LMFDB - Embedded newform 966.2.y.b.121.3

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			121.3
Character	$\chi$	$=$	966.121
Dual form			966.2.y.b.487.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0822082 - 1.72576i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.65083 + 2.06755i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})$	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0822082 - 1.72576i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.65083 + 2.06755i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-1.35808 + 1.06801i) q^{10} +(1.26911 - 1.78222i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(0.564714 + 3.92768i) q^{13} +(2.64175 + 0.145431i) q^{14} +(1.65774 - 0.486755i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-4.13648 - 0.797240i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-4.84598 + 0.933985i) q^{19} +(1.65774 + 0.486755i) q^{20} +(-2.39847 - 1.11685i) q^{21} -2.18791 q^{22} +(-2.04260 - 4.33910i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00586 - 0.191536i) q^{25} +(2.87182 - 2.73828i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-1.41390 - 2.23627i) q^{28} +(-3.71004 + 4.28162i) q^{29} +(-1.35808 - 1.06801i) q^{30} +(1.32572 + 1.26407i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(2.03119 + 0.813164i) q^{33} +(1.74998 + 3.83192i) q^{34} +(3.70381 + 2.67897i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.53462 + 3.36883i) q^{37} +(3.57174 + 3.40565i) q^{38} +(-3.68382 + 1.47478i) q^{39} +(-0.565082 - 1.63270i) q^{40} +(1.13163 - 0.727251i) q^{41} +(0.481485 + 2.60157i) q^{42} +(-3.97761 - 1.16793i) q^{43} +(1.26911 + 1.78222i) q^{44} +(0.863860 + 1.49625i) q^{45} +(-2.34970 + 4.18078i) q^{46} +(-6.16523 + 10.6785i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-1.54952 - 6.82635i) q^{49} +(-1.31953 - 1.52282i) q^{50} +(-0.200444 - 4.20783i) q^{51} +(-3.89636 - 0.750961i) q^{52} +(5.13199 - 2.05454i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-3.18002 - 2.04367i) q^{55} +(-1.00146 + 2.44889i) q^{56} +(-2.05014 - 4.48918i) q^{57} +(5.63974 + 0.538529i) q^{58} +(-2.80080 + 2.20257i) q^{59} +(-0.0822082 + 1.72576i) q^{60} +(-0.707305 + 2.91555i) q^{61} +(0.260690 - 1.81314i) q^{62} +(0.519911 - 2.59417i) q^{63} +(0.841254 - 0.540641i) q^{64} +(6.73181 - 1.29745i) q^{65} +(-0.515819 - 2.12624i) q^{66} +(-13.8629 + 1.32375i) q^{67} +(2.10630 - 3.64822i) q^{68} +(3.73522 - 3.00801i) q^{69} +(0.0338054 - 4.57099i) q^{70} +(-0.393494 + 0.861631i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(-1.19470 + 3.45186i) q^{73} +(6.53462 + 3.36883i) q^{74} +(0.659037 + 1.90416i) q^{75} +(0.702347 - 4.88493i) q^{76} +(1.58974 + 5.56609i) q^{77} +(3.33815 + 2.14530i) q^{78} +(-5.98114 - 2.39449i) q^{79} +(-1.00218 + 1.40736i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-1.24881 - 0.499948i) q^{82} +(-0.250227 - 0.160811i) q^{83} +(1.83989 - 1.90127i) q^{84} +(-1.03580 + 7.20412i) q^{85} +(1.35587 + 3.91753i) q^{86} +(-5.03560 - 2.59603i) q^{87} +(0.715595 - 2.06758i) q^{88} +(-7.20208 + 6.86717i) q^{89} +(0.717721 - 1.57159i) q^{90} +(-9.05291 - 5.31635i) q^{91} +(4.76852 - 0.511082i) q^{92} +(-0.915891 + 1.58637i) q^{93} +(12.2746 - 1.17208i) q^{94} +(2.01022 + 8.28622i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(7.74787 - 4.97925i) q^{97} +(-4.66177 + 5.22187i) q^{98} +(-0.311372 + 2.16564i) 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
$5$	−0.0822082	−	1.72576i	−0.0367646	−	0.771785i	−0.939698	−	0.342005i	$-0.888894\pi$
$5$	−0.0822082	−	1.72576i	−0.0367646	−	0.771785i	0.902934	−	0.429780i	$-0.141409\pi$
$6$	0.654861	−	0.755750i	0.267346	−	0.308533i
$7$	−1.65083	+	2.06755i	−0.623955	+	0.781460i
$7$	−1.65083	+	2.06755i	−0.623955	+	0.781460i
$8$	0.959493	−	0.281733i	0.339232	−	0.0996075i
$9$	−0.888835	+	0.458227i	−0.296278	+	0.152742i
$10$	−1.35808	+	1.06801i	−0.429463	+	0.337733i
$11$	1.26911	−	1.78222i	0.382652	−	0.537359i	−0.577664	−	0.816275i	$-0.696036\pi$
$11$	1.26911	−	1.78222i	0.382652	−	0.537359i	0.960316	+	0.278915i	$0.0899749\pi$
$12$	−0.995472	−	0.0950560i	−0.287368	−	0.0274403i
$13$	0.564714	+	3.92768i	0.156624	+	1.08934i	0.904799	+	0.425840i	$0.140021\pi$
$13$	0.564714	+	3.92768i	0.156624	+	1.08934i	−0.748175	+	0.663501i	$0.769070\pi$
$14$	2.64175	+	0.145431i	0.706038	+	0.0388680i
$15$	1.65774	−	0.486755i	0.428025	−	0.125680i
$16$	−0.786053	−	0.618159i	−0.196513	−	0.154540i
$17$	−4.13648	−	0.797240i	−1.00324	−	0.193359i	−0.338928	−	0.940812i	$-0.610064\pi$
$17$	−4.13648	−	0.797240i	−1.00324	−	0.193359i	−0.664315	+	0.747453i	$0.731276\pi$
$18$	0.888835	+	0.458227i	0.209501	+	0.108005i
$19$	−4.84598	+	0.933985i	−1.11174	+	0.214271i	−0.711878	−	0.702303i	$-0.752155\pi$
$19$	−4.84598	+	0.933985i	−1.11174	+	0.214271i	−0.399865	+	0.916574i	$0.630943\pi$
$20$	1.65774	+	0.486755i	0.370681	+	0.108842i
$21$	−2.39847	−	1.11685i	−0.523388	−	0.243717i
$22$	−2.18791			−0.466464
$23$	−2.04260	−	4.33910i	−0.425912	−	0.904764i
$23$	−2.04260	−	4.33910i	−0.425912	−	0.904764i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.00586	−	0.191536i	0.401172	−	0.0383073i
$26$	2.87182	−	2.73828i	0.563211	−	0.537021i
$27$	−0.654861	−	0.755750i	−0.126028	−	0.145444i
$28$	−1.41390	−	2.23627i	−0.267202	−	0.422614i
$29$	−3.71004	+	4.28162i	−0.688937	+	0.795076i	−0.987214	−	0.159404i	$-0.949043\pi$
$29$	−3.71004	+	4.28162i	−0.688937	+	0.795076i	0.298276	+	0.954480i	$0.403588\pi$
$30$	−1.35808	−	1.06801i	−0.247950	−	0.194990i
$31$	1.32572	+	1.26407i	0.238107	+	0.227034i	0.799732	−	0.600358i	$-0.204975\pi$
$31$	1.32572	+	1.26407i	0.238107	+	0.227034i	−0.561625	+	0.827392i	$0.689824\pi$
$32$	−0.0475819	+	0.998867i	−0.00841137	+	0.176576i
$33$	2.03119	+	0.813164i	0.353584	+	0.141554i
$34$	1.74998	+	3.83192i	0.300119	+	0.657169i
$35$	3.70381	+	2.67897i	0.626058	+	0.452829i
$36$	−0.142315	−	0.989821i	−0.0237191	−	0.164970i
$37$	−6.53462	+	3.36883i	−1.07428	+	0.553832i	−0.902230	−	0.431256i	$-0.858071\pi$
$37$	−6.53462	+	3.36883i	−1.07428	+	0.553832i	−0.172054	+	0.985087i	$0.555040\pi$
$38$	3.57174	+	3.40565i	0.579413	+	0.552469i
$39$	−3.68382	+	1.47478i	−0.589884	+	0.236154i
$40$	−0.565082	−	1.63270i	−0.0893473	−	0.258152i
$41$	1.13163	−	0.727251i	0.176730	−	0.113578i	−0.449285	−	0.893389i	$-0.648321\pi$
$41$	1.13163	−	0.727251i	0.176730	−	0.113578i	0.626015	+	0.779811i	$0.284685\pi$
$42$	0.481485	+	2.60157i	0.0742948	+	0.401431i
$43$	−3.97761	−	1.16793i	−0.606580	−	0.178108i	−0.0360024	−	0.999352i	$-0.511462\pi$
$43$	−3.97761	−	1.16793i	−0.606580	−	0.178108i	−0.570577	+	0.821244i	$0.693281\pi$
$44$	1.26911	+	1.78222i	0.191326	+	0.268680i
$45$	0.863860	+	1.49625i	0.128777	+	0.223048i
$46$	−2.34970	+	4.18078i	−0.346444	+	0.616422i
$47$	−6.16523	+	10.6785i	−0.899291	+	1.55762i	−0.0708894	+	0.997484i	$0.522584\pi$
$47$	−6.16523	+	10.6785i	−0.899291	+	1.55762i	−0.828402	+	0.560134i	$0.810750\pi$
$48$	0.415415	−	0.909632i	0.0599600	−	0.131294i
$49$	−1.54952	−	6.82635i	−0.221360	−	0.975192i
$50$	−1.31953	−	1.52282i	−0.186610	−	0.215360i
$51$	−0.200444	−	4.20783i	−0.0280677	−	0.589214i
$52$	−3.89636	−	0.750961i	−0.540327	−	0.104140i
$53$	5.13199	−	2.05454i	0.704933	−	0.282213i	0.00863210	−	0.999963i	$-0.497252\pi$
$53$	5.13199	−	2.05454i	0.704933	−	0.282213i	0.696301	+	0.717750i	$0.254828\pi$
$54$	−0.235759	+	0.971812i	−0.0320827	+	0.132247i
$55$	−3.18002	−	2.04367i	−0.428794	−	0.275569i
$56$	−1.00146	+	2.44889i	−0.133826	+	0.327247i
$57$	−2.05014	−	4.48918i	−0.271548	−	0.594606i
$58$	5.63974	+	0.538529i	0.740534	+	0.0707124i
$59$	−2.80080	+	2.20257i	−0.364633	+	0.286750i	−0.783618	−	0.621243i	$-0.786628\pi$
$59$	−2.80080	+	2.20257i	−0.364633	+	0.286750i	0.418986	+	0.907993i	$0.362386\pi$
$60$	−0.0822082	+	1.72576i	−0.0106130	+	0.222795i
$61$	−0.707305	+	2.91555i	−0.0905611	+	0.373298i	−0.999000	−	0.0447207i	$-0.985760\pi$
$61$	−0.707305	+	2.91555i	−0.0905611	+	0.373298i	0.908438	+	0.418019i	$0.137275\pi$
$62$	0.260690	−	1.81314i	0.0331076	−	0.230269i
$63$	0.519911	−	2.59417i	0.0655026	−	0.326834i
$64$	0.841254	−	0.540641i	0.105157	−	0.0675801i
$65$	6.73181	−	1.29745i	0.834979	−	0.160929i
$66$	−0.515819	−	2.12624i	−0.0634930	−	0.261722i
$67$	−13.8629	+	1.32375i	−1.69363	+	0.161722i	−0.896786	−	0.442465i	$-0.854104\pi$
$67$	−13.8629	+	1.32375i	−1.69363	+	0.161722i	−0.796842	+	0.604187i	$0.793498\pi$
$68$	2.10630	−	3.64822i	0.255427	−	0.442412i
$69$	3.73522	−	3.00801i	0.449668	−	0.362121i
$70$	0.0338054	−	4.57099i	0.00404052	−	0.546338i
$71$	−0.393494	+	0.861631i	−0.0466991	+	0.102257i	−0.931544	−	0.363630i	$-0.881537\pi$
$71$	−0.393494	+	0.861631i	−0.0466991	+	0.102257i	0.884844	+	0.465887i	$0.154265\pi$
$72$	−0.723734	+	0.690079i	−0.0852929	+	0.0813266i
$73$	−1.19470	+	3.45186i	−0.139829	+	0.404009i	−0.993072	−	0.117503i	$-0.962511\pi$
$73$	−1.19470	+	3.45186i	−0.139829	+	0.404009i	0.853244	+	0.521513i	$0.174632\pi$
$74$	6.53462	+	3.36883i	0.759634	+	0.391618i
$75$	0.659037	+	1.90416i	0.0760990	+	0.219874i
$76$	0.702347	−	4.88493i	0.0805647	−	0.560340i
$77$	1.58974	+	5.56609i	0.181167	+	0.634315i
$78$	3.33815	+	2.14530i	0.377971	+	0.242907i
$79$	−5.98114	−	2.39449i	−0.672931	−	0.269401i	0.00992869	−	0.999951i	$-0.496840\pi$
$79$	−5.98114	−	2.39449i	−0.672931	−	0.269401i	−0.682859	+	0.730550i	$0.739264\pi$
$80$	−1.00218	+	1.40736i	−0.112047	+	0.157348i
$81$	0.580057	−	0.814576i	0.0644508	−	0.0905084i
$82$	−1.24881	−	0.499948i	−0.137908	−	0.0552100i
$83$	−0.250227	−	0.160811i	−0.0274660	−	0.0176513i	0.526836	−	0.849967i	$-0.323378\pi$
$83$	−0.250227	−	0.160811i	−0.0274660	−	0.0176513i	−0.554302	+	0.832316i	$0.687015\pi$
$84$	1.83989	−	1.90127i	0.200748	−	0.207445i
$85$	−1.03580	+	7.20412i	−0.112348	+	0.781396i
$86$	1.35587	+	3.91753i	0.146207	+	0.422438i
$87$	−5.03560	−	2.59603i	−0.539873	−	0.278324i
$88$	0.715595	−	2.06758i	0.0762827	−	0.220404i
$89$	−7.20208	+	6.86717i	−0.763419	+	0.727919i	−0.968005	−	0.250930i	$-0.919264\pi$
$89$	−7.20208	+	6.86717i	−0.763419	+	0.727919i	0.204586	+	0.978849i	$0.434415\pi$
$90$	0.717721	−	1.57159i	0.0756544	−	0.165660i
$91$	−9.05291	−	5.31635i	−0.949003	−	0.557305i
$92$	4.76852	−	0.511082i	0.497153	−	0.0532840i
$93$	−0.915891	+	1.58637i	−0.0949734	+	0.164499i
$94$	12.2746	−	1.17208i	1.26603	−	0.120891i
$95$	2.01022	+	8.28622i	0.206244	+	0.850149i
$96$	−0.981929	+	0.189251i	−0.100218	+	0.0193154i
$97$	7.74787	−	4.97925i	0.786677	−	0.505566i	−0.0845666	−	0.996418i	$-0.526951\pi$
$97$	7.74787	−	4.97925i	0.786677	−	0.505566i	0.871243	+	0.490851i	$0.163314\pi$
$98$	−4.66177	+	5.22187i	−0.470910	+	0.527488i
$99$	−0.311372	+	2.16564i	−0.0312941	+	0.217655i
$100$	−0.475050	+	1.95818i	−0.0475050	+	0.195818i
$101$	0.421084	−	8.83963i	0.0418994	−	0.879576i	−0.875891	−	0.482510i	$-0.839725\pi$
$101$	0.421084	−	8.83963i	0.0418994	−	0.879576i	0.917790	−	0.397066i	$-0.129972\pi$
$102$	−3.31133	+	2.60406i	−0.327870	+	0.257840i
$103$	−18.0325	−	1.72190i	−1.77680	−	0.169664i	−0.845513	−	0.533955i	$-0.820705\pi$
$103$	−18.0325	−	1.72190i	−1.77680	−	0.169664i	−0.931285	+	0.364292i	$0.881311\pi$
$104$	1.64839	+	3.60948i	0.161638	+	0.353939i
$105$	−1.73025	+	4.23100i	−0.168855	+	0.412903i
$106$	−4.65042	−	2.98864i	−0.451689	−	0.290283i
$107$	0.563971	−	2.32472i	0.0545211	−	0.224739i	−0.938033	−	0.346547i	$-0.887354\pi$
$107$	0.563971	−	2.32472i	0.0545211	−	0.224739i	0.992554	+	0.121808i	$0.0388692\pi$
$108$	0.928368	−	0.371662i	0.0893322	−	0.0357632i
$109$	14.5866	+	2.81134i	1.39714	+	0.269278i	0.831570	−	0.555420i	$-0.187442\pi$
$109$	14.5866	+	2.81134i	1.39714	+	0.269278i	0.565574	+	0.824697i	$0.308655\pi$
$110$	0.179864	+	3.77582i	0.0171494	+	0.360010i
$111$	−4.81446	−	5.55618i	−0.456968	−	0.527370i
$112$	2.57571	−	0.604727i	0.243382	−	0.0571414i
$113$	−4.81584	+	10.5452i	−0.453036	+	0.992010i	0.535984	+	0.844228i	$0.319941\pi$
$113$	−4.81584	+	10.5452i	−0.453036	+	0.992010i	−0.989020	+	0.147782i	$0.952787\pi$
$114$	−2.46758	+	4.27397i	−0.231110	+	0.400294i
$115$	−7.32034	+	3.88176i	−0.682625	+	0.361976i
$116$	−2.83269	−	4.90637i	−0.263009	−	0.455545i
$117$	−2.30170	−	3.23229i	−0.212793	−	0.298825i
$118$	3.41878	+	1.00385i	0.314724	+	0.0924114i
$119$	8.47695	−	7.23626i	0.777081	−	0.663347i
$120$	1.45345	−	0.934076i	0.132681	−	0.0852691i
$121$	2.03209	+	5.87134i	0.184735	+	0.533758i
$122$	2.78521	−	1.11503i	0.252161	−	0.100950i
$123$	0.973542	+	0.928270i	0.0877813	+	0.0836993i
$124$	−1.62815	+	0.839371i	−0.146212	+	0.0753777i
$125$	−1.72485	−	11.9966i	−0.154275	−	1.07301i
$126$	−2.41472	+	1.08126i	−0.215121	+	0.0963260i
$127$	5.73695	+	12.5622i	0.509072	+	1.11471i	0.973413	+	0.229056i	$0.0735638\pi$
$127$	5.73695	+	12.5622i	0.509072	+	1.11471i	−0.464341	+	0.885656i	$0.653709\pi$
$128$	−0.928368	−	0.371662i	−0.0820569	−	0.0328506i
$129$	0.197252	−	4.14084i	0.0173671	−	0.364580i
$130$	−4.96171	−	4.73098i	−0.435171	−	0.414934i
$131$	15.6356	+	12.2960i	1.36609	+	1.07430i	0.988966	+	0.148141i	$0.0473290\pi$
$131$	15.6356	+	12.2960i	1.36609	+	1.07430i	0.377123	+	0.926163i	$0.376913\pi$
$132$	−1.43278	+	1.65351i	−0.124707	+	0.143920i
$133$	6.06882	−	11.5611i	0.526234	−	1.00248i
$134$	9.11959	+	10.5246i	0.787813	+	0.909184i
$135$	−1.25041	+	1.19226i	−0.107618	+	0.102614i
$136$	−4.19353	+	0.400433i	−0.359592	+	0.0343369i
$137$	−5.29400	−	9.16948i	−0.452297	−	0.783401i	0.546231	−	0.837634i	$-0.316062\pi$
$137$	−5.29400	−	9.16948i	−0.452297	−	0.783401i	−0.998528	+	0.0542330i	$0.982729\pi$
$138$	−4.61689	−	1.29781i	−0.393016	−	0.110477i
$139$	−3.00805			−0.255140			−0.127570	−	0.991830i	$-0.540718\pi$
$139$	−3.00805			−0.255140			−0.127570	+	0.991830i	$0.540718\pi$
$140$	−3.74303	+	2.62390i	−0.316344	+	0.221760i
$141$	−11.8310	−	3.47389i	−0.996349	−	0.292555i
$142$	0.930113	−	0.179265i	0.0780534	−	0.0150436i
$143$	7.71666	+	3.97822i	0.645300	+	0.332675i
$144$	0.981929	+	0.189251i	0.0818274	+	0.0157709i
$145$	7.69405	+	6.05067i	0.638956	+	0.502481i
$146$	3.50479	−	1.02910i	0.290059	−	0.0851689i
$147$	6.26861	−	3.11521i	0.517026	−	0.256938i
$148$	−1.04628	−	7.27705i	−0.0860039	−	0.598170i
$149$	17.5243	+	1.67337i	1.43565	+	0.137088i	0.783684	−	0.621160i	$-0.213338\pi$
$149$	17.5243	+	1.67337i	1.43565	+	0.137088i	0.651966	+	0.758248i	$0.273944\pi$
$150$	1.16881	−	1.64136i	0.0954325	−	0.134016i
$151$	14.4758	−	11.3839i	1.17803	−	0.926409i	0.179669	−	0.983727i	$-0.442497\pi$
$151$	14.4758	−	11.3839i	1.17803	−	0.926409i	0.998356	+	0.0573178i	$0.0182548\pi$
$152$	−4.38655	+	2.26142i	−0.355796	+	0.183425i
$153$	4.04196	−	1.18683i	0.326773	−	0.0959493i
$154$	3.61187	−	4.52361i	0.291053	−	0.364523i
$155$	2.07251	−	2.39180i	0.166468	−	0.192114i
$156$	−0.188808	−	3.96357i	−0.0151167	−	0.317340i
$157$	−0.646609	+	1.86825i	−0.0516050	+	0.149103i	−0.967858	−	0.251497i	$-0.919077\pi$
$157$	−0.646609	+	1.86825i	−0.0516050	+	0.149103i	0.916253	+	0.400600i	$0.131198\pi$
$158$	1.51891	+	6.26103i	0.120838	+	0.498101i
$159$	3.20654	+	4.50295i	0.254295	+	0.357107i
$160$	1.72772			0.136588
$161$	12.3433	+	2.93993i	0.972787	+	0.231699i
$162$	−1.00000			−0.0785674
$163$	−2.28266	−	3.20555i	−0.178792	−	0.251078i	0.715448	−	0.698666i	$-0.246223\pi$
$163$	−2.28266	−	3.20555i	−0.178792	−	0.251078i	−0.894240	+	0.447588i	$0.852283\pi$
$164$	0.317135	+	1.30725i	0.0247641	+	0.102079i
$165$	1.23635	−	3.57219i	0.0962496	−	0.278095i
$166$	0.0141530	+	0.297109i	0.00109849	+	0.0230601i
$167$	1.26260	−	1.45712i	0.0977031	−	0.112755i	−0.704792	−	0.709414i	$-0.748960\pi$
$167$	1.26260	−	1.45712i	0.0977031	−	0.112755i	0.802495	+	0.596658i	$0.203505\pi$
$168$	−2.61597	−	0.395887i	−0.201826	−	0.0305433i
$169$	−2.63432	+	0.773507i	−0.202640	+	0.0595006i
$170$	6.46912	−	3.33506i	0.496159	−	0.255788i
$171$	3.87930	−	3.05071i	0.296657	−	0.233294i
$172$	2.40465	−	3.37685i	0.183352	−	0.257483i
$173$	14.4666	+	1.38139i	1.09988	+	0.105025i	0.629172	−	0.777266i	$-0.283394\pi$
$173$	14.4666	+	1.38139i	1.09988	+	0.105025i	0.470703	+	0.882291i	$0.344000\pi$
$174$	0.806269	+	5.60772i	0.0611231	+	0.425120i
$175$	−2.91532	+	4.46341i	−0.220378	+	0.337402i
$176$	−2.09928	+	0.616406i	−0.158240	+	0.0464633i
$177$	−2.80080	−	2.20257i	−0.210521	−	0.165555i
$178$	9.77145	+	1.88329i	0.732401	+	0.141159i
$179$	−19.5475	−	10.0774i	−1.46105	−	0.753221i	−0.469494	−	0.882936i	$-0.655564\pi$
$179$	−19.5475	−	10.0774i	−1.46105	−	0.753221i	−0.991551	+	0.129714i	$0.958594\pi$
$180$	−1.69650	+	0.326973i	−0.126449	+	0.0243711i
$181$	0.412208	+	0.121035i	0.0306391	+	0.00899647i	0.297016	−	0.954872i	$-0.404008\pi$
$181$	0.412208	+	0.121035i	0.0306391	+	0.00899647i	−0.266377	+	0.963869i	$0.585827\pi$
$182$	0.920630	+	10.4581i	0.0682416	+	0.775204i
$183$	−3.00012			−0.221775
$184$	−3.18233	−	3.58787i	−0.234604	−	0.264501i
$185$	6.35100	+	11.0003i	0.466935	+	0.808755i
$186$	1.82349	−	0.174122i	0.133705	−	0.0127672i
$187$	−6.67051	+	6.36032i	−0.487796	+	0.465113i
$188$	−8.07474	−	9.31874i	−0.588911	−	0.679639i
$189$	2.64361	−	0.106342i	0.192295	−	0.00773525i
$190$	5.58372	−	6.44396i	0.405086	−	0.467494i
$191$	−5.00542	−	3.93631i	−0.362180	−	0.284821i	0.420441	−	0.907320i	$-0.361875\pi$
$191$	−5.00542	−	3.93631i	−0.362180	−	0.284821i	−0.782621	+	0.622498i	$0.786118\pi$
$192$	0.723734	+	0.690079i	0.0522310	+	0.0498022i
$193$	0.556318	−	11.6786i	0.0400447	−	0.840641i	−0.886105	−	0.463485i	$-0.846599\pi$
$193$	0.556318	−	11.6786i	0.0400447	−	0.840641i	0.926150	−	0.377156i	$-0.123098\pi$
$194$	−8.55018	−	3.42298i	−0.613867	−	0.245755i
$195$	2.84796	+	6.23617i	0.203947	+	0.446581i
$196$	6.95770	+	0.768384i	0.496979	+	0.0548846i
$197$	−1.11315	−	7.74215i	−0.0793089	−	0.551606i	−0.990275	−	0.139124i	$-0.955571\pi$
$197$	−1.11315	−	7.74215i	−0.0793089	−	0.551606i	0.910966	−	0.412481i	$-0.135338\pi$
$198$	1.94469	−	1.00256i	0.138203	−	0.0712487i
$199$	12.1461	+	11.5813i	0.861017	+	0.820978i	0.985223	−	0.171278i	$-0.0547897\pi$
$199$	12.1461	+	11.5813i	0.861017	+	0.820978i	−0.124205	+	0.992257i	$0.539638\pi$
$200$	1.87065	−	0.748894i	0.132275	−	0.0529548i
$201$	−4.55475	−	13.1601i	−0.321267	−	0.928241i
$202$	−7.44480	+	4.78449i	−0.523815	+	0.336635i
$203$	−2.72780	−	14.7389i	−0.191454	−	1.03447i
$204$	4.04196	+	1.18683i	0.282994	+	0.0830945i
$205$	−1.34809	−	1.89313i	−0.0941549	−	0.132222i
$206$	9.05728	+	15.6877i	0.631050	+	1.09301i
$207$	3.80383	+	2.92077i	0.264384	+	0.203007i
$208$	1.98403	−	3.43644i	0.137568	−	0.238275i
$209$	−4.48552	+	9.82192i	−0.310270	+	0.679397i
$210$	4.45011	−	1.04480i	0.307087	−	0.0720980i
$211$	1.22645	+	1.41539i	0.0844320	+	0.0974397i	0.796394	−	0.604779i	$-0.206738\pi$
$211$	1.22645	+	1.41539i	0.0844320	+	0.0974397i	−0.711962	+	0.702218i	$0.752193\pi$
$212$	0.263031	+	5.52171i	0.0180651	+	0.379232i
$213$	−0.930113	−	0.179265i	−0.0637303	−	0.0122830i
$214$	−2.22080	+	0.889072i	−0.151810	+	0.0607757i
$215$	−1.68858	+	6.96043i	−0.115160	+	0.474697i
$216$	−0.841254	−	0.540641i	−0.0572401	−	0.0367859i
$217$	−4.80208	+	0.654224i	−0.325986	+	0.0444116i
$218$	−6.17102	−	13.5126i	−0.417954	−	0.915192i
$219$	−3.63621	−	0.347216i	−0.245713	−	0.0234627i
$220$	2.97136	−	2.33670i	0.200329	−	0.157540i
$221$	0.795374	−	16.6969i	0.0535026	−	1.12316i
$222$	−1.73327	+	7.14465i	−0.116330	+	0.479517i
$223$	−1.66468	+	11.5781i	−0.111476	+	0.775329i	0.855011	+	0.518610i	$0.173551\pi$
$223$	−1.66468	+	11.5781i	−0.111476	+	0.775329i	−0.966486	+	0.256719i	$0.917359\pi$
$224$	−1.98666	−	1.74734i	−0.132739	−	0.116749i
$225$	−1.69511	+	1.08938i	−0.113007	+	0.0726255i
$226$	11.3833	−	2.19396i	0.757208	−	0.145940i
$227$	4.05606	+	16.7193i	0.269210	+	1.10970i	0.932452	+	0.361295i	$0.117665\pi$
$227$	4.05606	+	16.7193i	0.269210	+	1.10970i	−0.663241	+	0.748406i	$0.730820\pi$
$228$	4.91281	−	0.469117i	0.325359	−	0.0310680i
$229$	7.40329	−	12.8229i	0.489223	−	0.847360i	−0.510700	−	0.859759i	$-0.670614\pi$
$229$	7.40329	−	12.8229i	0.489223	−	0.847360i	0.999923	+	0.0123994i	$0.00394695\pi$
$230$	7.40820	+	3.71133i	0.488482	+	0.244718i
$231$	−5.03440	+	2.85718i	−0.331239	+	0.187989i
$232$	−2.35349	+	5.15342i	−0.154514	+	0.338339i
$233$	18.1732	−	17.3281i	1.19057	−	1.13520i	0.202805	−	0.979219i	$-0.434994\pi$
$233$	18.1732	−	17.3281i	1.19057	−	1.13520i	0.987760	−	0.155983i	$-0.0498544\pi$
$234$	−1.29783	+	3.74982i	−0.0848416	+	0.245134i
$235$	18.9354	+	9.76187i	1.23521	+	0.636794i
$236$	−1.16538	−	3.36715i	−0.0758598	−	0.219183i
$237$	0.916883	−	6.37706i	0.0595579	−	0.414235i
$238$	−10.8116	−	2.70768i	−0.700812	−	0.175513i
$239$	−16.0381	−	10.3070i	−1.03742	−	0.666707i	−0.0930697	−	0.995660i	$-0.529668\pi$
$239$	−16.0381	−	10.3070i	−1.03742	−	0.666707i	−0.944346	+	0.328953i	$0.893304\pi$
$240$	−1.60396	−	0.642129i	−0.103535	−	0.0414492i
$241$	9.27727	−	13.0281i	0.597602	−	0.839214i	−0.399385	−	0.916783i	$-0.630776\pi$
$241$	9.27727	−	13.0281i	0.597602	−	0.839214i	0.996987	+	0.0775690i	$0.0247158\pi$
$242$	3.60392	−	5.06100i	0.231669	−	0.325333i
$243$	0.928368	+	0.371662i	0.0595548	+	0.0238422i
$244$	−2.52386	−	1.62199i	−0.161574	−	0.103837i
$245$	−11.6533	+	3.23528i	−0.744500	+	0.206695i
$246$	0.191437	−	1.33147i	0.0122056	−	0.0848917i
$247$	−6.40498	−	18.5060i	−0.407539	−	1.17751i
$248$	1.62815	+	0.839371i	0.103388	+	0.0533001i
$249$	0.0972849	−	0.281086i	0.00616518	−	0.0178131i
$250$	−8.77160	+	8.36371i	−0.554765	+	0.528967i
$251$	9.74170	−	21.3313i	0.614891	−	1.34642i	−0.304288	−	0.952580i	$-0.598418\pi$
$251$	9.74170	−	21.3313i	0.614891	−	1.34642i	0.919178	−	0.393842i	$-0.128854\pi$
$252$	2.28144	+	1.33978i	0.143717	+	0.0843985i
$253$	−10.3255	−	1.86644i	−0.649160	−	0.117342i
$254$	6.90508	−	11.9600i	0.433263	−	0.750434i
$255$	−7.24524	+	0.691837i	−0.453715	+	0.0433245i
$256$	0.235759	+	0.971812i	0.0147349	+	0.0607382i
$257$	−5.61918	+	1.08301i	−0.350515	+	0.0675562i	−0.361470	−	0.932384i	$-0.617725\pi$
$257$	−5.61918	+	1.08301i	−0.350515	+	0.0675562i	0.0109550	+	0.999940i	$0.496513\pi$
$258$	−3.48744	+	2.24124i	−0.217119	+	0.139534i
$259$	3.82232	−	19.0720i	0.237508	−	1.18508i
$260$	−0.975669	+	6.78592i	−0.0605084	+	0.420845i
$261$	1.33567	−	5.50569i	0.0826757	−	0.340794i
$262$	0.946465	−	19.8688i	0.0584728	−	1.22750i
$263$	16.1513	−	12.7015i	0.995929	−	0.783208i	0.0196687	−	0.999807i	$-0.493739\pi$
$263$	16.1513	−	12.7015i	0.995929	−	0.783208i	0.976261	+	0.216599i	$0.0694964\pi$
$264$	2.17800	+	0.207974i	0.134047	+	0.0127999i
$265$	−3.96754	−	8.68770i	−0.243724	−	0.533681i
$266$	−12.9377	+	1.76260i	−0.793261	+	0.108072i
$267$	−8.37155	−	5.38007i	−0.512331	−	0.329255i
$268$	3.28318	−	13.5334i	0.200552	−	0.826687i
$269$	3.04699	−	1.21983i	0.185779	−	0.0743745i	−0.276908	−	0.960896i	$-0.589310\pi$
$269$	3.04699	−	1.21983i	0.185779	−	0.0743745i	0.462687	+	0.886522i	$0.346886\pi$
$270$	1.69650	+	0.326973i	0.103246	+	0.0198990i
$271$	−0.581824	−	12.2140i	−0.0353433	−	0.741948i	−0.945095	−	0.326795i	$-0.894031\pi$
$271$	−0.581824	−	12.2140i	−0.0353433	−	0.741948i	0.909752	−	0.415152i	$-0.136272\pi$
$272$	2.75867	+	3.18367i	0.167269	+	0.193039i
$273$	3.03219	−	10.0511i	0.183516	−	0.608320i
$274$	−4.39841	+	9.63118i	−0.265718	+	0.581841i
$275$	2.20430	−	3.81796i	0.132924	−	0.230232i
$276$	1.62090	+	4.51361i	0.0975665	+	0.271688i
$277$	2.62847	+	4.55265i	0.157930	+	0.273542i	0.934122	−	0.356954i	$-0.116185\pi$
$277$	2.62847	+	4.55265i	0.157930	+	0.273542i	−0.776192	+	0.630496i	$0.782851\pi$
$278$	1.74484	+	2.45029i	0.104649	+	0.146958i
$279$	−1.75758	−	0.516072i	−0.105224	−	0.0308964i
$280$	4.30854	+	1.52697i	0.257484	+	0.0912540i
$281$	−13.0425	+	8.38188i	−0.778047	+	0.500021i	−0.868385	−	0.495890i	$-0.834842\pi$
$281$	−13.0425	+	8.38188i	−0.778047	+	0.500021i	0.0903376	+	0.995911i	$0.471205\pi$
$282$	4.03290	+	11.6523i	0.240156	+	0.693884i
$283$	−17.6368	+	7.06069i	−1.04840	+	0.419715i	−0.830944	−	0.556356i	$-0.812199\pi$
$283$	−17.6368	+	7.06069i	−1.04840	+	0.419715i	−0.217452	+	0.976071i	$0.569775\pi$
$284$	−0.685543	−	0.653664i	−0.0406795	−	0.0387878i
$285$	−7.57872	+	3.90710i	−0.448925	+	0.231437i
$286$	−1.23554	−	8.59340i	−0.0730593	−	0.508139i
$287$	−0.364494	+	3.54026i	−0.0215154	+	0.208975i
$288$	−0.415415	−	0.909632i	−0.0244786	−	0.0536006i
$289$	0.692583	+	0.277268i	0.0407402	+	0.0163099i
$290$	0.465742	−	9.77712i	0.0273493	−	0.574132i
$291$	6.66552	+	6.35556i	0.390740	+	0.372570i
$292$	−2.87126	−	2.25798i	−0.168028	−	0.132138i
$293$	−13.0118	+	15.0165i	−0.760159	+	0.877271i	−0.995512	−	0.0946395i	$-0.969830\pi$
$293$	−13.0118	+	15.0165i	−0.760159	+	0.877271i	0.235352	+	0.971910i	$0.424376\pi$
$294$	−6.17373	−	3.29926i	−0.360059	−	0.192417i
$295$	4.03136	+	4.65244i	0.234715	+	0.270876i
$296$	−5.32081	+	5.07338i	−0.309266	+	0.294884i
$297$	−2.17800	+	0.207974i	−0.126381	+	0.0120679i
$298$	−8.80203	−	15.2456i	−0.509888	−	0.883151i
$299$	15.8891	−	10.4730i	0.918889	−	0.605671i
$300$	−2.01498			−0.116335
$301$	8.98112	−	6.29585i	0.517663	−	0.362887i
$302$	−17.6699	−	5.18834i	−1.01679	−	0.298555i
$303$	8.68973	−	1.67481i	0.499212	−	0.0962152i
$304$	4.38655	+	2.26142i	0.251586	+	0.129701i
$305$	5.08970	+	0.980959i	0.291435	+	0.0561695i
$306$	−3.31133	−	2.60406i	−0.189296	−	0.148864i
$307$	19.3648	−	5.68601i	1.10521	−	0.324518i	0.322287	−	0.946642i	$-0.395548\pi$
$307$	19.3648	−	5.68601i	1.10521	−	0.324518i	0.782918	+	0.622124i	$0.213730\pi$
$308$	−5.77992	−	0.318190i	−0.329341	−	0.0181305i
$309$	−2.57797	−	17.9302i	−0.146656	−	1.02001i
$310$	−3.15047	−	0.300834i	−0.178935	−	0.0170862i
$311$	−9.21392	+	12.9391i	−0.522474	+	0.733712i	−0.988527	−	0.151045i	$-0.951736\pi$
$311$	−9.21392	+	12.9391i	−0.522474	+	0.733712i	0.466053	+	0.884757i	$0.345676\pi$
$312$	−3.11911	+	2.45289i	−0.176585	+	0.138868i
$313$	−18.3343	+	9.45197i	−1.03631	+	0.534257i	−0.890466	−	0.455050i	$-0.849621\pi$
$313$	−18.3343	+	9.45197i	−1.03631	+	0.534257i	−0.145848	+	0.989307i	$0.546591\pi$
$314$	1.89690	−	0.556981i	0.107048	−	0.0314323i
$315$	−4.51966	−	0.683981i	−0.254654	−	0.0385380i
$316$	4.21903	−	4.86902i	0.237339	−	0.273904i
$317$	−0.746258	−	15.6659i	−0.0419140	−	0.879884i	−0.917722	−	0.397224i	$-0.869974\pi$
$317$	−0.746258	−	15.6659i	−0.0419140	−	0.879884i	0.875808	−	0.482660i	$-0.160329\pi$
$318$	1.80802	−	5.22393i	0.101389	−	0.292944i
$319$	2.92232	+	12.0460i	0.163618	+	0.674444i
$320$	−1.00218	−	1.40736i	−0.0560233	−	0.0786738i
$321$	2.39215			0.133517
$322$	−4.76501	−	11.7599i	−0.265544	−	0.655352i
$323$	20.7899			1.15678
$324$	0.580057	+	0.814576i	0.0322254	+	0.0452542i
$325$	1.88503	+	7.77020i	0.104563	+	0.431013i
$326$	−1.28709	+	3.71881i	−0.0712854	+	0.205966i
$327$	0.706832	+	14.8382i	0.0390879	+	0.820557i
$328$	0.880896	−	1.01661i	0.0486393	−	0.0561328i
$329$	−11.9006	−	30.3753i	−0.656099	−	1.67464i
$330$	−3.62698	+	1.06498i	−0.199658	+	0.0586250i
$331$	−14.6844	+	7.57034i	−0.807129	+	0.416104i	−0.811836	−	0.583885i	$-0.801532\pi$
$331$	−14.6844	+	7.57034i	−0.807129	+	0.416104i	0.00470761	+	0.999989i	$0.498502\pi$
$332$	0.233808	−	0.183869i	0.0128319	−	0.0100911i
$333$	4.26451	−	5.98867i	0.233694	−	0.328177i
$334$	−1.91932	−	0.183273i	−0.105020	−	0.0100282i
$335$	3.42413	+	23.8153i	0.187080	+	1.30117i
$336$	1.19493	+	2.36054i	0.0651887	+	0.128778i
$337$	−23.0476	+	6.76737i	−1.25548	+	0.368642i	−0.840811	−	0.541329i	$-0.817921\pi$
$337$	−23.0476	+	6.76737i	−1.25548	+	0.368642i	−0.414670	+	0.909972i	$0.636103\pi$
$338$	2.15814	+	1.69718i	0.117387	+	0.0923144i
$339$	−11.3833	−	2.19396i	−0.618258	−	0.119159i
$340$	−6.46912	−	3.33506i	−0.350837	−	0.180869i
$341$	3.93535	−	0.758476i	0.213111	−	0.0410738i
$342$	−4.73525	−	1.39040i	−0.256053	−	0.0751840i
$343$	16.6718	+	8.06544i	0.900192	+	0.435493i
$344$	−4.14553			−0.223512
$345$	−5.49817	−	6.19883i	−0.296012	−	0.333734i
$346$	−7.26620	−	12.5854i	−0.390633	−	0.676597i
$347$	0.800986	−	0.0764849i	0.0429992	−	0.00410592i	−0.0735343	−	0.997293i	$-0.523428\pi$
$347$	0.800986	−	0.0764849i	0.0429992	−	0.00410592i	0.116533	+	0.993187i	$0.462822\pi$
$348$	4.10023	−	3.90957i	0.219796	−	0.209575i
$349$	23.0445	+	26.5948i	1.23355	+	1.42359i	0.870754	+	0.491718i	$0.163631\pi$
$349$	23.0445	+	26.5948i	1.23355	+	1.42359i	0.362792	+	0.931870i	$0.381824\pi$
$350$	5.32684	−	0.214278i	0.284731	−	0.0114536i
$351$	2.59853	−	2.99886i	0.138699	−	0.160067i
$352$	1.71981	+	1.35248i	0.0916664	+	0.0720872i
$353$	18.4683	+	17.6095i	0.982967	+	0.937257i	0.998037	−	0.0626296i	$-0.0199487\pi$
$353$	18.4683	+	17.6095i	0.982967	+	0.937257i	−0.0150701	+	0.999886i	$0.504797\pi$
$354$	−0.169540	+	3.55908i	−0.00901094	+	0.189163i
$355$	1.51932	+	0.608244i	0.0806372	+	0.0322822i
$356$	−4.13391	−	9.05200i	−0.219097	−	0.479755i
$357$	9.03080	+	6.53199i	0.477960	+	0.345710i
$358$	3.12982	+	21.7684i	0.165416	+	1.15049i
$359$	21.2167	−	10.9380i	1.11978	−	0.577285i	0.203999	−	0.978971i	$-0.434606\pi$
$359$	21.2167	−	10.9380i	1.11978	−	0.577285i	0.915777	+	0.401686i	$0.131576\pi$
$360$	1.25041	+	1.19226i	0.0659024	+	0.0628378i
$361$	4.97216	−	1.99055i	0.261693	−	0.104766i
$362$	−0.140512	−	0.405982i	−0.00738513	−	0.0213379i
$363$	−5.22675	+	3.35903i	−0.274333	+	0.176303i
$364$	7.98487	−	6.81620i	0.418521	−	0.357266i
$365$	6.05530	+	1.77800i	0.316949	+	0.0930646i
$366$	1.74024	+	2.44383i	0.0909638	+	0.127741i
$367$	13.7377	+	23.7944i	0.717102	+	1.24206i	0.962143	+	0.272544i	$0.0878651\pi$
$367$	13.7377	+	23.7944i	0.717102	+	1.24206i	−0.245041	+	0.969513i	$0.578802\pi$
$368$	−1.07666	+	4.67342i	−0.0561247	+	0.243619i
$369$	−0.672583	+	1.16495i	−0.0350133	+	0.0606447i
$370$	5.27660	−	11.5541i	0.274317	−	0.600671i
$371$	−4.22418	+	14.0023i	−0.219309	+	0.726965i
$372$	−1.19956	−	1.38437i	−0.0621944	−	0.0717761i
$373$	−0.330939	−	6.94726i	−0.0171354	−	0.359716i	−0.991109	−	0.133054i	$-0.957522\pi$
$373$	−0.330939	−	6.94726i	−0.0171354	−	0.359716i	0.973973	−	0.226662i	$-0.0727813\pi$
$374$	9.05024	+	1.74429i	0.467977	+	0.0901951i
$375$	11.2518	−	4.50452i	0.581038	−	0.232613i
$376$	−2.90702	+	11.9829i	−0.149918	+	0.617970i
$377$	−18.9119	−	12.1539i	−0.974013	−	0.625960i
$378$	−1.62007	−	2.09174i	−0.0833274	−	0.107587i
$379$	6.82917	+	14.9538i	0.350791	+	0.768125i	0.999972	+	0.00749096i	$0.00238447\pi$
$379$	6.82917	+	14.9538i	0.350791	+	0.768125i	−0.649181	+	0.760634i	$0.724888\pi$
$380$	−8.48797	−	0.810503i	−0.435423	−	0.0415779i
$381$	−10.8555	+	8.53688i	−0.556145	+	0.437358i
$382$	−0.302992	+	6.36058i	−0.0155024	+	0.325436i
$383$	−4.09102	+	16.8634i	−0.209042	+	0.861681i	0.766567	+	0.642164i	$0.221963\pi$
$383$	−4.09102	+	16.8634i	−0.209042	+	0.861681i	−0.975609	+	0.219517i	$0.929552\pi$
$384$	0.142315	−	0.989821i	0.00726247	−	0.0505116i
$385$	9.47507	−	3.20109i	0.482894	−	0.163142i
$386$	−9.83577	+	6.32106i	−0.500627	+	0.321734i
$387$	4.07062	−	0.784547i	0.206921	−	0.0398808i
$388$	2.17132	+	8.95029i	0.110232	+	0.454382i
$389$	1.14300	−	0.109144i	0.0579526	−	0.00553380i	−0.0660395	−	0.997817i	$-0.521036\pi$
$389$	1.14300	−	0.109144i	0.0579526	−	0.00553380i	0.123992	+	0.992283i	$0.460430\pi$
$390$	3.42785	−	5.93721i	0.173576	−	0.300643i
$391$	4.98987	+	19.5770i	0.252349	+	0.990052i
$392$	−3.40995	−	6.11328i	−0.172229	−	0.308767i
$393$	−8.26314	+	18.0937i	−0.416820	+	0.912709i
$394$	−5.66088	+	5.39764i	−0.285191	+	0.271929i
$395$	−3.64062	+	10.5189i	−0.183179	+	0.529262i
$396$	−1.94469	−	1.00256i	−0.0977245	−	0.0503805i
$397$	9.70433	+	28.0388i	0.487047	+	1.40723i	0.874359	+	0.485280i	$0.161282\pi$
$397$	9.70433	+	28.0388i	0.487047	+	1.40723i	−0.387312	+	0.921949i	$0.626596\pi$
$398$	2.38841	−	16.6118i	0.119720	−	0.832674i
$399$	12.6660	+	3.17211i	0.634095	+	0.158804i
$400$	−1.69511	−	1.08938i	−0.0847556	−	0.0544691i
$401$	−15.2049	−	6.08713i	−0.759297	−	0.303977i	−0.0404842	−	0.999180i	$-0.512890\pi$
$401$	−15.2049	−	6.08713i	−0.759297	−	0.303977i	−0.718813	+	0.695203i	$0.755314\pi$
$402$	−8.07787	+	11.3438i	−0.402888	+	0.565777i
$403$	−4.21622	+	5.92085i	−0.210025	+	0.294938i
$404$	8.21574	+	3.28908i	0.408748	+	0.163638i
$405$	−1.45345	−	0.934076i	−0.0722225	−	0.0464146i
$406$	−10.4237	+	10.7714i	−0.517319	+	0.534576i
$407$	−2.28917	+	15.9215i	−0.113470	+	0.789201i
$408$	−1.37781	−	3.98091i	−0.0682116	−	0.197085i
$409$	−10.1994	−	5.25815i	−0.504327	−	0.259999i	0.187236	−	0.982315i	$-0.440047\pi$
$409$	−10.1994	−	5.25815i	−0.504327	−	0.259999i	−0.691563	+	0.722316i	$0.743078\pi$
$410$	−0.760129	+	2.19625i	−0.0375401	+	0.108465i
$411$	7.66290	−	7.30656i	0.377983	−	0.360406i
$412$	7.52506	−	16.4776i	0.370733	−	0.811792i
$413$	0.0697177	−	9.42686i	0.00343058	−	0.463865i
$414$	0.172752	−	4.79272i	0.00849028	−	0.235549i
$415$	−0.256951	+	0.445053i	−0.0126132	+	0.0218468i
$416$	−3.95010	+	0.377189i	−0.193669	+	0.0184932i
$417$	−0.709175	−	2.92326i	−0.0347285	−	0.143153i
$418$	10.6026	−	2.04348i	0.518588	−	0.0999497i
$419$	−15.2389	+	9.79344i	−0.744468	+	0.478441i	−0.857070	−	0.515199i	$-0.827718\pi$
$419$	−15.2389	+	9.79344i	−0.744468	+	0.478441i	0.112602	+	0.993640i	$0.464082\pi$
$420$	−3.43239	−	3.01891i	−0.167483	−	0.147308i
$421$	2.00908	−	13.9735i	0.0979166	−	0.681025i	−0.880449	−	0.474141i	$-0.842759\pi$
$421$	2.00908	−	13.9735i	0.0979166	−	0.681025i	0.978366	−	0.206884i	$-0.0663322\pi$
$422$	0.441537	−	1.82004i	0.0214937	−	0.0885983i
$423$	0.586707	−	12.3165i	0.0285267	−	0.598849i
$424$	4.34528	−	3.41716i	0.211025	−	0.165952i
$425$	−8.44989	−	0.806867i	−0.409880	−	0.0391388i
$426$	0.393494	+	0.861631i	0.0190648	+	0.0417462i
$427$	−4.86040	−	6.27547i	−0.235211	−	0.303691i
$428$	2.01240	+	1.29329i	0.0972732	+	0.0625137i
$429$	−2.04680	+	8.43704i	−0.0988207	+	0.407344i
$430$	6.64927	−	2.66197i	0.320656	−	0.128371i
$431$	−8.43487	−	1.62569i	−0.406293	−	0.0783066i	−0.0179898	−	0.999838i	$-0.505727\pi$
$431$	−8.43487	−	1.62569i	−0.406293	−	0.0783066i	−0.388303	+	0.921532i	$0.626939\pi$
$432$	0.0475819	+	0.998867i	0.00228929	+	0.0480580i
$433$	13.1345	+	15.1580i	0.631202	+	0.728446i	0.977794	−	0.209570i	$-0.0672065\pi$
$433$	13.1345	+	15.1580i	0.631202	+	0.728446i	−0.346592	+	0.938016i	$0.612661\pi$
$434$	3.31839	+	3.53217i	0.159288	+	0.169550i
$435$	−4.06617	+	8.90367i	−0.194958	+	0.426898i
$436$	−7.42753	+	12.8649i	−0.355714	+	0.616115i
$437$	13.9511	+	19.1194i	0.667370	+	0.914605i
$438$	1.82638	+	3.16338i	0.0872677	+	0.151152i
$439$	−13.6661	−	19.1914i	−0.652249	−	0.915956i	0.347515	−	0.937674i	$-0.387026\pi$
$439$	−13.6661	−	19.1914i	−0.652249	−	0.915956i	−0.999764	+	0.0217187i	$0.993086\pi$
$440$	−3.62698	−	1.06498i	−0.172909	−	0.0507708i
$441$	4.50528	+	5.35747i	0.214537	+	0.255118i
$442$	−14.0623	+	9.03729i	−0.668875	+	0.429860i
$443$	−6.68467	−	19.3141i	−0.317598	−	0.917640i	−0.984941	−	0.172889i	$-0.944690\pi$
$443$	−6.68467	−	19.3141i	−0.317598	−	0.917640i	0.667343	−	0.744750i	$-0.267432\pi$
$444$	6.82525	−	2.73242i	0.323912	−	0.129675i
$445$	12.4432	+	11.8645i	0.589863	+	0.562433i
$446$	10.3969	−	5.35997i	0.492307	−	0.253802i
$447$	2.50532	+	17.4249i	0.118497	+	0.824168i
$448$	−0.270966	+	2.63184i	−0.0128019	+	0.124343i
$449$	−1.54956	−	3.39306i	−0.0731282	−	0.160128i	0.869537	−	0.493867i	$-0.164417\pi$
$449$	−1.54956	−	3.39306i	−0.0731282	−	0.160128i	−0.942666	+	0.333738i	$0.891690\pi$
$450$	1.87065	+	0.748894i	0.0881831	+	0.0353032i
$451$	0.140038	−	2.93977i	0.00659415	−	0.138428i
$452$	−8.39013	−	7.99997i	−0.394638	−	0.376287i
$453$	14.4758	+	11.3839i	0.680133	+	0.534863i
$454$	11.2664	−	13.0021i	0.528759	−	0.610220i
$455$	−8.43054	+	16.0602i	−0.395230	+	0.752915i
$456$	−3.23184	−	3.72975i	−0.151345	−	0.174661i
$457$	−0.260485	+	0.248372i	−0.0121850	+	0.0116183i	−0.696147	−	0.717899i	$-0.745104\pi$
$457$	−0.260485	+	0.248372i	−0.0121850	+	0.0116183i	0.683962	+	0.729518i	$0.260255\pi$
$458$	−14.7395	+	1.40746i	−0.688734	+	0.0657661i
$459$	2.10630	+	3.64822i	0.0983137	+	0.170284i
$460$	−1.27402	−	8.18732i	−0.0594014	−	0.381736i
$461$	−5.52236			−0.257202			−0.128601	−	0.991696i	$-0.541049\pi$
$461$	−5.52236			−0.257202			−0.128601	+	0.991696i	$0.541049\pi$
$462$	5.24763	+	2.44357i	0.244142	+	0.113685i
$463$	27.1039	+	7.95844i	1.25963	+	0.369860i	0.842356	−	0.538922i	$-0.181168\pi$
$463$	27.1039	+	7.95844i	1.25963	+	0.369860i	0.417271	+	0.908782i	$0.362986\pi$
$464$	5.56301	−	1.07218i	0.258256	−	0.0497748i
$465$	2.81299	+	1.45020i	0.130449	+	0.0672513i
$466$	−24.6565	−	4.75216i	−1.14219	−	0.220139i
$467$	13.1465	+	10.3385i	0.608346	+	0.478408i	0.874174	−	0.485612i	$-0.161403\pi$
$467$	13.1465	+	10.3385i	0.608346	+	0.478408i	−0.265829	+	0.964020i	$0.585646\pi$
$468$	3.80733	−	1.11793i	0.175994	−	0.0516765i
$469$	20.1485	−	30.8476i	0.930369	−	1.42441i
$470$	−3.03182	−	21.0867i	−0.139847	−	0.972659i
$471$	−1.96803	−	0.187924i	−0.0906822	−	0.00865910i
$472$	−2.06681	+	2.90243i	−0.0951326	+	0.133595i
$473$	−7.12955	+	5.60674i	−0.327817	+	0.257798i
$474$	−5.72644	+	2.95219i	−0.263024	+	0.135598i
$475$	−9.54145	+	2.80162i	−0.437792	+	0.128547i
$476$	4.06573	+	10.3775i	0.186352	+	0.475651i
$477$	−3.62005	+	4.17776i	−0.165751	+	0.191286i
$478$	0.907125	+	19.0429i	0.0414909	+	0.871001i
$479$	−9.16531	+	26.4814i	−0.418774	+	1.20997i	0.516576	+	0.856241i	$0.327206\pi$
$479$	−9.16531	+	26.4814i	−0.418774	+	1.20997i	−0.935349	+	0.353725i	$0.884915\pi$
$480$	0.407325	+	1.67902i	0.0185918	+	0.0766364i
$481$	−16.9219	−	23.7634i	−0.771570	−	1.08352i
$482$	−15.9937			−0.728494
$483$	0.0529796	+	12.6885i	0.00241065	+	0.577345i
$484$	−6.21305			−0.282411
$485$	−9.22995	−	12.9616i	−0.419110	−	0.588558i
$486$	−0.235759	−	0.971812i	−0.0106942	−	0.0440823i
$487$	−12.6546	+	36.5630i	−0.573434	+	1.65683i	0.167987	+	0.985789i	$0.446273\pi$
$487$	−12.6546	+	36.5630i	−0.573434	+	1.65683i	−0.741421	+	0.671040i	$0.765848\pi$
$488$	0.142751	+	2.99672i	0.00646205	+	0.135655i
$489$	2.57704	−	2.97406i	0.116538	−	0.134492i
$490$	9.39494	+	7.61583i	0.424420	+	0.344048i
$491$	−5.43370	+	1.59548i	−0.245219	+	0.0720029i	−0.402033	−	0.915625i	$-0.631696\pi$
$491$	−5.43370	+	1.59548i	−0.245219	+	0.0720029i	0.156813	+	0.987628i	$0.449878\pi$
$492$	−1.19563	+	0.616391i	−0.0539032	+	0.0277890i
$493$	18.7600	−	14.7530i	0.844907	−	0.664442i
$494$	−11.3593	+	15.9519i	−0.511078	+	0.717709i
$495$	3.76298	+	0.359321i	0.169133	+	0.0161503i
$496$	−0.260690	−	1.81314i	−0.0117053	−	0.0814122i
$497$	−1.13187	−	2.23598i	−0.0507715	−	0.100297i
$498$	−0.285397	+	0.0838001i	−0.0127889	+	0.00375517i
$499$	5.14198	+	4.04370i	0.230187	+	0.181021i	0.726590	−	0.687071i	$-0.241104\pi$
$499$	5.14198	+	4.04370i	0.230187	+	0.181021i	−0.496404	+	0.868092i	$0.665346\pi$
$500$	11.9009	+	2.29371i	0.532225	+	0.102578i
$501$	1.71372	+	0.883482i	0.0765632	+	0.0394711i
$502$	−23.0267	+	4.43804i	−1.02773	+	0.198079i
$503$	−17.1141	−	5.02516i	−0.763081	−	0.224061i	−0.123040	−	0.992402i	$-0.539264\pi$
$503$	−17.1141	−	5.02516i	−0.763081	−	0.224061i	−0.640041	+	0.768341i	$0.721083\pi$
$504$	−0.232010	−	2.63556i	−0.0103345	−	0.117397i
$505$	−15.2897			−0.680384
$506$	4.46903	+	9.49356i	0.198673	+	0.422040i
$507$	−1.37277	−	2.37771i	−0.0609668	−	0.105598i
$508$	−13.7476	+	1.31274i	−0.609953	+	0.0582434i
$509$	−15.7356	+	15.0039i	−0.697468	+	0.665035i	−0.953417	−	0.301656i	$-0.902461\pi$
$509$	−15.7356	+	15.0039i	−0.697468	+	0.665035i	0.255949	+	0.966690i	$0.417612\pi$
$510$	4.76621	+	5.50050i	0.211051	+	0.243566i
$511$	−5.16464	−	8.16853i	−0.228470	−	0.361354i
$512$	0.654861	−	0.755750i	0.0289410	−	0.0333997i
$513$	3.87930	+	3.05071i	0.171275	+	0.134692i
$514$	4.14164	+	3.94904i	0.182680	+	0.174185i
$515$	−1.48917	+	31.2614i	−0.0656205	+	1.37754i
$516$	3.84858	+	1.54074i	0.169424	+	0.0678273i
$517$	11.2070	+	24.5400i	0.492885	+	1.07927i
$518$	−17.7528	+	7.94927i	−0.780011	+	0.349271i
$519$	2.06818	+	14.3845i	0.0907829	+	0.631409i
$520$	6.09359	−	3.14147i	0.267222	−	0.137762i
$521$	−5.70920	−	5.44371i	−0.250125	−	0.238493i	0.554636	−	0.832093i	$-0.312858\pi$
$521$	−5.70920	−	5.44371i	−0.250125	−	0.238493i	−0.804760	+	0.593600i	$0.797706\pi$
$522$	−5.25957	+	2.10561i	−0.230205	+	0.0921602i
$523$	−4.78478	−	13.8247i	−0.209224	−	0.604512i	0.790747	−	0.612143i	$-0.209692\pi$
$523$	−4.78478	−	13.8247i	−0.209224	−	0.604512i	−0.999971	+	0.00763083i	$0.997571\pi$
$524$	−16.7336	+	10.7540i	−0.731011	+	0.469792i
$525$	−5.02490	−	1.78086i	−0.219305	−	0.0777230i
$526$	−19.7150	−	5.78884i	−0.859614	−	0.252405i
$527$	−4.47605	−	6.28573i	−0.194980	−	0.273811i
$528$	−1.09396	−	1.89479i	−0.0476083	−	0.0824600i
$529$	−14.6555	+	17.7261i	−0.637198	+	0.770701i
$530$	−4.77539	+	8.27122i	−0.207430	+	0.359279i
$531$	1.48017	−	3.24112i	0.0642340	−	0.140653i
$532$	8.94037	+	9.51632i	0.387614	+	0.412585i
$533$	3.49545	+	4.03397i	0.151405	+	0.174731i
$534$	0.473501	+	9.94001i	0.0204904	+	0.430146i
$535$	−4.05828	−	0.782169i	−0.175455	−	0.0338161i
$536$	−12.9285	+	5.17577i	−0.558424	+	0.223559i
$537$	5.18486	−	21.3723i	0.223743	−	0.922282i
$538$	−2.76108	−	1.77444i	−0.119038	−	0.0765014i
$539$	−14.1326	−	5.90182i	−0.608732	−	0.254209i
$540$	−0.717721	−	1.57159i	−0.0308858	−	0.0676304i
$541$	17.3802	+	1.65960i	0.747231	+	0.0713519i	0.461723	−	0.887024i	$-0.347231\pi$
$541$	17.3802	+	1.65960i	0.747231	+	0.0713519i	0.285508	+	0.958376i	$0.407838\pi$
$542$	−9.61174	+	7.55875i	−0.412859	+	0.324676i
$543$	−0.0204417	+	0.429123i	−0.000877235	+	0.0184154i
$544$	0.993159	−	4.09386i	0.0425813	−	0.175523i
$545$	3.65257	−	25.4042i	0.156459	−	1.08819i
$546$	−9.94623	+	3.36026i	−0.425659	+	0.143806i
$547$	−34.3527	+	22.0771i	−1.46882	+	0.943950i	−0.470719	+	0.882283i	$0.656005\pi$
$547$	−34.3527	+	22.0771i	−1.46882	+	0.943950i	−0.998097	+	0.0616671i	$0.980358\pi$
$548$	10.3967	−	2.00379i	0.444123	−	0.0855978i
$549$	−0.707305	−	2.91555i	−0.0301870	−	0.124433i
$550$	−4.38864	+	0.419064i	−0.187132	+	0.0178690i
$551$	13.9798	−	24.2137i	0.595560	−	1.03154i
$552$	2.73647	−	3.93850i	0.116472	−	0.167633i
$553$	14.8246	−	8.41340i	0.630405	−	0.357774i
$554$	2.18382	−	4.78189i	0.0927814	−	0.203163i
$555$	−9.19287	+	8.76538i	−0.390216	+	0.372070i
$556$	0.983838	−	2.84261i	0.0417240	−	0.120554i
$557$	18.8790	+	9.73278i	0.799928	+	0.412391i	0.809176	−	0.587566i	$-0.199914\pi$
$557$	18.8790	+	9.73278i	0.799928	+	0.412391i	−0.00924876	+	0.999957i	$0.502944\pi$
$558$	0.599117	+	1.73103i	0.0253626	+	0.0732805i
$559$	2.34104	−	16.2823i	0.0990156	−	0.688668i
$560$	−1.25536	−	4.39536i	−0.0530487	−	0.185738i
$561$	−7.75366	−	4.98298i	−0.327360	−	0.210381i
$562$	14.3930	+	5.76210i	0.607134	+	0.243060i
$563$	−14.5638	+	20.4521i	−0.613793	+	0.861952i	−0.998123	−	0.0612442i	$-0.980493\pi$
$563$	−14.5638	+	20.4521i	−0.613793	+	0.861952i	0.384330	+	0.923196i	$0.374433\pi$
$564$	7.15237	−	10.0441i	0.301169	−	0.422933i
$565$	18.5944	+	7.44409i	0.782274	+	0.313175i
$566$	15.9818	+	10.2709i	0.671765	+	0.431717i
$567$	0.726600	+	2.54402i	0.0305143	+	0.106839i
$568$	−0.134805	+	0.937589i	−0.00565629	+	0.0393404i
$569$	−13.3326	−	38.5219i	−0.558930	−	1.61492i	−0.770417	−	0.637540i	$-0.779952\pi$
$569$	−13.3326	−	38.5219i	−0.558930	−	1.61492i	0.211487	−	0.977381i	$-0.432169\pi$
$570$	7.57872	+	3.90710i	0.317438	+	0.163651i
$571$	−3.11612	+	9.00342i	−0.130405	+	0.376782i	−0.991235	−	0.132112i	$-0.957824\pi$
$571$	−3.11612	+	9.00342i	−0.130405	+	0.376782i	0.860829	+	0.508894i	$0.169945\pi$
$572$	−6.28329	+	5.99111i	−0.262718	+	0.250501i
$573$	2.64528	−	5.79235i	0.110508	−	0.241979i
$574$	3.09524	−	1.75664i	0.129193	−	0.0733209i
$575$	−4.92827	−	8.31239i	−0.205523	−	0.346651i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	39.6126	−	3.78255i	1.64910	−	0.157470i	0.771289	−	0.636485i	$-0.219612\pi$
$577$	39.6126	−	3.78255i	1.64910	−	0.157470i	0.877807	+	0.479015i	$0.159006\pi$
$578$	−0.175881	−	0.724993i	−0.00731570	−	0.0301557i
$579$	11.4805	−	2.21269i	0.477114	−	0.0919562i
$580$	−8.23436	+	5.29190i	−0.341913	+	0.219734i
$581$	0.745568	−	0.251885i	0.0309314	−	0.0104499i
$582$	1.31071	−	9.11616i	0.0543305	−	0.377877i
$583$	2.85143	−	11.7538i	0.118094	−	0.486791i
$584$	−0.173805	+	3.64862i	−0.00719210	+	0.150981i
$585$	−5.38895	+	4.23792i	−0.222806	+	0.175216i
$586$	19.7796	+	1.88873i	0.817090	+	0.0780226i
$587$	13.3320	+	29.1930i	0.550270	+	1.20492i	0.956656	+	0.291222i	$0.0940618\pi$
$587$	13.3320	+	29.1930i	0.550270	+	1.20492i	−0.406385	+	0.913702i	$0.633211\pi$
$588$	0.893615	+	6.94273i	0.0368521	+	0.286313i
$589$	−7.60504	−	4.88747i	−0.313360	−	0.201385i
$590$	1.45135	−	5.98253i	0.0597510	−	0.246297i
$591$	7.26148	−	2.90706i	0.298697	−	0.119580i
$592$	7.21903	+	1.39135i	0.296700	+	0.0571843i
$593$	−0.879949	−	18.4724i	−0.0361352	−	0.758571i	−0.942123	−	0.335267i	$-0.891173\pi$
$593$	−0.879949	−	18.4724i	−0.0361352	−	0.758571i	0.905988	−	0.423303i	$-0.139130\pi$
$594$	1.43278	+	1.65351i	0.0587875	+	0.0678444i
$595$	−13.1849	−	14.0343i	−0.540530	−	0.575352i
$596$	−7.31299	+	16.0132i	−0.299552	+	0.655927i
$597$	−8.39130	+	14.5342i	−0.343433	+	0.594844i
$598$	−17.7477	−	6.86791i	−0.725756	−	0.280850i
$599$	−22.8599	−	39.5946i	−0.934032	−	1.61779i	−0.776352	−	0.630300i	$-0.782932\pi$
$599$	−22.8599	−	39.5946i	−0.934032	−	1.61779i	−0.157680	−	0.987490i	$-0.550401\pi$
$600$	1.16881	+	1.64136i	0.0477163	+	0.0670081i
$601$	−4.79848	−	1.40896i	−0.195734	−	0.0574727i	0.182396	−	0.983225i	$-0.441615\pi$
$601$	−4.79848	−	1.40896i	−0.195734	−	0.0574727i	−0.378130	+	0.925752i	$0.623433\pi$
$602$	−10.3380	−	3.66385i	−0.421346	−	0.149327i
$603$	11.7153	−	7.52896i	0.477084	−	0.306603i
$604$	6.02323	+	17.4030i	0.245082	+	0.708117i
$605$	9.96548	−	3.98958i	0.405154	−	0.162199i
$606$	−6.40480	−	6.10696i	−0.260177	−	0.248078i
$607$	−20.3886	+	10.5110i	−0.827546	+	0.426630i	−0.819320	−	0.573336i	$-0.805649\pi$
$607$	−20.3886	+	10.5110i	−0.827546	+	0.426630i	−0.00822622	+	0.999966i	$0.502619\pi$
$608$	−0.702347	−	4.88493i	−0.0284839	−	0.198110i
$609$	13.6803	−	6.12574i	0.554355	−	0.248227i
$610$	−2.15325	−	4.71496i	−0.0871825	−	0.190903i
$611$	−45.4233	−	18.1847i	−1.83763	−	0.735675i
$612$	−0.200444	+	4.20783i	−0.00810246	+	0.170092i
$613$	21.6817	+	20.6735i	0.875717	+	0.834995i	0.987317	−	0.158759i	$-0.0507492\pi$
$613$	21.6817	+	20.6735i	0.875717	+	0.834995i	−0.111600	+	0.993753i	$0.535598\pi$
$614$	−15.8644	−	12.4759i	−0.640233	−	0.503485i
$615$	1.52194	−	1.75641i	0.0613706	−	0.0708255i
$616$	3.09349	+	4.89275i	0.124640	+	0.197134i
$617$	−15.5714	−	17.9703i	−0.626879	−	0.723457i	0.350119	−	0.936705i	$-0.386141\pi$
$617$	−15.5714	−	17.9703i	−0.626879	−	0.723457i	−0.976998	+	0.213248i	$0.931596\pi$
$618$	−13.1101	+	12.5005i	−0.527366	+	0.502843i
$619$	−31.6721	+	3.02432i	−1.27301	+	0.121558i	−0.709591	−	0.704613i	$-0.751120\pi$
$619$	−31.6721	+	3.02432i	−1.27301	+	0.121558i	−0.563419	+	0.826171i	$0.690514\pi$
$620$	1.58240	+	2.74080i	0.0635508	+	0.110073i
$621$	−1.94165	+	4.38520i	−0.0779158	+	0.175972i
$622$	15.8845			0.636911
$623$	−2.30880	−	26.2272i	−0.0924999	−	1.05077i
$624$	3.80733	+	1.11793i	0.152415	+	0.0447531i
$625$	−10.6686	+	2.05620i	−0.426743	+	0.0822480i
$626$	18.3343	+	9.45197i	0.732784	+	0.377777i
$627$	−10.6026	−	2.04348i	−0.423425	−	0.0816086i
$628$	−1.55402	−	1.22209i	−0.0620120	−	0.0487668i
$629$	29.7160	−	8.72542i	1.18486	−	0.347905i
$630$	2.06450	+	4.07835i	0.0822518	+	0.162485i
$631$	−5.50643	−	38.2980i	−0.219207	−	1.52462i	−0.740975	−	0.671533i	$-0.765636\pi$
$631$	−5.50643	−	38.2980i	−0.219207	−	1.52462i	0.521767	−	0.853088i	$-0.325273\pi$
$632$	−6.41346	−	0.612412i	−0.255114	−	0.0243604i
$633$	−1.08635	+	1.52557i	−0.0431786	+	0.0606358i
$634$	−12.3282	+	9.69499i	−0.489615	+	0.385037i
$635$	21.2077	−	10.9333i	0.841602	−	0.433876i
$636$	−5.30405	+	1.55741i	−0.210319	+	0.0617553i
$637$	25.9366	−	9.94094i	1.02765	−	0.393874i
$638$	8.11724	−	9.36779i	0.321364	−	0.370874i
$639$	−0.0450711	−	0.946158i	−0.00178298	−	0.0374294i
$640$	−0.565082	+	1.63270i	−0.0223368	+	0.0645380i
$641$	−2.89482	−	11.9326i	−0.114339	−	0.471310i	−0.999976	−	0.00693245i	$-0.997793\pi$
$641$	−2.89482	−	11.9326i	−0.114339	−	0.471310i	0.885637	−	0.464377i	$-0.153722\pi$
$642$	−1.38758	−	1.94859i	−0.0547635	−	0.0769046i
$643$	−26.9688			−1.06354			−0.531772	−	0.846888i	$-0.678474\pi$
$643$	−26.9688			−1.06354			−0.531772	+	0.846888i	$0.678474\pi$
$644$	−6.81533	+	10.7029i	−0.268562	+	0.421752i
$645$	−7.16232			−0.282016
$646$	−12.0593	−	16.9349i	−0.474467	−	0.666296i
$647$	−2.58150	−	10.6411i	−0.101489	−	0.418344i	0.898289	−	0.439405i	$-0.144811\pi$
$647$	−2.58150	−	10.6411i	−0.101489	−	0.418344i	−0.999778	+	0.0210612i	$0.993296\pi$
$648$	0.327068	−	0.945001i	0.0128484	−	0.0371231i
$649$	0.370938	+	7.78694i	0.0145606	+	0.305664i
$650$	5.23599	−	6.04266i	0.205373	−	0.237013i
$651$	−1.76792	−	4.51248i	−0.0692901	−	0.176858i
$652$	3.77584	−	1.10869i	0.147873	−	0.0434195i
$653$	−15.0054	+	7.73584i	−0.587208	+	0.302727i	−0.726109	−	0.687579i	$-0.758673\pi$
$653$	−15.0054	+	7.73584i	−0.587208	+	0.302727i	0.138901	+	0.990306i	$0.455643\pi$
$654$	11.6769	−	9.18279i	0.456602	−	0.359076i
$655$	19.9346	−	27.9942i	0.778908	−	1.09382i
$656$	−1.33907	−	0.127866i	−0.0522821	−	0.00499233i
$657$	−0.519841	−	3.61557i	−0.0202809	−	0.141057i
$658$	−17.8400	+	27.3133i	−0.695475	+	1.06478i
$659$	24.4169	−	7.16944i	0.951146	−	0.279282i	0.230882	−	0.972982i	$-0.425839\pi$
$659$	24.4169	−	7.16944i	0.951146	−	0.279282i	0.720264	+	0.693700i	$0.244021\pi$
$660$	2.97136	+	2.33670i	0.115660	+	0.0909560i
$661$	−15.8331	−	3.05158i	−0.615836	−	0.118693i	−0.128212	−	0.991747i	$-0.540924\pi$
$661$	−15.8331	−	3.05158i	−0.615836	−	0.118693i	−0.487623	+	0.873054i	$0.662136\pi$
$662$	14.6844	+	7.57034i	0.570726	+	0.294230i
$663$	16.4138	−	3.16350i	0.637459	−	0.122860i
$664$	−0.285397	−	0.0838001i	−0.0110755	−	0.00325207i
$665$	−20.4507	−	9.52293i	−0.793044	−	0.369283i
$666$	−7.35188			−0.284880
$667$	26.1565	+	7.35259i	1.01278	+	0.284693i
$668$	0.964024	+	1.66974i	0.0372992	+	0.0646041i
$669$	−11.6442	+	1.11189i	−0.450192	+	0.0429881i
$670$	17.4132	−	16.6035i	0.672731	−	0.641448i
$671$	4.29850	+	4.96073i	0.165942	+	0.191507i
$672$	1.22971	−	2.34261i	0.0474372	−	0.0903680i
$673$	−27.9887	+	32.3007i	−1.07888	+	1.24510i	−0.110969	+	0.993824i	$0.535395\pi$
$673$	−27.9887	+	32.3007i	−1.07888	+	1.24510i	−0.967916	+	0.251275i	$0.919150\pi$
$674$	18.8814	+	14.8485i	0.727286	+	0.571944i
$675$	−1.45831	−	1.39050i	−0.0561305	−	0.0535203i
$676$	0.130638	−	2.74243i	0.00502454	−	0.105478i
$677$	−17.9094	−	7.16983i	−0.688313	−	0.275559i	0.00102426	−	0.999999i	$-0.499674\pi$
$677$	−17.9094	−	7.16983i	−0.688313	−	0.275559i	−0.689337	+	0.724440i	$0.742098\pi$
$678$	4.81584	+	10.5452i	0.184951	+	0.404986i
$679$	−2.49557	+	24.2390i	−0.0957711	+	0.930207i
$680$	1.03580	+	7.20412i	0.0397209	+	0.276265i
$681$	−15.2918	+	7.88346i	−0.585982	+	0.302095i
$682$	−2.90056	−	2.76568i	−0.111068	−	0.105903i
$683$	−20.7492	+	8.30672i	−0.793946	+	0.317848i	−0.732943	−	0.680290i	$-0.761854\pi$
$683$	−20.7492	+	8.30672i	−0.793946	+	0.317848i	−0.0610023	+	0.998138i	$0.519430\pi$
$684$	1.61413	+	4.66373i	0.0617179	+	0.178322i
$685$	−15.3891	+	9.89000i	−0.587989	+	0.377877i
$686$	−3.10068	−	18.2589i	−0.118384	−	0.697126i
$687$	14.2068	+	4.17150i	0.542024	+	0.159153i
$688$	2.40465	+	3.37685i	0.0916762	+	0.128741i
$689$	10.9677	+	18.9966i	0.417835	+	0.723711i
$690$	−1.86016	+	8.07435i	−0.0708152	+	0.307385i
$691$	−11.9360	+	20.6738i	−0.454068	+	0.786469i	−0.998634	−	0.0522493i	$-0.983361\pi$
$691$	−11.9360	+	20.6738i	−0.454068	+	0.786469i	0.544566	+	0.838718i	$0.316694\pi$
$692$	−6.03698	+	13.2191i	−0.229492	+	0.502516i
$693$	−3.96355	−	4.21888i	−0.150563	−	0.160262i
$694$	−0.526920	−	0.608098i	−0.0200016	−	0.0230831i
$695$	0.247287	+	5.19119i	0.00938012	+	0.196913i
$696$	−5.56301	−	1.07218i	−0.210865	−	0.0406410i
$697$	−5.26073	+	2.10608i	−0.199265	+	0.0797735i
$698$	8.29636	−	34.1980i	0.314022	−	1.29442i
$699$	21.1241	+	13.5757i	0.798988	+	0.513479i
$700$	−3.26441	−	4.21482i	−0.123383	−	0.159305i
$701$	17.9442	+	39.2924i	0.677744	+	1.48405i	0.865016	+	0.501745i	$0.167308\pi$
$701$	17.9442	+	39.2924i	0.677744	+	1.48405i	−0.187271	+	0.982308i	$0.559964\pi$
$702$	−3.95010	−	0.377189i	−0.149087	−	0.0142361i
$703$	28.5201	−	22.4285i	1.07566	−	0.845907i
$704$	0.104105	−	2.18543i	0.00392360	−	0.0823666i
$705$	−5.02251	+	20.7031i	−0.189159	+	0.779723i
$706$	3.63159	−	25.2583i	0.136677	−	0.950608i
$707$	17.5812	+	15.4633i	0.661210	+	0.581559i
$708$	2.99748	−	1.92636i	0.112652	−	0.0723972i
$709$	43.6842	−	8.41943i	1.64059	−	0.316198i	0.716274	−	0.697819i	$-0.245846\pi$
$709$	43.6842	−	8.41943i	1.64059	−	0.316198i	0.924319	+	0.381621i	$0.124634\pi$
$710$	−0.385831	−	1.59042i	−0.0144800	−	0.0596873i
$711$	6.41346	−	0.612412i	0.240524	−	0.0229672i
$712$	−4.97564	+	8.61806i	−0.186470	+	0.322976i
$713$	2.77702	−	8.33444i	0.104000	−	0.312127i
$714$	0.0824259	−	11.1452i	0.00308471	−	0.417098i
$715$	6.23109	−	13.6442i	0.233029	−	0.510263i
$716$	15.9165	−	15.1764i	0.594828	−	0.567167i
$717$	6.23538	−	18.0160i	0.232865	−	0.672818i
$718$	−21.2167	−	10.9380i	−0.791801	−	0.408202i
$719$	−3.79290	−	10.9589i	−0.141451	−	0.408697i	0.851916	−	0.523678i	$-0.175440\pi$
$719$	−3.79290	−	10.9589i	−0.141451	−	0.408697i	−0.993368	+	0.114981i	$0.963319\pi$
$720$	0.245880	−	1.71013i	0.00916341	−	0.0637329i
$721$	33.3288	−	34.4406i	1.24123	−	1.28263i
$722$	−4.50559	−	2.89557i	−0.167681	−	0.107762i
$723$	14.8481	+	5.94427i	0.552205	+	0.221070i
$724$	−0.249198	+	0.349950i	−0.00926138	+	0.0130058i
$725$	−6.62174	+	9.29893i	−0.245925	+	0.345353i
$726$	5.76799	+	2.30916i	0.214070	+	0.0857008i
$727$	−2.08909	−	1.34258i	−0.0774801	−	0.0497934i	0.501327	−	0.865258i	$-0.332845\pi$
$727$	−2.08909	−	1.34258i	−0.0774801	−	0.0497934i	−0.578807	+	0.815464i	$0.696482\pi$
$728$	−10.1840	−	2.55050i	−0.377444	−	0.0945279i
$729$	−0.142315	+	0.989821i	−0.00527092	+	0.0366601i
$730$	−2.06411	−	5.96384i	−0.0763960	−	0.220732i
$731$	15.5222	+	8.00223i	0.574108	+	0.295973i
$732$	0.981243	−	2.83512i	0.0362678	−	0.104789i
$733$	22.6204	−	21.5685i	0.835504	−	0.796651i	−0.145760	−	0.989320i	$-0.546563\pi$
$733$	22.6204	−	21.5685i	0.835504	−	0.796651i	0.981264	+	0.192669i	$0.0617142\pi$
$734$	11.4137	−	24.9925i	0.421287	−	0.922490i
$735$	−5.89145	−	10.5620i	−0.217309	−	0.389587i
$736$	4.43137	−	1.83383i	0.163343	−	0.0675958i
$737$	−15.2344	+	26.3868i	−0.561167	+	0.971970i
$738$	1.33907	−	0.127866i	0.0492920	−	0.00470682i
$739$	9.33026	+	38.4598i	0.343219	+	1.41477i	0.837962	+	0.545729i	$0.183747\pi$
$739$	9.33026	+	38.4598i	0.343219	+	1.41477i	−0.494743	+	0.869040i	$0.664738\pi$
$740$	−12.4725	+	2.40387i	−0.458497	+	0.0883680i
$741$	16.4743	−	10.5874i	0.605198	−	0.388937i
$742$	13.8562	−	4.68123i	0.508678	−	0.171853i
$743$	5.39063	−	37.4927i	0.197763	−	1.37547i	−0.612993	−	0.790089i	$-0.710035\pi$
$743$	5.39063	−	37.4927i	0.197763	−	1.37547i	0.810756	−	0.585384i	$-0.199056\pi$
$744$	−0.431859	+	1.78015i	−0.0158327	+	0.0652633i
$745$	1.44720	−	30.3804i	0.0530212	−	1.11305i
$746$	−5.46711	+	4.29938i	−0.200165	+	0.157412i
$747$	0.296099	+	0.0282740i	0.0108337	+	0.00103449i
$748$	−3.82880	−	8.38389i	−0.139995	−	0.306546i
$749$	3.87545	+	5.00375i	0.141606	+	0.182833i
$750$	−10.1959	−	6.55253i	−0.372303	−	0.239264i
$751$	−11.5217	+	47.4929i	−0.420431	+	1.73304i	0.229739	+	0.973252i	$0.426213\pi$
$751$	−11.5217	+	47.4929i	−0.420431	+	1.73304i	−0.650170	+	0.759789i	$0.725302\pi$
$752$	11.4472	−	4.58277i	0.417437	−	0.167116i
$753$	23.0267	+	4.43804i	0.839141	+	0.161731i
$754$	1.06967	+	22.4552i	0.0389551	+	0.817769i
$755$	−20.8360	−	24.0460i	−0.758298	−	0.875123i
$756$	−0.764148	+	2.53300i	−0.0277918	+	0.0921242i
$757$	−5.56730	+	12.1907i	−0.202347	+	0.443078i	−0.983415	−	0.181367i	$-0.941948\pi$
$757$	−5.56730	+	12.1907i	−0.202347	+	0.443078i	0.781068	+	0.624445i	$0.214675\pi$
$758$	8.21970	−	14.2369i	0.298553	−	0.517109i
$759$	−0.620508	−	10.4745i	−0.0225230	−	0.380200i
$760$	4.26329	+	7.38423i	0.154646	+	0.267854i
$761$	−5.44287	−	7.64344i	−0.197304	−	0.277075i	0.704057	−	0.710144i	$-0.251370\pi$
$761$	−5.44287	−	7.64344i	−0.197304	−	0.277075i	−0.901361	+	0.433069i	$0.857431\pi$
$762$	13.2508	+	3.89077i	0.480024	+	0.140948i
$763$	−29.8926	+	25.5175i	−1.08219	+	0.923795i
$764$	5.35693	−	3.44269i	0.193807	−	0.124552i
$765$	−2.38047	−	6.87790i	−0.0860659	−	0.248671i
$766$	16.1096	−	6.44930i	0.582062	−	0.233023i
$767$	−10.2326	−	9.75680i	−0.369479	−	0.352298i
$768$	−0.888835	+	0.458227i	−0.0320731	+	0.0165348i
$769$	4.92839	+	34.2777i	0.177722	+	1.23608i	0.862017	+	0.506879i	$0.169201\pi$
$769$	4.92839	+	34.2777i	0.177722	+	1.23608i	−0.684295	+	0.729205i	$0.739890\pi$
$770$	−8.10361	−	5.86135i	−0.292034	−	0.211228i
$771$	−2.37725	−	5.20546i	−0.0856146	−	0.187470i
$772$	10.8543	+	4.34540i	0.390654	+	0.156394i
$773$	−0.0770615	+	1.61772i	−0.00277171	+	0.0581853i	−0.999829	−	0.0184691i	$-0.994121\pi$
$773$	−0.0770615	+	1.61772i	−0.00277171	+	0.0581853i	0.997058	+	0.0766544i	$0.0244238\pi$
$774$	−3.00026	−	2.86075i	−0.107842	−	0.102827i
$775$	2.90133	+	2.28163i	0.104219	+	0.0819586i
$776$	6.03121	−	6.96038i	0.216508	−	0.249863i
$777$	19.4355	−	0.781815i	0.697246	−	0.0280475i
$778$	−0.751913	−	0.867754i	−0.0269574	−	0.0311105i
$779$	−4.80459	+	4.58116i	−0.172142	+	0.164137i
$780$	−6.82466	+	0.651676i	−0.244362	+	0.0233338i
$781$	1.03623	+	1.79480i	0.0370792	+	0.0642230i
$782$	13.0526	−	15.4204i	0.466758	−	0.551433i
$783$	5.66539			0.202464
$784$	−3.00176	+	6.32372i	−0.107206	+	0.225847i
$785$	3.27732	+	0.962308i	0.116973	+	0.0343462i
$786$	19.5318	−	3.76445i	0.696677	−	0.134273i
$787$	−14.3838	−	7.41537i	−0.512728	−	0.264330i	0.182389	−	0.983226i	$-0.441617\pi$
$787$	−14.3838	−	7.41537i	−0.512728	−	0.264330i	−0.695117	+	0.718897i	$0.744647\pi$
$788$	7.68042	+	1.48028i	0.273604	+	0.0527328i
$789$	16.1513	+	12.7015i	0.575000	+	0.452185i
$790$	10.6802	−	3.13599i	0.379984	−	0.111573i
$791$	−13.8526	−	27.3653i	−0.492542	−	0.972999i
$792$	0.311372	+	2.16564i	0.0110641	+	0.0769527i
$793$	−11.8508	−	1.13161i	−0.420833	−	0.0401847i
$794$	17.2107	−	24.1690i	0.610785	−	0.857727i
$795$	7.50742	−	5.90390i	0.266261	−	0.209390i
$796$	−14.9170	+	7.69024i	−0.528718	+	0.272573i
$797$	−23.6904	+	6.95614i	−0.839159	+	0.246399i	−0.672947	−	0.739691i	$-0.734972\pi$
$797$	−23.6904	+	6.95614i	−0.839159	+	0.246399i	−0.166212	+	0.986090i	$0.553154\pi$
$798$	−4.76309	−	12.1574i	−0.168612	−	0.430369i
$799$	34.0157	−	39.2562i	1.20339	−	1.38878i
$800$	0.0958768	+	2.01270i	0.00338976	+	0.0711597i
$801$	3.25474	−	9.40397i	0.115001	−	0.332273i
$802$	3.86129	+	15.9164i	0.136347	+	0.562029i
$803$	4.63576	+	6.51001i	0.163592	+	0.229733i
$804$	13.9260			0.491132
$805$	4.05891	−	21.5433i	0.143058	−	0.759301i
$806$	7.26863			0.256026
$807$	1.90380	+	2.67352i	0.0670171	+	0.0941123i
$808$	−2.08639	−	8.60020i	−0.0733988	−	0.302554i
$809$	3.54475	−	10.2419i	0.124627	−	0.360086i	−0.865378	−	0.501120i	$-0.832922\pi$
$809$	3.54475	−	10.2419i	0.124627	−	0.360086i	0.990005	+	0.141034i	$0.0450428\pi$
$810$	0.0822082	+	1.72576i	0.00288850	+	0.0606371i
$811$	−5.52955	+	6.38144i	−0.194169	+	0.224083i	−0.844483	−	0.535583i	$-0.820092\pi$
$811$	−5.52955	+	6.38144i	−0.194169	+	0.224083i	0.650314	+	0.759666i	$0.274637\pi$
$812$	14.8205	+	2.24285i	0.520096	+	0.0787087i
$813$	11.7325	−	3.44498i	0.411478	−	0.120821i
$814$	14.2972	−	7.37069i	0.501115	−	0.258343i
$815$	−5.34437	+	4.20286i	−0.187205	+	0.147220i
$816$	−2.44355	+	3.43148i	−0.0855413	+	0.120126i
$817$	20.3662	+	1.94474i	0.712524	+	0.0680378i
$818$	1.63306	+	11.3582i	0.0570987	+	0.397130i
$819$	10.4826	+	0.577079i	0.366293	+	0.0201648i
$820$	2.22993	−	0.654766i	0.0778725	−	0.0228654i
$821$	4.36753	+	3.43466i	0.152428	+	0.119871i	0.691460	−	0.722414i	$-0.256968\pi$
$821$	4.36753	+	3.43466i	0.152428	+	0.119871i	−0.539033	+	0.842285i	$0.681210\pi$
$822$	−10.3967	−	2.00379i	−0.362625	−	0.0698903i
$823$	−45.6483	−	23.5333i	−1.59120	−	0.820320i	−0.999904	−	0.0138646i	$-0.995587\pi$
$823$	−45.6483	−	23.5333i	−1.59120	−	0.820320i	−0.591295	−	0.806455i	$-0.701383\pi$
$824$	−17.7872	+	3.42820i	−0.619646	+	0.119427i
$825$	4.23002	+	1.24205i	0.147271	+	0.0432425i
$826$	−7.71933	+	5.41132i	−0.268590	+	0.188284i
$827$	−10.0350			−0.348950			−0.174475	−	0.984662i	$-0.555823\pi$
$827$	−10.0350			−0.348950			−0.174475	+	0.984662i	$0.555823\pi$
$828$	−4.00424	+	2.63933i	−0.139157	+	0.0917231i
$829$	−25.3560	−	43.9179i	−0.880651	−	1.52533i	−0.850619	−	0.525783i	$-0.823773\pi$
$829$	−25.3560	−	43.9179i	−0.880651	−	1.52533i	−0.0300315	−	0.999549i	$-0.509561\pi$
$830$	0.511576	−	0.0488496i	0.0177571	−	0.00169559i
$831$	−3.80463	+	3.62771i	−0.131981	+	0.125844i
$832$	2.59853	+	2.99886i	0.0900878	+	0.103967i
$833$	0.967301	+	29.4724i	0.0335150	+	1.02116i
$834$	−1.96986	+	2.27333i	−0.0682105	+	0.0787191i
$835$	−2.61844	−	2.05917i	−0.0906149	−	0.0712604i
$836$	−7.81465	−	7.45126i	−0.270275	−	0.257707i
$837$	0.0871597	−	1.82971i	0.00301268	−	0.0632439i
$838$	16.8169	+	6.73248i	0.580931	+	0.232570i
$839$	6.49220	+	14.2159i	0.224136	+	0.490788i	0.987974	−	0.154619i	$-0.0494149\pi$
$839$	6.49220	+	14.2159i	0.224136	+	0.490788i	−0.763839	+	0.645407i	$0.776688\pi$
$840$	−0.468153	+	4.54708i	−0.0161528	+	0.156889i
$841$	−0.440697	−	3.06511i	−0.0151964	−	0.105694i
$842$	−12.5478	+	6.46885i	−0.432426	+	0.222931i
$843$	−11.2205	−	10.6987i	−0.386454	−	0.368483i
$844$	−1.73868	+	0.696062i	−0.0598478	+	0.0239594i
$845$	1.55145	+	4.48263i	0.0533716	+	0.154207i
$846$	−10.3730	+	6.66635i	−0.356633	+	0.229194i
$847$	−15.4939	−	5.49114i	−0.532377	−	0.188678i
$848$	−5.30405	−	1.55741i	−0.182142	−	0.0534816i
$849$	−11.0197	−	15.4750i	−0.378195	−	0.531100i
$850$	4.24416	+	7.35110i	0.145574	+	0.252141i
$851$	27.9653	+	21.4732i	0.958638	+	0.736090i
$852$	0.473615	−	0.820326i	0.0162258	−	0.0281039i
$853$	−14.2471	+	31.1967i	−0.487811	+	1.06816i	0.492431	+	0.870352i	$0.336108\pi$
$853$	−14.2471	+	31.1967i	−0.487811	+	1.06816i	−0.980241	+	0.197805i	$0.936619\pi$
$854$	−2.29253	+	7.59930i	−0.0784489	+	0.260043i
$855$	−5.58372	−	6.44396i	−0.190959	−	0.220379i
$856$	−0.113823	−	2.38944i	−0.00389039	−	0.0816694i
$857$	−28.1958	−	5.43430i	−0.963151	−	0.185632i	−0.316648	−	0.948543i	$-0.602557\pi$
$857$	−28.1958	−	5.43430i	−0.963151	−	0.185632i	−0.646503	+	0.762911i	$0.723769\pi$
$858$	8.05988	−	3.22669i	0.275160	−	0.110157i
$859$	−0.612297	+	2.52392i	−0.0208913	+	0.0861151i	−0.981303	−	0.192470i	$-0.938350\pi$
$859$	−0.612297	+	2.52392i	−0.0208913	+	0.0861151i	0.960412	+	0.278585i	$0.0898654\pi$
$860$	−6.02533	−	3.87224i	−0.205462	−	0.132042i
$861$	−3.52640	+	0.480429i	−0.120179	+	0.0163730i
$862$	3.56846	+	7.81383i	0.121542	+	0.266140i
$863$	28.7760	+	2.74778i	0.979548	+	0.0935355i	0.572529	−	0.819884i	$-0.305962\pi$
$863$	28.7760	+	2.74778i	0.979548	+	0.0935355i	0.407019	+	0.913420i	$0.366568\pi$
$864$	0.786053	−	0.618159i	0.0267421	−	0.0210302i
$865$	1.19468	−	25.0795i	0.0406205	−	0.852728i
$866$	4.72859	−	19.4915i	0.160684	−	0.662348i
$867$	−0.106170	+	0.738429i	−0.00360572	+	0.0250784i
$868$	0.952363	−	4.75194i	0.0323253	−	0.161291i
$869$	−11.8582	+	7.62083i	−0.402263	+	0.258519i
$870$	9.61132	−	1.85243i	0.325854	−	0.0628033i
$871$	−13.0279	−	53.7016i	−0.441432	−	1.81961i
$872$	14.7878	−	1.41206i	0.500778	−	0.0478185i
$873$	−4.60495	+	7.97601i	−0.155854	+	0.269947i
$874$	7.48180	−	22.4545i	0.253076	−	0.759536i
$875$	27.6509	+	16.2381i	0.934771	+	0.548948i
$876$	1.51741	−	3.32266i	0.0512685	−	0.112262i
$877$	−14.2467	+	13.5842i	−0.481077	+	0.458706i	−0.891389	−	0.453239i	$-0.850268\pi$
$877$	−14.2467	+	13.5842i	−0.481077	+	0.458706i	0.410312	+	0.911945i	$0.365420\pi$
$878$	−7.70572	+	22.2642i	−0.260055	+	0.751381i
$879$	−17.6608	−	9.10479i	−0.595685	−	0.307097i
$880$	1.23635	+	3.57219i	0.0416773	+	0.120419i
$881$	2.46243	−	17.1266i	0.0829614	−	0.577009i	−0.905362	−	0.424640i	$-0.860401\pi$
$881$	2.46243	−	17.1266i	0.0829614	−	0.577009i	0.988324	−	0.152369i	$-0.0486902\pi$
$882$	1.75075	−	6.77753i	0.0589507	−	0.228211i
$883$	−24.3451	−	15.6456i	−0.819277	−	0.526517i	0.0625771	−	0.998040i	$-0.480068\pi$
$883$	−24.3451	−	15.6456i	−0.819277	−	0.526517i	−0.881854	+	0.471523i	$0.843704\pi$
$884$	15.5185	+	6.21267i	0.521943	+	0.208955i
$885$	−3.57087	+	5.01458i	−0.120033	+	0.168563i
$886$	−11.8553	+	16.6484i	−0.398287	+	0.559315i
$887$	−11.8116	−	4.72866i	−0.396596	−	0.158773i	0.164787	−	0.986329i	$-0.447306\pi$
$887$	−11.8116	−	4.72866i	−0.396596	−	0.158773i	−0.561383	+	0.827556i	$0.689731\pi$
$888$	−6.18480	−	3.97473i	−0.207548	−	0.133383i
$889$	−35.4436	−	8.87659i	−1.18874	−	0.297711i
$890$	2.44682	−	17.0180i	0.0820177	−	0.570446i
$891$	−0.715595	−	2.06758i	−0.0239733	−	0.0692664i
$892$	−10.3969	−	5.35997i	−0.348113	−	0.179465i
$893$	19.9030	−	57.5059i	0.666029	−	1.92436i
$894$	12.7407	−	12.1482i	0.426111	−	0.406296i
$895$	−15.7843	+	34.5627i	−0.527610	+	1.15530i
$896$	2.30101	−	1.30589i	0.0768713	−	0.0436269i
$897$	13.9238	+	12.9721i	0.464902	+	0.433125i
$898$	−1.86507	+	3.23040i	−0.0622383	+	0.107800i
$899$	−10.3308	+	0.986468i	−0.344550	+	0.0329006i
$900$	−0.475050	−	1.95818i	−0.0158350	−	0.0652728i
$901$	−22.8663	+	4.40712i	−0.761787	+	0.146822i
$902$	−2.47589	+	1.59116i	−0.0824383	+	0.0529799i
$903$	8.23575	+	7.24365i	0.274069	+	0.241054i
$904$	−1.64983	+	11.4748i	−0.0548726	+	0.381647i
$905$	0.174991	−	0.721323i	0.00581690	−	0.0239776i
$906$	0.876260	−	18.3950i	0.0291118	−	0.611132i
$907$	31.0295	−	24.4019i	1.03032	−	0.810250i	0.0482603	−	0.998835i	$-0.484632\pi$
$907$	31.0295	−	24.4019i	1.03032	−	0.810250i	0.982057	+	0.188584i	$0.0603899\pi$
$908$	−17.1264	−	1.63537i	−0.568359	−	0.0542717i
$909$	3.67628	+	8.04993i	0.121935	+	0.266999i
$910$	17.9725	−	2.44853i	0.595781	−	0.0811679i
$911$	29.5811	+	19.0106i	0.980067	+	0.629851i	0.929481	−	0.368869i	$-0.120255\pi$
$911$	29.5811	+	19.0106i	0.980067	+	0.629851i	0.0505857	+	0.998720i	$0.483891\pi$
$912$	−1.16351	+	4.79605i	−0.0385276	+	0.158813i
$913$	−0.604167	+	0.241872i	−0.0199950	+	0.00800480i
$914$	0.353414	+	0.0681149i	0.0116899	+	0.00225304i
$915$	0.246635	+	5.17750i	0.00815349	+	0.171163i
$916$	9.69625	+	11.1901i	0.320373	+	0.369730i
$917$	−51.2343	+	12.0288i	−1.69190	+	0.397226i
$918$	1.74998	−	3.83192i	0.0577579	−	0.126472i
$919$	−23.8970	+	41.3908i	−0.788289	+	1.36536i	0.138725	+	0.990331i	$0.455699\pi$
$919$	−23.8970	+	41.3908i	−0.788289	+	1.36536i	−0.927014	+	0.375026i	$0.877634\pi$
$920$	−5.93019	+	5.78690i	−0.195513	+	0.190788i
$921$	10.0911	+	17.4784i	0.332515	+	0.575932i
$922$	3.20328	+	4.49838i	0.105495	+	0.148146i
$923$	−3.60642	−	1.05894i	−0.118707	−	0.0348555i
$924$	−1.05345	−	5.69200i	−0.0346558	−	0.187253i
$925$	−12.4623	+	8.00901i	−0.409757	+	0.263335i
$926$	−9.23908	−	26.6946i	−0.303615	−	0.877238i
$927$	16.8170	−	6.73250i	0.552342	−	0.221124i
$928$	−4.10023	−	3.90957i	−0.134597	−	0.128338i
$929$	27.4427	−	14.1477i	0.900367	−	0.464172i	0.0550790	−	0.998482i	$-0.482459\pi$
$929$	27.4427	−	14.1477i	0.900367	−	0.464172i	0.845288	+	0.534310i	$0.179429\pi$
$930$	−0.450399	−	3.13259i	−0.0147692	−	0.102722i
$931$	13.8846	+	31.6331i	0.455050	+	1.03673i
$932$	10.4312	+	22.8411i	0.341685	+	0.748187i
$933$	−14.7467	−	5.90368i	−0.482785	−	0.193278i
$934$	0.795791	−	16.7057i	0.0260391	−	0.546627i
$935$	11.5248	+	10.9888i	0.376900	+	0.359374i
$936$	−3.11911	−	2.45289i	−0.101951	−	0.0801754i
$937$	12.8026	−	14.7749i	0.418241	−	0.482676i	−0.507059	−	0.861911i	$-0.669267\pi$
$937$	12.8026	−	14.7749i	0.418241	−	0.482676i	0.925300	+	0.379235i	$0.123813\pi$
$938$	−36.8150	+	1.48092i	−1.20205	+	0.0483538i
$939$	−13.5080	−	15.5891i	−0.440817	−	0.508730i
$940$	−15.4181	+	14.7012i	−0.502884	+	0.479499i
$941$	37.1515	−	3.54754i	1.21110	−	0.115646i	0.530106	−	0.847932i	$-0.322152\pi$
$941$	37.1515	−	3.54754i	1.21110	−	0.115646i	0.680998	+	0.732285i	$0.261546\pi$
$942$	0.988493	+	1.71212i	0.0322068	+	0.0557839i
$943$	−5.46708	−	3.42475i	−0.178033	−	0.111525i
$944$	3.56311			0.115969
$945$	−0.400848	−	4.55351i	−0.0130396	−	0.148126i
$946$	8.70265	+	2.55533i	0.282948	+	0.0830809i
$947$	6.79870	−	1.31034i	0.220928	−	0.0425804i	−0.0775858	−	0.996986i	$-0.524721\pi$
$947$	6.79870	−	1.31034i	0.220928	−	0.0425804i	0.298514	+	0.954405i	$0.403509\pi$
$948$	5.72644	+	2.95219i	0.185986	+	0.0958826i
$949$	−14.2324	−	2.74308i	−0.462004	−	0.0890440i
$950$	7.81672	+	6.14714i	0.253608	+	0.199439i
$951$	15.0484	−	4.41860i	0.487976	−	0.143283i
$952$	6.09489	−	9.33137i	0.197536	−	0.302431i
$953$	−7.84483	−	54.5620i	−0.254119	−	1.76744i	−0.572916	−	0.819614i	$-0.694188\pi$
$953$	−7.84483	−	54.5620i	−0.254119	−	1.76744i	0.318797	−	0.947823i	$-0.396721\pi$
$954$	5.50294	+	0.525467i	0.178164	+	0.0170126i
$955$	−6.38165	+	8.96177i	−0.206505	+	0.289996i
$956$	14.9857	−	11.7849i	0.484672	−	0.381150i
$957$	−11.0174	+	5.67988i	−0.356143	+	0.183605i
$958$	26.8875	−	7.89489i	0.868696	−	0.255072i
$959$	27.6978	+	4.19165i	0.894410	+	0.135355i
$960$	1.13142	−	1.30572i	0.0365163	−	0.0421421i
$961$	−1.31538	−	27.6133i	−0.0424317	−	0.890751i
$962$	−9.54147	+	27.5683i	−0.307629	+	0.888837i
$963$	0.563971	+	2.32472i	0.0181737	+	0.0749130i
$964$	9.27727	+	13.0281i	0.298801	+	0.419607i
$965$	−20.2002			−0.650266
$966$	10.3050	−	7.40319i	0.331558	−	0.238194i
$967$	6.99012			0.224787			0.112394	−	0.993664i	$-0.464148\pi$
$967$	6.99012			0.224787			0.112394	+	0.993664i	$0.464148\pi$
$968$	3.60392	+	5.06100i	0.115834	+	0.162667i
$969$	4.90140	+	20.2038i	0.157456	+	0.649041i
$970$	−5.20435	+	15.0370i	−0.167102	+	0.482809i
$971$	0.348942	+	7.32520i	0.0111981	+	0.235077i	0.997527	+	0.0702871i	$0.0223916\pi$
$971$	0.348942	+	7.32520i	0.0111981	+	0.235077i	−0.986329	+	0.164790i	$0.947305\pi$
$972$	−0.654861	+	0.755750i	−0.0210047	+	0.0242407i
$973$	4.96579	−	6.21930i	0.159196	−	0.199381i
$974$	37.1237	−	10.9005i	1.18952	−	0.349275i
$975$	−7.10676	+	3.66379i	−0.227598	+	0.117335i
$976$	2.35825	−	1.85455i	0.0754858	−	0.0593627i
$977$	−24.0469	+	33.7692i	−0.769330	+	1.08037i	0.225034	+	0.974351i	$0.427751\pi$
$977$	−24.0469	+	33.7692i	−0.769330	+	1.08037i	−0.994364	+	0.106021i	$0.966189\pi$
$978$	−3.91742	−	0.374068i	−0.125265	−	0.0119614i
$979$	3.09855	+	21.5509i	0.0990301	+	0.688770i
$980$	0.754069	−	12.0705i	0.0240878	−	0.385578i
$981$	−14.2533	+	4.18516i	−0.455074	+	0.133622i
$982$	4.45149	+	3.50069i	0.142053	+	0.111712i
$983$	5.98216	+	1.15297i	0.190801	+	0.0367739i	0.283757	−	0.958896i	$-0.408419\pi$
$983$	5.98216	+	1.15297i	0.190801	+	0.0367739i	−0.0929553	+	0.995670i	$0.529631\pi$
$984$	1.19563	+	0.616391i	0.0381153	+	0.0196498i
$985$	−13.2696	+	2.55751i	−0.422805	+	0.0814890i
$986$	−22.8993	−	6.72384i	−0.729262	−	0.214131i
$987$	26.7134	−	18.7263i	0.850297	−	0.596066i
$988$	19.5830			0.623019
$989$	3.05691	+	19.6449i	0.0972041	+	0.624670i
$990$	−1.89005	−	3.27366i	−0.0600697	−	0.104044i
$991$	48.5335	−	4.63439i	1.54172	−	0.147216i	0.710713	−	0.703482i	$-0.248372\pi$
$991$	48.5335	−	4.63439i	1.54172	−	0.147216i	0.831004	+	0.556266i	$0.187766\pi$
$992$	−1.32572	+	1.26407i	−0.0420917	+	0.0401344i
$993$	−10.8189	−	12.4857i	−0.343328	−	0.396222i
$994$	−1.16482	+	2.21899i	−0.0369459	+	0.0703821i
$995$	18.9881	−	21.9135i	0.601964	−	0.694703i
$996$	0.233808	+	0.183869i	0.00740849	+	0.00582610i
$997$	13.3770	+	12.7549i	0.423653	+	0.403952i	0.871686	−	0.490065i	$-0.163027\pi$
$997$	13.3770	+	12.7549i	0.423653	+	0.403952i	−0.448033	+	0.894017i	$0.647875\pi$
$998$	0.311258	−	6.53410i	0.00985269	−	0.206833i
$999$	6.82525	+	2.73242i	0.215941	+	0.0864499i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.121.3	✓	160
7.4	even	3	inner	966.2.y.b.949.6	yes	160
23.4	even	11	inner	966.2.y.b.625.6	yes	160
161.4	even	33	inner	966.2.y.b.487.3	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.121.3	✓	160	1.1	even	1	trivial
966.2.y.b.487.3	yes	160	161.4	even	33	inner
966.2.y.b.625.6	yes	160	23.4	even	11	inner
966.2.y.b.949.6	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)

\(f(q)\)	\(=\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0822082 - 1.72576i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.65083 + 2.06755i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +O(q^{10})\)	\(q+(-0.580057 - 0.814576i) q^{2} +(0.235759 + 0.971812i) q^{3} +(-0.327068 + 0.945001i) q^{4} +(-0.0822082 - 1.72576i) q^{5} +(0.654861 - 0.755750i) q^{6} +(-1.65083 + 2.06755i) q^{7} +(0.959493 - 0.281733i) q^{8} +(-0.888835 + 0.458227i) q^{9} +(-1.35808 + 1.06801i) q^{10} +(1.26911 - 1.78222i) q^{11} +(-0.995472 - 0.0950560i) q^{12} +(0.564714 + 3.92768i) q^{13} +(2.64175 + 0.145431i) q^{14} +(1.65774 - 0.486755i) q^{15} +(-0.786053 - 0.618159i) q^{16} +(-4.13648 - 0.797240i) q^{17} +(0.888835 + 0.458227i) q^{18} +(-4.84598 + 0.933985i) q^{19} +(1.65774 + 0.486755i) q^{20} +(-2.39847 - 1.11685i) q^{21} -2.18791 q^{22} +(-2.04260 - 4.33910i) q^{23} +(0.500000 + 0.866025i) q^{24} +(2.00586 - 0.191536i) q^{25} +(2.87182 - 2.73828i) q^{26} +(-0.654861 - 0.755750i) q^{27} +(-1.41390 - 2.23627i) q^{28} +(-3.71004 + 4.28162i) q^{29} +(-1.35808 - 1.06801i) q^{30} +(1.32572 + 1.26407i) q^{31} +(-0.0475819 + 0.998867i) q^{32} +(2.03119 + 0.813164i) q^{33} +(1.74998 + 3.83192i) q^{34} +(3.70381 + 2.67897i) q^{35} +(-0.142315 - 0.989821i) q^{36} +(-6.53462 + 3.36883i) q^{37} +(3.57174 + 3.40565i) q^{38} +(-3.68382 + 1.47478i) q^{39} +(-0.565082 - 1.63270i) q^{40} +(1.13163 - 0.727251i) q^{41} +(0.481485 + 2.60157i) q^{42} +(-3.97761 - 1.16793i) q^{43} +(1.26911 + 1.78222i) q^{44} +(0.863860 + 1.49625i) q^{45} +(-2.34970 + 4.18078i) q^{46} +(-6.16523 + 10.6785i) q^{47} +(0.415415 - 0.909632i) q^{48} +(-1.54952 - 6.82635i) q^{49} +(-1.31953 - 1.52282i) q^{50} +(-0.200444 - 4.20783i) q^{51} +(-3.89636 - 0.750961i) q^{52} +(5.13199 - 2.05454i) q^{53} +(-0.235759 + 0.971812i) q^{54} +(-3.18002 - 2.04367i) q^{55} +(-1.00146 + 2.44889i) q^{56} +(-2.05014 - 4.48918i) q^{57} +(5.63974 + 0.538529i) q^{58} +(-2.80080 + 2.20257i) q^{59} +(-0.0822082 + 1.72576i) q^{60} +(-0.707305 + 2.91555i) q^{61} +(0.260690 - 1.81314i) q^{62} +(0.519911 - 2.59417i) q^{63} +(0.841254 - 0.540641i) q^{64} +(6.73181 - 1.29745i) q^{65} +(-0.515819 - 2.12624i) q^{66} +(-13.8629 + 1.32375i) q^{67} +(2.10630 - 3.64822i) q^{68} +(3.73522 - 3.00801i) q^{69} +(0.0338054 - 4.57099i) q^{70} +(-0.393494 + 0.861631i) q^{71} +(-0.723734 + 0.690079i) q^{72} +(-1.19470 + 3.45186i) q^{73} +(6.53462 + 3.36883i) q^{74} +(0.659037 + 1.90416i) q^{75} +(0.702347 - 4.88493i) q^{76} +(1.58974 + 5.56609i) q^{77} +(3.33815 + 2.14530i) q^{78} +(-5.98114 - 2.39449i) q^{79} +(-1.00218 + 1.40736i) q^{80} +(0.580057 - 0.814576i) q^{81} +(-1.24881 - 0.499948i) q^{82} +(-0.250227 - 0.160811i) q^{83} +(1.83989 - 1.90127i) q^{84} +(-1.03580 + 7.20412i) q^{85} +(1.35587 + 3.91753i) q^{86} +(-5.03560 - 2.59603i) q^{87} +(0.715595 - 2.06758i) q^{88} +(-7.20208 + 6.86717i) q^{89} +(0.717721 - 1.57159i) q^{90} +(-9.05291 - 5.31635i) q^{91} +(4.76852 - 0.511082i) q^{92} +(-0.915891 + 1.58637i) q^{93} +(12.2746 - 1.17208i) q^{94} +(2.01022 + 8.28622i) q^{95} +(-0.981929 + 0.189251i) q^{96} +(7.74787 - 4.97925i) q^{97} +(-4.66177 + 5.22187i) q^{98} +(-0.311372 + 2.16564i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9}+O(q^{10}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9	\( 160 q - 8 q^{2} + 8 q^{3} + 8 q^{4} + 6 q^{5} + 16 q^{6} - 10 q^{7} + 16 q^{8} + 8 q^{9} - 6 q^{10} + 8 q^{11} + 8 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 8 q^{16} + 9 q^{17} - 8 q^{18} - 8 q^{19} + 10 q^{20} - 3 q^{21} - 28 q^{22} + 22 q^{23} + 80 q^{24} + 46 q^{25} + 2 q^{26} - 16 q^{27} - 14 q^{28} + 62 q^{29} - 6 q^{30} + 7 q^{31} - 8 q^{32} - 14 q^{33} - 4 q^{34} + 24 q^{35} - 16 q^{36} + 15 q^{37} + 19 q^{38} - 2 q^{39} + 5 q^{40} - 14 q^{41} + 10 q^{42} - 56 q^{43} + 8 q^{44} - 16 q^{45} + 66 q^{47} - 16 q^{48} + 42 q^{49} + 4 q^{50} + 9 q^{51} - 2 q^{52} + 12 q^{53} - 8 q^{54} - 14 q^{55} + 10 q^{56} - 6 q^{57} - 13 q^{58} + 62 q^{59} + 6 q^{60} + 16 q^{61} - 8 q^{62} + 2 q^{63} - 16 q^{64} + 70 q^{65} - 8 q^{66} - 14 q^{67} - 46 q^{68} + 22 q^{69} + 24 q^{70} - 108 q^{71} - 8 q^{72} + 40 q^{73} - 15 q^{74} + 2 q^{75} + 16 q^{76} + 29 q^{77} + 18 q^{78} + 22 q^{79} + 6 q^{80} + 8 q^{81} - 7 q^{82} - 18 q^{83} - 9 q^{84} + 26 q^{85} - 6 q^{86} + 2 q^{87} + 3 q^{88} + 112 q^{89} + 12 q^{90} + 18 q^{91} - 66 q^{92} - 26 q^{93} + 23 q^{95} - 8 q^{96} + 8 q^{97} + 9 q^{98} + 28 q^{99}+O(q^{100}) \) 160 * q - 8 * q^2 + 8 * q^3 + 8 * q^4 + 6 * q^5 + 16 * q^6 - 10 * q^7 + 16 * q^8 + 8 * q^9 - 6 * q^10 + 8 * q^11 + 8 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 8 * q^16 + 9 * q^17 - 8 * q^18 - 8 * q^19 + 10 * q^20 - 3 * q^21 - 28 * q^22 + 22 * q^23 + 80 * q^24 + 46 * q^25 + 2 * q^26 - 16 * q^27 - 14 * q^28 + 62 * q^29 - 6 * q^30 + 7 * q^31 - 8 * q^32 - 14 * q^33 - 4 * q^34 + 24 * q^35 - 16 * q^36 + 15 * q^37 + 19 * q^38 - 2 * q^39 + 5 * q^40 - 14 * q^41 + 10 * q^42 - 56 * q^43 + 8 * q^44 - 16 * q^45 + 66 * q^47 - 16 * q^48 + 42 * q^49 + 4 * q^50 + 9 * q^51 - 2 * q^52 + 12 * q^53 - 8 * q^54 - 14 * q^55 + 10 * q^56 - 6 * q^57 - 13 * q^58 + 62 * q^59 + 6 * q^60 + 16 * q^61 - 8 * q^62 + 2 * q^63 - 16 * q^64 + 70 * q^65 - 8 * q^66 - 14 * q^67 - 46 * q^68 + 22 * q^69 + 24 * q^70 - 108 * q^71 - 8 * q^72 + 40 * q^73 - 15 * q^74 + 2 * q^75 + 16 * q^76 + 29 * q^77 + 18 * q^78 + 22 * q^79 + 6 * q^80 + 8 * q^81 - 7 * q^82 - 18 * q^83 - 9 * q^84 + 26 * q^85 - 6 * q^86 + 2 * q^87 + 3 * q^88 + 112 * q^89 + 12 * q^90 + 18 * q^91 - 66 * q^92 - 26 * q^93 + 23 * q^95 - 8 * q^96 + 8 * q^97 + 9 * q^98 + 28 * q^99

Introduction

L-functions

Modular forms

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Database

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