LMFDB - Embedded newform 966.2.be.a.493.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(19,966)]

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, 55, 45]))

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

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

chi := DirichletCharacter("966.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.be (of order $66$, 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:	$320$
Relative dimension:	$16$ over $\Q(\zeta_{66})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{66}]$

Embedding invariants

Embedding label			493.12
Character	$\chi$	$=$	966.493
Dual form			966.2.be.a.145.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.614573 + 0.0586846i) q^{5} +(0.989821 - 0.142315i) q^{6} +(2.12691 - 1.57361i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})$	\(q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.614573 + 0.0586846i) q^{5} +(0.989821 - 0.142315i) q^{6} +(2.12691 - 1.57361i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.145550 + 0.599966i) q^{10} +(0.580686 - 0.200977i) q^{11} +(0.189251 - 0.981929i) q^{12} +(-0.399400 - 1.36023i) q^{13} +(-0.791414 - 2.52461i) q^{14} +(-0.333775 - 0.519363i) q^{15} +(0.235759 + 0.971812i) q^{16} +(3.61808 + 1.44846i) q^{17} +(0.580057 + 0.814576i) q^{18} +(3.76979 - 1.50920i) q^{19} +(0.519363 + 0.333775i) q^{20} +(2.37329 + 1.16941i) q^{21} -0.614482i q^{22} +(-0.0117961 - 4.79582i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-4.53539 + 0.874124i) q^{25} +(-1.41605 - 0.0674548i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-2.64461 - 0.0778322i) q^{28} +(-0.716899 - 4.98614i) q^{29} +(-0.599966 + 0.145550i) q^{30} +(8.57576 - 0.408514i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.444722 + 0.424041i) q^{33} +(2.55216 - 2.94534i) q^{34} +(-1.21480 + 1.09191i) q^{35} +(0.959493 - 0.281733i) q^{36} +(6.40415 + 4.56038i) q^{37} +(-0.193214 - 4.05607i) q^{38} +(1.02601 - 0.978294i) q^{39} +(0.485284 - 0.381632i) q^{40} +(-1.48674 - 0.678974i) q^{41} +(1.88132 - 1.86028i) q^{42} +(4.17496 - 6.49637i) q^{43} +(-0.580686 - 0.200977i) q^{44} +(0.308684 - 0.534657i) q^{45} +(-4.53591 - 1.55741i) q^{46} +(-6.20400 + 3.58188i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(2.04752 - 6.69385i) q^{49} +(-0.657332 + 4.57184i) q^{50} +(0.370457 + 3.87960i) q^{51} +(-0.526889 + 1.31611i) q^{52} +(3.49197 + 3.66227i) q^{53} +(-0.458227 + 0.888835i) q^{54} +(-0.345080 + 0.157593i) q^{55} +(-0.938517 + 2.47370i) q^{56} +(3.06885 + 2.65917i) q^{57} +(-4.94638 - 0.953338i) q^{58} +(-0.698741 - 0.169513i) q^{59} +(-0.0586846 + 0.614573i) q^{60} +(-3.40416 - 1.75497i) q^{61} +(2.41881 - 8.23771i) q^{62} +(0.0480914 + 2.64531i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.325285 + 0.812522i) q^{65} +(0.546173 - 0.281572i) q^{66} +(-0.973476 - 5.05088i) q^{67} +(-1.94862 - 3.37512i) q^{68} +(4.25729 - 2.20806i) q^{69} +(0.634538 + 1.50511i) q^{70} +(6.76690 + 7.80941i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(6.98307 - 8.87970i) q^{73} +(6.40415 - 4.56038i) q^{74} +(-2.85519 - 3.63067i) q^{75} +(-3.89618 - 1.14402i) q^{76} +(0.918810 - 1.34123i) q^{77} +(-0.588915 - 1.28954i) q^{78} +(-0.242561 + 0.254391i) q^{79} +(-0.201921 - 0.583414i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-1.12790 + 1.18290i) q^{82} +(-1.67276 - 3.66282i) q^{83} +(-1.14265 - 2.38628i) q^{84} +(-2.30858 - 0.677859i) q^{85} +(-4.77358 - 6.07010i) q^{86} +(4.10336 - 2.92199i) q^{87} +(-0.379848 + 0.483015i) q^{88} +(0.104186 - 2.18713i) q^{89} +(-0.404290 - 0.466576i) q^{90} +(-2.98996 - 2.26459i) q^{91} +(-2.95531 + 3.77706i) q^{92} +(4.29274 + 7.43525i) q^{93} +(1.35575 + 7.03430i) q^{94} +(-2.22824 + 1.14874i) q^{95} +(0.371662 + 0.928368i) q^{96} +(2.07909 - 4.55257i) q^{97} +(-5.65602 - 4.12426i) q^{98} +(-0.173120 + 0.589591i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	$ 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) $ 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{22}\right)$

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 $

$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$2$	0.327068	−	0.945001i	0.231272	−	0.668216i
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$3$	0.458227	+	0.888835i	0.264557	+	0.513169i
$4$	−0.786053	−	0.618159i	−0.393027	−	0.309079i
$5$	−0.614573	+	0.0586846i	−0.274845	+	0.0262445i	−0.231569	−	0.972819i	$-0.574386\pi$
$5$	−0.614573	+	0.0586846i	−0.274845	+	0.0262445i	−0.0432767	+	0.999063i	$0.513780\pi$
$6$	0.989821	−	0.142315i	0.404093	−	0.0580998i
$7$	2.12691	−	1.57361i	0.803898	−	0.594767i
$7$	2.12691	−	1.57361i	0.803898	−	0.594767i
$8$	−0.841254	+	0.540641i	−0.297428	+	0.191145i
$9$	−0.580057	+	0.814576i	−0.193352	+	0.271525i
$10$	−0.145550	+	0.599966i	−0.0460270	+	0.189726i
$11$	0.580686	−	0.200977i	0.175083	−	0.0605970i	−0.238120	−	0.971236i	$-0.576531\pi$
$11$	0.580686	−	0.200977i	0.175083	−	0.0605970i	0.413203	+	0.910639i	$0.364410\pi$
$12$	0.189251	−	0.981929i	0.0546321	−	0.283458i
$13$	−0.399400	−	1.36023i	−0.110774	−	0.377260i	0.885382	−	0.464865i	$-0.153897\pi$
$13$	−0.399400	−	1.36023i	−0.110774	−	0.377260i	−0.996155	+	0.0876045i	$0.972079\pi$
$14$	−0.791414	−	2.52461i	−0.211514	−	0.674731i
$15$	−0.333775	−	0.519363i	−0.0861802	−	0.134099i
$16$	0.235759	+	0.971812i	0.0589397	+	0.242953i
$17$	3.61808	+	1.44846i	0.877514	+	0.351303i	0.766292	−	0.642492i	$-0.222100\pi$
$17$	3.61808	+	1.44846i	0.877514	+	0.351303i	0.111221	+	0.993796i	$0.464524\pi$
$18$	0.580057	+	0.814576i	0.136721	+	0.191997i
$19$	3.76979	−	1.50920i	0.864849	−	0.346233i	0.103542	−	0.994625i	$-0.466982\pi$
$19$	3.76979	−	1.50920i	0.864849	−	0.346233i	0.761307	+	0.648392i	$0.224558\pi$
$20$	0.519363	+	0.333775i	0.116133	+	0.0746343i
$21$	2.37329	+	1.16941i	0.517893	+	0.255186i
$22$		−	0.614482i		−	0.131008i
$23$	−0.0117961	−	4.79582i	−0.00245965	−	0.999997i
$23$	−0.0117961	−	4.79582i	−0.00245965	−	0.999997i
$24$	−0.866025	−	0.500000i	−0.176777	−	0.102062i
$25$	−4.53539	+	0.874124i	−0.907078	+	0.174825i
$26$	−1.41605	−	0.0674548i	−0.277710	−	0.0132290i
$27$	−0.989821	−	0.142315i	−0.190491	−	0.0273885i
$28$	−2.64461	−	0.0778322i	−0.499784	−	0.0147089i
$29$	−0.716899	−	4.98614i	−0.133125	−	0.925904i	−0.941446	−	0.337162i	$-0.890533\pi$
$29$	−0.716899	−	4.98614i	−0.133125	−	0.925904i	0.808322	−	0.588741i	$-0.200376\pi$
$30$	−0.599966	+	0.145550i	−0.109538	+	0.0265737i
$31$	8.57576	−	0.408514i	1.54025	−	0.0733712i	0.739824	−	0.672800i	$-0.234909\pi$
$31$	8.57576	−	0.408514i	1.54025	−	0.0733712i	0.800428	+	0.599429i	$0.204606\pi$
$32$	0.995472	+	0.0950560i	0.175976	+	0.0168037i
$33$	0.444722	+	0.424041i	0.0774161	+	0.0738161i
$34$	2.55216	−	2.94534i	0.437691	−	0.505122i
$35$	−1.21480	+	1.09191i	−0.205338	+	0.184567i
$36$	0.959493	−	0.281733i	0.159915	−	0.0469554i
$37$	6.40415	+	4.56038i	1.05284	+	0.749721i	0.969075	−	0.246765i	$-0.0793675\pi$
$37$	6.40415	+	4.56038i	1.05284	+	0.749721i	0.0837606	+	0.996486i	$0.473307\pi$
$38$	−0.193214	−	4.05607i	−0.0313435	−	0.657981i
$39$	1.02601	−	0.978294i	0.164292	−	0.156652i
$40$	0.485284	−	0.381632i	0.0767302	−	0.0603413i
$41$	−1.48674	−	0.678974i	−0.232191	−	0.106038i	0.295922	−	0.955212i	$-0.404373\pi$
$41$	−1.48674	−	0.678974i	−0.232191	−	0.106038i	−0.528113	+	0.849174i	$0.677100\pi$
$42$	1.88132	−	1.86028i	0.290294	−	0.287048i
$43$	4.17496	−	6.49637i	0.636676	−	0.990687i	−0.361620	−	0.932326i	$-0.617776\pi$
$43$	4.17496	−	6.49637i	0.636676	−	0.990687i	0.998296	−	0.0583612i	$-0.0185875\pi$
$44$	−0.580686	−	0.200977i	−0.0875417	−	0.0302985i
$45$	0.308684	−	0.534657i	0.0460159	−	0.0797019i
$46$	−4.53591	−	1.55741i	−0.668783	−	0.229628i
$47$	−6.20400	+	3.58188i	−0.904946	+	0.522471i	−0.878802	−	0.477187i	$-0.841656\pi$
$47$	−6.20400	+	3.58188i	−0.904946	+	0.522471i	−0.0261443	+	0.999658i	$0.508323\pi$
$48$	−0.755750	+	0.654861i	−0.109083	+	0.0945210i
$49$	2.04752	−	6.69385i	0.292503	−	0.956265i
$50$	−0.657332	+	4.57184i	−0.0929608	+	0.646556i
$51$	0.370457	+	3.87960i	0.0518744	+	0.543253i
$52$	−0.526889	+	1.31611i	−0.0730664	+	0.182511i
$53$	3.49197	+	3.66227i	0.479659	+	0.503052i	0.918450	−	0.395537i	$-0.129442\pi$
$53$	3.49197	+	3.66227i	0.479659	+	0.503052i	−0.438791	+	0.898589i	$0.644593\pi$
$54$	−0.458227	+	0.888835i	−0.0623567	+	0.120955i
$55$	−0.345080	+	0.157593i	−0.0465305	+	0.0212498i
$56$	−0.938517	+	2.47370i	−0.125415	+	0.330562i
$57$	3.06885	+	2.65917i	0.406479	+	0.352216i
$58$	−4.94638	−	0.953338i	−0.649492	−	0.125179i
$59$	−0.698741	−	0.169513i	−0.0909683	−	0.0220687i	0.190016	−	0.981781i	$-0.439146\pi$
$59$	−0.698741	−	0.169513i	−0.0909683	−	0.0220687i	−0.280985	+	0.959712i	$0.590661\pi$
$60$	−0.0586846	+	0.614573i	−0.00757615	+	0.0793410i
$61$	−3.40416	−	1.75497i	−0.435858	−	0.224700i	0.226311	−	0.974055i	$-0.427334\pi$
$61$	−3.40416	−	1.75497i	−0.435858	−	0.224700i	−0.662169	+	0.749355i	$0.730364\pi$
$62$	2.41881	−	8.23771i	0.307189	−	1.04619i
$63$	0.0480914	+	2.64531i	0.00605895	+	0.333278i
$64$	0.415415	−	0.909632i	0.0519269	−	0.113704i
$65$	0.325285	+	0.812522i	0.0403466	+	0.100781i
$66$	0.546173	−	0.281572i	0.0672293	−	0.0346591i
$67$	−0.973476	−	5.05088i	−0.118929	−	0.617063i	−0.991662	−	0.128865i	$-0.958867\pi$
$67$	−0.973476	−	5.05088i	−0.118929	−	0.617063i	0.872733	−	0.488198i	$-0.162345\pi$
$68$	−1.94862	−	3.37512i	−0.236305	−	0.409293i
$69$	4.25729	−	2.20806i	0.512517	−	0.265819i
$70$	0.634538	+	1.50511i	0.0758418	+	0.179896i
$71$	6.76690	+	7.80941i	0.803083	+	0.926807i	0.998546	−	0.0539040i	$-0.0171665\pi$
$71$	6.76690	+	7.80941i	0.803083	+	0.926807i	−0.195463	+	0.980711i	$0.562621\pi$
$72$	0.0475819	−	0.998867i	0.00560758	−	0.117718i
$73$	6.98307	−	8.87970i	0.817307	−	1.03929i	−0.181133	−	0.983459i	$-0.557977\pi$
$73$	6.98307	−	8.87970i	0.817307	−	1.03929i	0.998440	−	0.0558316i	$-0.0177810\pi$
$74$	6.40415	−	4.56038i	0.744467	−	0.530133i
$75$	−2.85519	−	3.63067i	−0.329689	−	0.419233i
$76$	−3.89618	−	1.14402i	−0.446922	−	0.131228i
$77$	0.918810	−	1.34123i	0.104708	−	0.152848i
$78$	−0.588915	−	1.28954i	−0.0666815	−	0.146012i
$79$	−0.242561	+	0.254391i	−0.0272903	+	0.0286212i	−0.737238	−	0.675633i	$-0.763870\pi$
$79$	−0.242561	+	0.254391i	−0.0272903	+	0.0286212i	0.709947	+	0.704255i	$0.248719\pi$
$80$	−0.201921	−	0.583414i	−0.0225755	−	0.0652276i
$81$	−0.327068	−	0.945001i	−0.0363409	−	0.105000i
$82$	−1.12790	+	1.18290i	−0.124555	+	0.130630i
$83$	−1.67276	−	3.66282i	−0.183609	−	0.402047i	0.795337	−	0.606168i	$-0.207294\pi$
$83$	−1.67276	−	3.66282i	−0.183609	−	0.402047i	−0.978946	+	0.204120i	$0.934567\pi$
$84$	−1.14265	−	2.38628i	−0.124673	−	0.260365i
$85$	−2.30858	−	0.677859i	−0.250400	−	0.0735242i
$86$	−4.77358	−	6.07010i	−0.514748	−	0.654555i
$87$	4.10336	−	2.92199i	0.439926	−	0.313270i
$88$	−0.379848	+	0.483015i	−0.0404919	+	0.0514896i
$89$	0.104186	−	2.18713i	0.0110437	−	0.231835i	−0.986597	−	0.163178i	$-0.947825\pi$
$89$	0.104186	−	2.18713i	0.0110437	−	0.231835i	0.997640	−	0.0686573i	$-0.0218715\pi$
$90$	−0.404290	−	0.466576i	−0.0426159	−	0.0491814i
$91$	−2.98996	−	2.26459i	−0.313433	−	0.237394i
$92$	−2.95531	+	3.77706i	−0.308112	+	0.393786i
$93$	4.29274	+	7.43525i	0.445137	+	0.770999i
$94$	1.35575	+	7.03430i	0.139835	+	0.725533i
$95$	−2.22824	+	1.14874i	−0.228613	+	0.117858i
$96$	0.371662	+	0.928368i	0.0379326	+	0.0947512i
$97$	2.07909	−	4.55257i	0.211099	−	0.462243i	−0.774230	−	0.632904i	$-0.781863\pi$
$97$	2.07909	−	4.55257i	0.211099	−	0.462243i	0.985330	+	0.170660i	$0.0545901\pi$
$98$	−5.65602	−	4.12426i	−0.571344	−	0.416613i
$99$	−0.173120	+	0.589591i	−0.0173992	+	0.0592561i
$100$	4.10540	+	2.11648i	0.410540	+	0.211648i
$101$	−0.637677	+	6.67805i	−0.0634512	+	0.664491i	0.906665	+	0.421851i	$0.138619\pi$
$101$	−0.637677	+	6.67805i	−0.0634512	+	0.664491i	−0.970116	+	0.242640i	$0.921987\pi$
$102$	3.78739	+	0.918811i	0.375008	+	0.0909759i
$103$	1.00397	+	0.193500i	0.0989243	+	0.0190661i	0.238473	−	0.971149i	$-0.423353\pi$
$103$	1.00397	+	0.193500i	0.0989243	+	0.0190661i	−0.139549	+	0.990215i	$0.544565\pi$
$104$	1.07139	+	0.928367i	0.105059	+	0.0910339i
$105$	−1.52718	−	0.579411i	−0.149038	−	0.0565447i
$106$	4.60296	−	2.10210i	0.447079	−	0.204174i
$107$	−8.46601	+	16.4218i	−0.818440	+	1.58755i	−0.00928485	+	0.999957i	$0.502956\pi$
$107$	−8.46601	+	16.4218i	−0.818440	+	1.58755i	−0.809155	+	0.587595i	$0.800075\pi$
$108$	0.690079	+	0.723734i	0.0664029	+	0.0696413i
$109$	−2.88145	+	7.19753i	−0.275993	+	0.689398i	−1.00000		0.000395105i	$-0.999874\pi$
$109$	−2.88145	+	7.19753i	−0.275993	+	0.689398i	0.724007	+	0.689793i	$0.242298\pi$
$110$	0.0360606	+	0.377644i	0.00343825	+	0.0360069i
$111$	−1.11887	+	7.78192i	−0.106199	+	0.738627i
$112$	2.03069	+	1.69597i	0.191882	+	0.160254i
$113$	−12.3280	+	10.6823i	−1.15972	+	1.00491i	−0.159882	+	0.987136i	$0.551111\pi$
$113$	−12.3280	+	10.6823i	−1.15972	+	1.00491i	−0.999842	+	0.0177701i	$0.994343\pi$
$114$	3.51664	−	2.03033i	0.329363	−	0.190158i
$115$	0.288690	+	2.94669i	0.0269205	+	0.274780i
$116$	−2.51871	+	4.36253i	−0.233856	+	0.405051i
$117$	1.33969	+	0.463670i	0.123854	+	0.0428663i
$118$	−0.388725	+	0.604868i	−0.0357851	+	0.0556826i
$119$	9.97465	−	2.61269i	0.914375	−	0.239504i
$120$	0.561578	+	0.256464i	0.0512648	+	0.0234119i
$121$	−8.34978	+	6.56634i	−0.759071	+	0.596940i
$122$	−2.77184	+	2.64294i	−0.250950	+	0.239281i
$123$	−0.0777701	−	1.63260i	−0.00701229	−	0.147206i
$124$	−6.99353	−	4.98007i	−0.628037	−	0.447223i
$125$	5.69783	−	1.67303i	0.509630	−	0.149641i
$126$	2.51555	+	0.819751i	0.224103	+	0.0730292i
$127$	−7.68100	+	8.86435i	−0.681579	+	0.786584i	−0.986141	−	0.165909i	$-0.946944\pi$
$127$	−7.68100	+	8.86435i	−0.681579	+	0.786584i	0.304563	+	0.952492i	$0.401490\pi$
$128$	−0.723734	−	0.690079i	−0.0639697	−	0.0609949i
$129$	7.68728	+	0.734046i	0.676827	+	0.0646292i
$130$	0.874224	−	0.0416444i	0.0766745	−	0.00365246i
$131$	−18.6531	+	4.52519i	−1.62973	+	0.395368i	−0.943330	−	0.331857i	$-0.892325\pi$
$131$	−18.6531	+	4.52519i	−1.62973	+	0.395368i	−0.686399	+	0.727225i	$0.740810\pi$
$132$	−0.0874499	−	0.608227i	−0.00761154	−	0.0529394i
$133$	5.64314	−	9.14210i	0.489322	−	0.792721i
$134$	−5.09147	−	0.732043i	−0.439836	−	0.0632389i
$135$	0.616669	+	0.0293756i	0.0530744	+	0.00252825i
$136$	−3.82682	+	0.737559i	−0.328147	+	0.0632452i
$137$	−8.85717	−	5.11369i	−0.756719	−	0.436892i	0.0713976	−	0.997448i	$-0.477254\pi$
$137$	−8.85717	−	5.11369i	−0.756719	−	0.436892i	−0.828116	+	0.560556i	$0.810587\pi$
$138$	−0.694192	−	4.74532i	−0.0590935	−	0.403949i
$139$		−	13.8080i		−	1.17118i	−0.810609	−	0.585588i	$-0.800864\pi$
$139$		−	13.8080i		−	1.17118i	0.810609	−	0.585588i	$-0.199136\pi$
$140$	1.62987	−	0.107364i	0.137749	−	0.00907392i
$141$	−6.02654	−	3.87302i	−0.507526	−	0.326167i
$142$	9.59314	−	3.84051i	0.805038	−	0.322289i
$143$	−0.505301	−	0.709596i	−0.0422554	−	0.0593394i
$144$	−0.928368	−	0.371662i	−0.0773640	−	0.0309719i
$145$	0.733197	+	3.02228i	0.0608887	+	0.250987i
$146$	−6.10738	−	9.50327i	−0.505451	−	0.786497i
$147$	6.88796	−	1.24739i	0.568110	−	0.102883i
$148$	−2.21497	−	7.54348i	−0.182069	−	0.620070i
$149$	−2.74648	+	14.2501i	−0.225000	+	1.16741i	0.677102	+	0.735889i	$0.263236\pi$
$149$	−2.74648	+	14.2501i	−0.225000	+	1.16741i	−0.902102	+	0.431523i	$0.857977\pi$
$150$	−4.36482	+	1.51068i	−0.356386	+	0.123346i
$151$	0.183312	−	0.755623i	0.0149177	−	0.0614917i	−0.963866	−	0.266387i	$-0.914170\pi$
$151$	0.183312	−	0.755623i	0.0149177	−	0.0614917i	0.978784	+	0.204895i	$0.0656853\pi$
$152$	−2.35542	+	3.30772i	−0.191050	+	0.268292i
$153$	−3.27857	+	2.10701i	−0.265057	+	0.170342i
$154$	−0.966953	−	1.30695i	−0.0779193	−	0.105317i
$155$	−5.24646	+	0.754326i	−0.421405	+	0.0605890i
$156$	−1.41124	+	0.134757i	−0.112989	+	0.0107892i
$157$	9.03921	+	7.10852i	0.721408	+	0.567321i	0.909937	−	0.414746i	$-0.136130\pi$
$157$	9.03921	+	7.10852i	0.721408	+	0.567321i	−0.188529	+	0.982068i	$0.560372\pi$
$158$	0.161066	+	0.312424i	0.0128137	+	0.0248551i
$159$	−1.65504	+	4.78193i	−0.131254	+	0.379232i
$160$	−0.617368			−0.0488073
$161$	−7.57182	−	10.1817i	−0.596743	−	0.802432i
$162$	−1.00000			−0.0785674
$163$	−5.14950	+	14.8785i	−0.403340	+	1.16537i	0.542307	+	0.840180i	$0.317551\pi$
$163$	−5.14950	+	14.8785i	−0.403340	+	1.16537i	−0.945647	+	0.325194i	$0.894570\pi$
$164$	0.748947	+	1.45275i	0.0584829	+	0.113441i
$165$	−0.298198	−	0.234506i	−0.0232147	−	0.0182563i
$166$	−4.00848	+	0.382763i	−0.311118	+	0.0297082i
$167$	12.2533	−	1.76176i	0.948192	−	0.136329i	0.349168	−	0.937060i	$-0.386464\pi$
$167$	12.2533	−	1.76176i	0.948192	−	0.136329i	0.599024	+	0.800731i	$0.295555\pi$
$168$	−2.62876	+	0.299327i	−0.202814	+	0.0230936i
$169$	9.24559	−	5.94178i	0.711199	−	0.457060i
$170$	−1.39564	+	1.95990i	−0.107041	+	0.150318i
$171$	−0.957338	+	3.94620i	−0.0732095	+	0.301774i
$172$	−7.29753	+	2.52570i	−0.556431	+	0.192583i
$173$	0.527843	−	2.73871i	0.0401312	−	0.208220i	−0.956328	−	0.292295i	$-0.905581\pi$
$173$	0.527843	−	2.73871i	0.0401312	−	0.208220i	0.996459	+	0.0840744i	$0.0267933\pi$
$174$	−1.41920	−	4.83337i	−0.107590	−	0.366417i
$175$	−8.27085	+	8.99610i	−0.625217	+	0.680042i
$176$	0.332214	+	0.516935i	0.0250416	+	0.0389655i
$177$	−0.169513	−	0.698741i	−0.0127414	−	0.0525206i
$178$	−2.03276	−	0.813796i	−0.152362	−	0.0609966i
$179$	5.13290	+	7.20815i	0.383651	+	0.538763i	0.960570	−	0.278039i	$-0.0896845\pi$
$179$	5.13290	+	7.20815i	0.383651	+	0.538763i	−0.576919	+	0.816802i	$0.695745\pi$
$180$	−0.573145	+	0.229453i	−0.0427197	+	0.0171024i
$181$	−12.0129	−	7.72024i	−0.892914	−	0.573841i	0.0117667	−	0.999931i	$-0.496254\pi$
$181$	−12.0129	−	7.72024i	−0.892914	−	0.573841i	−0.904681	+	0.426090i	$0.859891\pi$
$182$	−3.11796	+	2.08484i	−0.231119	+	0.154538i
$183$		−	3.82991i		−	0.283115i
$184$	2.60274	+	4.02812i	0.191876	+	0.296957i
$185$	−4.20344	−	2.42686i	−0.309043	−	0.178426i
$186$	8.43033	−	1.62481i	0.618142	−	0.119137i
$187$	2.39208	+	0.113949i	0.174926	+	0.00833275i
$188$	7.09084	+	1.01951i	0.517153	+	0.0743553i
$189$	−2.32921	+	1.25490i	−0.169425	+	0.0912804i
$190$	0.356773	+	2.48141i	0.0258830	+	0.180020i
$191$	−12.2919	+	2.98199i	−0.889414	+	0.215770i	−0.654333	−	0.756206i	$-0.727051\pi$
$191$	−12.2919	+	2.98199i	−0.889414	+	0.215770i	−0.235081	+	0.971976i	$0.575535\pi$
$192$	0.998867	−	0.0475819i	0.0720870	−	0.00343393i
$193$	23.9965	+	2.29139i	1.72731	+	0.164938i	0.910924	−	0.412573i	$-0.135370\pi$
$193$	23.9965	+	2.29139i	1.72731	+	0.164938i	0.816383	+	0.577511i	$0.195976\pi$
$194$	−3.62218	−	3.45374i	−0.260057	−	0.247964i
$195$	−0.573144	+	0.661444i	−0.0410437	+	0.0473670i
$196$	−5.74733	+	3.99603i	−0.410523	+	0.285431i
$197$	−21.7773	+	6.39440i	−1.55157	+	0.455582i	−0.941569	−	0.336820i	$-0.890649\pi$
$197$	−21.7773	+	6.39440i	−1.55157	+	0.455582i	−0.610000	+	0.792401i	$0.708831\pi$
$198$	0.500542	+	0.356435i	0.0355720	+	0.0253307i
$199$	0.519285	+	10.9011i	0.0368111	+	0.772761i	0.939517	+	0.342503i	$0.111275\pi$
$199$	0.519285	+	10.9011i	0.0368111	+	0.772761i	−0.902706	+	0.430258i	$0.858422\pi$
$200$	3.34282	−	3.18738i	0.236373	−	0.225382i
$201$	4.04332	−	3.17971i	0.285194	−	0.224279i
$202$	6.10220	+	2.78678i	0.429349	+	0.196077i
$203$	−9.37101	−	9.47698i	−0.657716	−	0.665154i
$204$	2.10701	−	3.27857i	0.147520	−	0.229546i
$205$	0.953558	+	0.330030i	0.0665994	+	0.0230503i
$206$	0.511224	−	0.885467i	0.0356187	−	0.0616934i
$207$	3.91340	+	2.77224i	0.272000	+	0.192684i
$208$	1.22773	−	0.708828i	0.0851275	−	0.0491484i
$209$	1.88575	−	1.63401i	0.130440	−	0.113027i
$210$	−1.04704	+	1.25368i	−0.0722524	+	0.0865123i
$211$	−3.57021	+	24.8314i	−0.245784	+	1.70946i	0.376289	+	0.926502i	$0.377200\pi$
$211$	−3.57021	+	24.8314i	−0.245784	+	1.70946i	−0.622072	+	0.782960i	$0.713709\pi$
$212$	−0.481007	−	5.03733i	−0.0330357	−	0.345965i
$213$	−3.84051	+	9.59314i	−0.263148	+	0.657311i
$214$	12.7496	+	13.3714i	0.871546	+	0.914051i
$215$	−2.18458	+	4.23750i	−0.148987	+	0.288995i
$216$	0.909632	−	0.415415i	0.0618926	−	0.0282654i
$217$	17.5971	−	14.3637i	1.19457	−	0.975075i
$218$	5.85924	+	5.07706i	0.396838	+	0.343862i
$219$	11.0924	+	2.13789i	0.749556	+	0.144465i
$220$	0.368668	+	0.0894379i	0.0248556	+	0.00602990i
$221$	0.525180	−	5.49994i	0.0353275	−	0.369966i
$222$	6.98798	+	3.60255i	0.469002	+	0.241787i
$223$	2.92300	−	9.95483i	0.195739	−	0.666625i	−0.801869	−	0.597500i	$-0.796161\pi$
$223$	2.92300	−	9.95483i	0.195739	−	0.666625i	0.997608	−	0.0691254i	$-0.0220209\pi$
$224$	2.26686	−	1.36431i	0.151461	−	0.0911565i
$225$	1.91874	−	4.20146i	0.127916	−	0.280097i
$226$	6.06268	+	15.1438i	0.403283	+	1.00735i
$227$	−0.0615341	+	0.0317230i	−0.00408416	+	0.00210553i	−0.460267	−	0.887780i	$-0.652246\pi$
$227$	−0.0615341	+	0.0317230i	−0.00408416	+	0.00210553i	0.456183	+	0.889886i	$0.349216\pi$
$228$	−0.768486	−	3.98728i	−0.0508942	−	0.264064i
$229$	−1.14757	−	1.98765i	−0.0758335	−	0.131348i	0.825615	−	0.564234i	$-0.190828\pi$
$229$	−1.14757	−	1.98765i	−0.0758335	−	0.131348i	−0.901448	+	0.432886i	$0.857495\pi$
$230$	2.87904	+	0.690954i	0.189838	+	0.0455602i
$231$	1.61316	+	0.202082i	0.106138	+	0.0132960i
$232$	3.29881	+	3.80703i	0.216577	+	0.249944i
$233$	0.685627	−	14.3931i	0.0449169	−	0.942923i	−0.858144	−	0.513410i	$-0.828382\pi$
$233$	0.685627	−	14.3931i	0.0449169	−	0.942923i	0.903061	−	0.429513i	$-0.141315\pi$
$234$	0.876336	−	1.11435i	0.0572879	−	0.0728475i
$235$	3.60261	−	2.56540i	0.235008	−	0.167349i
$236$	0.444462	+	0.565179i	0.0289320	+	0.0367900i
$237$	−0.337260	−	0.0990283i	−0.0219074	−	0.00643258i
$238$	0.793400	−	10.2806i	0.0514285	−	0.666391i
$239$	6.28806	+	13.7689i	0.406741	+	0.890638i	0.996542	+	0.0830895i	$0.0264787\pi$
$239$	6.28806	+	13.7689i	0.406741	+	0.890638i	−0.589801	+	0.807548i	$0.700794\pi$
$240$	0.426033	−	0.446811i	0.0275003	−	0.0288415i
$241$	−5.56771	−	16.0868i	−0.358647	−	1.03624i	−0.969625	−	0.244596i	$-0.921345\pi$
$241$	−5.56771	−	16.0868i	−0.358647	−	1.03624i	0.610978	−	0.791648i	$-0.290777\pi$
$242$	3.47425	+	10.0382i	0.223333	+	0.645279i
$243$	0.690079	−	0.723734i	0.0442686	−	0.0464276i
$244$	1.59100	+	3.48381i	0.101853	+	0.223028i
$245$	−0.865526	+	4.23402i	−0.0552964	+	0.270501i
$246$	−1.56824	−	0.460477i	−0.0999873	−	0.0293589i
$247$	−3.55851	−	4.52501i	−0.226422	−	0.287920i
$248$	−6.99353	+	4.98007i	−0.444090	+	0.316235i
$249$	2.48915	−	3.16521i	0.157743	−	0.200587i
$250$	0.282559	−	5.93165i	0.0178706	−	0.375151i
$251$	−4.81023	−	5.55131i	−0.303619	−	0.350395i	0.583352	−	0.812219i	$-0.301741\pi$
$251$	−4.81023	−	5.55131i	−0.303619	−	0.350395i	−0.886972	+	0.461824i	$0.847195\pi$
$252$	1.59742	−	2.10909i	0.100628	−	0.132860i
$253$	−0.970701	−	2.78249i	−0.0610274	−	0.174934i
$254$	5.86461	+	10.1578i	0.367978	+	0.637357i
$255$	−0.455346	−	2.36256i	−0.0285149	−	0.147949i
$256$	−0.888835	+	0.458227i	−0.0555522	+	0.0286392i
$257$	−3.46620	−	8.65815i	−0.216216	−	0.540081i	0.780118	−	0.625632i	$-0.215159\pi$
$257$	−3.46620	−	8.65815i	−0.216216	−	0.540081i	−0.996334	+	0.0855517i	$0.972735\pi$
$258$	3.20794	−	7.02440i	0.199717	−	0.437320i
$259$	20.7973	−	0.378092i	1.29228	−	0.0234935i
$260$	0.246577	−	0.839763i	0.0152920	−	0.0520799i
$261$	4.47744	+	2.30828i	0.277146	+	0.142879i
$262$	−1.82452	+	19.1072i	−0.112719	+	1.18045i
$263$	−0.0420869	−	0.0102102i	−0.00259519	−	0.000629587i	0.234461	−	0.972125i	$-0.424667\pi$
$263$	−0.0420869	−	0.0102102i	−0.00259519	−	0.000629587i	−0.237056	+	0.971496i	$0.576183\pi$
$264$	−0.603378	−	0.116291i	−0.0371353	−	0.00715725i
$265$	−2.36099	−	2.04581i	−0.145034	−	0.125673i
$266$	−6.79360	−	8.32286i	−0.416542	−	0.510307i
$267$	1.99174	−	0.909597i	0.121893	−	0.0556665i
$268$	−2.35704	+	4.57202i	−0.143979	+	0.279281i
$269$	−17.8542	−	18.7249i	−1.08859	−	1.14168i	−0.989192	−	0.146629i	$-0.953158\pi$
$269$	−17.8542	−	18.7249i	−1.08859	−	1.14168i	−0.0993952	−	0.995048i	$-0.531691\pi$
$270$	0.229453	−	0.573145i	0.0139640	−	0.0348805i
$271$	3.02816	+	31.7123i	0.183948	+	1.92639i	0.343414	+	0.939184i	$0.388417\pi$
$271$	3.02816	+	31.7123i	0.183948	+	1.92639i	−0.159466	+	0.987203i	$0.550977\pi$
$272$	−0.554636	+	3.85758i	−0.0336298	+	0.233900i
$273$	0.642774	−	3.69528i	0.0389025	−	0.223648i
$274$	−7.72933	+	6.69751i	−0.466946	+	0.404611i
$275$	−2.45796	+	1.41910i	−0.148220	+	0.0855751i
$276$	−4.71138	−	0.896031i	−0.283592	−	0.0539348i
$277$	−1.54770	+	2.68070i	−0.0929925	+	0.161068i	−0.908769	−	0.417300i	$-0.862977\pi$
$277$	−1.54770	+	2.68070i	−0.0929925	+	0.161068i	0.815776	+	0.578367i	$0.196310\pi$
$278$	−13.0485	−	4.51614i	−0.782599	−	0.270860i
$279$	−4.64166	+	7.22257i	−0.277889	+	0.432404i
$280$	0.431619	−	1.57534i	0.0257942	−	0.0941448i
$281$	17.2777	+	7.89044i	1.03070	+	0.470704i	0.857664	−	0.514211i	$-0.171915\pi$
$281$	17.2777	+	7.89044i	1.03070	+	0.470704i	0.173035	+	0.984916i	$0.444643\pi$
$282$	−5.63109	+	4.42834i	−0.335327	+	0.263704i
$283$	−20.0465	+	19.1143i	−1.19164	+	1.13623i	−0.204089	+	0.978952i	$0.565423\pi$
$283$	−20.0465	+	19.1143i	−1.19164	+	1.13623i	−0.987555	+	0.157277i	$0.949728\pi$
$284$	−0.491680	−	10.3216i	−0.0291758	−	0.612476i
$285$	−2.04208	−	1.45416i	−0.120962	−	0.0861370i
$286$	−0.835837	+	0.245424i	−0.0494241	+	0.0145122i
$287$	−4.23062	+	0.895434i	−0.249725	+	0.0528558i
$288$	−0.654861	+	0.755750i	−0.0385880	+	0.0445330i
$289$	−1.31101	−	1.25004i	−0.0771181	−	0.0735320i
$290$	3.09586	+	0.295619i	0.181795	+	0.0173593i
$291$	4.99918	−	0.238140i	0.293057	−	0.0139600i
$292$	−10.9781	+	2.66327i	−0.642447	+	0.155856i
$293$	1.74318	+	12.1241i	0.101838	+	0.708297i	0.975216	+	0.221255i	$0.0710152\pi$
$293$	1.74318	+	12.1241i	0.101838	+	0.708297i	−0.873378	+	0.487042i	$0.838076\pi$
$294$	1.07405	−	6.91711i	0.0626397	−	0.403414i
$295$	0.439375	+	0.0631726i	0.0255814	+	0.00367805i
$296$	−7.85304	−	0.374086i	−0.456449	−	0.0217433i
$297$	−0.603378	+	0.116291i	−0.0350115	+	0.00674792i
$298$	12.5681	+	7.25617i	0.728048	+	0.420338i
$299$	−6.51871	+	1.93149i	−0.376986	+	0.111701i
$300$			4.61886i			0.266670i
$301$	−1.34295	−	20.3870i	−0.0774061	−	1.17509i
$302$	−0.654108	−	0.420370i	−0.0376397	−	0.0241896i
$303$	−6.22789	+	2.49327i	−0.357783	+	0.143235i
$304$	2.35542	+	3.30772i	0.135092	+	0.189711i
$305$	2.19509	+	0.878783i	0.125691	+	0.0503190i
$306$	0.918811	+	3.78739i	0.0525249	+	0.216511i
$307$	7.96517	+	12.3940i	0.454596	+	0.707366i	0.990591	−	0.136856i	$-0.0436997\pi$
$307$	7.96517	+	12.3940i	0.454596	+	0.707366i	−0.535995	+	0.844221i	$0.680063\pi$
$308$	−1.55133	+	0.486310i	−0.0883951	+	0.0277101i
$309$	0.288057	+	0.981032i	0.0163870	+	0.0558090i
$310$	−1.00311	+	5.20462i	−0.0569727	+	0.295603i
$311$	6.84825	−	2.37020i	0.388329	−	0.134402i	−0.125926	−	0.992040i	$-0.540190\pi$
$311$	6.84825	−	2.37020i	0.388329	−	0.134402i	0.514254	+	0.857638i	$0.328069\pi$
$312$	−0.334225	+	1.37769i	−0.0189218	+	0.0779966i
$313$	3.90277	−	5.48067i	0.220597	−	0.309786i	−0.689415	−	0.724366i	$-0.742132\pi$
$313$	3.90277	−	5.48067i	0.220597	−	0.309786i	0.910012	+	0.414581i	$0.136072\pi$
$314$	9.67399	−	6.21710i	0.545935	−	0.350851i
$315$	−0.184795	−	1.62292i	−0.0104120	−	0.0914410i
$316$	0.347920	−	0.0500233i	0.0195720	−	0.00281403i
$317$	19.0002	−	1.81430i	1.06716	−	0.101901i	0.453330	−	0.891343i	$-0.350236\pi$
$317$	19.0002	−	1.81430i	1.06716	−	0.101901i	0.613826	+	0.789441i	$0.289630\pi$
$318$	3.97762	+	3.12804i	0.223054	+	0.175412i
$319$	−1.41840	−	2.75130i	−0.0794149	−	0.154043i
$320$	−0.201921	+	0.583414i	−0.0112878	+	0.0326138i
$321$	−18.4756			−1.03121
$322$	−12.0982	+	3.82526i	−0.674209	+	0.213173i
$323$	15.8254			0.880550
$324$	−0.327068	+	0.945001i	−0.0181704	+	0.0525000i
$325$	3.00044	+	5.82005i	0.166435	+	0.322838i
$326$	12.3760	+	9.73256i	0.685441	+	0.539037i
$327$	−7.71777	+	0.736958i	−0.426794	+	0.0407539i
$328$	1.61781	−	0.232606i	0.0893286	−	0.0128435i
$329$	−7.55889	+	17.3810i	−0.416735	+	0.958245i
$330$	−0.319139	+	0.205098i	−0.0175680	+	0.0112903i
$331$	−6.68077	+	9.38183i	−0.367208	+	0.515672i	−0.956297	−	0.292396i	$-0.905547\pi$
$331$	−6.68077	+	9.38183i	−0.367208	+	0.515672i	0.589089	+	0.808068i	$0.299487\pi$
$332$	−0.949333	+	3.91320i	−0.0521014	+	0.214765i
$333$	−7.42954	+	2.57139i	−0.407137	+	0.140911i
$334$	2.34281	−	12.1556i	0.128193	−	0.665127i
$335$	0.894681	+	3.04700i	0.0488816	+	0.166476i
$336$	−0.576921	+	2.58208i	−0.0314736	+	0.140864i
$337$	−3.57325	−	5.56008i	−0.194647	−	0.302877i	0.730187	−	0.683247i	$-0.239433\pi$
$337$	−3.57325	−	5.56008i	−0.194647	−	0.302877i	−0.924834	+	0.380370i	$0.875797\pi$
$338$	−2.59105	−	10.6805i	−0.140935	−	0.580940i
$339$	−15.1438	−	6.06268i	−0.822500	−	0.329279i
$340$	1.39564	+	1.95990i	0.0756892	+	0.106291i
$341$	4.89772	−	1.96075i	0.265226	−	0.106181i
$342$	3.41605	+	2.19536i	0.184719	+	0.118712i
$343$	−6.17859	−	17.4592i	−0.333612	−	0.942710i
$344$			7.72225i			0.416356i
$345$	−2.48683	+	1.60685i	−0.133887	+	0.0865098i
$346$	−2.41544	−	1.39456i	−0.129855	−	0.0749718i
$347$	−0.438163	+	0.0844490i	−0.0235218	+	0.00453346i	−0.200999	−	0.979592i	$-0.564419\pi$
$347$	−0.438163	+	0.0844490i	−0.0235218	+	0.00453346i	0.177477	+	0.984125i	$0.443207\pi$
$348$	−5.03171	−	0.239690i	−0.269728	−	0.0128487i
$349$	11.5895	+	1.66632i	0.620374	+	0.0891963i	0.445333	−	0.895365i	$-0.353085\pi$
$349$	11.5895	+	1.66632i	0.620374	+	0.0891963i	0.175041	+	0.984561i	$0.443994\pi$
$350$	5.79620	+	10.7583i	0.309820	+	0.575055i
$351$	0.201753	+	1.40323i	0.0107688	+	0.0748987i
$352$	0.597161	−	0.144870i	0.0318288	−	0.00772158i
$353$	32.1646	−	1.53219i	1.71195	−	0.0815502i	0.831451	−	0.555599i	$-0.187511\pi$
$353$	32.1646	−	1.53219i	1.71195	−	0.0815502i	0.880499	+	0.474048i	$0.157208\pi$
$354$	−0.715753	−	0.0683461i	−0.0380418	−	0.00363255i
$355$	−4.61704	−	4.40234i	−0.245047	−	0.233652i
$356$	−1.43389	+	1.65480i	−0.0759960	+	0.0877041i
$357$	6.89290	+	7.66862i	0.364811	+	0.405867i
$358$	8.49052	−	2.49304i	0.448738	−	0.131761i
$359$	13.6760	+	9.73863i	0.721791	+	0.513985i	0.880916	−	0.473273i	$-0.156928\pi$
$359$	13.6760	+	9.73863i	0.721791	+	0.513985i	−0.159124	+	0.987259i	$0.550867\pi$
$360$	0.0293756	+	0.616669i	0.00154823	+	0.0325013i
$361$	−1.81730	+	1.73279i	−0.0956473	+	0.0911995i
$362$	−11.2247	+	8.82719i	−0.589956	+	0.463947i
$363$	−9.66249	−	4.41271i	−0.507149	−	0.231607i
$364$	0.950385	+	3.62836i	0.0498137	+	0.190178i
$365$	−3.77051	+	5.86702i	−0.197357	+	0.307094i
$366$	−3.61927	−	1.25264i	−0.189182	−	0.0654766i
$367$	−7.07004	+	12.2457i	−0.369053	+	0.639218i	−0.989418	−	0.145095i	$-0.953651\pi$
$367$	−7.07004	+	12.2457i	−0.369053	+	0.639218i	0.620365	+	0.784313i	$0.286985\pi$
$368$	4.65785	−	1.14212i	0.242807	−	0.0595371i
$369$	1.41547	−	0.817223i	0.0736865	−	0.0425429i
$370$	−3.66819	+	3.17851i	−0.190700	+	0.165243i
$371$	13.1901	+	2.29435i	0.684795	+	0.119117i
$372$	1.22184	−	8.49810i	0.0633495	−	0.440606i
$373$	−1.10874	−	11.6112i	−0.0574082	−	0.601206i	−0.977705	−	0.209984i	$-0.932659\pi$
$373$	−1.10874	−	11.6112i	−0.0574082	−	0.601206i	0.920296	−	0.391222i	$-0.127947\pi$
$374$	0.890053	−	2.22325i	0.0460236	−	0.114961i
$375$	4.09795	+	4.29781i	0.211617	+	0.221938i
$376$	3.28262	−	6.36740i	0.169288	−	0.328374i
$377$	−6.49598	+	2.96661i	−0.334560	+	0.152788i
$378$	0.424069	+	2.61154i	0.0218118	+	0.134323i
$379$	−3.11351	−	2.69787i	−0.159930	−	0.138580i	0.571220	−	0.820797i	$-0.306470\pi$
$379$	−3.11351	−	2.69787i	−0.159930	−	0.138580i	−0.731150	+	0.682217i	$0.761016\pi$
$380$	2.46162	+	0.474439i	0.126279	+	0.0243382i
$381$	−11.3986	−	2.76527i	−0.583967	−	0.141669i
$382$	−1.20232	+	12.5912i	−0.0615158	+	0.644223i
$383$	−10.6167	−	5.47331i	−0.542490	−	0.279673i	0.165123	−	0.986273i	$-0.447198\pi$
$383$	−10.6167	−	5.47331i	−0.542490	−	0.279673i	−0.707613	+	0.706600i	$0.750228\pi$
$384$	0.281733	−	0.959493i	0.0143771	−	0.0489639i
$385$	−0.485966	+	0.878205i	−0.0247671	+	0.0447575i
$386$	10.0139	−	21.9273i	0.509692	−	1.11607i
$387$	2.87007	+	7.16909i	0.145894	+	0.364425i
$388$	−4.44849	+	2.29335i	−0.225838	+	0.116427i
$389$	−4.71749	−	24.4767i	−0.239186	−	1.24102i	−0.880615	−	0.473833i	$-0.842870\pi$
$389$	−4.71749	−	24.4767i	−0.239186	−	1.24102i	0.641428	−	0.767183i	$-0.278342\pi$
$390$	0.437608	+	0.757959i	0.0221591	+	0.0383807i
$391$	6.90388	−	17.3687i	0.349144	−	0.878375i
$392$	1.89648	+	6.73820i	0.0957869	+	0.340331i
$393$	−12.5695	−	14.5060i	−0.634047	−	0.731729i
$394$	−1.07995	+	22.6710i	−0.0544072	+	1.14215i
$395$	0.134143	−	0.170576i	0.00674945	−	0.00858263i
$396$	0.500542	−	0.356435i	0.0251532	−	0.0179115i
$397$	−12.0433	−	15.3142i	−0.604433	−	0.768600i	0.383490	−	0.923545i	$-0.374722\pi$
$397$	−12.0433	−	15.3142i	−0.604433	−	0.768600i	−0.987923	+	0.154946i	$0.950480\pi$
$398$	10.4714	+	3.07469i	0.524885	+	0.154120i
$399$	10.7117	+	0.826668i	0.536254	+	0.0413852i
$400$	−1.91874	−	4.20146i	−0.0959371	−	0.210073i
$401$	−13.0330	+	13.6687i	−0.650839	+	0.682581i	−0.963630	−	0.267242i	$-0.913888\pi$
$401$	−13.0330	+	13.6687i	−0.650839	+	0.682581i	0.312790	+	0.949822i	$0.398736\pi$
$402$	−1.68238	−	4.86092i	−0.0839096	−	0.242441i
$403$	−3.98083	−	11.5018i	−0.198299	−	0.572948i
$404$	4.62935	−	4.85512i	0.230319	−	0.241551i
$405$	0.256464	+	0.561578i	0.0127438	+	0.0279050i
$406$	−12.0207	+	5.75600i	−0.596578	+	0.285665i
$407$	4.63533	+	1.36106i	0.229765	+	0.0674651i
$408$	−2.40912	−	3.06344i	−0.119269	−	0.151663i
$409$	28.5952	−	20.3626i	1.41394	−	1.00686i	0.418836	−	0.908062i	$-0.362438\pi$
$409$	28.5952	−	20.3626i	1.41394	−	1.00686i	0.995107	−	0.0988028i	$-0.0315013\pi$
$410$	0.623757	−	0.793171i	0.0308051	−	0.0391719i
$411$	0.486638	−	10.2158i	0.0240041	−	0.503908i
$412$	−0.669562	−	0.772715i	−0.0329869	−	0.0380689i
$413$	−1.75291	+	0.739004i	−0.0862549	+	0.0363640i
$414$	3.89971	−	2.79146i	0.191661	−	0.137193i
$415$	1.24298	+	2.15291i	0.0610156	+	0.105682i
$416$	−0.268293	−	1.39204i	−0.0131541	−	0.0682502i
$417$	12.2730	−	6.32718i	0.601012	−	0.309843i
$418$	−0.927374	−	2.31647i	−0.0453594	−	0.113302i
$419$	10.8472	−	23.7521i	0.529921	−	1.16037i	−0.435623	−	0.900129i	$-0.643472\pi$
$419$	10.8472	−	23.7521i	0.529921	−	1.16037i	0.965545	−	0.260237i	$-0.0838007\pi$
$420$	0.842279	+	1.39949i	0.0410990	+	0.0682881i
$421$	−0.862602	+	2.93775i	−0.0420407	+	0.143177i	−0.977839	−	0.209359i	$-0.932862\pi$
$421$	−0.862602	+	2.93775i	−0.0420407	+	0.143177i	0.935798	+	0.352536i	$0.114681\pi$
$422$	22.2980	+	11.4954i	1.08545	+	0.559587i
$423$	0.680958	−	7.13132i	0.0331093	−	0.346737i
$424$	−4.91760	−	1.19300i	−0.238820	−	0.0579371i
$425$	−17.6755	−	3.40668i	−0.857389	−	0.165248i
$426$	7.80941	+	6.76690i	0.378367	+	0.327857i
$427$	−10.0020	+	1.62415i	−0.484030	+	0.0785980i
$428$	16.8060	−	7.67504i	0.812348	−	0.370987i
$429$	0.399172	−	0.774286i	0.0192722	−	0.0373829i
$430$	3.28993	+	3.45038i	0.158655	+	0.166392i
$431$	12.5374	−	31.3169i	0.603904	−	1.50848i	−0.239333	−	0.970938i	$-0.576929\pi$
$431$	12.5374	−	31.3169i	0.603904	−	1.50848i	0.843237	−	0.537542i	$-0.180647\pi$
$432$	−0.0950560	−	0.995472i	−0.00457339	−	0.0478947i
$433$	−0.282476	+	1.96466i	−0.0135749	+	0.0944157i	−0.995483	−	0.0949450i	$-0.969732\pi$
$433$	−0.282476	+	1.96466i	−0.0135749	+	0.0944157i	0.981908	+	0.189361i	$0.0606416\pi$
$434$	−7.81832	−	21.3272i	−0.375291	−	1.02374i
$435$	−2.35034	+	2.03658i	−0.112690	+	0.0976465i
$436$	6.71419	−	3.87644i	0.321551	−	0.185648i
$437$	−7.28230	−	18.0614i	−0.348360	−	0.863995i
$438$	5.64828	−	9.78311i	0.269885	−	0.467455i
$439$	20.1203	+	6.96370i	0.960289	+	0.332359i	0.761850	−	0.647754i	$-0.224291\pi$
$439$	20.1203	+	6.96370i	0.960289	+	0.332359i	0.198439	+	0.980113i	$0.436413\pi$
$440$	0.205098	−	0.319139i	0.00977768	−	0.0152144i
$441$	4.26497	+	5.55068i	0.203094	+	0.264318i
$442$	−5.02568	−	2.29515i	−0.239047	−	0.109169i
$443$	−17.9228	+	14.0947i	−0.851539	+	0.669657i	−0.945394	−	0.325928i	$-0.894323\pi$
$443$	−17.9228	+	14.0947i	−0.851539	+	0.669657i	0.0938558	+	0.995586i	$0.470081\pi$
$444$	5.68996	−	5.42536i	0.270033	−	0.257476i
$445$	0.0643211	+	1.35027i	0.00304911	+	0.0640087i
$446$	−8.45131	−	6.01815i	−0.400181	−	0.284968i
$447$	−13.9245	+	4.08860i	−0.658605	+	0.193384i
$448$	−0.547851	−	2.58841i	−0.0258835	−	0.122291i
$449$	13.3330	−	15.3871i	0.629222	−	0.726161i	−0.348209	−	0.937417i	$-0.613210\pi$
$449$	13.3330	−	15.3871i	0.629222	−	0.726161i	0.977431	+	0.211256i	$0.0677555\pi$
$450$	−3.34282	−	3.18738i	−0.157582	−	0.150254i
$451$	−0.999790	−	0.0954684i	−0.0470783	−	0.00449543i
$452$	16.2938	−	0.776172i	0.766398	−	0.0365080i
$453$	0.755623	−	0.183312i	0.0355022	−	0.00861275i
$454$	0.00985245	+	0.0685253i	0.000462399	+	0.00321605i
$455$	1.97044	+	1.21629i	0.0923758	+	0.0570207i
$456$	−4.01933	−	0.577893i	−0.188223	−	0.0270623i
$457$	−18.6430	−	0.888076i	−0.872083	−	0.0415424i	−0.393233	−	0.919439i	$-0.628643\pi$
$457$	−18.6430	−	0.888076i	−0.872083	−	0.0415424i	−0.478850	+	0.877897i	$0.658946\pi$
$458$	−2.25366	+	0.434358i	−0.105307	+	0.0202962i
$459$	−3.37512	−	1.94862i	−0.157537	−	0.0909540i
$460$	1.59460	−	2.49471i	0.0743484	−	0.116316i
$461$			10.5342i			0.490629i	0.969444	+	0.245314i	$0.0788912\pi$
$461$			10.5342i			0.490629i	−0.969444	+	0.245314i	$0.921109\pi$
$462$	0.718580	−	1.45834i	0.0334314	−	0.0678482i
$463$	−5.42150	−	3.48419i	−0.251959	−	0.161924i	0.408565	−	0.912729i	$-0.366029\pi$
$463$	−5.42150	−	3.48419i	−0.251959	−	0.161924i	−0.660524	+	0.750805i	$0.729666\pi$
$464$	4.67658	−	1.87222i	0.217105	−	0.0869156i
$465$	−3.07454	−	4.31758i	−0.142578	−	0.200223i
$466$	−13.3772	−	5.35544i	−0.619688	−	0.248086i
$467$	−4.75696	−	19.6084i	−0.220126	−	0.907371i	−0.969474	−	0.245194i	$-0.921148\pi$
$467$	−4.75696	−	19.6084i	−0.220126	−	0.907371i	0.749348	−	0.662176i	$-0.230367\pi$
$468$	−0.766442	−	1.19261i	−0.0354288	−	0.0551283i
$469$	−10.0186	−	9.21091i	−0.462616	−	0.425320i
$470$	−1.24601	−	4.24353i	−0.0574743	−	0.195739i
$471$	−2.17629	+	11.2917i	−0.100278	+	0.520293i
$472$	0.679464	−	0.235165i	0.0312748	−	0.0108243i
$473$	1.11872	−	4.61142i	0.0514388	−	0.212033i
$474$	−0.203889	+	0.286322i	−0.00936492	+	0.0131512i
$475$	−15.7782	+	10.1401i	−0.723955	+	0.465258i
$476$	−9.45566	−	4.11221i	−0.433400	−	0.188483i
$477$	−5.00874	+	0.720148i	−0.229334	+	0.0329733i
$478$	15.0683	−	1.43885i	0.689207	−	0.0658113i
$479$	0.0889319	+	0.0699369i	0.00406340	+	0.00319550i	0.620189	−	0.784453i	$-0.287056\pi$
$479$	0.0889319	+	0.0699369i	0.00406340	+	0.00319550i	−0.616125	+	0.787648i	$0.711298\pi$
$480$	−0.282895	−	0.548739i	−0.0129123	−	0.0250464i
$481$	3.64535	−	10.5325i	0.166213	−	0.480242i
$482$	−17.0231			−0.775380
$483$	5.58027	−	11.3956i	0.253911	−	0.518520i
$484$	10.6224			0.482837
$485$	−1.01059	+	2.91990i	−0.0458883	+	0.132586i
$486$	−0.458227	−	0.888835i	−0.0207856	−	0.0403184i
$487$	3.20948	+	2.52396i	0.145435	+	0.114372i	0.688226	−	0.725497i	$-0.258390\pi$
$487$	3.20948	+	2.52396i	0.145435	+	0.114372i	−0.542791	+	0.839868i	$0.682632\pi$
$488$	3.81257	−	0.364056i	0.172587	−	0.0164800i
$489$	−15.5842	+	2.24067i	−0.704741	+	0.101326i
$490$	3.71806	+	2.20273i	0.167965	+	0.0995094i
$491$	−0.649848	+	0.417632i	−0.0293272	+	0.0188475i	−0.555222	−	0.831702i	$-0.687367\pi$
$491$	−0.649848	+	0.417632i	−0.0293272	+	0.0188475i	0.525895	+	0.850549i	$0.323730\pi$
$492$	−0.948072	+	1.33138i	−0.0427424	+	0.0600233i
$493$	4.62844	−	19.0787i	0.208454	−	0.859260i
$494$	−5.44001	+	1.88281i	−0.244758	+	0.0847115i
$495$	0.0717947	−	0.372506i	0.00322693	−	0.0167429i
$496$	2.41881	+	8.23771i	0.108608	+	0.369884i
$497$	26.6816	+	5.96152i	1.19683	+	0.267411i
$498$	−2.17700	−	3.38748i	−0.0975539	−	0.151797i
$499$	−4.15581	−	17.1305i	−0.186040	−	0.766865i	−0.985991	−	0.166800i	$-0.946656\pi$
$499$	−4.15581	−	17.1305i	−0.186040	−	0.766865i	0.799951	−	0.600065i	$-0.204859\pi$
$500$	−5.51300	−	2.20707i	−0.246549	−	0.0987033i
$501$	7.18073	+	10.0839i	0.320811	+	0.450516i
$502$	−6.81926	+	2.73002i	−0.304359	+	0.121847i
$503$	18.2763	+	11.7455i	0.814900	+	0.523704i	0.880447	−	0.474145i	$-0.157243\pi$
$503$	18.2763	+	11.7455i	0.814900	+	0.523704i	−0.0655470	+	0.997849i	$0.520879\pi$
$504$	−1.47062	−	2.19938i	−0.0655067	−	0.0979682i
$505$		−	4.14157i		−	0.184298i
$506$	−2.94694	+	0.00724848i	−0.131008	+	0.000322234i
$507$	9.51784	+	5.49513i	0.422702	+	0.244047i
$508$	11.5173	−	2.21977i	0.510995	−	0.0984863i
$509$	−25.9572	−	1.23649i	−1.15053	−	0.0548066i	−0.536368	−	0.843984i	$-0.680204\pi$
$509$	−25.9572	−	1.23649i	−1.15053	−	0.0548066i	−0.614165	+	0.789178i	$0.710507\pi$
$510$	−2.38155	−	0.342415i	−0.105457	−	0.0151624i
$511$	0.879236	−	29.8750i	0.0388951	−	1.32159i
$512$	0.142315	+	0.989821i	0.00628949	+	0.0437443i
$513$	−3.94620	+	0.957338i	−0.174229	+	0.0422675i
$514$	−9.31564	+	0.443759i	−0.410895	+	0.0195734i
$515$	−0.628369	−	0.0600020i	−0.0276893	−	0.00264400i
$516$	−5.58885	−	5.32896i	−0.246036	−	0.234594i
$517$	−2.88270	+	3.32681i	−0.126781	+	0.146313i
$518$	6.44484	−	19.7771i	0.283170	−	0.868958i
$519$	2.67613	−	0.785784i	0.117469	−	0.0344921i
$520$	−0.712930	−	0.507675i	−0.0312640	−	0.0222630i
$521$	−0.914737	−	19.2027i	−0.0400753	−	0.841285i	−0.926016	−	0.377485i	$-0.876789\pi$
$521$	−0.914737	−	19.2027i	−0.0400753	−	0.841285i	0.885940	−	0.463800i	$-0.153514\pi$
$522$	3.64575	−	3.47622i	0.159570	−	0.152150i
$523$	−28.0043	+	22.0228i	−1.22454	+	0.962991i	−0.999934	−	0.0114587i	$-0.996352\pi$
$523$	−28.0043	+	22.0228i	−1.22454	+	0.962991i	−0.224608	+	0.974449i	$0.572110\pi$
$524$	17.4596	+	7.97354i	0.762727	+	0.348326i
$525$	−11.7860	−	3.22917i	−0.514382	−	0.140933i
$526$	−0.0234139	+	0.0364328i	−0.00102090	+	0.00158854i
$527$	31.6195	+	10.9436i	1.37737	+	0.476712i
$528$	−0.307241	+	0.532157i	−0.0133709	+	0.0231592i
$529$	−22.9997	+	0.113144i	−0.999988	+	0.00491929i
$530$	−2.70549	+	1.56202i	−0.117519	+	0.0678497i
$531$	0.543390	−	0.470850i	0.0235811	−	0.0204332i
$532$	−10.0871	+	3.69782i	−0.437330	+	0.160321i
$533$	−0.329755	+	2.29350i	−0.0142833	+	0.0993424i
$534$	−0.208136	−	2.17970i	−0.00900692	−	0.0943247i
$535$	4.23927	−	10.5892i	0.183280	−	0.457811i
$536$	3.54965	+	3.72277i	0.153322	+	0.160799i
$537$	−4.05483	+	7.86527i	−0.174979	+	0.339411i
$538$	−23.5346	+	10.7479i	−1.01465	+	0.463374i
$539$	−0.156345	−	4.29853i	−0.00673425	−	0.185151i
$540$	−0.466576	−	0.404290i	−0.0200782	−	0.0173979i
$541$	−23.3103	−	4.49270i	−1.00219	−	0.193156i	−0.338341	−	0.941024i	$-0.609866\pi$
$541$	−23.3103	−	4.49270i	−1.00219	−	0.193156i	−0.663848	+	0.747868i	$0.731078\pi$
$542$	30.9586	+	7.51048i	1.32979	+	0.322603i
$543$	1.35738	−	14.2151i	0.0582508	−	0.610030i
$544$	3.46401	+	1.78582i	0.148518	+	0.0765665i
$545$	1.34848	−	4.59250i	0.0577625	−	0.196721i
$546$	−3.28181	−	1.81603i	−0.140448	−	0.0777189i
$547$	10.5026	−	22.9975i	0.449060	−	0.983304i	−0.540786	−	0.841160i	$-0.681873\pi$
$547$	10.5026	−	22.9975i	0.449060	−	0.983304i	0.989846	−	0.142144i	$-0.0453996\pi$
$548$	3.80113	+	9.49477i	0.162376	+	0.405596i
$549$	3.40416	−	1.75497i	0.145286	−	0.0749001i
$550$	0.537134	+	2.78691i	0.0229035	+	0.118834i
$551$	−10.2276	−	17.7148i	−0.435712	−	0.754675i
$552$	−2.38769	+	4.15920i	−0.101627	+	0.177027i
$553$	−0.115595	+	0.922763i	−0.00491562	+	0.0392399i
$554$	2.02706	+	2.33935i	0.0861216	+	0.0993896i
$555$	0.230949	−	4.84822i	0.00980324	−	0.205795i
$556$	−8.53552	+	10.8538i	−0.361987	+	0.460303i
$557$	−16.8445	+	11.9949i	−0.713724	+	0.508240i	−0.878292	−	0.478126i	$-0.841316\pi$
$557$	−16.8445	+	11.9949i	−0.713724	+	0.508240i	0.164568	+	0.986366i	$0.447377\pi$
$558$	5.30719	+	6.74865i	0.224671	+	0.285693i
$559$	−10.5040	−	3.08426i	−0.444273	−	0.130450i
$560$	−1.34753	−	0.923125i	−0.0569437	−	0.0390092i
$561$	0.994831	+	2.17838i	0.0420018	+	0.0919712i
$562$	13.1074	−	13.7467i	0.552904	−	0.579869i
$563$	1.54326	+	4.45896i	0.0650407	+	0.187923i	0.972838	−	0.231486i	$-0.0743587\pi$
$563$	1.54326	+	4.45896i	0.0650407	+	0.187923i	−0.907798	+	0.419409i	$0.862237\pi$
$564$	2.34304	+	6.76976i	0.0986596	+	0.285058i
$565$	6.94959	−	7.28852i	0.292371	−	0.306630i
$566$	11.5065	+	25.1957i	0.483654	+	1.05905i
$567$	−2.18271	−	1.49526i	−0.0916650	−	0.0627950i
$568$	−9.91476	−	2.91124i	−0.416014	−	0.122153i
$569$	−23.3660	−	29.7123i	−0.979554	−	1.24560i	−0.969357	−	0.245656i	$-0.920997\pi$
$569$	−23.3660	−	29.7123i	−0.979554	−	1.24560i	−0.0101966	−	0.999948i	$-0.503246\pi$
$570$	−2.04208	+	1.45416i	−0.0855334	+	0.0609080i
$571$	22.1831	−	28.2081i	0.928335	−	1.18047i	−0.0549662	−	0.998488i	$-0.517505\pi$
$571$	22.1831	−	28.2081i	0.928335	−	1.18047i	0.983301	−	0.181986i	$-0.0582525\pi$
$572$	−0.0414497	+	0.870137i	−0.00173310	+	0.0363823i
$573$	−8.28300	−	9.55909i	−0.346027	−	0.399337i
$574$	−0.537513	+	4.29080i	−0.0224354	+	0.179095i
$575$	4.24564	+	21.7406i	0.177055	+	0.906645i
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	3.66128	+	18.9965i	0.152421	+	0.790835i	0.975004	+	0.222189i	$0.0713202\pi$
$577$	3.66128	+	18.9965i	0.152421	+	0.790835i	−0.822583	+	0.568645i	$0.807468\pi$
$578$	−1.61008	+	0.830054i	−0.0669705	+	0.0345257i
$579$	8.95917	+	22.3789i	0.372330	+	0.930037i
$580$	1.29192	−	2.82890i	0.0536439	−	0.117464i
$581$	−9.32165	−	5.15825i	−0.386727	−	0.214000i
$582$	1.41003	−	4.80212i	0.0584476	−	0.199054i
$583$	2.76377	+	1.42482i	0.114464	+	0.0590101i
$584$	−1.07381	+	11.2454i	−0.0444344	+	0.465338i
$585$	−0.850545	−	0.206340i	−0.0351657	−	0.00853111i
$586$	12.0274	+	2.31809i	0.496848	+	0.0957596i
$587$	24.6994	+	21.4021i	1.01945	+	0.883360i	0.993215	−	0.116295i	$-0.0371019\pi$
$587$	24.6994	+	21.4021i	1.01945	+	0.883360i	0.0262376	+	0.999656i	$0.491647\pi$
$588$	−6.18539	−	3.27734i	−0.255081	−	0.135155i
$589$	31.7123	−	14.4825i	1.30668	−	0.596742i
$590$	0.203404	−	0.394548i	0.00837399	−	0.0162433i
$591$	−15.6625	−	16.4264i	−0.644269	−	0.675690i
$592$	−2.92199	+	7.29878i	−0.120093	+	0.299978i
$593$	−2.58131	−	27.0327i	−0.106002	−	1.11010i	−0.879369	−	0.476141i	$-0.842035\pi$
$593$	−2.58131	−	27.0327i	−0.106002	−	1.11010i	0.773367	−	0.633958i	$-0.218571\pi$
$594$	−0.0874499	+	0.608227i	−0.00358811	+	0.0249559i
$595$	−5.97683	+	2.19104i	−0.245026	+	0.0898241i
$596$	10.9677	−	9.50356i	0.449254	−	0.389281i
$597$	−9.45136	+	5.45675i	−0.386819	+	0.223330i
$598$	−0.306797	+	6.79191i	−0.0125459	+	0.277742i
$599$	5.17138	−	8.95709i	0.211297	−	0.365977i	−0.740824	−	0.671699i	$-0.765565\pi$
$599$	5.17138	−	8.95709i	0.211297	−	0.365977i	0.952121	+	0.305723i	$0.0988980\pi$
$600$	4.36482	+	1.51068i	0.178193	+	0.0616732i
$601$	7.73262	−	12.0322i	0.315420	−	0.490804i	−0.646955	−	0.762528i	$-0.723958\pi$
$601$	7.73262	−	12.0322i	0.315420	−	0.490804i	0.962375	+	0.271725i	$0.0875941\pi$
$602$	−19.7049	−	5.39884i	−0.803113	−	0.220040i
$603$	4.67899	+	2.13682i	0.190543	+	0.0870182i
$604$	−0.611188	+	0.480643i	−0.0248689	+	0.0195571i
$605$	4.74621	−	4.52550i	0.192961	−	0.183988i
$606$	0.319200	+	6.70083i	0.0129666	+	0.272203i
$607$	33.6528	+	23.9640i	1.36592	+	0.972670i	0.999102	+	0.0423783i	$0.0134935\pi$
$607$	33.6528	+	23.9640i	1.36592	+	0.972670i	0.366822	+	0.930291i	$0.380446\pi$
$608$	3.89618	−	1.14402i	0.158011	−	0.0463962i
$609$	4.12943	−	12.6719i	0.167333	−	0.513491i
$610$	1.54840	−	1.78694i	0.0626927	−	0.0723512i
$611$	7.35005	+	7.00826i	0.297351	+	0.283524i
$612$	3.87960	+	0.370457i	0.156824	+	0.0149748i
$613$	−36.8634	+	1.75602i	−1.48890	+	0.0709249i	−0.776173	−	0.630520i	$-0.782842\pi$
$613$	−36.8634	+	1.75602i	−1.48890	+	0.0709249i	−0.712724	+	0.701445i	$0.752539\pi$
$614$	14.3175	−	3.47340i	0.577809	−	0.140175i
$615$	0.143604	+	0.998785i	0.00579065	+	0.0402749i
$616$	−0.0478265	+	1.62506i	−0.00192698	+	0.0654757i
$617$	−9.36954	−	1.34714i	−0.377203	−	0.0542337i	−0.0488942	−	0.998804i	$-0.515570\pi$
$617$	−9.36954	−	1.34714i	−0.377203	−	0.0542337i	−0.328309	+	0.944570i	$0.606479\pi$
$618$	1.02129	+	0.0486501i	0.0410823	+	0.00195699i
$619$	−29.1245	+	5.61330i	−1.17061	+	0.225617i	−0.737262	−	0.675607i	$-0.763882\pi$
$619$	−29.1245	+	5.61330i	−1.17061	+	0.225617i	−0.433352	+	0.901225i	$0.642669\pi$
$620$	4.59029	+	2.65020i	0.184350	+	0.106435i
$621$	−0.670840	+	4.74868i	−0.0269199	+	0.190558i
$622$		−	7.24682i		−	0.290571i
$623$	−3.22009	−	4.81579i	−0.129010	−	0.192940i
$624$	1.19261	+	0.766442i	0.0477425	+	0.0306823i
$625$	18.0364	−	7.22070i	0.721458	−	0.288828i
$626$	−3.90277	−	5.48067i	−0.155986	−	0.219052i
$627$	2.31647	+	0.927374i	0.0925108	+	0.0370358i
$628$	−2.71111	−	11.1753i	−0.108185	−	0.445945i
$629$	16.5652	+	25.7760i	0.660498	+	1.02776i
$630$	−1.59410	−	0.356173i	−0.0635104	−	0.0141903i
$631$	0.443111	+	1.50910i	0.0176400	+	0.0600763i	0.967843	−	0.251556i	$-0.0809424\pi$
$631$	0.443111	+	1.50910i	0.0176400	+	0.0600763i	−0.950203	+	0.311633i	$0.899124\pi$
$632$	0.0665214	−	0.345146i	0.00264608	−	0.0137292i
$633$	−23.7070	+	8.20506i	−0.942267	+	0.326122i
$634$	4.49984	−	18.5486i	0.178711	−	0.736658i
$635$	4.20033	−	5.89854i	0.166685	−	0.234077i
$636$	4.25695	−	2.73577i	0.168799	−	0.108481i
$637$	−9.92296	−	0.111581i	−0.393162	−	0.00442098i
$638$	−3.06390	+	0.440522i	−0.121301	+	0.0174404i
$639$	−10.2865	+	0.982246i	−0.406929	+	0.0388571i
$640$	0.485284	+	0.381632i	0.0191825	+	0.0150853i
$641$	0.0276714	+	0.0536750i	0.00109295	+	0.00212004i	0.889381	−	0.457166i	$-0.151136\pi$
$641$	0.0276714	+	0.0536750i	0.00109295	+	0.00212004i	−0.888288	+	0.459286i	$0.848105\pi$
$642$	−6.04278	+	17.4595i	−0.238489	+	0.689070i
$643$	−4.94557			−0.195034			−0.0975171	−	0.995234i	$-0.531090\pi$
$643$	−4.94557			−0.195034			−0.0975171	+	0.995234i	$0.531090\pi$
$644$	−0.342073	+	12.6840i	−0.0134796	+	0.499818i
$645$	−4.76747			−0.187719
$646$	5.17599	−	14.9550i	0.203647	−	0.588398i
$647$	1.77103	+	3.43532i	0.0696265	+	0.135057i	0.921080	−	0.389374i	$-0.127309\pi$
$647$	1.77103	+	3.43532i	0.0696265	+	0.135057i	−0.851453	+	0.524430i	$0.824278\pi$
$648$	0.786053	+	0.618159i	0.0308791	+	0.0242836i
$649$	−0.439817	+	0.0419974i	−0.0172643	+	0.00164854i
$650$	6.48130	−	0.931870i	0.254217	−	0.0365509i
$651$	20.8304	+	9.05904i	0.816410	+	0.355052i
$652$	13.2451	−	8.51208i	0.518717	−	0.333359i
$653$	6.67921	−	9.37964i	0.261378	−	0.367054i	−0.662943	−	0.748670i	$-0.730693\pi$
$653$	6.67921	−	9.37964i	0.261378	−	0.367054i	0.924321	+	0.381616i	$0.124632\pi$
$654$	−1.82781	+	7.53434i	−0.0714731	+	0.294616i
$655$	11.1981	−	3.87571i	0.437547	−	0.151437i
$656$	0.309321	−	1.60491i	0.0120770	−	0.0626612i
$657$	3.18261	+	10.8390i	0.124165	+	0.422869i
$658$	13.9528	+	12.8279i	0.543936	+	0.500085i
$659$	14.4289	+	22.4519i	0.562071	+	0.874600i	0.999698	−	0.0245564i	$-0.00781735\pi$
$659$	14.4289	+	22.4519i	0.562071	+	0.874600i	−0.437627	+	0.899157i	$0.644181\pi$
$660$	0.0894379	+	0.368668i	0.00348137	+	0.0143504i
$661$	11.2246	+	4.49365i	0.436586	+	0.174783i	0.579535	−	0.814947i	$-0.303234\pi$
$661$	11.2246	+	4.49365i	0.436586	+	0.174783i	−0.142949	+	0.989730i	$0.545659\pi$
$662$	6.68077	+	9.38183i	0.259655	+	0.364635i
$663$	5.12919	−	2.05342i	0.199201	−	0.0797482i
$664$	3.38748	+	2.17700i	0.131460	+	0.0844841i
$665$	−2.93162	+	5.94965i	−0.113683	+	0.230718i
$666$			7.86195i			0.304644i
$667$	−23.9042	+	3.49693i	−0.925573	+	0.135402i
$668$	−10.7208	−	6.18967i	−0.414801	−	0.239486i
$669$	10.1876	−	1.96350i	0.393876	−	0.0759133i
$670$	3.17204	+	0.151103i	0.122547	+	0.00583762i
$671$	−2.32946	−	0.334925i	−0.0899277	−	0.0129296i
$672$	2.25138	+	1.38971i	0.0868489	+	0.0536091i
$673$	5.89342	+	40.9896i	0.227175	+	1.58003i	0.709926	+	0.704276i	$0.248728\pi$
$673$	5.89342	+	40.9896i	0.227175	+	1.58003i	−0.482751	+	0.875757i	$0.660363\pi$
$674$	−6.42297	+	1.55820i	−0.247404	+	0.0600195i
$675$	4.61362	−	0.219774i	0.177578	−	0.00845911i
$676$	−10.9405	−	1.04469i	−0.420788	−	0.0401804i
$677$	−12.7690	−	12.1752i	−0.490751	−	0.467930i	0.403831	−	0.914834i	$-0.367678\pi$
$677$	−12.7690	−	12.1752i	−0.490751	−	0.467930i	−0.894582	+	0.446903i	$0.852527\pi$
$678$	−10.6823	+	12.3280i	−0.410251	+	0.473455i
$679$	−2.74191	−	12.9546i	−0.105225	−	0.497151i
$680$	2.30858	−	0.677859i	0.0885299	−	0.0259947i
$681$	−0.0563931	−	0.0401573i	−0.00216099	−	0.00153883i
$682$	−0.251024	−	5.26965i	−0.00961222	−	0.201785i
$683$	15.1132	−	14.4104i	0.578289	−	0.551397i	−0.343469	−	0.939164i	$-0.611602\pi$
$683$	15.1132	−	14.4104i	0.578289	−	0.551397i	0.921757	+	0.387767i	$0.126753\pi$
$684$	3.19190	−	2.51014i	0.122045	−	0.0959775i
$685$	5.74347	+	2.62295i	0.219447	+	0.100218i
$686$	−18.5198	+	0.128412i	−0.707090	+	0.00490278i
$687$	1.24085	−	1.93079i	0.0473412	−	0.0736644i
$688$	7.29753	+	2.52570i	0.278216	+	0.0962914i
$689$	3.58684	−	6.21259i	0.136648	−	0.236681i
$690$	0.705109	+	2.87561i	0.0268430	+	0.109473i
$691$	−11.8302	+	6.83018i	−0.450043	+	0.259832i	−0.707848	−	0.706364i	$-0.750334\pi$
$691$	−11.8302	+	6.83018i	−0.450043	+	0.259832i	0.257805	+	0.966197i	$0.417001\pi$
$692$	−2.10787	+	1.82648i	−0.0801292	+	0.0694324i
$693$	0.559574	+	1.52643i	0.0212565	+	0.0579843i
$694$	−0.0635047	+	0.441685i	−0.00241061	+	0.0167661i
$695$	0.810315	+	8.48600i	0.0307370	+	0.321892i
$696$	−1.87222	+	4.67658i	−0.0709663	+	0.177265i
$697$	−4.39570	−	4.61007i	−0.166499	−	0.174619i
$698$	5.36524	−	10.4071i	0.203078	−	0.393915i
$699$	13.1073	−	5.98589i	0.495762	−	0.226407i
$700$	12.0623	−	1.95872i	0.455914	−	0.0740325i
$701$	29.0637	+	25.1839i	1.09772	+	0.951182i	0.999034	−	0.0439363i	$-0.0139899\pi$
$701$	29.0637	+	25.1839i	1.09772	+	0.951182i	0.0986883	+	0.995118i	$0.468535\pi$
$702$	1.39204	+	0.268293i	0.0525390	+	0.0101261i
$703$	31.0248	+	7.52654i	1.17012	+	0.283869i
$704$	0.0584102	−	0.611700i	0.00220142	−	0.0230543i
$705$	3.93103	+	2.02659i	0.148051	+	0.0763257i
$706$	9.07209	−	30.8967i	0.341433	−	1.16281i
$707$	9.15235	+	15.2071i	0.344209	+	0.571922i
$708$	−0.298687	+	0.654033i	−0.0112253	+	0.0245801i
$709$	−10.0842	−	25.1892i	−0.378721	−	0.945999i	−0.988196	−	0.153194i	$-0.951044\pi$
$709$	−10.0842	−	25.1892i	−0.378721	−	0.945999i	0.609475	−	0.792805i	$-0.291380\pi$
$710$	−5.67030	+	2.92324i	−0.212803	+	0.109707i
$711$	−0.0665214	−	0.345146i	−0.00249475	−	0.0129440i
$712$	1.09481	+	1.89626i	0.0410296	+	0.0710653i
$713$	−2.06032	−	41.1230i	−0.0771595	−	1.54007i
$714$	9.50130	−	4.00563i	0.355577	−	0.149907i
$715$	0.352187	+	0.406445i	0.0131710	+	0.0152002i
$716$	0.421051	−	8.83894i	0.0157354	−	0.330327i
$717$	−9.35696	+	11.8983i	−0.349442	+	0.444352i
$718$	13.6760	−	9.73863i	0.510384	−	0.363443i
$719$	−5.97124	−	7.59305i	−0.222690	−	0.283173i	0.661852	−	0.749635i	$-0.269771\pi$
$719$	−5.97124	−	7.59305i	−0.222690	−	0.283173i	−0.884541	+	0.466462i	$0.845528\pi$
$720$	0.592361	+	0.173933i	0.0220760	+	0.00648209i
$721$	2.43985	−	1.16830i	0.0908649	−	0.0435098i
$722$	1.04311	+	2.28409i	0.0388205	+	0.0850050i
$723$	11.7473	−	12.3202i	0.436886	−	0.458193i
$724$	4.67047	+	13.4944i	0.173576	+	0.501516i
$725$	7.60993	+	21.9874i	0.282626	+	0.816593i
$726$	−7.33030	+	7.68780i	−0.272053	+	0.285321i
$727$	8.85108	+	19.3812i	0.328268	+	0.718807i	0.999753	−	0.0222107i	$-0.00707047\pi$
$727$	8.85108	+	19.3812i	0.328268	+	0.718807i	−0.671485	+	0.741018i	$0.734343\pi$
$728$	3.73964	+	0.288606i	0.138600	+	0.0106964i
$729$	0.959493	+	0.281733i	0.0355368	+	0.0104345i
$730$	4.31113	+	5.48205i	0.159562	+	0.202900i
$731$	24.5151	−	17.4571i	0.906723	−	0.645675i
$732$	−2.36749	+	3.01051i	−0.0875051	+	0.111272i
$733$	−2.34229	+	49.1707i	−0.0865144	+	1.81616i	0.372826	+	0.927901i	$0.378389\pi$
$733$	−2.34229	+	49.1707i	−0.0865144	+	1.81616i	−0.459340	+	0.888260i	$0.651914\pi$
$734$	9.25978	+	10.6864i	0.341785	+	0.394441i
$735$	−4.15995	+	1.17083i	−0.153442	+	0.0431867i
$736$	0.444129	−	4.77522i	0.0163708	−	0.176017i
$737$	−1.58040	−	2.73733i	−0.0582146	−	0.100831i
$738$	−0.309321	−	1.60491i	−0.0113863	−	0.0590775i
$739$	−22.7541	+	11.7306i	−0.837024	+	0.431516i	−0.822765	−	0.568382i	$-0.807569\pi$
$739$	−22.7541	+	11.7306i	−0.837024	+	0.431516i	−0.0142597	+	0.999898i	$0.504539\pi$
$740$	1.80394	+	4.50603i	0.0663143	+	0.165645i
$741$	2.39139	−	5.23641i	0.0878498	−	0.192364i
$742$	6.48222	−	11.7142i	0.237970	−	0.430043i
$743$	−8.49813	+	28.9420i	−0.311766	+	1.06178i	0.643356	+	0.765567i	$0.277541\pi$
$743$	−8.49813	+	28.9420i	−0.311766	+	1.06178i	−0.955122	+	0.296211i	$0.904277\pi$
$744$	−7.63108	−	3.93410i	−0.279769	−	0.144231i
$745$	0.851650	−	8.91889i	0.0312021	−	0.326763i
$746$	−11.3352	−	2.74990i	−0.415013	−	0.100681i
$747$	3.95394	+	0.762060i	0.144667	+	0.0278823i
$748$	−1.80986	−	1.56825i	−0.0661751	−	0.0573410i
$749$	7.83493	+	48.2498i	0.286282	+	1.76301i
$750$	5.40174	−	2.46689i	0.197244	−	0.0900781i
$751$	−9.95766	+	19.3152i	−0.363360	+	0.704820i	−0.997668	−	0.0682607i	$-0.978255\pi$
$751$	−9.95766	+	19.3152i	−0.363360	+	0.704820i	0.634307	+	0.773081i	$0.281285\pi$
$752$	−4.94356	−	5.18466i	−0.180273	−	0.189065i
$753$	2.73002	−	6.81926i	0.0994875	−	0.248508i
$754$	0.678826	+	7.10899i	0.0247214	+	0.258894i
$755$	−0.0683152	+	0.475143i	−0.00248625	+	0.0172922i
$756$	2.60661	+	0.453407i	0.0948015	+	0.0164902i
$757$	14.2157	−	12.3180i	0.516680	−	0.447706i	−0.357073	−	0.934077i	$-0.616225\pi$
$757$	14.2157	−	12.3180i	0.516680	−	0.447706i	0.873752	+	0.486371i	$0.161680\pi$
$758$	−3.56782	+	2.05988i	−0.129589	+	0.0748183i
$759$	2.02838	−	2.13781i	0.0736254	−	0.0775974i
$760$	1.25346	−	2.17106i	0.0454679	−	0.0787527i
$761$	39.2586	+	13.5875i	1.42312	+	0.492548i	0.926789	−	0.375584i	$-0.122558\pi$
$761$	39.2586	+	13.5875i	1.42312	+	0.492548i	0.496335	+	0.868131i	$0.334679\pi$
$762$	−6.34129	+	9.86724i	−0.229721	+	0.357452i
$763$	5.19747	+	19.8428i	0.188161	+	0.718357i
$764$	11.5055	+	5.25437i	0.416253	+	0.190096i
$765$	1.89127	−	1.48731i	0.0683792	−	0.0537740i
$766$	−8.64468	+	8.24269i	−0.312345	+	0.297820i
$767$	0.0485005	+	1.01815i	0.00175125	+	0.0367633i
$768$	−0.814576	−	0.580057i	−0.0293935	−	0.0209310i
$769$	40.3249	−	11.8405i	1.45415	−	0.426978i	0.543241	−	0.839577i	$-0.317197\pi$
$769$	40.3249	−	11.8405i	1.45415	−	0.426978i	0.910913	+	0.412599i	$0.135379\pi$
$770$	0.670961	+	0.746471i	0.0241798	+	0.0269009i
$771$	6.10737	−	7.04828i	0.219951	−	0.253837i
$772$	−17.4461	−	16.6348i	−0.627899	−	0.598700i
$773$	29.1836	+	2.78670i	1.04966	+	0.100230i	0.605603	−	0.795767i	$-0.292932\pi$
$773$	29.1836	+	2.78670i	1.04966	+	0.100230i	0.444059	+	0.895998i	$0.353538\pi$
$774$	7.71350	−	0.367439i	0.277256	−	0.0132073i
$775$	−38.5373	+	9.34905i	−1.38430	+	0.335828i
$776$	0.712264	+	4.95390i	0.0255688	+	0.177835i
$777$	9.86594	+	18.3121i	0.353939	+	0.656944i
$778$	−24.6734	−	3.54750i	−0.884585	−	0.127184i
$779$	−6.62942	−	0.315798i	−0.237524	−	0.0113146i
$780$	0.859399	−	0.165636i	0.0307714	−	0.00593071i
$781$	5.49896	+	3.17482i	0.196768	+	0.113604i
$782$	−14.1554	−	12.2049i	−0.506197	−	0.436447i
$783$			5.03742i			0.180023i
$784$	6.98788	+	0.411671i	0.249567	+	0.0147025i
$785$	−5.97242	−	3.83824i	−0.213165	−	0.136993i
$786$	−17.8192	+	7.13374i	−0.635591	+	0.254452i
$787$	−28.7936	−	40.4349i	−1.02638	−	1.44135i	−0.892878	−	0.450300i	$-0.851317\pi$
$787$	−28.7936	−	40.4349i	−1.02638	−	1.44135i	−0.133502	−	0.991049i	$-0.542622\pi$
$788$	21.0709	+	8.43551i	0.750619	+	0.300502i
$789$	−0.0102102	−	0.0420869i	−0.000363492	−	0.00149834i
$790$	−0.117321	−	0.182555i	−0.00417409	−	0.00649502i
$791$	−9.41092	+	42.1198i	−0.334614	+	1.49761i
$792$	−0.173120	−	0.589591i	−0.00615154	−	0.0209502i
$793$	−1.02754	+	5.33138i	−0.0364890	+	0.189323i
$794$	−18.4109	+	6.37208i	−0.653379	+	0.226137i
$795$	0.736519	−	3.03597i	0.0261216	−	0.107675i
$796$	6.33045	−	8.88987i	0.224377	−	0.315093i
$797$	5.23984	−	3.36744i	0.185605	−	0.119281i	−0.444539	−	0.895760i	$-0.646632\pi$
$797$	5.23984	−	3.36744i	0.185605	−	0.119281i	0.630144	+	0.776479i	$0.282996\pi$
$798$	4.28464	−	9.85215i	0.151675	−	0.348762i
$799$	−27.6348	+	3.97328i	−0.977648	+	0.140565i
$800$	−4.59794	+	0.439050i	−0.162562	+	0.0155228i
$801$	1.72115	+	1.35353i	0.0608139	+	0.0478246i
$802$	8.65421	+	16.7868i	0.305591	+	0.592763i
$803$	2.27035	−	6.55976i	0.0801190	−	0.231489i
$804$	−5.14383			−0.181409
$805$	5.25095	+	5.81306i	0.185072	+	0.204884i
$806$	−12.1713			−0.428714
$807$	8.46210	−	24.4496i	0.297880	−	0.860668i
$808$	−3.07398	−	5.96269i	−0.108142	−	0.209767i
$809$	−14.2682	−	11.2207i	−0.501645	−	0.394498i	0.335022	−	0.942210i	$-0.391256\pi$
$809$	−14.2682	−	11.2207i	−0.501645	−	0.394498i	−0.836666	+	0.547713i	$0.815499\pi$
$810$	0.614573	−	0.0586846i	0.0215939	−	0.00206197i
$811$	−52.6853	+	7.57500i	−1.85003	+	0.265994i	−0.975664	−	0.219272i	$-0.929632\pi$
$811$	−52.6853	+	7.57500i	−1.85003	+	0.265994i	−0.874366	+	0.485267i	$0.838723\pi$
$812$	1.50783	+	13.2422i	0.0529146	+	0.464710i
$813$	−26.7995	+	17.2230i	−0.939898	+	0.604036i
$814$	2.80227	−	3.93524i	0.0982195	−	0.137930i
$815$	2.29160	−	9.44612i	0.0802714	−	0.330883i
$816$	−3.68290	+	1.27467i	−0.128927	+	0.0446222i
$817$	5.93444	−	30.7908i	0.207620	−	1.07723i
$818$	−9.89006	−	33.6825i	−0.345798	−	1.17768i
$819$	3.57903	−	1.12195i	0.125061	−	0.0392042i
$820$	−0.545537	−	0.848872i	−0.0190510	−	0.0296439i
$821$	5.02098	+	20.6967i	0.175233	+	0.722321i	0.989825	+	0.142287i	$0.0454457\pi$
$821$	5.02098	+	20.6967i	0.175233	+	0.722321i	−0.814592	+	0.580034i	$0.803039\pi$
$822$	−9.49477	−	3.80113i	−0.331168	−	0.132580i
$823$	2.89900	+	4.07108i	0.101053	+	0.141909i	0.862006	−	0.506898i	$-0.169208\pi$
$823$	2.89900	+	4.07108i	0.101053	+	0.141909i	−0.760953	+	0.648807i	$0.775268\pi$
$824$	−0.949209	+	0.380006i	−0.0330672	+	0.0132381i
$825$	−2.38765	−	1.53445i	−0.0831273	−	0.0534227i
$826$	0.125040	+	1.89820i	0.00435070	+	0.0660470i
$827$			41.5458i			1.44469i	0.691533	+	0.722344i	$0.256935\pi$
$827$			41.5458i			1.44469i	−0.691533	+	0.722344i	$0.743065\pi$
$828$	−1.36246	−	4.59823i	−0.0473486	−	0.159800i
$829$	17.6456	+	10.1877i	0.612857	+	0.353833i	0.774083	−	0.633084i	$-0.218211\pi$
$829$	17.6456	+	10.1877i	0.612857	+	0.353833i	−0.161226	+	0.986918i	$0.551545\pi$
$830$	2.44104	−	0.470472i	0.0847297	−	0.0163303i
$831$	−3.09190	−	0.147285i	−0.107257	−	0.00510928i
$832$	−1.40323	−	0.201753i	−0.0486481	−	0.00699454i
$833$	17.1039	−	21.2531i	0.592615	−	0.736378i
$834$	−1.96508	−	13.6674i	−0.0680451	−	0.473264i
$835$	−7.42718	+	1.80182i	−0.257028	+	0.0623544i
$836$	−2.49238	+	0.118727i	−0.0862007	+	0.00410625i
$837$	−8.54661	−	0.816102i	−0.295414	−	0.0282086i
$838$	−18.8980	−	18.0192i	−0.652820	−	0.622462i
$839$	−27.1815	+	31.3691i	−0.938410	+	1.08298i	0.0579993	+	0.998317i	$0.481528\pi$
$839$	−27.1815	+	31.3691i	−0.938410	+	1.08298i	−0.996409	+	0.0846663i	$0.973018\pi$
$840$	1.59800	−	0.338226i	0.0551363	−	0.0116699i
$841$	3.47761	−	1.02112i	0.119918	−	0.0352110i
$842$	2.49405	+	1.77600i	0.0859506	+	0.0612052i
$843$	0.903777	+	18.9726i	0.0311277	+	0.653451i
$844$	18.1561	−	17.3118i	0.624959	−	0.595897i
$845$	−5.33340	+	4.19423i	−0.183474	+	0.144286i
$846$	−6.51638	−	2.97593i	−0.224038	−	0.102315i
$847$	−7.42642	+	27.1053i	−0.255175	+	0.931349i
$848$	−2.73577	+	4.25695i	−0.0939469	+	0.146184i
$849$	−26.1754	−	9.05938i	−0.898336	−	0.310917i
$850$	−9.00042	+	15.5892i	−0.308712	+	0.534704i
$851$	21.7952	−	30.7669i	0.747129	−	1.05468i
$852$	8.94893	−	5.16667i	0.306585	−	0.177007i
$853$	−12.0356	+	10.4289i	−0.412093	+	0.357080i	−0.836099	−	0.548579i	$-0.815169\pi$
$853$	−12.0356	+	10.4289i	−0.412093	+	0.357080i	0.424006	+	0.905659i	$0.360624\pi$
$854$	−1.73651	+	9.98309i	−0.0594220	+	0.341614i
$855$	0.356773	−	2.48141i	0.0122014	−	0.0848624i
$856$	−1.75622	−	18.3919i	−0.0600263	−	0.628624i
$857$	−2.37493	+	5.93229i	−0.0811261	+	0.202643i	−0.963385	−	0.268121i	$-0.913597\pi$
$857$	−2.37493	+	5.93229i	−0.0811261	+	0.202643i	0.882259	+	0.470764i	$0.156022\pi$
$858$	−0.601144	−	0.630462i	−0.0205227	−	0.0215236i
$859$	3.78282	−	7.33766i	0.129068	−	0.250358i	−0.815442	−	0.578838i	$-0.803506\pi$
$859$	3.78282	−	7.33766i	0.129068	−	0.250358i	0.944511	+	0.328481i	$0.106537\pi$
$860$	4.33664	−	1.98048i	0.147878	−	0.0675338i
$861$	−2.73447	−	3.35001i	−0.0931906	−	0.114168i
$862$	−25.4939	−	22.0906i	−0.868325	−	0.752408i
$863$	26.9167	+	5.18777i	0.916255	+	0.176594i	0.625518	−	0.780210i	$-0.284888\pi$
$863$	26.9167	+	5.18777i	0.916255	+	0.176594i	0.290736	+	0.956803i	$0.406100\pi$
$864$	−0.971812	−	0.235759i	−0.0330617	−	0.00802068i
$865$	−0.163678	+	1.71411i	−0.00556522	+	0.0582816i
$866$	1.76422	+	0.909519i	0.0599506	+	0.0309067i
$867$	0.510344	−	1.73807i	0.0173322	−	0.0590281i
$868$	−22.7113	+	0.412888i	−0.770872	+	0.0140143i
$869$	−0.0897251	+	0.196471i	−0.00304371	+	0.00666481i
$870$	1.15585	+	2.88717i	0.0391869	+	0.0978842i
$871$	−6.48155	+	3.34147i	−0.219619	+	0.113221i
$872$	−1.46724	−	7.61278i	−0.0496871	−	0.257801i
$873$	2.50242	+	4.33432i	0.0846942	+	0.146695i
$874$	−19.4499	+	0.974466i	−0.657902	+	0.0329618i
$875$	9.48610	−	12.5245i	0.320689	−	0.423407i
$876$	−7.39768	−	8.53737i	−0.249944	−	0.288451i
$877$	0.0107451	−	0.225567i	0.000362836	−	0.00761686i	−0.998679	−	0.0513900i	$-0.983635\pi$
$877$	0.0107451	−	0.225567i	0.000362836	−	0.00761686i	0.999041	+	0.0437731i	$0.0139379\pi$
$878$	13.1614	−	16.7361i	0.444176	−	0.564816i
$879$	−9.97755	+	7.10498i	−0.336534	+	0.239645i
$880$	−0.234506	−	0.298198i	−0.00790519	−	0.0100523i
$881$	25.8567	+	7.59221i	0.871134	+	0.255788i	0.686598	−	0.727038i	$-0.259103\pi$
$881$	25.8567	+	7.59221i	0.871134	+	0.255788i	0.184536	+	0.982826i	$0.440922\pi$
$882$	6.64033	−	2.21495i	0.223592	−	0.0745813i
$883$	9.55496	+	20.9224i	0.321550	+	0.704096i	0.999520	−	0.0309938i	$-0.00986721\pi$
$883$	9.55496	+	20.9224i	0.321550	+	0.704096i	−0.677970	+	0.735090i	$0.737140\pi$
$884$	−3.81266	+	3.99860i	−0.128234	+	0.134487i
$885$	0.145183	+	0.419479i	0.00488028	+	0.0141006i
$886$	7.45748	+	21.5470i	0.250539	+	0.723885i
$887$	−28.5010	+	29.8910i	−0.956969	+	1.00364i	0.0430209	+	0.999074i	$0.486302\pi$
$887$	−28.5010	+	29.8910i	−0.956969	+	1.00364i	−0.999990	+	0.00456571i	$0.998547\pi$
$888$	−3.26597	−	7.15148i	−0.109599	−	0.239988i
$889$	−2.38783	+	30.9406i	−0.0800851	+	1.03771i
$890$	1.29704	+	0.380845i	0.0434769	+	0.0127660i
$891$	−0.379848	−	0.483015i	−0.0127254	−	0.0161816i
$892$	−8.45131	+	6.01815i	−0.282971	+	0.201502i
$893$	−17.9820	+	22.8660i	−0.601745	+	0.765181i
$894$	−0.690525	+	14.4959i	−0.0230946	+	0.484815i
$895$	−3.57755	−	4.12871i	−0.119584	−	0.138008i
$896$	−2.62523	−	0.328866i	−0.0877029	−	0.0109866i
$897$	−4.70382	−	4.90899i	−0.157056	−	0.163907i
$898$	−10.1800	−	17.6323i	−0.339711	−	0.588397i
$899$	−8.18486	−	42.4671i	−0.272980	−	1.41636i
$900$	−4.10540	+	2.11648i	−0.136847	+	0.0705494i
$901$	7.32957	+	18.3084i	0.244183	+	0.609940i
$902$	−0.417217	+	0.913578i	−0.0138918	+	0.0304188i
$903$	17.5053	−	10.5355i	0.582539	−	0.350600i
$904$	4.59571	−	15.6516i	0.152851	−	0.520563i
$905$	7.83588	+	4.03968i	0.260474	+	0.134283i
$906$	0.0739099	−	0.774019i	0.00245549	−	0.0257151i
$907$	29.6104	+	7.18339i	0.983196	+	0.238521i	0.694968	−	0.719041i	$-0.255419\pi$
$907$	29.6104	+	7.18339i	0.983196	+	0.238521i	0.288228	+	0.957562i	$0.406934\pi$
$908$	0.0679789	+	0.0131019i	0.00225596	+	0.000434800i
$909$	−5.06989	−	4.39309i	−0.168158	−	0.145709i
$910$	1.79387	−	1.46426i	0.0594661	−	0.0485397i
$911$	27.4882	−	12.5534i	0.910725	−	0.415914i	0.0957470	−	0.995406i	$-0.469476\pi$
$911$	27.4882	−	12.5534i	0.910725	−	0.415914i	0.814978	+	0.579491i	$0.196749\pi$
$912$	−1.86070	+	3.60926i	−0.0616141	+	0.119515i
$913$	−1.70749	−	1.79076i	−0.0565097	−	0.0592657i
$914$	−6.93676	+	17.3272i	−0.229448	+	0.573132i
$915$	0.224757	+	2.35376i	0.00743023	+	0.0778129i
$916$	−0.326632	+	2.27178i	−0.0107922	+	0.0750616i
$917$	−32.5527	+	38.9773i	−1.07498	+	1.28714i
$918$	−2.94534	+	2.55216i	−0.0972108	+	0.0842337i
$919$	−34.4269	+	19.8764i	−1.13564	+	0.655662i	−0.945347	−	0.326066i	$-0.894277\pi$
$919$	−34.4269	+	19.8764i	−1.13564	+	0.655662i	−0.190292	+	0.981728i	$0.560944\pi$
$920$	−1.83596	−	2.32283i	−0.0605298	−	0.0765815i
$921$	−7.36641	+	12.7590i	−0.242732	+	0.420424i
$922$	9.95487	+	3.44542i	0.327846	+	0.113469i
$923$	7.91991	−	12.3236i	0.260687	−	0.405637i
$924$	−1.14311	−	1.15604i	−0.0376055	−	0.0380308i
$925$	−33.0316	−	15.0850i	−1.08607	−	0.495993i
$926$	−5.06576	+	3.98376i	−0.166471	+	0.130914i
$927$	−0.739981	+	0.705570i	−0.0243042	+	0.0231740i
$928$	−0.239690	−	5.03171i	−0.00786821	−	0.165174i
$929$	21.1008	+	15.0258i	0.692294	+	0.492980i	0.871227	−	0.490881i	$-0.163325\pi$
$929$	21.1008	+	15.0258i	0.692294	+	0.492980i	−0.178933	+	0.983861i	$0.557264\pi$
$930$	−5.08570	+	1.49330i	−0.166767	+	0.0489671i
$931$	−2.38361	−	28.3245i	−0.0781195	−	0.928299i
$932$	−9.43616	+	10.8899i	−0.309092	+	0.356711i
$933$	5.24477	+	5.00088i	0.171706	+	0.163721i
$934$	−20.0858	−	1.91797i	−0.657229	−	0.0627577i
$935$	−1.47679	+	0.0703483i	−0.0482963	+	0.00230064i
$936$	−1.37769	+	0.334225i	−0.0450313	+	0.0109245i
$937$	3.30447	+	22.9831i	0.107952	+	0.750825i	0.969843	+	0.243731i	$0.0783713\pi$
$937$	3.30447	+	22.9831i	0.107952	+	0.750825i	−0.861891	+	0.507094i	$0.830720\pi$
$938$	−11.9811	+	6.45499i	−0.391196	+	0.210763i
$939$	6.65976	+	0.957529i	0.217333	+	0.0312478i
$940$	−4.41767	−	0.210439i	−0.144088	−	0.00686378i
$941$	−17.0497	+	3.28606i	−0.555805	+	0.107123i	−0.459416	−	0.888221i	$-0.651941\pi$
$941$	−17.0497	+	3.28606i	−0.555805	+	0.107123i	−0.0963888	+	0.995344i	$0.530729\pi$
$942$	9.95885	+	5.74975i	0.324477	+	0.187337i
$943$	−3.23870	+	7.13816i	−0.105466	+	0.232451i
$944$		−	0.719008i		−	0.0234017i
$945$	1.35783	−	0.907915i	0.0441701	−	0.0295345i
$946$	−3.99190	−	2.56544i	−0.129788	−	0.0834096i
$947$	47.0317	−	18.8287i	1.52833	−	0.611849i	0.553111	−	0.833108i	$-0.313441\pi$
$947$	47.0317	−	18.8287i	1.52833	−	0.611849i	0.975215	+	0.221258i	$0.0710165\pi$
$948$	0.203889	+	0.286322i	0.00662200	+	0.00929929i
$949$	−14.8675	−	5.95204i	−0.482619	−	0.193211i
$950$	4.42181	+	18.2269i	0.143462	+	0.591360i
$951$	10.3190	+	16.0567i	0.334616	+	0.520673i
$952$	−6.97869	+	7.59064i	−0.226181	+	0.246014i
$953$	16.9848	+	57.8449i	0.550192	+	1.87378i	0.482130	+	0.876100i	$0.339863\pi$
$953$	16.9848	+	57.8449i	0.550192	+	1.87378i	0.0680617	+	0.997681i	$0.478319\pi$
$954$	−0.957658	+	4.96880i	−0.0310053	+	0.160871i
$955$	7.37930	−	2.55400i	0.238789	−	0.0826455i
$956$	3.56864	−	14.7101i	0.115418	−	0.475760i
$957$	1.79551	−	2.52144i	0.0580406	−	0.0815066i
$958$	0.0951772	−	0.0611667i	0.00307504	−	0.00197621i
$959$	−26.8854	+	3.06133i	−0.868174	+	0.0988554i
$960$	−0.611084	+	0.0878607i	−0.0197227	+	0.00283569i
$961$	42.5171	−	4.05989i	1.37152	−	0.130964i
$962$	−8.76098	−	6.88971i	−0.282465	−	0.222133i
$963$	−8.46601	−	16.4218i	−0.272813	−	0.529184i
$964$	−5.56771	+	16.0868i	−0.179324	+	0.518122i
$965$	−14.8821			−0.479071
$966$	−8.94376	−	9.00051i	−0.287761	−	0.289587i
$967$	16.2030			0.521054			0.260527	−	0.965467i	$-0.416104\pi$
$967$	16.2030			0.521054			0.260527	+	0.965467i	$0.416104\pi$
$968$	3.47425	−	10.0382i	0.111667	−	0.322640i
$969$	7.25163	+	14.0662i	0.232956	+	0.451871i
$970$	2.42877	+	1.91001i	0.0779832	+	0.0613267i
$971$	13.3384	−	1.27366i	0.428050	−	0.0408738i	0.121192	−	0.992629i	$-0.461328\pi$
$971$	13.3384	−	1.27366i	0.428050	−	0.0408738i	0.306858	+	0.951755i	$0.400722\pi$
$972$	−0.989821	+	0.142315i	−0.0317485	+	0.00456475i
$973$	−21.7283	−	29.3684i	−0.696578	−	0.941506i
$974$	3.43486	−	2.20745i	0.110060	−	0.0707313i
$975$	−3.79818	+	5.33380i	−0.121639	+	0.170818i
$976$	0.902936	−	3.72195i	0.0289023	−	0.119137i
$977$	−50.2716	+	17.3992i	−1.60833	+	0.556649i	−0.975947	−	0.218007i	$-0.930044\pi$
$977$	−50.2716	+	17.3992i	−1.60833	+	0.556649i	−0.632383	+	0.774656i	$0.717923\pi$
$978$	−2.97965	+	15.4599i	−0.0952788	+	0.494353i
$979$	−0.379065	−	1.29098i	−0.0121150	−	0.0412598i
$980$	3.29765	−	2.79313i	0.105339	−	0.0892233i
$981$	−4.19152	−	6.52214i	−0.133825	−	0.208236i
$982$	0.182118	+	0.750701i	0.00581162	+	0.0239558i
$983$	−19.4040	−	7.76819i	−0.618891	−	0.247767i	0.0409625	−	0.999161i	$-0.486958\pi$
$983$	−19.4040	−	7.76819i	−0.618891	−	0.247767i	−0.659854	+	0.751394i	$0.729382\pi$
$984$	0.948072	+	1.33138i	0.0302234	+	0.0424429i
$985$	13.0085	−	5.20782i	0.414485	−	0.165935i
$986$	−16.5155	−	10.6139i	−0.525962	−	0.338015i
$987$	−18.9125	+	1.24582i	−0.601993	+	0.0396549i
$988$			5.75662i			0.183143i
$989$	−31.2046	−	19.9457i	−0.992250	−	0.634237i
$990$	−0.328537	−	0.189681i	−0.0104416	−	0.00602845i
$991$	−8.30931	+	1.60149i	−0.263954	+	0.0508729i	−0.319511	−	0.947583i	$-0.603519\pi$
$991$	−8.30931	+	1.60149i	−0.263954	+	0.0508729i	0.0555571	+	0.998456i	$0.482307\pi$
$992$	8.57576	+	0.408514i	0.272281	+	0.0129703i
$993$	−11.4002	−	1.63910i	−0.361775	−	0.0520153i
$994$	14.3603	−	23.2643i	0.455482	−	0.737898i
$995$	−0.958867	−	6.66907i	−0.0303981	−	0.211424i
$996$	−3.91320	+	0.949333i	−0.123995	+	0.0300808i
$997$	36.5256	−	1.73993i	1.15678	−	0.0551042i	0.539596	−	0.841924i	$-0.318577\pi$
$997$	36.5256	−	1.73993i	1.15678	−	0.0551042i	0.617183	+	0.786820i	$0.288274\pi$
$998$	−17.5475	−	1.67559i	−0.555458	−	0.0530398i
$999$	−5.68996	−	5.42536i	−0.180022	−	0.171651i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.be.a.493.12	yes	320
7.5	odd	6	inner	966.2.be.a.355.12	yes	320
23.7	odd	22	inner	966.2.be.a.283.12	yes	320
161.145	even	66	inner	966.2.be.a.145.12	✓	320

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.be.a.145.12	✓	320	161.145	even	66	inner
966.2.be.a.283.12	yes	320	23.7	odd	22	inner
966.2.be.a.355.12	yes	320	7.5	odd	6	inner
966.2.be.a.493.12	yes	320	1.1	even	1	trivial

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.be (of order \(66\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.614573 + 0.0586846i) q^{5} +(0.989821 - 0.142315i) q^{6} +(2.12691 - 1.57361i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +O(q^{10})\)	\(q+(0.327068 - 0.945001i) q^{2} +(0.458227 + 0.888835i) q^{3} +(-0.786053 - 0.618159i) q^{4} +(-0.614573 + 0.0586846i) q^{5} +(0.989821 - 0.142315i) q^{6} +(2.12691 - 1.57361i) q^{7} +(-0.841254 + 0.540641i) q^{8} +(-0.580057 + 0.814576i) q^{9} +(-0.145550 + 0.599966i) q^{10} +(0.580686 - 0.200977i) q^{11} +(0.189251 - 0.981929i) q^{12} +(-0.399400 - 1.36023i) q^{13} +(-0.791414 - 2.52461i) q^{14} +(-0.333775 - 0.519363i) q^{15} +(0.235759 + 0.971812i) q^{16} +(3.61808 + 1.44846i) q^{17} +(0.580057 + 0.814576i) q^{18} +(3.76979 - 1.50920i) q^{19} +(0.519363 + 0.333775i) q^{20} +(2.37329 + 1.16941i) q^{21} -0.614482i q^{22} +(-0.0117961 - 4.79582i) q^{23} +(-0.866025 - 0.500000i) q^{24} +(-4.53539 + 0.874124i) q^{25} +(-1.41605 - 0.0674548i) q^{26} +(-0.989821 - 0.142315i) q^{27} +(-2.64461 - 0.0778322i) q^{28} +(-0.716899 - 4.98614i) q^{29} +(-0.599966 + 0.145550i) q^{30} +(8.57576 - 0.408514i) q^{31} +(0.995472 + 0.0950560i) q^{32} +(0.444722 + 0.424041i) q^{33} +(2.55216 - 2.94534i) q^{34} +(-1.21480 + 1.09191i) q^{35} +(0.959493 - 0.281733i) q^{36} +(6.40415 + 4.56038i) q^{37} +(-0.193214 - 4.05607i) q^{38} +(1.02601 - 0.978294i) q^{39} +(0.485284 - 0.381632i) q^{40} +(-1.48674 - 0.678974i) q^{41} +(1.88132 - 1.86028i) q^{42} +(4.17496 - 6.49637i) q^{43} +(-0.580686 - 0.200977i) q^{44} +(0.308684 - 0.534657i) q^{45} +(-4.53591 - 1.55741i) q^{46} +(-6.20400 + 3.58188i) q^{47} +(-0.755750 + 0.654861i) q^{48} +(2.04752 - 6.69385i) q^{49} +(-0.657332 + 4.57184i) q^{50} +(0.370457 + 3.87960i) q^{51} +(-0.526889 + 1.31611i) q^{52} +(3.49197 + 3.66227i) q^{53} +(-0.458227 + 0.888835i) q^{54} +(-0.345080 + 0.157593i) q^{55} +(-0.938517 + 2.47370i) q^{56} +(3.06885 + 2.65917i) q^{57} +(-4.94638 - 0.953338i) q^{58} +(-0.698741 - 0.169513i) q^{59} +(-0.0586846 + 0.614573i) q^{60} +(-3.40416 - 1.75497i) q^{61} +(2.41881 - 8.23771i) q^{62} +(0.0480914 + 2.64531i) q^{63} +(0.415415 - 0.909632i) q^{64} +(0.325285 + 0.812522i) q^{65} +(0.546173 - 0.281572i) q^{66} +(-0.973476 - 5.05088i) q^{67} +(-1.94862 - 3.37512i) q^{68} +(4.25729 - 2.20806i) q^{69} +(0.634538 + 1.50511i) q^{70} +(6.76690 + 7.80941i) q^{71} +(0.0475819 - 0.998867i) q^{72} +(6.98307 - 8.87970i) q^{73} +(6.40415 - 4.56038i) q^{74} +(-2.85519 - 3.63067i) q^{75} +(-3.89618 - 1.14402i) q^{76} +(0.918810 - 1.34123i) q^{77} +(-0.588915 - 1.28954i) q^{78} +(-0.242561 + 0.254391i) q^{79} +(-0.201921 - 0.583414i) q^{80} +(-0.327068 - 0.945001i) q^{81} +(-1.12790 + 1.18290i) q^{82} +(-1.67276 - 3.66282i) q^{83} +(-1.14265 - 2.38628i) q^{84} +(-2.30858 - 0.677859i) q^{85} +(-4.77358 - 6.07010i) q^{86} +(4.10336 - 2.92199i) q^{87} +(-0.379848 + 0.483015i) q^{88} +(0.104186 - 2.18713i) q^{89} +(-0.404290 - 0.466576i) q^{90} +(-2.98996 - 2.26459i) q^{91} +(-2.95531 + 3.77706i) q^{92} +(4.29274 + 7.43525i) q^{93} +(1.35575 + 7.03430i) q^{94} +(-2.22824 + 1.14874i) q^{95} +(0.371662 + 0.928368i) q^{96} +(2.07909 - 4.55257i) q^{97} +(-5.65602 - 4.12426i) q^{98} +(-0.173120 + 0.589591i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9}+O(q^{10}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9	\( 320 q - 16 q^{2} + 16 q^{4} + 32 q^{8} - 16 q^{9} - 22 q^{14} + 16 q^{16} + 66 q^{17} + 16 q^{18} + 40 q^{23} - 48 q^{25} + 12 q^{26} + 44 q^{28} - 24 q^{29} + 24 q^{31} - 16 q^{32} + 98 q^{35} + 32 q^{36} - 22 q^{37} - 66 q^{38} - 8 q^{39} - 88 q^{43} + 4 q^{46} - 144 q^{47} - 24 q^{49} + 80 q^{50} - 22 q^{51} + 12 q^{52} + 44 q^{53} + 44 q^{57} + 10 q^{58} + 12 q^{59} - 32 q^{64} + 108 q^{70} - 16 q^{71} + 16 q^{72} - 180 q^{73} - 22 q^{74} - 12 q^{75} + 18 q^{77} - 16 q^{78} + 44 q^{79} + 16 q^{81} + 36 q^{82} + 22 q^{84} + 68 q^{85} - 22 q^{86} + 48 q^{87} + 22 q^{88} + 8 q^{92} + 8 q^{93} - 12 q^{94} + 66 q^{95} - 90 q^{98}+O(q^{100}) \) 320 * q - 16 * q^2 + 16 * q^4 + 32 * q^8 - 16 * q^9 - 22 * q^14 + 16 * q^16 + 66 * q^17 + 16 * q^18 + 40 * q^23 - 48 * q^25 + 12 * q^26 + 44 * q^28 - 24 * q^29 + 24 * q^31 - 16 * q^32 + 98 * q^35 + 32 * q^36 - 22 * q^37 - 66 * q^38 - 8 * q^39 - 88 * q^43 + 4 * q^46 - 144 * q^47 - 24 * q^49 + 80 * q^50 - 22 * q^51 + 12 * q^52 + 44 * q^53 + 44 * q^57 + 10 * q^58 + 12 * q^59 - 32 * q^64 + 108 * q^70 - 16 * q^71 + 16 * q^72 - 180 * q^73 - 22 * q^74 - 12 * q^75 + 18 * q^77 - 16 * q^78 + 44 * q^79 + 16 * q^81 + 36 * q^82 + 22 * q^84 + 68 * q^85 - 22 * q^86 + 48 * q^87 + 22 * q^88 + 8 * q^92 + 8 * q^93 - 12 * q^94 + 66 * q^95 - 90 * q^98

Introduction

L-functions

Modular forms

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