LMFDB - Embedded newform 966.2.y.b.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("966.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$160$
Relative dimension:	$8$ over $\Q(\zeta_{33})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{33}]$

Embedding invariants

Embedding label			163.2
Character	$\chi$	$=$	966.163
Dual form			966.2.y.b.403.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-1.51894 + 1.44831i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.846978 - 2.50652i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})$	\(q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-1.51894 + 1.44831i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.846978 - 2.50652i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(-0.686435 + 1.98332i) q^{10} +(0.565097 + 0.291328i) q^{11} +(0.0475819 + 0.998867i) q^{12} +(2.58082 + 2.97842i) q^{13} +(-1.90138 - 1.83977i) q^{14} +(0.298684 - 2.07739i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(7.32287 - 0.699249i) q^{17} +(-0.235759 - 0.971812i) q^{18} +(-1.42138 - 0.135725i) q^{19} +(0.298684 + 2.07739i) q^{20} +(2.21520 + 1.44669i) q^{21} +0.635773 q^{22} +(0.166161 - 4.79295i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.0283222 + 0.594556i) q^{25} +(3.65872 + 1.46473i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.53304 - 0.763995i) q^{28} +(3.42151 - 7.49206i) q^{29} +(-0.686435 - 1.98332i) q^{30} +(2.68605 - 1.07533i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(-0.624283 + 0.120321i) q^{33} +(6.18841 - 3.97705i) q^{34} +(4.91671 + 2.58057i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.689161 - 2.84076i) q^{37} +(-1.32556 + 0.530676i) q^{38} +(-3.86980 - 0.745843i) q^{39} +(1.21740 + 1.70959i) q^{40} +(7.09296 + 2.08268i) q^{41} +(2.63186 + 0.270807i) q^{42} +(0.439493 + 3.05674i) q^{43} +(0.565097 - 0.291328i) q^{44} +(1.04938 + 1.81757i) q^{45} +(-2.04857 - 4.33629i) q^{46} +(5.96276 - 10.3278i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-5.56526 + 4.24593i) q^{49} +(0.247268 + 0.541440i) q^{50} +(-5.32392 + 5.07634i) q^{51} +(3.92318 - 0.374618i) q^{52} +(5.28315 + 1.01824i) q^{53} +(0.786053 + 0.618159i) q^{54} +(-1.28028 + 0.375924i) q^{55} +(-2.60154 + 0.481642i) q^{56} +(1.20118 - 0.771950i) q^{57} +(-0.391902 - 8.22703i) q^{58} +(-1.62759 + 4.70261i) q^{59} +(-1.51894 - 1.44831i) q^{60} +(6.27928 + 4.93808i) q^{61} +(1.89471 - 2.18662i) q^{62} +(-2.63555 + 0.232169i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-8.23378 - 0.786231i) q^{65} +(-0.499751 + 0.393009i) q^{66} +(-0.284851 + 5.97976i) q^{67} +(3.67809 - 6.37064i) q^{68} +(2.83220 + 3.87023i) q^{69} +(5.55263 + 0.0407301i) q^{70} +(-0.235891 - 0.151598i) q^{71} +(-0.928368 - 0.371662i) q^{72} +(1.82156 - 2.55803i) q^{73} +(-0.689161 - 2.84076i) q^{74} +(-0.345267 - 0.484860i) q^{75} +(-0.935038 + 1.07909i) q^{76} +(0.251594 - 1.66317i) q^{77} +(-3.78138 + 1.11031i) q^{78} +(4.06553 - 0.783568i) q^{79} +(1.86545 + 0.961705i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(7.25881 - 1.39902i) q^{82} +(-13.5362 + 3.97459i) q^{83} +(2.46338 - 0.965283i) q^{84} +(-10.1103 + 11.6679i) q^{85} +(1.79131 + 2.51555i) q^{86} +(1.94180 + 8.00419i) q^{87} +(0.368784 - 0.517885i) q^{88} +(5.66211 + 2.26677i) q^{89} +(1.76558 + 1.13467i) q^{90} +(5.27958 - 8.99153i) q^{91} +(-3.80784 - 2.91554i) q^{92} +(-1.44665 + 2.50568i) q^{93} +(0.567439 - 11.9120i) q^{94} +(2.35556 - 1.85243i) q^{95} +(0.995472 + 0.0950560i) q^{96} +(-8.33765 - 2.44815i) q^{97} +(-3.00100 + 6.32408i) q^{98} +(0.416342 - 0.480485i) 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$2$	0.888835	−	0.458227i	0.628502	−	0.324015i
$3$	−0.786053	+	0.618159i	−0.453828	+	0.356894i
$3$	−0.786053	+	0.618159i	−0.453828	+	0.356894i
$4$	0.580057	−	0.814576i	0.290028	−	0.407288i
$5$	−1.51894	+	1.44831i	−0.679291	+	0.647702i	−0.949013	−	0.315236i	$-0.897916\pi$
$5$	−1.51894	+	1.44831i	−0.679291	+	0.647702i	0.269723	+	0.962938i	$0.413068\pi$
$6$	−0.415415	+	0.909632i	−0.169592	+	0.371356i
$7$	−0.846978	−	2.50652i	−0.320128	−	0.947374i
$7$	−0.846978	−	2.50652i	−0.320128	−	0.947374i
$8$	0.142315	−	0.989821i	0.0503159	−	0.349955i
$9$	0.235759	−	0.971812i	0.0785863	−	0.323937i
$10$	−0.686435	+	1.98332i	−0.217070	+	0.627182i
$11$	0.565097	+	0.291328i	0.170383	+	0.0878387i	0.541309	−	0.840824i	$-0.317929\pi$
$11$	0.565097	+	0.291328i	0.170383	+	0.0878387i	−0.370925	+	0.928663i	$0.620959\pi$
$12$	0.0475819	+	0.998867i	0.0137357	+	0.288348i
$13$	2.58082	+	2.97842i	0.715791	+	0.826066i	0.990794	−	0.135377i	$-0.0432245\pi$
$13$	2.58082	+	2.97842i	0.715791	+	0.826066i	−0.275004	+	0.961443i	$0.588679\pi$
$14$	−1.90138	−	1.83977i	−0.508164	−	0.491700i
$15$	0.298684	−	2.07739i	0.0771198	−	0.536380i
$16$	−0.327068	−	0.945001i	−0.0817670	−	0.236250i
$17$	7.32287	−	0.699249i	1.77606	−	0.169593i	0.845072	−	0.534652i	$-0.179557\pi$
$17$	7.32287	−	0.699249i	1.77606	−	0.169593i	0.930984	+	0.365060i	$0.118951\pi$
$18$	−0.235759	−	0.971812i	−0.0555689	−	0.229058i
$19$	−1.42138	−	0.135725i	−0.326086	−	0.0311375i	−0.0692707	−	0.997598i	$-0.522067\pi$
$19$	−1.42138	−	0.135725i	−0.326086	−	0.0311375i	−0.256816	+	0.966460i	$0.582673\pi$
$20$	0.298684	+	2.07739i	0.0667877	+	0.464519i
$21$	2.21520	+	1.44669i	0.483395	+	0.315693i
$22$	0.635773			0.135547
$23$	0.166161	−	4.79295i	0.0346469	−	0.999400i
$23$	0.166161	−	4.79295i	0.0346469	−	0.999400i
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	−0.0283222	+	0.594556i	−0.00566444	+	0.118911i
$26$	3.65872	+	1.46473i	0.717533	+	0.287257i
$27$	0.415415	+	0.909632i	0.0799467	+	0.175059i
$28$	−2.53304	−	0.763995i	−0.478700	−	0.144381i
$29$	3.42151	−	7.49206i	0.635358	−	1.39124i	−0.268446	−	0.963295i	$-0.586510\pi$
$29$	3.42151	−	7.49206i	0.635358	−	1.39124i	0.903804	−	0.427946i	$-0.140763\pi$
$30$	−0.686435	−	1.98332i	−0.125325	−	0.362104i
$31$	2.68605	−	1.07533i	0.482429	−	0.193136i	−0.117683	−	0.993051i	$-0.537547\pi$
$31$	2.68605	−	1.07533i	0.482429	−	0.193136i	0.600113	+	0.799916i	$0.295122\pi$
$32$	−0.723734	−	0.690079i	−0.127939	−	0.121990i
$33$	−0.624283	+	0.120321i	−0.108674	+	0.0209452i
$34$	6.18841	−	3.97705i	1.06130	−	0.682058i
$35$	4.91671	+	2.58057i	0.831076	+	0.436195i
$36$	−0.654861	−	0.755750i	−0.109143	−	0.125958i
$37$	0.689161	−	2.84076i	0.113297	−	0.467018i	−0.886692	−	0.462361i	$-0.847002\pi$
$37$	0.689161	−	2.84076i	0.113297	−	0.467018i	0.999989	−	0.00465722i	$-0.00148245\pi$
$38$	−1.32556	+	0.530676i	−0.215035	+	0.0860869i
$39$	−3.86980	−	0.745843i	−0.619664	−	0.119430i
$40$	1.21740	+	1.70959i	0.192487	+	0.270311i
$41$	7.09296	+	2.08268i	1.10773	+	0.325260i	0.783921	−	0.620861i	$-0.213217\pi$
$41$	7.09296	+	2.08268i	1.10773	+	0.325260i	0.323813	+	0.946121i	$0.395035\pi$
$42$	2.63186	+	0.270807i	0.406104	+	0.0417864i
$43$	0.439493	+	3.05674i	0.0670220	+	0.466148i	0.995500	+	0.0947609i	$0.0302087\pi$
$43$	0.439493	+	3.05674i	0.0670220	+	0.466148i	−0.928478	+	0.371387i	$0.878882\pi$
$44$	0.565097	−	0.291328i	0.0851916	−	0.0439193i
$45$	1.04938	+	1.81757i	0.156432	+	0.270948i
$46$	−2.04857	−	4.33629i	−0.302045	−	0.639350i
$47$	5.96276	−	10.3278i	0.869758	−	1.50646i	0.00751311	−	0.999972i	$-0.497608\pi$
$47$	5.96276	−	10.3278i	0.869758	−	1.50646i	0.862244	−	0.506492i	$-0.169058\pi$
$48$	0.841254	+	0.540641i	0.121424	+	0.0780348i
$49$	−5.56526	+	4.24593i	−0.795037	+	0.606561i
$50$	0.247268	+	0.541440i	0.0349689	+	0.0765712i
$51$	−5.32392	+	5.07634i	−0.745497	+	0.710830i
$52$	3.92318	−	0.374618i	0.544046	−	0.0519501i
$53$	5.28315	+	1.01824i	0.725697	+	0.139867i	0.538705	−	0.842495i	$-0.318914\pi$
$53$	5.28315	+	1.01824i	0.725697	+	0.139867i	0.186992	+	0.982361i	$0.440126\pi$
$54$	0.786053	+	0.618159i	0.106968	+	0.0841208i
$55$	−1.28028	+	0.375924i	−0.172633	+	0.0506896i
$56$	−2.60154	+	0.481642i	−0.347646	+	0.0643621i
$57$	1.20118	−	0.771950i	0.159100	−	0.102247i
$58$	−0.391902	−	8.22703i	−0.0514592	−	1.08026i
$59$	−1.62759	+	4.70261i	−0.211894	+	0.612227i	−0.999994	−	0.00331912i	$-0.998943\pi$
$59$	−1.62759	+	4.70261i	−0.211894	+	0.612227i	0.788101	+	0.615547i	$0.211065\pi$
$60$	−1.51894	−	1.44831i	−0.196094	−	0.186976i
$61$	6.27928	+	4.93808i	0.803980	+	0.632257i	0.933199	−	0.359359i	$-0.117005\pi$
$61$	6.27928	+	4.93808i	0.803980	+	0.632257i	−0.129219	+	0.991616i	$0.541247\pi$
$62$	1.89471	−	2.18662i	0.240629	−	0.277700i
$63$	−2.63555	+	0.232169i	−0.332047	+	0.0292505i
$64$	−0.959493	−	0.281733i	−0.119937	−	0.0352166i
$65$	−8.23378	−	0.786231i	−1.02127	−	0.0975199i
$66$	−0.499751	+	0.393009i	−0.0615151	+	0.0483760i
$67$	−0.284851	+	5.97976i	−0.0348001	+	0.730544i	0.912284	+	0.409558i	$0.134317\pi$
$67$	−0.284851	+	5.97976i	−0.0348001	+	0.730544i	−0.947084	+	0.320986i	$0.895986\pi$
$68$	3.67809	−	6.37064i	0.446034	−	0.772553i
$69$	2.83220	+	3.87023i	0.340956	+	0.465921i
$70$	5.55263	+	0.0407301i	0.663667	+	0.00486817i
$71$	−0.235891	−	0.151598i	−0.0279951	−	0.0179913i	0.526568	−	0.850133i	$-0.323478\pi$
$71$	−0.235891	−	0.151598i	−0.0279951	−	0.0179913i	−0.554564	+	0.832141i	$0.687115\pi$
$72$	−0.928368	−	0.371662i	−0.109409	−	0.0438008i
$73$	1.82156	−	2.55803i	0.213198	−	0.299395i	−0.694104	−	0.719875i	$-0.744199\pi$
$73$	1.82156	−	2.55803i	0.213198	−	0.299395i	0.907302	+	0.420480i	$0.138138\pi$
$74$	−0.689161	−	2.84076i	−0.0801134	−	0.330232i
$75$	−0.345267	−	0.484860i	−0.0398680	−	0.0559868i
$76$	−0.935038	+	1.07909i	−0.107256	+	0.123780i
$77$	0.251594	−	1.66317i	0.0286717	−	0.189536i
$78$	−3.78138	+	1.11031i	−0.428157	+	0.125718i
$79$	4.06553	−	0.783568i	0.457408	−	0.0881582i	0.0446578	−	0.999002i	$-0.485780\pi$
$79$	4.06553	−	0.783568i	0.457408	−	0.0881582i	0.412751	+	0.910844i	$0.364568\pi$
$80$	1.86545	+	0.961705i	0.208563	+	0.107522i
$81$	−0.888835	−	0.458227i	−0.0987595	−	0.0509141i
$82$	7.25881	−	1.39902i	0.801602	−	0.154496i
$83$	−13.5362	+	3.97459i	−1.48579	+	0.436268i	−0.921196	−	0.389098i	$-0.872787\pi$
$83$	−13.5362	+	3.97459i	−1.48579	+	0.436268i	−0.564597	+	0.825367i	$0.690968\pi$
$84$	2.46338	−	0.965283i	0.268777	−	0.105321i
$85$	−10.1103	+	11.6679i	−1.09661	+	1.26556i
$86$	1.79131	+	2.51555i	0.193162	+	0.271259i
$87$	1.94180	+	8.00419i	0.208182	+	0.858139i
$88$	0.368784	−	0.517885i	0.0393125	−	0.0552067i
$89$	5.66211	+	2.26677i	0.600182	+	0.240277i	0.651801	−	0.758390i	$-0.274014\pi$
$89$	5.66211	+	2.26677i	0.600182	+	0.240277i	−0.0516187	+	0.998667i	$0.516438\pi$
$90$	1.76558	+	1.13467i	0.186109	+	0.119605i
$91$	5.27958	−	8.99153i	0.553450	−	0.942568i
$92$	−3.80784	−	2.91554i	−0.396995	−	0.303966i
$93$	−1.44665	+	2.50568i	−0.150011	+	0.259827i
$94$	0.567439	−	11.9120i	0.0585268	−	1.22863i
$95$	2.35556	−	1.85243i	0.241675	−	0.190055i
$96$	0.995472	+	0.0950560i	0.101600	+	0.00970162i
$97$	−8.33765	−	2.44815i	−0.846560	−	0.248572i	−0.170444	−	0.985367i	$-0.554520\pi$
$97$	−8.33765	−	2.44815i	−0.846560	−	0.248572i	−0.676116	+	0.736795i	$0.736338\pi$
$98$	−3.00100	+	6.32408i	−0.303147	+	0.638829i
$99$	0.416342	−	0.480485i	0.0418440	−	0.0482905i
$100$	0.467883	+	0.367947i	0.0467883	+	0.0367947i
$101$	0.111006	+	0.105844i	0.0110455	+	0.0105318i	0.695582	−	0.718447i	$-0.255147\pi$
$101$	0.111006	+	0.105844i	0.0110455	+	0.0105318i	−0.684536	+	0.728979i	$0.739995\pi$
$102$	−2.40597	+	6.95159i	−0.238226	+	0.688310i
$103$	0.388490	+	8.15540i	0.0382790	+	0.803576i	0.933635	+	0.358225i	$0.116618\pi$
$103$	0.388490	+	8.15540i	0.0382790	+	0.803576i	−0.895356	+	0.445351i	$0.853079\pi$
$104$	3.31540	−	2.13068i	0.325101	−	0.208930i
$105$	−5.46000	+	1.01085i	−0.532841	+	0.0986487i
$106$	5.16244	−	1.51583i	0.501421	−	0.147230i
$107$	−5.70759	−	4.48850i	−0.551774	−	0.433920i	0.302947	−	0.953007i	$-0.402029\pi$
$107$	−5.70759	−	4.48850i	−0.551774	−	0.433920i	−0.854721	+	0.519088i	$0.826272\pi$
$108$	0.981929	+	0.189251i	0.0944861	+	0.0182107i
$109$	−4.03060	+	0.384876i	−0.386062	+	0.0368644i	−0.286283	−	0.958145i	$-0.592420\pi$
$109$	−4.03060	+	0.384876i	−0.386062	+	0.0368644i	−0.0997790	+	0.995010i	$0.531814\pi$
$110$	−0.965700	+	0.920793i	−0.0920759	+	0.0877942i
$111$	1.21432	+	2.65900i	0.115259	+	0.252381i
$112$	−2.09164	+	1.62020i	−0.197642	+	0.153094i
$113$	−15.9726	−	10.2650i	−1.50257	−	0.965646i	−0.994545	−	0.104306i	$-0.966738\pi$
$113$	−15.9726	−	10.2650i	−1.50257	−	0.965646i	−0.508029	−	0.861340i	$-0.669626\pi$
$114$	0.713921	−	1.23655i	0.0668649	−	0.115813i
$115$	6.68927	+	7.52086i	0.623778	+	0.701324i
$116$	−4.11818	−	7.13290i	−0.382364	−	0.662273i
$117$	3.50292	−	1.80588i	0.323845	−	0.166954i
$118$	0.708201	+	4.92565i	0.0651952	+	0.453443i
$119$	−7.95499	−	17.7626i	−0.729232	−	1.62830i
$120$	−2.01374	−	0.591287i	−0.183828	−	0.0539769i
$121$	−6.14616	−	8.63108i	−0.558742	−	0.784643i
$122$	7.84401	+	1.51181i	0.710163	+	0.136873i
$123$	−6.86287	+	2.74748i	−0.618804	+	0.247732i
$124$	0.682123	−	2.81175i	0.0612565	−	0.252503i
$125$	−7.69004	−	8.87478i	−0.687818	−	0.793784i
$126$	−2.23618	+	1.41404i	−0.199215	+	0.125972i
$127$	−4.86579	+	3.12705i	−0.431769	+	0.277481i	−0.738420	−	0.674341i	$-0.764428\pi$
$127$	−4.86579	+	3.12705i	−0.431769	+	0.277481i	0.306651	+	0.951822i	$0.400792\pi$
$128$	−0.981929	+	0.189251i	−0.0867911	+	0.0167276i
$129$	−2.23501	−	2.13108i	−0.196782	−	0.187631i
$130$	−7.67875	+	3.07411i	−0.673471	+	0.269617i
$131$	−2.75532	−	7.96097i	−0.240733	−	0.695553i	−0.999046	−	0.0436624i	$-0.986097\pi$
$131$	−2.75532	−	7.96097i	−0.240733	−	0.695553i	0.758313	−	0.651890i	$-0.226024\pi$
$132$	−0.264109	+	0.578319i	−0.0229878	+	0.0503362i
$133$	0.863678	+	3.67766i	0.0748904	+	0.318894i
$134$	2.48690	+	5.44555i	0.214835	+	0.470424i
$135$	−1.94842	−	0.780028i	−0.167693	−	0.0671341i
$136$	0.350021	−	7.34784i	0.0300141	−	0.630072i
$137$	−2.07884	−	3.60066i	−0.177607	−	0.307625i	0.763453	−	0.645863i	$-0.223502\pi$
$137$	−2.07884	−	3.60066i	−0.177607	−	0.307625i	−0.941060	+	0.338238i	$0.890169\pi$
$138$	4.29080	+	2.14221i	0.365257	+	0.182357i
$139$	−3.51350			−0.298011			−0.149006	−	0.988836i	$-0.547607\pi$
$139$	−3.51350			−0.298011			−0.149006	+	0.988836i	$0.547607\pi$
$140$	4.95404	−	2.50816i	0.418693	−	0.211978i
$141$	1.69718	+	11.8041i	0.142928	+	0.994087i
$142$	−0.279134	−	0.0266541i	−0.0234244	−	0.00223676i
$143$	0.590716	+	2.43496i	0.0493981	+	0.203622i
$144$	−0.995472	+	0.0950560i	−0.0829560	+	0.00792134i
$145$	5.65373	+	16.3354i	0.469517	+	1.35658i
$146$	0.446914	−	3.10836i	0.0369869	−	0.257249i
$147$	1.74993	−	6.77774i	0.144332	−	0.559019i
$148$	−1.91426	−	2.20918i	−0.157351	−	0.181593i
$149$	0.234355	+	4.91972i	0.0191991	+	0.403039i	0.987928	+	0.154916i	$0.0495107\pi$
$149$	0.234355	+	4.91972i	0.0191991	+	0.403039i	−0.968729	+	0.248123i	$0.920186\pi$
$150$	−0.529062	−	0.272750i	−0.0431977	−	0.0222700i
$151$	−0.0881684	+	0.254746i	−0.00717505	+	0.0207309i	−0.948531	−	0.316683i	$-0.897431\pi$
$151$	−0.0881684	+	0.254746i	−0.00717505	+	0.0207309i	0.941356	+	0.337414i	$0.109552\pi$
$152$	−0.336627	+	1.38759i	−0.0273040	+	0.112549i
$153$	1.04689	−	7.28130i	0.0846363	−	0.588658i
$154$	−0.538485	−	1.59357i	−0.0433924	−	0.128414i
$155$	−2.52254	+	5.52360i	−0.202615	+	0.443666i
$156$	−2.85225	+	2.71962i	−0.228363	+	0.217743i
$157$	−3.20760	+	4.50444i	−0.255994	+	0.359494i	−0.922494	−	0.386012i	$-0.873852\pi$
$157$	−3.20760	+	4.50444i	−0.255994	+	0.359494i	0.666500	+	0.745505i	$0.267792\pi$
$158$	3.25454	−	2.55940i	0.258917	−	0.203615i
$159$	−4.78228	+	2.46543i	−0.379259	+	0.195522i
$160$	2.09875			0.165921
$161$	−12.1544	+	3.64304i	−0.957897	+	0.287112i
$162$	−1.00000			−0.0785674
$163$	16.1215	−	8.31122i	1.26273	−	0.650985i	0.308836	−	0.951115i	$-0.400060\pi$
$163$	16.1215	−	8.31122i	1.26273	−	0.650985i	0.953898	+	0.300130i	$0.0970302\pi$
$164$	5.81082	−	4.56968i	0.453749	−	0.356832i
$165$	0.773988	−	1.08691i	0.0602549	−	0.0846161i
$166$	−10.2102	+	9.73541i	−0.792466	+	0.755615i
$167$	0.839545	−	1.83835i	0.0649660	−	0.142256i	−0.874364	−	0.485271i	$-0.838721\pi$
$167$	0.839545	−	1.83835i	0.0649660	−	0.142256i	0.939330	+	0.343015i	$0.111448\pi$
$168$	1.74722	−	1.98676i	0.134801	−	0.153282i
$169$	−0.360290	+	2.50587i	−0.0277146	+	0.192759i
$170$	−3.63984	+	15.0036i	−0.279163	+	1.15072i
$171$	−0.467002	+	1.34931i	−0.0357125	+	0.103185i
$172$	2.74488	+	1.41508i	0.209295	+	0.107899i
$173$	1.03885	+	21.8082i	0.0789825	+	1.65805i	0.596678	+	0.802481i	$0.296487\pi$
$173$	1.03885	+	21.8082i	0.0789825	+	1.65805i	−0.517695	+	0.855565i	$0.673210\pi$
$174$	5.39367	+	6.22463i	0.408893	+	0.471888i
$175$	1.51425	−	0.432586i	0.114467	−	0.0327004i
$176$	0.0904799	−	0.629301i	0.00682018	−	0.0474354i
$177$	−1.62759	−	4.70261i	−0.122337	−	0.353470i
$178$	6.07137	−	0.579746i	0.455069	−	0.0434538i
$179$	0.948901	+	3.91142i	0.0709242	+	0.292353i	0.996217	−	0.0868999i	$-0.0276960\pi$
$179$	0.948901	+	3.91142i	0.0709242	+	0.292353i	−0.925293	+	0.379253i	$0.876181\pi$
$180$	2.08925	+	0.199499i	0.155724	+	0.0148698i
$181$	2.25223	+	15.6646i	0.167407	+	1.16434i	0.884219	+	0.467073i	$0.154691\pi$
$181$	2.25223	+	15.6646i	0.167407	+	1.16434i	−0.716812	+	0.697266i	$0.754400\pi$
$182$	0.572517	−	10.4112i	0.0424378	−	0.771732i
$183$	−7.98837			−0.590517
$184$	−4.72052	−	0.846578i	−0.348001	−	0.0624105i
$185$	3.06750	+	5.31306i	0.225527	+	0.390624i
$186$	−0.137669	+	2.89003i	−0.0100944	+	0.211907i
$187$	4.34184	+	1.73821i	0.317507	+	0.127111i
$188$	−4.95404	−	10.8478i	−0.361310	−	0.791159i
$189$	1.92816	−	1.81168i	0.140253	−	0.131781i
$190$	1.24487	−	2.72589i	0.0903124	−	0.197757i
$191$	−1.91842	−	5.54292i	−0.138812	−	0.401072i	0.854072	−	0.520155i	$-0.174126\pi$
$191$	−1.91842	−	5.54292i	−0.138812	−	0.401072i	−0.992884	+	0.119083i	$0.962005\pi$
$192$	0.928368	−	0.371662i	0.0669992	−	0.0268224i
$193$	5.13571	+	4.89689i	0.369676	+	0.352486i	0.852032	−	0.523490i	$-0.175370\pi$
$193$	5.13571	+	4.89689i	0.369676	+	0.352486i	−0.482356	+	0.875976i	$0.660219\pi$
$194$	−8.53261	+	1.64452i	−0.612605	+	0.118070i
$195$	6.95820	−	4.47177i	0.498287	−	0.320230i
$196$	0.230466	+	6.99621i	0.0164618	+	0.499729i
$197$	13.4896	+	15.5678i	0.961092	+	1.10916i	0.993965	+	0.109700i	$0.0349890\pi$
$197$	13.4896	+	15.5678i	0.961092	+	1.10916i	−0.0328725	+	0.999460i	$0.510466\pi$
$198$	0.149889	−	0.617851i	0.0106522	−	0.0439088i
$199$	−4.75326	+	1.90292i	−0.336950	+	0.134894i	−0.533966	−	0.845506i	$-0.679299\pi$
$199$	−4.75326	+	1.90292i	−0.336950	+	0.134894i	0.197016	+	0.980400i	$0.436875\pi$
$200$	0.584474	+	0.112648i	0.0413285	+	0.00796542i
$201$	−3.47254	−	4.87649i	−0.244934	−	0.343961i
$202$	0.147166	+	0.0432118i	0.0103546	+	0.00304037i
$203$	−21.6769	−	2.23046i	−1.52142	−	0.156548i
$204$	1.04689	+	7.28130i	0.0732972	+	0.509793i
$205$	−13.7901	+	7.10931i	−0.963145	+	0.496536i
$206$	4.08233	+	7.07080i	0.284429	+	0.492646i
$207$	−4.61867	−	1.29146i	−0.321020	−	0.0897625i
$208$	1.97051	−	3.41302i	0.136630	−	0.236651i
$209$	−0.763676	−	0.490785i	−0.0528246	−	0.0339483i
$210$	−4.38984	+	3.40039i	−0.302928	+	0.234649i
$211$	−2.95385	−	6.46804i	−0.203352	−	0.445278i	0.780289	−	0.625419i	$-0.215072\pi$
$211$	−2.95385	−	6.46804i	−0.203352	−	0.445278i	−0.983641	+	0.180141i	$0.942345\pi$
$212$	3.89397	−	3.71289i	0.267439	−	0.255002i
$213$	0.279134	−	0.0266541i	0.0191259	−	0.00182631i
$214$	−7.12986	−	1.37417i	−0.487387	−	0.0939362i
$215$	−5.09466	−	4.00648i	−0.347453	−	0.273240i
$216$	0.959493	−	0.281733i	0.0652852	−	0.0191695i
$217$	−4.97037	−	5.82186i	−0.337411	−	0.395213i
$218$	−3.40618	+	2.18902i	−0.230696	+	0.148259i
$219$	0.149422	+	3.13676i	0.0100970	+	0.211963i
$220$	−0.436417	+	1.26094i	−0.0294232	+	0.0850128i
$221$	20.9817	+	20.0060i	1.41138	+	1.34575i
$222$	2.29776	+	1.80698i	0.154216	+	0.121276i
$223$	4.46741	−	5.15567i	0.299160	−	0.345249i	−0.586191	−	0.810173i	$-0.699373\pi$
$223$	4.46741	−	5.15567i	0.299160	−	0.345249i	0.885350	+	0.464924i	$0.153918\pi$
$224$	−1.11671	+	2.39853i	−0.0746132	+	0.160259i
$225$	0.571119	+	0.167696i	0.0380746	+	0.0111797i
$226$	−18.9007	−	1.80480i	−1.25725	−	0.120053i
$227$	13.8416	−	10.8852i	0.918699	−	0.722473i	−0.0422766	−	0.999106i	$-0.513461\pi$
$227$	13.8416	−	10.8852i	0.918699	−	0.722473i	0.960976	+	0.276633i	$0.0892186\pi$
$228$	0.0679395	−	1.42623i	0.00449940	−	0.0944541i
$229$	−3.01973	+	5.23033i	−0.199549	+	0.345630i	−0.948382	−	0.317129i	$-0.897281\pi$
$229$	−3.01973	+	5.23033i	−0.199549	+	0.345630i	0.748833	+	0.662759i	$0.230615\pi$
$230$	9.39192	+	3.61960i	0.619285	+	0.238670i
$231$	0.830340	+	1.46287i	0.0546324	+	0.0962496i
$232$	−6.92887	−	4.45291i	−0.454903	−	0.292348i
$233$	18.3258	+	7.33655i	1.20056	+	0.480633i	0.883797	−	0.467870i	$-0.154979\pi$
$233$	18.3258	+	7.33655i	1.20056	+	0.480633i	0.316766	+	0.948504i	$0.397403\pi$
$234$	2.28602	−	3.21026i	0.149442	−	0.209861i
$235$	5.90075	+	24.3232i	0.384922	+	1.58667i
$236$	2.88654	+	4.05357i	0.187898	+	0.263865i
$237$	−2.71136	+	3.12907i	−0.176122	+	0.203255i
$238$	−15.2100	−	12.1429i	−0.985917	−	0.787106i
$239$	0.536820	−	0.157625i	0.0347240	−	0.0101959i	−0.264324	−	0.964434i	$-0.585149\pi$
$239$	0.536820	−	0.157625i	0.0347240	−	0.0101959i	0.299048	+	0.954238i	$0.403331\pi$
$240$	−2.06083	+	0.397192i	−0.133026	+	0.0256386i
$241$	−23.5461	−	12.1388i	−1.51674	−	0.781931i	−0.519375	−	0.854546i	$-0.673835\pi$
$241$	−23.5461	−	12.1388i	−1.51674	−	0.781931i	−0.997360	+	0.0726147i	$0.976866\pi$
$242$	−9.41792	−	4.85527i	−0.605407	−	0.312109i
$243$	0.981929	−	0.189251i	0.0629908	−	0.0121405i
$244$	7.66479	−	2.25058i	0.490688	−	0.144079i
$245$	2.30389	−	14.5095i	0.147190	−	0.926978i
$246$	−4.84100	+	5.58681i	−0.308651	+	0.356202i
$247$	−3.26407	−	4.58375i	−0.207688	−	0.291657i
$248$	−0.682123	−	2.81175i	−0.0433149	−	0.178546i
$249$	8.18326	−	11.4918i	0.518593	−	0.728262i
$250$	−10.9018	−	4.36444i	−0.689493	−	0.276031i
$251$	−24.7445	−	15.9023i	−1.56186	−	1.00375i	−0.981967	−	0.189053i	$-0.939458\pi$
$251$	−24.7445	−	15.9023i	−1.56186	−	1.00375i	−0.579892	−	0.814693i	$-0.696905\pi$
$252$	−1.33965	+	2.28152i	−0.0843898	+	0.143722i
$253$	1.49022	−	2.66008i	0.0936892	−	0.167238i
$254$	−2.89199	+	5.00907i	−0.181460	+	0.314297i
$255$	0.734608	−	15.4213i	0.0460029	−	0.965721i
$256$	−0.786053	+	0.618159i	−0.0491283	+	0.0386349i
$257$	26.5564	+	2.53583i	1.65655	+	0.158181i	0.881002	−	0.473113i	$-0.156870\pi$
$257$	26.5564	+	2.53583i	1.65655	+	0.158181i	0.775544	+	0.631294i	$0.217476\pi$
$258$	−2.96308	−	0.870038i	−0.184473	−	0.0541662i
$259$	−7.70412	+	0.678667i	−0.478711	+	0.0421703i
$260$	−5.41651	+	6.25098i	−0.335917	+	0.387669i
$261$	−6.47422	−	5.09138i	−0.400744	−	0.315149i
$262$	−6.09695	−	5.81343i	−0.376671	−	0.359155i
$263$	9.05143	−	26.1524i	0.558135	−	1.61263i	−0.213767	−	0.976885i	$-0.568573\pi$
$263$	9.05143	−	26.1524i	0.558135	−	1.61263i	0.771902	−	0.635741i	$-0.219305\pi$
$264$	0.0302513	+	0.635052i	0.00186184	+	0.0390848i
$265$	−9.49952	+	6.10497i	−0.583551	+	0.375026i
$266$	2.45287	+	2.87308i	0.150395	+	0.176160i
$267$	−5.85194	+	1.71828i	−0.358133	+	0.105157i
$268$	4.70574	+	3.70063i	0.287449	+	0.226052i
$269$	7.78093	+	1.49965i	0.474411	+	0.0914353i	0.420852	−	0.907129i	$-0.361731\pi$
$269$	7.78093	+	1.49965i	0.474411	+	0.0914353i	0.0535595	+	0.998565i	$0.482943\pi$
$270$	−2.08925	+	0.199499i	−0.127148	+	0.0121411i
$271$	−16.7526	+	15.9736i	−1.01765	+	0.970325i	−0.999564	−	0.0295117i	$-0.990605\pi$
$271$	−16.7526	+	15.9736i	−1.01765	+	0.970325i	−0.0180830	+	0.999836i	$0.505756\pi$
$272$	−3.05587	−	6.69141i	−0.185289	−	0.405727i
$273$	1.40817	+	10.3314i	0.0852262	+	0.625287i
$274$	−3.49766	−	2.24781i	−0.211302	−	0.135795i
$275$	−0.189216	+	0.327731i	−0.0114101	+	0.0197629i
$276$	4.79543	−	0.0620853i	0.288651	−	0.00373710i
$277$	8.16315	+	14.1390i	0.490476	+	0.849529i	0.999940	−	0.0109628i	$-0.00348964\pi$
$277$	8.16315	+	14.1390i	0.490476	+	0.849529i	−0.509464	+	0.860492i	$0.670156\pi$
$278$	−3.12292	+	1.60998i	−0.187301	+	0.0965601i
$279$	−0.411761	−	2.86386i	−0.0246515	−	0.171455i
$280$	3.25402	−	4.49942i	0.194465	−	0.268891i
$281$	−7.65201	−	2.24683i	−0.456481	−	0.134035i	0.0454051	−	0.998969i	$-0.485542\pi$
$281$	−7.65201	−	2.24683i	−0.456481	−	0.134035i	−0.501886	+	0.864934i	$0.667360\pi$
$282$	6.91748	+	9.71424i	0.411930	+	0.578474i
$283$	1.48491	+	0.286192i	0.0882685	+	0.0170124i	0.233194	−	0.972430i	$-0.425082\pi$
$283$	1.48491	+	0.286192i	0.0882685	+	0.0170124i	−0.144926	+	0.989443i	$0.546294\pi$
$284$	−0.260318	+	0.104216i	−0.0154470	+	0.00618405i
$285$	−0.706497	+	2.91222i	−0.0418493	+	0.172505i
$286$	1.64081	+	1.89360i	0.0970234	+	0.111971i
$287$	−0.787304	−	19.5426i	−0.0464731	−	1.15356i
$288$	−0.841254	+	0.540641i	−0.0495713	+	0.0318576i
$289$	36.4426	−	7.02374i	2.14369	−	0.413161i
$290$	12.5105	+	11.9288i	0.734644	+	0.700482i
$291$	8.06718	−	3.22961i	0.472907	−	0.189323i
$292$	−1.02710	−	2.96761i	−0.0601064	−	0.173666i
$293$	−11.6808	+	25.5774i	−0.682400	+	1.49425i	0.177680	+	0.984088i	$0.443141\pi$
$293$	−11.6808	+	25.5774i	−0.682400	+	1.49425i	−0.860080	+	0.510159i	$0.829586\pi$
$294$	−1.55034	−	6.82616i	−0.0904177	−	0.398110i
$295$	−4.33861	−	9.50023i	−0.252604	−	0.553125i
$296$	−2.71377	−	1.08643i	−0.157735	−	0.0631474i
$297$	−0.0302513	+	0.635052i	−0.00175536	+	0.0368495i
$298$	2.46265	+	4.26543i	0.142657	+	0.247090i
$299$	14.7043	−	11.8748i	0.850370	−	0.686740i
$300$	−0.595230			−0.0343656
$301$	7.28953	−	3.69058i	0.420161	−	0.212722i
$302$	0.0383641	+	0.266828i	0.00220761	+	0.0153542i
$303$	−0.152684	−	0.0145796i	−0.00877149	−	0.000837575i
$304$	0.336627	+	1.38759i	0.0193069	+	0.0795840i
$305$	−16.6897	+	1.59367i	−0.955650	+	0.0912535i
$306$	−2.40597	−	6.95159i	−0.137540	−	0.397396i
$307$	1.10716	−	7.70043i	0.0631887	−	0.439487i	−0.933527	−	0.358507i	$-0.883286\pi$
$307$	1.10716	−	7.70043i	0.0631887	−	0.439487i	0.996716	−	0.0809800i	$-0.0258050\pi$
$308$	−1.20884	−	1.16968i	−0.0688802	−	0.0666486i
$309$	−5.34671	−	6.17043i	−0.304164	−	0.351024i
$310$	0.288934	+	6.06546i	0.0164103	+	0.344495i
$311$	29.4974	+	15.2070i	1.67265	+	0.862309i	0.991492	+	0.130169i	$0.0415521\pi$
$311$	29.4974	+	15.2070i	1.67265	+	0.862309i	0.681155	+	0.732140i	$0.261478\pi$
$312$	−1.28898	+	3.72427i	−0.0729742	+	0.210845i
$313$	−3.92069	+	16.1613i	−0.221610	+	0.913491i	0.746983	+	0.664843i	$0.231501\pi$
$313$	−3.92069	+	16.1613i	−0.221610	+	0.913491i	−0.968594	+	0.248648i	$0.920014\pi$
$314$	−0.786973	+	5.47351i	−0.0444114	+	0.308888i
$315$	3.66698	−	4.16973i	0.206611	−	0.234938i
$316$	1.71997	−	3.76620i	0.0967557	−	0.211865i
$317$	15.2959	−	14.5846i	0.859101	−	0.819151i	−0.125839	−	0.992051i	$-0.540162\pi$
$317$	15.2959	−	14.5846i	0.859101	−	0.819151i	0.984939	+	0.172900i	$0.0553137\pi$
$318$	−3.12093	+	4.38273i	−0.175013	+	0.245771i
$319$	4.11613	−	3.23696i	0.230459	−	0.181235i
$320$	1.86545	−	0.961705i	0.104282	−	0.0537609i
$321$	7.26108			0.405274
$322$	−9.13388	+	8.80751i	−0.509011	+	0.490823i
$323$	−10.5035			−0.584428
$324$	−0.888835	+	0.458227i	−0.0493797	+	0.0254570i
$325$	−1.84393	+	1.45009i	−0.102283	+	0.0804363i
$326$	10.5210	−	14.7746i	0.582702	−	0.818290i
$327$	2.93035	−	2.79409i	0.162049	−	0.154513i
$328$	3.07092	−	6.72437i	0.169563	−	0.371291i
$329$	−30.9371	−	6.19834i	−1.70562	−	0.341725i
$330$	0.189895	−	1.32075i	0.0104534	−	0.0727048i
$331$	−3.46447	+	14.2807i	−0.190424	+	0.784940i	0.793824	+	0.608148i	$0.208087\pi$
$331$	−3.46447	+	14.2807i	−0.190424	+	0.784940i	−0.984248	+	0.176792i	$0.943428\pi$
$332$	−4.61417	+	13.3318i	−0.253235	+	0.731676i
$333$	−2.59821	−	1.33947i	−0.142381	−	0.0734025i
$334$	−0.0961621	−	2.01869i	−0.00526175	−	0.110458i
$335$	−8.22785	−	9.49545i	−0.449536	−	0.518792i
$336$	0.642602	−	2.56653i	0.0350568	−	0.140016i
$337$	−4.69315	+	32.6416i	−0.255652	+	1.77810i	0.307302	+	0.951612i	$0.400574\pi$
$337$	−4.69315	+	32.6416i	−0.255652	+	1.77810i	−0.562954	+	0.826488i	$0.690335\pi$
$338$	0.828019	+	2.39240i	0.0450383	+	0.130130i
$339$	18.9007	−	1.80480i	1.02654	−	0.0980230i
$340$	3.63984	+	15.0036i	0.197398	+	0.813685i
$341$	1.83116	+	0.174854i	0.0991626	+	0.00946888i
$342$	0.203203	+	1.41331i	0.0109880	+	0.0764230i
$343$	15.3561	+	10.3532i	0.829154	+	0.559021i
$344$	3.08817			0.166503
$345$	−9.90721	−	1.77676i	−0.533386	−	0.0956575i
$346$	10.9165	+	18.9079i	0.586872	+	1.01649i
$347$	−0.485610	+	10.1942i	−0.0260689	+	0.547254i	0.947624	+	0.319389i	$0.103478\pi$
$347$	−0.485610	+	10.1942i	−0.0260689	+	0.547254i	−0.973693	+	0.227865i	$0.926825\pi$
$348$	7.64637	+	3.06115i	0.409889	+	0.164095i
$349$	−13.0469	−	28.5688i	−0.698385	−	1.52925i	−0.841918	−	0.539605i	$-0.818573\pi$
$349$	−13.0469	−	28.5688i	−0.698385	−	1.52925i	0.143533	−	0.989646i	$-0.454154\pi$
$350$	1.14770	−	1.07837i	0.0613471	−	0.0576412i
$351$	−1.63716	+	3.58488i	−0.0873851	+	0.191347i
$352$	−0.207941	−	0.600806i	−0.0110833	−	0.0320230i
$353$	−16.8090	+	6.72931i	−0.894654	+	0.358165i	−0.772999	−	0.634407i	$-0.781244\pi$
$353$	−16.8090	+	6.72931i	−0.894654	+	0.358165i	−0.121655	+	0.992573i	$0.538820\pi$
$354$	−3.60152	−	3.43404i	−0.191419	−	0.182517i
$355$	0.577863	−	0.111374i	0.0306698	−	0.00591112i
$356$	5.13080	−	3.29736i	0.271932	−	0.174760i
$357$	17.2332	+	9.04494i	0.912077	+	0.478709i
$358$	2.63573	+	3.04180i	0.139303	+	0.160764i
$359$	7.00565	−	28.8777i	0.369744	−	1.52411i	−0.418197	−	0.908356i	$-0.637338\pi$
$359$	7.00565	−	28.8777i	0.369744	−	1.52411i	0.787941	−	0.615750i	$-0.211147\pi$
$360$	1.94842	−	0.780028i	0.102691	−	0.0411111i
$361$	−16.6548	−	3.20994i	−0.876566	−	0.168944i
$362$	9.17978	+	12.8912i	0.482479	+	0.677546i
$363$	10.1666	+	2.98518i	0.533608	+	0.156681i
$364$	−4.26183	−	9.51621i	−0.223380	−	0.498785i
$365$	0.937963	+	6.52368i	0.0490952	+	0.341465i
$366$	−7.10035	+	3.66048i	−0.371141	+	0.191337i
$367$	5.49222	+	9.51281i	0.286692	+	0.496565i	0.973018	−	0.230729i	$-0.0741111\pi$
$367$	5.49222	+	9.51281i	0.286692	+	0.496565i	−0.686326	+	0.727294i	$0.740778\pi$
$368$	−4.58369	+	1.41060i	−0.238941	+	0.0735326i
$369$	3.69620	−	6.40201i	0.192417	−	0.333275i
$370$	5.16109	+	3.31683i	0.268312	+	0.172434i
$371$	−1.92247	−	14.1047i	−0.0998095	−	0.732282i
$372$	1.20192	+	2.63184i	0.0623168	+	0.136455i
$373$	−13.2021	+	12.5882i	−0.683578	+	0.651790i	−0.950066	−	0.312048i	$-0.898985\pi$
$373$	−13.2021	+	12.5882i	−0.683578	+	0.651790i	0.266488	+	0.963838i	$0.414137\pi$
$374$	4.65568	−	0.444563i	0.240739	−	0.0229878i
$375$	11.5308	+	2.22238i	0.595448	+	0.114763i
$376$	−9.37409	−	7.37186i	−0.483432	−	0.380175i
$377$	31.1448	−	9.14495i	1.60404	−	0.470989i
$378$	0.883657	−	2.49382i	0.0454504	−	0.128268i
$379$	−19.0478	+	12.2413i	−0.978419	+	0.628792i	−0.929037	−	0.369988i	$-0.879362\pi$
$379$	−19.0478	+	12.2413i	−0.978419	+	0.628792i	−0.0493828	+	0.998780i	$0.515725\pi$
$380$	−0.142588	−	2.99330i	−0.00731463	−	0.153553i
$381$	1.89175	−	5.46586i	0.0969175	−	0.280025i
$382$	−4.24508	−	4.04767i	−0.217197	−	0.207097i
$383$	3.77325	+	2.96732i	0.192804	+	0.151623i	0.709895	−	0.704308i	$-0.248743\pi$
$383$	3.77325	+	2.96732i	0.192804	+	0.151623i	−0.517091	+	0.855931i	$0.672985\pi$
$384$	0.654861	−	0.755750i	0.0334182	−	0.0385667i
$385$	2.02663	+	2.89065i	0.103287	+	0.147321i
$386$	6.80868	+	1.99921i	0.346553	+	0.101757i
$387$	3.07419	+	0.293549i	0.156270	+	0.0149220i
$388$	−6.83052	+	5.37158i	−0.346767	+	0.272701i
$389$	1.35091	−	28.3591i	0.0684940	−	1.43787i	−0.659202	−	0.751966i	$-0.729106\pi$
$389$	1.35091	−	28.3591i	0.0684940	−	1.43787i	0.727696	−	0.685900i	$-0.240591\pi$
$390$	4.13562	−	7.16310i	0.209415	−	0.362718i
$391$	−2.13469	−	35.2143i	−0.107956	−	1.78087i
$392$	3.41069	+	6.11287i	0.172266	+	0.308747i
$393$	7.08697	+	4.55452i	0.357490	+	0.229745i
$394$	19.1236	+	7.65593i	0.963432	+	0.385700i
$395$	−5.04046	+	7.07833i	−0.253613	+	0.356149i
$396$	−0.149889	−	0.617851i	−0.00753221	−	0.0310482i
$397$	12.3014	+	17.2749i	0.617390	+	0.867003i	0.998340	−	0.0575929i	$-0.0183425\pi$
$397$	12.3014	+	17.2749i	0.617390	+	0.867003i	−0.380950	+	0.924595i	$0.624403\pi$
$398$	−3.35290	+	3.86945i	−0.168066	+	0.193958i
$399$	−2.95228	−	2.35695i	−0.147799	−	0.117995i
$400$	0.571119	−	0.167696i	0.0285560	−	0.00838479i
$401$	11.4332	−	2.20357i	0.570947	−	0.110041i	0.104397	−	0.994536i	$-0.466709\pi$
$401$	11.4332	−	2.20357i	0.570947	−	0.110041i	0.466550	+	0.884495i	$0.345497\pi$
$402$	−5.32105	−	2.74319i	−0.265390	−	0.136818i
$403$	10.1350	+	5.22497i	0.504861	+	0.260274i
$404$	0.150607	−	0.0290271i	0.00749298	−	0.00144415i
$405$	2.01374	−	0.591287i	0.100064	−	0.0293813i
$406$	−20.2893	+	7.95042i	−1.00694	+	0.394573i
$407$	1.21704	−	1.40453i	0.0603262	−	0.0696202i
$408$	4.26700	+	5.99216i	0.211248	+	0.296656i
$409$	−8.25136	−	34.0126i	−0.408003	−	1.68181i	−0.691130	−	0.722730i	$-0.742887\pi$
$409$	−8.25136	−	34.0126i	−0.408003	−	1.68181i	0.283127	−	0.959082i	$-0.408628\pi$
$410$	−8.99949	+	12.6380i	−0.444453	+	0.624147i
$411$	3.85986	+	1.54525i	0.190393	+	0.0762217i
$412$	6.86854	+	4.41414i	0.338389	+	0.217469i
$413$	13.1657	+	0.0965740i	0.647842	+	0.00475209i
$414$	−4.69702	+	0.968504i	−0.230846	+	0.0475994i
$415$	14.8043	−	25.6418i	0.726713	−	1.25870i
$416$	0.187521	−	3.93656i	0.00919399	−	0.193006i
$417$	2.76180	−	2.17190i	0.135246	−	0.106358i
$418$	−0.903673	−	0.0862903i	−0.0442001	−	0.00422060i
$419$	16.7988	+	4.93257i	0.820674	+	0.240972i	0.665006	−	0.746838i	$-0.268429\pi$
$419$	16.7988	+	4.93257i	0.820674	+	0.240972i	0.155668	+	0.987809i	$0.450247\pi$
$420$	−2.34370	+	5.03393i	−0.114361	+	0.245631i
$421$	16.2220	−	18.7212i	0.790612	−	0.912415i	−0.207215	−	0.978295i	$-0.566440\pi$
$421$	16.2220	−	18.7212i	0.790612	−	0.912415i	0.997828	+	0.0658803i	$0.0209855\pi$
$422$	−5.58932	−	4.39549i	−0.272084	−	0.213969i
$423$	−8.63090	−	8.22955i	−0.419649	−	0.400134i
$424$	1.75975	−	5.08447i	0.0854611	−	0.246924i
$425$	0.208343	+	4.37366i	0.0101061	+	0.212154i
$426$	0.235891	−	0.151598i	0.0114289	−	0.00734493i
$427$	7.05898	−	19.9216i	0.341608	−	0.964073i
$428$	−6.96695	+	2.04568i	−0.336760	+	0.0988818i
$429$	−1.96953	−	1.54885i	−0.0950897	−	0.0747794i
$430$	−6.36419	−	1.22660i	−0.306908	−	0.0591517i
$431$	−3.53090	+	0.337160i	−0.170078	+	0.0162404i	−0.179747	−	0.983713i	$-0.557528\pi$
$431$	−3.53090	+	0.337160i	−0.170078	+	0.0162404i	0.00966975	+	0.999953i	$0.496922\pi$
$432$	0.723734	−	0.690079i	0.0348207	−	0.0332014i
$433$	12.8761	+	28.1947i	0.618785	+	1.35495i	0.916400	+	0.400264i	$0.131081\pi$
$433$	12.8761	+	28.1947i	0.618785	+	1.35495i	−0.297615	+	0.954686i	$0.596191\pi$
$434$	−7.08557	−	2.89712i	−0.340118	−	0.139066i
$435$	−14.5420	−	9.34557i	−0.697235	−	0.448086i
$436$	−2.02447	+	3.50648i	−0.0969544	+	0.167930i
$437$	−0.886701	+	6.79004i	−0.0424167	+	0.324812i
$438$	1.57016	+	2.71960i	0.0750252	+	0.129947i
$439$	−18.1028	+	9.33265i	−0.864000	+	0.445423i	−0.832464	−	0.554080i	$-0.813070\pi$
$439$	−18.1028	+	9.33265i	−0.864000	+	0.445423i	−0.0315362	+	0.999503i	$0.510040\pi$
$440$	0.189895	+	1.32075i	0.00905289	+	0.0629642i
$441$	2.81418	+	6.40940i	0.134009	+	0.305209i
$442$	27.8165	+	8.16766i	1.32310	+	0.388496i
$443$	0.791901	+	1.11207i	0.0376244	+	0.0528360i	0.832960	−	0.553334i	$-0.186645\pi$
$443$	0.791901	+	1.11207i	0.0376244	+	0.0528360i	−0.795335	+	0.606170i	$0.792705\pi$
$444$	2.87034	+	0.553212i	0.136220	+	0.0262543i
$445$	−11.8834	+	4.75738i	−0.563326	+	0.225522i
$446$	1.60833	−	6.62963i	0.0761566	−	0.313922i
$447$	−3.22538	−	3.72229i	−0.152555	−	0.176058i
$448$	0.106502	+	2.64361i	0.00503173	+	0.124899i
$449$	−15.9050	+	10.2215i	−0.750605	+	0.482384i	−0.859161	−	0.511706i	$-0.829014\pi$
$449$	−15.9050	+	10.2215i	−0.750605	+	0.482384i	0.108556	+	0.994090i	$0.465377\pi$
$450$	0.584474	−	0.112648i	0.0275524	−	0.00531028i
$451$	3.40147	+	3.24329i	0.160169	+	0.152721i
$452$	−17.6266	+	7.05662i	−0.829085	+	0.331916i
$453$	−0.0881684	−	0.254746i	−0.00414251	−	0.0119690i
$454$	7.31504	−	16.0177i	0.343312	−	0.751748i
$455$	5.00313	+	21.3040i	0.234550	+	0.998748i
$456$	−0.593147	−	1.29881i	−0.0277767	−	0.0608224i
$457$	−30.8575	−	12.3535i	−1.44345	−	0.577871i	−0.487955	−	0.872869i	$-0.662257\pi$
$457$	−30.8575	−	12.3535i	−1.44345	−	0.577871i	−0.955498	+	0.294998i	$0.904681\pi$
$458$	−0.287369	+	6.03262i	−0.0134279	+	0.281886i
$459$	3.67809	+	6.37064i	0.171678	+	0.297356i
$460$	10.0065	−	1.08640i	0.466554	−	0.0506535i
$461$	9.78295			0.455637			0.227819	−	0.973704i	$-0.426841\pi$
$461$	9.78295			0.455637			0.227819	+	0.973704i	$0.426841\pi$
$462$	1.40836	+	0.919765i	0.0655229	+	0.0427913i
$463$	4.67051	+	32.4841i	0.217057	+	1.50966i	0.748822	+	0.662772i	$0.230620\pi$
$463$	4.67051	+	32.4841i	0.217057	+	1.50966i	−0.531765	+	0.846892i	$0.678471\pi$
$464$	−8.19907	−	0.782916i	−0.380632	−	0.0363460i
$465$	−1.43161	−	5.90117i	−0.0663893	−	0.273660i
$466$	19.6504	−	1.87639i	0.910288	−	0.0869220i
$467$	−5.68194	−	16.4169i	−0.262929	−	0.759683i	−0.996766	−	0.0803579i	$-0.974394\pi$
$467$	−5.68194	−	16.4169i	−0.262929	−	0.759683i	0.733837	−	0.679325i	$-0.237728\pi$
$468$	0.560866	−	3.90091i	0.0259260	−	0.180319i
$469$	15.2296	−	4.35074i	0.703239	−	0.200899i
$470$	16.3903	+	18.9154i	0.756029	+	0.872505i
$471$	−0.263118	−	5.52354i	−0.0121239	−	0.254511i
$472$	4.42311	+	2.28027i	0.203590	+	0.104958i
$473$	−0.642157	+	1.85539i	−0.0295264	+	0.0853109i
$474$	−0.976126	+	4.02365i	−0.0448349	+	0.184812i
$475$	0.120953	−	0.841244i	0.00554969	−	0.0385989i
$476$	−19.0834	−	3.82340i	−0.874685	−	0.175245i
$477$	2.23509	−	4.89417i	0.102338	−	0.224089i
$478$	0.404917	−	0.386088i	0.0185205	−	0.0176592i
$479$	−24.6754	+	34.6518i	−1.12745	+	1.58328i	−0.371790	+	0.928317i	$0.621256\pi$
$479$	−24.6754	+	34.6518i	−1.12745	+	1.58328i	−0.755659	+	0.654965i	$0.772683\pi$
$480$	−1.64973	+	1.29736i	−0.0752996	+	0.0592163i
$481$	10.2396	−	5.27888i	0.466885	−	0.240696i
$482$	−26.4909			−1.20663
$483$	7.30199	−	10.3769i	0.332252	−	0.472167i
$484$	−10.5958			−0.481627
$485$	16.2101	−	8.35687i	0.736061	−	0.379466i
$486$	0.786053	−	0.618159i	0.0356561	−	0.0280403i
$487$	5.28819	−	7.42623i	0.239631	−	0.336514i	−0.677194	−	0.735805i	$-0.736804\pi$
$487$	5.28819	−	7.42623i	0.239631	−	0.336514i	0.916825	+	0.399290i	$0.130743\pi$
$488$	5.78146	−	5.51261i	0.261714	−	0.249544i
$489$	−7.53471	+	16.4987i	−0.340731	+	0.746098i
$490$	−4.60087	−	13.9523i	−0.207846	−	0.630299i
$491$	−2.36593	+	16.4554i	−0.106773	+	0.742622i	0.864151	+	0.503233i	$0.167856\pi$
$491$	−2.36593	+	16.4554i	−0.106773	+	0.742622i	−0.970924	+	0.239389i	$0.923053\pi$
$492$	−1.74283	+	7.18402i	−0.0785726	+	0.323881i
$493$	19.8164	−	57.2558i	0.892487	−	2.57867i
$494$	−5.00162	−	2.57851i	−0.225033	−	0.116013i
$495$	0.0634900	+	1.33282i	0.00285366	+	0.0599058i
$496$	−1.89471	−	2.18662i	−0.0850751	−	0.0981819i
$497$	−0.180188	+	0.719664i	−0.00808254	+	0.0322813i
$498$	2.00773	−	13.9641i	0.0899686	−	0.625746i
$499$	−12.8160	−	37.0293i	−0.573722	−	1.65766i	−0.740808	−	0.671717i	$-0.765557\pi$
$499$	−12.8160	−	37.0293i	−0.573722	−	1.65766i	0.167086	−	0.985942i	$-0.446564\pi$
$500$	−11.6898	+	1.11624i	−0.522786	+	0.0499200i
$501$	0.476464	+	1.96401i	0.0212868	+	0.0877455i
$502$	−29.2807	−	2.79596i	−1.30686	−	0.124790i
$503$	−1.02098	−	7.10105i	−0.0455231	−	0.316620i	−0.999841	−	0.0178272i	$-0.994325\pi$
$503$	−1.02098	−	7.10105i	−0.0455231	−	0.316620i	0.954318	−	0.298793i	$-0.0965840\pi$
$504$	−0.145271	+	2.64176i	−0.00647090	+	0.117673i
$505$	−0.321905			−0.0143246
$506$	0.105640	−	3.04723i	0.00469629	−	0.135466i
$507$	−1.26582	−	2.19247i	−0.0562171	−	0.0973708i
$508$	−0.275213	+	5.77743i	−0.0122106	+	0.256332i
$509$	−32.3570	−	12.9538i	−1.43420	−	0.574167i	−0.481057	−	0.876689i	$-0.659747\pi$
$509$	−32.3570	−	12.9538i	−1.43420	−	0.574167i	−0.953142	+	0.302523i	$0.902171\pi$
$510$	−6.41351	−	14.0436i	−0.283995	−	0.621863i
$511$	−7.95457	−	2.39919i	−0.351890	−	0.106134i
$512$	−0.415415	+	0.909632i	−0.0183589	+	0.0402004i
$513$	−0.467002	−	1.34931i	−0.0206186	−	0.0595736i
$514$	24.7663	−	9.91493i	1.09239	−	0.437329i
$515$	−12.4016	−	11.8249i	−0.546480	−	0.521068i
$516$	−3.03236	+	0.584440i	−0.133492	+	0.0257285i
$517$	6.37831	−	4.09909i	0.280518	−	0.180278i
$518$	−6.53671	+	4.13346i	−0.287207	+	0.181614i
$519$	−14.2975	−	16.5002i	−0.627592	−	0.724279i
$520$	−1.95002	+	8.03808i	−0.0855139	+	0.352493i
$521$	15.5415	−	6.22188i	0.680885	−	0.272585i	−0.00532788	−	0.999986i	$-0.501696\pi$
$521$	15.5415	−	6.22188i	0.680885	−	0.272585i	0.686213	+	0.727400i	$0.259272\pi$
$522$	−8.08752	−	1.55874i	−0.353981	−	0.0682243i
$523$	−18.3277	−	25.7377i	−0.801415	−	1.12543i	−0.989678	−	0.143311i	$-0.954225\pi$
$523$	−18.3277	−	25.7377i	−0.801415	−	1.12543i	0.188263	−	0.982119i	$-0.439714\pi$
$524$	−8.08305	−	2.37340i	−0.353110	−	0.103682i
$525$	−0.922877	+	1.27608i	−0.0402776	+	0.0556929i
$526$	−3.93849	−	27.3928i	−0.171726	−	1.19438i
$527$	18.9177	−	9.75275i	0.824067	−	0.424836i
$528$	0.317886	+	0.550595i	0.0138342	+	0.0239616i
$529$	−22.9448	−	1.59280i	−0.997599	−	0.0692522i
$530$	−5.64605	+	9.77925i	−0.245249	+	0.424783i
$531$	4.18633	+	2.69039i	0.181671	+	0.116753i
$532$	3.49672	+	1.42972i	0.151602	+	0.0619863i
$533$	12.1025	+	26.5009i	0.524219	+	1.14788i
$534$	−4.41405	+	4.20879i	−0.191014	+	0.182132i
$535$	15.1702	−	1.44858i	0.655865	−	0.0626276i
$536$	5.87836	+	1.13296i	0.253906	+	0.0489364i
$537$	−3.16377	−	2.48801i	−0.136527	−	0.107366i
$538$	7.60314	−	2.23248i	0.327795	−	0.0962492i
$539$	−4.38187	+	0.778048i	−0.188740	+	0.0335129i
$540$	−1.76558	+	1.13467i	−0.0759787	+	0.0488285i
$541$	−0.515340	−	10.8183i	−0.0221562	−	0.465116i	−0.982496	−	0.186284i	$-0.940356\pi$
$541$	−0.515340	−	10.8183i	−0.0221562	−	0.465116i	0.960340	−	0.278832i	$-0.0899473\pi$
$542$	−7.57079	+	21.8744i	−0.325193	+	0.939584i
$543$	−11.4536	−	10.9210i	−0.491520	−	0.468663i
$544$	−5.78235	−	4.54729i	−0.247916	−	0.194963i
$545$	5.56482	−	6.42215i	0.238371	−	0.275095i
$546$	5.98577	+	8.53769i	0.256167	+	0.365379i
$547$	37.0243	+	10.8713i	1.58304	+	0.464824i	0.950764	−	0.309916i	$-0.100301\pi$
$547$	37.0243	+	10.8713i	1.58304	+	0.464824i	0.632280	+	0.774740i	$0.282119\pi$
$548$	−4.13885	−	0.395213i	−0.176803	−	0.0168826i
$549$	6.27928	−	4.93808i	0.267993	−	0.210752i
$550$	−0.0180065	+	0.378002i	−0.000767799	+	0.0161181i
$551$	−5.88011	+	10.1847i	−0.250501	+	0.433881i
$552$	4.23390	−	2.25258i	0.180207	−	0.0958760i
$553$	−5.40744	−	9.52667i	−0.229948	−	0.405115i
$554$	13.7345	+	8.82666i	0.583525	+	0.375009i
$555$	−5.69553	−	2.28015i	−0.241762	−	0.0967869i
$556$	−2.03803	+	2.86201i	−0.0864317	+	0.121376i
$557$	9.91318	+	40.8627i	0.420035	+	1.73141i	0.651577	+	0.758583i	$0.274108\pi$
$557$	9.91318	+	40.8627i	0.420035	+	1.73141i	−0.231542	+	0.972825i	$0.574377\pi$
$558$	−1.67828	−	2.35682i	−0.0710474	−	0.0997721i
$559$	−7.97001	+	9.19788i	−0.337096	+	0.389029i
$560$	0.830538	−	5.49032i	0.0350966	−	0.232008i
$561$	−4.48741	+	1.31762i	−0.189459	+	0.0556301i
$562$	−7.83094	+	1.50929i	−0.330328	+	0.0636656i
$563$	−16.2237	−	8.36389i	−0.683747	−	0.352496i	0.0811021	−	0.996706i	$-0.474156\pi$
$563$	−16.2237	−	8.36389i	−0.683747	−	0.352496i	−0.764849	+	0.644210i	$0.777186\pi$
$564$	10.5998	+	5.46459i	0.446333	+	0.230101i
$565$	39.1282	−	7.54134i	1.64614	−	0.317267i
$566$	1.45098	−	0.426046i	0.0609892	−	0.0179080i
$567$	−0.395729	+	2.61599i	−0.0166190	+	0.109861i
$568$	−0.183625	+	0.211915i	−0.00770475	+	0.00889175i
$569$	−14.9203	−	20.9526i	−0.625492	−	0.878380i	0.373290	−	0.927715i	$-0.378229\pi$
$569$	−14.9203	−	20.9526i	−0.625492	−	0.878380i	−0.998782	+	0.0493341i	$0.984290\pi$
$570$	0.706497	+	2.91222i	0.0295919	+	0.121979i
$571$	−3.42797	+	4.81390i	−0.143456	+	0.201456i	−0.880052	−	0.474877i	$-0.842492\pi$
$571$	−3.42797	+	4.81390i	−0.143456	+	0.201456i	0.736596	+	0.676333i	$0.236432\pi$
$572$	2.32611	+	0.931235i	0.0972596	+	0.0389369i
$573$	4.93439	+	3.17114i	0.206137	+	0.132476i
$574$	−9.65473	−	17.0094i	−0.402980	−	0.709959i
$575$	2.84497	+	0.234539i	0.118644	+	0.00978094i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	1.55639	−	32.6726i	0.0647932	−	1.36018i	−0.699188	−	0.714938i	$-0.746455\pi$
$577$	1.55639	−	32.6726i	0.0647932	−	1.36018i	0.763981	−	0.645239i	$-0.223242\pi$
$578$	29.1730	−	22.9419i	1.21344	−	0.954259i
$579$	−7.06399	−	0.674530i	−0.293570	−	0.0280325i
$580$	16.5859	+	4.87006i	0.688692	+	0.202218i
$581$	21.4273	+	30.5624i	0.888953	+	1.26794i
$582$	5.69050	−	6.56719i	0.235879	−	0.272219i
$583$	2.68885	+	2.11454i	0.111361	+	0.0875752i
$584$	−2.27276	−	2.16707i	−0.0940474	−	0.0896740i
$585$	−2.70526	+	7.81632i	−0.111849	+	0.323165i
$586$	1.33793	+	28.0866i	0.0552693	+	1.16025i
$587$	−36.9657	+	23.7564i	−1.52574	+	0.980533i	−0.534986	+	0.844861i	$0.679683\pi$
$587$	−36.9657	+	23.7564i	−1.52574	+	0.980533i	−0.990754	+	0.135672i	$0.956681\pi$
$588$	−4.50593	−	5.35692i	−0.185821	−	0.220916i
$589$	−3.96385	+	1.16389i	−0.163327	+	0.0479572i
$590$	−8.20956	−	6.45607i	−0.337982	−	0.265792i
$591$	−20.2269	−	3.89841i	−0.832023	−	0.160359i
$592$	−2.90992	+	0.277864i	−0.119597	+	0.0114201i
$593$	−12.1546	+	11.5894i	−0.499129	+	0.475919i	−0.897318	−	0.441385i	$-0.854487\pi$
$593$	−12.1546	+	11.5894i	−0.499129	+	0.475919i	0.398189	+	0.917303i	$0.369639\pi$
$594$	0.264109	+	0.578319i	0.0108365	+	0.0237287i
$595$	37.8089	+	15.4591i	1.55001	+	0.633763i
$596$	4.14342	+	2.66282i	0.169721	+	0.109073i
$597$	2.56001	−	4.43407i	0.104774	−	0.181474i
$598$	7.62831	−	17.2927i	0.311945	−	0.707150i
$599$	−10.0688	−	17.4396i	−0.411398	−	0.712563i	0.583645	−	0.812009i	$-0.301626\pi$
$599$	−10.0688	−	17.4396i	−0.411398	−	0.712563i	−0.995043	+	0.0994465i	$0.968293\pi$
$600$	−0.529062	+	0.272750i	−0.0215989	+	0.0111350i
$601$	4.07097	+	28.3142i	0.166058	+	1.15496i	0.886934	+	0.461897i	$0.152831\pi$
$601$	4.07097	+	28.3142i	0.166058	+	1.15496i	−0.720875	+	0.693065i	$0.756260\pi$
$602$	4.78807	−	6.62058i	0.195147	−	0.269835i
$603$	5.74405	+	1.68660i	0.233916	+	0.0686838i
$604$	0.156367	+	0.219587i	0.00636249	+	0.00893487i
$605$	21.8361	+	4.20856i	0.887764	+	0.171102i
$606$	−0.142392	+	0.0570052i	−0.00578428	+	0.00231568i
$607$	−2.14497	+	8.84167i	−0.0870615	+	0.358872i	−0.998633	−	0.0522692i	$-0.983355\pi$
$607$	−2.14497	+	8.84167i	−0.0870615	+	0.358872i	0.911572	+	0.411141i	$0.134870\pi$
$608$	0.935038	+	1.07909i	0.0379208	+	0.0437629i
$609$	18.4180	−	11.6465i	0.746334	−	0.471941i
$610$	−14.1041	+	9.06418i	−0.571060	+	0.366998i
$611$	46.1494	−	8.89456i	1.86700	−	0.359835i
$612$	−5.32392	−	5.07634i	−0.215207	−	0.205199i
$613$	24.0547	−	9.63004i	0.971559	−	0.388954i	0.169059	−	0.985606i	$-0.445927\pi$
$613$	24.0547	−	9.63004i	0.971559	−	0.388954i	0.802500	+	0.596652i	$0.203503\pi$
$614$	−2.54446	−	7.35175i	−0.102686	−	0.296692i
$615$	6.44510	−	14.1128i	0.259891	−	0.569083i
$616$	−1.61044	−	0.485727i	−0.0648865	−	0.0195705i
$617$	2.06207	+	4.51530i	0.0830157	+	0.181779i	0.946588	−	0.322447i	$-0.104505\pi$
$617$	2.06207	+	4.51530i	0.0830157	+	0.181779i	−0.863572	+	0.504226i	$0.831778\pi$
$618$	−7.57980	−	3.03449i	−0.304904	−	0.122065i
$619$	0.376812	−	7.91026i	0.0151454	−	0.317940i	−0.978563	−	0.205945i	$-0.933973\pi$
$619$	0.376812	−	7.91026i	0.0151454	−	0.317940i	0.993709	−	0.111995i	$-0.0357239\pi$
$620$	3.03617	+	5.25880i	0.121936	+	0.211199i
$621$	4.42885	−	1.83992i	0.177724	−	0.0738334i
$622$	33.1866			1.33066
$623$	0.886008	−	16.1121i	0.0354972	−	0.645516i
$624$	0.560866	+	3.90091i	0.0224526	+	0.156161i
$625$	21.5714	+	2.05982i	0.862857	+	0.0823929i
$626$	3.92069	+	16.1613i	0.156702	+	0.645935i
$627$	0.903673	−	0.0862903i	0.0360892	−	0.00344610i
$628$	1.80862	+	5.22567i	0.0721718	+	0.208527i
$629$	3.06024	−	21.2844i	0.122020	−	0.848665i
$630$	1.34866	−	5.38651i	0.0537321	−	0.214604i
$631$	5.68047	+	6.55561i	0.226136	+	0.260975i	0.857467	−	0.514538i	$-0.172037\pi$
$631$	5.68047	+	6.55561i	0.226136	+	0.260975i	−0.631331	+	0.775513i	$0.717491\pi$
$632$	−0.197006	−	4.13567i	−0.00783648	−	0.164508i
$633$	6.32016	+	3.25827i	0.251204	+	0.129505i
$634$	6.91246	−	19.9722i	0.274529	−	0.793199i
$635$	2.86191	−	11.7970i	0.113572	−	0.468148i
$636$	−0.765709	+	5.32562i	−0.0303623	+	0.211175i
$637$	−27.0091	−	5.61772i	−1.07014	−	0.222582i
$638$	2.17530	−	4.76325i	0.0861210	−	0.188579i
$639$	−0.202938	+	0.193501i	−0.00802809	+	0.00765477i
$640$	1.21740	−	1.70959i	0.0481218	−	0.0675777i
$641$	−24.8808	+	19.5665i	−0.982733	+	0.772830i	−0.973864	−	0.227131i	$-0.927066\pi$
$641$	−24.8808	+	19.5665i	−0.982733	+	0.772830i	−0.00886908	+	0.999961i	$0.502823\pi$
$642$	6.45390	−	3.32722i	0.254715	−	0.131315i
$643$	18.8890			0.744908			0.372454	−	0.928051i	$-0.378516\pi$
$643$	18.8890			0.744908			0.372454	+	0.928051i	$0.378516\pi$
$644$	−4.08268	+	12.0138i	−0.160880	+	0.473411i
$645$	6.48131			0.255201
$646$	−9.33585	+	4.81297i	−0.367314	+	0.189364i
$647$	−15.2776	+	12.0144i	−0.600625	+	0.472337i	−0.871579	−	0.490256i	$-0.836903\pi$
$647$	−15.2776	+	12.0144i	−0.600625	+	0.472337i	0.270954	+	0.962592i	$0.412661\pi$
$648$	−0.580057	+	0.814576i	−0.0227868	+	0.0319996i
$649$	−2.28975	+	2.18327i	−0.0898804	+	0.0857008i
$650$	−0.974487	+	2.13383i	−0.0382225	+	0.0836956i
$651$	7.50581	+	1.50381i	0.294176	+	0.0589389i
$652$	2.58128	−	17.9532i	0.101091	−	0.703101i
$653$	4.12254	−	16.9933i	0.161327	−	0.665001i	−0.832496	−	0.554031i	$-0.813089\pi$
$653$	4.12254	−	16.9933i	0.161327	−	0.665001i	0.993824	−	0.110970i	$-0.0353958\pi$
$654$	1.32428	−	3.82625i	0.0517833	−	0.149618i
$655$	15.7151	+	8.10169i	0.614039	+	0.316559i
$656$	−0.351745	−	7.38403i	−0.0137333	−	0.288298i
$657$	−2.05647	−	2.37330i	−0.0802307	−	0.0925911i
$658$	−30.3383	+	8.66691i	−1.18271	+	0.337871i
$659$	1.01236	−	7.04109i	0.0394358	−	0.274282i	−0.960557	−	0.278083i	$-0.910301\pi$
$659$	1.01236	−	7.04109i	0.0394358	−	0.274282i	0.999993	+	0.00380129i	$0.00120999\pi$
$660$	−0.436417	−	1.26094i	−0.0169875	−	0.0490822i
$661$	31.3260	−	2.99127i	1.21844	−	0.116347i	0.534044	−	0.845457i	$-0.320672\pi$
$661$	31.3260	−	2.99127i	1.21844	−	0.116347i	0.684397	+	0.729110i	$0.260066\pi$
$662$	3.46447	+	14.2807i	0.134650	+	0.555036i
$663$	−28.8596	−	2.75575i	−1.12081	−	0.107025i
$664$	2.00773	+	13.9641i	0.0779151	+	0.541912i
$665$	−6.63826	−	4.33528i	−0.257421	−	0.168115i
$666$	−2.92316			−0.113270
$667$	−35.3406	−	17.6440i	−1.36839	−	0.683179i
$668$	−1.01049	−	1.75022i	−0.0390970	−	0.0677180i
$669$	−0.324600	+	6.81420i	−0.0125498	+	0.263452i
$670$	−11.6643	−	4.66967i	−0.450630	−	0.180405i
$671$	2.10980	+	4.61983i	0.0814481	+	0.178346i
$672$	−0.604883	−	2.57568i	−0.0233339	−	0.0993589i
$673$	−17.1769	+	37.6122i	−0.662122	+	1.44984i	0.218410	+	0.975857i	$0.429913\pi$
$673$	−17.1769	+	37.6122i	−0.662122	+	1.44984i	−0.880532	+	0.473987i	$0.842814\pi$
$674$	10.7858	+	31.1635i	0.415453	+	1.20037i
$675$	−0.552593	+	0.221225i	−0.0212693	+	0.00851494i
$676$	1.83223	+	1.74703i	0.0704706	+	0.0671935i
$677$	−28.7578	+	5.54262i	−1.10525	+	0.213020i	−0.709061	−	0.705147i	$-0.750881\pi$
$677$	−28.7578	+	5.54262i	−1.10525	+	0.213020i	−0.396193	+	0.918167i	$0.629669\pi$
$678$	15.9726	−	10.2650i	0.613423	−	0.394223i
$679$	0.925462	+	22.9720i	0.0355160	+	0.881584i
$680$	10.1103	+	11.6679i	0.387711	+	0.447442i
$681$	−4.15148	+	17.1126i	−0.159085	+	0.655757i
$682$	1.70772	−	0.683668i	0.0653919	−	0.0261790i
$683$	32.2046	+	6.20693i	1.23227	+	0.237501i	0.763495	−	0.645814i	$-0.223482\pi$
$683$	32.2046	+	6.20693i	1.23227	+	0.237501i	0.468780	+	0.883315i	$0.344694\pi$
$684$	0.828230	+	1.16309i	0.0316682	+	0.0444717i
$685$	8.37249	+	2.45838i	0.319896	+	0.0939300i
$686$	18.3932	+	2.16570i	0.702256	+	0.0826870i
$687$	−0.859505	−	5.97799i	−0.0327922	−	0.228075i
$688$	2.74488	−	1.41508i	0.104647	−	0.0539495i
$689$	10.6021	+	18.3634i	0.403908	+	0.699589i
$690$	−9.62004	+	2.96050i	−0.366229	+	0.112704i
$691$	−16.2713	+	28.1828i	−0.618991	+	1.07212i	0.370680	+	0.928761i	$0.379125\pi$
$691$	−16.2713	+	28.1828i	−0.618991	+	1.07212i	−0.989670	+	0.143362i	$0.954209\pi$
$692$	18.3670	+	11.8038i	0.698209	+	0.448712i
$693$	−1.55698	−	0.636610i	−0.0591446	−	0.0241828i
$694$	4.23963	+	9.28350i	0.160934	+	0.352397i
$695$	5.33680	−	5.08863i	0.202436	−	0.193023i
$696$	8.19907	−	0.782916i	0.310785	−	0.0296764i
$697$	53.3971	+	10.2915i	2.02256	+	0.389816i
$698$	−24.6875	−	19.4145i	−0.934437	−	0.734849i
$699$	−18.9402	+	5.56135i	−0.716384	+	0.210349i
$700$	0.525979	−	1.48440i	0.0198801	−	0.0561050i
$701$	−20.1241	+	12.9330i	−0.760077	+	0.488472i	−0.862368	−	0.506283i	$-0.831019\pi$
$701$	−20.1241	+	12.9330i	−0.760077	+	0.488472i	0.102291	+	0.994755i	$0.467383\pi$
$702$	0.187521	+	3.93656i	0.00707754	+	0.148576i
$703$	−1.36512	+	3.94426i	−0.0514865	+	0.148760i
$704$	−0.460130	−	0.438733i	−0.0173418	−	0.0165354i
$705$	−19.6739	−	15.4717i	−0.740962	−	0.582699i
$706$	−11.8569	+	13.6836i	−0.446240	+	0.514989i
$707$	0.171279	−	0.367884i	0.00644163	−	0.0138357i
$708$	−4.77473	−	1.40199i	−0.179445	−	0.0526899i
$709$	−14.2923	−	1.36475i	−0.536760	−	0.0512544i	−0.176844	−	0.984239i	$-0.556589\pi$
$709$	−14.2923	−	1.36475i	−0.536760	−	0.0512544i	−0.359916	+	0.932985i	$0.617195\pi$
$710$	0.462591	−	0.363786i	0.0173607	−	0.0136526i
$711$	0.197006	−	4.13567i	0.00738830	−	0.155100i
$712$	3.04950	−	5.28188i	0.114285	−	0.197947i
$713$	−4.70771	−	13.0528i	−0.176305	−	0.488831i
$714$	19.4621	+	0.142760i	0.728350	+	0.00534265i
$715$	−4.42384	−	2.84303i	−0.165442	−	0.106323i
$716$	3.73657	+	1.49590i	0.139642	+	0.0559042i
$717$	−0.324532	+	0.455742i	−0.0121199	+	0.0170200i
$718$	−7.00565	−	28.8777i	−0.261449	−	1.07771i
$719$	13.9443	+	19.5821i	0.520035	+	0.730287i	0.988169	−	0.153370i	$-0.0490127\pi$
$719$	13.9443	+	19.5821i	0.520035	+	0.730287i	−0.468133	+	0.883658i	$0.655073\pi$
$720$	1.37439	−	1.58613i	0.0512206	−	0.0591117i
$721$	20.1126	−	7.88120i	0.749033	−	0.293511i
$722$	−16.2742	+	4.77854i	−0.605664	+	0.177839i
$723$	26.0122	−	5.01344i	0.967404	−	0.186452i
$724$	14.0664	+	7.25174i	0.522774	+	0.269509i
$725$	4.35754	+	2.24647i	0.161835	+	0.0834318i
$726$	10.4043	−	2.00527i	0.386140	−	0.0744224i
$727$	28.2706	−	8.30099i	1.04850	−	0.307867i	0.288287	−	0.957544i	$-0.406914\pi$
$727$	28.2706	−	8.30099i	1.04850	−	0.307867i	0.760210	+	0.649677i	$0.225096\pi$
$728$	−8.14864	−	6.50546i	−0.302009	−	0.241109i
$729$	−0.654861	+	0.755750i	−0.0242541	+	0.0279907i
$730$	3.82302	+	5.36868i	0.141496	+	0.198704i
$731$	5.35577	+	22.0768i	0.198090	+	0.816539i
$732$	−4.63371	+	6.50714i	−0.171267	+	0.240511i
$733$	−19.8793	−	7.95848i	−0.734260	−	0.293953i	−0.0257636	−	0.999668i	$-0.508202\pi$
$733$	−19.8793	−	7.95848i	−0.734260	−	0.293953i	−0.708496	+	0.705715i	$0.750626\pi$
$734$	9.24070	+	5.93864i	0.341081	+	0.219199i
$735$	7.15821	+	12.8294i	0.264034	+	0.473220i
$736$	−3.42777	+	3.35416i	−0.126349	+	0.123636i
$737$	−1.90304	+	3.29616i	−0.0700994	+	0.121416i
$738$	0.351745	−	7.38403i	0.0129479	−	0.271810i
$739$	13.2809	−	10.4442i	0.488547	−	0.384198i	−0.343280	−	0.939233i	$-0.611538\pi$
$739$	13.2809	−	10.4442i	0.488547	−	0.384198i	0.831827	+	0.555036i	$0.187295\pi$
$740$	6.10722	+	0.583168i	0.224506	+	0.0214377i
$741$	5.39922	+	1.58535i	0.198345	+	0.0582394i
$742$	−8.17193	−	11.6559i	−0.300001	−	0.427901i
$743$	−0.152161	+	0.175603i	−0.00558224	+	0.00644224i	−0.758534	−	0.651634i	$-0.774084\pi$
$743$	−0.152161	+	0.175603i	−0.00558224	+	0.00644224i	0.752952	+	0.658076i	$0.228629\pi$
$744$	2.27429	+	1.78852i	0.0833796	+	0.0655705i
$745$	−7.48123	−	7.13334i	−0.274091	−	0.261345i
$746$	−5.96625	+	17.2383i	−0.218440	+	0.631141i
$747$	0.671270	+	14.0917i	0.0245605	+	0.515588i
$748$	3.93442	−	2.52850i	0.143857	−	0.0924511i
$749$	−6.41630	+	18.1078i	−0.234446	+	0.661646i
$750$	11.2673	−	3.30839i	0.411425	−	0.120805i
$751$	−27.4985	−	21.6251i	−1.00343	−	0.789110i	−0.0258527	−	0.999666i	$-0.508230\pi$
$751$	−27.4985	−	21.6251i	−1.00343	−	0.789110i	−0.977582	+	0.210556i	$0.932473\pi$
$752$	−11.7100	−	2.25692i	−0.427020	−	0.0823013i
$753$	29.2807	−	2.79596i	1.06705	−	0.101891i
$754$	23.4922	−	22.3997i	0.855534	−	0.815750i
$755$	−0.235028	−	0.514639i	−0.00855353	−	0.0187296i
$756$	−0.357310	−	2.62151i	−0.0129952	−	0.0953435i
$757$	30.4129	+	19.5452i	1.10538	+	0.710382i	0.960281	−	0.279036i	$-0.0900150\pi$
$757$	30.4129	+	19.5452i	1.10538	+	0.710382i	0.145095	+	0.989418i	$0.453651\pi$
$758$	−11.3211	+	19.6087i	−0.411200	+	0.712219i
$759$	0.472960	+	3.01215i	0.0171674	+	0.109334i
$760$	−1.49835	−	2.59521i	−0.0543507	−	0.0941382i
$761$	20.8931	−	10.7712i	0.757375	−	0.390454i	−0.0358698	−	0.999356i	$-0.511420\pi$
$761$	20.8931	−	10.7712i	0.757375	−	0.390454i	0.793245	+	0.608902i	$0.208390\pi$
$762$	−0.823146	−	5.72511i	−0.0298194	−	0.207399i
$763$	4.37853	+	9.77679i	0.158513	+	0.353944i
$764$	−5.62793	−	1.65251i	−0.203611	−	0.0597857i
$765$	8.95539	+	12.5761i	0.323783	+	0.454689i
$766$	4.71350	+	0.908453i	0.170306	+	0.0328238i
$767$	−18.2069	+	7.28893i	−0.657412	+	0.263188i
$768$	0.235759	−	0.971812i	0.00850722	−	0.0350672i
$769$	−32.4200	−	37.4147i	−1.16909	−	1.34921i	−0.925234	−	0.379397i	$-0.876131\pi$
$769$	−32.4200	−	37.4147i	−1.16909	−	1.34921i	−0.243861	−	0.969810i	$-0.578414\pi$
$770$	3.12591	+	1.64065i	0.112650	+	0.0591250i
$771$	−22.4423	+	14.4228i	−0.808240	+	0.519425i
$772$	6.96789	−	1.34295i	0.250780	−	0.0483338i
$773$	−10.8698	−	10.3643i	−0.390960	−	0.372779i	0.468951	−	0.883224i	$-0.344632\pi$
$773$	−10.8698	−	10.3643i	−0.390960	−	0.372779i	−0.859910	+	0.510445i	$0.829481\pi$
$774$	2.86696	−	1.14776i	0.103051	−	0.0412553i
$775$	0.563271	+	1.62747i	0.0202333	+	0.0584603i
$776$	−3.60981	+	7.90437i	−0.129584	+	0.283750i
$777$	5.63632	−	5.29584i	0.202202	−	0.189987i
$778$	−11.7942	−	25.8256i	−0.422842	−	0.925894i
$779$	−9.79910	−	3.92297i	−0.351089	−	0.140555i
$780$	0.393561	−	8.26186i	0.0140917	−	0.295822i
$781$	−0.0891365	−	0.154389i	−0.00318955	−	0.00552447i
$782$	−18.0335	−	30.3216i	−0.644878	−	1.08430i
$783$	8.23636			0.294344
$784$	5.83262	+	3.87047i	0.208308	+	0.138231i
$785$	−1.65166	−	11.4876i	−0.0589503	−	0.410009i
$786$	8.38615	+	0.800780i	0.299124	+	0.0285629i
$787$	7.60705	+	31.3567i	0.271162	+	1.11774i	0.930615	+	0.365999i	$0.119273\pi$
$787$	7.60705	+	31.3567i	0.271162	+	1.11774i	−0.659453	+	0.751746i	$0.729212\pi$
$788$	20.5059	−	1.95807i	0.730491	−	0.0697535i
$789$	9.05143	+	26.1524i	0.322240	+	0.931050i
$790$	−1.23666	+	8.60114i	−0.0439983	+	0.306015i
$791$	−12.2009	+	48.7297i	−0.433813	+	1.73263i
$792$	−0.416342	−	0.480485i	−0.0147941	−	0.0170733i
$793$	1.49799	+	31.4467i	0.0531952	+	1.11670i
$794$	18.8497	+	9.71772i	0.668952	+	0.344869i
$795$	3.69329	−	10.6710i	0.130987	−	0.378463i
$796$	−1.20709	+	4.97569i	−0.0427842	+	0.176359i
$797$	−1.71150	+	11.9037i	−0.0606243	+	0.421652i	0.936796	+	0.349875i	$0.113776\pi$
$797$	−1.71150	+	11.9037i	−0.0606243	+	0.421652i	−0.997421	+	0.0717766i	$0.977133\pi$
$798$	−3.70410	−	0.742127i	−0.131124	−	0.0262710i
$799$	36.4428	−	79.7985i	1.28925	−	2.82307i
$800$	0.430788	−	0.410756i	0.0152307	−	0.0145224i
$801$	3.53776	−	4.96809i	0.125001	−	0.175539i
$802$	9.15251	−	7.19761i	0.323186	−	0.254156i
$803$	1.77459	−	0.914863i	0.0626238	−	0.0322848i
$804$	−5.98654			−0.211129
$805$	13.1855	−	23.1368i	0.464728	−	0.815464i
$806$	11.4026			0.401639
$807$	−7.04324	+	3.63104i	−0.247934	+	0.127819i
$808$	0.120564	−	0.0948125i	0.00424142	−	0.00333549i
$809$	27.9677	−	39.2751i	0.983291	−	1.38084i	0.0593791	−	0.998236i	$-0.481088\pi$
$809$	27.9677	−	39.2751i	0.983291	−	1.38084i	0.923912	−	0.382604i	$-0.124973\pi$
$810$	1.51894	−	1.44831i	0.0533701	−	0.0508883i
$811$	−10.0074	+	21.9131i	−0.351406	+	0.769472i	0.648560	+	0.761164i	$0.275372\pi$
$811$	−10.0074	+	21.9131i	−0.351406	+	0.769472i	−0.999965	+	0.00830773i	$0.997356\pi$
$812$	−14.3907	+	16.3637i	−0.505015	+	0.574253i
$813$	3.29422	−	22.9118i	0.115533	−	0.803553i
$814$	0.438150	−	1.80608i	0.0153571	−	0.0633030i
$815$	−12.4504	+	35.9731i	−0.436119	+	1.26008i
$816$	6.53843	+	3.37080i	0.228891	+	0.118001i
$817$	−0.209809	−	4.40443i	−0.00734028	−	0.154091i
$818$	−22.9196	−	26.4506i	−0.801363	−	0.924823i
$819$	−7.49336	−	7.25059i	−0.261839	−	0.253356i
$820$	−2.20799	+	15.3569i	−0.0771064	+	0.536287i
$821$	−0.961633	−	2.77846i	−0.0335612	−	0.0969688i	0.926976	−	0.375122i	$-0.122399\pi$
$821$	−0.961633	−	2.77846i	−0.0335612	−	0.0969688i	−0.960537	+	0.278153i	$0.910278\pi$
$822$	4.13885	−	0.395213i	0.144359	−	0.0137846i
$823$	−8.82928	−	36.3948i	−0.307769	−	1.26864i	−0.890128	−	0.455710i	$-0.849385\pi$
$823$	−8.82928	−	36.3948i	−0.307769	−	1.26864i	0.582359	−	0.812932i	$-0.302130\pi$
$824$	8.12768	+	0.776099i	0.283141	+	0.0270367i
$825$	−0.0538564	−	0.374579i	−0.00187504	−	0.0130412i
$826$	11.7464	−	5.94703i	0.408709	−	0.206924i
$827$	11.7044			0.407002			0.203501	−	0.979075i	$-0.434768\pi$
$827$	11.7044			0.407002			0.203501	+	0.979075i	$0.434768\pi$
$828$	−3.73108	+	3.01314i	−0.129664	+	0.104714i
$829$	−5.16005	−	8.93746i	−0.179216	−	0.310411i	0.762396	−	0.647110i	$-0.224023\pi$
$829$	−5.16005	−	8.93746i	−0.179216	−	0.310411i	−0.941612	+	0.336699i	$0.890689\pi$
$830$	1.40883	−	29.5750i	0.0489013	−	1.02656i
$831$	−15.1568	−	6.06787i	−0.525784	−	0.210492i
$832$	−1.63716	−	3.58488i	−0.0567583	−	0.124283i
$833$	−37.7847	+	34.9839i	−1.30916	+	1.21212i
$834$	1.45956	−	3.19599i	0.0505405	−	0.110668i
$835$	1.38727	+	4.00826i	0.0480085	+	0.138711i
$836$	−0.842757	+	0.337389i	−0.0291474	+	0.0116688i
$837$	2.09398	+	1.99661i	0.0723787	+	0.0690130i
$838$	17.1916	−	3.31341i	0.593873	−	0.114460i
$839$	−12.8219	+	8.24012i	−0.442660	+	0.284481i	−0.742924	−	0.669376i	$-0.766562\pi$
$839$	−12.8219	+	8.24012i	−0.442660	+	0.284481i	0.300264	+	0.953856i	$0.402925\pi$
$840$	0.223521	+	5.54828i	0.00771221	+	0.191434i
$841$	−25.4333	−	29.3515i	−0.877009	−	1.01212i
$842$	5.84015	−	24.0734i	0.201265	−	0.829625i
$843$	7.40379	−	2.96403i	0.255000	−	0.102087i
$844$	−6.98211	−	1.34569i	−0.240334	−	0.0463206i
$845$	−3.08201	−	4.32808i	−0.106024	−	0.148890i
$846$	−11.4424	−	3.35981i	−0.393399	−	0.115512i
$847$	−16.4283	+	22.7158i	−0.564482	+	0.780524i
$848$	−0.765709	−	5.32562i	−0.0262945	−	0.182883i
$849$	−1.34413	+	0.692946i	−0.0461303	+	0.0237818i
$850$	2.18931	+	3.79200i	0.0750927	+	0.130064i
$851$	−13.5011	−	3.77514i	−0.462812	−	0.129410i
$852$	0.140202	−	0.242837i	0.00480324	−	0.00831945i
$853$	−35.2095	−	22.6278i	−1.20555	−	0.774760i	−0.225642	−	0.974210i	$-0.572448\pi$
$853$	−35.2095	−	22.6278i	−1.20555	−	0.774760i	−0.979908	+	0.199451i	$0.936084\pi$
$854$	−2.85433	−	20.9416i	−0.0976731	−	0.716607i
$855$	−1.24487	−	2.72589i	−0.0425737	−	0.0932233i
$856$	−5.25509	+	5.01072i	−0.179615	+	0.171263i
$857$	−10.4589	+	0.998701i	−0.357268	+	0.0341150i	−0.272147	−	0.962256i	$-0.587734\pi$
$857$	−10.4589	+	0.998701i	−0.357268	+	0.0341150i	−0.0851211	+	0.996371i	$0.527128\pi$
$858$	−2.46031	−	0.474187i	−0.0839937	−	0.0161885i
$859$	−0.925479	−	0.727804i	−0.0315769	−	0.0248324i	0.602246	−	0.798311i	$-0.294273\pi$
$859$	−0.925479	−	0.727804i	−0.0315769	−	0.0248324i	−0.633823	+	0.773478i	$0.718515\pi$
$860$	−6.21877	+	1.82600i	−0.212058	+	0.0622660i
$861$	12.6993	+	14.8749i	0.432791	+	0.506934i
$862$	−2.98390	+	1.91763i	−0.101632	+	0.0653149i
$863$	1.10078	+	23.1082i	0.0374710	+	0.786613i	0.936911	+	0.349569i	$0.113672\pi$
$863$	1.10078	+	23.1082i	0.0374710	+	0.786613i	−0.899440	+	0.437045i	$0.856025\pi$
$864$	0.327068	−	0.945001i	0.0111271	−	0.0321496i
$865$	−33.1629	−	31.6208i	−1.12757	−	1.07514i
$866$	24.3643	+	19.1603i	0.827931	+	0.651092i
$867$	−24.3041	+	28.0484i	−0.825409	+	0.952573i
$868$	−7.62544	+	0.671736i	−0.258824	+	0.0228002i
$869$	2.52570	+	0.741612i	0.0856784	+	0.0251574i
$870$	−17.2078	−	1.64315i	−0.583400	−	0.0557079i
$871$	−18.5454	+	14.5843i	−0.628387	+	0.494169i
$872$	−0.192656	+	4.04435i	−0.00652416	+	0.136959i
$873$	−4.34482	+	7.52545i	−0.147050	+	0.254698i
$874$	2.32325	+	6.44154i	0.0785850	+	0.217888i
$875$	−15.7315	+	26.7920i	−0.531821	+	0.905733i
$876$	2.64181	+	1.69779i	0.0892584	+	0.0573629i
$877$	−42.0889	−	16.8499i	−1.42124	−	0.568980i	−0.471459	−	0.881888i	$-0.656272\pi$
$877$	−42.0889	−	16.8499i	−1.42124	−	0.568980i	−0.949783	+	0.312908i	$0.898697\pi$
$878$	−11.8140	+	16.5904i	−0.398702	+	0.559898i
$879$	−6.62917	−	27.3258i	−0.223596	−	0.921676i
$880$	0.773988	+	1.08691i	0.0260911	+	0.0366398i
$881$	−22.3848	+	25.8334i	−0.754163	+	0.870351i	−0.994965	−	0.100224i	$-0.968044\pi$
$881$	−22.3848	+	25.8334i	−0.754163	+	0.870351i	0.240802	+	0.970574i	$0.422590\pi$
$882$	5.43830	+	4.40737i	0.183117	+	0.148404i
$883$	−10.8548	+	3.18725i	−0.365293	+	0.107260i	−0.459227	−	0.888319i	$-0.651874\pi$
$883$	−10.8548	+	3.18725i	−0.365293	+	0.107260i	0.0939348	+	0.995578i	$0.470055\pi$
$884$	28.4669	−	5.48655i	0.957447	−	0.184533i
$885$	9.28303	+	4.78573i	0.312046	+	0.160871i
$886$	1.21345	+	0.625577i	0.0407667	+	0.0210167i
$887$	−1.44592	+	0.278679i	−0.0485493	+	0.00935712i	−0.213468	−	0.976950i	$-0.568476\pi$
$887$	−1.44592	+	0.278679i	−0.0485493	+	0.00935712i	0.164919	+	0.986307i	$0.447264\pi$
$888$	2.80475	−	0.823550i	0.0941213	−	0.0276365i
$889$	11.9592	+	9.54765i	0.401100	+	0.320218i
$890$	−8.38240	+	9.67381i	−0.280979	+	0.324267i
$891$	−0.368784	−	0.517885i	−0.0123547	−	0.0173498i
$892$	−1.60833	−	6.62963i	−0.0538509	−	0.221976i
$893$	−9.87707	+	13.8704i	−0.330523	+	0.464155i
$894$	−4.57249	−	1.83055i	−0.152927	−	0.0612227i
$895$	−7.10626	−	4.56692i	−0.237536	−	0.152655i
$896$	1.30603	+	2.30093i	0.0436315	+	0.0768687i
$897$	−4.21780	+	18.4238i	−0.140828	+	0.615154i
$898$	−9.45317	+	16.3734i	−0.315456	+	0.546386i
$899$	1.13389	−	23.8033i	0.0378174	−	0.793886i
$900$	0.467883	−	0.367947i	0.0155961	−	0.0122649i
$901$	39.3998	+	3.76223i	1.31260	+	0.125338i
$902$	4.50951	+	1.32411i	0.150150	+	0.0440881i
$903$	−3.44859	+	7.40708i	−0.114762	+	0.246492i
$904$	−12.4336	+	14.3491i	−0.413536	+	0.477246i
$905$	−26.1081	−	20.5316i	−0.867863	−	0.682495i
$906$	−0.195099	−	0.186026i	−0.00648172	−	0.00618030i
$907$	−12.7177	+	36.7455i	−0.422285	+	1.22011i	0.510562	+	0.859841i	$0.329437\pi$
$907$	−12.7177	+	36.7455i	−0.422285	+	1.22011i	−0.932847	+	0.360272i	$0.882684\pi$
$908$	−0.837869	−	17.5890i	−0.0278057	−	0.583713i
$909$	0.129031	−	0.0829229i	0.00427967	−	0.00275038i
$910$	14.2090	+	16.6432i	0.471025	+	0.551717i
$911$	−22.1011	+	6.48946i	−0.732241	+	0.215005i	−0.626536	−	0.779392i	$-0.715528\pi$
$911$	−22.1011	+	6.48946i	−0.732241	+	0.215005i	−0.105705	+	0.994398i	$0.533710\pi$
$912$	−1.12236	−	0.882634i	−0.0371651	−	0.0292269i
$913$	−8.80719	−	1.69745i	−0.291475	−	0.0561773i
$914$	−33.0879	+	3.15951i	−1.09445	+	0.104507i
$915$	12.1339	−	11.5696i	0.401133	−	0.382479i
$916$	2.50888	+	5.49369i	0.0828959	+	0.181517i
$917$	−17.6206	+	13.6490i	−0.581884	+	0.450730i
$918$	6.18841	+	3.97705i	0.204248	+	0.131262i
$919$	−25.7807	+	44.6535i	−0.850427	+	1.47298i	0.0303972	+	0.999538i	$0.490323\pi$
$919$	−25.7807	+	44.6535i	−0.850427	+	1.47298i	−0.880824	+	0.473444i	$0.843011\pi$
$920$	8.39629	−	5.55086i	0.276817	−	0.183006i
$921$	3.88981	+	6.73735i	0.128174	+	0.222003i
$922$	8.69543	−	4.48281i	0.286369	−	0.147633i
$923$	−0.157269	−	1.09383i	−0.00517656	−	0.0360038i
$924$	1.67326	+	0.172172i	0.0550463	+	0.00566403i
$925$	1.66947	+	0.490202i	0.0548919	+	0.0161177i
$926$	19.0364	+	26.7329i	0.625574	+	0.878496i
$927$	8.01711	+	1.54517i	0.263316	+	0.0507501i
$928$	−7.64637	+	3.06115i	−0.251005	+	0.100487i
$929$	4.18276	−	17.2416i	0.137232	−	0.565678i	−0.861126	−	0.508392i	$-0.830240\pi$
$929$	4.18276	−	17.2416i	0.137232	−	0.565678i	0.998358	−	0.0572862i	$-0.0182447\pi$
$930$	−3.97654	−	4.58917i	−0.130396	−	0.150485i
$931$	8.48661	−	5.27972i	0.278137	−	0.173036i
$932$	16.6062	−	10.6721i	0.543954	−	0.349578i
$933$	−32.5869	+	6.28061i	−1.06685	+	0.205618i
$934$	−12.5730	−	11.9883i	−0.411400	−	0.392269i
$935$	−9.11246	+	3.64808i	−0.298009	+	0.119305i
$936$	−1.28898	−	3.72427i	−0.0421317	−	0.121731i
$937$	−6.81789	+	14.9291i	−0.222731	+	0.487712i	−0.987701	−	0.156353i	$-0.950026\pi$
$937$	−6.81789	+	14.9291i	−0.222731	+	0.487712i	0.764970	+	0.644065i	$0.222754\pi$
$938$	11.5430	−	10.8457i	0.376893	−	0.354125i
$939$	−6.90838	−	15.1272i	−0.225447	−	0.493659i
$940$	23.2359	+	9.30224i	0.757870	+	0.303406i
$941$	0.299923	−	6.29617i	0.00977722	−	0.205249i	−0.988693	−	0.149955i	$-0.952087\pi$
$941$	0.299923	−	6.29617i	0.00977722	−	0.205249i	0.998470	−	0.0552945i	$-0.0176098\pi$
$942$	−2.76490	−	4.78895i	−0.0900853	−	0.156032i
$943$	11.1608	−	33.6502i	0.363444	−	1.09580i
$944$	4.97630			0.161965
$945$	−0.304889	+	5.54441i	−0.00991803	+	0.180360i
$946$	0.279417	+	1.94339i	0.00908464	+	0.0631851i
$947$	−41.9945	−	4.00999i	−1.36464	−	0.130307i	−0.613104	−	0.790002i	$-0.710079\pi$
$947$	−41.9945	−	4.00999i	−1.36464	−	0.130307i	−0.751533	+	0.659695i	$0.770685\pi$
$948$	0.976126	+	4.02365i	0.0317031	+	0.130682i
$949$	12.3200	−	1.17642i	0.399925	−	0.0381882i
$950$	−0.277973	−	0.803152i	−0.00901865	−	0.0260577i
$951$	−3.00777	+	20.9195i	−0.0975337	+	0.678362i
$952$	−18.7140	+	5.34613i	−0.606523	+	0.173269i
$953$	10.5125	+	12.1320i	0.340532	+	0.392995i	0.900024	−	0.435841i	$-0.143549\pi$
$953$	10.5125	+	12.1320i	0.340532	+	0.392995i	−0.559491	+	0.828836i	$0.689003\pi$
$954$	−0.256009	−	5.37429i	−0.00828860	−	0.173999i
$955$	10.9418	+	5.64090i	0.354069	+	0.182535i
$956$	0.182989	−	0.528712i	0.00591829	−	0.0170998i
$957$	−1.23454	+	5.08885i	−0.0399070	+	0.164499i
$958$	−6.05403	+	42.1067i	−0.195597	+	1.36041i
$959$	−7.26438	+	8.26032i	−0.234579	+	0.266740i
$960$	−0.871854	+	1.90909i	−0.0281390	+	0.0616157i
$961$	−16.3772	+	15.6156i	−0.528297	+	0.503730i
$962$	6.68239	−	9.38411i	0.215449	−	0.302556i
$963$	−5.70759	+	4.48850i	−0.183925	+	0.144640i
$964$	−23.5461	+	12.1388i	−0.758368	+	0.390966i
$965$	−14.8930			−0.479423
$966$	1.73527	−	12.5694i	0.0558316	−	0.404413i
$967$	−42.9524			−1.38125			−0.690627	−	0.723211i	$-0.742666\pi$
$967$	−42.9524			−1.38125			−0.690627	+	0.723211i	$0.742666\pi$
$968$	−9.41792	+	4.85527i	−0.302703	+	0.156054i
$969$	8.25628	−	6.49281i	0.265230	−	0.208579i
$970$	10.5787	−	14.8558i	0.339663	−	0.476990i
$971$	−14.6670	+	13.9849i	−0.470685	+	0.448797i	−0.887918	−	0.460002i	$-0.847849\pi$
$971$	−14.6670	+	13.9849i	−0.470685	+	0.448797i	0.417233	+	0.908800i	$0.363000\pi$
$972$	0.415415	−	0.909632i	0.0133244	−	0.0291765i
$973$	2.97586	+	8.80665i	0.0954016	+	0.282328i
$974$	1.29744	−	9.02388i	0.0415726	−	0.289144i
$975$	0.553047	−	2.27969i	0.0177117	−	0.0730085i
$976$	2.61274	−	7.54902i	0.0836318	−	0.241638i
$977$	−17.3666	−	8.95310i	−0.555606	−	0.286435i	0.157467	−	0.987524i	$-0.449667\pi$
$977$	−17.3666	−	8.95310i	−0.555606	−	0.286435i	−0.713073	+	0.701089i	$0.752697\pi$
$978$	0.863031	+	18.1173i	0.0275967	+	0.579326i
$979$	2.53927	+	2.93047i	0.0811554	+	0.0936583i
$980$	−10.4827	−	10.2930i	−0.334858	−	0.328799i
$981$	−0.576224	+	4.00772i	−0.0183974	+	0.127957i
$982$	5.43738	+	15.7103i	0.173514	+	0.501335i
$983$	−48.8945	+	4.66886i	−1.55949	+	0.148913i	−0.838838	−	0.544381i	$-0.816765\pi$
$983$	−48.8945	+	4.66886i	−1.55949	+	0.148913i	−0.720654	+	0.693295i	$0.756158\pi$
$984$	1.74283	+	7.18402i	0.0555592	+	0.229018i
$985$	−43.0368	−	4.10952i	−1.37127	−	0.130940i
$986$	−8.62259	−	59.9714i	−0.274599	−	1.90988i
$987$	28.1498	−	14.2518i	0.896017	−	0.453641i
$988$	−5.62716			−0.179024
$989$	14.7238	−	1.59856i	0.468190	−	0.0508312i
$990$	0.667165	+	1.15556i	0.0212039	+	0.0367262i
$991$	−1.99566	+	41.8940i	−0.0633941	+	1.33081i	0.713269	+	0.700890i	$0.247214\pi$
$991$	−1.99566	+	41.8940i	−0.0633941	+	1.33081i	−0.776664	+	0.629916i	$0.783089\pi$
$992$	−2.68605	−	1.07533i	−0.0852823	−	0.0341419i
$993$	−6.10450	−	13.3670i	−0.193721	−	0.424189i
$994$	0.169611	+	0.722229i	0.00537975	+	0.0229077i
$995$	4.46391	−	9.77460i	0.141515	−	0.309876i
$996$	−4.61417	−	13.3318i	−0.146206	−	0.422433i
$997$	−48.4719	+	19.4052i	−1.53512	+	0.614569i	−0.976627	−	0.214941i	$-0.931044\pi$
$997$	−48.4719	+	19.4052i	−1.53512	+	0.614569i	−0.558492	+	0.829510i	$0.688620\pi$
$998$	−28.3591	−	27.0403i	−0.897692	−	0.855947i
$999$	2.87034	−	0.553212i	0.0908134	−	0.0175028i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.y.b.163.2	yes	160
7.4	even	3	inner	966.2.y.b.25.2	✓	160
23.12	even	11	inner	966.2.y.b.541.2	yes	160
161.81	even	33	inner	966.2.y.b.403.2	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.y.b.25.2	✓	160	7.4	even	3	inner
966.2.y.b.163.2	yes	160	1.1	even	1	trivial
966.2.y.b.403.2	yes	160	161.81	even	33	inner
966.2.y.b.541.2	yes	160	23.12	even	11	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)

\(f(q)\)	\(=\)	\(q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-1.51894 + 1.44831i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.846978 - 2.50652i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +O(q^{10})\)	\(q+(0.888835 - 0.458227i) q^{2} +(-0.786053 + 0.618159i) q^{3} +(0.580057 - 0.814576i) q^{4} +(-1.51894 + 1.44831i) q^{5} +(-0.415415 + 0.909632i) q^{6} +(-0.846978 - 2.50652i) q^{7} +(0.142315 - 0.989821i) q^{8} +(0.235759 - 0.971812i) q^{9} +(-0.686435 + 1.98332i) q^{10} +(0.565097 + 0.291328i) q^{11} +(0.0475819 + 0.998867i) q^{12} +(2.58082 + 2.97842i) q^{13} +(-1.90138 - 1.83977i) q^{14} +(0.298684 - 2.07739i) q^{15} +(-0.327068 - 0.945001i) q^{16} +(7.32287 - 0.699249i) q^{17} +(-0.235759 - 0.971812i) q^{18} +(-1.42138 - 0.135725i) q^{19} +(0.298684 + 2.07739i) q^{20} +(2.21520 + 1.44669i) q^{21} +0.635773 q^{22} +(0.166161 - 4.79295i) q^{23} +(0.500000 + 0.866025i) q^{24} +(-0.0283222 + 0.594556i) q^{25} +(3.65872 + 1.46473i) q^{26} +(0.415415 + 0.909632i) q^{27} +(-2.53304 - 0.763995i) q^{28} +(3.42151 - 7.49206i) q^{29} +(-0.686435 - 1.98332i) q^{30} +(2.68605 - 1.07533i) q^{31} +(-0.723734 - 0.690079i) q^{32} +(-0.624283 + 0.120321i) q^{33} +(6.18841 - 3.97705i) q^{34} +(4.91671 + 2.58057i) q^{35} +(-0.654861 - 0.755750i) q^{36} +(0.689161 - 2.84076i) q^{37} +(-1.32556 + 0.530676i) q^{38} +(-3.86980 - 0.745843i) q^{39} +(1.21740 + 1.70959i) q^{40} +(7.09296 + 2.08268i) q^{41} +(2.63186 + 0.270807i) q^{42} +(0.439493 + 3.05674i) q^{43} +(0.565097 - 0.291328i) q^{44} +(1.04938 + 1.81757i) q^{45} +(-2.04857 - 4.33629i) q^{46} +(5.96276 - 10.3278i) q^{47} +(0.841254 + 0.540641i) q^{48} +(-5.56526 + 4.24593i) q^{49} +(0.247268 + 0.541440i) q^{50} +(-5.32392 + 5.07634i) q^{51} +(3.92318 - 0.374618i) q^{52} +(5.28315 + 1.01824i) q^{53} +(0.786053 + 0.618159i) q^{54} +(-1.28028 + 0.375924i) q^{55} +(-2.60154 + 0.481642i) q^{56} +(1.20118 - 0.771950i) q^{57} +(-0.391902 - 8.22703i) q^{58} +(-1.62759 + 4.70261i) q^{59} +(-1.51894 - 1.44831i) q^{60} +(6.27928 + 4.93808i) q^{61} +(1.89471 - 2.18662i) q^{62} +(-2.63555 + 0.232169i) q^{63} +(-0.959493 - 0.281733i) q^{64} +(-8.23378 - 0.786231i) q^{65} +(-0.499751 + 0.393009i) q^{66} +(-0.284851 + 5.97976i) q^{67} +(3.67809 - 6.37064i) q^{68} +(2.83220 + 3.87023i) q^{69} +(5.55263 + 0.0407301i) q^{70} +(-0.235891 - 0.151598i) q^{71} +(-0.928368 - 0.371662i) q^{72} +(1.82156 - 2.55803i) q^{73} +(-0.689161 - 2.84076i) q^{74} +(-0.345267 - 0.484860i) q^{75} +(-0.935038 + 1.07909i) q^{76} +(0.251594 - 1.66317i) q^{77} +(-3.78138 + 1.11031i) q^{78} +(4.06553 - 0.783568i) q^{79} +(1.86545 + 0.961705i) q^{80} +(-0.888835 - 0.458227i) q^{81} +(7.25881 - 1.39902i) q^{82} +(-13.5362 + 3.97459i) q^{83} +(2.46338 - 0.965283i) q^{84} +(-10.1103 + 11.6679i) q^{85} +(1.79131 + 2.51555i) q^{86} +(1.94180 + 8.00419i) q^{87} +(0.368784 - 0.517885i) q^{88} +(5.66211 + 2.26677i) q^{89} +(1.76558 + 1.13467i) q^{90} +(5.27958 - 8.99153i) q^{91} +(-3.80784 - 2.91554i) q^{92} +(-1.44665 + 2.50568i) q^{93} +(0.567439 - 11.9120i) q^{94} +(2.35556 - 1.85243i) q^{95} +(0.995472 + 0.0950560i) q^{96} +(-8.33765 - 2.44815i) q^{97} +(-3.00100 + 6.32408i) q^{98} +(0.416342 - 0.480485i) 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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