.521401	+	0.497154i	−0.383053	+	0.923726i	$0.625127\pi$
$614$	−1.05325	−	0.828285i	−0.0425057	−	0.0334269i
$615$	−21.9694	+	25.3540i	−0.885892	+	1.02237i
$616$	−9.88243	−	1.87505i	−0.398174	−	0.0755479i
$617$	−13.5966	−	15.6913i	−0.547380	−	0.631710i	0.412891	−	0.910780i	$-0.364519\pi$
$617$	−13.5966	−	15.6913i	−0.547380	−	0.631710i	−0.960271	+	0.279071i	$0.909974\pi$
$618$	−9.80124	+	9.34546i	−0.394264	+	0.375930i
$619$	−15.0684	+	1.43886i	−0.605649	+	0.0578325i	−0.393376	−	0.919378i	$-0.628693\pi$
$619$	−15.0684	+	1.43886i	−0.605649	+	0.0578325i	−0.212274	+	0.977210i	$0.568087\pi$
$620$	−11.7980	−	20.4347i	−0.473818	−	0.820677i
$621$	1.13432	−	4.65975i	0.0455188	−	0.186990i
$622$	−15.7731			−0.632443
$623$	−35.7777	−	27.9688i	−1.43340	−	1.12054i
$624$	−1.10272	−	0.323789i	−0.0441442	−	0.0129619i
$625$	89.3809	−	17.2268i	3.57524	−	0.689070i
$626$	−9.40246	−	4.84731i	−0.375798	−	0.193737i
$627$	−14.6029	−	2.81448i	−0.583183	−	0.112399i
$628$	−6.57199	−	5.16827i	−0.262251	−	0.206236i
$629$	15.9861	−	4.69393i	0.637406	−	0.187159i
$630$	−10.9451	−	3.17942i	−0.436065	−	0.126671i
$631$	−4.99569	−	34.7458i	−0.198875	−	1.38321i	−0.807555	−	0.589793i	$-0.799209\pi$
$631$	−4.99569	−	34.7458i	−0.198875	−	1.38321i	0.608679	−	0.793416i	$-0.291700\pi$
$632$	1.78322	+	0.170277i	0.0709328	+	0.00677326i
$633$	3.22106	−	4.52334i	0.128026	−	0.179787i
$634$	15.1433	−	11.9088i	0.601417	−	0.472960i
$635$	−80.9924	+	41.7545i	−3.21409	+	1.65698i
$636$	−4.38284	+	1.28692i	−0.173791	+	0.0510296i
$637$	3.38427	+	7.29847i	0.134089	+	0.289176i
$638$	15.5428	−	17.9374i	0.615347	−	0.710148i
$639$	0.687655	+	14.4357i	0.0272032	+	0.571066i
$640$	−1.40897	+	4.07095i	−0.0556944	+	0.160918i
$641$	9.75024	+	40.1910i	0.385111	+	1.58745i	0.753286	+	0.657693i	$0.228468\pi$
$641$	9.75024	+	40.1910i	0.385111	+	1.58745i	−0.368175	+	0.929757i	$0.620017\pi$
$642$	1.46749	+	2.06080i	0.0579172	+	0.0813333i
$643$	10.3523			0.408254			0.204127	−	0.978944i	$-0.434564\pi$
$643$	10.3523			0.408254			0.204127	+	0.978944i	$0.434564\pi$
$644$	5.29533	+	11.5308i	0.208665	+	0.454377i
$645$	24.9246			0.981405
$646$	5.34028	+	7.49938i	0.210111	+	0.295059i
$647$	−9.52848	−	39.2769i	−0.374603	−	1.54413i	−0.777496	−	0.628888i	$-0.783511\pi$
$647$	−9.52848	−	39.2769i	−0.374603	−	1.54413i	0.402893	−	0.915247i	$-0.368005\pi$
$648$	0.327068	−	0.945001i	0.0128484	−	0.0371231i
$649$	−0.567775	−	11.9191i	−0.0222871	−	0.467864i
$650$	10.2038	−	11.7759i	0.400228	−	0.461887i
$651$	−13.4693	−	5.34712i	−0.527902	−	0.209570i
$652$	0.457896	−	0.134450i	0.0179326	−	0.00526548i
$653$	−14.9683	+	7.71669i	−0.585755	+	0.301978i	−0.725513	−	0.688208i	$-0.758398\pi$
$653$	−14.9683	+	7.71669i	−0.585755	+	0.301978i	0.139759	+	0.990186i	$0.455367\pi$
$654$	14.5934	−	11.4764i	0.570646	−	0.448761i
$655$	23.0865	−	32.4204i	0.902064	−	1.26677i
$656$	7.75237	+	0.740262i	0.302679	+	0.0289024i
$657$	−0.645646	−	4.49057i	−0.0251891	−	0.175194i
$658$	2.86931	+	11.6799i	0.111857	+	0.455330i
$659$	26.4494	−	7.76625i	1.03032	−	0.302530i	0.277481	−	0.960731i	$-0.410500\pi$
$659$	26.4494	−	7.76625i	1.03032	−	0.302530i	0.752842	+	0.658201i	$0.228682\pi$
$660$	12.8739	+	10.1241i	0.501116	+	0.394082i
$661$	−24.4783	−	4.71780i	−0.952094	−	0.183501i	−0.310524	−	0.950565i	$-0.600505\pi$
$661$	−24.4783	−	4.71780i	−0.952094	−	0.183501i	−0.641570	+	0.767064i	$0.721717\pi$
$662$	19.2220	+	9.90961i	0.747083	+	0.385148i
$663$	2.65603	−	0.511908i	0.103152	−	0.0198809i
$664$	−9.84659	−	2.89122i	−0.382122	−	0.112201i
$665$	41.3421	−	16.6898i	1.60318	−	0.647202i
$666$	7.07898			0.274305
$667$	−29.8021	−	2.86939i	−1.15394	−	0.111103i
$668$	3.43754	+	5.95400i	0.133003	+	0.230367i
$669$	5.19531	−	0.496092i	0.200862	−	0.0191800i
$670$	39.8625	−	38.0088i	1.54002	−	1.46841i
$671$	−13.0861	−	15.1021i	−0.505182	−	0.583011i
$672$	0.872569	+	2.49772i	0.0336601	+	0.0963518i
$673$	29.2802	−	33.7912i	1.12867	−	1.30255i	0.180935	−	0.983495i	$-0.442088\pi$
$673$	29.2802	−	33.7912i	1.12867	−	1.30255i	0.947735	−	0.319059i	$-0.103367\pi$
$674$	−12.7425	−	10.0208i	−0.490823	−	0.385987i
$675$	9.81227	+	9.35598i	0.377675	+	0.360112i
$676$	−0.555717	+	11.6659i	−0.0213737	+	0.448690i
$677$	26.1906	+	10.4851i	1.00659	+	0.402976i	0.815599	−	0.578617i	$-0.196407\pi$
$677$	26.1906	+	10.4851i	1.00659	+	0.402976i	0.190986	+	0.981593i	$0.438832\pi$
$678$	4.26839	+	9.34647i	0.163926	+	0.358949i
$679$	1.64937	+	1.89239i	0.0632972	+	0.0726233i
$680$	−1.44292	−	10.0357i	−0.0553335	−	0.384853i
$681$	25.0445	−	12.9113i	0.959708	−	0.494764i
$682$	15.0712	+	14.3703i	0.577105	+	0.550268i
$683$	−27.2827	+	10.9223i	−1.04394	+	0.417932i	−0.829325	−	0.558766i	$-0.811275\pi$
$683$	−27.2827	+	10.9223i	−1.04394	+	0.417932i	−0.214618	+	0.976698i	$0.568851\pi$
$684$	1.27939	+	3.69655i	0.0489187	+	0.141341i
$685$	−17.1917	+	11.0485i	−0.656863	+	0.422140i
$686$	9.12060	−	16.1188i	0.348226	−	0.615417i
$687$	9.40007	+	2.76011i	0.358635	+	0.105305i
$688$	−3.35610	−	4.71298i	−0.127950	−	0.179681i
$689$	−2.62487	−	4.54641i	−0.0999996	−	0.173204i
$690$	0.999251	−	20.6357i	0.0380408	−	0.785587i
$691$	−0.213683	+	0.370109i	−0.00812887	+	0.0140796i	−0.870061	−	0.492944i	$-0.835921\pi$
$691$	−0.213683	+	0.370109i	−0.00812887	+	0.0140796i	0.861932	+	0.507023i	$0.169254\pi$
$692$	−7.79317	+	17.0647i	−0.296252	+	0.648701i
$693$	10.0587	−	0.0290962i	0.382098	−	0.00110527i
$694$	−1.35116	−	1.55933i	−0.0512895	−	0.0591912i
$695$	−0.279089	−	5.85879i	−0.0105864	−	0.222237i
$696$	−6.13010	−	1.18148i	−0.232361	−	0.0447838i
$697$	−17.0159	+	6.81214i	−0.644523	+	0.258028i
$698$	−8.01239	+	33.0275i	−0.303273	+	1.25011i
$699$	2.16746	+	1.39294i	0.0819809	+	0.0526859i
$700$	−35.7180	−	3.30642i	−1.35001	−	0.124971i
$701$	14.0141	+	30.6867i	0.529307	+	1.15902i	0.965794	+	0.259310i	$0.0834951\pi$
$701$	14.0141	+	30.6867i	0.529307	+	1.15902i	−0.436487	+	0.899710i	$0.643778\pi$
$702$	1.14407	+	0.109246i	0.0431802	+	0.00412321i
$703$	−21.7664	+	17.1173i	−0.820936	+	0.645591i
$704$	0.180899	−	3.79754i	0.00681789	−	0.143125i
$705$	4.61686	−	19.0309i	0.173881	−	0.716747i
$706$	−2.61451	+	18.1843i	−0.0983983	+	0.684376i
$707$	26.8409	−	2.64136i	1.00945	−	0.0993387i
$708$	−2.64038	+	1.69687i	−0.0992316	+	0.0637723i
$709$	18.6246	−	3.58960i	0.699462	−	0.134810i	0.172890	−	0.984941i	$-0.444689\pi$
$709$	18.6246	−	3.58960i	0.699462	−	0.134810i	0.526571	+	0.850131i	$0.323477\pi$
$710$	14.6778	+	60.5027i	0.550848	+	2.27062i
$711$	−1.78322	+	0.170277i	−0.0668761	+	0.00638589i
$712$	8.58215	−	14.8647i	0.321630	−	0.557079i
$713$	3.75884	−	25.9983i	0.140770	−	0.973644i
$714$	−4.51909	−	4.28406i	−0.169123	−	0.160327i
$715$	−7.81924	+	17.1218i	−0.292423	+	0.640317i
$716$	−13.9582	+	13.3091i	−0.521642	+	0.497385i
$717$	−4.56562	+	13.1915i	−0.170506	+	0.492645i
$718$	−0.302667	−	0.156036i	−0.0112954	−	0.00582320i
$719$	0.111154	+	0.321158i	0.00414534	+	0.0119772i	0.947055	−	0.321073i	$-0.104043\pi$
$719$	0.111154	+	0.321158i	0.00414534	+	0.0119772i	−0.942909	+	0.333050i	$0.891922\pi$
$720$	0.613075	−	4.26403i	0.0228480	−	0.158911i
$721$	1.80840	+	35.7847i	0.0673482	+	1.33269i
$722$	3.11151	+	1.99965i	0.115799	+	0.0744192i
$723$	22.8098	+	9.13165i	0.848304	+	0.339610i
$724$	3.92862	−	5.51697i	0.146006	−	0.205037i
$725$	49.0963	−	68.9461i	1.82339	−	2.56059i
$726$	−3.20660	−	1.28373i	−0.119008	−	0.0476437i
$727$	33.9446	+	21.8149i	1.25894	+	0.809069i	0.988138	−	0.153567i	$-0.0490761\pi$
$727$	33.9446	+	21.8149i	1.25894	+	0.809069i	0.270798	+	0.962636i	$0.412712\pi$
$728$	−2.55323	+	1.65132i	−0.0946291	+	0.0612019i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−6.39214	−	18.4689i	−0.236584	−	0.683564i
$731$	12.1036	+	6.23984i	0.447668	+	0.230789i
$732$	−1.71911	+	4.96704i	−0.0635401	+	0.183587i
$733$	−25.9030	+	24.6984i	−0.956748	+	0.912258i	−0.996212	−	0.0869632i	$-0.972284\pi$
$733$	−25.9030	+	24.6984i	−0.956748	+	0.912258i	0.0394630	+	0.999221i	$0.487435\pi$
$734$	7.62643	−	16.6995i	0.281496	−	0.616391i
$735$	−25.2734	+	16.4496i	−0.932223	+	0.606753i
$736$	−4.03655	+	2.58965i	−0.148789	+	0.0954558i
$737$	−24.3045	+	42.0965i	−0.895266	+	1.55065i
$738$	−7.75237	+	0.740262i	−0.285369	+	0.0272494i
$739$	−1.30981	−	5.39913i	−0.0481823	−	0.198610i	0.942633	−	0.333830i	$-0.108341\pi$
$739$	−1.30981	−	5.39913i	−0.0481823	−	0.198610i	−0.990816	+	0.135220i	$0.956826\pi$
$740$	29.9443	−	5.77129i	1.10077	−	0.212157i
$741$	−3.78195	+	2.43051i	−0.138933	+	0.0892871i
$742$	−4.98866	+	11.0078i	−0.183139	+	0.404109i
$743$	−6.86717	+	47.7622i	−0.251932	+	1.75223i	0.334656	+	0.942340i	$0.391380\pi$
$743$	−6.86717	+	47.7622i	−0.251932	+	1.75223i	−0.586588	+	0.809885i	$0.699529\pi$
$744$	1.29134	−	5.32299i	0.0473429	−	0.195150i
$745$	−2.62685	+	55.1444i	−0.0962405	+	2.02034i
$746$	−17.0934	+	13.4424i	−0.625833	+	0.492160i
$747$	10.2158	+	0.975492i	0.373777	+	0.0356914i
$748$	3.71711	+	8.13934i	0.135911	+	0.297604i
$749$	6.66500	+	0.616981i	0.243534	+	0.0225440i
$750$	31.0138	+	19.9314i	1.13246	+	0.727790i
$751$	2.04534	−	8.43099i	0.0746354	−	0.307651i	−0.922242	−	0.386612i	$-0.873645\pi$
$751$	2.04534	−	8.43099i	0.0746354	−	0.307651i	0.996878	+	0.0789611i	$0.0251603\pi$
$752$	−4.22021	+	1.68952i	−0.153895	+	0.0616104i
$753$	24.1499	+	4.65452i	0.880072	+	0.169620i
$754$	−0.341392	−	7.16670i	−0.0124328	−	0.260996i
$755$	2.49622	+	2.88079i	0.0908468	+	0.104843i
$756$	−1.32950	−	2.28745i	−0.0483534	−	0.0831938i
$757$	−16.2105	+	35.4960i	−0.589181	+	1.29013i	0.346755	+	0.937956i	$0.387283\pi$
$757$	−16.2105	+	35.4960i	−0.589181	+	1.29013i	−0.935936	+	0.352170i	$0.885444\pi$
$758$	13.9908	−	24.2328i	0.508170	−	0.880177i
$759$	4.28467	+	17.7224i	0.155524	+	0.643283i
$760$	8.42555	+	14.5935i	0.305627	+	0.529361i
$761$	9.75943	+	13.7052i	0.353779	+	0.496813i	0.952665	−	0.304021i	$-0.0983293\pi$
$761$	9.75943	+	13.7052i	0.353779	+	0.496813i	−0.598886	+	0.800834i	$0.704390\pi$
$762$	−20.2956	−	5.95931i	−0.735230	−	0.215883i
$763$	2.19526	−	49.0703i	0.0794738	−	1.77647i
$764$	−9.93143	+	6.38254i	−0.359307	+	0.230912i
$765$	3.31612	+	9.58131i	0.119895	+	0.346413i
$766$	−12.1697	+	4.87203i	−0.439710	+	0.176033i
$767$	−2.61062	−	2.48922i	−0.0942639	−	0.0898805i
$768$	−0.888835	+	0.458227i	−0.0320731	+	0.0165348i
$769$	5.44151	+	37.8465i	0.196226	+	1.36478i	0.815114	+	0.579301i	$0.196674\pi$
$769$	5.44151	+	37.8465i	0.196226	+	1.36478i	−0.618888	+	0.785479i	$0.712416\pi$
$770$	42.5249	−	8.32365i	1.53249	−	0.299963i
$771$	−3.73559	−	8.17981i	−0.134534	−	0.294589i
$772$	−7.50975	−	3.00645i	−0.270282	−	0.108205i
$773$	0.732674	−	15.3807i	0.0263525	−	0.553206i	−0.946629	−	0.322324i	$-0.895536\pi$
$773$	0.732674	−	15.3807i	0.0263525	−	0.553206i	0.972982	−	0.230882i	$-0.0741611\pi$
$774$	4.18739	+	3.99267i	0.150513	+	0.143513i
$775$	58.3735	+	45.9055i	2.09684	+	1.64897i
$776$	−0.621333	+	0.717057i	−0.0223046	+	0.0257408i
$777$	12.2240	−	14.1900i	0.438535	−	0.509064i
$778$	1.50275	+	1.73427i	0.0538763	+	0.0621765i
$779$	22.0470	−	21.0218i	0.789915	−	0.753183i
$780$	4.92853	−	0.470617i	0.176470	−	0.0168508i
$781$	−27.4722	−	47.5832i	−0.983032	−	1.70266i
$782$	5.65137	−	9.77072i	0.202092	−	0.349400i
$783$	6.24291			0.223103
$784$	6.51352	+	2.56400i	0.232626	+	0.0915714i
$785$	34.5582	+	10.1472i	1.23343	+	0.362169i
$786$	9.07201	−	1.74849i	0.323588	−	0.0623664i
$787$	−20.4218	−	10.5282i	−0.727958	−	0.375288i	0.0540657	−	0.998537i	$-0.482782\pi$
$787$	−20.4218	−	10.5282i	−0.727958	−	0.375288i	−0.782023	+	0.623249i	$0.785812\pi$
$788$	−2.19213	−	0.422499i	−0.0780915	−	0.0150509i
$789$	−14.6540	−	11.5240i	−0.521696	−	0.410266i
$790$	−7.40427	+	2.17409i	−0.263432	+	0.0773506i
$791$	26.1059	+	7.58344i	0.928221	+	0.269636i
$792$	0.541059	+	3.76315i	0.0192257	+	0.133718i
$793$	−6.01339	−	0.574209i	−0.213542	−	0.0203908i
$794$	18.3354	−	25.7485i	0.650699	−	0.913780i
$795$	15.4678	−	12.1640i	0.548587	−	0.431414i
$796$	19.0477	−	9.81976i	0.675127	−	0.348052i
$797$	−7.28801	+	2.13995i	−0.258154	+	0.0758010i	−0.408249	−	0.912871i	$-0.633860\pi$
$797$	−7.28801	+	2.13995i	−0.258154	+	0.0758010i	0.150094	+	0.988672i	$0.452042\pi$
$798$	9.61910	+	3.81866i	0.340513	+	0.135179i
$799$	7.00636	−	8.08577i	0.247867	−	0.286054i
$800$	−0.645108	−	13.5425i	−0.0228080	−	0.478799i
$801$	−5.61390	+	16.2203i	−0.198357	+	0.573116i
$802$	−3.84375	−	15.8442i	−0.135728	−	0.559476i
$803$	10.0048	+	14.0498i	0.353062	+	0.495807i
$804$	12.7856			0.450914
$805$	−39.6393	−	37.6369i	−1.39710	−	1.32653i
$806$	6.29503			0.221733
$807$	15.0828	+	21.1809i	0.530940	+	0.745601i
$808$	2.40330	+	9.90655i	0.0845479	+	0.348511i
$809$	−9.30731	+	26.8917i	−0.327228	+	0.945462i	0.654648	+	0.755934i	$0.272817\pi$
$809$	−9.30731	+	26.8917i	−0.327228	+	0.945462i	−0.981875	+	0.189528i	$0.939304\pi$
$810$	0.204977	+	4.30300i	0.00720217	+	0.151192i
$811$	−16.0313	+	18.5011i	−0.562934	+	0.649660i	−0.963847	−	0.266456i	$-0.914147\pi$
$811$	−16.0313	+	18.5011i	−0.562934	+	0.649660i	0.400913	+	0.916116i	$0.368693\pi$
$812$	−12.9538	+	10.2478i	−0.454589	+	0.359626i
$813$	−13.8441	+	4.06500i	−0.485534	+	0.142566i
$814$	−23.9214	+	12.3323i	−0.838444	+	0.432248i
$815$	−1.61600	+	1.27083i	−0.0566059	+	0.0445154i
$816$	1.36521	−	1.91717i	0.0477919	−	0.0671144i
$817$	−22.5298	−	2.15134i	−0.788219	−	0.0752658i
$818$	−0.701008	−	4.87561i	−0.0245102	−	0.170472i
$819$	2.19458	−	2.10468i	0.0766848	−	0.0735434i
$820$	−32.1893	+	9.45162i	−1.12410	+	0.330065i
$821$	−22.6096	−	17.7803i	−0.789079	−	0.620538i	0.140113	−	0.990135i	$-0.455253\pi$
$821$	−22.6096	−	17.7803i	−0.789079	−	0.620538i	−0.929192	+	0.369597i	$0.879496\pi$
$822$	−4.65811	−	0.897776i	−0.162470	−	0.0313135i
$823$	4.00410	+	2.06426i	0.139574	+	0.0719554i	0.526599	−	0.850114i	$-0.323467\pi$
$823$	4.00410	+	2.06426i	0.139574	+	0.0719554i	−0.387025	+	0.922069i	$0.626497\pi$
$824$	−13.2979	+	2.56295i	−0.463253	+	0.0892847i
$825$	−49.4569	−	14.5218i	−1.72187	−	0.505586i
$826$	−1.15801	+	8.22289i	−0.0402922	+	0.286111i
$827$	−32.4618			−1.12881			−0.564404	−	0.825499i	$-0.690894\pi$
$827$	−32.4618			−1.12881			−0.564404	+	0.825499i	$0.690894\pi$
$828$	3.47351	−	3.30677i	0.120713	−	0.114918i
$829$	10.1300	+	17.5457i	0.351830	+	0.609387i	0.986570	−	0.163338i	$-0.0522262\pi$
$829$	10.1300	+	17.5457i	0.351830	+	0.609387i	−0.634740	+	0.772726i	$0.718893\pi$
$830$	44.0085	−	4.20230i	1.52756	−	0.145864i
$831$	−7.70289	+	7.34469i	−0.267210	+	0.254785i
$832$	−0.752616	−	0.868565i	−0.0260923	−	0.0301121i
$833$	−16.3911	+	1.66091i	−0.567919	+	0.0575471i
$834$	0.891632	−	1.02900i	0.0308747	−	0.0356313i
$835$	−23.2806	−	18.3080i	−0.805657	−	0.633576i
$836$	−10.7631	−	10.2626i	−0.372250	−	0.354940i
$837$	−0.260625	+	5.47118i	−0.00900850	+	0.189112i
$838$	−18.6641	−	7.47197i	−0.644740	−	0.258115i
$839$	−17.8378	−	39.0594i	−0.615830	−	1.34848i	−0.918514	−	0.395389i	$-0.870610\pi$
$839$	−17.8378	−	39.0594i	−0.615830	−	1.34848i	0.302683	−	0.953091i	$-0.402118\pi$
$840$	−7.48871	−	8.59209i	−0.258385	−	0.296455i
$841$	−1.41944	−	9.87244i	−0.0489463	−	0.340429i
$842$	16.7349	−	8.62744i	0.576723	−	0.297321i
$843$	23.4543	+	22.3636i	0.807810	+	0.770245i
$844$	5.15523	−	2.06384i	0.177450	−	0.0710404i
$845$	−16.4556	−	47.5453i	−0.566090	−	1.63561i
$846$	3.82421	−	2.45767i	0.131479	−	0.0844964i
$847$	−8.11046	+	4.21097i	−0.278679	+	0.144691i
$848$	−4.38284	−	1.28692i	−0.150507	−	0.0441929i
$849$	−0.564434	−	0.792636i	−0.0193713	−	0.0272032i
$850$	15.9547	+	27.6344i	0.547243	+	0.947852i
$851$	30.1634	+	15.5803i	1.03399	+	0.534086i
$852$	−7.22601	+	12.5158i	−0.247559	+	0.428785i
$853$	−10.1563	+	22.2391i	−0.347744	+	0.761453i	0.652250	+	0.758004i	$0.273825\pi$
$853$	−10.1563	+	22.2391i	−0.347744	+	0.761453i	−0.999994	+	0.00344916i	$0.998902\pi$
$854$	6.98801	+	12.0231i	0.239125	+	0.411423i
$855$	−11.0351	−	12.7352i	−0.377393	−	0.435535i
$856$	0.120378	+	2.52704i	0.00411443	+	0.0863724i
$857$	23.9382	+	4.61370i	0.817712	+	0.157601i	0.580921	−	0.813960i	$-0.302692\pi$
$857$	23.9382	+	4.61370i	0.817712	+	0.157601i	0.236790	+	0.971561i	$0.423905\pi$
$858$	−4.05638	+	1.62393i	−0.138483	+	0.0554401i
$859$	5.67700	−	23.4009i	0.193697	−	0.798428i	−0.789180	−	0.614162i	$-0.789494\pi$
$859$	5.67700	−	23.4009i	0.193697	−	0.798428i	0.982876	−	0.184266i	$-0.0589908\pi$
$860$	20.9679	+	13.4752i	0.714999	+	0.459502i
$861$	−11.9030	+	16.8181i	−0.405652	+	0.573161i
$862$	−4.19033	−	9.17554i	−0.142723	−	0.312520i
$863$	41.3559	+	3.94901i	1.40777	+	0.134426i	0.771102	−	0.636712i	$-0.219706\pi$
$863$	41.3559	+	3.94901i	1.40777	+	0.134426i	0.636668	+	0.771138i	$0.280312\pi$
$864$	0.786053	−	0.618159i	0.0267421	−	0.0210302i
$865$	3.84537	−	80.7242i	0.130746	−	2.74470i
$866$	−1.98987	+	8.20234i	−0.0676184	+	0.278727i
$867$	1.63102	−	11.3440i	0.0553924	−	0.385263i
$868$	−8.44018	−	11.7803i	−0.286479	−	0.399850i
$869$	5.72925	−	3.68197i	0.194352	−	0.124902i
$870$	26.4077	−	5.08967i	0.895306	−	0.172556i
$871$	3.46429	+	14.2800i	0.117383	+	0.483859i
$872$	18.4813	−	1.76475i	0.625857	−	0.0597621i
$873$	0.474401	−	0.821687i	0.0160560	−	0.0278099i
$874$	−2.68439	+	18.5668i	−0.0908008	+	0.628030i
$875$	93.5078	−	27.7504i	3.16114	−	0.938136i
$876$	1.88463	−	4.12677i	0.0636758	−	0.139431i
$877$	−24.7738	+	23.6218i	−0.836553	+	0.797652i	−0.981435	−	0.191797i	$-0.938568\pi$
$877$	−24.7738	+	23.6218i	−0.836553	+	0.797652i	0.144881	+	0.989449i	$0.453720\pi$
$878$	2.39825	−	6.92930i	0.0809371	−	0.233853i
$879$	18.8722	+	9.72930i	0.636543	+	0.328161i
$880$	5.35668	+	15.4771i	0.180574	+	0.521734i
$881$	3.24261	−	22.5529i	0.109246	−	0.759826i	−0.859386	−	0.511328i	$-0.829154\pi$
$881$	3.24261	−	22.5529i	0.109246	−	0.759826i	0.968632	−	0.248498i	$-0.0799370\pi$
$882$	−6.88105	−	1.28497i	−0.231697	−	0.0432672i
$883$	14.1549	+	9.09683i	0.476352	+	0.306133i	0.756696	−	0.653767i	$-0.226812\pi$
$883$	14.1549	+	9.09683i	0.476352	+	0.306133i	−0.280344	+	0.959899i	$0.590449\pi$
$884$	2.51116	+	1.00531i	0.0844593	+	0.0338124i
$885$	7.84286	−	11.0137i	0.263635	−	0.370223i
$886$	3.77896	−	5.30681i	0.126957	−	0.178286i
$887$	−53.1149	−	21.2640i	−1.78342	−	0.713975i	−0.995118	−	0.0986898i	$-0.968535\pi$
$887$	−53.1149	−	21.2640i	−1.78342	−	0.713975i	−0.788305	−	0.615285i	$-0.789041\pi$
$888$	5.95521	+	3.82718i	0.199844	+	0.128432i
$889$	−46.9921	+	30.3924i	−1.57607	+	1.01933i
$890$	−10.5230	+	73.1892i	−0.352732	+	2.45331i
$891$	−1.24346	−	3.59275i	−0.0416575	−	0.120362i
$892$	4.63878	+	2.39146i	0.155318	+	0.0800719i
$893$	−5.81590	+	16.8039i	−0.194622	+	0.562323i
$894$	−9.27490	+	8.84360i	−0.310199	+	0.295774i
$895$	34.5141	−	75.5752i	1.15368	−	2.52620i
$896$	−0.616319	+	2.57297i	−0.0205898	+	0.0859567i
$897$	4.63442	+	2.98351i	0.154739	+	0.0996165i
$898$	−3.84116	+	6.65308i	−0.128181	+	0.222016i
$899$	34.0400	−	3.25043i	1.13530	−	0.108408i
$900$	3.19638	+	13.1757i	0.106546	+	0.439189i
$901$	10.5566	−	2.03461i	0.351690	−	0.0677827i
$902$	24.9073	−	16.0070i	0.829323	−	0.532973i
$903$	15.2342	−	1.49917i	0.506963	−	0.0498894i
$904$	−1.46228	+	10.1704i	−0.0486349	+	0.338263i
$905$	−6.87862	+	28.3540i	−0.228653	+	0.942520i
$906$	−0.0421029	+	0.883849i	−0.00139878	+	0.0293639i
$907$	−10.5617	+	8.30584i	−0.350696	+	0.275791i	−0.777931	−	0.628350i	$-0.783730\pi$
$907$	−10.5617	+	8.30584i	−0.350696	+	0.275791i	0.427234	+	0.904141i	$0.359488\pi$
$908$	28.0492	+	2.67837i	0.930845	+	0.0888849i
$909$	−4.23470	−	9.27269i	−0.140456	−	0.307556i
$910$	7.56725	−	10.6920i	0.250852	−	0.354438i
$911$	−42.7490	−	27.4731i	−1.41634	−	0.910224i	−0.999999	−	0.00101319i	$-0.999677\pi$
$911$	−42.7490	−	27.4731i	−1.41634	−	0.910224i	−0.416336	−	0.909211i	$-0.636686\pi$
$912$	−0.922216	+	3.80143i	−0.0305376	+	0.125878i
$913$	−36.2208	+	14.5006i	−1.19873	+	0.479901i
$914$	13.4854	+	2.59909i	0.446056	+	0.0859702i
$915$	−1.07739	−	22.6171i	−0.0356173	−	0.747699i
$916$	6.41561	+	7.40401i	0.211978	+	0.244635i
$917$	12.1607	−	21.2044i	0.401582	−	0.700231i
$918$	−0.977713	+	2.14089i	−0.0322693	+	0.0706600i
$919$	18.9416	−	32.8078i	0.624825	−	1.08223i	−0.363750	−	0.931497i	$-0.618504\pi$
$919$	18.9416	−	32.8078i	0.624825	−	1.08223i	0.988575	−	0.150731i	$-0.0481629\pi$
$920$	11.9971	−	16.8196i	0.395533	−	0.554526i
$921$	0.669961	+	1.16041i	0.0220760	+	0.0382367i
$922$	−6.36739	−	8.94175i	−0.209699	−	0.294481i
$923$	−15.9366	−	4.67940i	−0.524559	−	0.154024i
$924$	8.47764	+	5.41366i	0.278894	+	0.178096i
$925$	−80.7399	+	51.8884i	−2.65471	+	1.70608i
$926$	6.53174	+	18.8722i	0.214646	+	0.620180i
$927$	12.5725	−	5.03328i	0.412936	−	0.165314i
$928$	−4.51821	−	4.30810i	−0.148317	−	0.141420i
$929$	43.0342	−	22.1857i	1.41191	−	0.727888i	0.427535	−	0.903999i	$-0.359382\pi$
$929$	43.0342	−	22.1857i	1.41191	−	0.727888i	0.984370	+	0.176111i	$0.0563517\pi$
$930$	3.35805	+	23.3558i	0.110115	+	0.765866i
$931$	24.2650	−	12.6877i	0.795252	−	0.415822i
$932$	1.07030	+	2.34363i	0.0350589	+	0.0767683i
$933$	14.6432	+	5.86226i	0.479397	+	0.191922i
$934$	−1.24928	+	26.2256i	−0.0408777	+	0.858128i
$935$	−27.8975	−	26.6003i	−0.912347	−	0.869922i
$936$	0.903392	+	0.710435i	0.0295283	+	0.0232213i
$937$	−29.6217	+	34.1852i	−0.967698	+	1.11678i	0.0254217	+	0.999677i	$0.491907\pi$
$937$	−29.6217	+	34.1852i	−0.967698	+	1.11678i	−0.993119	+	0.117106i	$0.962638\pi$
$938$	22.0783	−	25.6291i	0.720882	−	0.836821i
$939$	6.92738	+	7.99463i	0.226067	+	0.260895i
$940$	14.1728	−	13.5138i	0.462267	−	0.440771i
$941$	−38.2314	+	3.65066i	−1.24631	+	0.119008i	−0.697282	−	0.716797i	$-0.745608\pi$
$941$	−38.2314	+	3.65066i	−1.24631	+	0.119008i	−0.549027	+	0.835805i	$0.685002\pi$
$942$	4.18037	+	7.24062i	0.136204	+	0.235912i
$943$	−34.6619	−	13.9082i	−1.12875	−	0.452912i
$944$	−3.13863			−0.102154
$945$	8.97945	+	7.01957i	0.292101	+	0.228347i
$946$	−21.1057	−	6.19720i	−0.686206	−	0.201488i
$947$	40.4535	−	7.79678i	1.31456	−	0.253361i	0.516683	−	0.856177i	$-0.327167\pi$
$947$	40.4535	−	7.79678i	1.31456	−	0.253361i	0.797880	+	0.602816i	$0.205955\pi$
$948$	−1.59220	−	0.820837i	−0.0517123	−	0.0266595i
$949$	5.11975	+	0.986751i	0.166194	+	0.0320313i
$950$	−41.6876	−	32.7835i	−1.35253	−	1.06364i
$951$	−18.4846	+	5.42757i	−0.599405	+	0.176001i
$952$	−1.48557	−	6.04719i	−0.0481475	−	0.195990i
$953$	−1.81732	−	12.6397i	−0.0588688	−	0.409442i	−0.997854	−	0.0654831i	$-0.979141\pi$
$953$	−1.81732	−	12.6397i	−0.0588688	−	0.409442i	0.938985	−	0.343958i	$-0.111768\pi$
$954$	4.54719	+	0.434204i	0.147221	+	0.0140579i
$955$	29.4998	−	41.4267i	0.954592	−	1.34054i
$956$	−10.9727	+	8.62902i	−0.354882	+	0.279083i
$957$	−21.0961	+	10.8758i	−0.681941	+	0.351565i
$958$	19.1870	−	5.63380i	0.619903	−	0.182020i
$959$	−9.84327	+	7.78702i	−0.317856	+	0.251456i
$960$	2.82106	−	3.25568i	0.0910494	−	0.105077i
$961$	−0.0474973	−	0.997090i	−0.00153217	−	0.0321642i
$962$	−2.66093	+	7.68824i	−0.0857917	+	0.247879i
$963$	−0.596448	−	2.45859i	−0.0192203	−	0.0792270i
$964$	14.2519	+	20.0139i	0.459021	+	0.644605i
$965$	34.8473			1.12177
$966$	−0.630449	−	12.6729i	−0.0202844	−	0.407744i
$967$	23.1344			0.743951			0.371976	−	0.928242i	$-0.378680\pi$
$967$	23.1344			0.743951			0.371976	+	0.928242i	$0.378680\pi$
$968$	−2.00353	−	2.81356i	−0.0643958	−	0.0904313i
$969$	−2.17051	−	8.94697i	−0.0697268	−	0.287418i
$970$	1.33683	−	3.86253i	0.0429232	−	0.124018i
$971$	1.55816	+	32.7098i	0.0500038	+	1.04971i	0.874863	+	0.484370i	$0.160951\pi$
$971$	1.55816	+	32.7098i	0.0500038	+	1.04971i	−0.824859	+	0.565338i	$0.808746\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	−0.522980	−	3.56418i	−0.0167660	−	0.114262i
$974$	−6.79504	+	1.99520i	−0.217727	+	0.0639304i
$975$	−13.8496	+	7.13995i	−0.443541	+	0.228661i
$976$	−4.13159	+	3.24912i	−0.132249	+	0.104002i
$977$	14.1656	−	19.8928i	0.453198	−	0.636428i	−0.523250	−	0.852179i	$-0.675281\pi$
$977$	14.1656	−	19.8928i	0.453198	−	0.636428i	0.976448	+	0.215751i	$0.0692201\pi$
$978$	−0.475066	−	0.0453633i	−0.0151909	−	0.00145056i
$979$	−9.28690	−	64.5918i	−0.296811	−	2.06436i
$980$	−30.1547	+	0.174455i	−0.963255	+	0.00557275i
$981$	−17.8134	+	5.23047i	−0.568737	+	0.166996i
$982$	0.217092	+	0.170723i	0.00692770	+	0.00544800i
$983$	4.24398	+	0.817959i	0.135362	+	0.0260888i	0.256482	−	0.966549i	$-0.417437\pi$
$983$	4.24398	+	0.817959i	0.135362	+	0.0260888i	−0.121120	+	0.992638i	$0.538649\pi$
$984$	−6.92193	−	3.56850i	−0.220663	−	0.113760i
$985$	9.44344	−	1.82007i	0.300893	−	0.0579924i
$986$	14.0980	+	4.13955i	0.448972	+	0.131830i
$987$	1.67720	−	11.9097i	0.0533859	−	0.379088i
$988$	−4.49561			−0.143025
$989$	9.05480	+	26.2288i	0.287926	+	0.834027i
$990$	−8.18895	−	14.1837i	−0.260262	−	0.450787i
$991$	48.7142	−	4.65164i	1.54746	−	0.147764i	0.713920	−	0.700227i	$-0.246918\pi$
$991$	48.7142	−	4.65164i	1.54746	−	0.147764i	0.833538	+	0.552463i	$0.186312\pi$
$992$	3.96417	−	3.77983i	0.125863	−	0.120010i
$993$	−14.1620	−	16.3438i	−0.449418	−	0.518656i
$994$	12.6104	+	36.0972i	0.399977	+	1.14493i
$995$	−60.4551	+	69.7689i	−1.91656	+	2.21182i
$996$	8.06670	+	6.34372i	0.255603	+	0.201009i
$997$	5.26088	+	5.01624i	0.166614	+	0.158866i	0.768799	−	0.639490i	$-0.220855\pi$
$997$	5.26088	+	5.01624i	0.166614	+	0.158866i	−0.602185	+	0.798356i	$0.705703\pi$
$998$	−1.55462	+	32.6355i	−0.0492106	+	1.03306i
$999$	−6.57190	−	2.63099i	−0.207926	−	0.0832408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.121.1	✓	160
7.4	even	3	inner	966.2.y.b.949.8	yes	160
23.4	even	11	inner	966.2.y.b.625.8	yes	160
161.4	even	33	inner	966.2.y.b.487.1	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.121.1	✓	160	1.1	even	1	trivial
966.2.y.b.487.1	yes	160	161.4	even	33	inner
966.2.y.b.625.8	yes	160	23.4	even	11	inner
966.2.y.b.949.8	yes	160	7.4	even	3	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)

\(f(q)\)	\(=\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.204977 - 4.30300i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.384103 - 2.61772i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.204977 - 4.30300i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-0.384103 - 2.61772i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-3.38622 + 2.66296i) q^{10} +(2.20529 - 3.09689i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(-0.163559 - 1.13758i) q^{13} +(-1.90953 + 1.83131i) q^{14} +(4.13338 - 1.21367i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(2.31105 + 0.445418i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-3.84100 + 0.740293i) q^{19} +(4.13338 + 1.21367i) q^{20} +(2.45338 - 0.990427i) q^{21} -3.80184 q^{22} +(2.77878 + 3.90875i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-13.4965 + 1.28875i) q^{25} +(-0.831770 + 0.793091i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(2.59938 + 0.493195i) q^{28} +(-4.08824 + 4.71808i) q^{29} +(-3.38622 - 2.66296i) q^{30} +(-3.96417 - 3.77983i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(3.52951 + 1.41300i) q^{33} +(-0.977713 - 2.14089i) q^{34} +(-11.1853 + 2.18937i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(6.29205 - 3.24378i) q^{37} +(2.83102 + 2.69938i) q^{38} +(1.06695 - 0.427143i) q^{39} +(-1.40897 - 4.07095i) q^{40} +(-6.55138 + 4.21031i) q^{41} +(-2.22988 - 1.42396i) q^{42} +(5.55144 + 1.63005i) q^{43} +(2.20529 + 3.09689i) q^{44} +(2.15394 + 3.73073i) q^{45} +(1.57212 - 4.53083i) q^{46} +(2.27292 - 3.93682i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-6.70493 + 2.01095i) q^{49} +(8.87850 + 10.2463i) q^{50} +(0.111988 + 2.35091i) q^{51} +(1.12851 + 0.217502i) q^{52} +(4.24066 - 1.69771i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-13.7780 - 8.85456i) q^{55} +(-1.10604 - 2.40347i) q^{56} +(-1.62498 - 3.55820i) q^{57} +(6.21464 + 0.593427i) q^{58} +(2.46713 - 1.94017i) q^{59} +(-0.204977 + 4.30300i) q^{60} +(1.23918 - 5.10796i) q^{61} +(-0.779514 + 5.42164i) q^{62} +(1.54091 + 2.15072i) q^{63} +(0.841254 - 0.540641i) q^{64} +(-4.86148 + 0.936973i) q^{65} +(-0.896319 - 3.69468i) q^{66} +(-12.7277 + 1.21535i) q^{67} +(-1.17679 + 2.03826i) q^{68} +(-3.14345 + 3.62198i) q^{69} +(8.27154 + 7.84134i) q^{70} +(6.00359 - 13.1460i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(-1.48382 + 4.28723i) q^{73} +(-6.29205 - 3.24378i) q^{74} +(-4.43434 - 12.8122i) q^{75} +(0.556692 - 3.87188i) q^{76} +(-8.95385 - 4.58330i) q^{77} +(-0.966833 - 0.621346i) q^{78} +(1.66302 + 0.665772i) q^{79} +(-2.49882 + 3.50910i) q^{80} +(0.580057 - 0.814576i) q^{81} +(7.22979 + 2.89437i) q^{82} +(-8.63318 - 5.54821i) q^{83} +(0.133534 + 2.64238i) q^{84} +(1.44292 - 10.0357i) q^{85} +(-1.89235 - 5.46760i) q^{86} +(-5.54892 - 2.86067i) q^{87} +(1.24346 - 3.59275i) q^{88} +(12.4224 - 11.8447i) q^{89} +(1.78956 - 3.91859i) q^{90} +(-2.91504 + 0.865100i) q^{91} +(-4.60263 + 1.34753i) q^{92} +(2.73869 - 4.74356i) q^{93} +(-4.52526 + 0.432110i) q^{94} +(3.97280 + 16.3761i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(-0.798183 + 0.512961i) q^{97} +(5.52731 + 4.29521i) q^{98} +(-0.541059 + 3.76315i) 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

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