LMFDB - Embedded newform 69.2.e.c.58.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [69,2,Mod(4,69)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(69, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("69.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 69 = 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	69.e (of order $11$, 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:	$0.550967773947$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 7 x^{19} + 24 x^{18} - 70 x^{17} + 209 x^{16} - 527 x^{15} + 1115 x^{14} - 2187 x^{13} + \cdots + 529 $ x^20 - 7x^19 + 24x^18 - 70x^17 + 209x^16 - 527x^15 + 1115x^14 - 2187x^13 + 4165x^12 - 7040x^11 + 10649x^10 - 13519x^9 + 15111x^8 - 12101x^7 + 8244x^6 - 2837x^5 + 1859x^4 - 1730x^3 + 1957x^2 - 1656*x + 529
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			58.1
Root			$-0.201819 - 1.40368i$ of defining polynomial
Character	$\chi$	$=$	69.58
Dual form			69.2.e.c.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.733503 + 0.471394i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(-0.515016 + 1.12773i) q^{4} +(-1.20424 + 0.353596i) q^{5} +(-0.362207 - 0.793123i) q^{6} +(1.95301 + 2.25389i) q^{7} +(-0.402011 - 2.79605i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})$	\(q+(-0.733503 + 0.471394i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(-0.515016 + 1.12773i) q^{4} +(-1.20424 + 0.353596i) q^{5} +(-0.362207 - 0.793123i) q^{6} +(1.95301 + 2.25389i) q^{7} +(-0.402011 - 2.79605i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.716629 - 0.827034i) q^{10} +(1.82789 + 1.17472i) q^{11} +(-1.04295 - 0.670266i) q^{12} +(2.53697 - 2.92782i) q^{13} +(-2.49500 - 0.732599i) q^{14} +(-0.178616 - 1.24230i) q^{15} +(-0.0108276 - 0.0124957i) q^{16} +(0.279567 + 0.612167i) q^{17} +(0.836598 - 0.245647i) q^{18} +(1.71250 - 3.74986i) q^{19} +(0.221442 - 1.54016i) q^{20} +(-2.50889 + 1.61236i) q^{21} -1.89452 q^{22} +(0.811247 - 4.72672i) q^{23} +2.82480 q^{24} +(-2.88111 + 1.85157i) q^{25} +(-0.480720 + 3.34348i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-3.54760 + 1.04167i) q^{28} +(3.63733 + 7.96463i) q^{29} +(0.716629 + 0.827034i) q^{30} +(0.717223 + 4.98839i) q^{31} +(5.43459 + 1.59574i) q^{32} +(-1.42289 + 1.64211i) q^{33} +(-0.493635 - 0.317240i) q^{34} +(-3.14885 - 2.02364i) q^{35} +(0.811872 - 0.936950i) q^{36} +(-8.56168 - 2.51394i) q^{37} +(0.511534 + 3.55779i) q^{38} +(2.53697 + 2.92782i) q^{39} +(1.47279 + 3.22496i) q^{40} +(-5.37386 + 1.57791i) q^{41} +(1.08022 - 2.36535i) q^{42} +(1.20980 - 8.41433i) q^{43} +(-2.26615 + 1.45637i) q^{44} +1.25508 q^{45} +(1.63309 + 3.84948i) q^{46} +8.72071 q^{47} +(0.0139094 - 0.00893903i) q^{48} +(-0.269579 + 1.87496i) q^{49} +(1.24048 - 2.71627i) q^{50} +(-0.645722 + 0.189601i) q^{51} +(1.99521 + 4.36889i) q^{52} +(-7.25079 - 8.36786i) q^{53} +(0.124087 + 0.863041i) q^{54} +(-2.61659 - 0.768301i) q^{55} +(5.51685 - 6.36679i) q^{56} +(3.46798 + 2.22873i) q^{57} +(-6.42247 - 4.12747i) q^{58} +(3.81005 - 4.39703i) q^{59} +(1.49297 + 0.438375i) q^{60} +(-0.635567 - 4.42047i) q^{61} +(-2.87758 - 3.32091i) q^{62} +(-1.23890 - 2.71282i) q^{63} +(-4.70678 + 1.38203i) q^{64} +(-2.01986 + 4.42287i) q^{65} +(0.269618 - 1.87523i) q^{66} +(4.74190 - 3.04743i) q^{67} -0.834339 q^{68} +(4.56316 + 1.47567i) q^{69} +3.26362 q^{70} +(-6.66525 + 4.28350i) q^{71} +(-0.402011 + 2.79605i) q^{72} +(2.65322 - 5.80973i) q^{73} +(7.46507 - 2.19194i) q^{74} +(-1.42270 - 3.11529i) q^{75} +(3.34685 + 3.86247i) q^{76} +(0.922207 + 6.41409i) q^{77} +(-3.24103 - 0.951654i) q^{78} +(-4.70947 + 5.43502i) q^{79} +(0.0174574 + 0.0112192i) q^{80} +(0.841254 + 0.540641i) q^{81} +(3.19793 - 3.69060i) q^{82} +(-11.4263 - 3.35507i) q^{83} +(-0.526191 - 3.65974i) q^{84} +(-0.553126 - 0.638341i) q^{85} +(3.07907 + 6.74222i) q^{86} +(-8.40121 + 2.46682i) q^{87} +(2.54973 - 5.58312i) q^{88} +(-0.0515079 + 0.358245i) q^{89} +(-0.920603 + 0.591636i) q^{90} +11.5537 q^{91} +(4.91265 + 3.34920i) q^{92} -5.03969 q^{93} +(-6.39666 + 4.11088i) q^{94} +(-0.736326 + 5.12126i) q^{95} +(-2.35292 + 5.15217i) q^{96} +(-11.7625 + 3.45378i) q^{97} +(-0.686108 - 1.50237i) q^{98} +(-1.42289 - 1.64211i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/69\mathbb{Z}\right)^\times$.

$n$	$28$	$47$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$1$

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 $

$2$	−0.733503	+	0.471394i	−0.518665	+	0.333326i	−0.773644	−	0.633621i	$-0.781568\pi$
$2$	−0.733503	+	0.471394i	−0.518665	+	0.333326i	0.254979	+	0.966947i	$0.417931\pi$
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$3$	−0.142315	+	0.989821i	−0.0821655	+	0.571474i
$4$	−0.515016	+	1.12773i	−0.257508	+	0.563864i
$5$	−1.20424	+	0.353596i	−0.538552	+	0.158133i	−0.539686	−	0.841866i	$-0.681457\pi$
$5$	−1.20424	+	0.353596i	−0.538552	+	0.158133i	0.00113425	+	0.999999i	$0.499639\pi$
$6$	−0.362207	−	0.793123i	−0.147870	−	0.323791i
$7$	1.95301	+	2.25389i	0.738167	+	0.851890i	0.993366	−	0.114999i	$-0.0366864\pi$
$7$	1.95301	+	2.25389i	0.738167	+	0.851890i	−0.255199	+	0.966889i	$0.582141\pi$
$8$	−0.402011	−	2.79605i	−0.142132	−	0.988553i
$9$	−0.959493	−	0.281733i	−0.319831	−	0.0939109i
$10$	0.716629	−	0.827034i	0.226618	−	0.261531i
$11$	1.82789	+	1.17472i	0.551130	+	0.354190i	0.786378	−	0.617745i	$-0.211954\pi$
$11$	1.82789	+	1.17472i	0.551130	+	0.354190i	−0.235248	+	0.971935i	$0.575590\pi$
$12$	−1.04295	−	0.670266i	−0.301075	−	0.193489i
$13$	2.53697	−	2.92782i	0.703630	−	0.812032i	−0.285608	−	0.958347i	$-0.592196\pi$
$13$	2.53697	−	2.92782i	0.703630	−	0.812032i	0.989238	+	0.146314i	$0.0467410\pi$
$14$	−2.49500	−	0.732599i	−0.666818	−	0.195795i
$15$	−0.178616	−	1.24230i	−0.0461185	−	0.320761i
$16$	−0.0108276	−	0.0124957i	−0.00270689	−	0.00312392i
$17$	0.279567	+	0.612167i	0.0678050	+	0.148472i	0.940500	−	0.339793i	$-0.110357\pi$
$17$	0.279567	+	0.612167i	0.0678050	+	0.148472i	−0.872695	+	0.488265i	$0.837630\pi$
$18$	0.836598	−	0.245647i	0.197188	−	0.0578996i
$19$	1.71250	−	3.74986i	0.392875	−	0.860277i	−0.605068	−	0.796174i	$-0.706854\pi$
$19$	1.71250	−	3.74986i	0.392875	−	0.860277i	0.997943	−	0.0641030i	$-0.0204186\pi$
$20$	0.221442	−	1.54016i	0.0495159	−	0.344390i
$21$	−2.50889	+	1.61236i	−0.547484	+	0.351847i
$22$	−1.89452			−0.403912
$23$	0.811247	−	4.72672i	0.169157	−	0.985589i
$23$	0.811247	−	4.72672i	0.169157	−	0.985589i
$24$	2.82480			0.576610
$25$	−2.88111	+	1.85157i	−0.576221	+	0.370315i
$26$	−0.480720	+	3.34348i	−0.0942769	+	0.655710i
$27$	0.415415	−	0.909632i	0.0799467	−	0.175059i
$28$	−3.54760	+	1.04167i	−0.670433	+	0.196857i
$29$	3.63733	+	7.96463i	0.675435	+	1.47900i	0.867409	+	0.497596i	$0.165784\pi$
$29$	3.63733	+	7.96463i	0.675435	+	1.47900i	−0.191974	+	0.981400i	$0.561489\pi$
$30$	0.716629	+	0.827034i	0.130838	+	0.150995i
$31$	0.717223	+	4.98839i	0.128817	+	0.895942i	0.947057	+	0.321065i	$0.104041\pi$
$31$	0.717223	+	4.98839i	0.128817	+	0.895942i	−0.818240	+	0.574877i	$0.805050\pi$
$32$	5.43459	+	1.59574i	0.960708	+	0.282089i
$33$	−1.42289	+	1.64211i	−0.247694	+	0.285854i
$34$	−0.493635	−	0.317240i	−0.0846577	−	0.0544062i
$35$	−3.14885	−	2.02364i	−0.532253	−	0.342058i
$36$	0.811872	−	0.936950i	0.135312	−	0.156158i
$37$	−8.56168	−	2.51394i	−1.40753	−	0.413289i	−0.512268	−	0.858826i	$-0.671195\pi$
$37$	−8.56168	−	2.51394i	−1.40753	−	0.413289i	−0.895264	+	0.445537i	$0.853013\pi$
$38$	0.511534	+	3.55779i	0.0829817	+	0.577150i
$39$	2.53697	+	2.92782i	0.406241	+	0.468827i
$40$	1.47279	+	3.22496i	0.232869	+	0.509911i
$41$	−5.37386	+	1.57791i	−0.839256	+	0.246428i	−0.672989	−	0.739653i	$-0.734990\pi$
$41$	−5.37386	+	1.57791i	−0.839256	+	0.246428i	−0.166268	+	0.986081i	$0.553172\pi$
$42$	1.08022	−	2.36535i	0.166681	−	0.364981i
$43$	1.20980	−	8.41433i	0.184492	−	1.28317i	−0.661487	−	0.749957i	$-0.730074\pi$
$43$	1.20980	−	8.41433i	0.184492	−	1.28317i	0.845979	−	0.533216i	$-0.179017\pi$
$44$	−2.26615	+	1.45637i	−0.341635	+	0.219556i
$45$	1.25508			0.187096
$46$	1.63309	+	3.84948i	0.240786	+	0.567575i
$47$	8.72071			1.27205			0.636023	−	0.771670i	$-0.280578\pi$
$47$	8.72071			1.27205			0.636023	+	0.771670i	$0.280578\pi$
$48$	0.0139094	−	0.00893903i	0.00200765	−	0.00129024i
$49$	−0.269579	+	1.87496i	−0.0385113	+	0.267852i
$50$	1.24048	−	2.71627i	0.175430	−	0.384139i
$51$	−0.645722	+	0.189601i	−0.0904192	+	0.0265495i
$52$	1.99521	+	4.36889i	0.276685	+	0.605856i
$53$	−7.25079	−	8.36786i	−0.995973	−	1.14941i	−0.988771	−	0.149440i	$-0.952253\pi$
$53$	−7.25079	−	8.36786i	−0.995973	−	1.14941i	−0.00720166	−	0.999974i	$-0.502292\pi$
$54$	0.124087	+	0.863041i	0.0168860	+	0.117445i
$55$	−2.61659	−	0.768301i	−0.352822	−	0.103598i
$56$	5.51685	−	6.36679i	0.737220	−	0.850798i
$57$	3.46798	+	2.22873i	0.459345	+	0.295203i
$58$	−6.42247	−	4.12747i	−0.843311	−	0.541963i
$59$	3.81005	−	4.39703i	0.496027	−	0.572445i	−0.451439	−	0.892302i	$-0.649089\pi$
$59$	3.81005	−	4.39703i	0.496027	−	0.572445i	0.947466	+	0.319857i	$0.103635\pi$
$60$	1.49297	+	0.438375i	0.192742	+	0.0565940i
$61$	−0.635567	−	4.42047i	−0.0813760	−	0.565983i	−0.989193	−	0.146617i	$-0.953162\pi$
$61$	−0.635567	−	4.42047i	−0.0813760	−	0.565983i	0.907817	−	0.419366i	$-0.137748\pi$
$62$	−2.87758	−	3.32091i	−0.365453	−	0.421755i
$63$	−1.23890	−	2.71282i	−0.156087	−	0.341783i
$64$	−4.70678	+	1.38203i	−0.588347	+	0.172754i
$65$	−2.01986	+	4.42287i	−0.250532	+	0.548589i
$66$	0.269618	−	1.87523i	0.0331877	−	0.230825i
$67$	4.74190	−	3.04743i	0.579315	−	0.372303i	−0.217925	−	0.975966i	$-0.569929\pi$
$67$	4.74190	−	3.04743i	0.579315	−	0.372303i	0.797240	+	0.603662i	$0.206292\pi$
$68$	−0.834339			−0.101178
$69$	4.56316	+	1.47567i	0.549339	+	0.177650i
$70$	3.26362			0.390078
$71$	−6.66525	+	4.28350i	−0.791020	+	0.508358i	−0.872674	−	0.488303i	$-0.837616\pi$
$71$	−6.66525	+	4.28350i	−0.791020	+	0.508358i	0.0816541	+	0.996661i	$0.473980\pi$
$72$	−0.402011	+	2.79605i	−0.0473775	+	0.329518i
$73$	2.65322	−	5.80973i	0.310535	−	0.679978i	−0.688437	−	0.725296i	$-0.741703\pi$
$73$	2.65322	−	5.80973i	0.310535	−	0.679978i	0.998973	+	0.0453182i	$0.0144302\pi$
$74$	7.46507	−	2.19194i	0.867797	−	0.254808i
$75$	−1.42270	−	3.11529i	−0.164280	−	0.359722i
$76$	3.34685	+	3.86247i	0.383910	+	0.443056i
$77$	0.922207	+	6.41409i	0.105095	+	0.730953i
$78$	−3.24103	−	0.951654i	−0.366975	−	0.107754i
$79$	−4.70947	+	5.43502i	−0.529857	+	0.611488i	−0.956071	−	0.293135i	$-0.905302\pi$
$79$	−4.70947	+	5.43502i	−0.529857	+	0.611488i	0.426214	+	0.904622i	$0.359847\pi$
$80$	0.0174574	+	0.0112192i	0.00195180	+	0.00125434i
$81$	0.841254	+	0.540641i	0.0934726	+	0.0600712i
$82$	3.19793	−	3.69060i	0.353152	−	0.407559i
$83$	−11.4263	−	3.35507i	−1.25420	−	0.368267i	−0.413868	−	0.910337i	$-0.635823\pi$
$83$	−11.4263	−	3.35507i	−1.25420	−	0.368267i	−0.840333	+	0.542070i	$0.817641\pi$
$84$	−0.526191	−	3.65974i	−0.0574121	−	0.399310i
$85$	−0.553126	−	0.638341i	−0.0599949	−	0.0692378i
$86$	3.07907	+	6.74222i	0.332025	+	0.727033i
$87$	−8.40121	+	2.46682i	−0.900704	+	0.264471i
$88$	2.54973	−	5.58312i	0.271802	−	0.595163i
$89$	−0.0515079	+	0.358245i	−0.00545982	+	0.0379739i	−0.992369	−	0.123302i	$-0.960652\pi$
$89$	−0.0515079	+	0.358245i	−0.00545982	+	0.0379739i	0.986909	+	0.161276i	$0.0515608\pi$
$90$	−0.920603	+	0.591636i	−0.0970401	+	0.0623639i
$91$	11.5537			1.21116
$92$	4.91265	+	3.34920i	0.512179	+	0.349178i
$93$	−5.03969			−0.522592
$94$	−6.39666	+	4.11088i	−0.659765	+	0.424005i
$95$	−0.736326	+	5.12126i	−0.0755455	+	0.525430i
$96$	−2.35292	+	5.15217i	−0.240144	+	0.525841i
$97$	−11.7625	+	3.45378i	−1.19430	+	0.350679i	−0.817671	−	0.575685i	$-0.804735\pi$
$97$	−11.7625	+	3.45378i	−1.19430	+	0.350679i	−0.376630	+	0.926364i	$0.622917\pi$
$98$	−0.686108	−	1.50237i	−0.0693074	−	0.151762i
$99$	−1.42289	−	1.64211i	−0.143006	−	0.165038i
$100$	−0.604256	−	4.20269i	−0.0604256	−	0.420269i
$101$	15.2598	+	4.48067i	1.51840	+	0.445844i	0.931478	−	0.363797i	$-0.118520\pi$
$101$	15.2598	+	4.48067i	1.51840	+	0.445844i	0.586926	+	0.809641i	$0.300338\pi$
$102$	0.384262	−	0.443462i	0.0380476	−	0.0439093i
$103$	15.7202	+	10.1028i	1.54896	+	0.995455i	0.985571	+	0.169263i	$0.0541387\pi$
$103$	15.7202	+	10.1028i	1.54896	+	0.995455i	0.563388	+	0.826193i	$0.309498\pi$
$104$	−9.20623	−	5.91649i	−0.902745	−	0.580159i
$105$	2.45117	−	2.82881i	0.239210	−	0.276063i
$106$	9.26303	+	2.71987i	0.899705	+	0.264177i
$107$	−0.867913	−	6.03647i	−0.0839044	−	0.583568i	−0.987790	−	0.155793i	$-0.950207\pi$
$107$	−0.867913	−	6.03647i	−0.0839044	−	0.583568i	0.903885	−	0.427775i	$-0.140702\pi$
$108$	0.811872	+	0.936950i	0.0781224	+	0.0901580i
$109$	3.78448	+	8.28687i	0.362488	+	0.793738i	0.999734	+	0.0230771i	$0.00734633\pi$
$109$	3.78448	+	8.28687i	0.362488	+	0.793738i	−0.637246	+	0.770661i	$0.719926\pi$
$110$	2.28145	−	0.669894i	0.217528	−	0.0638719i
$111$	3.70680	−	8.11677i	0.351834	−	0.770409i
$112$	0.00701756	−	0.0488082i	0.000663097	−	0.00461194i
$113$	−7.92976	+	5.09615i	−0.745969	+	0.479405i	−0.857582	−	0.514347i	$-0.828034\pi$
$113$	−7.92976	+	5.09615i	−0.745969	+	0.479405i	0.111614	+	0.993752i	$0.464398\pi$
$114$	−3.59438			−0.336645
$115$	0.694416	+	5.97895i	0.0647546	+	0.557540i
$116$	−10.8552			−1.00788
$117$	−3.25907	+	2.09448i	−0.301301	+	0.193635i
$118$	−0.721950	+	5.02127i	−0.0664609	+	0.462245i
$119$	−0.833759	+	1.82568i	−0.0764306	+	0.167360i
$120$	−3.40174	+	0.998840i	−0.310535	+	0.0911812i
$121$	−2.60833	−	5.71145i	−0.237121	−	0.519222i
$122$	2.54997	+	2.94282i	0.230863	+	0.266431i
$123$	−0.797067	−	5.54372i	−0.0718691	−	0.499861i
$124$	−5.99493	−	1.76027i	−0.538361	−	0.158077i
$125$	6.92434	−	7.99111i	0.619332	−	0.714747i
$126$	2.18754	+	1.40585i	0.194882	+	0.125243i
$127$	4.93475	+	3.17137i	0.437888	+	0.281414i	0.740954	−	0.671556i	$-0.234374\pi$
$127$	4.93475	+	3.17137i	0.437888	+	0.281414i	−0.303065	+	0.952970i	$0.598010\pi$
$128$	−4.61734	+	5.32869i	−0.408119	+	0.470994i
$129$	8.15651	+	2.39497i	0.718141	+	0.210865i
$130$	−0.603341	−	4.19633i	−0.0529165	−	0.368042i
$131$	−5.64905	−	6.51936i	−0.493560	−	0.569599i	0.453253	−	0.891382i	$-0.350263\pi$
$131$	−5.64905	−	6.51936i	−0.493560	−	0.569599i	−0.946813	+	0.321783i	$0.895718\pi$
$132$	−1.11904	−	2.45035i	−0.0973996	−	0.213275i
$133$	11.7963	−	3.46370i	1.02287	−	0.300341i
$134$	−2.04166	+	4.47060i	−0.176372	+	0.386201i
$135$	−0.178616	+	1.24230i	−0.0153728	+	0.106920i
$136$	1.59926	−	1.02778i	0.137135	−	0.0881315i
$137$	1.98038			0.169195			0.0845977	−	0.996415i	$-0.473040\pi$
$137$	1.98038			0.169195			0.0845977	+	0.996415i	$0.473040\pi$
$138$	−4.04271	+	1.06863i	−0.344138	+	0.0909680i
$139$	−5.82311			−0.493910			−0.246955	−	0.969027i	$-0.579430\pi$
$139$	−5.82311			−0.493910			−0.246955	+	0.969027i	$0.579430\pi$
$140$	3.90383	−	2.50884i	0.329934	−	0.212035i
$141$	−1.24109	+	8.63194i	−0.104518	+	0.726941i
$142$	2.86977	−	6.28391i	0.240826	−	0.527334i
$143$	8.07668	−	2.37153i	0.675406	−	0.198317i
$144$	0.00686853	+	0.0150400i	0.000572378	+	0.00125333i
$145$	−7.19648	−	8.30518i	−0.597635	−	0.689707i
$146$	0.792529	+	5.51216i	0.0655902	+	0.456190i
$147$	−1.81751	−	0.533670i	−0.149906	−	0.0440163i
$148$	7.24444	−	8.36052i	0.595489	−	0.687231i
$149$	−14.6598	−	9.42125i	−1.20097	−	0.771819i	−0.221849	−	0.975081i	$-0.571209\pi$
$149$	−14.6598	−	9.42125i	−1.20097	−	0.771819i	−0.979124	+	0.203262i	$0.934846\pi$
$150$	2.51208	+	1.61442i	0.205111	+	0.131817i
$151$	−8.54313	+	9.85930i	−0.695230	+	0.802339i	−0.988100	−	0.153814i	$-0.950844\pi$
$151$	−8.54313	+	9.85930i	−0.695230	+	0.802339i	0.292869	+	0.956152i	$0.405390\pi$
$152$	−11.1732	−	3.28076i	−0.906269	−	0.266105i
$153$	−0.0957755	−	0.666133i	−0.00774299	−	0.0538537i
$154$	−3.70000	−	4.27003i	−0.298155	−	0.344089i
$155$	−2.62759	−	5.75361i	−0.211053	−	0.462141i
$156$	−4.60837	+	1.35314i	−0.368965	+	0.108338i
$157$	3.64988	−	7.99213i	0.291292	−	0.637841i	−0.706246	−	0.707967i	$-0.749613\pi$
$157$	3.64988	−	7.99213i	0.291292	−	0.637841i	0.997538	+	0.0701254i	$0.0223399\pi$
$158$	0.892377	−	6.20662i	0.0709937	−	0.493772i
$159$	9.31458	−	5.98612i	0.738694	−	0.474730i
$160$	−7.10879			−0.561999
$161$	12.2379	−	7.40285i	0.964479	−	0.583426i
$162$	−0.871916			−0.0685042
$163$	−7.01613	+	4.50899i	−0.549546	+	0.353172i	−0.785762	−	0.618529i	$-0.787729\pi$
$163$	−7.01613	+	4.50899i	−0.549546	+	0.353172i	0.236216	+	0.971700i	$0.424093\pi$
$164$	0.988174	−	6.87290i	0.0771634	−	0.536683i
$165$	1.13286	−	2.48062i	0.0881931	−	0.193116i
$166$	9.96280	−	2.92534i	0.773263	−	0.227050i
$167$	4.90225	+	10.7344i	0.379347	+	0.830654i	0.998953	+	0.0457416i	$0.0145651\pi$
$167$	4.90225	+	10.7344i	0.379347	+	0.830654i	−0.619606	+	0.784913i	$0.712708\pi$
$168$	5.51685	+	6.36679i	0.425634	+	0.491208i
$169$	−0.285825	−	1.98795i	−0.0219865	−	0.152920i
$170$	0.706629	+	0.207485i	0.0541960	+	0.0159134i
$171$	−2.69959	+	3.11550i	−0.206443	+	0.238248i
$172$	8.86600	+	5.69783i	0.676026	+	0.434456i
$173$	13.0011	+	8.35530i	0.988455	+	0.635241i	0.931731	−	0.363149i	$-0.118298\pi$
$173$	13.0011	+	8.35530i	0.988455	+	0.635241i	0.0567236	+	0.998390i	$0.481935\pi$
$174$	4.99947	−	5.76969i	0.379009	−	0.437399i
$175$	−9.80006	−	2.87756i	−0.740815	−	0.217523i
$176$	−0.00511276	−	0.0355600i	−0.000385389	−	0.00268044i
$177$	3.81005	+	4.39703i	0.286381	+	0.330501i
$178$	−0.131093	−	0.287054i	−0.00982585	−	0.0215156i
$179$	17.7101	−	5.20015i	1.32371	−	0.388677i	0.457882	−	0.889013i	$-0.348608\pi$
$179$	17.7101	−	5.20015i	1.32371	−	0.388677i	0.865831	+	0.500336i	$0.166790\pi$
$180$	−0.646385	+	1.41539i	−0.0481787	+	0.105497i
$181$	−0.990548	+	6.88941i	−0.0736268	+	0.512086i	0.919319	+	0.393514i	$0.128741\pi$
$181$	−0.990548	+	6.88941i	−0.0736268	+	0.512086i	−0.992945	+	0.118572i	$0.962168\pi$
$182$	−8.47468	+	5.44635i	−0.628185	+	0.403710i
$183$	4.46592			0.330130
$184$	−13.5423	−	0.368093i	−0.998349	−	0.0271362i
$185$	11.1992			0.823384
$186$	3.69663	−	2.37568i	0.271050	−	0.174193i
$187$	−0.208103	+	1.44739i	−0.0152180	+	0.105843i
$188$	−4.49130	+	9.83458i	−0.327562	+	0.717260i
$189$	2.86152	−	0.840217i	0.208145	−	0.0611168i
$190$	−1.87403	−	4.10356i	−0.135957	−	0.297703i
$191$	−9.80772	−	11.3187i	−0.709662	−	0.818993i	0.280362	−	0.959894i	$-0.409546\pi$
$191$	−9.80772	−	11.3187i	−0.709662	−	0.818993i	−0.990024	+	0.140901i	$0.955000\pi$
$192$	−0.698123	−	4.85555i	−0.0503827	−	0.350419i
$193$	−16.9034	−	4.96330i	−1.21674	−	0.357266i	−0.390507	−	0.920600i	$-0.627700\pi$
$193$	−16.9034	−	4.96330i	−1.21674	−	0.357266i	−0.826229	+	0.563334i	$0.809518\pi$
$194$	6.99974	−	8.07813i	0.502552	−	0.579976i
$195$	−4.09039	−	2.62874i	−0.292919	−	0.188248i
$196$	−1.97561	−	1.26965i	−0.141115	−	0.0906890i
$197$	−12.0284	+	13.8815i	−0.856990	+	0.989019i	−1.00000		0.000702196i	$-0.999776\pi$
$197$	−12.0284	+	13.8815i	−0.856990	+	0.989019i	0.143010	+	0.989721i	$0.454322\pi$
$198$	1.81778	+	0.533747i	0.129184	+	0.0379318i
$199$	2.58580	+	17.9846i	0.183302	+	1.27489i	0.848888	+	0.528573i	$0.177273\pi$
$199$	2.58580	+	17.9846i	0.183302	+	1.27489i	−0.665586	+	0.746322i	$0.731818\pi$
$200$	6.33533	+	7.31136i	0.447976	+	0.516991i
$201$	2.34157	+	5.12733i	0.165162	+	0.361654i
$202$	−13.3052	+	3.90677i	−0.936153	+	0.274879i
$203$	−10.8477	+	23.7531i	−0.761358	+	1.66714i
$204$	0.118739	−	0.825846i	0.00831338	−	0.0578208i
$205$	5.91347	−	3.80036i	0.413015	−	0.265428i
$206$	−16.2932			−1.13520
$207$	−2.11006	+	4.30670i	−0.146659	+	0.299336i
$208$	−0.0640544			−0.00444137
$209$	7.53529	−	4.84264i	0.521227	−	0.334972i
$210$	−0.464462	+	3.23040i	−0.0320509	+	0.222919i
$211$	−4.38868	+	9.60987i	−0.302129	+	0.661571i	−0.998420	−	0.0561890i	$-0.982105\pi$
$211$	−4.38868	+	9.60987i	−0.302129	+	0.661571i	0.696291	+	0.717760i	$0.254832\pi$
$212$	13.1709	−	3.86733i	0.904583	−	0.265610i
$213$	−3.29133	−	7.20702i	−0.225518	−	0.493817i
$214$	3.48217	+	4.01864i	0.238036	+	0.274708i
$215$	1.51839	+	10.5606i	0.103553	+	0.720230i
$216$	−2.71038	−	0.795838i	−0.184418	−	0.0541499i
$217$	−9.84254	+	11.3589i	−0.668155	+	0.771092i
$218$	−6.68230	−	4.29446i	−0.452583	−	0.290857i
$219$	5.37301	+	3.45302i	0.363074	+	0.233334i
$220$	2.21402	−	2.55512i	0.149269	−	0.172266i
$221$	2.50157	+	0.734528i	0.168274	+	0.0494097i
$222$	1.10724	+	7.70103i	0.0743132	+	0.516859i
$223$	4.12016	+	4.75492i	0.275906	+	0.318413i	0.876743	−	0.480959i	$-0.159711\pi$
$223$	4.12016	+	4.75492i	0.275906	+	0.318413i	−0.600837	+	0.799372i	$0.705166\pi$
$224$	7.01716	+	15.3654i	0.468854	+	1.02665i
$225$	3.28605	−	0.964872i	0.219070	−	0.0643248i
$226$	3.41421	−	7.47607i	0.227110	−	0.497301i
$227$	0.999968	−	6.95493i	0.0663702	−	0.461615i	−0.929350	−	0.369199i	$-0.879632\pi$
$227$	0.999968	−	6.95493i	0.0663702	−	0.461615i	0.995720	−	0.0924159i	$-0.0294589\pi$
$228$	−4.29947	+	2.76310i	−0.284739	+	0.182991i
$229$	0.341930			0.0225954			0.0112977	−	0.999936i	$-0.496404\pi$
$229$	0.341930			0.0225954			0.0112977	+	0.999936i	$0.496404\pi$
$230$	−3.32780	−	4.05824i	−0.219428	−	0.267592i
$231$	−6.48005			−0.426356
$232$	20.8073	−	13.3720i	1.36606	−	0.877916i
$233$	1.57250	−	10.9370i	0.103018	−	0.716504i	−0.871206	−	0.490918i	$-0.836661\pi$
$233$	1.57250	−	10.9370i	0.103018	−	0.716504i	0.974223	−	0.225586i	$-0.0724296\pi$
$234$	1.40321	−	3.07261i	0.0917310	−	0.200863i
$235$	−10.5018	+	3.08361i	−0.685063	+	0.201153i
$236$	2.99642	+	6.56124i	0.195050	+	0.427100i
$237$	−4.70947	−	5.43502i	−0.305913	−	0.353042i
$238$	−0.249048	−	1.73217i	−0.0161434	−	0.112280i
$239$	4.91021	+	1.44177i	0.317615	+	0.0932601i	0.436654	−	0.899629i	$-0.356163\pi$
$239$	4.91021	+	1.44177i	0.317615	+	0.0932601i	−0.119039	+	0.992890i	$0.537982\pi$
$240$	−0.0135894	+	0.0156830i	−0.000877194	+	0.00101234i
$241$	−13.9668	−	8.97590i	−0.899679	−	0.578189i	0.00701599	−	0.999975i	$-0.497767\pi$
$241$	−13.9668	−	8.97590i	−0.899679	−	0.578189i	−0.906695	+	0.421787i	$0.861403\pi$
$242$	4.60556	+	2.95981i	0.296056	+	0.190264i
$243$	−0.654861	+	0.755750i	−0.0420093	+	0.0484814i
$244$	5.31241	+	1.55986i	0.340092	+	0.0998600i
$245$	−0.338342	−	2.35322i	−0.0216159	−	0.150342i
$246$	3.19793	+	3.69060i	0.203892	+	0.235304i
$247$	−6.63435	−	14.5272i	−0.422134	−	0.924344i
$248$	13.6595	−	4.01078i	0.867377	−	0.254685i
$249$	4.94706	−	10.8325i	0.313507	−	0.686484i
$250$	−1.31206	+	9.12559i	−0.0829821	+	0.577153i
$251$	13.6488	−	8.77152i	0.861502	−	0.553654i	−0.0336406	−	0.999434i	$-0.510710\pi$
$251$	13.6488	−	8.77152i	0.861502	−	0.553654i	0.895142	+	0.445780i	$0.147074\pi$
$252$	3.69737			0.232912
$253$	7.03542	−	7.68695i	0.442313	−	0.483274i
$254$	−5.11462			−0.320920
$255$	0.710562	−	0.456650i	0.0444971	−	0.0285965i
$256$	2.27116	−	15.7963i	0.141948	−	0.987268i
$257$	7.32756	−	16.0451i	0.457081	−	1.00087i	−0.531062	−	0.847333i	$-0.678207\pi$
$257$	7.32756	−	16.0451i	0.457081	−	1.00087i	0.988143	−	0.153535i	$-0.0490657\pi$
$258$	−7.11180	+	2.08821i	−0.442761	+	0.130006i
$259$	−11.0549	−	24.2068i	−0.686917	−	1.50414i
$260$	−3.94753	−	4.55569i	−0.244815	−	0.282532i
$261$	−1.24609	−	8.66676i	−0.0771312	−	0.536459i
$262$	7.21678	+	2.11904i	0.445854	+	0.130915i
$263$	−10.9629	+	12.6519i	−0.676004	+	0.780150i	−0.985303	−	0.170815i	$-0.945360\pi$
$263$	−10.9629	+	12.6519i	−0.676004	+	0.780150i	0.309299	+	0.950965i	$0.399906\pi$
$264$	5.16343	+	3.31834i	0.317787	+	0.204230i
$265$	11.6905	+	7.51305i	0.718143	+	0.461523i
$266$	−7.01984	+	8.10133i	−0.430414	+	0.496724i
$267$	−0.347268	−	0.101967i	−0.0212525	−	0.00624029i
$268$	0.994521	+	6.91705i	0.0607501	+	0.422526i
$269$	−5.18567	−	5.98459i	−0.316176	−	0.364887i	0.575309	−	0.817936i	$-0.304882\pi$
$269$	−5.18567	−	5.98459i	−0.316176	−	0.364887i	−0.891486	+	0.453049i	$0.850336\pi$
$270$	−0.454598	−	0.995431i	−0.0276660	−	0.0605800i
$271$	2.74288	−	0.805381i	0.166618	−	0.0489234i	−0.197360	−	0.980331i	$-0.563237\pi$
$271$	2.74288	−	0.805381i	0.166618	−	0.0489234i	0.363978	+	0.931408i	$0.381418\pi$
$272$	0.00462240	−	0.0101217i	0.000280274	−	0.000613715i
$273$	−1.64426	+	11.4361i	−0.0995154	+	0.692145i
$274$	−1.45261	+	0.933539i	−0.0877556	+	0.0563971i
$275$	−7.44143			−0.448735
$276$	−4.01425	+	4.38600i	−0.241630	+	0.264006i
$277$	−3.94930			−0.237290			−0.118645	−	0.992937i	$-0.537855\pi$
$277$	−3.94930			−0.237290			−0.118645	+	0.992937i	$0.537855\pi$
$278$	4.27127	−	2.74498i	0.256174	−	0.164633i
$279$	0.717223	−	4.98839i	0.0429390	−	0.298647i
$280$	−4.39233	+	9.61787i	−0.262492	+	0.574778i
$281$	−12.0525	+	3.53892i	−0.718990	+	0.211114i	−0.620705	−	0.784044i	$-0.713154\pi$
$281$	−12.0525	+	3.53892i	−0.718990	+	0.211114i	−0.0982845	+	0.995158i	$0.531336\pi$
$282$	−3.15870	−	6.91659i	−0.188098	−	0.411877i
$283$	10.1011	+	11.6573i	0.600447	+	0.692953i	0.971872	−	0.235510i	$-0.0756761\pi$
$283$	10.1011	+	11.6573i	0.600447	+	0.692953i	−0.371425	+	0.928463i	$0.621131\pi$
$284$	−1.39791	−	9.72266i	−0.0829505	−	0.576934i
$285$	−4.96434	−	1.45766i	−0.294062	−	0.0863445i
$286$	−4.80634	+	5.54681i	−0.284205	+	0.327990i
$287$	−14.0516	−	9.03042i	−0.829440	−	0.533049i
$288$	−4.76488	−	3.06220i	−0.280773	−	0.180442i
$289$	10.8360	−	12.5055i	0.637414	−	0.735615i
$290$	9.19364	+	2.69950i	0.539869	+	0.158520i
$291$	−1.74465	−	12.1343i	−0.102273	−	0.711326i
$292$	5.18535	+	5.98421i	0.303449	+	0.350199i
$293$	−8.45722	−	18.5187i	−0.494076	−	1.08188i	−0.978350	−	0.206959i	$-0.933643\pi$
$293$	−8.45722	−	18.5187i	−0.494076	−	1.08188i	0.484274	−	0.874916i	$-0.339084\pi$
$294$	1.58472	−	0.465315i	0.0924226	−	0.0271377i
$295$	−3.03344	+	6.64230i	−0.176614	+	0.386730i
$296$	−3.58720	+	24.9495i	−0.208502	+	1.45016i
$297$	1.82789	−	1.17472i	0.106065	−	0.0681639i
$298$	15.1941			0.880170
$299$	−11.7809	−	14.3668i	−0.681307	−	0.830851i
$300$	4.24591			0.245138
$301$	21.3277	−	13.7065i	1.22931	−	0.790028i
$302$	1.61880	−	11.2590i	0.0931515	−	0.647883i
$303$	−6.60676	+	14.4668i	−0.379548	+	0.831095i
$304$	−0.0653992	+	0.0192029i	−0.00375090	+	0.00110136i
$305$	2.32844	+	5.09856i	0.133326	+	0.291943i
$306$	0.384262	+	0.443462i	0.0219668	+	0.0253511i
$307$	0.660443	+	4.59348i	0.0376935	+	0.262164i	0.999950	−	0.00997947i	$-0.00317662\pi$
$307$	0.660443	+	4.59348i	0.0376935	+	0.262164i	−0.962257	+	0.272143i	$0.912268\pi$
$308$	−7.70830	−	2.26336i	−0.439221	−	0.128967i
$309$	−12.2372	+	14.1224i	−0.696148	+	0.803397i
$310$	4.63956	+	2.98166i	0.263509	+	0.169347i
$311$	−8.82107	−	5.66896i	−0.500197	−	0.321457i	0.266098	−	0.963946i	$-0.414265\pi$
$311$	−8.82107	−	5.66896i	−0.500197	−	0.321457i	−0.766295	+	0.642489i	$0.777902\pi$
$312$	7.16645	−	8.27052i	0.405720	−	0.468226i
$313$	29.7304	+	8.72962i	1.68046	+	0.493427i	0.976265	−	0.216580i	$-0.0694902\pi$
$313$	29.7304	+	8.72962i	1.68046	+	0.493427i	0.704194	+	0.710007i	$0.251308\pi$
$314$	1.09024	+	7.58278i	0.0615257	+	0.427921i
$315$	2.45117	+	2.82881i	0.138108	+	0.159385i
$316$	−3.70377	−	8.11012i	−0.208353	−	0.456230i
$317$	−12.8931	+	3.78575i	−0.724148	+	0.212629i	−0.622977	−	0.782240i	$-0.714077\pi$
$317$	−12.8931	+	3.78575i	−0.724148	+	0.212629i	−0.101171	+	0.994869i	$0.532259\pi$
$318$	−4.01045	+	8.78166i	−0.224895	+	0.492451i
$319$	−2.70753	+	18.8313i	−0.151593	+	1.05435i
$320$	5.17940	−	3.32860i	0.289537	−	0.186074i
$321$	6.09854			0.340388
$322$	−5.48685	+	11.1989i	−0.305770	+	0.624088i
$323$	2.77430			0.154366
$324$	−1.04295	+	0.670266i	−0.0579419	+	0.0372370i
$325$	−1.88821	+	13.1328i	−0.104739	+	0.728475i
$326$	3.02084	−	6.61472i	0.167309	−	0.366355i
$327$	−8.74111	+	2.56662i	−0.483384	+	0.141934i
$328$	6.57226	+	14.3912i	0.362892	+	0.794624i
$329$	17.0316	+	19.6555i	0.938982	+	1.08364i
$330$	0.338392	+	2.35357i	0.0186278	+	0.129559i
$331$	−2.57921	−	0.757325i	−0.141766	−	0.0416263i	0.210080	−	0.977684i	$-0.432628\pi$
$331$	−2.57921	−	0.757325i	−0.141766	−	0.0416263i	−0.351846	+	0.936058i	$0.614446\pi$
$332$	9.66834	−	11.1579i	0.530619	−	0.612367i
$333$	7.50662	+	4.82421i	0.411360	+	0.264365i
$334$	−8.65595	−	5.56284i	−0.473632	−	0.304385i
$335$	−4.63282	+	5.34656i	−0.253118	+	0.292114i
$336$	0.0473127	+	0.0138923i	0.00258112	+	0.000757885i
$337$	−1.45758	−	10.1377i	−0.0793992	−	0.552233i	−0.990229	−	0.139451i	$-0.955466\pi$
$337$	−1.45758	−	10.1377i	−0.0793992	−	0.552233i	0.910830	−	0.412782i	$-0.135443\pi$
$338$	1.14676	+	1.32343i	0.0623756	+	0.0719853i
$339$	−3.91575	−	8.57430i	−0.212674	−	0.465692i
$340$	1.00474	−	0.295019i	0.0544898	−	0.0159997i
$341$	−4.54894	+	9.96078i	−0.246339	+	0.539406i
$342$	0.511534	−	3.55779i	0.0276606	−	0.192383i
$343$	12.8098	−	8.23234i	0.691663	−	0.444505i
$344$	−24.0132			−1.29471
$345$	−6.01692	−	0.163546i	−0.323940	−	0.00880504i
$346$	−13.4750			−0.724419
$347$	−22.2235	+	14.2822i	−1.19302	+	0.766708i	−0.977735	−	0.209844i	$-0.932705\pi$
$347$	−22.2235	+	14.2822i	−1.19302	+	0.766708i	−0.215285	+	0.976551i	$0.569068\pi$
$348$	1.54486	−	10.7447i	0.0828131	−	0.575978i
$349$	−4.22532	+	9.25217i	−0.226176	+	0.495257i	−0.988366	−	0.152097i	$-0.951397\pi$
$349$	−4.22532	+	9.25217i	−0.226176	+	0.495257i	0.762189	+	0.647354i	$0.224125\pi$
$350$	8.54483	−	2.50899i	0.456740	−	0.134111i
$351$	−1.60935	−	3.52398i	−0.0859005	−	0.188096i
$352$	8.05930	+	9.30093i	0.429562	+	0.495741i
$353$	0.825737	+	5.74313i	0.0439496	+	0.305676i	0.999925	+	0.0122299i	$0.00389299\pi$
$353$	0.825737	+	5.74313i	0.0439496	+	0.305676i	−0.955976	+	0.293446i	$0.905198\pi$
$354$	−4.86742	−	1.42920i	−0.258700	−	0.0759613i
$355$	6.51193	−	7.51517i	0.345617	−	0.398864i
$356$	−0.377475	−	0.242589i	−0.0200062	−	0.0128572i
$357$	−1.68844	−	1.08509i	−0.0893617	−	0.0574293i
$358$	−10.5391	+	12.1627i	−0.557007	+	0.642820i
$359$	24.1166	+	7.08128i	1.27283	+	0.373736i	0.847254	−	0.531188i	$-0.178254\pi$
$359$	24.1166	+	7.08128i	1.27283	+	0.373736i	0.425574	+	0.904924i	$0.360072\pi$
$360$	−0.504555	−	3.50926i	−0.0265924	−	0.184954i
$361$	1.31358	+	1.51595i	0.0691356	+	0.0797868i
$362$	−2.52105	−	5.52034i	−0.132504	−	0.290143i
$363$	6.02452	−	1.76896i	0.316205	−	0.0928462i
$364$	−5.95035	+	13.0294i	−0.311883	+	0.682928i
$365$	−1.14081	+	7.93447i	−0.0597125	+	0.415309i
$366$	−3.27577	+	2.10521i	−0.171227	+	0.110041i
$367$	3.87312			0.202175			0.101087	−	0.994878i	$-0.467768\pi$
$367$	3.87312			0.202175			0.101087	+	0.994878i	$0.467768\pi$
$368$	−0.0678474	+	0.0410418i	−0.00353679	+	0.00213945i
$369$	5.60073			0.291562
$370$	−8.21466	+	5.27924i	−0.427060	+	0.274455i
$371$	4.69938	−	32.6849i	0.243980	−	1.69692i
$372$	2.59552	−	5.68340i	0.134571	−	0.294670i
$373$	3.77864	−	1.10951i	0.195651	−	0.0574482i	−0.182439	−	0.983217i	$-0.558399\pi$
$373$	3.77864	−	1.10951i	0.195651	−	0.0574482i	0.378090	+	0.925769i	$0.376581\pi$
$374$	−0.529645	−	1.15976i	−0.0273873	−	0.0599698i
$375$	6.92434	+	7.99111i	0.357571	+	0.412659i
$376$	−3.50582	−	24.3835i	−0.180799	−	1.25748i
$377$	32.5469	+	9.55662i	1.67625	+	0.492191i
$378$	−1.70286	+	1.96520i	−0.0875855	+	0.101079i
$379$	−27.9697	−	17.9750i	−1.43671	−	0.923315i	−0.999716	−	0.0238483i	$-0.992408\pi$
$379$	−27.9697	−	17.9750i	−1.43671	−	0.923315i	−0.436990	−	0.899466i	$-0.643955\pi$
$380$	−5.39617	−	3.46791i	−0.276818	−	0.177900i
$381$	−3.84138	+	4.43319i	−0.196800	+	0.227119i
$382$	12.5296	+	3.67901i	0.641068	+	0.188235i
$383$	4.78313	+	33.2674i	0.244407	+	1.69988i	0.629495	+	0.777005i	$0.283262\pi$
$383$	4.78313	+	33.2674i	0.244407	+	1.69988i	−0.385088	+	0.922880i	$0.625829\pi$
$384$	−4.61734	−	5.32869i	−0.235627	−	0.271929i
$385$	−3.37856	−	7.39801i	−0.172187	−	0.377037i
$386$	14.7384	−	4.32758i	0.750164	−	0.220268i
$387$	−3.53138	+	7.73265i	−0.179510	+	0.393073i
$388$	2.16295	−	15.0437i	0.109807	−	0.763726i
$389$	−6.86901	+	4.41445i	−0.348273	+	0.223821i	−0.703068	−	0.711123i	$-0.748187\pi$
$389$	−6.86901	+	4.41445i	−0.348273	+	0.223821i	0.354795	+	0.934944i	$0.384551\pi$
$390$	4.23948			0.214675
$391$	3.12034	−	0.824817i	0.157802	−	0.0417128i
$392$	5.35086			0.270259
$393$	7.25694	−	4.66375i	0.366064	−	0.235255i
$394$	2.27921	−	15.8523i	0.114825	−	0.798626i
$395$	3.74953	−	8.21031i	0.188659	−	0.413106i
$396$	2.58466	−	0.758925i	0.129884	−	0.0381374i
$397$	−7.20880	−	15.7851i	−0.361799	−	0.792230i	−0.999755	−	0.0221563i	$-0.992947\pi$
$397$	−7.20880	−	15.7851i	−0.361799	−	0.792230i	0.637955	−	0.770073i	$-0.279780\pi$
$398$	−10.3745	−	11.9728i	−0.520027	−	0.600143i
$399$	1.74966	+	12.1692i	0.0875926	+	0.609220i
$400$	0.0543320	+	0.0159533i	0.00271660	+	0.000797666i
$401$	−13.6945	+	15.8044i	−0.683873	+	0.789232i	−0.986480	−	0.163884i	$-0.947598\pi$
$401$	−13.6945	+	15.8044i	−0.683873	+	0.789232i	0.302606	+	0.953116i	$0.402143\pi$
$402$	−4.13454	−	2.65711i	−0.206212	−	0.132524i
$403$	16.4247	+	10.5555i	0.818174	+	0.525808i
$404$	−12.9120	+	14.9012i	−0.642396	+	0.741364i
$405$	−1.20424	−	0.353596i	−0.0598391	−	0.0175703i
$406$	−3.24026	−	22.5365i	−0.160811	−	1.11847i
$407$	−12.6967	−	14.6527i	−0.629351	−	0.726309i
$408$	0.789722	+	1.72925i	0.0390971	+	0.0856106i
$409$	−11.3282	+	3.32627i	−0.560144	+	0.164473i	−0.549535	−	0.835470i	$-0.685195\pi$
$409$	−11.3282	+	3.32627i	−0.560144	+	0.164473i	−0.0106091	+	0.999944i	$0.503377\pi$
$410$	−2.54608	+	5.57514i	−0.125742	+	0.275337i
$411$	−0.281838	+	1.96022i	−0.0139020	+	0.0966907i
$412$	−19.4893	+	12.5250i	−0.960170	+	0.617064i
$413$	17.3515			0.853810
$414$	−0.482418	−	4.15364i	−0.0237095	−	0.204140i
$415$	14.9464			0.733688
$416$	18.4594	−	11.8632i	0.905049	−	0.581640i
$417$	0.828716	−	5.76384i	0.0405824	−	0.282257i
$418$	−3.24437	+	7.10417i	−0.158687	+	0.347476i
$419$	27.1112	−	7.96056i	1.32447	−	0.388899i	0.458364	−	0.888764i	$-0.348435\pi$
$419$	27.1112	−	7.96056i	1.32447	−	0.388899i	0.866103	+	0.499866i	$0.166617\pi$
$420$	1.92773	+	4.22114i	0.0940635	+	0.205970i
$421$	−6.80446	−	7.85277i	−0.331629	−	0.382721i	0.565307	−	0.824881i	$-0.308758\pi$
$421$	−6.80446	−	7.85277i	−0.331629	−	0.382721i	−0.896936	+	0.442160i	$0.854212\pi$
$422$	−1.31092	−	9.11766i	−0.0638146	−	0.443841i
$423$	−8.36746	−	2.45691i	−0.406840	−	0.119459i
$424$	−20.4820	+	23.6375i	−0.994696	+	1.14794i
$425$	−1.93894	−	1.24608i	−0.0940522	−	0.0604437i
$426$	5.81154	+	3.73485i	0.281570	+	0.180954i
$427$	8.72197	−	10.0657i	0.422086	−	0.487113i
$428$	7.25448	+	2.13011i	0.350659	+	0.102963i
$429$	1.19796	+	8.33197i	0.0578379	+	0.402271i
$430$	−6.09196	−	7.03050i	−0.293781	−	0.339041i
$431$	−3.86029	−	8.45285i	−0.185944	−	0.407160i	0.793587	−	0.608457i	$-0.208211\pi$
$431$	−3.86029	−	8.45285i	−0.185944	−	0.407160i	−0.979530	+	0.201298i	$0.935484\pi$
$432$	−0.0158644	+	0.00465821i	−0.000763276	+	0.000224118i
$433$	−1.81253	+	3.96888i	−0.0871045	+	0.190732i	−0.948171	−	0.317760i	$-0.897070\pi$
$433$	−1.81253	+	3.96888i	−0.0871045	+	0.190732i	0.861067	+	0.508492i	$0.169797\pi$
$434$	1.86502	−	12.9715i	0.0895238	−	0.622652i
$435$	9.24481	−	5.94128i	0.443255	−	0.284862i
$436$	−11.2944			−0.540903
$437$	−16.3353	−	11.1366i	−0.781422	−	0.532735i
$438$	−5.56885			−0.266090
$439$	6.13769	−	3.94445i	0.292936	−	0.188258i	−0.385916	−	0.922534i	$-0.626114\pi$
$439$	6.13769	−	3.94445i	0.292936	−	0.188258i	0.678851	+	0.734276i	$0.262478\pi$
$440$	−1.09631	+	7.62499i	−0.0522644	+	0.363507i
$441$	0.786897	−	1.72306i	0.0374713	−	0.0820506i
$442$	−2.18116	+	0.640447i	−0.103747	+	0.0304629i
$443$	8.73293	+	19.1224i	0.414914	+	0.908535i	0.995538	+	0.0943631i	$0.0300814\pi$
$443$	8.73293	+	19.1224i	0.414914	+	0.908535i	−0.580624	+	0.814172i	$0.697191\pi$
$444$	7.24444	+	8.36052i	0.343806	+	0.396773i
$445$	−0.0646464	−	0.449626i	−0.00306453	−	0.0213143i
$446$	−5.26358	−	1.54553i	−0.249238	−	0.0731829i
$447$	11.4117	−	13.1698i	0.539753	−	0.622908i
$448$	−12.3073	−	7.90943i	−0.581466	−	0.373685i
$449$	9.06779	+	5.82751i	0.427935	+	0.275017i	0.736829	−	0.676079i	$-0.236322\pi$
$449$	9.06779	+	5.82751i	0.427935	+	0.275017i	−0.308894	+	0.951097i	$0.599959\pi$
$450$	−1.95549	+	2.25676i	−0.0921828	+	0.106385i
$451$	−11.6764	−	3.42851i	−0.549822	−	0.161442i
$452$	−1.66311	−	11.5672i	−0.0782262	−	0.544075i
$453$	−8.54313	−	9.85930i	−0.401391	−	0.463230i
$454$	2.54503	+	5.57284i	0.119444	+	0.261546i
$455$	−13.9134	+	4.08535i	−0.652272	+	0.191524i
$456$	4.83748	−	10.5926i	0.226536	−	0.496044i
$457$	0.473005	−	3.28982i	0.0221262	−	0.153891i	−0.975763	−	0.218830i	$-0.929776\pi$
$457$	0.473005	−	3.28982i	0.0221262	−	0.153891i	0.997889	+	0.0649385i	$0.0206851\pi$
$458$	−0.250806	+	0.161183i	−0.0117194	+	0.00753161i
$459$	0.672983			0.0314122
$460$	−7.10026	−	2.29614i	−0.331052	−	0.107058i
$461$	−16.7849			−0.781749			−0.390874	−	0.920444i	$-0.627827\pi$
$461$	−16.7849			−0.781749			−0.390874	+	0.920444i	$0.627827\pi$
$462$	4.75313	−	3.05465i	0.221136	−	0.142115i
$463$	1.99892	−	13.9028i	0.0928975	−	0.646117i	−0.889169	−	0.457580i	$-0.848716\pi$
$463$	1.99892	−	13.9028i	0.0928975	−	0.646117i	0.982066	−	0.188537i	$-0.0603745\pi$
$464$	0.0601401	−	0.131688i	0.00279193	−	0.00611348i
$465$	6.06899	−	1.78202i	0.281443	−	0.0826390i
$466$	4.00218	+	8.76356i	0.185398	+	0.405964i
$467$	13.5172	+	15.5996i	0.625500	+	0.721865i	0.976742	−	0.214419i	$-0.0687859\pi$
$467$	13.5172	+	15.5996i	0.625500	+	0.721865i	−0.351242	+	0.936285i	$0.614240\pi$
$468$	−0.683527	−	4.75403i	−0.0315960	−	0.219755i
$469$	16.1295	+	4.73606i	0.744793	+	0.218691i
$470$	6.24951	−	7.21232i	0.288269	−	0.332680i
$471$	7.39135	+	4.75013i	0.340575	+	0.218874i
$472$	−13.8260	−	8.88544i	−0.636394	−	0.408985i
$473$	12.0958	−	13.9593i	0.556166	−	0.641850i
$474$	6.01644	+	1.76659i	0.276344	+	0.0811420i
$475$	2.00924	+	13.9746i	0.0921903	+	0.641197i
$476$	−1.62947	−	1.88051i	−0.0746865	−	0.0861929i
$477$	4.59958	+	10.0717i	0.210600	+	0.461151i
$478$	−4.28129	+	1.25710i	−0.195822	+	0.0574984i
$479$	−1.19040	+	2.60662i	−0.0543909	+	0.119100i	−0.934876	−	0.354974i	$-0.884490\pi$
$479$	−1.19040	+	2.60662i	−0.0543909	+	0.119100i	0.880485	+	0.474074i	$0.157217\pi$
$480$	1.01169	−	7.03643i	0.0461769	−	0.321168i
$481$	−29.0811	+	18.6893i	−1.32599	+	0.852159i
$482$	14.4758			0.659357
$483$	5.58587	+	13.1668i	0.254166	+	0.599112i
$484$	7.78428			0.353831
$485$	12.9436	−	8.31836i	0.587740	−	0.377717i
$486$	0.124087	−	0.863041i	0.00562868	−	0.0391484i
$487$	8.00013	−	17.5178i	0.362520	−	0.793809i	−0.637212	−	0.770688i	$-0.719913\pi$
$487$	8.00013	−	17.5178i	0.362520	−	0.793809i	0.999733	−	0.0231206i	$-0.00736016\pi$
$488$	−12.1043	+	3.55415i	−0.547937	+	0.160889i
$489$	−3.46460	−	7.58641i	−0.156675	−	0.343069i
$490$	1.35747	+	1.56660i	0.0613242	+	0.0707719i
$491$	2.38639	+	16.5977i	0.107696	+	0.749043i	0.970079	+	0.242787i	$0.0780618\pi$
$491$	2.38639	+	16.5977i	0.107696	+	0.749043i	−0.862383	+	0.506256i	$0.831029\pi$
$492$	6.66231	+	1.95623i	0.300360	+	0.0881937i
$493$	−3.85881	+	4.45330i	−0.173792	+	0.200567i
$494$	11.7143	+	7.52835i	0.527053	+	0.338717i
$495$	2.29415	+	1.47436i	0.103114	+	0.0662675i
$496$	0.0545676	−	0.0629743i	0.00245016	−	0.00282763i
$497$	−22.6718	−	6.65704i	−1.01697	−	0.298609i
$498$	1.47771	+	10.2777i	0.0662178	+	0.460555i
$499$	13.4411	+	15.5118i	0.601705	+	0.694405i	0.972126	−	0.234459i	$-0.0753319\pi$
$499$	13.4411	+	15.5118i	0.601705	+	0.694405i	−0.370421	+	0.928864i	$0.620786\pi$
$500$	5.44565	+	11.9243i	0.243537	+	0.533272i
$501$	−11.3228	+	3.32468i	−0.505866	+	0.148536i
$502$	−5.87656	+	12.8679i	−0.262284	+	0.574321i
$503$	1.61504	−	11.2328i	0.0720111	−	0.500848i	−0.921614	−	0.388109i	$-0.873128\pi$
$503$	1.61504	−	11.2328i	0.0720111	−	0.500848i	0.993625	−	0.112739i	$-0.0359624\pi$
$504$	−7.08711	+	4.55461i	−0.315685	+	0.202878i
$505$	−19.9608			−0.888242
$506$	−1.53692	+	8.95485i	−0.0683245	+	0.398092i
$507$	2.00840			0.0891960
$508$	−6.11792	+	3.93175i	−0.271439	+	0.174443i
$509$	−0.261891	+	1.82149i	−0.0116081	+	0.0807363i	−0.994802	−	0.101828i	$-0.967531\pi$
$509$	−0.261891	+	1.82149i	−0.0116081	+	0.0807363i	0.983194	+	0.182565i	$0.0584399\pi$
$510$	−0.305937	+	0.669908i	−0.0135471	+	0.0296640i
$511$	18.2762	−	5.36639i	0.808493	−	0.237395i
$512$	−0.0777080	−	0.170157i	−0.00343424	−	0.00751993i
$513$	−2.69959	−	3.11550i	−0.119190	−	0.137552i
$514$	2.18878	+	15.2233i	0.0965430	+	0.671471i
$515$	−22.5032	−	6.60754i	−0.991609	−	0.291163i
$516$	−6.90160	+	7.96487i	−0.303826	+	0.350634i
$517$	15.9405	+	10.2443i	0.701063	+	0.450546i
$518$	19.5197	+	12.5446i	0.857647	+	0.551176i
$519$	−10.1205	+	11.6797i	−0.444241	+	0.512681i
$520$	13.1786	+	3.86957i	0.577918	+	0.169692i
$521$	−0.142144	−	0.988632i	−0.00622744	−	0.0433128i	0.986471	−	0.163937i	$-0.0524194\pi$
$521$	−0.142144	−	0.988632i	−0.00622744	−	0.0433128i	−0.992698	+	0.120624i	$0.961510\pi$
$522$	4.99947	+	5.76969i	0.218821	+	0.252533i
$523$	−11.1818	−	24.4847i	−0.488945	−	1.07064i	−0.979906	−	0.199459i	$-0.936081\pi$
$523$	−11.1818	−	24.4847i	−0.488945	−	1.07064i	0.490961	−	0.871182i	$-0.336646\pi$
$524$	10.2614	−	3.01302i	0.448272	−	0.131624i
$525$	4.24296	−	9.29079i	0.185178	−	0.405483i
$526$	2.07732	−	14.4481i	0.0905754	−	0.629966i
$527$	−2.85322	+	1.83365i	−0.124288	+	0.0798751i
$528$	0.0359257			0.00156347
$529$	−21.6838	−	7.66908i	−0.942772	−	0.333438i
$530$	−12.1166			−0.526313
$531$	−4.89451	+	3.14551i	−0.212403	+	0.136503i
$532$	−2.16916	+	15.0869i	−0.0940452	+	0.654098i
$533$	−9.01351	+	19.7368i	−0.390419	+	0.854897i
$534$	0.302789	−	0.0889068i	0.0131030	−	0.00384738i
$535$	3.17965	+	6.96246i	0.137468	+	0.301013i
$536$	−10.4271	−	12.0335i	−0.450381	−	0.519767i
$537$	2.62681	+	18.2699i	0.113355	+	0.788403i
$538$	6.62480	+	1.94522i	0.285615	+	0.0838643i
$539$	−2.69531	+	3.11055i	−0.116095	+	0.133981i
$540$	−1.30899	−	0.841236i	−0.0563299	−	0.0362010i
$541$	36.6814	+	23.5737i	1.57706	+	1.01351i	0.976918	+	0.213617i	$0.0685243\pi$
$541$	36.6814	+	23.5737i	1.57706	+	1.01351i	0.600139	+	0.799896i	$0.295112\pi$
$542$	−1.63226	+	1.88372i	−0.0701114	+	0.0809128i
$543$	−6.67832	−	1.96093i	−0.286594	−	0.0841516i
$544$	0.542474	+	3.77299i	0.0232584	+	0.161766i
$545$	−7.48763	−	8.64119i	−0.320735	−	0.370148i
$546$	−4.18484	−	9.16352i	−0.179095	−	0.392162i
$547$	9.08055	−	2.66629i	0.388256	−	0.114002i	−0.0817779	−	0.996651i	$-0.526060\pi$
$547$	9.08055	−	2.66629i	0.388256	−	0.114002i	0.470034	+	0.882648i	$0.344242\pi$
$548$	−1.01993	+	2.23333i	−0.0435691	+	0.0954031i
$549$	−0.635567	+	4.42047i	−0.0271253	+	0.188661i
$550$	5.45831	−	3.50784i	0.232743	−	0.149575i
$551$	36.0952			1.53771
$552$	2.29161	−	13.3520i	0.0975375	−	0.568301i
$553$	−21.4476			−0.912043
$554$	2.89682	−	1.86167i	0.123074	−	0.0790950i
$555$	−1.59382	+	11.0852i	−0.0676537	+	0.470542i
$556$	2.99900	−	6.56688i	0.127186	−	0.278498i
$557$	−34.7965	+	10.2172i	−1.47437	+	0.432916i	−0.917518	−	0.397693i	$-0.869811\pi$
$557$	−34.7965	+	10.2172i	−1.47437	+	0.432916i	−0.556856	+	0.830609i	$0.687993\pi$
$558$	1.82541	+	3.99709i	0.0772758	+	0.169210i
$559$	−21.5665	−	24.8890i	−0.912164	−	1.05269i
$560$	0.00880759	+	0.0612581i	0.000372189	+	0.00258863i
$561$	−1.40304	−	0.411969i	−0.0592363	−	0.0173934i
$562$	7.17229	−	8.27726i	0.302545	−	0.349155i
$563$	−9.41346	−	6.04966i	−0.396730	−	0.254963i	0.327031	−	0.945014i	$-0.393952\pi$
$563$	−9.41346	−	6.04966i	−0.396730	−	0.254963i	−0.723761	+	0.690051i	$0.757588\pi$
$564$	−9.09530	−	5.84519i	−0.382981	−	0.246127i
$565$	7.74734	−	8.94091i	0.325933	−	0.376147i
$566$	−12.9043	−	3.78905i	−0.542410	−	0.159266i
$567$	0.424429	+	2.95197i	0.0178243	+	0.123971i
$568$	14.6564	+	16.9144i	0.614968	+	0.709711i
$569$	−0.961001	−	2.10430i	−0.0402872	−	0.0882168i	0.888418	−	0.459035i	$-0.151805\pi$
$569$	−0.961001	−	2.10430i	−0.0402872	−	0.0882168i	−0.928706	+	0.370818i	$0.879077\pi$
$570$	4.32849	−	1.27096i	0.181301	−	0.0532347i
$571$	1.67055	−	3.65800i	0.0699104	−	0.153082i	−0.871451	−	0.490483i	$-0.836820\pi$
$571$	1.67055	−	3.65800i	0.0699104	−	0.153082i	0.941361	+	0.337401i	$0.109548\pi$
$572$	−1.48518	+	10.3297i	−0.0620985	+	0.431905i
$573$	12.5993	−	8.09707i	0.526343	−	0.338260i
$574$	14.5638			0.607880
$575$	6.41459	+	15.1203i	0.267507	+	0.630559i
$576$	4.90548			0.204395
$577$	−26.8793	+	17.2743i	−1.11900	+	0.719138i	−0.963236	−	0.268656i	$-0.913420\pi$
$577$	−26.8793	+	17.2743i	−1.11900	+	0.719138i	−0.155764	+	0.987794i	$0.549784\pi$
$578$	−2.05327	+	14.2808i	−0.0854049	+	0.594004i
$579$	7.31839	−	16.0250i	0.304142	−	0.665978i
$580$	13.0723	−	3.83837i	0.542797	−	0.159379i
$581$	−14.7537	−	32.3061i	−0.612087	−	1.34028i
$582$	6.99974	+	8.07813i	0.290148	+	0.334849i
$583$	−3.42381	−	23.8132i	−0.141800	−	0.986240i
$584$	−17.3109	−	5.08294i	−0.716331	−	0.210334i
$585$	3.18410	−	3.67465i	0.131646	−	0.151928i
$586$	14.9330	+	9.59685i	0.616876	+	0.396442i
$587$	−16.8842	−	10.8508i	−0.696886	−	0.447861i	0.143642	−	0.989630i	$-0.454119\pi$
$587$	−16.8842	−	10.8508i	−0.696886	−	0.447861i	−0.840528	+	0.541768i	$0.817755\pi$
$588$	1.53788	−	1.77481i	0.0634212	−	0.0731919i
$589$	19.9340	+	5.85316i	0.821367	+	0.241175i
$590$	−0.906103	−	6.30209i	−0.0373037	−	0.259453i
$591$	−12.0284	−	13.8815i	−0.494783	−	0.571010i
$592$	0.0612888	+	0.134204i	0.00251895	+	0.00551574i
$593$	−10.8129	+	3.17495i	−0.444032	+	0.130380i	−0.496103	−	0.868264i	$-0.665236\pi$
$593$	−10.8129	+	3.17495i	−0.444032	+	0.130380i	0.0520707	+	0.998643i	$0.483418\pi$
$594$	−0.787011	+	1.72331i	−0.0322914	+	0.0707084i
$595$	0.358492	−	2.49337i	0.0146967	−	0.102218i
$596$	18.1746	−	11.6801i	0.744461	−	0.478436i
$597$	−18.1695			−0.743630
$598$	15.4137	+	4.98462i	0.630314	+	0.203836i
$599$	31.2141			1.27537			0.637687	−	0.770295i	$-0.279891\pi$
$599$	31.2141			1.27537			0.637687	+	0.770295i	$0.279891\pi$
$600$	−8.13855	+	5.23033i	−0.332255	+	0.213527i
$601$	−4.54076	+	31.5817i	−0.185222	+	1.28824i	0.658956	+	0.752181i	$0.270998\pi$
$601$	−4.54076	+	31.5817i	−0.185222	+	1.28824i	−0.844178	+	0.536063i	$0.819911\pi$
$602$	−9.18278	+	20.1075i	−0.374262	+	0.819520i
$603$	−5.40838	+	1.58804i	−0.220246	+	0.0646702i
$604$	−6.71876	−	14.7120i	−0.273382	−	0.598624i
$605$	5.16060	+	5.95565i	0.209808	+	0.242132i
$606$	−1.97347	−	13.7258i	−0.0801668	−	0.557573i
$607$	−20.1003	−	5.90199i	−0.815848	−	0.239555i	−0.152921	−	0.988238i	$-0.548868\pi$
$607$	−20.1003	−	5.90199i	−0.815848	−	0.239555i	−0.662927	+	0.748684i	$0.730686\pi$
$608$	15.2905	−	17.6462i	0.620113	−	0.715649i
$609$	−21.9675	−	14.1177i	−0.890170	−	0.572077i
$610$	−4.11134	−	2.64220i	−0.166463	−	0.106980i
$611$	22.1242	−	25.5327i	0.895050	−	1.03294i
$612$	0.800542	+	0.235060i	0.0323600	+	0.00950175i
$613$	−2.81397	−	19.5716i	−0.113655	−	0.790490i	−0.964312	−	0.264768i	$-0.914704\pi$
$613$	−2.81397	−	19.5716i	−0.113655	−	0.790490i	0.850657	−	0.525722i	$-0.176205\pi$
$614$	−2.64977	−	3.05800i	−0.106936	−	0.123411i
$615$	2.92010	+	6.39413i	0.117750	+	0.257836i
$616$	17.5634	−	5.15707i	0.707648	−	0.207784i
$617$	14.8212	−	32.4540i	0.596680	−	1.30655i	−0.334640	−	0.942346i	$-0.608615\pi$
$617$	14.8212	−	32.4540i	0.596680	−	1.30655i	0.931320	−	0.364201i	$-0.118658\pi$
$618$	2.31876	−	16.1274i	0.0932744	−	0.648737i
$619$	12.3010	−	7.90539i	0.494420	−	0.317744i	−0.269561	−	0.962983i	$-0.586879\pi$
$619$	12.3010	−	7.90539i	0.494420	−	0.317744i	0.763981	+	0.645239i	$0.223242\pi$
$620$	7.84175			0.314932
$621$	−3.96257	−	2.70149i	−0.159012	−	0.108407i
$622$	9.14258			0.366584
$623$	−0.908040	+	0.583562i	−0.0363798	+	0.0233799i
$624$	0.00911589	−	0.0634024i	0.000364928	−	0.00253813i
$625$	1.60059	−	3.50481i	0.0640237	−	0.140192i
$626$	−25.9224	+	7.61150i	−1.03607	+	0.304217i
$627$	3.72096	+	8.14777i	0.148601	+	0.325391i
$628$	7.13319	+	8.23215i	0.284645	+	0.328498i
$629$	−0.854617	−	5.94399i	−0.0340758	−	0.237002i
$630$	−3.13142	−	0.919469i	−0.124759	−	0.0366325i
$631$	11.2905	−	13.0299i	0.449468	−	0.518713i	−0.485119	−	0.874448i	$-0.661224\pi$
$631$	11.2905	−	13.0299i	0.449468	−	0.518713i	0.934587	+	0.355735i	$0.115769\pi$
$632$	17.0898	+	10.9830i	0.679797	+	0.436879i
$633$	−8.88748	−	5.71164i	−0.353246	−	0.227017i
$634$	7.67254	−	8.85458i	0.304715	−	0.351660i
$635$	−7.06401	−	2.07418i	−0.280326	−	0.0823113i
$636$	1.95355	+	13.5872i	0.0774634	+	0.538769i
$637$	4.80564	+	5.54601i	0.190407	+	0.219741i
$638$	−6.89098	−	15.0891i	−0.272816	−	0.597385i
$639$	7.60206	−	2.23217i	0.300733	−	0.0883032i
$640$	3.67617	−	8.04969i	0.145313	−	0.318192i
$641$	2.39733	−	16.6738i	0.0946887	−	0.658574i	−0.886099	−	0.463496i	$-0.846595\pi$
$641$	2.39733	−	16.6738i	0.0946887	−	0.658574i	0.980788	−	0.195078i	$-0.0624961\pi$
$642$	−4.47330	+	2.87481i	−0.176547	+	0.113460i
$643$	−22.2079			−0.875796			−0.437898	−	0.899025i	$-0.644277\pi$
$643$	−22.2079			−0.875796			−0.437898	+	0.899025i	$0.644277\pi$
$644$	2.04570	+	17.6136i	0.0806118	+	0.694072i
$645$	−10.6692			−0.420101
$646$	−2.03496	+	1.30779i	−0.0800643	+	0.0514542i
$647$	−0.769102	+	5.34922i	−0.0302365	+	0.210300i	−0.999339	−	0.0363597i	$-0.988424\pi$
$647$	−0.769102	+	5.34922i	−0.0302365	+	0.210300i	0.969102	+	0.246659i	$0.0793329\pi$
$648$	1.17346	−	2.56953i	0.0460981	−	0.100941i
$649$	12.1296	−	3.56158i	0.476130	−	0.139804i
$650$	−4.80570	−	10.5230i	−0.188495	−	0.412747i
$651$	−9.84254	−	11.3589i	−0.385760	−	0.445190i
$652$	−1.47150	−	10.2345i	−0.0576282	−	0.400813i
$653$	19.7469	+	5.79821i	0.772755	+	0.226901i	0.644258	−	0.764808i	$-0.277166\pi$
$653$	19.7469	+	5.79821i	0.772755	+	0.226901i	0.128498	+	0.991710i	$0.458985\pi$
$654$	5.20174	−	6.00312i	0.203404	−	0.234741i
$655$	9.10803	+	5.85338i	0.355880	+	0.228710i
$656$	0.0779029	+	0.0500651i	0.00304160	+	0.00195471i
$657$	−4.18253	+	4.82690i	−0.163176	+	0.188315i
$658$	−21.7582	−	6.38878i	−0.848223	−	0.249061i
$659$	3.64872	+	25.3774i	0.142134	+	0.988565i	0.928640	+	0.370982i	$0.120979\pi$
$659$	3.64872	+	25.3774i	0.142134	+	0.988565i	−0.786506	+	0.617583i	$0.788112\pi$
$660$	2.21402	+	2.55512i	0.0861807	+	0.0994578i
$661$	19.7714	+	43.2933i	0.769017	+	1.68391i	0.728805	+	0.684722i	$0.240076\pi$
$661$	19.7714	+	43.2933i	0.769017	+	1.68391i	0.0402123	+	0.999191i	$0.487197\pi$
$662$	2.24886	−	0.660324i	0.0874043	−	0.0256642i
$663$	−1.08306	+	2.37158i	−0.0420626	+	0.0921043i
$664$	−4.78743	+	33.2973i	−0.185788	+	1.29219i
$665$	−12.9808	+	8.34225i	−0.503374	+	0.323499i
$666$	−7.78022			−0.301478
$667$	40.5974	−	10.7313i	1.57194	−	0.415519i
$668$	−14.6302			−0.566061
$669$	−5.29288	+	3.40153i	−0.204635	+	0.131511i
$670$	0.877852	−	6.10560i	0.0339144	−	0.235880i
$671$	4.03104	−	8.82675i	0.155617	−	0.340753i
$672$	−16.2077	+	4.75901i	−0.625225	+	0.183583i
$673$	6.29846	+	13.7917i	0.242788	+	0.531631i	0.991321	−	0.131467i	$-0.0419686\pi$
$673$	6.29846	+	13.7917i	0.242788	+	0.531631i	−0.748533	+	0.663098i	$0.769241\pi$
$674$	5.84796	+	6.74891i	0.225255	+	0.259958i
$675$	0.487397	+	3.38992i	0.0187599	+	0.130478i
$676$	2.38907	+	0.701495i	0.0918875	+	0.0269806i
$677$	−17.7655	+	20.5025i	−0.682784	+	0.787975i	−0.986319	−	0.164845i	$-0.947288\pi$
$677$	−17.7655	+	20.5025i	−0.682784	+	0.787975i	0.303535	+	0.952820i	$0.401833\pi$
$678$	6.91408	+	4.44341i	0.265534	+	0.170648i
$679$	−30.7567	−	19.7661i	−1.18033	−	0.758554i
$680$	−1.56247	+	1.80319i	−0.0599180	+	0.0691491i
$681$	6.74183	+	1.97958i	0.258348	+	0.0758577i
$682$	−1.35879	−	9.45060i	−0.0520308	−	0.361882i
$683$	13.5189	+	15.6016i	0.517286	+	0.596980i	0.952949	−	0.303130i	$-0.0980316\pi$
$683$	13.5189	+	15.6016i	0.517286	+	0.596980i	−0.435663	+	0.900110i	$0.643486\pi$
$684$	−2.12310	−	4.64893i	−0.0811786	−	0.177756i
$685$	−2.38485	+	0.700256i	−0.0911205	+	0.0267554i
$686$	−5.51533	+	12.0769i	−0.210576	+	0.461098i
$687$	−0.0486617	+	0.338449i	−0.00185656	+	0.0129126i
$688$	−0.118242	+	0.0759894i	−0.00450793	+	0.00289707i
$689$	−42.8947			−1.63416
$690$	4.49052	−	2.71638i	0.170951	−	0.103411i
$691$	−17.3303			−0.659276			−0.329638	−	0.944107i	$-0.606927\pi$
$691$	−17.3303			−0.659276			−0.329638	+	0.944107i	$0.606927\pi$
$692$	−16.1183	+	10.3586i	−0.612724	+	0.393774i
$693$	0.922207	−	6.41409i	0.0350317	−	0.243651i
$694$	9.56847	−	20.9520i	0.363214	−	0.795328i
$695$	7.01242	−	2.05903i	0.265996	−	0.0781036i
$696$	10.2747	+	22.4985i	0.389462	+	0.852804i
$697$	−2.46830	−	2.84857i	−0.0934935	−	0.107897i
$698$	−1.26213	−	8.77828i	−0.0477722	−	0.332263i
$699$	10.6019	+	3.11298i	0.400999	+	0.117744i
$700$	8.29228	−	9.56981i	0.313419	−	0.361705i
$701$	26.0430	+	16.7368i	0.983632	+	0.632142i	0.930441	−	0.366442i	$-0.119424\pi$
$701$	26.0430	+	16.7368i	0.983632	+	0.632142i	0.0531914	+	0.998584i	$0.483061\pi$
$702$	2.84164	+	1.82621i	0.107251	+	0.0689259i
$703$	−24.0888	+	27.8000i	−0.908527	+	1.04850i
$704$	−10.2270	−	3.00291i	−0.385444	−	0.113176i
$705$	−1.55766	−	10.8338i	−0.0586649	−	0.408023i
$706$	−3.31295	−	3.82335i	−0.124685	−	0.143894i
$707$	19.7035	+	43.1446i	0.741025	+	1.62262i
$708$	−6.92089	+	2.03216i	−0.260103	+	0.0763732i
$709$	−1.01923	+	2.23181i	−0.0382782	+	0.0838175i	−0.927805	−	0.373065i	$-0.878307\pi$
$709$	−1.01923	+	2.23181i	−0.0382782	+	0.0838175i	0.889527	+	0.456883i	$0.151034\pi$
$710$	−1.23392	+	8.58207i	−0.0463080	+	0.322079i
$711$	6.04993	−	3.88805i	0.226890	−	0.145813i
$712$	1.02238			0.0383152
$713$	24.1606	+	0.656710i	0.904821	+	0.0245940i
$714$	1.74998			0.0654914
$715$	−8.88768	+	5.71177i	−0.332381	+	0.213608i
$716$	−3.25662	+	22.6503i	−0.121706	+	0.846481i
$717$	−2.12589	+	4.65504i	−0.0793927	+	0.173846i
$718$	−21.0277	+	6.17429i	−0.784746	+	0.230422i
$719$	−15.0744	−	33.0083i	−0.562180	−	1.23100i	−0.950858	−	0.309628i	$-0.899795\pi$
$719$	−15.0744	−	33.0083i	−0.562180	−	1.23100i	0.388678	−	0.921374i	$-0.372932\pi$
$720$	−0.0135894	−	0.0156830i	−0.000506448	−	0.000584473i
$721$	7.93115	+	55.1624i	0.295372	+	2.05435i
$722$	−1.67812	−	0.492741i	−0.0624532	−	0.0183379i
$723$	10.8722	−	12.5472i	0.404342	−	0.466636i
$724$	−7.25923	−	4.66522i	−0.269787	−	0.173382i
$725$	−25.2266	−	16.2122i	−0.936894	−	0.602105i
$726$	−3.58512	+	4.13745i	−0.133056	+	0.153555i
$727$	−32.4855	−	9.53859i	−1.20482	−	0.353767i	−0.383125	−	0.923696i	$-0.625152\pi$
$727$	−32.4855	−	9.53859i	−1.20482	−	0.353767i	−0.821694	+	0.569930i	$0.806970\pi$
$728$	−4.64472	−	32.3047i	−0.172145	−	1.19729i
$729$	−0.654861	−	0.755750i	−0.0242541	−	0.0279907i
$730$	−2.90348	−	6.35773i	−0.107462	−	0.235310i
$731$	5.48919	−	1.61177i	0.203025	−	0.0596136i
$732$	−2.30002	+	5.03634i	−0.0850112	+	0.186149i
$733$	0.930131	−	6.46920i	0.0343552	−	0.238946i	−0.965407	−	0.260747i	$-0.916031\pi$
$733$	0.930131	−	6.46920i	0.0343552	−	0.238946i	0.999762	+	0.0218016i	$0.00694021\pi$
$734$	−2.84094	+	1.82576i	−0.104861	+	0.0673901i
$735$	2.37742			0.0876925
$736$	11.9514	−	24.3932i	0.440535	−	0.899146i
$737$	12.2476			0.451144
$738$	−4.10815	+	2.64015i	−0.151223	+	0.0971852i
$739$	−5.74842	+	39.9811i	−0.211459	+	1.47073i	0.556830	+	0.830626i	$0.312017\pi$
$739$	−5.74842	+	39.9811i	−0.211459	+	1.47073i	−0.768289	+	0.640103i	$0.778892\pi$
$740$	−5.76778	+	12.6297i	−0.212028	+	0.464276i
$741$	15.3235	−	4.49939i	0.562923	−	0.165289i
$742$	11.9605	+	26.1897i	0.439082	+	0.961456i
$743$	3.77789	+	4.35992i	0.138597	+	0.159950i	0.820805	−	0.571209i	$-0.193525\pi$
$743$	3.77789	+	4.35992i	0.138597	+	0.159950i	−0.682207	+	0.731159i	$0.738980\pi$
$744$	2.02601	+	14.0912i	0.0742772	+	0.516609i
$745$	20.9852	+	6.16180i	0.768837	+	0.225751i
$746$	−2.24863	+	2.59506i	−0.0823281	+	0.0950117i
$747$	10.0182	+	6.43833i	0.366548	+	0.235566i
$748$	−1.52508	−	0.980110i	−0.0557625	−	0.0358364i
$749$	11.9105	−	13.7454i	0.435200	−	0.502247i
$750$	−8.84598	−	2.59741i	−0.323009	−	0.0948441i
$751$	−1.05748	−	7.35492i	−0.0385879	−	0.268385i	0.961389	−	0.275193i	$-0.0887419\pi$
$751$	−1.05748	−	7.35492i	−0.0385879	−	0.268385i	−0.999977	+	0.00680848i	$0.997833\pi$
$752$	−0.0944240	−	0.108971i	−0.00344329	−	0.00397377i
$753$	6.73982	+	14.7581i	0.245613	+	0.537817i
$754$	−28.3781	+	8.33257i	−1.03347	+	0.303454i
$755$	6.80176	−	14.8938i	0.247541	−	0.542040i
$756$	−0.526191	+	3.65974i	−0.0191374	+	0.133103i
$757$	7.66876	−	4.92841i	0.278726	−	0.179126i	−0.393808	−	0.919193i	$-0.628842\pi$
$757$	7.66876	−	4.92841i	0.278726	−	0.179126i	0.672534	+	0.740067i	$0.265206\pi$
$758$	28.9891			1.05293
$759$	6.60746	+	8.05778i	0.239836	+	0.292479i
$760$	14.6153			0.530153
$761$	9.14969	−	5.88015i	0.331676	−	0.213155i	−0.364194	−	0.931323i	$-0.618655\pi$
$761$	9.14969	−	5.88015i	0.331676	−	0.213155i	0.695870	+	0.718168i	$0.255019\pi$
$762$	0.727886	−	5.06256i	0.0263685	−	0.183397i
$763$	−11.2866	+	24.7141i	−0.408601	+	0.894710i
$764$	17.8156	−	5.23112i	0.644544	−	0.189255i
$765$	0.350879	+	0.768317i	0.0126860	+	0.0277786i
$766$	−19.1905	−	22.1470i	−0.693380	−	0.800203i
$767$	−3.20774	−	22.3103i	−0.115825	−	0.805579i
$768$	15.3123	+	4.49609i	0.552535	+	0.162239i
$769$	34.3044	−	39.5894i	1.23705	−	1.42763i	0.370278	−	0.928921i	$-0.379263\pi$
$769$	34.3044	−	39.5894i	1.23705	−	1.42763i	0.866770	−	0.498708i	$-0.166192\pi$
$770$	5.96555	+	3.83383i	0.214984	+	0.138162i
$771$	14.8390	+	9.53644i	0.534413	+	0.343446i
$772$	14.3028	−	16.5063i	0.514768	−	0.594075i
$773$	−24.1303	−	7.08528i	−0.867905	−	0.254840i	−0.182681	−	0.983172i	$-0.558478\pi$
$773$	−24.1303	−	7.08528i	−0.867905	−	0.254840i	−0.685224	+	0.728332i	$0.740296\pi$
$774$	−1.05484	−	7.33659i	−0.0379155	−	0.263708i
$775$	−11.3028	−	13.0441i	−0.406008	−	0.468558i
$776$	14.3856	+	31.5001i	0.516413	+	1.13079i
$777$	25.5337	−	7.49737i	0.916016	−	0.268967i
$778$	2.95750	−	6.47602i	0.106031	−	0.232176i
$779$	−3.28582	+	22.8534i	−0.117727	+	0.818808i
$780$	5.07111	−	3.25901i	0.181575	−	0.116691i
$781$	−17.2153			−0.616010
$782$	−1.89996	+	2.07591i	−0.0679425	+	0.0742345i
$783$	8.75589			0.312910
$784$	0.0263478	−	0.0169327i	0.000940992	−	0.000604739i
$785$	−1.56934	+	10.9150i	−0.0560122	+	0.389574i
$786$	−3.12452	+	6.84175i	−0.111448	+	0.244037i
$787$	−2.02473	+	0.594516i	−0.0721740	+	0.0211922i	−0.317620	−	0.948218i	$-0.602884\pi$
$787$	−2.02473	+	0.594516i	−0.0721740	+	0.0211922i	0.245446	+	0.969410i	$0.421066\pi$
$788$	−9.45977	−	20.7140i	−0.336990	−	0.737906i
$789$	−10.9629	−	12.6519i	−0.390291	−	0.450420i
$790$	1.12000	+	7.78979i	0.0398479	+	0.277148i
$791$	−26.9730	−	7.91999i	−0.959050	−	0.281602i
$792$	−4.01939	+	4.63863i	−0.142823	+	0.164826i
$793$	−14.5548	−	9.35378i	−0.516855	−	0.332162i
$794$	12.7286	+	8.18020i	0.451723	+	0.290305i
$795$	−9.10031	+	10.5023i	−0.322755	+	0.372479i
$796$	−21.6135	−	6.34628i	−0.766068	−	0.224938i
$797$	−4.22546	−	29.3887i	−0.149673	−	1.04100i	−0.916754	−	0.399452i	$-0.869201\pi$
$797$	−4.22546	−	29.3887i	−0.149673	−	1.04100i	0.767081	−	0.641550i	$-0.221709\pi$
$798$	−7.01984	−	8.10133i	−0.248500	−	0.286784i
$799$	2.43802	+	5.33853i	0.0862511	+	0.188864i
$800$	−18.6123	+	5.46505i	−0.658042	+	0.193219i
$801$	0.150351	−	0.329222i	0.00531238	−	0.0116325i
$802$	2.59492	−	18.0481i	0.0916298	−	0.637299i
$803$	11.6746	−	7.50279i	0.411987	−	0.264768i
$804$	−6.98818			−0.246454
$805$	−12.1197	+	13.2421i	−0.427163	+	0.466721i
$806$	−17.0234			−0.599623
$807$	6.66167	−	4.28120i	0.234502	−	0.150705i
$808$	6.39358	−	44.4683i	0.224925	−	1.56439i
$809$	14.4613	−	31.6658i	0.508432	−	1.11331i	−0.465205	−	0.885203i	$-0.654019\pi$
$809$	14.4613	−	31.6658i	0.508432	−	1.11331i	0.973636	−	0.228107i	$-0.0732535\pi$
$810$	1.05000	−	0.308306i	0.0368931	−	0.0108328i
$811$	12.3329	+	27.0052i	0.433066	+	0.948282i	0.992819	+	0.119623i	$0.0381686\pi$
$811$	12.3329	+	27.0052i	0.433066	+	0.948282i	−0.559753	+	0.828659i	$0.689104\pi$
$812$	−21.2003	−	24.4664i	−0.743985	−	0.858604i
$813$	0.406831	+	2.82957i	0.0142682	+	0.0992375i
$814$	16.2203	+	4.76270i	0.568519	+	0.166932i
$815$	6.85473	−	7.91078i	0.240111	−	0.277103i
$816$	0.00936079	+	0.00601582i	0.000327693	+	0.000210596i
$817$	−29.4808	−	18.9461i	−1.03140	−	0.662842i
$818$	6.74130	−	7.77987i	0.235704	−	0.272017i
$819$	−11.0857	−	3.25506i	−0.387366	−	0.113741i
$820$	1.24024	+	8.62603i	0.0433109	+	0.301234i
$821$	29.9418	+	34.5547i	1.04498	+	1.20597i	0.978085	+	0.208208i	$0.0667632\pi$
$821$	29.9418	+	34.5547i	1.04498	+	1.20597i	0.0668930	+	0.997760i	$0.478691\pi$
$822$	−0.717308	−	1.57069i	−0.0250190	−	0.0547839i
$823$	−3.72764	+	1.09453i	−0.129937	+	0.0381530i	−0.346055	−	0.938214i	$-0.612479\pi$
$823$	−3.72764	+	1.09453i	−0.129937	+	0.0381530i	0.216117	+	0.976367i	$0.430661\pi$
$824$	21.9281	−	48.0159i	0.763903	−	1.67271i
$825$	1.05903	−	7.36568i	0.0368705	−	0.256440i
$826$	−12.7274	+	8.17937i	−0.442841	+	0.284597i
$827$	11.4728			0.398948			0.199474	−	0.979903i	$-0.436077\pi$
$827$	11.4728			0.398948			0.199474	+	0.979903i	$0.436077\pi$
$828$	−3.77007	−	4.59759i	−0.131019	−	0.159777i
$829$	30.5516			1.06110			0.530550	−	0.847654i	$-0.321985\pi$
$829$	30.5516			1.06110			0.530550	+	0.847654i	$0.321985\pi$
$830$	−10.9632	+	7.04562i	−0.380538	+	0.244557i
$831$	0.562044	−	3.90910i	0.0194971	−	0.135605i
$832$	−7.89462	+	17.2868i	−0.273697	+	0.599312i
$833$	−1.22315	+	0.359151i	−0.0423798	+	0.0124438i
$834$	2.10917	+	4.61845i	0.0730347	+	0.159924i
$835$	−9.69913	−	11.1934i	−0.335652	−	0.387363i
$836$	1.58038	+	10.9918i	0.0546586	+	0.380159i
$837$	4.83555	+	1.41984i	0.167141	+	0.0490770i
$838$	−16.1336	+	18.6191i	−0.557325	+	0.643187i
$839$	−0.687141	−	0.441599i	−0.0237227	−	0.0152457i	0.528726	−	0.848793i	$-0.322670\pi$
$839$	−0.687141	−	0.441599i	−0.0237227	−	0.0152457i	−0.552448	+	0.833547i	$0.686306\pi$
$840$	−8.89488	−	5.71639i	−0.306903	−	0.197234i
$841$	−31.2143	+	36.0232i	−1.07636	+	1.24218i
$842$	8.69284	+	2.55245i	0.299575	+	0.0879631i
$843$	−1.78766	−	12.4334i	−0.0615702	−	0.428230i
$844$	−8.57707	−	9.89847i	−0.295235	−	0.340719i
$845$	1.04713	+	2.29290i	0.0360225	+	0.0788783i
$846$	7.29572	−	2.14222i	0.250832	−	0.0736509i
$847$	7.77888	−	17.0334i	0.267285	−	0.585274i
$848$	−0.0260536	+	0.181207i	−0.000894685	+	0.00622267i
$849$	−12.9762	+	8.33927i	−0.445340	+	0.286203i
$850$	2.00961			0.0689290
$851$	−18.8283	+	38.4292i	−0.645426	+	1.31734i
$852$	9.82264			0.336518
$853$	23.0710	−	14.8268i	0.789937	−	0.507662i	−0.0823810	−	0.996601i	$-0.526252\pi$
$853$	23.0710	−	14.8268i	0.789937	−	0.507662i	0.872318	+	0.488939i	$0.162616\pi$
$854$	−1.65269	+	11.4947i	−0.0565538	+	0.393340i
$855$	2.14933	−	4.70637i	0.0735054	−	0.160954i
$856$	−16.5294	+	4.85346i	−0.564962	+	0.165888i
$857$	23.9708	+	52.4887i	0.818826	+	1.79298i	0.563480	+	0.826129i	$0.309462\pi$
$857$	23.9708	+	52.4887i	0.818826	+	1.79298i	0.255346	+	0.966850i	$0.417811\pi$
$858$	−4.80634	−	5.54681i	−0.164086	−	0.189365i
$859$	−7.73937	−	53.8285i	−0.264064	−	1.83660i	−0.501447	−	0.865188i	$-0.667199\pi$
$859$	−7.73937	−	53.8285i	−0.264064	−	1.83660i	0.237383	−	0.971416i	$-0.423710\pi$
$860$	−12.6915	−	3.72657i	−0.432777	−	0.127075i
$861$	10.9383	−	12.6234i	0.372775	−	0.430205i
$862$	6.81615	+	4.38047i	0.232159	+	0.149200i
$863$	−20.9782	−	13.4819i	−0.714106	−	0.458928i	0.132476	−	0.991186i	$-0.457707\pi$
$863$	−20.9782	−	13.4819i	−0.714106	−	0.458928i	−0.846582	+	0.532258i	$0.821344\pi$
$864$	3.70914	−	4.28058i	0.126188	−	0.145628i
$865$	−18.6108	−	5.46463i	−0.632787	−	0.185803i
$866$	−0.541411	−	3.76560i	−0.0183979	−	0.127960i
$867$	10.8360	+	12.5055i	0.368011	+	0.424708i
$868$	−7.74068	−	16.9497i	−0.262736	−	0.575311i
$869$	−14.9930	+	4.40234i	−0.508603	+	0.149339i
$870$	−3.98041	+	8.71589i	−0.134949	+	0.295496i
$871$	3.10773	−	21.6147i	0.105301	−	0.732387i
$872$	21.6491	−	13.9130i	0.733130	−	0.471154i
$873$	12.2591			0.414907
$874$	17.2317	+	0.468375i	0.582870	+	0.0158430i
$875$	31.5343			1.06606
$876$	−6.66125	+	4.28093i	−0.225063	+	0.144639i
$877$	−5.18888	+	36.0894i	−0.175216	+	1.21865i	0.692435	+	0.721480i	$0.256538\pi$
$877$	−5.18888	+	36.0894i	−0.175216	+	1.21865i	−0.867651	+	0.497174i	$0.834371\pi$
$878$	−2.64262	+	5.78653i	−0.0891841	+	0.195286i
$879$	19.5338	−	5.73564i	0.658859	−	0.193458i
$880$	0.0187309	+	0.0410149i	0.000631418	+	0.00138261i
$881$	6.12793	+	7.07201i	0.206455	+	0.238262i	0.849529	−	0.527542i	$-0.176886\pi$
$881$	6.12793	+	7.07201i	0.206455	+	0.238262i	−0.643073	+	0.765805i	$0.722341\pi$
$882$	0.235050	+	1.63481i	0.00791455	+	0.0550469i
$883$	−17.0772	−	5.01431i	−0.574692	−	0.168745i	−0.0185440	−	0.999828i	$-0.505903\pi$
$883$	−17.0772	−	5.01431i	−0.574692	−	0.168745i	−0.556148	+	0.831083i	$0.687721\pi$
$884$	−2.11670	+	2.44280i	−0.0711922	+	0.0821602i
$885$	−6.14299	−	3.94786i	−0.206494	−	0.132706i
$886$	−15.4198	−	9.90972i	−0.518039	−	0.332924i
$887$	19.9904	−	23.0701i	0.671210	−	0.774618i	−0.313355	−	0.949636i	$-0.601453\pi$
$887$	19.9904	−	23.0701i	0.671210	−	0.774618i	0.984565	+	0.175018i	$0.0559984\pi$
$888$	−24.1850	−	7.10137i	−0.811597	−	0.238306i
$889$	2.48968	+	17.3161i	0.0835011	+	0.580763i
$890$	0.259369	+	0.299328i	0.00869407	+	0.0100335i
$891$	0.902622	+	1.97647i	0.0302390	+	0.0662141i
$892$	−7.48420	+	2.19756i	−0.250589	+	0.0735797i
$893$	14.9342	−	32.7014i	0.499755	−	1.09431i
$894$	−2.16234	+	15.0394i	−0.0723196	+	0.502994i
$895$	−19.4884	+	12.5244i	−0.651426	+	0.418646i
$896$	−21.0280			−0.702495
$897$	15.8971	−	9.61638i	0.530789	−	0.321081i
$898$	−9.39830			−0.313625
$899$	−37.1220	+	23.8568i	−1.23809	+	0.795670i
$900$	−0.604256	+	4.20269i	−0.0201419	+	0.140090i
$901$	3.09544	−	6.77807i	0.103124	−	0.225810i
$902$	10.1809	−	2.98937i	0.338986	−	0.0995353i
$903$	10.5317	+	23.0613i	0.350474	+	0.767430i
$904$	17.4369	+	20.1233i	0.579943	+	0.669290i
$905$	−1.24321	−	8.64675i	−0.0413259	−	0.287428i
$906$	10.9140	+	3.20465i	0.362594	+	0.106467i
$907$	9.99447	−	11.5342i	0.331861	−	0.382988i	−0.565156	−	0.824984i	$-0.691184\pi$
$907$	9.99447	−	11.5342i	0.331861	−	0.382988i	0.897017	+	0.441996i	$0.145730\pi$
$908$	7.32827	+	4.70959i	0.243197	+	0.156293i
$909$	−13.3793	−	8.59835i	−0.443763	−	0.285189i
$910$	8.27973	−	9.55532i	0.274470	−	0.316756i
$911$	28.1955	+	8.27895i	0.934159	+	0.274294i	0.713177	−	0.700984i	$-0.247256\pi$
$911$	28.1955	+	8.27895i	0.934159	+	0.274294i	0.220982	+	0.975278i	$0.429074\pi$
$912$	−0.00970021	−	0.0674664i	−0.000321206	−	0.00223404i
$913$	−16.9448	−	19.5554i	−0.560792	−	0.647189i
$914$	1.20385	+	2.63606i	0.0398198	+	0.0871932i
$915$	−5.37804	+	1.57913i	−0.177792	+	0.0522046i
$916$	−0.176099	+	0.385603i	−0.00581848	+	0.0127407i
$917$	3.66127	−	25.4647i	0.120906	−	0.840918i
$918$	−0.493635	+	0.317240i	−0.0162924	+	0.0104705i
$919$	38.9857			1.28602			0.643010	−	0.765858i	$-0.277686\pi$
$919$	38.9857			1.28602			0.643010	+	0.765858i	$0.277686\pi$
$920$	16.4383	−	4.34523i	0.541954	−	0.143258i
$921$	−4.64072			−0.152917
$922$	12.3117	−	7.91227i	0.405465	−	0.260577i
$923$	−4.36825	+	30.3818i	−0.143783	+	1.00003i
$924$	3.33733	−	7.30773i	0.109790	−	0.240407i
$925$	29.3219	−	8.60967i	0.964097	−	0.283084i
$926$	5.08747	+	11.1400i	0.167184	+	0.366083i
$927$	−12.2372	−	14.1224i	−0.401921	−	0.463842i
$928$	7.05789	+	49.0887i	0.231687	+	1.61142i
$929$	−20.6895	−	6.07499i	−0.678801	−	0.199314i	−0.0758824	−	0.997117i	$-0.524177\pi$
$929$	−20.6895	−	6.07499i	−0.678801	−	0.199314i	−0.602918	+	0.797803i	$0.705996\pi$
$930$	−3.61159	+	4.16800i	−0.118429	+	0.136674i
$931$	6.56919	+	4.22176i	0.215296	+	0.138363i
$932$	11.5241	+	7.40606i	0.377483	+	0.242593i
$933$	6.86662	−	7.92450i	0.224803	−	0.259437i
$934$	−17.2684	−	5.07047i	−0.565041	−	0.165911i
$935$	−0.261185	−	1.81658i	−0.00854167	−	0.0594086i
$936$	7.16645	+	8.27052i	0.234243	+	0.270330i
$937$	14.0487	+	30.7623i	0.458950	+	1.00496i	0.987726	+	0.156198i	$0.0499240\pi$
$937$	14.0487	+	30.7623i	0.458950	+	1.00496i	−0.528776	+	0.848762i	$0.677349\pi$
$938$	−14.0636	+	4.12945i	−0.459193	+	0.134831i
$939$	−12.8718	+	28.1854i	−0.420057	+	0.919796i
$940$	1.93113	−	13.4313i	0.0629865	−	0.438080i
$941$	2.77201	−	1.78147i	0.0903651	−	0.0580741i	−0.494678	−	0.869076i	$-0.664714\pi$
$941$	2.77201	−	1.78147i	0.0903651	−	0.0580741i	0.585043	+	0.811002i	$0.301078\pi$
$942$	−7.66075			−0.249601
$943$	3.09880	+	26.6808i	0.100911	+	0.868847i
$944$	−0.0961975			−0.00313096
$945$	−3.14885	+	2.02364i	−0.102432	+	0.0658292i
$946$	−2.29198	+	15.9411i	−0.0745188	+	0.518290i
$947$	−8.94946	+	19.5966i	−0.290819	+	0.636804i	−0.997495	−	0.0707328i	$-0.977466\pi$
$947$	−8.94946	+	19.5966i	−0.290819	+	0.636804i	0.706677	+	0.707537i	$0.250194\pi$
$948$	8.55467	−	2.51188i	0.277843	−	0.0815820i
$949$	−10.2787	−	22.5073i	−0.333662	−	0.730618i
$950$	−8.06131	−	9.30324i	−0.261543	−	0.301837i
$951$	−1.91234	−	13.3006i	−0.0620119	−	0.431302i
$952$	5.43987	+	1.59729i	0.176307	+	0.0517684i
$953$	−22.3186	+	25.7571i	−0.722971	+	0.834353i	−0.991661	−	0.128874i	$-0.958864\pi$
$953$	−22.3186	+	25.7571i	−0.722971	+	0.834353i	0.268690	+	0.963227i	$0.413409\pi$
$954$	−8.12153	−	5.21939i	−0.262944	−	0.168984i
$955$	15.8131	+	10.1625i	0.511700	+	0.328849i
$956$	−4.15475	+	4.79484i	−0.134374	+	0.155076i
$957$	−18.2543	−	5.35995i	−0.590078	−	0.173263i
$958$	−0.355580	−	2.47311i	−0.0114883	−	0.0799026i
$959$	3.86769	+	4.46356i	0.124894	+	0.144136i
$960$	2.55761	+	5.60039i	0.0825466	+	0.180752i
$961$	5.37462	−	1.57813i	0.173375	−	0.0509074i
$962$	12.5211	−	27.4173i	0.403695	−	0.883970i
$963$	−0.867913	+	6.03647i	−0.0279681	+	0.194523i
$964$	17.3155	−	11.1280i	0.557694	−	0.358408i
$965$	22.1108			0.711771
$966$	−10.3040	−	7.02477i	−0.331526	−	0.226018i
$967$	5.29658			0.170327			0.0851633	−	0.996367i	$-0.472859\pi$
$967$	5.29658			0.170327			0.0851633	+	0.996367i	$0.472859\pi$
$968$	−14.9209	+	9.58908i	−0.479576	+	0.308205i
$969$	−0.394824	+	2.74606i	−0.0126836	+	0.0882162i
$970$	−5.57296	+	12.2031i	−0.178937	+	0.391817i
$971$	−54.3549	+	15.9600i	−1.74433	+	0.512182i	−0.989599	−	0.143851i	$-0.954051\pi$
$971$	−54.3549	+	15.9600i	−1.74433	+	0.512182i	−0.754732	+	0.656033i	$0.772233\pi$
$972$	−0.515016	−	1.12773i	−0.0165191	−	0.0361719i
$973$	−11.3726	−	13.1246i	−0.364588	−	0.420757i
$974$	2.38968	+	16.6206i	0.0765703	+	0.532558i
$975$	−12.7304	−	3.73798i	−0.407698	−	0.119711i
$976$	−0.0483550	+	0.0558047i	−0.00154781	+	0.00178626i
$977$	45.9836	+	29.5518i	1.47114	+	0.945447i	0.997917	+	0.0645067i	$0.0205474\pi$
$977$	45.9836	+	29.5518i	1.47114	+	0.945447i	0.473227	+	0.880940i	$0.343089\pi$
$978$	6.11748	+	3.93146i	0.195615	+	0.125714i
$979$	−0.514987	+	0.594326i	−0.0164590	+	0.0189948i
$980$	2.82805	+	0.830389i	0.0903386	+	0.0265258i
$981$	−1.29651	−	9.01740i	−0.0413943	−	0.287903i
$982$	−9.57447	−	11.0495i	−0.305533	−	0.352604i
$983$	−21.1998	−	46.4210i	−0.676168	−	1.48060i	−0.866653	−	0.498911i	$-0.833733\pi$
$983$	−21.1998	−	46.4210i	−0.676168	−	1.48060i	0.190485	−	0.981690i	$-0.438994\pi$
$984$	−15.1801	+	4.45728i	−0.483924	+	0.142093i
$985$	9.57663	−	20.9699i	0.305137	−	0.668157i
$986$	0.731188	−	5.08553i	0.0232858	−	0.161956i
$987$	−21.8793	+	14.0610i	−0.696425	+	0.447565i
$988$	19.7995			0.629907
$989$	−38.7907	−	12.5445i	−1.23347	−	0.398891i
$990$	−2.37777			−0.0755704
$991$	−34.6859	+	22.2913i	−1.10183	+	0.708106i	−0.959499	−	0.281713i	$-0.909097\pi$
$991$	−34.6859	+	22.2913i	−1.10183	+	0.708106i	−0.142335	+	0.989819i	$0.545461\pi$
$992$	−4.06236	+	28.2544i	−0.128980	+	0.897077i
$993$	1.11668	−	2.44518i	0.0354367	−	0.0775955i
$994$	19.7679	−	5.80438i	0.627000	−	0.184104i
$995$	−9.47321	−	20.7434i	−0.300321	−	0.657611i
$996$	9.66834	+	11.1579i	0.306353	+	0.353550i
$997$	2.96444	+	20.6181i	0.0938846	+	0.652982i	0.981367	+	0.192141i	$0.0615430\pi$
$997$	2.96444	+	20.6181i	0.0938846	+	0.652982i	−0.887483	+	0.460841i	$0.847548\pi$
$998$	−17.1712	−	5.04193i	−0.543546	−	0.159600i
$999$	−5.84341	+	6.74365i	−0.184877	+	0.213360i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	69.2.e.c.58.1	yes	20
3.2	odd	2		207.2.i.d.127.2		20
23.2	even	11	inner	69.2.e.c.25.1	✓	20
23.5	odd	22		1587.2.a.t.1.4		10
23.18	even	11		1587.2.a.u.1.4		10
69.2	odd	22		207.2.i.d.163.2		20
69.5	even	22		4761.2.a.bu.1.7		10
69.41	odd	22		4761.2.a.bt.1.7		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.25.1	✓	20	23.2	even	11	inner
69.2.e.c.58.1	yes	20	1.1	even	1	trivial
207.2.i.d.127.2		20	3.2	odd	2
207.2.i.d.163.2		20	69.2	odd	22
1587.2.a.t.1.4		10	23.5	odd	22
1587.2.a.u.1.4		10	23.18	even	11
4761.2.a.bt.1.7		10	69.41	odd	22
4761.2.a.bu.1.7		10	69.5	even	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:	\( N \)	\(=\)	\( 69 = 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	69.e (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.733503 + 0.471394i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(-0.515016 + 1.12773i) q^{4} +(-1.20424 + 0.353596i) q^{5} +(-0.362207 - 0.793123i) q^{6} +(1.95301 + 2.25389i) q^{7} +(-0.402011 - 2.79605i) q^{8} +(-0.959493 - 0.281733i) q^{9} +O(q^{10})\)	\(q+(-0.733503 + 0.471394i) q^{2} +(-0.142315 + 0.989821i) q^{3} +(-0.515016 + 1.12773i) q^{4} +(-1.20424 + 0.353596i) q^{5} +(-0.362207 - 0.793123i) q^{6} +(1.95301 + 2.25389i) q^{7} +(-0.402011 - 2.79605i) q^{8} +(-0.959493 - 0.281733i) q^{9} +(0.716629 - 0.827034i) q^{10} +(1.82789 + 1.17472i) q^{11} +(-1.04295 - 0.670266i) q^{12} +(2.53697 - 2.92782i) q^{13} +(-2.49500 - 0.732599i) q^{14} +(-0.178616 - 1.24230i) q^{15} +(-0.0108276 - 0.0124957i) q^{16} +(0.279567 + 0.612167i) q^{17} +(0.836598 - 0.245647i) q^{18} +(1.71250 - 3.74986i) q^{19} +(0.221442 - 1.54016i) q^{20} +(-2.50889 + 1.61236i) q^{21} -1.89452 q^{22} +(0.811247 - 4.72672i) q^{23} +2.82480 q^{24} +(-2.88111 + 1.85157i) q^{25} +(-0.480720 + 3.34348i) q^{26} +(0.415415 - 0.909632i) q^{27} +(-3.54760 + 1.04167i) q^{28} +(3.63733 + 7.96463i) q^{29} +(0.716629 + 0.827034i) q^{30} +(0.717223 + 4.98839i) q^{31} +(5.43459 + 1.59574i) q^{32} +(-1.42289 + 1.64211i) q^{33} +(-0.493635 - 0.317240i) q^{34} +(-3.14885 - 2.02364i) q^{35} +(0.811872 - 0.936950i) q^{36} +(-8.56168 - 2.51394i) q^{37} +(0.511534 + 3.55779i) q^{38} +(2.53697 + 2.92782i) q^{39} +(1.47279 + 3.22496i) q^{40} +(-5.37386 + 1.57791i) q^{41} +(1.08022 - 2.36535i) q^{42} +(1.20980 - 8.41433i) q^{43} +(-2.26615 + 1.45637i) q^{44} +1.25508 q^{45} +(1.63309 + 3.84948i) q^{46} +8.72071 q^{47} +(0.0139094 - 0.00893903i) q^{48} +(-0.269579 + 1.87496i) q^{49} +(1.24048 - 2.71627i) q^{50} +(-0.645722 + 0.189601i) q^{51} +(1.99521 + 4.36889i) q^{52} +(-7.25079 - 8.36786i) q^{53} +(0.124087 + 0.863041i) q^{54} +(-2.61659 - 0.768301i) q^{55} +(5.51685 - 6.36679i) q^{56} +(3.46798 + 2.22873i) q^{57} +(-6.42247 - 4.12747i) q^{58} +(3.81005 - 4.39703i) q^{59} +(1.49297 + 0.438375i) q^{60} +(-0.635567 - 4.42047i) q^{61} +(-2.87758 - 3.32091i) q^{62} +(-1.23890 - 2.71282i) q^{63} +(-4.70678 + 1.38203i) q^{64} +(-2.01986 + 4.42287i) q^{65} +(0.269618 - 1.87523i) q^{66} +(4.74190 - 3.04743i) q^{67} -0.834339 q^{68} +(4.56316 + 1.47567i) q^{69} +3.26362 q^{70} +(-6.66525 + 4.28350i) q^{71} +(-0.402011 + 2.79605i) q^{72} +(2.65322 - 5.80973i) q^{73} +(7.46507 - 2.19194i) q^{74} +(-1.42270 - 3.11529i) q^{75} +(3.34685 + 3.86247i) q^{76} +(0.922207 + 6.41409i) q^{77} +(-3.24103 - 0.951654i) q^{78} +(-4.70947 + 5.43502i) q^{79} +(0.0174574 + 0.0112192i) q^{80} +(0.841254 + 0.540641i) q^{81} +(3.19793 - 3.69060i) q^{82} +(-11.4263 - 3.35507i) q^{83} +(-0.526191 - 3.65974i) q^{84} +(-0.553126 - 0.638341i) q^{85} +(3.07907 + 6.74222i) q^{86} +(-8.40121 + 2.46682i) q^{87} +(2.54973 - 5.58312i) q^{88} +(-0.0515079 + 0.358245i) q^{89} +(-0.920603 + 0.591636i) q^{90} +11.5537 q^{91} +(4.91265 + 3.34920i) q^{92} -5.03969 q^{93} +(-6.39666 + 4.11088i) q^{94} +(-0.736326 + 5.12126i) q^{95} +(-2.35292 + 5.15217i) q^{96} +(-11.7625 + 3.45378i) q^{97} +(-0.686108 - 1.50237i) q^{98} +(-1.42289 - 1.64211i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9	\( 20 q - 4 q^{2} - 2 q^{3} - 6 q^{4} - 6 q^{5} + 7 q^{6} - 6 q^{7} + 10 q^{8} - 2 q^{9} - 18 q^{10} - 16 q^{11} - 6 q^{12} + 14 q^{13} - 22 q^{14} + 5 q^{15} - 8 q^{16} + 11 q^{17} - 4 q^{18} - 11 q^{19} + 57 q^{20} - 6 q^{21} + 26 q^{22} - 12 q^{24} - 4 q^{25} - 14 q^{26} - 2 q^{27} - 14 q^{28} + 12 q^{29} - 18 q^{30} + 41 q^{31} - 46 q^{32} - 5 q^{33} - 3 q^{34} - 26 q^{35} + 5 q^{36} - 18 q^{37} + 70 q^{38} + 14 q^{39} - 13 q^{40} + 44 q^{42} - 10 q^{43} - 3 q^{44} + 16 q^{45} - 24 q^{46} + 18 q^{47} + 25 q^{48} - 10 q^{49} + 33 q^{50} + 61 q^{52} - 20 q^{53} + 7 q^{54} - 17 q^{55} + 6 q^{56} + 11 q^{57} - 37 q^{58} + 40 q^{59} - 31 q^{60} - 12 q^{61} - 89 q^{62} - 6 q^{63} - 2 q^{64} - 51 q^{65} + 15 q^{66} - 47 q^{67} - 12 q^{68} - 22 q^{69} + 32 q^{70} - 47 q^{71} + 10 q^{72} + 39 q^{73} - 50 q^{74} - 26 q^{75} - 39 q^{76} + 22 q^{77} - 14 q^{78} - 2 q^{79} + 12 q^{80} - 2 q^{81} + 26 q^{82} - 52 q^{83} - 14 q^{84} + 35 q^{85} + 34 q^{86} - 32 q^{87} + 30 q^{88} + 36 q^{89} - 18 q^{90} + 8 q^{91} - 19 q^{92} - 14 q^{93} + 21 q^{94} + 89 q^{95} - 2 q^{96} + 85 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q - 4 * q^2 - 2 * q^3 - 6 * q^4 - 6 * q^5 + 7 * q^6 - 6 * q^7 + 10 * q^8 - 2 * q^9 - 18 * q^10 - 16 * q^11 - 6 * q^12 + 14 * q^13 - 22 * q^14 + 5 * q^15 - 8 * q^16 + 11 * q^17 - 4 * q^18 - 11 * q^19 + 57 * q^20 - 6 * q^21 + 26 * q^22 - 12 * q^24 - 4 * q^25 - 14 * q^26 - 2 * q^27 - 14 * q^28 + 12 * q^29 - 18 * q^30 + 41 * q^31 - 46 * q^32 - 5 * q^33 - 3 * q^34 - 26 * q^35 + 5 * q^36 - 18 * q^37 + 70 * q^38 + 14 * q^39 - 13 * q^40 + 44 * q^42 - 10 * q^43 - 3 * q^44 + 16 * q^45 - 24 * q^46 + 18 * q^47 + 25 * q^48 - 10 * q^49 + 33 * q^50 + 61 * q^52 - 20 * q^53 + 7 * q^54 - 17 * q^55 + 6 * q^56 + 11 * q^57 - 37 * q^58 + 40 * q^59 - 31 * q^60 - 12 * q^61 - 89 * q^62 - 6 * q^63 - 2 * q^64 - 51 * q^65 + 15 * q^66 - 47 * q^67 - 12 * q^68 - 22 * q^69 + 32 * q^70 - 47 * q^71 + 10 * q^72 + 39 * q^73 - 50 * q^74 - 26 * q^75 - 39 * q^76 + 22 * q^77 - 14 * q^78 - 2 * q^79 + 12 * q^80 - 2 * q^81 + 26 * q^82 - 52 * q^83 - 14 * q^84 + 35 * q^85 + 34 * q^86 - 32 * q^87 + 30 * q^88 + 36 * q^89 - 18 * q^90 + 8 * q^91 - 19 * q^92 - 14 * q^93 + 21 * q^94 + 89 * q^95 - 2 * q^96 + 85 * q^98 - 5 * q^99

Introduction

L-functions

Modular forms

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