LMFDB - Embedded newform 966.2.r.a.113.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(113,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 0, 13]))

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

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

chi := DirichletCharacter("966.113");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.r (of order $22$, degree $10$, 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:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			113.12
Character	$\chi$	$=$	966.113
Dual form			966.2.r.a.701.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.540641 + 0.841254i) q^{2} +(1.57548 + 0.719621i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.33211 - 0.684769i) q^{5} +(-1.45715 + 0.936324i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.96429 + 2.26750i) q^{9} +O(q^{10})$	\(q+(-0.540641 + 0.841254i) q^{2} +(1.57548 + 0.719621i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.33211 - 0.684769i) q^{5} +(-1.45715 + 0.936324i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.96429 + 2.26750i) q^{9} +(1.83690 - 1.59168i) q^{10} +(0.775581 - 0.498436i) q^{11} +(0.000111226 - 1.73205i) q^{12} +(2.56284 + 2.95768i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-3.18142 - 2.75708i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.52134 + 3.33127i) q^{17} +(-2.96952 + 0.426563i) q^{18} +(6.24594 - 2.85243i) q^{19} +(0.345905 + 2.40582i) q^{20} +(-0.719419 - 1.57558i) q^{21} +0.921935i q^{22} +(4.30503 + 2.11346i) q^{23} +(1.45703 + 0.936511i) q^{24} +(0.763555 + 0.490707i) q^{25} +(-3.87373 + 0.556958i) q^{26} +(1.46296 + 4.98595i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(-6.62648 - 3.02621i) q^{29} +(4.03941 - 1.18580i) q^{30} +(-0.503887 + 3.50461i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(1.58060 - 0.227152i) q^{33} +(-1.97994 - 3.08085i) q^{34} +(1.31406 + 2.04472i) q^{35} +(1.24660 - 2.72874i) q^{36} +(3.05253 + 10.3960i) q^{37} +(-0.977198 + 6.79656i) q^{38} +(1.90930 + 6.50404i) q^{39} +(-2.21092 - 1.00969i) q^{40} +(-0.299028 + 1.01840i) q^{41} +(1.71441 + 0.246607i) q^{42} +(8.13447 - 1.16956i) q^{43} +(-0.775581 - 0.498436i) q^{44} +(-3.02823 - 6.63314i) q^{45} +(-4.10543 + 2.47900i) q^{46} +8.81744i q^{47} +(-1.57558 + 0.719419i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-0.825618 + 0.377047i) q^{50} +(-4.79409 + 4.15357i) q^{51} +(1.62575 - 3.55990i) q^{52} +(-8.99806 + 10.3843i) q^{53} +(-4.98539 - 1.46489i) q^{54} +(-2.15005 + 0.631313i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(11.8930 + 0.000763727i) q^{57} +(6.12835 - 3.93845i) q^{58} +(3.74136 - 3.24191i) q^{59} +(-1.18631 + 4.03925i) q^{60} +(9.48450 + 1.36366i) q^{61} +(-2.67584 - 2.31863i) q^{62} +(0.000385298 - 3.00000i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-3.95150 - 8.65257i) q^{65} +(-0.663444 + 1.45249i) q^{66} +(-5.05903 + 7.87200i) q^{67} +3.66221 q^{68} +(5.26161 + 6.42771i) q^{69} -2.43056 q^{70} +(-2.11966 + 3.29825i) q^{71} +(1.62160 + 2.52397i) q^{72} +(-1.01635 - 2.22549i) q^{73} +(-10.3960 - 3.05253i) q^{74} +(0.849844 + 1.32257i) q^{75} +(-5.18932 - 4.49657i) q^{76} +(-0.912551 - 0.131205i) q^{77} +(-6.50379 - 1.91014i) q^{78} +(9.73714 - 8.43728i) q^{79} +(2.04472 - 1.31406i) q^{80} +(-1.28312 + 8.90806i) q^{81} +(-0.695063 - 0.802146i) q^{82} +(7.18205 - 2.10884i) q^{83} +(-1.13434 + 1.30892i) q^{84} +(5.82907 - 6.72711i) q^{85} +(-3.41393 + 7.47547i) q^{86} +(-8.26217 - 9.53629i) q^{87} +(0.838622 - 0.382986i) q^{88} +(-2.36722 - 16.4644i) q^{89} +(7.21734 + 1.03864i) q^{90} -3.91356i q^{91} +(0.134095 - 4.79396i) q^{92} +(-3.31586 + 5.15884i) q^{93} +(-7.41770 - 4.76707i) q^{94} +(-16.5195 + 2.37514i) q^{95} +(0.246607 - 1.71441i) q^{96} +(5.04241 - 17.1729i) q^{97} +(-0.909632 - 0.415415i) q^{98} +(2.65367 + 0.779558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9}+O(q^{10}) $ 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9	$ 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} + 24 q^{14} + 18 q^{15} - 24 q^{16} + 32 q^{17} - 4 q^{18} + 4 q^{20} - 8 q^{23} + 12 q^{25} - 148 q^{27} + 40 q^{30} + 16 q^{31} + 42 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} + 154 q^{41} + 4 q^{42} + 22 q^{43} + 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} + 88 q^{50} + 24 q^{51} + 8 q^{52} - 108 q^{53} + 12 q^{54} - 16 q^{55} - 24 q^{56} - 62 q^{57} - 4 q^{58} + 22 q^{59} - 18 q^{60} - 4 q^{63} + 24 q^{64} - 100 q^{66} - 44 q^{67} - 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} - 16 q^{74} - 26 q^{75} - 78 q^{78} - 4 q^{80} + 52 q^{81} + 8 q^{82} + 16 q^{83} - 28 q^{85} + 16 q^{86} - 196 q^{87} + 24 q^{89} + 126 q^{90} + 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} + 172 q^{99}+O(q^{100}) $ 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 + 24 * q^14 + 18 * q^15 - 24 * q^16 + 32 * q^17 - 4 * q^18 + 4 * q^20 - 8 * q^23 + 12 * q^25 - 148 * q^27 + 40 * q^30 + 16 * q^31 + 42 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 + 154 * q^41 + 4 * q^42 + 22 * q^43 + 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 + 88 * q^50 + 24 * q^51 + 8 * q^52 - 108 * q^53 + 12 * q^54 - 16 * q^55 - 24 * q^56 - 62 * q^57 - 4 * q^58 + 22 * q^59 - 18 * q^60 - 4 * q^63 + 24 * q^64 - 100 * q^66 - 44 * q^67 - 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 - 16 * q^74 - 26 * q^75 - 78 * q^78 - 4 * q^80 + 52 * q^81 + 8 * q^82 + 16 * q^83 - 28 * q^85 + 16 * q^86 - 196 * q^87 + 24 * q^89 + 126 * q^90 + 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 + 172 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$1$	$e\left(\frac{13}{22}\right)$

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 $

$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$2$	−0.540641	+	0.841254i	−0.382291	+	0.594856i
$3$	1.57548	+	0.719621i	0.909605	+	0.415473i
$3$	1.57548	+	0.719621i	0.909605	+	0.415473i
$4$	−0.415415	−	0.909632i	−0.207708	−	0.454816i
$5$	−2.33211	−	0.684769i	−1.04295	−	0.306238i	−0.284985	−	0.958532i	$-0.591989\pi$
$5$	−2.33211	−	0.684769i	−1.04295	−	0.306238i	−0.757966	+	0.652294i	$0.773807\pi$
$6$	−1.45715	+	0.936324i	−0.594881	+	0.382253i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$7$	−0.755750	−	0.654861i	−0.285646	−	0.247514i
$8$	0.989821	+	0.142315i	0.349955	+	0.0503159i
$9$	1.96429	+	2.26750i	0.654764	+	0.755834i
$10$	1.83690	−	1.59168i	0.580878	−	0.503334i
$11$	0.775581	−	0.498436i	0.233847	−	0.150284i	−0.418470	−	0.908231i	$-0.637434\pi$
$11$	0.775581	−	0.498436i	0.233847	−	0.150284i	0.652317	+	0.757946i	$0.273797\pi$
$12$	0.000111226	−	1.73205i	3.21081e−5	−	0.500000i
$13$	2.56284	+	2.95768i	0.710804	+	0.820311i	0.990169	−	0.139873i	$-0.0446695\pi$
$13$	2.56284	+	2.95768i	0.710804	+	0.820311i	−0.279365	+	0.960185i	$0.590124\pi$
$14$	0.959493	−	0.281733i	0.256435	−	0.0752962i
$15$	−3.18142	−	2.75708i	−0.821440	−	0.711874i
$16$	−0.654861	+	0.755750i	−0.163715	+	0.188937i
$17$	−1.52134	+	3.33127i	−0.368979	+	0.807951i	0.630516	+	0.776176i	$0.282843\pi$
$17$	−1.52134	+	3.33127i	−0.368979	+	0.807951i	−0.999495	+	0.0317748i	$0.989884\pi$
$18$	−2.96952	+	0.426563i	−0.699922	+	0.100542i
$19$	6.24594	−	2.85243i	1.43292	−	0.654391i	0.460504	−	0.887657i	$-0.347669\pi$
$19$	6.24594	−	2.85243i	1.43292	−	0.654391i	0.972413	+	0.233266i	$0.0749413\pi$
$20$	0.345905	+	2.40582i	0.0773468	+	0.537959i
$21$	−0.719419	−	1.57558i	−0.156990	−	0.343819i
$22$			0.921935i			0.196557i
$23$	4.30503	+	2.11346i	0.897661	+	0.440687i
$23$	4.30503	+	2.11346i	0.897661	+	0.440687i
$24$	1.45703	+	0.936511i	0.297416	+	0.191164i
$25$	0.763555	+	0.490707i	0.152711	+	0.0981414i
$26$	−3.87373	+	0.556958i	−0.759701	+	0.109229i
$27$	1.46296	+	4.98595i	0.281548	+	0.959547i
$28$	−0.281733	+	0.959493i	−0.0532424	+	0.181327i
$29$	−6.62648	−	3.02621i	−1.23051	−	0.561953i	−0.309276	−	0.950972i	$-0.600087\pi$
$29$	−6.62648	−	3.02621i	−1.23051	−	0.561953i	−0.921230	+	0.389019i	$0.872814\pi$
$30$	4.03941	−	1.18580i	0.737491	−	0.216496i
$31$	−0.503887	+	3.50461i	−0.0905007	+	0.629446i	0.893204	+	0.449652i	$0.148452\pi$
$31$	−0.503887	+	3.50461i	−0.0905007	+	0.629446i	−0.983704	+	0.179794i	$0.942457\pi$
$32$	−0.281733	−	0.959493i	−0.0498038	−	0.169616i
$33$	1.58060	−	0.227152i	0.275147	−	0.0395422i
$34$	−1.97994	−	3.08085i	−0.339557	−	0.528361i
$35$	1.31406	+	2.04472i	0.222117	+	0.345621i
$36$	1.24660	−	2.72874i	0.207766	−	0.454789i
$37$	3.05253	+	10.3960i	0.501833	+	1.70909i	0.687246	+	0.726425i	$0.258820\pi$
$37$	3.05253	+	10.3960i	0.501833	+	1.70909i	−0.185413	+	0.982661i	$0.559362\pi$
$38$	−0.977198	+	6.79656i	−0.158522	+	1.10255i
$39$	1.90930	+	6.50404i	0.305733	+	1.04148i
$40$	−2.21092	−	1.00969i	−0.349577	−	0.159646i
$41$	−0.299028	+	1.01840i	−0.0467004	+	0.159047i	−0.979542	−	0.201240i	$-0.935503\pi$
$41$	−0.299028	+	1.01840i	−0.0467004	+	0.159047i	0.932842	+	0.360287i	$0.117321\pi$
$42$	1.71441	+	0.246607i	0.264538	+	0.0380522i
$43$	8.13447	−	1.16956i	1.24050	−	0.178356i	0.509339	−	0.860566i	$-0.329890\pi$
$43$	8.13447	−	1.16956i	1.24050	−	0.178356i	0.731157	+	0.682210i	$0.238981\pi$
$44$	−0.775581	−	0.498436i	−0.116923	−	0.0751420i
$45$	−3.02823	−	6.63314i	−0.451421	−	0.988811i
$46$	−4.10543	+	2.47900i	−0.605313	+	0.365509i
$47$			8.81744i			1.28616i	0.765801	+	0.643078i	$0.222343\pi$
$47$			8.81744i			1.28616i	−0.765801	+	0.643078i	$0.777657\pi$
$48$	−1.57558	+	0.719419i	−0.227415	+	0.103839i
$49$	0.142315	+	0.989821i	0.0203307	+	0.141403i
$50$	−0.825618	+	0.377047i	−0.116760	+	0.0533225i
$51$	−4.79409	+	4.15357i	−0.671307	+	0.581616i
$52$	1.62575	−	3.55990i	0.225451	−	0.493670i
$53$	−8.99806	+	10.3843i	−1.23598	+	1.42639i	−0.367975	+	0.929836i	$0.619949\pi$
$53$	−8.99806	+	10.3843i	−1.23598	+	1.42639i	−0.868003	+	0.496559i	$0.834596\pi$
$54$	−4.98539	−	1.46489i	−0.678426	−	0.199346i
$55$	−2.15005	+	0.631313i	−0.289913	+	0.0851262i
$56$	−0.654861	−	0.755750i	−0.0875094	−	0.100991i
$57$	11.8930		0.000763727i	1.57527		0.000101158i
$58$	6.12835	−	3.93845i	0.804692	−	0.517144i
$59$	3.74136	−	3.24191i	0.487084	−	0.422060i	−0.376385	−	0.926464i	$-0.622833\pi$
$59$	3.74136	−	3.24191i	0.487084	−	0.422060i	0.863468	+	0.504403i	$0.168287\pi$
$60$	−1.18631	+	4.03925i	−0.153152	+	0.521466i
$61$	9.48450	+	1.36366i	1.21437	+	0.174599i	0.719576	−	0.694414i	$-0.244336\pi$
$61$	9.48450	+	1.36366i	1.21437	+	0.174599i	0.494789	+	0.869013i	$0.335245\pi$
$62$	−2.67584	−	2.31863i	−0.339832	−	0.294466i
$63$	0.000385298	−	3.00000i	4.85430e−5	−	0.377964i
$64$	0.959493	+	0.281733i	0.119937	+	0.0352166i
$65$	−3.95150	−	8.65257i	−0.490123	−	1.07322i
$66$	−0.663444	+	1.45249i	−0.0816643	+	0.178790i
$67$	−5.05903	+	7.87200i	−0.618059	+	0.961718i	0.381247	+	0.924473i	$0.375495\pi$
$67$	−5.05903	+	7.87200i	−0.618059	+	0.961718i	−0.999306	+	0.0372452i	$0.988142\pi$
$68$	3.66221			0.444109
$69$	5.26161	+	6.42771i	0.633424	+	0.773805i
$70$	−2.43056			−0.290508
$71$	−2.11966	+	3.29825i	−0.251557	+	0.391430i	−0.943949	−	0.330091i	$-0.892921\pi$
$71$	−2.11966	+	3.29825i	−0.251557	+	0.391430i	0.692392	+	0.721521i	$0.256557\pi$
$72$	1.62160	+	2.52397i	0.191107	+	0.297453i
$73$	−1.01635	−	2.22549i	−0.118954	−	0.260474i	0.840783	−	0.541372i	$-0.182095\pi$
$73$	−1.01635	−	2.22549i	−0.118954	−	0.260474i	−0.959738	+	0.280898i	$0.909368\pi$
$74$	−10.3960	−	3.05253i	−1.20851	−	0.354849i
$75$	0.849844	+	1.32257i	0.0981316	+	0.152717i
$76$	−5.18932	−	4.49657i	−0.595255	−	0.515792i
$77$	−0.912551	−	0.131205i	−0.103995	−	0.0149522i
$78$	−6.50379	−	1.91014i	−0.736410	−	0.216281i
$79$	9.73714	−	8.43728i	1.09551	−	0.949269i	0.0965755	−	0.995326i	$-0.469211\pi$
$79$	9.73714	−	8.43728i	1.09551	−	0.949269i	0.998939	+	0.0460571i	$0.0146656\pi$
$80$	2.04472	−	1.31406i	0.228607	−	0.146917i
$81$	−1.28312	+	8.90806i	−0.142569	+	0.989785i
$82$	−0.695063	−	0.802146i	−0.0767569	−	0.0885822i
$83$	7.18205	−	2.10884i	0.788332	−	0.231475i	0.137304	−	0.990529i	$-0.456156\pi$
$83$	7.18205	−	2.10884i	0.788332	−	0.231475i	0.651028	+	0.759054i	$0.274338\pi$
$84$	−1.13434	+	1.30892i	−0.123766	+	0.142815i
$85$	5.82907	−	6.72711i	0.632252	−	0.729658i
$86$	−3.41393	+	7.47547i	−0.368134	+	0.806100i
$87$	−8.26217	−	9.53629i	−0.885798	−	1.02240i
$88$	0.838622	−	0.382986i	0.0893974	−	0.0408264i
$89$	−2.36722	−	16.4644i	−0.250925	−	1.74522i	−0.592686	−	0.805434i	$-0.701933\pi$
$89$	−2.36722	−	16.4644i	−0.250925	−	1.74522i	0.341761	−	0.939787i	$-0.388977\pi$
$90$	7.21734	+	1.03864i	0.760774	+	0.109483i
$91$		−	3.91356i		−	0.410253i
$92$	0.134095	−	4.79396i	0.0139804	−	0.499805i
$93$	−3.31586	+	5.15884i	−0.343838	+	0.534947i
$94$	−7.41770	−	4.76707i	−0.765078	−	0.491686i
$95$	−16.5195	+	2.37514i	−1.69486	+	0.243684i
$96$	0.246607	−	1.71441i	0.0251692	−	0.174976i
$97$	5.04241	−	17.1729i	0.511979	−	1.74364i	−0.144704	−	0.989475i	$-0.546223\pi$
$97$	5.04241	−	17.1729i	0.511979	−	1.74364i	0.656684	−	0.754166i	$-0.271959\pi$
$98$	−0.909632	−	0.415415i	−0.0918867	−	0.0419633i
$99$	2.65367	+	0.779558i	0.266704	+	0.0783486i
$100$	0.129171	−	0.898401i	0.0129171	−	0.0898401i
$101$	0.702322	+	2.39189i	0.0698836	+	0.238002i	0.987027	−	0.160556i	$-0.0513289\pi$
$101$	0.702322	+	2.39189i	0.0698836	+	0.238002i	−0.917143	+	0.398558i	$0.869511\pi$
$102$	−0.902320	−	6.27863i	−0.0893430	−	0.621677i
$103$	−6.56299	−	10.2122i	−0.646670	−	1.00624i	−0.997559	−	0.0698218i	$-0.977757\pi$
$103$	−6.56299	−	10.2122i	−0.646670	−	1.00624i	0.350889	−	0.936417i	$-0.385879\pi$
$104$	2.11583	+	3.29230i	0.207474	+	0.322837i
$105$	0.598858	+	4.16705i	0.0584425	+	0.406662i
$106$	−3.87112	−	13.1838i	−0.375997	−	1.28053i
$107$	1.79711	−	12.4992i	0.173733	−	1.20834i	−0.697178	−	0.716898i	$-0.745561\pi$
$107$	1.79711	−	12.4992i	0.173733	−	1.20834i	0.870911	−	0.491441i	$-0.163530\pi$
$108$	3.92765	−	3.40200i	0.377938	−	0.327358i
$109$	−0.572223	−	0.261326i	−0.0548090	−	0.0250305i	0.387822	−	0.921734i	$-0.373228\pi$
$109$	−0.572223	−	0.261326i	−0.0548090	−	0.0250305i	−0.442631	+	0.896704i	$0.645955\pi$
$110$	0.631313	−	2.15005i	0.0601933	−	0.205000i
$111$	−2.67195	+	18.5753i	−0.253610	+	1.76309i
$112$	0.989821	−	0.142315i	0.0935293	−	0.0134475i
$113$	8.49932	+	5.46218i	0.799549	+	0.513839i	0.875469	−	0.483275i	$-0.160553\pi$
$113$	8.49932	+	5.46218i	0.799549	+	0.513839i	−0.0759196	+	0.997114i	$0.524189\pi$
$114$	−6.43050	+	10.0046i	−0.602272	+	0.937021i
$115$	−8.59257	−	7.87677i	−0.801261	−	0.734512i
$116$			7.28479i			0.676376i
$117$	−1.67237	+	11.6210i	−0.154610	+	1.07436i
$118$	0.704534	+	4.90014i	0.0648576	+	0.451095i
$119$	3.33127	−	1.52134i	0.305377	−	0.139461i
$120$	−2.75667	−	3.18178i	−0.251648	−	0.290455i
$121$	−4.21648	+	9.23280i	−0.383316	+	0.839345i
$122$	−6.27489	+	7.24161i	−0.568102	+	0.655625i
$123$	−1.20397	+	1.38928i	−0.108559	+	0.125267i
$124$	3.39723	−	0.997516i	0.305080	−	0.0895796i
$125$	6.51373	+	7.51725i	0.582606	+	0.672363i
$126$	2.52355	+	1.62225i	0.224816	+	0.144521i
$127$	−13.0499	+	8.38663i	−1.15799	+	0.744193i	−0.971214	−	0.238210i	$-0.923439\pi$
$127$	−13.0499	+	8.38663i	−1.15799	+	0.744193i	−0.186773	+	0.982403i	$0.559803\pi$
$128$	−0.755750	+	0.654861i	−0.0667995	+	0.0578821i
$129$	13.6574	+	4.01112i	1.20246	+	0.353159i
$130$	9.41535	+	1.35372i	0.825781	+	0.118729i
$131$	−2.90148	−	2.51415i	−0.253503	−	0.219662i	0.518833	−	0.854876i	$-0.326367\pi$
$131$	−2.90148	−	2.51415i	−0.253503	−	0.219662i	−0.772337	+	0.635214i	$0.780912\pi$
$132$	−0.863230	−	1.34340i	−0.0751345	−	0.116928i
$133$	−6.58831	−	1.93450i	−0.571279	−	0.167743i
$134$	−3.88723	−	8.51185i	−0.335806	−	0.735312i
$135$	0.00243307	−	12.6296i	0.000209406	−	1.08698i
$136$	−1.97994	+	3.08085i	−0.169779	+	0.264181i
$137$	6.47830			0.553479			0.276739	−	0.960945i	$-0.410746\pi$
$137$	6.47830			0.553479			0.276739	+	0.960945i	$0.410746\pi$
$138$	−8.25197	+	0.951269i	−0.702455	+	0.0809774i
$139$	−5.54670			−0.470465			−0.235232	−	0.971939i	$-0.575585\pi$
$139$	−5.54670			−0.470465			−0.235232	+	0.971939i	$0.575585\pi$
$140$	1.31406	−	2.04472i	0.111058	−	0.172810i
$141$	−6.34522	+	13.8917i	−0.534364	+	1.16989i
$142$	−1.62869	−	3.56634i	−0.136677	−	0.299280i
$143$	3.46190	+	1.01651i	0.289499	+	0.0850045i
$144$	−3.00000		0.000385298i	−0.250000		3.21081e-5i
$145$	13.3814	+	11.5951i	1.11127	+	0.962917i
$146$	2.42168	+	0.348185i	0.200419	+	0.0288160i
$147$	−0.488082	+	1.66186i	−0.0402563	+	0.137068i
$148$	8.18843	−	7.09532i	0.673085	−	0.583232i
$149$	5.28975	−	3.39952i	0.433353	−	0.278499i	−0.305724	−	0.952120i	$-0.598898\pi$
$149$	5.28975	−	3.39952i	0.433353	−	0.278499i	0.739077	+	0.673621i	$0.235262\pi$
$150$	−1.57208		0.000100953i	−0.128360		8.24278e-6i
$151$	4.74982	+	5.48158i	0.386535	+	0.446085i	0.915354	−	0.402650i	$-0.131911\pi$
$151$	4.74982	+	5.48158i	0.386535	+	0.446085i	−0.528820	+	0.848734i	$0.677365\pi$
$152$	6.58831	−	1.93450i	0.534382	−	0.156909i
$153$	−10.5420	+	3.09394i	−0.852270	+	0.250130i
$154$	0.603739	−	0.696752i	0.0486507	−	0.0561459i
$155$	3.57497	−	7.82808i	0.287148	−	0.628767i
$156$	5.12313	−	4.43864i	0.410179	−	0.355376i
$157$	−9.83149	+	4.48989i	−0.784639	+	0.358332i	−0.767111	−	0.641514i	$-0.778307\pi$
$157$	−9.83149	+	4.48989i	−0.784639	+	0.358332i	−0.0175272	+	0.999846i	$0.505579\pi$
$158$	1.83360	+	12.7529i	0.145873	+	1.01457i
$159$	−21.6491	+	9.88511i	−1.71688	+	0.783940i
$160$			2.43056i			0.192153i
$161$	−1.86950	−	4.41644i	−0.147338	−	0.348064i
$162$	−6.80023	−	5.89549i	−0.534277	−	0.463194i
$163$	−10.8544	−	6.97569i	−0.850181	−	0.546378i	0.0414505	−	0.999141i	$-0.486802\pi$
$163$	−10.8544	−	6.97569i	−0.850181	−	0.546378i	−0.891631	+	0.452763i	$0.850438\pi$
$164$	1.05059	−	0.151052i	0.0820371	−	0.0117952i
$165$	−3.84168	−	0.552602i	−0.299074	−	0.0430200i
$166$	−2.10884	+	7.18205i	−0.163678	+	0.557435i
$167$	−5.46626	−	2.49636i	−0.422992	−	0.193174i	0.192534	−	0.981290i	$-0.438329\pi$
$167$	−5.46626	−	2.49636i	−0.422992	−	0.193174i	−0.615526	+	0.788116i	$0.711057\pi$
$168$	−0.487868	−	1.66192i	−0.0376399	−	0.128220i
$169$	−0.329600	+	2.29242i	−0.0253538	+	0.176340i
$170$	2.50777	+	8.54068i	0.192337	+	0.655040i
$171$	18.7367	+	8.55968i	1.43283	+	0.654575i
$172$	−4.44305	−	6.91353i	−0.338780	−	0.527151i
$173$	−0.912225	−	1.41945i	−0.0693552	−	0.107919i	0.804844	−	0.593487i	$-0.202249\pi$
$173$	−0.912225	−	1.41945i	−0.0693552	−	0.107919i	−0.874199	+	0.485568i	$0.838613\pi$
$174$	12.4893	−	1.79487i	0.946812	−	0.136069i
$175$	−0.255712	−	0.870874i	−0.0193300	−	0.0658319i
$176$	−0.131205	+	0.912551i	−0.00988996	+	0.0687862i
$177$	8.22739	−	2.41521i	0.618409	−	0.181538i
$178$	15.1305	+	6.90988i	1.13408	+	0.517918i
$179$	1.75710	−	5.98413i	0.131332	−	0.447275i	−0.867401	−	0.497610i	$-0.834211\pi$
$179$	1.75710	−	5.98413i	0.131332	−	0.447275i	0.998732	+	0.0503358i	$0.0160291\pi$
$180$	−4.77575	+	5.51008i	−0.355963	+	0.410697i
$181$	5.04308	−	0.725085i	0.374849	−	0.0538952i	0.0476843	−	0.998862i	$-0.484816\pi$
$181$	5.04308	−	0.725085i	0.374849	−	0.0538952i	0.327165	+	0.944967i	$0.393907\pi$
$182$	3.29230	+	2.11583i	0.244042	+	0.156836i
$183$	13.9613	+	8.97367i	1.03205	+	0.663353i
$184$	3.96044	+	2.70462i	0.291967	+	0.199387i
$185$		−	26.3348i		−	1.93617i
$186$	−2.54721	−	5.57856i	−0.186770	−	0.409040i
$187$	0.480501	+	3.34196i	0.0351377	+	0.244388i
$188$	8.02063	−	3.66290i	0.584964	−	0.267144i
$189$	2.15947	−	4.72617i	0.157078	−	0.343778i
$190$	6.93300	−	15.1812i	0.502973	−	1.10136i
$191$	11.8883	−	13.7198i	0.860205	−	0.992730i	−0.139792	−	0.990181i	$-0.544643\pi$
$191$	11.8883	−	13.7198i	0.860205	−	0.992730i	0.999997	−	0.00254878i	$-0.000811304\pi$
$192$	1.30892	+	1.13434i	0.0944634	+	0.0818637i
$193$	−6.84418	+	2.00963i	−0.492655	+	0.144657i	−0.518618	−	0.855006i	$-0.673553\pi$
$193$	−6.84418	+	2.00963i	−0.492655	+	0.144657i	0.0259625	+	0.999663i	$0.491735\pi$
$194$	11.7206	+	13.5263i	0.841491	+	0.971132i
$195$	0.00105800	−	16.4756i	7.57649e−5	−	1.17984i
$196$	0.841254	−	0.540641i	0.0600895	−	0.0386172i
$197$	18.2213	−	15.7889i	1.29822	−	1.12491i	0.313718	−	0.949516i	$-0.398425\pi$
$197$	18.2213	−	15.7889i	1.29822	−	1.12491i	0.984498	−	0.175395i	$-0.0561201\pi$
$198$	−2.09049	+	1.81095i	−0.148565	+	0.128699i
$199$	−19.4429	−	2.79546i	−1.37827	−	0.198165i	−0.586976	−	0.809604i	$-0.699682\pi$
$199$	−19.4429	−	2.79546i	−1.37827	−	0.198165i	−0.791291	+	0.611439i	$0.790591\pi$
$200$	0.685948	+	0.594377i	0.0485039	+	0.0420288i
$201$	−13.6353	+	8.76162i	−0.961758	+	0.617997i
$202$	−2.39189	−	0.702322i	−0.168293	−	0.0494152i
$203$	3.02621	+	6.62648i	0.212398	+	0.465087i
$204$	5.76975	+	2.63541i	0.403964	+	0.184515i
$205$	1.39473	−	2.17025i	0.0974124	−	0.151577i
$206$	12.1393			0.845783
$207$	3.66406	+	13.9131i	0.254670	+	0.967028i
$208$	−3.91356			−0.271357
$209$	3.42248	−	5.32549i	0.236738	−	0.368372i
$210$	−3.82931	−	1.74908i	−0.264248	−	0.120698i
$211$	−0.773259	−	1.69320i	−0.0532333	−	0.116565i	0.881146	−	0.472844i	$-0.156773\pi$
$211$	−0.773259	−	1.69320i	−0.0532333	−	0.116565i	−0.934380	+	0.356279i	$0.884045\pi$
$212$	13.1838	+	3.87112i	0.905469	+	0.265870i
$213$	−5.71297	+	3.67099i	−0.391446	+	0.251532i
$214$	9.54337	+	8.26937i	0.652371	+	0.565283i
$215$	−19.7714	−	2.84269i	−1.34840	−	0.193870i
$216$	0.738499	+	5.14341i	0.0502485	+	0.349964i
$217$	2.67584	−	2.31863i	0.181648	−	0.157399i
$218$	0.529208	−	0.340102i	0.0358425	−	0.0230346i
$219$	0.000272123	−	4.23760i	1.83884e−5	−	0.286351i
$220$	1.46743	+	1.69350i	0.0989339	+	0.114176i
$221$	−13.7518	+	4.03788i	−0.925043	+	0.271617i
$222$	−14.1820	−	12.2904i	−0.951833	−	0.824875i
$223$	5.95480	−	6.87220i	0.398763	−	0.460197i	−0.520488	−	0.853869i	$-0.674250\pi$
$223$	5.95480	−	6.87220i	0.398763	−	0.460197i	0.919251	+	0.393672i	$0.128795\pi$
$224$	−0.415415	+	0.909632i	−0.0277561	+	0.0607773i
$225$	0.387166	+	2.69525i	0.0258110	+	0.179684i
$226$	−9.19016	+	4.19701i	−0.611320	+	0.279181i
$227$	0.629722	+	4.37981i	0.0417961	+	0.290698i	0.999990	+	0.00457703i	$0.00145692\pi$
$227$	0.629722	+	4.37981i	0.0417961	+	0.290698i	−0.958193	+	0.286121i	$0.907634\pi$
$228$	−4.93985	−	10.8186i	−0.327150	−	0.716480i
$229$		−	13.3542i		−	0.882471i	−0.897391	−	0.441236i	$-0.854540\pi$
$229$		−	13.3542i		−	0.882471i	0.897391	−	0.441236i	$-0.145460\pi$
$230$	11.2719	−	2.97003i	0.743244	−	0.195838i
$231$	−1.34329	−	0.863403i	−0.0883821	−	0.0568077i
$232$	−6.12835	−	3.93845i	−0.402346	−	0.258572i
$233$	−20.5208	+	2.95044i	−1.34436	+	0.193290i	−0.776647	−	0.629936i	$-0.783081\pi$
$233$	−20.5208	+	2.95044i	−1.34436	+	0.193290i	−0.567714	+	0.823226i	$0.692172\pi$
$234$	−8.87204	−	7.68966i	−0.579983	−	0.502689i
$235$	6.03791	−	20.5632i	0.393870	−	1.34140i
$236$	−4.50316	−	2.05652i	−0.293131	−	0.133868i
$237$	21.4123	−	6.28574i	1.39088	−	0.408303i
$238$	−0.521187	+	3.62494i	−0.0337836	+	0.234970i
$239$	6.89963	+	23.4980i	0.446300	+	1.51996i	0.808862	+	0.587999i	$0.200084\pi$
$239$	6.89963	+	23.4980i	0.446300	+	1.51996i	−0.362562	+	0.931960i	$0.618098\pi$
$240$	4.16705	−	0.598858i	0.268982	−	0.0386561i
$241$	−8.03271	−	12.4991i	−0.517432	−	0.805140i	0.479962	−	0.877290i	$-0.340651\pi$
$241$	−8.03271	−	12.4991i	−0.517432	−	0.805140i	−0.997394	+	0.0721492i	$0.977014\pi$
$242$	−5.48752	−	8.53875i	−0.352751	−	0.548892i
$243$	−8.43197	+	13.1111i	−0.540911	+	0.841080i
$244$	−2.69957	−	9.19389i	−0.172822	−	0.588578i
$245$	0.345905	−	2.40582i	0.0220991	−	0.153702i
$246$	−0.517819	−	1.76395i	−0.0330149	−	0.112465i
$247$	24.4439	+	11.1632i	1.55533	+	0.710294i
$248$	−0.997516	+	3.39723i	−0.0633423	+	0.215724i
$249$	12.8328	+	1.84591i	0.813243	+	0.116980i
$250$	−9.84550	+	1.41557i	−0.622684	+	0.0895284i
$251$	−3.23951	−	2.08190i	−0.204476	−	0.131409i	0.434396	−	0.900722i	$-0.356962\pi$
$251$	−3.23951	−	2.08190i	−0.204476	−	0.131409i	−0.638871	+	0.769314i	$0.720598\pi$
$252$	−2.72906	+	1.24589i	−0.171914	+	0.0784840i
$253$	4.39233	−	0.506623i	0.276143	−	0.0318511i
$254$		−	15.5124i		−	0.973334i
$255$	14.0246	−	6.40372i	0.878253	−	0.401017i
$256$	−0.142315	−	0.989821i	−0.00889468	−	0.0618638i
$257$	13.2346	−	6.04403i	0.825550	−	0.377016i	0.0425936	−	0.999092i	$-0.486438\pi$
$257$	13.2346	−	6.04403i	0.825550	−	0.377016i	0.782957	+	0.622076i	$0.213711\pi$
$258$	−10.7581	+	9.32073i	−0.669770	+	0.580283i
$259$	4.50096	−	9.85573i	0.279676	−	0.612405i
$260$	−6.22915	+	7.18882i	−0.386315	+	0.445832i
$261$	−6.15439	−	20.9699i	−0.380947	−	1.29800i
$262$	3.68369	−	1.08163i	0.227579	−	0.0668233i
$263$	−8.46216	−	9.76585i	−0.521799	−	0.602188i	0.432281	−	0.901739i	$-0.357709\pi$
$263$	−8.46216	−	9.76585i	−0.521799	−	0.602188i	−0.954080	+	0.299551i	$0.903163\pi$
$264$	1.59684		0.000102543i	0.0982786		6.31109e-6i
$265$	28.0953	−	18.0558i	1.72588	−	1.10916i
$266$	5.18932	−	4.49657i	0.318177	−	0.275702i
$267$	8.11860	−	27.6428i	0.496850	−	1.69171i
$268$	9.26222	+	1.33171i	0.565780	+	0.0813469i
$269$	−7.40791	−	6.41899i	−0.451669	−	0.391373i	0.399105	−	0.916905i	$-0.369321\pi$
$269$	−7.40791	−	6.41899i	−0.451669	−	0.391373i	−0.850774	+	0.525532i	$0.823866\pi$
$270$	10.6234	+	6.83011i	0.646517	+	0.415667i
$271$	17.3626	+	5.09812i	1.05470	+	0.309689i	0.762716	−	0.646734i	$-0.223866\pi$
$271$	17.3626	+	5.09812i	1.05470	+	0.309689i	0.291987	+	0.956422i	$0.405684\pi$
$272$	−1.52134	−	3.33127i	−0.0922447	−	0.201988i
$273$	2.81628	−	6.16575i	0.170449	−	0.373168i
$274$	−3.50243	+	5.44989i	−0.211590	+	0.329240i
$275$	0.836785			0.0504600
$276$	3.66110	−	7.45630i	0.220372	−	0.448816i
$277$	−20.3953			−1.22544			−0.612719	−	0.790301i	$-0.709924\pi$
$277$	−20.3953			−1.22544			−0.612719	+	0.790301i	$0.709924\pi$
$278$	2.99877	−	4.66618i	0.179854	−	0.279859i
$279$	−8.93648	+	5.74151i	−0.535013	+	0.343735i
$280$	1.00969	+	2.21092i	0.0603407	+	0.132128i
$281$	2.28387	+	0.670605i	0.136244	+	0.0400050i	0.349144	−	0.937069i	$-0.386472\pi$
$281$	2.28387	+	0.670605i	0.136244	+	0.0400050i	−0.212899	+	0.977074i	$0.568291\pi$
$282$	−8.25598	−	12.8484i	−0.491636	−	0.765109i
$283$	2.26404	+	1.96181i	0.134583	+	0.116617i	0.719551	−	0.694439i	$-0.244347\pi$
$283$	2.26404	+	1.96181i	0.134583	+	0.116617i	−0.584968	+	0.811056i	$0.698893\pi$
$284$	3.88073	+	0.557965i	0.230279	+	0.0331091i
$285$	−27.7353	−	8.14576i	−1.64290	−	0.482513i
$286$	−2.72679	+	2.36277i	−0.161238	+	0.139714i
$287$	0.892899	−	0.573831i	0.0527062	−	0.0338722i
$288$	1.62225	−	2.52355i	0.0955918	−	0.148702i
$289$	2.34977	+	2.71177i	0.138222	+	0.159516i
$290$	−16.9889	+	4.98840i	−0.997623	+	0.292929i
$291$	20.3022	−	23.4269i	1.19014	−	1.37331i
$292$	−1.60217	+	1.84900i	−0.0937599	+	0.108205i
$293$	2.01795	−	4.41870i	0.117890	−	0.258143i	−0.841483	−	0.540283i	$-0.818317\pi$
$293$	2.01795	−	4.41870i	0.117890	−	0.258143i	0.959373	+	0.282140i	$0.0910443\pi$
$294$	−1.13417	−	1.30907i	−0.0661460	−	0.0763465i
$295$	−10.9452	+	4.99851i	−0.637255	+	0.291025i
$296$	1.54196	+	10.7246i	0.0896246	+	0.623353i
$297$	3.61983	+	3.13782i	0.210044	+	0.182075i
$298$			6.28794i			0.364250i
$299$	4.78218	+	18.1493i	0.276561	+	1.04960i
$300$	0.850014	−	1.32246i	0.0490756	−	0.0763523i
$301$	−6.91353	−	4.44305i	−0.398489	−	0.256093i
$302$	−7.17934	+	1.03223i	−0.413125	+	0.0593984i
$303$	−0.614758	+	4.27378i	−0.0353169	+	0.245523i
$304$	−1.93450	+	6.58831i	−0.110951	+	0.377865i
$305$	−21.1851	−	9.67490i	−1.21305	−	0.553983i
$306$	3.09665	−	10.5412i	0.177024	−	0.602601i
$307$	−3.19064	+	22.1914i	−0.182099	+	1.26653i	0.669688	+	0.742642i	$0.266428\pi$
$307$	−3.19064	+	22.1914i	−0.182099	+	1.26653i	−0.851788	+	0.523887i	$0.824481\pi$
$308$	0.259739	+	0.884591i	0.0148000	+	0.0504042i
$309$	−2.99095	−	20.8120i	−0.170149	−	1.18395i
$310$	4.65263	+	7.23963i	0.264252	+	0.411184i
$311$	3.01936	+	4.69821i	0.171212	+	0.266411i	0.916247	−	0.400615i	$-0.131203\pi$
$311$	3.01936	+	4.69821i	0.171212	+	0.266411i	−0.745035	+	0.667026i	$0.767567\pi$
$312$	0.964249	+	6.70956i	0.0545899	+	0.379854i
$313$	−3.53749	−	12.0476i	−0.199951	−	0.680970i	−0.997024	−	0.0770875i	$-0.975438\pi$
$313$	−3.53749	−	12.0476i	−0.199951	−	0.680970i	0.797074	−	0.603882i	$-0.206380\pi$
$314$	1.53817	−	10.6982i	0.0868039	−	0.603734i
$315$	−2.05521	+	6.99606i	−0.115798	+	0.394183i
$316$	−11.7198	−	5.35224i	−0.659289	−	0.301087i
$317$	0.0664275	−	0.226231i	0.00373094	−	0.0127064i	−0.957606	−	0.288080i	$-0.906983\pi$
$317$	0.0664275	−	0.226231i	0.00373094	−	0.0127064i	0.961337	+	0.275373i	$0.0888014\pi$
$318$	3.38848	−	23.5566i	0.190016	−	1.32099i
$319$	−6.64774	+	0.955801i	−0.372202	+	0.0535146i
$320$	−2.04472	−	1.31406i	−0.114303	−	0.0734583i
$321$	11.8260	−	18.3990i	0.660061	−	1.02693i
$322$	4.72608	+	0.814981i	0.263374	+	0.0454171i
$323$			25.1464i			1.39918i
$324$	8.63609	−	2.53337i	0.479783	−	0.140743i
$325$	0.505517	+	3.51595i	0.0280411	+	0.195030i
$326$	11.7366	−	5.35994i	0.650032	−	0.296860i
$327$	−0.713472	−	0.823498i	−0.0394551	−	0.0455395i
$328$	−0.440918	+	0.965475i	−0.0243456	+	0.0533095i
$329$	5.77420	−	6.66378i	0.318342	−	0.367386i
$330$	2.54185	−	2.93307i	0.139924	−	0.161460i
$331$	−29.7170	+	8.72569i	−1.63339	+	0.479607i	−0.964573	−	0.263817i	$-0.915018\pi$
$331$	−29.7170	+	8.72569i	−1.63339	+	0.479607i	−0.668820	+	0.743424i	$0.733200\pi$
$332$	−4.90180	−	5.65698i	−0.269021	−	0.310467i
$333$	−17.5768	+	27.3423i	−0.963203	+	1.49835i
$334$	5.05535	−	3.24888i	0.276617	−	0.177771i
$335$	17.1887	−	14.8941i	0.939120	−	0.813752i
$336$	1.66186	+	0.488082i	0.0906619	+	0.0266270i
$337$	21.4112	+	3.07847i	1.16634	+	0.167695i	0.698163	−	0.715939i	$-0.254001\pi$
$337$	21.4112	+	3.07847i	1.16634	+	0.167695i	0.468179	+	0.883633i	$0.344910\pi$
$338$	−1.75031	−	1.51665i	−0.0952043	−	0.0824950i
$339$	9.45983	+	14.7219i	0.513788	+	0.799582i
$340$	−8.54068	−	2.50777i	−0.463183	−	0.136003i
$341$	1.35602	+	2.96926i	0.0734325	+	0.160795i
$342$	−17.3307	+	11.1346i	−0.937137	+	0.602091i
$343$	0.540641	−	0.841254i	0.0291919	−	0.0454234i
$344$	8.21812			0.443092
$345$	−7.86916	−	18.5931i	−0.423661	−	1.00102i
$346$	1.68730			0.0907100
$347$	−10.7050	+	16.6574i	−0.574677	+	0.894214i	−0.999941	−	0.0108548i	$-0.996545\pi$
$347$	−10.7050	+	16.6574i	−0.574677	+	0.894214i	0.425264	+	0.905069i	$0.360181\pi$
$348$	−5.24229	+	11.4771i	−0.281016	+	0.615235i
$349$	−12.7845	−	27.9942i	−0.684339	−	1.49849i	−0.857979	−	0.513685i	$-0.828280\pi$
$349$	−12.7845	−	27.9942i	−0.684339	−	1.49849i	0.173640	−	0.984809i	$-0.444447\pi$
$350$	0.870874	+	0.255712i	0.0465502	+	0.0136684i
$351$	−10.9975	+	17.1052i	−0.587002	+	0.913007i
$352$	−0.696752	−	0.603739i	−0.0371370	−	0.0321794i
$353$	27.5926	+	3.96721i	1.46861	+	0.211154i	0.829733	−	0.558160i	$-0.188492\pi$
$353$	27.5926	+	3.96721i	1.46861	+	0.211154i	0.638872	+	0.769313i	$0.279401\pi$
$354$	−2.41626	+	8.22708i	−0.128423	+	0.437265i
$355$	7.20181	−	6.24040i	0.382232	−	0.331206i
$356$	−13.9931	+	8.99285i	−0.741635	+	0.476620i
$357$	6.34314		0.000407333i	0.335715		2.15583e-5i
$358$	4.08421	+	4.71343i	0.215857	+	0.249112i
$359$	6.65291	−	1.95347i	0.351127	−	0.103100i	−0.101413	−	0.994844i	$-0.532336\pi$
$359$	6.65291	−	1.95347i	0.351127	−	0.103100i	0.452540	+	0.891744i	$0.350518\pi$
$360$	−2.05341	−	6.99659i	−0.108224	−	0.368753i
$361$	18.4331	−	21.2729i	0.970163	−	1.11963i
$362$	−2.11651	+	4.63452i	−0.111242	+	0.243585i
$363$	−13.2871	+	11.5118i	−0.697392	+	0.604215i
$364$	−3.55990	+	1.62575i	−0.186590	+	0.0852126i
$365$	0.846285	+	5.88604i	0.0442966	+	0.308089i
$366$	−15.0972	+	6.89349i	−0.789143	+	0.360328i
$367$		−	23.6405i		−	1.23402i	−0.786954	−	0.617011i	$-0.788343\pi$
$367$		−	23.6405i		−	1.23402i	0.786954	−	0.617011i	$-0.211657\pi$
$368$	−4.41644	+	1.86950i	−0.230223	+	0.0974547i
$369$	−2.89660	+	1.32238i	−0.150791	+	0.0688404i
$370$	22.1542	+	14.2377i	1.15174	+	0.740181i
$371$	13.6006	−	1.95546i	0.706106	−	0.101523i
$372$	6.07010	+	0.873147i	0.314720	+	0.0452706i
$373$	−8.14128	+	27.7267i	−0.421540	+	1.43563i	0.425914	+	0.904763i	$0.359952\pi$
$373$	−8.14128	+	27.7267i	−0.421540	+	1.43563i	−0.847454	+	0.530869i	$0.821866\pi$
$374$	−3.07121	−	1.40258i	−0.158809	−	0.0725255i
$375$	4.85270	+	16.5307i	0.250592	+	0.853642i
$376$	−1.25485	+	8.72769i	−0.0647141	+	0.450096i
$377$	−8.03205	−	27.3547i	−0.413672	−	1.40884i
$378$	2.80841	+	4.37182i	0.144449	+	0.224862i
$379$	10.7002	+	16.6498i	0.549633	+	0.855245i	0.999279	−	0.0379615i	$-0.0120864\pi$
$379$	10.7002	+	16.6498i	0.549633	+	0.855245i	−0.449647	+	0.893207i	$0.648450\pi$
$380$	9.02294	+	14.0400i	0.462867	+	0.720235i
$381$	−26.5950	+	3.82204i	−1.36250	+	0.195809i
$382$	5.11454	+	17.4185i	0.261683	+	0.891210i
$383$	−3.08626	+	21.4654i	−0.157700	+	1.09683i	0.745157	+	0.666889i	$0.232375\pi$
$383$	−3.08626	+	21.4654i	−0.157700	+	1.09683i	−0.902857	+	0.429940i	$0.858535\pi$
$384$	−1.66192	+	0.487868i	−0.0848096	+	0.0248964i
$385$	2.03832	+	0.930871i	0.103883	+	0.0474416i
$386$	2.00963	−	6.84418i	0.102288	−	0.348360i
$387$	18.6305	+	16.1476i	0.947039	+	0.820827i
$388$	−17.7157	+	2.54713i	−0.899378	+	0.129311i
$389$	−29.1706	−	18.7468i	−1.47901	−	0.950501i	−0.997243	−	0.0741999i	$-0.976360\pi$
$389$	−29.1706	−	18.7468i	−1.47901	−	0.950501i	−0.481765	−	0.876301i	$-0.660004\pi$
$390$	13.8596	+	8.90825i	0.701806	+	0.451087i
$391$	−13.5899	+	11.1259i	−0.687271	+	0.562662i
$392$			1.00000i			0.0505076i
$393$	−2.76200	−	6.04896i	−0.139324	−	0.305130i
$394$	3.43125	+	23.8649i	0.172864	+	1.20229i
$395$	−28.4857	+	13.0090i	−1.43327	+	0.654552i
$396$	−0.393264	−	2.73770i	−0.0197622	−	0.137575i
$397$	10.6545	−	23.3301i	0.534734	−	1.17090i	−0.428820	−	0.903390i	$-0.641071\pi$
$397$	10.6545	−	23.3301i	0.534734	−	1.17090i	0.963554	−	0.267514i	$-0.0862022\pi$
$398$	12.8633	−	14.8450i	0.644778	−	0.744114i
$399$	−8.98766	−	7.78886i	−0.449946	−	0.389931i
$400$	−0.870874	+	0.255712i	−0.0435437	+	0.0127856i
$401$	4.46424	+	5.15201i	0.222934	+	0.257279i	0.856188	−	0.516665i	$-0.172827\pi$
$401$	4.46424	+	5.15201i	0.222934	+	0.257279i	−0.633254	+	0.773944i	$0.718281\pi$
$402$	0.00104079	−	16.2076i	5.19100e−5	−	0.808362i
$403$	−11.6569	+	7.49142i	−0.580670	+	0.373174i
$404$	1.88398	−	1.63248i	0.0937317	−	0.0812190i
$405$	9.09234	−	19.8959i	0.451802	−	0.988637i
$406$	−7.21064	−	1.03673i	−0.357858	−	0.0514522i
$407$	7.54921	+	6.54142i	0.374200	+	0.324246i
$408$	−5.33641	+	3.42902i	−0.264192	+	0.169762i
$409$	30.4293	+	8.93484i	1.50463	+	0.441800i	0.927177	−	0.374624i	$-0.122228\pi$
$409$	30.4293	+	8.93484i	1.50463	+	0.441800i	0.577454	+	0.816423i	$0.304046\pi$
$410$	1.07168	+	2.34665i	0.0529264	+	0.115893i
$411$	10.2064	+	4.66192i	0.503447	+	0.229956i
$412$	−6.56299	+	10.2122i	−0.323335	+	0.503119i
$413$	−4.95053			−0.243600
$414$	−13.6854	−	4.43959i	−0.672601	−	0.218194i
$415$	−18.1934			−0.893078
$416$	2.11583	−	3.29230i	0.103737	−	0.161418i
$417$	−8.73872	−	3.99152i	−0.427937	−	0.195466i
$418$	2.62975	+	5.75835i	0.128625	+	0.281650i
$419$	−22.8864	−	6.72005i	−1.11807	−	0.328296i	−0.330064	−	0.943959i	$-0.607070\pi$
$419$	−22.8864	−	6.72005i	−1.11807	−	0.328296i	−0.788010	+	0.615663i	$0.788888\pi$
$420$	3.54171	−	2.27579i	0.172818	−	0.111047i
$421$	−11.1516	−	9.66289i	−0.543494	−	0.470941i	0.339314	−	0.940673i	$-0.389805\pi$
$421$	−11.1516	−	9.66289i	−0.543494	−	0.470941i	−0.882809	+	0.469732i	$0.844350\pi$
$422$	1.84247	+	0.264907i	0.0896899	+	0.0128955i
$423$	−19.9936	+	17.3200i	−0.972120	+	0.842128i
$424$	−10.3843	+	8.99806i	−0.504307	+	0.436984i
$425$	−2.79630	+	1.79707i	−0.135641	+	0.0871709i
$426$	0.000436076	−	6.79074i	2.11280e−5	−	0.329013i
$427$	−6.27489	−	7.24161i	−0.303663	−	0.350446i
$428$	−12.1162	+	3.55763i	−0.585657	+	0.171964i
$429$	4.72267	+	4.09275i	0.228013	+	0.197600i
$430$	13.0806	−	15.0958i	0.630804	−	0.727986i
$431$	−3.87779	+	8.49119i	−0.186787	+	0.409006i	−0.979739	−	0.200278i	$-0.935816\pi$
$431$	−3.87779	+	8.49119i	−0.186787	+	0.409006i	0.792952	+	0.609284i	$0.208543\pi$
$432$	−4.72617	−	2.15947i	−0.227388	−	0.103898i
$433$	−9.07795	+	4.14576i	−0.436258	+	0.199233i	−0.621423	−	0.783475i	$-0.713445\pi$
$433$	−9.07795	+	4.14576i	−0.436258	+	0.199233i	0.185165	+	0.982707i	$0.440718\pi$
$434$	0.503887	+	3.50461i	0.0241873	+	0.168227i
$435$	12.7381	+	27.8974i	0.610746	+	1.33758i
$436$			0.629071i			0.0301270i
$437$	32.9175	+	0.920756i	1.57466	+	0.0440457i
$438$	3.56475	+	2.29125i	0.170330	+	0.109480i
$439$	2.05376	+	1.31987i	0.0980205	+	0.0629939i	0.588733	−	0.808328i	$-0.299627\pi$
$439$	2.05376	+	1.31987i	0.0980205	+	0.0629939i	−0.490712	+	0.871322i	$0.663263\pi$
$440$	−2.21801	+	0.318902i	−0.105740	+	0.0152031i
$441$	−1.96487	+	2.26700i	−0.0935654	+	0.107952i
$442$	4.03788	−	13.7518i	0.192062	−	0.654104i
$443$	15.5933	+	7.12121i	0.740859	+	0.338339i	0.749839	−	0.661621i	$-0.230131\pi$
$443$	15.5933	+	7.12121i	0.740859	+	0.338339i	−0.00897946	+	0.999960i	$0.502858\pi$
$444$	18.0067	−	5.28598i	0.854559	−	0.250862i
$445$	−5.75368	+	40.0177i	−0.272751	+	1.89702i
$446$	2.56186	+	8.72489i	0.121308	+	0.413135i
$447$	10.7803	−	1.54926i	0.509889	−	0.0732776i
$448$	−0.540641	−	0.841254i	−0.0255429	−	0.0397455i
$449$	22.6188	+	35.1955i	1.06745	+	1.66098i	0.667867	+	0.744280i	$0.267207\pi$
$449$	22.6188	+	35.1955i	1.06745	+	1.66098i	0.399579	+	0.916699i	$0.369156\pi$
$450$	−2.47671	−	1.13146i	−0.116753	−	0.0533375i
$451$	0.275685	+	0.938897i	0.0129815	+	0.0442109i
$452$	1.43783	−	10.0003i	0.0676298	−	0.470376i
$453$	3.53859	+	12.0542i	0.166258	+	0.566356i
$454$	−4.02498	−	1.83815i	−0.188902	−	0.0862686i
$455$	−2.67989	+	9.12686i	−0.125635	+	0.427874i
$456$	11.7719	+	1.69331i	0.551269	+	0.0792966i
$457$	−19.3214	+	2.77800i	−0.903818	+	0.129949i	−0.578526	−	0.815664i	$-0.696372\pi$
$457$	−19.3214	+	2.77800i	−0.903818	+	0.129949i	−0.325292	+	0.945613i	$0.605463\pi$
$458$	11.2343	+	7.21983i	0.524943	+	0.337361i
$459$	−18.8352	−	2.71180i	−0.879152	−	0.126576i
$460$	−3.59548	+	11.0882i	−0.167640	+	0.516990i
$461$		−	15.6186i		−	0.727430i	−0.931510	−	0.363715i	$-0.881508\pi$
$461$		−	15.6186i		−	0.727430i	0.931510	−	0.363715i	$-0.118492\pi$
$462$	1.45258	−	0.663258i	0.0675801	−	0.0308575i
$463$	−0.0123900	−	0.0861747i	−0.000575814	−	0.00400488i	0.989532	−	0.144317i	$-0.0460985\pi$
$463$	−0.0123900	−	0.0861747i	−0.000575814	−	0.00400488i	−0.990107	+	0.140312i	$0.955189\pi$
$464$	6.62648	−	3.02621i	0.307626	−	0.140488i
$465$	11.2656	−	9.76039i	0.522427	−	0.452627i
$466$	8.61230	−	18.8583i	0.398957	−	0.873594i
$467$	6.51651	−	7.52045i	0.301548	−	0.348005i	−0.584672	−	0.811270i	$-0.698777\pi$
$467$	6.51651	−	7.52045i	0.301548	−	0.348005i	0.886220	+	0.463265i	$0.153322\pi$
$468$	11.2655	−	3.30629i	0.520750	−	0.152833i
$469$	8.97843	−	2.63630i	0.414585	−	0.121733i
$470$	14.0345	+	16.1967i	0.647365	+	0.747100i
$471$	−18.7204	−	0.00120215i	−0.862589	−	5.53923e-5i
$472$	4.16465	−	2.67646i	0.191694	−	0.123194i
$473$	5.72600	−	4.96160i	0.263282	−	0.228135i
$474$	−6.28849	+	21.4115i	−0.288840	+	0.983465i
$475$	6.16882	+	0.886943i	0.283045	+	0.0406957i
$476$	−2.76772	−	2.39824i	−0.126858	−	0.109923i
$477$	−41.2212	−	0.00529415i	−1.88739	−	0.000242402i
$478$	−23.4980	−	6.89963i	−1.07477	−	0.315582i
$479$	−5.95053	−	13.0298i	−0.271887	−	0.595349i	0.723603	−	0.690216i	$-0.242485\pi$
$479$	−5.95053	−	13.0298i	−0.271887	−	0.595349i	−0.995490	+	0.0948673i	$0.969757\pi$
$480$	−1.74908	+	3.82931i	−0.0798344	+	0.174783i
$481$	−22.9247	+	35.6716i	−1.04528	+	1.62648i
$482$	14.8578			0.676752
$483$	0.232792	−	8.30336i	0.0105924	−	0.377816i
$484$	10.1500			0.461365
$485$	−23.5189	+	36.5961i	−1.06794	+	1.66174i
$486$	−6.47113	−	14.1818i	−0.293536	−	0.643301i
$487$	8.94159	+	19.5794i	0.405182	+	0.887225i	0.996718	+	0.0809468i	$0.0257944\pi$
$487$	8.94159	+	19.5794i	0.405182	+	0.887225i	−0.591536	+	0.806278i	$0.701478\pi$
$488$	9.19389	+	2.69957i	0.416188	+	0.122204i
$489$	−12.0810	−	18.8011i	−0.546323	−	0.850216i
$490$	1.83690	+	1.59168i	0.0829826	+	0.0719048i
$491$	−35.4301	−	5.09408i	−1.59894	−	0.229893i	−0.715560	−	0.698551i	$-0.753828\pi$
$491$	−35.4301	−	5.09408i	−1.59894	−	0.229893i	−0.883379	+	0.468659i	$0.844737\pi$
$492$	1.76388	+	0.518046i	0.0795220	+	0.0233553i
$493$	20.1622	−	17.4707i	0.908061	−	0.786839i
$494$	−22.6064	+	14.5283i	−1.01711	+	0.653657i
$495$	−5.65483	−	3.63517i	−0.254166	−	0.163389i
$496$	−2.31863	−	2.67584i	−0.104110	−	0.120149i
$497$	3.76182	−	1.10457i	0.168741	−	0.0495468i
$498$	−8.49080	+	9.79763i	−0.380482	+	0.439042i
$499$	22.1034	−	25.5087i	0.989484	−	1.14193i	−0.000392985	−	1.00000i	$-0.500125\pi$
$499$	22.1034	−	25.5087i	0.989484	−	1.14193i	0.989877	−	0.141926i	$-0.0453295\pi$
$500$	4.13203	−	9.04788i	0.184790	−	0.404633i
$501$	−6.81557	−	7.86660i	−0.304497	−	0.351454i
$502$	3.50282	−	1.59968i	0.156338	−	0.0713974i
$503$	2.27396	+	15.8157i	0.101391	+	0.705189i	0.975587	+	0.219615i	$0.0704802\pi$
$503$	2.27396	+	15.8157i	0.101391	+	0.705189i	−0.874196	+	0.485574i	$0.838611\pi$
$504$	0.427326	−	2.96941i	0.0190346	−	0.132268i
$505$		−	6.05907i		−	0.269625i
$506$	−1.94847	+	3.96896i	−0.0866202	+	0.176442i
$507$	−2.16895	+	3.37448i	−0.0963265	+	0.149866i
$508$	13.0499	+	8.38663i	0.578993	+	0.372097i
$509$	−23.0650	+	3.31625i	−1.02234	+	0.146990i	−0.633038	−	0.774121i	$-0.718192\pi$
$509$	−23.0650	+	3.31625i	−1.02234	+	0.146990i	−0.389300	+	0.921111i	$0.627283\pi$
$510$	−2.19511	+	15.2603i	−0.0972009	+	0.675739i
$511$	−0.689281	+	2.34748i	−0.0304920	+	0.103846i
$512$	0.909632	+	0.415415i	0.0402004	+	0.0183589i
$513$	23.3597	+	26.9690i	1.03135	+	1.19071i
$514$	−2.07059	+	14.4013i	−0.0913299	+	0.635213i
$515$	8.31260	+	28.3101i	0.366297	+	1.24749i
$516$	−2.02483	−	14.0895i	−0.0891384	−	0.620254i
$517$	4.39493	+	6.83864i	0.193289	+	0.300763i
$518$	5.85776	+	9.11486i	0.257375	+	0.400484i
$519$	−0.415729	−	2.89278i	−0.0182485	−	0.126979i
$520$	−2.67989	−	9.12686i	−0.117521	−	0.400239i
$521$	4.26868	−	29.6893i	0.187014	−	1.30071i	−0.652672	−	0.757641i	$-0.726352\pi$
$521$	4.26868	−	29.6893i	0.187014	−	1.30071i	0.839686	−	0.543072i	$-0.182739\pi$
$522$	20.9683	+	6.15978i	0.917758	+	0.269606i
$523$	2.75830	+	1.25968i	0.120612	+	0.0550818i	0.474807	−	0.880090i	$-0.342518\pi$
$523$	2.75830	+	1.25968i	0.120612	+	0.0550818i	−0.354195	+	0.935172i	$0.615245\pi$
$524$	−1.08163	+	3.68369i	−0.0472512	+	0.160923i
$525$	0.223830	−	1.55606i	0.00976874	−	0.0679121i
$526$	12.7905	−	1.83900i	0.557694	−	0.0801843i
$527$	−10.9082	−	7.01028i	−0.475169	−	0.305372i
$528$	−0.863403	+	1.34329i	−0.0375748	+	0.0584592i
$529$	14.0666	+	18.1970i	0.611591	+	0.791174i
$530$			33.3969i			1.45067i
$531$	14.7002	+	2.11549i	0.637932	+	0.0918044i
$532$	0.977198	+	6.79656i	0.0423669	+	0.294668i
$533$	−3.77845	+	1.72556i	−0.163663	+	0.0747423i
$534$	18.8654	+	21.7746i	0.816385	+	0.942281i
$535$	−12.7501	+	27.9188i	−0.551234	+	1.20703i
$536$	−6.12784	+	7.07190i	−0.264682	+	0.305460i
$537$	7.07458	−	8.16344i	0.305291	−	0.352279i
$538$	9.40502	−	2.76156i	0.405479	−	0.119059i
$539$	0.603739	+	0.696752i	0.0260049	+	0.0300112i
$540$	−11.4893	+	5.24430i	−0.494420	+	0.225679i
$541$	−15.8727	+	10.2008i	−0.682420	+	0.438565i	−0.835384	−	0.549667i	$-0.814755\pi$
$541$	−15.8727	+	10.2008i	−0.682420	+	0.438565i	0.152964	+	0.988232i	$0.451118\pi$
$542$	−13.6757	+	11.8501i	−0.587423	+	0.509005i
$543$	8.46707	+	2.48675i	0.363357	+	0.106717i
$544$	3.62494	+	0.521187i	0.155418	+	0.0223457i
$545$	1.15554	+	1.00128i	0.0494979	+	0.0428901i
$546$	3.66436	+	5.70267i	0.156820	+	0.244052i
$547$	13.7256	+	4.03020i	0.586865	+	0.172319i	0.561667	−	0.827363i	$-0.310160\pi$
$547$	13.7256	+	4.03020i	0.586865	+	0.172319i	0.0251978	+	0.999682i	$0.491978\pi$
$548$	−2.69118	−	5.89287i	−0.114962	−	0.251731i
$549$	15.5382	+	24.1847i	0.663154	+	1.03218i
$550$	−0.452400	+	0.703948i	−0.0192904	+	0.0300165i
$551$	−50.0206			−2.13095
$552$	4.29330	+	7.11109i	0.182735	+	0.302668i
$553$	−12.8841			−0.547887
$554$	11.0266	−	17.1576i	0.468473	−	0.728959i
$555$	18.9511	−	41.4900i	0.804428	−	1.76115i
$556$	2.30418	+	5.04545i	0.0977190	+	0.213975i
$557$	39.8091	+	11.6890i	1.68676	+	0.495278i	0.977725	−	0.209891i	$-0.0673109\pi$
$557$	39.8091	+	11.6890i	1.68676	+	0.495278i	0.709039	+	0.705169i	$0.249129\pi$
$558$	0.00136420	−	10.6219i	5.77513e−5	−	0.449663i
$559$	24.3065	+	21.0617i	1.02806	+	0.890816i
$560$	−2.40582	−	0.345905i	−0.101665	−	0.0146172i
$561$	−1.64792	+	5.61098i	−0.0695753	+	0.236896i
$562$	−1.79890	+	1.55876i	−0.0758822	+	0.0657523i
$563$	17.9831	−	11.5570i	0.757896	−	0.487070i	−0.103735	−	0.994605i	$-0.533079\pi$
$563$	17.9831	−	11.5570i	0.757896	−	0.487070i	0.861631	+	0.507535i	$0.169443\pi$
$564$	15.2723		0.000980727i	0.643078		4.12961e-5i
$565$	−16.0810	−	18.5585i	−0.676533	−	0.780761i
$566$	−2.87441	+	0.844003i	−0.120820	+	0.0354761i
$567$	6.80326	−	5.89200i	0.285710	−	0.247441i
$568$	−2.56747	+	2.96302i	−0.107729	+	0.124326i
$569$	−12.3505	+	27.0438i	−0.517759	+	1.13373i	0.452522	+	0.891753i	$0.350524\pi$
$569$	−12.3505	+	27.0438i	−0.517759	+	1.13373i	−0.970281	+	0.241981i	$0.922203\pi$
$570$	21.8475	−	18.9285i	0.915091	−	0.792828i
$571$	−34.5301	+	15.7694i	−1.44504	+	0.659928i	−0.974896	−	0.222662i	$-0.928526\pi$
$571$	−34.5301	+	15.7694i	−1.44504	+	0.659928i	−0.470145	+	0.882589i	$0.655798\pi$
$572$	−0.513480	−	3.57133i	−0.0214697	−	0.149325i
$573$	28.6028	−	13.0603i	1.19490	−	0.545600i
$574$			1.06139i			0.0443016i
$575$	2.25004	+	3.72625i	0.0938331	+	0.155395i
$576$	1.24589	+	2.72906i	0.0519123	+	0.113711i
$577$	1.04658	+	0.672598i	0.0435698	+	0.0280006i	0.562244	−	0.826971i	$-0.309938\pi$
$577$	1.04658	+	0.672598i	0.0435698	+	0.0280006i	−0.518675	+	0.854972i	$0.673574\pi$
$578$	−3.55167	+	0.510653i	−0.147730	+	0.0212404i
$579$	−12.2291	−	1.75908i	−0.508223	−	0.0731047i
$580$	4.98840	−	16.9889i	0.207132	−	0.705426i
$581$	−6.80883	−	3.10949i	−0.282478	−	0.129003i
$582$	8.73180	+	29.7449i	0.361945	+	1.23296i
$583$	−1.80281	+	12.5388i	−0.0746649	+	0.519305i
$584$	−0.689281	−	2.34748i	−0.0285227	−	0.0971393i
$585$	11.8578	−	25.9562i	0.490261	−	1.07316i
$586$	2.62626	+	4.08654i	0.108490	+	0.168813i
$587$	−0.864854	−	1.34574i	−0.0356964	−	0.0555446i	0.822947	−	0.568118i	$-0.192328\pi$
$587$	−0.864854	−	1.34574i	−0.0356964	−	0.0555446i	−0.858643	+	0.512574i	$0.828692\pi$
$588$	1.71444	−	0.246386i	0.0707022	−	0.0101608i
$589$	6.84939	+	23.3269i	0.282224	+	0.961167i
$590$	1.71241	−	11.9101i	0.0704990	−	0.490331i
$591$	40.0694	−	11.7626i	1.64823	−	0.483850i
$592$	−9.85573	−	4.50096i	−0.405068	−	0.184988i
$593$	5.00401	−	17.0421i	0.205490	−	0.699835i	−0.790667	−	0.612247i	$-0.790266\pi$
$593$	5.00401	−	17.0421i	0.205490	−	0.699835i	0.996157	−	0.0875882i	$-0.0279160\pi$
$594$	−4.59673	+	1.34876i	−0.188606	+	0.0553403i
$595$	−8.81064	+	1.26678i	−0.361201	+	0.0519329i
$596$	−5.28975	−	3.39952i	−0.216677	−	0.139250i
$597$	−28.6202	−	18.3957i	−1.17135	−	0.752885i
$598$	−17.8536	−	5.78925i	−0.730090	−	0.236740i
$599$		−	30.5728i		−	1.24917i	−0.780957	−	0.624585i	$-0.785268\pi$
$599$		−	30.5728i		−	1.24917i	0.780957	−	0.624585i	$-0.214732\pi$
$600$	0.652973	+	1.43005i	0.0266575	+	0.0583817i
$601$	−3.14357	−	21.8640i	−0.128229	−	0.891852i	−0.947798	−	0.318872i	$-0.896696\pi$
$601$	−3.14357	−	21.8640i	−0.128229	−	0.891852i	0.819569	−	0.572981i	$-0.194213\pi$
$602$	7.47547	−	3.41393i	0.304677	−	0.139141i
$603$	−27.7872	+	3.99155i	−1.13158	+	0.162549i
$604$	3.01308	−	6.59771i	0.122600	−	0.268457i
$605$	16.1556	−	18.6446i	0.656819	−	0.758010i
$606$	−3.26297	−	2.82775i	−0.132549	−	0.114869i
$607$	28.9499	−	8.50046i	1.17504	−	0.345023i	0.364780	−	0.931094i	$-0.381144\pi$
$607$	28.9499	−	8.50046i	1.17504	−	0.345023i	0.810260	+	0.586071i	$0.199326\pi$
$608$	−4.49657	−	5.18932i	−0.182360	−	0.210455i
$609$	−0.000810257		12.6176i	−3.28333e−5		0.511292i
$610$	19.5926	−	12.5914i	0.793280	−	0.509810i
$611$	−26.0791	+	22.5977i	−1.05505	+	0.914205i
$612$	7.19365	+	8.30407i	0.290786	+	0.335672i
$613$	−33.8783	−	4.87096i	−1.36833	−	0.196736i	−0.581320	−	0.813675i	$-0.697463\pi$
$613$	−33.8783	−	4.87096i	−1.36833	−	0.196736i	−0.787011	+	0.616939i	$0.788373\pi$
$614$	−16.9436	−	14.6817i	−0.683788	−	0.592506i
$615$	3.75913	−	2.41551i	0.151583	−	0.0974027i
$616$	−0.884591	−	0.259739i	−0.0356412	−	0.0104652i
$617$	−5.51733	−	12.0813i	−0.222119	−	0.486373i	0.765462	−	0.643481i	$-0.222510\pi$
$617$	−5.51733	−	12.0813i	−0.222119	−	0.486373i	−0.987582	+	0.157107i	$0.949783\pi$
$618$	19.1252	+	8.73568i	0.769329	+	0.351401i
$619$	−13.9341	+	21.6819i	−0.560058	+	0.871467i	−0.999643	−	0.0267339i	$-0.991489\pi$
$619$	−13.9341	+	21.6819i	−0.560058	+	0.871467i	0.439585	+	0.898201i	$0.355126\pi$
$620$	−8.60577			−0.345616
$621$	−4.23950	+	24.5566i	−0.170125	+	0.985422i
$622$	−5.58478			−0.223929
$623$	−8.99285	+	13.9931i	−0.360291	+	0.560624i
$624$	−6.16575	−	2.81628i	−0.246828	−	0.112742i
$625$	−11.9284	−	26.1195i	−0.477136	−	1.04478i
$626$	12.0476	+	3.53749i	0.481518	+	0.141387i
$627$	9.22440	−	5.92732i	0.368387	−	0.236715i
$628$	8.16830	+	7.07787i	0.325951	+	0.282438i
$629$	−39.2757	−	5.64699i	−1.56602	−	0.225160i
$630$	−4.77433	−	5.51131i	−0.190214	−	0.219576i
$631$	−14.6383	+	12.6841i	−0.582741	+	0.504948i	−0.895605	−	0.444850i	$-0.853257\pi$
$631$	−14.6383	+	12.6841i	−0.582741	+	0.504948i	0.312864	+	0.949798i	$0.398712\pi$
$632$	10.8388	−	6.96566i	0.431144	−	0.277079i
$633$	0.000207037	−	3.22406i	8.22899e−6	−	0.128145i
$634$	0.154404	+	0.178192i	0.00613219	+	0.00707692i
$635$	36.1766	−	10.6224i	1.43562	−	0.421537i
$636$	17.9852	+	15.5862i	0.713158	+	0.618035i
$637$	−2.56284	+	2.95768i	−0.101543	+	0.117187i
$638$	2.78997	−	6.10918i	0.110456	−	0.241865i
$639$	−11.6424	+	1.67240i	−0.460567	+	0.0661591i
$640$	2.21092	−	1.00969i	0.0873942	−	0.0399116i
$641$	−1.56491	−	10.8842i	−0.0618103	−	0.429900i	−0.997105	−	0.0760313i	$-0.975775\pi$
$641$	−1.56491	−	10.8842i	−0.0618103	−	0.429900i	0.935295	−	0.353869i	$-0.115134\pi$
$642$	9.08459	+	19.8959i	0.358540	+	0.785227i
$643$			2.01691i			0.0795390i	0.999209	+	0.0397695i	$0.0126624\pi$
$643$			2.01691i			0.0795390i	−0.999209	+	0.0397695i	$0.987338\pi$
$644$	−3.24072	+	3.53522i	−0.127702	+	0.139307i
$645$	−29.1038	−	18.7065i	−1.14596	−	0.736568i
$646$	−21.1545	−	13.5952i	−0.832313	−	0.534895i
$647$	−0.832554	+	0.119703i	−0.0327311	+	0.00470602i	−0.158661	−	0.987333i	$-0.550718\pi$
$647$	−0.832554	+	0.119703i	−0.0327311	+	0.00470602i	0.125930	+	0.992039i	$0.459809\pi$
$648$	−2.53781	+	8.63479i	−0.0996946	+	0.339206i
$649$	1.28585	−	4.37919i	0.0504739	−	0.171898i
$650$	−3.23111	−	1.47560i	−0.126735	−	0.0578777i
$651$	5.88428	−	1.72737i	0.230623	−	0.0677010i
$652$	−1.83623	+	12.7713i	−0.0719125	+	0.500163i
$653$	−6.48288	−	22.0787i	−0.253695	−	0.864004i	−0.983586	−	0.180441i	$-0.942247\pi$
$653$	−6.48288	−	22.0787i	−0.253695	−	0.864004i	0.729891	−	0.683563i	$-0.239571\pi$
$654$	1.07850	−	0.154995i	0.0421728	−	0.00606077i
$655$	5.04496	+	7.85010i	0.197123	+	0.306729i
$656$	−0.573831	−	0.892899i	−0.0224044	−	0.0348619i
$657$	3.04990	−	6.67607i	0.118988	−	0.260458i
$658$	2.48416	+	8.46027i	0.0968426	+	0.329816i
$659$	3.87581	−	26.9568i	0.150980	−	1.05009i	−0.763602	−	0.645687i	$-0.776571\pi$
$659$	3.87581	−	26.9568i	0.150980	−	1.05009i	0.914582	−	0.404401i	$-0.132520\pi$
$660$	1.09323	+	3.72407i	0.0425538	+	0.144959i
$661$	−10.2061	−	4.66098i	−0.396972	−	0.181291i	0.206919	−	0.978358i	$-0.433656\pi$
$661$	−10.2061	−	4.66098i	−0.396972	−	0.181291i	−0.603891	+	0.797067i	$0.706384\pi$
$662$	8.72569	−	29.7170i	0.339134	−	1.15498i
$663$	−24.5714	−	3.53444i	−0.954274	−	0.137266i
$664$	7.40907	−	1.06526i	0.287528	−	0.0413402i
$665$	14.0400	+	9.02294i	0.544447	+	0.349895i
$666$	−13.4991	−	29.5689i	−0.523079	−	1.14577i
$667$	−22.1314	−	27.0327i	−0.856932	−	1.04671i
$668$			6.00931i			0.232507i
$669$	14.3271	−	6.54184i	0.553916	−	0.252922i
$670$	3.23680	+	22.5124i	0.125048	+	0.869731i
$671$	8.03570	−	3.66978i	0.310215	−	0.141670i
$672$	−1.30907	+	1.13417i	−0.0504985	+	0.0437515i
$673$	6.15840	−	13.4850i	0.237389	−	0.519809i	−0.753017	−	0.658002i	$-0.771402\pi$
$673$	6.15840	−	13.4850i	0.237389	−	0.519809i	0.990405	+	0.138193i	$0.0441293\pi$
$674$	−14.1655	+	16.3479i	−0.545636	+	0.629698i
$675$	−1.32959	+	4.52494i	−0.0511759	+	0.174165i
$676$	2.22218	−	0.652490i	0.0854683	−	0.0250958i
$677$	−13.9669	−	16.1187i	−0.536793	−	0.619492i	0.420962	−	0.907078i	$-0.361693\pi$
$677$	−13.9669	−	16.1187i	−0.536793	−	0.619492i	−0.957755	+	0.287586i	$0.907147\pi$
$678$	−17.4992	−	0.00112373i	−0.672052	−	4.31567e-5i
$679$	−15.0566	+	9.67632i	−0.577821	+	0.371343i
$680$	6.72711	−	5.82907i	0.257973	−	0.223535i
$681$	−2.15969	+	7.35348i	−0.0827594	+	0.281786i
$682$	−3.23102	−	0.464551i	−0.123722	−	0.0177886i
$683$	−24.4731	−	21.2061i	−0.936437	−	0.811427i	0.0458232	−	0.998950i	$-0.485409\pi$
$683$	−24.4731	−	21.2061i	−0.936437	−	0.811427i	−0.982260	+	0.187522i	$0.939954\pi$
$684$	0.00264563	−	20.5993i	0.000101158	−	0.787636i
$685$	−15.1081	−	4.43614i	−0.577251	−	0.169496i
$686$	0.415415	+	0.909632i	0.0158606	+	0.0347299i
$687$	9.60997	−	21.0393i	0.366643	−	0.802700i
$688$	−4.44305	+	6.91353i	−0.169390	+	0.263576i
$689$	−53.7740			−2.04863
$690$	19.8959	+	3.43223i	0.757424	+	0.130663i
$691$	47.7028			1.81470			0.907350	−	0.420376i	$-0.138102\pi$
$691$	47.7028			1.81470			0.907350	+	0.420376i	$0.138102\pi$
$692$	−0.912225	+	1.41945i	−0.0346776	+	0.0539594i
$693$	−1.49501	−	2.32694i	−0.0567907	−	0.0883930i
$694$	−8.22549	−	18.0113i	−0.312235	−	0.683700i
$695$	12.9355	+	3.79821i	0.490671	+	0.144074i
$696$	−6.82092	−	10.6151i	−0.258546	−	0.402363i
$697$	−2.93763	−	2.54547i	−0.111271	−	0.0964166i
$698$	30.4620	+	4.37978i	1.15300	+	0.165777i
$699$	−34.4533	−	10.1188i	−1.30314	−	0.382729i
$700$	−0.685948	+	0.594377i	−0.0259264	+	0.0224654i
$701$	10.4799	−	6.73500i	0.395819	−	0.254378i	−0.327557	−	0.944831i	$-0.606225\pi$
$701$	10.4799	−	6.73500i	0.395819	−	0.254378i	0.723377	+	0.690454i	$0.242589\pi$
$702$	−8.44410	−	18.4994i	−0.318702	−	0.698216i
$703$	48.7196	+	56.2255i	1.83750	+	2.12058i
$704$	0.884591	−	0.259739i	0.0333393	−	0.00978929i
$705$	24.3104	−	28.0520i	0.915581	−	1.05650i
$706$	−18.2551	+	21.0675i	−0.687040	+	0.792887i
$707$	1.03557	−	2.26759i	0.0389468	−	0.0852816i
$708$	−5.61473	−	6.48059i	−0.211015	−	0.243555i
$709$	14.3845	−	6.56919i	0.540222	−	0.246711i	−0.126566	−	0.991958i	$-0.540396\pi$
$709$	14.3845	−	6.56919i	0.540222	−	0.246711i	0.666789	+	0.745247i	$0.267668\pi$
$710$	1.35617	+	9.43236i	0.0508961	+	0.353990i
$711$	38.2581	+	5.50570i	1.43479	+	0.206480i
$712$		−	16.6337i		−	0.623374i
$713$	−9.57609	+	14.0225i	−0.358628	+	0.525147i
$714$	−3.42970	+	5.33597i	−0.128353	+	0.199694i
$715$	−7.37746	−	4.74121i	−0.275901	−	0.177311i
$716$	−6.17328	+	0.887583i	−0.230706	+	0.0331705i
$717$	−6.03940	+	41.9858i	−0.225545	+	1.56799i
$718$	−1.95347	+	6.65291i	−0.0729029	+	0.248285i
$719$	9.96123	+	4.54914i	0.371491	+	0.169654i	0.592408	−	0.805638i	$-0.298178\pi$
$719$	9.96123	+	4.54914i	0.371491	+	0.169654i	−0.220916	+	0.975293i	$0.570905\pi$
$720$	6.99606	+	2.05521i	0.260728	+	0.0765930i
$721$	−1.72760	+	12.0157i	−0.0643392	+	0.447489i
$722$	7.93024	+	27.0079i	0.295133	+	1.00513i
$723$	−3.66075	−	25.4727i	−0.136145	−	0.947339i
$724$	−2.75453	−	4.28614i	−0.102371	−	0.159293i
$725$	−3.57470	−	5.56233i	−0.132761	−	0.206580i
$726$	−2.50083	−	17.4016i	−0.0928145	−	0.645834i
$727$	−5.26299	−	17.9241i	−0.195193	−	0.664768i	−0.997679	−	0.0680960i	$-0.978308\pi$
$727$	−5.26299	−	17.9241i	−0.195193	−	0.664768i	0.802485	−	0.596672i	$-0.203511\pi$
$728$	0.556958	−	3.87373i	0.0206423	−	0.143570i
$729$	−22.7195	+	14.5885i	−0.841462	+	0.540317i
$730$	−5.40919	−	2.47029i	−0.200203	−	0.0914297i
$731$	−8.47917	+	28.8774i	−0.313613	+	1.06807i
$732$	2.36299	−	16.4275i	0.0873387	−	0.607177i
$733$	31.2088	−	4.48715i	1.15272	−	0.165736i	0.460662	−	0.887576i	$-0.347612\pi$
$733$	31.2088	−	4.48715i	1.15272	−	0.165736i	0.692061	+	0.721839i	$0.256703\pi$
$734$	19.8876	+	12.7810i	0.734066	+	0.471755i
$735$	2.27625	−	3.54141i	0.0839607	−	0.130627i
$736$	0.814981	−	4.72608i	0.0300406	−	0.174206i
$737$			8.62698i			0.317779i
$738$	0.453560	−	3.15170i	0.0166958	−	0.116016i
$739$	2.22939	+	15.5058i	0.0820095	+	0.570389i	0.988850	+	0.148915i	$0.0475780\pi$
$739$	2.22939	+	15.5058i	0.0820095	+	0.570389i	−0.906840	+	0.421474i	$0.861513\pi$
$740$	−23.9550	+	10.9399i	−0.880602	+	0.402158i
$741$	30.4777	+	35.1777i	1.11963	+	1.29229i
$742$	−5.70797	+	12.4987i	−0.209546	+	0.458842i
$743$	14.4917	−	16.7244i	0.531651	−	0.613557i	−0.424859	−	0.905260i	$-0.639676\pi$
$743$	14.4917	−	16.7244i	0.531651	−	0.613557i	0.956509	+	0.291702i	$0.0942217\pi$
$744$	−4.01628	+	4.63444i	−0.147244	+	0.169907i
$745$	−14.6642	+	4.30578i	−0.537253	+	0.157752i
$746$	−18.9236	−	21.8390i	−0.692844	−	0.799584i
$747$	18.8894	+	12.1429i	0.691128	+	0.444287i
$748$	2.84034	−	1.82538i	0.103853	−	0.0667425i
$749$	−9.54337	+	8.26937i	−0.348707	+	0.302156i
$750$	−16.5301	−	4.85482i	−0.603593	−	0.177273i
$751$	−24.7577	−	3.55963i	−0.903423	−	0.129893i	−0.325080	−	0.945686i	$-0.605391\pi$
$751$	−24.7577	−	3.55963i	−0.903423	−	0.129893i	−0.578343	+	0.815794i	$0.696300\pi$
$752$	−6.66378	−	5.77420i	−0.243003	−	0.210563i
$753$	−3.60560	−	5.61122i	−0.131395	−	0.204484i
$754$	27.3547	+	8.03205i	0.996198	+	0.292510i
$755$	−7.32347	−	16.0362i	−0.266528	−	0.583616i
$756$	−5.19615	−	0.00100103i	−0.188982	−	3.64072e-5i
$757$	−9.59004	+	14.9224i	−0.348556	+	0.542363i	−0.970625	−	0.240599i	$-0.922656\pi$
$757$	−9.59004	+	14.9224i	−0.348556	+	0.542363i	0.622069	+	0.782963i	$0.286292\pi$
$758$	−19.7917			−0.718867
$759$	7.28461	+	2.36263i	0.264415	+	0.0857582i
$760$	−16.6893			−0.605386
$761$	−14.1910	+	22.0817i	−0.514424	+	0.800460i	−0.997160	−	0.0753061i	$-0.976007\pi$
$761$	−14.1910	+	22.0817i	−0.514424	+	0.800460i	0.482736	+	0.875766i	$0.339643\pi$
$762$	11.1630	−	24.4395i	0.404394	−	0.885350i
$763$	0.261326	+	0.572223i	0.00946062	+	0.0207159i
$764$	−17.4185	−	5.11454i	−0.630180	−	0.185038i
$765$	26.7037	+	0.00342963i	0.965475	+	0.000123998i
$766$	−16.3893	−	14.2014i	−0.592168	−	0.513117i
$767$	19.1770	+	2.75724i	0.692442	+	0.0995581i
$768$	0.488082	−	1.66186i	0.0176121	−	0.0599672i
$769$	20.7497	−	17.9797i	0.748253	−	0.648365i	−0.194862	−	0.980831i	$-0.562426\pi$
$769$	20.7497	−	17.9797i	0.748253	−	0.648365i	0.943115	+	0.332466i	$0.107881\pi$
$770$	−1.88510	+	1.21148i	−0.0679343	+	0.0436587i
$771$	25.2003	+	0.00161827i	0.907565	+	5.82805e-5i
$772$	4.67120	+	5.39086i	0.168120	+	0.194021i
$773$	21.1458	−	6.20898i	0.760563	−	0.223321i	0.121621	−	0.992577i	$-0.461191\pi$
$773$	21.1458	−	6.20898i	0.760563	−	0.223321i	0.638942	+	0.769255i	$0.279373\pi$
$774$	−23.6566	+	6.94290i	−0.850318	+	0.249557i
$775$	−2.10448	+	2.42870i	−0.0755952	+	0.0872415i
$776$	7.43504	−	16.2805i	0.266902	−	0.584435i
$777$	14.1836	−	12.2885i	0.508833	−	0.440849i
$778$	31.5416	−	14.4046i	1.13082	−	0.516429i
$779$	1.03719	+	7.21381i	0.0371611	+	0.258461i
$780$	−14.9871	+	6.84323i	−0.536626	+	0.245027i
$781$			3.61457i			0.129340i
$782$	−2.01246	−	17.4477i	−0.0719656	−	0.623928i
$783$	5.39424	−	37.4665i	0.192774	−	1.33894i
$784$	−0.841254	−	0.540641i	−0.0300448	−	0.0193086i
$785$	26.0027	−	3.73862i	0.928074	−	0.133437i
$786$	6.58196	+	0.946774i	0.234771	+	0.0337703i
$787$	−2.52730	+	8.60719i	−0.0900885	+	0.306813i	−0.992194	−	0.124702i	$-0.960203\pi$
$787$	−2.52730	+	8.60719i	−0.0900885	+	0.306813i	0.902106	+	0.431515i	$0.142021\pi$
$788$	−21.9315	−	10.0158i	−0.781277	−	0.356797i
$789$	−6.30427	−	21.4755i	−0.224438	−	0.764547i
$790$	4.45667	−	30.9968i	0.158561	−	1.10282i
$791$	−2.84639	−	9.69391i	−0.101206	−	0.344676i
$792$	2.51572	+	1.14928i	0.0893922	+	0.0408379i
$793$	20.2740	+	31.5469i	0.719950	+	1.12026i
$794$	13.8663	+	21.5763i	0.492095	+	0.765716i
$795$	57.2570	−	8.22856i	2.03070	−	0.291837i
$796$	5.53401	+	18.8471i	0.196148	+	0.668018i
$797$	4.15033	−	28.8662i	0.147012	−	1.02249i	−0.774063	−	0.633109i	$-0.781779\pi$
$797$	4.15033	−	28.8662i	0.147012	−	1.02249i	0.921075	−	0.389384i	$-0.127312\pi$
$798$	11.4115	−	3.34992i	0.403963	−	0.118586i
$799$	−29.3732	−	13.4143i	−1.03915	−	0.474564i
$800$	0.255712	−	0.870874i	0.00904077	−	0.0307900i
$801$	32.6831	−	37.7085i	1.15480	−	1.33236i
$802$	−6.74770	+	0.970172i	−0.238269	+	0.0342580i
$803$	−1.89752	−	1.21946i	−0.0669621	−	0.0430339i
$804$	13.6341	+	8.76337i	0.480839	+	0.309060i
$805$	1.33565	+	11.5798i	0.0470753	+	0.408134i
$806$		−	13.8566i		−	0.488076i
$807$	−7.05180	−	15.4439i	−0.248235	−	0.543651i
$808$	0.354772	+	2.46749i	0.0124808	+	0.0868061i
$809$	10.7346	−	4.90232i	0.377408	−	0.172356i	−0.217674	−	0.976022i	$-0.569847\pi$
$809$	10.7346	−	4.90232i	0.377408	−	0.172356i	0.595082	+	0.803665i	$0.297120\pi$
$810$	11.8218	+	18.4055i	0.415377	+	0.646704i
$811$	13.0904	−	28.6640i	0.459666	−	1.00653i	−0.527898	−	0.849308i	$-0.677020\pi$
$811$	13.0904	−	28.6640i	0.459666	−	1.00653i	0.987564	−	0.157220i	$-0.0502531\pi$
$812$	4.77052	−	5.50547i	0.167412	−	0.193204i
$813$	23.6858	+	20.5265i	0.830696	+	0.719895i
$814$	−9.58441	+	2.81424i	−0.335933	+	0.0986389i
$815$	20.5369	+	23.7008i	0.719375	+	0.830203i
$816$	0.000407333	−	6.34314i	1.42595e−5	−	0.222054i
$817$	47.4714	−	30.5080i	1.66081	−	1.06734i
$818$	−23.9678	+	20.7682i	−0.838014	+	0.726143i
$819$	8.87401	−	7.68738i	0.310083	−	0.268619i
$820$	−2.55352	−	0.367141i	−0.0891728	−	0.0128211i
$821$	16.6256	+	14.4062i	0.580238	+	0.502779i	0.894805	−	0.446456i	$-0.147314\pi$
$821$	16.6256	+	14.4062i	0.580238	+	0.502779i	−0.314568	+	0.949235i	$0.601860\pi$
$822$	−9.43988	+	6.06579i	−0.329254	+	0.211569i
$823$	−19.9851	−	5.86815i	−0.696637	−	0.204551i	−0.0858056	−	0.996312i	$-0.527346\pi$
$823$	−19.9851	−	5.86815i	−0.696637	−	0.204551i	−0.610831	+	0.791761i	$0.709165\pi$
$824$	−5.04284	−	11.0423i	−0.175676	−	0.384676i
$825$	1.31834	+	0.602168i	0.0458987	+	0.0209648i
$826$	2.67646	−	4.16465i	0.0931259	−	0.144907i
$827$	4.92443			0.171239			0.0856195	−	0.996328i	$-0.472713\pi$
$827$	4.92443			0.171239			0.0856195	+	0.996328i	$0.472713\pi$
$828$	11.1337	−	9.11267i	0.386923	−	0.316687i
$829$	0.667073			0.0231684			0.0115842	−	0.999933i	$-0.496313\pi$
$829$	0.667073			0.0231684			0.0115842	+	0.999933i	$0.496313\pi$
$830$	9.83609	−	15.3053i	0.341416	−	0.531253i
$831$	−32.1325	−	14.6769i	−1.11466	−	0.509137i
$832$	1.62575	+	3.55990i	0.0563629	+	0.123417i
$833$	−3.51387	−	1.03176i	−0.121748	−	0.0357485i
$834$	8.08239	−	5.19350i	0.279870	−	0.179836i
$835$	11.0385	+	9.56490i	0.382003	+	0.331007i
$836$	−6.26599	−	0.900913i	−0.216714	−	0.0311587i
$837$	−18.2110	+	2.61476i	−0.629464	+	0.0903795i
$838$	18.0266	−	15.6201i	0.622718	−	0.539588i
$839$	−40.7827	+	26.2094i	−1.40797	+	0.904850i	−0.999967	−	0.00812881i	$-0.997412\pi$
$839$	−40.7827	+	26.2094i	−1.40797	+	0.904850i	−0.408007	+	0.912979i	$0.633776\pi$
$840$	−0.000270342		4.20986i	−9.32767e−6		0.145254i
$841$	15.7613	+	18.1895i	0.543492	+	0.627223i
$842$	14.1579	−	4.15715i	0.487915	−	0.143265i
$843$	3.11562	+	2.70005i	0.107308	+	0.0929947i
$844$	−1.21897	+	1.40676i	−0.0419586	+	0.0484228i
$845$	2.33844	−	5.12047i	0.0804447	−	0.176149i
$846$	−3.76119	−	26.1836i	−0.129313	−	0.900209i
$847$	9.23280	−	4.21648i	0.317243	−	0.144880i
$848$	−1.95546	−	13.6006i	−0.0671509	−	0.467045i
$849$	2.15521	+	4.72004i	0.0739665	+	0.161992i
$850$		−	3.32397i		−	0.114011i
$851$	−8.83020	+	51.2063i	−0.302695	+	1.75533i
$852$	5.71250	+	3.67172i	0.195707	+	0.125791i
$853$	−12.9950	−	8.35139i	−0.444941	−	0.285946i	0.298923	−	0.954277i	$-0.403373\pi$
$853$	−12.9950	−	8.35139i	−0.444941	−	0.285946i	−0.743864	+	0.668331i	$0.767009\pi$
$854$	9.48450	−	1.36366i	0.324553	−	0.0466636i
$855$	−37.8347	−	32.7924i	−1.29392	−	1.12148i
$856$	3.55763	−	12.1162i	0.121597	−	0.414122i
$857$	33.0922	+	15.1127i	1.13041	+	0.516239i	0.890694	−	0.454604i	$-0.150219\pi$
$857$	33.0922	+	15.1127i	1.13041	+	0.516239i	0.239713	+	0.970844i	$0.422947\pi$
$858$	−5.99630	+	1.76026i	−0.204710	+	0.0600941i
$859$	0.0525305	−	0.365358i	0.00179232	−	0.0124658i	−0.988906	−	0.148545i	$-0.952541\pi$
$859$	0.0525305	−	0.365358i	0.00179232	−	0.0124658i	0.990698	+	0.136079i	$0.0434501\pi$
$860$	5.62752	+	19.1656i	0.191897	+	0.653540i
$861$	1.81969	−	0.261512i	0.0620148	−	0.00891232i
$862$	−5.04675	−	7.85289i	−0.171893	−	0.267471i
$863$	−0.350530	−	0.545436i	−0.0119322	−	0.0185668i	0.835236	−	0.549891i	$-0.185331\pi$
$863$	−0.350530	−	0.545436i	−0.0119322	−	0.0185668i	−0.847168	+	0.531324i	$0.821695\pi$
$864$	4.37182	−	2.80841i	0.148732	−	0.0955440i
$865$	1.15541	+	3.93498i	0.0392852	+	0.133793i
$866$	1.42027	−	9.87823i	0.0482629	−	0.335676i
$867$	1.75057	+	5.96329i	0.0594523	+	0.202524i
$868$	−3.22069	−	1.47084i	−0.109317	−	0.0499235i
$869$	3.34650	−	11.3971i	0.113522	−	0.386622i
$870$	−30.3555	−	4.36645i	−1.02915	−	0.148037i
$871$	−36.2483	+	5.21172i	−1.22823	+	0.176592i
$872$	−0.529208	−	0.340102i	−0.0179213	−	0.0115173i
$873$	48.8443	−	22.2989i	1.65313	−	0.754702i
$874$	−18.5711	+	27.1941i	−0.628177	+	0.919855i
$875$		−	9.94674i		−	0.336261i
$876$	−3.85477	+	1.76012i	−0.130241	+	0.0594688i
$877$	−3.47235	−	24.1507i	−0.117253	−	0.815512i	−0.960559	−	0.278078i	$-0.910303\pi$
$877$	−3.47235	−	24.1507i	−0.117253	−	0.815512i	0.843306	−	0.537434i	$-0.180606\pi$
$878$	−2.22069	+	1.01416i	−0.0749447	+	0.0342261i
$879$	6.35904	−	5.50942i	0.214485	−	0.185828i
$880$	0.930871	−	2.03832i	0.0313797	−	0.0687119i
$881$	−23.0412	+	26.5910i	−0.776278	+	0.895872i	−0.996835	−	0.0795017i	$-0.974667\pi$
$881$	−23.0412	+	26.5910i	−0.776278	+	0.895872i	0.220557	+	0.975374i	$0.429213\pi$
$882$	−0.844828	−	2.87859i	−0.0284468	−	0.0969271i
$883$	−35.3006	+	10.3652i	−1.18796	+	0.348816i	−0.815237	−	0.579127i	$-0.803394\pi$
$883$	−35.3006	+	10.3652i	−1.18796	+	0.348816i	−0.372722	+	0.927943i	$0.621575\pi$
$884$	9.38567	+	10.8316i	0.315674	+	0.364307i
$885$	−20.8410	−	0.00133833i	−0.700564	−	4.49876e-5i
$886$	−14.4211	+	9.26789i	−0.484487	+	0.311361i
$887$	19.6550	−	17.0312i	0.659950	−	0.571850i	−0.259168	−	0.965832i	$-0.583448\pi$
$887$	19.6550	−	17.0312i	0.659950	−	0.571850i	0.919118	+	0.393982i	$0.128903\pi$
$888$	−5.28829	+	18.0060i	−0.177464	+	0.604242i
$889$	15.3545	+	2.20764i	0.514973	+	0.0740420i
$890$	−30.5544	−	26.4755i	−1.02418	−	0.887461i
$891$	3.44493	+	7.54848i	0.115410	+	0.252884i
$892$	−8.72489	−	2.56186i	−0.292131	−	0.0857774i
$893$	25.1511	+	55.0732i	0.841649	+	1.84295i
$894$	−4.52493	+	9.90653i	−0.151336	+	0.331324i
$895$	−8.19549	+	12.7524i	−0.273945	+	0.426267i
$896$	1.00000			0.0334077
$897$	−5.52640	+	32.0353i	−0.184521	+	1.06963i
$898$	−41.8370			−1.39612
$899$	13.9447	−	21.6983i	0.465081	−	0.723680i
$900$	2.29085	−	1.47183i	0.0763618	−	0.0490609i
$901$	−20.9038	−	45.7730i	−0.696407	−	1.52492i
$902$	−0.938897	−	0.275685i	−0.0312618	−	0.00917930i
$903$	−7.69482	−	11.9751i	−0.256068	−	0.398505i
$904$	7.63546	+	6.61616i	0.253952	+	0.220050i
$905$	−12.2575	−	1.76237i	−0.407454	−	0.0585830i
$906$	−12.0537	−	3.54014i	−0.400459	−	0.117613i
$907$	−5.24122	+	4.54154i	−0.174032	+	0.150800i	−0.737521	−	0.675324i	$-0.764004\pi$
$907$	−5.24122	+	4.54154i	−0.174032	+	0.150800i	0.563490	+	0.826123i	$0.309458\pi$
$908$	3.72242	−	2.39225i	0.123533	−	0.0793897i
$909$	−4.04405	+	6.29088i	−0.134133	+	0.208655i
$910$	−6.22915	−	7.18882i	−0.206494	−	0.238307i
$911$	33.0186	−	9.69514i	1.09396	−	0.321214i	0.315508	−	0.948923i	$-0.397825\pi$
$911$	33.0186	−	9.69514i	1.09396	−	0.321214i	0.778448	+	0.627709i	$0.216007\pi$
$912$	−7.78886	+	8.98766i	−0.257915	+	0.297611i
$913$	4.51914	−	5.21537i	0.149562	−	0.172604i
$914$	8.10895	−	17.7561i	0.268220	−	0.587320i
$915$	−26.4145	−	30.4879i	−0.873235	−	1.00790i
$916$	−12.1474	+	5.54754i	−0.401362	+	0.183296i
$917$	0.546376	+	3.80013i	0.0180429	+	0.125491i
$918$	12.4644	−	14.3791i	0.411386	−	0.474580i
$919$			9.23017i			0.304475i	0.988344	+	0.152238i	$0.0486479\pi$
$919$			9.23017i			0.304475i	−0.988344	+	0.152238i	$0.951352\pi$
$920$	−7.38413	−	9.01944i	−0.243448	−	0.297362i
$921$	−20.9962	+	32.6661i	−0.691848	+	1.07638i
$922$	13.1392	+	8.44404i	0.432716	+	0.278090i
$923$	−15.1875	+	2.18363i	−0.499902	+	0.0718751i
$924$	−0.227355	+	1.58057i	−0.00747944	+	0.0519970i
$925$	−2.77060	+	9.43578i	−0.0910967	+	0.310247i
$926$	0.0791933	+	0.0361664i	0.00260245	+	0.00118850i
$927$	10.2646	−	34.9413i	0.337133	−	1.14762i
$928$	−1.03673	+	7.21064i	−0.0340324	+	0.236701i
$929$	−2.89477	−	9.85867i	−0.0949742	−	0.323452i	0.898278	−	0.439428i	$-0.144819\pi$
$929$	−2.89477	−	9.85867i	−0.0949742	−	0.323452i	−0.993252	+	0.115975i	$0.963001\pi$
$930$	2.12034	+	14.7540i	0.0695288	+	0.483804i
$931$	3.71228	+	5.77642i	0.121665	+	0.189315i
$932$	11.2085	+	17.4407i	0.367145	+	0.571289i
$933$	1.37601	+	9.57474i	0.0450486	+	0.313463i
$934$	2.80352	+	9.54790i	0.0917339	+	0.312417i
$935$	1.16789	−	8.12284i	0.0381940	−	0.265645i
$936$	−3.30918	+	11.2647i	−0.108164	+	0.368198i
$937$	3.76154	+	1.71784i	0.122884	+	0.0561193i	0.475908	−	0.879495i	$-0.342119\pi$
$937$	3.76154	+	1.71784i	0.122884	+	0.0561193i	−0.353024	+	0.935614i	$0.614847\pi$
$938$	−2.63630	+	8.97843i	−0.0860784	+	0.293156i
$939$	3.09644	−	21.5264i	0.101049	−	0.702488i
$940$	−21.2132	+	3.05000i	−0.691899	+	0.0994800i
$941$	−27.0932	−	17.4118i	−0.883214	−	0.567607i	0.0185539	−	0.999828i	$-0.494094\pi$
$941$	−27.0932	−	17.4118i	−0.883214	−	0.567607i	−0.901768	+	0.432221i	$0.857730\pi$
$942$	10.1220	−	15.7479i	0.329793	−	0.513095i
$943$	−3.43967	+	3.75225i	−0.112011	+	0.122190i
$944$			4.95053i			0.161126i
$945$	−8.27245	+	9.54321i	−0.269103	+	0.310440i
$946$	1.07826	+	7.49946i	0.0350572	+	0.243828i
$947$	18.5215	−	8.45847i	0.601867	−	0.274864i	−0.0910896	−	0.995843i	$-0.529035\pi$
$947$	18.5215	−	8.45847i	0.601867	−	0.274864i	0.692957	+	0.720979i	$0.256308\pi$
$948$	−14.6127	−	16.8662i	−0.474599	−	0.547788i
$949$	3.97754	−	8.70959i	0.129116	−	0.282725i
$950$	−4.08126	+	4.71003i	−0.132414	+	0.152813i
$951$	0.267456	−	0.308621i	0.00867286	−	0.0100077i
$952$	3.51387	−	1.03176i	0.113885	−	0.0334397i
$953$	−14.9800	−	17.2879i	−0.485251	−	0.560009i	0.459340	−	0.888261i	$-0.348086\pi$
$953$	−14.9800	−	17.2879i	−0.485251	−	0.560009i	−0.944590	+	0.328251i	$0.893541\pi$
$954$	22.2903	−	34.6747i	0.721676	−	1.12263i
$955$	−37.1196	+	23.8553i	−1.20116	+	0.771941i
$956$	18.5083	−	16.0375i	0.598602	−	0.518691i
$957$	−11.1612	−	3.27801i	−0.360791	−	0.105963i
$958$	14.1785	+	2.03856i	0.458087	+	0.0658629i
$959$	−4.89597	−	4.24238i	−0.158099	−	0.136994i
$960$	−2.27579	−	3.54171i	−0.0734510	−	0.114308i
$961$	17.7159	+	5.20186i	0.571481	+	0.167802i
$962$	−17.6148	−	38.5710i	−0.567924	−	1.24358i
$963$	31.8719	−	20.4770i	1.02706	−	0.659863i
$964$	−8.03271	+	12.4991i	−0.258716	+	0.402570i
$965$	17.3375			0.558114
$966$	6.85937	+	4.68497i	0.220697	+	0.150737i
$967$	28.5102			0.916826			0.458413	−	0.888739i	$-0.348418\pi$
$967$	28.5102			0.916826			0.458413	+	0.888739i	$0.348418\pi$
$968$	−5.48752	+	8.53875i	−0.176376	+	0.274446i
$969$	−18.0959	+	39.6177i	−0.581323	+	1.27270i
$970$	−18.0713	−	39.5707i	−0.580236	−	1.27054i
$971$	12.7777	+	3.75186i	0.410055	+	0.120403i	0.480253	−	0.877130i	$-0.340545\pi$
$971$	12.7777	+	3.75186i	0.410055	+	0.120403i	−0.0701980	+	0.997533i	$0.522363\pi$
$972$	15.4291	+	2.22342i	0.494888	+	0.0713163i
$973$	4.19191	+	3.63231i	0.134387	+	0.116447i
$974$	−21.3054	−	3.06325i	−0.682669	−	0.0981529i
$975$	−1.73372	+	5.90310i	−0.0555234	+	0.189050i
$976$	−7.24161	+	6.27489i	−0.231798	+	0.200854i
$977$	30.2728	−	19.4551i	0.968512	−	0.622425i	0.0421706	−	0.999110i	$-0.486573\pi$
$977$	30.2728	−	19.4551i	0.968512	−	0.622425i	0.926341	+	0.376686i	$0.122936\pi$
$978$	22.3480	+	0.00143511i	0.714610	+	4.58896e-5i
$979$	−10.0424	−	11.5896i	−0.320957	−	0.370404i
$980$	−2.33211	+	0.684769i	−0.0744965	+	0.0218741i
$981$	−0.531457	−	1.81084i	−0.0169681	−	0.0578155i
$982$	23.4404	−	27.0516i	0.748013	−	0.863253i
$983$	15.8119	−	34.6233i	0.504323	−	1.10431i	−0.470717	−	0.882284i	$-0.656005\pi$
$983$	15.8119	−	34.6233i	0.504323	−	1.10431i	0.975040	−	0.222029i	$-0.0712679\pi$
$984$	−1.38943	+	1.20380i	−0.0442936	+	0.0383756i
$985$	−53.3059	+	24.3440i	−1.69847	+	0.775663i
$986$	3.79674	+	26.4069i	0.120913	+	0.840967i
$987$	13.8925	−	6.34343i	0.442204	−	0.201914i
$988$		−	26.8723i		−	0.854922i
$989$	37.4910	+	12.1569i	1.19214	+	0.386566i
$990$	6.11533	−	2.79183i	0.194358	−	0.0887301i
$991$	20.0581	+	12.8906i	0.637167	+	0.409482i	0.818957	−	0.573855i	$-0.194553\pi$
$991$	20.0581	+	12.8906i	0.637167	+	0.409482i	−0.181790	+	0.983337i	$0.558189\pi$
$992$	3.50461	−	0.503887i	0.111271	−	0.0159984i
$993$	−53.0978	−	7.63779i	−1.68501	−	0.242378i
$994$	−1.10457	+	3.76182i	−0.0350349	+	0.119318i
$995$	43.4286	+	19.8332i	1.37678	+	0.628754i
$996$	−3.65182	−	12.4399i	−0.115712	−	0.394174i
$997$	3.46386	−	24.0917i	0.109702	−	0.762992i	−0.858499	−	0.512816i	$-0.828602\pi$
$997$	3.46386	−	24.0917i	0.109702	−	0.762992i	0.968200	−	0.250176i	$-0.0804885\pi$
$998$	9.50927	+	32.3856i	0.301011	+	1.02515i
$999$	−47.3680	+	30.4287i	−1.49866	+	0.962721i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.r.a.113.12	✓	240
3.2	odd	2		966.2.r.b.113.14	yes	240
23.11	odd	22		966.2.r.b.701.14	yes	240
69.11	even	22	inner	966.2.r.a.701.12	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.r.a.113.12	✓	240	1.1	even	1	trivial
966.2.r.a.701.12	yes	240	69.11	even	22	inner
966.2.r.b.113.14	yes	240	3.2	odd	2
966.2.r.b.701.14	yes	240	23.11	odd	22

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.r (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.57548 + 0.719621i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.33211 - 0.684769i) q^{5} +(-1.45715 + 0.936324i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.96429 + 2.26750i) q^{9} +O(q^{10})\)	\(q+(-0.540641 + 0.841254i) q^{2} +(1.57548 + 0.719621i) q^{3} +(-0.415415 - 0.909632i) q^{4} +(-2.33211 - 0.684769i) q^{5} +(-1.45715 + 0.936324i) q^{6} +(-0.755750 - 0.654861i) q^{7} +(0.989821 + 0.142315i) q^{8} +(1.96429 + 2.26750i) q^{9} +(1.83690 - 1.59168i) q^{10} +(0.775581 - 0.498436i) q^{11} +(0.000111226 - 1.73205i) q^{12} +(2.56284 + 2.95768i) q^{13} +(0.959493 - 0.281733i) q^{14} +(-3.18142 - 2.75708i) q^{15} +(-0.654861 + 0.755750i) q^{16} +(-1.52134 + 3.33127i) q^{17} +(-2.96952 + 0.426563i) q^{18} +(6.24594 - 2.85243i) q^{19} +(0.345905 + 2.40582i) q^{20} +(-0.719419 - 1.57558i) q^{21} +0.921935i q^{22} +(4.30503 + 2.11346i) q^{23} +(1.45703 + 0.936511i) q^{24} +(0.763555 + 0.490707i) q^{25} +(-3.87373 + 0.556958i) q^{26} +(1.46296 + 4.98595i) q^{27} +(-0.281733 + 0.959493i) q^{28} +(-6.62648 - 3.02621i) q^{29} +(4.03941 - 1.18580i) q^{30} +(-0.503887 + 3.50461i) q^{31} +(-0.281733 - 0.959493i) q^{32} +(1.58060 - 0.227152i) q^{33} +(-1.97994 - 3.08085i) q^{34} +(1.31406 + 2.04472i) q^{35} +(1.24660 - 2.72874i) q^{36} +(3.05253 + 10.3960i) q^{37} +(-0.977198 + 6.79656i) q^{38} +(1.90930 + 6.50404i) q^{39} +(-2.21092 - 1.00969i) q^{40} +(-0.299028 + 1.01840i) q^{41} +(1.71441 + 0.246607i) q^{42} +(8.13447 - 1.16956i) q^{43} +(-0.775581 - 0.498436i) q^{44} +(-3.02823 - 6.63314i) q^{45} +(-4.10543 + 2.47900i) q^{46} +8.81744i q^{47} +(-1.57558 + 0.719419i) q^{48} +(0.142315 + 0.989821i) q^{49} +(-0.825618 + 0.377047i) q^{50} +(-4.79409 + 4.15357i) q^{51} +(1.62575 - 3.55990i) q^{52} +(-8.99806 + 10.3843i) q^{53} +(-4.98539 - 1.46489i) q^{54} +(-2.15005 + 0.631313i) q^{55} +(-0.654861 - 0.755750i) q^{56} +(11.8930 + 0.000763727i) q^{57} +(6.12835 - 3.93845i) q^{58} +(3.74136 - 3.24191i) q^{59} +(-1.18631 + 4.03925i) q^{60} +(9.48450 + 1.36366i) q^{61} +(-2.67584 - 2.31863i) q^{62} +(0.000385298 - 3.00000i) q^{63} +(0.959493 + 0.281733i) q^{64} +(-3.95150 - 8.65257i) q^{65} +(-0.663444 + 1.45249i) q^{66} +(-5.05903 + 7.87200i) q^{67} +3.66221 q^{68} +(5.26161 + 6.42771i) q^{69} -2.43056 q^{70} +(-2.11966 + 3.29825i) q^{71} +(1.62160 + 2.52397i) q^{72} +(-1.01635 - 2.22549i) q^{73} +(-10.3960 - 3.05253i) q^{74} +(0.849844 + 1.32257i) q^{75} +(-5.18932 - 4.49657i) q^{76} +(-0.912551 - 0.131205i) q^{77} +(-6.50379 - 1.91014i) q^{78} +(9.73714 - 8.43728i) q^{79} +(2.04472 - 1.31406i) q^{80} +(-1.28312 + 8.90806i) q^{81} +(-0.695063 - 0.802146i) q^{82} +(7.18205 - 2.10884i) q^{83} +(-1.13434 + 1.30892i) q^{84} +(5.82907 - 6.72711i) q^{85} +(-3.41393 + 7.47547i) q^{86} +(-8.26217 - 9.53629i) q^{87} +(0.838622 - 0.382986i) q^{88} +(-2.36722 - 16.4644i) q^{89} +(7.21734 + 1.03864i) q^{90} -3.91356i q^{91} +(0.134095 - 4.79396i) q^{92} +(-3.31586 + 5.15884i) q^{93} +(-7.41770 - 4.76707i) q^{94} +(-16.5195 + 2.37514i) q^{95} +(0.246607 - 1.71441i) q^{96} +(5.04241 - 17.1729i) q^{97} +(-0.909632 - 0.415415i) q^{98} +(2.65367 + 0.779558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9}+O(q^{10}) \) 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9	\( 240 q - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{9} + 4 q^{12} - 8 q^{13} + 24 q^{14} + 18 q^{15} - 24 q^{16} + 32 q^{17} - 4 q^{18} + 4 q^{20} - 8 q^{23} + 12 q^{25} - 148 q^{27} + 40 q^{30} + 16 q^{31} + 42 q^{33} - 4 q^{36} + 22 q^{37} + 8 q^{39} + 154 q^{41} + 4 q^{42} + 22 q^{43} + 24 q^{45} + 4 q^{46} - 4 q^{48} + 24 q^{49} + 88 q^{50} + 24 q^{51} + 8 q^{52} - 108 q^{53} + 12 q^{54} - 16 q^{55} - 24 q^{56} - 62 q^{57} - 4 q^{58} + 22 q^{59} - 18 q^{60} - 4 q^{63} + 24 q^{64} - 100 q^{66} - 44 q^{67} - 32 q^{68} - 86 q^{69} + 4 q^{70} + 4 q^{72} - 12 q^{73} - 16 q^{74} - 26 q^{75} - 78 q^{78} - 4 q^{80} + 52 q^{81} + 8 q^{82} + 16 q^{83} - 28 q^{85} + 16 q^{86} - 196 q^{87} + 24 q^{89} + 126 q^{90} + 8 q^{92} - 16 q^{93} - 8 q^{94} + 132 q^{97} + 172 q^{99}+O(q^{100}) \) 240 * q - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^9 + 4 * q^12 - 8 * q^13 + 24 * q^14 + 18 * q^15 - 24 * q^16 + 32 * q^17 - 4 * q^18 + 4 * q^20 - 8 * q^23 + 12 * q^25 - 148 * q^27 + 40 * q^30 + 16 * q^31 + 42 * q^33 - 4 * q^36 + 22 * q^37 + 8 * q^39 + 154 * q^41 + 4 * q^42 + 22 * q^43 + 24 * q^45 + 4 * q^46 - 4 * q^48 + 24 * q^49 + 88 * q^50 + 24 * q^51 + 8 * q^52 - 108 * q^53 + 12 * q^54 - 16 * q^55 - 24 * q^56 - 62 * q^57 - 4 * q^58 + 22 * q^59 - 18 * q^60 - 4 * q^63 + 24 * q^64 - 100 * q^66 - 44 * q^67 - 32 * q^68 - 86 * q^69 + 4 * q^70 + 4 * q^72 - 12 * q^73 - 16 * q^74 - 26 * q^75 - 78 * q^78 - 4 * q^80 + 52 * q^81 + 8 * q^82 + 16 * q^83 - 28 * q^85 + 16 * q^86 - 196 * q^87 + 24 * q^89 + 126 * q^90 + 8 * q^92 - 16 * q^93 - 8 * q^94 + 132 * q^97 + 172 * q^99

Introduction

L-functions

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